id	sid	tid	token	lemma	pos
ejpam-6458	1	1	european	european	PROPN
ejpam-6458	1	2	journal	journal	PROPN
ejpam-6458	1	3	of	of	ADP
ejpam-6458	1	4	pure	pure	ADJ
ejpam-6458	1	5	and	and	CCONJ
ejpam-6458	1	6	applied	applied	ADJ
ejpam-6458	1	7	mathematics	mathematic	NOUN
ejpam-6458	1	8	2025	2025	NUM
ejpam-6458	1	9	,	,	PUNCT
ejpam-6458	1	10	vol	vol	NOUN
ejpam-6458	1	11	.	.	PROPN
ejpam-6458	1	12	18	18	NUM
ejpam-6458	1	13	,	,	PUNCT
ejpam-6458	1	14	issue	issue	NOUN
ejpam-6458	1	15	3	3	NUM
ejpam-6458	1	16	,	,	PUNCT
ejpam-6458	1	17	article	article	NOUN
ejpam-6458	1	18	number	number	NOUN
ejpam-6458	1	19	6458	6458	NUM
ejpam-6458	1	20	issn	issn	PROPN
ejpam-6458	1	21	1307	1307	NUM
ejpam-6458	1	22	-	-	SYM
ejpam-6458	1	23	5543	5543	NUM
ejpam-6458	1	24	–	–	PUNCT
ejpam-6458	1	25	ejpam.com	ejpam.com	X
ejpam-6458	1	26	published	publish	VERB
ejpam-6458	1	27	by	by	ADP
ejpam-6458	1	28	new	new	PROPN
ejpam-6458	1	29	york	york	PROPN
ejpam-6458	1	30	business	business	PROPN
ejpam-6458	1	31	global	global	PROPN
ejpam-6458	1	32	gelfand	gelfand	PROPN
ejpam-6458	1	33	-	-	PUNCT
ejpam-6458	1	34	tsetlin	tsetlin	PROPN
ejpam-6458	1	35	modules	module	NOUN
ejpam-6458	1	36	for	for	ADP
ejpam-6458	1	37	lie	lie	NOUN
ejpam-6458	1	38	algebras	algebra	NOUN
ejpam-6458	1	39	of	of	ADP
ejpam-6458	1	40	rank	rank	PROPN
ejpam-6458	1	41	2	2	NUM
ejpam-6458	1	42	milica	milica	PROPN
ejpam-6458	1	43	andelić,1,∗	andelić,1,∗	PROPN
ejpam-6458	1	44	,	,	PUNCT
ejpam-6458	1	45	carlos	carlos	PROPN
ejpam-6458	1	46	m.	m.	PROPN
ejpam-6458	1	47	da	da	PROPN
ejpam-6458	1	48	fonseca2,3	fonseca2,3	PROPN
ejpam-6458	1	49	,	,	PUNCT
ejpam-6458	1	50	vyacheslav	vyacheslav	NOUN
ejpam-6458	1	51	futorny4	futorny4	PROPN
ejpam-6458	1	52	,	,	PUNCT
ejpam-6458	1	53	andrew	andrew	PROPN
ejpam-6458	1	54	tsylke5	tsylke5	PROPN
ejpam-6458	1	55	1	1	NUM
ejpam-6458	1	56	department	department	NOUN
ejpam-6458	1	57	of	of	ADP
ejpam-6458	1	58	mathematics	mathematics	PROPN
ejpam-6458	1	59	,	,	PUNCT
ejpam-6458	1	60	kuwait	kuwait	PROPN
ejpam-6458	1	61	university	university	PROPN
ejpam-6458	1	62	,	,	PUNCT
ejpam-6458	1	63	al	al	PROPN
ejpam-6458	1	64	-	-	PUNCT
ejpam-6458	1	65	shadadiyah	shadadiyah	PROPN
ejpam-6458	1	66	,	,	PUNCT
ejpam-6458	1	67	kuwait	kuwait	PROPN
ejpam-6458	1	68	2	2	NUM
ejpam-6458	1	69	kuwait	kuwait	PROPN
ejpam-6458	1	70	college	college	PROPN
ejpam-6458	1	71	of	of	ADP
ejpam-6458	1	72	science	science	NOUN
ejpam-6458	1	73	and	and	CCONJ
ejpam-6458	1	74	technology	technology	NOUN
ejpam-6458	1	75	,	,	PUNCT
ejpam-6458	1	76	doha	doha	PROPN
ejpam-6458	1	77	district	district	PROPN
ejpam-6458	1	78	,	,	PUNCT
ejpam-6458	1	79	safat	safat	NOUN
ejpam-6458	1	80	13133	13133	NUM
ejpam-6458	1	81	,	,	PUNCT
ejpam-6458	1	82	kuwait	kuwait	PROPN
ejpam-6458	1	83	3	3	NUM
ejpam-6458	1	84	faculty	faculty	NOUN
ejpam-6458	1	85	of	of	ADP
ejpam-6458	1	86	applied	apply	VERB
ejpam-6458	1	87	mathematics	mathematic	NOUN
ejpam-6458	1	88	and	and	CCONJ
ejpam-6458	1	89	informatics	informatic	NOUN
ejpam-6458	1	90	,	,	PUNCT
ejpam-6458	1	91	technical	technical	ADJ
ejpam-6458	1	92	university	university	PROPN
ejpam-6458	1	93	of	of	ADP
ejpam-6458	1	94	sofia	sofia	PROPN
ejpam-6458	1	95	,	,	PUNCT
ejpam-6458	1	96	kliment	kliment	PROPN
ejpam-6458	1	97	ohridski	ohridski	PROPN
ejpam-6458	1	98	blvd	blvd	PROPN
ejpam-6458	1	99	.	.	PUNCT
ejpam-6458	2	1	8	8	NUM
ejpam-6458	2	2	,	,	PUNCT
ejpam-6458	2	3	1000	1000	NUM
ejpam-6458	2	4	sofia	sofia	NOUN
ejpam-6458	2	5	,	,	PUNCT
ejpam-6458	2	6	bulgaria	bulgaria	PROPN
ejpam-6458	2	7	4	4	NUM
ejpam-6458	2	8	shenzhen	shenzhen	PROPN
ejpam-6458	2	9	international	international	ADJ
ejpam-6458	2	10	center	center	NOUN
ejpam-6458	2	11	for	for	ADP
ejpam-6458	2	12	mathematics	mathematic	NOUN
ejpam-6458	2	13	,	,	PUNCT
ejpam-6458	2	14	southern	southern	ADJ
ejpam-6458	2	15	university	university	PROPN
ejpam-6458	2	16	of	of	ADP
ejpam-6458	2	17	science	science	NOUN
ejpam-6458	2	18	and	and	CCONJ
ejpam-6458	2	19	technology	technology	NOUN
ejpam-6458	2	20	,	,	PUNCT
ejpam-6458	2	21	china	china	PROPN
ejpam-6458	2	22	5	5	NUM
ejpam-6458	2	23	kyiv	kyiv	ADJ
ejpam-6458	2	24	taras	taras	PROPN
ejpam-6458	2	25	shevchenko	shevchenko	PROPN
ejpam-6458	2	26	university	university	PROPN
ejpam-6458	2	27	,	,	PUNCT
ejpam-6458	2	28	kyiv	kyiv	PROPN
ejpam-6458	2	29	,	,	PUNCT
ejpam-6458	2	30	ukraine	ukraine	ADJ
ejpam-6458	2	31	abstract	abstract	NOUN
ejpam-6458	2	32	.	.	PUNCT
ejpam-6458	3	1	we	we	PRON
ejpam-6458	3	2	explicitly	explicitly	ADV
ejpam-6458	3	3	construct	construct	VERB
ejpam-6458	3	4	families	family	NOUN
ejpam-6458	3	5	of	of	ADP
ejpam-6458	3	6	simple	simple	ADJ
ejpam-6458	3	7	modules	module	NOUN
ejpam-6458	3	8	for	for	ADP
ejpam-6458	3	9	all	all	DET
ejpam-6458	3	10	simple	simple	ADJ
ejpam-6458	3	11	lie	lie	NOUN
ejpam-6458	3	12	algebras	algebra	NOUN
ejpam-6458	3	13	of	of	ADP
ejpam-6458	3	14	rank	rank	NOUN
ejpam-6458	3	15	2	2	NUM
ejpam-6458	3	16	on	on	ADP
ejpam-6458	3	17	which	which	PRON
ejpam-6458	3	18	a	a	DET
ejpam-6458	3	19	certain	certain	ADJ
ejpam-6458	3	20	commutative	commutative	ADJ
ejpam-6458	3	21	subalgebra	subalgebra	NOUN
ejpam-6458	3	22	acts	act	VERB
ejpam-6458	3	23	diagonally	diagonally	ADV
ejpam-6458	3	24	with	with	ADP
ejpam-6458	3	25	a	a	DET
ejpam-6458	3	26	simple	simple	ADJ
ejpam-6458	3	27	spectrum	spectrum	NOUN
ejpam-6458	3	28	.	.	PUNCT
ejpam-6458	4	1	in	in	ADP
ejpam-6458	4	2	type	type	NOUN
ejpam-6458	4	3	a	a	PRON
ejpam-6458	4	4	,	,	PUNCT
ejpam-6458	4	5	these	these	DET
ejpam-6458	4	6	modules	module	NOUN
ejpam-6458	4	7	are	be	AUX
ejpam-6458	4	8	the	the	DET
ejpam-6458	4	9	well	well	ADV
ejpam-6458	4	10	-	-	PUNCT
ejpam-6458	4	11	known	know	VERB
ejpam-6458	4	12	generic	generic	ADJ
ejpam-6458	4	13	gelfand	gelfand	PROPN
ejpam-6458	4	14	-	-	PUNCT
ejpam-6458	4	15	tsetlin	tsetlin	PROPN
ejpam-6458	4	16	modules	module	NOUN
ejpam-6458	4	17	.	.	PUNCT
ejpam-6458	5	1	2020	2020	NUM
ejpam-6458	5	2	mathematics	mathematic	NOUN
ejpam-6458	5	3	subject	subject	NOUN
ejpam-6458	5	4	classifications	classification	NOUN
ejpam-6458	5	5	:	:	PUNCT
ejpam-6458	5	6	17b10	17b10	NUM
ejpam-6458	5	7	,	,	PUNCT
ejpam-6458	5	8	16g99	16g99	NUM
ejpam-6458	5	9	key	key	ADJ
ejpam-6458	5	10	words	word	NOUN
ejpam-6458	5	11	and	and	CCONJ
ejpam-6458	5	12	phrases	phrase	NOUN
ejpam-6458	5	13	:	:	PUNCT
ejpam-6458	5	14	gelfand	gelfand	ADJ
ejpam-6458	5	15	-	-	PUNCT
ejpam-6458	5	16	tsetlin	tsetlin	PROPN
ejpam-6458	5	17	module	module	NOUN
ejpam-6458	5	18	,	,	PUNCT
ejpam-6458	5	19	gelfand	gelfand	NOUN
ejpam-6458	5	20	-	-	PUNCT
ejpam-6458	5	21	tsetlin	tsetlin	PROPN
ejpam-6458	5	22	basis	basis	NOUN
ejpam-6458	5	23	,	,	PUNCT
ejpam-6458	5	24	lie	lie	VERB
ejpam-6458	5	25	algebras	algebras	PROPN
ejpam-6458	5	26	1	1	X
ejpam-6458	5	27	.	.	X
ejpam-6458	5	28	introduction	introduction	NOUN
ejpam-6458	5	29	let	let	VERB
ejpam-6458	5	30	g	g	PRON
ejpam-6458	5	31	be	be	AUX
ejpam-6458	5	32	a	a	DET
ejpam-6458	5	33	simple	simple	ADJ
ejpam-6458	5	34	finite	finite	ADJ
ejpam-6458	5	35	-	-	ADJ
ejpam-6458	5	36	dimensional	dimensional	ADJ
ejpam-6458	5	37	simple	simple	ADJ
ejpam-6458	5	38	lie	lie	NOUN
ejpam-6458	5	39	algebra	algebra	NOUN
ejpam-6458	5	40	over	over	ADP
ejpam-6458	5	41	the	the	DET
ejpam-6458	5	42	complex	complex	ADJ
ejpam-6458	5	43	numbers	number	NOUN
ejpam-6458	5	44	and	and	CCONJ
ejpam-6458	5	45	let	let	VERB
ejpam-6458	5	46	h	h	PRON
ejpam-6458	5	47	be	be	AUX
ejpam-6458	5	48	a	a	DET
ejpam-6458	5	49	fixed	fix	VERB
ejpam-6458	5	50	cartan	cartan	ADJ
ejpam-6458	5	51	subalgebra	subalgebra	NOUN
ejpam-6458	5	52	of	of	ADP
ejpam-6458	5	53	g.	g.	PROPN
ejpam-6458	5	54	a	a	DET
ejpam-6458	5	55	g	g	NOUN
ejpam-6458	5	56	-	-	PUNCT
ejpam-6458	5	57	module	module	NOUN
ejpam-6458	5	58	m	m	NOUN
ejpam-6458	5	59	is	be	AUX
ejpam-6458	5	60	weight	weight	NOUN
ejpam-6458	5	61	(	(	PUNCT
ejpam-6458	5	62	with	with	ADP
ejpam-6458	5	63	respect	respect	NOUN
ejpam-6458	5	64	to	to	ADP
ejpam-6458	5	65	h	h	NOUN
ejpam-6458	5	66	)	)	PUNCT
ejpam-6458	5	67	if	if	SCONJ
ejpam-6458	5	68	h	h	NOUN
ejpam-6458	5	69	is	be	AUX
ejpam-6458	5	70	diagonalizable	diagonalizable	ADJ
ejpam-6458	5	71	on	on	ADP
ejpam-6458	5	72	m	m	PROPN
ejpam-6458	5	73	,	,	PUNCT
ejpam-6458	5	74	that	that	PRON
ejpam-6458	5	75	is	is	ADV
ejpam-6458	5	76	m	m	PROPN
ejpam-6458	5	77	=	=	PUNCT
ejpam-6458	5	78	⊕	⊕	PROPN
ejpam-6458	5	79	λ∈h∗	λ∈h∗	PROPN
ejpam-6458	5	80	mλ	mλ	INTJ
ejpam-6458	5	81	,	,	PUNCT
ejpam-6458	5	82	where	where	SCONJ
ejpam-6458	5	83	hv	hv	PROPN
ejpam-6458	5	84	=	=	PROPN
ejpam-6458	5	85	λ(h)v	λ(h)v	PROPN
ejpam-6458	5	86	,	,	PUNCT
ejpam-6458	5	87	for	for	ADP
ejpam-6458	5	88	any	any	DET
ejpam-6458	5	89	v	v	NOUN
ejpam-6458	5	90	∈	∈	PROPN
ejpam-6458	5	91	mλ	mλ	NOUN
ejpam-6458	5	92	and	and	CCONJ
ejpam-6458	5	93	h	h	NOUN
ejpam-6458	5	94	∈	∈	PROPN
ejpam-6458	5	95	h.	h.	NOUN
ejpam-6458	6	1	the	the	DET
ejpam-6458	6	2	subspace	subspace	PROPN
ejpam-6458	6	3	mλ	mλ	NOUN
ejpam-6458	6	4	is	be	AUX
ejpam-6458	6	5	called	call	VERB
ejpam-6458	6	6	a	a	DET
ejpam-6458	6	7	weight	weight	NOUN
ejpam-6458	6	8	subspace	subspace	NOUN
ejpam-6458	6	9	of	of	ADP
ejpam-6458	6	10	weight	weight	NOUN
ejpam-6458	6	11	λ	λ	PROPN
ejpam-6458	6	12	,	,	PUNCT
ejpam-6458	6	13	if	if	SCONJ
ejpam-6458	6	14	mλ	mλ	NOUN
ejpam-6458	6	15	̸=	̸=	PROPN
ejpam-6458	6	16	0	0	NUM
ejpam-6458	6	17	.	.	PUNCT
ejpam-6458	7	1	simple	simple	ADJ
ejpam-6458	7	2	weight	weight	NOUN
ejpam-6458	7	3	modules	module	NOUN
ejpam-6458	7	4	were	be	AUX
ejpam-6458	7	5	studied	study	VERB
ejpam-6458	7	6	extensively	extensively	ADV
ejpam-6458	7	7	in	in	ADP
ejpam-6458	7	8	the	the	DET
ejpam-6458	7	9	last	last	ADJ
ejpam-6458	7	10	50	50	NUM
ejpam-6458	7	11	years	year	NOUN
ejpam-6458	7	12	.	.	PUNCT
ejpam-6458	8	1	classical	classical	ADJ
ejpam-6458	8	2	results	result	NOUN
ejpam-6458	8	3	of	of	ADP
ejpam-6458	8	4	fernando	fernando	NOUN
ejpam-6458	8	5	[	[	X
ejpam-6458	8	6	1	1	NUM
ejpam-6458	8	7	]	]	PUNCT
ejpam-6458	8	8	and	and	CCONJ
ejpam-6458	8	9	mathieu	mathieu	NOUN
ejpam-6458	9	1	[	[	X
ejpam-6458	9	2	2	2	NUM
ejpam-6458	9	3	]	]	PUNCT
ejpam-6458	9	4	provided	provide	VERB
ejpam-6458	9	5	a	a	DET
ejpam-6458	9	6	complete	complete	ADJ
ejpam-6458	9	7	classification	classification	NOUN
ejpam-6458	9	8	of	of	ADP
ejpam-6458	9	9	simple	simple	ADJ
ejpam-6458	9	10	weight	weight	NOUN
ejpam-6458	9	11	modules	module	NOUN
ejpam-6458	9	12	with	with	ADP
ejpam-6458	9	13	finite	finite	ADJ
ejpam-6458	9	14	-	-	ADJ
ejpam-6458	9	15	dimensional	dimensional	ADJ
ejpam-6458	9	16	weight	weight	NOUN
ejpam-6458	9	17	subspaces	subspace	NOUN
ejpam-6458	9	18	.	.	PUNCT
ejpam-6458	10	1	on	on	ADP
ejpam-6458	10	2	the	the	DET
ejpam-6458	10	3	other	other	ADJ
ejpam-6458	10	4	hand	hand	NOUN
ejpam-6458	10	5	,	,	PUNCT
ejpam-6458	10	6	the	the	DET
ejpam-6458	10	7	classification	classification	NOUN
ejpam-6458	10	8	of	of	ADP
ejpam-6458	10	9	simple	simple	ADJ
ejpam-6458	10	10	weight	weight	NOUN
ejpam-6458	10	11	modules	module	NOUN
ejpam-6458	10	12	with	with	ADP
ejpam-6458	10	13	infinite	infinite	ADJ
ejpam-6458	10	14	-	-	PUNCT
ejpam-6458	10	15	dimensional	dimensional	ADJ
ejpam-6458	10	16	weight	weight	NOUN
ejpam-6458	10	17	subspaces	subspace	NOUN
ejpam-6458	10	18	is	be	AUX
ejpam-6458	10	19	still	still	ADV
ejpam-6458	10	20	an	an	DET
ejpam-6458	10	21	open	open	ADJ
ejpam-6458	10	22	problem	problem	NOUN
ejpam-6458	10	23	.	.	PUNCT
ejpam-6458	11	1	the	the	DET
ejpam-6458	11	2	most	most	ADJ
ejpam-6458	11	3	progress	progress	NOUN
ejpam-6458	11	4	has	have	AUX
ejpam-6458	11	5	been	be	AUX
ejpam-6458	11	6	achieved	achieve	VERB
ejpam-6458	11	7	in	in	ADP
ejpam-6458	11	8	the	the	DET
ejpam-6458	11	9	case	case	NOUN
ejpam-6458	11	10	of	of	ADP
ejpam-6458	11	11	lie	lie	NOUN
ejpam-6458	11	12	algebras	algebra	NOUN
ejpam-6458	11	13	of	of	ADP
ejpam-6458	11	14	type	type	NOUN
ejpam-6458	11	15	a	a	PRON
ejpam-6458	11	16	,	,	PUNCT
ejpam-6458	11	17	where	where	SCONJ
ejpam-6458	11	18	simple	simple	ADJ
ejpam-6458	11	19	gelfandtsetlin	gelfandtsetlin	NOUN
ejpam-6458	11	20	modules	module	NOUN
ejpam-6458	11	21	were	be	AUX
ejpam-6458	11	22	classified	classify	VERB
ejpam-6458	11	23	(	(	PUNCT
ejpam-6458	11	24	see	see	VERB
ejpam-6458	11	25	[	[	X
ejpam-6458	11	26	3–6	3–6	X
ejpam-6458	11	27	]	]	X
ejpam-6458	11	28	and	and	CCONJ
ejpam-6458	11	29	references	reference	NOUN
ejpam-6458	11	30	therein	therein	ADV
ejpam-6458	11	31	)	)	PUNCT
ejpam-6458	11	32	.	.	PUNCT
ejpam-6458	12	1	these	these	PRON
ejpam-6458	12	2	are	be	AUX
ejpam-6458	12	3	weight	weight	NOUN
ejpam-6458	12	4	modules	module	NOUN
ejpam-6458	12	5	with	with	ADP
ejpam-6458	12	6	diagonalizable	diagonalizable	ADJ
ejpam-6458	12	7	action	action	NOUN
ejpam-6458	12	8	of	of	ADP
ejpam-6458	12	9	a	a	DET
ejpam-6458	12	10	certain	certain	ADJ
ejpam-6458	12	11	commutative	commutative	ADJ
ejpam-6458	12	12	subalgebra	subalgebra	NOUN
ejpam-6458	12	13	of	of	ADP
ejpam-6458	12	14	the	the	DET
ejpam-6458	12	15	universal	universal	ADJ
ejpam-6458	12	16	enveloping	enveloping	NOUN
ejpam-6458	12	17	algebra	algebra	NOUN
ejpam-6458	12	18	u(g	u(g	PROPN
ejpam-6458	12	19	)	)	PUNCT
ejpam-6458	12	20	,	,	PUNCT
ejpam-6458	12	21	called	call	VERB
ejpam-6458	12	22	the	the	DET
ejpam-6458	12	23	gelfand	gelfand	PROPN
ejpam-6458	12	24	-	-	PUNCT
ejpam-6458	12	25	tsetlin	tsetlin	PROPN
ejpam-6458	12	26	subalgebra	subalgebra	NOUN
ejpam-6458	12	27	.	.	PUNCT
ejpam-6458	13	1	generically	generically	ADV
ejpam-6458	13	2	,	,	PUNCT
ejpam-6458	13	3	such	such	ADJ
ejpam-6458	13	4	simple	simple	ADJ
ejpam-6458	13	5	gelfand	gelfand	ADJ
ejpam-6458	13	6	-	-	PUNCT
ejpam-6458	13	7	tsetlin	tsetlin	PROPN
ejpam-6458	13	8	modules	module	NOUN
ejpam-6458	13	9	have	have	VERB
ejpam-6458	13	10	infinite	infinite	ADJ
ejpam-6458	13	11	-	-	PUNCT
ejpam-6458	13	12	dimensional	dimensional	ADJ
ejpam-6458	13	13	weight	weight	NOUN
ejpam-6458	13	14	subspaces	subspace	NOUN
ejpam-6458	13	15	.	.	PUNCT
ejpam-6458	14	1	in	in	ADP
ejpam-6458	14	2	particular	particular	ADJ
ejpam-6458	14	3	,	,	PUNCT
ejpam-6458	14	4	in	in	ADP
ejpam-6458	14	5	the	the	DET
ejpam-6458	14	6	case	case	NOUN
ejpam-6458	14	7	of	of	ADP
ejpam-6458	14	8	sl(2	sl(2	PROPN
ejpam-6458	14	9	)	)	PUNCT
ejpam-6458	14	10	we	we	PRON
ejpam-6458	14	11	obtain	obtain	VERB
ejpam-6458	14	12	in	in	ADP
ejpam-6458	14	13	this	this	DET
ejpam-6458	14	14	way	way	NOUN
ejpam-6458	14	15	all	all	DET
ejpam-6458	14	16	simple	simple	ADJ
ejpam-6458	14	17	weight	weight	NOUN
ejpam-6458	14	18	modules	module	NOUN
ejpam-6458	14	19	.	.	PUNCT
ejpam-6458	15	1	they	they	PRON
ejpam-6458	15	2	depend	depend	VERB
ejpam-6458	15	3	on	on	ADP
ejpam-6458	15	4	two	two	NUM
ejpam-6458	15	5	parameters	parameter	NOUN
ejpam-6458	15	6	and	and	CCONJ
ejpam-6458	15	7	have	have	VERB
ejpam-6458	15	8	∗corresponding	∗corresponde	VERB
ejpam-6458	15	9	author	author	NOUN
ejpam-6458	15	10	.	.	PUNCT
ejpam-6458	16	1	doi	doi	NOUN
ejpam-6458	16	2	:	:	PUNCT
ejpam-6458	16	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6458	https://doi.org/10.29020/nybg.ejpam.v18i3.6458	PROPN
ejpam-6458	16	4	email	email	NOUN
ejpam-6458	16	5	addresses	address	NOUN
ejpam-6458	16	6	:	:	PUNCT
ejpam-6458	16	7	milica.andelic@ku.edu.kw	milica.andelic@ku.edu.kw	VERB
ejpam-6458	16	8	(	(	PUNCT
ejpam-6458	16	9	m.	m.	NOUN
ejpam-6458	16	10	andelić	andelić	ADV
ejpam-6458	16	11	)	)	PUNCT
ejpam-6458	16	12	,	,	PUNCT
ejpam-6458	16	13	c.dafonseca@kcst.edu.kw	c.dafonseca@kcst.edu.kw	NOUN
ejpam-6458	16	14	,	,	PUNCT
ejpam-6458	16	15	carlos.fonseca@tu-sofia.bg	carlos.fonseca@tu-sofia.bg	PUNCT
ejpam-6458	16	16	(	(	PUNCT
ejpam-6458	16	17	c.m	c.m	NOUN
ejpam-6458	16	18	.	.	PROPN
ejpam-6458	16	19	da	da	PROPN
ejpam-6458	16	20	fonseca	fonseca	PROPN
ejpam-6458	16	21	)	)	PUNCT
ejpam-6458	16	22	,	,	PUNCT
ejpam-6458	16	23	vfutorny@gmail.com	vfutorny@gmail.com	X
ejpam-6458	16	24	(	(	PUNCT
ejpam-6458	16	25	v.	v.	ADP
ejpam-6458	16	26	futorny	futorny	NOUN
ejpam-6458	16	27	)	)	PUNCT
ejpam-6458	16	28	,	,	PUNCT
ejpam-6458	16	29	andrew4tsylke@gmail.com	andrew4tsylke@gmail.com	X
ejpam-6458	16	30	(	(	PUNCT
ejpam-6458	16	31	a.	a.	PROPN
ejpam-6458	16	32	tsylke	tsylke	PROPN
ejpam-6458	16	33	)	)	PUNCT
ejpam-6458	16	34	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6458	17	1	1	1	NUM
ejpam-6458	17	2	copyright	copyright	NOUN
ejpam-6458	17	3	:	:	PUNCT
ejpam-6458	17	4	©	©	PROPN
ejpam-6458	17	5	2025	2025	NUM
ejpam-6458	17	6	the	the	DET
ejpam-6458	17	7	author(s	author(s	NOUN
ejpam-6458	17	8	)	)	PUNCT
ejpam-6458	17	9	.	.	PUNCT
ejpam-6458	18	1	(	(	PUNCT
ejpam-6458	18	2	cc	cc	NOUN
ejpam-6458	18	3	by	by	ADP
ejpam-6458	18	4	-	-	PUNCT
ejpam-6458	18	5	nc	nc	PROPN
ejpam-6458	18	6	4.0	4.0	NUM
ejpam-6458	18	7	)	)	PUNCT
ejpam-6458	18	8	m.	m.	NOUN
ejpam-6458	18	9	andelić	andelić	PROPN
ejpam-6458	18	10	et	et	PROPN
ejpam-6458	18	11	al	al	PROPN
ejpam-6458	18	12	.	.	PUNCT
ejpam-6458	18	13	/	/	SYM
ejpam-6458	18	14	eur	eur	PROPN
ejpam-6458	18	15	.	.	PUNCT
ejpam-6458	19	1	j.	j.	PROPN
ejpam-6458	19	2	pure	pure	PROPN
ejpam-6458	19	3	appl	appl	PROPN
ejpam-6458	19	4	.	.	PROPN
ejpam-6458	19	5	math	math	PROPN
ejpam-6458	19	6	,	,	PUNCT
ejpam-6458	19	7	18	18	NUM
ejpam-6458	19	8	(	(	PUNCT
ejpam-6458	19	9	3	3	NUM
ejpam-6458	19	10	)	)	PUNCT
ejpam-6458	19	11	(	(	PUNCT
ejpam-6458	19	12	2025	2025	NUM
ejpam-6458	19	13	)	)	PUNCT
ejpam-6458	19	14	,	,	PUNCT
ejpam-6458	19	15	6458	6458	NUM
ejpam-6458	19	16	2	2	NUM
ejpam-6458	19	17	of	of	ADP
ejpam-6458	19	18	21	21	NUM
ejpam-6458	19	19	1	1	NUM
ejpam-6458	19	20	-	-	PUNCT
ejpam-6458	19	21	dimensional	dimensional	ADJ
ejpam-6458	19	22	weight	weight	NOUN
ejpam-6458	19	23	subspaces	subspace	NOUN
ejpam-6458	19	24	.	.	PUNCT
ejpam-6458	20	1	in	in	ADP
ejpam-6458	20	2	the	the	DET
ejpam-6458	20	3	case	case	NOUN
ejpam-6458	20	4	of	of	ADP
ejpam-6458	20	5	g	g	PROPN
ejpam-6458	20	6	=	=	SYM
ejpam-6458	20	7	sl(3	sl(3	PROPN
ejpam-6458	20	8	)	)	PUNCT
ejpam-6458	20	9	a	a	DET
ejpam-6458	20	10	complete	complete	ADJ
ejpam-6458	20	11	description	description	NOUN
ejpam-6458	20	12	of	of	ADP
ejpam-6458	20	13	simple	simple	ADJ
ejpam-6458	20	14	gelfand	gelfand	PROPN
ejpam-6458	20	15	-	-	PUNCT
ejpam-6458	20	16	tsetlin	tsetlin	PROPN
ejpam-6458	20	17	modules	module	NOUN
ejpam-6458	20	18	was	be	AUX
ejpam-6458	20	19	given	give	VERB
ejpam-6458	20	20	in	in	ADP
ejpam-6458	20	21	[	[	X
ejpam-6458	20	22	7	7	NUM
ejpam-6458	20	23	]	]	PUNCT
ejpam-6458	20	24	.	.	PUNCT
ejpam-6458	21	1	the	the	DET
ejpam-6458	21	2	original	original	ADJ
ejpam-6458	21	3	approach	approach	NOUN
ejpam-6458	21	4	to	to	ADP
ejpam-6458	21	5	the	the	DET
ejpam-6458	21	6	study	study	NOUN
ejpam-6458	21	7	of	of	ADP
ejpam-6458	21	8	weight	weight	NOUN
ejpam-6458	21	9	modules	module	NOUN
ejpam-6458	21	10	was	be	AUX
ejpam-6458	21	11	based	base	VERB
ejpam-6458	21	12	on	on	ADP
ejpam-6458	21	13	the	the	DET
ejpam-6458	21	14	reduction	reduction	NOUN
ejpam-6458	21	15	to	to	ADP
ejpam-6458	21	16	the	the	DET
ejpam-6458	21	17	study	study	NOUN
ejpam-6458	21	18	of	of	ADP
ejpam-6458	21	19	simple	simple	ADJ
ejpam-6458	21	20	modules	module	NOUN
ejpam-6458	21	21	over	over	ADP
ejpam-6458	21	22	the	the	DET
ejpam-6458	21	23	centralizer	centralizer	NOUN
ejpam-6458	21	24	u0(g	u0(g	NOUN
ejpam-6458	21	25	)	)	PUNCT
ejpam-6458	21	26	of	of	ADP
ejpam-6458	21	27	the	the	DET
ejpam-6458	21	28	cartan	cartan	ADJ
ejpam-6458	21	29	subalgebra	subalgebra	PROPN
ejpam-6458	21	30	h	h	PROPN
ejpam-6458	21	31	in	in	ADP
ejpam-6458	21	32	the	the	DET
ejpam-6458	21	33	universal	universal	ADJ
ejpam-6458	21	34	enveloping	enveloping	NOUN
ejpam-6458	21	35	algebra	algebra	NOUN
ejpam-6458	21	36	u(g	u(g	PROPN
ejpam-6458	21	37	):	):	PUNCT
ejpam-6458	21	38	ifm	ifm	PROPN
ejpam-6458	21	39	is	be	AUX
ejpam-6458	21	40	a	a	DET
ejpam-6458	21	41	simple	simple	ADJ
ejpam-6458	21	42	weight	weight	NOUN
ejpam-6458	21	43	g	g	NOUN
ejpam-6458	21	44	-	-	PUNCT
ejpam-6458	21	45	module	module	NOUN
ejpam-6458	21	46	,	,	PUNCT
ejpam-6458	21	47	thenmλ	thenmλ	PROPN
ejpam-6458	21	48	is	be	AUX
ejpam-6458	21	49	a	a	DET
ejpam-6458	21	50	simple	simple	ADJ
ejpam-6458	21	51	u0(g)-module	u0(g)-module	NOUN
ejpam-6458	21	52	,	,	PUNCT
ejpam-6458	21	53	for	for	ADP
ejpam-6458	21	54	any	any	DET
ejpam-6458	21	55	weight	weight	NOUN
ejpam-6458	21	56	λ	λ	NOUN
ejpam-6458	21	57	of	of	ADP
ejpam-6458	21	58	m	m	PROPN
ejpam-6458	21	59	.	.	PUNCT
ejpam-6458	22	1	hence	hence	ADV
ejpam-6458	22	2	,	,	PUNCT
ejpam-6458	22	3	every	every	DET
ejpam-6458	22	4	simple	simple	ADJ
ejpam-6458	22	5	weight	weight	NOUN
ejpam-6458	22	6	g	g	NOUN
ejpam-6458	22	7	-	-	PUNCT
ejpam-6458	22	8	module	module	NOUN
ejpam-6458	22	9	corresponds	correspond	VERB
ejpam-6458	22	10	to	to	ADP
ejpam-6458	22	11	a	a	DET
ejpam-6458	22	12	simple	simple	ADJ
ejpam-6458	22	13	(	(	PUNCT
ejpam-6458	22	14	not	not	PART
ejpam-6458	22	15	unique	unique	ADJ
ejpam-6458	22	16	)	)	PUNCT
ejpam-6458	22	17	u0(g)-module	u0(g)-module	NOUN
ejpam-6458	22	18	and	and	CCONJ
ejpam-6458	22	19	,	,	PUNCT
ejpam-6458	22	20	in	in	ADP
ejpam-6458	22	21	its	its	PRON
ejpam-6458	22	22	turn	turn	NOUN
ejpam-6458	22	23	,	,	PUNCT
ejpam-6458	22	24	any	any	DET
ejpam-6458	22	25	simple	simple	ADJ
ejpam-6458	22	26	u0(g)-module	u0(g)-module	NOUN
ejpam-6458	22	27	corresponds	correspond	VERB
ejpam-6458	22	28	to	to	ADP
ejpam-6458	22	29	a	a	DET
ejpam-6458	22	30	unique	unique	ADJ
ejpam-6458	22	31	simple	simple	ADJ
ejpam-6458	22	32	weight	weight	NOUN
ejpam-6458	22	33	g	g	NOUN
ejpam-6458	22	34	-	-	PUNCT
ejpam-6458	22	35	module	module	NOUN
ejpam-6458	22	36	.	.	PUNCT
ejpam-6458	23	1	this	this	DET
ejpam-6458	23	2	approach	approach	NOUN
ejpam-6458	23	3	was	be	AUX
ejpam-6458	23	4	successfully	successfully	ADV
ejpam-6458	23	5	used	use	VERB
ejpam-6458	23	6	in	in	ADP
ejpam-6458	23	7	the	the	DET
ejpam-6458	23	8	case	case	NOUN
ejpam-6458	23	9	of	of	ADP
ejpam-6458	23	10	g	g	PROPN
ejpam-6458	23	11	=	=	SYM
ejpam-6458	23	12	sl(3	sl(3	PROPN
ejpam-6458	23	13	)	)	PUNCT
ejpam-6458	24	1	[	[	X
ejpam-6458	24	2	8–15	8–15	PROPN
ejpam-6458	24	3	]	]	PUNCT
ejpam-6458	24	4	,	,	PUNCT
ejpam-6458	24	5	etc	etc	X
ejpam-6458	24	6	.	.	X
ejpam-6458	25	1	as	as	SCONJ
ejpam-6458	25	2	the	the	DET
ejpam-6458	25	3	structure	structure	NOUN
ejpam-6458	25	4	of	of	ADP
ejpam-6458	25	5	u0(g	u0(g	NOUN
ejpam-6458	25	6	)	)	PUNCT
ejpam-6458	25	7	is	be	AUX
ejpam-6458	25	8	rather	rather	ADV
ejpam-6458	25	9	complicated	complicated	ADJ
ejpam-6458	25	10	(	(	PUNCT
ejpam-6458	25	11	there	there	PRON
ejpam-6458	25	12	are	be	VERB
ejpam-6458	25	13	two	two	NUM
ejpam-6458	25	14	commuting	commuting	NOUN
ejpam-6458	25	15	generators	generator	NOUN
ejpam-6458	25	16	for	for	ADP
ejpam-6458	25	17	sl(2	sl(2	PROPN
ejpam-6458	25	18	)	)	PUNCT
ejpam-6458	25	19	,	,	PUNCT
ejpam-6458	25	20	and	and	CCONJ
ejpam-6458	25	21	there	there	PRON
ejpam-6458	25	22	are	be	VERB
ejpam-6458	25	23	six	six	NUM
ejpam-6458	25	24	generators	generator	NOUN
ejpam-6458	25	25	for	for	ADP
ejpam-6458	25	26	sl(3	sl(3	PROPN
ejpam-6458	25	27	)	)	PUNCT
ejpam-6458	25	28	with	with	ADP
ejpam-6458	25	29	three	three	NUM
ejpam-6458	25	30	polynomial	polynomial	ADJ
ejpam-6458	25	31	relations	relation	NOUN
ejpam-6458	25	32	and	and	CCONJ
ejpam-6458	25	33	five	five	NUM
ejpam-6458	25	34	commuting	commuting	NOUN
ejpam-6458	25	35	generators	generator	NOUN
ejpam-6458	25	36	among	among	ADP
ejpam-6458	25	37	them	they	PRON
ejpam-6458	25	38	)	)	PUNCT
ejpam-6458	25	39	,	,	PUNCT
ejpam-6458	25	40	there	there	PRON
ejpam-6458	25	41	were	be	VERB
ejpam-6458	25	42	essentially	essentially	ADV
ejpam-6458	25	43	no	no	DET
ejpam-6458	25	44	attempts	attempt	NOUN
ejpam-6458	25	45	beyond	beyond	ADP
ejpam-6458	25	46	the	the	DET
ejpam-6458	25	47	sl(3	sl(3	PROPN
ejpam-6458	25	48	)	)	PUNCT
ejpam-6458	25	49	case	case	NOUN
ejpam-6458	25	50	.	.	PUNCT
ejpam-6458	26	1	the	the	DET
ejpam-6458	26	2	goal	goal	NOUN
ejpam-6458	26	3	of	of	ADP
ejpam-6458	26	4	the	the	DET
ejpam-6458	26	5	paper	paper	NOUN
ejpam-6458	26	6	is	be	AUX
ejpam-6458	26	7	to	to	PART
ejpam-6458	26	8	revise	revise	VERB
ejpam-6458	26	9	the	the	DET
ejpam-6458	26	10	centralizer	centralizer	NOUN
ejpam-6458	26	11	approach	approach	NOUN
ejpam-6458	26	12	and	and	CCONJ
ejpam-6458	26	13	to	to	PART
ejpam-6458	26	14	construct	construct	VERB
ejpam-6458	26	15	new	new	ADJ
ejpam-6458	26	16	simple	simple	ADJ
ejpam-6458	26	17	weight	weight	NOUN
ejpam-6458	26	18	modules	module	NOUN
ejpam-6458	26	19	with	with	ADP
ejpam-6458	26	20	infinite	infinite	ADJ
ejpam-6458	26	21	-	-	PUNCT
ejpam-6458	26	22	dimensional	dimensional	ADJ
ejpam-6458	26	23	weight	weight	NOUN
ejpam-6458	26	24	subspaces	subspace	NOUN
ejpam-6458	26	25	for	for	ADP
ejpam-6458	26	26	all	all	DET
ejpam-6458	26	27	simple	simple	ADJ
ejpam-6458	26	28	lie	lie	NOUN
ejpam-6458	26	29	algebras	algebra	NOUN
ejpam-6458	26	30	of	of	ADP
ejpam-6458	26	31	rank	rank	NOUN
ejpam-6458	26	32	2	2	NUM
ejpam-6458	26	33	.	.	PUNCT
ejpam-6458	27	1	we	we	PRON
ejpam-6458	27	2	explicitly	explicitly	ADV
ejpam-6458	27	3	construct	construct	VERB
ejpam-6458	27	4	simple	simple	ADJ
ejpam-6458	27	5	generic	generic	ADJ
ejpam-6458	27	6	modules	module	NOUN
ejpam-6458	27	7	in	in	ADP
ejpam-6458	27	8	the	the	DET
ejpam-6458	27	9	category	category	NOUN
ejpam-6458	27	10	of	of	ADP
ejpam-6458	27	11	γ	γ	PROPN
ejpam-6458	27	12	-	-	PUNCT
ejpam-6458	27	13	pointed	point	VERB
ejpam-6458	27	14	modules	module	NOUN
ejpam-6458	27	15	for	for	ADP
ejpam-6458	27	16	a	a	DET
ejpam-6458	27	17	commutative	commutative	ADJ
ejpam-6458	27	18	subalgebra	subalgebra	NOUN
ejpam-6458	27	19	γ	γ	NOUN
ejpam-6458	27	20	of	of	ADP
ejpam-6458	27	21	the	the	DET
ejpam-6458	27	22	centralizer	centralizer	NOUN
ejpam-6458	27	23	u0(g	u0(g	NOUN
ejpam-6458	27	24	)	)	PUNCT
ejpam-6458	27	25	.	.	PUNCT
ejpam-6458	28	1	in	in	ADP
ejpam-6458	28	2	type	type	NOUN
ejpam-6458	28	3	a	a	PRON
ejpam-6458	28	4	,	,	PUNCT
ejpam-6458	28	5	γ	γ	ADJ
ejpam-6458	28	6	-	-	PUNCT
ejpam-6458	28	7	pointed	point	VERB
ejpam-6458	28	8	modules	module	NOUN
ejpam-6458	28	9	are	be	AUX
ejpam-6458	28	10	the	the	DET
ejpam-6458	28	11	celebrated	celebrate	VERB
ejpam-6458	28	12	gelfand	gelfand	PROPN
