id	sid	tid	token	lemma	pos
ejpam-3245	1	1	european	european	PROPN
ejpam-3245	1	2	journal	journal	PROPN
ejpam-3245	1	3	of	of	ADP
ejpam-3245	1	4	pure	pure	ADJ
ejpam-3245	1	5	and	and	CCONJ
ejpam-3245	1	6	applied	apply	VERB
ejpam-3245	1	7	mathematics	mathematic	NOUN
ejpam-3245	1	8	vol	vol	NOUN
ejpam-3245	1	9	.	.	PUNCT
ejpam-3245	2	1	11	11	NUM
ejpam-3245	2	2	,	,	PUNCT
ejpam-3245	2	3	no	no	INTJ
ejpam-3245	2	4	.	.	NOUN
ejpam-3245	2	5	3	3	NUM
ejpam-3245	2	6	,	,	PUNCT
ejpam-3245	2	7	2018	2018	NUM
ejpam-3245	2	8	,	,	PUNCT
ejpam-3245	2	9	803	803	NUM
ejpam-3245	2	10	-	-	SYM
ejpam-3245	2	11	814	814	NUM
ejpam-3245	2	12	issn	issn	PROPN
ejpam-3245	2	13	1307	1307	NUM
ejpam-3245	2	14	-	-	SYM
ejpam-3245	2	15	5543	5543	NUM
ejpam-3245	2	16	–	–	PUNCT
ejpam-3245	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3245	2	18	published	publish	VERB
ejpam-3245	2	19	by	by	ADP
ejpam-3245	2	20	new	new	PROPN
ejpam-3245	2	21	york	york	PROPN
ejpam-3245	2	22	business	business	PROPN
ejpam-3245	2	23	global	global	PROPN
ejpam-3245	2	24	on	on	ADP
ejpam-3245	2	25	the	the	DET
ejpam-3245	2	26	existence	existence	NOUN
ejpam-3245	2	27	of	of	ADP
ejpam-3245	2	28	roots	root	NOUN
ejpam-3245	2	29	of	of	ADP
ejpam-3245	2	30	some	some	DET
ejpam-3245	2	31	p	p	ADJ
ejpam-3245	2	32	-	-	PUNCT
ejpam-3245	2	33	adic	adic	ADJ
ejpam-3245	2	34	exponential	exponential	NOUN
ejpam-3245	2	35	-	-	PUNCT
ejpam-3245	2	36	polynomials	polynomial	NOUN
ejpam-3245	2	37	amran	amran	ADJ
ejpam-3245	2	38	dalloul	dalloul	PROPN
ejpam-3245	2	39	department	department	PROPN
ejpam-3245	2	40	of	of	ADP
ejpam-3245	2	41	mathematics	mathematics	PROPN
ejpam-3245	2	42	,	,	PUNCT
ejpam-3245	2	43	beirut	beirut	PROPN
ejpam-3245	2	44	arab	arab	PROPN
ejpam-3245	2	45	university	university	PROPN
ejpam-3245	2	46	,	,	PUNCT
ejpam-3245	2	47	beirut	beirut	PROPN
ejpam-3245	2	48	,	,	PUNCT
ejpam-3245	2	49	lebanon	lebanon	PROPN
ejpam-3245	2	50	abstract	abstract	NOUN
ejpam-3245	2	51	.	.	PUNCT
ejpam-3245	3	1	in	in	ADP
ejpam-3245	3	2	this	this	DET
ejpam-3245	3	3	paper	paper	NOUN
ejpam-3245	3	4	,	,	PUNCT
ejpam-3245	3	5	we	we	PRON
ejpam-3245	3	6	apply	apply	VERB
ejpam-3245	3	7	newton	newton	PROPN
ejpam-3245	3	8	polygon	polygon	PROPN
ejpam-3245	3	9	method	method	NOUN
ejpam-3245	3	10	in	in	ADP
ejpam-3245	3	11	order	order	NOUN
ejpam-3245	3	12	to	to	PART
ejpam-3245	3	13	derive	derive	VERB
ejpam-3245	3	14	sufficient	sufficient	ADJ
ejpam-3245	3	15	conditions	condition	NOUN
ejpam-3245	3	16	for	for	ADP
ejpam-3245	3	17	the	the	DET
ejpam-3245	3	18	existence	existence	NOUN
ejpam-3245	3	19	of	of	ADP
ejpam-3245	3	20	zeros	zero	NOUN
ejpam-3245	3	21	of	of	ADP
ejpam-3245	3	22	some	some	DET
ejpam-3245	3	23	p	p	ADJ
ejpam-3245	3	24	-	-	PUNCT
ejpam-3245	3	25	adic	adic	ADJ
ejpam-3245	3	26	exponential	exponential	NOUN
ejpam-3245	3	27	-	-	PUNCT
ejpam-3245	3	28	polynomials	polynomial	NOUN
ejpam-3245	3	29	.	.	PUNCT
ejpam-3245	4	1	1	1	X
ejpam-3245	4	2	.	.	X
ejpam-3245	4	3	introduction	introduction	NOUN
ejpam-3245	4	4	let	let	VERB
ejpam-3245	4	5	k	k	PROPN
ejpam-3245	4	6	be	be	AUX
ejpam-3245	4	7	an	an	DET
ejpam-3245	4	8	algebraically	algebraically	ADV
ejpam-3245	4	9	closed	closed	ADJ
ejpam-3245	4	10	field	field	NOUN
ejpam-3245	4	11	of	of	ADP
ejpam-3245	4	12	characteristic	characteristic	ADJ
ejpam-3245	4	13	zero	zero	NUM
ejpam-3245	4	14	,	,	PUNCT
ejpam-3245	4	15	and	and	CCONJ
ejpam-3245	4	16	let	let	VERB
ejpam-3245	4	17	exp	exp	NOUN
ejpam-3245	4	18	be	be	AUX
ejpam-3245	4	19	a	a	DET
ejpam-3245	4	20	(	(	PUNCT
ejpam-3245	4	21	partial	partial	ADJ
ejpam-3245	4	22	)	)	PUNCT
ejpam-3245	4	23	exponential	exponential	ADJ
ejpam-3245	4	24	map	map	NOUN
ejpam-3245	4	25	exp	exp	NOUN
ejpam-3245	4	26	:	:	PUNCT
ejpam-3245	4	27	e	e	X
ejpam-3245	4	28	→	→	SYM
ejpam-3245	4	29	k×	k×	PROPN
ejpam-3245	4	30	,	,	PUNCT
ejpam-3245	4	31	e	e	PROPN
ejpam-3245	4	32	⊂	⊂	PROPN
ejpam-3245	4	33	k	k	X
ejpam-3245	4	34	being	be	AUX
ejpam-3245	4	35	the	the	DET
ejpam-3245	4	36	domain	domain	NOUN
ejpam-3245	4	37	of	of	ADP
ejpam-3245	4	38	the	the	DET
ejpam-3245	4	39	exponential	exponential	ADJ
ejpam-3245	4	40	map	map	NOUN
ejpam-3245	4	41	.	.	PUNCT
ejpam-3245	5	1	an	an	DET
ejpam-3245	5	2	exponential	exponential	ADJ
ejpam-3245	5	3	-	-	PUNCT
ejpam-3245	5	4	polynomial	polynomial	ADJ
ejpam-3245	5	5	is	be	AUX
ejpam-3245	5	6	any	any	DET
ejpam-3245	5	7	expression	expression	NOUN
ejpam-3245	5	8	of	of	ADP
ejpam-3245	5	9	the	the	DET
ejpam-3245	5	10	form	form	NOUN
ejpam-3245	5	11	a(x	a(x	NOUN
ejpam-3245	5	12	)	)	PUNCT
ejpam-3245	5	13	=	=	SYM
ejpam-3245	5	14	p1(x	p1(x	NOUN
ejpam-3245	5	15	)	)	PUNCT
ejpam-3245	5	16	exp(w1x	exp(w1x	PROPN
ejpam-3245	5	17	)	)	PUNCT
ejpam-3245	6	1	+	+	CCONJ
ejpam-3245	6	2	...	...	PUNCT
ejpam-3245	7	1	+	+	NUM
ejpam-3245	7	2	pd(x	pd(x	NOUN
ejpam-3245	7	3	)	)	PUNCT
ejpam-3245	7	4	exp(wdx	exp(wdx	PROPN
ejpam-3245	7	5	)	)	PUNCT
ejpam-3245	7	6	,	,	PUNCT
ejpam-3245	7	7	(	(	PUNCT
ejpam-3245	7	8	1	1	X
ejpam-3245	7	9	)	)	PUNCT
ejpam-3245	7	10	where	where	SCONJ
ejpam-3245	7	11	the	the	DET
ejpam-3245	7	12	pi	pi	NOUN
ejpam-3245	7	13	’s	’s	X
ejpam-3245	7	14	(	(	PUNCT
ejpam-3245	7	15	i	i	NOUN
ejpam-3245	7	16	=	=	NOUN
ejpam-3245	7	17	1	1	NUM
ejpam-3245	7	18	,	,	PUNCT
ejpam-3245	7	19	.	.	PUNCT
ejpam-3245	7	20	.	.	PUNCT
ejpam-3245	7	21	.	.	PUNCT
ejpam-3245	8	1	,	,	PUNCT
ejpam-3245	8	2	d	d	X
ejpam-3245	8	3	)	)	PUNCT
ejpam-3245	8	4	are	be	AUX
ejpam-3245	8	5	polynomials	polynomial	NOUN
ejpam-3245	8	6	in	in	ADP
ejpam-3245	8	7	k[x	k[x	NOUN
ejpam-3245	8	8	]	]	PUNCT
ejpam-3245	8	9	,	,	PUNCT
ejpam-3245	8	10	and	and	CCONJ
ejpam-3245	9	1	wi	wi	PROPN
ejpam-3245	9	2	∈	∈	PROPN
ejpam-3245	9	3	k	k	PROPN
ejpam-3245	9	4	for	for	ADP
ejpam-3245	9	5	i	i	PRON
ejpam-3245	9	6	=	=	NOUN
ejpam-3245	9	7	1	1	NUM
ejpam-3245	9	8	,	,	PUNCT
ejpam-3245	9	9	2	2	NUM
ejpam-3245	9	10	,	,	PUNCT
ejpam-3245	9	11	.	.	PUNCT
ejpam-3245	9	12	.	.	PUNCT
ejpam-3245	9	13	.	.	PUNCT
ejpam-3245	10	1	,	,	PUNCT
ejpam-3245	10	2	d.	d.	PROPN
ejpam-3245	10	3	the	the	DET
ejpam-3245	10	4	theory	theory	NOUN
ejpam-3245	10	5	of	of	ADP
ejpam-3245	10	6	exponential	exponential	ADJ
ejpam-3245	10	7	polynomials	polynomial	NOUN
ejpam-3245	10	8	is	be	AUX
ejpam-3245	10	9	an	an	DET
ejpam-3245	10	10	important	important	ADJ
ejpam-3245	10	11	topic	topic	NOUN
ejpam-3245	10	12	in	in	ADP
ejpam-3245	10	13	transcendental	transcendental	ADJ
ejpam-3245	10	14	number	number	NOUN
ejpam-3245	10	15	theory	theory	NOUN
ejpam-3245	10	16	.	.	PUNCT
ejpam-3245	11	1	a	a	DET
ejpam-3245	11	2	remarkable	remarkable	ADJ
ejpam-3245	11	3	work	work	NOUN
ejpam-3245	11	4	has	have	AUX
ejpam-3245	11	5	been	be	AUX
ejpam-3245	11	6	made	make	VERB
ejpam-3245	11	7	by	by	ADP
ejpam-3245	11	8	p.	p.	PROPN
ejpam-3245	11	9	d’a	d’a	PROPN
ejpam-3245	11	10	quino	quino	PROPN
ejpam-3245	11	11	,	,	PUNCT
ejpam-3245	11	12	a.	a.	PROPN
ejpam-3245	11	13	macintyre	macintyre	PROPN
ejpam-3245	11	14	and	and	CCONJ
ejpam-3245	11	15	g.	g.	PROPN
ejpam-3245	11	16	terzo	terzo	PROPN
ejpam-3245	12	1	[	[	X
ejpam-3245	12	2	1	1	NUM
ejpam-3245	12	3	]	]	PUNCT
ejpam-3245	12	4	,	,	PUNCT
ejpam-3245	12	5	where	where	SCONJ
ejpam-3245	12	6	they	they	PRON
ejpam-3245	12	7	proved	prove	VERB
ejpam-3245	12	8	that	that	SCONJ
ejpam-3245	12	9	shapiro	shapiro	PROPN
ejpam-3245	12	10	’s	’s	PART
ejpam-3245	12	11	conjecture	conjecture	NOUN
ejpam-3245	12	12	(	(	PUNCT
ejpam-3245	12	13	over	over	ADP
ejpam-3245	12	14	an	an	DET
ejpam-3245	12	15	algebraically	algebraically	ADV
ejpam-3245	12	16	closed	close	VERB
ejpam-3245	12	17	exponential	exponential	ADJ
ejpam-3245	12	18	field	field	NOUN
ejpam-3245	12	19	of	of	ADP
ejpam-3245	12	20	characteristic	characteristic	ADJ
ejpam-3245	12	21	zero	zero	NUM
ejpam-3245	12	22	having	have	VERB
ejpam-3245	12	23	an	an	DET
ejpam-3245	12	24	infinite	infinite	ADJ
ejpam-3245	12	25	cyclic	cyclic	ADJ
ejpam-3245	12	26	group	group	NOUN
ejpam-3245	12	27	of	of	ADP
ejpam-3245	12	28	periods	period	NOUN
ejpam-3245	12	29	and	and	CCONJ
ejpam-3245	12	30	the	the	DET
ejpam-3245	12	31	exponential	exponential	NOUN
ejpam-3245	12	32	is	be	AUX
ejpam-3245	12	33	surjective	surjective	ADJ
ejpam-3245	12	34	onto	onto	ADP
ejpam-3245	12	35	the	the	DET
ejpam-3245	12	36	multiplicative	multiplicative	ADJ
ejpam-3245	12	37	group	group	NOUN
ejpam-3245	12	38	)	)	PUNCT
ejpam-3245	12	39	is	be	AUX
ejpam-3245	12	40	true	true	ADJ
ejpam-3245	12	41	with	with	ADP
ejpam-3245	12	42	an	an	DET
ejpam-3245	12	43	extra	extra	ADJ
ejpam-3245	12	44	assumption	assumption	NOUN
ejpam-3245	12	45	,	,	PUNCT
ejpam-3245	12	46	schanuel	schanuel	NOUN
ejpam-3245	12	47	’s	’s	PART
ejpam-3245	12	48	conjecture	conjecture	NOUN
ejpam-3245	12	49	.	.	PUNCT
ejpam-3245	13	1	in	in	ADP
ejpam-3245	13	2	2017	2017	NUM
ejpam-3245	13	3	,	,	PUNCT
ejpam-3245	13	4	they	they	PRON
ejpam-3245	13	5	proved	prove	VERB
ejpam-3245	13	6	the	the	DET
ejpam-3245	13	7	following	following	NOUN
ejpam-3245	13	8	[	[	X
ejpam-3245	13	9	2	2	NUM
ejpam-3245	13	10	]	]	PUNCT
ejpam-3245	13	11	:	:	PUNCT
ejpam-3245	13	12	assume	assume	VERB
ejpam-3245	13	13	schanuel	schanuel	PROPN
ejpam-3245	13	14	’s	’s	PART
ejpam-3245	13	15	conjecture	conjecture	NOUN
ejpam-3245	13	16	.	.	PUNCT
ejpam-3245	14	1	let	let	VERB
ejpam-3245	14	2	z(f	z(f	NOUN
ejpam-3245	14	3	)	)	PUNCT
ejpam-3245	14	4	be	be	AUX
ejpam-3245	14	5	the	the	DET
ejpam-3245	14	6	zero	zero	NUM
ejpam-3245	14	7	set	set	NOUN
ejpam-3245	14	8	of	of	ADP
ejpam-3245	14	9	the	the	DET
ejpam-3245	14	10	exponential	exponential	ADJ
ejpam-3245	14	11	polynomial	polynomial	ADJ
ejpam-3245	14	12	f(x	f(x	PROPN
ejpam-3245	14	13	)	)	PUNCT
ejpam-3245	15	1	=	=	SYM
ejpam-3245	15	2	α1	α1	PROPN
ejpam-3245	15	3	exp(w1x	exp(w1x	PROPN
ejpam-3245	15	4	)	)	PUNCT
ejpam-3245	16	1	+	+	CCONJ
ejpam-3245	16	2	...	...	PUNCT
ejpam-3245	16	3	+	+	CCONJ
ejpam-3245	16	4	αd	αd	PROPN
ejpam-3245	16	5	exp(wdx	exp(wdx	NOUN
ejpam-3245	16	6	)	)	PUNCT
ejpam-3245	16	7	,	,	PUNCT
ejpam-3245	16	8	where	where	SCONJ
ejpam-3245	16	9	αi	αi	NOUN
ejpam-3245	16	10	,	,	PUNCT
ejpam-3245	16	11	wi	wi	PROPN
ejpam-3245	16	12	are	be	AUX
ejpam-3245	16	13	constants	constant	NOUN
ejpam-3245	16	14	in	in	ADP
ejpam-3245	16	15	k.	k.	PROPN
ejpam-3245	16	16	if	if	SCONJ
ejpam-3245	16	17	z(f	z(f	NOUN
ejpam-3245	16	18	)	)	PUNCT
ejpam-3245	16	19	is	be	AUX
ejpam-3245	16	20	infinite	infinite	ADJ
ejpam-3245	16	21	,	,	PUNCT
ejpam-3245	16	22	then	then	ADV
ejpam-3245	16	23	each	each	DET
ejpam-3245	16	24	infinite	infinite	NOUN
ejpam-3245	16	25	subset	subset	NOUN
ejpam-3245	16	26	x	x	PUNCT
ejpam-3245	16	27	⊆	⊆	NUM
ejpam-3245	16	28	z(f	z(f	NOUN
ejpam-3245	16	29	)	)	PUNCT
ejpam-3245	16	30	has	have	VERB
ejpam-3245	16	31	an	an	DET
ejpam-3245	16	32	infinite	infinite	ADJ
ejpam-3245	16	33	transcendence	transcendence	NOUN
ejpam-3245	16	34	degree	degree	NOUN
ejpam-3245	16	35	over	over	ADP
ejpam-3245	16	36	q.	q.	NOUN
ejpam-3245	16	37	in	in	ADP
ejpam-3245	16	38	this	this	DET
ejpam-3245	16	39	paper	paper	NOUN
ejpam-3245	16	40	,	,	PUNCT
ejpam-3245	16	41	we	we	PRON
ejpam-3245	16	42	work	work	VERB
ejpam-3245	16	43	in	in	ADP
ejpam-3245	16	44	the	the	DET
ejpam-3245	16	45	non	non	ADJ
ejpam-3245	16	46	-	-	ADJ
ejpam-3245	16	47	archimedean	archimedean	ADJ
ejpam-3245	16	48	fields	field	NOUN
ejpam-3245	16	49	,	,	PUNCT
ejpam-3245	16	50	namely	namely	ADV
ejpam-3245	16	51	the	the	DET
ejpam-3245	16	52	p−adic	p−adic	ADJ
ejpam-3245	16	53	fields	field	NOUN
ejpam-3245	16	54	.	.	PUNCT
ejpam-3245	17	1	here	here	ADV
ejpam-3245	17	2	,	,	PUNCT
ejpam-3245	17	3	the	the	DET
ejpam-3245	17	4	situation	situation	NOUN
ejpam-3245	17	5	is	be	AUX
ejpam-3245	17	6	different	different	ADJ
ejpam-3245	17	7	to	to	ADP
ejpam-3245	17	8	some	some	DET
ejpam-3245	17	9	extend	extend	NOUN
ejpam-3245	17	10	.	.	PUNCT
ejpam-3245	18	1	in	in	ADP
ejpam-3245	18	2	fact	fact	NOUN
ejpam-3245	18	3	,	,	PUNCT
ejpam-3245	18	4	poorten	poorten	VERB
ejpam-3245	18	5	and	and	CCONJ
ejpam-3245	18	6	rumely	rumely	ADV
ejpam-3245	19	1	[	[	X
ejpam-3245	19	2	pr	pr	X
ejpam-3245	19	3	]	]	PUNCT
ejpam-3245	19	4	proved	prove	VERB
ejpam-3245	19	5	that	that	SCONJ
ejpam-3245	19	6	each	each	DET
ejpam-3245	19	7	exponential	exponential	ADJ
ejpam-3245	19	8	polynomial	polynomial	NOUN
ejpam-3245	19	9	of	of	ADP
ejpam-3245	19	10	the	the	DET
ejpam-3245	19	11	form	form	NOUN
ejpam-3245	19	12	(	(	PUNCT
ejpam-3245	19	13	1.1	1.1	NUM
ejpam-3245	19	14	)	)	PUNCT
ejpam-3245	19	15	has	have	VERB
ejpam-3245	19	16	at	at	ADP
ejpam-3245	19	17	most	most	ADV
ejpam-3245	19	18	finitely	finitely	ADV
ejpam-3245	19	19	many	many	ADJ
ejpam-3245	19	20	roots	root	NOUN
ejpam-3245	19	21	in	in	ADP
ejpam-3245	19	22	the	the	DET
ejpam-3245	19	23	domain	domain	NOUN
ejpam-3245	19	24	of	of	ADP
ejpam-3245	19	25	convergence	convergence	NOUN
ejpam-3245	19	26	.	.	PUNCT
ejpam-3245	20	1	their	their	PRON
ejpam-3245	20	2	proof	proof	NOUN
ejpam-3245	20	3	relies	rely	VERB
ejpam-3245	20	4	on	on	ADP
ejpam-3245	20	5	a	a	DET
ejpam-3245	20	6	geometric	geometric	ADJ
ejpam-3245	20	7	approach	approach	NOUN
ejpam-3245	20	8	,	,	PUNCT
ejpam-3245	20	9	namely	namely	ADV
ejpam-3245	20	10	the	the	DET
ejpam-3245	20	11	newton	newton	PROPN
ejpam-3245	20	12	polygon	polygon	PROPN
ejpam-3245	20	13	of	of	ADP
ejpam-3245	20	14	power	power	NOUN
ejpam-3245	20	15	series	series	NOUN
ejpam-3245	20	16	,	,	PUNCT
ejpam-3245	20	17	where	where	SCONJ
ejpam-3245	20	18	they	they	PRON
ejpam-3245	20	19	proved	prove	VERB
ejpam-3245	20	20	that	that	SCONJ
ejpam-3245	20	21	the	the	DET
ejpam-3245	20	22	newton	newton	PROPN
ejpam-3245	20	23	polygon	polygon	PROPN
ejpam-3245	20	24	of	of	ADP
ejpam-3245	20	25	the	the	DET
ejpam-3245	20	26	exponential	exponential	ADJ
ejpam-3245	20	27	doi	doi	NOUN
ejpam-3245	20	28	:	:	PUNCT
ejpam-3245	20	29	https://doi.org/10.29020/nybg.ejpam.v11i3.3245	https://doi.org/10.29020/nybg.ejpam.v11i3.3245	PROPN
ejpam-3245	20	30	email	email	NOUN
ejpam-3245	20	31	address	address	NOUN
ejpam-3245	20	32	:	:	PUNCT
ejpam-3245	20	33	amrandalloul@hotmail.com	amrandalloul@hotmail.com	X
ejpam-3245	20	34	(	(	PUNCT
ejpam-3245	20	35	a.	a.	NOUN
ejpam-3245	20	36	dalloul	dalloul	PROPN
ejpam-3245	20	37	)	)	PUNCT
ejpam-3245	20	38	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3245	21	1	803	803	NUM
ejpam-3245	21	2	c	c	NOUN
ejpam-3245	21	3	©	©	PROPN
ejpam-3245	21	4	2018	2018	NUM
ejpam-3245	21	5	ejpam	ejpam	VERB
ejpam-3245	21	6	all	all	DET
ejpam-3245	21	7	rights	right	NOUN
ejpam-3245	21	8	reserved	reserve	VERB
ejpam-3245	21	9	.	.	PUNCT
ejpam-3245	22	1	a.	a.	PROPN
ejpam-3245	22	2	dalloul	dalloul	PROPN
ejpam-3245	22	3	/	/	SYM
ejpam-3245	22	4	eur	eur	PROPN
ejpam-3245	22	5	.	.	PUNCT
ejpam-3245	23	1	j.	j.	PROPN
ejpam-3245	23	2	pure	pure	PROPN
ejpam-3245	23	3	appl	appl	PROPN
ejpam-3245	23	4	.	.	PROPN
ejpam-3245	23	5	math	math	PROPN
ejpam-3245	23	6	,	,	PUNCT
ejpam-3245	23	7	11	11	NUM
ejpam-3245	23	8	(	(	PUNCT
ejpam-3245	23	9	3	3	NUM
ejpam-3245	23	10	)	)	PUNCT
ejpam-3245	23	11	(	(	PUNCT
ejpam-3245	23	12	2018	2018	NUM
ejpam-3245	23	13	)	)	PUNCT
ejpam-3245	23	14	,	,	PUNCT
ejpam-3245	23	15	803	803	NUM
ejpam-3245	23	16	-	-	SYM
ejpam-3245	23	17	814	814	NUM
ejpam-3245	23	18	804	804	NUM
ejpam-3245	23	19	polynomial	polynomial	ADJ
ejpam-3245	23	20	(	(	PUNCT
ejpam-3245	23	21	1.1	1.1	NUM
ejpam-3245	23	22	)	)	PUNCT
ejpam-3245	23	23	ends	end	VERB
ejpam-3245	23	24	with	with	ADP
ejpam-3245	23	25	a	a	DET
ejpam-3245	23	26	straight	straight	ADJ
ejpam-3245	23	27	line	line	NOUN
ejpam-3245	23	28	.	.	PUNCT
ejpam-3245	24	1	that	that	PRON
ejpam-3245	24	2	guarantees	guarantee	VERB
ejpam-3245	24	3	the	the	DET
ejpam-3245	24	4	existence	existence	NOUN
ejpam-3245	24	5	of	of	ADP
ejpam-3245	24	6	a	a	DET
ejpam-3245	24	7	bound	bind	VERB
ejpam-3245	24	8	on	on	ADP
ejpam-3245	24	9	the	the	DET
ejpam-3245	24	10	number	number	NOUN
ejpam-3245	24	11	of	of	ADP
ejpam-3245	24	12	zeros	zero	NOUN
ejpam-3245	24	13	.	.	PUNCT
ejpam-3245	25	1	furthermore	furthermore	ADV
ejpam-3245	25	2	,	,	PUNCT
ejpam-3245	25	3	the	the	DET
ejpam-3245	25	4	p	p	ADJ
ejpam-3245	25	5	-	-	PUNCT
ejpam-3245	25	6	adic	adic	ADJ
ejpam-3245	25	7	exponential	exponential	ADJ
ejpam-3245	25	8	function	function	NOUN
ejpam-3245	25	9	and	and	CCONJ
ejpam-3245	25	10	the	the	DET
ejpam-3245	25	11	p	p	NOUN
ejpam-3245	25	12	-	-	PUNCT
ejpam-3245	25	13	adic	adic	NOUN
ejpam-3245	25	14	trigonometric	trigonometric	NOUN
ejpam-3245	25	15	functions	function	NOUN
ejpam-3245	25	16	are	be	AUX
ejpam-3245	25	17	not	not	PART
ejpam-3245	25	18	periodic	periodic	ADJ
ejpam-3245	25	19	.	.	PUNCT
ejpam-3245	26	1	many	many	ADJ
ejpam-3245	26	2	results	result	NOUN
ejpam-3245	26	3	,	,	PUNCT
ejpam-3245	26	4	however	however	ADV
ejpam-3245	26	5	,	,	PUNCT
ejpam-3245	26	6	have	have	AUX
ejpam-3245	26	7	been	be	AUX
ejpam-3245	26	8	made	make	VERB
ejpam-3245	26	9	in	in	ADP
ejpam-3245	26	10	the	the	DET
ejpam-3245	26	11	p−adic	p−adic	ADJ
ejpam-3245	26	12	exponential	exponential	ADJ
ejpam-3245	26	13	polynomials	polynomial	NOUN
ejpam-3245	26	14	.	.	PUNCT
ejpam-3245	27	1	for	for	ADP
ejpam-3245	27	2	example	example	NOUN
ejpam-3245	27	3	,	,	PUNCT
ejpam-3245	27	4	poorten	poorten	VERB
ejpam-3245	27	5	,	,	PUNCT
ejpam-3245	27	6	[	[	X
ejpam-3245	27	7	5	5	NUM
ejpam-3245	27	8	]	]	PUNCT
ejpam-3245	27	9	,	,	PUNCT
ejpam-3245	27	10	used	use	VERB
ejpam-3245	27	11	strassmann	strassmann	NOUN
ejpam-3245	27	12	theorem	theorem	VERB
ejpam-3245	27	13	to	to	PART
ejpam-3245	27	14	prove	prove	VERB
ejpam-3245	27	15	that	that	SCONJ
ejpam-3245	27	16	the	the	DET
ejpam-3245	27	17	exponential	exponential	ADJ
ejpam-3245	27	18	polynomial	polynomial	ADJ
ejpam-3245	27	19	b(z	b(z	NOUN
ejpam-3245	27	20	)	)	PUNCT
ejpam-3245	27	21	=	=	SYM
ejpam-3245	27	22	p1[z	p1[z	NOUN
ejpam-3245	27	23	]	]	PUNCT
ejpam-3245	27	24	exp(w1z	exp(w1z	PROPN
ejpam-3245	27	25	)	)	PUNCT
ejpam-3245	27	26	+	+	CCONJ
ejpam-3245	27	27	...	...	PUNCT
ejpam-3245	28	1	+	+	X
ejpam-3245	28	2	pd[z	pd[z	NOUN
ejpam-3245	28	3	]	]	PUNCT
ejpam-3245	28	4	exp(wdz	exp(wdz	PROPN
ejpam-3245	28	5	)	)	PUNCT
ejpam-3245	28	6	,	,	PUNCT
ejpam-3245	28	7	(	(	PUNCT
ejpam-3245	28	8	2	2	X
ejpam-3245	28	9	)	)	PUNCT
ejpam-3245	28	10	with	with	ADP
ejpam-3245	28	11	pi[z	pi[z	PROPN
ejpam-3245	28	12	]	]	PUNCT
ejpam-3245	28	13	∈	∈	PROPN
ejpam-3245	28	14	cp[z	cp[z	PROPN
ejpam-3245	28	15	]	]	PUNCT
ejpam-3245	28	16	and	and	CCONJ
ejpam-3245	28	17	ord(wi	ord(wi	NOUN
ejpam-3245	28	18	)	)	PUNCT
ejpam-3245	28	19	>	>	X
ejpam-3245	28	20	1	1	NUM
ejpam-3245	28	21	p−1+ε	p−1+ε	NOUN
ejpam-3245	28	22	,	,	PUNCT
ejpam-3245	28	23	i	i	PRON
ejpam-3245	28	24	=	=	NOUN
ejpam-3245	28	25	1	1	NUM
ejpam-3245	28	26	,	,	PUNCT
ejpam-3245	28	27	2	2	NUM
ejpam-3245	28	28	,	,	PUNCT
ejpam-3245	28	29	..	..	PUNCT
ejpam-3245	28	30	,	,	PUNCT
ejpam-3245	28	31	d	d	AUX
ejpam-3245	28	32	,	,	PUNCT
ejpam-3245	28	33	has	have	VERB
ejpam-3245	28	34	at	at	ADP
ejpam-3245	28	35	most	most	ADV
ejpam-3245	28	36	(	(	PUNCT
ejpam-3245	28	37	d−1	d−1	PROPN
ejpam-3245	28	38	+	+	PROPN
ejpam-3245	28	39	∑d	∑d	PROPN
ejpam-3245	28	40	i=1	i=1	PROPN
ejpam-3245	28	41	degpi[z])(1	degpi[z])(1	PROPN
ejpam-3245	28	42	+	+	CCONJ
ejpam-3245	28	43	1	1	NUM
ejpam-3245	28	44	ε(p−1	ε(p−1	NUM
ejpam-3245	28	45	)	)	PUNCT
ejpam-3245	28	46	)	)	PUNCT
ejpam-3245	28	47	roots	root	NOUN
ejpam-3245	28	48	in	in	ADP
ejpam-3245	28	49	the	the	DET
ejpam-3245	28	50	unit	unit	NOUN
ejpam-3245	28	51	disk	disk	NOUN
ejpam-3245	28	52	.	.	PUNCT
ejpam-3245	29	1	poorten	poorten	VERB
ejpam-3245	29	2	and	and	CCONJ
ejpam-3245	29	3	rumely	rumely	ADV
ejpam-3245	29	4	,	,	PUNCT
ejpam-3245	29	5	[	[	X
ejpam-3245	29	6	6	6	NUM
ejpam-3245	29	7	]	]	PUNCT
ejpam-3245	29	8	,	,	PUNCT
ejpam-3245	29	9	proved	prove	VERB
ejpam-3245	29	10	that	that	SCONJ
ejpam-3245	29	11	the	the	DET
ejpam-3245	29	12	exponential	exponential	ADJ
ejpam-3245	29	13	polynomial	polynomial	NOUN
ejpam-3245	29	14	(	(	PUNCT
ejpam-3245	29	15	1.2	1.2	NUM
ejpam-3245	29	16	)	)	PUNCT
ejpam-3245	29	17	over	over	ADP
ejpam-3245	29	18	qp	qp	PROPN
ejpam-3245	29	19	(	(	PUNCT
ejpam-3245	29	20	for	for	ADP
ejpam-3245	29	21	large	large	ADJ
ejpam-3245	29	22	enough	enough	ADJ
ejpam-3245	29	23	p	p	NOUN
ejpam-3245	29	24	)	)	PUNCT
ejpam-3245	29	25	has	have	VERB
ejpam-3245	29	26	at	at	ADP
ejpam-3245	29	27	most	most	ADJ
ejpam-3245	29	28	(	(	PUNCT
ejpam-3245	29	29	d	d	NOUN
ejpam-3245	29	30	−	−	PROPN
ejpam-3245	29	31	2	2	NUM
ejpam-3245	29	32	+	+	NUM
ejpam-3245	29	33	∑d	∑d	CCONJ
ejpam-3245	29	34	i=1	i=1	PROPN
ejpam-3245	29	35	degpi[z])p	degpi[z])p	NOUN
ejpam-3245	29	36	roots	root	NOUN
ejpam-3245	29	37	in	in	ADP
ejpam-3245	29	38	its	its	PRON
ejpam-3245	29	39	domain	domain	NOUN
ejpam-3245	29	40	of	of	ADP
ejpam-3245	29	41	convergence	convergence	NOUN
ejpam-3245	29	42	using	use	VERB
ejpam-3245	29	43	the	the	DET
ejpam-3245	29	44	newton	newton	PROPN
ejpam-3245	29	45	polygon	polygon	PROPN
ejpam-3245	29	46	method	method	NOUN
ejpam-3245	29	47	and	and	CCONJ
ejpam-3245	29	48	concepts	concept	NOUN
ejpam-3245	29	49	of	of	ADP
ejpam-3245	29	50	recurrence	recurrence	NOUN
ejpam-3245	29	51	sequences	sequence	NOUN
ejpam-3245	29	52	and	and	CCONJ
ejpam-3245	29	53	generalized	generalized	ADJ
ejpam-3245	29	54	sums	sum	NOUN
ejpam-3245	29	55	.	.	PUNCT
ejpam-3245	30	1	in	in	ADP
ejpam-3245	30	2	this	this	DET
ejpam-3245	30	3	work	work	NOUN
ejpam-3245	30	4	,	,	PUNCT
ejpam-3245	30	5	we	we	PRON
ejpam-3245	30	6	consider	consider	VERB
ejpam-3245	30	7	some	some	DET
ejpam-3245	30	8	p−adic	p−adic	ADJ
ejpam-3245	30	9	exponential	exponential	ADJ
ejpam-3245	30	10	polynomials	polynomial	NOUN
ejpam-3245	30	11	,	,	PUNCT
ejpam-3245	30	12	where	where	SCONJ
ejpam-3245	30	13	we	we	PRON
ejpam-3245	30	14	put	put	VERB
ejpam-3245	30	15	a	a	DET
ejpam-3245	30	16	least	least	ADV
ejpam-3245	30	17	bound	bind	VERB
ejpam-3245	30	18	on	on	ADP
ejpam-3245	30	19	the	the	DET
ejpam-3245	30	20	number	number	NOUN
ejpam-3245	30	21	of	of	ADP
ejpam-3245	30	22	zeros	zero	NOUN
ejpam-3245	30	23	(	(	PUNCT
ejpam-3245	30	24	counting	count	VERB
ejpam-3245	30	25	multiplicity	multiplicity	NOUN
ejpam-3245	30	26	)	)	PUNCT
ejpam-3245	30	27	of	of	ADP
ejpam-3245	30	28	the	the	DET
ejpam-3245	30	29	p−adic	p−adic	ADJ
ejpam-3245	30	30	exponential	exponential	ADJ
ejpam-3245	30	31	polynomials	polynomial	NOUN
ejpam-3245	30	32	.	.	PUNCT
ejpam-3245	31	1	we	we	PRON
ejpam-3245	31	2	mainly	mainly	ADV
ejpam-3245	31	3	use	use	VERB
ejpam-3245	31	4	here	here	ADV
ejpam-3245	31	5	the	the	DET
ejpam-3245	31	6	newton	newton	PROPN
ejpam-3245	31	7	polygon	polygon	PROPN
ejpam-3245	31	8	of	of	ADP
ejpam-3245	31	9	power	power	NOUN
ejpam-3245	31	10	series	series	PROPN
ejpam-3245	31	11	method	method	NOUN
ejpam-3245	31	12	which	which	PRON
ejpam-3245	31	13	assures	assure	VERB
ejpam-3245	31	14	that	that	SCONJ
ejpam-3245	31	15	the	the	DET
ejpam-3245	31	16	roots	root	NOUN
ejpam-3245	31	17	of	of	ADP
ejpam-3245	31	18	the	the	DET
ejpam-3245	31	19	power	power	NOUN
ejpam-3245	31	20	series	series	PROPN
ejpam-3245	31	21	yield	yield	VERB
ejpam-3245	31	22	from	from	ADP
ejpam-3245	31	23	the	the	DET
ejpam-3245	31	24	finite	finite	ADJ
ejpam-3245	31	25	segments	segment	NOUN
ejpam-3245	31	26	of	of	ADP
ejpam-3245	31	27	the	the	DET
ejpam-3245	31	28	polygon	polygon	NOUN
ejpam-3245	31	29	.	.	PUNCT
ejpam-3245	32	1	in	in	ADP
ejpam-3245	32	2	other	other	ADJ
ejpam-3245	32	3	words	word	NOUN
ejpam-3245	32	4	,	,	PUNCT
ejpam-3245	32	5	if	if	SCONJ
ejpam-3245	32	6	the	the	DET
ejpam-3245	32	7	newton	newton	PROPN
ejpam-3245	32	8	polygon	polygon	PROPN
ejpam-3245	32	9	of	of	ADP
ejpam-3245	32	10	the	the	DET
ejpam-3245	32	11	power	power	NOUN
ejpam-3245	32	12	series	series	PROPN
ejpam-3245	32	13	f	f	PROPN
ejpam-3245	32	14	has	have	VERB
ejpam-3245	32	15	a	a	DET
ejpam-3245	32	16	finite	finite	ADJ
ejpam-3245	32	17	segment	segment	NOUN
