id	sid	tid	token	lemma	pos
ejpam-2623	1	1	european	european	PROPN
ejpam-2623	1	2	journal	journal	PROPN
ejpam-2623	1	3	of	of	ADP
ejpam-2623	1	4	pure	pure	ADJ
ejpam-2623	1	5	and	and	CCONJ
ejpam-2623	1	6	applied	apply	VERB
ejpam-2623	1	7	mathematics	mathematic	NOUN
ejpam-2623	1	8	vol	vol	NOUN
ejpam-2623	1	9	.	.	PROPN
ejpam-2623	2	1	10	10	NUM
ejpam-2623	2	2	,	,	PUNCT
ejpam-2623	2	3	no	no	INTJ
ejpam-2623	2	4	.	.	NOUN
ejpam-2623	2	5	2	2	NUM
ejpam-2623	2	6	,	,	PUNCT
ejpam-2623	2	7	2017	2017	NUM
ejpam-2623	2	8	,	,	PUNCT
ejpam-2623	2	9	363	363	NUM
ejpam-2623	2	10	-	-	SYM
ejpam-2623	2	11	391	391	NUM
ejpam-2623	2	12	issn	issn	PROPN
ejpam-2623	2	13	1307	1307	NUM
ejpam-2623	2	14	-	-	SYM
ejpam-2623	2	15	5543	5543	NUM
ejpam-2623	2	16	–	–	PUNCT
ejpam-2623	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2623	2	18	published	publish	VERB
ejpam-2623	2	19	by	by	ADP
ejpam-2623	2	20	new	new	PROPN
ejpam-2623	2	21	york	york	PROPN
ejpam-2623	2	22	business	business	PROPN
ejpam-2623	2	23	global	global	ADJ
ejpam-2623	2	24	on	on	ADP
ejpam-2623	2	25	indifferentiable	indifferentiable	ADJ
ejpam-2623	2	26	deterministic	deterministic	ADJ
ejpam-2623	2	27	hashing	hashing	NOUN
ejpam-2623	2	28	into	into	ADP
ejpam-2623	2	29	elliptic	elliptic	ADJ
ejpam-2623	2	30	curves	curve	NOUN
ejpam-2623	2	31	nafissatou	nafissatou	ADJ
ejpam-2623	2	32	diarra1	diarra1	PROPN
ejpam-2623	2	33	,	,	PUNCT
ejpam-2623	2	34	djiby	djiby	PROPN
ejpam-2623	2	35	sow1,∗	sow1,∗	PROPN
ejpam-2623	2	36	,	,	PUNCT
ejpam-2623	3	1	ahmed	ahmed	PROPN
ejpam-2623	3	2	youssef	youssef	PROPN
ejpam-2623	3	3	ould	ould	AUX
ejpam-2623	3	4	cheikh	cheikh	PROPN
ejpam-2623	3	5	khlil1	khlil1	PROPN
ejpam-2623	3	6	1	1	NUM
ejpam-2623	3	7	laboratoire	laboratoire	PROPN
ejpam-2623	3	8	d’algèbre	d’algèbre	PROPN
ejpam-2623	3	9	,	,	PUNCT
ejpam-2623	3	10	de	de	X
ejpam-2623	3	11	cryptographie	cryptographie	NOUN
ejpam-2623	3	12	,	,	PUNCT
ejpam-2623	3	13	de	de	X
ejpam-2623	3	14	géométrie	géométrie	X
ejpam-2623	3	15	algébrique	algébrique	PROPN
ejpam-2623	3	16	et	et	NOUN
ejpam-2623	3	17	aplications	aplication	NOUN
ejpam-2623	3	18	(	(	PUNCT
ejpam-2623	3	19	lacgaa	lacgaa	NOUN
ejpam-2623	3	20	,	,	PUNCT
ejpam-2623	3	21	cheikh	cheikh	PROPN
ejpam-2623	3	22	anta	anta	PROPN
ejpam-2623	3	23	diop	diop	PROPN
ejpam-2623	3	24	university	university	PROPN
ejpam-2623	3	25	,	,	PUNCT
ejpam-2623	3	26	dakar	dakar	NOUN
ejpam-2623	3	27	,	,	PUNCT
ejpam-2623	3	28	senegal	senegal	ADJ
ejpam-2623	3	29	abstract	abstract	NOUN
ejpam-2623	3	30	.	.	PUNCT
ejpam-2623	4	1	in	in	ADP
ejpam-2623	4	2	this	this	DET
ejpam-2623	4	3	paper	paper	NOUN
ejpam-2623	4	4	,	,	PUNCT
ejpam-2623	4	5	we	we	PRON
ejpam-2623	4	6	give	give	VERB
ejpam-2623	4	7	new	new	ADJ
ejpam-2623	4	8	deterministic	deterministic	ADJ
ejpam-2623	4	9	encodings	encoding	NOUN
ejpam-2623	4	10	based	base	VERB
ejpam-2623	4	11	on	on	ADP
ejpam-2623	4	12	elligator	elligator	NOUN
ejpam-2623	4	13	’s	’s	PART
ejpam-2623	4	14	model	model	NOUN
ejpam-2623	4	15	,	,	PUNCT
ejpam-2623	4	16	for	for	ADP
ejpam-2623	4	17	some	some	DET
ejpam-2623	4	18	families	family	NOUN
ejpam-2623	4	19	of	of	ADP
ejpam-2623	4	20	elliptic	elliptic	ADJ
ejpam-2623	4	21	curves	curve	NOUN
ejpam-2623	4	22	.	.	PUNCT
ejpam-2623	5	1	these	these	DET
ejpam-2623	5	2	encodings	encoding	NOUN
ejpam-2623	5	3	are	be	AUX
ejpam-2623	5	4	almost	almost	ADV
ejpam-2623	5	5	-	-	PUNCT
ejpam-2623	5	6	injective	injective	ADJ
ejpam-2623	5	7	and	and	CCONJ
ejpam-2623	5	8	easily	easily	ADV
ejpam-2623	5	9	invertible	invertible	ADJ
ejpam-2623	5	10	.	.	PUNCT
ejpam-2623	6	1	this	this	PRON
ejpam-2623	6	2	allows	allow	VERB
ejpam-2623	6	3	to	to	PART
ejpam-2623	6	4	make	make	VERB
ejpam-2623	6	5	points	point	NOUN
ejpam-2623	6	6	in	in	ADP
ejpam-2623	6	7	the	the	DET
ejpam-2623	6	8	image	image	NOUN
ejpam-2623	6	9	set	set	NOUN
ejpam-2623	6	10	of	of	ADP
ejpam-2623	6	11	the	the	DET
ejpam-2623	6	12	encoding	encoding	NOUN
ejpam-2623	6	13	indistinguishable	indistinguishable	ADJ
ejpam-2623	6	14	from	from	ADP
ejpam-2623	6	15	uniform	uniform	ADJ
ejpam-2623	6	16	string	string	NOUN
ejpam-2623	6	17	of	of	ADP
ejpam-2623	6	18	bits	bit	NOUN
ejpam-2623	6	19	,	,	PUNCT
ejpam-2623	6	20	which	which	PRON
ejpam-2623	6	21	is	be	AUX
ejpam-2623	6	22	useful	useful	ADJ
ejpam-2623	6	23	for	for	ADP
ejpam-2623	6	24	applications	application	NOUN
ejpam-2623	6	25	in	in	ADP
ejpam-2623	6	26	censorship	censorship	NOUN
ejpam-2623	6	27	circumvention	circumvention	NOUN
ejpam-2623	6	28	.	.	PUNCT
ejpam-2623	7	1	following	follow	VERB
ejpam-2623	7	2	the	the	DET
ejpam-2623	7	3	idea	idea	NOUN
ejpam-2623	7	4	of	of	ADP
ejpam-2623	7	5	farashahi	farashahi	NOUN
ejpam-2623	7	6	et	et	PROPN
ejpam-2623	7	7	al	al	PROPN
ejpam-2623	7	8	.	.	PROPN
ejpam-2623	7	9	,	,	PUNCT
ejpam-2623	7	10	we	we	PRON
ejpam-2623	7	11	show	show	VERB
ejpam-2623	7	12	that	that	SCONJ
ejpam-2623	7	13	our	our	PRON
ejpam-2623	7	14	encodings	encoding	NOUN
ejpam-2623	7	15	are	be	AUX
ejpam-2623	7	16	well	well	ADV
ejpam-2623	7	17	-	-	PUNCT
ejpam-2623	7	18	distributed	distribute	VERB
ejpam-2623	7	19	.	.	PUNCT
ejpam-2623	8	1	and	and	CCONJ
ejpam-2623	8	2	thus	thus	ADV
ejpam-2623	8	3	they	they	PRON
ejpam-2623	8	4	give	give	VERB
ejpam-2623	8	5	rise	rise	NOUN
ejpam-2623	8	6	to	to	ADP
ejpam-2623	8	7	hash	hash	NOUN
ejpam-2623	8	8	functions	function	NOUN
ejpam-2623	8	9	constructions	construction	NOUN
ejpam-2623	8	10	indifferentiable	indifferentiable	ADJ
ejpam-2623	8	11	from	from	ADP
ejpam-2623	8	12	random	random	ADJ
ejpam-2623	8	13	oracles	oracle	NOUN
ejpam-2623	8	14	.	.	PUNCT
ejpam-2623	9	1	key	key	ADJ
ejpam-2623	9	2	words	word	NOUN
ejpam-2623	9	3	and	and	CCONJ
ejpam-2623	9	4	phrases	phrase	NOUN
ejpam-2623	9	5	:	:	PUNCT
ejpam-2623	9	6	deterministic	deterministic	ADJ
ejpam-2623	9	7	encodings	encoding	NOUN
ejpam-2623	9	8	,	,	PUNCT
ejpam-2623	9	9	elliptic	elliptic	ADJ
ejpam-2623	9	10	curves	curve	NOUN
ejpam-2623	9	11	,	,	PUNCT
ejpam-2623	9	12	random	random	ADJ
ejpam-2623	9	13	oracle	oracle	NOUN
ejpam-2623	9	14	,	,	PUNCT
ejpam-2623	9	15	indifferentiable	indifferentiable	ADJ
ejpam-2623	9	16	hashing	hash	VERB
ejpam-2623	9	17	1	1	NUM
ejpam-2623	9	18	.	.	PUNCT
ejpam-2623	9	19	introduction	introduction	NOUN
ejpam-2623	9	20	in	in	ADP
ejpam-2623	9	21	elliptic	elliptic	ADJ
ejpam-2623	9	22	curve	curve	NOUN
ejpam-2623	9	23	cryptography	cryptography	NOUN
ejpam-2623	9	24	,	,	PUNCT
ejpam-2623	9	25	many	many	ADJ
ejpam-2623	9	26	protocols	protocol	NOUN
ejpam-2623	10	1	[	[	X
ejpam-2623	10	2	18	18	NUM
ejpam-2623	10	3	]	]	PUNCT
ejpam-2623	10	4	and	and	CCONJ
ejpam-2623	10	5	encryption	encryption	NOUN
ejpam-2623	10	6	schemes	scheme	NOUN
ejpam-2623	10	7	(	(	PUNCT
ejpam-2623	10	8	like	like	ADP
ejpam-2623	10	9	the	the	DET
ejpam-2623	10	10	the	the	DET
ejpam-2623	10	11	identity	identity	NOUN
ejpam-2623	10	12	based	base	VERB
ejpam-2623	10	13	-	-	PUNCT
ejpam-2623	10	14	encryption	encryption	NOUN
ejpam-2623	10	15	of	of	ADP
ejpam-2623	10	16	boneh	boneh	PROPN
ejpam-2623	10	17	and	and	CCONJ
ejpam-2623	10	18	franklin	franklin	PROPN
ejpam-2623	11	1	[	[	X
ejpam-2623	11	2	2	2	NUM
ejpam-2623	11	3	]	]	PUNCT
ejpam-2623	11	4	)	)	PUNCT
ejpam-2623	11	5	need	need	VERB
ejpam-2623	11	6	to	to	PART
ejpam-2623	11	7	hash	hash	VERB
ejpam-2623	11	8	into	into	ADP
ejpam-2623	11	9	the	the	DET
ejpam-2623	11	10	group	group	NOUN
ejpam-2623	11	11	of	of	ADP
ejpam-2623	11	12	points	point	NOUN
ejpam-2623	11	13	of	of	ADP
ejpam-2623	11	14	an	an	DET
ejpam-2623	11	15	elliptic	elliptic	ADJ
ejpam-2623	11	16	curve	curve	NOUN
ejpam-2623	11	17	.	.	PUNCT
ejpam-2623	12	1	the	the	DET
ejpam-2623	12	2	main	main	ADJ
ejpam-2623	12	3	idea	idea	NOUN
ejpam-2623	12	4	is	be	AUX
ejpam-2623	12	5	the	the	DET
ejpam-2623	12	6	following	following	NOUN
ejpam-2623	12	7	:	:	PUNCT
ejpam-2623	12	8	the	the	DET
ejpam-2623	12	9	image	image	NOUN
ejpam-2623	12	10	of	of	ADP
ejpam-2623	12	11	a	a	DET
ejpam-2623	12	12	message	message	NOUN
ejpam-2623	12	13	(	(	PUNCT
ejpam-2623	12	14	a	a	DET
ejpam-2623	12	15	random	random	ADJ
ejpam-2623	12	16	string	string	NOUN
ejpam-2623	12	17	)	)	PUNCT
ejpam-2623	12	18	m	m	VERB
ejpam-2623	12	19	by	by	ADP
ejpam-2623	12	20	the	the	DET
ejpam-2623	12	21	hash	hash	NOUN
ejpam-2623	12	22	function	function	NOUN
ejpam-2623	12	23	f	f	PROPN
ejpam-2623	12	24	is	be	AUX
ejpam-2623	12	25	f	f	PROPN
ejpam-2623	12	26	(	(	PUNCT
ejpam-2623	12	27	m	m	NOUN
ejpam-2623	12	28	)	)	PUNCT
ejpam-2623	12	29	=	=	SYM
ejpam-2623	12	30	f(h(m	f(h(m	NOUN
ejpam-2623	12	31	)	)	PUNCT
ejpam-2623	12	32	)	)	PUNCT
ejpam-2623	12	33	,	,	PUNCT
ejpam-2623	12	34	where	where	SCONJ
ejpam-2623	12	35	h	h	NOUN
ejpam-2623	12	36	is	be	AUX
ejpam-2623	12	37	a	a	DET
ejpam-2623	12	38	classical	classical	ADJ
ejpam-2623	12	39	hash	hash	NOUN
ejpam-2623	12	40	function	function	NOUN
ejpam-2623	12	41	and	and	CCONJ
ejpam-2623	12	42	f	f	PROPN
ejpam-2623	12	43	is	be	AUX
ejpam-2623	12	44	an	an	DET
ejpam-2623	12	45	encoding	encoding	NOUN
ejpam-2623	12	46	function	function	NOUN
ejpam-2623	12	47	that	that	PRON
ejpam-2623	12	48	maps	map	VERB
ejpam-2623	12	49	a	a	DET
ejpam-2623	12	50	point	point	NOUN
ejpam-2623	12	51	of	of	ADP
ejpam-2623	12	52	fq	fq	PROPN
ejpam-2623	12	53	to	to	ADP
ejpam-2623	12	54	an	an	DET
ejpam-2623	12	55	element	element	NOUN
ejpam-2623	12	56	of	of	ADP
ejpam-2623	12	57	the	the	DET
ejpam-2623	12	58	elliptic	elliptic	ADJ
ejpam-2623	12	59	curve	curve	NOUN
ejpam-2623	12	60	.	.	PUNCT
ejpam-2623	13	1	as	as	SCONJ
ejpam-2623	13	2	discussed	discuss	VERB
ejpam-2623	13	3	by	by	ADP
ejpam-2623	13	4	brier	brier	PROPN
ejpam-2623	13	5	et	et	PROPN
ejpam-2623	13	6	al	al	PROPN
ejpam-2623	13	7	.	.	PUNCT
ejpam-2623	14	1	in	in	ADP
ejpam-2623	14	2	[	[	X
ejpam-2623	14	3	6	6	NUM
ejpam-2623	14	4	]	]	PUNCT
ejpam-2623	14	5	,	,	PUNCT
ejpam-2623	14	6	the	the	DET
ejpam-2623	14	7	construction	construction	NOUN
ejpam-2623	14	8	h(m	h(m	NOUN
ejpam-2623	14	9	)	)	PUNCT
ejpam-2623	14	10	=	=	SYM
ejpam-2623	14	11	f(h(m	f(h(m	NOUN
ejpam-2623	14	12	)	)	PUNCT
ejpam-2623	14	13	)	)	PUNCT
ejpam-2623	14	14	,	,	PUNCT
ejpam-2623	14	15	where	where	SCONJ
ejpam-2623	14	16	f	f	PROPN
ejpam-2623	14	17	is	be	AUX
ejpam-2623	14	18	a	a	DET
ejpam-2623	14	19	constant	constant	ADJ
ejpam-2623	14	20	-	-	PUNCT
ejpam-2623	14	21	time	time	NOUN
ejpam-2623	14	22	encoding	encoding	NOUN
ejpam-2623	14	23	and	and	CCONJ
ejpam-2623	14	24	h	h	NOUN
ejpam-2623	14	25	is	be	AUX
ejpam-2623	14	26	a	a	DET
ejpam-2623	14	27	classical	classical	ADJ
ejpam-2623	14	28	hash	hash	NOUN
ejpam-2623	14	29	function	function	NOUN
ejpam-2623	14	30	modeled	model	VERB
ejpam-2623	14	31	as	as	ADP
ejpam-2623	14	32	a	a	DET
ejpam-2623	14	33	random	random	ADJ
ejpam-2623	14	34	oracle	oracle	NOUN
ejpam-2623	14	35	,	,	PUNCT
ejpam-2623	14	36	can	can	AUX
ejpam-2623	14	37	not	not	PART
ejpam-2623	14	38	replace	replace	VERB
ejpam-2623	14	39	a	a	DET
ejpam-2623	14	40	random	random	ADJ
ejpam-2623	14	41	oracle	oracle	NOUN
ejpam-2623	14	42	to	to	ADP
ejpam-2623	14	43	the	the	DET
ejpam-2623	14	44	group	group	NOUN
ejpam-2623	14	45	of	of	ADP
ejpam-2623	14	46	points	point	NOUN
ejpam-2623	14	47	of	of	ADP
ejpam-2623	14	48	the	the	DET
ejpam-2623	14	49	elliptic	elliptic	ADJ
ejpam-2623	14	50	curve	curve	NOUN
ejpam-2623	14	51	(	(	PUNCT
ejpam-2623	14	52	excepted	except	VERB
ejpam-2623	14	53	for	for	ADP
ejpam-2623	14	54	some	some	DET
ejpam-2623	14	55	special	special	ADJ
ejpam-2623	14	56	encodings	encoding	NOUN
ejpam-2623	14	57	,	,	PUNCT
ejpam-2623	14	58	such	such	ADJ
ejpam-2623	14	59	as	as	ADP
ejpam-2623	14	60	boneh	boneh	PROPN
ejpam-2623	14	61	and	and	CCONJ
ejpam-2623	14	62	franklin	franklin	PROPN
ejpam-2623	14	63	’s	’s	PART
ejpam-2623	14	64	one	one	NUM
ejpam-2623	14	65	[	[	X
ejpam-2623	14	66	2	2	NUM
ejpam-2623	14	67	]	]	NUM
ejpam-2623	14	68	)	)	PUNCT
ejpam-2623	14	69	.	.	PUNCT
ejpam-2623	15	1	in	in	ADP
ejpam-2623	15	2	2013	2013	NUM
ejpam-2623	15	3	,	,	PUNCT
ejpam-2623	15	4	farashahi	farashahi	NOUN
ejpam-2623	15	5	et	et	PROPN
ejpam-2623	15	6	al	al	PROPN
ejpam-2623	15	7	.	.	PUNCT
ejpam-2623	16	1	[	[	X
ejpam-2623	16	2	14	14	NUM
ejpam-2623	16	3	]	]	PUNCT
ejpam-2623	16	4	defined	define	VERB
ejpam-2623	16	5	the	the	DET
ejpam-2623	16	6	notion	notion	NOUN
ejpam-2623	16	7	of	of	ADP
ejpam-2623	16	8	admissible	admissible	ADJ
ejpam-2623	16	9	encodings	encoding	NOUN
ejpam-2623	16	10	,	,	PUNCT
ejpam-2623	16	11	which	which	PRON
ejpam-2623	16	12	allow	allow	VERB
ejpam-2623	16	13	them	they	PRON
ejpam-2623	16	14	to	to	PART
ejpam-2623	16	15	give	give	VERB
ejpam-2623	16	16	a	a	DET
ejpam-2623	16	17	sufficient	sufficient	ADJ
ejpam-2623	16	18	condition	condition	NOUN
ejpam-2623	16	19	for	for	SCONJ
ejpam-2623	16	20	an	an	DET
ejpam-2623	16	21	encoding	encoding	NOUN
ejpam-2623	16	22	f	f	PROPN
ejpam-2623	16	23	to	to	PART
ejpam-2623	16	24	be	be	AUX
ejpam-2623	16	25	indifferentiable	indifferentiable	ADJ
ejpam-2623	16	26	from	from	ADP
ejpam-2623	16	27	a	a	DET
ejpam-2623	16	28	random	random	ADJ
ejpam-2623	16	29	oracle	oracle	NOUN
ejpam-2623	16	30	.	.	PUNCT
ejpam-2623	17	1	but	but	CCONJ
ejpam-2623	17	2	this	this	PRON
ejpam-2623	17	3	is	be	AUX
ejpam-2623	17	4	not	not	PART
ejpam-2623	17	5	applicable	applicable	ADJ
ejpam-2623	17	6	to	to	ADP
ejpam-2623	17	7	the	the	DET
ejpam-2623	17	8	constant	constant	ADJ
ejpam-2623	17	9	-	-	PUNCT
ejpam-2623	17	10	time	time	NOUN
ejpam-2623	17	11	encodings	encoding	NOUN
ejpam-2623	17	12	(	(	PUNCT
ejpam-2623	17	13	such	such	ADJ
ejpam-2623	17	14	as	as	ADP
ejpam-2623	17	15	icart	icart	PROPN
ejpam-2623	17	16	’s	’s	PART
ejpam-2623	17	17	encoding	encoding	NOUN
ejpam-2623	17	18	)	)	PUNCT
ejpam-2623	17	19	since	since	SCONJ
ejpam-2623	17	20	they	they	PRON
ejpam-2623	17	21	are	be	AUX
ejpam-2623	17	22	not	not	PART
ejpam-2623	17	23	admissible	admissible	ADJ
ejpam-2623	17	24	.	.	PUNCT
ejpam-2623	18	1	hence	hence	ADV
ejpam-2623	18	2	,	,	PUNCT
ejpam-2623	18	3	farashahi	farashahi	NOUN
ejpam-2623	18	4	et	et	PROPN
ejpam-2623	18	5	al	al	PROPN
ejpam-2623	18	6	.	.	PUNCT
ejpam-2623	19	1	[	[	X
ejpam-2623	19	2	14	14	NUM
ejpam-2623	19	3	]	]	PUNCT
ejpam-2623	19	4	proposed	propose	VERB
ejpam-2623	19	5	a	a	DET
ejpam-2623	19	6	more	more	ADV
ejpam-2623	19	7	general	general	ADJ
ejpam-2623	19	8	construction	construction	NOUN
ejpam-2623	19	9	h(m	h(m	NOUN
ejpam-2623	19	10	)	)	PUNCT
ejpam-2623	19	11	=	=	PUNCT
ejpam-2623	19	12	f(h1(m	f(h1(m	NOUN
ejpam-2623	19	13	)	)	PUNCT
ejpam-2623	19	14	)	)	PUNCT
ejpam-2623	20	1	+	+	CCONJ
ejpam-2623	20	2	.	.	PUNCT
ejpam-2623	20	3	.	.	PUNCT
ejpam-2623	21	1	.+	.+	NUM
ejpam-2623	21	2	f(hs(m	f(hs(m	PROPN
ejpam-2623	21	3	)	)	PUNCT
ejpam-2623	21	4	)	)	PUNCT
ejpam-2623	21	5	,	,	PUNCT
ejpam-2623	21	6	which	which	PRON
ejpam-2623	21	7	preserves	preserve	VERB
ejpam-2623	21	8	the	the	DET
ejpam-2623	21	9	indifferentiability	indifferentiability	NOUN
ejpam-2623	21	10	notion	notion	NOUN
ejpam-2623	21	11	if	if	SCONJ
ejpam-2623	21	12	the	the	DET
ejpam-2623	21	13	hi	hi	NOUN
ejpam-2623	21	14	are	be	AUX
ejpam-2623	21	15	modeled	model	VERB
ejpam-2623	21	16	as	as	ADP
ejpam-2623	21	17	random	random	ADJ
ejpam-2623	21	18	oracles	oracle	NOUN
ejpam-2623	21	19	and	and	CCONJ
ejpam-2623	21	20	s	s	NOUN
ejpam-2623	21	21	is	be	AUX
ejpam-2623	21	22	strictly	strictly	ADV
ejpam-2623	21	23	greater	great	ADJ
ejpam-2623	21	24	than	than	ADP
ejpam-2623	21	25	the	the	DET
ejpam-2623	21	26	genus	genus	NOUN
ejpam-2623	21	27	of	of	ADP
ejpam-2623	21	28	the	the	DET
ejpam-2623	21	29	curve	curve	NOUN
ejpam-2623	21	30	.	.	PUNCT
ejpam-2623	22	1	∗corresponding	∗corresponde	VERB
ejpam-2623	22	2	author	author	NOUN
ejpam-2623	22	3	.	.	PUNCT
ejpam-2623	23	1	email	email	NOUN
ejpam-2623	23	2	addresses	address	NOUN
ejpam-2623	23	3	:	:	PUNCT
ejpam-2623	23	4	fifiramatou@gmail.com	fifiramatou@gmail.com	X
ejpam-2623	23	5	(	(	PUNCT
ejpam-2623	23	6	n.	n.	PROPN
ejpam-2623	23	7	diarra	diarra	PROPN
ejpam-2623	23	8	)	)	PUNCT
ejpam-2623	23	9	,	,	PUNCT
ejpam-2623	23	10	sowdjibab@yahoo.fr	sowdjibab@yahoo.fr	NOUN
ejpam-2623	23	11	(	(	PUNCT
ejpam-2623	23	12	d.	d.	PROPN
ejpam-2623	23	13	sow	sow	PROPN
ejpam-2623	23	14	)	)	PUNCT
ejpam-2623	23	15	,	,	PUNCT
ejpam-2623	23	16	ahmed.youssef@ucad.edu.sn	ahmed.youssef@ucad.edu.sn	PROPN
ejpam-2623	23	17	(	(	PUNCT
ejpam-2623	23	18	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	23	19	.	.	PUNCT
ejpam-2623	23	20	khlil	khlil	PROPN
ejpam-2623	23	21	)	)	PUNCT
ejpam-2623	23	22	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2623	24	1	363	363	NUM
ejpam-2623	24	2	c	c	NOUN
ejpam-2623	24	3	©	©	PROPN
ejpam-2623	24	4	2017	2017	NUM
ejpam-2623	24	5	ejpam	ejpam	NOUN
ejpam-2623	24	6	all	all	DET
ejpam-2623	24	7	rights	right	NOUN
ejpam-2623	24	8	reserved	reserve	VERB
ejpam-2623	24	9	.	.	PUNCT
ejpam-2623	25	1	n.	n.	PROPN
ejpam-2623	25	2	diarra	diarra	PROPN
ejpam-2623	25	3	,	,	PUNCT
ejpam-2623	25	4	d.	d.	PROPN
ejpam-2623	25	5	sow	sow	PROPN
ejpam-2623	25	6	,	,	PUNCT
ejpam-2623	25	7	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	25	8	.	.	PUNCT
ejpam-2623	25	9	khlil	khlil	PROPN
ejpam-2623	25	10	/	/	SYM
ejpam-2623	25	11	eur	eur	PROPN
ejpam-2623	25	12	.	.	PUNCT
ejpam-2623	26	1	j.	j.	PROPN
ejpam-2623	26	2	pure	pure	PROPN
ejpam-2623	26	3	appl	appl	PROPN
ejpam-2623	26	4	.	.	PROPN
ejpam-2623	26	5	math	math	PROPN
ejpam-2623	26	6	,	,	PUNCT
ejpam-2623	26	7	10	10	NUM
ejpam-2623	26	8	(	(	PUNCT
ejpam-2623	26	9	2	2	NUM
ejpam-2623	26	10	)	)	PUNCT
ejpam-2623	26	11	(	(	PUNCT
ejpam-2623	26	12	2017	2017	NUM
ejpam-2623	26	13	)	)	PUNCT
ejpam-2623	26	14	,	,	PUNCT
ejpam-2623	26	15	363	363	NUM
ejpam-2623	26	16	-	-	SYM
ejpam-2623	26	17	391	391	NUM
ejpam-2623	26	18	364	364	NUM
ejpam-2623	26	19	on	on	ADP
ejpam-2623	26	20	another	another	DET
ejpam-2623	26	21	side	side	NOUN
ejpam-2623	27	1	,	,	PUNCT
ejpam-2623	27	2	ecc	ecc	PROPN
ejpam-2623	27	3	has	have	VERB
ejpam-2623	27	4	many	many	ADJ
ejpam-2623	27	5	applications	application	NOUN
ejpam-2623	27	6	on	on	ADP
ejpam-2623	27	7	internet	internet	NOUN
ejpam-2623	27	8	(	(	PUNCT
ejpam-2623	27	9	ssl	ssl	PROPN
ejpam-2623	27	10	/	/	SYM
ejpam-2623	27	11	tls	tls	PROPN
ejpam-2623	27	12	,	,	PUNCT
ejpam-2623	27	13	ssh	ssh	NOUN
ejpam-2623	27	14	,	,	PUNCT
ejpam-2623	27	15	tor	tor	NOUN
ejpam-2623	28	1	[	[	X
ejpam-2623	28	2	10	10	NUM
ejpam-2623	28	3	]	]	PUNCT
ejpam-2623	28	4	,	,	PUNCT
ejpam-2623	28	5	bitcoin	bitcoin	NOUN
ejpam-2623	28	6	,	,	PUNCT
ejpam-2623	28	7	...	...	PUNCT
ejpam-2623	28	8	)	)	PUNCT
ejpam-2623	28	9	;	;	PUNCT
ejpam-2623	28	10	but	but	CCONJ
ejpam-2623	28	11	it	it	PRON
ejpam-2623	28	12	presents	present	VERB
ejpam-2623	28	13	at	at	ADV
ejpam-2623	28	14	least	least	ADV
ejpam-2623	28	15	one	one	NUM
ejpam-2623	28	16	drawback	drawback	NOUN
ejpam-2623	28	17	:	:	PUNCT
ejpam-2623	28	18	for	for	ADP
ejpam-2623	28	19	applications	application	NOUN
ejpam-2623	28	20	in	in	ADP
ejpam-2623	28	21	censorship	censorship	NOUN
ejpam-2623	28	22	circumvention	circumvention	NOUN
ejpam-2623	28	23	,	,	PUNCT
ejpam-2623	28	24	points	point	NOUN
ejpam-2623	28	25	of	of	ADP
ejpam-2623	28	26	elliptic	elliptic	ADJ
ejpam-2623	28	27	curves	curve	NOUN
ejpam-2623	28	28	are	be	AUX
ejpam-2623	28	29	easy	easy	ADJ
ejpam-2623	28	30	to	to	PART
ejpam-2623	28	31	distinguish	distinguish	VERB
ejpam-2623	28	32	from	from	ADP
ejpam-2623	28	33	uniform	uniform	ADJ
ejpam-2623	28	34	random	random	ADJ
ejpam-2623	28	35	strings	string	NOUN
ejpam-2623	28	36	if	if	SCONJ
ejpam-2623	28	37	a	a	DET
ejpam-2623	28	38	suitable	suitable	ADJ
ejpam-2623	28	39	implementation	implementation	NOUN
ejpam-2623	28	40	is	be	AUX
ejpam-2623	28	41	not	not	PART
ejpam-2623	28	42	used	use	VERB
ejpam-2623	28	43	.	.	PUNCT
ejpam-2623	29	1	the	the	DET
ejpam-2623	29	2	problem	problem	NOUN
ejpam-2623	29	3	of	of	ADP
ejpam-2623	29	4	making	make	VERB
ejpam-2623	29	5	points	point	NOUN
ejpam-2623	29	6	of	of	ADP
ejpam-2623	29	7	elliptic	elliptic	ADJ
ejpam-2623	29	8	curves	curve	NOUN
ejpam-2623	29	9	indistinguishable	indistinguishable	ADJ
ejpam-2623	29	10	from	from	ADP
ejpam-2623	29	11	uniform	uniform	ADJ
ejpam-2623	29	12	random	random	ADJ
ejpam-2623	29	13	strings	string	NOUN
ejpam-2623	29	14	was	be	AUX
ejpam-2623	29	15	investigated	investigate	VERB
ejpam-2623	29	16	by	by	ADP
ejpam-2623	29	17	möller	möller	NOUN
ejpam-2623	29	18	[	[	X
ejpam-2623	29	19	11	11	NUM
ejpam-2623	29	20	]	]	PUNCT
ejpam-2623	29	21	,	,	PUNCT
ejpam-2623	29	22	bernstein	bernstein	PROPN
ejpam-2623	29	23	et	et	PROPN
ejpam-2623	29	24	al	al	PROPN
ejpam-2623	29	25	.	.	PUNCT
ejpam-2623	30	1	[	[	X
ejpam-2623	30	2	4	4	NUM
ejpam-2623	30	3	]	]	PUNCT
ejpam-2623	30	4	,	,	PUNCT
ejpam-2623	30	5	tibouchi	tibouchi	NOUN
ejpam-2623	30	6	[	[	X
ejpam-2623	30	7	17	17	NUM
ejpam-2623	30	8	]	]	PUNCT
ejpam-2623	30	9	.	.	PUNCT
ejpam-2623	31	1	the	the	DET
ejpam-2623	31	2	first	first	ADJ
ejpam-2623	31	3	approach	approach	NOUN
ejpam-2623	31	4	is	be	AUX
ejpam-2623	31	5	möller	möller	NOUN
ejpam-2623	31	6	’s	’s	NOUN
ejpam-2623	31	7	one	one	NUM
ejpam-2623	31	8	.	.	PUNCT
ejpam-2623	32	1	in	in	ADP
ejpam-2623	32	2	2004	2004	NUM
ejpam-2623	32	3	[	[	X
ejpam-2623	32	4	11	11	NUM
ejpam-2623	32	5	]	]	PUNCT
ejpam-2623	32	6	,	,	PUNCT
ejpam-2623	32	7	möller	möller	NOUN
ejpam-2623	32	8	proposed	propose	VERB
ejpam-2623	32	9	to	to	PART
ejpam-2623	32	10	modify	modify	VERB
ejpam-2623	32	11	protocols	protocol	NOUN
ejpam-2623	32	12	so	so	SCONJ
ejpam-2623	32	13	that	that	SCONJ
ejpam-2623	32	14	transmitted	transmit	VERB
ejpam-2623	32	15	points	point	NOUN
ejpam-2623	32	16	lie	lie	VERB
ejpam-2623	32	17	either	either	CCONJ
ejpam-2623	32	18	on	on	ADP
ejpam-2623	32	19	the	the	DET
ejpam-2623	32	20	given	give	VERB
ejpam-2623	32	21	elliptic	elliptic	ADJ
ejpam-2623	32	22	curve	curve	NOUN
ejpam-2623	32	23	or	or	CCONJ
ejpam-2623	32	24	in	in	ADP
ejpam-2623	32	25	its	its	PRON
ejpam-2623	32	26	quadratic	quadratic	ADJ
ejpam-2623	32	27	twist	twist	NOUN
ejpam-2623	32	28	[	[	X
ejpam-2623	32	29	5	5	NUM
ejpam-2623	32	30	]	]	PUNCT
ejpam-2623	32	31	.	.	PUNCT
ejpam-2623	33	1	but	but	CCONJ
ejpam-2623	33	2	this	this	DET
ejpam-2623	33	3	approach	approach	NOUN
ejpam-2623	33	4	imposes	impose	VERB
ejpam-2623	33	5	twist	twist	NOUN
ejpam-2623	33	6	-	-	PUNCT
ejpam-2623	33	7	security	security	NOUN
ejpam-2623	33	8	.	.	PUNCT
ejpam-2623	34	1	the	the	DET
ejpam-2623	34	2	second	second	ADJ
ejpam-2623	34	3	approach	approach	NOUN
ejpam-2623	34	4	,	,	PUNCT
ejpam-2623	34	5	called	call	VERB
ejpam-2623	34	6	elligator	elligator	NOUN
ejpam-2623	34	7	,	,	PUNCT
ejpam-2623	34	8	is	be	AUX
ejpam-2623	34	9	the	the	DET
ejpam-2623	34	10	one	one	NOUN
ejpam-2623	34	11	proposed	propose	VERB
ejpam-2623	34	12	by	by	ADP
ejpam-2623	34	13	bernstein	bernstein	PROPN
ejpam-2623	34	14	et	et	PROPN
ejpam-2623	34	15	al	al	PROPN
ejpam-2623	34	16	.	.	PUNCT
ejpam-2623	35	1	in	in	ADP
ejpam-2623	35	2	[	[	X
ejpam-2623	35	3	4	4	NUM
ejpam-2623	35	4	]	]	PUNCT
ejpam-2623	35	5	.	.	PUNCT
ejpam-2623	36	1	it	it	PRON
ejpam-2623	36	2	is	be	AUX
ejpam-2623	36	3	based	base	VERB
ejpam-2623	36	4	on	on	ADP
ejpam-2623	36	5	the	the	DET
ejpam-2623	36	6	construction	construction	NOUN
ejpam-2623	36	7	of	of	ADP
ejpam-2623	36	8	an	an	DET
ejpam-2623	36	9	efficient	efficient	ADJ
ejpam-2623	36	10	injective	injective	ADJ
ejpam-2623	36	11	and	and	CCONJ
ejpam-2623	36	12	invertible	invertible	ADJ
ejpam-2623	36	13	encoding	encoding	NOUN
ejpam-2623	36	14	ψ	ψ	NOUN
ejpam-2623	36	15	that	that	PRON
ejpam-2623	36	16	maps	map	VERB
ejpam-2623	36	17	a	a	DET
ejpam-2623	36	18	subset	subset	NOUN
ejpam-2623	36	19	s	s	PART
ejpam-2623	36	20	⊆	⊆	NUM
ejpam-2623	36	21	fq	fq	NOUN
ejpam-2623	36	22	(	(	PUNCT
ejpam-2623	36	23	where	where	SCONJ
ejpam-2623	36	24	q	q	ADJ
ejpam-2623	36	25	prime	prime	NOUN
ejpam-2623	36	26	and	and	CCONJ
ejpam-2623	36	27	s	s	NOUN
ejpam-2623	36	28	∩	∩	ADJ
ejpam-2623	36	29	−s	−s	NOUN
ejpam-2623	36	30	=	=	SYM
ejpam-2623	36	31	{	{	PUNCT
ejpam-2623	36	32	0	0	NUM
ejpam-2623	36	33	}	}	PUNCT
ejpam-2623	36	34	)	)	PUNCT
ejpam-2623	36	35	,	,	PUNCT
ejpam-2623	36	36	to	to	ADP
ejpam-2623	36	37	the	the	DET
ejpam-2623	36	38	group	group	NOUN
ejpam-2623	36	39	e(fq	e(fq	PROPN
ejpam-2623	36	40	)	)	PUNCT
ejpam-2623	36	41	of	of	ADP
ejpam-2623	36	42	an	an	DET
ejpam-2623	36	43	elliptic	elliptic	ADJ
ejpam-2623	36	44	curve	curve	NOUN
ejpam-2623	36	45	e	e	PROPN
ejpam-2623	36	46	over	over	ADP
ejpam-2623	36	47	fq	fq	PROPN
ejpam-2623	36	48	.	.	PUNCT
ejpam-2623	37	1	since	since	SCONJ
ejpam-2623	37	2	the	the	DET
ejpam-2623	37	3	map	map	NOUN
ejpam-2623	37	4	is	be	AUX
ejpam-2623	37	5	injective	injective	ADJ
ejpam-2623	37	6	and	and	CCONJ
ejpam-2623	37	7	invertible	invertible	ADJ
ejpam-2623	37	8	,	,	PUNCT
ejpam-2623	37	9	bernstein	bernstein	PROPN
ejpam-2623	37	10	et	et	PROPN
ejpam-2623	37	11	al	al	PROPN
ejpam-2623	37	12	.	.	PROPN
ejpam-2623	37	13	consider	consider	VERB
ejpam-2623	37	14	that	that	SCONJ
ejpam-2623	37	15	a	a	DET
ejpam-2623	37	16	point	point	NOUN
ejpam-2623	37	17	p	p	X
ejpam-2623	37	18	∈	∈	PROPN
ejpam-2623	37	19	im(ψ	im(ψ	NOUN
ejpam-2623	37	20	)	)	PUNCT
ejpam-2623	37	21	of	of	ADP
ejpam-2623	37	22	the	the	DET
ejpam-2623	37	23	curve	curve	NOUN
ejpam-2623	37	24	can	can	AUX
ejpam-2623	37	25	be	be	AUX
ejpam-2623	37	26	viewed	view	VERB
ejpam-2623	37	27	as	as	ADP
ejpam-2623	37	28	the	the	DET
ejpam-2623	37	29	string	string	NOUN
ejpam-2623	37	30	representation	representation	NOUN
ejpam-2623	37	31	of	of	ADP
ejpam-2623	37	32	the	the	DET
ejpam-2623	37	33	unique	unique	ADJ
ejpam-2623	37	34	ψ−1(p	ψ−1(p	NOUN
ejpam-2623	37	35	)	)	PUNCT
ejpam-2623	37	36	.	.	PUNCT
ejpam-2623	38	1	moreover	moreover	ADV
ejpam-2623	38	2	,	,	PUNCT
ejpam-2623	38	3	if	if	SCONJ
ejpam-2623	38	4	q	q	NOUN
ejpam-2623	38	5	is	be	AUX
ejpam-2623	38	6	chosen	choose	VERB
ejpam-2623	38	7	such	such	ADJ
ejpam-2623	38	8	that	that	SCONJ
ejpam-2623	38	9	#	#	NOUN
ejpam-2623	38	10	s	s	NOUN
ejpam-2623	38	11	is	be	AUX
ejpam-2623	38	12	relatively	relatively	ADV
ejpam-2623	38	13	close	close	ADJ
ejpam-2623	38	14	to	to	ADP
ejpam-2623	38	15	a	a	DET
ejpam-2623	38	16	power	power	NOUN
ejpam-2623	38	17	of	of	ADP
ejpam-2623	38	18	2	2	NUM
ejpam-2623	38	19	,	,	PUNCT
ejpam-2623	38	20	then	then	ADV
ejpam-2623	38	21	a	a	DET
ejpam-2623	38	22	uniform	uniform	NOUN
ejpam-2623	38	23	p	p	X
ejpam-2623	38	24	∈	∈	PROPN
ejpam-2623	38	25	im(ψ	im(ψ	NOUN
ejpam-2623	38	26	)	)	PUNCT
ejpam-2623	38	27	will	will	AUX
ejpam-2623	38	28	have	have	VERB
ejpam-2623	38	29	a	a	DET
ejpam-2623	38	30	close	close	NOUN
ejpam-2623	38	31	to	to	PART
ejpam-2623	38	32	uniform	uniform	ADJ
ejpam-2623	38	33	bit	bit	NOUN
ejpam-2623	38	34	string	string	NOUN
ejpam-2623	38	35	representation	representation	NOUN
ejpam-2623	38	36	.	.	PUNCT
ejpam-2623	39	1	this	this	DET
ejpam-2623	39	2	method	method	NOUN
ejpam-2623	39	3	has	have	VERB
ejpam-2623	39	4	the	the	DET
ejpam-2623	39	5	advantage	advantage	NOUN
ejpam-2623	39	6	to	to	PART
ejpam-2623	39	7	not	not	PART
ejpam-2623	39	8	impose	impose	VERB
ejpam-2623	39	9	additional	additional	ADJ
ejpam-2623	39	10	security	security	NOUN
ejpam-2623	39	11	requirements	requirement	NOUN
ejpam-2623	39	12	on	on	ADP
ejpam-2623	39	13	the	the	DET
ejpam-2623	39	14	quadratic	quadratic	ADJ
ejpam-2623	39	15	twist	twist	NOUN
ejpam-2623	39	16	of	of	ADP
ejpam-2623	39	17	the	the	DET
ejpam-2623	39	18	curve	curve	NOUN
ejpam-2623	39	19	,	,	PUNCT
ejpam-2623	39	20	but	but	CCONJ
ejpam-2623	39	21	it	it	PRON
ejpam-2623	39	22	relies	rely	VERB
ejpam-2623	39	23	on	on	ADP
ejpam-2623	39	24	the	the	DET
ejpam-2623	39	25	existence	existence	NOUN
ejpam-2623	39	26	of	of	ADP
ejpam-2623	39	27	the	the	DET
ejpam-2623	39	28	injective	injective	ADJ
ejpam-2623	39	29	encoding	encoding	NOUN
ejpam-2623	39	30	ψ	ψ	X
ejpam-2623	39	31	.	.	PUNCT
ejpam-2623	40	1	recently	recently	ADV
ejpam-2623	40	2	[	[	X
ejpam-2623	40	3	17	17	NUM
ejpam-2623	40	4	]	]	PUNCT
ejpam-2623	40	5	,	,	PUNCT
ejpam-2623	40	6	tibouchi	tibouchi	PROPN
ejpam-2623	40	7	proposed	propose	VERB
ejpam-2623	40	8	a	a	DET
ejpam-2623	40	9	new	new	ADJ
ejpam-2623	40	10	method	method	NOUN
ejpam-2623	40	11	,	,	PUNCT
ejpam-2623	40	12	called	call	VERB
ejpam-2623	40	13	elligator	elligator	NOUN
ejpam-2623	40	14	-	-	PUNCT
ejpam-2623	40	15	squared	square	VERB
ejpam-2623	40	16	,	,	PUNCT
ejpam-2623	40	17	which	which	PRON
ejpam-2623	40	18	supports	support	VERB
ejpam-2623	40	19	more	more	ADJ
ejpam-2623	40	20	elliptic	elliptic	ADJ
ejpam-2623	40	21	curves	curve	NOUN
ejpam-2623	40	22	than	than	ADP
ejpam-2623	40	23	elligator	elligator	NOUN
ejpam-2623	40	24	.	.	PUNCT
ejpam-2623	41	1	while	while	SCONJ
ejpam-2623	41	2	elligator	elligator	NOUN
ejpam-2623	41	3	is	be	AUX
ejpam-2623	41	4	used	use	VERB
ejpam-2623	41	5	to	to	PART
ejpam-2623	41	6	represent	represent	VERB
ejpam-2623	41	7	a	a	DET
ejpam-2623	41	8	point	point	NOUN
ejpam-2623	41	9	p	p	NOUN
ejpam-2623	41	10	in	in	ADP
ejpam-2623	41	11	the	the	DET
ejpam-2623	41	12	curve	curve	NOUN
ejpam-2623	41	13	by	by	ADP
ejpam-2623	41	14	a	a	DET
ejpam-2623	41	15	preimage	preimage	NOUN
ejpam-2623	41	16	under	under	ADP
ejpam-2623	41	17	an	an	DET
ejpam-2623	41	18	injective	injective	ADJ
ejpam-2623	41	19	encoding	encoding	NOUN
ejpam-2623	41	20	,	,	PUNCT
ejpam-2623	41	21	in	in	ADP
ejpam-2623	41	22	elligator	elligator	NOUN
ejpam-2623	41	23	-	-	PUNCT
ejpam-2623	41	24	squared	square	VERB
ejpam-2623	41	25	,	,	PUNCT
ejpam-2623	41	26	a	a	DET
ejpam-2623	41	27	point	point	NOUN
ejpam-2623	41	28	p	p	NOUN
ejpam-2623	41	29	in	in	ADP
ejpam-2623	41	30	the	the	DET
ejpam-2623	41	31	curve	curve	NOUN
ejpam-2623	41	32	is	be	AUX
ejpam-2623	41	33	represented	represent	VERB
ejpam-2623	41	34	by	by	ADP
ejpam-2623	41	35	a	a	DET
ejpam-2623	41	36	randomly	randomly	ADV
ejpam-2623	41	37	sampled	sample	VERB
ejpam-2623	41	38	preimage	preimage	NOUN
ejpam-2623	41	39	under	under	ADP
ejpam-2623	41	40	a	a	DET
ejpam-2623	41	41	surjective	surjective	ADJ
ejpam-2623	41	42	map	map	NOUN
ejpam-2623	41	43	.	.	PUNCT
ejpam-2623	42	1	in	in	ADP
ejpam-2623	42	2	binary	binary	ADJ
ejpam-2623	42	3	-	-	PUNCT
ejpam-2623	42	4	elligator	elligator	NOUN
ejpam-2623	42	5	-	-	PUNCT
ejpam-2623	42	6	squared	square	VERB
ejpam-2623	42	7	[	[	X
ejpam-2623	42	8	5	5	NUM
ejpam-2623	42	9	]	]	PUNCT
ejpam-2623	42	10	,	,	PUNCT
ejpam-2623	42	11	a	a	DET
ejpam-2623	42	12	comparison	comparison	NOUN
ejpam-2623	42	13	between	between	ADP
ejpam-2623	42	14	elligator	elligator	NOUN
ejpam-2623	42	15	and	and	CCONJ
ejpam-2623	42	16	elligator	elligator	NOUN
ejpam-2623	42	17	-	-	PUNCT
ejpam-2623	42	18	squared	square	VERB
ejpam-2623	42	19	is	be	AUX
ejpam-2623	42	20	done	do	VERB
ejpam-2623	42	21	.	.	PUNCT
ejpam-2623	43	1	elligator	elligator	NOUN
ejpam-2623	43	2	is	be	AUX
ejpam-2623	43	3	better	well	ADJ
ejpam-2623	43	4	for	for	ADP
ejpam-2623	43	5	protocols	protocol	NOUN
ejpam-2623	43	6	using	use	VERB
ejpam-2623	43	7	a	a	DET
ejpam-2623	43	8	fixed	fix	VERB
ejpam-2623	43	9	base	base	NOUN
ejpam-2623	43	10	point	point	NOUN
ejpam-2623	43	11	(	(	PUNCT
ejpam-2623	43	12	such	such	ADJ
ejpam-2623	43	13	as	as	ADP
ejpam-2623	43	14	static	static	ADJ
ejpam-2623	43	15	ecdh	ecdh	NOUN
ejpam-2623	43	16	)	)	PUNCT
ejpam-2623	43	17	,	,	PUNCT
ejpam-2623	43	18	but	but	CCONJ
ejpam-2623	43	19	elligator	elligator	NOUN
ejpam-2623	43	20	-	-	PUNCT
ejpam-2623	43	21	squared	square	VERB
ejpam-2623	43	22	is	be	AUX
ejpam-2623	43	23	better	well	ADJ
ejpam-2623	43	24	for	for	ADP
ejpam-2623	43	25	protocols	protocol	NOUN
ejpam-2623	43	26	using	use	VERB
ejpam-2623	43	27	a	a	DET
ejpam-2623	43	28	variable	variable	ADJ
ejpam-2623	43	29	base	base	NOUN
ejpam-2623	43	30	point	point	NOUN
ejpam-2623	43	31	(	(	PUNCT
ejpam-2623	43	32	such	such	ADJ
ejpam-2623	43	33	as	as	ADP
ejpam-2623	43	34	elgamal	elgamal	ADJ
ejpam-2623	43	35	encryption	encryption	NOUN
ejpam-2623	43	36	)	)	PUNCT
ejpam-2623	43	37	.	.	PUNCT
ejpam-2623	44	1	even	even	ADV
ejpam-2623	44	2	if	if	SCONJ
ejpam-2623	44	3	elligator	elligator	NOUN
ejpam-2623	44	4	-	-	PUNCT
ejpam-2623	44	5	squared	square	VERB
ejpam-2623	44	6	constructs	construct	VERB
ejpam-2623	44	7	a	a	DET
ejpam-2623	44	8	surjective	surjective	ADJ
ejpam-2623	44	9	map	map	NOUN
ejpam-2623	44	10	,	,	PUNCT
ejpam-2623	44	11	it	it	PRON
ejpam-2623	44	12	uses	use	VERB
ejpam-2623	44	13	an	an	DET
ejpam-2623	44	14	injective	injective	ADJ
ejpam-2623	44	15	encoding	encoding	NOUN
ejpam-2623	44	16	as	as	ADP
ejpam-2623	44	17	elligator	elligator	NOUN
ejpam-2623	44	18	.	.	PUNCT
ejpam-2623	45	1	to	to	ADP
ejpam-2623	45	2	our	our	PRON
ejpam-2623	45	3	knowledge	knowledge	NOUN
ejpam-2623	45	4	,	,	PUNCT
ejpam-2623	45	5	only	only	ADV
ejpam-2623	45	6	a	a	DET
ejpam-2623	45	7	few	few	ADJ
ejpam-2623	45	8	examples	example	NOUN
ejpam-2623	45	9	of	of	ADP
ejpam-2623	45	10	such	such	ADJ
ejpam-2623	45	11	encodings	encoding	NOUN
ejpam-2623	45	12	exist	exist	VERB
ejpam-2623	45	13	[	[	X
ejpam-2623	45	14	5	5	NUM
ejpam-2623	45	15	,	,	PUNCT
ejpam-2623	45	16	4	4	NUM
ejpam-2623	45	17	,	,	PUNCT
ejpam-2623	45	18	13	13	NUM
ejpam-2623	45	19	,	,	PUNCT
ejpam-2623	45	20	12	12	NUM
ejpam-2623	45	21	]	]	PUNCT
ejpam-2623	45	22	.	.	PUNCT
ejpam-2623	46	1	this	this	PRON
ejpam-2623	46	2	is	be	AUX
ejpam-2623	46	3	one	one	NUM
ejpam-2623	46	4	of	of	ADP
ejpam-2623	46	5	the	the	DET
ejpam-2623	46	6	motivations	motivation	NOUN
ejpam-2623	46	7	of	of	ADP
ejpam-2623	46	8	this	this	DET
ejpam-2623	46	9	paper	paper	NOUN
ejpam-2623	46	10	.	.	PUNCT
ejpam-2623	47	1	organization	organization	NOUN
ejpam-2623	47	2	of	of	ADP
ejpam-2623	47	3	the	the	DET
ejpam-2623	47	4	paper	paper	NOUN
ejpam-2623	47	5	:	:	PUNCT
ejpam-2623	47	6	•	•	NUM
ejpam-2623	47	7	section	section	NOUN
ejpam-2623	47	8	2	2	NUM
ejpam-2623	47	9	recalls	recall	VERB
ejpam-2623	47	10	some	some	DET
ejpam-2623	47	11	definitions	definition	NOUN
ejpam-2623	47	12	about	about	ADP
ejpam-2623	47	13	square	square	ADJ
ejpam-2623	47	14	roots	root	NOUN
ejpam-2623	47	15	in	in	ADP
ejpam-2623	47	16	finite	finite	ADJ
ejpam-2623	47	17	fields	field	NOUN
ejpam-2623	47	18	(	(	PUNCT
ejpam-2623	47	19	2.1	2.1	NUM
ejpam-2623	47	20	)	)	PUNCT
ejpam-2623	47	21	and	and	CCONJ
ejpam-2623	47	22	gives	give	VERB
ejpam-2623	47	23	an	an	DET
ejpam-2623	47	24	overview	overview	NOUN
ejpam-2623	47	25	of	of	ADP
ejpam-2623	47	26	existing	exist	VERB
ejpam-2623	47	27	encodings	encoding	NOUN
ejpam-2623	47	28	into	into	ADP
ejpam-2623	47	29	elliptic	elliptic	ADJ
ejpam-2623	47	30	curves	curve	NOUN
ejpam-2623	47	31	(	(	PUNCT
ejpam-2623	47	32	2.2	2.2	NUM
ejpam-2623	47	33	)	)	PUNCT
ejpam-2623	47	34	.	.	PUNCT
ejpam-2623	48	1	•	•	NUM
ejpam-2623	48	2	sections	section	NOUN
ejpam-2623	48	3	3	3	NUM
ejpam-2623	48	4	and	and	CCONJ
ejpam-2623	48	5	4	4	NUM
ejpam-2623	48	6	present	present	VERB
ejpam-2623	48	7	the	the	DET
ejpam-2623	48	8	contributions	contribution	NOUN
ejpam-2623	48	9	of	of	ADP
ejpam-2623	48	10	this	this	DET
ejpam-2623	48	11	paper	paper	NOUN
ejpam-2623	48	12	as	as	SCONJ
ejpam-2623	48	13	follows	follow	VERB
ejpam-2623	48	14	:	:	PUNCT
ejpam-2623	48	15	–	–	PUNCT
ejpam-2623	48	16	in	in	ADP
ejpam-2623	48	17	section	section	NOUN
ejpam-2623	48	18	3	3	NUM
ejpam-2623	48	19	,	,	PUNCT
ejpam-2623	48	20	we	we	PRON
ejpam-2623	48	21	revisit	revisit	VERB
ejpam-2623	48	22	elligator	elligator	NOUN
ejpam-2623	48	23	’s	’s	PART
ejpam-2623	48	24	methods	method	NOUN
ejpam-2623	48	25	for	for	ADP
ejpam-2623	48	26	constructing	construct	VERB
ejpam-2623	48	27	almost	almost	ADV
ejpam-2623	48	28	-	-	PUNCT
ejpam-2623	48	29	injective	injective	ADJ
ejpam-2623	48	30	and	and	CCONJ
ejpam-2623	48	31	invertible	invertible	ADJ
ejpam-2623	48	32	encodings	encoding	NOUN
ejpam-2623	48	33	for	for	ADP
ejpam-2623	48	34	some	some	DET
ejpam-2623	48	35	models	model	NOUN
ejpam-2623	48	36	of	of	ADP
ejpam-2623	48	37	curves	curve	NOUN
ejpam-2623	48	38	:	:	PUNCT
ejpam-2623	48	39	(	(	PUNCT
ejpam-2623	48	40	3.1	3.1	NUM
ejpam-2623	48	41	)	)	PUNCT
ejpam-2623	48	42	generalized	generalize	VERB
ejpam-2623	48	43	huff	huff	NOUN
ejpam-2623	48	44	curves	curve	NOUN
ejpam-2623	48	45	x(ay2	x(ay2	PUNCT
ejpam-2623	49	1	−	−	ADP
ejpam-2623	49	2	1	1	NUM
ejpam-2623	49	3	)	)	PUNCT
ejpam-2623	49	4	=	=	PUNCT
ejpam-2623	50	1	y(bx2	y(bx2	NOUN
ejpam-2623	51	1	−	−	NOUN
ejpam-2623	51	2	1	1	NUM
ejpam-2623	51	3	)	)	PUNCT
ejpam-2623	51	4	,	,	PUNCT
ejpam-2623	51	5	(	(	PUNCT
ejpam-2623	51	6	3.2	3.2	NUM
ejpam-2623	51	7	)	)	PUNCT
ejpam-2623	51	8	classical	classical	ADJ
ejpam-2623	51	9	huff	huff	NOUN
ejpam-2623	51	10	curves	curve	NOUN
ejpam-2623	51	11	αx(y2	αx(y2	ADP
ejpam-2623	51	12	−	−	NOUN
ejpam-2623	51	13	1	1	NUM
ejpam-2623	51	14	)	)	PUNCT
ejpam-2623	51	15	=	=	SYM
ejpam-2623	51	16	βy(x2	βy(x2	NOUN
ejpam-2623	52	1	−	−	NOUN
ejpam-2623	52	2	1	1	NUM
ejpam-2623	52	3	)	)	PUNCT
ejpam-2623	52	4	,	,	PUNCT
ejpam-2623	52	5	(	(	PUNCT
ejpam-2623	52	6	3.3	3.3	NUM
ejpam-2623	52	7	)	)	PUNCT
ejpam-2623	52	8	edwards	edwards	PROPN
ejpam-2623	52	9	curves	curve	VERB
ejpam-2623	52	10	x2	x2	PROPN
ejpam-2623	53	1	+	+	CCONJ
ejpam-2623	53	2	y2	y2	NOUN
ejpam-2623	53	3	=	=	SYM
ejpam-2623	53	4	1	1	NUM
ejpam-2623	53	5	+	+	CCONJ
ejpam-2623	53	6	dx2y2	dx2y2	PROPN
ejpam-2623	53	7	and	and	CCONJ
ejpam-2623	53	8	(	(	PUNCT
ejpam-2623	53	9	3.4	3.4	NUM
ejpam-2623	53	10	)	)	PUNCT
ejpam-2623	53	11	weierstrass	weierstrass	NOUN
ejpam-2623	53	12	model	model	NOUN
ejpam-2623	53	13	y2	y2	PROPN
ejpam-2623	53	14	=	=	PUNCT
ejpam-2623	54	1	x3	x3	PROPN
ejpam-2623	54	2	+	+	CCONJ
ejpam-2623	54	3	ax2	ax2	NOUN
ejpam-2623	54	4	+	+	CCONJ
ejpam-2623	54	5	c.	c.	NOUN
ejpam-2623	54	6	–	–	PUNCT
ejpam-2623	54	7	section	section	NOUN
ejpam-2623	54	8	4	4	NUM
ejpam-2623	54	9	begins	begin	VERB
ejpam-2623	54	10	by	by	ADP
ejpam-2623	54	11	a	a	DET
ejpam-2623	54	12	review	review	NOUN
ejpam-2623	54	13	of	of	ADP
ejpam-2623	54	14	well	well	ADV
ejpam-2623	54	15	-	-	PUNCT
ejpam-2623	54	16	distributed	distribute	VERB
ejpam-2623	54	17	encodings	encoding	NOUN
ejpam-2623	54	18	(	(	PUNCT
ejpam-2623	54	19	4.1	4.1	NUM
ejpam-2623	54	20	)	)	PUNCT
ejpam-2623	54	21	,	,	PUNCT
ejpam-2623	54	22	as	as	SCONJ
ejpam-2623	54	23	defined	define	VERB
ejpam-2623	54	24	in	in	ADP
ejpam-2623	54	25	[	[	X
ejpam-2623	54	26	6	6	NUM
ejpam-2623	54	27	,	,	PUNCT
ejpam-2623	54	28	14	14	NUM
ejpam-2623	54	29	]	]	PUNCT
ejpam-2623	54	30	.	.	PUNCT
ejpam-2623	55	1	then	then	ADV
ejpam-2623	55	2	we	we	PRON
ejpam-2623	55	3	show	show	VERB
ejpam-2623	55	4	(	(	PUNCT
ejpam-2623	55	5	4.3	4.3	NUM
ejpam-2623	55	6	)	)	PUNCT
ejpam-2623	55	7	how	how	SCONJ
ejpam-2623	55	8	one	one	PRON
ejpam-2623	55	9	can	can	AUX
ejpam-2623	55	10	obtain	obtain	VERB
ejpam-2623	55	11	a	a	DET
ejpam-2623	55	12	hash	hash	NOUN
ejpam-2623	55	13	function	function	NOUN
ejpam-2623	55	14	indifferentiable	indifferentiable	ADJ
ejpam-2623	55	15	from	from	ADP
ejpam-2623	55	16	a	a	DET
ejpam-2623	55	17	random	random	ADJ
ejpam-2623	55	18	oracle	oracle	NOUN
ejpam-2623	55	19	using	use	VERB
ejpam-2623	55	20	one	one	NUM
ejpam-2623	55	21	of	of	ADP
ejpam-2623	55	22	the	the	DET
ejpam-2623	55	23	previous	previous	ADJ
ejpam-2623	55	24	encodings	encoding	NOUN
ejpam-2623	55	25	and	and	CCONJ
ejpam-2623	55	26	following	follow	VERB
ejpam-2623	55	27	the	the	DET
ejpam-2623	55	28	methodology	methodology	NOUN
ejpam-2623	55	29	in	in	ADP
ejpam-2623	55	30	[	[	X
ejpam-2623	55	31	6	6	NUM
ejpam-2623	55	32	,	,	PUNCT
ejpam-2623	55	33	14	14	NUM
ejpam-2623	55	34	]	]	PUNCT
ejpam-2623	55	35	.	.	PUNCT
ejpam-2623	56	1	n.	n.	PROPN
ejpam-2623	56	2	diarra	diarra	PROPN
ejpam-2623	56	3	,	,	PUNCT
ejpam-2623	56	4	d.	d.	PROPN
ejpam-2623	56	5	sow	sow	PROPN
ejpam-2623	56	6	,	,	PUNCT
ejpam-2623	56	7	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	56	8	.	.	PUNCT
ejpam-2623	56	9	khlil	khlil	PROPN
ejpam-2623	56	10	/	/	SYM
ejpam-2623	56	11	eur	eur	PROPN
ejpam-2623	56	12	.	.	PUNCT
ejpam-2623	57	1	j.	j.	PROPN
ejpam-2623	57	2	pure	pure	PROPN
ejpam-2623	57	3	appl	appl	PROPN
ejpam-2623	57	4	.	.	PROPN
ejpam-2623	57	5	math	math	PROPN
ejpam-2623	57	6	,	,	PUNCT
ejpam-2623	57	7	10	10	NUM
ejpam-2623	57	8	(	(	PUNCT
ejpam-2623	57	9	2	2	NUM
ejpam-2623	57	10	)	)	PUNCT
ejpam-2623	57	11	(	(	PUNCT
ejpam-2623	57	12	2017	2017	NUM
ejpam-2623	57	13	)	)	PUNCT
ejpam-2623	57	14	,	,	PUNCT
ejpam-2623	57	15	363	363	NUM
ejpam-2623	57	16	-	-	SYM
ejpam-2623	57	17	391	391	NUM
ejpam-2623	57	18	365	365	NUM
ejpam-2623	57	19	2	2	NUM
ejpam-2623	57	20	.	.	PUNCT
ejpam-2623	57	21	preliminaries	preliminary	NOUN
ejpam-2623	57	22	2.1	2.1	NUM
ejpam-2623	57	23	.	.	PUNCT
ejpam-2623	58	1	squares	square	NOUN
ejpam-2623	58	2	and	and	CCONJ
ejpam-2623	58	3	square	square	ADJ
ejpam-2623	58	4	roots	root	NOUN
ejpam-2623	58	5	let	let	VERB
ejpam-2623	58	6	q	q	NOUN
ejpam-2623	58	7	be	be	AUX
ejpam-2623	58	8	an	an	DET
ejpam-2623	58	9	odd	odd	ADJ
ejpam-2623	58	10	prime	prime	ADJ
ejpam-2623	58	11	power	power	NOUN
ejpam-2623	58	12	.	.	PUNCT
ejpam-2623	59	1	(	(	PUNCT
ejpam-2623	59	2	i	i	NOUN
ejpam-2623	59	3	)	)	PUNCT
ejpam-2623	59	4	the	the	DET
ejpam-2623	59	5	quadratic	quadratic	ADJ
ejpam-2623	59	6	character	character	NOUN
ejpam-2623	59	7	is	be	AUX
ejpam-2623	59	8	the	the	DET
ejpam-2623	59	9	function	function	NOUN
ejpam-2623	59	10	χ	χ	NOUN
ejpam-2623	59	11	defined	define	VERB
ejpam-2623	59	12	by	by	ADP
ejpam-2623	59	13	χ	χ	X
ejpam-2623	59	14	:	:	PUNCT
ejpam-2623	59	15	fq	fq	PROPN
ejpam-2623	59	16	→	→	SYM
ejpam-2623	59	17	fq	fq	PROPN
ejpam-2623	59	18	:	:	PUNCT
ejpam-2623	59	19	u	u	PROPN
ejpam-2623	59	20	7→	7→	NUM
ejpam-2623	59	21	χ(u	χ(u	NOUN
ejpam-2623	59	22	)	)	PUNCT
ejpam-2623	60	1	=	=	SYM
ejpam-2623	61	1	u(q−1)/2	u(q−1)/2	PROPN
ejpam-2623	61	2	and	and	CCONJ
ejpam-2623	61	3	verifying	verifying	NOUN
ejpam-2623	61	4	:	:	PUNCT
ejpam-2623	61	5	χ(u	χ(u	NOUN
ejpam-2623	61	6	)	)	PUNCT
ejpam-2623	61	7	=	=	SYM
ejpam-2623	61	8	1	1	NUM
ejpam-2623	61	9	if	if	SCONJ
ejpam-2623	61	10	u	u	NOUN
ejpam-2623	61	11	is	be	AUX
ejpam-2623	61	12	a	a	DET
ejpam-2623	61	13	non	non	ADJ
ejpam-2623	61	14	-	-	ADJ
ejpam-2623	61	15	zero	zero	NUM
ejpam-2623	61	16	square	square	NOUN
ejpam-2623	61	17	;	;	PUNCT
ejpam-2623	61	18	χ(u	χ(u	NOUN
ejpam-2623	61	19	)	)	PUNCT
ejpam-2623	61	20	=	=	PUNCT
ejpam-2623	62	1	−1	−1	NOUN
ejpam-2623	62	2	if	if	SCONJ
ejpam-2623	62	3	u	u	NOUN
ejpam-2623	62	4	is	be	AUX
ejpam-2623	62	5	a	a	DET
ejpam-2623	62	6	non	non	ADJ
ejpam-2623	62	7	-	-	ADJ
ejpam-2623	62	8	square	square	ADJ
ejpam-2623	62	9	;	;	PUNCT
ejpam-2623	62	10	and	and	CCONJ
ejpam-2623	62	11	χ(u	χ(u	NOUN
ejpam-2623	62	12	)	)	PUNCT
ejpam-2623	63	1	=	=	SYM
ejpam-2623	63	2	0	0	PUNCT
ejpam-2623	64	1	if	if	SCONJ
ejpam-2623	64	2	u	u	NOUN
ejpam-2623	64	3	=	=	NOUN
ejpam-2623	64	4	0	0	NUM
ejpam-2623	64	5	.	.	PUNCT
ejpam-2623	65	1	the	the	DET
ejpam-2623	65	2	following	follow	VERB
ejpam-2623	65	3	properties	property	NOUN
ejpam-2623	65	4	are	be	AUX
ejpam-2623	65	5	also	also	ADV
ejpam-2623	65	6	verified	verify	VERB
ejpam-2623	65	7	:	:	PUNCT
ejpam-2623	65	8	χ(uv	χ(uv	X
ejpam-2623	65	9	)	)	PUNCT
ejpam-2623	65	10	=	=	SYM
ejpam-2623	65	11	χ(u	χ(u	NOUN
ejpam-2623	65	12	)	)	PUNCT
ejpam-2623	65	13	·	·	PUNCT
ejpam-2623	65	14	χ(v	χ(v	NOUN
ejpam-2623	65	15	)	)	PUNCT
ejpam-2623	65	16	for	for	ADP
ejpam-2623	65	17	any	any	DET
ejpam-2623	65	18	u	u	NOUN
ejpam-2623	65	19	,	,	PUNCT
ejpam-2623	65	20	v	v	PROPN
ejpam-2623	65	21	∈	∈	PROPN
ejpam-2623	65	22	fq	fq	NOUN
ejpam-2623	65	23	;	;	PUNCT
ejpam-2623	65	24	χ(a2	χ(a2	NOUN
ejpam-2623	65	25	)	)	PUNCT
ejpam-2623	65	26	=	=	SYM
ejpam-2623	65	27	1	1	NUM
ejpam-2623	65	28	for	for	ADP
ejpam-2623	65	29	any	any	DET
ejpam-2623	65	30	a	a	DET
ejpam-2623	65	31	∈	∈	NOUN
ejpam-2623	65	32	f∗q	f∗q	NOUN
ejpam-2623	65	33	;	;	PUNCT
ejpam-2623	65	34	and	and	CCONJ
ejpam-2623	65	35	if	if	SCONJ
ejpam-2623	65	36	q	q	PRON
ejpam-2623	65	37	≡	≡	PROPN
ejpam-2623	65	38	3	3	NUM
ejpam-2623	65	39	mod	mod	NOUN
ejpam-2623	65	40	4	4	NUM
ejpam-2623	65	41	,	,	PUNCT
ejpam-2623	65	42	χ(−1	χ(−1	PROPN
ejpam-2623	65	43	)	)	PUNCT
ejpam-2623	65	44	=	=	SYM
ejpam-2623	65	45	−1	−1	NOUN
ejpam-2623	65	46	,	,	PUNCT
ejpam-2623	65	47	χ(χ(u	χ(χ(u	PROPN
ejpam-2623	65	48	)	)	PUNCT
ejpam-2623	65	49	)	)	PUNCT
ejpam-2623	66	1	=	=	SYM
ejpam-2623	66	2	χ(u	χ(u	NOUN
ejpam-2623	66	3	)	)	PUNCT
ejpam-2623	66	4	,	,	PUNCT
ejpam-2623	66	5	for	for	ADP
ejpam-2623	66	6	any	any	DET
ejpam-2623	66	7	u	u	PROPN
ejpam-2623	66	8	∈	∈	PROPN
ejpam-2623	66	9	fq	fq	NOUN
ejpam-2623	66	10	.	.	PROPN
ejpam-2623	67	1	if	if	SCONJ
ejpam-2623	67	2	q	q	PRON
ejpam-2623	67	3	≡	≡	PROPN
ejpam-2623	67	4	1	1	NUM
ejpam-2623	67	5	mod	mod	NOUN
ejpam-2623	67	6	4	4	NUM
ejpam-2623	67	7	,	,	PUNCT
ejpam-2623	67	8	then	then	ADV
ejpam-2623	67	9	χ(−1	χ(−1	VERB
ejpam-2623	67	10	)	)	PUNCT
ejpam-2623	67	11	=	=	SYM
ejpam-2623	68	1	1	1	X
ejpam-2623	68	2	.	.	PUNCT
ejpam-2623	68	3	(	(	PUNCT
ejpam-2623	68	4	ii	ii	NOUN
ejpam-2623	68	5	)	)	PUNCT
ejpam-2623	68	6	define	define	VERB
ejpam-2623	68	7	f2	f2	PROPN
ejpam-2623	68	8	q	q	NOUN
ejpam-2623	68	9	=	=	SYM
ejpam-2623	68	10	{	{	PUNCT
ejpam-2623	68	11	a2	a2	PROPN
ejpam-2623	68	12	:	:	PUNCT
ejpam-2623	68	13	a	a	DET
ejpam-2623	68	14	∈	∈	PROPN
ejpam-2623	68	15	fq	fq	PROPN
ejpam-2623	68	16	}	}	PUNCT
ejpam-2623	68	17	(	(	PUNCT
ejpam-2623	68	18	see	see	VERB
ejpam-2623	68	19	[	[	X
ejpam-2623	68	20	4	4	NUM
ejpam-2623	68	21	]	]	NUM
ejpam-2623	68	22	)	)	PUNCT
ejpam-2623	68	23	.	.	PUNCT
ejpam-2623	69	1	a	a	DET
ejpam-2623	69	2	square	square	ADJ
ejpam-2623	69	3	root	root	NOUN
ejpam-2623	69	4	function	function	NOUN
ejpam-2623	69	5	√	√	PROPN
ejpam-2623	69	6	for	for	ADP
ejpam-2623	69	7	fq	fq	PROPN
ejpam-2623	69	8	is	be	AUX
ejpam-2623	69	9	defined	define	VERB
ejpam-2623	69	10	by	by	ADP
ejpam-2623	69	11	:	:	PUNCT
ejpam-2623	69	12	√	√	NUM
ejpam-2623	69	13	:	:	PUNCT
ejpam-2623	69	14	f2	f2	PROPN
ejpam-2623	69	15	q	q	PROPN
ejpam-2623	69	16	→	→	SYM
ejpam-2623	69	17	fq	fq	PROPN
ejpam-2623	69	18	:	:	PUNCT
ejpam-2623	69	19	a2	a2	PROPN
ejpam-2623	69	20	7→	7→	NUM
ejpam-2623	69	21	√	√	PROPN
ejpam-2623	69	22	a2	a2	PROPN
ejpam-2623	69	23	=	=	SYM
ejpam-2623	70	1	±a	±a	PROPN
ejpam-2623	70	2	.	.	PROPN
ejpam-2623	70	3	for	for	ADP
ejpam-2623	70	4	q	q	PROPN
ejpam-2623	70	5	≡	≡	PROPN
ejpam-2623	70	6	3	3	NUM
ejpam-2623	70	7	mod	mod	NOUN
ejpam-2623	70	8	4	4	NUM
ejpam-2623	70	9	,	,	PUNCT
ejpam-2623	70	10	a	a	DET
ejpam-2623	70	11	q+1	q+1	NUM
ejpam-2623	70	12	4	4	NUM
ejpam-2623	70	13	is	be	AUX
ejpam-2623	70	14	called	call	VERB
ejpam-2623	70	15	the	the	DET
ejpam-2623	70	16	principal	principal	ADJ
ejpam-2623	70	17	square	square	ADJ
ejpam-2623	70	18	root	root	NOUN
ejpam-2623	70	19	of	of	ADP
ejpam-2623	70	20	a	a	PRON
ejpam-2623	70	21	;	;	PUNCT
ejpam-2623	70	22	therefore	therefore	ADV
ejpam-2623	70	23	one	one	PRON
ejpam-2623	70	24	can	can	AUX
ejpam-2623	70	25	take	take	VERB
ejpam-2623	70	26	the	the	DET
ejpam-2623	70	27	principal	principal	ADJ
ejpam-2623	70	28	square	square	ADJ
ejpam-2623	70	29	root	root	NOUN
ejpam-2623	70	30	as	as	ADP
ejpam-2623	70	31	a	a	DET
ejpam-2623	70	32	square	square	ADJ
ejpam-2623	70	33	-	-	PUNCT
ejpam-2623	70	34	root	root	NOUN
ejpam-2623	70	35	function	function	NOUN
ejpam-2623	70	36	,	,	PUNCT
ejpam-2623	70	37	i.e.	i.e.	X
ejpam-2623	70	38	,	,	PUNCT
ejpam-2623	70	39	take	take	VERB
ejpam-2623	70	40	√	√	ADP
ejpam-2623	70	41	f2	f2	PROPN
ejpam-2623	70	42	q	q	NOUN
ejpam-2623	70	43	=	=	PUNCT
ejpam-2623	70	44	f2	f2	PROPN
ejpam-2623	70	45	q	q	NOUN
ejpam-2623	70	46	.	.	PUNCT
ejpam-2623	71	1	for	for	ADP
ejpam-2623	71	2	an	an	DET
ejpam-2623	71	3	odd	odd	ADJ
ejpam-2623	71	4	prime	prime	ADJ
ejpam-2623	71	5	q	q	NOUN
ejpam-2623	71	6	,	,	PUNCT
ejpam-2623	71	7	one	one	PRON
ejpam-2623	71	8	can	can	AUX
ejpam-2623	71	9	take	take	VERB
ejpam-2623	71	10	√	√	ADP
ejpam-2623	71	11	f2	f2	PROPN
ejpam-2623	71	12	q	q	NOUN
ejpam-2623	71	13	=	=	PUNCT
ejpam-2623	71	14	{	{	PUNCT
ejpam-2623	71	15	0	0	NUM
ejpam-2623	71	16	,	,	PUNCT
ejpam-2623	71	17	1	1	NUM
ejpam-2623	71	18	,	,	PUNCT
ejpam-2623	71	19	...	...	PUNCT
ejpam-2623	71	20	,	,	PUNCT
ejpam-2623	71	21	q−12	q−12	PROPN
ejpam-2623	71	22	}	}	PUNCT
ejpam-2623	71	23	.	.	PUNCT
ejpam-2623	72	1	2.2	2.2	NUM
ejpam-2623	72	2	.	.	PUNCT
ejpam-2623	73	1	an	an	DET
ejpam-2623	73	2	overview	overview	NOUN
ejpam-2623	73	3	of	of	ADP
ejpam-2623	73	4	existing	exist	VERB
ejpam-2623	73	5	encodings	encoding	NOUN
ejpam-2623	73	6	into	into	ADP
ejpam-2623	73	7	elliptic	elliptic	ADJ
ejpam-2623	73	8	curves	curve	NOUN
ejpam-2623	73	9	we	we	PRON
ejpam-2623	73	10	give	give	VERB
ejpam-2623	73	11	here	here	ADV
ejpam-2623	73	12	an	an	DET
ejpam-2623	73	13	overview	overview	NOUN
ejpam-2623	73	14	of	of	ADP
ejpam-2623	73	15	main	main	ADJ
ejpam-2623	73	16	existing	exist	VERB
ejpam-2623	73	17	encodings	encoding	NOUN
ejpam-2623	73	18	for	for	ADP
ejpam-2623	73	19	elliptic	elliptic	ADJ
ejpam-2623	73	20	curves	curve	NOUN
ejpam-2623	73	21	.	.	PUNCT
ejpam-2623	74	1	2.2.1	2.2.1	NUM
ejpam-2623	74	2	.	.	PUNCT
ejpam-2623	74	3	trivial	trivial	ADJ
ejpam-2623	74	4	encoding	encoding	NOUN
ejpam-2623	74	5	for	for	ADP
ejpam-2623	74	6	an	an	DET
ejpam-2623	74	7	elliptic	elliptic	ADJ
ejpam-2623	74	8	curve	curve	NOUN
ejpam-2623	74	9	ea	ea	PROPN
ejpam-2623	74	10	,	,	PUNCT
ejpam-2623	74	11	b	b	NOUN
ejpam-2623	74	12	:	:	PUNCT
ejpam-2623	74	13	y2	y2	NOUN
ejpam-2623	74	14	=	=	SYM
ejpam-2623	75	1	x3	x3	VERB
ejpam-2623	75	2	+	+	CCONJ
ejpam-2623	75	3	ax	ax	NOUN
ejpam-2623	75	4	+	+	CCONJ
ejpam-2623	75	5	b	b	NOUN
ejpam-2623	75	6	,	,	PUNCT
ejpam-2623	75	7	the	the	DET
ejpam-2623	75	8	simplest	simple	ADJ
ejpam-2623	75	9	way	way	NOUN
ejpam-2623	75	10	to	to	PART
ejpam-2623	75	11	construct	construct	VERB
ejpam-2623	75	12	a	a	DET
ejpam-2623	75	13	point	point	NOUN
ejpam-2623	75	14	of	of	ADP
ejpam-2623	75	15	ea	ea	NOUN
ejpam-2623	75	16	,	,	PUNCT
ejpam-2623	75	17	b	b	PROPN
ejpam-2623	75	18	is	be	AUX
ejpam-2623	75	19	to	to	PART
ejpam-2623	75	20	use	use	VERB
ejpam-2623	75	21	the	the	DET
ejpam-2623	75	22	trivial	trivial	ADJ
ejpam-2623	75	23	encoding	encoding	NOUN
ejpam-2623	75	24	,	,	PUNCT
ejpam-2623	75	25	also	also	ADV
ejpam-2623	75	26	known	know	VERB
ejpam-2623	75	27	as	as	ADP
ejpam-2623	75	28	the	the	DET
ejpam-2623	75	29	try	try	VERB
ejpam-2623	75	30	-	-	PUNCT
ejpam-2623	75	31	and	and	CCONJ
ejpam-2623	75	32	-	-	PUNCT
ejpam-2623	75	33	increment	increment	NOUN
ejpam-2623	75	34	method	method	NOUN
ejpam-2623	75	35	.	.	PUNCT
ejpam-2623	76	1	the	the	DET
ejpam-2623	76	2	idea	idea	NOUN
ejpam-2623	76	3	is	be	AUX
ejpam-2623	76	4	to	to	PART
ejpam-2623	76	5	pick	pick	VERB
ejpam-2623	76	6	a	a	DET
ejpam-2623	76	7	x	x	NOUN
ejpam-2623	76	8	-	-	NOUN
ejpam-2623	76	9	coordinate	coordinate	NOUN
ejpam-2623	76	10	and	and	CCONJ
ejpam-2623	76	11	try	try	VERB
ejpam-2623	76	12	to	to	PART
ejpam-2623	76	13	deduce	deduce	VERB
ejpam-2623	76	14	the	the	DET
ejpam-2623	76	15	y	y	NOUN
ejpam-2623	76	16	-	-	PUNCT
ejpam-2623	76	17	coordinate	coordinate	NOUN
ejpam-2623	76	18	by	by	ADP
ejpam-2623	76	19	computing	compute	VERB
ejpam-2623	76	20	a	a	DET
ejpam-2623	76	21	square	square	ADJ
ejpam-2623	76	22	root	root	NOUN
ejpam-2623	76	23	:	:	PUNCT
ejpam-2623	76	24	choose	choose	VERB
ejpam-2623	76	25	a	a	DET
ejpam-2623	76	26	random	random	ADJ
ejpam-2623	76	27	element	element	NOUN
ejpam-2623	76	28	u	u	PROPN
ejpam-2623	76	29	∈	∈	PROPN
ejpam-2623	76	30	f∗q	f∗q	NOUN
ejpam-2623	76	31	and	and	CCONJ
ejpam-2623	76	32	compute	compute	NOUN
ejpam-2623	76	33	u3	u3	NOUN
ejpam-2623	76	34	+	+	CCONJ
ejpam-2623	76	35	au	au	X
ejpam-2623	76	36	+	+	CCONJ
ejpam-2623	76	37	b	b	NOUN
ejpam-2623	76	38	;	;	PUNCT
ejpam-2623	76	39	and	and	CCONJ
ejpam-2623	76	40	then	then	ADV
ejpam-2623	76	41	test	test	VERB
ejpam-2623	76	42	whether	whether	SCONJ
ejpam-2623	76	43	u3	u3	PROPN
ejpam-2623	76	44	+	+	CCONJ
ejpam-2623	76	45	au+	au+	PROPN
ejpam-2623	76	46	b	b	PROPN
ejpam-2623	76	47	is	be	AUX
ejpam-2623	76	48	a	a	DET
ejpam-2623	76	49	square	square	NOUN
ejpam-2623	76	50	in	in	ADP
ejpam-2623	76	51	fq	fq	PROPN
ejpam-2623	76	52	.	.	PUNCT
ejpam-2623	77	1	if	if	SCONJ
ejpam-2623	77	2	it	it	PRON
ejpam-2623	77	3	’s	’	VERB
ejpam-2623	77	4	the	the	DET
ejpam-2623	77	5	case	case	NOUN
ejpam-2623	77	6	,	,	PUNCT
ejpam-2623	77	7	then	then	ADV
ejpam-2623	77	8	returns	return	VERB
ejpam-2623	77	9	(	(	PUNCT
ejpam-2623	77	10	x	x	X
ejpam-2623	77	11	,	,	PUNCT
ejpam-2623	77	12	y	y	NOUN
ejpam-2623	77	13	)	)	PUNCT
ejpam-2623	77	14	=	=	PUNCT
ejpam-2623	77	15	(	(	PUNCT
ejpam-2623	77	16	u,±	u,±	PROPN
ejpam-2623	77	17	√	√	PROPN
ejpam-2623	77	18	u3	u3	NOUN
ejpam-2623	77	19	+	+	CCONJ
ejpam-2623	77	20	au+	au+	PROPN
ejpam-2623	77	21	b	b	X
ejpam-2623	77	22	)	)	PUNCT
ejpam-2623	77	23	as	as	ADP
ejpam-2623	77	24	a	a	DET
ejpam-2623	77	25	point	point	NOUN
ejpam-2623	77	26	of	of	ADP
ejpam-2623	77	27	the	the	DET
ejpam-2623	77	28	curve	curve	NOUN
ejpam-2623	77	29	.	.	PUNCT
ejpam-2623	78	1	otherwise	otherwise	ADV
ejpam-2623	78	2	,	,	PUNCT
ejpam-2623	78	3	one	one	PRON
ejpam-2623	78	4	can	can	AUX
ejpam-2623	78	5	choose	choose	VERB
ejpam-2623	78	6	another	another	DET
ejpam-2623	78	7	u	u	NOUN
ejpam-2623	78	8	in	in	ADP
ejpam-2623	78	9	fq	fq	PROPN
ejpam-2623	78	10	and	and	CCONJ
ejpam-2623	78	11	try	try	VERB
ejpam-2623	78	12	again	again	ADV
ejpam-2623	78	13	.	.	PUNCT
ejpam-2623	79	1	but	but	CCONJ
ejpam-2623	79	2	this	this	DET
ejpam-2623	79	3	method	method	NOUN
ejpam-2623	79	4	has	have	VERB
ejpam-2623	79	5	at	at	ADV
ejpam-2623	79	6	least	least	ADJ
ejpam-2623	79	7	one	one	NUM
ejpam-2623	79	8	drawback	drawback	NOUN
ejpam-2623	79	9	,	,	PUNCT
ejpam-2623	79	10	that	that	PRON
ejpam-2623	79	11	is	is	ADV
ejpam-2623	79	12	it	it	PRON
ejpam-2623	79	13	can	can	AUX
ejpam-2623	79	14	not	not	PART
ejpam-2623	79	15	run	run	VERB
ejpam-2623	79	16	in	in	ADP
ejpam-2623	79	17	constant	constant	ADJ
ejpam-2623	79	18	time	time	NOUN
ejpam-2623	79	19	:	:	PUNCT
ejpam-2623	79	20	the	the	DET
ejpam-2623	79	21	number	number	NOUN
ejpam-2623	79	22	of	of	ADP
ejpam-2623	79	23	operations	operation	NOUN
ejpam-2623	79	24	depends	depend	VERB
ejpam-2623	79	25	on	on	ADP
ejpam-2623	79	26	the	the	DET
ejpam-2623	79	27	input	input	NOUN
ejpam-2623	79	28	u.	u.	ADV
ejpam-2623	79	29	in	in	ADP
ejpam-2623	79	30	practice	practice	NOUN
ejpam-2623	79	31	the	the	DET
ejpam-2623	79	32	input	input	NOUN
ejpam-2623	79	33	u	u	NOUN
ejpam-2623	79	34	is	be	AUX
ejpam-2623	79	35	the	the	DET
ejpam-2623	79	36	message	message	NOUN
ejpam-2623	79	37	m	m	VERB
ejpam-2623	79	38	we	we	PRON
ejpam-2623	79	39	want	want	VERB
ejpam-2623	79	40	to	to	PART
ejpam-2623	79	41	hash	hash	VERB
ejpam-2623	79	42	;	;	PUNCT
ejpam-2623	79	43	thus	thus	ADV
ejpam-2623	79	44	running	run	VERB
ejpam-2623	79	45	this	this	DET
ejpam-2623	79	46	algorithm	algorithm	NOUN
ejpam-2623	79	47	can	can	AUX
ejpam-2623	79	48	allow	allow	VERB
ejpam-2623	79	49	the	the	DET
ejpam-2623	79	50	attacker	attacker	NOUN
ejpam-2623	79	51	to	to	PART
ejpam-2623	79	52	guess	guess	VERB
ejpam-2623	79	53	some	some	DET
ejpam-2623	79	54	information	information	NOUN
ejpam-2623	79	55	about	about	ADP
ejpam-2623	79	56	m.	m.	NOUN
ejpam-2623	79	57	2.2.2	2.2.2	NUM
ejpam-2623	79	58	.	.	PUNCT
ejpam-2623	80	1	encoding	encode	VERB
ejpam-2623	80	2	for	for	ADP
ejpam-2623	80	3	supersingular	supersingular	ADJ
ejpam-2623	80	4	curves	curve	NOUN
ejpam-2623	80	5	a	a	DET
ejpam-2623	80	6	supersingular	supersingular	ADJ
ejpam-2623	80	7	curve	curve	NOUN
ejpam-2623	80	8	over	over	ADP
ejpam-2623	80	9	fq	fq	PROPN
ejpam-2623	80	10	is	be	AUX
ejpam-2623	80	11	an	an	DET
ejpam-2623	80	12	elliptic	elliptic	ADJ
ejpam-2623	80	13	curve	curve	NOUN
ejpam-2623	80	14	e	e	NOUN
ejpam-2623	80	15	such	such	ADJ
ejpam-2623	80	16	that	that	SCONJ
ejpam-2623	80	17	|e(fq)|	|e(fq)|	NOUN
ejpam-2623	80	18	=	=	PUNCT
ejpam-2623	80	19	q	q	NOUN
ejpam-2623	81	1	+	+	NOUN
ejpam-2623	81	2	1	1	X
ejpam-2623	81	3	.	.	X
ejpam-2623	81	4	for	for	ADP
ejpam-2623	81	5	q	q	PROPN
ejpam-2623	81	6	≡	≡	PROPN
ejpam-2623	81	7	2	2	NUM
ejpam-2623	81	8	mod	mod	NOUN
ejpam-2623	81	9	3	3	NUM
ejpam-2623	81	10	,	,	PUNCT
ejpam-2623	81	11	the	the	DET
ejpam-2623	81	12	curve	curve	NOUN
ejpam-2623	81	13	defined	define	VERB
ejpam-2623	81	14	by	by	ADP
ejpam-2623	81	15	eb	eb	PROPN
ejpam-2623	81	16	:	:	PUNCT
ejpam-2623	81	17	y2	y2	PROPN
ejpam-2623	81	18	=	=	PUNCT
ejpam-2623	82	1	x3+b	x3+b	PROPN
ejpam-2623	82	2	is	be	AUX
ejpam-2623	82	3	a	a	DET
ejpam-2623	82	4	supersingular	supersingular	ADJ
ejpam-2623	82	5	one	one	NOUN
ejpam-2623	82	6	.	.	PUNCT
ejpam-2623	83	1	in	in	ADP
ejpam-2623	83	2	their	their	PRON
ejpam-2623	83	3	identity	identity	NOUN
ejpam-2623	83	4	-	-	PUNCT
ejpam-2623	83	5	based	base	VERB
ejpam-2623	83	6	scheme[2	scheme[2	PROPN
ejpam-2623	83	7	]	]	PUNCT
ejpam-2623	83	8	,	,	PUNCT
ejpam-2623	83	9	boneh	boneh	PROPN
ejpam-2623	83	10	and	and	CCONJ
ejpam-2623	83	11	franklin	franklin	PROPN
ejpam-2623	83	12	proposed	propose	VERB
ejpam-2623	83	13	the	the	DET
ejpam-2623	83	14	function	function	NOUN
ejpam-2623	83	15	f	f	NOUN
ejpam-2623	83	16	:	:	PUNCT
ejpam-2623	83	17	u	u	NOUN
ejpam-2623	83	18	7→	7→	PROPN
ejpam-2623	83	19	(	(	PUNCT
ejpam-2623	83	20	(	(	PUNCT
ejpam-2623	83	21	u2−b	u2−b	PROPN
ejpam-2623	83	22	)	)	PUNCT
ejpam-2623	83	23	1	1	NUM
ejpam-2623	83	24	3	3	NUM
ejpam-2623	83	25	,	,	PUNCT
ejpam-2623	83	26	u	u	NOUN
ejpam-2623	83	27	)	)	PUNCT
ejpam-2623	83	28	that	that	PRON
ejpam-2623	83	29	constructs	construct	VERB
ejpam-2623	83	30	a	a	DET
ejpam-2623	83	31	point	point	NOUN
ejpam-2623	83	32	of	of	ADP
ejpam-2623	83	33	eb	eb	PROPN
ejpam-2623	83	34	,	,	PUNCT
ejpam-2623	83	35	given	give	VERB
ejpam-2623	83	36	any	any	DET
ejpam-2623	83	37	u	u	PROPN
ejpam-2623	83	38	∈	∈	PROPN
ejpam-2623	83	39	fq	fq	PROPN
ejpam-2623	83	40	.	.	PROPN
ejpam-2623	84	1	this	this	DET
ejpam-2623	84	2	function	function	NOUN
ejpam-2623	84	3	allows	allow	VERB
ejpam-2623	84	4	them	they	PRON
ejpam-2623	84	5	to	to	PART
ejpam-2623	84	6	construct	construct	VERB
ejpam-2623	84	7	the	the	DET
ejpam-2623	84	8	public	public	ADJ
ejpam-2623	84	9	key	key	ADJ
ejpam-2623	84	10	qid(a	qid(a	PROPN
ejpam-2623	84	11	point	point	NOUN
ejpam-2623	84	12	on	on	ADP
ejpam-2623	84	13	the	the	DET
ejpam-2623	84	14	supersingular	supersingular	ADJ
ejpam-2623	84	15	curve	curve	NOUN
ejpam-2623	84	16	)	)	PUNCT
ejpam-2623	84	17	corresponding	correspond	VERB
ejpam-2623	84	18	to	to	ADP
ejpam-2623	84	19	the	the	DET
ejpam-2623	84	20	identity	identity	NOUN
ejpam-2623	84	21	i	i	PROPN
ejpam-2623	84	22	d	d	PROPN
ejpam-2623	84	23	∈	∈	PROPN
ejpam-2623	84	24	{	{	PUNCT
ejpam-2623	84	25	0	0	NUM
ejpam-2623	84	26	,	,	PUNCT
ejpam-2623	84	27	1}∗.	1}∗.	NUM
ejpam-2623	85	1	but	but	CCONJ
ejpam-2623	85	2	it	it	PRON
ejpam-2623	85	3	is	be	AUX
ejpam-2623	85	4	well	well	ADV
ejpam-2623	85	5	-	-	PUNCT
ejpam-2623	85	6	known	know	VERB
ejpam-2623	85	7	that	that	SCONJ
ejpam-2623	85	8	supersingular	supersingular	ADJ
ejpam-2623	85	9	curves	curve	NOUN
ejpam-2623	85	10	are	be	AUX
ejpam-2623	85	11	useless	useless	ADJ
ejpam-2623	85	12	for	for	ADP
ejpam-2623	85	13	cryptographic	cryptographic	ADJ
ejpam-2623	85	14	concerns	concern	NOUN
ejpam-2623	85	15	because	because	SCONJ
ejpam-2623	85	16	of	of	ADP
ejpam-2623	85	17	the	the	DET
ejpam-2623	85	18	mov	mov	NOUN
ejpam-2623	85	19	attack[1	attack[1	PROPN
ejpam-2623	85	20	]	]	PUNCT
ejpam-2623	85	21	:	:	PUNCT
ejpam-2623	85	22	that	that	PRON
ejpam-2623	85	23	is	be	AUX
ejpam-2623	85	24	the	the	DET
ejpam-2623	85	25	dlp	dlp	PROPN
ejpam-2623	85	26	on	on	ADP
ejpam-2623	85	27	eb	eb	PROPN
ejpam-2623	85	28	can	can	AUX
ejpam-2623	85	29	be	be	AUX
ejpam-2623	85	30	reduced	reduce	VERB
ejpam-2623	85	31	to	to	ADP
ejpam-2623	85	32	the	the	DET
ejpam-2623	85	33	dlp	dlp	NOUN
ejpam-2623	85	34	in	in	ADP
ejpam-2623	85	35	fq	fq	PROPN
ejpam-2623	85	36	.	.	PROPN
ejpam-2623	85	37	to	to	PART
ejpam-2623	85	38	avoid	avoid	VERB
ejpam-2623	85	39	these	these	DET
ejpam-2623	85	40	attack	attack	NOUN
ejpam-2623	85	41	,	,	PUNCT
ejpam-2623	85	42	a	a	DET
ejpam-2623	85	43	large	large	ADJ
ejpam-2623	85	44	q	q	NOUN
ejpam-2623	85	45	should	should	AUX
ejpam-2623	85	46	be	be	AUX
ejpam-2623	85	47	used	use	VERB
ejpam-2623	85	48	.	.	PUNCT
ejpam-2623	86	1	n.	n.	PROPN
ejpam-2623	86	2	diarra	diarra	PROPN
ejpam-2623	86	3	,	,	PUNCT
ejpam-2623	86	4	d.	d.	PROPN
ejpam-2623	86	5	sow	sow	PROPN
ejpam-2623	86	6	,	,	PUNCT
ejpam-2623	86	7	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	86	8	.	.	PUNCT
ejpam-2623	86	9	khlil	khlil	PROPN
ejpam-2623	86	10	/	/	SYM
ejpam-2623	86	11	eur	eur	PROPN
ejpam-2623	86	12	.	.	PUNCT
ejpam-2623	87	1	j.	j.	PROPN
ejpam-2623	87	2	pure	pure	PROPN
ejpam-2623	87	3	appl	appl	PROPN
ejpam-2623	87	4	.	.	PROPN
ejpam-2623	87	5	math	math	PROPN
ejpam-2623	87	6	,	,	PUNCT
ejpam-2623	87	7	10	10	NUM
ejpam-2623	87	8	(	(	PUNCT
ejpam-2623	87	9	2	2	NUM
ejpam-2623	87	10	)	)	PUNCT
ejpam-2623	87	11	(	(	PUNCT
ejpam-2623	87	12	2017	2017	NUM
ejpam-2623	87	13	)	)	PUNCT
ejpam-2623	87	14	,	,	PUNCT
ejpam-2623	87	15	363	363	NUM
ejpam-2623	87	16	-	-	SYM
ejpam-2623	87	17	391	391	NUM
ejpam-2623	87	18	366	366	NUM
ejpam-2623	87	19	2.2.3	2.2.3	NUM
ejpam-2623	87	20	.	.	PUNCT
ejpam-2623	88	1	the	the	DET
ejpam-2623	88	2	swu	swu	PROPN
ejpam-2623	88	3	algorithm	algorithm	NOUN
ejpam-2623	88	4	in	in	ADP
ejpam-2623	88	5	2006[15	2006[15	NUM
ejpam-2623	88	6	]	]	PUNCT
ejpam-2623	88	7	,	,	PUNCT
ejpam-2623	88	8	shallue	shallue	NOUN
ejpam-2623	88	9	and	and	CCONJ
ejpam-2623	88	10	van	van	PROPN
ejpam-2623	88	11	de	de	PROPN
ejpam-2623	88	12	woestjine	woestjine	PROPN
ejpam-2623	88	13	proposed	propose	VERB
ejpam-2623	88	14	an	an	DET
ejpam-2623	88	15	algorithm	algorithm	NOUN
ejpam-2623	88	16	that	that	PRON
ejpam-2623	88	17	generates	generate	VERB
ejpam-2623	88	18	,	,	PUNCT
ejpam-2623	88	19	in	in	ADP
ejpam-2623	88	20	polynomial	polynomial	ADJ
ejpam-2623	88	21	time	time	NOUN
ejpam-2623	88	22	,	,	PUNCT
ejpam-2623	88	23	a	a	DET
ejpam-2623	88	24	point	point	NOUN
ejpam-2623	88	25	of	of	ADP
ejpam-2623	88	26	an	an	DET
ejpam-2623	88	27	elliptic	elliptic	ADJ
ejpam-2623	88	28	curve	curve	NOUN
ejpam-2623	88	29	ea	ea	PROPN
ejpam-2623	88	30	,	,	PUNCT
ejpam-2623	88	31	b	b	NOUN
ejpam-2623	88	32	given	give	VERB
ejpam-2623	88	33	by	by	ADP
ejpam-2623	88	34	its	its	PRON
ejpam-2623	88	35	weierstrass	weierstrass	NOUN
ejpam-2623	88	36	equation	equation	NOUN
ejpam-2623	88	37	.	.	PUNCT
ejpam-2623	89	1	let	let	VERB
ejpam-2623	89	2	fq	fq	PRON
ejpam-2623	89	3	be	be	AUX
ejpam-2623	89	4	a	a	DET
ejpam-2623	89	5	finite	finite	ADJ
ejpam-2623	89	6	field	field	NOUN
ejpam-2623	89	7	of	of	ADP
ejpam-2623	89	8	characteristic	characteristic	ADJ
ejpam-2623	89	9	at	at	ADV
ejpam-2623	89	10	least	least	ADV
ejpam-2623	89	11	5	5	NUM
ejpam-2623	89	12	,	,	PUNCT
ejpam-2623	89	13	and	and	CCONJ
ejpam-2623	89	14	g(x	g(x	NOUN
ejpam-2623	89	15	)	)	PUNCT
ejpam-2623	90	1	=	=	PUNCT
ejpam-2623	90	2	x3	x3	VERB
ejpam-2623	90	3	+	+	CCONJ
ejpam-2623	90	4	ax	ax	NOUN
ejpam-2623	90	5	+	+	CCONJ
ejpam-2623	90	6	b	b	AUX
ejpam-2623	90	7	be	be	AUX
ejpam-2623	90	8	a	a	DET
ejpam-2623	90	9	polynomial	polynomial	NOUN
ejpam-2623	90	10	in	in	ADP
ejpam-2623	90	11	fq[x	fq[x	PROPN
ejpam-2623	90	12	]	]	PUNCT
ejpam-2623	90	13	,	,	PUNCT
ejpam-2623	90	14	with	with	ADP
ejpam-2623	90	15	a	a	DET
ejpam-2623	90	16	6=	6=	NUM
ejpam-2623	90	17	0	0	NUM
ejpam-2623	90	18	.	.	PUNCT
ejpam-2623	91	1	we	we	PRON
ejpam-2623	91	2	know	know	VERB
ejpam-2623	91	3	from	from	ADP
ejpam-2623	91	4	the	the	DET
ejpam-2623	91	5	skalba	skalba	PROPN
ejpam-2623	91	6	’s	’s	PART
ejpam-2623	91	7	theorem	theorem	NOUN
ejpam-2623	91	8	[	[	X
ejpam-2623	91	9	16	16	NUM
ejpam-2623	91	10	]	]	PUNCT
ejpam-2623	91	11	that	that	SCONJ
ejpam-2623	91	12	there	there	PRON
ejpam-2623	91	13	exist	exist	VERB
ejpam-2623	91	14	four	four	NUM
ejpam-2623	91	15	non	non	ADJ
ejpam-2623	91	16	-	-	ADJ
ejpam-2623	91	17	constant	constant	ADJ
ejpam-2623	91	18	rational	rational	ADJ
ejpam-2623	91	19	functions	function	NOUN
ejpam-2623	91	20	x1(t	x1(t	NUM
ejpam-2623	91	21	)	)	PUNCT
ejpam-2623	91	22	,	,	PUNCT
ejpam-2623	91	23	x2(t	x2(t	PROPN
ejpam-2623	91	24	)	)	PUNCT
ejpam-2623	91	25	,	,	PUNCT
ejpam-2623	91	26	x3(t	x3(t	PROPN
ejpam-2623	91	27	)	)	PUNCT
ejpam-2623	91	28	,	,	PUNCT
ejpam-2623	91	29	x4(t	x4(t	PROPN
ejpam-2623	91	30	)	)	PUNCT
ejpam-2623	91	31	∈	∈	PROPN
ejpam-2623	91	32	fq(x	fq(x	NOUN
ejpam-2623	91	33	)	)	PUNCT
ejpam-2623	91	34	such	such	ADJ
ejpam-2623	91	35	that	that	SCONJ
ejpam-2623	91	36	:	:	PUNCT
ejpam-2623	91	37	g(x1(t	g(x1(t	ADJ
ejpam-2623	91	38	2	2	NUM
ejpam-2623	91	39	)	)	PUNCT
ejpam-2623	91	40	)	)	PUNCT
ejpam-2623	91	41	·	·	PUNCT
ejpam-2623	92	1	g(x2(t	g(x2(t	NOUN
ejpam-2623	92	2	2	2	NUM
ejpam-2623	92	3	)	)	PUNCT
ejpam-2623	92	4	)	)	PUNCT
ejpam-2623	92	5	·	·	PUNCT
ejpam-2623	93	1	g(x3(t	g(x3(t	NOUN
ejpam-2623	93	2	2	2	NUM
ejpam-2623	93	3	)	)	PUNCT
ejpam-2623	93	4	)	)	PUNCT
ejpam-2623	94	1	=	=	PRON
ejpam-2623	94	2	(	(	PUNCT
ejpam-2623	94	3	x4(t	x4(t	PROPN
ejpam-2623	94	4	)	)	PUNCT
ejpam-2623	94	5	)	)	PUNCT
ejpam-2623	94	6	2	2	NUM
ejpam-2623	94	7	(	(	PUNCT
ejpam-2623	94	8	1	1	X
ejpam-2623	94	9	)	)	PUNCT
ejpam-2623	94	10	it	it	PRON
ejpam-2623	94	11	follows	follow	VERB
ejpam-2623	94	12	that	that	SCONJ
ejpam-2623	94	13	at	at	ADP
ejpam-2623	94	14	less	less	ADJ
ejpam-2623	94	15	one	one	NUM
ejpam-2623	94	16	one	one	NUM
ejpam-2623	94	17	the	the	DET
ejpam-2623	94	18	g(xi(u	g(xi(u	PROPN
ejpam-2623	94	19	2	2	NUM
ejpam-2623	94	20	)	)	PUNCT
ejpam-2623	94	21	)	)	PUNCT
ejpam-2623	94	22	must	must	AUX
ejpam-2623	94	23	be	be	AUX
ejpam-2623	94	24	a	a	DET
ejpam-2623	94	25	quadratic	quadratic	ADJ
ejpam-2623	94	26	residue	residue	NOUN
ejpam-2623	94	27	in	in	ADP
ejpam-2623	94	28	the	the	DET
ejpam-2623	94	29	finite	finite	ADJ
ejpam-2623	94	30	field	field	NOUN
ejpam-2623	94	31	fq	fq	PROPN
ejpam-2623	94	32	,	,	PUNCT
ejpam-2623	94	33	given	give	VERB
ejpam-2623	94	34	any	any	DET
ejpam-2623	94	35	u	u	NOUN
ejpam-2623	94	36	∈	∈	PROPN
ejpam-2623	94	37	fq	fq	NOUN
ejpam-2623	94	38	such	such	ADJ
ejpam-2623	94	39	that	that	SCONJ
ejpam-2623	94	40	u2	u2	NOUN
ejpam-2623	94	41	is	be	AUX
ejpam-2623	94	42	not	not	PART
ejpam-2623	94	43	a	a	DET
ejpam-2623	94	44	pole	pole	NOUN
ejpam-2623	94	45	of	of	ADP
ejpam-2623	94	46	the	the	DET
ejpam-2623	94	47	xi	xi	NOUN
ejpam-2623	94	48	’s	’s	NOUN
ejpam-2623	94	49	,	,	PUNCT
ejpam-2623	94	50	i	i	PRON
ejpam-2623	94	51	=	=	NOUN
ejpam-2623	94	52	1	1	NUM
ejpam-2623	94	53	,	,	PUNCT
ejpam-2623	94	54	2	2	NUM
ejpam-2623	94	55	,	,	PUNCT
ejpam-2623	94	56	3	3	NUM
ejpam-2623	94	57	.	.	NOUN
ejpam-2623	94	58	from	from	ADP
ejpam-2623	94	59	identity	identity	NOUN
ejpam-2623	94	60	(	(	PUNCT
ejpam-2623	94	61	1	1	NUM
ejpam-2623	94	62	)	)	PUNCT
ejpam-2623	94	63	,	,	PUNCT
ejpam-2623	94	64	one	one	PRON
ejpam-2623	94	65	can	can	AUX
ejpam-2623	94	66	deduce	deduce	VERB
ejpam-2623	94	67	an	an	DET
ejpam-2623	94	68	encoding	encoding	NOUN
ejpam-2623	94	69	function	function	NOUN
ejpam-2623	94	70	to	to	ADP
ejpam-2623	94	71	the	the	DET
ejpam-2623	94	72	curve	curve	NOUN
ejpam-2623	94	73	ea	ea	PROPN
ejpam-2623	94	74	,	,	PUNCT
ejpam-2623	94	75	b	b	NOUN
ejpam-2623	94	76	:	:	PUNCT
ejpam-2623	94	77	y2	y2	PROPN
ejpam-2623	94	78	=	=	SYM
ejpam-2623	94	79	g(x	g(x	NOUN
ejpam-2623	94	80	)	)	PUNCT
ejpam-2623	94	81	.	.	PUNCT
ejpam-2623	95	1	it	it	PRON
ejpam-2623	95	2	suffices	suffice	VERB
ejpam-2623	95	3	to	to	PART
ejpam-2623	95	4	set	set	VERB
ejpam-2623	95	5	(	(	PUNCT
ejpam-2623	95	6	x	x	NOUN
ejpam-2623	95	7	,	,	PUNCT
ejpam-2623	95	8	y	y	NOUN
ejpam-2623	95	9	)	)	PUNCT
ejpam-2623	95	10	=	=	SYM
ejpam-2623	95	11	(	(	PUNCT
ejpam-2623	95	12	xi(u	xi(u	NOUN
ejpam-2623	95	13	2	2	NUM
ejpam-2623	95	14	)	)	PUNCT
ejpam-2623	95	15	,	,	PUNCT
ejpam-2623	95	16	√	√	NUM
ejpam-2623	95	17	g(xi(u2	g(xi(u2	NOUN
ejpam-2623	95	18	)	)	PUNCT
ejpam-2623	95	19	)	)	PUNCT
ejpam-2623	95	20	)	)	PUNCT
ejpam-2623	95	21	,	,	PUNCT
ejpam-2623	95	22	where	where	SCONJ
ejpam-2623	95	23	i	i	PRON
ejpam-2623	95	24	is	be	AUX
ejpam-2623	95	25	the	the	DET
ejpam-2623	95	26	smallest	small	ADJ
ejpam-2623	95	27	indice	indice	NOUN
ejpam-2623	95	28	such	such	ADJ
ejpam-2623	95	29	that	that	SCONJ
ejpam-2623	95	30	g(xi(u	g(xi(u	PROPN
ejpam-2623	95	31	2	2	NUM
ejpam-2623	95	32	)	)	PUNCT
ejpam-2623	95	33	)	)	PUNCT
ejpam-2623	96	1	is	be	AUX
ejpam-2623	96	2	a	a	DET
ejpam-2623	96	3	quadratic	quadratic	ADJ
ejpam-2623	96	4	residue	residue	NOUN
ejpam-2623	96	5	.	.	PUNCT
ejpam-2623	97	1	even	even	ADV
ejpam-2623	97	2	if	if	SCONJ
ejpam-2623	97	3	this	this	DET
ejpam-2623	97	4	construction	construction	NOUN
ejpam-2623	97	5	defines	define	VERB
ejpam-2623	97	6	a	a	DET
ejpam-2623	97	7	constant	constant	ADJ
ejpam-2623	97	8	-	-	PUNCT
ejpam-2623	97	9	time	time	NOUN
ejpam-2623	97	10	encoding	encoding	NOUN
ejpam-2623	97	11	,	,	PUNCT
ejpam-2623	97	12	it	it	PRON
ejpam-2623	97	13	presents	present	VERB
ejpam-2623	97	14	at	at	ADV
ejpam-2623	97	15	least	least	ADV
ejpam-2623	97	16	one	one	NUM
ejpam-2623	97	17	drawback	drawback	NOUN
ejpam-2623	97	18	.	.	PUNCT
ejpam-2623	98	1	in	in	ADP
ejpam-2623	98	2	fact	fact	NOUN
ejpam-2623	98	3	,	,	PUNCT
ejpam-2623	98	4	the	the	DET
ejpam-2623	98	5	rational	rational	ADJ
ejpam-2623	98	6	functions	function	NOUN
ejpam-2623	98	7	xi(t	xi(t	PUNCT
ejpam-2623	98	8	)	)	PUNCT
ejpam-2623	98	9	are	be	AUX
ejpam-2623	98	10	large	large	ADJ
ejpam-2623	98	11	and	and	CCONJ
ejpam-2623	98	12	complex	complex	ADJ
ejpam-2623	98	13	enough	enough	ADV
ejpam-2623	98	14	to	to	PART
ejpam-2623	98	15	make	make	VERB
ejpam-2623	98	16	them	they	PRON
ejpam-2623	98	17	difficult	difficult	ADJ
ejpam-2623	98	18	to	to	PART
ejpam-2623	98	19	implement	implement	VERB
ejpam-2623	98	20	.	.	PUNCT
ejpam-2623	99	1	and	and	CCONJ
ejpam-2623	99	2	there	there	PRON
ejpam-2623	99	3	is	be	VERB
ejpam-2623	99	4	no	no	DET
ejpam-2623	99	5	deterministic	deterministic	ADJ
ejpam-2623	99	6	polynomial	polynomial	ADJ
ejpam-2623	99	7	time	time	NOUN
ejpam-2623	99	8	for	for	ADP
ejpam-2623	99	9	computing	compute	VERB
ejpam-2623	99	10	a	a	DET
ejpam-2623	99	11	square	square	ADJ
ejpam-2623	99	12	root	root	NOUN
ejpam-2623	99	13	in	in	ADP
ejpam-2623	99	14	fq	fq	PROPN
ejpam-2623	99	15	,	,	PUNCT
ejpam-2623	99	16	unless	unless	SCONJ
ejpam-2623	99	17	making	make	VERB
ejpam-2623	99	18	additional	additional	ADJ
ejpam-2623	99	19	hypotheses	hypothesis	NOUN
ejpam-2623	99	20	on	on	ADP
ejpam-2623	99	21	q.	q.	NOUN
ejpam-2623	99	22	for	for	ADP
ejpam-2623	99	23	example	example	NOUN
ejpam-2623	99	24	,	,	PUNCT
ejpam-2623	99	25	when	when	SCONJ
ejpam-2623	99	26	q	q	PROPN
ejpam-2623	99	27	≡	≡	PROPN
ejpam-2623	99	28	3	3	NUM
ejpam-2623	99	29	mod	mod	NOUN
ejpam-2623	99	30	4	4	NUM
ejpam-2623	99	31	,	,	PUNCT
ejpam-2623	99	32	then	then	ADV