ejpam-6458	28	13	-	-	PUNCT
ejpam-6458	28	14	tsetlin	tsetlin	PROPN
ejpam-6458	28	15	modules	module	NOUN
ejpam-6458	28	16	,	,	PUNCT
ejpam-6458	28	17	and	and	CCONJ
ejpam-6458	28	18	similar	similar	ADJ
ejpam-6458	28	19	constructions	construction	NOUN
ejpam-6458	28	20	can	can	AUX
ejpam-6458	28	21	be	be	AUX
ejpam-6458	28	22	viewed	view	VERB
ejpam-6458	28	23	analogously	analogously	ADV
ejpam-6458	28	24	in	in	ADP
ejpam-6458	28	25	other	other	ADJ
ejpam-6458	28	26	types	type	NOUN
ejpam-6458	28	27	.	.	PUNCT
ejpam-6458	29	1	the	the	DET
ejpam-6458	29	2	structure	structure	NOUN
ejpam-6458	29	3	of	of	ADP
ejpam-6458	29	4	the	the	DET
ejpam-6458	29	5	paper	paper	NOUN
ejpam-6458	29	6	is	be	AUX
ejpam-6458	29	7	the	the	DET
ejpam-6458	29	8	following	following	NOUN
ejpam-6458	29	9	.	.	PUNCT
ejpam-6458	30	1	in	in	ADP
ejpam-6458	30	2	section	section	NOUN
ejpam-6458	30	3	2	2	NUM
ejpam-6458	30	4	we	we	PRON
ejpam-6458	30	5	discuss	discuss	VERB
ejpam-6458	30	6	the	the	DET
ejpam-6458	30	7	structure	structure	NOUN
ejpam-6458	30	8	of	of	ADP
ejpam-6458	30	9	the	the	DET
ejpam-6458	30	10	centralizer	centralizer	NOUN
ejpam-6458	30	11	u0(g	u0(g	NOUN
ejpam-6458	30	12	)	)	PUNCT
ejpam-6458	30	13	of	of	ADP
ejpam-6458	30	14	the	the	DET
ejpam-6458	30	15	cartan	cartan	ADJ
ejpam-6458	30	16	subalgebra	subalgebra	PROPN
ejpam-6458	30	17	h	h	PROPN
ejpam-6458	30	18	in	in	ADP
ejpam-6458	30	19	the	the	DET
ejpam-6458	30	20	universal	universal	ADJ
ejpam-6458	30	21	enveloping	enveloping	NOUN
ejpam-6458	30	22	algebra	algebra	NOUN
ejpam-6458	30	23	u(g	u(g	PROPN
ejpam-6458	30	24	)	)	PUNCT
ejpam-6458	30	25	,	,	PUNCT
ejpam-6458	30	26	prove	prove	VERB
ejpam-6458	30	27	that	that	SCONJ
ejpam-6458	30	28	u0(g	u0(g	NOUN
ejpam-6458	30	29	)	)	PUNCT
ejpam-6458	30	30	is	be	AUX
ejpam-6458	30	31	finitely	finitely	ADV
ejpam-6458	30	32	generated	generate	VERB
ejpam-6458	30	33	and	and	CCONJ
ejpam-6458	30	34	finitely	finitely	ADV
ejpam-6458	30	35	presented	present	VERB
ejpam-6458	30	36	.	.	PUNCT
ejpam-6458	31	1	we	we	PRON
ejpam-6458	31	2	give	give	VERB
ejpam-6458	31	3	a	a	DET
ejpam-6458	31	4	generating	generate	VERB
ejpam-6458	31	5	set	set	NOUN
ejpam-6458	31	6	of	of	ADP
ejpam-6458	31	7	elements	element	NOUN
ejpam-6458	31	8	and	and	CCONJ
ejpam-6458	31	9	describe	describe	VERB
ejpam-6458	31	10	an	an	DET
ejpam-6458	31	11	algorithm	algorithm	NOUN
ejpam-6458	31	12	for	for	ADP
ejpam-6458	31	13	computing	compute	VERB
ejpam-6458	31	14	all	all	DET
ejpam-6458	31	15	relations	relation	NOUN
ejpam-6458	31	16	between	between	ADP
ejpam-6458	31	17	them	they	PRON
ejpam-6458	31	18	.	.	PUNCT
ejpam-6458	32	1	in	in	ADP
ejpam-6458	32	2	section	section	NOUN
ejpam-6458	32	3	4	4	NUM
ejpam-6458	32	4	we	we	PRON
ejpam-6458	32	5	consider	consider	VERB
ejpam-6458	32	6	the	the	DET
ejpam-6458	32	7	lie	lie	NOUN
ejpam-6458	32	8	algebra	algebra	NOUN
ejpam-6458	32	9	of	of	ADP
ejpam-6458	32	10	type	type	NOUN
ejpam-6458	32	11	a2	a2	PROPN
ejpam-6458	32	12	.	.	PUNCT
ejpam-6458	33	1	our	our	PRON
ejpam-6458	33	2	approach	approach	NOUN
ejpam-6458	33	3	is	be	AUX
ejpam-6458	33	4	a	a	DET
ejpam-6458	33	5	suitable	suitable	ADJ
ejpam-6458	33	6	modification	modification	NOUN
ejpam-6458	33	7	of	of	ADP
ejpam-6458	33	8	[	[	X
ejpam-6458	33	9	9	9	NUM
ejpam-6458	33	10	]	]	PUNCT
ejpam-6458	33	11	and	and	CCONJ
ejpam-6458	33	12	[	[	X
ejpam-6458	33	13	14	14	NUM
ejpam-6458	33	14	]	]	PUNCT
ejpam-6458	33	15	,	,	PUNCT
ejpam-6458	33	16	and	and	CCONJ
ejpam-6458	33	17	we	we	PRON
ejpam-6458	33	18	recover	recover	VERB
ejpam-6458	33	19	a	a	DET
ejpam-6458	33	20	construction	construction	NOUN
ejpam-6458	33	21	of	of	ADP
ejpam-6458	33	22	generic	generic	ADJ
ejpam-6458	33	23	torsion	torsion	NOUN
ejpam-6458	33	24	free	free	PROPN
ejpam-6458	33	25	a2	a2	NOUN
ejpam-6458	33	26	-	-	PUNCT
ejpam-6458	33	27	modules	module	NOUN
ejpam-6458	33	28	with	with	ADP
ejpam-6458	33	29	infinite	infinite	ADJ
ejpam-6458	33	30	-	-	PUNCT
ejpam-6458	33	31	dimensional	dimensional	ADJ
ejpam-6458	33	32	weight	weight	NOUN
ejpam-6458	33	33	spaces	space	NOUN
ejpam-6458	33	34	obtained	obtain	VERB
ejpam-6458	33	35	in	in	ADP
ejpam-6458	33	36	[	[	X
ejpam-6458	33	37	14	14	NUM
ejpam-6458	33	38	]	]	PUNCT
ejpam-6458	33	39	and	and	CCONJ
ejpam-6458	33	40	[	[	X
ejpam-6458	33	41	7	7	NUM
ejpam-6458	33	42	]	]	PUNCT
ejpam-6458	33	43	.	.	PUNCT
ejpam-6458	34	1	they	they	PRON
ejpam-6458	34	2	are	be	AUX
ejpam-6458	34	3	tame	tame	ADJ
ejpam-6458	34	4	gelfand	gelfand	PROPN
ejpam-6458	34	5	-	-	PUNCT
ejpam-6458	34	6	tsetlin	tsetlin	PROPN
ejpam-6458	34	7	modules	module	NOUN
ejpam-6458	34	8	with	with	ADP
ejpam-6458	34	9	diagonalizable	diagonalizable	ADJ
ejpam-6458	34	10	action	action	NOUN
ejpam-6458	34	11	of	of	ADP
ejpam-6458	34	12	the	the	DET
ejpam-6458	34	13	gelfand	gelfand	PROPN
ejpam-6458	34	14	-	-	PUNCT
ejpam-6458	34	15	tsetlin	tsetlin	PROPN
ejpam-6458	34	16	subalgebra	subalgebra	NOUN
ejpam-6458	34	17	.	.	PUNCT
ejpam-6458	35	1	in	in	ADP
ejpam-6458	35	2	section	section	NOUN
ejpam-6458	35	3	5	5	NUM
ejpam-6458	35	4	we	we	PRON
ejpam-6458	35	5	consider	consider	VERB
ejpam-6458	35	6	the	the	DET
ejpam-6458	35	7	lie	lie	NOUN
ejpam-6458	35	8	algebra	algebra	NOUN
ejpam-6458	35	9	g	g	PROPN
ejpam-6458	35	10	of	of	ADP
ejpam-6458	35	11	type	type	NOUN
ejpam-6458	35	12	c2	c2	PROPN
ejpam-6458	35	13	and	and	CCONJ
ejpam-6458	35	14	give	give	VERB
ejpam-6458	35	15	the	the	DET
ejpam-6458	35	16	generators	generator	NOUN
ejpam-6458	35	17	and	and	CCONJ
ejpam-6458	35	18	the	the	DET
ejpam-6458	35	19	defining	define	VERB
ejpam-6458	35	20	relations	relation	NOUN
ejpam-6458	35	21	of	of	ADP
ejpam-6458	35	22	the	the	DET
ejpam-6458	35	23	centralizer	centralizer	NOUN
ejpam-6458	35	24	u0(g	u0(g	NOUN
ejpam-6458	35	25	)	)	PUNCT
ejpam-6458	35	26	.	.	PUNCT
ejpam-6458	36	1	we	we	PRON
ejpam-6458	36	2	construct	construct	VERB
ejpam-6458	36	3	two	two	NUM
ejpam-6458	36	4	4	4	NUM
ejpam-6458	36	5	-	-	PUNCT
ejpam-6458	36	6	parameter	parameter	NOUN
ejpam-6458	36	7	families	family	NOUN
ejpam-6458	36	8	of	of	ADP
ejpam-6458	36	9	simple	simple	ADJ
ejpam-6458	36	10	torsion	torsion	NOUN
ejpam-6458	36	11	free	free	ADJ
ejpam-6458	36	12	c2	c2	PROPN
ejpam-6458	36	13	-	-	PUNCT
ejpam-6458	36	14	modules	module	NOUN
ejpam-6458	36	15	with	with	ADP
ejpam-6458	36	16	infinite	infinite	ADJ
ejpam-6458	36	17	-	-	PUNCT
ejpam-6458	36	18	dimensional	dimensional	ADJ
ejpam-6458	36	19	weight	weight	NOUN
ejpam-6458	36	20	spaces	space	NOUN
ejpam-6458	36	21	.	.	PUNCT
ejpam-6458	37	1	these	these	DET
ejpam-6458	37	2	modules	module	NOUN
ejpam-6458	37	3	are	be	AUX
ejpam-6458	37	4	γ	γ	X
ejpam-6458	37	5	-	-	ADJ
ejpam-6458	37	6	pointed	pointed	ADJ
ejpam-6458	37	7	,	,	PUNCT
ejpam-6458	37	8	where	where	SCONJ
ejpam-6458	37	9	γ	γ	PROPN
ejpam-6458	37	10	is	be	AUX
ejpam-6458	37	11	the	the	DET
ejpam-6458	37	12	4	4	NUM
ejpam-6458	37	13	-	-	PUNCT
ejpam-6458	37	14	generated	generate	VERB
ejpam-6458	37	15	gelfand	gelfand	PROPN
ejpam-6458	37	16	-	-	PUNCT
ejpam-6458	37	17	tsetlin	tsetlin	PROPN
ejpam-6458	37	18	subalgebra	subalgebra	NOUN
ejpam-6458	37	19	of	of	ADP
ejpam-6458	37	20	u0(g	u0(g	NOUN
ejpam-6458	37	21	)	)	PUNCT
ejpam-6458	37	22	which	which	PRON
ejpam-6458	37	23	has	have	VERB
ejpam-6458	37	24	a	a	DET
ejpam-6458	37	25	simple	simple	ADJ
ejpam-6458	37	26	spectrum	spectrum	NOUN
ejpam-6458	37	27	on	on	ADP
ejpam-6458	37	28	such	such	ADJ
ejpam-6458	37	29	representations	representation	NOUN
ejpam-6458	37	30	.	.	PUNCT
ejpam-6458	38	1	finally	finally	ADV
ejpam-6458	38	2	,	,	PUNCT
ejpam-6458	38	3	in	in	ADP
ejpam-6458	38	4	section	section	NOUN
ejpam-6458	38	5	6	6	NUM
ejpam-6458	38	6	we	we	PRON
ejpam-6458	38	7	construct	construct	VERB
ejpam-6458	38	8	a	a	DET
ejpam-6458	38	9	3	3	NUM
ejpam-6458	38	10	-	-	PUNCT
ejpam-6458	38	11	parameter	parameter	NOUN
ejpam-6458	38	12	family	family	NOUN
ejpam-6458	38	13	of	of	ADP
ejpam-6458	38	14	simple	simple	ADJ
ejpam-6458	38	15	torsion	torsion	NOUN
ejpam-6458	38	16	free	free	ADJ
ejpam-6458	38	17	g2	g2	NOUN
ejpam-6458	38	18	-	-	PUNCT
ejpam-6458	38	19	modules	module	NOUN
ejpam-6458	38	20	with	with	ADP
ejpam-6458	38	21	infinite	infinite	ADJ
ejpam-6458	38	22	-	-	PUNCT
ejpam-6458	38	23	dimensional	dimensional	ADJ
ejpam-6458	38	24	weight	weight	NOUN
ejpam-6458	38	25	spaces	space	NOUN
ejpam-6458	38	26	.	.	PUNCT
ejpam-6458	39	1	these	these	DET
ejpam-6458	39	2	modules	module	NOUN
ejpam-6458	39	3	are	be	AUX
ejpam-6458	39	4	γ	γ	X
ejpam-6458	39	5	-	-	PUNCT
ejpam-6458	39	6	pointed	point	VERB
ejpam-6458	39	7	with	with	ADP
ejpam-6458	39	8	respect	respect	NOUN
ejpam-6458	39	9	to	to	ADP
ejpam-6458	39	10	a	a	DET
ejpam-6458	39	11	4	4	NUM
ejpam-6458	39	12	-	-	PUNCT
ejpam-6458	39	13	generated	generate	VERB
ejpam-6458	39	14	gelfand	gelfand	PROPN
ejpam-6458	39	15	-	-	PUNCT
ejpam-6458	39	16	tsetlin	tsetlin	PROPN
ejpam-6458	39	17	subalgebra	subalgebra	PROPN
ejpam-6458	39	18	γ	γ	PROPN
ejpam-6458	39	19	of	of	ADP
ejpam-6458	39	20	u0(g	u0(g	NOUN
ejpam-6458	39	21	)	)	PUNCT
ejpam-6458	39	22	which	which	PRON
ejpam-6458	39	23	has	have	VERB
ejpam-6458	39	24	a	a	DET
ejpam-6458	39	25	simple	simple	ADJ
ejpam-6458	39	26	spectrum	spectrum	NOUN
ejpam-6458	39	27	on	on	ADP
ejpam-6458	39	28	such	such	ADJ
ejpam-6458	39	29	representations	representation	NOUN
ejpam-6458	39	30	.	.	PUNCT
ejpam-6458	40	1	we	we	PRON
ejpam-6458	40	2	hope	hope	VERB
ejpam-6458	40	3	to	to	PART
ejpam-6458	40	4	use	use	VERB
ejpam-6458	40	5	the	the	DET
ejpam-6458	40	6	defined	define	VERB
ejpam-6458	40	7	representations	representation	NOUN
ejpam-6458	40	8	to	to	PART
ejpam-6458	40	9	construct	construct	VERB
ejpam-6458	40	10	new	new	ADJ
ejpam-6458	40	11	simple	simple	ADJ
ejpam-6458	40	12	modules	module	NOUN
ejpam-6458	40	13	for	for	ADP
ejpam-6458	40	14	all	all	DET
ejpam-6458	40	15	simple	simple	ADJ
ejpam-6458	40	16	finite	finite	ADJ
ejpam-6458	40	17	-	-	ADJ
ejpam-6458	40	18	dimensional	dimensional	ADJ
ejpam-6458	40	19	and	and	CCONJ
ejpam-6458	40	20	affine	affine	NOUN
ejpam-6458	40	21	lie	lie	NOUN
ejpam-6458	40	22	algebras	algebra	NOUN
ejpam-6458	40	23	via	via	ADP
ejpam-6458	40	24	the	the	DET
ejpam-6458	40	25	parabolic	parabolic	ADJ
ejpam-6458	40	26	induction	induction	NOUN
ejpam-6458	40	27	.	.	PUNCT
ejpam-6458	41	1	2	2	X
ejpam-6458	41	2	.	.	X
ejpam-6458	41	3	cartan	cartan	PROPN
ejpam-6458	41	4	centralizers	centralizer	NOUN
ejpam-6458	41	5	let	let	VERB
ejpam-6458	41	6	∆	∆	PROPN
ejpam-6458	41	7	=	=	SYM
ejpam-6458	41	8	{	{	PUNCT
ejpam-6458	41	9	α1	α1	PROPN
ejpam-6458	41	10	,	,	PUNCT
ejpam-6458	41	11	.	.	PUNCT
ejpam-6458	41	12	.	.	PUNCT
ejpam-6458	41	13	.	.	PUNCT
ejpam-6458	42	1	,	,	PUNCT
ejpam-6458	42	2	αk1	αk1	AUX
ejpam-6458	42	3	}	}	PUNCT
ejpam-6458	42	4	be	be	VERB
ejpam-6458	42	5	the	the	DET
ejpam-6458	42	6	root	root	NOUN
ejpam-6458	42	7	system	system	NOUN
ejpam-6458	42	8	of	of	ADP
ejpam-6458	42	9	(	(	PUNCT
ejpam-6458	42	10	g	g	PROPN
ejpam-6458	42	11	,	,	PUNCT
ejpam-6458	42	12	h	h	NOUN
ejpam-6458	42	13	)	)	PUNCT
ejpam-6458	42	14	,	,	PUNCT
ejpam-6458	42	15	and	and	CCONJ
ejpam-6458	42	16	let	let	VERB
ejpam-6458	42	17	π	π	PROPN
ejpam-6458	42	18	=	=	PRON
ejpam-6458	42	19	{	{	PUNCT
ejpam-6458	42	20	β1	β1	PROPN
ejpam-6458	42	21	,	,	PUNCT
ejpam-6458	42	22	.	.	PUNCT
ejpam-6458	42	23	.	.	PUNCT
ejpam-6458	43	1	.	.	PUNCT
ejpam-6458	44	1	,	,	PUNCT
ejpam-6458	44	2	βk0	βk0	AUX
ejpam-6458	44	3	}	}	PUNCT
ejpam-6458	44	4	be	be	AUX
ejpam-6458	44	5	a	a	DET
ejpam-6458	44	6	basis	basis	NOUN
ejpam-6458	44	7	of	of	ADP
ejpam-6458	44	8	∆.	∆.	NOUN
ejpam-6458	44	9	with	with	ADP
ejpam-6458	44	10	respect	respect	NOUN
ejpam-6458	44	11	to	to	ADP
ejpam-6458	44	12	the	the	DET
ejpam-6458	44	13	basis	basis	NOUN
ejpam-6458	44	14	π	π	NOUN
ejpam-6458	44	15	,	,	PUNCT
ejpam-6458	44	16	we	we	PRON
ejpam-6458	44	17	have	have	VERB
ejpam-6458	44	18	the	the	DET
ejpam-6458	44	19	decomposition	decomposition	NOUN
ejpam-6458	44	20	of	of	ADP
ejpam-6458	44	21	∆	∆	PROPN
ejpam-6458	44	22	into	into	ADP
ejpam-6458	44	23	positive	positive	ADJ
ejpam-6458	44	24	and	and	CCONJ
ejpam-6458	44	25	negative	negative	ADJ
ejpam-6458	44	26	roots	root	NOUN
ejpam-6458	44	27	:	:	PUNCT
ejpam-6458	45	1	∆	∆	PROPN
ejpam-6458	45	2	=	=	PUNCT
ejpam-6458	45	3	∆+	∆+	SYM
ejpam-6458	45	4	∪	∪	X
ejpam-6458	45	5	∆−.	∆−.	PROPN
ejpam-6458	45	6	let	let	VERB
ejpam-6458	45	7	w	w	NOUN
ejpam-6458	45	8	be	be	AUX
ejpam-6458	45	9	the	the	DET
ejpam-6458	45	10	weyl	weyl	VERB
ejpam-6458	45	11	group	group	NOUN
ejpam-6458	45	12	of	of	ADP
ejpam-6458	45	13	the	the	DET
ejpam-6458	45	14	root	root	NOUN
ejpam-6458	45	15	system	system	NOUN
ejpam-6458	45	16	∆.	∆.	NOUN
ejpam-6458	45	17	choose	choose	VERB
ejpam-6458	45	18	a	a	DET
ejpam-6458	45	19	basis	basis	NOUN
ejpam-6458	45	20	g	g	PROPN
ejpam-6458	45	21	=	=	PROPN
ejpam-6458	45	22	g0	g0	PROPN
ejpam-6458	45	23	∪	∪	NOUN
ejpam-6458	45	24	g1	g1	NOUN
ejpam-6458	45	25	of	of	ADP
ejpam-6458	45	26	the	the	DET
ejpam-6458	45	27	lie	lie	NOUN
ejpam-6458	45	28	algebra	algebra	VERB
ejpam-6458	45	29	g	g	PROPN
ejpam-6458	45	30	,	,	PUNCT
ejpam-6458	45	31	where	where	SCONJ
ejpam-6458	45	32	g0	g0	NOUN
ejpam-6458	45	33	=	=	PUNCT
ejpam-6458	45	34	{	{	PUNCT
ejpam-6458	45	35	hβ	hβ	NOUN
ejpam-6458	45	36	∈	∈	PROPN
ejpam-6458	45	37	h	h	NOUN
ejpam-6458	45	38	|β	|β	VERB
ejpam-6458	45	39	∈	∈	PROPN
ejpam-6458	45	40	π	π	NOUN
ejpam-6458	45	41	}	}	PUNCT
ejpam-6458	45	42	and	and	CCONJ
ejpam-6458	45	43	g1	g1	PROPN
ejpam-6458	45	44	=	=	SYM
ejpam-6458	45	45	{	{	PUNCT
ejpam-6458	45	46	eα	eα	NOUN
ejpam-6458	45	47	∈	∈	NOUN
ejpam-6458	45	48	gα	gα	ADP
ejpam-6458	45	49	\	\	PROPN
ejpam-6458	45	50	{	{	PUNCT
ejpam-6458	45	51	0	0	NUM
ejpam-6458	45	52	}	}	PUNCT
ejpam-6458	45	53	|α	|α	NOUN
ejpam-6458	45	54	∈	∈	NOUN
ejpam-6458	45	55	∆	∆	X
ejpam-6458	45	56	}	}	PUNCT
ejpam-6458	45	57	.	.	PUNCT
ejpam-6458	46	1	set	set	VERB
ejpam-6458	46	2	fα	fα	NOUN
ejpam-6458	46	3	=	=	PUNCT
ejpam-6458	46	4	e−α	e−α	PROPN
ejpam-6458	46	5	.	.	PUNCT
ejpam-6458	47	1	denote	denote	VERB
ejpam-6458	47	2	by	by	ADP
ejpam-6458	47	3	u0(g	u0(g	NOUN
ejpam-6458	47	4	)	)	PUNCT
ejpam-6458	47	5	the	the	DET
ejpam-6458	47	6	centralizer	centralizer	NOUN
ejpam-6458	47	7	of	of	ADP
ejpam-6458	47	8	the	the	DET
ejpam-6458	47	9	cartan	cartan	ADJ
ejpam-6458	47	10	subalgebra	subalgebra	PROPN
ejpam-6458	47	11	h	h	PROPN
ejpam-6458	47	12	in	in	ADP
ejpam-6458	47	13	the	the	DET
ejpam-6458	47	14	universal	universal	ADJ
ejpam-6458	47	15	enveloping	enveloping	NOUN
ejpam-6458	47	16	algebra	algebra	NOUN
ejpam-6458	47	17	u(g	u(g	PROPN
ejpam-6458	47	18	)	)	PUNCT
ejpam-6458	47	19	.	.	PUNCT
ejpam-6458	48	1	for	for	ADP
ejpam-6458	48	2	each	each	DET
ejpam-6458	48	3	i	i	PRON
ejpam-6458	48	4	∈	∈	PROPN
ejpam-6458	48	5	n	n	PRON
ejpam-6458	48	6	denote	denote	VERB
ejpam-6458	48	7	by	by	ADP
ejpam-6458	48	8	u	u	PROPN
ejpam-6458	48	9	(	(	PUNCT
ejpam-6458	48	10	i)(g	i)(g	PROPN
ejpam-6458	48	11	)	)	PUNCT
ejpam-6458	48	12	the	the	DET
ejpam-6458	48	13	vector	vector	NOUN
ejpam-6458	48	14	subspace	subspace	NOUN
ejpam-6458	48	15	of	of	ADP
ejpam-6458	48	16	u(g	u(g	PROPN
ejpam-6458	48	17	)	)	PUNCT
ejpam-6458	48	18	spanned	span	VERB
ejpam-6458	48	19	by	by	ADP
ejpam-6458	48	20	the	the	DET
ejpam-6458	48	21	monomials	monomial	NOUN
ejpam-6458	48	22	x1x2	x1x2	X
ejpam-6458	48	23	·	·	PUNCT
ejpam-6458	48	24	·	·	PUNCT
ejpam-6458	49	1	·	·	PUNCT
ejpam-6458	49	2	xj	xj	PROPN
ejpam-6458	49	3	,	,	PUNCT
ejpam-6458	49	4	where	where	SCONJ
ejpam-6458	49	5	x1	x1	ADJ
ejpam-6458	49	6	,	,	PUNCT
ejpam-6458	49	7	.	.	PUNCT
ejpam-6458	49	8	.	.	PUNCT
ejpam-6458	49	9	.	.	PUNCT
ejpam-6458	50	1	,	,	PUNCT
ejpam-6458	50	2	xj	xj	PROPN
ejpam-6458	50	3	∈	∈	PROPN
ejpam-6458	50	4	g	g	PROPN
ejpam-6458	50	5	and	and	CCONJ
ejpam-6458	50	6	j	j	PROPN
ejpam-6458	50	7	≤	≤	PROPN
ejpam-6458	50	8	i.	i.	NOUN
ejpam-6458	51	1	then	then	ADV
ejpam-6458	51	2	we	we	PRON
ejpam-6458	51	3	get	get	VERB
ejpam-6458	51	4	an	an	DET
ejpam-6458	51	5	increasing	increase	VERB
ejpam-6458	51	6	sequence	sequence	NOUN
ejpam-6458	51	7	m.	m.	NOUN
ejpam-6458	51	8	andelić	andelić	PROPN
ejpam-6458	51	9	et	et	PROPN
ejpam-6458	51	10	al	al	PROPN
ejpam-6458	51	11	.	.	PUNCT
ejpam-6458	51	12	/	/	SYM
ejpam-6458	51	13	eur	eur	PROPN
ejpam-6458	51	14	.	.	PUNCT
ejpam-6458	52	1	j.	j.	PROPN
ejpam-6458	52	2	pure	pure	PROPN
ejpam-6458	52	3	appl	appl	PROPN
ejpam-6458	52	4	.	.	PROPN
ejpam-6458	52	5	math	math	PROPN
ejpam-6458	52	6	,	,	PUNCT
ejpam-6458	52	7	18	18	NUM
ejpam-6458	52	8	(	(	PUNCT
ejpam-6458	52	9	3	3	NUM
ejpam-6458	52	10	)	)	PUNCT
ejpam-6458	52	11	(	(	PUNCT
ejpam-6458	52	12	2025	2025	NUM
ejpam-6458	52	13	)	)	PUNCT
ejpam-6458	52	14	,	,	PUNCT
ejpam-6458	52	15	6458	6458	NUM
ejpam-6458	52	16	3	3	NUM
ejpam-6458	52	17	of	of	ADP
ejpam-6458	52	18	21	21	NUM
ejpam-6458	52	19	of	of	ADP
ejpam-6458	52	20	subspaces	subspace	NOUN
ejpam-6458	52	21	u	u	NOUN
ejpam-6458	52	22	(	(	PUNCT
ejpam-6458	52	23	1)(g	1)(g	NUM
ejpam-6458	52	24	)	)	PUNCT
ejpam-6458	52	25	⊂	⊂	PROPN
ejpam-6458	52	26	u	u	X
ejpam-6458	52	27	(	(	PUNCT
ejpam-6458	52	28	2)(g	2)(g	NUM
ejpam-6458	52	29	)	)	PUNCT
ejpam-6458	52	30	⊂	⊂	X
ejpam-6458	52	31	·	·	PUNCT
ejpam-6458	52	32	·	·	PUNCT
ejpam-6458	52	33	·	·	PUNCT
ejpam-6458	53	1	⊂	⊂	PRON
ejpam-6458	53	2	u	u	X
ejpam-6458	53	3	(	(	PUNCT
ejpam-6458	53	4	i)(g	i)(g	PROPN
ejpam-6458	53	5	)	)	PUNCT
ejpam-6458	53	6	⊂	⊂	X
ejpam-6458	53	7	·	·	PUNCT
ejpam-6458	53	8	·	·	PUNCT
ejpam-6458	53	9	·	·	PUNCT
ejpam-6458	53	10	,	,	PUNCT
ejpam-6458	53	11	which	which	PRON
ejpam-6458	53	12	defines	define	VERB
ejpam-6458	53	13	a	a	DET
ejpam-6458	53	14	canonical	canonical	ADJ
ejpam-6458	53	15	filtration	filtration	NOUN
ejpam-6458	53	16	of	of	ADP
ejpam-6458	53	17	u(g	u(g	PROPN
ejpam-6458	53	18	)	)	PUNCT
ejpam-6458	53	19	.	.	PUNCT
ejpam-6458	54	1	the	the	DET
ejpam-6458	54	2	canonical	canonical	ADJ
ejpam-6458	54	3	filtration	filtration	NOUN
ejpam-6458	54	4	of	of	ADP
ejpam-6458	54	5	u0(g	u0(g	NOUN
ejpam-6458	54	6	)	)	PUNCT
ejpam-6458	54	7	is	be	AUX
ejpam-6458	54	8	the	the	DET
ejpam-6458	54	9	sequence	sequence	NOUN
ejpam-6458	54	10	of	of	ADP
ejpam-6458	54	11	subspaces	subspace	NOUN
ejpam-6458	54	12	u	u	NOUN
ejpam-6458	54	13	(	(	PUNCT
ejpam-6458	54	14	1	1	NUM
ejpam-6458	54	15	)	)	PUNCT
ejpam-6458	54	16	0	0	NUM
ejpam-6458	55	1	(	(	PUNCT
ejpam-6458	55	2	g	g	NOUN
ejpam-6458	55	3	)	)	PUNCT
ejpam-6458	55	4	⊂	⊂	PROPN
ejpam-6458	55	5	u	u	NOUN
ejpam-6458	55	6	(	(	PUNCT
ejpam-6458	55	7	2	2	NUM
ejpam-6458	55	8	)	)	PUNCT
ejpam-6458	55	9	0	0	NUM
ejpam-6458	56	1	(	(	PUNCT
ejpam-6458	56	2	g	g	NOUN
ejpam-6458	56	3	)	)	PUNCT
ejpam-6458	56	4	⊂	⊂	X
ejpam-6458	56	5	·	·	PUNCT
ejpam-6458	56	6	·	·	PUNCT
ejpam-6458	56	7	·	·	PUNCT
ejpam-6458	57	1	⊂	⊂	PRON
ejpam-6458	57	2	u	u	X
ejpam-6458	57	3	(	(	PUNCT
ejpam-6458	57	4	i	i	NOUN
ejpam-6458	57	5	)	)	PUNCT
ejpam-6458	57	6	0	0	PUNCT
ejpam-6458	58	1	(	(	PUNCT
ejpam-6458	58	2	g	g	NOUN
ejpam-6458	58	3	)	)	PUNCT
ejpam-6458	58	4	⊂	⊂	X
ejpam-6458	58	5	·	·	PUNCT
ejpam-6458	58	6	·	·	PUNCT
ejpam-6458	58	7	·	·	PUNCT
ejpam-6458	58	8	,	,	PUNCT
ejpam-6458	58	9	where	where	SCONJ
ejpam-6458	58	10	u	u	PROPN
ejpam-6458	58	11	(	(	PUNCT
ejpam-6458	58	12	i	i	NOUN
ejpam-6458	58	13	)	)	PUNCT
ejpam-6458	58	14	0	0	PUNCT
ejpam-6458	58	15	(	(	PUNCT
ejpam-6458	58	16	g	g	NOUN
ejpam-6458	58	17	)	)	PUNCT
ejpam-6458	58	18	=	=	SYM
ejpam-6458	58	19	u	u	NOUN
ejpam-6458	58	20	(	(	PUNCT
ejpam-6458	58	21	i)(g	i)(g	ADJ
ejpam-6458	58	22	)	)	PUNCT
ejpam-6458	58	23	∩	∩	ADJ
ejpam-6458	58	24	u0(g	u0(g	NOUN
ejpam-6458	58	25	)	)	PUNCT
ejpam-6458	58	26	.	.	PUNCT
ejpam-6458	59	1	for	for	ADP
ejpam-6458	59	2	any	any	DET
ejpam-6458	59	3	monomial	monomial	NOUN
ejpam-6458	59	4	x	x	PUNCT
ejpam-6458	59	5	=	=	PUNCT
ejpam-6458	59	6	x1x2	x1x2	X
ejpam-6458	59	7	·	·	PUNCT
ejpam-6458	59	8	·	·	PUNCT
ejpam-6458	59	9	·	·	PUNCT
ejpam-6458	59	10	xj	xj	PROPN
ejpam-6458	59	11	denote	denote	VERB
ejpam-6458	59	12	by	by	ADP
ejpam-6458	59	13	t0(x	t0(x	NOUN
ejpam-6458	59	14	)	)	PUNCT
ejpam-6458	59	15	the	the	DET
ejpam-6458	59	16	set	set	NOUN
ejpam-6458	59	17	of	of	ADP
ejpam-6458	59	18	monomials	monomial	NOUN
ejpam-6458	59	19	obtained	obtain	VERB
ejpam-6458	59	20	from	from	ADP
ejpam-6458	59	21	x	x	PUNCT
ejpam-6458	59	22	by	by	ADP
ejpam-6458	59	23	permuting	permute	VERB
ejpam-6458	59	24	the	the	DET
ejpam-6458	59	25	variables	variable	NOUN
ejpam-6458	59	26	xi	xi	PROPN
ejpam-6458	59	27	.	.	PUNCT
ejpam-6458	60	1	we	we	PRON
ejpam-6458	60	2	will	will	AUX
ejpam-6458	60	3	treat	treat	VERB
ejpam-6458	60	4	each	each	DET
ejpam-6458	60	5	monomial	monomial	NOUN
ejpam-6458	60	6	as	as	ADP
ejpam-6458	60	7	an	an	DET
ejpam-6458	60	8	element	element	NOUN
ejpam-6458	60	9	of	of	ADP
ejpam-6458	60	10	the	the	DET
ejpam-6458	60	11	algebra	algebra	NOUN
ejpam-6458	60	12	u(g	u(g	PROPN
ejpam-6458	60	13	)	)	PUNCT
ejpam-6458	60	14	,	,	PUNCT
ejpam-6458	60	15	considering	consider	VERB
ejpam-6458	60	16	it	it	PRON
ejpam-6458	60	17	as	as	ADP
ejpam-6458	60	18	a	a	DET
ejpam-6458	60	19	monomial	monomial	NOUN
ejpam-6458	60	20	with	with	ADP
ejpam-6458	60	21	coefficient	coefficient	NOUN
ejpam-6458	60	22	1	1	X
ejpam-6458	60	23	.	.	PUNCT
ejpam-6458	60	24	define	define	VERB
ejpam-6458	60	25	the	the	DET
ejpam-6458	60	26	degree	degree	NOUN
ejpam-6458	60	27	function	function	NOUN
ejpam-6458	60	28	deg(y	deg(y	PROPN
ejpam-6458	60	29	)	)	PUNCT
ejpam-6458	60	30	as	as	SCONJ
ejpam-6458	60	31	follows	follow	VERB
ejpam-6458	60	32	:	:	PUNCT
ejpam-6458	60	33	deg(y	deg(y	PROPN
ejpam-6458	60	34	)	)	PUNCT
ejpam-6458	61	1	=	=	PUNCT
ejpam-6458	61	2	i	i	PRON
ejpam-6458	61	3	if	if	SCONJ
ejpam-6458	61	4	y	y	PROPN
ejpam-6458	61	5	∈	∈	PROPN
ejpam-6458	61	6	u	u	PROPN
ejpam-6458	61	7	(	(	PUNCT
ejpam-6458	61	8	i)(g	i)(g	PROPN
ejpam-6458	61	9	)	)	PUNCT
ejpam-6458	61	10	,	,	PUNCT
ejpam-6458	61	11	but	but	CCONJ
ejpam-6458	61	12	y	y	PROPN
ejpam-6458	61	13	/∈	/∈	PUNCT
ejpam-6458	62	1	u	u	PROPN
ejpam-6458	62	2	(	(	PUNCT
ejpam-6458	62	3	i−1)(g	i−1)(g	PROPN
ejpam-6458	62	4	)	)	PUNCT
ejpam-6458	62	5	.	.	PUNCT
ejpam-6458	63	1	now	now	ADV
ejpam-6458	63	2	,	,	PUNCT
ejpam-6458	63	3	fix	fix	VERB
ejpam-6458	63	4	some	some	DET
ejpam-6458	63	5	order	order	NOUN
ejpam-6458	63	6	on	on	ADP
ejpam-6458	63	7	the	the	DET
ejpam-6458	63	8	set	set	NOUN
ejpam-6458	63	9	g	g	NOUN
ejpam-6458	63	10	:	:	PUNCT
ejpam-6458	64	1	x1	x1	ADJ
ejpam-6458	64	2	≤	≤	NUM
ejpam-6458	64	3	x2	x2	ADJ
ejpam-6458	64	4	≤	≤	NOUN
ejpam-6458	64	5	·	·	PUNCT
ejpam-6458	64	6	·	·	PUNCT
ejpam-6458	64	7	·	·	PUNCT
ejpam-6458	65	1	≤	≤	NUM
ejpam-6458	65	2	xk	xk	PROPN
ejpam-6458	65	3	,	,	PUNCT
ejpam-6458	65	4	(	(	PUNCT
ejpam-6458	65	5	2.1	2.1	NUM
ejpam-6458	65	6	)	)	PUNCT
ejpam-6458	65	7	where	where	SCONJ
ejpam-6458	65	8	k	k	PROPN
ejpam-6458	65	9	is	be	AUX
ejpam-6458	65	10	the	the	DET
ejpam-6458	65	11	dimension	dimension	NOUN
ejpam-6458	65	12	of	of	ADP
ejpam-6458	65	13	g.	g.	PROPN
ejpam-6458	65	14	define	define	VERB
ejpam-6458	65	15	standard	standard	ADJ
ejpam-6458	65	16	monomials	monomial	NOUN
ejpam-6458	65	17	of	of	ADP
ejpam-6458	65	18	u(g	u(g	PROPN
ejpam-6458	65	19	)	)	PUNCT
ejpam-6458	65	20	with	with	ADP
ejpam-6458	65	21	respect	respect	NOUN
ejpam-6458	65	22	to	to	ADP
ejpam-6458	65	23	this	this	DET
ejpam-6458	65	24	order	order	NOUN
ejpam-6458	65	25	as	as	SCONJ
ejpam-6458	65	26	follows	follow	VERB
ejpam-6458	65	27	:	:	PUNCT
ejpam-6458	65	28	xs	xs	PROPN
ejpam-6458	65	29	=	=	PUNCT
ejpam-6458	65	30	xs11	xs11	PROPN
ejpam-6458	65	31	x	x	SYM
ejpam-6458	65	32	s2	s2	NOUN
ejpam-6458	65	33	2	2	NUM
ejpam-6458	65	34	·	·	PUNCT
ejpam-6458	65	35	·	·	PUNCT
ejpam-6458	65	36	·	·	PUNCT
ejpam-6458	65	37	xskk	xskk	PROPN
ejpam-6458	65	38	.	.	PUNCT
ejpam-6458	66	1	where	where	SCONJ
ejpam-6458	66	2	s	s	VERB
ejpam-6458	66	3	=	=	SYM
ejpam-6458	66	4	(	(	PUNCT
ejpam-6458	66	5	s1	s1	PROPN
ejpam-6458	66	6	,	,	PUNCT
ejpam-6458	66	7	.	.	PUNCT
ejpam-6458	66	8	.	.	PUNCT
ejpam-6458	66	9	.	.	PUNCT
ejpam-6458	67	1	,	,	PUNCT
ejpam-6458	67	2	sk	sk	PROPN
ejpam-6458	67	3	)	)	PUNCT
ejpam-6458	67	4	is	be	AUX
ejpam-6458	67	5	a	a	DET
ejpam-6458	67	6	k	k	NOUN
ejpam-6458	67	7	-	-	NOUN
ejpam-6458	67	8	tuple	tuple	NOUN
ejpam-6458	67	9	of	of	ADP
ejpam-6458	67	10	nonnegative	nonnegative	ADJ
ejpam-6458	67	11	integers	integer	NOUN
ejpam-6458	67	12	,	,	PUNCT
ejpam-6458	67	13	with	with	ADP
ejpam-6458	67	14	at	at	ADV
ejpam-6458	67	15	least	least	ADV
ejpam-6458	67	16	one	one	NUM
ejpam-6458	67	17	si	si	NOUN
ejpam-6458	67	18	̸=	̸=	PROPN
ejpam-6458	67	19	0	0	NUM
ejpam-6458	67	20	.	.	PUNCT
ejpam-6458	68	1	for	for	ADP
ejpam-6458	68	2	every	every	DET
ejpam-6458	68	3	monomial	monomial	NOUN
ejpam-6458	68	4	x	x	AUX
ejpam-6458	68	5	define	define	VERB
ejpam-6458	68	6	a	a	DET
ejpam-6458	68	7	lexicographical	lexicographical	ADJ
ejpam-6458	68	8	order	order	NOUN
ejpam-6458	68	9	on	on	ADP
ejpam-6458	68	10	the	the	DET
ejpam-6458	68	11	set	set	NOUN
ejpam-6458	68	12	t0(x	t0(x	NOUN
ejpam-6458	68	13	)	)	PUNCT
ejpam-6458	68	14	with	with	ADP
ejpam-6458	68	15	respect	respect	NOUN
ejpam-6458	68	16	to	to	ADP
ejpam-6458	68	17	the	the	DET
ejpam-6458	68	18	order	order	NOUN
ejpam-6458	68	19	(	(	PUNCT
ejpam-6458	68	20	2.1	2.1	NUM
ejpam-6458	68	21	):	):	PUNCT
ejpam-6458	68	22	if	if	SCONJ
ejpam-6458	68	23	x1	x1	PROPN
ejpam-6458	68	24	=	=	X
ejpam-6458	68	25	xi1xi2	xi1xi2	PROPN
ejpam-6458	68	26	·	·	PUNCT
ejpam-6458	68	27	·	·	PUNCT
ejpam-6458	68	28	·	·	PUNCT
ejpam-6458	68	29	xin	xin	PROPN
ejpam-6458	68	30	and	and	CCONJ
ejpam-6458	68	31	x2	x2	PROPN
ejpam-6458	69	1	=	=	PUNCT
ejpam-6458	69	2	xj1xj2	xj1xj2	PROPN
ejpam-6458	69	3	·	·	PUNCT
ejpam-6458	69	4	·	·	PUNCT
ejpam-6458	69	5	·	·	PUNCT
ejpam-6458	69	6	xjn	xjn	NOUN
ejpam-6458	69	7	,	,	PUNCT
ejpam-6458	69	8	with	with	ADP
ejpam-6458	69	9	x1	x1	PROPN
ejpam-6458	69	10	,	,	PUNCT
ejpam-6458	69	11	x2	x2	PROPN
ejpam-6458	69	12	∈	∈	PROPN
ejpam-6458	69	13	t0(x	t0(x	NOUN
ejpam-6458	69	14	)	)	PUNCT
ejpam-6458	69	15	,	,	PUNCT
ejpam-6458	69	16	then	then	ADV
ejpam-6458	69	17	x1	x1	INTJ
ejpam-6458	69	18	<	<	X
ejpam-6458	69	19	x2	x2	PROPN
ejpam-6458	69	20	if	if	SCONJ
