id	sid	tid	token	lemma	pos
ejpam-5996	1	1	european	european	PROPN
ejpam-5996	1	2	journal	journal	PROPN
ejpam-5996	1	3	of	of	ADP
ejpam-5996	1	4	pure	pure	ADJ
ejpam-5996	1	5	and	and	CCONJ
ejpam-5996	1	6	applied	applied	ADJ
ejpam-5996	1	7	mathematics	mathematic	NOUN
ejpam-5996	1	8	2025	2025	NUM
ejpam-5996	1	9	,	,	PUNCT
ejpam-5996	1	10	vol	vol	NOUN
ejpam-5996	1	11	.	.	PROPN
ejpam-5996	1	12	18	18	NUM
ejpam-5996	1	13	,	,	PUNCT
ejpam-5996	1	14	issue	issue	NOUN
ejpam-5996	1	15	2	2	NUM
ejpam-5996	1	16	,	,	PUNCT
ejpam-5996	1	17	article	article	NOUN
ejpam-5996	1	18	number	number	NOUN
ejpam-5996	1	19	5996	5996	NUM
ejpam-5996	1	20	issn	issn	PROPN
ejpam-5996	1	21	1307	1307	NUM
ejpam-5996	1	22	-	-	SYM
ejpam-5996	1	23	5543	5543	NUM
ejpam-5996	1	24	–	–	PUNCT
ejpam-5996	1	25	ejpam.com	ejpam.com	X
ejpam-5996	1	26	published	publish	VERB
ejpam-5996	1	27	by	by	ADP
ejpam-5996	1	28	new	new	PROPN
ejpam-5996	1	29	york	york	PROPN
ejpam-5996	1	30	business	business	NOUN
ejpam-5996	1	31	global	global	ADJ
ejpam-5996	1	32	some	some	DET
ejpam-5996	1	33	irreducible	irreducible	ADJ
ejpam-5996	1	34	polynomials	polynomial	NOUN
ejpam-5996	1	35	over	over	ADP
ejpam-5996	1	36	a	a	DET
ejpam-5996	1	37	finite	finite	ADJ
ejpam-5996	1	38	field	field	NOUN
ejpam-5996	1	39	amara	amara	PROPN
ejpam-5996	1	40	chandoul1,∗	chandoul1,∗	NOUN
ejpam-5996	1	41	,	,	PUNCT
ejpam-5996	1	42	abdallah	abdallah	PROPN
ejpam-5996	1	43	assiry2	assiry2	PROPN
ejpam-5996	1	44	1{department	1{department	NOUN
ejpam-5996	1	45	of	of	ADP
ejpam-5996	1	46	mathematics	mathematic	NOUN
ejpam-5996	1	47	,	,	PUNCT
ejpam-5996	1	48	higher	high	ADJ
ejpam-5996	1	49	institute	institute	PROPN
ejpam-5996	1	50	of	of	ADP
ejpam-5996	1	51	informatics	informatic	NOUN
ejpam-5996	1	52	and	and	CCONJ
ejpam-5996	1	53	multimedia	multimedia	NOUN
ejpam-5996	1	54	of	of	ADP
ejpam-5996	1	55	sfax	sfax	NOUN
ejpam-5996	1	56	(	(	PUNCT
ejpam-5996	1	57	isims	isim	NOUN
ejpam-5996	1	58	)	)	PUNCT
ejpam-5996	1	59	,	,	PUNCT
ejpam-5996	1	60	sfax	sfax	PROPN
ejpam-5996	1	61	university	university	NOUN
ejpam-5996	1	62	,	,	PUNCT
ejpam-5996	1	63	sfax	sfax	NOUN
ejpam-5996	1	64	,	,	PUNCT
ejpam-5996	1	65	tunisia	tunisia	NOUN
ejpam-5996	1	66	2	2	NUM
ejpam-5996	1	67	departement	departement	NOUN
ejpam-5996	1	68	of	of	ADP
ejpam-5996	1	69	mathematics	mathematic	NOUN
ejpam-5996	1	70	,	,	PUNCT
ejpam-5996	1	71	college	college	NOUN
ejpam-5996	1	72	of	of	ADP
ejpam-5996	1	73	science	science	NOUN
ejpam-5996	1	74	,	,	PUNCT
ejpam-5996	1	75	umm	umm	INTJ
ejpam-5996	1	76	al	al	PROPN
ejpam-5996	1	77	-	-	PUNCT
ejpam-5996	1	78	qura	qura	PROPN
ejpam-5996	1	79	university	university	NOUN
ejpam-5996	1	80	.	.	PUNCT
ejpam-5996	2	1	mecca	mecca	PROPN
ejpam-5996	2	2	21955	21955	NUM
ejpam-5996	2	3	,	,	PUNCT
ejpam-5996	2	4	saudi	saudi	PROPN
ejpam-5996	2	5	arabia	arabia	PROPN
ejpam-5996	2	6	abstract	abstract	NOUN
ejpam-5996	2	7	.	.	PUNCT
ejpam-5996	3	1	the	the	DET
ejpam-5996	3	2	irreducibility	irreducibility	NOUN
ejpam-5996	3	3	of	of	ADP
ejpam-5996	3	4	a	a	DET
ejpam-5996	3	5	polynomial	polynomial	NOUN
ejpam-5996	3	6	over	over	ADP
ejpam-5996	3	7	a	a	DET
ejpam-5996	3	8	finite	finite	ADJ
ejpam-5996	3	9	field	field	NOUN
ejpam-5996	3	10	refers	refer	VERB
ejpam-5996	3	11	to	to	ADP
ejpam-5996	3	12	whether	whether	SCONJ
ejpam-5996	3	13	the	the	DET
ejpam-5996	3	14	polynomial	polynomial	ADJ
ejpam-5996	3	15	,	,	PUNCT
ejpam-5996	3	16	with	with	ADP
ejpam-5996	3	17	coefficients	coefficient	NOUN
ejpam-5996	3	18	in	in	ADP
ejpam-5996	3	19	that	that	DET
ejpam-5996	3	20	field	field	NOUN
ejpam-5996	3	21	,	,	PUNCT
ejpam-5996	3	22	can	can	AUX
ejpam-5996	3	23	not	not	PART
ejpam-5996	3	24	be	be	AUX
ejpam-5996	3	25	factored	factor	VERB
ejpam-5996	3	26	into	into	ADP
ejpam-5996	3	27	nontrivial	nontrivial	ADJ
ejpam-5996	3	28	polynomials	polynomial	NOUN
ejpam-5996	3	29	.	.	PUNCT
ejpam-5996	4	1	it	it	PRON
ejpam-5996	4	2	is	be	AUX
ejpam-5996	4	3	surprising	surprising	ADJ
ejpam-5996	4	4	to	to	PART
ejpam-5996	4	5	discover	discover	VERB
ejpam-5996	4	6	that	that	SCONJ
ejpam-5996	4	7	there	there	PRON
ejpam-5996	4	8	exist	exist	VERB
ejpam-5996	4	9	very	very	ADV
ejpam-5996	4	10	efficient	efficient	ADJ
ejpam-5996	4	11	but	but	CCONJ
ejpam-5996	4	12	still	still	ADV
ejpam-5996	4	13	little	little	ADV
ejpam-5996	4	14	-	-	PUNCT
ejpam-5996	4	15	known	know	VERB
ejpam-5996	4	16	divisibility	divisibility	NOUN
ejpam-5996	4	17	criteria	criterion	NOUN
ejpam-5996	4	18	.	.	PUNCT
ejpam-5996	5	1	in	in	ADP
ejpam-5996	5	2	this	this	DET
ejpam-5996	5	3	paper	paper	NOUN
ejpam-5996	5	4	,	,	PUNCT
ejpam-5996	5	5	we	we	PRON
ejpam-5996	5	6	give	give	VERB
ejpam-5996	5	7	some	some	DET
ejpam-5996	5	8	irreducibility	irreducibility	NOUN
ejpam-5996	5	9	criterions	criterion	NOUN
ejpam-5996	5	10	of	of	ADP
ejpam-5996	5	11	a	a	DET
ejpam-5996	5	12	given	give	VERB
ejpam-5996	5	13	polynomial	polynomial	NOUN
ejpam-5996	5	14	with	with	ADP
ejpam-5996	5	15	coefficients	coefficient	NOUN
ejpam-5996	5	16	in	in	ADP
ejpam-5996	5	17	fq[x	fq[x	PROPN
ejpam-5996	5	18	]	]	PUNCT
ejpam-5996	5	19	,	,	PUNCT
ejpam-5996	5	20	were	be	AUX
ejpam-5996	5	21	fq	fq	NOUN
ejpam-5996	5	22	is	be	AUX
ejpam-5996	5	23	a	a	DET
ejpam-5996	5	24	finite	finite	ADJ
ejpam-5996	5	25	field	field	NOUN
ejpam-5996	5	26	.	.	PUNCT
ejpam-5996	6	1	the	the	DET
ejpam-5996	6	2	arguments	argument	NOUN
ejpam-5996	6	3	can	can	AUX
ejpam-5996	6	4	be	be	AUX
ejpam-5996	6	5	extended	extend	VERB
ejpam-5996	6	6	to	to	PART
ejpam-5996	6	7	discuss	discuss	VERB
ejpam-5996	6	8	our	our	PRON
ejpam-5996	6	9	results	result	NOUN
ejpam-5996	6	10	,	,	PUNCT
ejpam-5996	6	11	including	include	VERB
ejpam-5996	6	12	potential	potential	ADJ
ejpam-5996	6	13	applications	application	NOUN
ejpam-5996	6	14	or	or	CCONJ
ejpam-5996	6	15	future	future	ADJ
ejpam-5996	6	16	research	research	NOUN
ejpam-5996	6	17	directions	direction	NOUN
ejpam-5996	6	18	.	.	PUNCT
ejpam-5996	7	1	2020	2020	NUM
ejpam-5996	7	2	mathematics	mathematic	NOUN
ejpam-5996	7	3	subject	subject	NOUN
ejpam-5996	7	4	classifications	classification	NOUN
ejpam-5996	7	5	:	:	PUNCT
ejpam-5996	7	6	11a05	11a05	NUM
ejpam-5996	7	7	,	,	PUNCT
ejpam-5996	7	8	11c08	11c08	NUM
ejpam-5996	7	9	,	,	PUNCT
ejpam-5996	7	10	11t06	11t06	NUM
ejpam-5996	7	11	,	,	PUNCT
ejpam-5996	7	12	11t55	11t55	NUM
ejpam-5996	7	13	,	,	PUNCT
ejpam-5996	7	14	12e05	12e05	NUM
ejpam-5996	7	15	key	key	ADJ
ejpam-5996	7	16	words	word	NOUN
ejpam-5996	7	17	and	and	CCONJ
ejpam-5996	7	18	phrases	phrase	NOUN
ejpam-5996	7	19	:	:	PUNCT
ejpam-5996	7	20	polynomial	polynomial	ADJ
ejpam-5996	7	21	,	,	PUNCT
ejpam-5996	7	22	irreducible	irreducible	ADJ
ejpam-5996	7	23	polynomial	polynomial	ADJ
ejpam-5996	7	24	,	,	PUNCT
ejpam-5996	7	25	finite	finite	ADJ
ejpam-5996	7	26	field	field	NOUN
ejpam-5996	7	27	,	,	PUNCT
ejpam-5996	7	28	divisibility	divisibility	NOUN
ejpam-5996	7	29	,	,	PUNCT
ejpam-5996	7	30	divisibility	divisibility	NOUN
ejpam-5996	7	31	criteria	criterion	NOUN
ejpam-5996	7	32	1	1	NUM
ejpam-5996	7	33	.	.	PUNCT
ejpam-5996	8	1	introduction	introduction	NOUN
ejpam-5996	8	2	finite	finite	PROPN
ejpam-5996	8	3	fields	field	NOUN
ejpam-5996	8	4	,	,	PUNCT
ejpam-5996	8	5	also	also	ADV
ejpam-5996	8	6	known	know	VERB
ejpam-5996	8	7	as	as	ADP
ejpam-5996	8	8	galois	galois	PROPN
ejpam-5996	8	9	fields	field	NOUN
ejpam-5996	8	10	,	,	PUNCT
ejpam-5996	8	11	are	be	AUX
ejpam-5996	8	12	fundamental	fundamental	ADJ
ejpam-5996	8	13	structures	structure	NOUN
ejpam-5996	8	14	in	in	ADP
ejpam-5996	8	15	mathematics	mathematic	NOUN
ejpam-5996	8	16	with	with	ADP
ejpam-5996	8	17	far	far	ADV
ejpam-5996	8	18	-	-	PUNCT
ejpam-5996	8	19	reaching	reach	VERB
ejpam-5996	8	20	applications	application	NOUN
ejpam-5996	8	21	in	in	ADP
ejpam-5996	8	22	coding	code	VERB
ejpam-5996	8	23	theory	theory	NOUN
ejpam-5996	8	24	,	,	PUNCT
ejpam-5996	8	25	cryptography	cryptography	NOUN
ejpam-5996	8	26	,	,	PUNCT
ejpam-5996	8	27	combinatorics	combinatoric	NOUN
ejpam-5996	8	28	,	,	PUNCT
ejpam-5996	8	29	and	and	CCONJ
ejpam-5996	8	30	computational	computational	ADJ
ejpam-5996	8	31	algebra	algebra	NOUN
ejpam-5996	8	32	.	.	PUNCT
ejpam-5996	9	1	at	at	ADP
ejpam-5996	9	2	the	the	DET
ejpam-5996	9	3	heart	heart	NOUN
ejpam-5996	9	4	of	of	ADP
ejpam-5996	9	5	many	many	ADJ
ejpam-5996	9	6	of	of	ADP
ejpam-5996	9	7	these	these	DET
ejpam-5996	9	8	applications	application	NOUN
ejpam-5996	9	9	lies	lie	VERB
ejpam-5996	9	10	the	the	DET
ejpam-5996	9	11	study	study	NOUN
ejpam-5996	9	12	of	of	ADP
ejpam-5996	9	13	irreducible	irreducible	ADJ
ejpam-5996	9	14	polynomials	polynomial	NOUN
ejpam-5996	9	15	over	over	ADP
ejpam-5996	9	16	finite	finite	ADJ
ejpam-5996	9	17	fields	field	NOUN
ejpam-5996	9	18	.	.	PUNCT
ejpam-5996	10	1	these	these	DET
ejpam-5996	10	2	polynomials	polynomial	NOUN
ejpam-5996	10	3	serve	serve	VERB
ejpam-5996	10	4	as	as	ADP
ejpam-5996	10	5	the	the	DET
ejpam-5996	10	6	building	building	NOUN
ejpam-5996	10	7	blocks	block	NOUN
ejpam-5996	10	8	for	for	ADP
ejpam-5996	10	9	constructing	construct	VERB
ejpam-5996	10	10	finite	finite	ADJ
ejpam-5996	10	11	field	field	NOUN
ejpam-5996	10	12	extensions	extension	NOUN
ejpam-5996	10	13	,	,	PUNCT
ejpam-5996	10	14	enabling	enable	VERB
ejpam-5996	10	15	the	the	DET
ejpam-5996	10	16	representation	representation	NOUN
ejpam-5996	10	17	and	and	CCONJ
ejpam-5996	10	18	manipulation	manipulation	NOUN
ejpam-5996	10	19	of	of	ADP
ejpam-5996	10	20	elements	element	NOUN
ejpam-5996	10	21	in	in	ADP
ejpam-5996	10	22	higher	high	ADJ
ejpam-5996	10	23	-	-	PUNCT
ejpam-5996	10	24	dimensional	dimensional	ADJ
ejpam-5996	10	25	spaces	space	NOUN
ejpam-5996	10	26	.	.	PUNCT
ejpam-5996	11	1	the	the	DET
ejpam-5996	11	2	theory	theory	NOUN
ejpam-5996	11	3	of	of	ADP
ejpam-5996	11	4	irreducible	irreducible	ADJ
ejpam-5996	11	5	polynomials	polynomial	NOUN
ejpam-5996	11	6	over	over	ADP
ejpam-5996	11	7	finite	finite	ADJ
ejpam-5996	11	8	fields	field	NOUN
ejpam-5996	11	9	is	be	AUX
ejpam-5996	11	10	both	both	CCONJ
ejpam-5996	11	11	rich	rich	ADJ
ejpam-5996	11	12	and	and	CCONJ
ejpam-5996	11	13	elegant	elegant	ADJ
ejpam-5996	11	14	,	,	PUNCT
ejpam-5996	11	15	blending	blend	VERB
ejpam-5996	11	16	algebraic	algebraic	ADJ
ejpam-5996	11	17	rigor	rigor	NOUN
ejpam-5996	11	18	with	with	ADP
ejpam-5996	11	19	practical	practical	ADJ
ejpam-5996	11	20	utility	utility	NOUN
ejpam-5996	11	21	.	.	PUNCT
ejpam-5996	12	1	from	from	ADP
ejpam-5996	12	2	the	the	DET
ejpam-5996	12	3	enumeration	enumeration	NOUN
ejpam-5996	12	4	of	of	ADP
ejpam-5996	12	5	irreducible	irreducible	ADJ
ejpam-5996	12	6	polynomials	polynomial	NOUN
ejpam-5996	12	7	to	to	ADP
ejpam-5996	12	8	the	the	DET
ejpam-5996	12	9	development	development	NOUN
ejpam-5996	12	10	of	of	ADP
ejpam-5996	12	11	efficient	efficient	ADJ
ejpam-5996	12	12	algorithms	algorithm	NOUN
ejpam-5996	12	13	for	for	ADP
ejpam-5996	12	14	their	their	PRON
ejpam-5996	12	15	construction	construction	NOUN
ejpam-5996	12	16	and	and	CCONJ
ejpam-5996	12	17	testing	testing	NOUN
ejpam-5996	12	18	,	,	PUNCT
ejpam-5996	12	19	this	this	DET
ejpam-5996	12	20	area	area	NOUN
ejpam-5996	12	21	of	of	ADP
ejpam-5996	12	22	research	research	NOUN
ejpam-5996	12	23	has	have	AUX
ejpam-5996	12	24	witnessed	witness	VERB
ejpam-5996	12	25	significant	significant	ADJ
ejpam-5996	12	26	advancements	advancement	NOUN
ejpam-5996	12	27	over	over	ADP
ejpam-5996	12	28	the	the	DET
ejpam-5996	12	29	past	past	ADJ
ejpam-5996	12	30	century	century	NOUN
ejpam-5996	12	31	.	.	PUNCT
ejpam-5996	13	1	moreover	moreover	ADV
ejpam-5996	13	2	,	,	PUNCT
ejpam-5996	13	3	the	the	DET
ejpam-5996	13	4	study	study	NOUN
ejpam-5996	13	5	of	of	ADP
ejpam-5996	13	6	specific	specific	ADJ
ejpam-5996	13	7	families	family	NOUN
ejpam-5996	13	8	of	of	ADP
ejpam-5996	13	9	irreducible	irreducible	ADJ
ejpam-5996	13	10	polynomials	polynomial	NOUN
ejpam-5996	13	11	—	—	PUNCT
ejpam-5996	13	12	such	such	ADJ
ejpam-5996	13	13	as	as	ADP
ejpam-5996	13	14	binomials	binomial	NOUN
ejpam-5996	13	15	,	,	PUNCT
ejpam-5996	13	16	trinomials	trinomial	NOUN
ejpam-5996	13	17	,	,	PUNCT
ejpam-5996	13	18	and	and	CCONJ
ejpam-5996	13	19	cyclotomic	cyclotomic	ADJ
ejpam-5996	13	20	polynomials	polynomial	NOUN
ejpam-5996	13	21	—	—	PUNCT
ejpam-5996	13	22	has	have	AUX
ejpam-5996	13	23	led	lead	VERB
ejpam-5996	13	24	to	to	ADP
ejpam-5996	13	25	deep	deep	ADJ
ejpam-5996	13	26	insights	insight	NOUN
ejpam-5996	13	27	into	into	ADP
ejpam-5996	13	28	their	their	PRON
ejpam-5996	13	29	structural	structural	ADJ
ejpam-5996	13	30	properties	property	NOUN
ejpam-5996	13	31	and	and	CCONJ
ejpam-5996	13	32	their	their	PRON
ejpam-5996	13	33	role	role	NOUN
ejpam-5996	13	34	in	in	ADP
ejpam-5996	13	35	theoretical	theoretical	ADJ
ejpam-5996	13	36	and	and	CCONJ
ejpam-5996	13	37	applied	applied	ADJ
ejpam-5996	13	38	contexts	contexts	NOUN
ejpam-5996	13	39	.	.	PUNCT
ejpam-5996	14	1	∗corresponding	∗corresponde	VERB
ejpam-5996	14	2	author	author	NOUN
ejpam-5996	14	3	.	.	PUNCT
ejpam-5996	15	1	doi	doi	NOUN
ejpam-5996	15	2	:	:	PUNCT
ejpam-5996	15	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5996	https://doi.org/10.29020/nybg.ejpam.v18i2.5996	NOUN
ejpam-5996	15	4	email	email	NOUN
ejpam-5996	15	5	addresses	address	VERB
ejpam-5996	15	6	:	:	PUNCT
ejpam-5996	15	7	amarachandoul@yahoo.fr	amarachandoul@yahoo.fr	PROPN
ejpam-5996	15	8	(	(	PUNCT
ejpam-5996	15	9	amara	amara	PROPN
ejpam-5996	15	10	chandoul	chandoul	PROPN
ejpam-5996	15	11	)	)	PUNCT
ejpam-5996	15	12	,	,	PUNCT
ejpam-5996	15	13	aaassiry@uqu.edu.sa	aaassiry@uqu.edu.sa	PROPN
ejpam-5996	15	14	(	(	PUNCT
ejpam-5996	15	15	a.	a.	NOUN
ejpam-5996	15	16	assiry	assiry	PROPN
ejpam-5996	15	17	)	)	PUNCT
ejpam-5996	15	18	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5996	15	19	1	1	NUM
ejpam-5996	15	20	copyright	copyright	NOUN
ejpam-5996	15	21	:	:	PUNCT
ejpam-5996	16	1	©	©	PROPN
ejpam-5996	16	2	2025	2025	NUM
ejpam-5996	16	3	the	the	DET
ejpam-5996	16	4	author(s	author(s	NOUN
ejpam-5996	16	5	)	)	PUNCT
ejpam-5996	16	6	.	.	PUNCT
ejpam-5996	17	1	(	(	PUNCT
ejpam-5996	17	2	cc	cc	NOUN
ejpam-5996	17	3	by	by	ADP
ejpam-5996	17	4	-	-	PUNCT
ejpam-5996	17	5	nc	nc	PROPN
ejpam-5996	17	6	4.0	4.0	NUM
ejpam-5996	17	7	)	)	PUNCT
ejpam-5996	17	8	a.	a.	NOUN
ejpam-5996	17	9	chandoul	chandoul	PROPN
ejpam-5996	17	10	,	,	PUNCT
ejpam-5996	17	11	a.	a.	NOUN
ejpam-5996	17	12	assiry	assiry	NOUN
ejpam-5996	17	13	/	/	SYM
ejpam-5996	17	14	eur	eur	PROPN
ejpam-5996	17	15	.	.	PUNCT
ejpam-5996	18	1	j.	j.	PROPN
ejpam-5996	18	2	pure	pure	PROPN
ejpam-5996	18	3	appl	appl	PROPN
ejpam-5996	18	4	.	.	PROPN
ejpam-5996	18	5	math	math	PROPN
ejpam-5996	18	6	,	,	PUNCT
ejpam-5996	18	7	18	18	NUM
ejpam-5996	18	8	(	(	PUNCT
ejpam-5996	18	9	2	2	NUM
ejpam-5996	18	10	)	)	PUNCT
ejpam-5996	18	11	(	(	PUNCT
ejpam-5996	18	12	2025	2025	NUM
ejpam-5996	18	13	)	)	PUNCT
ejpam-5996	18	14	,	,	PUNCT
ejpam-5996	18	15	5996	5996	NUM
ejpam-5996	18	16	2	2	NUM
ejpam-5996	18	17	of	of	ADP
ejpam-5996	18	18	9	9	NUM
ejpam-5996	18	19	some	some	PRON
ejpam-5996	18	20	of	of	ADP
ejpam-5996	18	21	application	application	NOUN
ejpam-5996	18	22	of	of	ADP
ejpam-5996	18	23	irreducibility	irreducibility	NOUN
ejpam-5996	18	24	is	be	AUX
ejpam-5996	18	25	to	to	PART