ejpam-2623	99	33	computing	compute	VERB
ejpam-2623	99	34	a	a	DET
ejpam-2623	99	35	square	square	ADJ
ejpam-2623	99	36	root	root	NOUN
ejpam-2623	99	37	is	be	AUX
ejpam-2623	99	38	simply	simply	ADV
ejpam-2623	99	39	an	an	DET
ejpam-2623	99	40	exponentiation	exponentiation	NOUN
ejpam-2623	99	41	.	.	PUNCT
ejpam-2623	100	1	2.2.4	2.2.4	X
ejpam-2623	100	2	.	.	X
ejpam-2623	100	3	icart	icart	PROPN
ejpam-2623	100	4	’s	’s	PART
ejpam-2623	100	5	function	function	NOUN
ejpam-2623	100	6	let	let	VERB
ejpam-2623	100	7	q	q	NOUN
ejpam-2623	100	8	=	=	SYM
ejpam-2623	100	9	2	2	NUM
ejpam-2623	100	10	mod	mod	NOUN
ejpam-2623	100	11	3	3	NUM
ejpam-2623	100	12	;	;	PUNCT
ejpam-2623	100	13	so	so	SCONJ
ejpam-2623	100	14	the	the	DET
ejpam-2623	100	15	map	map	NOUN
ejpam-2623	100	16	x	x	X
ejpam-2623	100	17	7→	7→	NUM
ejpam-2623	100	18	x3	x3	ADJ
ejpam-2623	100	19	is	be	AUX
ejpam-2623	100	20	a	a	DET
ejpam-2623	100	21	bijection	bijection	NOUN
ejpam-2623	100	22	and	and	CCONJ
ejpam-2623	100	23	then	then	ADV
ejpam-2623	100	24	computation	computation	NOUN
ejpam-2623	100	25	of	of	ADP
ejpam-2623	100	26	a	a	DET
ejpam-2623	100	27	cubic	cubic	ADJ
ejpam-2623	100	28	root	root	NOUN
ejpam-2623	100	29	can	can	AUX
ejpam-2623	100	30	be	be	AUX
ejpam-2623	100	31	done	do	VERB
ejpam-2623	100	32	as	as	ADP
ejpam-2623	100	33	an	an	DET
ejpam-2623	100	34	exponentiation	exponentiation	NOUN
ejpam-2623	100	35	.	.	PUNCT
ejpam-2623	101	1	in	in	ADP
ejpam-2623	101	2	[	[	X
ejpam-2623	101	3	9	9	NUM
ejpam-2623	101	4	]	]	PUNCT
ejpam-2623	101	5	,	,	PUNCT
ejpam-2623	101	6	icart	icart	PROPN
ejpam-2623	101	7	defined	define	VERB
ejpam-2623	101	8	a	a	DET
ejpam-2623	101	9	new	new	ADJ
ejpam-2623	101	10	encoding	encoding	NOUN
ejpam-2623	101	11	function	function	NOUN
ejpam-2623	101	12	,	,	PUNCT
ejpam-2623	101	13	based	base	VERB
ejpam-2623	101	14	on	on	ADP
ejpam-2623	101	15	the	the	DET
ejpam-2623	101	16	following	follow	VERB
ejpam-2623	101	17	idea	idea	NOUN
ejpam-2623	101	18	:	:	PUNCT
ejpam-2623	101	19	intersect	intersect	ADJ
ejpam-2623	101	20	the	the	DET
ejpam-2623	101	21	line	line	NOUN
ejpam-2623	101	22	y	y	PROPN
ejpam-2623	101	23	=	=	PUNCT
ejpam-2623	101	24	ux	ux	PROPN
ejpam-2623	102	1	+	+	CCONJ
ejpam-2623	102	2	v	v	NOUN
ejpam-2623	102	3	with	with	ADP
ejpam-2623	102	4	the	the	DET
ejpam-2623	102	5	weierstrass	weierstrass	NOUN
ejpam-2623	102	6	curve	curve	NOUN
ejpam-2623	102	7	ea	ea	PROPN
ejpam-2623	102	8	,	,	PUNCT
ejpam-2623	102	9	b	b	NOUN
ejpam-2623	102	10	:	:	PUNCT
ejpam-2623	102	11	y2	y2	NOUN
ejpam-2623	102	12	=	=	SYM
ejpam-2623	103	1	x3	x3	ADJ
ejpam-2623	103	2	+	+	CCONJ
ejpam-2623	103	3	ax+	ax+	PROPN
ejpam-2623	103	4	b	b	NOUN
ejpam-2623	103	5	,	,	PUNCT
ejpam-2623	103	6	with	with	ADP
ejpam-2623	103	7	a	a	PRON
ejpam-2623	103	8	,	,	PUNCT
ejpam-2623	103	9	b	b	PROPN
ejpam-2623	103	10	∈	∈	PROPN
ejpam-2623	103	11	fq	fq	PROPN
ejpam-2623	103	12	.	.	PUNCT
ejpam-2623	104	1	he	he	PRON
ejpam-2623	104	2	defined	define	VERB
ejpam-2623	104	3	the	the	DET
ejpam-2623	104	4	encoding	encoding	NOUN
ejpam-2623	104	5	function	function	NOUN
ejpam-2623	104	6	:	:	PUNCT
ejpam-2623	104	7	fa	fa	PROPN
ejpam-2623	104	8	,	,	PUNCT
ejpam-2623	104	9	b	b	NOUN
ejpam-2623	104	10	:	:	PUNCT
ejpam-2623	104	11	fq	fq	PROPN
ejpam-2623	104	12	→	→	SYM
ejpam-2623	104	13	ea	ea	PROPN
ejpam-2623	104	14	,	,	PUNCT
ejpam-2623	104	15	b	b	PROPN
ejpam-2623	104	16	x	x	SYM
ejpam-2623	104	17	7→	7→	NUM
ejpam-2623	104	18	fa	fa	PROPN
ejpam-2623	104	19	,	,	PUNCT
ejpam-2623	104	20	b(u	b(u	PROPN
ejpam-2623	104	21	)	)	PUNCT
ejpam-2623	104	22	=	=	SYM
ejpam-2623	104	23	(	(	PUNCT
ejpam-2623	104	24	(	(	PUNCT
ejpam-2623	104	25	v2	v2	VERB
ejpam-2623	104	26	−	−	NOUN
ejpam-2623	104	27	b−	b−	PROPN
ejpam-2623	104	28	u6	u6	PROPN
ejpam-2623	104	29	27	27	NUM
ejpam-2623	104	30	)	)	PUNCT
ejpam-2623	104	31	1/3	1/3	PRON
ejpam-2623	105	1	+	+	CCONJ
ejpam-2623	105	2	u2	u2	PROPN
ejpam-2623	105	3	3	3	NUM
ejpam-2623	105	4	,	,	PUNCT
ejpam-2623	105	5	ux+	ux+	ADJ
ejpam-2623	105	6	v	v	NOUN
ejpam-2623	105	7	)	)	PUNCT
ejpam-2623	105	8	where	where	SCONJ
ejpam-2623	105	9	v	v	NOUN
ejpam-2623	105	10	=	=	SYM
ejpam-2623	105	11	(	(	PUNCT
ejpam-2623	105	12	3a	3a	NUM
ejpam-2623	105	13	−	−	NUM
ejpam-2623	105	14	u4)/6u	u4)/6u	ADJ
ejpam-2623	105	15	.	.	PUNCT
ejpam-2623	106	1	as	as	SCONJ
ejpam-2623	106	2	shown	show	VERB
ejpam-2623	106	3	in	in	ADP
ejpam-2623	106	4	the	the	DET
ejpam-2623	106	5	paper	paper	NOUN
ejpam-2623	106	6	,	,	PUNCT
ejpam-2623	106	7	this	this	DET
ejpam-2623	106	8	function	function	NOUN
ejpam-2623	106	9	presents	present	VERB
ejpam-2623	106	10	many	many	ADJ
ejpam-2623	106	11	interesting	interesting	ADJ
ejpam-2623	106	12	properties	property	NOUN
ejpam-2623	106	13	.	.	PUNCT
ejpam-2623	107	1	in	in	ADP
ejpam-2623	107	2	fact	fact	NOUN
ejpam-2623	107	3	,	,	PUNCT
ejpam-2623	107	4	it	it	PRON
ejpam-2623	107	5	can	can	AUX
ejpam-2623	107	6	be	be	AUX
ejpam-2623	107	7	implemented	implement	VERB
ejpam-2623	107	8	in	in	ADP
ejpam-2623	107	9	polynomial	polynomial	ADJ
ejpam-2623	107	10	time	time	NOUN
ejpam-2623	107	11	with	with	ADP
ejpam-2623	107	12	o(log3	o(log3	NUM
ejpam-2623	107	13	q	q	NOUN
ejpam-2623	107	14	)	)	PUNCT
ejpam-2623	107	15	operations	operation	NOUN
ejpam-2623	107	16	.	.	PUNCT
ejpam-2623	108	1	the	the	DET
ejpam-2623	108	2	inverse	inverse	NOUN
ejpam-2623	108	3	function	function	NOUN
ejpam-2623	108	4	f−1a	f−1a	PROPN
ejpam-2623	108	5	,	,	PUNCT
ejpam-2623	108	6	b	b	PROPN
ejpam-2623	108	7	is	be	AUX
ejpam-2623	108	8	also	also	ADV
ejpam-2623	108	9	computable	computable	ADJ
ejpam-2623	108	10	in	in	ADP
ejpam-2623	108	11	polynomial	polynomial	ADJ
ejpam-2623	108	12	time	time	NOUN
ejpam-2623	108	13	.	.	PUNCT
ejpam-2623	109	1	icart	icart	PROPN
ejpam-2623	109	2	also	also	ADV
ejpam-2623	109	3	showed	show	VERB
ejpam-2623	109	4	that	that	SCONJ
ejpam-2623	109	5	|f−1a	|f−1a	NOUN
ejpam-2623	109	6	,	,	PUNCT
ejpam-2623	109	7	b	b	PROPN
ejpam-2623	109	8	(	(	PUNCT
ejpam-2623	109	9	p	p	NOUN
ejpam-2623	109	10	)	)	PUNCT
ejpam-2623	109	11	|	|	ADV
ejpam-2623	109	12	≤	≤	NUM
ejpam-2623	109	13	4	4	NUM
ejpam-2623	109	14	,	,	PUNCT
ejpam-2623	109	15	given	give	VERB
ejpam-2623	109	16	a	a	DET
ejpam-2623	109	17	point	point	NOUN
ejpam-2623	109	18	p	p	NOUN
ejpam-2623	109	19	on	on	ADP
ejpam-2623	109	20	the	the	DET
ejpam-2623	109	21	elliptic	elliptic	ADJ
ejpam-2623	109	22	curve	curve	NOUN
ejpam-2623	109	23	.	.	PUNCT
ejpam-2623	110	1	this	this	PRON
ejpam-2623	110	2	results	result	VERB
ejpam-2623	110	3	from	from	ADP
ejpam-2623	110	4	the	the	DET
ejpam-2623	110	5	fact	fact	NOUN
ejpam-2623	110	6	that	that	SCONJ
ejpam-2623	110	7	to	to	PART
ejpam-2623	110	8	compute	compute	VERB
ejpam-2623	110	9	f−1a	f−1a	PROPN
ejpam-2623	110	10	,	,	PUNCT
ejpam-2623	110	11	b	b	PROPN
ejpam-2623	110	12	(	(	PUNCT
ejpam-2623	110	13	p	p	NOUN
ejpam-2623	110	14	)	)	PUNCT
ejpam-2623	110	15	,	,	PUNCT
ejpam-2623	110	16	it	it	PRON
ejpam-2623	110	17	’s	’	VERB
ejpam-2623	110	18	sufficient	sufficient	ADJ
ejpam-2623	110	19	to	to	PART
ejpam-2623	110	20	solve	solve	VERB
ejpam-2623	110	21	the	the	DET
ejpam-2623	110	22	degree	degree	NOUN
ejpam-2623	110	23	4	4	NUM
ejpam-2623	110	24	polynomial	polynomial	ADJ
ejpam-2623	110	25	over	over	ADP
ejpam-2623	110	26	fq	fq	PROPN
ejpam-2623	110	27	:	:	PUNCT
ejpam-2623	110	28	u4	u4	PROPN
ejpam-2623	111	1	−	−	PROPN
ejpam-2623	111	2	6u2x+	6u2x+	NUM
ejpam-2623	111	3	6uy	6uy	NOUN
ejpam-2623	111	4	−	−	PROPN
ejpam-2623	111	5	3a	3a	NUM
ejpam-2623	111	6	=	=	SYM
ejpam-2623	111	7	0	0	PUNCT
ejpam-2623	112	1	moreover	moreover	ADV
ejpam-2623	112	2	,	,	PUNCT
ejpam-2623	112	3	icart	icart	PROPN
ejpam-2623	112	4	showed	show	VERB
ejpam-2623	112	5	that	that	SCONJ
ejpam-2623	112	6	the	the	DET
ejpam-2623	112	7	cardinal	cardinal	NOUN
ejpam-2623	112	8	of	of	ADP
ejpam-2623	112	9	the	the	DET
ejpam-2623	112	10	image	image	NOUN
ejpam-2623	112	11	set	set	VERB
ejpam-2623	112	12	im(fa	im(fa	NOUN
ejpam-2623	112	13	,	,	PUNCT
ejpam-2623	112	14	b	b	NOUN
ejpam-2623	112	15	)	)	PUNCT
ejpam-2623	112	16	is	be	AUX
ejpam-2623	112	17	greater	great	ADJ
ejpam-2623	112	18	than	than	ADP
ejpam-2623	112	19	q/4	q/4	PUNCT
ejpam-2623	112	20	and	and	CCONJ
ejpam-2623	112	21	made	make	VERB
ejpam-2623	112	22	the	the	DET
ejpam-2623	112	23	following	following	NOUN
ejpam-2623	112	24	conjecture(proved	conjecture(prove	VERB
ejpam-2623	112	25	later	later	ADV
ejpam-2623	112	26	by	by	ADP
ejpam-2623	112	27	tibouchi	tibouchi	NOUN
ejpam-2623	112	28	and	and	CCONJ
ejpam-2623	112	29	fouque	fouque	NOUN
ejpam-2623	112	30	in	in	ADP
ejpam-2623	112	31	[	[	X
ejpam-2623	112	32	8	8	NUM
ejpam-2623	112	33	]	]	PUNCT
ejpam-2623	112	34	):	):	PUNCT
ejpam-2623	112	35	the	the	DET
ejpam-2623	112	36	size	size	NOUN
ejpam-2623	112	37	of	of	ADP
ejpam-2623	112	38	im(fa	im(fa	NOUN
ejpam-2623	112	39	,	,	PUNCT
ejpam-2623	112	40	b	b	NOUN
ejpam-2623	112	41	)	)	PUNCT
ejpam-2623	112	42	is	be	AUX
ejpam-2623	112	43	approximately	approximately	ADV
ejpam-2623	112	44	5	5	NUM
ejpam-2623	112	45	8	8	NUM
ejpam-2623	112	46	of	of	ADP
ejpam-2623	112	47	the	the	DET
ejpam-2623	112	48	size	size	NOUN
ejpam-2623	112	49	of	of	ADP
ejpam-2623	112	50	the	the	DET
ejpam-2623	112	51	curve	curve	NOUN
ejpam-2623	112	52	ea	ea	PROPN
ejpam-2623	112	53	,	,	PUNCT
ejpam-2623	112	54	b.	b.	PROPN
ejpam-2623	112	55	n.	n.	PROPN
ejpam-2623	112	56	diarra	diarra	PROPN
ejpam-2623	112	57	,	,	PUNCT
ejpam-2623	112	58	d.	d.	PROPN
ejpam-2623	112	59	sow	sow	PROPN
ejpam-2623	112	60	,	,	PUNCT
ejpam-2623	112	61	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	112	62	.	.	PUNCT
ejpam-2623	112	63	khlil	khlil	PROPN
ejpam-2623	112	64	/	/	SYM
ejpam-2623	112	65	eur	eur	PROPN
ejpam-2623	112	66	.	.	PUNCT
ejpam-2623	113	1	j.	j.	PROPN
ejpam-2623	113	2	pure	pure	PROPN
ejpam-2623	113	3	appl	appl	PROPN
ejpam-2623	113	4	.	.	PROPN
ejpam-2623	113	5	math	math	PROPN
ejpam-2623	113	6	,	,	PUNCT
ejpam-2623	113	7	10	10	NUM
ejpam-2623	113	8	(	(	PUNCT
ejpam-2623	113	9	2	2	NUM
ejpam-2623	113	10	)	)	PUNCT
ejpam-2623	113	11	(	(	PUNCT
ejpam-2623	113	12	2017	2017	NUM
ejpam-2623	113	13	)	)	PUNCT
ejpam-2623	113	14	,	,	PUNCT
ejpam-2623	113	15	363	363	NUM
ejpam-2623	113	16	-	-	SYM
ejpam-2623	113	17	391	391	NUM
ejpam-2623	113	18	367	367	NUM
ejpam-2623	113	19	2.2.5	2.2.5	NUM
ejpam-2623	113	20	.	.	PUNCT
ejpam-2623	114	1	encoding	encoding	NOUN
ejpam-2623	114	2	and	and	CCONJ
ejpam-2623	114	3	extraction	extraction	NOUN
ejpam-2623	114	4	for	for	ADP
ejpam-2623	114	5	hessian	hessian	ADJ
ejpam-2623	114	6	curves	curve	NOUN
ejpam-2623	114	7	let	let	VERB
ejpam-2623	114	8	d	d	X
ejpam-2623	114	9	∈	∈	PROPN
ejpam-2623	114	10	fq	fq	PROPN
ejpam-2623	114	11	with	with	ADP
ejpam-2623	114	12	d3	d3	PROPN
ejpam-2623	114	13	6=	6=	ADP
ejpam-2623	114	14	1	1	NUM
ejpam-2623	114	15	.	.	PUNCT
ejpam-2623	115	1	a	a	DET
ejpam-2623	115	2	hessian	hessian	ADJ
ejpam-2623	115	3	curve(a	curve(a	PROPN
ejpam-2623	115	4	curve	curve	NOUN
ejpam-2623	115	5	with	with	ADP
ejpam-2623	115	6	a	a	DET
ejpam-2623	115	7	point	point	NOUN
ejpam-2623	115	8	of	of	ADP
ejpam-2623	115	9	order	order	NOUN
ejpam-2623	115	10	3	3	X
ejpam-2623	115	11	)	)	PUNCT
ejpam-2623	115	12	hd	hd	NOUN
ejpam-2623	115	13	over	over	ADP
ejpam-2623	115	14	fq	fq	PROPN
ejpam-2623	115	15	is	be	AUX
ejpam-2623	115	16	given	give	VERB
ejpam-2623	115	17	by	by	ADP
ejpam-2623	115	18	the	the	DET
ejpam-2623	115	19	equation	equation	NOUN
ejpam-2623	115	20	x3	x3	VERB
ejpam-2623	116	1	+	+	CCONJ
ejpam-2623	116	2	y3	y3	NOUN
ejpam-2623	116	3	+	+	CCONJ
ejpam-2623	116	4	1	1	NUM
ejpam-2623	116	5	=	=	SYM
ejpam-2623	116	6	3dxy	3dxy	PROPN
ejpam-2623	116	7	.	.	PUNCT
ejpam-2623	117	1	for	for	ADP
ejpam-2623	117	2	q	q	PROPN
ejpam-2623	117	3	≡	≡	PROPN
ejpam-2623	117	4	2	2	NUM
ejpam-2623	117	5	mod	mod	NOUN
ejpam-2623	117	6	3	3	NUM
ejpam-2623	117	7	,	,	PUNCT
ejpam-2623	117	8	farashahi[7	farashahi[7	CCONJ
ejpam-2623	117	9	]	]	PUNCT
ejpam-2623	117	10	applied	apply	VERB
ejpam-2623	117	11	icart	icart	PROPN
ejpam-2623	117	12	’s	’s	PART
ejpam-2623	117	13	method	method	NOUN
ejpam-2623	117	14	to	to	ADP
ejpam-2623	117	15	the	the	DET
ejpam-2623	117	16	set	set	NOUN
ejpam-2623	117	17	hd(fq	hd(fq	PROPN
ejpam-2623	117	18	)	)	PUNCT
ejpam-2623	117	19	of	of	ADP
ejpam-2623	117	20	fq	fq	PROPN
ejpam-2623	117	21	-	-	ADJ
ejpam-2623	117	22	rational	rational	ADJ
ejpam-2623	117	23	points	point	NOUN
ejpam-2623	117	24	of	of	ADP
ejpam-2623	117	25	hd	hd	NOUN
ejpam-2623	117	26	.	.	PUNCT
ejpam-2623	118	1	he	he	PRON
ejpam-2623	118	2	obtained	obtain	VERB
ejpam-2623	118	3	the	the	DET
ejpam-2623	118	4	function	function	NOUN
ejpam-2623	118	5	:	:	PUNCT
ejpam-2623	118	6	hd	hd	PROPN
ejpam-2623	118	7	:	:	PUNCT
ejpam-2623	119	1	fq	fq	PROPN
ejpam-2623	119	2	7→	7→	NUM
ejpam-2623	119	3	hd(fq	hd(fq	NOUN
ejpam-2623	119	4	)	)	PUNCT
ejpam-2623	119	5	u	u	PROPN
ejpam-2623	119	6	7→	7→	NUM
ejpam-2623	119	7	hd(u	hd(u	NOUN
ejpam-2623	119	8	)	)	PUNCT
ejpam-2623	119	9	=	=	SYM
ejpam-2623	119	10	(	(	PUNCT
ejpam-2623	119	11	x	x	X
ejpam-2623	119	12	,	,	PUNCT
ejpam-2623	119	13	y	y	NOUN
ejpam-2623	119	14	)	)	PUNCT
ejpam-2623	119	15	defined	define	VERB
ejpam-2623	119	16	by	by	ADP
ejpam-2623	119	17	•	•	NUM
ejpam-2623	119	18	hd(u	hd(u	PRON
ejpam-2623	119	19	)	)	PUNCT
ejpam-2623	119	20	=	=	SYM
ejpam-2623	119	21	(	(	PUNCT
ejpam-2623	119	22	x	x	X
ejpam-2623	119	23	,	,	PUNCT
ejpam-2623	119	24	y	y	PROPN
ejpam-2623	119	25	)	)	PUNCT
ejpam-2623	120	1	if	if	SCONJ
ejpam-2623	120	2	u	u	PROPN
ejpam-2623	120	3	6=	6=	SYM
ejpam-2623	120	4	−1	−1	NOUN
ejpam-2623	120	5	,	,	PUNCT
ejpam-2623	120	6	where	where	SCONJ
ejpam-2623	120	7	x	x	X
ejpam-2623	120	8	=	=	VERB
ejpam-2623	120	9	−u	−u	PROPN
ejpam-2623	120	10	(	(	PUNCT
ejpam-2623	120	11	d3u3	d3u3	X
ejpam-2623	120	12	+	+	X
ejpam-2623	120	13	u3	u3	NOUN
ejpam-2623	120	14	+	+	CCONJ
ejpam-2623	120	15	1	1	NUM
ejpam-2623	120	16	)	)	PUNCT
ejpam-2623	120	17	1/3	1/3	NUM
ejpam-2623	120	18	,	,	PUNCT
ejpam-2623	120	19	v	v	NOUN
ejpam-2623	120	20	=	=	SYM
ejpam-2623	120	21	−	−	PROPN
ejpam-2623	120	22	(	(	PUNCT
ejpam-2623	120	23	d3u3	d3u3	X
ejpam-2623	120	24	+	+	X
ejpam-2623	120	25	u3	u3	NOUN
ejpam-2623	120	26	+	+	CCONJ
ejpam-2623	120	27	1	1	NUM
ejpam-2623	120	28	)	)	PUNCT
ejpam-2623	120	29	1/3	1/3	NOUN
ejpam-2623	120	30	+	+	CCONJ
ejpam-2623	120	31	du	du	NOUN
ejpam-2623	120	32	;	;	PUNCT
ejpam-2623	120	33	•	•	NOUN
ejpam-2623	120	34	and	and	CCONJ
ejpam-2623	120	35	hd(u	hd(u	PRON
ejpam-2623	120	36	)	)	PUNCT
ejpam-2623	121	1	=	=	PUNCT
ejpam-2623	121	2	o	o	NOUN
ejpam-2623	121	3	if	if	SCONJ
ejpam-2623	121	4	u	u	PROPN
ejpam-2623	121	5	=	=	SYM
ejpam-2623	121	6	−1	−1	NOUN
ejpam-2623	121	7	,	,	PUNCT
ejpam-2623	121	8	where	where	SCONJ
ejpam-2623	121	9	o	o	NOUN
ejpam-2623	121	10	is	be	AUX
ejpam-2623	121	11	the	the	DET
ejpam-2623	121	12	point	point	NOUN
ejpam-2623	121	13	at	at	ADP
ejpam-2623	121	14	infinity	infinity	NOUN
ejpam-2623	121	15	.	.	PUNCT
ejpam-2623	122	1	the	the	DET
ejpam-2623	122	2	map	map	NOUN
ejpam-2623	122	3	hd	hd	NOUN
ejpam-2623	122	4	is	be	AUX
ejpam-2623	122	5	well	well	ADV
ejpam-2623	122	6	-	-	PUNCT
ejpam-2623	122	7	defined	define	VERB
ejpam-2623	122	8	since	since	SCONJ
ejpam-2623	122	9	hd(u	hd(u	PRON
ejpam-2623	122	10	)	)	PUNCT
ejpam-2623	122	11	is	be	AUX
ejpam-2623	122	12	a	a	DET
ejpam-2623	122	13	point	point	NOUN
ejpam-2623	122	14	of	of	ADP
ejpam-2623	122	15	hd(fq	hd(fq	PROPN
ejpam-2623	122	16	)	)	PUNCT
ejpam-2623	122	17	,	,	PUNCT
ejpam-2623	122	18	for	for	ADP
ejpam-2623	122	19	u	u	PROPN
ejpam-2623	122	20	∈	∈	PROPN
ejpam-2623	122	21	fq	fq	PROPN
ejpam-2623	122	22	.	.	PROPN
ejpam-2623	123	1	this	this	DET
ejpam-2623	123	2	encoding	encoding	NOUN
ejpam-2623	123	3	function	function	NOUN
ejpam-2623	123	4	for	for	ADP
ejpam-2623	123	5	hessian	hessian	ADJ
ejpam-2623	123	6	curves	curve	NOUN
ejpam-2623	123	7	is	be	AUX
ejpam-2623	123	8	less	less	ADV
ejpam-2623	123	9	general	general	ADJ
ejpam-2623	123	10	than	than	ADP
ejpam-2623	123	11	icart	icart	PROPN
ejpam-2623	123	12	’s	’s	PART
ejpam-2623	123	13	one	one	NUM
ejpam-2623	123	14	,	,	PUNCT
ejpam-2623	123	15	but	but	CCONJ
ejpam-2623	123	16	has	have	VERB
ejpam-2623	123	17	many	many	ADJ
ejpam-2623	123	18	other	other	ADJ
ejpam-2623	123	19	interesting	interesting	ADJ
ejpam-2623	123	20	properties	property	NOUN
ejpam-2623	123	21	.	.	PUNCT
ejpam-2623	124	1	in	in	ADP
ejpam-2623	124	2	fact	fact	NOUN
ejpam-2623	124	3	,	,	PUNCT
ejpam-2623	124	4	farashahi	farashahi	NOUN
ejpam-2623	124	5	showed	show	VERB
ejpam-2623	124	6	that	that	SCONJ
ejpam-2623	124	7	the	the	DET
ejpam-2623	124	8	size	size	NOUN
ejpam-2623	124	9	of	of	ADP
ejpam-2623	124	10	the	the	DET
ejpam-2623	124	11	image	image	NOUN
ejpam-2623	124	12	set	set	VERB
ejpam-2623	124	13	hd(fq	hd(fq	PROPN
ejpam-2623	124	14	)	)	PUNCT
ejpam-2623	124	15	is	be	AUX
ejpam-2623	124	16	at	at	ADP
ejpam-2623	124	17	least	least	ADJ
ejpam-2623	124	18	q/2	q/2	NOUN
ejpam-2623	124	19	an	an	DET
ejpam-2623	124	20	that	that	SCONJ
ejpam-2623	124	21	the	the	DET
ejpam-2623	124	22	inverse	inverse	NOUN
ejpam-2623	124	23	function	function	NOUN
ejpam-2623	124	24	h−1d	h−1d	PRON
ejpam-2623	124	25	can	can	AUX
ejpam-2623	124	26	be	be	AUX
ejpam-2623	124	27	easily	easily	ADV
ejpam-2623	124	28	described	describe	VERB
ejpam-2623	124	29	.	.	PUNCT
ejpam-2623	125	1	he	he	PRON
ejpam-2623	125	2	also	also	ADV
ejpam-2623	125	3	studied	study	VERB
ejpam-2623	125	4	the	the	DET
ejpam-2623	125	5	possibility	possibility	NOUN
ejpam-2623	125	6	to	to	PART
ejpam-2623	125	7	extract	extract	VERB
ejpam-2623	125	8	random	random	ADJ
ejpam-2623	125	9	bits	bit	NOUN
ejpam-2623	125	10	from	from	ADP
ejpam-2623	125	11	the	the	DET
ejpam-2623	125	12	image	image	NOUN
ejpam-2623	125	13	hd(u	hd(u	NOUN
ejpam-2623	125	14	)	)	PUNCT
ejpam-2623	125	15	of	of	ADP
ejpam-2623	125	16	an	an	DET
ejpam-2623	125	17	element	element	NOUN
ejpam-2623	125	18	u	u	PROPN
ejpam-2623	125	19	∈	∈	PROPN
ejpam-2623	125	20	fq	fq	PROPN
ejpam-2623	125	21	.	.	PROPN
ejpam-2623	125	22	2.2.6	2.2.6	NUM
ejpam-2623	125	23	.	.	PUNCT
ejpam-2623	125	24	injective	injective	ADJ
ejpam-2623	125	25	encoding	encoding	NOUN
ejpam-2623	125	26	for	for	ADP
ejpam-2623	125	27	edwards	edwards	PROPN
ejpam-2623	125	28	curves	curve	NOUN
ejpam-2623	125	29	:	:	PUNCT
ejpam-2623	125	30	elligator-1	elligator-1	NUM
ejpam-2623	125	31	an	an	DET
ejpam-2623	125	32	edwards	edwards	PROPN
ejpam-2623	125	33	curve	curve	PROPN
ejpam-2623	125	34	ed	ed	PROPN
ejpam-2623	125	35	defined	define	VERB
ejpam-2623	125	36	over	over	ADP
ejpam-2623	125	37	fq	fq	PROPN
ejpam-2623	125	38	is	be	AUX
ejpam-2623	125	39	a	a	DET
ejpam-2623	125	40	model	model	NOUN
ejpam-2623	125	41	of	of	ADP
ejpam-2623	125	42	elliptic	elliptic	ADJ
ejpam-2623	125	43	curve	curve	NOUN
ejpam-2623	125	44	given	give	VERB
ejpam-2623	125	45	by	by	ADP
ejpam-2623	125	46	the	the	DET
ejpam-2623	125	47	equation	equation	NOUN
ejpam-2623	125	48	:	:	PUNCT
ejpam-2623	125	49	ed	ed	NOUN
ejpam-2623	125	50	:	:	PUNCT
ejpam-2623	126	1	x2	x2	PROPN
ejpam-2623	127	1	+	+	PUNCT
ejpam-2623	127	2	y2	y2	NOUN
ejpam-2623	127	3	=	=	SYM
ejpam-2623	127	4	1	1	NUM
ejpam-2623	127	5	+	+	CCONJ
ejpam-2623	127	6	dx2y2	dx2y2	VERB
ejpam-2623	127	7	with	with	ADP
ejpam-2623	127	8	d	d	PROPN
ejpam-2623	127	9	/∈	/∈	PUNCT
ejpam-2623	127	10	{	{	PUNCT
ejpam-2623	127	11	0	0	NUM
ejpam-2623	127	12	,	,	PUNCT
ejpam-2623	127	13	1	1	NUM
ejpam-2623	127	14	}	}	PUNCT
ejpam-2623	127	15	and	and	CCONJ
ejpam-2623	127	16	d	d	NOUN
ejpam-2623	127	17	is	be	AUX
ejpam-2623	127	18	not	not	PART
ejpam-2623	127	19	a	a	DET
ejpam-2623	127	20	square	square	NOUN
ejpam-2623	127	21	.	.	PUNCT
ejpam-2623	128	1	in	in	ADP
ejpam-2623	128	2	[	[	X
ejpam-2623	128	3	4	4	NUM
ejpam-2623	128	4	]	]	PUNCT
ejpam-2623	128	5	,	,	PUNCT
ejpam-2623	128	6	bernstein	bernstein	PROPN
ejpam-2623	128	7	et	et	PROPN
ejpam-2623	128	8	al	al	PROPN
ejpam-2623	128	9	.	.	PROPN
ejpam-2623	128	10	defined	define	VERB
ejpam-2623	128	11	an	an	DET
ejpam-2623	128	12	encoding	encoding	NOUN
ejpam-2623	128	13	that	that	PRON
ejpam-2623	128	14	maps	map	VERB
ejpam-2623	128	15	an	an	DET
ejpam-2623	128	16	element	element	NOUN
ejpam-2623	128	17	of	of	ADP
ejpam-2623	128	18	fq	fq	PROPN
ejpam-2623	128	19	to	to	ADP
ejpam-2623	128	20	a	a	DET
ejpam-2623	128	21	point	point	NOUN
ejpam-2623	128	22	of	of	ADP
ejpam-2623	128	23	the	the	DET
ejpam-2623	128	24	curve	curve	NOUN
ejpam-2623	128	25	ed	ed	NOUN
ejpam-2623	128	26	.	.	PUNCT
ejpam-2623	129	1	their	their	PRON
ejpam-2623	129	2	work	work	NOUN
ejpam-2623	129	3	used	use	VERB
ejpam-2623	129	4	the	the	DET
ejpam-2623	129	5	general	general	ADJ
ejpam-2623	129	6	method	method	NOUN
ejpam-2623	129	7	proposed	propose	VERB
ejpam-2623	129	8	by	by	ADP
ejpam-2623	129	9	fouque	fouque	PROPN
ejpam-2623	129	10	et	et	PROPN
ejpam-2623	129	11	al	al	PROPN
ejpam-2623	129	12	.	.	PUNCT
ejpam-2623	130	1	in	in	ADP
ejpam-2623	130	2	[	[	X
ejpam-2623	130	3	13	13	NUM
ejpam-2623	130	4	]	]	PUNCT
ejpam-2623	130	5	.	.	PUNCT
ejpam-2623	131	1	note	note	VERB
ejpam-2623	131	2	that	that	SCONJ
ejpam-2623	131	3	,	,	PUNCT
ejpam-2623	131	4	in	in	ADP
ejpam-2623	131	5	their	their	PRON
ejpam-2623	131	6	updated	update	VERB
ejpam-2623	131	7	paper	paper	NOUN
ejpam-2623	131	8	[	[	X
ejpam-2623	131	9	12	12	NUM
ejpam-2623	131	10	]	]	PUNCT
ejpam-2623	131	11	,	,	PUNCT
ejpam-2623	131	12	fouque	fouque	PROPN
ejpam-2623	131	13	et	et	PROPN
ejpam-2623	131	14	al	al	PROPN
ejpam-2623	131	15	.	.	PROPN
ejpam-2623	131	16	have	have	AUX
ejpam-2623	131	17	also	also	ADV
ejpam-2623	131	18	proposed	propose	VERB
ejpam-2623	131	19	an	an	DET
ejpam-2623	131	20	explicit	explicit	ADJ
ejpam-2623	131	21	encoding	encoding	NOUN
ejpam-2623	131	22	for	for	ADP
ejpam-2623	131	23	edwards	edwards	PROPN
ejpam-2623	131	24	curves	curve	NOUN
ejpam-2623	131	25	,	,	PUNCT
ejpam-2623	131	26	based	base	VERB
ejpam-2623	131	27	on	on	ADP
ejpam-2623	131	28	their	their	PRON
ejpam-2623	131	29	previous	previous	ADJ
ejpam-2623	131	30	work	work	NOUN
ejpam-2623	131	31	[	[	X
ejpam-2623	131	32	13	13	NUM
ejpam-2623	131	33	]	]	PUNCT
ejpam-2623	131	34	.	.	PUNCT
ejpam-2623	132	1	the	the	DET
ejpam-2623	132	2	encoding	encoding	NOUN
ejpam-2623	132	3	process	process	NOUN
ejpam-2623	132	4	of	of	ADP
ejpam-2623	132	5	bernstein	bernstein	PROPN
ejpam-2623	132	6	et	et	PROPN
ejpam-2623	132	7	al	al	PROPN
ejpam-2623	132	8	.	.	PUNCT
ejpam-2623	133	1	in	in	ADP
ejpam-2623	133	2	[	[	X
ejpam-2623	133	3	4	4	X
ejpam-2623	133	4	]	]	PUNCT
ejpam-2623	133	5	is	be	AUX
ejpam-2623	133	6	described	describe	VERB
ejpam-2623	133	7	in	in	ADP
ejpam-2623	133	8	the	the	DET
ejpam-2623	133	9	following	following	NOUN
ejpam-2623	133	10	theorem	theorem	NOUN
ejpam-2623	133	11	:	:	PUNCT
ejpam-2623	133	12	theorem	theorem	NOUN
ejpam-2623	133	13	1	1	X
ejpam-2623	133	14	.	.	PUNCT
ejpam-2623	134	1	let	let	VERB
ejpam-2623	134	2	q	q	PART
ejpam-2623	134	3	be	be	AUX
ejpam-2623	134	4	a	a	DET
ejpam-2623	134	5	prime	prime	ADJ
ejpam-2623	134	6	power	power	NOUN
ejpam-2623	134	7	congruent	congruent	NOUN
ejpam-2623	134	8	to	to	ADP
ejpam-2623	134	9	3	3	NUM
ejpam-2623	134	10	modulo	modulo	NOUN
ejpam-2623	134	11	4	4	NUM
ejpam-2623	134	12	.	.	PUNCT
ejpam-2623	135	1	let	let	VERB
ejpam-2623	135	2	s	s	PRON
ejpam-2623	135	3	be	be	AUX
ejpam-2623	135	4	a	a	DET
ejpam-2623	135	5	nonzero	nonzero	ADJ
ejpam-2623	135	6	element	element	NOUN
ejpam-2623	135	7	of	of	ADP
ejpam-2623	135	8	fq	fq	PROPN
ejpam-2623	135	9	with	with	ADP
ejpam-2623	135	10	(	(	PUNCT
ejpam-2623	135	11	s2	s2	NOUN
ejpam-2623	135	12	−	−	PROPN
ejpam-2623	135	13	2)(s2	2)(s2	NUM
ejpam-2623	136	1	+	+	CCONJ
ejpam-2623	136	2	2	2	NUM
ejpam-2623	136	3	)	)	PUNCT
ejpam-2623	136	4	6=	6=	ADP
ejpam-2623	136	5	0	0	X
ejpam-2623	136	6	.	.	PUNCT
ejpam-2623	137	1	define	define	VERB
ejpam-2623	137	2	c	c	NOUN
ejpam-2623	137	3	=	=	SYM
ejpam-2623	137	4	2	2	NUM
ejpam-2623	137	5	/	/	SYM
ejpam-2623	137	6	s2	s2	PROPN
ejpam-2623	137	7	.	.	PUNCT
ejpam-2623	138	1	then	then	ADV
ejpam-2623	138	2	c(c	c(c	PROPN
ejpam-2623	138	3	−	−	PROPN
ejpam-2623	138	4	1)(c	1)(c	NUM
ejpam-2623	139	1	+	+	CCONJ
ejpam-2623	139	2	1	1	NUM
ejpam-2623	139	3	)	)	PUNCT
ejpam-2623	139	4	6=	6=	ADP
ejpam-2623	139	5	0	0	X
ejpam-2623	139	6	.	.	PUNCT
ejpam-2623	140	1	define	define	VERB
ejpam-2623	140	2	r	r	NOUN
ejpam-2623	140	3	=	=	NOUN
ejpam-2623	140	4	c+	c+	VERB
ejpam-2623	140	5	1	1	NUM
ejpam-2623	140	6	/	/	SYM
ejpam-2623	140	7	c	c	NOUN
ejpam-2623	140	8	and	and	CCONJ
ejpam-2623	140	9	d	d	NOUN
ejpam-2623	140	10	=	=	SYM
ejpam-2623	141	1	−(c+	−(c+	NUM
ejpam-2623	141	2	1)2/(c−	1)2/(c−	NUM
ejpam-2623	141	3	1)2	1)2	NUM
ejpam-2623	141	4	.	.	PUNCT
ejpam-2623	142	1	then	then	ADV
ejpam-2623	142	2	r	r	PROPN
ejpam-2623	142	3	6=	6=	PROPN
ejpam-2623	142	4	0	0	NUM
ejpam-2623	142	5	,	,	PUNCT
ejpam-2623	142	6	and	and	CCONJ
ejpam-2623	142	7	d	d	NOUN
ejpam-2623	142	8	is	be	AUX
ejpam-2623	142	9	not	not	PART
ejpam-2623	142	10	a	a	DET
ejpam-2623	142	11	square	square	NOUN
ejpam-2623	142	12	.	.	PUNCT
ejpam-2623	143	1	the	the	DET
ejpam-2623	143	2	following	follow	VERB
ejpam-2623	143	3	elements	element	NOUN
ejpam-2623	143	4	of	of	ADP
ejpam-2623	143	5	fq	fq	PROPN
ejpam-2623	143	6	are	be	AUX
ejpam-2623	143	7	defined	define	VERB
ejpam-2623	143	8	for	for	ADP
ejpam-2623	143	9	each	each	DET
ejpam-2623	143	10	t	t	NOUN
ejpam-2623	143	11	∈	∈	PROPN
ejpam-2623	143	12	fq	fq	PROPN
ejpam-2623	143	13	\	\	PROPN
ejpam-2623	143	14	{	{	PUNCT
ejpam-2623	143	15	0	0	NUM
ejpam-2623	143	16	,	,	PUNCT
ejpam-2623	143	17	1	1	NUM
ejpam-2623	143	18	}	}	PUNCT
ejpam-2623	143	19	:	:	PUNCT
ejpam-2623	143	20	u	u	NOUN
ejpam-2623	143	21	=	=	PUNCT
ejpam-2623	143	22	(	(	PUNCT
ejpam-2623	143	23	1−	1−	NUM
ejpam-2623	143	24	t)/(1	t)/(1	NUM
ejpam-2623	143	25	+	+	CCONJ
ejpam-2623	143	26	t	t	NOUN
ejpam-2623	143	27	)	)	PUNCT
ejpam-2623	143	28	,	,	PUNCT
ejpam-2623	143	29	v	v	X
ejpam-2623	143	30	=	=	SYM
ejpam-2623	143	31	u5	u5	PROPN
ejpam-2623	143	32	+	+	CCONJ
ejpam-2623	143	33	(	(	PUNCT
ejpam-2623	143	34	r2	r2	PROPN
ejpam-2623	143	35	−	−	PROPN
ejpam-2623	143	36	2)u3	2)u3	NUM
ejpam-2623	143	37	+	+	NUM
ejpam-2623	143	38	u	u	NOUN
ejpam-2623	143	39	;	;	PUNCT
ejpam-2623	143	40	x	x	SYM
ejpam-2623	143	41	=	=	PUNCT
ejpam-2623	143	42	χ(v)u	χ(v)u	PROPN
ejpam-2623	143	43	,	,	PUNCT
ejpam-2623	143	44	y	y	NOUN
ejpam-2623	143	45	=	=	PUNCT
ejpam-2623	143	46	(	(	PUNCT
ejpam-2623	143	47	χ(v)v)(q+1)/4χ(v)χ(u2	χ(v)v)(q+1)/4χ(v)χ(u2	PROPN
ejpam-2623	143	48	+	+	PUNCT
ejpam-2623	143	49	1	1	NUM
ejpam-2623	143	50	/	/	SYM
ejpam-2623	143	51	c2	c2	PROPN
ejpam-2623	143	52	)	)	PUNCT
ejpam-2623	143	53	;	;	PUNCT
ejpam-2623	143	54	x	x	SYM
ejpam-2623	143	55	=	=	SYM
ejpam-2623	143	56	(	(	PUNCT
ejpam-2623	143	57	c−	c−	X
ejpam-2623	143	58	1)sx(1	1)sx(1	NUM
ejpam-2623	143	59	+	+	ADJ
ejpam-2623	143	60	x)/y	x)/y	PROPN
ejpam-2623	143	61	,	,	PUNCT
ejpam-2623	143	62	y	y	PROPN
ejpam-2623	143	63	=	=	PUNCT
ejpam-2623	143	64	(	(	PUNCT
ejpam-2623	143	65	rx	rx	ADP
ejpam-2623	143	66	−	−	PROPN
ejpam-2623	143	67	(	(	PUNCT
ejpam-2623	143	68	1	1	NUM
ejpam-2623	143	69	+	+	NOUN
ejpam-2623	143	70	x)2)/(rx	x)2)/(rx	NOUN
ejpam-2623	143	71	+	+	X
ejpam-2623	143	72	(	(	PUNCT
ejpam-2623	143	73	1	1	NUM
ejpam-2623	143	74	+	+	NOUN
ejpam-2623	143	75	x)2	x)2	NOUN
ejpam-2623	143	76	)	)	PUNCT
ejpam-2623	143	77	.	.	PUNCT
ejpam-2623	144	1	furthermore	furthermore	ADV
ejpam-2623	144	2	x2	x2	PROPN
ejpam-2623	145	1	+	+	CCONJ
ejpam-2623	146	1	y2	y2	NOUN
ejpam-2623	146	2	=	=	SYM
ejpam-2623	146	3	1	1	NUM
ejpam-2623	146	4	+	+	CCONJ
ejpam-2623	146	5	dx2y2	dx2y2	PROPN
ejpam-2623	146	6	;	;	PUNCT
ejpam-2623	146	7	uvxy	uvxy	PROPN
ejpam-2623	146	8	x(y	x(y	PUNCT
ejpam-2623	147	1	+	+	PUNCT
ejpam-2623	147	2	1	1	NUM
ejpam-2623	147	3	)	)	PUNCT
ejpam-2623	147	4	6=	6=	ADP
ejpam-2623	147	5	0	0	NUM
ejpam-2623	147	6	and	and	CCONJ
ejpam-2623	147	7	y	y	PROPN
ejpam-2623	147	8	2	2	NUM
ejpam-2623	147	9	=	=	SYM
ejpam-2623	147	10	x5	x5	PROPN
ejpam-2623	147	11	+	+	CCONJ
ejpam-2623	147	12	(	(	PUNCT
ejpam-2623	147	13	r2	r2	PROPN
ejpam-2623	147	14	−	−	PROPN
ejpam-2623	147	15	2)x3	2)x3	NUM
ejpam-2623	148	1	+	+	NOUN
ejpam-2623	148	2	x.	x.	NOUN
ejpam-2623	148	3	the	the	DET
ejpam-2623	148	4	authors	author	NOUN
ejpam-2623	148	5	also	also	ADV
ejpam-2623	148	6	showed	show	VERB
ejpam-2623	148	7	that	that	SCONJ
ejpam-2623	148	8	the	the	DET
ejpam-2623	148	9	image	image	NOUN
ejpam-2623	148	10	set	set	NOUN
ejpam-2623	148	11	of	of	ADP
ejpam-2623	148	12	the	the	DET
ejpam-2623	148	13	map	map	NOUN
ejpam-2623	148	14	can	can	AUX
ejpam-2623	148	15	be	be	AUX
ejpam-2623	148	16	easily	easily	ADV
ejpam-2623	148	17	described	describe	VERB
ejpam-2623	148	18	.	.	PUNCT
ejpam-2623	149	1	furthermore	furthermore	ADV
ejpam-2623	149	2	,	,	PUNCT
ejpam-2623	149	3	this	this	DET
ejpam-2623	149	4	map	map	NOUN
ejpam-2623	149	5	can	can	AUX
ejpam-2623	149	6	be	be	AUX
ejpam-2623	149	7	used	use	VERB
ejpam-2623	149	8	for	for	ADP
ejpam-2623	149	9	injective	injective	ADJ
ejpam-2623	149	10	encoding	encoding	NOUN
ejpam-2623	149	11	into	into	ADP
ejpam-2623	149	12	the	the	DET
ejpam-2623	149	13	curve	curve	NOUN
ejpam-2623	149	14	,	,	PUNCT
ejpam-2623	149	15	considering	consider	VERB
ejpam-2623	149	16	only	only	ADV
ejpam-2623	149	17	half	half	NOUN
ejpam-2623	149	18	of	of	ADP
ejpam-2623	149	19	the	the	DET
ejpam-2623	149	20	points	point	NOUN
ejpam-2623	149	21	of	of	ADP
ejpam-2623	149	22	fq	fq	PROPN
ejpam-2623	149	23	.	.	PROPN
ejpam-2623	149	24	n.	n.	PROPN
ejpam-2623	149	25	diarra	diarra	PROPN
ejpam-2623	149	26	,	,	PUNCT
ejpam-2623	149	27	d.	d.	PROPN
ejpam-2623	149	28	sow	sow	PROPN
ejpam-2623	149	29	,	,	PUNCT
ejpam-2623	149	30	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	149	31	.	.	PUNCT
ejpam-2623	149	32	khlil	khlil	PROPN
ejpam-2623	149	33	/	/	SYM
ejpam-2623	149	34	eur	eur	PROPN
ejpam-2623	149	35	.	.	PUNCT
ejpam-2623	150	1	j.	j.	PROPN
ejpam-2623	150	2	pure	pure	PROPN
ejpam-2623	150	3	appl	appl	PROPN
ejpam-2623	150	4	.	.	PROPN
ejpam-2623	150	5	math	math	PROPN
ejpam-2623	150	6	,	,	PUNCT
ejpam-2623	150	7	10	10	NUM
ejpam-2623	150	8	(	(	PUNCT
ejpam-2623	150	9	2	2	NUM
ejpam-2623	150	10	)	)	PUNCT
ejpam-2623	150	11	(	(	PUNCT
ejpam-2623	150	12	2017	2017	NUM
ejpam-2623	150	13	)	)	PUNCT
ejpam-2623	150	14	,	,	PUNCT
ejpam-2623	150	15	363	363	NUM
ejpam-2623	150	16	-	-	SYM
ejpam-2623	150	17	391	391	NUM
ejpam-2623	150	18	368	368	NUM
ejpam-2623	150	19	3	3	NUM
ejpam-2623	150	20	.	.	PUNCT
ejpam-2623	150	21	elligator	elligator	NOUN
ejpam-2623	150	22	’s	’s	PART
ejpam-2623	150	23	methods	method	NOUN
ejpam-2623	150	24	revisited	revisit	VERB
ejpam-2623	150	25	for	for	ADP
ejpam-2623	150	26	various	various	ADJ
ejpam-2623	150	27	curves	curve	NOUN
ejpam-2623	150	28	in	in	ADP
ejpam-2623	150	29	this	this	DET
ejpam-2623	150	30	section	section	NOUN
ejpam-2623	150	31	,	,	PUNCT
ejpam-2623	150	32	we	we	PRON
ejpam-2623	150	33	investigate	investigate	VERB
ejpam-2623	150	34	the	the	DET
ejpam-2623	150	35	problem	problem	NOUN
ejpam-2623	150	36	of	of	ADP
ejpam-2623	150	37	constructing	construct	VERB
ejpam-2623	150	38	almost	almost	ADV
ejpam-2623	150	39	-	-	PUNCT
ejpam-2623	150	40	injective	injective	ADJ
ejpam-2623	150	41	and	and	CCONJ
ejpam-2623	150	42	invertible	invertible	ADJ
ejpam-2623	150	43	encodings	encoding	NOUN
ejpam-2623	150	44	(	(	PUNCT
ejpam-2623	150	45	aiie	aiie	NOUN
ejpam-2623	150	46	)	)	PUNCT
ejpam-2623	150	47	for	for	ADP
ejpam-2623	150	48	some	some	DET
ejpam-2623	150	49	forms	form	NOUN
ejpam-2623	150	50	of	of	ADP
ejpam-2623	150	51	curves	curve	NOUN
ejpam-2623	150	52	,	,	PUNCT
ejpam-2623	150	53	such	such	ADJ
ejpam-2623	150	54	as	as	ADP
ejpam-2623	150	55	generalized	generalize	VERB
ejpam-2623	150	56	huff	huff	NOUN
ejpam-2623	150	57	curves	curve	NOUN
ejpam-2623	150	58	x(ay2	x(ay2	PUNCT
ejpam-2623	151	1	−	−	ADP
ejpam-2623	151	2	1	1	NUM
ejpam-2623	151	3	)	)	PUNCT
ejpam-2623	151	4	=	=	PUNCT
ejpam-2623	152	1	y(bx2	y(bx2	NOUN
ejpam-2623	153	1	−	−	NOUN
ejpam-2623	153	2	1	1	NUM
ejpam-2623	153	3	)	)	PUNCT
ejpam-2623	153	4	,	,	PUNCT
ejpam-2623	153	5	classical	classical	ADJ
ejpam-2623	153	6	huff	huff	NOUN
ejpam-2623	153	7	curves	curve	VERB
ejpam-2623	153	8	αx(y2	αx(y2	ADP
ejpam-2623	153	9	−	−	NOUN
ejpam-2623	153	10	1	1	NUM
ejpam-2623	153	11	)	)	PUNCT
ejpam-2623	153	12	=	=	SYM
ejpam-2623	153	13	βy(x2	βy(x2	NOUN
ejpam-2623	154	1	−	−	NOUN
ejpam-2623	154	2	1	1	NUM
ejpam-2623	154	3	)	)	PUNCT
ejpam-2623	155	1	,	,	PUNCT
ejpam-2623	155	2	edwards	edwards	PROPN
ejpam-2623	155	3	curves	curve	VERB
ejpam-2623	155	4	x2	x2	PROPN
ejpam-2623	156	1	+	+	ADJ
ejpam-2623	156	2	y2	y2	NOUN
ejpam-2623	156	3	=	=	SYM
ejpam-2623	156	4	1+dx2y2	1+dx2y2	NUM
ejpam-2623	156	5	and	and	CCONJ
ejpam-2623	156	6	the	the	DET
ejpam-2623	156	7	weierstrass	weierstrass	NOUN
ejpam-2623	156	8	model	model	NOUN
ejpam-2623	157	1	y2	y2	PROPN
ejpam-2623	157	2	=	=	PUNCT
ejpam-2623	158	1	x3	x3	VERB
ejpam-2623	158	2	+	+	NOUN
ejpam-2623	158	3	ax2	ax2	NOUN
ejpam-2623	158	4	+	+	PROPN
ejpam-2623	158	5	c.	c.	NOUN
ejpam-2623	158	6	our	our	PRON
ejpam-2623	158	7	encodings	encoding	NOUN
ejpam-2623	158	8	are	be	AUX
ejpam-2623	158	9	based	base	VERB
ejpam-2623	158	10	on	on	ADP
ejpam-2623	158	11	the	the	DET
ejpam-2623	158	12	elligator	elligator	NOUN
ejpam-2623	158	13	method	method	NOUN
ejpam-2623	158	14	due	due	ADP
ejpam-2623	158	15	to	to	ADP
ejpam-2623	158	16	bernstein	bernstein	PROPN
ejpam-2623	158	17	et	et	PROPN
ejpam-2623	158	18	al	al	PROPN
ejpam-2623	158	19	.	.	PUNCT
ejpam-2623	159	1	[	[	X
ejpam-2623	159	2	4	4	NUM
ejpam-2623	159	3	]	]	PUNCT
ejpam-2623	159	4	,	,	PUNCT
ejpam-2623	159	5	and	and	CCONJ
ejpam-2623	159	6	their	their	PRON
ejpam-2623	159	7	almost	almost	ADV
ejpam-2623	159	8	-	-	PUNCT
ejpam-2623	159	9	injectivity	injectivity	NOUN
ejpam-2623	159	10	means	mean	VERB
ejpam-2623	159	11	that	that	SCONJ
ejpam-2623	159	12	their	their	PRON
ejpam-2623	159	13	restriction	restriction	NOUN
ejpam-2623	159	14	to	to	ADP
ejpam-2623	159	15	a	a	DET
ejpam-2623	159	16	large	large	ADJ
ejpam-2623	159	17	enough	enough	ADJ
ejpam-2623	159	18	subset	subset	NOUN
ejpam-2623	159	19	of	of	ADP
ejpam-2623	159	20	fq	fq	PROPN
ejpam-2623	159	21	is	be	AUX
ejpam-2623	159	22	injective	injective	ADJ
ejpam-2623	159	23	.	.	PUNCT
ejpam-2623	160	1	3.1	3.1	NUM
ejpam-2623	160	2	.	.	PUNCT
ejpam-2623	161	1	an	an	DET
ejpam-2623	161	2	aiee	aiee	NOUN
ejpam-2623	161	3	for	for	ADP
ejpam-2623	161	4	the	the	DET
ejpam-2623	161	5	generalized	generalize	VERB
ejpam-2623	161	6	huff	huff	PROPN
ejpam-2623	161	7	model	model	NOUN
ejpam-2623	161	8	x(ay2	x(ay2	PUNCT
ejpam-2623	162	1	−	−	NOUN
ejpam-2623	162	2	1	1	NUM
ejpam-2623	162	3	)	)	PUNCT
ejpam-2623	162	4	=	=	PUNCT
ejpam-2623	163	1	y(bx2	y(bx2	NOUN
ejpam-2623	164	1	−	−	NUM
ejpam-2623	164	2	1	1	X
ejpam-2623	164	3	)	)	PUNCT
ejpam-2623	164	4	fouque	fouque	NOUN
ejpam-2623	164	5	,	,	PUNCT
ejpam-2623	164	6	joux	joux	PROPN
ejpam-2623	164	7	and	and	CCONJ
ejpam-2623	164	8	tibouchi	tibouchi	PROPN
ejpam-2623	164	9	proposed	propose	VERB
ejpam-2623	164	10	a	a	DET
ejpam-2623	164	11	method	method	NOUN
ejpam-2623	164	12	in	in	ADP
ejpam-2623	164	13	[	[	X
ejpam-2623	164	14	13	13	NUM
ejpam-2623	164	15	]	]	PUNCT
ejpam-2623	164	16	,	,	PUNCT
ejpam-2623	164	17	to	to	PART
ejpam-2623	164	18	construct	construct	VERB
ejpam-2623	164	19	an	an	DET
ejpam-2623	164	20	injective	injective	ADJ
ejpam-2623	164	21	encoding	encoding	NOUN
ejpam-2623	164	22	for	for	ADP
ejpam-2623	164	23	an	an	DET
ejpam-2623	164	24	elliptic	elliptic	ADJ
ejpam-2623	164	25	curve	curve	NOUN
ejpam-2623	164	26	,	,	PUNCT
ejpam-2623	164	27	viewed	view	VERB
ejpam-2623	164	28	as	as	ADP
ejpam-2623	164	29	a	a	DET
ejpam-2623	164	30	quotient	quotient	NOUN
ejpam-2623	164	31	of	of	ADP
ejpam-2623	164	32	an	an	DET
ejpam-2623	164	33	odd	odd	ADJ
ejpam-2623	164	34	hyperelliptic	hyperelliptic	ADJ
ejpam-2623	164	35	curve	curve	NOUN
ejpam-2623	164	36	.	.	PUNCT
ejpam-2623	165	1	the	the	DET
ejpam-2623	165	2	elliptic	elliptic	ADJ
ejpam-2623	165	3	curves	curve	NOUN
ejpam-2623	165	4	compatible	compatible	ADJ
ejpam-2623	165	5	with	with	ADP
ejpam-2623	165	6	their	their	PRON
ejpam-2623	165	7	encoding	encoding	NOUN
ejpam-2623	165	8	are	be	AUX
ejpam-2623	165	9	of	of	ADP
ejpam-2623	165	10	the	the	DET
ejpam-2623	165	11	form	form	NOUN
ejpam-2623	165	12	:	:	PUNCT
ejpam-2623	165	13	y2	y2	X
ejpam-2623	165	14	=	=	PUNCT
ejpam-2623	166	1	x3±4x2	x3±4x2	PROPN
ejpam-2623	167	1	+	+	PUNCT
ejpam-2623	167	2	ax	ax	NOUN
ejpam-2623	167	3	(	(	PUNCT
ejpam-2623	167	4	see	see	VERB
ejpam-2623	167	5	[	[	X
ejpam-2623	167	6	13	13	NUM
ejpam-2623	167	7	]	]	PUNCT
ejpam-2623	167	8	,	,	PUNCT
ejpam-2623	167	9	pages	page	NOUN
ejpam-2623	167	10	11	11	NUM
ejpam-2623	167	11	-	-	SYM
ejpam-2623	167	12	12	12	NUM
ejpam-2623	167	13	)	)	PUNCT
ejpam-2623	167	14	.	.	PUNCT
ejpam-2623	168	1	they	they	PRON
ejpam-2623	168	2	have	have	AUX
ejpam-2623	168	3	updated	update	VERB
ejpam-2623	168	4	their	their	PRON
ejpam-2623	168	5	work	work	NOUN
ejpam-2623	168	6	in	in	ADP
ejpam-2623	168	7	[	[	X
ejpam-2623	168	8	12	12	NUM
ejpam-2623	168	9	]	]	PUNCT
ejpam-2623	168	10	.	.	PUNCT
ejpam-2623	169	1	bernstein	bernstein	PROPN
ejpam-2623	169	2	et	et	PROPN
ejpam-2623	169	3	al	al	PROPN
ejpam-2623	169	4	.	.	PROPN
ejpam-2623	169	5	,	,	PUNCT
ejpam-2623	169	6	based	base	VERB
ejpam-2623	169	7	on	on	ADP
ejpam-2623	169	8	the	the	DET
ejpam-2623	169	9	work	work	NOUN
ejpam-2623	169	10	in	in	ADP
ejpam-2623	169	11	[	[	X
ejpam-2623	169	12	13	13	NUM
ejpam-2623	169	13	]	]	PUNCT
ejpam-2623	169	14	,	,	PUNCT
ejpam-2623	169	15	have	have	AUX
ejpam-2623	169	16	proposed	propose	VERB
ejpam-2623	169	17	in	in	ADP
ejpam-2623	169	18	[	[	X
ejpam-2623	169	19	4	4	NUM
ejpam-2623	169	20	]	]	PUNCT
ejpam-2623	169	21	,	,	PUNCT
ejpam-2623	169	22	an	an	DET
ejpam-2623	169	23	injective	injective	ADJ
ejpam-2623	169	24	encoding	encoding	NOUN
ejpam-2623	169	25	for	for	ADP
ejpam-2623	169	26	the	the	DET
ejpam-2623	169	27	edward	edward	NOUN
ejpam-2623	169	28	’s	’s	PART
ejpam-2623	169	29	curve	curve	PROPN
ejpam-2623	169	30	ed	ed	NOUN
ejpam-2623	169	31	:	:	PUNCT
ejpam-2623	169	32	x2+y2	x2+y2	PROPN
ejpam-2623	169	33	=	=	SYM
ejpam-2623	169	34	1+dx2y2	1+dx2y2	NUM
ejpam-2623	169	35	,	,	PUNCT
ejpam-2623	169	36	where	where	SCONJ
ejpam-2623	169	37	d	d	NOUN
ejpam-2623	169	38	is	be	AUX
ejpam-2623	169	39	not	not	PART
ejpam-2623	169	40	a	a	DET
ejpam-2623	169	41	square	square	NOUN
ejpam-2623	169	42	.	.	PUNCT
ejpam-2623	170	1	in	in	ADP
ejpam-2623	170	2	[	[	X
ejpam-2623	170	3	13	13	NUM
ejpam-2623	170	4	]	]	PUNCT
ejpam-2623	170	5	and	and	CCONJ
ejpam-2623	170	6	[	[	X
ejpam-2623	170	7	12	12	NUM
ejpam-2623	170	8	]	]	X
ejpam-2623	170	9	,	,	PUNCT
ejpam-2623	170	10	an	an	DET
ejpam-2623	170	11	explicit	explicit	ADJ
ejpam-2623	170	12	encoding	encoding	NOUN
ejpam-2623	170	13	was	be	AUX
ejpam-2623	170	14	not	not	PART
ejpam-2623	170	15	proposed	propose	VERB
ejpam-2623	170	16	for	for	ADP
ejpam-2623	170	17	the	the	DET
ejpam-2623	170	18	special	special	ADJ
ejpam-2623	170	19	case	case	NOUN
ejpam-2623	170	20	of	of	ADP
ejpam-2623	170	21	generalized	generalized	ADJ
ejpam-2623	170	22	huff	huff	NOUN
ejpam-2623	170	23	curve	curve	NOUN
ejpam-2623	170	24	x(ay2	x(ay2	PUNCT
ejpam-2623	171	1	−	−	NOUN
ejpam-2623	171	2	1	1	NUM
ejpam-2623	171	3	)	)	PUNCT
ejpam-2623	171	4	=	=	PUNCT
ejpam-2623	172	1	y(bx2	y(bx2	NOUN
ejpam-2623	173	1	−	−	NOUN
ejpam-2623	173	2	1	1	NUM
ejpam-2623	173	3	)	)	PUNCT
ejpam-2623	173	4	,	,	PUNCT
ejpam-2623	173	5	with	with	ADP
ejpam-2623	173	6	ab(a−	ab(a−	PROPN
ejpam-2623	173	7	b	b	PROPN
ejpam-2623	173	8	)	)	PUNCT
ejpam-2623	173	9	6=	6=	ADP
ejpam-2623	173	10	0	0	NUM
ejpam-2623	173	11	.	.	PUNCT
ejpam-2623	174	1	as	as	ADP
ejpam-2623	174	2	in	in	ADP
ejpam-2623	174	3	[	[	X
ejpam-2623	174	4	4	4	NUM
ejpam-2623	174	5	]	]	PUNCT
ejpam-2623	174	6	,	,	PUNCT
ejpam-2623	174	7	our	our	PRON
ejpam-2623	174	8	main	main	ADJ
ejpam-2623	174	9	contribution	contribution	NOUN
ejpam-2623	174	10	in	in	ADP
ejpam-2623	174	11	this	this	DET
ejpam-2623	174	12	section	section	NOUN
ejpam-2623	174	13	is	be	AUX
ejpam-2623	174	14	to	to	PART
ejpam-2623	174	15	adapt	adapt	VERB
ejpam-2623	174	16	elligator-1	elligator-1	PROPN
ejpam-2623	174	17	’s	’s	PART
ejpam-2623	174	18	method	method	NOUN
ejpam-2623	174	19	(	(	PUNCT
ejpam-2623	174	20	as	as	ADV
ejpam-2623	174	21	well	well	ADV
ejpam-2623	174	22	as	as	ADP
ejpam-2623	174	23	those	those	PRON
ejpam-2623	174	24	of	of	ADP
ejpam-2623	174	25	fouque	fouque	PROPN
ejpam-2623	174	26	et	et	PROPN
ejpam-2623	174	27	al	al	PROPN
ejpam-2623	174	28	.	.	PROPN
ejpam-2623	174	29	)	)	PUNCT
ejpam-2623	174	30	to	to	PART
ejpam-2623	174	31	generalized	generalize	VERB
ejpam-2623	174	32	huff	huff	NOUN
ejpam-2623	174	33	curves	curve	NOUN
ejpam-2623	174	34	.	.	PUNCT
ejpam-2623	175	1	theorem	theorem	NOUN
ejpam-2623	175	2	2	2	NUM
ejpam-2623	175	3	.	.	PUNCT
ejpam-2623	176	1	let	let	VERB
ejpam-2623	176	2	q	q	PROPN
ejpam-2623	176	3	≡	≡	PROPN
ejpam-2623	176	4	3	3	NUM
ejpam-2623	176	5	mod	mod	NOUN
ejpam-2623	176	6	4	4	X
ejpam-2623	176	7	.	.	PUNCT
ejpam-2623	177	1	let	let	VERB
ejpam-2623	177	2	c	c	PROPN
ejpam-2623	177	3	∈	∈	PROPN
ejpam-2623	177	4	fq	fq	PROPN
ejpam-2623	177	5	such	such	ADJ
ejpam-2623	177	6	that	that	SCONJ
ejpam-2623	177	7	c(c−1)(c+1	c(c−1)(c+1	NOUN
ejpam-2623	177	8	)	)	PUNCT
ejpam-2623	177	9	6=	6=	ADP
ejpam-2623	177	10	0	0	X
ejpam-2623	177	11	.	.	PUNCT
ejpam-2623	178	1	let	let	VERB
ejpam-2623	178	2	a	a	PRON
ejpam-2623	178	3	=	=	PUNCT
ejpam-2623	178	4	−(c−	−(c−	NOUN
ejpam-2623	178	5	1	1	NUM
ejpam-2623	178	6	c	c	NOUN
ejpam-2623	178	7	)	)	PUNCT
ejpam-2623	178	8	2	2	NUM
ejpam-2623	178	9	;	;	PUNCT
ejpam-2623	178	10	then	then	ADV
ejpam-2623	178	11	a	a	DET
ejpam-2623	178	12	6=	6=	PROPN
ejpam-2623	178	13	0	0	NUM
ejpam-2623	178	14	and	and	CCONJ
ejpam-2623	178	15	a	a	PRON
ejpam-2623	178	16	is	be	AUX
ejpam-2623	178	17	not	not	PART
ejpam-2623	178	18	a	a	DET
ejpam-2623	178	19	square	square	NOUN
ejpam-2623	178	20	.	.	PUNCT
ejpam-2623	179	1	let	let	VERB
ejpam-2623	179	2	s	s	PRON
ejpam-2623	179	3	=	=	PUNCT
ejpam-2623	179	4	c+	c+	VERB
ejpam-2623	179	5	1	1	NUM
ejpam-2623	179	6	c−	c−	NOUN
ejpam-2623	179	7	1	1	NUM
ejpam-2623	179	8	;	;	PUNCT
ejpam-2623	179	9	then	then	ADV
ejpam-2623	179	10	s	s	PROPN
ejpam-2623	179	11	6=	6=	NUM
ejpam-2623	179	12	±1	±1	VERB
ejpam-2623	179	13	.	.	PUNCT
ejpam-2623	180	1	let	let	VERB
ejpam-2623	180	2	λ	λ	X
ejpam-2623	180	3	∈	∈	NOUN
ejpam-2623	180	4	f∗q	f∗q	NOUN
ejpam-2623	180	5	;	;	PUNCT
ejpam-2623	180	6	define	define	VERB
ejpam-2623	180	7	b	b	NOUN
ejpam-2623	180	8	=	=	SYM
ejpam-2623	180	9	λ2	λ2	NOUN
ejpam-2623	180	10	1−	1−	NUM
ejpam-2623	180	11	s2	s2	NOUN
ejpam-2623	180	12	and	and	CCONJ
ejpam-2623	180	13	a	a	DET
ejpam-2623	180	14	=	=	SYM
ejpam-2623	180	15	−bs2	−bs2	PROPN
ejpam-2623	180	16	.	.	PUNCT
ejpam-2623	181	1	then	then	ADV
ejpam-2623	181	2	a	a	PRON
ejpam-2623	181	3	+	+	NOUN
ejpam-2623	181	4	b	b	NOUN
ejpam-2623	181	5	is	be	AUX
ejpam-2623	181	6	a	a	DET
ejpam-2623	181	7	square	square	NOUN
ejpam-2623	181	8	,	,	PUNCT
ejpam-2623	181	9	ab	ab	PROPN
ejpam-2623	181	10	is	be	AUX
ejpam-2623	181	11	not	not	PART
ejpam-2623	181	12	a	a	DET
ejpam-2623	181	13	square	square	ADJ
ejpam-2623	181	14	and	and	CCONJ
ejpam-2623	181	15	ab(a	ab(a	NUM
ejpam-2623	182	1	−	−	PROPN
ejpam-2623	182	2	b	b	X
ejpam-2623	182	3	)	)	PUNCT
ejpam-2623	182	4	6=	6=	ADP
ejpam-2623	182	5	0	0	X
ejpam-2623	182	6	.	.	PUNCT
ejpam-2623	183	1	under	under	ADP
ejpam-2623	183	2	the	the	DET
ejpam-2623	183	3	previous	previous	ADJ
ejpam-2623	183	4	hypotheses	hypothesis	NOUN
ejpam-2623	183	5	,	,	PUNCT
ejpam-2623	183	6	for	for	ADP
ejpam-2623	183	7	each	each	DET
ejpam-2623	183	8	element	element	NOUN
ejpam-2623	183	9	z	z	PROPN
ejpam-2623	183	10	∈	∈	PROPN
ejpam-2623	184	1	fq	fq	PROPN
ejpam-2623	184	2	\	\	PROPN
ejpam-2623	184	3	{	{	PUNCT
ejpam-2623	184	4	−1	−1	NOUN
ejpam-2623	184	5	,	,	PUNCT
ejpam-2623	184	6	1	1	NUM
ejpam-2623	184	7	}	}	PUNCT
ejpam-2623	184	8	,	,	PUNCT
ejpam-2623	184	9	the	the	DET
ejpam-2623	184	10	following	follow	VERB
ejpam-2623	184	11	elements	element	NOUN
ejpam-2623	184	12	are	be	AUX
ejpam-2623	184	13	well	well	ADV
ejpam-2623	184	14	-	-	PUNCT
ejpam-2623	184	15	defined	define	VERB
ejpam-2623	184	16	:	:	PUNCT
ejpam-2623	184	17	u	u	NOUN
ejpam-2623	184	18	=	=	SYM
ejpam-2623	184	19	(	(	PUNCT
ejpam-2623	184	20	1−	1−	NUM
ejpam-2623	184	21	z)/(1	z)/(1	NUM
ejpam-2623	184	22	+	+	CCONJ
ejpam-2623	184	23	z	z	NOUN
ejpam-2623	184	24	)	)	PUNCT
ejpam-2623	184	25	;	;	PUNCT
ejpam-2623	184	26	v	v	X
ejpam-2623	184	27	=	=	SYM
ejpam-2623	184	28	−u5	−u5	NOUN
ejpam-2623	185	1	+	+	CCONJ
ejpam-2623	185	2	(	(	PUNCT
ejpam-2623	185	3	c2	c2	PROPN
ejpam-2623	185	4	+	+	CCONJ
ejpam-2623	185	5	1	1	NUM
ejpam-2623	185	6	/	/	SYM
ejpam-2623	185	7	c2)u3	c2)u3	NOUN
ejpam-2623	185	8	−	−	PROPN
ejpam-2623	185	9	u	u	NOUN
ejpam-2623	185	10	;	;	PUNCT
ejpam-2623	185	11	x	x	SYM
ejpam-2623	185	12	=	=	PUNCT
ejpam-2623	185	13	χ(v)u	χ(v)u	PROPN
ejpam-2623	185	14	;	;	PUNCT
ejpam-2623	185	15	y	y	PROPN
ejpam-2623	185	16	=	=	SYM
ejpam-2623	185	17	χ(v	χ(v	PROPN
ejpam-2623	185	18	·	·	PUNCT
ejpam-2623	185	19	(	(	PUNCT
ejpam-2623	185	20	c2u2	c2u2	PUNCT
ejpam-2623	185	21	−	−	NOUN
ejpam-2623	185	22	1	1	NUM
ejpam-2623	185	23	)	)	PUNCT
ejpam-2623	185	24	)	)	PUNCT
ejpam-2623	186	1	√	√	ADP
ejpam-2623	186	2	χ(v)v	χ(v)v	PROPN
ejpam-2623	186	3	;	;	PUNCT
ejpam-2623	186	4	α	α	NOUN
ejpam-2623	186	5	=	=	SYM
ejpam-2623	186	6	λ	λ	X
ejpam-2623	186	7	2	2	NUM
ejpam-2623	186	8	=	=	SYM
ejpam-2623	186	9	√	√	PROPN
ejpam-2623	186	10	a+	a+	PUNCT
ejpam-2623	186	11	b	b	PROPN
ejpam-2623	186	12	2	2	NUM
ejpam-2623	186	13	;	;	PUNCT
ejpam-2623	187	1	x	x	SYM
ejpam-2623	187	2	=	=	SYM
ejpam-2623	187	3	(	(	PUNCT
ejpam-2623	187	4	1	1	NUM
ejpam-2623	187	5	+	+	NOUN
ejpam-2623	187	6	x)(bx	x)(bx	X
ejpam-2623	187	7	−	−	PROPN
ejpam-2623	187	8	α2(1	α2(1	NOUN
ejpam-2623	187	9	+	+	NOUN
ejpam-2623	187	10	x)2	x)2	NOUN
ejpam-2623	187	11	)	)	PUNCT
ejpam-2623	187	12	bαy	bαy	ADV
ejpam-2623	187	13	and	and	CCONJ
ejpam-2623	187	14	y	y	PROPN
ejpam-2623	187	15	=	=	PUNCT
ejpam-2623	187	16	(	(	PUNCT
ejpam-2623	187	17	1	1	NUM
ejpam-2623	187	18	+	+	NOUN
ejpam-2623	187	19	x)(ax	x)(ax	NOUN
ejpam-2623	187	20	−	−	PROPN
ejpam-2623	187	21	α2(1	α2(1	NOUN
ejpam-2623	187	22	+	+	NOUN
ejpam-2623	187	23	x)2	x)2	PROPN
ejpam-2623	187	24	)	)	PUNCT
ejpam-2623	187	25	aαy	aαy	NOUN
ejpam-2623	187	26	.	.	PUNCT
ejpam-2623	188	1	moreover	moreover	ADV
ejpam-2623	188	2	,	,	PUNCT
ejpam-2623	188	3	we	we	PRON
ejpam-2623	188	4	have	have	VERB
ejpam-2623	188	5	:	:	PUNCT
ejpam-2623	188	6	y	y	PROPN
ejpam-2623	188	7	2	2	NUM
ejpam-2623	188	8	=	=	SYM
ejpam-2623	188	9	−x5	−x5	PROPN
ejpam-2623	188	10	+	+	CCONJ
ejpam-2623	188	11	(	(	PUNCT
ejpam-2623	188	12	2−a)x3	2−a)x3	NUM
ejpam-2623	188	13	−x	−x	NOUN
ejpam-2623	188	14	and	and	CCONJ
ejpam-2623	188	15	x(ay2	x(ay2	ADJ
ejpam-2623	189	1	−	−	NOUN
ejpam-2623	189	2	1	1	X
ejpam-2623	189	3	)	)	PUNCT
ejpam-2623	189	4	=	=	PUNCT
ejpam-2623	190	1	y(bx2	y(bx2	NOUN
ejpam-2623	191	1	−	−	NOUN
ejpam-2623	191	2	1	1	NUM
ejpam-2623	191	3	)	)	PUNCT
ejpam-2623	191	4	.	.	PUNCT
ejpam-2623	192	1	proof	proof	NOUN
ejpam-2623	192	2	.	.	PUNCT
ejpam-2623	193	1	(	(	PUNCT
ejpam-2623	193	2	i	i	NOUN
ejpam-2623	193	3	)	)	PUNCT
ejpam-2623	193	4	let	let	VERB
ejpam-2623	193	5	us	we	PRON
ejpam-2623	193	6	show	show	VERB
ejpam-2623	193	7	that	that	SCONJ
ejpam-2623	193	8	a	a	DET
ejpam-2623	193	9	6=	6=	NUM
ejpam-2623	193	10	0	0	NUM
ejpam-2623	193	11	and	and	CCONJ
ejpam-2623	193	12	a	a	PRON
ejpam-2623	193	13	is	be	AUX
ejpam-2623	193	14	not	not	PART
ejpam-2623	193	15	a	a	DET
ejpam-2623	193	16	square	square	NOUN
ejpam-2623	193	17	.	.	PUNCT
ejpam-2623	194	1	•	•	NOUN
ejpam-2623	194	2	if	if	SCONJ
ejpam-2623	194	3	a	a	DET
ejpam-2623	194	4	=	=	NOUN
ejpam-2623	194	5	0	0	PUNCT
ejpam-2623	194	6	then	then	ADV
ejpam-2623	194	7	c	c	X
ejpam-2623	194	8	=	=	NOUN
ejpam-2623	194	9	1	1	NUM
ejpam-2623	194	10	/	/	SYM
ejpam-2623	194	11	c	c	NOUN
ejpam-2623	195	1	so	so	ADV
ejpam-2623	195	2	we	we	PRON
ejpam-2623	195	3	have	have	VERB
ejpam-2623	195	4	c2	c2	PROPN
ejpam-2623	195	5	=	=	SYM
ejpam-2623	195	6	1	1	NUM
ejpam-2623	195	7	and	and	CCONJ
ejpam-2623	195	8	c	c	NOUN
ejpam-2623	195	9	=	=	PRON
ejpam-2623	195	10	±1	±1	VERB
ejpam-2623	195	11	which	which	PRON
ejpam-2623	195	12	is	be	AUX
ejpam-2623	195	13	a	a	DET
ejpam-2623	195	14	contradiction	contradiction	NOUN
ejpam-2623	195	15	.	.	PUNCT
ejpam-2623	196	1	•	•	INTJ
ejpam-2623	196	2	if	if	SCONJ
ejpam-2623	196	3	a	a	PRON
ejpam-2623	196	4	is	be	AUX
ejpam-2623	196	5	a	a	DET
ejpam-2623	196	6	square	square	NOUN
ejpam-2623	196	7	,	,	PUNCT
ejpam-2623	196	8	then	then	ADV
ejpam-2623	196	9	we	we	PRON
ejpam-2623	196	10	have	have	VERB
ejpam-2623	196	11	−1	−1	NOUN
ejpam-2623	196	12	=	=	SYM
ejpam-2623	196	13	a(c	a(c	PROPN
ejpam-2623	196	14	/	/	SYM
ejpam-2623	196	15	c2	c2	PROPN
ejpam-2623	196	16	−	−	PROPN
ejpam-2623	196	17	1)2	1)2	NUM
ejpam-2623	196	18	is	be	AUX
ejpam-2623	196	19	a	a	DET
ejpam-2623	196	20	square	square	NOUN
ejpam-2623	196	21	which	which	PRON
ejpam-2623	196	22	is	be	AUX
ejpam-2623	196	23	a	a	DET
ejpam-2623	196	24	contradiction	contradiction	NOUN
ejpam-2623	196	25	since	since	SCONJ
ejpam-2623	196	26	q	q	PROPN
ejpam-2623	196	27	=	=	SYM
ejpam-2623	196	28	3	3	NUM
ejpam-2623	196	29	mod	mod	NOUN
ejpam-2623	196	30	4	4	NUM
ejpam-2623	196	31	.	.	PUNCT
ejpam-2623	196	32	(	(	PUNCT
ejpam-2623	196	33	ii	ii	NOUN
ejpam-2623	196	34	)	)	PUNCT
ejpam-2623	196	35	let	let	VERB
ejpam-2623	196	36	us	we	PRON
ejpam-2623	196	37	show	show	VERB
ejpam-2623	196	38	that	that	SCONJ
ejpam-2623	196	39	s	s	PROPN
ejpam-2623	196	40	6=	6=	NUM
ejpam-2623	196	41	±1	±1	ADJ
ejpam-2623	196	42	and	and	CCONJ
ejpam-2623	196	43	b	b	NOUN
ejpam-2623	196	44	is	be	AUX
ejpam-2623	196	45	well	well	ADV
ejpam-2623	196	46	-	-	PUNCT
ejpam-2623	196	47	defined	define	VERB
ejpam-2623	196	48	.	.	PUNCT
ejpam-2623	197	1	n.	n.	PROPN
ejpam-2623	197	2	diarra	diarra	PROPN
ejpam-2623	197	3	,	,	PUNCT
ejpam-2623	197	4	d.	d.	PROPN
ejpam-2623	197	5	sow	sow	PROPN
ejpam-2623	197	6	,	,	PUNCT
ejpam-2623	197	7	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	197	8	.	.	PUNCT
ejpam-2623	197	9	khlil	khlil	PROPN
ejpam-2623	197	10	/	/	SYM
ejpam-2623	197	11	eur	eur	PROPN
ejpam-2623	197	12	.	.	PUNCT
ejpam-2623	198	1	j.	j.	PROPN
ejpam-2623	198	2	pure	pure	PROPN
ejpam-2623	198	3	appl	appl	PROPN
ejpam-2623	198	4	.	.	PROPN
ejpam-2623	198	5	math	math	PROPN
ejpam-2623	198	6	,	,	PUNCT
ejpam-2623	198	7	10	10	NUM
ejpam-2623	198	8	(	(	PUNCT
ejpam-2623	198	9	2	2	NUM
ejpam-2623	198	10	)	)	PUNCT
ejpam-2623	198	11	(	(	PUNCT
ejpam-2623	198	12	2017	2017	NUM
ejpam-2623	198	13	)	)	PUNCT
ejpam-2623	198	14	,	,	PUNCT
ejpam-2623	198	15	363	363	NUM
ejpam-2623	198	16	-	-	SYM
ejpam-2623	198	17	391	391	NUM
ejpam-2623	198	18	369	369	NUM
ejpam-2623	198	19	•	•	NOUN
ejpam-2623	198	20	s	s	PART
ejpam-2623	198	21	=	=	X
ejpam-2623	198	22	1⇒	1⇒	X
ejpam-2623	198	23	c−	c−	ADJ
ejpam-2623	198	24	1	1	NUM
ejpam-2623	198	25	=	=	PUNCT
ejpam-2623	198	26	c+	c+	X
ejpam-2623	198	27	1	1	NUM
ejpam-2623	198	28	which	which	PRON
ejpam-2623	198	29	is	be	AUX
ejpam-2623	198	30	impossible	impossible	ADJ
ejpam-2623	198	31	.	.	PUNCT
ejpam-2623	199	1	•	•	NUM
ejpam-2623	199	2	s	s	X
ejpam-2623	199	3	=	=	X
ejpam-2623	199	4	−1⇒	−1⇒	VERB
ejpam-2623	199	5	c−	c−	ADJ
ejpam-2623	199	6	1	1	NUM
ejpam-2623	199	7	=	=	SYM
ejpam-2623	199	8	−c−	−c−	NOUN
ejpam-2623	199	9	1⇒	1⇒	PROPN
ejpam-2623	199	10	2c	2c	NUM
ejpam-2623	199	11	=	=	SYM
ejpam-2623	199	12	0	0	NUM
ejpam-2623	199	13	which	which	PRON
ejpam-2623	199	14	is	be	AUX
ejpam-2623	199	15	impossible	impossible	ADJ
ejpam-2623	199	16	since	since	SCONJ
ejpam-2623	199	17	c	c	PROPN
ejpam-2623	199	18	6=	6=	PROPN
ejpam-2623	199	19	0	0	NUM
ejpam-2623	199	20	.	.	PUNCT
ejpam-2623	200	1	(	(	PUNCT
ejpam-2623	200	2	iii	iii	X
ejpam-2623	200	3	)	)	PUNCT
ejpam-2623	200	4	let	let	VERB
ejpam-2623	200	5	us	we	PRON
ejpam-2623	200	6	show	show	VERB
ejpam-2623	200	7	that	that	SCONJ
ejpam-2623	200	8	a+	a+	PUNCT
ejpam-2623	200	9	b	b	NOUN
ejpam-2623	200	10	is	be	AUX
ejpam-2623	200	11	a	a	DET
ejpam-2623	200	12	square	square	ADJ
ejpam-2623	200	13	and	and	CCONJ
ejpam-2623	200	14	ab(a−	ab(a−	PROPN
ejpam-2623	200	15	b	b	PROPN
ejpam-2623	200	16	)	)	PUNCT
ejpam-2623	200	17	6=	6=	ADP
ejpam-2623	200	18	0	0	NUM
ejpam-2623	200	19	.	.	NOUN
ejpam-2623	200	20	•	•	NUM
ejpam-2623	200	21	in	in	ADP
ejpam-2623	200	22	fact	fact	NOUN
ejpam-2623	200	23	,	,	PUNCT
ejpam-2623	200	24	we	we	PRON
ejpam-2623	200	25	have	have	VERB
ejpam-2623	200	26	a+	a+	PRON
ejpam-2623	200	27	b	b	X
ejpam-2623	200	28	=	=	SYM
ejpam-2623	200	29	−bs2	−bs2	PROPN
ejpam-2623	200	30	+	+	CCONJ
ejpam-2623	200	31	b	b	PROPN
ejpam-2623	200	32	=	=	SYM
ejpam-2623	200	33	b(1−	b(1−	PROPN
ejpam-2623	200	34	s2	s2	PROPN
ejpam-2623	200	35	)	)	PUNCT
ejpam-2623	200	36	=	=	SYM
ejpam-2623	200	37	λ2	λ2	NOUN
ejpam-2623	200	38	which	which	PRON
ejpam-2623	200	39	is	be	AUX
ejpam-2623	200	40	a	a	DET
ejpam-2623	200	41	square	square	NOUN
ejpam-2623	200	42	.	.	PUNCT
ejpam-2623	201	1	•	•	NUM
ejpam-2623	201	2	ab	ab	PROPN
ejpam-2623	201	3	6=	6=	ADP
ejpam-2623	201	4	0	0	NUM
ejpam-2623	201	5	since	since	SCONJ
ejpam-2623	201	6	a	a	PRON
ejpam-2623	201	7	and	and	CCONJ
ejpam-2623	201	8	b	b	NOUN
ejpam-2623	201	9	are	be	AUX
ejpam-2623	201	10	both	both	PRON
ejpam-2623	201	11	non	non	ADJ
ejpam-2623	201	12	-	-	NOUN
ejpam-2623	201	13	zero	zero	NUM
ejpam-2623	201	14	.	.	PUNCT
ejpam-2623	202	1	we	we	PRON
ejpam-2623	202	2	have	have	VERB
ejpam-2623	202	3	a−	a−	PROPN
ejpam-2623	202	4	b	b	X
ejpam-2623	202	5	=	=	NOUN
ejpam-2623	202	6	0⇒	0⇒	NOUN
ejpam-2623	202	7	−b(s2	−b(s2	NOUN
ejpam-2623	202	8	+	+	CCONJ
ejpam-2623	202	9	1	1	X
ejpam-2623	202	10	)	)	PUNCT
ejpam-2623	202	11	=	=	SYM
ejpam-2623	202	12	0	0	NUM
ejpam-2623	202	13	,	,	PUNCT
ejpam-2623	202	14	which	which	PRON
ejpam-2623	202	15	is	be	AUX
ejpam-2623	202	16	impossible	impossible	ADJ
ejpam-2623	202	17	.	.	PUNCT
ejpam-2623	203	1	(	(	PUNCT
ejpam-2623	203	2	iv	iv	X
ejpam-2623	203	3	)	)	PUNCT
ejpam-2623	203	4	by	by	ADP
ejpam-2623	203	5	hypothesis	hypothesis	NOUN
ejpam-2623	203	6	,	,	PUNCT
ejpam-2623	203	7	u	u	NOUN
ejpam-2623	203	8	is	be	AUX
ejpam-2623	203	9	well	well	ADV
ejpam-2623	203	10	-	-	PUNCT
ejpam-2623	203	11	defined	define	VERB
ejpam-2623	203	12	and	and	CCONJ
ejpam-2623	203	13	u	u	NOUN
ejpam-2623	203	14	6=	6=	PROPN
ejpam-2623	203	15	0	0	NUM
ejpam-2623	203	16	.	.	PUNCT
ejpam-2623	204	1	suppose	suppose	VERB
ejpam-2623	204	2	that	that	SCONJ
ejpam-2623	204	3	v	v	NOUN
ejpam-2623	204	4	=	=	SYM
ejpam-2623	204	5	0	0	NUM
ejpam-2623	204	6	;	;	PUNCT
ejpam-2623	204	7	so	so	ADV
ejpam-2623	204	8	u(−u4	u(−u4	PROPN
ejpam-2623	204	9	+	+	CCONJ
ejpam-2623	204	10	(	(	PUNCT
ejpam-2623	204	11	c2	c2	PROPN
ejpam-2623	204	12	+	+	CCONJ
ejpam-2623	204	13	1	1	NUM
ejpam-2623	204	14	/	/	SYM
ejpam-2623	204	15	c2)u2	c2)u2	NOUN
ejpam-2623	204	16	−	−	NOUN
ejpam-2623	204	17	1	1	NUM
ejpam-2623	204	18	)	)	PUNCT
ejpam-2623	204	19	=	=	SYM
ejpam-2623	205	1	0	0	X
ejpam-2623	205	2	.	.	PUNCT
ejpam-2623	206	1	since	since	SCONJ
ejpam-2623	206	2	u	u	PROPN
ejpam-2623	206	3	6=	6=	PROPN
ejpam-2623	206	4	0	0	NUM
ejpam-2623	206	5	,	,	PUNCT
ejpam-2623	206	6	then	then	ADV
ejpam-2623	206	7	we	we	PRON
ejpam-2623	206	8	have	have	VERB
ejpam-2623	206	9	−u4	−u4	NOUN
ejpam-2623	206	10	+	+	CCONJ
ejpam-2623	206	11	(	(	PUNCT
ejpam-2623	206	12	c2	c2	PROPN
ejpam-2623	206	13	+	+	CCONJ
ejpam-2623	206	14	1	1	NUM
ejpam-2623	206	15	/	/	SYM
ejpam-2623	206	16	c2)u2	c2)u2	NOUN
ejpam-2623	206	17	−	−	NOUN
ejpam-2623	206	18	1	1	NUM
ejpam-2623	206	19	=	=	SYM
ejpam-2623	206	20	0	0	NUM
ejpam-2623	206	21	.	.	PUNCT
ejpam-2623	207	1	thus	thus	ADV
ejpam-2623	207	2	u2	u2	PROPN
ejpam-2623	207	3	=	=	SYM
ejpam-2623	207	4	−c2	−c2	PROPN
ejpam-2623	207	5	or	or	CCONJ
ejpam-2623	207	6	u2	u2	PROPN
ejpam-2623	207	7	=	=	PUNCT
ejpam-2623	207	8	−1	−1	NOUN
ejpam-2623	207	9	/	/	SYM
ejpam-2623	207	10	c2	c2	PROPN
ejpam-2623	207	11	contradicting	contradict	VERB
ejpam-2623	207	12	the	the	DET
ejpam-2623	207	13	fact	fact	NOUN
ejpam-2623	207	14	that	that	SCONJ
ejpam-2623	207	15	−1	−1	NOUN
ejpam-2623	207	16	is	be	AUX
ejpam-2623	207	17	not	not	PART
ejpam-2623	207	18	a	a	DET
ejpam-2623	207	19	square	square	NOUN
ejpam-2623	207	20	.	.	PUNCT
ejpam-2623	208	1	(	(	PUNCT
ejpam-2623	208	2	v	v	NOUN
ejpam-2623	208	3	)	)	PUNCT
ejpam-2623	208	4	since	since	SCONJ
ejpam-2623	208	5	uv	uv	PROPN
ejpam-2623	208	6	6=	6=	ADP
ejpam-2623	208	7	0	0	NUM
ejpam-2623	208	8	by	by	ADP
ejpam-2623	208	9	above	above	ADP
ejpam-2623	208	10	results	result	NOUN
ejpam-2623	208	11	,	,	PUNCT
ejpam-2623	208	12	then	then	ADV
ejpam-2623	208	13	x	x	X
ejpam-2623	208	14	6=	6=	PROPN
ejpam-2623	208	15	0	0	NUM
ejpam-2623	208	16	.	.	PUNCT
ejpam-2623	209	1	(	(	PUNCT
ejpam-2623	209	2	vi	vi	X
ejpam-2623	209	3	)	)	PUNCT
ejpam-2623	209	4	let	let	VERB
ejpam-2623	209	5	us	we	PRON
ejpam-2623	209	6	show	show	VERB
ejpam-2623	209	7	that	that	SCONJ
ejpam-2623	209	8	1	1	NUM
ejpam-2623	209	9	+	+	NUM
ejpam-2623	209	10	x	x	SYM
ejpam-2623	209	11	6=	6=	ADP
ejpam-2623	209	12	0	0	NUM
ejpam-2623	209	13	.	.	PUNCT
ejpam-2623	210	1	if	if	SCONJ
ejpam-2623	210	2	1	1	NUM
ejpam-2623	210	3	+	+	NOUN
ejpam-2623	210	4	x	x	SYM
ejpam-2623	210	5	=	=	SYM
ejpam-2623	210	6	0	0	NUM
ejpam-2623	210	7	then	then	ADV
ejpam-2623	210	8	we	we	PRON
ejpam-2623	210	9	have	have	VERB
ejpam-2623	210	10	u	u	NOUN
ejpam-2623	210	11	=	=	NOUN
ejpam-2623	210	12	−χ(v	−χ(v	NOUN
ejpam-2623	210	13	)	)	PUNCT
ejpam-2623	210	14	and	and	CCONJ
ejpam-2623	210	15	v	v	NOUN
ejpam-2623	210	16	=	=	SYM
ejpam-2623	210	17	(	(	PUNCT
ejpam-2623	210	18	χ(v))5−(c2	χ(v))5−(c2	ADV
ejpam-2623	210	19	+	+	ADJ
ejpam-2623	210	20	1	1	NUM
ejpam-2623	210	21	/	/	SYM
ejpam-2623	210	22	c2)(χ(v))3+χ(v	c2)(χ(v))3+χ(v	NOUN
ejpam-2623	210	23	)	)	PUNCT
ejpam-2623	210	24	=	=	PUNCT
ejpam-2623	211	1	χ(v)−(c2	χ(v)−(c2	PROPN
ejpam-2623	211	2	+	+	ADJ
ejpam-2623	211	3	1	1	NUM
ejpam-2623	211	4	/	/	SYM
ejpam-2623	211	5	c2−1)χ(v	c2−1)χ(v	NOUN
ejpam-2623	211	6	)	)	PUNCT
ejpam-2623	211	7	=	=	PUNCT
ejpam-2623	212	1	−χ(v)(c2	−χ(v)(c2	PROPN
ejpam-2623	212	2	+	+	ADJ
ejpam-2623	212	3	1	1	NUM
ejpam-2623	212	4	/	/	SYM
ejpam-2623	212	5	c2−2	c2−2	NOUN
ejpam-2623	212	6	)	)	PUNCT
ejpam-2623	212	7	.	.	PUNCT
ejpam-2623	213	1	so	so	ADV
ejpam-2623	213	2	we	we	PRON
ejpam-2623	213	3	find	find	VERB
ejpam-2623	213	4	v	v	NOUN
ejpam-2623	213	5	=	=	NOUN
ejpam-2623	213	6	−χ(v)(c−	−χ(v)(c−	NOUN
ejpam-2623	213	7	1	1	NUM
ejpam-2623	213	8	/	/	SYM
ejpam-2623	213	9	c)2	c)2	NOUN
ejpam-2623	213	10	,	,	PUNCT
ejpam-2623	213	11	then	then	ADV
ejpam-2623	213	12	χ(v	χ(v	NOUN
ejpam-2623	213	13	)	)	PUNCT
ejpam-2623	213	14	=	=	SYM
ejpam-2623	213	15	−χ(v	−χ(v	NOUN
ejpam-2623	213	16	)	)	PUNCT
ejpam-2623	213	17	,	,	PUNCT
ejpam-2623	213	18	which	which	PRON
ejpam-2623	213	19	is	be	AUX
ejpam-2623	213	20	a	a	DET
ejpam-2623	213	21	contradiction	contradiction	NOUN
ejpam-2623	213	22	.	.	PUNCT
ejpam-2623	214	1	(	(	PUNCT
ejpam-2623	214	2	vii	vii	PROPN
ejpam-2623	214	3	)	)	PUNCT
ejpam-2623	214	4	since	since	SCONJ
ejpam-2623	214	5	x	x	PROPN
ejpam-2623	214	6	6=	6=	ADP
ejpam-2623	214	7	0	0	NUM
ejpam-2623	214	8	and	and	CCONJ
ejpam-2623	214	9	y	y	PROPN
ejpam-2623	214	10	2	2	X
ejpam-2623	214	11	=	=	SYM
ejpam-2623	214	12	−x5	−x5	PROPN
ejpam-2623	214	13	+	+	CCONJ
ejpam-2623	214	14	(	(	PUNCT
ejpam-2623	214	15	c2	c2	PROPN
ejpam-2623	214	16	+	+	CCONJ
ejpam-2623	214	17	1	1	NUM
ejpam-2623	214	18	/	/	SYM
ejpam-2623	214	19	c2)x3	c2)x3	NOUN
ejpam-2623	214	20	−x	−x	NOUN
ejpam-2623	214	21	,	,	PUNCT
ejpam-2623	214	22	similarly	similarly	ADV
ejpam-2623	214	23	as	as	ADP
ejpam-2623	214	24	4	4	NUM
ejpam-2623	214	25	,	,	PUNCT
ejpam-2623	214	26	we	we	PRON
ejpam-2623	214	27	have	have	VERB
ejpam-2623	214	28	y	y	PROPN
ejpam-2623	214	29	6=	6=	PROPN
ejpam-2623	214	30	0	0	NUM
ejpam-2623	214	31	.	.	PUNCT
ejpam-2623	215	1	(	(	PUNCT
ejpam-2623	215	2	viii	viii	NOUN
ejpam-2623	215	3	)	)	PUNCT
ejpam-2623	215	4	we	we	PRON
ejpam-2623	215	5	have−x5	have−x5	VERB
ejpam-2623	216	1	+	+	CCONJ
ejpam-2623	216	2	(	(	PUNCT
ejpam-2623	216	3	c2	c2	PROPN
ejpam-2623	216	4	+	+	CCONJ
ejpam-2623	216	5	1	1	NUM
ejpam-2623	216	6	/	/	SYM
ejpam-2623	216	7	c2)x3	c2)x3	NOUN
ejpam-2623	216	8	−	−	NOUN
ejpam-2623	216	9	x	x	SYM
ejpam-2623	217	1	=	=	SYM
ejpam-2623	217	2	−(χ(v)u)5	−(χ(v)u)5	NOUN
ejpam-2623	218	1	+	+	CCONJ
ejpam-2623	218	2	(	(	PUNCT
ejpam-2623	218	3	c2	c2	PROPN
ejpam-2623	218	4	+	+	CCONJ
ejpam-2623	218	5	1	1	NUM
ejpam-2623	218	6	/	/	SYM
ejpam-2623	218	7	c2)(χ(v)u)3	c2)(χ(v)u)3	NOUN
ejpam-2623	218	8	−	−	PROPN
ejpam-2623	218	9	χ(v)u	χ(v)u	PROPN
ejpam-2623	218	10	=	=	SYM
ejpam-2623	218	11	χ(v)[−u5	χ(v)[−u5	PROPN
ejpam-2623	218	12	+	+	CCONJ
ejpam-2623	218	13	(	(	PUNCT
ejpam-2623	218	14	c2	c2	PROPN
ejpam-2623	218	15	+	+	CCONJ
ejpam-2623	218	16	1	1	NUM
ejpam-2623	218	17	/	/	SYM
ejpam-2623	218	18	c2)u3	c2)u3	NOUN
ejpam-2623	218	19	−	−	PROPN
ejpam-2623	218	20	u	u	NOUN
ejpam-2623	218	21	]	]	X
ejpam-2623	218	22	=	=	PUNCT
ejpam-2623	218	23	χ(v)v	χ(v)v	PROPN
ejpam-2623	218	24	=	=	PUNCT
ejpam-2623	218	25	y	y	PROPN
ejpam-2623	218	26	2	2	NUM
ejpam-2623	218	27	.	.	PUNCT
ejpam-2623	218	28	(	(	PUNCT
ejpam-2623	218	29	ix	ix	PROPN
ejpam-2623	218	30	)	)	PUNCT
ejpam-2623	218	31	x	x	PUNCT
ejpam-2623	218	32	and	and	CCONJ
ejpam-2623	218	33	y	y	PROPN
ejpam-2623	218	34	are	be	AUX
ejpam-2623	218	35	well	well	ADV
ejpam-2623	218	36	-	-	PUNCT
ejpam-2623	218	37	defined	define	VERB
ejpam-2623	218	38	since	since	SCONJ
ejpam-2623	218	39	y	y	PROPN
ejpam-2623	218	40	6=	6=	PROPN
ejpam-2623	218	41	0	0	NUM
ejpam-2623	218	42	.	.	PUNCT
ejpam-2623	219	1	(	(	PUNCT
ejpam-2623	219	2	x	x	X
ejpam-2623	219	3	)	)	PUNCT
ejpam-2623	219	4	(	(	PUNCT
ejpam-2623	219	5	x	x	X
ejpam-2623	219	6	,	,	PUNCT
ejpam-2623	219	7	y	y	NOUN
ejpam-2623	219	8	)	)	PUNCT
ejpam-2623	219	9	verifies	verifie	NOUN
ejpam-2623	219	10	x(ay2	x(ay2	PUNCT
ejpam-2623	220	1	−	−	ADP
ejpam-2623	220	2	1	1	X
ejpam-2623	220	3	)	)	PUNCT
ejpam-2623	220	4	=	=	PUNCT
ejpam-2623	221	1	y(bx2	y(bx2	NOUN
ejpam-2623	222	1	−	−	NOUN
ejpam-2623	222	2	1	1	NUM
ejpam-2623	222	3	)	)	PUNCT
ejpam-2623	222	4	?	?	PUNCT
ejpam-2623	223	1	at	at	ADP
ejpam-2623	223	2	first	first	ADV
ejpam-2623	223	3	we	we	PRON
ejpam-2623	223	4	show	show	VERB
ejpam-2623	223	5	that	that	SCONJ
ejpam-2623	223	6	α4(x4−(2−a)x2	α4(x4−(2−a)x2	PROPN
ejpam-2623	223	7	+	+	NOUN
ejpam-2623	223	8	1	1	NUM
ejpam-2623	223	9	)	)	PUNCT
ejpam-2623	223	10	=	=	SYM
ejpam-2623	223	11	(	(	PUNCT
ejpam-2623	223	12	bx−α2(1+x)2)(ax−α2(1+x)2	bx−α2(1+x)2)(ax−α2(1+x)2	NOUN
ejpam-2623	223	13	)	)	PUNCT
ejpam-2623	223	14	.	.	PUNCT
ejpam-2623	224	1	in	in	ADP
ejpam-2623	224	2	fact	fact	NOUN
ejpam-2623	224	3	,	,	PUNCT
ejpam-2623	224	4	we	we	PRON
ejpam-2623	224	5	have	have	VERB
ejpam-2623	224	6	:	:	PUNCT
ejpam-2623	224	7	(	(	PUNCT
ejpam-2623	224	8	bx−α2(1+x)2)(ax−α2(1+x)2	bx−α2(1+x)2)(ax−α2(1+x)2	X
ejpam-2623	224	9	)	)	PUNCT
ejpam-2623	224	10	=	=	SYM
ejpam-2623	224	11	abx2−bα2x(x2	abx2−bα2x(x2	NOUN
ejpam-2623	225	1	+	+	PROPN
ejpam-2623	225	2	2x+1)−aα2(x3	2x+1)−aα2(x3	NUM
ejpam-2623	225	3	+	+	NOUN
ejpam-2623	225	4	2x2	2x2	NUM
ejpam-2623	225	5	+	+	SYM
ejpam-2623	225	6	x)+α4(1	x)+α4(1	NOUN
ejpam-2623	226	1	+	+	PROPN
ejpam-2623	226	2	4x+6x2	4x+6x2	PROPN
ejpam-2623	226	3	+4x3	+4x3	PROPN
ejpam-2623	226	4	+	+	NOUN
ejpam-2623	226	5	x4	x4	PROPN
ejpam-2623	226	6	)	)	PUNCT
ejpam-2623	227	1	=	=	SYM
ejpam-2623	227	2	x4(α4)+x3(4α4−	x4(α4)+x3(4α4−	PROPN
ejpam-2623	228	1	(	(	PUNCT
ejpam-2623	228	2	a+b)α2)+x2(ab+6α4−	a+b)α2)+x2(ab+6α4−	NOUN
ejpam-2623	228	3	2α2(a+	2α2(a+	NOUN
ejpam-2623	228	4	b	b	NOUN
ejpam-2623	228	5	)	)	PUNCT
ejpam-2623	228	6	)	)	PUNCT
ejpam-2623	229	1	+	+	ADP
ejpam-2623	229	2	x(4α4	x(4α4	DET
ejpam-2623	229	3	−	−	PROPN
ejpam-2623	229	4	α2(a+	α2(a+	PROPN
ejpam-2623	229	5	b	b	NOUN
ejpam-2623	229	6	)	)	PUNCT
ejpam-2623	229	7	)	)	PUNCT
ejpam-2623	230	1	+	+	NUM
ejpam-2623	230	2	α4	α4	NOUN
ejpam-2623	230	3	.	.	PUNCT
ejpam-2623	231	1	then	then	ADV
ejpam-2623	231	2	using	use	VERB
ejpam-2623	231	3	4	4	NUM
ejpam-2623	231	4	=	=	SYM
ejpam-2623	231	5	(	(	PUNCT
ejpam-2623	231	6	a+	a+	PUNCT
ejpam-2623	231	7	b)/α2	b)/α2	NOUN
ejpam-2623	231	8	and	and	CCONJ
ejpam-2623	231	9	a	a	DET
ejpam-2623	231	10	=	=	X
ejpam-2623	231	11	ab	ab	PROPN
ejpam-2623	231	12	/	/	SYM
ejpam-2623	231	13	α4	α4	PROPN
ejpam-2623	231	14	yields	yield	NOUN
ejpam-2623	231	15	that	that	PRON
ejpam-2623	231	16	(	(	PUNCT
ejpam-2623	231	17	bx	bx	NOUN
ejpam-2623	231	18	−	−	PROPN
ejpam-2623	231	19	α2(1	α2(1	PROPN
ejpam-2623	231	20	+	+	NOUN
ejpam-2623	231	21	x)2)(ax	x)2)(ax	PROPN
ejpam-2623	231	22	−	−	PROPN
ejpam-2623	231	23	α2(1	α2(1	NOUN
ejpam-2623	231	24	+	+	NOUN
ejpam-2623	231	25	x)2	x)2	NOUN
ejpam-2623	231	26	)	)	PUNCT
ejpam-2623	231	27	=	=	SYM
ejpam-2623	231	28	α4(x4	α4(x4	ADP
ejpam-2623	231	29	−	−	PROPN
ejpam-2623	231	30	(	(	PUNCT
ejpam-2623	231	31	2−a)x2	2−a)x2	NUM
ejpam-2623	231	32	+	+	NOUN
ejpam-2623	231	33	1	1	NUM
ejpam-2623	231	34	)	)	PUNCT
ejpam-2623	231	35	.	.	PUNCT
ejpam-2623	232	1	since	since	SCONJ
ejpam-2623	232	2	a	a	PRON
ejpam-2623	232	3	and	and	CCONJ
ejpam-2623	232	4	b	b	NOUN
ejpam-2623	232	5	are	be	AUX
ejpam-2623	232	6	not	not	PART
ejpam-2623	232	7	square	square	ADJ
ejpam-2623	232	8	,	,	PUNCT
ejpam-2623	232	9	thus	thus	ADV
ejpam-2623	232	10	(	(	PUNCT
ejpam-2623	232	11	ay2	ay2	NOUN
ejpam-2623	232	12	−	−	PROPN
ejpam-2623	232	13	1)(bx2	1)(bx2	NUM
ejpam-2623	232	14	−	−	NOUN
ejpam-2623	232	15	1	1	NUM
ejpam-2623	232	16	)	)	PUNCT
ejpam-2623	232	17	6=	6=	ADP
ejpam-2623	232	18	0	0	X
ejpam-2623	232	19	.	.	PUNCT
ejpam-2623	233	1	now	now	ADV
ejpam-2623	233	2	,	,	PUNCT
ejpam-2623	233	3	we	we	PRON
ejpam-2623	233	4	have	have	VERB
ejpam-2623	233	5	:	:	PUNCT
ejpam-2623	233	6	bx2	bx2	NOUN
ejpam-2623	233	7	−	−	PROPN
ejpam-2623	233	8	1	1	NUM
ejpam-2623	234	1	ay2	ay2	NOUN
ejpam-2623	234	2	−	−	NOUN
ejpam-2623	234	3	1	1	NUM
ejpam-2623	234	4	=	=	NOUN
ejpam-2623	234	5	a	a	DET
ejpam-2623	234	6	b	b	NOUN
ejpam-2623	234	7	·	·	PUNCT
ejpam-2623	234	8	(	(	PUNCT
ejpam-2623	234	9	1	1	NUM
ejpam-2623	234	10	+	+	NOUN
ejpam-2623	234	11	x)2(bx	x)2(bx	PROPN
ejpam-2623	234	12	−	−	PROPN
ejpam-2623	234	13	α2(1	α2(1	NOUN
ejpam-2623	234	14	+	+	NOUN
ejpam-2623	234	15	x)2)2	x)2)2	PROPN
ejpam-2623	234	16	−	−	NOUN
ejpam-2623	234	17	bα2y	bα2y	NOUN
ejpam-2623	234	18	2	2	NUM
ejpam-2623	234	19	(	(	PUNCT
ejpam-2623	234	20	1	1	NUM
ejpam-2623	234	21	+	+	NOUN
ejpam-2623	234	22	x)2(ax	x)2(ax	PROPN
ejpam-2623	234	23	−	−	PROPN
ejpam-2623	234	24	α2(1	α2(1	NOUN
ejpam-2623	234	25	+	+	NOUN
ejpam-2623	234	26	x)2)2	x)2)2	PROPN
ejpam-2623	234	27	−	−	X
ejpam-2623	235	1	aα2y	aα2y	NOUN
ejpam-2623	235	2	2	2	NUM
ejpam-2623	235	3	=	=	SYM
ejpam-2623	235	4	a	a	DET
ejpam-2623	235	5	b	b	NOUN
ejpam-2623	235	6	·	·	PUNCT
ejpam-2623	235	7	(	(	PUNCT
ejpam-2623	235	8	bx	bx	NOUN
ejpam-2623	235	9	−	−	PROPN
ejpam-2623	235	10	α2(1	α2(1	NOUN
ejpam-2623	235	11	+	+	NOUN
ejpam-2623	235	12	x)2	x)2	X
ejpam-2623	235	13	ax	ax	NOUN
ejpam-2623	235	14	−	−	PROPN
ejpam-2623	235	15	α2(1	α2(1	NOUN
ejpam-2623	235	16	+	+	NOUN
ejpam-2623	235	17	x)2	x)2	X
ejpam-2623	235	18	)	)	PUNCT
ejpam-2623	235	19	·	·	PUNCT
ejpam-2623	236	1			NOUN
ejpam-2623	236	2	(	(	PUNCT
ejpam-2623	236	3	1	1	NUM
ejpam-2623	236	4	+	+	NOUN
ejpam-2623	236	5	x)2(bx	x)2(bx	PROPN
ejpam-2623	236	6	−	−	PROPN
ejpam-2623	236	7	α2(1	α2(1	NOUN
ejpam-2623	236	8	+	+	NOUN
ejpam-2623	236	9	x)2)−	x)2)−	ADJ
ejpam-2623	236	10	bα2y	bα2y	NOUN
ejpam-2623	236	11	2	2	NUM
ejpam-2623	236	12	bx−α2(1+x)2	bx−α2(1+x)2	NOUN
ejpam-2623	236	13	(	(	PUNCT
ejpam-2623	236	14	1	1	NUM
ejpam-2623	236	15	+	+	NOUN
ejpam-2623	236	16	x)2(ax	x)2(ax	PROPN
ejpam-2623	236	17	−	−	PROPN
ejpam-2623	236	18	α2(1	α2(1	NOUN
ejpam-2623	236	19	+	+	NOUN
ejpam-2623	236	20	x)2)−	x)2)−	PROPN
ejpam-2623	236	21	aα2y	aα2y	PROPN
ejpam-2623	236	22	2	2	NUM
ejpam-2623	236	23	ax−α2(1+x)2	ax−α2(1+x)2	NOUN
ejpam-2623	236	24			NOUN
ejpam-2623	236	25	=	=	PUNCT
ejpam-2623	236	26	a	a	DET
ejpam-2623	236	27	b	b	PROPN
ejpam-2623	236	28	·	·	PUNCT
ejpam-2623	236	29	(	(	PUNCT
ejpam-2623	236	30	bx	bx	NOUN
ejpam-2623	236	31	−	−	PROPN
ejpam-2623	236	32	α2(1	α2(1	NOUN
ejpam-2623	236	33	+	+	NOUN
ejpam-2623	236	34	x)2	x)2	X
ejpam-2623	236	35	ax	ax	NOUN
ejpam-2623	236	36	−	−	PROPN
ejpam-2623	236	37	α2(1	α2(1	NOUN
ejpam-2623	236	38	+	+	NOUN
ejpam-2623	236	39	x)2	x)2	X
ejpam-2623	236	40	)	)	PUNCT
ejpam-2623	236	41	·	·	PUNCT
ejpam-2623	237	1			NOUN
ejpam-2623	237	2	(	(	PUNCT
ejpam-2623	237	3	1	1	NUM
ejpam-2623	237	4	+	+	NOUN
ejpam-2623	237	5	x)2(bx	x)2(bx	PROPN
ejpam-2623	237	6	−	−	PROPN
ejpam-2623	237	7	α2(1	α2(1	NOUN
ejpam-2623	237	8	+	+	NOUN
ejpam-2623	237	9	x)2	x)2	NOUN
ejpam-2623	237	10	)	)	PUNCT
ejpam-2623	238	1	+	+	PUNCT
ejpam-2623	238	2	bα2x(x4−(2−a)x2	bα2x(x4−(2−a)x2	VERB
ejpam-2623	238	3	+	+	ADJ
ejpam-2623	238	4	1	1	NUM
ejpam-2623	238	5	)	)	PUNCT
ejpam-2623	238	6	bx−α2(1+x)2	bx−α2(1+x)2	NOUN
ejpam-2623	238	7	(	(	PUNCT
ejpam-2623	238	8	1	1	NUM
ejpam-2623	238	9	+	+	NOUN
ejpam-2623	238	10	x)2(ax	x)2(ax	PROPN
ejpam-2623	238	11	−	−	PROPN
ejpam-2623	238	12	α2(1	α2(1	NOUN
ejpam-2623	238	13	+	+	NOUN
ejpam-2623	238	14	x)2	x)2	NOUN
ejpam-2623	238	15	)	)	PUNCT
ejpam-2623	239	1	+	+	CCONJ
ejpam-2623	239	2	aα2x(x4−(2−a)x2	aα2x(x4−(2−a)x2	X
ejpam-2623	239	3	+	+	NOUN
ejpam-2623	239	4	1	1	NUM
ejpam-2623	239	5	)	)	PUNCT
ejpam-2623	239	6	ax−α2(1+x)2	ax−α2(1+x)2	VERB
ejpam-2623	239	7			NOUN
ejpam-2623	239	8	=	=	PUNCT
ejpam-2623	239	9	a	a	DET
ejpam-2623	239	10	b	b	PROPN
ejpam-2623	239	11	·	·	PUNCT
ejpam-2623	239	12	(	(	PUNCT
ejpam-2623	239	13	bx	bx	NOUN
ejpam-2623	239	14	−	−	PROPN
ejpam-2623	239	15	α2(1	α2(1	NOUN
ejpam-2623	239	16	+	+	NOUN
ejpam-2623	239	17	x)2	x)2	X
ejpam-2623	239	18	ax	ax	NOUN
ejpam-2623	239	19	−	−	PROPN
ejpam-2623	239	20	α2(1	α2(1	NOUN
ejpam-2623	239	21	+	+	NOUN
ejpam-2623	239	22	x)2	x)2	X
ejpam-2623	239	23	)	)	PUNCT
ejpam-2623	239	24	·	·	PUNCT
ejpam-2623	240	1	[	[	PUNCT
ejpam-2623	240	2	α2(1	α2(1	NOUN
ejpam-2623	240	3	+	+	NOUN
ejpam-2623	240	4	x)2(bx	x)2(bx	PROPN
ejpam-2623	240	5	−	−	PROPN
ejpam-2623	240	6	α2(1	α2(1	NOUN
ejpam-2623	240	7	+	+	NOUN
ejpam-2623	240	8	x)2	x)2	NOUN
ejpam-2623	240	9	)	)	PUNCT
ejpam-2623	241	1	+	+	CCONJ
ejpam-2623	241	2	bx(ax	bx(ax	PROPN
ejpam-2623	241	3	−	−	PROPN
ejpam-2623	241	4	α2(1	α2(1	PROPN
ejpam-2623	241	5	+	+	NOUN
ejpam-2623	241	6	x)2	x)2	PROPN