ejpam-3245	32	18	with	with	ADP
ejpam-3245	32	19	projection	projection	NOUN
ejpam-3245	32	20	length	length	NOUN
ejpam-3245	32	21	on	on	ADP
ejpam-3245	32	22	the	the	DET
ejpam-3245	32	23	x	x	ADJ
ejpam-3245	32	24	-	-	ADJ
ejpam-3245	32	25	axis	axis	NOUN
ejpam-3245	32	26	equals	equal	VERB
ejpam-3245	32	27	to	to	ADP
ejpam-3245	32	28	m	m	PRON
ejpam-3245	32	29	,	,	PUNCT
ejpam-3245	32	30	then	then	ADV
ejpam-3245	32	31	there	there	PRON
ejpam-3245	32	32	exist	exist	VERB
ejpam-3245	32	33	m	m	VERB
ejpam-3245	32	34	roots	root	NOUN
ejpam-3245	32	35	(	(	PUNCT
ejpam-3245	32	36	counting	count	VERB
ejpam-3245	32	37	multiplicity	multiplicity	NOUN
ejpam-3245	32	38	)	)	PUNCT
ejpam-3245	32	39	of	of	ADP
ejpam-3245	32	40	f	f	PROPN
ejpam-3245	32	41	of	of	ADP
ejpam-3245	32	42	the	the	DET
ejpam-3245	32	43	same	same	ADJ
ejpam-3245	32	44	order	order	NOUN
ejpam-3245	32	45	.	.	PUNCT
ejpam-3245	33	1	similarly	similarly	ADV
ejpam-3245	33	2	,	,	PUNCT
ejpam-3245	33	3	we	we	PRON
ejpam-3245	33	4	use	use	VERB
ejpam-3245	33	5	the	the	DET
ejpam-3245	33	6	newton	newton	PROPN
ejpam-3245	33	7	polygon	polygon	PROPN
ejpam-3245	33	8	method	method	NOUN
ejpam-3245	33	9	to	to	PART
ejpam-3245	33	10	put	put	VERB
ejpam-3245	33	11	sufficient	sufficient	ADJ
ejpam-3245	33	12	conditions	condition	NOUN
ejpam-3245	33	13	on	on	ADP
ejpam-3245	33	14	some	some	DET
ejpam-3245	33	15	polynomials	polynomial	NOUN
ejpam-3245	34	1	p	p	X
ejpam-3245	34	2	[	[	X
ejpam-3245	34	3	x	x	X
ejpam-3245	34	4	,	,	PUNCT
ejpam-3245	34	5	y	y	PROPN
ejpam-3245	34	6	]	]	PUNCT
ejpam-3245	34	7	∈	∈	PROPN
ejpam-3245	34	8	q[x	q[x	PROPN
ejpam-3245	34	9	,	,	PUNCT
ejpam-3245	34	10	y	y	PROPN
ejpam-3245	34	11	]	]	PUNCT
ejpam-3245	34	12	to	to	PART
ejpam-3245	34	13	have	have	AUX
ejpam-3245	34	14	roots	root	NOUN
ejpam-3245	34	15	of	of	ADP
ejpam-3245	34	16	the	the	DET
ejpam-3245	34	17	form	form	NOUN
ejpam-3245	34	18	(	(	PUNCT
ejpam-3245	34	19	x	x	NOUN
ejpam-3245	34	20	,	,	PUNCT
ejpam-3245	34	21	exp(x	exp(x	PROPN
ejpam-3245	34	22	)	)	PUNCT
ejpam-3245	34	23	)	)	PUNCT
ejpam-3245	34	24	.	.	PUNCT
ejpam-3245	35	1	2	2	X
ejpam-3245	35	2	.	.	X
ejpam-3245	35	3	notation	notation	NOUN
ejpam-3245	35	4	and	and	CCONJ
ejpam-3245	35	5	preliminaries	preliminary	NOUN
ejpam-3245	35	6	let	let	VERB
ejpam-3245	35	7	p	p	PRON
ejpam-3245	35	8	be	be	AUX
ejpam-3245	35	9	a	a	DET
ejpam-3245	35	10	prime	prime	ADJ
ejpam-3245	35	11	number	number	NOUN
ejpam-3245	35	12	,	,	PUNCT
ejpam-3245	35	13	qp	qp	ADP
ejpam-3245	35	14	the	the	DET
ejpam-3245	35	15	completion	completion	NOUN
ejpam-3245	35	16	of	of	ADP
ejpam-3245	35	17	q	q	NOUN
ejpam-3245	35	18	with	with	ADP
ejpam-3245	35	19	respect	respect	NOUN
ejpam-3245	35	20	to	to	ADP
ejpam-3245	35	21	the	the	DET
ejpam-3245	35	22	p−adic	p−adic	ADJ
ejpam-3245	35	23	absolute	absolute	ADJ
ejpam-3245	35	24	value	value	NOUN
ejpam-3245	35	25	|.|	|.|	NOUN
ejpam-3245	35	26	and	and	CCONJ
ejpam-3245	35	27	cp	cp	VERB
ejpam-3245	35	28	the	the	DET
ejpam-3245	35	29	completion	completion	NOUN
ejpam-3245	35	30	of	of	ADP
ejpam-3245	35	31	an	an	DET
ejpam-3245	35	32	algebraic	algebraic	ADJ
ejpam-3245	35	33	closure	closure	NOUN
ejpam-3245	35	34	of	of	ADP
ejpam-3245	35	35	qp	qp	PROPN
ejpam-3245	35	36	.	.	PUNCT
ejpam-3245	36	1	the	the	DET
ejpam-3245	36	2	absolute	absolute	ADJ
ejpam-3245	36	3	value	value	NOUN
ejpam-3245	36	4	|	|	ADV
ejpam-3245	36	5	·	·	PUNCT
ejpam-3245	36	6	|	|	ADV
ejpam-3245	36	7	on	on	ADP
ejpam-3245	36	8	cp	cp	PROPN
ejpam-3245	36	9	is	be	AUX
ejpam-3245	36	10	the	the	DET
ejpam-3245	36	11	extension	extension	NOUN
ejpam-3245	36	12	of	of	ADP
ejpam-3245	36	13	the	the	DET
ejpam-3245	36	14	p−adic	p−adic	ADJ
ejpam-3245	36	15	absolute	absolute	ADJ
ejpam-3245	36	16	value	value	NOUN
ejpam-3245	36	17	|.|	|.|	NOUN
ejpam-3245	36	18	.	.	PUNCT
ejpam-3245	37	1	starting	start	VERB
ejpam-3245	37	2	from	from	ADP
ejpam-3245	37	3	|	|	ADV
ejpam-3245	37	4	·	·	PUNCT
ejpam-3245	37	5	|	|	ADV
ejpam-3245	37	6	,	,	PUNCT
ejpam-3245	37	7	one	one	PRON
ejpam-3245	37	8	can	can	AUX
ejpam-3245	37	9	define	define	VERB
ejpam-3245	37	10	a	a	DET
ejpam-3245	37	11	map	map	NOUN
ejpam-3245	37	12	ord	ord	NOUN
ejpam-3245	37	13	:	:	PUNCT
ejpam-3245	37	14	cp	cp	PROPN
ejpam-3245	37	15	→	→	SYM
ejpam-3245	37	16	q∪{∞	q∪{∞	PROPN
ejpam-3245	37	17	}	}	PUNCT
ejpam-3245	37	18	,	,	PUNCT
ejpam-3245	37	19	as	as	SCONJ
ejpam-3245	37	20	follows	follow	VERB
ejpam-3245	37	21	:	:	PUNCT
ejpam-3245	37	22	ord(0	ord(0	NUM
ejpam-3245	37	23	)	)	PUNCT
ejpam-3245	38	1	=	=	PUNCT
ejpam-3245	38	2	∞	∞	PROPN
ejpam-3245	38	3	,	,	PUNCT
ejpam-3245	38	4	and	and	CCONJ
ejpam-3245	38	5	ord(x	ord(x	NUM
ejpam-3245	38	6	)	)	PUNCT
ejpam-3245	38	7	=	=	SYM
ejpam-3245	38	8	−	−	PROPN
ejpam-3245	38	9	log(|x|	log(|x|	NUM
ejpam-3245	38	10	)	)	PUNCT
ejpam-3245	38	11	.	.	PUNCT
ejpam-3245	39	1	this	this	DET
ejpam-3245	39	2	map	map	NOUN
ejpam-3245	39	3	satisfies	satisfy	VERB
ejpam-3245	39	4	the	the	DET
ejpam-3245	39	5	properties	property	NOUN
ejpam-3245	39	6	:	:	PUNCT
ejpam-3245	39	7	ord(x±	ord(x±	PROPN
ejpam-3245	39	8	y	y	PROPN
ejpam-3245	39	9	)	)	PUNCT
ejpam-3245	39	10	≥	≥	PROPN
ejpam-3245	39	11	min	min	NOUN
ejpam-3245	39	12	{	{	PUNCT
ejpam-3245	39	13	ord(x	ord(x	PROPN
ejpam-3245	39	14	)	)	PUNCT
ejpam-3245	39	15	,	,	PUNCT
ejpam-3245	39	16	ord(y	ord(y	PROPN
ejpam-3245	39	17	)	)	PUNCT
ejpam-3245	39	18	}	}	PUNCT
ejpam-3245	39	19	,	,	PUNCT
ejpam-3245	39	20	ord(xy±1	ord(xy±1	PROPN
ejpam-3245	39	21	)	)	PUNCT
ejpam-3245	39	22	=	=	PUNCT
ejpam-3245	40	1	ord(x)±	ord(x)±	PROPN
ejpam-3245	40	2	ord(y	ord(y	PROPN
ejpam-3245	40	3	)	)	PUNCT
ejpam-3245	40	4	,	,	PUNCT
ejpam-3245	40	5	if	if	SCONJ
ejpam-3245	40	6	ord(x	ord(x	PROPN
ejpam-3245	40	7	)	)	PUNCT
ejpam-3245	41	1	6=	6=	ADP
ejpam-3245	41	2	ord(y	ord(y	PROPN
ejpam-3245	41	3	)	)	PUNCT
ejpam-3245	41	4	,	,	PUNCT
ejpam-3245	41	5	then	then	ADV
ejpam-3245	41	6	ord(x±	ord(x±	PROPN
ejpam-3245	41	7	y	y	NOUN
ejpam-3245	41	8	)	)	PUNCT
ejpam-3245	41	9	=	=	SYM
ejpam-3245	41	10	min{ord(x	min{ord(x	PROPN
ejpam-3245	41	11	)	)	PUNCT
ejpam-3245	41	12	,	,	PUNCT
ejpam-3245	41	13	ord(y	ord(y	PROPN
ejpam-3245	41	14	)	)	PUNCT
ejpam-3245	41	15	}	}	PUNCT
ejpam-3245	41	16	.	.	PUNCT
ejpam-3245	42	1	the	the	DET
ejpam-3245	42	2	set	set	NOUN
ejpam-3245	42	3	o	o	NOUN
ejpam-3245	42	4	:	:	PUNCT
ejpam-3245	42	5	=	=	SYM
ejpam-3245	42	6	{	{	PUNCT
ejpam-3245	42	7	x	x	SYM
ejpam-3245	42	8	∈	∈	PROPN
ejpam-3245	42	9	cp	cp	INTJ
ejpam-3245	42	10	:	:	PUNCT
ejpam-3245	42	11	ord(x	ord(x	PROPN
ejpam-3245	42	12	)	)	PUNCT
ejpam-3245	42	13	≥	≥	NOUN
ejpam-3245	42	14	0	0	NUM
ejpam-3245	42	15	}	}	PUNCT
ejpam-3245	42	16	forms	form	VERB
ejpam-3245	42	17	a	a	DET
ejpam-3245	42	18	local	local	ADJ
ejpam-3245	42	19	ring	ring	NOUN
ejpam-3245	42	20	called	call	VERB
ejpam-3245	42	21	the	the	DET
ejpam-3245	42	22	ring	ring	NOUN
ejpam-3245	42	23	of	of	ADP
ejpam-3245	42	24	integers	integer	NOUN
ejpam-3245	42	25	in	in	ADP
ejpam-3245	42	26	cp	cp	PROPN
ejpam-3245	42	27	.	.	PUNCT
ejpam-3245	43	1	let	let	VERB
ejpam-3245	43	2	n	n	PRON
ejpam-3245	43	3	∈	∈	PROPN
ejpam-3245	43	4	n	n	X
ejpam-3245	43	5	with	with	ADP
ejpam-3245	43	6	n	n	PRON
ejpam-3245	43	7	≥	≥	NUM
ejpam-3245	43	8	1	1	NUM
ejpam-3245	43	9	.	.	PUNCT
ejpam-3245	44	1	it	it	PRON
ejpam-3245	44	2	is	be	AUX
ejpam-3245	44	3	well	well	ADV
ejpam-3245	44	4	known	know	VERB
ejpam-3245	44	5	that	that	SCONJ
ejpam-3245	44	6	ord(n	ord(n	NOUN
ejpam-3245	44	7	!	!	PUNCT
ejpam-3245	44	8	)	)	PUNCT
ejpam-3245	45	1	=	=	PUNCT
ejpam-3245	46	1	n−	n−	NOUN
ejpam-3245	46	2	sn	sn	NOUN
ejpam-3245	46	3	p−	p−	NOUN
ejpam-3245	46	4	1	1	NUM
ejpam-3245	46	5	,	,	PUNCT
ejpam-3245	46	6	where	where	SCONJ
ejpam-3245	46	7	sn	sn	PROPN
ejpam-3245	46	8	is	be	AUX
ejpam-3245	46	9	the	the	DET
ejpam-3245	46	10	sum	sum	NOUN
ejpam-3245	46	11	of	of	ADP
ejpam-3245	46	12	digits	digit	NOUN
ejpam-3245	46	13	of	of	ADP
ejpam-3245	46	14	n	n	PRON
ejpam-3245	46	15	when	when	SCONJ
ejpam-3245	46	16	it	it	PRON
ejpam-3245	46	17	is	be	AUX
ejpam-3245	46	18	written	write	VERB
ejpam-3245	46	19	in	in	ADP
ejpam-3245	46	20	the	the	DET
ejpam-3245	46	21	base	base	NOUN
ejpam-3245	46	22	p.	p.	NOUN
ejpam-3245	46	23	in	in	ADP
ejpam-3245	46	24	particular	particular	ADJ
ejpam-3245	46	25	,	,	PUNCT
ejpam-3245	46	26	if	if	SCONJ
ejpam-3245	46	27	n	n	NOUN
ejpam-3245	46	28	=	=	SYM
ejpam-3245	46	29	pm	pm	NOUN
ejpam-3245	46	30	,	,	PUNCT
ejpam-3245	46	31	m	m	VERB
ejpam-3245	46	32	≥	≥	NOUN
ejpam-3245	46	33	1	1	NUM
ejpam-3245	46	34	,	,	PUNCT
ejpam-3245	46	35	then	then	ADV
ejpam-3245	46	36	sn	sn	PROPN
ejpam-3245	46	37	=	=	VERB
ejpam-3245	47	1	1	1	X
ejpam-3245	47	2	.	.	PUNCT
ejpam-3245	48	1	it	it	PRON
ejpam-3245	48	2	is	be	AUX
ejpam-3245	48	3	clear	clear	ADJ
ejpam-3245	48	4	that	that	SCONJ
ejpam-3245	48	5	sn	sn	PROPN
ejpam-3245	48	6	≥	≥	NUM
ejpam-3245	48	7	1,∀n	1,∀n	NUM
ejpam-3245	48	8	≥	≥	NOUN
ejpam-3245	48	9	1	1	NUM
ejpam-3245	48	10	.	.	PUNCT
ejpam-3245	49	1	this	this	PRON
ejpam-3245	49	2	implies	imply	VERB
ejpam-3245	49	3	that	that	SCONJ
ejpam-3245	49	4	ord	ord	PROPN
ejpam-3245	49	5	(	(	PUNCT
ejpam-3245	49	6	1	1	NUM
ejpam-3245	49	7	n	n	NOUN
ejpam-3245	49	8	!	!	PUNCT
ejpam-3245	49	9	)	)	PUNCT
ejpam-3245	50	1	≥	≥	PROPN
ejpam-3245	50	2	−n−	−n−	NOUN
ejpam-3245	50	3	1	1	NUM
ejpam-3245	50	4	p−	p−	NOUN
ejpam-3245	50	5	1	1	NUM
ejpam-3245	50	6	.	.	PUNCT
ejpam-3245	51	1	we	we	PRON
ejpam-3245	51	2	also	also	ADV
ejpam-3245	51	3	recall	recall	VERB
ejpam-3245	51	4	some	some	DET
ejpam-3245	51	5	basic	basic	ADJ
ejpam-3245	51	6	concepts	concept	NOUN
ejpam-3245	51	7	and	and	CCONJ
ejpam-3245	51	8	results	result	NOUN
ejpam-3245	51	9	concerning	concern	VERB
ejpam-3245	51	10	the	the	DET
ejpam-3245	51	11	newton	newton	PROPN
ejpam-3245	51	12	polygon	polygon	PROPN
ejpam-3245	51	13	method	method	NOUN
ejpam-3245	51	14	.	.	PUNCT
ejpam-3245	52	1	for	for	ADP
ejpam-3245	52	2	more	more	ADJ
ejpam-3245	52	3	details	detail	NOUN
ejpam-3245	52	4	,	,	PUNCT
ejpam-3245	52	5	see	see	VERB
ejpam-3245	52	6	[	[	X
ejpam-3245	52	7	4	4	X
ejpam-3245	52	8	]	]	PUNCT
ejpam-3245	52	9	and	and	CCONJ
ejpam-3245	53	1	[	[	X
ejpam-3245	53	2	3	3	NUM
ejpam-3245	53	3	]	]	PUNCT
ejpam-3245	53	4	.	.	PUNCT
ejpam-3245	53	5	a.	a.	PROPN
ejpam-3245	53	6	dalloul	dalloul	PROPN
ejpam-3245	53	7	/	/	SYM
ejpam-3245	53	8	eur	eur	PROPN
ejpam-3245	53	9	.	.	PUNCT
ejpam-3245	54	1	j.	j.	PROPN
ejpam-3245	54	2	pure	pure	PROPN
ejpam-3245	54	3	appl	appl	PROPN
ejpam-3245	54	4	.	.	PROPN
ejpam-3245	54	5	math	math	PROPN
ejpam-3245	54	6	,	,	PUNCT
ejpam-3245	54	7	11	11	NUM
ejpam-3245	54	8	(	(	PUNCT
ejpam-3245	54	9	3	3	NUM
ejpam-3245	54	10	)	)	PUNCT
ejpam-3245	54	11	(	(	PUNCT
ejpam-3245	54	12	2018	2018	NUM
ejpam-3245	54	13	)	)	PUNCT
ejpam-3245	54	14	,	,	PUNCT
ejpam-3245	54	15	803	803	NUM
ejpam-3245	54	16	-	-	SYM
ejpam-3245	54	17	814	814	NUM
ejpam-3245	54	18	805	805	NUM
ejpam-3245	54	19	2.1	2.1	NUM
ejpam-3245	54	20	.	.	PUNCT
ejpam-3245	55	1	the	the	DET
ejpam-3245	55	2	newton	newton	PROPN
ejpam-3245	55	3	polygon	polygon	PROPN
ejpam-3245	55	4	for	for	ADP
ejpam-3245	55	5	polynomials	polynomial	NOUN
ejpam-3245	55	6	let	let	VERB
ejpam-3245	55	7	f(x	f(x	PROPN
ejpam-3245	55	8	)	)	PUNCT
ejpam-3245	55	9	=	=	PUNCT
ejpam-3245	56	1	1	1	NUM
ejpam-3245	56	2	+	+	NUM
ejpam-3245	56	3	a1x	a1x	NOUN
ejpam-3245	56	4	+	+	CCONJ
ejpam-3245	56	5	·	·	PUNCT
ejpam-3245	56	6	·	·	PUNCT
ejpam-3245	56	7	·	·	PUNCT
ejpam-3245	57	1	+	+	NUM
ejpam-3245	57	2	anx	anx	ADJ
ejpam-3245	57	3	n	n	CCONJ
ejpam-3245	57	4	∈	∈	PROPN
ejpam-3245	57	5	1	1	NUM
ejpam-3245	57	6	+	+	NOUN
ejpam-3245	57	7	xcp[x	xcp[x	VERB
ejpam-3245	57	8	]	]	X
ejpam-3245	57	9	be	be	VERB
ejpam-3245	57	10	a	a	DET
ejpam-3245	57	11	polynomial	polynomial	ADJ
ejpam-3245	57	12	with	with	ADP
ejpam-3245	57	13	degree	degree	NOUN
ejpam-3245	57	14	n	n	NOUN
ejpam-3245	57	15	and	and	CCONJ
ejpam-3245	57	16	the	the	DET
ejpam-3245	57	17	constant	constant	ADJ
ejpam-3245	57	18	term	term	NOUN
ejpam-3245	57	19	is	be	AUX
ejpam-3245	57	20	1	1	NUM
ejpam-3245	57	21	.	.	PUNCT
ejpam-3245	58	1	we	we	PRON
ejpam-3245	58	2	plot	plot	VERB
ejpam-3245	58	3	the	the	DET
ejpam-3245	58	4	following	follow	VERB
ejpam-3245	58	5	points	point	NOUN
ejpam-3245	58	6	in	in	ADP
ejpam-3245	58	7	the	the	DET
ejpam-3245	58	8	euclidean	euclidean	ADJ
ejpam-3245	58	9	space	space	NOUN
ejpam-3245	58	10	r2	r2	NOUN
ejpam-3245	58	11	:	:	PUNCT
ejpam-3245	58	12	(	(	PUNCT
ejpam-3245	58	13	0	0	NUM
ejpam-3245	58	14	,	,	PUNCT
ejpam-3245	58	15	0	0	NUM
ejpam-3245	58	16	)	)	PUNCT
ejpam-3245	58	17	,	,	PUNCT
ejpam-3245	58	18	(	(	PUNCT
ejpam-3245	58	19	1	1	NUM
ejpam-3245	58	20	,	,	PUNCT
ejpam-3245	58	21	ord(a1	ord(a1	NOUN
ejpam-3245	58	22	)	)	PUNCT
ejpam-3245	58	23	)	)	PUNCT
ejpam-3245	58	24	,	,	PUNCT
ejpam-3245	58	25	(	(	PUNCT
ejpam-3245	58	26	2	2	NUM
ejpam-3245	58	27	,	,	PUNCT
ejpam-3245	58	28	ord(a2	ord(a2	PROPN
ejpam-3245	58	29	)	)	PUNCT
ejpam-3245	58	30	)	)	PUNCT
ejpam-3245	58	31	,	,	PUNCT
ejpam-3245	58	32	.	.	PUNCT
ejpam-3245	58	33	.	.	PUNCT
ejpam-3245	58	34	.	.	PUNCT
ejpam-3245	59	1	,	,	PUNCT
ejpam-3245	59	2	(	(	PUNCT
ejpam-3245	59	3	n	n	CCONJ
ejpam-3245	59	4	,	,	PUNCT
ejpam-3245	59	5	ord(an	ord(an	NOUN
ejpam-3245	59	6	)	)	PUNCT
ejpam-3245	59	7	)	)	PUNCT
ejpam-3245	59	8	.	.	PUNCT
ejpam-3245	60	1	if	if	SCONJ
ejpam-3245	60	2	ai	ai	VERB
ejpam-3245	60	3	=	=	NOUN
ejpam-3245	60	4	0	0	NUM
ejpam-3245	60	5	for	for	ADP
ejpam-3245	60	6	some	some	DET
ejpam-3245	60	7	i	i	PRON
ejpam-3245	60	8	,	,	PUNCT
ejpam-3245	60	9	we	we	PRON
ejpam-3245	60	10	omit	omit	VERB
ejpam-3245	60	11	this	this	DET
ejpam-3245	60	12	point	point	NOUN
ejpam-3245	60	13	(	(	PUNCT
ejpam-3245	60	14	considering	consider	VERB
ejpam-3245	60	15	it	it	PRON
ejpam-3245	60	16	as	as	ADP
ejpam-3245	60	17	a	a	DET
ejpam-3245	60	18	point	point	NOUN
ejpam-3245	60	19	at	at	ADP
ejpam-3245	60	20	infinity	infinity	NOUN
ejpam-3245	60	21	)	)	PUNCT
ejpam-3245	60	22	.	.	PUNCT
ejpam-3245	61	1	the	the	DET
ejpam-3245	61	2	newton	newton	PROPN
ejpam-3245	61	3	polygon	polygon	PROPN
ejpam-3245	61	4	of	of	ADP
ejpam-3245	61	5	the	the	DET
ejpam-3245	61	6	polynomial	polynomial	ADJ
ejpam-3245	61	7	f	f	PROPN
ejpam-3245	61	8	is	be	AUX
ejpam-3245	61	9	defined	define	VERB
ejpam-3245	61	10	as	as	ADP
ejpam-3245	61	11	the	the	DET
ejpam-3245	61	12	convex	convex	PROPN
ejpam-3245	61	13	hull	hull	NOUN
ejpam-3245	61	14	of	of	ADP
ejpam-3245	61	15	the	the	DET
ejpam-3245	61	16	points	point	NOUN
ejpam-3245	61	17	(	(	PUNCT
ejpam-3245	61	18	0	0	NUM
ejpam-3245	61	19	,	,	PUNCT
ejpam-3245	61	20	0	0	NUM
ejpam-3245	61	21	)	)	PUNCT
ejpam-3245	61	22	,	,	PUNCT
ejpam-3245	61	23	(	(	PUNCT
ejpam-3245	61	24	1	1	NUM
ejpam-3245	61	25	,	,	PUNCT
ejpam-3245	61	26	ord(a1	ord(a1	NOUN
ejpam-3245	61	27	)	)	PUNCT
ejpam-3245	61	28	)	)	PUNCT
ejpam-3245	61	29	,	,	PUNCT
ejpam-3245	61	30	(	(	PUNCT
ejpam-3245	61	31	2	2	NUM
ejpam-3245	61	32	,	,	PUNCT
ejpam-3245	61	33	ord(a2	ord(a2	PROPN
ejpam-3245	61	34	)	)	PUNCT
ejpam-3245	61	35	)	)	PUNCT
ejpam-3245	61	36	,	,	PUNCT
ejpam-3245	61	37	.	.	PUNCT
ejpam-3245	61	38	.	.	PUNCT
ejpam-3245	62	1	.	.	PUNCT
ejpam-3245	63	1	,	,	PUNCT
ejpam-3245	63	2	(	(	PUNCT
ejpam-3245	63	3	n	n	CCONJ
ejpam-3245	63	4	,	,	PUNCT
ejpam-3245	63	5	ord(an	ord(an	NOUN
ejpam-3245	63	6	)	)	PUNCT
ejpam-3245	63	7	)	)	PUNCT
ejpam-3245	63	8	.	.	PUNCT
ejpam-3245	64	1	that	that	PRON
ejpam-3245	64	2	is	be	AUX
ejpam-3245	64	3	the	the	DET
ejpam-3245	64	4	highest	high	ADJ
ejpam-3245	64	5	convex	convex	ADJ
ejpam-3245	64	6	polygonal	polygonal	ADJ
ejpam-3245	64	7	line	line	NOUN
ejpam-3245	64	8	joining	join	VERB
ejpam-3245	64	9	(	(	PUNCT
ejpam-3245	64	10	0	0	NUM
ejpam-3245	64	11	,	,	PUNCT
ejpam-3245	64	12	0	0	NUM
ejpam-3245	64	13	)	)	PUNCT
ejpam-3245	64	14	with	with	ADP
ejpam-3245	64	15	(	(	PUNCT
ejpam-3245	64	16	n	n	CCONJ
ejpam-3245	64	17	,	,	PUNCT
ejpam-3245	64	18	ord(an	ord(an	NOUN
ejpam-3245	64	19	)	)	PUNCT
ejpam-3245	64	20	)	)	PUNCT
ejpam-3245	64	21	and	and	CCONJ
ejpam-3245	64	22	passing	pass	VERB
ejpam-3245	64	23	through	through	ADP
ejpam-3245	64	24	or	or	CCONJ
ejpam-3245	64	25	below	below	ADP
ejpam-3245	64	26	all	all	DET
ejpam-3245	64	27	the	the	DET
ejpam-3245	64	28	points	point	NOUN
ejpam-3245	64	29	(	(	PUNCT
ejpam-3245	64	30	i	i	NOUN
ejpam-3245	64	31	,	,	PUNCT
ejpam-3245	64	32	ord(ai	ord(ai	NOUN
ejpam-3245	64	33	)	)	PUNCT
ejpam-3245	64	34	)	)	PUNCT
ejpam-3245	64	35	,	,	PUNCT
ejpam-3245	65	1	i	i	PRON
ejpam-3245	65	2	=	=	NOUN
ejpam-3245	65	3	1	1	NUM
ejpam-3245	65	4	,	,	PUNCT
ejpam-3245	65	5	2	2	NUM
ejpam-3245	65	6	,	,	PUNCT
ejpam-3245	65	7	..	..	PUNCT
ejpam-3245	65	8	,	,	PUNCT
ejpam-3245	65	9	n−	n−	NOUN
ejpam-3245	65	10	1	1	NUM
ejpam-3245	65	11	.	.	PUNCT
ejpam-3245	66	1	practically	practically	ADV
ejpam-3245	66	2	,	,	PUNCT
ejpam-3245	66	3	the	the	DET
ejpam-3245	66	4	newton	newton	PROPN
ejpam-3245	66	5	polygon	polygon	PROPN
ejpam-3245	66	6	of	of	ADP
ejpam-3245	66	7	polynomials	polynomial	NOUN
ejpam-3245	66	8	is	be	AUX
ejpam-3245	66	9	obtained	obtain	VERB
ejpam-3245	66	10	by	by	ADP
ejpam-3245	66	11	the	the	DET
ejpam-3245	66	12	following	follow	VERB
ejpam-3245	66	13	steps	step	NOUN
ejpam-3245	66	14	:	:	PUNCT
ejpam-3245	66	15	1	1	X
ejpam-3245	66	16	)	)	PUNCT
ejpam-3245	66	17	start	start	VERB
ejpam-3245	66	18	with	with	ADP
ejpam-3245	66	19	the	the	DET
ejpam-3245	66	20	vertical	vertical	ADJ
ejpam-3245	66	21	half	half	ADJ
ejpam-3245	66	22	-	-	PUNCT
ejpam-3245	66	23	line	line	NOUN
ejpam-3245	66	24	which	which	PRON
ejpam-3245	66	25	is	be	AUX
ejpam-3245	66	26	the	the	DET
ejpam-3245	66	27	negative	negative	ADJ
ejpam-3245	66	28	part	part	NOUN
ejpam-3245	66	29	of	of	ADP
ejpam-3245	66	30	the	the	DET
ejpam-3245	66	31	y	y	NOUN
ejpam-3245	66	32	-	-	PUNCT
ejpam-3245	66	33	axis	axis	NOUN
ejpam-3245	66	34	.	.	PUNCT
ejpam-3245	67	1	2	2	X
ejpam-3245	67	2	)	)	PUNCT
ejpam-3245	67	3	rotate	rotate	VERB
ejpam-3245	67	4	the	the	DET
ejpam-3245	67	5	line	line	NOUN
ejpam-3245	67	6	counter	counter	NOUN
ejpam-3245	67	7	-	-	NOUN
ejpam-3245	67	8	clockwise	clockwise	NOUN
ejpam-3245	67	9	until	until	SCONJ
ejpam-3245	67	10	it	it	PRON
ejpam-3245	67	11	hits	hit	VERB
ejpam-3245	67	12	one	one	NUM
ejpam-3245	67	13	of	of	ADP
ejpam-3245	67	14	the	the	DET
ejpam-3245	67	15	points	point	NOUN
ejpam-3245	67	16	we	we	PRON
ejpam-3245	67	17	have	have	AUX
ejpam-3245	67	18	plotted	plot	VERB
ejpam-3245	67	19	.	.	PUNCT
ejpam-3245	68	1	3	3	X
ejpam-3245	68	2	)	)	PUNCT
ejpam-3245	68	3	break	break	VERB
ejpam-3245	68	4	the	the	DET
ejpam-3245	68	5	line	line	NOUN
ejpam-3245	68	6	at	at	ADP
ejpam-3245	68	7	that	that	DET
ejpam-3245	68	8	point	point	NOUN
ejpam-3245	68	9	,	,	PUNCT
ejpam-3245	68	10	and	and	CCONJ
ejpam-3245	68	11	continue	continue	VERB
ejpam-3245	68	12	rotating	rotate	VERB
ejpam-3245	68	13	the	the	DET
ejpam-3245	68	14	remaining	remain	VERB
ejpam-3245	68	15	part	part	NOUN
ejpam-3245	68	16	until	until	SCONJ
ejpam-3245	68	17	another	another	DET
ejpam-3245	68	18	point	point	NOUN
ejpam-3245	68	19	is	be	AUX
ejpam-3245	68	20	hit	hit	VERB
ejpam-3245	68	21	.	.	PUNCT
ejpam-3245	69	1	4	4	X
ejpam-3245	69	2	)	)	PUNCT
ejpam-3245	69	3	continue	continue	VERB
ejpam-3245	69	4	until	until	SCONJ
ejpam-3245	69	5	all	all	DET
ejpam-3245	69	6	the	the	DET
ejpam-3245	69	7	points	point	NOUN
ejpam-3245	69	8	have	have	AUX
ejpam-3245	69	9	either	either	ADV
ejpam-3245	69	10	been	be	AUX
ejpam-3245	69	11	hit	hit	VERB
ejpam-3245	69	12	or	or	CCONJ
ejpam-3245	69	13	lie	lie	VERB
ejpam-3245	69	14	strictly	strictly	ADV
ejpam-3245	69	15	above	above	ADP
ejpam-3245	69	16	a	a	DET
ejpam-3245	69	17	portion	portion	NOUN
ejpam-3245	69	18	of	of	ADP
ejpam-3245	69	19	the	the	DET
ejpam-3245	69	20	polygon	polygon	NOUN
ejpam-3245	69	21	.	.	PUNCT
ejpam-3245	70	1	a	a	DET
ejpam-3245	70	2	vertex	vertex	NOUN
ejpam-3245	70	3	of	of	ADP
ejpam-3245	70	4	the	the	DET
ejpam-3245	70	5	newton	newton	PROPN
ejpam-3245	70	6	polygon	polygon	PROPN
ejpam-3245	70	7	is	be	AUX
ejpam-3245	70	8	a	a	DET
ejpam-3245	70	9	point	point	NOUN
ejpam-3245	70	10	(	(	PUNCT
ejpam-3245	70	11	i	i	NOUN
ejpam-3245	70	12	,	,	PUNCT
ejpam-3245	70	13	ord(ai	ord(ai	NOUN
ejpam-3245	70	14	)	)	PUNCT
ejpam-3245	70	15	)	)	PUNCT
ejpam-3245	70	16	where	where	SCONJ
ejpam-3245	70	17	the	the	DET
ejpam-3245	70	18	slopes	slope	NOUN
ejpam-3245	70	19	change	change	VERB
ejpam-3245	70	20	.	.	PUNCT
ejpam-3245	71	1	if	if	SCONJ
ejpam-3245	71	2	a	a	DET
ejpam-3245	71	3	segment	segment	NOUN
ejpam-3245	71	4	joins	join	VERB
ejpam-3245	71	5	the	the	DET
ejpam-3245	71	6	point	point	NOUN
ejpam-3245	71	7	(	(	PUNCT
ejpam-3245	71	8	i	i	PROPN
ejpam-3245	71	9	,	,	PUNCT
ejpam-3245	71	10	m	m	PROPN
ejpam-3245	71	11	)	)	PUNCT
ejpam-3245	71	12	to	to	ADP
ejpam-3245	71	13	the	the	DET
ejpam-3245	71	14	point	point	NOUN
ejpam-3245	71	15	(	(	PUNCT
ejpam-3245	71	16	i′,m′	i′,m′	PROPN
ejpam-3245	71	17	)	)	PUNCT
ejpam-3245	71	18	,	,	PUNCT
ejpam-3245	71	19	then	then	ADV
ejpam-3245	71	20	the	the	DET
ejpam-3245	71	21	slope	slope	NOUN
ejpam-3245	71	22	is	be	AUX
ejpam-3245	71	23	the	the	DET
ejpam-3245	71	24	quantity	quantity	NOUN
ejpam-3245	71	25	m−m′	m−m′	ADV
ejpam-3245	71	26	i−i′	i−i′	X
ejpam-3245	71	27	.	.	PUNCT
ejpam-3245	72	1	by	by	ADP
ejpam-3245	72	2	the	the	DET
ejpam-3245	72	3	length	length	NOUN
ejpam-3245	72	4	of	of	ADP
ejpam-3245	72	5	the	the	DET
ejpam-3245	72	6	slope	slope	NOUN
ejpam-3245	72	7	we	we	PRON
ejpam-3245	72	8	mean	mean	VERB
ejpam-3245	72	9	the	the	DET
ejpam-3245	72	10	quantity	quantity	NOUN
ejpam-3245	72	11	i−	i−	ADP
ejpam-3245	72	12	i′.	i′.	NOUN
ejpam-3245	72	13	if	if	SCONJ
ejpam-3245	72	14	the	the	DET
ejpam-3245	72	15	polygon	polygon	NOUN
ejpam-3245	72	16	has	have	VERB
ejpam-3245	72	17	a	a	DET
ejpam-3245	72	18	segment	segment	NOUN
ejpam-3245	72	19	ends	end	VERB
ejpam-3245	72	20	by	by	ADP
ejpam-3245	72	21	a	a	DET
ejpam-3245	72	22	point	point	NOUN
ejpam-3245	72	23	(	(	PUNCT
ejpam-3245	72	24	i	i	NOUN
ejpam-3245	72	25	,	,	PUNCT
ejpam-3245	72	26	ord(ai	ord(ai	NOUN
ejpam-3245	72	27	)	)	PUNCT
ejpam-3245	72	28	)	)	PUNCT
ejpam-3245	72	29	and	and	CCONJ
ejpam-3245	72	30	continues	continue	VERB
ejpam-3245	72	31	by	by	ADP
ejpam-3245	72	32	another	another	DET
ejpam-3245	72	33	segment	segment	NOUN
ejpam-3245	72	34	of	of	ADP
ejpam-3245	72	35	different	different	ADJ
ejpam-3245	72	36	slope	slope	NOUN
ejpam-3245	72	37	,	,	PUNCT
ejpam-3245	72	38	we	we	PRON
ejpam-3245	72	39	say	say	VERB
ejpam-3245	72	40	that	that	SCONJ
ejpam-3245	72	41	the	the	DET
ejpam-3245	72	42	newton	newton	PROPN
ejpam-3245	72	43	polygon	polygon	PROPN
ejpam-3245	72	44	has	have	VERB
ejpam-3245	72	45	a	a	DET
ejpam-3245	72	46	”	"	PUNCT
ejpam-3245	72	47	break	break	NOUN
ejpam-3245	72	48	”	"	PUNCT
ejpam-3245	72	49	at	at	ADP
ejpam-3245	72	50	the	the	DET
ejpam-3245	72	51	point	point	NOUN
ejpam-3245	72	52	(	(	PUNCT
ejpam-3245	72	53	i	i	NOUN
ejpam-3245	72	54	,	,	PUNCT
ejpam-3245	72	55	ord(ai	ord(ai	ADJ
ejpam-3245	72	56	)	)	PUNCT
ejpam-3245	72	57	)	)	PUNCT
ejpam-3245	72	58	.	.	PUNCT
ejpam-3245	73	1	theorem	theorem	NOUN
ejpam-3245	73	2	1	1	NUM
ejpam-3245	73	3	.	.	PUNCT
ejpam-3245	74	1	let	let	VERB
ejpam-3245	74	2	f(x	f(x	PROPN
ejpam-3245	74	3	)	)	PUNCT
ejpam-3245	74	4	=	=	PUNCT
ejpam-3245	75	1	1	1	NUM
ejpam-3245	75	2	+	+	NUM
ejpam-3245	75	3	a1x	a1x	NOUN
ejpam-3245	75	4	+	+	X
ejpam-3245	75	5	·	·	PUNCT
ejpam-3245	75	6	·	·	PUNCT
ejpam-3245	75	7	·	·	PUNCT
ejpam-3245	76	1	+	+	CCONJ
ejpam-3245	76	2	anx	anx	ADJ
ejpam-3245	76	3	n	n	CCONJ
ejpam-3245	76	4	∈	∈	PROPN
ejpam-3245	76	5	1	1	NUM
ejpam-3245	76	6	+	+	NUM
ejpam-3245	76	7	xcp[x	xcp[x	NUM
ejpam-3245	76	8	]	]	PUNCT
ejpam-3245	76	9	.	.	PUNCT
ejpam-3245	77	1	if	if	SCONJ
ejpam-3245	77	2	λ	λ	PROPN
ejpam-3245	77	3	is	be	AUX
ejpam-3245	77	4	a	a	DET
ejpam-3245	77	5	slope	slope	NOUN
ejpam-3245	77	6	of	of	ADP
ejpam-3245	77	7	the	the	DET
