id	sid	tid	token	lemma	pos
ejpam-3281	1	1	a	a	DET
ejpam-3281	1	2	note	note	NOUN
ejpam-3281	1	3	on	on	ADP
ejpam-3281	1	4	one	one	NUM
ejpam-3281	1	5	-	-	PUNCT
ejpam-3281	1	6	dimensional	dimensional	ADJ
ejpam-3281	1	7	varieties	variety	NOUN
ejpam-3281	1	8	over	over	ADP
ejpam-3281	1	9	the	the	DET
ejpam-3281	1	10	complex	complex	ADJ
ejpam-3281	1	11	$	$	SYM
ejpam-3281	1	12	p$-adic	p$-adic	ADJ
ejpam-3281	1	13	field	field	NOUN
ejpam-3281	1	14	european	european	ADJ
ejpam-3281	1	15	journal	journal	PROPN
ejpam-3281	1	16	of	of	ADP
ejpam-3281	1	17	pure	pure	ADJ
ejpam-3281	1	18	and	and	CCONJ
ejpam-3281	1	19	applied	apply	VERB
ejpam-3281	1	20	mathematics	mathematic	NOUN
ejpam-3281	1	21	vol	vol	NOUN
ejpam-3281	1	22	.	.	PUNCT
ejpam-3281	2	1	11	11	NUM
ejpam-3281	2	2	,	,	PUNCT
ejpam-3281	2	3	no	no	INTJ
ejpam-3281	2	4	.	.	NOUN
ejpam-3281	2	5	4	4	NUM
ejpam-3281	2	6	,	,	PUNCT
ejpam-3281	2	7	2018	2018	NUM
ejpam-3281	2	8	,	,	PUNCT
ejpam-3281	2	9	1046	1046	NUM
ejpam-3281	2	10	-	-	SYM
ejpam-3281	2	11	1057	1057	NUM
ejpam-3281	2	12	issn	issn	PROPN
ejpam-3281	2	13	1307	1307	NUM
ejpam-3281	2	14	-	-	SYM
ejpam-3281	2	15	5543	5543	NUM
ejpam-3281	2	16	–	–	PUNCT
ejpam-3281	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3281	2	18	published	publish	VERB
ejpam-3281	2	19	by	by	ADP
ejpam-3281	2	20	new	new	PROPN
ejpam-3281	2	21	york	york	PROPN
ejpam-3281	2	22	business	business	PROPN
ejpam-3281	2	23	global	global	PROPN
ejpam-3281	2	24	a	a	DET
ejpam-3281	2	25	note	note	NOUN
ejpam-3281	2	26	on	on	ADP
ejpam-3281	2	27	one	one	NUM
ejpam-3281	2	28	-	-	PUNCT
ejpam-3281	2	29	dimensional	dimensional	ADJ
ejpam-3281	2	30	varieties	variety	NOUN
ejpam-3281	2	31	over	over	ADP
ejpam-3281	2	32	the	the	DET
ejpam-3281	2	33	complex	complex	ADJ
ejpam-3281	2	34	p	p	ADJ
ejpam-3281	2	35	-	-	PUNCT
ejpam-3281	2	36	adic	adic	ADJ
ejpam-3281	2	37	field	field	NOUN
ejpam-3281	2	38	amran	amran	PROPN
ejpam-3281	2	39	dalloul	dalloul	PROPN
ejpam-3281	2	40	department	department	PROPN
ejpam-3281	2	41	of	of	ADP
ejpam-3281	2	42	mathematics	mathematics	PROPN
ejpam-3281	2	43	,	,	PUNCT
ejpam-3281	2	44	beirut	beirut	PROPN
ejpam-3281	2	45	arab	arab	PROPN
ejpam-3281	2	46	university	university	PROPN
ejpam-3281	2	47	,	,	PUNCT
ejpam-3281	2	48	beirut	beirut	PROPN
ejpam-3281	2	49	,	,	PUNCT
ejpam-3281	2	50	lebanon	lebanon	PROPN
ejpam-3281	2	51	abstract	abstract	NOUN
ejpam-3281	2	52	.	.	PUNCT
ejpam-3281	3	1	in	in	ADP
ejpam-3281	3	2	this	this	DET
ejpam-3281	3	3	paper	paper	NOUN
ejpam-3281	3	4	,	,	PUNCT
ejpam-3281	3	5	we	we	PRON
ejpam-3281	3	6	study	study	VERB
ejpam-3281	3	7	the	the	DET
ejpam-3281	3	8	varieties	variety	NOUN
ejpam-3281	3	9	v	v	ADP
ejpam-3281	3	10	⊆	⊆	NUM
ejpam-3281	3	11	c4	c4	NOUN
ejpam-3281	3	12	p	p	NOUN
ejpam-3281	3	13	of	of	ADP
ejpam-3281	3	14	dimension	dimension	NOUN
ejpam-3281	3	15	one	one	NOUN
ejpam-3281	3	16	that	that	PRON
ejpam-3281	3	17	contain	contain	VERB
ejpam-3281	3	18	points	point	NOUN
ejpam-3281	3	19	of	of	ADP
ejpam-3281	3	20	the	the	DET
ejpam-3281	3	21	form	form	NOUN
ejpam-3281	3	22	(	(	PUNCT
ejpam-3281	3	23	x1	x1	PROPN
ejpam-3281	3	24	,	,	PUNCT
ejpam-3281	3	25	x2	x2	PROPN
ejpam-3281	3	26	,	,	PUNCT
ejpam-3281	3	27	exp(x1	exp(x1	ADJ
ejpam-3281	3	28	)	)	PUNCT
ejpam-3281	3	29	,	,	PUNCT
ejpam-3281	3	30	exp(x2	exp(x2	NOUN
ejpam-3281	3	31	)	)	PUNCT
ejpam-3281	3	32	)	)	PUNCT
ejpam-3281	3	33	by	by	ADP
ejpam-3281	3	34	using	use	VERB
ejpam-3281	3	35	tools	tool	NOUN
ejpam-3281	3	36	from	from	ADP
ejpam-3281	3	37	non	non	ADJ
ejpam-3281	3	38	-	-	ADJ
ejpam-3281	3	39	archimedian	archimedian	ADJ
ejpam-3281	3	40	analysis	analysis	NOUN
ejpam-3281	3	41	.	.	PUNCT
ejpam-3281	4	1	2010	2010	NUM
ejpam-3281	4	2	mathematics	mathematic	NOUN
ejpam-3281	4	3	subject	subject	NOUN
ejpam-3281	4	4	classifications	classification	NOUN
ejpam-3281	4	5	:	:	PUNCT
ejpam-3281	4	6	11e95	11e95	NUM
ejpam-3281	4	7	,	,	PUNCT
ejpam-3281	4	8	11f85	11f85	NUM
ejpam-3281	4	9	,	,	PUNCT
ejpam-3281	4	10	11j81	11j81	NUM
ejpam-3281	4	11	key	key	ADJ
ejpam-3281	4	12	words	word	NOUN
ejpam-3281	4	13	and	and	CCONJ
ejpam-3281	4	14	phrases	phrase	NOUN
ejpam-3281	4	15	:	:	PUNCT
ejpam-3281	4	16	p	p	X
ejpam-3281	4	17	-	-	PUNCT
ejpam-3281	4	18	adic	adic	ADJ
ejpam-3281	4	19	analysis	analysis	NOUN
ejpam-3281	4	20	,	,	PUNCT
ejpam-3281	4	21	transcendence	transcendence	NOUN
ejpam-3281	4	22	theory	theory	NOUN
ejpam-3281	4	23	1	1	NUM
ejpam-3281	4	24	.	.	PUNCT
ejpam-3281	4	25	introduction	introduction	NOUN
ejpam-3281	4	26	the	the	DET
ejpam-3281	4	27	algebraic	algebraic	ADJ
ejpam-3281	4	28	(	(	PUNCT
ejpam-3281	4	29	in)dependence	in)dependence	NOUN
ejpam-3281	4	30	between	between	ADP
ejpam-3281	4	31	elements	element	NOUN
ejpam-3281	4	32	of	of	ADP
ejpam-3281	4	33	the	the	DET
ejpam-3281	4	34	form	form	NOUN
ejpam-3281	4	35	x	x	NOUN
ejpam-3281	4	36	,	,	PUNCT
ejpam-3281	4	37	exp(x	exp(x	PROPN
ejpam-3281	4	38	)	)	PUNCT
ejpam-3281	4	39	in	in	ADP
ejpam-3281	4	40	the	the	DET
ejpam-3281	4	41	p−adic	p−adic	ADJ
ejpam-3281	4	42	domain	domain	NOUN
ejpam-3281	4	43	plays	play	VERB
ejpam-3281	4	44	a	a	DET
ejpam-3281	4	45	fundamental	fundamental	ADJ
ejpam-3281	4	46	role	role	NOUN
ejpam-3281	4	47	in	in	ADP
ejpam-3281	4	48	the	the	DET
ejpam-3281	4	49	p−adic	p−adic	ADJ
ejpam-3281	4	50	transcendental	transcendental	ADJ
ejpam-3281	4	51	number	number	NOUN
ejpam-3281	4	52	theory	theory	NOUN
ejpam-3281	4	53	.	.	PUNCT
ejpam-3281	5	1	many	many	ADJ
ejpam-3281	5	2	results	result	NOUN
ejpam-3281	5	3	have	have	AUX
ejpam-3281	5	4	been	be	AUX
ejpam-3281	5	5	made	make	VERB
ejpam-3281	5	6	towards	towards	ADP
ejpam-3281	5	7	this	this	DET
ejpam-3281	5	8	direction	direction	NOUN
ejpam-3281	5	9	.	.	PUNCT
ejpam-3281	6	1	for	for	ADP
ejpam-3281	6	2	example	example	NOUN
ejpam-3281	6	3	,	,	PUNCT
ejpam-3281	6	4	in	in	ADP
ejpam-3281	6	5	1932	1932	NUM
ejpam-3281	6	6	k.mahler	k.mahler	NOUN
ejpam-3281	6	7	,	,	PUNCT
ejpam-3281	6	8	[	[	X
ejpam-3281	6	9	n	n	CCONJ
ejpam-3281	6	10	]	]	PUNCT
ejpam-3281	6	11	,	,	PUNCT
ejpam-3281	6	12	proved	prove	VERB
ejpam-3281	6	13	that	that	SCONJ
ejpam-3281	6	14	exp(α	exp(α	PROPN
ejpam-3281	6	15	)	)	PUNCT
ejpam-3281	6	16	is	be	AUX
ejpam-3281	6	17	transcendental	transcendental	ADJ
ejpam-3281	6	18	over	over	ADP
ejpam-3281	6	19	q	q	NOUN
ejpam-3281	6	20	for	for	ADP
ejpam-3281	6	21	any	any	DET
ejpam-3281	6	22	non	non	ADJ
ejpam-3281	6	23	-	-	ADJ
ejpam-3281	6	24	zero	zero	ADJ
ejpam-3281	6	25	algebraic	algebraic	ADJ
ejpam-3281	6	26	element	element	NOUN
ejpam-3281	6	27	α	α	PROPN
ejpam-3281	6	28	∈	∈	PROPN
ejpam-3281	6	29	e	e	X
ejpam-3281	6	30	(	(	PUNCT
ejpam-3281	6	31	the	the	DET
ejpam-3281	6	32	domain	domain	NOUN
ejpam-3281	6	33	of	of	ADP
ejpam-3281	6	34	convergence	convergence	NOUN
ejpam-3281	6	35	of	of	ADP
ejpam-3281	6	36	the	the	DET
ejpam-3281	6	37	exponential	exponential	ADJ
ejpam-3281	6	38	function	function	NOUN
ejpam-3281	6	39	)	)	PUNCT
ejpam-3281	6	40	.	.	PUNCT
ejpam-3281	7	1	in	in	ADP
ejpam-3281	7	2	2008	2008	NUM
ejpam-3281	7	3	,	,	PUNCT
ejpam-3281	7	4	yu.v	yu.v	X
ejpam-3281	7	5	.	.	PUNCT
ejpam-3281	8	1	nesterenko	nesterenko	PROPN
ejpam-3281	8	2	proved	prove	VERB
ejpam-3281	8	3	that	that	SCONJ
ejpam-3281	8	4	if	if	SCONJ
ejpam-3281	8	5	α1	α1	PROPN
ejpam-3281	8	6	,	,	PUNCT
ejpam-3281	8	7	...	...	PUNCT
ejpam-3281	8	8	,	,	PUNCT
ejpam-3281	8	9	αn	αn	X
ejpam-3281	8	10	∈	∈	PROPN
ejpam-3281	8	11	e	e	NOUN
ejpam-3281	8	12	are	be	AUX
ejpam-3281	8	13	algebraic	algebraic	ADJ
ejpam-3281	8	14	over	over	ADP
ejpam-3281	8	15	q	q	NOUN
ejpam-3281	8	16	and	and	CCONJ
ejpam-3281	8	17	form	form	VERB
ejpam-3281	8	18	a	a	DET
ejpam-3281	8	19	basis	basis	NOUN
ejpam-3281	8	20	of	of	ADP
ejpam-3281	8	21	a	a	DET
ejpam-3281	8	22	finite	finite	ADJ
ejpam-3281	8	23	extension	extension	NOUN
ejpam-3281	8	24	of	of	ADP
ejpam-3281	8	25	degree	degree	NOUN
ejpam-3281	8	26	n	n	PROPN
ejpam-3281	8	27	of	of	ADP
ejpam-3281	8	28	q.	q.	PROPN
ejpam-3281	8	29	then	then	ADV
ejpam-3281	8	30	,	,	PUNCT
ejpam-3281	8	31	there	there	PRON
ejpam-3281	8	32	exist	exist	VERB
ejpam-3281	8	33	at	at	ADP
ejpam-3281	8	34	least	least	ADJ
ejpam-3281	8	35	bn2	bn2	NOUN
ejpam-3281	8	36	c	c	NOUN
ejpam-3281	8	37	among	among	ADP
ejpam-3281	8	38	the	the	DET
ejpam-3281	8	39	elements	element	NOUN
ejpam-3281	8	40	exp(α1	exp(α1	PROPN
ejpam-3281	8	41	)	)	PUNCT
ejpam-3281	8	42	,	,	PUNCT
ejpam-3281	8	43	....	....	PUNCT
ejpam-3281	8	44	,	,	PUNCT
ejpam-3281	8	45	exp(αn	exp(αn	NOUN
ejpam-3281	8	46	)	)	PUNCT
ejpam-3281	8	47	which	which	PRON
ejpam-3281	8	48	are	be	AUX
ejpam-3281	8	49	q−algebraically	q−algebraically	ADV
ejpam-3281	8	50	independent	independent	ADJ
ejpam-3281	8	51	.	.	PUNCT
ejpam-3281	9	1	this	this	DET
ejpam-3281	9	2	result	result	NOUN
ejpam-3281	9	3	is	be	AUX
ejpam-3281	9	4	usually	usually	ADV
ejpam-3281	9	5	called	call	VERB
ejpam-3281	9	6	half	half	NOUN
ejpam-3281	9	7	of	of	ADP
ejpam-3281	9	8	lindemann	lindemann	PROPN
ejpam-3281	9	9	-	-	PUNCT
ejpam-3281	9	10	weierstrass	weierstrass	PROPN
ejpam-3281	9	11	conjecture	conjecture	NOUN
ejpam-3281	9	12	in	in	ADP
ejpam-3281	9	13	the	the	DET
ejpam-3281	9	14	p−adic	p−adic	ADJ
ejpam-3281	9	15	domain	domain	NOUN
ejpam-3281	9	16	,	,	PUNCT
ejpam-3281	9	17	[	[	X
ejpam-3281	9	18	n	n	X
ejpam-3281	9	19	]	]	PUNCT
ejpam-3281	9	20	.	.	PUNCT
ejpam-3281	10	1	in	in	ADP
ejpam-3281	10	2	this	this	DET
ejpam-3281	10	3	paper	paper	NOUN
ejpam-3281	10	4	,	,	PUNCT
ejpam-3281	10	5	we	we	PRON
ejpam-3281	10	6	use	use	VERB
ejpam-3281	10	7	weierstrass	weierstrass	NOUN
ejpam-3281	10	8	preparation	preparation	NOUN
ejpam-3281	10	9	theorem	theorem	VERB
ejpam-3281	10	10	to	to	PART
ejpam-3281	10	11	give	give	VERB
ejpam-3281	10	12	necessary	necessary	ADJ
ejpam-3281	10	13	and	and	CCONJ
ejpam-3281	10	14	sufficient	sufficient	ADJ
ejpam-3281	10	15	conditions	condition	NOUN
ejpam-3281	10	16	on	on	ADP
ejpam-3281	10	17	a	a	DET
ejpam-3281	10	18	class	class	NOUN
ejpam-3281	10	19	of	of	ADP
ejpam-3281	10	20	polynomials	polynomial	NOUN
ejpam-3281	10	21	over	over	ADP
ejpam-3281	10	22	z	z	NOUN
ejpam-3281	10	23	so	so	SCONJ
ejpam-3281	10	24	that	that	SCONJ
ejpam-3281	10	25	each	each	DET
ejpam-3281	10	26	one	one	NUM
ejpam-3281	10	27	of	of	ADP
ejpam-3281	10	28	them	they	PRON
ejpam-3281	10	29	has	have	VERB
ejpam-3281	10	30	a	a	DET
ejpam-3281	10	31	root	root	NOUN
ejpam-3281	10	32	of	of	ADP
ejpam-3281	10	33	the	the	DET
ejpam-3281	10	34	form	form	NOUN
ejpam-3281	10	35	(	(	PUNCT
ejpam-3281	10	36	x	x	NOUN
ejpam-3281	10	37	,	,	PUNCT
ejpam-3281	10	38	exp(x	exp(x	PROPN
ejpam-3281	10	39	)	)	PUNCT
ejpam-3281	10	40	)	)	PUNCT
ejpam-3281	10	41	.	.	PUNCT
ejpam-3281	11	1	similarly	similarly	ADV
ejpam-3281	11	2	,	,	PUNCT
ejpam-3281	11	3	we	we	PRON
ejpam-3281	11	4	use	use	VERB
ejpam-3281	11	5	hilbert	hilbert	NOUN
ejpam-3281	11	6	theorem	theorem	VERB
ejpam-3281	11	7	on	on	ADP
ejpam-3281	11	8	the	the	DET
ejpam-3281	11	9	ring	ring	NOUN
ejpam-3281	11	10	of	of	ADP
ejpam-3281	11	11	strictly	strictly	ADV
ejpam-3281	11	12	convergent	convergent	ADJ
ejpam-3281	11	13	power	power	NOUN
ejpam-3281	11	14	series	series	NOUN
ejpam-3281	11	15	to	to	PART
ejpam-3281	11	16	give	give	VERB
ejpam-3281	11	17	necessary	necessary	ADJ
ejpam-3281	11	18	and	and	CCONJ
ejpam-3281	11	19	sufficient	sufficient	ADJ
ejpam-3281	11	20	conditions	condition	NOUN
ejpam-3281	11	21	on	on	ADP
ejpam-3281	11	22	a	a	DET
ejpam-3281	11	23	class	class	NOUN
ejpam-3281	11	24	of	of	ADP
ejpam-3281	11	25	polynomials	polynomial	NOUN
ejpam-3281	11	26	over	over	ADP
ejpam-3281	11	27	z	z	NOUN
ejpam-3281	11	28	so	so	SCONJ
ejpam-3281	11	29	that	that	SCONJ
ejpam-3281	11	30	each	each	DET
ejpam-3281	11	31	one	one	NUM
ejpam-3281	11	32	of	of	ADP
ejpam-3281	11	33	them	they	PRON
ejpam-3281	11	34	has	have	VERB
ejpam-3281	11	35	a	a	DET
ejpam-3281	11	36	root	root	NOUN
ejpam-3281	11	37	of	of	ADP
ejpam-3281	11	38	the	the	DET
ejpam-3281	11	39	form	form	NOUN
ejpam-3281	11	40	(	(	PUNCT
ejpam-3281	11	41	exp(x1	exp(x1	ADJ
ejpam-3281	11	42	)	)	PUNCT
ejpam-3281	11	43	,	,	PUNCT
ejpam-3281	11	44	exp(x2	exp(x2	NOUN
ejpam-3281	11	45	)	)	PUNCT
ejpam-3281	11	46	)	)	PUNCT
ejpam-3281	11	47	.	.	PUNCT
ejpam-3281	12	1	that	that	PRON
ejpam-3281	12	2	enables	enable	VERB
ejpam-3281	12	3	us	we	PRON
ejpam-3281	12	4	to	to	PART
ejpam-3281	12	5	put	put	VERB
ejpam-3281	12	6	necessary	necessary	ADJ
ejpam-3281	12	7	conditions	condition	NOUN
ejpam-3281	12	8	on	on	ADP
ejpam-3281	12	9	certain	certain	ADJ
ejpam-3281	12	10	varieties	variety	NOUN
ejpam-3281	12	11	v	v	ADP
ejpam-3281	12	12	⊆	⊆	NUM
ejpam-3281	12	13	c4	c4	NOUN
ejpam-3281	12	14	p	p	NOUN
ejpam-3281	12	15	of	of	ADP
ejpam-3281	12	16	dimension	dimension	NOUN
ejpam-3281	12	17	one	one	NUM
ejpam-3281	12	18	over	over	ADP
ejpam-3281	12	19	q	q	NOUN
ejpam-3281	12	20	in	in	ADP
ejpam-3281	12	21	order	order	NOUN
ejpam-3281	12	22	to	to	PART
ejpam-3281	12	23	have	have	AUX
ejpam-3281	12	24	points	point	NOUN
ejpam-3281	12	25	of	of	ADP
ejpam-3281	12	26	the	the	DET
ejpam-3281	12	27	form	form	NOUN
ejpam-3281	12	28	(	(	PUNCT
ejpam-3281	12	29	x1	x1	PROPN
ejpam-3281	12	30	,	,	PUNCT
ejpam-3281	12	31	x2	x2	PROPN
ejpam-3281	12	32	,	,	PUNCT
ejpam-3281	12	33	exp(x1	exp(x1	ADJ
ejpam-3281	12	34	)	)	PUNCT
ejpam-3281	12	35	,	,	PUNCT
ejpam-3281	12	36	exp(x2	exp(x2	NOUN
ejpam-3281	12	37	)	)	PUNCT
ejpam-3281	12	38	)	)	PUNCT
ejpam-3281	12	39	.	.	PUNCT
ejpam-3281	13	1	also	also	ADV
ejpam-3281	13	2	,	,	PUNCT
ejpam-3281	13	3	we	we	PRON
ejpam-3281	13	4	give	give	VERB
ejpam-3281	13	5	a	a	DET
ejpam-3281	13	6	class	class	NOUN
ejpam-3281	13	7	of	of	ADP
ejpam-3281	13	8	varieties	variety	NOUN
ejpam-3281	13	9	v	v	ADP
ejpam-3281	13	10	⊆	⊆	NUM
ejpam-3281	13	11	c4	c4	NOUN
ejpam-3281	13	12	p	p	NOUN
ejpam-3281	13	13	of	of	ADP
ejpam-3281	13	14	dimension	dimension	NOUN
ejpam-3281	13	15	one	one	NUM
ejpam-3281	13	16	over	over	ADP
ejpam-3281	13	17	q	q	NOUN
ejpam-3281	13	18	such	such	ADJ
ejpam-3281	13	19	that	that	SCONJ
ejpam-3281	13	20	each	each	DET
ejpam-3281	13	21	variety	variety	NOUN
ejpam-3281	13	22	contains	contain	VERB
ejpam-3281	13	23	a	a	DET
ejpam-3281	13	24	point	point	NOUN
ejpam-3281	13	25	of	of	ADP
ejpam-3281	13	26	the	the	DET
ejpam-3281	13	27	form	form	NOUN
ejpam-3281	13	28	(	(	PUNCT
ejpam-3281	13	29	x1	x1	PROPN
ejpam-3281	13	30	,	,	PUNCT
ejpam-3281	13	31	x2	x2	PROPN
ejpam-3281	13	32	,	,	PUNCT
ejpam-3281	13	33	exp(x1	exp(x1	ADJ
ejpam-3281	13	34	)	)	PUNCT
ejpam-3281	13	35	,	,	PUNCT
ejpam-3281	13	36	exp(x2	exp(x2	NOUN
ejpam-3281	13	37	)	)	PUNCT
ejpam-3281	13	38	)	)	PUNCT
ejpam-3281	13	39	.	.	PUNCT
ejpam-3281	14	1	this	this	DET
ejpam-3281	14	2	point	point	NOUN
ejpam-3281	14	3	does	do	AUX
ejpam-3281	14	4	not	not	PART
ejpam-3281	14	5	contradict	contradict	VERB
ejpam-3281	14	6	schanuel	schanuel	NOUN
ejpam-3281	14	7	’s	’s	PART
ejpam-3281	14	8	conjecture	conjecture	NOUN
ejpam-3281	14	9	for	for	ADP
ejpam-3281	14	10	two	two	NUM
ejpam-3281	14	11	elements	element	NOUN
ejpam-3281	14	12	.	.	PUNCT
ejpam-3281	15	1	the	the	DET
ejpam-3281	15	2	conjecture	conjecture	NOUN
ejpam-3281	15	3	asserts	assert	VERB
ejpam-3281	15	4	that	that	SCONJ
ejpam-3281	15	5	for	for	ADP
ejpam-3281	15	6	a	a	DET
ejpam-3281	15	7	given	give	VERB
ejpam-3281	15	8	variety	variety	NOUN
ejpam-3281	15	9	v	v	ADP
ejpam-3281	15	10	⊆	⊆	NUM
ejpam-3281	15	11	c4	c4	NOUN
ejpam-3281	15	12	p	p	NOUN
ejpam-3281	15	13	over	over	ADP
ejpam-3281	15	14	q	q	NOUN
ejpam-3281	15	15	of	of	ADP
ejpam-3281	15	16	dimension	dimension	NOUN
ejpam-3281	15	17	one	one	NUM
ejpam-3281	15	18	and	and	CCONJ
ejpam-3281	15	19	a	a	DET
ejpam-3281	15	20	tuple	tuple	NOUN
ejpam-3281	15	21	(	(	PUNCT
ejpam-3281	15	22	x1	x1	PROPN
ejpam-3281	15	23	,	,	PUNCT
ejpam-3281	15	24	x2	x2	PROPN
ejpam-3281	15	25	,	,	PUNCT
ejpam-3281	15	26	exp(x1	exp(x1	ADJ
ejpam-3281	15	27	)	)	PUNCT
ejpam-3281	15	28	,	,	PUNCT
ejpam-3281	15	29	exp(x2	exp(x2	NOUN
ejpam-3281	15	30	)	)	PUNCT
ejpam-3281	15	31	)	)	PUNCT
ejpam-3281	16	1	∈	∈	PROPN
ejpam-3281	16	2	v	v	NOUN
ejpam-3281	16	3	,	,	PUNCT
ejpam-3281	16	4	then	then	ADV
ejpam-3281	16	5	x1	x1	NUM
ejpam-3281	16	6	,	,	PUNCT
ejpam-3281	16	7	x2	x2	PRON
ejpam-3281	16	8	are	be	AUX
ejpam-3281	16	9	q	q	ADJ
ejpam-3281	16	10	-	-	PUNCT
ejpam-3281	16	11	linearly	linearly	ADV
ejpam-3281	16	12	dependent	dependent	ADJ
ejpam-3281	16	13	.	.	PUNCT
ejpam-3281	17	1	finally	finally	ADV
ejpam-3281	17	2	,	,	PUNCT
ejpam-3281	17	3	doi	doi	PROPN
ejpam-3281	17	4	:	:	PUNCT
ejpam-3281	17	5	https://doi.org/10.29020/nybg.ejpam.v11i4.3281	https://doi.org/10.29020/nybg.ejpam.v11i4.3281	NUM
ejpam-3281	17	6	email	email	NOUN
ejpam-3281	17	7	address	address	NOUN
ejpam-3281	17	8	:	:	PUNCT
ejpam-3281	17	9	amrandalloul@hotmail.com	amrandalloul@hotmail.com	X
ejpam-3281	17	10	(	(	PUNCT
ejpam-3281	17	11	a.	a.	NOUN
ejpam-3281	17	12	dalloul	dalloul	PROPN
ejpam-3281	17	13	)	)	PUNCT
ejpam-3281	17	14	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3281	18	1	1046	1046	NUM
ejpam-3281	18	2	c	c	X
ejpam-3281	18	3	©	©	PROPN
ejpam-3281	18	4	2018	2018	NUM
ejpam-3281	18	5	ejpam	ejpam	VERB
ejpam-3281	18	6	all	all	DET
ejpam-3281	18	7	rights	right	NOUN
ejpam-3281	18	8	reserved	reserve	VERB
ejpam-3281	18	9	.	.	PUNCT
ejpam-3281	19	1	a.	a.	PROPN
ejpam-3281	19	2	dalloul	dalloul	PROPN
ejpam-3281	19	3	/	/	SYM
ejpam-3281	19	4	eur	eur	PROPN
ejpam-3281	19	5	.	.	PUNCT
ejpam-3281	20	1	j.	j.	PROPN
ejpam-3281	20	2	pure	pure	PROPN
ejpam-3281	20	3	appl	appl	PROPN
ejpam-3281	20	4	.	.	PROPN
ejpam-3281	20	5	math	math	PROPN
ejpam-3281	20	6	,	,	PUNCT
ejpam-3281	20	7	11	11	NUM
ejpam-3281	20	8	(	(	PUNCT
ejpam-3281	20	9	4	4	NUM
ejpam-3281	20	10	)	)	PUNCT
ejpam-3281	20	11	(	(	PUNCT
ejpam-3281	20	12	2018	2018	NUM
ejpam-3281	20	13	)	)	PUNCT
ejpam-3281	20	14	,	,	PUNCT
ejpam-3281	20	15	1046	1046	NUM
ejpam-3281	20	16	-	-	SYM
ejpam-3281	20	17	1057	1057	NUM
ejpam-3281	20	18	1047	1047	NUM
ejpam-3281	20	19	we	we	PRON
ejpam-3281	20	20	give	give	VERB
ejpam-3281	20	21	some	some	DET
ejpam-3281	20	22	applications	application	NOUN
ejpam-3281	20	23	on	on	ADP
ejpam-3281	20	24	weierstrass	weierstrass	NOUN
ejpam-3281	20	25	preparation	preparation	NOUN
ejpam-3281	20	26	theorem	theorem	NOUN
ejpam-3281	20	27	and	and	CCONJ
ejpam-3281	20	28	hilbert	hilbert	PROPN
ejpam-3281	20	29	theorem	theorem	PROPN
ejpam-3281	20	30	concerning	concern	VERB
ejpam-3281	20	31	the	the	DET
ejpam-3281	20	32	algebraic	algebraic	ADJ
ejpam-3281	20	33	dependence	dependence	NOUN
ejpam-3281	20	34	over	over	ADP
ejpam-3281	20	35	qp	qp	NOUN
ejpam-3281	20	36	and	and	CCONJ
ejpam-3281	20	37	other	other	ADJ
ejpam-3281	20	38	related	related	ADJ
ejpam-3281	20	39	topics	topic	NOUN
ejpam-3281	20	40	.	.	PUNCT
ejpam-3281	21	1	many	many	ADJ
ejpam-3281	21	2	results	result	NOUN
ejpam-3281	21	3	concerning	concern	VERB
ejpam-3281	21	4	the	the	DET
ejpam-3281	21	5	existence	existence	NOUN
ejpam-3281	21	6	of	of	ADP
ejpam-3281	21	7	roots	root	NOUN
ejpam-3281	21	8	of	of	ADP
ejpam-3281	21	9	p−adic	p−adic	ADJ
ejpam-3281	21	10	exponential	exponential	ADJ
ejpam-3281	21	11	polynomials	polynomial	NOUN
ejpam-3281	21	12	have	have	AUX
ejpam-3281	21	13	been	be	AUX
ejpam-3281	21	14	made	make	VERB
ejpam-3281	21	15	by	by	ADP
ejpam-3281	21	16	poorten	poorten	NOUN
ejpam-3281	21	17	(	(	PUNCT
ejpam-3281	21	18	see	see	VERB
ejpam-3281	21	19	[	[	X
ejpam-3281	21	20	p	p	X
ejpam-3281	21	21	]	]	X
ejpam-3281	21	22	and	and	CCONJ
ejpam-3281	21	23	[	[	X
ejpam-3281	21	24	pr	pr	X
ejpam-3281	21	25	]	]	X
ejpam-3281	21	26	)	)	PUNCT
ejpam-3281	21	27	and	and	CCONJ
ejpam-3281	21	28	others	other	NOUN
ejpam-3281	21	29	.	.	PUNCT
ejpam-3281	22	1	these	these	DET
ejpam-3281	22	2	results	result	NOUN
ejpam-3281	22	3	imply	imply	VERB
ejpam-3281	22	4	the	the	DET
ejpam-3281	22	5	existence	existence	NOUN
ejpam-3281	22	6	of	of	ADP
ejpam-3281	22	7	roots	root	NOUN
ejpam-3281	22	8	of	of	ADP
ejpam-3281	22	9	polynomials	polynomial	NOUN
ejpam-3281	22	10	p	p	X
ejpam-3281	23	1	[	[	X
ejpam-3281	23	2	x	x	X
ejpam-3281	23	3	,	,	PUNCT
ejpam-3281	23	4	y	y	PROPN
ejpam-3281	23	5	]	]	PUNCT
ejpam-3281	23	6	∈	∈	PROPN
ejpam-3281	23	7	q[x	q[x	PROPN
ejpam-3281	23	8	,	,	PUNCT
ejpam-3281	23	9	y	y	PROPN
ejpam-3281	23	10	]	]	PUNCT
ejpam-3281	23	11	of	of	ADP
ejpam-3281	23	12	the	the	DET
ejpam-3281	23	13	form	form	NOUN
ejpam-3281	23	14	(	(	PUNCT
ejpam-3281	23	15	x	x	NOUN
ejpam-3281	23	16	,	,	PUNCT
ejpam-3281	23	17	exp(x	exp(x	PROPN
ejpam-3281	23	18	)	)	PUNCT
ejpam-3281	23	19	)	)	PUNCT
ejpam-3281	23	20	.	.	PUNCT
ejpam-3281	24	1	in	in	ADP
ejpam-3281	24	2	our	our	PRON
ejpam-3281	24	3	work	work	NOUN
ejpam-3281	24	4	,	,	PUNCT
ejpam-3281	24	5	we	we	PRON
ejpam-3281	24	6	consider	consider	VERB
ejpam-3281	24	7	these	these	DET
ejpam-3281	24	8	polynomials	polynomial	NOUN
ejpam-3281	24	9	directly	directly	ADV
ejpam-3281	24	10	where	where	SCONJ
ejpam-3281	24	11	the	the	DET
ejpam-3281	24	12	coefficients	coefficient	NOUN
ejpam-3281	24	13	and	and	CCONJ
ejpam-3281	24	14	degrees	degree	NOUN
ejpam-3281	24	15	of	of	ADP
ejpam-3281	24	16	the	the	DET
ejpam-3281	24	17	variables	variable	NOUN
ejpam-3281	24	18	play	play	VERB
ejpam-3281	24	19	a	a	DET
ejpam-3281	24	20	role	role	NOUN
ejpam-3281	24	21	in	in	ADP
ejpam-3281	24	22	the	the	DET
ejpam-3281	24	23	existence	existence	NOUN
ejpam-3281	24	24	of	of	ADP
ejpam-3281	24	25	such	such	ADJ
ejpam-3281	24	26	roots	root	NOUN
ejpam-3281	24	27	.	.	PUNCT
ejpam-3281	25	1	we	we	PRON
ejpam-3281	25	2	prove	prove	VERB
ejpam-3281	25	3	,	,	PUNCT
ejpam-3281	25	4	as	as	ADP
ejpam-3281	25	5	a	a	DET
ejpam-3281	25	6	corollary	corollary	NOUN
ejpam-3281	25	7	,	,	PUNCT
ejpam-3281	25	8	that	that	SCONJ
ejpam-3281	25	9	there	there	PRON
ejpam-3281	25	10	exist	exist	VERB
ejpam-3281	25	11	polynomials	polynomial	NOUN
ejpam-3281	25	12	in	in	ADP
ejpam-3281	25	13	q[x	q[x	PROPN
ejpam-3281	25	14	,	,	PUNCT
ejpam-3281	25	15	y	y	PROPN
ejpam-3281	25	16	]	]	PUNCT
ejpam-3281	25	17	which	which	PRON
ejpam-3281	25	18	do	do	AUX
ejpam-3281	25	19	not	not	PART
ejpam-3281	25	20	contain	contain	VERB
ejpam-3281	25	21	any	any	DET
ejpam-3281	25	22	root	root	NOUN
ejpam-3281	25	23	of	of	ADP
ejpam-3281	25	24	the	the	DET
ejpam-3281	25	25	form	form	NOUN
ejpam-3281	25	26	(	(	PUNCT
ejpam-3281	25	27	x	x	NOUN
ejpam-3281	25	28	,	,	PUNCT
ejpam-3281	25	29	exp(x	exp(x	PROPN
ejpam-3281	25	30	)	)	PUNCT
ejpam-3281	25	31	)	)	PUNCT
ejpam-3281	25	32	.	.	PUNCT
ejpam-3281	26	1	this	this	PRON
ejpam-3281	26	2	implies	imply	VERB
ejpam-3281	26	3	the	the	DET
ejpam-3281	26	4	existence	existence	NOUN
ejpam-3281	26	5	of	of	ADP
ejpam-3281	26	6	varieties	variety	NOUN
ejpam-3281	26	7	v	v	ADP
ejpam-3281	26	8	⊆	⊆	NUM
ejpam-3281	26	9	c4	c4	NOUN
ejpam-3281	26	10	p	p	NOUN
ejpam-3281	26	11	over	over	ADP
ejpam-3281	26	12	q	q	NOUN
ejpam-3281	26	13	of	of	ADP
ejpam-3281	26	14	dimension	dimension	NOUN
ejpam-3281	26	15	one	one	NUM
ejpam-3281	26	16	which	which	PRON
ejpam-3281	26	17	do	do	AUX
ejpam-3281	26	18	not	not	PART
ejpam-3281	26	19	contain	contain	VERB
ejpam-3281	26	20	points	point	NOUN
ejpam-3281	26	21	of	of	ADP
ejpam-3281	26	22	the	the	DET
ejpam-3281	26	23	form	form	NOUN
ejpam-3281	26	24	(	(	PUNCT
ejpam-3281	26	25	x1	x1	PROPN
ejpam-3281	26	26	,	,	PUNCT
ejpam-3281	26	27	x2	x2	PROPN
ejpam-3281	26	28	,	,	PUNCT
ejpam-3281	26	29	exp(x1	exp(x1	ADJ
ejpam-3281	26	30	)	)	PUNCT
ejpam-3281	26	31	,	,	PUNCT
ejpam-3281	26	32	exp(x2	exp(x2	NOUN
ejpam-3281	26	33	)	)	PUNCT
ejpam-3281	26	34	)	)	PUNCT
ejpam-3281	26	35	.	.	PUNCT
ejpam-3281	27	1	using	use	VERB
ejpam-3281	27	2	the	the	DET
ejpam-3281	27	3	same	same	ADJ
ejpam-3281	27	4	technic	technic	NOUN
ejpam-3281	27	5	,	,	PUNCT
ejpam-3281	27	6	we	we	PRON
ejpam-3281	27	7	prove	prove	VERB
ejpam-3281	27	8	that	that	SCONJ
ejpam-3281	27	9	there	there	PRON
ejpam-3281	27	10	exist	exist	VERB
ejpam-3281	27	11	polynomials	polynomial	NOUN
ejpam-3281	27	12	over	over	ADP
ejpam-3281	27	13	z	z	NOUN
ejpam-3281	27	14	with	with	ADP
ejpam-3281	27	15	2n	2n	NUM
ejpam-3281	27	16	variables	variable	NOUN
ejpam-3281	27	17	which	which	PRON
ejpam-3281	27	18	do	do	AUX
ejpam-3281	27	19	not	not	PART
ejpam-3281	27	20	contain	contain	VERB
ejpam-3281	27	21	any	any	DET
ejpam-3281	27	22	root	root	NOUN
ejpam-3281	27	23	of	of	ADP
ejpam-3281	27	24	the	the	DET
ejpam-3281	27	25	form	form	NOUN
ejpam-3281	27	26	(	(	PUNCT
ejpam-3281	27	27	x1	x1	PROPN
ejpam-3281	27	28	,	,	PUNCT
ejpam-3281	27	29	..	..	PUNCT
ejpam-3281	27	30	,	,	PUNCT
ejpam-3281	27	31	xn	xn	PROPN
ejpam-3281	27	32	,	,	PUNCT
ejpam-3281	27	33	exp(x1	exp(x1	ADJ
ejpam-3281	27	34	)	)	PUNCT
ejpam-3281	27	35	,	,	PUNCT
ejpam-3281	27	36	..	..	PUNCT
ejpam-3281	27	37	,	,	PUNCT
ejpam-3281	27	38	exp(xn	exp(xn	NOUN
ejpam-3281	27	39	)	)	PUNCT
ejpam-3281	27	40	)	)	PUNCT
ejpam-3281	27	41	.	.	PUNCT
ejpam-3281	28	1	furthermore	furthermore	ADV
ejpam-3281	28	2	,	,	PUNCT
ejpam-3281	28	3	we	we	PRON
ejpam-3281	28	4	use	use	VERB
ejpam-3281	28	5	weierstrass	weierstrass	NOUN
ejpam-3281	28	6	preparation	preparation	NOUN
ejpam-3281	28	7	theorem	theorem	VERB
ejpam-3281	28	8	to	to	PART
ejpam-3281	28	9	prove	prove	VERB
ejpam-3281	28	10	the	the	DET
ejpam-3281	28	11	existence	existence	NOUN
ejpam-3281	28	12	of	of	ADP
ejpam-3281	28	13	varieties	variety	NOUN
ejpam-3281	28	14	v	v	ADP
ejpam-3281	28	15	⊆	⊆	NUM
ejpam-3281	28	16	c4	c4	NOUN
ejpam-3281	28	17	p	p	NOUN
ejpam-3281	28	18	over	over	ADP
ejpam-3281	28	19	qp	qp	NOUN
ejpam-3281	28	20	of	of	ADP
ejpam-3281	28	21	dimension	dimension	NOUN
ejpam-3281	28	22	one	one	NOUN
ejpam-3281	28	23	that	that	PRON
ejpam-3281	28	24	contain	contain	VERB
ejpam-3281	28	25	points	point	NOUN
ejpam-3281	28	26	of	of	ADP
ejpam-3281	28	27	the	the	DET
ejpam-3281	28	28	form	form	NOUN
ejpam-3281	28	29	(	(	PUNCT
ejpam-3281	28	30	x1	x1	PROPN
ejpam-3281	28	31	,	,	PUNCT
ejpam-3281	28	32	x2	x2	PROPN
ejpam-3281	28	33	,	,	PUNCT
ejpam-3281	28	34	exp(x1	exp(x1	ADJ
ejpam-3281	28	35	)	)	PUNCT
ejpam-3281	28	36	,	,	PUNCT
ejpam-3281	28	37	exp(x2	exp(x2	NOUN
ejpam-3281	28	38	)	)	PUNCT
ejpam-3281	28	39	)	)	PUNCT
ejpam-3281	28	40	.	.	PUNCT
ejpam-3281	29	1	2	2	X
ejpam-3281	29	2	.	.	X
ejpam-3281	29	3	background	background	NOUN
ejpam-3281	29	4	we	we	PRON
ejpam-3281	29	5	recall	recall	VERB
ejpam-3281	29	6	some	some	DET
ejpam-3281	29	7	basic	basic	ADJ
ejpam-3281	29	8	notations	notation	NOUN
ejpam-3281	29	9	and	and	CCONJ
ejpam-3281	29	10	results	result	NOUN
ejpam-3281	29	11	regarding	regard	VERB
ejpam-3281	29	12	the	the	DET
ejpam-3281	29	13	field	field	NOUN
ejpam-3281	29	14	of	of	ADP
ejpam-3281	29	15	p−adic	p−adic	ADJ
ejpam-3281	29	16	numbers	number	NOUN
ejpam-3281	29	17	and	and	CCONJ
ejpam-3281	29	18	some	some	DET
ejpam-3281	29	19	elementary	elementary	ADJ
ejpam-3281	29	20	non	non	ADJ
ejpam-3281	29	21	-	-	ADJ
ejpam-3281	29	22	archimedian	archimedian	ADJ
ejpam-3281	29	23	analysis	analysis	NOUN
ejpam-3281	29	24	that	that	PRON
ejpam-3281	29	25	will	will	AUX
ejpam-3281	29	26	be	be	AUX
ejpam-3281	29	27	needed	need	VERB
ejpam-3281	29	28	later	later	ADV
ejpam-3281	29	29	.	.	PUNCT
ejpam-3281	30	1	for	for	ADP
ejpam-3281	30	2	more	more	ADJ
ejpam-3281	30	3	details	detail	NOUN
ejpam-3281	30	4	,	,	PUNCT
ejpam-3281	30	5	see	see	VERB
ejpam-3281	30	6	[	[	X
ejpam-3281	30	7	bgr	bgr	X
ejpam-3281	30	8	]	]	X
ejpam-3281	30	9	and	and	CCONJ
ejpam-3281	30	10	[	[	X
ejpam-3281	30	11	g	g	X
ejpam-3281	30	12	]	]	PUNCT
ejpam-3281	30	13	.	.	PUNCT
ejpam-3281	31	1	let	let	VERB
ejpam-3281	31	2	p	p	PRON
ejpam-3281	31	3	be	be	AUX
ejpam-3281	31	4	a	a	DET
ejpam-3281	31	5	prime	prime	ADJ