ejpam-2623	241	7	)	)	PUNCT
ejpam-2623	241	8	α2(1	α2(1	NOUN
ejpam-2623	241	9	+	+	NOUN
ejpam-2623	241	10	x)2(ax	x)2(ax	PROPN
ejpam-2623	241	11	−	−	PROPN
ejpam-2623	241	12	α2(1	α2(1	NOUN
ejpam-2623	241	13	+	+	NOUN
ejpam-2623	241	14	x)2	x)2	NOUN
ejpam-2623	241	15	)	)	PUNCT
ejpam-2623	242	1	+	+	CCONJ
ejpam-2623	242	2	ax(bx	ax(bx	PROPN
ejpam-2623	242	3	−	−	PRON
ejpam-2623	242	4	α2(1	α2(1	NOUN
ejpam-2623	242	5	+	+	NOUN
ejpam-2623	242	6	x)2	x)2	NOUN
ejpam-2623	242	7	)	)	PUNCT
ejpam-2623	242	8	]	]	PUNCT
ejpam-2623	243	1	=	=	PUNCT
ejpam-2623	243	2	a	a	DET
ejpam-2623	243	3	b	b	PROPN
ejpam-2623	243	4	·	·	PUNCT
ejpam-2623	243	5	(	(	PUNCT
ejpam-2623	243	6	bx	bx	NOUN
ejpam-2623	243	7	−	−	PROPN
ejpam-2623	243	8	α2(1	α2(1	NOUN
ejpam-2623	243	9	+	+	NOUN
ejpam-2623	243	10	x)2	x)2	X
ejpam-2623	243	11	ax	ax	NOUN
ejpam-2623	243	12	−	−	PROPN
ejpam-2623	243	13	α2(1	α2(1	NOUN
ejpam-2623	243	14	+	+	NOUN
ejpam-2623	243	15	x)2	x)2	X
ejpam-2623	243	16	)	)	PUNCT
ejpam-2623	243	17	·	·	PUNCT
ejpam-2623	244	1	(	(	PUNCT
ejpam-2623	244	2	abx2	abx2	PROPN
ejpam-2623	244	3	−	−	PROPN
ejpam-2623	244	4	α4(1	α4(1	NOUN
ejpam-2623	244	5	+	+	ADJ
ejpam-2623	244	6	x)4	x)4	VERB
ejpam-2623	244	7	abx2	abx2	NOUN
ejpam-2623	244	8	−	−	PROPN
ejpam-2623	244	9	α4(1	α4(1	NOUN
ejpam-2623	244	10	+	+	ADJ
ejpam-2623	244	11	x)4	x)4	X
ejpam-2623	244	12	)	)	PUNCT
ejpam-2623	245	1	=	=	PUNCT
ejpam-2623	245	2	a	a	DET
ejpam-2623	245	3	b	b	PROPN
ejpam-2623	245	4	·	·	PUNCT
ejpam-2623	245	5	(	(	PUNCT
ejpam-2623	245	6	bx	bx	NOUN
ejpam-2623	245	7	−	−	PROPN
ejpam-2623	245	8	α2(1	α2(1	NOUN
ejpam-2623	246	1	+	+	NOUN
ejpam-2623	246	2	x)2	x)2	X
ejpam-2623	246	3	ax	ax	NOUN
ejpam-2623	246	4	−	−	PROPN
ejpam-2623	246	5	α2(1	α2(1	NOUN
ejpam-2623	246	6	+	+	NOUN
ejpam-2623	246	7	x)2	x)2	X
ejpam-2623	246	8	)	)	PUNCT
ejpam-2623	247	1	=	=	PUNCT
ejpam-2623	247	2	x	x	PUNCT
ejpam-2623	247	3	y	y	PROPN
ejpam-2623	247	4	n.	n.	PROPN
ejpam-2623	247	5	diarra	diarra	PROPN
ejpam-2623	247	6	,	,	PUNCT
ejpam-2623	247	7	d.	d.	PROPN
ejpam-2623	247	8	sow	sow	PROPN
ejpam-2623	247	9	,	,	PUNCT
ejpam-2623	247	10	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	247	11	.	.	PUNCT
ejpam-2623	247	12	khlil	khlil	PROPN
ejpam-2623	247	13	/	/	SYM
ejpam-2623	247	14	eur	eur	PROPN
ejpam-2623	247	15	.	.	PUNCT
ejpam-2623	248	1	j.	j.	PROPN
ejpam-2623	248	2	pure	pure	PROPN
ejpam-2623	248	3	appl	appl	PROPN
ejpam-2623	248	4	.	.	PROPN
ejpam-2623	248	5	math	math	PROPN
ejpam-2623	248	6	,	,	PUNCT
ejpam-2623	248	7	10	10	NUM
ejpam-2623	248	8	(	(	PUNCT
ejpam-2623	248	9	2	2	NUM
ejpam-2623	248	10	)	)	PUNCT
ejpam-2623	248	11	(	(	PUNCT
ejpam-2623	248	12	2017	2017	NUM
ejpam-2623	248	13	)	)	PUNCT
ejpam-2623	248	14	,	,	PUNCT
ejpam-2623	248	15	363	363	NUM
ejpam-2623	248	16	-	-	SYM
ejpam-2623	248	17	391	391	NUM
ejpam-2623	248	18	370	370	NUM
ejpam-2623	248	19	in	in	ADP
ejpam-2623	248	20	the	the	DET
ejpam-2623	248	21	situation	situation	NOUN
ejpam-2623	248	22	of	of	ADP
ejpam-2623	248	23	the	the	DET
ejpam-2623	248	24	previous	previous	ADJ
ejpam-2623	248	25	theorem	theorem	NOUN
ejpam-2623	248	26	,	,	PUNCT
ejpam-2623	248	27	we	we	PRON
ejpam-2623	248	28	can	can	AUX
ejpam-2623	248	29	write	write	VERB
ejpam-2623	248	30	x	x	X
ejpam-2623	249	1	=	=	PUNCT
ejpam-2623	250	1	(	(	PUNCT
ejpam-2623	250	2	1	1	NUM
ejpam-2623	250	3	+	+	NOUN
ejpam-2623	250	4	x)(bx	x)(bx	X
ejpam-2623	250	5	−	−	PROPN
ejpam-2623	250	6	α2(1	α2(1	NOUN
ejpam-2623	250	7	+	+	NOUN
ejpam-2623	250	8	x)2	x)2	NOUN
ejpam-2623	250	9	)	)	PUNCT
ejpam-2623	251	1	bαy	bαy	VERB
ejpam-2623	251	2	=	=	PUNCT
ejpam-2623	251	3	g(z	g(z	PROPN
ejpam-2623	251	4	)	)	PUNCT
ejpam-2623	251	5	and	and	CCONJ
ejpam-2623	251	6	y	y	PROPN
ejpam-2623	251	7	=	=	PUNCT
ejpam-2623	251	8	(	(	PUNCT
ejpam-2623	251	9	1	1	NUM
ejpam-2623	251	10	+	+	NOUN
ejpam-2623	251	11	x)(ax	x)(ax	NOUN
ejpam-2623	251	12	−	−	PROPN
ejpam-2623	251	13	α2(1	α2(1	NOUN
ejpam-2623	251	14	+	+	NOUN
ejpam-2623	251	15	x)2	x)2	PROPN
ejpam-2623	251	16	)	)	PUNCT
ejpam-2623	251	17	aαy	aαy	NOUN
ejpam-2623	252	1	=	=	SYM
ejpam-2623	252	2	h(z	h(z	NOUN
ejpam-2623	252	3	)	)	PUNCT
ejpam-2623	252	4	.	.	PUNCT
ejpam-2623	253	1	therefore	therefore	ADV
ejpam-2623	253	2	,	,	PUNCT
ejpam-2623	253	3	we	we	PRON
ejpam-2623	253	4	can	can	AUX
ejpam-2623	253	5	define	define	VERB
ejpam-2623	253	6	the	the	DET
ejpam-2623	253	7	encoding	encoding	NOUN
ejpam-2623	253	8	function	function	NOUN
ejpam-2623	253	9	as	as	SCONJ
ejpam-2623	253	10	follows	follow	VERB
ejpam-2623	253	11	.	.	PUNCT
ejpam-2623	254	1	definition	definition	NOUN
ejpam-2623	254	2	1	1	NUM
ejpam-2623	254	3	.	.	PUNCT
ejpam-2623	255	1	the	the	DET
ejpam-2623	255	2	encoding	encoding	NOUN
ejpam-2623	255	3	function	function	NOUN
ejpam-2623	255	4	for	for	ADP
ejpam-2623	255	5	the	the	DET
ejpam-2623	255	6	generalized	generalize	VERB
ejpam-2623	255	7	huff	huff	PROPN
ejpam-2623	255	8	curve	curve	NOUN
ejpam-2623	255	9	e	e	NOUN
ejpam-2623	255	10	:	:	PUNCT
ejpam-2623	255	11	x(ay2	x(ay2	X
ejpam-2623	256	1	−	−	NOUN
ejpam-2623	256	2	1	1	X
ejpam-2623	256	3	)	)	PUNCT
ejpam-2623	256	4	=	=	PUNCT
ejpam-2623	257	1	y(bx2	y(bx2	NOUN
ejpam-2623	258	1	−	−	NOUN
ejpam-2623	258	2	1	1	X
ejpam-2623	258	3	)	)	PUNCT
ejpam-2623	258	4	with	with	ADP
ejpam-2623	258	5	ab(a−	ab(a−	PROPN
ejpam-2623	258	6	b	b	PROPN
ejpam-2623	258	7	)	)	PUNCT
ejpam-2623	258	8	6=	6=	ADP
ejpam-2623	258	9	0	0	NUM
ejpam-2623	258	10	is	be	AUX
ejpam-2623	258	11	the	the	DET
ejpam-2623	258	12	function	function	NOUN
ejpam-2623	258	13	φa	φa	ADP
ejpam-2623	258	14	,	,	PUNCT
ejpam-2623	258	15	b	b	X
ejpam-2623	258	16	:	:	PUNCT
ejpam-2623	258	17	fq	fq	PROPN
ejpam-2623	258	18	→	→	SYM
ejpam-2623	258	19	e(fq	e(fq	PROPN
ejpam-2623	258	20	)	)	PUNCT
ejpam-2623	258	21	defined	define	VERB
ejpam-2623	258	22	as	as	SCONJ
ejpam-2623	258	23	follows	follow	VERB
ejpam-2623	258	24	:	:	PUNCT
ejpam-2623	258	25	φa	φa	ADP
ejpam-2623	258	26	,	,	PUNCT
ejpam-2623	258	27	b(±1	b(±1	NOUN
ejpam-2623	258	28	)	)	PUNCT
ejpam-2623	258	29	=	=	SYM
ejpam-2623	258	30	(	(	PUNCT
ejpam-2623	258	31	0	0	NUM
ejpam-2623	258	32	,	,	PUNCT
ejpam-2623	258	33	0	0	NUM
ejpam-2623	258	34	)	)	PUNCT
ejpam-2623	258	35	;	;	PUNCT
ejpam-2623	258	36	and	and	CCONJ
ejpam-2623	258	37	φa	φa	ADP
ejpam-2623	258	38	,	,	PUNCT
ejpam-2623	258	39	b(z	b(z	NOUN
ejpam-2623	258	40	)	)	PUNCT
ejpam-2623	258	41	=	=	PUNCT
ejpam-2623	259	1	(	(	PUNCT
ejpam-2623	259	2	x	x	X
ejpam-2623	259	3	,	,	PUNCT
ejpam-2623	259	4	y	y	NOUN
ejpam-2623	259	5	)	)	PUNCT
ejpam-2623	259	6	=	=	SYM
ejpam-2623	259	7	(	(	PUNCT
ejpam-2623	259	8	g(z	g(z	PROPN
ejpam-2623	259	9	)	)	PUNCT
ejpam-2623	259	10	,	,	PUNCT
ejpam-2623	259	11	h(z	h(z	NOUN
ejpam-2623	259	12	)	)	PUNCT
ejpam-2623	259	13	)	)	PUNCT
ejpam-2623	260	1	if	if	SCONJ
ejpam-2623	260	2	z	z	PROPN
ejpam-2623	260	3	6=	6=	NUM
ejpam-2623	260	4	±1	±1	VERB
ejpam-2623	260	5	.	.	PUNCT
ejpam-2623	261	1	nb	nb	NOUN
ejpam-2623	261	2	:	:	PUNCT
ejpam-2623	261	3	our	our	PRON
ejpam-2623	261	4	encoding	encoding	NOUN
ejpam-2623	261	5	function	function	NOUN
ejpam-2623	261	6	for	for	ADP
ejpam-2623	261	7	generalized	generalized	ADJ
ejpam-2623	261	8	huff	huff	NOUN
ejpam-2623	261	9	curves	curve	NOUN
ejpam-2623	261	10	does	do	AUX
ejpam-2623	261	11	not	not	PART
ejpam-2623	261	12	include	include	VERB
ejpam-2623	261	13	classical	classical	ADJ
ejpam-2623	261	14	huff	huff	NOUN
ejpam-2623	261	15	curves	curve	NOUN
ejpam-2623	261	16	,	,	PUNCT
ejpam-2623	261	17	because	because	SCONJ
ejpam-2623	261	18	in	in	ADP
ejpam-2623	261	19	our	our	PRON
ejpam-2623	261	20	algorithm	algorithm	NOUN
ejpam-2623	261	21	,	,	PUNCT
ejpam-2623	261	22	ab	ab	PROPN
ejpam-2623	261	23	is	be	AUX
ejpam-2623	261	24	not	not	PART
ejpam-2623	261	25	a	a	DET
ejpam-2623	261	26	square	square	NOUN
ejpam-2623	261	27	,	,	PUNCT
ejpam-2623	261	28	hence	hence	ADV
ejpam-2623	261	29	a	a	PRON
ejpam-2623	261	30	and	and	CCONJ
ejpam-2623	261	31	b	b	NOUN
ejpam-2623	261	32	can	can	AUX
ejpam-2623	261	33	not	not	PART
ejpam-2623	261	34	be	be	AUX
ejpam-2623	261	35	square	square	ADJ
ejpam-2623	261	36	simultaneously	simultaneously	ADV
ejpam-2623	261	37	.	.	PUNCT
ejpam-2623	262	1	proposition	proposition	NOUN
ejpam-2623	262	2	1	1	NUM
ejpam-2623	262	3	.	.	PUNCT
ejpam-2623	263	1	in	in	ADP
ejpam-2623	263	2	the	the	DET
ejpam-2623	263	3	situation	situation	NOUN
ejpam-2623	263	4	of	of	ADP
ejpam-2623	263	5	definition	definition	NOUN
ejpam-2623	263	6	(	(	PUNCT
ejpam-2623	263	7	1	1	NUM
ejpam-2623	263	8	)	)	PUNCT
ejpam-2623	263	9	,	,	PUNCT
ejpam-2623	263	10	if	if	SCONJ
ejpam-2623	263	11	z	z	PROPN
ejpam-2623	263	12	∈	∈	PROPN
ejpam-2623	263	13	fq	fq	NOUN
ejpam-2623	263	14	then	then	ADV
ejpam-2623	263	15	−z	−z	PROPN
ejpam-2623	263	16	∈	∈	PROPN
ejpam-2623	263	17	φ−1a	φ−1a	PROPN
ejpam-2623	263	18	,	,	PUNCT
ejpam-2623	263	19	b(φa	b(φa	PROPN
ejpam-2623	263	20	,	,	PUNCT
ejpam-2623	263	21	b(z	b(z	NOUN
ejpam-2623	263	22	)	)	PUNCT
ejpam-2623	263	23	)	)	PUNCT
ejpam-2623	263	24	.	.	PUNCT
ejpam-2623	264	1	proof	proof	NOUN
ejpam-2623	264	2	.	.	PUNCT
ejpam-2623	265	1	let	let	VERB
ejpam-2623	265	2	z	z	NOUN
ejpam-2623	265	3	∈	∈	PROPN
ejpam-2623	265	4	fq	fq	NOUN
ejpam-2623	265	5	;	;	PUNCT
ejpam-2623	265	6	if	if	SCONJ
ejpam-2623	265	7	z	z	NOUN
ejpam-2623	265	8	=	=	SYM
ejpam-2623	265	9	±1	±1	VERB
ejpam-2623	265	10	then	then	ADV
ejpam-2623	265	11	φa	φa	ADP
ejpam-2623	265	12	,	,	PUNCT
ejpam-2623	265	13	b(z	b(z	NOUN
ejpam-2623	265	14	)	)	PUNCT
ejpam-2623	265	15	=	=	SYM
ejpam-2623	266	1	(	(	PUNCT
ejpam-2623	266	2	0	0	NUM
ejpam-2623	266	3	,	,	PUNCT
ejpam-2623	266	4	0	0	NUM
ejpam-2623	266	5	)	)	PUNCT
ejpam-2623	267	1	=	=	SYM
ejpam-2623	267	2	φa	φa	NOUN
ejpam-2623	267	3	,	,	PUNCT
ejpam-2623	267	4	b(−z	b(−z	NOUN
ejpam-2623	267	5	)	)	PUNCT
ejpam-2623	267	6	by	by	ADP
ejpam-2623	267	7	definition	definition	NOUN
ejpam-2623	267	8	.	.	PUNCT
ejpam-2623	268	1	so	so	ADV
ejpam-2623	268	2	we	we	PRON
ejpam-2623	268	3	can	can	AUX
ejpam-2623	268	4	suppose	suppose	VERB
ejpam-2623	268	5	that	that	SCONJ
ejpam-2623	268	6	z	z	PROPN
ejpam-2623	268	7	6=	6=	NUM
ejpam-2623	268	8	1,−1	1,−1	PROPN
ejpam-2623	268	9	.	.	PUNCT
ejpam-2623	269	1	let	let	VERB
ejpam-2623	269	2	z′	z′	NUM
ejpam-2623	269	3	=	=	PUNCT
ejpam-2623	269	4	−z	−z	NOUN
ejpam-2623	269	5	and	and	CCONJ
ejpam-2623	269	6	define	define	VERB
ejpam-2623	269	7	u′	u′	PROPN
ejpam-2623	269	8	,	,	PUNCT
ejpam-2623	269	9	v′	v′	PROPN
ejpam-2623	269	10	,	,	PUNCT
ejpam-2623	269	11	x	x	SYM
ejpam-2623	269	12	′	′	NUM
ejpam-2623	269	13	,	,	PUNCT
ejpam-2623	269	14	y	y	PROPN
ejpam-2623	269	15	′	′	PROPN
ejpam-2623	269	16	,	,	PUNCT
ejpam-2623	269	17	x′	x′	PROPN
ejpam-2623	269	18	,	,	PUNCT
ejpam-2623	269	19	y′	y′	ADV
ejpam-2623	269	20	from	from	ADP
ejpam-2623	269	21	z′	z′	NUM
ejpam-2623	269	22	,	,	PUNCT
ejpam-2623	269	23	with	with	ADP
ejpam-2623	269	24	(	(	PUNCT
ejpam-2623	269	25	x′	x′	NUM
ejpam-2623	269	26	,	,	PUNCT
ejpam-2623	269	27	y′	y′	NUM
ejpam-2623	269	28	)	)	PUNCT
ejpam-2623	270	1	=	=	SYM
ejpam-2623	270	2	φa	φa	PROPN
ejpam-2623	270	3	,	,	PUNCT
ejpam-2623	270	4	b(z	b(z	NOUN
ejpam-2623	270	5	′	′	NOUN
ejpam-2623	270	6	)	)	PUNCT
ejpam-2623	270	7	.	.	PUNCT
ejpam-2623	271	1	to	to	PART
ejpam-2623	271	2	show	show	VERB
ejpam-2623	271	3	that	that	SCONJ
ejpam-2623	271	4	(	(	PUNCT
ejpam-2623	271	5	x	x	NOUN
ejpam-2623	271	6	,	,	PUNCT
ejpam-2623	271	7	y	y	NOUN
ejpam-2623	271	8	)	)	PUNCT
ejpam-2623	271	9	=	=	SYM
ejpam-2623	271	10	(	(	PUNCT
ejpam-2623	271	11	x′	x′	NUM
ejpam-2623	271	12	,	,	PUNCT
ejpam-2623	271	13	y′	y′	NUM
ejpam-2623	271	14	)	)	PUNCT
ejpam-2623	271	15	,	,	PUNCT
ejpam-2623	271	16	as	as	ADP
ejpam-2623	271	17	in	in	ADP
ejpam-2623	271	18	[	[	X
ejpam-2623	271	19	4	4	NUM
ejpam-2623	271	20	]	]	PUNCT
ejpam-2623	271	21	,	,	PUNCT
ejpam-2623	271	22	we	we	PRON
ejpam-2623	271	23	will	will	AUX
ejpam-2623	271	24	compare	compare	VERB
ejpam-2623	271	25	u′	u′	PRON
ejpam-2623	271	26	to	to	ADP
ejpam-2623	271	27	u	u	PROPN
ejpam-2623	271	28	,	,	PUNCT
ejpam-2623	271	29	v′	v′	NUM
ejpam-2623	271	30	to	to	ADP
ejpam-2623	271	31	v	v	NOUN
ejpam-2623	271	32	,	,	PUNCT
ejpam-2623	271	33	x	x	NOUN
ejpam-2623	271	34	′	′	NOUN
ejpam-2623	271	35	to	to	PART
ejpam-2623	271	36	x	x	SYM
ejpam-2623	271	37	,	,	PUNCT
ejpam-2623	271	38	y	y	PROPN
ejpam-2623	271	39	to	to	ADP
ejpam-2623	271	40	y	y	PROPN
ejpam-2623	271	41	′	′	NOUN
ejpam-2623	271	42	and	and	CCONJ
ejpam-2623	271	43	finally	finally	ADV
ejpam-2623	271	44	compute	compute	VERB
ejpam-2623	271	45	(	(	PUNCT
ejpam-2623	271	46	x′	x′	NUM
ejpam-2623	271	47	,	,	PUNCT
ejpam-2623	271	48	y′	y′	NUM
ejpam-2623	271	49	)	)	PUNCT
ejpam-2623	272	1	=	=	SYM
ejpam-2623	272	2	φa	φa	PROPN
ejpam-2623	272	3	,	,	PUNCT
ejpam-2623	272	4	b(z	b(z	NOUN
ejpam-2623	272	5	′	′	NOUN
ejpam-2623	272	6	)	)	PUNCT
ejpam-2623	272	7	.	.	PUNCT
ejpam-2623	273	1	(	(	PUNCT
ejpam-2623	273	2	i	i	NOUN
ejpam-2623	273	3	)	)	PUNCT
ejpam-2623	273	4	u′	u′	PROPN
ejpam-2623	273	5	=	=	SYM
ejpam-2623	274	1	1−z′	1−z′	PROPN
ejpam-2623	274	2	1+z′	1+z′	NUM
ejpam-2623	274	3	=	=	SYM
ejpam-2623	274	4	1+z	1+z	NUM
ejpam-2623	274	5	1−z	1−z	NUM
ejpam-2623	274	6	=	=	SYM
ejpam-2623	274	7	1	1	NUM
ejpam-2623	274	8	u	u	NOUN
ejpam-2623	274	9	.	.	PUNCT
ejpam-2623	275	1	(	(	PUNCT
ejpam-2623	275	2	ii	ii	NOUN
ejpam-2623	275	3	)	)	PUNCT
ejpam-2623	275	4	v′	v′	PROPN
ejpam-2623	275	5	=	=	PUNCT
ejpam-2623	276	1	−u′5+(c2	−u′5+(c2	NUM
ejpam-2623	276	2	+	+	NOUN
ejpam-2623	276	3	1	1	NUM
ejpam-2623	276	4	/	/	SYM
ejpam-2623	276	5	c2)u′3−u′	c2)u′3−u′	NOUN
ejpam-2623	277	1	=	=	SYM
ejpam-2623	277	2	−	−	PROPN
ejpam-2623	277	3	1	1	NUM
ejpam-2623	277	4	u5	u5	NOUN
ejpam-2623	277	5	+	+	PROPN
ejpam-2623	277	6	(	(	PUNCT
ejpam-2623	277	7	c2	c2	PROPN
ejpam-2623	277	8	+	+	PROPN
ejpam-2623	277	9	1	1	PROPN
ejpam-2623	277	10	/	/	SYM
ejpam-2623	277	11	c2	c2	PROPN
ejpam-2623	277	12	)	)	PUNCT
ejpam-2623	277	13	1	1	NUM
ejpam-2623	277	14	u3	u3	NOUN
ejpam-2623	277	15	−	−	PROPN
ejpam-2623	277	16	1	1	NUM
ejpam-2623	277	17	u	u	NOUN
ejpam-2623	277	18	=	=	PROPN
ejpam-2623	277	19	v	v	NUM
ejpam-2623	277	20	u6	u6	NOUN
ejpam-2623	277	21	.	.	PUNCT
ejpam-2623	278	1	note	note	VERB
ejpam-2623	278	2	that	that	SCONJ
ejpam-2623	278	3	χ(v′	χ(v′	PROPN
ejpam-2623	278	4	)	)	PUNCT
ejpam-2623	278	5	=	=	SYM
ejpam-2623	278	6	χ(v	χ(v	NOUN
ejpam-2623	278	7	)	)	PUNCT
ejpam-2623	278	8	.	.	PUNCT
ejpam-2623	279	1	(	(	PUNCT
ejpam-2623	279	2	iii	iii	X
ejpam-2623	279	3	)	)	PUNCT
ejpam-2623	279	4	x	x	SYM
ejpam-2623	279	5	′	′	NUM
ejpam-2623	279	6	=	=	PUNCT
ejpam-2623	279	7	χ(v′)u′	χ(v′)u′	NOUN
ejpam-2623	279	8	=	=	PUNCT
ejpam-2623	279	9	χ(v)u′	χ(v)u′	PROPN
ejpam-2623	279	10	=	=	SYM
ejpam-2623	279	11	χ(v	χ(v	NOUN
ejpam-2623	279	12	)	)	PUNCT
ejpam-2623	279	13	u	u	NOUN
ejpam-2623	279	14	=	=	NOUN
ejpam-2623	279	15	1	1	NUM
ejpam-2623	279	16	uχ(v	uχ(v	NOUN
ejpam-2623	279	17	)	)	PUNCT
ejpam-2623	279	18	=	=	SYM
ejpam-2623	279	19	1	1	NUM
ejpam-2623	279	20	x	x	X
ejpam-2623	279	21	.	.	PUNCT
ejpam-2623	280	1	(	(	PUNCT
ejpam-2623	280	2	iv	iv	X
ejpam-2623	280	3	)	)	PUNCT
ejpam-2623	280	4	y	y	PROPN
ejpam-2623	280	5	′	′	NUM
ejpam-2623	281	1	=	=	PUNCT
ejpam-2623	281	2	χ(v′	χ(v′	PROPN
ejpam-2623	281	3	·	·	PUNCT
ejpam-2623	281	4	(	(	PUNCT
ejpam-2623	281	5	c2u′2	c2u′2	PROPN
ejpam-2623	281	6	−	−	PROPN
ejpam-2623	281	7	1)/c	1)/c	NUM
ejpam-2623	281	8	)	)	PUNCT
ejpam-2623	281	9	√	√	ADP
ejpam-2623	281	10	χ(v′)v′	χ(v′)v′	NOUN
ejpam-2623	281	11	=	=	SYM
ejpam-2623	281	12	χ(v′	χ(v′	PROPN
ejpam-2623	281	13	)	)	PUNCT
ejpam-2623	281	14	·	·	PUNCT
ejpam-2623	281	15	χ(u′2	χ(u′2	X
ejpam-2623	282	1	−	−	ADP
ejpam-2623	282	2	1	1	NUM
ejpam-2623	282	3	/	/	SYM
ejpam-2623	282	4	c2	c2	PROPN
ejpam-2623	282	5	)	)	PUNCT
ejpam-2623	283	1	√	√	PROPN
ejpam-2623	283	2	χ(v′)v′.	χ(v′)v′.	NOUN
ejpam-2623	283	3	for	for	ADP
ejpam-2623	283	4	the	the	DET
ejpam-2623	283	5	second	second	ADJ
ejpam-2623	283	6	factor	factor	NOUN
ejpam-2623	283	7	of	of	ADP
ejpam-2623	283	8	y	y	PROPN
ejpam-2623	283	9	′	′	PROPN
ejpam-2623	283	10	,	,	PUNCT
ejpam-2623	283	11	recall	recall	VERB
ejpam-2623	283	12	that	that	DET
ejpam-2623	283	13	v′	v′	NOUN
ejpam-2623	283	14	=	=	SYM
ejpam-2623	283	15	v	v	NOUN
ejpam-2623	283	16	/	/	SYM
ejpam-2623	283	17	u6	u6	NOUN
ejpam-2623	283	18	and	and	CCONJ
ejpam-2623	283	19	χ(v′	χ(v′	NUM
ejpam-2623	283	20	)	)	PUNCT
ejpam-2623	283	21	=	=	SYM
ejpam-2623	283	22	χ(v	χ(v	NOUN
ejpam-2623	283	23	)	)	PUNCT
ejpam-2623	283	24	;	;	PUNCT
ejpam-2623	283	25	so	so	ADV
ejpam-2623	283	26	√	√	VERB
ejpam-2623	283	27	χ(v′)v′	χ(v′)v′	NOUN
ejpam-2623	283	28	=	=	NOUN
ejpam-2623	283	29	√	√	ADP
ejpam-2623	283	30	χ(v)v	χ(v)v	PROPN
ejpam-2623	283	31	u6	u6	NOUN
ejpam-2623	283	32	=	=	NOUN
ejpam-2623	283	33	√	√	PROPN
ejpam-2623	283	34	χ(v)v	χ(v)v	PROPN
ejpam-2623	283	35	χ(u)2u6	χ(u)2u6	AUX
ejpam-2623	283	36	=	=	SYM
ejpam-2623	283	37	χ(u	χ(u	NOUN
ejpam-2623	283	38	)	)	PUNCT
ejpam-2623	283	39	√	√	X
ejpam-2623	283	40	χ(v)v	χ(v)v	PROPN
ejpam-2623	283	41	u3	u3	NOUN
ejpam-2623	283	42	.	.	PUNCT
ejpam-2623	284	1	since	since	SCONJ
ejpam-2623	284	2	χ((u2−1	χ((u2−1	NOUN
ejpam-2623	284	3	/	/	SYM
ejpam-2623	284	4	c2)2c2u4	c2)2c2u4	NOUN
ejpam-2623	284	5	)	)	PUNCT
ejpam-2623	284	6	=	=	SYM
ejpam-2623	284	7	1	1	X
ejpam-2623	284	8	,	,	PUNCT
ejpam-2623	284	9	we	we	PRON
ejpam-2623	284	10	have	have	VERB
ejpam-2623	284	11	χ(u′2−1	χ(u′2−1	NOUN
ejpam-2623	284	12	/	/	SYM
ejpam-2623	284	13	c2	c2	PROPN
ejpam-2623	284	14	)	)	PUNCT
ejpam-2623	285	1	=	=	PUNCT
ejpam-2623	285	2	χ((u′2−1	χ((u′2−1	NOUN
ejpam-2623	285	3	/	/	SYM
ejpam-2623	285	4	c2)(u2−1	c2)(u2−1	NOUN
ejpam-2623	285	5	/	/	SYM
ejpam-2623	285	6	c2)2c2u4	c2)2c2u4	NOUN
ejpam-2623	285	7	)	)	PUNCT
ejpam-2623	285	8	.	.	PUNCT
ejpam-2623	286	1	thus	thus	ADV
ejpam-2623	286	2	,	,	PUNCT
ejpam-2623	286	3	we	we	PRON
ejpam-2623	286	4	have	have	VERB
ejpam-2623	286	5	:	:	PUNCT
ejpam-2623	286	6	χ(u′2	χ(u′2	X
ejpam-2623	286	7	−	−	PROPN
ejpam-2623	286	8	1	1	NUM
ejpam-2623	286	9	/	/	SYM
ejpam-2623	286	10	c2	c2	PROPN
ejpam-2623	286	11	)	)	PUNCT
ejpam-2623	287	1	=	=	PROPN
ejpam-2623	287	2	χ(u2(c2	χ(u2(c2	PROPN
ejpam-2623	287	3	−	−	PROPN
ejpam-2623	287	4	u2)(u2	u2)(u2	PROPN
ejpam-2623	287	5	−	−	PROPN
ejpam-2623	287	6	1	1	NUM
ejpam-2623	287	7	/	/	SYM
ejpam-2623	287	8	c2)2	c2)2	NOUN
ejpam-2623	287	9	)	)	PUNCT
ejpam-2623	287	10	.	.	PUNCT
ejpam-2623	288	1	since	since	SCONJ
ejpam-2623	288	2	v	v	NOUN
ejpam-2623	288	3	=	=	SYM
ejpam-2623	288	4	−u5	−u5	NOUN
ejpam-2623	288	5	+	+	CCONJ
ejpam-2623	288	6	(	(	PUNCT
ejpam-2623	288	7	c2	c2	PROPN
ejpam-2623	288	8	+	+	CCONJ
ejpam-2623	288	9	1	1	NUM
ejpam-2623	288	10	/	/	SYM
ejpam-2623	288	11	c2)u3	c2)u3	NOUN
ejpam-2623	288	12	−	−	PROPN
ejpam-2623	288	13	u	u	NOUN
ejpam-2623	288	14	=	=	PROPN
ejpam-2623	288	15	−u(u2	−u(u2	PROPN
ejpam-2623	288	16	−	−	PROPN
ejpam-2623	288	17	c2)(u2	c2)(u2	PROPN
ejpam-2623	288	18	−	−	NUM
ejpam-2623	288	19	1	1	NUM
ejpam-2623	288	20	/	/	SYM
ejpam-2623	288	21	c2	c2	PROPN
ejpam-2623	288	22	)	)	PUNCT
ejpam-2623	288	23	,	,	PUNCT
ejpam-2623	288	24	we	we	PRON
ejpam-2623	288	25	then	then	ADV
ejpam-2623	288	26	have	have	VERB
ejpam-2623	288	27	χ(u′2	χ(u′2	NUM
ejpam-2623	288	28	−	−	ADP
ejpam-2623	288	29	1	1	NUM
ejpam-2623	288	30	/	/	SYM
ejpam-2623	288	31	c2	c2	PROPN
ejpam-2623	288	32	)	)	PUNCT
ejpam-2623	289	1	=	=	PUNCT
ejpam-2623	289	2	χ(uv(u2	χ(uv(u2	ADJ
ejpam-2623	289	3	−	−	NUM
ejpam-2623	289	4	1	1	NUM
ejpam-2623	289	5	/	/	SYM
ejpam-2623	289	6	c2	c2	PROPN
ejpam-2623	289	7	)	)	PUNCT
ejpam-2623	289	8	)	)	PUNCT
ejpam-2623	289	9	.	.	PUNCT
ejpam-2623	290	1	finally	finally	ADV
ejpam-2623	290	2	,	,	PUNCT
ejpam-2623	290	3	y	y	PROPN
ejpam-2623	290	4	′	′	NUM
ejpam-2623	290	5	=	=	SYM
ejpam-2623	290	6	χ(v′)·χ(u′2−1	χ(v′)·χ(u′2−1	PROPN
ejpam-2623	290	7	/	/	SYM
ejpam-2623	290	8	c2	c2	PROPN
ejpam-2623	290	9	)	)	PUNCT
ejpam-2623	291	1	√	√	VERB
ejpam-2623	291	2	χ(v′)v′	χ(v′)v′	NOUN
ejpam-2623	291	3	=	=	SYM
ejpam-2623	291	4	1	1	NUM
ejpam-2623	291	5	u3	u3	NOUN
ejpam-2623	291	6	(	(	PUNCT
ejpam-2623	291	7	χ(u2)χ(v2)χ(u2	χ(u2)χ(v2)χ(u2	NUM
ejpam-2623	291	8	−	−	PROPN
ejpam-2623	291	9	1	1	NUM
ejpam-2623	291	10	/	/	SYM
ejpam-2623	291	11	c2	c2	PROPN
ejpam-2623	291	12	)	)	PUNCT
ejpam-2623	291	13	√	√	PROPN
ejpam-2623	291	14	χ(v′)v′	χ(v′)v′	NOUN
ejpam-2623	291	15	)	)	PUNCT
ejpam-2623	292	1	=	=	SYM
ejpam-2623	292	2	y	y	PROPN
ejpam-2623	292	3	χ(v)u3	χ(v)u3	PROPN
ejpam-2623	292	4	=	=	SYM
ejpam-2623	292	5	y	y	PROPN
ejpam-2623	292	6	(	(	PUNCT
ejpam-2623	292	7	χ(v)u)3	χ(v)u)3	NOUN
ejpam-2623	292	8	=	=	SYM
ejpam-2623	292	9	y	y	NOUN
ejpam-2623	292	10	x3	x3	VERB
ejpam-2623	292	11	.	.	PUNCT
ejpam-2623	293	1	(	(	PUNCT
ejpam-2623	293	2	v	v	NOUN
ejpam-2623	293	3	)	)	PUNCT
ejpam-2623	293	4	since	since	SCONJ
ejpam-2623	293	5	y′	y′	NUM
ejpam-2623	293	6	=	=	SYM
ejpam-2623	293	7	(	(	PUNCT
ejpam-2623	293	8	1+x′)(ax′−α2(1+x′)2	1+x′)(ax′−α2(1+x′)2	NUM
ejpam-2623	293	9	)	)	PUNCT
ejpam-2623	293	10	aαy	aαy	NOUN
ejpam-2623	293	11	′	′	NOUN
ejpam-2623	293	12	,	,	PUNCT
ejpam-2623	293	13	x	x	PUNCT
ejpam-2623	294	1	′	′	NUM
ejpam-2623	294	2	=	=	VERB
ejpam-2623	294	3	1	1	NUM
ejpam-2623	294	4	/	/	SYM
ejpam-2623	294	5	x	x	PROPN
ejpam-2623	294	6	and	and	CCONJ
ejpam-2623	294	7	y	y	PROPN
ejpam-2623	295	1	′	′	NUM
ejpam-2623	295	2	=	=	PUNCT
ejpam-2623	295	3	y	y	PROPN
ejpam-2623	295	4	/	/	SYM
ejpam-2623	295	5	x3	x3	PROPN
ejpam-2623	295	6	,	,	PUNCT
ejpam-2623	295	7	then	then	ADV
ejpam-2623	295	8	we	we	PRON
ejpam-2623	295	9	have	have	VERB
ejpam-2623	295	10	y′	y′	NOUN
ejpam-2623	295	11	=	=	SYM
ejpam-2623	296	1	x3	x3	ADJ
ejpam-2623	296	2	(	(	PUNCT
ejpam-2623	296	3	(	(	PUNCT
ejpam-2623	296	4	1	1	NUM
ejpam-2623	296	5	+	+	SYM
ejpam-2623	296	6	1	1	NUM
ejpam-2623	296	7	/	/	SYM
ejpam-2623	296	8	x)(a	x)(a	NUM
ejpam-2623	296	9	/	/	SYM
ejpam-2623	296	10	x	x	SYM
ejpam-2623	296	11	−	−	PROPN
ejpam-2623	296	12	α2(1	α2(1	NOUN
ejpam-2623	296	13	+	+	CCONJ
ejpam-2623	296	14	1	1	NUM
ejpam-2623	296	15	/	/	SYM
ejpam-2623	296	16	x)2	x)2	PROPN
ejpam-2623	296	17	aαy	aαy	VERB
ejpam-2623	296	18	)	)	PUNCT
ejpam-2623	297	1	=	=	SYM
ejpam-2623	297	2	x(x	x(x	PROPN
ejpam-2623	298	1	+	+	CCONJ
ejpam-2623	298	2	1)(ax	1)(ax	NUM
ejpam-2623	298	3	−	−	NOUN
ejpam-2623	298	4	α2(1	α2(1	NOUN
ejpam-2623	298	5	+	+	NOUN
ejpam-2623	298	6	x)2	x)2	PROPN
ejpam-2623	298	7	)	)	PUNCT
ejpam-2623	298	8	aαy	aαy	NOUN
ejpam-2623	298	9	=	=	SYM
ejpam-2623	298	10	y	y	PROPN
ejpam-2623	298	11	,	,	PUNCT
ejpam-2623	298	12	as	as	SCONJ
ejpam-2623	298	13	desired	desire	VERB
ejpam-2623	298	14	.	.	PUNCT
ejpam-2623	299	1	(	(	PUNCT
ejpam-2623	299	2	vi	vi	NOUN
ejpam-2623	299	3	)	)	PUNCT
ejpam-2623	299	4	as	as	ADP
ejpam-2623	299	5	for	for	ADP
ejpam-2623	299	6	y′	y′	NUM
ejpam-2623	299	7	,	,	PUNCT
ejpam-2623	299	8	one	one	PRON
ejpam-2623	299	9	can	can	AUX
ejpam-2623	299	10	show	show	VERB
ejpam-2623	299	11	that	that	PRON
ejpam-2623	299	12	x′	x′	PROPN
ejpam-2623	299	13	=	=	PUNCT
ejpam-2623	299	14	x.	x.	PROPN
ejpam-2623	299	15	n.	n.	PROPN
ejpam-2623	299	16	diarra	diarra	PROPN
ejpam-2623	299	17	,	,	PUNCT
ejpam-2623	299	18	d.	d.	PROPN
ejpam-2623	299	19	sow	sow	PROPN
ejpam-2623	299	20	,	,	PUNCT
ejpam-2623	299	21	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	299	22	.	.	PUNCT
ejpam-2623	299	23	khlil	khlil	PROPN
ejpam-2623	299	24	/	/	SYM
ejpam-2623	299	25	eur	eur	PROPN
ejpam-2623	299	26	.	.	PUNCT
ejpam-2623	300	1	j.	j.	PROPN
ejpam-2623	300	2	pure	pure	PROPN
ejpam-2623	300	3	appl	appl	PROPN
ejpam-2623	300	4	.	.	PROPN
ejpam-2623	300	5	math	math	PROPN
ejpam-2623	300	6	,	,	PUNCT
ejpam-2623	300	7	10	10	NUM
ejpam-2623	300	8	(	(	PUNCT
ejpam-2623	300	9	2	2	NUM
ejpam-2623	300	10	)	)	PUNCT
ejpam-2623	300	11	(	(	PUNCT
ejpam-2623	300	12	2017	2017	NUM
ejpam-2623	300	13	)	)	PUNCT
ejpam-2623	300	14	,	,	PUNCT
ejpam-2623	300	15	363	363	NUM
ejpam-2623	300	16	-	-	SYM
ejpam-2623	300	17	391	391	NUM
ejpam-2623	300	18	371	371	NUM
ejpam-2623	300	19	hence	hence	ADV
ejpam-2623	300	20	we	we	PRON
ejpam-2623	300	21	conclude	conclude	VERB
ejpam-2623	300	22	that	that	SCONJ
ejpam-2623	300	23	φa	φa	ADP
ejpam-2623	300	24	,	,	PUNCT
ejpam-2623	300	25	b(−z	b(−z	NOUN
ejpam-2623	300	26	)	)	PUNCT
ejpam-2623	300	27	=	=	SYM
ejpam-2623	300	28	φa	φa	PROPN
ejpam-2623	300	29	,	,	PUNCT
ejpam-2623	300	30	b(z	b(z	NOUN
ejpam-2623	300	31	)	)	PUNCT
ejpam-2623	300	32	,	,	PUNCT
ejpam-2623	300	33	for	for	ADP
ejpam-2623	300	34	every	every	DET
ejpam-2623	300	35	z	z	PROPN
ejpam-2623	300	36	∈	∈	PROPN
ejpam-2623	300	37	fq	fq	PROPN
ejpam-2623	300	38	.	.	PROPN
ejpam-2623	300	39	proposition	proposition	PROPN
ejpam-2623	300	40	2	2	NUM
ejpam-2623	300	41	.	.	PUNCT
ejpam-2623	301	1	in	in	ADP
ejpam-2623	301	2	the	the	DET
ejpam-2623	301	3	situation	situation	NOUN
ejpam-2623	301	4	of	of	ADP
ejpam-2623	301	5	definition	definition	NOUN
ejpam-2623	301	6	1	1	NUM
ejpam-2623	301	7	,	,	PUNCT
ejpam-2623	301	8	if	if	SCONJ
ejpam-2623	301	9	(	(	PUNCT
ejpam-2623	301	10	x	x	NOUN
ejpam-2623	301	11	,	,	PUNCT
ejpam-2623	301	12	y	y	PROPN
ejpam-2623	301	13	)	)	PUNCT
ejpam-2623	301	14	∈	∈	PROPN
ejpam-2623	301	15	φa	φa	ADP
ejpam-2623	301	16	,	,	PUNCT
ejpam-2623	301	17	b(fq	b(fq	PROPN
ejpam-2623	301	18	)	)	PUNCT
ejpam-2623	301	19	then	then	ADV
ejpam-2623	301	20	:	:	PUNCT
ejpam-2623	301	21	x	x	X
ejpam-2623	301	22	6=	6=	NUM
ejpam-2623	301	23	y	y	PROPN
ejpam-2623	301	24	and	and	CCONJ
ejpam-2623	301	25	1−	1−	NUM
ejpam-2623	301	26	4α2η	4α2η	NOUN
ejpam-2623	301	27	is	be	AUX
ejpam-2623	301	28	a	a	DET
ejpam-2623	301	29	square	square	NOUN
ejpam-2623	301	30	,	,	PUNCT
ejpam-2623	301	31	where	where	SCONJ
ejpam-2623	301	32	η	η	PROPN
ejpam-2623	301	33	=	=	SYM
ejpam-2623	301	34	bx−	bx−	PROPN
ejpam-2623	301	35	ay	ay	PROPN
ejpam-2623	301	36	ab(x−	ab(x−	X
ejpam-2623	301	37	y	y	NOUN
ejpam-2623	301	38	)	)	PUNCT
ejpam-2623	301	39	with	with	ADP
ejpam-2623	301	40	α2	α2	ADJ
ejpam-2623	301	41	=	=	SYM
ejpam-2623	301	42	a+	a+	PUNCT
ejpam-2623	301	43	b	b	PROPN
ejpam-2623	301	44	4	4	NUM
ejpam-2623	301	45	.	.	PUNCT
ejpam-2623	302	1	proof	proof	NOUN
ejpam-2623	302	2	.	.	PUNCT
ejpam-2623	303	1	let	let	VERB
ejpam-2623	303	2	(	(	PUNCT
ejpam-2623	303	3	x	x	NOUN
ejpam-2623	303	4	,	,	PUNCT
ejpam-2623	303	5	y	y	PROPN
ejpam-2623	303	6	)	)	PUNCT
ejpam-2623	303	7	∈	∈	PROPN
ejpam-2623	303	8	φa	φa	ADP
ejpam-2623	303	9	,	,	PUNCT
ejpam-2623	303	10	b(fq	b(fq	PROPN
ejpam-2623	303	11	)	)	PUNCT
ejpam-2623	303	12	;	;	PUNCT
ejpam-2623	303	13	by	by	ADP
ejpam-2623	303	14	theorem	theorem	NOUN
ejpam-2623	303	15	2	2	NUM
ejpam-2623	303	16	,	,	PUNCT
ejpam-2623	303	17	we	we	PRON
ejpam-2623	303	18	know	know	VERB
ejpam-2623	303	19	that	that	SCONJ
ejpam-2623	303	20	x	x	X
ejpam-2623	304	1	=	=	PUNCT
ejpam-2623	304	2	(	(	PUNCT
ejpam-2623	304	3	1	1	NUM
ejpam-2623	304	4	+	+	NOUN
ejpam-2623	304	5	x)(bx	x)(bx	X
ejpam-2623	304	6	−	−	PROPN
ejpam-2623	304	7	α2(1	α2(1	NOUN
ejpam-2623	304	8	+	+	NOUN
ejpam-2623	304	9	x)2	x)2	NOUN
ejpam-2623	304	10	)	)	PUNCT
ejpam-2623	304	11	bαy	bαy	ADV
ejpam-2623	304	12	and	and	CCONJ
ejpam-2623	304	13	y	y	PROPN
ejpam-2623	304	14	=	=	PUNCT
ejpam-2623	304	15	(	(	PUNCT
ejpam-2623	304	16	1	1	NUM
ejpam-2623	304	17	+	+	NOUN
ejpam-2623	304	18	x)(ax	x)(ax	NOUN
ejpam-2623	304	19	−	−	PROPN
ejpam-2623	304	20	α2(1	α2(1	NOUN
ejpam-2623	304	21	+	+	NOUN
ejpam-2623	304	22	x)2	x)2	PROPN
ejpam-2623	304	23	)	)	PUNCT
ejpam-2623	304	24	aαy	aαy	NOUN
ejpam-2623	304	25	.	.	PUNCT
ejpam-2623	305	1	•	•	NUM
ejpam-2623	305	2	x	x	X
ejpam-2623	305	3	=	=	SYM
ejpam-2623	305	4	y	y	PROPN
ejpam-2623	305	5	⇒	⇒	VERB
ejpam-2623	305	6	a	a	DET
ejpam-2623	305	7	=	=	SYM
ejpam-2623	305	8	b	b	NOUN
ejpam-2623	305	9	which	which	PRON
ejpam-2623	305	10	is	be	AUX
ejpam-2623	305	11	impossible	impossible	ADJ
ejpam-2623	305	12	.	.	PUNCT
ejpam-2623	306	1	•	•	INTJ
ejpam-2623	306	2	we	we	PRON
ejpam-2623	306	3	have	have	VERB
ejpam-2623	306	4	x	x	X
ejpam-2623	306	5	y	y	VERB
ejpam-2623	306	6	=	=	PUNCT
ejpam-2623	306	7	a	a	PRON
ejpam-2623	306	8	b	b	PROPN
ejpam-2623	306	9	(	(	PUNCT
ejpam-2623	306	10	bx	bx	NOUN
ejpam-2623	306	11	−	−	PROPN
ejpam-2623	306	12	α2(1	α2(1	NOUN
ejpam-2623	307	1	+	+	NOUN
ejpam-2623	307	2	x)2	x)2	X
ejpam-2623	307	3	ax	ax	NOUN
ejpam-2623	307	4	−	−	PROPN
ejpam-2623	307	5	α2(1	α2(1	NOUN
ejpam-2623	307	6	+	+	NOUN
ejpam-2623	307	7	x)2	x)2	X
ejpam-2623	307	8	)	)	PUNCT
ejpam-2623	308	1	and	and	CCONJ
ejpam-2623	308	2	we	we	PRON
ejpam-2623	308	3	obtain	obtain	VERB
ejpam-2623	308	4	the	the	DET
ejpam-2623	308	5	equation	equation	NOUN
ejpam-2623	308	6	x2+x(2−	x2+x(2−	PROPN
ejpam-2623	308	7	1	1	NUM
ejpam-2623	308	8	ηα2	ηα2	NOUN
ejpam-2623	308	9	)	)	PUNCT
ejpam-2623	309	1	+	+	CCONJ
ejpam-2623	309	2	1	1	NUM
ejpam-2623	309	3	=	=	SYM
ejpam-2623	309	4	0	0	NUM
ejpam-2623	309	5	,	,	PUNCT
ejpam-2623	309	6	where	where	SCONJ
ejpam-2623	309	7	η	η	PROPN
ejpam-2623	309	8	=	=	SYM
ejpam-2623	309	9	bx−	bx−	PROPN
ejpam-2623	309	10	ay	ay	PROPN
ejpam-2623	309	11	ab(x−	ab(x−	X
ejpam-2623	309	12	y	y	PROPN
ejpam-2623	309	13	)	)	PUNCT
ejpam-2623	309	14	.	.	PUNCT
ejpam-2623	310	1	the	the	DET
ejpam-2623	310	2	discriminant	discriminant	NOUN
ejpam-2623	310	3	δ	δ	PROPN
ejpam-2623	310	4	=	=	SYM
ejpam-2623	310	5	1	1	NUM
ejpam-2623	310	6	(	(	PUNCT
ejpam-2623	310	7	ηα2)2	ηα2)2	NOUN
ejpam-2623	310	8	(	(	PUNCT
ejpam-2623	310	9	1−4ηα2	1−4ηα2	NUM
ejpam-2623	310	10	)	)	PUNCT
ejpam-2623	310	11	of	of	ADP
ejpam-2623	310	12	this	this	DET
ejpam-2623	310	13	equation	equation	NOUN
ejpam-2623	310	14	has	have	VERB
ejpam-2623	310	15	to	to	PART
ejpam-2623	310	16	be	be	AUX
ejpam-2623	310	17	a	a	DET
ejpam-2623	310	18	square	square	NOUN
ejpam-2623	310	19	.	.	PUNCT
ejpam-2623	311	1	this	this	PRON
ejpam-2623	311	2	leads	lead	VERB
ejpam-2623	311	3	to	to	ADP
ejpam-2623	311	4	1−	1−	NUM
ejpam-2623	311	5	4ηα2	4ηα2	NUM
ejpam-2623	311	6	is	be	AUX
ejpam-2623	311	7	a	a	DET
ejpam-2623	311	8	square	square	NOUN
ejpam-2623	311	9	,	,	PUNCT
ejpam-2623	311	10	as	as	SCONJ
ejpam-2623	311	11	desired	desire	VERB
ejpam-2623	311	12	.	.	PUNCT
ejpam-2623	312	1	proposition	proposition	NOUN
ejpam-2623	312	2	3	3	NUM
ejpam-2623	312	3	.	.	PUNCT
ejpam-2623	313	1	for	for	ADP
ejpam-2623	313	2	z	z	PROPN
ejpam-2623	313	3	∈	∈	PROPN
ejpam-2623	313	4	fq	fq	PROPN
ejpam-2623	313	5	\	\	PROPN
ejpam-2623	313	6	{	{	PUNCT
ejpam-2623	313	7	±1	±1	PROPN
ejpam-2623	313	8	}	}	PUNCT
ejpam-2623	313	9	,	,	PUNCT
ejpam-2623	313	10	the	the	DET
ejpam-2623	313	11	set	set	NOUN
ejpam-2623	313	12	of	of	ADP
ejpam-2623	313	13	preimages	preimage	NOUN
ejpam-2623	313	14	of	of	ADP
ejpam-2623	313	15	φa	φa	ADP
ejpam-2623	313	16	,	,	PUNCT
ejpam-2623	313	17	b(z	b(z	NOUN
ejpam-2623	313	18	)	)	PUNCT
ejpam-2623	313	19	is	be	AUX
ejpam-2623	313	20	{	{	PUNCT
ejpam-2623	313	21	−z	−z	NOUN
ejpam-2623	313	22	,	,	PUNCT
ejpam-2623	313	23	z	z	NOUN
ejpam-2623	313	24	}	}	PUNCT
ejpam-2623	313	25	.	.	PUNCT
ejpam-2623	314	1	proof	proof	NOUN
ejpam-2623	314	2	.	.	PUNCT
ejpam-2623	315	1	•	•	NUM
ejpam-2623	315	2	{	{	PUNCT
ejpam-2623	315	3	z,−z	z,−z	NOUN
ejpam-2623	315	4	}	}	PUNCT
ejpam-2623	315	5	⊆	⊆	NUM
ejpam-2623	315	6	φ−1a	φ−1a	ADJ
ejpam-2623	315	7	,	,	PUNCT
ejpam-2623	315	8	b(φa	b(φa	PROPN
ejpam-2623	315	9	,	,	PUNCT
ejpam-2623	315	10	b(z	b(z	NOUN
ejpam-2623	315	11	)	)	PUNCT
ejpam-2623	315	12	)	)	PUNCT
ejpam-2623	315	13	follows	follow	VERB
ejpam-2623	315	14	from	from	ADP
ejpam-2623	315	15	proposition	proposition	NOUN
ejpam-2623	315	16	1	1	NUM
ejpam-2623	315	17	.	.	NOUN
ejpam-2623	316	1	•	•	INTJ
ejpam-2623	316	2	let	let	VERB
ejpam-2623	316	3	z	z	NOUN
ejpam-2623	316	4	∈	∈	PROPN
ejpam-2623	316	5	fq	fq	PROPN
ejpam-2623	316	6	and	and	CCONJ
ejpam-2623	316	7	z′	z′	NUM
ejpam-2623	316	8	∈	∈	PROPN
ejpam-2623	316	9	fq	fq	NOUN
ejpam-2623	316	10	such	such	ADJ
ejpam-2623	316	11	that	that	SCONJ
ejpam-2623	316	12	φa	φa	ADP
ejpam-2623	316	13	,	,	PUNCT
ejpam-2623	316	14	b(z	b(z	NOUN
ejpam-2623	316	15	′	′	NOUN
ejpam-2623	316	16	)	)	PUNCT
ejpam-2623	316	17	=	=	SYM
ejpam-2623	317	1	φa	φa	ADP
ejpam-2623	317	2	,	,	PUNCT
ejpam-2623	317	3	b(z	b(z	NOUN
ejpam-2623	317	4	)	)	PUNCT
ejpam-2623	317	5	.	.	PUNCT
ejpam-2623	318	1	define	define	VERB
ejpam-2623	318	2	,	,	PUNCT
ejpam-2623	318	3	as	as	ADP
ejpam-2623	318	4	in	in	ADP
ejpam-2623	318	5	the	the	DET
ejpam-2623	318	6	proof	proof	NOUN
ejpam-2623	318	7	of	of	ADP
ejpam-2623	318	8	theorem	theorem	NOUN
ejpam-2623	318	9	1	1	NUM
ejpam-2623	318	10	and	and	CCONJ
ejpam-2623	318	11	in	in	ADP
ejpam-2623	318	12	proposition	proposition	NOUN
ejpam-2623	318	13	2	2	NUM
ejpam-2623	318	14	,	,	PUNCT
ejpam-2623	318	15	the	the	DET
ejpam-2623	318	16	following	follow	VERB
ejpam-2623	318	17	elements	element	NOUN
ejpam-2623	318	18	:	:	PUNCT
ejpam-2623	318	19	–	–	PUNCT
ejpam-2623	318	20	for	for	ADP
ejpam-2623	318	21	z	z	NOUN
ejpam-2623	318	22	:	:	PUNCT
ejpam-2623	318	23	u	u	NOUN
ejpam-2623	318	24	,	,	PUNCT
ejpam-2623	318	25	v	v	NOUN
ejpam-2623	318	26	,	,	PUNCT
ejpam-2623	318	27	x	x	NOUN
ejpam-2623	318	28	,	,	PUNCT
ejpam-2623	318	29	y	y	PROPN
ejpam-2623	318	30	,	,	PUNCT
ejpam-2623	318	31	x	x	PROPN
ejpam-2623	318	32	,	,	PUNCT
ejpam-2623	318	33	y	y	PROPN
ejpam-2623	318	34	;	;	PUNCT
ejpam-2623	318	35	–	–	PUNCT
ejpam-2623	318	36	for	for	ADP
ejpam-2623	318	37	z1	z1	NOUN
ejpam-2623	318	38	=	=	SYM
ejpam-2623	318	39	−z	−z	NOUN
ejpam-2623	318	40	:	:	PUNCT
ejpam-2623	318	41	u1	u1	NOUN
ejpam-2623	318	42	,	,	PUNCT
ejpam-2623	318	43	v1	v1	PROPN
ejpam-2623	318	44	,	,	PUNCT
ejpam-2623	318	45	x1	x1	PROPN
ejpam-2623	318	46	,	,	PUNCT
ejpam-2623	318	47	y1	y1	PROPN
ejpam-2623	318	48	,	,	PUNCT
ejpam-2623	318	49	x1	x1	PROPN
ejpam-2623	318	50	=	=	SYM
ejpam-2623	318	51	x	x	X
ejpam-2623	318	52	,	,	PUNCT
ejpam-2623	318	53	y1	y1	INTJ
ejpam-2623	318	54	=	=	SYM
ejpam-2623	318	55	y	y	PROPN
ejpam-2623	318	56	;	;	PUNCT
ejpam-2623	318	57	–	–	PUNCT
ejpam-2623	318	58	for	for	ADP
ejpam-2623	318	59	z′	z′	NUM
ejpam-2623	318	60	:	:	PUNCT
ejpam-2623	318	61	u′	u′	PROPN
ejpam-2623	318	62	,	,	PUNCT
ejpam-2623	318	63	v′	v′	PROPN
ejpam-2623	318	64	,	,	PUNCT
ejpam-2623	318	65	x	x	SYM
ejpam-2623	318	66	′	′	NUM
ejpam-2623	318	67	,	,	PUNCT
ejpam-2623	318	68	y	y	PROPN
ejpam-2623	318	69	′	′	NOUN
ejpam-2623	318	70	,	,	PUNCT
ejpam-2623	318	71	x′	x′	PROPN
ejpam-2623	319	1	=	=	SYM
ejpam-2623	319	2	x	x	NOUN
ejpam-2623	319	3	,	,	PUNCT
ejpam-2623	319	4	y′	y′	X
ejpam-2623	319	5	=	=	PUNCT
ejpam-2623	319	6	y.	y.	NOUN
ejpam-2623	319	7	by	by	ADP
ejpam-2623	319	8	the	the	DET
ejpam-2623	319	9	previous	previous	ADJ
ejpam-2623	319	10	proposition	proposition	NOUN
ejpam-2623	319	11	and	and	CCONJ
ejpam-2623	319	12	since	since	SCONJ
ejpam-2623	319	13	x	x	X
ejpam-2623	319	14	=	=	PUNCT
ejpam-2623	319	15	x′	x′	X
ejpam-2623	319	16	=	=	SYM
ejpam-2623	319	17	x1	x1	PROPN
ejpam-2623	319	18	,	,	PUNCT
ejpam-2623	319	19	y	y	PROPN
ejpam-2623	319	20	=	=	SYM
ejpam-2623	319	21	y′	y′	NOUN
ejpam-2623	319	22	=	=	SYM
ejpam-2623	319	23	y1	y1	PROPN
ejpam-2623	319	24	,	,	PUNCT
ejpam-2623	319	25	we	we	PRON
ejpam-2623	319	26	have	have	VERB
ejpam-2623	319	27	η	η	NOUN
ejpam-2623	319	28	=	=	NOUN
ejpam-2623	319	29	η′	η′	NOUN
ejpam-2623	319	30	=	=	SYM
ejpam-2623	319	31	η1	η1	NOUN
ejpam-2623	319	32	.	.	PUNCT
ejpam-2623	320	1	so	so	ADV
ejpam-2623	320	2	x	x	X
ejpam-2623	320	3	,	,	PUNCT
ejpam-2623	320	4	as	as	ADV
ejpam-2623	320	5	well	well	ADV
ejpam-2623	320	6	as	as	ADP
ejpam-2623	320	7	x1	x1	NUM
ejpam-2623	320	8	and	and	CCONJ
ejpam-2623	320	9	x	x	SYM
ejpam-2623	320	10	′	′	NOUN
ejpam-2623	320	11	are	be	AUX
ejpam-2623	320	12	solutions	solution	NOUN
ejpam-2623	320	13	of	of	ADP
ejpam-2623	320	14	the	the	DET
ejpam-2623	320	15	equation	equation	NOUN
ejpam-2623	320	16	f	f	PROPN
ejpam-2623	320	17	2	2	NUM
ejpam-2623	321	1	+	+	CCONJ
ejpam-2623	321	2	f	f	X
ejpam-2623	321	3	(	(	PUNCT
ejpam-2623	321	4	2−	2−	NUM
ejpam-2623	321	5	1	1	NUM
ejpam-2623	321	6	ηα2	ηα2	NOUN
ejpam-2623	321	7	)	)	PUNCT
ejpam-2623	322	1	+	+	CCONJ
ejpam-2623	322	2	1	1	NUM
ejpam-2623	322	3	=	=	SYM
ejpam-2623	322	4	0	0	NUM
ejpam-2623	322	5	.	.	PUNCT
ejpam-2623	323	1	since	since	SCONJ
ejpam-2623	323	2	x	x	PROPN
ejpam-2623	323	3	=	=	SYM
ejpam-2623	323	4	1	1	NUM
ejpam-2623	323	5	/	/	SYM
ejpam-2623	323	6	x1	x1	PROPN
ejpam-2623	323	7	then	then	ADV
ejpam-2623	323	8	x	x	X
ejpam-2623	323	9	6=	6=	NUM
ejpam-2623	323	10	x1	x1	PROPN
ejpam-2623	323	11	.	.	PUNCT
ejpam-2623	324	1	in	in	ADP
ejpam-2623	324	2	fact	fact	NOUN
ejpam-2623	324	3	x	x	X
ejpam-2623	324	4	=	=	SYM
ejpam-2623	324	5	x1	x1	PROPN
ejpam-2623	324	6	implies	imply	VERB
ejpam-2623	324	7	that	that	SCONJ
ejpam-2623	324	8	x2	x2	PRON
ejpam-2623	324	9	=	=	PUNCT
ejpam-2623	325	1	1⇒	1⇒	NUM
ejpam-2623	325	2	x	x	X
ejpam-2623	326	1	=	=	PUNCT
ejpam-2623	326	2	±1⇒	±1⇒	ADJ
ejpam-2623	326	3	χ(v)u	χ(v)u	PROPN
ejpam-2623	326	4	=	=	PUNCT
ejpam-2623	326	5	±1	±1	VERB
ejpam-2623	326	6	;	;	PUNCT
ejpam-2623	326	7	thus	thus	ADV
ejpam-2623	326	8	u	u	X
ejpam-2623	326	9	=	=	VERB
ejpam-2623	326	10	±1	±1	ADJ
ejpam-2623	326	11	and	and	CCONJ
ejpam-2623	326	12	1−z	1−z	NUM
ejpam-2623	326	13	1+z	1+z	NUM
ejpam-2623	326	14	=	=	SYM
ejpam-2623	326	15	±1	±1	NOUN
ejpam-2623	326	16	,	,	PUNCT
ejpam-2623	326	17	which	which	PRON
ejpam-2623	326	18	is	be	AUX
ejpam-2623	326	19	impossible	impossible	ADJ
ejpam-2623	326	20	if	if	SCONJ
ejpam-2623	326	21	z	z	NOUN
ejpam-2623	326	22	6=	6=	ADP
ejpam-2623	326	23	0	0	NUM
ejpam-2623	326	24	.	.	PUNCT
ejpam-2623	327	1	now	now	ADV
ejpam-2623	327	2	let	let	VERB
ejpam-2623	327	3	us	we	PRON
ejpam-2623	327	4	discuss	discuss	VERB
ejpam-2623	327	5	the	the	DET
ejpam-2623	327	6	following	follow	VERB
ejpam-2623	327	7	cases	case	NOUN
ejpam-2623	327	8	.	.	PUNCT
ejpam-2623	328	1	–	–	PUNCT
ejpam-2623	328	2	if	if	SCONJ
ejpam-2623	328	3	x	x	PRON
ejpam-2623	328	4	′	′	NOUN
ejpam-2623	328	5	=	=	PUNCT
ejpam-2623	329	1	x	x	X
ejpam-2623	329	2	:	:	PUNCT
ejpam-2623	329	3	let	let	VERB
ejpam-2623	329	4	us	we	PRON
ejpam-2623	329	5	prove	prove	VERB
ejpam-2623	329	6	that	that	SCONJ
ejpam-2623	329	7	χ(v	χ(v	NOUN
ejpam-2623	329	8	)	)	PUNCT
ejpam-2623	329	9	=	=	SYM
ejpam-2623	329	10	χ(v′	χ(v′	PROPN
ejpam-2623	329	11	)	)	PUNCT
ejpam-2623	329	12	,	,	PUNCT
ejpam-2623	329	13	u′	u′	PROPN
ejpam-2623	329	14	=	=	SYM
ejpam-2623	329	15	u	u	NOUN
ejpam-2623	329	16	and	and	CCONJ
ejpam-2623	329	17	z′	z′	NUM
ejpam-2623	329	18	=	=	PUNCT
ejpam-2623	330	1	z.	z.	PROPN
ejpam-2623	330	2	now	now	ADV
ejpam-2623	330	3	we	we	PRON
ejpam-2623	330	4	have	have	VERB
ejpam-2623	330	5	x	x	NOUN
ejpam-2623	330	6	=	=	SYM
ejpam-2623	330	7	(	(	PUNCT
ejpam-2623	330	8	1	1	NUM
ejpam-2623	330	9	+	+	NOUN
ejpam-2623	330	10	x)(bx	x)(bx	X
ejpam-2623	330	11	−	−	PROPN
ejpam-2623	330	12	α2(1	α2(1	NOUN
ejpam-2623	330	13	+	+	NOUN
ejpam-2623	330	14	x)2	x)2	NOUN
ejpam-2623	330	15	)	)	PUNCT
ejpam-2623	330	16	bαy	bαy	ADV
ejpam-2623	331	1	=	=	PRON
ejpam-2623	331	2	(	(	PUNCT
ejpam-2623	331	3	1	1	NUM
ejpam-2623	331	4	+	+	NOUN
ejpam-2623	331	5	x)(bx	x)(bx	X
ejpam-2623	331	6	−	−	PROPN
ejpam-2623	331	7	α2(1	α2(1	NOUN
ejpam-2623	331	8	+	+	NOUN
ejpam-2623	331	9	x)2)χ(v	x)2)χ(v	NOUN
ejpam-2623	331	10	)	)	PUNCT
ejpam-2623	331	11	bαχ(c2u2	bαχ(c2u2	NOUN
ejpam-2623	331	12	−	−	NOUN
ejpam-2623	331	13	1	1	X
ejpam-2623	331	14	)	)	PUNCT
ejpam-2623	331	15	√	√	ADP
ejpam-2623	331	16	χ(v)v	χ(v)v	PROPN
ejpam-2623	331	17	;	;	PUNCT
ejpam-2623	331	18	but	but	CCONJ
ejpam-2623	331	19	u	u	X
ejpam-2623	331	20	=	=	PROPN
ejpam-2623	331	21	χ(v)x	χ(v)x	PROPN
ejpam-2623	332	1	so	so	ADV
ejpam-2623	332	2	x	x	SYM
ejpam-2623	332	3	=	=	SYM
ejpam-2623	332	4	(	(	PUNCT
ejpam-2623	332	5	1	1	NUM
ejpam-2623	333	1	+	+	NOUN
ejpam-2623	333	2	x)(bx	x)(bx	X
ejpam-2623	333	3	−	−	PROPN
ejpam-2623	333	4	α2(1	α2(1	NOUN
ejpam-2623	333	5	+	+	NOUN
ejpam-2623	333	6	x)2)χ(v	x)2)χ(v	NOUN
ejpam-2623	333	7	)	)	PUNCT
ejpam-2623	334	1	bαχ(c2x2	bαχ(c2x2	VERB
ejpam-2623	335	1	−	−	NOUN
ejpam-2623	335	2	1	1	X
ejpam-2623	335	3	)	)	PUNCT
ejpam-2623	335	4	√	√	ADP
ejpam-2623	335	5	χ(v)v	χ(v)v	PROPN
ejpam-2623	335	6	and	and	CCONJ
ejpam-2623	335	7	thus	thus	ADV
ejpam-2623	335	8	χ(v	χ(v	NOUN
ejpam-2623	335	9	)	)	PUNCT
ejpam-2623	336	1	=	=	SYM
ejpam-2623	337	1	χ	χ	X
ejpam-2623	337	2	(	(	PUNCT
ejpam-2623	337	3	bα(1	bα(1	PROPN
ejpam-2623	337	4	+	+	NOUN
ejpam-2623	337	5	x)(bx	x)(bx	X
ejpam-2623	337	6	−	−	PROPN
ejpam-2623	337	7	α2(1	α2(1	NOUN
ejpam-2623	337	8	+	+	NOUN
ejpam-2623	337	9	x)2)(c2x2	x)2)(c2x2	PROPN
ejpam-2623	337	10	−	−	NOUN
ejpam-2623	337	11	1	1	NUM
ejpam-2623	337	12	)	)	PUNCT
ejpam-2623	337	13	)	)	PUNCT
ejpam-2623	337	14	.	.	PUNCT
ejpam-2623	338	1	similarly	similarly	ADV
ejpam-2623	338	2	we	we	PRON
ejpam-2623	338	3	have	have	AUX
ejpam-2623	338	4	χ(v′	χ(v′	VERB
ejpam-2623	338	5	)	)	PUNCT
ejpam-2623	339	1	=	=	SYM
ejpam-2623	340	1	χ	χ	X
ejpam-2623	340	2	(	(	PUNCT
ejpam-2623	340	3	bα(1	bα(1	PROPN
ejpam-2623	340	4	+	+	PROPN
ejpam-2623	340	5	x	x	PROPN
ejpam-2623	340	6	′)(bx	′)(bx	PROPN
ejpam-2623	340	7	′	′	NOUN
ejpam-2623	340	8	−	−	PROPN
ejpam-2623	340	9	α2(1	α2(1	NOUN
ejpam-2623	340	10	+	+	NOUN
ejpam-2623	340	11	x	x	SYM
ejpam-2623	340	12	′)2)(c2x	′)2)(c2x	NOUN
ejpam-2623	340	13	′2	′2	X
ejpam-2623	340	14	−	−	PROPN
ejpam-2623	340	15	1	1	NUM
ejpam-2623	340	16	)	)	PUNCT
ejpam-2623	340	17	)	)	PUNCT
ejpam-2623	340	18	.	.	PUNCT
ejpam-2623	341	1	since	since	SCONJ
ejpam-2623	341	2	x	x	PROPN
ejpam-2623	341	3	=	=	PUNCT
ejpam-2623	341	4	x′	x′	PROPN
ejpam-2623	341	5	and	and	CCONJ
ejpam-2623	341	6	x	x	X
ejpam-2623	341	7	=	=	SYM
ejpam-2623	341	8	x	x	SYM
ejpam-2623	341	9	′	′	NOUN
ejpam-2623	341	10	,	,	PUNCT
ejpam-2623	341	11	we	we	PRON
ejpam-2623	341	12	have	have	VERB
ejpam-2623	341	13	χ(v	χ(v	NOUN
ejpam-2623	341	14	)	)	PUNCT
ejpam-2623	342	1	=	=	SYM
ejpam-2623	342	2	χ(v′	χ(v′	PROPN
ejpam-2623	342	3	)	)	PUNCT
ejpam-2623	342	4	;	;	PUNCT
ejpam-2623	342	5	therefore	therefore	ADV
ejpam-2623	342	6	u′	u′	PROPN
ejpam-2623	342	7	=	=	SYM
ejpam-2623	342	8	u	u	NOUN
ejpam-2623	342	9	and	and	CCONJ
ejpam-2623	342	10	z′	z′	NUM
ejpam-2623	342	11	=	=	PUNCT
ejpam-2623	342	12	z.	z.	PROPN
ejpam-2623	342	13	n.	n.	PROPN
ejpam-2623	342	14	diarra	diarra	PROPN
ejpam-2623	342	15	,	,	PUNCT
ejpam-2623	342	16	d.	d.	PROPN
ejpam-2623	342	17	sow	sow	PROPN
ejpam-2623	342	18	,	,	PUNCT
ejpam-2623	342	19	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	342	20	.	.	PUNCT
ejpam-2623	342	21	khlil	khlil	PROPN
ejpam-2623	342	22	/	/	SYM
ejpam-2623	342	23	eur	eur	PROPN
ejpam-2623	342	24	.	.	PUNCT
ejpam-2623	343	1	j.	j.	PROPN
ejpam-2623	343	2	pure	pure	PROPN
ejpam-2623	343	3	appl	appl	PROPN
ejpam-2623	343	4	.	.	PROPN
ejpam-2623	343	5	math	math	PROPN
ejpam-2623	343	6	,	,	PUNCT
ejpam-2623	343	7	10	10	NUM
ejpam-2623	343	8	(	(	PUNCT
ejpam-2623	343	9	2	2	NUM
ejpam-2623	343	10	)	)	PUNCT
ejpam-2623	343	11	(	(	PUNCT
ejpam-2623	343	12	2017	2017	NUM
ejpam-2623	343	13	)	)	PUNCT
ejpam-2623	343	14	,	,	PUNCT
ejpam-2623	343	15	363	363	NUM
ejpam-2623	343	16	-	-	SYM
ejpam-2623	343	17	391	391	NUM
ejpam-2623	343	18	372	372	NUM
ejpam-2623	343	19	–	–	PUNCT
ejpam-2623	343	20	if	if	SCONJ
ejpam-2623	343	21	x	x	PRON
ejpam-2623	343	22	′	′	NUM
ejpam-2623	344	1	=	=	SYM
ejpam-2623	344	2	x1	x1	NUM
ejpam-2623	344	3	:	:	PUNCT
ejpam-2623	344	4	as	as	ADP
ejpam-2623	344	5	above	above	ADV
ejpam-2623	344	6	we	we	PRON
ejpam-2623	344	7	have	have	AUX
ejpam-2623	344	8	χ(v′	χ(v′	PROPN
ejpam-2623	344	9	)	)	PUNCT
ejpam-2623	344	10	=	=	SYM
ejpam-2623	344	11	χ(v1	χ(v1	ADJ
ejpam-2623	344	12	)	)	PUNCT
ejpam-2623	344	13	,	,	PUNCT
ejpam-2623	344	14	u	u	NOUN
ejpam-2623	344	15	′	′	NOUN
ejpam-2623	344	16	=	=	SYM
ejpam-2623	344	17	u1	u1	NOUN
ejpam-2623	344	18	and	and	CCONJ
ejpam-2623	344	19	z′	z′	NUM
ejpam-2623	344	20	=	=	SYM
ejpam-2623	344	21	z1	z1	PROPN
ejpam-2623	344	22	.	.	PUNCT
ejpam-2623	345	1	proposition	proposition	NOUN
ejpam-2623	345	2	4	4	NUM
ejpam-2623	345	3	.	.	PUNCT
ejpam-2623	346	1	let	let	VERB
ejpam-2623	346	2	(	(	PUNCT
ejpam-2623	346	3	x	x	NOUN
ejpam-2623	346	4	,	,	PUNCT
ejpam-2623	346	5	y	y	NOUN
ejpam-2623	346	6	)	)	PUNCT
ejpam-2623	346	7	∈	∈	PROPN
ejpam-2623	346	8	e(fq	e(fq	PROPN
ejpam-2623	346	9	)	)	PUNCT
ejpam-2623	346	10	.	.	PUNCT
ejpam-2623	347	1	if	if	SCONJ
ejpam-2623	347	2	x	x	PRON
ejpam-2623	347	3	−	−	PROPN
ejpam-2623	347	4	y	y	PROPN
ejpam-2623	347	5	6=	6=	ADP
ejpam-2623	347	6	0	0	NUM
ejpam-2623	347	7	and	and	CCONJ
ejpam-2623	347	8	1	1	NUM
ejpam-2623	347	9	−	−	NOUN
ejpam-2623	347	10	4α2η	4α2η	NOUN
ejpam-2623	347	11	is	be	AUX
ejpam-2623	347	12	a	a	DET
ejpam-2623	347	13	square	square	NOUN
ejpam-2623	347	14	,	,	PUNCT
ejpam-2623	347	15	with	with	ADP
ejpam-2623	347	16	η	η	PROPN
ejpam-2623	347	17	=	=	SYM
ejpam-2623	347	18	bx−	bx−	PROPN
ejpam-2623	347	19	ay	ay	PROPN
ejpam-2623	347	20	ab(x−	ab(x−	X
ejpam-2623	347	21	y	y	PROPN
ejpam-2623	347	22	)	)	PUNCT
ejpam-2623	347	23	,	,	PUNCT
ejpam-2623	347	24	there	there	PRON
ejpam-2623	347	25	exists	exist	VERB
ejpam-2623	347	26	z	z	PROPN
ejpam-2623	347	27	∈	∈	PROPN
ejpam-2623	347	28	fq	fq	NOUN
ejpam-2623	347	29	such	such	ADJ
ejpam-2623	347	30	that	that	SCONJ
ejpam-2623	347	31	φa	φa	ADP
ejpam-2623	347	32	,	,	PUNCT
ejpam-2623	347	33	b(z	b(z	NOUN
ejpam-2623	347	34	)	)	PUNCT
ejpam-2623	347	35	=	=	PUNCT
ejpam-2623	348	1	(	(	PUNCT
ejpam-2623	348	2	x	x	X
ejpam-2623	348	3	,	,	PUNCT
ejpam-2623	348	4	y	y	PROPN
ejpam-2623	348	5	)	)	PUNCT
ejpam-2623	348	6	.	.	PUNCT
ejpam-2623	349	1	proof	proof	NOUN
ejpam-2623	349	2	.	.	PUNCT
ejpam-2623	350	1	let	let	VERB
ejpam-2623	350	2	(	(	PUNCT
ejpam-2623	350	3	x	x	NOUN
ejpam-2623	350	4	,	,	PUNCT
ejpam-2623	350	5	y	y	NOUN
ejpam-2623	350	6	)	)	PUNCT
ejpam-2623	350	7	∈	∈	PROPN
ejpam-2623	350	8	e(fq	e(fq	PROPN
ejpam-2623	350	9	)	)	PUNCT
ejpam-2623	350	10	such	such	ADJ
ejpam-2623	350	11	that	that	SCONJ
ejpam-2623	350	12	x	x	X
ejpam-2623	350	13	−	−	PROPN
ejpam-2623	350	14	y	y	PROPN
ejpam-2623	350	15	6=	6=	ADP
ejpam-2623	350	16	0	0	NUM
ejpam-2623	350	17	and	and	CCONJ
ejpam-2623	350	18	1	1	NUM
ejpam-2623	350	19	−	−	NOUN
ejpam-2623	350	20	4α2η	4α2η	NOUN
ejpam-2623	350	21	is	be	AUX
ejpam-2623	350	22	a	a	DET
ejpam-2623	350	23	square	square	NOUN
ejpam-2623	350	24	,	,	PUNCT
ejpam-2623	350	25	where	where	SCONJ
ejpam-2623	350	26	η	η	PROPN
ejpam-2623	350	27	=	=	SYM
ejpam-2623	350	28	bx−	bx−	PROPN
ejpam-2623	350	29	ay	ay	PROPN
ejpam-2623	350	30	ab(x−	ab(x−	X
ejpam-2623	350	31	y	y	PROPN
ejpam-2623	350	32	)	)	PUNCT
ejpam-2623	350	33	.	.	PUNCT
ejpam-2623	351	1	the	the	DET
ejpam-2623	351	2	discriminant	discriminant	ADJ
ejpam-2623	351	3	δ	δ	PROPN
ejpam-2623	351	4	of	of	ADP
ejpam-2623	351	5	the	the	DET
ejpam-2623	351	6	equation	equation	NOUN
ejpam-2623	351	7	f	f	PROPN
ejpam-2623	351	8	2	2	NUM
ejpam-2623	351	9	+	+	CCONJ
ejpam-2623	351	10	f	f	X
ejpam-2623	351	11	(	(	PUNCT
ejpam-2623	351	12	2	2	NUM
ejpam-2623	351	13	−	−	NUM
ejpam-2623	351	14	1	1	NUM
ejpam-2623	351	15	ηα2	ηα2	NOUN
ejpam-2623	351	16	)	)	PUNCT
ejpam-2623	352	1	+	+	CCONJ
ejpam-2623	352	2	1	1	NUM
ejpam-2623	352	3	=	=	SYM
ejpam-2623	352	4	0	0	NUM
ejpam-2623	352	5	is	be	AUX
ejpam-2623	352	6	then	then	ADV
ejpam-2623	352	7	a	a	DET
ejpam-2623	352	8	square	square	NOUN
ejpam-2623	352	9	,	,	PUNCT
ejpam-2623	352	10	since	since	SCONJ
ejpam-2623	352	11	1	1	NUM
ejpam-2623	352	12	−	−	NOUN
ejpam-2623	352	13	4α2η	4α2η	NOUN
ejpam-2623	352	14	is	be	AUX
ejpam-2623	352	15	a	a	DET
ejpam-2623	352	16	square	square	NOUN
ejpam-2623	352	17	.	.	PUNCT
ejpam-2623	353	1	so	so	ADV
ejpam-2623	353	2	there	there	PRON
ejpam-2623	353	3	is	be	VERB
ejpam-2623	353	4	at	at	ADV
ejpam-2623	353	5	least	least	ADJ
ejpam-2623	353	6	one	one	NUM
ejpam-2623	353	7	solution	solution	NOUN
ejpam-2623	353	8	x	x	NOUN
ejpam-2623	353	9	=	=	PUNCT
ejpam-2623	353	10	−1	−1	NOUN
ejpam-2623	353	11	2(2	2(2	NUM
ejpam-2623	353	12	−	−	NOUN
ejpam-2623	353	13	1	1	NUM
ejpam-2623	353	14	ηα2	ηα2	NOUN
ejpam-2623	353	15	)	)	PUNCT
ejpam-2623	354	1	+	+	CCONJ
ejpam-2623	354	2	1	1	NUM
ejpam-2623	354	3	2ηα2	2ηα2	NUM
ejpam-2623	354	4	(	(	PUNCT
ejpam-2623	354	5	1−	1−	NUM
ejpam-2623	354	6	4α2η)(q+1)/4	4α2η)(q+1)/4	NUM
ejpam-2623	354	7	.	.	PUNCT
ejpam-2623	355	1	note	note	VERB
ejpam-2623	355	2	that	that	SCONJ
ejpam-2623	355	3	the	the	DET
ejpam-2623	355	4	two	two	NUM
ejpam-2623	355	5	quantities	quantity	NOUN
ejpam-2623	355	6	(	(	PUNCT
ejpam-2623	355	7	1	1	NUM
ejpam-2623	355	8	+	+	NOUN
ejpam-2623	355	9	x)(bx	x)(bx	X
ejpam-2623	355	10	−	−	PROPN
ejpam-2623	355	11	α2(1	α2(1	NOUN
ejpam-2623	355	12	+	+	NOUN
ejpam-2623	355	13	x)2	x)2	PROPN
ejpam-2623	355	14	)	)	PUNCT
ejpam-2623	355	15	αbx	αbx	NOUN
ejpam-2623	355	16	and	and	CCONJ
ejpam-2623	355	17	(	(	PUNCT
ejpam-2623	355	18	1	1	NUM
ejpam-2623	355	19	+	+	NOUN
ejpam-2623	355	20	x)(ax	x)(ax	NOUN
ejpam-2623	355	21	−	−	PROPN
ejpam-2623	355	22	α2(1	α2(1	NOUN
ejpam-2623	355	23	+	+	NOUN
ejpam-2623	355	24	x)2	x)2	PROPN
ejpam-2623	355	25	)	)	PUNCT
ejpam-2623	355	26	αay	αay	NOUN
ejpam-2623	355	27	are	be	AUX
ejpam-2623	355	28	the	the	DET
ejpam-2623	355	29	same	same	ADJ
ejpam-2623	355	30	.	.	PUNCT
ejpam-2623	356	1	in	in	ADP
ejpam-2623	356	2	fact	fact	NOUN
ejpam-2623	356	3	,	,	PUNCT
ejpam-2623	356	4	as	as	ADP
ejpam-2623	356	5	a	a	DET
ejpam-2623	356	6	solution	solution	NOUN
ejpam-2623	356	7	of	of	ADP
ejpam-2623	356	8	the	the	DET
ejpam-2623	356	9	previous	previous	ADJ
ejpam-2623	356	10	equation	equation	NOUN
ejpam-2623	356	11	,	,	PUNCT
ejpam-2623	356	12	x	x	PRON
ejpam-2623	356	13	verifies	verifie	NOUN
ejpam-2623	356	14	x2	x2	NOUN
ejpam-2623	357	1	=	=	PUNCT
ejpam-2623	357	2	−x(2−	−x(2−	NOUN
ejpam-2623	357	3	1	1	NUM
ejpam-2623	357	4	ηα2	ηα2	NOUN
ejpam-2623	357	5	)	)	PUNCT
ejpam-2623	357	6	−1	−1	NOUN
ejpam-2623	357	7	;	;	PUNCT
ejpam-2623	357	8	so	so	ADV
ejpam-2623	357	9	bx−α2(1+x)2	bx−α2(1+x)2	VERB
ejpam-2623	357	10	=	=	SYM
ejpam-2623	357	11	x(bη	x(bη	PROPN
ejpam-2623	358	1	−	−	NOUN
ejpam-2623	358	2	1	1	NUM
ejpam-2623	358	3	)	)	PUNCT
ejpam-2623	358	4	η	η	PROPN
ejpam-2623	358	5	and	and	CCONJ
ejpam-2623	358	6	ax−α2(1+x)2	ax−α2(1+x)2	NOUN
ejpam-2623	359	1	=	=	SYM
ejpam-2623	359	2	x(aη	x(aη	PROPN
ejpam-2623	359	3	−	−	NOUN
ejpam-2623	359	4	1	1	NUM
ejpam-2623	359	5	)	)	PUNCT
ejpam-2623	359	6	η	η	PROPN
ejpam-2623	359	7	.	.	PUNCT
ejpam-2623	360	1	thus	thus	ADV
ejpam-2623	360	2	,	,	PUNCT
ejpam-2623	360	3	we	we	PRON
ejpam-2623	360	4	have	have	VERB
ejpam-2623	360	5	bx	bx	VERB
ejpam-2623	360	6	−	−	PROPN
ejpam-2623	360	7	α2(1	α2(1	NOUN
ejpam-2623	360	8	+	+	NOUN
ejpam-2623	360	9	x)2	x)2	X
ejpam-2623	360	10	ax	ax	NOUN
ejpam-2623	360	11	−	−	PROPN
ejpam-2623	360	12	α2(1	α2(1	NOUN
ejpam-2623	360	13	+	+	NOUN
ejpam-2623	360	14	x)2	x)2	NOUN
ejpam-2623	360	15	=	=	SYM
ejpam-2623	360	16	1−	1−	NUM
ejpam-2623	360	17	bη	bη	VERB
ejpam-2623	360	18	1−	1−	NUM
ejpam-2623	360	19	aη	aη	INTJ
ejpam-2623	360	20	.	.	PUNCT
ejpam-2623	361	1	from	from	ADP
ejpam-2623	361	2	η	η	PROPN
ejpam-2623	361	3	=	=	SYM
ejpam-2623	361	4	bx−	bx−	PROPN
ejpam-2623	361	5	ay	ay	PROPN
ejpam-2623	361	6	ab(x−	ab(x−	X
ejpam-2623	361	7	y	y	PROPN
ejpam-2623	361	8	)	)	PUNCT
ejpam-2623	361	9	,	,	PUNCT
ejpam-2623	361	10	we	we	PRON
ejpam-2623	361	11	deduce	deduce	VERB
ejpam-2623	361	12	that	that	SCONJ
ejpam-2623	361	13	x	x	PUNCT
ejpam-2623	361	14	y	y	PROPN
ejpam-2623	361	15	=	=	PUNCT
ejpam-2623	361	16	a(1−	a(1−	NOUN
ejpam-2623	361	17	bη	bη	NOUN
ejpam-2623	361	18	)	)	PUNCT
ejpam-2623	361	19	b(1−	b(1−	PROPN
ejpam-2623	361	20	aη	aη	PROPN
ejpam-2623	361	21	)	)	PUNCT
ejpam-2623	361	22	;	;	PUNCT
ejpam-2623	361	23	so	so	ADV
ejpam-2623	361	24	a(bx	a(bx	PROPN
ejpam-2623	361	25	−	−	PROPN
ejpam-2623	361	26	α2(1	α2(1	NOUN
ejpam-2623	361	27	+	+	NOUN
ejpam-2623	361	28	x)2	x)2	PROPN
ejpam-2623	361	29	)	)	PUNCT
ejpam-2623	361	30	b(ax	b(ax	PROPN
ejpam-2623	361	31	−	−	PROPN
ejpam-2623	361	32	α2(1	α2(1	NOUN
ejpam-2623	361	33	+	+	NOUN
ejpam-2623	361	34	x)2	x)2	NOUN
ejpam-2623	361	35	)	)	PUNCT
ejpam-2623	361	36	=	=	PUNCT
ejpam-2623	362	1	x	x	PUNCT
ejpam-2623	362	2	y	y	PROPN
ejpam-2623	362	3	and	and	CCONJ
ejpam-2623	362	4	(	(	PUNCT
ejpam-2623	362	5	1	1	NUM
ejpam-2623	362	6	+	+	NOUN
ejpam-2623	362	7	x)(bx	x)(bx	X
ejpam-2623	362	8	−	−	PROPN
ejpam-2623	362	9	α2(1	α2(1	NOUN
ejpam-2623	362	10	+	+	NOUN
ejpam-2623	362	11	x)2	x)2	PROPN
ejpam-2623	362	12	)	)	PUNCT
ejpam-2623	362	13	αbx	αbx	NOUN
ejpam-2623	362	14	=	=	PUNCT
ejpam-2623	363	1	(	(	PUNCT
ejpam-2623	363	2	1	1	NUM
ejpam-2623	363	3	+	+	NOUN
ejpam-2623	363	4	x)(ax	x)(ax	NOUN
ejpam-2623	363	5	−	−	PROPN
ejpam-2623	363	6	α2(1	α2(1	NOUN
ejpam-2623	363	7	+	+	NOUN
ejpam-2623	363	8	x)2	x)2	PROPN
ejpam-2623	363	9	)	)	PUNCT
ejpam-2623	363	10	αay	αay	NOUN
ejpam-2623	363	11	.	.	PUNCT
ejpam-2623	364	1	now	now	ADV
ejpam-2623	364	2	we	we	PRON
ejpam-2623	364	3	define	define	VERB
ejpam-2623	364	4	y	y	PROPN
ejpam-2623	364	5	=	=	PUNCT
ejpam-2623	364	6	(	(	PUNCT
ejpam-2623	364	7	1	1	NUM
ejpam-2623	364	8	+	+	NOUN
ejpam-2623	364	9	x)(bx	x)(bx	X
ejpam-2623	364	10	−	−	PROPN
ejpam-2623	364	11	α2(1	α2(1	NOUN
ejpam-2623	364	12	+	+	NOUN
ejpam-2623	364	13	x)2	x)2	PROPN
ejpam-2623	364	14	)	)	PUNCT
ejpam-2623	364	15	αbx	αbx	NOUN
ejpam-2623	364	16	=	=	PUNCT
ejpam-2623	365	1	(	(	PUNCT
ejpam-2623	365	2	1	1	NUM
ejpam-2623	365	3	+	+	NOUN
ejpam-2623	365	4	x)(ax	x)(ax	NOUN
ejpam-2623	365	5	−	−	PROPN
ejpam-2623	365	6	α2(1	α2(1	NOUN
ejpam-2623	365	7	+	+	NOUN
ejpam-2623	365	8	x)2	x)2	PROPN
ejpam-2623	365	9	)	)	PUNCT
ejpam-2623	365	10	αay	αay	NOUN
ejpam-2623	365	11	.	.	PUNCT
ejpam-2623	366	1	(	(	PUNCT
ejpam-2623	366	2	i	i	NOUN
ejpam-2623	366	3	)	)	PUNCT
ejpam-2623	366	4	first	first	ADV
ejpam-2623	366	5	,	,	PUNCT
ejpam-2623	366	6	we	we	PRON
ejpam-2623	366	7	verify	verify	VERB
ejpam-2623	366	8	that	that	SCONJ
ejpam-2623	366	9	y	y	PROPN
ejpam-2623	366	10	2	2	NUM
ejpam-2623	366	11	=	=	SYM
ejpam-2623	366	12	−x5	−x5	PROPN
ejpam-2623	366	13	+	+	CCONJ
ejpam-2623	366	14	(	(	PUNCT
ejpam-2623	366	15	2	2	NUM
ejpam-2623	366	16	−	−	PROPN
ejpam-2623	366	17	a)x3	a)x3	PROPN
ejpam-2623	366	18	−	−	PROPN
ejpam-2623	366	19	x.	x.	NOUN
ejpam-2623	366	20	in	in	ADP
ejpam-2623	366	21	fact	fact	NOUN
ejpam-2623	366	22	,	,	PUNCT
ejpam-2623	366	23	x	x	PUNCT
ejpam-2623	366	24	and	and	CCONJ
ejpam-2623	366	25	y	y	PROPN
ejpam-2623	366	26	are	be	AUX
ejpam-2623	366	27	such	such	ADJ
ejpam-2623	366	28	that	that	SCONJ
ejpam-2623	366	29	bx2	bx2	NOUN
ejpam-2623	366	30	−	−	PROPN
ejpam-2623	366	31	1	1	NUM
ejpam-2623	366	32	ay2	ay2	NOUN
ejpam-2623	366	33	−	−	NOUN
ejpam-2623	366	34	1	1	NUM
ejpam-2623	366	35	=	=	SYM
ejpam-2623	366	36	x	x	SYM
ejpam-2623	366	37	y	y	NOUN
ejpam-2623	366	38	;	;	PUNCT
ejpam-2623	366	39	that	that	PRON
ejpam-2623	366	40	is	be	AUX
ejpam-2623	366	41	a	a	DET
ejpam-2623	366	42	b	b	PROPN
ejpam-2623	366	43	(	(	PUNCT
ejpam-2623	366	44	(	(	PUNCT
ejpam-2623	366	45	1	1	NUM
ejpam-2623	366	46	+	+	NOUN
ejpam-2623	366	47	x)2(bx	x)2(bx	NOUN
ejpam-2623	366	48	−	−	PROPN
ejpam-2623	366	49	α2(1	α2(1	NOUN
ejpam-2623	366	50	+	+	NOUN
ejpam-2623	366	51	x)2)2	x)2)2	PROPN
ejpam-2623	366	52	−	−	NOUN
ejpam-2623	366	53	bα2y	bα2y	NOUN
ejpam-2623	366	54	2	2	NUM
ejpam-2623	366	55	(	(	PUNCT
ejpam-2623	366	56	1	1	NUM
ejpam-2623	366	57	+	+	NOUN
ejpam-2623	366	58	x)2(ax	x)2(ax	PROPN
ejpam-2623	366	59	−	−	PROPN
ejpam-2623	366	60	α2(1	α2(1	NOUN
ejpam-2623	366	61	+	+	NOUN
ejpam-2623	366	62	x)2)2	x)2)2	PROPN
ejpam-2623	366	63	−	−	X
ejpam-2623	367	1	aα2y	aα2y	NOUN
ejpam-2623	367	2	2	2	NUM
ejpam-2623	367	3	)	)	PUNCT
ejpam-2623	367	4	=	=	PUNCT
ejpam-2623	368	1	a	a	DET
ejpam-2623	368	2	b	b	PROPN
ejpam-2623	368	3	(	(	PUNCT
ejpam-2623	368	4	bx	bx	NOUN
ejpam-2623	368	5	−	−	PROPN
ejpam-2623	368	6	α2(1	α2(1	NOUN
ejpam-2623	368	7	+	+	NOUN
ejpam-2623	368	8	x)2	x)2	X
ejpam-2623	368	9	ax	ax	NOUN
ejpam-2623	368	10	−	−	PROPN
ejpam-2623	368	11	α2(1	α2(1	NOUN
ejpam-2623	368	12	+	+	NOUN
ejpam-2623	368	13	x)2	x)2	NOUN
ejpam-2623	368	14	)	)	PUNCT
ejpam-2623	368	15	.	.	PUNCT
ejpam-2623	369	1	we	we	PRON
ejpam-2623	369	2	have	have	VERB
ejpam-2623	369	3	(	(	PUNCT
ejpam-2623	369	4	1	1	NUM
ejpam-2623	369	5	+	+	NOUN
ejpam-2623	369	6	x)2(bx	x)2(bx	PROPN
ejpam-2623	369	7	−α2(1	−α2(1	NUM
ejpam-2623	370	1	+	+	NOUN
ejpam-2623	370	2	x)2(ax−α2(1	x)2(ax−α2(1	NOUN
ejpam-2623	370	3	+	+	ADJ
ejpam-2623	370	4	x)2)2−aα2y	x)2)2−aα2y	PROPN
ejpam-2623	370	5	2(bx	2(bx	NUM
ejpam-2623	370	6	−α2(1	−α2(1	NUM
ejpam-2623	370	7	+	+	NOUN
ejpam-2623	370	8	x)2	x)2	NOUN
ejpam-2623	370	9	)	)	PUNCT
ejpam-2623	370	10	=	=	PUNCT
ejpam-2623	371	1	(	(	PUNCT
ejpam-2623	371	2	1	1	NUM
ejpam-2623	371	3	+	+	NOUN
ejpam-2623	371	4	x)2(ax	x)2(ax	PROPN
ejpam-2623	371	5	−	−	PROPN
ejpam-2623	372	1	α2(1	α2(1	NOUN
ejpam-2623	372	2	+	+	NOUN
ejpam-2623	372	3	x)2(bx−	x)2(bx−	PROPN
ejpam-2623	372	4	α2(1	α2(1	NOUN
ejpam-2623	372	5	+	+	NOUN
ejpam-2623	372	6	x)2)2	x)2)2	PROPN
ejpam-2623	372	7	−	−	NOUN
ejpam-2623	372	8	bα2y	bα2y	NOUN
ejpam-2623	372	9	2(ax	2(ax	NUM
ejpam-2623	372	10	−	−	NOUN
ejpam-2623	372	11	α2(1	α2(1	NOUN
ejpam-2623	372	12	+	+	NOUN
ejpam-2623	372	13	x)2	x)2	NOUN
ejpam-2623	372	14	)	)	PUNCT
ejpam-2623	372	15	.	.	PUNCT
ejpam-2623	373	1	⇒	⇒	PROPN
ejpam-2623	373	2	α4y	α4y	PROPN
ejpam-2623	373	3	2(1	2(1	NUM
ejpam-2623	373	4	+	+	NOUN
ejpam-2623	373	5	x)2(b−a	x)2(b−a	X
ejpam-2623	373	6	)	)	PUNCT
ejpam-2623	374	1	=	=	PUNCT
ejpam-2623	374	2	x(1	x(1	PROPN
ejpam-2623	375	1	+	+	PROPN
ejpam-2623	375	2	x)2(a−	x)2(a−	PROPN
ejpam-2623	375	3	b)(bx−α2(1	b)(bx−α2(1	X
ejpam-2623	376	1	+	+	ADJ
ejpam-2623	376	2	x)2)(ax−α2(1	x)2)(ax−α2(1	X
ejpam-2623	376	3	+	+	NOUN
ejpam-2623	376	4	x)2	x)2	NOUN
ejpam-2623	376	5	)	)	PUNCT
ejpam-2623	376	6	.	.	PUNCT
ejpam-2623	377	1	(	(	PUNCT
ejpam-2623	377	2	*	*	PUNCT
ejpam-2623	377	3	)	)	PUNCT
ejpam-2623	377	4	but	but	CCONJ
ejpam-2623	377	5	recall	recall	VERB
ejpam-2623	377	6	from	from	ADP
ejpam-2623	377	7	the	the	DET
ejpam-2623	377	8	proof	proof	NOUN
ejpam-2623	377	9	of	of	ADP
ejpam-2623	377	10	theorem	theorem	NOUN
ejpam-2623	377	11	2	2	NUM
ejpam-2623	377	12	that	that	PRON
ejpam-2623	377	13	(	(	PUNCT
ejpam-2623	377	14	bx	bx	NOUN
ejpam-2623	377	15	−α2(1	−α2(1	SYM
ejpam-2623	377	16	+	+	NOUN
ejpam-2623	377	17	x)2)(ax	x)2)(ax	PROPN
ejpam-2623	377	18	−α2(1	−α2(1	PUNCT
ejpam-2623	377	19	+	+	NOUN
ejpam-2623	377	20	x)2	x)2	NOUN
ejpam-2623	377	21	)	)	PUNCT
ejpam-2623	377	22	=	=	SYM
ejpam-2623	378	1	α4(x4	α4(x4	ADP
ejpam-2623	378	2	−	−	PROPN
ejpam-2623	378	3	(	(	PUNCT
ejpam-2623	378	4	2−a)x2	2−a)x2	NUM
ejpam-2623	378	5	+	+	NOUN
ejpam-2623	378	6	1	1	NUM
ejpam-2623	378	7	)	)	PUNCT
ejpam-2623	378	8	.	.	PUNCT
ejpam-2623	379	1	so	so	ADV
ejpam-2623	379	2	(	(	PUNCT
ejpam-2623	379	3	*	*	NOUN
ejpam-2623	379	4	)	)	PUNCT
ejpam-2623	379	5	yields	yield	NOUN
ejpam-2623	379	6	to	to	PART
ejpam-2623	379	7	:	:	PUNCT
ejpam-2623	379	8	α4y	α4y	NUM
ejpam-2623	379	9	2(1	2(1	NUM
ejpam-2623	380	1	+	+	NOUN
ejpam-2623	380	2	x)2(b−	x)2(b−	PROPN
ejpam-2623	380	3	a	a	X
ejpam-2623	380	4	)	)	PUNCT
ejpam-2623	380	5	=	=	SYM
ejpam-2623	380	6	α4x(1	α4x(1	PROPN
ejpam-2623	380	7	+	+	PROPN
ejpam-2623	380	8	x)2(a−	x)2(a−	PROPN
ejpam-2623	380	9	b)(x4	b)(x4	NOUN
ejpam-2623	380	10	−	−	PROPN
ejpam-2623	380	11	(	(	PUNCT
ejpam-2623	380	12	2−a)x2	2−a)x2	NUM
ejpam-2623	380	13	+	+	NOUN
ejpam-2623	380	14	1	1	NUM
ejpam-2623	380	15	)	)	PUNCT
ejpam-2623	380	16	.	.	PUNCT
ejpam-2623	381	1	finally	finally	ADV
ejpam-2623	381	2	we	we	PRON
ejpam-2623	381	3	have	have	VERB
ejpam-2623	381	4	y	y	PROPN
ejpam-2623	381	5	2	2	NUM
ejpam-2623	381	6	=	=	SYM
ejpam-2623	381	7	−x5	−x5	PROPN
ejpam-2623	381	8	+	+	CCONJ
ejpam-2623	381	9	(	(	PUNCT
ejpam-2623	381	10	2−a)x3	2−a)x3	NUM
ejpam-2623	381	11	−x	−x	NOUN
ejpam-2623	381	12	as	as	SCONJ
ejpam-2623	381	13	desired	desire	VERB
ejpam-2623	381	14	.	.	PUNCT
ejpam-2623	382	1	(	(	PUNCT
ejpam-2623	382	2	ii	ii	NOUN
ejpam-2623	382	3	)	)	PUNCT
ejpam-2623	382	4	define	define	VERB
ejpam-2623	382	5	β	β	NOUN
ejpam-2623	382	6	=	=	SYM
ejpam-2623	382	7	χ	χ	X
ejpam-2623	382	8	(	(	PUNCT
ejpam-2623	382	9	y	y	PROPN
ejpam-2623	382	10	(	(	PUNCT
ejpam-2623	382	11	c2x2	c2x2	INTJ
ejpam-2623	382	12	−	−	NOUN
ejpam-2623	382	13	1	1	NUM
ejpam-2623	382	14	)	)	PUNCT
ejpam-2623	382	15	)	)	PUNCT
ejpam-2623	382	16	and	and	CCONJ
ejpam-2623	382	17	u	u	X
ejpam-2623	382	18	=	=	NOUN
ejpam-2623	382	19	βx	βx	PROPN
ejpam-2623	382	20	.	.	PUNCT
ejpam-2623	383	1	(	(	PUNCT
ejpam-2623	383	2	iii	iii	NOUN
ejpam-2623	383	3	)	)	PUNCT
ejpam-2623	383	4	define	define	VERB
ejpam-2623	383	5	v	v	NOUN
ejpam-2623	383	6	=	=	SYM
ejpam-2623	383	7	−u5	−u5	NOUN
ejpam-2623	383	8	+	+	CCONJ
ejpam-2623	383	9	(	(	PUNCT
ejpam-2623	383	10	c2	c2	PROPN
ejpam-2623	383	11	+	+	CCONJ
ejpam-2623	383	12	1	1	NUM
ejpam-2623	383	13	/	/	SYM
ejpam-2623	383	14	c2)u3	c2)u3	NOUN
ejpam-2623	383	15	−	−	PROPN
ejpam-2623	383	16	u.	u.	ADV
ejpam-2623	383	17	now	now	ADV
ejpam-2623	383	18	,	,	PUNCT
ejpam-2623	383	19	we	we	PRON
ejpam-2623	383	20	have	have	VERB
ejpam-2623	383	21	v	v	NOUN
ejpam-2623	383	22	=	=	SYM
ejpam-2623	383	23	β	β	X
ejpam-2623	383	24	(	(	PUNCT
ejpam-2623	383	25	−x5	−x5	PROPN
ejpam-2623	383	26	+	+	CCONJ
ejpam-2623	383	27	(	(	PUNCT
ejpam-2623	383	28	c2	c2	PROPN
ejpam-2623	383	29	+	+	CCONJ
ejpam-2623	383	30	1	1	NUM
ejpam-2623	383	31	/	/	SYM
ejpam-2623	383	32	c2)x3	c2)x3	ADJ
ejpam-2623	383	33	−x	−x	NOUN
ejpam-2623	383	34	)	)	PUNCT
ejpam-2623	383	35	.	.	PUNCT
ejpam-2623	384	1	since	since	SCONJ
ejpam-2623	384	2	y	y	PROPN
ejpam-2623	384	3	2	2	NUM
ejpam-2623	384	4	=	=	NOUN
ejpam-2623	384	5	−x5+(2−a)x3−x	−x5+(2−a)x3−x	NOUN
ejpam-2623	384	6	and	and	CCONJ
ejpam-2623	384	7	q	q	PROPN
ejpam-2623	384	8	≡	≡	PROPN
ejpam-2623	384	9	3	3	NUM
ejpam-2623	384	10	mod	mod	NOUN
ejpam-2623	384	11	4	4	NUM
ejpam-2623	384	12	,	,	PUNCT
ejpam-2623	384	13	then	then	ADV
ejpam-2623	384	14	v	v	NOUN
ejpam-2623	384	15	=	=	SYM
ejpam-2623	384	16	βy	βy	ADJ
ejpam-2623	384	17	2	2	NUM
ejpam-2623	384	18	and	and	CCONJ
ejpam-2623	384	19	χ(v	χ(v	NOUN
ejpam-2623	384	20	)	)	PUNCT
ejpam-2623	384	21	=	=	SYM
ejpam-2623	384	22	χ(β	χ(β	NOUN
ejpam-2623	384	23	)	)	PUNCT
ejpam-2623	384	24	=	=	PUNCT
ejpam-2623	385	1	β	β	X
ejpam-2623	385	2	.	.	PUNCT
ejpam-2623	386	1	from	from	ADP
ejpam-2623	386	2	u	u	NOUN
ejpam-2623	386	3	=	=	X
ejpam-2623	386	4	βx	βx	PROPN
ejpam-2623	386	5	and	and	CCONJ
ejpam-2623	386	6	β	β	X
ejpam-2623	386	7	=	=	SYM
ejpam-2623	386	8	χ(v	χ(v	PROPN
ejpam-2623	386	9	)	)	PUNCT
ejpam-2623	386	10	,	,	PUNCT
ejpam-2623	386	11	we	we	PRON
ejpam-2623	386	12	deduce	deduce	VERB
ejpam-2623	386	13	that	that	SCONJ
ejpam-2623	386	14	x	x	NOUN
ejpam-2623	386	15	=	=	PUNCT
ejpam-2623	386	16	χ(v)u	χ(v)u	PROPN
ejpam-2623	386	17	and	and	CCONJ
ejpam-2623	386	18	y	y	PROPN
ejpam-2623	386	19	2	2	NUM
ejpam-2623	386	20	=	=	SYM
ejpam-2623	386	21	βv	βv	PUNCT
ejpam-2623	386	22	=	=	SYM
ejpam-2623	386	23	χ(v)v	χ(v)v	PROPN
ejpam-2623	386	24	.	.	PUNCT
ejpam-2623	387	1	(	(	PUNCT
ejpam-2623	387	2	iv	iv	X
ejpam-2623	387	3	)	)	PUNCT
ejpam-2623	387	4	χ(v	χ(v	NOUN
ejpam-2623	387	5	)	)	PUNCT
ejpam-2623	388	1	=	=	SYM
ejpam-2623	388	2	β	β	X
ejpam-2623	388	3	=	=	SYM
ejpam-2623	389	1	χ	χ	X
ejpam-2623	389	2	(	(	PUNCT
ejpam-2623	389	3	y	y	PROPN
ejpam-2623	389	4	(	(	PUNCT
ejpam-2623	389	5	c2x2	c2x2	INTJ
ejpam-2623	389	6	−	−	NOUN
ejpam-2623	389	7	1	1	NUM
ejpam-2623	389	8	)	)	PUNCT
ejpam-2623	389	9	)	)	PUNCT
ejpam-2623	390	1	=	=	SYM
ejpam-2623	391	1	χ	χ	X
ejpam-2623	391	2	(	(	PUNCT
ejpam-2623	391	3	y	y	PROPN
ejpam-2623	391	4	(	(	PUNCT
ejpam-2623	391	5	x2	x2	INTJ
ejpam-2623	391	6	−	−	PROPN
ejpam-2623	391	7	1	1	NUM
ejpam-2623	391	8	/	/	SYM
ejpam-2623	391	9	c2	c2	PROPN
ejpam-2623	391	10	)	)	PUNCT
ejpam-2623	391	11	)	)	PUNCT
ejpam-2623	391	12	⇒	⇒	PROPN
ejpam-2623	391	13	χ(y	χ(y	PROPN
ejpam-2623	391	14	)	)	PUNCT
ejpam-2623	392	1	=	=	SYM
ejpam-2623	392	2	χ(v)χ	χ(v)χ	PROPN
ejpam-2623	392	3	(	(	PUNCT
ejpam-2623	392	4	x2	x2	INTJ
ejpam-2623	392	5	−	−	PROPN
ejpam-2623	392	6	1	1	NUM
ejpam-2623	392	7	/	/	SYM
ejpam-2623	392	8	c2	c2	PROPN
ejpam-2623	392	9	)	)	PUNCT
ejpam-2623	392	10	.	.	PUNCT
ejpam-2623	393	1	so	so	ADV
ejpam-2623	393	2	y	y	PROPN
ejpam-2623	393	3	=	=	PRON
ejpam-2623	393	4	(	(	PUNCT
ejpam-2623	393	5	χ(v)v)(q+1)/4χ(v)χ	χ(v)v)(q+1)/4χ(v)χ	PROPN
ejpam-2623	393	6	(	(	PUNCT
ejpam-2623	393	7	x2	x2	INTJ
ejpam-2623	393	8	−	−	PROPN
ejpam-2623	393	9	1	1	NUM
ejpam-2623	393	10	/	/	SYM
ejpam-2623	393	11	c2	c2	PROPN
ejpam-2623	393	12	)	)	PUNCT
ejpam-2623	393	13	.	.	PUNCT
ejpam-2623	394	1	n.	n.	PROPN
ejpam-2623	394	2	diarra	diarra	PROPN
ejpam-2623	394	3	,	,	PUNCT
ejpam-2623	394	4	d.	d.	PROPN
ejpam-2623	394	5	sow	sow	PROPN
ejpam-2623	394	6	,	,	PUNCT
ejpam-2623	394	7	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	394	8	.	.	PUNCT
ejpam-2623	394	9	khlil	khlil	PROPN
ejpam-2623	394	10	/	/	SYM
ejpam-2623	394	11	eur	eur	PROPN
ejpam-2623	394	12	.	.	PUNCT
ejpam-2623	395	1	j.	j.	PROPN
ejpam-2623	395	2	pure	pure	PROPN
ejpam-2623	395	3	appl	appl	PROPN
ejpam-2623	395	4	.	.	PROPN
ejpam-2623	395	5	math	math	PROPN
ejpam-2623	395	6	,	,	PUNCT
ejpam-2623	395	7	10	10	NUM
ejpam-2623	395	8	(	(	PUNCT
ejpam-2623	395	9	2	2	NUM
ejpam-2623	395	10	)	)	PUNCT
ejpam-2623	395	11	(	(	PUNCT
ejpam-2623	395	12	2017	2017	NUM
ejpam-2623	395	13	)	)	PUNCT
ejpam-2623	395	14	,	,	PUNCT
ejpam-2623	395	15	363	363	NUM
ejpam-2623	395	16	-	-	SYM
ejpam-2623	395	17	391	391	NUM
ejpam-2623	395	18	373	373	NUM
ejpam-2623	395	19	(	(	PUNCT
ejpam-2623	395	20	v	v	NOUN
ejpam-2623	395	21	)	)	PUNCT
ejpam-2623	395	22	finally	finally	ADV
ejpam-2623	395	23	let	let	VERB
ejpam-2623	395	24	z	z	NOUN
ejpam-2623	395	25	=	=	SYM
ejpam-2623	395	26	1−	1−	NUM
ejpam-2623	395	27	u	u	NOUN
ejpam-2623	395	28	1	1	NUM
ejpam-2623	395	29	+	+	NUM
ejpam-2623	395	30	u	u	NOUN
ejpam-2623	395	31	;	;	PUNCT
ejpam-2623	395	32	so	so	ADV
ejpam-2623	395	33	φa	φa	ADP
ejpam-2623	395	34	,	,	PUNCT
ejpam-2623	395	35	b(t	b(t	NOUN
ejpam-2623	395	36	)	)	PUNCT
ejpam-2623	395	37	=	=	PUNCT
ejpam-2623	395	38	(	(	PUNCT
ejpam-2623	395	39	x	x	X
ejpam-2623	395	40	,	,	PUNCT
ejpam-2623	395	41	y	y	PROPN
ejpam-2623	395	42	)	)	PUNCT
ejpam-2623	395	43	by	by	ADP
ejpam-2623	395	44	the	the	DET
ejpam-2623	395	45	previous	previous	ADJ
ejpam-2623	395	46	construction	construction	NOUN
ejpam-2623	395	47	.	.	PUNCT
ejpam-2623	396	1	note	note	VERB
ejpam-2623	396	2	that	that	SCONJ
ejpam-2623	396	3	z	z	NOUN
ejpam-2623	396	4	is	be	AUX
ejpam-2623	396	5	well	well	ADV
ejpam-2623	396	6	-	-	PUNCT
ejpam-2623	396	7	defined	define	VERB
ejpam-2623	396	8	since	since	SCONJ
ejpam-2623	396	9	u	u	NOUN
ejpam-2623	396	10	=	=	PROPN
ejpam-2623	396	11	±x	±x	PROPN
ejpam-2623	396	12	and	and	CCONJ
ejpam-2623	396	13	x	x	SYM
ejpam-2623	396	14	6=	6=	NUM
ejpam-2623	396	15	1	1	NUM
ejpam-2623	396	16	,	,	PUNCT
ejpam-2623	396	17	and	and	CCONJ
ejpam-2623	396	18	z	z	AUX
ejpam-2623	396	19	6=	6=	NUM
ejpam-2623	396	20	±1	±1	VERB
ejpam-2623	396	21	.	.	PUNCT
ejpam-2623	397	1	efficiency	efficiency	NOUN
ejpam-2623	397	2	of	of	ADP
ejpam-2623	397	3	φa	φa	ADP
ejpam-2623	397	4	,	,	PUNCT
ejpam-2623	397	5	b	b	NOUN
ejpam-2623	397	6	and	and	CCONJ
ejpam-2623	397	7	φ−13	φ−13	NOUN
ejpam-2623	397	8	:	:	PUNCT
ejpam-2623	397	9	as	as	ADP
ejpam-2623	397	10	in	in	ADP
ejpam-2623	397	11	elligator-1	elligator-1	NUM
ejpam-2623	397	12	[	[	X
ejpam-2623	397	13	4	4	NUM
ejpam-2623	397	14	]	]	PUNCT
ejpam-2623	397	15	,	,	PUNCT
ejpam-2623	397	16	the	the	DET
ejpam-2623	397	17	definitions	definition	NOUN
ejpam-2623	397	18	of	of	ADP
ejpam-2623	397	19	u	u	NOUN
ejpam-2623	397	20	,	,	PUNCT
ejpam-2623	397	21	v	v	NOUN
ejpam-2623	397	22	,	,	PUNCT
ejpam-2623	397	23	x	x	NOUN
ejpam-2623	397	24	,	,	PUNCT
ejpam-2623	397	25	y	y	PROPN
ejpam-2623	397	26	,	,	PUNCT
ejpam-2623	397	27	x	x	PRON
ejpam-2623	397	28	,	,	PUNCT
ejpam-2623	397	29	y	y	PROPN
ejpam-2623	397	30	in	in	ADP
ejpam-2623	397	31	theorem	theorem	NOUN
ejpam-2623	397	32	2	2	NUM
ejpam-2623	397	33	involve	involve	VERB
ejpam-2623	397	34	divisions	division	NOUN
ejpam-2623	397	35	by	by	ADP
ejpam-2623	397	36	c	c	PROPN
ejpam-2623	397	37	,	,	PUNCT
ejpam-2623	397	38	1	1	NUM
ejpam-2623	397	39	+	+	CCONJ
ejpam-2623	397	40	c	c	X
ejpam-2623	397	41	,	,	PUNCT
ejpam-2623	397	42	1−	1−	NUM
ejpam-2623	397	43	c	c	NOUN
ejpam-2623	397	44	and	and	CCONJ
ejpam-2623	397	45	αy	αy	INTJ
ejpam-2623	397	46	,	,	PUNCT
ejpam-2623	397	47	two	two	NUM
ejpam-2623	397	48	computations	computation	NOUN
ejpam-2623	397	49	of	of	ADP
ejpam-2623	397	50	the	the	DET
ejpam-2623	397	51	quadratic	quadratic	ADJ
ejpam-2623	397	52	character	character	NOUN
ejpam-2623	397	53	χ	χ	X
ejpam-2623	397	54	(	(	PUNCT
ejpam-2623	397	55	namely	namely	ADV
ejpam-2623	397	56	χ(v	χ(v	NOUN
ejpam-2623	397	57	)	)	PUNCT
ejpam-2623	397	58	and	and	CCONJ
ejpam-2623	397	59	χ(u2	χ(u2	PROPN
ejpam-2623	398	1	−	−	PROPN
ejpam-2623	398	2	1	1	NUM
ejpam-2623	398	3	/	/	SYM
ejpam-2623	398	4	c2	c2	PROPN
ejpam-2623	398	5	)	)	PUNCT
ejpam-2623	398	6	)	)	PUNCT
ejpam-2623	398	7	,	,	PUNCT
ejpam-2623	398	8	a	a	DET
ejpam-2623	398	9	square	square	ADJ
ejpam-2623	398	10	-	-	PUNCT
ejpam-2623	398	11	root	root	NOUN
ejpam-2623	398	12	computation	computation	NOUN
ejpam-2623	398	13	and	and	CCONJ
ejpam-2623	398	14	some	some	DET
ejpam-2623	398	15	multiplications	multiplication	NOUN
ejpam-2623	398	16	.	.	PUNCT
ejpam-2623	399	1	one	one	PRON
ejpam-2623	399	2	can	can	AUX
ejpam-2623	399	3	reduce	reduce	VERB
ejpam-2623	399	4	the	the	DET
ejpam-2623	399	5	number	number	NOUN
ejpam-2623	399	6	of	of	ADP
ejpam-2623	399	7	multiplications	multiplication	NOUN
ejpam-2623	399	8	,	,	PUNCT
ejpam-2623	399	9	for	for	ADP
ejpam-2623	399	10	example	example	NOUN
ejpam-2623	399	11	by	by	ADP
ejpam-2623	399	12	factoring	factor	VERB
ejpam-2623	399	13	v	v	NOUN
ejpam-2623	399	14	=	=	SYM
ejpam-2623	399	15	−u5	−u5	NOUN
ejpam-2623	399	16	+	+	CCONJ
ejpam-2623	399	17	(	(	PUNCT
ejpam-2623	399	18	c2	c2	PROPN
ejpam-2623	399	19	+	+	CCONJ
ejpam-2623	399	20	1	1	NUM
ejpam-2623	399	21	/	/	SYM
ejpam-2623	399	22	c2)u3	c2)u3	NOUN
ejpam-2623	399	23	−	−	PROPN
ejpam-2623	399	24	u	u	NOUN
ejpam-2623	399	25	as	as	ADP
ejpam-2623	399	26	v	v	NOUN
ejpam-2623	399	27	=	=	SYM
ejpam-2623	399	28	−u(u2	−u(u2	PROPN
ejpam-2623	399	29	−	−	PROPN
ejpam-2623	399	30	c2)(u2	c2)(u2	PROPN
ejpam-2623	399	31	−	−	NUM
ejpam-2623	399	32	1	1	NUM
ejpam-2623	399	33	/	/	SYM
ejpam-2623	399	34	c2	c2	PROPN
ejpam-2623	399	35	)	)	PUNCT
ejpam-2623	399	36	.	.	PUNCT
ejpam-2623	400	1	and	and	CCONJ
ejpam-2623	400	2	u2	u2	PROPN
ejpam-2623	400	3	−	−	PROPN
ejpam-2623	400	4	1	1	NUM
ejpam-2623	400	5	/	/	SYM
ejpam-2623	400	6	c2	c2	PROPN
ejpam-2623	400	7	can	can	AUX
ejpam-2623	400	8	be	be	AUX
ejpam-2623	400	9	reused	reuse	VERB
ejpam-2623	400	10	when	when	SCONJ
ejpam-2623	400	11	computing	compute	VERB
ejpam-2623	400	12	y	y	PROPN
ejpam-2623	400	13	=	=	SYM
ejpam-2623	400	14	χ(v	χ(v	PROPN
ejpam-2623	400	15	)	)	PUNCT