ejpam-3245	77	8	newton	newton	PROPN
ejpam-3245	77	9	polygon	polygon	PROPN
ejpam-3245	77	10	associated	associate	VERB
ejpam-3245	77	11	to	to	ADP
ejpam-3245	77	12	the	the	DET
ejpam-3245	77	13	polynomial	polynomial	ADJ
ejpam-3245	77	14	f	f	PROPN
ejpam-3245	77	15	with	with	ADP
ejpam-3245	77	16	the	the	DET
ejpam-3245	77	17	length	length	NOUN
ejpam-3245	77	18	m	m	PROPN
ejpam-3245	77	19	,	,	PUNCT
ejpam-3245	77	20	then	then	ADV
ejpam-3245	77	21	there	there	PRON
ejpam-3245	77	22	exist	exist	VERB
ejpam-3245	77	23	the	the	DET
ejpam-3245	77	24	numbers	number	NOUN
ejpam-3245	77	25	α1	α1	PROPN
ejpam-3245	77	26	,	,	PUNCT
ejpam-3245	77	27	α2	α2	ADJ
ejpam-3245	77	28	,	,	PUNCT
ejpam-3245	77	29	..	..	PUNCT
ejpam-3245	77	30	,	,	PUNCT
ejpam-3245	77	31	αm	αm	PROPN
ejpam-3245	77	32	∈	∈	PROPN
ejpam-3245	77	33	cp	cp	INTJ
ejpam-3245	77	34	(	(	PUNCT
ejpam-3245	77	35	counting	count	VERB
ejpam-3245	77	36	multiplicity	multiplicity	NOUN
ejpam-3245	77	37	)	)	PUNCT
ejpam-3245	77	38	such	such	ADJ
ejpam-3245	77	39	that	that	DET
ejpam-3245	77	40	f(αi	f(αi	NOUN
ejpam-3245	77	41	)	)	PUNCT
ejpam-3245	77	42	=	=	SYM
ejpam-3245	77	43	0	0	NUM
ejpam-3245	77	44	and	and	CCONJ
ejpam-3245	77	45	ord(αi	ord(αi	ADJ
ejpam-3245	77	46	)	)	PUNCT
ejpam-3245	77	47	=	=	SYM
ejpam-3245	77	48	−λ	−λ	VERB
ejpam-3245	77	49	,	,	PUNCT
ejpam-3245	77	50	∀i	∀i	NOUN
ejpam-3245	77	51	=	=	SYM
ejpam-3245	77	52	1	1	NUM
ejpam-3245	77	53	,	,	PUNCT
ejpam-3245	77	54	2	2	NUM
ejpam-3245	77	55	,	,	PUNCT
ejpam-3245	77	56	..	..	PUNCT
ejpam-3245	77	57	,	,	PUNCT
ejpam-3245	77	58	m.	m.	NOUN
ejpam-3245	77	59	2.2	2.2	NUM
ejpam-3245	77	60	.	.	PUNCT
ejpam-3245	78	1	the	the	DET
ejpam-3245	78	2	newton	newton	PROPN
ejpam-3245	78	3	polygon	polygon	PROPN
ejpam-3245	78	4	for	for	ADP
ejpam-3245	78	5	power	power	NOUN
ejpam-3245	78	6	series	series	NOUN
ejpam-3245	78	7	the	the	DET
ejpam-3245	78	8	definition	definition	NOUN
ejpam-3245	78	9	is	be	AUX
ejpam-3245	78	10	formally	formally	ADV
ejpam-3245	78	11	identical	identical	ADJ
ejpam-3245	78	12	to	to	ADP
ejpam-3245	78	13	that	that	PRON
ejpam-3245	78	14	given	give	VERB
ejpam-3245	78	15	for	for	ADP
ejpam-3245	78	16	polynomials	polynomial	NOUN
ejpam-3245	78	17	:	:	PUNCT
ejpam-3245	78	18	consider	consider	VERB
ejpam-3245	78	19	the	the	DET
ejpam-3245	78	20	power	power	NOUN
ejpam-3245	78	21	series	series	PROPN
ejpam-3245	78	22	f(x	f(x	PROPN
ejpam-3245	78	23	)	)	PUNCT
ejpam-3245	78	24	=	=	SYM
ejpam-3245	79	1	1	1	NUM
ejpam-3245	79	2	+	+	NUM
ejpam-3245	79	3	a1x	a1x	X
ejpam-3245	79	4	+	+	CCONJ
ejpam-3245	79	5	a2x	a2x	ADP
ejpam-3245	79	6	2	2	NUM
ejpam-3245	79	7	+	+	NOUN
ejpam-3245	79	8	·	·	PUNCT
ejpam-3245	79	9	·	·	PUNCT
ejpam-3245	79	10	·	·	PUNCT
ejpam-3245	80	1	+	+	NUM
ejpam-3245	80	2	anx	anx	ADJ
ejpam-3245	80	3	n	n	NOUN
ejpam-3245	80	4	+	+	X
ejpam-3245	80	5	.	.	PUNCT
ejpam-3245	80	6	.	.	PUNCT
ejpam-3245	81	1	.	.	PUNCT
ejpam-3245	82	1	we	we	PRON
ejpam-3245	82	2	plot	plot	VERB
ejpam-3245	82	3	the	the	DET
ejpam-3245	82	4	points	point	NOUN
ejpam-3245	82	5	(	(	PUNCT
ejpam-3245	82	6	i	i	NOUN
ejpam-3245	82	7	,	,	PUNCT
ejpam-3245	82	8	ord(ai	ord(ai	NOUN
ejpam-3245	82	9	)	)	PUNCT
ejpam-3245	82	10	)	)	PUNCT
ejpam-3245	82	11	,	,	PUNCT
ejpam-3245	82	12	i	i	PRON
ejpam-3245	82	13	=	=	NOUN
ejpam-3245	82	14	1	1	NUM
ejpam-3245	82	15	,	,	PUNCT
ejpam-3245	82	16	2	2	NUM
ejpam-3245	82	17	,	,	PUNCT
ejpam-3245	82	18	...	...	PUNCT
ejpam-3245	82	19	,	,	PUNCT
ejpam-3245	82	20	ignoring	ignore	VERB
ejpam-3245	82	21	as	as	ADP
ejpam-3245	82	22	before	before	ADP
ejpam-3245	82	23	any	any	DET
ejpam-3245	82	24	points	point	NOUN
ejpam-3245	82	25	where	where	SCONJ
ejpam-3245	82	26	ai	ai	VERB
ejpam-3245	82	27	=	=	NOUN
ejpam-3245	82	28	0	0	PROPN
ejpam-3245	82	29	.	.	PUNCT
ejpam-3245	83	1	the	the	DET
ejpam-3245	83	2	newton	newton	PROPN
ejpam-3245	83	3	polygon	polygon	PROPN
ejpam-3245	83	4	of	of	ADP
ejpam-3245	83	5	f(x	f(x	PROPN
ejpam-3245	83	6	)	)	PUNCT
ejpam-3245	83	7	is	be	AUX
ejpam-3245	83	8	again	again	ADV
ejpam-3245	83	9	obtained	obtain	VERB
ejpam-3245	83	10	by	by	ADP
ejpam-3245	83	11	the	the	DET
ejpam-3245	83	12	rotating	rotate	VERB
ejpam-3245	83	13	line	line	NOUN
ejpam-3245	83	14	procedure	procedure	NOUN
ejpam-3245	83	15	.	.	PUNCT
ejpam-3245	84	1	in	in	ADP
ejpam-3245	84	2	this	this	DET
ejpam-3245	84	3	case	case	NOUN
ejpam-3245	84	4	,	,	PUNCT
ejpam-3245	84	5	the	the	DET
ejpam-3245	84	6	things	thing	NOUN
ejpam-3245	84	7	become	become	VERB
ejpam-3245	84	8	more	more	ADV
ejpam-3245	84	9	complicated	complicated	ADJ
ejpam-3245	84	10	than	than	ADP
ejpam-3245	84	11	the	the	DET
ejpam-3245	84	12	case	case	NOUN
ejpam-3245	84	13	of	of	ADP
ejpam-3245	84	14	polynomials	polynomial	NOUN
ejpam-3245	84	15	.	.	PUNCT
ejpam-3245	85	1	for	for	ADP
ejpam-3245	85	2	example	example	NOUN
ejpam-3245	85	3	,	,	PUNCT
ejpam-3245	85	4	the	the	DET
ejpam-3245	85	5	newton	newton	PROPN
ejpam-3245	85	6	polygon	polygon	PROPN
ejpam-3245	85	7	of	of	ADP
ejpam-3245	85	8	the	the	DET
ejpam-3245	85	9	power	power	NOUN
ejpam-3245	85	10	series	series	PROPN
ejpam-3245	85	11	f(x	f(x	PROPN
ejpam-3245	85	12	)	)	PUNCT
ejpam-3245	85	13	=	=	SYM
ejpam-3245	86	1	1	1	NUM
ejpam-3245	86	2	+	+	NUM
ejpam-3245	86	3	px	px	X
ejpam-3245	86	4	+	+	CCONJ
ejpam-3245	86	5	px2	px2	PROPN
ejpam-3245	86	6	+	+	X
ejpam-3245	86	7	..	..	PUNCT
ejpam-3245	87	1	+	+	CCONJ
ejpam-3245	87	2	pxn	pxn	VERB
ejpam-3245	87	3	+	+	CCONJ
ejpam-3245	87	4	...	...	PUNCT
ejpam-3245	87	5	is	be	AUX
ejpam-3245	87	6	just	just	ADV
ejpam-3245	87	7	the	the	DET
ejpam-3245	87	8	horizontal	horizontal	ADJ
ejpam-3245	87	9	line	line	NOUN
ejpam-3245	87	10	ox	ox	NOUN
ejpam-3245	87	11	which	which	PRON
ejpam-3245	87	12	does	do	AUX
ejpam-3245	87	13	not	not	PART
ejpam-3245	87	14	hit	hit	VERB
ejpam-3245	87	15	any	any	PRON
ejpam-3245	87	16	of	of	ADP
ejpam-3245	87	17	the	the	DET
ejpam-3245	87	18	points	point	NOUN
ejpam-3245	87	19	(	(	PUNCT
ejpam-3245	87	20	i	i	NOUN
ejpam-3245	87	21	,	,	PUNCT
ejpam-3245	87	22	ord(ai	ord(ai	NOUN
ejpam-3245	87	23	)	)	PUNCT
ejpam-3245	87	24	)	)	PUNCT
ejpam-3245	87	25	,	,	PUNCT
ejpam-3245	87	26	i	i	PRON
ejpam-3245	87	27	=	=	NOUN
ejpam-3245	87	28	1	1	NUM
ejpam-3245	87	29	,	,	PUNCT
ejpam-3245	87	30	2	2	NUM
ejpam-3245	87	31	,	,	PUNCT
ejpam-3245	87	32	....	....	PUNCT
ejpam-3245	88	1	for	for	ADP
ejpam-3245	88	2	this	this	DET
ejpam-3245	88	3	case	case	NOUN
ejpam-3245	88	4	and	and	CCONJ
ejpam-3245	88	5	other	other	ADJ
ejpam-3245	88	6	cases	case	NOUN
ejpam-3245	88	7	,	,	PUNCT
ejpam-3245	88	8	we	we	PRON
ejpam-3245	88	9	must	must	AUX
ejpam-3245	88	10	modify	modify	VERB
ejpam-3245	88	11	the	the	DET
ejpam-3245	88	12	rules	rule	NOUN
ejpam-3245	88	13	to	to	PART
ejpam-3245	88	14	obtain	obtain	VERB
ejpam-3245	88	15	the	the	DET
ejpam-3245	88	16	newton	newton	PROPN
ejpam-3245	88	17	polygon	polygon	PROPN
ejpam-3245	88	18	of	of	ADP
ejpam-3245	88	19	power	power	NOUN
ejpam-3245	88	20	series	series	NOUN
ejpam-3245	88	21	as	as	ADP
ejpam-3245	88	22	the	the	DET
ejpam-3245	88	23	following	follow	VERB
ejpam-3245	88	24	steps	step	NOUN
ejpam-3245	88	25	:	:	PUNCT
ejpam-3245	88	26	start	start	VERB
ejpam-3245	88	27	with	with	ADP
ejpam-3245	88	28	the	the	DET
ejpam-3245	88	29	half	half	ADJ
ejpam-3245	88	30	-	-	PUNCT
ejpam-3245	88	31	line	line	NOUN
ejpam-3245	88	32	which	which	PRON
ejpam-3245	88	33	is	be	AUX
ejpam-3245	88	34	the	the	DET
ejpam-3245	88	35	negative	negative	ADJ
ejpam-3245	88	36	part	part	NOUN
ejpam-3245	88	37	of	of	ADP
ejpam-3245	88	38	the	the	DET
ejpam-3245	88	39	y	y	NOUN
ejpam-3245	88	40	-	-	PUNCT
ejpam-3245	88	41	axis	axis	NOUN
ejpam-3245	88	42	.	.	PUNCT
ejpam-3245	89	1	rotate	rotate	VERB
ejpam-3245	89	2	that	that	DET
ejpam-3245	89	3	line	line	NOUN
ejpam-3245	89	4	counterclockwise	counterclockwise	NOUN
ejpam-3245	89	5	until	until	SCONJ
ejpam-3245	89	6	one	one	NUM
ejpam-3245	89	7	of	of	ADP
ejpam-3245	89	8	the	the	DET
ejpam-3245	89	9	following	following	NOUN
ejpam-3245	89	10	happens	happen	VERB
ejpam-3245	89	11	:	:	PUNCT
ejpam-3245	89	12	a.	a.	NOUN
ejpam-3245	89	13	dalloul	dalloul	PROPN
ejpam-3245	89	14	/	/	SYM
ejpam-3245	89	15	eur	eur	PROPN
ejpam-3245	89	16	.	.	PUNCT
ejpam-3245	90	1	j.	j.	PROPN
ejpam-3245	90	2	pure	pure	PROPN
ejpam-3245	90	3	appl	appl	PROPN
ejpam-3245	90	4	.	.	PROPN
ejpam-3245	90	5	math	math	PROPN
ejpam-3245	90	6	,	,	PUNCT
ejpam-3245	90	7	11	11	NUM
ejpam-3245	90	8	(	(	PUNCT
ejpam-3245	90	9	3	3	NUM
ejpam-3245	90	10	)	)	PUNCT
ejpam-3245	90	11	(	(	PUNCT
ejpam-3245	90	12	2018	2018	NUM
ejpam-3245	90	13	)	)	PUNCT
ejpam-3245	90	14	,	,	PUNCT
ejpam-3245	90	15	803	803	NUM
ejpam-3245	90	16	-	-	SYM
ejpam-3245	90	17	814	814	NUM
ejpam-3245	90	18	806	806	NUM
ejpam-3245	90	19	i	i	NOUN
ejpam-3245	90	20	)	)	PUNCT
ejpam-3245	90	21	the	the	DET
ejpam-3245	90	22	line	line	NOUN
ejpam-3245	90	23	simultaneously	simultaneously	ADV
ejpam-3245	90	24	hits	hit	VERB
ejpam-3245	90	25	infinitely	infinitely	ADV
ejpam-3245	90	26	many	many	ADJ
ejpam-3245	90	27	of	of	ADP
ejpam-3245	90	28	the	the	DET
ejpam-3245	90	29	points	point	NOUN
ejpam-3245	90	30	we	we	PRON
ejpam-3245	90	31	have	have	AUX
ejpam-3245	90	32	plotted	plot	VERB
ejpam-3245	90	33	.	.	PUNCT
ejpam-3245	91	1	in	in	ADP
ejpam-3245	91	2	this	this	DET
ejpam-3245	91	3	case	case	NOUN
ejpam-3245	91	4	,	,	PUNCT
ejpam-3245	91	5	stop	stop	VERB
ejpam-3245	91	6	and	and	CCONJ
ejpam-3245	91	7	the	the	DET
ejpam-3245	91	8	polygon	polygon	NOUN
ejpam-3245	91	9	is	be	AUX
ejpam-3245	91	10	complete	complete	ADJ
ejpam-3245	91	11	.	.	PUNCT
ejpam-3245	92	1	for	for	ADP
ejpam-3245	92	2	example	example	NOUN
ejpam-3245	92	3	the	the	DET
ejpam-3245	92	4	newton	newton	PROPN
ejpam-3245	92	5	polygon	polygon	PROPN
ejpam-3245	92	6	of	of	ADP
ejpam-3245	92	7	the	the	DET
ejpam-3245	92	8	power	power	NOUN
ejpam-3245	92	9	series	series	PROPN
ejpam-3245	92	10	f(x	f(x	PROPN
ejpam-3245	92	11	)	)	PUNCT
ejpam-3245	92	12	=	=	SYM
ejpam-3245	93	1	1	1	NUM
ejpam-3245	93	2	+	+	NUM
ejpam-3245	93	3	∑∞	∑∞	NOUN
ejpam-3245	93	4	i=1	i=1	X
ejpam-3245	94	1	p	p	PROPN
ejpam-3245	94	2	ixi	ixi	PROPN
ejpam-3245	94	3	is	be	AUX
ejpam-3245	94	4	just	just	ADV
ejpam-3245	94	5	the	the	DET
ejpam-3245	94	6	line	line	NOUN
ejpam-3245	94	7	y	y	PROPN
ejpam-3245	94	8	=	=	SYM
ejpam-3245	94	9	x.	x.	PROPN
ejpam-3245	94	10	ii	ii	PROPN
ejpam-3245	94	11	)	)	PUNCT
ejpam-3245	94	12	the	the	DET
ejpam-3245	94	13	line	line	NOUN
ejpam-3245	94	14	reaches	reach	VERB
ejpam-3245	94	15	a	a	DET
ejpam-3245	94	16	position	position	NOUN
ejpam-3245	94	17	where	where	SCONJ
ejpam-3245	94	18	it	it	PRON
ejpam-3245	94	19	contains	contain	VERB
ejpam-3245	94	20	only	only	ADV
ejpam-3245	94	21	one	one	NUM
ejpam-3245	94	22	of	of	ADP
ejpam-3245	94	23	our	our	PRON
ejpam-3245	94	24	points	point	NOUN
ejpam-3245	94	25	that	that	PRON
ejpam-3245	94	26	serves	serve	VERB
ejpam-3245	94	27	as	as	ADP
ejpam-3245	94	28	a	a	DET
ejpam-3245	94	29	center	center	NOUN
ejpam-3245	94	30	of	of	ADP
ejpam-3245	94	31	rotation	rotation	NOUN
ejpam-3245	94	32	,	,	PUNCT
ejpam-3245	94	33	but	but	CCONJ
ejpam-3245	94	34	can	can	AUX
ejpam-3245	94	35	be	be	AUX
ejpam-3245	94	36	rotated	rotate	VERB
ejpam-3245	94	37	no	no	ADV
ejpam-3245	94	38	further	far	ADV
ejpam-3245	94	39	without	without	ADP
ejpam-3245	94	40	leaving	leave	VERB
ejpam-3245	94	41	behind	behind	ADV
ejpam-3245	94	42	some	some	DET
ejpam-3245	94	43	points	point	NOUN
ejpam-3245	94	44	.	.	PUNCT
ejpam-3245	95	1	in	in	ADP
ejpam-3245	95	2	this	this	DET
ejpam-3245	95	3	case	case	NOUN
ejpam-3245	95	4	,	,	PUNCT
ejpam-3245	95	5	stop	stop	VERB
ejpam-3245	95	6	and	and	CCONJ
ejpam-3245	95	7	the	the	DET
ejpam-3245	95	8	polygon	polygon	NOUN
ejpam-3245	95	9	is	be	AUX
ejpam-3245	95	10	complete	complete	ADJ
ejpam-3245	95	11	.	.	PUNCT
ejpam-3245	96	1	we	we	PRON
ejpam-3245	96	2	will	will	AUX
ejpam-3245	96	3	counter	counter	VERB
ejpam-3245	96	4	this	this	DET
ejpam-3245	96	5	case	case	NOUN
ejpam-3245	96	6	in	in	ADP
ejpam-3245	96	7	section	section	NOUN
ejpam-3245	96	8	4	4	NUM
ejpam-3245	96	9	.	.	X
ejpam-3245	96	10	iii	iii	X
ejpam-3245	96	11	)	)	PUNCT
ejpam-3245	96	12	the	the	DET
ejpam-3245	96	13	line	line	NOUN
ejpam-3245	96	14	hits	hit	VERB
ejpam-3245	96	15	a	a	DET
ejpam-3245	96	16	finite	finite	ADJ
ejpam-3245	96	17	number	number	NOUN
ejpam-3245	96	18	of	of	ADP
ejpam-3245	96	19	points	point	NOUN
ejpam-3245	96	20	.	.	PUNCT
ejpam-3245	97	1	in	in	ADP
ejpam-3245	97	2	this	this	DET
ejpam-3245	97	3	case	case	NOUN
ejpam-3245	97	4	,	,	PUNCT
ejpam-3245	97	5	break	break	VERB
ejpam-3245	97	6	the	the	DET
ejpam-3245	97	7	line	line	NOUN
ejpam-3245	97	8	at	at	ADP
ejpam-3245	97	9	the	the	DET
ejpam-3245	97	10	last	last	ADJ
ejpam-3245	97	11	point	point	NOUN
ejpam-3245	97	12	it	it	PRON
ejpam-3245	97	13	was	be	AUX
ejpam-3245	97	14	hit	hit	VERB
ejpam-3245	97	15	,	,	PUNCT
ejpam-3245	97	16	and	and	CCONJ
ejpam-3245	97	17	repeat	repeat	VERB
ejpam-3245	97	18	the	the	DET
ejpam-3245	97	19	whole	whole	ADJ
ejpam-3245	97	20	procedure	procedure	NOUN
ejpam-3245	97	21	again	again	ADV
ejpam-3245	97	22	.	.	PUNCT
ejpam-3245	98	1	using	use	VERB
ejpam-3245	98	2	the	the	DET
ejpam-3245	98	3	above	above	ADJ
ejpam-3245	98	4	procedure	procedure	NOUN
ejpam-3245	98	5	,	,	PUNCT
ejpam-3245	98	6	it	it	PRON
ejpam-3245	98	7	can	can	AUX
ejpam-3245	98	8	be	be	AUX
ejpam-3245	98	9	seen	see	VERB
ejpam-3245	98	10	that	that	SCONJ
ejpam-3245	98	11	the	the	DET
ejpam-3245	98	12	newton	newton	PROPN
ejpam-3245	98	13	polygon	polygon	PROPN
ejpam-3245	98	14	of	of	ADP
ejpam-3245	98	15	power	power	NOUN
ejpam-3245	98	16	series	series	PROPN
ejpam-3245	98	17	either	either	CCONJ
ejpam-3245	98	18	ends	end	VERB
ejpam-3245	98	19	by	by	ADP
ejpam-3245	98	20	a	a	DET
ejpam-3245	98	21	ray	ray	NOUN
ejpam-3245	98	22	(	(	PUNCT
ejpam-3245	98	23	see	see	VERB
ejpam-3245	98	24	the	the	DET
ejpam-3245	98	25	appendix	appendix	NOUN
ejpam-3245	98	26	)	)	PUNCT
ejpam-3245	98	27	or	or	CCONJ
ejpam-3245	98	28	has	have	VERB
ejpam-3245	98	29	an	an	DET
ejpam-3245	98	30	infinite	infinite	ADJ
ejpam-3245	98	31	number	number	NOUN
ejpam-3245	98	32	of	of	ADP
ejpam-3245	98	33	finite	finite	ADJ
ejpam-3245	98	34	segments	segment	NOUN
ejpam-3245	98	35	(	(	PUNCT
ejpam-3245	98	36	for	for	ADP
ejpam-3245	98	37	example	example	NOUN
ejpam-3245	98	38	,	,	PUNCT
ejpam-3245	98	39	the	the	DET
ejpam-3245	98	40	newton	newton	PROPN
ejpam-3245	98	41	polygon	polygon	PROPN
ejpam-3245	98	42	of	of	ADP
ejpam-3245	98	43	the	the	DET
ejpam-3245	98	44	power	power	NOUN
ejpam-3245	98	45	series	series	NOUN
ejpam-3245	98	46	1	1	NUM
ejpam-3245	98	47	+	+	NUM
ejpam-3245	98	48	∑∞	∑∞	X
ejpam-3245	98	49	i=1	i=1	X
ejpam-3245	98	50	p	p	X
ejpam-3245	98	51	i2xi	i2xi	PUNCT
ejpam-3245	98	52	)	)	PUNCT
ejpam-3245	98	53	.	.	PUNCT
ejpam-3245	99	1	furthermore	furthermore	ADV
ejpam-3245	99	2	,	,	PUNCT
ejpam-3245	99	3	it	it	PRON
ejpam-3245	99	4	is	be	AUX
ejpam-3245	99	5	well	well	ADV
ejpam-3245	99	6	known	know	VERB
ejpam-3245	99	7	that	that	SCONJ
ejpam-3245	99	8	if	if	SCONJ
ejpam-3245	99	9	the	the	DET
ejpam-3245	99	10	newton	newton	PROPN
ejpam-3245	99	11	polygon	polygon	PROPN
ejpam-3245	99	12	of	of	ADP
ejpam-3245	99	13	a	a	DET
ejpam-3245	99	14	power	power	NOUN
ejpam-3245	99	15	series	series	NOUN
ejpam-3245	99	16	f	f	PROPN
ejpam-3245	99	17	ends	end	VERB
ejpam-3245	99	18	by	by	ADP
ejpam-3245	99	19	a	a	DET
ejpam-3245	99	20	ray	ray	NOUN
ejpam-3245	99	21	,	,	PUNCT
ejpam-3245	99	22	then	then	ADV
ejpam-3245	99	23	f	f	PROPN
ejpam-3245	99	24	has	have	VERB
ejpam-3245	99	25	at	at	ADV
ejpam-3245	99	26	most	most	ADV
ejpam-3245	99	27	finitely	finitely	ADV
ejpam-3245	99	28	many	many	ADJ
ejpam-3245	99	29	zeros	zero	NOUN
ejpam-3245	99	30	in	in	ADP
ejpam-3245	99	31	its	its	PRON
ejpam-3245	99	32	disk	disk	NOUN
ejpam-3245	99	33	of	of	ADP
ejpam-3245	99	34	convergence	convergence	NOUN
ejpam-3245	99	35	.	.	PUNCT
ejpam-3245	100	1	the	the	DET
ejpam-3245	100	2	following	follow	VERB
ejpam-3245	100	3	lemma	lemma	PROPN
ejpam-3245	100	4	is	be	AUX
ejpam-3245	100	5	a	a	DET
ejpam-3245	100	6	connection	connection	NOUN
ejpam-3245	100	7	between	between	ADP
ejpam-3245	100	8	the	the	DET
ejpam-3245	100	9	domain	domain	NOUN
ejpam-3245	100	10	of	of	ADP
ejpam-3245	100	11	convergence	convergence	NOUN
ejpam-3245	100	12	of	of	ADP
ejpam-3245	100	13	a	a	DET
ejpam-3245	100	14	power	power	NOUN
ejpam-3245	100	15	series	series	NOUN
ejpam-3245	100	16	and	and	CCONJ
ejpam-3245	100	17	the	the	DET
ejpam-3245	100	18	slopes	slope	NOUN
ejpam-3245	100	19	of	of	ADP
ejpam-3245	100	20	its	its	PRON
ejpam-3245	100	21	polygon	polygon	NOUN
ejpam-3245	100	22	.	.	PUNCT
ejpam-3245	101	1	lemma	lemma	PROPN
ejpam-3245	101	2	1	1	X
ejpam-3245	101	3	.	.	PUNCT
ejpam-3245	102	1	let	let	VERB
ejpam-3245	102	2	m	m	PRON
ejpam-3245	102	3	be	be	AUX
ejpam-3245	102	4	the	the	DET
ejpam-3245	102	5	sup	sup	NOUN
ejpam-3245	102	6	of	of	ADP
ejpam-3245	102	7	all	all	DET
ejpam-3245	102	8	slopes	slope	NOUN
ejpam-3245	102	9	appearing	appear	VERB
ejpam-3245	102	10	in	in	ADP
ejpam-3245	102	11	the	the	DET
ejpam-3245	102	12	newton	newton	PROPN
ejpam-3245	102	13	polygon	polygon	PROPN
ejpam-3245	102	14	of	of	ADP
ejpam-3245	102	15	a	a	DET
ejpam-3245	102	16	power	power	NOUN
ejpam-3245	102	17	series	series	NOUN
ejpam-3245	102	18	f(x	f(x	PROPN
ejpam-3245	102	19	)	)	PUNCT
ejpam-3245	103	1	=	=	SYM
ejpam-3245	104	1	1	1	NUM
ejpam-3245	104	2	+	+	NUM
ejpam-3245	104	3	∑∞	∑∞	X
ejpam-3245	104	4	i=1	i=1	PROPN
ejpam-3245	104	5	aix	aix	PROPN
ejpam-3245	104	6	i.	i.	PROPN
ejpam-3245	104	7	then	then	ADV
ejpam-3245	104	8	,	,	PUNCT
ejpam-3245	104	9	the	the	DET
ejpam-3245	104	10	domain	domain	NOUN
ejpam-3245	104	11	of	of	ADP
ejpam-3245	104	12	f	f	PROPN
ejpam-3245	104	13	is	be	AUX
ejpam-3245	104	14	the	the	DET
ejpam-3245	104	15	set	set	NOUN
ejpam-3245	104	16	{	{	PUNCT
ejpam-3245	104	17	x	x	SYM
ejpam-3245	104	18	∈	∈	PROPN
ejpam-3245	104	19	cp	cp	INTJ
ejpam-3245	104	20	:	:	PUNCT
ejpam-3245	104	21	ord(x	ord(x	PROPN
ejpam-3245	104	22	)	)	PUNCT
ejpam-3245	104	23	>	>	X
ejpam-3245	105	1	−m	−m	NOUN
ejpam-3245	105	2	}	}	PUNCT
ejpam-3245	105	3	.	.	PUNCT
ejpam-3245	106	1	in	in	ADP
ejpam-3245	106	2	the	the	DET
ejpam-3245	106	3	case	case	NOUN
ejpam-3245	106	4	m	m	NOUN
ejpam-3245	106	5	is	be	AUX
ejpam-3245	106	6	infinite	infinite	ADJ
ejpam-3245	106	7	.	.	PUNCT
ejpam-3245	107	1	then	then	ADV
ejpam-3245	107	2	f	f	PROPN
ejpam-3245	107	3	converges	converge	VERB
ejpam-3245	107	4	on	on	ADP
ejpam-3245	107	5	all	all	PRON
ejpam-3245	107	6	of	of	ADP
ejpam-3245	107	7	cp	cp	PROPN
ejpam-3245	107	8	.	.	PROPN
ejpam-3245	108	1	in	in	ADP
ejpam-3245	108	2	particular	particular	ADJ
ejpam-3245	108	3	,	,	PUNCT
ejpam-3245	108	4	if	if	SCONJ
ejpam-3245	108	5	the	the	DET
ejpam-3245	108	6	newton	newton	PROPN
ejpam-3245	108	7	polygon	polygon	PROPN
ejpam-3245	108	8	of	of	ADP
ejpam-3245	108	9	f	f	PROPN
ejpam-3245	108	10	ends	end	VERB
ejpam-3245	108	11	by	by	ADP
ejpam-3245	108	12	a	a	DET
ejpam-3245	108	13	ray	ray	NOUN
ejpam-3245	108	14	of	of	ADP
ejpam-3245	108	15	slope	slope	NOUN
ejpam-3245	108	16	m	m	PROPN
ejpam-3245	108	17	,	,	PUNCT
ejpam-3245	108	18	then	then	ADV
ejpam-3245	108	19	the	the	DET
ejpam-3245	108	20	domain	domain	NOUN
ejpam-3245	108	21	is	be	AUX
ejpam-3245	108	22	{	{	PUNCT
ejpam-3245	108	23	x	x	SYM
ejpam-3245	108	24	∈	∈	PROPN
ejpam-3245	108	25	cp	cp	INTJ
ejpam-3245	108	26	:	:	PUNCT
ejpam-3245	108	27	ord(x	ord(x	PROPN
ejpam-3245	108	28	)	)	PUNCT
ejpam-3245	108	29	>	>	X
ejpam-3245	109	1	−m	−m	NOUN
ejpam-3245	109	2	}	}	PUNCT
ejpam-3245	109	3	.	.	PUNCT
ejpam-3245	110	1	finally	finally	ADV
ejpam-3245	110	2	,	,	PUNCT
ejpam-3245	110	3	we	we	PRON
ejpam-3245	110	4	need	need	VERB
ejpam-3245	110	5	the	the	DET
ejpam-3245	110	6	following	follow	VERB
ejpam-3245	110	7	:	:	PUNCT
ejpam-3245	110	8	corollary	corollary	ADJ
ejpam-3245	110	9	1	1	NUM
ejpam-3245	110	10	.	.	PUNCT
ejpam-3245	111	1	(	(	PUNCT
ejpam-3245	111	2	[	[	X
ejpam-3245	111	3	4	4	NUM
ejpam-3245	111	4	]	]	PUNCT
ejpam-3245	111	5	,	,	PUNCT
ejpam-3245	111	6	p.106	p.106	NOUN
ejpam-3245	111	7	)	)	PUNCT
ejpam-3245	111	8	if	if	SCONJ
ejpam-3245	111	9	a	a	DET
ejpam-3245	111	10	segment	segment	NOUN
ejpam-3245	111	11	of	of	ADP
ejpam-3245	111	12	the	the	DET
ejpam-3245	111	13	newton	newton	PROPN
ejpam-3245	111	14	polygon	polygon	PROPN
ejpam-3245	111	15	of	of	ADP
ejpam-3245	111	16	f(x	f(x	PROPN
ejpam-3245	111	17	)	)	PUNCT
ejpam-3245	111	18	∈	∈	NOUN
ejpam-3245	111	19	1	1	NUM
ejpam-3245	112	1	+	+	CCONJ
ejpam-3245	112	2	cp[[x	cp[[x	PROPN
ejpam-3245	112	3	]	]	X
ejpam-3245	112	4	]	]	X
ejpam-3245	112	5	has	have	VERB
ejpam-3245	112	6	finite	finite	ADJ
ejpam-3245	112	7	length	length	NOUN
ejpam-3245	112	8	n	n	PROPN
ejpam-3245	112	9	and	and	CCONJ
ejpam-3245	112	10	slope	slope	NOUN
ejpam-3245	112	11	λ	λ	PROPN
ejpam-3245	112	12	,	,	PUNCT
ejpam-3245	112	13	then	then	ADV
ejpam-3245	112	14	there	there	PRON
ejpam-3245	112	15	are	be	VERB
ejpam-3245	112	16	precisely	precisely	ADV
ejpam-3245	112	17	n	n	PRON
ejpam-3245	112	18	values	value	NOUN
ejpam-3245	112	19	of	of	ADP
ejpam-3245	112	20	x	x	PUNCT
ejpam-3245	112	21	counting	count	VERB
ejpam-3245	112	22	multiplicity	multiplicity	NOUN
ejpam-3245	112	23	for	for	ADP
ejpam-3245	112	24	which	which	PRON
ejpam-3245	112	25	f(x	f(x	PROPN
ejpam-3245	112	26	)	)	PUNCT
ejpam-3245	113	1	=	=	SYM
ejpam-3245	113	2	0	0	NUM
ejpam-3245	113	3	and	and	CCONJ
ejpam-3245	113	4	ord(x	ord(x	NUM
ejpam-3245	113	5	)	)	PUNCT
ejpam-3245	113	6	=	=	SYM
ejpam-3245	113	7	−λ	−λ	PROPN
ejpam-3245	113	8	.	.	PUNCT
ejpam-3245	114	1	we	we	PRON
ejpam-3245	114	2	summarize	summarize	VERB
ejpam-3245	114	3	what	what	PRON
ejpam-3245	114	4	we	we	PRON
ejpam-3245	114	5	need	need	VERB
ejpam-3245	114	6	as	as	ADP
ejpam-3245	114	7	the	the	DET
ejpam-3245	114	8	following	following	NOUN
ejpam-3245	114	9	:	:	PUNCT
ejpam-3245	114	10	fact	fact	NOUN
ejpam-3245	114	11	1	1	NUM
ejpam-3245	114	12	.	.	PUNCT
ejpam-3245	115	1	the	the	DET
ejpam-3245	115	2	points	point	NOUN
ejpam-3245	115	3	(	(	PUNCT
ejpam-3245	115	4	i	i	PRON
ejpam-3245	115	5	,	,	PUNCT
ejpam-3245	115	6	ord	ord	PROPN
ejpam-3245	115	7	(	(	PUNCT
ejpam-3245	115	8	1	1	NUM
ejpam-3245	115	9	i	i	NOUN
ejpam-3245	115	10	!	!	PUNCT
ejpam-3245	115	11	)	)	PUNCT
ejpam-3245	115	12	)	)	PUNCT
ejpam-3245	115	13	;	;	PUNCT
ejpam-3245	115	14	i	i	PRON
ejpam-3245	115	15	>	>	X
ejpam-3245	115	16	1	1	NUM
ejpam-3245	115	17	are	be	AUX
ejpam-3245	115	18	on	on	ADP
ejpam-3245	115	19	or	or	CCONJ
ejpam-3245	115	20	above	above	ADP
ejpam-3245	115	21	the	the	DET
ejpam-3245	115	22	line	line	NOUN
ejpam-3245	115	23	y	y	PROPN
ejpam-3245	115	24	=	=	PUNCT
ejpam-3245	115	25	−1	−1	NOUN
ejpam-3245	115	26	p−1(x	p−1(x	NOUN
ejpam-3245	115	27	−	−	NOUN
ejpam-3245	115	28	1	1	NUM
ejpam-3245	115	29	)	)	PUNCT
ejpam-3245	115	30	.	.	PUNCT
ejpam-3245	116	1	it	it	PRON
ejpam-3245	116	2	algebraically	algebraically	ADV
ejpam-3245	116	3	means	mean	VERB
ejpam-3245	116	4	that	that	SCONJ
ejpam-3245	116	5	ord	ord	PROPN
ejpam-3245	116	6	(	(	PUNCT
ejpam-3245	116	7	1	1	NUM
ejpam-3245	116	8	i	i	NOUN
ejpam-3245	116	9	!	!	PUNCT
ejpam-3245	116	10	)	)	PUNCT
ejpam-3245	116	11	>	>	X
ejpam-3245	117	1	−1	−1	NOUN
ejpam-3245	117	2	p−1(i−	p−1(i−	NOUN
ejpam-3245	117	3	1	1	NUM
ejpam-3245	117	4	)	)	PUNCT
ejpam-3245	117	5	,	,	PUNCT
ejpam-3245	117	6	∀i	∀i	X
ejpam-3245	117	7	>	>	X
ejpam-3245	117	8	1	1	NUM
ejpam-3245	117	9	.	.	PUNCT
ejpam-3245	117	10	fact	fact	NOUN
ejpam-3245	117	11	2	2	NUM
ejpam-3245	117	12	.	.	PUNCT
ejpam-3245	117	13	a	a	DET
ejpam-3245	117	14	finite	finite	ADJ
ejpam-3245	117	15	segment	segment	NOUN
ejpam-3245	117	16	of	of	ADP
ejpam-3245	117	17	the	the	DET
ejpam-3245	117	18	length	length	NOUN
ejpam-3245	117	19	m	m	PROPN
ejpam-3245	117	20	of	of	ADP
ejpam-3245	117	21	the	the	DET