ejpam-6458	69	21	either	either	CCONJ
ejpam-6458	69	22	xi1	xi1	PROPN
ejpam-6458	69	23	<	<	X
ejpam-6458	69	24	xj1	xj1	PROPN
ejpam-6458	69	25	or	or	CCONJ
ejpam-6458	69	26	there	there	PRON
ejpam-6458	69	27	exists	exist	VERB
ejpam-6458	69	28	an	an	DET
ejpam-6458	69	29	index	index	NOUN
ejpam-6458	69	30	1	1	NUM
ejpam-6458	69	31	<	<	X
ejpam-6458	69	32	s	s	PART
ejpam-6458	69	33	≤	≤	NUM
ejpam-6458	69	34	n	n	CCONJ
ejpam-6458	69	35	such	such	ADJ
ejpam-6458	69	36	that	that	SCONJ
ejpam-6458	69	37	xis	xis	PROPN
ejpam-6458	69	38	<	<	X
ejpam-6458	69	39	xjs	xjs	PROPN
ejpam-6458	69	40	and	and	CCONJ
ejpam-6458	69	41	xit	xit	PROPN
ejpam-6458	69	42	=	=	SYM
ejpam-6458	69	43	xjt	xjt	PROPN
ejpam-6458	69	44	,	,	PUNCT
ejpam-6458	69	45	for	for	ADP
ejpam-6458	69	46	1	1	NUM
ejpam-6458	69	47	≤	≤	NOUN
ejpam-6458	69	48	t	t	PROPN
ejpam-6458	69	49	<	<	X
ejpam-6458	69	50	s.	s.	PROPN
ejpam-6458	69	51	denote	denote	VERB
ejpam-6458	69	52	by	by	ADP
ejpam-6458	69	53	p	p	X
ejpam-6458	69	54	the	the	DET
ejpam-6458	69	55	set	set	NOUN
ejpam-6458	69	56	of	of	ADP
ejpam-6458	69	57	all	all	DET
ejpam-6458	69	58	standard	standard	ADJ
ejpam-6458	69	59	monomials	monomial	NOUN
ejpam-6458	69	60	and	and	CCONJ
ejpam-6458	69	61	by	by	ADP
ejpam-6458	69	62	p	p	PROPN
ejpam-6458	69	63	(	(	PUNCT
ejpam-6458	69	64	i	i	NOUN
ejpam-6458	69	65	)	)	PUNCT
ejpam-6458	69	66	the	the	DET
ejpam-6458	69	67	set	set	NOUN
ejpam-6458	69	68	of	of	ADP
ejpam-6458	69	69	all	all	DET
ejpam-6458	69	70	standard	standard	ADJ
ejpam-6458	69	71	monomials	monomial	NOUN
ejpam-6458	69	72	of	of	ADP
ejpam-6458	69	73	degree	degree	NOUN
ejpam-6458	69	74	i.	i.	NOUN
ejpam-6458	69	75	set	set	VERB
ejpam-6458	69	76	p0	p0	NOUN
ejpam-6458	69	77	=	=	SYM
ejpam-6458	69	78	p∩u0(g	p∩u0(g	NOUN
ejpam-6458	69	79	)	)	PUNCT
ejpam-6458	69	80	and	and	CCONJ
ejpam-6458	69	81	p	p	X
ejpam-6458	69	82	(	(	PUNCT
ejpam-6458	69	83	i	i	NOUN
ejpam-6458	69	84	)	)	PUNCT
ejpam-6458	69	85	0	0	PUNCT
ejpam-6458	70	1	=	=	SYM
ejpam-6458	70	2	p	p	X
ejpam-6458	70	3	(	(	PUNCT
ejpam-6458	70	4	i)∩u0(g	i)∩u0(g	NOUN
ejpam-6458	70	5	)	)	PUNCT
ejpam-6458	70	6	.	.	PUNCT
ejpam-6458	71	1	in	in	ADP
ejpam-6458	71	2	particular	particular	ADJ
ejpam-6458	71	3	,	,	PUNCT
ejpam-6458	71	4	t0(p	t0(p	X
ejpam-6458	71	5	)	)	PUNCT
ejpam-6458	72	1	=	=	SYM
ejpam-6458	72	2	⋃	⋃	ADP
ejpam-6458	72	3	x∈p	x∈p	NOUN
ejpam-6458	72	4	t0(x	t0(x	NOUN
ejpam-6458	72	5	)	)	PUNCT
ejpam-6458	72	6	will	will	AUX
ejpam-6458	72	7	denote	denote	VERB
ejpam-6458	72	8	the	the	DET
ejpam-6458	72	9	set	set	NOUN
ejpam-6458	72	10	of	of	ADP
ejpam-6458	72	11	all	all	DET
ejpam-6458	72	12	monomials	monomial	NOUN
ejpam-6458	72	13	in	in	ADP
ejpam-6458	72	14	the	the	DET
ejpam-6458	72	15	algebra	algebra	NOUN
ejpam-6458	72	16	u(g	u(g	PROPN
ejpam-6458	72	17	)	)	PUNCT
ejpam-6458	72	18	.	.	PUNCT
ejpam-6458	73	1	the	the	DET
ejpam-6458	73	2	following	follow	VERB
ejpam-6458	73	3	lemma	lemma	PROPN
ejpam-6458	73	4	is	be	AUX
ejpam-6458	73	5	an	an	DET
ejpam-6458	73	6	immediate	immediate	ADJ
ejpam-6458	73	7	consequence	consequence	NOUN
ejpam-6458	73	8	of	of	ADP
ejpam-6458	73	9	the	the	DET
ejpam-6458	73	10	pbw	pbw	NOUN
ejpam-6458	73	11	theorem	theorem	NOUN
ejpam-6458	73	12	.	.	PUNCT
ejpam-6458	74	1	lemma	lemma	PROPN
ejpam-6458	74	2	2.1	2.1	NUM
ejpam-6458	74	3	.	.	PUNCT
ejpam-6458	74	4	1	1	NUM
ejpam-6458	74	5	.	.	PUNCT
ejpam-6458	75	1	the	the	DET
ejpam-6458	75	2	set	set	NOUN
ejpam-6458	75	3	of	of	ADP
ejpam-6458	75	4	the	the	DET
ejpam-6458	75	5	following	follow	VERB
ejpam-6458	75	6	standard	standard	ADJ
ejpam-6458	75	7	monomials	monomial	NOUN
ejpam-6458	75	8	p̄	p̄	NOUN
ejpam-6458	75	9	(	(	PUNCT
ejpam-6458	75	10	i	i	NOUN
ejpam-6458	75	11	)	)	PUNCT
ejpam-6458	76	1	=	=	SYM
ejpam-6458	76	2	p	p	X
ejpam-6458	76	3	(	(	PUNCT
ejpam-6458	76	4	1)∪p	1)∪p	X
ejpam-6458	76	5	(	(	PUNCT
ejpam-6458	76	6	2)∪	2)∪	NOUN
ejpam-6458	76	7	·	·	PUNCT
ejpam-6458	76	8	·	·	PUNCT
ejpam-6458	76	9	·	·	PUNCT
ejpam-6458	76	10	∪p	∪p	NUM
ejpam-6458	76	11	(	(	PUNCT
ejpam-6458	76	12	i	i	NOUN
ejpam-6458	76	13	)	)	PUNCT
ejpam-6458	76	14	forms	form	VERB
ejpam-6458	76	15	a	a	DET
ejpam-6458	76	16	basis	basis	NOUN
ejpam-6458	76	17	for	for	ADP
ejpam-6458	76	18	the	the	DET
ejpam-6458	76	19	vector	vector	NOUN
ejpam-6458	76	20	space	space	NOUN
ejpam-6458	76	21	u	u	NOUN
ejpam-6458	76	22	(	(	PUNCT
ejpam-6458	76	23	i)(g	i)(g	PROPN
ejpam-6458	76	24	)	)	PUNCT
ejpam-6458	76	25	.	.	PUNCT
ejpam-6458	77	1	2	2	X
ejpam-6458	77	2	.	.	X
ejpam-6458	77	3	the	the	DET
ejpam-6458	77	4	set	set	NOUN
ejpam-6458	77	5	of	of	ADP
ejpam-6458	77	6	the	the	DET
ejpam-6458	77	7	standard	standard	ADJ
ejpam-6458	77	8	monomials	monomial	NOUN
ejpam-6458	77	9	p̄	p̄	NOUN
ejpam-6458	77	10	(	(	PUNCT
ejpam-6458	77	11	i	i	NOUN
ejpam-6458	77	12	)	)	PUNCT
ejpam-6458	77	13	0	0	PUNCT
ejpam-6458	78	1	=	=	SYM
ejpam-6458	78	2	p	p	X
ejpam-6458	78	3	(	(	PUNCT
ejpam-6458	78	4	1	1	NUM
ejpam-6458	78	5	)	)	PUNCT
ejpam-6458	78	6	0	0	NUM
ejpam-6458	78	7	∪	∪	PROPN
ejpam-6458	78	8	p	p	X
ejpam-6458	78	9	(	(	PUNCT
ejpam-6458	78	10	2	2	NUM
ejpam-6458	78	11	)	)	PUNCT
ejpam-6458	78	12	0	0	NUM
ejpam-6458	78	13	∪	∪	X
ejpam-6458	78	14	·	·	PUNCT
ejpam-6458	78	15	·	·	PUNCT
ejpam-6458	78	16	·	·	PUNCT
ejpam-6458	78	17	∪	∪	ADP
ejpam-6458	78	18	p	p	X
ejpam-6458	78	19	(	(	PUNCT
ejpam-6458	78	20	i	i	NOUN
ejpam-6458	78	21	)	)	PUNCT
ejpam-6458	78	22	0	0	NUM
ejpam-6458	78	23	forms	form	VERB
ejpam-6458	78	24	a	a	DET
ejpam-6458	78	25	basis	basis	NOUN
ejpam-6458	78	26	for	for	ADP
ejpam-6458	78	27	the	the	DET
ejpam-6458	78	28	vector	vector	NOUN
ejpam-6458	78	29	space	space	NOUN
ejpam-6458	78	30	u	u	NOUN
ejpam-6458	78	31	(	(	PUNCT
ejpam-6458	78	32	i	i	NOUN
ejpam-6458	78	33	)	)	PUNCT
ejpam-6458	78	34	0	0	PUNCT
ejpam-6458	79	1	(	(	PUNCT
ejpam-6458	79	2	g	g	NOUN
ejpam-6458	79	3	)	)	PUNCT
ejpam-6458	79	4	.	.	PUNCT
ejpam-6458	80	1	3	3	X
ejpam-6458	80	2	.	.	X
ejpam-6458	80	3	if	if	SCONJ
ejpam-6458	80	4	a	a	DET
ejpam-6458	80	5	∈	∈	PROPN
ejpam-6458	80	6	u	u	NOUN
ejpam-6458	80	7	(	(	PUNCT
ejpam-6458	80	8	i)(g	i)(g	PROPN
ejpam-6458	80	9	)	)	PUNCT
ejpam-6458	80	10	and	and	CCONJ
ejpam-6458	80	11	b	b	X
ejpam-6458	80	12	∈	∈	PROPN
ejpam-6458	80	13	u	u	NOUN
ejpam-6458	80	14	(	(	PUNCT
ejpam-6458	80	15	j)(g	j)(g	PROPN
ejpam-6458	80	16	)	)	PUNCT
ejpam-6458	80	17	,	,	PUNCT
ejpam-6458	80	18	then	then	ADV
ejpam-6458	80	19	ab	ab	PROPN
ejpam-6458	80	20	∈	∈	PROPN
ejpam-6458	80	21	u	u	PROPN
ejpam-6458	80	22	(	(	PUNCT
ejpam-6458	80	23	i+j)(g	i+j)(g	ADP
ejpam-6458	80	24	)	)	PUNCT
ejpam-6458	80	25	and	and	CCONJ
ejpam-6458	80	26	ab−	ab−	NUM
ejpam-6458	80	27	ba	ba	PROPN
ejpam-6458	80	28	∈	∈	PROPN
ejpam-6458	80	29	u	u	PROPN
ejpam-6458	80	30	(	(	PUNCT
ejpam-6458	80	31	i+j−1)(g	i+j−1)(g	PROPN
ejpam-6458	80	32	)	)	PUNCT
ejpam-6458	80	33	.	.	PUNCT
ejpam-6458	81	1	4	4	X
ejpam-6458	81	2	.	.	X
ejpam-6458	82	1	if	if	SCONJ
ejpam-6458	82	2	x	x	SYM
ejpam-6458	82	3	∈	∈	PROPN
ejpam-6458	82	4	p	p	X
ejpam-6458	82	5	(	(	PUNCT
ejpam-6458	82	6	i	i	NOUN
ejpam-6458	82	7	)	)	PUNCT
ejpam-6458	82	8	0	0	NUM
ejpam-6458	82	9	and	and	CCONJ
ejpam-6458	82	10	x1	x1	NUM
ejpam-6458	82	11	,	,	PUNCT
ejpam-6458	82	12	x2	x2	PROPN
ejpam-6458	82	13	∈	∈	PROPN
ejpam-6458	82	14	t0(x	t0(x	NOUN
ejpam-6458	82	15	)	)	PUNCT
ejpam-6458	82	16	,	,	PUNCT
ejpam-6458	82	17	then	then	ADV
ejpam-6458	82	18	x1	x1	NUM
ejpam-6458	82	19	−x2	−x2	PROPN
ejpam-6458	82	20	∈	∈	PROPN
ejpam-6458	82	21	u	u	NOUN
ejpam-6458	82	22	(	(	PUNCT
ejpam-6458	82	23	i−1	i−1	PROPN
ejpam-6458	82	24	)	)	PUNCT
ejpam-6458	82	25	0	0	NUM
ejpam-6458	83	1	(	(	PUNCT
ejpam-6458	83	2	g	g	NOUN
ejpam-6458	83	3	)	)	PUNCT
ejpam-6458	83	4	.	.	PUNCT
ejpam-6458	84	1	5	5	X
ejpam-6458	84	2	.	.	X
ejpam-6458	84	3	for	for	ADP
ejpam-6458	84	4	every	every	DET
ejpam-6458	84	5	monomial	monomial	NOUN
ejpam-6458	84	6	x	x	SYM
ejpam-6458	84	7	∈	∈	PROPN
ejpam-6458	84	8	t0(p	t0(p	X
ejpam-6458	84	9	)	)	PUNCT
ejpam-6458	84	10	,	,	PUNCT
ejpam-6458	84	11	the	the	DET
ejpam-6458	84	12	minimal	minimal	ADJ
ejpam-6458	84	13	element	element	NOUN
ejpam-6458	84	14	of	of	ADP
ejpam-6458	84	15	the	the	DET
ejpam-6458	84	16	set	set	NOUN
ejpam-6458	84	17	t0(x	t0(x	NOUN
ejpam-6458	84	18	)	)	PUNCT
ejpam-6458	84	19	with	with	ADP
ejpam-6458	84	20	respect	respect	NOUN
ejpam-6458	84	21	to	to	ADP
ejpam-6458	84	22	the	the	DET
ejpam-6458	84	23	above	above	ADJ
ejpam-6458	84	24	lexicographical	lexicographical	ADJ
ejpam-6458	84	25	order	order	NOUN
ejpam-6458	84	26	is	be	AUX
ejpam-6458	84	27	a	a	DET
ejpam-6458	84	28	standard	standard	ADJ
ejpam-6458	84	29	monomial	monomial	NOUN
ejpam-6458	84	30	.	.	PUNCT
ejpam-6458	85	1	6	6	X
ejpam-6458	85	2	.	.	X
ejpam-6458	85	3	let	let	VERB
ejpam-6458	85	4	p	p	PRON
ejpam-6458	85	5	′	′	NOUN
ejpam-6458	85	6	be	be	AUX
ejpam-6458	85	7	a	a	DET
ejpam-6458	85	8	set	set	NOUN
ejpam-6458	85	9	of	of	ADP
ejpam-6458	85	10	monomials	monomial	NOUN
ejpam-6458	85	11	of	of	ADP
ejpam-6458	85	12	degree	degree	NOUN
ejpam-6458	85	13	≤	≤	X
ejpam-6458	86	1	i	i	PRON
ejpam-6458	86	2	,	,	PUNCT
ejpam-6458	86	3	such	such	ADJ
ejpam-6458	86	4	that	that	PRON
ejpam-6458	86	5	for	for	ADP
ejpam-6458	86	6	every	every	DET
ejpam-6458	86	7	monomial	monomial	NOUN
ejpam-6458	86	8	x	x	SYM
ejpam-6458	86	9	∈	∈	PROPN
ejpam-6458	86	10	p̄	p̄	NOUN
ejpam-6458	86	11	(	(	PUNCT
ejpam-6458	86	12	i	i	NOUN
ejpam-6458	86	13	)	)	PUNCT
ejpam-6458	86	14	,	,	PUNCT
ejpam-6458	86	15	there	there	PRON
ejpam-6458	86	16	exist	exist	VERB
ejpam-6458	86	17	a	a	DET
ejpam-6458	86	18	unique	unique	ADJ
ejpam-6458	86	19	x	x	SYM
ejpam-6458	86	20	′	′	NUM
ejpam-6458	86	21	∈	∈	NOUN
ejpam-6458	86	22	p	p	NOUN
ejpam-6458	86	23	′	′	NUM
ejpam-6458	86	24	satisfying	satisfying	ADJ
ejpam-6458	86	25	t0(x	t0(x	NOUN
ejpam-6458	86	26	)	)	PUNCT
ejpam-6458	86	27	=	=	SYM
ejpam-6458	86	28	t0(x	t0(x	NOUN
ejpam-6458	86	29	′	′	NOUN
ejpam-6458	86	30	)	)	PUNCT
ejpam-6458	86	31	.	.	PUNCT
ejpam-6458	87	1	then	then	ADV
ejpam-6458	87	2	p	p	NOUN
ejpam-6458	87	3	′	′	NOUN
ejpam-6458	87	4	is	be	AUX
ejpam-6458	87	5	a	a	DET
ejpam-6458	87	6	basis	basis	NOUN
ejpam-6458	87	7	of	of	ADP
ejpam-6458	87	8	u	u	PROPN
ejpam-6458	87	9	(	(	PUNCT
ejpam-6458	87	10	i)(g	i)(g	PROPN
ejpam-6458	87	11	)	)	PUNCT
ejpam-6458	87	12	and	and	CCONJ
ejpam-6458	87	13	p	p	X
ejpam-6458	87	14	′	′	NOUN
ejpam-6458	87	15	0	0	NUM
ejpam-6458	88	1	=	=	SYM
ejpam-6458	88	2	p	p	ADJ
ejpam-6458	88	3	′	′	NUM
ejpam-6458	88	4	∩	∩	ADJ
ejpam-6458	88	5	u	u	NOUN
ejpam-6458	88	6	(	(	PUNCT
ejpam-6458	88	7	i	i	NOUN
ejpam-6458	88	8	)	)	PUNCT
ejpam-6458	88	9	0	0	PUNCT
ejpam-6458	89	1	(	(	PUNCT
ejpam-6458	89	2	g	g	NOUN
ejpam-6458	89	3	)	)	PUNCT
ejpam-6458	89	4	is	be	AUX
ejpam-6458	89	5	a	a	DET
ejpam-6458	89	6	basis	basis	NOUN
ejpam-6458	89	7	of	of	ADP
ejpam-6458	89	8	u	u	PROPN
ejpam-6458	89	9	(	(	PUNCT
ejpam-6458	89	10	i	i	NOUN
ejpam-6458	89	11	)	)	PUNCT
ejpam-6458	89	12	0	0	PUNCT
ejpam-6458	90	1	(	(	PUNCT
ejpam-6458	90	2	g	g	NOUN
ejpam-6458	90	3	)	)	PUNCT
ejpam-6458	90	4	.	.	PUNCT
ejpam-6458	91	1	m.	m.	PROPN
ejpam-6458	91	2	andelić	andelić	PROPN
ejpam-6458	91	3	et	et	PROPN
ejpam-6458	91	4	al	al	PROPN
ejpam-6458	91	5	.	.	PUNCT
ejpam-6458	91	6	/	/	SYM
ejpam-6458	91	7	eur	eur	PROPN
ejpam-6458	91	8	.	.	PUNCT
ejpam-6458	92	1	j.	j.	PROPN
ejpam-6458	92	2	pure	pure	PROPN
ejpam-6458	92	3	appl	appl	PROPN
ejpam-6458	92	4	.	.	PROPN
ejpam-6458	92	5	math	math	PROPN
ejpam-6458	92	6	,	,	PUNCT
ejpam-6458	92	7	18	18	NUM
ejpam-6458	92	8	(	(	PUNCT
ejpam-6458	92	9	3	3	NUM
ejpam-6458	92	10	)	)	PUNCT
ejpam-6458	92	11	(	(	PUNCT
ejpam-6458	92	12	2025	2025	NUM
ejpam-6458	92	13	)	)	PUNCT
ejpam-6458	92	14	,	,	PUNCT
ejpam-6458	92	15	6458	6458	NUM
ejpam-6458	92	16	4	4	NUM
ejpam-6458	92	17	of	of	ADP
ejpam-6458	92	18	21	21	NUM
ejpam-6458	92	19	denote	denote	VERB
ejpam-6458	92	20	by	by	ADP
ejpam-6458	92	21	p̂	p̂	X
ejpam-6458	92	22	(	(	PUNCT
ejpam-6458	92	23	i	i	NOUN
ejpam-6458	92	24	)	)	PUNCT
ejpam-6458	92	25	0	0	PUNCT
ejpam-6458	93	1	⊂	⊂	PROPN
ejpam-6458	93	2	p	p	X
ejpam-6458	93	3	(	(	PUNCT
ejpam-6458	93	4	i	i	NOUN
ejpam-6458	93	5	)	)	PUNCT
ejpam-6458	93	6	0	0	PUNCT
ejpam-6458	94	1	the	the	DET
ejpam-6458	94	2	subset	subset	NOUN
ejpam-6458	94	3	of	of	ADP
ejpam-6458	94	4	monomials	monomial	NOUN
ejpam-6458	94	5	of	of	ADP
ejpam-6458	94	6	degree	degree	NOUN
ejpam-6458	94	7	i	i	PRON
ejpam-6458	94	8	generated	generate	VERB
ejpam-6458	94	9	by	by	ADP
ejpam-6458	94	10	g1	g1	NOUN
ejpam-6458	94	11	,	,	PUNCT
ejpam-6458	94	12	and	and	CCONJ
ejpam-6458	94	13	set	set	VERB
ejpam-6458	94	14	p̂0	p̂0	NOUN
ejpam-6458	94	15	=	=	PUNCT
ejpam-6458	95	1	⋃	⋃	PUNCT
ejpam-6458	95	2	i	i	PRON
ejpam-6458	95	3	p̂	p̂	X
ejpam-6458	95	4	(	(	PUNCT
ejpam-6458	95	5	i	i	NOUN
ejpam-6458	95	6	)	)	PUNCT
ejpam-6458	95	7	0	0	PUNCT
ejpam-6458	95	8	.	.	PUNCT
ejpam-6458	96	1	letx	letx	PROPN
ejpam-6458	96	2	∈	∈	PROPN
ejpam-6458	96	3	t0(p	t0(p	X
ejpam-6458	96	4	)	)	PUNCT
ejpam-6458	96	5	.	.	PUNCT
ejpam-6458	97	1	thenx	thenx	NOUN
ejpam-6458	98	1	=	=	PUNCT
ejpam-6458	98	2	hβ1	hβ1	NOUN
ejpam-6458	98	3	·	·	PUNCT
ejpam-6458	98	4	·	·	PUNCT
ejpam-6458	98	5	·	·	PUNCT
ejpam-6458	98	6	hβmeα1	hβmeα1	X
ejpam-6458	98	7	·	·	PUNCT
ejpam-6458	98	8	·	·	PUNCT
ejpam-6458	98	9	·	·	PUNCT
ejpam-6458	98	10	eαn	eαn	X
ejpam-6458	98	11	,	,	PUNCT
ejpam-6458	98	12	for	for	ADP
ejpam-6458	98	13	some	some	DET
ejpam-6458	98	14	α1	α1	NOUN
ejpam-6458	98	15	,	,	PUNCT
ejpam-6458	98	16	.	.	PUNCT
ejpam-6458	98	17	.	.	PUNCT
ejpam-6458	98	18	.	.	PUNCT
ejpam-6458	99	1	,	,	PUNCT
ejpam-6458	99	2	αn	αn	NOUN
ejpam-6458	99	3	∈	∈	PROPN
ejpam-6458	99	4	∆	∆	X
ejpam-6458	99	5	,	,	PUNCT
ejpam-6458	99	6	β1	β1	PROPN
ejpam-6458	99	7	,	,	PUNCT
ejpam-6458	99	8	.	.	PUNCT
ejpam-6458	99	9	.	.	PUNCT
ejpam-6458	99	10	.	.	PUNCT
ejpam-6458	100	1	,	,	PUNCT
ejpam-6458	100	2	βm	βm	VERB
ejpam-6458	100	3	∈	∈	PROPN
ejpam-6458	100	4	π	π	PROPN
ejpam-6458	100	5	.	.	PUNCT
ejpam-6458	101	1	define	define	VERB
ejpam-6458	101	2	two	two	NUM
ejpam-6458	101	3	lists	list	NOUN
ejpam-6458	101	4	of	of	ADP
ejpam-6458	101	5	roots	root	NOUN
ejpam-6458	101	6	associated	associate	VERB
ejpam-6458	101	7	with	with	ADP
ejpam-6458	101	8	x	x	PUNCT
ejpam-6458	101	9	as	as	SCONJ
ejpam-6458	101	10	follows	follow	VERB
ejpam-6458	101	11	:	:	PUNCT
ejpam-6458	101	12	l0(x	l0(x	NOUN
ejpam-6458	101	13	)	)	PUNCT
ejpam-6458	101	14	=	=	SYM
ejpam-6458	101	15	(	(	PUNCT
ejpam-6458	101	16	β1	β1	PROPN
ejpam-6458	101	17	,	,	PUNCT
ejpam-6458	101	18	.	.	PUNCT
ejpam-6458	101	19	.	.	PUNCT
ejpam-6458	101	20	.	.	PUNCT
ejpam-6458	102	1	,	,	PUNCT
ejpam-6458	102	2	βm	βm	VERB
ejpam-6458	102	3	)	)	PUNCT
ejpam-6458	102	4	and	and	CCONJ
ejpam-6458	102	5	l1(x	l1(x	NUM
ejpam-6458	102	6	)	)	PUNCT
ejpam-6458	102	7	=	=	SYM
ejpam-6458	102	8	(	(	PUNCT
ejpam-6458	102	9	α1	α1	PROPN
ejpam-6458	102	10	,	,	PUNCT
ejpam-6458	102	11	.	.	PUNCT
ejpam-6458	102	12	.	.	PUNCT
ejpam-6458	103	1	.	.	PUNCT
ejpam-6458	104	1	,	,	PUNCT
ejpam-6458	104	2	αm	αm	X
ejpam-6458	104	3	)	)	PUNCT
ejpam-6458	104	4	.	.	PUNCT
ejpam-6458	105	1	extend	extend	VERB
ejpam-6458	105	2	this	this	DET
ejpam-6458	105	3	definition	definition	NOUN
ejpam-6458	105	4	to	to	ADP
ejpam-6458	105	5	the	the	DET
ejpam-6458	105	6	set	set	NOUN
ejpam-6458	105	7	of	of	ADP
ejpam-6458	105	8	all	all	DET
ejpam-6458	105	9	monomials	monomial	NOUN
ejpam-6458	105	10	as	as	SCONJ
ejpam-6458	105	11	follows	follow	VERB
ejpam-6458	105	12	:	:	PUNCT
ejpam-6458	105	13	if	if	SCONJ
ejpam-6458	105	14	x	x	NUM
ejpam-6458	105	15	′	′	NUM
ejpam-6458	105	16	∈	∈	PROPN
ejpam-6458	105	17	t0(x	t0(x	NOUN
ejpam-6458	105	18	)	)	PUNCT
ejpam-6458	105	19	,	,	PUNCT
ejpam-6458	105	20	then	then	ADV
ejpam-6458	105	21	l0(x	l0(x	ADP
ejpam-6458	105	22	′	′	X
ejpam-6458	105	23	)	)	PUNCT
ejpam-6458	105	24	=	=	PUNCT
ejpam-6458	106	1	l0(x	l0(x	NOUN
ejpam-6458	106	2	)	)	PUNCT
ejpam-6458	106	3	,	,	PUNCT
ejpam-6458	106	4	l1(x	l1(x	NOUN
ejpam-6458	106	5	′	′	NOUN
ejpam-6458	106	6	)	)	PUNCT
ejpam-6458	106	7	=	=	SYM
ejpam-6458	106	8	l1(x	l1(x	NOUN
ejpam-6458	106	9	)	)	PUNCT
ejpam-6458	106	10	.	.	PUNCT
ejpam-6458	107	1	for	for	ADP
ejpam-6458	107	2	any	any	DET
ejpam-6458	107	3	monomial	monomial	NOUN
ejpam-6458	107	4	x	x	SYM
ejpam-6458	107	5	∈	∈	PROPN
ejpam-6458	107	6	t0(p	t0(p	X
ejpam-6458	107	7	)	)	PUNCT
ejpam-6458	107	8	,	,	PUNCT
ejpam-6458	107	9	the	the	DET
ejpam-6458	107	10	sum	sum	NOUN
ejpam-6458	107	11	of	of	ADP
ejpam-6458	107	12	all	all	DET
ejpam-6458	107	13	roots	root	NOUN
ejpam-6458	107	14	in	in	ADP
ejpam-6458	107	15	the	the	DET
ejpam-6458	107	16	list	list	NOUN
ejpam-6458	107	17	l1(x	l1(x	NOUN
ejpam-6458	107	18	)	)	PUNCT
ejpam-6458	107	19	is	be	AUX
ejpam-6458	107	20	called	call	VERB
ejpam-6458	107	21	the	the	DET
ejpam-6458	107	22	weight	weight	NOUN
ejpam-6458	107	23	of	of	ADP
ejpam-6458	107	24	the	the	DET
ejpam-6458	107	25	list	list	NOUN
ejpam-6458	107	26	l1(x	l1(x	NOUN
ejpam-6458	107	27	)	)	PUNCT
ejpam-6458	107	28	.	.	PUNCT
ejpam-6458	108	1	clearly	clearly	ADV
ejpam-6458	108	2	,	,	PUNCT
ejpam-6458	108	3	the	the	DET
ejpam-6458	108	4	weight	weight	NOUN
ejpam-6458	108	5	of	of	ADP
ejpam-6458	108	6	the	the	DET
ejpam-6458	108	7	list	list	NOUN
ejpam-6458	108	8	l1(x	l1(x	NOUN
ejpam-6458	108	9	)	)	PUNCT
ejpam-6458	108	10	is	be	AUX
ejpam-6458	108	11	zero	zero	NUM
ejpam-6458	108	12	if	if	SCONJ
ejpam-6458	108	13	and	and	CCONJ
ejpam-6458	108	14	only	only	ADV
ejpam-6458	108	15	if	if	SCONJ
ejpam-6458	108	16	x	x	PROPN
ejpam-6458	108	17	∈	∈	PROPN
ejpam-6458	108	18	t0(p0	t0(p0	NOUN
ejpam-6458	108	19	)	)	PUNCT
ejpam-6458	108	20	.	.	PUNCT
ejpam-6458	109	1	denote	denote	VERB
ejpam-6458	109	2	by	by	ADP
ejpam-6458	109	3	b(∆	b(∆	PROPN
ejpam-6458	109	4	)	)	PUNCT
ejpam-6458	109	5	the	the	DET
ejpam-6458	109	6	set	set	NOUN
ejpam-6458	109	7	of	of	ADP
ejpam-6458	109	8	all	all	DET
ejpam-6458	109	9	zero	zero	NUM
ejpam-6458	109	10	-	-	PUNCT
ejpam-6458	109	11	weight	weight	NOUN
ejpam-6458	109	12	lists	list	NOUN
ejpam-6458	109	13	of	of	ADP
ejpam-6458	109	14	roots	root	NOUN
ejpam-6458	109	15	.	.	PUNCT
ejpam-6458	110	1	furthermore	furthermore	ADV
ejpam-6458	110	2	,	,	PUNCT
ejpam-6458	110	3	if	if	SCONJ
ejpam-6458	110	4	l0(x	l0(x	ADP
ejpam-6458	110	5	)	)	PUNCT
ejpam-6458	110	6	=	=	SYM
ejpam-6458	110	7	l0(y	l0(y	X
ejpam-6458	110	8	)	)	PUNCT
ejpam-6458	110	9	and	and	CCONJ
ejpam-6458	110	10	l1(x	l1(x	NUM
ejpam-6458	110	11	)	)	PUNCT
ejpam-6458	110	12	=	=	SYM
ejpam-6458	111	1	l1(y	l1(y	PROPN
ejpam-6458	111	2	)	)	PUNCT
ejpam-6458	111	3	,	,	PUNCT
ejpam-6458	111	4	for	for	ADP
ejpam-6458	111	5	some	some	DET
ejpam-6458	111	6	monomials	monomial	NOUN
ejpam-6458	111	7	x	x	X
ejpam-6458	111	8	,	,	PUNCT
ejpam-6458	111	9	y	y	PROPN
ejpam-6458	111	10	,	,	PUNCT
ejpam-6458	111	11	then	then	ADV
ejpam-6458	111	12	t0(x	t0(x	NOUN
ejpam-6458	111	13	)	)	PUNCT
ejpam-6458	111	14	=	=	SYM
ejpam-6458	112	1	t0(y	t0(y	NUM
ejpam-6458	112	2	)	)	PUNCT
ejpam-6458	112	3	.	.	PUNCT
ejpam-6458	113	1	a	a	DET
ejpam-6458	113	2	list	list	NOUN
ejpam-6458	113	3	l1(x	l1(x	NOUN
ejpam-6458	113	4	)	)	PUNCT
ejpam-6458	113	5	for	for	ADP
ejpam-6458	113	6	x	x	PROPN
ejpam-6458	113	7	∈	∈	PROPN
ejpam-6458	113	8	p̄0	p̄0	PUNCT
ejpam-6458	113	9	is	be	AUX
ejpam-6458	113	10	called	call	VERB
ejpam-6458	113	11	decomposable	decomposable	ADJ
ejpam-6458	113	12	if	if	SCONJ
ejpam-6458	113	13	there	there	PRON
ejpam-6458	113	14	exist	exist	VERB
ejpam-6458	113	15	x1	x1	PROPN
ejpam-6458	114	1	,	,	PUNCT
ejpam-6458	114	2	x2	x2	PROPN
ejpam-6458	114	3	∈	∈	PROPN
ejpam-6458	114	4	p̄0	p̄0	NOUN
ejpam-6458	114	5	such	such	ADJ
ejpam-6458	114	6	that	that	DET
ejpam-6458	114	7	l1(x	l1(x	NOUN
ejpam-6458	114	8	)	)	PUNCT
ejpam-6458	114	9	=	=	SYM
ejpam-6458	115	1	l1(x1	l1(x1	X
ejpam-6458	115	2	)	)	PUNCT
ejpam-6458	115	3	⊔	⊔	NOUN
ejpam-6458	115	4	l1(x2	l1(x2	NOUN
ejpam-6458	115	5	)	)	PUNCT
ejpam-6458	115	6	(	(	PUNCT
ejpam-6458	115	7	disjoint	disjoint	NOUN
ejpam-6458	115	8	union	union	NOUN
ejpam-6458	115	9	of	of	ADP
ejpam-6458	115	10	two	two	NUM
ejpam-6458	115	11	lists	list	NOUN
ejpam-6458	115	12	)	)	PUNCT
ejpam-6458	115	13	.	.	PUNCT
ejpam-6458	116	1	in	in	ADP
ejpam-6458	116	2	this	this	DET
ejpam-6458	116	3	case	case	NOUN
ejpam-6458	116	4	,	,	PUNCT
ejpam-6458	116	5	it	it	PRON
ejpam-6458	116	6	follows	follow	VERB
ejpam-6458	116	7	that	that	PRON
ejpam-6458	116	8	t0(x	t0(x	NOUN
ejpam-6458	116	9	)	)	PUNCT
ejpam-6458	116	10	=	=	SYM
ejpam-6458	116	11	t0(x1x2	t0(x1x2	NOUN
ejpam-6458	116	12	)	)	PUNCT
ejpam-6458	116	13	.	.	PUNCT
ejpam-6458	117	1	conversely	conversely	ADV
ejpam-6458	117	2	,	,	PUNCT
ejpam-6458	117	3	if	if	SCONJ
ejpam-6458	117	4	no	no	DET
ejpam-6458	117	5	such	such	ADJ
ejpam-6458	117	6	decomposition	decomposition	NOUN
ejpam-6458	117	7	exists	exist	VERB
ejpam-6458	117	8	,	,	PUNCT
ejpam-6458	117	9	the	the	DET
ejpam-6458	117	10	list	list	NOUN
ejpam-6458	117	11	is	be	AUX
ejpam-6458	117	12	called	call	VERB
ejpam-6458	117	13	indecompossable	indecompossable	ADJ
ejpam-6458	117	14	.	.	PUNCT
ejpam-6458	118	1	note	note	VERB
ejpam-6458	118	2	that	that	SCONJ
ejpam-6458	118	3	decompositions	decomposition	NOUN
ejpam-6458	118	4	are	be	AUX
ejpam-6458	118	5	not	not	PART
ejpam-6458	118	6	unique	unique	ADJ
ejpam-6458	118	7	for	for	ADP
ejpam-6458	118	8	certain	certain	ADJ
ejpam-6458	118	9	monomials	monomial	NOUN
ejpam-6458	118	10	.	.	PUNCT
ejpam-6458	119	1	for	for	ADP
ejpam-6458	119	2	example	example	NOUN
ejpam-6458	119	3	,	,	PUNCT
ejpam-6458	119	4	in	in	ADP
ejpam-6458	119	5	the	the	DET
ejpam-6458	119	6	algebra	algebra	NOUN
ejpam-6458	119	7	a2	a2	PROPN
ejpam-6458	119	8	(	(	PUNCT
ejpam-6458	119	9	see	see	VERB
ejpam-6458	119	10	section	section	NOUN
ejpam-6458	119	11	4.1	4.1	NUM
ejpam-6458	119	12	)	)	PUNCT
ejpam-6458	119	13	,	,	PUNCT
ejpam-6458	119	14	(	(	PUNCT
ejpam-6458	119	15	α1	α1	PROPN
ejpam-6458	119	16	,	,	PUNCT
ejpam-6458	119	17	.	.	PUNCT
ejpam-6458	119	18	.	.	PUNCT
ejpam-6458	120	1	.	.	PUNCT
ejpam-6458	121	1	,	,	PUNCT
ejpam-6458	121	2	α6	α6	NOUN
ejpam-6458	121	3	)	)	PUNCT
ejpam-6458	122	1	=	=	PUNCT
ejpam-6458	122	2	(	(	PUNCT
ejpam-6458	122	3	α1	α1	PROPN
ejpam-6458	122	4	,	,	PUNCT
ejpam-6458	122	5	α6	α6	NOUN
ejpam-6458	122	6	)	)	PUNCT
ejpam-6458	122	7	⊔	⊔	PROPN
ejpam-6458	122	8	(	(	PUNCT
ejpam-6458	122	9	α2	α2	ADJ
ejpam-6458	122	10	,	,	PUNCT
ejpam-6458	122	11	α5	α5	NOUN
ejpam-6458	122	12	)	)	PUNCT
ejpam-6458	123	1	⊔	⊔	PROPN
ejpam-6458	123	2	(	(	PUNCT
ejpam-6458	123	3	α3	α3	PROPN
ejpam-6458	123	4	,	,	PUNCT
ejpam-6458	123	5	α4	α4	NOUN
ejpam-6458	123	6	)	)	PUNCT
ejpam-6458	123	7	=	=	SYM
ejpam-6458	123	8	(	(	PUNCT
ejpam-6458	123	9	α1	α1	PROPN
ejpam-6458	123	10	,	,	PUNCT
ejpam-6458	123	11	α2	α2	ADJ
ejpam-6458	123	12	,	,	PUNCT
ejpam-6458	123	13	α4	α4	NOUN
ejpam-6458	123	14	)	)	PUNCT
ejpam-6458	123	15	⊔	⊔	PROPN
ejpam-6458	123	16	(	(	PUNCT
ejpam-6458	123	17	α3	α3	PROPN
ejpam-6458	123	18	,	,	PUNCT
ejpam-6458	123	19	α5	α5	NOUN
ejpam-6458	123	20	,	,	PUNCT
ejpam-6458	123	21	α6	α6	NOUN
ejpam-6458	123	22	)	)	PUNCT
ejpam-6458	123	23	.	.	PUNCT
ejpam-6458	124	1	denote	denote	VERB
ejpam-6458	124	2	by	by	ADP
ejpam-6458	124	3	b1(∆	b1(∆	PROPN
ejpam-6458	124	4	)	)	PUNCT
ejpam-6458	125	1	⊂	⊂	PROPN
ejpam-6458	126	1	b(∆	b(∆	NOUN
ejpam-6458	126	2	)	)	PUNCT
ejpam-6458	126	3	the	the	DET
ejpam-6458	126	4	set	set	NOUN
ejpam-6458	126	5	of	of	ADP
ejpam-6458	126	6	all	all	DET
ejpam-6458	126	7	zero	zero	NUM
ejpam-6458	126	8	-	-	PUNCT
ejpam-6458	126	9	weight	weight	NOUN
ejpam-6458	126	10	indecomposable	indecomposable	ADJ
ejpam-6458	126	11	lists	list	NOUN
ejpam-6458	126	12	.	.	PUNCT
ejpam-6458	127	1	define	define	VERB
ejpam-6458	127	2	the	the	DET
ejpam-6458	127	3	action	action	NOUN
ejpam-6458	127	4	of	of	ADP
ejpam-6458	127	5	the	the	DET
ejpam-6458	127	6	weyl	weyl	PROPN
ejpam-6458	127	7	group	group	NOUN
ejpam-6458	127	8	w	w	PROPN
ejpam-6458	127	9	on	on	ADP
ejpam-6458	127	10	the	the	DET
ejpam-6458	127	11	list	list	NOUN
ejpam-6458	127	12	of	of	ADP
ejpam-6458	127	13	roots	root	NOUN
ejpam-6458	127	14	a	a	DET
ejpam-6458	127	15	=	=	SYM
ejpam-6458	127	16	(	(	PUNCT
ejpam-6458	127	17	α1	α1	PROPN
ejpam-6458	127	18	,	,	PUNCT
ejpam-6458	127	19	α2	α2	ADJ
ejpam-6458	127	20	,	,	PUNCT
ejpam-6458	127	21	.	.	PUNCT
ejpam-6458	127	22	.	.	PUNCT
ejpam-6458	128	1	.	.	PUNCT
ejpam-6458	129	1	,	,	PUNCT
ejpam-6458	129	2	αn	αn	X
ejpam-6458	129	3	)	)	PUNCT
ejpam-6458	129	4	as	as	SCONJ
ejpam-6458	129	5	follows	follow	VERB
ejpam-6458	129	6	:	:	PUNCT
ejpam-6458	129	7	w(a	w(a	X
ejpam-6458	129	8	)	)	PUNCT
ejpam-6458	130	1	=	=	SYM
ejpam-6458	130	2	(	(	PUNCT
ejpam-6458	130	3	wα1	wα1	NOUN
ejpam-6458	130	4	,	,	PUNCT
ejpam-6458	130	5	wα2	wα2	NOUN
ejpam-6458	130	6	,	,	PUNCT
ejpam-6458	130	7	.	.	PUNCT
ejpam-6458	130	8	.	.	PUNCT
ejpam-6458	131	1	.	.	PUNCT
ejpam-6458	132	1	,	,	PUNCT
ejpam-6458	132	2	wαn	wαn	NOUN
ejpam-6458	132	3	)	)	PUNCT
ejpam-6458	132	4	,	,	PUNCT
ejpam-6458	132	5	with	with	ADP
ejpam-6458	132	6	∈w	∈w	NOUN
ejpam-6458	132	7	.	.	PUNCT
ejpam-6458	133	1	clearly	clearly	ADV
ejpam-6458	133	2	,	,	PUNCT
ejpam-6458	133	3	if	if	SCONJ
ejpam-6458	133	4	a	a	PRON
ejpam-6458	133	5	is	be	AUX
ejpam-6458	133	6	indecomposable	indecomposable	ADJ
ejpam-6458	133	7	,	,	PUNCT
ejpam-6458	133	8	then	then	ADV
ejpam-6458	133	9	w(a	w(a	PROPN
ejpam-6458	133	10	)	)	PUNCT
ejpam-6458	133	11	is	be	AUX
ejpam-6458	133	12	also	also	ADV
ejpam-6458	133	13	indecomposable	indecomposable	ADJ
ejpam-6458	133	14	.	.	PUNCT
ejpam-6458	134	1	moreover	moreover	ADV
ejpam-6458	134	2	,	,	PUNCT
ejpam-6458	134	3	if	if	SCONJ
ejpam-6458	134	4	a	a	PRON
ejpam-6458	134	5	has	have	VERB
ejpam-6458	134	6	a	a	DET
ejpam-6458	134	7	zero	zero	NUM
ejpam-6458	134	8	weight	weight	NOUN
ejpam-6458	134	9	,	,	PUNCT
ejpam-6458	134	10	then	then	ADV
ejpam-6458	134	11	w(a	w(a	PROPN
ejpam-6458	134	12	)	)	PUNCT
ejpam-6458	134	13	also	also	ADV
ejpam-6458	134	14	has	have	VERB
ejpam-6458	134	15	a	a	DET
ejpam-6458	134	16	zero	zero	NUM
ejpam-6458	134	17	weight	weight	NOUN
ejpam-6458	134	18	.	.	PUNCT
ejpam-6458	135	1	the	the	DET
ejpam-6458	135	2	simplest	simple	ADJ
ejpam-6458	135	3	examples	example	NOUN
ejpam-6458	135	4	of	of	ADP
ejpam-6458	135	5	indecomposable	indecomposable	ADJ