ejpam-5996	18	26	explore	explore	VERB
ejpam-5996	18	27	its	its	PRON
ejpam-5996	18	28	relationship	relationship	NOUN
ejpam-5996	18	29	with	with	ADP
ejpam-5996	18	30	special	special	ADJ
ejpam-5996	18	31	elements	element	NOUN
ejpam-5996	18	32	,	,	PUNCT
ejpam-5996	18	33	as	as	SCONJ
ejpam-5996	18	34	salem	salem	PROPN
ejpam-5996	18	35	formal	formal	ADJ
ejpam-5996	18	36	power	power	NOUN
ejpam-5996	18	37	series	series	NOUN
ejpam-5996	18	38	,	,	PUNCT
ejpam-5996	18	39	which	which	PRON
ejpam-5996	18	40	are	be	AUX
ejpam-5996	18	41	algebraic	algebraic	ADJ
ejpam-5996	18	42	elements	element	NOUN
ejpam-5996	18	43	(	(	PUNCT
ejpam-5996	18	44	roots	root	NOUN
ejpam-5996	18	45	of	of	ADP
ejpam-5996	18	46	monic	monic	ADJ
ejpam-5996	18	47	integer	integer	NOUN
ejpam-5996	18	48	polynomials	polynomial	NOUN
ejpam-5996	18	49	)	)	PUNCT
ejpam-5996	18	50	with	with	ADP
ejpam-5996	18	51	a	a	DET
ejpam-5996	18	52	special	special	ADJ
ejpam-5996	18	53	property	property	NOUN
ejpam-5996	18	54	:	:	PUNCT
ejpam-5996	18	55	they	they	PRON
ejpam-5996	18	56	have	have	VERB
ejpam-5996	18	57	exactly	exactly	ADV
ejpam-5996	18	58	one	one	NUM
ejpam-5996	18	59	conjugate	conjugate	NOUN
ejpam-5996	18	60	outside	outside	ADP
ejpam-5996	18	61	the	the	DET
ejpam-5996	18	62	unit	unit	NOUN
ejpam-5996	18	63	circle	circle	NOUN
ejpam-5996	18	64	and	and	CCONJ
ejpam-5996	18	65	all	all	DET
ejpam-5996	18	66	other	other	ADJ
ejpam-5996	18	67	conjugates	conjugate	NOUN
ejpam-5996	18	68	on	on	ADP
ejpam-5996	18	69	the	the	DET
ejpam-5996	18	70	unit	unit	NOUN
ejpam-5996	18	71	circle	circle	NOUN
ejpam-5996	18	72	.	.	PUNCT
ejpam-5996	19	1	the	the	DET
ejpam-5996	19	2	connection	connection	NOUN
ejpam-5996	19	3	to	to	ADP
ejpam-5996	19	4	irreducible	irreducible	ADJ
ejpam-5996	19	5	polynomials	polynomial	NOUN
ejpam-5996	19	6	arises	arise	VERB
ejpam-5996	19	7	because	because	SCONJ
ejpam-5996	19	8	salem	salem	NOUN
ejpam-5996	19	9	numbers	number	NOUN
ejpam-5996	19	10	are	be	AUX
ejpam-5996	19	11	defined	define	VERB
ejpam-5996	19	12	by	by	ADP
ejpam-5996	19	13	their	their	PRON
ejpam-5996	19	14	minimal	minimal	ADJ
ejpam-5996	19	15	polynomials	polynomial	NOUN
ejpam-5996	19	16	,	,	PUNCT
ejpam-5996	19	17	which	which	PRON
ejpam-5996	19	18	are	be	AUX
ejpam-5996	19	19	irreducible	irreducible	ADJ
ejpam-5996	19	20	[	[	X
ejpam-5996	19	21	1	1	NUM
ejpam-5996	19	22	]	]	PUNCT
ejpam-5996	19	23	.	.	PUNCT
ejpam-5996	20	1	2	2	X
ejpam-5996	20	2	.	.	X
ejpam-5996	20	3	preliminaries	preliminary	NOUN
ejpam-5996	20	4	let	let	VERB
ejpam-5996	20	5	fq	fq	PROPN
ejpam-5996	20	6	represent	represent	VERB
ejpam-5996	20	7	the	the	DET
ejpam-5996	20	8	finite	finite	ADJ
ejpam-5996	20	9	field	field	NOUN
ejpam-5996	20	10	containing	contain	VERB
ejpam-5996	20	11	q	q	NOUN
ejpam-5996	20	12	elements	element	NOUN
ejpam-5996	20	13	,	,	PUNCT
ejpam-5996	20	14	with	with	ADP
ejpam-5996	20	15	q	q	NOUN
ejpam-5996	20	16	being	be	AUX
ejpam-5996	20	17	a	a	DET
ejpam-5996	20	18	power	power	NOUN
ejpam-5996	20	19	of	of	ADP
ejpam-5996	20	20	a	a	DET
ejpam-5996	20	21	prime	prime	NOUN
ejpam-5996	20	22	.	.	PUNCT
ejpam-5996	21	1	the	the	DET
ejpam-5996	21	2	ring	ring	NOUN
ejpam-5996	21	3	of	of	ADP
ejpam-5996	21	4	polynomials	polynomial	NOUN
ejpam-5996	21	5	whose	whose	DET
ejpam-5996	21	6	coefficients	coefficient	NOUN
ejpam-5996	21	7	lie	lie	VERB
ejpam-5996	21	8	in	in	ADP
ejpam-5996	21	9	fq	fq	PROPN
ejpam-5996	21	10	is	be	AUX
ejpam-5996	21	11	denoted	denote	VERB
ejpam-5996	21	12	by	by	ADP
ejpam-5996	21	13	fq[x	fq[x	PROPN
ejpam-5996	21	14	]	]	PUNCT
ejpam-5996	21	15	,	,	PUNCT
ejpam-5996	21	16	while	while	SCONJ
ejpam-5996	21	17	fq(x	fq(x	NOUN
ejpam-5996	21	18	)	)	PUNCT
ejpam-5996	21	19	signifies	signify	VERB
ejpam-5996	21	20	the	the	DET
ejpam-5996	21	21	field	field	NOUN
ejpam-5996	21	22	of	of	ADP
ejpam-5996	21	23	rational	rational	ADJ
ejpam-5996	21	24	functions	function	NOUN
ejpam-5996	21	25	over	over	ADP
ejpam-5996	21	26	fq	fq	PROPN
ejpam-5996	21	27	.	.	PUNCT
ejpam-5996	22	1	the	the	DET
ejpam-5996	22	2	field	field	NOUN
ejpam-5996	22	3	of	of	ADP
ejpam-5996	22	4	formal	formal	ADJ
ejpam-5996	22	5	laurent	laurent	NOUN
ejpam-5996	22	6	series	series	NOUN
ejpam-5996	22	7	in	in	ADP
ejpam-5996	22	8	x−1	x−1	PROPN
ejpam-5996	22	9	over	over	ADP
ejpam-5996	22	10	fq	fq	PROPN
ejpam-5996	22	11	is	be	AUX
ejpam-5996	22	12	denoted	denote	VERB
ejpam-5996	22	13	by	by	ADP
ejpam-5996	22	14	fq((x	fq((x	NOUN
ejpam-5996	22	15	−1	−1	NOUN
ejpam-5996	22	16	)	)	PUNCT
ejpam-5996	22	17	)	)	PUNCT
ejpam-5996	22	18	and	and	CCONJ
ejpam-5996	22	19	is	be	AUX
ejpam-5996	22	20	defined	define	VERB
ejpam-5996	22	21	as	as	ADP
ejpam-5996	22	22	:	:	PUNCT
ejpam-5996	22	23	fq((x	fq((x	NOUN
ejpam-5996	22	24	−1	−1	NOUN
ejpam-5996	22	25	)	)	PUNCT
ejpam-5996	22	26	)	)	PUNCT
ejpam-5996	23	1	=	=	PRON
ejpam-5996	23	2	{	{	PUNCT
ejpam-5996	23	3	∞∑	∞∑	NUM
ejpam-5996	23	4	n	n	CCONJ
ejpam-5996	23	5	=	=	SYM
ejpam-5996	23	6	n0	n0	X
ejpam-5996	23	7	anx	anx	NOUN
ejpam-5996	23	8	−n	−n	ADJ
ejpam-5996	23	9	∣∣∣	∣∣∣	NOUN
ejpam-5996	23	10	an	an	DET
ejpam-5996	23	11	∈	∈	PROPN
ejpam-5996	23	12	fq	fq	NOUN
ejpam-5996	23	13	for	for	ADP
ejpam-5996	23	14	some	some	DET
ejpam-5996	23	15	integer	integer	NOUN
ejpam-5996	23	16	n0	n0	PROPN
ejpam-5996	23	17	}	}	PUNCT
ejpam-5996	23	18	.	.	PUNCT
ejpam-5996	24	1	for	for	ADP
ejpam-5996	24	2	an	an	DET
ejpam-5996	24	3	element	element	NOUN
ejpam-5996	24	4	w	w	NOUN
ejpam-5996	24	5	=	=	PUNCT
ejpam-5996	24	6	∑+∞	∑+∞	ADJ
ejpam-5996	24	7	n	n	CCONJ
ejpam-5996	24	8	=	=	SYM
ejpam-5996	24	9	n0	n0	X
ejpam-5996	24	10	anx	anx	ADJ
ejpam-5996	24	11	−n	−n	PROPN
ejpam-5996	24	12	∈	∈	PROPN
ejpam-5996	24	13	fq((x	fq((x	NOUN
ejpam-5996	24	14	−1	−1	NOUN
ejpam-5996	24	15	)	)	PUNCT
ejpam-5996	24	16	)	)	PUNCT
ejpam-5996	24	17	,	,	PUNCT
ejpam-5996	24	18	we	we	PRON
ejpam-5996	24	19	define	define	VERB
ejpam-5996	24	20	its	its	PRON
ejpam-5996	24	21	integer	integer	NOUN
ejpam-5996	24	22	part	part	NOUN
ejpam-5996	25	1	[	[	X
ejpam-5996	25	2	w	w	X
ejpam-5996	25	3	]	]	X
ejpam-5996	25	4	as	as	ADP
ejpam-5996	25	5	:	:	PUNCT
ejpam-5996	25	6	[	[	X
ejpam-5996	25	7	w	w	X
ejpam-5996	25	8	]	]	X
ejpam-5996	25	9	=	=	SYM
ejpam-5996	25	10	{	{	PUNCT
ejpam-5996	25	11	∑0	∑0	PROPN
ejpam-5996	25	12	n	n	CCONJ
ejpam-5996	25	13	=	=	PROPN
ejpam-5996	25	14	n0	n0	X
ejpam-5996	25	15	anx	anx	NOUN
ejpam-5996	25	16	−n	−n	PROPN
ejpam-5996	26	1	if	if	SCONJ
ejpam-5996	26	2	n0	n0	ADJ
ejpam-5996	26	3	≤	≤	ADV
ejpam-5996	26	4	0	0	NUM
ejpam-5996	26	5	,	,	PUNCT
ejpam-5996	26	6	0	0	PUNCT
ejpam-5996	26	7	if	if	SCONJ
ejpam-5996	26	8	n0	n0	X
ejpam-5996	26	9	>	>	X
ejpam-5996	26	10	0	0	X
ejpam-5996	26	11	.	.	PUNCT
ejpam-5996	27	1	the	the	DET
ejpam-5996	27	2	fractional	fractional	ADJ
ejpam-5996	27	3	part	part	NOUN
ejpam-5996	27	4	of	of	ADP
ejpam-5996	27	5	w	w	PROPN
ejpam-5996	27	6	is	be	AUX
ejpam-5996	27	7	denoted	denote	VERB
ejpam-5996	27	8	by	by	ADP
ejpam-5996	27	9	{	{	PUNCT
ejpam-5996	27	10	w	w	NOUN
ejpam-5996	27	11	}	}	PUNCT
ejpam-5996	27	12	and	and	CCONJ
ejpam-5996	27	13	is	be	AUX
ejpam-5996	27	14	given	give	VERB
ejpam-5996	27	15	by	by	ADP
ejpam-5996	27	16	:	:	PUNCT
ejpam-5996	27	17	{	{	PUNCT
ejpam-5996	27	18	w	w	NOUN
ejpam-5996	27	19	}	}	PUNCT
ejpam-5996	27	20	=	=	PUNCT
ejpam-5996	27	21	w	w	NOUN
ejpam-5996	28	1	−	−	PROPN
ejpam-5996	29	1	[	[	X
ejpam-5996	29	2	w	w	X
ejpam-5996	29	3	]	]	X
ejpam-5996	29	4	=	=	PUNCT
ejpam-5996	30	1	+	+	ADJ
ejpam-5996	30	2	∞∑	∞∑	NUM
ejpam-5996	30	3	n=1	n=1	ADJ
ejpam-5996	30	4	anx	anx	ADJ
ejpam-5996	30	5	−n	−n	NOUN
ejpam-5996	30	6	.	.	PUNCT
ejpam-5996	31	1	a	a	DET
ejpam-5996	31	2	non	non	ADJ
ejpam-5996	31	3	-	-	ADJ
ejpam-5996	31	4	archimedean	archimedean	ADJ
ejpam-5996	31	5	absolute	absolute	ADJ
ejpam-5996	31	6	value	value	NOUN
ejpam-5996	31	7	|	|	ADV
ejpam-5996	31	8	·	·	PUNCT
ejpam-5996	32	1	|	|	ADV
ejpam-5996	32	2	defined	define	VERB
ejpam-5996	32	3	on	on	ADP
ejpam-5996	32	4	a	a	DET
ejpam-5996	32	5	field	field	NOUN
ejpam-5996	32	6	fq((x	fq((x	NOUN
ejpam-5996	32	7	−1))∗	−1))∗	NOUN
ejpam-5996	32	8	by	by	ADP
ejpam-5996	32	9	|w|	|w|	ADJ
ejpam-5996	32	10	=	=	PUNCT
ejpam-5996	32	11	e−n0	e−n0	NOUN
ejpam-5996	32	12	,	,	PUNCT
ejpam-5996	32	13	where	where	SCONJ
ejpam-5996	32	14	n0	n0	PROPN
ejpam-5996	32	15	is	be	AUX
ejpam-5996	32	16	the	the	DET
ejpam-5996	32	17	smallest	small	ADJ
ejpam-5996	32	18	index	index	NOUN
ejpam-5996	32	19	such	such	ADJ
ejpam-5996	32	20	that	that	SCONJ
ejpam-5996	32	21	an0	an0	PROPN
ejpam-5996	32	22	̸=	̸=	PROPN
ejpam-5996	32	23	0	0	NUM
ejpam-5996	32	24	.	.	PUNCT
ejpam-5996	33	1	if	if	SCONJ
ejpam-5996	33	2	w	w	PROPN
ejpam-5996	33	3	=	=	NOUN
ejpam-5996	33	4	0	0	NUM
ejpam-5996	33	5	,	,	PUNCT
ejpam-5996	33	6	we	we	PRON
ejpam-5996	33	7	set	set	VERB
ejpam-5996	33	8	|w|	|w|	PROPN
ejpam-5996	33	9	=	=	NOUN
ejpam-5996	33	10	0	0	NUM
ejpam-5996	33	11	.	.	PUNCT
ejpam-5996	34	1	this	this	DET
ejpam-5996	34	2	absolute	absolute	ADJ
ejpam-5996	34	3	value	value	NOUN
ejpam-5996	34	4	makes	make	VERB
ejpam-5996	34	5	fq((x	fq((x	NOUN
ejpam-5996	34	6	−1	−1	NOUN
ejpam-5996	34	7	)	)	PUNCT
ejpam-5996	34	8	)	)	PUNCT
ejpam-5996	35	1	a	a	DET
ejpam-5996	35	2	complete	complete	ADJ
ejpam-5996	35	3	and	and	CCONJ
ejpam-5996	35	4	locally	locally	ADV
ejpam-5996	35	5	compact	compact	ADJ
ejpam-5996	35	6	metric	metric	ADJ
ejpam-5996	35	7	space	space	NOUN
ejpam-5996	35	8	.	.	PUNCT
ejpam-5996	36	1	let	let	VERB
ejpam-5996	36	2	fq((x	fq((x	NOUN
ejpam-5996	36	3	−1	−1	NOUN
ejpam-5996	36	4	)	)	PUNCT
ejpam-5996	36	5	)	)	PUNCT
ejpam-5996	37	1	denote	denote	VERB
ejpam-5996	37	2	the	the	DET
ejpam-5996	37	3	algebraic	algebraic	ADJ
ejpam-5996	37	4	closure	closure	NOUN
ejpam-5996	37	5	of	of	ADP
ejpam-5996	37	6	fq((x	fq((x	NOUN
ejpam-5996	37	7	−1	−1	NOUN
ejpam-5996	37	8	)	)	PUNCT
ejpam-5996	37	9	)	)	PUNCT
ejpam-5996	37	10	.	.	PUNCT
ejpam-5996	38	1	the	the	DET
ejpam-5996	38	2	absolute	absolute	ADJ
ejpam-5996	38	3	value	value	NOUN
ejpam-5996	38	4	|	|	ADV
ejpam-5996	38	5	·	·	PUNCT
ejpam-5996	38	6	|	|	ADV
ejpam-5996	38	7	extends	extend	VERB
ejpam-5996	38	8	uniquely	uniquely	ADV
ejpam-5996	38	9	to	to	ADP
ejpam-5996	38	10	fq((x	fq((x	NOUN
ejpam-5996	38	11	−1	−1	NOUN
ejpam-5996	38	12	)	)	PUNCT
ejpam-5996	38	13	)	)	PUNCT
ejpam-5996	38	14	,	,	PUNCT
ejpam-5996	38	15	and	and	CCONJ
ejpam-5996	38	16	we	we	PRON
ejpam-5996	38	17	use	use	VERB
ejpam-5996	38	18	the	the	DET
ejpam-5996	38	19	same	same	ADJ
ejpam-5996	38	20	notation	notation	NOUN
ejpam-5996	38	21	for	for	ADP
ejpam-5996	38	22	this	this	DET
ejpam-5996	38	23	extended	extended	ADJ
ejpam-5996	38	24	absolute	absolute	ADJ
ejpam-5996	38	25	value	value	NOUN
ejpam-5996	38	26	.	.	PUNCT
ejpam-5996	39	1	we	we	PRON
ejpam-5996	39	2	define	define	VERB
ejpam-5996	39	3	a	a	DET
ejpam-5996	39	4	non	non	ADJ
ejpam-5996	39	5	-	-	ADJ
ejpam-5996	39	6	constant	constant	ADJ
ejpam-5996	39	7	polynomial	polynomial	NOUN
ejpam-5996	39	8	p	p	NOUN
ejpam-5996	39	9	over	over	ADP
ejpam-5996	39	10	f	f	PROPN
ejpam-5996	39	11	as	as	ADV
ejpam-5996	39	12	irreducible	irreducible	ADJ
ejpam-5996	39	13	if	if	SCONJ
ejpam-5996	39	14	p	p	PROPN
ejpam-5996	39	15	=	=	PUNCT
ejpam-5996	39	16	qh	qh	PROPN
ejpam-5996	39	17	with	with	ADP
ejpam-5996	39	18	q	q	PROPN
ejpam-5996	39	19	and	and	CCONJ
ejpam-5996	39	20	h	h	NOUN
ejpam-5996	39	21	in	in	ADP
ejpam-5996	39	22	f	f	PROPN
ejpam-5996	39	23	,	,	PUNCT
ejpam-5996	39	24	which	which	PRON
ejpam-5996	39	25	implies	imply	VERB
ejpam-5996	39	26	that	that	SCONJ
ejpam-5996	39	27	either	either	CCONJ
ejpam-5996	39	28	q	q	PROPN
ejpam-5996	39	29	or	or	CCONJ
ejpam-5996	39	30	h	h	NOUN
ejpam-5996	39	31	is	be	AUX
ejpam-5996	39	32	a	a	DET
ejpam-5996	39	33	constant	constant	ADJ
ejpam-5996	39	34	.	.	PUNCT
ejpam-5996	40	1	otherwise	otherwise	ADV
ejpam-5996	40	2	,	,	PUNCT
ejpam-5996	40	3	it	it	PRON
ejpam-5996	40	4	is	be	AUX
ejpam-5996	40	5	called	call	VERB
ejpam-5996	40	6	to	to	PART
ejpam-5996	40	7	be	be	AUX
ejpam-5996	40	8	reducible	reducible	ADJ
ejpam-5996	40	9	.	.	PUNCT
ejpam-5996	41	1	irreducible	irreducible	ADJ
ejpam-5996	41	2	polynomials	polynomial	NOUN
ejpam-5996	41	3	are	be	AUX
ejpam-5996	41	4	commonly	commonly	ADV
ejpam-5996	41	5	studied	study	VERB
ejpam-5996	41	6	in	in	ADP
ejpam-5996	41	7	fields	field	NOUN
ejpam-5996	41	8	such	such	ADJ
ejpam-5996	41	9	as	as	ADP
ejpam-5996	41	10	number	number	NOUN
ejpam-5996	41	11	theory	theory	NOUN
ejpam-5996	41	12	,	,	PUNCT
ejpam-5996	41	13	combinatorics	combinatoric	NOUN
ejpam-5996	41	14	,	,	PUNCT
ejpam-5996	41	15	and	and	CCONJ
ejpam-5996	41	16	algebraic	algebraic	ADJ
ejpam-5996	41	17	geometry	geometry	NOUN
ejpam-5996	41	18	.	.	PUNCT
ejpam-5996	42	1	they	they	PRON
ejpam-5996	42	2	also	also	ADV
ejpam-5996	42	3	play	play	VERB
ejpam-5996	42	4	a	a	DET
ejpam-5996	42	5	significant	significant	ADJ
ejpam-5996	42	6	role	role	NOUN
ejpam-5996	42	7	in	in	ADP
ejpam-5996	42	8	practical	practical	ADJ
ejpam-5996	42	9	domains	domain	NOUN
ejpam-5996	42	10	,	,	PUNCT
ejpam-5996	42	11	including	include	VERB
ejpam-5996	42	12	coding	code	VERB
ejpam-5996	42	13	theory	theory	NOUN
ejpam-5996	42	14	,	,	PUNCT
ejpam-5996	42	15	cryptography	cryptography	NOUN
ejpam-5996	42	16	,	,	PUNCT
ejpam-5996	42	17	complexity	complexity	NOUN
ejpam-5996	42	18	theory	theory	NOUN
ejpam-5996	42	19	,	,	PUNCT
ejpam-5996	42	20	and	and	CCONJ
ejpam-5996	42	21	computer	computer	NOUN
ejpam-5996	42	22	science[2	science[2	PROPN
ejpam-5996	42	23	]	]	PUNCT
ejpam-5996	42	24	.	.	PUNCT
ejpam-5996	43	1	a.	a.	PROPN
ejpam-5996	43	2	chandoul	chandoul	PROPN
ejpam-5996	43	3	,	,	PUNCT
ejpam-5996	43	4	a.	a.	NOUN
ejpam-5996	43	5	assiry	assiry	NOUN
ejpam-5996	43	6	/	/	SYM
ejpam-5996	43	7	eur	eur	PROPN
ejpam-5996	43	8	.	.	PUNCT
ejpam-5996	44	1	j.	j.	PROPN
ejpam-5996	44	2	pure	pure	PROPN
ejpam-5996	44	3	appl	appl	PROPN
ejpam-5996	44	4	.	.	PROPN
ejpam-5996	44	5	math	math	PROPN
ejpam-5996	44	6	,	,	PUNCT
ejpam-5996	44	7	18	18	NUM
ejpam-5996	44	8	(	(	PUNCT
ejpam-5996	44	9	2	2	NUM
ejpam-5996	44	10	)	)	PUNCT
ejpam-5996	44	11	(	(	PUNCT
ejpam-5996	44	12	2025	2025	NUM
ejpam-5996	44	13	)	)	PUNCT
ejpam-5996	44	14	,	,	PUNCT
ejpam-5996	44	15	5996	5996	NUM
ejpam-5996	44	16	3	3	NUM
ejpam-5996	44	17	of	of	ADP
ejpam-5996	44	18	9	9	NUM
ejpam-5996	44	19	constructing	construct	VERB
ejpam-5996	44	20	and	and	CCONJ
ejpam-5996	44	21	characterizing	characterize	VERB
ejpam-5996	44	22	irreducible	irreducible	ADJ
ejpam-5996	44	23	polynomials	polynomial	NOUN
ejpam-5996	44	24	over	over	ADP
ejpam-5996	44	25	finite	finite	ADJ
ejpam-5996	44	26	fields	field	NOUN
ejpam-5996	44	27	fq	fq	PROPN
ejpam-5996	44	28	is	be	AUX
ejpam-5996	44	29	one	one	NUM
ejpam-5996	44	30	of	of	ADP
ejpam-5996	44	31	the	the	DET
ejpam-5996	44	32	main	main	ADJ
ejpam-5996	44	33	challenges	challenge	NOUN
ejpam-5996	44	34	in	in	ADP
ejpam-5996	44	35	the	the	DET
ejpam-5996	44	36	theory	theory	NOUN
ejpam-5996	44	37	of	of	ADP
ejpam-5996	44	38	finite	finite	ADJ
ejpam-5996	44	39	fields	field	NOUN
ejpam-5996	44	40	that	that	PRON
ejpam-5996	44	41	has	have	AUX
ejpam-5996	44	42	just	just	ADV
ejpam-5996	44	43	lately	lately	ADV
ejpam-5996	44	44	received	receive	VERB
ejpam-5996	44	45	attention	attention	NOUN
ejpam-5996	44	46	.	.	PUNCT
ejpam-5996	45	1	during	during	ADP