ejpam-2623	400	16	·	·	PUNCT
ejpam-2623	400	17	χ(u2	χ(u2	PROPN
ejpam-2623	401	1	−	−	ADP
ejpam-2623	401	2	1	1	NUM
ejpam-2623	401	3	/	/	SYM
ejpam-2623	401	4	c2	c2	PROPN
ejpam-2623	401	5	)	)	PUNCT
ejpam-2623	401	6	·	·	PUNCT
ejpam-2623	402	1	√	√	NUM
ejpam-2623	402	2	χ(v)v	χ(v)v	PROPN
ejpam-2623	402	3	.	.	PUNCT
ejpam-2623	403	1	the	the	DET
ejpam-2623	403	2	computation	computation	NOUN
ejpam-2623	403	3	of	of	ADP
ejpam-2623	403	4	χ(v	χ(v	NOUN
ejpam-2623	403	5	)	)	PUNCT
ejpam-2623	403	6	and	and	CCONJ
ejpam-2623	403	7	χ(u2	χ(u2	PROPN
ejpam-2623	403	8	−	−	PROPN
ejpam-2623	403	9	1	1	NUM
ejpam-2623	403	10	/	/	SYM
ejpam-2623	403	11	c2	c2	PROPN
ejpam-2623	403	12	)	)	PUNCT
ejpam-2623	403	13	can	can	AUX
ejpam-2623	403	14	be	be	AUX
ejpam-2623	403	15	replaced	replace	VERB
ejpam-2623	403	16	by	by	ADP
ejpam-2623	403	17	exponentiations	exponentiation	NOUN
ejpam-2623	403	18	,	,	PUNCT
ejpam-2623	403	19	and	and	CCONJ
ejpam-2623	403	20	the	the	DET
ejpam-2623	403	21	square	square	ADJ
ejpam-2623	403	22	-	-	PUNCT
ejpam-2623	403	23	root	root	NOUN
ejpam-2623	403	24	computation	computation	NOUN
ejpam-2623	403	25	is	be	AUX
ejpam-2623	403	26	also	also	ADV
ejpam-2623	403	27	replaced	replace	VERB
ejpam-2623	403	28	by	by	ADP
ejpam-2623	403	29	an	an	DET
ejpam-2623	403	30	exponentiation	exponentiation	NOUN
ejpam-2623	403	31	with	with	ADP
ejpam-2623	403	32	exponent	exponent	PROPN
ejpam-2623	403	33	a(q+1)/4	a(q+1)/4	PROPN
ejpam-2623	404	1	since	since	SCONJ
ejpam-2623	404	2	q	q	PROPN
ejpam-2623	404	3	≡	≡	PROPN
ejpam-2623	404	4	3	3	NUM
ejpam-2623	404	5	mod	mod	NOUN
ejpam-2623	404	6	4	4	NUM
ejpam-2623	404	7	.	.	X
ejpam-2623	405	1	for	for	ADP
ejpam-2623	405	2	p	p	NOUN
ejpam-2623	405	3	=	=	SYM
ejpam-2623	405	4	(	(	PUNCT
ejpam-2623	405	5	x	x	NOUN
ejpam-2623	405	6	,	,	PUNCT
ejpam-2623	405	7	y	y	NOUN
ejpam-2623	405	8	)	)	PUNCT
ejpam-2623	405	9	∈	∈	PROPN
ejpam-2623	405	10	ea	ea	PROPN
ejpam-2623	405	11	,	,	PUNCT
ejpam-2623	405	12	b	b	PROPN
ejpam-2623	405	13	,	,	PUNCT
ejpam-2623	405	14	checking	check	VERB
ejpam-2623	405	15	wether	wether	NOUN
ejpam-2623	405	16	or	or	CCONJ
ejpam-2623	405	17	not	not	PART
ejpam-2623	405	18	p	p	NOUN
ejpam-2623	405	19	is	be	AUX
ejpam-2623	405	20	in	in	ADP
ejpam-2623	405	21	im(φa	im(φa	PROPN
ejpam-2623	405	22	,	,	PUNCT
ejpam-2623	405	23	b	b	NOUN
ejpam-2623	405	24	)	)	PUNCT
ejpam-2623	405	25	requires	require	VERB
ejpam-2623	405	26	few	few	ADJ
ejpam-2623	405	27	multiplications	multiplication	NOUN
ejpam-2623	405	28	,	,	PUNCT
ejpam-2623	405	29	one	one	NUM
ejpam-2623	405	30	inversion	inversion	NOUN
ejpam-2623	405	31	and	and	CCONJ
ejpam-2623	405	32	a	a	DET
ejpam-2623	405	33	computation	computation	NOUN
ejpam-2623	405	34	of	of	ADP
ejpam-2623	405	35	χ(1−	χ(1−	ADJ
ejpam-2623	405	36	4α2η	4α2η	NOUN
ejpam-2623	405	37	)	)	PUNCT
ejpam-2623	405	38	,	,	PUNCT
ejpam-2623	405	39	where	where	SCONJ
ejpam-2623	405	40	η	η	PROPN
ejpam-2623	405	41	=	=	SYM
ejpam-2623	405	42	(	(	PUNCT
ejpam-2623	405	43	bx−	bx−	PROPN
ejpam-2623	405	44	ay)/(ab(x−	ay)/(ab(x−	X
ejpam-2623	405	45	y	y	NOUN
ejpam-2623	405	46	)	)	PUNCT
ejpam-2623	405	47	)	)	PUNCT
ejpam-2623	405	48	.	.	PUNCT
ejpam-2623	406	1	elligator	elligator	NOUN
ejpam-2623	406	2	-	-	PUNCT
ejpam-2623	406	3	squared	square	VERB
ejpam-2623	406	4	approach	approach	NOUN
ejpam-2623	406	5	with	with	ADP
ejpam-2623	406	6	elligator-3	elligator-3	PROPN
ejpam-2623	406	7	encoding	encoding	NOUN
ejpam-2623	406	8	:	:	PUNCT
ejpam-2623	406	9	recently	recently	ADV
ejpam-2623	406	10	[	[	X
ejpam-2623	406	11	17	17	NUM
ejpam-2623	406	12	]	]	PUNCT
ejpam-2623	406	13	,	,	PUNCT
ejpam-2623	406	14	tibouchi	tibouchi	PROPN
ejpam-2623	406	15	proposed	propose	VERB
ejpam-2623	406	16	a	a	DET
ejpam-2623	406	17	new	new	ADJ
ejpam-2623	406	18	method	method	NOUN
ejpam-2623	406	19	,	,	PUNCT
ejpam-2623	406	20	called	call	VERB
ejpam-2623	406	21	elligator	elligator	NOUN
ejpam-2623	406	22	-	-	PUNCT
ejpam-2623	406	23	squared	square	VERB
ejpam-2623	406	24	,	,	PUNCT
ejpam-2623	406	25	which	which	PRON
ejpam-2623	406	26	supports	support	VERB
ejpam-2623	406	27	more	more	ADJ
ejpam-2623	406	28	elliptic	elliptic	ADJ
ejpam-2623	406	29	curves	curve	NOUN
ejpam-2623	406	30	than	than	ADP
ejpam-2623	406	31	elligator	elligator	NOUN
ejpam-2623	406	32	,	,	PUNCT
ejpam-2623	406	33	and	and	CCONJ
ejpam-2623	406	34	uses	use	VERB
ejpam-2623	406	35	a	a	DET
ejpam-2623	406	36	surjective	surjective	ADJ
ejpam-2623	406	37	map	map	NOUN
ejpam-2623	406	38	to	to	PART
ejpam-2623	406	39	represent	represent	VERB
ejpam-2623	406	40	a	a	DET
ejpam-2623	406	41	point	point	NOUN
ejpam-2623	406	42	in	in	ADP
ejpam-2623	406	43	the	the	DET
ejpam-2623	406	44	curve	curve	NOUN
ejpam-2623	406	45	by	by	ADP
ejpam-2623	406	46	its	its	PRON
ejpam-2623	406	47	preimage	preimage	NOUN
ejpam-2623	406	48	under	under	ADP
ejpam-2623	406	49	this	this	DET
ejpam-2623	406	50	map	map	NOUN
ejpam-2623	406	51	.	.	PUNCT
ejpam-2623	407	1	in	in	ADP
ejpam-2623	407	2	fact	fact	NOUN
ejpam-2623	407	3	,	,	PUNCT
ejpam-2623	407	4	any	any	DET
ejpam-2623	407	5	p	p	PROPN
ejpam-2623	407	6	∈	∈	PROPN
ejpam-2623	407	7	e(fq	e(fq	X
ejpam-2623	407	8	)	)	PUNCT
ejpam-2623	407	9	is	be	AUX
ejpam-2623	407	10	represented	represent	VERB
ejpam-2623	407	11	by	by	ADP
ejpam-2623	407	12	its	its	PRON
ejpam-2623	407	13	randomly	randomly	ADV
ejpam-2623	407	14	sampled	sample	VERB
ejpam-2623	407	15	preimage	preimage	NOUN
ejpam-2623	407	16	under	under	ADP
ejpam-2623	407	17	an	an	DET
ejpam-2623	407	18	admissible	admissible	ADJ
ejpam-2623	407	19	encoding	encoding	NOUN
ejpam-2623	407	20	of	of	ADP
ejpam-2623	407	21	the	the	DET
ejpam-2623	407	22	form	form	NOUN
ejpam-2623	407	23	f⊗2	f⊗2	NOUN
ejpam-2623	407	24	:	:	PUNCT
ejpam-2623	407	25	(	(	PUNCT
ejpam-2623	407	26	u	u	NOUN
ejpam-2623	407	27	,	,	PUNCT
ejpam-2623	407	28	v	v	NOUN
ejpam-2623	407	29	)	)	PUNCT
ejpam-2623	407	30	7→	7→	PROPN
ejpam-2623	407	31	f(u	f(u	PROPN
ejpam-2623	407	32	)	)	PUNCT
ejpam-2623	407	33	+	+	NUM
ejpam-2623	407	34	f(v	f(v	NOUN
ejpam-2623	407	35	)	)	PUNCT
ejpam-2623	407	36	,	,	PUNCT
ejpam-2623	407	37	where	where	SCONJ
ejpam-2623	407	38	f	f	X
ejpam-2623	407	39	:	:	PUNCT
ejpam-2623	407	40	fq	fq	PROPN
ejpam-2623	407	41	→	→	SYM
ejpam-2623	407	42	e(fq	e(fq	PROPN
ejpam-2623	407	43	)	)	PUNCT
ejpam-2623	407	44	is	be	AUX
ejpam-2623	407	45	any	any	DET
ejpam-2623	407	46	encoding	encoding	NOUN
ejpam-2623	407	47	.	.	PUNCT
ejpam-2623	408	1	in	in	ADP
ejpam-2623	408	2	the	the	DET
ejpam-2623	408	3	same	same	ADJ
ejpam-2623	408	4	paper	paper	NOUN
ejpam-2623	408	5	,	,	PUNCT
ejpam-2623	408	6	tibouchi	tibouchi	PROPN
ejpam-2623	408	7	gave	give	VERB
ejpam-2623	408	8	a	a	DET
ejpam-2623	408	9	list	list	NOUN
ejpam-2623	408	10	of	of	ADP
ejpam-2623	408	11	known	know	VERB
ejpam-2623	408	12	encodings	encoding	NOUN
ejpam-2623	408	13	that	that	PRON
ejpam-2623	408	14	meet	meet	VERB
ejpam-2623	408	15	the	the	DET
ejpam-2623	408	16	requirements	requirement	NOUN
ejpam-2623	408	17	of	of	ADP
ejpam-2623	408	18	elligator	elligator	NOUN
ejpam-2623	408	19	-	-	PUNCT
ejpam-2623	408	20	squared	square	VERB
ejpam-2623	408	21	construction	construction	NOUN
ejpam-2623	408	22	,	,	PUNCT
ejpam-2623	408	23	namely	namely	ADV
ejpam-2623	408	24	well	well	ADV
ejpam-2623	408	25	-	-	PUNCT
ejpam-2623	408	26	bounded	bound	VERB
ejpam-2623	408	27	encodings	encoding	NOUN
ejpam-2623	408	28	.	.	PUNCT
ejpam-2623	409	1	as	as	ADP
ejpam-2623	409	2	for	for	ADP
ejpam-2623	409	3	elligator-1	elligator-1	NUM
ejpam-2623	409	4	encoding	encode	VERB
ejpam-2623	409	5	[	[	X
ejpam-2623	409	6	4	4	NUM
ejpam-2623	409	7	]	]	PUNCT
ejpam-2623	409	8	,	,	PUNCT
ejpam-2623	409	9	the	the	DET
ejpam-2623	409	10	elligator	elligator	NOUN
ejpam-2623	409	11	-	-	PUNCT
ejpam-2623	409	12	squared	square	VERB
ejpam-2623	409	13	construction	construction	NOUN
ejpam-2623	409	14	can	can	AUX
ejpam-2623	409	15	be	be	AUX
ejpam-2623	409	16	applied	apply	VERB
ejpam-2623	409	17	to	to	ADP
ejpam-2623	409	18	our	our	PRON
ejpam-2623	409	19	new	new	ADJ
ejpam-2623	409	20	elligator-3	elligator-3	PROPN
ejpam-2623	409	21	encoding	encoding	NOUN
ejpam-2623	409	22	.	.	PUNCT
ejpam-2623	410	1	in	in	ADP
ejpam-2623	410	2	fact	fact	NOUN
ejpam-2623	410	3	,	,	PUNCT
ejpam-2623	410	4	φa	φa	ADP
ejpam-2623	410	5	,	,	PUNCT
ejpam-2623	410	6	b	b	NOUN
ejpam-2623	410	7	can	can	AUX
ejpam-2623	410	8	be	be	AUX
ejpam-2623	410	9	expressed	express	VERB
ejpam-2623	410	10	in	in	ADP
ejpam-2623	410	11	terms	term	NOUN
ejpam-2623	410	12	of	of	ADP
ejpam-2623	410	13	a	a	DET
ejpam-2623	410	14	degree	degree	NOUN
ejpam-2623	410	15	2	2	NUM
ejpam-2623	410	16	covering	covering	NOUN
ejpam-2623	410	17	h	h	NOUN
ejpam-2623	410	18	:	:	PUNCT
ejpam-2623	410	19	h	h	NOUN
ejpam-2623	410	20	→	→	SYM
ejpam-2623	410	21	e	e	PROPN
ejpam-2623	410	22	of	of	ADP
ejpam-2623	410	23	e	e	PROPN
ejpam-2623	410	24	by	by	ADP
ejpam-2623	410	25	a	a	DET
ejpam-2623	410	26	certain	certain	ADJ
ejpam-2623	410	27	elliptic	elliptic	ADJ
ejpam-2623	410	28	curve	curve	NOUN
ejpam-2623	410	29	h	h	NOUN
ejpam-2623	410	30	of	of	ADP
ejpam-2623	410	31	genus	genus	NOUN
ejpam-2623	410	32	2	2	NUM
ejpam-2623	411	1	[	[	X
ejpam-2623	411	2	17	17	NUM
ejpam-2623	411	3	,	,	PUNCT
ejpam-2623	411	4	13	13	NUM
ejpam-2623	411	5	]	]	PUNCT
ejpam-2623	411	6	.	.	PUNCT
ejpam-2623	412	1	hence	hence	ADV
ejpam-2623	412	2	,	,	PUNCT
ejpam-2623	412	3	using	use	VERB
ejpam-2623	412	4	lemma	lemma	PROPN
ejpam-2623	412	5	3	3	NUM
ejpam-2623	412	6	in	in	ADP
ejpam-2623	412	7	[	[	X
ejpam-2623	412	8	17	17	NUM
ejpam-2623	412	9	]	]	PUNCT
ejpam-2623	412	10	,	,	PUNCT
ejpam-2623	412	11	one	one	PRON
ejpam-2623	412	12	shows	show	VERB
ejpam-2623	412	13	that	that	SCONJ
ejpam-2623	412	14	φa	φa	ADP
ejpam-2623	412	15	,	,	PUNCT
ejpam-2623	412	16	b	b	PROPN
ejpam-2623	412	17	is	be	AUX
ejpam-2623	412	18	2−well	2−well	NOUN
ejpam-2623	412	19	-	-	PUNCT
ejpam-2623	412	20	distributed	distribute	VERB
ejpam-2623	412	21	and	and	CCONJ
ejpam-2623	412	22	is	be	AUX
ejpam-2623	412	23	also	also	ADV
ejpam-2623	412	24	a	a	DET
ejpam-2623	412	25	(	(	PUNCT
ejpam-2623	412	26	2	2	NUM
ejpam-2623	412	27	,	,	PUNCT
ejpam-2623	412	28	2)-well	2)-well	NUM
ejpam-2623	412	29	-	-	PUNCT
ejpam-2623	412	30	bounded	bound	VERB
ejpam-2623	412	31	encoding	encoding	NOUN
ejpam-2623	412	32	,	,	PUNCT
ejpam-2623	412	33	since	since	SCONJ
ejpam-2623	412	34	any	any	DET
ejpam-2623	412	35	p	p	PROPN
ejpam-2623	412	36	∈	∈	PROPN
ejpam-2623	412	37	e(fq	e(fq	X
ejpam-2623	412	38	)	)	PUNCT
ejpam-2623	412	39	has	have	VERB
ejpam-2623	412	40	at	at	ADP
ejpam-2623	412	41	most	most	ADJ
ejpam-2623	412	42	2	2	NUM
ejpam-2623	412	43	preimages	preimage	NOUN
ejpam-2623	412	44	(	(	PUNCT
ejpam-2623	412	45	see	see	VERB
ejpam-2623	412	46	proposition	proposition	NOUN
ejpam-2623	412	47	3	3	NUM
ejpam-2623	412	48	)	)	PUNCT
ejpam-2623	412	49	.	.	PUNCT
ejpam-2623	413	1	also	also	ADV
ejpam-2623	413	2	note	note	VERB
ejpam-2623	413	3	that	that	SCONJ
ejpam-2623	413	4	elligator-3	elligator-3	PROPN
ejpam-2623	413	5	encoding	encoding	NOUN
ejpam-2623	413	6	φa	φa	ADP
ejpam-2623	413	7	,	,	PUNCT
ejpam-2623	413	8	b	b	NOUN
ejpam-2623	413	9	can	can	AUX
ejpam-2623	413	10	be	be	AUX
ejpam-2623	413	11	used	use	VERB
ejpam-2623	413	12	to	to	PART
ejpam-2623	413	13	build	build	VERB
ejpam-2623	413	14	a	a	DET
ejpam-2623	413	15	hash	hash	NOUN
ejpam-2623	413	16	function	function	NOUN
ejpam-2623	413	17	into	into	ADP
ejpam-2623	413	18	the	the	DET
ejpam-2623	413	19	elliptic	elliptic	ADJ
ejpam-2623	413	20	curve	curve	NOUN
ejpam-2623	413	21	.	.	PUNCT
ejpam-2623	414	1	but	but	CCONJ
ejpam-2623	414	2	it	it	PRON
ejpam-2623	414	3	can	can	AUX
ejpam-2623	414	4	not	not	PART
ejpam-2623	414	5	be	be	AUX
ejpam-2623	414	6	directly	directly	ADV
ejpam-2623	414	7	used	use	VERB
ejpam-2623	414	8	in	in	ADP
ejpam-2623	414	9	the	the	DET
ejpam-2623	414	10	bls	bls	PROPN
ejpam-2623	414	11	signature	signature	NOUN
ejpam-2623	414	12	scheme	scheme	NOUN
ejpam-2623	414	13	[	[	X
ejpam-2623	414	14	3	3	NUM
ejpam-2623	414	15	]	]	PUNCT
ejpam-2623	414	16	.	.	PUNCT
ejpam-2623	415	1	this	this	PRON
ejpam-2623	415	2	results	result	VERB
ejpam-2623	415	3	from	from	ADP
ejpam-2623	415	4	the	the	DET
ejpam-2623	415	5	fact	fact	NOUN
ejpam-2623	415	6	that	that	SCONJ
ejpam-2623	415	7	not	not	PART
ejpam-2623	415	8	all	all	DET
ejpam-2623	415	9	points	point	NOUN
ejpam-2623	415	10	of	of	ADP
ejpam-2623	415	11	the	the	DET
ejpam-2623	415	12	elliptic	elliptic	ADJ
ejpam-2623	415	13	curve	curve	NOUN
ejpam-2623	415	14	are	be	AUX
ejpam-2623	415	15	representable	representable	ADJ
ejpam-2623	415	16	since	since	SCONJ
ejpam-2623	415	17	the	the	DET
ejpam-2623	415	18	image	image	NOUN
ejpam-2623	415	19	set	set	NOUN
ejpam-2623	415	20	does	do	AUX
ejpam-2623	415	21	not	not	PART
ejpam-2623	415	22	cover	cover	VERB
ejpam-2623	415	23	the	the	DET
ejpam-2623	415	24	whole	whole	ADJ
ejpam-2623	415	25	curve	curve	NOUN
ejpam-2623	415	26	.	.	PUNCT
ejpam-2623	416	1	and	and	CCONJ
ejpam-2623	416	2	in	in	ADP
ejpam-2623	416	3	the	the	DET
ejpam-2623	416	4	bls	bls	PROPN
ejpam-2623	416	5	signature	signature	NOUN
ejpam-2623	416	6	scheme	scheme	NOUN
ejpam-2623	416	7	,	,	PUNCT
ejpam-2623	416	8	which	which	PRON
ejpam-2623	416	9	is	be	AUX
ejpam-2623	416	10	a	a	DET
ejpam-2623	416	11	full	full	ADJ
ejpam-2623	416	12	-	-	PUNCT
ejpam-2623	416	13	domain	domain	NOUN
ejpam-2623	416	14	signature	signature	NOUN
ejpam-2623	416	15	scheme	scheme	NOUN
ejpam-2623	416	16	,	,	PUNCT
ejpam-2623	416	17	all	all	DET
ejpam-2623	416	18	points	point	NOUN
ejpam-2623	416	19	need	need	VERB
ejpam-2623	416	20	to	to	PART
ejpam-2623	416	21	be	be	AUX
ejpam-2623	416	22	representable	representable	ADJ
ejpam-2623	416	23	.	.	PUNCT
ejpam-2623	417	1	nevertheless	nevertheless	ADV
ejpam-2623	417	2	,	,	PUNCT
ejpam-2623	417	3	we	we	PRON
ejpam-2623	417	4	can	can	AUX
ejpam-2623	417	5	overcome	overcome	VERB
ejpam-2623	417	6	this	this	DET
ejpam-2623	417	7	limitation	limitation	NOUN
ejpam-2623	417	8	by	by	ADP
ejpam-2623	417	9	combining	combine	VERB
ejpam-2623	417	10	elligator-3	elligator-3	PROPN
ejpam-2623	417	11	encoding	encoding	NOUN
ejpam-2623	417	12	and	and	CCONJ
ejpam-2623	417	13	elligator	elligator	NOUN
ejpam-2623	417	14	-	-	PUNCT
ejpam-2623	417	15	squared	square	VERB
ejpam-2623	417	16	approach	approach	NOUN
ejpam-2623	417	17	.	.	PUNCT
ejpam-2623	418	1	in	in	ADP
ejpam-2623	418	2	fact	fact	NOUN
ejpam-2623	418	3	,	,	PUNCT
ejpam-2623	418	4	the	the	DET
ejpam-2623	418	5	resulting	result	VERB
ejpam-2623	418	6	construction	construction	NOUN
ejpam-2623	418	7	φ⊗2a	φ⊗2a	PROPN
ejpam-2623	418	8	,	,	PUNCT
ejpam-2623	418	9	b	b	NOUN
ejpam-2623	418	10	:	:	PUNCT
ejpam-2623	418	11	(	(	PUNCT
ejpam-2623	418	12	u	u	NOUN
ejpam-2623	418	13	,	,	PUNCT
ejpam-2623	418	14	v	v	NOUN
ejpam-2623	418	15	)	)	PUNCT
ejpam-2623	418	16	7→	7→	NUM
ejpam-2623	418	17	φa	φa	ADP
ejpam-2623	418	18	,	,	PUNCT
ejpam-2623	418	19	b(u	b(u	PROPN
ejpam-2623	418	20	)	)	PUNCT
ejpam-2623	418	21	+	+	CCONJ
ejpam-2623	418	22	φa	φa	PROPN
ejpam-2623	418	23	,	,	PUNCT
ejpam-2623	418	24	b(v	b(v	NOUN
ejpam-2623	418	25	)	)	PUNCT
ejpam-2623	418	26	,	,	PUNCT
ejpam-2623	418	27	which	which	PRON
ejpam-2623	418	28	we	we	PRON
ejpam-2623	418	29	call	call	VERB
ejpam-2623	418	30	elligator-3	elligator-3	PROPN
ejpam-2623	418	31	-	-	PUNCT
ejpam-2623	418	32	squared	square	VERB
ejpam-2623	418	33	,	,	PUNCT
ejpam-2623	418	34	is	be	AUX
ejpam-2623	418	35	a	a	DET
ejpam-2623	418	36	surjective	surjective	ADJ
ejpam-2623	418	37	one	one	NUM
ejpam-2623	418	38	.	.	PUNCT
ejpam-2623	419	1	3.2	3.2	NUM
ejpam-2623	419	2	.	.	PUNCT
ejpam-2623	420	1	an	an	DET
ejpam-2623	420	2	aiee	aiee	NOUN
ejpam-2623	420	3	for	for	ADP
ejpam-2623	420	4	the	the	DET
ejpam-2623	420	5	classical	classical	ADJ
ejpam-2623	420	6	huff	huff	NOUN
ejpam-2623	420	7	model	model	NOUN
ejpam-2623	420	8	αx(y2	αx(y2	ADP
ejpam-2623	420	9	−	−	PROPN
ejpam-2623	420	10	1	1	NUM
ejpam-2623	420	11	)	)	PUNCT
ejpam-2623	420	12	=	=	SYM
ejpam-2623	420	13	βy(x2	βy(x2	NOUN
ejpam-2623	421	1	−	−	NOUN
ejpam-2623	421	2	1	1	X
ejpam-2623	421	3	)	)	PUNCT
ejpam-2623	421	4	the	the	DET
ejpam-2623	421	5	classical	classical	ADJ
ejpam-2623	421	6	huff	huff	NOUN
ejpam-2623	421	7	model	model	NOUN
ejpam-2623	421	8	αx′(y′2−	αx′(y′2−	PROPN
ejpam-2623	421	9	1	1	NUM
ejpam-2623	421	10	)	)	PUNCT
ejpam-2623	421	11	=	=	SYM
ejpam-2623	421	12	βy′(x′2−	βy′(x′2−	ADJ
ejpam-2623	421	13	1	1	X
ejpam-2623	421	14	)	)	PUNCT
ejpam-2623	421	15	is	be	AUX
ejpam-2623	421	16	included	include	VERB
ejpam-2623	421	17	in	in	ADP
ejpam-2623	421	18	the	the	DET
ejpam-2623	421	19	generalized	generalize	VERB
ejpam-2623	421	20	huff	huff	PROPN
ejpam-2623	421	21	model	model	PROPN
ejpam-2623	421	22	x(ay2−1	x(ay2−1	PROPN
ejpam-2623	421	23	)	)	PUNCT
ejpam-2623	421	24	=	=	PUNCT
ejpam-2623	421	25	y(bx2−1	y(bx2−1	NOUN
ejpam-2623	421	26	)	)	PUNCT
ejpam-2623	421	27	.	.	PUNCT
ejpam-2623	422	1	in	in	ADP
ejpam-2623	422	2	fact	fact	NOUN
ejpam-2623	422	3	,	,	PUNCT
ejpam-2623	422	4	one	one	PRON
ejpam-2623	422	5	can	can	AUX
ejpam-2623	422	6	simply	simply	ADV
ejpam-2623	422	7	set	set	VERB
ejpam-2623	422	8	a	a	DET
ejpam-2623	422	9	=	=	X
ejpam-2623	422	10	α2	α2	PROPN
ejpam-2623	422	11	,	,	PUNCT
ejpam-2623	422	12	b	b	X
ejpam-2623	422	13	=	=	PUNCT
ejpam-2623	422	14	β2	β2	NOUN
ejpam-2623	422	15	and	and	CCONJ
ejpam-2623	422	16	then	then	ADV
ejpam-2623	422	17	use	use	VERB
ejpam-2623	422	18	the	the	DET
ejpam-2623	422	19	change	change	NOUN
ejpam-2623	422	20	of	of	ADP
ejpam-2623	422	21	variables	variable	NOUN
ejpam-2623	422	22	(	(	PUNCT
ejpam-2623	422	23	x	x	X
ejpam-2623	422	24	,	,	PUNCT
ejpam-2623	422	25	y	y	PROPN
ejpam-2623	422	26	)	)	PUNCT
ejpam-2623	422	27	→	→	PUNCT
ejpam-2623	422	28	(	(	PUNCT
ejpam-2623	422	29	x′	x′	X
ejpam-2623	422	30	=	=	SYM
ejpam-2623	422	31	βx	βx	PROPN
ejpam-2623	422	32	,	,	PUNCT
ejpam-2623	422	33	y′	y′	PUNCT
ejpam-2623	422	34	=	=	SYM
ejpam-2623	422	35	αy	αy	NOUN
ejpam-2623	422	36	)	)	PUNCT
ejpam-2623	422	37	.	.	PUNCT
ejpam-2623	423	1	but	but	CCONJ
ejpam-2623	423	2	the	the	DET
ejpam-2623	423	3	previous	previous	ADJ
ejpam-2623	423	4	method	method	NOUN
ejpam-2623	423	5	is	be	AUX
ejpam-2623	423	6	not	not	PART
ejpam-2623	423	7	directly	directly	ADV
ejpam-2623	423	8	applicable	applicable	ADJ
ejpam-2623	423	9	to	to	ADP
ejpam-2623	423	10	the	the	DET
ejpam-2623	423	11	classical	classical	ADJ
ejpam-2623	423	12	huff	huff	NOUN
ejpam-2623	423	13	model	model	NOUN
ejpam-2623	423	14	,	,	PUNCT
ejpam-2623	423	15	since	since	SCONJ
ejpam-2623	423	16	the	the	DET
ejpam-2623	423	17	product	product	NOUN
ejpam-2623	423	18	ab	ab	PROPN
ejpam-2623	423	19	has	have	VERB
ejpam-2623	423	20	to	to	PART
ejpam-2623	423	21	be	be	AUX
ejpam-2623	423	22	a	a	DET
ejpam-2623	423	23	non	non	ADJ
ejpam-2623	423	24	-	-	ADJ
ejpam-2623	423	25	square	square	ADJ
ejpam-2623	423	26	in	in	ADP
ejpam-2623	423	27	fq	fq	PROPN
ejpam-2623	423	28	.	.	PUNCT
ejpam-2623	424	1	this	this	PRON
ejpam-2623	424	2	is	be	AUX
ejpam-2623	424	3	not	not	PART
ejpam-2623	424	4	the	the	DET
ejpam-2623	424	5	case	case	NOUN
ejpam-2623	424	6	when	when	SCONJ
ejpam-2623	424	7	a	a	DET
ejpam-2623	424	8	=	=	SYM
ejpam-2623	424	9	α2	α2	PROPN
ejpam-2623	424	10	and	and	CCONJ
ejpam-2623	424	11	b	b	X
ejpam-2623	424	12	=	=	SYM
ejpam-2623	424	13	β2	β2	PROPN
ejpam-2623	424	14	.	.	PUNCT
ejpam-2623	425	1	to	to	PART
ejpam-2623	425	2	avoid	avoid	VERB
ejpam-2623	425	3	these	these	DET
ejpam-2623	425	4	problems	problem	NOUN
ejpam-2623	425	5	,	,	PUNCT
ejpam-2623	425	6	one	one	PRON
ejpam-2623	425	7	can	can	AUX
ejpam-2623	425	8	possibly	possibly	ADV
ejpam-2623	425	9	n.	n.	PROPN
ejpam-2623	425	10	diarra	diarra	PROPN
ejpam-2623	425	11	,	,	PUNCT
ejpam-2623	425	12	d.	d.	PROPN
ejpam-2623	425	13	sow	sow	PROPN
ejpam-2623	425	14	,	,	PUNCT
ejpam-2623	425	15	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	425	16	.	.	PUNCT
ejpam-2623	425	17	khlil	khlil	PROPN
ejpam-2623	425	18	/	/	SYM
ejpam-2623	425	19	eur	eur	PROPN
ejpam-2623	425	20	.	.	PUNCT
ejpam-2623	426	1	j.	j.	PROPN
ejpam-2623	426	2	pure	pure	PROPN
ejpam-2623	426	3	appl	appl	PROPN
ejpam-2623	426	4	.	.	PROPN
ejpam-2623	426	5	math	math	PROPN
ejpam-2623	426	6	,	,	PUNCT
ejpam-2623	426	7	10	10	NUM
ejpam-2623	426	8	(	(	PUNCT
ejpam-2623	426	9	2	2	NUM
ejpam-2623	426	10	)	)	PUNCT
ejpam-2623	426	11	(	(	PUNCT
ejpam-2623	426	12	2017	2017	NUM
ejpam-2623	426	13	)	)	PUNCT
ejpam-2623	426	14	,	,	PUNCT
ejpam-2623	426	15	363	363	NUM
ejpam-2623	426	16	-	-	SYM
ejpam-2623	426	17	391	391	NUM
ejpam-2623	426	18	374	374	NUM
ejpam-2623	426	19	use	use	NOUN
ejpam-2623	426	20	the	the	DET
ejpam-2623	426	21	translation	translation	NOUN
ejpam-2623	426	22	suggested	suggest	VERB
ejpam-2623	426	23	in	in	ADP
ejpam-2623	426	24	[	[	X
ejpam-2623	426	25	12	12	NUM
ejpam-2623	426	26	]	]	PUNCT
ejpam-2623	426	27	,	,	PUNCT
ejpam-2623	426	28	page	page	NOUN
ejpam-2623	426	29	13	13	NUM
ejpam-2623	426	30	.	.	PUNCT
ejpam-2623	427	1	in	in	ADP
ejpam-2623	427	2	this	this	DET
ejpam-2623	427	3	section	section	NOUN
ejpam-2623	427	4	,	,	PUNCT
ejpam-2623	427	5	we	we	PRON
ejpam-2623	427	6	propose	propose	VERB
ejpam-2623	427	7	an	an	DET
ejpam-2623	427	8	encoding	encoding	NOUN
ejpam-2623	427	9	function	function	NOUN
ejpam-2623	427	10	for	for	ADP
ejpam-2623	427	11	the	the	DET
ejpam-2623	427	12	classical	classical	ADJ
ejpam-2623	427	13	huff	huff	NOUN
ejpam-2623	427	14	model	model	NOUN
ejpam-2623	427	15	αx(y2	αx(y2	ADP
ejpam-2623	427	16	−	−	PROPN
ejpam-2623	427	17	1	1	NUM
ejpam-2623	427	18	)	)	PUNCT
ejpam-2623	427	19	=	=	SYM
ejpam-2623	427	20	βy(x2	βy(x2	NOUN
ejpam-2623	428	1	−	−	NOUN
ejpam-2623	428	2	1	1	NUM
ejpam-2623	428	3	)	)	PUNCT
ejpam-2623	428	4	with	with	ADP
ejpam-2623	428	5	αβ(α2	αβ(α2	PRON
ejpam-2623	428	6	−	−	NOUN
ejpam-2623	428	7	β2)(α2	β2)(α2	PUNCT
ejpam-2623	429	1	+	+	CCONJ
ejpam-2623	429	2	β2	β2	ADJ
ejpam-2623	429	3	)	)	PUNCT
ejpam-2623	429	4	6=	6=	ADP
ejpam-2623	429	5	0	0	NUM
ejpam-2623	429	6	,	,	PUNCT
ejpam-2623	429	7	using	use	VERB
ejpam-2623	429	8	elligator-2	elligator-2	NUM
ejpam-2623	429	9	method	method	NOUN
ejpam-2623	429	10	as	as	ADP
ejpam-2623	429	11	in	in	ADP
ejpam-2623	429	12	[	[	X
ejpam-2623	429	13	4	4	NUM
ejpam-2623	429	14	]	]	PUNCT
ejpam-2623	429	15	.	.	PUNCT
ejpam-2623	430	1	elligator-2	elligator-2	PRON
ejpam-2623	430	2	method	method	PROPN
ejpam-2623	430	3	’s	’s	PART
ejpam-2623	430	4	propose	propose	VERB
ejpam-2623	430	5	an	an	DET
ejpam-2623	430	6	injective	injective	ADJ
ejpam-2623	430	7	encoding	encoding	NOUN
ejpam-2623	430	8	for	for	ADP
ejpam-2623	430	9	weierstrass	weierstrass	NOUN
ejpam-2623	430	10	curves	curve	NOUN
ejpam-2623	430	11	of	of	ADP
ejpam-2623	430	12	the	the	DET
ejpam-2623	430	13	form	form	NOUN
ejpam-2623	430	14	y2	y2	NOUN
ejpam-2623	430	15	=	=	SYM
ejpam-2623	431	1	x3	x3	VERB
ejpam-2623	431	2	+	+	CCONJ
ejpam-2623	431	3	ax2	ax2	NOUN
ejpam-2623	431	4	+	+	CCONJ
ejpam-2623	431	5	bx	bx	PROPN
ejpam-2623	431	6	.	.	PUNCT
ejpam-2623	432	1	with	with	ADP
ejpam-2623	432	2	this	this	DET
ejpam-2623	432	3	method	method	NOUN
ejpam-2623	432	4	,	,	PUNCT
ejpam-2623	432	5	to	to	PART
ejpam-2623	432	6	encode	encode	VERB
ejpam-2623	432	7	into	into	ADP
ejpam-2623	432	8	another	another	DET
ejpam-2623	432	9	form	form	NOUN
ejpam-2623	432	10	(	(	PUNCT
ejpam-2623	432	11	such	such	ADJ
ejpam-2623	432	12	as	as	ADP
ejpam-2623	432	13	edwards	edwards	PROPN
ejpam-2623	432	14	,	,	PUNCT
ejpam-2623	432	15	huff	huff	PROPN
ejpam-2623	432	16	,	,	PUNCT
ejpam-2623	432	17	...	...	PUNCT
ejpam-2623	432	18	)	)	PUNCT
ejpam-2623	432	19	,	,	PUNCT
ejpam-2623	432	20	it	it	PRON
ejpam-2623	432	21	is	be	AUX
ejpam-2623	432	22	necessary	necessary	ADJ
ejpam-2623	432	23	to	to	PART
ejpam-2623	432	24	use	use	VERB
ejpam-2623	432	25	a	a	DET
ejpam-2623	432	26	birational	birational	ADJ
ejpam-2623	432	27	equivalence	equivalence	NOUN
ejpam-2623	432	28	.	.	PUNCT
ejpam-2623	433	1	we	we	PRON
ejpam-2623	433	2	propose	propose	VERB
ejpam-2623	433	3	the	the	DET
ejpam-2623	433	4	following	follow	VERB
ejpam-2623	433	5	algorithm	algorithm	NOUN
ejpam-2623	433	6	which	which	PRON
ejpam-2623	433	7	allows	allow	VERB
ejpam-2623	433	8	to	to	PART
ejpam-2623	433	9	encode	encode	VERB
ejpam-2623	433	10	directly	directly	ADV
ejpam-2623	433	11	into	into	ADP
ejpam-2623	433	12	huff	huff	NOUN
ejpam-2623	433	13	curves	curve	NOUN
ejpam-2623	433	14	,	,	PUNCT
ejpam-2623	433	15	without	without	ADP
ejpam-2623	433	16	using	use	VERB
ejpam-2623	433	17	any	any	DET
ejpam-2623	433	18	birational	birational	ADJ
ejpam-2623	433	19	equivalence	equivalence	NOUN
ejpam-2623	433	20	.	.	PUNCT
ejpam-2623	434	1	we	we	PRON
ejpam-2623	434	2	begin	begin	VERB
ejpam-2623	434	3	by	by	ADP
ejpam-2623	434	4	giving	give	VERB
ejpam-2623	434	5	the	the	DET
ejpam-2623	434	6	following	follow	VERB
ejpam-2623	434	7	algorithm	algorithm	NOUN
ejpam-2623	434	8	.	.	PUNCT
ejpam-2623	435	1	algorithm	algorithm	NOUN
ejpam-2623	435	2	1	1	NUM
ejpam-2623	435	3	.	.	PUNCT
ejpam-2623	436	1	input	input	NOUN
ejpam-2623	436	2	:	:	PUNCT
ejpam-2623	436	3	α	α	X
ejpam-2623	436	4	,	,	PUNCT
ejpam-2623	436	5	β	β	PROPN
ejpam-2623	436	6	∈	∈	PROPN
ejpam-2623	436	7	fq	fq	NOUN
ejpam-2623	436	8	such	such	ADJ
ejpam-2623	436	9	that	that	DET
ejpam-2623	436	10	αβ(α2−β2)(α2+β2	αβ(α2−β2)(α2+β2	NOUN
ejpam-2623	436	11	)	)	PUNCT
ejpam-2623	436	12	6=	6=	ADP
ejpam-2623	436	13	0	0	NUM
ejpam-2623	436	14	,	,	PUNCT
ejpam-2623	436	15	u	u	PROPN
ejpam-2623	436	16	a	a	DET
ejpam-2623	436	17	non	non	ADJ
ejpam-2623	436	18	-	-	ADJ
ejpam-2623	436	19	square	square	ADJ
ejpam-2623	436	20	in	in	ADP
ejpam-2623	436	21	fq	fq	PROPN
ejpam-2623	436	22	and	and	CCONJ
ejpam-2623	436	23	r	r	PROPN
ejpam-2623	436	24	∈	∈	PROPN
ejpam-2623	436	25	fq	fq	NOUN
ejpam-2623	436	26	verifying	verify	VERB
ejpam-2623	436	27	α2	α2	NOUN
ejpam-2623	436	28	+	+	CCONJ
ejpam-2623	437	1	uβ2r2	uβ2r2	PROPN
ejpam-2623	437	2	6=	6=	NUM
ejpam-2623	437	3	0	0	NUM
ejpam-2623	437	4	;	;	PUNCT
ejpam-2623	437	5	output	output	NOUN
ejpam-2623	437	6	:	:	PUNCT
ejpam-2623	437	7	a	a	DET
ejpam-2623	437	8	point	point	NOUN
ejpam-2623	437	9	(	(	PUNCT
ejpam-2623	437	10	x	x	NOUN
ejpam-2623	437	11	,	,	PUNCT
ejpam-2623	437	12	y	y	PROPN
ejpam-2623	437	13	)	)	PUNCT
ejpam-2623	437	14	∈	∈	PROPN
ejpam-2623	437	15	eα	eα	NOUN
ejpam-2623	437	16	,	,	PUNCT
ejpam-2623	437	17	β	β	X
ejpam-2623	437	18	:	:	PUNCT
ejpam-2623	437	19	αx(y2	αx(y2	PRON
ejpam-2623	437	20	−	−	PROPN
ejpam-2623	437	21	1	1	NUM
ejpam-2623	437	22	)	)	PUNCT
ejpam-2623	437	23	=	=	SYM
ejpam-2623	437	24	βy(x2	βy(x2	NOUN
ejpam-2623	438	1	−	−	NOUN
ejpam-2623	438	2	1	1	NUM
ejpam-2623	438	3	)	)	PUNCT
ejpam-2623	438	4	;	;	PUNCT
ejpam-2623	439	1	1	1	X
ejpam-2623	439	2	.	.	X
ejpam-2623	439	3	v	v	NOUN
ejpam-2623	439	4	=	=	PRON
ejpam-2623	439	5	β(α2	β(α2	X
ejpam-2623	439	6	+	+	CCONJ
ejpam-2623	439	7	uβ2r2	uβ2r2	PROPN
ejpam-2623	439	8	)	)	PUNCT
ejpam-2623	439	9	α(α2	α(α2	NOUN
ejpam-2623	440	1	+	+	CCONJ
ejpam-2623	440	2	β2	β2	VERB
ejpam-2623	440	3	)	)	PUNCT
ejpam-2623	440	4	;	;	PUNCT
ejpam-2623	441	1	2	2	X
ejpam-2623	441	2	.	.	X
ejpam-2623	441	3	ε	ε	PROPN
ejpam-2623	441	4	=	=	SYM
ejpam-2623	441	5	χ	χ	PROPN
ejpam-2623	441	6	(	(	PUNCT
ejpam-2623	441	7	v(αv	v(αv	NUM
ejpam-2623	441	8	−	−	PROPN
ejpam-2623	441	9	β)(α−	β)(α−	PROPN
ejpam-2623	441	10	βv	βv	PROPN
ejpam-2623	441	11	)	)	PUNCT
ejpam-2623	441	12	)	)	PUNCT
ejpam-2623	441	13	;	;	PUNCT
ejpam-2623	442	1	3	3	X
ejpam-2623	442	2	.	.	X
ejpam-2623	442	3	t	t	NOUN
ejpam-2623	443	1	=	=	SYM
ejpam-2623	444	1	1	1	NUM
ejpam-2623	444	2	2	2	NUM
ejpam-2623	444	3	(	(	PUNCT
ejpam-2623	444	4	ε	ε	PROPN
ejpam-2623	444	5	(	(	PUNCT
ejpam-2623	444	6	1	1	NUM
ejpam-2623	444	7	+	+	NUM
ejpam-2623	444	8	v2	v2	NOUN
ejpam-2623	444	9	v	v	ADP
ejpam-2623	444	10	−	−	PROPN
ejpam-2623	444	11	α	α	NOUN
ejpam-2623	444	12	β	β	NOUN
ejpam-2623	444	13	−	−	X
ejpam-2623	444	14	β	β	X
ejpam-2623	444	15	α	α	NOUN
ejpam-2623	444	16	)	)	PUNCT
ejpam-2623	445	1	+	+	CCONJ
ejpam-2623	445	2	(	(	PUNCT
ejpam-2623	445	3	α	α	X
ejpam-2623	445	4	β	β	X
ejpam-2623	445	5	+	+	X
ejpam-2623	445	6	β	β	X
ejpam-2623	445	7	α	α	NOUN
ejpam-2623	445	8	+	+	X
ejpam-2623	445	9	v2	v2	PROPN
ejpam-2623	445	10	−	−	NOUN
ejpam-2623	445	11	1	1	NUM
ejpam-2623	445	12	v	v	NOUN
ejpam-2623	445	13	)	)	PUNCT
ejpam-2623	445	14	)	)	PUNCT
ejpam-2623	445	15	;	;	PUNCT
ejpam-2623	446	1	4	4	X
ejpam-2623	446	2	.	.	NUM
ejpam-2623	446	3	x	x	X
ejpam-2623	447	1	=	=	PUNCT
ejpam-2623	447	2	−ε	−ε	PROPN
ejpam-2623	447	3	√	√	NUM
ejpam-2623	447	4	t(αt−	t(αt−	NUM
ejpam-2623	447	5	β	β	NOUN
ejpam-2623	447	6	)	)	PUNCT
ejpam-2623	447	7	α−	α−	AUX
ejpam-2623	447	8	βt	βt	VERB
ejpam-2623	447	9	;	;	PUNCT
ejpam-2623	447	10	5	5	X
ejpam-2623	447	11	.	.	X
ejpam-2623	447	12	y	y	NOUN
ejpam-2623	447	13	=	=	PUNCT
ejpam-2623	447	14	x	x	SYM
ejpam-2623	447	15	t	t	NOUN
ejpam-2623	447	16	;	;	PUNCT
ejpam-2623	447	17	6	6	NUM
ejpam-2623	447	18	.	.	X
ejpam-2623	447	19	return	return	NOUN
ejpam-2623	447	20	(	(	PUNCT
ejpam-2623	447	21	x	x	X
ejpam-2623	447	22	,	,	PUNCT
ejpam-2623	447	23	y	y	PROPN
ejpam-2623	447	24	)	)	PUNCT
ejpam-2623	447	25	;	;	PUNCT
ejpam-2623	447	26	theorem	theorem	VERB
ejpam-2623	447	27	3	3	X
ejpam-2623	447	28	.	.	PUNCT
ejpam-2623	448	1	let	let	VERB
ejpam-2623	448	2	q	q	PART
ejpam-2623	448	3	be	be	AUX
ejpam-2623	448	4	a	a	DET
ejpam-2623	448	5	prime	prime	ADJ
ejpam-2623	448	6	power	power	NOUN
ejpam-2623	448	7	,	,	PUNCT
ejpam-2623	448	8	α	α	X
ejpam-2623	448	9	,	,	PUNCT
ejpam-2623	448	10	β	β	X
ejpam-2623	448	11	∈	∈	PROPN
ejpam-2623	448	12	fq	fq	NOUN
ejpam-2623	448	13	such	such	ADJ
ejpam-2623	448	14	that	that	SCONJ
ejpam-2623	448	15	αβ(α2	αβ(α2	ADP
ejpam-2623	448	16	−	−	NOUN
ejpam-2623	448	17	β2)(α2	β2)(α2	PUNCT
ejpam-2623	449	1	+	+	CCONJ
ejpam-2623	449	2	β2	β2	ADJ
ejpam-2623	449	3	)	)	PUNCT
ejpam-2623	449	4	6=	6=	ADP
ejpam-2623	449	5	0	0	NUM
ejpam-2623	449	6	,	,	PUNCT
ejpam-2623	449	7	u	u	PROPN
ejpam-2623	449	8	a	a	DET
ejpam-2623	449	9	non	non	ADJ
ejpam-2623	449	10	-	-	ADJ
ejpam-2623	449	11	square	square	ADJ
ejpam-2623	449	12	in	in	ADP
ejpam-2623	449	13	fq	fq	PROPN
ejpam-2623	449	14	and	and	CCONJ
ejpam-2623	449	15	define	define	VERB
ejpam-2623	449	16	the	the	DET
ejpam-2623	449	17	set	set	NOUN
ejpam-2623	449	18	r	r	NOUN
ejpam-2623	449	19	=	=	PUNCT
ejpam-2623	449	20	{	{	PUNCT
ejpam-2623	449	21	r	r	NOUN
ejpam-2623	449	22	∈	∈	PROPN
ejpam-2623	449	23	fq	fq	NOUN
ejpam-2623	449	24	:	:	PUNCT
ejpam-2623	449	25	α2	α2	PROPN
ejpam-2623	449	26	+	+	CCONJ
ejpam-2623	450	1	uβ2r2	uβ2r2	PROPN
ejpam-2623	450	2	6=	6=	ADP
ejpam-2623	450	3	0	0	NUM
ejpam-2623	450	4	}	}	PUNCT
ejpam-2623	450	5	.	.	PUNCT
ejpam-2623	451	1	let	let	VERB
ejpam-2623	451	2	eα	eα	PRON
ejpam-2623	451	3	,	,	PUNCT
ejpam-2623	451	4	β	β	X
ejpam-2623	451	5	be	be	VERB
ejpam-2623	451	6	the	the	DET
ejpam-2623	451	7	elliptic	elliptic	ADJ
ejpam-2623	451	8	curve	curve	NOUN
ejpam-2623	451	9	defined	define	VERB
ejpam-2623	451	10	over	over	ADP
ejpam-2623	451	11	fq	fq	PROPN
ejpam-2623	451	12	by	by	ADP
ejpam-2623	451	13	αx(y2	αx(y2	PRON
ejpam-2623	451	14	−	−	PROPN
ejpam-2623	451	15	1	1	NUM
ejpam-2623	451	16	)	)	PUNCT
ejpam-2623	451	17	=	=	SYM
ejpam-2623	452	1	βy(x2	βy(x2	NOUN
ejpam-2623	453	1	−	−	NOUN
ejpam-2623	453	2	1	1	NUM
ejpam-2623	453	3	)	)	PUNCT
ejpam-2623	453	4	.	.	PUNCT
ejpam-2623	454	1	then	then	ADV
ejpam-2623	454	2	algorithm	algorithm	NOUN
ejpam-2623	454	3	1	1	NUM
ejpam-2623	454	4	defines	define	VERB
ejpam-2623	454	5	a	a	DET
ejpam-2623	454	6	deterministic	deterministic	ADJ
ejpam-2623	454	7	encoding	encoding	NOUN
ejpam-2623	454	8	φα	φα	PROPN
ejpam-2623	454	9	,	,	PUNCT
ejpam-2623	454	10	β	β	X
ejpam-2623	454	11	:	:	PUNCT
ejpam-2623	455	1	r→	r→	PROPN
ejpam-2623	455	2	eα	eα	PROPN
ejpam-2623	455	3	,	,	PUNCT
ejpam-2623	455	4	β	β	X
ejpam-2623	455	5	,	,	PUNCT
ejpam-2623	455	6	r	r	PROPN
ejpam-2623	455	7	7→	7→	NUM
ejpam-2623	455	8	φα	φα	ADP
ejpam-2623	455	9	,	,	PUNCT
ejpam-2623	455	10	β(r	β(r	NOUN
ejpam-2623	455	11	)	)	PUNCT
ejpam-2623	455	12	=	=	SYM
ejpam-2623	455	13	(	(	PUNCT
ejpam-2623	455	14	x	x	X
ejpam-2623	455	15	,	,	PUNCT
ejpam-2623	455	16	y	y	PROPN
ejpam-2623	455	17	)	)	PUNCT
ejpam-2623	455	18	.	.	PUNCT
ejpam-2623	456	1	proof	proof	NOUN
ejpam-2623	456	2	.	.	PUNCT
ejpam-2623	457	1	(	(	PUNCT
ejpam-2623	457	2	i	i	NOUN
ejpam-2623	457	3	)	)	PUNCT
ejpam-2623	457	4	let	let	VERB
ejpam-2623	457	5	us	we	PRON
ejpam-2623	457	6	show	show	VERB
ejpam-2623	457	7	that	that	SCONJ
ejpam-2623	457	8	v	v	NOUN
ejpam-2623	457	9	is	be	AUX
ejpam-2623	457	10	well	well	ADV
ejpam-2623	457	11	-	-	PUNCT
ejpam-2623	457	12	defined	define	VERB
ejpam-2623	457	13	and	and	CCONJ
ejpam-2623	457	14	v	v	ADP
ejpam-2623	457	15	6=	6=	NUM
ejpam-2623	457	16	0	0	NUM
ejpam-2623	457	17	:	:	PUNCT
ejpam-2623	457	18	by	by	ADP
ejpam-2623	457	19	the	the	DET
ejpam-2623	457	20	hypothesis	hypothesis	NOUN
ejpam-2623	457	21	on	on	ADP
ejpam-2623	457	22	α	α	PROPN
ejpam-2623	457	23	and	and	CCONJ
ejpam-2623	457	24	β	β	X
ejpam-2623	457	25	,	,	PUNCT
ejpam-2623	457	26	we	we	PRON
ejpam-2623	457	27	have	have	VERB
ejpam-2623	457	28	α(α2	α(α2	NOUN
ejpam-2623	458	1	+	+	ADJ
ejpam-2623	458	2	β2	β2	ADJ
ejpam-2623	458	3	)	)	PUNCT
ejpam-2623	458	4	6=	6=	ADP
ejpam-2623	458	5	0	0	NUM
ejpam-2623	458	6	;	;	PUNCT
ejpam-2623	458	7	so	so	SCONJ
ejpam-2623	458	8	v	v	NOUN
ejpam-2623	458	9	is	be	AUX
ejpam-2623	458	10	well	well	ADV
ejpam-2623	458	11	-	-	PUNCT
ejpam-2623	458	12	defined	define	VERB
ejpam-2623	458	13	.	.	PUNCT
ejpam-2623	459	1	suppose	suppose	VERB
ejpam-2623	459	2	that	that	SCONJ
ejpam-2623	459	3	v	v	NOUN
ejpam-2623	459	4	=	=	SYM
ejpam-2623	459	5	0	0	NUM
ejpam-2623	459	6	;	;	PUNCT
ejpam-2623	459	7	this	this	PRON
ejpam-2623	459	8	implies	imply	VERB
ejpam-2623	459	9	that	that	SCONJ
ejpam-2623	459	10	α2	α2	ADJ
ejpam-2623	459	11	+	+	CCONJ
ejpam-2623	459	12	uβ2r2	uβ2r2	PROPN
ejpam-2623	459	13	=	=	SYM
ejpam-2623	459	14	0	0	NUM
ejpam-2623	459	15	,	,	PUNCT
ejpam-2623	459	16	which	which	PRON
ejpam-2623	459	17	is	be	AUX
ejpam-2623	459	18	impossible	impossible	ADJ
ejpam-2623	459	19	by	by	ADP
ejpam-2623	459	20	the	the	DET
ejpam-2623	459	21	definition	definition	NOUN
ejpam-2623	459	22	of	of	ADP
ejpam-2623	459	23	r.	r.	PROPN
ejpam-2623	459	24	thus	thus	ADV
ejpam-2623	459	25	v	v	ADP
ejpam-2623	459	26	6=	6=	PROPN
ejpam-2623	459	27	0	0	NUM
ejpam-2623	459	28	.	.	PUNCT
ejpam-2623	460	1	n.	n.	PROPN
ejpam-2623	460	2	diarra	diarra	PROPN
ejpam-2623	460	3	,	,	PUNCT
ejpam-2623	460	4	d.	d.	PROPN
ejpam-2623	460	5	sow	sow	PROPN
ejpam-2623	460	6	,	,	PUNCT
ejpam-2623	460	7	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	460	8	.	.	PUNCT
ejpam-2623	460	9	khlil	khlil	PROPN
ejpam-2623	460	10	/	/	SYM
ejpam-2623	460	11	eur	eur	PROPN
ejpam-2623	460	12	.	.	PUNCT
ejpam-2623	461	1	j.	j.	PROPN
ejpam-2623	461	2	pure	pure	PROPN
ejpam-2623	461	3	appl	appl	PROPN
ejpam-2623	461	4	.	.	PROPN
ejpam-2623	461	5	math	math	PROPN
ejpam-2623	461	6	,	,	PUNCT
ejpam-2623	461	7	10	10	NUM
ejpam-2623	461	8	(	(	PUNCT
ejpam-2623	461	9	2	2	NUM
ejpam-2623	461	10	)	)	PUNCT
ejpam-2623	461	11	(	(	PUNCT
ejpam-2623	461	12	2017	2017	NUM
ejpam-2623	461	13	)	)	PUNCT
ejpam-2623	461	14	,	,	PUNCT
ejpam-2623	461	15	363	363	NUM
ejpam-2623	461	16	-	-	SYM
ejpam-2623	461	17	391	391	NUM
ejpam-2623	461	18	375	375	NUM
ejpam-2623	461	19	(	(	PUNCT
ejpam-2623	461	20	ii	ii	NOUN
ejpam-2623	461	21	)	)	PUNCT
ejpam-2623	461	22	we	we	PRON
ejpam-2623	461	23	show	show	VERB
ejpam-2623	461	24	that	that	SCONJ
ejpam-2623	461	25	ε	ε	PROPN
ejpam-2623	461	26	is	be	AUX
ejpam-2623	461	27	well	well	ADV
ejpam-2623	461	28	-	-	PUNCT
ejpam-2623	461	29	defined	define	VERB
ejpam-2623	461	30	and	and	CCONJ
ejpam-2623	461	31	ε	ε	PROPN
ejpam-2623	461	32	6=	6=	NUM
ejpam-2623	461	33	0	0	NUM
ejpam-2623	461	34	:	:	PUNCT
ejpam-2623	461	35	in	in	ADP
ejpam-2623	461	36	fact	fact	NOUN
ejpam-2623	461	37	,	,	PUNCT
ejpam-2623	461	38	suppose	suppose	VERB
ejpam-2623	461	39	that	that	SCONJ
ejpam-2623	461	40	α−βv	α−βv	NOUN
ejpam-2623	461	41	=	=	SYM
ejpam-2623	461	42	0	0	NUM
ejpam-2623	461	43	;	;	PUNCT
ejpam-2623	461	44	this	this	PRON
ejpam-2623	461	45	implies	imply	VERB
ejpam-2623	461	46	that	that	SCONJ
ejpam-2623	461	47	α2(α2	α2(α2	NUM
ejpam-2623	461	48	+	+	ADJ
ejpam-2623	461	49	β2)−β2(α2	β2)−β2(α2	PROPN
ejpam-2623	461	50	+	+	ADJ
ejpam-2623	461	51	uβ2r2	uβ2r2	NOUN
ejpam-2623	461	52	)	)	PUNCT
ejpam-2623	461	53	=	=	SYM
ejpam-2623	461	54	0	0	PUNCT
ejpam-2623	461	55	and	and	CCONJ
ejpam-2623	461	56	then	then	ADV
ejpam-2623	461	57	r2	r2	PROPN
ejpam-2623	461	58	=	=	SYM
ejpam-2623	461	59	α4	α4	PROPN
ejpam-2623	461	60	uβ4	uβ4	PROPN
ejpam-2623	461	61	.	.	PUNCT
ejpam-2623	462	1	this	this	PRON
ejpam-2623	462	2	can	can	AUX
ejpam-2623	462	3	not	not	PART
ejpam-2623	462	4	happen	happen	VERB
ejpam-2623	462	5	since	since	SCONJ
ejpam-2623	462	6	u	u	NOUN
ejpam-2623	462	7	is	be	AUX
ejpam-2623	462	8	not	not	PART
ejpam-2623	462	9	a	a	DET
ejpam-2623	462	10	square	square	NOUN
ejpam-2623	462	11	in	in	ADP
ejpam-2623	462	12	fq	fq	PROPN
ejpam-2623	462	13	;	;	PUNCT
ejpam-2623	462	14	so	so	ADV
ejpam-2623	462	15	ε	ε	PROPN
ejpam-2623	462	16	is	be	AUX
ejpam-2623	462	17	well	well	ADV
ejpam-2623	462	18	-	-	PUNCT
ejpam-2623	462	19	defined	define	VERB
ejpam-2623	462	20	.	.	PUNCT
ejpam-2623	463	1	now	now	ADV
ejpam-2623	463	2	suppose	suppose	VERB
ejpam-2623	463	3	that	that	SCONJ
ejpam-2623	463	4	ε	ε	PROPN
ejpam-2623	463	5	=	=	SYM
ejpam-2623	463	6	0	0	NUM
ejpam-2623	463	7	;	;	PUNCT
ejpam-2623	463	8	so	so	ADV
ejpam-2623	463	9	v(αv	v(αv	NUM
ejpam-2623	463	10	−	−	PROPN
ejpam-2623	463	11	β	β	X
ejpam-2623	463	12	)	)	PUNCT
ejpam-2623	463	13	=	=	SYM
ejpam-2623	463	14	0	0	PUNCT
ejpam-2623	464	1	and	and	CCONJ
ejpam-2623	464	2	then	then	ADV
ejpam-2623	464	3	αv	αv	ADP
ejpam-2623	464	4	−	−	PROPN
ejpam-2623	464	5	β	β	X
ejpam-2623	464	6	since	since	SCONJ
ejpam-2623	464	7	v	v	NUM
ejpam-2623	464	8	6=	6=	PROPN
ejpam-2623	464	9	0	0	NUM
ejpam-2623	464	10	.	.	PUNCT
ejpam-2623	465	1	but	but	CCONJ
ejpam-2623	465	2	αv	αv	ADP
ejpam-2623	465	3	−	−	PROPN
ejpam-2623	465	4	β	β	NOUN
ejpam-2623	465	5	=	=	SYM
ejpam-2623	465	6	0	0	NUM
ejpam-2623	465	7	⇒	⇒	NOUN
ejpam-2623	465	8	αβ(α2	αβ(α2	X
ejpam-2623	465	9	+	+	CCONJ
ejpam-2623	465	10	uβ2r2	uβ2r2	NOUN
ejpam-2623	465	11	)	)	PUNCT
ejpam-2623	465	12	−	−	PROPN
ejpam-2623	465	13	αβ(α2	αβ(α2	X
ejpam-2623	466	1	+	+	CCONJ
ejpam-2623	466	2	β2	β2	ADJ
ejpam-2623	466	3	)	)	PUNCT
ejpam-2623	466	4	=	=	SYM
ejpam-2623	466	5	0	0	NUM
ejpam-2623	466	6	⇒	⇒	NOUN
ejpam-2623	466	7	uαβ3r2	uαβ3r2	ADV
ejpam-2623	466	8	−	−	PROPN
ejpam-2623	466	9	αβ3	αβ3	NOUN
ejpam-2623	466	10	=	=	SYM
ejpam-2623	466	11	0	0	NUM
ejpam-2623	466	12	⇒	⇒	NOUN
ejpam-2623	466	13	r2	r2	NOUN
ejpam-2623	466	14	=	=	SYM
ejpam-2623	466	15	1	1	NUM
ejpam-2623	466	16	u	u	NOUN
ejpam-2623	466	17	;	;	PUNCT
ejpam-2623	466	18	contradiction	contradiction	NOUN
ejpam-2623	466	19	since	since	SCONJ
ejpam-2623	466	20	u	u	NOUN
ejpam-2623	466	21	is	be	AUX
ejpam-2623	466	22	not	not	PART
ejpam-2623	466	23	a	a	DET
ejpam-2623	466	24	square	square	NOUN
ejpam-2623	466	25	.	.	PUNCT
ejpam-2623	467	1	finally	finally	ADV
ejpam-2623	467	2	we	we	PRON
ejpam-2623	467	3	have	have	VERB
ejpam-2623	467	4	ε	ε	PROPN
ejpam-2623	467	5	6=	6=	ADP
ejpam-2623	467	6	0	0	NUM
ejpam-2623	467	7	,	,	PUNCT
ejpam-2623	467	8	that	that	PRON
ejpam-2623	467	9	is	be	AUX
ejpam-2623	467	10	ε	ε	PROPN
ejpam-2623	467	11	=	=	SYM
ejpam-2623	467	12	±1	±1	VERB
ejpam-2623	467	13	.	.	PUNCT
ejpam-2623	468	1	(	(	PUNCT
ejpam-2623	468	2	iii	iii	X
ejpam-2623	468	3	)	)	PUNCT
ejpam-2623	468	4	let	let	VERB
ejpam-2623	468	5	us	we	PRON
ejpam-2623	468	6	show	show	VERB
ejpam-2623	468	7	that	that	SCONJ
ejpam-2623	468	8	t	t	PROPN
ejpam-2623	468	9	is	be	AUX
ejpam-2623	468	10	well	well	ADV
ejpam-2623	468	11	-	-	PUNCT
ejpam-2623	468	12	defined	define	VERB
ejpam-2623	468	13	and	and	CCONJ
ejpam-2623	468	14	t	t	PROPN
ejpam-2623	468	15	6=	6=	NUM
ejpam-2623	468	16	0	0	NUM
ejpam-2623	468	17	:	:	PUNCT
ejpam-2623	468	18	first	first	ADV
ejpam-2623	468	19	see	see	VERB
ejpam-2623	468	20	that	that	SCONJ
ejpam-2623	468	21	αβv	αβv	PRON
ejpam-2623	468	22	6=	6=	ADP
ejpam-2623	468	23	0	0	NUM
ejpam-2623	468	24	;	;	PUNCT
ejpam-2623	468	25	so	so	SCONJ
ejpam-2623	468	26	t	t	PROPN
ejpam-2623	468	27	is	be	AUX
ejpam-2623	468	28	well	well	ADV
ejpam-2623	468	29	-	-	PUNCT
ejpam-2623	468	30	defined	define	VERB
ejpam-2623	468	31	.	.	PUNCT
ejpam-2623	469	1	to	to	PART
ejpam-2623	469	2	show	show	VERB
ejpam-2623	469	3	that	that	PRON
ejpam-2623	469	4	t	t	PROPN
ejpam-2623	469	5	6=	6=	PRON
ejpam-2623	469	6	0	0	NUM
ejpam-2623	469	7	,	,	PUNCT
ejpam-2623	469	8	we	we	PRON
ejpam-2623	469	9	have	have	VERB
ejpam-2623	469	10	to	to	PART
ejpam-2623	469	11	consider	consider	VERB
ejpam-2623	469	12	the	the	DET
ejpam-2623	469	13	cases	case	NOUN
ejpam-2623	469	14	where	where	SCONJ
ejpam-2623	469	15	ε	ε	PROPN
ejpam-2623	469	16	=	=	SYM
ejpam-2623	469	17	1	1	NUM
ejpam-2623	469	18	and	and	CCONJ
ejpam-2623	469	19	where	where	SCONJ
ejpam-2623	469	20	ε	ε	PROPN
ejpam-2623	469	21	=	=	SYM
ejpam-2623	469	22	−1	−1	PROPN
ejpam-2623	469	23	.	.	PUNCT
ejpam-2623	470	1	•	•	INTJ
ejpam-2623	470	2	if	if	SCONJ
ejpam-2623	470	3	ε	ε	PROPN
ejpam-2623	470	4	=	=	SYM
ejpam-2623	470	5	1	1	NUM
ejpam-2623	470	6	,	,	PUNCT
ejpam-2623	470	7	then	then	ADV
ejpam-2623	470	8	t	t	PROPN
ejpam-2623	470	9	=	=	SYM
ejpam-2623	470	10	v	v	PROPN
ejpam-2623	470	11	6=	6=	PROPN
ejpam-2623	470	12	0	0	NUM
ejpam-2623	470	13	.	.	NOUN
ejpam-2623	471	1	•	•	NUM
ejpam-2623	471	2	if	if	SCONJ
ejpam-2623	471	3	ε	ε	PROPN
ejpam-2623	471	4	=	=	SYM
ejpam-2623	471	5	−1	−1	NOUN
ejpam-2623	471	6	,	,	PUNCT
ejpam-2623	471	7	then	then	ADV
ejpam-2623	471	8	t	t	PROPN
ejpam-2623	471	9	=	=	PUNCT
ejpam-2623	471	10	v(α2	v(α2	X
ejpam-2623	472	1	+	+	CCONJ
ejpam-2623	473	1	β2)−	β2)−	ADJ
ejpam-2623	473	2	αβ	αβ	NUM
ejpam-2623	473	3	αβv	αβv	PRON
ejpam-2623	473	4	.	.	PUNCT
ejpam-2623	474	1	suppose	suppose	VERB
ejpam-2623	474	2	that	that	SCONJ
ejpam-2623	474	3	v(α2	v(α2	PROPN
ejpam-2623	474	4	+	+	CCONJ
ejpam-2623	474	5	β2	β2	NOUN
ejpam-2623	474	6	)	)	PUNCT
ejpam-2623	474	7	−	−	PROPN
ejpam-2623	475	1	αβ	αβ	INTJ
ejpam-2623	475	2	=	=	NOUN
ejpam-2623	475	3	0	0	NUM
ejpam-2623	475	4	;	;	PUNCT
ejpam-2623	475	5	so	so	SCONJ
ejpam-2623	475	6	β(α2	β(α2	PRON
ejpam-2623	476	1	+	+	CCONJ
ejpam-2623	476	2	uβ2r2	uβ2r2	ADJ
ejpam-2623	476	3	)	)	PUNCT
ejpam-2623	476	4	α(α2	α(α2	NOUN
ejpam-2623	477	1	+	+	CCONJ
ejpam-2623	477	2	β2	β2	VERB
ejpam-2623	477	3	)	)	PUNCT
ejpam-2623	477	4	=	=	SYM
ejpam-2623	478	1	v	v	NOUN
ejpam-2623	478	2	=	=	SYM
ejpam-2623	478	3	αβ	αβ	INTJ
ejpam-2623	478	4	α2	α2	ADJ
ejpam-2623	478	5	+	+	CCONJ
ejpam-2623	478	6	β2	β2	VERB
ejpam-2623	478	7	.	.	PUNCT
ejpam-2623	479	1	this	this	PRON
ejpam-2623	479	2	implies	imply	VERB
ejpam-2623	479	3	that	that	SCONJ
ejpam-2623	479	4	uβ2r2	uβ2r2	PROPN
ejpam-2623	479	5	=	=	SYM
ejpam-2623	479	6	0	0	NUM
ejpam-2623	479	7	which	which	PRON
ejpam-2623	479	8	is	be	AUX
ejpam-2623	479	9	impossible	impossible	ADJ
ejpam-2623	479	10	since	since	SCONJ
ejpam-2623	479	11	r	r	NOUN
ejpam-2623	479	12	∈	∈	PROPN
ejpam-2623	479	13	r	r	NOUN
ejpam-2623	479	14	\	\	PUNCT
ejpam-2623	479	15	{	{	PUNCT
ejpam-2623	479	16	0	0	NUM
ejpam-2623	479	17	}	}	PUNCT
ejpam-2623	479	18	.	.	PUNCT
ejpam-2623	480	1	hence	hence	ADV
ejpam-2623	480	2	t	t	PROPN
ejpam-2623	480	3	6=	6=	PROPN
ejpam-2623	480	4	0	0	X
ejpam-2623	480	5	.	.	PUNCT
ejpam-2623	481	1	finally	finally	ADV
ejpam-2623	481	2	t	t	PROPN
ejpam-2623	481	3	is	be	AUX
ejpam-2623	481	4	well	well	ADV
ejpam-2623	481	5	-	-	PUNCT
ejpam-2623	481	6	defined	define	VERB
ejpam-2623	481	7	and	and	CCONJ
ejpam-2623	481	8	t	t	PROPN
ejpam-2623	481	9	6=	6=	PROPN
ejpam-2623	481	10	0	0	NUM
ejpam-2623	481	11	.	.	PUNCT
ejpam-2623	482	1	(	(	PUNCT
ejpam-2623	482	2	iv	iv	X
ejpam-2623	482	3	)	)	PUNCT
ejpam-2623	482	4	we	we	PRON
ejpam-2623	482	5	show	show	VERB
ejpam-2623	482	6	that	that	SCONJ
ejpam-2623	482	7	x	x	PRON
ejpam-2623	482	8	is	be	AUX
ejpam-2623	482	9	well	well	ADV
ejpam-2623	482	10	-	-	PUNCT
ejpam-2623	482	11	defined	define	VERB
ejpam-2623	482	12	and	and	CCONJ
ejpam-2623	482	13	x	x	SYM
ejpam-2623	482	14	6=	6=	ADP
ejpam-2623	482	15	0	0	NUM
ejpam-2623	482	16	:	:	PUNCT
ejpam-2623	482	17	for	for	ADP
ejpam-2623	482	18	this	this	PRON
ejpam-2623	482	19	,	,	PUNCT
ejpam-2623	482	20	we	we	PRON
ejpam-2623	482	21	must	must	AUX
ejpam-2623	482	22	show	show	VERB
ejpam-2623	482	23	that	that	SCONJ
ejpam-2623	482	24	t(αt−	t(αt−	NOUN
ejpam-2623	482	25	β	β	NOUN
ejpam-2623	482	26	)	)	PUNCT
ejpam-2623	482	27	α−	α−	AUX
ejpam-2623	482	28	βt	βt	VERB
ejpam-2623	482	29	is	be	AUX
ejpam-2623	482	30	well	well	ADV
ejpam-2623	482	31	-	-	PUNCT
ejpam-2623	482	32	defined	define	VERB
ejpam-2623	482	33	and	and	CCONJ
ejpam-2623	482	34	is	be	AUX
ejpam-2623	482	35	a	a	DET
ejpam-2623	482	36	non	non	ADJ
ejpam-2623	482	37	-	-	ADJ
ejpam-2623	482	38	zero	zero	NUM
ejpam-2623	482	39	square	square	NOUN
ejpam-2623	482	40	.	.	PUNCT
ejpam-2623	483	1	as	as	SCONJ
ejpam-2623	483	2	previously	previously	ADV
ejpam-2623	483	3	,	,	PUNCT
ejpam-2623	483	4	for	for	ADP
ejpam-2623	483	5	t	t	PROPN
ejpam-2623	483	6	,	,	PUNCT
ejpam-2623	483	7	we	we	PRON
ejpam-2623	483	8	have	have	VERB
ejpam-2623	483	9	to	to	PART
ejpam-2623	483	10	consider	consider	VERB
ejpam-2623	483	11	the	the	DET
ejpam-2623	483	12	cases	case	NOUN
ejpam-2623	483	13	where	where	SCONJ
ejpam-2623	483	14	ε	ε	PROPN
ejpam-2623	483	15	=	=	SYM
ejpam-2623	483	16	1	1	NUM
ejpam-2623	483	17	and	and	CCONJ
ejpam-2623	483	18	where	where	SCONJ
ejpam-2623	483	19	ε	ε	PROPN
ejpam-2623	483	20	=	=	SYM
ejpam-2623	483	21	−1	−1	PROPN
ejpam-2623	483	22	.	.	PUNCT
ejpam-2623	484	1	•	•	INTJ
ejpam-2623	484	2	if	if	SCONJ
ejpam-2623	484	3	ε	ε	PROPN
ejpam-2623	484	4	=	=	SYM
ejpam-2623	484	5	1	1	NUM
ejpam-2623	484	6	,	,	PUNCT
ejpam-2623	484	7	then	then	ADV
ejpam-2623	484	8	t	t	PROPN
ejpam-2623	484	9	=	=	SYM
ejpam-2623	484	10	v	v	PROPN
ejpam-2623	484	11	and	and	CCONJ
ejpam-2623	484	12	α−	α−	ADP
ejpam-2623	484	13	βt	βt	NOUN
ejpam-2623	485	1	=	=	PUNCT
ejpam-2623	485	2	α−	α−	ADP
ejpam-2623	485	3	βv	βv	PUNCT
ejpam-2623	485	4	=	=	NOUN
ejpam-2623	485	5	0	0	NUM
ejpam-2623	485	6	which	which	PRON
ejpam-2623	485	7	is	be	AUX
ejpam-2623	485	8	impossible	impossible	ADJ
ejpam-2623	485	9	as	as	SCONJ
ejpam-2623	485	10	previously	previously	ADV
ejpam-2623	485	11	shown	show	VERB
ejpam-2623	485	12	.	.	PUNCT
ejpam-2623	486	1	moreover	moreover	ADV
ejpam-2623	486	2	we	we	PRON
ejpam-2623	486	3	have	have	VERB
ejpam-2623	486	4	χ	χ	X
ejpam-2623	486	5	(	(	PUNCT
ejpam-2623	486	6	t(αt−	t(αt−	NUM
ejpam-2623	486	7	β	β	NOUN
ejpam-2623	486	8	)	)	PUNCT
ejpam-2623	486	9	α−	α−	ADP
ejpam-2623	486	10	βt	βt	NOUN
ejpam-2623	486	11	)	)	PUNCT
ejpam-2623	487	1	=	=	SYM
ejpam-2623	488	1	χ	χ	X
ejpam-2623	488	2	(	(	PUNCT
ejpam-2623	488	3	v(αv	v(αv	NUM
ejpam-2623	488	4	−	−	NOUN
ejpam-2623	488	5	β	β	NOUN
ejpam-2623	488	6	)	)	PUNCT
ejpam-2623	488	7	α−	α−	ADP
ejpam-2623	488	8	βv	βv	PUNCT
ejpam-2623	488	9	)	)	PUNCT
ejpam-2623	488	10	=	=	PUNCT
ejpam-2623	488	11	ε	ε	PROPN
ejpam-2623	488	12	=	=	SYM
ejpam-2623	488	13	1	1	X
ejpam-2623	488	14	.	.	PUNCT
ejpam-2623	488	15	hence	hence	ADV
ejpam-2623	488	16	we	we	PRON
ejpam-2623	488	17	conclude	conclude	VERB
ejpam-2623	488	18	that	that	SCONJ
ejpam-2623	488	19	x	x	PRON
ejpam-2623	488	20	is	be	AUX
ejpam-2623	488	21	well	well	ADV
ejpam-2623	488	22	-	-	PUNCT
ejpam-2623	488	23	defined	define	VERB
ejpam-2623	488	24	when	when	SCONJ
ejpam-2623	488	25	ε	ε	PROPN
ejpam-2623	488	26	=	=	SYM
ejpam-2623	488	27	1	1	NUM
ejpam-2623	488	28	.	.	NOUN
ejpam-2623	488	29	•	•	NOUN
ejpam-2623	488	30	if	if	SCONJ
ejpam-2623	488	31	ε	ε	PROPN
ejpam-2623	488	32	=	=	SYM
ejpam-2623	488	33	−1	−1	NOUN
ejpam-2623	488	34	,	,	PUNCT
ejpam-2623	488	35	then	then	ADV
ejpam-2623	488	36	t	t	PROPN
ejpam-2623	488	37	=	=	PUNCT
ejpam-2623	488	38	v(α2	v(α2	X
ejpam-2623	488	39	+	+	CCONJ
ejpam-2623	488	40	β2)−	β2)−	ADJ
ejpam-2623	488	41	αβ	αβ	NUM
ejpam-2623	488	42	αβv	αβv	PRON
ejpam-2623	488	43	.	.	PUNCT
ejpam-2623	489	1	suppose	suppose	VERB
ejpam-2623	489	2	that	that	SCONJ
ejpam-2623	489	3	α	α	PRON
ejpam-2623	489	4	−	−	NOUN
ejpam-2623	489	5	βt	βt	NOUN
ejpam-2623	489	6	=	=	SYM
ejpam-2623	489	7	0	0	NUM
ejpam-2623	489	8	;	;	PUNCT
ejpam-2623	489	9	this	this	PRON
ejpam-2623	489	10	implies	imply	VERB
ejpam-2623	489	11	that	that	SCONJ
ejpam-2623	489	12	βv	βv	PRON
ejpam-2623	489	13	=	=	SYM
ejpam-2623	489	14	α	α	PROPN
ejpam-2623	489	15	and	and	CCONJ
ejpam-2623	489	16	then	then	ADV
ejpam-2623	489	17	r2	r2	PROPN
ejpam-2623	489	18	=	=	SYM
ejpam-2623	489	19	α4	α4	PROPN
ejpam-2623	489	20	uβ4	uβ4	NOUN
ejpam-2623	489	21	;	;	PUNCT
ejpam-2623	489	22	contradiction	contradiction	NOUN
ejpam-2623	489	23	since	since	SCONJ
ejpam-2623	489	24	χ(u	χ(u	NOUN
ejpam-2623	489	25	)	)	PUNCT
ejpam-2623	489	26	=	=	SYM
ejpam-2623	489	27	−1	−1	NOUN
ejpam-2623	489	28	.	.	PUNCT
ejpam-2623	490	1	thus	thus	ADV
ejpam-2623	490	2	the	the	DET
ejpam-2623	490	3	quantity	quantity	NOUN
ejpam-2623	490	4	t(αt−	t(αt−	NUM
ejpam-2623	490	5	β	β	NOUN
ejpam-2623	490	6	)	)	PUNCT
ejpam-2623	490	7	α−	α−	AUX
ejpam-2623	490	8	βt	βt	VERB
ejpam-2623	490	9	is	be	AUX
ejpam-2623	490	10	well	well	ADV
ejpam-2623	490	11	-	-	PUNCT
ejpam-2623	490	12	defined	define	VERB
ejpam-2623	490	13	.	.	PUNCT
ejpam-2623	491	1	moreover	moreover	ADV
ejpam-2623	491	2	we	we	PRON
ejpam-2623	491	3	have	have	VERB
ejpam-2623	491	4	:	:	PUNCT
ejpam-2623	491	5	χ	χ	X
ejpam-2623	491	6	(	(	PUNCT
ejpam-2623	491	7	t(αt−	t(αt−	NUM
ejpam-2623	491	8	β	β	NOUN
ejpam-2623	491	9	)	)	PUNCT
ejpam-2623	491	10	α−	α−	ADP
ejpam-2623	491	11	βt	βt	VERB
ejpam-2623	491	12	)	)	PUNCT
ejpam-2623	492	1	=	=	SYM
ejpam-2623	492	2	χ	χ	X
ejpam-2623	492	3	(	(	PUNCT
ejpam-2623	492	4	α(αv	α(αv	NUM
ejpam-2623	492	5	−	−	PROPN
ejpam-2623	492	6	β)(v(α2	β)(v(α2	NOUN
ejpam-2623	492	7	+	+	CCONJ
ejpam-2623	492	8	β2)−	β2)−	ADJ
ejpam-2623	492	9	αβ	αβ	INTJ
ejpam-2623	492	10	)	)	PUNCT
ejpam-2623	492	11	vβ3(α−	vβ3(α−	NOUN
ejpam-2623	492	12	βv	βv	PUNCT
ejpam-2623	492	13	)	)	PUNCT
ejpam-2623	492	14	)	)	PUNCT
ejpam-2623	493	1	=	=	SYM
ejpam-2623	493	2	χ	χ	X
ejpam-2623	493	3	(	(	PUNCT
ejpam-2623	493	4	αv	αv	INTJ
ejpam-2623	493	5	−	−	PROPN
ejpam-2623	493	6	β	β	X
ejpam-2623	493	7	v(α−	v(α−	X
ejpam-2623	493	8	βv	βv	PUNCT
ejpam-2623	493	9	)	)	PUNCT
ejpam-2623	493	10	)	)	PUNCT
ejpam-2623	493	11	·	·	PUNCT
ejpam-2623	494	1	χ	χ	X
ejpam-2623	494	2	(	(	PUNCT
ejpam-2623	494	3	αβ	αβ	INTJ
ejpam-2623	494	4	(	(	PUNCT
ejpam-2623	494	5	v(α2	v(α2	NOUN
ejpam-2623	494	6	+	+	CCONJ
ejpam-2623	494	7	β2)−	β2)−	ADJ
ejpam-2623	494	8	αβ	αβ	NOUN
ejpam-2623	494	9	)	)	PUNCT
ejpam-2623	494	10	)	)	PUNCT
ejpam-2623	495	1	=	=	X
ejpam-2623	495	2	ε	ε	X
ejpam-2623	495	3	·	·	PUNCT
ejpam-2623	495	4	χ	χ	X
ejpam-2623	495	5	(	(	PUNCT
ejpam-2623	495	6	αβ	αβ	INTJ
ejpam-2623	495	7	(	(	PUNCT
ejpam-2623	495	8	v(α2	v(α2	NOUN
ejpam-2623	495	9	+	+	CCONJ
ejpam-2623	495	10	β2)−	β2)−	ADJ
ejpam-2623	495	11	αβ	αβ	NOUN
ejpam-2623	495	12	)	)	PUNCT
ejpam-2623	495	13	)	)	PUNCT
ejpam-2623	496	1	=	=	PUNCT
ejpam-2623	496	2	−χ	−χ	NOUN
ejpam-2623	496	3	(	(	PUNCT
ejpam-2623	496	4	αβ	αβ	INTJ
ejpam-2623	496	5	(	(	PUNCT
ejpam-2623	496	6	v(α2	v(α2	NOUN
ejpam-2623	496	7	+	+	CCONJ
ejpam-2623	496	8	β2)−	β2)−	ADJ
ejpam-2623	496	9	αβ	αβ	NOUN
ejpam-2623	496	10	)	)	PUNCT
ejpam-2623	496	11	)	)	PUNCT
ejpam-2623	496	12	n.	n.	PROPN
ejpam-2623	496	13	diarra	diarra	PROPN
ejpam-2623	496	14	,	,	PUNCT
ejpam-2623	496	15	d.	d.	PROPN
ejpam-2623	496	16	sow	sow	PROPN
ejpam-2623	496	17	,	,	PUNCT
ejpam-2623	496	18	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	496	19	.	.	PUNCT
ejpam-2623	496	20	khlil	khlil	PROPN
ejpam-2623	496	21	/	/	SYM
ejpam-2623	496	22	eur	eur	PROPN
ejpam-2623	496	23	.	.	PUNCT
ejpam-2623	497	1	j.	j.	PROPN
ejpam-2623	497	2	pure	pure	PROPN
ejpam-2623	497	3	appl	appl	PROPN
ejpam-2623	497	4	.	.	PROPN
ejpam-2623	497	5	math	math	PROPN
ejpam-2623	497	6	,	,	PUNCT
ejpam-2623	497	7	10	10	NUM
ejpam-2623	497	8	(	(	PUNCT
ejpam-2623	497	9	2	2	NUM
ejpam-2623	497	10	)	)	PUNCT
ejpam-2623	497	11	(	(	PUNCT
ejpam-2623	497	12	2017	2017	NUM
ejpam-2623	497	13	)	)	PUNCT
ejpam-2623	497	14	,	,	PUNCT
ejpam-2623	497	15	363	363	NUM
ejpam-2623	497	16	-	-	SYM
ejpam-2623	497	17	391	391	NUM
ejpam-2623	497	18	376	376	NUM
ejpam-2623	497	19	but	but	CCONJ
ejpam-2623	497	20	χ	χ	X
ejpam-2623	497	21	(	(	PUNCT
ejpam-2623	497	22	αβ	αβ	INTJ
ejpam-2623	497	23	(	(	PUNCT
ejpam-2623	497	24	v(α2	v(α2	NOUN
ejpam-2623	497	25	+	+	CCONJ
ejpam-2623	497	26	β2)−	β2)−	ADJ
ejpam-2623	497	27	αβ	αβ	NOUN
ejpam-2623	497	28	)	)	PUNCT
ejpam-2623	497	29	)	)	PUNCT
ejpam-2623	498	1	=	=	SYM
ejpam-2623	499	1	χ	χ	X
ejpam-2623	499	2	(	(	PUNCT
ejpam-2623	499	3	αβ	αβ	INTJ
ejpam-2623	499	4	(	(	PUNCT
ejpam-2623	499	5	uβ3r2	uβ3r2	PROPN
ejpam-2623	499	6	α	α	NOUN
ejpam-2623	499	7	)	)	PUNCT
ejpam-2623	499	8	)	)	PUNCT
ejpam-2623	500	1	=	=	PUNCT
ejpam-2623	500	2	χ(u	χ(u	NOUN
ejpam-2623	500	3	)	)	PUNCT
ejpam-2623	500	4	=	=	SYM
ejpam-2623	501	1	−1	−1	NOUN
ejpam-2623	501	2	.	.	PUNCT
ejpam-2623	502	1	hence	hence	ADV
ejpam-2623	502	2	we	we	PRON
ejpam-2623	502	3	conclude	conclude	VERB
ejpam-2623	502	4	that	that	SCONJ
ejpam-2623	502	5	χ	χ	X
ejpam-2623	502	6	(	(	PUNCT
ejpam-2623	502	7	t(αt−	t(αt−	NUM
ejpam-2623	502	8	β	β	NOUN
ejpam-2623	502	9	)	)	PUNCT
ejpam-2623	502	10	α−	α−	ADP
ejpam-2623	502	11	βt	βt	NOUN
ejpam-2623	502	12	)	)	PUNCT
ejpam-2623	503	1	=	=	SYM
ejpam-2623	503	2	1	1	NUM
ejpam-2623	503	3	and	and	CCONJ
ejpam-2623	503	4	x	x	PRON
ejpam-2623	503	5	is	be	AUX
ejpam-2623	503	6	well	well	ADV
ejpam-2623	503	7	-	-	PUNCT
ejpam-2623	503	8	defined	define	VERB
ejpam-2623	503	9	when	when	SCONJ
ejpam-2623	503	10	ε	ε	PROPN
ejpam-2623	503	11	=	=	SYM
ejpam-2623	503	12	−1	−1	NOUN
ejpam-2623	503	13	.	.	PUNCT
ejpam-2623	504	1	furthermore	furthermore	ADV
ejpam-2623	504	2	x	x	X
ejpam-2623	504	3	is	be	AUX
ejpam-2623	504	4	a	a	DET
ejpam-2623	504	5	non	non	ADJ
ejpam-2623	504	6	-	-	ADJ
ejpam-2623	504	7	zero	zero	NUM
ejpam-2623	504	8	element	element	NOUN
ejpam-2623	504	9	of	of	ADP
ejpam-2623	504	10	fq	fq	PROPN
ejpam-2623	504	11	.	.	PUNCT
ejpam-2623	505	1	(	(	PUNCT
ejpam-2623	505	2	v	v	NOUN
ejpam-2623	505	3	)	)	PUNCT
ejpam-2623	505	4	y	y	PROPN
ejpam-2623	505	5	is	be	AUX
ejpam-2623	505	6	well	well	ADV
ejpam-2623	505	7	-	-	PUNCT
ejpam-2623	505	8	defined	define	VERB
ejpam-2623	505	9	since	since	SCONJ
ejpam-2623	505	10	t	t	PROPN
ejpam-2623	505	11	6=	6=	ADP
ejpam-2623	505	12	0	0	NUM
ejpam-2623	505	13	and	and	CCONJ
ejpam-2623	505	14	y	y	PROPN
ejpam-2623	505	15	6=	6=	PROPN
ejpam-2623	505	16	0	0	NUM
ejpam-2623	505	17	since	since	SCONJ
ejpam-2623	505	18	x	x	PROPN
ejpam-2623	505	19	6=	6=	ADP
ejpam-2623	505	20	0	0	NUM
ejpam-2623	505	21	.	.	PUNCT
ejpam-2623	506	1	(	(	PUNCT
ejpam-2623	506	2	vi	vi	X
ejpam-2623	506	3	)	)	PUNCT
ejpam-2623	506	4	we	we	PRON
ejpam-2623	506	5	show	show	VERB
ejpam-2623	506	6	that	that	SCONJ
ejpam-2623	506	7	(	(	PUNCT
ejpam-2623	506	8	x	x	NOUN
ejpam-2623	506	9	,	,	PUNCT
ejpam-2623	506	10	y	y	PROPN
ejpam-2623	506	11	)	)	PUNCT
ejpam-2623	506	12	∈	∈	PROPN
ejpam-2623	506	13	eα	eα	NOUN
ejpam-2623	506	14	,	,	PUNCT
ejpam-2623	506	15	β	β	X
ejpam-2623	506	16	:	:	PUNCT
ejpam-2623	506	17	αx(y2	αx(y2	DET
ejpam-2623	506	18	−	−	PROPN
ejpam-2623	506	19	1	1	NUM
ejpam-2623	506	20	)	)	PUNCT
ejpam-2623	506	21	=	=	SYM
ejpam-2623	507	1	βy(x2	βy(x2	NOUN
ejpam-2623	508	1	−	−	NOUN
ejpam-2623	508	2	1	1	NUM
ejpam-2623	508	3	):	):	PUNCT
ejpam-2623	508	4	in	in	ADP
ejpam-2623	508	5	fact	fact	NOUN
ejpam-2623	509	1	y2	y2	INTJ
ejpam-2623	509	2	−	−	PROPN
ejpam-2623	509	3	1	1	NUM
ejpam-2623	510	1	x2	x2	NOUN
ejpam-2623	510	2	−	−	NOUN
ejpam-2623	510	3	1	1	NUM
ejpam-2623	510	4	=	=	SYM
ejpam-2623	510	5	x2	x2	PROPN
ejpam-2623	510	6	t2	t2	PROPN
ejpam-2623	510	7	−	−	PROPN
ejpam-2623	510	8	1	1	NUM
ejpam-2623	510	9	x2	x2	NOUN
ejpam-2623	510	10	−	−	NOUN
ejpam-2623	510	11	1	1	NUM
ejpam-2623	510	12	=	=	SYM
ejpam-2623	510	13	x2	x2	PROPN
ejpam-2623	510	14	−	−	PROPN
ejpam-2623	510	15	t2	t2	NOUN
ejpam-2623	510	16	t2(x2	t2(x2	NOUN
ejpam-2623	510	17	−	−	PROPN
ejpam-2623	510	18	1	1	NUM
ejpam-2623	510	19	)	)	PUNCT
ejpam-2623	510	20	=	=	SYM
ejpam-2623	510	21	1	1	NUM
ejpam-2623	510	22	t2	t2	NOUN
ejpam-2623	510	23			PROPN
ejpam-2623	510	24	t(αt−β	t(αt−β	NOUN
ejpam-2623	510	25	)	)	PUNCT
ejpam-2623	510	26	α−βt	α−βt	NOUN
ejpam-2623	510	27	−	−	PROPN
ejpam-2623	510	28	t	t	NOUN
ejpam-2623	510	29	2	2	NUM
ejpam-2623	510	30	t(αt−β	t(αt−β	NOUN
ejpam-2623	510	31	)	)	PUNCT
ejpam-2623	510	32	α−βt	α−βt	NOUN
ejpam-2623	510	33	−	−	NOUN
ejpam-2623	510	34	1	1	NUM
ejpam-2623	510	35			PROPN
ejpam-2623	510	36	=	=	SYM
ejpam-2623	510	37	β	β	X
ejpam-2623	510	38	αt2	αt2	NOUN
ejpam-2623	510	39	(	(	PUNCT
ejpam-2623	510	40	t3	t3	PROPN
ejpam-2623	510	41	−	−	PROPN
ejpam-2623	510	42	t	t	PROPN
ejpam-2623	510	43	t2	t2	NOUN
ejpam-2623	510	44	−	−	PROPN
ejpam-2623	510	45	1	1	NUM
ejpam-2623	510	46	)	)	PUNCT
ejpam-2623	510	47	=	=	PUNCT
ejpam-2623	510	48	β	β	X
ejpam-2623	510	49	αt	αt	NOUN
ejpam-2623	510	50	=	=	PUNCT
ejpam-2623	510	51	βy	βy	NOUN
ejpam-2623	510	52	αx	αx	INTJ
ejpam-2623	510	53	.	.	PUNCT
ejpam-2623	511	1	hence	hence	ADV
ejpam-2623	511	2	we	we	PRON
ejpam-2623	511	3	have	have	VERB
ejpam-2623	511	4	αx(y2	αx(y2	PRON
ejpam-2623	511	5	−	−	NOUN
ejpam-2623	511	6	1	1	NUM
ejpam-2623	511	7	)	)	PUNCT
ejpam-2623	511	8	=	=	SYM
ejpam-2623	511	9	βy(x2	βy(x2	NOUN
ejpam-2623	512	1	−	−	NOUN
ejpam-2623	512	2	1	1	NUM
ejpam-2623	512	3	)	)	PUNCT
ejpam-2623	512	4	,	,	PUNCT
ejpam-2623	512	5	which	which	PRON
ejpam-2623	512	6	ends	end	VERB
ejpam-2623	512	7	the	the	DET
ejpam-2623	512	8	proof	proof	NOUN
ejpam-2623	512	9	.	.	PUNCT
ejpam-2623	513	1	proposition	proposition	NOUN
ejpam-2623	513	2	5	5	NUM
ejpam-2623	513	3	.	.	PUNCT
ejpam-2623	514	1	for	for	ADP
ejpam-2623	514	2	any	any	DET
ejpam-2623	514	3	r	r	NOUN
ejpam-2623	514	4	∈	∈	NOUN
ejpam-2623	514	5	r	r	NOUN
ejpam-2623	514	6	,	,	PUNCT
ejpam-2623	514	7	the	the	DET
ejpam-2623	514	8	set	set	NOUN
ejpam-2623	514	9	of	of	ADP
ejpam-2623	514	10	preimages	preimage	NOUN
ejpam-2623	514	11	of	of	ADP
ejpam-2623	514	12	φα	φα	PROPN
ejpam-2623	514	13	,	,	PUNCT
ejpam-2623	514	14	β(r	β(r	NOUN
ejpam-2623	514	15	)	)	PUNCT
ejpam-2623	514	16	is	be	AUX
ejpam-2623	514	17	{	{	PUNCT
ejpam-2623	514	18	r,−r	r,−r	NOUN
ejpam-2623	514	19	}	}	PUNCT
ejpam-2623	514	20	.	.	PUNCT
ejpam-2623	515	1	proof	proof	NOUN
ejpam-2623	515	2	.	.	PUNCT
ejpam-2623	516	1	it	it	PRON
ejpam-2623	516	2	is	be	AUX
ejpam-2623	516	3	obvious	obvious	ADJ
ejpam-2623	516	4	that	that	SCONJ
ejpam-2623	516	5	φα	φα	ADP
ejpam-2623	516	6	,	,	PUNCT
ejpam-2623	516	7	β(−r	β(−r	VERB
ejpam-2623	516	8	)	)	PUNCT
ejpam-2623	516	9	=	=	SYM
ejpam-2623	516	10	φα	φα	PROPN
ejpam-2623	516	11	,	,	PUNCT
ejpam-2623	516	12	β(r	β(r	PROPN
ejpam-2623	516	13	)	)	PUNCT
ejpam-2623	516	14	since	since	SCONJ
ejpam-2623	516	15	the	the	DET
ejpam-2623	516	16	definition	definition	NOUN
ejpam-2623	516	17	of	of	ADP
ejpam-2623	516	18	φα	φα	PROPN
ejpam-2623	516	19	,	,	PUNCT
ejpam-2623	516	20	β	β	X
ejpam-2623	516	21	only	only	ADV
ejpam-2623	516	22	uses	use	VERB
ejpam-2623	516	23	r2	r2	PROPN
ejpam-2623	516	24	.	.	PUNCT
ejpam-2623	517	1	now	now	ADV
ejpam-2623	517	2	let	let	VERB
ejpam-2623	517	3	r′	r′	DET
ejpam-2623	517	4	∈	∈	PROPN
ejpam-2623	517	5	r	r	NOUN
ejpam-2623	517	6	such	such	ADJ
ejpam-2623	517	7	that	that	DET
ejpam-2623	517	8	φα	φα	PROPN
ejpam-2623	517	9	,	,	PUNCT
ejpam-2623	517	10	β(r′	β(r′	PROPN
ejpam-2623	517	11	)	)	PUNCT
ejpam-2623	517	12	=	=	SYM
ejpam-2623	517	13	φα	φα	PROPN
ejpam-2623	517	14	,	,	PUNCT
ejpam-2623	517	15	β(r	β(r	NOUN
ejpam-2623	517	16	)	)	PUNCT
ejpam-2623	517	17	.	.	PUNCT
ejpam-2623	518	1	we	we	PRON
ejpam-2623	518	2	want	want	VERB
ejpam-2623	518	3	to	to	PART
ejpam-2623	518	4	show	show	VERB
ejpam-2623	518	5	that	that	PRON
ejpam-2623	518	6	r′	r′	NOUN
ejpam-2623	518	7	=	=	SYM
ejpam-2623	518	8	r	r	NOUN
ejpam-2623	518	9	or	or	CCONJ
ejpam-2623	518	10	r′	r′	PROPN
ejpam-2623	518	11	=	=	SYM
ejpam-2623	518	12	−r	−r	PROPN
ejpam-2623	518	13	.	.	PUNCT
ejpam-2623	519	1	from	from	ADP
ejpam-2623	519	2	r′	r′	PROPN
ejpam-2623	519	3	we	we	PRON
ejpam-2623	519	4	define	define	VERB
ejpam-2623	519	5	the	the	DET
ejpam-2623	519	6	elements	element	NOUN
ejpam-2623	519	7	v′	v′	NOUN
ejpam-2623	519	8	,	,	PUNCT
ejpam-2623	519	9	ε′	ε′	NUM
ejpam-2623	519	10	,	,	PUNCT
ejpam-2623	519	11	t′	t′	NUM
ejpam-2623	519	12	,	,	PUNCT
ejpam-2623	519	13	x′	x′	NUM
ejpam-2623	519	14	,	,	PUNCT
ejpam-2623	519	15	y′	y′	ADV
ejpam-2623	519	16	as	as	ADP
ejpam-2623	519	17	in	in	ADP
ejpam-2623	519	18	theorem	theorem	NOUN
ejpam-2623	519	19	3	3	X
ejpam-2623	519	20	.	.	PUNCT
ejpam-2623	520	1	so	so	ADV
ejpam-2623	520	2	φα	φα	PROPN
ejpam-2623	520	3	,	,	PUNCT
ejpam-2623	520	4	β(r′	β(r′	PROPN
ejpam-2623	520	5	)	)	PUNCT
ejpam-2623	520	6	=	=	SYM
ejpam-2623	520	7	φα	φα	PROPN
ejpam-2623	520	8	,	,	PUNCT
ejpam-2623	520	9	β(r	β(r	NOUN
ejpam-2623	520	10	)	)	PUNCT
ejpam-2623	520	11	⇒	⇒	NOUN
ejpam-2623	520	12	x′	x′	X
ejpam-2623	521	1	=	=	PUNCT
ejpam-2623	521	2	x	x	PROPN
ejpam-2623	521	3	and	and	CCONJ
ejpam-2623	521	4	y′	y′	NUM
ejpam-2623	521	5	=	=	PUNCT
ejpam-2623	521	6	y.	y.	NOUN
ejpam-2623	521	7	furthermore	furthermore	ADV
ejpam-2623	521	8	we	we	PRON
ejpam-2623	521	9	have	have	VERB
ejpam-2623	521	10	t′	t′	NUM
ejpam-2623	521	11	=	=	SYM
ejpam-2623	521	12	t	t	PROPN
ejpam-2623	521	13	and	and	CCONJ
ejpam-2623	521	14	then	then	ADV
ejpam-2623	521	15	−ε′	−ε′	ADJ
ejpam-2623	521	16	√	√	ADP
ejpam-2623	521	17	t(αt−β	t(αt−β	NOUN
ejpam-2623	521	18	)	)	PUNCT
ejpam-2623	521	19	α−βt	α−βt	NOUN
ejpam-2623	521	20	=	=	SYM
ejpam-2623	521	21	−ε	−ε	NOUN
ejpam-2623	521	22	√	√	NOUN
ejpam-2623	521	23	t(αt−β	t(αt−β	NUM
ejpam-2623	521	24	)	)	PUNCT
ejpam-2623	521	25	α−βt	α−βt	NOUN
ejpam-2623	521	26	.	.	PUNCT
ejpam-2623	522	1	so	so	ADV
ejpam-2623	522	2	ε′	ε′	X
ejpam-2623	522	3	=	=	SYM
ejpam-2623	522	4	ε	ε	PROPN
ejpam-2623	522	5	;	;	PUNCT
ejpam-2623	522	6	and	and	CCONJ
ejpam-2623	522	7	we	we	PRON
ejpam-2623	522	8	have	have	VERB
ejpam-2623	522	9	v′	v′	NOUN
ejpam-2623	522	10	=	=	SYM
ejpam-2623	522	11	v	v	NOUN
ejpam-2623	522	12	by	by	ADP
ejpam-2623	522	13	replacing	replace	VERB
ejpam-2623	522	14	ε′	ε′	NOUN
ejpam-2623	522	15	by	by	ADP
ejpam-2623	522	16	ε	ε	PROPN
ejpam-2623	522	17	in	in	ADP
ejpam-2623	522	18	t′	t′	NUM
ejpam-2623	523	1	=	=	PUNCT
ejpam-2623	524	1	t.	t.	NOUN
ejpam-2623	524	2	finally	finally	ADV
ejpam-2623	524	3	v	v	NOUN
ejpam-2623	524	4	=	=	SYM
ejpam-2623	524	5	v′	v′	NOUN
ejpam-2623	524	6	implies	imply	VERB
ejpam-2623	524	7	that	that	SCONJ
ejpam-2623	524	8	r′2	r′2	NOUN
ejpam-2623	524	9	=	=	SYM
ejpam-2623	524	10	r2	r2	NOUN
ejpam-2623	524	11	,	,	PUNCT
ejpam-2623	524	12	that	that	PRON
ejpam-2623	524	13	is	be	AUX
ejpam-2623	524	14	r′	r′	PROPN
ejpam-2623	524	15	=	=	SYM
ejpam-2623	524	16	±r	±r	PROPN
ejpam-2623	524	17	.	.	PUNCT
ejpam-2623	525	1	proposition	proposition	NOUN
ejpam-2623	525	2	6	6	NUM
ejpam-2623	525	3	.	.	PUNCT
ejpam-2623	526	1	in	in	ADP
ejpam-2623	526	2	the	the	DET
ejpam-2623	526	3	situation	situation	NOUN
ejpam-2623	526	4	of	of	ADP
ejpam-2623	526	5	theorem	theorem	NOUN
ejpam-2623	526	6	3	3	NUM
ejpam-2623	526	7	,	,	PUNCT
ejpam-2623	526	8	we	we	PRON
ejpam-2623	526	9	have	have	VERB
ejpam-2623	526	10	:	:	PUNCT
ejpam-2623	526	11	(	(	PUNCT
ejpam-2623	526	12	i	i	NOUN
ejpam-2623	526	13	)	)	PUNCT
ejpam-2623	526	14	im(φα	im(φα	PROPN
ejpam-2623	526	15	,	,	PUNCT
ejpam-2623	526	16	β	β	NOUN
ejpam-2623	526	17	)	)	PUNCT
ejpam-2623	526	18	is	be	AUX
ejpam-2623	526	19	the	the	DET
ejpam-2623	526	20	set	set	NOUN
ejpam-2623	526	21	of	of	ADP
ejpam-2623	526	22	(	(	PUNCT
ejpam-2623	526	23	x	x	NOUN
ejpam-2623	526	24	,	,	PUNCT
ejpam-2623	526	25	y	y	PROPN
ejpam-2623	526	26	)	)	PUNCT
ejpam-2623	526	27	∈	∈	PROPN
ejpam-2623	526	28	eα	eα	NOUN
ejpam-2623	526	29	,	,	PUNCT
ejpam-2623	526	30	β	β	X
ejpam-2623	526	31	such	such	ADJ
ejpam-2623	526	32	that	that	PRON
ejpam-2623	526	33	:	:	PUNCT
ejpam-2623	526	34	•	•	NUM
ejpam-2623	526	35	χ	χ	X
ejpam-2623	526	36	(	(	PUNCT
ejpam-2623	526	37	uαβxy(α2	uαβxy(α2	X
ejpam-2623	526	38	+	+	CCONJ
ejpam-2623	526	39	β2	β2	NOUN
ejpam-2623	526	40	−	−	PROPN
ejpam-2623	526	41	αβ	αβ	INTJ
ejpam-2623	526	42	y	y	NOUN
ejpam-2623	526	43	x	x	PROPN
ejpam-2623	526	44	)	)	PUNCT
ejpam-2623	526	45	)	)	PUNCT
ejpam-2623	527	1	=	=	SYM
ejpam-2623	527	2	1	1	NUM
ejpam-2623	527	3	if	if	SCONJ
ejpam-2623	527	4	x	x	X
ejpam-2623	527	5	/∈	/∈	NOUN
ejpam-2623	527	6	√	√	VERB
ejpam-2623	527	7	f2	f2	PROPN
ejpam-2623	527	8	q.	q.	PROPN
ejpam-2623	527	9	•	•	NOUN
ejpam-2623	528	1	and	and	CCONJ
ejpam-2623	528	2	χ	χ	X
ejpam-2623	528	3	(	(	PUNCT
ejpam-2623	528	4	uαβxy(α2	uαβxy(α2	X
ejpam-2623	528	5	+	+	CCONJ
ejpam-2623	528	6	β2	β2	NOUN
ejpam-2623	528	7	−	−	PROPN
ejpam-2623	528	8	αβx	αβx	NOUN
ejpam-2623	528	9	y	y	PROPN
ejpam-2623	528	10	)	)	PUNCT
ejpam-2623	528	11	)	)	PUNCT
ejpam-2623	529	1	=	=	PUNCT
ejpam-2623	529	2	1	1	NUM
ejpam-2623	529	3	if	if	SCONJ
ejpam-2623	529	4	x	x	SYM
ejpam-2623	529	5	∈	∈	NOUN
ejpam-2623	529	6	√	√	VERB
ejpam-2623	529	7	f2	f2	PROPN
ejpam-2623	529	8	q	q	NOUN
ejpam-2623	529	9	;	;	PUNCT
ejpam-2623	529	10	(	(	PUNCT
ejpam-2623	529	11	ii	ii	NOUN
ejpam-2623	529	12	)	)	PUNCT
ejpam-2623	529	13	for	for	ADP
ejpam-2623	529	14	(	(	PUNCT
ejpam-2623	529	15	x	x	NOUN
ejpam-2623	529	16	,	,	PUNCT
ejpam-2623	529	17	y	y	NOUN
ejpam-2623	529	18	)	)	PUNCT
ejpam-2623	529	19	∈	∈	PROPN
ejpam-2623	529	20	im(φα	im(φα	PROPN
ejpam-2623	529	21	,	,	PUNCT
ejpam-2623	529	22	β	β	NOUN
ejpam-2623	529	23	)	)	PUNCT
ejpam-2623	529	24	,	,	PUNCT
ejpam-2623	529	25	define	define	VERB
ejpam-2623	529	26	t	t	NOUN
ejpam-2623	530	1	=	=	PUNCT
ejpam-2623	531	1	x	x	SYM
ejpam-2623	531	2	y	y	PROPN
ejpam-2623	531	3	and	and	CCONJ
ejpam-2623	531	4	z	z	NOUN
ejpam-2623	531	5	=	=	SYM
ejpam-2623	531	6	t(αt−	t(αt−	NUM
ejpam-2623	531	7	β	β	NOUN
ejpam-2623	531	8	)	)	PUNCT
ejpam-2623	531	9	α−	α−	AUX
ejpam-2623	531	10	βt	βt	VERB
ejpam-2623	531	11	;	;	PUNCT
ejpam-2623	531	12	so	so	ADV
ejpam-2623	531	13	x	x	SYM
ejpam-2623	531	14	∈	∈	PROPN
ejpam-2623	531	15	{	{	PUNCT
ejpam-2623	531	16	√	√	PROPN
ejpam-2623	531	17	z,−	z,−	PROPN
ejpam-2623	532	1	√	√	PROPN
ejpam-2623	532	2	z	z	NOUN
ejpam-2623	532	3	}	}	PUNCT
ejpam-2623	532	4	.	.	PUNCT
ejpam-2623	533	1	let	let	VERB
ejpam-2623	533	2	r	r	NOUN
ejpam-2623	533	3	defined	define	VERB
ejpam-2623	533	4	as	as	SCONJ
ejpam-2623	533	5	follows	follow	VERB
ejpam-2623	533	6	:	:	PUNCT
ejpam-2623	533	7	r	r	NOUN
ejpam-2623	533	8	=	=	SYM
ejpam-2623	533	9	1	1	NUM
ejpam-2623	533	10	β	β	SYM
ejpam-2623	533	11	√	√	NUM
ejpam-2623	533	12	α(x(α2	α(x(α2	PROPN
ejpam-2623	533	13	+	+	CCONJ
ejpam-2623	533	14	β2)−	β2)−	ADJ
ejpam-2623	533	15	αβy	αβy	ADJ
ejpam-2623	533	16	)	)	PUNCT
ejpam-2623	533	17	uβy	uβy	VERB
ejpam-2623	533	18	if	if	SCONJ
ejpam-2623	533	19	x	x	PROPN
ejpam-2623	533	20	=	=	PUNCT
ejpam-2623	534	1	−	−	PROPN
ejpam-2623	534	2	√	√	PROPN
ejpam-2623	534	3	z	z	NOUN
ejpam-2623	534	4	;	;	PUNCT
ejpam-2623	534	5	and	and	CCONJ
ejpam-2623	534	6	r	r	NOUN
ejpam-2623	534	7	=	=	SYM
ejpam-2623	534	8	α	α	NOUN
ejpam-2623	534	9	√	√	VERB
ejpam-2623	534	10	αx	αx	ADP
ejpam-2623	534	11	uβ(y(α2	uβ(y(α2	PROPN
ejpam-2623	534	12	+	+	CCONJ
ejpam-2623	534	13	β2)−	β2)−	ADJ
ejpam-2623	534	14	αβx	αβx	NOUN
ejpam-2623	534	15	)	)	PUNCT
ejpam-2623	534	16	if	if	SCONJ
ejpam-2623	534	17	x	x	X
ejpam-2623	534	18	=	=	PUNCT
ejpam-2623	534	19	√	√	PROPN
ejpam-2623	534	20	z.	z.	PROPN
ejpam-2623	535	1	then	then	ADV
ejpam-2623	535	2	r	r	NOUN
ejpam-2623	535	3	∈	∈	PROPN
ejpam-2623	535	4	r	r	NOUN
ejpam-2623	535	5	and	and	CCONJ
ejpam-2623	535	6	φα	φα	NOUN
ejpam-2623	535	7	,	,	PUNCT
ejpam-2623	535	8	β(r	β(r	NOUN
ejpam-2623	535	9	)	)	PUNCT
ejpam-2623	535	10	=	=	SYM
ejpam-2623	535	11	(	(	PUNCT
ejpam-2623	535	12	x	x	X
ejpam-2623	535	13	,	,	PUNCT
ejpam-2623	535	14	y	y	PROPN
ejpam-2623	535	15	)	)	PUNCT
ejpam-2623	535	16	.	.	PUNCT
ejpam-2623	536	1	proof	proof	NOUN
ejpam-2623	536	2	.	.	PUNCT
ejpam-2623	537	1	(	(	PUNCT
ejpam-2623	537	2	i	i	NOUN
ejpam-2623	537	3	)	)	PUNCT
ejpam-2623	537	4	for	for	ADP
ejpam-2623	537	5	this	this	DET
ejpam-2623	537	6	statement	statement	NOUN
ejpam-2623	537	7	,	,	PUNCT
ejpam-2623	537	8	we	we	PRON
ejpam-2623	537	9	have	have	VERB
ejpam-2623	537	10	to	to	PART
ejpam-2623	537	11	show	show	VERB
ejpam-2623	537	12	two	two	NUM
ejpam-2623	537	13	things	thing	NOUN
ejpam-2623	537	14	.	.	PUNCT
ejpam-2623	538	1	the	the	DET
ejpam-2623	538	2	first	first	ADJ
ejpam-2623	538	3	one	one	NUM
ejpam-2623	538	4	is	be	AUX
ejpam-2623	538	5	that	that	SCONJ
ejpam-2623	538	6	every	every	DET
ejpam-2623	538	7	(	(	PUNCT
ejpam-2623	538	8	x	x	NOUN
ejpam-2623	538	9	,	,	PUNCT
ejpam-2623	538	10	y	y	NOUN
ejpam-2623	538	11	)	)	PUNCT
ejpam-2623	538	12	∈	∈	PROPN
ejpam-2623	538	13	im(φα	im(φα	PROPN
ejpam-2623	538	14	,	,	PUNCT
ejpam-2623	538	15	β	β	NOUN
ejpam-2623	538	16	)	)	PUNCT
ejpam-2623	538	17	verifies	verifie	NOUN
ejpam-2623	538	18	the	the	DET
ejpam-2623	538	19	conditions	condition	NOUN
ejpam-2623	538	20	mentioned	mention	VERB
ejpam-2623	538	21	above	above	ADV
ejpam-2623	538	22	;	;	PUNCT
ejpam-2623	538	23	the	the	DET
ejpam-2623	538	24	second	second	NOUN
ejpam-2623	538	25	is	be	AUX
ejpam-2623	538	26	that	that	SCONJ
ejpam-2623	538	27	any	any	DET
ejpam-2623	538	28	point	point	NOUN
ejpam-2623	538	29	(	(	PUNCT
ejpam-2623	538	30	x	x	NOUN
ejpam-2623	538	31	,	,	PUNCT
ejpam-2623	538	32	y	y	NOUN
ejpam-2623	538	33	)	)	PUNCT
ejpam-2623	538	34	∈	∈	PROPN
ejpam-2623	538	35	ea	ea	PROPN
ejpam-2623	538	36	,	,	PUNCT
ejpam-2623	538	37	b	b	X
ejpam-2623	538	38	verifying	verify	VERB
ejpam-2623	538	39	these	these	DET
ejpam-2623	538	40	conditions	condition	NOUN
ejpam-2623	538	41	,	,	PUNCT
ejpam-2623	538	42	is	be	AUX
ejpam-2623	538	43	in	in	ADP
ejpam-2623	538	44	im(φα	im(φα	NOUN
ejpam-2623	538	45	,	,	PUNCT
ejpam-2623	538	46	β	β	NOUN
ejpam-2623	538	47	)	)	PUNCT
ejpam-2623	538	48	.	.	PUNCT
ejpam-2623	539	1	n.	n.	PROPN
ejpam-2623	539	2	diarra	diarra	PROPN
ejpam-2623	539	3	,	,	PUNCT
ejpam-2623	539	4	d.	d.	PROPN
ejpam-2623	539	5	sow	sow	PROPN
ejpam-2623	539	6	,	,	PUNCT
ejpam-2623	539	7	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	539	8	.	.	PUNCT
ejpam-2623	539	9	khlil	khlil	PROPN
ejpam-2623	539	10	/	/	SYM
ejpam-2623	539	11	eur	eur	PROPN
ejpam-2623	539	12	.	.	PUNCT
ejpam-2623	540	1	j.	j.	PROPN
ejpam-2623	540	2	pure	pure	PROPN