ejpam-3281	31	6	number	number	NOUN
ejpam-3281	31	7	,	,	PUNCT
ejpam-3281	31	8	qp	qp	ADP
ejpam-3281	31	9	the	the	DET
ejpam-3281	31	10	completion	completion	NOUN
ejpam-3281	31	11	of	of	ADP
ejpam-3281	31	12	q	q	NOUN
ejpam-3281	31	13	with	with	ADP
ejpam-3281	31	14	respect	respect	NOUN
ejpam-3281	31	15	to	to	ADP
ejpam-3281	31	16	the	the	DET
ejpam-3281	31	17	non	non	ADJ
ejpam-3281	31	18	-	-	ADJ
ejpam-3281	31	19	archimedian	archimedian	ADJ
ejpam-3281	31	20	absolute	absolute	ADJ
ejpam-3281	31	21	value	value	NOUN
ejpam-3281	31	22	|.|	|.|	NOUN
ejpam-3281	31	23	and	and	CCONJ
ejpam-3281	31	24	cp	cp	VERB
ejpam-3281	31	25	the	the	DET
ejpam-3281	31	26	completion	completion	NOUN
ejpam-3281	31	27	of	of	ADP
ejpam-3281	31	28	the	the	DET
ejpam-3281	31	29	algebraic	algebraic	ADJ
ejpam-3281	31	30	closure	closure	NOUN
ejpam-3281	31	31	of	of	ADP
ejpam-3281	31	32	qp	qp	PROPN
ejpam-3281	31	33	.	.	PUNCT
ejpam-3281	32	1	this	this	DET
ejpam-3281	32	2	field	field	NOUN
ejpam-3281	32	3	is	be	AUX
ejpam-3281	32	4	non	non	ADJ
ejpam-3281	32	5	-	-	ADJ
ejpam-3281	32	6	archimedian	archimedian	ADJ
ejpam-3281	32	7	(	(	PUNCT
ejpam-3281	32	8	with	with	ADP
ejpam-3281	32	9	respect	respect	NOUN
ejpam-3281	32	10	to	to	ADP
ejpam-3281	32	11	the	the	DET
ejpam-3281	32	12	extended	extended	ADJ
ejpam-3281	32	13	p	p	NOUN
ejpam-3281	32	14	-	-	PUNCT
ejpam-3281	32	15	adic	adic	ADJ
ejpam-3281	32	16	absolute	absolute	ADJ
ejpam-3281	32	17	value	value	NOUN
ejpam-3281	32	18	|.|	|.|	NOUN
ejpam-3281	32	19	)	)	PUNCT
ejpam-3281	32	20	,	,	PUNCT
ejpam-3281	32	21	complete	complete	ADJ
ejpam-3281	32	22	and	and	CCONJ
ejpam-3281	32	23	algebraically	algebraically	ADV
ejpam-3281	32	24	closed	close	VERB
ejpam-3281	32	25	with	with	ADP
ejpam-3281	32	26	the	the	DET
ejpam-3281	32	27	residue	residue	NOUN
ejpam-3281	32	28	class	class	NOUN
ejpam-3281	32	29	field	field	NOUN
ejpam-3281	32	30	f̄p	f̄p	PROPN
ejpam-3281	32	31	(	(	PUNCT
ejpam-3281	32	32	the	the	DET
ejpam-3281	32	33	algebraic	algebraic	ADJ
ejpam-3281	32	34	closure	closure	NOUN
ejpam-3281	32	35	of	of	ADP
ejpam-3281	32	36	the	the	DET
ejpam-3281	32	37	field	field	NOUN
ejpam-3281	32	38	fp	fp	NOUN
ejpam-3281	32	39	)	)	PUNCT
ejpam-3281	32	40	and	and	CCONJ
ejpam-3281	32	41	the	the	DET
ejpam-3281	32	42	value	value	NOUN
ejpam-3281	32	43	group	group	NOUN
ejpam-3281	32	44	pq∪{0	pq∪{0	PROPN
ejpam-3281	32	45	}	}	PUNCT
ejpam-3281	32	46	.	.	PUNCT
ejpam-3281	33	1	moreover	moreover	ADV
ejpam-3281	33	2	,	,	PUNCT
ejpam-3281	33	3	the	the	DET
ejpam-3281	33	4	field	field	NOUN
ejpam-3281	33	5	cp	cp	INTJ
ejpam-3281	33	6	is	be	AUX
ejpam-3281	33	7	endowed	endow	VERB
ejpam-3281	33	8	by	by	ADP
ejpam-3281	33	9	the	the	DET
ejpam-3281	33	10	exponential	exponential	ADJ
ejpam-3281	33	11	map	map	NOUN
ejpam-3281	33	12	:	:	PUNCT
ejpam-3281	33	13	exp	exp	NOUN
ejpam-3281	33	14	:	:	PUNCT
ejpam-3281	33	15	e	e	X
ejpam-3281	33	16	→	→	SYM
ejpam-3281	33	17	1	1	NUM
ejpam-3281	33	18	+	+	CCONJ
ejpam-3281	33	19	e	e	NOUN
ejpam-3281	33	20	,	,	PUNCT
ejpam-3281	33	21	x	x	X
ejpam-3281	33	22	7−→	7−→	NOUN
ejpam-3281	33	23	∑	∑	PROPN
ejpam-3281	33	24	n≥0	n≥0	PROPN
ejpam-3281	33	25	xn	xn	PROPN
ejpam-3281	33	26	n	n	NUM
ejpam-3281	33	27	!	!	PUNCT
ejpam-3281	33	28	where	where	SCONJ
ejpam-3281	33	29	e	e	NOUN
ejpam-3281	33	30	=	=	PRON
ejpam-3281	33	31	{	{	PUNCT
ejpam-3281	33	32	x	x	SYM
ejpam-3281	33	33	∈	∈	PROPN
ejpam-3281	33	34	cp	cp	NOUN
ejpam-3281	33	35	;	;	PUNCT
ejpam-3281	33	36	|x|	|x|	PROPN
ejpam-3281	33	37	<	<	X
ejpam-3281	33	38	p	p	X
ejpam-3281	33	39	−1	−1	NOUN
ejpam-3281	33	40	p−1	p−1	PROPN
ejpam-3281	33	41	}	}	PUNCT
ejpam-3281	33	42	.	.	PUNCT
ejpam-3281	34	1	it	it	PRON
ejpam-3281	34	2	is	be	AUX
ejpam-3281	34	3	well	well	ADV
ejpam-3281	34	4	-	-	PUNCT
ejpam-3281	34	5	known	know	VERB
ejpam-3281	34	6	in	in	ADP
ejpam-3281	34	7	the	the	DET
ejpam-3281	34	8	non	non	ADJ
ejpam-3281	34	9	-	-	ADJ
ejpam-3281	34	10	archimedian	archimedian	ADJ
ejpam-3281	34	11	fields	field	NOUN
ejpam-3281	34	12	that	that	PRON
ejpam-3281	34	13	a	a	DET
ejpam-3281	34	14	series	series	NOUN
ejpam-3281	34	15	∑	∑	PROPN
ejpam-3281	34	16	n	n	PROPN
ejpam-3281	34	17	an	an	PRON
ejpam-3281	34	18	is	be	AUX
ejpam-3281	34	19	convergent	convergent	ADJ
ejpam-3281	34	20	if	if	SCONJ
ejpam-3281	34	21	and	and	CCONJ
ejpam-3281	34	22	only	only	ADV
ejpam-3281	35	1	if	if	SCONJ
ejpam-3281	35	2	lim	lim	PROPN
ejpam-3281	35	3	n→∞	n→∞	NOUN
ejpam-3281	35	4	|an|	|an|	NOUN
ejpam-3281	35	5	=	=	NOUN
ejpam-3281	35	6	0	0	X
ejpam-3281	35	7	.	.	PUNCT
ejpam-3281	35	8	therefore	therefore	ADV
ejpam-3281	35	9	,	,	PUNCT
ejpam-3281	35	10	let	let	VERB
ejpam-3281	35	11	f(x	f(x	PROPN
ejpam-3281	35	12	)	)	PUNCT
ejpam-3281	35	13	=	=	PUNCT
ejpam-3281	35	14	∑∞	∑∞	NOUN
ejpam-3281	35	15	n=0	n=0	X
ejpam-3281	35	16	anx	anx	ADJ
ejpam-3281	35	17	n	n	CCONJ
ejpam-3281	35	18	∈	∈	PROPN
ejpam-3281	35	19	cp[[x	cp[[x	PROPN
ejpam-3281	35	20	]	]	X
ejpam-3281	35	21	]	]	PUNCT
ejpam-3281	35	22	be	be	AUX
ejpam-3281	35	23	a	a	DET
ejpam-3281	35	24	power	power	NOUN
ejpam-3281	35	25	series	series	NOUN
ejpam-3281	35	26	.	.	PUNCT
ejpam-3281	36	1	then	then	ADV
ejpam-3281	36	2	,	,	PUNCT
ejpam-3281	36	3	f(x	f(x	PROPN
ejpam-3281	36	4	)	)	PUNCT
ejpam-3281	36	5	is	be	AUX
ejpam-3281	36	6	convergent	convergent	ADJ
ejpam-3281	36	7	for	for	ADP
ejpam-3281	36	8	each	each	DET
ejpam-3281	36	9	x	x	PUNCT
ejpam-3281	36	10	in	in	ADP
ejpam-3281	36	11	the	the	DET
ejpam-3281	36	12	closed	closed	ADJ
ejpam-3281	36	13	ball	ball	NOUN
ejpam-3281	36	14	b(0	b(0	NOUN
ejpam-3281	36	15	,	,	PUNCT
ejpam-3281	36	16	c	c	NOUN
ejpam-3281	36	17	)	)	PUNCT
ejpam-3281	36	18	if	if	SCONJ
ejpam-3281	37	1	and	and	CCONJ
ejpam-3281	37	2	only	only	ADV
ejpam-3281	37	3	if	if	SCONJ
ejpam-3281	37	4	lim	lim	PROPN
ejpam-3281	37	5	n→∞	n→∞	X
ejpam-3281	37	6	|an|cn	|an|cn	ADV
ejpam-3281	37	7	=	=	PUNCT
ejpam-3281	37	8	0	0	X
ejpam-3281	37	9	.	.	PUNCT
ejpam-3281	38	1	since	since	SCONJ
ejpam-3281	38	2	(	(	PUNCT
ejpam-3281	38	3	|an|cn	|an|cn	X
ejpam-3281	38	4	)	)	PUNCT
ejpam-3281	38	5	is	be	AUX
ejpam-3281	38	6	convergent	convergent	ADJ
ejpam-3281	38	7	,	,	PUNCT
ejpam-3281	38	8	it	it	PRON
ejpam-3281	38	9	is	be	AUX
ejpam-3281	38	10	bounded	bound	VERB
ejpam-3281	38	11	.	.	PUNCT
ejpam-3281	39	1	i.e	i.e	PRON
ejpam-3281	39	2	,	,	PUNCT
ejpam-3281	39	3	it	it	PRON
ejpam-3281	39	4	has	have	VERB
ejpam-3281	39	5	a	a	DET
ejpam-3281	39	6	maximum	maximum	NOUN
ejpam-3281	39	7	.	.	PUNCT
ejpam-3281	40	1	therefore	therefore	ADV
ejpam-3281	40	2	,	,	PUNCT
ejpam-3281	40	3	the	the	DET
ejpam-3281	40	4	norm	norm	NOUN
ejpam-3281	40	5	‖	‖	PROPN
ejpam-3281	40	6	.	.	PUNCT
ejpam-3281	41	1	‖c	‖c	NOUN
ejpam-3281	41	2	on	on	ADP
ejpam-3281	41	3	f(x	f(x	PROPN
ejpam-3281	41	4	)	)	PUNCT
ejpam-3281	41	5	is	be	AUX
ejpam-3281	41	6	defined	define	VERB
ejpam-3281	41	7	as	as	SCONJ
ejpam-3281	41	8	follows	follow	VERB
ejpam-3281	41	9	:	:	PUNCT
ejpam-3281	42	1	‖	‖	PROPN
ejpam-3281	42	2	f(x	f(x	PROPN
ejpam-3281	42	3	)	)	PUNCT
ejpam-3281	42	4	‖c:=	‖c:=	ADJ
ejpam-3281	42	5	max{|an|cn	max{|an|cn	NOUN
ejpam-3281	42	6	}	}	PUNCT
ejpam-3281	42	7	.	.	PUNCT
ejpam-3281	43	1	we	we	PRON
ejpam-3281	43	2	summaries	summarie	VERB
ejpam-3281	43	3	the	the	DET
ejpam-3281	43	4	properties	property	NOUN
ejpam-3281	43	5	of	of	ADP
ejpam-3281	43	6	‖	‖	PROPN
ejpam-3281	43	7	.	.	PUNCT
ejpam-3281	44	1	‖c	‖c	NOUN
ejpam-3281	44	2	as	as	SCONJ
ejpam-3281	44	3	follows	follow	VERB
ejpam-3281	44	4	,	,	PUNCT
ejpam-3281	45	1	[	[	X
ejpam-3281	45	2	g	g	X
ejpam-3281	45	3	]	]	X
ejpam-3281	45	4	:	:	PUNCT
ejpam-3281	45	5	1	1	X
ejpam-3281	45	6	)	)	PUNCT
ejpam-3281	45	7	‖	‖	PROPN
ejpam-3281	45	8	f(x	f(x	PROPN
ejpam-3281	45	9	)	)	PUNCT
ejpam-3281	46	1	‖c=	‖c=	ADP
ejpam-3281	46	2	0⇔	0⇔	NOUN
ejpam-3281	46	3	f(x	f(x	PROPN
ejpam-3281	46	4	)	)	PUNCT
ejpam-3281	46	5	≡	≡	PROPN
ejpam-3281	46	6	0	0	NUM
ejpam-3281	46	7	,	,	PUNCT
ejpam-3281	46	8	2	2	NUM
ejpam-3281	46	9	)	)	PUNCT
ejpam-3281	46	10	‖	‖	PROPN
ejpam-3281	46	11	f(x	f(x	PROPN
ejpam-3281	46	12	)	)	PUNCT
ejpam-3281	47	1	+	+	CCONJ
ejpam-3281	47	2	g(x	g(x	NOUN
ejpam-3281	47	3	)	)	PUNCT
ejpam-3281	47	4	‖c≤	‖c≤	PRON
ejpam-3281	47	5	max{‖	max{‖	PROPN
ejpam-3281	47	6	f(x	f(x	PROPN
ejpam-3281	47	7	)	)	PUNCT
ejpam-3281	47	8	‖c	‖c	NOUN
ejpam-3281	47	9	,	,	PUNCT
ejpam-3281	47	10	‖	‖	PROPN
ejpam-3281	47	11	g(x	g(x	NOUN
ejpam-3281	47	12	)	)	PUNCT
ejpam-3281	47	13	‖c	‖c	NOUN
ejpam-3281	47	14	}	}	PUNCT
ejpam-3281	47	15	,	,	PUNCT
ejpam-3281	47	16	3	3	X
ejpam-3281	47	17	)	)	PUNCT
ejpam-3281	47	18	‖	‖	PROPN
ejpam-3281	48	1	α	α	X
ejpam-3281	48	2	‖c=	‖c=	ADP
ejpam-3281	48	3	|α|	|α|	PROPN
ejpam-3281	48	4	,	,	PUNCT
ejpam-3281	48	5	for	for	ADP
ejpam-3281	48	6	any	any	DET
ejpam-3281	48	7	constant	constant	ADJ
ejpam-3281	48	8	α	α	PROPN
ejpam-3281	48	9	∈	∈	PROPN
ejpam-3281	48	10	cp	cp	PROPN
ejpam-3281	48	11	.	.	PUNCT
ejpam-3281	48	12	a.	a.	PROPN
ejpam-3281	48	13	dalloul	dalloul	PROPN
ejpam-3281	48	14	/	/	SYM
ejpam-3281	48	15	eur	eur	PROPN
ejpam-3281	48	16	.	.	PUNCT
ejpam-3281	49	1	j.	j.	PROPN
ejpam-3281	49	2	pure	pure	PROPN
ejpam-3281	49	3	appl	appl	PROPN
ejpam-3281	49	4	.	.	PROPN
ejpam-3281	49	5	math	math	PROPN
ejpam-3281	49	6	,	,	PUNCT
ejpam-3281	49	7	11	11	NUM
ejpam-3281	49	8	(	(	PUNCT
ejpam-3281	49	9	4	4	NUM
ejpam-3281	49	10	)	)	PUNCT
ejpam-3281	49	11	(	(	PUNCT
ejpam-3281	49	12	2018	2018	NUM
ejpam-3281	49	13	)	)	PUNCT
ejpam-3281	49	14	,	,	PUNCT
ejpam-3281	49	15	1046	1046	NUM
ejpam-3281	49	16	-	-	SYM
ejpam-3281	49	17	1057	1057	NUM
ejpam-3281	49	18	1048	1048	NUM
ejpam-3281	49	19	4	4	NUM
ejpam-3281	49	20	)	)	PUNCT
ejpam-3281	49	21	|f(x)|	|f(x)|	PROPN
ejpam-3281	49	22	≤‖	≤‖	PROPN
ejpam-3281	49	23	f(x	f(x	PROPN
ejpam-3281	49	24	)	)	PUNCT
ejpam-3281	49	25	‖c	‖c	NOUN
ejpam-3281	49	26	,	,	PUNCT
ejpam-3281	49	27	for	for	ADP
ejpam-3281	49	28	any	any	DET
ejpam-3281	49	29	x	x	SYM
ejpam-3281	49	30	∈	∈	PROPN
ejpam-3281	49	31	b(0	b(0	NOUN
ejpam-3281	49	32	,	,	PUNCT
ejpam-3281	49	33	c	c	NOUN
ejpam-3281	49	34	)	)	PUNCT
ejpam-3281	49	35	,	,	PUNCT
ejpam-3281	49	36	where	where	SCONJ
ejpam-3281	49	37	f(x	f(x	PROPN
ejpam-3281	49	38	)	)	PUNCT
ejpam-3281	49	39	,	,	PUNCT
ejpam-3281	49	40	g(x	g(x	NOUN
ejpam-3281	49	41	)	)	PUNCT
ejpam-3281	49	42	are	be	AUX
ejpam-3281	49	43	convergent	convergent	ADJ
ejpam-3281	49	44	power	power	NOUN
ejpam-3281	49	45	series	series	NOUN
ejpam-3281	49	46	on	on	ADP
ejpam-3281	49	47	b(0	b(0	PROPN
ejpam-3281	49	48	,	,	PUNCT
ejpam-3281	49	49	c	c	NOUN
ejpam-3281	49	50	)	)	PUNCT
ejpam-3281	49	51	and	and	CCONJ
ejpam-3281	49	52	|.|	|.|	NOUN
ejpam-3281	49	53	stands	stand	VERB
ejpam-3281	49	54	for	for	ADP
ejpam-3281	49	55	the	the	DET
ejpam-3281	49	56	p−adic	p−adic	ADJ
ejpam-3281	49	57	absolute	absolute	ADJ
ejpam-3281	49	58	value	value	NOUN
ejpam-3281	49	59	on	on	ADP
ejpam-3281	49	60	cp	cp	PROPN
ejpam-3281	49	61	.	.	PUNCT
ejpam-3281	50	1	now	now	ADV
ejpam-3281	50	2	,	,	PUNCT
ejpam-3281	50	3	we	we	PRON
ejpam-3281	50	4	are	be	AUX
ejpam-3281	50	5	able	able	ADJ
ejpam-3281	50	6	to	to	PART
ejpam-3281	50	7	state	state	VERB
ejpam-3281	50	8	weierstrass	weierstrass	NOUN
ejpam-3281	50	9	preparation	preparation	NOUN
ejpam-3281	50	10	theorem	theorem	NOUN
ejpam-3281	50	11	:	:	PUNCT
ejpam-3281	50	12	theorem	theorem	NOUN
ejpam-3281	50	13	1	1	NUM
ejpam-3281	50	14	.	.	PUNCT
ejpam-3281	51	1	(	(	PUNCT
ejpam-3281	51	2	weierstrass	weierstrass	NOUN
ejpam-3281	51	3	preparation	preparation	NOUN
ejpam-3281	51	4	theorem	theorem	VERB
ejpam-3281	51	5	[	[	X
ejpam-3281	51	6	g	g	NOUN
ejpam-3281	51	7	]	]	PUNCT
ejpam-3281	51	8	)	)	PUNCT
ejpam-3281	51	9	let	let	VERB
ejpam-3281	51	10	c	c	NOUN
ejpam-3281	51	11	be	be	AUX
ejpam-3281	51	12	a	a	DET
ejpam-3281	51	13	positive	positive	ADJ
ejpam-3281	51	14	real	real	ADJ
ejpam-3281	51	15	number	number	NOUN
ejpam-3281	51	16	of	of	ADP
ejpam-3281	51	17	the	the	DET
ejpam-3281	51	18	form	form	NOUN
ejpam-3281	51	19	pα	pα	VERB
ejpam-3281	51	20	,	,	PUNCT
ejpam-3281	51	21	α	α	PROPN
ejpam-3281	51	22	∈	∈	PROPN
ejpam-3281	51	23	q	q	X
ejpam-3281	51	24	,	,	PUNCT
ejpam-3281	51	25	and	and	CCONJ
ejpam-3281	51	26	let	let	VERB
ejpam-3281	51	27	f(x	f(x	PROPN
ejpam-3281	51	28	)	)	PUNCT
ejpam-3281	52	1	=	=	SYM
ejpam-3281	52	2	a0	a0	PROPN
ejpam-3281	52	3	+	+	CCONJ
ejpam-3281	52	4	a1x	a1x	NOUN
ejpam-3281	52	5	+	+	PUNCT
ejpam-3281	52	6	..	..	PUNCT
ejpam-3281	52	7	+	+	X
ejpam-3281	52	8	anx	anx	ADJ
ejpam-3281	52	9	n	n	NOUN
ejpam-3281	52	10	+	+	CCONJ
ejpam-3281	52	11	..	..	PUNCT
ejpam-3281	52	12	∈	∈	PROPN
ejpam-3281	53	1	cp[[x	cp[[x	PROPN
ejpam-3281	53	2	]	]	X
ejpam-3281	53	3	]	]	PUNCT
ejpam-3281	53	4	be	be	AUX
ejpam-3281	53	5	a	a	DET
ejpam-3281	53	6	power	power	NOUN
ejpam-3281	53	7	series	series	NOUN
ejpam-3281	53	8	convergent	convergent	NOUN
ejpam-3281	53	9	on	on	ADP
ejpam-3281	53	10	the	the	DET
ejpam-3281	53	11	closed	close	VERB
ejpam-3281	53	12	ball	ball	NOUN
ejpam-3281	53	13	b(0	b(0	NOUN
ejpam-3281	53	14	,	,	PUNCT
ejpam-3281	53	15	c	c	NOUN
ejpam-3281	53	16	)	)	PUNCT
ejpam-3281	53	17	.	.	PUNCT
ejpam-3281	54	1	let	let	VERB
ejpam-3281	54	2	n	n	PRON
ejpam-3281	54	3	∈	∈	PROPN
ejpam-3281	54	4	n	n	AUX
ejpam-3281	54	5	be	be	AUX
ejpam-3281	54	6	a	a	DET
ejpam-3281	54	7	number	number	NOUN
ejpam-3281	54	8	defined	define	VERB
ejpam-3281	54	9	by	by	ADP
ejpam-3281	54	10	the	the	DET
ejpam-3281	54	11	conditions	condition	NOUN
ejpam-3281	54	12	:	:	PUNCT
ejpam-3281	54	13	|an	|an	X
ejpam-3281	54	14	|cn	|cn	NUM
ejpam-3281	54	15	=	=	SYM
ejpam-3281	54	16	maxn{|an|cn	maxn{|an|cn	NOUN
ejpam-3281	54	17	}	}	PUNCT
ejpam-3281	54	18	and	and	CCONJ
ejpam-3281	54	19	|an	|an	X
ejpam-3281	54	20	|cn	|cn	NUM
ejpam-3281	54	21	>	>	X
ejpam-3281	54	22	|an|cn	|an|cn	NOUN
ejpam-3281	54	23	,	,	PUNCT
ejpam-3281	55	1	∀n	∀n	NUM
ejpam-3281	55	2	>	>	X
ejpam-3281	55	3	n.	n.	NOUN
ejpam-3281	55	4	then	then	ADV
ejpam-3281	55	5	,	,	PUNCT
ejpam-3281	55	6	there	there	PRON
ejpam-3281	55	7	exist	exist	VERB
ejpam-3281	55	8	a	a	DET
ejpam-3281	55	9	polynomial	polynomial	ADJ
ejpam-3281	55	10	g(x	g(x	NOUN
ejpam-3281	55	11	)	)	PUNCT
ejpam-3281	55	12	∈	∈	PROPN
ejpam-3281	55	13	cp[x	cp[x	PROPN
ejpam-3281	55	14	]	]	PUNCT
ejpam-3281	55	15	of	of	ADP
ejpam-3281	55	16	degree	degree	NOUN
ejpam-3281	55	17	n	n	NOUN
ejpam-3281	55	18	,	,	PUNCT
ejpam-3281	55	19	and	and	CCONJ
ejpam-3281	55	20	a	a	DET
ejpam-3281	55	21	power	power	NOUN
ejpam-3281	55	22	series	series	NOUN
ejpam-3281	55	23	h(x	h(x	PROPN
ejpam-3281	55	24	)	)	PUNCT
ejpam-3281	55	25	convergent	convergent	NOUN
ejpam-3281	55	26	on	on	ADP
ejpam-3281	55	27	the	the	DET
ejpam-3281	55	28	closed	close	VERB
ejpam-3281	55	29	ball	ball	NOUN
ejpam-3281	55	30	b(0	b(0	NOUN
ejpam-3281	55	31	,	,	PUNCT
ejpam-3281	55	32	c	c	NOUN
ejpam-3281	55	33	)	)	PUNCT
ejpam-3281	55	34	such	such	ADJ
ejpam-3281	55	35	that	that	DET
ejpam-3281	55	36	1	1	NUM
ejpam-3281	55	37	)	)	PUNCT
ejpam-3281	55	38	f(x	f(x	PROPN
ejpam-3281	55	39	)	)	PUNCT
ejpam-3281	55	40	=	=	PUNCT
ejpam-3281	55	41	h(x)g(x	h(x)g(x	NOUN
ejpam-3281	55	42	)	)	PUNCT
ejpam-3281	55	43	.	.	PUNCT
ejpam-3281	56	1	in	in	ADP
ejpam-3281	56	2	addition	addition	NOUN
ejpam-3281	56	3	,	,	PUNCT
ejpam-3281	56	4	each	each	DET
ejpam-3281	56	5	root	root	NOUN
ejpam-3281	56	6	of	of	ADP
ejpam-3281	56	7	g(x	g(x	NOUN
ejpam-3281	56	8	)	)	PUNCT
ejpam-3281	56	9	,	,	PUNCT
ejpam-3281	56	10	if	if	SCONJ
ejpam-3281	56	11	exists	exist	VERB
ejpam-3281	56	12	,	,	PUNCT
ejpam-3281	56	13	belongs	belong	VERB
ejpam-3281	56	14	to	to	PART
ejpam-3281	56	15	b(0	b(0	VERB
ejpam-3281	56	16	,	,	PUNCT
ejpam-3281	56	17	c	c	NOUN
ejpam-3281	56	18	)	)	PUNCT
ejpam-3281	56	19	.	.	PUNCT
ejpam-3281	57	1	2	2	X
ejpam-3281	57	2	)	)	PUNCT
ejpam-3281	57	3	‖	‖	PROPN
ejpam-3281	57	4	h(x)−	h(x)−	PROPN
ejpam-3281	57	5	1	1	NUM
ejpam-3281	57	6	‖c	‖c	X
ejpam-3281	57	7	<	<	X
ejpam-3281	57	8	1	1	NUM
ejpam-3281	57	9	.	.	PUNCT
ejpam-3281	58	1	in	in	ADP
ejpam-3281	58	2	particular	particular	ADJ
ejpam-3281	58	3	,	,	PUNCT
ejpam-3281	58	4	h(x	h(x	PROPN
ejpam-3281	58	5	)	)	PUNCT
ejpam-3281	58	6	has	have	VERB
ejpam-3281	58	7	no	no	DET
ejpam-3281	58	8	roots	root	NOUN
ejpam-3281	58	9	in	in	ADP
ejpam-3281	58	10	b(0	b(0	NOUN
ejpam-3281	58	11	,	,	PUNCT
ejpam-3281	58	12	c	c	NOUN
ejpam-3281	58	13	)	)	PUNCT
ejpam-3281	58	14	.	.	PUNCT
ejpam-3281	59	1	we	we	PRON
ejpam-3281	59	2	need	need	VERB
ejpam-3281	59	3	the	the	DET
ejpam-3281	59	4	following	follow	VERB
ejpam-3281	59	5	notions	notion	NOUN
ejpam-3281	59	6	and	and	CCONJ
ejpam-3281	59	7	results	result	NOUN
ejpam-3281	59	8	related	relate	VERB
ejpam-3281	59	9	to	to	ADP
ejpam-3281	59	10	the	the	DET
ejpam-3281	59	11	ring	ring	NOUN
ejpam-3281	59	12	of	of	ADP
ejpam-3281	59	13	strictly	strictly	ADV
ejpam-3281	59	14	convergent	convergent	ADJ
ejpam-3281	59	15	power	power	NOUN
ejpam-3281	59	16	series	series	NOUN
ejpam-3281	59	17	in	in	ADP
ejpam-3281	59	18	order	order	NOUN
ejpam-3281	59	19	to	to	PART
ejpam-3281	59	20	study	study	VERB
ejpam-3281	59	21	the	the	DET
ejpam-3281	59	22	polynomials	polynomial	NOUN
ejpam-3281	59	23	in	in	ADP
ejpam-3281	59	24	z[x1	z[x1	ADP
ejpam-3281	59	25	,	,	PUNCT
ejpam-3281	59	26	x2	x2	PROPN
ejpam-3281	59	27	]	]	PUNCT
ejpam-3281	59	28	that	that	PRON
ejpam-3281	59	29	admit	admit	VERB
ejpam-3281	59	30	roots	root	NOUN
ejpam-3281	59	31	of	of	ADP
ejpam-3281	59	32	the	the	DET
ejpam-3281	59	33	form	form	NOUN
ejpam-3281	59	34	(	(	PUNCT
ejpam-3281	59	35	exp(x1	exp(x1	ADJ
ejpam-3281	59	36	)	)	PUNCT
ejpam-3281	59	37	,	,	PUNCT
ejpam-3281	59	38	exp(x2	exp(x2	NOUN
ejpam-3281	59	39	)	)	PUNCT
ejpam-3281	59	40	)	)	PUNCT
ejpam-3281	59	41	.	.	PUNCT
ejpam-3281	60	1	see	see	VERB
ejpam-3281	61	1	[	[	X
ejpam-3281	61	2	s	s	X
ejpam-3281	61	3	]	]	X
ejpam-3281	61	4	and	and	CCONJ
ejpam-3281	61	5	[	[	X
ejpam-3281	61	6	bgr	bgr	NOUN
ejpam-3281	61	7	]	]	X
ejpam-3281	61	8	for	for	ADP
ejpam-3281	61	9	more	more	ADJ
ejpam-3281	61	10	details	detail	NOUN
ejpam-3281	61	11	.	.	PUNCT
ejpam-3281	62	1	let	let	AUX
ejpam-3281	62	2	(	(	PUNCT
ejpam-3281	62	3	k	k	NOUN
ejpam-3281	62	4	,	,	PUNCT
ejpam-3281	62	5	|.|	|.|	NOUN
ejpam-3281	62	6	)	)	PUNCT
ejpam-3281	62	7	be	be	VERB
ejpam-3281	62	8	a	a	DET
ejpam-3281	62	9	non	non	ADJ
ejpam-3281	62	10	-	-	ADJ
ejpam-3281	62	11	archimedian	archimedian	ADJ
ejpam-3281	62	12	,	,	PUNCT
ejpam-3281	62	13	complete	complete	ADJ
ejpam-3281	62	14	and	and	CCONJ
ejpam-3281	62	15	algebraically	algebraically	ADV
ejpam-3281	62	16	closed	closed	ADJ
ejpam-3281	62	17	field	field	NOUN
ejpam-3281	62	18	.	.	PUNCT
ejpam-3281	63	1	then	then	ADV
ejpam-3281	63	2	,	,	PUNCT
ejpam-3281	63	3	a	a	DET
ejpam-3281	63	4	formal	formal	ADJ
ejpam-3281	63	5	power	power	NOUN
ejpam-3281	63	6	series	series	NOUN
ejpam-3281	63	7	f(x1	f(x1	PROPN
ejpam-3281	63	8	,	,	PUNCT
ejpam-3281	63	9	..	..	PUNCT
ejpam-3281	63	10	,	,	PUNCT
ejpam-3281	63	11	xn	xn	X
ejpam-3281	63	12	)	)	PUNCT
ejpam-3281	64	1	=	=	SYM
ejpam-3281	64	2	∑	∑	PUNCT
ejpam-3281	64	3	i=(i1,	i=(i1,	PROPN
ejpam-3281	64	4	..	..	SYM
ejpam-3281	64	5	,in	,in	PUNCT
ejpam-3281	64	6	)	)	PUNCT
ejpam-3281	64	7	aix	aix	PROPN
ejpam-3281	64	8	i1	i1	PROPN
ejpam-3281	64	9	1	1	NUM
ejpam-3281	64	10	...	...	PUNCT
ejpam-3281	64	11	x	x	X
ejpam-3281	64	12	in	in	ADP
ejpam-3281	64	13	n	n	PRON
ejpam-3281	64	14	∈	∈	PROPN
ejpam-3281	64	15	k[[x1	k[[x1	PROPN
ejpam-3281	64	16	,	,	PUNCT
ejpam-3281	64	17	..	..	PUNCT
ejpam-3281	64	18	,	,	PUNCT
ejpam-3281	64	19	xn	xn	PROPN
ejpam-3281	64	20	]	]	X
ejpam-3281	64	21	]	]	X
ejpam-3281	64	22	is	be	AUX
ejpam-3281	64	23	convergent	convergent	NOUN
ejpam-3281	64	24	on	on	ADP
ejpam-3281	64	25	a	a	DET
ejpam-3281	64	26	ball	ball	NOUN
ejpam-3281	64	27	b(0	b(0	NOUN
ejpam-3281	64	28	,	,	PUNCT
ejpam-3281	64	29	ρ	ρ	NOUN
ejpam-3281	64	30	)	)	PUNCT
ejpam-3281	64	31	:	:	PUNCT
ejpam-3281	64	32	=	=	SYM
ejpam-3281	64	33	{	{	PUNCT
ejpam-3281	64	34	x̄	x̄	NOUN
ejpam-3281	64	35	=	=	SYM
ejpam-3281	64	36	(	(	PUNCT
ejpam-3281	64	37	x1	x1	PROPN
ejpam-3281	64	38	,	,	PUNCT
ejpam-3281	64	39	..	..	PUNCT
ejpam-3281	64	40	,	,	PUNCT
ejpam-3281	64	41	xn	xn	X
ejpam-3281	64	42	)	)	PUNCT
ejpam-3281	65	1	∈	∈	PROPN
ejpam-3281	65	2	cnp	cnp	PROPN
ejpam-3281	65	3	:	:	PUNCT
ejpam-3281	65	4	max	max	PROPN
ejpam-3281	65	5	|xi|	|xi|	PROPN
ejpam-3281	65	6	≤	≤	PROPN
ejpam-3281	65	7	ρ	ρ	PROPN
ejpam-3281	65	8	}	}	PUNCT
ejpam-3281	65	9	if	if	SCONJ
ejpam-3281	65	10	and	and	CCONJ
ejpam-3281	65	11	only	only	ADV
ejpam-3281	65	12	if	if	SCONJ
ejpam-3281	65	13	|ai	|ai	NUM
ejpam-3281	65	14	|ρ(i1+	|ρ(i1+	ADJ
ejpam-3281	65	15	...	...	PUNCT
ejpam-3281	65	16	+in	+in	ADJ
ejpam-3281	65	17	)	)	PUNCT
ejpam-3281	65	18	→	→	SYM
ejpam-3281	65	19	0	0	PUNCT
ejpam-3281	65	20	as	as	ADP
ejpam-3281	65	21	i1	i1	PROPN
ejpam-3281	65	22	+	+	CCONJ
ejpam-3281	65	23	...	...	PUNCT
ejpam-3281	65	24	+	+	CCONJ
ejpam-3281	65	25	in	in	ADP
ejpam-3281	65	26	→∞.	→∞.	X
ejpam-3281	65	27	we	we	PRON
ejpam-3281	65	28	define	define	VERB
ejpam-3281	65	29	a	a	DET
ejpam-3281	65	30	norm	norm	NOUN
ejpam-3281	65	31	|.|ρ	|.|ρ	PROPN
ejpam-3281	65	32	on	on	ADP
ejpam-3281	65	33	f	f	PROPN
ejpam-3281	65	34	as	as	SCONJ
ejpam-3281	65	35	follows	follow	VERB
ejpam-3281	65	36	:	:	PUNCT
ejpam-3281	65	37	|f	|f	PROPN
ejpam-3281	65	38	|ρ	|ρ	NOUN
ejpam-3281	65	39	:	:	PUNCT
ejpam-3281	65	40	=	=	SYM
ejpam-3281	65	41	max	max	PROPN
ejpam-3281	65	42	i=(i1,	i=(i1,	PROPN
ejpam-3281	65	43	..	..	PUNCT
ejpam-3281	65	44	,in	,in	NUM
ejpam-3281	65	45	)	)	PUNCT
ejpam-3281	65	46	{	{	PUNCT
ejpam-3281	65	47	|ai	|ai	NUM
ejpam-3281	65	48	|ρ(i1+	|ρ(i1+	ADJ
ejpam-3281	65	49	...	...	PUNCT
ejpam-3281	65	50	+in	+in	ADJ
ejpam-3281	65	51	)	)	PUNCT
ejpam-3281	65	52	}	}	PUNCT
ejpam-3281	65	53	.	.	PUNCT
ejpam-3281	66	1	this	this	DET
ejpam-3281	66	2	norm	norm	NOUN
ejpam-3281	66	3	is	be	AUX
ejpam-3281	66	4	usually	usually	ADV
ejpam-3281	66	5	called	call	VERB
ejpam-3281	66	6	gauss	gauss	NOUN
ejpam-3281	66	7	norm	norm	NOUN
ejpam-3281	66	8	,	,	PUNCT
ejpam-3281	66	9	[	[	X
ejpam-3281	66	10	s	s	X
ejpam-3281	66	11	]	]	X
ejpam-3281	66	12	.	.	PUNCT
ejpam-3281	67	1	let	let	AUX
ejpam-3281	67	2	tn(ρ	tn(ρ	NUM
ejpam-3281	67	3	)	)	PUNCT
ejpam-3281	67	4	be	be	AUX
ejpam-3281	67	5	the	the	DET
ejpam-3281	67	6	set	set	NOUN
ejpam-3281	67	7	of	of	ADP
ejpam-3281	67	8	all	all	DET
ejpam-3281	67	9	formal	formal	ADJ
ejpam-3281	67	10	power	power	NOUN
ejpam-3281	67	11	series	series	NOUN
ejpam-3281	67	12	in	in	ADP
ejpam-3281	67	13	k[[x1	k[[x1	PROPN
ejpam-3281	67	14	,	,	PUNCT
ejpam-3281	67	15	..	..	PUNCT
ejpam-3281	67	16	,	,	PUNCT
ejpam-3281	67	17	xn	xn	PROPN
ejpam-3281	67	18	]	]	X
ejpam-3281	67	19	]	]	X
ejpam-3281	67	20	which	which	PRON
ejpam-3281	67	21	are	be	AUX
ejpam-3281	67	22	convergent	convergent	ADJ
ejpam-3281	67	23	on	on	ADP
ejpam-3281	67	24	the	the	DET
ejpam-3281	67	25	ball	ball	NOUN
ejpam-3281	67	26	b(0	b(0	PROPN
ejpam-3281	67	27	,	,	PUNCT
ejpam-3281	67	28	ρ	ρ	NOUN
ejpam-3281	67	29	)	)	PUNCT
ejpam-3281	67	30	.	.	PUNCT
ejpam-3281	68	1	then	then	ADV
ejpam-3281	68	2	,	,	PUNCT
ejpam-3281	68	3	tn(ρ	tn(ρ	NUM
ejpam-3281	68	4	)	)	PUNCT
ejpam-3281	68	5	forms	form	VERB
ejpam-3281	68	6	a	a	DET
ejpam-3281	68	7	complete	complete	ADJ
ejpam-3281	68	8	normed	norme	VERB
ejpam-3281	68	9	k−algebra	k−algebra	PROPN
ejpam-3281	68	10	embeds	embed	VERB
ejpam-3281	68	11	k[x1	k[x1	PROPN
ejpam-3281	68	12	,	,	PUNCT
ejpam-3281	68	13	..	..	PUNCT
ejpam-3281	68	14	,	,	PUNCT
ejpam-3281	68	15	xn	xn	PROPN
ejpam-3281	68	16	]	]	X
ejpam-3281	68	17	as	as	ADP
ejpam-3281	68	18	a	a	DET
ejpam-3281	68	19	dense	dense	ADJ
ejpam-3281	68	20	k−	k−	NOUN
ejpam-3281	68	21	subalgebra	subalgebra	NOUN
ejpam-3281	68	22	.	.	PUNCT
ejpam-3281	69	1	in	in	ADP
ejpam-3281	69	2	particular	particular	ADJ
ejpam-3281	69	3	,	,	PUNCT
ejpam-3281	69	4	for	for	ADP
ejpam-3281	69	5	ρ	ρ	PROPN
ejpam-3281	69	6	=	=	SYM
ejpam-3281	69	7	1	1	NUM
ejpam-3281	69	8	,	,	PUNCT
ejpam-3281	69	9	k〈x1	k〈x1	NOUN
ejpam-3281	69	10	,	,	PUNCT
ejpam-3281	69	11	..	..	PUNCT
ejpam-3281	69	12	,	,	PUNCT
ejpam-3281	69	13	xn	xn	PROPN
ejpam-3281	69	14	〉	〉	PROPN
ejpam-3281	69	15	denotes	denote	VERB
ejpam-3281	69	16	the	the	DET
ejpam-3281	69	17	ring	ring	NOUN
ejpam-3281	69	18	of	of	ADP
ejpam-3281	69	19	all	all	DET
ejpam-3281	69	20	power	power	NOUN
ejpam-3281	69	21	series	series	NOUN
ejpam-3281	69	22	which	which	PRON
ejpam-3281	69	23	are	be	AUX
ejpam-3281	69	24	convergent	convergent	ADJ
ejpam-3281	69	25	on	on	ADP
ejpam-3281	69	26	the	the	DET
ejpam-3281	69	27	unit	unit	NOUN
ejpam-3281	69	28	ball	ball	NOUN
ejpam-3281	69	29	.	.	PUNCT
ejpam-3281	70	1	each	each	DET
ejpam-3281	70	2	element	element	NOUN
ejpam-3281	70	3	of	of	ADP
ejpam-3281	70	4	this	this	DET
ejpam-3281	70	5	ring	ring	NOUN
ejpam-3281	70	6	is	be	AUX
ejpam-3281	70	7	usually	usually	ADV
ejpam-3281	70	8	called	call	VERB
ejpam-3281	70	9	strictly	strictly	ADV
ejpam-3281	70	10	convergent	convergent	ADJ
ejpam-3281	70	11	power	power	NOUN
ejpam-3281	70	12	series	series	NOUN
ejpam-3281	70	13	,	,	PUNCT
ejpam-3281	70	14	[	[	X
ejpam-3281	70	15	s	s	X
ejpam-3281	70	16	]	]	X
ejpam-3281	70	17	.	.	PUNCT
ejpam-3281	71	1	then	then	ADV
ejpam-3281	71	2	,	,	PUNCT
ejpam-3281	71	3	we	we	PRON
ejpam-3281	71	4	have	have	VERB
ejpam-3281	71	5	the	the	DET
ejpam-3281	71	6	following	following	NOUN
ejpam-3281	71	7	:	:	PUNCT
ejpam-3281	71	8	lemma	lemma	PROPN
ejpam-3281	71	9	1	1	NUM
ejpam-3281	71	10	.	.	PUNCT
ejpam-3281	72	1	(	(	PUNCT
ejpam-3281	72	2	[	[	X
ejpam-3281	72	3	s	s	X
ejpam-3281	72	4	]	]	X
ejpam-3281	72	5	lemma	lemma	PROPN
ejpam-3281	72	6	4.9	4.9	NUM
ejpam-3281	72	7	,	,	PUNCT
ejpam-3281	72	8	p.9	p.9	NOUN
ejpam-3281	72	9	)	)	PUNCT
ejpam-3281	72	10	a	a	DET
ejpam-3281	72	11	strictly	strictly	ADV
ejpam-3281	72	12	convergent	convergent	ADJ
ejpam-3281	72	13	power	power	NOUN
ejpam-3281	72	14	series	series	NOUN
ejpam-3281	72	15	f	f	PROPN
ejpam-3281	72	16	=	=	X
ejpam-3281	72	17	∑	∑	PUNCT
ejpam-3281	72	18	i=(i1,	i=(i1,	PROPN
ejpam-3281	72	19	..	..	SYM
ejpam-3281	72	20	,in	,in	PUNCT
ejpam-3281	72	21	)	)	PUNCT
ejpam-3281	72	22	aix	aix	PROPN
ejpam-3281	72	23	i1	i1	PROPN
ejpam-3281	72	24	1	1	NUM
ejpam-3281	72	25	...	...	PUNCT
ejpam-3281	72	26	x	x	X
ejpam-3281	72	27	in	in	ADP
ejpam-3281	72	28	n	n	PRON
ejpam-3281	72	29	∈	∈	PROPN
ejpam-3281	72	30	k〈x1	k〈x1	NOUN
ejpam-3281	72	31	,	,	PUNCT
ejpam-3281	72	32	..	..	PUNCT
ejpam-3281	72	33	,	,	PUNCT
ejpam-3281	72	34	xn	xn	PROPN
ejpam-3281	72	35	〉	〉	PROPN
ejpam-3281	72	36	is	be	AUX
ejpam-3281	72	37	unit	unit	NOUN
ejpam-3281	72	38	in	in	ADP
ejpam-3281	72	39	k〈x1	k〈x1	NOUN
ejpam-3281	72	40	,	,	PUNCT
ejpam-3281	72	41	..	..	PUNCT
ejpam-3281	72	42	,	,	PUNCT
ejpam-3281	72	43	xn	xn	PROPN
ejpam-3281	72	44	〉	〉	NOUN
ejpam-3281	72	45	if	if	SCONJ
ejpam-3281	72	46	and	and	CCONJ
ejpam-3281	72	47	only	only	ADV
ejpam-3281	72	48	if	if	SCONJ
ejpam-3281	72	49	|a(0,	|a(0,	NOUN
ejpam-3281	72	50	..	..	PUNCT
ejpam-3281	72	51	,0)|	,0)|	PUNCT
ejpam-3281	72	52	=	=	SYM
ejpam-3281	72	53	|f	|f	PROPN
ejpam-3281	73	1	|	|	ADV
ejpam-3281	73	2	and	and	CCONJ
ejpam-3281	73	3	|a(i1,	|a(i1,	PROPN
ejpam-3281	73	4	..	..	PUNCT
ejpam-3281	73	5	,in)|	,in)|	PUNCT
ejpam-3281	73	6	<	<	X
ejpam-3281	73	7	|f	|f	X
ejpam-3281	73	8	|	|	ADV
ejpam-3281	73	9	for	for	ADP
ejpam-3281	73	10	all	all	DET
ejpam-3281	73	11	i1	i1	PROPN
ejpam-3281	73	12	+	+	CCONJ
ejpam-3281	73	13	..	..	PUNCT
ejpam-3281	73	14	+	+	CCONJ
ejpam-3281	73	15	in	in	ADP
ejpam-3281	73	16	>	>	PRON
ejpam-3281	73	17	0	0	X
ejpam-3281	73	18	.	.	PUNCT
ejpam-3281	74	1	this	this	DET
ejpam-3281	74	2	lemma	lemma	PROPN
ejpam-3281	74	3	immediately	immediately	ADV
ejpam-3281	74	4	implies	imply	VERB
ejpam-3281	74	5	that	that	SCONJ