ejpam-5996	45	2	the	the	DET
ejpam-5996	45	3	last	last	ADJ
ejpam-5996	45	4	fifty	fifty	NUM
ejpam-5996	45	5	years	year	NOUN
ejpam-5996	45	6	,	,	PUNCT
ejpam-5996	45	7	constructions	construction	NOUN
ejpam-5996	45	8	of	of	ADP
ejpam-5996	45	9	irreducible	irreducible	ADJ
ejpam-5996	45	10	polynomials	polynomial	NOUN
ejpam-5996	45	11	over	over	ADP
ejpam-5996	45	12	finite	finite	ADJ
ejpam-5996	45	13	fields	field	NOUN
ejpam-5996	45	14	have	have	AUX
ejpam-5996	45	15	been	be	AUX
ejpam-5996	45	16	extensively	extensively	ADV
ejpam-5996	45	17	studied	study	VERB
ejpam-5996	45	18	.	.	PUNCT
ejpam-5996	46	1	however	however	ADV
ejpam-5996	46	2	,	,	PUNCT
ejpam-5996	46	3	it	it	PRON
ejpam-5996	46	4	is	be	AUX
ejpam-5996	46	5	recognized	recognize	VERB
ejpam-5996	46	6	that	that	SCONJ
ejpam-5996	46	7	there	there	PRON
ejpam-5996	46	8	is	be	VERB
ejpam-5996	46	9	no	no	DET
ejpam-5996	46	10	general	general	ADJ
ejpam-5996	46	11	criteria	criterion	NOUN
ejpam-5996	46	12	for	for	ADP
ejpam-5996	46	13	determining	determine	VERB
ejpam-5996	46	14	whether	whether	SCONJ
ejpam-5996	46	15	such	such	DET
ejpam-5996	46	16	a	a	DET
ejpam-5996	46	17	polynomial	polynomial	NOUN
ejpam-5996	46	18	is	be	AUX
ejpam-5996	46	19	reducible	reducible	ADJ
ejpam-5996	46	20	or	or	CCONJ
ejpam-5996	46	21	irreducible	irreducible	ADJ
ejpam-5996	46	22	.	.	PUNCT
ejpam-5996	47	1	despite	despite	SCONJ
ejpam-5996	47	2	this	this	PRON
ejpam-5996	47	3	,	,	PUNCT
ejpam-5996	47	4	numerous	numerous	ADJ
ejpam-5996	47	5	tests	test	NOUN
ejpam-5996	47	6	referred	refer	VERB
ejpam-5996	47	7	to	to	ADP
ejpam-5996	47	8	as	as	SCONJ
ejpam-5996	47	9	irreducibility	irreducibility	NOUN
ejpam-5996	47	10	criteria	criterion	NOUN
ejpam-5996	47	11	have	have	AUX
ejpam-5996	47	12	been	be	AUX
ejpam-5996	47	13	established	establish	VERB
ejpam-5996	47	14	to	to	PART
ejpam-5996	47	15	offer	offer	VERB
ejpam-5996	47	16	valuable	valuable	ADJ
ejpam-5996	47	17	insights	insight	NOUN
ejpam-5996	47	18	into	into	ADP
ejpam-5996	47	19	specific	specific	ADJ
ejpam-5996	47	20	classes	class	NOUN
ejpam-5996	47	21	of	of	ADP
ejpam-5996	47	22	polynomials	polynomial	NOUN
ejpam-5996	47	23	.	.	PUNCT
ejpam-5996	48	1	in	in	ADP
ejpam-5996	48	2	[	[	X
ejpam-5996	48	3	3	3	NUM
ejpam-5996	48	4	]	]	PUNCT
ejpam-5996	48	5	,	,	PUNCT
ejpam-5996	48	6	lipka	lipka	NOUN
ejpam-5996	48	7	derived	derive	VERB
ejpam-5996	48	8	conditions	condition	NOUN
ejpam-5996	48	9	for	for	ADP
ejpam-5996	48	10	the	the	DET
ejpam-5996	48	11	irreducibility	irreducibility	NOUN
ejpam-5996	48	12	of	of	ADP
ejpam-5996	48	13	integer	integer	NOUN
ejpam-5996	48	14	polynomials	polynomial	NOUN
ejpam-5996	48	15	of	of	ADP
ejpam-5996	48	16	the	the	DET
ejpam-5996	48	17	form	form	NOUN
ejpam-5996	48	18	f(x	f(x	PROPN
ejpam-5996	48	19	)	)	PUNCT
ejpam-5996	48	20	=	=	PUNCT
ejpam-5996	49	1	anx	anx	ADJ
ejpam-5996	49	2	n	n	PROPN
ejpam-5996	49	3	+	+	CCONJ
ejpam-5996	49	4	·	·	PUNCT
ejpam-5996	49	5	·	·	PUNCT
ejpam-5996	49	6	·	·	PUNCT
ejpam-5996	50	1	+	+	NUM
ejpam-5996	50	2	a1x	a1x	ADJ
ejpam-5996	50	3	+	+	ADJ
ejpam-5996	50	4	a0p	a0p	PROPN
ejpam-5996	50	5	k	k	PROPN
ejpam-5996	50	6	,	,	PUNCT
ejpam-5996	50	7	where	where	SCONJ
ejpam-5996	50	8	p	p	NOUN
ejpam-5996	50	9	is	be	AUX
ejpam-5996	50	10	a	a	DET
ejpam-5996	50	11	prime	prime	ADJ
ejpam-5996	50	12	number	number	NOUN
ejpam-5996	50	13	and	and	CCONJ
ejpam-5996	50	14	p	p	PROPN
ejpam-5996	50	15	∤	∤	PROPN
ejpam-5996	50	16	a0	a0	PROPN
ejpam-5996	50	17	.	.	PROPN
ejpam-5996	51	1	for	for	ADP
ejpam-5996	51	2	instance	instance	NOUN
ejpam-5996	51	3	,	,	PUNCT
ejpam-5996	51	4	he	he	PRON
ejpam-5996	51	5	demonstrated	demonstrate	VERB
ejpam-5996	51	6	that	that	SCONJ
ejpam-5996	51	7	such	such	DET
ejpam-5996	51	8	a	a	DET
ejpam-5996	51	9	polynomial	polynomial	NOUN
ejpam-5996	51	10	is	be	AUX
ejpam-5996	51	11	irreducible	irreducible	ADJ
ejpam-5996	51	12	over	over	ADP
ejpam-5996	51	13	q	q	NOUN
ejpam-5996	51	14	for	for	ADP
ejpam-5996	51	15	all	all	PRON
ejpam-5996	51	16	but	but	ADV
ejpam-5996	51	17	finitely	finitely	ADV
ejpam-5996	51	18	many	many	ADJ
ejpam-5996	51	19	positive	positive	ADJ
ejpam-5996	51	20	integers	integer	NOUN
ejpam-5996	51	21	k.	k.	X
ejpam-5996	51	22	for	for	ADP
ejpam-5996	51	23	older	old	ADJ
ejpam-5996	51	24	results	result	NOUN
ejpam-5996	51	25	,	,	PUNCT
ejpam-5996	51	26	one	one	PRON
ejpam-5996	51	27	can	can	AUX
ejpam-5996	51	28	see	see	VERB
ejpam-5996	51	29	[	[	X
ejpam-5996	51	30	4	4	NUM
ejpam-5996	51	31	,	,	PUNCT
ejpam-5996	51	32	5	5	NUM
ejpam-5996	51	33	]	]	PUNCT
ejpam-5996	51	34	.	.	PUNCT
ejpam-5996	52	1	in	in	ADP
ejpam-5996	52	2	the	the	DET
ejpam-5996	52	3	first	first	ADJ
ejpam-5996	52	4	part	part	NOUN
ejpam-5996	52	5	of	of	ADP
ejpam-5996	52	6	this	this	DET
ejpam-5996	52	7	paper	paper	NOUN
ejpam-5996	52	8	we	we	PRON
ejpam-5996	52	9	prove	prove	VERB
ejpam-5996	52	10	an	an	DET
ejpam-5996	52	11	irreducibility	irreducibility	NOUN
ejpam-5996	52	12	criterion	criterion	NOUN
ejpam-5996	52	13	for	for	ADP
ejpam-5996	52	14	lacunary	lacunary	ADJ
ejpam-5996	52	15	polynomials	polynomial	NOUN
ejpam-5996	52	16	with	with	ADP
ejpam-5996	52	17	coefficients	coefficient	NOUN
ejpam-5996	52	18	in	in	ADP
ejpam-5996	52	19	fq[x	fq[x	PROPN
ejpam-5996	52	20	]	]	PUNCT
ejpam-5996	52	21	,	,	PUNCT
ejpam-5996	52	22	which	which	PRON
ejpam-5996	52	23	is	be	AUX
ejpam-5996	52	24	similar	similar	ADJ
ejpam-5996	52	25	to	to	ADP
ejpam-5996	52	26	the	the	DET
ejpam-5996	52	27	first	first	ADJ
ejpam-5996	52	28	result	result	NOUN
ejpam-5996	52	29	of	of	ADP
ejpam-5996	52	30	lipka	lipka	NOUN
ejpam-5996	52	31	.	.	PUNCT
ejpam-5996	53	1	in	in	ADP
ejpam-5996	53	2	[	[	X
ejpam-5996	53	3	6	6	NUM
ejpam-5996	53	4	]	]	PUNCT
ejpam-5996	53	5	,	,	PUNCT
ejpam-5996	53	6	ben	ben	PROPN
ejpam-5996	53	7	nasr	nasr	PROPN
ejpam-5996	53	8	and	and	CCONJ
ejpam-5996	53	9	kthiri	kthiri	PROPN
ejpam-5996	53	10	proved	prove	VERB
ejpam-5996	53	11	,	,	PUNCT
ejpam-5996	53	12	using	use	VERB
ejpam-5996	53	13	the	the	DET
ejpam-5996	53	14	upper	upper	ADJ
ejpam-5996	53	15	newton	newton	PROPN
ejpam-5996	53	16	polygon	polygon	PROPN
ejpam-5996	53	17	,	,	PUNCT
ejpam-5996	53	18	that	that	PRON
ejpam-5996	53	19	theorem	theorem	VERB
ejpam-5996	53	20	1	1	NUM
ejpam-5996	53	21	.	.	PUNCT
ejpam-5996	54	1	let	let	VERB
ejpam-5996	54	2	λ(y	λ(y	PRON
ejpam-5996	54	3	)	)	PUNCT
ejpam-5996	55	1	=	=	PUNCT
ejpam-5996	56	1	y	y	PROPN
ejpam-5996	56	2	d	d	PROPN
ejpam-5996	56	3	+	+	CCONJ
ejpam-5996	56	4	λd−1y	λd−1y	PROPN
ejpam-5996	56	5	d−1	d−1	PROPN
ejpam-5996	56	6	+	+	CCONJ
ejpam-5996	56	7	·	·	PUNCT
ejpam-5996	56	8	·	·	PUNCT
ejpam-5996	56	9	·	·	PUNCT
ejpam-5996	57	1	+	+	PUNCT
ejpam-5996	57	2	λ0	λ0	NOUN
ejpam-5996	57	3	be	be	VERB
ejpam-5996	57	4	a	a	DET
ejpam-5996	57	5	polynomial	polynomial	NOUN
ejpam-5996	57	6	with	with	ADP
ejpam-5996	57	7	λi	λi	X
ejpam-5996	57	8	∈	∈	PROPN
ejpam-5996	57	9	fq[x	fq[x	PROPN
ejpam-5996	57	10	]	]	PUNCT
ejpam-5996	57	11	,	,	PUNCT
ejpam-5996	57	12	λ0	λ0	NOUN
ejpam-5996	57	13	̸=	̸=	PROPN
ejpam-5996	57	14	0	0	NUM
ejpam-5996	57	15	,	,	PUNCT
ejpam-5996	57	16	and	and	CCONJ
ejpam-5996	57	17	deg	deg	VERB
ejpam-5996	57	18	λd−2	λd−2	PROPN
ejpam-5996	57	19	>	>	X
ejpam-5996	57	20	deg	deg	PROPN
ejpam-5996	57	21	λi	λi	ADP
ejpam-5996	57	22	for	for	ADP
ejpam-5996	57	23	all	all	PRON
ejpam-5996	57	24	i	i	PRON
ejpam-5996	57	25	̸=	̸=	PROPN
ejpam-5996	57	26	d−	d−	PROPN
ejpam-5996	57	27	2	2	NUM
ejpam-5996	57	28	.	.	PUNCT
ejpam-5996	57	29	suppose	suppose	VERB
ejpam-5996	57	30	further	far	ADV
ejpam-5996	57	31	that	that	SCONJ
ejpam-5996	57	32	deg	deg	NOUN
ejpam-5996	57	33	λd−2	λd−2	PROPN
ejpam-5996	57	34	is	be	AUX
ejpam-5996	57	35	odd	odd	ADJ
ejpam-5996	57	36	and	and	CCONJ
ejpam-5996	57	37	satisfies	satisfie	NOUN
ejpam-5996	57	38	deg	deg	PROPN
ejpam-5996	57	39	λd−2	λd−2	X
ejpam-5996	57	40	≥	≥	NUM
ejpam-5996	57	41	2	2	NUM
ejpam-5996	57	42	deg	deg	NOUN
ejpam-5996	57	43	λd−1	λd−1	PROPN
ejpam-5996	57	44	.	.	PROPN
ejpam-5996	58	1	then	then	ADV
ejpam-5996	58	2	,	,	PUNCT
ejpam-5996	58	3	λ(y	λ(y	PROPN
ejpam-5996	58	4	)	)	PUNCT
ejpam-5996	58	5	is	be	AUX
ejpam-5996	58	6	irreducible	irreducible	ADJ
ejpam-5996	58	7	over	over	ADP
ejpam-5996	58	8	fq[x	fq[x	PROPN
ejpam-5996	58	9	]	]	PUNCT
ejpam-5996	58	10	.	.	PUNCT
ejpam-5996	59	1	recall	recall	VERB
ejpam-5996	59	2	that	that	SCONJ
ejpam-5996	59	3	newton	newton	PROPN
ejpam-5996	59	4	polygons	polygon	NOUN
ejpam-5996	59	5	can	can	AUX
ejpam-5996	59	6	be	be	AUX
ejpam-5996	59	7	used	use	VERB
ejpam-5996	59	8	to	to	PART
ejpam-5996	59	9	determine	determine	VERB
ejpam-5996	59	10	the	the	DET
ejpam-5996	59	11	behavior	behavior	NOUN
ejpam-5996	59	12	of	of	ADP
ejpam-5996	59	13	roots	root	NOUN
ejpam-5996	59	14	in	in	ADP
ejpam-5996	59	15	polynomials	polynomial	NOUN
ejpam-5996	59	16	over	over	ADP
ejpam-5996	59	17	a	a	DET
ejpam-5996	59	18	field	field	NOUN
ejpam-5996	59	19	.	.	PUNCT
ejpam-5996	60	1	let	let	VERB
ejpam-5996	60	2	p	p	NOUN
ejpam-5996	60	3	(	(	PUNCT
ejpam-5996	60	4	y	y	PROPN
ejpam-5996	60	5	)	)	PUNCT
ejpam-5996	60	6	=	=	PUNCT
ejpam-5996	61	1	asy	asy	PROPN
ejpam-5996	61	2	s	s	PART
ejpam-5996	62	1	+	+	ADJ
ejpam-5996	62	2	as−1y	as−1y	ADJ
ejpam-5996	62	3	s−1	s−1	NOUN
ejpam-5996	62	4	+	+	PROPN
ejpam-5996	62	5	as−3y	as−3y	PROPN
ejpam-5996	62	6	s−3	s−3	NOUN
ejpam-5996	62	7	+	+	CCONJ
ejpam-5996	62	8	·	·	PUNCT
ejpam-5996	62	9	·	·	PUNCT
ejpam-5996	62	10	·	·	PUNCT
ejpam-5996	63	1	+	+	ADJ
ejpam-5996	63	2	a1y	a1y	PROPN
ejpam-5996	63	3	+	+	SYM
ejpam-5996	63	4	a0	a0	NOUN
ejpam-5996	63	5	be	be	VERB
ejpam-5996	63	6	a	a	DET
ejpam-5996	63	7	polynomial	polynomial	NOUN
ejpam-5996	63	8	over	over	ADP
ejpam-5996	63	9	fq[x	fq[x	PROPN
ejpam-5996	63	10	]	]	PUNCT
ejpam-5996	63	11	,	,	PUNCT
ejpam-5996	63	12	and	and	CCONJ
ejpam-5996	63	13	assume	assume	VERB
ejpam-5996	63	14	,	,	PUNCT
ejpam-5996	63	15	for	for	ADP
ejpam-5996	63	16	simplicity	simplicity	NOUN
ejpam-5996	63	17	,	,	PUNCT
ejpam-5996	63	18	that	that	SCONJ
ejpam-5996	63	19	asa0	asa0	NOUN
ejpam-5996	63	20	̸=	̸=	PROPN
ejpam-5996	63	21	0	0	NUM
ejpam-5996	63	22	.	.	PUNCT
ejpam-5996	64	1	to	to	ADP
ejpam-5996	64	2	each	each	DET
ejpam-5996	64	3	term	term	NOUN
ejpam-5996	64	4	ai	ai	VERB
ejpam-5996	64	5	of	of	ADP
ejpam-5996	64	6	p	p	PROPN
ejpam-5996	64	7	(	(	PUNCT
ejpam-5996	64	8	y	y	PROPN
ejpam-5996	64	9	)	)	PUNCT
ejpam-5996	64	10	,	,	PUNCT
ejpam-5996	64	11	we	we	PRON
ejpam-5996	64	12	assign	assign	VERB
ejpam-5996	64	13	the	the	DET
ejpam-5996	64	14	point	point	NOUN
ejpam-5996	64	15	in	in	ADP
ejpam-5996	64	16	the	the	DET
ejpam-5996	64	17	following	follow	VERB
ejpam-5996	64	18	manner	manner	NOUN
ejpam-5996	64	19	:	:	PUNCT
ejpam-5996	64	20	•	•	ADP
ejpam-5996	64	21	if	if	SCONJ
ejpam-5996	64	22	ai	ai	AUX
ejpam-5996	64	23	̸=	̸=	PROPN
ejpam-5996	64	24	0	0	NUM
ejpam-5996	64	25	take	take	VERB
ejpam-5996	64	26	the	the	DET
ejpam-5996	64	27	point	point	NOUN
ejpam-5996	64	28	:	:	PUNCT
ejpam-5996	64	29	(	(	PUNCT
ejpam-5996	64	30	i	i	NOUN
ejpam-5996	64	31	,	,	PUNCT
ejpam-5996	64	32	degai	degai	PROPN
ejpam-5996	64	33	)	)	PUNCT
ejpam-5996	64	34	•	•	ADV
ejpam-5996	64	35	if	if	SCONJ
ejpam-5996	64	36	ai	ai	VERB
ejpam-5996	64	37	=	=	SYM
ejpam-5996	64	38	0	0	NUM
ejpam-5996	64	39	disregard	disregard	NOUN
ejpam-5996	64	40	the	the	DET
ejpam-5996	64	41	nonexistent	nonexistent	ADJ
ejpam-5996	64	42	point	point	NOUN
ejpam-5996	64	43	:	:	PUNCT
ejpam-5996	64	44	(	(	PUNCT
ejpam-5996	64	45	i,∞	i,∞	PROPN
ejpam-5996	64	46	)	)	PUNCT
ejpam-5996	64	47	then	then	ADV
ejpam-5996	64	48	,	,	PUNCT
ejpam-5996	64	49	the	the	DET
ejpam-5996	64	50	points	point	NOUN
ejpam-5996	64	51	we	we	PRON
ejpam-5996	64	52	plot	plot	VERB
ejpam-5996	64	53	for	for	ADP
ejpam-5996	64	54	the	the	DET
ejpam-5996	64	55	polynomial	polynomial	ADJ
ejpam-5996	64	56	p	p	NOUN
ejpam-5996	64	57	(	(	PUNCT
ejpam-5996	64	58	y	y	PROPN
ejpam-5996	64	59	)	)	PUNCT
ejpam-5996	64	60	are	be	AUX
ejpam-5996	64	61	(	(	PUNCT
ejpam-5996	64	62	0,dega0	0,dega0	NUM
ejpam-5996	64	63	)	)	PUNCT
ejpam-5996	64	64	,	,	PUNCT
ejpam-5996	64	65	·	·	PUNCT
ejpam-5996	64	66	·	·	PUNCT
ejpam-5996	64	67	·	·	PUNCT
ejpam-5996	64	68	(	(	PUNCT
ejpam-5996	64	69	s	s	X
ejpam-5996	64	70	,	,	PUNCT
ejpam-5996	64	71	degas	dega	NOUN
ejpam-5996	64	72	)	)	PUNCT
ejpam-5996	64	73	we	we	PRON
ejpam-5996	64	74	begin	begin	VERB
ejpam-5996	64	75	by	by	ADP
ejpam-5996	64	76	connecting	connect	VERB
ejpam-5996	64	77	the	the	DET
ejpam-5996	64	78	points	point	NOUN
ejpam-5996	64	79	with	with	ADP
ejpam-5996	64	80	line	line	NOUN
ejpam-5996	64	81	segments	segment	NOUN
ejpam-5996	64	82	.	.	PUNCT
ejpam-5996	65	1	the	the	DET
ejpam-5996	65	2	process	process	NOUN
ejpam-5996	65	3	starts	start	VERB
ejpam-5996	65	4	at	at	ADP
ejpam-5996	65	5	the	the	DET
ejpam-5996	65	6	point	point	NOUN
ejpam-5996	65	7	(	(	PUNCT
ejpam-5996	65	8	0	0	NUM
ejpam-5996	65	9	,	,	PUNCT
ejpam-5996	65	10	dega0	dega0	PROPN
ejpam-5996	65	11	)	)	PUNCT
ejpam-5996	65	12	,	,	PUNCT
ejpam-5996	65	13	which	which	PRON
ejpam-5996	65	14	is	be	AUX
ejpam-5996	65	15	connected	connect	VERB
ejpam-5996	65	16	to	to	ADP
ejpam-5996	65	17	a	a	DET
ejpam-5996	65	18	point	point	NOUN
ejpam-5996	65	19	,	,	PUNCT
ejpam-5996	65	20	denoted	denote	VERB
ejpam-5996	65	21	as	as	ADP
ejpam-5996	65	22	b	b	NOUN
ejpam-5996	65	23	,	,	PUNCT
ejpam-5996	65	24	that	that	PRON
ejpam-5996	65	25	yields	yield	VERB
ejpam-5996	65	26	the	the	DET
ejpam-5996	65	27	least	least	ADV
ejpam-5996	65	28	feasible	feasible	ADJ
ejpam-5996	65	29	slope	slope	NOUN
ejpam-5996	65	30	for	for	ADP
ejpam-5996	65	31	the	the	DET
ejpam-5996	65	32	first	first	ADJ
ejpam-5996	65	33	line	line	NOUN
ejpam-5996	65	34	segment	segment	NOUN
ejpam-5996	65	35	.	.	PUNCT
ejpam-5996	66	1	subsequently	subsequently	ADV
ejpam-5996	66	2	,	,	PUNCT
ejpam-5996	66	3	b	b	PROPN
ejpam-5996	66	4	is	be	AUX
ejpam-5996	66	5	connected	connect	VERB
ejpam-5996	66	6	to	to	ADP
ejpam-5996	66	7	the	the	DET
ejpam-5996	66	8	next	next	ADJ
ejpam-5996	66	9	point	point	NOUN
ejpam-5996	66	10	to	to	ADP
ejpam-5996	66	11	its	its	PRON
ejpam-5996	66	12	right	right	NOUN
ejpam-5996	66	13	,	,	PUNCT
ejpam-5996	66	14	ensuring	ensure	VERB
ejpam-5996	66	15	the	the	DET
ejpam-5996	66	16	smallest	small	ADJ
ejpam-5996	66	17	possible	possible	ADJ
ejpam-5996	66	18	slope	slope	NOUN
ejpam-5996	66	19	for	for	ADP
ejpam-5996	66	20	the	the	DET
ejpam-5996	66	21	second	second	ADJ
ejpam-5996	66	22	line	line	NOUN
ejpam-5996	66	23	segment	segment	NOUN
ejpam-5996	66	24	,	,	PUNCT
ejpam-5996	66	25	and	and	CCONJ
ejpam-5996	66	26	so	so	ADV
ejpam-5996	66	27	forth	forth	ADV
ejpam-5996	66	28	.	.	PUNCT
ejpam-5996	67	1	to	to	PART
ejpam-5996	67	2	geometrically	geometrically	ADV
ejpam-5996	67	3	visualize	visualize	VERB
ejpam-5996	67	4	this	this	DET
ejpam-5996	67	5	construction	construction	NOUN
ejpam-5996	67	6	,	,	PUNCT
ejpam-5996	67	7	imagine	imagine	VERB
ejpam-5996	67	8	a	a	DET
ejpam-5996	67	9	string	string	NOUN
ejpam-5996	67	10	fixed	fix	VERB
ejpam-5996	67	11	at	at	ADP
ejpam-5996	67	12	one	one	NUM
ejpam-5996	67	13	end	end	NOUN
ejpam-5996	67	14	to	to	ADP
ejpam-5996	67	15	the	the	DET
ejpam-5996	67	16	point	point	NOUN
ejpam-5996	67	17	(	(	PUNCT
ejpam-5996	67	18	0,dega0	0,dega0	NUM
ejpam-5996	67	19	)	)	PUNCT
ejpam-5996	67	20	and	and	CCONJ