ejpam-2623	540	3	appl	appl	PROPN
ejpam-2623	540	4	.	.	PROPN
ejpam-2623	540	5	math	math	PROPN
ejpam-2623	540	6	,	,	PUNCT
ejpam-2623	540	7	10	10	NUM
ejpam-2623	540	8	(	(	PUNCT
ejpam-2623	540	9	2	2	NUM
ejpam-2623	540	10	)	)	PUNCT
ejpam-2623	540	11	(	(	PUNCT
ejpam-2623	540	12	2017	2017	NUM
ejpam-2623	540	13	)	)	PUNCT
ejpam-2623	540	14	,	,	PUNCT
ejpam-2623	540	15	363	363	NUM
ejpam-2623	540	16	-	-	SYM
ejpam-2623	540	17	391	391	NUM
ejpam-2623	540	18	377	377	NUM
ejpam-2623	540	19	•	•	NOUN
ejpam-2623	540	20	let	let	VERB
ejpam-2623	540	21	(	(	PUNCT
ejpam-2623	540	22	x	x	NOUN
ejpam-2623	540	23	,	,	PUNCT
ejpam-2623	540	24	y	y	NOUN
ejpam-2623	540	25	)	)	PUNCT
ejpam-2623	540	26	∈	∈	PROPN
ejpam-2623	540	27	im(φα	im(φα	PROPN
ejpam-2623	540	28	,	,	PUNCT
ejpam-2623	540	29	β	β	NOUN
ejpam-2623	540	30	)	)	PUNCT
ejpam-2623	540	31	;	;	PUNCT
ejpam-2623	540	32	so	so	CCONJ
ejpam-2623	540	33	there	there	PRON
ejpam-2623	540	34	exists	exist	VERB
ejpam-2623	540	35	r	r	NOUN
ejpam-2623	540	36	∈	∈	PROPN
ejpam-2623	540	37	r	r	NOUN
ejpam-2623	540	38	\	\	PUNCT
ejpam-2623	540	39	{	{	PUNCT
ejpam-2623	540	40	0	0	NUM
ejpam-2623	540	41	}	}	PUNCT
ejpam-2623	540	42	such	such	ADJ
ejpam-2623	540	43	that	that	SCONJ
ejpam-2623	540	44	the	the	DET
ejpam-2623	540	45	elements	element	NOUN
ejpam-2623	540	46	t	t	X
ejpam-2623	541	1	=	=	PUNCT
ejpam-2623	541	2	x	x	SYM
ejpam-2623	541	3	y	y	PROPN
ejpam-2623	541	4	,	,	PUNCT
ejpam-2623	541	5	ε	ε	PROPN
ejpam-2623	541	6	,	,	PUNCT
ejpam-2623	541	7	v	v	NUM
ejpam-2623	541	8	are	be	AUX
ejpam-2623	541	9	defined	define	VERB
ejpam-2623	541	10	as	as	ADP
ejpam-2623	541	11	in	in	ADP
ejpam-2623	541	12	theorem	theorem	NOUN
ejpam-2623	541	13	3	3	X
ejpam-2623	541	14	.	.	X
ejpam-2623	541	15	we	we	PRON
ejpam-2623	541	16	consider	consider	VERB
ejpam-2623	541	17	two	two	NUM
ejpam-2623	541	18	cases	case	NOUN
ejpam-2623	541	19	:	:	PUNCT
ejpam-2623	541	20	–	–	PUNCT
ejpam-2623	541	21	if	if	SCONJ
ejpam-2623	541	22	ε	ε	PROPN
ejpam-2623	541	23	=	=	SYM
ejpam-2623	541	24	1	1	NUM
ejpam-2623	541	25	,	,	PUNCT
ejpam-2623	541	26	so	so	ADV
ejpam-2623	541	27	x	x	ADP
ejpam-2623	541	28	=	=	PUNCT
ejpam-2623	542	1	−	−	NOUN
ejpam-2623	542	2	√	√	NUM
ejpam-2623	542	3	t(αt−	t(αt−	NUM
ejpam-2623	542	4	β	β	NOUN
ejpam-2623	542	5	)	)	PUNCT
ejpam-2623	542	6	α−	α−	ADP
ejpam-2623	542	7	βt	βt	VERB
ejpam-2623	542	8	/∈	/∈	PUNCT
ejpam-2623	543	1	√	√	VERB
ejpam-2623	543	2	f2	f2	PROPN
ejpam-2623	543	3	q	q	NOUN
ejpam-2623	544	1	and	and	CCONJ
ejpam-2623	544	2	x	x	SYM
ejpam-2623	544	3	y	y	PROPN
ejpam-2623	544	4	=	=	SYM
ejpam-2623	544	5	t	t	PROPN
ejpam-2623	544	6	=	=	SYM
ejpam-2623	544	7	v	v	NOUN
ejpam-2623	544	8	=	=	PUNCT
ejpam-2623	544	9	β(α2	β(α2	X
ejpam-2623	544	10	+	+	CCONJ
ejpam-2623	544	11	uβ2r2	uβ2r2	PROPN
ejpam-2623	544	12	)	)	PUNCT
ejpam-2623	544	13	α(α2	α(α2	NOUN
ejpam-2623	545	1	+	+	CCONJ
ejpam-2623	545	2	β2	β2	VERB
ejpam-2623	545	3	)	)	PUNCT
ejpam-2623	545	4	.	.	PUNCT
ejpam-2623	546	1	let	let	VERB
ejpam-2623	546	2	us	we	PRON
ejpam-2623	546	3	show	show	VERB
ejpam-2623	546	4	that	that	SCONJ
ejpam-2623	546	5	χ	χ	X
ejpam-2623	546	6	(	(	PUNCT
ejpam-2623	546	7	uαβxy(α2	uαβxy(α2	X
ejpam-2623	546	8	+	+	CCONJ
ejpam-2623	546	9	β2	β2	NOUN
ejpam-2623	546	10	−	−	PROPN
ejpam-2623	547	1	αβ	αβ	INTJ
ejpam-2623	547	2	y	y	NOUN
ejpam-2623	547	3	x	x	PROPN
ejpam-2623	547	4	)	)	PUNCT
ejpam-2623	547	5	)	)	PUNCT
ejpam-2623	548	1	=	=	PUNCT
ejpam-2623	548	2	1	1	X
ejpam-2623	548	3	.	.	PUNCT
ejpam-2623	548	4	in	in	ADP
ejpam-2623	548	5	fact	fact	NOUN
ejpam-2623	548	6	,	,	PUNCT
ejpam-2623	548	7	we	we	PRON
ejpam-2623	548	8	have	have	VERB
ejpam-2623	548	9	:	:	PUNCT
ejpam-2623	548	10	uαβxy(α2	uαβxy(α2	PROPN
ejpam-2623	549	1	+	+	CCONJ
ejpam-2623	549	2	β2	β2	VERB
ejpam-2623	549	3	−	−	PROPN
ejpam-2623	550	1	αβ	αβ	INTJ
ejpam-2623	550	2	y	y	NOUN
ejpam-2623	550	3	x	x	X
ejpam-2623	550	4	)	)	PUNCT
ejpam-2623	551	1	=	=	NUM
ejpam-2623	551	2	uαby2(t(α2	uαby2(t(α2	X
ejpam-2623	551	3	+	+	CCONJ
ejpam-2623	551	4	b2)−	b2)−	PROPN
ejpam-2623	551	5	αb	αb	NOUN
ejpam-2623	551	6	)	)	PUNCT
ejpam-2623	551	7	=	=	SYM
ejpam-2623	551	8	uαβy2	uαβy2	PROPN
ejpam-2623	551	9	(	(	PUNCT
ejpam-2623	551	10	β(α2	β(α2	NOUN
ejpam-2623	551	11	+	+	CCONJ
ejpam-2623	551	12	uβ2r2	uβ2r2	NOUN
ejpam-2623	551	13	)	)	PUNCT
ejpam-2623	551	14	α	α	NOUN
ejpam-2623	551	15	−	−	NOUN
ejpam-2623	551	16	αβ	αβ	INTJ
ejpam-2623	551	17	)	)	PUNCT
ejpam-2623	552	1	=	=	NOUN
ejpam-2623	552	2	uαβy2	uαβy2	NOUN
ejpam-2623	552	3	(	(	PUNCT
ejpam-2623	552	4	uβ3r2	uβ3r2	NOUN
ejpam-2623	552	5	α	α	NOUN
ejpam-2623	552	6	)	)	PUNCT
ejpam-2623	553	1	=	=	SYM
ejpam-2623	553	2	u2β4r2y2	u2β4r2y2	NOUN
ejpam-2623	553	3	which	which	PRON
ejpam-2623	553	4	is	be	AUX
ejpam-2623	553	5	a	a	DET
ejpam-2623	553	6	square	square	NOUN
ejpam-2623	553	7	.	.	PUNCT
ejpam-2623	554	1	–	–	PUNCT
ejpam-2623	554	2	if	if	SCONJ
ejpam-2623	554	3	ε	ε	PROPN
ejpam-2623	554	4	=	=	SYM
ejpam-2623	554	5	−1	−1	NOUN
ejpam-2623	554	6	,	,	PUNCT
ejpam-2623	554	7	so	so	ADV
ejpam-2623	554	8	x	x	X
ejpam-2623	554	9	=	=	PUNCT
ejpam-2623	555	1	√	√	PART
ejpam-2623	555	2	t(αt−	t(αt−	NUM
ejpam-2623	555	3	β	β	NOUN
ejpam-2623	555	4	)	)	PUNCT
ejpam-2623	555	5	α−	α−	ADP
ejpam-2623	555	6	βt	βt	ADP
ejpam-2623	555	7	∈	∈	NOUN
ejpam-2623	555	8	√	√	ADP
ejpam-2623	555	9	f2	f2	PROPN
ejpam-2623	555	10	q	q	PROPN
ejpam-2623	556	1	and	and	CCONJ
ejpam-2623	556	2	x	x	SYM
ejpam-2623	556	3	y	y	PROPN
ejpam-2623	556	4	=	=	SYM
ejpam-2623	556	5	t	t	PROPN
ejpam-2623	556	6	=	=	PUNCT
ejpam-2623	556	7	v(a2	v(a2	NOUN
ejpam-2623	556	8	+	+	CCONJ
ejpam-2623	556	9	b2)−	b2)−	PROPN
ejpam-2623	556	10	ab	ab	PROPN
ejpam-2623	556	11	abv	abv	PROPN
ejpam-2623	556	12	.	.	PUNCT
ejpam-2623	557	1	let	let	VERB
ejpam-2623	557	2	us	we	PRON
ejpam-2623	557	3	show	show	VERB
ejpam-2623	557	4	that	that	SCONJ
ejpam-2623	557	5	χ	χ	X
ejpam-2623	557	6	(	(	PUNCT
ejpam-2623	557	7	uαβxy(α2	uαβxy(α2	X
ejpam-2623	557	8	+	+	CCONJ
ejpam-2623	557	9	β2	β2	NOUN
ejpam-2623	557	10	−	−	PROPN
ejpam-2623	557	11	αβx	αβx	NOUN
ejpam-2623	557	12	y	y	PROPN
ejpam-2623	557	13	)	)	PUNCT
ejpam-2623	557	14	)	)	PUNCT
ejpam-2623	558	1	=	=	PUNCT
ejpam-2623	558	2	1	1	X
ejpam-2623	558	3	.	.	PUNCT
ejpam-2623	558	4	in	in	ADP
ejpam-2623	558	5	fact	fact	NOUN
ejpam-2623	558	6	,	,	PUNCT
ejpam-2623	558	7	we	we	PRON
ejpam-2623	558	8	have	have	VERB
ejpam-2623	558	9	:	:	PUNCT
ejpam-2623	558	10	uαβxy(α2	uαβxy(α2	PROPN
ejpam-2623	559	1	+	+	CCONJ
ejpam-2623	559	2	β2	β2	NOUN
ejpam-2623	559	3	−	−	PROPN
ejpam-2623	559	4	αβx	αβx	NOUN
ejpam-2623	559	5	y	y	PROPN
ejpam-2623	559	6	)	)	PUNCT
ejpam-2623	560	1	=	=	PRON
ejpam-2623	560	2	uαβx2	uαβx2	PROPN
ejpam-2623	560	3	(	(	PUNCT
ejpam-2623	560	4	α2	α2	PROPN
ejpam-2623	560	5	+	+	CCONJ
ejpam-2623	560	6	β2	β2	PROPN
ejpam-2623	560	7	−	−	PROPN
ejpam-2623	560	8	αβt	αβt	NOUN
ejpam-2623	560	9	t	t	NOUN
ejpam-2623	560	10	)	)	PUNCT
ejpam-2623	560	11	=	=	SYM
ejpam-2623	561	1	uαβx2	uαβx2	PROPN
ejpam-2623	561	2	(	(	PUNCT
ejpam-2623	561	3	αβ	αβ	INTJ
ejpam-2623	561	4	vt	vt	INTJ
ejpam-2623	561	5	)	)	PUNCT
ejpam-2623	562	1	=	=	VERB
ejpam-2623	562	2	uαβx2	uαβx2	X
ejpam-2623	562	3	(	(	PUNCT
ejpam-2623	562	4	α2β2	α2β2	ADP
ejpam-2623	562	5	v(α2	v(α2	NOUN
ejpam-2623	562	6	+	+	CCONJ
ejpam-2623	562	7	β2)−	β2)−	ADJ
ejpam-2623	562	8	αβ	αβ	NOUN
ejpam-2623	562	9	)	)	PUNCT
ejpam-2623	562	10	=	=	SYM
ejpam-2623	562	11	uαβx2	uαβx2	PROPN
ejpam-2623	563	1	(	(	PUNCT
ejpam-2623	563	2	α3	α3	ADJ
ejpam-2623	563	3	uβr2	uβr2	NOUN
ejpam-2623	563	4	)	)	PUNCT
ejpam-2623	564	1	=	=	PUNCT
ejpam-2623	565	1	α4x2	α4x2	PROPN
ejpam-2623	565	2	r2	r2	NOUN
ejpam-2623	565	3	which	which	PRON
ejpam-2623	565	4	is	be	AUX
ejpam-2623	565	5	a	a	DET
ejpam-2623	565	6	square	square	NOUN
ejpam-2623	565	7	.	.	PUNCT
ejpam-2623	566	1	•	•	NUM
ejpam-2623	566	2	now	now	ADV
ejpam-2623	566	3	let	let	VERB
ejpam-2623	566	4	(	(	PUNCT
ejpam-2623	566	5	x	x	NOUN
ejpam-2623	566	6	,	,	PUNCT
ejpam-2623	566	7	y	y	PROPN
ejpam-2623	566	8	)	)	PUNCT
ejpam-2623	566	9	∈	∈	PROPN
ejpam-2623	566	10	eα	eα	NOUN
ejpam-2623	566	11	,	,	PUNCT
ejpam-2623	566	12	β	β	NOUN
ejpam-2623	566	13	such	such	ADJ
ejpam-2623	566	14	that	that	SCONJ
ejpam-2623	566	15	χ	χ	PROPN
ejpam-2623	566	16	(	(	PUNCT
ejpam-2623	566	17	uαβxy(α2	uαβxy(α2	X
ejpam-2623	566	18	+	+	CCONJ
ejpam-2623	566	19	β2	β2	NOUN
ejpam-2623	566	20	−	−	PROPN
ejpam-2623	567	1	αβ	αβ	INTJ
ejpam-2623	567	2	y	y	NOUN
ejpam-2623	567	3	x	x	PROPN
ejpam-2623	567	4	)	)	PUNCT
ejpam-2623	567	5	)	)	PUNCT
ejpam-2623	568	1	=	=	SYM
ejpam-2623	568	2	1	1	NUM
ejpam-2623	568	3	if	if	SCONJ
ejpam-2623	568	4	x	x	X
ejpam-2623	568	5	/∈	/∈	NOUN
ejpam-2623	568	6	√	√	VERB
ejpam-2623	568	7	f2	f2	PROPN
ejpam-2623	568	8	q	q	NOUN
ejpam-2623	568	9	and	and	CCONJ
ejpam-2623	568	10	χ	χ	X
ejpam-2623	568	11	(	(	PUNCT
ejpam-2623	568	12	uαβxy(α2	uαβxy(α2	X
ejpam-2623	568	13	+	+	CCONJ
ejpam-2623	569	1	β2	β2	NOUN
ejpam-2623	569	2	−	−	PROPN
ejpam-2623	569	3	αβx	αβx	NOUN
ejpam-2623	569	4	y	y	PROPN
ejpam-2623	569	5	)	)	PUNCT
ejpam-2623	569	6	)	)	PUNCT
ejpam-2623	570	1	=	=	PUNCT
ejpam-2623	570	2	1	1	NUM
ejpam-2623	570	3	if	if	SCONJ
ejpam-2623	570	4	x	x	SYM
ejpam-2623	570	5	∈	∈	NOUN
ejpam-2623	570	6	√	√	VERB
ejpam-2623	570	7	f2	f2	PROPN
ejpam-2623	570	8	q	q	NOUN
ejpam-2623	570	9	.	.	PUNCT
ejpam-2623	571	1	we	we	PRON
ejpam-2623	571	2	define	define	VERB
ejpam-2623	571	3	r	r	NOUN
ejpam-2623	571	4	=	=	SYM
ejpam-2623	571	5	1	1	NUM
ejpam-2623	571	6	β	β	SYM
ejpam-2623	571	7	√	√	NUM
ejpam-2623	571	8	α(x(α2	α(x(α2	PROPN
ejpam-2623	571	9	+	+	CCONJ
ejpam-2623	571	10	β2)−	β2)−	ADJ
ejpam-2623	571	11	αβy	αβy	ADJ
ejpam-2623	571	12	)	)	PUNCT
ejpam-2623	571	13	uβy	uβy	VERB
ejpam-2623	571	14	if	if	SCONJ
ejpam-2623	571	15	the	the	DET
ejpam-2623	571	16	first	first	ADJ
ejpam-2623	571	17	condition	condition	NOUN
ejpam-2623	571	18	is	be	AUX
ejpam-2623	571	19	verified	verify	VERB
ejpam-2623	571	20	;	;	PUNCT
ejpam-2623	571	21	and	and	CCONJ
ejpam-2623	572	1	r	r	X
ejpam-2623	572	2	=	=	PUNCT
ejpam-2623	572	3	a	a	PRON
ejpam-2623	572	4	√	√	NOUN
ejpam-2623	572	5	αx	αx	ADP
ejpam-2623	572	6	uβ(y(α2	uβ(y(α2	PROPN
ejpam-2623	572	7	+	+	CCONJ
ejpam-2623	572	8	β2)−	β2)−	ADJ
ejpam-2623	572	9	αβx	αβx	NOUN
ejpam-2623	572	10	)	)	PUNCT
ejpam-2623	572	11	otherwise	otherwise	ADV
ejpam-2623	572	12	.	.	PUNCT
ejpam-2623	573	1	first	first	ADV
ejpam-2623	573	2	see	see	VERB
ejpam-2623	573	3	that	that	SCONJ
ejpam-2623	573	4	r	r	NOUN
ejpam-2623	573	5	is	be	AUX
ejpam-2623	573	6	well	well	ADV
ejpam-2623	573	7	-	-	PUNCT
ejpam-2623	573	8	defined	define	VERB
ejpam-2623	573	9	and	and	CCONJ
ejpam-2623	573	10	r	r	NOUN
ejpam-2623	573	11	6=	6=	ADP
ejpam-2623	573	12	0	0	NUM
ejpam-2623	573	13	in	in	ADP
ejpam-2623	573	14	both	both	DET
ejpam-2623	573	15	cases	case	NOUN
ejpam-2623	573	16	since	since	SCONJ
ejpam-2623	573	17	uαβxy(α2	uαβxy(α2	NOUN
ejpam-2623	573	18	+	+	CCONJ
ejpam-2623	573	19	β2	β2	NOUN
ejpam-2623	573	20	−	−	PROPN
ejpam-2623	574	1	αβ	αβ	INTJ
ejpam-2623	574	2	y	y	NOUN
ejpam-2623	574	3	x	x	PROPN
ejpam-2623	574	4	)	)	PUNCT
ejpam-2623	574	5	and	and	CCONJ
ejpam-2623	574	6	uαβxy(α2	uαβxy(α2	X
ejpam-2623	575	1	+	+	CCONJ
ejpam-2623	575	2	β2	β2	NOUN
ejpam-2623	575	3	−	−	PROPN
ejpam-2623	575	4	αβx	αβx	NOUN
ejpam-2623	575	5	y	y	PROPN
ejpam-2623	575	6	)	)	PUNCT
ejpam-2623	575	7	are	be	AUX
ejpam-2623	575	8	non	non	ADJ
ejpam-2623	575	9	-	-	ADJ
ejpam-2623	575	10	zero	zero	NUM
ejpam-2623	575	11	squares	square	NOUN
ejpam-2623	575	12	.	.	PUNCT
ejpam-2623	576	1	now	now	ADV
ejpam-2623	576	2	let	let	VERB
ejpam-2623	576	3	us	we	PRON
ejpam-2623	576	4	show	show	VERB
ejpam-2623	576	5	that	that	SCONJ
ejpam-2623	576	6	r	r	PROPN
ejpam-2623	576	7	∈	∈	PROPN
ejpam-2623	576	8	r.	r.	PROPN
ejpam-2623	576	9	–	–	PUNCT
ejpam-2623	576	10	if	if	SCONJ
ejpam-2623	576	11	r	r	NOUN
ejpam-2623	576	12	=	=	SYM
ejpam-2623	576	13	1	1	NUM
ejpam-2623	576	14	β	β	SYM
ejpam-2623	576	15	√	√	NUM
ejpam-2623	576	16	α(x(α2	α(x(α2	PROPN
ejpam-2623	576	17	+	+	CCONJ
ejpam-2623	576	18	β2)−	β2)−	ADJ
ejpam-2623	576	19	αβy	αβy	ADJ
ejpam-2623	576	20	)	)	PUNCT
ejpam-2623	576	21	uβy	uβy	NOUN
ejpam-2623	576	22	,	,	PUNCT
ejpam-2623	576	23	then	then	ADV
ejpam-2623	576	24	α2+uβ2r2	α2+uβ2r2	X
ejpam-2623	576	25	=	=	SYM
ejpam-2623	576	26	α2+uβ2	α2+uβ2	NOUN
ejpam-2623	576	27	(	(	PUNCT
ejpam-2623	576	28	α	α	PROPN
ejpam-2623	576	29	(	(	PUNCT
ejpam-2623	576	30	x(α2	x(α2	PROPN
ejpam-2623	576	31	+	+	CCONJ
ejpam-2623	576	32	β2)−	β2)−	ADJ
ejpam-2623	576	33	αβy	αβy	ADJ
ejpam-2623	576	34	)	)	PUNCT
ejpam-2623	576	35	uβ3y	uβ3y	PROPN
ejpam-2623	576	36	)	)	PUNCT
ejpam-2623	576	37	=	=	PUNCT
ejpam-2623	577	1	αx(α2	αx(α2	NOUN
ejpam-2623	577	2	+	+	CCONJ
ejpam-2623	577	3	β2	β2	ADJ
ejpam-2623	577	4	)	)	PUNCT
ejpam-2623	577	5	βy	βy	PRON
ejpam-2623	578	1	6=	6=	ADP
ejpam-2623	578	2	0	0	NUM
ejpam-2623	578	3	since	since	SCONJ
ejpam-2623	578	4	x	x	PROPN
ejpam-2623	578	5	6=	6=	ADP
ejpam-2623	578	6	0	0	NUM
ejpam-2623	578	7	and	and	CCONJ
ejpam-2623	578	8	α(α2	α(α2	PRON
ejpam-2623	578	9	+	+	CCONJ
ejpam-2623	578	10	β2	β2	NOUN
ejpam-2623	578	11	)	)	PUNCT
ejpam-2623	578	12	6=	6=	ADP
ejpam-2623	578	13	0	0	NUM
ejpam-2623	578	14	.	.	PUNCT
ejpam-2623	579	1	–	–	PUNCT
ejpam-2623	579	2	if	if	SCONJ
ejpam-2623	579	3	r	r	NOUN
ejpam-2623	579	4	=	=	SYM
ejpam-2623	579	5	α	α	NOUN
ejpam-2623	579	6	√	√	VERB
ejpam-2623	579	7	αx	αx	ADP
ejpam-2623	579	8	uβ(y(α2	uβ(y(α2	PROPN
ejpam-2623	579	9	+	+	CCONJ
ejpam-2623	579	10	β2)−	β2)−	ADJ
ejpam-2623	579	11	αβx	αβx	NOUN
ejpam-2623	579	12	)	)	PUNCT
ejpam-2623	579	13	,	,	PUNCT
ejpam-2623	579	14	then	then	ADV
ejpam-2623	579	15	α2+uβ2r2	α2+uβ2r2	X
ejpam-2623	579	16	=	=	SYM
ejpam-2623	579	17	α2+uβ2	α2+uβ2	NOUN
ejpam-2623	579	18	(	(	PUNCT
ejpam-2623	579	19	α2(αx	α2(αx	NUM
ejpam-2623	579	20	)	)	PUNCT
ejpam-2623	579	21	uβ	uβ	PROPN
ejpam-2623	579	22	(	(	PUNCT
ejpam-2623	579	23	y(α2	y(α2	PROPN
ejpam-2623	579	24	+	+	CCONJ
ejpam-2623	579	25	β2)−	β2)−	ADJ
ejpam-2623	579	26	αbx	αbx	NOUN
ejpam-2623	579	27	)	)	PUNCT
ejpam-2623	579	28	)	)	PUNCT
ejpam-2623	580	1	=	=	PUNCT
ejpam-2623	580	2	α2y(α2	α2y(α2	PROPN
ejpam-2623	580	3	+	+	CCONJ
ejpam-2623	580	4	β2	β2	PROPN
ejpam-2623	580	5	)	)	PUNCT
ejpam-2623	580	6	y(α2	y(α2	PROPN
ejpam-2623	581	1	+	+	CCONJ
ejpam-2623	581	2	β2)−	β2)−	ADJ
ejpam-2623	581	3	αβx	αβx	NOUN
ejpam-2623	581	4	6=	6=	SYM
ejpam-2623	581	5	0	0	NUM
ejpam-2623	581	6	since	since	SCONJ
ejpam-2623	581	7	y	y	PROPN
ejpam-2623	581	8	6=	6=	ADP
ejpam-2623	581	9	0	0	NUM
ejpam-2623	581	10	and	and	CCONJ
ejpam-2623	581	11	α(α2	α(α2	PRON
ejpam-2623	582	1	+	+	CCONJ
ejpam-2623	582	2	β2	β2	NOUN
ejpam-2623	582	3	)	)	PUNCT
ejpam-2623	582	4	6=	6=	ADP
ejpam-2623	582	5	0	0	X
ejpam-2623	582	6	.	.	PUNCT
ejpam-2623	583	1	n.	n.	PROPN
ejpam-2623	583	2	diarra	diarra	PROPN
ejpam-2623	583	3	,	,	PUNCT
ejpam-2623	583	4	d.	d.	PROPN
ejpam-2623	583	5	sow	sow	PROPN
ejpam-2623	583	6	,	,	PUNCT
ejpam-2623	583	7	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	583	8	.	.	PUNCT
ejpam-2623	583	9	khlil	khlil	PROPN
ejpam-2623	583	10	/	/	SYM
ejpam-2623	583	11	eur	eur	PROPN
ejpam-2623	583	12	.	.	PUNCT
ejpam-2623	584	1	j.	j.	PROPN
ejpam-2623	584	2	pure	pure	PROPN
ejpam-2623	584	3	appl	appl	PROPN
ejpam-2623	584	4	.	.	PROPN
ejpam-2623	584	5	math	math	PROPN
ejpam-2623	584	6	,	,	PUNCT
ejpam-2623	584	7	10	10	NUM
ejpam-2623	584	8	(	(	PUNCT
ejpam-2623	584	9	2	2	NUM
ejpam-2623	584	10	)	)	PUNCT
ejpam-2623	584	11	(	(	PUNCT
ejpam-2623	584	12	2017	2017	NUM
ejpam-2623	584	13	)	)	PUNCT
ejpam-2623	584	14	,	,	PUNCT
ejpam-2623	584	15	363	363	NUM
ejpam-2623	584	16	-	-	SYM
ejpam-2623	584	17	391	391	NUM
ejpam-2623	584	18	378	378	NUM
ejpam-2623	584	19	hence	hence	ADV
ejpam-2623	584	20	we	we	PRON
ejpam-2623	584	21	have	have	AUX
ejpam-2623	584	22	showed	show	VERB
ejpam-2623	584	23	that	that	SCONJ
ejpam-2623	584	24	r	r	NOUN
ejpam-2623	584	25	is	be	AUX
ejpam-2623	584	26	well	well	ADV
ejpam-2623	584	27	-	-	PUNCT
ejpam-2623	584	28	defined	define	VERB
ejpam-2623	584	29	and	and	CCONJ
ejpam-2623	584	30	that	that	SCONJ
ejpam-2623	584	31	r	r	NOUN
ejpam-2623	584	32	∈	∈	PROPN
ejpam-2623	584	33	r	r	NOUN
ejpam-2623	584	34	\	\	PUNCT
ejpam-2623	584	35	{	{	PUNCT
ejpam-2623	584	36	0	0	NUM
ejpam-2623	584	37	}	}	PUNCT
ejpam-2623	584	38	.	.	PUNCT
ejpam-2623	585	1	then	then	ADV
ejpam-2623	585	2	φα	φα	ADP
ejpam-2623	585	3	,	,	PUNCT
ejpam-2623	585	4	β(r	β(r	PROPN
ejpam-2623	585	5	)	)	PUNCT
ejpam-2623	585	6	=	=	SYM
ejpam-2623	585	7	(	(	PUNCT
ejpam-2623	585	8	x	x	X
ejpam-2623	585	9	,	,	PUNCT
ejpam-2623	585	10	y	y	NOUN
ejpam-2623	585	11	)	)	PUNCT
ejpam-2623	585	12	follows	follow	VERB
ejpam-2623	585	13	from	from	ADP
ejpam-2623	585	14	the	the	DET
ejpam-2623	585	15	following	following	ADJ
ejpam-2623	585	16	proof	proof	NOUN
ejpam-2623	585	17	.	.	PUNCT
ejpam-2623	586	1	(	(	PUNCT
ejpam-2623	586	2	ii	ii	NOUN
ejpam-2623	586	3	)	)	PUNCT
ejpam-2623	586	4	as	as	ADP
ejpam-2623	586	5	previously	previously	ADV
ejpam-2623	586	6	,	,	PUNCT
ejpam-2623	586	7	we	we	PRON
ejpam-2623	586	8	consider	consider	VERB
ejpam-2623	586	9	two	two	NUM
ejpam-2623	586	10	cases	case	NOUN
ejpam-2623	586	11	:	:	PUNCT
ejpam-2623	586	12	•	•	NUM
ejpam-2623	586	13	first	first	ADJ
ejpam-2623	586	14	case	case	NOUN
ejpam-2623	586	15	:	:	PUNCT
ejpam-2623	586	16	x	x	X
ejpam-2623	586	17	=	=	PUNCT
ejpam-2623	587	1	−	−	PROPN
ejpam-2623	587	2	√	√	PROPN
ejpam-2623	587	3	z	z	NOUN
ejpam-2623	587	4	/∈	/∈	PUNCT
ejpam-2623	587	5	√	√	VERB
ejpam-2623	588	1	f2	f2	PROPN
ejpam-2623	588	2	q	q	NOUN
ejpam-2623	588	3	and	and	CCONJ
ejpam-2623	588	4	r	r	NOUN
ejpam-2623	588	5	=	=	SYM
ejpam-2623	588	6	1	1	NUM
ejpam-2623	588	7	β	β	SYM
ejpam-2623	588	8	√	√	NUM
ejpam-2623	588	9	α(x(α2	α(x(α2	PROPN
ejpam-2623	588	10	+	+	CCONJ
ejpam-2623	588	11	β2)−	β2)−	ADJ
ejpam-2623	588	12	αβy	αβy	ADJ
ejpam-2623	588	13	)	)	PUNCT
ejpam-2623	588	14	uβy	uβy	PROPN
ejpam-2623	588	15	.	.	PUNCT
ejpam-2623	589	1	since	since	SCONJ
ejpam-2623	589	2	r	r	NOUN
ejpam-2623	589	3	∈	∈	PROPN
ejpam-2623	589	4	r	r	NOUN
ejpam-2623	589	5	\	\	PUNCT
ejpam-2623	589	6	{	{	PUNCT
ejpam-2623	589	7	0	0	NUM
ejpam-2623	589	8	}	}	PUNCT
ejpam-2623	589	9	,	,	PUNCT
ejpam-2623	589	10	we	we	PRON
ejpam-2623	589	11	can	can	AUX
ejpam-2623	589	12	define	define	VERB
ejpam-2623	589	13	v	v	ADP
ejpam-2623	589	14	,	,	PUNCT
ejpam-2623	589	15	ε	ε	PROPN
ejpam-2623	589	16	,	,	PUNCT
ejpam-2623	589	17	t	t	PROPN
ejpam-2623	589	18	,	,	PUNCT
ejpam-2623	589	19	x	x	X
ejpam-2623	589	20	and	and	CCONJ
ejpam-2623	589	21	y	y	PROPN
ejpam-2623	589	22	from	from	ADP
ejpam-2623	589	23	r	r	NOUN
ejpam-2623	589	24	as	as	ADP
ejpam-2623	589	25	in	in	ADP
ejpam-2623	589	26	theorem	theorem	NOUN
ejpam-2623	589	27	3	3	X
ejpam-2623	589	28	.	.	X
ejpam-2623	590	1	we	we	PRON
ejpam-2623	590	2	have	have	VERB
ejpam-2623	590	3	:	:	PUNCT
ejpam-2623	590	4	v	v	X
ejpam-2623	590	5	=	=	PUNCT
ejpam-2623	590	6	β(α2	β(α2	X
ejpam-2623	590	7	+	+	CCONJ
ejpam-2623	590	8	uβ2r2	uβ2r2	PROPN
ejpam-2623	590	9	)	)	PUNCT
ejpam-2623	590	10	α(α2	α(α2	NOUN
ejpam-2623	591	1	+	+	CCONJ
ejpam-2623	591	2	β2	β2	VERB
ejpam-2623	591	3	)	)	PUNCT
ejpam-2623	591	4	=	=	PUNCT
ejpam-2623	591	5	β	β	X
ejpam-2623	591	6	α(α2	α(α2	NOUN
ejpam-2623	592	1	+	+	CCONJ
ejpam-2623	592	2	β2	β2	NOUN
ejpam-2623	592	3	)	)	PUNCT
ejpam-2623	592	4	(	(	PUNCT
ejpam-2623	592	5	α2	α2	PROPN
ejpam-2623	592	6	+	+	CCONJ
ejpam-2623	592	7	α	α	PROPN
ejpam-2623	592	8	(	(	PUNCT
ejpam-2623	592	9	x(α2	x(α2	PROPN
ejpam-2623	592	10	+	+	CCONJ
ejpam-2623	592	11	β2)−	β2)−	ADJ
ejpam-2623	592	12	αβy	αβy	ADJ
ejpam-2623	592	13	)	)	PUNCT
ejpam-2623	592	14	βy	βy	PRON
ejpam-2623	592	15	)	)	PUNCT
ejpam-2623	592	16	=	=	SYM
ejpam-2623	593	1	αx(α2	αx(α2	NOUN
ejpam-2623	594	1	+	+	CCONJ
ejpam-2623	594	2	β2	β2	ADJ
ejpam-2623	594	3	)	)	PUNCT
ejpam-2623	594	4	αy(α2	αy(α2	NOUN
ejpam-2623	595	1	+	+	CCONJ
ejpam-2623	595	2	β2	β2	VERB
ejpam-2623	595	3	)	)	PUNCT
ejpam-2623	595	4	=	=	PUNCT
ejpam-2623	596	1	x	x	PUNCT
ejpam-2623	596	2	y	y	PROPN
ejpam-2623	596	3	.	.	PUNCT
ejpam-2623	597	1	ε	ε	PROPN
ejpam-2623	598	1	=	=	PRON
ejpam-2623	598	2	χ	χ	X
ejpam-2623	598	3	(	(	PUNCT
ejpam-2623	598	4	v(αv	v(αv	NUM
ejpam-2623	598	5	−	−	NOUN
ejpam-2623	598	6	β	β	NOUN
ejpam-2623	598	7	)	)	PUNCT
ejpam-2623	598	8	α−	α−	ADP
ejpam-2623	598	9	βv	βv	PUNCT
ejpam-2623	598	10	)	)	PUNCT
ejpam-2623	598	11	=	=	SYM
ejpam-2623	599	1	χ	χ	X
ejpam-2623	599	2	(	(	PUNCT
ejpam-2623	599	3	x	x	SYM
ejpam-2623	599	4	y	y	PROPN
ejpam-2623	599	5	(	(	PUNCT
ejpam-2623	599	6	αxy	αxy	NOUN
ejpam-2623	599	7	−	−	PROPN
ejpam-2623	599	8	β	β	NOUN
ejpam-2623	599	9	)	)	PUNCT
ejpam-2623	599	10	α−	α−	ADP
ejpam-2623	599	11	β	β	X
ejpam-2623	599	12	xy	xy	PROPN
ejpam-2623	599	13	)	)	PUNCT
ejpam-2623	600	1	=	=	SYM
ejpam-2623	601	1	χ	χ	X
ejpam-2623	601	2	(	(	PUNCT
ejpam-2623	601	3	x(αx−	x(αx−	NUM
ejpam-2623	601	4	βy	βy	NOUN
ejpam-2623	601	5	)	)	PUNCT
ejpam-2623	601	6	y(αy	y(αy	PROPN
ejpam-2623	601	7	−	−	PROPN
ejpam-2623	601	8	βx	βx	NOUN
ejpam-2623	601	9	)	)	PUNCT
ejpam-2623	601	10	)	)	PUNCT
ejpam-2623	602	1	but	but	CCONJ
ejpam-2623	602	2	from	from	ADP
ejpam-2623	602	3	the	the	DET
ejpam-2623	602	4	curve	curve	NOUN
ejpam-2623	602	5	equation	equation	NOUN
ejpam-2623	602	6	we	we	PRON
ejpam-2623	602	7	know	know	VERB
ejpam-2623	602	8	that	that	SCONJ
ejpam-2623	602	9	αx−	αx−	NUM
ejpam-2623	602	10	βy	βy	NOUN
ejpam-2623	602	11	αy	αy	ADP
ejpam-2623	602	12	−	−	NOUN
ejpam-2623	603	1	βx	βx	NOUN
ejpam-2623	603	2	=	=	PUNCT
ejpam-2623	603	3	xy	xy	PROPN
ejpam-2623	603	4	;	;	PUNCT
ejpam-2623	603	5	so	so	ADV
ejpam-2623	603	6	ε	ε	PROPN
ejpam-2623	603	7	=	=	SYM
ejpam-2623	603	8	χ(x2	χ(x2	PROPN
ejpam-2623	603	9	)	)	PUNCT
ejpam-2623	603	10	=	=	SYM
ejpam-2623	604	1	1	1	X
ejpam-2623	604	2	.	.	PUNCT
ejpam-2623	604	3	then	then	ADV
ejpam-2623	604	4	t	t	PROPN
ejpam-2623	604	5	=	=	SYM
ejpam-2623	604	6	v	v	PROPN
ejpam-2623	604	7	=	=	SYM
ejpam-2623	604	8	x	x	SYM
ejpam-2623	604	9	y	y	PROPN
ejpam-2623	604	10	=	=	SYM
ejpam-2623	604	11	t	t	PROPN
ejpam-2623	604	12	,	,	PUNCT
ejpam-2623	604	13	x	x	PUNCT
ejpam-2623	604	14	=	=	PUNCT
ejpam-2623	605	1	−	−	NOUN
ejpam-2623	605	2	√	√	NUM
ejpam-2623	605	3	t(αt−	t(αt−	NUM
ejpam-2623	605	4	β	β	NOUN
ejpam-2623	605	5	)	)	PUNCT
ejpam-2623	605	6	α−	α−	ADP
ejpam-2623	605	7	βt	βt	NOUN
ejpam-2623	606	1	=	=	SYM
ejpam-2623	606	2	−	−	PROPN
ejpam-2623	606	3	√	√	NUM
ejpam-2623	606	4	t(αt−	t(αt−	NUM
ejpam-2623	606	5	β	β	NOUN
ejpam-2623	606	6	)	)	PUNCT
ejpam-2623	606	7	α−	α−	ADP
ejpam-2623	606	8	βt	βt	NOUN
ejpam-2623	607	1	=	=	SYM
ejpam-2623	607	2	−	−	PROPN
ejpam-2623	608	1	√	√	NOUN
ejpam-2623	608	2	z	z	NOUN
ejpam-2623	609	1	=	=	PUNCT
ejpam-2623	610	1	x	x	PROPN
ejpam-2623	610	2	and	and	CCONJ
ejpam-2623	610	3	y	y	PROPN
ejpam-2623	610	4	=	=	PUNCT
ejpam-2623	611	1	x	x	PUNCT
ejpam-2623	611	2	t	t	NOUN
ejpam-2623	611	3	=	=	PUNCT
ejpam-2623	611	4	x	x	SYM
ejpam-2623	611	5	t	t	NOUN
ejpam-2623	611	6	=	=	PUNCT
ejpam-2623	611	7	y.	y.	NOUN
ejpam-2623	611	8	hence	hence	ADV
ejpam-2623	611	9	we	we	PRON
ejpam-2623	611	10	conclude	conclude	VERB
ejpam-2623	611	11	that	that	SCONJ
ejpam-2623	611	12	φ′(r	φ′(r	NOUN
ejpam-2623	611	13	)	)	PUNCT
ejpam-2623	611	14	=	=	SYM
ejpam-2623	612	1	(	(	PUNCT
ejpam-2623	612	2	x	x	X
ejpam-2623	612	3	,	,	PUNCT
ejpam-2623	612	4	y	y	NOUN
ejpam-2623	612	5	)	)	PUNCT
ejpam-2623	612	6	=	=	SYM
ejpam-2623	612	7	(	(	PUNCT
ejpam-2623	612	8	x	x	X
ejpam-2623	612	9	,	,	PUNCT
ejpam-2623	612	10	y	y	PROPN
ejpam-2623	612	11	)	)	PUNCT
ejpam-2623	612	12	.	.	PUNCT
ejpam-2623	613	1	•	•	NUM
ejpam-2623	613	2	second	second	ADJ
ejpam-2623	613	3	case	case	NOUN
ejpam-2623	613	4	:	:	PUNCT
ejpam-2623	613	5	x	x	X
ejpam-2623	613	6	=	=	PUNCT
ejpam-2623	613	7	√	√	PROPN
ejpam-2623	613	8	z	z	NOUN
ejpam-2623	613	9	∈	∈	PROPN
ejpam-2623	613	10	√	√	ADP
ejpam-2623	613	11	f2	f2	PROPN
ejpam-2623	613	12	q	q	NOUN
ejpam-2623	613	13	and	and	CCONJ
ejpam-2623	613	14	r	r	NOUN
ejpam-2623	613	15	=	=	SYM
ejpam-2623	613	16	α	α	NOUN
ejpam-2623	613	17	√	√	VERB
ejpam-2623	613	18	αx	αx	ADP
ejpam-2623	613	19	uβ(y(α2	uβ(y(α2	PROPN
ejpam-2623	613	20	+	+	CCONJ
ejpam-2623	613	21	β2)−	β2)−	ADJ
ejpam-2623	613	22	αβx	αβx	NOUN
ejpam-2623	613	23	)	)	PUNCT
ejpam-2623	613	24	.	.	PUNCT
ejpam-2623	614	1	since	since	SCONJ
ejpam-2623	614	2	r	r	NOUN
ejpam-2623	614	3	∈	∈	PROPN
ejpam-2623	614	4	r	r	NOUN
ejpam-2623	614	5	\	\	PUNCT
ejpam-2623	614	6	{	{	PUNCT
ejpam-2623	614	7	0	0	NUM
ejpam-2623	614	8	}	}	PUNCT
ejpam-2623	614	9	,	,	PUNCT
ejpam-2623	614	10	we	we	PRON
ejpam-2623	614	11	can	can	AUX
ejpam-2623	614	12	define	define	VERB
ejpam-2623	614	13	v	v	ADP
ejpam-2623	614	14	,	,	PUNCT
ejpam-2623	614	15	ε	ε	PROPN
ejpam-2623	614	16	,	,	PUNCT
ejpam-2623	614	17	t	t	PROPN
ejpam-2623	614	18	,	,	PUNCT
ejpam-2623	614	19	x	x	X
ejpam-2623	614	20	and	and	CCONJ
ejpam-2623	614	21	y	y	PROPN
ejpam-2623	614	22	from	from	ADP
ejpam-2623	614	23	r	r	NOUN
ejpam-2623	614	24	as	as	ADP
ejpam-2623	614	25	in	in	ADP
ejpam-2623	614	26	theorem	theorem	NOUN
ejpam-2623	614	27	3	3	X
ejpam-2623	614	28	.	.	X
ejpam-2623	615	1	we	we	PRON
ejpam-2623	615	2	have	have	VERB
ejpam-2623	615	3	:	:	PUNCT
ejpam-2623	615	4	v	v	X
ejpam-2623	615	5	=	=	PUNCT
ejpam-2623	615	6	β(α2	β(α2	X
ejpam-2623	615	7	+	+	CCONJ
ejpam-2623	615	8	uβ2r2	uβ2r2	PROPN
ejpam-2623	615	9	)	)	PUNCT
ejpam-2623	615	10	α(α2	α(α2	NOUN
ejpam-2623	616	1	+	+	CCONJ
ejpam-2623	616	2	β2	β2	VERB
ejpam-2623	616	3	)	)	PUNCT
ejpam-2623	616	4	=	=	PUNCT
ejpam-2623	616	5	β	β	X
ejpam-2623	616	6	α(α2	α(α2	NOUN
ejpam-2623	617	1	+	+	CCONJ
ejpam-2623	617	2	β2	β2	NOUN
ejpam-2623	617	3	)	)	PUNCT
ejpam-2623	617	4	(	(	PUNCT
ejpam-2623	617	5	α2	α2	ADJ
ejpam-2623	617	6	+	+	CCONJ
ejpam-2623	617	7	α3βx	α3βx	PROPN
ejpam-2623	617	8	y(α2	y(α2	NOUN
ejpam-2623	618	1	+	+	CCONJ
ejpam-2623	618	2	β2)−	β2)−	ADJ
ejpam-2623	618	3	αβx	αβx	NOUN
ejpam-2623	618	4	)	)	PUNCT
ejpam-2623	618	5	=	=	PUNCT
ejpam-2623	618	6	αβy	αβy	PROPN
ejpam-2623	618	7	y(α2	y(α2	PROPN
ejpam-2623	618	8	+	+	CCONJ
ejpam-2623	618	9	β2)−	β2)−	ADJ
ejpam-2623	618	10	αβx	αβx	NOUN
ejpam-2623	618	11	.	.	PUNCT
ejpam-2623	619	1	ε	ε	PROPN
ejpam-2623	620	1	=	=	PRON
ejpam-2623	620	2	χ	χ	X
ejpam-2623	620	3	(	(	PUNCT
ejpam-2623	620	4	v(αv	v(αv	NUM
ejpam-2623	620	5	−	−	NOUN
ejpam-2623	620	6	β	β	NOUN
ejpam-2623	620	7	)	)	PUNCT
ejpam-2623	620	8	α−	α−	ADP
ejpam-2623	620	9	βv	βv	PUNCT
ejpam-2623	620	10	)	)	PUNCT
ejpam-2623	620	11	=	=	PUNCT
ejpam-2623	621	1	χ	χ	PRON
ejpam-2623	621	2			PROPN
ejpam-2623	621	3	αβy	αβy	ADJ
ejpam-2623	621	4	y(α2+β2)−αβx	y(α2+β2)−αβx	NUM
ejpam-2623	621	5	(	(	PUNCT
ejpam-2623	621	6	α2βy	α2βy	NUM
ejpam-2623	621	7	y(α2+β2)−αβx	y(α2+β2)−αβx	NUM
ejpam-2623	621	8	−	−	NUM
ejpam-2623	621	9	β	β	NOUN
ejpam-2623	621	10	)	)	PUNCT
ejpam-2623	621	11	α−	α−	ADP
ejpam-2623	621	12	αβ2y	αβ2y	NOUN
ejpam-2623	621	13	y(α2+β2)−αβx	y(α2+β2)−αβx	NUM
ejpam-2623	621	14			PROPN
ejpam-2623	621	15	=	=	SYM
ejpam-2623	621	16	χ	χ	X
ejpam-2623	621	17	(	(	PUNCT
ejpam-2623	621	18	β3y(αx−	β3y(αx−	PUNCT
ejpam-2623	621	19	βy	βy	ADJ
ejpam-2623	621	20	)	)	PUNCT
ejpam-2623	621	21	α(αy	α(αy	NOUN
ejpam-2623	621	22	−	−	NOUN
ejpam-2623	621	23	βx	βx	NOUN
ejpam-2623	621	24	)	)	PUNCT
ejpam-2623	621	25	(	(	PUNCT
ejpam-2623	621	26	y(α2	y(α2	X
ejpam-2623	621	27	+	+	CCONJ
ejpam-2623	621	28	β2)−	β2)−	ADJ
ejpam-2623	621	29	αβx	αβx	NOUN
ejpam-2623	621	30	)	)	PUNCT
ejpam-2623	621	31	)	)	PUNCT
ejpam-2623	622	1	=	=	SYM
ejpam-2623	623	1	χ	χ	X
ejpam-2623	623	2	(	(	PUNCT
ejpam-2623	623	3	β3xy2	β3xy2	PROPN
ejpam-2623	623	4	α	α	PROPN
ejpam-2623	623	5	(	(	PUNCT
ejpam-2623	623	6	y(α2	y(α2	X
ejpam-2623	623	7	+	+	CCONJ
ejpam-2623	623	8	β2)−	β2)−	ADJ
ejpam-2623	623	9	αβx	αβx	NOUN
ejpam-2623	623	10	)	)	PUNCT
ejpam-2623	623	11	)	)	PUNCT
ejpam-2623	624	1	=	=	SYM
ejpam-2623	624	2	χ	χ	X
ejpam-2623	624	3	(	(	PUNCT
ejpam-2623	624	4	αβx	αβx	INTJ
ejpam-2623	624	5	(	(	PUNCT
ejpam-2623	624	6	y(α2	y(α2	PROPN
ejpam-2623	624	7	+	+	CCONJ
ejpam-2623	624	8	β2)−	β2)−	ADJ
ejpam-2623	624	9	αβx	αβx	NOUN
ejpam-2623	624	10	)	)	PUNCT
ejpam-2623	624	11	)	)	PUNCT
ejpam-2623	625	1	=	=	PUNCT
ejpam-2623	625	2	−1	−1	NOUN
ejpam-2623	625	3	since	since	SCONJ
ejpam-2623	625	4	χ	χ	PROPN
ejpam-2623	625	5	(	(	PUNCT
ejpam-2623	625	6	uαβxy(α2	uαβxy(α2	X
ejpam-2623	625	7	+	+	CCONJ
ejpam-2623	625	8	β2	β2	NOUN
ejpam-2623	625	9	−	−	PROPN
ejpam-2623	626	1	αβ	αβ	INTJ
ejpam-2623	626	2	y	y	NOUN
ejpam-2623	626	3	x	x	PROPN
ejpam-2623	626	4	)	)	PUNCT
ejpam-2623	626	5	)	)	PUNCT
ejpam-2623	627	1	=	=	PUNCT
ejpam-2623	627	2	1	1	X
ejpam-2623	627	3	.	.	PUNCT
ejpam-2623	627	4	ε	ε	PROPN
ejpam-2623	627	5	=	=	PUNCT
ejpam-2623	627	6	−1	−1	NOUN
ejpam-2623	627	7	implies	imply	VERB
ejpam-2623	627	8	that	that	SCONJ
ejpam-2623	627	9	t	t	NOUN
ejpam-2623	627	10	=	=	SYM
ejpam-2623	627	11	v(α2	v(α2	PROPN
ejpam-2623	627	12	+	+	CCONJ
ejpam-2623	627	13	β2)−	β2)−	ADJ
ejpam-2623	627	14	αβ	αβ	NUM
ejpam-2623	627	15	αβv	αβv	NUM
ejpam-2623	627	16	=	=	SYM
ejpam-2623	627	17	αβy(α2+β2	αβy(α2+β2	X
ejpam-2623	627	18	)	)	PUNCT
ejpam-2623	627	19	y(α2+β2)−αβx	y(α2+β2)−αβx	NUM
ejpam-2623	627	20	−	−	PROPN
ejpam-2623	628	1	αβ	αβ	INTJ
ejpam-2623	628	2	α2β2y	α2β2y	NUM
ejpam-2623	628	3	y(α2+β2)−αβx	y(α2+β2)−αβx	NOUN
ejpam-2623	628	4	=	=	PUNCT
ejpam-2623	629	1	x	x	PUNCT
ejpam-2623	629	2	y	y	NOUN
ejpam-2623	629	3	=	=	PUNCT
ejpam-2623	629	4	t.	t.	PROPN
ejpam-2623	630	1	so	so	ADV
ejpam-2623	630	2	x	x	SYM
ejpam-2623	631	1	=	=	PUNCT
ejpam-2623	631	2	√	√	PART
ejpam-2623	631	3	t(αt−	t(αt−	NUM
ejpam-2623	631	4	β	β	NOUN
ejpam-2623	631	5	)	)	PUNCT
ejpam-2623	631	6	α−	α−	ADP
ejpam-2623	631	7	βt	βt	NOUN
ejpam-2623	631	8	=	=	SYM
ejpam-2623	631	9	√	√	PROPN
ejpam-2623	631	10	t(αt−	t(αt−	NUM
ejpam-2623	631	11	β	β	NOUN
ejpam-2623	631	12	)	)	PUNCT
ejpam-2623	631	13	α−	α−	ADP
ejpam-2623	631	14	βt	βt	NOUN
ejpam-2623	632	1	=	=	PUNCT
ejpam-2623	632	2	√	√	ADJ
ejpam-2623	632	3	z	z	NOUN
ejpam-2623	632	4	=	=	PUNCT
ejpam-2623	633	1	x	x	PROPN
ejpam-2623	633	2	and	and	CCONJ
ejpam-2623	633	3	y	y	PROPN
ejpam-2623	633	4	=	=	PUNCT
ejpam-2623	634	1	x	x	PUNCT
ejpam-2623	634	2	t	t	NOUN
ejpam-2623	634	3	=	=	PUNCT
ejpam-2623	634	4	x	x	SYM
ejpam-2623	634	5	t	t	NOUN
ejpam-2623	634	6	=	=	PUNCT
ejpam-2623	634	7	y.	y.	PROPN
ejpam-2623	634	8	n.	n.	PROPN
ejpam-2623	634	9	diarra	diarra	PROPN
ejpam-2623	634	10	,	,	PUNCT
ejpam-2623	634	11	d.	d.	PROPN
ejpam-2623	634	12	sow	sow	PROPN
ejpam-2623	634	13	,	,	PUNCT
ejpam-2623	634	14	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	634	15	.	.	PUNCT
ejpam-2623	634	16	khlil	khlil	PROPN
ejpam-2623	634	17	/	/	SYM
ejpam-2623	634	18	eur	eur	PROPN
ejpam-2623	634	19	.	.	PUNCT
ejpam-2623	635	1	j.	j.	PROPN
ejpam-2623	635	2	pure	pure	PROPN
ejpam-2623	635	3	appl	appl	PROPN
ejpam-2623	635	4	.	.	PROPN
ejpam-2623	635	5	math	math	PROPN
ejpam-2623	635	6	,	,	PUNCT
ejpam-2623	635	7	10	10	NUM
ejpam-2623	635	8	(	(	PUNCT
ejpam-2623	635	9	2	2	NUM
ejpam-2623	635	10	)	)	PUNCT
ejpam-2623	635	11	(	(	PUNCT
ejpam-2623	635	12	2017	2017	NUM
ejpam-2623	635	13	)	)	PUNCT
ejpam-2623	635	14	,	,	PUNCT
ejpam-2623	635	15	363	363	NUM
ejpam-2623	635	16	-	-	SYM
ejpam-2623	635	17	391	391	NUM
ejpam-2623	635	18	379	379	NUM
ejpam-2623	635	19	hence	hence	ADV
ejpam-2623	635	20	we	we	PRON
ejpam-2623	635	21	conclude	conclude	VERB
ejpam-2623	635	22	that	that	SCONJ
ejpam-2623	635	23	(	(	PUNCT
ejpam-2623	635	24	x	x	X
ejpam-2623	635	25	,	,	PUNCT
ejpam-2623	635	26	y	y	NOUN
ejpam-2623	635	27	)	)	PUNCT
ejpam-2623	635	28	∈	∈	PROPN
ejpam-2623	635	29	im(φα	im(φα	PROPN
ejpam-2623	635	30	,	,	PUNCT
ejpam-2623	635	31	β	β	NOUN
ejpam-2623	635	32	)	)	PUNCT
ejpam-2623	635	33	.	.	PUNCT
ejpam-2623	636	1	efficiency	efficiency	NOUN
ejpam-2623	636	2	of	of	ADP
ejpam-2623	636	3	φα	φα	PROPN
ejpam-2623	636	4	,	,	PUNCT
ejpam-2623	636	5	β	β	X
ejpam-2623	636	6	and	and	CCONJ
ejpam-2623	636	7	φ−1α	φ−1α	NOUN
ejpam-2623	636	8	,	,	PUNCT
ejpam-2623	636	9	β	β	NOUN
ejpam-2623	636	10	:	:	PUNCT
ejpam-2623	636	11	for	for	ADP
ejpam-2623	636	12	any	any	DET
ejpam-2623	636	13	r	r	NOUN
ejpam-2623	636	14	∈	∈	NOUN
ejpam-2623	636	15	r	r	NOUN
ejpam-2623	636	16	,	,	PUNCT
ejpam-2623	636	17	computing	computing	NOUN
ejpam-2623	636	18	φα	φα	ADP
ejpam-2623	636	19	,	,	PUNCT
ejpam-2623	636	20	β(r	β(r	NOUN
ejpam-2623	636	21	)	)	PUNCT
ejpam-2623	636	22	takes	take	VERB
ejpam-2623	636	23	2	2	NUM
ejpam-2623	636	24	inversions	inversion	NOUN
ejpam-2623	636	25	,	,	PUNCT
ejpam-2623	636	26	1	1	NUM
ejpam-2623	636	27	square	square	ADJ
ejpam-2623	636	28	-	-	PUNCT
ejpam-2623	636	29	root	root	NOUN
ejpam-2623	636	30	computation	computation	NOUN
ejpam-2623	636	31	,	,	PUNCT
ejpam-2623	636	32	one	one	NUM
ejpam-2623	636	33	computation	computation	NOUN
ejpam-2623	636	34	of	of	ADP
ejpam-2623	636	35	the	the	DET
ejpam-2623	636	36	quadratic	quadratic	ADJ
ejpam-2623	636	37	character	character	NOUN
ejpam-2623	636	38	χ	χ	NOUN
ejpam-2623	636	39	and	and	CCONJ
ejpam-2623	636	40	some	some	DET
ejpam-2623	636	41	multiplications	multiplication	NOUN
ejpam-2623	636	42	.	.	PUNCT
ejpam-2623	637	1	one	one	PRON
ejpam-2623	637	2	can	can	AUX
ejpam-2623	637	3	use	use	VERB
ejpam-2623	637	4	euclid	euclid	PROPN
ejpam-2623	637	5	’s	’s	PART
ejpam-2623	637	6	algorithm	algorithm	NOUN
ejpam-2623	637	7	to	to	PART
ejpam-2623	637	8	compute	compute	VERB
ejpam-2623	637	9	the	the	DET
ejpam-2623	637	10	inverses	inverse	NOUN
ejpam-2623	637	11	;	;	PUNCT
ejpam-2623	637	12	note	note	VERB
ejpam-2623	637	13	that	that	SCONJ
ejpam-2623	637	14	the	the	DET
ejpam-2623	637	15	computation	computation	NOUN
ejpam-2623	637	16	of	of	ADP
ejpam-2623	637	17	χ	χ	NOUN
ejpam-2623	637	18	can	can	AUX
ejpam-2623	637	19	be	be	AUX
ejpam-2623	637	20	replaced	replace	VERB
ejpam-2623	637	21	by	by	ADP
ejpam-2623	637	22	an	an	DET
ejpam-2623	637	23	exponentiation	exponentiation	NOUN
ejpam-2623	637	24	(	(	PUNCT
ejpam-2623	637	25	with	with	ADP
ejpam-2623	637	26	exponent	exponent	NOUN
ejpam-2623	637	27	(	(	PUNCT
ejpam-2623	637	28	q	q	PROPN
ejpam-2623	637	29	−	−	PROPN
ejpam-2623	637	30	1)/2	1)/2	NUM
ejpam-2623	637	31	)	)	PUNCT
ejpam-2623	637	32	;	;	PUNCT
ejpam-2623	637	33	and	and	CCONJ
ejpam-2623	637	34	if	if	SCONJ
ejpam-2623	637	35	q	q	PRON
ejpam-2623	637	36	≡	≡	PROPN
ejpam-2623	637	37	3	3	NUM
ejpam-2623	637	38	mod	mod	NOUN
ejpam-2623	637	39	4	4	NUM
ejpam-2623	637	40	,	,	PUNCT
ejpam-2623	637	41	the	the	DET
ejpam-2623	637	42	square	square	ADJ
ejpam-2623	637	43	-	-	PUNCT
ejpam-2623	637	44	root	root	NOUN
ejpam-2623	637	45	computation	computation	NOUN
ejpam-2623	637	46	is	be	AUX
ejpam-2623	637	47	also	also	ADV
ejpam-2623	637	48	replaced	replace	VERB
ejpam-2623	637	49	by	by	ADP
ejpam-2623	637	50	an	an	DET
ejpam-2623	637	51	exponentiation	exponentiation	NOUN
ejpam-2623	637	52	.	.	PUNCT
ejpam-2623	638	1	inverting	invert	VERB
ejpam-2623	638	2	φα	φα	PROPN
ejpam-2623	638	3	,	,	PUNCT
ejpam-2623	638	4	β	β	PROPN
ejpam-2623	638	5	takes	take	VERB
ejpam-2623	638	6	one	one	NUM
ejpam-2623	638	7	essential	essential	ADJ
ejpam-2623	638	8	exponentiation	exponentiation	NOUN
ejpam-2623	638	9	,	,	PUNCT
ejpam-2623	638	10	the	the	DET
ejpam-2623	638	11	square	square	ADJ
ejpam-2623	638	12	-	-	PUNCT
ejpam-2623	638	13	root	root	NOUN
ejpam-2623	638	14	computation	computation	NOUN
ejpam-2623	638	15	to	to	PART
ejpam-2623	638	16	obtain	obtain	VERB
ejpam-2623	638	17	r	r	NOUN
ejpam-2623	638	18	,	,	PUNCT
ejpam-2623	638	19	and	and	CCONJ
ejpam-2623	638	20	one	one	NUM
ejpam-2623	638	21	inversion	inversion	NOUN
ejpam-2623	638	22	.	.	PUNCT
ejpam-2623	639	1	extending	extend	VERB
ejpam-2623	639	2	φα	φα	PROPN
ejpam-2623	639	3	,	,	PUNCT
ejpam-2623	639	4	β	β	X
ejpam-2623	639	5	:	:	PUNCT
ejpam-2623	639	6	we	we	PRON
ejpam-2623	639	7	can	can	AUX
ejpam-2623	639	8	extend	extend	VERB
ejpam-2623	639	9	the	the	DET
ejpam-2623	639	10	definition	definition	NOUN
ejpam-2623	639	11	of	of	ADP
ejpam-2623	639	12	φα	φα	PROPN
ejpam-2623	639	13	,	,	PUNCT
ejpam-2623	639	14	β	β	PROPN
ejpam-2623	639	15	on	on	ADP
ejpam-2623	639	16	fq	fq	PROPN
ejpam-2623	639	17	as	as	SCONJ
ejpam-2623	639	18	follows	follow	VERB
ejpam-2623	639	19	:	:	PUNCT
ejpam-2623	639	20	(	(	PUNCT
ejpam-2623	639	21	i	i	NOUN
ejpam-2623	639	22	)	)	PUNCT
ejpam-2623	639	23	if	if	SCONJ
ejpam-2623	639	24	q	q	PRON
ejpam-2623	639	25	≡	≡	PROPN
ejpam-2623	639	26	1	1	NUM
ejpam-2623	639	27	mod	mod	NOUN
ejpam-2623	639	28	4	4	NUM
ejpam-2623	639	29	:	:	PUNCT
ejpam-2623	639	30	we	we	PRON
ejpam-2623	639	31	have	have	VERB
ejpam-2623	639	32	r	r	NOUN
ejpam-2623	639	33	=	=	SYM
ejpam-2623	639	34	f∗q	f∗q	NOUN
ejpam-2623	639	35	.	.	PUNCT
ejpam-2623	640	1	define	define	VERB
ejpam-2623	640	2	the	the	DET
ejpam-2623	640	3	function	function	NOUN
ejpam-2623	640	4	φα	φα	PROPN
ejpam-2623	640	5	,	,	PUNCT
ejpam-2623	640	6	β	β	X
ejpam-2623	640	7	by	by	ADP
ejpam-2623	640	8	φα	φα	PROPN
ejpam-2623	640	9	,	,	PUNCT
ejpam-2623	640	10	β(r	β(r	PROPN
ejpam-2623	640	11	)	)	PUNCT
ejpam-2623	640	12	=	=	SYM
ejpam-2623	640	13	φα	φα	PROPN
ejpam-2623	640	14	,	,	PUNCT
ejpam-2623	640	15	β(r	β(r	PROPN
ejpam-2623	640	16	)	)	PUNCT
ejpam-2623	640	17	if	if	SCONJ
ejpam-2623	640	18	r	r	NOUN
ejpam-2623	640	19	∈	∈	PROPN
ejpam-2623	640	20	r	r	NOUN
ejpam-2623	640	21	,	,	PUNCT
ejpam-2623	640	22	and	and	CCONJ
ejpam-2623	640	23	φα	φα	ADV
ejpam-2623	640	24	,	,	PUNCT
ejpam-2623	640	25	β(0	β(0	PROPN
ejpam-2623	640	26	)	)	PUNCT
ejpam-2623	640	27	=	=	SYM
ejpam-2623	640	28	(	(	PUNCT
ejpam-2623	640	29	0	0	NUM
ejpam-2623	640	30	,	,	PUNCT
ejpam-2623	640	31	0	0	NUM
ejpam-2623	640	32	)	)	PUNCT
ejpam-2623	640	33	.	.	PUNCT
ejpam-2623	641	1	(	(	PUNCT
ejpam-2623	641	2	ii	ii	NOUN
ejpam-2623	641	3	)	)	PUNCT
ejpam-2623	641	4	if	if	SCONJ
ejpam-2623	641	5	q	q	PRON
ejpam-2623	641	6	≡	≡	PROPN
ejpam-2623	641	7	3	3	NUM
ejpam-2623	641	8	mod	mod	NOUN
ejpam-2623	641	9	4	4	NUM
ejpam-2623	641	10	:	:	PUNCT
ejpam-2623	641	11	we	we	PRON
ejpam-2623	641	12	choose	choose	VERB
ejpam-2623	641	13	u	u	NOUN
ejpam-2623	641	14	=	=	PROPN
ejpam-2623	641	15	−1	−1	NOUN
ejpam-2623	641	16	;	;	PUNCT
ejpam-2623	641	17	then	then	ADV
ejpam-2623	641	18	we	we	PRON
ejpam-2623	641	19	have	have	VERB
ejpam-2623	641	20	r	r	NOUN
ejpam-2623	641	21	=	=	SYM
ejpam-2623	641	22	f∗q	f∗q	X
ejpam-2623	641	23	\	\	NOUN
ejpam-2623	641	24	{	{	PUNCT
ejpam-2623	641	25	±α	±α	PROPN
ejpam-2623	641	26	β	β	X
ejpam-2623	641	27	}	}	PUNCT
ejpam-2623	641	28	.	.	PUNCT
ejpam-2623	642	1	if	if	SCONJ
ejpam-2623	642	2	in	in	ADP
ejpam-2623	642	3	addition	addition	NOUN
ejpam-2623	642	4	α2	α2	ADJ
ejpam-2623	642	5	+	+	CCONJ
ejpam-2623	642	6	β2	β2	NOUN
ejpam-2623	642	7	is	be	AUX
ejpam-2623	642	8	not	not	PART
ejpam-2623	642	9	a	a	DET
ejpam-2623	642	10	square	square	NOUN
ejpam-2623	642	11	,	,	PUNCT
ejpam-2623	642	12	define	define	VERB
ejpam-2623	642	13	the	the	DET
ejpam-2623	642	14	function	function	NOUN
ejpam-2623	642	15	φα	φα	PROPN
ejpam-2623	642	16	,	,	PUNCT
ejpam-2623	642	17	β	β	X
ejpam-2623	642	18	by	by	ADP
ejpam-2623	642	19	:	:	PUNCT
ejpam-2623	642	20	•	•	NUM
ejpam-2623	642	21	φα	φα	INTJ
ejpam-2623	642	22	,	,	PUNCT
ejpam-2623	642	23	β(r	β(r	NOUN
ejpam-2623	642	24	)	)	PUNCT
ejpam-2623	642	25	=	=	SYM
ejpam-2623	642	26	φα	φα	PROPN
ejpam-2623	642	27	,	,	PUNCT
ejpam-2623	642	28	β(r	β(r	PROPN
ejpam-2623	642	29	)	)	PUNCT
ejpam-2623	642	30	if	if	SCONJ
ejpam-2623	642	31	r	r	NOUN
ejpam-2623	642	32	∈	∈	PROPN
ejpam-2623	642	33	r	r	NOUN
ejpam-2623	642	34	;	;	PUNCT
ejpam-2623	642	35	•	•	NUM
ejpam-2623	642	36	φα	φα	INTJ
ejpam-2623	642	37	,	,	PUNCT
ejpam-2623	642	38	β(r	β(r	NOUN
ejpam-2623	642	39	)	)	PUNCT
ejpam-2623	642	40	=	=	SYM
ejpam-2623	642	41	(	(	PUNCT
ejpam-2623	642	42	β	β	X
ejpam-2623	642	43	√	√	NUM
ejpam-2623	642	44	−(α2	−(α2	VERB
ejpam-2623	642	45	+	+	CCONJ
ejpam-2623	642	46	β2	β2	ADJ
ejpam-2623	642	47	)	)	PUNCT
ejpam-2623	642	48	α2	α2	PROPN
ejpam-2623	642	49	,	,	PUNCT
ejpam-2623	642	50	β2	β2	NOUN
ejpam-2623	642	51	√	√	PROPN
ejpam-2623	642	52	−(α2	−(α2	PRON
ejpam-2623	643	1	+	+	CCONJ
ejpam-2623	643	2	β2	β2	ADJ
ejpam-2623	643	3	)	)	PUNCT
ejpam-2623	643	4	α(α2	α(α2	NOUN
ejpam-2623	644	1	+	+	CCONJ
ejpam-2623	644	2	β2	β2	NOUN
ejpam-2623	644	3	)	)	PUNCT
ejpam-2623	644	4	)	)	PUNCT
ejpam-2623	645	1	if	if	SCONJ
ejpam-2623	645	2	r	r	NOUN
ejpam-2623	645	3	=	=	SYM
ejpam-2623	645	4	±α	±α	NOUN
ejpam-2623	645	5	β	β	NOUN
ejpam-2623	645	6	;	;	PUNCT
ejpam-2623	645	7	•	•	ADP
ejpam-2623	645	8	φα	φα	INTJ
ejpam-2623	645	9	,	,	PUNCT
ejpam-2623	645	10	β(0	β(0	PROPN
ejpam-2623	645	11	)	)	PUNCT
ejpam-2623	645	12	=	=	SYM
ejpam-2623	645	13	(	(	PUNCT
ejpam-2623	645	14	0	0	NUM
ejpam-2623	645	15	,	,	PUNCT
ejpam-2623	645	16	0	0	NUM
ejpam-2623	645	17	)	)	PUNCT
ejpam-2623	645	18	.	.	PUNCT
ejpam-2623	646	1	we	we	PRON
ejpam-2623	646	2	call	call	VERB
ejpam-2623	646	3	φα	φα	PROPN
ejpam-2623	646	4	,	,	PUNCT
ejpam-2623	646	5	β	β	PROPN
ejpam-2623	646	6	the	the	DET
ejpam-2623	646	7	aiee	aiee	PROPN
ejpam-2623	646	8	-	-	PUNCT
ejpam-2623	646	9	for	for	ADP
ejpam-2623	646	10	-	-	PUNCT
ejpam-2623	646	11	huff	huff	NOUN
ejpam-2623	646	12	.	.	PUNCT
ejpam-2623	647	1	3.3	3.3	NUM
ejpam-2623	647	2	.	.	PUNCT
ejpam-2623	648	1	an	an	DET
ejpam-2623	648	2	aiie	aiie	NOUN
ejpam-2623	648	3	for	for	ADP
ejpam-2623	648	4	the	the	DET
ejpam-2623	648	5	classical	classical	ADJ
ejpam-2623	648	6	edwards	edwards	PROPN
ejpam-2623	648	7	model	model	NOUN
ejpam-2623	648	8	x2	x2	PROPN
ejpam-2623	649	1	+	+	CCONJ
ejpam-2623	649	2	y2	y2	NOUN
ejpam-2623	649	3	=	=	SYM
ejpam-2623	649	4	1	1	NUM
ejpam-2623	649	5	+	+	CCONJ
ejpam-2623	649	6	dx2y2	dx2y2	VERB
ejpam-2623	649	7	with	with	ADP
ejpam-2623	649	8	elligator-2	elligator-2	PROPN
ejpam-2623	649	9	’s	’s	PART
ejpam-2623	649	10	method	method	NOUN
ejpam-2623	649	11	[	[	X
ejpam-2623	649	12	4	4	NUM
ejpam-2623	649	13	]	]	PUNCT
ejpam-2623	649	14	,	,	PUNCT
ejpam-2623	649	15	to	to	PART
ejpam-2623	649	16	encode	encode	VERB
ejpam-2623	649	17	on	on	ADP
ejpam-2623	649	18	edwards	edwards	PROPN
ejpam-2623	649	19	curves	curve	NOUN
ejpam-2623	649	20	,	,	PUNCT
ejpam-2623	649	21	it	it	PRON
ejpam-2623	649	22	is	be	AUX
ejpam-2623	649	23	necessary	necessary	ADJ
ejpam-2623	649	24	to	to	PART
ejpam-2623	649	25	use	use	VERB
ejpam-2623	649	26	a	a	DET
ejpam-2623	649	27	birational	birational	ADJ
ejpam-2623	649	28	equivalence	equivalence	NOUN
ejpam-2623	649	29	.	.	PUNCT
ejpam-2623	650	1	in	in	ADP
ejpam-2623	650	2	this	this	DET
ejpam-2623	650	3	section	section	NOUN
ejpam-2623	650	4	,	,	PUNCT
ejpam-2623	650	5	we	we	PRON
ejpam-2623	650	6	propose	propose	VERB
ejpam-2623	650	7	an	an	DET
ejpam-2623	650	8	algorithm	algorithm	NOUN
ejpam-2623	650	9	which	which	PRON
ejpam-2623	650	10	encodes	encode	VERB
ejpam-2623	650	11	directly	directly	ADV
ejpam-2623	650	12	an	an	DET
ejpam-2623	650	13	element	element	NOUN
ejpam-2623	650	14	of	of	ADP
ejpam-2623	650	15	fq	fq	PROPN
ejpam-2623	650	16	to	to	ADP
ejpam-2623	650	17	a	a	DET
ejpam-2623	650	18	point	point	NOUN
ejpam-2623	650	19	of	of	ADP
ejpam-2623	650	20	an	an	DET
ejpam-2623	650	21	edwards	edwards	PROPN
ejpam-2623	650	22	curves	curves	PROPN
ejpam-2623	651	1	ed	ed	NOUN
ejpam-2623	651	2	:	:	PUNCT
ejpam-2623	652	1	x2	x2	PROPN
ejpam-2623	653	1	+	+	PUNCT
ejpam-2623	653	2	y2	y2	NOUN
ejpam-2623	653	3	=	=	SYM
ejpam-2623	653	4	1	1	NUM
ejpam-2623	653	5	+	+	CCONJ
ejpam-2623	653	6	dx2y2	dx2y2	PROPN
ejpam-2623	653	7	,	,	PUNCT
ejpam-2623	653	8	where	where	SCONJ
ejpam-2623	653	9	d	d	NOUN
ejpam-2623	653	10	is	be	AUX
ejpam-2623	653	11	not	not	PART
ejpam-2623	653	12	a	a	DET
ejpam-2623	653	13	square	square	NOUN
ejpam-2623	653	14	,	,	PUNCT
ejpam-2623	653	15	and	and	CCONJ
ejpam-2623	653	16	without	without	ADP
ejpam-2623	653	17	any	any	DET
ejpam-2623	653	18	birational	birational	ADJ
ejpam-2623	653	19	equivalence	equivalence	NOUN
ejpam-2623	653	20	.	.	PUNCT
ejpam-2623	654	1	theorem	theorem	NOUN
ejpam-2623	654	2	4	4	NUM
ejpam-2623	654	3	.	.	PUNCT
ejpam-2623	655	1	let	let	VERB
ejpam-2623	655	2	q	q	PART
ejpam-2623	655	3	be	be	AUX
ejpam-2623	655	4	an	an	DET
ejpam-2623	655	5	odd	odd	ADJ
ejpam-2623	655	6	prime	prime	ADJ
ejpam-2623	655	7	power	power	NOUN
ejpam-2623	655	8	,	,	PUNCT
ejpam-2623	655	9	and	and	CCONJ
ejpam-2623	655	10	d	d	PROPN
ejpam-2623	655	11	∈	∈	NOUN
ejpam-2623	655	12	f∗q	f∗q	NOUN
ejpam-2623	655	13	such	such	ADJ
ejpam-2623	655	14	that	that	DET
ejpam-2623	655	15	d	d	PROPN
ejpam-2623	655	16	6=	6=	PROPN
ejpam-2623	655	17	±1,−2	±1,−2	PROPN
ejpam-2623	656	1	and	and	CCONJ
ejpam-2623	656	2	d	d	PROPN
ejpam-2623	656	3	is	be	AUX
ejpam-2623	656	4	not	not	PART
ejpam-2623	656	5	a	a	DET
ejpam-2623	656	6	square	square	NOUN
ejpam-2623	656	7	.	.	PUNCT
ejpam-2623	657	1	let	let	VERB
ejpam-2623	657	2	u	u	PRON
ejpam-2623	657	3	be	be	AUX
ejpam-2623	657	4	a	a	DET
ejpam-2623	657	5	nonzero	nonzero	ADJ
ejpam-2623	657	6	non	non	ADJ
ejpam-2623	657	7	-	-	ADJ
ejpam-2623	657	8	square	square	ADJ
ejpam-2623	657	9	and	and	CCONJ
ejpam-2623	657	10	let	let	VERB
ejpam-2623	657	11	r	r	PRON
ejpam-2623	657	12	be	be	AUX
ejpam-2623	657	13	a	a	DET
ejpam-2623	657	14	subset	subset	NOUN
ejpam-2623	657	15	of	of	ADP
ejpam-2623	657	16	fq	fq	PROPN
ejpam-2623	657	17	defined	define	VERB
ejpam-2623	657	18	by	by	ADP
ejpam-2623	657	19	r	r	NOUN
ejpam-2623	657	20	=	=	PUNCT
ejpam-2623	657	21	{	{	PUNCT
ejpam-2623	657	22	r	r	NOUN
ejpam-2623	657	23	∈	∈	PROPN
ejpam-2623	657	24	f∗q	f∗q	NOUN
ejpam-2623	657	25	:	:	PUNCT
ejpam-2623	657	26	ur2	ur2	X
ejpam-2623	658	1	+	+	CCONJ
ejpam-2623	658	2	1	1	NUM
ejpam-2623	658	3	6=	6=	NUM
ejpam-2623	658	4	0	0	NUM
ejpam-2623	658	5	,	,	PUNCT
ejpam-2623	658	6	ur2(1−	ur2(1−	ADJ
ejpam-2623	658	7	d)−	d)−	PROPN
ejpam-2623	658	8	(	(	PUNCT
ejpam-2623	658	9	1	1	NUM
ejpam-2623	658	10	+	+	NUM
ejpam-2623	658	11	3d	3d	NUM
ejpam-2623	658	12	)	)	PUNCT
ejpam-2623	658	13	6=	6=	ADP
ejpam-2623	658	14	0	0	NUM
ejpam-2623	658	15	,	,	PUNCT
ejpam-2623	658	16	ur2(1	ur2(1	NOUN
ejpam-2623	659	1	+	+	CCONJ
ejpam-2623	659	2	3d)−	3d)−	NUM
ejpam-2623	659	3	(	(	PUNCT
ejpam-2623	659	4	1−	1−	NUM
ejpam-2623	659	5	d	d	NOUN
ejpam-2623	659	6	)	)	PUNCT
ejpam-2623	659	7	6=	6=	ADP
ejpam-2623	659	8	0	0	NUM
ejpam-2623	659	9	}	}	PUNCT
ejpam-2623	659	10	.	.	PUNCT
ejpam-2623	660	1	for	for	ADP
ejpam-2623	660	2	any	any	DET
ejpam-2623	660	3	non	non	ADJ
ejpam-2623	660	4	-	-	ADJ
ejpam-2623	660	5	zero	zero	NUM
ejpam-2623	660	6	r	r	NOUN
ejpam-2623	660	7	∈	∈	NOUN
ejpam-2623	660	8	r	r	NOUN
ejpam-2623	660	9	,	,	PUNCT
ejpam-2623	660	10	the	the	DET
ejpam-2623	660	11	following	follow	VERB
ejpam-2623	660	12	elements	element	NOUN
ejpam-2623	660	13	are	be	AUX
ejpam-2623	660	14	well	well	ADV
ejpam-2623	660	15	-	-	PUNCT
ejpam-2623	660	16	defined	define	VERB
ejpam-2623	660	17	:	:	PUNCT
ejpam-2623	660	18	v	v	X
ejpam-2623	660	19	=	=	PUNCT
ejpam-2623	660	20	(	(	PUNCT
ejpam-2623	660	21	d−	d−	PROPN
ejpam-2623	660	22	1)ur2	1)ur2	PROPN
ejpam-2623	660	23	−	−	PROPN
ejpam-2623	661	1	3−	3−	NUM
ejpam-2623	661	2	d	d	PROPN
ejpam-2623	661	3	ur2(d−	ur2(d−	PROPN
ejpam-2623	661	4	1	1	NUM
ejpam-2623	661	5	)	)	PUNCT
ejpam-2623	661	6	+	+	CCONJ
ejpam-2623	661	7	1	1	NUM
ejpam-2623	662	1	+	+	NUM
ejpam-2623	662	2	3d	3d	NUM
ejpam-2623	662	3	;	;	PUNCT
ejpam-2623	662	4	ε	ε	PROPN
ejpam-2623	662	5	=	=	SYM
ejpam-2623	662	6	χ[(1−	χ[(1−	NOUN
ejpam-2623	662	7	v2)(1−	v2)(1−	ADJ
ejpam-2623	662	8	dv2	dv2	NOUN
ejpam-2623	662	9	)	)	PUNCT
ejpam-2623	662	10	]	]	PUNCT
ejpam-2623	662	11	;	;	PUNCT
ejpam-2623	662	12	x	x	SYM
ejpam-2623	662	13	=	=	PUNCT
ejpam-2623	662	14	ε(v	ε(v	PROPN
ejpam-2623	662	15	+	+	CCONJ
ejpam-2623	662	16	1)(dv	1)(dv	NUM
ejpam-2623	662	17	+	+	NUM
ejpam-2623	662	18	1	1	NUM
ejpam-2623	662	19	)	)	PUNCT
ejpam-2623	663	1	+	+	NUM
ejpam-2623	663	2	dv2	dv2	NOUN
ejpam-2623	663	3	−	−	NOUN
ejpam-2623	663	4	1	1	NUM
ejpam-2623	663	5	2d(v	2d(v	NUM
ejpam-2623	663	6	+	+	CCONJ
ejpam-2623	663	7	1	1	NUM
ejpam-2623	663	8	)	)	PUNCT
ejpam-2623	663	9	+	+	CCONJ
ejpam-2623	663	10	(	(	PUNCT
ejpam-2623	663	11	1−	1−	NUM
ejpam-2623	663	12	d	d	NOUN
ejpam-2623	663	13	)	)	PUNCT
ejpam-2623	663	14	;	;	PUNCT
ejpam-2623	663	15	y	y	PROPN
ejpam-2623	663	16	=	=	PUNCT
ejpam-2623	663	17	−ε	−ε	PROPN
ejpam-2623	663	18	√	√	NOUN
ejpam-2623	663	19	1−	1−	NUM
ejpam-2623	663	20	x2	x2	NOUN
ejpam-2623	663	21	1−	1−	NUM
ejpam-2623	663	22	dx2	dx2	PROPN
ejpam-2623	663	23	.	.	PUNCT
ejpam-2623	664	1	furthermore	furthermore	ADV
ejpam-2623	664	2	,	,	PUNCT
ejpam-2623	664	3	ε	ε	PROPN
ejpam-2623	664	4	6=	6=	NUM
ejpam-2623	664	5	0	0	NUM
ejpam-2623	664	6	and	and	CCONJ
ejpam-2623	664	7	x2	x2	PROPN
ejpam-2623	665	1	+	+	CCONJ
ejpam-2623	665	2	y2	y2	NOUN
ejpam-2623	665	3	=	=	SYM
ejpam-2623	665	4	1	1	NUM
ejpam-2623	665	5	+	+	CCONJ
ejpam-2623	665	6	dx2y2	dx2y2	PROPN
ejpam-2623	665	7	.	.	PUNCT
ejpam-2623	666	1	proof	proof	NOUN
ejpam-2623	666	2	.	.	PUNCT
ejpam-2623	667	1	n.	n.	PROPN
ejpam-2623	667	2	diarra	diarra	PROPN
ejpam-2623	667	3	,	,	PUNCT
ejpam-2623	667	4	d.	d.	PROPN
ejpam-2623	667	5	sow	sow	PROPN
ejpam-2623	667	6	,	,	PUNCT
ejpam-2623	667	7	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	667	8	.	.	PUNCT
ejpam-2623	667	9	khlil	khlil	PROPN
ejpam-2623	667	10	/	/	SYM
ejpam-2623	667	11	eur	eur	PROPN
ejpam-2623	667	12	.	.	PUNCT
ejpam-2623	668	1	j.	j.	PROPN
ejpam-2623	668	2	pure	pure	PROPN
ejpam-2623	668	3	appl	appl	PROPN
ejpam-2623	668	4	.	.	PROPN
ejpam-2623	668	5	math	math	PROPN
ejpam-2623	668	6	,	,	PUNCT
ejpam-2623	668	7	10	10	NUM
ejpam-2623	668	8	(	(	PUNCT
ejpam-2623	668	9	2	2	NUM
ejpam-2623	668	10	)	)	PUNCT
ejpam-2623	668	11	(	(	PUNCT
ejpam-2623	668	12	2017	2017	NUM
ejpam-2623	668	13	)	)	PUNCT
ejpam-2623	668	14	,	,	PUNCT
ejpam-2623	668	15	363	363	NUM
ejpam-2623	668	16	-	-	SYM
ejpam-2623	668	17	391	391	NUM
ejpam-2623	668	18	380	380	NUM
ejpam-2623	668	19	(	(	PUNCT
ejpam-2623	668	20	i	i	NOUN
ejpam-2623	668	21	)	)	PUNCT
ejpam-2623	668	22	v	v	NOUN
ejpam-2623	668	23	is	be	AUX
ejpam-2623	668	24	well	well	ADV
ejpam-2623	668	25	-	-	PUNCT
ejpam-2623	668	26	defined	define	VERB
ejpam-2623	668	27	by	by	ADP
ejpam-2623	668	28	the	the	DET
ejpam-2623	668	29	definition	definition	NOUN
ejpam-2623	668	30	of	of	ADP
ejpam-2623	668	31	the	the	DET
ejpam-2623	668	32	set	set	PROPN
ejpam-2623	668	33	r.	r.	PROPN
ejpam-2623	668	34	(	(	PUNCT
ejpam-2623	668	35	ii	ii	PROPN
ejpam-2623	668	36	)	)	PUNCT
ejpam-2623	668	37	since	since	SCONJ
ejpam-2623	668	38	d	d	PROPN
ejpam-2623	668	39	is	be	AUX
ejpam-2623	668	40	not	not	PART
ejpam-2623	668	41	a	a	DET
ejpam-2623	668	42	square	square	NOUN
ejpam-2623	668	43	,	,	PUNCT
ejpam-2623	668	44	then	then	ADV
ejpam-2623	668	45	ε	ε	PROPN
ejpam-2623	668	46	is	be	AUX
ejpam-2623	668	47	well	well	ADV
ejpam-2623	668	48	-	-	PUNCT
ejpam-2623	668	49	defined	define	VERB
ejpam-2623	668	50	.	.	PUNCT
ejpam-2623	669	1	now	now	ADV
ejpam-2623	669	2	let	let	VERB
ejpam-2623	669	3	us	we	PRON
ejpam-2623	669	4	show	show	VERB
ejpam-2623	669	5	that	that	SCONJ
ejpam-2623	669	6	ε	ε	PROPN
ejpam-2623	669	7	6=	6=	PRON
ejpam-2623	669	8	0	0	NUM
ejpam-2623	669	9	.	.	PUNCT
ejpam-2623	669	10	suppose	suppose	VERB
ejpam-2623	669	11	that	that	SCONJ
ejpam-2623	669	12	1−v	1−v	PROPN
ejpam-2623	670	1	=	=	SYM
ejpam-2623	670	2	0	0	NUM
ejpam-2623	670	3	;	;	PUNCT
ejpam-2623	670	4	this	this	PRON
ejpam-2623	670	5	implies	imply	VERB
ejpam-2623	670	6	that	that	SCONJ
ejpam-2623	670	7	ur2(d−1)+3d+1−(d−1)ur2	ur2(d−1)+3d+1−(d−1)ur2	VERB
ejpam-2623	670	8	+	+	NOUN
ejpam-2623	670	9	3+d	3+d	NUM
ejpam-2623	670	10	=	=	SYM
ejpam-2623	670	11	0⇒	0⇒	NOUN
ejpam-2623	671	1	d	d	NOUN
ejpam-2623	671	2	=	=	SYM
ejpam-2623	671	3	−1	−1	NOUN
ejpam-2623	671	4	;	;	PUNCT
ejpam-2623	671	5	impossible	impossible	ADJ
ejpam-2623	671	6	by	by	ADP
ejpam-2623	671	7	our	our	PRON
ejpam-2623	671	8	hypothesis	hypothesis	NOUN
ejpam-2623	671	9	on	on	ADP
ejpam-2623	671	10	d.	d.	PROPN
ejpam-2623	671	11	suppose	suppose	VERB
ejpam-2623	671	12	that	that	SCONJ
ejpam-2623	671	13	1+v	1+v	NUM
ejpam-2623	672	1	=	=	SYM
ejpam-2623	672	2	0	0	NUM
ejpam-2623	672	3	;	;	PUNCT
ejpam-2623	672	4	thus	thus	ADV
ejpam-2623	672	5	ur2(d−1)+d−1	ur2(d−1)+d−1	PROPN
ejpam-2623	672	6	=	=	SYM
ejpam-2623	672	7	0	0	NUM
ejpam-2623	672	8	and	and	CCONJ
ejpam-2623	672	9	ur2	ur2	PRON
ejpam-2623	672	10	+	+	CCONJ
ejpam-2623	672	11	1	1	NUM
ejpam-2623	672	12	=	=	SYM
ejpam-2623	672	13	0	0	NUM
ejpam-2623	672	14	.	.	PUNCT
ejpam-2623	673	1	this	this	PRON
ejpam-2623	673	2	is	be	AUX
ejpam-2623	673	3	impossible	impossible	ADJ
ejpam-2623	673	4	by	by	ADP
ejpam-2623	673	5	the	the	DET
ejpam-2623	673	6	definition	definition	NOUN
ejpam-2623	673	7	of	of	ADP
ejpam-2623	673	8	the	the	DET
ejpam-2623	673	9	set	set	NOUN
ejpam-2623	673	10	r.	r.	PROPN
ejpam-2623	673	11	finally	finally	ADV
ejpam-2623	673	12	ε	ε	PROPN
ejpam-2623	673	13	is	be	AUX
ejpam-2623	673	14	welldefined	welldefine	VERB
ejpam-2623	673	15	and	and	CCONJ
ejpam-2623	673	16	is	be	AUX
ejpam-2623	673	17	non	non	ADJ
ejpam-2623	673	18	-	-	ADJ
ejpam-2623	673	19	zero	zero	NUM
ejpam-2623	673	20	.	.	PUNCT
ejpam-2623	674	1	(	(	PUNCT
ejpam-2623	674	2	iii	iii	X
ejpam-2623	674	3	)	)	PUNCT
ejpam-2623	674	4	x	x	PRON
ejpam-2623	674	5	is	be	AUX
ejpam-2623	674	6	well	well	ADV
ejpam-2623	674	7	-	-	PUNCT
ejpam-2623	674	8	defined	define	VERB
ejpam-2623	674	9	when	when	SCONJ
ejpam-2623	674	10	2d(v+	2d(v+	NUM
ejpam-2623	674	11	1	1	NUM
ejpam-2623	674	12	)	)	PUNCT
ejpam-2623	674	13	+	+	NUM
ejpam-2623	674	14	1−d	1−d	NUM
ejpam-2623	674	15	6=	6=	ADP
ejpam-2623	674	16	0	0	X
ejpam-2623	674	17	.	.	PUNCT
ejpam-2623	675	1	suppose	suppose	VERB
ejpam-2623	675	2	that	that	SCONJ
ejpam-2623	675	3	2d(v+	2d(v+	NUM
ejpam-2623	675	4	1	1	NUM
ejpam-2623	675	5	)	)	PUNCT
ejpam-2623	675	6	+	+	NUM
ejpam-2623	675	7	1−d	1−d	NUM
ejpam-2623	675	8	=	=	SYM
ejpam-2623	675	9	0	0	NUM
ejpam-2623	675	10	;	;	PUNCT
ejpam-2623	675	11	this	this	PRON
ejpam-2623	675	12	implies	imply	VERB
ejpam-2623	675	13	that	that	SCONJ
ejpam-2623	676	1	2d(d−1)ur2−2d(3+d)+2dur2(d−1)+2d(1	2d(d−1)ur2−2d(3+d)+2dur2(d−1)+2d(1	PROPN
ejpam-2623	676	2	+	+	NOUN
ejpam-2623	676	3	3d)+ur2(1−d)(d−1)+	3d)+ur2(1−d)(d−1)+	NUM
ejpam-2623	676	4	(	(	PUNCT
ejpam-2623	676	5	1−	1−	NUM
ejpam-2623	676	6	d)(1	d)(1	X
ejpam-2623	676	7	+	+	CCONJ
ejpam-2623	676	8	3d	3d	NUM
ejpam-2623	676	9	)	)	PUNCT
ejpam-2623	676	10	=	=	SYM
ejpam-2623	677	1	0⇒	0⇒	NOUN
ejpam-2623	678	1	4dur2(d−	4dur2(d−	NUM
ejpam-2623	678	2	1)−ur2(d−	1)−ur2(d−	NUM
ejpam-2623	679	1	1)2−	1)2−	NUM
ejpam-2623	679	2	4d(1−	4d(1−	NUM
ejpam-2623	679	3	d	d	NOUN
ejpam-2623	679	4	)	)	PUNCT
ejpam-2623	680	1	+	+	CCONJ
ejpam-2623	680	2	(	(	PUNCT
ejpam-2623	680	3	1−	1−	NUM
ejpam-2623	680	4	d)(1	d)(1	X
ejpam-2623	681	1	+	+	CCONJ
ejpam-2623	681	2	3d	3d	NUM
ejpam-2623	681	3	)	)	PUNCT
ejpam-2623	682	1	=	=	SYM
ejpam-2623	682	2	0⇒	0⇒	NOUN
ejpam-2623	682	3	(	(	PUNCT
ejpam-2623	682	4	d−1	d−1	PROPN
ejpam-2623	682	5	)	)	PUNCT
ejpam-2623	682	6	(	(	PUNCT
ejpam-2623	682	7	4dur2	4dur2	X
ejpam-2623	682	8	−	−	NOUN
ejpam-2623	682	9	ur2(d−	ur2(d−	PROPN
ejpam-2623	682	10	1	1	NUM
ejpam-2623	682	11	)	)	PUNCT
ejpam-2623	682	12	+	+	PUNCT
ejpam-2623	683	1	4d−	4d−	NUM
ejpam-2623	683	2	1−	1−	NUM
ejpam-2623	683	3	3d	3d	NUM
ejpam-2623	683	4	)	)	PUNCT
ejpam-2623	684	1	=	=	PUNCT
ejpam-2623	684	2	0	0	X
ejpam-2623	684	3	.	.	PUNCT
ejpam-2623	685	1	this	this	PRON
ejpam-2623	685	2	leads	lead	VERB
ejpam-2623	685	3	to	to	ADP
ejpam-2623	685	4	ur2(1	ur2(1	NOUN
ejpam-2623	685	5	+	+	NOUN
ejpam-2623	685	6	3d)+(d−1	3d)+(d−1	NUM
ejpam-2623	685	7	)	)	PUNCT
ejpam-2623	685	8	=	=	SYM
ejpam-2623	685	9	0	0	NUM
ejpam-2623	685	10	,	,	PUNCT
ejpam-2623	685	11	which	which	PRON
ejpam-2623	685	12	contradicts	contradict	VERB
ejpam-2623	685	13	the	the	DET
ejpam-2623	685	14	definition	definition	NOUN
ejpam-2623	685	15	of	of	ADP
ejpam-2623	685	16	r.	r.	PROPN
ejpam-2623	685	17	(	(	PUNCT
ejpam-2623	685	18	iv	iv	X
ejpam-2623	685	19	)	)	PUNCT
ejpam-2623	685	20	y	y	PROPN
ejpam-2623	685	21	is	be	AUX
ejpam-2623	685	22	well	well	ADV
ejpam-2623	685	23	-	-	PUNCT
ejpam-2623	685	24	defined	define	VERB
ejpam-2623	685	25	when	when	SCONJ
ejpam-2623	685	26	1−	1−	NUM
ejpam-2623	685	27	dx2	dx2	PROPN
ejpam-2623	685	28	6=	6=	ADP
ejpam-2623	685	29	0	0	NUM
ejpam-2623	685	30	and	and	CCONJ
ejpam-2623	685	31	χ	χ	X
ejpam-2623	685	32	(	(	PUNCT
ejpam-2623	685	33	1−x2	1−x2	NUM
ejpam-2623	685	34	1−dx2	1−dx2	NUM
ejpam-2623	685	35	)	)	PUNCT
ejpam-2623	685	36	=	=	SYM
ejpam-2623	686	1	1	1	X
ejpam-2623	686	2	.	.	PUNCT
ejpam-2623	686	3	at	at	ADP
ejpam-2623	686	4	first	first	ADV
ejpam-2623	686	5	,	,	PUNCT
ejpam-2623	686	6	recall	recall	VERB
ejpam-2623	686	7	that	that	SCONJ
ejpam-2623	686	8	d	d	NOUN
ejpam-2623	686	9	is	be	AUX
ejpam-2623	686	10	not	not	PART
ejpam-2623	686	11	a	a	DET
ejpam-2623	686	12	square	square	NOUN
ejpam-2623	686	13	by	by	ADP
ejpam-2623	686	14	hypothesis	hypothesis	NOUN
ejpam-2623	686	15	;	;	PUNCT
ejpam-2623	686	16	so	so	ADV
ejpam-2623	686	17	1−	1−	NUM
ejpam-2623	686	18	dx2	dx2	PROPN
ejpam-2623	686	19	6=	6=	PROPN
ejpam-2623	686	20	0	0	NUM
ejpam-2623	686	21	.	.	PUNCT
ejpam-2623	687	1	now	now	ADV
ejpam-2623	687	2	let	let	VERB
ejpam-2623	687	3	us	we	PRON
ejpam-2623	687	4	show	show	VERB
ejpam-2623	687	5	that	that	SCONJ
ejpam-2623	687	6	1−	1−	NUM
ejpam-2623	688	1	x2	x2	NUM
ejpam-2623	688	2	1−	1−	NUM
ejpam-2623	688	3	dx2	dx2	PROPN
ejpam-2623	688	4	is	be	AUX
ejpam-2623	688	5	a	a	DET
ejpam-2623	688	6	non	non	ADJ
ejpam-2623	688	7	-	-	ADJ
ejpam-2623	688	8	zero	zero	NUM
ejpam-2623	688	9	square	square	NOUN
ejpam-2623	688	10	.	.	PUNCT
ejpam-2623	689	1	for	for	ADP
ejpam-2623	689	2	this	this	PRON
ejpam-2623	689	3	,	,	PUNCT
ejpam-2623	689	4	we	we	PRON
ejpam-2623	689	5	must	must	AUX
ejpam-2623	689	6	consider	consider	VERB
ejpam-2623	689	7	two	two	NUM
ejpam-2623	689	8	cases	case	NOUN
ejpam-2623	689	9	:	:	PUNCT
ejpam-2623	689	10	•	•	INTJ
ejpam-2623	689	11	if	if	SCONJ
ejpam-2623	689	12	ε	ε	PROPN
ejpam-2623	689	13	=	=	SYM
ejpam-2623	689	14	1	1	NUM
ejpam-2623	689	15	,	,	PUNCT
ejpam-2623	689	16	then	then	ADV
ejpam-2623	689	17	x	x	X
ejpam-2623	689	18	=	=	SYM
ejpam-2623	689	19	v	v	PROPN
ejpam-2623	689	20	and	and	CCONJ
ejpam-2623	689	21	χ	χ	X
ejpam-2623	689	22	(	(	PUNCT
ejpam-2623	689	23	1−x2	1−x2	NUM
ejpam-2623	689	24	1−dx2	1−dx2	NUM
ejpam-2623	689	25	)	)	PUNCT
ejpam-2623	690	1	=	=	SYM
ejpam-2623	691	1	χ	χ	X
ejpam-2623	691	2	(	(	PUNCT
ejpam-2623	691	3	1−v2	1−v2	NUM
ejpam-2623	691	4	1−dv2	1−dv2	NUM
ejpam-2623	691	5	)	)	PUNCT
ejpam-2623	691	6	=	=	PUNCT
ejpam-2623	691	7	ε	ε	PROPN
ejpam-2623	691	8	=	=	SYM
ejpam-2623	691	9	1	1	NUM
ejpam-2623	691	10	.	.	NOUN
ejpam-2623	691	11	•	•	NOUN
ejpam-2623	691	12	if	if	SCONJ
ejpam-2623	691	13	ε	ε	PROPN
ejpam-2623	691	14	=	=	SYM
ejpam-2623	691	15	−1	−1	NOUN
ejpam-2623	691	16	,	,	PUNCT
ejpam-2623	691	17	then	then	ADV
ejpam-2623	691	18	x	x	X
ejpam-2623	691	19	=	=	SYM
ejpam-2623	691	20	−(v+1)(d+1)+(d−1	−(v+1)(d+1)+(d−1	NOUN
ejpam-2623	691	21	)	)	PUNCT
ejpam-2623	691	22	2d(v+1)+(1−d	2d(v+1)+(1−d	PROPN
ejpam-2623	691	23	)	)	PUNCT
ejpam-2623	691	24	.	.	PUNCT
ejpam-2623	692	1	let	let	VERB
ejpam-2623	692	2	h(x	h(x	PROPN
ejpam-2623	692	3	)	)	PUNCT
ejpam-2623	693	1	=	=	PUNCT
ejpam-2623	694	1	1−x2	1−x2	NUM
ejpam-2623	694	2	1−dx2	1−dx2	NUM
ejpam-2623	694	3	=	=	SYM
ejpam-2623	694	4	(	(	PUNCT
ejpam-2623	694	5	1−x)(1+x	1−x)(1+x	NUM
ejpam-2623	694	6	)	)	PUNCT
ejpam-2623	694	7	1−dx2	1−dx2	PROPN
ejpam-2623	694	8	.	.	PUNCT
ejpam-2623	695	1	our	our	PRON
ejpam-2623	695	2	objective	objective	NOUN
ejpam-2623	695	3	now	now	ADV
ejpam-2623	695	4	is	be	AUX
ejpam-2623	695	5	to	to	PART
ejpam-2623	695	6	write	write	VERB
ejpam-2623	695	7	χ(h(x	χ(h(x	PROPN
ejpam-2623	695	8	)	)	PUNCT
ejpam-2623	695	9	)	)	PUNCT
ejpam-2623	695	10	in	in	ADP
ejpam-2623	695	11	function	function	NOUN
ejpam-2623	695	12	of	of	ADP
ejpam-2623	695	13	χ(h(v	χ(h(v	NOUN
ejpam-2623	695	14	)	)	PUNCT
ejpam-2623	695	15	)	)	PUNCT
ejpam-2623	695	16	,	,	PUNCT
ejpam-2623	695	17	and	and	CCONJ
ejpam-2623	695	18	then	then	ADV
ejpam-2623	695	19	use	use	VERB
ejpam-2623	695	20	the	the	DET
ejpam-2623	695	21	fact	fact	NOUN
ejpam-2623	695	22	that	that	SCONJ
ejpam-2623	695	23	χ(h(v	χ(h(v	NOUN
ejpam-2623	695	24	)	)	PUNCT
ejpam-2623	695	25	)	)	PUNCT
ejpam-2623	696	1	=	=	PUNCT
ejpam-2623	696	2	ε	ε	PROPN
ejpam-2623	696	3	=	=	SYM
ejpam-2623	696	4	−1	−1	NOUN
ejpam-2623	696	5	.	.	PUNCT
ejpam-2623	697	1	first	first	ADV
ejpam-2623	697	2	we	we	PRON
ejpam-2623	697	3	compute	compute	VERB
ejpam-2623	697	4	1−	1−	NUM
ejpam-2623	697	5	x	x	NOUN
ejpam-2623	697	6	,	,	PUNCT
ejpam-2623	697	7	1	1	NUM
ejpam-2623	697	8	+	+	CCONJ
ejpam-2623	697	9	x	x	SYM
ejpam-2623	697	10	,	,	PUNCT
ejpam-2623	697	11	1−	1−	NUM
ejpam-2623	697	12	dx2	dx2	NOUN
ejpam-2623	697	13	and	and	CCONJ
ejpam-2623	697	14	find	find	VERB
ejpam-2623	697	15	:	:	PUNCT
ejpam-2623	698	1	[	[	X
ejpam-2623	698	2	2d(v	2d(v	NOUN
ejpam-2623	698	3	+	+	CCONJ
ejpam-2623	698	4	1	1	NUM
ejpam-2623	698	5	)	)	PUNCT
ejpam-2623	698	6	+	+	CCONJ
ejpam-2623	698	7	(	(	PUNCT
ejpam-2623	698	8	1−	1−	NUM
ejpam-2623	698	9	d	d	NOUN
ejpam-2623	698	10	)	)	PUNCT
ejpam-2623	698	11	]	]	PUNCT
ejpam-2623	698	12	(	(	PUNCT
ejpam-2623	698	13	1	1	NUM
ejpam-2623	698	14	+	+	CCONJ
ejpam-2623	698	15	x	x	X
ejpam-2623	698	16	)	)	PUNCT
ejpam-2623	698	17	=	=	SYM
ejpam-2623	698	18	(	(	PUNCT
ejpam-2623	698	19	v	v	NOUN
ejpam-2623	698	20	+	+	CCONJ
ejpam-2623	698	21	1)(d−	1)(d−	PROPN
ejpam-2623	698	22	1	1	NUM
ejpam-2623	698	23	)	)	PUNCT
ejpam-2623	698	24	;	;	PUNCT
ejpam-2623	699	1	[	[	X
ejpam-2623	699	2	2d(v	2d(v	NOUN
ejpam-2623	699	3	+	+	CCONJ
ejpam-2623	699	4	1	1	NUM
ejpam-2623	699	5	)	)	PUNCT
ejpam-2623	699	6	+	+	CCONJ
ejpam-2623	699	7	(	(	PUNCT
ejpam-2623	699	8	1−	1−	NUM
ejpam-2623	699	9	d	d	NOUN
ejpam-2623	699	10	)	)	PUNCT
ejpam-2623	699	11	]	]	PUNCT
ejpam-2623	699	12	(	(	PUNCT
ejpam-2623	699	13	1−	1−	NUM
ejpam-2623	699	14	x	x	NOUN
ejpam-2623	699	15	)	)	PUNCT
ejpam-2623	699	16	=	=	SYM
ejpam-2623	699	17	(	(	PUNCT
ejpam-2623	699	18	v	v	NOUN
ejpam-2623	699	19	+	+	CCONJ
ejpam-2623	699	20	1)(3d+	1)(3d+	NUM
ejpam-2623	699	21	1	1	NUM
ejpam-2623	699	22	)	)	PUNCT
ejpam-2623	699	23	+	+	CCONJ
ejpam-2623	699	24	2(1−	2(1−	NUM
ejpam-2623	699	25	d	d	NOUN
ejpam-2623	699	26	)	)	PUNCT
ejpam-2623	699	27	;	;	PUNCT
ejpam-2623	699	28	and	and	CCONJ
ejpam-2623	699	29	[	[	X
ejpam-2623	699	30	2d(v	2d(v	NUM
ejpam-2623	699	31	+	+	CCONJ
ejpam-2623	699	32	1	1	NUM
ejpam-2623	699	33	)	)	PUNCT
ejpam-2623	699	34	+	+	CCONJ
ejpam-2623	699	35	(	(	PUNCT
ejpam-2623	699	36	1−	1−	NUM
ejpam-2623	699	37	d)]2	d)]2	INTJ
ejpam-2623	699	38	(	(	PUNCT
ejpam-2623	699	39	1−	1−	NUM
ejpam-2623	699	40	dx2	dx2	PROPN
ejpam-2623	699	41	)	)	PUNCT
ejpam-2623	699	42	=	=	PUNCT
ejpam-2623	699	43	(	(	PUNCT
ejpam-2623	699	44	d−	d−	PROPN
ejpam-2623	699	45	1)2(1−	1)2(1−	NUM
ejpam-2623	699	46	dv2	dv2	NOUN
ejpam-2623	699	47	)	)	PUNCT
ejpam-2623	699	48	.	.	PUNCT
ejpam-2623	700	1	then	then	ADV
ejpam-2623	700	2	h(x	h(x	PROPN
ejpam-2623	700	3	)	)	PUNCT
ejpam-2623	700	4	=	=	PUNCT
ejpam-2623	700	5	(	(	PUNCT
ejpam-2623	700	6	1−	1−	NUM
ejpam-2623	700	7	x)(1	x)(1	PUNCT
ejpam-2623	701	1	+	+	NUM
ejpam-2623	701	2	x	x	X
ejpam-2623	701	3	)	)	PUNCT
ejpam-2623	701	4	1−	1−	NUM
ejpam-2623	701	5	dx2	dx2	NOUN
ejpam-2623	701	6	=	=	SYM
ejpam-2623	701	7	(	(	PUNCT
ejpam-2623	701	8	(	(	PUNCT
ejpam-2623	701	9	v	v	NOUN
ejpam-2623	701	10	+	+	CCONJ
ejpam-2623	701	11	1)(3d+	1)(3d+	NUM
ejpam-2623	701	12	1	1	NUM
ejpam-2623	701	13	)	)	PUNCT
ejpam-2623	701	14	+	+	CCONJ
ejpam-2623	701	15	2(1−	2(1−	NUM
ejpam-2623	701	16	d	d	NOUN
ejpam-2623	701	17	)	)	PUNCT
ejpam-2623	701	18	)	)	PUNCT
ejpam-2623	701	19	·	·	PUNCT
ejpam-2623	702	1	[	[	X
ejpam-2623	702	2	(	(	PUNCT
ejpam-2623	702	3	v	v	NOUN
ejpam-2623	702	4	+	+	X
ejpam-2623	702	5	1)(d−	1)(d−	PROPN
ejpam-2623	702	6	1	1	NUM
ejpam-2623	702	7	)	)	PUNCT
ejpam-2623	702	8	]	]	PUNCT
ejpam-2623	702	9	(	(	PUNCT
ejpam-2623	702	10	d−	d−	PROPN
ejpam-2623	702	11	1)2(1−	1)2(1−	NUM
ejpam-2623	702	12	dv2	dv2	NOUN
ejpam-2623	702	13	)	)	PUNCT
ejpam-2623	702	14	=	=	SYM
ejpam-2623	703	1	(	(	PUNCT
ejpam-2623	703	2	v	v	NOUN
ejpam-2623	703	3	+	+	NOUN
ejpam-2623	703	4	1)[(v	1)[(v	NUM
ejpam-2623	703	5	+	+	CCONJ
ejpam-2623	703	6	1)(3d+	1)(3d+	NUM
ejpam-2623	703	7	1	1	NUM
ejpam-2623	703	8	)	)	PUNCT
ejpam-2623	704	1	+	+	CCONJ
ejpam-2623	705	1	2(1−	2(1−	NUM
ejpam-2623	705	2	d	d	NOUN
ejpam-2623	705	3	)	)	PUNCT
ejpam-2623	705	4	]	]	PUNCT
ejpam-2623	705	5	(	(	PUNCT
ejpam-2623	705	6	d−	d−	PROPN
ejpam-2623	705	7	1)(1−	1)(1−	NUM
ejpam-2623	705	8	dv2	dv2	NOUN
ejpam-2623	705	9	)	)	PUNCT
ejpam-2623	705	10	=	=	SYM
ejpam-2623	706	1	h(v	h(v	NOUN
ejpam-2623	706	2	)	)	PUNCT
ejpam-2623	706	3	1−	1−	NUM
ejpam-2623	706	4	v	v	NOUN
ejpam-2623	706	5	(	(	PUNCT
ejpam-2623	706	6	(	(	PUNCT
ejpam-2623	706	7	v	v	NOUN
ejpam-2623	706	8	+	+	CCONJ
ejpam-2623	706	9	1)(3d+	1)(3d+	NUM
ejpam-2623	706	10	1	1	NUM
ejpam-2623	706	11	)	)	PUNCT
ejpam-2623	706	12	+	+	CCONJ
ejpam-2623	706	13	2(1−	2(1−	NUM
ejpam-2623	706	14	d	d	NOUN
ejpam-2623	706	15	)	)	PUNCT
ejpam-2623	706	16	d−	d−	PROPN
ejpam-2623	706	17	1	1	NUM
ejpam-2623	706	18	)	)	PUNCT
ejpam-2623	706	19	,	,	PUNCT
ejpam-2623	706	20	where	where	SCONJ
ejpam-2623	706	21	h(v	h(v	NOUN
ejpam-2623	706	22	)	)	PUNCT
ejpam-2623	706	23	=	=	PUNCT
ejpam-2623	706	24	(	(	PUNCT
ejpam-2623	706	25	1−	1−	NUM
ejpam-2623	706	26	v)(1	v)(1	NUM
ejpam-2623	706	27	+	+	CCONJ
ejpam-2623	706	28	v)/(1−	v)/(1−	PROPN
ejpam-2623	706	29	dv2	dv2	NOUN
ejpam-2623	706	30	)	)	PUNCT
ejpam-2623	706	31	.	.	PUNCT
ejpam-2623	707	1	replace	replace	VERB
ejpam-2623	707	2	v	v	NOUN
ejpam-2623	707	3	by	by	ADP
ejpam-2623	707	4	its	its	PRON
ejpam-2623	707	5	value	value	NOUN
ejpam-2623	707	6	to	to	PART
ejpam-2623	707	7	see	see	VERB
ejpam-2623	707	8	that	that	PRON
ejpam-2623	707	9	:	:	PUNCT
ejpam-2623	707	10	(	(	PUNCT
ejpam-2623	707	11	v+	v+	X
ejpam-2623	707	12	1)(1	1)(1	NUM
ejpam-2623	707	13	+	+	NOUN
ejpam-2623	707	14	3d	3d	NUM
ejpam-2623	707	15	)	)	PUNCT
ejpam-2623	708	1	+	+	NUM
ejpam-2623	708	2	2(1−d	2(1−d	NUM
ejpam-2623	708	3	)	)	PUNCT
ejpam-2623	709	1	=	=	SYM
ejpam-2623	710	1	2(d−	2(d−	NUM
ejpam-2623	710	2	1)[(1	1)[(1	NOUN
ejpam-2623	710	3	+	+	X
ejpam-2623	710	4	ur2)(1	ur2)(1	NOUN
ejpam-2623	710	5	+	+	CCONJ
ejpam-2623	710	6	3d)−	3d)−	NUM
ejpam-2623	710	7	ur2(d−	ur2(d−	PROPN
ejpam-2623	710	8	1)−	1)−	PROPN
ejpam-2623	710	9	(	(	PUNCT
ejpam-2623	710	10	1	1	NUM
ejpam-2623	710	11	+	+	NUM
ejpam-2623	710	12	3d	3d	NUM
ejpam-2623	710	13	)	)	PUNCT
ejpam-2623	710	14	]	]	PUNCT
ejpam-2623	710	15	ur2(d−	ur2(d−	PROPN
ejpam-2623	710	16	1	1	NUM
ejpam-2623	710	17	)	)	PUNCT
ejpam-2623	710	18	+	+	CCONJ
ejpam-2623	710	19	(	(	PUNCT
ejpam-2623	710	20	1	1	NUM
ejpam-2623	710	21	+	+	NUM
ejpam-2623	710	22	3d	3d	NUM
ejpam-2623	710	23	)	)	PUNCT
ejpam-2623	710	24	and	and	CCONJ
ejpam-2623	710	25	(	(	PUNCT
ejpam-2623	710	26	1−	1−	NUM
ejpam-2623	710	27	v)(d−	v)(d−	PROPN
ejpam-2623	710	28	1	1	NUM
ejpam-2623	710	29	)	)	PUNCT
ejpam-2623	710	30	=	=	VERB
ejpam-2623	711	1	4(d+	4(d+	NOUN
ejpam-2623	712	1	1)(d−	1)(d−	NUM
ejpam-2623	712	2	1	1	X
ejpam-2623	712	3	)	)	PUNCT
ejpam-2623	712	4	ur2(d−	ur2(d−	PROPN
ejpam-2623	712	5	1	1	NUM
ejpam-2623	712	6	)	)	PUNCT
ejpam-2623	712	7	+	+	CCONJ
ejpam-2623	712	8	(	(	PUNCT
ejpam-2623	712	9	1	1	NUM
ejpam-2623	712	10	+	+	NUM
ejpam-2623	712	11	3d	3d	NUM
ejpam-2623	712	12	)	)	PUNCT
ejpam-2623	712	13	;	;	PUNCT
ejpam-2623	713	1	so	so	CCONJ
ejpam-2623	713	2	(	(	PUNCT
ejpam-2623	713	3	v+1)(3d+1)+2(1−d	v+1)(3d+1)+2(1−d	PROPN
ejpam-2623	713	4	)	)	PUNCT
ejpam-2623	713	5	(	(	PUNCT
ejpam-2623	713	6	1−v)(d−1	1−v)(d−1	NUM
ejpam-2623	713	7	)	)	PUNCT
ejpam-2623	713	8	=	=	VERB
ejpam-2623	713	9	ur2	ur2	NOUN
ejpam-2623	713	10	.	.	PUNCT
ejpam-2623	714	1	since	since	SCONJ
ejpam-2623	714	2	r	r	NOUN
ejpam-2623	714	3	6=	6=	ADP
ejpam-2623	714	4	0	0	NUM
ejpam-2623	714	5	in	in	ADP
ejpam-2623	714	6	r	r	NOUN
ejpam-2623	714	7	,	,	PUNCT
ejpam-2623	714	8	then	then	ADV
ejpam-2623	714	9	χ(h(x	χ(h(x	PROPN
ejpam-2623	714	10	)	)	PUNCT
ejpam-2623	714	11	)	)	PUNCT
ejpam-2623	714	12	=	=	SYM
ejpam-2623	714	13	χ(h(v	χ(h(v	NOUN
ejpam-2623	714	14	)	)	PUNCT
ejpam-2623	714	15	)	)	PUNCT
ejpam-2623	714	16	·	·	PUNCT
ejpam-2623	715	1	χ(ur2	χ(ur2	X
ejpam-2623	715	2	)	)	PUNCT
ejpam-2623	715	3	=	=	SYM
ejpam-2623	715	4	1	1	NUM
ejpam-2623	715	5	as	as	SCONJ
ejpam-2623	715	6	desired	desire	VERB
ejpam-2623	715	7	.	.	PUNCT
ejpam-2623	716	1	hence	hence	ADV
ejpam-2623	716	2	(	(	PUNCT
ejpam-2623	716	3	1−x2)/(1−dx2	1−x2)/(1−dx2	X
ejpam-2623	716	4	)	)	PUNCT
ejpam-2623	716	5	is	be	AUX
ejpam-2623	716	6	a	a	DET
ejpam-2623	716	7	non	non	ADJ
ejpam-2623	716	8	-	-	ADJ
ejpam-2623	716	9	zero	zero	NUM
ejpam-2623	716	10	square	square	NOUN
ejpam-2623	716	11	and	and	CCONJ
ejpam-2623	716	12	y	y	PROPN
ejpam-2623	716	13	is	be	AUX
ejpam-2623	716	14	well	well	ADV
ejpam-2623	716	15	-	-	PUNCT
ejpam-2623	716	16	defined	define	VERB
ejpam-2623	716	17	.	.	PUNCT
ejpam-2623	717	1	moreover	moreover	ADV
ejpam-2623	717	2	(	(	PUNCT
ejpam-2623	717	3	x	x	NOUN
ejpam-2623	717	4	,	,	PUNCT
ejpam-2623	717	5	y	y	NOUN
ejpam-2623	717	6	)	)	PUNCT
ejpam-2623	717	7	verifies	verifie	NOUN
ejpam-2623	717	8	x2	x2	NOUN
ejpam-2623	718	1	+	+	CCONJ
ejpam-2623	719	1	y2	y2	NOUN
ejpam-2623	719	2	=	=	SYM
ejpam-2623	719	3	1	1	NUM
ejpam-2623	719	4	+	+	CCONJ
ejpam-2623	719	5	dx2y2	dx2y2	PROPN
ejpam-2623	719	6	.	.	PUNCT
ejpam-2623	720	1	definition	definition	NOUN
ejpam-2623	720	2	2	2	NUM
ejpam-2623	720	3	.	.	PUNCT
ejpam-2623	721	1	in	in	ADP
ejpam-2623	721	2	the	the	DET
ejpam-2623	721	3	situation	situation	NOUN
ejpam-2623	721	4	of	of	ADP
ejpam-2623	721	5	theorem	theorem	NOUN
ejpam-2623	721	6	4	4	NUM
ejpam-2623	721	7	,	,	PUNCT
ejpam-2623	721	8	the	the	DET
ejpam-2623	721	9	encoding	encoding	NOUN
ejpam-2623	721	10	function	function	NOUN
ejpam-2623	721	11	for	for	ADP
ejpam-2623	721	12	the	the	DET
ejpam-2623	721	13	edwards	edwards	PROPN
ejpam-2623	721	14	curve	curve	PROPN
ejpam-2623	721	15	ed	ed	NOUN
ejpam-2623	721	16	:	:	PUNCT
ejpam-2623	722	1	x2	x2	PROPN
ejpam-2623	722	2	+	+	PUNCT
ejpam-2623	722	3	y2	y2	NOUN
ejpam-2623	722	4	=	=	SYM
ejpam-2623	722	5	1	1	NUM
ejpam-2623	722	6	+	+	CCONJ
ejpam-2623	722	7	dx2y2	dx2y2	PROPN
ejpam-2623	722	8	is	be	AUX
ejpam-2623	722	9	the	the	DET
ejpam-2623	722	10	function	function	NOUN
ejpam-2623	722	11	φd	φd	VERB
ejpam-2623	722	12	:	:	PUNCT
ejpam-2623	722	13	r→	r→	PROPN
ejpam-2623	722	14	ed	ed	NOUN
ejpam-2623	722	15	:	:	PUNCT
ejpam-2623	722	16	r	r	NOUN
ejpam-2623	722	17	7→	7→	NUM
ejpam-2623	722	18	φd(r	φd(r	NOUN
ejpam-2623	722	19	)	)	PUNCT
ejpam-2623	722	20	=	=	PRON
ejpam-2623	722	21	(	(	PUNCT
ejpam-2623	722	22	x	x	X
ejpam-2623	722	23	,	,	PUNCT
ejpam-2623	722	24	y	y	PROPN
ejpam-2623	722	25	)	)	PUNCT