ejpam-6458	135	6	lists	list	NOUN
ejpam-6458	135	7	are	be	AUX
ejpam-6458	135	8	those	those	PRON
ejpam-6458	135	9	containing	contain	VERB
ejpam-6458	135	10	only	only	ADV
ejpam-6458	135	11	one	one	NUM
ejpam-6458	135	12	positive	positive	ADJ
ejpam-6458	135	13	or	or	CCONJ
ejpam-6458	135	14	only	only	ADV
ejpam-6458	135	15	one	one	NUM
ejpam-6458	135	16	negative	negative	ADJ
ejpam-6458	135	17	root	root	NOUN
ejpam-6458	135	18	.	.	PUNCT
ejpam-6458	136	1	define	define	VERB
ejpam-6458	136	2	the	the	DET
ejpam-6458	136	3	set	set	NOUN
ejpam-6458	136	4	of	of	ADP
ejpam-6458	136	5	primitive	primitive	ADJ
ejpam-6458	136	6	lists	list	NOUN
ejpam-6458	136	7	b2(∆	b2(∆	VERB
ejpam-6458	136	8	)	)	PUNCT
ejpam-6458	136	9	⊆	⊆	NUM
ejpam-6458	136	10	b1(∆	b1(∆	NOUN
ejpam-6458	136	11	)	)	PUNCT
ejpam-6458	136	12	as	as	SCONJ
ejpam-6458	136	13	follows	follow	VERB
ejpam-6458	136	14	:	:	PUNCT
ejpam-6458	136	15	r	r	NOUN
ejpam-6458	136	16	∈	∈	PROPN
ejpam-6458	136	17	b2(∆	b2(∆	PROPN
ejpam-6458	136	18	)	)	PUNCT
ejpam-6458	136	19	if	if	SCONJ
ejpam-6458	136	20	there	there	PRON
ejpam-6458	136	21	exists	exist	VERB
ejpam-6458	136	22	w	w	NOUN
ejpam-6458	136	23	∈w	∈w	NOUN
ejpam-6458	136	24	such	such	ADJ
ejpam-6458	136	25	that	that	SCONJ
ejpam-6458	136	26	the	the	DET
ejpam-6458	136	27	list	list	NOUN
ejpam-6458	136	28	w(r	w(r	PROPN
ejpam-6458	136	29	)	)	PUNCT
ejpam-6458	136	30	contains	contain	VERB
ejpam-6458	136	31	only	only	ADV
ejpam-6458	136	32	one	one	NUM
ejpam-6458	136	33	negative	negative	ADJ
ejpam-6458	136	34	or	or	CCONJ
ejpam-6458	136	35	only	only	ADV
ejpam-6458	136	36	one	one	NUM
ejpam-6458	136	37	positive	positive	ADJ
ejpam-6458	136	38	root	root	NOUN
ejpam-6458	136	39	.	.	PUNCT
ejpam-6458	137	1	let	let	VERB
ejpam-6458	137	2	mk	mk	PROPN
ejpam-6458	137	3	=	=	PRON
ejpam-6458	137	4	{	{	PUNCT
ejpam-6458	137	5	(	(	PUNCT
ejpam-6458	137	6	n1	n1	NOUN
ejpam-6458	137	7	,	,	PUNCT
ejpam-6458	137	8	n2	n2	NOUN
ejpam-6458	137	9	,	,	PUNCT
ejpam-6458	137	10	.	.	PUNCT
ejpam-6458	137	11	.	.	PUNCT
ejpam-6458	138	1	.	.	PUNCT
ejpam-6458	139	1	,	,	PUNCT
ejpam-6458	139	2	nk	nk	PROPN
ejpam-6458	139	3	)	)	PUNCT
ejpam-6458	139	4	|ni	|ni	PROPN
ejpam-6458	139	5	∈	∈	PROPN
ejpam-6458	139	6	n	n	CCONJ
ejpam-6458	139	7	}	}	PUNCT
ejpam-6458	139	8	be	be	AUX
ejpam-6458	139	9	the	the	DET
ejpam-6458	139	10	set	set	NOUN
ejpam-6458	139	11	of	of	ADP
ejpam-6458	139	12	vectors	vector	NOUN
ejpam-6458	139	13	with	with	ADP
ejpam-6458	139	14	nonnegative	nonnegative	ADJ
ejpam-6458	139	15	integer	integer	NOUN
ejpam-6458	139	16	coordinates	coordinate	NOUN
ejpam-6458	139	17	.	.	PUNCT
ejpam-6458	140	1	define	define	VERB
ejpam-6458	140	2	a	a	DET
ejpam-6458	140	3	partial	partial	ADJ
ejpam-6458	140	4	order	order	NOUN
ejpam-6458	140	5	on	on	ADP
ejpam-6458	140	6	the	the	DET
ejpam-6458	140	7	set	set	VERB
ejpam-6458	140	8	mk	mk	NOUN
ejpam-6458	140	9	as	as	SCONJ
ejpam-6458	140	10	follows	follow	VERB
ejpam-6458	140	11	:	:	PUNCT
ejpam-6458	140	12	(	(	PUNCT
ejpam-6458	140	13	n1	n1	NOUN
ejpam-6458	140	14	,	,	PUNCT
ejpam-6458	140	15	n2	n2	NOUN
ejpam-6458	140	16	,	,	PUNCT
ejpam-6458	140	17	.	.	PUNCT
ejpam-6458	140	18	.	.	PUNCT
ejpam-6458	141	1	.	.	PUNCT
ejpam-6458	142	1	,	,	PUNCT
ejpam-6458	142	2	nk	nk	PROPN
ejpam-6458	142	3	)	)	PUNCT
ejpam-6458	142	4	≤	≤	NOUN
ejpam-6458	142	5	(	(	PUNCT
ejpam-6458	142	6	m1,m2	m1,m2	PROPN
ejpam-6458	142	7	,	,	PUNCT
ejpam-6458	142	8	.	.	PUNCT
ejpam-6458	142	9	.	.	PUNCT
ejpam-6458	143	1	.	.	PUNCT
ejpam-6458	144	1	,	,	PUNCT
ejpam-6458	144	2	mk	mk	PROPN
ejpam-6458	144	3	)	)	PUNCT
ejpam-6458	144	4	if	if	SCONJ
ejpam-6458	144	5	ni	ni	PROPN
ejpam-6458	144	6	≤	≤	PROPN
ejpam-6458	144	7	mi	mi	PROPN
ejpam-6458	144	8	,	,	PUNCT
ejpam-6458	144	9	for	for	ADP
ejpam-6458	144	10	all	all	DET
ejpam-6458	144	11	i	i	PRON
ejpam-6458	144	12	=	=	NOUN
ejpam-6458	144	13	1	1	NUM
ejpam-6458	144	14	,	,	PUNCT
ejpam-6458	144	15	.	.	PUNCT
ejpam-6458	144	16	.	.	PUNCT
ejpam-6458	145	1	.	.	PUNCT
ejpam-6458	146	1	,	,	PUNCT
ejpam-6458	146	2	k.	k.	PROPN
ejpam-6458	146	3	we	we	PRON
ejpam-6458	146	4	will	will	AUX
ejpam-6458	146	5	be	be	AUX
ejpam-6458	146	6	using	use	VERB
ejpam-6458	146	7	the	the	DET
ejpam-6458	146	8	following	following	ADJ
ejpam-6458	146	9	result	result	NOUN
ejpam-6458	146	10	[	[	X
ejpam-6458	146	11	16	16	NUM
ejpam-6458	146	12	,	,	PUNCT
ejpam-6458	146	13	lemma	lemma	PROPN
ejpam-6458	146	14	2.6.2	2.6.2	PROPN
ejpam-6458	146	15	]	]	PUNCT
ejpam-6458	146	16	.	.	PUNCT
ejpam-6458	147	1	lemma	lemma	PROPN
ejpam-6458	147	2	2.2	2.2	NUM
ejpam-6458	147	3	.	.	PUNCT
ejpam-6458	148	1	if	if	SCONJ
ejpam-6458	148	2	sk	sk	PROPN
ejpam-6458	148	3	⊂	⊂	PROPN
ejpam-6458	148	4	mk	mk	PROPN
ejpam-6458	148	5	is	be	AUX
ejpam-6458	148	6	any	any	DET
ejpam-6458	148	7	infinite	infinite	ADJ
ejpam-6458	148	8	subset	subset	NOUN
ejpam-6458	148	9	,	,	PUNCT
ejpam-6458	148	10	then	then	ADV
ejpam-6458	148	11	there	there	PRON
ejpam-6458	148	12	exist	exist	VERB
ejpam-6458	148	13	two	two	NUM
ejpam-6458	148	14	elements	element	NOUN
ejpam-6458	148	15	r1	r1	NOUN
ejpam-6458	148	16	,	,	PUNCT
ejpam-6458	148	17	r2	r2	PROPN
ejpam-6458	148	18	∈	∈	PROPN
ejpam-6458	148	19	sk	sk	VERB
ejpam-6458	148	20	such	such	ADJ
ejpam-6458	148	21	that	that	SCONJ
ejpam-6458	148	22	r1	r1	NOUN
ejpam-6458	148	23	≤	≤	ADJ
ejpam-6458	148	24	r2	r2	NOUN
ejpam-6458	148	25	.	.	PUNCT
ejpam-6458	149	1	we	we	PRON
ejpam-6458	149	2	have	have	VERB
ejpam-6458	149	3	the	the	DET
ejpam-6458	149	4	following	follow	VERB
ejpam-6458	149	5	properties	property	NOUN
ejpam-6458	149	6	of	of	ADP
ejpam-6458	149	7	indecomposable	indecomposable	ADJ
ejpam-6458	149	8	lists	list	NOUN
ejpam-6458	149	9	of	of	ADP
ejpam-6458	149	10	roots	root	NOUN
ejpam-6458	149	11	.	.	PUNCT
ejpam-6458	150	1	lemma	lemma	PROPN
ejpam-6458	150	2	2.3	2.3	NUM
ejpam-6458	150	3	.	.	PUNCT
ejpam-6458	151	1	let	let	VERB
ejpam-6458	151	2	g	g	PRON
ejpam-6458	151	3	be	be	AUX
ejpam-6458	151	4	a	a	DET
ejpam-6458	151	5	simple	simple	ADJ
ejpam-6458	151	6	finite	finite	ADJ
ejpam-6458	151	7	-	-	ADJ
ejpam-6458	151	8	dimensional	dimensional	ADJ
ejpam-6458	151	9	lie	lie	NOUN
ejpam-6458	151	10	algebra	algebra	NOUN
ejpam-6458	151	11	with	with	ADP
ejpam-6458	151	12	root	root	NOUN
ejpam-6458	151	13	system	system	NOUN
ejpam-6458	152	1	∆.	∆.	X
ejpam-6458	152	2	then	then	ADV
ejpam-6458	152	3	1	1	X
ejpam-6458	152	4	.	.	PUNCT
ejpam-6458	153	1	the	the	DET
ejpam-6458	153	2	set	set	NOUN
ejpam-6458	153	3	of	of	ADP
ejpam-6458	153	4	indecomposable	indecomposable	ADJ
ejpam-6458	153	5	lists	list	NOUN
ejpam-6458	153	6	b1(∆	b1(∆	VERB
ejpam-6458	153	7	)	)	PUNCT
ejpam-6458	153	8	is	be	AUX
ejpam-6458	153	9	finite	finite	ADJ
ejpam-6458	153	10	.	.	PUNCT
ejpam-6458	154	1	2	2	X
ejpam-6458	154	2	.	.	X
ejpam-6458	155	1	if	if	SCONJ
ejpam-6458	155	2	g	g	PROPN
ejpam-6458	155	3	∈	∈	PROPN
ejpam-6458	155	4	{	{	PUNCT
ejpam-6458	155	5	a2	a2	PROPN
ejpam-6458	155	6	,	,	PUNCT
ejpam-6458	155	7	c2	c2	PROPN
ejpam-6458	155	8	,	,	PUNCT
ejpam-6458	155	9	g2	g2	PROPN
ejpam-6458	155	10	}	}	PUNCT
ejpam-6458	155	11	,	,	PUNCT
ejpam-6458	155	12	then	then	ADV
ejpam-6458	155	13	all	all	DET
ejpam-6458	155	14	indecomposable	indecomposable	ADJ
ejpam-6458	155	15	lists	list	NOUN
ejpam-6458	155	16	are	be	AUX
ejpam-6458	155	17	primitive	primitive	ADJ
ejpam-6458	155	18	and	and	CCONJ
ejpam-6458	155	19	hence	hence	ADV
ejpam-6458	155	20	b1(∆	b1(∆	VERB
ejpam-6458	155	21	)	)	PUNCT
ejpam-6458	155	22	=	=	SYM
ejpam-6458	155	23	b2(∆	b2(∆	PROPN
ejpam-6458	155	24	)	)	PUNCT
ejpam-6458	155	25	.	.	PUNCT
ejpam-6458	156	1	proof	proof	NOUN
ejpam-6458	156	2	.	.	PUNCT
ejpam-6458	157	1	define	define	VERB
ejpam-6458	157	2	the	the	DET
ejpam-6458	157	3	function	function	NOUN
ejpam-6458	157	4	σ	σ	NOUN
ejpam-6458	157	5	on	on	ADP
ejpam-6458	157	6	the	the	DET
ejpam-6458	157	7	setb(∆	setb(∆	NOUN
ejpam-6458	157	8	)	)	PUNCT
ejpam-6458	157	9	as	as	SCONJ
ejpam-6458	157	10	follows	follow	VERB
ejpam-6458	157	11	:	:	PUNCT
ejpam-6458	157	12	σ(α1	σ(α1	NOUN
ejpam-6458	157	13	,	,	PUNCT
ejpam-6458	157	14	α2	α2	ADJ
ejpam-6458	157	15	,	,	PUNCT
ejpam-6458	157	16	.	.	PUNCT
ejpam-6458	157	17	.	.	PUNCT
ejpam-6458	158	1	.	.	PUNCT
ejpam-6458	159	1	,	,	PUNCT
ejpam-6458	159	2	αm	αm	X
ejpam-6458	159	3	)	)	PUNCT
ejpam-6458	159	4	=	=	SYM
ejpam-6458	159	5	(	(	PUNCT
ejpam-6458	159	6	n1	n1	NOUN
ejpam-6458	159	7	,	,	PUNCT
ejpam-6458	159	8	n2	n2	NOUN
ejpam-6458	159	9	,	,	PUNCT
ejpam-6458	159	10	.	.	PUNCT
ejpam-6458	159	11	.	.	PUNCT
ejpam-6458	159	12	.	.	PUNCT
ejpam-6458	160	1	,	,	PUNCT
ejpam-6458	160	2	n|∆|	n|∆|	ADP
ejpam-6458	160	3	)	)	PUNCT
ejpam-6458	160	4	,	,	PUNCT
ejpam-6458	160	5	where	where	SCONJ
ejpam-6458	160	6	ni	ni	PROPN
ejpam-6458	160	7	is	be	AUX
ejpam-6458	160	8	the	the	DET
ejpam-6458	160	9	number	number	NOUN
ejpam-6458	160	10	of	of	ADP
ejpam-6458	160	11	occurrences	occurrence	NOUN
ejpam-6458	160	12	of	of	ADP
ejpam-6458	160	13	the	the	DET
ejpam-6458	160	14	i	i	PROPN
ejpam-6458	160	15	-	-	PUNCT
ejpam-6458	160	16	th	th	X
ejpam-6458	160	17	root	root	NOUN
ejpam-6458	160	18	of	of	ADP
ejpam-6458	160	19	∆	∆	PROPN
ejpam-6458	160	20	(	(	PUNCT
ejpam-6458	160	21	with	with	ADP
ejpam-6458	160	22	respect	respect	NOUN
ejpam-6458	160	23	to	to	ADP
ejpam-6458	160	24	the	the	DET
ejpam-6458	160	25	ordering	ordering	NOUN
ejpam-6458	160	26	in	in	ADP
ejpam-6458	160	27	(	(	PUNCT
ejpam-6458	160	28	2.1	2.1	NUM
ejpam-6458	160	29	)	)	PUNCT
ejpam-6458	160	30	in	in	ADP
ejpam-6458	160	31	the	the	DET
ejpam-6458	160	32	list	list	NOUN
ejpam-6458	160	33	(	(	PUNCT
ejpam-6458	160	34	α1	α1	PROPN
ejpam-6458	160	35	,	,	PUNCT
ejpam-6458	160	36	α2	α2	ADJ
ejpam-6458	160	37	,	,	PUNCT
ejpam-6458	160	38	.	.	PUNCT
ejpam-6458	160	39	.	.	PUNCT
ejpam-6458	161	1	.	.	PUNCT
ejpam-6458	162	1	,	,	PUNCT
ejpam-6458	162	2	αm	αm	X
ejpam-6458	162	3	)	)	PUNCT
ejpam-6458	162	4	.	.	PUNCT
ejpam-6458	163	1	it	it	PRON
ejpam-6458	163	2	is	be	AUX
ejpam-6458	163	3	clear	clear	ADJ
ejpam-6458	163	4	that	that	SCONJ
ejpam-6458	163	5	a	a	DET
ejpam-6458	163	6	list	list	NOUN
ejpam-6458	163	7	r1	r1	NOUN
ejpam-6458	163	8	is	be	AUX
ejpam-6458	163	9	a	a	DET
ejpam-6458	163	10	sublist	sublist	NOUN
ejpam-6458	163	11	of	of	ADP
ejpam-6458	163	12	a	a	DET
ejpam-6458	163	13	list	list	NOUN
ejpam-6458	163	14	r2	r2	NOUN
ejpam-6458	163	15	if	if	SCONJ
ejpam-6458	163	16	and	and	CCONJ
ejpam-6458	163	17	only	only	ADV
ejpam-6458	163	18	if	if	SCONJ
ejpam-6458	163	19	σ(r1	σ(r1	NOUN
ejpam-6458	163	20	)	)	PUNCT
ejpam-6458	163	21	≤	≤	NUM
ejpam-6458	163	22	σ(r2	σ(r2	NOUN
ejpam-6458	163	23	)	)	PUNCT
ejpam-6458	163	24	.	.	PUNCT
ejpam-6458	164	1	now	now	ADV
ejpam-6458	164	2	,	,	PUNCT
ejpam-6458	164	3	the	the	DET
ejpam-6458	164	4	proof	proof	NOUN
ejpam-6458	164	5	of	of	ADP
ejpam-6458	164	6	the	the	DET
ejpam-6458	164	7	first	first	ADJ
ejpam-6458	164	8	statement	statement	NOUN
ejpam-6458	164	9	follows	follow	VERB
ejpam-6458	164	10	from	from	ADP
ejpam-6458	164	11	the	the	DET
ejpam-6458	164	12	previous	previous	ADJ
ejpam-6458	164	13	lemma	lemma	PROPN
ejpam-6458	164	14	.	.	PUNCT
ejpam-6458	165	1	the	the	DET
ejpam-6458	165	2	second	second	ADJ
ejpam-6458	165	3	statement	statement	NOUN
ejpam-6458	165	4	for	for	ADP
ejpam-6458	165	5	the	the	DET
ejpam-6458	165	6	case	case	NOUN
ejpam-6458	165	7	a2	a2	PROPN
ejpam-6458	165	8	is	be	AUX
ejpam-6458	165	9	obvious	obvious	ADJ
ejpam-6458	165	10	.	.	PUNCT
ejpam-6458	166	1	we	we	PRON
ejpam-6458	166	2	will	will	AUX
ejpam-6458	166	3	now	now	ADV
ejpam-6458	166	4	prove	prove	VERB
ejpam-6458	166	5	the	the	DET
ejpam-6458	166	6	second	second	ADJ
ejpam-6458	166	7	statement	statement	NOUN
ejpam-6458	166	8	for	for	ADP
ejpam-6458	166	9	the	the	DET
ejpam-6458	166	10	case	case	NOUN
ejpam-6458	166	11	c2	c2	PROPN
ejpam-6458	166	12	.	.	PUNCT
ejpam-6458	167	1	let	let	VERB
ejpam-6458	167	2	π	π	NOUN
ejpam-6458	167	3	=	=	PRON
ejpam-6458	167	4	{	{	PUNCT
ejpam-6458	167	5	β1	β1	PROPN
ejpam-6458	167	6	,	,	PUNCT
ejpam-6458	167	7	β2	β2	PROPN
ejpam-6458	167	8	}	}	PUNCT
ejpam-6458	167	9	be	be	AUX
ejpam-6458	167	10	a	a	DET
ejpam-6458	167	11	basis	basis	NOUN
ejpam-6458	167	12	of	of	ADP
ejpam-6458	167	13	the	the	DET
ejpam-6458	167	14	root	root	NOUN
ejpam-6458	167	15	system	system	NOUN
ejpam-6458	167	16	.	.	PUNCT
ejpam-6458	168	1	for	for	ADP
ejpam-6458	168	2	convenience	convenience	NOUN
ejpam-6458	168	3	,	,	PUNCT
ejpam-6458	168	4	m.	m.	NOUN
ejpam-6458	168	5	andelić	andelić	PROPN
ejpam-6458	168	6	et	et	PROPN
ejpam-6458	168	7	al	al	PROPN
ejpam-6458	168	8	.	.	PUNCT
ejpam-6458	168	9	/	/	SYM
ejpam-6458	168	10	eur	eur	PROPN
ejpam-6458	168	11	.	.	PUNCT
ejpam-6458	169	1	j.	j.	PROPN
ejpam-6458	169	2	pure	pure	PROPN
ejpam-6458	169	3	appl	appl	PROPN
ejpam-6458	169	4	.	.	PROPN
ejpam-6458	169	5	math	math	PROPN
ejpam-6458	169	6	,	,	PUNCT
ejpam-6458	169	7	18	18	NUM
ejpam-6458	169	8	(	(	PUNCT
ejpam-6458	169	9	3	3	NUM
ejpam-6458	169	10	)	)	PUNCT
ejpam-6458	169	11	(	(	PUNCT
ejpam-6458	169	12	2025	2025	NUM
ejpam-6458	169	13	)	)	PUNCT
ejpam-6458	169	14	,	,	PUNCT
ejpam-6458	169	15	6458	6458	NUM
ejpam-6458	169	16	5	5	NUM
ejpam-6458	169	17	of	of	ADP
ejpam-6458	169	18	21	21	NUM
ejpam-6458	169	19	we	we	PRON
ejpam-6458	169	20	will	will	AUX
ejpam-6458	169	21	represent	represent	VERB
ejpam-6458	169	22	the	the	DET
ejpam-6458	169	23	roots	root	NOUN
ejpam-6458	169	24	of	of	ADP
ejpam-6458	169	25	∆	∆	PROPN
ejpam-6458	169	26	as	as	ADP
ejpam-6458	169	27	vectors	vector	NOUN
ejpam-6458	169	28	in	in	ADP
ejpam-6458	169	29	this	this	DET
ejpam-6458	169	30	basis	basis	NOUN
ejpam-6458	169	31	:	:	PUNCT
ejpam-6458	169	32	(	(	PUNCT
ejpam-6458	169	33	i	i	PRON
ejpam-6458	169	34	,	,	PUNCT
ejpam-6458	169	35	j	j	PROPN
ejpam-6458	169	36	)	)	PUNCT
ejpam-6458	169	37	=	=	PUNCT
ejpam-6458	170	1	iβ1	iβ1	NOUN
ejpam-6458	170	2	+	+	CCONJ
ejpam-6458	170	3	jβ2	jβ2	ADJ
ejpam-6458	170	4	.	.	PUNCT
ejpam-6458	171	1	then	then	ADV
ejpam-6458	171	2	∆	∆	PROPN
ejpam-6458	171	3	=	=	PRON
ejpam-6458	171	4	{	{	PUNCT
ejpam-6458	171	5	(	(	PUNCT
ejpam-6458	171	6	1	1	NUM
ejpam-6458	171	7	,	,	PUNCT
ejpam-6458	171	8	0	0	NUM
ejpam-6458	171	9	)	)	PUNCT
ejpam-6458	171	10	,	,	PUNCT
ejpam-6458	171	11	(	(	PUNCT
ejpam-6458	171	12	0	0	NUM
ejpam-6458	171	13	,	,	PUNCT
ejpam-6458	171	14	1	1	NUM
ejpam-6458	171	15	)	)	PUNCT
ejpam-6458	171	16	,	,	PUNCT
ejpam-6458	171	17	(	(	PUNCT
ejpam-6458	171	18	1	1	NUM
ejpam-6458	171	19	,	,	PUNCT
ejpam-6458	171	20	1	1	NUM
ejpam-6458	171	21	)	)	PUNCT
ejpam-6458	171	22	,	,	PUNCT
ejpam-6458	171	23	(	(	PUNCT
ejpam-6458	171	24	2	2	NUM
ejpam-6458	171	25	,	,	PUNCT
ejpam-6458	171	26	1	1	NUM
ejpam-6458	171	27	)	)	PUNCT
ejpam-6458	171	28	,	,	PUNCT
ejpam-6458	171	29	(	(	PUNCT
ejpam-6458	171	30	−1	−1	NOUN
ejpam-6458	171	31	,	,	PUNCT
ejpam-6458	171	32	0	0	NUM
ejpam-6458	171	33	)	)	PUNCT
ejpam-6458	171	34	,	,	PUNCT
ejpam-6458	171	35	(	(	PUNCT
ejpam-6458	171	36	0,−1	0,−1	NOUN
ejpam-6458	171	37	)	)	PUNCT
ejpam-6458	171	38	,	,	PUNCT
ejpam-6458	171	39	(	(	PUNCT
ejpam-6458	171	40	−1,−1	−1,−1	NOUN
ejpam-6458	171	41	)	)	PUNCT
ejpam-6458	171	42	,	,	PUNCT
ejpam-6458	171	43	(	(	PUNCT
ejpam-6458	171	44	−2,−1	−2,−1	ADV
ejpam-6458	171	45	)	)	PUNCT
ejpam-6458	171	46	}	}	PUNCT
ejpam-6458	171	47	.	.	PUNCT
ejpam-6458	172	1	let	let	VERB
ejpam-6458	172	2	v	v	NOUN
ejpam-6458	172	3	=	=	SYM
ejpam-6458	172	4	(	(	PUNCT
ejpam-6458	172	5	i	i	PROPN
ejpam-6458	172	6	,	,	PUNCT
ejpam-6458	172	7	j	j	PROPN
ejpam-6458	172	8	)	)	PUNCT
ejpam-6458	172	9	∈	∈	PROPN
ejpam-6458	172	10	∆	∆	PROPN
ejpam-6458	172	11	be	be	VERB
ejpam-6458	172	12	any	any	DET
ejpam-6458	172	13	root	root	NOUN
ejpam-6458	172	14	.	.	PUNCT
ejpam-6458	173	1	the	the	DET
ejpam-6458	173	2	action	action	NOUN
ejpam-6458	173	3	of	of	ADP
ejpam-6458	173	4	the	the	DET
ejpam-6458	173	5	weyl	weyl	VERB
ejpam-6458	173	6	group	group	NOUN
ejpam-6458	173	7	is	be	AUX
ejpam-6458	173	8	given	give	VERB
ejpam-6458	173	9	by	by	ADP
ejpam-6458	173	10	w1(v	w1(v	PROPN
ejpam-6458	173	11	)	)	PUNCT
ejpam-6458	173	12	=	=	PRON
ejpam-6458	174	1	(	(	PUNCT
ejpam-6458	174	2	2j	2j	NUM
ejpam-6458	174	3	−	−	PROPN
ejpam-6458	175	1	i	i	PRON
ejpam-6458	175	2	,	,	PUNCT
ejpam-6458	175	3	j	j	PROPN
ejpam-6458	175	4	)	)	PUNCT
ejpam-6458	175	5	and	and	CCONJ
ejpam-6458	175	6	w2(v	w2(v	NUM
ejpam-6458	175	7	)	)	PUNCT
ejpam-6458	175	8	=	=	PUNCT
ejpam-6458	175	9	(	(	PUNCT
ejpam-6458	175	10	i	i	PROPN
ejpam-6458	175	11	,	,	PUNCT
ejpam-6458	175	12	i−	i−	PROPN
ejpam-6458	175	13	j	j	PROPN
ejpam-6458	175	14	)	)	PUNCT
ejpam-6458	175	15	,	,	PUNCT
ejpam-6458	175	16	where	where	SCONJ
ejpam-6458	175	17	w1	w1	NOUN
ejpam-6458	175	18	and	and	CCONJ
ejpam-6458	175	19	w2	w2	NOUN
ejpam-6458	175	20	are	be	AUX
ejpam-6458	175	21	simple	simple	ADJ
ejpam-6458	175	22	reflections	reflection	NOUN
ejpam-6458	175	23	.	.	PUNCT
ejpam-6458	176	1	we	we	PRON
ejpam-6458	176	2	will	will	AUX
ejpam-6458	176	3	prove	prove	VERB
ejpam-6458	176	4	that	that	SCONJ
ejpam-6458	176	5	non	non	ADJ
ejpam-6458	176	6	-	-	ADJ
ejpam-6458	176	7	primitive	primitive	ADJ
ejpam-6458	176	8	indecomposable	indecomposable	ADJ
ejpam-6458	176	9	lists	list	NOUN
ejpam-6458	176	10	do	do	AUX
ejpam-6458	176	11	not	not	PART
ejpam-6458	176	12	exist	exist	VERB
ejpam-6458	176	13	for	for	ADP
ejpam-6458	176	14	c2	c2	PROPN
ejpam-6458	176	15	.	.	PUNCT
ejpam-6458	177	1	by	by	ADP
ejpam-6458	177	2	the	the	DET
ejpam-6458	177	3	definition	definition	NOUN
ejpam-6458	177	4	of	of	ADP
ejpam-6458	177	5	a	a	DET
ejpam-6458	177	6	primitive	primitive	ADJ
ejpam-6458	177	7	list	list	NOUN
ejpam-6458	177	8	,	,	PUNCT
ejpam-6458	177	9	any	any	DET
ejpam-6458	177	10	list	list	NOUN
ejpam-6458	177	11	consisting	consist	VERB
ejpam-6458	177	12	of	of	ADP
ejpam-6458	177	13	two	two	NUM
ejpam-6458	177	14	or	or	CCONJ
ejpam-6458	177	15	three	three	NUM
ejpam-6458	177	16	roots	root	NOUN
ejpam-6458	177	17	is	be	AUX
ejpam-6458	177	18	primitive	primitive	ADJ
ejpam-6458	177	19	.	.	PUNCT
ejpam-6458	178	1	suppose	suppose	VERB
ejpam-6458	178	2	there	there	PRON
ejpam-6458	178	3	exists	exist	VERB
ejpam-6458	178	4	a	a	DET
ejpam-6458	178	5	non	non	ADJ
ejpam-6458	178	6	-	-	ADJ
ejpam-6458	178	7	primitive	primitive	ADJ
ejpam-6458	178	8	indecomposable	indecomposable	ADJ
ejpam-6458	178	9	list	list	NOUN
ejpam-6458	178	10	r	r	NOUN
ejpam-6458	178	11	with	with	ADP
ejpam-6458	178	12	more	more	ADJ
ejpam-6458	178	13	than	than	ADP
ejpam-6458	178	14	three	three	NUM
ejpam-6458	178	15	roots	root	NOUN
ejpam-6458	178	16	.	.	PUNCT
ejpam-6458	179	1	first	first	ADV
ejpam-6458	179	2	,	,	PUNCT
ejpam-6458	179	3	observe	observe	VERB
ejpam-6458	179	4	that	that	SCONJ
ejpam-6458	179	5	if	if	SCONJ
ejpam-6458	179	6	(	(	PUNCT
ejpam-6458	179	7	2	2	NUM
ejpam-6458	179	8	,	,	PUNCT
ejpam-6458	179	9	1	1	NUM
ejpam-6458	179	10	)	)	PUNCT
ejpam-6458	179	11	,	,	PUNCT
ejpam-6458	179	12	(	(	PUNCT
ejpam-6458	179	13	−2,−1	−2,−1	ADV
ejpam-6458	179	14	)	)	PUNCT
ejpam-6458	179	15	/∈	/∈	PUNCT
ejpam-6458	180	1	r	r	NOUN
ejpam-6458	180	2	,	,	PUNCT
ejpam-6458	180	3	then	then	ADV
ejpam-6458	180	4	r	r	NOUN
ejpam-6458	180	5	can	can	AUX
ejpam-6458	180	6	not	not	PART
ejpam-6458	180	7	contain	contain	VERB
ejpam-6458	180	8	more	more	ADJ
ejpam-6458	180	9	than	than	ADP
ejpam-6458	180	10	three	three	NUM
ejpam-6458	180	11	roots	root	NOUN
ejpam-6458	180	12	.	.	PUNCT
ejpam-6458	181	1	consider	consider	VERB
ejpam-6458	181	2	the	the	DET
ejpam-6458	181	3	case	case	NOUN
ejpam-6458	181	4	(	(	PUNCT
ejpam-6458	181	5	2	2	NUM
ejpam-6458	181	6	,	,	PUNCT
ejpam-6458	181	7	1	1	NUM
ejpam-6458	181	8	)	)	PUNCT
ejpam-6458	181	9	∈	∈	PROPN
ejpam-6458	181	10	r.	r.	PROPN
ejpam-6458	181	11	(	(	PUNCT
ejpam-6458	181	12	the	the	DET
ejpam-6458	181	13	case	case	NOUN
ejpam-6458	181	14	(	(	PUNCT
ejpam-6458	181	15	−2,−1	−2,−1	ADJ
ejpam-6458	181	16	)	)	PUNCT
ejpam-6458	181	17	∈	∈	NOUN
ejpam-6458	181	18	r	r	NOUN
ejpam-6458	181	19	is	be	AUX
ejpam-6458	181	20	miror	miror	NOUN
ejpam-6458	181	21	of	of	ADP
ejpam-6458	181	22	first	first	ADJ
ejpam-6458	181	23	case	case	NOUN
ejpam-6458	181	24	.	.	PUNCT
ejpam-6458	181	25	)	)	PUNCT
ejpam-6458	182	1	then	then	ADV
ejpam-6458	182	2	necessarily	necessarily	ADV
ejpam-6458	182	3	(	(	PUNCT
ejpam-6458	182	4	−2,−1	−2,−1	ADJ
ejpam-6458	182	5	)	)	PUNCT
ejpam-6458	182	6	/∈	/∈	PUNCT
ejpam-6458	182	7	r.	r.	PROPN
ejpam-6458	182	8	consider	consider	VERB
ejpam-6458	182	9	the	the	DET
ejpam-6458	182	10	list	list	NOUN
ejpam-6458	182	11	w1(r	w1(r	PROPN
ejpam-6458	182	12	)	)	PUNCT
ejpam-6458	182	13	.	.	PUNCT
ejpam-6458	183	1	then	then	ADV
ejpam-6458	183	2	w1(2	w1(2	PROPN
ejpam-6458	183	3	,	,	PUNCT
ejpam-6458	183	4	1	1	NUM
ejpam-6458	183	5	)	)	PUNCT
ejpam-6458	183	6	=	=	SYM
ejpam-6458	183	7	(	(	PUNCT
ejpam-6458	183	8	0	0	NUM
ejpam-6458	183	9	,	,	PUNCT
ejpam-6458	183	10	1	1	X
ejpam-6458	183	11	)	)	PUNCT
ejpam-6458	183	12	∈	∈	PROPN
ejpam-6458	183	13	w1(r	w1(r	PROPN
ejpam-6458	183	14	)	)	PUNCT
ejpam-6458	183	15	.	.	PUNCT
ejpam-6458	184	1	first	first	ADV
ejpam-6458	184	2	,	,	PUNCT
ejpam-6458	184	3	suppose	suppose	VERB
ejpam-6458	184	4	(	(	PUNCT
ejpam-6458	184	5	2	2	NUM
ejpam-6458	184	6	,	,	PUNCT
ejpam-6458	184	7	1	1	NUM
ejpam-6458	184	8	)	)	PUNCT
ejpam-6458	184	9	,	,	PUNCT
ejpam-6458	184	10	(	(	PUNCT
ejpam-6458	184	11	−2,−1	−2,−1	ADV
ejpam-6458	184	12	)	)	PUNCT
ejpam-6458	184	13	/∈	/∈	PUNCT
ejpam-6458	185	1	w1(r	w1(r	PROPN
ejpam-6458	185	2	)	)	PUNCT
ejpam-6458	185	3	.	.	PUNCT
ejpam-6458	186	1	in	in	ADP
ejpam-6458	186	2	this	this	DET
ejpam-6458	186	3	case	case	NOUN
ejpam-6458	186	4	,	,	PUNCT
ejpam-6458	186	5	w1(r	w1(r	PROPN
ejpam-6458	186	6	)	)	PUNCT
ejpam-6458	186	7	is	be	AUX
ejpam-6458	186	8	primitive	primitive	ADJ
ejpam-6458	186	9	,	,	PUNCT
ejpam-6458	186	10	and	and	CCONJ
ejpam-6458	186	11	consequently	consequently	ADV
ejpam-6458	186	12	,	,	PUNCT
ejpam-6458	186	13	so	so	ADV
ejpam-6458	186	14	is	be	AUX
ejpam-6458	186	15	r.	r.	PROPN
ejpam-6458	186	16	second	second	ADJ
ejpam-6458	186	17	,	,	PUNCT
ejpam-6458	186	18	if	if	SCONJ
ejpam-6458	186	19	(	(	PUNCT
ejpam-6458	186	20	2	2	NUM
ejpam-6458	186	21	,	,	PUNCT
ejpam-6458	186	22	1	1	NUM
ejpam-6458	186	23	)	)	PUNCT
ejpam-6458	186	24	∈	∈	PROPN
ejpam-6458	186	25	w1(r	w1(r	PROPN
ejpam-6458	186	26	)	)	PUNCT
ejpam-6458	186	27	,	,	PUNCT
ejpam-6458	186	28	then	then	ADV
ejpam-6458	186	29	both	both	PRON
ejpam-6458	186	30	(	(	PUNCT
ejpam-6458	186	31	2	2	NUM
ejpam-6458	186	32	,	,	PUNCT
ejpam-6458	186	33	1	1	NUM
ejpam-6458	186	34	)	)	PUNCT
ejpam-6458	186	35	and	and	CCONJ
ejpam-6458	186	36	(	(	PUNCT
ejpam-6458	186	37	0	0	NUM
ejpam-6458	186	38	,	,	PUNCT
ejpam-6458	186	39	1	1	NUM
ejpam-6458	186	40	)	)	PUNCT
ejpam-6458	186	41	belong	belong	VERB
ejpam-6458	186	42	to	to	ADP
ejpam-6458	186	43	w1(r	w1(r	PROPN
ejpam-6458	186	44	)	)	PUNCT
ejpam-6458	186	45	.	.	PUNCT
ejpam-6458	187	1	finally	finally	ADV
ejpam-6458	187	2	,	,	PUNCT
ejpam-6458	187	3	if	if	SCONJ
ejpam-6458	187	4	(	(	PUNCT
ejpam-6458	187	5	−2,−1	−2,−1	ADJ
ejpam-6458	187	6	)	)	PUNCT
ejpam-6458	187	7	∈	∈	PROPN
ejpam-6458	187	8	w1(r	w1(r	PROPN
ejpam-6458	187	9	)	)	PUNCT
ejpam-6458	187	10	,	,	PUNCT
ejpam-6458	187	11	then	then	ADV
ejpam-6458	187	12	we	we	PRON
ejpam-6458	187	13	obtain	obtain	VERB
ejpam-6458	187	14	(	(	PUNCT
ejpam-6458	187	15	2	2	NUM
ejpam-6458	187	16	,	,	PUNCT
ejpam-6458	187	17	1	1	NUM
ejpam-6458	187	18	)	)	PUNCT
ejpam-6458	187	19	,	,	PUNCT
ejpam-6458	187	20	(	(	PUNCT
ejpam-6458	187	21	0	0	NUM
ejpam-6458	187	22	,	,	PUNCT
ejpam-6458	187	23	1	1	X
ejpam-6458	187	24	)	)	PUNCT
ejpam-6458	187	25	∈	∈	PROPN
ejpam-6458	187	26	w1w2(r	w1w2(r	PROPN
ejpam-6458	187	27	)	)	PUNCT
ejpam-6458	187	28	.	.	PUNCT
ejpam-6458	188	1	now	now	ADV
ejpam-6458	188	2	,	,	PUNCT
ejpam-6458	188	3	suppose	suppose	VERB
ejpam-6458	188	4	there	there	PRON
ejpam-6458	188	5	exists	exist	VERB
ejpam-6458	188	6	w	w	NOUN
ejpam-6458	188	7	∈w	∈w	NOUN
ejpam-6458	188	8	such	such	ADJ
ejpam-6458	188	9	that	that	SCONJ
ejpam-6458	188	10	(	(	PUNCT
ejpam-6458	188	11	2	2	NUM
ejpam-6458	188	12	,	,	PUNCT
ejpam-6458	188	13	1	1	NUM
ejpam-6458	188	14	)	)	PUNCT
ejpam-6458	188	15	,	,	PUNCT
ejpam-6458	188	16	(	(	PUNCT
ejpam-6458	188	17	0	0	NUM
ejpam-6458	188	18	,	,	PUNCT
ejpam-6458	188	19	1	1	X
ejpam-6458	188	20	)	)	PUNCT
ejpam-6458	188	21	∈	∈	PROPN
ejpam-6458	188	22	r′	r′	NOUN
ejpam-6458	188	23	=	=	SYM
ejpam-6458	188	24	w(r	w(r	PROPN
ejpam-6458	188	25	)	)	PUNCT
ejpam-6458	188	26	.	.	PUNCT
ejpam-6458	189	1	the	the	DET
ejpam-6458	189	2	possible	possible	ADJ
ejpam-6458	189	3	negative	negative	ADJ
ejpam-6458	189	4	roots	root	NOUN
ejpam-6458	189	5	in	in	ADP
ejpam-6458	189	6	the	the	DET
ejpam-6458	189	7	list	list	NOUN
ejpam-6458	189	8	r′	r′	NOUN
ejpam-6458	189	9	are	be	AUX
ejpam-6458	189	10	(	(	PUNCT
ejpam-6458	189	11	−1,−1	−1,−1	NOUN
ejpam-6458	189	12	)	)	PUNCT
ejpam-6458	189	13	and	and	CCONJ
ejpam-6458	189	14	(	(	PUNCT
ejpam-6458	189	15	−1	−1	NOUN
ejpam-6458	189	16	,	,	PUNCT
ejpam-6458	189	17	0	0	NUM
ejpam-6458	189	18	)	)	PUNCT
ejpam-6458	189	19	.	.	PUNCT
ejpam-6458	190	1	since	since	SCONJ
ejpam-6458	190	2	the	the	DET
ejpam-6458	190	3	second	second	ADJ
ejpam-6458	190	4	coordinate	coordinate	NOUN
ejpam-6458	190	5	of	of	ADP
ejpam-6458	190	6	the	the	DET
ejpam-6458	190	7	sum	sum	NOUN
ejpam-6458	190	8	of	of	ADP
ejpam-6458	190	9	all	all	DET
ejpam-6458	190	10	positive	positive	ADJ
ejpam-6458	190	11	roots	root	NOUN
ejpam-6458	190	12	is	be	AUX
ejpam-6458	190	13	at	at	ADP
ejpam-6458	190	14	least	least	ADJ
ejpam-6458	190	15	two	two	NUM
ejpam-6458	190	16	,	,	PUNCT
ejpam-6458	190	17	r′	r′	PROPN
ejpam-6458	190	18	must	must	AUX
ejpam-6458	190	19	contain	contain	VERB
ejpam-6458	190	20	at	at	ADV
ejpam-6458	190	21	least	least	ADV
ejpam-6458	190	22	two	two	NUM
ejpam-6458	190	23	occurrences	occurrence	NOUN
ejpam-6458	190	24	of	of	ADP
ejpam-6458	190	25	(	(	PUNCT
ejpam-6458	190	26	−1,−1	−1,−1	NOUN
ejpam-6458	190	27	)	)	PUNCT
ejpam-6458	190	28	.	.	PUNCT
ejpam-6458	191	1	thus	thus	ADV
ejpam-6458	191	2	we	we	PRON
ejpam-6458	191	3	have	have	VERB
ejpam-6458	191	4	r′	r′	ADJ
ejpam-6458	191	5	=	=	SYM
ejpam-6458	191	6	{	{	PUNCT