ejpam-5996	67	21	being	be	AUX
ejpam-5996	67	22	pulled	pull	VERB
ejpam-5996	67	23	counterclockwise	counterclockwise	ADV
ejpam-5996	67	24	around	around	ADP
ejpam-5996	67	25	the	the	DET
ejpam-5996	67	26	points	point	NOUN
ejpam-5996	67	27	by	by	ADP
ejpam-5996	67	28	the	the	DET
ejpam-5996	67	29	other	other	ADJ
ejpam-5996	67	30	end	end	NOUN
ejpam-5996	67	31	.	.	PUNCT
ejpam-5996	68	1	as	as	ADP
ejpam-5996	68	2	the	the	DET
ejpam-5996	68	3	string	string	NOUN
ejpam-5996	68	4	wraps	wrap	NOUN
ejpam-5996	68	5	around	around	ADP
ejpam-5996	68	6	each	each	DET
ejpam-5996	68	7	point	point	NOUN
ejpam-5996	68	8	,	,	PUNCT
ejpam-5996	68	9	it	it	PRON
ejpam-5996	68	10	forms	form	VERB
ejpam-5996	68	11	a	a	DET
ejpam-5996	68	12	“	"	PUNCT
ejpam-5996	68	13	bend	bend	NOUN
ejpam-5996	68	14	”	"	PUNCT
ejpam-5996	68	15	at	at	ADP
ejpam-5996	68	16	that	that	DET
ejpam-5996	68	17	location	location	NOUN
ejpam-5996	68	18	.	.	PUNCT
ejpam-5996	69	1	the	the	DET
ejpam-5996	69	2	process	process	NOUN
ejpam-5996	69	3	concludes	conclude	VERB
ejpam-5996	69	4	once	once	ADV
ejpam-5996	69	5	all	all	DET
ejpam-5996	69	6	finite	finite	ADJ
ejpam-5996	69	7	points	point	NOUN
ejpam-5996	69	8	have	have	AUX
ejpam-5996	69	9	been	be	AUX
ejpam-5996	69	10	wrapped	wrap	VERB
ejpam-5996	69	11	in	in	ADP
ejpam-5996	69	12	this	this	DET
ejpam-5996	69	13	manner	manner	NOUN
ejpam-5996	69	14	.	.	PUNCT
ejpam-5996	70	1	a.	a.	PROPN
ejpam-5996	70	2	chandoul	chandoul	PROPN
ejpam-5996	70	3	,	,	PUNCT
ejpam-5996	70	4	a.	a.	NOUN
ejpam-5996	70	5	assiry	assiry	NOUN
ejpam-5996	70	6	/	/	SYM
ejpam-5996	70	7	eur	eur	PROPN
ejpam-5996	70	8	.	.	PUNCT
ejpam-5996	71	1	j.	j.	PROPN
ejpam-5996	71	2	pure	pure	PROPN
ejpam-5996	71	3	appl	appl	PROPN
ejpam-5996	71	4	.	.	PROPN
ejpam-5996	71	5	math	math	PROPN
ejpam-5996	71	6	,	,	PUNCT
ejpam-5996	71	7	18	18	NUM
ejpam-5996	71	8	(	(	PUNCT
ejpam-5996	71	9	2	2	NUM
ejpam-5996	71	10	)	)	PUNCT
ejpam-5996	71	11	(	(	PUNCT
ejpam-5996	71	12	2025	2025	NUM
ejpam-5996	71	13	)	)	PUNCT
ejpam-5996	71	14	,	,	PUNCT
ejpam-5996	71	15	5996	5996	NUM
ejpam-5996	71	16	4	4	NUM
ejpam-5996	71	17	of	of	ADP
ejpam-5996	71	18	9	9	NUM
ejpam-5996	71	19	there	there	PRON
ejpam-5996	71	20	should	should	AUX
ejpam-5996	71	21	be	be	AUX
ejpam-5996	71	22	a	a	DET
ejpam-5996	71	23	note	note	NOUN
ejpam-5996	71	24	here	here	ADV
ejpam-5996	71	25	for	for	ADP
ejpam-5996	71	26	points	point	NOUN
ejpam-5996	71	27	of	of	ADP
ejpam-5996	71	28	the	the	DET
ejpam-5996	71	29	form	form	NOUN
ejpam-5996	71	30	(	(	PUNCT
ejpam-5996	71	31	i	i	PRON
ejpam-5996	71	32	,	,	PUNCT
ejpam-5996	71	33	deg	deg	NOUN
ejpam-5996	71	34	0	0	NUM
ejpam-5996	71	35	)	)	PUNCT
ejpam-5996	71	36	.	.	PUNCT
ejpam-5996	72	1	because	because	SCONJ
ejpam-5996	72	2	deg	deg	NOUN
ejpam-5996	72	3	0	0	NUM
ejpam-5996	72	4	=	=	SYM
ejpam-5996	72	5	∞	∞	PROPN
ejpam-5996	72	6	,	,	PUNCT
ejpam-5996	72	7	these	these	DET
ejpam-5996	72	8	points	point	NOUN
ejpam-5996	72	9	have	have	VERB
ejpam-5996	72	10	no	no	DET
ejpam-5996	72	11	interfer	interfer	NOUN
ejpam-5996	72	12	on	on	ADP
ejpam-5996	72	13	our	our	PRON
ejpam-5996	72	14	construction	construction	NOUN
ejpam-5996	72	15	because	because	SCONJ
ejpam-5996	72	16	it	it	PRON
ejpam-5996	72	17	does	do	AUX
ejpam-5996	72	18	not	not	PART
ejpam-5996	72	19	yield	yield	VERB
ejpam-5996	72	20	small	small	ADJ
ejpam-5996	72	21	slopes	slope	NOUN
ejpam-5996	72	22	while	while	SCONJ
ejpam-5996	72	23	constructing	construct	VERB
ejpam-5996	72	24	line	line	NOUN
ejpam-5996	72	25	segments	segment	NOUN
ejpam-5996	72	26	.	.	PUNCT
ejpam-5996	73	1	it	it	PRON
ejpam-5996	73	2	is	be	AUX
ejpam-5996	73	3	better	well	ADJ
ejpam-5996	73	4	to	to	PART
ejpam-5996	73	5	completely	completely	ADV
ejpam-5996	73	6	ignore	ignore	VERB
ejpam-5996	73	7	such	such	ADJ
ejpam-5996	73	8	points	point	NOUN
ejpam-5996	73	9	together	together	ADV
ejpam-5996	73	10	.	.	PUNCT
ejpam-5996	74	1	the	the	DET
ejpam-5996	74	2	final	final	ADJ
ejpam-5996	74	3	structure	structure	NOUN
ejpam-5996	74	4	is	be	AUX
ejpam-5996	74	5	referred	refer	VERB
ejpam-5996	74	6	to	to	ADP
ejpam-5996	74	7	as	as	ADP
ejpam-5996	74	8	the	the	DET
ejpam-5996	74	9	upper	upper	ADJ
ejpam-5996	74	10	newton	newton	PROPN
ejpam-5996	74	11	polygon	polygon	PROPN
ejpam-5996	74	12	of	of	ADP
ejpam-5996	74	13	p	p	PROPN
ejpam-5996	74	14	(	(	PUNCT
ejpam-5996	74	15	y	y	PROPN
ejpam-5996	74	16	)	)	PUNCT
ejpam-5996	74	17	.	.	PUNCT
ejpam-5996	75	1	observe	observe	VERB
ejpam-5996	75	2	that	that	SCONJ
ejpam-5996	75	3	the	the	DET
ejpam-5996	75	4	upper	upper	ADJ
ejpam-5996	75	5	newton	newton	PROPN
ejpam-5996	75	6	polygon	polygon	PROPN
ejpam-5996	75	7	consists	consist	VERB
ejpam-5996	75	8	of	of	ADP
ejpam-5996	75	9	a	a	DET
ejpam-5996	75	10	sequence	sequence	NOUN
ejpam-5996	75	11	of	of	ADP
ejpam-5996	75	12	line	line	NOUN
ejpam-5996	75	13	segments	segment	NOUN
ejpam-5996	75	14	with	with	ADP
ejpam-5996	75	15	strictly	strictly	ADV
ejpam-5996	75	16	decreasing	decrease	VERB
ejpam-5996	75	17	and	and	CCONJ
ejpam-5996	75	18	distinct	distinct	ADJ
ejpam-5996	75	19	slopes	slope	NOUN
ejpam-5996	75	20	.	.	PUNCT
ejpam-5996	76	1	the	the	DET
ejpam-5996	76	2	condition	condition	NOUN
ejpam-5996	76	3	asa0	asa0	NOUN
ejpam-5996	76	4	̸=	̸=	PROPN
ejpam-5996	76	5	0	0	NUM
ejpam-5996	76	6	ensures	ensure	VERB
ejpam-5996	76	7	that	that	SCONJ
ejpam-5996	76	8	the	the	DET
ejpam-5996	76	9	polygon	polygon	NOUN
ejpam-5996	76	10	begins	begin	VERB
ejpam-5996	76	11	at	at	ADP
ejpam-5996	76	12	a	a	DET
ejpam-5996	76	13	finite	finite	ADJ
ejpam-5996	76	14	point	point	NOUN
ejpam-5996	76	15	and	and	CCONJ
ejpam-5996	76	16	terminates	terminate	VERB
ejpam-5996	76	17	at	at	ADP
ejpam-5996	76	18	another	another	DET
ejpam-5996	76	19	finite	finite	ADJ
ejpam-5996	76	20	point	point	NOUN
ejpam-5996	76	21	.	.	PUNCT
ejpam-5996	77	1	for	for	ADP
ejpam-5996	77	2	example	example	NOUN
ejpam-5996	77	3	,	,	PUNCT
ejpam-5996	77	4	the	the	DET
ejpam-5996	77	5	slope	slope	NOUN
ejpam-5996	77	6	of	of	ADP
ejpam-5996	77	7	a	a	DET
ejpam-5996	77	8	line	line	NOUN
ejpam-5996	77	9	segment	segment	NOUN
ejpam-5996	77	10	in	in	ADP
ejpam-5996	77	11	the	the	DET
ejpam-5996	77	12	newton	newton	PROPN
ejpam-5996	77	13	polygon	polygon	PROPN
ejpam-5996	77	14	of	of	ADP
ejpam-5996	77	15	p	p	PROPN
ejpam-5996	77	16	(	(	PUNCT
ejpam-5996	77	17	y	y	PROPN
ejpam-5996	77	18	)	)	PUNCT
ejpam-5996	77	19	connecting	connect	VERB
ejpam-5996	77	20	the	the	DET
ejpam-5996	77	21	point	point	NOUN
ejpam-5996	77	22	(	(	PUNCT
ejpam-5996	77	23	r	r	NOUN
ejpam-5996	77	24	,	,	PUNCT
ejpam-5996	77	25	degar	degar	NOUN
ejpam-5996	77	26	)	)	PUNCT
ejpam-5996	77	27	to	to	ADP
ejpam-5996	77	28	the	the	DET
ejpam-5996	77	29	point	point	NOUN
ejpam-5996	77	30	(	(	PUNCT
ejpam-5996	77	31	r	r	NOUN
ejpam-5996	77	32	+	+	NOUN
ejpam-5996	77	33	m	m	NOUN
ejpam-5996	77	34	,	,	PUNCT
ejpam-5996	77	35	degar+m	degar+m	PROPN
ejpam-5996	77	36	)	)	PUNCT
ejpam-5996	77	37	is	be	AUX
ejpam-5996	77	38	computed	compute	VERB
ejpam-5996	77	39	as	as	ADP
ejpam-5996	77	40	:	:	PUNCT
ejpam-5996	77	41	slope	slope	NOUN
ejpam-5996	77	42	=	=	SYM
ejpam-5996	77	43	k	k	PROPN
ejpam-5996	78	1	=	=	PRON
ejpam-5996	78	2	degar+m	degar+m	VERB
ejpam-5996	78	3	−	−	PROPN
ejpam-5996	78	4	degar	degar	VERB
ejpam-5996	78	5	m	m	PROPN
ejpam-5996	78	6	.	.	PUNCT
ejpam-5996	79	1	denote	denote	VERB
ejpam-5996	79	2	by	by	ADP
ejpam-5996	79	3	kp	kp	PROPN
ejpam-5996	79	4	the	the	DET
ejpam-5996	79	5	set	set	NOUN
ejpam-5996	79	6	of	of	ADP
ejpam-5996	79	7	slopes	slope	NOUN
ejpam-5996	79	8	.	.	PUNCT
ejpam-5996	80	1	this	this	DET
ejpam-5996	80	2	result	result	NOUN
ejpam-5996	80	3	of	of	ADP
ejpam-5996	80	4	ben	ben	PROPN
ejpam-5996	80	5	nasr	nasr	PROPN
ejpam-5996	80	6	and	and	CCONJ
ejpam-5996	80	7	kthiri	kthiri	PROPN
ejpam-5996	80	8	was	be	AUX
ejpam-5996	80	9	a	a	DET
ejpam-5996	80	10	continuation	continuation	NOUN
ejpam-5996	80	11	of	of	ADP
ejpam-5996	80	12	an	an	DET
ejpam-5996	80	13	idea	idea	NOUN
ejpam-5996	80	14	we	we	PRON
ejpam-5996	80	15	started	start	VERB
ejpam-5996	80	16	in	in	ADP
ejpam-5996	80	17	[	[	X
ejpam-5996	80	18	7	7	NUM
ejpam-5996	80	19	]	]	PUNCT
ejpam-5996	80	20	.	.	PUNCT
ejpam-5996	81	1	we	we	PRON
ejpam-5996	81	2	established	establish	VERB
ejpam-5996	81	3	a	a	DET
ejpam-5996	81	4	well	well	ADV
ejpam-5996	81	5	-	-	PUNCT
ejpam-5996	81	6	known	know	VERB
ejpam-5996	81	7	criterion	criterion	NOUN
ejpam-5996	81	8	for	for	ADP
ejpam-5996	81	9	irreducibility	irreducibility	NOUN
ejpam-5996	81	10	,	,	PUNCT
ejpam-5996	81	11	which	which	PRON
ejpam-5996	81	12	can	can	AUX
ejpam-5996	81	13	be	be	AUX
ejpam-5996	81	14	formulated	formulate	VERB
ejpam-5996	81	15	as	as	SCONJ
ejpam-5996	81	16	follows	follow	VERB
ejpam-5996	81	17	:	:	PUNCT
ejpam-5996	81	18	theorem	theorem	NOUN
ejpam-5996	81	19	2	2	NUM
ejpam-5996	81	20	.	.	PUNCT
ejpam-5996	81	21	let	let	VERB
ejpam-5996	81	22	λ(y	λ(y	PRON
ejpam-5996	81	23	)	)	PUNCT
ejpam-5996	82	1	=	=	PUNCT
ejpam-5996	83	1	y	y	PROPN
ejpam-5996	83	2	d	d	PROPN
ejpam-5996	83	3	+	+	CCONJ
ejpam-5996	83	4	λd−1y	λd−1y	PROPN
ejpam-5996	83	5	d−1	d−1	PROPN
ejpam-5996	83	6	+	+	CCONJ
ejpam-5996	83	7	·	·	PUNCT
ejpam-5996	83	8	·	·	PUNCT
ejpam-5996	83	9	·	·	PUNCT
ejpam-5996	84	1	+	+	PUNCT
ejpam-5996	84	2	λ0	λ0	NOUN
ejpam-5996	84	3	be	be	VERB
ejpam-5996	84	4	a	a	DET
ejpam-5996	84	5	polynomial	polynomial	NOUN
ejpam-5996	84	6	with	with	ADP
ejpam-5996	84	7	coefficients	coefficient	NOUN
ejpam-5996	84	8	λi	λi	X
ejpam-5996	84	9	∈	∈	NOUN
ejpam-5996	84	10	fq[x	fq[x	PROPN
ejpam-5996	84	11	]	]	PUNCT
ejpam-5996	84	12	,	,	PUNCT
ejpam-5996	84	13	where	where	SCONJ
ejpam-5996	84	14	λ0	λ0	NOUN
ejpam-5996	84	15	̸=	̸=	PROPN
ejpam-5996	84	16	0	0	NUM
ejpam-5996	84	17	.	.	PUNCT
ejpam-5996	85	1	if	if	SCONJ
ejpam-5996	85	2	deg	deg	PROPN
ejpam-5996	85	3	λd−1	λd−1	PROPN
ejpam-5996	85	4	>	>	X
ejpam-5996	85	5	deg	deg	PROPN
ejpam-5996	85	6	λi	λi	ADP
ejpam-5996	85	7	for	for	ADP
ejpam-5996	85	8	all	all	DET
ejpam-5996	85	9	i	i	PRON
ejpam-5996	85	10	̸=	̸=	PROPN
ejpam-5996	85	11	d−	d−	PROPN
ejpam-5996	85	12	1	1	NUM
ejpam-5996	85	13	,	,	PUNCT
ejpam-5996	85	14	then	then	ADV
ejpam-5996	85	15	λ	λ	PROPN
ejpam-5996	85	16	is	be	AUX
ejpam-5996	85	17	irreducible	irreducible	ADJ
ejpam-5996	85	18	over	over	ADP
ejpam-5996	85	19	fq[x	fq[x	PROPN
ejpam-5996	85	20	]	]	PUNCT
ejpam-5996	85	21	.	.	PUNCT
ejpam-5996	86	1	however	however	ADV
ejpam-5996	86	2	,	,	PUNCT
ejpam-5996	86	3	the	the	DET
ejpam-5996	86	4	authors	author	NOUN
ejpam-5996	86	5	did	do	AUX
ejpam-5996	86	6	not	not	PART
ejpam-5996	86	7	refer	refer	VERB
ejpam-5996	86	8	to	to	ADP
ejpam-5996	86	9	our	our	PRON
ejpam-5996	86	10	findings	finding	NOUN
ejpam-5996	86	11	,	,	PUNCT
ejpam-5996	86	12	maybe	maybe	ADV
ejpam-5996	86	13	because	because	SCONJ
ejpam-5996	86	14	they	they	PRON
ejpam-5996	86	15	were	be	AUX
ejpam-5996	86	16	unaware	unaware	ADJ
ejpam-5996	86	17	of	of	ADP
ejpam-5996	86	18	it	it	PRON
ejpam-5996	86	19	or	or	CCONJ
ejpam-5996	86	20	because	because	SCONJ
ejpam-5996	86	21	they	they	PRON
ejpam-5996	86	22	were	be	AUX
ejpam-5996	86	23	focused	focus	VERB
ejpam-5996	86	24	on	on	ADP
ejpam-5996	86	25	studying	study	VERB
ejpam-5996	86	26	pisot	pisot	ADJ
ejpam-5996	86	27	numbers	number	NOUN
ejpam-5996	86	28	.	.	PUNCT
ejpam-5996	87	1	then	then	ADV
ejpam-5996	87	2	their	their	PRON
ejpam-5996	87	3	results	result	NOUN
ejpam-5996	87	4	on	on	ADP
ejpam-5996	87	5	irreducibility	irreducibility	NOUN
ejpam-5996	87	6	was	be	AUX
ejpam-5996	87	7	an	an	DET
ejpam-5996	87	8	unintended	unintended	ADJ
ejpam-5996	87	9	incidental	incidental	ADJ
ejpam-5996	87	10	result	result	NOUN
ejpam-5996	87	11	.	.	PUNCT
ejpam-5996	88	1	in	in	ADP
ejpam-5996	88	2	a	a	DET
ejpam-5996	88	3	second	second	ADJ
ejpam-5996	88	4	part	part	NOUN
ejpam-5996	88	5	of	of	ADP
ejpam-5996	88	6	this	this	DET
ejpam-5996	88	7	paper	paper	NOUN
ejpam-5996	88	8	,	,	PUNCT
ejpam-5996	88	9	we	we	PRON
ejpam-5996	88	10	generalize	generalize	VERB
ejpam-5996	88	11	these	these	DET
ejpam-5996	88	12	two	two	NUM
ejpam-5996	88	13	results	result	NOUN
ejpam-5996	88	14	and	and	CCONJ
ejpam-5996	88	15	provide	provide	VERB
ejpam-5996	88	16	a	a	DET
ejpam-5996	88	17	new	new	ADJ
ejpam-5996	88	18	criterion	criterion	NOUN
ejpam-5996	88	19	of	of	ADP
ejpam-5996	88	20	polynomials	polynomial	NOUN
ejpam-5996	88	21	’s	’s	PART
ejpam-5996	88	22	irreducibility	irreducibility	NOUN
ejpam-5996	88	23	over	over	ADP
ejpam-5996	88	24	fq[x	fq[x	PROPN
ejpam-5996	88	25	]	]	PUNCT
ejpam-5996	88	26	.	.	PUNCT
ejpam-5996	89	1	3	3	X
ejpam-5996	89	2	.	.	X
ejpam-5996	89	3	results	result	NOUN
ejpam-5996	89	4	now	now	ADV
ejpam-5996	89	5	,	,	PUNCT
ejpam-5996	89	6	we	we	PRON
ejpam-5996	89	7	are	be	AUX
ejpam-5996	89	8	prepared	prepared	ADJ
ejpam-5996	89	9	to	to	PART
ejpam-5996	89	10	give	give	VERB
ejpam-5996	89	11	the	the	DET
ejpam-5996	89	12	main	main	ADJ
ejpam-5996	89	13	results	result	NOUN
ejpam-5996	89	14	.	.	PUNCT
ejpam-5996	90	1	theorem	theorem	NOUN
ejpam-5996	90	2	3	3	X
ejpam-5996	90	3	.	.	PUNCT
ejpam-5996	91	1	let	let	AUX
ejpam-5996	91	2	fq	fq	PROPN
ejpam-5996	91	3	(	(	PUNCT
ejpam-5996	91	4	q	q	PROPN
ejpam-5996	91	5	=	=	SYM
ejpam-5996	91	6	pn	pn	PROPN
ejpam-5996	91	7	,	,	PUNCT
ejpam-5996	91	8	n	n	X
ejpam-5996	91	9	≥	≥	NOUN
ejpam-5996	91	10	2	2	NUM
ejpam-5996	91	11	and	and	CCONJ
ejpam-5996	91	12	p	p	NOUN
ejpam-5996	91	13	be	be	AUX
ejpam-5996	91	14	a	a	DET
ejpam-5996	91	15	prime	prime	NOUN
ejpam-5996	91	16	)	)	PUNCT
ejpam-5996	91	17	be	be	AUX
ejpam-5996	91	18	a	a	DET
ejpam-5996	91	19	finite	finite	ADJ
ejpam-5996	91	20	field	field	NOUN
ejpam-5996	91	21	of	of	ADP
ejpam-5996	91	22	characteristic	characteristic	ADJ
ejpam-5996	91	23	p.	p.	NOUN
ejpam-5996	91	24	consider	consider	VERB
ejpam-5996	91	25	the	the	DET
ejpam-5996	91	26	polynomial	polynomial	ADJ
ejpam-5996	91	27	p	p	X
ejpam-5996	91	28	(	(	PUNCT
ejpam-5996	91	29	y	y	PROPN
ejpam-5996	91	30	)	)	PUNCT
ejpam-5996	92	1	=	=	PUNCT
ejpam-5996	93	1	bnasy	bnasy	NOUN
ejpam-5996	93	2	s	s	PART
ejpam-5996	93	3	+	+	ADJ
ejpam-5996	93	4	bmas−1y	bmas−1y	ADJ
ejpam-5996	93	5	s−1	s−1	NOUN
ejpam-5996	93	6	+	+	PROPN
ejpam-5996	93	7	as−2y	as−2y	PROPN
ejpam-5996	93	8	s−2	s−2	PROPN
ejpam-5996	93	9	+	+	CCONJ
ejpam-5996	93	10	·	·	PUNCT
ejpam-5996	93	11	·	·	PUNCT
ejpam-5996	93	12	·	·	PUNCT
ejpam-5996	93	13	+	+	ADJ
ejpam-5996	93	14	a1y	a1y	PROPN
ejpam-5996	93	15	+	+	ADJ
ejpam-5996	93	16	a0	a0	NOUN
ejpam-5996	93	17	,	,	PUNCT
ejpam-5996	93	18	defined	define	VERB
ejpam-5996	93	19	over	over	ADP
ejpam-5996	93	20	fq[x	fq[x	PROPN
ejpam-5996	93	21	]	]	PUNCT
ejpam-5996	93	22	,	,	PUNCT
ejpam-5996	93	23	such	such	ADJ
ejpam-5996	93	24	that	that	DET
ejpam-5996	93	25	asas−1a0	asas−1a0	NOUN
ejpam-5996	93	26	̸=	̸=	PROPN
ejpam-5996	93	27	0	0	NUM
ejpam-5996	93	28	.	.	PUNCT
ejpam-5996	94	1	here	here	ADV
ejpam-5996	94	2	,	,	PUNCT
ejpam-5996	94	3	b	b	PROPN
ejpam-5996	94	4	is	be	AUX
ejpam-5996	94	5	an	an	DET
ejpam-5996	94	6	irreducible	irreducible	ADJ
ejpam-5996	94	7	factor	factor	NOUN
ejpam-5996	94	8	of	of	ADP
ejpam-5996	94	9	both	both	PRON
ejpam-5996	94	10	as	as	ADP
ejpam-5996	94	11	and	and	CCONJ
ejpam-5996	94	12	as−1	as−1	NOUN
ejpam-5996	94	13	,	,	PUNCT
ejpam-5996	94	14	but	but	CCONJ
ejpam-5996	94	15	b	b	NOUN
ejpam-5996	94	16	does	do	AUX