ejpam-3281	74	6	if	if	SCONJ
ejpam-3281	74	7	|a(0,0,	|a(0,0,	PRON
ejpam-3281	74	8	..	..	PUNCT
ejpam-3281	74	9	,0)|	,0)|	PUNCT
ejpam-3281	74	10	<	<	X
ejpam-3281	74	11	|f	|f	PROPN
ejpam-3281	74	12	|	|	PROPN
ejpam-3281	74	13	,	,	PUNCT
ejpam-3281	74	14	then	then	ADV
ejpam-3281	74	15	f	f	PROPN
ejpam-3281	74	16	is	be	AUX
ejpam-3281	74	17	not	not	PART
ejpam-3281	74	18	unit	unit	NOUN
ejpam-3281	74	19	ink〈x1	ink〈x1	NOUN
ejpam-3281	74	20	,	,	PUNCT
ejpam-3281	74	21	..	..	PUNCT
ejpam-3281	74	22	,	,	PUNCT
ejpam-3281	74	23	xn	xn	PROPN
ejpam-3281	74	24	〉	〉	NUM
ejpam-3281	74	25	.	.	PUNCT
ejpam-3281	75	1	lemma	lemma	PROPN
ejpam-3281	75	2	2	2	NUM
ejpam-3281	75	3	.	.	PUNCT
ejpam-3281	76	1	(	(	PUNCT
ejpam-3281	76	2	hilbert	hilbert	PROPN
ejpam-3281	76	3	theorem	theorem	VERB
ejpam-3281	76	4	[	[	X
ejpam-3281	76	5	s	s	X
ejpam-3281	76	6	]	]	X
ejpam-3281	76	7	,	,	PUNCT
ejpam-3281	76	8	corollary	corollary	ADJ
ejpam-3281	76	9	5.10	5.10	NUM
ejpam-3281	76	10	,	,	PUNCT
ejpam-3281	76	11	p.14	p.14	NOUN
ejpam-3281	76	12	)	)	PUNCT
ejpam-3281	76	13	there	there	PRON
ejpam-3281	76	14	is	be	VERB
ejpam-3281	76	15	a	a	DET
ejpam-3281	76	16	one	one	NUM
ejpam-3281	76	17	to	to	ADP
ejpam-3281	76	18	one	one	NUM
ejpam-3281	76	19	correspondence	correspondence	NOUN
ejpam-3281	76	20	between	between	ADP
ejpam-3281	76	21	the	the	DET
ejpam-3281	76	22	maximal	maximal	ADJ
ejpam-3281	76	23	ideals	ideal	NOUN
ejpam-3281	76	24	of	of	ADP
ejpam-3281	76	25	k〈x1	k〈x1	NOUN
ejpam-3281	76	26	,	,	PUNCT
ejpam-3281	76	27	..	..	PUNCT
ejpam-3281	76	28	,	,	PUNCT
ejpam-3281	76	29	xn	xn	PROPN
ejpam-3281	76	30	〉	〉	NUM
ejpam-3281	76	31	and	and	CCONJ
ejpam-3281	76	32	the	the	DET
ejpam-3281	76	33	points	point	NOUN
ejpam-3281	76	34	in	in	ADP
ejpam-3281	76	35	the	the	DET
ejpam-3281	76	36	unit	unit	NOUN
ejpam-3281	76	37	ball	ball	NOUN
ejpam-3281	76	38	b(0	b(0	PROPN
ejpam-3281	76	39	,	,	PUNCT
ejpam-3281	76	40	1	1	NUM
ejpam-3281	76	41	)	)	PUNCT
ejpam-3281	76	42	:	:	PUNCT
ejpam-3281	77	1	=	=	SYM
ejpam-3281	77	2	{	{	PUNCT
ejpam-3281	77	3	x̄	x̄	NOUN
ejpam-3281	77	4	=	=	SYM
ejpam-3281	77	5	(	(	PUNCT
ejpam-3281	77	6	x1	x1	PROPN
ejpam-3281	77	7	,	,	PUNCT
ejpam-3281	77	8	..	..	PUNCT
ejpam-3281	77	9	,	,	PUNCT
ejpam-3281	77	10	xn	xn	X
ejpam-3281	77	11	)	)	PUNCT
ejpam-3281	77	12	∈	∈	PROPN
ejpam-3281	77	13	cnp	cnp	NOUN
ejpam-3281	77	14	:	:	PUNCT
ejpam-3281	77	15	max{|xi|	max{|xi|	ADJ
ejpam-3281	77	16	}	}	PUNCT
ejpam-3281	77	17	≤	≤	NUM
ejpam-3281	77	18	1	1	NUM
ejpam-3281	77	19	}	}	PUNCT
ejpam-3281	77	20	.	.	PUNCT
ejpam-3281	78	1	under	under	ADP
ejpam-3281	78	2	this	this	DET
ejpam-3281	78	3	correspondence	correspondence	NOUN
ejpam-3281	78	4	,	,	PUNCT
ejpam-3281	78	5	a	a	DET
ejpam-3281	78	6	point	point	NOUN
ejpam-3281	78	7	x̄	x̄	PUNCT
ejpam-3281	78	8	=	=	PUNCT
ejpam-3281	79	1	(	(	PUNCT
ejpam-3281	79	2	x1	x1	PROPN
ejpam-3281	79	3	,	,	PUNCT
ejpam-3281	79	4	..	..	PUNCT
ejpam-3281	79	5	,	,	PUNCT
ejpam-3281	79	6	xn	xn	X
ejpam-3281	79	7	)	)	PUNCT
ejpam-3281	79	8	∈	∈	PROPN
ejpam-3281	79	9	b(0	b(0	NOUN
ejpam-3281	79	10	,	,	PUNCT
ejpam-3281	79	11	1	1	NUM
ejpam-3281	79	12	)	)	PUNCT
ejpam-3281	79	13	determines	determine	VERB
ejpam-3281	79	14	the	the	DET
ejpam-3281	79	15	maximal	maximal	ADJ
ejpam-3281	79	16	ideal	ideal	NOUN
ejpam-3281	79	17	〈	〈	PROPN
ejpam-3281	79	18	x1	x1	NOUN
ejpam-3281	79	19	−	−	PROPN
ejpam-3281	79	20	x1	x1	PROPN
ejpam-3281	79	21	,	,	PUNCT
ejpam-3281	79	22	..	..	PUNCT
ejpam-3281	79	23	,	,	PUNCT
ejpam-3281	79	24	xn	xn	PROPN
ejpam-3281	80	1	−	−	PROPN
ejpam-3281	80	2	xn	xn	SYM
ejpam-3281	80	3	〉	〉	NUM
ejpam-3281	80	4	.	.	PUNCT
ejpam-3281	81	1	throughout	throughout	ADP
ejpam-3281	81	2	the	the	DET
ejpam-3281	81	3	paper	paper	NOUN
ejpam-3281	81	4	,	,	PUNCT
ejpam-3281	81	5	we	we	PRON
ejpam-3281	81	6	use	use	VERB
ejpam-3281	81	7	the	the	DET
ejpam-3281	81	8	standard	standard	ADJ
ejpam-3281	81	9	notation	notation	NOUN
ejpam-3281	81	10	(	(	PUNCT
ejpam-3281	81	11	x̄	x̄	NOUN
ejpam-3281	81	12	,	,	PUNCT
ejpam-3281	81	13	exp(x̄	exp(x̄	PRON
ejpam-3281	81	14	)	)	PUNCT
ejpam-3281	81	15	)	)	PUNCT
ejpam-3281	81	16	for	for	ADP
ejpam-3281	81	17	the	the	DET
ejpam-3281	81	18	2ntuple	2ntuple	NUM
ejpam-3281	81	19	(	(	PUNCT
ejpam-3281	81	20	x1	x1	PROPN
ejpam-3281	81	21	,	,	PUNCT
ejpam-3281	81	22	...	...	PUNCT
ejpam-3281	81	23	,	,	PUNCT
ejpam-3281	81	24	xn	xn	PROPN
ejpam-3281	81	25	,	,	PUNCT
ejpam-3281	81	26	exp(x1	exp(x1	ADJ
ejpam-3281	81	27	)	)	PUNCT
ejpam-3281	81	28	,	,	PUNCT
ejpam-3281	81	29	...	...	PUNCT
ejpam-3281	81	30	,	,	PUNCT
ejpam-3281	81	31	exp(xn	exp(xn	NOUN
ejpam-3281	81	32	)	)	PUNCT
ejpam-3281	81	33	)	)	PUNCT
ejpam-3281	81	34	,	,	PUNCT
ejpam-3281	82	1	[	[	X
ejpam-3281	82	2	k	k	X
ejpam-3281	82	3	]	]	X
ejpam-3281	82	4	.	.	PUNCT
ejpam-3281	82	5	a.	a.	PROPN
ejpam-3281	82	6	dalloul	dalloul	PROPN
ejpam-3281	82	7	/	/	SYM
ejpam-3281	82	8	eur	eur	PROPN
ejpam-3281	82	9	.	.	PUNCT
ejpam-3281	83	1	j.	j.	PROPN
ejpam-3281	83	2	pure	pure	PROPN
ejpam-3281	83	3	appl	appl	PROPN
ejpam-3281	83	4	.	.	PROPN
ejpam-3281	83	5	math	math	PROPN
ejpam-3281	83	6	,	,	PUNCT
ejpam-3281	83	7	11	11	NUM
ejpam-3281	83	8	(	(	PUNCT
ejpam-3281	83	9	4	4	NUM
ejpam-3281	83	10	)	)	PUNCT
ejpam-3281	83	11	(	(	PUNCT
ejpam-3281	83	12	2018	2018	NUM
ejpam-3281	83	13	)	)	PUNCT
ejpam-3281	83	14	,	,	PUNCT
ejpam-3281	83	15	1046	1046	NUM
ejpam-3281	83	16	-	-	SYM
ejpam-3281	83	17	1057	1057	NUM
ejpam-3281	83	18	1049	1049	NUM
ejpam-3281	83	19	3	3	NUM
ejpam-3281	83	20	.	.	PUNCT
ejpam-3281	84	1	the	the	DET
ejpam-3281	84	2	main	main	ADJ
ejpam-3281	84	3	results	result	NOUN
ejpam-3281	84	4	it	it	PRON
ejpam-3281	84	5	is	be	AUX
ejpam-3281	84	6	clear	clear	ADJ
ejpam-3281	84	7	that	that	SCONJ
ejpam-3281	84	8	finding	find	VERB
ejpam-3281	84	9	roots	root	NOUN
ejpam-3281	84	10	of	of	ADP
ejpam-3281	84	11	a	a	DET
ejpam-3281	84	12	polynomial	polynomial	NOUN
ejpam-3281	84	13	with	with	ADP
ejpam-3281	84	14	rational	rational	ADJ
ejpam-3281	84	15	coefficients	coefficient	NOUN
ejpam-3281	84	16	can	can	AUX
ejpam-3281	84	17	be	be	AUX
ejpam-3281	84	18	reduced	reduce	VERB
ejpam-3281	84	19	to	to	ADP
ejpam-3281	84	20	the	the	DET
ejpam-3281	84	21	case	case	NOUN
ejpam-3281	84	22	of	of	ADP
ejpam-3281	84	23	coefficients	coefficient	NOUN
ejpam-3281	84	24	in	in	ADP
ejpam-3281	84	25	z.	z.	PROPN
ejpam-3281	84	26	therefore	therefore	ADV
ejpam-3281	84	27	,	,	PUNCT
ejpam-3281	84	28	without	without	ADP
ejpam-3281	84	29	loss	loss	NOUN
ejpam-3281	84	30	of	of	ADP
ejpam-3281	84	31	generality	generality	NOUN
ejpam-3281	84	32	,	,	PUNCT
ejpam-3281	84	33	we	we	PRON
ejpam-3281	84	34	can	can	AUX
ejpam-3281	84	35	take	take	VERB
ejpam-3281	84	36	the	the	DET
ejpam-3281	84	37	polynomials	polynomial	NOUN
ejpam-3281	84	38	over	over	ADP
ejpam-3281	84	39	z.	z.	PROPN
ejpam-3281	85	1	we	we	PRON
ejpam-3281	85	2	only	only	ADV
ejpam-3281	85	3	consider	consider	VERB
ejpam-3281	85	4	the	the	DET
ejpam-3281	85	5	class	class	NOUN
ejpam-3281	85	6	of	of	ADP
ejpam-3281	85	7	polynomials	polynomial	NOUN
ejpam-3281	85	8	p	p	X
ejpam-3281	85	9	[	[	X
ejpam-3281	85	10	x	x	X
ejpam-3281	85	11	,	,	PUNCT
ejpam-3281	85	12	y	y	PROPN
ejpam-3281	85	13	]	]	PUNCT
ejpam-3281	85	14	∈	∈	PROPN
ejpam-3281	85	15	z[x	z[x	PROPN
ejpam-3281	85	16	,	,	PUNCT
ejpam-3281	85	17	y	y	PROPN
ejpam-3281	85	18	]	]	PUNCT
ejpam-3281	85	19	in	in	ADP
ejpam-3281	85	20	which	which	PRON
ejpam-3281	85	21	at	at	ADP
ejpam-3281	85	22	least	least	ADJ
ejpam-3281	85	23	one	one	NUM
ejpam-3281	85	24	of	of	ADP
ejpam-3281	85	25	the	the	DET
ejpam-3281	85	26	degrees	degree	NOUN
ejpam-3281	85	27	of	of	ADP
ejpam-3281	85	28	the	the	DET
ejpam-3281	85	29	variable	variable	ADJ
ejpam-3281	85	30	y	y	PROPN
ejpam-3281	85	31	is	be	AUX
ejpam-3281	85	32	relatively	relatively	ADV
ejpam-3281	85	33	prime	prime	ADJ
ejpam-3281	85	34	to	to	ADP
ejpam-3281	85	35	p.	p.	NOUN
ejpam-3281	85	36	furthermore	furthermore	ADV
ejpam-3281	85	37	,	,	PUNCT
ejpam-3281	85	38	we	we	PRON
ejpam-3281	85	39	exclude	exclude	VERB
ejpam-3281	85	40	the	the	DET
ejpam-3281	85	41	case	case	NOUN
ejpam-3281	85	42	of	of	ADP
ejpam-3281	85	43	polynomials	polynomial	NOUN
ejpam-3281	85	44	that	that	PRON
ejpam-3281	85	45	contain	contain	VERB
ejpam-3281	85	46	the	the	DET
ejpam-3281	85	47	variable	variable	NOUN
ejpam-3281	85	48	x	x	NOUN
ejpam-3281	85	49	in	in	ADP
ejpam-3281	85	50	each	each	DET
ejpam-3281	85	51	term	term	NOUN
ejpam-3281	85	52	since	since	SCONJ
ejpam-3281	85	53	they	they	PRON
ejpam-3281	85	54	have	have	VERB
ejpam-3281	85	55	the	the	DET
ejpam-3281	85	56	trivial	trivial	ADJ
ejpam-3281	85	57	root	root	NOUN
ejpam-3281	85	58	(	(	PUNCT
ejpam-3281	85	59	0	0	NUM
ejpam-3281	85	60	,	,	PUNCT
ejpam-3281	85	61	exp(0	exp(0	NOUN
ejpam-3281	85	62	)	)	PUNCT
ejpam-3281	85	63	)	)	PUNCT
ejpam-3281	85	64	.	.	PUNCT
ejpam-3281	86	1	theorem	theorem	NOUN
ejpam-3281	86	2	2	2	NUM
ejpam-3281	86	3	.	.	PUNCT
ejpam-3281	87	1	the	the	DET
ejpam-3281	87	2	polynomial	polynomial	ADJ
ejpam-3281	87	3	with	with	ADP
ejpam-3281	87	4	rational	rational	ADJ
ejpam-3281	87	5	integer	integer	NOUN
ejpam-3281	87	6	coefficients	coefficient	NOUN
ejpam-3281	87	7	p	p	X
ejpam-3281	88	1	[	[	X
ejpam-3281	88	2	x	x	X
ejpam-3281	88	3	,	,	PUNCT
ejpam-3281	88	4	y	y	PROPN
ejpam-3281	88	5	]	]	PUNCT
ejpam-3281	88	6	=	=	PUNCT
ejpam-3281	88	7	c+	c+	VERB
ejpam-3281	88	8	m∑	m∑	VERB
ejpam-3281	88	9	i=1	i=1	PROPN
ejpam-3281	88	10	diy	diy	NOUN
ejpam-3281	88	11	αi	αi	NOUN
ejpam-3281	88	12	+	+	X
ejpam-3281	88	13	e1xy	e1xy	PUNCT
ejpam-3281	88	14	β1,2	β1,2	NUM
ejpam-3281	89	1	+	+	CCONJ
ejpam-3281	89	2	s∑	s∑	PROPN
ejpam-3281	89	3	k=1	k=1	PROPN
ejpam-3281	89	4	fkx	fkx	VERB
ejpam-3281	89	5	γk,1y	γk,1y	PRON
ejpam-3281	89	6	γk,2	γk,2	PROPN
ejpam-3281	89	7	;	;	PUNCT
ejpam-3281	89	8	γk,1	γk,1	NOUN
ejpam-3281	89	9	≥	≥	NOUN
ejpam-3281	89	10	2	2	NUM
ejpam-3281	89	11	,	,	PUNCT
ejpam-3281	89	12	in	in	ADP
ejpam-3281	89	13	which	which	PRON
ejpam-3281	89	14	(	(	PUNCT
ejpam-3281	89	15	d1α1	d1α1	X
ejpam-3281	89	16	+	+	X
ejpam-3281	89	17	..	..	PUNCT
ejpam-3281	90	1	+	+	ADJ
ejpam-3281	90	2	dmαm+e1	dmαm+e1	ADJ
ejpam-3281	90	3	,	,	PUNCT
ejpam-3281	90	4	p	p	NOUN
ejpam-3281	90	5	)	)	PUNCT
ejpam-3281	90	6	=	=	SYM
ejpam-3281	90	7	1	1	NUM
ejpam-3281	90	8	,	,	PUNCT
ejpam-3281	90	9	has	have	VERB
ejpam-3281	90	10	a	a	DET
ejpam-3281	90	11	root	root	NOUN
ejpam-3281	90	12	of	of	ADP
ejpam-3281	90	13	the	the	DET
ejpam-3281	90	14	form	form	NOUN
ejpam-3281	90	15	(	(	PUNCT
ejpam-3281	90	16	x	x	NOUN
ejpam-3281	90	17	,	,	PUNCT
ejpam-3281	90	18	exp(x	exp(x	PROPN
ejpam-3281	90	19	)	)	PUNCT
ejpam-3281	90	20	)	)	PUNCT
ejpam-3281	91	1	∈	∈	PROPN
ejpam-3281	91	2	cp×c∗p	cp×c∗p	NOUN
ejpam-3281	91	3	;	;	PUNCT
ejpam-3281	91	4	p	p	PRON
ejpam-3281	91	5	≥	≥	NUM
ejpam-3281	91	6	3	3	NUM
ejpam-3281	91	7	if	if	SCONJ
ejpam-3281	91	8	and	and	CCONJ
ejpam-3281	91	9	only	only	ADV
ejpam-3281	91	10	if	if	SCONJ
ejpam-3281	91	11	|c+	|c+	NOUN
ejpam-3281	91	12	d1	d1	PROPN
ejpam-3281	91	13	+	+	X
ejpam-3281	91	14	..	..	PUNCT
ejpam-3281	91	15	+	+	CCONJ
ejpam-3281	91	16	dm|	dm|	VERB
ejpam-3281	91	17	≤	≤	PROPN
ejpam-3281	91	18	p−1	p−1	PROPN
ejpam-3281	91	19	.	.	PUNCT
ejpam-3281	92	1	proof	proof	NOUN
ejpam-3281	92	2	.	.	PUNCT
ejpam-3281	93	1	(	(	PUNCT
ejpam-3281	93	2	proof	proof	NOUN
ejpam-3281	93	3	of	of	ADP
ejpam-3281	93	4	the	the	DET
ejpam-3281	93	5	necessary	necessary	ADJ
ejpam-3281	93	6	condition	condition	NOUN
ejpam-3281	93	7	)	)	PUNCT
ejpam-3281	93	8	if	if	SCONJ
ejpam-3281	93	9	(	(	PUNCT
ejpam-3281	93	10	x	x	NOUN
ejpam-3281	93	11	,	,	PUNCT
ejpam-3281	93	12	exp(x	exp(x	PROPN
ejpam-3281	93	13	)	)	PUNCT
ejpam-3281	93	14	)	)	PUNCT
ejpam-3281	93	15	is	be	AUX
ejpam-3281	93	16	a	a	DET
ejpam-3281	93	17	root	root	NOUN
ejpam-3281	93	18	of	of	ADP
ejpam-3281	93	19	p	p	NOUN
ejpam-3281	93	20	[	[	X
ejpam-3281	93	21	x	x	X
ejpam-3281	93	22	,	,	PUNCT
ejpam-3281	93	23	y	y	PROPN
ejpam-3281	93	24	]	]	PUNCT
ejpam-3281	93	25	,	,	PUNCT
ejpam-3281	93	26	then	then	ADV
ejpam-3281	93	27	x	x	PUNCT
ejpam-3281	93	28	is	be	AUX
ejpam-3281	93	29	a	a	DET
ejpam-3281	93	30	root	root	NOUN
ejpam-3281	93	31	of	of	ADP
ejpam-3281	93	32	the	the	DET
ejpam-3281	93	33	power	power	NOUN
ejpam-3281	93	34	series	series	PROPN
ejpam-3281	93	35	f(x	f(x	PROPN
ejpam-3281	93	36	)	)	PUNCT
ejpam-3281	93	37	:	:	PUNCT
ejpam-3281	94	1	=	=	PUNCT
ejpam-3281	94	2	p	p	X
ejpam-3281	95	1	[	[	X
ejpam-3281	95	2	x	x	X
ejpam-3281	95	3	,	,	PUNCT
ejpam-3281	95	4	exp(x	exp(x	PROPN
ejpam-3281	95	5	)	)	PUNCT
ejpam-3281	95	6	]	]	PUNCT
ejpam-3281	96	1	which	which	PRON
ejpam-3281	96	2	is	be	AUX
ejpam-3281	96	3	convergent	convergent	NOUN
ejpam-3281	96	4	on	on	ADP
ejpam-3281	96	5	e	e	PROPN
ejpam-3281	96	6	(	(	PUNCT
ejpam-3281	96	7	since	since	SCONJ
ejpam-3281	96	8	at	at	ADV
ejpam-3281	96	9	least	least	ADV
ejpam-3281	96	10	one	one	NUM
ejpam-3281	96	11	of	of	ADP
ejpam-3281	96	12	the	the	DET
ejpam-3281	96	13	degrees	degree	NOUN
ejpam-3281	96	14	of	of	ADP
ejpam-3281	96	15	the	the	DET
ejpam-3281	96	16	variable	variable	ADJ
ejpam-3281	96	17	y	y	PROPN
ejpam-3281	96	18	is	be	AUX
ejpam-3281	96	19	relatively	relatively	ADV
ejpam-3281	96	20	prime	prime	ADJ
ejpam-3281	96	21	to	to	ADP
ejpam-3281	96	22	p	p	PRON
ejpam-3281	96	23	,	,	PUNCT
ejpam-3281	96	24	see	see	VERB
ejpam-3281	96	25	[	[	X
ejpam-3281	96	26	pr	pr	X
ejpam-3281	96	27	,	,	PUNCT
ejpam-3281	96	28	theorem	theorem	VERB
ejpam-3281	96	29	1	1	NUM
ejpam-3281	96	30	]	]	PUNCT
ejpam-3281	96	31	)	)	PUNCT
ejpam-3281	96	32	.	.	PUNCT
ejpam-3281	97	1	thus	thus	ADV
ejpam-3281	97	2	,	,	PUNCT
ejpam-3281	97	3	x	x	PROPN
ejpam-3281	97	4	∈	∈	PROPN
ejpam-3281	97	5	e.	e.	PROPN
ejpam-3281	97	6	so	so	ADV
ejpam-3281	97	7	,	,	PUNCT
ejpam-3281	97	8	c+	c+	VERB
ejpam-3281	97	9	m∑	m∑	X
ejpam-3281	97	10	i=1	i=1	PROPN
ejpam-3281	97	11	di	di	PROPN
ejpam-3281	97	12	exp(αix	exp(αix	PROPN
ejpam-3281	97	13	)	)	PUNCT
ejpam-3281	98	1	=	=	SYM
ejpam-3281	99	1	−	−	PROPN
ejpam-3281	99	2	(	(	PUNCT
ejpam-3281	99	3	e1x	e1x	PROPN
ejpam-3281	99	4	exp(β1,2x	exp(β1,2x	NUM
ejpam-3281	99	5	)	)	PUNCT
ejpam-3281	100	1	+	+	CCONJ
ejpam-3281	100	2	s∑	s∑	PROPN
ejpam-3281	100	3	k=1	k=1	PROPN
ejpam-3281	100	4	fkx	fkx	PROPN
ejpam-3281	100	5	γk,1	γk,1	PROPN
ejpam-3281	100	6	exp(γk,2x	exp(γk,2x	PUNCT
ejpam-3281	100	7	)	)	PUNCT
ejpam-3281	100	8	)	)	PUNCT
ejpam-3281	100	9	.	.	PUNCT
ejpam-3281	101	1	we	we	PRON
ejpam-3281	101	2	have	have	VERB
ejpam-3281	101	3	z	z	PROPN
ejpam-3281	101	4	⊆	⊆	NUM
ejpam-3281	101	5	zp	zp	PROPN
ejpam-3281	101	6	and	and	CCONJ
ejpam-3281	101	7	|	|	ADV
ejpam-3281	101	8	exp(w)|	exp(w)|	VERB
ejpam-3281	101	9	=	=	NOUN
ejpam-3281	101	10	1	1	NUM
ejpam-3281	101	11	for	for	ADP
ejpam-3281	101	12	every	every	DET
ejpam-3281	101	13	w	w	PROPN
ejpam-3281	101	14	∈	∈	PROPN
ejpam-3281	101	15	e.	e.	NOUN
ejpam-3281	101	16	using	use	VERB
ejpam-3281	101	17	the	the	DET
ejpam-3281	101	18	strong	strong	ADJ
ejpam-3281	101	19	triangle	triangle	NOUN
ejpam-3281	101	20	inequality	inequality	NOUN
ejpam-3281	101	21	,	,	PUNCT
ejpam-3281	101	22	it	it	PRON
ejpam-3281	101	23	follows	follow	VERB
ejpam-3281	101	24	that	that	SCONJ
ejpam-3281	101	25	|c+	|c+	NOUN
ejpam-3281	101	26	m∑	m∑	VERB
ejpam-3281	101	27	i=1	i=1	PROPN
ejpam-3281	101	28	di	di	PROPN
ejpam-3281	101	29	exp(αix)|	exp(αix)|	PROPN
ejpam-3281	101	30	≤	≤	NUM
ejpam-3281	101	31	max	max	PROPN
ejpam-3281	101	32	k	k	PROPN
ejpam-3281	101	33	{	{	PUNCT
ejpam-3281	101	34	|e1x	|e1x	PROPN
ejpam-3281	101	35	exp(β1,2x)|	exp(β1,2x)|	PROPN
ejpam-3281	101	36	,	,	PUNCT
ejpam-3281	101	37	|fkxγk,1	|fkxγk,1	PROPN
ejpam-3281	101	38	exp(γk,2x)|	exp(γk,2x)|	PROPN
ejpam-3281	101	39	}	}	PUNCT
ejpam-3281	101	40	≤	≤	NUM
ejpam-3281	101	41	max	max	PROPN
ejpam-3281	101	42	k	k	PROPN
ejpam-3281	101	43	{	{	PUNCT
ejpam-3281	101	44	|e1||x||	|e1||x||	NOUN
ejpam-3281	101	45	exp(β1,2x)|	exp(β1,2x)|	NOUN
ejpam-3281	101	46	,	,	PUNCT
ejpam-3281	101	47	|fk||xγk,1	|fk||xγk,1	NOUN
ejpam-3281	101	48	||	||	NOUN
ejpam-3281	102	1	exp(γk,2x)|	exp(γk,2x)|	ADJ
ejpam-3281	102	2	)	)	PUNCT
ejpam-3281	102	3	}	}	PUNCT
ejpam-3281	102	4	≤	≤	NUM
ejpam-3281	102	5	max	max	PROPN
ejpam-3281	102	6	k	k	PROPN
ejpam-3281	102	7	{	{	PUNCT
ejpam-3281	102	8	|x|	|x|	PROPN
ejpam-3281	102	9	,	,	PUNCT
ejpam-3281	102	10	|x|γk,1	|x|γk,1	VERB
ejpam-3281	102	11	}	}	PUNCT
ejpam-3281	102	12	<	<	X
ejpam-3281	102	13	p	p	X
ejpam-3281	102	14	−1	−1	NOUN
ejpam-3281	102	15	p−1	p−1	NOUN
ejpam-3281	102	16	<	<	X
ejpam-3281	102	17	1	1	NUM
ejpam-3281	102	18	.	.	PUNCT
ejpam-3281	103	1	we	we	PRON
ejpam-3281	103	2	define	define	VERB
ejpam-3281	103	3	zi	zi	NOUN
ejpam-3281	103	4	=	=	SYM
ejpam-3281	103	5	αix	αix	NOUN
ejpam-3281	103	6	;	;	PUNCT
ejpam-3281	103	7	i	i	NOUN
ejpam-3281	103	8	=	=	NOUN
ejpam-3281	103	9	1	1	NUM
ejpam-3281	103	10	,	,	PUNCT
ejpam-3281	103	11	2	2	NUM
ejpam-3281	103	12	,	,	PUNCT
ejpam-3281	103	13	..	..	PUNCT
ejpam-3281	103	14	,	,	PUNCT
ejpam-3281	103	15	m.	m.	NOUN
ejpam-3281	103	16	then	then	ADV
ejpam-3281	103	17	,	,	PUNCT
ejpam-3281	103	18	|c+	|c+	PROPN
ejpam-3281	103	19	d1	d1	PROPN
ejpam-3281	103	20	exp(z1	exp(z1	NOUN
ejpam-3281	103	21	)	)	PUNCT
ejpam-3281	104	1	+	+	CCONJ
ejpam-3281	104	2	...	...	PUNCT
ejpam-3281	105	1	+	+	CCONJ
ejpam-3281	105	2	dm	dm	NUM
ejpam-3281	105	3	exp(zm)|	exp(zm)|	NOUN
ejpam-3281	105	4	<	<	X
ejpam-3281	105	5	1	1	NUM
ejpam-3281	105	6	.	.	PUNCT
ejpam-3281	105	7	(	(	PUNCT
ejpam-3281	105	8	1	1	NUM
ejpam-3281	105	9	)	)	PUNCT
ejpam-3281	105	10	therefore	therefore	ADV
ejpam-3281	105	11	,	,	PUNCT
ejpam-3281	105	12	|c+	|c+	NUM
ejpam-3281	105	13	d1	d1	PROPN
ejpam-3281	105	14	+	+	CCONJ
ejpam-3281	105	15	...	...	PUNCT
ejpam-3281	105	16	+	+	CCONJ
ejpam-3281	105	17	dm|	dm|	VERB
ejpam-3281	105	18	<	<	X
ejpam-3281	105	19	1	1	NUM
ejpam-3281	105	20	.	.	PUNCT
ejpam-3281	106	1	this	this	PRON
ejpam-3281	106	2	is	be	AUX
ejpam-3281	106	3	because	because	SCONJ
ejpam-3281	106	4	,	,	PUNCT
ejpam-3281	106	5	|c+d1	|c+d1	PROPN
ejpam-3281	106	6	exp(z1)+	exp(z1)+	PROPN
ejpam-3281	106	7	...	...	PUNCT
ejpam-3281	106	8	+dm	+dm	NOUN
ejpam-3281	106	9	exp(zm)|	exp(zm)|	NOUN
ejpam-3281	106	10	=	=	SYM
ejpam-3281	106	11	|c+d1+	|c+d1+	PROPN
ejpam-3281	106	12	...	...	PUNCT
ejpam-3281	106	13	+dm+d1(exp(z1)−1)+	+dm+d1(exp(z1)−1)+	PROPN
ejpam-3281	106	14	..	..	PUNCT
ejpam-3281	106	15	+dm(exp(zm)−1)|	+dm(exp(zm)−1)|	PROPN
ejpam-3281	106	16	.	.	PUNCT
ejpam-3281	107	1	if	if	SCONJ
ejpam-3281	107	2	|c+	|c+	NOUN
ejpam-3281	107	3	d1	d1	PROPN
ejpam-3281	107	4	+	+	CCONJ
ejpam-3281	107	5	...	...	PUNCT
ejpam-3281	108	1	+	+	CCONJ
ejpam-3281	108	2	dm|	dm|	VERB
ejpam-3281	108	3	=	=	SYM
ejpam-3281	108	4	1	1	NUM
ejpam-3281	108	5	,	,	PUNCT
ejpam-3281	108	6	then	then	ADV
ejpam-3281	108	7	we	we	PRON
ejpam-3281	108	8	find	find	VERB
ejpam-3281	108	9	that	that	SCONJ
ejpam-3281	108	10	|d1(exp(z1)−	|d1(exp(z1)−	PROPN
ejpam-3281	108	11	1	1	NUM
ejpam-3281	108	12	)	)	PUNCT
ejpam-3281	108	13	+	+	CCONJ
ejpam-3281	108	14	..	..	PUNCT
ejpam-3281	109	1	+	+	CCONJ
ejpam-3281	109	2	dm(exp(zm)−	dm(exp(zm)−	ADJ
ejpam-3281	109	3	1)|	1)|	NUM
ejpam-3281	109	4	≤	≤	NUM
ejpam-3281	109	5	max	max	PROPN
ejpam-3281	109	6	1≤i≤m	1≤i≤m	NUM
ejpam-3281	109	7	{	{	PUNCT
ejpam-3281	109	8	|di(exp(zi)−	|di(exp(zi)−	NOUN
ejpam-3281	109	9	1)|	1)|	NUM
ejpam-3281	109	10	}	}	PUNCT
ejpam-3281	109	11	a.	a.	NOUN
ejpam-3281	109	12	dalloul	dalloul	PROPN
ejpam-3281	109	13	/	/	SYM
ejpam-3281	109	14	eur	eur	PROPN
ejpam-3281	109	15	.	.	PUNCT
ejpam-3281	110	1	j.	j.	PROPN
ejpam-3281	110	2	pure	pure	PROPN
ejpam-3281	110	3	appl	appl	PROPN
ejpam-3281	110	4	.	.	PROPN
ejpam-3281	110	5	math	math	PROPN
ejpam-3281	110	6	,	,	PUNCT
ejpam-3281	110	7	11	11	NUM
ejpam-3281	110	8	(	(	PUNCT
ejpam-3281	110	9	4	4	NUM
ejpam-3281	110	10	)	)	PUNCT
ejpam-3281	110	11	(	(	PUNCT
ejpam-3281	110	12	2018	2018	NUM
ejpam-3281	110	13	)	)	PUNCT
ejpam-3281	110	14	,	,	PUNCT
ejpam-3281	110	15	1046	1046	NUM
ejpam-3281	110	16	-	-	SYM
ejpam-3281	110	17	1057	1057	NUM
ejpam-3281	110	18	1050	1050	NUM
ejpam-3281	110	19	≤	≤	NUM
ejpam-3281	110	20	max	max	PROPN
ejpam-3281	110	21	1≤i≤m	1≤i≤m	NUM
ejpam-3281	110	22	{	{	PUNCT
ejpam-3281	110	23	|(exp(zi)−	|(exp(zi)−	NOUN
ejpam-3281	110	24	1)|	1)|	NUM
ejpam-3281	110	25	}	}	PUNCT
ejpam-3281	110	26	(	(	PUNCT
ejpam-3281	110	27	using	use	VERB
ejpam-3281	110	28	the	the	DET
ejpam-3281	110	29	fact	fact	NOUN
ejpam-3281	110	30	|w|	|w|	ADJ
ejpam-3281	110	31	=	=	SYM
ejpam-3281	110	32	|	|	ADV
ejpam-3281	110	33	exp(w)−	exp(w)−	PROPN
ejpam-3281	110	34	1|	1|	NUM
ejpam-3281	110	35	,	,	PUNCT
ejpam-3281	110	36	∀w	∀w	X
ejpam-3281	110	37	∈	∈	PROPN
ejpam-3281	110	38	e	e	NOUN
ejpam-3281	110	39	)	)	PUNCT
ejpam-3281	110	40	≤	≤	NUM
ejpam-3281	111	1	max	max	PROPN
ejpam-3281	111	2	1≤i≤m	1≤i≤m	NUM
ejpam-3281	111	3	{	{	PUNCT
ejpam-3281	111	4	|(zi|	|(zi|	ADV
ejpam-3281	111	5	}	}	PUNCT
ejpam-3281	111	6	<	<	X
ejpam-3281	111	7	p	p	X
ejpam-3281	111	8	−1	−1	NOUN
ejpam-3281	111	9	p−1	p−1	NOUN
ejpam-3281	111	10	<	<	X
ejpam-3281	111	11	1	1	NUM
ejpam-3281	111	12	.	.	PUNCT
ejpam-3281	112	1	so	so	ADV
ejpam-3281	112	2	,	,	PUNCT
ejpam-3281	112	3	by	by	ADP
ejpam-3281	112	4	the	the	DET
ejpam-3281	112	5	isosceles	isoscele	NOUN
ejpam-3281	112	6	triangle	triangle	NOUN
ejpam-3281	112	7	inequality	inequality	NOUN
ejpam-3281	112	8	,	,	PUNCT
ejpam-3281	112	9	we	we	PRON
ejpam-3281	112	10	find	find	VERB
ejpam-3281	112	11	that	that	SCONJ
ejpam-3281	112	12	|c+	|c+	NOUN
ejpam-3281	112	13	d1	d1	PROPN
ejpam-3281	112	14	exp(z1	exp(z1	NOUN
ejpam-3281	112	15	)	)	PUNCT
ejpam-3281	113	1	+	+	CCONJ
ejpam-3281	113	2	...	...	PUNCT
ejpam-3281	114	1	+	+	CCONJ
ejpam-3281	114	2	dm	dm	NUM
ejpam-3281	114	3	exp(zm)|	exp(zm)|	NOUN
ejpam-3281	114	4	=	=	SYM
ejpam-3281	114	5	=	=	SYM
ejpam-3281	114	6	max{|c+	max{|c+	NOUN
ejpam-3281	114	7	d1	d1	NOUN
ejpam-3281	114	8	+	+	CCONJ
ejpam-3281	114	9	...	...	PUNCT
ejpam-3281	114	10	+	+	CCONJ
ejpam-3281	114	11	dm|	dm|	ADJ
ejpam-3281	114	12	,	,	PUNCT
ejpam-3281	114	13	|d1(exp(z1)−	|d1(exp(z1)−	NOUN
ejpam-3281	114	14	1	1	NUM
ejpam-3281	114	15	)	)	PUNCT
ejpam-3281	114	16	+	+	CCONJ
ejpam-3281	114	17	..	..	PUNCT
ejpam-3281	115	1	+	+	CCONJ
ejpam-3281	115	2	dm(exp(zm)−	dm(exp(zm)−	ADJ
ejpam-3281	115	3	1)|	1)|	NOUN
ejpam-3281	115	4	}	}	PUNCT
ejpam-3281	115	5	=	=	NOUN
ejpam-3281	115	6	=	=	SYM
ejpam-3281	115	7	|c+	|c+	NUM
ejpam-3281	115	8	d1	d1	NOUN
ejpam-3281	115	9	+	+	CCONJ
ejpam-3281	115	10	...	...	PUNCT
ejpam-3281	115	11	+	+	CCONJ
ejpam-3281	115	12	dm|	dm|	VERB
ejpam-3281	115	13	=	=	SYM
ejpam-3281	115	14	1	1	X
ejpam-3281	115	15	.	.	PUNCT
ejpam-3281	116	1	this	this	PRON
ejpam-3281	116	2	contradicts	contradict	VERB
ejpam-3281	116	3	(	(	PUNCT
ejpam-3281	116	4	1	1	NUM
ejpam-3281	116	5	)	)	PUNCT
ejpam-3281	116	6	.	.	PUNCT
ejpam-3281	117	1	therefore	therefore	ADV
ejpam-3281	117	2	,	,	PUNCT
ejpam-3281	117	3	|c+	|c+	NUM
ejpam-3281	117	4	d1	d1	PROPN
ejpam-3281	117	5	+	+	CCONJ
ejpam-3281	117	6	...	...	PUNCT
ejpam-3281	117	7	+	+	CCONJ
ejpam-3281	117	8	dm|	dm|	VERB
ejpam-3281	117	9	<	<	X
ejpam-3281	117	10	1	1	NUM
ejpam-3281	117	11	,	,	PUNCT
ejpam-3281	117	12	so	so	ADV
ejpam-3281	117	13	|c+	|c+	NUM
ejpam-3281	117	14	d1	d1	PROPN
ejpam-3281	117	15	+	+	CCONJ
ejpam-3281	117	16	...	...	PUNCT
ejpam-3281	117	17	+	+	CCONJ
ejpam-3281	117	18	dm|	dm|	VERB
ejpam-3281	117	19	≤	≤	PROPN
ejpam-3281	117	20	p−1	p−1	PROPN
ejpam-3281	117	21	.	.	PUNCT
ejpam-3281	118	1	this	this	PRON
ejpam-3281	118	2	is	be	AUX
ejpam-3281	118	3	because	because	SCONJ
ejpam-3281	118	4	,	,	PUNCT
ejpam-3281	118	5	c+	c+	VERB
ejpam-3281	118	6	d1	d1	PROPN
ejpam-3281	118	7	+	+	CCONJ
ejpam-3281	118	8	...	...	PUNCT
ejpam-3281	119	1	+	+	CCONJ
ejpam-3281	119	2	dm	dm	X
ejpam-3281	119	3	∈	∈	PROPN
ejpam-3281	119	4	z	z	NOUN
ejpam-3281	119	5	,	,	PUNCT
ejpam-3281	119	6	and	and	CCONJ
ejpam-3281	119	7	the	the	DET
ejpam-3281	119	8	value	value	NOUN
ejpam-3281	119	9	group	group	NOUN
ejpam-3281	119	10	of	of	ADP
ejpam-3281	119	11	z	z	PROPN
ejpam-3281	119	12	is	be	AUX
ejpam-3281	119	13	pz	pz	NOUN
ejpam-3281	119	14	∪	∪	X
ejpam-3281	119	15	{	{	PUNCT
ejpam-3281	119	16	0}.i.e	0}.i.e	PROPN
ejpam-3281	119	17	,	,	PUNCT
ejpam-3281	119	18	for	for	ADP
ejpam-3281	119	19	each	each	DET
ejpam-3281	119	20	q	q	PROPN
ejpam-3281	119	21	∈	∈	PROPN
ejpam-3281	119	22	z∗	z∗	NOUN
ejpam-3281	119	23	,	,	PUNCT
ejpam-3281	119	24	|q|	|q|	PROPN
ejpam-3281	119	25	=	=	SYM
ejpam-3281	119	26	ps	ps	NOUN
ejpam-3281	119	27	,	,	PUNCT
ejpam-3281	119	28	for	for	ADP
ejpam-3281	119	29	some	some	DET
ejpam-3281	119	30	s	s	NOUN
ejpam-3281	119	31	∈	∈	PROPN
ejpam-3281	119	32	z.	z.	NOUN
ejpam-3281	119	33	proof	proof	NOUN
ejpam-3281	119	34	of	of	ADP
ejpam-3281	119	35	the	the	DET
ejpam-3281	119	36	sufficient	sufficient	ADJ
ejpam-3281	119	37	condition	condition	NOUN
ejpam-3281	119	38	.	.	PUNCT
ejpam-3281	120	1	consider	consider	VERB
ejpam-3281	121	1	the	the	DET
ejpam-3281	121	2	polynomial	polynomial	ADJ
ejpam-3281	121	3	p	p	NOUN
ejpam-3281	121	4	[	[	X
ejpam-3281	121	5	x	x	X
ejpam-3281	121	6	,	,	PUNCT
ejpam-3281	121	7	y	y	PROPN
ejpam-3281	121	8	]	]	PUNCT
ejpam-3281	121	9	=	=	PUNCT
ejpam-3281	121	10	c+	c+	VERB
ejpam-3281	122	1	m∑	m∑	AUX
ejpam-3281	122	2	i=1	i=1	PROPN
ejpam-3281	122	3	diy	diy	NOUN
ejpam-3281	122	4	αi	αi	NOUN
ejpam-3281	122	5	+	+	X
ejpam-3281	122	6	e1xy	e1xy	PUNCT
ejpam-3281	122	7	β1,2	β1,2	NUM
ejpam-3281	123	1	+	+	CCONJ
ejpam-3281	123	2	s∑	s∑	PROPN
ejpam-3281	123	3	k=1	k=1	PROPN
ejpam-3281	123	4	fkx	fkx	VERB
ejpam-3281	123	5	γk,1y	γk,1y	PRON
ejpam-3281	123	6	γk,2	γk,2	PROPN
ejpam-3281	123	7	∈	∈	PROPN
ejpam-3281	123	8	z[x	z[x	NOUN
ejpam-3281	123	9	,	,	PUNCT
ejpam-3281	123	10	y	y	PROPN
ejpam-3281	123	11	]	]	PUNCT
ejpam-3281	123	12	,	,	PUNCT
ejpam-3281	123	13	with	with	SCONJ
ejpam-3281	123	14	the	the	DET
ejpam-3281	123	15	condition	condition	NOUN
ejpam-3281	123	16	|c	|c	VERB
ejpam-3281	123	17	+	+	CCONJ
ejpam-3281	123	18	d1	d1	PROPN
ejpam-3281	123	19	+	+	CCONJ
ejpam-3281	123	20	...	...	PUNCT
ejpam-3281	124	1	+	+	CCONJ
ejpam-3281	124	2	dm|	dm|	VERB
ejpam-3281	124	3	≤	≤	PROPN
ejpam-3281	124	4	p−1	p−1	PROPN
ejpam-3281	124	5	.	.	PUNCT
ejpam-3281	125	1	we	we	PRON
ejpam-3281	125	2	have	have	VERB
ejpam-3281	125	3	to	to	PART
ejpam-3281	125	4	prove	prove	VERB
ejpam-3281	125	5	that	that	SCONJ
ejpam-3281	125	6	p	p	X
ejpam-3281	125	7	[	[	X
ejpam-3281	125	8	x	x	X
ejpam-3281	125	9	,	,	PUNCT
ejpam-3281	125	10	y	y	PROPN
ejpam-3281	125	11	]	]	PUNCT
ejpam-3281	125	12	has	have	VERB
ejpam-3281	125	13	a	a	DET
ejpam-3281	125	14	root	root	NOUN
ejpam-3281	125	15	of	of	ADP
ejpam-3281	125	16	the	the	DET
ejpam-3281	125	17	form	form	NOUN
ejpam-3281	125	18	(	(	PUNCT
ejpam-3281	125	19	x	x	NOUN
ejpam-3281	125	20	,	,	PUNCT
ejpam-3281	125	21	exp(x	exp(x	PROPN
ejpam-3281	125	22	)	)	PUNCT
ejpam-3281	125	23	)	)	PUNCT
ejpam-3281	125	24	,	,	PUNCT
ejpam-3281	125	25	x	x	PUNCT
ejpam-3281	125	26	∈	∈	PROPN
ejpam-3281	125	27	e.	e.	PROPN
ejpam-3281	125	28	this	this	PRON
ejpam-3281	125	29	is	be	AUX
ejpam-3281	125	30	equivalent	equivalent	ADJ
ejpam-3281	125	31	to	to	PART
ejpam-3281	125	32	prove	prove	VERB
ejpam-3281	125	33	that	that	SCONJ
ejpam-3281	125	34	the	the	DET
ejpam-3281	125	35	power	power	NOUN
ejpam-3281	125	36	series	series	PROPN
ejpam-3281	125	37	f(x	f(x	PROPN
ejpam-3281	125	38	)	)	PUNCT
ejpam-3281	125	39	:	:	PUNCT
ejpam-3281	126	1	=	=	PUNCT
ejpam-3281	126	2	p	p	X
ejpam-3281	127	1	[	[	X
ejpam-3281	127	2	x	x	X
ejpam-3281	127	3	,	,	PUNCT
ejpam-3281	127	4	exp(x	exp(x	PROPN
ejpam-3281	127	5	)	)	PUNCT
ejpam-3281	127	6	]	]	PUNCT