ejpam-3245	117	22	newton	newton	PROPN
ejpam-3245	117	23	polygon	polygon	PROPN
ejpam-3245	117	24	of	of	ADP
ejpam-3245	117	25	the	the	DET
ejpam-3245	117	26	power	power	NOUN
ejpam-3245	117	27	series	series	PROPN
ejpam-3245	117	28	f	f	PROPN
ejpam-3245	117	29	determines	determine	VERB
ejpam-3245	117	30	at	at	ADP
ejpam-3245	117	31	least	least	ADJ
ejpam-3245	117	32	m	m	VERB
ejpam-3245	117	33	roots	root	NOUN
ejpam-3245	117	34	(	(	PUNCT
ejpam-3245	117	35	counting	count	VERB
ejpam-3245	117	36	multiplicity	multiplicity	NOUN
ejpam-3245	117	37	)	)	PUNCT
ejpam-3245	117	38	of	of	ADP
ejpam-3245	117	39	f	f	PROPN
ejpam-3245	117	40	of	of	ADP
ejpam-3245	117	41	the	the	DET
ejpam-3245	117	42	same	same	ADJ
ejpam-3245	117	43	order	order	NOUN
ejpam-3245	117	44	.	.	PUNCT
ejpam-3245	118	1	3	3	X
ejpam-3245	118	2	.	.	X
ejpam-3245	118	3	the	the	DET
ejpam-3245	118	4	main	main	ADJ
ejpam-3245	118	5	results	result	NOUN
ejpam-3245	118	6	keep	keep	VERB
ejpam-3245	118	7	the	the	DET
ejpam-3245	118	8	notation	notation	NOUN
ejpam-3245	118	9	as	as	ADP
ejpam-3245	118	10	above	above	ADV
ejpam-3245	118	11	.	.	PUNCT
ejpam-3245	119	1	we	we	PRON
ejpam-3245	119	2	prove	prove	VERB
ejpam-3245	119	3	the	the	DET
ejpam-3245	119	4	following	following	NOUN
ejpam-3245	119	5	:	:	PUNCT
ejpam-3245	119	6	theorem	theorem	NOUN
ejpam-3245	119	7	2	2	NUM
ejpam-3245	119	8	.	.	PUNCT
ejpam-3245	119	9	consider	consider	VERB
ejpam-3245	119	10	the	the	DET
ejpam-3245	119	11	polynomials	polynomial	NOUN
ejpam-3245	119	12	over	over	ADP
ejpam-3245	119	13	o	o	NOUN
ejpam-3245	119	14	:	:	PUNCT
ejpam-3245	119	15	p1(z	p1(z	NUM
ejpam-3245	119	16	)	)	PUNCT
ejpam-3245	119	17	=	=	SYM
ejpam-3245	119	18	n1∑	n1∑	PROPN
ejpam-3245	119	19	j=0	j=0	VERB
ejpam-3245	119	20	a	a	DET
ejpam-3245	119	21	(	(	PUNCT
ejpam-3245	119	22	1	1	NUM
ejpam-3245	119	23	)	)	PUNCT
ejpam-3245	119	24	j	j	PROPN
ejpam-3245	119	25	zj	zj	PROPN
ejpam-3245	119	26	,	,	PUNCT
ejpam-3245	119	27	p2(z	p2(z	X
ejpam-3245	119	28	)	)	PUNCT
ejpam-3245	119	29	=	=	SYM
ejpam-3245	119	30	n2∑	n2∑	PROPN
ejpam-3245	119	31	j=0	j=0	VERB
ejpam-3245	119	32	a	a	DET
ejpam-3245	119	33	(	(	PUNCT
ejpam-3245	119	34	2	2	NUM
ejpam-3245	119	35	)	)	PUNCT
ejpam-3245	119	36	j	j	PROPN
ejpam-3245	119	37	zj	zj	PROPN
ejpam-3245	119	38	,	,	PUNCT
ejpam-3245	119	39	.	.	PUNCT
ejpam-3245	119	40	.	.	PUNCT
ejpam-3245	119	41	.	.	PUNCT
ejpam-3245	120	1	.	.	PUNCT
ejpam-3245	120	2	,	,	PUNCT
ejpam-3245	120	3	pd(z	pd(z	X
ejpam-3245	120	4	)	)	PUNCT
ejpam-3245	120	5	=	=	SYM
ejpam-3245	120	6	nd∑	nd∑	PROPN
ejpam-3245	120	7	j=0	j=0	VERB
ejpam-3245	120	8	a	a	DET
ejpam-3245	120	9	(	(	PUNCT
ejpam-3245	120	10	d	d	NOUN
ejpam-3245	120	11	)	)	PUNCT
ejpam-3245	120	12	j	j	PROPN
ejpam-3245	120	13	zj	zj	PROPN
ejpam-3245	120	14	,	,	PUNCT
ejpam-3245	120	15	a.	a.	NOUN
ejpam-3245	120	16	dalloul	dalloul	PROPN
ejpam-3245	120	17	/	/	SYM
ejpam-3245	120	18	eur	eur	PROPN
ejpam-3245	120	19	.	.	PUNCT
ejpam-3245	121	1	j.	j.	PROPN
ejpam-3245	121	2	pure	pure	PROPN
ejpam-3245	121	3	appl	appl	PROPN
ejpam-3245	121	4	.	.	PROPN
ejpam-3245	121	5	math	math	PROPN
ejpam-3245	121	6	,	,	PUNCT
ejpam-3245	121	7	11	11	NUM
ejpam-3245	121	8	(	(	PUNCT
ejpam-3245	121	9	3	3	NUM
ejpam-3245	121	10	)	)	PUNCT
ejpam-3245	121	11	(	(	PUNCT
ejpam-3245	121	12	2018	2018	NUM
ejpam-3245	121	13	)	)	PUNCT
ejpam-3245	121	14	,	,	PUNCT
ejpam-3245	121	15	803	803	NUM
ejpam-3245	121	16	-	-	SYM
ejpam-3245	121	17	814	814	NUM
ejpam-3245	121	18	807	807	NUM
ejpam-3245	121	19	where	where	SCONJ
ejpam-3245	121	20	nd	nd	ADV
ejpam-3245	121	21	>	>	X
ejpam-3245	121	22	max1≤i≤d−1{degpi	max1≤i≤d−1{degpi	PROPN
ejpam-3245	121	23	,	,	PUNCT
ejpam-3245	121	24	1	1	NUM
ejpam-3245	121	25	}	}	PUNCT
ejpam-3245	121	26	.	.	PUNCT
ejpam-3245	122	1	let	let	VERB
ejpam-3245	122	2	w1	w1	NOUN
ejpam-3245	122	3	,	,	PUNCT
ejpam-3245	122	4	.	.	PUNCT
ejpam-3245	122	5	.	.	PUNCT
ejpam-3245	123	1	.	.	PUNCT
ejpam-3245	124	1	,	,	PUNCT
ejpam-3245	124	2	wd	wd	PROPN
ejpam-3245	124	3	∈	∈	PROPN
ejpam-3245	124	4	cp	cp	INTJ
ejpam-3245	124	5	with	with	ADP
ejpam-3245	124	6	ord(wi	ord(wi	NOUN
ejpam-3245	124	7	)	)	PUNCT
ejpam-3245	124	8	>	>	X
ejpam-3245	124	9	1	1	NUM
ejpam-3245	124	10	p−1	p−1	PROPN
ejpam-3245	124	11	,	,	PUNCT
ejpam-3245	124	12	i	i	PRON
ejpam-3245	124	13	=	=	NOUN
ejpam-3245	124	14	1	1	NUM
ejpam-3245	124	15	,	,	PUNCT
ejpam-3245	124	16	2	2	NUM
ejpam-3245	124	17	,	,	PUNCT
ejpam-3245	124	18	..	..	PUNCT
ejpam-3245	124	19	,	,	PUNCT
ejpam-3245	124	20	d.	d.	PROPN
ejpam-3245	124	21	then	then	ADV
ejpam-3245	124	22	,	,	PUNCT
ejpam-3245	124	23	the	the	DET
ejpam-3245	124	24	exponential	exponential	ADJ
ejpam-3245	124	25	polynomial	polynomial	ADJ
ejpam-3245	124	26	b(z	b(z	NOUN
ejpam-3245	124	27	)	)	PUNCT
ejpam-3245	124	28	=	=	SYM
ejpam-3245	124	29	p1(z	p1(z	PROPN
ejpam-3245	124	30	)	)	PUNCT
ejpam-3245	124	31	exp(w1z	exp(w1z	PROPN
ejpam-3245	124	32	)	)	PUNCT
ejpam-3245	124	33	+	+	NUM
ejpam-3245	124	34	p2(z	p2(z	X
ejpam-3245	124	35	)	)	PUNCT
ejpam-3245	124	36	exp(w2z	exp(w2z	PROPN
ejpam-3245	124	37	)	)	PUNCT
ejpam-3245	124	38	+	+	CCONJ
ejpam-3245	124	39	.	.	PUNCT
ejpam-3245	124	40	.	.	PUNCT
ejpam-3245	124	41	.	.	PUNCT
ejpam-3245	125	1	.+	.+	NOUN
ejpam-3245	125	2	pd(z	pd(z	PRON
ejpam-3245	125	3	)	)	PUNCT
ejpam-3245	125	4	exp(wdz	exp(wdz	PROPN
ejpam-3245	125	5	)	)	PUNCT
ejpam-3245	125	6	,	,	PUNCT
ejpam-3245	125	7	with	with	ADP
ejpam-3245	125	8	ord(a	ord(a	PROPN
ejpam-3245	125	9	(	(	PUNCT
ejpam-3245	125	10	1	1	NUM
ejpam-3245	125	11	)	)	PUNCT
ejpam-3245	125	12	0	0	PUNCT
ejpam-3245	126	1	+	+	CCONJ
ejpam-3245	126	2	·	·	PUNCT
ejpam-3245	126	3	·	·	PUNCT
ejpam-3245	126	4	·	·	PUNCT
ejpam-3245	126	5	+	+	CCONJ
ejpam-3245	126	6	a	a	DET
ejpam-3245	126	7	(	(	PUNCT
ejpam-3245	126	8	d	d	NOUN
ejpam-3245	126	9	)	)	PUNCT
ejpam-3245	126	10	0	0	NUM
ejpam-3245	126	11	)	)	PUNCT
ejpam-3245	127	1	=	=	SYM
ejpam-3245	128	1	ord(a	ord(a	PROPN
ejpam-3245	128	2	(	(	PUNCT
ejpam-3245	128	3	d	d	NOUN
ejpam-3245	128	4	)	)	PUNCT
ejpam-3245	128	5	nd	nd	NUM
ejpam-3245	128	6	)	)	PUNCT
ejpam-3245	128	7	=	=	SYM
ejpam-3245	128	8	0	0	NUM
ejpam-3245	128	9	,	,	PUNCT
ejpam-3245	128	10	has	have	VERB
ejpam-3245	128	11	at	at	ADV
ejpam-3245	128	12	least	least	ADJ
ejpam-3245	128	13	nd	nd	NUM
ejpam-3245	128	14	roots	root	NOUN
ejpam-3245	128	15	(	(	PUNCT
ejpam-3245	128	16	counting	count	VERB
ejpam-3245	128	17	multiplicity	multiplicity	NOUN
ejpam-3245	128	18	)	)	PUNCT
ejpam-3245	128	19	in	in	ADP
ejpam-3245	128	20	the	the	DET
ejpam-3245	128	21	unit	unit	NOUN
ejpam-3245	128	22	disk	disk	NOUN
ejpam-3245	128	23	.	.	PUNCT
ejpam-3245	129	1	proof	proof	NOUN
ejpam-3245	129	2	.	.	PUNCT
ejpam-3245	130	1	as	as	ADP
ejpam-3245	130	2	ord(wj	ord(wj	ADV
ejpam-3245	130	3	)	)	PUNCT
ejpam-3245	130	4	>	>	X
ejpam-3245	130	5	1	1	NUM
ejpam-3245	130	6	p−1	p−1	PROPN
ejpam-3245	130	7	for	for	ADP
ejpam-3245	130	8	j	j	PROPN
ejpam-3245	130	9	=	=	SYM
ejpam-3245	130	10	1	1	NUM
ejpam-3245	130	11	,	,	PUNCT
ejpam-3245	130	12	2	2	NUM
ejpam-3245	130	13	,	,	PUNCT
ejpam-3245	130	14	..	..	PUNCT
ejpam-3245	130	15	,	,	PUNCT
ejpam-3245	131	1	d	d	X
ejpam-3245	131	2	,	,	PUNCT
ejpam-3245	131	3	the	the	DET
ejpam-3245	131	4	domain	domain	NOUN
ejpam-3245	131	5	of	of	ADP
ejpam-3245	131	6	convergence	convergence	NOUN
ejpam-3245	131	7	is	be	AUX
ejpam-3245	131	8	the	the	DET
ejpam-3245	131	9	unit	unit	NOUN
ejpam-3245	131	10	disk	disk	NOUN
ejpam-3245	131	11	.	.	PUNCT
ejpam-3245	132	1	let	let	VERB
ejpam-3245	132	2	c	c	NOUN
ejpam-3245	132	3	=	=	PUNCT
ejpam-3245	132	4	a	a	X
ejpam-3245	132	5	(	(	PUNCT
ejpam-3245	132	6	1	1	NUM
ejpam-3245	132	7	)	)	PUNCT
ejpam-3245	132	8	0	0	PUNCT
ejpam-3245	133	1	+	+	CCONJ
ejpam-3245	133	2	....	....	PUNCT
ejpam-3245	133	3	+	+	CCONJ
ejpam-3245	133	4	a	a	DET
ejpam-3245	133	5	(	(	PUNCT
ejpam-3245	133	6	d	d	NOUN
ejpam-3245	133	7	)	)	PUNCT
ejpam-3245	133	8	0	0	NUM
ejpam-3245	133	9	,	,	PUNCT
ejpam-3245	133	10	then	then	ADV
ejpam-3245	133	11	,	,	PUNCT
ejpam-3245	133	12	by	by	ADP
ejpam-3245	133	13	expanding	expand	VERB
ejpam-3245	133	14	a(z	a(z	NOUN
ejpam-3245	133	15	)	)	PUNCT
ejpam-3245	133	16	as	as	ADP
ejpam-3245	133	17	a	a	DET
ejpam-3245	133	18	power	power	NOUN
ejpam-3245	133	19	series	series	NOUN
ejpam-3245	133	20	in	in	ADP
ejpam-3245	133	21	z	z	PROPN
ejpam-3245	133	22	,	,	PUNCT
ejpam-3245	133	23	one	one	PRON
ejpam-3245	133	24	finds	find	VERB
ejpam-3245	133	25	:	:	PUNCT
ejpam-3245	133	26	a(z	a(z	NOUN
ejpam-3245	133	27	)	)	PUNCT
ejpam-3245	133	28	c	c	NOUN
ejpam-3245	134	1	=	=	SYM
ejpam-3245	134	2	1	1	NUM
ejpam-3245	134	3	+	+	CCONJ
ejpam-3245	134	4	c−1	c−1	PROPN
ejpam-3245	134	5	∞∑	∞∑	PROPN
ejpam-3245	134	6	i=1	i=1	X
ejpam-3245	134	7	(	(	PUNCT
ejpam-3245	134	8	d∑	d∑	PROPN
ejpam-3245	134	9	j=1	j=1	PROPN
ejpam-3245	134	10	a	a	DET
ejpam-3245	134	11	(	(	PUNCT
ejpam-3245	134	12	j	j	NOUN
ejpam-3245	134	13	)	)	PUNCT
ejpam-3245	134	14	0	0	NUM
ejpam-3245	134	15	wij	wij	PROPN
ejpam-3245	134	16	(	(	PUNCT
ejpam-3245	134	17	i	i	NOUN
ejpam-3245	134	18	)	)	PUNCT
ejpam-3245	134	19	!	!	PUNCT
ejpam-3245	135	1	+	+	CCONJ
ejpam-3245	135	2	....	....	PUNCT
ejpam-3245	136	1	+	+	CCONJ
ejpam-3245	136	2	a(j)nj	a(j)nj	PROPN
ejpam-3245	136	3	w	w	NOUN
ejpam-3245	136	4	i−nj	i−nj	ADJ
ejpam-3245	136	5	j	j	PROPN
ejpam-3245	136	6	(	(	PUNCT
ejpam-3245	136	7	i−	i−	PROPN
ejpam-3245	136	8	nj	nj	PROPN
ejpam-3245	136	9	)	)	PUNCT
ejpam-3245	136	10	!	!	PUNCT
ejpam-3245	136	11	)	)	PUNCT
ejpam-3245	137	1	zi	zi	NOUN
ejpam-3245	138	1	=	=	NOUN
ejpam-3245	138	2	:	:	PUNCT
ejpam-3245	138	3	1	1	NUM
ejpam-3245	138	4	+	+	CCONJ
ejpam-3245	138	5	∞∑	∞∑	NUM
ejpam-3245	138	6	i=1	i=1	PROPN
ejpam-3245	138	7	miz	miz	PROPN
ejpam-3245	138	8	i.	i.	NOUN
ejpam-3245	138	9	we	we	PRON
ejpam-3245	138	10	have	have	VERB
ejpam-3245	138	11	ord(wj	ord(wj	ADV
ejpam-3245	138	12	)	)	PUNCT
ejpam-3245	138	13	>	>	X
ejpam-3245	138	14	1	1	NUM
ejpam-3245	138	15	p−	p−	NOUN
ejpam-3245	138	16	1	1	NUM
ejpam-3245	138	17	=	=	SYM
ejpam-3245	138	18	i	i	PRON
ejpam-3245	138	19	i(p−	i(p−	VERB
ejpam-3245	138	20	1	1	NUM
ejpam-3245	138	21	)	)	PUNCT
ejpam-3245	138	22	>	>	PUNCT
ejpam-3245	139	1	i−	i−	PROPN
ejpam-3245	139	2	si	si	X
ejpam-3245	139	3	i(p−	i(p−	VERB
ejpam-3245	139	4	1	1	NUM
ejpam-3245	139	5	)	)	PUNCT
ejpam-3245	139	6	,	,	PUNCT
ejpam-3245	139	7	∀i	∀i	NOUN
ejpam-3245	139	8	≥	≥	NOUN
ejpam-3245	139	9	1,∀j	1,∀j	NUM
ejpam-3245	139	10	=	=	SYM
ejpam-3245	139	11	1	1	NUM
ejpam-3245	139	12	,	,	PUNCT
ejpam-3245	139	13	2	2	NUM
ejpam-3245	139	14	,	,	PUNCT
ejpam-3245	139	15	..	..	PUNCT
ejpam-3245	139	16	,	,	PUNCT
ejpam-3245	139	17	d.	d.	PROPN
ejpam-3245	139	18	hence	hence	ADV
ejpam-3245	139	19	,	,	PUNCT
ejpam-3245	139	20	i	i	PRON
ejpam-3245	139	21	ord(wj	ord(wj	ADV
ejpam-3245	139	22	)	)	PUNCT
ejpam-3245	139	23	>	>	X
ejpam-3245	140	1	i−	i−	PROPN
ejpam-3245	140	2	si	si	INTJ
ejpam-3245	140	3	p−	p−	NOUN
ejpam-3245	140	4	1	1	NUM
ejpam-3245	140	5	=	=	SYM
ejpam-3245	140	6	ord(i!)⇒	ord(i!)⇒	NOUN
ejpam-3245	140	7	i	i	PROPN
ejpam-3245	140	8	ord(wj)−	ord(wj)−	PROPN
ejpam-3245	140	9	ord(i	ord(i	PROPN
ejpam-3245	140	10	!	!	PUNCT
ejpam-3245	140	11	)	)	PUNCT
ejpam-3245	140	12	>	>	X
ejpam-3245	141	1	0	0	X
ejpam-3245	141	2	.	.	PUNCT
ejpam-3245	141	3	therefore	therefore	ADV
ejpam-3245	141	4	,	,	PUNCT
ejpam-3245	141	5	ord	ord	PROPN
ejpam-3245	141	6	(	(	PUNCT
ejpam-3245	141	7	wij	wij	PROPN
ejpam-3245	141	8	i	i	PROPN
ejpam-3245	141	9	!	!	PUNCT
ejpam-3245	141	10	)	)	PUNCT
ejpam-3245	142	1	>	>	X
ejpam-3245	143	1	0	0	X
ejpam-3245	143	2	.	.	PUNCT
ejpam-3245	144	1	(	(	PUNCT
ejpam-3245	144	2	3	3	X
ejpam-3245	144	3	)	)	PUNCT
ejpam-3245	144	4	using	use	VERB
ejpam-3245	144	5	(	(	PUNCT
ejpam-3245	144	6	3	3	NUM
ejpam-3245	144	7	)	)	PUNCT
ejpam-3245	144	8	,	,	PUNCT
ejpam-3245	144	9	the	the	DET
ejpam-3245	144	10	assumptions	assumption	NOUN
ejpam-3245	144	11	of	of	ADP
ejpam-3245	144	12	the	the	DET
ejpam-3245	144	13	theorem	theorem	NOUN
ejpam-3245	144	14	that	that	PRON
ejpam-3245	144	15	ord(c	ord(c	PROPN
ejpam-3245	144	16	)	)	PUNCT
ejpam-3245	144	17	=	=	SYM
ejpam-3245	144	18	0	0	NUM
ejpam-3245	144	19	and	and	CCONJ
ejpam-3245	144	20	the	the	DET
ejpam-3245	144	21	coefficients	coefficient	NOUN
ejpam-3245	144	22	of	of	ADP
ejpam-3245	144	23	pj	pj	PROPN
ejpam-3245	144	24	,	,	PUNCT
ejpam-3245	144	25	j	j	PROPN
ejpam-3245	144	26	=	=	SYM
ejpam-3245	144	27	1	1	NUM
ejpam-3245	144	28	,	,	PUNCT
ejpam-3245	144	29	2	2	NUM
ejpam-3245	144	30	,	,	PUNCT
ejpam-3245	144	31	...	...	PUNCT
ejpam-3245	144	32	,	,	PUNCT
ejpam-3245	144	33	d	d	X
ejpam-3245	144	34	are	be	AUX
ejpam-3245	144	35	in	in	ADP
ejpam-3245	144	36	o	o	NOUN
ejpam-3245	144	37	,	,	PUNCT
ejpam-3245	144	38	we	we	PRON
ejpam-3245	144	39	find	find	VERB
ejpam-3245	144	40	that	that	SCONJ
ejpam-3245	144	41	ord(mi	ord(mi	NOUN
ejpam-3245	144	42	)	)	PUNCT
ejpam-3245	144	43	≥	≥	NOUN
ejpam-3245	144	44	0	0	NUM
ejpam-3245	144	45	,	,	PUNCT
ejpam-3245	144	46	i	i	PRON
ejpam-3245	144	47	=	=	NOUN
ejpam-3245	144	48	1	1	NUM
ejpam-3245	144	49	,	,	PUNCT
ejpam-3245	144	50	2	2	NUM
ejpam-3245	144	51	,	,	PUNCT
ejpam-3245	144	52	...	...	PUNCT
ejpam-3245	144	53	that	that	PRON
ejpam-3245	144	54	means	mean	VERB
ejpam-3245	144	55	the	the	DET
ejpam-3245	144	56	points	point	NOUN
ejpam-3245	144	57	(	(	PUNCT
ejpam-3245	144	58	i	i	NOUN
ejpam-3245	144	59	,	,	PUNCT
ejpam-3245	144	60	ord(mi	ord(mi	NOUN
ejpam-3245	144	61	)	)	PUNCT
ejpam-3245	144	62	)	)	PUNCT
ejpam-3245	144	63	,	,	PUNCT
ejpam-3245	144	64	i	i	PRON
ejpam-3245	144	65	=	=	NOUN
ejpam-3245	144	66	1	1	NUM
ejpam-3245	144	67	,	,	PUNCT
ejpam-3245	144	68	2	2	NUM
ejpam-3245	144	69	,	,	PUNCT
ejpam-3245	144	70	..	..	PUNCT
ejpam-3245	144	71	are	be	AUX
ejpam-3245	144	72	on	on	ADP
ejpam-3245	144	73	or	or	CCONJ
ejpam-3245	144	74	above	above	ADP
ejpam-3245	144	75	the	the	DET
ejpam-3245	144	76	x	x	NOUN
ejpam-3245	144	77	-	-	NOUN
ejpam-3245	144	78	axis	axis	NOUN
ejpam-3245	144	79	.	.	PUNCT
ejpam-3245	145	1	consider	consider	VERB
ejpam-3245	145	2	the	the	DET
ejpam-3245	145	3	coefficient	coefficient	NOUN
ejpam-3245	145	4	mnd	mnd	PROPN
ejpam-3245	145	5	in	in	ADP
ejpam-3245	145	6	the	the	DET
ejpam-3245	145	7	series	series	NOUN
ejpam-3245	145	8	a(z	a(z	PROPN
ejpam-3245	145	9	)	)	PUNCT
ejpam-3245	145	10	c	c	NOUN
ejpam-3245	145	11	.	.	PUNCT
ejpam-3245	146	1	the	the	DET
ejpam-3245	146	2	assumption	assumption	NOUN
ejpam-3245	146	3	that	that	SCONJ
ejpam-3245	146	4	ord(and	ord(and	ADV
ejpam-3245	146	5	)	)	PUNCT
ejpam-3245	147	1	=	=	SYM
ejpam-3245	147	2	ord(c	ord(c	PROPN
ejpam-3245	147	3	)	)	PUNCT
ejpam-3245	147	4	=	=	SYM
ejpam-3245	147	5	0	0	NUM
ejpam-3245	148	1	and	and	CCONJ
ejpam-3245	148	2	(	(	PUNCT
ejpam-3245	148	3	3	3	X
ejpam-3245	148	4	)	)	PUNCT
ejpam-3245	148	5	guarantee	guarantee	VERB
ejpam-3245	148	6	that	that	SCONJ
ejpam-3245	148	7	ord(mnd	ord(mnd	NOUN
ejpam-3245	148	8	)	)	PUNCT
ejpam-3245	149	1	=	=	SYM
ejpam-3245	149	2	0	0	X
ejpam-3245	149	3	.	.	X
ejpam-3245	149	4	assume	assume	VERB
ejpam-3245	149	5	that	that	SCONJ
ejpam-3245	149	6	ord(w1	ord(w1	VERB
ejpam-3245	149	7	)	)	PUNCT
ejpam-3245	149	8	=	=	PUNCT
ejpam-3245	149	9	min{ord(wj	min{ord(wj	NOUN
ejpam-3245	149	10	)	)	PUNCT
ejpam-3245	149	11	,	,	PUNCT
ejpam-3245	149	12	j	j	PROPN
ejpam-3245	150	1	=	=	SYM
ejpam-3245	150	2	1	1	NUM
ejpam-3245	150	3	,	,	PUNCT
ejpam-3245	150	4	2	2	NUM
ejpam-3245	150	5	,	,	PUNCT
ejpam-3245	150	6	..	..	PUNCT
ejpam-3245	150	7	,	,	PUNCT
ejpam-3245	150	8	d	d	AUX
ejpam-3245	150	9	}	}	PUNCT
ejpam-3245	150	10	(	(	PUNCT
ejpam-3245	150	11	the	the	DET
ejpam-3245	150	12	other	other	ADJ
ejpam-3245	150	13	cases	case	NOUN
ejpam-3245	150	14	can	can	AUX
ejpam-3245	150	15	be	be	AUX
ejpam-3245	150	16	done	do	VERB
ejpam-3245	150	17	similarly	similarly	ADV
ejpam-3245	150	18	)	)	PUNCT
ejpam-3245	150	19	.	.	PUNCT
ejpam-3245	151	1	therefore	therefore	ADV
ejpam-3245	151	2	,	,	PUNCT
ejpam-3245	151	3	we	we	PRON
ejpam-3245	151	4	have	have	VERB
ejpam-3245	151	5	for	for	ADP
ejpam-3245	151	6	all	all	PRON
ejpam-3245	152	1	i	i	PRON
ejpam-3245	152	2	>	>	X
ejpam-3245	152	3	nd	nd	INTJ
ejpam-3245	152	4	min	min	PROPN
ejpam-3245	152	5	{	{	PUNCT
ejpam-3245	152	6	ord	ord	PROPN
ejpam-3245	152	7	(	(	PUNCT
ejpam-3245	152	8	1	1	NUM
ejpam-3245	152	9	(	(	PUNCT
ejpam-3245	152	10	i−	i−	PROPN
ejpam-3245	152	11	j	j	PROPN
ejpam-3245	152	12	)	)	PUNCT
ejpam-3245	152	13	!	!	PUNCT
ejpam-3245	152	14	)	)	PUNCT
ejpam-3245	153	1	:	:	PUNCT
ejpam-3245	154	1	0	0	NUM
ejpam-3245	154	2	≤	≤	NUM
ejpam-3245	154	3	j	j	PROPN
ejpam-3245	154	4	≤	≤	ADV
ejpam-3245	154	5	nd	nd	ADV
ejpam-3245	154	6	}	}	PUNCT
ejpam-3245	154	7	=	=	SYM
ejpam-3245	154	8	ord	ord	PROPN
ejpam-3245	154	9	(	(	PUNCT
ejpam-3245	154	10	1	1	NUM
ejpam-3245	154	11	i	i	NOUN
ejpam-3245	154	12	!	!	PUNCT
ejpam-3245	154	13	)	)	PUNCT
ejpam-3245	154	14	.	.	PUNCT
ejpam-3245	155	1	hence	hence	ADV
ejpam-3245	155	2	,	,	PUNCT
ejpam-3245	155	3	ord(mi	ord(mi	NOUN
ejpam-3245	155	4	)	)	PUNCT
ejpam-3245	155	5	≥	≥	PROPN
ejpam-3245	155	6	min	min	PROPN
ejpam-3245	155	7	{	{	PUNCT
ejpam-3245	155	8	ord(ord	ord(ord	NOUN
ejpam-3245	155	9	(	(	PUNCT
ejpam-3245	155	10	wi−kj	wi−kj	NOUN
ejpam-3245	155	11	(	(	PUNCT
ejpam-3245	155	12	i−	i−	PROPN
ejpam-3245	155	13	k	k	PROPN
ejpam-3245	155	14	)	)	PUNCT
ejpam-3245	155	15	!	!	PUNCT
ejpam-3245	155	16	)	)	PUNCT
ejpam-3245	155	17	)	)	PUNCT
ejpam-3245	155	18	:	:	PUNCT
ejpam-3245	156	1	j	j	X
ejpam-3245	156	2	=	=	SYM
ejpam-3245	156	3	1	1	NUM
ejpam-3245	156	4	,	,	PUNCT
ejpam-3245	156	5	.	.	PUNCT
ejpam-3245	156	6	.	.	PUNCT
ejpam-3245	157	1	.	.	PUNCT
ejpam-3245	158	1	,	,	PUNCT
ejpam-3245	159	1	d	d	X
ejpam-3245	159	2	,	,	PUNCT
ejpam-3245	159	3	0	0	NUM
ejpam-3245	159	4	≤	≤	NUM
ejpam-3245	159	5	k	k	PROPN
ejpam-3245	159	6	≤	≤	PROPN
ejpam-3245	159	7	nj	nj	PROPN
ejpam-3245	159	8	}	}	PUNCT
ejpam-3245	159	9	≥	≥	PROPN
ejpam-3245	159	10	(	(	PUNCT
ejpam-3245	159	11	i−	i−	PROPN
ejpam-3245	159	12	nd)ord(w1	nd)ord(w1	PROPN
ejpam-3245	159	13	)	)	PUNCT
ejpam-3245	159	14	+	+	CCONJ
ejpam-3245	159	15	ord	ord	NOUN
ejpam-3245	159	16	(	(	PUNCT
ejpam-3245	159	17	1	1	NUM
ejpam-3245	159	18	i	i	NOUN
ejpam-3245	159	19	!	!	PUNCT
ejpam-3245	159	20	)	)	PUNCT
ejpam-3245	159	21	a.	a.	NOUN
ejpam-3245	159	22	dalloul	dalloul	PROPN
ejpam-3245	159	23	/	/	SYM
ejpam-3245	159	24	eur	eur	PROPN
ejpam-3245	159	25	.	.	PUNCT
ejpam-3245	160	1	j.	j.	PROPN
ejpam-3245	160	2	pure	pure	PROPN
ejpam-3245	160	3	appl	appl	PROPN
ejpam-3245	160	4	.	.	PROPN
ejpam-3245	160	5	math	math	PROPN
ejpam-3245	160	6	,	,	PUNCT
ejpam-3245	160	7	11	11	NUM
ejpam-3245	160	8	(	(	PUNCT
ejpam-3245	160	9	3	3	NUM
ejpam-3245	160	10	)	)	PUNCT
ejpam-3245	160	11	(	(	PUNCT
ejpam-3245	160	12	2018	2018	NUM
ejpam-3245	160	13	)	)	PUNCT
ejpam-3245	160	14	,	,	PUNCT
ejpam-3245	160	15	803	803	NUM
ejpam-3245	160	16	-	-	SYM
ejpam-3245	160	17	814	814	NUM
ejpam-3245	160	18	808	808	NUM
ejpam-3245	160	19	figure	figure	NOUN
ejpam-3245	160	20	1	1	NUM
ejpam-3245	160	21	:	:	PUNCT
ejpam-3245	160	22	the	the	DET
ejpam-3245	160	23	newton	newton	PROPN
ejpam-3245	160	24	polygon	polygon	PROPN
ejpam-3245	160	25	of	of	ADP
ejpam-3245	160	26	a(z	a(z	PROPN
ejpam-3245	160	27	)	)	PUNCT
ejpam-3245	160	28	c	c	NOUN
ejpam-3245	160	29	≥	≥	X
ejpam-3245	160	30	(	(	PUNCT
ejpam-3245	160	31	i−	i−	PROPN
ejpam-3245	160	32	nd)ord(w1)−	nd)ord(w1)−	NOUN
ejpam-3245	160	33	i−	i−	PROPN
ejpam-3245	160	34	1	1	NUM
ejpam-3245	160	35	p−	p−	NOUN
ejpam-3245	160	36	1	1	NUM
ejpam-3245	160	37	.	.	PUNCT
ejpam-3245	161	1	therefore	therefore	ADV
ejpam-3245	161	2	,	,	PUNCT
ejpam-3245	161	3	for	for	ADP
ejpam-3245	161	4	all	all	PRON
ejpam-3245	161	5	i	i	PRON
ejpam-3245	161	6	>	>	X
ejpam-3245	161	7	nd	nd	ADP
ejpam-3245	161	8	the	the	DET
ejpam-3245	161	9	points	point	NOUN
ejpam-3245	161	10	(	(	PUNCT
ejpam-3245	161	11	i	i	NOUN
ejpam-3245	161	12	,	,	PUNCT
ejpam-3245	161	13	ord(mi	ord(mi	NOUN
ejpam-3245	161	14	)	)	PUNCT
ejpam-3245	161	15	)	)	PUNCT
ejpam-3245	161	16	are	be	AUX
ejpam-3245	161	17	on	on	ADP
ejpam-3245	161	18	or	or	CCONJ
ejpam-3245	161	19	above	above	ADP
ejpam-3245	161	20	the	the	DET
ejpam-3245	161	21	line	line	NOUN
ejpam-3245	161	22	l	l	NOUN
ejpam-3245	161	23	:	:	PUNCT
ejpam-3245	162	1	y	y	PROPN
ejpam-3245	162	2	+	+	CCONJ
ejpam-3245	162	3	nd.ord(w1)−	nd.ord(w1)−	PROPN
ejpam-3245	162	4	1	1	NUM
ejpam-3245	162	5	p−	p−	NOUN
ejpam-3245	162	6	1	1	NUM
ejpam-3245	162	7	=	=	SYM
ejpam-3245	162	8	(	(	PUNCT
ejpam-3245	162	9	ord(w1)−	ord(w1)−	ADJ
ejpam-3245	162	10	1	1	NUM
ejpam-3245	162	11	p−	p−	NOUN
ejpam-3245	162	12	1	1	NUM
ejpam-3245	162	13	)	)	PUNCT
ejpam-3245	162	14	x.	x.	NOUN
ejpam-3245	162	15	this	this	DET
ejpam-3245	162	16	line	line	NOUN
ejpam-3245	162	17	has	have	VERB
ejpam-3245	162	18	a	a	DET
ejpam-3245	162	19	positive	positive	ADJ
ejpam-3245	162	20	slope	slope	NOUN
ejpam-3245	162	21	λ	λ	NOUN
ejpam-3245	162	22	=	=	NOUN
ejpam-3245	162	23	ord(w1)−	ord(w1)−	VERB
ejpam-3245	162	24	1	1	NUM
ejpam-3245	162	25	p−1	p−1	PROPN
ejpam-3245	162	26	>	>	X
ejpam-3245	162	27	0	0	PUNCT
ejpam-3245	162	28	and	and	CCONJ
ejpam-3245	162	29	intersects	intersect	NOUN
ejpam-3245	162	30	with	with	ADP
ejpam-3245	162	31	the	the	DET
ejpam-3245	162	32	x	x	NOUN
ejpam-3245	162	33	-	-	NOUN
ejpam-3245	162	34	axis	axis	NOUN
ejpam-3245	162	35	in	in	ADP
ejpam-3245	162	36	the	the	DET
ejpam-3245	162	37	point	point	NOUN
ejpam-3245	162	38	(	(	PUNCT
ejpam-3245	162	39	nd.ord(w1)−	nd.ord(w1)−	PUNCT
ejpam-3245	162	40	1	1	X
ejpam-3245	162	41	p−1	p−1	PROPN
ejpam-3245	162	42	ord(w1)−	ord(w1)−	VERB
ejpam-3245	162	43	1	1	NUM
ejpam-3245	162	44	p−1	p−1	PROPN
ejpam-3245	162	45	,	,	PUNCT
ejpam-3245	162	46	0	0	NUM
ejpam-3245	162	47	)	)	PUNCT
ejpam-3245	162	48	which	which	PRON
ejpam-3245	162	49	lies	lie	VERB
ejpam-3245	162	50	on	on	ADP
ejpam-3245	162	51	the	the	DET
ejpam-3245	162	52	right	right	NOUN
ejpam-3245	162	53	of	of	ADP
ejpam-3245	162	54	the	the	DET
ejpam-3245	162	55	point	point	NOUN
ejpam-3245	162	56	(	(	PUNCT
ejpam-3245	162	57	nd	nd	NOUN
ejpam-3245	162	58	,	,	PUNCT
ejpam-3245	162	59	0	0	NUM
ejpam-3245	162	60	)	)	PUNCT
ejpam-3245	162	61	since	since	SCONJ
ejpam-3245	162	62	nd	nd	X
ejpam-3245	162	63	>	>	X
ejpam-3245	162	64	1	1	NUM
ejpam-3245	162	65	.	.	PUNCT
ejpam-3245	163	1	the	the	DET
ejpam-3245	163	2	points	point	NOUN
ejpam-3245	163	3	(	(	PUNCT
ejpam-3245	163	4	i	i	NOUN
ejpam-3245	163	5	,	,	PUNCT
ejpam-3245	163	6	ord(mi	ord(mi	NOUN
ejpam-3245	163	7	)	)	PUNCT
ejpam-3245	163	8	)	)	PUNCT
ejpam-3245	163	9	,	,	PUNCT
ejpam-3245	163	10	i	i	PRON
ejpam-3245	163	11	=	=	NOUN
ejpam-3245	163	12	1	1	NUM
ejpam-3245	163	13	,	,	PUNCT
ejpam-3245	163	14	2	2	NUM
ejpam-3245	163	15	,	,	PUNCT
ejpam-3245	163	16	3	3	NUM
ejpam-3245	163	17	,	,	PUNCT
ejpam-3245	163	18	.	.	PUNCT
ejpam-3245	163	19	.	.	PUNCT
ejpam-3245	164	1	.	.	PUNCT
ejpam-3245	165	1	are	be	AUX
ejpam-3245	165	2	thus	thus	ADV
ejpam-3245	165	3	distributed	distribute	VERB
ejpam-3245	165	4	as	as	SCONJ
ejpam-3245	165	5	follows	follow	VERB
ejpam-3245	165	6	:	:	PUNCT
ejpam-3245	165	7	1	1	X
ejpam-3245	165	8	)	)	PUNCT
ejpam-3245	165	9	the	the	DET
ejpam-3245	165	10	points	point	NOUN
ejpam-3245	165	11	(	(	PUNCT
ejpam-3245	165	12	1	1	NUM
ejpam-3245	165	13	,	,	PUNCT
ejpam-3245	165	14	ord(m1	ord(m1	NOUN
ejpam-3245	165	15	)	)	PUNCT
ejpam-3245	165	16	)	)	PUNCT
ejpam-3245	165	17	,	,	PUNCT
ejpam-3245	165	18	.	.	PUNCT
ejpam-3245	165	19	.	.	PUNCT
ejpam-3245	166	1	.	.	PUNCT
ejpam-3245	167	1	,	,	PUNCT
ejpam-3245	167	2	(	(	PUNCT
ejpam-3245	167	3	nd	nd	ADV
ejpam-3245	167	4	−	−	PROPN
ejpam-3245	167	5	1	1	NUM
ejpam-3245	167	6	,	,	PUNCT
ejpam-3245	167	7	ord(mnd−1	ord(mnd−1	NOUN
ejpam-3245	167	8	)	)	PUNCT
ejpam-3245	167	9	)	)	PUNCT
ejpam-3245	167	10	are	be	AUX
ejpam-3245	167	11	on	on	ADP
ejpam-3245	167	12	or	or	CCONJ
ejpam-3245	167	13	above	above	ADP
ejpam-3245	167	14	the	the	DET
ejpam-3245	167	15	x	x	NOUN