ejpam-5996	94	17	not	not	PART
ejpam-5996	94	18	divide	divide	VERB
ejpam-5996	94	19	asas−1	asas−1	PROPN
ejpam-5996	94	20	.	.	PUNCT
ejpam-5996	95	1	if	if	SCONJ
ejpam-5996	95	2	the	the	DET
ejpam-5996	95	3	inequality	inequality	NOUN
ejpam-5996	95	4	n	n	CCONJ
ejpam-5996	95	5	>	>	X
ejpam-5996	95	6	ms+	ms+	NOUN
ejpam-5996	95	7	(	(	PUNCT
ejpam-5996	95	8	s−	s−	PROPN
ejpam-5996	95	9	1)(degas	1)(degas	NUM
ejpam-5996	95	10	−m	−m	ADJ
ejpam-5996	95	11	degb	degb	NOUN
ejpam-5996	95	12	)	)	PUNCT
ejpam-5996	96	1	+	+	CCONJ
ejpam-5996	96	2	max	max	PROPN
ejpam-5996	96	3	(	(	PUNCT
ejpam-5996	96	4	max0≤i≤s−2	max0≤i≤s−2	PROPN
ejpam-5996	96	5	degai	degai	VERB
ejpam-5996	96	6	,	,	PUNCT
ejpam-5996	96	7	deg(b	deg(b	X
ejpam-5996	96	8	mas−1	mas−1	PROPN
ejpam-5996	96	9	)	)	PUNCT
ejpam-5996	96	10	)	)	PUNCT
ejpam-5996	96	11	degb	degb	PROPN
ejpam-5996	96	12	holds	hold	VERB
ejpam-5996	96	13	,	,	PUNCT
ejpam-5996	96	14	then	then	ADV
ejpam-5996	96	15	the	the	DET
ejpam-5996	96	16	polynomial	polynomial	ADJ
ejpam-5996	96	17	p	p	NOUN
ejpam-5996	96	18	is	be	AUX
ejpam-5996	96	19	irreducible	irreducible	ADJ
ejpam-5996	96	20	over	over	ADP
ejpam-5996	96	21	fq[x	fq[x	PROPN
ejpam-5996	96	22	]	]	PUNCT
ejpam-5996	96	23	.	.	PUNCT
ejpam-5996	97	1	proof	proof	NOUN
ejpam-5996	97	2	.	.	PUNCT
ejpam-5996	98	1	assume	assume	VERB
ejpam-5996	98	2	that	that	SCONJ
ejpam-5996	98	3	p	p	PROPN
ejpam-5996	98	4	can	can	AUX
ejpam-5996	98	5	be	be	AUX
ejpam-5996	98	6	expressed	express	VERB
ejpam-5996	98	7	as	as	ADP
ejpam-5996	98	8	the	the	DET
ejpam-5996	98	9	product	product	NOUN
ejpam-5996	98	10	p	p	NOUN
ejpam-5996	98	11	(	(	PUNCT
ejpam-5996	98	12	y	y	PROPN
ejpam-5996	98	13	)	)	PUNCT
ejpam-5996	99	1	=	=	SYM
ejpam-5996	99	2	q(y	q(y	NOUN
ejpam-5996	99	3	)	)	PUNCT
ejpam-5996	99	4	h(y	h(y	ADV
ejpam-5996	99	5	)	)	PUNCT
ejpam-5996	99	6	,	,	PUNCT
ejpam-5996	99	7	where	where	SCONJ
ejpam-5996	99	8	q	q	NOUN
ejpam-5996	99	9	and	and	CCONJ
ejpam-5996	99	10	h	h	NOUN
ejpam-5996	99	11	are	be	AUX
ejpam-5996	99	12	in	in	ADP
ejpam-5996	99	13	fq[x][y	fq[x][y	NOUN
ejpam-5996	99	14	]	]	PUNCT
ejpam-5996	99	15	.	.	PUNCT
ejpam-5996	100	1	let	let	VERB
ejpam-5996	100	2	a.	a.	PROPN
ejpam-5996	100	3	chandoul	chandoul	PROPN
ejpam-5996	100	4	,	,	PUNCT
ejpam-5996	100	5	a.	a.	NOUN
ejpam-5996	100	6	assiry	assiry	NOUN
ejpam-5996	100	7	/	/	SYM
ejpam-5996	100	8	eur	eur	PROPN
ejpam-5996	100	9	.	.	PUNCT
ejpam-5996	101	1	j.	j.	PROPN
ejpam-5996	101	2	pure	pure	PROPN
ejpam-5996	101	3	appl	appl	PROPN
ejpam-5996	101	4	.	.	PROPN
ejpam-5996	101	5	math	math	PROPN
ejpam-5996	101	6	,	,	PUNCT
ejpam-5996	101	7	18	18	NUM
ejpam-5996	101	8	(	(	PUNCT
ejpam-5996	101	9	2	2	NUM
ejpam-5996	101	10	)	)	PUNCT
ejpam-5996	101	11	(	(	PUNCT
ejpam-5996	101	12	2025	2025	NUM
ejpam-5996	101	13	)	)	PUNCT
ejpam-5996	101	14	,	,	PUNCT
ejpam-5996	101	15	5996	5996	NUM
ejpam-5996	101	16	5	5	NUM
ejpam-5996	101	17	of	of	ADP
ejpam-5996	101	18	9	9	NUM
ejpam-5996	101	19	q(y)=	q(y)=	NOUN
ejpam-5996	101	20	bdqjy	bdqjy	NOUN
ejpam-5996	101	21	j	j	NOUN
ejpam-5996	102	1	+	+	PROPN
ejpam-5996	102	2	qj−1y	qj−1y	PROPN
ejpam-5996	102	3	j−1	j−1	PROPN
ejpam-5996	102	4	+	+	NOUN
ejpam-5996	102	5	qj−2y	qj−2y	PROPN
ejpam-5996	102	6	j−2	j−2	PROPN
ejpam-5996	102	7	+	+	CCONJ
ejpam-5996	102	8	·	·	PUNCT
ejpam-5996	102	9	·	·	PUNCT
ejpam-5996	102	10	·	·	PUNCT
ejpam-5996	102	11	+	+	PUNCT
ejpam-5996	102	12	q1y	q1y	ADJ
ejpam-5996	102	13	+	+	ADJ
ejpam-5996	102	14	q0	q0	ADJ
ejpam-5996	102	15	and	and	CCONJ
ejpam-5996	102	16	h(y)=	h(y)=	ADP
ejpam-5996	102	17	bn−dhky	bn−dhky	PROPN
ejpam-5996	102	18	k	k	PROPN
ejpam-5996	102	19	+	+	PROPN
ejpam-5996	102	20	hk−1y	hk−1y	PROPN
ejpam-5996	102	21	k−1	k−1	PROPN
ejpam-5996	102	22	+	+	PROPN
ejpam-5996	102	23	hk−2y	hk−2y	PROPN
ejpam-5996	102	24	k−2	k−2	PROPN
ejpam-5996	102	25	+	+	CCONJ
ejpam-5996	102	26	·	·	PUNCT
ejpam-5996	102	27	·	·	PUNCT
ejpam-5996	102	28	·	·	PUNCT
ejpam-5996	102	29	+	+	NUM
ejpam-5996	102	30	h1y	h1y	NOUN
ejpam-5996	102	31	+	+	NOUN
ejpam-5996	102	32	h0	h0	NOUN
ejpam-5996	102	33	where	where	SCONJ
ejpam-5996	102	34	j+k	j+k	ADJ
ejpam-5996	102	35	=	=	SYM
ejpam-5996	102	36	s	s	NOUN
ejpam-5996	102	37	,	,	PUNCT
ejpam-5996	102	38	qjhk	qjhk	NOUN
ejpam-5996	102	39	=	=	PUNCT
ejpam-5996	102	40	as	as	ADP
ejpam-5996	102	41	,	,	PUNCT
ejpam-5996	102	42	q0h0	q0h0	PROPN
ejpam-5996	102	43	=	=	SYM
ejpam-5996	102	44	a0	a0	PROPN
ejpam-5996	102	45	,	,	PUNCT
ejpam-5996	102	46	as−1	as−1	PROPN
ejpam-5996	102	47	=	=	SYM
ejpam-5996	102	48	bdqjhk−1+bm−dhkqj−1	bdqjhk−1+bm−dhkqj−1	PROPN
ejpam-5996	102	49	.	.	PUNCT
ejpam-5996	102	50	assume	assume	VERB
ejpam-5996	102	51	that	that	SCONJ
ejpam-5996	102	52	d	d	PROPN
ejpam-5996	102	53	≤	≤	ADJ
ejpam-5996	102	54	n−	n−	NOUN
ejpam-5996	102	55	d.	d.	PROPN
ejpam-5996	102	56	consider	consider	VERB
ejpam-5996	102	57	the	the	DET
ejpam-5996	102	58	factorization	factorization	NOUN
ejpam-5996	102	59	of	of	ADP
ejpam-5996	102	60	the	the	DET
ejpam-5996	102	61	polynomials	polynomial	NOUN
ejpam-5996	102	62	p	p	NOUN
ejpam-5996	102	63	and	and	CCONJ
ejpam-5996	102	64	q	q	NOUN
ejpam-5996	102	65	in	in	ADP
ejpam-5996	102	66	the	the	DET
ejpam-5996	102	67	algebraic	algebraic	ADJ
ejpam-5996	102	68	closure	closure	NOUN
ejpam-5996	102	69	of	of	ADP
ejpam-5996	102	70	the	the	DET
ejpam-5996	102	71	field	field	NOUN
ejpam-5996	102	72	of	of	ADP
ejpam-5996	102	73	formal	formal	ADJ
ejpam-5996	102	74	laurent	laurent	PROPN
ejpam-5996	102	75	series	series	PROPN
ejpam-5996	102	76	fq((x−1	fq((x−1	PROPN
ejpam-5996	102	77	)	)	PUNCT
ejpam-5996	102	78	)	)	PUNCT
ejpam-5996	102	79	.	.	PUNCT
ejpam-5996	103	1	we	we	PRON
ejpam-5996	103	2	can	can	AUX
ejpam-5996	103	3	express	express	VERB
ejpam-5996	103	4	p	p	NOUN
ejpam-5996	103	5	and	and	CCONJ
ejpam-5996	103	6	q	q	NOUN
ejpam-5996	103	7	as	as	ADP
ejpam-5996	103	8	:	:	PUNCT
ejpam-5996	103	9	p	p	X
ejpam-5996	103	10	(	(	PUNCT
ejpam-5996	103	11	y	y	PROPN
ejpam-5996	103	12	)	)	PUNCT
ejpam-5996	103	13	=	=	PUNCT
ejpam-5996	103	14	as	as	ADP
ejpam-5996	103	15	n∏	n∏	PROPN
ejpam-5996	103	16	i=1	i=1	PROPN
ejpam-5996	103	17	(	(	PUNCT
ejpam-5996	103	18	y	y	PROPN
ejpam-5996	103	19	−	−	PROPN
ejpam-5996	103	20	ωi	ωi	PROPN
ejpam-5996	103	21	)	)	PUNCT
ejpam-5996	103	22	and	and	CCONJ
ejpam-5996	103	23	q(y	q(y	PROPN
ejpam-5996	103	24	)	)	PUNCT
ejpam-5996	104	1	=	=	PUNCT
ejpam-5996	105	1	qj	qj	PROPN
ejpam-5996	105	2	j∏	j∏	PROPN
ejpam-5996	106	1	i=1	i=1	PROPN
ejpam-5996	106	2	(	(	PUNCT
ejpam-5996	106	3	y	y	PROPN
ejpam-5996	106	4	−	−	PROPN
ejpam-5996	106	5	ωi	ωi	PROPN
ejpam-5996	106	6	)	)	PUNCT
ejpam-5996	106	7	,	,	PUNCT
ejpam-5996	106	8	where	where	SCONJ
ejpam-5996	106	9	ωi	ωi	PROPN
ejpam-5996	106	10	are	be	AUX
ejpam-5996	106	11	in	in	ADP
ejpam-5996	106	12	fq((x−1	fq((x−1	NOUN
ejpam-5996	106	13	)	)	PUNCT
ejpam-5996	106	14	)	)	PUNCT
ejpam-5996	107	1	for	for	ADP
ejpam-5996	107	2	all	all	DET
ejpam-5996	107	3	i	i	PRON
ejpam-5996	107	4	=	=	NOUN
ejpam-5996	107	5	1	1	NUM
ejpam-5996	107	6	,	,	PUNCT
ejpam-5996	107	7	.	.	PUNCT
ejpam-5996	107	8	.	.	PUNCT
ejpam-5996	107	9	.	.	PUNCT
ejpam-5996	108	1	,	,	PUNCT
ejpam-5996	108	2	n.	n.	PROPN
ejpam-5996	108	3	consider	consider	VERB
ejpam-5996	108	4	now	now	ADV
ejpam-5996	108	5	the	the	DET
ejpam-5996	108	6	non	non	ADJ
ejpam-5996	108	7	-	-	ADJ
ejpam-5996	108	8	archimedean	archimedean	ADJ
ejpam-5996	108	9	absolute	absolute	ADJ
ejpam-5996	108	10	value	value	NOUN
ejpam-5996	108	11	defined	define	VERB
ejpam-5996	108	12	over	over	ADP
ejpam-5996	108	13	a	a	DET
ejpam-5996	108	14	field	field	NOUN
ejpam-5996	108	15	where	where	SCONJ
ejpam-5996	108	16	each	each	DET
ejpam-5996	108	17	element	element	NOUN
ejpam-5996	108	18	ωi	ωi	NUM
ejpam-5996	108	19	belongs	belong	VERB
ejpam-5996	108	20	to	to	ADP
ejpam-5996	108	21	the	the	DET
ejpam-5996	108	22	algebraic	algebraic	ADJ
ejpam-5996	108	23	closure	closure	NOUN
ejpam-5996	108	24	of	of	ADP
ejpam-5996	108	25	fq((x	fq((x	NOUN
ejpam-5996	108	26	−1	−1	NOUN
ejpam-5996	108	27	)	)	PUNCT
ejpam-5996	108	28	)	)	PUNCT
ejpam-5996	108	29	for	for	ADP
ejpam-5996	108	30	all	all	DET
ejpam-5996	108	31	i	i	PRON
ejpam-5996	108	32	=	=	NOUN
ejpam-5996	108	33	1	1	NUM
ejpam-5996	108	34	,	,	PUNCT
ejpam-5996	108	35	.	.	PUNCT
ejpam-5996	108	36	.	.	PUNCT
ejpam-5996	109	1	.	.	PUNCT
ejpam-5996	110	1	,	,	PUNCT
ejpam-5996	111	1	n	n	CCONJ
ejpam-5996	111	2	,	,	PUNCT
ejpam-5996	112	1	and	and	CCONJ
ejpam-5996	112	2	set	set	VERB
ejpam-5996	112	3	a	a	DET
ejpam-5996	112	4	real	real	ADJ
ejpam-5996	112	5	number	number	NOUN
ejpam-5996	112	6	α	α	NOUN
ejpam-5996	112	7	≥	≥	NOUN
ejpam-5996	112	8	0	0	NUM
ejpam-5996	112	9	such	such	ADJ
ejpam-5996	112	10	that	that	SCONJ
ejpam-5996	112	11	|as|	|as|	PROPN
ejpam-5996	112	12	>	>	X
ejpam-5996	112	13	eαmax	eαmax	PROPN
ejpam-5996	112	14	|ai|	|ai|	NOUN
ejpam-5996	112	15	i	i	PRON
ejpam-5996	112	16	̸=s	̸=s	PROPN
ejpam-5996	112	17	then	then	ADV
ejpam-5996	112	18	,	,	PUNCT
ejpam-5996	112	19	applying	apply	VERB
ejpam-5996	112	20	viète	viète	NOUN
ejpam-5996	112	21	’s	’s	PART
ejpam-5996	112	22	theorem	theorem	ADJ
ejpam-5996	112	23	,	,	PUNCT
ejpam-5996	112	24	we	we	PRON
ejpam-5996	112	25	obtain	obtain	VERB
ejpam-5996	112	26	|ω1	|ω1	NUM
ejpam-5996	112	27	·	·	PUNCT
ejpam-5996	112	28	·	·	PUNCT
ejpam-5996	113	1	·	·	PUNCT
ejpam-5996	113	2	ωs|	ωs|	NUM
ejpam-5996	113	3	=	=	PRON
ejpam-5996	113	4	|ω1|	|ω1|	NOUN
ejpam-5996	113	5	·	·	PUNCT
ejpam-5996	113	6	·	·	PUNCT
ejpam-5996	113	7	·	·	PUNCT
ejpam-5996	114	1	|ωs|	|ωs|	NUM
ejpam-5996	114	2	=	=	PUNCT
ejpam-5996	114	3	|a0|	|a0|	NOUN
ejpam-5996	114	4	|as|	|as|	X
ejpam-5996	114	5	<	<	X
ejpam-5996	114	6	|a0|	|a0|	NOUN
ejpam-5996	114	7	eαmax	eαmax	VERB
ejpam-5996	114	8	|ai|	|ai|	NUM
ejpam-5996	114	9	i	i	PRON
ejpam-5996	114	10	̸=s	̸=s	PROPN
ejpam-5996	114	11	<	<	X
ejpam-5996	114	12	1	1	NUM
ejpam-5996	114	13	eα	eα	NOUN
ejpam-5996	114	14	,	,	PUNCT
ejpam-5996	114	15	thus	thus	ADV
ejpam-5996	114	16	,	,	PUNCT
ejpam-5996	114	17	we	we	PRON
ejpam-5996	114	18	must	must	AUX
ejpam-5996	114	19	have	have	AUX
ejpam-5996	114	20	,	,	PUNCT
ejpam-5996	114	21	for	for	ADP
ejpam-5996	114	22	any	any	DET
ejpam-5996	114	23	j	j	NOUN
ejpam-5996	114	24	:	:	PUNCT
ejpam-5996	114	25	=	=	SYM
ejpam-5996	114	26	1	1	NUM
ejpam-5996	114	27	,	,	PUNCT
ejpam-5996	114	28	·	·	PUNCT
ejpam-5996	114	29	·	·	PUNCT
ejpam-5996	114	30	·	·	PUNCT
ejpam-5996	114	31	,	,	PUNCT
ejpam-5996	114	32	n	n	CCONJ
ejpam-5996	114	33	,	,	PUNCT
ejpam-5996	114	34	|ωj	|ωj	VERB
ejpam-5996	114	35	|	|	ADV
ejpam-5996	114	36	<	<	X
ejpam-5996	114	37	1	1	NUM
ejpam-5996	114	38	eα	eα	NOUN
ejpam-5996	114	39	/	/	SYM
ejpam-5996	114	40	s	s	PART
ejpam-5996	114	41	.	.	PUNCT
ejpam-5996	115	1	consequently	consequently	ADV
ejpam-5996	115	2	,	,	PUNCT
ejpam-5996	115	3	we	we	PRON
ejpam-5996	115	4	find	find	VERB
ejpam-5996	115	5	|ω1	|ω1	NUM
ejpam-5996	115	6	·	·	PUNCT
ejpam-5996	115	7	·	·	PUNCT
ejpam-5996	115	8	·	·	PUNCT
ejpam-5996	115	9	ωj	ωj	ADP
ejpam-5996	115	10	|	|	ADV
ejpam-5996	115	11	<	<	X
ejpam-5996	115	12	1	1	NUM
ejpam-5996	115	13	ejα	ejα	NOUN
ejpam-5996	115	14	/	/	SYM
ejpam-5996	115	15	s	s	NOUN
ejpam-5996	115	16	.	.	PUNCT
ejpam-5996	116	1	on	on	ADP
ejpam-5996	116	2	the	the	DET
ejpam-5996	116	3	other	other	ADJ
ejpam-5996	116	4	hand	hand	NOUN
ejpam-5996	116	5	,	,	PUNCT
ejpam-5996	116	6	we	we	PRON
ejpam-5996	116	7	have	have	VERB
ejpam-5996	116	8	|ω1	|ω1	PRON
ejpam-5996	116	9	·	·	PUNCT
ejpam-5996	116	10	·	·	PUNCT
ejpam-5996	116	11	·	·	PUNCT
ejpam-5996	117	1	ωj	ωj	ADP
ejpam-5996	117	2	|	|	ADV
ejpam-5996	117	3	=	=	SYM
ejpam-5996	117	4	∣∣∣∣q0	∣∣∣∣q0	PROPN
ejpam-5996	117	5	qj	qj	PROPN
ejpam-5996	117	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5996	117	7	=	=	PUNCT
ejpam-5996	117	8	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5996	117	9	q0	q0	PROPN
ejpam-5996	117	10	bdqj	bdqj	NOUN
ejpam-5996	117	11	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5996	117	12	≥	≥	NUM
ejpam-5996	117	13	1	1	NUM
ejpam-5996	117	14	|bm|	|bm|	PROPN
ejpam-5996	117	15	|as|	|as|	PROPN
ejpam-5996	117	16	.	.	PUNCT
ejpam-5996	118	1	to	to	PART
ejpam-5996	118	2	reach	reach	VERB
ejpam-5996	118	3	a	a	DET
ejpam-5996	118	4	contraduction	contraduction	NOUN
ejpam-5996	118	5	,	,	PUNCT
ejpam-5996	118	6	it	it	PRON
ejpam-5996	118	7	is	be	AUX
ejpam-5996	118	8	still	still	ADV
ejpam-5996	118	9	necessary	necessary	ADJ
ejpam-5996	118	10	to	to	PART
ejpam-5996	118	11	chose	chose	VERB
ejpam-5996	118	12	α	α	PRON
ejpam-5996	118	13	such	such	ADJ
ejpam-5996	118	14	that	that	SCONJ
ejpam-5996	118	15	1	1	NUM
ejpam-5996	118	16	|bm|	|bm|	PROPN
ejpam-5996	118	17	|as|	|as|	PROPN
ejpam-5996	118	18	≥	≥	NOUN
ejpam-5996	118	19	1	1	NUM
ejpam-5996	118	20	ejα	ejα	NOUN
ejpam-5996	118	21	/	/	SYM
ejpam-5996	118	22	s	s	NOUN
ejpam-5996	118	23	.	.	PUNCT
ejpam-5996	119	1	it	it	PRON
ejpam-5996	119	2	can	can	AUX
ejpam-5996	119	3	be	be	AUX
ejpam-5996	119	4	sufficient	sufficient	ADJ
ejpam-5996	119	5	to	to	PART
ejpam-5996	119	6	choose	choose	VERB
ejpam-5996	119	7	α	α	PRON
ejpam-5996	119	8	such	such	ADJ
ejpam-5996	119	9	that	that	SCONJ
ejpam-5996	119	10	|bm|	|bm|	PROPN
ejpam-5996	119	11	|as|	|as|	PROPN
ejpam-5996	119	12	≤	≤	NUM
ejpam-5996	119	13	eα	eα	PROPN
ejpam-5996	119	14	/	/	SYM
ejpam-5996	119	15	s.	s.	PROPN
ejpam-5996	119	16	or	or	CCONJ
ejpam-5996	119	17	,	,	PUNCT
ejpam-5996	119	18	equivalently	equivalently	ADV
ejpam-5996	119	19	α	α	PROPN
ejpam-5996	119	20	is	be	AUX
ejpam-5996	119	21	greater	great	ADJ
ejpam-5996	119	22	than	than	ADP
ejpam-5996	119	23	or	or	CCONJ
ejpam-5996	119	24	equal	equal	ADJ
ejpam-5996	119	25	to	to	ADP
ejpam-5996	119	26	the	the	DET
ejpam-5996	119	27	quantity	quantity	NOUN
ejpam-5996	119	28	smdeg(b	smdeg(b	NOUN
ejpam-5996	119	29	)	)	PUNCT
ejpam-5996	119	30	+	+	SYM
ejpam-5996	119	31	s	s	X
ejpam-5996	119	32	(	(	PUNCT
ejpam-5996	119	33	deg(as)−	deg(as)−	PROPN
ejpam-5996	119	34	n	n	PRON
ejpam-5996	119	35	deg(b	deg(b	NUM
ejpam-5996	119	36	)	)	PUNCT
ejpam-5996	119	37	)	)	PUNCT
ejpam-5996	119	38	.	.	PUNCT
ejpam-5996	120	1	a.	a.	PROPN
ejpam-5996	120	2	chandoul	chandoul	PROPN
ejpam-5996	120	3	,	,	PUNCT
ejpam-5996	120	4	a.	a.	NOUN
ejpam-5996	120	5	assiry	assiry	NOUN
ejpam-5996	120	6	/	/	SYM
ejpam-5996	120	7	eur	eur	PROPN
ejpam-5996	120	8	.	.	PUNCT
ejpam-5996	121	1	j.	j.	PROPN
ejpam-5996	121	2	pure	pure	PROPN
ejpam-5996	121	3	appl	appl	PROPN
ejpam-5996	121	4	.	.	PROPN
ejpam-5996	121	5	math	math	PROPN
ejpam-5996	121	6	,	,	PUNCT
ejpam-5996	121	7	18	18	NUM
ejpam-5996	121	8	(	(	PUNCT
ejpam-5996	121	9	2	2	NUM
ejpam-5996	121	10	)	)	PUNCT
ejpam-5996	121	11	(	(	PUNCT
ejpam-5996	121	12	2025	2025	NUM
ejpam-5996	121	13	)	)	PUNCT
ejpam-5996	121	14	,	,	PUNCT
ejpam-5996	121	15	5996	5996	NUM
ejpam-5996	121	16	6	6	NUM
ejpam-5996	121	17	of	of	ADP
ejpam-5996	121	18	9	9	NUM
ejpam-5996	121	19	a	a	DET
ejpam-5996	121	20	possible	possible	ADJ
ejpam-5996	121	21	expression	expression	NOUN
ejpam-5996	121	22	for	for	ADP
ejpam-5996	121	23	α	α	NOUN
ejpam-5996	121	24	could	could	AUX
ejpam-5996	121	25	be	be	AUX
ejpam-5996	121	26	smdegb	smdegb	ADJ
ejpam-5996	121	27	+	+	CCONJ
ejpam-5996	121	28	s(degas	s(degas	NOUN
ejpam-5996	121	29	−	−	NOUN
ejpam-5996	121	30	n	n	CCONJ
ejpam-5996	121	31	degb	degb	NOUN