ejpam-6458	191	7	(	(	PUNCT
ejpam-6458	191	8	2	2	NUM
ejpam-6458	191	9	,	,	PUNCT
ejpam-6458	191	10	1	1	NUM
ejpam-6458	191	11	)	)	PUNCT
ejpam-6458	191	12	,	,	PUNCT
ejpam-6458	191	13	(	(	PUNCT
ejpam-6458	191	14	0	0	NUM
ejpam-6458	191	15	,	,	PUNCT
ejpam-6458	191	16	1	1	NUM
ejpam-6458	191	17	)	)	PUNCT
ejpam-6458	191	18	,	,	PUNCT
ejpam-6458	191	19	(	(	PUNCT
ejpam-6458	191	20	−1,−1	−1,−1	NOUN
ejpam-6458	191	21	)	)	PUNCT
ejpam-6458	191	22	,	,	PUNCT
ejpam-6458	191	23	(	(	PUNCT
ejpam-6458	191	24	−1,−1	−1,−1	NOUN
ejpam-6458	191	25	)	)	PUNCT
ejpam-6458	191	26	}	}	PUNCT
ejpam-6458	191	27	.	.	PUNCT
ejpam-6458	192	1	now	now	ADV
ejpam-6458	192	2	,	,	PUNCT
ejpam-6458	192	3	applying	apply	VERB
ejpam-6458	192	4	w2	w2	NOUN
ejpam-6458	192	5	,	,	PUNCT
ejpam-6458	192	6	we	we	PRON
ejpam-6458	192	7	obtain	obtain	VERB
ejpam-6458	192	8	w2(r	w2(r	PROPN
ejpam-6458	192	9	′	′	NOUN
ejpam-6458	192	10	)	)	PUNCT
ejpam-6458	192	11	=	=	SYM
ejpam-6458	193	1	=	=	PRON
ejpam-6458	193	2	{	{	PUNCT
ejpam-6458	193	3	(	(	PUNCT
ejpam-6458	193	4	2	2	NUM
ejpam-6458	193	5	,	,	PUNCT
ejpam-6458	193	6	1	1	NUM
ejpam-6458	193	7	)	)	PUNCT
ejpam-6458	193	8	,	,	PUNCT
ejpam-6458	193	9	(	(	PUNCT
ejpam-6458	193	10	0,−1	0,−1	NOUN
ejpam-6458	193	11	)	)	PUNCT
ejpam-6458	193	12	,	,	PUNCT
ejpam-6458	193	13	(	(	PUNCT
ejpam-6458	193	14	−1	−1	NOUN
ejpam-6458	193	15	,	,	PUNCT
ejpam-6458	193	16	0	0	NUM
ejpam-6458	193	17	)	)	PUNCT
ejpam-6458	193	18	,	,	PUNCT
ejpam-6458	193	19	(	(	PUNCT
ejpam-6458	193	20	−1	−1	NOUN
ejpam-6458	193	21	,	,	PUNCT
ejpam-6458	193	22	0	0	NUM
ejpam-6458	193	23	)	)	PUNCT
ejpam-6458	193	24	}	}	PUNCT
ejpam-6458	193	25	,	,	PUNCT
ejpam-6458	193	26	which	which	PRON
ejpam-6458	193	27	is	be	AUX
ejpam-6458	193	28	primitive	primitive	ADJ
ejpam-6458	193	29	.	.	PUNCT
ejpam-6458	194	1	consequently	consequently	ADV
ejpam-6458	194	2	r	r	NOUN
ejpam-6458	194	3	is	be	AUX
ejpam-6458	194	4	also	also	ADV
ejpam-6458	194	5	primitive	primitive	ADJ
ejpam-6458	194	6	.	.	PUNCT
ejpam-6458	195	1	the	the	DET
ejpam-6458	195	2	proof	proof	NOUN
ejpam-6458	195	3	of	of	ADP
ejpam-6458	195	4	the	the	DET
ejpam-6458	195	5	second	second	ADJ
ejpam-6458	195	6	statement	statement	NOUN
ejpam-6458	195	7	for	for	ADP
ejpam-6458	195	8	g2	g2	PROPN
ejpam-6458	195	9	is	be	AUX
ejpam-6458	195	10	similar	similar	ADJ
ejpam-6458	195	11	to	to	ADP
ejpam-6458	195	12	the	the	DET
ejpam-6458	195	13	case	case	NOUN
ejpam-6458	195	14	of	of	ADP
ejpam-6458	195	15	c2	c2	PROPN
ejpam-6458	195	16	.	.	PUNCT
ejpam-6458	196	1	for	for	ADP
ejpam-6458	196	2	the	the	DET
ejpam-6458	196	3	sets	set	NOUN
ejpam-6458	196	4	of	of	ADP
ejpam-6458	196	5	all	all	DET
ejpam-6458	196	6	primitive	primitive	ADJ
ejpam-6458	196	7	lists	list	NOUN
ejpam-6458	196	8	in	in	ADP
ejpam-6458	196	9	all	all	DET
ejpam-6458	196	10	three	three	NUM
ejpam-6458	196	11	cases	case	NOUN
ejpam-6458	196	12	,	,	PUNCT
ejpam-6458	196	13	see	see	VERB
ejpam-6458	196	14	sections	section	NOUN
ejpam-6458	196	15	4	4	NUM
ejpam-6458	196	16	-	-	SYM
ejpam-6458	196	17	6	6	NUM
ejpam-6458	196	18	.	.	PUNCT
ejpam-6458	196	19	□	□	PUNCT
ejpam-6458	196	20	define	define	VERB
ejpam-6458	196	21	the	the	DET
ejpam-6458	196	22	following	follow	VERB
ejpam-6458	196	23	order	order	NOUN
ejpam-6458	196	24	on	on	ADP
ejpam-6458	196	25	the	the	DET
ejpam-6458	196	26	set	set	NOUN
ejpam-6458	196	27	of	of	ADP
ejpam-6458	196	28	roots	root	NOUN
ejpam-6458	196	29	∆	∆	PROPN
ejpam-6458	196	30	,	,	PUNCT
ejpam-6458	196	31	derived	derive	VERB
ejpam-6458	196	32	from	from	ADP
ejpam-6458	196	33	(	(	PUNCT
ejpam-6458	196	34	2.1	2.1	NUM
ejpam-6458	196	35	)	)	PUNCT
ejpam-6458	196	36	.	.	PUNCT
ejpam-6458	197	1	for	for	ADP
ejpam-6458	197	2	α1	α1	PROPN
ejpam-6458	197	3	,	,	PUNCT
ejpam-6458	197	4	α2	α2	PROPN
ejpam-6458	197	5	∈	∈	PROPN
ejpam-6458	197	6	∆	∆	PROPN
ejpam-6458	197	7	α1	α1	PROPN
ejpam-6458	197	8	≤	≤	ADV
ejpam-6458	197	9	α2	α2	PROPN
ejpam-6458	197	10	if	if	SCONJ
ejpam-6458	197	11	and	and	CCONJ
ejpam-6458	197	12	only	only	ADV
ejpam-6458	197	13	if	if	SCONJ
ejpam-6458	197	14	eα1	eα1	X
ejpam-6458	197	15	≤	≤	X
ejpam-6458	197	16	eα2	eα2	PROPN
ejpam-6458	197	17	.	.	PUNCT
ejpam-6458	198	1	(	(	PUNCT
ejpam-6458	198	2	2.2	2.2	NUM
ejpam-6458	198	3	)	)	PUNCT
ejpam-6458	198	4	a	a	DET
ejpam-6458	198	5	monomial	monomial	NOUN
ejpam-6458	198	6	x	x	AUX
ejpam-6458	198	7	is	be	AUX
ejpam-6458	198	8	called	call	VERB
ejpam-6458	198	9	perfect	perfect	ADJ
ejpam-6458	198	10	if	if	SCONJ
ejpam-6458	198	11	either	either	CCONJ
ejpam-6458	198	12	x	x	X
ejpam-6458	198	13	=	=	VERB
ejpam-6458	198	14	hβ	hβ	PROPN
ejpam-6458	198	15	∈	∈	PROPN
ejpam-6458	198	16	g0	g0	NOUN
ejpam-6458	198	17	,	,	PUNCT
ejpam-6458	198	18	or	or	CCONJ
ejpam-6458	198	19	x	x	X
ejpam-6458	198	20	=	=	PRON
ejpam-6458	198	21	eα1	eα1	X
ejpam-6458	198	22	·	·	PUNCT
ejpam-6458	198	23	eα2	eα2	X
ejpam-6458	198	24	·	·	PUNCT
ejpam-6458	198	25	·	·	PUNCT
ejpam-6458	198	26	·	·	PUNCT
ejpam-6458	198	27	·	·	PUNCT
ejpam-6458	198	28	·	·	PUNCT
ejpam-6458	198	29	eαn	eαn	X
ejpam-6458	198	30	and	and	CCONJ
ejpam-6458	198	31	the	the	DET
ejpam-6458	198	32	associated	associated	ADJ
ejpam-6458	198	33	list	list	NOUN
ejpam-6458	198	34	l1(x	l1(x	NOUN
ejpam-6458	198	35	)	)	PUNCT
ejpam-6458	198	36	=	=	SYM
ejpam-6458	198	37	(	(	PUNCT
ejpam-6458	198	38	α1	α1	PROPN
ejpam-6458	198	39	,	,	PUNCT
ejpam-6458	198	40	α2	α2	ADJ
ejpam-6458	198	41	,	,	PUNCT
ejpam-6458	198	42	.	.	PUNCT
ejpam-6458	198	43	.	.	PUNCT
ejpam-6458	199	1	.	.	PUNCT
ejpam-6458	200	1	,	,	PUNCT
ejpam-6458	200	2	αn	αn	X
ejpam-6458	200	3	)	)	PUNCT
ejpam-6458	200	4	is	be	AUX
ejpam-6458	200	5	both	both	CCONJ
ejpam-6458	200	6	indecomposable	indecomposable	ADJ
ejpam-6458	200	7	and	and	CCONJ
ejpam-6458	200	8	ordered	order	VERB
ejpam-6458	200	9	according	accord	VERB
ejpam-6458	200	10	to	to	ADP
ejpam-6458	200	11	(	(	PUNCT
ejpam-6458	200	12	2.2	2.2	NUM
ejpam-6458	200	13	)	)	PUNCT
ejpam-6458	200	14	,	,	PUNCT
ejpam-6458	200	15	i.e.	i.e.	X
ejpam-6458	200	16	,	,	PUNCT
ejpam-6458	200	17	α1	α1	PROPN
ejpam-6458	200	18	≤	≤	ADV
ejpam-6458	200	19	α2	α2	ADJ
ejpam-6458	200	20	≤	≤	NOUN
ejpam-6458	200	21	·	·	PUNCT
ejpam-6458	200	22	·	·	PUNCT
ejpam-6458	200	23	·	·	PUNCT
ejpam-6458	201	1	≤	≤	NUM
ejpam-6458	201	2	αn	αn	NOUN
ejpam-6458	201	3	.	.	PUNCT
ejpam-6458	202	1	since	since	SCONJ
ejpam-6458	202	2	the	the	DET
ejpam-6458	202	3	set	set	NOUN
ejpam-6458	202	4	of	of	ADP
ejpam-6458	202	5	all	all	DET
ejpam-6458	202	6	indecomposable	indecomposable	ADJ
ejpam-6458	202	7	lists	list	NOUN
ejpam-6458	202	8	is	be	AUX
ejpam-6458	202	9	finite	finite	ADJ
ejpam-6458	202	10	,	,	PUNCT
ejpam-6458	202	11	the	the	DET
ejpam-6458	202	12	set	set	NOUN
ejpam-6458	202	13	of	of	ADP
ejpam-6458	202	14	all	all	DET
ejpam-6458	202	15	perfect	perfect	ADJ
ejpam-6458	202	16	monomials	monomial	NOUN
ejpam-6458	202	17	is	be	AUX
ejpam-6458	202	18	also	also	ADV
ejpam-6458	202	19	finite	finite	ADJ
ejpam-6458	202	20	.	.	PUNCT
ejpam-6458	203	1	let	let	VERB
ejpam-6458	203	2	i(g	i(g	NOUN
ejpam-6458	203	3	)	)	PUNCT
ejpam-6458	204	1	=	=	PRON
ejpam-6458	204	2	{	{	PUNCT
ejpam-6458	204	3	p1	p1	NOUN
ejpam-6458	204	4	,	,	PUNCT
ejpam-6458	204	5	.	.	PUNCT
ejpam-6458	204	6	.	.	PUNCT
ejpam-6458	205	1	.	.	PUNCT
ejpam-6458	206	1	,	,	PUNCT
ejpam-6458	206	2	pq	pq	X
ejpam-6458	206	3	}	}	PUNCT
ejpam-6458	206	4	denote	denote	VERB
ejpam-6458	206	5	the	the	DET
ejpam-6458	206	6	set	set	NOUN
ejpam-6458	206	7	of	of	ADP
ejpam-6458	206	8	all	all	DET
ejpam-6458	206	9	perfect	perfect	ADJ
ejpam-6458	206	10	monomials	monomial	NOUN
ejpam-6458	206	11	with	with	ADP
ejpam-6458	206	12	degree	degree	NOUN
ejpam-6458	206	13	greater	great	ADJ
ejpam-6458	206	14	than	than	ADP
ejpam-6458	206	15	one	one	NUM
ejpam-6458	206	16	.	.	PUNCT
ejpam-6458	207	1	then	then	ADV
ejpam-6458	207	2	i(g	i(g	ADV
ejpam-6458	207	3	)	)	PUNCT
ejpam-6458	207	4	∪g0	∪g0	PROPN
ejpam-6458	207	5	is	be	AUX
ejpam-6458	207	6	a	a	DET
ejpam-6458	207	7	generating	generate	VERB
ejpam-6458	207	8	set	set	NOUN
ejpam-6458	207	9	of	of	ADP
ejpam-6458	207	10	u0(g	u0(g	NOUN
ejpam-6458	207	11	)	)	PUNCT
ejpam-6458	207	12	consisting	consist	VERB
ejpam-6458	207	13	of	of	ADP
ejpam-6458	207	14	all	all	DET
ejpam-6458	207	15	perfect	perfect	ADJ
ejpam-6458	207	16	monomials	monomial	NOUN
ejpam-6458	207	17	.	.	PUNCT
ejpam-6458	208	1	denote	denote	VERB
ejpam-6458	208	2	by	by	ADP
ejpam-6458	208	3	d0	d0	NOUN
ejpam-6458	208	4	the	the	DET
ejpam-6458	208	5	maximal	maximal	ADJ
ejpam-6458	208	6	degree	degree	NOUN
ejpam-6458	208	7	of	of	ADP
ejpam-6458	208	8	perfect	perfect	ADJ
ejpam-6458	208	9	monomials	monomial	NOUN
ejpam-6458	208	10	in	in	ADP
ejpam-6458	208	11	i(g	i(g	NOUN
ejpam-6458	208	12	)	)	PUNCT
ejpam-6458	208	13	.	.	PUNCT
ejpam-6458	209	1	let	let	VERB
ejpam-6458	209	2	j(g	j(g	NOUN
ejpam-6458	209	3	)	)	PUNCT
ejpam-6458	209	4	=	=	SYM
ejpam-6458	209	5	{	{	PUNCT
ejpam-6458	209	6	c1	c1	NOUN
ejpam-6458	209	7	,	,	PUNCT
ejpam-6458	209	8	.	.	PUNCT
ejpam-6458	209	9	.	.	PUNCT
ejpam-6458	210	1	.	.	PUNCT
ejpam-6458	211	1	,	,	PUNCT
ejpam-6458	211	2	cq	cq	AUX
ejpam-6458	211	3	}	}	PUNCT
ejpam-6458	211	4	be	be	AUX
ejpam-6458	211	5	the	the	DET
ejpam-6458	211	6	set	set	NOUN
ejpam-6458	211	7	of	of	ADP
ejpam-6458	211	8	new	new	ADJ
ejpam-6458	211	9	indeterminates	indeterminate	NOUN
ejpam-6458	211	10	,	,	PUNCT
ejpam-6458	211	11	ri	ri	PROPN
ejpam-6458	211	12	=	=	SYM
ejpam-6458	211	13	ci	ci	PROPN
ejpam-6458	212	1	−	−	PROPN
ejpam-6458	212	2	pi	pi	NOUN
ejpam-6458	212	3	,	,	PUNCT
ejpam-6458	212	4	i	i	PRON
ejpam-6458	212	5	=	=	NOUN
ejpam-6458	212	6	1	1	NUM
ejpam-6458	212	7	,	,	PUNCT
ejpam-6458	212	8	.	.	PUNCT
ejpam-6458	212	9	.	.	PUNCT
ejpam-6458	212	10	.	.	PUNCT
ejpam-6458	213	1	,	,	PUNCT
ejpam-6458	213	2	q	q	NOUN
ejpam-6458	213	3	and	and	CCONJ
ejpam-6458	213	4	d	d	PROPN
ejpam-6458	213	5	=	=	SYM
ejpam-6458	213	6	⟨r1	⟨r1	PROPN
ejpam-6458	213	7	,	,	PUNCT
ejpam-6458	213	8	.	.	PUNCT
ejpam-6458	213	9	.	.	PUNCT
ejpam-6458	214	1	.	.	PUNCT
ejpam-6458	215	1	,	,	PUNCT
ejpam-6458	215	2	rq⟩	rq⟩	NOUN
ejpam-6458	215	3	the	the	DET
ejpam-6458	215	4	2	2	NUM
ejpam-6458	215	5	-	-	PUNCT
ejpam-6458	215	6	sided	sided	ADJ
ejpam-6458	215	7	ideal	ideal	NOUN
ejpam-6458	215	8	of	of	ADP
ejpam-6458	215	9	u0(g)[c1	u0(g)[c1	PRON
ejpam-6458	215	10	,	,	PUNCT
ejpam-6458	215	11	.	.	PUNCT
ejpam-6458	215	12	.	.	PUNCT
ejpam-6458	216	1	.	.	PUNCT
ejpam-6458	217	1	,	,	PUNCT
ejpam-6458	217	2	cq	cq	AUX
ejpam-6458	217	3	]	]	PUNCT
ejpam-6458	217	4	generated	generate	VERB
ejpam-6458	217	5	by	by	ADP
ejpam-6458	217	6	these	these	DET
ejpam-6458	217	7	elements	element	NOUN
ejpam-6458	217	8	.	.	PUNCT
ejpam-6458	218	1	define	define	VERB
ejpam-6458	218	2	û0(g	û0(g	NOUN
ejpam-6458	218	3	)	)	PUNCT
ejpam-6458	218	4	=	=	PUNCT
ejpam-6458	218	5	u0(g)[c1	u0(g)[c1	PROPN
ejpam-6458	218	6	,	,	PUNCT
ejpam-6458	218	7	.	.	PUNCT
ejpam-6458	218	8	.	.	PUNCT
ejpam-6458	219	1	.	.	PUNCT
ejpam-6458	220	1	,	,	PUNCT
ejpam-6458	220	2	cq]/d	cq]/d	PROPN
ejpam-6458	220	3	.	.	PUNCT
ejpam-6458	221	1	clearly	clearly	ADV
ejpam-6458	221	2	,	,	PUNCT
ejpam-6458	221	3	û0(g	û0(g	NOUN
ejpam-6458	221	4	)	)	PUNCT
ejpam-6458	221	5	∼=	∼=	PROPN
ejpam-6458	221	6	u0(g	u0(g	NOUN
ejpam-6458	221	7	)	)	PUNCT
ejpam-6458	221	8	and	and	CCONJ
ejpam-6458	221	9	û0(g	û0(g	NOUN
ejpam-6458	221	10	)	)	PUNCT
ejpam-6458	221	11	is	be	AUX
ejpam-6458	221	12	generated	generate	VERB
ejpam-6458	221	13	by	by	ADP
ejpam-6458	221	14	j(g	j(g	PROPN
ejpam-6458	221	15	)	)	PUNCT
ejpam-6458	221	16	∪	∪	X
ejpam-6458	221	17	g0	g0	PROPN
ejpam-6458	221	18	with	with	ADP
ejpam-6458	221	19	the	the	DET
ejpam-6458	221	20	ideal	ideal	NOUN
ejpam-6458	221	21	of	of	ADP
ejpam-6458	221	22	relations	relation	NOUN
ejpam-6458	221	23	k	k	PROPN
ejpam-6458	221	24	inherited	inherit	VERB
ejpam-6458	221	25	from	from	ADP
ejpam-6458	221	26	u0(g	u0(g	NOUN
ejpam-6458	221	27	)	)	PUNCT
ejpam-6458	221	28	.	.	PUNCT
ejpam-6458	222	1	define	define	VERB
ejpam-6458	222	2	the	the	DET
ejpam-6458	222	3	degrees	degree	NOUN
ejpam-6458	222	4	of	of	ADP
ejpam-6458	222	5	new	new	ADJ
ejpam-6458	222	6	indeterminates	indeterminate	NOUN
ejpam-6458	222	7	ci	ci	NOUN
ejpam-6458	222	8	by	by	ADP
ejpam-6458	222	9	:	:	PUNCT
ejpam-6458	222	10	deg(ci	deg(ci	X
ejpam-6458	222	11	)	)	PUNCT
ejpam-6458	222	12	=	=	SYM
ejpam-6458	222	13	deg(pi	deg(pi	NOUN
ejpam-6458	222	14	)	)	PUNCT
ejpam-6458	222	15	.	.	PUNCT
ejpam-6458	223	1	denote	denote	VERB
ejpam-6458	223	2	by	by	ADP
ejpam-6458	223	3	q0(g	q0(g	NOUN
ejpam-6458	223	4	)	)	PUNCT
ejpam-6458	223	5	the	the	DET
ejpam-6458	223	6	set	set	NOUN
ejpam-6458	223	7	of	of	ADP
ejpam-6458	223	8	all	all	DET
ejpam-6458	223	9	monomials	monomial	NOUN
ejpam-6458	223	10	generated	generate	VERB
ejpam-6458	223	11	by	by	ADP
ejpam-6458	223	12	j(g	j(g	PROPN
ejpam-6458	223	13	)	)	PUNCT
ejpam-6458	223	14	∪	∪	X
ejpam-6458	223	15	g0	g0	NOUN
ejpam-6458	223	16	and	and	CCONJ
ejpam-6458	223	17	set	set	VERB
ejpam-6458	223	18	q	q	PROPN
ejpam-6458	224	1	(	(	PUNCT
ejpam-6458	224	2	i	i	NOUN
ejpam-6458	224	3	)	)	PUNCT
ejpam-6458	224	4	0	0	PUNCT
ejpam-6458	225	1	(	(	PUNCT
ejpam-6458	225	2	g	g	NOUN
ejpam-6458	225	3	)	)	PUNCT
ejpam-6458	225	4	=	=	SYM
ejpam-6458	226	1	q0(g	q0(g	NOUN
ejpam-6458	226	2	)	)	PUNCT
ejpam-6458	226	3	∩	∩	NOUN
ejpam-6458	226	4	u	u	SYM
ejpam-6458	226	5	(	(	PUNCT
ejpam-6458	226	6	i	i	NOUN
ejpam-6458	226	7	)	)	PUNCT
ejpam-6458	226	8	0	0	PUNCT
ejpam-6458	226	9	(	(	PUNCT
ejpam-6458	226	10	g	g	NOUN
ejpam-6458	226	11	)	)	PUNCT
ejpam-6458	226	12	.	.	PUNCT
ejpam-6458	227	1	define	define	VERB
ejpam-6458	227	2	the	the	DET
ejpam-6458	227	3	function	function	NOUN
ejpam-6458	227	4	from	from	ADP
ejpam-6458	227	5	q0(g	q0(g	NOUN
ejpam-6458	227	6	)	)	PUNCT
ejpam-6458	227	7	to	to	ADP
ejpam-6458	227	8	i(g	i(g	NOUN
ejpam-6458	227	9	)	)	PUNCT
ejpam-6458	227	10	∪g0	∪g0	NOUN
ejpam-6458	227	11	as	as	SCONJ
ejpam-6458	227	12	follows	follow	VERB
ejpam-6458	227	13	:	:	PUNCT
ejpam-6458	227	14	ω	ω	NOUN
ejpam-6458	227	15	:	:	PUNCT
ejpam-6458	227	16	q0(g	q0(g	X
ejpam-6458	227	17	)	)	PUNCT
ejpam-6458	227	18	→	→	SYM
ejpam-6458	227	19	i(g	i(g	NOUN
ejpam-6458	227	20	)	)	PUNCT
ejpam-6458	227	21	∪g0	∪g0	NOUN
ejpam-6458	227	22	,	,	PUNCT
ejpam-6458	227	23	ω(ci	ω(ci	NOUN
ejpam-6458	227	24	)	)	PUNCT
ejpam-6458	227	25	=	=	SYM
ejpam-6458	227	26	pi	pi	NOUN
ejpam-6458	227	27	,	,	PUNCT
ejpam-6458	227	28	ω(h	ω(h	NUM
ejpam-6458	227	29	)	)	PUNCT
ejpam-6458	228	1	=	=	SYM
ejpam-6458	228	2	h	h	NOUN
ejpam-6458	228	3	,	,	PUNCT
ejpam-6458	228	4	h	h	PROPN
ejpam-6458	228	5	∈	∈	PROPN
ejpam-6458	228	6	g0	g0	PROPN
ejpam-6458	228	7	.	.	PUNCT
ejpam-6458	229	1	let	let	VERB
ejpam-6458	229	2	us	we	PRON
ejpam-6458	229	3	fix	fix	VERB
ejpam-6458	229	4	some	some	DET
ejpam-6458	229	5	order	order	NOUN
ejpam-6458	229	6	on	on	ADP
ejpam-6458	229	7	the	the	DET
ejpam-6458	229	8	set	set	NOUN
ejpam-6458	229	9	j(g	j(g	NOUN
ejpam-6458	229	10	)	)	PUNCT
ejpam-6458	229	11	∪g0	∪g0	PROPN
ejpam-6458	229	12	:	:	PUNCT
ejpam-6458	230	1	x1	x1	PROPN
ejpam-6458	230	2	≤	≤	NUM
ejpam-6458	230	3	x2	x2	ADJ
ejpam-6458	230	4	≤	≤	NOUN
ejpam-6458	230	5	·	·	PUNCT
ejpam-6458	230	6	·	·	PUNCT
ejpam-6458	230	7	·	·	PUNCT
ejpam-6458	231	1	≤	≤	NUM
ejpam-6458	231	2	xq+k0	xq+k0	PROPN
ejpam-6458	231	3	,	,	PUNCT
ejpam-6458	231	4	xi	xi	PROPN
ejpam-6458	231	5	∈	∈	PROPN
ejpam-6458	231	6	j(g	j(g	PROPN
ejpam-6458	231	7	)	)	PUNCT
ejpam-6458	231	8	∪g0	∪g0	NOUN
ejpam-6458	231	9	,	,	PUNCT
ejpam-6458	231	10	i	i	NOUN
ejpam-6458	231	11	=	=	NOUN
ejpam-6458	231	12	1	1	NUM
ejpam-6458	231	13	,	,	PUNCT
ejpam-6458	231	14	.	.	PUNCT
ejpam-6458	231	15	.	.	PUNCT
ejpam-6458	231	16	.	.	PUNCT
ejpam-6458	232	1	,	,	PUNCT
ejpam-6458	232	2	q	q	X
ejpam-6458	233	1	+	+	X
ejpam-6458	233	2	k0	k0	PROPN
ejpam-6458	233	3	.	.	PUNCT
ejpam-6458	234	1	(	(	PUNCT
ejpam-6458	234	2	2.3	2.3	NUM
ejpam-6458	234	3	)	)	PUNCT
ejpam-6458	234	4	m.	m.	NOUN
ejpam-6458	234	5	andelić	andelić	PROPN
ejpam-6458	234	6	et	et	PROPN
ejpam-6458	234	7	al	al	PROPN
ejpam-6458	234	8	.	.	PUNCT
ejpam-6458	234	9	/	/	SYM
ejpam-6458	234	10	eur	eur	PROPN
ejpam-6458	234	11	.	.	PUNCT
ejpam-6458	235	1	j.	j.	PROPN
ejpam-6458	235	2	pure	pure	PROPN
ejpam-6458	235	3	appl	appl	PROPN
ejpam-6458	235	4	.	.	PROPN
ejpam-6458	235	5	math	math	PROPN
ejpam-6458	235	6	,	,	PUNCT
ejpam-6458	235	7	18	18	NUM
ejpam-6458	235	8	(	(	PUNCT
ejpam-6458	235	9	3	3	NUM
ejpam-6458	235	10	)	)	PUNCT
ejpam-6458	235	11	(	(	PUNCT
ejpam-6458	235	12	2025	2025	NUM
ejpam-6458	235	13	)	)	PUNCT
ejpam-6458	235	14	,	,	PUNCT
ejpam-6458	235	15	6458	6458	NUM
ejpam-6458	235	16	6	6	NUM
ejpam-6458	235	17	of	of	ADP
ejpam-6458	235	18	21	21	NUM
ejpam-6458	235	19	for	for	ADP
ejpam-6458	235	20	any	any	DET
ejpam-6458	235	21	monomial	monomial	ADJ
ejpam-6458	235	22	y	y	PROPN
ejpam-6458	235	23	∈	∈	PROPN
ejpam-6458	235	24	q0(g	q0(g	NOUN
ejpam-6458	235	25	)	)	PUNCT
ejpam-6458	235	26	,	,	PUNCT
ejpam-6458	235	27	denote	denote	VERB
ejpam-6458	235	28	by	by	ADP
ejpam-6458	235	29	t1(y	t1(y	PRON
ejpam-6458	235	30	)	)	PUNCT
ejpam-6458	235	31	the	the	DET
ejpam-6458	235	32	set	set	NOUN
ejpam-6458	235	33	of	of	ADP
ejpam-6458	235	34	all	all	DET
ejpam-6458	235	35	monomials	monomial	NOUN
ejpam-6458	235	36	x	x	X
ejpam-6458	235	37	∈	∈	NOUN
ejpam-6458	235	38	q0(g	q0(g	NOUN
ejpam-6458	235	39	)	)	PUNCT
ejpam-6458	235	40	such	such	ADJ
ejpam-6458	235	41	that	that	SCONJ
ejpam-6458	235	42	t0(ω(y	t0(ω(y	NOUN
ejpam-6458	235	43	)	)	PUNCT
ejpam-6458	235	44	)	)	PUNCT
ejpam-6458	236	1	=	=	PUNCT
ejpam-6458	236	2	t0(ω(x	t0(ω(x	NOUN
ejpam-6458	236	3	)	)	PUNCT
ejpam-6458	236	4	)	)	PUNCT
ejpam-6458	236	5	.	.	PUNCT
ejpam-6458	237	1	note	note	VERB
ejpam-6458	237	2	that	that	SCONJ
ejpam-6458	237	3	all	all	DET
ejpam-6458	237	4	monomials	monomial	NOUN
ejpam-6458	237	5	in	in	ADP
ejpam-6458	237	6	the	the	DET
ejpam-6458	237	7	sets	set	NOUN
ejpam-6458	237	8	t0(ω(y	t0(ω(y	X
ejpam-6458	237	9	)	)	PUNCT
ejpam-6458	237	10	)	)	PUNCT
ejpam-6458	238	1	and	and	CCONJ
ejpam-6458	238	2	t1(y	t1(y	PRON
ejpam-6458	238	3	)	)	PUNCT
ejpam-6458	238	4	have	have	VERB
ejpam-6458	238	5	the	the	DET
ejpam-6458	238	6	same	same	ADJ
ejpam-6458	238	7	degree	degree	NOUN
ejpam-6458	238	8	.	.	PUNCT
ejpam-6458	239	1	extend	extend	VERB
ejpam-6458	239	2	function	function	NOUN
ejpam-6458	239	3	l1	l1	PROPN
ejpam-6458	239	4	on	on	ADP
ejpam-6458	239	5	the	the	DET
ejpam-6458	239	6	set	set	NOUN
ejpam-6458	239	7	j(g	j(g	NOUN
ejpam-6458	239	8	)	)	PUNCT
ejpam-6458	239	9	as	as	SCONJ
ejpam-6458	239	10	follows	follow	VERB
ejpam-6458	239	11	:	:	PUNCT
ejpam-6458	239	12	l1(x	l1(x	NUM
ejpam-6458	239	13	)	)	PUNCT
ejpam-6458	239	14	=	=	SYM
ejpam-6458	239	15	l1(ω(x	l1(ω(x	NOUN
ejpam-6458	239	16	)	)	PUNCT
ejpam-6458	239	17	)	)	PUNCT
ejpam-6458	239	18	,	,	PUNCT
ejpam-6458	239	19	x	x	PUNCT
ejpam-6458	239	20	∈	∈	PROPN
ejpam-6458	239	21	q0(g	q0(g	NOUN
ejpam-6458	239	22	)	)	PUNCT
ejpam-6458	239	23	.	.	PUNCT
ejpam-6458	240	1	define	define	VERB
ejpam-6458	240	2	a	a	DET
ejpam-6458	240	3	lexicographical	lexicographical	ADJ
ejpam-6458	240	4	order	order	NOUN
ejpam-6458	240	5	on	on	ADP
ejpam-6458	240	6	the	the	DET
ejpam-6458	240	7	set	set	NOUN
ejpam-6458	240	8	t1(y	t1(y	NUM
ejpam-6458	240	9	)	)	PUNCT
ejpam-6458	240	10	with	with	ADP
ejpam-6458	240	11	respect	respect	NOUN
ejpam-6458	240	12	to	to	ADP
ejpam-6458	240	13	the	the	DET
ejpam-6458	240	14	order	order	NOUN
ejpam-6458	240	15	given	give	VERB
ejpam-6458	240	16	in	in	ADP
ejpam-6458	240	17	(	(	PUNCT
ejpam-6458	240	18	2.3	2.3	NUM
ejpam-6458	240	19	)	)	PUNCT
ejpam-6458	240	20	as	as	SCONJ
ejpam-6458	240	21	follows	follow	VERB
ejpam-6458	240	22	:	:	PUNCT
ejpam-6458	240	23	if	if	SCONJ
ejpam-6458	240	24	y1	y1	NOUN
ejpam-6458	240	25	=	=	SYM
ejpam-6458	240	26	a1a2	a1a2	X
ejpam-6458	240	27	·	·	PUNCT
ejpam-6458	240	28	·	·	PUNCT
ejpam-6458	240	29	·	·	PUNCT
ejpam-6458	241	1	an	an	X
ejpam-6458	241	2	,	,	PUNCT
ejpam-6458	241	3	y2	y2	PROPN
ejpam-6458	241	4	=	=	SYM
ejpam-6458	241	5	b1b2	b1b2	PROPN
ejpam-6458	241	6	·	·	PUNCT
ejpam-6458	241	7	·	·	PUNCT
ejpam-6458	241	8	·	·	PUNCT
ejpam-6458	241	9	bm	bm	PROPN
ejpam-6458	241	10	,	,	PUNCT
ejpam-6458	241	11	for	for	ADP
ejpam-6458	241	12	ai	ai	NOUN
ejpam-6458	241	13	,	,	PUNCT
ejpam-6458	241	14	bj	bj	ADP
ejpam-6458	241	15	∈	∈	PROPN
ejpam-6458	241	16	j0(g	j0(g	NOUN
ejpam-6458	241	17	)	)	PUNCT
ejpam-6458	241	18	∪g0	∪g0	NOUN
ejpam-6458	241	19	and	and	CCONJ
ejpam-6458	241	20	y1	y1	NOUN
ejpam-6458	241	21	,	,	PUNCT
ejpam-6458	241	22	y2	y2	NOUN
ejpam-6458	241	23	∈	∈	PROPN
ejpam-6458	242	1	t1(y	t1(y	X
ejpam-6458	242	2	)	)	PUNCT
ejpam-6458	242	3	,	,	PUNCT
ejpam-6458	242	4	then	then	ADV
ejpam-6458	242	5	y1	y1	VERB
ejpam-6458	242	6	<	<	X
ejpam-6458	242	7	y2	y2	INTJ
ejpam-6458	242	8	if	if	SCONJ
ejpam-6458	242	9	there	there	PRON
ejpam-6458	242	10	exists	exist	VERB
ejpam-6458	242	11	an	an	DET
ejpam-6458	242	12	index	index	NOUN
ejpam-6458	242	13	1	1	NUM
ejpam-6458	242	14	≤	≤	NOUN
ejpam-6458	242	15	s	s	PART
ejpam-6458	242	16	≤	≤	ADJ
ejpam-6458	242	17	min(n	min(n	PROPN
ejpam-6458	242	18	,	,	PUNCT
ejpam-6458	242	19	m	m	PROPN
ejpam-6458	242	20	)	)	PUNCT
ejpam-6458	242	21	,	,	PUNCT
ejpam-6458	242	22	such	such	ADJ
ejpam-6458	242	23	that	that	SCONJ
ejpam-6458	242	24	as	as	ADP
ejpam-6458	242	25	<	<	X
ejpam-6458	242	26	bs	bs	NOUN
ejpam-6458	242	27	and	and	CCONJ
ejpam-6458	242	28	at	at	ADP
ejpam-6458	242	29	=	=	PUNCT
ejpam-6458	242	30	bt	bt	PROPN
ejpam-6458	242	31	,	,	PUNCT
ejpam-6458	242	32	for	for	ADP
ejpam-6458	242	33	all	all	PRON
ejpam-6458	242	34	0	0	NUM
ejpam-6458	242	35	<	<	X
ejpam-6458	242	36	t	t	X
ejpam-6458	242	37	<	<	X
ejpam-6458	242	38	s.	s.	PROPN
ejpam-6458	242	39	note	note	VERB
ejpam-6458	242	40	that	that	SCONJ
ejpam-6458	242	41	neither	neither	CCONJ
ejpam-6458	242	42	y1	y1	NOUN
ejpam-6458	242	43	nor	nor	CCONJ
ejpam-6458	242	44	y2	y2	NOUN
ejpam-6458	242	45	can	can	AUX
ejpam-6458	242	46	be	be	AUX
ejpam-6458	242	47	a	a	DET
ejpam-6458	242	48	prefix	prefix	NOUN
ejpam-6458	242	49	of	of	ADP
ejpam-6458	242	50	the	the	DET
ejpam-6458	242	51	other	other	ADJ
ejpam-6458	242	52	,	,	PUNCT
ejpam-6458	242	53	which	which	PRON
ejpam-6458	242	54	ensure	ensure	VERB
ejpam-6458	242	55	that	that	SCONJ
ejpam-6458	242	56	our	our	PRON
ejpam-6458	242	57	definition	definition	NOUN
ejpam-6458	242	58	is	be	AUX
ejpam-6458	242	59	well	well	ADV
ejpam-6458	242	60	-	-	PUNCT
ejpam-6458	242	61	defined	define	VERB
ejpam-6458	242	62	and	and	CCONJ
ejpam-6458	242	63	that	that	SCONJ
ejpam-6458	242	64	any	any	DET
ejpam-6458	242	65	two	two	NUM
ejpam-6458	242	66	distinct	distinct	ADJ
ejpam-6458	242	67	elements	element	NOUN
ejpam-6458	242	68	are	be	AUX
ejpam-6458	242	69	comparable	comparable	ADJ
ejpam-6458	242	70	.	.	PUNCT
ejpam-6458	243	1	a	a	DET
ejpam-6458	243	2	monomial	monomial	ADJ
ejpam-6458	243	3	y	y	PROPN
ejpam-6458	243	4	∈	∈	PROPN
ejpam-6458	243	5	q0(g	q0(g	NOUN
ejpam-6458	243	6	)	)	PUNCT
ejpam-6458	243	7	is	be	AUX
ejpam-6458	243	8	called	call	VERB
ejpam-6458	243	9	semi	semi	ADJ
ejpam-6458	243	10	-	-	ADJ
ejpam-6458	243	11	perfect	perfect	ADJ
ejpam-6458	243	12	if	if	SCONJ
ejpam-6458	243	13	it	it	PRON
ejpam-6458	243	14	is	be	AUX
ejpam-6458	243	15	the	the	DET
ejpam-6458	243	16	minimal	minimal	ADJ
ejpam-6458	243	17	element	element	NOUN
ejpam-6458	243	18	of	of	ADP
ejpam-6458	243	19	the	the	DET
ejpam-6458	243	20	set	set	NOUN
ejpam-6458	243	21	t1(y	t1(y	X
ejpam-6458	243	22	)	)	PUNCT
ejpam-6458	243	23	under	under	ADP
ejpam-6458	243	24	this	this	DET
ejpam-6458	243	25	lexicographical	lexicographical	ADJ
ejpam-6458	243	26	order	order	NOUN
ejpam-6458	243	27	.	.	PUNCT
ejpam-6458	244	1	denote	denote	VERB
ejpam-6458	244	2	by	by	ADP
ejpam-6458	244	3	s(g	s(g	PROPN
ejpam-6458	244	4	)	)	PUNCT
ejpam-6458	244	5	the	the	DET
ejpam-6458	244	6	set	set	NOUN
ejpam-6458	244	7	of	of	ADP
ejpam-6458	244	8	all	all	DET
ejpam-6458	244	9	semi	semi	ADJ
ejpam-6458	244	10	-	-	ADJ
ejpam-6458	244	11	perfect	perfect	ADJ
ejpam-6458	244	12	monomials	monomial	NOUN
ejpam-6458	244	13	,	,	PUNCT
ejpam-6458	244	14	and	and	CCONJ
ejpam-6458	244	15	set	set	VERB
ejpam-6458	244	16	s(i)(g	s(i)(g	NOUN
ejpam-6458	244	17	)	)	PUNCT
ejpam-6458	244	18	=	=	SYM
ejpam-6458	244	19	s(g	s(g	PROPN
ejpam-6458	244	20	)	)	PUNCT
ejpam-6458	244	21	∩	∩	NOUN
ejpam-6458	244	22	û	û	NUM
ejpam-6458	244	23	(	(	PUNCT
ejpam-6458	244	24	i	i	NOUN
ejpam-6458	244	25	)	)	PUNCT
ejpam-6458	244	26	0	0	PUNCT
ejpam-6458	245	1	(	(	PUNCT
ejpam-6458	245	2	g	g	NOUN
ejpam-6458	245	3	)	)	PUNCT
ejpam-6458	245	4	.	.	PUNCT
ejpam-6458	246	1	lemma	lemma	PROPN
ejpam-6458	246	2	2.4	2.4	NUM
ejpam-6458	246	3	.	.	NOUN
ejpam-6458	247	1	1	1	NUM
ejpam-6458	247	2	.	.	X
ejpam-6458	248	1	for	for	ADP
ejpam-6458	248	2	any	any	DET
ejpam-6458	248	3	i	i	PRON
ejpam-6458	248	4	≥	≥	NOUN
ejpam-6458	248	5	1	1	NUM
ejpam-6458	248	6	and	and	CCONJ
ejpam-6458	248	7	x	x	PUNCT
ejpam-6458	248	8	∈	∈	PROPN
ejpam-6458	248	9	p	p	X
ejpam-6458	248	10	(	(	PUNCT
ejpam-6458	248	11	i	i	NOUN
ejpam-6458	248	12	)	)	PUNCT
ejpam-6458	248	13	0	0	PUNCT
ejpam-6458	249	1	there	there	PRON
ejpam-6458	249	2	exists	exist	VERB
ejpam-6458	249	3	a	a	DET
ejpam-6458	249	4	unique	unique	ADJ
ejpam-6458	249	5	semi	semi	ADJ
ejpam-6458	249	6	-	-	ADJ
ejpam-6458	249	7	perfect	perfect	ADJ
ejpam-6458	249	8	monomial	monomial	ADJ
ejpam-6458	249	9	y	y	PROPN
ejpam-6458	249	10	∈	∈	PROPN
ejpam-6458	249	11	s(i)(g	s(i)(g	NOUN
ejpam-6458	249	12	)	)	PUNCT
ejpam-6458	249	13	such	such	ADJ
ejpam-6458	249	14	that	that	DET
ejpam-6458	249	15	t0(x	t0(x	NOUN
ejpam-6458	249	16	)	)	PUNCT
ejpam-6458	249	17	=	=	SYM
ejpam-6458	249	18	t0(ω(y	t0(ω(y	NOUN
ejpam-6458	249	19	)	)	PUNCT
ejpam-6458	249	20	)	)	PUNCT
ejpam-6458	249	21	.	.	PUNCT
ejpam-6458	250	1	2	2	X
ejpam-6458	250	2	.	.	X
ejpam-6458	250	3	let	let	VERB
ejpam-6458	250	4	x	x	X
ejpam-6458	250	5	=	=	PUNCT
ejpam-6458	250	6	a1a2	a1a2	X
ejpam-6458	250	7	·	·	PUNCT
ejpam-6458	250	8	·	·	PUNCT
ejpam-6458	250	9	·	·	PUNCT
ejpam-6458	250	10	am	be	AUX
ejpam-6458	250	11	with	with	ADP
ejpam-6458	250	12	ai	ai	PROPN
ejpam-6458	250	13	∈	∈	PROPN
ejpam-6458	250	14	j0(g	j0(g	NOUN