ejpam-3281	127	7	has	have	VERB
ejpam-3281	127	8	a	a	DET
ejpam-3281	127	9	root	root	NOUN
ejpam-3281	127	10	x	x	SYM
ejpam-3281	127	11	∈	∈	PROPN
ejpam-3281	127	12	e.	e.	PROPN
ejpam-3281	127	13	suppose	suppose	VERB
ejpam-3281	127	14	that	that	SCONJ
ejpam-3281	127	15	the	the	DET
ejpam-3281	127	16	power	power	NOUN
ejpam-3281	127	17	series	series	PROPN
ejpam-3281	127	18	f(x	f(x	PROPN
ejpam-3281	127	19	)	)	PUNCT
ejpam-3281	127	20	takes	take	VERB
ejpam-3281	127	21	the	the	DET
ejpam-3281	127	22	form	form	NOUN
ejpam-3281	127	23	f(x	f(x	PROPN
ejpam-3281	127	24	)	)	PUNCT
ejpam-3281	128	1	=	=	SYM
ejpam-3281	128	2	a0	a0	PROPN
ejpam-3281	128	3	+	+	CCONJ
ejpam-3281	128	4	a1x	a1x	NOUN
ejpam-3281	128	5	+	+	PUNCT
ejpam-3281	128	6	..	..	PUNCT
ejpam-3281	128	7	+	+	X
ejpam-3281	128	8	anx	anx	ADJ
ejpam-3281	128	9	n	n	NOUN
ejpam-3281	128	10	+	+	CCONJ
ejpam-3281	128	11	..	..	PUNCT
ejpam-3281	128	12	in	in	ADP
ejpam-3281	128	13	our	our	PRON
ejpam-3281	128	14	case	case	NOUN
ejpam-3281	128	15	,	,	PUNCT
ejpam-3281	128	16	we	we	PRON
ejpam-3281	128	17	have	have	VERB
ejpam-3281	128	18	a0	a0	NOUN
ejpam-3281	128	19	=	=	PUNCT
ejpam-3281	128	20	c+	c+	X
ejpam-3281	128	21	d1	d1	PROPN
ejpam-3281	128	22	+	+	CCONJ
ejpam-3281	128	23	..	..	PUNCT
ejpam-3281	129	1	+	+	CCONJ
ejpam-3281	129	2	dm	dm	X
ejpam-3281	129	3	,	,	PUNCT
ejpam-3281	129	4	a1	a1	NOUN
ejpam-3281	129	5	=	=	SYM
ejpam-3281	129	6	d1α1	d1α1	PROPN
ejpam-3281	129	7	+	+	NUM
ejpam-3281	129	8	..	..	PUNCT
ejpam-3281	129	9	+	+	NUM
ejpam-3281	129	10	dmαm	dmαm	NOUN
ejpam-3281	129	11	+	+	CCONJ
ejpam-3281	129	12	e1	e1	NOUN
ejpam-3281	129	13	,	,	PUNCT
ejpam-3281	129	14	an	an	DET
ejpam-3281	129	15	=	=	PUNCT
ejpam-3281	129	16	d1α	d1α	PROPN
ejpam-3281	129	17	n	n	X
ejpam-3281	129	18	1	1	NUM
ejpam-3281	129	19	+	+	CCONJ
ejpam-3281	129	20	..	..	PUNCT
ejpam-3281	129	21	+	+	NUM
ejpam-3281	129	22	dmα	dmα	PROPN
ejpam-3281	129	23	n	n	INTJ
ejpam-3281	129	24	m	m	VERB
ejpam-3281	129	25	n	n	NUM
ejpam-3281	129	26	!	!	PUNCT
ejpam-3281	130	1	+	+	CCONJ
ejpam-3281	130	2	e1	e1	PROPN
ejpam-3281	130	3	βn−11,2	βn−11,2	NOUN
ejpam-3281	130	4	(	(	PUNCT
ejpam-3281	130	5	n−	n−	NOUN
ejpam-3281	130	6	1	1	NUM
ejpam-3281	130	7	)	)	PUNCT
ejpam-3281	130	8	!	!	PUNCT
ejpam-3281	131	1	;	;	PUNCT
ejpam-3281	131	2	n	n	CCONJ
ejpam-3281	131	3	<	<	X
ejpam-3281	131	4	min	min	X
ejpam-3281	131	5	1≤j≤s	1≤j≤s	NUM
ejpam-3281	131	6	{	{	PUNCT
ejpam-3281	131	7	γj,1	γj,1	NOUN
ejpam-3281	131	8	}	}	PUNCT
ejpam-3281	131	9	,	,	PUNCT
ejpam-3281	131	10	an	an	DET
ejpam-3281	131	11	=	=	PUNCT
ejpam-3281	131	12	d1α	d1α	PROPN
ejpam-3281	131	13	n	n	X
ejpam-3281	131	14	1	1	NUM
ejpam-3281	131	15	+	+	CCONJ
ejpam-3281	131	16	..	..	PUNCT
ejpam-3281	131	17	+	+	NUM
ejpam-3281	131	18	dmα	dmα	PROPN
ejpam-3281	131	19	n	n	INTJ
ejpam-3281	131	20	m	m	VERB
ejpam-3281	131	21	n	n	NUM
ejpam-3281	131	22	!	!	PUNCT
ejpam-3281	132	1	+	+	CCONJ
ejpam-3281	132	2	e1	e1	PROPN
ejpam-3281	132	3	βn−11,2	βn−11,2	NOUN
ejpam-3281	132	4	(	(	PUNCT
ejpam-3281	132	5	n−	n−	NOUN
ejpam-3281	132	6	1	1	NUM
ejpam-3281	132	7	)	)	PUNCT
ejpam-3281	132	8	!	!	PUNCT
ejpam-3281	133	1	+	+	CCONJ
ejpam-3281	133	2	f1	f1	ADJ
ejpam-3281	133	3	γ	γ	NOUN
ejpam-3281	133	4	n−γ1,1	n−γ1,1	PROPN
ejpam-3281	133	5	1,2	1,2	NUM
ejpam-3281	133	6	(	(	PUNCT
ejpam-3281	133	7	n−	n−	NOUN
ejpam-3281	133	8	γ1,1	γ1,1	NUM
ejpam-3281	133	9	)	)	PUNCT
ejpam-3281	133	10	!	!	PUNCT
ejpam-3281	134	1	+	+	CCONJ
ejpam-3281	134	2	..	..	PUNCT
ejpam-3281	134	3	+	+	CCONJ
ejpam-3281	134	4	fs	fs	ADP
ejpam-3281	134	5	γ	γ	X
ejpam-3281	134	6	n−γs,1	n−γs,1	ADJ
ejpam-3281	134	7	s,2	s,2	X
ejpam-3281	134	8	(	(	PUNCT
ejpam-3281	134	9	n−	n−	NOUN
ejpam-3281	134	10	γs,1	γs,1	ADJ
ejpam-3281	134	11	)	)	PUNCT
ejpam-3281	134	12	!	!	PUNCT
ejpam-3281	135	1	;	;	PUNCT
ejpam-3281	135	2	n	n	NUM
ejpam-3281	135	3	≥	≥	NOUN
ejpam-3281	135	4	min	min	PROPN
ejpam-3281	135	5	1≤i≤s	1≤i≤s	NUM
ejpam-3281	135	6	{	{	PUNCT
ejpam-3281	135	7	γj,1	γj,1	NOUN
ejpam-3281	135	8	}	}	PUNCT
ejpam-3281	135	9	.	.	PUNCT
ejpam-3281	136	1	let	let	VERB
ejpam-3281	136	2	α	α	PRON
ejpam-3281	136	3	be	be	AUX
ejpam-3281	136	4	any	any	DET
ejpam-3281	136	5	rational	rational	ADJ
ejpam-3281	136	6	number	number	NOUN
ejpam-3281	136	7	satisfying	satisfy	VERB
ejpam-3281	136	8	−1	−1	NOUN
ejpam-3281	136	9	<	<	X
ejpam-3281	136	10	α	α	PRON
ejpam-3281	136	11	<	<	X
ejpam-3281	136	12	−1	−1	NOUN
ejpam-3281	136	13	p−1	p−1	PROPN
ejpam-3281	136	14	.	.	PUNCT
ejpam-3281	137	1	in	in	ADP
ejpam-3281	137	2	fact	fact	NOUN
ejpam-3281	137	3	,	,	PUNCT
ejpam-3281	137	4	we	we	PRON
ejpam-3281	137	5	have	have	AUX
ejpam-3281	137	6	chosen	choose	VERB
ejpam-3281	137	7	α	α	PRON
ejpam-3281	137	8	∈	∈	PROPN
ejpam-3281	137	9	q	q	PUNCT
ejpam-3281	137	10	to	to	PART
ejpam-3281	137	11	guarantee	guarantee	VERB
ejpam-3281	137	12	that	that	SCONJ
ejpam-3281	137	13	pα	pα	NOUN
ejpam-3281	137	14	∈	∈	PROPN
ejpam-3281	137	15	|cp|	|cp|	PROPN
ejpam-3281	137	16	.	.	PUNCT
ejpam-3281	138	1	then	then	ADV
ejpam-3281	138	2	f(x	f(x	PROPN
ejpam-3281	138	3	)	)	PUNCT
ejpam-3281	138	4	is	be	AUX
ejpam-3281	138	5	convergent	convergent	ADJ
ejpam-3281	138	6	on	on	ADP
ejpam-3281	138	7	the	the	DET
ejpam-3281	138	8	closed	close	VERB
ejpam-3281	138	9	ball	ball	NOUN
ejpam-3281	138	10	b(0	b(0	NOUN
ejpam-3281	138	11	,	,	PUNCT
ejpam-3281	138	12	pα	pα	NOUN
ejpam-3281	138	13	)	)	PUNCT
ejpam-3281	138	14	.	.	PUNCT
ejpam-3281	139	1	the	the	DET
ejpam-3281	139	2	general	general	ADJ
ejpam-3281	139	3	assumption	assumption	NOUN
ejpam-3281	139	4	of	of	ADP
ejpam-3281	139	5	the	the	DET
ejpam-3281	139	6	theorem	theorem	NOUN
ejpam-3281	139	7	guarantees	guarantee	NOUN
ejpam-3281	139	8	that	that	SCONJ
ejpam-3281	139	9	ord(a1	ord(a1	VERB
ejpam-3281	139	10	)	)	PUNCT
ejpam-3281	139	11	=	=	SYM
ejpam-3281	139	12	0	0	X
ejpam-3281	139	13	.	.	PUNCT
ejpam-3281	140	1	therefore	therefore	ADV
ejpam-3281	140	2	,	,	PUNCT
ejpam-3281	140	3	|a1|	|a1|	X
ejpam-3281	140	4	=	=	SYM
ejpam-3281	140	5	1	1	X
ejpam-3281	140	6	.	.	PUNCT
ejpam-3281	141	1	also	also	ADV
ejpam-3281	141	2	,	,	PUNCT
ejpam-3281	141	3	by	by	ADP
ejpam-3281	141	4	definition	definition	NOUN
ejpam-3281	141	5	of	of	ADP
ejpam-3281	141	6	α	α	NOUN
ejpam-3281	141	7	,	,	PUNCT
ejpam-3281	141	8	we	we	PRON
ejpam-3281	141	9	find	find	VERB
ejpam-3281	141	10	that	that	SCONJ
ejpam-3281	141	11	p−1	p−1	PROPN
ejpam-3281	141	12	<	<	X
ejpam-3281	141	13	pα	pα	NOUN
ejpam-3281	141	14	.	.	PUNCT
ejpam-3281	142	1	thus	thus	ADV
ejpam-3281	142	2	,	,	PUNCT
ejpam-3281	142	3	|a0|	|a0|	NOUN
ejpam-3281	142	4	≤	≤	X
ejpam-3281	142	5	p−1	p−1	PROPN
ejpam-3281	142	6	<	<	X
ejpam-3281	142	7	|a1|p1.α	|a1|p1.α	PUNCT
ejpam-3281	142	8	≤	≤	ADJ
ejpam-3281	142	9	max	max	PROPN
ejpam-3281	142	10	n≥1	n≥1	PROPN
ejpam-3281	142	11	{	{	PUNCT
ejpam-3281	142	12	|an|pnα	|an|pnα	ADV
ejpam-3281	142	13	}	}	PUNCT
ejpam-3281	142	14	.	.	PUNCT
ejpam-3281	143	1	therefore	therefore	ADV
ejpam-3281	143	2	,	,	PUNCT
ejpam-3281	143	3	the	the	DET
ejpam-3281	143	4	number	number	NOUN
ejpam-3281	143	5	n	n	NOUN
ejpam-3281	143	6	,	,	PUNCT
ejpam-3281	143	7	defined	define	VERB
ejpam-3281	143	8	in	in	ADP
ejpam-3281	143	9	weierstrass	weierstrass	NOUN
ejpam-3281	143	10	preparation	preparation	NOUN
ejpam-3281	143	11	theorem	theorem	NOUN
ejpam-3281	143	12	,	,	PUNCT
ejpam-3281	143	13	is	be	AUX
ejpam-3281	143	14	strictly	strictly	ADV
ejpam-3281	143	15	larger	large	ADJ
ejpam-3281	143	16	than	than	ADP
ejpam-3281	143	17	zero.i.e	zero.i.e	NOUN
ejpam-3281	143	18	,	,	PUNCT
ejpam-3281	143	19	n	n	CCONJ
ejpam-3281	143	20	>	>	X
ejpam-3281	143	21	0	0	X
ejpam-3281	143	22	.	.	PUNCT
ejpam-3281	144	1	weierstrass	weierstrass	PROPN
ejpam-3281	144	2	preparation	preparation	NOUN
ejpam-3281	144	3	theorem	theorem	NOUN
ejpam-3281	144	4	guarantees	guarantee	NOUN
ejpam-3281	144	5	that	that	SCONJ
ejpam-3281	144	6	f(x	f(x	PROPN
ejpam-3281	144	7	)	)	PUNCT
ejpam-3281	144	8	can	can	AUX
ejpam-3281	144	9	be	be	AUX
ejpam-3281	144	10	written	write	VERB
ejpam-3281	144	11	in	in	ADP
ejpam-3281	144	12	the	the	DET
ejpam-3281	144	13	form	form	NOUN
ejpam-3281	144	14	f(x	f(x	PROPN
ejpam-3281	144	15	)	)	PUNCT
ejpam-3281	144	16	=	=	PUNCT
ejpam-3281	144	17	h(x)g(x	h(x)g(x	X
ejpam-3281	144	18	)	)	PUNCT
ejpam-3281	144	19	;	;	PUNCT
ejpam-3281	144	20	h(x	h(x	PROPN
ejpam-3281	144	21	)	)	PUNCT
ejpam-3281	144	22	is	be	AUX
ejpam-3281	144	23	a	a	DET
ejpam-3281	144	24	power	power	NOUN
ejpam-3281	144	25	series	series	NOUN
ejpam-3281	144	26	convergent	convergent	NOUN
ejpam-3281	144	27	and	and	CCONJ
ejpam-3281	144	28	non	non	ADJ
ejpam-3281	144	29	-	-	ADJ
ejpam-3281	144	30	vanishing	vanishing	ADJ
ejpam-3281	144	31	a.	a.	NOUN
ejpam-3281	144	32	dalloul	dalloul	PROPN
ejpam-3281	144	33	/	/	SYM
ejpam-3281	144	34	eur	eur	PROPN
ejpam-3281	144	35	.	.	PUNCT
ejpam-3281	145	1	j.	j.	PROPN
ejpam-3281	145	2	pure	pure	PROPN
ejpam-3281	145	3	appl	appl	PROPN
ejpam-3281	145	4	.	.	PROPN
ejpam-3281	145	5	math	math	PROPN
ejpam-3281	145	6	,	,	PUNCT
ejpam-3281	145	7	11	11	NUM
ejpam-3281	145	8	(	(	PUNCT
ejpam-3281	145	9	4	4	NUM
ejpam-3281	145	10	)	)	PUNCT
ejpam-3281	145	11	(	(	PUNCT
ejpam-3281	145	12	2018	2018	NUM
ejpam-3281	145	13	)	)	PUNCT
ejpam-3281	145	14	,	,	PUNCT
ejpam-3281	145	15	1046	1046	NUM
ejpam-3281	145	16	-	-	SYM
ejpam-3281	145	17	1057	1057	NUM
ejpam-3281	145	18	1051	1051	NUM
ejpam-3281	145	19	on	on	ADP
ejpam-3281	145	20	b(0	b(0	PROPN
ejpam-3281	145	21	,	,	PUNCT
ejpam-3281	145	22	pα	pα	NOUN
ejpam-3281	145	23	)	)	PUNCT
ejpam-3281	145	24	and	and	CCONJ
ejpam-3281	145	25	g(x	g(x	NOUN
ejpam-3281	145	26	)	)	PUNCT
ejpam-3281	145	27	is	be	AUX
ejpam-3281	145	28	a	a	DET
ejpam-3281	145	29	polynomial	polynomial	NOUN
ejpam-3281	145	30	with	with	ADP
ejpam-3281	145	31	p	p	NOUN
ejpam-3281	145	32	-	-	PUNCT
ejpam-3281	145	33	adic	adic	ADJ
ejpam-3281	145	34	complex	complex	ADJ
ejpam-3281	145	35	coefficients	coefficient	NOUN
ejpam-3281	145	36	of	of	ADP
ejpam-3281	145	37	degree	degree	NOUN
ejpam-3281	145	38	n	n	CCONJ
ejpam-3281	145	39	>	>	X
ejpam-3281	145	40	0	0	X
ejpam-3281	145	41	.	.	PUNCT
ejpam-3281	146	1	since	since	SCONJ
ejpam-3281	146	2	cp	cp	PROPN
ejpam-3281	146	3	is	be	AUX
ejpam-3281	146	4	algebraically	algebraically	ADV
ejpam-3281	146	5	closes	close	VERB
ejpam-3281	146	6	field	field	NOUN
ejpam-3281	146	7	,	,	PUNCT
ejpam-3281	146	8	it	it	PRON
ejpam-3281	146	9	follows	follow	VERB
ejpam-3281	146	10	that	that	SCONJ
ejpam-3281	146	11	g(x	g(x	NOUN
ejpam-3281	146	12	)	)	PUNCT
ejpam-3281	146	13	has	have	VERB
ejpam-3281	146	14	a	a	DET
ejpam-3281	146	15	root	root	NOUN
ejpam-3281	146	16	x.	x.	NOUN
ejpam-3281	147	1	this	this	DET
ejpam-3281	147	2	root	root	NOUN
ejpam-3281	147	3	belongs	belong	VERB
ejpam-3281	147	4	to	to	ADP
ejpam-3281	147	5	b(0	b(0	VERB
ejpam-3281	147	6	,	,	PUNCT
ejpam-3281	147	7	pα).i.e	pα).i.e	NOUN
ejpam-3281	147	8	.	.	PUNCT
ejpam-3281	147	9	,	,	PUNCT
ejpam-3281	147	10	x	x	PUNCT
ejpam-3281	147	11	∈	∈	PROPN
ejpam-3281	147	12	e.	e.	PROPN
ejpam-3281	147	13	therefore	therefore	ADV
ejpam-3281	147	14	,	,	PUNCT
ejpam-3281	147	15	f(x	f(x	PROPN
ejpam-3281	147	16	)	)	PUNCT
ejpam-3281	147	17	=	=	PUNCT
ejpam-3281	148	1	h(x).0	h(x).0	X
ejpam-3281	148	2	=	=	SYM
ejpam-3281	148	3	0	0	X
ejpam-3281	148	4	.	.	PUNCT
ejpam-3281	149	1	thus	thus	ADV
ejpam-3281	149	2	,	,	PUNCT
ejpam-3281	149	3	p	p	X
ejpam-3281	149	4	(	(	PUNCT
ejpam-3281	149	5	x	x	NOUN
ejpam-3281	149	6	,	,	PUNCT
ejpam-3281	149	7	exp(x	exp(x	PROPN
ejpam-3281	149	8	)	)	PUNCT
ejpam-3281	149	9	)	)	PUNCT
ejpam-3281	149	10	=	=	PUNCT
ejpam-3281	149	11	0	0	X
ejpam-3281	149	12	.	.	PUNCT
ejpam-3281	149	13	remark	remark	PROPN
ejpam-3281	149	14	1	1	NUM
ejpam-3281	149	15	.	.	PUNCT
ejpam-3281	150	1	in	in	ADP
ejpam-3281	150	2	the	the	DET
ejpam-3281	150	3	proof	proof	NOUN
ejpam-3281	150	4	of	of	ADP
ejpam-3281	150	5	the	the	DET
ejpam-3281	150	6	necessary	necessary	ADJ
ejpam-3281	150	7	condition	condition	NOUN
ejpam-3281	150	8	,	,	PUNCT
ejpam-3281	150	9	we	we	PRON
ejpam-3281	150	10	did	do	AUX
ejpam-3281	150	11	not	not	PART
ejpam-3281	150	12	use	use	VERB
ejpam-3281	150	13	the	the	DET
ejpam-3281	150	14	assumption	assumption	NOUN
ejpam-3281	150	15	(	(	PUNCT
ejpam-3281	150	16	d1α1	d1α1	X
ejpam-3281	150	17	+	+	NUM
ejpam-3281	150	18	..	..	PUNCT
ejpam-3281	150	19	+	+	NUM
ejpam-3281	150	20	dmαm	dmαm	NOUN
ejpam-3281	150	21	+	+	CCONJ
ejpam-3281	150	22	e1	e1	NOUN
ejpam-3281	150	23	,	,	PUNCT
ejpam-3281	150	24	p	p	NOUN
ejpam-3281	150	25	)	)	PUNCT
ejpam-3281	151	1	=	=	SYM
ejpam-3281	151	2	1	1	X
ejpam-3281	151	3	.	.	PUNCT
ejpam-3281	152	1	this	this	PRON
ejpam-3281	152	2	implies	imply	VERB
ejpam-3281	152	3	that	that	SCONJ
ejpam-3281	152	4	any	any	DET
ejpam-3281	152	5	polynomial	polynomial	NOUN
ejpam-3281	152	6	of	of	ADP
ejpam-3281	152	7	the	the	DET
ejpam-3281	152	8	form	form	NOUN
ejpam-3281	152	9	p	p	X
ejpam-3281	152	10	[	[	X
ejpam-3281	152	11	x	x	X
ejpam-3281	152	12	,	,	PUNCT
ejpam-3281	152	13	y	y	PROPN
ejpam-3281	152	14	]	]	PUNCT
ejpam-3281	152	15	=	=	PUNCT
ejpam-3281	152	16	c+	c+	VERB
ejpam-3281	152	17	m∑	m∑	VERB
ejpam-3281	152	18	i=1	i=1	PROPN
ejpam-3281	152	19	diy	diy	NOUN
ejpam-3281	152	20	αi	αi	NOUN
ejpam-3281	152	21	+	+	CCONJ
ejpam-3281	152	22	s∑	s∑	PROPN
ejpam-3281	152	23	k=1	k=1	PROPN
ejpam-3281	152	24	fkx	fkx	PROPN
ejpam-3281	152	25	ξk,1y	ξk,1y	NUM
ejpam-3281	152	26	ξk,2	ξk,2	PROPN
ejpam-3281	152	27	;	;	PUNCT
ejpam-3281	152	28	ξk,1	ξk,1	NOUN
ejpam-3281	152	29	≥	≥	NOUN
ejpam-3281	152	30	1	1	NUM
ejpam-3281	152	31	,	,	PUNCT
ejpam-3281	152	32	with	with	ADP
ejpam-3281	152	33	(	(	PUNCT
ejpam-3281	152	34	c+	c+	VERB
ejpam-3281	152	35	d1	d1	PROPN
ejpam-3281	152	36	+	+	X
ejpam-3281	152	37	..	..	PUNCT
ejpam-3281	153	1	+	+	CCONJ
ejpam-3281	153	2	dm	dm	VERB
ejpam-3281	153	3	,	,	PUNCT
ejpam-3281	153	4	p	p	NOUN
ejpam-3281	153	5	)	)	PUNCT
ejpam-3281	153	6	=	=	SYM
ejpam-3281	153	7	1	1	NUM
ejpam-3281	153	8	and	and	CCONJ
ejpam-3281	153	9	at	at	ADV
ejpam-3281	153	10	least	least	ADJ
ejpam-3281	153	11	one	one	NUM
ejpam-3281	153	12	of	of	ADP
ejpam-3281	153	13	the	the	DET
ejpam-3281	153	14	degrees	degree	NOUN
ejpam-3281	153	15	of	of	ADP
ejpam-3281	153	16	the	the	DET
ejpam-3281	153	17	variable	variable	ADJ
ejpam-3281	153	18	y	y	PROPN
ejpam-3281	153	19	is	be	AUX
ejpam-3281	153	20	relatively	relatively	ADV
ejpam-3281	153	21	prime	prime	ADJ
ejpam-3281	153	22	to	to	ADP
ejpam-3281	153	23	p	p	NOUN
ejpam-3281	153	24	does	do	AUX
ejpam-3281	153	25	not	not	PART
ejpam-3281	153	26	have	have	VERB
ejpam-3281	153	27	any	any	DET
ejpam-3281	153	28	root	root	NOUN
ejpam-3281	153	29	of	of	ADP
ejpam-3281	153	30	the	the	DET
ejpam-3281	153	31	form	form	NOUN
ejpam-3281	153	32	(	(	PUNCT
ejpam-3281	153	33	x	x	NOUN
ejpam-3281	153	34	,	,	PUNCT
ejpam-3281	153	35	exp(x	exp(x	PROPN
ejpam-3281	153	36	)	)	PUNCT
ejpam-3281	153	37	)	)	PUNCT
ejpam-3281	153	38	.	.	PUNCT
ejpam-3281	154	1	example	example	NOUN
ejpam-3281	155	1	1	1	X
ejpam-3281	155	2	.	.	PUNCT
ejpam-3281	155	3	we	we	PRON
ejpam-3281	155	4	can	can	AUX
ejpam-3281	155	5	use	use	VERB
ejpam-3281	155	6	remark	remark	NOUN
ejpam-3281	155	7	1	1	NUM
ejpam-3281	155	8	to	to	PART
ejpam-3281	155	9	prove	prove	VERB
ejpam-3281	155	10	that	that	SCONJ
ejpam-3281	155	11	the	the	DET
ejpam-3281	155	12	polynomial	polynomial	ADJ
ejpam-3281	155	13	p	p	X
ejpam-3281	156	1	[	[	X
ejpam-3281	156	2	x	x	X
ejpam-3281	156	3	,	,	PUNCT
ejpam-3281	156	4	y	y	NOUN
ejpam-3281	156	5	]	]	PUNCT
ejpam-3281	157	1	=	=	PUNCT
ejpam-3281	157	2	x2	x2	PROPN
ejpam-3281	158	1	+	+	CCONJ
ejpam-3281	158	2	y	y	PROPN
ejpam-3281	158	3	2	2	NUM
ejpam-3281	158	4	has	have	VERB
ejpam-3281	158	5	no	no	DET
ejpam-3281	158	6	roots	root	NOUN
ejpam-3281	158	7	of	of	ADP
ejpam-3281	158	8	the	the	DET
ejpam-3281	158	9	form	form	NOUN
ejpam-3281	158	10	(	(	PUNCT
ejpam-3281	158	11	x	x	NOUN
ejpam-3281	158	12	,	,	PUNCT
ejpam-3281	158	13	exp(x	exp(x	PROPN
ejpam-3281	158	14	)	)	PUNCT
ejpam-3281	158	15	)	)	PUNCT
ejpam-3281	159	1	∈	∈	PROPN
ejpam-3281	160	1	cp	cp	INTJ
ejpam-3281	160	2	×	×	PROPN
ejpam-3281	160	3	c∗p	c∗p	PROPN
ejpam-3281	160	4	;	;	PUNCT
ejpam-3281	160	5	p	p	PRON
ejpam-3281	160	6	≥	≥	NUM
ejpam-3281	160	7	3	3	NUM
ejpam-3281	160	8	.	.	PUNCT
ejpam-3281	160	9	example	example	NOUN
ejpam-3281	160	10	2	2	NUM
ejpam-3281	160	11	.	.	X
ejpam-3281	160	12	consider	consider	VERB
ejpam-3281	160	13	the	the	DET
ejpam-3281	160	14	polynomial	polynomial	ADJ
ejpam-3281	160	15	p	p	NOUN
ejpam-3281	161	1	[	[	X
ejpam-3281	161	2	x	x	X
ejpam-3281	161	3	,	,	PUNCT
ejpam-3281	161	4	y	y	PROPN
ejpam-3281	161	5	]	]	PUNCT
ejpam-3281	162	1	=	=	PUNCT
ejpam-3281	162	2	p−	p−	NOUN
ejpam-3281	162	3	1	1	NUM
ejpam-3281	162	4	+	+	CCONJ
ejpam-3281	162	5	(	(	PUNCT
ejpam-3281	162	6	p+	p+	NOUN
ejpam-3281	162	7	1)y	1)y	NUM
ejpam-3281	162	8	p	p	X
ejpam-3281	162	9	+	+	PROPN
ejpam-3281	162	10	x	x	PROPN
ejpam-3281	162	11	+	+	ADJ
ejpam-3281	162	12	x3y	x3y	PROPN
ejpam-3281	162	13	p−1	p−1	PROPN
ejpam-3281	162	14	+	+	PROPN
ejpam-3281	162	15	x7y	x7y	PROPN
ejpam-3281	162	16	15	15	NUM
ejpam-3281	162	17	.	.	PUNCT
ejpam-3281	163	1	then	then	ADV
ejpam-3281	163	2	,	,	PUNCT
ejpam-3281	163	3	the	the	DET
ejpam-3281	163	4	domain	domain	NOUN
ejpam-3281	163	5	of	of	ADP
ejpam-3281	163	6	f(x	f(x	PROPN
ejpam-3281	163	7	)	)	PUNCT
ejpam-3281	164	1	=	=	PUNCT
ejpam-3281	165	1	p	p	X
ejpam-3281	166	1	[	[	X
ejpam-3281	166	2	x	x	X
ejpam-3281	166	3	,	,	PUNCT
ejpam-3281	166	4	exp(x	exp(x	PROPN
ejpam-3281	166	5	)	)	PUNCT
ejpam-3281	166	6	]	]	PUNCT
ejpam-3281	166	7	is	be	AUX
ejpam-3281	166	8	e	e	NOUN
ejpam-3281	166	9	,	,	PUNCT
ejpam-3281	166	10	(	(	PUNCT
ejpam-3281	166	11	d1α1	d1α1	X
ejpam-3281	166	12	+	+	X
ejpam-3281	166	13	..	..	PUNCT
ejpam-3281	166	14	+	+	NUM
ejpam-3281	166	15	dmαm	dmαm	NOUN
ejpam-3281	166	16	+	+	CCONJ
ejpam-3281	166	17	e1	e1	NOUN
ejpam-3281	166	18	,	,	PUNCT
ejpam-3281	166	19	p	p	NOUN
ejpam-3281	166	20	)	)	PUNCT
ejpam-3281	166	21	=	=	SYM
ejpam-3281	166	22	(	(	PUNCT
ejpam-3281	166	23	p(p+	p(p+	PROPN
ejpam-3281	166	24	1	1	NUM
ejpam-3281	166	25	)	)	PUNCT
ejpam-3281	167	1	+	+	NUM
ejpam-3281	167	2	1	1	NUM
ejpam-3281	167	3	,	,	PUNCT
ejpam-3281	167	4	p	p	NOUN
ejpam-3281	167	5	)	)	PUNCT
ejpam-3281	167	6	=	=	SYM
ejpam-3281	167	7	1	1	NUM
ejpam-3281	167	8	and	and	CCONJ
ejpam-3281	167	9	|c+d1	|c+d1	PROPN
ejpam-3281	167	10	+	+	NUM
ejpam-3281	167	11	..	..	PUNCT
ejpam-3281	168	1	+	+	PROPN
ejpam-3281	168	2	dm|	dm|	VERB
ejpam-3281	168	3	=	=	PUNCT
ejpam-3281	168	4	|2p|	|2p|	NUM
ejpam-3281	168	5	=	=	SYM
ejpam-3281	168	6	p−1	p−1	PROPN
ejpam-3281	168	7	.	.	PUNCT
ejpam-3281	169	1	according	accord	VERB
ejpam-3281	169	2	to	to	ADP
ejpam-3281	169	3	theorem	theorem	NOUN
ejpam-3281	169	4	2	2	NUM
ejpam-3281	169	5	,	,	PUNCT
ejpam-3281	169	6	we	we	PRON
ejpam-3281	169	7	find	find	VERB
ejpam-3281	169	8	that	that	SCONJ
ejpam-3281	169	9	p	p	X
ejpam-3281	169	10	[	[	X
ejpam-3281	169	11	x	x	X
ejpam-3281	169	12	,	,	PUNCT
ejpam-3281	169	13	y	y	PROPN
ejpam-3281	169	14	]	]	PUNCT
ejpam-3281	169	15	has	have	VERB
ejpam-3281	169	16	a	a	DET
ejpam-3281	169	17	root	root	NOUN
ejpam-3281	169	18	of	of	ADP
ejpam-3281	169	19	the	the	DET
ejpam-3281	169	20	form	form	NOUN
ejpam-3281	169	21	(	(	PUNCT
ejpam-3281	169	22	x	x	NOUN
ejpam-3281	169	23	,	,	PUNCT
ejpam-3281	169	24	exp(x	exp(x	PROPN
ejpam-3281	169	25	)	)	PUNCT
ejpam-3281	169	26	)	)	PUNCT
ejpam-3281	170	1	∈	∈	PROPN
ejpam-3281	171	1	cp	cp	INTJ
ejpam-3281	171	2	×	×	PROPN
ejpam-3281	171	3	c∗p	c∗p	PROPN
ejpam-3281	171	4	;	;	PUNCT
ejpam-3281	171	5	p	p	PRON
ejpam-3281	171	6	≥	≥	NUM
ejpam-3281	171	7	3	3	NUM
ejpam-3281	171	8	.	.	PUNCT
ejpam-3281	172	1	this	this	DET
ejpam-3281	172	2	example	example	NOUN
ejpam-3281	172	3	shows	show	VERB
ejpam-3281	172	4	that	that	SCONJ
ejpam-3281	172	5	there	there	PRON
ejpam-3281	172	6	exists	exist	VERB
ejpam-3281	172	7	a	a	DET
ejpam-3281	172	8	non	non	ADJ
ejpam-3281	172	9	trivial	trivial	ADJ
ejpam-3281	172	10	tuple	tuple	NOUN
ejpam-3281	172	11	of	of	ADP
ejpam-3281	172	12	the	the	DET
ejpam-3281	172	13	form	form	NOUN
ejpam-3281	172	14	(	(	PUNCT
ejpam-3281	172	15	x	x	NOUN
ejpam-3281	172	16	,	,	PUNCT
ejpam-3281	172	17	exp(x	exp(x	PROPN
ejpam-3281	172	18	)	)	PUNCT
ejpam-3281	172	19	)	)	PUNCT
ejpam-3281	172	20	satisfies	satisfy	VERB
ejpam-3281	172	21	an	an	DET
ejpam-3281	172	22	algebraic	algebraic	ADJ
ejpam-3281	172	23	dependence	dependence	NOUN
ejpam-3281	172	24	relation	relation	NOUN
ejpam-3281	172	25	with	with	ADP
ejpam-3281	172	26	rational	rational	ADJ
ejpam-3281	172	27	integer	integer	NOUN
ejpam-3281	172	28	coefficients	coefficient	NOUN
ejpam-3281	172	29	relatively	relatively	ADV
ejpam-3281	172	30	prime	prime	ADJ
ejpam-3281	172	31	to	to	ADP
ejpam-3281	172	32	p.	p.	NOUN
ejpam-3281	172	33	also	also	ADV
ejpam-3281	172	34	we	we	PRON
ejpam-3281	172	35	can	can	AUX
ejpam-3281	172	36	use	use	VERB
ejpam-3281	172	37	hilbert	hilbert	NOUN
ejpam-3281	172	38	theorem	theorem	VERB
ejpam-3281	172	39	to	to	PART
ejpam-3281	172	40	get	get	VERB
ejpam-3281	172	41	a	a	DET
ejpam-3281	172	42	result	result	NOUN
ejpam-3281	172	43	concerning	concern	VERB
ejpam-3281	172	44	the	the	DET
ejpam-3281	172	45	roots	root	NOUN
ejpam-3281	172	46	of	of	ADP
ejpam-3281	172	47	the	the	DET
ejpam-3281	172	48	form	form	NOUN
ejpam-3281	172	49	(	(	PUNCT
ejpam-3281	172	50	exp(x1	exp(x1	ADJ
ejpam-3281	172	51	)	)	PUNCT
ejpam-3281	172	52	,	,	PUNCT
ejpam-3281	172	53	exp(x2	exp(x2	NOUN
ejpam-3281	172	54	)	)	PUNCT
ejpam-3281	172	55	)	)	PUNCT
ejpam-3281	172	56	to	to	ADP
ejpam-3281	172	57	the	the	DET
ejpam-3281	172	58	polynomials	polynomial	NOUN
ejpam-3281	172	59	with	with	ADP
ejpam-3281	172	60	rational	rational	ADJ
ejpam-3281	172	61	integer	integer	NOUN
ejpam-3281	172	62	coefficients	coefficient	NOUN
ejpam-3281	172	63	and	and	CCONJ
ejpam-3281	172	64	two	two	NUM
ejpam-3281	172	65	variables	variable	NOUN
ejpam-3281	172	66	.	.	PUNCT
ejpam-3281	173	1	theorem	theorem	VERB
ejpam-3281	173	2	3	3	NUM
ejpam-3281	173	3	.	.	PUNCT
ejpam-3281	174	1	the	the	DET
ejpam-3281	174	2	polynomial	polynomial	ADJ
ejpam-3281	174	3	p	p	PROPN
ejpam-3281	175	1	[	[	X
ejpam-3281	175	2	x1	x1	PROPN
ejpam-3281	175	3	,	,	PUNCT
ejpam-3281	175	4	x2	x2	PROPN
ejpam-3281	175	5	]	]	X
ejpam-3281	175	6	=	=	PUNCT
ejpam-3281	175	7	ai0	ai0	PROPN
ejpam-3281	175	8	+	+	CCONJ
ejpam-3281	175	9	ai1x	ai1x	PROPN
ejpam-3281	175	10	i1,1	i1,1	NOUN
ejpam-3281	175	11	1	1	NUM
ejpam-3281	175	12	x	x	SYM
ejpam-3281	175	13	i1,2	i1,2	ADJ
ejpam-3281	175	14	2	2	NUM
ejpam-3281	175	15	+	+	CCONJ
ejpam-3281	175	16	...	...	PUNCT
ejpam-3281	176	1	+	+	CCONJ
ejpam-3281	176	2	aimx	aimx	PROPN
ejpam-3281	176	3	im,1	im,1	PROPN
ejpam-3281	176	4	1	1	NUM
ejpam-3281	176	5	x	x	X
ejpam-3281	176	6	im,2	im,2	PROPN
ejpam-3281	176	7	2	2	NUM
ejpam-3281	176	8	∈	∈	NOUN
ejpam-3281	176	9	z[x1	z[x1	X
ejpam-3281	176	10	,	,	PUNCT
ejpam-3281	176	11	x2	x2	PROPN
ejpam-3281	176	12	]	]	X
ejpam-3281	176	13	,	,	PUNCT
ejpam-3281	176	14	in	in	ADP
ejpam-3281	176	15	which	which	PRON
ejpam-3281	176	16	at	at	ADP
ejpam-3281	176	17	least	least	ADJ
ejpam-3281	176	18	one	one	NUM
ejpam-3281	176	19	of	of	ADP
ejpam-3281	176	20	the	the	DET
ejpam-3281	176	21	elements	element	NOUN
ejpam-3281	176	22	ai1i1,1	ai1i1,1	PUNCT
ejpam-3281	176	23	+	+	CCONJ
ejpam-3281	176	24	....	....	PUNCT
ejpam-3281	176	25	+	+	X
ejpam-3281	176	26	aimim,1	aimim,1	ADJ
ejpam-3281	176	27	,	,	PUNCT
ejpam-3281	176	28	ai1i1,2	ai1i1,2	PROPN
ejpam-3281	176	29	+	+	X
ejpam-3281	176	30	....	....	PUNCT
ejpam-3281	176	31	+	+	X
ejpam-3281	176	32	aimim,2	aimim,2	X
ejpam-3281	176	33	and	and	CCONJ
ejpam-3281	176	34	all	all	DET
ejpam-3281	176	35	the	the	DET
ejpam-3281	176	36	degrees	degree	NOUN
ejpam-3281	176	37	of	of	ADP
ejpam-3281	176	38	x1	x1	PROPN
ejpam-3281	176	39	and	and	CCONJ
ejpam-3281	176	40	x2	x2	PROPN
ejpam-3281	176	41	are	be	AUX
ejpam-3281	176	42	relatively	relatively	ADV
ejpam-3281	176	43	prime	prime	ADJ
ejpam-3281	176	44	to	to	ADP
ejpam-3281	176	45	p	p	NOUN
ejpam-3281	176	46	has	have	AUX
ejpam-3281	176	47	a	a	DET
ejpam-3281	176	48	root	root	NOUN
ejpam-3281	176	49	of	of	ADP
ejpam-3281	176	50	the	the	DET
ejpam-3281	176	51	form	form	NOUN
ejpam-3281	176	52	(	(	PUNCT
ejpam-3281	176	53	exp(x1	exp(x1	ADJ
ejpam-3281	176	54	)	)	PUNCT
ejpam-3281	176	55	,	,	PUNCT
ejpam-3281	176	56	exp(x2	exp(x2	NOUN
ejpam-3281	176	57	)	)	PUNCT
ejpam-3281	176	58	)	)	PUNCT
ejpam-3281	177	1	if	if	SCONJ
ejpam-3281	177	2	and	and	CCONJ
ejpam-3281	177	3	only	only	ADV
ejpam-3281	177	4	if	if	SCONJ
ejpam-3281	177	5	|ai0	|ai0	PROPN
ejpam-3281	177	6	+	+	CCONJ
ejpam-3281	177	7	....	....	PUNCT
ejpam-3281	178	1	+	+	CCONJ
ejpam-3281	178	2	aim	aim	VERB
ejpam-3281	178	3	|	|	ADV
ejpam-3281	178	4	≤	≤	PROPN
ejpam-3281	178	5	p−1	p−1	PROPN
ejpam-3281	178	6	.	.	PUNCT
ejpam-3281	179	1	proof	proof	NOUN
ejpam-3281	179	2	.	.	PUNCT
ejpam-3281	180	1	(	(	PUNCT
ejpam-3281	180	2	proof	proof	NOUN
ejpam-3281	180	3	of	of	ADP
ejpam-3281	180	4	the	the	DET
ejpam-3281	180	5	necessary	necessary	ADJ
ejpam-3281	180	6	condition	condition	NOUN
ejpam-3281	180	7	)	)	PUNCT
ejpam-3281	180	8	.	.	PUNCT
ejpam-3281	181	1	if	if	SCONJ
ejpam-3281	181	2	p	p	NOUN
ejpam-3281	181	3	has	have	VERB
ejpam-3281	181	4	a	a	DET
ejpam-3281	181	5	root	root	NOUN
ejpam-3281	181	6	of	of	ADP
ejpam-3281	181	7	the	the	DET
ejpam-3281	181	8	form	form	NOUN
ejpam-3281	181	9	(	(	PUNCT
ejpam-3281	181	10	exp(x1	exp(x1	ADJ
ejpam-3281	181	11	)	)	PUNCT
ejpam-3281	181	12	,	,	PUNCT
ejpam-3281	181	13	exp(x2	exp(x2	NOUN
ejpam-3281	181	14	)	)	PUNCT
ejpam-3281	181	15	)	)	PUNCT
ejpam-3281	181	16	for	for	ADP
ejpam-3281	181	17	some	some	DET
ejpam-3281	181	18	elements	element	NOUN
ejpam-3281	181	19	x1	x1	NUM
ejpam-3281	181	20	,	,	PUNCT
ejpam-3281	181	21	x2	x2	PROPN
ejpam-3281	181	22	∈	∈	PROPN
ejpam-3281	181	23	e	e	NOUN
ejpam-3281	181	24	,	,	PUNCT
ejpam-3281	181	25	then	then	ADV
ejpam-3281	181	26	p	p	X
ejpam-3281	181	27	(	(	PUNCT
ejpam-3281	181	28	exp(x1	exp(x1	ADJ
ejpam-3281	181	29	)	)	PUNCT
ejpam-3281	181	30	,	,	PUNCT
ejpam-3281	181	31	exp(x2	exp(x2	NOUN
ejpam-3281	181	32	)	)	PUNCT
ejpam-3281	181	33	)	)	PUNCT
ejpam-3281	181	34	=	=	PUNCT
ejpam-3281	182	1	ai0	ai0	PROPN
ejpam-3281	182	2	+	+	NUM
ejpam-3281	182	3	ai1(exp(x1	ai1(exp(x1	NOUN
ejpam-3281	182	4	)	)	PUNCT
ejpam-3281	182	5	)	)	PUNCT
ejpam-3281	182	6	i1,1(exp(x2	i1,1(exp(x2	NOUN
ejpam-3281	182	7	)	)	PUNCT
ejpam-3281	182	8	)	)	PUNCT
ejpam-3281	183	1	i1,2	i1,2	PROPN
ejpam-3281	183	2	+	+	CCONJ
ejpam-3281	183	3	...	...	PUNCT
ejpam-3281	184	1	+	+	CCONJ
ejpam-3281	184	2	aim(exp(x1	aim(exp(x1	ADJ
ejpam-3281	184	3	)	)	PUNCT
ejpam-3281	184	4	)	)	PUNCT
ejpam-3281	184	5	im,1(exp(x2	im,1(exp(x2	PROPN
ejpam-3281	184	6	)	)	PUNCT
ejpam-3281	184	7	)	)	PUNCT
ejpam-3281	185	1	im,2	im,2	PROPN
ejpam-3281	185	2	=	=	SYM
ejpam-3281	185	3	0	0	X
ejpam-3281	185	4	.	.	PUNCT
ejpam-3281	186	1	let	let	VERB
ejpam-3281	186	2	zj	zj	NOUN
ejpam-3281	186	3	:	:	PUNCT
ejpam-3281	186	4	=	=	SYM
ejpam-3281	186	5	ij,1x1	ij,1x1	PROPN
ejpam-3281	186	6	+	+	CCONJ
ejpam-3281	186	7	ij,2x2	ij,2x2	NOUN
ejpam-3281	186	8	,	,	PUNCT
ejpam-3281	186	9	∀j	∀j	NOUN
ejpam-3281	186	10	=	=	SYM
ejpam-3281	186	11	1	1	NUM
ejpam-3281	186	12	,	,	PUNCT
ejpam-3281	186	13	2	2	NUM
ejpam-3281	186	14	,	,	PUNCT
ejpam-3281	186	15	..	..	PUNCT
ejpam-3281	186	16	,	,	PUNCT
ejpam-3281	186	17	m.	m.	NOUN
ejpam-3281	186	18	then	then	ADV
ejpam-3281	186	19	zj	zj	PROPN
ejpam-3281	186	20	∈	∈	PROPN
ejpam-3281	186	21	e.	e.	PROPN
ejpam-3281	186	22	using	use	VERB
ejpam-3281	186	23	the	the	DET
ejpam-3281	186	24	universal	universal	ADJ