ejpam-5996	121	32	)	)	PUNCT
ejpam-5996	121	33	.	.	PUNCT
ejpam-5996	122	1	however	however	ADV
ejpam-5996	122	2	,	,	PUNCT
ejpam-5996	122	3	this	this	PRON
ejpam-5996	122	4	results	result	VERB
ejpam-5996	122	5	in	in	ADP
ejpam-5996	122	6	a	a	DET
ejpam-5996	122	7	contradiction	contradiction	NOUN
ejpam-5996	122	8	when	when	SCONJ
ejpam-5996	122	9	n	n	CCONJ
ejpam-5996	122	10	>	>	X
ejpam-5996	122	11	ms+	ms+	NOUN
ejpam-5996	122	12	(	(	PUNCT
ejpam-5996	122	13	s−	s−	PROPN
ejpam-5996	122	14	1)(degas	1)(degas	NUM
ejpam-5996	122	15	−mdegb	−mdegb	NOUN
ejpam-5996	122	16	)	)	PUNCT
ejpam-5996	123	1	+	+	CCONJ
ejpam-5996	123	2	max	max	PROPN
ejpam-5996	123	3	(	(	PUNCT
ejpam-5996	123	4	degai	degai	PROPN
ejpam-5996	123	5	0≤i≤s−2	0≤i≤s−2	NUM
ejpam-5996	123	6	,	,	PUNCT
ejpam-5996	123	7	bmas−1	bmas−1	NOUN
ejpam-5996	123	8	)	)	PUNCT
ejpam-5996	123	9	degb	degb	NOUN
ejpam-5996	123	10	.	.	PUNCT
ejpam-5996	124	1	what	what	PRON
ejpam-5996	124	2	was	be	AUX
ejpam-5996	124	3	to	to	PART
ejpam-5996	124	4	be	be	AUX
ejpam-5996	124	5	proved	prove	VERB
ejpam-5996	124	6	.	.	PUNCT
ejpam-5996	125	1	theorem	theorem	ADJ
ejpam-5996	125	2	4	4	NUM
ejpam-5996	125	3	.	.	PUNCT
ejpam-5996	126	1	let	let	VERB
ejpam-5996	126	2	fq	fq	PROPN
ejpam-5996	126	3	(	(	PUNCT
ejpam-5996	126	4	q	q	PROPN
ejpam-5996	126	5	=	=	SYM
ejpam-5996	126	6	pn	pn	PROPN
ejpam-5996	126	7	,	,	PUNCT
ejpam-5996	126	8	n	n	X
ejpam-5996	126	9	≥	≥	NOUN
ejpam-5996	126	10	2	2	NUM
ejpam-5996	126	11	and	and	CCONJ
ejpam-5996	126	12	p	p	NOUN
ejpam-5996	126	13	be	be	AUX
ejpam-5996	126	14	a	a	DET
ejpam-5996	126	15	prime	prime	NOUN
ejpam-5996	126	16	)	)	PUNCT
ejpam-5996	126	17	be	be	AUX
ejpam-5996	126	18	a	a	DET
ejpam-5996	126	19	finite	finite	ADJ
ejpam-5996	126	20	field	field	NOUN
ejpam-5996	126	21	of	of	ADP
ejpam-5996	126	22	characteristic	characteristic	ADJ
ejpam-5996	126	23	p	p	NOUN
ejpam-5996	126	24	and	and	CCONJ
ejpam-5996	126	25	let	let	VERB
ejpam-5996	126	26	p	p	PROPN
ejpam-5996	126	27	(	(	PUNCT
ejpam-5996	126	28	y	y	PROPN
ejpam-5996	126	29	)	)	PUNCT
ejpam-5996	127	1	=	=	PUNCT
ejpam-5996	128	1	bnasy	bnasy	NOUN
ejpam-5996	128	2	s	s	X
ejpam-5996	128	3	+	+	NOUN
ejpam-5996	128	4	bmas−2y	bmas−2y	PROPN
ejpam-5996	128	5	s−2	s−2	PROPN
ejpam-5996	128	6	+	+	PROPN
ejpam-5996	128	7	as−3y	as−3y	PROPN
ejpam-5996	128	8	s−3	s−3	NOUN
ejpam-5996	128	9	+	+	CCONJ
ejpam-5996	128	10	·	·	PUNCT
ejpam-5996	128	11	·	·	PUNCT
ejpam-5996	128	12	·	·	PUNCT
ejpam-5996	129	1	+	+	ADJ
ejpam-5996	129	2	a1y	a1y	PROPN
ejpam-5996	129	3	+	+	SYM
ejpam-5996	129	4	a0	a0	NOUN
ejpam-5996	129	5	be	be	VERB
ejpam-5996	129	6	a	a	DET
ejpam-5996	129	7	polynomial	polynomial	NOUN
ejpam-5996	129	8	over	over	ADP
ejpam-5996	129	9	fq[x	fq[x	PROPN
ejpam-5996	129	10	]	]	PUNCT
ejpam-5996	129	11	,	,	PUNCT
ejpam-5996	129	12	such	such	ADJ
ejpam-5996	129	13	that	that	SCONJ
ejpam-5996	129	14	asas−2a0	asas−2a0	PROPN
ejpam-5996	129	15	̸=	̸=	PROPN
ejpam-5996	129	16	0	0	NUM
ejpam-5996	129	17	,	,	PUNCT
ejpam-5996	129	18	b	b	NOUN
ejpam-5996	129	19	is	be	AUX
ejpam-5996	129	20	an	an	DET
ejpam-5996	129	21	irreducible	irreducible	ADJ
ejpam-5996	129	22	polynomial	polynomial	NOUN
ejpam-5996	129	23	over	over	ADP
ejpam-5996	129	24	fq	fq	PROPN
ejpam-5996	129	25	and	and	CCONJ
ejpam-5996	129	26	b	b	PROPN
ejpam-5996	129	27	∤	∤	PROPN
ejpam-5996	129	28	asas−2	asas−2	PROPN
ejpam-5996	129	29	.	.	PUNCT
ejpam-5996	130	1	if	if	SCONJ
ejpam-5996	130	2	n−m	n−m	PROPN
ejpam-5996	130	3	is	be	AUX
ejpam-5996	130	4	odd	odd	ADJ
ejpam-5996	130	5	,	,	PUNCT
ejpam-5996	130	6	and	and	CCONJ
ejpam-5996	130	7	n	n	CCONJ
ejpam-5996	130	8	>	>	X
ejpam-5996	130	9	ms+	ms+	NOUN
ejpam-5996	130	10	(	(	PUNCT
ejpam-5996	130	11	s−	s−	PROPN
ejpam-5996	130	12	1)(degas	1)(degas	NUM
ejpam-5996	130	13	−mdegb	−mdegb	NOUN
ejpam-5996	130	14	)	)	PUNCT
ejpam-5996	131	1	+	+	CCONJ
ejpam-5996	131	2	max	max	PROPN
ejpam-5996	131	3	(	(	PUNCT
ejpam-5996	131	4	degai	degai	PROPN
ejpam-5996	131	5	0≤i≤s−3	0≤i≤s−3	NUM
ejpam-5996	131	6	,	,	PUNCT
ejpam-5996	131	7	bmas−2	bmas−2	PROPN
ejpam-5996	131	8	)	)	PUNCT
ejpam-5996	131	9	degb	degb	NOUN
ejpam-5996	131	10	,	,	PUNCT
ejpam-5996	131	11	then	then	ADV
ejpam-5996	131	12	p	p	NOUN
ejpam-5996	131	13	is	be	AUX
ejpam-5996	131	14	irreducible	irreducible	ADJ
ejpam-5996	131	15	over	over	ADP
ejpam-5996	131	16	fq[x	fq[x	PROPN
ejpam-5996	131	17	]	]	PUNCT
ejpam-5996	131	18	.	.	PUNCT
ejpam-5996	132	1	proof	proof	NOUN
ejpam-5996	132	2	.	.	PUNCT
ejpam-5996	133	1	suppose	suppose	VERB
ejpam-5996	134	1	that	that	SCONJ
ejpam-5996	134	2	p	p	PROPN
ejpam-5996	134	3	(	(	PUNCT
ejpam-5996	134	4	y	y	PROPN
ejpam-5996	134	5	)	)	PUNCT
ejpam-5996	134	6	=	=	SYM
ejpam-5996	134	7	q(y	q(y	NOUN
ejpam-5996	134	8	)	)	PUNCT
ejpam-5996	134	9	h(y	h(y	ADV
ejpam-5996	134	10	)	)	PUNCT
ejpam-5996	134	11	,	,	PUNCT
ejpam-5996	134	12	where	where	SCONJ
ejpam-5996	134	13	q	q	X
ejpam-5996	134	14	,	,	PUNCT
ejpam-5996	134	15	h	h	PROPN
ejpam-5996	134	16	∈	∈	PROPN
ejpam-5996	134	17	fq[x][y	fq[x][y	NOUN
ejpam-5996	134	18	]	]	PUNCT
ejpam-5996	134	19	.	.	PUNCT
ejpam-5996	135	1	let	let	VERB
ejpam-5996	135	2	q(y)=	q(y)=	AUX
ejpam-5996	135	3	qjy	qjy	VERB
ejpam-5996	135	4	j	j	NOUN
ejpam-5996	135	5	+	+	NOUN
ejpam-5996	135	6	qj−1y	qj−1y	NOUN
ejpam-5996	135	7	j−1	j−1	PROPN
ejpam-5996	135	8	+	+	NOUN
ejpam-5996	135	9	qj−2y	qj−2y	PROPN
ejpam-5996	135	10	j−2	j−2	PROPN
ejpam-5996	135	11	+	+	CCONJ
ejpam-5996	135	12	·	·	PUNCT
ejpam-5996	135	13	·	·	PUNCT
ejpam-5996	135	14	·	·	PUNCT
ejpam-5996	136	1	+	+	PUNCT
ejpam-5996	136	2	q1y	q1y	ADJ
ejpam-5996	136	3	+	+	ADJ
ejpam-5996	136	4	q0	q0	ADJ
ejpam-5996	136	5	and	and	CCONJ
ejpam-5996	136	6	h(y)=	h(y)=	ADP
ejpam-5996	136	7	hky	hky	PROPN
ejpam-5996	136	8	k	k	PROPN
ejpam-5996	137	1	+	+	PROPN
ejpam-5996	137	2	hk−1y	hk−1y	PROPN
ejpam-5996	137	3	k−1	k−1	PROPN
ejpam-5996	137	4	+	+	PROPN
ejpam-5996	137	5	hk−2y	hk−2y	PROPN
ejpam-5996	137	6	k−2	k−2	PROPN
ejpam-5996	137	7	+	+	CCONJ
ejpam-5996	137	8	·	·	PUNCT
ejpam-5996	137	9	·	·	PUNCT
ejpam-5996	137	10	·	·	PUNCT
ejpam-5996	137	11	+	+	NUM
ejpam-5996	137	12	h1y	h1y	NOUN
ejpam-5996	137	13	+	+	NOUN
ejpam-5996	137	14	h0	h0	PROPN
ejpam-5996	137	15	where	where	SCONJ
ejpam-5996	137	16	j+	j+	PROPN
ejpam-5996	137	17	k	k	NOUN
ejpam-5996	137	18	=	=	SYM
ejpam-5996	137	19	s	s	PROPN
ejpam-5996	137	20	,	,	PUNCT
ejpam-5996	137	21	qjhk	qjhk	NOUN
ejpam-5996	137	22	=	=	PUNCT
ejpam-5996	137	23	as	as	ADP
ejpam-5996	137	24	,	,	PUNCT
ejpam-5996	137	25	q0h0	q0h0	PROPN
ejpam-5996	137	26	=	=	SYM
ejpam-5996	137	27	a0	a0	PROPN
ejpam-5996	137	28	and	and	CCONJ
ejpam-5996	137	29	bmas−1	bmas−1	PROPN
ejpam-5996	137	30	=	=	SYM
ejpam-5996	137	31	qjhk−1	qjhk−1	X
ejpam-5996	137	32	+	+	NOUN
ejpam-5996	137	33	hkqj−1	hkqj−1	NOUN
ejpam-5996	137	34	.	.	PROPN
ejpam-5996	137	35	assume	assume	VERB
ejpam-5996	137	36	that	that	SCONJ
ejpam-5996	137	37	n−d	n−d	PROPN
ejpam-5996	137	38	≥	≥	PRON
ejpam-5996	137	39	d.	d.	PROPN
ejpam-5996	137	40	then	then	ADV
ejpam-5996	137	41	,	,	PUNCT
ejpam-5996	137	42	using	use	VERB
ejpam-5996	137	43	precisely	precisely	ADV
ejpam-5996	137	44	the	the	DET
ejpam-5996	137	45	same	same	ADJ
ejpam-5996	137	46	justifications	justification	NOUN
ejpam-5996	137	47	as	as	ADP
ejpam-5996	137	48	in	in	ADP
ejpam-5996	137	49	the	the	DET
ejpam-5996	137	50	proof	proof	NOUN
ejpam-5996	137	51	of	of	ADP
ejpam-5996	137	52	theorem	theorem	NOUN
ejpam-5996	137	53	3	3	NUM
ejpam-5996	137	54	.	.	PUNCT
ejpam-5996	137	55	the	the	DET
ejpam-5996	137	56	remainder	remainder	NOUN
ejpam-5996	137	57	of	of	ADP
ejpam-5996	137	58	the	the	DET
ejpam-5996	137	59	proof	proof	NOUN
ejpam-5996	137	60	is	be	AUX
ejpam-5996	137	61	similar	similar	ADJ
ejpam-5996	137	62	to	to	ADP
ejpam-5996	137	63	that	that	PRON
ejpam-5996	137	64	of	of	ADP
ejpam-5996	137	65	theorem	theorem	NOUN
ejpam-5996	137	66	4	4	NUM
ejpam-5996	137	67	,	,	PUNCT
ejpam-5996	137	68	using	use	VERB
ejpam-5996	137	69	max	max	PROPN
ejpam-5996	137	70	(	(	PUNCT
ejpam-5996	137	71	degai	degai	PROPN
ejpam-5996	137	72	0≤i≤s−3	0≤i≤s−3	NUM
ejpam-5996	137	73	,	,	PUNCT
ejpam-5996	137	74	bmas−2	bmas−2	PROPN
ejpam-5996	137	75	)	)	PUNCT
ejpam-5996	137	76	instead	instead	ADV
ejpam-5996	137	77	of	of	ADP
ejpam-5996	137	78	max	max	PROPN
ejpam-5996	137	79	(	(	PUNCT
ejpam-5996	137	80	degai	degai	PROPN
ejpam-5996	137	81	0≤i≤s−2	0≤i≤s−2	NUM
ejpam-5996	137	82	,	,	PUNCT
ejpam-5996	137	83	bmas−1	bmas−1	NOUN
ejpam-5996	137	84	)	)	PUNCT
ejpam-5996	137	85	theorem	theorem	NOUN
ejpam-5996	137	86	5	5	NUM
ejpam-5996	137	87	.	.	PUNCT
ejpam-5996	138	1	let	let	VERB
ejpam-5996	138	2	p	p	NOUN
ejpam-5996	138	3	(	(	PUNCT
ejpam-5996	138	4	y	y	PROPN
ejpam-5996	138	5	)	)	PUNCT
ejpam-5996	139	1	=	=	PUNCT
ejpam-5996	140	1	y	y	PROPN
ejpam-5996	140	2	n	n	PROPN
ejpam-5996	140	3	+	+	CCONJ
ejpam-5996	140	4	an−1y	an−1y	PROPN
ejpam-5996	140	5	n−1	n−1	PROPN
ejpam-5996	140	6	+	+	PROPN
ejpam-5996	140	7	·	·	PUNCT
ejpam-5996	140	8	·	·	PUNCT
ejpam-5996	140	9	·	·	PUNCT
ejpam-5996	141	1	+	+	CCONJ
ejpam-5996	141	2	an−k+1y	an−k+1y	ADP
ejpam-5996	141	3	n−k+1	n−k+1	ADJ
ejpam-5996	141	4	+	+	NUM
ejpam-5996	141	5	an−ky	an−ky	ADP
ejpam-5996	141	6	n−k	n−k	NOUN
ejpam-5996	141	7	+	+	X
ejpam-5996	141	8	·	·	PUNCT
ejpam-5996	141	9	·	·	PUNCT
ejpam-5996	141	10	·	·	PUNCT
ejpam-5996	141	11	+	+	PUNCT
ejpam-5996	141	12	a1y	a1y	NOUN
ejpam-5996	141	13	+	+	SYM
ejpam-5996	141	14	a0	a0	PROPN
ejpam-5996	141	15	with	with	ADP
ejpam-5996	141	16	a0	a0	PROPN
ejpam-5996	141	17	̸=	̸=	PROPN
ejpam-5996	141	18	0	0	NUM
ejpam-5996	141	19	and	and	CCONJ
ejpam-5996	141	20	|an−k|	|an−k|	X
ejpam-5996	141	21	>	>	X
ejpam-5996	141	22	|ai|	|ai|	PROPN
ejpam-5996	141	23	i	i	PROPN
ejpam-5996	141	24	̸=n−k	̸=n−k	PROPN
ejpam-5996	141	25	be	be	VERB
ejpam-5996	141	26	a	a	DET
ejpam-5996	141	27	polynomial	polynomial	NOUN
ejpam-5996	141	28	over	over	ADP
ejpam-5996	141	29	fq[x	fq[x	PROPN
ejpam-5996	141	30	]	]	PUNCT
ejpam-5996	141	31	of	of	ADP
ejpam-5996	141	32	degree	degree	NOUN
ejpam-5996	141	33	≥	≥	X
ejpam-5996	141	34	k	k	NOUN
ejpam-5996	142	1	+	+	NOUN
ejpam-5996	143	1	1	1	X
ejpam-5996	143	2	.	.	PUNCT
ejpam-5996	143	3	if	if	SCONJ
ejpam-5996	143	4	degan−k	degan−k	AUX
ejpam-5996	143	5	>	>	X
ejpam-5996	143	6	k	k	PROPN
ejpam-5996	143	7	maxdegan−i	maxdegan−i	PROPN
ejpam-5996	143	8	1≤i≤k−1	1≤i≤k−1	NUM
ejpam-5996	143	9	and	and	CCONJ
ejpam-5996	143	10	k	k	PROPN
ejpam-5996	143	11	̸	̸	PUNCT
ejpam-5996	143	12	|	|	ADV
ejpam-5996	143	13	degan−k	degan−k	VERB
ejpam-5996	143	14	,	,	PUNCT
ejpam-5996	143	15	then	then	ADV
ejpam-5996	143	16	,	,	PUNCT
ejpam-5996	143	17	p	p	PROPN
ejpam-5996	143	18	has	have	VERB
ejpam-5996	143	19	no	no	DET
ejpam-5996	143	20	root	root	NOUN
ejpam-5996	143	21	in	in	ADP
ejpam-5996	143	22	fq((x	fq((x	NOUN
ejpam-5996	143	23	−1	−1	NOUN
ejpam-5996	143	24	)	)	PUNCT
ejpam-5996	143	25	)	)	PUNCT
ejpam-5996	143	26	with	with	ADP
ejpam-5996	143	27	modulus	modulus	NOUN
ejpam-5996	143	28	strictly	strictly	ADV
ejpam-5996	143	29	greater	great	ADJ
ejpam-5996	143	30	than	than	ADP
ejpam-5996	143	31	1	1	NUM
ejpam-5996	143	32	.	.	PUNCT
ejpam-5996	144	1	moreover	moreover	ADV
ejpam-5996	144	2	p	p	PROPN
ejpam-5996	144	3	is	be	AUX
ejpam-5996	144	4	irreducible	irreducible	ADJ
ejpam-5996	144	5	over	over	ADP
ejpam-5996	144	6	fq[x	fq[x	PROPN
ejpam-5996	144	7	−1	−1	NOUN
ejpam-5996	144	8	]	]	PUNCT
ejpam-5996	144	9	.	.	PUNCT
ejpam-5996	145	1	to	to	PART
ejpam-5996	145	2	prove	prove	VERB
ejpam-5996	145	3	this	this	DET
ejpam-5996	145	4	theorem	theorem	NOUN
ejpam-5996	145	5	,	,	PUNCT
ejpam-5996	145	6	we	we	PRON
ejpam-5996	145	7	use	use	VERB
ejpam-5996	145	8	the	the	DET
ejpam-5996	145	9	idea	idea	NOUN
ejpam-5996	145	10	of	of	ADP
ejpam-5996	145	11	a	a	DET
ejpam-5996	145	12	newton	newton	PROPN
ejpam-5996	145	13	polygon	polygon	PROPN
ejpam-5996	145	14	and	and	CCONJ
ejpam-5996	145	15	the	the	DET
ejpam-5996	145	16	following	follow	VERB
ejpam-5996	145	17	proposition	proposition	NOUN
ejpam-5996	145	18	:	:	PUNCT
ejpam-5996	145	19	proposition	proposition	NOUN
ejpam-5996	145	20	1	1	NUM
ejpam-5996	145	21	.	.	PUNCT
ejpam-5996	146	1	(	(	PUNCT
ejpam-5996	146	2	weiss	weiss	PROPN
ejpam-5996	146	3	,	,	PUNCT
ejpam-5996	146	4	pp	pp	ADV
ejpam-5996	146	5	73	73	NUM
ejpam-5996	146	6	-	-	SYM
ejpam-5996	146	7	75	75	NUM
ejpam-5996	146	8	)	)	PUNCT
ejpam-5996	146	9	let	let	VERB
ejpam-5996	146	10	p	p	PROPN
ejpam-5996	146	11	(	(	PUNCT
ejpam-5996	146	12	y	y	PROPN
ejpam-5996	146	13	)	)	PUNCT
ejpam-5996	146	14	=	=	PUNCT
ejpam-5996	147	1	any	any	DET
ejpam-5996	147	2	n	n	PRON
ejpam-5996	147	3	+	+	ADJ
ejpam-5996	147	4	an−1y	an−1y	PROPN
ejpam-5996	147	5	n−1	n−1	PROPN
ejpam-5996	147	6	+	+	PROPN
ejpam-5996	147	7	·	·	PUNCT
ejpam-5996	147	8	·	·	PUNCT
ejpam-5996	147	9	·	·	PUNCT
ejpam-5996	147	10	+	+	ADJ
ejpam-5996	147	11	a1y	a1y	NOUN
ejpam-5996	147	12	+	+	ADJ
ejpam-5996	147	13	a0	a0	NOUN
ejpam-5996	147	14	with	with	ADP
ejpam-5996	147	15	ana0	ana0	NOUN
ejpam-5996	147	16	̸=	̸=	PROPN
ejpam-5996	147	17	0	0	NUM
ejpam-5996	147	18	be	be	AUX
ejpam-5996	147	19	a	a	DET
ejpam-5996	147	20	polynomial	polynomial	NOUN
ejpam-5996	147	21	over	over	ADP
ejpam-5996	147	22	fq[x	fq[x	PROPN
ejpam-5996	147	23	]	]	PUNCT
ejpam-5996	147	24	.	.	PUNCT
ejpam-5996	148	1	let	let	VERB
ejpam-5996	148	2	kp	kp	PROPN
ejpam-5996	148	3	the	the	DET
ejpam-5996	148	4	set	set	NOUN
ejpam-5996	148	5	of	of	ADP
ejpam-5996	148	6	slopes	slope	NOUN
ejpam-5996	148	7	of	of	ADP
ejpam-5996	148	8	its	its	PRON
ejpam-5996	148	9	newton	newton	PROPN
ejpam-5996	148	10	polygon	polygon	PROPN
ejpam-5996	148	11	.	.	PUNCT
ejpam-5996	149	1	then	then	ADV
ejpam-5996	149	2	for	for	ADP
ejpam-5996	149	3	all	all	PRON
ejpam-5996	149	4	k	k	NOUN
ejpam-5996	149	5	=	=	PUNCT
ejpam-5996	149	6	degar+m	degar+m	VERB
ejpam-5996	149	7	−	−	NOUN
ejpam-5996	149	8	degar	degar	VERB
ejpam-5996	149	9	m	m	PROPN
ejpam-5996	149	10	∈	∈	PROPN
ejpam-5996	149	11	kp	kp	PROPN
ejpam-5996	149	12	a.	a.	PROPN
ejpam-5996	149	13	chandoul	chandoul	PROPN
ejpam-5996	149	14	,	,	PUNCT
ejpam-5996	149	15	a.	a.	NOUN
ejpam-5996	149	16	assiry	assiry	NOUN
ejpam-5996	149	17	/	/	SYM
ejpam-5996	149	18	eur	eur	PROPN
ejpam-5996	149	19	.	.	PUNCT
ejpam-5996	150	1	j.	j.	PROPN
ejpam-5996	150	2	pure	pure	PROPN
ejpam-5996	150	3	appl	appl	PROPN
ejpam-5996	150	4	.	.	PROPN
ejpam-5996	150	5	math	math	PROPN
ejpam-5996	150	6	,	,	PUNCT
ejpam-5996	150	7	18	18	NUM
ejpam-5996	150	8	(	(	PUNCT
ejpam-5996	150	9	2	2	NUM
ejpam-5996	150	10	)	)	PUNCT
ejpam-5996	150	11	(	(	PUNCT
ejpam-5996	150	12	2025	2025	NUM
ejpam-5996	150	13	)	)	PUNCT
ejpam-5996	150	14	,	,	PUNCT
ejpam-5996	150	15	5996	5996	NUM
ejpam-5996	150	16	7	7	NUM
ejpam-5996	150	17	of	of	ADP
ejpam-5996	150	18	9	9	NUM
ejpam-5996	150	19	•	•	NOUN
ejpam-5996	150	20	(	(	PUNCT
ejpam-5996	150	21	i	i	NOUN
ejpam-5996	150	22	)	)	PUNCT
ejpam-5996	151	1	p	p	NOUN
ejpam-5996	151	2	has	have	VERB
ejpam-5996	151	3	m	m	PROPN
ejpam-5996	151	4	roots	root	NOUN
ejpam-5996	151	5	α1	α1	NOUN
ejpam-5996	151	6	,	,	PUNCT
ejpam-5996	151	7	·	·	PUNCT
ejpam-5996	151	8	·	·	PUNCT
ejpam-5996	151	9	·	·	PUNCT
ejpam-5996	151	10	,	,	PUNCT
ejpam-5996	151	11	αm	αm	NOUN
ejpam-5996	151	12	such	such	ADJ
ejpam-5996	151	13	that	that	SCONJ
ejpam-5996	151	14	|	|	ADV
ejpam-5996	151	15	α1	α1	NOUN