ejpam-6458	250	15	)	)	PUNCT
ejpam-6458	250	16	∪	∪	PROPN
ejpam-6458	250	17	g0	g0	PROPN
ejpam-6458	250	18	,	,	PUNCT
ejpam-6458	250	19	be	be	AUX
ejpam-6458	250	20	a	a	DET
ejpam-6458	250	21	semi	semi	ADJ
ejpam-6458	250	22	-	-	ADJ
ejpam-6458	250	23	perfect	perfect	ADJ
ejpam-6458	250	24	monomial	monomial	NOUN
ejpam-6458	250	25	.	.	PUNCT
ejpam-6458	251	1	then	then	ADV
ejpam-6458	251	2	,	,	PUNCT
ejpam-6458	251	3	for	for	ADP
ejpam-6458	251	4	any	any	DET
ejpam-6458	251	5	s	s	X
ejpam-6458	251	6	∈	∈	NOUN
ejpam-6458	251	7	{	{	PUNCT
ejpam-6458	251	8	1	1	NUM
ejpam-6458	251	9	,	,	PUNCT
ejpam-6458	251	10	.	.	PUNCT
ejpam-6458	251	11	.	.	PUNCT
ejpam-6458	251	12	.	.	PUNCT
ejpam-6458	252	1	,	,	PUNCT
ejpam-6458	252	2	m	m	PROPN
ejpam-6458	252	3	}	}	PUNCT
ejpam-6458	252	4	,	,	PUNCT
ejpam-6458	252	5	the	the	DET
ejpam-6458	252	6	monomial	monomial	NOUN
ejpam-6458	252	7	x	x	NOUN
ejpam-6458	252	8	′	′	NOUN
ejpam-6458	252	9	=	=	NOUN
ejpam-6458	252	10	a1	a1	NOUN
ejpam-6458	252	11	·	·	PUNCT
ejpam-6458	252	12	·	·	PUNCT
ejpam-6458	252	13	·	·	PUNCT
ejpam-6458	253	1	as−1as+1	as−1as+1	CCONJ
ejpam-6458	253	2	·	·	PUNCT
ejpam-6458	253	3	·	·	PUNCT
ejpam-6458	253	4	·	·	PUNCT
ejpam-6458	253	5	am	am	VERB
ejpam-6458	253	6	is	be	AUX
ejpam-6458	253	7	also	also	ADV
ejpam-6458	253	8	semi	semi	ADJ
ejpam-6458	253	9	-	-	ADJ
ejpam-6458	253	10	perfect	perfect	ADJ
ejpam-6458	253	11	.	.	PUNCT
ejpam-6458	254	1	3	3	X
ejpam-6458	254	2	.	.	X
ejpam-6458	254	3	the	the	DET
ejpam-6458	254	4	set	set	NOUN
ejpam-6458	254	5	of	of	ADP
ejpam-6458	254	6	semi	semi	ADJ
ejpam-6458	254	7	-	-	ADJ
ejpam-6458	254	8	perfect	perfect	ADJ
ejpam-6458	254	9	monomials	monomial	NOUN
ejpam-6458	254	10	s(i)(g	s(i)(g	NOUN
ejpam-6458	254	11	)	)	PUNCT
ejpam-6458	254	12	is	be	AUX
ejpam-6458	254	13	a	a	DET
ejpam-6458	254	14	basis	basis	NOUN
ejpam-6458	254	15	of	of	ADP
ejpam-6458	254	16	the	the	DET
ejpam-6458	254	17	vector	vector	NOUN
ejpam-6458	254	18	space	space	NOUN
ejpam-6458	254	19	û	û	NUM
ejpam-6458	254	20	(	(	PUNCT
ejpam-6458	254	21	i	i	NOUN
ejpam-6458	254	22	)	)	PUNCT
ejpam-6458	254	23	0	0	PUNCT
ejpam-6458	255	1	(	(	PUNCT
ejpam-6458	255	2	g	g	NOUN
ejpam-6458	255	3	)	)	PUNCT
ejpam-6458	255	4	.	.	PUNCT
ejpam-6458	256	1	proof	proof	NOUN
ejpam-6458	256	2	.	.	PUNCT
ejpam-6458	257	1	the	the	DET
ejpam-6458	257	2	one	one	NUM
ejpam-6458	257	3	-	-	PUNCT
ejpam-6458	257	4	to	to	ADP
ejpam-6458	257	5	-	-	PUNCT
ejpam-6458	257	6	one	one	NUM
ejpam-6458	257	7	correspondence	correspondence	NOUN
ejpam-6458	257	8	between	between	ADP
ejpam-6458	257	9	standard	standard	ADJ
ejpam-6458	257	10	monomials	monomial	NOUN
ejpam-6458	257	11	in	in	ADP
ejpam-6458	257	12	u	u	NOUN
ejpam-6458	257	13	(	(	PUNCT
ejpam-6458	257	14	i	i	NOUN
ejpam-6458	257	15	)	)	PUNCT
ejpam-6458	257	16	0	0	PUNCT
ejpam-6458	258	1	(	(	PUNCT
ejpam-6458	258	2	g	g	NOUN
ejpam-6458	258	3	)	)	PUNCT
ejpam-6458	258	4	and	and	CCONJ
ejpam-6458	258	5	semiperfect	semiperfect	ADJ
ejpam-6458	258	6	monomials	monomial	NOUN
ejpam-6458	258	7	in	in	ADP
ejpam-6458	258	8	û	û	PROPN
ejpam-6458	258	9	(	(	PUNCT
ejpam-6458	258	10	i	i	NOUN
ejpam-6458	258	11	)	)	PUNCT
ejpam-6458	258	12	0	0	PUNCT
ejpam-6458	259	1	(	(	PUNCT
ejpam-6458	259	2	g	g	NOUN
ejpam-6458	259	3	)	)	PUNCT
ejpam-6458	259	4	follows	follow	VERB
ejpam-6458	259	5	from	from	ADP
ejpam-6458	259	6	lemma	lemma	PROPN
ejpam-6458	259	7	2.1	2.1	NUM
ejpam-6458	259	8	and	and	CCONJ
ejpam-6458	259	9	the	the	DET
ejpam-6458	259	10	definition	definition	NOUN
ejpam-6458	259	11	of	of	ADP
ejpam-6458	259	12	semi	semi	ADJ
ejpam-6458	259	13	-	-	ADJ
ejpam-6458	259	14	perfect	perfect	ADJ
ejpam-6458	259	15	monomials	monomial	NOUN
ejpam-6458	259	16	.	.	PUNCT
ejpam-6458	260	1	since	since	SCONJ
ejpam-6458	260	2	û	û	NUM
ejpam-6458	260	3	(	(	PUNCT
ejpam-6458	260	4	i	i	NOUN
ejpam-6458	260	5	)	)	PUNCT
ejpam-6458	260	6	0	0	PUNCT
ejpam-6458	261	1	(	(	PUNCT
ejpam-6458	261	2	g	g	NOUN
ejpam-6458	261	3	)	)	PUNCT
ejpam-6458	261	4	is	be	AUX
ejpam-6458	261	5	a	a	DET
ejpam-6458	261	6	finite	finite	ADJ
ejpam-6458	261	7	-	-	ADJ
ejpam-6458	261	8	dimensional	dimensional	ADJ
ejpam-6458	261	9	vector	vector	NOUN
ejpam-6458	261	10	space	space	NOUN
ejpam-6458	261	11	and	and	CCONJ
ejpam-6458	261	12	the	the	DET
ejpam-6458	261	13	set	set	NOUN
ejpam-6458	261	14	of	of	ADP
ejpam-6458	261	15	semi	semi	ADJ
ejpam-6458	261	16	-	-	ADJ
ejpam-6458	261	17	perfect	perfect	ADJ
ejpam-6458	261	18	monomials	monomial	NOUN
ejpam-6458	261	19	s(i)(g	s(i)(g	NOUN
ejpam-6458	261	20	)	)	PUNCT
ejpam-6458	261	21	satisfy	satisfy	VERB
ejpam-6458	261	22	the	the	DET
ejpam-6458	261	23	condition	condition	NOUN
ejpam-6458	261	24	for	for	ADP
ejpam-6458	261	25	the	the	DET
ejpam-6458	261	26	set	set	NOUN
ejpam-6458	261	27	p	p	NOUN
ejpam-6458	261	28	′	′	NOUN
ejpam-6458	261	29	in	in	ADP
ejpam-6458	261	30	the	the	DET
ejpam-6458	261	31	part	part	NOUN
ejpam-6458	261	32	6	6	NUM
ejpam-6458	261	33	of	of	ADP
ejpam-6458	261	34	the	the	DET
ejpam-6458	261	35	lemma	lemma	PROPN
ejpam-6458	261	36	2.1	2.1	NUM
ejpam-6458	261	37	,	,	PUNCT
ejpam-6458	261	38	the	the	DET
ejpam-6458	261	39	lemma	lemma	PROPN
ejpam-6458	261	40	follows	follow	VERB
ejpam-6458	261	41	.	.	PUNCT
ejpam-6458	262	1	□	□	PUNCT
ejpam-6458	262	2	since	since	SCONJ
ejpam-6458	262	3	the	the	DET
ejpam-6458	262	4	set	set	NOUN
ejpam-6458	262	5	of	of	ADP
ejpam-6458	262	6	semi	semi	ADJ
ejpam-6458	262	7	-	-	ADJ
ejpam-6458	262	8	perfect	perfect	ADJ
ejpam-6458	262	9	monomials	monomial	NOUN
ejpam-6458	262	10	s(i)(g	s(i)(g	NOUN
ejpam-6458	262	11	)	)	PUNCT
ejpam-6458	262	12	forms	form	VERB
ejpam-6458	262	13	a	a	DET
ejpam-6458	262	14	basis	basis	NOUN
ejpam-6458	262	15	of	of	ADP
ejpam-6458	262	16	the	the	DET
ejpam-6458	262	17	algebra	algebra	NOUN
ejpam-6458	262	18	u	u	NOUN
ejpam-6458	262	19	(	(	PUNCT
ejpam-6458	262	20	i	i	NOUN
ejpam-6458	262	21	)	)	PUNCT
ejpam-6458	262	22	0	0	PUNCT
ejpam-6458	263	1	(	(	PUNCT
ejpam-6458	263	2	g	g	NOUN
ejpam-6458	263	3	)	)	PUNCT
ejpam-6458	263	4	,	,	PUNCT
ejpam-6458	263	5	any	any	DET
ejpam-6458	263	6	element	element	NOUN
ejpam-6458	263	7	x	x	SYM
ejpam-6458	263	8	∈	∈	PROPN
ejpam-6458	263	9	û0(g	û0(g	NOUN
ejpam-6458	263	10	)	)	PUNCT
ejpam-6458	263	11	can	can	AUX
ejpam-6458	263	12	be	be	AUX
ejpam-6458	263	13	expressed	express	VERB
ejpam-6458	263	14	as	as	ADP
ejpam-6458	263	15	a	a	DET
ejpam-6458	263	16	linear	linear	ADJ
ejpam-6458	263	17	combination	combination	NOUN
ejpam-6458	263	18	of	of	ADP
ejpam-6458	263	19	semi	semi	ADJ
ejpam-6458	263	20	-	-	ADJ
ejpam-6458	263	21	perfect	perfect	ADJ
ejpam-6458	263	22	elements	element	NOUN
ejpam-6458	263	23	.	.	PUNCT
ejpam-6458	264	1	we	we	PRON
ejpam-6458	264	2	need	need	VERB
ejpam-6458	264	3	to	to	PART
ejpam-6458	264	4	determine	determine	VERB
ejpam-6458	264	5	how	how	SCONJ
ejpam-6458	264	6	to	to	PART
ejpam-6458	264	7	multiply	multiply	VERB
ejpam-6458	264	8	any	any	DET
ejpam-6458	264	9	two	two	NUM
ejpam-6458	264	10	semi	semi	ADJ
ejpam-6458	264	11	-	-	ADJ
ejpam-6458	264	12	perfect	perfect	ADJ
ejpam-6458	264	13	monomials	monomial	NOUN
ejpam-6458	264	14	and	and	CCONJ
ejpam-6458	264	15	express	express	VERB
ejpam-6458	264	16	their	their	PRON
ejpam-6458	264	17	product	product	NOUN
ejpam-6458	264	18	as	as	ADP
ejpam-6458	264	19	a	a	DET
ejpam-6458	264	20	linear	linear	ADJ
ejpam-6458	264	21	combination	combination	NOUN
ejpam-6458	264	22	of	of	ADP
ejpam-6458	264	23	elements	element	NOUN
ejpam-6458	264	24	of	of	ADP
ejpam-6458	264	25	s(g	s(g	PROPN
ejpam-6458	264	26	)	)	PUNCT
ejpam-6458	264	27	.	.	PUNCT
ejpam-6458	265	1	if	if	SCONJ
ejpam-6458	265	2	an	an	DET
ejpam-6458	265	3	element	element	NOUN
ejpam-6458	265	4	x	x	SYM
ejpam-6458	265	5	∈	∈	PROPN
ejpam-6458	265	6	û0(g	û0(g	NOUN
ejpam-6458	265	7	)	)	PUNCT
ejpam-6458	265	8	is	be	AUX
ejpam-6458	265	9	expressed	express	VERB
ejpam-6458	265	10	as	as	ADP
ejpam-6458	265	11	a	a	DET
ejpam-6458	265	12	linear	linear	ADJ
ejpam-6458	265	13	combination	combination	NOUN
ejpam-6458	265	14	of	of	ADP
ejpam-6458	265	15	semi	semi	ADJ
ejpam-6458	265	16	-	-	ADJ
ejpam-6458	265	17	perfect	perfect	ADJ
ejpam-6458	265	18	monomials	monomial	NOUN
ejpam-6458	265	19	,	,	PUNCT
ejpam-6458	265	20	we	we	PRON
ejpam-6458	265	21	say	say	VERB
ejpam-6458	265	22	that	that	SCONJ
ejpam-6458	265	23	x	x	PRON
ejpam-6458	265	24	is	be	AUX
ejpam-6458	265	25	in	in	ADP
ejpam-6458	265	26	a	a	DET
ejpam-6458	265	27	normal	normal	ADJ
ejpam-6458	265	28	form	form	NOUN
ejpam-6458	265	29	,	,	PUNCT
ejpam-6458	265	30	denoted	denote	VERB
ejpam-6458	265	31	by	by	ADP
ejpam-6458	265	32	n	n	PROPN
ejpam-6458	265	33	(	(	PUNCT
ejpam-6458	265	34	x	x	NOUN
ejpam-6458	265	35	)	)	PUNCT
ejpam-6458	265	36	.	.	PUNCT
ejpam-6458	266	1	the	the	DET
ejpam-6458	266	2	process	process	NOUN
ejpam-6458	266	3	of	of	ADP
ejpam-6458	266	4	converting	convert	VERB
ejpam-6458	266	5	a	a	DET
ejpam-6458	266	6	given	give	VERB
ejpam-6458	266	7	element	element	NOUN
ejpam-6458	266	8	into	into	ADP
ejpam-6458	266	9	its	its	PRON
ejpam-6458	266	10	normal	normal	ADJ
ejpam-6458	266	11	form	form	NOUN
ejpam-6458	266	12	is	be	AUX
ejpam-6458	266	13	called	call	VERB
ejpam-6458	266	14	normalization	normalization	NOUN
ejpam-6458	266	15	.	.	PUNCT
ejpam-6458	267	1	define	define	VERB
ejpam-6458	267	2	the	the	DET
ejpam-6458	267	3	set	set	NOUN
ejpam-6458	267	4	of	of	ADP
ejpam-6458	267	5	relations	relation	NOUN
ejpam-6458	267	6	as	as	SCONJ
ejpam-6458	267	7	follows	follow	VERB
ejpam-6458	267	8	:	:	PUNCT
ejpam-6458	267	9	k	k	X
ejpam-6458	267	10	′	′	NUM
ejpam-6458	268	1	=	=	SYM
ejpam-6458	268	2	{	{	PUNCT
ejpam-6458	268	3	ci1ci2	ci1ci2	PROPN
ejpam-6458	268	4	·	·	PUNCT
ejpam-6458	268	5	·	·	PUNCT
ejpam-6458	268	6	·	·	PUNCT
ejpam-6458	268	7	cim	cim	PROPN
ejpam-6458	268	8	−n	−n	PROPN
ejpam-6458	268	9	(	(	PUNCT
ejpam-6458	268	10	ci1ci2	ci1ci2	PROPN
ejpam-6458	268	11	·	·	PUNCT
ejpam-6458	268	12	·	·	PUNCT
ejpam-6458	268	13	·	·	PUNCT
ejpam-6458	268	14	cim	cim	PROPN
ejpam-6458	268	15	)	)	PUNCT
ejpam-6458	268	16	|m	|m	VERB
ejpam-6458	268	17	≤	≤	ADJ
ejpam-6458	268	18	d0	d0	NOUN
ejpam-6458	268	19	,	,	PUNCT
ejpam-6458	268	20	ci	ci	PROPN
ejpam-6458	268	21	∈	∈	PROPN
ejpam-6458	268	22	j(g	j(g	PROPN
ejpam-6458	268	23	)	)	PUNCT
ejpam-6458	268	24	}	}	PUNCT
ejpam-6458	268	25	.	.	PUNCT
ejpam-6458	269	1	(	(	PUNCT
ejpam-6458	269	2	2.4	2.4	NUM
ejpam-6458	269	3	)	)	PUNCT
ejpam-6458	269	4	additionally	additionally	ADV
ejpam-6458	269	5	,	,	PUNCT
ejpam-6458	269	6	define	define	VERB
ejpam-6458	269	7	the	the	DET
ejpam-6458	269	8	length	length	NOUN
ejpam-6458	269	9	function	function	NOUN
ejpam-6458	269	10	on	on	ADP
ejpam-6458	269	11	k	k	PROPN
ejpam-6458	269	12	′	′	NUM
ejpam-6458	270	1	⊆	⊆	NUM
ejpam-6458	270	2	k	k	NOUN
ejpam-6458	270	3	as	as	ADP
ejpam-6458	270	4	:	:	PUNCT
ejpam-6458	270	5	len(ci1	len(ci1	X
ejpam-6458	270	6	·	·	PUNCT
ejpam-6458	270	7	·	·	PUNCT
ejpam-6458	270	8	·	·	PUNCT
ejpam-6458	270	9	cim	cim	PROPN
ejpam-6458	270	10	−n	−n	PROPN
ejpam-6458	270	11	(	(	PUNCT
ejpam-6458	270	12	ci1	ci1	PROPN
ejpam-6458	270	13	·	·	PUNCT
ejpam-6458	270	14	·	·	PUNCT
ejpam-6458	270	15	·	·	PUNCT
ejpam-6458	270	16	cim	cim	NOUN
ejpam-6458	270	17	)	)	PUNCT
ejpam-6458	270	18	)	)	PUNCT
ejpam-6458	271	1	=	=	PUNCT
ejpam-6458	271	2	m.	m.	NOUN
ejpam-6458	271	3	thus	thus	ADV
ejpam-6458	271	4	,	,	PUNCT
ejpam-6458	271	5	k	k	PROPN
ejpam-6458	271	6	′	′	NOUN
ejpam-6458	271	7	is	be	AUX
ejpam-6458	271	8	the	the	DET
ejpam-6458	271	9	set	set	NOUN
ejpam-6458	271	10	of	of	ADP
ejpam-6458	271	11	all	all	DET
ejpam-6458	271	12	relations	relation	NOUN
ejpam-6458	271	13	with	with	ADP
ejpam-6458	271	14	length	length	NOUN
ejpam-6458	271	15	less	less	ADV
ejpam-6458	271	16	or	or	CCONJ
ejpam-6458	271	17	equal	equal	ADJ
ejpam-6458	271	18	to	to	ADP
ejpam-6458	271	19	d0	d0	NOUN
ejpam-6458	271	20	.	.	PUNCT
ejpam-6458	272	1	we	we	PRON
ejpam-6458	272	2	are	be	AUX
ejpam-6458	272	3	now	now	ADV
ejpam-6458	272	4	ready	ready	ADJ
ejpam-6458	272	5	to	to	PART
ejpam-6458	272	6	state	state	VERB
ejpam-6458	272	7	the	the	DET
ejpam-6458	272	8	main	main	ADJ
ejpam-6458	272	9	result	result	NOUN
ejpam-6458	272	10	regarding	regard	VERB
ejpam-6458	272	11	the	the	DET
ejpam-6458	272	12	cartan	cartan	ADJ
ejpam-6458	272	13	centralizers	centralizer	NOUN
ejpam-6458	272	14	of	of	ADP
ejpam-6458	272	15	the	the	DET
ejpam-6458	272	16	universal	universal	ADJ
ejpam-6458	272	17	enveloping	enveloping	NOUN
ejpam-6458	272	18	algebras	algebra	NOUN
ejpam-6458	272	19	.	.	PUNCT
ejpam-6458	273	1	theorem	theorem	VERB
ejpam-6458	273	2	2.5	2.5	NUM
ejpam-6458	273	3	.	.	PUNCT
ejpam-6458	274	1	the	the	DET
ejpam-6458	274	2	ideal	ideal	NOUN
ejpam-6458	274	3	of	of	ADP
ejpam-6458	274	4	relations	relation	NOUN
ejpam-6458	274	5	k	k	PROPN
ejpam-6458	274	6	is	be	AUX
ejpam-6458	274	7	generated	generate	VERB
ejpam-6458	274	8	by	by	ADP
ejpam-6458	274	9	the	the	DET
ejpam-6458	274	10	set	set	PROPN
ejpam-6458	274	11	k	k	PROPN
ejpam-6458	274	12	′.	′.	PROPN
ejpam-6458	274	13	proof	proof	NOUN
ejpam-6458	274	14	.	.	PUNCT
ejpam-6458	275	1	we	we	PRON
ejpam-6458	275	2	prove	prove	VERB
ejpam-6458	275	3	that	that	SCONJ
ejpam-6458	275	4	the	the	DET
ejpam-6458	275	5	product	product	NOUN
ejpam-6458	275	6	of	of	ADP
ejpam-6458	275	7	semi	semi	ADJ
ejpam-6458	275	8	-	-	ADJ
ejpam-6458	275	9	perfect	perfect	ADJ
ejpam-6458	275	10	elements	element	NOUN
ejpam-6458	275	11	can	can	AUX
ejpam-6458	275	12	be	be	AUX
ejpam-6458	275	13	expressed	express	VERB
ejpam-6458	275	14	as	as	ADP
ejpam-6458	275	15	a	a	DET
ejpam-6458	275	16	linear	linear	ADJ
ejpam-6458	275	17	combination	combination	NOUN
ejpam-6458	275	18	of	of	ADP
ejpam-6458	275	19	semi	semi	ADJ
ejpam-6458	275	20	-	-	ADJ
ejpam-6458	275	21	perfect	perfect	ADJ
ejpam-6458	275	22	elements	element	NOUN
ejpam-6458	275	23	using	use	VERB
ejpam-6458	275	24	only	only	ADV
ejpam-6458	275	25	the	the	DET
ejpam-6458	275	26	relations	relation	NOUN
ejpam-6458	275	27	k	k	PROPN
ejpam-6458	275	28	′.	′.	PROPN
ejpam-6458	275	29	this	this	PRON
ejpam-6458	275	30	follows	follow	VERB
ejpam-6458	275	31	from	from	ADP
ejpam-6458	275	32	the	the	DET
ejpam-6458	275	33	reduction	reduction	NOUN
ejpam-6458	275	34	algorithm	algorithm	NOUN
ejpam-6458	275	35	described	describe	VERB
ejpam-6458	275	36	below	below	ADV
ejpam-6458	275	37	.	.	PUNCT
ejpam-6458	276	1	we	we	PRON
ejpam-6458	276	2	will	will	AUX
ejpam-6458	276	3	show	show	VERB
ejpam-6458	276	4	that	that	SCONJ
ejpam-6458	276	5	any	any	DET
ejpam-6458	276	6	monomial	monomial	NOUN
ejpam-6458	276	7	,	,	PUNCT
ejpam-6458	276	8	written	write	VERB
ejpam-6458	276	9	as	as	ADP
ejpam-6458	276	10	product	product	NOUN
ejpam-6458	276	11	of	of	ADP
ejpam-6458	276	12	perfect	perfect	ADJ
ejpam-6458	276	13	monomials	monomial	NOUN
ejpam-6458	276	14	in	in	ADP
ejpam-6458	276	15	arbitrary	arbitrary	ADJ
ejpam-6458	276	16	order	order	NOUN
ejpam-6458	276	17	,	,	PUNCT
ejpam-6458	276	18	can	can	AUX
ejpam-6458	276	19	be	be	AUX
ejpam-6458	276	20	transformed	transform	VERB
ejpam-6458	276	21	into	into	ADP
ejpam-6458	276	22	a	a	DET
ejpam-6458	276	23	linear	linear	ADJ
ejpam-6458	276	24	combination	combination	NOUN
ejpam-6458	276	25	of	of	ADP
ejpam-6458	276	26	semi	semi	ADJ
ejpam-6458	276	27	-	-	ADJ
ejpam-6458	276	28	perfect	perfect	ADJ
ejpam-6458	276	29	monomial	monomial	NOUN
ejpam-6458	276	30	.	.	PUNCT
ejpam-6458	277	1	m.	m.	NOUN
ejpam-6458	277	2	andelić	andelić	PROPN
ejpam-6458	277	3	et	et	PROPN
ejpam-6458	277	4	al	al	PROPN
ejpam-6458	277	5	.	.	PUNCT
ejpam-6458	277	6	/	/	SYM
ejpam-6458	277	7	eur	eur	PROPN
ejpam-6458	277	8	.	.	PUNCT
ejpam-6458	278	1	j.	j.	PROPN
ejpam-6458	278	2	pure	pure	PROPN
ejpam-6458	278	3	appl	appl	PROPN
ejpam-6458	278	4	.	.	PROPN
ejpam-6458	278	5	math	math	PROPN
ejpam-6458	278	6	,	,	PUNCT
ejpam-6458	278	7	18	18	NUM
ejpam-6458	278	8	(	(	PUNCT
ejpam-6458	278	9	3	3	NUM
ejpam-6458	278	10	)	)	PUNCT
ejpam-6458	278	11	(	(	PUNCT
ejpam-6458	278	12	2025	2025	NUM
ejpam-6458	278	13	)	)	PUNCT
ejpam-6458	278	14	,	,	PUNCT
ejpam-6458	278	15	6458	6458	NUM
ejpam-6458	278	16	7	7	NUM
ejpam-6458	278	17	of	of	ADP
ejpam-6458	278	18	21	21	NUM
ejpam-6458	278	19	let	let	VERB
ejpam-6458	278	20	x	x	PUNCT
ejpam-6458	278	21	=	=	PUNCT
ejpam-6458	278	22	a1a2	a1a2	X
ejpam-6458	278	23	·	·	PUNCT
ejpam-6458	278	24	·	·	PUNCT
ejpam-6458	278	25	·	·	PUNCT
ejpam-6458	278	26	am	be	AUX
ejpam-6458	278	27	∈	∈	PROPN
ejpam-6458	278	28	q	q	X
ejpam-6458	278	29	(	(	PUNCT
ejpam-6458	278	30	i	i	NOUN
ejpam-6458	278	31	)	)	PUNCT
ejpam-6458	278	32	0	0	PUNCT
ejpam-6458	279	1	(	(	PUNCT
ejpam-6458	279	2	g	g	NOUN
ejpam-6458	279	3	)	)	PUNCT
ejpam-6458	279	4	be	be	AUX
ejpam-6458	279	5	a	a	DET
ejpam-6458	279	6	monomial	monomial	NOUN
ejpam-6458	279	7	of	of	ADP
ejpam-6458	279	8	degree	degree	NOUN
ejpam-6458	279	9	i	i	PRON
ejpam-6458	279	10	that	that	PRON
ejpam-6458	279	11	is	be	AUX
ejpam-6458	279	12	a	a	DET
ejpam-6458	279	13	product	product	NOUN
ejpam-6458	279	14	of	of	ADP
ejpam-6458	279	15	perfect	perfect	ADJ
ejpam-6458	279	16	elements	element	NOUN
ejpam-6458	279	17	.	.	PUNCT
ejpam-6458	280	1	by	by	ADP
ejpam-6458	280	2	lemmas	lemmas	PROPN
ejpam-6458	280	3	2.1	2.1	NUM
ejpam-6458	280	4	and	and	CCONJ
ejpam-6458	280	5	2.4	2.4	NUM
ejpam-6458	280	6	,	,	PUNCT
ejpam-6458	280	7	there	there	PRON
ejpam-6458	280	8	exists	exist	VERB
ejpam-6458	280	9	a	a	DET
ejpam-6458	280	10	semi	semi	ADJ
ejpam-6458	280	11	-	-	ADJ
ejpam-6458	280	12	perfect	perfect	ADJ
ejpam-6458	280	13	element	element	NOUN
ejpam-6458	280	14	y	y	PROPN
ejpam-6458	280	15	=	=	SYM
ejpam-6458	280	16	b1b2	b1b2	PROPN
ejpam-6458	280	17	·	·	PUNCT
ejpam-6458	280	18	·	·	PUNCT
ejpam-6458	280	19	·	·	PUNCT
ejpam-6458	281	1	bn	bn	X
ejpam-6458	281	2	∈	∈	PROPN
ejpam-6458	281	3	q	q	X
ejpam-6458	281	4	(	(	PUNCT
ejpam-6458	281	5	i	i	NOUN
ejpam-6458	281	6	)	)	PUNCT
ejpam-6458	281	7	0	0	PUNCT
ejpam-6458	282	1	(	(	PUNCT
ejpam-6458	282	2	g	g	NOUN
ejpam-6458	282	3	)	)	PUNCT
ejpam-6458	282	4	,	,	PUNCT
ejpam-6458	282	5	such	such	ADJ
ejpam-6458	282	6	that	that	DET
ejpam-6458	282	7	t1(x	t1(x	NOUN
ejpam-6458	282	8	)	)	PUNCT
ejpam-6458	283	1	=	=	SYM
ejpam-6458	284	1	t1(y	t1(y	NUM
ejpam-6458	284	2	)	)	PUNCT
ejpam-6458	285	1	and	and	CCONJ
ejpam-6458	285	2	x	x	SYM
ejpam-6458	285	3	−	−	PROPN
ejpam-6458	285	4	y	y	PROPN
ejpam-6458	285	5	∈	∈	PROPN
ejpam-6458	285	6	û	û	X
ejpam-6458	285	7	(	(	PUNCT
ejpam-6458	285	8	i−1	i−1	PROPN
ejpam-6458	285	9	)	)	PUNCT
ejpam-6458	285	10	0	0	NUM
ejpam-6458	285	11	(	(	PUNCT
ejpam-6458	285	12	g	g	NOUN
ejpam-6458	285	13	)	)	PUNCT
ejpam-6458	285	14	.	.	PUNCT
ejpam-6458	286	1	the	the	DET
ejpam-6458	286	2	proof	proof	NOUN
ejpam-6458	286	3	proceeds	proceed	VERB
ejpam-6458	286	4	by	by	ADP
ejpam-6458	286	5	induction	induction	NOUN
ejpam-6458	286	6	on	on	ADP
ejpam-6458	286	7	the	the	DET
ejpam-6458	286	8	degree	degree	NOUN
ejpam-6458	286	9	of	of	ADP
ejpam-6458	286	10	the	the	DET
ejpam-6458	286	11	monomials	monomial	NOUN
ejpam-6458	286	12	.	.	PUNCT
ejpam-6458	287	1	the	the	DET
ejpam-6458	287	2	statement	statement	NOUN
ejpam-6458	287	3	is	be	AUX
ejpam-6458	287	4	obvious	obvious	ADJ
ejpam-6458	287	5	for	for	ADP
ejpam-6458	287	6	the	the	DET
ejpam-6458	287	7	case	case	NOUN
ejpam-6458	287	8	i	i	PRON
ejpam-6458	287	9	=	=	NOUN
ejpam-6458	288	1	1	1	X
ejpam-6458	288	2	.	.	X
ejpam-6458	288	3	assume	assume	VERB
ejpam-6458	288	4	that	that	SCONJ
ejpam-6458	288	5	the	the	DET
ejpam-6458	288	6	statement	statement	NOUN
ejpam-6458	288	7	holds	hold	VERB
ejpam-6458	288	8	for	for	ADP
ejpam-6458	288	9	all	all	DET
ejpam-6458	288	10	elements	element	NOUN
ejpam-6458	288	11	in	in	ADP
ejpam-6458	288	12	û	û	PROPN
ejpam-6458	288	13	(	(	PUNCT
ejpam-6458	288	14	i−1	i−1	PROPN
ejpam-6458	288	15	)	)	PUNCT
ejpam-6458	288	16	0	0	NUM
ejpam-6458	289	1	(	(	PUNCT
ejpam-6458	289	2	g	g	NOUN
ejpam-6458	289	3	)	)	PUNCT
ejpam-6458	289	4	,	,	PUNCT
ejpam-6458	289	5	that	that	ADV
ejpam-6458	289	6	is	is	ADV
ejpam-6458	289	7	,	,	PUNCT
ejpam-6458	289	8	any	any	DET
ejpam-6458	289	9	such	such	ADJ
ejpam-6458	289	10	element	element	NOUN
ejpam-6458	289	11	can	can	AUX
ejpam-6458	289	12	be	be	AUX
ejpam-6458	289	13	transformed	transform	VERB
ejpam-6458	289	14	into	into	ADP
ejpam-6458	289	15	the	the	DET
ejpam-6458	289	16	normal	normal	ADJ
ejpam-6458	289	17	form	form	NOUN
ejpam-6458	289	18	.	.	PUNCT
ejpam-6458	290	1	we	we	PRON
ejpam-6458	290	2	will	will	AUX
ejpam-6458	290	3	show	show	VERB
ejpam-6458	290	4	that	that	SCONJ
ejpam-6458	290	5	,	,	PUNCT
ejpam-6458	290	6	using	use	VERB
ejpam-6458	290	7	only	only	ADV
ejpam-6458	290	8	relations	relation	NOUN
ejpam-6458	290	9	k	k	PROPN
ejpam-6458	290	10	′	′	NOUN
ejpam-6458	290	11	,	,	PUNCT
ejpam-6458	290	12	x	x	PRON
ejpam-6458	290	13	can	can	AUX
ejpam-6458	290	14	be	be	AUX
ejpam-6458	290	15	transformed	transform	VERB
ejpam-6458	290	16	into	into	ADP
ejpam-6458	290	17	a	a	DET
ejpam-6458	290	18	sum	sum	NOUN
ejpam-6458	290	19	x	x	PUNCT
ejpam-6458	291	1	=	=	PUNCT
ejpam-6458	291	2	y	y	PROPN
ejpam-6458	291	3	+	+	PROPN
ejpam-6458	291	4	y1	y1	PROPN
ejpam-6458	291	5	,	,	PUNCT
ejpam-6458	291	6	where	where	SCONJ
ejpam-6458	291	7	y	y	PROPN
ejpam-6458	291	8	is	be	AUX
ejpam-6458	291	9	above	above	ADP
ejpam-6458	291	10	semi	semi	ADJ
ejpam-6458	291	11	-	-	ADJ
ejpam-6458	291	12	perfect	perfect	ADJ
ejpam-6458	291	13	monomial	monomial	NOUN
ejpam-6458	291	14	and	and	CCONJ
ejpam-6458	291	15	y1	y1	NOUN
ejpam-6458	291	16	∈	∈	PROPN
ejpam-6458	291	17	û	û	X
ejpam-6458	291	18	(	(	PUNCT
ejpam-6458	291	19	i−1	i−1	PROPN
ejpam-6458	291	20	)	)	PUNCT
ejpam-6458	291	21	0	0	NUM
ejpam-6458	292	1	(	(	PUNCT
ejpam-6458	292	2	g	g	NOUN
ejpam-6458	292	3	)	)	PUNCT
ejpam-6458	292	4	.	.	PUNCT
ejpam-6458	293	1	denote	denote	VERB
ejpam-6458	293	2	y	y	PROPN
ejpam-6458	293	3	′	′	NUM
ejpam-6458	293	4	=	=	SYM
ejpam-6458	293	5	b2	b2	NOUN
ejpam-6458	293	6	·	·	PUNCT
ejpam-6458	293	7	·	·	PUNCT
ejpam-6458	293	8	·	·	PUNCT
ejpam-6458	294	1	bn	bn	X
ejpam-6458	294	2	.	.	PUNCT
ejpam-6458	294	3	there	there	PRON
ejpam-6458	294	4	are	be	VERB
ejpam-6458	294	5	two	two	NUM
ejpam-6458	294	6	cases	case	NOUN
ejpam-6458	294	7	to	to	PART
ejpam-6458	294	8	consider	consider	VERB
ejpam-6458	294	9	.	.	PUNCT
ejpam-6458	295	1	1	1	X
ejpam-6458	295	2	.	.	X
ejpam-6458	295	3	let	let	VERB
ejpam-6458	295	4	b1	b1	PROPN
ejpam-6458	295	5	∈	∈	PROPN
ejpam-6458	295	6	g0	g0	PROPN
ejpam-6458	295	7	.	.	PUNCT
ejpam-6458	296	1	since	since	SCONJ
ejpam-6458	296	2	l0(x	l0(x	NOUN
ejpam-6458	296	3	)	)	PUNCT
ejpam-6458	296	4	=	=	SYM
ejpam-6458	296	5	l0(y	l0(y	X
ejpam-6458	296	6	)	)	PUNCT
ejpam-6458	296	7	,	,	PUNCT
ejpam-6458	296	8	by	by	ADP
ejpam-6458	296	9	lemma	lemma	PROPN
ejpam-6458	296	10	2.4	2.4	NUM
ejpam-6458	296	11	,	,	PUNCT
ejpam-6458	296	12	it	it	PRON
ejpam-6458	296	13	follows	follow	VERB
ejpam-6458	296	14	that	that	SCONJ
ejpam-6458	296	15	b1	b1	NOUN
ejpam-6458	296	16	=	=	PUNCT
ejpam-6458	296	17	as	as	ADP
ejpam-6458	296	18	for	for	ADP
ejpam-6458	296	19	some	some	DET
ejpam-6458	296	20	1	1	NUM
ejpam-6458	296	21	≤	≤	NUM
ejpam-6458	296	22	s	s	PART
ejpam-6458	296	23	≤	≤	NOUN
ejpam-6458	296	24	m.	m.	NOUN
ejpam-6458	296	25	as	as	SCONJ
ejpam-6458	296	26	b1	b1	NOUN
ejpam-6458	296	27	belongs	belong	VERB
ejpam-6458	296	28	to	to	ADP
ejpam-6458	296	29	the	the	DET
ejpam-6458	296	30	center	center	NOUN
ejpam-6458	296	31	of	of	ADP
ejpam-6458	296	32	û0(g	û0(g	NOUN
ejpam-6458	296	33	)	)	PUNCT
ejpam-6458	296	34	,	,	PUNCT
ejpam-6458	296	35	we	we	PRON
ejpam-6458	296	36	can	can	AUX
ejpam-6458	296	37	rewrite	rewrite	VERB
ejpam-6458	296	38	x	x	PUNCT
ejpam-6458	296	39	as	as	ADP
ejpam-6458	296	40	x	x	X
ejpam-6458	296	41	=	=	SYM
ejpam-6458	296	42	b1a1a2	b1a1a2	PROPN
ejpam-6458	296	43	·	·	PUNCT
ejpam-6458	296	44	·	·	PUNCT
ejpam-6458	296	45	·	·	PUNCT
ejpam-6458	297	1	as−1as+1	as−1as+1	CCONJ
ejpam-6458	297	2	·	·	PUNCT
ejpam-6458	297	3	·	·	PUNCT
ejpam-6458	297	4	·	·	PUNCT
ejpam-6458	297	5	am	be	AUX
ejpam-6458	297	6	=	=	PUNCT
ejpam-6458	297	7	b1x	b1x	PROPN
ejpam-6458	297	8	′.	′.	NOUN
ejpam-6458	297	9	thus	thus	ADV
ejpam-6458	297	10	,	,	PUNCT
ejpam-6458	297	11	we	we	PRON
ejpam-6458	297	12	obtain	obtain	VERB
ejpam-6458	297	13	x	x	X
ejpam-6458	298	1	=	=	PUNCT
ejpam-6458	298	2	y	y	PROPN
ejpam-6458	298	3	+	+	CCONJ
ejpam-6458	298	4	b1(x	b1(x	NOUN
ejpam-6458	299	1	′	′	NUM
ejpam-6458	299	2	−	−	NOUN
ejpam-6458	300	1	y	y	PROPN
ejpam-6458	300	2	′	′	NUM
ejpam-6458	300	3	)	)	PUNCT
ejpam-6458	300	4	.	.	PUNCT
ejpam-6458	301	1	it	it	PRON
ejpam-6458	301	2	is	be	AUX
ejpam-6458	301	3	easy	easy	ADJ
ejpam-6458	301	4	to	to	PART
ejpam-6458	301	5	see	see	VERB
ejpam-6458	301	6	that	that	PRON
ejpam-6458	301	7	t1(x	t1(x	PROPN
ejpam-6458	301	8	′	′	NUM
ejpam-6458	301	9	)	)	PUNCT
ejpam-6458	302	1	=	=	SYM
ejpam-6458	302	2	t1(y	t1(y	NUM
ejpam-6458	302	3	′	′	NUM
ejpam-6458	302	4	)	)	PUNCT
ejpam-6458	302	5	,	,	PUNCT
ejpam-6458	302	6	and	and	CCONJ
ejpam-6458	302	7	y	y	PROPN
ejpam-6458	302	8	′	′	NOUN
ejpam-6458	302	9	is	be	AUX
ejpam-6458	302	10	semi	semi	ADJ
ejpam-6458	302	11	-	-	ADJ
ejpam-6458	302	12	perfect	perfect	ADJ
ejpam-6458	302	13	.	.	PUNCT
ejpam-6458	303	1	by	by	ADP
ejpam-6458	303	2	the	the	DET
ejpam-6458	303	3	induction	induction	NOUN
ejpam-6458	303	4	hypothesis	hypothesis	NOUN
ejpam-6458	303	5	,	,	PUNCT
ejpam-6458	303	6	we	we	PRON
ejpam-6458	303	7	can	can	AUX
ejpam-6458	303	8	apply	apply	VERB
ejpam-6458	303	9	our	our	PRON
ejpam-6458	303	10	algorithm	algorithm	NOUN
ejpam-6458	303	11	to	to	ADP
ejpam-6458	303	12	the	the	DET
ejpam-6458	303	13	pair	pair	NOUN
ejpam-6458	303	14	x	x	NOUN
ejpam-6458	303	15	′	′	NOUN
ejpam-6458	303	16	,	,	PUNCT
ejpam-6458	303	17	y	y	PROPN
ejpam-6458	303	18	′.	′.	NOUN
ejpam-6458	303	19	this	this	PRON
ejpam-6458	303	20	gives	give	VERB
ejpam-6458	303	21	(	(	PUNCT
ejpam-6458	303	22	x	x	PART
ejpam-6458	303	23	′−y	′−y	NOUN
ejpam-6458	303	24	′	′	NUM
ejpam-6458	303	25	)	)	PUNCT
ejpam-6458	304	1	=	=	PUNCT
ejpam-6458	304	2	x	x	X
ejpam-6458	304	3	′′	′′	NOUN
ejpam-6458	304	4	∈	∈	PROPN
ejpam-6458	304	5	û	û	NUM
ejpam-6458	304	6	(	(	PUNCT
ejpam-6458	304	7	i−2	i−2	PROPN