ejpam-2623	722	26	.	.	PUNCT
ejpam-2623	723	1	the	the	DET
ejpam-2623	723	2	following	follow	VERB
ejpam-2623	723	3	proposition	proposition	NOUN
ejpam-2623	723	4	characterizes	characterize	VERB
ejpam-2623	723	5	the	the	DET
ejpam-2623	723	6	image	image	NOUN
ejpam-2623	723	7	set	set	NOUN
ejpam-2623	723	8	of	of	ADP
ejpam-2623	723	9	the	the	DET
ejpam-2623	723	10	function	function	NOUN
ejpam-2623	723	11	φd	φd	PROPN
ejpam-2623	723	12	.	.	PUNCT
ejpam-2623	723	13	n.	n.	PROPN
ejpam-2623	723	14	diarra	diarra	PROPN
ejpam-2623	723	15	,	,	PUNCT
ejpam-2623	723	16	d.	d.	PROPN
ejpam-2623	723	17	sow	sow	PROPN
ejpam-2623	723	18	,	,	PUNCT
ejpam-2623	723	19	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	723	20	.	.	PUNCT
ejpam-2623	723	21	khlil	khlil	PROPN
ejpam-2623	723	22	/	/	SYM
ejpam-2623	723	23	eur	eur	PROPN
ejpam-2623	723	24	.	.	PUNCT
ejpam-2623	724	1	j.	j.	PROPN
ejpam-2623	724	2	pure	pure	PROPN
ejpam-2623	724	3	appl	appl	PROPN
ejpam-2623	724	4	.	.	PROPN
ejpam-2623	724	5	math	math	PROPN
ejpam-2623	724	6	,	,	PUNCT
ejpam-2623	724	7	10	10	NUM
ejpam-2623	724	8	(	(	PUNCT
ejpam-2623	724	9	2	2	NUM
ejpam-2623	724	10	)	)	PUNCT
ejpam-2623	724	11	(	(	PUNCT
ejpam-2623	724	12	2017	2017	NUM
ejpam-2623	724	13	)	)	PUNCT
ejpam-2623	724	14	,	,	PUNCT
ejpam-2623	724	15	363	363	NUM
ejpam-2623	724	16	-	-	SYM
ejpam-2623	724	17	391	391	NUM
ejpam-2623	724	18	381	381	NUM
ejpam-2623	724	19	proposition	proposition	NOUN
ejpam-2623	724	20	7	7	NUM
ejpam-2623	724	21	.	.	PUNCT
ejpam-2623	725	1	(	(	PUNCT
ejpam-2623	725	2	i	i	NOUN
ejpam-2623	725	3	)	)	PUNCT
ejpam-2623	725	4	for	for	ADP
ejpam-2623	725	5	r	r	NOUN
ejpam-2623	725	6	∈	∈	PROPN
ejpam-2623	725	7	r	r	NOUN
ejpam-2623	725	8	,	,	PUNCT
ejpam-2623	725	9	the	the	DET
ejpam-2623	725	10	set	set	NOUN
ejpam-2623	725	11	of	of	ADP
ejpam-2623	725	12	preimages	preimage	NOUN
ejpam-2623	725	13	of	of	ADP
ejpam-2623	725	14	φd(r	φd(r	NOUN
ejpam-2623	725	15	)	)	PUNCT
ejpam-2623	725	16	is	be	AUX
ejpam-2623	725	17	{	{	PUNCT
ejpam-2623	725	18	−r	−r	ADJ
ejpam-2623	725	19	,	,	PUNCT
ejpam-2623	725	20	r	r	NOUN
ejpam-2623	725	21	}	}	PUNCT
ejpam-2623	725	22	.	.	PUNCT
ejpam-2623	726	1	(	(	PUNCT
ejpam-2623	726	2	ii	ii	NOUN
ejpam-2623	726	3	)	)	PUNCT
ejpam-2623	726	4	im(φd	im(φd	PROPN
ejpam-2623	726	5	)	)	PUNCT
ejpam-2623	726	6	is	be	AUX
ejpam-2623	726	7	the	the	DET
ejpam-2623	726	8	set	set	NOUN
ejpam-2623	726	9	of	of	ADP
ejpam-2623	726	10	(	(	PUNCT
ejpam-2623	726	11	x	x	NOUN
ejpam-2623	726	12	,	,	PUNCT
ejpam-2623	726	13	y	y	NOUN
ejpam-2623	726	14	)	)	PUNCT
ejpam-2623	726	15	∈	∈	PROPN
ejpam-2623	726	16	ed	ed	NOUN
ejpam-2623	726	17	such	such	ADJ
ejpam-2623	726	18	that	that	SCONJ
ejpam-2623	726	19	1	1	NUM
ejpam-2623	726	20	−	−	NUM
ejpam-2623	726	21	x2	x2	PROPN
ejpam-2623	726	22	6=	6=	ADP
ejpam-2623	726	23	0	0	NUM
ejpam-2623	726	24	,	,	PUNCT
ejpam-2623	726	25	x	x	SYM
ejpam-2623	726	26	6=	6=	NUM
ejpam-2623	726	27	−(d+	−(d+	NUM
ejpam-2623	726	28	1	1	NUM
ejpam-2623	726	29	)	)	PUNCT
ejpam-2623	726	30	2d	2d	NOUN
ejpam-2623	726	31	and	and	CCONJ
ejpam-2623	726	32	χ[u(d	χ[u(d	NOUN
ejpam-2623	726	33	−	−	PROPN
ejpam-2623	726	34	1)(1−	1)(1−	NUM
ejpam-2623	726	35	x)(x(3d+	x)(x(3d+	PROPN
ejpam-2623	726	36	1	1	NUM
ejpam-2623	726	37	)	)	PUNCT
ejpam-2623	726	38	+	+	NUM
ejpam-2623	726	39	d+	d+	NOUN
ejpam-2623	726	40	3	3	NUM
ejpam-2623	726	41	)	)	PUNCT
ejpam-2623	726	42	]	]	PUNCT
ejpam-2623	727	1	=	=	PUNCT
ejpam-2623	727	2	1	1	X
ejpam-2623	727	3	.	.	PUNCT
ejpam-2623	727	4	(	(	PUNCT
ejpam-2623	727	5	iii	iii	X
ejpam-2623	727	6	)	)	PUNCT
ejpam-2623	727	7	let	let	VERB
ejpam-2623	727	8	(	(	PUNCT
ejpam-2623	727	9	x	x	NOUN
ejpam-2623	727	10	,	,	PUNCT
ejpam-2623	727	11	y	y	NOUN
ejpam-2623	727	12	)	)	PUNCT
ejpam-2623	727	13	∈	∈	PROPN
ejpam-2623	727	14	im(φd	im(φd	PROPN
ejpam-2623	727	15	)	)	PUNCT
ejpam-2623	727	16	and	and	CCONJ
ejpam-2623	727	17	define	define	VERB
ejpam-2623	727	18	r	r	NOUN
ejpam-2623	727	19	as	as	SCONJ
ejpam-2623	727	20	follows	follow	VERB
ejpam-2623	727	21	:	:	PUNCT
ejpam-2623	727	22	r	r	NOUN
ejpam-2623	727	23	=	=	PUNCT
ejpam-2623	727	24	√	√	PROPN
ejpam-2623	727	25	x(3d+	x(3d+	NOUN
ejpam-2623	727	26	1	1	NUM
ejpam-2623	727	27	)	)	PUNCT
ejpam-2623	728	1	+	+	CCONJ
ejpam-2623	728	2	d+	d+	SYM
ejpam-2623	728	3	3	3	NUM
ejpam-2623	728	4	u(d−	u(d−	PROPN
ejpam-2623	728	5	1)(1−	1)(1−	NUM
ejpam-2623	728	6	x	x	NOUN
ejpam-2623	728	7	)	)	PUNCT
ejpam-2623	728	8	,	,	PUNCT
ejpam-2623	728	9	if	if	SCONJ
ejpam-2623	728	10	y	y	PROPN
ejpam-2623	728	11	/∈	/∈	PUNCT
ejpam-2623	728	12	√	√	VERB
ejpam-2623	728	13	f2	f2	PROPN
ejpam-2623	728	14	q	q	NOUN
ejpam-2623	728	15	,	,	PUNCT
ejpam-2623	728	16	and	and	CCONJ
ejpam-2623	728	17	r	r	NOUN
ejpam-2623	728	18	=	=	SYM
ejpam-2623	728	19	√	√	PROPN
ejpam-2623	728	20	(	(	PUNCT
ejpam-2623	728	21	d−	d−	PROPN
ejpam-2623	728	22	1)(1−	1)(1−	NUM
ejpam-2623	728	23	x	x	SYM
ejpam-2623	728	24	)	)	PUNCT
ejpam-2623	728	25	u[x(3d+	u[x(3d+	NOUN
ejpam-2623	728	26	1	1	NUM
ejpam-2623	728	27	)	)	PUNCT
ejpam-2623	728	28	+	+	NUM
ejpam-2623	728	29	d+	d+	NOUN
ejpam-2623	728	30	3	3	NUM
ejpam-2623	728	31	)	)	PUNCT
ejpam-2623	728	32	]	]	PUNCT
ejpam-2623	728	33	,	,	PUNCT
ejpam-2623	728	34	if	if	SCONJ
ejpam-2623	728	35	y	y	PROPN
ejpam-2623	728	36	∈	∈	PROPN
ejpam-2623	728	37	√	√	ADP
ejpam-2623	728	38	f2	f2	PROPN
ejpam-2623	728	39	q.	q.	PROPN
ejpam-2623	728	40	then	then	ADV
ejpam-2623	728	41	r	r	NOUN
ejpam-2623	728	42	∈	∈	PROPN
ejpam-2623	728	43	r	r	NOUN
ejpam-2623	728	44	and	and	CCONJ
ejpam-2623	728	45	φd(r	φd(r	NUM
ejpam-2623	728	46	)	)	PUNCT
ejpam-2623	728	47	=	=	PRON
ejpam-2623	728	48	(	(	PUNCT
ejpam-2623	728	49	x	x	X
ejpam-2623	728	50	,	,	PUNCT
ejpam-2623	728	51	y	y	PROPN
ejpam-2623	728	52	)	)	PUNCT
ejpam-2623	728	53	.	.	PUNCT
ejpam-2623	729	1	proof	proof	NOUN
ejpam-2623	729	2	.	.	PUNCT
ejpam-2623	730	1	(	(	PUNCT
ejpam-2623	730	2	i	i	NOUN
ejpam-2623	730	3	)	)	PUNCT
ejpam-2623	730	4	it	it	PRON
ejpam-2623	730	5	is	be	AUX
ejpam-2623	730	6	obvious	obvious	ADJ
ejpam-2623	730	7	that	that	SCONJ
ejpam-2623	730	8	φd(−r	φd(−r	NOUN
ejpam-2623	730	9	)	)	PUNCT
ejpam-2623	730	10	=	=	SYM
ejpam-2623	730	11	φd(r	φd(r	NOUN
ejpam-2623	730	12	)	)	PUNCT
ejpam-2623	730	13	since	since	SCONJ
ejpam-2623	730	14	the	the	DET
ejpam-2623	730	15	definition	definition	NOUN
ejpam-2623	730	16	of	of	ADP
ejpam-2623	730	17	φd	φd	PRON
ejpam-2623	730	18	only	only	ADV
ejpam-2623	730	19	uses	use	VERB
ejpam-2623	730	20	r2	r2	PROPN
ejpam-2623	730	21	.	.	PUNCT
ejpam-2623	731	1	now	now	ADV
ejpam-2623	731	2	let	let	VERB
ejpam-2623	731	3	r′	r′	DET
ejpam-2623	731	4	∈	∈	PROPN
ejpam-2623	731	5	r	r	NOUN
ejpam-2623	732	1	such	such	ADJ
ejpam-2623	732	2	that	that	DET
ejpam-2623	732	3	φd(r	φd(r	NUM
ejpam-2623	732	4	′	′	NUM
ejpam-2623	732	5	)	)	PUNCT
ejpam-2623	732	6	=	=	NOUN
ejpam-2623	733	1	φd(r	φd(r	NOUN
ejpam-2623	733	2	)	)	PUNCT
ejpam-2623	733	3	.	.	PUNCT
ejpam-2623	734	1	we	we	PRON
ejpam-2623	734	2	want	want	VERB
ejpam-2623	734	3	to	to	PART
ejpam-2623	734	4	show	show	VERB
ejpam-2623	734	5	that	that	PRON
ejpam-2623	734	6	r′	r′	NOUN
ejpam-2623	734	7	=	=	SYM
ejpam-2623	734	8	r	r	NOUN
ejpam-2623	734	9	or	or	CCONJ
ejpam-2623	734	10	r′	r′	PROPN
ejpam-2623	734	11	=	=	SYM
ejpam-2623	734	12	−r	−r	PROPN
ejpam-2623	734	13	.	.	PUNCT
ejpam-2623	735	1	from	from	ADP
ejpam-2623	735	2	r′	r′	PROPN
ejpam-2623	735	3	we	we	PRON
ejpam-2623	735	4	define	define	VERB
ejpam-2623	735	5	the	the	DET
ejpam-2623	735	6	elements	element	NOUN
ejpam-2623	735	7	v′	v′	NOUN
ejpam-2623	735	8	,	,	PUNCT
ejpam-2623	735	9	ε′	ε′	NUM
ejpam-2623	735	10	,	,	PUNCT
ejpam-2623	735	11	t′	t′	NUM
ejpam-2623	735	12	,	,	PUNCT
ejpam-2623	735	13	x′	x′	NUM
ejpam-2623	735	14	,	,	PUNCT
ejpam-2623	735	15	y′	y′	ADV
ejpam-2623	735	16	as	as	ADP
ejpam-2623	735	17	in	in	ADP
ejpam-2623	735	18	theorem	theorem	NOUN
ejpam-2623	735	19	4	4	NUM
ejpam-2623	735	20	.	.	PUNCT
ejpam-2623	736	1	so	so	ADV
ejpam-2623	736	2	φd(r	φd(r	NUM
ejpam-2623	736	3	′	′	NOUN
ejpam-2623	736	4	)	)	PUNCT
ejpam-2623	736	5	=	=	SYM
ejpam-2623	737	1	φd(r	φd(r	NOUN
ejpam-2623	737	2	)	)	PUNCT
ejpam-2623	737	3	⇒	⇒	VERB
ejpam-2623	737	4	x′	x′	X
ejpam-2623	738	1	=	=	PUNCT
ejpam-2623	738	2	x	x	PROPN
ejpam-2623	738	3	and	and	CCONJ
ejpam-2623	738	4	y′	y′	NUM
ejpam-2623	738	5	=	=	PUNCT
ejpam-2623	738	6	y.	y.	NOUN
ejpam-2623	738	7	thus	thus	ADV
ejpam-2623	738	8	we	we	PRON
ejpam-2623	738	9	have	have	VERB
ejpam-2623	738	10	−ε′	−ε′	ADJ
ejpam-2623	738	11	√	√	PROPN
ejpam-2623	738	12	(	(	PUNCT
ejpam-2623	738	13	1−x2	1−x2	NUM
ejpam-2623	738	14	)	)	PUNCT
ejpam-2623	738	15	1−dx2	1−dx2	PROPN
ejpam-2623	738	16	=	=	PUNCT
ejpam-2623	738	17	−ε	−ε	PROPN
ejpam-2623	738	18	√	√	PROPN
ejpam-2623	738	19	(	(	PUNCT
ejpam-2623	738	20	1−x2	1−x2	NUM
ejpam-2623	738	21	)	)	PUNCT
ejpam-2623	738	22	1−dx2	1−dx2	PROPN
ejpam-2623	738	23	.	.	PUNCT
ejpam-2623	739	1	so	so	ADV
ejpam-2623	739	2	ε′	ε′	X
ejpam-2623	739	3	=	=	SYM
ejpam-2623	739	4	ε	ε	PROPN
ejpam-2623	739	5	;	;	PUNCT
ejpam-2623	739	6	and	and	CCONJ
ejpam-2623	739	7	we	we	PRON
ejpam-2623	739	8	have	have	VERB
ejpam-2623	739	9	v′	v′	NOUN
ejpam-2623	739	10	=	=	SYM
ejpam-2623	739	11	v	v	NOUN
ejpam-2623	739	12	by	by	ADP
ejpam-2623	739	13	replacing	replace	VERB
ejpam-2623	739	14	ε′	ε′	NOUN
ejpam-2623	739	15	by	by	ADP
ejpam-2623	739	16	ε	ε	PROPN
ejpam-2623	739	17	in	in	ADP
ejpam-2623	739	18	x′	x′	PROPN
ejpam-2623	740	1	=	=	PUNCT
ejpam-2623	740	2	x.	x.	NOUN
ejpam-2623	740	3	finally	finally	ADV
ejpam-2623	740	4	v	v	X
ejpam-2623	740	5	=	=	SYM
ejpam-2623	740	6	v′	v′	NOUN
ejpam-2623	740	7	implies	imply	VERB
ejpam-2623	740	8	that	that	SCONJ
ejpam-2623	740	9	r′2	r′2	NOUN
ejpam-2623	740	10	=	=	SYM
ejpam-2623	740	11	r2	r2	NOUN
ejpam-2623	740	12	,	,	PUNCT
ejpam-2623	740	13	that	that	PRON
ejpam-2623	740	14	is	be	AUX
ejpam-2623	740	15	r′	r′	PROPN
ejpam-2623	740	16	=	=	SYM
ejpam-2623	740	17	±r	±r	PROPN
ejpam-2623	740	18	.	.	PUNCT
ejpam-2623	741	1	(	(	PUNCT
ejpam-2623	741	2	ii	ii	NOUN
ejpam-2623	741	3	)	)	PUNCT
ejpam-2623	741	4	forward	forward	ADV
ejpam-2623	741	5	part	part	NOUN
ejpam-2623	741	6	:	:	PUNCT
ejpam-2623	741	7	let	let	VERB
ejpam-2623	741	8	(	(	PUNCT
ejpam-2623	741	9	x	x	NOUN
ejpam-2623	741	10	,	,	PUNCT
ejpam-2623	741	11	y	y	NOUN
ejpam-2623	741	12	)	)	PUNCT
ejpam-2623	741	13	∈	∈	PROPN
ejpam-2623	741	14	im(φ4	im(φ4	NOUN
ejpam-2623	741	15	)	)	PUNCT
ejpam-2623	741	16	,	,	PUNCT
ejpam-2623	741	17	we	we	PRON
ejpam-2623	741	18	need	need	VERB
ejpam-2623	741	19	to	to	PART
ejpam-2623	741	20	show	show	VERB
ejpam-2623	741	21	1	1	NUM
ejpam-2623	741	22	−	−	PROPN
ejpam-2623	741	23	x2	x2	PROPN
ejpam-2623	741	24	6=	6=	ADP
ejpam-2623	741	25	0	0	NUM
ejpam-2623	741	26	,	,	PUNCT
ejpam-2623	741	27	x	x	SYM
ejpam-2623	741	28	6=	6=	ADP
ejpam-2623	741	29	−d+1	−d+1	PROPN
ejpam-2623	741	30	2d	2d	PROPN
ejpam-2623	741	31	and	and	CCONJ
ejpam-2623	741	32	χ[u(d	χ[u(d	PROPN
ejpam-2623	741	33	−	−	PROPN
ejpam-2623	741	34	1)(1	1)(1	NUM
ejpam-2623	741	35	−	−	ADP
ejpam-2623	741	36	x)(x(3d	x)(x(3d	PROPN
ejpam-2623	742	1	+	+	CCONJ
ejpam-2623	742	2	1	1	NUM
ejpam-2623	742	3	)	)	PUNCT
ejpam-2623	742	4	+	+	CCONJ
ejpam-2623	743	1	d	d	NOUN
ejpam-2623	743	2	+	+	NOUN
ejpam-2623	743	3	3	3	NUM
ejpam-2623	743	4	)	)	PUNCT
ejpam-2623	743	5	]	]	PUNCT
ejpam-2623	744	1	=	=	PUNCT
ejpam-2623	744	2	1	1	X
ejpam-2623	744	3	.	.	PUNCT
ejpam-2623	744	4	since	since	SCONJ
ejpam-2623	744	5	(	(	PUNCT
ejpam-2623	744	6	x	x	NOUN
ejpam-2623	744	7	,	,	PUNCT
ejpam-2623	744	8	y	y	NOUN
ejpam-2623	744	9	)	)	PUNCT
ejpam-2623	744	10	∈	∈	PROPN
ejpam-2623	744	11	im(φ4	im(φ4	NOUN
ejpam-2623	744	12	)	)	PUNCT
ejpam-2623	744	13	,	,	PUNCT
ejpam-2623	744	14	then	then	ADV
ejpam-2623	744	15	there	there	PRON
ejpam-2623	744	16	exists	exist	VERB
ejpam-2623	744	17	r	r	NOUN
ejpam-2623	744	18	∈	∈	PROPN
ejpam-2623	744	19	r	r	NOUN
ejpam-2623	744	20	such	such	DET
ejpam-2623	745	1	that	that	DET
ejpam-2623	745	2	φ4(r	φ4(r	NOUN
ejpam-2623	745	3	)	)	PUNCT
ejpam-2623	745	4	=	=	SYM
ejpam-2623	745	5	(	(	PUNCT
ejpam-2623	745	6	x	x	X
ejpam-2623	745	7	,	,	PUNCT
ejpam-2623	745	8	y	y	PROPN
ejpam-2623	745	9	)	)	PUNCT
ejpam-2623	745	10	.	.	PUNCT
ejpam-2623	746	1	from	from	ADP
ejpam-2623	746	2	r	r	NOUN
ejpam-2623	746	3	,	,	PUNCT
ejpam-2623	746	4	define	define	VERB
ejpam-2623	746	5	v	v	NOUN
ejpam-2623	746	6	and	and	CCONJ
ejpam-2623	746	7	ε	ε	PROPN
ejpam-2623	746	8	as	as	ADP
ejpam-2623	746	9	in	in	ADP
ejpam-2623	746	10	theorem	theorem	NOUN
ejpam-2623	746	11	4	4	NUM
ejpam-2623	746	12	.	.	PUNCT
ejpam-2623	747	1	if	if	SCONJ
ejpam-2623	747	2	ε	ε	PROPN
ejpam-2623	747	3	=	=	SYM
ejpam-2623	747	4	1	1	NUM
ejpam-2623	747	5	,	,	PUNCT
ejpam-2623	747	6	then	then	ADV
ejpam-2623	747	7	x	x	X
ejpam-2623	747	8	=	=	SYM
ejpam-2623	747	9	v	v	NOUN
ejpam-2623	747	10	=	=	PUNCT
ejpam-2623	747	11	(	(	PUNCT
ejpam-2623	747	12	d−	d−	PROPN
ejpam-2623	747	13	1)ur2	1)ur2	PROPN
ejpam-2623	747	14	−	−	PROPN
ejpam-2623	748	1	3−	3−	NUM
ejpam-2623	748	2	d	d	PROPN
ejpam-2623	748	3	ur2(d−	ur2(d−	PROPN
ejpam-2623	748	4	1	1	NUM
ejpam-2623	748	5	)	)	PUNCT
ejpam-2623	748	6	+	+	CCONJ
ejpam-2623	748	7	1	1	NUM
ejpam-2623	749	1	+	+	NUM
ejpam-2623	749	2	3d	3d	NUM
ejpam-2623	749	3	.	.	PUNCT
ejpam-2623	750	1	we	we	PRON
ejpam-2623	750	2	have	have	VERB
ejpam-2623	750	3	1	1	NUM
ejpam-2623	750	4	+	+	NOUN
ejpam-2623	750	5	x	x	SYM
ejpam-2623	750	6	=	=	SYM
ejpam-2623	750	7	2(d−	2(d−	NUM
ejpam-2623	751	1	1)(ur2	1)(ur2	NUM
ejpam-2623	751	2	+	+	NOUN
ejpam-2623	751	3	1	1	X
ejpam-2623	751	4	)	)	PUNCT
ejpam-2623	751	5	ur2(d−	ur2(d−	PROPN
ejpam-2623	751	6	1	1	NUM
ejpam-2623	751	7	)	)	PUNCT
ejpam-2623	751	8	+	+	CCONJ
ejpam-2623	751	9	1	1	NUM
ejpam-2623	752	1	+	+	NUM
ejpam-2623	752	2	3d	3d	NUM
ejpam-2623	752	3	,	,	PUNCT
ejpam-2623	752	4	1	1	NUM
ejpam-2623	752	5	−	−	NOUN
ejpam-2623	752	6	x	x	X
ejpam-2623	753	1	=	=	PUNCT
ejpam-2623	753	2	4(d+	4(d+	NOUN
ejpam-2623	753	3	1	1	X
ejpam-2623	753	4	)	)	PUNCT
ejpam-2623	753	5	ur2(d−	ur2(d−	PROPN
ejpam-2623	753	6	1	1	NUM
ejpam-2623	753	7	)	)	PUNCT
ejpam-2623	753	8	+	+	CCONJ
ejpam-2623	753	9	1	1	NUM
ejpam-2623	754	1	+	+	NUM
ejpam-2623	754	2	3d	3d	NUM
ejpam-2623	754	3	and	and	CCONJ
ejpam-2623	754	4	x	x	SYM
ejpam-2623	755	1	+	+	NUM
ejpam-2623	755	2	d+1	d+1	PROPN
ejpam-2623	755	3	2d	2d	NUM
ejpam-2623	755	4	=	=	SYM
ejpam-2623	755	5	(	(	PUNCT
ejpam-2623	755	6	d−	d−	PROPN
ejpam-2623	755	7	1)[(3d+	1)[(3d+	NUM
ejpam-2623	755	8	1)ur2	1)ur2	NUM
ejpam-2623	755	9	+	+	CCONJ
ejpam-2623	755	10	d−	d−	PROPN
ejpam-2623	755	11	1	1	NUM
ejpam-2623	755	12	]	]	SYM
ejpam-2623	755	13	2d[(d−	2d[(d−	NUM
ejpam-2623	755	14	1)ur2	1)ur2	NUM
ejpam-2623	756	1	+	+	CCONJ
ejpam-2623	756	2	1	1	NUM
ejpam-2623	756	3	+	+	NUM
ejpam-2623	756	4	3d	3d	NUM
ejpam-2623	756	5	]	]	PUNCT
ejpam-2623	756	6	,	,	PUNCT
ejpam-2623	756	7	thus	thus	ADV
ejpam-2623	756	8	1	1	NUM
ejpam-2623	756	9	+	+	NUM
ejpam-2623	756	10	x	x	SYM
ejpam-2623	756	11	6=	6=	ADP
ejpam-2623	756	12	0	0	NUM
ejpam-2623	756	13	,	,	PUNCT
ejpam-2623	756	14	1	1	NUM
ejpam-2623	756	15	−	−	NOUN
ejpam-2623	756	16	x	x	SYM
ejpam-2623	756	17	6=	6=	ADP
ejpam-2623	756	18	0	0	NUM
ejpam-2623	756	19	and	and	CCONJ
ejpam-2623	756	20	x	x	SYM
ejpam-2623	756	21	6=	6=	PROPN
ejpam-2623	756	22	−d+1	−d+1	PROPN
ejpam-2623	756	23	2d	2d	PROPN
ejpam-2623	756	24	,	,	PUNCT
ejpam-2623	756	25	by	by	ADP
ejpam-2623	756	26	definition	definition	NOUN
ejpam-2623	756	27	of	of	ADP
ejpam-2623	756	28	r.	r.	PROPN
ejpam-2623	756	29	moreover	moreover	ADV
ejpam-2623	756	30	,	,	PUNCT
ejpam-2623	756	31	we	we	PRON
ejpam-2623	756	32	have	have	VERB
ejpam-2623	756	33	x(3d+	x(3d+	NOUN
ejpam-2623	756	34	1	1	NUM
ejpam-2623	756	35	)	)	PUNCT
ejpam-2623	756	36	+	+	NUM
ejpam-2623	756	37	d+	d+	SYM
ejpam-2623	756	38	3	3	NUM
ejpam-2623	756	39	=	=	SYM
ejpam-2623	756	40	4ur2(d−	4ur2(d−	NUM
ejpam-2623	756	41	1)(d+	1)(d+	NUM
ejpam-2623	756	42	1	1	NUM
ejpam-2623	756	43	)	)	PUNCT
ejpam-2623	756	44	ur2(d−	ur2(d−	PROPN
ejpam-2623	756	45	1	1	NUM
ejpam-2623	756	46	)	)	PUNCT
ejpam-2623	757	1	+	+	CCONJ
ejpam-2623	757	2	1	1	NUM
ejpam-2623	757	3	+	+	NUM
ejpam-2623	757	4	3d	3d	NOUN
ejpam-2623	757	5	;	;	PUNCT
ejpam-2623	757	6	hence	hence	ADV
ejpam-2623	757	7	u(d−	u(d−	PROPN
ejpam-2623	757	8	1)(1−	1)(1−	PROPN
ejpam-2623	757	9	x)(x(3d+	x)(x(3d+	PROPN
ejpam-2623	757	10	1	1	NUM
ejpam-2623	757	11	)	)	PUNCT
ejpam-2623	757	12	+	+	NUM
ejpam-2623	757	13	d+	d+	NOUN
ejpam-2623	757	14	3	3	X
ejpam-2623	757	15	)	)	PUNCT
ejpam-2623	757	16	=	=	SYM
ejpam-2623	758	1	16u2r2(d−	16u2r2(d−	NUM
ejpam-2623	758	2	1)2(d+	1)2(d+	NUM
ejpam-2623	758	3	1)2	1)2	NUM
ejpam-2623	758	4	(	(	PUNCT
ejpam-2623	758	5	ur2(d−	ur2(d−	PROPN
ejpam-2623	758	6	1	1	NUM
ejpam-2623	758	7	)	)	PUNCT
ejpam-2623	759	1	+	+	CCONJ
ejpam-2623	759	2	1	1	NUM
ejpam-2623	759	3	+	+	NUM
ejpam-2623	759	4	3d)2	3d)2	NUM
ejpam-2623	759	5	which	which	PRON
ejpam-2623	759	6	is	be	AUX
ejpam-2623	759	7	a	a	DET
ejpam-2623	759	8	nonzero	nonzero	ADJ
ejpam-2623	759	9	square	square	NOUN
ejpam-2623	759	10	by	by	ADP
ejpam-2623	759	11	definition	definition	NOUN
ejpam-2623	759	12	of	of	ADP
ejpam-2623	759	13	r	r	NOUN
ejpam-2623	759	14	,	,	PUNCT
ejpam-2623	759	15	as	as	SCONJ
ejpam-2623	759	16	desired	desire	VERB
ejpam-2623	759	17	.	.	PUNCT
ejpam-2623	760	1	if	if	SCONJ
ejpam-2623	760	2	ε	ε	PROPN
ejpam-2623	760	3	=	=	SYM
ejpam-2623	760	4	−1	−1	NOUN
ejpam-2623	760	5	,	,	PUNCT
ejpam-2623	760	6	then	then	ADV
ejpam-2623	760	7	x	x	X
ejpam-2623	760	8	=	=	SYM
ejpam-2623	760	9	−(v	−(v	NOUN
ejpam-2623	761	1	+	+	X
ejpam-2623	761	2	1)(d+	1)(d+	NUM
ejpam-2623	761	3	1	1	NUM
ejpam-2623	761	4	)	)	PUNCT
ejpam-2623	761	5	+	+	CCONJ
ejpam-2623	761	6	(	(	PUNCT
ejpam-2623	761	7	d−	d−	PROPN
ejpam-2623	761	8	1	1	NUM
ejpam-2623	761	9	)	)	PUNCT
ejpam-2623	761	10	2d(v	2d(v	NOUN
ejpam-2623	762	1	+	+	CCONJ
ejpam-2623	762	2	1	1	X
ejpam-2623	762	3	)	)	PUNCT
ejpam-2623	762	4	+	+	CCONJ
ejpam-2623	762	5	(	(	PUNCT
ejpam-2623	762	6	1−	1−	NUM
ejpam-2623	762	7	d	d	NOUN
ejpam-2623	762	8	)	)	PUNCT
ejpam-2623	762	9	=	=	SYM
ejpam-2623	762	10	d−	d−	PROPN
ejpam-2623	762	11	1−	1−	NUM
ejpam-2623	762	12	ur2(d+	ur2(d+	NUM
ejpam-2623	762	13	3	3	NUM
ejpam-2623	762	14	)	)	PUNCT
ejpam-2623	762	15	ur2(3d+	ur2(3d+	NOUN
ejpam-2623	762	16	1	1	NUM
ejpam-2623	762	17	)	)	PUNCT
ejpam-2623	763	1	+	+	CCONJ
ejpam-2623	763	2	d−	d−	PROPN
ejpam-2623	763	3	1	1	NUM
ejpam-2623	763	4	.	.	PUNCT
ejpam-2623	764	1	we	we	PRON
ejpam-2623	764	2	have	have	VERB
ejpam-2623	764	3	1−	1−	NUM
ejpam-2623	764	4	x	x	SYM
ejpam-2623	764	5	=	=	SYM
ejpam-2623	764	6	4ur2(d+	4ur2(d+	PROPN
ejpam-2623	764	7	1	1	NUM
ejpam-2623	764	8	)	)	PUNCT
ejpam-2623	764	9	ur2(3d+	ur2(3d+	NOUN
ejpam-2623	764	10	1	1	NUM
ejpam-2623	764	11	)	)	PUNCT
ejpam-2623	764	12	+	+	CCONJ
ejpam-2623	764	13	d−	d−	PROPN
ejpam-2623	764	14	1	1	NUM
ejpam-2623	764	15	,	,	PUNCT
ejpam-2623	764	16	1+x	1+x	NUM
ejpam-2623	764	17	=	=	SYM
ejpam-2623	764	18	2(d−	2(d−	NUM
ejpam-2623	764	19	1)(ur2	1)(ur2	NUM
ejpam-2623	765	1	+	+	NOUN
ejpam-2623	765	2	1	1	X
ejpam-2623	765	3	)	)	PUNCT
ejpam-2623	765	4	ur2(1	ur2(1	NOUN
ejpam-2623	766	1	+	+	CCONJ
ejpam-2623	766	2	3d	3d	NUM
ejpam-2623	766	3	)	)	PUNCT
ejpam-2623	767	1	+	+	CCONJ
ejpam-2623	767	2	d−	d−	PROPN
ejpam-2623	767	3	1	1	NUM
ejpam-2623	767	4	and	and	CCONJ
ejpam-2623	767	5	x+d+1	x+d+1	PROPN
ejpam-2623	767	6	2d	2d	PROPN
ejpam-2623	768	1	=	=	SYM
ejpam-2623	768	2	(	(	PUNCT
ejpam-2623	768	3	d−	d−	PROPN
ejpam-2623	768	4	1)[ur2(d−	1)[ur2(d−	NUM
ejpam-2623	768	5	1	1	NUM
ejpam-2623	768	6	)	)	PUNCT
ejpam-2623	768	7	+	+	CCONJ
ejpam-2623	768	8	1	1	NUM
ejpam-2623	768	9	+	+	NUM
ejpam-2623	768	10	3d	3d	NUM
ejpam-2623	768	11	]	]	X
ejpam-2623	769	1	2d[ur2(1	2d[ur2(1	NUM
ejpam-2623	769	2	+	+	CCONJ
ejpam-2623	769	3	3d	3d	NUM
ejpam-2623	769	4	)	)	PUNCT
ejpam-2623	770	1	+	+	CCONJ
ejpam-2623	770	2	d−	d−	PROPN
ejpam-2623	770	3	1	1	NUM
ejpam-2623	770	4	]	]	PUNCT
ejpam-2623	770	5	,	,	PUNCT
ejpam-2623	770	6	thus	thus	ADV
ejpam-2623	770	7	1	1	NUM
ejpam-2623	770	8	+	+	NUM
ejpam-2623	770	9	x	x	SYM
ejpam-2623	770	10	6=	6=	ADP
ejpam-2623	770	11	0	0	NUM
ejpam-2623	770	12	,	,	PUNCT
ejpam-2623	770	13	1	1	NUM
ejpam-2623	770	14	−	−	NOUN
ejpam-2623	770	15	x	x	SYM
ejpam-2623	770	16	6=	6=	ADP
ejpam-2623	770	17	0	0	NUM
ejpam-2623	771	1	and	and	CCONJ
ejpam-2623	771	2	x	x	SYM
ejpam-2623	771	3	6=	6=	PROPN
ejpam-2623	771	4	−d+1	−d+1	PROPN
ejpam-2623	771	5	2d	2d	PROPN
ejpam-2623	771	6	,	,	PUNCT
ejpam-2623	771	7	by	by	ADP
ejpam-2623	771	8	definition	definition	NOUN
ejpam-2623	771	9	of	of	ADP
ejpam-2623	771	10	r.	r.	PROPN
ejpam-2623	771	11	moreover	moreover	ADV
ejpam-2623	771	12	,	,	PUNCT
ejpam-2623	771	13	we	we	PRON
ejpam-2623	771	14	have	have	VERB
ejpam-2623	771	15	x(3d+	x(3d+	NOUN
ejpam-2623	771	16	1	1	NUM
ejpam-2623	771	17	)	)	PUNCT
ejpam-2623	771	18	+	+	NUM
ejpam-2623	771	19	d+	d+	SYM
ejpam-2623	771	20	3	3	NUM
ejpam-2623	771	21	=	=	SYM
ejpam-2623	771	22	4(d−	4(d−	PROPN
ejpam-2623	771	23	1)(d+	1)(d+	NUM
ejpam-2623	771	24	1	1	NUM
ejpam-2623	771	25	)	)	PUNCT
ejpam-2623	771	26	ur2(3d+	ur2(3d+	NOUN
ejpam-2623	771	27	1	1	NUM
ejpam-2623	771	28	)	)	PUNCT
ejpam-2623	771	29	+	+	CCONJ
ejpam-2623	771	30	d−	d−	PROPN
ejpam-2623	771	31	1	1	NUM
ejpam-2623	771	32	;	;	PUNCT
ejpam-2623	771	33	hence	hence	ADV
ejpam-2623	771	34	u(d−	u(d−	PROPN
ejpam-2623	771	35	1)(1−	1)(1−	PROPN
ejpam-2623	771	36	x)(x(3d+	x)(x(3d+	PROPN
ejpam-2623	771	37	1	1	NUM
ejpam-2623	771	38	)	)	PUNCT
ejpam-2623	771	39	+	+	NUM
ejpam-2623	771	40	d+	d+	NOUN
ejpam-2623	771	41	3	3	X
ejpam-2623	771	42	)	)	PUNCT
ejpam-2623	771	43	=	=	SYM
ejpam-2623	772	1	16u2r2(d−	16u2r2(d−	NUM
ejpam-2623	772	2	1)2(d+	1)2(d+	NUM
ejpam-2623	772	3	1)2	1)2	NUM
ejpam-2623	772	4	(	(	PUNCT
ejpam-2623	772	5	ur2(d−	ur2(d−	PROPN
ejpam-2623	772	6	1	1	NUM
ejpam-2623	772	7	)	)	PUNCT
ejpam-2623	773	1	+	+	CCONJ
ejpam-2623	773	2	1	1	NUM
ejpam-2623	773	3	+	+	NUM
ejpam-2623	773	4	3d)2	3d)2	NUM
ejpam-2623	773	5	,	,	PUNCT
ejpam-2623	773	6	which	which	PRON
ejpam-2623	773	7	is	be	AUX
ejpam-2623	773	8	a	a	DET
ejpam-2623	773	9	nonzero	nonzero	ADJ
ejpam-2623	773	10	square	square	NOUN
ejpam-2623	773	11	by	by	ADP
ejpam-2623	773	12	definition	definition	NOUN
ejpam-2623	773	13	of	of	ADP
ejpam-2623	773	14	r	r	NOUN
ejpam-2623	773	15	,	,	PUNCT
ejpam-2623	773	16	as	as	SCONJ
ejpam-2623	773	17	desired	desire	VERB
ejpam-2623	773	18	.	.	PUNCT
ejpam-2623	774	1	n.	n.	PROPN
ejpam-2623	774	2	diarra	diarra	PROPN
ejpam-2623	774	3	,	,	PUNCT
ejpam-2623	774	4	d.	d.	PROPN
ejpam-2623	774	5	sow	sow	PROPN
ejpam-2623	774	6	,	,	PUNCT
ejpam-2623	774	7	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	774	8	.	.	PUNCT
ejpam-2623	774	9	khlil	khlil	PROPN
ejpam-2623	774	10	/	/	SYM
ejpam-2623	774	11	eur	eur	PROPN
ejpam-2623	774	12	.	.	PUNCT
ejpam-2623	775	1	j.	j.	PROPN
ejpam-2623	775	2	pure	pure	PROPN
ejpam-2623	775	3	appl	appl	PROPN
ejpam-2623	775	4	.	.	PROPN
ejpam-2623	775	5	math	math	PROPN
ejpam-2623	775	6	,	,	PUNCT
ejpam-2623	775	7	10	10	NUM
ejpam-2623	775	8	(	(	PUNCT
ejpam-2623	775	9	2	2	NUM
ejpam-2623	775	10	)	)	PUNCT
ejpam-2623	775	11	(	(	PUNCT
ejpam-2623	775	12	2017	2017	NUM
ejpam-2623	775	13	)	)	PUNCT
ejpam-2623	775	14	,	,	PUNCT
ejpam-2623	775	15	363	363	NUM
ejpam-2623	775	16	-	-	SYM
ejpam-2623	775	17	391	391	NUM
ejpam-2623	775	18	382	382	NUM
ejpam-2623	775	19	reverse	reverse	NOUN
ejpam-2623	775	20	part	part	NOUN
ejpam-2623	775	21	:	:	PUNCT
ejpam-2623	775	22	let	let	VERB
ejpam-2623	775	23	(	(	PUNCT
ejpam-2623	775	24	x	x	NOUN
ejpam-2623	775	25	,	,	PUNCT
ejpam-2623	775	26	y	y	NOUN
ejpam-2623	775	27	)	)	PUNCT
ejpam-2623	775	28	∈	∈	PROPN
ejpam-2623	775	29	ed	ed	NOUN
ejpam-2623	775	30	such	such	ADJ
ejpam-2623	775	31	that	that	SCONJ
ejpam-2623	775	32	1	1	NUM
ejpam-2623	775	33	−	−	NUM
ejpam-2623	775	34	x2	x2	PROPN
ejpam-2623	775	35	6=	6=	ADP
ejpam-2623	775	36	0	0	NUM
ejpam-2623	775	37	,	,	PUNCT
ejpam-2623	775	38	x	x	SYM
ejpam-2623	775	39	6=	6=	ADP
ejpam-2623	775	40	−d+1	−d+1	PROPN
ejpam-2623	775	41	2d	2d	PROPN
ejpam-2623	775	42	and	and	CCONJ
ejpam-2623	775	43	χ[u(d	χ[u(d	PROPN
ejpam-2623	775	44	−	−	PROPN
ejpam-2623	775	45	1)(1	1)(1	NUM
ejpam-2623	775	46	−	−	PROPN
ejpam-2623	775	47	x)(x(3d+1)+d+3	x)(x(3d+1)+d+3	NUM
ejpam-2623	775	48	)	)	PUNCT
ejpam-2623	775	49	]	]	PUNCT
ejpam-2623	776	1	=	=	PUNCT
ejpam-2623	776	2	1	1	X
ejpam-2623	776	3	.	.	X
ejpam-2623	777	1	we	we	PRON
ejpam-2623	777	2	want	want	VERB
ejpam-2623	777	3	to	to	PART
ejpam-2623	777	4	show	show	VERB
ejpam-2623	777	5	that	that	SCONJ
ejpam-2623	777	6	(	(	PUNCT
ejpam-2623	777	7	x	x	NOUN
ejpam-2623	777	8	,	,	PUNCT
ejpam-2623	777	9	y	y	NOUN
ejpam-2623	777	10	)	)	PUNCT
ejpam-2623	777	11	∈	∈	PROPN
ejpam-2623	777	12	im(φd	im(φd	PROPN
ejpam-2623	777	13	)	)	PUNCT
ejpam-2623	777	14	.	.	PUNCT
ejpam-2623	778	1	for	for	ADP
ejpam-2623	778	2	this	this	PRON
ejpam-2623	778	3	,	,	PUNCT
ejpam-2623	778	4	we	we	PRON
ejpam-2623	778	5	consider	consider	VERB
ejpam-2623	778	6	the	the	DET
ejpam-2623	778	7	cases	case	NOUN
ejpam-2623	778	8	where	where	SCONJ
ejpam-2623	778	9	y	y	NOUN
ejpam-2623	778	10	=	=	PUNCT
ejpam-2623	778	11	−	−	PROPN
ejpam-2623	778	12	√	√	NUM
ejpam-2623	778	13	(	(	PUNCT
ejpam-2623	778	14	1−	1−	NUM
ejpam-2623	778	15	x2)/(1−	x2)/(1−	PROPN
ejpam-2623	778	16	dx2	dx2	PROPN
ejpam-2623	778	17	)	)	PUNCT
ejpam-2623	778	18	and	and	CCONJ
ejpam-2623	778	19	where	where	SCONJ
ejpam-2623	778	20	y	y	PROPN
ejpam-2623	778	21	=	=	PUNCT
ejpam-2623	778	22	√	√	PROPN
ejpam-2623	778	23	(	(	PUNCT
ejpam-2623	778	24	1−	1−	NUM
ejpam-2623	778	25	x2)/(1−	x2)/(1−	PROPN
ejpam-2623	778	26	dx2	dx2	PROPN
ejpam-2623	778	27	)	)	PUNCT
ejpam-2623	778	28	.	.	PUNCT
ejpam-2623	779	1	•	•	INTJ
ejpam-2623	779	2	if	if	SCONJ
ejpam-2623	779	3	y	y	PROPN
ejpam-2623	779	4	=	=	PUNCT
ejpam-2623	779	5	−	−	PROPN
ejpam-2623	780	1	√	√	NUM
ejpam-2623	780	2	(	(	PUNCT
ejpam-2623	780	3	1−	1−	NUM
ejpam-2623	780	4	x2)/(1−	x2)/(1−	PROPN
ejpam-2623	780	5	dx2	dx2	PROPN
ejpam-2623	780	6	)	)	PUNCT
ejpam-2623	780	7	,	,	PUNCT
ejpam-2623	780	8	put	put	VERB
ejpam-2623	780	9	r	r	NOUN
ejpam-2623	780	10	=	=	PUNCT
ejpam-2623	780	11	√	√	PROPN
ejpam-2623	780	12	x(3d+1)+d+3	x(3d+1)+d+3	PUNCT
ejpam-2623	780	13	u(d−1)(1−x	u(d−1)(1−x	PROPN
ejpam-2623	780	14	)	)	PUNCT
ejpam-2623	781	1	then	then	ADV
ejpam-2623	781	2	r	r	NOUN
ejpam-2623	781	3	is	be	AUX
ejpam-2623	781	4	well	well	ADV
ejpam-2623	781	5	defined	define	VERB
ejpam-2623	781	6	.	.	PUNCT
ejpam-2623	782	1	first	first	ADV
ejpam-2623	782	2	we	we	PRON
ejpam-2623	782	3	need	need	VERB
ejpam-2623	782	4	to	to	PART
ejpam-2623	782	5	show	show	VERB
ejpam-2623	782	6	that	that	SCONJ
ejpam-2623	782	7	r	r	PROPN
ejpam-2623	782	8	∈	∈	PROPN
ejpam-2623	782	9	r.	r.	NOUN
ejpam-2623	782	10	we	we	PRON
ejpam-2623	782	11	have	have	VERB
ejpam-2623	782	12	:	:	PUNCT
ejpam-2623	782	13	r	r	NOUN
ejpam-2623	782	14	6=	6=	NUM
ejpam-2623	782	15	0	0	NUM
ejpam-2623	782	16	,	,	PUNCT
ejpam-2623	782	17	since	since	SCONJ
ejpam-2623	782	18	χ[u(d−	χ[u(d−	PROPN
ejpam-2623	782	19	1)(1−	1)(1−	NUM
ejpam-2623	782	20	x)(x(3d+	x)(x(3d+	PROPN
ejpam-2623	782	21	1	1	NUM
ejpam-2623	782	22	)	)	PUNCT
ejpam-2623	782	23	+	+	NUM
ejpam-2623	782	24	d+	d+	NOUN
ejpam-2623	782	25	3	3	NUM
ejpam-2623	782	26	)	)	PUNCT
ejpam-2623	782	27	]	]	PUNCT
ejpam-2623	783	1	=	=	PUNCT
ejpam-2623	783	2	1	1	NUM
ejpam-2623	783	3	,	,	PUNCT
ejpam-2623	783	4	ur2	ur2	VERB
ejpam-2623	783	5	+	+	CCONJ
ejpam-2623	783	6	1	1	NUM
ejpam-2623	783	7	=	=	NOUN
ejpam-2623	783	8	0⇒	0⇒	NOUN
ejpam-2623	783	9	1	1	NUM
ejpam-2623	784	1	+	+	NOUN
ejpam-2623	784	2	x	x	SYM
ejpam-2623	784	3	=	=	SYM
ejpam-2623	784	4	0	0	NUM
ejpam-2623	784	5	which	which	PRON
ejpam-2623	784	6	is	be	AUX
ejpam-2623	784	7	impossible	impossible	ADJ
ejpam-2623	784	8	,	,	PUNCT
ejpam-2623	784	9	ur2(1−	ur2(1−	X
ejpam-2623	784	10	d)−	d)−	PROPN
ejpam-2623	784	11	(	(	PUNCT
ejpam-2623	784	12	1	1	NUM
ejpam-2623	784	13	+	+	NUM
ejpam-2623	784	14	3d	3d	NUM
ejpam-2623	784	15	)	)	PUNCT
ejpam-2623	785	1	=	=	SYM
ejpam-2623	785	2	0⇒	0⇒	NOUN
ejpam-2623	786	1	4(d−	4(d−	PROPN
ejpam-2623	786	2	1)(d+	1)(d+	NUM
ejpam-2623	786	3	1	1	NUM
ejpam-2623	786	4	)	)	PUNCT
ejpam-2623	786	5	=	=	SYM
ejpam-2623	786	6	0	0	NUM
ejpam-2623	786	7	which	which	PRON
ejpam-2623	786	8	is	be	AUX
ejpam-2623	786	9	impossible	impossible	ADJ
ejpam-2623	786	10	,	,	PUNCT
ejpam-2623	786	11	ur2(1	ur2(1	NOUN
ejpam-2623	787	1	+	+	CCONJ
ejpam-2623	788	1	3d)−	3d)−	NUM
ejpam-2623	788	2	(	(	PUNCT
ejpam-2623	788	3	1−	1−	NUM
ejpam-2623	788	4	d	d	NOUN
ejpam-2623	788	5	)	)	PUNCT
ejpam-2623	789	1	=	=	SYM
ejpam-2623	789	2	0⇒	0⇒	NOUN
ejpam-2623	789	3	x	x	X
ejpam-2623	790	1	=	=	PUNCT
ejpam-2623	790	2	−d+1	−d+1	PROPN
ejpam-2623	790	3	2d	2d	NUM
ejpam-2623	790	4	which	which	PRON
ejpam-2623	790	5	is	be	AUX
ejpam-2623	790	6	impossible	impossible	ADJ
ejpam-2623	790	7	.	.	PUNCT
ejpam-2623	791	1	now	now	ADV
ejpam-2623	791	2	,	,	PUNCT
ejpam-2623	791	3	from	from	ADP
ejpam-2623	791	4	r	r	NOUN
ejpam-2623	791	5	,	,	PUNCT
ejpam-2623	791	6	define	define	VERB
ejpam-2623	791	7	v	v	ADP
ejpam-2623	791	8	,	,	PUNCT
ejpam-2623	791	9	ε	ε	PROPN
ejpam-2623	791	10	,	,	PUNCT
ejpam-2623	791	11	x	x	X
ejpam-2623	791	12	and	and	CCONJ
ejpam-2623	791	13	y	y	PROPN
ejpam-2623	791	14	as	as	ADP
ejpam-2623	791	15	in	in	ADP
ejpam-2623	791	16	theorem	theorem	NOUN
ejpam-2623	791	17	4	4	NUM
ejpam-2623	791	18	.	.	PUNCT
ejpam-2623	792	1	our	our	PRON
ejpam-2623	792	2	objective	objective	NOUN
ejpam-2623	792	3	is	be	AUX
ejpam-2623	792	4	to	to	PART
ejpam-2623	792	5	show	show	VERB
ejpam-2623	792	6	that	that	SCONJ
ejpam-2623	792	7	x	x	NOUN
ejpam-2623	793	1	=	=	PUNCT
ejpam-2623	793	2	x	x	X
ejpam-2623	793	3	and	and	CCONJ
ejpam-2623	793	4	y	y	PROPN
ejpam-2623	793	5	=	=	SYM
ejpam-2623	793	6	y.	y.	NOUN
ejpam-2623	793	7	from	from	ADP
ejpam-2623	793	8	(	(	PUNCT
ejpam-2623	793	9	d	d	PROPN
ejpam-2623	793	10	−	−	PROPN
ejpam-2623	793	11	1)ur2	1)ur2	NUM
ejpam-2623	793	12	−	−	NOUN
ejpam-2623	793	13	(	(	PUNCT
ejpam-2623	793	14	3	3	NUM
ejpam-2623	793	15	+	+	CCONJ
ejpam-2623	793	16	d	d	NOUN
ejpam-2623	793	17	)	)	PUNCT
ejpam-2623	793	18	=	=	SYM
ejpam-2623	794	1	4x(d	4x(d	NOUN
ejpam-2623	795	1	+	+	CCONJ
ejpam-2623	796	1	1)/(1	1)/(1	NUM
ejpam-2623	796	2	−	−	NOUN
ejpam-2623	796	3	x	x	NOUN
ejpam-2623	796	4	)	)	PUNCT
ejpam-2623	796	5	and	and	CCONJ
ejpam-2623	796	6	ur2(d	ur2(d	INTJ
ejpam-2623	796	7	−	−	NOUN
ejpam-2623	796	8	1	1	NUM
ejpam-2623	796	9	)	)	PUNCT
ejpam-2623	796	10	+	+	CCONJ
ejpam-2623	796	11	(	(	PUNCT
ejpam-2623	796	12	1	1	NUM
ejpam-2623	796	13	+	+	NUM
ejpam-2623	796	14	3d	3d	NUM
ejpam-2623	796	15	)	)	PUNCT
ejpam-2623	797	1	=	=	NOUN
ejpam-2623	797	2	4(d	4(d	NUM
ejpam-2623	798	1	+	+	CCONJ
ejpam-2623	798	2	1)/(1	1)/(1	NUM
ejpam-2623	798	3	−	−	NOUN
ejpam-2623	798	4	x	x	NOUN
ejpam-2623	798	5	)	)	PUNCT
ejpam-2623	798	6	,	,	PUNCT
ejpam-2623	798	7	we	we	PRON
ejpam-2623	798	8	deduce	deduce	VERB
ejpam-2623	798	9	v	v	VERB
ejpam-2623	798	10	=	=	PUNCT
ejpam-2623	798	11	x.	x.	NOUN
ejpam-2623	799	1	so	so	ADV
ejpam-2623	799	2	ε	ε	PROPN
ejpam-2623	799	3	=	=	SYM
ejpam-2623	799	4	χ	χ	PROPN
ejpam-2623	799	5	(	(	PUNCT
ejpam-2623	799	6	1−x2	1−x2	NUM
ejpam-2623	799	7	1−dx2	1−dx2	PROPN
ejpam-2623	799	8	)	)	PUNCT
ejpam-2623	799	9	=	=	SYM
ejpam-2623	799	10	1	1	NUM
ejpam-2623	799	11	and	and	CCONJ
ejpam-2623	799	12	x	x	X
ejpam-2623	799	13	=	=	SYM
ejpam-2623	799	14	v	v	X
ejpam-2623	799	15	=	=	PUNCT
ejpam-2623	799	16	x.	x.	NOUN
ejpam-2623	800	1	finally	finally	ADV
ejpam-2623	800	2	we	we	PRON
ejpam-2623	800	3	have	have	VERB
ejpam-2623	800	4	y	y	PROPN
ejpam-2623	800	5	=	=	PUNCT
ejpam-2623	800	6	−ε	−ε	PROPN
ejpam-2623	800	7	√	√	NOUN
ejpam-2623	800	8	1−x2	1−x2	NUM
ejpam-2623	801	1	1−dx2	1−dx2	NUM
ejpam-2623	801	2	=	=	PUNCT
ejpam-2623	801	3	y.	y.	NOUN
ejpam-2623	801	4	•	•	NOUN
ejpam-2623	802	1	if	if	SCONJ
ejpam-2623	802	2	y	y	PROPN
ejpam-2623	802	3	=	=	PUNCT
ejpam-2623	802	4	√	√	PROPN
ejpam-2623	802	5	(	(	PUNCT
ejpam-2623	802	6	1−	1−	NUM
ejpam-2623	802	7	x2)/(1−	x2)/(1−	PROPN
ejpam-2623	802	8	dx2	dx2	PROPN
ejpam-2623	802	9	)	)	PUNCT
ejpam-2623	802	10	,	,	PUNCT
ejpam-2623	802	11	put	put	VERB
ejpam-2623	802	12	r	r	NOUN
ejpam-2623	802	13	=	=	PUNCT
ejpam-2623	802	14	√	√	PROPN
ejpam-2623	802	15	(	(	PUNCT
ejpam-2623	802	16	d−1)(1−x	d−1)(1−x	NOUN
ejpam-2623	802	17	)	)	PUNCT
ejpam-2623	802	18	u[x(3d+1)+d+3	u[x(3d+1)+d+3	PROPN
ejpam-2623	802	19	)	)	PUNCT
ejpam-2623	802	20	]	]	PUNCT
ejpam-2623	802	21	,	,	PUNCT
ejpam-2623	802	22	then	then	ADV
ejpam-2623	802	23	r	r	NOUN
ejpam-2623	802	24	is	be	AUX
ejpam-2623	802	25	well	well	ADV
ejpam-2623	802	26	defined	define	VERB
ejpam-2623	802	27	.	.	PUNCT
ejpam-2623	803	1	as	as	ADP
ejpam-2623	803	2	for	for	ADP
ejpam-2623	803	3	previous	previous	ADJ
ejpam-2623	803	4	case	case	NOUN
ejpam-2623	803	5	,	,	PUNCT
ejpam-2623	803	6	first	first	ADV
ejpam-2623	803	7	,	,	PUNCT
ejpam-2623	803	8	we	we	PRON
ejpam-2623	803	9	need	need	VERB
ejpam-2623	803	10	to	to	PART
ejpam-2623	803	11	prove	prove	VERB
ejpam-2623	803	12	that	that	SCONJ
ejpam-2623	803	13	r	r	PROPN
ejpam-2623	803	14	∈	∈	PROPN
ejpam-2623	803	15	r.	r.	NOUN
ejpam-2623	803	16	we	we	PRON
ejpam-2623	803	17	have	have	VERB
ejpam-2623	803	18	:	:	PUNCT
ejpam-2623	803	19	r	r	NOUN
ejpam-2623	803	20	6=	6=	NUM
ejpam-2623	803	21	0	0	NUM
ejpam-2623	803	22	,	,	PUNCT
ejpam-2623	803	23	since	since	SCONJ
ejpam-2623	803	24	χ[u(d−	χ[u(d−	PROPN
ejpam-2623	803	25	1)(1−	1)(1−	NUM
ejpam-2623	803	26	x)(x(3d+	x)(x(3d+	PROPN
ejpam-2623	803	27	1	1	NUM
ejpam-2623	803	28	)	)	PUNCT
ejpam-2623	804	1	+	+	NUM
ejpam-2623	804	2	d+	d+	NOUN
ejpam-2623	804	3	3	3	NUM
ejpam-2623	804	4	)	)	PUNCT
ejpam-2623	804	5	]	]	PUNCT
ejpam-2623	805	1	=	=	PUNCT
ejpam-2623	805	2	1	1	NUM
ejpam-2623	805	3	,	,	PUNCT
ejpam-2623	805	4	ur2	ur2	VERB
ejpam-2623	805	5	+	+	CCONJ
ejpam-2623	805	6	1	1	NUM
ejpam-2623	805	7	=	=	NOUN
ejpam-2623	805	8	0⇒	0⇒	NOUN
ejpam-2623	805	9	1	1	NUM
ejpam-2623	806	1	+	+	NOUN
ejpam-2623	806	2	x	x	SYM
ejpam-2623	806	3	=	=	SYM
ejpam-2623	806	4	0	0	NUM
ejpam-2623	806	5	which	which	PRON
ejpam-2623	806	6	is	be	AUX
ejpam-2623	806	7	impossible	impossible	ADJ
ejpam-2623	806	8	,	,	PUNCT
ejpam-2623	806	9	ur2(1−	ur2(1−	X
ejpam-2623	806	10	d)−	d)−	PROPN
ejpam-2623	806	11	(	(	PUNCT
ejpam-2623	806	12	1	1	NUM
ejpam-2623	806	13	+	+	NUM
ejpam-2623	806	14	3d	3d	NUM
ejpam-2623	806	15	)	)	PUNCT
ejpam-2623	807	1	=	=	SYM
ejpam-2623	807	2	0⇒	0⇒	NOUN
ejpam-2623	807	3	x	x	X
ejpam-2623	808	1	=	=	PUNCT
ejpam-2623	808	2	−d+1	−d+1	PROPN
ejpam-2623	808	3	2d	2d	NUM
ejpam-2623	808	4	=	=	SYM
ejpam-2623	808	5	0	0	NUM
ejpam-2623	808	6	which	which	PRON
ejpam-2623	808	7	is	be	AUX
ejpam-2623	808	8	impossible	impossible	ADJ
ejpam-2623	808	9	,	,	PUNCT
ejpam-2623	808	10	ur2(1	ur2(1	NOUN
ejpam-2623	809	1	+	+	CCONJ
ejpam-2623	810	1	3d)−	3d)−	NUM
ejpam-2623	810	2	(	(	PUNCT
ejpam-2623	810	3	1−	1−	NUM
ejpam-2623	810	4	d	d	NOUN
ejpam-2623	810	5	)	)	PUNCT
ejpam-2623	810	6	=	=	SYM
ejpam-2623	810	7	0⇒	0⇒	NOUN
ejpam-2623	811	1	4(d−	4(d−	PROPN
ejpam-2623	811	2	1)(d+	1)(d+	NUM
ejpam-2623	811	3	1	1	NUM
ejpam-2623	811	4	)	)	PUNCT
ejpam-2623	811	5	=	=	SYM
ejpam-2623	811	6	0	0	NUM
ejpam-2623	811	7	which	which	PRON
ejpam-2623	811	8	is	be	AUX
ejpam-2623	811	9	impossible	impossible	ADJ
ejpam-2623	811	10	.	.	PUNCT
ejpam-2623	812	1	now	now	ADV
ejpam-2623	812	2	let	let	VERB
ejpam-2623	812	3	us	we	PRON
ejpam-2623	812	4	define	define	VERB
ejpam-2623	812	5	v	v	ADP
ejpam-2623	812	6	,	,	PUNCT
ejpam-2623	812	7	ε	ε	PROPN
ejpam-2623	812	8	,	,	PUNCT
ejpam-2623	812	9	x	x	X
ejpam-2623	812	10	and	and	CCONJ
ejpam-2623	812	11	y	y	PROPN
ejpam-2623	812	12	from	from	ADP
ejpam-2623	812	13	r.	r.	PROPN
ejpam-2623	812	14	replacing	replace	VERB
ejpam-2623	812	15	r	r	NOUN
ejpam-2623	812	16	by	by	ADP
ejpam-2623	812	17	its	its	PRON
ejpam-2623	812	18	value	value	NOUN
ejpam-2623	812	19	in	in	ADP
ejpam-2623	812	20	v	v	NOUN
ejpam-2623	812	21	,	,	PUNCT
ejpam-2623	812	22	we	we	PRON
ejpam-2623	812	23	find	find	VERB
ejpam-2623	812	24	v	v	NOUN
ejpam-2623	812	25	=	=	SYM
ejpam-2623	813	1	−2−	−2−	NUM
ejpam-2623	813	2	x(d+	x(d+	PROPN
ejpam-2623	813	3	1	1	NUM
ejpam-2623	813	4	)	)	PUNCT
ejpam-2623	813	5	d+	d+	NOUN
ejpam-2623	813	6	1	1	NUM
ejpam-2623	814	1	+	+	NUM
ejpam-2623	814	2	2dx	2dx	NUM
ejpam-2623	814	3	and	and	CCONJ
ejpam-2623	814	4	1−	1−	NUM
ejpam-2623	814	5	v2	v2	NOUN
ejpam-2623	814	6	1−	1−	NUM
ejpam-2623	814	7	dv2	dv2	NOUN
ejpam-2623	814	8	=	=	SYM
ejpam-2623	814	9	(	(	PUNCT
ejpam-2623	814	10	d−	d−	PROPN
ejpam-2623	814	11	1)(1	1)(1	NUM
ejpam-2623	814	12	+	+	CCONJ
ejpam-2623	814	13	x)(x(1	x)(x(1	PROPN
ejpam-2623	814	14	+	+	NOUN
ejpam-2623	814	15	3d	3d	NUM
ejpam-2623	814	16	)	)	PUNCT
ejpam-2623	815	1	+	+	NUM
ejpam-2623	815	2	d+	d+	NOUN
ejpam-2623	815	3	3	3	X
ejpam-2623	815	4	)	)	PUNCT
ejpam-2623	815	5	(	(	PUNCT
ejpam-2623	815	6	d−	d−	PROPN
ejpam-2623	815	7	1)2(1−	1)2(1−	PROPN
ejpam-2623	815	8	dx2	dx2	PROPN
ejpam-2623	815	9	)	)	PUNCT
ejpam-2623	815	10	=(	=(	NOUN
ejpam-2623	815	11	(	(	PUNCT
ejpam-2623	815	12	1	1	NUM
ejpam-2623	815	13	+	+	CCONJ
ejpam-2623	815	14	x)(1−	x)(1−	PROPN
ejpam-2623	815	15	x	x	SYM
ejpam-2623	815	16	)	)	PUNCT
ejpam-2623	815	17	1−	1−	NUM
ejpam-2623	815	18	dx2	dx2	PROPN
ejpam-2623	815	19	)	)	PUNCT
ejpam-2623	815	20	(	(	PUNCT
ejpam-2623	815	21	(	(	PUNCT
ejpam-2623	815	22	x(1	x(1	PROPN
ejpam-2623	815	23	+	+	NOUN
ejpam-2623	815	24	3d	3d	NUM
ejpam-2623	815	25	)	)	PUNCT
ejpam-2623	816	1	+	+	NUM
ejpam-2623	816	2	d+	d+	NOUN
ejpam-2623	816	3	3	3	X
ejpam-2623	816	4	)	)	PUNCT
ejpam-2623	816	5	(	(	PUNCT
ejpam-2623	816	6	d−	d−	PROPN
ejpam-2623	816	7	1)(1−	1)(1−	NUM
ejpam-2623	816	8	x	x	NOUN
ejpam-2623	816	9	)	)	PUNCT
ejpam-2623	816	10	)	)	PUNCT
ejpam-2623	816	11	.	.	PUNCT
ejpam-2623	817	1	recall	recall	VERB
ejpam-2623	817	2	that	that	PRON
ejpam-2623	817	3	(	(	PUNCT
ejpam-2623	817	4	x	x	X
ejpam-2623	817	5	,	,	PUNCT
ejpam-2623	817	6	y	y	NOUN
ejpam-2623	817	7	)	)	PUNCT
ejpam-2623	817	8	is	be	AUX
ejpam-2623	817	9	in	in	ADP
ejpam-2623	817	10	ed	ed	NOUN
ejpam-2623	817	11	and	and	CCONJ
ejpam-2623	817	12	that	that	SCONJ
ejpam-2623	817	13	χ	χ	X
ejpam-2623	817	14	(	(	PUNCT
ejpam-2623	817	15	(	(	PUNCT
ejpam-2623	817	16	x(1	x(1	PROPN
ejpam-2623	817	17	+	+	NOUN
ejpam-2623	817	18	3d	3d	NUM
ejpam-2623	817	19	)	)	PUNCT
ejpam-2623	818	1	+	+	NUM
ejpam-2623	818	2	d+	d+	NOUN
ejpam-2623	818	3	3	3	X
ejpam-2623	818	4	)	)	PUNCT
ejpam-2623	818	5	(	(	PUNCT
ejpam-2623	818	6	d−	d−	PROPN
ejpam-2623	818	7	1)(1−	1)(1−	NUM
ejpam-2623	818	8	x	x	NOUN
ejpam-2623	818	9	)	)	PUNCT
ejpam-2623	818	10	)	)	PUNCT
ejpam-2623	819	1	=	=	PUNCT
ejpam-2623	819	2	−1	−1	NOUN
ejpam-2623	819	3	by	by	ADP
ejpam-2623	819	4	hypothesis	hypothesis	NOUN
ejpam-2623	819	5	,	,	PUNCT
ejpam-2623	819	6	thus	thus	ADV
ejpam-2623	819	7	ε	ε	X
ejpam-2623	819	8	=	=	SYM
ejpam-2623	819	9	−1	−1	NOUN
ejpam-2623	819	10	.	.	PUNCT
ejpam-2623	820	1	from	from	ADP
ejpam-2623	820	2	v	v	NOUN
ejpam-2623	820	3	=	=	SYM
ejpam-2623	820	4	−2−	−2−	NUM
ejpam-2623	820	5	x(d+	x(d+	PROPN
ejpam-2623	820	6	1	1	NUM
ejpam-2623	820	7	)	)	PUNCT
ejpam-2623	820	8	d+	d+	NOUN
ejpam-2623	820	9	1	1	NUM
ejpam-2623	820	10	+	+	NUM
ejpam-2623	820	11	2dx	2dx	NUM
ejpam-2623	820	12	,	,	PUNCT
ejpam-2623	820	13	we	we	PRON
ejpam-2623	820	14	have	have	VERB
ejpam-2623	820	15	x	x	NOUN
ejpam-2623	820	16	=	=	SYM
ejpam-2623	820	17	−(v	−(v	NOUN
ejpam-2623	821	1	+	+	X
ejpam-2623	821	2	1)(d+	1)(d+	NUM
ejpam-2623	821	3	1	1	NUM
ejpam-2623	821	4	)	)	PUNCT
ejpam-2623	821	5	+	+	CCONJ
ejpam-2623	821	6	(	(	PUNCT
ejpam-2623	821	7	d−	d−	PROPN
ejpam-2623	821	8	1	1	NUM
ejpam-2623	821	9	)	)	PUNCT
ejpam-2623	821	10	2d(v	2d(v	NOUN
ejpam-2623	822	1	+	+	CCONJ
ejpam-2623	822	2	1	1	X
ejpam-2623	822	3	)	)	PUNCT
ejpam-2623	822	4	+	+	CCONJ
ejpam-2623	822	5	(	(	PUNCT
ejpam-2623	822	6	1−	1−	NUM
ejpam-2623	822	7	d	d	NOUN
ejpam-2623	822	8	)	)	PUNCT
ejpam-2623	822	9	=	=	PUNCT
ejpam-2623	823	1	x.	x.	NOUN
ejpam-2623	823	2	we	we	PRON
ejpam-2623	823	3	deduce	deduce	VERB
ejpam-2623	823	4	that	that	SCONJ
ejpam-2623	823	5	y	y	PROPN
ejpam-2623	823	6	=	=	PUNCT
ejpam-2623	823	7	−ε	−ε	PROPN
ejpam-2623	823	8	√	√	NOUN
ejpam-2623	823	9	1−	1−	NUM
ejpam-2623	824	1	x2	x2	NOUN
ejpam-2623	824	2	1−	1−	NUM
ejpam-2623	824	3	dx2	dx2	PROPN
ejpam-2623	824	4	=	=	PROPN
ejpam-2623	824	5	√	√	PROPN
ejpam-2623	824	6	1−	1−	NUM
ejpam-2623	824	7	x2	x2	NOUN
ejpam-2623	824	8	1−	1−	NUM
ejpam-2623	824	9	dx2	dx2	PROPN
ejpam-2623	824	10	=	=	PROPN
ejpam-2623	824	11	y.	y.	PROPN
ejpam-2623	824	12	thus	thus	ADV
ejpam-2623	824	13	φd(r	φd(r	NOUN
ejpam-2623	824	14	)	)	PUNCT
ejpam-2623	824	15	=	=	PRON
ejpam-2623	824	16	(	(	PUNCT
ejpam-2623	824	17	x	x	X
ejpam-2623	824	18	,	,	PUNCT
ejpam-2623	824	19	y	y	NOUN
ejpam-2623	824	20	)	)	PUNCT
ejpam-2623	824	21	as	as	SCONJ
ejpam-2623	824	22	desired	desire	VERB
ejpam-2623	824	23	.	.	PUNCT
ejpam-2623	825	1	(	(	PUNCT
ejpam-2623	825	2	iii	iii	NOUN
ejpam-2623	825	3	)	)	PUNCT
ejpam-2623	825	4	follows	follow	VERB
ejpam-2623	825	5	from	from	ADP
ejpam-2623	825	6	the	the	DET
ejpam-2623	825	7	previous	previous	ADJ
ejpam-2623	825	8	part	part	NOUN
ejpam-2623	825	9	of	of	ADP
ejpam-2623	825	10	the	the	DET
ejpam-2623	825	11	proof	proof	NOUN
ejpam-2623	825	12	.	.	PUNCT
ejpam-2623	826	1	efficiency	efficiency	NOUN
ejpam-2623	826	2	of	of	ADP
ejpam-2623	826	3	φd	φd	PRON
ejpam-2623	826	4	and	and	CCONJ
ejpam-2623	826	5	φ−1d	φ−1d	VERB
ejpam-2623	826	6	:	:	PUNCT
ejpam-2623	826	7	for	for	ADP
ejpam-2623	826	8	any	any	DET
ejpam-2623	826	9	r	r	NOUN
ejpam-2623	826	10	∈	∈	NOUN
ejpam-2623	826	11	r	r	NOUN
ejpam-2623	826	12	,	,	PUNCT
ejpam-2623	826	13	computing	computing	NOUN
ejpam-2623	826	14	φd(r	φd(r	NOUN
ejpam-2623	826	15	)	)	PUNCT
ejpam-2623	826	16	takes	take	VERB
ejpam-2623	826	17	3	3	NUM
ejpam-2623	826	18	inversions	inversion	NOUN
ejpam-2623	826	19	,	,	PUNCT
ejpam-2623	826	20	one	one	NUM
ejpam-2623	826	21	computation	computation	NOUN
ejpam-2623	826	22	of	of	ADP
ejpam-2623	826	23	χ	χ	NOUN
ejpam-2623	826	24	,	,	PUNCT
ejpam-2623	826	25	one	one	NUM
ejpam-2623	826	26	squareroot	squareroot	NOUN
ejpam-2623	826	27	computation	computation	NOUN
ejpam-2623	826	28	and	and	CCONJ
ejpam-2623	826	29	some	some	DET
ejpam-2623	826	30	multiplications	multiplication	NOUN
ejpam-2623	826	31	.	.	PUNCT
ejpam-2623	827	1	elligator-2	elligator-2	PRON
ejpam-2623	827	2	method	method	NOUN
ejpam-2623	827	3	[	[	X
ejpam-2623	827	4	4	4	NUM
ejpam-2623	827	5	]	]	PUNCT
ejpam-2623	827	6	applied	apply	VERB
ejpam-2623	827	7	to	to	ADP
ejpam-2623	827	8	edwards	edwards	PROPN
ejpam-2623	827	9	n.	n.	PROPN
ejpam-2623	827	10	diarra	diarra	PROPN
ejpam-2623	827	11	,	,	PUNCT
ejpam-2623	827	12	d.	d.	PROPN
ejpam-2623	827	13	sow	sow	PROPN
ejpam-2623	827	14	,	,	PUNCT
ejpam-2623	827	15	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	827	16	.	.	PUNCT
ejpam-2623	827	17	khlil	khlil	PROPN
ejpam-2623	827	18	/	/	SYM
ejpam-2623	827	19	eur	eur	PROPN
ejpam-2623	827	20	.	.	PUNCT
ejpam-2623	828	1	j.	j.	PROPN
ejpam-2623	828	2	pure	pure	PROPN
ejpam-2623	828	3	appl	appl	PROPN
ejpam-2623	828	4	.	.	PROPN
ejpam-2623	828	5	math	math	PROPN
ejpam-2623	828	6	,	,	PUNCT
ejpam-2623	828	7	10	10	NUM
ejpam-2623	828	8	(	(	PUNCT
ejpam-2623	828	9	2	2	NUM
ejpam-2623	828	10	)	)	PUNCT
ejpam-2623	828	11	(	(	PUNCT
ejpam-2623	828	12	2017	2017	NUM
ejpam-2623	828	13	)	)	PUNCT
ejpam-2623	828	14	,	,	PUNCT
ejpam-2623	828	15	363	363	NUM
ejpam-2623	828	16	-	-	SYM
ejpam-2623	828	17	391	391	NUM
ejpam-2623	828	18	383	383	NUM
ejpam-2623	828	19	curves	curve	NOUN
ejpam-2623	828	20	by	by	ADP
ejpam-2623	828	21	using	use	VERB
ejpam-2623	828	22	a	a	DET
ejpam-2623	828	23	birational	birational	ADJ
ejpam-2623	828	24	equivalence	equivalence	NOUN
ejpam-2623	828	25	,	,	PUNCT
ejpam-2623	828	26	takes	take	VERB
ejpam-2623	828	27	5	5	NUM
ejpam-2623	828	28	inversions	inversion	NOUN
ejpam-2623	828	29	,	,	PUNCT
ejpam-2623	828	30	one	one	NUM
ejpam-2623	828	31	computation	computation	NOUN
ejpam-2623	828	32	of	of	ADP
ejpam-2623	828	33	χ	χ	NOUN
ejpam-2623	828	34	,	,	PUNCT
ejpam-2623	828	35	one	one	NUM
ejpam-2623	828	36	square	square	ADJ
ejpam-2623	828	37	-	-	PUNCT
ejpam-2623	828	38	root	root	NOUN
ejpam-2623	828	39	computation	computation	NOUN
ejpam-2623	828	40	and	and	CCONJ
ejpam-2623	828	41	some	some	DET
ejpam-2623	828	42	multiplications	multiplication	NOUN
ejpam-2623	828	43	.	.	PUNCT
ejpam-2623	829	1	one	one	PRON
ejpam-2623	829	2	can	can	AUX
ejpam-2623	829	3	use	use	VERB
ejpam-2623	829	4	euclid	euclid	PROPN
ejpam-2623	829	5	’s	’s	PART
ejpam-2623	829	6	algorithm	algorithm	NOUN
ejpam-2623	829	7	to	to	PART
ejpam-2623	829	8	compute	compute	VERB
ejpam-2623	829	9	the	the	DET
ejpam-2623	829	10	inverses	inverse	NOUN
ejpam-2623	829	11	,	,	PUNCT
ejpam-2623	829	12	or	or	CCONJ
ejpam-2623	829	13	use	use	VERB
ejpam-2623	829	14	an	an	DET
ejpam-2623	829	15	exponentiation	exponentiation	NOUN
ejpam-2623	829	16	;	;	PUNCT
ejpam-2623	829	17	note	note	VERB
ejpam-2623	829	18	that	that	SCONJ
ejpam-2623	829	19	the	the	DET
ejpam-2623	829	20	computation	computation	NOUN
ejpam-2623	829	21	of	of	ADP
ejpam-2623	829	22	χ	χ	NOUN
ejpam-2623	829	23	can	can	AUX
ejpam-2623	829	24	be	be	AUX
ejpam-2623	829	25	replaced	replace	VERB
ejpam-2623	829	26	by	by	ADP
ejpam-2623	829	27	an	an	DET
ejpam-2623	829	28	exponentiation	exponentiation	NOUN
ejpam-2623	829	29	(	(	PUNCT
ejpam-2623	829	30	with	with	ADP
ejpam-2623	829	31	exponent	exponent	NOUN
ejpam-2623	829	32	(	(	PUNCT
ejpam-2623	829	33	q−1)/2	q−1)/2	PROPN
ejpam-2623	829	34	)	)	PUNCT
ejpam-2623	829	35	;	;	PUNCT
ejpam-2623	829	36	and	and	CCONJ
ejpam-2623	829	37	if	if	SCONJ
ejpam-2623	829	38	q	q	PRON
ejpam-2623	829	39	≡	≡	PROPN
ejpam-2623	829	40	3	3	NUM
ejpam-2623	829	41	mod	mod	NOUN
ejpam-2623	829	42	4	4	NUM
ejpam-2623	829	43	,	,	PUNCT
ejpam-2623	829	44	the	the	DET
ejpam-2623	829	45	squareroot	squareroot	NOUN
ejpam-2623	829	46	computation	computation	NOUN
ejpam-2623	829	47	is	be	AUX
ejpam-2623	829	48	also	also	ADV
ejpam-2623	829	49	replaced	replace	VERB
ejpam-2623	829	50	by	by	ADP
ejpam-2623	829	51	an	an	DET
ejpam-2623	829	52	exponentiation	exponentiation	NOUN
ejpam-2623	829	53	.	.	PUNCT
ejpam-2623	830	1	and	and	CCONJ
ejpam-2623	830	2	as	as	ADP
ejpam-2623	830	3	in	in	ADP
ejpam-2623	830	4	[	[	X
ejpam-2623	830	5	4	4	NUM
ejpam-2623	830	6	]	]	PUNCT
ejpam-2623	830	7	,	,	PUNCT
ejpam-2623	830	8	the	the	DET
ejpam-2623	830	9	computation	computation	NOUN
ejpam-2623	830	10	of	of	ADP
ejpam-2623	830	11	χ	χ	NOUN
ejpam-2623	830	12	can	can	AUX
ejpam-2623	830	13	be	be	AUX
ejpam-2623	830	14	combined	combine	VERB
ejpam-2623	830	15	into	into	ADP
ejpam-2623	830	16	the	the	DET
ejpam-2623	830	17	square	square	ADJ
ejpam-2623	830	18	-	-	PUNCT
ejpam-2623	830	19	root	root	NOUN
ejpam-2623	830	20	computation	computation	NOUN
ejpam-2623	830	21	as	as	SCONJ
ejpam-2623	830	22	follows	follow	VERB
ejpam-2623	830	23	.	.	PUNCT
ejpam-2623	831	1	first	first	ADV
ejpam-2623	831	2	compute	compute	VERB
ejpam-2623	831	3	a	a	DET
ejpam-2623	831	4	power	power	NOUN
ejpam-2623	831	5	of	of	ADP
ejpam-2623	831	6	1−v2	1−v2	NUM
ejpam-2623	831	7	1−dv2	1−dv2	NUM
ejpam-2623	831	8	as	as	ADP
ejpam-2623	831	9	above	above	ADV
ejpam-2623	831	10	,	,	PUNCT
ejpam-2623	831	11	obtaining	obtain	VERB
ejpam-2623	831	12	a	a	DET
ejpam-2623	831	13	square	square	ADJ
ejpam-2623	831	14	root	root	NOUN
ejpam-2623	831	15	of	of	ADP
ejpam-2623	831	16	1−	1−	NUM
ejpam-2623	831	17	v2	v2	NOUN
ejpam-2623	831	18	1−	1−	NUM
ejpam-2623	831	19	dv2	dv2	NOUN
ejpam-2623	831	20	if	if	SCONJ
ejpam-2623	831	21	1−	1−	NUM
ejpam-2623	831	22	v2	v2	NOUN
ejpam-2623	831	23	1−	1−	NUM
ejpam-2623	831	24	dv2	dv2	NOUN
ejpam-2623	831	25	is	be	AUX
ejpam-2623	831	26	a	a	DET
ejpam-2623	831	27	square	square	NOUN
ejpam-2623	831	28	.	.	PUNCT
ejpam-2623	832	1	if	if	SCONJ
ejpam-2623	832	2	the	the	DET
ejpam-2623	832	3	square	square	NOUN
ejpam-2623	832	4	of	of	ADP
ejpam-2623	832	5	this	this	DET
ejpam-2623	832	6	power	power	NOUN
ejpam-2623	832	7	turns	turn	VERB
ejpam-2623	832	8	out	out	ADP
ejpam-2623	832	9	to	to	PART
ejpam-2623	832	10	match	match	VERB
ejpam-2623	832	11	1−	1−	NUM
ejpam-2623	832	12	v2	v2	NOUN
ejpam-2623	832	13	1−	1−	NUM
ejpam-2623	832	14	dv2	dv2	NOUN
ejpam-2623	832	15	then	then	ADV
ejpam-2623	832	16	ε	ε	PROPN
ejpam-2623	832	17	=	=	SYM
ejpam-2623	832	18	1	1	NUM
ejpam-2623	832	19	and	and	CCONJ
ejpam-2623	832	20	x	x	X
ejpam-2623	833	1	=	=	NOUN
ejpam-2623	833	2	v.	v.	CCONJ
ejpam-2623	833	3	otherwise	otherwise	ADV
ejpam-2623	833	4	ε	ε	PROPN
ejpam-2623	833	5	=	=	SYM
ejpam-2623	833	6	−1	−1	NOUN
ejpam-2623	833	7	and	and	CCONJ
ejpam-2623	833	8	1−	1−	NUM
ejpam-2623	833	9	x2	x2	NOUN
ejpam-2623	833	10	1−	1−	NUM
ejpam-2623	833	11	dx2	dx2	PROPN
ejpam-2623	833	12	=	=	SYM
ejpam-2623	833	13	ur2	ur2	NOUN
ejpam-2623	833	14	(	(	PUNCT
ejpam-2623	833	15	1−	1−	NUM
ejpam-2623	833	16	v2	v2	NOUN
ejpam-2623	833	17	1−	1−	NUM
ejpam-2623	833	18	dv2	dv2	NOUN
ejpam-2623	833	19	)	)	PUNCT
ejpam-2623	833	20	(	(	PUNCT
ejpam-2623	833	21	by	by	ADP
ejpam-2623	833	22	definition	definition	NOUN
ejpam-2623	833	23	of	of	ADP
ejpam-2623	833	24	ur2	ur2	NOUN
ejpam-2623	833	25	,	,	PUNCT
ejpam-2623	833	26	see	see	VERB
ejpam-2623	833	27	proof	proof	NOUN
ejpam-2623	833	28	of	of	ADP
ejpam-2623	833	29	theorem	theorem	NOUN
ejpam-2623	833	30	4	4	NUM
ejpam-2623	833	31	)	)	PUNCT
ejpam-2623	833	32	;	;	PUNCT
ejpam-2623	833	33	multiply	multiply	VERB
ejpam-2623	833	34	the	the	DET
ejpam-2623	833	35	previous	previous	ADJ
ejpam-2623	833	36	power	power	NOUN
ejpam-2623	833	37	by	by	ADP
ejpam-2623	833	38	r	r	NOUN
ejpam-2623	833	39	and	and	CCONJ
ejpam-2623	833	40	by	by	ADP
ejpam-2623	833	41	a	a	DET
ejpam-2623	833	42	precomputed	precompute	VERB
ejpam-2623	833	43	power	power	NOUN
ejpam-2623	833	44	of	of	ADP
ejpam-2623	833	45	u	u	PRON
ejpam-2623	833	46	to	to	PART
ejpam-2623	833	47	obtain	obtain	VERB
ejpam-2623	833	48	a	a	DET
ejpam-2623	833	49	square	square	ADJ
ejpam-2623	833	50	root	root	NOUN
ejpam-2623	833	51	of	of	ADP
ejpam-2623	833	52	1−	1−	NUM
ejpam-2623	833	53	x2	x2	NOUN
ejpam-2623	833	54	1−	1−	NUM
ejpam-2623	833	55	dx2	dx2	PROPN
ejpam-2623	833	56	.	.	PUNCT
ejpam-2623	834	1	similar	similar	ADJ
ejpam-2623	834	2	comments	comment	NOUN
ejpam-2623	834	3	apply	apply	VERB
ejpam-2623	834	4	to	to	ADP
ejpam-2623	834	5	computing	compute	VERB
ejpam-2623	834	6	φ−1d	φ−1d	NOUN
ejpam-2623	834	7	;	;	PUNCT
ejpam-2623	834	8	there	there	PRON
ejpam-2623	834	9	is	be	VERB
ejpam-2623	834	10	one	one	NUM
ejpam-2623	834	11	square	square	ADJ
ejpam-2623	834	12	-	-	PUNCT
ejpam-2623	834	13	root	root	NOUN
ejpam-2623	834	14	computation	computation	NOUN
ejpam-2623	834	15	,	,	PUNCT
ejpam-2623	834	16	one	one	NUM
ejpam-2623	834	17	inversion	inversion	NOUN
ejpam-2623	834	18	and	and	CCONJ
ejpam-2623	834	19	few	few	ADJ
ejpam-2623	834	20	multiplications	multiplication	NOUN
ejpam-2623	834	21	.	.	PUNCT
ejpam-2623	835	1	also	also	ADV
ejpam-2623	835	2	note	note	VERB
ejpam-2623	835	3	that	that	SCONJ
ejpam-2623	835	4	q	q	NOUN
ejpam-2623	835	5	is	be	AUX
ejpam-2623	835	6	not	not	PART
ejpam-2623	835	7	required	require	VERB
ejpam-2623	835	8	to	to	PART
ejpam-2623	835	9	be	be	AUX
ejpam-2623	835	10	congruent	congruent	ADJ
ejpam-2623	835	11	to	to	ADP
ejpam-2623	835	12	3	3	NUM
ejpam-2623	835	13	modulo	modulo	NOUN
ejpam-2623	835	14	4	4	NUM
ejpam-2623	835	15	to	to	PART
ejpam-2623	835	16	encode	encode	VERB
ejpam-2623	835	17	all	all	DET
ejpam-2623	835	18	points	point	NOUN
ejpam-2623	835	19	of	of	ADP
ejpam-2623	835	20	fq	fq	PROPN
ejpam-2623	835	21	,	,	PUNCT
ejpam-2623	835	22	as	as	SCONJ
ejpam-2623	835	23	said	say	VERB
ejpam-2623	835	24	in	in	ADP
ejpam-2623	835	25	the	the	DET
ejpam-2623	835	26	next	next	ADJ
ejpam-2623	835	27	remark	remark	NOUN
ejpam-2623	835	28	.	.	PUNCT
ejpam-2623	836	1	extension	extension	NOUN
ejpam-2623	836	2	of	of	ADP
ejpam-2623	836	3	φd	φd	PROPN
ejpam-2623	836	4	:	:	PUNCT
ejpam-2623	836	5	our	our	PRON
ejpam-2623	836	6	objective	objective	NOUN
ejpam-2623	836	7	now	now	ADV
ejpam-2623	836	8	is	be	AUX
ejpam-2623	836	9	to	to	PART
ejpam-2623	836	10	extend	extend	VERB
ejpam-2623	836	11	the	the	DET
ejpam-2623	836	12	encoding	encoding	NOUN
ejpam-2623	836	13	function	function	NOUN
ejpam-2623	836	14	φd	φd	VERB
ejpam-2623	836	15	:	:	PUNCT
ejpam-2623	836	16	r	r	X
ejpam-2623	836	17	→	→	SYM
ejpam-2623	836	18	e(fq	e(fq	PROPN
ejpam-2623	836	19	)	)	PUNCT
ejpam-2623	836	20	to	to	PART
ejpam-2623	836	21	φd	φd	VERB
ejpam-2623	836	22	:	:	PUNCT
ejpam-2623	836	23	fq	fq	PROPN
ejpam-2623	836	24	→	→	SYM
ejpam-2623	836	25	e(fq	e(fq	PROPN
ejpam-2623	836	26	)	)	PUNCT
ejpam-2623	836	27	.	.	PUNCT
ejpam-2623	837	1	for	for	ADP
ejpam-2623	837	2	this	this	PRON
ejpam-2623	837	3	,	,	PUNCT
ejpam-2623	837	4	we	we	PRON
ejpam-2623	837	5	put	put	VERB
ejpam-2623	837	6	φd(r	φd(r	NOUN
ejpam-2623	837	7	)	)	PUNCT
ejpam-2623	837	8	=	=	SYM
ejpam-2623	837	9	φd(r	φd(r	NOUN
ejpam-2623	837	10	)	)	PUNCT
ejpam-2623	837	11	∀r	∀r	NOUN
ejpam-2623	837	12	∈	∈	NOUN
ejpam-2623	837	13	r	r	NOUN
ejpam-2623	837	14	and	and	CCONJ
ejpam-2623	837	15	we	we	PRON
ejpam-2623	837	16	must	must	AUX
ejpam-2623	837	17	send	send	VERB
ejpam-2623	837	18	all	all	DET
ejpam-2623	837	19	points	point	NOUN
ejpam-2623	837	20	r	r	NOUN
ejpam-2623	837	21	in	in	ADP
ejpam-2623	837	22	fq	fq	PROPN
ejpam-2623	837	23	\	\	NOUN
ejpam-2623	837	24	r	r	NOUN
ejpam-2623	837	25	to	to	AUX
ejpam-2623	837	26	points	point	NOUN
ejpam-2623	837	27	p	p	PROPN
ejpam-2623	837	28	in	in	ADP
ejpam-2623	837	29	e(fq)\im(φd	e(fq)\im(φd	PROPN
ejpam-2623	837	30	)	)	PUNCT
ejpam-2623	837	31	via	via	ADP
ejpam-2623	837	32	φd	φd	PROPN
ejpam-2623	837	33	.	.	PROPN
ejpam-2623	837	34	for	for	ADP
ejpam-2623	837	35	constructing	construct	VERB
ejpam-2623	837	36	such	such	DET
ejpam-2623	837	37	a	a	DET
ejpam-2623	837	38	point	point	NOUN
ejpam-2623	837	39	p	p	NOUN
ejpam-2623	837	40	in	in	ADP
ejpam-2623	837	41	e(fq)\im(φd	e(fq)\im(φd	PROPN
ejpam-2623	837	42	)	)	PUNCT
ejpam-2623	837	43	,	,	PUNCT
ejpam-2623	837	44	we	we	PRON
ejpam-2623	837	45	use	use	VERB
ejpam-2623	837	46	the	the	DET
ejpam-2623	837	47	characterization	characterization	NOUN
ejpam-2623	837	48	of	of	ADP
ejpam-2623	837	49	the	the	DET
ejpam-2623	837	50	encoding	encoding	NOUN
ejpam-2623	837	51	φd	φd	VERB
ejpam-2623	837	52	(	(	PUNCT
ejpam-2623	837	53	see	see	VERB
ejpam-2623	837	54	proposition	proposition	NOUN
ejpam-2623	837	55	7	7	NUM
ejpam-2623	837	56	)	)	PUNCT
ejpam-2623	837	57	.	.	PUNCT
ejpam-2623	838	1	furthermore	furthermore	ADV
ejpam-2623	838	2	,	,	PUNCT
ejpam-2623	838	3	if	if	SCONJ
ejpam-2623	838	4	r	r	NOUN
ejpam-2623	838	5	,	,	PUNCT
ejpam-2623	838	6	r′	r′	PROPN
ejpam-2623	838	7	∈	∈	PROPN
ejpam-2623	838	8	fq	fq	PROPN
ejpam-2623	838	9	\r	\r	X
ejpam-2623	838	10	,	,	PUNCT
ejpam-2623	838	11	with	with	ADP
ejpam-2623	838	12	r	r	PROPN
ejpam-2623	838	13	6=	6=	SYM
ejpam-2623	838	14	r′	r′	PROPN
ejpam-2623	838	15	,	,	PUNCT
ejpam-2623	838	16	we	we	PRON
ejpam-2623	838	17	need	need	VERB
ejpam-2623	838	18	to	to	PART
ejpam-2623	838	19	have	have	VERB
ejpam-2623	838	20	φd(r	φd(r	NOUN
ejpam-2623	838	21	)	)	PUNCT
ejpam-2623	838	22	6=	6=	ADP
ejpam-2623	838	23	φd(r	φd(r	NUM
ejpam-2623	838	24	′	′	NOUN
ejpam-2623	838	25	)	)	PUNCT
ejpam-2623	838	26	in	in	ADP
ejpam-2623	838	27	order	order	NOUN
ejpam-2623	838	28	to	to	PART
ejpam-2623	838	29	preserve	preserve	VERB
ejpam-2623	838	30	the	the	DET
ejpam-2623	838	31	almost	almost	ADV
ejpam-2623	838	32	-	-	PUNCT
ejpam-2623	838	33	injectivity	injectivity	NOUN
ejpam-2623	838	34	of	of	ADP
ejpam-2623	838	35	φd	φd	PROPN
ejpam-2623	838	36	.	.	PUNCT
ejpam-2623	839	1	we	we	PRON
ejpam-2623	839	2	can	can	AUX
ejpam-2623	839	3	extend	extend	VERB
ejpam-2623	839	4	the	the	DET
ejpam-2623	839	5	definition	definition	NOUN
ejpam-2623	839	6	of	of	ADP
ejpam-2623	839	7	φd	φd	PROPN
ejpam-2623	839	8	on	on	ADP
ejpam-2623	839	9	fq	fq	PROPN
ejpam-2623	839	10	as	as	SCONJ
ejpam-2623	839	11	follows	follow	VERB
ejpam-2623	839	12	.	.	PUNCT
ejpam-2623	840	1	(	(	PUNCT
ejpam-2623	840	2	i	i	NOUN
ejpam-2623	840	3	)	)	PUNCT
ejpam-2623	840	4	if	if	SCONJ
ejpam-2623	840	5	χ((1	χ((1	PROPN
ejpam-2623	840	6	−	−	PROPN
ejpam-2623	840	7	d)(1	d)(1	X
ejpam-2623	840	8	+	+	SYM
ejpam-2623	840	9	3d	3d	NUM
ejpam-2623	840	10	)	)	PUNCT
ejpam-2623	840	11	)	)	PUNCT
ejpam-2623	841	1	=	=	PUNCT
ejpam-2623	841	2	1	1	NUM
ejpam-2623	841	3	then	then	ADV
ejpam-2623	841	4	r	r	NOUN
ejpam-2623	841	5	=	=	NOUN
ejpam-2623	841	6	f∗q	f∗q	NOUN
ejpam-2623	841	7	when	when	SCONJ
ejpam-2623	841	8	q	q	PROPN
ejpam-2623	841	9	≡	≡	PROPN
ejpam-2623	841	10	1	1	NUM
ejpam-2623	841	11	mod	mod	NOUN
ejpam-2623	841	12	4	4	NUM
ejpam-2623	841	13	and	and	CCONJ
ejpam-2623	841	14	r	r	NOUN
ejpam-2623	841	15	=	=	SYM
ejpam-2623	841	16	f∗q	f∗q	X
ejpam-2623	841	17	\	\	NOUN
ejpam-2623	841	18	{	{	PUNCT
ejpam-2623	841	19	±	±	NOUN
ejpam-2623	841	20	√	√	NUM
ejpam-2623	841	21	−1	−1	NOUN
ejpam-2623	841	22	u	u	PROPN
ejpam-2623	841	23	}	}	PUNCT
ejpam-2623	841	24	when	when	SCONJ
ejpam-2623	841	25	q	q	PROPN
ejpam-2623	841	26	≡	≡	PROPN
ejpam-2623	841	27	3	3	NUM
ejpam-2623	841	28	mod	mod	NOUN
ejpam-2623	841	29	4	4	NUM
ejpam-2623	841	30	,	,	PUNCT
ejpam-2623	841	31	thus	thus	ADV
ejpam-2623	841	32	we	we	PRON
ejpam-2623	841	33	need	need	VERB
ejpam-2623	841	34	1	1	NUM
ejpam-2623	841	35	and	and	CCONJ
ejpam-2623	841	36	2	2	NUM
ejpam-2623	841	37	points	point	NOUN
ejpam-2623	841	38	in	in	ADP
ejpam-2623	841	39	e(fq	e(fq	PROPN
ejpam-2623	841	40	)	)	PUNCT
ejpam-2623	841	41	\	\	PROPN
ejpam-2623	841	42	im(φd	im(φd	PROPN
ejpam-2623	841	43	)	)	PUNCT
ejpam-2623	841	44	respectively	respectively	ADV
ejpam-2623	841	45	in	in	ADP
ejpam-2623	841	46	order	order	NOUN
ejpam-2623	841	47	to	to	PART
ejpam-2623	841	48	extend	extend	VERB
ejpam-2623	841	49	φ4	φ4	NOUN
ejpam-2623	841	50	.	.	PUNCT
ejpam-2623	842	1	since	since	SCONJ
ejpam-2623	842	2	(	(	PUNCT
ejpam-2623	842	3	1	1	NUM
ejpam-2623	842	4	,	,	PUNCT
ejpam-2623	842	5	0	0	NUM
ejpam-2623	842	6	)	)	PUNCT
ejpam-2623	842	7	and	and	CCONJ
ejpam-2623	842	8	(	(	PUNCT
ejpam-2623	842	9	−1	−1	NOUN
ejpam-2623	842	10	,	,	PUNCT
ejpam-2623	842	11	0	0	NUM
ejpam-2623	842	12	)	)	PUNCT
ejpam-2623	842	13	are	be	AUX
ejpam-2623	842	14	in	in	ADP
ejpam-2623	842	15	e(fq	e(fq	PROPN
ejpam-2623	842	16	)	)	PUNCT
ejpam-2623	842	17	\	\	PROPN
ejpam-2623	842	18	im(φd	im(φd	PROPN
ejpam-2623	842	19	)	)	PUNCT
ejpam-2623	842	20	by	by	ADP
ejpam-2623	842	21	the	the	DET
ejpam-2623	842	22	above	above	ADJ
ejpam-2623	842	23	characterization	characterization	NOUN
ejpam-2623	842	24	of	of	ADP
ejpam-2623	842	25	im(φd	im(φd	PROPN
ejpam-2623	842	26	)	)	PUNCT
ejpam-2623	842	27	,	,	PUNCT
ejpam-2623	842	28	then	then	ADV
ejpam-2623	842	29	we	we	PRON
ejpam-2623	842	30	propose	propose	VERB
ejpam-2623	842	31	the	the	DET
ejpam-2623	842	32	following	following	NOUN
ejpam-2623	842	33	:	:	PUNCT
ejpam-2623	842	34	(	(	PUNCT
ejpam-2623	842	35	a	a	X
ejpam-2623	842	36	)	)	PUNCT
ejpam-2623	842	37	if	if	SCONJ
ejpam-2623	842	38	q	q	PRON
ejpam-2623	842	39	≡	≡	PROPN
ejpam-2623	842	40	1	1	NUM
ejpam-2623	842	41	mod	mod	NOUN
ejpam-2623	842	42	4	4	NUM
ejpam-2623	842	43	:	:	PUNCT
ejpam-2623	842	44	put	put	VERB
ejpam-2623	842	45	φd(0	φd(0	PRON
ejpam-2623	842	46	)	)	PUNCT
ejpam-2623	842	47	=	=	PUNCT
ejpam-2623	842	48	(	(	PUNCT
ejpam-2623	842	49	1	1	NUM
ejpam-2623	842	50	,	,	PUNCT
ejpam-2623	842	51	0	0	NUM
ejpam-2623	842	52	)	)	PUNCT
ejpam-2623	842	53	.	.	PUNCT
ejpam-2623	843	1	(	(	PUNCT
ejpam-2623	843	2	b	b	X
ejpam-2623	843	3	)	)	PUNCT
ejpam-2623	843	4	if	if	SCONJ
ejpam-2623	843	5	q	q	PRON
ejpam-2623	843	6	≡	≡	PROPN
ejpam-2623	843	7	3	3	NUM
ejpam-2623	843	8	mod	mod	NOUN
ejpam-2623	843	9	4	4	NUM
ejpam-2623	843	10	:	:	PUNCT
ejpam-2623	843	11	put	put	VERB
ejpam-2623	843	12	φd(0	φd(0	PRON
ejpam-2623	843	13	)	)	PUNCT
ejpam-2623	843	14	=	=	PUNCT
ejpam-2623	844	1	(	(	PUNCT
ejpam-2623	844	2	1	1	NUM
ejpam-2623	844	3	,	,	PUNCT
ejpam-2623	844	4	0	0	NUM
ejpam-2623	844	5	)	)	PUNCT
ejpam-2623	844	6	and	and	CCONJ
ejpam-2623	844	7	φ4(±	φ4(±	NOUN
ejpam-2623	844	8	√	√	NUM
ejpam-2623	844	9	−1	−1	NOUN
ejpam-2623	844	10	u	u	NOUN
ejpam-2623	844	11	)	)	PUNCT
ejpam-2623	844	12	=	=	SYM
ejpam-2623	844	13	(	(	PUNCT
ejpam-2623	844	14	−1	−1	NOUN
ejpam-2623	844	15	,	,	PUNCT
ejpam-2623	844	16	0	0	NUM
ejpam-2623	844	17	)	)	PUNCT
ejpam-2623	844	18	.	.	PUNCT
ejpam-2623	845	1	(	(	PUNCT
ejpam-2623	845	2	ii	ii	NOUN
ejpam-2623	845	3	)	)	PUNCT
ejpam-2623	845	4	if	if	SCONJ
ejpam-2623	845	5	χ((1	χ((1	PROPN
ejpam-2623	845	6	−	−	PROPN
ejpam-2623	845	7	d)(1	d)(1	X
ejpam-2623	846	1	+	+	SYM
ejpam-2623	846	2	3d	3d	NUM
ejpam-2623	846	3	)	)	PUNCT
ejpam-2623	846	4	)	)	PUNCT
ejpam-2623	847	1	=	=	PUNCT
ejpam-2623	848	1	−1	−1	NOUN
ejpam-2623	848	2	then	then	ADV
ejpam-2623	848	3	r	r	NOUN
ejpam-2623	848	4	=	=	SYM
ejpam-2623	848	5	f∗q	f∗q	X
ejpam-2623	848	6	\	\	NOUN
ejpam-2623	848	7	{	{	PUNCT
ejpam-2623	848	8	±	±	NUM
ejpam-2623	848	9	√	√	NOUN
ejpam-2623	848	10	1−d	1−d	NUM
ejpam-2623	849	1	u(1	u(1	PROPN
ejpam-2623	849	2	+	+	NOUN
ejpam-2623	849	3	3d	3d	NUM
ejpam-2623	849	4	)	)	PUNCT
ejpam-2623	849	5	,	,	PUNCT
ejpam-2623	849	6	±	±	NOUN
ejpam-2623	850	1	√	√	NOUN
ejpam-2623	850	2	1	1	NUM
ejpam-2623	850	3	+	+	SYM
ejpam-2623	850	4	3d	3d	PROPN
ejpam-2623	850	5	u(1−d	u(1−d	PROPN
ejpam-2623	850	6	)	)	PUNCT
ejpam-2623	850	7	}	}	PUNCT
ejpam-2623	851	1	when	when	SCONJ
ejpam-2623	851	2	q	q	PRON
ejpam-2623	851	3	≡	≡	PROPN
ejpam-2623	851	4	1	1	NUM
ejpam-2623	851	5	mod	mod	NOUN
ejpam-2623	851	6	4	4	NUM
ejpam-2623	851	7	and	and	CCONJ
ejpam-2623	851	8	r	r	NOUN
ejpam-2623	851	9	=	=	SYM
ejpam-2623	851	10	f∗q	f∗q	X
ejpam-2623	851	11	\	\	NOUN
ejpam-2623	851	12	{	{	PUNCT
ejpam-2623	851	13	±	±	NOUN
ejpam-2623	851	14	√	√	NUM
ejpam-2623	851	15	−1	−1	NOUN
ejpam-2623	851	16	u	u	PROPN
ejpam-2623	851	17	,	,	PUNCT
ejpam-2623	851	18	±	±	NOUN
ejpam-2623	851	19	√	√	NOUN
ejpam-2623	851	20	1−d	1−d	NUM
ejpam-2623	852	1	u(1	u(1	PROPN
ejpam-2623	852	2	+	+	NOUN
ejpam-2623	852	3	3d	3d	NUM
ejpam-2623	852	4	)	)	PUNCT
ejpam-2623	852	5	,	,	PUNCT
ejpam-2623	852	6	±	±	NOUN
ejpam-2623	853	1	√	√	NOUN
ejpam-2623	853	2	1	1	NUM
ejpam-2623	853	3	+	+	SYM
ejpam-2623	853	4	3d	3d	PROPN
ejpam-2623	853	5	u(1−d	u(1−d	PROPN
ejpam-2623	853	6	)	)	PUNCT
ejpam-2623	853	7	}	}	PUNCT
ejpam-2623	854	1	when	when	SCONJ
ejpam-2623	854	2	q	q	PROPN
ejpam-2623	854	3	≡	≡	PROPN
ejpam-2623	854	4	3	3	NUM
ejpam-2623	854	5	mod	mod	NOUN
ejpam-2623	854	6	4	4	NUM
ejpam-2623	854	7	,	,	PUNCT
ejpam-2623	854	8	thus	thus	ADV
ejpam-2623	854	9	we	we	PRON
ejpam-2623	854	10	need	need	VERB
ejpam-2623	854	11	3	3	NUM
ejpam-2623	854	12	and	and	CCONJ
ejpam-2623	854	13	4	4	NUM
ejpam-2623	854	14	points	point	NOUN
ejpam-2623	854	15	in	in	ADP
ejpam-2623	854	16	e(fq)\	e(fq)\	PROPN
ejpam-2623	854	17	im(φd	im(φd	PROPN
ejpam-2623	854	18	)	)	PUNCT
ejpam-2623	854	19	respectively	respectively	ADV
ejpam-2623	854	20	in	in	ADP
ejpam-2623	854	21	order	order	NOUN
ejpam-2623	854	22	to	to	PART
ejpam-2623	854	23	extend	extend	VERB
ejpam-2623	854	24	φ4	φ4	NOUN
ejpam-2623	854	25	.	.	PUNCT
ejpam-2623	855	1	since	since	SCONJ
ejpam-2623	855	2	(	(	PUNCT
ejpam-2623	855	3	1	1	NUM
ejpam-2623	855	4	,	,	PUNCT
ejpam-2623	855	5	0	0	NUM
ejpam-2623	855	6	)	)	PUNCT
ejpam-2623	855	7	and	and	CCONJ
ejpam-2623	855	8	(	(	PUNCT
ejpam-2623	855	9	−1	−1	NOUN
ejpam-2623	855	10	,	,	PUNCT
ejpam-2623	855	11	0	0	NUM
ejpam-2623	855	12	)	)	PUNCT
ejpam-2623	855	13	are	be	AUX
ejpam-2623	855	14	in	in	ADP
ejpam-2623	855	15	e(fq	e(fq	PROPN
ejpam-2623	855	16	)	)	PUNCT
ejpam-2623	855	17	\	\	PROPN
ejpam-2623	855	18	im(φd	im(φd	PROPN
ejpam-2623	855	19	)	)	PUNCT
ejpam-2623	855	20	by	by	ADP
ejpam-2623	855	21	the	the	DET
ejpam-2623	855	22	above	above	ADJ
ejpam-2623	855	23	characterization	characterization	NOUN
ejpam-2623	855	24	of	of	ADP
ejpam-2623	855	25	im(φd	im(φd	PROPN
ejpam-2623	855	26	)	)	PUNCT
ejpam-2623	855	27	,	,	PUNCT
ejpam-2623	855	28	then	then	ADV
ejpam-2623	855	29	we	we	PRON
ejpam-2623	855	30	need	need	VERB
ejpam-2623	855	31	two	two	NUM
ejpam-2623	855	32	other	other	ADJ
ejpam-2623	855	33	points	point	NOUN
ejpam-2623	855	34	in	in	ADP
ejpam-2623	855	35	e(fq	e(fq	PROPN
ejpam-2623	855	36	)	)	PUNCT
ejpam-2623	855	37	\	\	PROPN
ejpam-2623	855	38	im(φd	im(φd	PROPN
ejpam-2623	855	39	)	)	PUNCT
ejpam-2623	855	40	.	.	PUNCT
ejpam-2623	856	1	there	there	PRON
ejpam-2623	856	2	exist	exist	VERB
ejpam-2623	856	3	different	different	ADJ
ejpam-2623	856	4	methods	method	NOUN
ejpam-2623	856	5	for	for	ADP
ejpam-2623	856	6	doing	do	VERB
ejpam-2623	856	7	this	this	PRON
ejpam-2623	856	8	.	.	PUNCT
ejpam-2623	857	1	we	we	PRON
ejpam-2623	857	2	propose	propose	VERB
ejpam-2623	857	3	in	in	ADP
ejpam-2623	857	4	the	the	DET
ejpam-2623	857	5	following	following	NOUN
ejpam-2623	857	6	at	at	ADV
ejpam-2623	857	7	least	least	ADV
ejpam-2623	857	8	two	two	NUM
ejpam-2623	857	9	examples	example	NOUN
ejpam-2623	857	10	.	.	PUNCT
ejpam-2623	858	1	(	(	PUNCT
ejpam-2623	858	2	a	a	X
ejpam-2623	858	3	)	)	PUNCT
ejpam-2623	858	4	example	example	NOUN
ejpam-2623	858	5	1	1	NUM
ejpam-2623	858	6	:	:	PUNCT
ejpam-2623	858	7	if	if	SCONJ
ejpam-2623	858	8	χ((d	χ((d	NOUN
ejpam-2623	858	9	−	−	PROPN
ejpam-2623	859	1	1)(d	1)(d	NUM
ejpam-2623	859	2	+	+	CCONJ
ejpam-2623	859	3	3	3	NUM
ejpam-2623	859	4	)	)	PUNCT
ejpam-2623	859	5	)	)	PUNCT
ejpam-2623	860	1	=	=	SYM
ejpam-2623	860	2	1	1	NUM
ejpam-2623	860	3	,	,	PUNCT
ejpam-2623	860	4	then	then	ADV
ejpam-2623	860	5	(	(	PUNCT
ejpam-2623	860	6	0	0	NUM
ejpam-2623	860	7	,	,	PUNCT
ejpam-2623	860	8	1	1	NUM
ejpam-2623	860	9	)	)	PUNCT
ejpam-2623	860	10	,	,	PUNCT
ejpam-2623	860	11	(	(	PUNCT
ejpam-2623	860	12	0,−1	0,−1	NUM
ejpam-2623	860	13	)	)	PUNCT
ejpam-2623	860	14	∈	∈	PROPN
ejpam-2623	860	15	e(fq	e(fq	PROPN
ejpam-2623	860	16	)	)	PUNCT
ejpam-2623	860	17	\	\	PROPN
ejpam-2623	860	18	im(φd	im(φd	PROPN
ejpam-2623	860	19	)	)	PUNCT
ejpam-2623	860	20	,	,	PUNCT
ejpam-2623	860	21	therefore	therefore	ADV
ejpam-2623	860	22	,	,	PUNCT
ejpam-2623	860	23	we	we	PRON
ejpam-2623	860	24	choose	choose	VERB
ejpam-2623	860	25	:	:	PUNCT
ejpam-2623	860	26	n.	n.	PROPN
ejpam-2623	860	27	diarra	diarra	PROPN
ejpam-2623	860	28	,	,	PUNCT
ejpam-2623	860	29	d.	d.	PROPN
ejpam-2623	860	30	sow	sow	PROPN
ejpam-2623	860	31	,	,	PUNCT
ejpam-2623	860	32	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	860	33	.	.	PUNCT
ejpam-2623	860	34	khlil	khlil	PROPN
ejpam-2623	860	35	/	/	SYM
ejpam-2623	860	36	eur	eur	PROPN
ejpam-2623	860	37	.	.	PUNCT
ejpam-2623	861	1	j.	j.	PROPN
ejpam-2623	861	2	pure	pure	PROPN
ejpam-2623	861	3	appl	appl	PROPN
ejpam-2623	861	4	.	.	PROPN
ejpam-2623	861	5	math	math	PROPN
ejpam-2623	861	6	,	,	PUNCT
ejpam-2623	861	7	10	10	NUM
ejpam-2623	861	8	(	(	PUNCT
ejpam-2623	861	9	2	2	NUM
ejpam-2623	861	10	)	)	PUNCT
ejpam-2623	861	11	(	(	PUNCT
ejpam-2623	861	12	2017	2017	NUM
ejpam-2623	861	13	)	)	PUNCT
ejpam-2623	861	14	,	,	PUNCT
ejpam-2623	861	15	363	363	NUM
ejpam-2623	861	16	-	-	SYM
ejpam-2623	861	17	391	391	NUM
ejpam-2623	861	18	384	384	NUM
ejpam-2623	861	19	i.	i.	NOUN
ejpam-2623	861	20	φd(0	φd(0	PROPN
ejpam-2623	861	21	)	)	PUNCT
ejpam-2623	861	22	=	=	PUNCT
ejpam-2623	861	23	(	(	PUNCT
ejpam-2623	861	24	1	1	NUM
ejpam-2623	861	25	,	,	PUNCT
ejpam-2623	861	26	0	0	NUM
ejpam-2623	861	27	)	)	PUNCT
ejpam-2623	861	28	,	,	PUNCT
ejpam-2623	861	29	φ4	φ4	NOUN
ejpam-2623	861	30	(	(	PUNCT
ejpam-2623	861	31	±	±	NOUN
ejpam-2623	861	32	√	√	NOUN
ejpam-2623	861	33	1−d	1−d	NUM
ejpam-2623	862	1	u(1	u(1	PROPN
ejpam-2623	862	2	+	+	NOUN
ejpam-2623	862	3	3d	3d	NUM
ejpam-2623	862	4	)	)	PUNCT
ejpam-2623	862	5	)	)	PUNCT
ejpam-2623	863	1	=	=	PUNCT
ejpam-2623	863	2	(	(	PUNCT
ejpam-2623	863	3	0,−1	0,−1	PROPN
ejpam-2623	863	4	)	)	PUNCT
ejpam-2623	863	5	and	and	CCONJ
ejpam-2623	863	6	φ4	φ4	PROPN
ejpam-2623	863	7	(	(	PUNCT
ejpam-2623	863	8	±	±	NOUN
ejpam-2623	863	9	√	√	PROPN
ejpam-2623	863	10	1	1	NUM
ejpam-2623	863	11	+	+	SYM
ejpam-2623	863	12	3d	3d	PROPN
ejpam-2623	863	13	u(1−d	u(1−d	NOUN
ejpam-2623	863	14	)	)	PUNCT
ejpam-2623	863	15	)	)	PUNCT
ejpam-2623	864	1	=	=	PUNCT
ejpam-2623	864	2	(	(	PUNCT
ejpam-2623	864	3	0	0	NUM
ejpam-2623	864	4	,	,	PUNCT
ejpam-2623	864	5	1	1	NUM
ejpam-2623	864	6	)	)	PUNCT
ejpam-2623	864	7	,	,	PUNCT
ejpam-2623	864	8	when	when	SCONJ
ejpam-2623	864	9	q	q	PROPN
ejpam-2623	864	10	≡	≡	PROPN
ejpam-2623	864	11	1	1	NUM
ejpam-2623	864	12	mod	mod	PROPN
ejpam-2623	864	13	4	4	NUM
ejpam-2623	864	14	.	.	PUNCT
ejpam-2623	864	15	ii	ii	PROPN
ejpam-2623	864	16	.	.	PUNCT
ejpam-2623	865	1	φd(0	φd(0	X
ejpam-2623	865	2	)	)	PUNCT
ejpam-2623	866	1	=	=	SYM
ejpam-2623	866	2	(	(	PUNCT
ejpam-2623	866	3	1	1	NUM
ejpam-2623	866	4	,	,	PUNCT
ejpam-2623	866	5	0	0	NUM
ejpam-2623	866	6	)	)	PUNCT
ejpam-2623	866	7	,	,	PUNCT
ejpam-2623	866	8	φ4(±	φ4(±	NOUN
ejpam-2623	866	9	√	√	NUM
ejpam-2623	866	10	−1	−1	NOUN
ejpam-2623	866	11	/	/	SYM
ejpam-2623	866	12	u	u	NOUN
ejpam-2623	866	13	)	)	PUNCT
ejpam-2623	866	14	=	=	SYM
ejpam-2623	866	15	(	(	PUNCT
ejpam-2623	866	16	−1	−1	NOUN
ejpam-2623	866	17	,	,	PUNCT
ejpam-2623	866	18	0	0	NUM
ejpam-2623	866	19	)	)	PUNCT
ejpam-2623	866	20	,	,	PUNCT
ejpam-2623	866	21	φ4	φ4	NOUN
ejpam-2623	866	22	(	(	PUNCT
ejpam-2623	866	23	±	±	NOUN
ejpam-2623	866	24	√	√	NOUN
ejpam-2623	866	25	1−d	1−d	NUM
ejpam-2623	867	1	u(1	u(1	PROPN
ejpam-2623	867	2	+	+	NOUN
ejpam-2623	867	3	3d	3d	NUM
ejpam-2623	867	4	)	)	PUNCT
ejpam-2623	867	5	)	)	PUNCT
ejpam-2623	868	1	=	=	PUNCT
ejpam-2623	868	2	(	(	PUNCT
ejpam-2623	868	3	0,−1	0,−1	PROPN
ejpam-2623	868	4	)	)	PUNCT
ejpam-2623	868	5	and	and	CCONJ
ejpam-2623	868	6	φ4	φ4	PROPN
ejpam-2623	868	7	(	(	PUNCT
ejpam-2623	868	8	±	±	NOUN
ejpam-2623	868	9	√	√	PROPN
ejpam-2623	868	10	1	1	NUM
ejpam-2623	868	11	+	+	SYM
ejpam-2623	868	12	3d	3d	PROPN
ejpam-2623	868	13	u(1−d	u(1−d	NOUN
ejpam-2623	868	14	)	)	PUNCT
ejpam-2623	868	15	)	)	PUNCT
ejpam-2623	869	1	=	=	PUNCT
ejpam-2623	869	2	(	(	PUNCT
ejpam-2623	869	3	0	0	NUM
ejpam-2623	869	4	,	,	PUNCT
ejpam-2623	869	5	1	1	NUM
ejpam-2623	869	6	)	)	PUNCT
ejpam-2623	869	7	when	when	SCONJ
ejpam-2623	869	8	q	q	PROPN
ejpam-2623	869	9	≡	≡	PROPN
ejpam-2623	869	10	3	3	NUM
ejpam-2623	869	11	mod	mod	NOUN
ejpam-2623	869	12	4	4	X
ejpam-2623	869	13	.	.	PUNCT
ejpam-2623	869	14	(	(	PUNCT
ejpam-2623	869	15	b	b	X
ejpam-2623	869	16	)	)	PUNCT
ejpam-2623	869	17	example	example	NOUN
ejpam-2623	869	18	2	2	NUM
ejpam-2623	869	19	:	:	PUNCT
ejpam-2623	869	20	if	if	SCONJ
ejpam-2623	869	21	χ(−2(1	χ(−2(1	PROPN
ejpam-2623	869	22	+	+	NUM
ejpam-2623	869	23	d	d	NOUN
ejpam-2623	869	24	)	)	PUNCT
ejpam-2623	869	25	)	)	PUNCT