ejpam-5996	151	16	|=	|=	X
ejpam-5996	151	17	·	·	PUNCT
ejpam-5996	151	18	·	·	PUNCT
ejpam-5996	151	19	·	·	PUNCT
ejpam-5996	152	1	=|	=|	NOUN
ejpam-5996	152	2	αm	αm	NOUN
ejpam-5996	152	3	|=	|=	PUNCT
ejpam-5996	152	4	e−k	e−k	X
ejpam-5996	152	5	•	•	NOUN
ejpam-5996	152	6	(	(	PUNCT
ejpam-5996	152	7	ii	ii	NOUN
ejpam-5996	152	8	)	)	PUNCT
ejpam-5996	152	9	the	the	DET
ejpam-5996	152	10	polynomial	polynomial	ADJ
ejpam-5996	152	11	pk(y	pk(y	PUNCT
ejpam-5996	152	12	)	)	PUNCT
ejpam-5996	152	13	=	=	PUNCT
ejpam-5996	153	1	m∏	m∏	PROPN
ejpam-5996	153	2	i=1	i=1	X
ejpam-5996	154	1	(	(	PUNCT
ejpam-5996	154	2	y	y	PROPN
ejpam-5996	154	3	−	−	PROPN
ejpam-5996	154	4	αi	αi	NOUN
ejpam-5996	154	5	)	)	PUNCT
ejpam-5996	154	6	and	and	CCONJ
ejpam-5996	154	7	p	p	X
ejpam-5996	154	8	(	(	PUNCT
ejpam-5996	154	9	y	y	PROPN
ejpam-5996	154	10	)	)	PUNCT
ejpam-5996	155	1	=	=	SYM
ejpam-5996	155	2	∏	∏	PROPN
ejpam-5996	155	3	k∈kp	k∈kp	NOUN
ejpam-5996	155	4	pk(y	pk(y	NUM
ejpam-5996	155	5	)	)	PUNCT
ejpam-5996	155	6	proposition	proposition	NOUN
ejpam-5996	155	7	2	2	NUM
ejpam-5996	155	8	.	.	PUNCT
ejpam-5996	155	9	let	let	VERB
ejpam-5996	155	10	p	p	NOUN
ejpam-5996	155	11	(	(	PUNCT
ejpam-5996	155	12	y	y	PROPN
ejpam-5996	155	13	)	)	PUNCT
ejpam-5996	156	1	=	=	PUNCT
ejpam-5996	157	1	y	y	PROPN
ejpam-5996	157	2	n+an−1y	n+an−1y	PROPN
ejpam-5996	157	3	n−1	n−1	PROPN
ejpam-5996	157	4	+	+	PROPN
ejpam-5996	157	5	·	·	PUNCT
ejpam-5996	157	6	·	·	PUNCT
ejpam-5996	157	7	·	·	PUNCT
ejpam-5996	157	8	+	+	ADJ
ejpam-5996	157	9	a1y	a1y	NOUN
ejpam-5996	157	10	+	+	ADJ
ejpam-5996	157	11	a0	a0	NOUN
ejpam-5996	157	12	with	with	ADP
ejpam-5996	157	13	a0	a0	PROPN
ejpam-5996	157	14	̸=	̸=	PROPN
ejpam-5996	157	15	0	0	NUM
ejpam-5996	157	16	be	be	AUX
ejpam-5996	157	17	a	a	DET
ejpam-5996	157	18	polynomial	polynomial	NOUN
ejpam-5996	157	19	over	over	ADP
ejpam-5996	157	20	fq[x	fq[x	PROPN
ejpam-5996	157	21	]	]	PUNCT
ejpam-5996	157	22	of	of	ADP
ejpam-5996	157	23	degree	degree	NOUN
ejpam-5996	157	24	≥	≥	X
ejpam-5996	157	25	k	k	NOUN
ejpam-5996	158	1	+	+	CCONJ
ejpam-5996	158	2	1	1	X
ejpam-5996	158	3	.	.	PUNCT
ejpam-5996	158	4	then	then	ADV
ejpam-5996	158	5	,	,	PUNCT
ejpam-5996	158	6	p	p	PROPN
ejpam-5996	158	7	has	have	VERB
ejpam-5996	158	8	exactly	exactly	ADV
ejpam-5996	158	9	k	k	ADJ
ejpam-5996	158	10	roots	root	NOUN
ejpam-5996	158	11	with	with	ADP
ejpam-5996	158	12	modulus	modulus	NOUN
ejpam-5996	158	13	strictly	strictly	ADV
ejpam-5996	158	14	greater	great	ADJ
ejpam-5996	158	15	than	than	ADP
ejpam-5996	158	16	1	1	NUM
ejpam-5996	158	17	and	and	CCONJ
ejpam-5996	158	18	all	all	DET
ejpam-5996	158	19	the	the	DET
ejpam-5996	158	20	remaining	remain	VERB
ejpam-5996	158	21	roots	root	NOUN
ejpam-5996	158	22	lie	lie	VERB
ejpam-5996	158	23	inside	inside	ADV
ejpam-5996	158	24	of	of	ADP
ejpam-5996	158	25	the	the	DET
ejpam-5996	158	26	unit	unit	NOUN
ejpam-5996	158	27	disc	disc	VERB
ejpam-5996	158	28	if	if	SCONJ
ejpam-5996	158	29	and	and	CCONJ
ejpam-5996	158	30	only	only	ADV
ejpam-5996	158	31	if	if	SCONJ
ejpam-5996	158	32	|an−k|	|an−k|	PROPN
ejpam-5996	158	33	>	>	X
ejpam-5996	158	34	|ai|	|ai|	PROPN
ejpam-5996	158	35	for	for	ADP
ejpam-5996	158	36	all	all	PRON
ejpam-5996	158	37	i	i	PRON
ejpam-5996	158	38	̸=	̸=	PROPN
ejpam-5996	158	39	n−	n−	PROPN
ejpam-5996	158	40	k.	k.	NOUN
ejpam-5996	158	41	proof	proof	NOUN
ejpam-5996	158	42	.	.	PUNCT
ejpam-5996	159	1	”	"	PUNCT
ejpam-5996	159	2	=	=	SYM
ejpam-5996	159	3	⇒	⇒	NOUN
ejpam-5996	159	4	”	"	PUNCT
ejpam-5996	159	5	let	let	VERB
ejpam-5996	159	6	ω1	ω1	PROPN
ejpam-5996	159	7	,	,	PUNCT
ejpam-5996	159	8	·	·	PUNCT
ejpam-5996	159	9	·	·	PUNCT
ejpam-5996	159	10	·	·	PUNCT
ejpam-5996	159	11	,	,	PUNCT
ejpam-5996	159	12	ωn	ωn	PRON
ejpam-5996	159	13	be	be	AUX
ejpam-5996	159	14	the	the	DET
ejpam-5996	159	15	roots	root	NOUN
ejpam-5996	159	16	of	of	ADP
ejpam-5996	159	17	p	p	NOUN
ejpam-5996	159	18	.	.	PUNCT
ejpam-5996	160	1	assuming	assume	VERB
ejpam-5996	160	2	that	that	SCONJ
ejpam-5996	160	3	|ω1|	|ω1|	VERB
ejpam-5996	160	4	≥	≥	PRON
ejpam-5996	160	5	·	·	PUNCT
ejpam-5996	160	6	·	·	PUNCT
ejpam-5996	160	7	·	·	PUNCT
ejpam-5996	160	8	≥	≥	X
ejpam-5996	160	9	|ωk|	|ωk|	PROPN
ejpam-5996	160	10	>	>	X
ejpam-5996	160	11	|ωn−k+1|	|ωn−k+1|	PROPN
ejpam-5996	160	12	≥	≥	NOUN
ejpam-5996	160	13	·	·	PUNCT
ejpam-5996	160	14	·	·	PUNCT
ejpam-5996	160	15	·	·	PUNCT
ejpam-5996	160	16	≥	≥	X
ejpam-5996	160	17	|ωn|	|ωn|	NUM
ejpam-5996	160	18	using	use	VERB
ejpam-5996	160	19	the	the	DET
ejpam-5996	160	20	viète	viète	NOUN
ejpam-5996	160	21	theorem	theorem	VERB
ejpam-5996	160	22	,	,	PUNCT
ejpam-5996	160	23	we	we	PRON
ejpam-5996	160	24	get	get	VERB
ejpam-5996	160	25	|an−l|	|an−l|	PROPN
ejpam-5996	160	26	=	=	SYM
ejpam-5996	160	27	|	|	ADV
ejpam-5996	160	28	∑	∑	ADV
ejpam-5996	160	29	i1<···<il≤n	i1<···<il≤n	NOUN
ejpam-5996	160	30	ωi1	ωi1	PROPN
ejpam-5996	160	31	·	·	PUNCT
ejpam-5996	160	32	·	·	PUNCT
ejpam-5996	160	33	·	·	PUNCT
ejpam-5996	160	34	ωil	ωil	NUM
ejpam-5996	160	35	|≤|	|≤|	X
ejpam-5996	160	36	ω1	ω1	X
ejpam-5996	160	37	·	·	PUNCT
ejpam-5996	160	38	·	·	PUNCT
ejpam-5996	160	39	·	·	PUNCT
ejpam-5996	160	40	ωl	ωl	PRON
ejpam-5996	160	41	|<|	|<|	PROPN
ejpam-5996	160	42	ω1	ω1	PROPN
ejpam-5996	160	43	·	·	PUNCT
ejpam-5996	160	44	·	·	PUNCT
ejpam-5996	160	45	·	·	PUNCT
ejpam-5996	160	46	ωk	ωk	ADP
ejpam-5996	160	47	|=	|=	X
ejpam-5996	160	48	|an−k|	|an−k|	X
ejpam-5996	160	49	”	"	PUNCT
ejpam-5996	160	50	⇐	⇐	NOUN
ejpam-5996	160	51	=	=	NOUN
ejpam-5996	160	52	”	"	PUNCT
ejpam-5996	160	53	suppose	suppose	VERB
ejpam-5996	160	54	that	that	SCONJ
ejpam-5996	160	55	|an−k|	|an−k|	PROPN
ejpam-5996	160	56	>	>	X
ejpam-5996	160	57	|ai|	|ai|	PROPN
ejpam-5996	160	58	for	for	ADP
ejpam-5996	160	59	all	all	PRON
ejpam-5996	160	60	i	i	PRON
ejpam-5996	160	61	̸=	̸=	PROPN
ejpam-5996	160	62	n	n	CCONJ
ejpam-5996	160	63	−	−	PROPN
ejpam-5996	160	64	k.	k.	PROPN
ejpam-5996	161	1	it	it	PRON
ejpam-5996	161	2	is	be	AUX
ejpam-5996	161	3	easy	easy	ADJ
ejpam-5996	161	4	to	to	PART
ejpam-5996	161	5	remark	remark	VERB
ejpam-5996	161	6	,	,	PUNCT
ejpam-5996	161	7	using	use	VERB
ejpam-5996	161	8	the	the	DET
ejpam-5996	161	9	viète	viète	NOUN
ejpam-5996	161	10	theorem	theorem	VERB
ejpam-5996	161	11	,	,	PUNCT
ejpam-5996	161	12	that	that	SCONJ
ejpam-5996	161	13	p	p	NOUN
ejpam-5996	161	14	has	have	VERB
ejpam-5996	161	15	at	at	ADV
ejpam-5996	161	16	least	least	ADV
ejpam-5996	161	17	one	one	NUM
ejpam-5996	161	18	root	root	NOUN
ejpam-5996	161	19	with	with	ADP
ejpam-5996	161	20	modulus	modulus	NOUN
ejpam-5996	161	21	strictly	strictly	ADV
ejpam-5996	161	22	greater	great	ADJ
ejpam-5996	161	23	than	than	ADP
ejpam-5996	161	24	1	1	NUM
ejpam-5996	161	25	.	.	PUNCT
ejpam-5996	162	1	assume	assume	VERB
ejpam-5996	162	2	now	now	ADV
ejpam-5996	162	3	,	,	PUNCT
ejpam-5996	162	4	that	that	SCONJ
ejpam-5996	162	5	p	p	PROPN
ejpam-5996	162	6	has	have	VERB
ejpam-5996	162	7	l	l	NOUN
ejpam-5996	162	8	̸=	̸=	PROPN
ejpam-5996	162	9	k	k	PROPN
ejpam-5996	162	10	roots	root	NOUN
ejpam-5996	162	11	ω1	ω1	PROPN
ejpam-5996	162	12	,	,	PUNCT
ejpam-5996	162	13	·	·	PUNCT
ejpam-5996	162	14	·	·	PUNCT
ejpam-5996	162	15	·	·	PUNCT
ejpam-5996	162	16	,	,	PUNCT
ejpam-5996	162	17	ωl	ωl	ADP
ejpam-5996	162	18	such	such	ADJ
ejpam-5996	162	19	that	that	PRON
ejpam-5996	162	20	|ω1|	|ω1|	VERB
ejpam-5996	162	21	≥	≥	PRON
ejpam-5996	162	22	·	·	PUNCT
ejpam-5996	162	23	·	·	PUNCT
ejpam-5996	162	24	·	·	PUNCT
ejpam-5996	162	25	≥	≥	PRON
ejpam-5996	162	26	|ωl|	|ωl|	VERB
ejpam-5996	162	27	>	>	X
ejpam-5996	162	28	|ωn−l+1|	|ωn−l+1|	PROPN
ejpam-5996	162	29	≥	≥	X
ejpam-5996	162	30	·	·	PUNCT
ejpam-5996	162	31	·	·	PUNCT
ejpam-5996	162	32	·	·	PUNCT
ejpam-5996	162	33	≥	≥	NUM
ejpam-5996	162	34	|ωn|	|ωn|	NUM
ejpam-5996	162	35	.	.	PUNCT
ejpam-5996	163	1	therefore	therefore	ADV
ejpam-5996	163	2	,	,	PUNCT
ejpam-5996	163	3	we	we	PRON
ejpam-5996	163	4	get	get	VERB
ejpam-5996	163	5	two	two	NUM
ejpam-5996	163	6	cases	case	NOUN
ejpam-5996	163	7	:	:	PUNCT
ejpam-5996	163	8	case	case	NOUN
ejpam-5996	163	9	1	1	NUM
ejpam-5996	163	10	:	:	PUNCT
ejpam-5996	163	11	l	l	X
ejpam-5996	163	12	<	<	X
ejpam-5996	163	13	k	k	X
ejpam-5996	163	14	,	,	PUNCT
ejpam-5996	163	15	then	then	ADV
ejpam-5996	163	16	from	from	ADP
ejpam-5996	163	17	the	the	DET
ejpam-5996	163	18	above	above	NOUN
ejpam-5996	163	19	we	we	PRON
ejpam-5996	163	20	can	can	AUX
ejpam-5996	163	21	conclude	conclude	VERB
ejpam-5996	163	22	that	that	SCONJ
ejpam-5996	163	23	|an−l|	|an−l|	PROPN
ejpam-5996	163	24	>	>	X
ejpam-5996	163	25	|ai|	|ai|	PROPN
ejpam-5996	163	26	for	for	ADP
ejpam-5996	163	27	all	all	PRON
ejpam-5996	163	28	i	i	PRON
ejpam-5996	163	29	̸=	̸=	PROPN
ejpam-5996	163	30	n−	n−	PROPN
ejpam-5996	163	31	l	l	NOUN
ejpam-5996	163	32	,	,	PUNCT
ejpam-5996	163	33	which	which	PRON
ejpam-5996	163	34	contraduct	contraduct	VERB
ejpam-5996	163	35	our	our	PRON
ejpam-5996	163	36	assume	assume	NOUN
ejpam-5996	163	37	.	.	PUNCT
ejpam-5996	164	1	case	case	NOUN
ejpam-5996	164	2	2	2	NUM
ejpam-5996	164	3	:	:	PUNCT
ejpam-5996	165	1	l	l	NOUN
ejpam-5996	165	2	>	>	X
ejpam-5996	166	1	k	k	X
ejpam-5996	166	2	,	,	PUNCT
ejpam-5996	166	3	we	we	PRON
ejpam-5996	166	4	have	have	VERB
ejpam-5996	166	5	|an−l|	|an−l|	PROPN
ejpam-5996	166	6	=	=	SYM
ejpam-5996	166	7	|	|	ADV
ejpam-5996	166	8	∑	∑	ADV
ejpam-5996	166	9	i1<···<il≤n	i1<···<il≤n	NOUN
ejpam-5996	166	10	ωi1	ωi1	PROPN
ejpam-5996	166	11	·	·	PUNCT
ejpam-5996	166	12	·	·	PUNCT
ejpam-5996	166	13	·	·	PUNCT
ejpam-5996	166	14	ωil	ωil	PROPN
ejpam-5996	166	15	|	|	ADV
ejpam-5996	166	16	=|	=|	NOUN
ejpam-5996	166	17	ω1	ω1	PROPN
ejpam-5996	166	18	·	·	PUNCT
ejpam-5996	166	19	·	·	PUNCT
ejpam-5996	166	20	·	·	PUNCT
ejpam-5996	166	21	ωl	ωl	ADP
ejpam-5996	167	1	|	|	ADV
ejpam-5996	167	2	>	>	X
ejpam-5996	167	3	|	|	ADV
ejpam-5996	167	4	∑	∑	ADV
ejpam-5996	167	5	i1<···<il≤n	i1<···<il≤n	NOUN
ejpam-5996	167	6	ωi1	ωi1	PROPN
ejpam-5996	167	7	·	·	PUNCT
ejpam-5996	167	8	·	·	PUNCT
ejpam-5996	168	1	·	·	PUNCT
ejpam-5996	168	2	ωik	ωik	PROPN
ejpam-5996	168	3	|	|	ADV
ejpam-5996	168	4	≥	≥	NOUN
ejpam-5996	168	5	|an−k|	|an−k|	X
ejpam-5996	168	6	contraduction	contraduction	NOUN
ejpam-5996	168	7	.	.	PUNCT
ejpam-5996	169	1	proof	proof	NOUN
ejpam-5996	169	2	.	.	PUNCT
ejpam-5996	170	1	of	of	ADP
ejpam-5996	170	2	theorem	theorem	NOUN
ejpam-5996	170	3	5	5	NUM
ejpam-5996	170	4	;	;	PUNCT
ejpam-5996	170	5	using	use	VERB
ejpam-5996	170	6	the	the	DET
ejpam-5996	170	7	proposition	proposition	NOUN
ejpam-5996	170	8	2	2	NUM
ejpam-5996	170	9	,	,	PUNCT
ejpam-5996	170	10	p	p	NOUN
ejpam-5996	170	11	has	have	VERB
ejpam-5996	170	12	exactly	exactly	ADV
ejpam-5996	170	13	k	k	ADJ
ejpam-5996	170	14	-	-	PUNCT
ejpam-5996	170	15	pisot	pisot	ADJ
ejpam-5996	170	16	elements	element	NOUN
ejpam-5996	170	17	.	.	PUNCT
ejpam-5996	171	1	since	since	SCONJ
ejpam-5996	171	2	degan−k	degan−k	VERB
ejpam-5996	171	3	>	>	X
ejpam-5996	171	4	k	k	PROPN
ejpam-5996	171	5	maxdegan−i	maxdegan−i	PROPN
ejpam-5996	171	6	1≤i≤k−1	1≤i≤k−1	NUM
ejpam-5996	171	7	,	,	PUNCT
ejpam-5996	171	8	therefore	therefore	ADV
ejpam-5996	171	9	,	,	PUNCT
ejpam-5996	171	10	the	the	DET
ejpam-5996	171	11	upper	upper	ADJ
ejpam-5996	171	12	newton	newton	PROPN
ejpam-5996	171	13	polygon	polygon	PROPN
ejpam-5996	171	14	of	of	ADP
ejpam-5996	171	15	p	p	PROPN
ejpam-5996	171	16	contains	contain	VERB
ejpam-5996	171	17	the	the	DET
ejpam-5996	171	18	line	line	NOUN
ejpam-5996	171	19	segment	segment	NOUN
ejpam-5996	171	20	joining	join	VERB
ejpam-5996	171	21	(	(	PUNCT
ejpam-5996	171	22	n	n	CCONJ
ejpam-5996	171	23	,	,	PUNCT
ejpam-5996	171	24	0	0	NUM
ejpam-5996	171	25	)	)	PUNCT
ejpam-5996	171	26	to	to	ADP
ejpam-5996	171	27	(	(	PUNCT
ejpam-5996	171	28	n−	n−	NOUN
ejpam-5996	171	29	1	1	NUM
ejpam-5996	171	30	,	,	PUNCT
ejpam-5996	171	31	dega−	dega−	VERB
ejpam-5996	171	32	n−	n−	NOUN
ejpam-5996	171	33	1	1	NUM
ejpam-5996	171	34	)	)	PUNCT
ejpam-5996	171	35	.	.	PUNCT
ejpam-5996	172	1	the	the	DET
ejpam-5996	172	2	slope	slope	NOUN
ejpam-5996	172	3	of	of	ADP
ejpam-5996	172	4	this	this	DET
ejpam-5996	172	5	line	line	NOUN
ejpam-5996	172	6	segment	segment	NOUN
ejpam-5996	172	7	is	be	AUX
ejpam-5996	172	8	−degan−k	−degan−k	PROPN
ejpam-5996	172	9	k	k	X
ejpam-5996	172	10	.	.	PUNCT
ejpam-5996	173	1	applaying	applaye	VERB
ejpam-5996	173	2	the	the	DET
ejpam-5996	173	3	proposition	proposition	NOUN
ejpam-5996	173	4	1	1	NUM
ejpam-5996	173	5	,	,	PUNCT
ejpam-5996	173	6	item	item	NOUN
ejpam-5996	173	7	(	(	PUNCT
ejpam-5996	173	8	i	i	NOUN
ejpam-5996	173	9	)	)	PUNCT
ejpam-5996	173	10	,	,	PUNCT
ejpam-5996	173	11	p	p	NOUN
ejpam-5996	173	12	has	have	VERB
ejpam-5996	173	13	n−	n−	PROPN
ejpam-5996	173	14	(	(	PUNCT
ejpam-5996	173	15	n−	n−	NOUN
ejpam-5996	173	16	k	k	NOUN
ejpam-5996	173	17	)	)	PUNCT
ejpam-5996	173	18	=	=	SYM
ejpam-5996	174	1	k	k	X
ejpam-5996	174	2	pisot	pisot	ADJ
ejpam-5996	174	3	elements	element	NOUN
ejpam-5996	174	4	with	with	ADP
ejpam-5996	174	5	same	same	ADJ
ejpam-5996	174	6	absolute	absolute	ADJ
ejpam-5996	174	7	value	value	NOUN
ejpam-5996	174	8	|	|	NOUN
ejpam-5996	174	9	ω1	ω1	PROPN
ejpam-5996	174	10	|=	|=	X
ejpam-5996	174	11	·	·	PUNCT
ejpam-5996	174	12	·	·	PUNCT
ejpam-5996	174	13	·	·	PUNCT
ejpam-5996	175	1	=|	=|	NOUN
ejpam-5996	175	2	ωk	ωk	ADP
ejpam-5996	175	3	|=	|=	X
ejpam-5996	175	4	q	q	X
ejpam-5996	175	5	degan−k	degan−k	PUNCT
ejpam-5996	175	6	k	k	PROPN
ejpam-5996	175	7	a.	a.	PROPN
ejpam-5996	175	8	chandoul	chandoul	PROPN
ejpam-5996	175	9	,	,	PUNCT
ejpam-5996	175	10	a.	a.	NOUN
ejpam-5996	175	11	assiry	assiry	NOUN
ejpam-5996	175	12	/	/	SYM
ejpam-5996	175	13	eur	eur	PROPN
ejpam-5996	175	14	.	.	PUNCT
ejpam-5996	176	1	j.	j.	PROPN
ejpam-5996	176	2	pure	pure	PROPN
ejpam-5996	176	3	appl	appl	PROPN
ejpam-5996	176	4	.	.	PROPN
ejpam-5996	176	5	math	math	PROPN
ejpam-5996	176	6	,	,	PUNCT
ejpam-5996	176	7	18	18	NUM
ejpam-5996	176	8	(	(	PUNCT
ejpam-5996	176	9	2	2	NUM
ejpam-5996	176	10	)	)	PUNCT
ejpam-5996	176	11	(	(	PUNCT
ejpam-5996	176	12	2025	2025	NUM
ejpam-5996	176	13	)	)	PUNCT
ejpam-5996	176	14	,	,	PUNCT
ejpam-5996	176	15	5996	5996	NUM
ejpam-5996	176	16	8	8	NUM
ejpam-5996	176	17	of	of	ADP
ejpam-5996	176	18	9	9	NUM
ejpam-5996	176	19	so	so	SCONJ
ejpam-5996	176	20	that	that	SCONJ
ejpam-5996	176	21	,	,	PUNCT
ejpam-5996	176	22	ω1	ω1	PROPN
ejpam-5996	176	23	,	,	PUNCT
ejpam-5996	176	24	·	·	PUNCT
ejpam-5996	176	25	·	·	PUNCT
ejpam-5996	176	26	·	·	PUNCT
ejpam-5996	176	27	,	,	PUNCT
ejpam-5996	176	28	ωk	ωk	ADP
ejpam-5996	176	29	/∈	/∈	ADJ
ejpam-5996	176	30	fq((x	fq((x	NOUN
ejpam-5996	176	31	−1	−1	NOUN
ejpam-5996	176	32	)	)	PUNCT
ejpam-5996	176	33	)	)	PUNCT
ejpam-5996	176	34	.	.	PUNCT
ejpam-5996	177	1	now	now	ADV
ejpam-5996	177	2	,	,	PUNCT
ejpam-5996	177	3	assume	assume	VERB
ejpam-5996	177	4	that	that	SCONJ
ejpam-5996	177	5	p	p	NOUN
ejpam-5996	177	6	decomposes	decompose	VERB
ejpam-5996	177	7	as	as	ADP
ejpam-5996	177	8	p	p	PROPN
ejpam-5996	177	9	(	(	PUNCT
ejpam-5996	177	10	y	y	NOUN
ejpam-5996	177	11	)	)	PUNCT
ejpam-5996	178	1	=	=	SYM
ejpam-5996	178	2	q(y	q(y	NOUN
ejpam-5996	178	3	)	)	PUNCT
ejpam-5996	178	4	h(y	h(y	ADV
ejpam-5996	178	5	)	)	PUNCT
ejpam-5996	178	6	,	,	PUNCT
ejpam-5996	178	7	such	such	ADJ
ejpam-5996	178	8	that	that	PRON
ejpam-5996	178	9	q	q	NOUN
ejpam-5996	178	10	,	,	PUNCT