ejpam-3245	167	16	-	-	NOUN
ejpam-3245	167	17	axis	axis	ADJ
ejpam-3245	167	18	.	.	PUNCT
ejpam-3245	168	1	2	2	X
ejpam-3245	168	2	)	)	PUNCT
ejpam-3245	168	3	the	the	DET
ejpam-3245	168	4	point	point	NOUN
ejpam-3245	168	5	(	(	PUNCT
ejpam-3245	168	6	nd	nd	NOUN
ejpam-3245	168	7	,	,	PUNCT
ejpam-3245	168	8	ord(mnd	ord(mnd	NOUN
ejpam-3245	168	9	)	)	PUNCT
ejpam-3245	168	10	)	)	PUNCT
ejpam-3245	168	11	is	be	AUX
ejpam-3245	168	12	on	on	ADP
ejpam-3245	168	13	the	the	DET
ejpam-3245	168	14	x	x	NOUN
ejpam-3245	168	15	-	-	NOUN
ejpam-3245	168	16	axis	axis	ADJ
ejpam-3245	168	17	.	.	PUNCT
ejpam-3245	169	1	3	3	X
ejpam-3245	169	2	)	)	PUNCT
ejpam-3245	169	3	the	the	DET
ejpam-3245	169	4	points	point	NOUN
ejpam-3245	169	5	(	(	PUNCT
ejpam-3245	169	6	i	i	NOUN
ejpam-3245	169	7	,	,	PUNCT
ejpam-3245	169	8	ord(mi	ord(mi	NOUN
ejpam-3245	169	9	)	)	PUNCT
ejpam-3245	169	10	)	)	PUNCT
ejpam-3245	169	11	,	,	PUNCT
ejpam-3245	170	1	i	i	PRON
ejpam-3245	170	2	>	>	X
ejpam-3245	170	3	nd	nd	PRON
ejpam-3245	170	4	are	be	AUX
ejpam-3245	170	5	on	on	ADP
ejpam-3245	170	6	or	or	CCONJ
ejpam-3245	170	7	above	above	ADP
ejpam-3245	170	8	the	the	DET
ejpam-3245	170	9	line	line	NOUN
ejpam-3245	170	10	l	l	NOUN
ejpam-3245	170	11	and	and	CCONJ
ejpam-3245	170	12	above	above	ADP
ejpam-3245	170	13	x	x	NOUN
ejpam-3245	170	14	-	-	NOUN
ejpam-3245	170	15	axis	axis	ADJ
ejpam-3245	170	16	.	.	PUNCT
ejpam-3245	171	1	it	it	PRON
ejpam-3245	171	2	follows	follow	VERB
ejpam-3245	171	3	that	that	SCONJ
ejpam-3245	171	4	there	there	PRON
ejpam-3245	171	5	exists	exist	VERB
ejpam-3245	171	6	a	a	DET
ejpam-3245	171	7	finite	finite	ADJ
ejpam-3245	171	8	number	number	NOUN
ejpam-3245	171	9	of	of	ADP
ejpam-3245	171	10	points	point	NOUN
ejpam-3245	171	11	(	(	PUNCT
ejpam-3245	171	12	i	i	NOUN
ejpam-3245	171	13	,	,	PUNCT
ejpam-3245	171	14	ord(mi	ord(mi	NOUN
ejpam-3245	171	15	)	)	PUNCT
ejpam-3245	171	16	)	)	PUNCT
ejpam-3245	171	17	lying	lie	VERB
ejpam-3245	171	18	on	on	ADP
ejpam-3245	171	19	a	a	DET
ejpam-3245	171	20	horizontal	horizontal	ADJ
ejpam-3245	171	21	line	line	NOUN
ejpam-3245	171	22	above	above	ADP
ejpam-3245	171	23	the	the	DET
ejpam-3245	171	24	x	x	NOUN
ejpam-3245	171	25	-	-	NOUN
ejpam-3245	171	26	axis	axis	NOUN
ejpam-3245	171	27	.	.	PUNCT
ejpam-3245	172	1	now	now	ADV
ejpam-3245	172	2	,	,	PUNCT
ejpam-3245	172	3	we	we	PRON
ejpam-3245	172	4	apply	apply	VERB
ejpam-3245	172	5	the	the	DET
ejpam-3245	172	6	previous	previous	ADJ
ejpam-3245	172	7	steps	step	NOUN
ejpam-3245	172	8	to	to	PART
ejpam-3245	172	9	obtain	obtain	VERB
ejpam-3245	172	10	the	the	DET
ejpam-3245	172	11	newton	newton	PROPN
ejpam-3245	172	12	polygon	polygon	PROPN
ejpam-3245	172	13	of	of	ADP
ejpam-3245	172	14	a(z)c	a(z)c	PROPN
ejpam-3245	172	15	as	as	SCONJ
ejpam-3245	172	16	follows	follow	VERB
ejpam-3245	172	17	:	:	PUNCT
ejpam-3245	172	18	rotate	rotate	VERB
ejpam-3245	172	19	the	the	DET
ejpam-3245	172	20	vertical	vertical	ADJ
ejpam-3245	172	21	half	half	ADJ
ejpam-3245	172	22	-	-	PUNCT
ejpam-3245	172	23	line	line	NOUN
ejpam-3245	172	24	of	of	ADP
ejpam-3245	172	25	the	the	DET
ejpam-3245	172	26	negative	negative	ADJ
ejpam-3245	172	27	part	part	NOUN
ejpam-3245	172	28	of	of	ADP
ejpam-3245	172	29	the	the	DET
ejpam-3245	172	30	y	y	NOUN
ejpam-3245	172	31	-	-	PUNCT
ejpam-3245	172	32	axis	axis	NOUN
ejpam-3245	172	33	until	until	SCONJ
ejpam-3245	172	34	it	it	PRON
ejpam-3245	172	35	hits	hit	VERB
ejpam-3245	172	36	the	the	DET
ejpam-3245	172	37	point	point	NOUN
ejpam-3245	172	38	(	(	PUNCT
ejpam-3245	172	39	nd	nd	NOUN
ejpam-3245	172	40	,	,	PUNCT
ejpam-3245	172	41	0	0	NUM
ejpam-3245	172	42	)	)	PUNCT
ejpam-3245	172	43	.	.	PUNCT
ejpam-3245	173	1	break	break	VERB
ejpam-3245	173	2	the	the	DET
ejpam-3245	173	3	line	line	NOUN
ejpam-3245	173	4	at	at	ADP
ejpam-3245	173	5	this	this	DET
ejpam-3245	173	6	point	point	NOUN
ejpam-3245	173	7	(	(	PUNCT
ejpam-3245	173	8	the	the	DET
ejpam-3245	173	9	existence	existence	NOUN
ejpam-3245	173	10	of	of	ADP
ejpam-3245	173	11	the	the	DET
ejpam-3245	173	12	break	break	NOUN
ejpam-3245	173	13	is	be	AUX
ejpam-3245	173	14	because	because	SCONJ
ejpam-3245	173	15	there	there	PRON
ejpam-3245	173	16	is	be	VERB
ejpam-3245	173	17	at	at	ADP
ejpam-3245	173	18	most	most	ADV
ejpam-3245	173	19	finitely	finitely	ADV
ejpam-3245	173	20	many	many	ADJ
ejpam-3245	173	21	points	point	NOUN
ejpam-3245	173	22	(	(	PUNCT
ejpam-3245	173	23	i	i	NOUN
ejpam-3245	173	24	,	,	PUNCT
ejpam-3245	173	25	ord(mi	ord(mi	NOUN
ejpam-3245	173	26	)	)	PUNCT
ejpam-3245	173	27	)	)	PUNCT
ejpam-3245	173	28	lying	lie	VERB
ejpam-3245	173	29	on	on	ADP
ejpam-3245	173	30	a	a	DET
ejpam-3245	173	31	horizontal	horizontal	ADJ
ejpam-3245	173	32	line	line	NOUN
ejpam-3245	173	33	above	above	ADP
ejpam-3245	173	34	the	the	DET
ejpam-3245	173	35	x	x	NOUN
ejpam-3245	173	36	-	-	NOUN
ejpam-3245	173	37	axis	axis	NOUN
ejpam-3245	173	38	)	)	PUNCT
ejpam-3245	173	39	.	.	PUNCT
ejpam-3245	174	1	rotate	rotate	VERB
ejpam-3245	174	2	it	it	PRON
ejpam-3245	174	3	around	around	ADP
ejpam-3245	174	4	this	this	DET
ejpam-3245	174	5	point	point	NOUN
ejpam-3245	174	6	until	until	SCONJ
ejpam-3245	174	7	it	it	PRON
ejpam-3245	174	8	hits	hit	VERB
ejpam-3245	174	9	another	another	DET
ejpam-3245	174	10	point	point	NOUN
ejpam-3245	174	11	or	or	CCONJ
ejpam-3245	174	12	continues	continue	VERB
ejpam-3245	174	13	until	until	SCONJ
ejpam-3245	174	14	it	it	PRON
ejpam-3245	174	15	reaches	reach	VERB
ejpam-3245	174	16	a	a	DET
ejpam-3245	174	17	position	position	NOUN
ejpam-3245	174	18	parallel	parallel	ADJ
ejpam-3245	174	19	to	to	ADP
ejpam-3245	174	20	a	a	DET
ejpam-3245	174	21	line	line	NOUN
ejpam-3245	174	22	with	with	ADP
ejpam-3245	174	23	a	a	DET
ejpam-3245	174	24	positive	positive	ADJ
ejpam-3245	174	25	slope	slope	NOUN
ejpam-3245	174	26	.	.	PUNCT
ejpam-3245	175	1	in	in	ADP
ejpam-3245	175	2	all	all	DET
ejpam-3245	175	3	cases	case	NOUN
ejpam-3245	175	4	,	,	PUNCT
ejpam-3245	175	5	the	the	DET
ejpam-3245	175	6	newton	newton	PROPN
ejpam-3245	175	7	polygon	polygon	PROPN
ejpam-3245	175	8	of	of	ADP
ejpam-3245	175	9	a(z)c	a(z)c	PROPN
ejpam-3245	175	10	starts	start	VERB
ejpam-3245	175	11	with	with	ADP
ejpam-3245	175	12	a	a	DET
ejpam-3245	175	13	segment	segment	NOUN
ejpam-3245	175	14	of	of	ADP
ejpam-3245	175	15	the	the	DET
ejpam-3245	175	16	length	length	NOUN
ejpam-3245	175	17	nd	nd	ADV
ejpam-3245	175	18	and	and	CCONJ
ejpam-3245	175	19	has	have	VERB
ejpam-3245	175	20	a	a	DET
ejpam-3245	175	21	break	break	NOUN
ejpam-3245	175	22	at	at	ADP
ejpam-3245	175	23	the	the	DET
ejpam-3245	175	24	point	point	NOUN
ejpam-3245	175	25	(	(	PUNCT
ejpam-3245	175	26	nd	nd	NOUN
ejpam-3245	175	27	,	,	PUNCT
ejpam-3245	175	28	0	0	NUM
ejpam-3245	175	29	)	)	PUNCT
ejpam-3245	175	30	(	(	PUNCT
ejpam-3245	175	31	see	see	VERB
ejpam-3245	175	32	figure	figure	NOUN
ejpam-3245	175	33	1	1	NUM
ejpam-3245	175	34	)	)	PUNCT
ejpam-3245	175	35	.	.	PUNCT
ejpam-3245	176	1	therefore	therefore	ADV
ejpam-3245	176	2	,	,	PUNCT
ejpam-3245	176	3	using	use	VERB
ejpam-3245	176	4	fact	fact	NOUN
ejpam-3245	176	5	2	2	NUM
ejpam-3245	176	6	,	,	PUNCT
ejpam-3245	176	7	we	we	PRON
ejpam-3245	176	8	find	find	VERB
ejpam-3245	176	9	that	that	SCONJ
ejpam-3245	176	10	a(z	a(z	NOUN
ejpam-3245	176	11	)	)	PUNCT
ejpam-3245	176	12	c	c	NOUN
ejpam-3245	176	13	(	(	PUNCT
ejpam-3245	176	14	and	and	CCONJ
ejpam-3245	176	15	hence	hence	ADV
ejpam-3245	176	16	a(z	a(z	NOUN
ejpam-3245	176	17	)	)	PUNCT
ejpam-3245	176	18	)	)	PUNCT
ejpam-3245	176	19	has	have	VERB
ejpam-3245	176	20	at	at	ADV
ejpam-3245	176	21	least	least	ADJ
ejpam-3245	176	22	nd	nd	NUM
ejpam-3245	176	23	roots	root	NOUN
ejpam-3245	176	24	.	.	PUNCT
ejpam-3245	177	1	a.	a.	NOUN
ejpam-3245	177	2	dalloul	dalloul	PROPN
ejpam-3245	177	3	/	/	SYM
ejpam-3245	177	4	eur	eur	PROPN
ejpam-3245	177	5	.	.	PUNCT
ejpam-3245	178	1	j.	j.	PROPN
ejpam-3245	178	2	pure	pure	PROPN
ejpam-3245	178	3	appl	appl	PROPN
ejpam-3245	178	4	.	.	PROPN
ejpam-3245	178	5	math	math	PROPN
ejpam-3245	178	6	,	,	PUNCT
ejpam-3245	178	7	11	11	NUM
ejpam-3245	178	8	(	(	PUNCT
ejpam-3245	178	9	3	3	NUM
ejpam-3245	178	10	)	)	PUNCT
ejpam-3245	178	11	(	(	PUNCT
ejpam-3245	178	12	2018	2018	NUM
ejpam-3245	178	13	)	)	PUNCT
ejpam-3245	178	14	,	,	PUNCT
ejpam-3245	178	15	803	803	NUM
ejpam-3245	178	16	-	-	SYM
ejpam-3245	178	17	814	814	NUM
ejpam-3245	178	18	809	809	NUM
ejpam-3245	178	19	remark	remark	NOUN
ejpam-3245	178	20	1	1	NUM
ejpam-3245	178	21	.	.	PUNCT
ejpam-3245	178	22	theorem	theorem	ADJ
ejpam-3245	178	23	2	2	NUM
ejpam-3245	178	24	covers	cover	VERB
ejpam-3245	178	25	only	only	ADV
ejpam-3245	178	26	certain	certain	ADJ
ejpam-3245	178	27	cases	case	NOUN
ejpam-3245	178	28	of	of	ADP
ejpam-3245	178	29	exponential	exponential	ADJ
ejpam-3245	178	30	polynomials	polynomial	NOUN
ejpam-3245	178	31	.	.	PUNCT
ejpam-3245	179	1	the	the	DET
ejpam-3245	179	2	assumption	assumption	NOUN
ejpam-3245	179	3	ord(wj	ord(wj	NOUN
ejpam-3245	179	4	)	)	PUNCT
ejpam-3245	180	1	=	=	PUNCT
ejpam-3245	180	2	0,∀j	0,∀j	NUM
ejpam-3245	181	1	=	=	SYM
ejpam-3245	181	2	1	1	NUM
ejpam-3245	181	3	,	,	PUNCT
ejpam-3245	181	4	2	2	NUM
ejpam-3245	181	5	,	,	PUNCT
ejpam-3245	181	6	..	..	PUNCT
ejpam-3245	181	7	,	,	PUNCT
ejpam-3245	182	1	d	d	X
ejpam-3245	182	2	is	be	AUX
ejpam-3245	182	3	crucial	crucial	ADJ
ejpam-3245	182	4	.	.	PUNCT
ejpam-3245	183	1	in	in	ADP
ejpam-3245	183	2	fact	fact	NOUN
ejpam-3245	183	3	,	,	PUNCT
ejpam-3245	183	4	there	there	PRON
ejpam-3245	183	5	exists	exist	VERB
ejpam-3245	183	6	a	a	DET
ejpam-3245	183	7	very	very	ADV
ejpam-3245	183	8	big	big	ADJ
ejpam-3245	183	9	class	class	NOUN
ejpam-3245	183	10	of	of	ADP
ejpam-3245	183	11	exponential	exponential	ADJ
ejpam-3245	183	12	polynomials	polynomial	NOUN
ejpam-3245	183	13	that	that	PRON
ejpam-3245	183	14	have	have	VERB
ejpam-3245	183	15	no	no	DET
ejpam-3245	183	16	roots	root	NOUN
ejpam-3245	183	17	.	.	PUNCT
ejpam-3245	184	1	for	for	ADP
ejpam-3245	184	2	example	example	NOUN
ejpam-3245	184	3	,	,	PUNCT
ejpam-3245	184	4	the	the	DET
ejpam-3245	184	5	exponential	exponential	ADJ
ejpam-3245	184	6	polynomial	polynomial	NOUN
ejpam-3245	184	7	over	over	ADP
ejpam-3245	184	8	o	o	NOUN
ejpam-3245	184	9	:	:	PUNCT
ejpam-3245	184	10	a(z	a(z	NOUN
ejpam-3245	184	11	)	)	PUNCT
ejpam-3245	184	12	=	=	SYM
ejpam-3245	184	13	a	a	DET
ejpam-3245	184	14	exp(w1z	exp(w1z	PROPN
ejpam-3245	184	15	)	)	PUNCT
ejpam-3245	185	1	+	+	CCONJ
ejpam-3245	185	2	(	(	PUNCT
ejpam-3245	185	3	a1z	a1z	PROPN
ejpam-3245	185	4	+	+	CCONJ
ejpam-3245	185	5	·	·	PUNCT
ejpam-3245	185	6	·	·	PUNCT
ejpam-3245	185	7	·	·	PUNCT
ejpam-3245	185	8	+	+	NUM
ejpam-3245	185	9	anz	anz	PROPN
ejpam-3245	185	10	n	n	CCONJ
ejpam-3245	185	11	)	)	PUNCT
ejpam-3245	185	12	exp(w2z	exp(w2z	PROPN
ejpam-3245	185	13	)	)	PUNCT
ejpam-3245	186	1	+	+	CCONJ
ejpam-3245	186	2	(	(	PUNCT
ejpam-3245	186	3	b1z	b1z	X
ejpam-3245	186	4	+	+	X
ejpam-3245	186	5	·	·	PUNCT
ejpam-3245	186	6	·	·	PUNCT
ejpam-3245	186	7	·	·	PUNCT
ejpam-3245	186	8	+	+	NUM
ejpam-3245	186	9	bmz	bmz	NOUN
ejpam-3245	186	10	m	m	NOUN
ejpam-3245	186	11	)	)	PUNCT
ejpam-3245	186	12	exp(w3z	exp(w3z	PROPN
ejpam-3245	186	13	)	)	PUNCT
ejpam-3245	186	14	,	,	PUNCT
ejpam-3245	186	15	where	where	SCONJ
ejpam-3245	186	16	ord(wj	ord(wj	ADV
ejpam-3245	186	17	)	)	PUNCT
ejpam-3245	186	18	=	=	PUNCT
ejpam-3245	187	1	0,∀j	0,∀j	NOUN
ejpam-3245	188	1	=	=	SYM
ejpam-3245	188	2	1	1	NUM
ejpam-3245	188	3	,	,	PUNCT
ejpam-3245	188	4	2	2	NUM
ejpam-3245	188	5	,	,	PUNCT
ejpam-3245	188	6	3	3	NUM
ejpam-3245	188	7	,	,	PUNCT
ejpam-3245	188	8	.	.	PUNCT
ejpam-3245	188	9	.	.	PUNCT
ejpam-3245	189	1	.	.	PUNCT
ejpam-3245	190	1	,	,	PUNCT
ejpam-3245	190	2	n	n	CCONJ
ejpam-3245	190	3	<	<	X
ejpam-3245	190	4	m	m	PROPN
ejpam-3245	190	5	,	,	PUNCT
ejpam-3245	190	6	has	have	VERB
ejpam-3245	190	7	no	no	DET
ejpam-3245	190	8	roots	root	NOUN
ejpam-3245	190	9	it	it	PRON
ejpam-3245	190	10	its	its	PRON
ejpam-3245	190	11	domain	domain	NOUN
ejpam-3245	190	12	even	even	ADV
ejpam-3245	190	13	if	if	SCONJ
ejpam-3245	190	14	ord(a	ord(a	PROPN
ejpam-3245	190	15	)	)	PUNCT
ejpam-3245	190	16	=	=	SYM
ejpam-3245	190	17	ord(bm	ord(bm	NOUN
ejpam-3245	190	18	)	)	PUNCT
ejpam-3245	190	19	=	=	SYM
ejpam-3245	191	1	0	0	X
ejpam-3245	191	2	.	.	PUNCT
ejpam-3245	192	1	the	the	DET
ejpam-3245	192	2	above	above	ADJ
ejpam-3245	192	3	follows	follow	VERB
ejpam-3245	192	4	since	since	ADV
ejpam-3245	192	5	,	,	PUNCT
ejpam-3245	192	6	if	if	SCONJ
ejpam-3245	192	7	z0	z0	PROPN
ejpam-3245	192	8	∈	∈	PROPN
ejpam-3245	192	9	{	{	PUNCT
ejpam-3245	192	10	z	z	NOUN
ejpam-3245	192	11	∈	∈	PROPN
ejpam-3245	193	1	cp	cp	INTJ
ejpam-3245	193	2	:	:	PUNCT
ejpam-3245	193	3	ord(z	ord(z	X
ejpam-3245	193	4	)	)	PUNCT
ejpam-3245	193	5	>	>	X
ejpam-3245	193	6	1	1	NUM
ejpam-3245	193	7	p−1	p−1	PROPN
ejpam-3245	193	8	}	}	PUNCT
ejpam-3245	193	9	is	be	AUX
ejpam-3245	193	10	a	a	DET
ejpam-3245	193	11	root	root	NOUN
ejpam-3245	193	12	of	of	ADP
ejpam-3245	193	13	a(z	a(z	NOUN
ejpam-3245	193	14	)	)	PUNCT
ejpam-3245	193	15	,	,	PUNCT
ejpam-3245	193	16	then	then	ADV
ejpam-3245	193	17	a	a	DET
ejpam-3245	193	18	exp(w1z0	exp(w1z0	ADJ
ejpam-3245	193	19	)	)	PUNCT
ejpam-3245	193	20	=	=	SYM
ejpam-3245	194	1	−	−	PROPN
ejpam-3245	194	2	(	(	PUNCT
ejpam-3245	194	3	(	(	PUNCT
ejpam-3245	194	4	a1z0	a1z0	X
ejpam-3245	194	5	+	+	X
ejpam-3245	194	6	·	·	PUNCT
ejpam-3245	194	7	·	·	PUNCT
ejpam-3245	194	8	·	·	PUNCT
ejpam-3245	195	1	+	+	NUM
ejpam-3245	195	2	anz	anz	PROPN
ejpam-3245	195	3	n	n	CCONJ
ejpam-3245	195	4	0	0	NUM
ejpam-3245	195	5	)	)	PUNCT
ejpam-3245	195	6	exp(w2z0	exp(w2z0	CCONJ
ejpam-3245	195	7	)	)	PUNCT
ejpam-3245	196	1	+	+	CCONJ
ejpam-3245	196	2	(	(	PUNCT
ejpam-3245	196	3	b1z0	b1z0	X
ejpam-3245	196	4	+	+	X
ejpam-3245	196	5	·	·	PUNCT
ejpam-3245	196	6	·	·	PUNCT
ejpam-3245	196	7	·	·	PUNCT
ejpam-3245	196	8	+	+	NUM
ejpam-3245	196	9	bmz	bmz	NOUN
ejpam-3245	196	10	m	m	NOUN
ejpam-3245	196	11	0	0	NUM
ejpam-3245	196	12	)	)	PUNCT
ejpam-3245	196	13	exp(w3z0	exp(w3z0	PROPN
ejpam-3245	196	14	)	)	PUNCT
ejpam-3245	196	15	)	)	PUNCT
ejpam-3245	196	16	.	.	PUNCT
ejpam-3245	197	1	therefore	therefore	ADV
ejpam-3245	197	2	,	,	PUNCT
ejpam-3245	197	3	|a	|a	VERB
ejpam-3245	197	4	exp(w1z0)|	exp(w1z0)|	X
ejpam-3245	197	5	=	=	SYM
ejpam-3245	197	6	∣∣∣(a1z0	∣∣∣(a1z0	PRON
ejpam-3245	197	7	+	+	X
ejpam-3245	197	8	·	·	PUNCT
ejpam-3245	197	9	·	·	PUNCT
ejpam-3245	197	10	·	·	PUNCT
ejpam-3245	197	11	+	+	NUM
ejpam-3245	197	12	anz	anz	PROPN
ejpam-3245	197	13	n	n	CCONJ
ejpam-3245	197	14	0	0	NUM
ejpam-3245	197	15	)	)	PUNCT
ejpam-3245	197	16	exp(w2z0	exp(w2z0	CCONJ
ejpam-3245	197	17	)	)	PUNCT
ejpam-3245	198	1	+	+	CCONJ
ejpam-3245	198	2	(	(	PUNCT
ejpam-3245	198	3	b1z0	b1z0	X
ejpam-3245	198	4	+	+	X
ejpam-3245	198	5	·	·	PUNCT
ejpam-3245	198	6	·	·	PUNCT
ejpam-3245	198	7	·	·	PUNCT
ejpam-3245	198	8	+	+	NUM
ejpam-3245	198	9	bmz	bmz	NOUN
ejpam-3245	198	10	m	m	NOUN
ejpam-3245	198	11	0	0	NUM
ejpam-3245	198	12	)	)	PUNCT
ejpam-3245	198	13	exp(w3z0	exp(w3z0	PROPN
ejpam-3245	198	14	)	)	PUNCT
ejpam-3245	198	15	∣∣∣	∣∣∣	ADJ
ejpam-3245	198	16	≤	≤	PROPN
ejpam-3245	198	17	max{|(a1z0	max{|(a1z0	PROPN
ejpam-3245	198	18	+	+	CCONJ
ejpam-3245	198	19	·	·	PUNCT
ejpam-3245	198	20	·	·	PUNCT
ejpam-3245	198	21	·	·	PUNCT
ejpam-3245	199	1	+	+	NUM
ejpam-3245	199	2	anz	anz	PROPN
ejpam-3245	199	3	n	n	CCONJ
ejpam-3245	199	4	0	0	NUM
ejpam-3245	199	5	)	)	PUNCT
ejpam-3245	199	6	exp(w2z0)|	exp(w2z0)|	PROPN
ejpam-3245	199	7	,	,	PUNCT
ejpam-3245	199	8	|(b1z0	|(b1z0	ADJ
ejpam-3245	199	9	+	+	X
ejpam-3245	199	10	·	·	PUNCT
ejpam-3245	199	11	·	·	PUNCT
ejpam-3245	199	12	·	·	PUNCT
ejpam-3245	199	13	+	+	NUM
ejpam-3245	199	14	bmz	bmz	NOUN
ejpam-3245	199	15	m	m	NOUN
ejpam-3245	199	16	0	0	NUM
ejpam-3245	199	17	)	)	PUNCT
ejpam-3245	199	18	exp(w3z0)|	exp(w3z0)|	NOUN
ejpam-3245	199	19	}	}	PUNCT
ejpam-3245	199	20	<	<	X
ejpam-3245	199	21	p	p	X
ejpam-3245	199	22	−1	−1	NOUN
ejpam-3245	199	23	p−1	p−1	PROPN
ejpam-3245	199	24	<	<	X
ejpam-3245	199	25	1	1	NUM
ejpam-3245	199	26	,	,	PUNCT
ejpam-3245	199	27	since	since	SCONJ
ejpam-3245	199	28	|	|	ADV
ejpam-3245	199	29	exp(wjz0)|	exp(wjz0)|	VERB
ejpam-3245	199	30	=	=	SYM
ejpam-3245	199	31	1	1	NUM
ejpam-3245	199	32	,	,	PUNCT
ejpam-3245	199	33	j	j	PROPN
ejpam-3245	199	34	=	=	SYM
ejpam-3245	199	35	2	2	NUM
ejpam-3245	199	36	,	,	PUNCT
ejpam-3245	199	37	3	3	NUM
ejpam-3245	199	38	and	and	CCONJ
ejpam-3245	199	39	|z0|	|z0|	NOUN
ejpam-3245	199	40	<	<	X
ejpam-3245	199	41	p	p	X
ejpam-3245	199	42	−1	−1	NOUN
ejpam-3245	199	43	p−1	p−1	NOUN
ejpam-3245	199	44	<	<	X
ejpam-3245	199	45	1	1	NUM
ejpam-3245	199	46	.	.	PUNCT
ejpam-3245	200	1	on	on	ADP
ejpam-3245	200	2	the	the	DET
ejpam-3245	200	3	other	other	ADJ
ejpam-3245	200	4	hand	hand	NOUN
ejpam-3245	200	5	,	,	PUNCT
ejpam-3245	200	6	we	we	PRON
ejpam-3245	200	7	have	have	AUX
ejpam-3245	200	8	|a	|a	VERB
ejpam-3245	200	9	exp(w1z0)|	exp(w1z0)|	PROPN
ejpam-3245	200	10	=	=	SYM
ejpam-3245	201	1	|	|	ADV
ejpam-3245	201	2	exp(w1z0)|	exp(w1z0)|	NOUN
ejpam-3245	201	3	=	=	SYM
ejpam-3245	201	4	1	1	X
ejpam-3245	201	5	.	.	PUNCT
ejpam-3245	202	1	this	this	DET
ejpam-3245	202	2	contradiction	contradiction	NOUN
ejpam-3245	202	3	shows	show	VERB
ejpam-3245	202	4	that	that	SCONJ
ejpam-3245	202	5	a(z	a(z	PROPN
ejpam-3245	202	6	)	)	PUNCT
ejpam-3245	202	7	has	have	VERB
ejpam-3245	202	8	no	no	DET
ejpam-3245	202	9	roots	root	NOUN
ejpam-3245	202	10	in	in	ADP
ejpam-3245	202	11	its	its	PRON
ejpam-3245	202	12	domain	domain	NOUN
ejpam-3245	202	13	.	.	PUNCT
ejpam-3245	203	1	corollary	corollary	ADJ
ejpam-3245	203	2	2	2	NUM
ejpam-3245	203	3	.	.	PUNCT
ejpam-3245	203	4	consider	consider	VERB
ejpam-3245	203	5	the	the	DET
ejpam-3245	203	6	polynomial	polynomial	ADJ
ejpam-3245	203	7	p	p	NOUN
ejpam-3245	204	1	[	[	X
ejpam-3245	204	2	x	x	X
ejpam-3245	204	3	,	,	PUNCT
ejpam-3245	204	4	y	y	PROPN
ejpam-3245	204	5	]	]	PUNCT
ejpam-3245	204	6	=	=	PUNCT
ejpam-3245	204	7	a+	a+	PUNCT
ejpam-3245	205	1	by	by	ADP
ejpam-3245	205	2	m	m	PROPN
ejpam-3245	205	3	+	+	PUNCT
ejpam-3245	205	4	a(i1,j1)x	a(i1,j1)x	NOUN
ejpam-3245	205	5	i1y	i1y	ADJ
ejpam-3245	205	6	j1	j1	NOUN
ejpam-3245	205	7	+	+	CCONJ
ejpam-3245	205	8	·	·	PUNCT
ejpam-3245	205	9	·	·	PUNCT
ejpam-3245	205	10	·	·	PUNCT
ejpam-3245	205	11	+	+	NUM
ejpam-3245	205	12	a(id	a(id	NOUN
ejpam-3245	205	13	,	,	PUNCT
ejpam-3245	205	14	jd)x	jd)x	PROPN
ejpam-3245	205	15	idy	idy	PROPN
ejpam-3245	205	16	jd	jd	PROPN
ejpam-3245	205	17	∈	∈	PROPN
ejpam-3245	205	18	z[x	z[x	PROPN
ejpam-3245	205	19	,	,	PUNCT
ejpam-3245	205	20	y	y	PROPN
ejpam-3245	205	21	]	]	PUNCT
ejpam-3245	205	22	,	,	PUNCT
ejpam-3245	205	23	with	with	ADP
ejpam-3245	205	24	p|	p|	ADV
ejpam-3245	205	25	gcd(m	gcd(m	NOUN
ejpam-3245	205	26	,	,	PUNCT
ejpam-3245	205	27	j1	j1	PROPN
ejpam-3245	205	28	,	,	PUNCT
ejpam-3245	205	29	..	..	PUNCT
ejpam-3245	205	30	,	,	PUNCT
ejpam-3245	205	31	jd	jd	PROPN
ejpam-3245	205	32	)	)	PUNCT
ejpam-3245	205	33	,	,	PUNCT
ejpam-3245	205	34	0	0	NUM
ejpam-3245	205	35	<	<	X
ejpam-3245	205	36	i1	i1	X
ejpam-3245	205	37	<	<	X
ejpam-3245	205	38	·	·	PUNCT
ejpam-3245	205	39	·	·	PUNCT
ejpam-3245	205	40	·	·	PUNCT
ejpam-3245	206	1	<	<	X
ejpam-3245	206	2	i	i	PROPN
ejpam-3245	206	3	d	d	PROPN
ejpam-3245	206	4	,	,	PUNCT
ejpam-3245	206	5	and	and	CCONJ
ejpam-3245	206	6	(	(	PUNCT
ejpam-3245	206	7	a+	a+	X
ejpam-3245	206	8	b	b	PROPN
ejpam-3245	206	9	,	,	PUNCT
ejpam-3245	206	10	p	p	NOUN
ejpam-3245	206	11	)	)	PUNCT
ejpam-3245	206	12	=	=	SYM
ejpam-3245	206	13	(	(	PUNCT
ejpam-3245	206	14	a(id	a(id	PROPN
ejpam-3245	206	15	,	,	PUNCT
ejpam-3245	206	16	jd	jd	PROPN
ejpam-3245	206	17	)	)	PUNCT
ejpam-3245	206	18	,	,	PUNCT
ejpam-3245	206	19	p	p	NOUN
ejpam-3245	206	20	)	)	PUNCT
ejpam-3245	206	21	=	=	SYM
ejpam-3245	206	22	1	1	X
ejpam-3245	206	23	.	.	PUNCT
ejpam-3245	207	1	then	then	ADV
ejpam-3245	207	2	,	,	PUNCT
ejpam-3245	207	3	p	p	NOUN
ejpam-3245	207	4	has	have	VERB
ejpam-3245	207	5	at	at	ADV
ejpam-3245	207	6	least	least	ADJ
ejpam-3245	207	7	i	i	PRON
ejpam-3245	207	8	d	d	ADJ
ejpam-3245	207	9	roots	root	NOUN
ejpam-3245	207	10	of	of	ADP
ejpam-3245	207	11	the	the	DET
ejpam-3245	207	12	form	form	NOUN
ejpam-3245	207	13	(	(	PUNCT
ejpam-3245	207	14	x	x	NOUN
ejpam-3245	207	15	,	,	PUNCT
ejpam-3245	207	16	exp(x	exp(x	PROPN
ejpam-3245	207	17	)	)	PUNCT
ejpam-3245	207	18	)	)	PUNCT
ejpam-3245	207	19	.	.	PUNCT
ejpam-3245	208	1	proof	proof	NOUN
ejpam-3245	208	2	.	.	PUNCT
ejpam-3245	209	1	consider	consider	VERB
ejpam-3245	209	2	the	the	DET
ejpam-3245	209	3	exponential	exponential	ADJ
ejpam-3245	209	4	polynomial	polynomial	ADJ
ejpam-3245	209	5	b(z	b(z	NOUN
ejpam-3245	209	6	)	)	PUNCT
ejpam-3245	210	1	=	=	PUNCT
ejpam-3245	210	2	(	(	PUNCT
ejpam-3245	210	3	a	a	DET
ejpam-3245	210	4	·	·	PUNCT
ejpam-3245	210	5	z0	z0	PROPN
ejpam-3245	210	6	)	)	PUNCT
ejpam-3245	210	7	+	+	CCONJ
ejpam-3245	210	8	(	(	PUNCT
ejpam-3245	210	9	b	b	X
ejpam-3245	210	10	·	·	SYM
ejpam-3245	210	11	z0	z0	PROPN
ejpam-3245	210	12	)	)	PUNCT
ejpam-3245	210	13	exp(mz	exp(mz	NOUN
ejpam-3245	210	14	)	)	PUNCT
ejpam-3245	211	1	+	+	CCONJ
ejpam-3245	211	2	a(i1,j1)z	a(i1,j1)z	PROPN
ejpam-3245	211	3	i1	i1	PROPN
ejpam-3245	211	4	exp	exp	PROPN
ejpam-3245	211	5	(	(	PUNCT
ejpam-3245	211	6	j1z	j1z	PROPN
ejpam-3245	211	7	)	)	PUNCT
ejpam-3245	211	8	+	+	CCONJ
ejpam-3245	211	9	·	·	PUNCT
ejpam-3245	211	10	·	·	PUNCT
ejpam-3245	211	11	·	·	PUNCT
ejpam-3245	211	12	+	+	NUM
ejpam-3245	211	13	a(id	a(id	NOUN
ejpam-3245	211	14	,	,	PUNCT
ejpam-3245	211	15	jd)z	jd)z	PROPN
ejpam-3245	211	16	i	i	PROPN
ejpam-3245	211	17	d	d	PROPN
ejpam-3245	211	18	exp	exp	X
ejpam-3245	211	19	(	(	PUNCT
ejpam-3245	211	20	jdz	jdz	PROPN
ejpam-3245	211	21	)	)	PUNCT
ejpam-3245	211	22	.	.	PUNCT
ejpam-3245	212	1	then	then	ADV
ejpam-3245	212	2	,	,	PUNCT
ejpam-3245	212	3	we	we	PRON
ejpam-3245	212	4	have	have	VERB
ejpam-3245	212	5	ord(m	ord(m	PROPN
ejpam-3245	212	6	)	)	PUNCT
ejpam-3245	212	7	≥	≥	NOUN
ejpam-3245	212	8	1	1	NUM
ejpam-3245	212	9	>	>	SYM
ejpam-3245	212	10	1	1	NUM
ejpam-3245	212	11	p−	p−	NOUN
ejpam-3245	212	12	1	1	NUM
ejpam-3245	212	13	,	,	PUNCT
ejpam-3245	212	14	ord(jk	ord(jk	PROPN
ejpam-3245	212	15	)	)	PUNCT
ejpam-3245	212	16	≥	≥	NOUN
ejpam-3245	212	17	1	1	NUM
ejpam-3245	212	18	>	>	SYM
ejpam-3245	212	19	1	1	NUM
ejpam-3245	212	20	p−	p−	NOUN
ejpam-3245	212	21	1	1	NUM
ejpam-3245	212	22	,	,	PUNCT
ejpam-3245	212	23	k	k	PROPN
ejpam-3245	212	24	=	=	SYM
ejpam-3245	212	25	1	1	NUM
ejpam-3245	212	26	,	,	PUNCT
ejpam-3245	212	27	2	2	NUM
ejpam-3245	212	28	,	,	PUNCT
ejpam-3245	212	29	.	.	PUNCT
ejpam-3245	212	30	.	.	PUNCT
ejpam-3245	212	31	.	.	PUNCT
ejpam-3245	213	1	,	,	PUNCT
ejpam-3245	213	2	d.	d.	PROPN
ejpam-3245	213	3	also	also	ADV
ejpam-3245	213	4	,	,	PUNCT
ejpam-3245	213	5	the	the	DET
ejpam-3245	213	6	polynomial	polynomial	ADJ
ejpam-3245	213	7	pd(z	pd(z	X
ejpam-3245	213	8	)	)	PUNCT
ejpam-3245	213	9	=	=	SYM
ejpam-3245	213	10	a(id	a(id	PROPN
ejpam-3245	213	11	,	,	PUNCT
ejpam-3245	213	12	jd)z	jd)z	PROPN
ejpam-3245	213	13	i	i	PROPN
ejpam-3245	213	14	d	d	PROPN
ejpam-3245	213	15	has	have	VERB
ejpam-3245	213	16	the	the	DET
ejpam-3245	213	17	largest	large	ADJ
ejpam-3245	213	18	degree	degree	NOUN
ejpam-3245	213	19	with	with	ADP
ejpam-3245	213	20	ord(a(id	ord(a(id	NOUN
ejpam-3245	213	21	,	,	PUNCT
ejpam-3245	213	22	jd	jd	PROPN
ejpam-3245	213	23	)	)	PUNCT
ejpam-3245	213	24	)	)	PUNCT
ejpam-3245	214	1	=	=	PUNCT
ejpam-3245	214	2	ord(a+	ord(a+	NOUN
ejpam-3245	214	3	b	b	X
ejpam-3245	214	4	)	)	PUNCT
ejpam-3245	214	5	=	=	SYM
ejpam-3245	214	6	0	0	X
ejpam-3245	214	7	.	.	PUNCT
ejpam-3245	215	1	this	this	PRON
ejpam-3245	215	2	implies	imply	VERB
ejpam-3245	215	3	,	,	PUNCT
ejpam-3245	215	4	by	by	ADP
ejpam-3245	215	5	theorem	theorem	NOUN
ejpam-3245	215	6	2	2	NUM
ejpam-3245	215	7	,	,	PUNCT
ejpam-3245	215	8	that	that	SCONJ