ejpam-3281	186	25	property	property	NOUN
ejpam-3281	186	26	of	of	ADP
ejpam-3281	186	27	the	the	DET
ejpam-3281	186	28	exponential	exponential	ADJ
ejpam-3281	186	29	function	function	NOUN
ejpam-3281	186	30	,	,	PUNCT
ejpam-3281	186	31	we	we	PRON
ejpam-3281	186	32	obtain	obtain	VERB
ejpam-3281	186	33	ai0	ai0	PROPN
ejpam-3281	186	34	+	+	CCONJ
ejpam-3281	186	35	ai1	ai1	VERB
ejpam-3281	186	36	exp(z1	exp(z1	ADJ
ejpam-3281	186	37	)	)	PUNCT
ejpam-3281	187	1	+	+	CCONJ
ejpam-3281	187	2	...	...	PUNCT
ejpam-3281	188	1	+	+	CCONJ
ejpam-3281	188	2	aim	aim	VERB
ejpam-3281	188	3	exp(zm	exp(zm	X
ejpam-3281	188	4	)	)	PUNCT
ejpam-3281	188	5	=	=	SYM
ejpam-3281	188	6	0	0	X
ejpam-3281	188	7	.	.	PUNCT
ejpam-3281	188	8	a.	a.	PROPN
ejpam-3281	188	9	dalloul	dalloul	PROPN
ejpam-3281	188	10	/	/	SYM
ejpam-3281	188	11	eur	eur	PROPN
ejpam-3281	188	12	.	.	PUNCT
ejpam-3281	189	1	j.	j.	PROPN
ejpam-3281	189	2	pure	pure	PROPN
ejpam-3281	189	3	appl	appl	PROPN
ejpam-3281	189	4	.	.	PROPN
ejpam-3281	189	5	math	math	PROPN
ejpam-3281	189	6	,	,	PUNCT
ejpam-3281	189	7	11	11	NUM
ejpam-3281	189	8	(	(	PUNCT
ejpam-3281	189	9	4	4	NUM
ejpam-3281	189	10	)	)	PUNCT
ejpam-3281	189	11	(	(	PUNCT
ejpam-3281	189	12	2018	2018	NUM
ejpam-3281	189	13	)	)	PUNCT
ejpam-3281	189	14	,	,	PUNCT
ejpam-3281	189	15	1046	1046	NUM
ejpam-3281	189	16	-	-	SYM
ejpam-3281	189	17	1057	1057	NUM
ejpam-3281	189	18	1052	1052	NUM
ejpam-3281	189	19	thus	thus	ADV
ejpam-3281	189	20	,	,	PUNCT
ejpam-3281	189	21	|ai0	|ai0	PROPN
ejpam-3281	189	22	+	+	CCONJ
ejpam-3281	189	23	ai1	ai1	VERB
ejpam-3281	189	24	exp(z1	exp(z1	ADJ
ejpam-3281	189	25	)	)	PUNCT
ejpam-3281	190	1	+	+	CCONJ
ejpam-3281	190	2	...	...	PUNCT
ejpam-3281	191	1	+	+	CCONJ
ejpam-3281	191	2	aim	aim	VERB
ejpam-3281	191	3	exp(zm)|	exp(zm)|	NOUN
ejpam-3281	191	4	=	=	SYM
ejpam-3281	191	5	0	0	PUNCT
ejpam-3281	191	6	<	<	X
ejpam-3281	191	7	1	1	NUM
ejpam-3281	191	8	.	.	PUNCT
ejpam-3281	191	9	by	by	ADP
ejpam-3281	191	10	a	a	DET
ejpam-3281	191	11	similar	similar	ADJ
ejpam-3281	191	12	argument	argument	NOUN
ejpam-3281	191	13	to	to	ADP
ejpam-3281	191	14	the	the	DET
ejpam-3281	191	15	necessary	necessary	ADJ
ejpam-3281	191	16	proof	proof	NOUN
ejpam-3281	191	17	of	of	ADP
ejpam-3281	191	18	theorem	theorem	NOUN
ejpam-3281	191	19	2	2	NUM
ejpam-3281	191	20	,	,	PUNCT
ejpam-3281	191	21	we	we	PRON
ejpam-3281	191	22	find	find	VERB
ejpam-3281	191	23	that	that	SCONJ
ejpam-3281	191	24	|ai0	|ai0	PROPN
ejpam-3281	192	1	+	+	CCONJ
ejpam-3281	192	2	....	....	PUNCT
ejpam-3281	192	3	+	+	CCONJ
ejpam-3281	192	4	aim	aim	VERB
ejpam-3281	192	5	|	|	ADV
ejpam-3281	192	6	≤	≤	PROPN
ejpam-3281	192	7	p−1	p−1	PROPN
ejpam-3281	192	8	.	.	PUNCT
ejpam-3281	193	1	proof	proof	NOUN
ejpam-3281	193	2	of	of	ADP
ejpam-3281	193	3	the	the	DET
ejpam-3281	193	4	sufficient	sufficient	ADJ
ejpam-3281	193	5	condition	condition	NOUN
ejpam-3281	193	6	.	.	PUNCT
ejpam-3281	194	1	consider	consider	VERB
ejpam-3281	194	2	the	the	DET
ejpam-3281	194	3	polynomial	polynomial	ADJ
ejpam-3281	194	4	p	p	PROPN
ejpam-3281	195	1	[	[	X
ejpam-3281	195	2	x1	x1	PROPN
ejpam-3281	195	3	,	,	PUNCT
ejpam-3281	195	4	x2	x2	PROPN
ejpam-3281	195	5	]	]	X
ejpam-3281	195	6	=	=	PUNCT
ejpam-3281	195	7	ai0	ai0	PROPN
ejpam-3281	195	8	+	+	CCONJ
ejpam-3281	195	9	ai1x	ai1x	PROPN
ejpam-3281	195	10	i1,1	i1,1	NOUN
ejpam-3281	195	11	1	1	NUM
ejpam-3281	195	12	x	x	SYM
ejpam-3281	195	13	i1,2	i1,2	ADJ
ejpam-3281	195	14	2	2	NUM
ejpam-3281	195	15	+	+	CCONJ
ejpam-3281	195	16	...	...	PUNCT
ejpam-3281	196	1	+	+	CCONJ
ejpam-3281	196	2	aimx	aimx	PROPN
ejpam-3281	196	3	im,1	im,1	PROPN
ejpam-3281	196	4	1	1	NUM
ejpam-3281	196	5	x	x	X
ejpam-3281	196	6	im,2	im,2	PROPN
ejpam-3281	196	7	2	2	NUM
ejpam-3281	196	8	∈	∈	NOUN
ejpam-3281	196	9	z[x1	z[x1	X
ejpam-3281	196	10	,	,	PUNCT
ejpam-3281	196	11	x2	x2	PROPN
ejpam-3281	196	12	]	]	X
ejpam-3281	196	13	,	,	PUNCT
ejpam-3281	196	14	in	in	ADP
ejpam-3281	196	15	which	which	PRON
ejpam-3281	196	16	at	at	ADP
ejpam-3281	196	17	least	least	ADJ
ejpam-3281	196	18	one	one	NUM
ejpam-3281	196	19	of	of	ADP
ejpam-3281	196	20	the	the	DET
ejpam-3281	196	21	elements	element	NOUN
ejpam-3281	196	22	ai1i1,1	ai1i1,1	PUNCT
ejpam-3281	196	23	+	+	CCONJ
ejpam-3281	196	24	....	....	PUNCT
ejpam-3281	196	25	+	+	X
ejpam-3281	196	26	aimim,1	aimim,1	ADJ
ejpam-3281	196	27	,	,	PUNCT
ejpam-3281	196	28	ai1i1,2	ai1i1,2	PROPN
ejpam-3281	196	29	+	+	X
ejpam-3281	196	30	....	....	PUNCT
ejpam-3281	196	31	+	+	X
ejpam-3281	196	32	aimim,2	aimim,2	X
ejpam-3281	196	33	and	and	CCONJ
ejpam-3281	196	34	all	all	DET
ejpam-3281	196	35	the	the	DET
ejpam-3281	196	36	degrees	degree	NOUN
ejpam-3281	196	37	of	of	ADP
ejpam-3281	196	38	x1	x1	PROPN
ejpam-3281	196	39	and	and	CCONJ
ejpam-3281	196	40	x2	x2	PROPN
ejpam-3281	196	41	are	be	AUX
ejpam-3281	196	42	relatively	relatively	ADV
ejpam-3281	196	43	prime	prime	ADJ
ejpam-3281	196	44	to	to	ADP
ejpam-3281	196	45	p.	p.	NOUN
ejpam-3281	196	46	let	let	VERB
ejpam-3281	196	47	f	f	PROPN
ejpam-3281	196	48	∈	∈	PROPN
ejpam-3281	196	49	cp[[x1	cp[[x1	PROPN
ejpam-3281	196	50	,	,	PUNCT
ejpam-3281	196	51	x2	x2	PROPN
ejpam-3281	196	52	]	]	X
ejpam-3281	196	53	]	]	PUNCT
ejpam-3281	196	54	be	be	VERB
ejpam-3281	196	55	an	an	DET
ejpam-3281	196	56	element	element	NOUN
ejpam-3281	196	57	defined	define	VERB
ejpam-3281	196	58	by	by	ADP
ejpam-3281	196	59	the	the	DET
ejpam-3281	196	60	relation	relation	NOUN
ejpam-3281	196	61	f(x1	f(x1	NOUN
ejpam-3281	196	62	,	,	PUNCT
ejpam-3281	196	63	x2	x2	PROPN
ejpam-3281	196	64	)	)	PUNCT
ejpam-3281	196	65	=	=	PUNCT
ejpam-3281	197	1	p	p	X
ejpam-3281	198	1	[	[	X
ejpam-3281	198	2	exp(x1	exp(x1	ADJ
ejpam-3281	198	3	)	)	PUNCT
ejpam-3281	198	4	,	,	PUNCT
ejpam-3281	198	5	exp(x2	exp(x2	PROPN
ejpam-3281	198	6	)	)	PUNCT
ejpam-3281	198	7	]	]	PUNCT
ejpam-3281	198	8	.	.	PUNCT
ejpam-3281	199	1	then	then	ADV
ejpam-3281	199	2	,	,	PUNCT
ejpam-3281	199	3	p	p	X
ejpam-3281	200	1	[	[	X
ejpam-3281	200	2	x1	x1	PROPN
ejpam-3281	200	3	,	,	PUNCT
ejpam-3281	200	4	x2	x2	PROPN
ejpam-3281	200	5	]	]	PUNCT
ejpam-3281	200	6	has	have	VERB
ejpam-3281	200	7	a	a	DET
ejpam-3281	200	8	root	root	NOUN
ejpam-3281	200	9	of	of	ADP
ejpam-3281	200	10	the	the	DET
ejpam-3281	200	11	form	form	NOUN
ejpam-3281	200	12	(	(	PUNCT
ejpam-3281	200	13	exp(x1	exp(x1	ADJ
ejpam-3281	200	14	)	)	PUNCT
ejpam-3281	200	15	,	,	PUNCT
ejpam-3281	200	16	exp(x2	exp(x2	NOUN
ejpam-3281	200	17	)	)	PUNCT
ejpam-3281	200	18	)	)	PUNCT
ejpam-3281	201	1	if	if	SCONJ
ejpam-3281	201	2	and	and	CCONJ
ejpam-3281	201	3	only	only	ADV
ejpam-3281	201	4	if	if	SCONJ
ejpam-3281	201	5	(	(	PUNCT
ejpam-3281	201	6	x1	x1	ADJ
ejpam-3281	201	7	,	,	PUNCT
ejpam-3281	201	8	x2	x2	PROPN
ejpam-3281	201	9	)	)	PUNCT
ejpam-3281	201	10	is	be	AUX
ejpam-3281	201	11	a	a	DET
ejpam-3281	201	12	root	root	NOUN
ejpam-3281	201	13	of	of	ADP
ejpam-3281	201	14	f.	f.	PROPN
ejpam-3281	201	15	it	it	PRON
ejpam-3281	201	16	is	be	AUX
ejpam-3281	201	17	clear	clear	ADJ
ejpam-3281	201	18	that	that	SCONJ
ejpam-3281	201	19	f	f	PROPN
ejpam-3281	201	20	is	be	AUX
ejpam-3281	201	21	convergent	convergent	ADJ
ejpam-3281	201	22	on	on	ADP
ejpam-3281	201	23	the	the	DET
ejpam-3281	201	24	ball	ball	NOUN
ejpam-3281	201	25	b(0	b(0	PROPN
ejpam-3281	201	26	,	,	PUNCT
ejpam-3281	201	27	ρ	ρ	NOUN
ejpam-3281	201	28	)	)	PUNCT
ejpam-3281	201	29	:	:	PUNCT
ejpam-3281	202	1	=	=	SYM
ejpam-3281	202	2	{	{	PUNCT
ejpam-3281	202	3	(	(	PUNCT
ejpam-3281	202	4	x1	x1	PROPN
ejpam-3281	202	5	,	,	PUNCT
ejpam-3281	202	6	x2	x2	PROPN
ejpam-3281	202	7	)	)	PUNCT
ejpam-3281	202	8	:	:	PUNCT
ejpam-3281	202	9	max	max	PROPN
ejpam-3281	202	10	|xi|	|xi|	PROPN
ejpam-3281	202	11	≤	≤	PROPN
ejpam-3281	202	12	ρ	ρ	PROPN
ejpam-3281	202	13	,	,	PUNCT
ejpam-3281	202	14	i	i	NOUN
ejpam-3281	202	15	=	=	NOUN
ejpam-3281	202	16	1	1	NUM
ejpam-3281	202	17	,	,	PUNCT
ejpam-3281	202	18	2	2	NUM
ejpam-3281	202	19	}	}	PUNCT
ejpam-3281	202	20	for	for	ADP
ejpam-3281	202	21	every	every	DET
ejpam-3281	202	22	ρ	ρ	NOUN
ejpam-3281	202	23	<	<	X
ejpam-3281	202	24	p	p	X
ejpam-3281	202	25	−1	−1	NOUN
ejpam-3281	202	26	p−1	p−1	PROPN
ejpam-3281	202	27	(	(	PUNCT
ejpam-3281	202	28	since	since	SCONJ
ejpam-3281	202	29	all	all	DET
ejpam-3281	202	30	the	the	DET
ejpam-3281	202	31	degrees	degree	NOUN
ejpam-3281	202	32	of	of	ADP
ejpam-3281	202	33	the	the	DET
ejpam-3281	202	34	variables	variable	NOUN
ejpam-3281	202	35	x1	x1	PROPN
ejpam-3281	202	36	and	and	CCONJ
ejpam-3281	202	37	x2	x2	PROPN
ejpam-3281	202	38	are	be	AUX
ejpam-3281	202	39	relatively	relatively	ADV
ejpam-3281	202	40	prime	prime	ADJ
ejpam-3281	202	41	to	to	ADP
ejpam-3281	202	42	p	p	NOUN
ejpam-3281	202	43	)	)	PUNCT
ejpam-3281	202	44	.	.	PUNCT
ejpam-3281	203	1	let	let	VERB
ejpam-3281	203	2	α	α	PRON
ejpam-3281	203	3	be	be	AUX
ejpam-3281	203	4	a	a	DET
ejpam-3281	203	5	rational	rational	ADJ
ejpam-3281	203	6	number	number	NOUN
ejpam-3281	203	7	satisfying	satisfy	VERB
ejpam-3281	203	8	the	the	DET
ejpam-3281	203	9	relation	relation	NOUN
ejpam-3281	203	10	−1	−1	NOUN
ejpam-3281	203	11	<	<	X
ejpam-3281	203	12	α	α	X
ejpam-3281	203	13	<	<	X
ejpam-3281	203	14	−1	−1	NOUN
ejpam-3281	203	15	p−1	p−1	PROPN
ejpam-3281	203	16	.	.	PUNCT
ejpam-3281	204	1	then	then	ADV
ejpam-3281	204	2	,	,	PUNCT
ejpam-3281	204	3	f(x1	f(x1	ADJ
ejpam-3281	204	4	,	,	PUNCT
ejpam-3281	204	5	x2	x2	PROPN
ejpam-3281	204	6	)	)	PUNCT
ejpam-3281	204	7	is	be	AUX
ejpam-3281	204	8	convergent	convergent	ADJ
ejpam-3281	204	9	on	on	ADP
ejpam-3281	204	10	the	the	DET
ejpam-3281	204	11	ball	ball	NOUN
ejpam-3281	204	12	b(0	b(0	NOUN
ejpam-3281	204	13	,	,	PUNCT
ejpam-3281	204	14	pα	pα	NOUN
ejpam-3281	204	15	)	)	PUNCT
ejpam-3281	204	16	.	.	PUNCT
ejpam-3281	205	1	we	we	PRON
ejpam-3281	205	2	define	define	VERB
ejpam-3281	205	3	new	new	ADJ
ejpam-3281	205	4	variables	variable	NOUN
ejpam-3281	205	5	:	:	PUNCT
ejpam-3281	205	6	z1	z1	NOUN
ejpam-3281	205	7	:	:	PUNCT
ejpam-3281	205	8	=	=	SYM
ejpam-3281	205	9	pαx1	pαx1	PROPN
ejpam-3281	205	10	,	,	PUNCT
ejpam-3281	205	11	z2	z2	PROPN
ejpam-3281	205	12	:	:	PUNCT
ejpam-3281	205	13	=	=	SYM
ejpam-3281	205	14	pαx2	pαx2	PROPN
ejpam-3281	205	15	.	.	PUNCT
ejpam-3281	206	1	also	also	ADV
ejpam-3281	206	2	,	,	PUNCT
ejpam-3281	206	3	we	we	PRON
ejpam-3281	206	4	define	define	VERB
ejpam-3281	206	5	a	a	DET
ejpam-3281	206	6	new	new	ADJ
ejpam-3281	206	7	power	power	NOUN
ejpam-3281	206	8	series	series	NOUN
ejpam-3281	206	9	g(z1	g(z1	NOUN
ejpam-3281	206	10	,	,	PUNCT
ejpam-3281	206	11	z2	z2	PROPN
ejpam-3281	206	12	)	)	PUNCT
ejpam-3281	206	13	by	by	ADP
ejpam-3281	206	14	the	the	DET
ejpam-3281	206	15	relation	relation	NOUN
ejpam-3281	206	16	g(z1	g(z1	NOUN
ejpam-3281	206	17	,	,	PUNCT
ejpam-3281	206	18	z2	z2	PROPN
ejpam-3281	206	19	)	)	PUNCT
ejpam-3281	206	20	:	:	PUNCT
ejpam-3281	207	1	=	=	PUNCT
ejpam-3281	207	2	f(p−αz1	f(p−αz1	PROPN
ejpam-3281	207	3	,	,	PUNCT
ejpam-3281	207	4	p	p	PROPN
ejpam-3281	207	5	−αz2	−αz2	PROPN
ejpam-3281	207	6	)	)	PUNCT
ejpam-3281	207	7	.	.	PUNCT
ejpam-3281	208	1	it	it	PRON
ejpam-3281	208	2	’s	’	VERB
ejpam-3281	208	3	clear	clear	ADJ
ejpam-3281	208	4	that	that	SCONJ
ejpam-3281	208	5	g(z1	g(z1	NOUN
ejpam-3281	208	6	,	,	PUNCT
ejpam-3281	208	7	z2	z2	PROPN
ejpam-3281	208	8	)	)	PUNCT
ejpam-3281	208	9	is	be	AUX
ejpam-3281	208	10	convergent	convergent	ADJ
ejpam-3281	208	11	on	on	ADP
ejpam-3281	208	12	the	the	DET
ejpam-3281	208	13	unit	unit	NOUN
ejpam-3281	208	14	ball	ball	NOUN
ejpam-3281	208	15	b(0	b(0	PROPN
ejpam-3281	208	16	,	,	PUNCT
ejpam-3281	208	17	1	1	NUM
ejpam-3281	208	18	)	)	PUNCT
ejpam-3281	208	19	.	.	PUNCT
ejpam-3281	209	1	furthermore	furthermore	ADV
ejpam-3281	209	2	,	,	PUNCT
ejpam-3281	209	3	f(x1	f(x1	ADJ
ejpam-3281	209	4	,	,	PUNCT
ejpam-3281	209	5	x2	x2	PROPN
ejpam-3281	209	6	)	)	PUNCT
ejpam-3281	209	7	has	have	VERB
ejpam-3281	209	8	a	a	DET
ejpam-3281	209	9	root	root	NOUN
ejpam-3281	209	10	in	in	ADP
ejpam-3281	209	11	the	the	DET
ejpam-3281	209	12	ball	ball	NOUN
ejpam-3281	209	13	b(0	b(0	NOUN
ejpam-3281	209	14	,	,	PUNCT
ejpam-3281	209	15	pα	pα	NOUN
ejpam-3281	209	16	)	)	PUNCT
ejpam-3281	209	17	if	if	SCONJ
ejpam-3281	210	1	and	and	CCONJ
ejpam-3281	210	2	only	only	ADV
ejpam-3281	210	3	if	if	SCONJ
ejpam-3281	210	4	g(z1	g(z1	NOUN
ejpam-3281	210	5	,	,	PUNCT
ejpam-3281	210	6	z2	z2	PROPN
ejpam-3281	210	7	)	)	PUNCT
ejpam-3281	210	8	has	have	VERB
ejpam-3281	210	9	a	a	DET
ejpam-3281	210	10	root	root	NOUN
ejpam-3281	210	11	in	in	ADP
ejpam-3281	210	12	the	the	DET
ejpam-3281	210	13	unit	unit	NOUN
ejpam-3281	210	14	ball	ball	NOUN
ejpam-3281	210	15	.	.	PUNCT
ejpam-3281	211	1	since	since	SCONJ
ejpam-3281	211	2	g(z1	g(z1	NOUN
ejpam-3281	211	3	,	,	PUNCT
ejpam-3281	211	4	z2	z2	PROPN
ejpam-3281	211	5	)	)	PUNCT
ejpam-3281	211	6	is	be	AUX
ejpam-3281	211	7	convergent	convergent	ADJ
ejpam-3281	211	8	on	on	ADP
ejpam-3281	211	9	the	the	DET
ejpam-3281	211	10	unit	unit	NOUN
ejpam-3281	211	11	ball	ball	NOUN
ejpam-3281	211	12	,	,	PUNCT
ejpam-3281	211	13	it	it	PRON
ejpam-3281	211	14	follows	follow	VERB
ejpam-3281	211	15	that	that	PRON
ejpam-3281	211	16	g(z1	g(z1	NOUN
ejpam-3281	211	17	,	,	PUNCT
ejpam-3281	211	18	z2	z2	PROPN
ejpam-3281	211	19	)	)	PUNCT
ejpam-3281	211	20	∈	∈	PROPN
ejpam-3281	211	21	cp〈z1	cp〈z1	NOUN
ejpam-3281	211	22	,	,	PUNCT
ejpam-3281	211	23	z2	z2	PROPN
ejpam-3281	211	24	〉	〉	PROPN
ejpam-3281	211	25	.	.	PUNCT
ejpam-3281	212	1	suppose	suppose	VERB
ejpam-3281	212	2	that	that	SCONJ
ejpam-3281	212	3	g(z1	g(z1	NOUN
ejpam-3281	212	4	,	,	PUNCT
ejpam-3281	212	5	z2	z2	PROPN
ejpam-3281	212	6	)	)	PUNCT
ejpam-3281	212	7	takes	take	VERB
ejpam-3281	212	8	the	the	DET
ejpam-3281	212	9	form	form	NOUN
ejpam-3281	212	10	g	g	NOUN
ejpam-3281	212	11	=	=	SYM
ejpam-3281	212	12	(	(	PUNCT
ejpam-3281	212	13	g0	g0	PROPN
ejpam-3281	212	14	,	,	PUNCT
ejpam-3281	212	15	g1	g1	NOUN
ejpam-3281	212	16	,	,	PUNCT
ejpam-3281	212	17	...	...	PUNCT
ejpam-3281	212	18	,	,	PUNCT
ejpam-3281	212	19	gq	gq	PROPN
ejpam-3281	212	20	,	,	PUNCT
ejpam-3281	212	21	...	...	PUNCT
ejpam-3281	212	22	)	)	PUNCT
ejpam-3281	212	23	,	,	PUNCT
ejpam-3281	212	24	where	where	SCONJ
ejpam-3281	212	25	gi	gi	PRON
ejpam-3281	212	26	is	be	AUX
ejpam-3281	212	27	homogeneous	homogeneous	ADJ
ejpam-3281	212	28	polynomial	polynomial	NOUN
ejpam-3281	212	29	of	of	ADP
ejpam-3281	212	30	degree	degree	NOUN
ejpam-3281	212	31	i.	i.	NOUN
ejpam-3281	212	32	then	then	ADV
ejpam-3281	212	33	,	,	PUNCT
ejpam-3281	212	34	in	in	ADP
ejpam-3281	212	35	our	our	PRON
ejpam-3281	212	36	case	case	NOUN
ejpam-3281	212	37	,	,	PUNCT
ejpam-3281	212	38	we	we	PRON
ejpam-3281	212	39	have	have	VERB
ejpam-3281	212	40	g0	g0	NOUN
ejpam-3281	212	41	=	=	SYM
ejpam-3281	212	42	g(0	g(0	PROPN
ejpam-3281	212	43	,	,	PUNCT
ejpam-3281	212	44	0	0	NUM
ejpam-3281	212	45	)	)	PUNCT
ejpam-3281	212	46	=	=	VERB
ejpam-3281	213	1	ai0	ai0	PROPN
ejpam-3281	213	2	+	+	CCONJ
ejpam-3281	213	3	....	....	PUNCT
ejpam-3281	213	4	+	+	NUM
ejpam-3281	213	5	aim	aim	NOUN
ejpam-3281	213	6	,	,	PUNCT
ejpam-3281	213	7	g1	g1	PROPN
ejpam-3281	213	8	=	=	SYM
ejpam-3281	213	9	(	(	PUNCT
ejpam-3281	213	10	ai1i1,1	ai1i1,1	CCONJ
ejpam-3281	213	11	+	+	CCONJ
ejpam-3281	213	12	....	....	PUNCT
ejpam-3281	214	1	+	+	ADJ
ejpam-3281	214	2	aimim,1)p	aimim,1)p	ADJ
ejpam-3281	214	3	−αz1	−αz1	X
ejpam-3281	214	4	+	+	CCONJ
ejpam-3281	214	5	(	(	PUNCT
ejpam-3281	214	6	ai1i1,2	ai1i1,2	PROPN
ejpam-3281	214	7	+	+	NUM
ejpam-3281	214	8	....	....	PUNCT
ejpam-3281	214	9	+	+	NUM
ejpam-3281	214	10	aimim,2)p	aimim,2)p	PROPN
ejpam-3281	214	11	−αz2	−αz2	PROPN
ejpam-3281	214	12	.	.	PUNCT
ejpam-3281	214	13	suppose	suppose	VERB
ejpam-3281	214	14	that	that	SCONJ
ejpam-3281	214	15	α	α	PRON
ejpam-3281	214	16	takes	take	VERB
ejpam-3281	214	17	the	the	DET
ejpam-3281	214	18	form	form	NOUN
ejpam-3281	214	19	α	α	NOUN
ejpam-3281	214	20	=	=	SYM
ejpam-3281	214	21	−m	−m	NOUN
ejpam-3281	214	22	n	n	NOUN
ejpam-3281	214	23	.	.	PUNCT
ejpam-3281	215	1	then	then	ADV
ejpam-3281	215	2	,	,	PUNCT
ejpam-3281	215	3	we	we	PRON
ejpam-3281	215	4	have	have	VERB
ejpam-3281	215	5	|p−α|n	|p−α|n	NOUN
ejpam-3281	215	6	=	=	SYM
ejpam-3281	215	7	|pm|	|pm|	PROPN
ejpam-3281	215	8	=	=	PUNCT
ejpam-3281	215	9	p−m	p−m	X
ejpam-3281	215	10	⇒	⇒	NOUN
ejpam-3281	215	11	|p−α|	|p−α|	PUNCT
ejpam-3281	215	12	=	=	PUNCT
ejpam-3281	216	1	p	p	X
ejpam-3281	216	2	−m	−m	NOUN
ejpam-3281	216	3	n	n	PROPN
ejpam-3281	216	4	=	=	SYM
ejpam-3281	216	5	pα	pα	NOUN
ejpam-3281	216	6	.	.	PUNCT
ejpam-3281	217	1	we	we	PRON
ejpam-3281	217	2	assume	assume	VERB
ejpam-3281	217	3	that	that	SCONJ
ejpam-3281	217	4	(	(	PUNCT
ejpam-3281	217	5	ai1i1,1	ai1i1,1	PUNCT
ejpam-3281	217	6	+	+	CCONJ
ejpam-3281	217	7	....	....	PUNCT
ejpam-3281	217	8	+	+	NOUN
ejpam-3281	217	9	aimim,1	aimim,1	ADJ
ejpam-3281	217	10	,	,	PUNCT
ejpam-3281	217	11	p	p	NOUN
ejpam-3281	217	12	)	)	PUNCT
ejpam-3281	217	13	=	=	SYM
ejpam-3281	217	14	1	1	NUM
ejpam-3281	217	15	(	(	PUNCT
ejpam-3281	217	16	the	the	DET
ejpam-3281	217	17	other	other	ADJ
ejpam-3281	217	18	case	case	NOUN
ejpam-3281	217	19	can	can	AUX
ejpam-3281	217	20	be	be	AUX
ejpam-3281	217	21	done	do	VERB
ejpam-3281	217	22	similarly	similarly	ADV
ejpam-3281	217	23	)	)	PUNCT
ejpam-3281	217	24	.	.	PUNCT
ejpam-3281	218	1	this	this	PRON
ejpam-3281	218	2	implies	imply	VERB
ejpam-3281	218	3	that	that	SCONJ
ejpam-3281	218	4	|ai1i1,1	|ai1i1,1	PROPN
ejpam-3281	218	5	+	+	CCONJ
ejpam-3281	218	6	....	....	PUNCT
ejpam-3281	219	1	+	+	NUM
ejpam-3281	219	2	aimim,1|	aimim,1|	ADJ
ejpam-3281	219	3	=	=	SYM
ejpam-3281	219	4	1	1	X
ejpam-3281	219	5	.	.	PUNCT
ejpam-3281	220	1	now	now	ADV
ejpam-3281	220	2	,	,	PUNCT
ejpam-3281	220	3	since	since	SCONJ
ejpam-3281	220	4	−1	−1	NOUN
ejpam-3281	220	5	<	<	X
ejpam-3281	220	6	α	α	X
ejpam-3281	220	7	<	<	X
ejpam-3281	220	8	−1	−1	NOUN
ejpam-3281	220	9	p−1	p−1	PROPN
ejpam-3281	220	10	,	,	PUNCT
ejpam-3281	220	11	it	it	PRON
ejpam-3281	220	12	follows	follow	VERB
ejpam-3281	220	13	that	that	SCONJ
ejpam-3281	220	14	p−1	p−1	PROPN
ejpam-3281	220	15	<	<	X
ejpam-3281	220	16	pα	pα	NOUN
ejpam-3281	220	17	.	.	PUNCT
ejpam-3281	221	1	hence	hence	ADV
ejpam-3281	221	2	,	,	PUNCT
ejpam-3281	221	3	we	we	PRON
ejpam-3281	221	4	obtain	obtain	VERB
ejpam-3281	221	5	the	the	DET
ejpam-3281	221	6	inequalities	inequality	NOUN
ejpam-3281	221	7	|g0|	|g0|	ADV
ejpam-3281	221	8	=	=	SYM
ejpam-3281	221	9	|ai0	|ai0	PROPN
ejpam-3281	221	10	+	+	CCONJ
ejpam-3281	221	11	....	....	PUNCT
ejpam-3281	221	12	+	+	CCONJ
ejpam-3281	221	13	aim	aim	VERB
ejpam-3281	221	14	|	|	ADV
ejpam-3281	221	15	≤	≤	NUM
ejpam-3281	221	16	p−1	p−1	PROPN
ejpam-3281	221	17	<	<	X
ejpam-3281	221	18	pα	pα	PROPN
ejpam-3281	221	19	=	=	PUNCT
ejpam-3281	221	20	|(ai1i1,1	|(ai1i1,1	NOUN
ejpam-3281	222	1	+	+	CCONJ
ejpam-3281	222	2	....	....	PUNCT
ejpam-3281	222	3	+	+	CCONJ
ejpam-3281	222	4	aimim,1)p	aimim,1)p	ADJ
ejpam-3281	222	5	−α|	−α|	DET
ejpam-3281	222	6	≤	≤	PROPN
ejpam-3281	222	7	≤	≤	NUM
ejpam-3281	222	8	max	max	PROPN
ejpam-3281	222	9	j	j	PROPN
ejpam-3281	222	10	{	{	PUNCT
ejpam-3281	222	11	|bj	|bj	PROPN
ejpam-3281	222	12	|	|	ADV
ejpam-3281	222	13	}	}	PUNCT
ejpam-3281	222	14	=	=	SYM
ejpam-3281	222	15	|g|	|g|	ADJ
ejpam-3281	222	16	,	,	PUNCT
ejpam-3281	222	17	a.	a.	NOUN
ejpam-3281	222	18	dalloul	dalloul	PROPN
ejpam-3281	222	19	/	/	SYM
ejpam-3281	222	20	eur	eur	PROPN
ejpam-3281	222	21	.	.	PUNCT
ejpam-3281	223	1	j.	j.	PROPN
ejpam-3281	223	2	pure	pure	PROPN
ejpam-3281	223	3	appl	appl	PROPN
ejpam-3281	223	4	.	.	PROPN
ejpam-3281	223	5	math	math	PROPN
ejpam-3281	223	6	,	,	PUNCT
ejpam-3281	223	7	11	11	NUM
ejpam-3281	223	8	(	(	PUNCT
ejpam-3281	223	9	4	4	NUM
ejpam-3281	223	10	)	)	PUNCT
ejpam-3281	223	11	(	(	PUNCT
ejpam-3281	223	12	2018	2018	NUM
ejpam-3281	223	13	)	)	PUNCT
ejpam-3281	223	14	,	,	PUNCT
ejpam-3281	223	15	1046	1046	NUM
ejpam-3281	223	16	-	-	SYM
ejpam-3281	223	17	1057	1057	NUM
ejpam-3281	223	18	1053	1053	NUM
ejpam-3281	223	19	where	where	SCONJ
ejpam-3281	223	20	{	{	PUNCT
ejpam-3281	223	21	bj	bj	AUX
ejpam-3281	223	22	}	}	PUNCT
ejpam-3281	223	23	are	be	AUX
ejpam-3281	223	24	the	the	DET
ejpam-3281	223	25	coefficients	coefficient	NOUN
ejpam-3281	223	26	of	of	ADP
ejpam-3281	223	27	the	the	DET
ejpam-3281	223	28	power	power	NOUN
ejpam-3281	223	29	series	series	PROPN
ejpam-3281	223	30	g.	g.	PROPN
ejpam-3281	223	31	thus	thus	ADV
ejpam-3281	223	32	,	,	PUNCT
ejpam-3281	223	33	|g(0	|g(0	NOUN
ejpam-3281	223	34	,	,	PUNCT
ejpam-3281	223	35	0)|	0)|	NOUN
ejpam-3281	223	36	<	<	X
ejpam-3281	223	37	|g|	|g|	PROPN
ejpam-3281	223	38	.	.	PUNCT
ejpam-3281	224	1	using	use	VERB
ejpam-3281	224	2	lemma	lemma	PROPN
ejpam-3281	224	3	1	1	NUM
ejpam-3281	224	4	,	,	PUNCT
ejpam-3281	224	5	it	it	PRON
ejpam-3281	224	6	implies	imply	VERB
ejpam-3281	224	7	that	that	SCONJ
ejpam-3281	224	8	g	g	PROPN
ejpam-3281	224	9	is	be	AUX
ejpam-3281	224	10	not	not	PART
ejpam-3281	224	11	unit	unit	NOUN
ejpam-3281	224	12	in	in	ADP
ejpam-3281	224	13	the	the	DET
ejpam-3281	224	14	ring	ring	NOUN
ejpam-3281	224	15	cp〈z1	cp〈z1	NOUN
ejpam-3281	224	16	,	,	PUNCT
ejpam-3281	224	17	z2	z2	PROPN
ejpam-3281	224	18	〉	〉	PROPN
ejpam-3281	224	19	.	.	PUNCT
ejpam-3281	225	1	therefore	therefore	ADV
ejpam-3281	225	2	,	,	PUNCT
ejpam-3281	225	3	there	there	PRON
ejpam-3281	225	4	exits	exit	VERB
ejpam-3281	225	5	a	a	DET
ejpam-3281	225	6	maximal	maximal	ADJ
ejpam-3281	225	7	ideal	ideal	ADJ
ejpam-3281	225	8	%	%	NOUN
ejpam-3281	225	9	in	in	ADP
ejpam-3281	225	10	cp〈z1	cp〈z1	PROPN
ejpam-3281	225	11	,	,	PUNCT
ejpam-3281	225	12	z2	z2	PROPN
ejpam-3281	225	13	〉	〉	PROPN
ejpam-3281	225	14	such	such	ADJ
ejpam-3281	225	15	that	that	SCONJ
ejpam-3281	225	16	g	g	PROPN
ejpam-3281	225	17	∈	∈	PROPN
ejpam-3281	225	18	%	%	NOUN
ejpam-3281	225	19	.	.	PUNCT
ejpam-3281	226	1	using	use	VERB
ejpam-3281	226	2	lemma	lemma	PROPN
ejpam-3281	226	3	2	2	NUM
ejpam-3281	226	4	and	and	CCONJ
ejpam-3281	226	5	the	the	DET
ejpam-3281	226	6	fact	fact	NOUN
ejpam-3281	226	7	that	that	SCONJ
ejpam-3281	226	8	cp	cp	PROPN
ejpam-3281	226	9	is	be	AUX
ejpam-3281	226	10	algebraically	algebraically	ADV
ejpam-3281	226	11	closed	close	VERB
ejpam-3281	226	12	field	field	NOUN
ejpam-3281	226	13	,	,	PUNCT
ejpam-3281	226	14	it	it	PRON
ejpam-3281	226	15	follows	follow	VERB
ejpam-3281	226	16	that	that	SCONJ
ejpam-3281	226	17	there	there	PRON
ejpam-3281	226	18	exist	exist	VERB
ejpam-3281	226	19	the	the	DET
ejpam-3281	226	20	elements	element	NOUN
ejpam-3281	226	21	z1	z1	VERB
ejpam-3281	226	22	,	,	PUNCT
ejpam-3281	226	23	z2	z2	PROPN
ejpam-3281	226	24	∈	∈	PROPN
ejpam-3281	226	25	b(0	b(0	NOUN
ejpam-3281	226	26	,	,	PUNCT
ejpam-3281	226	27	1	1	NUM
ejpam-3281	226	28	)	)	PUNCT
ejpam-3281	226	29	such	such	ADJ
ejpam-3281	226	30	that	that	DET
ejpam-3281	226	31	%	%	NOUN
ejpam-3281	226	32	=	=	SYM
ejpam-3281	227	1	〈	〈	PROPN
ejpam-3281	227	2	z1	z1	PROPN
ejpam-3281	227	3	−	−	PROPN
ejpam-3281	227	4	z1	z1	PROPN
ejpam-3281	227	5	,	,	PUNCT
ejpam-3281	227	6	z2	z2	PROPN
ejpam-3281	227	7	−	−	PROPN
ejpam-3281	227	8	z2	z2	PROPN
ejpam-3281	227	9	〉	〉	PROPN
ejpam-3281	227	10	.	.	PUNCT
ejpam-3281	228	1	therefore	therefore	ADV
ejpam-3281	228	2	,	,	PUNCT
ejpam-3281	228	3	g	g	PROPN
ejpam-3281	228	4	can	can	AUX
ejpam-3281	228	5	be	be	AUX
ejpam-3281	228	6	written	write	VERB
ejpam-3281	228	7	in	in	ADP
ejpam-3281	228	8	the	the	DET
ejpam-3281	228	9	form	form	NOUN
ejpam-3281	228	10	g	g	NOUN
ejpam-3281	228	11	=	=	NOUN
ejpam-3281	228	12	r1(z1	r1(z1	NOUN
ejpam-3281	228	13	−	−	PROPN
ejpam-3281	228	14	z1	z1	PROPN
ejpam-3281	228	15	)	)	PUNCT
ejpam-3281	228	16	+	+	NUM
ejpam-3281	228	17	r2(z2	r2(z2	NOUN
ejpam-3281	228	18	−	−	PROPN
ejpam-3281	228	19	z2	z2	PROPN
ejpam-3281	228	20	)	)	PUNCT
ejpam-3281	228	21	,	,	PUNCT
ejpam-3281	228	22	for	for	ADP
ejpam-3281	228	23	some	some	DET
ejpam-3281	228	24	r1	r1	NOUN
ejpam-3281	228	25	,	,	PUNCT
ejpam-3281	228	26	r2	r2	PROPN
ejpam-3281	228	27	∈	∈	PROPN
ejpam-3281	228	28	cp〈z1	cp〈z1	NOUN
ejpam-3281	228	29	,	,	PUNCT
ejpam-3281	228	30	z2	z2	PROPN
ejpam-3281	228	31	〉	〉	PROPN
ejpam-3281	228	32	.	.	PUNCT
ejpam-3281	229	1	thus	thus	ADV
ejpam-3281	229	2	,	,	PUNCT
ejpam-3281	229	3	it	it	PRON
ejpam-3281	229	4	is	be	AUX
ejpam-3281	229	5	clear	clear	ADJ
ejpam-3281	229	6	that	that	SCONJ
ejpam-3281	229	7	g(z1	g(z1	NOUN
ejpam-3281	229	8	,	,	PUNCT
ejpam-3281	229	9	z2	z2	PROPN
ejpam-3281	229	10	)	)	PUNCT
ejpam-3281	229	11	=	=	SYM
ejpam-3281	230	1	0	0	X
ejpam-3281	230	2	.	.	PUNCT
ejpam-3281	231	1	hence	hence	ADV
ejpam-3281	231	2	,	,	PUNCT
ejpam-3281	231	3	g	g	PROPN
ejpam-3281	231	4	has	have	VERB
ejpam-3281	231	5	a	a	DET
ejpam-3281	231	6	root	root	NOUN
ejpam-3281	231	7	in	in	ADP
ejpam-3281	231	8	the	the	DET
ejpam-3281	231	9	unit	unit	NOUN
ejpam-3281	231	10	ball	ball	NOUN
ejpam-3281	231	11	.	.	PUNCT
ejpam-3281	232	1	therefore	therefore	ADV
ejpam-3281	232	2	,	,	PUNCT
ejpam-3281	232	3	f	f	PROPN
ejpam-3281	232	4	has	have	VERB
ejpam-3281	232	5	a	a	DET
ejpam-3281	232	6	root	root	NOUN
ejpam-3281	232	7	in	in	ADP
ejpam-3281	232	8	the	the	DET
ejpam-3281	232	9	ball	ball	NOUN
ejpam-3281	232	10	b(0	b(0	NOUN
ejpam-3281	232	11	,	,	PUNCT
ejpam-3281	232	12	pα	pα	NOUN
ejpam-3281	232	13	)	)	PUNCT
ejpam-3281	232	14	.	.	PUNCT
ejpam-3281	233	1	thus	thus	ADV
ejpam-3281	233	2	,	,	PUNCT
ejpam-3281	233	3	the	the	DET
ejpam-3281	233	4	original	original	ADJ
ejpam-3281	233	5	polynomial	polynomial	NOUN
ejpam-3281	233	6	p	p	NOUN
ejpam-3281	234	1	[	[	X
ejpam-3281	234	2	x1	x1	PROPN
ejpam-3281	234	3	,	,	PUNCT
ejpam-3281	234	4	x2	x2	PROPN
ejpam-3281	234	5	]	]	PUNCT
ejpam-3281	234	6	has	have	VERB
ejpam-3281	234	7	a	a	DET
ejpam-3281	234	8	root	root	NOUN
ejpam-3281	234	9	of	of	ADP
ejpam-3281	234	10	the	the	DET
ejpam-3281	234	11	form	form	NOUN
ejpam-3281	234	12	(	(	PUNCT
ejpam-3281	234	13	exp(x1	exp(x1	ADJ
ejpam-3281	234	14	)	)	PUNCT
ejpam-3281	234	15	,	,	PUNCT
ejpam-3281	234	16	exp(x2	exp(x2	NOUN
ejpam-3281	234	17	)	)	PUNCT
ejpam-3281	234	18	)	)	PUNCT
ejpam-3281	234	19	.	.	PUNCT
ejpam-3281	235	1	corollary	corollary	ADJ
ejpam-3281	235	2	1	1	NUM
ejpam-3281	235	3	.	.	PUNCT
ejpam-3281	236	1	let	let	VERB
ejpam-3281	236	2	v	v	PRON
ejpam-3281	236	3	⊆	⊆	NUM
ejpam-3281	236	4	c4	c4	NOUN
ejpam-3281	236	5	p	p	NOUN
ejpam-3281	236	6	be	be	AUX
ejpam-3281	236	7	a	a	DET
ejpam-3281	236	8	variety	variety	NOUN
ejpam-3281	236	9	over	over	ADP
ejpam-3281	236	10	q	q	NOUN
ejpam-3281	236	11	of	of	ADP
ejpam-3281	236	12	dimension	dimension	NOUN
ejpam-3281	236	13	one	one	NUM
ejpam-3281	236	14	defined	define	VERB
ejpam-3281	236	15	by	by	ADP
ejpam-3281	236	16	a	a	DET
ejpam-3281	236	17	system	system	NOUN
ejpam-3281	236	18	of	of	ADP
ejpam-3281	236	19	polynomials	polynomial	NOUN
ejpam-3281	236	20	with	with	ADP
ejpam-3281	236	21	rational	rational	ADJ
ejpam-3281	236	22	integer	integer	NOUN
ejpam-3281	236	23	coefficients	coefficient	NOUN
ejpam-3281	236	24	of	of	ADP
ejpam-3281	236	25	the	the	DET
ejpam-3281	236	26	form	form	NOUN
ejpam-3281	236	27	p1[x1	p1[x1	SYM
ejpam-3281	236	28	,	,	PUNCT
ejpam-3281	236	29	x3	x3	ADJ
ejpam-3281	236	30	]	]	X
ejpam-3281	236	31	=	=	PUNCT
ejpam-3281	236	32	c(1	c(1	NOUN
ejpam-3281	236	33	)	)	PUNCT
ejpam-3281	237	1	+	+	CCONJ
ejpam-3281	237	2	m∑	m∑	X
ejpam-3281	237	3	i=1	i=1	PROPN
ejpam-3281	237	4	d	d	X
ejpam-3281	237	5	(	(	PUNCT
ejpam-3281	237	6	1	1	X
ejpam-3281	237	7	)	)	PUNCT
ejpam-3281	237	8	i	i	NOUN
ejpam-3281	237	9	x	x	VERB
ejpam-3281	238	1	α	α	PRON
ejpam-3281	238	2	(	(	PUNCT
ejpam-3281	238	3	1	1	NUM
ejpam-3281	238	4	)	)	PUNCT
ejpam-3281	238	5	i	i	NOUN
ejpam-3281	238	6	3	3	NUM
ejpam-3281	239	1	+	+	CCONJ