ejpam-2623	870	1	=	=	SYM
ejpam-2623	870	2	1	1	NUM
ejpam-2623	870	3	,	,	PUNCT
ejpam-2623	870	4	then	then	ADV
ejpam-2623	870	5	(	(	PUNCT
ejpam-2623	870	6	−	−	PROPN
ejpam-2623	870	7	d+3	d+3	PROPN
ejpam-2623	870	8	1	1	NUM
ejpam-2623	870	9	+	+	NOUN
ejpam-2623	870	10	3d	3d	NOUN
ejpam-2623	870	11	,	,	PUNCT
ejpam-2623	870	12	2	2	NUM
ejpam-2623	870	13	√	√	NUM
ejpam-2623	870	14	−2(d+	−2(d+	VERB
ejpam-2623	870	15	1)/(d−	1)/(d−	NUM
ejpam-2623	870	16	1	1	NUM
ejpam-2623	870	17	)	)	PUNCT
ejpam-2623	870	18	)	)	PUNCT
ejpam-2623	870	19	,	,	PUNCT
ejpam-2623	870	20	(	(	PUNCT
ejpam-2623	870	21	−	−	PROPN
ejpam-2623	870	22	d+3	d+3	PROPN
ejpam-2623	870	23	1	1	NUM
ejpam-2623	870	24	+	+	NOUN
ejpam-2623	870	25	3d	3d	NOUN
ejpam-2623	870	26	,	,	PUNCT
ejpam-2623	870	27	−2	−2	NOUN
ejpam-2623	870	28	√	√	PROPN
ejpam-2623	870	29	−2(d+	−2(d+	VERB
ejpam-2623	870	30	1)/(d−	1)/(d−	NUM
ejpam-2623	870	31	1	1	NUM
ejpam-2623	870	32	)	)	PUNCT
ejpam-2623	870	33	)	)	PUNCT
ejpam-2623	871	1	∈	∈	PROPN
ejpam-2623	871	2	e(fq	e(fq	PROPN
ejpam-2623	871	3	)	)	PUNCT
ejpam-2623	871	4	\	\	PROPN
ejpam-2623	871	5	im(φd	im(φd	PROPN
ejpam-2623	871	6	)	)	PUNCT
ejpam-2623	871	7	,	,	PUNCT
ejpam-2623	871	8	therefore	therefore	ADV
ejpam-2623	871	9	,	,	PUNCT
ejpam-2623	871	10	we	we	PRON
ejpam-2623	871	11	choose	choose	VERB
ejpam-2623	871	12	:	:	PUNCT
ejpam-2623	871	13	i.	i.	PROPN
ejpam-2623	871	14	φd(0	φd(0	PROPN
ejpam-2623	871	15	)	)	PUNCT
ejpam-2623	871	16	=	=	PUNCT
ejpam-2623	871	17	(	(	PUNCT
ejpam-2623	871	18	1	1	NUM
ejpam-2623	871	19	,	,	PUNCT
ejpam-2623	871	20	0	0	NUM
ejpam-2623	871	21	)	)	PUNCT
ejpam-2623	871	22	,	,	PUNCT
ejpam-2623	871	23	φ4	φ4	NOUN
ejpam-2623	871	24	(	(	PUNCT
ejpam-2623	871	25	±	±	NOUN
ejpam-2623	871	26	√	√	NOUN
ejpam-2623	871	27	1−d	1−d	NUM
ejpam-2623	872	1	u(1	u(1	PROPN
ejpam-2623	872	2	+	+	NOUN
ejpam-2623	872	3	3d	3d	NUM
ejpam-2623	872	4	)	)	PUNCT
ejpam-2623	872	5	)	)	PUNCT
ejpam-2623	873	1	=	=	PUNCT
ejpam-2623	873	2	(	(	PUNCT
ejpam-2623	873	3	−	−	PUNCT
ejpam-2623	873	4	d+3	d+3	PROPN
ejpam-2623	873	5	1	1	NUM
ejpam-2623	873	6	+	+	NOUN
ejpam-2623	873	7	3d	3d	NOUN
ejpam-2623	873	8	,	,	PUNCT
ejpam-2623	873	9	2	2	NUM
ejpam-2623	873	10	√	√	NUM
ejpam-2623	873	11	−2(d+	−2(d+	VERB
ejpam-2623	873	12	1)/(d−	1)/(d−	NUM
ejpam-2623	873	13	1	1	NUM
ejpam-2623	873	14	)	)	PUNCT
ejpam-2623	873	15	)	)	PUNCT
ejpam-2623	873	16	and	and	CCONJ
ejpam-2623	873	17	φ4	φ4	PROPN
ejpam-2623	873	18	(	(	PUNCT
ejpam-2623	873	19	±	±	NOUN
ejpam-2623	873	20	√	√	PROPN
ejpam-2623	873	21	1	1	NUM
ejpam-2623	873	22	+	+	SYM
ejpam-2623	873	23	3d	3d	PROPN
ejpam-2623	873	24	u(1−d	u(1−d	NOUN
ejpam-2623	873	25	)	)	PUNCT
ejpam-2623	873	26	)	)	PUNCT
ejpam-2623	874	1	=	=	PUNCT
ejpam-2623	874	2	(	(	PUNCT
ejpam-2623	874	3	−	−	PUNCT
ejpam-2623	874	4	d+3	d+3	PROPN
ejpam-2623	874	5	1	1	NUM
ejpam-2623	874	6	+	+	NOUN
ejpam-2623	874	7	3d	3d	NOUN
ejpam-2623	874	8	,	,	PUNCT
ejpam-2623	874	9	−2	−2	NOUN
ejpam-2623	874	10	√	√	PROPN
ejpam-2623	874	11	−2(d+	−2(d+	VERB
ejpam-2623	874	12	1)/(d−	1)/(d−	NUM
ejpam-2623	874	13	1	1	NUM
ejpam-2623	874	14	)	)	PUNCT
ejpam-2623	874	15	)	)	PUNCT
ejpam-2623	875	1	,	,	PUNCT
ejpam-2623	875	2	when	when	SCONJ
ejpam-2623	875	3	q	q	PRON
ejpam-2623	875	4	≡	≡	PROPN
ejpam-2623	875	5	1	1	NUM
ejpam-2623	875	6	mod	mod	PROPN
ejpam-2623	875	7	4	4	NUM
ejpam-2623	875	8	.	.	PUNCT
ejpam-2623	875	9	ii	ii	PROPN
ejpam-2623	875	10	.	.	PUNCT
ejpam-2623	876	1	φd(0	φd(0	X
ejpam-2623	876	2	)	)	PUNCT
ejpam-2623	877	1	=	=	SYM
ejpam-2623	877	2	(	(	PUNCT
ejpam-2623	877	3	1	1	NUM
ejpam-2623	877	4	,	,	PUNCT
ejpam-2623	877	5	0	0	NUM
ejpam-2623	877	6	)	)	PUNCT
ejpam-2623	877	7	,	,	PUNCT
ejpam-2623	877	8	φ4(±	φ4(±	NOUN
ejpam-2623	877	9	√	√	NUM
ejpam-2623	877	10	−1	−1	NOUN
ejpam-2623	877	11	/	/	SYM
ejpam-2623	877	12	u	u	NOUN
ejpam-2623	877	13	)	)	PUNCT
ejpam-2623	877	14	=	=	SYM
ejpam-2623	877	15	(	(	PUNCT
ejpam-2623	877	16	−1	−1	NOUN
ejpam-2623	877	17	,	,	PUNCT
ejpam-2623	877	18	0	0	NUM
ejpam-2623	877	19	)	)	PUNCT
ejpam-2623	877	20	,	,	PUNCT
ejpam-2623	877	21	φ4	φ4	NOUN
ejpam-2623	877	22	(	(	PUNCT
ejpam-2623	877	23	±	±	NOUN
ejpam-2623	877	24	√	√	NOUN
ejpam-2623	877	25	1−d	1−d	NUM
ejpam-2623	878	1	u(1	u(1	PROPN
ejpam-2623	878	2	+	+	NOUN
ejpam-2623	878	3	3d	3d	NUM
ejpam-2623	878	4	)	)	PUNCT
ejpam-2623	878	5	)	)	PUNCT
ejpam-2623	879	1	=	=	PUNCT
ejpam-2623	879	2	(	(	PUNCT
ejpam-2623	879	3	−	−	PUNCT
ejpam-2623	879	4	d+3	d+3	PROPN
ejpam-2623	879	5	1	1	NUM
ejpam-2623	879	6	+	+	NOUN
ejpam-2623	879	7	3d	3d	NOUN
ejpam-2623	879	8	,	,	PUNCT
ejpam-2623	879	9	2	2	NUM
ejpam-2623	879	10	√	√	NUM
ejpam-2623	879	11	−2(d+	−2(d+	VERB
ejpam-2623	879	12	1)/(d−	1)/(d−	NUM
ejpam-2623	879	13	1	1	NUM
ejpam-2623	879	14	)	)	PUNCT
ejpam-2623	879	15	)	)	PUNCT
ejpam-2623	879	16	and	and	CCONJ
ejpam-2623	879	17	φ4	φ4	PROPN
ejpam-2623	879	18	(	(	PUNCT
ejpam-2623	879	19	±	±	NOUN
ejpam-2623	879	20	√	√	PROPN
ejpam-2623	879	21	1	1	NUM
ejpam-2623	879	22	+	+	SYM
ejpam-2623	879	23	3d	3d	PROPN
ejpam-2623	879	24	u(1−d	u(1−d	PROPN
ejpam-2623	879	25	)	)	PUNCT
ejpam-2623	879	26	)	)	PUNCT
ejpam-2623	880	1	=(	=(	NOUN
ejpam-2623	881	1	−	−	PROPN
ejpam-2623	881	2	d+3	d+3	PROPN
ejpam-2623	881	3	1	1	NUM
ejpam-2623	881	4	+	+	NOUN
ejpam-2623	881	5	3d	3d	NOUN
ejpam-2623	881	6	,	,	PUNCT
ejpam-2623	881	7	−2	−2	NOUN
ejpam-2623	881	8	√	√	PROPN
ejpam-2623	881	9	−2(d+	−2(d+	VERB
ejpam-2623	881	10	1)/(d−	1)/(d−	NUM
ejpam-2623	881	11	1	1	NUM
ejpam-2623	881	12	)	)	PUNCT
ejpam-2623	881	13	)	)	PUNCT
ejpam-2623	881	14	when	when	SCONJ
ejpam-2623	881	15	q	q	PROPN
ejpam-2623	881	16	≡	≡	PROPN
ejpam-2623	881	17	3	3	NUM
ejpam-2623	881	18	mod	mod	NOUN
ejpam-2623	881	19	4	4	X
ejpam-2623	881	20	.	.	PUNCT
ejpam-2623	882	1	we	we	PRON
ejpam-2623	882	2	call	call	VERB
ejpam-2623	882	3	φd	φd	VERB
ejpam-2623	882	4	the	the	DET
ejpam-2623	882	5	aiee	aiee	PROPN
ejpam-2623	882	6	-	-	PUNCT
ejpam-2623	882	7	for	for	ADP
ejpam-2623	882	8	-	-	PUNCT
ejpam-2623	882	9	edwards	edward	NOUN
ejpam-2623	882	10	.	.	PUNCT
ejpam-2623	883	1	3.4	3.4	NUM
ejpam-2623	883	2	.	.	PUNCT
ejpam-2623	884	1	an	an	DET
ejpam-2623	884	2	aiie	aiie	NOUN
ejpam-2623	884	3	for	for	ADP
ejpam-2623	884	4	the	the	DET
ejpam-2623	884	5	weierstrass	weierstrass	NOUN
ejpam-2623	884	6	model	model	NOUN
ejpam-2623	884	7	y2	y2	PROPN
ejpam-2623	884	8	=	=	PUNCT
ejpam-2623	885	1	x3	x3	PROPN
ejpam-2623	885	2	+	+	CCONJ
ejpam-2623	885	3	ax2	ax2	NOUN
ejpam-2623	885	4	+	+	CCONJ
ejpam-2623	885	5	c	c	NOUN
ejpam-2623	885	6	in	in	ADP
ejpam-2623	885	7	this	this	DET
ejpam-2623	885	8	section	section	NOUN
ejpam-2623	885	9	,	,	PUNCT
ejpam-2623	885	10	we	we	PRON
ejpam-2623	885	11	propose	propose	VERB
ejpam-2623	885	12	an	an	DET
ejpam-2623	885	13	injective	injective	ADJ
ejpam-2623	885	14	encoding	encoding	NOUN
ejpam-2623	885	15	for	for	ADP
ejpam-2623	885	16	the	the	DET
ejpam-2623	885	17	the	the	DET
ejpam-2623	885	18	weierstrass	weierstrass	NOUN
ejpam-2623	885	19	model	model	NOUN
ejpam-2623	886	1	y2	y2	PROPN
ejpam-2623	886	2	=	=	PUNCT
ejpam-2623	887	1	x3	x3	PROPN
ejpam-2623	887	2	+	+	CCONJ
ejpam-2623	887	3	ax2	ax2	NOUN
ejpam-2623	887	4	+	+	CCONJ
ejpam-2623	887	5	c	c	NOUN
ejpam-2623	887	6	with	with	ADP
ejpam-2623	887	7	char(fq	char(fq	NOUN
ejpam-2623	887	8	)	)	PUNCT
ejpam-2623	887	9	=	=	SYM
ejpam-2623	888	1	3	3	X
ejpam-2623	888	2	.	.	X
ejpam-2623	889	1	the	the	DET
ejpam-2623	889	2	encoding	encoding	NOUN
ejpam-2623	889	3	comes	come	VERB
ejpam-2623	889	4	from	from	ADP
ejpam-2623	889	5	the	the	DET
ejpam-2623	889	6	following	follow	VERB
ejpam-2623	889	7	algorithm	algorithm	NOUN
ejpam-2623	889	8	.	.	PUNCT
ejpam-2623	890	1	algorithm	algorithm	NOUN
ejpam-2623	890	2	2	2	NUM
ejpam-2623	890	3	.	.	PUNCT
ejpam-2623	891	1	input	input	NOUN
ejpam-2623	891	2	:	:	PUNCT
ejpam-2623	891	3	a	a	X
ejpam-2623	891	4	,	,	PUNCT
ejpam-2623	891	5	c	c	PROPN
ejpam-2623	891	6	∈	∈	PROPN
ejpam-2623	891	7	fq	fq	PROPN
ejpam-2623	891	8	(	(	PUNCT
ejpam-2623	891	9	with	with	ADP
ejpam-2623	891	10	char(fq	char(fq	NOUN
ejpam-2623	891	11	)	)	PUNCT
ejpam-2623	891	12	=	=	SYM
ejpam-2623	891	13	3	3	X
ejpam-2623	891	14	)	)	PUNCT
ejpam-2623	891	15	such	such	ADJ
ejpam-2623	891	16	that	that	DET
ejpam-2623	891	17	χ(−ac	χ(−ac	NOUN
ejpam-2623	891	18	)	)	PUNCT
ejpam-2623	891	19	=	=	SYM
ejpam-2623	892	1	1	1	NUM
ejpam-2623	892	2	,	,	PUNCT
ejpam-2623	892	3	u	u	NOUN
ejpam-2623	892	4	a	a	DET
ejpam-2623	892	5	non	non	ADJ
ejpam-2623	892	6	-	-	ADJ
ejpam-2623	892	7	square	square	ADJ
ejpam-2623	892	8	in	in	ADP
ejpam-2623	892	9	fq	fq	PROPN
ejpam-2623	892	10	,	,	PUNCT
ejpam-2623	892	11	r	r	NOUN
ejpam-2623	892	12	∈	∈	PROPN
ejpam-2623	892	13	f∗q	f∗q	NOUN
ejpam-2623	892	14	;	;	PUNCT
ejpam-2623	892	15	output	output	NOUN
ejpam-2623	892	16	:	:	PUNCT
ejpam-2623	892	17	a	a	DET
ejpam-2623	892	18	point	point	NOUN
ejpam-2623	892	19	(	(	PUNCT
ejpam-2623	892	20	x	x	NOUN
ejpam-2623	892	21	,	,	PUNCT
ejpam-2623	892	22	y	y	NOUN
ejpam-2623	892	23	)	)	PUNCT
ejpam-2623	892	24	on	on	ADP
ejpam-2623	892	25	ea	ea	NUM
ejpam-2623	892	26	,	,	PUNCT
ejpam-2623	892	27	c	c	NOUN
ejpam-2623	892	28	:	:	PUNCT
ejpam-2623	893	1	y2	y2	X
ejpam-2623	893	2	=	=	SYM
ejpam-2623	894	1	x3	x3	VERB
ejpam-2623	894	2	+	+	CCONJ
ejpam-2623	894	3	ax2	ax2	NOUN
ejpam-2623	894	4	+	+	CCONJ
ejpam-2623	894	5	c	c	NOUN
ejpam-2623	894	6	;	;	PUNCT
ejpam-2623	894	7	1	1	X
ejpam-2623	895	1	.	.	X
ejpam-2623	895	2	s2	s2	NOUN
ejpam-2623	895	3	=	=	PUNCT
ejpam-2623	896	1	−	−	PROPN
ejpam-2623	896	2	c	c	NOUN
ejpam-2623	896	3	a	a	PRON
ejpam-2623	896	4	;	;	PUNCT
ejpam-2623	896	5	2	2	X
ejpam-2623	896	6	.	.	X
ejpam-2623	896	7	v	v	NOUN
ejpam-2623	896	8	=	=	NOUN
ejpam-2623	896	9	ur2	ur2	NOUN
ejpam-2623	896	10	−	−	PROPN
ejpam-2623	896	11	s2	s2	PROPN
ejpam-2623	896	12	s	s	PART
ejpam-2623	896	13	;	;	PUNCT
ejpam-2623	896	14	3	3	X
ejpam-2623	896	15	.	.	X
ejpam-2623	896	16	ε	ε	PROPN
ejpam-2623	897	1	=	=	SYM
ejpam-2623	898	1	χ(v3	χ(v3	PROPN
ejpam-2623	898	2	+	+	CCONJ
ejpam-2623	898	3	av2	av2	PROPN
ejpam-2623	898	4	+	+	CCONJ
ejpam-2623	898	5	c	c	X
ejpam-2623	898	6	)	)	PUNCT
ejpam-2623	898	7	;	;	PUNCT
ejpam-2623	899	1	4	4	X
ejpam-2623	899	2	.	.	NUM
ejpam-2623	899	3	x	x	X
ejpam-2623	900	1	=	=	SYM
ejpam-2623	900	2	v	v	NUM
ejpam-2623	900	3	2	2	NUM
ejpam-2623	900	4	(	(	PUNCT
ejpam-2623	900	5	1	1	NUM
ejpam-2623	900	6	+	+	CCONJ
ejpam-2623	900	7	s+	s+	PUNCT
ejpam-2623	900	8	εv	εv	NOUN
ejpam-2623	900	9	s+	s+	PUNCT
ejpam-2623	900	10	v	v	NOUN
ejpam-2623	900	11	)	)	PUNCT
ejpam-2623	900	12	;	;	PUNCT
ejpam-2623	900	13	5	5	X
ejpam-2623	900	14	.	.	X
ejpam-2623	900	15	y	y	PROPN
ejpam-2623	900	16	=	=	PUNCT
ejpam-2623	900	17	−ε	−ε	PROPN
ejpam-2623	900	18	√	√	NOUN
ejpam-2623	900	19	x3	x3	VERB
ejpam-2623	900	20	+	+	CCONJ
ejpam-2623	900	21	ax2	ax2	NOUN
ejpam-2623	900	22	+	+	CCONJ
ejpam-2623	900	23	c	c	NOUN
ejpam-2623	900	24	;	;	PUNCT
ejpam-2623	900	25	6	6	NUM
ejpam-2623	900	26	.	.	X
ejpam-2623	901	1	return	return	NOUN
ejpam-2623	901	2	(	(	PUNCT
ejpam-2623	901	3	x	x	X
ejpam-2623	901	4	,	,	PUNCT
ejpam-2623	901	5	y	y	PROPN
ejpam-2623	901	6	)	)	PUNCT
ejpam-2623	901	7	;	;	PUNCT
ejpam-2623	901	8	theorem	theorem	VERB
ejpam-2623	901	9	5	5	NUM
ejpam-2623	901	10	.	.	PUNCT
ejpam-2623	902	1	let	let	VERB
ejpam-2623	902	2	a	a	PRON
ejpam-2623	902	3	,	,	PUNCT
ejpam-2623	902	4	c	c	PROPN
ejpam-2623	902	5	∈	∈	PROPN
ejpam-2623	902	6	fq	fq	PROPN
ejpam-2623	902	7	(	(	PUNCT
ejpam-2623	902	8	with	with	ADP
ejpam-2623	902	9	char(fq	char(fq	NOUN
ejpam-2623	902	10	)	)	PUNCT
ejpam-2623	902	11	=	=	SYM
ejpam-2623	902	12	3	3	X
ejpam-2623	902	13	)	)	PUNCT
ejpam-2623	902	14	such	such	ADJ
ejpam-2623	902	15	that	that	DET
ejpam-2623	902	16	χ(−ac	χ(−ac	NOUN
ejpam-2623	902	17	)	)	PUNCT
ejpam-2623	902	18	=	=	SYM
ejpam-2623	903	1	1	1	NUM
ejpam-2623	903	2	,	,	PUNCT
ejpam-2623	903	3	u	u	NOUN
ejpam-2623	903	4	a	a	DET
ejpam-2623	903	5	non	non	ADJ
ejpam-2623	903	6	-	-	ADJ
ejpam-2623	903	7	square	square	ADJ
ejpam-2623	903	8	in	in	ADP
ejpam-2623	903	9	fq	fq	PROPN
ejpam-2623	903	10	and	and	CCONJ
ejpam-2623	903	11	r	r	NOUN
ejpam-2623	903	12	∈	∈	PROPN
ejpam-2623	903	13	f∗q	f∗q	NOUN
ejpam-2623	903	14	.	.	PUNCT
ejpam-2623	904	1	let	let	VERB
ejpam-2623	904	2	ea	ea	PRON
ejpam-2623	904	3	,	,	PUNCT
ejpam-2623	904	4	c	c	PROPN
ejpam-2623	904	5	be	be	AUX
ejpam-2623	904	6	the	the	DET
ejpam-2623	904	7	elliptic	elliptic	ADJ
ejpam-2623	904	8	curve	curve	NOUN
ejpam-2623	904	9	defined	define	VERB
ejpam-2623	904	10	over	over	ADP
ejpam-2623	904	11	fq	fq	PROPN
ejpam-2623	904	12	by	by	ADP
ejpam-2623	904	13	y2	y2	PROPN
ejpam-2623	904	14	=	=	SYM
ejpam-2623	905	1	x3	x3	VERB
ejpam-2623	905	2	+	+	CCONJ
ejpam-2623	905	3	ax2	ax2	NOUN
ejpam-2623	905	4	+	+	CCONJ
ejpam-2623	905	5	c.	c.	NOUN
ejpam-2623	905	6	then	then	ADV
ejpam-2623	905	7	algorithm	algorithm	NOUN
ejpam-2623	905	8	2	2	NUM
ejpam-2623	905	9	defines	define	VERB
ejpam-2623	905	10	a	a	DET
ejpam-2623	905	11	deterministic	deterministic	ADJ
ejpam-2623	905	12	encoding	encoding	NOUN
ejpam-2623	905	13	φa	φa	ADP
ejpam-2623	905	14	,	,	PUNCT
ejpam-2623	905	15	c	c	NOUN
ejpam-2623	905	16	:	:	PUNCT
ejpam-2623	905	17	f∗q	f∗q	X
ejpam-2623	905	18	→	→	SYM
ejpam-2623	905	19	ea	ea	PROPN
ejpam-2623	905	20	,	,	PUNCT
ejpam-2623	905	21	c	c	X
ejpam-2623	905	22	,	,	PUNCT
ejpam-2623	905	23	r	r	NOUN
ejpam-2623	905	24	7→	7→	NUM
ejpam-2623	905	25	φa	φa	NOUN
ejpam-2623	905	26	,	,	PUNCT
ejpam-2623	905	27	c(r	c(r	X
ejpam-2623	905	28	)	)	PUNCT
ejpam-2623	906	1	=	=	PRON
ejpam-2623	906	2	(	(	PUNCT
ejpam-2623	906	3	x	x	X
ejpam-2623	906	4	,	,	PUNCT
ejpam-2623	906	5	y	y	PROPN
ejpam-2623	906	6	)	)	PUNCT
ejpam-2623	906	7	.	.	PUNCT
ejpam-2623	907	1	n.	n.	PROPN
ejpam-2623	907	2	diarra	diarra	PROPN
ejpam-2623	907	3	,	,	PUNCT
ejpam-2623	907	4	d.	d.	PROPN
ejpam-2623	907	5	sow	sow	PROPN
ejpam-2623	907	6	,	,	PUNCT
ejpam-2623	907	7	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	907	8	.	.	PUNCT
ejpam-2623	907	9	khlil	khlil	PROPN
ejpam-2623	907	10	/	/	SYM
ejpam-2623	907	11	eur	eur	PROPN
ejpam-2623	907	12	.	.	PUNCT
ejpam-2623	908	1	j.	j.	PROPN
ejpam-2623	908	2	pure	pure	PROPN
ejpam-2623	908	3	appl	appl	PROPN
ejpam-2623	908	4	.	.	PROPN
ejpam-2623	908	5	math	math	PROPN
ejpam-2623	908	6	,	,	PUNCT
ejpam-2623	908	7	10	10	NUM
ejpam-2623	908	8	(	(	PUNCT
ejpam-2623	908	9	2	2	NUM
ejpam-2623	908	10	)	)	PUNCT
ejpam-2623	908	11	(	(	PUNCT
ejpam-2623	908	12	2017	2017	NUM
ejpam-2623	908	13	)	)	PUNCT
ejpam-2623	908	14	,	,	PUNCT
ejpam-2623	908	15	363	363	NUM
ejpam-2623	908	16	-	-	SYM
ejpam-2623	908	17	391	391	NUM
ejpam-2623	908	18	385	385	NUM
ejpam-2623	908	19	proof	proof	NOUN
ejpam-2623	908	20	.	.	PUNCT
ejpam-2623	909	1	(	(	PUNCT
ejpam-2623	909	2	i	i	NOUN
ejpam-2623	909	3	)	)	PUNCT
ejpam-2623	909	4	by	by	ADP
ejpam-2623	909	5	hypothesis	hypothesis	NOUN
ejpam-2623	909	6	c	c	PROPN
ejpam-2623	909	7	6=	6=	ADP
ejpam-2623	909	8	0	0	NUM
ejpam-2623	909	9	and	and	CCONJ
ejpam-2623	909	10	a	a	DET
ejpam-2623	909	11	6=	6=	NUM
ejpam-2623	909	12	0	0	NUM
ejpam-2623	909	13	;	;	PUNCT
ejpam-2623	909	14	so	so	SCONJ
ejpam-2623	909	15	v	v	NOUN
ejpam-2623	909	16	is	be	AUX
ejpam-2623	909	17	defined	define	VERB
ejpam-2623	909	18	.	.	PUNCT
ejpam-2623	910	1	v	v	X
ejpam-2623	910	2	=	=	SYM
ejpam-2623	910	3	0	0	NUM
ejpam-2623	910	4	⇔	⇔	X
ejpam-2623	910	5	u	u	NOUN
ejpam-2623	910	6	=	=	PUNCT
ejpam-2623	910	7	(	(	PUNCT
ejpam-2623	910	8	r	r	NOUN
ejpam-2623	910	9	/	/	SYM
ejpam-2623	910	10	s)2	s)2	NOUN
ejpam-2623	910	11	;	;	PUNCT
ejpam-2623	910	12	contradiction	contradiction	NOUN
ejpam-2623	910	13	since	since	SCONJ
ejpam-2623	910	14	u	u	NOUN
ejpam-2623	910	15	is	be	AUX
ejpam-2623	910	16	not	not	PART
ejpam-2623	910	17	a	a	DET
ejpam-2623	910	18	square	square	NOUN
ejpam-2623	910	19	.	.	PUNCT
ejpam-2623	911	1	(	(	PUNCT
ejpam-2623	911	2	ii	ii	NOUN
ejpam-2623	911	3	)	)	PUNCT
ejpam-2623	911	4	v3	v3	PROPN
ejpam-2623	911	5	+	+	CCONJ
ejpam-2623	911	6	av2	av2	PROPN
ejpam-2623	911	7	+	+	CCONJ
ejpam-2623	911	8	c	c	PROPN
ejpam-2623	911	9	6=	6=	ADP
ejpam-2623	911	10	0	0	NUM
ejpam-2623	911	11	since	since	SCONJ
ejpam-2623	911	12	c	c	PROPN
ejpam-2623	911	13	6=	6=	PROPN
ejpam-2623	911	14	0	0	NUM
ejpam-2623	911	15	.	.	PUNCT
ejpam-2623	912	1	this	this	PRON
ejpam-2623	912	2	implies	imply	VERB
ejpam-2623	912	3	that	that	SCONJ
ejpam-2623	912	4	ε	ε	PROPN
ejpam-2623	912	5	6=	6=	PRON
ejpam-2623	912	6	0	0	NUM
ejpam-2623	912	7	.	.	PUNCT
ejpam-2623	913	1	(	(	PUNCT
ejpam-2623	913	2	iii	iii	X
ejpam-2623	913	3	)	)	PUNCT
ejpam-2623	913	4	suppose	suppose	VERB
ejpam-2623	913	5	that	that	SCONJ
ejpam-2623	913	6	v	v	ADP
ejpam-2623	913	7	+	+	SYM
ejpam-2623	913	8	s	s	NOUN
ejpam-2623	913	9	=	=	SYM
ejpam-2623	913	10	0	0	NUM
ejpam-2623	913	11	;	;	PUNCT
ejpam-2623	913	12	so	so	ADV
ejpam-2623	913	13	ur2	ur2	NOUN
ejpam-2623	913	14	=	=	SYM
ejpam-2623	913	15	0	0	NUM
ejpam-2623	913	16	which	which	PRON
ejpam-2623	913	17	is	be	AUX
ejpam-2623	913	18	impossible	impossible	ADJ
ejpam-2623	913	19	by	by	ADP
ejpam-2623	913	20	our	our	PRON
ejpam-2623	913	21	hypothesis	hypothesis	NOUN
ejpam-2623	913	22	on	on	ADP
ejpam-2623	913	23	u	u	PROPN
ejpam-2623	913	24	and	and	CCONJ
ejpam-2623	913	25	r.	r.	PROPN
ejpam-2623	913	26	thus	thus	ADV
ejpam-2623	913	27	x	x	X
ejpam-2623	913	28	is	be	AUX
ejpam-2623	913	29	defined	define	VERB
ejpam-2623	913	30	and	and	CCONJ
ejpam-2623	913	31	x	x	SYM
ejpam-2623	913	32	6=	6=	ADP
ejpam-2623	913	33	0	0	NUM
ejpam-2623	913	34	,	,	PUNCT
ejpam-2623	913	35	since	since	SCONJ
ejpam-2623	913	36	v	v	NUM
ejpam-2623	913	37	6=	6=	PROPN
ejpam-2623	913	38	0	0	NUM
ejpam-2623	913	39	.	.	PUNCT
ejpam-2623	914	1	(	(	PUNCT
ejpam-2623	914	2	iv	iv	X
ejpam-2623	914	3	)	)	PUNCT
ejpam-2623	914	4	we	we	PRON
ejpam-2623	914	5	show	show	VERB
ejpam-2623	914	6	that	that	SCONJ
ejpam-2623	914	7	x3	x3	PROPN
ejpam-2623	914	8	+	+	CCONJ
ejpam-2623	915	1	bx2	bx2	NOUN
ejpam-2623	916	1	+	+	CCONJ
ejpam-2623	916	2	c	c	NOUN
ejpam-2623	916	3	is	be	AUX
ejpam-2623	916	4	a	a	DET
ejpam-2623	916	5	square	square	NOUN
ejpam-2623	916	6	.	.	PUNCT
ejpam-2623	917	1	the	the	DET
ejpam-2623	917	2	first	first	ADJ
ejpam-2623	917	3	case	case	NOUN
ejpam-2623	917	4	is	be	AUX
ejpam-2623	917	5	when	when	SCONJ
ejpam-2623	917	6	ε	ε	PROPN
ejpam-2623	917	7	=	=	SYM
ejpam-2623	917	8	1	1	NUM
ejpam-2623	917	9	;	;	PUNCT
ejpam-2623	917	10	so	so	ADV
ejpam-2623	917	11	x	x	X
ejpam-2623	917	12	=	=	SYM
ejpam-2623	917	13	v	v	NOUN
ejpam-2623	917	14	and	and	CCONJ
ejpam-2623	917	15	χ(x3	χ(x3	NOUN
ejpam-2623	918	1	+	+	CCONJ
ejpam-2623	918	2	ax2	ax2	NOUN
ejpam-2623	918	3	+	+	CCONJ
ejpam-2623	918	4	c	c	X
ejpam-2623	918	5	)	)	PUNCT
ejpam-2623	918	6	=	=	SYM
ejpam-2623	919	1	χ(v3	χ(v3	ADJ
ejpam-2623	919	2	+	+	CCONJ
ejpam-2623	919	3	av2	av2	PROPN
ejpam-2623	919	4	+	+	CCONJ
ejpam-2623	919	5	c	c	X
ejpam-2623	919	6	)	)	PUNCT
ejpam-2623	919	7	=	=	SYM
ejpam-2623	919	8	ε	ε	PROPN
ejpam-2623	919	9	=	=	SYM
ejpam-2623	919	10	1	1	X
ejpam-2623	919	11	.	.	X
ejpam-2623	920	1	for	for	ADP
ejpam-2623	920	2	the	the	DET
ejpam-2623	920	3	second	second	ADJ
ejpam-2623	920	4	case	case	NOUN
ejpam-2623	920	5	we	we	PRON
ejpam-2623	920	6	have	have	VERB
ejpam-2623	920	7	ε	ε	PROPN
ejpam-2623	920	8	=	=	SYM
ejpam-2623	920	9	−1	−1	NOUN
ejpam-2623	920	10	;	;	PUNCT
ejpam-2623	920	11	so	so	ADV
ejpam-2623	920	12	x	x	X
ejpam-2623	920	13	=	=	PUNCT
ejpam-2623	920	14	sv	sv	NOUN
ejpam-2623	920	15	v	v	NUM
ejpam-2623	920	16	+	+	SYM
ejpam-2623	920	17	s	s	PART
ejpam-2623	920	18	.	.	PUNCT
ejpam-2623	921	1	recall	recall	NOUN
ejpam-2623	921	2	that	that	DET
ejpam-2623	921	3	as2	as2	PROPN
ejpam-2623	921	4	=	=	SYM
ejpam-2623	921	5	−c	−c	NOUN
ejpam-2623	921	6	,	,	PUNCT
ejpam-2623	921	7	(	(	PUNCT
ejpam-2623	921	8	s	s	X
ejpam-2623	921	9	+	+	NUM
ejpam-2623	921	10	v)3	v)3	NOUN
ejpam-2623	921	11	=	=	SYM
ejpam-2623	921	12	s3	s3	PROPN
ejpam-2623	921	13	+	+	CCONJ
ejpam-2623	921	14	v3	v3	PROPN
ejpam-2623	921	15	and	and	CCONJ
ejpam-2623	921	16	sv	sv	PROPN
ejpam-2623	922	1	+	+	CCONJ
ejpam-2623	922	2	s2	s2	PROPN
ejpam-2623	922	3	=	=	SYM
ejpam-2623	922	4	ur2	ur2	NOUN
ejpam-2623	922	5	.	.	PUNCT
ejpam-2623	923	1	so	so	ADV
ejpam-2623	923	2	(	(	PUNCT
ejpam-2623	923	3	v+	v+	X
ejpam-2623	923	4	s)3(x3	s)3(x3	X
ejpam-2623	923	5	+	+	CCONJ
ejpam-2623	923	6	ax2	ax2	NOUN
ejpam-2623	923	7	+	+	CCONJ
ejpam-2623	923	8	c	c	X
ejpam-2623	923	9	)	)	PUNCT
ejpam-2623	923	10	=	=	PUNCT
ejpam-2623	924	1	s3v3	s3v3	NUM
ejpam-2623	924	2	+	+	CCONJ
ejpam-2623	924	3	as2v2(v+	as2v2(v+	NUM
ejpam-2623	924	4	s	s	AUX
ejpam-2623	924	5	)	)	PUNCT
ejpam-2623	925	1	+	+	CCONJ
ejpam-2623	925	2	cv3	cv3	PROPN
ejpam-2623	925	3	+	+	CCONJ
ejpam-2623	925	4	cs3	cs3	NOUN
ejpam-2623	925	5	=	=	SYM
ejpam-2623	925	6	s3(v3	s3(v3	PROPN
ejpam-2623	925	7	+	+	NUM
ejpam-2623	925	8	av2	av2	NOUN
ejpam-2623	925	9	+	+	CCONJ
ejpam-2623	925	10	c	c	X
ejpam-2623	925	11	)	)	PUNCT
ejpam-2623	925	12	and	and	CCONJ
ejpam-2623	925	13	then	then	ADV
ejpam-2623	925	14	χ(x3	χ(x3	PROPN
ejpam-2623	926	1	+	+	CCONJ
ejpam-2623	926	2	ax2	ax2	NOUN
ejpam-2623	926	3	+	+	CCONJ
ejpam-2623	926	4	c	c	X
ejpam-2623	926	5	)	)	PUNCT
ejpam-2623	926	6	=	=	PUNCT
ejpam-2623	927	1	χ(s(v	χ(s(v	PROPN
ejpam-2623	927	2	+	+	CCONJ
ejpam-2623	927	3	s))χ(v3	s))χ(v3	NOUN
ejpam-2623	927	4	+	+	CCONJ
ejpam-2623	927	5	av2	av2	NOUN
ejpam-2623	927	6	+	+	CCONJ
ejpam-2623	927	7	c	c	X
ejpam-2623	927	8	)	)	PUNCT
ejpam-2623	927	9	=	=	PUNCT
ejpam-2623	927	10	−χ(sv	−χ(sv	VERB
ejpam-2623	927	11	+	+	CCONJ
ejpam-2623	927	12	s2	s2	PROPN
ejpam-2623	927	13	)	)	PUNCT
ejpam-2623	927	14	=	=	SYM
ejpam-2623	927	15	−χ(ur2	−χ(ur2	NOUN
ejpam-2623	927	16	)	)	PUNCT
ejpam-2623	927	17	=	=	SYM
ejpam-2623	928	1	1	1	X
ejpam-2623	928	2	.	.	PUNCT
ejpam-2623	928	3	hence	hence	ADV
ejpam-2623	928	4	x3+ax2+c	x3+ax2+c	ADJ
ejpam-2623	928	5	is	be	AUX
ejpam-2623	928	6	a	a	DET
ejpam-2623	928	7	non	non	ADJ
ejpam-2623	928	8	-	-	ADJ
ejpam-2623	928	9	zero	zero	NUM
ejpam-2623	928	10	square	square	NOUN
ejpam-2623	928	11	in	in	ADP
ejpam-2623	928	12	both	both	DET
ejpam-2623	928	13	cases	case	NOUN
ejpam-2623	928	14	.	.	PUNCT
ejpam-2623	929	1	furthermore	furthermore	ADV
ejpam-2623	929	2	y2	y2	PROPN
ejpam-2623	929	3	=	=	SYM
ejpam-2623	929	4	x3+ax2+c	x3+ax2+c	ADJ
ejpam-2623	929	5	.	.	PUNCT
ejpam-2623	930	1	proposition	proposition	NOUN
ejpam-2623	930	2	8	8	NUM
ejpam-2623	930	3	.	.	PUNCT
ejpam-2623	931	1	in	in	ADP
ejpam-2623	931	2	the	the	DET
ejpam-2623	931	3	situation	situation	NOUN
ejpam-2623	931	4	of	of	ADP
ejpam-2623	931	5	theorem	theorem	NOUN
ejpam-2623	931	6	5	5	NUM
ejpam-2623	931	7	,	,	PUNCT
ejpam-2623	931	8	the	the	DET
ejpam-2623	931	9	following	follow	VERB
ejpam-2623	931	10	results	result	NOUN
ejpam-2623	931	11	hold	hold	VERB
ejpam-2623	931	12	:	:	PUNCT
ejpam-2623	931	13	(	(	PUNCT
ejpam-2623	931	14	i	i	NOUN
ejpam-2623	931	15	)	)	PUNCT
ejpam-2623	931	16	for	for	ADP
ejpam-2623	931	17	r	r	NOUN
ejpam-2623	931	18	∈	∈	PROPN
ejpam-2623	931	19	f∗q	f∗q	NOUN
ejpam-2623	931	20	,	,	PUNCT
ejpam-2623	931	21	the	the	DET
ejpam-2623	931	22	set	set	NOUN
ejpam-2623	931	23	of	of	ADP
ejpam-2623	931	24	preimages	preimage	NOUN
ejpam-2623	931	25	of	of	ADP
ejpam-2623	931	26	φa	φa	PROPN
ejpam-2623	931	27	,	,	PUNCT
ejpam-2623	931	28	c(r	c(r	NOUN
ejpam-2623	931	29	)	)	PUNCT
ejpam-2623	931	30	under	under	ADP
ejpam-2623	931	31	φa	φa	PROPN
ejpam-2623	931	32	,	,	PUNCT
ejpam-2623	931	33	c	c	PROPN
ejpam-2623	931	34	is	be	AUX
ejpam-2623	931	35	{	{	PUNCT
ejpam-2623	931	36	−r	−r	ADJ
ejpam-2623	931	37	,	,	PUNCT
ejpam-2623	931	38	r	r	NOUN
ejpam-2623	931	39	}	}	PUNCT
ejpam-2623	931	40	.	.	PUNCT
ejpam-2623	932	1	(	(	PUNCT
ejpam-2623	932	2	ii	ii	NOUN
ejpam-2623	932	3	)	)	PUNCT
ejpam-2623	932	4	im(φa	im(φa	PROPN
ejpam-2623	932	5	,	,	PUNCT
ejpam-2623	932	6	c	c	NOUN
ejpam-2623	932	7	)	)	PUNCT
ejpam-2623	932	8	is	be	AUX
ejpam-2623	932	9	the	the	DET
ejpam-2623	932	10	set	set	NOUN
ejpam-2623	932	11	of	of	ADP
ejpam-2623	932	12	(	(	PUNCT
ejpam-2623	932	13	x	x	NOUN
ejpam-2623	932	14	,	,	PUNCT
ejpam-2623	932	15	y	y	NOUN
ejpam-2623	932	16	)	)	PUNCT
ejpam-2623	932	17	∈	∈	PROPN
ejpam-2623	932	18	ea	ea	PROPN
ejpam-2623	932	19	,	,	PUNCT
ejpam-2623	932	20	c	c	X
ejpam-2623	932	21	such	such	ADJ
ejpam-2623	932	22	that	that	PRON
ejpam-2623	932	23	χ(us(s	χ(us(s	PROPN
ejpam-2623	932	24	+	+	NUM
ejpam-2623	932	25	x	x	NOUN
ejpam-2623	932	26	)	)	PUNCT
ejpam-2623	932	27	)	)	PUNCT
ejpam-2623	933	1	=	=	SYM
ejpam-2623	933	2	1	1	NUM
ejpam-2623	933	3	if	if	SCONJ
ejpam-2623	933	4	y	y	PROPN
ejpam-2623	933	5	/∈	/∈	PUNCT
ejpam-2623	933	6	√	√	VERB
ejpam-2623	934	1	f2	f2	PROPN
ejpam-2623	934	2	q	q	NOUN
ejpam-2623	934	3	,	,	PUNCT
ejpam-2623	934	4	and	and	CCONJ
ejpam-2623	934	5	χ(us(s−	χ(us(s−	PROPN
ejpam-2623	934	6	x	x	X
ejpam-2623	934	7	)	)	PUNCT
ejpam-2623	934	8	)	)	PUNCT
ejpam-2623	935	1	=	=	SYM
ejpam-2623	935	2	1	1	NUM
ejpam-2623	935	3	if	if	SCONJ
ejpam-2623	935	4	y	y	PROPN
ejpam-2623	935	5	∈	∈	PROPN
ejpam-2623	935	6	√	√	VERB
ejpam-2623	935	7	f2	f2	PROPN
ejpam-2623	935	8	q.	q.	PROPN
ejpam-2623	935	9	(	(	PUNCT
ejpam-2623	935	10	iii	iii	NOUN
ejpam-2623	935	11	)	)	PUNCT
ejpam-2623	935	12	for	for	ADP
ejpam-2623	935	13	(	(	PUNCT
ejpam-2623	935	14	x	x	NOUN
ejpam-2623	935	15	,	,	PUNCT
ejpam-2623	935	16	y	y	NOUN
ejpam-2623	935	17	)	)	PUNCT
ejpam-2623	935	18	∈	∈	PROPN
ejpam-2623	935	19	im(φa	im(φa	NOUN
ejpam-2623	935	20	,	,	PUNCT
ejpam-2623	935	21	c	c	NOUN
ejpam-2623	935	22	)	)	PUNCT
ejpam-2623	935	23	,	,	PUNCT
ejpam-2623	935	24	let	let	VERB
ejpam-2623	935	25	r	r	NOUN
ejpam-2623	935	26	defined	define	VERB
ejpam-2623	935	27	as	as	SCONJ
ejpam-2623	935	28	follows	follow	VERB
ejpam-2623	935	29	:	:	PUNCT
ejpam-2623	935	30	r	r	X
ejpam-2623	935	31	=	=	SYM
ejpam-2623	935	32	√	√	PROPN
ejpam-2623	935	33	(	(	PUNCT
ejpam-2623	935	34	s(s+	s(s+	VERB
ejpam-2623	935	35	x))/u	x))/u	PUNCT
ejpam-2623	936	1	if	if	SCONJ
ejpam-2623	936	2	y	y	PROPN
ejpam-2623	936	3	/∈	/∈	PUNCT
ejpam-2623	937	1	√	√	VERB
ejpam-2623	937	2	f2	f2	INTJ
ejpam-2623	937	3	q	q	NOUN
ejpam-2623	937	4	r	r	NOUN
ejpam-2623	937	5	=	=	PUNCT
ejpam-2623	937	6	s	s	PART
ejpam-2623	937	7	√	√	NOUN
ejpam-2623	937	8	s/(u(s−	s/(u(s−	PRON
ejpam-2623	937	9	x	x	NOUN
ejpam-2623	937	10	)	)	PUNCT
ejpam-2623	937	11	)	)	PUNCT
ejpam-2623	938	1	if	if	SCONJ
ejpam-2623	938	2	y	y	PROPN
ejpam-2623	938	3	∈	∈	PROPN
ejpam-2623	938	4	√	√	ADP
ejpam-2623	938	5	f2	f2	PROPN
ejpam-2623	938	6	q.	q.	PROPN
ejpam-2623	938	7	then	then	ADV
ejpam-2623	938	8	φa	φa	PROPN
ejpam-2623	938	9	,	,	PUNCT
ejpam-2623	938	10	c(r	c(r	X
ejpam-2623	938	11	)	)	PUNCT
ejpam-2623	938	12	=	=	PRON
ejpam-2623	938	13	(	(	PUNCT
ejpam-2623	938	14	x	x	X
ejpam-2623	938	15	,	,	PUNCT
ejpam-2623	938	16	y	y	PROPN
ejpam-2623	938	17	)	)	PUNCT
ejpam-2623	938	18	.	.	PUNCT
ejpam-2623	939	1	proof	proof	NOUN
ejpam-2623	939	2	.	.	PUNCT
ejpam-2623	940	1	(	(	PUNCT
ejpam-2623	940	2	i	i	NOUN
ejpam-2623	940	3	)	)	PUNCT
ejpam-2623	940	4	same	same	ADJ
ejpam-2623	940	5	proof	proof	NOUN
ejpam-2623	940	6	as	as	ADP
ejpam-2623	940	7	proof	proof	NOUN
ejpam-2623	940	8	of	of	ADP
ejpam-2623	940	9	proposition	proposition	NOUN
ejpam-2623	940	10	5	5	NUM
ejpam-2623	940	11	.	.	PUNCT
ejpam-2623	940	12	(	(	PUNCT
ejpam-2623	940	13	ii	ii	NOUN
ejpam-2623	940	14	)	)	PUNCT
ejpam-2623	940	15	forward	forward	ADV
ejpam-2623	940	16	part	part	NOUN
ejpam-2623	940	17	:	:	PUNCT
ejpam-2623	940	18	we	we	PRON
ejpam-2623	940	19	show	show	VERB
ejpam-2623	940	20	that	that	SCONJ
ejpam-2623	940	21	any	any	DET
ejpam-2623	940	22	(	(	PUNCT
ejpam-2623	940	23	x	x	NOUN
ejpam-2623	940	24	,	,	PUNCT
ejpam-2623	940	25	y	y	NOUN
ejpam-2623	940	26	)	)	PUNCT
ejpam-2623	940	27	∈	∈	PROPN
ejpam-2623	940	28	im(φa	im(φa	NOUN
ejpam-2623	940	29	,	,	PUNCT
ejpam-2623	940	30	c	c	NOUN
ejpam-2623	940	31	)	)	PUNCT
ejpam-2623	940	32	verifies	verifie	NOUN
ejpam-2623	940	33	χ(us(s+x	χ(us(s+x	PROPN
ejpam-2623	940	34	)	)	PUNCT
ejpam-2623	940	35	)	)	PUNCT
ejpam-2623	941	1	=	=	SYM
ejpam-2623	941	2	χ(us(s−	χ(us(s−	ADJ
ejpam-2623	941	3	x	x	X
ejpam-2623	941	4	)	)	PUNCT
ejpam-2623	941	5	)	)	PUNCT
ejpam-2623	942	1	=	=	SYM
ejpam-2623	942	2	1	1	X
ejpam-2623	942	3	.	.	PUNCT
ejpam-2623	943	1	in	in	ADP
ejpam-2623	943	2	fact	fact	NOUN
ejpam-2623	943	3	,	,	PUNCT
ejpam-2623	943	4	let	let	VERB
ejpam-2623	943	5	r	r	PRON
ejpam-2623	943	6	∈	∈	NOUN
ejpam-2623	943	7	f∗q	f∗q	NOUN
ejpam-2623	943	8	such	such	ADJ
ejpam-2623	943	9	that	that	SCONJ
ejpam-2623	943	10	φa	φa	NOUN
ejpam-2623	943	11	,	,	PUNCT
ejpam-2623	943	12	c(r	c(r	X
ejpam-2623	943	13	)	)	PUNCT
ejpam-2623	943	14	=	=	PRON
ejpam-2623	943	15	(	(	PUNCT
ejpam-2623	943	16	x	x	X
ejpam-2623	943	17	,	,	PUNCT
ejpam-2623	943	18	y	y	PROPN
ejpam-2623	943	19	)	)	PUNCT
ejpam-2623	943	20	;	;	PUNCT
ejpam-2623	943	21	and	and	CCONJ
ejpam-2623	943	22	define	define	VERB
ejpam-2623	943	23	v	v	NOUN
ejpam-2623	943	24	,	,	PUNCT
ejpam-2623	943	25	ε	ε	PROPN
ejpam-2623	943	26	from	from	ADP
ejpam-2623	943	27	r.	r.	PROPN
ejpam-2623	943	28	if	if	SCONJ
ejpam-2623	943	29	ε	ε	PROPN
ejpam-2623	943	30	=	=	SYM
ejpam-2623	943	31	1	1	NUM
ejpam-2623	943	32	,	,	PUNCT
ejpam-2623	943	33	then	then	ADV
ejpam-2623	943	34	x	x	X
ejpam-2623	943	35	=	=	SYM
ejpam-2623	943	36	v	v	NOUN
ejpam-2623	943	37	;	;	PUNCT
ejpam-2623	943	38	so	so	CCONJ
ejpam-2623	943	39	us(s	us(s	PUNCT
ejpam-2623	944	1	+	+	CCONJ
ejpam-2623	944	2	x	x	X
ejpam-2623	944	3	)	)	PUNCT
ejpam-2623	944	4	=	=	SYM
ejpam-2623	944	5	us(s	us(s	X
ejpam-2623	944	6	+	+	CCONJ
ejpam-2623	944	7	v	v	X
ejpam-2623	944	8	)	)	PUNCT
ejpam-2623	944	9	=	=	SYM
ejpam-2623	945	1	us	us	PROPN
ejpam-2623	945	2	(	(	PUNCT
ejpam-2623	945	3	s+	s+	ADV
ejpam-2623	945	4	ur2	ur2	VERB
ejpam-2623	945	5	−	−	PROPN
ejpam-2623	945	6	s2	s2	PROPN
ejpam-2623	945	7	s	s	PART
ejpam-2623	945	8	)	)	PUNCT
ejpam-2623	945	9	=	=	SYM
ejpam-2623	945	10	u2r2	u2r2	NOUN
ejpam-2623	945	11	.	.	PUNCT
ejpam-2623	946	1	thus	thus	ADV
ejpam-2623	946	2	χ(us(s	χ(us(s	X
ejpam-2623	946	3	+	+	NUM
ejpam-2623	946	4	x	x	NOUN
ejpam-2623	946	5	)	)	PUNCT
ejpam-2623	946	6	)	)	PUNCT
ejpam-2623	947	1	=	=	PUNCT
ejpam-2623	947	2	1	1	X
ejpam-2623	947	3	.	.	PUNCT
ejpam-2623	948	1	if	if	SCONJ
ejpam-2623	948	2	ε	ε	PROPN
ejpam-2623	948	3	=	=	SYM
ejpam-2623	948	4	−1	−1	NOUN
ejpam-2623	948	5	,	,	PUNCT
ejpam-2623	948	6	then	then	ADV
ejpam-2623	948	7	x	x	X
ejpam-2623	948	8	=	=	SYM
ejpam-2623	948	9	sv	sv	PROPN
ejpam-2623	948	10	s+	s+	ADV
ejpam-2623	948	11	v	v	X
ejpam-2623	948	12	;	;	PUNCT
ejpam-2623	948	13	so	so	CCONJ
ejpam-2623	948	14	us(s	us(s	PUNCT
ejpam-2623	948	15	−	−	PROPN
ejpam-2623	948	16	x	x	X
ejpam-2623	948	17	)	)	PUNCT
ejpam-2623	949	1	=	=	SYM
ejpam-2623	949	2	us	we	PRON
ejpam-2623	949	3	(	(	PUNCT
ejpam-2623	949	4	s−	s−	PROPN
ejpam-2623	949	5	sv	sv	PROPN
ejpam-2623	949	6	s+	s+	PROPN
ejpam-2623	949	7	v	v	NOUN
ejpam-2623	949	8	)	)	PUNCT
ejpam-2623	950	1	=	=	SYM
ejpam-2623	950	2	us3	us3	PROPN
ejpam-2623	950	3	s+	s+	PUNCT
ejpam-2623	950	4	v	v	NOUN
ejpam-2623	950	5	=	=	SYM
ejpam-2623	950	6	us3	us3	PROPN
ejpam-2623	950	7	(	(	PUNCT
ejpam-2623	950	8	1	1	NUM
ejpam-2623	950	9	s+	s+	NUM
ejpam-2623	950	10	ur2−s2	ur2−s2	PROPN
ejpam-2623	950	11	s	s	PART
ejpam-2623	950	12	)	)	PUNCT
ejpam-2623	950	13	=	=	SYM
ejpam-2623	950	14	s4	s4	PROPN
ejpam-2623	950	15	r2	r2	PROPN
ejpam-2623	950	16	.	.	PUNCT
ejpam-2623	951	1	thus	thus	ADV
ejpam-2623	951	2	χ(us(s−	χ(us(s−	PROPN
ejpam-2623	951	3	x	x	X
ejpam-2623	951	4	)	)	PUNCT
ejpam-2623	951	5	)	)	PUNCT
ejpam-2623	952	1	=	=	SYM
ejpam-2623	952	2	1	1	X
ejpam-2623	952	3	.	.	X
ejpam-2623	952	4	reverse	reverse	VERB
ejpam-2623	952	5	part	part	NOUN
ejpam-2623	952	6	:	:	PUNCT
ejpam-2623	952	7	let	let	VERB
ejpam-2623	952	8	(	(	PUNCT
ejpam-2623	952	9	x	x	NOUN
ejpam-2623	952	10	,	,	PUNCT
ejpam-2623	952	11	y	y	NOUN
ejpam-2623	952	12	)	)	PUNCT
ejpam-2623	952	13	∈	∈	PROPN
ejpam-2623	952	14	ea	ea	PROPN
ejpam-2623	952	15	,	,	PUNCT
ejpam-2623	952	16	c	c	X
ejpam-2623	952	17	such	such	ADJ
ejpam-2623	952	18	that	that	PRON
ejpam-2623	952	19	χ(us(s	χ(us(s	NOUN
ejpam-2623	952	20	−	−	NOUN
ejpam-2623	952	21	x))(if	x))(if	PROPN
ejpam-2623	953	1	y	y	PROPN
ejpam-2623	953	2	=	=	PUNCT
ejpam-2623	953	3	√	√	NUM
ejpam-2623	953	4	x3	x3	VERB
ejpam-2623	953	5	+	+	CCONJ
ejpam-2623	953	6	ax2	ax2	NOUN
ejpam-2623	953	7	+	+	CCONJ
ejpam-2623	953	8	c	c	NOUN
ejpam-2623	953	9	)	)	PUNCT
ejpam-2623	953	10	or	or	CCONJ
ejpam-2623	953	11	χ(us(s+	χ(us(s+	NOUN
ejpam-2623	953	12	x	x	NOUN
ejpam-2623	953	13	)	)	PUNCT
ejpam-2623	953	14	)	)	PUNCT
ejpam-2623	954	1	=	=	PUNCT
ejpam-2623	954	2	1(if	1(if	NUM
ejpam-2623	954	3	y	y	NOUN
ejpam-2623	954	4	=	=	PUNCT
ejpam-2623	954	5	−	−	PROPN
ejpam-2623	954	6	√	√	NUM
ejpam-2623	954	7	x3	x3	VERB
ejpam-2623	954	8	+	+	CCONJ
ejpam-2623	954	9	ax2	ax2	NOUN
ejpam-2623	954	10	+	+	CCONJ
ejpam-2623	954	11	c	c	NOUN
ejpam-2623	954	12	)	)	PUNCT
ejpam-2623	954	13	.	.	PUNCT
ejpam-2623	955	1	we	we	PRON
ejpam-2623	955	2	show	show	VERB
ejpam-2623	955	3	that	that	SCONJ
ejpam-2623	955	4	(	(	PUNCT
ejpam-2623	955	5	x	x	NOUN
ejpam-2623	955	6	,	,	PUNCT
ejpam-2623	955	7	y	y	NOUN
ejpam-2623	955	8	)	)	PUNCT
ejpam-2623	955	9	∈	∈	PROPN
ejpam-2623	955	10	im(φa	im(φa	NOUN
ejpam-2623	955	11	,	,	PUNCT
ejpam-2623	955	12	c	c	NOUN
ejpam-2623	955	13	)	)	PUNCT
ejpam-2623	955	14	.	.	PUNCT
ejpam-2623	956	1	we	we	PRON
ejpam-2623	956	2	consider	consider	VERB
ejpam-2623	956	3	the	the	DET
ejpam-2623	956	4	following	follow	VERB
ejpam-2623	956	5	two	two	NUM
ejpam-2623	956	6	cases	case	NOUN
ejpam-2623	956	7	:	:	PUNCT
ejpam-2623	956	8	n.	n.	PROPN
ejpam-2623	956	9	diarra	diarra	PROPN
ejpam-2623	956	10	,	,	PUNCT
ejpam-2623	956	11	d.	d.	PROPN
ejpam-2623	956	12	sow	sow	PROPN
ejpam-2623	956	13	,	,	PUNCT
ejpam-2623	956	14	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	956	15	.	.	PUNCT
ejpam-2623	956	16	khlil	khlil	PROPN
ejpam-2623	956	17	/	/	SYM
ejpam-2623	956	18	eur	eur	PROPN
ejpam-2623	956	19	.	.	PUNCT
ejpam-2623	957	1	j.	j.	PROPN
ejpam-2623	957	2	pure	pure	PROPN
ejpam-2623	957	3	appl	appl	PROPN
ejpam-2623	957	4	.	.	PROPN
ejpam-2623	957	5	math	math	PROPN
ejpam-2623	957	6	,	,	PUNCT
ejpam-2623	957	7	10	10	NUM
ejpam-2623	957	8	(	(	PUNCT
ejpam-2623	957	9	2	2	NUM
ejpam-2623	957	10	)	)	PUNCT
ejpam-2623	957	11	(	(	PUNCT
ejpam-2623	957	12	2017	2017	NUM
ejpam-2623	957	13	)	)	PUNCT
ejpam-2623	957	14	,	,	PUNCT
ejpam-2623	957	15	363	363	NUM
ejpam-2623	957	16	-	-	SYM
ejpam-2623	957	17	391	391	NUM
ejpam-2623	957	18	386	386	NUM
ejpam-2623	957	19	•	•	NOUN
ejpam-2623	957	20	if	if	SCONJ
ejpam-2623	957	21	y	y	PROPN
ejpam-2623	957	22	=	=	SYM
ejpam-2623	957	23	−	−	PROPN
ejpam-2623	958	1	√	√	NUM
ejpam-2623	958	2	x3	x3	VERB
ejpam-2623	958	3	+	+	CCONJ
ejpam-2623	958	4	ax2	ax2	NOUN
ejpam-2623	958	5	+	+	CCONJ
ejpam-2623	958	6	c	c	X
ejpam-2623	958	7	,	,	PUNCT
ejpam-2623	958	8	let	let	VERB
ejpam-2623	958	9	r	r	NOUN
ejpam-2623	958	10	=	=	PUNCT
ejpam-2623	958	11	√	√	NOUN
ejpam-2623	958	12	s(s+	s(s+	VERB
ejpam-2623	958	13	x)/u	x)/u	X
ejpam-2623	958	14	6=	6=	ADP
ejpam-2623	958	15	0	0	NUM
ejpam-2623	958	16	;	;	PUNCT
ejpam-2623	958	17	then	then	ADV
ejpam-2623	958	18	define	define	VERB
ejpam-2623	958	19	v	v	ADP
ejpam-2623	958	20	,	,	PUNCT
ejpam-2623	958	21	ε	ε	PROPN
ejpam-2623	958	22	,	,	PUNCT
ejpam-2623	958	23	x	x	PRON
ejpam-2623	958	24	,	,	PUNCT
ejpam-2623	958	25	y	y	PROPN
ejpam-2623	958	26	from	from	ADP
ejpam-2623	958	27	r	r	NOUN
ejpam-2623	958	28	as	as	ADP
ejpam-2623	958	29	in	in	ADP
ejpam-2623	958	30	theorem	theorem	NOUN
ejpam-2623	958	31	6	6	NUM
ejpam-2623	958	32	.	.	PUNCT
ejpam-2623	959	1	so	so	ADV
ejpam-2623	959	2	v	v	ADV
ejpam-2623	959	3	=	=	SYM
ejpam-2623	959	4	ur2	ur2	NOUN
ejpam-2623	959	5	−	−	PROPN
ejpam-2623	959	6	s2	s2	PROPN
ejpam-2623	959	7	s	s	PART
ejpam-2623	959	8	=	=	PUNCT
ejpam-2623	959	9	s(s+	s(s+	NOUN
ejpam-2623	959	10	x)−	x)−	PROPN
ejpam-2623	959	11	s2	s2	NOUN
ejpam-2623	959	12	s	s	PART
ejpam-2623	959	13	=	=	PUNCT
ejpam-2623	959	14	x	x	X
ejpam-2623	959	15	and	and	CCONJ
ejpam-2623	959	16	ε	ε	PROPN
ejpam-2623	959	17	=	=	SYM
ejpam-2623	959	18	χ(v3	χ(v3	PROPN
ejpam-2623	959	19	+	+	CCONJ
ejpam-2623	959	20	av2	av2	PROPN
ejpam-2623	959	21	+	+	CCONJ
ejpam-2623	959	22	c	c	X
ejpam-2623	959	23	)	)	PUNCT
ejpam-2623	959	24	=	=	SYM
ejpam-2623	959	25	χ(x3	χ(x3	NOUN
ejpam-2623	959	26	+	+	CCONJ
ejpam-2623	959	27	ax2	ax2	NOUN
ejpam-2623	959	28	+	+	CCONJ
ejpam-2623	959	29	c	c	X
ejpam-2623	959	30	)	)	PUNCT
ejpam-2623	959	31	=	=	SYM
ejpam-2623	960	1	1	1	X
ejpam-2623	960	2	.	.	PUNCT
ejpam-2623	961	1	this	this	PRON
ejpam-2623	961	2	implies	imply	VERB
ejpam-2623	961	3	that	that	SCONJ
ejpam-2623	961	4	x	x	X
ejpam-2623	961	5	=	=	SYM
ejpam-2623	961	6	v	v	NOUN
ejpam-2623	961	7	=	=	SYM
ejpam-2623	961	8	x	x	X
ejpam-2623	961	9	and	and	CCONJ
ejpam-2623	961	10	y	y	PROPN
ejpam-2623	961	11	=	=	PROPN
ejpam-2623	961	12	−ε	−ε	PROPN
ejpam-2623	961	13	√	√	NOUN
ejpam-2623	961	14	x3	x3	VERB
ejpam-2623	961	15	+	+	CCONJ
ejpam-2623	961	16	ax2	ax2	NOUN
ejpam-2623	961	17	+	+	CCONJ
ejpam-2623	961	18	c	c	NOUN
ejpam-2623	961	19	=	=	SYM
ejpam-2623	961	20	−	−	PROPN
ejpam-2623	961	21	√	√	NUM
ejpam-2623	961	22	x3	x3	VERB
ejpam-2623	961	23	+	+	CCONJ
ejpam-2623	961	24	ax2	ax2	NOUN
ejpam-2623	961	25	+	+	CCONJ
ejpam-2623	961	26	c	c	NOUN
ejpam-2623	961	27	=	=	SYM
ejpam-2623	961	28	y.	y.	NOUN
ejpam-2623	961	29	hence	hence	ADV
ejpam-2623	961	30	(	(	PUNCT
ejpam-2623	961	31	φa	φa	ADP
ejpam-2623	961	32	,	,	PUNCT
ejpam-2623	961	33	c)(r	c)(r	PROPN
ejpam-2623	961	34	)	)	PUNCT
ejpam-2623	962	1	=	=	SYM
ejpam-2623	962	2	(	(	PUNCT
ejpam-2623	962	3	x	x	X
ejpam-2623	962	4	,	,	PUNCT
ejpam-2623	962	5	y	y	PROPN
ejpam-2623	962	6	)	)	PUNCT
ejpam-2623	962	7	and	and	CCONJ
ejpam-2623	962	8	(	(	PUNCT
ejpam-2623	962	9	x	x	NOUN
ejpam-2623	962	10	,	,	PUNCT
ejpam-2623	962	11	y	y	NOUN
ejpam-2623	962	12	)	)	PUNCT
ejpam-2623	962	13	∈	∈	PROPN
ejpam-2623	962	14	im(φa	im(φa	NOUN
ejpam-2623	962	15	,	,	PUNCT
ejpam-2623	962	16	c	c	NOUN
ejpam-2623	962	17	)	)	PUNCT
ejpam-2623	962	18	.	.	PUNCT
ejpam-2623	963	1	•	•	INTJ
ejpam-2623	963	2	if	if	SCONJ
ejpam-2623	963	3	y	y	PROPN
ejpam-2623	963	4	=	=	PUNCT
ejpam-2623	963	5	√	√	NUM
ejpam-2623	963	6	x3	x3	VERB
ejpam-2623	963	7	+	+	CCONJ
ejpam-2623	963	8	ax2	ax2	NOUN
ejpam-2623	963	9	+	+	CCONJ
ejpam-2623	963	10	c	c	X
ejpam-2623	963	11	,	,	PUNCT
ejpam-2623	963	12	let	let	VERB
ejpam-2623	963	13	r	r	NOUN
ejpam-2623	963	14	=	=	PUNCT
ejpam-2623	963	15	s	s	PART
ejpam-2623	963	16	√	√	NOUN
ejpam-2623	963	17	s/(u(s−	s/(u(s−	PRON
ejpam-2623	963	18	x	x	NOUN
ejpam-2623	963	19	)	)	PUNCT
ejpam-2623	963	20	)	)	PUNCT
ejpam-2623	964	1	6=	6=	ADP
ejpam-2623	964	2	0	0	NUM
ejpam-2623	964	3	since	since	SCONJ
ejpam-2623	964	4	us(s	us(s	PUNCT
ejpam-2623	964	5	−	−	PROPN
ejpam-2623	964	6	x	x	X
ejpam-2623	964	7	)	)	PUNCT
ejpam-2623	964	8	is	be	AUX
ejpam-2623	964	9	a	a	DET
ejpam-2623	964	10	nonzero	nonzero	ADJ
ejpam-2623	964	11	square	square	NOUN
ejpam-2623	964	12	.	.	PUNCT
ejpam-2623	965	1	so	so	ADV
ejpam-2623	965	2	define	define	VERB
ejpam-2623	965	3	v	v	ADP
ejpam-2623	965	4	,	,	PUNCT
ejpam-2623	965	5	ε	ε	PROPN
ejpam-2623	965	6	,	,	PUNCT
ejpam-2623	965	7	x	x	PRON
ejpam-2623	965	8	,	,	PUNCT
ejpam-2623	965	9	y	y	PROPN
ejpam-2623	965	10	from	from	ADP
ejpam-2623	965	11	r	r	NOUN
ejpam-2623	965	12	as	as	ADP
ejpam-2623	965	13	in	in	ADP
ejpam-2623	965	14	theorem	theorem	NOUN
ejpam-2623	965	15	6	6	NUM
ejpam-2623	965	16	.	.	PUNCT
ejpam-2623	966	1	we	we	PRON
ejpam-2623	966	2	then	then	ADV
ejpam-2623	966	3	have	have	VERB
ejpam-2623	966	4	v	v	NOUN
ejpam-2623	966	5	=	=	SYM
ejpam-2623	966	6	ur2	ur2	NOUN
ejpam-2623	966	7	−	−	PROPN
ejpam-2623	966	8	s2	s2	NOUN
ejpam-2623	966	9	s	s	PART
ejpam-2623	966	10	=	=	SYM
ejpam-2623	966	11	s3	s3	PROPN
ejpam-2623	966	12	s−x	s−x	NOUN
ejpam-2623	966	13	−	−	PROPN
ejpam-2623	966	14	s	s	NOUN
ejpam-2623	966	15	2	2	NUM
ejpam-2623	966	16	s	s	NOUN
ejpam-2623	966	17	=	=	X
ejpam-2623	966	18	sx	sx	PROPN
ejpam-2623	966	19	s−	s−	PROPN
ejpam-2623	966	20	x	x	X
ejpam-2623	966	21	.	.	PUNCT
ejpam-2623	967	1	recall	recall	PROPN
ejpam-2623	967	2	that	that	DET
ejpam-2623	967	3	as2	as2	PROPN
ejpam-2623	968	1	=	=	PUNCT
ejpam-2623	968	2	−c	−c	NOUN
ejpam-2623	968	3	and	and	CCONJ
ejpam-2623	968	4	(	(	PUNCT
ejpam-2623	968	5	s−	s−	PROPN
ejpam-2623	968	6	v)3	v)3	PROPN
ejpam-2623	968	7	=	=	SYM
ejpam-2623	968	8	s3	s3	PROPN
ejpam-2623	968	9	−	−	PROPN
ejpam-2623	968	10	v3	v3	PROPN
ejpam-2623	968	11	;	;	PUNCT
ejpam-2623	968	12	so	so	CCONJ
ejpam-2623	968	13	(	(	PUNCT
ejpam-2623	968	14	s−	s−	PROPN
ejpam-2623	968	15	x)3(v3	x)3(v3	PROPN
ejpam-2623	969	1	+	+	CCONJ
ejpam-2623	969	2	av2	av2	PROPN
ejpam-2623	969	3	+	+	CCONJ
ejpam-2623	969	4	c	c	X
ejpam-2623	969	5	)	)	PUNCT
ejpam-2623	970	1	=	=	SYM
ejpam-2623	970	2	s3x3	s3x3	X
ejpam-2623	970	3	+	+	NOUN
ejpam-2623	970	4	as2x2(s−	as2x2(s−	PROPN
ejpam-2623	970	5	x	x	SYM
ejpam-2623	970	6	)	)	PUNCT
ejpam-2623	970	7	+	+	CCONJ
ejpam-2623	970	8	c(s3	c(s3	NOUN
ejpam-2623	970	9	−	−	ADP
ejpam-2623	970	10	x3	x3	ADJ
ejpam-2623	970	11	)	)	PUNCT
ejpam-2623	970	12	=	=	PUNCT
ejpam-2623	971	1	s3(x3	s3(x3	PROPN
ejpam-2623	971	2	+	+	CCONJ
ejpam-2623	971	3	ax2	ax2	NOUN
ejpam-2623	971	4	+	+	CCONJ
ejpam-2623	971	5	c)⇒	c)⇒	PROPN
ejpam-2623	971	6	ε	ε	PROPN
ejpam-2623	971	7	=	=	SYM
ejpam-2623	971	8	χ(v3	χ(v3	PROPN
ejpam-2623	971	9	+	+	CCONJ
ejpam-2623	971	10	av2	av2	PROPN
ejpam-2623	971	11	+	+	CCONJ
ejpam-2623	971	12	c	c	X
ejpam-2623	971	13	)	)	PUNCT
ejpam-2623	971	14	=	=	SYM
ejpam-2623	971	15	χ(s(s−	χ(s(s−	NUM
ejpam-2623	971	16	x	x	NOUN
ejpam-2623	971	17	)	)	PUNCT
ejpam-2623	971	18	)	)	PUNCT
ejpam-2623	972	1	=	=	PUNCT
ejpam-2623	972	2	−1	−1	NOUN
ejpam-2623	972	3	since	since	SCONJ
ejpam-2623	972	4	χ(us(s−	χ(us(s−	PROPN
ejpam-2623	972	5	x	x	X
ejpam-2623	972	6	)	)	PUNCT
ejpam-2623	972	7	)	)	PUNCT
ejpam-2623	973	1	=	=	SYM
ejpam-2623	973	2	1	1	NUM
ejpam-2623	973	3	by	by	ADP
ejpam-2623	973	4	hypothesis	hypothesis	NOUN
ejpam-2623	973	5	,	,	PUNCT
ejpam-2623	973	6	and	and	CCONJ
ejpam-2623	973	7	χ(u	χ(u	NOUN
ejpam-2623	973	8	)	)	PUNCT
ejpam-2623	973	9	=	=	SYM
ejpam-2623	973	10	−1	−1	NOUN
ejpam-2623	973	11	.	.	PUNCT
ejpam-2623	974	1	now	now	ADV
ejpam-2623	974	2	replacing	replace	VERB
ejpam-2623	974	3	ε	ε	PROPN
ejpam-2623	974	4	by	by	ADP
ejpam-2623	974	5	−1	−1	NOUN
ejpam-2623	974	6	and	and	CCONJ
ejpam-2623	974	7	v	v	NOUN
ejpam-2623	974	8	by	by	ADP
ejpam-2623	974	9	sx	sx	PROPN
ejpam-2623	974	10	s−	s−	PROPN
ejpam-2623	974	11	x	x	PUNCT
ejpam-2623	974	12	in	in	ADP
ejpam-2623	974	13	x	x	PROPN
ejpam-2623	974	14	shows	show	VERB
ejpam-2623	974	15	that	that	SCONJ
ejpam-2623	974	16	x	x	PUNCT
ejpam-2623	974	17	=	=	PUNCT
ejpam-2623	974	18	x.	x.	NOUN
ejpam-2623	974	19	furthermore	furthermore	ADV
ejpam-2623	974	20	we	we	PRON
ejpam-2623	974	21	have	have	AUX
ejpam-2623	974	22	y	y	PROPN
ejpam-2623	974	23	=	=	PUNCT
ejpam-2623	974	24	−ε	−ε	PROPN
ejpam-2623	974	25	√	√	NOUN
ejpam-2623	974	26	x3	x3	VERB
ejpam-2623	974	27	+	+	CCONJ
ejpam-2623	974	28	ax2	ax2	NOUN
ejpam-2623	974	29	+	+	CCONJ
ejpam-2623	974	30	c	c	NOUN
ejpam-2623	974	31	=	=	PUNCT
ejpam-2623	974	32	√	√	NOUN
ejpam-2623	974	33	x3	x3	VERB
ejpam-2623	974	34	+	+	CCONJ
ejpam-2623	974	35	ax2	ax2	NOUN
ejpam-2623	974	36	+	+	CCONJ
ejpam-2623	974	37	c	c	NOUN
ejpam-2623	974	38	=	=	SYM
ejpam-2623	974	39	y	y	PROPN
ejpam-2623	975	1	and	and	CCONJ
ejpam-2623	975	2	we	we	PRON
ejpam-2623	975	3	conclude	conclude	VERB
ejpam-2623	975	4	that	that	PRON
ejpam-2623	975	5	(	(	PUNCT
ejpam-2623	975	6	x	x	X
ejpam-2623	975	7	,	,	PUNCT
ejpam-2623	975	8	y	y	NOUN
ejpam-2623	975	9	)	)	PUNCT
ejpam-2623	975	10	∈	∈	PROPN
ejpam-2623	975	11	im(φa	im(φa	NOUN
ejpam-2623	975	12	,	,	PUNCT
ejpam-2623	975	13	c	c	NOUN
ejpam-2623	975	14	)	)	PUNCT
ejpam-2623	975	15	.	.	PUNCT
ejpam-2623	976	1	(	(	PUNCT
ejpam-2623	976	2	iii	iii	NOUN
ejpam-2623	976	3	)	)	PUNCT
ejpam-2623	976	4	follows	follow	VERB
ejpam-2623	976	5	from	from	ADP
ejpam-2623	976	6	the	the	DET
ejpam-2623	976	7	proof	proof	NOUN
ejpam-2623	976	8	of	of	ADP
ejpam-2623	976	9	the	the	DET
ejpam-2623	976	10	second	second	ADJ
ejpam-2623	976	11	statement	statement	NOUN
ejpam-2623	976	12	.	.	PUNCT
ejpam-2623	977	1	extending	extend	VERB
ejpam-2623	977	2	φa	φa	ADP
ejpam-2623	977	3	,	,	PUNCT
ejpam-2623	977	4	c	c	NOUN
ejpam-2623	977	5	:	:	PUNCT
ejpam-2623	977	6	as	as	ADP
ejpam-2623	977	7	above	above	ADV
ejpam-2623	977	8	,	,	PUNCT
ejpam-2623	977	9	if	if	SCONJ
ejpam-2623	977	10	f	f	PROPN
ejpam-2623	977	11	has	have	VERB
ejpam-2623	977	12	a	a	DET
ejpam-2623	977	13	root	root	NOUN
ejpam-2623	977	14	,	,	PUNCT
ejpam-2623	977	15	then	then	ADV
ejpam-2623	977	16	we	we	PRON
ejpam-2623	977	17	can	can	AUX
ejpam-2623	977	18	use	use	VERB
ejpam-2623	977	19	elligator-2	elligator-2	NUM
ejpam-2623	977	20	method	method	NOUN
ejpam-2623	977	21	[	[	X
ejpam-2623	977	22	4	4	NUM
ejpam-2623	977	23	]	]	PUNCT
ejpam-2623	977	24	.	.	PUNCT
ejpam-2623	978	1	for	for	ADP
ejpam-2623	978	2	this	this	DET
ejpam-2623	978	3	case	case	NOUN
ejpam-2623	978	4	also	also	ADV
ejpam-2623	978	5	,	,	PUNCT
ejpam-2623	978	6	suppose	suppose	VERB
ejpam-2623	978	7	that	that	SCONJ
ejpam-2623	978	8	f(x	f(x	PROPN
ejpam-2623	978	9	)	)	PUNCT
ejpam-2623	978	10	=	=	PUNCT
ejpam-2623	979	1	x3	x3	VERB
ejpam-2623	979	2	+	+	CCONJ
ejpam-2623	979	3	ax2	ax2	NOUN
ejpam-2623	979	4	+	+	CCONJ
ejpam-2623	979	5	c	c	PROPN
ejpam-2623	979	6	6=	6=	NUM
ejpam-2623	979	7	0	0	NUM
ejpam-2623	979	8	,	,	PUNCT
ejpam-2623	979	9	∀x	∀x	X
ejpam-2623	979	10	∈	∈	PROPN
ejpam-2623	979	11	fq	fq	PROPN
ejpam-2623	979	12	.	.	PROPN
ejpam-2623	980	1	then	then	ADV
ejpam-2623	980	2	r	r	NOUN
ejpam-2623	980	3	=	=	SYM
ejpam-2623	980	4	f∗q	f∗q	NOUN
ejpam-2623	980	5	.	.	PUNCT
ejpam-2623	981	1	we	we	PRON
ejpam-2623	981	2	propose	propose	VERB
ejpam-2623	981	3	here	here	ADV
ejpam-2623	981	4	to	to	PART
ejpam-2623	981	5	extend	extend	VERB
ejpam-2623	981	6	φa	φa	ADP
ejpam-2623	981	7	,	,	PUNCT
ejpam-2623	981	8	c	c	PROPN
ejpam-2623	981	9	to	to	ADP
ejpam-2623	981	10	fq	fq	PROPN
ejpam-2623	981	11	.	.	PROPN
ejpam-2623	981	12	let	let	VERB
ejpam-2623	981	13	φa	φa	ADP
ejpam-2623	981	14	,	,	PUNCT
ejpam-2623	981	15	c	c	NOUN
ejpam-2623	981	16	:	:	PUNCT
ejpam-2623	981	17	fq	fq	PROPN
ejpam-2623	981	18	→	→	SYM
ejpam-2623	981	19	e(fq	e(fq	PROPN
ejpam-2623	981	20	)	)	PUNCT
ejpam-2623	981	21	defined	define	VERB
ejpam-2623	981	22	as	as	SCONJ
ejpam-2623	981	23	follows	follow	VERB
ejpam-2623	981	24	:	:	PUNCT
ejpam-2623	981	25	•	•	NUM
ejpam-2623	981	26	φa	φa	PROPN
ejpam-2623	981	27	,	,	PUNCT
ejpam-2623	981	28	c(r	c(r	X
ejpam-2623	981	29	)	)	PUNCT
ejpam-2623	982	1	=	=	SYM
ejpam-2623	982	2	φa	φa	PROPN
ejpam-2623	982	3	,	,	PUNCT
ejpam-2623	982	4	c(r	c(r	X
ejpam-2623	982	5	)	)	PUNCT
ejpam-2623	982	6	=	=	PRON
ejpam-2623	982	7	(	(	PUNCT
ejpam-2623	982	8	x	x	X
ejpam-2623	982	9	,	,	PUNCT
ejpam-2623	982	10	y	y	PROPN
ejpam-2623	982	11	)	)	PUNCT
ejpam-2623	982	12	if	if	SCONJ
ejpam-2623	982	13	r	r	NOUN
ejpam-2623	982	14	∈	∈	NOUN
ejpam-2623	982	15	r	r	NOUN
ejpam-2623	982	16	=	=	NOUN
ejpam-2623	982	17	f∗q	f∗q	NOUN
ejpam-2623	982	18	;	;	PUNCT
ejpam-2623	982	19	•	•	ADP
ejpam-2623	982	20	for	for	ADP
ejpam-2623	982	21	r	r	NOUN
ejpam-2623	982	22	=	=	SYM
ejpam-2623	982	23	0	0	NUM
ejpam-2623	982	24	,	,	PUNCT
ejpam-2623	982	25	let	let	VERB
ejpam-2623	982	26	d	d	X
ejpam-2623	982	27	∈	∈	PROPN
ejpam-2623	982	28	fq	fq	PROPN
ejpam-2623	982	29	and	and	CCONJ
ejpam-2623	982	30	put	put	VERB
ejpam-2623	982	31	c	c	NOUN
ejpam-2623	982	32	=	=	SYM
ejpam-2623	982	33	−(d2	−(d2	SYM
ejpam-2623	982	34	−	−	PROPN
ejpam-2623	982	35	a3	a3	NOUN
ejpam-2623	982	36	+	+	CCONJ
ejpam-2623	982	37	a)2	a)2	PROPN
ejpam-2623	982	38	a5	a5	PROPN
ejpam-2623	982	39	.	.	PUNCT
ejpam-2623	983	1	then	then	ADV
ejpam-2623	983	2	−ac	−ac	NOUN
ejpam-2623	983	3	is	be	AUX
ejpam-2623	983	4	a	a	DET
ejpam-2623	983	5	square	square	ADJ
ejpam-2623	983	6	and	and	CCONJ
ejpam-2623	983	7	f(s	f(	NOUN
ejpam-2623	983	8	)	)	PUNCT
ejpam-2623	983	9	=	=	SYM
ejpam-2623	983	10	s2d2	s2d2	X
ejpam-2623	983	11	a2	a2	PROPN
ejpam-2623	983	12	is	be	AUX
ejpam-2623	983	13	also	also	ADV
ejpam-2623	983	14	a	a	DET
ejpam-2623	983	15	square	square	NOUN
ejpam-2623	983	16	.	.	PUNCT
ejpam-2623	984	1	we	we	PRON
ejpam-2623	984	2	use	use	VERB
ejpam-2623	984	3	this	this	DET
ejpam-2623	984	4	result	result	NOUN
ejpam-2623	984	5	to	to	PART
ejpam-2623	984	6	extend	extend	VERB
ejpam-2623	984	7	φa	φa	ADP
ejpam-2623	984	8	,	,	PUNCT
ejpam-2623	984	9	c	c	PROPN
ejpam-2623	984	10	as	as	SCONJ
ejpam-2623	984	11	follows	follow	VERB
ejpam-2623	984	12	:	:	PUNCT
ejpam-2623	984	13	φa	φa	ADP
ejpam-2623	984	14	,	,	PUNCT
ejpam-2623	984	15	c(0	c(0	NOUN
ejpam-2623	984	16	)	)	PUNCT
ejpam-2623	984	17	=(	=(	NOUN
ejpam-2623	984	18	s	s	PROPN
ejpam-2623	984	19	,	,	PUNCT
ejpam-2623	984	20	√	√	NUM
ejpam-2623	984	21	f(s	f(	NOUN
ejpam-2623	984	22	)	)	PUNCT
ejpam-2623	984	23	)	)	PUNCT
ejpam-2623	984	24	.	.	PUNCT
ejpam-2623	985	1	we	we	PRON
ejpam-2623	985	2	call	call	VERB
ejpam-2623	985	3	φa	φa	ADP
ejpam-2623	985	4	,	,	PUNCT
ejpam-2623	985	5	c	c	PROPN
ejpam-2623	985	6	the	the	DET
ejpam-2623	985	7	aiee	aiee	PROPN
ejpam-2623	985	8	-	-	PUNCT
ejpam-2623	985	9	for	for	ADP
ejpam-2623	985	10	-	-	PUNCT
ejpam-2623	985	11	weierstrasschar3	weierstrasschar3	NOUN
ejpam-2623	985	12	.	.	PUNCT
ejpam-2623	986	1	4	4	X
ejpam-2623	986	2	.	.	X
ejpam-2623	986	3	hashing	hash	VERB
ejpam-2623	986	4	into	into	ADP
ejpam-2623	986	5	elliptic	elliptic	ADJ
ejpam-2623	986	6	curves	curve	NOUN
ejpam-2623	986	7	brier	brier	PROPN
ejpam-2623	986	8	et	et	PROPN
ejpam-2623	986	9	al	al	PROPN
ejpam-2623	986	10	.	.	PUNCT
ejpam-2623	987	1	[	[	X
ejpam-2623	987	2	6	6	NUM
ejpam-2623	987	3	]	]	PUNCT
ejpam-2623	987	4	showed	show	VERB
ejpam-2623	987	5	that	that	SCONJ
ejpam-2623	987	6	the	the	DET
ejpam-2623	987	7	construction	construction	NOUN
ejpam-2623	987	8	h(m	h(m	X
ejpam-2623	987	9	)	)	PUNCT
ejpam-2623	987	10	=	=	PUNCT
ejpam-2623	987	11	f(h1(m	f(h1(m	NOUN
ejpam-2623	987	12	)	)	PUNCT
ejpam-2623	987	13	)	)	PUNCT
ejpam-2623	988	1	+	+	CCONJ
ejpam-2623	988	2	f(h2(m	f(h2(m	NOUN
ejpam-2623	988	3	)	)	PUNCT
ejpam-2623	988	4	)	)	PUNCT
ejpam-2623	988	5	is	be	AUX
ejpam-2623	988	6	indifferentiable	indifferentiable	ADJ
ejpam-2623	988	7	from	from	ADP
ejpam-2623	988	8	a	a	DET
ejpam-2623	988	9	random	random	ADJ
ejpam-2623	988	10	oracle	oracle	NOUN
ejpam-2623	988	11	,	,	PUNCT
ejpam-2623	988	12	where	where	SCONJ
ejpam-2623	988	13	f	f	PROPN
ejpam-2623	988	14	is	be	AUX
ejpam-2623	988	15	the	the	DET
ejpam-2623	988	16	icart	icart	NOUN
ejpam-2623	988	17	’s	’s	PART
ejpam-2623	988	18	encoding	encoding	NOUN
ejpam-2623	988	19	[	[	X
ejpam-2623	988	20	9	9	NUM
ejpam-2623	988	21	]	]	PUNCT
ejpam-2623	988	22	and	and	CCONJ
ejpam-2623	988	23	the	the	DET
ejpam-2623	988	24	h1	h1	PROPN
ejpam-2623	988	25	,	,	PUNCT
ejpam-2623	988	26	h2	h2	PROPN
ejpam-2623	988	27	are	be	AUX
ejpam-2623	988	28	modeled	model	VERB
ejpam-2623	988	29	as	as	ADP
ejpam-2623	988	30	random	random	ADJ
ejpam-2623	988	31	oracles	oracle	NOUN
ejpam-2623	988	32	.	.	PUNCT
ejpam-2623	989	1	to	to	PART
ejpam-2623	989	2	show	show	VERB
ejpam-2623	989	3	the	the	DET
ejpam-2623	989	4	indifferentiability	indifferentiability	NOUN
ejpam-2623	989	5	,	,	PUNCT
ejpam-2623	989	6	they	they	PRON
ejpam-2623	989	7	bounded	bound	VERB
ejpam-2623	989	8	the	the	DET
ejpam-2623	989	9	statistical	statistical	ADJ
ejpam-2623	989	10	distance	distance	NOUN
ejpam-2623	989	11	between	between	ADP
ejpam-2623	989	12	the	the	DET
ejpam-2623	989	13	distribution	distribution	NOUN
ejpam-2623	989	14	defined	define	VERB
ejpam-2623	989	15	by	by	ADP
ejpam-2623	989	16	their	their	PRON
ejpam-2623	989	17	construction	construction	NOUN
ejpam-2623	989	18	and	and	CCONJ
ejpam-2623	989	19	the	the	DET
ejpam-2623	989	20	uniform	uniform	ADJ
ejpam-2623	989	21	distribution	distribution	NOUN
ejpam-2623	989	22	.	.	PUNCT
ejpam-2623	990	1	farashahi	farashahi	NOUN
ejpam-2623	990	2	et	et	PROPN
ejpam-2623	990	3	al	al	PROPN
ejpam-2623	990	4	.	.	PUNCT
ejpam-2623	991	1	[	[	X
ejpam-2623	991	2	14	14	NUM
ejpam-2623	991	3	]	]	PUNCT
ejpam-2623	991	4	generalized	generalize	VERB
ejpam-2623	991	5	the	the	DET
ejpam-2623	991	6	result	result	NOUN
ejpam-2623	991	7	of	of	ADP
ejpam-2623	991	8	brier	brier	PROPN
ejpam-2623	991	9	et	et	PROPN
ejpam-2623	991	10	al	al	PROPN
ejpam-2623	991	11	.	.	PUNCT
ejpam-2623	991	12	to	to	ADP
ejpam-2623	991	13	all	all	DET
ejpam-2623	991	14	known	know	VERB
ejpam-2623	991	15	deterministic	deterministic	ADJ
ejpam-2623	991	16	encodings	encoding	NOUN
ejpam-2623	991	17	to	to	PART
ejpam-2623	991	18	elliptic	elliptic	ADJ
ejpam-2623	991	19	(	(	PUNCT
ejpam-2623	991	20	and	and	CCONJ
ejpam-2623	991	21	hyperelliptic	hyperelliptic	ADJ
ejpam-2623	991	22	curves	curve	NOUN
ejpam-2623	991	23	)	)	PUNCT
ejpam-2623	991	24	.	.	PUNCT
ejpam-2623	992	1	in	in	ADP
ejpam-2623	992	2	fact	fact	NOUN
ejpam-2623	992	3	,	,	PUNCT
ejpam-2623	992	4	they	they	PRON
ejpam-2623	992	5	showed	show	VERB
ejpam-2623	992	6	that	that	SCONJ
ejpam-2623	992	7	given	give	VERB
ejpam-2623	992	8	a	a	DET
ejpam-2623	992	9	deterministic	deterministic	ADJ
ejpam-2623	992	10	encoding	encoding	NOUN
ejpam-2623	992	11	f	f	NOUN
ejpam-2623	992	12	,	,	PUNCT
ejpam-2623	992	13	the	the	DET
ejpam-2623	992	14	construction	construction	NOUN
ejpam-2623	992	15	h(m	h(m	X
ejpam-2623	992	16	)	)	PUNCT
ejpam-2623	992	17	=	=	PUNCT
ejpam-2623	992	18	f(h1(m	f(h1(m	NOUN
ejpam-2623	992	19	)	)	PUNCT
ejpam-2623	992	20	)	)	PUNCT
ejpam-2623	993	1	+	+	CCONJ
ejpam-2623	993	2	.	.	PUNCT
ejpam-2623	993	3	.	.	PUNCT
ejpam-2623	993	4	.	.	PUNCT
ejpam-2623	994	1	f(hs(m	f(hs(m	PROPN
ejpam-2623	994	2	)	)	PUNCT
ejpam-2623	994	3	)	)	PUNCT
ejpam-2623	994	4	is	be	AUX
ejpam-2623	994	5	indifferentiable	indifferentiable	ADJ
ejpam-2623	994	6	from	from	ADP
ejpam-2623	994	7	a	a	DET
ejpam-2623	994	8	random	random	ADJ
ejpam-2623	994	9	oracle	oracle	NOUN
ejpam-2623	994	10	,	,	PUNCT
ejpam-2623	994	11	if	if	SCONJ
ejpam-2623	994	12	the	the	DET
ejpam-2623	994	13	hi	hi	NOUN
ejpam-2623	994	14	are	be	AUX
ejpam-2623	994	15	modeled	model	VERB
ejpam-2623	994	16	as	as	ADP
ejpam-2623	994	17	random	random	ADJ
ejpam-2623	994	18	oracles	oracle	NOUN
ejpam-2623	994	19	and	and	CCONJ
ejpam-2623	994	20	s	s	NOUN
ejpam-2623	994	21	is	be	AUX
ejpam-2623	994	22	strictly	strictly	ADV
ejpam-2623	994	23	greater	great	ADJ
ejpam-2623	994	24	than	than	ADP
ejpam-2623	994	25	the	the	DET
ejpam-2623	994	26	genus	genus	NOUN
ejpam-2623	994	27	of	of	ADP
ejpam-2623	994	28	the	the	DET
ejpam-2623	994	29	target	target	NOUN
ejpam-2623	994	30	curve	curve	NOUN
ejpam-2623	994	31	.	.	PUNCT
ejpam-2623	995	1	our	our	PRON
ejpam-2623	995	2	objective	objective	NOUN
ejpam-2623	995	3	here	here	ADV
ejpam-2623	995	4	is	be	AUX
ejpam-2623	995	5	to	to	PART
ejpam-2623	995	6	apply	apply	VERB
ejpam-2623	995	7	these	these	DET
ejpam-2623	995	8	results	result	NOUN
ejpam-2623	995	9	to	to	ADP
ejpam-2623	995	10	one	one	NUM
ejpam-2623	995	11	of	of	ADP
ejpam-2623	995	12	our	our	PRON
ejpam-2623	995	13	encodings	encoding	NOUN
ejpam-2623	995	14	,	,	PUNCT
ejpam-2623	995	15	namely	namely	ADV
ejpam-2623	995	16	the	the	DET
ejpam-2623	995	17	encoding	encoding	NOUN
ejpam-2623	995	18	φd	φd	VERB
ejpam-2623	995	19	for	for	ADP
ejpam-2623	995	20	the	the	DET
ejpam-2623	995	21	edwards	edwards	PROPN
ejpam-2623	995	22	curve	curve	PROPN
ejpam-2623	995	23	x2	x2	PROPN
ejpam-2623	996	1	+	+	CCONJ
ejpam-2623	996	2	y2	y2	NOUN
ejpam-2623	996	3	=	=	SYM
ejpam-2623	996	4	1	1	NUM
ejpam-2623	996	5	+	+	CCONJ
ejpam-2623	996	6	dx2y2	dx2y2	PROPN
ejpam-2623	996	7	.	.	PUNCT
ejpam-2623	996	8	n.	n.	PROPN
ejpam-2623	996	9	diarra	diarra	PROPN
ejpam-2623	996	10	,	,	PUNCT
ejpam-2623	996	11	d.	d.	PROPN
ejpam-2623	996	12	sow	sow	PROPN
ejpam-2623	996	13	,	,	PUNCT
ejpam-2623	996	14	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	996	15	.	.	PUNCT
ejpam-2623	996	16	khlil	khlil	PROPN
ejpam-2623	996	17	/	/	SYM
ejpam-2623	996	18	eur	eur	PROPN
ejpam-2623	996	19	.	.	PUNCT
ejpam-2623	997	1	j.	j.	PROPN
ejpam-2623	997	2	pure	pure	PROPN
ejpam-2623	997	3	appl	appl	PROPN
ejpam-2623	997	4	.	.	PROPN
ejpam-2623	997	5	math	math	PROPN
ejpam-2623	997	6	,	,	PUNCT
ejpam-2623	997	7	10	10	NUM
ejpam-2623	997	8	(	(	PUNCT
ejpam-2623	997	9	2	2	NUM
ejpam-2623	997	10	)	)	PUNCT
ejpam-2623	997	11	(	(	PUNCT
ejpam-2623	997	12	2017	2017	NUM
ejpam-2623	997	13	)	)	PUNCT
ejpam-2623	997	14	,	,	PUNCT
ejpam-2623	997	15	363	363	NUM
ejpam-2623	997	16	-	-	SYM
ejpam-2623	997	17	391	391	NUM
ejpam-2623	997	18	387	387	NUM
ejpam-2623	997	19	4.1	4.1	NUM
ejpam-2623	997	20	.	.	PUNCT
ejpam-2623	997	21	admissible	admissible	ADJ
ejpam-2623	997	22	and	and	CCONJ
ejpam-2623	997	23	well	well	ADV
ejpam-2623	997	24	-	-	PUNCT
ejpam-2623	997	25	distributed	distribute	VERB
ejpam-2623	997	26	encodings	encoding	NOUN
ejpam-2623	997	27	we	we	PRON
ejpam-2623	997	28	recall	recall	VERB
ejpam-2623	997	29	the	the	DET
ejpam-2623	997	30	following	follow	VERB
ejpam-2623	997	31	definitions	definition	NOUN
ejpam-2623	997	32	and	and	CCONJ
ejpam-2623	997	33	theorems	theorem	NOUN
ejpam-2623	997	34	from	from	ADP
ejpam-2623	997	35	[	[	X
ejpam-2623	997	36	14	14	NUM
ejpam-2623	997	37	]	]	PUNCT
ejpam-2623	997	38	and	and	CCONJ
ejpam-2623	997	39	[	[	X
ejpam-2623	997	40	17	17	NUM
ejpam-2623	997	41	]	]	PUNCT
ejpam-2623	997	42	.	.	PUNCT
ejpam-2623	998	1	definition	definition	NOUN
ejpam-2623	998	2	3	3	X
ejpam-2623	998	3	.	.	PUNCT
ejpam-2623	999	1	let	let	VERB
ejpam-2623	999	2	s	s	PRON
ejpam-2623	999	3	,	,	PUNCT
ejpam-2623	999	4	r	r	NOUN
ejpam-2623	999	5	be	be	AUX
ejpam-2623	999	6	two	two	NUM
ejpam-2623	999	7	finite	finite	ADJ
ejpam-2623	999	8	sets	set	NOUN
ejpam-2623	999	9	and	and	CCONJ
ejpam-2623	999	10	f	f	PROPN
ejpam-2623	999	11	a	a	DET
ejpam-2623	999	12	function	function	NOUN
ejpam-2623	999	13	from	from	ADP
ejpam-2623	999	14	s	s	PRON
ejpam-2623	999	15	to	to	ADP
ejpam-2623	999	16	r.	r.	PROPN
ejpam-2623	999	17	then	then	ADV
ejpam-2623	999	18	f	f	PROPN
ejpam-2623	999	19	is	be	AUX
ejpam-2623	999	20	an	an	DET
ejpam-2623	999	21	ε	ε	PROPN
ejpam-2623	999	22	-	-	PUNCT
ejpam-2623	999	23	admissible	admissible	ADJ
ejpam-2623	999	24	encoding	encoding	NOUN
ejpam-2623	999	25	if	if	SCONJ
ejpam-2623	999	26	it	it	PRON
ejpam-2623	999	27	satisfies	satisfy	VERB
ejpam-2623	999	28	the	the	DET
ejpam-2623	999	29	following	follow	VERB
ejpam-2623	999	30	properties	property	NOUN
ejpam-2623	999	31	:	:	PUNCT
ejpam-2623	999	32	(	(	PUNCT
ejpam-2623	999	33	i	i	NOUN
ejpam-2623	999	34	)	)	PUNCT
ejpam-2623	999	35	computable	computable	ADJ
ejpam-2623	999	36	,	,	PUNCT
ejpam-2623	999	37	that	that	PRON
ejpam-2623	999	38	is	is	ADV
ejpam-2623	999	39	f	f	PROPN
ejpam-2623	999	40	is	be	AUX
ejpam-2623	999	41	computable	computable	ADJ
ejpam-2623	999	42	in	in	ADP
ejpam-2623	999	43	deterministic	deterministic	ADJ
ejpam-2623	999	44	polynomial	polynomial	ADJ
ejpam-2623	999	45	time	time	NOUN
ejpam-2623	999	46	;	;	PUNCT
ejpam-2623	999	47	(	(	PUNCT
ejpam-2623	999	48	ii	ii	NOUN
ejpam-2623	999	49	)	)	PUNCT
ejpam-2623	999	50	regular	regular	ADJ
ejpam-2623	999	51	:	:	PUNCT
ejpam-2623	999	52	for	for	SCONJ
ejpam-2623	999	53	s	s	AUX
ejpam-2623	999	54	uniformly	uniformly	ADV
ejpam-2623	999	55	distributed	distribute	VERB
ejpam-2623	999	56	in	in	ADP
ejpam-2623	999	57	s	s	PROPN
ejpam-2623	999	58	,	,	PUNCT
ejpam-2623	999	59	the	the	DET
ejpam-2623	999	60	distribution	distribution	NOUN
ejpam-2623	999	61	of	of	ADP
ejpam-2623	999	62	f	f	PROPN
ejpam-2623	999	63	(	(	PUNCT
ejpam-2623	999	64	s	s	X
ejpam-2623	999	65	)	)	PUNCT
ejpam-2623	999	66	is	be	AUX
ejpam-2623	999	67	ε	ε	PROPN
ejpam-2623	999	68	-	-	PUNCT
ejpam-2623	999	69	statistically	statistically	ADV
ejpam-2623	999	70	indistinguishable	indistinguishable	ADJ
ejpam-2623	999	71	from	from	ADP
ejpam-2623	999	72	the	the	DET
ejpam-2623	999	73	uniform	uniform	ADJ
ejpam-2623	999	74	distribution	distribution	NOUN
ejpam-2623	999	75	in	in	ADP
ejpam-2623	999	76	r	r	NOUN
ejpam-2623	999	77	;	;	PUNCT
ejpam-2623	999	78	(	(	PUNCT
ejpam-2623	999	79	iii	iii	X
ejpam-2623	999	80	)	)	PUNCT
ejpam-2623	999	81	samplable	samplable	NOUN
ejpam-2623	999	82	:	:	PUNCT
ejpam-2623	999	83	there	there	PRON
ejpam-2623	999	84	is	be	VERB
ejpam-2623	999	85	an	an	DET
ejpam-2623	999	86	efficient	efficient	ADJ
ejpam-2623	999	87	randomized	randomized	ADJ
ejpam-2623	999	88	algorithm	algorithm	NOUN
ejpam-2623	999	89	i	i	PRON
ejpam-2623	999	90	such	such	VERB
ejpam-2623	999	91	that	that	PRON
ejpam-2623	999	92	for	for	ADP
ejpam-2623	999	93	any	any	DET
ejpam-2623	999	94	r	r	NOUN
ejpam-2623	999	95	∈	∈	NOUN
ejpam-2623	999	96	r	r	NOUN
ejpam-2623	999	97	,	,	PUNCT
ejpam-2623	999	98	i(r	i(r	PROPN
ejpam-2623	999	99	)	)	PUNCT
ejpam-2623	999	100	induces	induce	VERB
ejpam-2623	999	101	a	a	DET
ejpam-2623	999	102	distribution	distribution	NOUN
ejpam-2623	999	103	that	that	PRON
ejpam-2623	999	104	is	be	AUX
ejpam-2623	999	105	ε	ε	PROPN
ejpam-2623	999	106	-	-	PUNCT
ejpam-2623	999	107	statistically	statistically	ADV
ejpam-2623	999	108	indistinguishable	indistinguishable	ADJ
ejpam-2623	999	109	from	from	ADP
ejpam-2623	999	110	the	the	DET
ejpam-2623	999	111	uniform	uniform	ADJ
ejpam-2623	999	112	distribution	distribution	NOUN
ejpam-2623	999	113	in	in	ADP
ejpam-2623	999	114	f−1(r	f−1(r	NOUN
ejpam-2623	999	115	)	)	PUNCT
ejpam-2623	999	116	.	.	PUNCT
ejpam-2623	1000	1	f	f	PROPN
ejpam-2623	1000	2	is	be	AUX
ejpam-2623	1000	3	an	an	DET
ejpam-2623	1000	4	admissible	admissible	ADJ
ejpam-2623	1000	5	encoding	encoding	NOUN
ejpam-2623	1000	6	if	if	SCONJ
ejpam-2623	1000	7	ε	ε	PROPN
ejpam-2623	1000	8	is	be	AUX
ejpam-2623	1000	9	a	a	DET
ejpam-2623	1000	10	negligible	negligible	ADJ
ejpam-2623	1000	11	function	function	NOUN
ejpam-2623	1000	12	of	of	ADP
ejpam-2623	1000	13	the	the	DET
ejpam-2623	1000	14	security	security	NOUN
ejpam-2623	1000	15	parameter	parameter	NOUN
ejpam-2623	1000	16	.	.	PUNCT
ejpam-2623	1001	1	definition	definition	NOUN
ejpam-2623	1001	2	4	4	NUM
ejpam-2623	1001	3	.	.	PUNCT
ejpam-2623	1002	1	let	let	VERB
ejpam-2623	1002	2	e	e	PRON
ejpam-2623	1002	3	be	be	AUX
ejpam-2623	1002	4	an	an	DET
ejpam-2623	1002	5	elliptic	elliptic	ADJ
ejpam-2623	1002	6	curve	curve	NOUN
ejpam-2623	1002	7	over	over	ADP
ejpam-2623	1002	8	fq	fq	PROPN
ejpam-2623	1002	9	and	and	CCONJ
ejpam-2623	1002	10	a	a	DET
ejpam-2623	1002	11	function	function	NOUN
ejpam-2623	1002	12	φ	φ	NOUN
ejpam-2623	1002	13	:	:	PUNCT
ejpam-2623	1002	14	fq	fq	PROPN
ejpam-2623	1002	15	→	→	SYM
ejpam-2623	1002	16	e(fq	e(fq	PROPN
ejpam-2623	1002	17	)	)	PUNCT
ejpam-2623	1002	18	.	.	PUNCT
ejpam-2623	1003	1	(	(	PUNCT
ejpam-2623	1003	2	i	i	NOUN
ejpam-2623	1003	3	)	)	PUNCT
ejpam-2623	1003	4	φ	φ	PROPN
ejpam-2623	1003	5	is	be	AUX
ejpam-2623	1003	6	a	a	DET
ejpam-2623	1003	7	b	b	NOUN
ejpam-2623	1003	8	-	-	PUNCT
ejpam-2623	1003	9	well	well	ADV
ejpam-2623	1003	10	-	-	PUNCT
ejpam-2623	1003	11	distributed	distribute	VERB
ejpam-2623	1003	12	encoding	encoding	NOUN
ejpam-2623	1003	13	for	for	ADP
ejpam-2623	1003	14	a	a	DET
ejpam-2623	1003	15	certain	certain	ADJ
ejpam-2623	1003	16	constant	constant	ADJ
ejpam-2623	1003	17	b	b	PROPN
ejpam-2623	1003	18	>	>	PUNCT
ejpam-2623	1003	19	0	0	NUM
ejpam-2623	1003	20	,	,	PUNCT
ejpam-2623	1003	21	if	if	SCONJ
ejpam-2623	1003	22	for	for	ADP
ejpam-2623	1003	23	any	any	DET
ejpam-2623	1003	24	nontrivial	nontrivial	ADJ
ejpam-2623	1003	25	character	character	NOUN
ejpam-2623	1003	26	ξ	ξ	PROPN
ejpam-2623	1003	27	of	of	ADP
ejpam-2623	1003	28	e(fq	e(fq	PROPN
ejpam-2623	1003	29	)	)	PUNCT
ejpam-2623	1003	30	,	,	PUNCT
ejpam-2623	1003	31	the	the	DET
ejpam-2623	1003	32	following	follow	VERB
ejpam-2623	1003	33	holds	hold	VERB
ejpam-2623	1003	34	:	:	PUNCT
ejpam-2623	1003	35	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-2623	1003	36	∑	∑	PUNCT
ejpam-2623	1003	37	r∈fq	r∈fq	PROPN
ejpam-2623	1003	38	ξ(φ(r	ξ(φ(r	NOUN
ejpam-2623	1003	39	)	)	PUNCT
ejpam-2623	1003	40	)	)	PUNCT
ejpam-2623	1004	1	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-2623	1004	2	≤	≤	PROPN
ejpam-2623	1004	3	b	b	NOUN
ejpam-2623	1004	4	√	√	NOUN
ejpam-2623	1004	5	q.	q.	NOUN
ejpam-2623	1004	6	if	if	SCONJ
ejpam-2623	1004	7	b	b	NOUN
ejpam-2623	1004	8	does	do	AUX
ejpam-2623	1004	9	n’t	not	PART
ejpam-2623	1004	10	depend	depend	VERB
ejpam-2623	1004	11	on	on	ADP
ejpam-2623	1004	12	the	the	DET
ejpam-2623	1004	13	security	security	NOUN
ejpam-2623	1004	14	parameter	parameter	NOUN
ejpam-2623	1004	15	(	(	PUNCT
ejpam-2623	1004	16	that	that	PRON
ejpam-2623	1004	17	allows	allow	VERB
ejpam-2623	1004	18	to	to	PART
ejpam-2623	1004	19	chose	chose	VERB
ejpam-2623	1004	20	q	q	PROPN
ejpam-2623	1004	21	)	)	PUNCT
ejpam-2623	1004	22	then	then	ADV
ejpam-2623	1004	23	φ	φ	PROPN
ejpam-2623	1004	24	is	be	AUX
ejpam-2623	1004	25	said	say	VERB
ejpam-2623	1004	26	to	to	PART
ejpam-2623	1004	27	be	be	AUX
ejpam-2623	1004	28	well	well	ADV
ejpam-2623	1004	29	-	-	PUNCT
ejpam-2623	1004	30	distributed	distribute	VERB
ejpam-2623	1004	31	.	.	PUNCT
ejpam-2623	1005	1	(	(	PUNCT
ejpam-2623	1005	2	ii	ii	NOUN
ejpam-2623	1005	3	)	)	PUNCT
ejpam-2623	1005	4	φ	φ	PROPN
ejpam-2623	1005	5	is	be	AUX
ejpam-2623	1005	6	a	a	DET
ejpam-2623	1005	7	(	(	PUNCT
ejpam-2623	1005	8	d	d	NOUN
ejpam-2623	1005	9	,	,	PUNCT
ejpam-2623	1005	10	b)-well	b)-well	NOUN
ejpam-2623	1005	11	-	-	PUNCT
ejpam-2623	1005	12	bounded	bound	VERB
ejpam-2623	1005	13	encoding	encoding	NOUN
ejpam-2623	1005	14	,	,	PUNCT
ejpam-2623	1005	15	for	for	ADP
ejpam-2623	1005	16	positive	positive	ADJ
ejpam-2623	1005	17	constants	constant	NOUN
ejpam-2623	1005	18	d	d	NOUN
ejpam-2623	1005	19	,	,	PUNCT
ejpam-2623	1005	20	b	b	NOUN
ejpam-2623	1005	21	,	,	PUNCT
ejpam-2623	1005	22	if	if	SCONJ
ejpam-2623	1005	23	φ	φ	PROPN
ejpam-2623	1005	24	is	be	AUX
ejpam-2623	1005	25	b	b	ADV
ejpam-2623	1005	26	-	-	PUNCT
ejpam-2623	1005	27	welldistributed	welldistribute	VERB
ejpam-2623	1005	28	and	and	CCONJ
ejpam-2623	1005	29	each	each	DET
ejpam-2623	1005	30	point	point	NOUN
ejpam-2623	1005	31	in	in	ADP
ejpam-2623	1005	32	e(fq	e(fq	PROPN
ejpam-2623	1005	33	)	)	PUNCT
ejpam-2623	1005	34	have	have	AUX
ejpam-2623	1005	35	at	at	ADP
ejpam-2623	1005	36	most	most	ADJ
ejpam-2623	1005	37	d	d	ADP
ejpam-2623	1005	38	preimages	preimage	NOUN
ejpam-2623	1005	39	under	under	ADP
ejpam-2623	1005	40	φ	φ	PROPN
ejpam-2623	1005	41	.	.	PUNCT
ejpam-2623	1006	1	theorem	theorem	VERB
ejpam-2623	1006	2	6	6	NUM
ejpam-2623	1006	3	.	.	PUNCT
ejpam-2623	1007	1	let	let	VERB
ejpam-2623	1007	2	h	h	NOUN
ejpam-2623	1007	3	:	:	PUNCT
ejpam-2623	1007	4	t	t	PROPN
ejpam-2623	1007	5	=	=	SYM
ejpam-2623	1007	6	t	t	PROPN
ejpam-2623	1007	7	(	(	PUNCT
ejpam-2623	1007	8	fq	fq	PROPN
ejpam-2623	1007	9	)	)	PUNCT
ejpam-2623	1007	10	→	→	SYM
ejpam-2623	1007	11	e	e	X
ejpam-2623	1007	12	=	=	SYM
ejpam-2623	1007	13	e(fq	e(fq	X
ejpam-2623	1007	14	)	)	PUNCT
ejpam-2623	1007	15	be	be	VERB
ejpam-2623	1007	16	a	a	DET
ejpam-2623	1007	17	non	non	X
ejpam-2623	1007	18	constant	constant	ADJ
ejpam-2623	1007	19	morphism	morphism	NOUN
ejpam-2623	1007	20	of	of	ADP
ejpam-2623	1007	21	curves	curve	NOUN
ejpam-2623	1007	22	,	,	PUNCT
ejpam-2623	1007	23	and	and	CCONJ
ejpam-2623	1007	24	ξ	ξ	X
ejpam-2623	1007	25	be	be	VERB
ejpam-2623	1007	26	any	any	DET
ejpam-2623	1007	27	nontrivial	nontrivial	ADJ
ejpam-2623	1007	28	character	character	NOUN
ejpam-2623	1007	29	of	of	ADP
ejpam-2623	1007	30	e(fq	e(fq	PROPN
ejpam-2623	1007	31	)	)	PUNCT
ejpam-2623	1007	32	.	.	PUNCT
ejpam-2623	1008	1	assume	assume	VERB
ejpam-2623	1008	2	that	that	SCONJ
ejpam-2623	1008	3	h	h	NOUN
ejpam-2623	1008	4	does	do	AUX
ejpam-2623	1008	5	not	not	PART
ejpam-2623	1008	6	factor	factor	VERB
ejpam-2623	1008	7	through	through	ADP
ejpam-2623	1008	8	a	a	DET
ejpam-2623	1008	9	nontrivial	nontrivial	ADJ
ejpam-2623	1008	10	unramified	unramifie	VERB
ejpam-2623	1008	11	morphism	morphism	NOUN
ejpam-2623	1008	12	z	z	PROPN
ejpam-2623	1008	13	→	→	SYM
ejpam-2623	1008	14	e	e	PROPN
ejpam-2623	1008	15	,	,	PUNCT
ejpam-2623	1008	16	then∣∣∣∣∣∑	then∣∣∣∣∣∑	PROPN
ejpam-2623	1008	17	p∈t	p∈t	PROPN
ejpam-2623	1008	18	ξ(h(p	ξ(h(p	PROPN
ejpam-2623	1008	19	)	)	PUNCT
ejpam-2623	1008	20	)	)	PUNCT
ejpam-2623	1009	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-2623	1009	2	≤	≤	NUM
ejpam-2623	1009	3	(	(	PUNCT
ejpam-2623	1009	4	2ĝ	2ĝ	NUM
ejpam-2623	1009	5	−	−	NOUN
ejpam-2623	1009	6	2	2	NUM
ejpam-2623	1009	7	)	)	PUNCT
ejpam-2623	1009	8	√	√	PROPN
ejpam-2623	1009	9	q	q	NOUN
ejpam-2623	1009	10	,	,	PUNCT
ejpam-2623	1009	11	where	where	SCONJ
ejpam-2623	1009	12	ĝ	ĝ	PROPN
ejpam-2623	1009	13	is	be	AUX
ejpam-2623	1009	14	the	the	DET
ejpam-2623	1009	15	genus	genus	NOUN
ejpam-2623	1009	16	of	of	ADP
ejpam-2623	1009	17	t	t	PROPN
ejpam-2623	1009	18	.	.	PUNCT
ejpam-2623	1010	1	furthermore	furthermore	ADV
ejpam-2623	1010	2	,	,	PUNCT
ejpam-2623	1010	3	if	if	SCONJ
ejpam-2623	1010	4	q	q	NOUN
ejpam-2623	1010	5	is	be	AUX
ejpam-2623	1010	6	odd	odd	ADJ
ejpam-2623	1010	7	and	and	CCONJ
ejpam-2623	1010	8	λ	λ	PROPN
ejpam-2623	1010	9	is	be	AUX
ejpam-2623	1010	10	a	a	DET
ejpam-2623	1010	11	non	non	ADJ
ejpam-2623	1010	12	constant	constant	ADJ
ejpam-2623	1010	13	rational	rational	ADJ
ejpam-2623	1010	14	function	function	NOUN
ejpam-2623	1010	15	on	on	ADP
ejpam-2623	1010	16	t	t	PROPN
ejpam-2623	1010	17	,	,	PUNCT
ejpam-2623	1010	18	we	we	PRON
ejpam-2623	1010	19	have∣∣∣∣∣∑	have∣∣∣∣∣∑	VERB
ejpam-2623	1010	20	p∈t	p∈t	NOUN
ejpam-2623	1010	21	ξ(h(p	ξ(h(p	PROPN
ejpam-2623	1010	22	)	)	PUNCT
ejpam-2623	1010	23	)	)	PUNCT
ejpam-2623	1010	24	χ(λ(p	χ(λ(p	NUM
ejpam-2623	1010	25	)	)	PUNCT
ejpam-2623	1010	26	)	)	PUNCT
ejpam-2623	1011	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-2623	1011	2	≤	≤	NUM
ejpam-2623	1011	3	(	(	PUNCT
ejpam-2623	1011	4	2ĝ	2ĝ	NUM
ejpam-2623	1011	5	−	−	NOUN
ejpam-2623	1011	6	2	2	NUM
ejpam-2623	1011	7	+	+	SYM
ejpam-2623	1011	8	2	2	NUM
ejpam-2623	1011	9	deg	deg	NOUN
ejpam-2623	1011	10	λ	λ	PROPN
ejpam-2623	1011	11	)	)	PUNCT
ejpam-2623	1011	12	√	√	PROPN
ejpam-2623	1011	13	q	q	PROPN
ejpam-2623	1011	14	n.	n.	PROPN
ejpam-2623	1011	15	diarra	diarra	PROPN
ejpam-2623	1011	16	,	,	PUNCT
ejpam-2623	1011	17	d.	d.	PROPN
ejpam-2623	1011	18	sow	sow	PROPN
ejpam-2623	1011	19	,	,	PUNCT
ejpam-2623	1011	20	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	1011	21	.	.	PUNCT
ejpam-2623	1011	22	khlil	khlil	PROPN
ejpam-2623	1011	23	/	/	SYM
ejpam-2623	1011	24	eur	eur	PROPN
ejpam-2623	1011	25	.	.	PUNCT
ejpam-2623	1012	1	j.	j.	PROPN
ejpam-2623	1012	2	pure	pure	PROPN
ejpam-2623	1012	3	appl	appl	PROPN
ejpam-2623	1012	4	.	.	PROPN