ejpam-3245	215	9	b(z	b(z	NOUN
ejpam-3245	215	10	)	)	PUNCT
ejpam-3245	215	11	has	have	VERB
ejpam-3245	215	12	at	at	ADP
ejpam-3245	215	13	least	least	ADJ
ejpam-3245	215	14	i	i	PRON
ejpam-3245	215	15	d	d	ADJ
ejpam-3245	215	16	roots	root	NOUN
ejpam-3245	215	17	.	.	PUNCT
ejpam-3245	216	1	this	this	PRON
ejpam-3245	216	2	proves	prove	VERB
ejpam-3245	216	3	the	the	DET
ejpam-3245	216	4	corollary	corollary	ADJ
ejpam-3245	216	5	.	.	PUNCT
ejpam-3245	217	1	corollary	corollary	ADJ
ejpam-3245	217	2	3	3	X
ejpam-3245	217	3	.	.	PUNCT
ejpam-3245	218	1	let	let	VERB
ejpam-3245	218	2	p	p	PRON
ejpam-3245	218	3	[	[	X
ejpam-3245	218	4	x	x	X
ejpam-3245	218	5	,	,	PUNCT
ejpam-3245	218	6	y	y	PROPN
ejpam-3245	218	7	]	]	PUNCT
ejpam-3245	218	8	∈	∈	PROPN
ejpam-3245	218	9	q[x	q[x	PROPN
ejpam-3245	218	10	,	,	PUNCT
ejpam-3245	218	11	y	y	PROPN
ejpam-3245	218	12	]	]	PUNCT
ejpam-3245	218	13	be	be	AUX
ejpam-3245	218	14	polynomial	polynomial	ADJ
ejpam-3245	218	15	defined	define	VERB
ejpam-3245	218	16	by	by	ADP
ejpam-3245	218	17	the	the	DET
ejpam-3245	218	18	conditions	condition	NOUN
ejpam-3245	218	19	of	of	ADP
ejpam-3245	218	20	the	the	DET
ejpam-3245	218	21	previous	previous	ADJ
ejpam-3245	218	22	corollary	corollary	NOUN
ejpam-3245	218	23	.	.	PUNCT
ejpam-3245	219	1	then	then	ADV
ejpam-3245	219	2	there	there	PRON
ejpam-3245	219	3	exists	exist	VERB
ejpam-3245	219	4	a	a	DET
ejpam-3245	219	5	tuple	tuple	NOUN
ejpam-3245	219	6	(	(	PUNCT
ejpam-3245	219	7	x	x	NOUN
ejpam-3245	219	8	,	,	PUNCT
ejpam-3245	219	9	exp(x	exp(x	PROPN
ejpam-3245	219	10	)	)	PUNCT
ejpam-3245	219	11	)	)	PUNCT
ejpam-3245	219	12	,	,	PUNCT
ejpam-3245	219	13	x	x	PUNCT
ejpam-3245	219	14	∈	∈	NOUN
ejpam-3245	219	15	e	e	X
ejpam-3245	219	16	(	(	PUNCT
ejpam-3245	219	17	domain	domain	NOUN
ejpam-3245	219	18	of	of	ADP
ejpam-3245	219	19	the	the	DET
ejpam-3245	219	20	exponential	exponential	ADJ
ejpam-3245	219	21	function	function	NOUN
ejpam-3245	219	22	)	)	PUNCT
ejpam-3245	219	23	such	such	ADJ
ejpam-3245	219	24	that	that	SCONJ
ejpam-3245	219	25	p	p	X
ejpam-3245	219	26	(	(	PUNCT
ejpam-3245	219	27	x	x	NOUN
ejpam-3245	219	28	,	,	PUNCT
ejpam-3245	219	29	exp(x	exp(x	PROPN
ejpam-3245	219	30	)	)	PUNCT
ejpam-3245	219	31	)	)	PUNCT
ejpam-3245	220	1	=	=	PUNCT
ejpam-3245	221	1	0	0	X
ejpam-3245	221	2	.	.	PUNCT
ejpam-3245	222	1	in	in	ADP
ejpam-3245	222	2	other	other	ADJ
ejpam-3245	222	3	words	word	NOUN
ejpam-3245	222	4	,	,	PUNCT
ejpam-3245	222	5	the	the	DET
ejpam-3245	222	6	elements	element	NOUN
ejpam-3245	222	7	x	x	SYM
ejpam-3245	222	8	,	,	PUNCT
ejpam-3245	222	9	exp(x	exp(x	PROPN
ejpam-3245	222	10	)	)	PUNCT
ejpam-3245	222	11	are	be	AUX
ejpam-3245	222	12	q−algebraically	q−algebraically	ADV
ejpam-3245	222	13	dependent	dependent	ADJ
ejpam-3245	222	14	.	.	PUNCT
ejpam-3245	223	1	hence	hence	ADV
ejpam-3245	223	2	,	,	PUNCT
ejpam-3245	223	3	tdqq(x	tdqq(x	PROPN
ejpam-3245	223	4	,	,	PUNCT
ejpam-3245	223	5	exp(x	exp(x	PROPN
ejpam-3245	223	6	)	)	PUNCT
ejpam-3245	223	7	)	)	PUNCT
ejpam-3245	224	1	≤	≤	NUM
ejpam-3245	224	2	1	1	NUM
ejpam-3245	224	3	,	,	PUNCT
ejpam-3245	224	4	where	where	SCONJ
ejpam-3245	224	5	td	td	NOUN
ejpam-3245	224	6	stands	stand	VERB
ejpam-3245	224	7	for	for	ADP
ejpam-3245	224	8	the	the	DET
ejpam-3245	224	9	transcendence	transcendence	NOUN
ejpam-3245	224	10	degree	degree	NOUN
ejpam-3245	224	11	.	.	PUNCT
ejpam-3245	224	12	a.	a.	NOUN
ejpam-3245	224	13	dalloul	dalloul	PROPN
ejpam-3245	224	14	/	/	SYM
ejpam-3245	224	15	eur	eur	PROPN
ejpam-3245	224	16	.	.	PUNCT
ejpam-3245	225	1	j.	j.	PROPN
ejpam-3245	225	2	pure	pure	PROPN
ejpam-3245	225	3	appl	appl	PROPN
ejpam-3245	225	4	.	.	PROPN
ejpam-3245	225	5	math	math	PROPN
ejpam-3245	225	6	,	,	PUNCT
ejpam-3245	225	7	11	11	NUM
ejpam-3245	225	8	(	(	PUNCT
ejpam-3245	225	9	3	3	NUM
ejpam-3245	225	10	)	)	PUNCT
ejpam-3245	225	11	(	(	PUNCT
ejpam-3245	225	12	2018	2018	NUM
ejpam-3245	225	13	)	)	PUNCT
ejpam-3245	225	14	,	,	PUNCT
ejpam-3245	225	15	803	803	NUM
ejpam-3245	225	16	-	-	SYM
ejpam-3245	225	17	814	814	NUM
ejpam-3245	225	18	810	810	NUM
ejpam-3245	225	19	4	4	NUM
ejpam-3245	225	20	.	.	PUNCT
ejpam-3245	226	1	further	further	ADJ
ejpam-3245	226	2	applications	application	NOUN
ejpam-3245	226	3	of	of	ADP
ejpam-3245	226	4	the	the	DET
ejpam-3245	226	5	newton	newton	PROPN
ejpam-3245	226	6	polygon	polygon	PROPN
ejpam-3245	226	7	method	method	NOUN
ejpam-3245	226	8	one	one	PRON
ejpam-3245	226	9	can	can	AUX
ejpam-3245	226	10	also	also	ADV
ejpam-3245	226	11	use	use	VERB
ejpam-3245	226	12	the	the	DET
ejpam-3245	226	13	newton	newton	PROPN
ejpam-3245	226	14	polygon	polygon	PROPN
ejpam-3245	226	15	of	of	ADP
ejpam-3245	226	16	power	power	NOUN
ejpam-3245	226	17	series	series	NOUN
ejpam-3245	226	18	in	in	ADP
ejpam-3245	226	19	order	order	NOUN
ejpam-3245	226	20	to	to	PART
ejpam-3245	226	21	obtain	obtain	VERB
ejpam-3245	226	22	sufficient	sufficient	ADJ
ejpam-3245	226	23	conditions	condition	NOUN
ejpam-3245	226	24	on	on	ADP
ejpam-3245	226	25	a	a	DET
ejpam-3245	226	26	polynomial	polynomial	ADJ
ejpam-3245	226	27	p	p	NOUN
ejpam-3245	226	28	[	[	X
ejpam-3245	226	29	x	x	X
ejpam-3245	226	30	,	,	PUNCT
ejpam-3245	226	31	y	y	PROPN
ejpam-3245	226	32	]	]	PUNCT
ejpam-3245	226	33	∈	∈	PROPN
ejpam-3245	226	34	q[x	q[x	PROPN
ejpam-3245	226	35	,	,	PUNCT
ejpam-3245	226	36	y	y	PROPN
ejpam-3245	226	37	]	]	PUNCT
ejpam-3245	226	38	to	to	PART
ejpam-3245	226	39	have	have	VERB
ejpam-3245	226	40	roots	root	NOUN
ejpam-3245	226	41	of	of	ADP
ejpam-3245	226	42	the	the	DET
ejpam-3245	226	43	form	form	NOUN
ejpam-3245	226	44	(	(	PUNCT
ejpam-3245	226	45	x	x	NOUN
ejpam-3245	226	46	,	,	PUNCT
ejpam-3245	226	47	exp(x	exp(x	PROPN
ejpam-3245	226	48	)	)	PUNCT
ejpam-3245	226	49	)	)	PUNCT
ejpam-3245	226	50	,	,	PUNCT
ejpam-3245	226	51	as	as	SCONJ
ejpam-3245	226	52	done	do	VERB
ejpam-3245	226	53	in	in	ADP
ejpam-3245	226	54	what	what	PRON
ejpam-3245	226	55	follows	follow	VERB
ejpam-3245	226	56	.	.	PUNCT
ejpam-3245	227	1	theorem	theorem	NOUN
ejpam-3245	227	2	3	3	NUM
ejpam-3245	227	3	.	.	X
ejpam-3245	227	4	for	for	ADP
ejpam-3245	227	5	any	any	DET
ejpam-3245	227	6	polynomial	polynomial	ADJ
ejpam-3245	227	7	p	p	NOUN
ejpam-3245	228	1	[	[	X
ejpam-3245	228	2	x	x	X
ejpam-3245	228	3	,	,	PUNCT
ejpam-3245	228	4	y	y	PROPN
ejpam-3245	228	5	]	]	PUNCT
ejpam-3245	228	6	having	have	VERB
ejpam-3245	228	7	the	the	DET
ejpam-3245	228	8	form	form	NOUN
ejpam-3245	228	9	p	p	X
ejpam-3245	229	1	[	[	X
ejpam-3245	229	2	x	x	X
ejpam-3245	229	3	,	,	PUNCT
ejpam-3245	229	4	y	y	PROPN
ejpam-3245	229	5	]	]	PUNCT
ejpam-3245	229	6	=	=	PUNCT
ejpam-3245	229	7	dy	dy	NOUN
ejpam-3245	229	8	n	n	NOUN
ejpam-3245	229	9	+	+	CCONJ
ejpam-3245	229	10	cxm	cxm	PROPN
ejpam-3245	229	11	+	+	CCONJ
ejpam-3245	229	12	c1x	c1x	PROPN
ejpam-3245	229	13	m1y	m1y	PUNCT
ejpam-3245	229	14	n1	n1	PROPN
ejpam-3245	229	15	+	+	CCONJ
ejpam-3245	229	16	·	·	PUNCT
ejpam-3245	229	17	·	·	PUNCT
ejpam-3245	229	18	·	·	PUNCT
ejpam-3245	230	1	+	+	NUM
ejpam-3245	230	2	crx	crx	PROPN
ejpam-3245	230	3	mry	mry	PROPN
ejpam-3245	230	4	nr	nr	PROPN
ejpam-3245	230	5	∈	∈	PROPN
ejpam-3245	230	6	q[x	q[x	PROPN
ejpam-3245	230	7	,	,	PUNCT
ejpam-3245	230	8	y	y	PROPN
ejpam-3245	230	9	]	]	PUNCT
ejpam-3245	230	10	,	,	PUNCT
ejpam-3245	230	11	with	with	ADP
ejpam-3245	230	12	mi	mi	PROPN
ejpam-3245	230	13	,	,	PUNCT
ejpam-3245	230	14	m	m	PROPN
ejpam-3245	230	15	,	,	PUNCT
ejpam-3245	230	16	n	n	CCONJ
ejpam-3245	230	17	,	,	PUNCT
ejpam-3245	230	18	ni	ni	PROPN
ejpam-3245	230	19	∈	∈	PROPN
ejpam-3245	230	20	z≥1	z≥1	PROPN
ejpam-3245	230	21	,	,	PUNCT
ejpam-3245	230	22	(	(	PUNCT
ejpam-3245	230	23	ni	ni	PROPN
ejpam-3245	230	24	,	,	PUNCT
ejpam-3245	230	25	p	p	NOUN
ejpam-3245	230	26	)	)	PUNCT
ejpam-3245	230	27	=	=	SYM
ejpam-3245	230	28	(	(	PUNCT
ejpam-3245	230	29	n	n	X
ejpam-3245	230	30	,	,	PUNCT
ejpam-3245	230	31	p	p	NOUN
ejpam-3245	230	32	)	)	PUNCT
ejpam-3245	230	33	=	=	SYM
ejpam-3245	230	34	1	1	NUM
ejpam-3245	230	35	,	,	PUNCT
ejpam-3245	230	36	ord(d	ord(d	PROPN
ejpam-3245	230	37	)	)	PUNCT
ejpam-3245	230	38	=	=	SYM
ejpam-3245	230	39	ord(ci	ord(ci	NOUN
ejpam-3245	230	40	)	)	PUNCT
ejpam-3245	230	41	=	=	SYM
ejpam-3245	230	42	0	0	NUM
ejpam-3245	230	43	,	,	PUNCT
ejpam-3245	230	44	for	for	ADP
ejpam-3245	230	45	i	i	PROPN
ejpam-3245	230	46	=	=	SYM
ejpam-3245	230	47	1	1	NUM
ejpam-3245	230	48	,	,	PUNCT
ejpam-3245	230	49	2	2	NUM
ejpam-3245	230	50	,	,	PUNCT
ejpam-3245	230	51	.	.	PUNCT
ejpam-3245	230	52	.	.	PUNCT
ejpam-3245	230	53	.	.	PUNCT
ejpam-3245	231	1	r	r	NOUN
ejpam-3245	231	2	,	,	PUNCT
ejpam-3245	231	3	and	and	CCONJ
ejpam-3245	231	4	such	such	ADJ
ejpam-3245	231	5	that	that	DET
ejpam-3245	231	6	ord(c	ord(c	PROPN
ejpam-3245	231	7	)	)	PUNCT
ejpam-3245	231	8	<	<	X
ejpam-3245	231	9	−1	−1	NOUN
ejpam-3245	231	10	p−1	p−1	PROPN
ejpam-3245	231	11	m	m	PROPN
ejpam-3245	231	12	,	,	PUNCT
ejpam-3245	231	13	has	have	VERB
ejpam-3245	231	14	a	a	DET
ejpam-3245	231	15	root	root	NOUN
ejpam-3245	231	16	of	of	ADP
ejpam-3245	231	17	the	the	DET
ejpam-3245	231	18	form	form	NOUN
ejpam-3245	231	19	(	(	PUNCT
ejpam-3245	231	20	x	x	NOUN
ejpam-3245	231	21	,	,	PUNCT
ejpam-3245	231	22	exp(x	exp(x	PROPN
ejpam-3245	231	23	)	)	PUNCT
ejpam-3245	231	24	)	)	PUNCT
ejpam-3245	231	25	,	,	PUNCT
ejpam-3245	231	26	x	x	PUNCT
ejpam-3245	231	27	∈	∈	PROPN
ejpam-3245	231	28	cp	cp	INTJ
ejpam-3245	231	29	with	with	ADP
ejpam-3245	231	30	ord(x	ord(x	PROPN
ejpam-3245	231	31	)	)	PUNCT
ejpam-3245	231	32	>	>	X
ejpam-3245	231	33	1	1	NUM
ejpam-3245	231	34	p−1	p−1	PROPN
ejpam-3245	231	35	.	.	PUNCT
ejpam-3245	232	1	proof	proof	NOUN
ejpam-3245	232	2	.	.	PUNCT
ejpam-3245	233	1	let	let	VERB
ejpam-3245	233	2	f(x	f(x	PROPN
ejpam-3245	233	3	)	)	PUNCT
ejpam-3245	233	4	:	:	PUNCT
ejpam-3245	234	1	=	=	PUNCT
ejpam-3245	234	2	p	p	X
ejpam-3245	235	1	[	[	X
ejpam-3245	235	2	x	x	X
ejpam-3245	235	3	,	,	PUNCT
ejpam-3245	235	4	exp(x	exp(x	PROPN
ejpam-3245	235	5	)	)	PUNCT
ejpam-3245	235	6	]	]	PUNCT
ejpam-3245	235	7	be	be	AUX
ejpam-3245	235	8	the	the	DET
ejpam-3245	235	9	corresponding	corresponding	ADJ
ejpam-3245	235	10	power	power	NOUN
ejpam-3245	235	11	series	series	NOUN
ejpam-3245	235	12	associated	associate	VERB
ejpam-3245	235	13	with	with	ADP
ejpam-3245	235	14	the	the	DET
ejpam-3245	235	15	original	original	ADJ
ejpam-3245	235	16	polynomial	polynomial	ADJ
ejpam-3245	235	17	p	p	X
ejpam-3245	235	18	[	[	X
ejpam-3245	235	19	x	x	X
ejpam-3245	235	20	,	,	PUNCT
ejpam-3245	235	21	y	y	PROPN
ejpam-3245	235	22	]	]	PUNCT
ejpam-3245	235	23	.	.	PUNCT
ejpam-3245	236	1	then	then	ADV
ejpam-3245	236	2	,	,	PUNCT
ejpam-3245	236	3	f(x	f(x	PROPN
ejpam-3245	236	4	)	)	PUNCT
ejpam-3245	236	5	can	can	AUX
ejpam-3245	236	6	be	be	AUX
ejpam-3245	236	7	written	write	VERB
ejpam-3245	236	8	as	as	ADP
ejpam-3245	236	9	f(x	f(x	PROPN
ejpam-3245	236	10	)	)	PUNCT
ejpam-3245	236	11	=	=	PUNCT
ejpam-3245	237	1	d(1	d(1	VERB
ejpam-3245	237	2	+	+	PUNCT
ejpam-3245	237	3	b1x	b1x	PROPN
ejpam-3245	237	4	+	+	X
ejpam-3245	237	5	..	..	PUNCT
ejpam-3245	238	1	+	+	NUM
ejpam-3245	238	2	bm−1x	bm−1x	NOUN
ejpam-3245	238	3	m−1	m−1	PROPN
ejpam-3245	238	4	+	+	CCONJ
ejpam-3245	238	5	(	(	PUNCT
ejpam-3245	238	6	bm	bm	PROPN
ejpam-3245	238	7	+	+	CCONJ
ejpam-3245	238	8	c.d−1)xm	c.d−1)xm	X
ejpam-3245	238	9	+	+	CCONJ
ejpam-3245	238	10	bm+1x	bm+1x	NOUN
ejpam-3245	238	11	m+1	m+1	PRON
ejpam-3245	238	12	+	+	X
ejpam-3245	238	13	.	.	PUNCT
ejpam-3245	238	14	.	.	PUNCT
ejpam-3245	238	15	.	.	PUNCT
ejpam-3245	238	16	)	)	PUNCT
ejpam-3245	238	17	,	,	PUNCT
ejpam-3245	238	18	where	where	SCONJ
ejpam-3245	238	19	bi	bi	NOUN
ejpam-3245	238	20	=	=	PROPN
ejpam-3245	238	21	ni	ni	PROPN
ejpam-3245	238	22	i	i	PROPN
ejpam-3245	238	23	!	!	PUNCT
ejpam-3245	239	1	+	+	CCONJ
ejpam-3245	239	2	e1d	e1d	PROPN
ejpam-3245	239	3	−1	−1	VERB
ejpam-3245	239	4	n	n	CCONJ
ejpam-3245	239	5	i−m1	i−m1	ADV
ejpam-3245	239	6	1	1	NUM
ejpam-3245	239	7	(	(	PUNCT
ejpam-3245	239	8	i−m1	i−m1	NUM
ejpam-3245	239	9	)	)	PUNCT
ejpam-3245	239	10	!	!	PUNCT
ejpam-3245	240	1	+	+	CCONJ
ejpam-3245	240	2	·	·	PUNCT
ejpam-3245	240	3	·	·	PUNCT
ejpam-3245	240	4	·	·	PUNCT
ejpam-3245	240	5	+	+	NUM
ejpam-3245	240	6	erd	erd	PROPN
ejpam-3245	240	7	−1	−1	NOUN
ejpam-3245	240	8	ni−mr	ni−mr	PROPN
ejpam-3245	240	9	r	r	NOUN
ejpam-3245	240	10	(	(	PUNCT
ejpam-3245	240	11	i−mr	i−mr	NOUN
ejpam-3245	240	12	)	)	PUNCT
ejpam-3245	240	13	!	!	PUNCT
ejpam-3245	241	1	;	;	PUNCT
ejpam-3245	241	2	ek	ek	NOUN
ejpam-3245	241	3	=	=	SYM
ejpam-3245	241	4	0	0	NUM
ejpam-3245	241	5	or	or	CCONJ
ejpam-3245	241	6	ck	ck	INTJ
ejpam-3245	241	7	,	,	PUNCT
ejpam-3245	241	8	for	for	ADP
ejpam-3245	241	9	k	k	PROPN
ejpam-3245	241	10	=	=	SYM
ejpam-3245	241	11	0	0	PROPN
ejpam-3245	241	12	,	,	PUNCT
ejpam-3245	241	13	..	..	PUNCT
ejpam-3245	241	14	,	,	PUNCT
ejpam-3245	241	15	r.	r.	PROPN
ejpam-3245	241	16	according	accord	VERB
ejpam-3245	241	17	to	to	ADP
ejpam-3245	241	18	the	the	DET
ejpam-3245	241	19	assumption	assumption	NOUN
ejpam-3245	241	20	of	of	ADP
ejpam-3245	241	21	theorem	theorem	NOUN
ejpam-3245	241	22	(	(	PUNCT
ejpam-3245	241	23	the	the	DET
ejpam-3245	241	24	coefficients	coefficient	NOUN
ejpam-3245	241	25	d	d	PROPN
ejpam-3245	241	26	,	,	PUNCT
ejpam-3245	241	27	ci	ci	NOUN
ejpam-3245	241	28	,	,	PUNCT
ejpam-3245	241	29	and	and	CCONJ
ejpam-3245	241	30	the	the	DET
ejpam-3245	241	31	degrees	degree	NOUN
ejpam-3245	241	32	nj	nj	PROPN
ejpam-3245	241	33	have	have	VERB
ejpam-3245	241	34	the	the	DET
ejpam-3245	241	35	same	same	ADJ
ejpam-3245	241	36	order	order	NOUN
ejpam-3245	241	37	which	which	PRON
ejpam-3245	241	38	is	be	AUX
ejpam-3245	241	39	zero	zero	NUM
ejpam-3245	241	40	)	)	PUNCT
ejpam-3245	241	41	and	and	CCONJ
ejpam-3245	241	42	fact	fact	NOUN
ejpam-3245	241	43	(	(	PUNCT
ejpam-3245	241	44	1	1	NUM
ejpam-3245	241	45	)	)	PUNCT
ejpam-3245	241	46	,	,	PUNCT
ejpam-3245	241	47	we	we	PRON
ejpam-3245	241	48	find	find	VERB
ejpam-3245	241	49	that	that	SCONJ
ejpam-3245	241	50	the	the	DET
ejpam-3245	241	51	numbers	number	NOUN
ejpam-3245	241	52	bi	bi	NOUN
ejpam-3245	241	53	satisfy	satisfy	VERB
ejpam-3245	241	54	the	the	DET
ejpam-3245	241	55	inequality	inequality	NOUN
ejpam-3245	241	56	ord(bi	ord(bi	NOUN
ejpam-3245	241	57	)	)	PUNCT
ejpam-3245	241	58	≥	≥	X
ejpam-3245	242	1	−1	−1	NOUN
ejpam-3245	242	2	p−	p−	NOUN
ejpam-3245	242	3	1	1	NUM
ejpam-3245	242	4	(	(	PUNCT
ejpam-3245	242	5	i−	i−	PROPN
ejpam-3245	242	6	1	1	NUM
ejpam-3245	242	7	)	)	PUNCT
ejpam-3245	242	8	.	.	PUNCT
ejpam-3245	243	1	since	since	SCONJ
ejpam-3245	243	2	ord(c	ord(c	PROPN
ejpam-3245	243	3	)	)	PUNCT
ejpam-3245	243	4	<	<	X
ejpam-3245	243	5	−1	−1	NOUN
ejpam-3245	243	6	p−1	p−1	NOUN
ejpam-3245	243	7	m	m	PROPN
ejpam-3245	243	8	<	<	X
ejpam-3245	243	9	−1	−1	NOUN
ejpam-3245	243	10	p−1(m−	p−1(m−	PROPN
ejpam-3245	243	11	1	1	NUM
ejpam-3245	243	12	)	)	PUNCT
ejpam-3245	243	13	,	,	PUNCT
ejpam-3245	243	14	it	it	PRON
ejpam-3245	243	15	follows	follow	VERB
ejpam-3245	243	16	that	that	SCONJ
ejpam-3245	243	17	ord(bm	ord(bm	PRON
ejpam-3245	243	18	+	+	CCONJ
ejpam-3245	243	19	cd−1	cd−1	PROPN
ejpam-3245	243	20	)	)	PUNCT
ejpam-3245	243	21	=	=	PUNCT
ejpam-3245	243	22	min{ord(bm	min{ord(bm	X
ejpam-3245	243	23	)	)	PUNCT
ejpam-3245	243	24	,	,	PUNCT
ejpam-3245	243	25	ord(cd−1	ord(cd−1	PROPN
ejpam-3245	243	26	)	)	PUNCT
ejpam-3245	243	27	}	}	PUNCT
ejpam-3245	243	28	=	=	SYM
ejpam-3245	243	29	ord(c	ord(c	PROPN
ejpam-3245	243	30	)	)	PUNCT
ejpam-3245	243	31	<	<	X
ejpam-3245	243	32	−1	−1	NOUN
ejpam-3245	243	33	p−	p−	NOUN
ejpam-3245	243	34	1	1	NUM
ejpam-3245	243	35	m.	m.	NOUN
ejpam-3245	243	36	also	also	ADV
ejpam-3245	243	37	,	,	PUNCT
ejpam-3245	243	38	if	if	SCONJ
ejpam-3245	243	39	i	i	PRON
ejpam-3245	243	40	is	be	AUX
ejpam-3245	243	41	sufficiently	sufficiently	ADV
ejpam-3245	243	42	large	large	ADJ
ejpam-3245	243	43	index	index	NOUN
ejpam-3245	243	44	of	of	ADP
ejpam-3245	243	45	the	the	DET
ejpam-3245	243	46	form	form	NOUN
ejpam-3245	243	47	pj	pj	PROPN
ejpam-3245	243	48	,	,	PUNCT
ejpam-3245	243	49	then	then	ADV
ejpam-3245	243	50	ord(n	ord(n	NOUN
ejpam-3245	243	51	i	i	X
ejpam-3245	243	52	i	i	PRON
ejpam-3245	243	53	!	!	PUNCT
ejpam-3245	243	54	)	)	PUNCT
ejpam-3245	244	1	=	=	SYM
ejpam-3245	244	2	ord	ord	PROPN
ejpam-3245	244	3	(	(	PUNCT
ejpam-3245	244	4	1	1	NUM
ejpam-3245	244	5	i	i	NOUN
ejpam-3245	244	6	!	!	PUNCT
ejpam-3245	244	7	)	)	PUNCT
ejpam-3245	245	1	=	=	PUNCT
ejpam-3245	246	1	−	−	PROPN
ejpam-3245	246	2	i−1	i−1	PROPN
ejpam-3245	246	3	p−1	p−1	PROPN
ejpam-3245	246	4	.	.	PUNCT
ejpam-3245	247	1	clearly	clearly	ADV
ejpam-3245	247	2	,	,	PUNCT
ejpam-3245	247	3	mk	mk	PROPN
ejpam-3245	247	4	+	+	CCONJ
ejpam-3245	247	5	si−mk	si−mk	PROPN
ejpam-3245	247	6	>	>	X
ejpam-3245	247	7	1,∀k	1,∀k	NUM
ejpam-3245	247	8	=	=	SYM
ejpam-3245	247	9	1	1	NUM
ejpam-3245	247	10	,	,	PUNCT
ejpam-3245	247	11	2	2	NUM
ejpam-3245	247	12	,	,	PUNCT
ejpam-3245	247	13	..	..	PUNCT
ejpam-3245	247	14	,	,	PUNCT
ejpam-3245	247	15	r	r	NOUN
ejpam-3245	247	16	(	(	PUNCT
ejpam-3245	247	17	since	since	SCONJ
ejpam-3245	247	18	sn	sn	PROPN
ejpam-3245	247	19	≥	≥	NUM
ejpam-3245	247	20	1,∀n	1,∀n	NUM
ejpam-3245	247	21	≥	≥	NOUN
ejpam-3245	247	22	1	1	NUM
ejpam-3245	247	23	)	)	PUNCT
ejpam-3245	247	24	.	.	PUNCT
ejpam-3245	248	1	this	this	PRON
ejpam-3245	248	2	is	be	AUX
ejpam-3245	248	3	equivalent	equivalent	ADJ
ejpam-3245	248	4	to	to	ADP
ejpam-3245	248	5	−	−	PROPN
ejpam-3245	249	1	i−1	i−1	PROPN
ejpam-3245	249	2	p−1	p−1	PROPN
ejpam-3245	249	3	<	<	X
ejpam-3245	249	4	−	−	X
ejpam-3245	249	5	i−mk−si−mk	i−mk−si−mk	PROPN
ejpam-3245	249	6	p−1	p−1	PROPN
ejpam-3245	249	7	.	.	PUNCT
ejpam-3245	250	1	in	in	ADP
ejpam-3245	250	2	other	other	ADJ
ejpam-3245	250	3	words	word	NOUN
ejpam-3245	250	4	,	,	PUNCT
ejpam-3245	250	5	ord	ord	PROPN
ejpam-3245	250	6	(	(	PUNCT
ejpam-3245	250	7	1	1	NUM
ejpam-3245	250	8	i	i	NOUN
ejpam-3245	250	9	!	!	PUNCT
ejpam-3245	250	10	)	)	PUNCT
ejpam-3245	251	1	<	<	X
ejpam-3245	251	2	ord	ord	PROPN
ejpam-3245	251	3	(	(	PUNCT
ejpam-3245	251	4	1	1	NUM
ejpam-3245	251	5	(	(	PUNCT
ejpam-3245	251	6	i−mk	i−mk	PROPN
ejpam-3245	251	7	)	)	PUNCT
ejpam-3245	251	8	!	!	PUNCT
ejpam-3245	251	9	)	)	PUNCT
ejpam-3245	251	10	,	,	PUNCT
ejpam-3245	251	11	k	k	NOUN
ejpam-3245	251	12	=	=	SYM
ejpam-3245	251	13	1	1	NUM
ejpam-3245	251	14	,	,	PUNCT
ejpam-3245	251	15	2	2	NUM
ejpam-3245	251	16	,	,	PUNCT
ejpam-3245	251	17	.	.	PUNCT
ejpam-3245	251	18	.	.	PUNCT
ejpam-3245	251	19	.	.	PUNCT
ejpam-3245	252	1	,	,	PUNCT
ejpam-3245	252	2	r.	r.	PROPN
ejpam-3245	252	3	hence	hence	ADV
ejpam-3245	252	4	,	,	PUNCT
ejpam-3245	252	5	ord(bi	ord(bi	NOUN
ejpam-3245	252	6	)	)	PUNCT
ejpam-3245	252	7	=	=	SYM
ejpam-3245	252	8	min	min	PROPN
ejpam-3245	252	9	{	{	PUNCT
ejpam-3245	252	10	ord	ord	PROPN
ejpam-3245	252	11	(	(	PUNCT
ejpam-3245	252	12	ni	ni	PROPN
ejpam-3245	252	13	i	i	PROPN
ejpam-3245	252	14	!	!	PUNCT
ejpam-3245	252	15	)	)	PUNCT
ejpam-3245	252	16	,	,	PUNCT
ejpam-3245	252	17	ord	ord	PROPN
ejpam-3245	252	18	(	(	PUNCT
ejpam-3245	252	19	ni−m1	ni−m1	PROPN
ejpam-3245	252	20	1	1	NUM
ejpam-3245	252	21	(	(	PUNCT
ejpam-3245	252	22	i−m1	i−m1	NUM
ejpam-3245	252	23	)	)	PUNCT
ejpam-3245	252	24	!	!	PUNCT
ejpam-3245	253	1	+	+	CCONJ
ejpam-3245	253	2	...	...	PUNCT
ejpam-3245	254	1	+	+	CCONJ
ejpam-3245	254	2	ni−mr	ni−mr	NOUN
ejpam-3245	254	3	r	r	NOUN
ejpam-3245	254	4	(	(	PUNCT
ejpam-3245	254	5	i−mr	i−mr	NOUN
ejpam-3245	254	6	)	)	PUNCT
ejpam-3245	254	7	!	!	PUNCT
ejpam-3245	254	8	)	)	PUNCT
ejpam-3245	254	9	}	}	PUNCT
ejpam-3245	254	10	=	=	SYM
ejpam-3245	254	11	ord	ord	PROPN
ejpam-3245	254	12	(	(	PUNCT
ejpam-3245	254	13	1	1	NUM
ejpam-3245	254	14	i	i	NOUN
ejpam-3245	254	15	!	!	PUNCT
ejpam-3245	254	16	)	)	PUNCT
ejpam-3245	254	17	.	.	PUNCT
ejpam-3245	255	1	therefore	therefore	ADV
ejpam-3245	255	2	,	,	PUNCT
ejpam-3245	255	3	the	the	DET
ejpam-3245	255	4	points	point	NOUN
ejpam-3245	255	5	of	of	ADP
ejpam-3245	255	6	the	the	DET
ejpam-3245	255	7	power	power	NOUN
ejpam-3245	255	8	series	series	PROPN
ejpam-3245	255	9	f(x	f(x	PROPN
ejpam-3245	255	10	)	)	PUNCT
ejpam-3245	256	1	d	d	NOUN
ejpam-3245	256	2	are	be	AUX
ejpam-3245	256	3	distributed	distribute	VERB
ejpam-3245	256	4	as	as	SCONJ
ejpam-3245	256	5	follows	follow	VERB
ejpam-3245	256	6	(	(	PUNCT
ejpam-3245	256	7	for	for	ADP
ejpam-3245	256	8	more	more	ADJ
ejpam-3245	256	9	details	detail	NOUN
ejpam-3245	256	10	,	,	PUNCT
ejpam-3245	256	11	see	see	VERB
ejpam-3245	256	12	the	the	DET
ejpam-3245	256	13	appendix	appendix	NOUN
ejpam-3245	256	14	):	):	PUNCT
ejpam-3245	256	15	the	the	DET
ejpam-3245	256	16	points	point	NOUN
ejpam-3245	256	17	(	(	PUNCT
ejpam-3245	256	18	i	i	NOUN
ejpam-3245	256	19	,	,	PUNCT
ejpam-3245	256	20	ord(bi	ord(bi	NOUN
ejpam-3245	256	21	)	)	PUNCT
ejpam-3245	256	22	)	)	PUNCT
ejpam-3245	256	23	are	be	AUX
ejpam-3245	256	24	on	on	ADP
ejpam-3245	256	25	or	or	CCONJ
ejpam-3245	256	26	above	above	ADP
ejpam-3245	256	27	the	the	DET
ejpam-3245	256	28	line	line	NOUN
ejpam-3245	256	29	y	y	PROPN
ejpam-3245	256	30	=	=	PUNCT
ejpam-3245	256	31	−1	−1	NOUN
ejpam-3245	256	32	p−1(x−1	p−1(x−1	NOUN
ejpam-3245	256	33	)	)	PUNCT
ejpam-3245	256	34	,	,	PUNCT
ejpam-3245	256	35	the	the	DET
ejpam-3245	256	36	subsequence	subsequence	NOUN
ejpam-3245	256	37	(	(	PUNCT
ejpam-3245	256	38	pi	pi	NOUN
ejpam-3245	256	39	,	,	PUNCT
ejpam-3245	256	40	ord(bpi	ord(bpi	NOUN
ejpam-3245	256	41	)	)	PUNCT
ejpam-3245	256	42	)	)	PUNCT
ejpam-3245	256	43	,	,	PUNCT
ejpam-3245	256	44	for	for	ADP
ejpam-3245	256	45	large	large	ADJ
ejpam-3245	256	46	enough	enough	ADV
ejpam-3245	256	47	i	i	PRON
ejpam-3245	256	48	lies	lie	VERB
ejpam-3245	256	49	on	on	ADP
ejpam-3245	256	50	the	the	DET
ejpam-3245	256	51	previous	previous	ADJ
ejpam-3245	256	52	line	line	NOUN
ejpam-3245	256	53	and	and	CCONJ
ejpam-3245	256	54	the	the	DET
ejpam-3245	256	55	point	point	NOUN
ejpam-3245	256	56	(	(	PUNCT
ejpam-3245	256	57	m	m	NOUN
ejpam-3245	256	58	,	,	PUNCT
ejpam-3245	256	59	ord(bm	ord(bm	NOUN
ejpam-3245	256	60	+	+	CCONJ
ejpam-3245	256	61	d−1c	d−1c	ADJ
ejpam-3245	256	62	)	)	PUNCT
ejpam-3245	256	63	)	)	PUNCT
ejpam-3245	256	64	is	be	AUX
ejpam-3245	256	65	below	below	ADP
ejpam-3245	256	66	the	the	DET
ejpam-3245	256	67	line	line	NOUN
ejpam-3245	257	1	y	y	PROPN
ejpam-3245	257	2	=	=	SYM
ejpam-3245	258	1	−	−	PROPN
ejpam-3245	258	2	1	1	NUM
ejpam-3245	258	3	p−1x	p−1x	NOUN
ejpam-3245	258	4	.	.	PUNCT
ejpam-3245	259	1	a.	a.	NOUN
ejpam-3245	259	2	dalloul	dalloul	PROPN
ejpam-3245	259	3	/	/	SYM
ejpam-3245	259	4	eur	eur	PROPN
ejpam-3245	259	5	.	.	PUNCT
ejpam-3245	260	1	j.	j.	PROPN
ejpam-3245	260	2	pure	pure	PROPN
ejpam-3245	260	3	appl	appl	PROPN
ejpam-3245	260	4	.	.	PROPN
ejpam-3245	260	5	math	math	PROPN
ejpam-3245	260	6	,	,	PUNCT
ejpam-3245	260	7	11	11	NUM
ejpam-3245	260	8	(	(	PUNCT
ejpam-3245	260	9	3	3	NUM
ejpam-3245	260	10	)	)	PUNCT
ejpam-3245	260	11	(	(	PUNCT
ejpam-3245	260	12	2018	2018	NUM
ejpam-3245	260	13	)	)	PUNCT
ejpam-3245	260	14	,	,	PUNCT
ejpam-3245	260	15	803	803	NUM
ejpam-3245	260	16	-	-	SYM
ejpam-3245	260	17	814	814	NUM
ejpam-3245	260	18	811	811	NUM
ejpam-3245	260	19	figure	figure	NOUN
ejpam-3245	260	20	2	2	NUM
ejpam-3245	260	21	:	:	PUNCT
ejpam-3245	260	22	the	the	DET
ejpam-3245	260	23	newton	newton	PROPN
ejpam-3245	260	24	polygon	polygon	PROPN
ejpam-3245	260	25	of	of	ADP
ejpam-3245	260	26	f(x	f(x	PROPN
ejpam-3245	260	27	)	)	PUNCT
ejpam-3245	261	1	d	d	NOUN
ejpam-3245	261	2	now	now	ADV
ejpam-3245	261	3	,	,	PUNCT
ejpam-3245	261	4	we	we	PRON
ejpam-3245	261	5	apply	apply	VERB
ejpam-3245	261	6	the	the	DET
ejpam-3245	261	7	previous	previous	ADJ
ejpam-3245	261	8	steps	step	NOUN
ejpam-3245	261	9	to	to	PART
ejpam-3245	261	10	obtain	obtain	VERB
ejpam-3245	261	11	the	the	DET
ejpam-3245	261	12	newton	newton	PROPN
ejpam-3245	261	13	polygon	polygon	PROPN
ejpam-3245	261	14	of	of	ADP
ejpam-3245	261	15	the	the	DET