ejpam-5996	178	11	h	h	NOUN
ejpam-5996	178	12	are	be	AUX
ejpam-5996	178	13	defined	define	VERB
ejpam-5996	178	14	as	as	ADP
ejpam-5996	178	15	follow	follow	NOUN
ejpam-5996	178	16	:	:	PUNCT
ejpam-5996	178	17	q(y)=	q(y)=	VERB
ejpam-5996	178	18	ys	ys	NOUN
ejpam-5996	178	19	+	+	NOUN
ejpam-5996	178	20	qs−1y	qs−1y	ADJ
ejpam-5996	178	21	s−1	s−1	NOUN
ejpam-5996	178	22	+	+	PROPN
ejpam-5996	178	23	qs−2y	qs−2y	PROPN
ejpam-5996	178	24	s−2	s−2	PROPN
ejpam-5996	178	25	+	+	CCONJ
ejpam-5996	178	26	·	·	PUNCT
ejpam-5996	178	27	·	·	PUNCT
ejpam-5996	178	28	·	·	PUNCT
ejpam-5996	179	1	+	+	PUNCT
ejpam-5996	179	2	q1y	q1y	ADJ
ejpam-5996	179	3	+	+	ADJ
ejpam-5996	179	4	q0	q0	ADJ
ejpam-5996	179	5	and	and	CCONJ
ejpam-5996	179	6	h(y)=	h(y)=	NOUN
ejpam-5996	179	7	yt	yt	NOUN
ejpam-5996	179	8	+	+	ADJ
ejpam-5996	179	9	ht−1y	ht−1y	PROPN
ejpam-5996	179	10	t−1	t−1	NOUN
ejpam-5996	180	1	+	+	ADJ
ejpam-5996	180	2	ht−2y	ht−2y	PROPN
ejpam-5996	180	3	t−2	t−2	PROPN
ejpam-5996	180	4	+	+	CCONJ
ejpam-5996	180	5	·	·	PUNCT
ejpam-5996	180	6	·	·	PUNCT
ejpam-5996	180	7	·	·	PUNCT
ejpam-5996	181	1	+	+	NUM
ejpam-5996	181	2	h1y	h1y	NOUN
ejpam-5996	181	3	+	+	NOUN
ejpam-5996	181	4	h0	h0	NOUN
ejpam-5996	181	5	where	where	SCONJ
ejpam-5996	181	6	q(y	q(y	PROPN
ejpam-5996	181	7	)	)	PUNCT
ejpam-5996	181	8	,	,	PUNCT
ejpam-5996	181	9	h(y	h(y	ADV
ejpam-5996	181	10	)	)	PUNCT
ejpam-5996	181	11	∈	∈	PROPN
ejpam-5996	181	12	fq[x][y	fq[x][y	NOUN
ejpam-5996	181	13	]	]	PUNCT
ejpam-5996	181	14	\	\	PROPN
ejpam-5996	181	15	fq	fq	PROPN
ejpam-5996	181	16	.	.	PROPN
ejpam-5996	181	17	case	case	NOUN
ejpam-5996	181	18	1	1	NUM
ejpam-5996	181	19	:	:	PUNCT
ejpam-5996	181	20	if	if	SCONJ
ejpam-5996	181	21	one	one	NUM
ejpam-5996	181	22	of	of	ADP
ejpam-5996	181	23	the	the	DET
ejpam-5996	181	24	polynomials	polynomial	NOUN
ejpam-5996	181	25	q	q	NOUN
ejpam-5996	181	26	or	or	CCONJ
ejpam-5996	181	27	h	h	NOUN
ejpam-5996	181	28	,	,	PUNCT
ejpam-5996	181	29	say	say	VERB
ejpam-5996	181	30	q	q	INTJ
ejpam-5996	181	31	,	,	PUNCT
ejpam-5996	181	32	vanishes	vanish	VERB
ejpam-5996	181	33	all	all	DET
ejpam-5996	181	34	the	the	DET
ejpam-5996	181	35	k	k	PROPN
ejpam-5996	181	36	roots	root	NOUN
ejpam-5996	181	37	with	with	ADP
ejpam-5996	181	38	absolute	absolute	ADJ
ejpam-5996	181	39	values	value	NOUN
ejpam-5996	181	40	greater	great	ADJ
ejpam-5996	181	41	than	than	ADP
ejpam-5996	181	42	1	1	NUM
ejpam-5996	181	43	.	.	NOUN
ejpam-5996	182	1	which	which	PRON
ejpam-5996	182	2	implies	imply	VERB
ejpam-5996	182	3	that	that	SCONJ
ejpam-5996	182	4	everyone	everyone	PRON
ejpam-5996	182	5	of	of	ADP
ejpam-5996	182	6	the	the	DET
ejpam-5996	182	7	roots	root	NOUN
ejpam-5996	182	8	of	of	ADP
ejpam-5996	182	9	h	h	NOUN
ejpam-5996	182	10	have	have	VERB
ejpam-5996	182	11	an	an	DET
ejpam-5996	182	12	absolute	absolute	ADJ
ejpam-5996	182	13	values	value	NOUN
ejpam-5996	182	14	less	less	ADJ
ejpam-5996	182	15	than	than	ADP
ejpam-5996	182	16	1	1	NUM
ejpam-5996	182	17	.	.	NOUN
ejpam-5996	182	18	which	which	PRON
ejpam-5996	182	19	,	,	PUNCT
ejpam-5996	182	20	given	give	VERB
ejpam-5996	182	21	|	|	ADV
ejpam-5996	182	22	h0	h0	NOUN
ejpam-5996	182	23	|≥	|≥	ADJ
ejpam-5996	182	24	1	1	NUM
ejpam-5996	182	25	,	,	PUNCT
ejpam-5996	182	26	is	be	AUX
ejpam-5996	182	27	not	not	PART
ejpam-5996	182	28	possible	possible	ADJ
ejpam-5996	182	29	.	.	PUNCT
ejpam-5996	183	1	case	case	NOUN
ejpam-5996	183	2	2	2	NUM
ejpam-5996	183	3	:	:	PUNCT
ejpam-5996	183	4	if	if	SCONJ
ejpam-5996	183	5	q	q	X
ejpam-5996	183	6	have	have	VERB
ejpam-5996	183	7	l	l	NOUN
ejpam-5996	183	8	roots	root	NOUN
ejpam-5996	183	9	with	with	ADP
ejpam-5996	183	10	absolute	absolute	ADJ
ejpam-5996	183	11	values	value	NOUN
ejpam-5996	183	12	greater	great	ADJ
ejpam-5996	183	13	than	than	ADP
ejpam-5996	183	14	1	1	NUM
ejpam-5996	183	15	and	and	CCONJ
ejpam-5996	183	16	h	h	NOUN
ejpam-5996	183	17	have	have	VERB
ejpam-5996	183	18	l	l	NOUN
ejpam-5996	183	19	roots	root	NOUN
ejpam-5996	183	20	with	with	ADP
ejpam-5996	183	21	absolute	absolute	ADJ
ejpam-5996	183	22	values	value	NOUN
ejpam-5996	183	23	greater	great	ADJ
ejpam-5996	183	24	than	than	ADP
ejpam-5996	183	25	1	1	NUM
ejpam-5996	183	26	,	,	PUNCT
ejpam-5996	183	27	such	such	ADJ
ejpam-5996	183	28	that	that	SCONJ
ejpam-5996	183	29	l	l	NOUN
ejpam-5996	184	1	+	+	NOUN
ejpam-5996	184	2	m	m	NOUN
ejpam-5996	184	3	=	=	ADJ
ejpam-5996	184	4	k.	k.	PROPN
ejpam-5996	184	5	then	then	ADV
ejpam-5996	184	6	,	,	PUNCT
ejpam-5996	184	7	degqs−l	degqs−l	NOUN
ejpam-5996	184	8	>	>	PUNCT
ejpam-5996	184	9	degqi	degqi	NOUN
ejpam-5996	184	10	i	i	PRON
ejpam-5996	184	11	̸=s−l	̸=s−l	PROPN
ejpam-5996	184	12	,	,	PUNCT
ejpam-5996	184	13	and	and	CCONJ
ejpam-5996	184	14	deght−m	deght−m	PROPN
ejpam-5996	184	15	>	>	PUNCT
ejpam-5996	184	16	degqi	degqi	NOUN
ejpam-5996	184	17	i	i	PRON
ejpam-5996	184	18	̸=t−m	̸=t−m	PROPN
ejpam-5996	184	19	.	.	PUNCT
ejpam-5996	185	1	or	or	CCONJ
ejpam-5996	185	2	degan−k	degan−k	X
ejpam-5996	185	3	>	>	X
ejpam-5996	185	4	k	k	PROPN
ejpam-5996	185	5	maxdegan−i	maxdegan−i	PROPN
ejpam-5996	185	6	1≤i≤k−1	1≤i≤k−1	NUM
ejpam-5996	185	7	,	,	PUNCT
ejpam-5996	186	1	then	then	ADV
ejpam-5996	186	2	degqs−l	degqs−l	NOUN
ejpam-5996	186	3	=	=	SYM
ejpam-5996	186	4	deght−m	deght−m	PROPN
ejpam-5996	186	5	.	.	PUNCT
ejpam-5996	187	1	in	in	ADP
ejpam-5996	187	2	addition	addition	NOUN
ejpam-5996	187	3	degan−k	degan−k	VERB
ejpam-5996	187	4	=	=	SYM
ejpam-5996	187	5	deg	deg	X
ejpam-5996	187	6	∑	∑	PUNCT
ejpam-5996	187	7	i+j	i+j	NUM
ejpam-5996	187	8	=	=	PROPN
ejpam-5996	187	9	k	k	X
ejpam-5996	187	10	qs−iht−j	qs−iht−j	PROPN
ejpam-5996	187	11	=	=	SYM
ejpam-5996	187	12	degqs−l	degqs−l	PROPN
ejpam-5996	187	13	+	+	CCONJ
ejpam-5996	187	14	deght−m	deght−m	PROPN
ejpam-5996	187	15	=	=	SYM
ejpam-5996	187	16	2degqs−l	2degqs−l	X
ejpam-5996	187	17	.	.	PUNCT
ejpam-5996	188	1	absurd	absurd	ADJ
ejpam-5996	188	2	.	.	PUNCT
ejpam-5996	189	1	then	then	ADV
ejpam-5996	189	2	,	,	PUNCT
ejpam-5996	189	3	we	we	PRON
ejpam-5996	189	4	deduce	deduce	VERB
ejpam-5996	189	5	that	that	SCONJ
ejpam-5996	189	6	p	p	NOUN
ejpam-5996	189	7	is	be	AUX
ejpam-5996	189	8	irreducible	irreducible	ADJ
ejpam-5996	189	9	over	over	ADP
ejpam-5996	189	10	fq[x	fq[x	PROPN
ejpam-5996	189	11	]	]	PUNCT
ejpam-5996	189	12	.	.	PUNCT
ejpam-5996	190	1	acknowledgements	acknowledgement	NOUN
ejpam-5996	190	2	the	the	DET
ejpam-5996	190	3	authors	author	NOUN
ejpam-5996	190	4	extend	extend	VERB
ejpam-5996	190	5	their	their	PRON
ejpam-5996	190	6	appreciation	appreciation	NOUN
ejpam-5996	190	7	to	to	ADP
ejpam-5996	190	8	umm	umm	INTJ
ejpam-5996	190	9	al	al	PROPN
ejpam-5996	190	10	-	-	PUNCT
ejpam-5996	190	11	qura	qura	PROPN
ejpam-5996	190	12	university	university	PROPN
ejpam-5996	190	13	,	,	PUNCT
ejpam-5996	190	14	saudi	saudi	PROPN
ejpam-5996	190	15	arabia	arabia	PROPN
ejpam-5996	190	16	for	for	ADP
ejpam-5996	190	17	funding	fund	VERB
ejpam-5996	190	18	this	this	DET
ejpam-5996	190	19	research	research	NOUN
ejpam-5996	190	20	work	work	NOUN
ejpam-5996	190	21	through	through	ADP
ejpam-5996	190	22	grant	grant	NOUN
ejpam-5996	190	23	number	number	NOUN
ejpam-5996	190	24	:	:	PUNCT
ejpam-5996	190	25	25uqu4270201gssr01	25uqu4270201gssr01	PROPN
ejpam-5996	190	26	.	.	PUNCT
ejpam-5996	191	1	funding	fund	VERB
ejpam-5996	191	2	this	this	DET
ejpam-5996	191	3	research	research	NOUN
ejpam-5996	191	4	work	work	NOUN
ejpam-5996	191	5	was	be	AUX
ejpam-5996	191	6	funded	fund	VERB
ejpam-5996	191	7	by	by	ADP
ejpam-5996	191	8	umm	umm	INTJ
ejpam-5996	191	9	al	al	PROPN
ejpam-5996	191	10	-	-	PUNCT
ejpam-5996	191	11	qura	qura	PROPN
ejpam-5996	191	12	university	university	NOUN
ejpam-5996	191	13	,	,	PUNCT
ejpam-5996	191	14	saudi	saudi	PROPN
ejpam-5996	191	15	arabia	arabia	PROPN
ejpam-5996	191	16	under	under	ADP
ejpam-5996	191	17	grant	grant	NOUN
ejpam-5996	191	18	number	number	NOUN
ejpam-5996	191	19	:	:	PUNCT
ejpam-5996	191	20	25uqu4270201gssr01	25uqu4270201gssr01	NUM
ejpam-5996	191	21	.	.	PUNCT
ejpam-5996	192	1	references	reference	NOUN
ejpam-5996	192	2	[	[	X
ejpam-5996	192	3	1	1	X
ejpam-5996	192	4	]	]	X
ejpam-5996	192	5	oussama	oussama	PROPN
ejpam-5996	192	6	dammak	dammak	PROPN
ejpam-5996	192	7	and	and	CCONJ
ejpam-5996	192	8	saber	saber	PROPN
ejpam-5996	192	9	mansour	mansour	PROPN
ejpam-5996	192	10	.	.	PROPN
ejpam-5996	193	1	on	on	ADP
ejpam-5996	193	2	salem	salem	PROPN
ejpam-5996	193	3	formal	formal	ADJ
ejpam-5996	193	4	power	power	NOUN
ejpam-5996	193	5	series	series	NOUN
ejpam-5996	193	6	.	.	PUNCT
ejpam-5996	194	1	european	european	PROPN
ejpam-5996	194	2	journal	journal	PROPN
ejpam-5996	194	3	of	of	ADP
ejpam-5996	194	4	pure	pure	ADJ
ejpam-5996	194	5	and	and	CCONJ
ejpam-5996	194	6	applied	applied	ADJ
ejpam-5996	194	7	mathematics	mathematic	NOUN
ejpam-5996	194	8	,	,	PUNCT
ejpam-5996	194	9	15(3):1321–1330	15(3):1321–1330	NUM
ejpam-5996	194	10	,	,	PUNCT
ejpam-5996	194	11	2022	2022	NUM
ejpam-5996	194	12	.	.	PUNCT
ejpam-5996	195	1	[	[	X
ejpam-5996	195	2	2	2	NUM
ejpam-5996	195	3	]	]	X
ejpam-5996	195	4	ahmed	ahmed	PROPN
ejpam-5996	195	5	cherchem	cherchem	PROPN
ejpam-5996	195	6	,	,	PUNCT
ejpam-5996	195	7	soufyane	soufyane	NOUN
ejpam-5996	195	8	bouguebrine	bouguebrine	NOUN
ejpam-5996	195	9	,	,	PUNCT
ejpam-5996	195	10	and	and	CCONJ
ejpam-5996	195	11	hamza	hamza	PROPN
ejpam-5996	195	12	boughambouz	boughambouz	PROPN
ejpam-5996	195	13	.	.	PUNCT
ejpam-5996	196	1	on	on	ADP
ejpam-5996	196	2	the	the	DET
ejpam-5996	196	3	construction	construction	NOUN
ejpam-5996	196	4	of	of	ADP
ejpam-5996	196	5	irreducible	irreducible	ADJ
ejpam-5996	196	6	and	and	CCONJ
ejpam-5996	196	7	primitive	primitive	ADJ
ejpam-5996	196	8	polynomials	polynomial	NOUN
ejpam-5996	196	9	from	from	ADP
ejpam-5996	196	10	fqm	fqm	NOUN
ejpam-5996	196	11	[	[	X
ejpam-5996	196	12	x	x	X
ejpam-5996	196	13	]	]	X
ejpam-5996	196	14	to	to	ADP
ejpam-5996	196	15	fq	fq	PROPN
ejpam-5996	196	16	[	[	X
ejpam-5996	196	17	x	x	X
ejpam-5996	196	18	]	]	X
ejpam-5996	196	19	.	.	PUNCT
ejpam-5996	197	1	finite	finite	PROPN
ejpam-5996	197	2	fields	field	NOUN
ejpam-5996	197	3	and	and	CCONJ
ejpam-5996	197	4	their	their	PRON
ejpam-5996	197	5	applications	application	NOUN
ejpam-5996	197	6	,	,	PUNCT
ejpam-5996	197	7	78:101971	78:101971	NUM
ejpam-5996	197	8	,	,	PUNCT
ejpam-5996	197	9	2022	2022	NUM
ejpam-5996	197	10	.	.	PUNCT
ejpam-5996	198	1	[	[	X
ejpam-5996	198	2	3	3	NUM
ejpam-5996	198	3	]	]	X
ejpam-5996	198	4	stephan	stephan	PROPN
ejpam-5996	198	5	lipka	lipka	PROPN
ejpam-5996	198	6	.	.	PUNCT
ejpam-5996	199	1	über	über	PROPN
ejpam-5996	199	2	die	die	VERB
ejpam-5996	199	3	irreduzibilität	irreduzibilität	PROPN
ejpam-5996	199	4	von	von	PROPN
ejpam-5996	199	5	polynomen	polynoman	NOUN
ejpam-5996	199	6	.	.	PUNCT
ejpam-5996	200	1	mathematische	mathematische	PROPN
ejpam-5996	200	2	annalen	annalen	PROPN
ejpam-5996	200	3	,	,	PUNCT
ejpam-5996	200	4	118(1):235–245	118(1):235–245	NUM
ejpam-5996	200	5	,	,	PUNCT
ejpam-5996	200	6	1941	1941	NUM
ejpam-5996	200	7	.	.	PUNCT
ejpam-5996	201	1	a.	a.	PROPN
ejpam-5996	201	2	chandoul	chandoul	PROPN
ejpam-5996	201	3	,	,	PUNCT
ejpam-5996	201	4	a.	a.	NOUN
ejpam-5996	201	5	assiry	assiry	NOUN
ejpam-5996	201	6	/	/	SYM
ejpam-5996	201	7	eur	eur	PROPN
ejpam-5996	201	8	.	.	PUNCT
ejpam-5996	202	1	j.	j.	PROPN
ejpam-5996	202	2	pure	pure	PROPN
ejpam-5996	202	3	appl	appl	PROPN
ejpam-5996	202	4	.	.	PROPN
ejpam-5996	202	5	math	math	PROPN
ejpam-5996	202	6	,	,	PUNCT
ejpam-5996	202	7	18	18	NUM
ejpam-5996	202	8	(	(	PUNCT
ejpam-5996	202	9	2	2	NUM
ejpam-5996	202	10	)	)	PUNCT
ejpam-5996	202	11	(	(	PUNCT
ejpam-5996	202	12	2025	2025	NUM
ejpam-5996	202	13	)	)	PUNCT
ejpam-5996	202	14	,	,	PUNCT
ejpam-5996	202	15	5996	5996	NUM
ejpam-5996	202	16	9	9	NUM
ejpam-5996	202	17	of	of	ADP
ejpam-5996	202	18	9	9	NUM
ejpam-5996	202	19	[	[	SYM
ejpam-5996	202	20	4	4	NUM
ejpam-5996	202	21	]	]	PUNCT
ejpam-5996	202	22	ravindranathan	ravindranathan	NOUN
ejpam-5996	202	23	thangadurai	thangadurai	ADJ
ejpam-5996	202	24	.	.	PUNCT
ejpam-5996	203	1	irreducibility	irreducibility	NOUN
ejpam-5996	203	2	of	of	ADP
ejpam-5996	203	3	polynomials	polynomial	NOUN
ejpam-5996	203	4	whose	whose	DET
ejpam-5996	203	5	coefficients	coefficient	NOUN
ejpam-5996	203	6	are	be	AUX
ejpam-5996	203	7	integers	integer	NOUN
ejpam-5996	203	8	.	.	PUNCT
ejpam-5996	204	1	mathematics	mathematic	NOUN
ejpam-5996	204	2	newsletter	newsletter	NOUN
ejpam-5996	204	3	,	,	PUNCT
ejpam-5996	204	4	17:29–61	17:29–61	NUM
ejpam-5996	204	5	,	,	PUNCT
ejpam-5996	204	6	2007	2007	NUM
ejpam-5996	204	7	.	.	PUNCT
ejpam-5996	205	1	[	[	X
ejpam-5996	205	2	5	5	NUM
ejpam-5996	205	3	]	]	PUNCT
ejpam-5996	205	4	hl	hl	NOUN
ejpam-5996	205	5	dorwart	dorwart	NOUN
ejpam-5996	205	6	.	.	PUNCT
ejpam-5996	206	1	irreducibility	irreducibility	NOUN
ejpam-5996	206	2	of	of	ADP
ejpam-5996	206	3	polynomials	polynomial	NOUN
ejpam-5996	206	4	.	.	PUNCT
ejpam-5996	207	1	the	the	DET
ejpam-5996	207	2	american	american	PROPN
ejpam-5996	207	3	mathematical	mathematical	PROPN
ejpam-5996	207	4	monthly	monthly	PROPN
ejpam-5996	207	5	,	,	PUNCT
ejpam-5996	207	6	42(6):369–381	42(6):369–381	PROPN
ejpam-5996	207	7	,	,	PUNCT
ejpam-5996	207	8	1935	1935	NUM
ejpam-5996	207	9	.	.	PUNCT
ejpam-5996	208	1	[	[	X
ejpam-5996	208	2	6	6	NUM
ejpam-5996	208	3	]	]	X
ejpam-5996	208	4	m	m	VERB
ejpam-5996	208	5	ben	ben	PROPN
ejpam-5996	208	6	nasr	nasr	PROPN
ejpam-5996	208	7	and	and	CCONJ
ejpam-5996	208	8	hassen	hassen	PROPN
ejpam-5996	208	9	kthiri	kthiri	PROPN
ejpam-5996	208	10	.	.	PUNCT
ejpam-5996	209	1	characterization	characterization	NOUN
ejpam-5996	209	2	of	of	ADP
ejpam-5996	209	3	2	2	NUM
ejpam-5996	209	4	-	-	PUNCT
ejpam-5996	209	5	pisot	pisot	ADJ
ejpam-5996	209	6	elements	element	NOUN
ejpam-5996	209	7	in	in	ADP
ejpam-5996	209	8	the	the	DET
ejpam-5996	209	9	field	field	NOUN
ejpam-5996	209	10	of	of	ADP
ejpam-5996	209	11	laurent	laurent	PROPN
ejpam-5996	209	12	series	series	PROPN
ejpam-5996	209	13	over	over	ADP
ejpam-5996	209	14	a	a	DET
ejpam-5996	209	15	finite	finite	ADJ
ejpam-5996	209	16	field	field	NOUN
ejpam-5996	209	17	.	.	PUNCT
ejpam-5996	210	1	mathematical	mathematical	ADJ
ejpam-5996	210	2	notes	note	NOUN
ejpam-5996	210	3	,	,	PUNCT
ejpam-5996	210	4	107:552–558	107:552–558	NUM
ejpam-5996	210	5	,	,	PUNCT
ejpam-5996	210	6	2020	2020	NUM
ejpam-5996	210	7	.	.	PUNCT
ejpam-5996	211	1	[	[	X
ejpam-5996	211	2	7	7	X
ejpam-5996	211	3	]	]	X
ejpam-5996	211	4	a	a	DET
ejpam-5996	211	5	chandoul	chandoul	PROPN
ejpam-5996	211	6	,	,	PUNCT
ejpam-5996	211	7	m	m	PROPN
ejpam-5996	211	8	jellali	jellali	PROPN
ejpam-5996	211	9	,	,	PUNCT
ejpam-5996	211	10	and	and	CCONJ
ejpam-5996	211	11	m	m	PROPN
ejpam-5996	211	12	mkaouar	mkaouar	NOUN
ejpam-5996	211	13	.	.	PUNCT
ejpam-5996	212	1	irreducibility	irreducibility	NOUN
ejpam-5996	212	2	criterion	criterion	NOUN
ejpam-5996	212	3	over	over	ADP
ejpam-5996	212	4	finite	finite	ADJ
ejpam-5996	212	5	fields	field	NOUN
ejpam-5996	212	6	.	.	PUNCT
ejpam-5996	213	1	communications	communication	NOUN
ejpam-5996	213	2	in	in	ADP
ejpam-5996	213	3	algebra	algebra	NOUN
ejpam-5996	213	4	,	,	PUNCT
ejpam-5996	213	5	39(9):3133–3137	39(9):3133–3137	NUM
ejpam-5996	213	6	,	,	PUNCT
ejpam-5996	213	7	2011	2011	NUM
ejpam-5996	213	8	.	.	PUNCT