ejpam-3281	239	2	r∑	r∑	NOUN
ejpam-3281	240	1	l=1	l=1	NOUN
ejpam-3281	240	2	f	f	X
ejpam-3281	240	3	(	(	PUNCT
ejpam-3281	240	4	1	1	NUM
ejpam-3281	240	5	)	)	PUNCT
ejpam-3281	240	6	k	k	NOUN
ejpam-3281	240	7	x	x	SYM
ejpam-3281	240	8	ξ	ξ	X
ejpam-3281	240	9	(	(	PUNCT
ejpam-3281	240	10	1	1	NUM
ejpam-3281	240	11	)	)	PUNCT
ejpam-3281	240	12	k,1	k,1	PROPN
ejpam-3281	240	13	1	1	NUM
ejpam-3281	240	14	x	x	SYM
ejpam-3281	240	15	ξ	ξ	PROPN
ejpam-3281	240	16	(	(	PUNCT
ejpam-3281	240	17	1	1	NUM
ejpam-3281	240	18	)	)	PUNCT
ejpam-3281	240	19	k,2	k,2	X
ejpam-3281	240	20	3	3	NUM
ejpam-3281	240	21	;	;	PUNCT
ejpam-3281	240	22	ξ	ξ	X
ejpam-3281	240	23	(	(	PUNCT
ejpam-3281	240	24	1	1	NUM
ejpam-3281	240	25	)	)	PUNCT
ejpam-3281	240	26	k,1	k,1	PROPN
ejpam-3281	240	27	≥	≥	PROPN
ejpam-3281	240	28	1	1	NUM
ejpam-3281	240	29	p2[x2	p2[x2	PROPN
ejpam-3281	240	30	,	,	PUNCT
ejpam-3281	240	31	x4	x4	PROPN
ejpam-3281	240	32	]	]	X
ejpam-3281	240	33	=	=	PUNCT
ejpam-3281	240	34	c(2	c(2	PROPN
ejpam-3281	240	35	)	)	PUNCT
ejpam-3281	241	1	+	+	CCONJ
ejpam-3281	241	2	m∑	m∑	X
ejpam-3281	241	3	i=1	i=1	PROPN
ejpam-3281	242	1	d	d	X
ejpam-3281	242	2	(	(	PUNCT
ejpam-3281	242	3	2	2	NUM
ejpam-3281	242	4	)	)	PUNCT
ejpam-3281	242	5	i	i	NOUN
ejpam-3281	242	6	x	x	VERB
ejpam-3281	242	7	α	α	PRON
ejpam-3281	242	8	(	(	PUNCT
ejpam-3281	242	9	2	2	NUM
ejpam-3281	242	10	)	)	PUNCT
ejpam-3281	242	11	i	i	NOUN
ejpam-3281	242	12	4	4	NUM
ejpam-3281	243	1	+	+	CCONJ
ejpam-3281	243	2	r∑	r∑	NOUN
ejpam-3281	244	1	l=1	l=1	NOUN
ejpam-3281	244	2	f	f	X
ejpam-3281	244	3	(	(	PUNCT
ejpam-3281	244	4	2	2	NUM
ejpam-3281	244	5	)	)	PUNCT
ejpam-3281	244	6	k	k	NOUN
ejpam-3281	244	7	x	x	SYM
ejpam-3281	244	8	ξ	ξ	X
ejpam-3281	244	9	(	(	PUNCT
ejpam-3281	244	10	2	2	NUM
ejpam-3281	244	11	)	)	PUNCT
ejpam-3281	244	12	k,1	k,1	NOUN
ejpam-3281	244	13	2	2	NUM
ejpam-3281	244	14	x	x	SYM
ejpam-3281	244	15	ξ	ξ	PROPN
ejpam-3281	244	16	(	(	PUNCT
ejpam-3281	244	17	2	2	NUM
ejpam-3281	244	18	)	)	PUNCT
ejpam-3281	244	19	k,2	k,2	X
ejpam-3281	244	20	4	4	NUM
ejpam-3281	244	21	;	;	PUNCT
ejpam-3281	244	22	ξ	ξ	X
ejpam-3281	244	23	(	(	PUNCT
ejpam-3281	244	24	2	2	NUM
ejpam-3281	244	25	)	)	PUNCT
ejpam-3281	244	26	k,1	k,1	PROPN
ejpam-3281	244	27	≥	≥	PROPN
ejpam-3281	244	28	1	1	NUM
ejpam-3281	244	29	p3[x3	p3[x3	ADJ
ejpam-3281	244	30	,	,	PUNCT
ejpam-3281	244	31	x4	x4	X
ejpam-3281	244	32	]	]	X
ejpam-3281	244	33	=	=	PUNCT
ejpam-3281	244	34	ai0	ai0	PROPN
ejpam-3281	244	35	+	+	CCONJ
ejpam-3281	244	36	ai1x	ai1x	PROPN
ejpam-3281	244	37	i1,1	i1,1	NOUN
ejpam-3281	244	38	3	3	NUM
ejpam-3281	244	39	x	x	SYM
ejpam-3281	244	40	i1,2	i1,2	ADJ
ejpam-3281	244	41	4	4	NUM
ejpam-3281	244	42	+	+	NUM
ejpam-3281	244	43	...	...	PUNCT
ejpam-3281	245	1	+	+	CCONJ
ejpam-3281	245	2	aimx	aimx	PROPN
ejpam-3281	245	3	im,1	im,1	PROPN
ejpam-3281	245	4	3	3	NUM
ejpam-3281	245	5	x	x	NOUN
ejpam-3281	245	6	im,2	im,2	PROPN
ejpam-3281	245	7	4	4	NUM
ejpam-3281	245	8	,	,	PUNCT
ejpam-3281	245	9	such	such	ADJ
ejpam-3281	245	10	that	that	SCONJ
ejpam-3281	245	11	there	there	PRON
ejpam-3281	245	12	exists	exist	VERB
ejpam-3281	245	13	a	a	DET
ejpam-3281	245	14	degree	degree	NOUN
ejpam-3281	245	15	of	of	ADP
ejpam-3281	245	16	each	each	PRON
ejpam-3281	245	17	of	of	ADP
ejpam-3281	245	18	the	the	DET
ejpam-3281	245	19	variables	variable	NOUN
ejpam-3281	245	20	x3	x3	ADJ
ejpam-3281	245	21	and	and	CCONJ
ejpam-3281	245	22	x4	x4	PROPN
ejpam-3281	245	23	in	in	ADP
ejpam-3281	245	24	p1	p1	PROPN
ejpam-3281	245	25	and	and	CCONJ
ejpam-3281	245	26	p2	p2	PROPN
ejpam-3281	245	27	respectively	respectively	ADV
ejpam-3281	245	28	which	which	PRON
ejpam-3281	245	29	is	be	AUX
ejpam-3281	245	30	relatively	relatively	ADV
ejpam-3281	245	31	prime	prime	ADJ
ejpam-3281	245	32	to	to	ADP
ejpam-3281	245	33	p	p	NOUN
ejpam-3281	245	34	and	and	CCONJ
ejpam-3281	245	35	all	all	DET
ejpam-3281	245	36	the	the	DET
ejpam-3281	245	37	degrees	degree	NOUN
ejpam-3281	245	38	of	of	ADP
ejpam-3281	245	39	the	the	DET
ejpam-3281	245	40	variables	variable	NOUN
ejpam-3281	245	41	x3	x3	ADJ
ejpam-3281	245	42	and	and	CCONJ
ejpam-3281	245	43	x4	x4	PROPN
ejpam-3281	245	44	in	in	ADP
ejpam-3281	245	45	p3	p3	PROPN
ejpam-3281	245	46	are	be	AUX
ejpam-3281	245	47	also	also	ADV
ejpam-3281	245	48	relatively	relatively	ADV
ejpam-3281	245	49	prime	prime	ADJ
ejpam-3281	245	50	to	to	ADP
ejpam-3281	245	51	p.	p.	NOUN
ejpam-3281	245	52	if	if	SCONJ
ejpam-3281	245	53	v	v	NOUN
ejpam-3281	245	54	contains	contain	VERB
ejpam-3281	245	55	a	a	DET
ejpam-3281	245	56	point	point	NOUN
ejpam-3281	245	57	of	of	ADP
ejpam-3281	245	58	the	the	DET
ejpam-3281	245	59	form	form	NOUN
ejpam-3281	245	60	(	(	PUNCT
ejpam-3281	245	61	x1	x1	PROPN
ejpam-3281	245	62	,	,	PUNCT
ejpam-3281	245	63	x2	x2	PROPN
ejpam-3281	245	64	,	,	PUNCT
ejpam-3281	245	65	exp(x1	exp(x1	ADJ
ejpam-3281	245	66	)	)	PUNCT
ejpam-3281	245	67	,	,	PUNCT
ejpam-3281	245	68	exp(x2	exp(x2	NOUN
ejpam-3281	245	69	)	)	PUNCT
ejpam-3281	245	70	)	)	PUNCT
ejpam-3281	245	71	,	,	PUNCT
ejpam-3281	245	72	then	then	ADV
ejpam-3281	245	73	the	the	DET
ejpam-3281	245	74	quantities	quantity	NOUN
ejpam-3281	245	75	c(1	c(1	NOUN
ejpam-3281	245	76	)	)	PUNCT
ejpam-3281	246	1	+	+	CCONJ
ejpam-3281	247	1	∑m	∑m	ADJ
ejpam-3281	247	2	i=1	i=1	X
ejpam-3281	247	3	d	d	X
ejpam-3281	247	4	(	(	PUNCT
ejpam-3281	247	5	1	1	X
ejpam-3281	247	6	)	)	PUNCT
ejpam-3281	247	7	i	i	PRON
ejpam-3281	247	8	,	,	PUNCT
ejpam-3281	247	9	c(2	c(2	PROPN
ejpam-3281	247	10	)	)	PUNCT
ejpam-3281	248	1	+	+	CCONJ
ejpam-3281	249	1	∑m	∑m	ADJ
ejpam-3281	249	2	i=1	i=1	X
ejpam-3281	249	3	d	d	X
ejpam-3281	249	4	(	(	PUNCT
ejpam-3281	249	5	2	2	NUM
ejpam-3281	249	6	)	)	PUNCT
ejpam-3281	249	7	i	i	PRON
ejpam-3281	249	8	and	and	CCONJ
ejpam-3281	249	9	ai0	ai0	PROPN
ejpam-3281	249	10	+	+	CCONJ
ejpam-3281	249	11	...	...	PUNCT
ejpam-3281	249	12	+	+	CCONJ
ejpam-3281	249	13	aim	aim	NOUN
ejpam-3281	249	14	are	be	AUX
ejpam-3281	249	15	all	all	ADV
ejpam-3281	249	16	divisible	divisible	ADJ
ejpam-3281	249	17	by	by	ADP
ejpam-3281	249	18	p.	p.	NOUN
ejpam-3281	249	19	proof	proof	NOUN
ejpam-3281	249	20	.	.	PUNCT
ejpam-3281	250	1	if	if	SCONJ
ejpam-3281	250	2	v	v	NOUN
ejpam-3281	250	3	contains	contain	VERB
ejpam-3281	250	4	a	a	DET
ejpam-3281	250	5	point	point	NOUN
ejpam-3281	250	6	of	of	ADP
ejpam-3281	250	7	the	the	DET
ejpam-3281	250	8	form	form	NOUN
ejpam-3281	250	9	(	(	PUNCT
ejpam-3281	250	10	x1	x1	PROPN
ejpam-3281	250	11	,	,	PUNCT
ejpam-3281	250	12	x2	x2	PROPN
ejpam-3281	250	13	,	,	PUNCT
ejpam-3281	250	14	exp(x1	exp(x1	ADJ
ejpam-3281	250	15	)	)	PUNCT
ejpam-3281	250	16	,	,	PUNCT
ejpam-3281	250	17	exp(x2	exp(x2	NOUN
ejpam-3281	250	18	)	)	PUNCT
ejpam-3281	250	19	)	)	PUNCT
ejpam-3281	250	20	,	,	PUNCT
ejpam-3281	250	21	then	then	ADV
ejpam-3281	250	22	we	we	PRON
ejpam-3281	250	23	have	have	VERB
ejpam-3281	250	24	p1(x1	p1(x1	NOUN
ejpam-3281	250	25	,	,	PUNCT
ejpam-3281	250	26	exp(x1	exp(x1	ADJ
ejpam-3281	250	27	)	)	PUNCT
ejpam-3281	250	28	)	)	PUNCT
ejpam-3281	251	1	=	=	SYM
ejpam-3281	251	2	p2(x2	p2(x2	NOUN
ejpam-3281	251	3	,	,	PUNCT
ejpam-3281	251	4	exp(x2	exp(x2	NOUN
ejpam-3281	251	5	)	)	PUNCT
ejpam-3281	251	6	)	)	PUNCT
ejpam-3281	252	1	=	=	SYM
ejpam-3281	252	2	p3(exp(x1	p3(exp(x1	PROPN
ejpam-3281	252	3	)	)	PUNCT
ejpam-3281	252	4	,	,	PUNCT
ejpam-3281	252	5	exp(x2	exp(x2	NOUN
ejpam-3281	252	6	)	)	PUNCT
ejpam-3281	252	7	)	)	PUNCT
ejpam-3281	253	1	=	=	PUNCT
ejpam-3281	253	2	0	0	X
ejpam-3281	253	3	.	.	X
ejpam-3281	253	4	using	use	VERB
ejpam-3281	253	5	theorems	theorem	NOUN
ejpam-3281	253	6	2	2	NUM
ejpam-3281	253	7	and	and	CCONJ
ejpam-3281	253	8	3	3	NUM
ejpam-3281	253	9	,	,	PUNCT
ejpam-3281	253	10	we	we	PRON
ejpam-3281	253	11	find	find	VERB
ejpam-3281	253	12	that	that	SCONJ
ejpam-3281	253	13	the	the	DET
ejpam-3281	253	14	quantities	quantity	NOUN
ejpam-3281	253	15	c(1	c(1	NOUN
ejpam-3281	253	16	)	)	PUNCT
ejpam-3281	254	1	+	+	CCONJ
ejpam-3281	255	1	∑m	∑m	ADJ
ejpam-3281	255	2	i=1	i=1	X
ejpam-3281	255	3	d	d	X
ejpam-3281	255	4	(	(	PUNCT
ejpam-3281	255	5	1	1	X
ejpam-3281	255	6	)	)	PUNCT
ejpam-3281	255	7	i	i	PRON
ejpam-3281	255	8	,	,	PUNCT
ejpam-3281	255	9	c(2	c(2	PROPN
ejpam-3281	255	10	)	)	PUNCT
ejpam-3281	256	1	+	+	CCONJ
ejpam-3281	257	1	∑m	∑m	ADJ
ejpam-3281	257	2	i=1	i=1	X
ejpam-3281	257	3	d	d	X
ejpam-3281	257	4	(	(	PUNCT
ejpam-3281	257	5	2	2	NUM
ejpam-3281	257	6	)	)	PUNCT
ejpam-3281	257	7	i	i	PRON
ejpam-3281	257	8	and	and	CCONJ
ejpam-3281	257	9	ai0	ai0	PROPN
ejpam-3281	257	10	+	+	CCONJ
ejpam-3281	257	11	...	...	PUNCT
ejpam-3281	257	12	+	+	CCONJ
ejpam-3281	257	13	aim	aim	NOUN
ejpam-3281	257	14	are	be	AUX
ejpam-3281	257	15	all	all	ADV
ejpam-3281	257	16	divisible	divisible	ADJ
ejpam-3281	257	17	by	by	ADP
ejpam-3281	257	18	p.	p.	PROPN
ejpam-3281	257	19	remark	remark	NOUN
ejpam-3281	257	20	2	2	NUM
ejpam-3281	257	21	.	.	PUNCT
ejpam-3281	257	22	from	from	ADP
ejpam-3281	257	23	the	the	DET
ejpam-3281	257	24	previous	previous	ADJ
ejpam-3281	257	25	corollary	corollary	NOUN
ejpam-3281	257	26	,	,	PUNCT
ejpam-3281	257	27	we	we	PRON
ejpam-3281	257	28	can	can	AUX
ejpam-3281	257	29	deduce	deduce	VERB
ejpam-3281	257	30	that	that	SCONJ
ejpam-3281	257	31	if	if	SCONJ
ejpam-3281	257	32	we	we	PRON
ejpam-3281	257	33	have	have	VERB
ejpam-3281	257	34	a	a	DET
ejpam-3281	257	35	variety	variety	NOUN
ejpam-3281	257	36	v	v	ADP
ejpam-3281	257	37	⊆	⊆	NUM
ejpam-3281	257	38	c4	c4	NOUN
ejpam-3281	257	39	p	p	NOUN
ejpam-3281	257	40	defined	define	VERB
ejpam-3281	257	41	as	as	ADP
ejpam-3281	257	42	in	in	ADP
ejpam-3281	257	43	the	the	DET
ejpam-3281	257	44	previous	previous	ADJ
ejpam-3281	257	45	corollary	corollary	NOUN
ejpam-3281	257	46	in	in	ADP
ejpam-3281	257	47	which	which	PRON
ejpam-3281	257	48	one	one	NUM
ejpam-3281	257	49	of	of	ADP
ejpam-3281	257	50	the	the	DET
ejpam-3281	257	51	quantities	quantity	NOUN
ejpam-3281	257	52	c(1	c(1	NOUN
ejpam-3281	257	53	)	)	PUNCT
ejpam-3281	258	1	+	+	CCONJ
ejpam-3281	259	1	∑m	∑m	ADJ
ejpam-3281	259	2	i=1	i=1	X
ejpam-3281	259	3	d	d	X
ejpam-3281	259	4	(	(	PUNCT
ejpam-3281	259	5	1	1	X
ejpam-3281	259	6	)	)	PUNCT
ejpam-3281	259	7	i	i	PRON
ejpam-3281	259	8	,	,	PUNCT
ejpam-3281	259	9	c(2	c(2	PROPN
ejpam-3281	259	10	)	)	PUNCT
ejpam-3281	260	1	+	+	ADJ
ejpam-3281	260	2	∑m	∑m	PROPN
ejpam-3281	260	3	i=1	i=1	X
ejpam-3281	260	4	d	d	X
ejpam-3281	260	5	(	(	PUNCT
ejpam-3281	260	6	2	2	NUM
ejpam-3281	260	7	)	)	PUNCT
ejpam-3281	260	8	i	i	PRON
ejpam-3281	260	9	or	or	CCONJ
ejpam-3281	260	10	summation	summation	NOUN
ejpam-3281	260	11	of	of	ADP
ejpam-3281	260	12	coefficients	coefficient	NOUN
ejpam-3281	260	13	of	of	ADP
ejpam-3281	260	14	p3	p3	PROPN
ejpam-3281	260	15	is	be	AUX
ejpam-3281	260	16	relatively	relatively	ADV
ejpam-3281	260	17	prime	prime	ADJ
ejpam-3281	260	18	to	to	ADP
ejpam-3281	260	19	p	p	PRON
ejpam-3281	260	20	,	,	PUNCT
ejpam-3281	260	21	then	then	ADV
ejpam-3281	260	22	v	v	NOUN
ejpam-3281	260	23	has	have	VERB
ejpam-3281	260	24	no	no	DET
ejpam-3281	260	25	point	point	NOUN
ejpam-3281	260	26	of	of	ADP
ejpam-3281	260	27	the	the	DET
ejpam-3281	260	28	form	form	NOUN
ejpam-3281	260	29	(	(	PUNCT
ejpam-3281	260	30	x1	x1	PROPN
ejpam-3281	260	31	,	,	PUNCT
ejpam-3281	260	32	x2	x2	PROPN
ejpam-3281	260	33	,	,	PUNCT
ejpam-3281	260	34	exp(x1	exp(x1	ADJ
ejpam-3281	260	35	)	)	PUNCT
ejpam-3281	260	36	,	,	PUNCT
ejpam-3281	260	37	exp(x2	exp(x2	NOUN
ejpam-3281	260	38	)	)	PUNCT
ejpam-3281	260	39	)	)	PUNCT
ejpam-3281	260	40	.	.	PUNCT
ejpam-3281	261	1	we	we	PRON
ejpam-3281	261	2	can	can	AUX
ejpam-3281	261	3	also	also	ADV
ejpam-3281	261	4	give	give	VERB
ejpam-3281	261	5	sufficient	sufficient	ADJ
ejpam-3281	261	6	conditions	condition	NOUN
ejpam-3281	261	7	on	on	ADP
ejpam-3281	261	8	a	a	DET
ejpam-3281	261	9	class	class	NOUN
ejpam-3281	261	10	of	of	ADP
ejpam-3281	261	11	varieties	variety	NOUN
ejpam-3281	261	12	such	such	ADJ
ejpam-3281	261	13	that	that	SCONJ
ejpam-3281	261	14	each	each	DET
ejpam-3281	261	15	variety	variety	NOUN
ejpam-3281	261	16	admits	admit	VERB
ejpam-3281	261	17	a	a	DET
ejpam-3281	261	18	point	point	NOUN
ejpam-3281	261	19	of	of	ADP
ejpam-3281	261	20	the	the	DET
ejpam-3281	261	21	form	form	NOUN
ejpam-3281	261	22	(	(	PUNCT
ejpam-3281	261	23	x1	x1	PROPN
ejpam-3281	261	24	,	,	PUNCT
ejpam-3281	261	25	x2	x2	PROPN
ejpam-3281	261	26	,	,	PUNCT
ejpam-3281	261	27	exp(x1	exp(x1	ADJ
ejpam-3281	261	28	)	)	PUNCT
ejpam-3281	261	29	,	,	PUNCT
ejpam-3281	261	30	exp(x2	exp(x2	NOUN
ejpam-3281	261	31	)	)	PUNCT
ejpam-3281	261	32	)	)	PUNCT
ejpam-3281	261	33	as	as	SCONJ
ejpam-3281	261	34	follows	follow	VERB
ejpam-3281	261	35	.	.	PUNCT
ejpam-3281	262	1	a.	a.	PROPN
ejpam-3281	262	2	dalloul	dalloul	PROPN
ejpam-3281	262	3	/	/	SYM
ejpam-3281	262	4	eur	eur	PROPN
ejpam-3281	262	5	.	.	PUNCT
ejpam-3281	263	1	j.	j.	PROPN
ejpam-3281	263	2	pure	pure	PROPN
ejpam-3281	263	3	appl	appl	PROPN
ejpam-3281	263	4	.	.	PROPN
ejpam-3281	263	5	math	math	PROPN
ejpam-3281	263	6	,	,	PUNCT
ejpam-3281	263	7	11	11	NUM
ejpam-3281	263	8	(	(	PUNCT
ejpam-3281	263	9	4	4	NUM
ejpam-3281	263	10	)	)	PUNCT
ejpam-3281	263	11	(	(	PUNCT
ejpam-3281	263	12	2018	2018	NUM
ejpam-3281	263	13	)	)	PUNCT
ejpam-3281	263	14	,	,	PUNCT
ejpam-3281	263	15	1046	1046	NUM
ejpam-3281	263	16	-	-	SYM
ejpam-3281	263	17	1057	1057	NUM
ejpam-3281	263	18	1054	1054	NUM
ejpam-3281	263	19	corollary	corollary	NOUN
ejpam-3281	263	20	2	2	NUM
ejpam-3281	263	21	.	.	PUNCT
ejpam-3281	264	1	let	let	VERB
ejpam-3281	264	2	p	p	PRON
ejpam-3281	264	3	be	be	AUX
ejpam-3281	264	4	an	an	DET
ejpam-3281	264	5	odd	odd	ADJ
ejpam-3281	264	6	prime	prime	NOUN
ejpam-3281	264	7	and	and	CCONJ
ejpam-3281	264	8	let	let	VERB
ejpam-3281	264	9	c	c	X
ejpam-3281	264	10	,	,	PUNCT
ejpam-3281	264	11	d	d	NOUN
ejpam-3281	264	12	,	,	PUNCT
ejpam-3281	264	13	m	m	VERB
ejpam-3281	264	14	∈	∈	PROPN
ejpam-3281	264	15	z	z	PROPN
ejpam-3281	264	16	,	,	PUNCT
ejpam-3281	264	17	m	m	VERB
ejpam-3281	264	18	≥	≥	NOUN
ejpam-3281	264	19	1	1	NUM
ejpam-3281	264	20	with	with	ADP
ejpam-3281	264	21	the	the	DET
ejpam-3281	264	22	conditions	condition	NOUN
ejpam-3281	264	23	(	(	PUNCT
ejpam-3281	265	1	d	d	NOUN
ejpam-3281	265	2	+	+	NOUN
ejpam-3281	265	3	1	1	NUM
ejpam-3281	265	4	,	,	PUNCT
ejpam-3281	265	5	p	p	NOUN
ejpam-3281	265	6	)	)	PUNCT
ejpam-3281	265	7	=	=	SYM
ejpam-3281	265	8	(	(	PUNCT
ejpam-3281	265	9	m	m	PROPN
ejpam-3281	265	10	,	,	PUNCT
ejpam-3281	265	11	p	p	NOUN
ejpam-3281	265	12	)	)	PUNCT
ejpam-3281	265	13	=	=	SYM
ejpam-3281	265	14	1	1	NUM
ejpam-3281	265	15	,	,	PUNCT
ejpam-3281	265	16	p|(c	p|(c	NOUN
ejpam-3281	265	17	+	+	CCONJ
ejpam-3281	265	18	d	d	NOUN
ejpam-3281	265	19	)	)	PUNCT
ejpam-3281	265	20	.	.	PUNCT
ejpam-3281	266	1	then	then	ADV
ejpam-3281	266	2	the	the	DET
ejpam-3281	266	3	variety	variety	NOUN
ejpam-3281	266	4	v	v	ADP
ejpam-3281	266	5	⊆	⊆	NUM
ejpam-3281	266	6	c4	c4	NOUN
ejpam-3281	266	7	p	p	NOUN
ejpam-3281	266	8	of	of	ADP
ejpam-3281	266	9	dimension	dimension	NOUN
ejpam-3281	266	10	one	one	NUM
ejpam-3281	266	11	defined	define	VERB
ejpam-3281	266	12	by	by	ADP
ejpam-3281	266	13	the	the	DET
ejpam-3281	266	14	system	system	NOUN
ejpam-3281	266	15	of	of	ADP
ejpam-3281	266	16	polynomials	polynomial	NOUN
ejpam-3281	266	17	p1[x1	p1[x1	NOUN
ejpam-3281	266	18	,	,	PUNCT
ejpam-3281	266	19	x3	x3	ADJ
ejpam-3281	266	20	]	]	PUNCT
ejpam-3281	266	21	=	=	PUNCT
ejpam-3281	266	22	c+	c+	VERB
ejpam-3281	266	23	dxm	dxm	NOUN
ejpam-3281	266	24	3	3	NUM
ejpam-3281	267	1	+	+	NOUN
ejpam-3281	267	2	mx1	mx1	PROPN
ejpam-3281	267	3	p2[x2	p2[x2	PROPN
ejpam-3281	267	4	,	,	PUNCT
ejpam-3281	267	5	x4	x4	PROPN
ejpam-3281	267	6	]	]	X
ejpam-3281	267	7	=	=	PUNCT
ejpam-3281	267	8	c+	c+	VERB
ejpam-3281	267	9	dx4	dx4	INTJ
ejpam-3281	268	1	+	+	SYM
ejpam-3281	268	2	x2	x2	PROPN
ejpam-3281	268	3	p3[x3	p3[x3	PROPN
ejpam-3281	268	4	,	,	PUNCT
ejpam-3281	268	5	x4	x4	X
ejpam-3281	268	6	]	]	X
ejpam-3281	268	7	=	=	SYM
ejpam-3281	268	8	x4	x4	PROPN
ejpam-3281	268	9	−xm	−xm	PRON
ejpam-3281	268	10	3	3	NUM
ejpam-3281	268	11	,	,	PUNCT
ejpam-3281	268	12	has	have	VERB
ejpam-3281	268	13	a	a	DET
ejpam-3281	268	14	point	point	NOUN
ejpam-3281	268	15	of	of	ADP
ejpam-3281	268	16	the	the	DET
ejpam-3281	268	17	form	form	NOUN
ejpam-3281	268	18	(	(	PUNCT
ejpam-3281	268	19	x1	x1	PROPN
ejpam-3281	268	20	,	,	PUNCT
ejpam-3281	268	21	x2	x2	PROPN
ejpam-3281	268	22	,	,	PUNCT
ejpam-3281	268	23	exp(x1	exp(x1	ADJ
ejpam-3281	268	24	)	)	PUNCT
ejpam-3281	268	25	,	,	PUNCT
ejpam-3281	268	26	exp(x2	exp(x2	NOUN
ejpam-3281	268	27	)	)	PUNCT
ejpam-3281	268	28	)	)	PUNCT
ejpam-3281	268	29	.	.	PUNCT
ejpam-3281	269	1	proof	proof	NOUN
ejpam-3281	269	2	.	.	PUNCT
ejpam-3281	270	1	in	in	ADP
ejpam-3281	270	2	fact	fact	NOUN
ejpam-3281	270	3	,	,	PUNCT
ejpam-3281	270	4	theorem	theorem	VERB
ejpam-3281	270	5	2	2	NUM
ejpam-3281	270	6	guarantees	guarantee	NOUN
ejpam-3281	270	7	that	that	SCONJ
ejpam-3281	270	8	p1	p1	NOUN
ejpam-3281	270	9	has	have	VERB
ejpam-3281	270	10	a	a	DET
ejpam-3281	270	11	root	root	NOUN
ejpam-3281	270	12	of	of	ADP
ejpam-3281	270	13	the	the	DET
ejpam-3281	270	14	form	form	NOUN
ejpam-3281	270	15	(	(	PUNCT
ejpam-3281	270	16	x	x	NOUN
ejpam-3281	270	17	,	,	PUNCT
ejpam-3281	270	18	exp(x	exp(x	PROPN
ejpam-3281	270	19	)	)	PUNCT
ejpam-3281	270	20	)	)	PUNCT
ejpam-3281	270	21	.	.	PUNCT
ejpam-3281	271	1	by	by	ADP
ejpam-3281	271	2	a	a	DET
ejpam-3281	271	3	simple	simple	ADJ
ejpam-3281	271	4	calculation	calculation	NOUN
ejpam-3281	271	5	,	,	PUNCT
ejpam-3281	271	6	we	we	PRON
ejpam-3281	271	7	find	find	VERB
ejpam-3281	271	8	that	that	SCONJ
ejpam-3281	271	9	(	(	PUNCT
ejpam-3281	271	10	mx	mx	PROPN
ejpam-3281	271	11	,	,	PUNCT
ejpam-3281	271	12	exp(mx	exp(mx	NOUN
ejpam-3281	271	13	)	)	PUNCT
ejpam-3281	271	14	)	)	PUNCT
ejpam-3281	271	15	is	be	AUX
ejpam-3281	271	16	a	a	DET
ejpam-3281	271	17	root	root	NOUN
ejpam-3281	271	18	of	of	ADP
ejpam-3281	271	19	p2	p2	PROPN
ejpam-3281	271	20	which	which	PRON
ejpam-3281	271	21	admits	admit	VERB
ejpam-3281	271	22	roots	root	NOUN
ejpam-3281	271	23	of	of	ADP
ejpam-3281	271	24	the	the	DET
ejpam-3281	271	25	form	form	NOUN
ejpam-3281	271	26	(	(	PUNCT
ejpam-3281	271	27	x	x	NOUN
ejpam-3281	271	28	,	,	PUNCT
ejpam-3281	271	29	exp(x	exp(x	PROPN
ejpam-3281	271	30	)	)	PUNCT
ejpam-3281	271	31	)	)	PUNCT
ejpam-3281	271	32	according	accord	VERB
ejpam-3281	271	33	to	to	ADP
ejpam-3281	271	34	theorem	theorem	NOUN
ejpam-3281	271	35	2	2	NUM
ejpam-3281	271	36	.	.	PUNCT
ejpam-3281	272	1	it	it	PRON
ejpam-3281	272	2	’s	’	VERB
ejpam-3281	272	3	clear	clear	ADJ
ejpam-3281	272	4	that	that	SCONJ
ejpam-3281	272	5	(	(	PUNCT
ejpam-3281	272	6	exp(x	exp(x	PROPN
ejpam-3281	272	7	)	)	PUNCT
ejpam-3281	272	8	,	,	PUNCT
ejpam-3281	272	9	exp(mx	exp(mx	NOUN
ejpam-3281	272	10	)	)	PUNCT
ejpam-3281	272	11	)	)	PUNCT
ejpam-3281	273	1	is	be	AUX
ejpam-3281	273	2	a	a	DET
ejpam-3281	273	3	root	root	NOUN
ejpam-3281	273	4	of	of	ADP
ejpam-3281	273	5	p3	p3	PROPN
ejpam-3281	273	6	which	which	PRON
ejpam-3281	273	7	admits	admit	VERB
ejpam-3281	273	8	roots	root	NOUN
ejpam-3281	273	9	of	of	ADP
ejpam-3281	273	10	the	the	DET
ejpam-3281	273	11	form	form	NOUN
ejpam-3281	273	12	(	(	PUNCT
ejpam-3281	273	13	exp(x1	exp(x1	ADJ
ejpam-3281	273	14	)	)	PUNCT
ejpam-3281	273	15	,	,	PUNCT
ejpam-3281	273	16	exp(x2	exp(x2	NOUN
ejpam-3281	273	17	)	)	PUNCT
ejpam-3281	273	18	)	)	PUNCT
ejpam-3281	273	19	according	accord	VERB
ejpam-3281	273	20	to	to	ADP
ejpam-3281	273	21	theorem	theorem	NOUN
ejpam-3281	273	22	3	3	NUM
ejpam-3281	273	23	.	.	PUNCT
ejpam-3281	274	1	hence	hence	ADV
ejpam-3281	274	2	(	(	PUNCT
ejpam-3281	274	3	x	x	NOUN
ejpam-3281	274	4	,	,	PUNCT
ejpam-3281	274	5	mx	mx	PROPN
ejpam-3281	274	6	,	,	PUNCT
ejpam-3281	274	7	exp(x	exp(x	PROPN
ejpam-3281	274	8	)	)	PUNCT
ejpam-3281	274	9	,	,	PUNCT
ejpam-3281	274	10	exp(mx	exp(mx	NOUN
ejpam-3281	274	11	)	)	PUNCT
ejpam-3281	274	12	)	)	PUNCT
ejpam-3281	274	13	∈	∈	PROPN
ejpam-3281	274	14	v.	v.	ADP
ejpam-3281	274	15	remark	remark	NOUN
ejpam-3281	274	16	3	3	NUM
ejpam-3281	274	17	.	.	PUNCT
ejpam-3281	275	1	schanuel	schanuel	PROPN
ejpam-3281	275	2	’s	’s	PART
ejpam-3281	275	3	conjecture	conjecture	NOUN
ejpam-3281	275	4	in	in	ADP
ejpam-3281	275	5	the	the	DET
ejpam-3281	275	6	case	case	NOUN
ejpam-3281	275	7	of	of	ADP
ejpam-3281	275	8	two	two	NUM
ejpam-3281	275	9	variables	variable	NOUN
ejpam-3281	275	10	asserts	assert	VERB
ejpam-3281	275	11	that	that	SCONJ
ejpam-3281	275	12	if	if	SCONJ
ejpam-3281	275	13	v	v	NUM
ejpam-3281	275	14	⊆	⊆	NUM
ejpam-3281	275	15	c4	c4	NOUN
ejpam-3281	275	16	p	p	NOUN
ejpam-3281	275	17	is	be	AUX
ejpam-3281	275	18	a	a	DET
ejpam-3281	275	19	variety	variety	NOUN
ejpam-3281	275	20	of	of	ADP
ejpam-3281	275	21	dimension	dimension	NOUN
ejpam-3281	275	22	one	one	NUM
ejpam-3281	275	23	over	over	ADP
ejpam-3281	275	24	q	q	NOUN
ejpam-3281	275	25	and	and	CCONJ
ejpam-3281	275	26	has	have	VERB
ejpam-3281	275	27	a	a	DET
ejpam-3281	275	28	point	point	NOUN
ejpam-3281	275	29	of	of	ADP
ejpam-3281	275	30	the	the	DET
ejpam-3281	275	31	form	form	NOUN
ejpam-3281	275	32	(	(	PUNCT
ejpam-3281	275	33	x1	x1	PROPN
ejpam-3281	275	34	,	,	PUNCT
ejpam-3281	275	35	x2	x2	PROPN
ejpam-3281	275	36	,	,	PUNCT
ejpam-3281	275	37	exp(x1	exp(x1	ADJ
ejpam-3281	275	38	)	)	PUNCT
ejpam-3281	275	39	,	,	PUNCT
ejpam-3281	275	40	exp(x2	exp(x2	NOUN
ejpam-3281	275	41	)	)	PUNCT
ejpam-3281	275	42	)	)	PUNCT
ejpam-3281	275	43	,	,	PUNCT
ejpam-3281	275	44	then	then	ADV
ejpam-3281	275	45	the	the	DET
ejpam-3281	275	46	point	point	NOUN
ejpam-3281	275	47	must	must	AUX
ejpam-3281	275	48	take	take	VERB
ejpam-3281	275	49	the	the	DET
ejpam-3281	275	50	form	form	NOUN
ejpam-3281	275	51	(	(	PUNCT
ejpam-3281	275	52	x	x	NOUN
ejpam-3281	275	53	,	,	PUNCT
ejpam-3281	275	54	mx	mx	PROPN
ejpam-3281	275	55	,	,	PUNCT
ejpam-3281	275	56	exp(x	exp(x	PROPN
ejpam-3281	275	57	)	)	PUNCT
ejpam-3281	275	58	,	,	PUNCT
ejpam-3281	275	59	exp(mx	exp(mx	NOUN
ejpam-3281	275	60	)	)	PUNCT
ejpam-3281	275	61	)	)	PUNCT
ejpam-3281	275	62	,	,	PUNCT
ejpam-3281	275	63	for	for	ADP
ejpam-3281	275	64	some	some	DET
ejpam-3281	275	65	m	m	NOUN
ejpam-3281	275	66	∈	∈	NOUN
ejpam-3281	275	67	q.	q.	NOUN
ejpam-3281	275	68	4	4	X
ejpam-3281	275	69	.	.	PUNCT
ejpam-3281	275	70	further	further	ADJ
ejpam-3281	275	71	applications	application	NOUN
ejpam-3281	275	72	of	of	ADP
ejpam-3281	275	73	weierstrass	weierstrass	NOUN
ejpam-3281	275	74	preparation	preparation	NOUN
ejpam-3281	275	75	theorem	theorem	NOUN
ejpam-3281	275	76	and	and	CCONJ
ejpam-3281	275	77	hilbert	hilbert	PROPN
ejpam-3281	275	78	theorem	theorem	NOUN
ejpam-3281	275	79	we	we	PRON
ejpam-3281	275	80	can	can	AUX
ejpam-3281	275	81	use	use	VERB
ejpam-3281	275	82	weierstrass	weierstrass	NOUN
ejpam-3281	275	83	preparation	preparation	NOUN
ejpam-3281	275	84	theorem	theorem	VERB
ejpam-3281	275	85	to	to	PART
ejpam-3281	275	86	get	get	VERB
ejpam-3281	275	87	a	a	DET
ejpam-3281	275	88	result	result	NOUN
ejpam-3281	275	89	concerning	concern	VERB
ejpam-3281	275	90	the	the	DET
ejpam-3281	275	91	algebraic	algebraic	ADJ
ejpam-3281	275	92	dependence	dependence	NOUN
ejpam-3281	275	93	over	over	ADP
ejpam-3281	275	94	qp	qp	NOUN
ejpam-3281	275	95	as	as	SCONJ
ejpam-3281	275	96	follows	follow	NOUN
ejpam-3281	275	97	.	.	PUNCT
ejpam-3281	276	1	theorem	theorem	ADJ
ejpam-3281	276	2	4	4	NUM
ejpam-3281	276	3	.	.	PUNCT
ejpam-3281	277	1	let	let	VERB
ejpam-3281	277	2	p1	p1	PROPN
ejpam-3281	277	3	,	,	PUNCT
ejpam-3281	277	4	p2	p2	PROPN
ejpam-3281	277	5	∈	∈	PROPN
ejpam-3281	277	6	z[x	z[x	NOUN
ejpam-3281	277	7	,	,	PUNCT
ejpam-3281	277	8	y	y	PROPN
ejpam-3281	277	9	]	]	PUNCT
ejpam-3281	277	10	be	be	AUX
ejpam-3281	277	11	polynomials	polynomial	NOUN
ejpam-3281	277	12	defined	define	VERB
ejpam-3281	277	13	as	as	ADP
ejpam-3281	277	14	in	in	ADP
ejpam-3281	277	15	the	the	DET
ejpam-3281	277	16	beginning	beginning	NOUN
ejpam-3281	277	17	of	of	ADP
ejpam-3281	277	18	the	the	DET
ejpam-3281	277	19	previous	previous	ADJ
ejpam-3281	277	20	section	section	NOUN
ejpam-3281	277	21	of	of	ADP
ejpam-3281	277	22	the	the	DET
ejpam-3281	277	23	form	form	NOUN
ejpam-3281	277	24	p1[x	p1[x	NOUN
ejpam-3281	277	25	,	,	PUNCT
ejpam-3281	277	26	y	y	PROPN
ejpam-3281	277	27	]	]	PUNCT
ejpam-3281	278	1	=	=	PUNCT
ejpam-3281	278	2	c(1	c(1	NOUN
ejpam-3281	278	3	)	)	PUNCT
ejpam-3281	279	1	+	+	CCONJ
ejpam-3281	279	2	m∑	m∑	X
ejpam-3281	279	3	i=1	i=1	PROPN
ejpam-3281	280	1	d	d	X
ejpam-3281	280	2	(	(	PUNCT
ejpam-3281	280	3	1	1	NUM
ejpam-3281	280	4	)	)	PUNCT
ejpam-3281	280	5	i	i	PRON
ejpam-3281	280	6	y	y	PROPN
ejpam-3281	280	7	α	α	PROPN
ejpam-3281	280	8	(	(	PUNCT
ejpam-3281	280	9	1	1	X
ejpam-3281	280	10	)	)	PUNCT
ejpam-3281	281	1	i	i	PRON
ejpam-3281	281	2	i	i	PRON
ejpam-3281	282	1	+	+	CCONJ
ejpam-3281	282	2	e(1)xy	e(1)xy	PROPN
ejpam-3281	282	3	β	β	X
ejpam-3281	282	4	(	(	PUNCT
ejpam-3281	282	5	1	1	NUM
ejpam-3281	282	6	)	)	PUNCT
ejpam-3281	282	7	1,2	1,2	NUM
ejpam-3281	282	8	+	+	CCONJ
ejpam-3281	283	1	s∑	s∑	PROPN
ejpam-3281	283	2	k=1	k=1	PROPN
ejpam-3281	283	3	f	f	X
ejpam-3281	283	4	(	(	PUNCT
ejpam-3281	283	5	1	1	NUM
ejpam-3281	283	6	)	)	PUNCT
ejpam-3281	283	7	k	k	NOUN
ejpam-3281	283	8	xγ	xγ	PROPN
ejpam-3281	283	9	(	(	PUNCT
ejpam-3281	283	10	1	1	X
ejpam-3281	283	11	)	)	PUNCT
ejpam-3281	283	12	k,1y	k,1y	PROPN
ejpam-3281	283	13	γ	γ	X
ejpam-3281	283	14	(	(	PUNCT
ejpam-3281	283	15	1	1	NUM
ejpam-3281	283	16	)	)	PUNCT
ejpam-3281	283	17	k,2	k,2	X
ejpam-3281	283	18	;	;	PUNCT
ejpam-3281	283	19	γ	γ	X
ejpam-3281	283	20	(	(	PUNCT
ejpam-3281	283	21	1	1	NUM
ejpam-3281	283	22	)	)	PUNCT
ejpam-3281	283	23	k,1	k,1	PROPN
ejpam-3281	283	24	≥	≥	PROPN
ejpam-3281	283	25	2	2	NUM
ejpam-3281	283	26	,	,	PUNCT
ejpam-3281	283	27	p2[x	p2[x	NOUN
ejpam-3281	283	28	,	,	PUNCT
ejpam-3281	283	29	y	y	PROPN
ejpam-3281	283	30	]	]	PUNCT
ejpam-3281	283	31	=	=	PUNCT
ejpam-3281	283	32	c(2	c(2	PROPN
ejpam-3281	283	33	)	)	PUNCT
ejpam-3281	284	1	+	+	CCONJ
ejpam-3281	284	2	m∑	m∑	X
ejpam-3281	284	3	i=1	i=1	PROPN
ejpam-3281	285	1	d	d	X
ejpam-3281	285	2	(	(	PUNCT
ejpam-3281	285	3	2	2	NUM
ejpam-3281	285	4	)	)	PUNCT
ejpam-3281	285	5	i	i	PRON
ejpam-3281	285	6	y	y	PROPN
ejpam-3281	285	7	α	α	PROPN
ejpam-3281	285	8	(	(	PUNCT
ejpam-3281	285	9	2	2	NUM
ejpam-3281	285	10	)	)	PUNCT
ejpam-3281	286	1	i	i	PRON
ejpam-3281	286	2	i	i	PRON
ejpam-3281	287	1	+	+	NUM
ejpam-3281	287	2	e(2)xy	e(2)xy	PROPN
ejpam-3281	287	3	β	β	X
ejpam-3281	287	4	(	(	PUNCT
ejpam-3281	287	5	2	2	NUM
ejpam-3281	287	6	)	)	PUNCT
ejpam-3281	287	7	1,2	1,2	NUM
ejpam-3281	288	1	+	+	CCONJ
ejpam-3281	288	2	s∑	s∑	PROPN
ejpam-3281	288	3	k=1	k=1	PROPN
ejpam-3281	289	1	f	f	X
ejpam-3281	289	2	(	(	PUNCT
ejpam-3281	289	3	2	2	NUM
ejpam-3281	289	4	)	)	PUNCT
ejpam-3281	289	5	k	k	NOUN
ejpam-3281	289	6	xγ	xγ	PROPN
ejpam-3281	289	7	(	(	PUNCT
ejpam-3281	289	8	2	2	NUM
ejpam-3281	289	9	)	)	PUNCT
ejpam-3281	289	10	k,1y	k,1y	PROPN
ejpam-3281	289	11	γ	γ	X
ejpam-3281	289	12	(	(	PUNCT
ejpam-3281	289	13	2	2	NUM
ejpam-3281	289	14	)	)	PUNCT
ejpam-3281	289	15	k,2	k,2	NOUN
ejpam-3281	289	16	;	;	PUNCT
ejpam-3281	289	17	γ	γ	X
ejpam-3281	289	18	(	(	PUNCT
ejpam-3281	289	19	2	2	NUM
ejpam-3281	289	20	)	)	PUNCT
ejpam-3281	289	21	k,1	k,1	X
ejpam-3281	289	22	≥	≥	PROPN
ejpam-3281	289	23	2	2	NUM
ejpam-3281	289	24	,	,	PUNCT
ejpam-3281	289	25	in	in	ADP
ejpam-3281	289	26	which	which	PRON
ejpam-3281	289	27	(	(	PUNCT
ejpam-3281	289	28	d	d	X
ejpam-3281	289	29	(	(	PUNCT
ejpam-3281	289	30	1	1	NUM
ejpam-3281	289	31	)	)	SYM
ejpam-3281	289	32	1	1	NUM
ejpam-3281	289	33	α	α	NOUN
ejpam-3281	289	34	(	(	PUNCT
ejpam-3281	289	35	1	1	NUM