ejpam-3245	261	16	power	power	NOUN
ejpam-3245	261	17	series	series	PROPN
ejpam-3245	261	18	f(x	f(x	PROPN
ejpam-3245	261	19	)	)	PUNCT
ejpam-3245	262	1	d	d	NOUN
ejpam-3245	262	2	as	as	SCONJ
ejpam-3245	262	3	follows	follow	VERB
ejpam-3245	262	4	:	:	PUNCT
ejpam-3245	262	5	rotate	rotate	VERB
ejpam-3245	262	6	the	the	DET
ejpam-3245	262	7	vertical	vertical	ADJ
ejpam-3245	262	8	half	half	ADJ
ejpam-3245	262	9	-	-	PUNCT
ejpam-3245	262	10	line	line	NOUN
ejpam-3245	262	11	of	of	ADP
ejpam-3245	262	12	the	the	DET
ejpam-3245	262	13	negative	negative	ADJ
ejpam-3245	262	14	part	part	NOUN
ejpam-3245	262	15	of	of	ADP
ejpam-3245	262	16	the	the	DET
ejpam-3245	262	17	y	y	NOUN
ejpam-3245	262	18	-	-	PUNCT
ejpam-3245	262	19	axis	axis	NOUN
ejpam-3245	262	20	until	until	SCONJ
ejpam-3245	262	21	it	it	PRON
ejpam-3245	262	22	hits	hit	VERB
ejpam-3245	262	23	the	the	DET
ejpam-3245	262	24	point	point	NOUN
ejpam-3245	262	25	(	(	PUNCT
ejpam-3245	262	26	m	m	NOUN
ejpam-3245	262	27	,	,	PUNCT
ejpam-3245	262	28	ord(bm+d−1c	ord(bm+d−1c	ADJ
ejpam-3245	262	29	)	)	PUNCT
ejpam-3245	262	30	)	)	PUNCT
ejpam-3245	262	31	.	.	PUNCT
ejpam-3245	263	1	then	then	ADV
ejpam-3245	263	2	rotate	rotate	VERB
ejpam-3245	263	3	it	it	PRON
ejpam-3245	263	4	around	around	ADP
ejpam-3245	263	5	this	this	DET
ejpam-3245	263	6	point	point	NOUN
ejpam-3245	263	7	until	until	SCONJ
ejpam-3245	263	8	it	it	PRON
ejpam-3245	263	9	reaches	reach	VERB
ejpam-3245	263	10	a	a	DET
ejpam-3245	263	11	position	position	NOUN
ejpam-3245	263	12	parallel	parallel	ADJ
ejpam-3245	263	13	to	to	ADP
ejpam-3245	263	14	the	the	DET
ejpam-3245	263	15	line	line	NOUN
ejpam-3245	264	1	y	y	PROPN
ejpam-3245	264	2	=	=	SYM
ejpam-3245	264	3	−	−	PROPN
ejpam-3245	264	4	1	1	NUM
ejpam-3245	264	5	p−1(x	p−1(x	NOUN
ejpam-3245	264	6	−	−	PROPN
ejpam-3245	264	7	1	1	NUM
ejpam-3245	264	8	)	)	PUNCT
ejpam-3245	264	9	.	.	PUNCT
ejpam-3245	265	1	stop	stop	VERB
ejpam-3245	265	2	here	here	ADV
ejpam-3245	265	3	and	and	CCONJ
ejpam-3245	265	4	the	the	DET
ejpam-3245	265	5	polygon	polygon	NOUN
ejpam-3245	265	6	is	be	AUX
ejpam-3245	265	7	complete	complete	ADJ
ejpam-3245	265	8	.	.	PUNCT
ejpam-3245	266	1	any	any	DET
ejpam-3245	266	2	further	further	ADJ
ejpam-3245	266	3	rotation	rotation	NOUN
ejpam-3245	266	4	would	would	AUX
ejpam-3245	266	5	leave	leave	VERB
ejpam-3245	266	6	behind	behind	ADV
ejpam-3245	266	7	some	some	DET
ejpam-3245	266	8	points	point	NOUN
ejpam-3245	266	9	(	(	PUNCT
ejpam-3245	266	10	i	i	NOUN
ejpam-3245	266	11	,	,	PUNCT
ejpam-3245	266	12	ord(bi	ord(bi	NOUN
ejpam-3245	266	13	)	)	PUNCT
ejpam-3245	266	14	)	)	PUNCT
ejpam-3245	266	15	(	(	PUNCT
ejpam-3245	266	16	see	see	VERB
ejpam-3245	266	17	figure	figure	NOUN
ejpam-3245	266	18	2	2	NUM
ejpam-3245	266	19	and	and	CCONJ
ejpam-3245	266	20	the	the	DET
ejpam-3245	266	21	appendix	appendix	NOUN
ejpam-3245	266	22	)	)	PUNCT
ejpam-3245	266	23	.	.	PUNCT
ejpam-3245	267	1	therefore	therefore	ADV
ejpam-3245	267	2	,	,	PUNCT
ejpam-3245	267	3	the	the	DET
ejpam-3245	267	4	newton	newton	PROPN
ejpam-3245	267	5	polygon	polygon	PROPN
ejpam-3245	267	6	of	of	ADP
ejpam-3245	267	7	f(x	f(x	PROPN
ejpam-3245	267	8	)	)	PUNCT
ejpam-3245	268	1	d	d	NOUN
ejpam-3245	268	2	has	have	VERB
ejpam-3245	268	3	a	a	DET
ejpam-3245	268	4	break	break	NOUN
ejpam-3245	268	5	at	at	ADP
ejpam-3245	268	6	the	the	DET
ejpam-3245	268	7	point	point	NOUN
ejpam-3245	268	8	(	(	PUNCT
ejpam-3245	268	9	m	m	NOUN
ejpam-3245	268	10	,	,	PUNCT
ejpam-3245	268	11	ord(bm	ord(bm	NOUN
ejpam-3245	268	12	+	+	CCONJ
ejpam-3245	268	13	d−1c	d−1c	ADJ
ejpam-3245	268	14	)	)	PUNCT
ejpam-3245	268	15	)	)	PUNCT
ejpam-3245	268	16	.	.	PUNCT
ejpam-3245	269	1	this	this	PRON
ejpam-3245	269	2	implies	imply	VERB
ejpam-3245	269	3	,	,	PUNCT
ejpam-3245	269	4	that	that	SCONJ
ejpam-3245	269	5	the	the	DET
ejpam-3245	269	6	newton	newton	PROPN
ejpam-3245	269	7	polygon	polygon	PROPN
ejpam-3245	269	8	of	of	ADP
ejpam-3245	269	9	f(x	f(x	PROPN
ejpam-3245	269	10	)	)	PUNCT
ejpam-3245	270	1	d	d	PROPN
ejpam-3245	270	2	has	have	VERB
ejpam-3245	270	3	a	a	DET
ejpam-3245	270	4	finite	finite	ADJ
ejpam-3245	270	5	segment	segment	NOUN
ejpam-3245	270	6	of	of	ADP
ejpam-3245	270	7	the	the	DET
ejpam-3245	270	8	length	length	NOUN
ejpam-3245	270	9	m.	m.	NOUN
ejpam-3245	270	10	using	use	VERB
ejpam-3245	270	11	fact	fact	NOUN
ejpam-3245	270	12	2	2	NUM
ejpam-3245	270	13	,	,	PUNCT
ejpam-3245	270	14	f(x	f(x	PROPN
ejpam-3245	270	15	)	)	PUNCT
ejpam-3245	271	1	d	d	NOUN
ejpam-3245	271	2	(	(	PUNCT
ejpam-3245	271	3	and	and	CCONJ
ejpam-3245	271	4	hence	hence	ADV
ejpam-3245	271	5	f	f	X
ejpam-3245	271	6	)	)	PUNCT
ejpam-3245	271	7	has	have	VERB
ejpam-3245	271	8	at	at	ADP
ejpam-3245	271	9	least	least	ADJ
ejpam-3245	271	10	m	m	NOUN
ejpam-3245	271	11	roots	root	NOUN
ejpam-3245	271	12	.	.	PUNCT
ejpam-3245	272	1	so	so	ADV
ejpam-3245	272	2	,	,	PUNCT
ejpam-3245	272	3	the	the	DET
ejpam-3245	272	4	original	original	ADJ
ejpam-3245	272	5	polynomial	polynomial	ADJ
ejpam-3245	272	6	p	p	X
ejpam-3245	273	1	[	[	X
ejpam-3245	273	2	x	x	X
ejpam-3245	273	3	,	,	PUNCT
ejpam-3245	273	4	y	y	PROPN
ejpam-3245	273	5	]	]	PUNCT
ejpam-3245	273	6	has	have	VERB
ejpam-3245	273	7	m	m	PROPN
ejpam-3245	273	8	roots	root	NOUN
ejpam-3245	273	9	in	in	ADP
ejpam-3245	273	10	cp	cp	NUM
ejpam-3245	273	11	×	×	NOUN
ejpam-3245	273	12	c∗p	c∗p	PROPN
ejpam-3245	273	13	of	of	ADP
ejpam-3245	273	14	the	the	DET
ejpam-3245	273	15	form	form	NOUN
ejpam-3245	273	16	(	(	PUNCT
ejpam-3245	273	17	x	x	NOUN
ejpam-3245	273	18	,	,	PUNCT
ejpam-3245	273	19	exp(x	exp(x	PROPN
ejpam-3245	273	20	)	)	PUNCT
ejpam-3245	273	21	)	)	PUNCT
ejpam-3245	273	22	.	.	PUNCT
ejpam-3245	274	1	remark	remark	PROPN
ejpam-3245	274	2	2	2	NUM
ejpam-3245	274	3	.	.	PUNCT
ejpam-3245	274	4	newton	newton	PROPN
ejpam-3245	274	5	polygon	polygon	PROPN
ejpam-3245	274	6	method	method	NOUN
ejpam-3245	274	7	does	do	AUX
ejpam-3245	274	8	not	not	PART
ejpam-3245	274	9	only	only	ADV
ejpam-3245	274	10	guarantee	guarantee	VERB
ejpam-3245	274	11	the	the	DET
ejpam-3245	274	12	existence	existence	NOUN
ejpam-3245	274	13	of	of	ADP
ejpam-3245	274	14	polynomials	polynomial	NOUN
ejpam-3245	274	15	that	that	PRON
ejpam-3245	274	16	admit	admit	VERB
ejpam-3245	274	17	roots	root	NOUN
ejpam-3245	274	18	of	of	ADP
ejpam-3245	274	19	the	the	DET
ejpam-3245	274	20	form	form	NOUN
ejpam-3245	274	21	(	(	PUNCT
ejpam-3245	274	22	x	x	NOUN
ejpam-3245	274	23	,	,	PUNCT
ejpam-3245	274	24	exp(x	exp(x	PROPN
ejpam-3245	274	25	)	)	PUNCT
ejpam-3245	274	26	)	)	PUNCT
ejpam-3245	274	27	,	,	PUNCT
ejpam-3245	274	28	but	but	CCONJ
ejpam-3245	274	29	it	it	PRON
ejpam-3245	274	30	also	also	ADV
ejpam-3245	274	31	gives	give	VERB
ejpam-3245	274	32	us	we	PRON
ejpam-3245	274	33	information	information	NOUN
ejpam-3245	274	34	about	about	ADP
ejpam-3245	274	35	the	the	DET
ejpam-3245	274	36	order	order	NOUN
ejpam-3245	274	37	of	of	ADP
ejpam-3245	274	38	x.	x.	NOUN
ejpam-3245	274	39	example	example	NOUN
ejpam-3245	275	1	1	1	X
ejpam-3245	275	2	.	.	X
ejpam-3245	275	3	consider	consider	VERB
ejpam-3245	275	4	the	the	DET
ejpam-3245	275	5	polynomial	polynomial	ADJ
ejpam-3245	275	6	p	p	NOUN
ejpam-3245	276	1	[	[	X
ejpam-3245	276	2	x	x	X
ejpam-3245	276	3	,	,	PUNCT
ejpam-3245	276	4	y	y	NOUN
ejpam-3245	276	5	]	]	PUNCT
ejpam-3245	276	6	=	=	SYM
ejpam-3245	276	7	p−1x2	p−1x2	X
ejpam-3245	276	8	+	+	CCONJ
ejpam-3245	276	9	y	y	PROPN
ejpam-3245	276	10	2	2	NUM
ejpam-3245	276	11	;	;	PUNCT
ejpam-3245	276	12	p	p	X
ejpam-3245	276	13	>	>	X
ejpam-3245	276	14	5	5	X
ejpam-3245	276	15	.	.	PUNCT
ejpam-3245	277	1	let	let	VERB
ejpam-3245	277	2	f(x	f(x	PROPN
ejpam-3245	277	3	)	)	PUNCT
ejpam-3245	278	1	:	:	PUNCT
ejpam-3245	278	2	=	=	PUNCT
ejpam-3245	278	3	p	p	X
ejpam-3245	279	1	[	[	X
ejpam-3245	279	2	x	x	X
ejpam-3245	279	3	,	,	PUNCT
ejpam-3245	279	4	exp(x	exp(x	PROPN
ejpam-3245	279	5	)	)	PUNCT
ejpam-3245	279	6	]	]	PUNCT
ejpam-3245	279	7	=	=	SYM
ejpam-3245	279	8	p−1x2	p−1x2	X
ejpam-3245	279	9	+	+	CCONJ
ejpam-3245	279	10	(	(	PUNCT
ejpam-3245	279	11	exp(x))2	exp(x))2	NOUN
ejpam-3245	279	12	=	=	PUNCT
ejpam-3245	279	13	p−1x2	p−1x2	NOUN
ejpam-3245	279	14	+	+	CCONJ
ejpam-3245	279	15	exp(2x	exp(2x	PROPN
ejpam-3245	279	16	)	)	PUNCT
ejpam-3245	279	17	.	.	PUNCT
ejpam-3245	280	1	then	then	ADV
ejpam-3245	280	2	we	we	PRON
ejpam-3245	280	3	have	have	VERB
ejpam-3245	280	4	,	,	PUNCT
ejpam-3245	280	5	f(x	f(x	PROPN
ejpam-3245	280	6	)	)	PUNCT
ejpam-3245	280	7	=	=	SYM
ejpam-3245	281	1	1	1	NUM
ejpam-3245	281	2	+	+	NUM
ejpam-3245	281	3	2x	2x	NUM
ejpam-3245	281	4	1	1	NUM
ejpam-3245	281	5	!	!	PUNCT
ejpam-3245	282	1	+	+	CCONJ
ejpam-3245	282	2	(	(	PUNCT
ejpam-3245	282	3	22	22	NUM
ejpam-3245	282	4	2	2	NUM
ejpam-3245	282	5	!	!	PUNCT
ejpam-3245	283	1	+	+	CCONJ
ejpam-3245	284	1	p−1)x2	p−1)x2	NUM
ejpam-3245	284	2	+	+	CCONJ
ejpam-3245	284	3	23	23	NUM
ejpam-3245	284	4	3	3	NUM
ejpam-3245	284	5	!	!	X
ejpam-3245	284	6	x3	x3	VERB
ejpam-3245	284	7	+	+	CCONJ
ejpam-3245	284	8	·	·	PUNCT
ejpam-3245	284	9	·	·	PUNCT
ejpam-3245	284	10	·	·	PUNCT
ejpam-3245	285	1	+	+	NUM
ejpam-3245	285	2	2i	2i	NUM
ejpam-3245	285	3	i	i	PRON
ejpam-3245	285	4	!	!	PUNCT
ejpam-3245	285	5	xi	xi	X
ejpam-3245	286	1	+	+	CCONJ
ejpam-3245	286	2	.	.	PUNCT
ejpam-3245	286	3	.	.	PUNCT
ejpam-3245	286	4	.	.	PUNCT
ejpam-3245	286	5	.	.	PUNCT
ejpam-3245	287	1	a.	a.	NOUN
ejpam-3245	287	2	dalloul	dalloul	PROPN
ejpam-3245	287	3	/	/	SYM
ejpam-3245	287	4	eur	eur	PROPN
ejpam-3245	287	5	.	.	PUNCT
ejpam-3245	288	1	j.	j.	PROPN
ejpam-3245	288	2	pure	pure	PROPN
ejpam-3245	288	3	appl	appl	PROPN
ejpam-3245	288	4	.	.	PROPN
ejpam-3245	288	5	math	math	PROPN
ejpam-3245	288	6	,	,	PUNCT
ejpam-3245	288	7	11	11	NUM
ejpam-3245	288	8	(	(	PUNCT
ejpam-3245	288	9	3	3	NUM
ejpam-3245	288	10	)	)	PUNCT
ejpam-3245	288	11	(	(	PUNCT
ejpam-3245	288	12	2018	2018	NUM
ejpam-3245	288	13	)	)	PUNCT
ejpam-3245	288	14	,	,	PUNCT
ejpam-3245	288	15	803	803	NUM
ejpam-3245	288	16	-	-	SYM
ejpam-3245	288	17	814	814	NUM
ejpam-3245	288	18	812	812	NUM
ejpam-3245	288	19	therefore	therefore	ADV
ejpam-3245	288	20	,	,	PUNCT
ejpam-3245	288	21	ord	ord	PROPN
ejpam-3245	288	22	(	(	PUNCT
ejpam-3245	288	23	2	2	NUM
ejpam-3245	288	24	1	1	NUM
ejpam-3245	288	25	!	!	PUNCT
ejpam-3245	288	26	)	)	PUNCT
ejpam-3245	289	1	=	=	SYM
ejpam-3245	289	2	0	0	NUM
ejpam-3245	289	3	,	,	PUNCT
ejpam-3245	289	4	ord	ord	PROPN
ejpam-3245	289	5	(	(	PUNCT
ejpam-3245	289	6	2i	2i	NUM
ejpam-3245	289	7	i	i	PRON
ejpam-3245	289	8	!	!	PUNCT
ejpam-3245	289	9	)	)	PUNCT
ejpam-3245	290	1	=	=	SYM
ejpam-3245	290	2	ord	ord	PROPN
ejpam-3245	290	3	(	(	PUNCT
ejpam-3245	290	4	1	1	NUM
ejpam-3245	290	5	i	i	NOUN
ejpam-3245	290	6	!	!	PUNCT
ejpam-3245	290	7	)	)	PUNCT
ejpam-3245	290	8	,	,	PUNCT
ejpam-3245	290	9	∀i	∀i	X
ejpam-3245	290	10	>	>	X
ejpam-3245	290	11	3	3	NUM
ejpam-3245	290	12	.	.	PUNCT
ejpam-3245	291	1	this	this	PRON
ejpam-3245	291	2	is	be	AUX
ejpam-3245	291	3	because	because	SCONJ
ejpam-3245	291	4	,	,	PUNCT
ejpam-3245	291	5	ord(2	ord(2	NUM
ejpam-3245	291	6	)	)	PUNCT
ejpam-3245	292	1	=	=	SYM
ejpam-3245	292	2	0	0	NUM
ejpam-3245	293	1	for	for	ADP
ejpam-3245	293	2	p	p	X
ejpam-3245	293	3	>	>	X
ejpam-3245	293	4	5	5	NUM
ejpam-3245	293	5	.	.	PUNCT
ejpam-3245	293	6	furthermore	furthermore	ADV
ejpam-3245	293	7	,	,	PUNCT
ejpam-3245	293	8	we	we	PRON
ejpam-3245	293	9	find	find	VERB
ejpam-3245	293	10	ord	ord	NOUN
ejpam-3245	293	11	(	(	PUNCT
ejpam-3245	293	12	22	22	NUM
ejpam-3245	293	13	2	2	NUM
ejpam-3245	293	14	!	!	PUNCT
ejpam-3245	294	1	+	+	CCONJ
ejpam-3245	294	2	p−1	p−1	NOUN
ejpam-3245	294	3	)	)	PUNCT
ejpam-3245	294	4	=	=	PUNCT
ejpam-3245	294	5	−1	−1	NOUN
ejpam-3245	294	6	.	.	PUNCT
ejpam-3245	295	1	the	the	DET
ejpam-3245	295	2	assumption	assumption	NOUN
ejpam-3245	295	3	p	p	X
ejpam-3245	295	4	>	>	X
ejpam-3245	295	5	5	5	NUM
ejpam-3245	295	6	guarantees	guarantee	VERB
ejpam-3245	295	7	that	that	SCONJ
ejpam-3245	295	8	the	the	DET
ejpam-3245	295	9	point	point	NOUN
ejpam-3245	295	10	(	(	PUNCT
ejpam-3245	295	11	2,−1	2,−1	NUM
ejpam-3245	295	12	)	)	PUNCT
ejpam-3245	295	13	is	be	AUX
ejpam-3245	295	14	below	below	ADP
ejpam-3245	295	15	the	the	DET
ejpam-3245	295	16	line	line	NOUN
ejpam-3245	295	17	y	y	NOUN
ejpam-3245	295	18	=	=	PUNCT
ejpam-3245	295	19	−1	−1	NOUN
ejpam-3245	295	20	p−1x	p−1x	ADV
ejpam-3245	295	21	.	.	PUNCT
ejpam-3245	296	1	this	this	PRON
ejpam-3245	296	2	means	mean	VERB
ejpam-3245	296	3	that	that	SCONJ
ejpam-3245	296	4	the	the	DET
ejpam-3245	296	5	newton	newton	PROPN
ejpam-3245	296	6	polygon	polygon	PROPN
ejpam-3245	296	7	of	of	ADP
ejpam-3245	296	8	f(x	f(x	PROPN
ejpam-3245	296	9	)	)	PUNCT
ejpam-3245	296	10	starts	start	VERB
ejpam-3245	296	11	with	with	ADP
ejpam-3245	296	12	a	a	DET
ejpam-3245	296	13	segment	segment	NOUN
ejpam-3245	296	14	of	of	ADP
ejpam-3245	296	15	the	the	DET
ejpam-3245	296	16	slope	slope	NOUN
ejpam-3245	296	17	(	(	PUNCT
ejpam-3245	296	18	−12	−12	NOUN
ejpam-3245	296	19	)	)	PUNCT
ejpam-3245	296	20	and	and	CCONJ
ejpam-3245	296	21	ends	end	VERB
ejpam-3245	296	22	with	with	ADP
ejpam-3245	296	23	the	the	DET
ejpam-3245	296	24	point	point	NOUN
ejpam-3245	296	25	(	(	PUNCT
ejpam-3245	296	26	2,-1)while	2,-1)while	NOUN
ejpam-3245	296	27	the	the	DET
ejpam-3245	296	28	second	second	ADJ
ejpam-3245	296	29	segment	segment	NOUN
ejpam-3245	296	30	is	be	AUX
ejpam-3245	296	31	a	a	DET
ejpam-3245	296	32	half	half	ADJ
ejpam-3245	296	33	line	line	NOUN
ejpam-3245	296	34	which	which	PRON
ejpam-3245	296	35	starts	start	VERB
ejpam-3245	296	36	with	with	ADP
ejpam-3245	296	37	the	the	DET
ejpam-3245	296	38	point	point	NOUN
ejpam-3245	296	39	(	(	PUNCT
ejpam-3245	296	40	2,-1	2,-1	NUM
ejpam-3245	296	41	)	)	PUNCT
ejpam-3245	296	42	and	and	CCONJ
ejpam-3245	296	43	has	have	VERB
ejpam-3245	296	44	the	the	DET
ejpam-3245	296	45	slope	slope	NOUN
ejpam-3245	296	46	−1	−1	PROPN
ejpam-3245	296	47	p−1	p−1	PROPN
ejpam-3245	296	48	.	.	PUNCT
ejpam-3245	297	1	therefore	therefore	ADV
ejpam-3245	297	2	,	,	PUNCT
ejpam-3245	297	3	the	the	DET
ejpam-3245	297	4	newton	newton	PROPN
ejpam-3245	297	5	polygon	polygon	PROPN
ejpam-3245	297	6	of	of	ADP
ejpam-3245	297	7	f(x	f(x	PROPN
ejpam-3245	297	8	)	)	PUNCT
ejpam-3245	297	9	has	have	VERB
ejpam-3245	297	10	a	a	DET
ejpam-3245	297	11	break	break	NOUN
ejpam-3245	297	12	at	at	ADP
ejpam-3245	297	13	the	the	DET
ejpam-3245	297	14	point	point	NOUN
ejpam-3245	297	15	(	(	PUNCT
ejpam-3245	297	16	2,-1	2,-1	NUM
ejpam-3245	297	17	)	)	PUNCT
ejpam-3245	297	18	.	.	PUNCT
ejpam-3245	298	1	using	use	VERB
ejpam-3245	298	2	fact	fact	NOUN
ejpam-3245	298	3	(	(	PUNCT
ejpam-3245	298	4	2	2	NUM
ejpam-3245	298	5	)	)	PUNCT
ejpam-3245	298	6	,	,	PUNCT
ejpam-3245	298	7	we	we	PRON
ejpam-3245	298	8	find	find	VERB
ejpam-3245	298	9	that	that	SCONJ
ejpam-3245	298	10	the	the	DET
ejpam-3245	298	11	power	power	NOUN
ejpam-3245	298	12	series	series	PROPN
ejpam-3245	298	13	f(x	f(x	PROPN
ejpam-3245	298	14	)	)	PUNCT
ejpam-3245	298	15	has	have	VERB
ejpam-3245	298	16	at	at	ADV
ejpam-3245	298	17	least	least	ADV
ejpam-3245	298	18	two	two	NUM
ejpam-3245	298	19	roots	root	NOUN
ejpam-3245	298	20	of	of	ADP
ejpam-3245	298	21	the	the	DET
ejpam-3245	298	22	order	order	NOUN
ejpam-3245	298	23	1	1	NUM
ejpam-3245	298	24	2	2	NUM
ejpam-3245	298	25	.	.	PUNCT
ejpam-3245	299	1	so	so	ADV
ejpam-3245	299	2	,	,	PUNCT
ejpam-3245	299	3	the	the	DET
ejpam-3245	299	4	original	original	ADJ
ejpam-3245	299	5	polynomial	polynomial	ADJ
ejpam-3245	299	6	p	p	X
ejpam-3245	299	7	[	[	X
ejpam-3245	299	8	x	x	X
ejpam-3245	299	9	,	,	PUNCT
ejpam-3245	299	10	y	y	PROPN
ejpam-3245	299	11	]	]	PUNCT
ejpam-3245	299	12	has	have	VERB
ejpam-3245	299	13	at	at	ADV
ejpam-3245	299	14	least	least	ADV
ejpam-3245	299	15	two	two	NUM
ejpam-3245	299	16	roots	root	NOUN
ejpam-3245	299	17	of	of	ADP
ejpam-3245	299	18	the	the	DET
ejpam-3245	299	19	form	form	NOUN
ejpam-3245	299	20	(	(	PUNCT
ejpam-3245	299	21	x	x	NOUN
ejpam-3245	299	22	,	,	PUNCT
ejpam-3245	299	23	exp(x	exp(x	PROPN
ejpam-3245	299	24	)	)	PUNCT
ejpam-3245	299	25	)	)	PUNCT
ejpam-3245	299	26	.	.	PUNCT
ejpam-3245	300	1	5	5	X
ejpam-3245	300	2	.	.	X
ejpam-3245	300	3	appendix	appendix	VERB
ejpam-3245	300	4	the	the	DET
ejpam-3245	300	5	following	follow	VERB
ejpam-3245	300	6	known	know	VERB
ejpam-3245	300	7	lemma	lemma	PROPN
ejpam-3245	300	8	,	,	PUNCT
ejpam-3245	300	9	(	(	PUNCT
ejpam-3245	300	10	see	see	VERB
ejpam-3245	300	11	,	,	PUNCT
ejpam-3245	300	12	e.g.	e.g.	ADV
ejpam-3245	300	13	,	,	PUNCT
ejpam-3245	300	14	[	[	X
ejpam-3245	300	15	4	4	NUM
ejpam-3245	300	16	]	]	PUNCT
ejpam-3245	300	17	,	,	PUNCT
ejpam-3245	300	18	p.	p.	NOUN
ejpam-3245	300	19	143	143	NUM
ejpam-3245	300	20	)	)	PUNCT
ejpam-3245	300	21	,	,	PUNCT
ejpam-3245	300	22	determines	determine	VERB
ejpam-3245	300	23	the	the	DET
ejpam-3245	300	24	distribution	distribution	NOUN
ejpam-3245	300	25	of	of	ADP
ejpam-3245	300	26	vertices	vertex	NOUN
ejpam-3245	300	27	(	(	PUNCT
ejpam-3245	300	28	i	i	PRON
ejpam-3245	300	29	,	,	PUNCT
ejpam-3245	300	30	ord	ord	PROPN
ejpam-3245	300	31	(	(	PUNCT
ejpam-3245	300	32	1	1	NUM
ejpam-3245	300	33	i	i	NOUN
ejpam-3245	300	34	!	!	PUNCT
ejpam-3245	300	35	)	)	PUNCT
ejpam-3245	300	36	)	)	PUNCT
ejpam-3245	300	37	that	that	PRON
ejpam-3245	300	38	appear	appear	VERB
ejpam-3245	300	39	in	in	ADP
ejpam-3245	300	40	the	the	DET
ejpam-3245	300	41	newton	newton	PROPN
ejpam-3245	300	42	polygon	polygon	PROPN
ejpam-3245	300	43	of	of	ADP
ejpam-3245	300	44	the	the	DET
ejpam-3245	300	45	exponential	exponential	ADJ
ejpam-3245	300	46	map	map	NOUN
ejpam-3245	300	47	.	.	PUNCT
ejpam-3245	301	1	lemma	lemma	PROPN
ejpam-3245	301	2	2	2	NUM
ejpam-3245	301	3	.	.	PUNCT
ejpam-3245	302	1	the	the	DET
ejpam-3245	302	2	newton	newton	PROPN
ejpam-3245	302	3	polygon	polygon	PROPN
ejpam-3245	302	4	of	of	ADP
ejpam-3245	302	5	the	the	DET
ejpam-3245	302	6	exponential	exponential	ADJ
ejpam-3245	302	7	function	function	NOUN
ejpam-3245	302	8	is	be	AUX
ejpam-3245	302	9	a	a	DET
ejpam-3245	302	10	straight	straight	ADJ
ejpam-3245	302	11	line	line	NOUN
ejpam-3245	302	12	from	from	ADP
ejpam-3245	302	13	(	(	PUNCT
ejpam-3245	302	14	0	0	NUM
ejpam-3245	302	15	,	,	PUNCT
ejpam-3245	302	16	0	0	NUM
ejpam-3245	302	17	)	)	PUNCT
ejpam-3245	302	18	with	with	ADP
ejpam-3245	302	19	the	the	DET
ejpam-3245	302	20	slope	slope	NOUN
ejpam-3245	302	21	−1	−1	PROPN
ejpam-3245	302	22	p−1	p−1	PROPN
ejpam-3245	302	23	.	.	PUNCT
ejpam-3245	303	1	proof	proof	NOUN
ejpam-3245	303	2	.	.	PUNCT
ejpam-3245	304	1	we	we	PRON
ejpam-3245	304	2	know	know	VERB
ejpam-3245	304	3	that	that	SCONJ
ejpam-3245	304	4	the	the	DET
ejpam-3245	304	5	exponential	exponential	ADJ
ejpam-3245	304	6	function	function	NOUN
ejpam-3245	304	7	exp(x	exp(x	PROPN
ejpam-3245	304	8	)	)	PUNCT
ejpam-3245	304	9	is	be	AUX
ejpam-3245	304	10	defined	define	VERB
ejpam-3245	304	11	as	as	ADP
ejpam-3245	304	12	exp(x	exp(x	PROPN
ejpam-3245	304	13	)	)	PUNCT
ejpam-3245	304	14	=	=	SYM
ejpam-3245	305	1	1	1	NUM
ejpam-3245	305	2	+	+	CCONJ
ejpam-3245	305	3	x	x	SYM
ejpam-3245	305	4	1	1	NUM
ejpam-3245	305	5	+	+	NUM
ejpam-3245	305	6	x2	x2	PROPN
ejpam-3245	305	7	2	2	NUM
ejpam-3245	305	8	!	!	PUNCT
ejpam-3245	306	1	+	+	CCONJ
ejpam-3245	306	2	·	·	PUNCT
ejpam-3245	306	3	·	·	PUNCT
ejpam-3245	306	4	·	·	PUNCT
ejpam-3245	306	5	+	+	NUM
ejpam-3245	306	6	xi	xi	X
ejpam-3245	306	7	i	i	PRON
ejpam-3245	306	8	!	!	PUNCT
ejpam-3245	307	1	+	+	CCONJ
ejpam-3245	307	2	.	.	PUNCT
ejpam-3245	307	3	.	.	PUNCT
ejpam-3245	308	1	.	.	PUNCT
ejpam-3245	309	1	we	we	PRON
ejpam-3245	309	2	first	first	ADV
ejpam-3245	309	3	show	show	VERB
ejpam-3245	309	4	that	that	SCONJ
ejpam-3245	309	5	,	,	PUNCT
ejpam-3245	309	6	for	for	ADP
ejpam-3245	309	7	all	all	DET
ejpam-3245	309	8	i	i	PRON
ejpam-3245	309	9	>	>	X
ejpam-3245	309	10	0	0	PROPN
ejpam-3245	309	11	,	,	PUNCT
ejpam-3245	309	12	the	the	DET
ejpam-3245	309	13	points	point	NOUN
ejpam-3245	309	14	(	(	PUNCT
ejpam-3245	309	15	pi	pi	NOUN
ejpam-3245	309	16	,	,	PUNCT
ejpam-3245	309	17	ord(api	ord(api	NOUN
ejpam-3245	309	18	)	)	PUNCT
ejpam-3245	309	19	)	)	PUNCT
ejpam-3245	309	20	belong	belong	VERB
ejpam-3245	309	21	to	to	ADP
ejpam-3245	309	22	the	the	DET
ejpam-3245	309	23	line	line	NOUN
ejpam-3245	309	24	y	y	PROPN
ejpam-3245	309	25	=	=	PUNCT
ejpam-3245	309	26	−1	−1	NOUN
ejpam-3245	309	27	p−1(x−1	p−1(x−1	NOUN
ejpam-3245	309	28	)	)	PUNCT
ejpam-3245	309	29	and	and	CCONJ
ejpam-3245	309	30	the	the	DET
ejpam-3245	309	31	other	other	ADJ
ejpam-3245	309	32	points	point	NOUN
ejpam-3245	309	33	are	be	AUX
ejpam-3245	309	34	on	on	ADP
ejpam-3245	309	35	or	or	CCONJ
ejpam-3245	309	36	above	above	ADP
ejpam-3245	309	37	this	this	DET
ejpam-3245	309	38	line	line	NOUN
ejpam-3245	309	39	.	.	PUNCT
ejpam-3245	310	1	that	that	PRON
ejpam-3245	310	2	is	be	AUX
ejpam-3245	310	3	,	,	PUNCT
ejpam-3245	310	4	for	for	ADP
ejpam-3245	310	5	all	all	DET
ejpam-3245	310	6	j	j	PROPN
ejpam-3245	310	7	>	>	X
ejpam-3245	310	8	1	1	NUM
ejpam-3245	310	9	,	,	PUNCT
ejpam-3245	310	10	the	the	DET
ejpam-3245	310	11	points	point	NOUN
ejpam-3245	310	12	(	(	PUNCT
ejpam-3245	310	13	j	j	NOUN
ejpam-3245	310	14	,	,	PUNCT
ejpam-3245	310	15	ord(aj	ord(aj	PROPN
ejpam-3245	310	16	)	)	PUNCT
ejpam-3245	310	17	)	)	PUNCT
ejpam-3245	310	18	are	be	AUX
ejpam-3245	310	19	on	on	ADP
ejpam-3245	310	20	or	or	CCONJ
ejpam-3245	310	21	above	above	ADP
ejpam-3245	310	22	the	the	DET
ejpam-3245	310	23	line	line	NOUN
ejpam-3245	310	24	y	y	PROPN
ejpam-3245	310	25	=	=	PUNCT
ejpam-3245	310	26	−1	−1	NOUN
ejpam-3245	310	27	p−1(x	p−1(x	NOUN
ejpam-3245	310	28	−	−	NOUN
ejpam-3245	310	29	1	1	NUM
ejpam-3245	310	30	)	)	PUNCT
ejpam-3245	310	31	.	.	PUNCT
ejpam-3245	311	1	to	to	PART
ejpam-3245	311	2	do	do	VERB
ejpam-3245	311	3	that	that	PRON
ejpam-3245	311	4	,	,	PUNCT
ejpam-3245	311	5	we	we	PRON
ejpam-3245	311	6	prove	prove	VERB
ejpam-3245	311	7	that	that	SCONJ
ejpam-3245	311	8	the	the	DET
ejpam-3245	311	9	slope	slope	NOUN
ejpam-3245	311	10	of	of	ADP
ejpam-3245	311	11	the	the	DET
ejpam-3245	311	12	line	line	NOUN
ejpam-3245	311	13	which	which	PRON
ejpam-3245	311	14	passes	pass	VERB
ejpam-3245	311	15	through	through	ADP
ejpam-3245	311	16	any	any	DET
ejpam-3245	311	17	two	two	NUM
ejpam-3245	311	18	points	point	NOUN
ejpam-3245	311	19	(	(	PUNCT
ejpam-3245	311	20	pi	pi	NOUN
ejpam-3245	311	21	,	,	PUNCT
ejpam-3245	311	22	ord(api	ord(api	NOUN
ejpam-3245	311	23	)	)	PUNCT
ejpam-3245	311	24	)	)	PUNCT
ejpam-3245	311	25	,	,	PUNCT
ejpam-3245	311	26	(	(	PUNCT
ejpam-3245	311	27	pj	pj	PROPN
ejpam-3245	311	28	,	,	PUNCT
ejpam-3245	311	29	ord(apj	ord(apj	PROPN
ejpam-3245	311	30	)	)	PUNCT
ejpam-3245	311	31	)	)	PUNCT
ejpam-3245	311	32	;	;	PUNCT
ejpam-3245	311	33	(	(	PUNCT
ejpam-3245	311	34	i	i	PRON
ejpam-3245	311	35	>	>	X
ejpam-3245	311	36	j	j	PROPN
ejpam-3245	311	37	)	)	PUNCT
ejpam-3245	311	38	has	have	VERB
ejpam-3245	311	39	a	a	DET
ejpam-3245	311	40	slope	slope	NOUN
ejpam-3245	311	41	independent	independent	ADJ
ejpam-3245	311	42	of	of	ADP
ejpam-3245	311	43	i	i	PROPN
ejpam-3245	311	44	and	and	CCONJ
ejpam-3245	311	45	j	j	PROPN
ejpam-3245	311	46	and	and	CCONJ
ejpam-3245	311	47	indeed	indeed	ADV
ejpam-3245	311	48	has	have	VERB
ejpam-3245	311	49	the	the	DET
ejpam-3245	311	50	value	value	NOUN
ejpam-3245	311	51	−1	−1	NOUN
ejpam-3245	311	52	p−1	p−1	PROPN
ejpam-3245	311	53	.	.	PUNCT
ejpam-3245	312	1	let	let	VERB
ejpam-3245	312	2	m	m	PRON
ejpam-3245	312	3	be	be	AUX
ejpam-3245	312	4	the	the	DET
ejpam-3245	312	5	slope	slope	NOUN
ejpam-3245	312	6	of	of	ADP
ejpam-3245	312	7	the	the	DET
ejpam-3245	312	8	line	line	NOUN
ejpam-3245	312	9	through	through	ADP
ejpam-3245	312	10	any	any	DET
ejpam-3245	312	11	points	point	NOUN
ejpam-3245	312	12	(	(	PUNCT
ejpam-3245	312	13	pi	pi	NOUN
ejpam-3245	312	14	,	,	PUNCT
ejpam-3245	312	15	ord(api	ord(api	NOUN
ejpam-3245	312	16	)	)	PUNCT