ejpam-6458	304	8	)	)	PUNCT
ejpam-6458	304	9	0	0	PUNCT
ejpam-6458	304	10	,	,	PUNCT
ejpam-6458	304	11	implying	imply	VERB
ejpam-6458	304	12	that	that	SCONJ
ejpam-6458	304	13	b1x	b1x	PROPN
ejpam-6458	304	14	′′	′′	PROPN
ejpam-6458	304	15	∈	∈	PROPN
ejpam-6458	304	16	û	û	NUM
ejpam-6458	304	17	(	(	PUNCT
ejpam-6458	304	18	i−1	i−1	PROPN
ejpam-6458	304	19	)	)	PUNCT
ejpam-6458	304	20	0	0	NUM
ejpam-6458	304	21	.	.	PUNCT
ejpam-6458	305	1	therefore	therefore	ADV
ejpam-6458	305	2	,	,	PUNCT
ejpam-6458	305	3	the	the	DET
ejpam-6458	305	4	statement	statement	NOUN
ejpam-6458	305	5	follows	follow	VERB
ejpam-6458	305	6	by	by	ADP
ejpam-6458	305	7	the	the	DET
ejpam-6458	305	8	induction	induction	NOUN
ejpam-6458	305	9	hypothesis	hypothesis	NOUN
ejpam-6458	305	10	.	.	PUNCT
ejpam-6458	306	1	2	2	X
ejpam-6458	306	2	.	.	X
ejpam-6458	306	3	let	let	VERB
ejpam-6458	306	4	b1	b1	PROPN
ejpam-6458	306	5	∈	∈	PROPN
ejpam-6458	306	6	j0(g	j0(g	NOUN
ejpam-6458	306	7	)	)	PUNCT
ejpam-6458	306	8	.	.	PUNCT
ejpam-6458	307	1	since	since	SCONJ
ejpam-6458	307	2	l1(x	l1(x	NOUN
ejpam-6458	307	3	)	)	PUNCT
ejpam-6458	307	4	=	=	SYM
ejpam-6458	307	5	l1(y	l1(y	PROPN
ejpam-6458	307	6	)	)	PUNCT
ejpam-6458	307	7	,	,	PUNCT
ejpam-6458	307	8	it	it	PRON
ejpam-6458	307	9	follows	follow	VERB
ejpam-6458	307	10	that	that	PRON
ejpam-6458	307	11	l1(b1	l1(b1	VERB
ejpam-6458	307	12	)	)	PUNCT
ejpam-6458	307	13	is	be	AUX
ejpam-6458	307	14	a	a	DET
ejpam-6458	307	15	sublist	sublist	NOUN
ejpam-6458	307	16	of	of	ADP
ejpam-6458	307	17	l1(x	l1(x	NOUN
ejpam-6458	307	18	)	)	PUNCT
ejpam-6458	307	19	.	.	PUNCT
ejpam-6458	308	1	let	let	VERB
ejpam-6458	308	2	{	{	PUNCT
ejpam-6458	308	3	z1	z1	ADJ
ejpam-6458	308	4	,	,	PUNCT
ejpam-6458	308	5	z2	z2	PROPN
ejpam-6458	308	6	,	,	PUNCT
ejpam-6458	308	7	.	.	PUNCT
ejpam-6458	308	8	.	.	PUNCT
ejpam-6458	309	1	.	.	PUNCT
ejpam-6458	310	1	,	,	PUNCT
ejpam-6458	310	2	zt	zt	PROPN
ejpam-6458	310	3	}	}	PUNCT
ejpam-6458	310	4	⊂	⊂	PROPN
ejpam-6458	310	5	{	{	PUNCT
ejpam-6458	310	6	a1	a1	PROPN
ejpam-6458	310	7	,	,	PUNCT
ejpam-6458	310	8	a2	a2	PROPN
ejpam-6458	310	9	,	,	PUNCT
ejpam-6458	310	10	.	.	PUNCT
ejpam-6458	310	11	.	.	PUNCT
ejpam-6458	311	1	.	.	PUNCT
ejpam-6458	312	1	,	,	PUNCT
ejpam-6458	312	2	am	be	AUX
ejpam-6458	312	3	}	}	PUNCT
ejpam-6458	312	4	be	be	AUX
ejpam-6458	312	5	a	a	DET
ejpam-6458	312	6	minimal	minimal	ADJ
ejpam-6458	312	7	set	set	NOUN
ejpam-6458	312	8	of	of	ADP
ejpam-6458	312	9	perfect	perfect	ADJ
ejpam-6458	312	10	monomials	monomial	NOUN
ejpam-6458	312	11	such	such	ADJ
ejpam-6458	312	12	that	that	DET
ejpam-6458	312	13	l1(b1	l1(b1	NOUN
ejpam-6458	312	14	)	)	PUNCT
ejpam-6458	312	15	⊏	⊏	PROPN
ejpam-6458	312	16	l1(z1z2	l1(z1z2	X
ejpam-6458	312	17	·	·	PUNCT
ejpam-6458	312	18	·	·	PUNCT
ejpam-6458	312	19	·	·	PUNCT
ejpam-6458	313	1	zt	zt	X
ejpam-6458	313	2	)	)	PUNCT
ejpam-6458	313	3	.	.	PUNCT
ejpam-6458	314	1	set	set	VERB
ejpam-6458	314	2	z	z	PROPN
ejpam-6458	314	3	=	=	PUNCT
ejpam-6458	314	4	z1z2	z1z2	X
ejpam-6458	314	5	·	·	PUNCT
ejpam-6458	314	6	·	·	PUNCT
ejpam-6458	314	7	·	·	PUNCT
ejpam-6458	315	1	zt	zt	X
ejpam-6458	315	2	.	.	PROPN
ejpam-6458	316	1	since	since	SCONJ
ejpam-6458	316	2	the	the	DET
ejpam-6458	316	3	cardinality	cardinality	NOUN
ejpam-6458	316	4	of	of	ADP
ejpam-6458	316	5	any	any	DET
ejpam-6458	316	6	indecomposable	indecomposable	ADJ
ejpam-6458	316	7	list	list	NOUN
ejpam-6458	316	8	is	be	AUX
ejpam-6458	316	9	bounded	bound	VERB
ejpam-6458	316	10	by	by	ADP
ejpam-6458	316	11	d0	d0	NOUN
ejpam-6458	316	12	,	,	PUNCT
ejpam-6458	316	13	we	we	PRON
ejpam-6458	316	14	have	have	VERB
ejpam-6458	316	15	t	t	NOUN
ejpam-6458	316	16	≤	≤	NUM
ejpam-6458	316	17	d0	d0	NOUN
ejpam-6458	316	18	.	.	PUNCT
ejpam-6458	317	1	using	use	VERB
ejpam-6458	317	2	the	the	DET
ejpam-6458	317	3	commutation	commutation	NOUN
ejpam-6458	317	4	relations	relation	NOUN
ejpam-6458	317	5	for	for	ADP
ejpam-6458	317	6	two	two	NUM
ejpam-6458	317	7	perfect	perfect	ADJ
ejpam-6458	317	8	elements	element	NOUN
ejpam-6458	317	9	we	we	PRON
ejpam-6458	317	10	can	can	AUX
ejpam-6458	317	11	transform	transform	VERB
ejpam-6458	317	12	x	x	PUNCT
ejpam-6458	317	13	into	into	ADP
ejpam-6458	317	14	the	the	DET
ejpam-6458	317	15	following	follow	VERB
ejpam-6458	317	16	form	form	NOUN
ejpam-6458	317	17	:	:	PUNCT
ejpam-6458	317	18	x	x	SYM
ejpam-6458	317	19	=	=	PUNCT
ejpam-6458	318	1	zx1	zx1	PROPN
ejpam-6458	318	2	+	+	NOUN
ejpam-6458	318	3	x2	x2	PROPN
ejpam-6458	318	4	,	,	PUNCT
ejpam-6458	318	5	where	where	SCONJ
ejpam-6458	318	6	t1(x	t1(x	NOUN
ejpam-6458	318	7	)	)	PUNCT
ejpam-6458	318	8	=	=	SYM
ejpam-6458	318	9	t1(zx1	t1(zx1	NOUN
ejpam-6458	318	10	)	)	PUNCT
ejpam-6458	318	11	and	and	CCONJ
ejpam-6458	318	12	x2	x2	PROPN
ejpam-6458	318	13	∈	∈	PROPN
ejpam-6458	318	14	û	û	X
ejpam-6458	318	15	(	(	PUNCT
ejpam-6458	318	16	i−1	i−1	PROPN
ejpam-6458	318	17	)	)	PUNCT
ejpam-6458	318	18	0	0	NUM
ejpam-6458	318	19	(	(	PUNCT
ejpam-6458	318	20	g	g	NOUN
ejpam-6458	318	21	)	)	PUNCT
ejpam-6458	318	22	.	.	PUNCT
ejpam-6458	319	1	denote	denote	VERB
ejpam-6458	319	2	n	n	PROPN
ejpam-6458	319	3	=	=	SYM
ejpam-6458	319	4	deg(z	deg(z	PROPN
ejpam-6458	319	5	)	)	PUNCT
ejpam-6458	319	6	,	,	PUNCT
ejpam-6458	319	7	then	then	ADV
ejpam-6458	319	8	deg(x1	deg(x1	NOUN
ejpam-6458	319	9	)	)	PUNCT
ejpam-6458	319	10	=	=	NOUN
ejpam-6458	320	1	i	i	PRON
ejpam-6458	320	2	−	−	VERB
ejpam-6458	320	3	n.	n.	VERB
ejpam-6458	320	4	there	there	PRON
ejpam-6458	320	5	exists	exist	VERB
ejpam-6458	320	6	a	a	DET
ejpam-6458	320	7	semi	semi	ADJ
ejpam-6458	320	8	-	-	ADJ
ejpam-6458	320	9	perfect	perfect	ADJ
ejpam-6458	320	10	monomial	monomial	ADJ
ejpam-6458	320	11	z1	z1	NOUN
ejpam-6458	321	1	such	such	ADJ
ejpam-6458	321	2	that	that	DET
ejpam-6458	321	3	t1(z	t1(z	NOUN
ejpam-6458	321	4	)	)	PUNCT
ejpam-6458	321	5	=	=	SYM
ejpam-6458	321	6	t1(z1	t1(z1	NOUN
ejpam-6458	321	7	)	)	PUNCT
ejpam-6458	321	8	.	.	PUNCT
ejpam-6458	322	1	since	since	SCONJ
ejpam-6458	322	2	t	t	NOUN
ejpam-6458	322	3	≤	≤	NUM
ejpam-6458	322	4	d0	d0	NOUN
ejpam-6458	322	5	,	,	PUNCT
ejpam-6458	322	6	we	we	PRON
ejpam-6458	322	7	can	can	AUX
ejpam-6458	322	8	apply	apply	VERB
ejpam-6458	322	9	the	the	DET
ejpam-6458	322	10	normalization	normalization	NOUN
ejpam-6458	322	11	process	process	NOUN
ejpam-6458	322	12	to	to	ADP
ejpam-6458	322	13	the	the	DET
ejpam-6458	322	14	monomial	monomial	PROPN
ejpam-6458	322	15	z.	z.	PROPN
ejpam-6458	323	1	we	we	PRON
ejpam-6458	323	2	obtain	obtain	VERB
ejpam-6458	323	3	z	z	NOUN
ejpam-6458	323	4	=	=	SYM
ejpam-6458	323	5	z1	z1	PROPN
ejpam-6458	323	6	+	+	CCONJ
ejpam-6458	323	7	z2	z2	PROPN
ejpam-6458	323	8	,	,	PUNCT
ejpam-6458	323	9	where	where	SCONJ
ejpam-6458	323	10	z2	z2	PROPN
ejpam-6458	323	11	∈	∈	PROPN
ejpam-6458	323	12	û	û	X
ejpam-6458	323	13	(	(	PUNCT
ejpam-6458	323	14	n−1	n−1	PROPN
ejpam-6458	323	15	)	)	PUNCT
ejpam-6458	323	16	0	0	NUM
ejpam-6458	324	1	(	(	PUNCT
ejpam-6458	324	2	g	g	NOUN
ejpam-6458	324	3	)	)	PUNCT
ejpam-6458	324	4	.	.	PUNCT
ejpam-6458	325	1	since	since	SCONJ
ejpam-6458	325	2	z1	z1	PROPN
ejpam-6458	325	3	is	be	AUX
ejpam-6458	325	4	a	a	DET
ejpam-6458	325	5	semi	semi	ADJ
ejpam-6458	325	6	-	-	ADJ
ejpam-6458	325	7	perfect	perfect	ADJ
ejpam-6458	325	8	monomial	monomial	NOUN
ejpam-6458	325	9	,	,	PUNCT
ejpam-6458	325	10	the	the	DET
ejpam-6458	325	11	first	first	ADJ
ejpam-6458	325	12	perfect	perfect	ADJ
ejpam-6458	325	13	element	element	NOUN
ejpam-6458	325	14	z′1	z′1	NOUN
ejpam-6458	325	15	in	in	ADP
ejpam-6458	325	16	its	its	PRON
ejpam-6458	325	17	decomposition	decomposition	NOUN
ejpam-6458	325	18	z1	z1	NOUN
ejpam-6458	325	19	=	=	SYM
ejpam-6458	325	20	z′1z	z′1z	NUM
ejpam-6458	325	21	′	′	NUM
ejpam-6458	325	22	2	2	NUM
ejpam-6458	325	23	·	·	PUNCT
ejpam-6458	325	24	·	·	PUNCT
ejpam-6458	325	25	·	·	PUNCT
ejpam-6458	325	26	z′s	z′s	PUNCT
ejpam-6458	326	1	=	=	SYM
ejpam-6458	327	1	z′1z	z′1z	NUM
ejpam-6458	327	2	′	′	NOUN
ejpam-6458	327	3	1	1	NUM
ejpam-6458	327	4	is	be	AUX
ejpam-6458	327	5	the	the	DET
ejpam-6458	327	6	minimal	minimal	ADJ
ejpam-6458	327	7	perfect	perfect	ADJ
ejpam-6458	327	8	element	element	NOUN
ejpam-6458	327	9	with	with	ADP
ejpam-6458	327	10	respect	respect	NOUN
ejpam-6458	327	11	to	to	ADP
ejpam-6458	327	12	the	the	DET
ejpam-6458	327	13	order	order	NOUN
ejpam-6458	327	14	(	(	PUNCT
ejpam-6458	327	15	2.3	2.3	NUM
ejpam-6458	327	16	)	)	PUNCT
ejpam-6458	327	17	.	.	PUNCT
ejpam-6458	328	1	this	this	PRON
ejpam-6458	328	2	means	mean	VERB
ejpam-6458	328	3	that	that	SCONJ
ejpam-6458	328	4	for	for	SCONJ
ejpam-6458	328	5	every	every	DET
ejpam-6458	328	6	perfect	perfect	ADJ
ejpam-6458	328	7	monomial	monomial	NOUN
ejpam-6458	328	8	x	x	PUNCT
ejpam-6458	328	9	such	such	ADJ
ejpam-6458	328	10	that	that	DET
ejpam-6458	328	11	l1(x	l1(x	NOUN
ejpam-6458	328	12	)	)	PUNCT
ejpam-6458	328	13	⊑	⊑	X
ejpam-6458	328	14	l1(z1	l1(z1	ADJ
ejpam-6458	328	15	)	)	PUNCT
ejpam-6458	328	16	,	,	PUNCT
ejpam-6458	328	17	we	we	PRON
ejpam-6458	328	18	have	have	VERB
ejpam-6458	328	19	z′1	z′1	NOUN
ejpam-6458	328	20	≤	≤	NUM
ejpam-6458	328	21	x.	x.	NOUN
ejpam-6458	329	1	since	since	SCONJ
ejpam-6458	329	2	l1(b1	l1(b1	PROPN
ejpam-6458	329	3	)	)	PUNCT
ejpam-6458	329	4	,	,	PUNCT
ejpam-6458	329	5	l1(z1	l1(z1	NOUN
ejpam-6458	329	6	)	)	PUNCT
ejpam-6458	329	7	⊑	⊑	X
ejpam-6458	329	8	l1(z	l1(z	PROPN
ejpam-6458	329	9	)	)	PUNCT
ejpam-6458	329	10	⊑	⊑	X
ejpam-6458	329	11	l1(y	l1(y	PROPN
ejpam-6458	329	12	)	)	PUNCT
ejpam-6458	329	13	,	,	PUNCT
ejpam-6458	329	14	it	it	PRON
ejpam-6458	329	15	follows	follow	VERB
ejpam-6458	329	16	that	that	DET
ejpam-6458	329	17	z′1	z′1	NOUN
ejpam-6458	329	18	=	=	SYM
ejpam-6458	329	19	b1	b1	PROPN
ejpam-6458	329	20	.	.	PUNCT
ejpam-6458	330	1	now	now	ADV
ejpam-6458	330	2	we	we	PRON
ejpam-6458	330	3	have	have	VERB
ejpam-6458	330	4	x	x	NOUN
ejpam-6458	330	5	=	=	PUNCT
ejpam-6458	330	6	zx1	zx1	NOUN
ejpam-6458	331	1	+	+	NOUN
ejpam-6458	331	2	x2	x2	NOUN
ejpam-6458	331	3	=	=	SYM
ejpam-6458	331	4	(	(	PUNCT
ejpam-6458	331	5	z1	z1	NOUN
ejpam-6458	331	6	+	+	NUM
ejpam-6458	331	7	z2)x1	z2)x1	NOUN
ejpam-6458	331	8	+	+	NOUN
ejpam-6458	331	9	x2	x2	NOUN
ejpam-6458	331	10	=	=	SYM
ejpam-6458	331	11	(	(	PUNCT
ejpam-6458	331	12	b1z	b1z	NOUN
ejpam-6458	331	13	′	′	ADP
ejpam-6458	331	14	1	1	NUM
ejpam-6458	332	1	+	+	NUM
ejpam-6458	332	2	z2)x1	z2)x1	NOUN
ejpam-6458	332	3	+	+	NOUN
ejpam-6458	332	4	x2	x2	NOUN
ejpam-6458	332	5	=	=	SYM
ejpam-6458	332	6	y	y	PROPN
ejpam-6458	332	7	−	−	NOUN
ejpam-6458	332	8	b1y	b1y	ADP
ejpam-6458	333	1	′	′	NUM
ejpam-6458	334	1	+	+	CCONJ
ejpam-6458	334	2	(	(	PUNCT
ejpam-6458	334	3	b1z	b1z	VERB
ejpam-6458	334	4	′	′	NOUN
ejpam-6458	334	5	1	1	NUM
ejpam-6458	335	1	+	+	NUM
ejpam-6458	335	2	z2)x1	z2)x1	NOUN
ejpam-6458	335	3	+	+	NOUN
ejpam-6458	335	4	x2	x2	NOUN
ejpam-6458	335	5	=	=	SYM
ejpam-6458	335	6	y	y	PROPN
ejpam-6458	336	1	+	+	CCONJ
ejpam-6458	336	2	b1(z	b1(z	PROPN
ejpam-6458	337	1	′	′	NUM
ejpam-6458	337	2	1x1	1x1	NUM
ejpam-6458	337	3	−	−	PROPN
ejpam-6458	337	4	y	y	PROPN
ejpam-6458	337	5	′	′	NUM
ejpam-6458	337	6	)	)	PUNCT
ejpam-6458	338	1	+	+	CCONJ
ejpam-6458	339	1	z2x1	z2x1	X
ejpam-6458	340	1	+	+	NOUN
ejpam-6458	340	2	x2	x2	PROPN
ejpam-6458	340	3	.	.	PUNCT
ejpam-6458	341	1	it	it	PRON
ejpam-6458	341	2	is	be	AUX
ejpam-6458	341	3	easy	easy	ADJ
ejpam-6458	341	4	to	to	PART
ejpam-6458	341	5	see	see	VERB
ejpam-6458	341	6	that	that	SCONJ
ejpam-6458	341	7	the	the	DET
ejpam-6458	341	8	pair	pair	NOUN
ejpam-6458	341	9	of	of	ADP
ejpam-6458	341	10	monomials	monomial	NOUN
ejpam-6458	341	11	x3	x3	ADJ
ejpam-6458	341	12	=	=	SYM
ejpam-6458	342	1	z	z	NOUN
ejpam-6458	343	1	′	′	NOUN
ejpam-6458	343	2	1x1	1x1	NUM
ejpam-6458	343	3	and	and	CCONJ
ejpam-6458	343	4	y	y	PROPN
ejpam-6458	343	5	′	′	NUM
ejpam-6458	343	6	satisfies	satisfy	VERB
ejpam-6458	343	7	the	the	DET
ejpam-6458	343	8	initial	initial	ADJ
ejpam-6458	343	9	conditions	condition	NOUN
ejpam-6458	343	10	of	of	ADP
ejpam-6458	343	11	our	our	PRON
ejpam-6458	343	12	lemma	lemma	PROPN
ejpam-6458	343	13	,	,	PUNCT
ejpam-6458	343	14	with	with	ADP
ejpam-6458	343	15	degree	degree	NOUN
ejpam-6458	343	16	of	of	ADP
ejpam-6458	343	17	the	the	DET
ejpam-6458	343	18	monomials	monomial	NOUN
ejpam-6458	343	19	less	less	ADJ
ejpam-6458	343	20	than	than	ADP
ejpam-6458	343	21	i.	i.	NOUN
ejpam-6458	343	22	since	since	SCONJ
ejpam-6458	343	23	deg(y	deg(y	PROPN
ejpam-6458	343	24	′	′	NOUN
ejpam-6458	343	25	)	)	PUNCT
ejpam-6458	344	1	=	=	SYM
ejpam-6458	345	1	i	i	PRON
ejpam-6458	345	2	−	−	PROPN
ejpam-6458	346	1	k	k	NOUN
ejpam-6458	346	2	,	,	PUNCT
ejpam-6458	346	3	t1(x3	t1(x3	NUM
ejpam-6458	346	4	)	)	PUNCT
ejpam-6458	346	5	=	=	SYM
ejpam-6458	347	1	t1(y	t1(y	NUM
ejpam-6458	347	2	′	′	NUM
ejpam-6458	347	3	)	)	PUNCT
ejpam-6458	347	4	and	and	CCONJ
ejpam-6458	347	5	y	y	PROPN
ejpam-6458	347	6	′	′	NOUN
ejpam-6458	347	7	is	be	AUX
ejpam-6458	347	8	semi	semi	ADJ
ejpam-6458	347	9	-	-	ADJ
ejpam-6458	347	10	perfect	perfect	ADJ
ejpam-6458	347	11	,	,	PUNCT
ejpam-6458	347	12	we	we	PRON
ejpam-6458	347	13	can	can	AUX
ejpam-6458	347	14	apply	apply	VERB
ejpam-6458	347	15	,	,	PUNCT
ejpam-6458	347	16	by	by	ADP
ejpam-6458	347	17	the	the	DET
ejpam-6458	347	18	induction	induction	NOUN
ejpam-6458	347	19	hypothesis	hypothesis	NOUN
ejpam-6458	347	20	,	,	PUNCT
ejpam-6458	347	21	our	our	PRON
ejpam-6458	347	22	algorithm	algorithm	NOUN
ejpam-6458	347	23	to	to	ADP
ejpam-6458	347	24	the	the	DET
ejpam-6458	347	25	pair	pair	NOUN
ejpam-6458	347	26	x3	x3	VERB
ejpam-6458	347	27	,	,	PUNCT
ejpam-6458	347	28	y	y	PROPN
ejpam-6458	347	29	′	′	NOUN
ejpam-6458	347	30	this	this	PRON
ejpam-6458	347	31	gives	give	VERB
ejpam-6458	347	32	x3	x3	NOUN
ejpam-6458	347	33	=	=	SYM
ejpam-6458	347	34	y	y	PROPN
ejpam-6458	347	35	′	′	NUM
ejpam-6458	348	1	+	+	PUNCT
ejpam-6458	348	2	x4	x4	PROPN
ejpam-6458	348	3	,	,	PUNCT
ejpam-6458	348	4	where	where	SCONJ
ejpam-6458	348	5	x4	x4	PROPN
ejpam-6458	348	6	∈	∈	PROPN
ejpam-6458	348	7	û	û	X
ejpam-6458	348	8	(	(	PUNCT
ejpam-6458	348	9	i−k−1	i−k−1	NOUN
ejpam-6458	348	10	)	)	PUNCT
ejpam-6458	348	11	0	0	NUM
ejpam-6458	349	1	(	(	PUNCT
ejpam-6458	349	2	g	g	NOUN
ejpam-6458	349	3	)	)	PUNCT
ejpam-6458	349	4	.	.	PUNCT
ejpam-6458	350	1	finally	finally	ADV
ejpam-6458	350	2	,	,	PUNCT
ejpam-6458	350	3	we	we	PRON
ejpam-6458	350	4	have	have	VERB
ejpam-6458	350	5	x	x	NOUN
ejpam-6458	350	6	=	=	PUNCT
ejpam-6458	350	7	y	y	PROPN
ejpam-6458	350	8	+	+	PROPN
ejpam-6458	350	9	y1	y1	PROPN
ejpam-6458	350	10	,	,	PUNCT
ejpam-6458	350	11	where	where	SCONJ
ejpam-6458	350	12	y1	y1	NOUN
ejpam-6458	350	13	=	=	PUNCT
ejpam-6458	350	14	b1x4	b1x4	PUNCT
ejpam-6458	351	1	+	+	PUNCT
ejpam-6458	351	2	z2x1	z2x1	NUM
ejpam-6458	351	3	+	+	NUM
ejpam-6458	351	4	x2	x2	PROPN
ejpam-6458	351	5	∈	∈	PROPN
ejpam-6458	351	6	û	û	X
ejpam-6458	351	7	(	(	PUNCT
ejpam-6458	351	8	i−1	i−1	PROPN
ejpam-6458	351	9	)	)	PUNCT
ejpam-6458	351	10	0	0	NUM
ejpam-6458	351	11	(	(	PUNCT
ejpam-6458	351	12	g	g	NOUN
ejpam-6458	351	13	)	)	PUNCT
ejpam-6458	351	14	.	.	PUNCT
ejpam-6458	352	1	m.	m.	PROPN
ejpam-6458	352	2	andelić	andelić	PROPN
ejpam-6458	352	3	et	et	PROPN
ejpam-6458	352	4	al	al	PROPN
ejpam-6458	352	5	.	.	PUNCT
ejpam-6458	352	6	/	/	SYM
ejpam-6458	352	7	eur	eur	PROPN
ejpam-6458	352	8	.	.	PUNCT
ejpam-6458	353	1	j.	j.	PROPN
ejpam-6458	353	2	pure	pure	PROPN
ejpam-6458	353	3	appl	appl	PROPN
ejpam-6458	353	4	.	.	PROPN
ejpam-6458	353	5	math	math	PROPN
ejpam-6458	353	6	,	,	PUNCT
ejpam-6458	353	7	18	18	NUM
ejpam-6458	353	8	(	(	PUNCT
ejpam-6458	353	9	3	3	NUM
ejpam-6458	353	10	)	)	PUNCT
ejpam-6458	353	11	(	(	PUNCT
ejpam-6458	353	12	2025	2025	NUM
ejpam-6458	353	13	)	)	PUNCT
ejpam-6458	353	14	,	,	PUNCT
ejpam-6458	353	15	6458	6458	NUM
ejpam-6458	353	16	8	8	NUM
ejpam-6458	353	17	of	of	ADP
ejpam-6458	353	18	21	21	NUM
ejpam-6458	353	19	the	the	DET
ejpam-6458	353	20	statement	statement	NOUN
ejpam-6458	353	21	follows	follow	VERB
ejpam-6458	353	22	by	by	ADP
ejpam-6458	353	23	the	the	DET
ejpam-6458	353	24	induction	induction	NOUN
ejpam-6458	353	25	hypothesis	hypothesis	NOUN
ejpam-6458	353	26	.	.	PUNCT
ejpam-6458	354	1	note	note	VERB
ejpam-6458	354	2	that	that	SCONJ
ejpam-6458	354	3	we	we	PRON
ejpam-6458	354	4	used	use	VERB
ejpam-6458	354	5	relations	relation	NOUN
ejpam-6458	355	1	k	k	PROPN
ejpam-6458	355	2	′	′	NUM
ejpam-6458	355	3	twice	twice	ADV
ejpam-6458	355	4	:	:	PUNCT
ejpam-6458	355	5	for	for	ADP
ejpam-6458	355	6	commuting	commute	VERB
ejpam-6458	355	7	perfect	perfect	ADJ
ejpam-6458	355	8	elements	element	NOUN
ejpam-6458	355	9	and	and	CCONJ
ejpam-6458	355	10	for	for	ADP
ejpam-6458	355	11	normalizing	normalize	VERB
ejpam-6458	355	12	z.	z.	PROPN
ejpam-6458	355	13	□	□	PUNCT
ejpam-6458	355	14	let	let	VERB
ejpam-6458	355	15	a	a	PRON
ejpam-6458	355	16	be	be	AUX
ejpam-6458	355	17	an	an	DET
ejpam-6458	355	18	associative	associative	ADJ
ejpam-6458	355	19	algebra	algebra	NOUN
ejpam-6458	355	20	defined	define	VERB
ejpam-6458	355	21	by	by	ADP
ejpam-6458	355	22	a	a	DET
ejpam-6458	355	23	set	set	NOUN
ejpam-6458	355	24	of	of	ADP
ejpam-6458	355	25	generators	generator	NOUN
ejpam-6458	355	26	s	s	PART
ejpam-6458	355	27	and	and	CCONJ
ejpam-6458	355	28	a	a	DET
ejpam-6458	355	29	set	set	NOUN
ejpam-6458	355	30	of	of	ADP
ejpam-6458	355	31	relation	relation	NOUN
ejpam-6458	355	32	r	r	NOUN
ejpam-6458	355	33	(	(	PUNCT
ejpam-6458	355	34	as	as	ADP
ejpam-6458	355	35	polynomials	polynomial	NOUN
ejpam-6458	355	36	in	in	ADP
ejpam-6458	355	37	the	the	DET
ejpam-6458	355	38	generators	generator	NOUN
ejpam-6458	355	39	of	of	ADP
ejpam-6458	355	40	s	s	NOUN
ejpam-6458	355	41	)	)	PUNCT
ejpam-6458	355	42	.	.	PUNCT
ejpam-6458	356	1	the	the	DET
ejpam-6458	356	2	set	set	NOUN
ejpam-6458	356	3	of	of	ADP
ejpam-6458	356	4	generators	generator	NOUN
ejpam-6458	356	5	s	s	PART
ejpam-6458	356	6	can	can	AUX
ejpam-6458	356	7	be	be	AUX
ejpam-6458	356	8	partitioned	partition	VERB
ejpam-6458	356	9	into	into	ADP
ejpam-6458	356	10	three	three	NUM
ejpam-6458	356	11	subsets	subset	NOUN
ejpam-6458	356	12	,	,	PUNCT
ejpam-6458	356	13	s	s	NOUN
ejpam-6458	356	14	=	=	SYM
ejpam-6458	356	15	s1∪s2∪s3	s1∪s2∪s3	NOUN
ejpam-6458	356	16	,	,	PUNCT
ejpam-6458	356	17	where	where	SCONJ
ejpam-6458	356	18	s1	s1	NOUN
ejpam-6458	356	19	generates	generate	VERB
ejpam-6458	356	20	the	the	DET
ejpam-6458	356	21	center	center	NOUN
ejpam-6458	356	22	of	of	ADP
ejpam-6458	356	23	the	the	DET
ejpam-6458	356	24	algebra	algebra	NOUN
ejpam-6458	356	25	a	a	PRON
ejpam-6458	356	26	and	and	CCONJ
ejpam-6458	356	27	s1∪s2	s1∪s2	PROPN
ejpam-6458	356	28	generates	generate	VERB
ejpam-6458	356	29	a	a	DET
ejpam-6458	356	30	commutative	commutative	ADJ
ejpam-6458	356	31	subalgebra	subalgebra	NOUN
ejpam-6458	356	32	of	of	ADP
ejpam-6458	356	33	a.	a.	NOUN
ejpam-6458	356	34	the	the	DET
ejpam-6458	356	35	width	width	NOUN
ejpam-6458	356	36	of	of	ADP
ejpam-6458	356	37	a	a	DET
ejpam-6458	356	38	monomialx	monomialx	NOUN
ejpam-6458	356	39	,	,	PUNCT
ejpam-6458	356	40	denoted	denote	VERB
ejpam-6458	356	41	by	by	ADP
ejpam-6458	356	42	width(x	width(x	PROPN
ejpam-6458	356	43	)	)	PUNCT
ejpam-6458	356	44	,	,	PUNCT
ejpam-6458	356	45	is	be	AUX
ejpam-6458	356	46	defined	define	VERB
ejpam-6458	356	47	as	as	ADP
ejpam-6458	356	48	the	the	DET
ejpam-6458	356	49	number	number	NOUN
ejpam-6458	356	50	of	of	ADP
ejpam-6458	356	51	occurrences	occurrence	NOUN
ejpam-6458	356	52	of	of	ADP
ejpam-6458	356	53	variables	variable	NOUN
ejpam-6458	356	54	from	from	ADP
ejpam-6458	356	55	the	the	DET
ejpam-6458	356	56	set	set	ADJ
ejpam-6458	356	57	s3	s3	PROPN
ejpam-6458	356	58	in	in	ADP
ejpam-6458	356	59	the	the	DET
ejpam-6458	356	60	monomial	monomial	NOUN
ejpam-6458	356	61	.	.	PUNCT
ejpam-6458	357	1	the	the	DET
ejpam-6458	357	2	width	width	NOUN
ejpam-6458	357	3	of	of	ADP
ejpam-6458	357	4	a	a	DET
ejpam-6458	357	5	polynomial	polynomial	ADJ
ejpam-6458	357	6	p	p	NOUN
ejpam-6458	357	7	is	be	AUX
ejpam-6458	357	8	then	then	ADV
ejpam-6458	357	9	defined	define	VERB
ejpam-6458	357	10	as	as	ADP
ejpam-6458	357	11	the	the	DET
ejpam-6458	357	12	maximal	maximal	ADJ
ejpam-6458	357	13	width	width	NOUN
ejpam-6458	357	14	among	among	ADP
ejpam-6458	357	15	all	all	DET
ejpam-6458	357	16	monomials	monomial	NOUN
ejpam-6458	357	17	that	that	PRON
ejpam-6458	357	18	make	make	VERB
ejpam-6458	357	19	up	up	ADP
ejpam-6458	357	20	the	the	DET
ejpam-6458	357	21	polynomial	polynomial	NOUN
ejpam-6458	357	22	.	.	PUNCT
ejpam-6458	358	1	we	we	PRON
ejpam-6458	358	2	can	can	AUX
ejpam-6458	358	3	decompose	decompose	VERB
ejpam-6458	358	4	the	the	DET
ejpam-6458	358	5	set	set	NOUN
ejpam-6458	358	6	of	of	ADP
ejpam-6458	358	7	relation	relation	NOUN
ejpam-6458	358	8	r	r	NOUN
ejpam-6458	358	9	into	into	ADP
ejpam-6458	358	10	a	a	DET
ejpam-6458	358	11	union	union	NOUN
ejpam-6458	358	12	of	of	ADP
ejpam-6458	358	13	subsets	subset	NOUN
ejpam-6458	358	14	as	as	SCONJ
ejpam-6458	358	15	follows	follow	VERB
ejpam-6458	358	16	:	:	PUNCT
ejpam-6458	358	17	r	r	NOUN
ejpam-6458	358	18	=	=	SYM
ejpam-6458	358	19	r0∪r1∪	r0∪r1∪	X
ejpam-6458	358	20	·	·	PUNCT
ejpam-6458	358	21	·	·	PUNCT
ejpam-6458	358	22	·	·	PUNCT
ejpam-6458	358	23	,	,	PUNCT
ejpam-6458	358	24	where	where	SCONJ
ejpam-6458	358	25	ri	ri	NOUN
ejpam-6458	358	26	=	=	PRON
ejpam-6458	358	27	{	{	PUNCT
ejpam-6458	358	28	y	y	PROPN
ejpam-6458	358	29	∈	∈	PROPN
ejpam-6458	358	30	r	r	NOUN
ejpam-6458	358	31	|	|	NOUN
ejpam-6458	358	32	width(y	width(y	ADV
ejpam-6458	358	33	)	)	PUNCT
ejpam-6458	358	34	=	=	PUNCT
ejpam-6458	359	1	i	i	PROPN
ejpam-6458	359	2	}	}	PUNCT
ejpam-6458	359	3	,	,	PUNCT
ejpam-6458	359	4	for	for	ADP
ejpam-6458	359	5	i	i	PROPN
ejpam-6458	359	6	=	=	SYM
ejpam-6458	359	7	0	0	NUM
ejpam-6458	359	8	,	,	PUNCT
ejpam-6458	359	9	1	1	NUM
ejpam-6458	359	10	,	,	PUNCT
ejpam-6458	359	11	2	2	NUM
ejpam-6458	359	12	,	,	PUNCT
ejpam-6458	359	13	.	.	PUNCT
ejpam-6458	359	14	.	.	PUNCT
ejpam-6458	360	1	..	..	PUNCT
ejpam-6458	360	2	note	note	VERB
ejpam-6458	360	3	that	that	SCONJ
ejpam-6458	360	4	this	this	DET
ejpam-6458	360	5	decomposition	decomposition	NOUN
ejpam-6458	360	6	is	be	AUX
ejpam-6458	360	7	not	not	PART
ejpam-6458	360	8	unique	unique	ADJ
ejpam-6458	360	9	and	and	CCONJ
ejpam-6458	360	10	may	may	AUX
ejpam-6458	360	11	vary	vary	VERB
ejpam-6458	360	12	depending	depend	VERB
ejpam-6458	360	13	on	on	ADP
ejpam-6458	360	14	the	the	DET
ejpam-6458	360	15	choice	choice	NOUN
ejpam-6458	360	16	of	of	ADP
ejpam-6458	360	17	generators	generator	NOUN
ejpam-6458	360	18	s	s	PART
ejpam-6458	360	19	and	and	CCONJ
ejpam-6458	360	20	the	the	DET
ejpam-6458	360	21	subset	subset	ADJ
ejpam-6458	360	22	s2	s2	PROPN
ejpam-6458	360	23	.	.	PUNCT
ejpam-6458	361	1	our	our	PRON
ejpam-6458	361	2	goal	goal	NOUN
ejpam-6458	361	3	will	will	AUX
ejpam-6458	361	4	be	be	AUX
ejpam-6458	361	5	to	to	PART
ejpam-6458	361	6	identify	identify	VERB
ejpam-6458	361	7	the	the	DET
ejpam-6458	361	8	”	"	PUNCT
ejpam-6458	361	9	best	good	ADJ
ejpam-6458	361	10	”	"	PUNCT
ejpam-6458	361	11	set	set	NOUN
ejpam-6458	361	12	of	of	ADP
ejpam-6458	361	13	generators	generator	NOUN
ejpam-6458	361	14	s	s	PART
ejpam-6458	361	15	and	and	CCONJ
ejpam-6458	361	16	”	"	PUNCT
ejpam-6458	361	17	best	good	ADJ
ejpam-6458	361	18	”	"	PUNCT
ejpam-6458	361	19	decomposition	decomposition	NOUN
ejpam-6458	361	20	,	,	PUNCT
ejpam-6458	361	21	such	such	ADJ
ejpam-6458	361	22	that	that	SCONJ
ejpam-6458	361	23	the	the	DET
ejpam-6458	361	24	cardinality	cardinality	NOUN
ejpam-6458	361	25	of	of	ADP
ejpam-6458	361	26	the	the	DET
ejpam-6458	361	27	set	set	NOUN
ejpam-6458	361	28	s3	s3	PROPN
ejpam-6458	361	29	is	be	AUX
ejpam-6458	361	30	minimal	minimal	ADJ
ejpam-6458	361	31	.	.	PUNCT
ejpam-6458	362	1	3	3	X
ejpam-6458	362	2	.	.	X
ejpam-6458	362	3	category	category	NOUN
ejpam-6458	362	4	of	of	ADP
ejpam-6458	362	5	γ	γ	PROPN
ejpam-6458	362	6	-	-	PUNCT
ejpam-6458	362	7	pointed	point	VERB
ejpam-6458	362	8	modules	module	NOUN
ejpam-6458	362	9	let	let	VERB
ejpam-6458	362	10	γ	γ	NOUN
ejpam-6458	362	11	be	be	AUX
ejpam-6458	362	12	a	a	DET
ejpam-6458	362	13	commutative	commutative	ADJ
ejpam-6458	362	14	subalgebra	subalgebra	NOUN
ejpam-6458	362	15	of	of	ADP
ejpam-6458	362	16	u0(g	u0(g	NOUN
ejpam-6458	362	17	)	)	PUNCT
ejpam-6458	362	18	such	such	ADJ
ejpam-6458	362	19	that	that	SCONJ
ejpam-6458	362	20	h	h	NOUN
ejpam-6458	362	21	⊆	⊆	NUM
ejpam-6458	362	22	γ	γ	X
ejpam-6458	362	23	⊂	⊂	PROPN
ejpam-6458	362	24	u0(g	u0(g	PROPN
ejpam-6458	362	25	)	)	PUNCT
ejpam-6458	362	26	.	.	PUNCT
ejpam-6458	363	1	by	by	ADP
ejpam-6458	363	2	hom(γ	hom(γ	NOUN
ejpam-6458	363	3	,	,	PUNCT
ejpam-6458	363	4	c	c	NOUN
ejpam-6458	363	5	)	)	PUNCT
ejpam-6458	363	6	we	we	PRON
ejpam-6458	363	7	denote	denote	VERB
ejpam-6458	363	8	the	the	DET
ejpam-6458	363	9	set	set	NOUN
ejpam-6458	363	10	of	of	ADP
ejpam-6458	363	11	all	all	DET
ejpam-6458	363	12	characters	character	NOUN
ejpam-6458	363	13	of	of	ADP
ejpam-6458	363	14	γ	γ	PROPN
ejpam-6458	363	15	,	,	PUNCT
ejpam-6458	363	16	that	that	PRON
ejpam-6458	363	17	is	be	AUX
ejpam-6458	363	18	the	the	DET
ejpam-6458	363	19	set	set	NOUN
ejpam-6458	363	20	of	of	ADP
ejpam-6458	363	21	all	all	DET
ejpam-6458	363	22	c	c	NOUN
ejpam-6458	363	23	-	-	PUNCT
ejpam-6458	363	24	algebra	algebra	NOUN
ejpam-6458	363	25	homomorphisms	homomorphism	NOUN
ejpam-6458	363	26	from	from	ADP
ejpam-6458	363	27	γ	γ	NOUN
ejpam-6458	363	28	to	to	ADP
ejpam-6458	363	29	c.	c.	PROPN
ejpam-6458	363	30	let	let	VERB
ejpam-6458	363	31	m	m	PRON
ejpam-6458	363	32	be	be	AUX
ejpam-6458	363	33	a	a	DET
ejpam-6458	363	34	γ	γ	NOUN
ejpam-6458	363	35	-	-	NOUN
ejpam-6458	363	36	module	module	NOUN
ejpam-6458	363	37	.	.	PUNCT
ejpam-6458	364	1	for	for	ADP
ejpam-6458	364	2	each	each	DET
ejpam-6458	364	3	χ	χ	PRON
ejpam-6458	364	4	∈	∈	PROPN
ejpam-6458	364	5	hom(γ	hom(γ	PROPN
ejpam-6458	364	6	,	,	PUNCT
ejpam-6458	364	7	c	c	NOUN
ejpam-6458	364	8	)	)	PUNCT
ejpam-6458	364	9	we	we	PRON
ejpam-6458	364	10	set	set	VERB
ejpam-6458	364	11	mχ	mχ	ADP
ejpam-6458	364	12	=	=	PUNCT
ejpam-6458	364	13	{	{	PUNCT
ejpam-6458	364	14	v	v	NOUN
ejpam-6458	364	15	∈m	∈m	NOUN