ejpam-3281	289	36	)	)	PUNCT
ejpam-3281	289	37	1	1	NUM
ejpam-3281	289	38	+	+	NOUN
ejpam-3281	289	39	...	...	PUNCT
ejpam-3281	290	1	+	+	ADJ
ejpam-3281	290	2	d	d	X
ejpam-3281	290	3	(	(	PUNCT
ejpam-3281	290	4	1	1	NUM
ejpam-3281	290	5	)	)	PUNCT
ejpam-3281	290	6	m	m	VERB
ejpam-3281	290	7	α	α	PRON
ejpam-3281	290	8	(	(	PUNCT
ejpam-3281	290	9	1	1	NUM
ejpam-3281	290	10	)	)	PUNCT
ejpam-3281	290	11	m	m	VERB
ejpam-3281	290	12	,	,	PUNCT
ejpam-3281	290	13	p	p	X
ejpam-3281	290	14	)	)	PUNCT
ejpam-3281	290	15	=	=	SYM
ejpam-3281	290	16	(	(	PUNCT
ejpam-3281	290	17	d	d	X
ejpam-3281	290	18	(	(	PUNCT
ejpam-3281	290	19	2	2	NUM
ejpam-3281	290	20	)	)	PUNCT
ejpam-3281	290	21	1	1	NUM
ejpam-3281	290	22	α	α	NOUN
ejpam-3281	290	23	(	(	PUNCT
ejpam-3281	290	24	2	2	NUM
ejpam-3281	290	25	)	)	PUNCT
ejpam-3281	290	26	1	1	NUM
ejpam-3281	290	27	+	+	NOUN
ejpam-3281	290	28	...	...	PUNCT
ejpam-3281	291	1	+	+	ADJ
ejpam-3281	291	2	d	d	X
ejpam-3281	291	3	(	(	PUNCT
ejpam-3281	291	4	2	2	NUM
ejpam-3281	291	5	)	)	PUNCT
ejpam-3281	291	6	m	m	VERB
ejpam-3281	291	7	α	α	PRON
ejpam-3281	291	8	(	(	PUNCT
ejpam-3281	291	9	2	2	NUM
ejpam-3281	291	10	)	)	PUNCT
ejpam-3281	291	11	m	m	PROPN
ejpam-3281	291	12	,	,	PUNCT
ejpam-3281	291	13	p	p	X
ejpam-3281	291	14	)	)	PUNCT
ejpam-3281	291	15	=	=	SYM
ejpam-3281	291	16	1	1	X
ejpam-3281	291	17	.	.	PUNCT
ejpam-3281	292	1	if	if	SCONJ
ejpam-3281	292	2	the	the	DET
ejpam-3281	292	3	quantities	quantity	NOUN
ejpam-3281	292	4	c(1)+∑m	c(1)+∑m	VERB
ejpam-3281	292	5	i=1	i=1	PROPN
ejpam-3281	292	6	d	d	X
ejpam-3281	292	7	(	(	PUNCT
ejpam-3281	292	8	1	1	X
ejpam-3281	292	9	)	)	PUNCT
ejpam-3281	292	10	i	i	PRON
ejpam-3281	292	11	,	,	PUNCT
ejpam-3281	292	12	c(2	c(2	PROPN
ejpam-3281	292	13	)	)	PUNCT
ejpam-3281	293	1	+	+	CCONJ
ejpam-3281	293	2	∑m	∑m	ADJ
ejpam-3281	293	3	i=1	i=1	X
ejpam-3281	293	4	d	d	X
ejpam-3281	293	5	(	(	PUNCT
ejpam-3281	293	6	2	2	X
ejpam-3281	293	7	)	)	PUNCT
ejpam-3281	293	8	i	i	PRON
ejpam-3281	293	9	are	be	AUX
ejpam-3281	293	10	divisible	divisible	ADJ
ejpam-3281	293	11	by	by	ADP
ejpam-3281	293	12	p	p	PROPN
ejpam-3281	293	13	and	and	CCONJ
ejpam-3281	293	14	(	(	PUNCT
ejpam-3281	293	15	x1	x1	PROPN
ejpam-3281	293	16	,	,	PUNCT
ejpam-3281	293	17	exp(x1	exp(x1	ADJ
ejpam-3281	293	18	)	)	PUNCT
ejpam-3281	293	19	)	)	PUNCT
ejpam-3281	293	20	,	,	PUNCT
ejpam-3281	293	21	(	(	PUNCT
ejpam-3281	293	22	x2	x2	INTJ
ejpam-3281	293	23	,	,	PUNCT
ejpam-3281	293	24	exp(x2	exp(x2	NOUN
ejpam-3281	293	25	)	)	PUNCT
ejpam-3281	293	26	)	)	PUNCT
ejpam-3281	293	27	are	be	AUX
ejpam-3281	293	28	roots	root	NOUN
ejpam-3281	293	29	of	of	ADP
ejpam-3281	293	30	p1	p1	NOUN
ejpam-3281	293	31	,	,	PUNCT
ejpam-3281	293	32	p2	p2	NOUN
ejpam-3281	293	33	receptively	receptively	ADV
ejpam-3281	293	34	,	,	PUNCT
ejpam-3281	293	35	then	then	ADV
ejpam-3281	293	36	there	there	PRON
ejpam-3281	293	37	exists	exist	VERB
ejpam-3281	293	38	a	a	DET
ejpam-3281	293	39	variety	variety	NOUN
ejpam-3281	293	40	v	v	ADP
ejpam-3281	293	41	⊆	⊆	NUM
ejpam-3281	293	42	c4	c4	NOUN
ejpam-3281	293	43	p	p	NOUN
ejpam-3281	293	44	over	over	ADP
ejpam-3281	293	45	qp	qp	NOUN
ejpam-3281	293	46	of	of	ADP
ejpam-3281	293	47	dimension	dimension	NOUN
ejpam-3281	293	48	≤	≤	ADV
ejpam-3281	293	49	1	1	NUM
ejpam-3281	293	50	containing	contain	VERB
ejpam-3281	293	51	the	the	DET
ejpam-3281	293	52	point	point	NOUN
ejpam-3281	293	53	(	(	PUNCT
ejpam-3281	293	54	x1	x1	PROPN
ejpam-3281	293	55	,	,	PUNCT
ejpam-3281	293	56	x2	x2	PROPN
ejpam-3281	293	57	,	,	PUNCT
ejpam-3281	293	58	exp(x1	exp(x1	ADJ
ejpam-3281	293	59	)	)	PUNCT
ejpam-3281	293	60	,	,	PUNCT
ejpam-3281	293	61	exp(x2	exp(x2	NOUN
ejpam-3281	293	62	)	)	PUNCT
ejpam-3281	293	63	)	)	PUNCT
ejpam-3281	293	64	.	.	PUNCT
ejpam-3281	294	1	proof	proof	NOUN
ejpam-3281	294	2	.	.	PUNCT
ejpam-3281	295	1	since	since	SCONJ
ejpam-3281	295	2	q	q	PROPN
ejpam-3281	295	3	⊆	⊆	NUM
ejpam-3281	295	4	qp	qp	NOUN
ejpam-3281	295	5	and	and	CCONJ
ejpam-3281	295	6	p1(x1	p1(x1	ADJ
ejpam-3281	295	7	,	,	PUNCT
ejpam-3281	295	8	exp(x1	exp(x1	ADJ
ejpam-3281	295	9	)	)	PUNCT
ejpam-3281	295	10	)	)	PUNCT
ejpam-3281	295	11	=	=	SYM
ejpam-3281	295	12	0	0	X
ejpam-3281	295	13	,	,	PUNCT
ejpam-3281	295	14	it	it	PRON
ejpam-3281	295	15	follows	follow	VERB
ejpam-3281	295	16	that	that	SCONJ
ejpam-3281	295	17	x1	x1	PROPN
ejpam-3281	295	18	and	and	CCONJ
ejpam-3281	295	19	exp(x1	exp(x1	NOUN
ejpam-3281	295	20	)	)	PUNCT
ejpam-3281	295	21	are	be	AUX
ejpam-3281	295	22	qp−algebraically	qp−algebraically	ADV
ejpam-3281	295	23	dependent	dependent	ADJ
ejpam-3281	295	24	.	.	PUNCT
ejpam-3281	296	1	the	the	DET
ejpam-3281	296	2	same	same	ADJ
ejpam-3281	296	3	holds	hold	VERB
ejpam-3281	296	4	true	true	ADJ
ejpam-3281	296	5	for	for	ADP
ejpam-3281	296	6	x2	x2	PROPN
ejpam-3281	296	7	and	and	CCONJ
ejpam-3281	296	8	exp(x2	exp(x2	PROPN
ejpam-3281	296	9	)	)	PUNCT
ejpam-3281	296	10	.	.	PUNCT
ejpam-3281	297	1	it	it	PRON
ejpam-3281	297	2	remains	remain	VERB
ejpam-3281	297	3	to	to	PART
ejpam-3281	297	4	show	show	VERB
ejpam-3281	297	5	that	that	SCONJ
ejpam-3281	297	6	x1	x1	PROPN
ejpam-3281	297	7	and	and	CCONJ
ejpam-3281	297	8	x2	x2	PROPN
ejpam-3281	297	9	are	be	AUX
ejpam-3281	297	10	qp−algebraically	qp−algebraically	ADV
ejpam-3281	297	11	dependent	dependent	ADJ
ejpam-3281	297	12	.	.	PUNCT
ejpam-3281	298	1	for	for	ADP
ejpam-3281	298	2	this	this	PRON
ejpam-3281	298	3	,	,	PUNCT
ejpam-3281	298	4	it	it	PRON
ejpam-3281	298	5	suffices	suffice	VERB
ejpam-3281	298	6	to	to	PART
ejpam-3281	298	7	show	show	VERB
ejpam-3281	298	8	that	that	SCONJ
ejpam-3281	298	9	x1	x1	PROPN
ejpam-3281	298	10	and	and	CCONJ
ejpam-3281	298	11	x2	x2	PROPN
ejpam-3281	298	12	are	be	AUX
ejpam-3281	298	13	algebraic	algebraic	ADJ
ejpam-3281	298	14	over	over	ADP
ejpam-3281	298	15	qp	qp	NOUN
ejpam-3281	298	16	.	.	PUNCT
ejpam-3281	299	1	we	we	PRON
ejpam-3281	299	2	briefly	briefly	ADV
ejpam-3281	299	3	review	review	VERB
ejpam-3281	299	4	the	the	DET
ejpam-3281	299	5	proof	proof	NOUN
ejpam-3281	299	6	of	of	ADP
ejpam-3281	299	7	theorem	theorem	NOUN
ejpam-3281	299	8	2	2	X
ejpam-3281	299	9	.	.	X
ejpam-3281	300	1	we	we	PRON
ejpam-3281	300	2	have	have	AUX
ejpam-3281	300	3	considered	consider	VERB
ejpam-3281	300	4	a.	a.	NOUN
ejpam-3281	300	5	dalloul	dalloul	PROPN
ejpam-3281	300	6	/	/	SYM
ejpam-3281	300	7	eur	eur	PROPN
ejpam-3281	300	8	.	.	PUNCT
ejpam-3281	301	1	j.	j.	PROPN
ejpam-3281	301	2	pure	pure	PROPN
ejpam-3281	301	3	appl	appl	PROPN
ejpam-3281	301	4	.	.	PROPN
ejpam-3281	301	5	math	math	PROPN
ejpam-3281	301	6	,	,	PUNCT
ejpam-3281	301	7	11	11	NUM
ejpam-3281	301	8	(	(	PUNCT
ejpam-3281	301	9	4	4	NUM
ejpam-3281	301	10	)	)	PUNCT
ejpam-3281	301	11	(	(	PUNCT
ejpam-3281	301	12	2018	2018	NUM
ejpam-3281	301	13	)	)	PUNCT
ejpam-3281	301	14	,	,	PUNCT
ejpam-3281	301	15	1046	1046	NUM
ejpam-3281	301	16	-	-	SYM
ejpam-3281	301	17	1057	1057	NUM
ejpam-3281	301	18	1055	1055	NUM
ejpam-3281	301	19	the	the	DET
ejpam-3281	301	20	power	power	NOUN
ejpam-3281	301	21	series	series	PROPN
ejpam-3281	301	22	f	f	PROPN
ejpam-3281	302	1	[	[	X
ejpam-3281	302	2	x	x	X
ejpam-3281	302	3	]	]	X
ejpam-3281	302	4	:	:	PUNCT
ejpam-3281	302	5	=	=	PUNCT
ejpam-3281	303	1	p	p	X
ejpam-3281	304	1	[	[	X
ejpam-3281	304	2	x	x	X
ejpam-3281	304	3	,	,	PUNCT
ejpam-3281	304	4	exp(x	exp(x	PROPN
ejpam-3281	304	5	)	)	PUNCT
ejpam-3281	304	6	]	]	PUNCT
ejpam-3281	304	7	∈	∈	PROPN
ejpam-3281	304	8	q[[x	q[[x	PROPN
ejpam-3281	304	9	]	]	X
ejpam-3281	304	10	]	]	PUNCT
ejpam-3281	304	11	which	which	PRON
ejpam-3281	304	12	is	be	AUX
ejpam-3281	304	13	convergent	convergent	NOUN
ejpam-3281	304	14	on	on	ADP
ejpam-3281	304	15	the	the	DET
ejpam-3281	304	16	closed	close	VERB
ejpam-3281	304	17	ball	ball	NOUN
ejpam-3281	304	18	b(0	b(0	NOUN
ejpam-3281	304	19	,	,	PUNCT
ejpam-3281	304	20	pα	pα	NOUN
ejpam-3281	304	21	)	)	PUNCT
ejpam-3281	304	22	,	,	PUNCT
ejpam-3281	304	23	α	α	PROPN
ejpam-3281	304	24	∈	∈	PROPN
ejpam-3281	304	25	(	(	PUNCT
ejpam-3281	304	26	−1	−1	NOUN
ejpam-3281	304	27	,	,	PUNCT
ejpam-3281	304	28	−1p−1	−1p−1	PROPN
ejpam-3281	304	29	)	)	PUNCT
ejpam-3281	304	30	∩	∩	PROPN
ejpam-3281	304	31	q.	q.	PROPN
ejpam-3281	304	32	weierstrass	weierstrass	PROPN
ejpam-3281	304	33	preparation	preparation	NOUN
ejpam-3281	304	34	theorem	theorem	NOUN
ejpam-3281	304	35	can	can	AUX
ejpam-3281	304	36	be	be	AUX
ejpam-3281	304	37	applied	apply	VERB
ejpam-3281	304	38	over	over	ADP
ejpam-3281	304	39	any	any	DET
ejpam-3281	304	40	finite	finite	ADJ
ejpam-3281	304	41	extension	extension	NOUN
ejpam-3281	304	42	k	k	PROPN
ejpam-3281	304	43	of	of	ADP
ejpam-3281	304	44	qp	qp	PROPN
ejpam-3281	304	45	(	(	PUNCT
ejpam-3281	304	46	for	for	ADP
ejpam-3281	304	47	more	more	ADJ
ejpam-3281	304	48	details	detail	NOUN
ejpam-3281	304	49	,	,	PUNCT
ejpam-3281	304	50	see	see	VERB
ejpam-3281	304	51	[	[	X
ejpam-3281	304	52	g	g	NOUN
ejpam-3281	304	53	]	]	X
ejpam-3281	304	54	)	)	PUNCT
ejpam-3281	304	55	.	.	PUNCT
ejpam-3281	305	1	also	also	ADV
ejpam-3281	305	2	,	,	PUNCT
ejpam-3281	305	3	the	the	DET
ejpam-3281	305	4	coefficients	coefficient	NOUN
ejpam-3281	305	5	of	of	ADP
ejpam-3281	305	6	f(x	f(x	PROPN
ejpam-3281	305	7	)	)	PUNCT
ejpam-3281	305	8	(	(	PUNCT
ejpam-3281	305	9	which	which	PRON
ejpam-3281	305	10	are	be	AUX
ejpam-3281	305	11	rationals	rational	NOUN
ejpam-3281	305	12	)	)	PUNCT
ejpam-3281	305	13	can	can	AUX
ejpam-3281	305	14	be	be	AUX
ejpam-3281	305	15	considered	consider	VERB
ejpam-3281	305	16	as	as	ADP
ejpam-3281	305	17	elements	element	NOUN
ejpam-3281	305	18	in	in	ADP
ejpam-3281	305	19	any	any	DET
ejpam-3281	305	20	finite	finite	ADJ
ejpam-3281	305	21	extension	extension	NOUN
ejpam-3281	305	22	of	of	ADP
ejpam-3281	305	23	qp	qp	PROPN
ejpam-3281	305	24	.	.	PUNCT
ejpam-3281	306	1	hence	hence	ADV
ejpam-3281	306	2	,	,	PUNCT
ejpam-3281	306	3	we	we	PRON
ejpam-3281	306	4	can	can	AUX
ejpam-3281	306	5	take	take	VERB
ejpam-3281	306	6	k	k	PROPN
ejpam-3281	306	7	to	to	PART
ejpam-3281	306	8	be	be	AUX
ejpam-3281	306	9	qp	qp	ADP
ejpam-3281	306	10	.	.	PUNCT
ejpam-3281	307	1	then	then	ADV
ejpam-3281	307	2	,	,	PUNCT
ejpam-3281	307	3	f(x	f(x	PROPN
ejpam-3281	307	4	)	)	PUNCT
ejpam-3281	307	5	can	can	AUX
ejpam-3281	307	6	be	be	AUX
ejpam-3281	307	7	factored	factor	VERB
ejpam-3281	307	8	in	in	ADP
ejpam-3281	307	9	the	the	DET
ejpam-3281	307	10	form	form	NOUN
ejpam-3281	307	11	f(x	f(x	PROPN
ejpam-3281	307	12	)	)	PUNCT
ejpam-3281	307	13	=	=	SYM
ejpam-3281	307	14	g(x)h(x	g(x)h(x	X
ejpam-3281	307	15	)	)	PUNCT
ejpam-3281	307	16	,	,	PUNCT
ejpam-3281	307	17	where	where	SCONJ
ejpam-3281	307	18	g(x	g(x	NOUN
ejpam-3281	307	19	)	)	PUNCT
ejpam-3281	307	20	∈	∈	PROPN
ejpam-3281	307	21	qp[x	qp[x	PROPN
ejpam-3281	307	22	]	]	PUNCT
ejpam-3281	307	23	and	and	CCONJ
ejpam-3281	307	24	h(x	h(x	PROPN
ejpam-3281	307	25	)	)	PUNCT
ejpam-3281	307	26	∈	∈	PROPN
ejpam-3281	307	27	qp[[x	qp[[x	PROPN
ejpam-3281	307	28	]	]	X
ejpam-3281	307	29	]	]	X
ejpam-3281	307	30	is	be	AUX
ejpam-3281	307	31	non	non	ADJ
ejpam-3281	307	32	-	-	ADJ
ejpam-3281	307	33	vanishing	vanishing	ADJ
ejpam-3281	307	34	and	and	CCONJ
ejpam-3281	307	35	converging	converge	VERB
ejpam-3281	307	36	on	on	ADP
ejpam-3281	307	37	the	the	DET
ejpam-3281	307	38	ball	ball	NOUN
ejpam-3281	307	39	b(0	b(0	NOUN
ejpam-3281	307	40	,	,	PUNCT
ejpam-3281	307	41	pα	pα	NOUN
ejpam-3281	307	42	)	)	PUNCT
ejpam-3281	307	43	.	.	PUNCT
ejpam-3281	308	1	the	the	DET
ejpam-3281	308	2	roots	root	NOUN
ejpam-3281	308	3	of	of	ADP
ejpam-3281	308	4	f(x	f(x	PROPN
ejpam-3281	308	5	)	)	PUNCT
ejpam-3281	308	6	are	be	AUX
ejpam-3281	308	7	exactly	exactly	ADV
ejpam-3281	308	8	the	the	DET
ejpam-3281	308	9	roots	root	NOUN
ejpam-3281	308	10	of	of	ADP
ejpam-3281	308	11	the	the	DET
ejpam-3281	308	12	polynomial	polynomial	ADJ
ejpam-3281	308	13	g.	g.	PROPN
ejpam-3281	308	14	that	that	PRON
ejpam-3281	308	15	is	be	AUX
ejpam-3281	308	16	,	,	PUNCT
ejpam-3281	308	17	each	each	DET
ejpam-3281	308	18	root	root	NOUN
ejpam-3281	308	19	of	of	ADP
ejpam-3281	308	20	f(x	f(x	PROPN
ejpam-3281	308	21	)	)	PUNCT
ejpam-3281	308	22	is	be	AUX
ejpam-3281	308	23	algebraic	algebraic	ADJ
ejpam-3281	308	24	over	over	ADP
ejpam-3281	308	25	qp	qp	NOUN
ejpam-3281	308	26	.	.	PUNCT
ejpam-3281	309	1	from	from	ADP
ejpam-3281	309	2	this	this	DET
ejpam-3281	309	3	argument	argument	NOUN
ejpam-3281	309	4	,	,	PUNCT
ejpam-3281	309	5	we	we	PRON
ejpam-3281	309	6	deduce	deduce	VERB
ejpam-3281	309	7	that	that	SCONJ
ejpam-3281	309	8	x1	x1	PROPN
ejpam-3281	309	9	and	and	CCONJ
ejpam-3281	309	10	x2	x2	PROPN
ejpam-3281	309	11	are	be	AUX
ejpam-3281	309	12	algebraic	algebraic	ADJ
ejpam-3281	309	13	numbers	number	NOUN
ejpam-3281	309	14	over	over	ADP
ejpam-3281	309	15	qp	qp	NOUN
ejpam-3281	309	16	.	.	PUNCT
ejpam-3281	310	1	this	this	PRON
ejpam-3281	310	2	clearly	clearly	ADV
ejpam-3281	310	3	implies	imply	VERB
ejpam-3281	310	4	that	that	SCONJ
ejpam-3281	310	5	x1	x1	PROPN
ejpam-3281	310	6	and	and	CCONJ
ejpam-3281	310	7	x2	x2	PROPN
ejpam-3281	310	8	are	be	AUX
ejpam-3281	310	9	qp−algebraically	qp−algebraically	ADV
ejpam-3281	310	10	dependent	dependent	ADJ
ejpam-3281	310	11	.	.	PUNCT
ejpam-3281	311	1	thus	thus	ADV
ejpam-3281	311	2	,	,	PUNCT
ejpam-3281	311	3	tdqpqp(x1	tdqpqp(x1	NOUN
ejpam-3281	311	4	,	,	PUNCT
ejpam-3281	311	5	x2	x2	PROPN
ejpam-3281	311	6	,	,	PUNCT
ejpam-3281	311	7	exp(x1	exp(x1	ADJ
ejpam-3281	311	8	)	)	PUNCT
ejpam-3281	311	9	,	,	PUNCT
ejpam-3281	311	10	exp(x2	exp(x2	NOUN
ejpam-3281	311	11	)	)	PUNCT
ejpam-3281	311	12	≤	≤	NOUN
ejpam-3281	311	13	1	1	NUM
ejpam-3281	311	14	.	.	PUNCT
ejpam-3281	312	1	hence	hence	ADV
ejpam-3281	312	2	,	,	PUNCT
ejpam-3281	312	3	there	there	PRON
ejpam-3281	312	4	exists	exist	VERB
ejpam-3281	312	5	a	a	DET
ejpam-3281	312	6	variety	variety	NOUN
ejpam-3281	312	7	v	v	ADP
ejpam-3281	312	8	⊆	⊆	NUM
ejpam-3281	312	9	c4	c4	NOUN
ejpam-3281	312	10	p	p	NOUN
ejpam-3281	312	11	over	over	ADP
ejpam-3281	312	12	qp	qp	NOUN
ejpam-3281	312	13	of	of	ADP
ejpam-3281	312	14	dimension	dimension	NOUN
ejpam-3281	312	15	≤	≤	ADV
ejpam-3281	312	16	1	1	NUM
ejpam-3281	312	17	containing	contain	VERB
ejpam-3281	312	18	the	the	DET
ejpam-3281	312	19	point	point	NOUN
ejpam-3281	312	20	(	(	PUNCT
ejpam-3281	312	21	x1	x1	PROPN
ejpam-3281	312	22	,	,	PUNCT
ejpam-3281	312	23	x2	x2	PROPN
ejpam-3281	312	24	,	,	PUNCT
ejpam-3281	312	25	exp(x1	exp(x1	ADJ
ejpam-3281	312	26	)	)	PUNCT
ejpam-3281	312	27	,	,	PUNCT
ejpam-3281	312	28	exp(x2	exp(x2	NOUN
ejpam-3281	312	29	)	)	PUNCT
ejpam-3281	312	30	)	)	PUNCT
ejpam-3281	312	31	.	.	PUNCT
ejpam-3281	313	1	finally	finally	ADV
ejpam-3281	313	2	,	,	PUNCT
ejpam-3281	313	3	we	we	PRON
ejpam-3281	313	4	generalize	generalize	VERB
ejpam-3281	313	5	theorem	theorem	VERB
ejpam-3281	313	6	2	2	NUM
ejpam-3281	313	7	to	to	ADP
ejpam-3281	313	8	the	the	DET
ejpam-3281	313	9	case	case	NOUN
ejpam-3281	313	10	of	of	ADP
ejpam-3281	313	11	polynomials	polynomial	NOUN
ejpam-3281	313	12	p	p	X
ejpam-3281	314	1	[	[	X
ejpam-3281	314	2	x1	x1	PROPN
ejpam-3281	314	3	,	,	PUNCT
ejpam-3281	314	4	...	...	PUNCT
ejpam-3281	314	5	,	,	PUNCT
ejpam-3281	314	6	xn	xn	PROPN
ejpam-3281	314	7	,	,	PUNCT
ejpam-3281	314	8	y1	y1	NOUN
ejpam-3281	314	9	,	,	PUNCT
ejpam-3281	314	10	...	...	PUNCT
ejpam-3281	314	11	,	,	PUNCT
ejpam-3281	314	12	yn	yn	PRON
ejpam-3281	314	13	]	]	X
ejpam-3281	314	14	∈	∈	PROPN
ejpam-3281	314	15	q[x1	q[x1	NOUN
ejpam-3281	314	16	,	,	PUNCT
ejpam-3281	314	17	...	...	PUNCT
ejpam-3281	314	18	,	,	PUNCT
ejpam-3281	314	19	xn	xn	PROPN
ejpam-3281	314	20	,	,	PUNCT
ejpam-3281	314	21	y1	y1	NOUN
ejpam-3281	314	22	,	,	PUNCT
ejpam-3281	314	23	...	...	PUNCT
ejpam-3281	314	24	,	,	PUNCT
ejpam-3281	314	25	yn	yn	PRON
ejpam-3281	314	26	]	]	X
ejpam-3281	314	27	.	.	PUNCT
ejpam-3281	315	1	as	as	ADP
ejpam-3281	315	2	in	in	ADP
ejpam-3281	315	3	the	the	DET
ejpam-3281	315	4	two	two	NUM
ejpam-3281	315	5	variables	variable	NOUN
ejpam-3281	315	6	case	case	NOUN
ejpam-3281	315	7	,	,	PUNCT
ejpam-3281	315	8	we	we	PRON
ejpam-3281	315	9	reduce	reduce	VERB
ejpam-3281	315	10	the	the	DET
ejpam-3281	315	11	problem	problem	NOUN
ejpam-3281	315	12	to	to	PART
ejpam-3281	315	13	find	find	VERB
ejpam-3281	315	14	the	the	DET
ejpam-3281	315	15	roots	root	NOUN
ejpam-3281	315	16	of	of	ADP
ejpam-3281	315	17	polynomials	polynomial	NOUN
ejpam-3281	315	18	with	with	ADP
ejpam-3281	315	19	rational	rational	ADJ
ejpam-3281	315	20	integer	integer	NOUN
ejpam-3281	315	21	coefficients	coefficient	NOUN
ejpam-3281	315	22	and	and	CCONJ
ejpam-3281	315	23	exclude	exclude	VERB
ejpam-3281	315	24	the	the	DET
ejpam-3281	315	25	polynomials	polynomial	NOUN
ejpam-3281	315	26	that	that	PRON
ejpam-3281	315	27	have	have	VERB
ejpam-3281	315	28	at	at	ADV
ejpam-3281	315	29	least	least	ADJ
ejpam-3281	315	30	one	one	NUM
ejpam-3281	315	31	of	of	ADP
ejpam-3281	315	32	the	the	DET
ejpam-3281	315	33	variables	variable	NOUN
ejpam-3281	315	34	x1	x1	PROPN
ejpam-3281	315	35	,	,	PUNCT
ejpam-3281	315	36	..	..	PUNCT
ejpam-3281	315	37	,	,	PUNCT
ejpam-3281	315	38	xn	xn	PROPN
ejpam-3281	315	39	in	in	ADP
ejpam-3281	315	40	each	each	DET
ejpam-3281	315	41	term	term	NOUN
ejpam-3281	315	42	since	since	SCONJ
ejpam-3281	315	43	it	it	PRON
ejpam-3281	315	44	implies	imply	VERB
ejpam-3281	315	45	that	that	SCONJ
ejpam-3281	315	46	the	the	DET
ejpam-3281	315	47	trivial	trivial	ADJ
ejpam-3281	315	48	point(0	point(0	PROPN
ejpam-3281	315	49	,	,	PUNCT
ejpam-3281	315	50	..	..	PUNCT
ejpam-3281	315	51	,	,	PUNCT
ejpam-3281	315	52	0	0	NUM
ejpam-3281	315	53	,	,	PUNCT
ejpam-3281	315	54	exp(0	exp(0	NOUN
ejpam-3281	315	55	)	)	PUNCT
ejpam-3281	315	56	,	,	PUNCT
ejpam-3281	315	57	..	..	PUNCT
ejpam-3281	315	58	,	,	PUNCT
ejpam-3281	315	59	exp(0	exp(0	NOUN
ejpam-3281	315	60	)	)	PUNCT
ejpam-3281	315	61	)	)	PUNCT
ejpam-3281	315	62	is	be	AUX
ejpam-3281	315	63	a	a	DET
ejpam-3281	315	64	root	root	NOUN
ejpam-3281	315	65	of	of	ADP
ejpam-3281	315	66	these	these	DET
ejpam-3281	315	67	polynomials	polynomial	NOUN
ejpam-3281	315	68	.	.	PUNCT
ejpam-3281	316	1	also	also	ADV
ejpam-3281	316	2	,	,	PUNCT
ejpam-3281	316	3	we	we	PRON
ejpam-3281	316	4	only	only	ADV
ejpam-3281	316	5	consider	consider	VERB
ejpam-3281	316	6	the	the	DET
ejpam-3281	316	7	polynomials	polynomial	NOUN
ejpam-3281	316	8	in	in	ADP
ejpam-3281	316	9	which	which	PRON
ejpam-3281	316	10	all	all	DET
ejpam-3281	316	11	the	the	DET
ejpam-3281	316	12	degrees	degree	NOUN
ejpam-3281	316	13	of	of	ADP
ejpam-3281	316	14	the	the	DET
ejpam-3281	316	15	variables	variable	NOUN
ejpam-3281	316	16	y1	y1	PROPN
ejpam-3281	316	17	,	,	PUNCT
ejpam-3281	316	18	...	...	PUNCT
ejpam-3281	316	19	,	,	PUNCT
ejpam-3281	316	20	yn	yn	PRON
ejpam-3281	316	21	are	be	AUX
ejpam-3281	316	22	relatively	relatively	ADV
ejpam-3281	316	23	prime	prime	ADJ
ejpam-3281	316	24	to	to	ADP
ejpam-3281	316	25	p.	p.	NOUN
ejpam-3281	316	26	then	then	ADV
ejpam-3281	316	27	,	,	PUNCT
ejpam-3281	316	28	we	we	PRON
ejpam-3281	316	29	prove	prove	VERB
ejpam-3281	316	30	theorem	theorem	ADJ
ejpam-3281	316	31	5	5	NUM
ejpam-3281	316	32	.	.	PUNCT
ejpam-3281	317	1	the	the	DET
ejpam-3281	317	2	polynomial	polynomial	ADJ
ejpam-3281	317	3	with	with	ADP
ejpam-3281	317	4	rational	rational	ADJ
ejpam-3281	317	5	integer	integer	NOUN
ejpam-3281	317	6	coefficients	coefficient	NOUN
ejpam-3281	317	7	p	p	X
ejpam-3281	318	1	[	[	X
ejpam-3281	318	2	x1	x1	PROPN
ejpam-3281	318	3	,	,	PUNCT
ejpam-3281	318	4	...	...	PUNCT
ejpam-3281	318	5	,	,	PUNCT
ejpam-3281	318	6	xn	xn	PROPN
ejpam-3281	318	7	,	,	PUNCT
ejpam-3281	318	8	y1	y1	NOUN
ejpam-3281	318	9	,	,	PUNCT
ejpam-3281	318	10	...	...	PUNCT
ejpam-3281	318	11	,	,	PUNCT
ejpam-3281	318	12	yn	yn	PRON
ejpam-3281	318	13	]	]	X
ejpam-3281	318	14	=	=	PUNCT
ejpam-3281	318	15	c+	c+	VERB
ejpam-3281	318	16	m∑	m∑	VERB
ejpam-3281	318	17	i=1	i=1	PROPN
ejpam-3281	318	18	diy	diy	NOUN
ejpam-3281	318	19	αi,1	αi,1	PROPN
ejpam-3281	318	20	1	1	NUM
ejpam-3281	318	21	...	...	PUNCT
ejpam-3281	318	22	y	y	PROPN
ejpam-3281	318	23	αi	αi	PROPN
ejpam-3281	318	24	,	,	PUNCT
ejpam-3281	318	25	n	n	CCONJ
ejpam-3281	318	26	n	n	PROPN
ejpam-3281	318	27	+	+	NOUN
ejpam-3281	318	28	n∑	n∑	ADJ
ejpam-3281	318	29	j=1	j=1	ADJ
ejpam-3281	318	30	ejxjy	ejxjy	NOUN
ejpam-3281	318	31	βj,1	βj,1	VERB
ejpam-3281	318	32	1	1	NUM
ejpam-3281	318	33	....	....	PUNCT
ejpam-3281	318	34	y	y	PROPN
ejpam-3281	318	35	βj	βj	PROPN
ejpam-3281	318	36	,	,	PUNCT
ejpam-3281	318	37	n	n	PRON
ejpam-3281	318	38	n	n	PROPN
ejpam-3281	318	39	+	+	CCONJ
ejpam-3281	318	40	s∑	s∑	PROPN
ejpam-3281	319	1	k=1	k=1	PROPN
ejpam-3281	319	2	fkx	fkx	PROPN
ejpam-3281	319	3	γk,1	γk,1	PROPN
ejpam-3281	319	4	1	1	NUM
ejpam-3281	319	5	...	...	SYM
ejpam-3281	319	6	x	x	SYM
ejpam-3281	319	7	γk	γk	PROPN
ejpam-3281	319	8	,	,	PUNCT
ejpam-3281	319	9	n	n	CCONJ
ejpam-3281	319	10	n	n	PROPN
ejpam-3281	319	11	y	y	PROPN
ejpam-3281	319	12	γk	γk	PROPN
ejpam-3281	319	13	,	,	PUNCT
ejpam-3281	319	14	n+1	n+1	PROPN
ejpam-3281	319	15	1	1	NUM
ejpam-3281	319	16	...	...	PUNCT
ejpam-3281	319	17	y	y	PROPN
ejpam-3281	319	18	γk,2n	γk,2n	X
ejpam-3281	319	19	n	n	PROPN
ejpam-3281	319	20	;	;	PUNCT
ejpam-3281	319	21	γk,1	γk,1	PROPN
ejpam-3281	319	22	+	+	CCONJ
ejpam-3281	319	23	...	...	PUNCT
ejpam-3281	319	24	+	+	NUM
ejpam-3281	319	25	γk	γk	NOUN
ejpam-3281	319	26	,	,	PUNCT
ejpam-3281	319	27	n	n	PRON
ejpam-3281	319	28	≥	≥	NOUN
ejpam-3281	319	29	2	2	NUM
ejpam-3281	319	30	,	,	PUNCT
ejpam-3281	319	31	in	in	ADP
ejpam-3281	319	32	which	which	PRON
ejpam-3281	319	33	at	at	ADP
ejpam-3281	319	34	least	least	ADJ
ejpam-3281	319	35	one	one	NUM
ejpam-3281	319	36	of	of	ADP
ejpam-3281	319	37	the	the	DET
ejpam-3281	319	38	elements	element	NOUN
ejpam-3281	319	39	(	(	PUNCT
ejpam-3281	319	40	d1α1,1	d1α1,1	NOUN
ejpam-3281	319	41	+	+	NUM
ejpam-3281	319	42	...	...	PUNCT
ejpam-3281	319	43	+	+	NUM
ejpam-3281	319	44	dmαm,1	dmαm,1	NOUN
ejpam-3281	319	45	+	+	NUM
ejpam-3281	319	46	e1	e1	NOUN
ejpam-3281	319	47	)	)	PUNCT
ejpam-3281	319	48	,	,	PUNCT
ejpam-3281	319	49	...	...	PUNCT
ejpam-3281	319	50	,	,	PUNCT
ejpam-3281	319	51	(	(	PUNCT
ejpam-3281	319	52	d1α1,n	d1α1,n	X
ejpam-3281	319	53	+	+	NUM
ejpam-3281	319	54	...	...	PUNCT
ejpam-3281	320	1	+	+	CCONJ
ejpam-3281	320	2	dmαm	dmαm	ADJ
ejpam-3281	320	3	,	,	PUNCT
ejpam-3281	320	4	n	n	PROPN
ejpam-3281	320	5	+	+	X
ejpam-3281	320	6	en	en	X
ejpam-3281	320	7	)	)	PUNCT
ejpam-3281	320	8	is	be	AUX
ejpam-3281	320	9	relatively	relatively	ADV
ejpam-3281	320	10	prime	prime	ADJ
ejpam-3281	320	11	to	to	ADP
ejpam-3281	320	12	p	p	NOUN
ejpam-3281	320	13	;	;	PUNCT
ejpam-3281	320	14	p	p	PRON
ejpam-3281	320	15	≥	≥	NOUN
ejpam-3281	320	16	3	3	NUM
ejpam-3281	320	17	,	,	PUNCT
ejpam-3281	320	18	has	have	VERB
ejpam-3281	320	19	a	a	DET
ejpam-3281	320	20	root	root	NOUN
ejpam-3281	320	21	of	of	ADP
ejpam-3281	320	22	the	the	DET
ejpam-3281	320	23	form	form	NOUN
ejpam-3281	320	24	(	(	PUNCT
ejpam-3281	320	25	x̄	x̄	NOUN
ejpam-3281	320	26	,	,	PUNCT
ejpam-3281	320	27	exp(x̄	exp(x̄	PRON
ejpam-3281	320	28	)	)	PUNCT
ejpam-3281	320	29	)	)	PUNCT
ejpam-3281	321	1	if	if	SCONJ
ejpam-3281	321	2	and	and	CCONJ
ejpam-3281	321	3	only	only	ADV
ejpam-3281	321	4	if	if	SCONJ
ejpam-3281	321	5	|c+	|c+	NOUN
ejpam-3281	321	6	d1	d1	PROPN
ejpam-3281	321	7	+	+	CCONJ
ejpam-3281	321	8	...	...	PUNCT
ejpam-3281	321	9	+	+	CCONJ
ejpam-3281	321	10	dm|	dm|	VERB
ejpam-3281	321	11	≤	≤	PROPN
ejpam-3281	321	12	p−1	p−1	PROPN
ejpam-3281	321	13	.	.	PUNCT
ejpam-3281	322	1	proof	proof	NOUN
ejpam-3281	322	2	.	.	PUNCT
ejpam-3281	323	1	proof	proof	NOUN
ejpam-3281	323	2	of	of	ADP
ejpam-3281	323	3	the	the	DET
ejpam-3281	323	4	necessary	necessary	ADJ
ejpam-3281	323	5	condition	condition	NOUN
ejpam-3281	323	6	.	.	PUNCT
ejpam-3281	324	1	if	if	SCONJ
ejpam-3281	324	2	(	(	PUNCT
ejpam-3281	324	3	x̄	x̄	NOUN
ejpam-3281	324	4	,	,	PUNCT
ejpam-3281	324	5	exp(x̄	exp(x̄	PRON
ejpam-3281	324	6	)	)	PUNCT
ejpam-3281	324	7	)	)	PUNCT
ejpam-3281	324	8	is	be	AUX
ejpam-3281	324	9	a	a	DET
ejpam-3281	324	10	root	root	NOUN
ejpam-3281	324	11	of	of	ADP
ejpam-3281	324	12	the	the	DET
ejpam-3281	324	13	polynomial	polynomial	ADJ
ejpam-3281	324	14	p	p	PROPN
ejpam-3281	325	1	[	[	X
ejpam-3281	325	2	x1	x1	PROPN
ejpam-3281	325	3	,	,	PUNCT
ejpam-3281	325	4	...	...	PUNCT
ejpam-3281	325	5	,	,	PUNCT
ejpam-3281	325	6	xn	xn	PROPN
ejpam-3281	325	7	,	,	PUNCT
ejpam-3281	325	8	y1	y1	NOUN
ejpam-3281	325	9	,	,	PUNCT
ejpam-3281	325	10	...	...	PUNCT
ejpam-3281	325	11	,	,	PUNCT
ejpam-3281	325	12	yn	yn	PRON
ejpam-3281	325	13	]	]	PUNCT
ejpam-3281	325	14	,	,	PUNCT
ejpam-3281	325	15	then	then	ADV
ejpam-3281	325	16	x̄	x̄	PROPN
ejpam-3281	325	17	is	be	AUX
ejpam-3281	325	18	a	a	DET
ejpam-3281	325	19	root	root	NOUN
ejpam-3281	325	20	of	of	ADP
ejpam-3281	325	21	the	the	DET
ejpam-3281	325	22	power	power	NOUN
ejpam-3281	325	23	series	series	PROPN
ejpam-3281	325	24	f(x1	f(x1	PROPN
ejpam-3281	325	25	,	,	PUNCT
ejpam-3281	325	26	...	...	PUNCT
ejpam-3281	325	27	,	,	PUNCT
ejpam-3281	325	28	xn	xn	PROPN
ejpam-3281	325	29	)	)	PUNCT
ejpam-3281	325	30	:	:	PUNCT
ejpam-3281	326	1	=	=	PUNCT
ejpam-3281	326	2	p	p	X
ejpam-3281	327	1	[	[	X
ejpam-3281	327	2	x1	x1	PROPN
ejpam-3281	327	3	,	,	PUNCT
ejpam-3281	327	4	...	...	PUNCT
ejpam-3281	327	5	,	,	PUNCT
ejpam-3281	327	6	xn	xn	PROPN
ejpam-3281	327	7	,	,	PUNCT
ejpam-3281	327	8	exp(x1	exp(x1	ADJ
ejpam-3281	327	9	)	)	PUNCT
ejpam-3281	327	10	,	,	PUNCT
ejpam-3281	327	11	..	..	PUNCT
ejpam-3281	327	12	,	,	PUNCT
ejpam-3281	327	13	exp(xn	exp(xn	NOUN
ejpam-3281	327	14	)	)	PUNCT
ejpam-3281	327	15	]	]	PUNCT
ejpam-3281	327	16	which	which	PRON
ejpam-3281	327	17	is	be	AUX
ejpam-3281	327	18	convergent	convergent	NOUN
ejpam-3281	327	19	on	on	ADP
ejpam-3281	327	20	the	the	DET
ejpam-3281	327	21	disk	disk	NOUN
ejpam-3281	327	22	{	{	PUNCT
ejpam-3281	327	23	x̄	x̄	NOUN
ejpam-3281	327	24	:	:	PUNCT
ejpam-3281	327	25	max	max	PROPN
ejpam-3281	327	26	|xi|	|xi|	PROPN
ejpam-3281	327	27	<	<	X
ejpam-3281	327	28	p	p	X
ejpam-3281	327	29	−1	−1	NOUN
ejpam-3281	327	30	p−1	p−1	PROPN
ejpam-3281	327	31	}	}	PUNCT
ejpam-3281	327	32	.	.	PUNCT
ejpam-3281	328	1	thus	thus	ADV
ejpam-3281	328	2	,	,	PUNCT
ejpam-3281	328	3	x̄	x̄	PROPN
ejpam-3281	328	4	∈	∈	PROPN
ejpam-3281	328	5	en	en	PROPN
ejpam-3281	328	6	.	.	PUNCT
ejpam-3281	329	1	so	so	ADV
ejpam-3281	329	2	,	,	PUNCT
ejpam-3281	329	3	c+	c+	VERB
ejpam-3281	329	4	m∑	m∑	X
ejpam-3281	329	5	i=1	i=1	PROPN
ejpam-3281	329	6	di	di	PROPN
ejpam-3281	329	7	exp(αi,1x1	exp(αi,1x1	PROPN
ejpam-3281	329	8	)	)	PUNCT
ejpam-3281	329	9	...	...	PUNCT
ejpam-3281	330	1	exp(αi	exp(αi	NOUN
ejpam-3281	330	2	,	,	PUNCT
ejpam-3281	330	3	nxn	nxn	NOUN
ejpam-3281	330	4	)	)	PUNCT
ejpam-3281	330	5	=	=	SYM
ejpam-3281	330	6	a.	a.	NOUN
ejpam-3281	330	7	dalloul	dalloul	PROPN
ejpam-3281	330	8	/	/	SYM
ejpam-3281	330	9	eur	eur	PROPN
ejpam-3281	330	10	.	.	PUNCT
ejpam-3281	331	1	j.	j.	PROPN
ejpam-3281	331	2	pure	pure	PROPN
ejpam-3281	331	3	appl	appl	PROPN
ejpam-3281	331	4	.	.	PROPN
ejpam-3281	331	5	math	math	PROPN
ejpam-3281	331	6	,	,	PUNCT
ejpam-3281	331	7	11	11	NUM
ejpam-3281	331	8	(	(	PUNCT
ejpam-3281	331	9	4	4	NUM
ejpam-3281	331	10	)	)	PUNCT
ejpam-3281	331	11	(	(	PUNCT
ejpam-3281	331	12	2018	2018	NUM
ejpam-3281	331	13	)	)	PUNCT
ejpam-3281	331	14	,	,	PUNCT
ejpam-3281	331	15	1046	1046	NUM
ejpam-3281	331	16	-	-	SYM
ejpam-3281	331	17	1057	1057	NUM
ejpam-3281	331	18	1056	1056	NUM
ejpam-3281	331	19	=	=	SYM
ejpam-3281	332	1	−	−	PROPN
ejpam-3281	332	2	(	(	PUNCT
ejpam-3281	332	3	n∑	n∑	NOUN
ejpam-3281	332	4	j=1	j=1	PROPN
ejpam-3281	332	5	ejxj	ejxj	PROPN
ejpam-3281	332	6	exp(βj,1x1	exp(βj,1x1	PROPN