ejpam-3245	312	17	)	)	PUNCT
ejpam-3245	312	18	,	,	PUNCT
ejpam-3245	312	19	(	(	PUNCT
ejpam-3245	312	20	pj	pj	PROPN
ejpam-3245	312	21	,	,	PUNCT
ejpam-3245	312	22	ord(apj	ord(apj	PROPN
ejpam-3245	312	23	)	)	PUNCT
ejpam-3245	312	24	)	)	PUNCT
ejpam-3245	312	25	.	.	PUNCT
ejpam-3245	313	1	then	then	ADV
ejpam-3245	313	2	m	m	VERB
ejpam-3245	313	3	=	=	SYM
ejpam-3245	313	4	ord(api)−	ord(api)−	NOUN
ejpam-3245	313	5	ord(apj	ord(apj	NOUN
ejpam-3245	313	6	)	)	PUNCT
ejpam-3245	314	1	pi	pi	NOUN
ejpam-3245	315	1	−	−	PROPN
ejpam-3245	316	1	pj	pj	PROPN
ejpam-3245	316	2	=	=	PUNCT
ejpam-3245	316	3	−ord(pi	−ord(pi	PROPN
ejpam-3245	316	4	!	!	PUNCT
ejpam-3245	316	5	)	)	PUNCT
ejpam-3245	317	1	+	+	CCONJ
ejpam-3245	317	2	ord(pj	ord(pj	NOUN
ejpam-3245	317	3	!	!	PUNCT
ejpam-3245	317	4	)	)	PUNCT
ejpam-3245	318	1	pi	pi	NOUN
ejpam-3245	318	2	−	−	PROPN
ejpam-3245	318	3	pj	pj	PROPN
ejpam-3245	318	4	=	=	PUNCT
ejpam-3245	318	5	ord(pj	ord(pj	PROPN
ejpam-3245	318	6	!	!	PUNCT
ejpam-3245	318	7	)	)	PUNCT
ejpam-3245	319	1	−	−	NOUN
ejpam-3245	319	2	ord(pi	ord(pi	NOUN
ejpam-3245	319	3	!	!	PUNCT
ejpam-3245	319	4	)	)	PUNCT
ejpam-3245	320	1	pi	pi	NOUN
ejpam-3245	320	2	−	−	PROPN
ejpam-3245	320	3	pj	pj	PROPN
ejpam-3245	320	4	=	=	PROPN
ejpam-3245	320	5	pj−s	pj−s	PROPN
ejpam-3245	320	6	pj	pj	PROPN
ejpam-3245	320	7	p−1	p−1	PROPN
ejpam-3245	321	1	−	−	PROPN
ejpam-3245	321	2	pi−spi	pi−spi	PROPN
ejpam-3245	321	3	p−1	p−1	PROPN
ejpam-3245	321	4	pi	pi	NOUN
ejpam-3245	321	5	−	−	PROPN
ejpam-3245	322	1	pj	pj	PROPN
ejpam-3245	322	2	.	.	PUNCT
ejpam-3245	323	1	therefore	therefore	ADV
ejpam-3245	323	2	,	,	PUNCT
ejpam-3245	323	3	m	m	VERB
ejpam-3245	323	4	=	=	NUM
ejpam-3245	323	5	pj−1	pj−1	PROPN
ejpam-3245	323	6	p−1	p−1	PROPN
ejpam-3245	323	7	−	−	PROPN
ejpam-3245	323	8	pi−1	pi−1	PROPN
ejpam-3245	323	9	p−1	p−1	PROPN
ejpam-3245	323	10	pi	pi	NOUN
ejpam-3245	323	11	−	−	PROPN
ejpam-3245	323	12	pj	pj	PROPN
ejpam-3245	323	13	=	=	PUNCT
ejpam-3245	324	1	pj−pi	pj−pi	NOUN
ejpam-3245	324	2	p−1	p−1	PROPN
ejpam-3245	324	3	pi	pi	NOUN
ejpam-3245	324	4	−	−	PROPN
ejpam-3245	324	5	pj	pj	PROPN
ejpam-3245	324	6	=	=	PUNCT
ejpam-3245	324	7	−1	−1	NOUN
ejpam-3245	325	1	p−	p−	NOUN
ejpam-3245	325	2	1	1	NUM
ejpam-3245	325	3	.	.	PUNCT
ejpam-3245	326	1	references	reference	NOUN
ejpam-3245	326	2	813	813	NUM
ejpam-3245	326	3	so	so	ADV
ejpam-3245	326	4	,	,	PUNCT
ejpam-3245	326	5	all	all	DET
ejpam-3245	326	6	the	the	DET
ejpam-3245	326	7	points	point	NOUN
ejpam-3245	326	8	(	(	PUNCT
ejpam-3245	326	9	pi	pi	NOUN
ejpam-3245	326	10	,	,	PUNCT
ejpam-3245	326	11	ord(api	ord(api	NOUN
ejpam-3245	326	12	)	)	PUNCT
ejpam-3245	326	13	)	)	PUNCT
ejpam-3245	326	14	;	;	PUNCT
ejpam-3245	326	15	i	i	PRON
ejpam-3245	326	16	>	>	X
ejpam-3245	326	17	0	0	PUNCT
ejpam-3245	326	18	belong	belong	VERB
ejpam-3245	326	19	to	to	ADP
ejpam-3245	326	20	the	the	DET
ejpam-3245	326	21	line	line	NOUN
ejpam-3245	326	22	with	with	ADP
ejpam-3245	326	23	the	the	DET
ejpam-3245	326	24	slope	slope	NOUN
ejpam-3245	326	25	−1	−1	NOUN
ejpam-3245	326	26	p−1	p−1	PROPN
ejpam-3245	326	27	and	and	CCONJ
ejpam-3245	326	28	passes	pass	VERB
ejpam-3245	326	29	through	through	ADP
ejpam-3245	326	30	the	the	DET
ejpam-3245	326	31	point	point	NOUN
ejpam-3245	326	32	(	(	PUNCT
ejpam-3245	326	33	p0,ord(ap0))(which	p0,ord(ap0))(which	PRON
ejpam-3245	326	34	is	be	AUX
ejpam-3245	326	35	the	the	DET
ejpam-3245	326	36	point	point	NOUN
ejpam-3245	326	37	(	(	PUNCT
ejpam-3245	326	38	1,0	1,0	NUM
ejpam-3245	326	39	)	)	PUNCT
ejpam-3245	326	40	)	)	PUNCT
ejpam-3245	326	41	.	.	PUNCT
ejpam-3245	327	1	this	this	DET
ejpam-3245	327	2	line	line	NOUN
ejpam-3245	327	3	has	have	VERB
ejpam-3245	327	4	the	the	DET
ejpam-3245	327	5	equation	equation	NOUN
ejpam-3245	327	6	y	y	NOUN
ejpam-3245	327	7	=	=	PUNCT
ejpam-3245	327	8	−1	−1	NOUN
ejpam-3245	327	9	p−1(x	p−1(x	NOUN
ejpam-3245	327	10	−	−	NOUN
ejpam-3245	327	11	1	1	NUM
ejpam-3245	327	12	)	)	PUNCT
ejpam-3245	327	13	.	.	PUNCT
ejpam-3245	328	1	also	also	ADV
ejpam-3245	328	2	,	,	PUNCT
ejpam-3245	328	3	for	for	ADP
ejpam-3245	328	4	all	all	DET
ejpam-3245	328	5	i	i	PRON
ejpam-3245	328	6	>	>	X
ejpam-3245	328	7	1	1	NUM
ejpam-3245	328	8	,	,	PUNCT
ejpam-3245	328	9	we	we	PRON
ejpam-3245	328	10	have	have	VERB
ejpam-3245	328	11	ord(ai	ord(ai	PRON
ejpam-3245	328	12	)	)	PUNCT
ejpam-3245	328	13	=	=	SYM
ejpam-3245	328	14	ord	ord	PROPN
ejpam-3245	328	15	(	(	PUNCT
ejpam-3245	328	16	1	1	NUM
ejpam-3245	328	17	i	i	NOUN
ejpam-3245	328	18	!	!	PUNCT
ejpam-3245	328	19	)	)	PUNCT
ejpam-3245	329	1	≥	≥	NOUN
ejpam-3245	330	1	−	−	NOUN
ejpam-3245	330	2	1	1	NUM
ejpam-3245	330	3	p−	p−	NOUN
ejpam-3245	330	4	1	1	NUM
ejpam-3245	330	5	(	(	PUNCT
ejpam-3245	330	6	i−	i−	PROPN
ejpam-3245	330	7	1	1	NUM
ejpam-3245	330	8	)	)	PUNCT
ejpam-3245	330	9	.	.	PUNCT
ejpam-3245	331	1	this	this	PRON
ejpam-3245	331	2	implies	imply	VERB
ejpam-3245	331	3	that	that	SCONJ
ejpam-3245	331	4	all	all	DET
ejpam-3245	331	5	the	the	DET
ejpam-3245	331	6	points	point	NOUN
ejpam-3245	331	7	(	(	PUNCT
ejpam-3245	331	8	i	i	NOUN
ejpam-3245	331	9	,	,	PUNCT
ejpam-3245	331	10	ord(ai	ord(ai	NOUN
ejpam-3245	331	11	)	)	PUNCT
ejpam-3245	331	12	)	)	PUNCT
ejpam-3245	331	13	;	;	PUNCT
ejpam-3245	331	14	(	(	PUNCT
ejpam-3245	331	15	i	i	PRON
ejpam-3245	331	16	>	>	X
ejpam-3245	331	17	1	1	NUM
ejpam-3245	331	18	)	)	PUNCT
ejpam-3245	331	19	are	be	AUX
ejpam-3245	331	20	on	on	ADP
ejpam-3245	331	21	or	or	CCONJ
ejpam-3245	331	22	above	above	ADP
ejpam-3245	331	23	the	the	DET
ejpam-3245	331	24	line	line	NOUN
ejpam-3245	331	25	y	y	PROPN
ejpam-3245	331	26	=	=	PUNCT
ejpam-3245	331	27	−1	−1	NOUN
ejpam-3245	331	28	p−1(x−1	p−1(x−1	NOUN
ejpam-3245	331	29	)	)	PUNCT
ejpam-3245	331	30	.	.	PUNCT
ejpam-3245	332	1	from	from	ADP
ejpam-3245	332	2	that	that	DET
ejpam-3245	332	3	argument	argument	NOUN
ejpam-3245	332	4	,	,	PUNCT
ejpam-3245	332	5	we	we	PRON
ejpam-3245	332	6	deduce	deduce	VERB
ejpam-3245	332	7	that	that	SCONJ
ejpam-3245	332	8	the	the	DET
ejpam-3245	332	9	points	point	NOUN
ejpam-3245	332	10	(	(	PUNCT
ejpam-3245	332	11	i	i	NOUN
ejpam-3245	332	12	,	,	PUNCT
ejpam-3245	332	13	ord(ai	ord(ai	NOUN
ejpam-3245	332	14	)	)	PUNCT
ejpam-3245	332	15	)	)	PUNCT
ejpam-3245	332	16	;	;	PUNCT
ejpam-3245	332	17	(	(	PUNCT
ejpam-3245	332	18	i	i	PRON
ejpam-3245	332	19	≥	≥	VERB
ejpam-3245	332	20	1	1	NUM
ejpam-3245	332	21	)	)	PUNCT
ejpam-3245	332	22	are	be	AUX
ejpam-3245	332	23	distributed	distribute	VERB
ejpam-3245	332	24	as	as	SCONJ
ejpam-3245	332	25	follows	follow	VERB
ejpam-3245	332	26	:	:	PUNCT
ejpam-3245	332	27	1	1	X
ejpam-3245	332	28	)	)	PUNCT
ejpam-3245	332	29	the	the	DET
ejpam-3245	332	30	subsequence	subsequence	NOUN
ejpam-3245	332	31	(	(	PUNCT
ejpam-3245	332	32	pj	pj	PROPN
ejpam-3245	332	33	,	,	PUNCT
ejpam-3245	332	34	ord(apj	ord(apj	PROPN
ejpam-3245	332	35	)	)	PUNCT
ejpam-3245	332	36	)	)	PUNCT
ejpam-3245	332	37	,	,	PUNCT
ejpam-3245	332	38	j	j	PROPN
ejpam-3245	332	39	≥	≥	X
ejpam-3245	332	40	0	0	NUM
ejpam-3245	332	41	lies	lie	VERB
ejpam-3245	332	42	on	on	ADP
ejpam-3245	332	43	the	the	DET
ejpam-3245	332	44	line	line	NOUN
ejpam-3245	332	45	y	y	PROPN
ejpam-3245	332	46	=	=	PUNCT
ejpam-3245	332	47	−1	−1	NOUN
ejpam-3245	332	48	p−1(x	p−1(x	NOUN
ejpam-3245	332	49	−	−	PROPN
ejpam-3245	332	50	1	1	NUM
ejpam-3245	332	51	)	)	PUNCT
ejpam-3245	332	52	which	which	PRON
ejpam-3245	332	53	has	have	VERB
ejpam-3245	332	54	the	the	DET
ejpam-3245	332	55	slope	slope	NOUN
ejpam-3245	332	56	−	−	PROPN
ejpam-3245	332	57	1	1	NUM
ejpam-3245	332	58	p−1	p−1	PROPN
ejpam-3245	332	59	.	.	PUNCT
ejpam-3245	333	1	2	2	X
ejpam-3245	333	2	)	)	PUNCT
ejpam-3245	333	3	the	the	DET
ejpam-3245	333	4	other	other	ADJ
ejpam-3245	333	5	points	point	NOUN
ejpam-3245	333	6	are	be	AUX
ejpam-3245	333	7	on	on	ADP
ejpam-3245	333	8	or	or	CCONJ
ejpam-3245	333	9	above	above	ADP
ejpam-3245	333	10	this	this	DET
ejpam-3245	333	11	line	line	NOUN
ejpam-3245	333	12	.	.	PUNCT
ejpam-3245	334	1	now	now	ADV
ejpam-3245	334	2	apply	apply	VERB
ejpam-3245	334	3	the	the	DET
ejpam-3245	334	4	previous	previous	ADJ
ejpam-3245	334	5	steps	step	NOUN
ejpam-3245	334	6	to	to	PART
ejpam-3245	334	7	obtain	obtain	VERB
ejpam-3245	334	8	the	the	DET
ejpam-3245	334	9	newton	newton	PROPN
ejpam-3245	334	10	polygon	polygon	PROPN
ejpam-3245	334	11	of	of	ADP
ejpam-3245	334	12	exp(x	exp(x	PROPN
ejpam-3245	334	13	)	)	PUNCT
ejpam-3245	334	14	as	as	SCONJ
ejpam-3245	334	15	follows	follow	VERB
ejpam-3245	334	16	:	:	PUNCT
ejpam-3245	334	17	rotate	rotate	VERB
ejpam-3245	334	18	the	the	DET
ejpam-3245	334	19	vertical	vertical	ADJ
ejpam-3245	334	20	half	half	ADJ
ejpam-3245	334	21	-	-	PUNCT
ejpam-3245	334	22	line	line	NOUN
ejpam-3245	334	23	of	of	ADP
ejpam-3245	334	24	the	the	DET
ejpam-3245	334	25	negative	negative	ADJ
ejpam-3245	334	26	part	part	NOUN
ejpam-3245	334	27	of	of	ADP
ejpam-3245	334	28	the	the	DET
ejpam-3245	334	29	y	y	NOUN
ejpam-3245	334	30	-	-	PUNCT
ejpam-3245	334	31	axis	axis	NOUN
ejpam-3245	334	32	until	until	SCONJ
ejpam-3245	334	33	it	it	PRON
ejpam-3245	334	34	reaches	reach	VERB
ejpam-3245	334	35	to	to	ADP
ejpam-3245	334	36	a	a	DET
ejpam-3245	334	37	position	position	NOUN
ejpam-3245	334	38	parallel	parallel	ADJ
ejpam-3245	334	39	to	to	ADP
ejpam-3245	334	40	the	the	DET
ejpam-3245	334	41	line	line	NOUN
ejpam-3245	335	1	y	y	PROPN
ejpam-3245	335	2	=	=	SYM
ejpam-3245	335	3	−	−	PROPN
ejpam-3245	335	4	1	1	NUM
ejpam-3245	335	5	p−1(x	p−1(x	NOUN
ejpam-3245	335	6	−	−	NOUN
ejpam-3245	335	7	1	1	NUM
ejpam-3245	335	8	)	)	PUNCT
ejpam-3245	335	9	.	.	PUNCT
ejpam-3245	336	1	we	we	PRON
ejpam-3245	336	2	stop	stop	VERB
ejpam-3245	336	3	here	here	ADV
ejpam-3245	336	4	without	without	ADP
ejpam-3245	336	5	any	any	DET
ejpam-3245	336	6	further	further	ADJ
ejpam-3245	336	7	rotation	rotation	NOUN
ejpam-3245	336	8	.	.	PUNCT
ejpam-3245	337	1	this	this	PRON
ejpam-3245	337	2	is	be	AUX
ejpam-3245	337	3	because	because	SCONJ
ejpam-3245	337	4	,	,	PUNCT
ejpam-3245	337	5	for	for	ADP
ejpam-3245	337	6	any	any	DET
ejpam-3245	337	7	ε	ε	PROPN
ejpam-3245	337	8	>	>	PUNCT
ejpam-3245	337	9	−	−	PROPN
ejpam-3245	337	10	1	1	NUM
ejpam-3245	337	11	p−1	p−1	PROPN
ejpam-3245	337	12	,	,	PUNCT
ejpam-3245	337	13	the	the	DET
ejpam-3245	337	14	line	line	NOUN
ejpam-3245	338	1	y	y	PROPN
ejpam-3245	338	2	=	=	NOUN
ejpam-3245	338	3	εx	εx	PROPN
ejpam-3245	338	4	would	would	AUX
ejpam-3245	338	5	leave	leave	VERB
ejpam-3245	338	6	behind	behind	ADP
ejpam-3245	338	7	it	it	PRON
ejpam-3245	338	8	some	some	DET
ejpam-3245	338	9	points	point	NOUN
ejpam-3245	338	10	of	of	ADP
ejpam-3245	338	11	the	the	DET
ejpam-3245	338	12	form	form	NOUN
ejpam-3245	338	13	(	(	PUNCT
ejpam-3245	338	14	pi	pi	NOUN
ejpam-3245	338	15	,	,	PUNCT
ejpam-3245	338	16	ord	ord	PROPN
ejpam-3245	338	17	(	(	PUNCT
ejpam-3245	338	18	1	1	NUM
ejpam-3245	338	19	pi	pi	NOUN
ejpam-3245	338	20	!	!	PUNCT
ejpam-3245	338	21	)	)	PUNCT
ejpam-3245	338	22	)	)	PUNCT
ejpam-3245	338	23	.	.	PUNCT
ejpam-3245	339	1	since	since	SCONJ
ejpam-3245	339	2	ε	ε	PROPN
ejpam-3245	339	3	>	>	X
ejpam-3245	339	4	−1	−1	PROPN
ejpam-3245	339	5	p−1	p−1	PROPN
ejpam-3245	339	6	,	,	PUNCT
ejpam-3245	339	7	it	it	PRON
ejpam-3245	339	8	follows	follow	VERB
ejpam-3245	339	9	that	that	SCONJ
ejpam-3245	339	10	there	there	PRON
ejpam-3245	339	11	exists	exist	VERB
ejpam-3245	339	12	some	some	DET
ejpam-3245	339	13	positive	positive	ADJ
ejpam-3245	339	14	real	real	ADJ
ejpam-3245	339	15	number	number	NOUN
ejpam-3245	339	16	δ	δ	PROPN
ejpam-3245	339	17	>	>	X
ejpam-3245	339	18	0	0	NUM
ejpam-3245	340	1	such	such	ADJ
ejpam-3245	340	2	that	that	DET
ejpam-3245	340	3	ε	ε	PROPN
ejpam-3245	340	4	=	=	SYM
ejpam-3245	340	5	−1	−1	PROPN
ejpam-3245	340	6	p−1	p−1	PROPN
ejpam-3245	340	7	+	+	CCONJ
ejpam-3245	340	8	δ	δ	PROPN
ejpam-3245	340	9	.	.	PUNCT
ejpam-3245	341	1	therefore	therefore	ADV
ejpam-3245	341	2	,	,	PUNCT
ejpam-3245	341	3	ord(ai	ord(ai	ADJ
ejpam-3245	341	4	)	)	PUNCT
ejpam-3245	341	5	<	<	X
ejpam-3245	341	6	εi⇔	εi⇔	PROPN
ejpam-3245	341	7	−	−	PROPN
ejpam-3245	341	8	i−	i−	PROPN
ejpam-3245	341	9	si	si	NOUN
ejpam-3245	341	10	p−	p−	NOUN
ejpam-3245	341	11	1	1	NUM
ejpam-3245	341	12	<	<	X
ejpam-3245	341	13	εi⇔	εi⇔	PROPN
ejpam-3245	341	14	−	−	PROPN
ejpam-3245	341	15	i−	i−	PROPN
ejpam-3245	341	16	si	si	NOUN
ejpam-3245	341	17	p−	p−	NOUN
ejpam-3245	341	18	1	1	NUM
ejpam-3245	341	19	<	<	X
ejpam-3245	341	20	(	(	PUNCT
ejpam-3245	341	21	−1	−1	NOUN
ejpam-3245	341	22	p−	p−	NOUN
ejpam-3245	341	23	1	1	NUM
ejpam-3245	341	24	+	+	NUM
ejpam-3245	341	25	δ)i⇔	δ)i⇔	NOUN
ejpam-3245	341	26	i−	i−	PROPN
ejpam-3245	341	27	si	si	PROPN
ejpam-3245	341	28	>	>	X
ejpam-3245	341	29	i−	i−	PROPN
ejpam-3245	341	30	(	(	PUNCT
ejpam-3245	341	31	p−	p−	NOUN
ejpam-3245	341	32	1)δi⇔	1)δi⇔	NUM
ejpam-3245	341	33	(	(	PUNCT
ejpam-3245	341	34	p−	p−	NOUN
ejpam-3245	341	35	1)δi	1)δi	PROPN
ejpam-3245	341	36	>	>	X
ejpam-3245	341	37	si	si	PROPN
ejpam-3245	341	38	⇔	⇔	PROPN
ejpam-3245	341	39	i	i	PROPN
ejpam-3245	341	40	>	>	X
ejpam-3245	341	41	si	si	X
ejpam-3245	341	42	(	(	PUNCT
ejpam-3245	341	43	p−	p−	NOUN
ejpam-3245	341	44	1)δ	1)δ	NUM
ejpam-3245	341	45	.	.	PUNCT
ejpam-3245	342	1	we	we	PRON
ejpam-3245	342	2	can	can	AUX
ejpam-3245	342	3	choose	choose	VERB
ejpam-3245	342	4	i	i	PRON
ejpam-3245	342	5	to	to	PART
ejpam-3245	342	6	be	be	AUX
ejpam-3245	342	7	sufficiently	sufficiently	ADV
ejpam-3245	342	8	large	large	ADJ
ejpam-3245	342	9	and	and	CCONJ
ejpam-3245	342	10	has	have	VERB
ejpam-3245	342	11	the	the	DET
ejpam-3245	342	12	form	form	NOUN
ejpam-3245	342	13	pj	pj	PROPN
ejpam-3245	342	14	.	.	PUNCT
ejpam-3245	343	1	in	in	ADP
ejpam-3245	343	2	this	this	DET
ejpam-3245	343	3	case	case	NOUN
ejpam-3245	343	4	,	,	PUNCT
ejpam-3245	343	5	we	we	PRON
ejpam-3245	343	6	find	find	VERB
ejpam-3245	343	7	that	that	SCONJ
ejpam-3245	343	8	si	si	NOUN
ejpam-3245	343	9	=	=	SYM
ejpam-3245	343	10	1	1	NUM
ejpam-3245	343	11	,	,	PUNCT
ejpam-3245	343	12	so	so	ADV
ejpam-3245	343	13	the	the	DET
ejpam-3245	343	14	relation	relation	NOUN
ejpam-3245	343	15	i	i	PRON
ejpam-3245	343	16	>	>	X
ejpam-3245	343	17	1	1	NUM
ejpam-3245	343	18	δ(p−1	δ(p−1	PROPN
ejpam-3245	343	19	)	)	PUNCT
ejpam-3245	343	20	holds	hold	VERB
ejpam-3245	343	21	true	true	ADJ
ejpam-3245	343	22	for	for	ADP
ejpam-3245	343	23	the	the	DET
ejpam-3245	343	24	index	index	NOUN
ejpam-3245	344	1	i	i	PRON
ejpam-3245	344	2	:	:	PUNCT
ejpam-3245	344	3	=	=	PROPN
ejpam-3245	344	4	pj	pj	PROPN
ejpam-3245	344	5	.	.	PUNCT
ejpam-3245	345	1	this	this	PRON
ejpam-3245	345	2	implies	imply	VERB
ejpam-3245	345	3	that	that	SCONJ
ejpam-3245	345	4	there	there	PRON
ejpam-3245	345	5	is	be	VERB
ejpam-3245	345	6	no	no	DET
ejpam-3245	345	7	further	further	ADJ
ejpam-3245	345	8	rotation	rotation	NOUN
ejpam-3245	345	9	of	of	ADP
ejpam-3245	345	10	the	the	DET
ejpam-3245	345	11	line	line	NOUN
ejpam-3245	345	12	y	y	NOUN
ejpam-3245	345	13	=	=	PUNCT
ejpam-3245	345	14	−1	−1	NOUN
ejpam-3245	345	15	p−1x	p−1x	ADV
ejpam-3245	345	16	.	.	PUNCT
ejpam-3245	346	1	hence	hence	ADV
ejpam-3245	346	2	,	,	PUNCT
ejpam-3245	346	3	the	the	DET
ejpam-3245	346	4	newton	newton	PROPN
ejpam-3245	346	5	polygon	polygon	PROPN
ejpam-3245	346	6	of	of	ADP
ejpam-3245	346	7	the	the	DET
ejpam-3245	346	8	exponential	exponential	ADJ
ejpam-3245	346	9	function	function	NOUN
ejpam-3245	346	10	is	be	AUX
ejpam-3245	346	11	the	the	DET
ejpam-3245	346	12	straight	straight	ADJ
ejpam-3245	346	13	line	line	NOUN
ejpam-3245	346	14	y	y	PROPN
ejpam-3245	346	15	=	=	PUNCT
ejpam-3245	346	16	−1	−1	NOUN
ejpam-3245	346	17	p−1x	p−1x	ADV
ejpam-3245	346	18	from	from	ADP
ejpam-3245	346	19	(	(	PUNCT
ejpam-3245	346	20	0	0	NUM
ejpam-3245	346	21	,	,	PUNCT
ejpam-3245	346	22	0	0	NUM
ejpam-3245	346	23	)	)	PUNCT
ejpam-3245	346	24	.	.	PUNCT
ejpam-3245	347	1	acknowledgements	acknowledgement	NOUN
ejpam-3245	347	2	i	i	PRON
ejpam-3245	347	3	would	would	AUX
ejpam-3245	347	4	like	like	VERB
ejpam-3245	347	5	to	to	PART
ejpam-3245	347	6	thank	thank	VERB
ejpam-3245	347	7	the	the	DET
ejpam-3245	347	8	referees	referee	NOUN
ejpam-3245	347	9	for	for	ADP
ejpam-3245	347	10	their	their	PRON
ejpam-3245	347	11	constructive	constructive	ADJ
ejpam-3245	347	12	comments	comment	NOUN
ejpam-3245	347	13	.	.	PUNCT
ejpam-3245	348	1	also	also	ADV
ejpam-3245	348	2	,	,	PUNCT
ejpam-3245	348	3	i	i	PRON
ejpam-3245	348	4	would	would	AUX
ejpam-3245	348	5	like	like	VERB
ejpam-3245	348	6	to	to	PART
ejpam-3245	348	7	thank	thank	VERB
ejpam-3245	348	8	ali	ali	PROPN
ejpam-3245	348	9	bleybel	bleybel	PROPN
ejpam-3245	348	10	for	for	ADP
ejpam-3245	348	11	proposing	propose	VERB
ejpam-3245	348	12	this	this	DET
ejpam-3245	348	13	subject	subject	NOUN
ejpam-3245	348	14	,	,	PUNCT
ejpam-3245	348	15	as	as	ADV
ejpam-3245	348	16	well	well	ADV
ejpam-3245	348	17	as	as	ADP
ejpam-3245	348	18	his	his	PRON
ejpam-3245	348	19	constant	constant	ADJ
ejpam-3245	348	20	help	help	NOUN
ejpam-3245	348	21	and	and	CCONJ
ejpam-3245	348	22	support	support	NOUN
ejpam-3245	348	23	throughout	throughout	ADP
ejpam-3245	348	24	the	the	DET
ejpam-3245	348	25	preparation	preparation	NOUN
ejpam-3245	348	26	of	of	ADP
ejpam-3245	348	27	this	this	DET
ejpam-3245	348	28	paper	paper	NOUN
ejpam-3245	348	29	.	.	PUNCT
ejpam-3245	349	1	references	reference	NOUN
ejpam-3245	349	2	[	[	X
ejpam-3245	349	3	1	1	NUM
ejpam-3245	349	4	]	]	PUNCT
ejpam-3245	349	5	p.	p.	PROPN
ejpam-3245	349	6	d’a	d’a	PROPN
ejpam-3245	349	7	quino	quino	PROPN
ejpam-3245	349	8	,	,	PUNCT
ejpam-3245	349	9	a.	a.	PROPN
ejpam-3245	349	10	macintyre	macintyre	PROPN
ejpam-3245	349	11	and	and	CCONJ
ejpam-3245	349	12	g.	g.	PROPN
ejpam-3245	349	13	terzo	terzo	PROPN
ejpam-3245	349	14	.	.	PROPN
ejpam-3245	350	1	from	from	ADP
ejpam-3245	350	2	schanuels	schanuel	NOUN
ejpam-3245	350	3	conjecture	conjecture	VERB
ejpam-3245	350	4	to	to	ADP
ejpam-3245	350	5	shapiros	shapiros	PROPN
ejpam-3245	350	6	conjecture	conjecture	NOUN
ejpam-3245	350	7	,	,	PUNCT
ejpam-3245	350	8	available	available	ADJ
ejpam-3245	350	9	at	at	ADP
ejpam-3245	350	10	:	:	PUNCT
ejpam-3245	350	11	http://arxiv.org/abs/1206.6747v1	http://arxiv.org/abs/1206.6747v1	NOUN
ejpam-3245	350	12	.	.	NOUN
ejpam-3245	350	13	references	reference	NOUN
ejpam-3245	350	14	814	814	NUM
ejpam-3245	350	15	[	[	X
ejpam-3245	350	16	2	2	NUM
ejpam-3245	350	17	]	]	PUNCT
ejpam-3245	350	18	p.	p.	PROPN
ejpam-3245	350	19	d’a	d’a	PROPN
ejpam-3245	350	20	quino	quino	PROPN
ejpam-3245	350	21	,	,	PUNCT
ejpam-3245	350	22	a.	a.	PROPN
ejpam-3245	350	23	macintyre	macintyre	PROPN
ejpam-3245	350	24	and	and	CCONJ
ejpam-3245	350	25	g.	g.	PROPN
ejpam-3245	350	26	terzo	terzo	PROPN
ejpam-3245	350	27	.	.	PUNCT
ejpam-3245	351	1	comparing	compare	VERB
ejpam-3245	351	2	c	c	PROPN
ejpam-3245	351	3	and	and	CCONJ
ejpam-3245	351	4	zilbers	zilber	NOUN
ejpam-3245	351	5	exponential	exponential	ADJ
ejpam-3245	351	6	fields	field	NOUN
ejpam-3245	351	7	:	:	PUNCT
ejpam-3245	351	8	zero	zero	NUM
ejpam-3245	351	9	sets	set	NOUN
ejpam-3245	351	10	of	of	ADP
ejpam-3245	351	11	exponential	exponential	ADJ
ejpam-3245	351	12	polynomials	polynomial	NOUN
ejpam-3245	351	13	,	,	PUNCT
ejpam-3245	351	14	available	available	ADJ
ejpam-3245	351	15	at	at	ADP
ejpam-3245	351	16	:	:	PUNCT
ejpam-3245	351	17	http://arxiv.org/abs/1310.6891v1	http://arxiv.org/abs/1310.6891v1	PUNCT
ejpam-3245	351	18	.	.	PUNCT
ejpam-3245	352	1	[	[	X
ejpam-3245	352	2	3	3	X
ejpam-3245	352	3	]	]	PUNCT
ejpam-3245	352	4	f.	f.	PROPN
ejpam-3245	352	5	q.	q.	PROPN
ejpam-3245	352	6	gouvea	gouvea	PROPN
ejpam-3245	352	7	,	,	PUNCT
ejpam-3245	352	8	p	p	ADJ
ejpam-3245	352	9	-	-	PUNCT
ejpam-3245	352	10	adic	adic	ADJ
ejpam-3245	352	11	numbers	number	NOUN
ejpam-3245	352	12	:	:	PUNCT
ejpam-3245	352	13	an	an	DET
ejpam-3245	352	14	introduction	introduction	NOUN
ejpam-3245	352	15	,	,	PUNCT
ejpam-3245	352	16	springer	springer	NOUN
ejpam-3245	352	17	-	-	PUNCT
ejpam-3245	352	18	verlag	verlag	PROPN
ejpam-3245	352	19	,	,	PUNCT
ejpam-3245	352	20	berlin	berlin	PROPN
ejpam-3245	352	21	,	,	PUNCT
ejpam-3245	352	22	heidelberg	heidelberg	PROPN
ejpam-3245	352	23	,	,	PUNCT
ejpam-3245	352	24	new	new	PROPN
ejpam-3245	352	25	york	york	PROPN
ejpam-3245	352	26	,	,	PUNCT
ejpam-3245	352	27	second	second	ADJ
ejpam-3245	352	28	edition	edition	NOUN
ejpam-3245	352	29	,	,	PUNCT
ejpam-3245	352	30	universitext	universitext	PROPN
ejpam-3245	352	31	,	,	PUNCT
ejpam-3245	352	32	2000	2000	NUM
ejpam-3245	352	33	.	.	PUNCT
ejpam-3245	353	1	[	[	X
ejpam-3245	353	2	4	4	NUM
ejpam-3245	353	3	]	]	X
ejpam-3245	353	4	n.	n.	NOUN
ejpam-3245	353	5	koblitz	koblitz	PROPN
ejpam-3245	353	6	.	.	PUNCT
ejpam-3245	354	1	p	p	X
ejpam-3245	354	2	-	-	PUNCT
ejpam-3245	354	3	adic	adic	ADJ
ejpam-3245	354	4	numbers	number	NOUN
ejpam-3245	354	5	,	,	PUNCT
ejpam-3245	354	6	p	p	ADJ
ejpam-3245	354	7	-	-	PUNCT
ejpam-3245	354	8	adic	adic	ADJ
ejpam-3245	354	9	analysis	analysis	NOUN
ejpam-3245	354	10	,	,	PUNCT
ejpam-3245	354	11	and	and	CCONJ
ejpam-3245	354	12	zeta	zeta	NOUN
ejpam-3245	354	13	-	-	PUNCT
ejpam-3245	354	14	functions	function	NOUN
ejpam-3245	354	15	.	.	PUNCT
ejpam-3245	355	1	springer	springer	NOUN
ejpam-3245	355	2	-	-	PUNCT
ejpam-3245	355	3	verlag	verlag	PROPN
ejpam-3245	355	4	,	,	PUNCT
ejpam-3245	355	5	berlin	berlin	PROPN
ejpam-3245	355	6	,	,	PUNCT
ejpam-3245	355	7	heidelberg	heidelberg	PROPN
ejpam-3245	355	8	,	,	PUNCT
ejpam-3245	355	9	new	new	PROPN
ejpam-3245	355	10	york	york	PROPN
ejpam-3245	355	11	,	,	PUNCT
ejpam-3245	355	12	second	second	ADJ
ejpam-3245	355	13	edition	edition	NOUN
ejpam-3245	355	14	,	,	PUNCT
ejpam-3245	355	15	1984	1984	NUM
ejpam-3245	355	16	.	.	PUNCT
ejpam-3245	356	1	[	[	X
ejpam-3245	356	2	5	5	NUM
ejpam-3245	356	3	]	]	X
ejpam-3245	356	4	a.j.van	a.j.van	NOUN
ejpam-3245	356	5	der	der	NOUN
ejpam-3245	356	6	poorten	poorten	VERB
ejpam-3245	356	7	,	,	PUNCT
ejpam-3245	356	8	zeros	zero	NOUN
ejpam-3245	356	9	of	of	ADP
ejpam-3245	356	10	p	p	NOUN
ejpam-3245	356	11	-	-	PUNCT
ejpam-3245	356	12	adic	adic	ADJ
ejpam-3245	356	13	exponential	exponential	ADJ
ejpam-3245	356	14	polynomials	polynomial	NOUN
ejpam-3245	356	15	i	i	PRON
ejpam-3245	356	16	,	,	PUNCT
ejpam-3245	356	17	school	school	NOUN
ejpam-3245	356	18	of	of	ADP
ejpam-3245	356	19	mathematics	mathematics	PROPN
ejpam-3245	356	20	the	the	DET
ejpam-3245	356	21	university	university	PROPN
ejpam-3245	356	22	of	of	ADP
ejpam-3245	356	23	nsw	nsw	PROPN
ejpam-3245	356	24	kensington	kensington	PROPN
ejpam-3245	356	25	,	,	PUNCT
ejpam-3245	356	26	nsw	nsw	PROPN
ejpam-3245	356	27	2033	2033	NUM
ejpam-3245	356	28	,	,	PUNCT
ejpam-3245	356	29	australia	australia	PROPN
ejpam-3245	356	30	,	,	PUNCT
ejpam-3245	356	31	1975	1975	NUM
ejpam-3245	356	32	.	.	PUNCT
ejpam-3245	357	1	[	[	X
ejpam-3245	357	2	6	6	NUM
ejpam-3245	357	3	]	]	X
ejpam-3245	357	4	a.j.van	a.j.van	NOUN
ejpam-3245	357	5	der	der	NOUN
ejpam-3245	357	6	poorten	poorten	VERB
ejpam-3245	357	7	and	and	CCONJ
ejpam-3245	357	8	roberts	roberts	PROPN
ejpam-3245	357	9	rumely	rumely	ADV
ejpam-3245	357	10	,	,	PUNCT
ejpam-3245	357	11	zeros	zero	NOUN
ejpam-3245	357	12	of	of	ADP
ejpam-3245	357	13	p	p	NOUN
ejpam-3245	357	14	-	-	PUNCT
ejpam-3245	357	15	adic	adic	ADJ
ejpam-3245	357	16	exponential	exponential	ADJ
ejpam-3245	357	17	polynomials	polynomials	PROPN
ejpam-3245	357	18	ii	ii	PROPN
ejpam-3245	357	19	,	,	PUNCT
ejpam-3245	357	20	j.	j.	PROPN
ejpam-3245	357	21	london	london	PROPN
ejpam-3245	357	22	math	math	PROPN
ejpam-3245	357	23	.	.	PUNCT
ejpam-3245	358	1	soc	soc	PROPN
ejpam-3245	358	2	.	.	PUNCT
ejpam-3245	359	1	(	(	PUNCT
ejpam-3245	359	2	2	2	X
ejpam-3245	359	3	)	)	PUNCT
ejpam-3245	359	4	36	36	NUM
ejpam-3245	359	5	(	(	PUNCT
ejpam-3245	359	6	1987	1987	NUM
ejpam-3245	359	7	)	)	PUNCT
ejpam-3245	359	8	1	1	NUM
ejpam-3245	359	9	-	-	SYM
ejpam-3245	359	10	15	15	NUM
ejpam-3245	359	11	.	.	PUNCT