ejpam-2623	1012	5	math	math	PROPN
ejpam-2623	1012	6	,	,	PUNCT
ejpam-2623	1012	7	10	10	NUM
ejpam-2623	1012	8	(	(	PUNCT
ejpam-2623	1012	9	2	2	NUM
ejpam-2623	1012	10	)	)	PUNCT
ejpam-2623	1012	11	(	(	PUNCT
ejpam-2623	1012	12	2017	2017	NUM
ejpam-2623	1012	13	)	)	PUNCT
ejpam-2623	1012	14	,	,	PUNCT
ejpam-2623	1012	15	363	363	NUM
ejpam-2623	1012	16	-	-	SYM
ejpam-2623	1012	17	391	391	NUM
ejpam-2623	1012	18	388	388	NUM
ejpam-2623	1012	19	4.2	4.2	NUM
ejpam-2623	1012	20	.	.	PUNCT
ejpam-2623	1013	1	indifferentiable	indifferentiable	ADJ
ejpam-2623	1013	2	hashing	hashing	NOUN
ejpam-2623	1013	3	let	let	VERB
ejpam-2623	1013	4	e	e	PRON
ejpam-2623	1013	5	be	be	AUX
ejpam-2623	1013	6	a	a	DET
ejpam-2623	1013	7	curve	curve	NOUN
ejpam-2623	1013	8	with	with	ADP
ejpam-2623	1013	9	a	a	DET
ejpam-2623	1013	10	fq	fq	ADJ
ejpam-2623	1013	11	-	-	ADJ
ejpam-2623	1013	12	rational	rational	ADJ
ejpam-2623	1013	13	point	point	NOUN
ejpam-2623	1013	14	and	and	CCONJ
ejpam-2623	1013	15	j	j	PROPN
ejpam-2623	1013	16	be	be	AUX
ejpam-2623	1013	17	its	its	PRON
ejpam-2623	1013	18	jacobian	jacobian	ADJ
ejpam-2623	1013	19	.	.	PUNCT
ejpam-2623	1013	20	theorem	theorem	VERB
ejpam-2623	1013	21	7	7	NUM
ejpam-2623	1013	22	.	.	PUNCT
ejpam-2623	1014	1	[	[	X
ejpam-2623	1014	2	14	14	NUM
ejpam-2623	1014	3	]	]	X
ejpam-2623	1014	4	if	if	SCONJ
ejpam-2623	1014	5	f	f	PROPN
ejpam-2623	1014	6	:	:	PUNCT
ejpam-2623	1014	7	fq	fq	PROPN
ejpam-2623	1014	8	→	→	SYM
ejpam-2623	1014	9	e(fq	e(fq	PROPN
ejpam-2623	1014	10	)	)	PUNCT
ejpam-2623	1014	11	is	be	AUX
ejpam-2623	1014	12	a	a	DET
ejpam-2623	1014	13	b	b	NOUN
ejpam-2623	1014	14	-	-	PUNCT
ejpam-2623	1014	15	well	well	ADV
ejpam-2623	1014	16	-	-	PUNCT
ejpam-2623	1014	17	distributed	distribute	VERB
ejpam-2623	1014	18	encoding	encoding	NOUN
ejpam-2623	1014	19	into	into	ADP
ejpam-2623	1014	20	e	e	NOUN
ejpam-2623	1014	21	,	,	PUNCT
ejpam-2623	1014	22	then	then	ADV
ejpam-2623	1014	23	the	the	DET
ejpam-2623	1014	24	statistical	statistical	ADJ
ejpam-2623	1014	25	distance	distance	NOUN
ejpam-2623	1014	26	between	between	ADP
ejpam-2623	1014	27	the	the	DET
ejpam-2623	1014	28	distribution	distribution	NOUN
ejpam-2623	1014	29	defined	define	VERB
ejpam-2623	1014	30	by	by	ADP
ejpam-2623	1014	31	the	the	DET
ejpam-2623	1014	32	construction	construction	NOUN
ejpam-2623	1014	33	(	(	PUNCT
ejpam-2623	1014	34	u1	u1	NOUN
ejpam-2623	1014	35	,	,	PUNCT
ejpam-2623	1014	36	.	.	PUNCT
ejpam-2623	1014	37	.	.	PUNCT
ejpam-2623	1015	1	.	.	PUNCT
ejpam-2623	1016	1	,	,	PUNCT
ejpam-2623	1016	2	us	we	PRON
ejpam-2623	1016	3	)	)	PUNCT
ejpam-2623	1016	4	7→	7→	NUM
ejpam-2623	1016	5	f(u1	f(u1	NOUN
ejpam-2623	1016	6	)	)	PUNCT
ejpam-2623	1016	7	.	.	PUNCT
ejpam-2623	1016	8	.	.	PUNCT
ejpam-2623	1016	9	.	.	PUNCT
ejpam-2623	1017	1	f(us	f(us	NOUN
ejpam-2623	1017	2	)	)	PUNCT
ejpam-2623	1017	3	on	on	ADP
ejpam-2623	1017	4	j(fq	j(fq	PROPN
ejpam-2623	1017	5	)	)	PUNCT
ejpam-2623	1017	6	and	and	CCONJ
ejpam-2623	1017	7	the	the	DET
ejpam-2623	1017	8	uniform	uniform	ADJ
ejpam-2623	1017	9	distribution	distribution	NOUN
ejpam-2623	1017	10	is	be	AUX
ejpam-2623	1017	11	bounded	bound	VERB
ejpam-2623	1017	12	as	as	ADP
ejpam-2623	1017	13	follows:∑	follows:∑	PROPN
ejpam-2623	1017	14	d∈j(fq	d∈j(fq	NOUN
ejpam-2623	1017	15	)	)	PUNCT
ejpam-2623	1017	16	∣∣∣∣ns(d	∣∣∣∣ns(d	PROPN
ejpam-2623	1017	17	)	)	PUNCT
ejpam-2623	1017	18	qs	qs	ADP
ejpam-2623	1017	19	−	−	PROPN
ejpam-2623	1018	1	1	1	NUM
ejpam-2623	1018	2	#	#	SYM
ejpam-2623	1018	3	j(fq	j(fq	NUM
ejpam-2623	1018	4	)	)	PUNCT
ejpam-2623	1018	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-2623	1018	6	≤	≤	ADJ
ejpam-2623	1018	7	bs	b	NOUN
ejpam-2623	1018	8	qs/2	qs/2	ADP
ejpam-2623	1018	9	√	√	ADV
ejpam-2623	1018	10	#	#	SYM
ejpam-2623	1018	11	j(fq	j(fq	NOUN
ejpam-2623	1018	12	)	)	PUNCT
ejpam-2623	1019	1	where	where	SCONJ
ejpam-2623	1019	2	ns(d	ns(d	NUM
ejpam-2623	1019	3	)	)	PUNCT
ejpam-2623	1019	4	=	=	PUNCT
ejpam-2623	1019	5	#	#	SYM
ejpam-2623	1019	6	{	{	PUNCT
ejpam-2623	1019	7	(	(	PUNCT
ejpam-2623	1019	8	u1	u1	NOUN
ejpam-2623	1019	9	,	,	PUNCT
ejpam-2623	1019	10	.	.	PUNCT
ejpam-2623	1019	11	.	.	PUNCT
ejpam-2623	1019	12	.	.	PUNCT
ejpam-2623	1020	1	us	we	PRON
ejpam-2623	1020	2	∈	∈	PROPN
ejpam-2623	1020	3	(	(	PUNCT
ejpam-2623	1020	4	fq)s	fq)s	NOUN
ejpam-2623	1020	5	:	:	PUNCT
ejpam-2623	1020	6	f(u1	f(u1	NOUN
ejpam-2623	1020	7	)	)	PUNCT
ejpam-2623	1021	1	+	+	CCONJ
ejpam-2623	1021	2	.	.	PUNCT
ejpam-2623	1021	3	.	.	PUNCT
ejpam-2623	1021	4	.	.	PUNCT
ejpam-2623	1022	1	f(us	f(us	NOUN
ejpam-2623	1022	2	)	)	PUNCT
ejpam-2623	1022	3	=	=	SYM
ejpam-2623	1023	1	d	d	X
ejpam-2623	1023	2	}	}	PUNCT
ejpam-2623	1023	3	for	for	ADP
ejpam-2623	1023	4	d	d	PROPN
ejpam-2623	1023	5	∈	∈	PROPN
ejpam-2623	1023	6	j(fq	j(fq	PROPN
ejpam-2623	1023	7	)	)	PUNCT
ejpam-2623	1023	8	.	.	PUNCT
ejpam-2623	1024	1	as	as	SCONJ
ejpam-2623	1024	2	said	say	VERB
ejpam-2623	1024	3	in	in	ADP
ejpam-2623	1024	4	[	[	X
ejpam-2623	1024	5	14	14	NUM
ejpam-2623	1024	6	]	]	PUNCT
ejpam-2623	1024	7	,	,	PUNCT
ejpam-2623	1024	8	this	this	DET
ejpam-2623	1024	9	theorem	theorem	NOUN
ejpam-2623	1024	10	shows	show	VERB
ejpam-2623	1024	11	that	that	SCONJ
ejpam-2623	1024	12	f	f	PROPN
ejpam-2623	1024	13	is	be	AUX
ejpam-2623	1024	14	a	a	DET
ejpam-2623	1024	15	well	well	ADV
ejpam-2623	1024	16	-	-	PUNCT
ejpam-2623	1024	17	distributed	distribute	VERB
ejpam-2623	1024	18	encoding	encoding	NOUN
ejpam-2623	1024	19	and	and	CCONJ
ejpam-2623	1024	20	if	if	SCONJ
ejpam-2623	1024	21	s	s	VERB
ejpam-2623	1024	22	is	be	AUX
ejpam-2623	1024	23	greater	great	ADJ
ejpam-2623	1024	24	than	than	ADP
ejpam-2623	1024	25	the	the	DET
ejpam-2623	1024	26	genus	genus	NOUN
ejpam-2623	1024	27	of	of	ADP
ejpam-2623	1024	28	the	the	DET
ejpam-2623	1024	29	curve	curve	NOUN
ejpam-2623	1024	30	,	,	PUNCT
ejpam-2623	1024	31	the	the	DET
ejpam-2623	1024	32	distribution	distribution	NOUN
ejpam-2623	1024	33	of	of	ADP
ejpam-2623	1024	34	the	the	DET
ejpam-2623	1024	35	new	new	ADJ
ejpam-2623	1024	36	construction	construction	NOUN
ejpam-2623	1024	37	is	be	AUX
ejpam-2623	1024	38	statistically	statistically	ADV
ejpam-2623	1024	39	indistinguishable	indistinguishable	ADJ
ejpam-2623	1024	40	from	from	ADP
ejpam-2623	1024	41	the	the	DET
ejpam-2623	1024	42	uniform	uniform	ADJ
ejpam-2623	1024	43	distribution	distribution	NOUN
ejpam-2623	1024	44	.	.	PUNCT
ejpam-2623	1025	1	moreover	moreover	ADV
ejpam-2623	1025	2	,	,	PUNCT
ejpam-2623	1025	3	it	it	PRON
ejpam-2623	1025	4	is	be	AUX
ejpam-2623	1025	5	admissible	admissible	ADJ
ejpam-2623	1025	6	if	if	SCONJ
ejpam-2623	1025	7	f	f	PROPN
ejpam-2623	1025	8	is	be	AUX
ejpam-2623	1025	9	also	also	ADV
ejpam-2623	1025	10	computable	computable	ADJ
ejpam-2623	1025	11	and	and	CCONJ
ejpam-2623	1025	12	samplable	samplable	NOUN
ejpam-2623	1025	13	,	,	PUNCT
ejpam-2623	1025	14	and	and	CCONJ
ejpam-2623	1025	15	the	the	DET
ejpam-2623	1025	16	hash	hash	NOUN
ejpam-2623	1025	17	function	function	NOUN
ejpam-2623	1025	18	m	m	VERB
ejpam-2623	1025	19	7→	7→	NUM
ejpam-2623	1025	20	f(h1(m	f(h1(m	NUM
ejpam-2623	1025	21	)	)	PUNCT
ejpam-2623	1025	22	)	)	PUNCT
ejpam-2623	1026	1	+	+	CCONJ
ejpam-2623	1026	2	.	.	PUNCT
ejpam-2623	1026	3	.	.	PUNCT
ejpam-2623	1026	4	.	.	PUNCT
ejpam-2623	1027	1	+	+	CCONJ
ejpam-2623	1027	2	f(hs(m	f(hs(m	NOUN
ejpam-2623	1027	3	)	)	PUNCT
ejpam-2623	1027	4	)	)	PUNCT
ejpam-2623	1027	5	is	be	AUX
ejpam-2623	1027	6	indifferentiable	indifferentiable	ADJ
ejpam-2623	1027	7	from	from	ADP
ejpam-2623	1027	8	a	a	DET
ejpam-2623	1027	9	random	random	ADJ
ejpam-2623	1027	10	oracle	oracle	NOUN
ejpam-2623	1027	11	if	if	SCONJ
ejpam-2623	1027	12	the	the	DET
ejpam-2623	1027	13	h1	h1	NOUN
ejpam-2623	1027	14	,	,	PUNCT
ejpam-2623	1027	15	.	.	PUNCT
ejpam-2623	1027	16	.	.	PUNCT
ejpam-2623	1028	1	.	.	PUNCT
ejpam-2623	1029	1	,	,	PUNCT
ejpam-2623	1029	2	hs	hs	PROPN
ejpam-2623	1029	3	are	be	AUX
ejpam-2623	1029	4	modeled	model	VERB
ejpam-2623	1029	5	as	as	ADP
ejpam-2623	1029	6	random	random	ADJ
ejpam-2623	1029	7	oracles	oracle	NOUN
ejpam-2623	1029	8	into	into	ADP
ejpam-2623	1029	9	fq	fq	PROPN
ejpam-2623	1029	10	.	.	PROPN
ejpam-2623	1029	11	4.3	4.3	NUM
ejpam-2623	1029	12	.	.	PUNCT
ejpam-2623	1030	1	application	application	NOUN
ejpam-2623	1030	2	to	to	ADP
ejpam-2623	1030	3	the	the	DET
ejpam-2623	1030	4	encoding	encoding	NOUN
ejpam-2623	1030	5	φd	φd	AUX
ejpam-2623	1030	6	in	in	ADP
ejpam-2623	1030	7	this	this	DET
ejpam-2623	1030	8	section	section	NOUN
ejpam-2623	1030	9	,	,	PUNCT
ejpam-2623	1030	10	we	we	PRON
ejpam-2623	1030	11	apply	apply	VERB
ejpam-2623	1030	12	the	the	DET
ejpam-2623	1030	13	results	result	NOUN
ejpam-2623	1030	14	and	and	CCONJ
ejpam-2623	1030	15	proofs	proof	NOUN
ejpam-2623	1030	16	of	of	ADP
ejpam-2623	1030	17	farashahi	farashahi	NOUN
ejpam-2623	1030	18	et	et	PROPN
ejpam-2623	1030	19	al	al	PROPN
ejpam-2623	1030	20	.	.	PUNCT
ejpam-2623	1031	1	[	[	X
ejpam-2623	1031	2	14	14	NUM
ejpam-2623	1031	3	]	]	PUNCT
ejpam-2623	1031	4	(	(	PUNCT
ejpam-2623	1031	5	for	for	ADP
ejpam-2623	1031	6	the	the	DET
ejpam-2623	1031	7	shalluewoestijne	shalluewoestijne	NOUN
ejpam-2623	1031	8	-	-	PUNCT
ejpam-2623	1031	9	ulas	ulas	PROPN
ejpam-2623	1031	10	encoding	encoding	PROPN
ejpam-2623	1031	11	)	)	PUNCT
ejpam-2623	1031	12	to	to	ADP
ejpam-2623	1031	13	one	one	NUM
ejpam-2623	1031	14	of	of	ADP
ejpam-2623	1031	15	our	our	PRON
ejpam-2623	1031	16	previous	previous	ADJ
ejpam-2623	1031	17	encodings	encoding	NOUN
ejpam-2623	1031	18	.	.	PUNCT
ejpam-2623	1032	1	we	we	PRON
ejpam-2623	1032	2	will	will	AUX
ejpam-2623	1032	3	show	show	VERB
ejpam-2623	1032	4	that	that	SCONJ
ejpam-2623	1032	5	the	the	DET
ejpam-2623	1032	6	encoding	encoding	NOUN
ejpam-2623	1032	7	φd	φd	VERB
ejpam-2623	1032	8	over	over	ADP
ejpam-2623	1032	9	the	the	DET
ejpam-2623	1032	10	edwards	edwards	PROPN
ejpam-2623	1032	11	curve	curve	PROPN
ejpam-2623	1032	12	x2	x2	PROPN
ejpam-2623	1033	1	+	+	CCONJ
ejpam-2623	1033	2	y2	y2	NOUN
ejpam-2623	1033	3	=	=	SYM
ejpam-2623	1033	4	1	1	NUM
ejpam-2623	1034	1	+	+	CCONJ
ejpam-2623	1034	2	dx2y2	dx2y2	VERB
ejpam-2623	1034	3	when	when	SCONJ
ejpam-2623	1034	4	q	q	PROPN
ejpam-2623	1034	5	≡	≡	PROPN
ejpam-2623	1034	6	3	3	NUM
ejpam-2623	1034	7	mod	mod	NOUN
ejpam-2623	1034	8	4	4	NUM
ejpam-2623	1034	9	is	be	AUX
ejpam-2623	1034	10	well	well	ADV
ejpam-2623	1034	11	-	-	PUNCT
ejpam-2623	1034	12	distributed	distribute	VERB
ejpam-2623	1034	13	,	,	PUNCT
ejpam-2623	1034	14	and	and	CCONJ
ejpam-2623	1034	15	thus	thus	ADV
ejpam-2623	1034	16	give	give	VERB
ejpam-2623	1034	17	rise	rise	NOUN
ejpam-2623	1034	18	to	to	ADP
ejpam-2623	1034	19	a	a	DET
ejpam-2623	1034	20	indifferentiable	indifferentiable	ADJ
ejpam-2623	1034	21	hash	hash	NOUN
ejpam-2623	1034	22	function	function	NOUN
ejpam-2623	1034	23	construction	construction	NOUN
ejpam-2623	1034	24	.	.	PUNCT
ejpam-2623	1035	1	recall	recall	NOUN
ejpam-2623	1035	2	that	that	PRON
ejpam-2623	1035	3	φd	φd	AUX
ejpam-2623	1035	4	is	be	AUX
ejpam-2623	1035	5	an	an	DET
ejpam-2623	1035	6	efficient	efficient	ADJ
ejpam-2623	1035	7	almost	almost	ADV
ejpam-2623	1035	8	-	-	PUNCT
ejpam-2623	1035	9	injective	injective	ADJ
ejpam-2623	1035	10	and	and	CCONJ
ejpam-2623	1035	11	invertible	invertible	ADJ
ejpam-2623	1035	12	encoding	encoding	NOUN
ejpam-2623	1035	13	from	from	ADP
ejpam-2623	1035	14	the	the	DET
ejpam-2623	1035	15	subset	subset	NOUN
ejpam-2623	1035	16	r	r	NOUN
ejpam-2623	1035	17	=	=	PUNCT
ejpam-2623	1035	18	{	{	PUNCT
ejpam-2623	1035	19	r	r	NOUN
ejpam-2623	1035	20	∈	∈	PROPN
ejpam-2623	1035	21	f∗q	f∗q	NOUN
ejpam-2623	1035	22	:	:	PUNCT
ejpam-2623	1035	23	ur2	ur2	X
ejpam-2623	1036	1	+	+	CCONJ
ejpam-2623	1036	2	1	1	NUM
ejpam-2623	1036	3	6=	6=	NUM
ejpam-2623	1036	4	0	0	NUM
ejpam-2623	1036	5	,	,	PUNCT
ejpam-2623	1036	6	ur2(1	ur2(1	NOUN
ejpam-2623	1037	1	−	−	PROPN
ejpam-2623	1037	2	d	d	NOUN
ejpam-2623	1037	3	)	)	PUNCT
ejpam-2623	1037	4	−	−	PROPN
ejpam-2623	1037	5	(	(	PUNCT
ejpam-2623	1037	6	1	1	NUM
ejpam-2623	1037	7	+	+	NUM
ejpam-2623	1037	8	3d	3d	NUM
ejpam-2623	1037	9	)	)	PUNCT
ejpam-2623	1037	10	6=	6=	ADP
ejpam-2623	1037	11	0	0	NUM
ejpam-2623	1037	12	,	,	PUNCT
ejpam-2623	1037	13	ur2(1	ur2(1	NOUN
ejpam-2623	1037	14	+	+	CCONJ
ejpam-2623	1037	15	3d	3d	NUM
ejpam-2623	1037	16	)	)	PUNCT
ejpam-2623	1037	17	−	−	PROPN
ejpam-2623	1038	1	(	(	PUNCT
ejpam-2623	1038	2	1	1	NUM
ejpam-2623	1038	3	−	−	PROPN
ejpam-2623	1038	4	d	d	NOUN
ejpam-2623	1038	5	)	)	PUNCT
ejpam-2623	1038	6	6=	6=	ADP
ejpam-2623	1038	7	0	0	NUM
ejpam-2623	1038	8	}	}	PUNCT
ejpam-2623	1038	9	to	to	ADP
ejpam-2623	1038	10	the	the	DET
ejpam-2623	1038	11	elliptic	elliptic	ADJ
ejpam-2623	1038	12	curve	curve	NOUN
ejpam-2623	1038	13	ed	ed	NOUN
ejpam-2623	1038	14	:	:	PUNCT
ejpam-2623	1039	1	x2	x2	PROPN
ejpam-2623	1039	2	+	+	PUNCT
ejpam-2623	1039	3	y2	y2	NOUN
ejpam-2623	1039	4	=	=	SYM
ejpam-2623	1039	5	1	1	NUM
ejpam-2623	1039	6	+	+	CCONJ
ejpam-2623	1039	7	dx2y2	dx2y2	PROPN
ejpam-2623	1039	8	,	,	PUNCT
ejpam-2623	1039	9	and	and	CCONJ
ejpam-2623	1039	10	let	let	VERB
ejpam-2623	1039	11	ω	ω	PROPN
ejpam-2623	1039	12	=	=	SYM
ejpam-2623	1039	13	fq	fq	PROPN
ejpam-2623	1039	14	\r	\r	PROPN
ejpam-2623	1039	15	.	.	PUNCT
ejpam-2623	1040	1	by	by	ADP
ejpam-2623	1040	2	the	the	DET
ejpam-2623	1040	3	invertibility	invertibility	NOUN
ejpam-2623	1040	4	of	of	ADP
ejpam-2623	1040	5	φd	φd	PROPN
ejpam-2623	1040	6	,	,	PUNCT
ejpam-2623	1040	7	we	we	PRON
ejpam-2623	1040	8	know	know	VERB
ejpam-2623	1040	9	that	that	SCONJ
ejpam-2623	1040	10	for	for	ADP
ejpam-2623	1040	11	(	(	PUNCT
ejpam-2623	1040	12	x	x	NOUN
ejpam-2623	1040	13	,	,	PUNCT
ejpam-2623	1040	14	y	y	NOUN
ejpam-2623	1040	15	)	)	PUNCT
ejpam-2623	1040	16	∈	∈	PROPN
ejpam-2623	1040	17	im(φd	im(φd	PROPN
ejpam-2623	1040	18	)	)	PUNCT
ejpam-2623	1040	19	,	,	PUNCT
ejpam-2623	1040	20	there	there	PRON
ejpam-2623	1040	21	exists	exist	VERB
ejpam-2623	1040	22	two	two	NUM
ejpam-2623	1040	23	preimages	preimage	NOUN
ejpam-2623	1040	24	r,−r	r,−r	NOUN
ejpam-2623	1040	25	such	such	ADJ
ejpam-2623	1040	26	that	that	SCONJ
ejpam-2623	1040	27	φd(±r	φd(±r	NOUN
ejpam-2623	1040	28	)	)	PUNCT
ejpam-2623	1040	29	=	=	SYM
ejpam-2623	1040	30	(	(	PUNCT
ejpam-2623	1040	31	x	x	X
ejpam-2623	1040	32	,	,	PUNCT
ejpam-2623	1040	33	y	y	PROPN
ejpam-2623	1040	34	)	)	PUNCT
ejpam-2623	1040	35	.	.	PUNCT
ejpam-2623	1041	1	when	when	SCONJ
ejpam-2623	1041	2	q	q	NOUN
ejpam-2623	1041	3	=	=	SYM
ejpam-2623	1041	4	3	3	NUM
ejpam-2623	1041	5	mod	mod	NOUN
ejpam-2623	1041	6	4	4	NUM
ejpam-2623	1041	7	,	,	PUNCT
ejpam-2623	1041	8	we	we	PRON
ejpam-2623	1041	9	have	have	VERB
ejpam-2623	1041	10	:	:	PUNCT
ejpam-2623	1042	1	y	y	PROPN
ejpam-2623	1042	2	=	=	PUNCT
ejpam-2623	1042	3	√	√	PROPN
ejpam-2623	1042	4	1−	1−	NUM
ejpam-2623	1043	1	x2	x2	NOUN
ejpam-2623	1043	2	1−	1−	NUM
ejpam-2623	1043	3	dx2	dx2	PROPN
ejpam-2623	1043	4	⇒	⇒	PROPN
ejpam-2623	1043	5	χq(y	χq(y	NUM
ejpam-2623	1043	6	)	)	PUNCT
ejpam-2623	1043	7	=	=	SYM
ejpam-2623	1043	8	1	1	NUM
ejpam-2623	1043	9	and	and	CCONJ
ejpam-2623	1043	10	y	y	NOUN
ejpam-2623	1043	11	=	=	PUNCT
ejpam-2623	1044	1	−	−	PROPN
ejpam-2623	1044	2	√	√	NUM
ejpam-2623	1044	3	1−	1−	NUM
ejpam-2623	1045	1	x2	x2	NOUN
ejpam-2623	1045	2	1−	1−	NUM
ejpam-2623	1045	3	dx2	dx2	PROPN
ejpam-2623	1045	4	⇒	⇒	PROPN
ejpam-2623	1045	5	χq(y	χq(y	NUM
ejpam-2623	1045	6	)	)	PUNCT
ejpam-2623	1045	7	=	=	SYM
ejpam-2623	1045	8	−1	−1	NOUN
ejpam-2623	1045	9	.	.	PUNCT
ejpam-2623	1046	1	thus	thus	ADV
ejpam-2623	1046	2	:	:	PUNCT
ejpam-2623	1046	3	χq(y	χq(y	NUM
ejpam-2623	1046	4	)	)	PUNCT
ejpam-2623	1046	5	=	=	SYM
ejpam-2623	1047	1	−1⇔	−1⇔	PROPN
ejpam-2623	1047	2	r2	r2	NOUN
ejpam-2623	1047	3	=	=	PUNCT
ejpam-2623	1047	4	(	(	PUNCT
ejpam-2623	1047	5	d−	d−	PROPN
ejpam-2623	1047	6	1)(1−	1)(1−	NUM
ejpam-2623	1047	7	x	x	SYM
ejpam-2623	1047	8	)	)	PUNCT
ejpam-2623	1047	9	u[x(3d+	u[x(3d+	NOUN
ejpam-2623	1047	10	1	1	NUM
ejpam-2623	1047	11	)	)	PUNCT
ejpam-2623	1047	12	+	+	NUM
ejpam-2623	1047	13	d+	d+	NOUN
ejpam-2623	1047	14	3	3	NUM
ejpam-2623	1047	15	)	)	PUNCT
ejpam-2623	1047	16	]	]	PUNCT
ejpam-2623	1047	17	eq−	eq−	PROPN
ejpam-2623	1047	18	(	(	PUNCT
ejpam-2623	1047	19	0	0	NUM
ejpam-2623	1047	20	)	)	PUNCT
ejpam-2623	1047	21	χq(y	χq(y	NUM
ejpam-2623	1047	22	)	)	PUNCT
ejpam-2623	1047	23	=	=	SYM
ejpam-2623	1047	24	1⇔	1⇔	NUM
ejpam-2623	1047	25	r2	r2	NOUN
ejpam-2623	1047	26	=	=	PUNCT
ejpam-2623	1047	27	x(3d+	x(3d+	NOUN
ejpam-2623	1047	28	1	1	NUM
ejpam-2623	1047	29	)	)	PUNCT
ejpam-2623	1047	30	+	+	CCONJ
ejpam-2623	1047	31	d+	d+	SYM
ejpam-2623	1047	32	3	3	NUM
ejpam-2623	1047	33	u(d−	u(d−	PROPN
ejpam-2623	1047	34	1)(1−	1)(1−	NUM
ejpam-2623	1047	35	x	x	SYM
ejpam-2623	1047	36	)	)	PUNCT
ejpam-2623	1047	37	eq−	eq−	PROPN
ejpam-2623	1047	38	(	(	PUNCT
ejpam-2623	1047	39	1	1	NUM
ejpam-2623	1047	40	)	)	PUNCT
ejpam-2623	1047	41	.	.	PUNCT
ejpam-2623	1048	1	from	from	ADP
ejpam-2623	1048	2	now	now	ADV
ejpam-2623	1048	3	,	,	PUNCT
ejpam-2623	1048	4	the	the	DET
ejpam-2623	1048	5	proof	proof	NOUN
ejpam-2623	1048	6	is	be	AUX
ejpam-2623	1048	7	similar	similar	ADJ
ejpam-2623	1048	8	to	to	ADP
ejpam-2623	1048	9	the	the	DET
ejpam-2623	1048	10	one	one	NUM
ejpam-2623	1048	11	of	of	ADP
ejpam-2623	1048	12	of	of	ADP
ejpam-2623	1048	13	farashahi	farashahi	NOUN
ejpam-2623	1048	14	et	et	PROPN
ejpam-2623	1048	15	al	al	PROPN
ejpam-2623	1048	16	(	(	PUNCT
ejpam-2623	1048	17	in	in	ADP
ejpam-2623	1048	18	[	[	PUNCT
ejpam-2623	1048	19	14	14	NUM
ejpam-2623	1048	20	]	]	PUNCT
ejpam-2623	1048	21	subsection	subsection	NOUN
ejpam-2623	1048	22	5.3	5.3	NUM
ejpam-2623	1048	23	)	)	PUNCT
ejpam-2623	1048	24	.	.	PUNCT
ejpam-2623	1049	1	by	by	ADP
ejpam-2623	1049	2	equation	equation	NOUN
ejpam-2623	1049	3	eq	eq	ADP
ejpam-2623	1049	4	−	−	PROPN
ejpam-2623	1049	5	(	(	PUNCT
ejpam-2623	1049	6	1	1	NUM
ejpam-2623	1049	7	)	)	PUNCT
ejpam-2623	1049	8	,	,	PUNCT
ejpam-2623	1049	9	we	we	PRON
ejpam-2623	1049	10	define	define	VERB
ejpam-2623	1049	11	the	the	DET
ejpam-2623	1049	12	coverings	covering	NOUN
ejpam-2623	1049	13	hi	hi	INTJ
ejpam-2623	1049	14	:	:	PUNCT
ejpam-2623	1049	15	ci	ci	PROPN
ejpam-2623	1049	16	→	→	SYM
ejpam-2623	1049	17	e	e	PROPN
ejpam-2623	1049	18	,	,	PUNCT
ejpam-2623	1049	19	i	i	PRON
ejpam-2623	1049	20	=	=	NOUN
ejpam-2623	1049	21	0	0	NUM
ejpam-2623	1049	22	,	,	PUNCT
ejpam-2623	1049	23	1	1	NUM
ejpam-2623	1049	24	,	,	PUNCT
ejpam-2623	1049	25	by	by	ADP
ejpam-2623	1049	26	the	the	DET
ejpam-2623	1049	27	smooth	smooth	ADJ
ejpam-2623	1049	28	projective	projective	PROPN
ejpam-2623	1049	29	curve	curve	NOUN
ejpam-2623	1049	30	whose	whose	DET
ejpam-2623	1049	31	function	function	NOUN
ejpam-2623	1049	32	fields	field	NOUN
ejpam-2623	1049	33	(	(	PUNCT
ejpam-2623	1049	34	denoted	denote	VERB
ejpam-2623	1049	35	fq(x	fq(x	NOUN
ejpam-2623	1049	36	,	,	PUNCT
ejpam-2623	1049	37	y	y	PROPN
ejpam-2623	1049	38	,	,	PUNCT
ejpam-2623	1049	39	r	r	NOUN
ejpam-2623	1049	40	)	)	PUNCT
ejpam-2623	1049	41	)	)	PUNCT
ejpam-2623	1049	42	is	be	AUX
ejpam-2623	1049	43	the	the	DET
ejpam-2623	1049	44	extension	extension	NOUN
ejpam-2623	1049	45	of	of	ADP
ejpam-2623	1049	46	fq(x	fq(x	PROPN
ejpam-2623	1049	47	,	,	PUNCT
ejpam-2623	1049	48	y	y	NOUN
ejpam-2623	1049	49	)	)	PUNCT
ejpam-2623	1049	50	given	give	VERB
ejpam-2623	1049	51	by	by	ADP
ejpam-2623	1049	52	eq−	eq−	PROPN
ejpam-2623	1049	53	(	(	PUNCT
ejpam-2623	1049	54	i	i	NOUN
ejpam-2623	1049	55	)	)	PUNCT
ejpam-2623	1049	56	.	.	PUNCT
ejpam-2623	1050	1	since	since	SCONJ
ejpam-2623	1050	2	r	r	NOUN
ejpam-2623	1050	3	is	be	AUX
ejpam-2623	1050	4	a	a	DET
ejpam-2623	1050	5	rational	rational	ADJ
ejpam-2623	1050	6	function	function	NOUN
ejpam-2623	1050	7	on	on	ADP
ejpam-2623	1050	8	ci	ci	PROPN
ejpam-2623	1050	9	,	,	PUNCT
ejpam-2623	1050	10	we	we	PRON
ejpam-2623	1050	11	have	have	VERB
ejpam-2623	1050	12	a	a	DET
ejpam-2623	1050	13	morphism	morphism	NOUN
ejpam-2623	1050	14	fi	fi	NOUN
ejpam-2623	1050	15	:	:	PUNCT
ejpam-2623	1050	16	ci	ci	PROPN
ejpam-2623	1050	17	→	→	SYM
ejpam-2623	1050	18	p1	p1	PROPN
ejpam-2623	1050	19	,	,	PUNCT
ejpam-2623	1050	20	such	such	ADJ
ejpam-2623	1050	21	that	that	SCONJ
ejpam-2623	1050	22	any	any	DET
ejpam-2623	1050	23	point	point	NOUN
ejpam-2623	1050	24	in	in	ADP
ejpam-2623	1050	25	a1(fq	a1(fq	PROPN
ejpam-2623	1050	26	)	)	PUNCT
ejpam-2623	1050	27	\	\	PROPN
ejpam-2623	1050	28	ω	ω	PROPN
ejpam-2623	1050	29	has	have	VERB
ejpam-2623	1050	30	exactly	exactly	ADV
ejpam-2623	1050	31	two	two	NUM
ejpam-2623	1050	32	preimages	preimage	NOUN
ejpam-2623	1050	33	in	in	ADP
ejpam-2623	1050	34	ci	ci	NOUN
ejpam-2623	1050	35	for	for	ADP
ejpam-2623	1050	36	one	one	NUM
ejpam-2623	1050	37	of	of	ADP
ejpam-2623	1050	38	i	i	PRON
ejpam-2623	1050	39	=	=	PROPN
ejpam-2623	1050	40	0	0	NUM
ejpam-2623	1050	41	,	,	PUNCT
ejpam-2623	1050	42	1	1	NUM
ejpam-2623	1050	43	,	,	PUNCT
ejpam-2623	1050	44	and	and	CCONJ
ejpam-2623	1050	45	none	none	NOUN
ejpam-2623	1050	46	in	in	ADP
ejpam-2623	1050	47	n.	n.	PROPN
ejpam-2623	1050	48	diarra	diarra	PROPN
ejpam-2623	1050	49	,	,	PUNCT
ejpam-2623	1050	50	d.	d.	PROPN
ejpam-2623	1050	51	sow	sow	PROPN
ejpam-2623	1050	52	,	,	PUNCT
ejpam-2623	1050	53	a.y.o.c	a.y.o.c	PROPN
ejpam-2623	1050	54	.	.	PUNCT
ejpam-2623	1050	55	khlil	khlil	PROPN
ejpam-2623	1050	56	/	/	SYM
ejpam-2623	1050	57	eur	eur	PROPN
ejpam-2623	1050	58	.	.	PUNCT
ejpam-2623	1051	1	j.	j.	PROPN
ejpam-2623	1051	2	pure	pure	PROPN
ejpam-2623	1051	3	appl	appl	PROPN
ejpam-2623	1051	4	.	.	PROPN
ejpam-2623	1051	5	math	math	PROPN
ejpam-2623	1051	6	,	,	PUNCT
ejpam-2623	1051	7	10	10	NUM
ejpam-2623	1051	8	(	(	PUNCT
ejpam-2623	1051	9	2	2	NUM
ejpam-2623	1051	10	)	)	PUNCT
ejpam-2623	1051	11	(	(	PUNCT
ejpam-2623	1051	12	2017	2017	NUM
ejpam-2623	1051	13	)	)	PUNCT
ejpam-2623	1051	14	,	,	PUNCT
ejpam-2623	1051	15	363	363	NUM
ejpam-2623	1051	16	-	-	SYM
ejpam-2623	1051	17	391	391	NUM
ejpam-2623	1051	18	389	389	NUM
ejpam-2623	1051	19	the	the	DET
ejpam-2623	1051	20	other	other	ADJ
ejpam-2623	1051	21	.	.	PUNCT
ejpam-2623	1052	1	since	since	SCONJ
ejpam-2623	1052	2	q	q	PROPN
ejpam-2623	1052	3	=	=	SYM
ejpam-2623	1052	4	3	3	NUM
ejpam-2623	1052	5	mod	mod	NOUN
ejpam-2623	1052	6	4	4	NUM
ejpam-2623	1052	7	,	,	PUNCT
ejpam-2623	1052	8	then	then	ADV
ejpam-2623	1052	9	these	these	DET
ejpam-2623	1052	10	two	two	NUM
ejpam-2623	1052	11	preimages	preimage	NOUN
ejpam-2623	1052	12	are	be	AUX
ejpam-2623	1052	13	conjugate	conjugate	ADJ
ejpam-2623	1052	14	under	under	ADP
ejpam-2623	1052	15	y	y	PROPN
ejpam-2623	1052	16	→	→	SYM
ejpam-2623	1052	17	−y	−y	PROPN
ejpam-2623	1052	18	.	.	PUNCT
ejpam-2623	1053	1	therefore	therefore	ADV
ejpam-2623	1053	2	,	,	PUNCT
ejpam-2623	1053	3	exactly	exactly	ADV
ejpam-2623	1053	4	one	one	NUM
ejpam-2623	1053	5	of	of	ADP
ejpam-2623	1053	6	them	they	PRON
ejpam-2623	1053	7	satisfies	satisfy	VERB
ejpam-2623	1053	8	χq(y	χq(y	NUM
ejpam-2623	1053	9	)	)	PUNCT
ejpam-2623	1053	10	=	=	SYM
ejpam-2623	1053	11	(	(	PUNCT
ejpam-2623	1053	12	−1)i	−1)i	X
ejpam-2623	1053	13	.	.	PUNCT
ejpam-2623	1053	14	let	let	VERB
ejpam-2623	1053	15	p	p	PROPN
ejpam-2623	1053	16	∈	∈	PROPN
ejpam-2623	1053	17	ci	ci	NOUN
ejpam-2623	1053	18	be	be	AUX
ejpam-2623	1053	19	that	that	DET
ejpam-2623	1053	20	preimage	preimage	NOUN
ejpam-2623	1053	21	;	;	PUNCT
ejpam-2623	1053	22	so	so	ADV
ejpam-2623	1053	23	φd(u	φd(u	PUNCT
ejpam-2623	1053	24	)	)	PUNCT
ejpam-2623	1053	25	=	=	SYM
ejpam-2623	1053	26	hi(p	hi(p	PRON
ejpam-2623	1053	27	)	)	PUNCT
ejpam-2623	1053	28	.	.	PUNCT
ejpam-2623	1054	1	theorem	theorem	ADJ
ejpam-2623	1054	2	8	8	NUM
ejpam-2623	1054	3	.	.	PUNCT
ejpam-2623	1055	1	for	for	ADP
ejpam-2623	1055	2	any	any	DET
ejpam-2623	1055	3	nontrivial	nontrivial	ADJ
ejpam-2623	1055	4	character	character	NOUN
ejpam-2623	1055	5	ξ	ξ	PROPN
ejpam-2623	1055	6	of	of	ADP
ejpam-2623	1055	7	ed(fq	ed(fq	PROPN
ejpam-2623	1055	8	)	)	PUNCT
ejpam-2623	1055	9	,	,	PUNCT
ejpam-2623	1055	10	the	the	DET
ejpam-2623	1055	11	following	follow	VERB
ejpam-2623	1055	12	holds	hold	VERB
ejpam-2623	1055	13	when	when	SCONJ
ejpam-2623	1055	14	q	q	PROPN
ejpam-2623	1055	15	≡	≡	PROPN
ejpam-2623	1055	16	3	3	NUM
ejpam-2623	1055	17	mod	mod	NOUN
ejpam-2623	1055	18	4	4	NUM
ejpam-2623	1055	19	:	:	PUNCT
ejpam-2623	1055	20	∣∣∣∣∣∣	∣∣∣∣∣∣	ADJ
ejpam-2623	1055	21	∑	∑	PUNCT
ejpam-2623	1055	22	r∈fq	r∈fq	PROPN
ejpam-2623	1055	23	ξ(φd(r	ξ(φd(r	NOUN
ejpam-2623	1055	24	)	)	PUNCT
ejpam-2623	1055	25	)	)	PUNCT
ejpam-2623	1055	26	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-2623	1055	27	≤	≤	ADV
ejpam-2623	1055	28	12	12	NUM
ejpam-2623	1055	29	√	√	PROPN
ejpam-2623	1055	30	q	q	NOUN
ejpam-2623	1056	1	+	+	NOUN
ejpam-2623	1056	2	31	31	NUM
ejpam-2623	1056	3	.	.	PUNCT
ejpam-2623	1057	1	proof	proof	NOUN
ejpam-2623	1057	2	.	.	PUNCT
ejpam-2623	1058	1	let	let	VERB
ejpam-2623	1058	2	r	r	NOUN
ejpam-2623	1058	3	∈	∈	PROPN
ejpam-2623	1058	4	r	r	NOUN
ejpam-2623	1058	5	,	,	PUNCT
ejpam-2623	1058	6	ω	ω	X
ejpam-2623	1058	7	=	=	SYM
ejpam-2623	1058	8	fq	fq	PROPN
ejpam-2623	1058	9	\	\	NOUN
ejpam-2623	1058	10	r	r	NOUN
ejpam-2623	1058	11	and	and	CCONJ
ejpam-2623	1058	12	hi	hi	INTJ
ejpam-2623	1058	13	:	:	PUNCT
ejpam-2623	1058	14	ci	ci	PROPN
ejpam-2623	1058	15	→	→	SYM
ejpam-2623	1058	16	ed	ed	NOUN
ejpam-2623	1058	17	(	(	PUNCT
ejpam-2623	1058	18	i	i	NOUN
ejpam-2623	1058	19	=	=	NOUN
ejpam-2623	1058	20	0	0	NUM
ejpam-2623	1058	21	,	,	PUNCT
ejpam-2623	1058	22	1	1	NUM
ejpam-2623	1058	23	)	)	PUNCT
ejpam-2623	1058	24	defined	define	VERB
ejpam-2623	1058	25	as	as	ADP
ejpam-2623	1058	26	previously	previously	ADV
ejpam-2623	1058	27	;	;	PUNCT
ejpam-2623	1058	28	also	also	ADV
ejpam-2623	1058	29	define	define	VERB
ejpam-2623	1058	30	ωi	ωi	X
ejpam-2623	1058	31	=	=	PUNCT
ejpam-2623	1058	32	{	{	PUNCT
ejpam-2623	1058	33	p	p	NOUN
ejpam-2623	1058	34	∈	∈	PROPN
ejpam-2623	1058	35	ci	ci	NOUN
ejpam-2623	1058	36	:	:	PUNCT
ejpam-2623	1058	37	fi(p	fi(p	X
ejpam-2623	1058	38	)	)	PUNCT
ejpam-2623	1058	39	∈	∈	PROPN
ejpam-2623	1058	40	ω	ω	PROPN
ejpam-2623	1058	41	}	}	PUNCT
ejpam-2623	1058	42	.	.	PUNCT
ejpam-2623	1059	1	so	so	ADV
ejpam-2623	1059	2	we	we	PRON
ejpam-2623	1059	3	can	can	AUX
ejpam-2623	1059	4	write	write	VERB
ejpam-2623	1059	5	:	:	PUNCT
ejpam-2623	1059	6	∑	∑	PUNCT
ejpam-2623	1059	7	r∈r	r∈r	NOUN
ejpam-2623	1059	8	ξ(φd(r	ξ(φd(r	NOUN
ejpam-2623	1059	9	)	)	PUNCT
ejpam-2623	1059	10	)	)	PUNCT
ejpam-2623	1060	1	=	=	SYM
ejpam-2623	1060	2	∑	∑	ADV
ejpam-2623	1060	3	p∈c0(fq)\ω0	p∈c0(fq)\ω0	ADV
ejpam-2623	1060	4	,	,	PUNCT
ejpam-2623	1060	5	χ(y)=+1	χ(y)=+1	VERB
ejpam-2623	1060	6	ξ(h0(p	ξ(h0(p	NOUN
ejpam-2623	1060	7	)	)	PUNCT
ejpam-2623	1060	8	)	)	PUNCT
ejpam-2623	1061	1	+	+	CCONJ
ejpam-2623	1061	2	∑	∑	ADV
ejpam-2623	1061	3	p∈c1(fq)\ω1	p∈c1(fq)\ω1	ADJ
ejpam-2623	1061	4	,	,	PUNCT
ejpam-2623	1061	5	χ(y)=−1	χ(y)=−1	VERB
ejpam-2623	1061	6	ξ(h1(p	ξ(h1(p	NOUN
ejpam-2623	1061	7	)	)	PUNCT
ejpam-2623	1061	8	)	)	PUNCT
ejpam-2623	1061	9	(	(	PUNCT
ejpam-2623	1061	10	*	*	NOUN
ejpam-2623	1061	11	)	)	PUNCT
ejpam-2623	1061	12	.	.	PUNCT
ejpam-2623	1062	1	also	also	ADV
ejpam-2623	1062	2	observe	observe	VERB
ejpam-2623	1062	3	that	that	SCONJ
ejpam-2623	1062	4	:	:	PUNCT
ejpam-2623	1062	5	1	1	NUM
ejpam-2623	1062	6	2	2	NUM
ejpam-2623	1062	7	∑	∑	ADV
ejpam-2623	1062	8	p∈ci(fq	p∈ci(fq	NOUN
ejpam-2623	1062	9	)	)	PUNCT
ejpam-2623	1062	10	,	,	PUNCT
ejpam-2623	1062	11	χ(y)=0	χ(y)=0	ADV
ejpam-2623	1062	12	ξ(hi(p	ξ(hi(p	NOUN
ejpam-2623	1062	13	)	)	PUNCT
ejpam-2623	1062	14	)	)	PUNCT
ejpam-2623	1063	1	+	+	CCONJ
ejpam-2623	1063	2	∑	∑	ADP
ejpam-2623	1063	3	p∈ci(fq	p∈ci(fq	NOUN
ejpam-2623	1063	4	)	)	PUNCT
ejpam-2623	1063	5	,	,	PUNCT
ejpam-2623	1063	6	χ(y)=(−1)i	χ(y)=(−1)i	PROPN
ejpam-2623	1063	7	ξ(hi(p	ξ(hi(p	NOUN
ejpam-2623	1063	8	)	)	PUNCT
ejpam-2623	1063	9	)	)	PUNCT
ejpam-2623	1064	1	=	=	PUNCT
ejpam-2623	1064	2	∑	∑	PUNCT
ejpam-2623	1064	3	p∈ci(fq	p∈ci(fq	NOUN
ejpam-2623	1064	4	)	)	PUNCT
ejpam-2623	1064	5	ξ(hi(p	ξ(hi(p	NOUN
ejpam-2623	1064	6	)	)	PUNCT
ejpam-2623	1064	7	)	)	PUNCT
ejpam-2623	1064	8	·	·	PUNCT
ejpam-2623	1065	1	(	(	PUNCT
ejpam-2623	1065	2	1	1	NUM
ejpam-2623	1065	3	+	+	CCONJ
ejpam-2623	1065	4	(	(	PUNCT
ejpam-2623	1065	5	−1)iχ(y	−1)iχ(y	NOUN
ejpam-2623	1065	6	)	)	PUNCT
ejpam-2623	1065	7	2	2	NUM
ejpam-2623	1065	8	)	)	PUNCT
ejpam-2623	1065	9	.	.	PUNCT
ejpam-2623	1066	1	(	(	PUNCT
ejpam-2623	1066	2	*	*	PUNCT
ejpam-2623	1066	3	*	*	X
ejpam-2623	1066	4	)	)	PUNCT
ejpam-2623	1066	5	one	one	PRON
ejpam-2623	1066	6	can	can	AUX
ejpam-2623	1066	7	see	see	VERB
ejpam-2623	1066	8	that	that	SCONJ
ejpam-2623	1066	9	the	the	DET
ejpam-2623	1066	10	first	first	ADJ
ejpam-2623	1066	11	term	term	NOUN
ejpam-2623	1066	12	of	of	ADP
ejpam-2623	1066	13	the	the	DET
ejpam-2623	1066	14	left	left	ADJ
ejpam-2623	1066	15	-	-	PUNCT
ejpam-2623	1066	16	hand	hand	NOUN
ejpam-2623	1066	17	side	side	NOUN
ejpam-2623	1066	18	of	of	ADP
ejpam-2623	1066	19	this	this	DET
ejpam-2623	1066	20	equality	equality	NOUN
ejpam-2623	1066	21	contains	contain	VERB
ejpam-2623	1066	22	at	at	ADP
ejpam-2623	1066	23	most	most	ADJ
ejpam-2623	1066	24	2	2	NUM
ejpam-2623	1066	25	·	·	SYM
ejpam-2623	1066	26	2	2	NUM
ejpam-2623	1066	27	=	=	SYM
ejpam-2623	1066	28	4	4	NUM
ejpam-2623	1066	29	terms	term	NOUN
ejpam-2623	1066	30	,	,	PUNCT
ejpam-2623	1066	31	when	when	SCONJ
ejpam-2623	1066	32	expressing	express	VERB
ejpam-2623	1066	33	y2	y2	PROPN
ejpam-2623	1066	34	in	in	ADP
ejpam-2623	1066	35	terms	term	NOUN
ejpam-2623	1066	36	of	of	ADP
ejpam-2623	1066	37	x	x	X
ejpam-2623	1066	38	and	and	CCONJ
ejpam-2623	1066	39	by	by	ADP
ejpam-2623	1066	40	eq−	eq−	PROPN
ejpam-2623	1066	41	(	(	PUNCT
ejpam-2623	1066	42	0	0	NUM
ejpam-2623	1066	43	)	)	PUNCT
ejpam-2623	1066	44	and	and	CCONJ
ejpam-2623	1066	45	eq−	eq−	PROPN
ejpam-2623	1066	46	(	(	PUNCT
ejpam-2623	1066	47	1	1	NUM
ejpam-2623	1066	48	)	)	PUNCT
ejpam-2623	1066	49	.	.	PUNCT
ejpam-2623	1067	1	to	to	PART
ejpam-2623	1067	2	estimate	estimate	VERB
ejpam-2623	1067	3	the	the	DET
ejpam-2623	1067	4	right	right	ADJ
ejpam-2623	1067	5	-	-	PUNCT
ejpam-2623	1067	6	hand	hand	NOUN
ejpam-2623	1067	7	side	side	NOUN
ejpam-2623	1067	8	of	of	ADP
ejpam-2623	1067	9	the	the	DET
ejpam-2623	1067	10	equality	equality	NOUN
ejpam-2623	1067	11	,	,	PUNCT
ejpam-2623	1067	12	one	one	PRON
ejpam-2623	1067	13	can	can	AUX
ejpam-2623	1067	14	use	use	VERB
ejpam-2623	1067	15	theorem	theorem	NOUN
ejpam-2623	1067	16	6	6	NUM
ejpam-2623	1067	17	.	.	PUNCT
ejpam-2623	1068	1	in	in	ADP
ejpam-2623	1068	2	fact	fact	NOUN
ejpam-2623	1068	3	,	,	PUNCT
ejpam-2623	1068	4	by	by	ADP
ejpam-2623	1068	5	eiseinstein	eiseinstein	ADJ
ejpam-2623	1068	6	criterion	criterion	NOUN
ejpam-2623	1068	7	,	,	PUNCT
ejpam-2623	1068	8	h0	h0	NOUN
ejpam-2623	1068	9	and	and	CCONJ
ejpam-2623	1068	10	h1	h1	PROPN
ejpam-2623	1068	11	are	be	AUX
ejpam-2623	1068	12	totally	totally	ADV
ejpam-2623	1068	13	ramified	ramify	VERB
ejpam-2623	1068	14	over	over	ADP
ejpam-2623	1068	15	points	point	NOUN
ejpam-2623	1068	16	such	such	ADJ
ejpam-2623	1068	17	that	that	SCONJ
ejpam-2623	1068	18	x	x	X
ejpam-2623	1068	19	=	=	PRON
ejpam-2623	1068	20	−d−	−d−	VERB
ejpam-2623	1068	21	3	3	NUM
ejpam-2623	1068	22	3d+	3d+	NUM
ejpam-2623	1068	23	1	1	NUM
ejpam-2623	1068	24	;	;	PUNCT
ejpam-2623	1068	25	so	so	SCONJ
ejpam-2623	1068	26	they	they	PRON
ejpam-2623	1068	27	can	can	AUX
ejpam-2623	1068	28	not	not	PART
ejpam-2623	1068	29	factor	factor	VERB
ejpam-2623	1068	30	through	through	ADP
ejpam-2623	1068	31	any	any	DET
ejpam-2623	1068	32	unramified	unramifie	VERB
ejpam-2623	1068	33	covering	covering	NOUN
ejpam-2623	1068	34	of	of	ADP
ejpam-2623	1068	35	ed	ed	NOUN
ejpam-2623	1068	36	.	.	PUNCT
ejpam-2623	1069	1	hence	hence	ADV
ejpam-2623	1069	2	,	,	PUNCT
ejpam-2623	1069	3	applying	apply	VERB
ejpam-2623	1069	4	theorem	theorem	NOUN
ejpam-2623	1069	5	6	6	NUM
ejpam-2623	1069	6	,	,	PUNCT
ejpam-2623	1069	7	we	we	PRON
ejpam-2623	1069	8	have	have	VERB
ejpam-2623	1069	9	:	:	PUNCT
ejpam-2623	1069	10	∑	∑	ADV
ejpam-2623	1069	11	p∈ci(fq	p∈ci(fq	NOUN
ejpam-2623	1069	12	)	)	PUNCT
ejpam-2623	1069	13	ξ(hi(p	ξ(hi(p	NOUN
ejpam-2623	1069	14	)	)	PUNCT
ejpam-2623	1069	15	)	)	PUNCT
ejpam-2623	1069	16	·	·	PUNCT
ejpam-2623	1070	1	(	(	PUNCT
ejpam-2623	1070	2	1	1	NUM
ejpam-2623	1070	3	+	+	CCONJ
ejpam-2623	1070	4	(	(	PUNCT
ejpam-2623	1070	5	−1)iχ(y	−1)iχ(y	NOUN
ejpam-2623	1070	6	)	)	PUNCT
ejpam-2623	1070	7	2	2	NUM
ejpam-2623	1070	8	)	)	PUNCT
ejpam-2623	1070	9	≤	≤	NOUN
ejpam-2623	1070	10	(	(	PUNCT
ejpam-2623	1070	11	2gi	2gi	ADJ
ejpam-2623	1070	12	−	−	PROPN
ejpam-2623	1070	13	2	2	NUM
ejpam-2623	1070	14	+	+	NUM
ejpam-2623	1070	15	deg(y	deg(y	PROPN
ejpam-2623	1070	16	)	)	PUNCT
ejpam-2623	1070	17	)	)	PUNCT
ejpam-2623	1071	1	√	√	PROPN
ejpam-2623	1071	2	q	q	NOUN
ejpam-2623	1072	1	where	where	SCONJ
ejpam-2623	1072	2	gi	gi	PRON
ejpam-2623	1072	3	is	be	AUX
ejpam-2623	1072	4	the	the	DET
ejpam-2623	1072	5	genus	genus	NOUN
ejpam-2623	1072	6	of	of	ADP
ejpam-2623	1072	7	ci	ci	PROPN
ejpam-2623	1072	8	and	and	CCONJ
ejpam-2623	1072	9	deg(y	deg(y	PROPN
ejpam-2623	1072	10	)	)	PUNCT
ejpam-2623	1072	11	is	be	AUX
ejpam-2623	1072	12	the	the	DET
ejpam-2623	1072	13	degree	degree	NOUN
ejpam-2623	1072	14	of	of	ADP
ejpam-2623	1072	15	y	y	PROPN
ejpam-2623	1072	16	seen	see	VERB
ejpam-2623	1072	17	as	as	ADP
ejpam-2623	1072	18	a	a	DET
ejpam-2623	1072	19	rational	rational	ADJ
ejpam-2623	1072	20	function	function	NOUN
ejpam-2623	1072	21	on	on	ADP
ejpam-2623	1072	22	ci	ci	PROPN
ejpam-2623	1072	23	.	.	PROPN
ejpam-2623	1072	24	denote	denote	VERB
ejpam-2623	1072	25	by	by	ADP
ejpam-2623	1072	26	ep	ep	PROPN
ejpam-2623	1072	27	the	the	DET
ejpam-2623	1072	28	ramification	ramification	NOUN
ejpam-2623	1072	29	index	index	NOUN
ejpam-2623	1072	30	at	at	ADP
ejpam-2623	1072	31	p	p	NOUN
ejpam-2623	1072	32	and	and	CCONJ
ejpam-2623	1072	33	by	by	ADP
ejpam-2623	1072	34	di	di	X
ejpam-2623	1072	35	the	the	DET
ejpam-2623	1072	36	degree	degree	NOUN
ejpam-2623	1072	37	of	of	ADP
ejpam-2623	1072	38	hi	hi	INTJ
ejpam-2623	1072	39	;	;	PUNCT
ejpam-2623	1072	40	since	since	SCONJ
ejpam-2623	1072	41	the	the	DET
ejpam-2623	1072	42	hi	hi	PROPN
ejpam-2623	1072	43	are	be	AUX
ejpam-2623	1072	44	ramified	ramify	VERB
ejpam-2623	1072	45	only	only	ADV
ejpam-2623	1072	46	at	at	ADP
ejpam-2623	1072	47	x	x	X
ejpam-2623	1072	48	=	=	PRON
ejpam-2623	1072	49	−d−	−d−	VERB
ejpam-2623	1072	50	3	3	NUM
ejpam-2623	1072	51	3d+	3d+	NUM
ejpam-2623	1072	52	1	1	NUM
ejpam-2623	1072	53	,	,	PUNCT
ejpam-2623	1072	54	then	then	ADV
ejpam-2623	1072	55	by	by	ADP
ejpam-2623	1072	56	the	the	DET
ejpam-2623	1072	57	riemann	riemann	PROPN
ejpam-2623	1072	58	-	-	PUNCT
ejpam-2623	1072	59	hurwitz	hurwitz	PROPN
ejpam-2623	1072	60	formula	formula	NOUN
ejpam-2623	1072	61	and	and	CCONJ
ejpam-2623	1072	62	using	use	VERB
ejpam-2623	1072	63	the	the	DET
ejpam-2623	1072	64	fact	fact	NOUN
ejpam-2623	1072	65	that	that	SCONJ
ejpam-2623	1072	66	any	any	DET
ejpam-2623	1072	67	point	point	NOUN
ejpam-2623	1072	68	has	have	AUX
ejpam-2623	1072	69	two	two	NUM
ejpam-2623	1072	70	conjugate	conjugate	ADJ
ejpam-2623	1072	71	preimages	preimage	NOUN
ejpam-2623	1072	72	,	,	PUNCT
ejpam-2623	1072	73	we	we	PRON
ejpam-2623	1072	74	have	have	VERB
ejpam-2623	1072	75	2gi−2	2gi−2	NUM
ejpam-2623	1072	76	=	=	NOUN
ejpam-2623	1072	77	di(2ged−2)+	di(2ged−2)+	ADJ
ejpam-2623	1072	78	∑	∑	INTJ
ejpam-2623	1072	79	p∈ci(ep	p∈ci(ep	NOUN
ejpam-2623	1072	80	−1	−1	NOUN
ejpam-2623	1072	81	)	)	PUNCT
ejpam-2623	1072	82	=	=	SYM
ejpam-2623	1073	1	di(2	di(2	PROPN
ejpam-2623	1073	2	·	·	PUNCT
ejpam-2623	1073	3	1−	1−	NUM
ejpam-2623	1073	4	2	2	NUM
ejpam-2623	1073	5	)	)	PUNCT
ejpam-2623	1073	6	+	+	CCONJ
ejpam-2623	1073	7	2(2−	2(2−	NUM
ejpam-2623	1073	8	1	1	NUM
ejpam-2623	1073	9	)	)	PUNCT
ejpam-2623	1073	10	+	+	CCONJ
ejpam-2623	1073	11	∑	∑	ADV
ejpam-2623	1073	12	p∈ci	p∈ci	ADJ
ejpam-2623	1073	13	,	,	PUNCT
ejpam-2623	1073	14	x	x	PROPN
ejpam-2623	1073	15	6=−t	6=−t	NUM
ejpam-2623	1073	16	(	(	PUNCT
ejpam-2623	1073	17	ep	ep	PROPN
ejpam-2623	1073	18	−	−	PROPN
ejpam-2623	1073	19	1	1	NUM
ejpam-2623	1073	20	)	)	PUNCT
ejpam-2623	1073	21	=	=	SYM
ejpam-2623	1073	22	0	0	PUNCT
ejpam-2623	1074	1	+	+	NUM
ejpam-2623	1074	2	2	2	NUM
ejpam-2623	1074	3	+	+	SYM
ejpam-2623	1074	4	0	0	NUM
ejpam-2623	1074	5	=	=	SYM
ejpam-2623	1074	6	2	2	NUM
ejpam-2623	1074	7	.	.	X
ejpam-2623	1074	8	hence	hence	ADV
ejpam-2623	1074	9	ci	ci	PROPN
ejpam-2623	1074	10	is	be	AUX
ejpam-2623	1074	11	a	a	DET
ejpam-2623	1074	12	curve	curve	NOUN
ejpam-2623	1074	13	of	of	ADP
ejpam-2623	1074	14	genus	genus	NOUN
ejpam-2623	1074	15	gi	gi	NOUN
ejpam-2623	1074	16	=	=	SYM
ejpam-2623	1074	17	2	2	X
ejpam-2623	1074	18	.	.	PUNCT
ejpam-2623	1075	1	on	on	ADP
ejpam-2623	1075	2	the	the	DET
ejpam-2623	1075	3	other	other	ADJ
ejpam-2623	1075	4	side	side	NOUN
ejpam-2623	1075	5	,	,	PUNCT
ejpam-2623	1075	6	we	we	PRON
ejpam-2623	1075	7	have	have	VERB
ejpam-2623	1075	8	deg(y	deg(y	PROPN
ejpam-2623	1075	9	)	)	PUNCT
ejpam-2623	1075	10	=	=	PUNCT
ejpam-2623	1076	1	[	[	X
ejpam-2623	1076	2	fq(x	fq(x	NOUN
ejpam-2623	1076	3	,	,	PUNCT
ejpam-2623	1076	4	y	y	PROPN
ejpam-2623	1076	5	,	,	PUNCT
ejpam-2623	1076	6	r	r	NOUN
ejpam-2623	1076	7	)	)	PUNCT
ejpam-2623	1076	8	:	:	PUNCT
ejpam-2623	1076	9	fq(x	fq(x	X
ejpam-2623	1076	10	,	,	PUNCT
ejpam-2623	1076	11	y	y	PROPN
ejpam-2623	1076	12	)	)	PUNCT
ejpam-2623	1076	13	]	]	PUNCT
ejpam-2623	1076	14	·	·	PUNCT
ejpam-2623	1077	1	[	[	X
ejpam-2623	1077	2	fq(x	fq(x	ADP
ejpam-2623	1077	3	,	,	PUNCT
ejpam-2623	1077	4	y	y	PROPN
ejpam-2623	1077	5	)	)	PUNCT
ejpam-2623	1077	6	:	:	PUNCT
ejpam-2623	1077	7	fq(y	fq(y	X
ejpam-2623	1077	8	)	)	PUNCT
ejpam-2623	1077	9	]	]	PUNCT
ejpam-2623	1078	1	=	=	SYM
ejpam-2623	1078	2	2	2	NUM
ejpam-2623	1078	3	·	·	SYM
ejpam-2623	1078	4	2	2	NUM
ejpam-2623	1078	5	=	=	SYM
ejpam-2623	1078	6	4	4	NUM
ejpam-2623	1078	7	.	.	PUNCT
ejpam-2623	1079	1	finally	finally	ADV
ejpam-2623	1079	2	,	,	PUNCT
ejpam-2623	1079	3	we	we	PRON
ejpam-2623	1079	4	have:∑	have:∑	NOUN
ejpam-2623	1079	5	p∈ci(fq	p∈ci(fq	NOUN
ejpam-2623	1079	6	)	)	PUNCT
ejpam-2623	1079	7	ξ(hi(p	ξ(hi(p	NOUN
ejpam-2623	1079	8	)	)	PUNCT
ejpam-2623	1079	9	)	)	PUNCT
ejpam-2623	1079	10	·	·	PUNCT
ejpam-2623	1080	1	(	(	PUNCT
ejpam-2623	1080	2	1	1	NUM
ejpam-2623	1080	3	+	+	CCONJ
ejpam-2623	1080	4	(	(	PUNCT
ejpam-2623	1080	5	−1)iχ(y	−1)iχ(y	NOUN
ejpam-2623	1080	6	)	)	PUNCT
ejpam-2623	1080	7	2	2	NUM
ejpam-2623	1080	8	)	)	PUNCT
ejpam-2623	1080	9	≤	≤	NOUN
ejpam-2623	1080	10	(	(	PUNCT
ejpam-2623	1080	11	2	2	NUM
ejpam-2623	1080	12	·	·	SYM
ejpam-2623	1080	13	2−	2−	NUM
ejpam-2623	1080	14	2	2	NUM
ejpam-2623	1080	15	+	+	CCONJ
ejpam-2623	1080	16	4	4	NUM
ejpam-2623	1080	17	)	)	PUNCT
ejpam-2623	1080	18	√	√	NOUN
ejpam-2623	1080	19	q	q	NOUN
ejpam-2623	1081	1	=	=	NUM
ejpam-2623	1081	2	6	6	NUM
ejpam-2623	1081	3	√	√	PROPN
ejpam-2623	1081	4	q.	q.	NOUN
ejpam-2623	1081	5	references	reference	NOUN
ejpam-2623	1081	6	390	390	NUM
ejpam-2623	1081	7	now	now	ADV
ejpam-2623	1081	8	it	it	PRON
ejpam-2623	1081	9	follows	follow	VERB
ejpam-2623	1081	10	from	from	ADP
ejpam-2623	1081	11	(	(	PUNCT
ejpam-2623	1081	12	*	*	PUNCT
ejpam-2623	1081	13	)	)	PUNCT
ejpam-2623	1081	14	and	and	CCONJ
ejpam-2623	1081	15	(	(	PUNCT
ejpam-2623	1081	16	*	*	PUNCT
ejpam-2623	1081	17	*	*	PUNCT
ejpam-2623	1081	18	)	)	PUNCT
ejpam-2623	1082	1	that:∣∣∣∣∣∑	that:∣∣∣∣∣∑	NUM
ejpam-2623	1082	2	r∈r	r∈r	NOUN
ejpam-2623	1082	3	ξ(φd(r	ξ(φd(r	NOUN
ejpam-2623	1082	4	)	)	PUNCT
ejpam-2623	1082	5	)	)	PUNCT
ejpam-2623	1083	1	∣∣∣∣∣	∣∣∣∣∣	PUNCT
ejpam-2623	1083	2	=	=	SYM
ejpam-2623	1083	3	2	2	X
ejpam-2623	1083	4	·	·	PUNCT
ejpam-2623	1083	5			NOUN
ejpam-2623	1083	6	∑	∑	PUNCT
ejpam-2623	1083	7	p∈ci(fq	p∈ci(fq	NOUN
ejpam-2623	1083	8	)	)	PUNCT
ejpam-2623	1083	9	ξ(hi(p	ξ(hi(p	NOUN
ejpam-2623	1083	10	)	)	PUNCT
ejpam-2623	1083	11	)	)	PUNCT
ejpam-2623	1083	12	·	·	PUNCT
ejpam-2623	1084	1	(	(	PUNCT
ejpam-2623	1084	2	1	1	NUM
ejpam-2623	1084	3	+	+	CCONJ
ejpam-2623	1084	4	(	(	PUNCT
ejpam-2623	1084	5	−1)iχ(y	−1)iχ(y	NOUN
ejpam-2623	1084	6	)	)	PUNCT
ejpam-2623	1084	7	2	2	NUM
ejpam-2623	1084	8	)	)	PUNCT
ejpam-2623	1084	9	−	−	NOUN
ejpam-2623	1084	10	1	1	NUM
ejpam-2623	1084	11	2	2	NUM
ejpam-2623	1084	12	∑	∑	ADV
ejpam-2623	1084	13	p∈ci(fq	p∈ci(fq	NOUN
ejpam-2623	1084	14	)	)	PUNCT
ejpam-2623	1084	15	,	,	PUNCT
ejpam-2623	1084	16	χ(y)=0	χ(y)=0	ADV
ejpam-2623	1084	17	ξ(hi(p	ξ(hi(p	NOUN
ejpam-2623	1084	18	)	)	PUNCT
ejpam-2623	1084	19	)	)	PUNCT
ejpam-2623	1085	1			NOUN
ejpam-2623	1085	2	+	+	CCONJ
ejpam-2623	1085	3	#	#	SYM
ejpam-2623	1085	4	ω0	ω0	ADV
ejpam-2623	1085	5	+	+	CCONJ
ejpam-2623	1085	6	#	#	SYM
ejpam-2623	1085	7	ω1	ω1	ADJ
ejpam-2623	1085	8	≤	≤	NOUN
ejpam-2623	1085	9	2(6	2(6	NUM
ejpam-2623	1085	10	√	√	PROPN
ejpam-2623	1085	11	q	q	NOUN
ejpam-2623	1085	12	−	−	NOUN
ejpam-2623	1085	13	2	2	NUM
ejpam-2623	1085	14	)	)	PUNCT
ejpam-2623	1085	15	+	+	CCONJ
ejpam-2623	1085	16	#	#	SYM
ejpam-2623	1085	17	ω0	ω0	ADV
ejpam-2623	1085	18	+	+	CCONJ
ejpam-2623	1085	19	#	#	SYM
ejpam-2623	1085	20	ω1	ω1	NOUN
ejpam-2623	1085	21	=	=	NOUN
ejpam-2623	1085	22	12	12	NUM
ejpam-2623	1085	23	√	√	NUM
ejpam-2623	1085	24	q	q	NOUN
ejpam-2623	1085	25	−	−	PROPN
ejpam-2623	1085	26	4	4	NUM
ejpam-2623	1085	27	+	+	CCONJ
ejpam-2623	1085	28	#	#	SYM
ejpam-2623	1085	29	ω0	ω0	ADV
ejpam-2623	1085	30	+	+	CCONJ
ejpam-2623	1085	31	#	#	SYM
ejpam-2623	1085	32	ω1	ω1	PROPN
ejpam-2623	1085	33	.	.	PUNCT
ejpam-2623	1086	1	this	this	PRON
ejpam-2623	1086	2	leads	lead	VERB
ejpam-2623	1086	3	to	to	ADP
ejpam-2623	1086	4	∣∣∣∣∣∣	∣∣∣∣∣∣	ADJ
ejpam-2623	1086	5	∑	∑	PUNCT
ejpam-2623	1086	6	r∈fq	r∈fq	ADJ
ejpam-2623	1086	7	ξ(φd(r	ξ(φd(r	NOUN
ejpam-2623	1086	8	)	)	PUNCT
ejpam-2623	1086	9	)	)	PUNCT
ejpam-2623	1087	1	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-2623	1087	2	≤	≤	ADV
ejpam-2623	1087	3	12	12	NUM
ejpam-2623	1087	4	√	√	NUM
ejpam-2623	1087	5	q	q	NOUN
ejpam-2623	1087	6	−	−	PROPN
ejpam-2623	1087	7	4	4	NUM
ejpam-2623	1087	8	+	+	CCONJ
ejpam-2623	1087	9	#	#	SYM
ejpam-2623	1087	10	ω0	ω0	NOUN
ejpam-2623	1087	11	+	+	CCONJ
ejpam-2623	1087	12	#	#	SYM
ejpam-2623	1087	13	ω1	ω1	NOUN
ejpam-2623	1087	14	+	+	CCONJ
ejpam-2623	1087	15	#	#	SYM
ejpam-2623	1087	16	ω	ω	NUM
ejpam-2623	1087	17	.	.	PUNCT
ejpam-2623	1088	1	but	but	CCONJ
ejpam-2623	1088	2	from	from	ADP
ejpam-2623	1088	3	the	the	DET
ejpam-2623	1088	4	definition	definition	NOUN
ejpam-2623	1088	5	of	of	ADP
ejpam-2623	1088	6	the	the	DET
ejpam-2623	1088	7	set	set	PROPN
ejpam-2623	1088	8	r	r	NOUN
ejpam-2623	1088	9	,	,	PUNCT
ejpam-2623	1088	10	ω	ω	PROPN
ejpam-2623	1088	11	has	have	VERB
ejpam-2623	1088	12	at	at	ADP
ejpam-2623	1088	13	most	most	ADV
ejpam-2623	1088	14	1	1	NUM
ejpam-2623	1088	15	+	+	SYM
ejpam-2623	1088	16	6	6	NUM
ejpam-2623	1088	17	=	=	SYM
ejpam-2623	1088	18	7	7	NUM
ejpam-2623	1088	19	elements	element	NOUN
ejpam-2623	1088	20	.	.	PUNCT
ejpam-2623	1089	1	hence	hence	ADV
ejpam-2623	1089	2	using	use	VERB
ejpam-2623	1089	3	the	the	DET
ejpam-2623	1089	4	facts	fact	NOUN
ejpam-2623	1089	5	that	that	SCONJ
ejpam-2623	1089	6	ωi	ωi	PROPN
ejpam-2623	1089	7	=	=	SYM
ejpam-2623	1089	8	{	{	PUNCT
ejpam-2623	1089	9	p	p	NOUN
ejpam-2623	1089	10	∈	∈	PROPN
ejpam-2623	1089	11	ci	ci	NOUN
ejpam-2623	1089	12	:	:	PUNCT
ejpam-2623	1089	13	fi(p	fi(p	X
ejpam-2623	1089	14	)	)	PUNCT
ejpam-2623	1089	15	∈	∈	PROPN
ejpam-2623	1089	16	ω	ω	PROPN
ejpam-2623	1089	17	}	}	PUNCT
ejpam-2623	1089	18	and	and	CCONJ
ejpam-2623	1089	19	fi	fi	NOUN
ejpam-2623	1089	20	is	be	AUX
ejpam-2623	1089	21	of	of	ADP
ejpam-2623	1089	22	degree	degree	NOUN
ejpam-2623	1089	23	2	2	NUM
ejpam-2623	1089	24	(	(	PUNCT
ejpam-2623	1089	25	since	since	SCONJ
ejpam-2623	1089	26	any	any	DET
ejpam-2623	1089	27	point	point	NOUN
ejpam-2623	1089	28	in	in	ADP
ejpam-2623	1089	29	a1(fq	a1(fq	PROPN
ejpam-2623	1089	30	)	)	PUNCT
ejpam-2623	1089	31	\ω	\ω	NOUN
ejpam-2623	1089	32	has	have	VERB
ejpam-2623	1089	33	exactly	exactly	ADV
ejpam-2623	1089	34	two	two	NUM
ejpam-2623	1089	35	preimages	preimage	NOUN
ejpam-2623	1089	36	in	in	ADP
ejpam-2623	1089	37	ci	ci	NOUN
ejpam-2623	1089	38	)	)	PUNCT
ejpam-2623	1089	39	,	,	PUNCT
ejpam-2623	1089	40	so	so	ADV
ejpam-2623	1089	41	#	#	SYM
ejpam-2623	1089	42	ωi	ωi	ADJ
ejpam-2623	1089	43	≤	≤	NUM
ejpam-2623	1089	44	2#ω	2#ω	NOUN
ejpam-2623	1089	45	=	=	SYM
ejpam-2623	1090	1	14	14	NUM
ejpam-2623	1090	2	.	.	PUNCT
ejpam-2623	1091	1	finally	finally	ADV
ejpam-2623	1091	2	,	,	PUNCT
ejpam-2623	1091	3	we	we	PRON
ejpam-2623	1091	4	have	have	VERB
ejpam-2623	1091	5	∣∣∣∣∣∣	∣∣∣∣∣∣	ADJ
ejpam-2623	1091	6	∑	∑	PUNCT
ejpam-2623	1091	7	r∈fq	r∈fq	ADJ
ejpam-2623	1091	8	ξ(φd(r	ξ(φd(r	NOUN
ejpam-2623	1091	9	)	)	PUNCT
ejpam-2623	1091	10	)	)	PUNCT
ejpam-2623	1092	1	∣∣∣∣∣∣	∣∣∣∣∣∣	ADP
ejpam-2623	1092	2	≤	≤	ADV
ejpam-2623	1092	3	12	12	NUM
ejpam-2623	1092	4	√	√	PROPN
ejpam-2623	1092	5	q	q	NOUN
ejpam-2623	1093	1	+	+	NOUN
ejpam-2623	1093	2	31	31	NUM
ejpam-2623	1093	3	.	.	PUNCT
ejpam-2623	1094	1	corollary	corollary	ADJ
ejpam-2623	1094	2	1	1	NUM
ejpam-2623	1094	3	.	.	PUNCT
ejpam-2623	1095	1	let	let	VERB
ejpam-2623	1095	2	h1	h1	PROPN
ejpam-2623	1095	3	,	,	PUNCT
ejpam-2623	1095	4	h2	h2	NOUN
ejpam-2623	1095	5	:	:	PUNCT
ejpam-2623	1095	6	{	{	PUNCT
ejpam-2623	1095	7	0	0	NUM
ejpam-2623	1095	8	,	,	PUNCT
ejpam-2623	1095	9	1}∗	1}∗	PROPN
ejpam-2623	1095	10	→	→	SYM
ejpam-2623	1095	11	fq	fq	PROPN
ejpam-2623	1095	12	be	be	AUX
ejpam-2623	1095	13	two	two	NUM
ejpam-2623	1095	14	hash	hash	NOUN
ejpam-2623	1095	15	functions	function	NOUN
ejpam-2623	1095	16	modeled	model	VERB
ejpam-2623	1095	17	as	as	ADP
ejpam-2623	1095	18	random	random	ADJ
ejpam-2623	1095	19	oracles	oracle	NOUN
ejpam-2623	1095	20	.	.	PUNCT
ejpam-2623	1096	1	then	then	ADV
ejpam-2623	1096	2	the	the	DET
ejpam-2623	1096	3	construction	construction	NOUN
ejpam-2623	1096	4	h	h	NOUN
ejpam-2623	1096	5	:	:	PUNCT
ejpam-2623	1096	6	m	m	VERB
ejpam-2623	1096	7	7→	7→	NUM
ejpam-2623	1096	8	φd(h1(m	φd(h1(m	NOUN
ejpam-2623	1096	9	)	)	PUNCT
ejpam-2623	1096	10	)	)	PUNCT
ejpam-2623	1097	1	+	+	CCONJ
ejpam-2623	1097	2	φd(h2(m	φd(h2(m	NUM
ejpam-2623	1097	3	)	)	PUNCT
ejpam-2623	1097	4	)	)	PUNCT
ejpam-2623	1097	5	is	be	AUX
ejpam-2623	1097	6	indifferentiable	indifferentiable	ADJ
ejpam-2623	1097	7	from	from	ADP
ejpam-2623	1097	8	a	a	DET
ejpam-2623	1097	9	random	random	ADJ
ejpam-2623	1097	10	oracle	oracle	NOUN
ejpam-2623	1097	11	.	.	PUNCT
ejpam-2623	1098	1	proof	proof	NOUN
ejpam-2623	1098	2	.	.	PUNCT
ejpam-2623	1099	1	by	by	ADP
ejpam-2623	1099	2	the	the	DET
ejpam-2623	1099	3	previous	previous	ADJ
ejpam-2623	1099	4	theorem	theorem	NOUN
ejpam-2623	1099	5	,	,	PUNCT
ejpam-2623	1099	6	we	we	PRON
ejpam-2623	1099	7	know	know	VERB
ejpam-2623	1099	8	that	that	SCONJ
ejpam-2623	1099	9	the	the	DET
ejpam-2623	1099	10	encoding	encoding	NOUN
ejpam-2623	1099	11	φd	φd	VERB
ejpam-2623	1099	12	is	be	AUX
ejpam-2623	1099	13	(	(	PUNCT
ejpam-2623	1099	14	12	12	NUM
ejpam-2623	1099	15	+	+	CCONJ
ejpam-2623	1099	16	31q−1/2)-welldistributed	31q−1/2)-welldistribute	VERB
ejpam-2623	1099	17	.	.	PUNCT
ejpam-2623	1100	1	from	from	ADP
ejpam-2623	1100	2	theorem	theorem	ADJ
ejpam-2623	1100	3	1	1	NUM
ejpam-2623	1100	4	and	and	CCONJ
ejpam-2623	1100	5	theorem	theorem	VERB
ejpam-2623	1100	6	2	2	NUM
ejpam-2623	1100	7	in	in	ADP
ejpam-2623	1100	8	[	[	X
ejpam-2623	1100	9	14	14	NUM
ejpam-2623	1100	10	]	]	PUNCT
ejpam-2623	1100	11	,	,	PUNCT
ejpam-2623	1100	12	we	we	PRON
ejpam-2623	1100	13	deduce	deduce	VERB
ejpam-2623	1100	14	that	that	PRON
ejpam-2623	1100	15	is	be	AUX
ejpam-2623	1100	16	h	h	NOUN
ejpam-2623	1100	17	regular	regular	ADJ
ejpam-2623	1100	18	.	.	PUNCT
ejpam-2623	1101	1	it	it	PRON
ejpam-2623	1101	2	is	be	AUX
ejpam-2623	1101	3	admissible	admissible	ADJ
ejpam-2623	1101	4	since	since	SCONJ
ejpam-2623	1101	5	it	it	PRON
ejpam-2623	1101	6	is	be	AUX
ejpam-2623	1101	7	clearly	clearly	ADV
ejpam-2623	1101	8	computable	computable	ADJ
ejpam-2623	1101	9	and	and	CCONJ
ejpam-2623	1101	10	samplable	samplable	ADJ
ejpam-2623	1101	11	(	(	PUNCT
ejpam-2623	1101	12	see	see	VERB
ejpam-2623	1101	13	[	[	X
ejpam-2623	1101	14	6	6	NUM
ejpam-2623	1101	15	]	]	PUNCT
ejpam-2623	1101	16	,	,	PUNCT
ejpam-2623	1101	17	[	[	X
ejpam-2623	1101	18	14	14	NUM
ejpam-2623	1101	19	]	]	PUNCT
ejpam-2623	1101	20	)	)	PUNCT
ejpam-2623	1101	21	.	.	PUNCT
ejpam-2623	1102	1	hence	hence	ADV
ejpam-2623	1102	2	we	we	PRON
ejpam-2623	1102	3	conclude	conclude	VERB
ejpam-2623	1102	4	that	that	SCONJ
ejpam-2623	1102	5	m	m	VERB
ejpam-2623	1102	6	7→	7→	NUM
ejpam-2623	1102	7	f(h1(m	f(h1(m	NUM
ejpam-2623	1102	8	)	)	PUNCT
ejpam-2623	1102	9	)	)	PUNCT
ejpam-2623	1103	1	+	+	CCONJ
ejpam-2623	1103	2	f(h2(m	f(h2(m	NOUN
ejpam-2623	1103	3	)	)	PUNCT
ejpam-2623	1103	4	)	)	PUNCT
ejpam-2623	1103	5	is	be	AUX
ejpam-2623	1103	6	indifferentiable	indifferentiable	ADJ
ejpam-2623	1103	7	from	from	ADP
ejpam-2623	1103	8	a	a	DET
ejpam-2623	1103	9	random	random	ADJ
ejpam-2623	1103	10	oracle	oracle	NOUN
ejpam-2623	1103	11	when	when	SCONJ
ejpam-2623	1103	12	h1	h1	PROPN
ejpam-2623	1103	13	,	,	PUNCT
ejpam-2623	1103	14	h2	h2	PROPN
ejpam-2623	1103	15	are	be	AUX
ejpam-2623	1103	16	modeled	model	VERB
ejpam-2623	1103	17	as	as	ADP
ejpam-2623	1103	18	random	random	ADJ
ejpam-2623	1103	19	oracles	oracle	NOUN
ejpam-2623	1103	20	.	.	PUNCT
ejpam-2623	1104	1	5	5	NUM
ejpam-2623	1104	2	.	.	X
ejpam-2623	1104	3	conclusion	conclusion	NOUN
ejpam-2623	1104	4	we	we	PRON
ejpam-2623	1104	5	have	have	AUX
ejpam-2623	1104	6	proposed	propose	VERB
ejpam-2623	1104	7	new	new	ADJ
ejpam-2623	1104	8	encoding	encoding	NOUN
ejpam-2623	1104	9	functions	function	NOUN
ejpam-2623	1104	10	for	for	ADP
ejpam-2623	1104	11	various	various	ADJ
ejpam-2623	1104	12	forms	form	NOUN
ejpam-2623	1104	13	of	of	ADP
ejpam-2623	1104	14	elliptic	elliptic	ADJ
ejpam-2623	1104	15	curves	curve	NOUN
ejpam-2623	1104	16	.	.	PUNCT
ejpam-2623	1105	1	our	our	PRON
ejpam-2623	1105	2	encodings	encoding	NOUN
ejpam-2623	1105	3	are	be	AUX
ejpam-2623	1105	4	almost	almost	ADV
ejpam-2623	1105	5	injective	injective	ADJ
ejpam-2623	1105	6	and	and	CCONJ
ejpam-2623	1105	7	easily	easily	ADV
ejpam-2623	1105	8	invertible	invertible	ADJ
ejpam-2623	1105	9	.	.	PUNCT
ejpam-2623	1106	1	this	this	PRON
ejpam-2623	1106	2	is	be	AUX
ejpam-2623	1106	3	useful	useful	ADJ
ejpam-2623	1106	4	for	for	ADP
ejpam-2623	1106	5	constructing	construct	VERB
ejpam-2623	1106	6	indifferentiable	indifferentiable	ADJ
ejpam-2623	1106	7	hash	hash	NOUN
ejpam-2623	1106	8	functions	function	NOUN
ejpam-2623	1106	9	following	follow	VERB
ejpam-2623	1106	10	the	the	DET
ejpam-2623	1106	11	idea	idea	NOUN
ejpam-2623	1106	12	of	of	ADP
ejpam-2623	1106	13	farashahi	farashahi	NOUN
ejpam-2623	1106	14	et	et	PROPN
ejpam-2623	1106	15	al	al	PROPN
ejpam-2623	1106	16	.	.	PUNCT
ejpam-2623	1106	17	references	reference	NOUN
ejpam-2623	1106	18	[	[	X
ejpam-2623	1106	19	1	1	NUM
ejpam-2623	1106	20	]	]	PUNCT
ejpam-2623	1106	21	tatsuaki	tatsuaki	PROPN
ejpam-2623	1106	22	okamoto	okamoto	PROPN
ejpam-2623	1106	23	alfred	alfred	PROPN
ejpam-2623	1106	24	menezes	menezes	PROPN
ejpam-2623	1106	25	and	and	CCONJ
ejpam-2623	1106	26	scott	scott	PROPN
ejpam-2623	1106	27	a.	a.	NOUN
ejpam-2623	1106	28	vanstone	vanstone	NOUN
ejpam-2623	1106	29	.	.	PUNCT
ejpam-2623	1107	1	reducing	reduce	VERB
ejpam-2623	1107	2	elliptic	elliptic	ADJ
ejpam-2623	1107	3	curve	curve	NOUN
ejpam-2623	1107	4	logarithms	logarithm	NOUN
ejpam-2623	1107	5	to	to	ADP
ejpam-2623	1107	6	logarithms	logarithm	NOUN
ejpam-2623	1107	7	in	in	ADP
ejpam-2623	1107	8	a	a	DET
ejpam-2623	1107	9	finite	finite	ADJ
ejpam-2623	1107	10	field	field	NOUN
ejpam-2623	1107	11	.	.	PUNCT
ejpam-2623	1108	1	ieee	ieee	NOUN
ejpam-2623	1108	2	transactions	transaction	NOUN
ejpam-2623	1108	3	on	on	ADP
ejpam-2623	1108	4	information	information	NOUN
ejpam-2623	1108	5	theory	theory	NOUN
ejpam-2623	1108	6	,	,	PUNCT
ejpam-2623	1108	7	39(5):1639–1646	39(5):1639–1646	NUM
ejpam-2623	1108	8	,	,	PUNCT
ejpam-2623	1108	9	1993	1993	NUM
ejpam-2623	1108	10	.	.	PUNCT
ejpam-2623	1109	1	[	[	X
ejpam-2623	1109	2	2	2	X
ejpam-2623	1109	3	]	]	PUNCT
ejpam-2623	1109	4	dan	dan	PROPN
ejpam-2623	1109	5	boneh	boneh	PROPN
ejpam-2623	1109	6	and	and	CCONJ
ejpam-2623	1109	7	matthew	matthew	PROPN
ejpam-2623	1109	8	k.	k.	PROPN
ejpam-2623	1109	9	franklin	franklin	PROPN
ejpam-2623	1109	10	.	.	PUNCT
ejpam-2623	1110	1	identity	identity	NOUN
ejpam-2623	1110	2	-	-	PUNCT
ejpam-2623	1110	3	based	base	VERB
ejpam-2623	1110	4	encryption	encryption	NOUN
ejpam-2623	1110	5	from	from	ADP
ejpam-2623	1110	6	the	the	DET
ejpam-2623	1110	7	weil	weil	PROPN
ejpam-2623	1110	8	pairing	pairing	PROPN
ejpam-2623	1110	9	.	.	PUNCT
ejpam-2623	1111	1	in	in	ADP
ejpam-2623	1111	2	crypto	crypto	X
ejpam-2623	1111	3	(	(	PUNCT
ejpam-2623	1111	4	2001	2001	NUM
ejpam-2623	1111	5	)	)	PUNCT
ejpam-2623	1111	6	,	,	PUNCT
ejpam-2623	1111	7	lncs	lncs	PROPN
ejpam-2623	1111	8	,	,	PUNCT
ejpam-2623	1111	9	springer	springer	NOUN
ejpam-2623	1111	10	,	,	PUNCT
ejpam-2623	1111	11	2139(3):213–229	2139(3):213–229	NUM
ejpam-2623	1111	12	,	,	PUNCT
ejpam-2623	1111	13	2001	2001	NUM
ejpam-2623	1111	14	.	.	PUNCT
ejpam-2623	1112	1	[	[	X
ejpam-2623	1112	2	3	3	X
ejpam-2623	1112	3	]	]	X
ejpam-2623	1112	4	b.	b.	PROPN
ejpam-2623	1112	5	lynn	lynn	PROPN
ejpam-2623	1112	6	d.	d.	PROPN
ejpam-2623	1112	7	boneh	boneh	PROPN
ejpam-2623	1112	8	and	and	CCONJ
ejpam-2623	1112	9	h.	h.	PROPN
ejpam-2623	1112	10	shacham	shacham	PROPN
ejpam-2623	1112	11	.	.	PUNCT
ejpam-2623	1113	1	short	short	ADJ
ejpam-2623	1113	2	signatures	signature	NOUN
ejpam-2623	1113	3	from	from	ADP
ejpam-2623	1113	4	the	the	DET
ejpam-2623	1113	5	weil	weil	PROPN
ejpam-2623	1113	6	pairing	pairing	NOUN
ejpam-2623	1113	7	.	.	PUNCT
ejpam-2623	1114	1	in	in	ADP
ejpam-2623	1114	2	asiacrypt	asiacrypt	PROPN
ejpam-2623	1114	3	,	,	PUNCT
ejpam-2623	1114	4	lncs	lncs	PROPN
ejpam-2623	1114	5	,	,	PUNCT
ejpam-2623	1114	6	springer	springer	NOUN
ejpam-2623	1114	7	,	,	PUNCT
ejpam-2623	1114	8	2248:514–532	2248:514–532	NUM
ejpam-2623	1114	9	,	,	PUNCT
ejpam-2623	1114	10	2001	2001	NUM
ejpam-2623	1114	11	.	.	PUNCT
ejpam-2623	1115	1	[	[	X
ejpam-2623	1115	2	4	4	NUM
ejpam-2623	1115	3	]	]	PUNCT
ejpam-2623	1115	4	anna	anna	PROPN
ejpam-2623	1115	5	krasnova	krasnova	PROPN
ejpam-2623	1115	6	daniel	daniel	PROPN
ejpam-2623	1115	7	j.	j.	PROPN
ejpam-2623	1115	8	bernstein	bernstein	PROPN
ejpam-2623	1115	9	,	,	PUNCT
ejpam-2623	1115	10	mike	mike	PROPN
ejpam-2623	1115	11	hamburg	hamburg	PROPN
ejpam-2623	1115	12	and	and	CCONJ
ejpam-2623	1115	13	tanja	tanja	PROPN
ejpam-2623	1115	14	lange	lange	PROPN
ejpam-2623	1115	15	.	.	PUNCT
ejpam-2623	1116	1	elligator	elligator	NOUN
ejpam-2623	1116	2	:	:	PUNCT
ejpam-2623	1116	3	elliptic	elliptic	ADJ
ejpam-2623	1116	4	-	-	PUNCT
ejpam-2623	1116	5	curve	curve	NOUN
ejpam-2623	1116	6	points	point	NOUN
ejpam-2623	1116	7	indistinguishable	indistinguishable	ADJ
ejpam-2623	1116	8	from	from	ADP
ejpam-2623	1116	9	uniform	uniform	ADJ
ejpam-2623	1116	10	random	random	ADJ
ejpam-2623	1116	11	strings	string	NOUN
ejpam-2623	1116	12	.	.	PUNCT
ejpam-2623	1117	1	acm	acm	PROPN
ejpam-2623	1117	2	ccs	ccs	PROPN
ejpam-2623	1117	3	,	,	PUNCT
ejpam-2623	1117	4	2013	2013	NUM
ejpam-2623	1117	5	.	.	PUNCT
ejpam-2623	1118	1	references	reference	NOUN
ejpam-2623	1118	2	391	391	NUM
ejpam-2623	1118	3	[	[	X
ejpam-2623	1118	4	5	5	NUM
ejpam-2623	1118	5	]	]	PUNCT
ejpam-2623	1118	6	chen	chen	PROPN
ejpam-2623	1118	7	qian	qian	PROPN
ejpam-2623	1118	8	et	et	PROPN
ejpam-2623	1118	9	al	al	PROPN
ejpam-2623	1118	10	.	.	PROPN
ejpam-2623	1118	11	diego	diego	PROPN
ejpam-2623	1118	12	f.	f.	PROPN
ejpam-2623	1118	13	aranha	aranha	PROPN
ejpam-2623	1118	14	,	,	PUNCT
ejpam-2623	1118	15	pierre	pierre	NOUN
ejpam-2623	1118	16	-	-	PUNCT
ejpam-2623	1118	17	alain	alain	PROPN
ejpam-2623	1118	18	fouque	fouque	NOUN
ejpam-2623	1118	19	.	.	PUNCT
ejpam-2623	1119	1	binary	binary	ADJ
ejpam-2623	1119	2	elligator	elligator	PROPN
ejpam-2623	1119	3	squared	square	VERB
ejpam-2623	1119	4	.	.	PUNCT
ejpam-2623	1120	1	available	available	ADJ
ejpam-2623	1120	2	at	at	ADP
ejpam-2623	1120	3	http://www.researchgate.net/publication/268333288	http://www.researchgate.net/publication/268333288	PROPN
ejpam-2623	1120	4	,	,	PUNCT
ejpam-2623	1120	5	november	november	PROPN
ejpam-2623	1120	6	2004	2004	NUM
ejpam-2623	1120	7	.	.	PUNCT
ejpam-2623	1121	1	[	[	X
ejpam-2623	1121	2	6	6	NUM
ejpam-2623	1121	3	]	]	X
ejpam-2623	1121	4	jean	jean	PROPN
ejpam-2623	1121	5	-	-	PUNCT
ejpam-2623	1121	6	sébastien	sébastien	PROPN
ejpam-2623	1121	7	coron	coron	PROPN
ejpam-2623	1121	8	thomas	thomas	PROPN
ejpam-2623	1121	9	icart	icart	PROPN
ejpam-2623	1121	10	et	et	PROPN
ejpam-2623	1121	11	al	al	PROPN
ejpam-2623	1121	12	.	.	PROPN
ejpam-2623	1121	13	eric	eric	PROPN
ejpam-2623	1121	14	brier	brier	PROPN
ejpam-2623	1121	15	.	.	PUNCT
ejpam-2623	1122	1	efficient	efficient	ADJ
ejpam-2623	1122	2	indifferentiable	indifferentiable	ADJ
ejpam-2623	1122	3	hashing	hashing	NOUN
ejpam-2623	1122	4	into	into	ADP
ejpam-2623	1122	5	ordinary	ordinary	ADJ
ejpam-2623	1122	6	elliptic	elliptic	ADJ
ejpam-2623	1122	7	curves	curve	NOUN
ejpam-2623	1122	8	.	.	PUNCT
ejpam-2623	1123	1	in	in	ADP
ejpam-2623	1123	2	crypto	crypto	X
ejpam-2623	1123	3	(	(	PUNCT
ejpam-2623	1123	4	2010	2010	NUM
ejpam-2623	1123	5	)	)	PUNCT
ejpam-2623	1123	6	,	,	PUNCT
ejpam-2623	1123	7	lncs	lncs	PROPN
ejpam-2623	1123	8	,	,	PUNCT
ejpam-2623	1123	9	springer	springer	NOUN
ejpam-2623	1123	10	,	,	PUNCT
ejpam-2623	1123	11	6223:237	6223:237	NUM
ejpam-2623	1123	12	–	–	PUNCT
ejpam-2623	1123	13	254	254	NUM
ejpam-2623	1123	14	,	,	PUNCT
ejpam-2623	1123	15	2010	2010	NUM
ejpam-2623	1123	16	.	.	PUNCT
ejpam-2623	1124	1	[	[	X
ejpam-2623	1124	2	7	7	NUM
ejpam-2623	1124	3	]	]	X
ejpam-2623	1124	4	reza	reza	PROPN
ejpam-2623	1124	5	rezaeian	rezaeian	ADJ
ejpam-2623	1124	6	farashahi	farashahi	NOUN
ejpam-2623	1124	7	.	.	PUNCT
ejpam-2623	1125	1	efficient	efficient	ADJ
ejpam-2623	1125	2	indifferentiable	indifferentiable	ADJ
ejpam-2623	1125	3	hashing	hashing	NOUN
ejpam-2623	1125	4	into	into	ADP
ejpam-2623	1125	5	ordinary	ordinary	ADJ
ejpam-2623	1125	6	elliptic	elliptic	ADJ
ejpam-2623	1125	7	curves	curve	NOUN
ejpam-2623	1125	8	.	.	PUNCT
ejpam-2623	1126	1	in	in	ADP
ejpam-2623	1126	2	africacrypt	africacrypt	PROPN
ejpam-2623	1126	3	(	(	PUNCT
ejpam-2623	1126	4	2011	2011	NUM
ejpam-2623	1126	5	)	)	PUNCT
ejpam-2623	1126	6	,	,	PUNCT
ejpam-2623	1126	7	lncs	lncs	PROPN
ejpam-2623	1126	8	,	,	PUNCT
ejpam-2623	1126	9	springer	springer	NOUN
ejpam-2623	1126	10	,	,	PUNCT
ejpam-2623	1126	11	6737:278–289	6737:278–289	NOUN
ejpam-2623	1126	12	,	,	PUNCT
ejpam-2623	1126	13	2011	2011	NUM
ejpam-2623	1126	14	.	.	PUNCT
ejpam-2623	1127	1	[	[	X
ejpam-2623	1127	2	8	8	NUM
ejpam-2623	1127	3	]	]	PUNCT
ejpam-2623	1127	4	pierre	pierre	PROPN
ejpam-2623	1127	5	-	-	PUNCT
ejpam-2623	1127	6	alain	alain	PROPN
ejpam-2623	1127	7	fouque	fouque	PROPN
ejpam-2623	1127	8	and	and	CCONJ
ejpam-2623	1127	9	mehdi	mehdi	PROPN
ejpam-2623	1127	10	tibouchi	tibouchi	PROPN
ejpam-2623	1127	11	.	.	PUNCT
ejpam-2623	1128	1	estimating	estimate	VERB
ejpam-2623	1128	2	the	the	DET
ejpam-2623	1128	3	size	size	NOUN
ejpam-2623	1128	4	of	of	ADP
ejpam-2623	1128	5	the	the	DET
ejpam-2623	1128	6	image	image	NOUN
ejpam-2623	1128	7	of	of	ADP
ejpam-2623	1128	8	deterministic	deterministic	ADJ
ejpam-2623	1128	9	hash	hash	NOUN
ejpam-2623	1128	10	functions	function	NOUN
ejpam-2623	1128	11	to	to	ADP
ejpam-2623	1128	12	elliptic	elliptic	ADJ
ejpam-2623	1128	13	curves	curve	NOUN
ejpam-2623	1128	14	.	.	PUNCT
ejpam-2623	1129	1	in	in	ADP
ejpam-2623	1129	2	latincrypt	latincrypt	PROPN
ejpam-2623	1129	3	(	(	PUNCT
ejpam-2623	1129	4	2010	2010	NUM
ejpam-2623	1129	5	)	)	PUNCT
ejpam-2623	1129	6	,	,	PUNCT
ejpam-2623	1129	7	lncs	lncs	PROPN
ejpam-2623	1129	8	,	,	PUNCT
ejpam-2623	1129	9	springer	springer	NOUN
ejpam-2623	1129	10	,	,	PUNCT
ejpam-2623	1129	11	6212:81–91	6212:81–91	PROPN
ejpam-2623	1129	12	,	,	PUNCT
ejpam-2623	1129	13	2010	2010	NUM
ejpam-2623	1129	14	.	.	PUNCT
ejpam-2623	1130	1	[	[	X
ejpam-2623	1130	2	9	9	NUM
ejpam-2623	1130	3	]	]	PUNCT
ejpam-2623	1130	4	thomas	thomas	PROPN
ejpam-2623	1130	5	icart	icart	PROPN
ejpam-2623	1130	6	.	.	PUNCT
ejpam-2623	1131	1	how	how	SCONJ
ejpam-2623	1131	2	to	to	PART
ejpam-2623	1131	3	hash	hash	VERB
ejpam-2623	1131	4	into	into	ADP
ejpam-2623	1131	5	elliptic	elliptic	ADJ
ejpam-2623	1131	6	curves	curve	NOUN
ejpam-2623	1131	7	.	.	PUNCT
ejpam-2623	1132	1	in	in	ADP
ejpam-2623	1132	2	crypto	crypto	X
ejpam-2623	1132	3	(	(	PUNCT
ejpam-2623	1132	4	2009	2009	NUM
ejpam-2623	1132	5	)	)	PUNCT
ejpam-2623	1132	6	,	,	PUNCT
ejpam-2623	1132	7	lncs	lncs	PROPN
ejpam-2623	1132	8	,	,	PUNCT
ejpam-2623	1132	9	springer	springer	NOUN
ejpam-2623	1132	10	,	,	PUNCT
ejpam-2623	1132	11	5677:303–316	5677:303–316	PROPN
ejpam-2623	1132	12	,	,	PUNCT
ejpam-2623	1132	13	2009	2009	NUM
ejpam-2623	1132	14	.	.	PUNCT
ejpam-2623	1133	1	[	[	X
ejpam-2623	1133	2	10	10	NUM
ejpam-2623	1133	3	]	]	PUNCT
ejpam-2623	1133	4	the	the	DET
ejpam-2623	1133	5	tor	tor	PROPN
ejpam-2623	1133	6	project	project	PROPN
ejpam-2623	1133	7	inc	inc	PROPN
ejpam-2623	1133	8	.	.	PROPN
ejpam-2623	1133	9	tor	tor	PROPN
ejpam-2623	1133	10	.	.	PUNCT
ejpam-2623	1133	11	available	available	ADJ
ejpam-2623	1133	12	at	at	ADP
ejpam-2623	1133	13	www.torproject.org	www.torproject.org	PROPN
ejpam-2623	1133	14	,	,	PUNCT
ejpam-2623	1133	15	september	september	PROPN
ejpam-2623	1133	16	2015	2015	NUM
ejpam-2623	1133	17	.	.	PUNCT
ejpam-2623	1134	1	[	[	X
ejpam-2623	1134	2	11	11	NUM
ejpam-2623	1134	3	]	]	PUNCT
ejpam-2623	1134	4	bodo	bodo	PROPN
ejpam-2623	1134	5	möller	möller	PROPN
ejpam-2623	1134	6	.	.	PUNCT
ejpam-2623	1135	1	a	a	DET
ejpam-2623	1135	2	public	public	ADJ
ejpam-2623	1135	3	-	-	PUNCT
ejpam-2623	1135	4	key	key	NOUN
ejpam-2623	1135	5	encryption	encryption	NOUN
ejpam-2623	1135	6	scheme	scheme	NOUN
ejpam-2623	1135	7	with	with	ADP
ejpam-2623	1135	8	pseudo	pseudo	NOUN
ejpam-2623	1135	9	-	-	ADJ
ejpam-2623	1135	10	random	random	ADJ
ejpam-2623	1135	11	ciphertexts	ciphertext	NOUN
ejpam-2623	1135	12	.	.	PUNCT
ejpam-2623	1136	1	esorics	esoric	NOUN
ejpam-2623	1136	2	,	,	PUNCT
ejpam-2623	1136	3	lncs	lncs	PROPN
ejpam-2623	1136	4	,	,	PUNCT
ejpam-2623	1136	5	springer	springer	NOUN
ejpam-2623	1136	6	,	,	PUNCT
ejpam-2623	1136	7	3193:335–351	3193:335–351	NOUN
ejpam-2623	1136	8	,	,	PUNCT
ejpam-2623	1136	9	2004	2004	NUM
ejpam-2623	1136	10	.	.	PUNCT
ejpam-2623	1137	1	[	[	X
ejpam-2623	1137	2	12	12	NUM
ejpam-2623	1137	3	]	]	PUNCT
ejpam-2623	1137	4	a.	a.	NOUN
ejpam-2623	1137	5	joux	joux	PROPN
ejpam-2623	1137	6	p.-a	p.-a	PROPN
ejpam-2623	1137	7	.	.	PUNCT
ejpam-2623	1138	1	fouque	fouque	PROPN
ejpam-2623	1138	2	and	and	CCONJ
ejpam-2623	1138	3	m.	m.	NOUN
ejpam-2623	1138	4	tibouchi	tibouchi	PROPN
ejpam-2623	1138	5	.	.	PUNCT
ejpam-2623	1139	1	injective	injective	ADJ
ejpam-2623	1139	2	encodings	encoding	NOUN
ejpam-2623	1139	3	to	to	ADP
ejpam-2623	1139	4	elliptic	elliptic	ADJ
ejpam-2623	1139	5	curves	curve	NOUN
ejpam-2623	1139	6	.	.	PUNCT
ejpam-2623	1140	1	in	in	ADP
ejpam-2623	1140	2	information	information	NOUN
ejpam-2623	1140	3	security	security	NOUN
ejpam-2623	1140	4	and	and	CCONJ
ejpam-2623	1140	5	privacy	privacy	NOUN
ejpam-2623	1140	6	18th	18th	ADJ
ejpam-2623	1140	7	australasian	australasian	ADJ
ejpam-2623	1140	8	conference	conference	NOUN
ejpam-2623	1140	9	,	,	PUNCT
ejpam-2623	1140	10	lncs	lncs	PROPN
ejpam-2623	1140	11	,	,	PUNCT
ejpam-2623	1140	12	springer	springer	NOUN
ejpam-2623	1140	13	,	,	PUNCT
ejpam-2623	1140	14	7959:16	7959:16	NUM
ejpam-2623	1140	15	,	,	PUNCT
ejpam-2623	1140	16	july	july	PROPN
ejpam-2623	1140	17	2013	2013	NUM
ejpam-2623	1140	18	.	.	PUNCT
ejpam-2623	1141	1	[	[	X
ejpam-2623	1141	2	13	13	NUM
ejpam-2623	1141	3	]	]	PUNCT
ejpam-2623	1141	4	antoine	antoine	PROPN
ejpam-2623	1141	5	joux	joux	PROPN
ejpam-2623	1141	6	pierre	pierre	PROPN
ejpam-2623	1141	7	-	-	PUNCT
ejpam-2623	1141	8	alain	alain	PROPN
ejpam-2623	1141	9	fouque	fouque	PROPN
ejpam-2623	1141	10	and	and	CCONJ
ejpam-2623	1141	11	mehdi	mehdi	PROPN
ejpam-2623	1141	12	tibouchi	tibouchi	PROPN
ejpam-2623	1141	13	.	.	PUNCT
ejpam-2623	1142	1	injective	injective	ADJ
ejpam-2623	1142	2	encodings	encoding	NOUN
ejpam-2623	1142	3	to	to	ADP
ejpam-2623	1142	4	elliptic	elliptic	ADJ
ejpam-2623	1142	5	curves	curve	NOUN
ejpam-2623	1142	6	.	.	PUNCT
ejpam-2623	1143	1	in	in	ADP
ejpam-2623	1143	2	acisp	acisp	PROPN
ejpam-2623	1143	3	(	(	PUNCT
ejpam-2623	1143	4	2013	2013	NUM
ejpam-2623	1143	5	)	)	PUNCT
ejpam-2623	1143	6	,	,	PUNCT
ejpam-2623	1143	7	lncs	lncs	PROPN
ejpam-2623	1143	8	,	,	PUNCT
ejpam-2623	1143	9	springer	springer	NOUN
ejpam-2623	1143	10	,	,	PUNCT
ejpam-2623	1143	11	7959:203–218	7959:203–218	NOUN
ejpam-2623	1143	12	,	,	PUNCT
ejpam-2623	1143	13	2013	2013	NUM
ejpam-2623	1143	14	.	.	PUNCT
ejpam-2623	1144	1	[	[	X
ejpam-2623	1144	2	14	14	NUM
ejpam-2623	1144	3	]	]	X
ejpam-2623	1144	4	igor	igor	PROPN
ejpam-2623	1144	5	e.	e.	PROPN
ejpam-2623	1144	6	shparlinski	shparlinski	PROPN
ejpam-2623	1144	7	et	et	PROPN
ejpam-2623	1144	8	al	al	PROPN
ejpam-2623	1144	9	.	.	PUNCT
ejpam-2623	1145	1	reza	reza	PROPN
ejpam-2623	1145	2	r.	r.	PROPN
ejpam-2623	1145	3	farashahi	farashahi	PROPN
ejpam-2623	1145	4	,	,	PUNCT
ejpam-2623	1145	5	pierre	pierre	PROPN
ejpam-2623	1145	6	-	-	PUNCT
ejpam-2623	1145	7	alain	alain	PROPN
ejpam-2623	1145	8	fouque	fouque	NOUN
ejpam-2623	1145	9	.	.	PUNCT
ejpam-2623	1146	1	indifferentiable	indifferentiable	ADJ
ejpam-2623	1146	2	deterministic	deterministic	ADJ
ejpam-2623	1146	3	hashing	hashing	NOUN
ejpam-2623	1146	4	to	to	ADP
ejpam-2623	1146	5	elliptic	elliptic	ADJ
ejpam-2623	1146	6	and	and	CCONJ
ejpam-2623	1146	7	hyperelliptic	hyperelliptic	ADJ
ejpam-2623	1146	8	curves	curve	NOUN
ejpam-2623	1146	9	.	.	PUNCT
ejpam-2623	1147	1	mathematics	mathematic	NOUN
ejpam-2623	1147	2	of	of	ADP
ejpam-2623	1147	3	computation	computation	NOUN
ejpam-2623	1147	4	,	,	PUNCT
ejpam-2623	1147	5	82(281):491–512	82(281):491–512	PROPN
ejpam-2623	1147	6	,	,	PUNCT
ejpam-2623	1147	7	january	january	PROPN
ejpam-2623	1147	8	2013	2013	NUM
ejpam-2623	1147	9	.	.	PUNCT
ejpam-2623	1148	1	[	[	X
ejpam-2623	1148	2	15	15	NUM
ejpam-2623	1148	3	]	]	X
ejpam-2623	1148	4	andrew	andrew	PROPN
ejpam-2623	1148	5	shallue	shallue	PROPN
ejpam-2623	1148	6	and	and	CCONJ
ejpam-2623	1148	7	christiaan	christiaan	PROPN
ejpam-2623	1148	8	van	van	PROPN
ejpam-2623	1148	9	de	de	PROPN
ejpam-2623	1148	10	woestijne	woestijne	PROPN
ejpam-2623	1148	11	.	.	PUNCT
ejpam-2623	1149	1	construction	construction	NOUN
ejpam-2623	1149	2	of	of	ADP
ejpam-2623	1149	3	rational	rational	ADJ
ejpam-2623	1149	4	points	point	NOUN
ejpam-2623	1149	5	on	on	ADP
ejpam-2623	1149	6	elliptic	elliptic	ADJ
ejpam-2623	1149	7	curves	curve	NOUN
ejpam-2623	1149	8	over	over	ADP
ejpam-2623	1149	9	finite	finite	ADJ
ejpam-2623	1149	10	fields	field	NOUN
ejpam-2623	1149	11	.	.	PUNCT
ejpam-2623	1150	1	in	in	ADP
ejpam-2623	1150	2	ants	ant	NOUN
ejpam-2623	1150	3	(	(	PUNCT
ejpam-2623	1150	4	2006	2006	NUM
ejpam-2623	1150	5	)	)	PUNCT
ejpam-2623	1150	6	,	,	PUNCT
ejpam-2623	1150	7	lncs	lncs	PROPN
ejpam-2623	1150	8	,	,	PUNCT
ejpam-2623	1150	9	springer	springer	NOUN
ejpam-2623	1150	10	,	,	PUNCT
ejpam-2623	1150	11	4076:510–524	4076:510–524	PROPN
ejpam-2623	1150	12	,	,	PUNCT
ejpam-2623	1150	13	2006	2006	NUM
ejpam-2623	1150	14	.	.	PUNCT
ejpam-2623	1151	1	[	[	X
ejpam-2623	1151	2	16	16	NUM
ejpam-2623	1151	3	]	]	PUNCT
ejpam-2623	1151	4	mariusz	mariusz	PROPN
ejpam-2623	1151	5	skalba	skalba	PROPN
ejpam-2623	1151	6	.	.	PUNCT
ejpam-2623	1152	1	points	point	NOUN
ejpam-2623	1152	2	on	on	ADP
ejpam-2623	1152	3	elliptic	elliptic	ADJ
ejpam-2623	1152	4	curves	curve	NOUN
ejpam-2623	1152	5	over	over	ADP
ejpam-2623	1152	6	finite	finite	ADJ
ejpam-2623	1152	7	fields	field	NOUN
ejpam-2623	1152	8	.	.	PUNCT
ejpam-2623	1153	1	acta	acta	PROPN
ejpam-2623	1153	2	arith	arith	PROPN
ejpam-2623	1153	3	.	.	PUNCT
ejpam-2623	1153	4	,	,	PUNCT
ejpam-2623	1153	5	117:293–301	117:293–301	NUM
ejpam-2623	1153	6	,	,	PUNCT
ejpam-2623	1153	7	2005	2005	NUM
ejpam-2623	1153	8	.	.	PUNCT
ejpam-2623	1154	1	[	[	X
ejpam-2623	1154	2	17	17	NUM
ejpam-2623	1154	3	]	]	X
ejpam-2623	1154	4	mehdi	mehdi	PROPN
ejpam-2623	1154	5	tibouchi	tibouchi	PROPN
ejpam-2623	1154	6	.	.	PUNCT
ejpam-2623	1155	1	elligator	elligator	PROPN
ejpam-2623	1155	2	squared	square	VERB
ejpam-2623	1155	3	:	:	PUNCT
ejpam-2623	1155	4	uniform	uniform	ADJ
ejpam-2623	1155	5	points	point	NOUN
ejpam-2623	1155	6	on	on	ADP
ejpam-2623	1155	7	elliptic	elliptic	ADJ
ejpam-2623	1155	8	curves	curve	NOUN
ejpam-2623	1155	9	of	of	ADP
ejpam-2623	1155	10	prime	prime	ADJ
ejpam-2623	1155	11	order	order	NOUN
ejpam-2623	1155	12	as	as	ADP
ejpam-2623	1155	13	uniform	uniform	ADJ
ejpam-2623	1155	14	random	random	ADJ
ejpam-2623	1155	15	strings	string	NOUN
ejpam-2623	1155	16	.	.	PUNCT
ejpam-2623	1156	1	to	to	PART
ejpam-2623	1156	2	appear	appear	VERB
ejpam-2623	1156	3	in	in	ADP
ejpam-2623	1156	4	financial	financial	ADJ
ejpam-2623	1156	5	cryptography	cryptography	NOUN
ejpam-2623	1156	6	,	,	PUNCT
ejpam-2623	1156	7	lncs	lncs	PROPN
ejpam-2623	1156	8	,	,	PUNCT
ejpam-2623	1156	9	springer	springer	NOUN
ejpam-2623	1156	10	,	,	PUNCT
ejpam-2623	1156	11	2014	2014	NUM
ejpam-2623	1156	12	.	.	PUNCT
ejpam-2623	1157	1	[	[	X
ejpam-2623	1157	2	18	18	NUM
ejpam-2623	1157	3	]	]	X
ejpam-2623	1157	4	philip	philip	PROPN
ejpam-2623	1157	5	d.	d.	PROPN
ejpam-2623	1157	6	mackenzie	mackenzie	PROPN
ejpam-2623	1157	7	victor	victor	PROPN
ejpam-2623	1157	8	boyko	boyko	PROPN
ejpam-2623	1157	9	and	and	CCONJ
ejpam-2623	1157	10	sarvar	sarvar	NOUN
ejpam-2623	1157	11	patel	patel	PROPN
ejpam-2623	1157	12	.	.	PUNCT
ejpam-2623	1158	1	provably	provably	ADV
ejpam-2623	1158	2	secure	secure	ADJ
ejpam-2623	1158	3	passwordauthenticated	passwordauthenticate	VERB
ejpam-2623	1158	4	key	key	ADJ
ejpam-2623	1158	5	exchange	exchange	NOUN
ejpam-2623	1158	6	using	use	VERB
ejpam-2623	1158	7	diffie	diffie	PROPN
ejpam-2623	1158	8	-	-	PUNCT
ejpam-2623	1158	9	hellman	hellman	NOUN
ejpam-2623	1158	10	.	.	PUNCT
ejpam-2623	1159	1	in	in	ADP
ejpam-2623	1159	2	eurocrypt	eurocrypt	NOUN
ejpam-2623	1159	3	(	(	PUNCT
ejpam-2623	1159	4	2000	2000	NUM
ejpam-2623	1159	5	)	)	PUNCT
ejpam-2623	1159	6	,	,	PUNCT
ejpam-2623	1159	7	lncs	lncs	PROPN
ejpam-2623	1159	8	,	,	PUNCT
ejpam-2623	1159	9	springer	springer	NOUN
ejpam-2623	1159	10	,	,	PUNCT
ejpam-2623	1159	11	1807:156171	1807:156171	NUM
ejpam-2623	1159	12	,	,	PUNCT
ejpam-2623	1159	13	2001	2001	NUM
ejpam-2623	1159	14	.	.	PUNCT