ejpam-3281	332	7	)	)	PUNCT
ejpam-3281	332	8	....	....	PUNCT
ejpam-3281	332	9	exp(βj	exp(βj	NOUN
ejpam-3281	332	10	,	,	PUNCT
ejpam-3281	332	11	nxn)+	nxn)+	PROPN
ejpam-3281	333	1	s∑	s∑	PROPN
ejpam-3281	334	1	k=1	k=1	PROPN
ejpam-3281	334	2	fkx	fkx	PROPN
ejpam-3281	334	3	γk,1	γk,1	PROPN
ejpam-3281	334	4	1	1	NUM
ejpam-3281	334	5	...	...	SYM
ejpam-3281	334	6	x	x	SYM
ejpam-3281	334	7	γk	γk	PROPN
ejpam-3281	334	8	,	,	PUNCT
ejpam-3281	334	9	n	n	CCONJ
ejpam-3281	334	10	n	n	PRON
ejpam-3281	334	11	exp(γk	exp(γk	NOUN
ejpam-3281	334	12	,	,	PUNCT
ejpam-3281	334	13	n+1x1	n+1x1	PROPN
ejpam-3281	334	14	)	)	PUNCT
ejpam-3281	334	15	...	...	PUNCT
ejpam-3281	335	1	exp(γk,2nxn	exp(γk,2nxn	NUM
ejpam-3281	335	2	)	)	PUNCT
ejpam-3281	335	3	)	)	PUNCT
ejpam-3281	335	4	.	.	PUNCT
ejpam-3281	336	1	using	use	VERB
ejpam-3281	336	2	the	the	DET
ejpam-3281	336	3	fact	fact	NOUN
ejpam-3281	336	4	z	z	NOUN
ejpam-3281	336	5	⊆	⊆	NUM
ejpam-3281	336	6	zp	zp	NOUN
ejpam-3281	336	7	,	,	PUNCT
ejpam-3281	336	8	|	|	ADV
ejpam-3281	336	9	exp(w)|	exp(w)|	VERB
ejpam-3281	336	10	=	=	NOUN
ejpam-3281	336	11	1,∀w	1,∀w	NUM
ejpam-3281	336	12	∈	∈	NOUN
ejpam-3281	336	13	e	e	NOUN
ejpam-3281	336	14	and	and	CCONJ
ejpam-3281	336	15	the	the	DET
ejpam-3281	336	16	strong	strong	ADJ
ejpam-3281	336	17	triangle	triangle	NOUN
ejpam-3281	336	18	inequality	inequality	NOUN
ejpam-3281	336	19	,	,	PUNCT
ejpam-3281	336	20	we	we	PRON
ejpam-3281	336	21	find	find	VERB
ejpam-3281	336	22	that	that	SCONJ
ejpam-3281	336	23	|c+	|c+	NOUN
ejpam-3281	336	24	m∑	m∑	PUNCT
ejpam-3281	336	25	i=1	i=1	PROPN
ejpam-3281	336	26	di	di	PROPN
ejpam-3281	336	27	exp(αi,1x1	exp(αi,1x1	PROPN
ejpam-3281	336	28	)	)	PUNCT
ejpam-3281	336	29	...	...	PUNCT
ejpam-3281	337	1	exp(αi	exp(αi	NOUN
ejpam-3281	337	2	,	,	PUNCT
ejpam-3281	337	3	nxn)|	nxn)|	X
ejpam-3281	337	4	<	<	X
ejpam-3281	337	5	1	1	X
ejpam-3281	337	6	.	.	PUNCT
ejpam-3281	337	7	let	let	VERB
ejpam-3281	337	8	zi	zi	NOUN
ejpam-3281	337	9	=	=	PUNCT
ejpam-3281	337	10	αi,1x1	αi,1x1	PROPN
ejpam-3281	338	1	+	+	CCONJ
ejpam-3281	338	2	...	...	PUNCT
ejpam-3281	339	1	+	+	ADJ
ejpam-3281	339	2	αi	αi	NOUN
ejpam-3281	339	3	,	,	PUNCT
ejpam-3281	339	4	nxn	nxn	PROPN
ejpam-3281	339	5	;	;	PUNCT
ejpam-3281	339	6	i	i	PROPN
ejpam-3281	339	7	=	=	NOUN
ejpam-3281	339	8	1	1	NUM
ejpam-3281	339	9	,	,	PUNCT
ejpam-3281	339	10	2	2	NUM
ejpam-3281	339	11	,	,	PUNCT
ejpam-3281	339	12	..	..	PUNCT
ejpam-3281	339	13	,	,	PUNCT
ejpam-3281	339	14	m.	m.	NOUN
ejpam-3281	339	15	using	use	VERB
ejpam-3281	339	16	the	the	DET
ejpam-3281	339	17	universal	universal	ADJ
ejpam-3281	339	18	property	property	NOUN
ejpam-3281	339	19	of	of	ADP
ejpam-3281	339	20	the	the	DET
ejpam-3281	339	21	exponential	exponential	ADJ
ejpam-3281	339	22	function	function	NOUN
ejpam-3281	339	23	,	,	PUNCT
ejpam-3281	339	24	we	we	PRON
ejpam-3281	339	25	find	find	VERB
ejpam-3281	339	26	that	that	SCONJ
ejpam-3281	339	27	|c+	|c+	NOUN
ejpam-3281	339	28	d1	d1	PROPN
ejpam-3281	339	29	exp(z1	exp(z1	NOUN
ejpam-3281	339	30	)	)	PUNCT
ejpam-3281	340	1	+	+	CCONJ
ejpam-3281	340	2	...	...	PUNCT
ejpam-3281	341	1	+	+	CCONJ
ejpam-3281	341	2	dm	dm	NUM
ejpam-3281	341	3	exp(zm)|	exp(zm)|	NOUN
ejpam-3281	341	4	<	<	X
ejpam-3281	341	5	1	1	NUM
ejpam-3281	341	6	.	.	PUNCT
ejpam-3281	341	7	by	by	ADP
ejpam-3281	341	8	a	a	DET
ejpam-3281	341	9	similar	similar	ADJ
ejpam-3281	341	10	fashion	fashion	NOUN
ejpam-3281	341	11	to	to	ADP
ejpam-3281	341	12	the	the	DET
ejpam-3281	341	13	two	two	NUM
ejpam-3281	341	14	variables	variable	NOUN
ejpam-3281	341	15	case	case	NOUN
ejpam-3281	341	16	,	,	PUNCT
ejpam-3281	341	17	we	we	PRON
ejpam-3281	341	18	find	find	VERB
ejpam-3281	341	19	that	that	SCONJ
ejpam-3281	341	20	|c+	|c+	NUM
ejpam-3281	341	21	d1	d1	PROPN
ejpam-3281	341	22	+	+	CCONJ
ejpam-3281	341	23	...	...	PUNCT
ejpam-3281	341	24	+	+	CCONJ
ejpam-3281	341	25	dm|	dm|	VERB
ejpam-3281	341	26	≤	≤	PROPN
ejpam-3281	341	27	p−1	p−1	PROPN
ejpam-3281	341	28	.	.	PUNCT
ejpam-3281	342	1	proof	proof	NOUN
ejpam-3281	342	2	of	of	ADP
ejpam-3281	342	3	the	the	DET
ejpam-3281	342	4	sufficient	sufficient	ADJ
ejpam-3281	342	5	condition	condition	NOUN
ejpam-3281	342	6	.	.	PUNCT
ejpam-3281	343	1	consider	consider	VERB
ejpam-3281	343	2	the	the	DET
ejpam-3281	343	3	polynomial	polynomial	ADJ
ejpam-3281	343	4	p	p	NOUN
ejpam-3281	344	1	[	[	X
ejpam-3281	344	2	x1	x1	PROPN
ejpam-3281	344	3	,	,	PUNCT
ejpam-3281	344	4	...	...	PUNCT
ejpam-3281	344	5	,	,	PUNCT
ejpam-3281	344	6	xn	xn	PROPN
ejpam-3281	344	7	,	,	PUNCT
ejpam-3281	344	8	y1	y1	NOUN
ejpam-3281	344	9	,	,	PUNCT
ejpam-3281	344	10	...	...	PUNCT
ejpam-3281	344	11	,	,	PUNCT
ejpam-3281	344	12	yn	yn	PRON
ejpam-3281	344	13	]	]	X
ejpam-3281	345	1	=	=	NOUN
ejpam-3281	345	2	c+	c+	VERB
ejpam-3281	345	3	m∑	m∑	VERB
ejpam-3281	345	4	i=1	i=1	PROPN
ejpam-3281	345	5	diy	diy	NOUN
ejpam-3281	345	6	αi,1	αi,1	PROPN
ejpam-3281	345	7	1	1	NUM
ejpam-3281	345	8	...	...	PUNCT
ejpam-3281	345	9	y	y	PROPN
ejpam-3281	345	10	αi	αi	PROPN
ejpam-3281	345	11	,	,	PUNCT
ejpam-3281	345	12	n	n	CCONJ
ejpam-3281	345	13	n	n	PROPN
ejpam-3281	345	14	+	+	NOUN
ejpam-3281	345	15	n∑	n∑	ADJ
ejpam-3281	345	16	j=1	j=1	ADJ
ejpam-3281	345	17	ejxjy	ejxjy	NOUN
ejpam-3281	345	18	βj,1	βj,1	VERB
ejpam-3281	345	19	1	1	NUM
ejpam-3281	345	20	....	....	PUNCT
ejpam-3281	345	21	y	y	PROPN
ejpam-3281	345	22	βj	βj	PROPN
ejpam-3281	345	23	,	,	PUNCT
ejpam-3281	345	24	n	n	PRON
ejpam-3281	345	25	n	n	PROPN
ejpam-3281	345	26	+	+	CCONJ
ejpam-3281	345	27	s∑	s∑	PROPN
ejpam-3281	346	1	k=1	k=1	PROPN
ejpam-3281	346	2	fkx	fkx	PROPN
ejpam-3281	346	3	γk,1	γk,1	PROPN
ejpam-3281	346	4	1	1	NUM
ejpam-3281	346	5	...	...	SYM
ejpam-3281	346	6	x	x	SYM
ejpam-3281	346	7	γk	γk	PROPN
ejpam-3281	346	8	,	,	PUNCT
ejpam-3281	346	9	n	n	CCONJ
ejpam-3281	346	10	n	n	PROPN
ejpam-3281	346	11	y	y	PROPN
ejpam-3281	346	12	γk	γk	PROPN
ejpam-3281	346	13	,	,	PUNCT
ejpam-3281	346	14	n+1	n+1	PROPN
ejpam-3281	346	15	1	1	NUM
ejpam-3281	346	16	...	...	PUNCT
ejpam-3281	346	17	y	y	PROPN
ejpam-3281	346	18	γk,2n	γk,2n	X
ejpam-3281	346	19	n	n	PROPN
ejpam-3281	346	20	;	;	PUNCT
ejpam-3281	346	21	γk,1	γk,1	PROPN
ejpam-3281	346	22	+	+	CCONJ
ejpam-3281	346	23	...	...	PUNCT
ejpam-3281	346	24	+	+	NUM
ejpam-3281	346	25	γk	γk	NOUN
ejpam-3281	346	26	,	,	PUNCT
ejpam-3281	346	27	n	n	PRON
ejpam-3281	346	28	≥	≥	NOUN
ejpam-3281	346	29	2	2	NUM
ejpam-3281	346	30	,	,	PUNCT
ejpam-3281	346	31	with	with	ADP
ejpam-3281	346	32	the	the	DET
ejpam-3281	346	33	conditions	condition	NOUN
ejpam-3281	346	34	:	:	PUNCT
ejpam-3281	346	35	1	1	X
ejpam-3281	346	36	)	)	PUNCT
ejpam-3281	346	37	at	at	ADV
ejpam-3281	346	38	least	least	ADJ
ejpam-3281	346	39	one	one	NUM
ejpam-3281	346	40	of	of	ADP
ejpam-3281	346	41	the	the	DET
ejpam-3281	346	42	elements	element	NOUN
ejpam-3281	346	43	(	(	PUNCT
ejpam-3281	346	44	d1α1,1	d1α1,1	NOUN
ejpam-3281	346	45	+	+	NUM
ejpam-3281	346	46	...	...	PUNCT
ejpam-3281	346	47	+	+	NUM
ejpam-3281	346	48	dmαm,1	dmαm,1	NOUN
ejpam-3281	346	49	+	+	NUM
ejpam-3281	346	50	e1	e1	NOUN
ejpam-3281	346	51	)	)	PUNCT
ejpam-3281	346	52	,	,	PUNCT
ejpam-3281	346	53	...	...	PUNCT
ejpam-3281	346	54	,	,	PUNCT
ejpam-3281	346	55	(	(	PUNCT
ejpam-3281	346	56	d1α1,n	d1α1,n	X
ejpam-3281	346	57	+	+	NUM
ejpam-3281	346	58	...	...	PUNCT
ejpam-3281	347	1	+	+	CCONJ
ejpam-3281	347	2	dmαm	dmαm	ADJ
ejpam-3281	347	3	,	,	PUNCT
ejpam-3281	347	4	n	n	PROPN
ejpam-3281	347	5	+	+	X
ejpam-3281	347	6	en	en	X
ejpam-3281	347	7	)	)	PUNCT
ejpam-3281	347	8	is	be	AUX
ejpam-3281	347	9	relatively	relatively	ADV
ejpam-3281	347	10	prime	prime	ADJ
ejpam-3281	347	11	to	to	ADP
ejpam-3281	347	12	p	p	PRON
ejpam-3281	347	13	,	,	PUNCT
ejpam-3281	347	14	2	2	NUM
ejpam-3281	347	15	)	)	PUNCT
ejpam-3281	347	16	|c+	|c+	NOUN
ejpam-3281	347	17	d1	d1	PROPN
ejpam-3281	347	18	+	+	CCONJ
ejpam-3281	347	19	...	...	PUNCT
ejpam-3281	347	20	+	+	CCONJ
ejpam-3281	347	21	dm|	dm|	VERB
ejpam-3281	347	22	≤	≤	PROPN
ejpam-3281	347	23	p−1	p−1	PROPN
ejpam-3281	347	24	.	.	PUNCT
ejpam-3281	348	1	consider	consider	VERB
ejpam-3281	348	2	the	the	DET
ejpam-3281	348	3	ring	ring	NOUN
ejpam-3281	348	4	of	of	ADP
ejpam-3281	348	5	the	the	DET
ejpam-3281	348	6	formal	formal	ADJ
ejpam-3281	348	7	power	power	NOUN
ejpam-3281	348	8	series	series	PROPN
ejpam-3281	348	9	cp[[x1	cp[[x1	PROPN
ejpam-3281	348	10	,	,	PUNCT
ejpam-3281	348	11	...	...	PUNCT
ejpam-3281	348	12	,	,	PUNCT
ejpam-3281	348	13	xn	xn	PROPN
ejpam-3281	348	14	]	]	X
ejpam-3281	348	15	]	]	PUNCT
ejpam-3281	348	16	.	.	PUNCT
ejpam-3281	349	1	let	let	VERB
ejpam-3281	349	2	f	f	PROPN
ejpam-3281	349	3	∈	∈	PROPN
ejpam-3281	349	4	cp[[x1	cp[[x1	PROPN
ejpam-3281	349	5	,	,	PUNCT
ejpam-3281	349	6	...	...	PUNCT
ejpam-3281	349	7	,	,	PUNCT
ejpam-3281	349	8	xn	xn	PROPN
ejpam-3281	349	9	]	]	X
ejpam-3281	349	10	]	]	PUNCT
ejpam-3281	349	11	be	be	AUX
ejpam-3281	349	12	an	an	DET
ejpam-3281	349	13	element	element	NOUN
ejpam-3281	349	14	defined	define	VERB
ejpam-3281	349	15	by	by	ADP
ejpam-3281	349	16	the	the	DET
ejpam-3281	349	17	relation	relation	NOUN
ejpam-3281	349	18	f(x1	f(x1	NOUN
ejpam-3281	349	19	,	,	PUNCT
ejpam-3281	349	20	...	...	PUNCT
ejpam-3281	349	21	,	,	PUNCT
ejpam-3281	349	22	xn	xn	X
ejpam-3281	349	23	)	)	PUNCT
ejpam-3281	350	1	=	=	PUNCT
ejpam-3281	350	2	p	p	X
ejpam-3281	351	1	[	[	X
ejpam-3281	351	2	x1	x1	PROPN
ejpam-3281	351	3	,	,	PUNCT
ejpam-3281	351	4	...	...	PUNCT
ejpam-3281	351	5	,	,	PUNCT
ejpam-3281	351	6	xn	xn	PROPN
ejpam-3281	351	7	,	,	PUNCT
ejpam-3281	351	8	exp(x1	exp(x1	ADJ
ejpam-3281	351	9	)	)	PUNCT
ejpam-3281	351	10	,	,	PUNCT
ejpam-3281	351	11	..	..	PUNCT
ejpam-3281	351	12	,	,	PUNCT
ejpam-3281	351	13	exp(xn	exp(xn	NOUN
ejpam-3281	351	14	)	)	PUNCT
ejpam-3281	351	15	]	]	PUNCT
ejpam-3281	351	16	.	.	PUNCT
ejpam-3281	352	1	then	then	ADV
ejpam-3281	352	2	,	,	PUNCT
ejpam-3281	352	3	p	p	X
ejpam-3281	353	1	[	[	X
ejpam-3281	353	2	x1	x1	PROPN
ejpam-3281	353	3	,	,	PUNCT
ejpam-3281	353	4	...	...	PUNCT
ejpam-3281	353	5	,	,	PUNCT
ejpam-3281	353	6	xn	xn	PROPN
ejpam-3281	353	7	,	,	PUNCT
ejpam-3281	353	8	y1	y1	NOUN
ejpam-3281	353	9	,	,	PUNCT
ejpam-3281	353	10	...	...	PUNCT
ejpam-3281	353	11	,	,	PUNCT
ejpam-3281	353	12	yn	yn	PRON
ejpam-3281	353	13	]	]	PUNCT
ejpam-3281	353	14	has	have	VERB
ejpam-3281	353	15	a	a	DET
ejpam-3281	353	16	root	root	NOUN
ejpam-3281	353	17	of	of	ADP
ejpam-3281	353	18	the	the	DET
ejpam-3281	353	19	form	form	NOUN
ejpam-3281	353	20	(	(	PUNCT
ejpam-3281	353	21	x̄	x̄	NOUN
ejpam-3281	353	22	,	,	PUNCT
ejpam-3281	353	23	exp(x̄	exp(x̄	PRON
ejpam-3281	353	24	)	)	PUNCT
ejpam-3281	353	25	)	)	PUNCT
ejpam-3281	354	1	if	if	SCONJ
ejpam-3281	354	2	and	and	CCONJ
ejpam-3281	354	3	only	only	ADV
ejpam-3281	354	4	if	if	SCONJ
ejpam-3281	354	5	(	(	PUNCT
ejpam-3281	354	6	x1	x1	PROPN
ejpam-3281	354	7	,	,	PUNCT
ejpam-3281	354	8	..	..	PUNCT
ejpam-3281	354	9	,	,	PUNCT
ejpam-3281	354	10	xn	xn	X
ejpam-3281	354	11	)	)	PUNCT
ejpam-3281	354	12	is	be	AUX
ejpam-3281	354	13	a	a	DET
ejpam-3281	354	14	root	root	NOUN
ejpam-3281	354	15	of	of	ADP
ejpam-3281	354	16	f.	f.	PROPN
ejpam-3281	354	17	it	it	PRON
ejpam-3281	354	18	is	be	AUX
ejpam-3281	354	19	clear	clear	ADJ
ejpam-3281	354	20	that	that	SCONJ
ejpam-3281	354	21	f	f	PROPN
ejpam-3281	354	22	is	be	AUX
ejpam-3281	354	23	convergent	convergent	ADJ
ejpam-3281	354	24	on	on	ADP
ejpam-3281	354	25	the	the	DET
ejpam-3281	354	26	ball	ball	NOUN
ejpam-3281	354	27	b(0	b(0	PROPN
ejpam-3281	354	28	,	,	PUNCT
ejpam-3281	354	29	ρ	ρ	NOUN
ejpam-3281	354	30	)	)	PUNCT
ejpam-3281	354	31	for	for	ADP
ejpam-3281	354	32	every	every	DET
ejpam-3281	354	33	ρ	ρ	NOUN
ejpam-3281	354	34	<	<	X
ejpam-3281	354	35	p	p	X
ejpam-3281	354	36	−1	−1	NOUN
ejpam-3281	354	37	p−1	p−1	PROPN
ejpam-3281	354	38	.	.	PUNCT
ejpam-3281	355	1	applying	apply	VERB
ejpam-3281	355	2	the	the	DET
ejpam-3281	355	3	same	same	ADJ
ejpam-3281	355	4	argument	argument	NOUN
ejpam-3281	355	5	in	in	ADP
ejpam-3281	355	6	the	the	DET
ejpam-3281	355	7	proof	proof	NOUN
ejpam-3281	355	8	of	of	ADP
ejpam-3281	355	9	theorem	theorem	NOUN
ejpam-3281	355	10	3	3	NUM
ejpam-3281	355	11	,	,	PUNCT
ejpam-3281	355	12	we	we	PRON
ejpam-3281	355	13	find	find	VERB
ejpam-3281	355	14	that	that	SCONJ
ejpam-3281	355	15	p	p	NOUN
ejpam-3281	355	16	has	have	VERB
ejpam-3281	355	17	a	a	DET
ejpam-3281	355	18	root	root	NOUN
ejpam-3281	355	19	of	of	ADP
ejpam-3281	355	20	the	the	DET
ejpam-3281	355	21	form	form	NOUN
ejpam-3281	355	22	(	(	PUNCT
ejpam-3281	355	23	x̄	x̄	NOUN
ejpam-3281	355	24	,	,	PUNCT
ejpam-3281	355	25	exp(x̄	exp(x̄	PRON
ejpam-3281	355	26	)	)	PUNCT
ejpam-3281	355	27	)	)	PUNCT
ejpam-3281	355	28	.	.	PUNCT
ejpam-3281	356	1	remark	remark	NOUN
ejpam-3281	356	2	4	4	NUM
ejpam-3281	356	3	.	.	PUNCT
ejpam-3281	357	1	as	as	ADP
ejpam-3281	357	2	in	in	ADP
ejpam-3281	357	3	the	the	DET
ejpam-3281	357	4	two	two	NUM
ejpam-3281	357	5	variables	variable	NOUN
ejpam-3281	357	6	case	case	NOUN
ejpam-3281	357	7	,	,	PUNCT
ejpam-3281	357	8	the	the	DET
ejpam-3281	357	9	polynomial	polynomial	NOUN
ejpam-3281	357	10	over	over	ADP
ejpam-3281	357	11	z	z	PROPN
ejpam-3281	357	12	p	p	X
ejpam-3281	358	1	[	[	X
ejpam-3281	358	2	x1	x1	PROPN
ejpam-3281	358	3	,	,	PUNCT
ejpam-3281	358	4	...	...	PUNCT
ejpam-3281	358	5	,	,	PUNCT
ejpam-3281	358	6	xn	xn	PROPN
ejpam-3281	358	7	,	,	PUNCT
ejpam-3281	358	8	y1	y1	NOUN
ejpam-3281	358	9	,	,	PUNCT
ejpam-3281	358	10	...	...	PUNCT
ejpam-3281	358	11	,	,	PUNCT
ejpam-3281	358	12	yn	yn	PRON
ejpam-3281	358	13	]	]	X
ejpam-3281	358	14	=	=	PUNCT
ejpam-3281	358	15	c+	c+	VERB
ejpam-3281	358	16	m∑	m∑	VERB
ejpam-3281	358	17	i=1	i=1	PROPN
ejpam-3281	358	18	diy	diy	NOUN
ejpam-3281	358	19	αi,1	αi,1	PROPN
ejpam-3281	358	20	1	1	NUM
ejpam-3281	358	21	...	...	PUNCT
ejpam-3281	358	22	y	y	PROPN
ejpam-3281	358	23	αi	αi	PROPN
ejpam-3281	358	24	,	,	PUNCT
ejpam-3281	358	25	n	n	PRON
ejpam-3281	358	26	n	n	PROPN
ejpam-3281	358	27	+	+	CCONJ
ejpam-3281	358	28	s∑	s∑	PROPN
ejpam-3281	358	29	k=1	k=1	PROPN
ejpam-3281	358	30	fkx	fkx	PROPN
ejpam-3281	358	31	ξk,1	ξk,1	PROPN
ejpam-3281	358	32	1	1	NUM
ejpam-3281	358	33	...	...	PUNCT
ejpam-3281	358	34	x	x	X
ejpam-3281	359	1	ξk	ξk	ADP
ejpam-3281	359	2	,	,	PUNCT
ejpam-3281	359	3	n	n	PROPN
ejpam-3281	359	4	n	n	PROPN
ejpam-3281	359	5	y	y	PROPN
ejpam-3281	359	6	ξk	ξk	PROPN
ejpam-3281	359	7	,	,	PUNCT
ejpam-3281	359	8	n+1	n+1	PROPN
ejpam-3281	359	9	1	1	NUM
ejpam-3281	359	10	...	...	PUNCT
ejpam-3281	359	11	y	y	PROPN
ejpam-3281	359	12	ξk,2n	ξk,2n	PROPN
ejpam-3281	359	13	n	n	PROPN
ejpam-3281	359	14	;	;	PUNCT
ejpam-3281	359	15	ξk,1	ξk,1	NOUN
ejpam-3281	359	16	+	+	CCONJ
ejpam-3281	359	17	...	...	PUNCT
ejpam-3281	359	18	+	+	CCONJ
ejpam-3281	359	19	ξk	ξk	ADP
ejpam-3281	359	20	,	,	PUNCT
ejpam-3281	359	21	n	n	PRON
ejpam-3281	359	22	≥	≥	NOUN
ejpam-3281	359	23	1	1	NUM
ejpam-3281	359	24	,	,	PUNCT
ejpam-3281	359	25	with	with	ADP
ejpam-3281	359	26	(	(	PUNCT
ejpam-3281	359	27	c+	c+	VERB
ejpam-3281	359	28	d1	d1	PROPN
ejpam-3281	359	29	+	+	CCONJ
ejpam-3281	359	30	...	...	PUNCT
ejpam-3281	359	31	+	+	CCONJ
ejpam-3281	360	1	dm	dm	X
ejpam-3281	360	2	,	,	PUNCT
ejpam-3281	360	3	p	p	NOUN
ejpam-3281	360	4	)	)	PUNCT
ejpam-3281	360	5	=	=	SYM
ejpam-3281	360	6	1	1	NUM
ejpam-3281	360	7	has	have	VERB
ejpam-3281	360	8	no	no	DET
ejpam-3281	360	9	roots	root	NOUN
ejpam-3281	360	10	of	of	ADP
ejpam-3281	360	11	the	the	DET
ejpam-3281	360	12	form	form	NOUN
ejpam-3281	360	13	(	(	PUNCT
ejpam-3281	360	14	x̄	x̄	NOUN
ejpam-3281	360	15	,	,	PUNCT
ejpam-3281	360	16	exp(x̄	exp(x̄	PRON
ejpam-3281	360	17	)	)	PUNCT
ejpam-3281	360	18	)	)	PUNCT
ejpam-3281	360	19	.	.	PUNCT
ejpam-3281	361	1	references	reference	NOUN
ejpam-3281	361	2	1057	1057	NUM
ejpam-3281	361	3	acknowledgements	acknowledgement	NOUN
ejpam-3281	361	4	i	i	PRON
ejpam-3281	361	5	would	would	AUX
ejpam-3281	361	6	like	like	VERB
ejpam-3281	361	7	to	to	PART
ejpam-3281	361	8	thank	thank	VERB
ejpam-3281	361	9	the	the	DET
ejpam-3281	361	10	referees	referee	NOUN
ejpam-3281	361	11	for	for	ADP
ejpam-3281	361	12	their	their	PRON
ejpam-3281	361	13	constructive	constructive	ADJ
ejpam-3281	361	14	comments	comment	NOUN
ejpam-3281	361	15	.	.	PUNCT
ejpam-3281	362	1	also	also	ADV
ejpam-3281	362	2	,	,	PUNCT
ejpam-3281	362	3	i	i	PRON
ejpam-3281	362	4	would	would	AUX
ejpam-3281	362	5	like	like	VERB
ejpam-3281	362	6	to	to	PART
ejpam-3281	362	7	thank	thank	VERB
ejpam-3281	362	8	ali	ali	PROPN
ejpam-3281	362	9	bleybel	bleybel	PROPN
ejpam-3281	362	10	for	for	ADP
ejpam-3281	362	11	proposing	propose	VERB
ejpam-3281	362	12	this	this	DET
ejpam-3281	362	13	subject	subject	NOUN
ejpam-3281	362	14	,	,	PUNCT
ejpam-3281	362	15	as	as	ADV
ejpam-3281	362	16	well	well	ADV
ejpam-3281	362	17	as	as	ADP
ejpam-3281	362	18	his	his	PRON
ejpam-3281	362	19	constant	constant	ADJ
ejpam-3281	362	20	help	help	NOUN
ejpam-3281	362	21	and	and	CCONJ
ejpam-3281	362	22	support	support	NOUN
ejpam-3281	362	23	throughout	throughout	ADP
ejpam-3281	362	24	the	the	DET
ejpam-3281	362	25	preparation	preparation	NOUN
ejpam-3281	362	26	of	of	ADP
ejpam-3281	362	27	this	this	DET
ejpam-3281	362	28	paper	paper	NOUN
ejpam-3281	362	29	.	.	PUNCT
ejpam-3281	363	1	references	reference	NOUN
ejpam-3281	363	2	[	[	X
ejpam-3281	363	3	1	1	X
ejpam-3281	363	4	]	]	PUNCT
ejpam-3281	363	5	[	[	X
ejpam-3281	363	6	ad	ad	X
ejpam-3281	363	7	]	]	X
ejpam-3281	363	8	s.	s.	PROPN
ejpam-3281	363	9	araci	araci	PROPN
ejpam-3281	363	10	,	,	PUNCT
ejpam-3281	363	11	u.	u.	PROPN
ejpam-3281	363	12	duran	duran	PROPN
ejpam-3281	363	13	and	and	CCONJ
ejpam-3281	363	14	m.	m.	NOUN
ejpam-3281	363	15	acikgoz	acikgoz	PROPN
ejpam-3281	363	16	,	,	PUNCT
ejpam-3281	363	17	(	(	PUNCT
ejpam-3281	363	18	ρ	ρ	NOUN
ejpam-3281	363	19	,	,	PUNCT
ejpam-3281	363	20	q)-volkenborn	q)-volkenborn	PUNCT
ejpam-3281	363	21	integration	integration	NOUN
ejpam-3281	363	22	,	,	PUNCT
ejpam-3281	363	23	the	the	DET
ejpam-3281	363	24	journal	journal	NOUN
ejpam-3281	363	25	of	of	ADP
ejpam-3281	363	26	number	number	NOUN
ejpam-3281	363	27	theory	theory	NOUN
ejpam-3281	363	28	,	,	PUNCT
ejpam-3281	363	29	v.171	v.171	NOUN
ejpam-3281	363	30	,	,	PUNCT
ejpam-3281	363	31	2017	2017	NUM
ejpam-3281	363	32	,	,	PUNCT
ejpam-3281	363	33	pp.1830	pp.1830	PROPN
ejpam-3281	363	34	.	.	PUNCT
ejpam-3281	364	1	[	[	X
ejpam-3281	364	2	2	2	X
ejpam-3281	364	3	]	]	X
ejpam-3281	364	4	[	[	X
ejpam-3281	364	5	bgr	bgr	X
ejpam-3281	364	6	]	]	X
ejpam-3281	364	7	s.	s.	PROPN
ejpam-3281	364	8	bosch	bosch	PROPN
ejpam-3281	364	9	,	,	PUNCT
ejpam-3281	364	10	u.	u.	NOUN
ejpam-3281	364	11	guntzer	guntzer	PROPN
ejpam-3281	364	12	,	,	PUNCT
ejpam-3281	364	13	and	and	CCONJ
ejpam-3281	364	14	r.	r.	PROPN
ejpam-3281	364	15	remmert	remmert	PROPN
ejpam-3281	364	16	,	,	PUNCT
ejpam-3281	364	17	non	non	ADJ
ejpam-3281	364	18	-	-	ADJ
ejpam-3281	364	19	archimedian	archimedian	ADJ
ejpam-3281	364	20	analysis	analysis	NOUN
ejpam-3281	364	21	,	,	PUNCT
ejpam-3281	364	22	springerverlag	springerverlag	NOUN
ejpam-3281	364	23	,	,	PUNCT
ejpam-3281	364	24	berlin	berlin	PROPN
ejpam-3281	364	25	,	,	PUNCT
ejpam-3281	364	26	1984	1984	NUM
ejpam-3281	364	27	.	.	PUNCT
ejpam-3281	365	1	[	[	X
ejpam-3281	365	2	3	3	X
ejpam-3281	365	3	]	]	X
ejpam-3281	365	4	[	[	X
ejpam-3281	365	5	da	da	X
ejpam-3281	365	6	]	]	X
ejpam-3281	365	7	u.	u.	PROPN
ejpam-3281	365	8	duran	duran	PROPN
ejpam-3281	365	9	,	,	PUNCT
ejpam-3281	365	10	m.	m.	NOUN
ejpam-3281	365	11	acikgoz	acikgoz	VERB
ejpam-3281	365	12	,	,	PUNCT
ejpam-3281	365	13	on	on	ADP
ejpam-3281	365	14	(	(	PUNCT
ejpam-3281	365	15	ρ	ρ	PROPN
ejpam-3281	365	16	,	,	PUNCT
ejpam-3281	365	17	q)-euler	q)-euler	NOUN
ejpam-3281	365	18	numbers	number	NOUN
ejpam-3281	365	19	and	and	CCONJ
ejpam-3281	365	20	polynomials	polynomial	NOUN
ejpam-3281	365	21	associated	associate	VERB
ejpam-3281	365	22	with	with	ADP
ejpam-3281	365	23	(	(	PUNCT
ejpam-3281	365	24	ρ	ρ	PROPN
ejpam-3281	365	25	,	,	PUNCT
ejpam-3281	365	26	q)-volkenborn	q)-volkenborn	PUNCT
ejpam-3281	365	27	integrals	integral	NOUN
ejpam-3281	365	28	,	,	PUNCT
ejpam-3281	365	29	international	international	ADJ
ejpam-3281	365	30	journal	journal	NOUN
ejpam-3281	365	31	of	of	ADP
ejpam-3281	365	32	number	number	NOUN
ejpam-3281	365	33	theory	theory	NOUN
ejpam-3281	365	34	,	,	PUNCT
ejpam-3281	365	35	14	14	NUM
ejpam-3281	365	36	(	(	PUNCT
ejpam-3281	365	37	1	1	NUM
ejpam-3281	365	38	)	)	PUNCT
ejpam-3281	365	39	,	,	PUNCT
ejpam-3281	365	40	2018	2018	NUM
ejpam-3281	365	41	,	,	PUNCT
ejpam-3281	365	42	241	241	NUM
ejpam-3281	365	43	-	-	SYM
ejpam-3281	365	44	253	253	NUM
ejpam-3281	365	45	.	.	PUNCT
ejpam-3281	366	1	https://doi.org/10.1142/s179304211850015x	https://doi.org/10.1142/s179304211850015x	INTJ
ejpam-3281	366	2	.	.	PUNCT
ejpam-3281	367	1	[	[	X
ejpam-3281	367	2	4	4	X
ejpam-3281	367	3	]	]	X
ejpam-3281	367	4	[	[	X
ejpam-3281	367	5	g	g	X
ejpam-3281	367	6	]	]	X
ejpam-3281	367	7	f.	f.	PROPN
ejpam-3281	367	8	q.	q.	PROPN
ejpam-3281	367	9	gouvea	gouvea	PROPN
ejpam-3281	367	10	,	,	PUNCT
ejpam-3281	367	11	p	p	ADJ
ejpam-3281	367	12	-	-	PUNCT
ejpam-3281	367	13	adic	adic	ADJ
ejpam-3281	367	14	numbers	number	NOUN
ejpam-3281	367	15	,	,	PUNCT
ejpam-3281	367	16	2nd	2nd	ADJ
ejpam-3281	367	17	edition	edition	NOUN
ejpam-3281	367	18	,	,	PUNCT
ejpam-3281	367	19	springer	springer	NOUN
ejpam-3281	367	20	,	,	PUNCT
ejpam-3281	367	21	new	new	PROPN
ejpam-3281	367	22	york	york	PROPN
ejpam-3281	367	23	,	,	PUNCT
ejpam-3281	367	24	2003	2003	NUM
ejpam-3281	367	25	.	.	PUNCT
ejpam-3281	368	1	[	[	X
ejpam-3281	368	2	5	5	X
ejpam-3281	368	3	]	]	PUNCT
ejpam-3281	368	4	[	[	X
ejpam-3281	368	5	k	k	X
ejpam-3281	368	6	]	]	X
ejpam-3281	368	7	j.	j.	PROPN
ejpam-3281	368	8	kirby	kirby	PROPN
ejpam-3281	368	9	,	,	PUNCT
ejpam-3281	368	10	exponential	exponential	ADJ
ejpam-3281	368	11	algebraicity	algebraicity	NOUN
ejpam-3281	368	12	in	in	ADP
ejpam-3281	368	13	exponential	exponential	ADJ
ejpam-3281	368	14	fields	field	NOUN
ejpam-3281	368	15	,	,	PUNCT
ejpam-3281	368	16	bull	bull	NOUN
ejpam-3281	368	17	.	.	PUNCT
ejpam-3281	369	1	lond	lond	PROPN
ejpam-3281	369	2	.	.	PUNCT
ejpam-3281	370	1	math	math	NOUN
ejpam-3281	370	2	.	.	PUNCT
ejpam-3281	371	1	soc	soc	PROPN
ejpam-3281	371	2	.	.	PUNCT
ejpam-3281	372	1	42:5(2010	42:5(2010	NOUN
ejpam-3281	372	2	)	)	PUNCT
ejpam-3281	372	3	,	,	PUNCT
ejpam-3281	372	4	879890	879890	NUM
ejpam-3281	372	5	.	.	PUNCT
ejpam-3281	373	1	mr	mr	PROPN
ejpam-3281	373	2	2011k:03070	2011k:03070	PROPN
ejpam-3281	373	3	zbl	zbl	PROPN
ejpam-3281	373	4	1203.03050	1203.03050	PROPN
ejpam-3281	373	5	.	.	PUNCT
ejpam-3281	374	1	[	[	X
ejpam-3281	374	2	6	6	NUM
ejpam-3281	374	3	]	]	PUNCT
ejpam-3281	374	4	[	[	X
ejpam-3281	374	5	n	n	X
ejpam-3281	374	6	]	]	X
ejpam-3281	374	7	yu	yu	PROPN
ejpam-3281	374	8	.	.	PROPN
ejpam-3281	375	1	v.	v.	ADP
ejpam-3281	375	2	nesterenko	nesterenko	ADJ
ejpam-3281	375	3	,	,	PUNCT
ejpam-3281	375	4	algebraic	algebraic	ADJ
ejpam-3281	375	5	independence	independence	NOUN
ejpam-3281	375	6	of	of	ADP
ejpam-3281	375	7	p	p	NOUN
ejpam-3281	375	8	-	-	PUNCT
ejpam-3281	375	9	adic	adic	ADJ
ejpam-3281	375	10	numbers	number	NOUN
ejpam-3281	375	11	,	,	PUNCT
ejpam-3281	375	12	izvestiya	izvestiya	NOUN
ejpam-3281	375	13	:	:	PUNCT
ejpam-3281	375	14	mathematics	mathematic	NOUN
ejpam-3281	375	15	72:3	72:3	NUM
ejpam-3281	375	16	565	565	NUM
ejpam-3281	375	17	-	-	SYM
ejpam-3281	375	18	579	579	NUM
ejpam-3281	375	19	(	(	PUNCT
ejpam-3281	375	20	2008	2008	NUM
ejpam-3281	375	21	)	)	PUNCT
ejpam-3281	375	22	.	.	PUNCT
ejpam-3281	376	1	[	[	X
ejpam-3281	376	2	7	7	X
ejpam-3281	376	3	]	]	X
ejpam-3281	376	4	[	[	X
ejpam-3281	376	5	p	p	X
ejpam-3281	376	6	]	]	X
ejpam-3281	376	7	a.j.van	a.j.van	NOUN
ejpam-3281	376	8	der	der	NOUN
ejpam-3281	376	9	poorten	poorten	VERB
ejpam-3281	376	10	,	,	PUNCT
ejpam-3281	376	11	zeros	zero	NOUN
ejpam-3281	376	12	of	of	ADP
ejpam-3281	376	13	p	p	NOUN
ejpam-3281	376	14	-	-	PUNCT
ejpam-3281	376	15	adic	adic	ADJ
ejpam-3281	376	16	exponential	exponential	ADJ
ejpam-3281	376	17	polynomials	polynomial	NOUN
ejpam-3281	376	18	i	i	PRON
ejpam-3281	376	19	,	,	PUNCT
ejpam-3281	376	20	school	school	NOUN
ejpam-3281	376	21	of	of	ADP
ejpam-3281	376	22	mathematics	mathematics	PROPN
ejpam-3281	376	23	the	the	DET
ejpam-3281	376	24	university	university	PROPN
ejpam-3281	376	25	of	of	ADP
ejpam-3281	376	26	nsw	nsw	PROPN
ejpam-3281	376	27	kensington	kensington	PROPN
ejpam-3281	376	28	,	,	PUNCT
ejpam-3281	376	29	nsw	nsw	PROPN
ejpam-3281	376	30	2033	2033	NUM
ejpam-3281	376	31	,	,	PUNCT
ejpam-3281	376	32	australia	australia	PROPN
ejpam-3281	376	33	,	,	PUNCT
ejpam-3281	376	34	1975	1975	NUM
ejpam-3281	376	35	.	.	PUNCT
ejpam-3281	377	1	[	[	X
ejpam-3281	377	2	8	8	X
ejpam-3281	377	3	]	]	X
ejpam-3281	377	4	[	[	X
ejpam-3281	377	5	pr	pr	X
ejpam-3281	377	6	]	]	X
ejpam-3281	377	7	a.j.van	a.j.van	NOUN
ejpam-3281	377	8	der	der	NOUN
ejpam-3281	377	9	poorten	poorten	VERB
ejpam-3281	377	10	and	and	CCONJ
ejpam-3281	377	11	roberts	roberts	PROPN
ejpam-3281	377	12	rumely	rumely	ADV
ejpam-3281	377	13	,	,	PUNCT
ejpam-3281	377	14	zeros	zero	NOUN
ejpam-3281	377	15	of	of	ADP
ejpam-3281	377	16	p	p	NOUN
ejpam-3281	377	17	-	-	PUNCT
ejpam-3281	377	18	adic	adic	ADJ
ejpam-3281	377	19	exponential	exponential	ADJ
ejpam-3281	377	20	polynomials	polynomial	NOUN
ejpam-3281	377	21	ii	ii	NOUN
ejpam-3281	377	22	.j.london	.j.london	PUNCT
ejpam-3281	378	1	math.soc.(2)36(1987)1	math.soc.(2)36(1987)1	NOUN
ejpam-3281	378	2	-	-	PUNCT
ejpam-3281	378	3	15	15	NUM
ejpam-3281	378	4	.	.	PUNCT
ejpam-3281	379	1	[	[	X
ejpam-3281	379	2	9	9	X
ejpam-3281	379	3	]	]	X
ejpam-3281	379	4	[	[	X
ejpam-3281	379	5	r	r	X
ejpam-3281	379	6	]	]	X
ejpam-3281	379	7	a.	a.	NOUN
ejpam-3281	379	8	robert	robert	PROPN
ejpam-3281	379	9	,	,	PUNCT
ejpam-3281	379	10	a	a	DET
ejpam-3281	379	11	course	course	NOUN
ejpam-3281	379	12	in	in	ADP
ejpam-3281	379	13	p	p	ADJ
ejpam-3281	379	14	-	-	PUNCT
ejpam-3281	379	15	adic	adic	ADJ
ejpam-3281	379	16	analysis	analysis	NOUN
ejpam-3281	379	17	,	,	PUNCT
ejpam-3281	379	18	graduate	graduate	NOUN
ejpam-3281	379	19	texts	text	NOUN
ejpam-3281	379	20	in	in	ADP
ejpam-3281	379	21	mathematics	mathematics	PROPN
ejpam-3281	379	22	198	198	NUM
ejpam-3281	379	23	,	,	PUNCT
ejpam-3281	379	24	springer	springer	NOUN
ejpam-3281	379	25	-	-	PUNCT
ejpam-3281	379	26	verlag	verlag	PROPN
ejpam-3281	379	27	2000	2000	NUM
ejpam-3281	379	28	.	.	PUNCT
ejpam-3281	380	1	[	[	X
ejpam-3281	380	2	10	10	NUM
ejpam-3281	380	3	]	]	X
ejpam-3281	380	4	[	[	X
ejpam-3281	380	5	s	s	X
ejpam-3281	380	6	]	]	X
ejpam-3281	380	7	h.schoutens	h.schouten	NOUN
ejpam-3281	380	8	,	,	PUNCT
ejpam-3281	380	9	an	an	DET
ejpam-3281	380	10	introduction	introduction	NOUN
ejpam-3281	380	11	to	to	ADP
ejpam-3281	380	12	rigid	rigid	ADJ
ejpam-3281	380	13	analytic	analytic	ADJ
ejpam-3281	380	14	geometry	geometry	NOUN
ejpam-3281	380	15	,	,	PUNCT
ejpam-3281	380	16	ohio	ohio	PROPN
ejpam-3281	380	17	state	state	PROPN
ejpam-3281	380	18	university	university	PROPN
ejpam-3281	380	19	,	,	PUNCT
ejpam-3281	380	20	june	june	PROPN
ejpam-3281	380	21	2002	2002	NUM
ejpam-3281	380	22	,	,	PUNCT
ejpam-3281	380	23	lecture	lecture	NOUN
ejpam-3281	380	24	notes	note	NOUN
ejpam-3281	380	25	,	,	PUNCT
ejpam-3281	380	26	available	available	ADJ
ejpam-3281	380	27	at	at	ADP
ejpam-3281	380	28	websupport1.citytech.cuny.edu/faculty/hschoutens/pdf/rag	websupport1.citytech.cuny.edu/faculty/hschoutens/pdf/rag	NOUN
ejpam-3281	380	29	lecture	lecture	PROPN
ejpam-3281	380	30	notes.pdf	notes.pdf	PROPN
ejpam-3281	380	31	.	.	PUNCT