ejpam-6458	364	16	;	;	PUNCT
ejpam-6458	364	17	av	av	PROPN
ejpam-6458	364	18	=	=	SYM
ejpam-6458	364	19	χ(a)v	χ(a)v	PROPN
ejpam-6458	364	20	,	,	PUNCT
ejpam-6458	364	21	∀a	∀a	NOUN
ejpam-6458	364	22	∈	∈	PROPN
ejpam-6458	364	23	γ	γ	X
ejpam-6458	364	24	}	}	PUNCT
ejpam-6458	364	25	,	,	PUNCT
ejpam-6458	364	26	and	and	CCONJ
ejpam-6458	364	27	call	call	VERB
ejpam-6458	364	28	it	it	PRON
ejpam-6458	364	29	the	the	DET
ejpam-6458	364	30	γ	γ	NOUN
ejpam-6458	364	31	-	-	PUNCT
ejpam-6458	364	32	weight	weight	NOUN
ejpam-6458	364	33	space	space	NOUN
ejpam-6458	364	34	of	of	ADP
ejpam-6458	364	35	m	m	PROPN
ejpam-6458	364	36	with	with	ADP
ejpam-6458	364	37	weight	weight	NOUN
ejpam-6458	364	38	χ	χ	NOUN
ejpam-6458	364	39	.	.	PUNCT
ejpam-6458	365	1	when	when	SCONJ
ejpam-6458	365	2	mχ	mχ	ADP
ejpam-6458	365	3	̸=	̸=	PROPN
ejpam-6458	365	4	{	{	PUNCT
ejpam-6458	365	5	0	0	NUM
ejpam-6458	365	6	}	}	PUNCT
ejpam-6458	365	7	,	,	PUNCT
ejpam-6458	365	8	we	we	PRON
ejpam-6458	365	9	say	say	VERB
ejpam-6458	365	10	that	that	SCONJ
ejpam-6458	365	11	χ	χ	NOUN
ejpam-6458	365	12	is	be	AUX
ejpam-6458	365	13	a	a	DET
ejpam-6458	365	14	γ	γ	NOUN
ejpam-6458	365	15	-	-	PUNCT
ejpam-6458	365	16	weight	weight	NOUN
ejpam-6458	365	17	of	of	ADP
ejpam-6458	365	18	m	m	NOUN
ejpam-6458	365	19	and	and	CCONJ
ejpam-6458	365	20	the	the	DET
ejpam-6458	365	21	elements	element	NOUN
ejpam-6458	365	22	of	of	ADP
ejpam-6458	365	23	mχ	mχ	NOUN
ejpam-6458	365	24	are	be	AUX
ejpam-6458	365	25	called	call	VERB
ejpam-6458	365	26	γ	γ	NOUN
ejpam-6458	365	27	-	-	PUNCT
ejpam-6458	365	28	weight	weight	NOUN
ejpam-6458	365	29	vectors	vector	NOUN
ejpam-6458	365	30	of	of	ADP
ejpam-6458	365	31	weight	weight	NOUN
ejpam-6458	365	32	χ	χ	NOUN
ejpam-6458	365	33	.	.	PUNCT
ejpam-6458	366	1	if	if	SCONJ
ejpam-6458	366	2	a	a	DET
ejpam-6458	366	3	γ	γ	NOUN
ejpam-6458	366	4	-	-	PUNCT
ejpam-6458	366	5	module	module	NOUN
ejpam-6458	366	6	m	m	NOUN
ejpam-6458	366	7	satisfies	satisfie	NOUN
ejpam-6458	366	8	m	m	PROPN
ejpam-6458	366	9	=	=	PROPN
ejpam-6458	366	10	⊕	⊕	PROPN
ejpam-6458	366	11	χ∈hom(γ	χ∈hom(γ	PROPN
ejpam-6458	366	12	,	,	PUNCT
ejpam-6458	366	13	c	c	NOUN
ejpam-6458	366	14	)	)	PUNCT
ejpam-6458	366	15	mχ	mχ	ADP
ejpam-6458	366	16	,	,	PUNCT
ejpam-6458	366	17	then	then	ADV
ejpam-6458	366	18	we	we	PRON
ejpam-6458	366	19	call	call	VERB
ejpam-6458	366	20	m	m	VERB
ejpam-6458	366	21	a	a	DET
ejpam-6458	366	22	γ	γ	ADJ
ejpam-6458	366	23	-	-	PUNCT
ejpam-6458	366	24	weight	weight	NOUN
ejpam-6458	366	25	module	module	NOUN
ejpam-6458	366	26	.	.	PUNCT
ejpam-6458	367	1	the	the	DET
ejpam-6458	367	2	dimension	dimension	NOUN
ejpam-6458	367	3	of	of	ADP
ejpam-6458	367	4	the	the	DET
ejpam-6458	367	5	vector	vector	NOUN
ejpam-6458	367	6	space	space	NOUN
ejpam-6458	367	7	mχ	mχ	ADP
ejpam-6458	367	8	̸=	̸=	PROPN
ejpam-6458	367	9	0	0	NUM
ejpam-6458	367	10	will	will	AUX
ejpam-6458	367	11	be	be	AUX
ejpam-6458	367	12	called	call	VERB
ejpam-6458	367	13	the	the	DET
ejpam-6458	367	14	γ	γ	NOUN
ejpam-6458	367	15	-	-	PUNCT
ejpam-6458	367	16	multiplicity	multiplicity	NOUN
ejpam-6458	367	17	of	of	ADP
ejpam-6458	367	18	χ	χ	NOUN
ejpam-6458	367	19	in	in	ADP
ejpam-6458	367	20	m	m	PROPN
ejpam-6458	367	21	.	.	PUNCT
ejpam-6458	368	1	module	module	NOUN
ejpam-6458	368	2	is	be	AUX
ejpam-6458	368	3	called	call	VERB
ejpam-6458	368	4	γ	γ	NOUN
ejpam-6458	368	5	-	-	PUNCT
ejpam-6458	368	6	pointed	point	VERB
ejpam-6458	368	7	if	if	SCONJ
ejpam-6458	368	8	γ	γ	NOUN
ejpam-6458	368	9	-	-	PUNCT
ejpam-6458	368	10	multiplicity	multiplicity	NOUN
ejpam-6458	368	11	of	of	ADP
ejpam-6458	368	12	any	any	DET
ejpam-6458	368	13	character	character	NOUN
ejpam-6458	368	14	χ	χ	NOUN
ejpam-6458	368	15	equals	equal	VERB
ejpam-6458	368	16	1	1	NUM
ejpam-6458	368	17	,	,	PUNCT
ejpam-6458	368	18	that	that	PRON
ejpam-6458	368	19	is	be	AUX
ejpam-6458	368	20	γ	γ	NOUN
ejpam-6458	368	21	separates	separate	VERB
ejpam-6458	368	22	the	the	DET
ejpam-6458	368	23	basis	basis	NOUN
ejpam-6458	368	24	elements	element	NOUN
ejpam-6458	368	25	of	of	ADP
ejpam-6458	368	26	m	m	PROPN
ejpam-6458	368	27	.	.	PUNCT
ejpam-6458	369	1	in	in	ADP
ejpam-6458	369	2	particular	particular	ADJ
ejpam-6458	369	3	,	,	PUNCT
ejpam-6458	369	4	m	m	VERB
ejpam-6458	369	5	is	be	AUX
ejpam-6458	369	6	a	a	DET
ejpam-6458	369	7	tame	tame	ADJ
ejpam-6458	369	8	module	module	NOUN
ejpam-6458	369	9	with	with	ADP
ejpam-6458	369	10	diagonalizable	diagonalizable	ADJ
ejpam-6458	369	11	action	action	NOUN
ejpam-6458	369	12	of	of	ADP
ejpam-6458	369	13	γ	γ	PROPN
ejpam-6458	369	14	.	.	PUNCT
ejpam-6458	370	1	a	a	DET
ejpam-6458	370	2	weight	weight	NOUN
ejpam-6458	370	3	module	module	NOUN
ejpam-6458	370	4	m	m	NOUN
ejpam-6458	370	5	is	be	AUX
ejpam-6458	370	6	torsion	torsion	NOUN
ejpam-6458	370	7	free	free	ADJ
ejpam-6458	370	8	provided	provide	VERB
ejpam-6458	370	9	all	all	DET
ejpam-6458	370	10	root	root	NOUN
ejpam-6458	370	11	vectors	vector	NOUN
ejpam-6458	370	12	of	of	ADP
ejpam-6458	370	13	g	g	PROPN
ejpam-6458	370	14	act	act	VERB
ejpam-6458	370	15	injectively	injectively	ADV
ejpam-6458	370	16	on	on	ADP
ejpam-6458	370	17	m	m	PRON
ejpam-6458	370	18	.	.	PUNCT
ejpam-6458	371	1	in	in	ADP
ejpam-6458	371	2	particular	particular	ADJ
ejpam-6458	371	3	,	,	PUNCT
ejpam-6458	371	4	if	if	SCONJ
ejpam-6458	371	5	γ	γ	X
ejpam-6458	371	6	=	=	SYM
ejpam-6458	371	7	u(h	u(h	PROPN
ejpam-6458	371	8	)	)	PUNCT
ejpam-6458	371	9	,	,	PUNCT
ejpam-6458	371	10	then	then	ADV
ejpam-6458	371	11	γ	γ	PROPN
ejpam-6458	371	12	-	-	PUNCT
ejpam-6458	371	13	weight	weight	NOUN
ejpam-6458	371	14	module	module	NOUN
ejpam-6458	371	15	is	be	AUX
ejpam-6458	371	16	a	a	DET
ejpam-6458	371	17	classical	classical	ADJ
ejpam-6458	371	18	weight	weight	NOUN
ejpam-6458	371	19	module	module	NOUN
ejpam-6458	371	20	.	.	PUNCT
ejpam-6458	372	1	suppose	suppose	VERB
ejpam-6458	372	2	g	g	PROPN
ejpam-6458	372	3	is	be	AUX
ejpam-6458	372	4	of	of	ADP
ejpam-6458	372	5	type	type	NOUN
ejpam-6458	372	6	a	a	PRON
ejpam-6458	372	7	and	and	CCONJ
ejpam-6458	372	8	γ	γ	NOUN
ejpam-6458	372	9	is	be	AUX
ejpam-6458	372	10	a	a	DET
ejpam-6458	372	11	gelfand	gelfand	ADJ
ejpam-6458	372	12	-	-	PUNCT
ejpam-6458	372	13	tsetlin	tsetlin	ADJ
ejpam-6458	372	14	subalgebra	subalgebra	NOUN
ejpam-6458	372	15	of	of	ADP
ejpam-6458	372	16	g	g	PROPN
ejpam-6458	373	1	[	[	X
ejpam-6458	373	2	17	17	NUM
ejpam-6458	373	3	]	]	PUNCT
ejpam-6458	373	4	.	.	PUNCT
ejpam-6458	374	1	then	then	ADV
ejpam-6458	374	2	γ	γ	PROPN
ejpam-6458	374	3	⊂	⊂	PROPN
ejpam-6458	374	4	u0(g	u0(g	PROPN
ejpam-6458	374	5	)	)	PUNCT
ejpam-6458	374	6	and	and	CCONJ
ejpam-6458	374	7	every	every	DET
ejpam-6458	374	8	generic	generic	ADJ
ejpam-6458	374	9	gelfand	gelfand	PROPN
ejpam-6458	374	10	-	-	PUNCT
ejpam-6458	374	11	tsetlin	tsetlin	PROPN
ejpam-6458	374	12	g	g	NOUN
ejpam-6458	374	13	-	-	PUNCT
ejpam-6458	374	14	module	module	NOUN
ejpam-6458	374	15	is	be	AUX
ejpam-6458	374	16	γ	γ	NOUN
ejpam-6458	374	17	-	-	PUNCT
ejpam-6458	374	18	pointed	pointed	ADJ
ejpam-6458	374	19	.	.	PUNCT
ejpam-6458	375	1	we	we	PRON
ejpam-6458	375	2	refer	refer	VERB
ejpam-6458	375	3	to	to	ADP
ejpam-6458	375	4	[	[	X
ejpam-6458	375	5	17	17	NUM
ejpam-6458	375	6	]	]	PUNCT
ejpam-6458	375	7	for	for	ADP
ejpam-6458	375	8	details	detail	NOUN
ejpam-6458	375	9	.	.	PUNCT
ejpam-6458	376	1	clearly	clearly	ADV
ejpam-6458	376	2	,	,	PUNCT
ejpam-6458	376	3	every	every	DET
ejpam-6458	376	4	finite	finite	ADJ
ejpam-6458	376	5	-	-	ADJ
ejpam-6458	376	6	dimensional	dimensional	ADJ
ejpam-6458	376	7	g	g	NOUN
ejpam-6458	376	8	-	-	PUNCT
ejpam-6458	376	9	module	module	NOUN
ejpam-6458	376	10	is	be	AUX
ejpam-6458	376	11	also	also	ADV
ejpam-6458	376	12	γ	γ	PROPN
ejpam-6458	376	13	-	-	PUNCT
ejpam-6458	376	14	pointed	pointed	ADJ
ejpam-6458	376	15	.	.	PUNCT
ejpam-6458	377	1	a	a	DET
ejpam-6458	377	2	family	family	NOUN
ejpam-6458	377	3	of	of	ADP
ejpam-6458	377	4	simple	simple	ADJ
ejpam-6458	377	5	γ	γ	PROPN
ejpam-6458	377	6	-	-	PUNCT
ejpam-6458	377	7	pointed	point	VERB
ejpam-6458	377	8	modules	module	NOUN
ejpam-6458	377	9	in	in	ADP
ejpam-6458	377	10	type	type	NOUN
ejpam-6458	377	11	a	a	PRON
ejpam-6458	377	12	was	be	AUX
ejpam-6458	377	13	studied	study	VERB
ejpam-6458	377	14	in	in	ADP
ejpam-6458	377	15	[	[	X
ejpam-6458	377	16	18	18	NUM
ejpam-6458	377	17	]	]	PUNCT
ejpam-6458	377	18	.	.	PUNCT
ejpam-6458	378	1	on	on	ADP
ejpam-6458	378	2	the	the	DET
ejpam-6458	378	3	other	other	ADJ
ejpam-6458	378	4	hand	hand	NOUN
ejpam-6458	378	5	,	,	PUNCT
ejpam-6458	378	6	there	there	PRON
ejpam-6458	378	7	exist	exist	VERB
ejpam-6458	378	8	gelfand	gelfand	PROPN
ejpam-6458	378	9	-	-	PUNCT
ejpam-6458	378	10	tsetlin	tsetlin	PROPN
ejpam-6458	378	11	modules	module	NOUN
ejpam-6458	378	12	which	which	PRON
ejpam-6458	378	13	are	be	AUX
ejpam-6458	378	14	not	not	PART
ejpam-6458	378	15	pointed	point	VERB
ejpam-6458	378	16	.	.	PUNCT
ejpam-6458	379	1	4	4	X
ejpam-6458	379	2	.	.	X
ejpam-6458	379	3	construction	construction	NOUN
ejpam-6458	379	4	of	of	ADP
ejpam-6458	379	5	simple	simple	ADJ
ejpam-6458	379	6	weight	weight	NOUN
ejpam-6458	379	7	a2	a2	NOUN
ejpam-6458	379	8	-	-	PUNCT
ejpam-6458	379	9	modules	module	NOUN
ejpam-6458	379	10	in	in	ADP
ejpam-6458	379	11	this	this	DET
ejpam-6458	379	12	section	section	NOUN
ejpam-6458	379	13	we	we	PRON
ejpam-6458	379	14	consider	consider	VERB
ejpam-6458	379	15	the	the	DET
ejpam-6458	379	16	lie	lie	NOUN
ejpam-6458	379	17	algebra	algebra	NOUN
ejpam-6458	379	18	g	g	PROPN
ejpam-6458	379	19	=	=	SYM
ejpam-6458	379	20	sl(3	sl(3	PROPN
ejpam-6458	379	21	)	)	PUNCT
ejpam-6458	379	22	.	.	PUNCT
ejpam-6458	380	1	even	even	ADV
ejpam-6458	380	2	though	though	SCONJ
ejpam-6458	380	3	this	this	DET
ejpam-6458	380	4	case	case	NOUN
ejpam-6458	380	5	is	be	AUX
ejpam-6458	380	6	well	well	ADV
ejpam-6458	380	7	understood	understand	VERB
ejpam-6458	380	8	we	we	PRON
ejpam-6458	380	9	give	give	VERB
ejpam-6458	380	10	some	some	DET
ejpam-6458	380	11	details	detail	NOUN
ejpam-6458	380	12	to	to	PART
ejpam-6458	380	13	illustrate	illustrate	VERB
ejpam-6458	380	14	our	our	PRON
ejpam-6458	380	15	approach	approach	NOUN
ejpam-6458	380	16	.	.	PUNCT
ejpam-6458	381	1	m.	m.	NOUN
ejpam-6458	381	2	andelić	andelić	PROPN
ejpam-6458	381	3	et	et	PROPN
ejpam-6458	381	4	al	al	PROPN
ejpam-6458	381	5	.	.	PUNCT
ejpam-6458	381	6	/	/	SYM
ejpam-6458	381	7	eur	eur	PROPN
ejpam-6458	381	8	.	.	PUNCT
ejpam-6458	382	1	j.	j.	PROPN
ejpam-6458	382	2	pure	pure	PROPN
ejpam-6458	382	3	appl	appl	PROPN
ejpam-6458	382	4	.	.	PROPN
ejpam-6458	382	5	math	math	PROPN
ejpam-6458	382	6	,	,	PUNCT
ejpam-6458	382	7	18	18	NUM
ejpam-6458	382	8	(	(	PUNCT
ejpam-6458	382	9	3	3	NUM
ejpam-6458	382	10	)	)	PUNCT
ejpam-6458	382	11	(	(	PUNCT
ejpam-6458	382	12	2025	2025	NUM
ejpam-6458	382	13	)	)	PUNCT
ejpam-6458	382	14	,	,	PUNCT
ejpam-6458	382	15	6458	6458	NUM
ejpam-6458	382	16	9	9	NUM
ejpam-6458	382	17	of	of	ADP
ejpam-6458	382	18	21	21	NUM
ejpam-6458	382	19	4.1	4.1	NUM
ejpam-6458	382	20	.	.	PUNCT
ejpam-6458	382	21	centralizer	centralizer	NOUN
ejpam-6458	382	22	of	of	ADP
ejpam-6458	382	23	the	the	DET
ejpam-6458	382	24	cartan	cartan	ADJ
ejpam-6458	382	25	subalgebra	subalgebra	NOUN
ejpam-6458	382	26	of	of	ADP
ejpam-6458	382	27	a2	a2	PROPN
ejpam-6458	382	28	let	let	VERB
ejpam-6458	382	29	∆	∆	PROPN
ejpam-6458	382	30	=	=	SYM
ejpam-6458	382	31	{	{	PUNCT
ejpam-6458	382	32	α1	α1	PROPN
ejpam-6458	382	33	,	,	PUNCT
ejpam-6458	382	34	α2	α2	ADJ
ejpam-6458	382	35	,	,	PUNCT
ejpam-6458	382	36	α3	α3	PROPN
ejpam-6458	382	37	=	=	SYM
ejpam-6458	382	38	α1+α2	α1+α2	PROPN
ejpam-6458	382	39	,	,	PUNCT
ejpam-6458	382	40	α4	α4	NOUN
ejpam-6458	382	41	=	=	SYM
ejpam-6458	382	42	−α1−α2	−α1−α2	PROPN
ejpam-6458	382	43	,	,	PUNCT
ejpam-6458	382	44	α5	α5	PROPN
ejpam-6458	382	45	=	=	SYM
ejpam-6458	382	46	−α2	−α2	PROPN
ejpam-6458	382	47	,	,	PUNCT
ejpam-6458	382	48	α6	α6	NOUN
ejpam-6458	382	49	=	=	SYM
ejpam-6458	382	50	−α1	−α1	PROPN
ejpam-6458	382	51	}	}	PUNCT
ejpam-6458	382	52	be	be	VERB
ejpam-6458	382	53	the	the	DET
ejpam-6458	382	54	root	root	NOUN
ejpam-6458	382	55	system	system	NOUN
ejpam-6458	382	56	of	of	ADP
ejpam-6458	382	57	g.	g.	PROPN
ejpam-6458	382	58	fix	fix	VERB
ejpam-6458	382	59	a	a	DET
ejpam-6458	382	60	chevalley	chevalley	ADJ
ejpam-6458	382	61	basis	basis	NOUN
ejpam-6458	382	62	g	g	NOUN
ejpam-6458	382	63	:	:	PUNCT
ejpam-6458	382	64	e10	e10	PROPN
ejpam-6458	382	65	=	=	SYM
ejpam-6458	382	66	e12	e12	NOUN
ejpam-6458	382	67	,	,	PUNCT
ejpam-6458	382	68	f10	f10	NOUN
ejpam-6458	382	69	=	=	SYM
ejpam-6458	382	70	e21	e21	PROPN
ejpam-6458	382	71	,	,	PUNCT
ejpam-6458	382	72	e01	e01	NOUN
ejpam-6458	382	73	=	=	SYM
ejpam-6458	382	74	e23	e23	NOUN
ejpam-6458	382	75	,	,	PUNCT
ejpam-6458	382	76	f01	f01	NOUN
ejpam-6458	382	77	=	=	SYM
ejpam-6458	382	78	e32	e32	PROPN
ejpam-6458	382	79	,	,	PUNCT
ejpam-6458	382	80	e11	e11	ADJ
ejpam-6458	382	81	=	=	SYM
ejpam-6458	382	82	e13	e13	PROPN
ejpam-6458	382	83	,	,	PUNCT
ejpam-6458	382	84	f11	f11	PROPN
ejpam-6458	382	85	=	=	SYM
ejpam-6458	382	86	e31	e31	PROPN
ejpam-6458	382	87	,	,	PUNCT
ejpam-6458	382	88	h10	h10	NOUN
ejpam-6458	382	89	=	=	SYM
ejpam-6458	382	90	e11	e11	PROPN
ejpam-6458	382	91	−	−	PROPN
ejpam-6458	382	92	e22	e22	NOUN
ejpam-6458	382	93	,	,	PUNCT
ejpam-6458	382	94	h01	h01	PROPN
ejpam-6458	382	95	=	=	SYM
ejpam-6458	382	96	e22	e22	PROPN
ejpam-6458	382	97	−	−	PROPN
ejpam-6458	382	98	e33	e33	PROPN
ejpam-6458	382	99	.	.	PUNCT
ejpam-6458	383	1	let	let	VERB
ejpam-6458	383	2	us	we	PRON
ejpam-6458	383	3	define	define	VERB
ejpam-6458	383	4	the	the	DET
ejpam-6458	383	5	following	follow	VERB
ejpam-6458	383	6	order	order	NOUN
ejpam-6458	383	7	on	on	ADP
ejpam-6458	383	8	the	the	DET
ejpam-6458	383	9	elements	element	NOUN
ejpam-6458	383	10	of	of	ADP
ejpam-6458	383	11	g	g	NOUN
ejpam-6458	383	12	:	:	PUNCT
ejpam-6458	383	13	h01	h01	PROPN
ejpam-6458	383	14	<	<	X
ejpam-6458	383	15	h10	h10	PROPN
ejpam-6458	383	16	<	<	X
ejpam-6458	383	17	f01	f01	PROPN
ejpam-6458	383	18	<	<	X
ejpam-6458	383	19	f10	f10	X
ejpam-6458	383	20	<	<	X
ejpam-6458	383	21	f11	f11	X
ejpam-6458	383	22	<	<	X
ejpam-6458	383	23	e11	e11	X
ejpam-6458	383	24	<	<	X
ejpam-6458	383	25	e10	e10	X
ejpam-6458	383	26	<	<	X
ejpam-6458	383	27	e01	e01	X
ejpam-6458	383	28	.	.	PUNCT
ejpam-6458	384	1	we	we	PRON
ejpam-6458	384	2	have	have	VERB
ejpam-6458	384	3	the	the	DET
ejpam-6458	384	4	following	follow	VERB
ejpam-6458	384	5	set	set	NOUN
ejpam-6458	384	6	of	of	ADP
ejpam-6458	384	7	indecomposable	indecomposable	ADJ
ejpam-6458	384	8	lists	list	NOUN
ejpam-6458	384	9	of	of	ADP
ejpam-6458	384	10	roots	root	NOUN
ejpam-6458	384	11	:	:	PUNCT
ejpam-6458	384	12	{	{	PUNCT
ejpam-6458	384	13	α1	α1	PROPN
ejpam-6458	384	14	,	,	PUNCT
ejpam-6458	384	15	α6	α6	NOUN
ejpam-6458	384	16	}	}	PUNCT
ejpam-6458	384	17	,	,	PUNCT
ejpam-6458	384	18	{	{	PUNCT
ejpam-6458	384	19	α2	α2	ADJ
ejpam-6458	384	20	,	,	PUNCT
ejpam-6458	384	21	α5	α5	PROPN
ejpam-6458	384	22	}	}	PUNCT
ejpam-6458	384	23	,	,	PUNCT
ejpam-6458	384	24	{	{	PUNCT
ejpam-6458	384	25	α3	α3	NOUN
ejpam-6458	384	26	,	,	PUNCT
ejpam-6458	384	27	α4	α4	NOUN
ejpam-6458	384	28	}	}	PUNCT
ejpam-6458	384	29	,	,	PUNCT
ejpam-6458	384	30	{	{	PUNCT
ejpam-6458	384	31	α1	α1	PROPN
ejpam-6458	384	32	,	,	PUNCT
ejpam-6458	384	33	α2	α2	ADJ
ejpam-6458	384	34	,	,	PUNCT
ejpam-6458	384	35	α4	α4	NOUN
ejpam-6458	384	36	}	}	PUNCT
ejpam-6458	384	37	,	,	PUNCT
ejpam-6458	384	38	{	{	PUNCT
ejpam-6458	384	39	α3	α3	NOUN
ejpam-6458	384	40	,	,	PUNCT
ejpam-6458	384	41	α5	α5	NOUN
ejpam-6458	384	42	,	,	PUNCT
ejpam-6458	384	43	α6	α6	NOUN
ejpam-6458	384	44	}	}	PUNCT
ejpam-6458	384	45	,	,	PUNCT
ejpam-6458	384	46	and	and	CCONJ
ejpam-6458	384	47	the	the	DET
ejpam-6458	384	48	following	follow	VERB
ejpam-6458	384	49	set	set	NOUN
ejpam-6458	384	50	of	of	ADP
ejpam-6458	384	51	perfect	perfect	ADJ
ejpam-6458	384	52	monomials	monomial	NOUN
ejpam-6458	384	53	:	:	PUNCT
ejpam-6458	384	54	h1	h1	PROPN
ejpam-6458	384	55	=	=	SYM
ejpam-6458	384	56	h01	h01	PROPN
ejpam-6458	384	57	,	,	PUNCT
ejpam-6458	384	58	h2	h2	NOUN
ejpam-6458	384	59	=	=	SYM
ejpam-6458	384	60	h10	h10	PROPN
ejpam-6458	384	61	,	,	PUNCT
ejpam-6458	384	62	c1	c1	PROPN
ejpam-6458	384	63	=	=	PUNCT
ejpam-6458	384	64	f01e01	f01e01	PROPN
ejpam-6458	384	65	,	,	PUNCT
ejpam-6458	384	66	c2	c2	PROPN
ejpam-6458	384	67	=	=	SYM
ejpam-6458	384	68	f10e10	f10e10	PROPN
ejpam-6458	384	69	,	,	PUNCT
ejpam-6458	384	70	c3	c3	PROPN
ejpam-6458	384	71	=	=	SYM
ejpam-6458	384	72	f11e11	f11e11	PROPN
ejpam-6458	384	73	,	,	PUNCT
ejpam-6458	384	74	c4	c4	NOUN
ejpam-6458	384	75	=	=	SYM
ejpam-6458	384	76	f11e10e01	f11e10e01	PROPN
ejpam-6458	384	77	,	,	PUNCT
ejpam-6458	384	78	c5	c5	PROPN
ejpam-6458	384	79	=	=	PUNCT
ejpam-6458	384	80	f01f10e11	f01f10e11	PROPN
ejpam-6458	384	81	.	.	X
ejpam-6458	384	82	define	define	VERB
ejpam-6458	384	83	the	the	DET
ejpam-6458	384	84	order	order	NOUN
ejpam-6458	384	85	on	on	ADP
ejpam-6458	384	86	the	the	DET
ejpam-6458	384	87	set	set	NOUN
ejpam-6458	384	88	of	of	ADP
ejpam-6458	384	89	perfect	perfect	ADJ
ejpam-6458	384	90	monomials	monomial	NOUN
ejpam-6458	384	91	:	:	PUNCT
ejpam-6458	384	92	h1	h1	VERB
ejpam-6458	384	93	<	<	X
ejpam-6458	384	94	h2	h2	PROPN
ejpam-6458	384	95	<	<	X
ejpam-6458	384	96	c1	c1	PROPN
ejpam-6458	384	97	<	<	X
ejpam-6458	384	98	c2	c2	PROPN
ejpam-6458	384	99	<	<	X
ejpam-6458	384	100	c3	c3	PROPN
ejpam-6458	384	101	<	<	X
ejpam-6458	384	102	c4	c4	PROPN
ejpam-6458	384	103	<	<	X
ejpam-6458	384	104	c5	c5	PROPN
ejpam-6458	384	105	.	.	PUNCT
ejpam-6458	385	1	note	note	VERB
ejpam-6458	385	2	that	that	SCONJ
ejpam-6458	385	3	any	any	DET
ejpam-6458	385	4	monomial	monomial	NOUN
ejpam-6458	385	5	containing	contain	VERB
ejpam-6458	385	6	both	both	DET
ejpam-6458	385	7	variables	variable	NOUN
ejpam-6458	385	8	c4	c4	NOUN
ejpam-6458	385	9	and	and	CCONJ
ejpam-6458	385	10	c5	c5	PROPN
ejpam-6458	385	11	is	be	AUX
ejpam-6458	385	12	not	not	PART
ejpam-6458	385	13	semi	semi	ADJ
ejpam-6458	385	14	-	-	ADJ
ejpam-6458	385	15	perfect	perfect	ADJ
ejpam-6458	385	16	since	since	SCONJ
ejpam-6458	385	17	m′	m′	NOUN
ejpam-6458	385	18	=	=	NOUN
ejpam-6458	385	19	c1c2c3	c1c2c3	NOUN
ejpam-6458	385	20	has	have	VERB
ejpam-6458	385	21	the	the	DET
ejpam-6458	385	22	same	same	ADJ
ejpam-6458	385	23	associated	associated	ADJ
ejpam-6458	385	24	list	list	NOUN
ejpam-6458	385	25	of	of	ADP
ejpam-6458	385	26	roots	root	NOUN
ejpam-6458	385	27	as	as	ADP
ejpam-6458	385	28	m	m	NOUN
ejpam-6458	385	29	=	=	SYM
ejpam-6458	385	30	c4c5	c4c5	NOUN
ejpam-6458	385	31	,	,	PUNCT
ejpam-6458	385	32	but	but	CCONJ
ejpam-6458	385	33	c1	c1	PROPN
ejpam-6458	385	34	<	<	X
ejpam-6458	385	35	c4	c4	PROPN
ejpam-6458	385	36	.	.	PUNCT
ejpam-6458	386	1	applying	apply	VERB
ejpam-6458	386	2	the	the	DET
ejpam-6458	386	3	relations	relation	NOUN
ejpam-6458	386	4	between	between	ADP
ejpam-6458	386	5	the	the	DET
ejpam-6458	386	6	generators	generator	NOUN
ejpam-6458	386	7	we	we	PRON
ejpam-6458	386	8	easily	easily	ADV
ejpam-6458	386	9	obtain	obtain	VERB
ejpam-6458	386	10	the	the	DET
ejpam-6458	386	11	following	follow	VERB
ejpam-6458	386	12	statement	statement	NOUN
ejpam-6458	386	13	.	.	PUNCT
ejpam-6458	387	1	proposition	proposition	NOUN
ejpam-6458	387	2	4.1	4.1	NUM
ejpam-6458	387	3	.	.	NOUN
ejpam-6458	388	1	•	•	NUM
ejpam-6458	388	2	the	the	DET
ejpam-6458	388	3	following	follow	VERB
ejpam-6458	388	4	set	set	NOUN
ejpam-6458	388	5	of	of	ADP
ejpam-6458	388	6	monomials	monomial	NOUN
ejpam-6458	388	7	is	be	AUX
ejpam-6458	388	8	a	a	DET
ejpam-6458	388	9	basis	basis	NOUN
ejpam-6458	388	10	of	of	ADP
ejpam-6458	388	11	û0(g	û0(g	NOUN
ejpam-6458	388	12	):	):	PUNCT
ejpam-6458	388	13	p	p	X
ejpam-6458	388	14	=	=	X
ejpam-6458	388	15	{	{	PUNCT
ejpam-6458	388	16	hs11	hs11	PROPN
ejpam-6458	388	17	h	h	NOUN
ejpam-6458	388	18	s2	s2	VERB
ejpam-6458	388	19	2	2	NUM
ejpam-6458	388	20	c	c	NOUN
ejpam-6458	388	21	s3	s3	PROPN
ejpam-6458	388	22	1	1	NUM
ejpam-6458	388	23	c	c	NOUN
ejpam-6458	388	24	s4	s4	PROPN
ejpam-6458	388	25	2	2	PROPN
ejpam-6458	388	26	c	c	NOUN
ejpam-6458	388	27	s5	s5	X
ejpam-6458	388	28	3	3	NUM
ejpam-6458	388	29	c	c	PROPN
ejpam-6458	388	30	s6	s6	PROPN
ejpam-6458	388	31	4	4	NUM
ejpam-6458	388	32	|	|	NOUN
ejpam-6458	388	33	s1	s1	NOUN
ejpam-6458	388	34	,	,	PUNCT
ejpam-6458	388	35	.	.	PUNCT
ejpam-6458	388	36	.	.	PUNCT
ejpam-6458	389	1	.	.	PUNCT
ejpam-6458	390	1	,	,	PUNCT
ejpam-6458	390	2	s6	s6	PROPN
ejpam-6458	390	3	∈	∈	PROPN
ejpam-6458	390	4	n	n	CCONJ
ejpam-6458	390	5	}	}	PUNCT
ejpam-6458	390	6	∪	∪	NOUN
ejpam-6458	390	7	{	{	PUNCT
ejpam-6458	390	8	hs11	hs11	PROPN
ejpam-6458	390	9	h	h	NOUN
ejpam-6458	390	10	s2	s2	VERB
ejpam-6458	390	11	2	2	NUM
ejpam-6458	390	12	c	c	NOUN
ejpam-6458	390	13	s3	s3	PROPN
ejpam-6458	390	14	1	1	NUM
ejpam-6458	390	15	c	c	NOUN
ejpam-6458	390	16	s4	s4	PROPN
ejpam-6458	390	17	2	2	PROPN
ejpam-6458	390	18	c	c	NOUN
ejpam-6458	390	19	s5	s5	X
ejpam-6458	390	20	3	3	NUM
ejpam-6458	390	21	c	c	PROPN
ejpam-6458	390	22	s6	s6	PROPN
ejpam-6458	390	23	5	5	NUM
ejpam-6458	390	24	|	|	NOUN
ejpam-6458	390	25	s1	s1	NOUN
ejpam-6458	390	26	,	,	PUNCT
ejpam-6458	390	27	.	.	PUNCT
ejpam-6458	390	28	.	.	PUNCT
ejpam-6458	390	29	.	.	PUNCT
ejpam-6458	391	1	,	,	PUNCT
ejpam-6458	391	2	s6	s6	PROPN
ejpam-6458	391	3	∈	∈	PROPN
ejpam-6458	391	4	n	n	CCONJ
ejpam-6458	391	5	}	}	PUNCT
ejpam-6458	391	6	.	.	PUNCT
ejpam-6458	392	1	•	•	NOUN
ejpam-6458	392	2	the	the	DET
ejpam-6458	392	3	set	set	NOUN
ejpam-6458	392	4	k̃	k̃	PROPN
ejpam-6458	392	5	=	=	SYM
ejpam-6458	392	6	{	{	PUNCT
ejpam-6458	392	7	x	x	SYM
ejpam-6458	392	8	|x	|x	NOUN
ejpam-6458	392	9	∈	∈	PROPN
ejpam-6458	392	10	k	k	X
ejpam-6458	392	11	′,len(x	′,len(x	PROPN
ejpam-6458	392	12	)	)	PUNCT
ejpam-6458	392	13	=	=	SYM
ejpam-6458	393	1	2	2	X
ejpam-6458	393	2	}	}	PUNCT
ejpam-6458	393	3	is	be	AUX
ejpam-6458	393	4	a	a	DET
ejpam-6458	393	5	generating	generate	VERB
ejpam-6458	393	6	set	set	NOUN
ejpam-6458	393	7	of	of	ADP
ejpam-6458	393	8	the	the	DET
ejpam-6458	393	9	ideal	ideal	NOUN
ejpam-6458	393	10	of	of	ADP
ejpam-6458	393	11	relations	relation	NOUN
ejpam-6458	393	12	k.	k.	PROPN
ejpam-6458	394	1	the	the	DET
ejpam-6458	394	2	following	follow	VERB
ejpam-6458	394	3	k̃	k̃	PROPN
ejpam-6458	394	4	is	be	AUX
ejpam-6458	394	5	the	the	DET
ejpam-6458	394	6	list	list	NOUN
ejpam-6458	394	7	of	of	ADP
ejpam-6458	394	8	all	all	DET
ejpam-6458	394	9	relations	relation	NOUN
ejpam-6458	394	10	of	of	ADP
ejpam-6458	394	11	length	length	NOUN
ejpam-6458	394	12	two	two	NUM
ejpam-6458	394	13	:	:	PUNCT
ejpam-6458	394	14	cjhi	cjhi	NOUN
ejpam-6458	394	15	=	=	PUNCT
ejpam-6458	394	16	hicj	hicj	NOUN
ejpam-6458	394	17	,	,	PUNCT
ejpam-6458	394	18	i	i	PRON
ejpam-6458	394	19	=	=	NOUN
ejpam-6458	394	20	1	1	NUM
ejpam-6458	394	21	,	,	PUNCT
ejpam-6458	394	22	2	2	NUM
ejpam-6458	394	23	,	,	PUNCT
ejpam-6458	394	24	j	j	NOUN
ejpam-6458	394	25	=	=	SYM
ejpam-6458	394	26	1	1	NUM
ejpam-6458	394	27	,	,	PUNCT
ejpam-6458	394	28	.	.	PUNCT
ejpam-6458	394	29	.	.	PUNCT
ejpam-6458	395	1	.	.	PUNCT
ejpam-6458	396	1	,	,	PUNCT
ejpam-6458	396	2	5	5	NUM
ejpam-6458	396	3	(	(	PUNCT
ejpam-6458	396	4	4.1	4.1	NUM
ejpam-6458	396	5	)	)	PUNCT
ejpam-6458	396	6	c2c1	c2c1	NOUN
ejpam-6458	396	7	=	=	PUNCT
ejpam-6458	396	8	−c5	−c5	NOUN
ejpam-6458	396	9	+	+	CCONJ
ejpam-6458	396	10	c4	c4	NOUN
ejpam-6458	396	11	+	+	CCONJ
ejpam-6458	396	12	c1c2	c1c2	ADJ
ejpam-6458	396	13	,	,	PUNCT
ejpam-6458	396	14	(	(	PUNCT
ejpam-6458	396	15	4.2	4.2	NUM
ejpam-6458	396	16	)	)	PUNCT
ejpam-6458	396	17	c3c1	c3c1	NOUN
ejpam-6458	396	18	=	=	SYM
ejpam-6458	396	19	c5	c5	PROPN
ejpam-6458	396	20	−	−	PROPN
ejpam-6458	396	21	c4	c4	NOUN
ejpam-6458	396	22	+	+	CCONJ
ejpam-6458	396	23	c1c3	c1c3	NOUN
ejpam-6458	396	24	,	,	PUNCT
ejpam-6458	396	25	(	(	PUNCT
ejpam-6458	396	26	4.3	4.3	NUM
ejpam-6458	396	27	)	)	PUNCT
ejpam-6458	396	28	c4c1	c4c1	NOUN
ejpam-6458	396	29	=	=	SYM
ejpam-6458	396	30	−2c5	−2c5	PUNCT
ejpam-6458	397	1	+	+	CCONJ
ejpam-6458	397	2	(	(	PUNCT
ejpam-6458	397	3	2	2	NUM
ejpam-6458	397	4	+	+	NUM
ejpam-6458	397	5	h1)c4	h1)c4	NOUN
ejpam-6458	397	6	+	+	CCONJ
ejpam-6458	398	1	c1c4	c1c4	NOUN
ejpam-6458	398	2	−	−	NOUN
ejpam-6458	398	3	c1c3	c1c3	NOUN
ejpam-6458	399	1	+	+	CCONJ
ejpam-6458	399	2	c1c2	c1c2	ADJ
ejpam-6458	399	3	,	,	PUNCT
ejpam-6458	399	4	(	(	PUNCT
ejpam-6458	399	5	4.4	4.4	NUM
ejpam-6458	399	6	)	)	PUNCT
ejpam-6458	399	7	c5c1	c5c1	VERB
ejpam-6458	399	8	=	=	SYM
ejpam-6458	399	9	−h1c5	−h1c5	X
ejpam-6458	399	10	+	+	CCONJ
ejpam-6458	399	11	c1c5	c1c5	X
ejpam-6458	399	12	+	+	NOUN
ejpam-6458	399	13	c1c3	c1c3	NOUN
ejpam-6458	400	1	−	−	NOUN
ejpam-6458	400	2	c1c2	c1c2	NOUN
ejpam-6458	400	3	,	,	PUNCT
ejpam-6458	400	4	(	(	PUNCT
ejpam-6458	400	5	4.5	4.5	NUM
ejpam-6458	400	6	)	)	PUNCT
ejpam-6458	401	1	c3c2	c3c2	X
ejpam-6458	401	2	=	=	PUNCT
ejpam-6458	401	3	−c5	−c5	NOUN
ejpam-6458	401	4	+	+	CCONJ
ejpam-6458	401	5	c4	c4	NOUN
ejpam-6458	401	6	+	+	CCONJ
ejpam-6458	401	7	c2c3	c2c3	PROPN
ejpam-6458	401	8	,	,	PUNCT
ejpam-6458	401	9	(	(	PUNCT
ejpam-6458	401	10	4.6	4.6	NUM
ejpam-6458	401	11	)	)	PUNCT
ejpam-6458	401	12	c4c2	c4c2	NOUN
ejpam-6458	401	13	=	=	SYM
ejpam-6458	401	14	h2c3	h2c3	PROPN
ejpam-6458	401	15	+	+	CCONJ
ejpam-6458	401	16	h2c4	h2c4	PROPN
ejpam-6458	401	17	+	+	CCONJ
ejpam-6458	401	18	c2c4	c2c4	NOUN
ejpam-6458	401	19	+	+	CCONJ
ejpam-6458	401	20	c2c3	c2c3	NOUN
ejpam-6458	401	21	−	−	NOUN
ejpam-6458	401	22	c1c2	c1c2	NOUN
ejpam-6458	401	23	,	,	PUNCT
ejpam-6458	401	24	(	(	PUNCT
ejpam-6458	401	25	4.7	4.7	NUM
ejpam-6458	401	26	)	)	PUNCT
ejpam-6458	401	27	c5c2	c5c2	NOUN
ejpam-6458	401	28	=	=	SYM
ejpam-6458	401	29	−h2c3	−h2c3	NOUN
ejpam-6458	401	30	−	−	NOUN
ejpam-6458	402	1	h2c5	h2c5	PROPN
ejpam-6458	403	1	+	+	CCONJ
ejpam-6458	403	2	c2c5	c2c5	ADP
ejpam-6458	403	3	−	−	PROPN
ejpam-6458	403	4	c2c3	c2c3	X
ejpam-6458	403	5	+	+	CCONJ
ejpam-6458	403	6	c1c2	c1c2	ADJ
ejpam-6458	403	7	,	,	PUNCT
ejpam-6458	403	8	(	(	PUNCT
ejpam-6458	403	9	4.8	4.8	NUM
ejpam-6458	403	10	)	)	PUNCT
ejpam-6458	403	11	c4c3	c4c3	X
ejpam-6458	403	12	=	=	SYM
ejpam-6458	403	13	2c5	2c5	PROPN
ejpam-6458	403	14	−	−	PROPN
ejpam-6458	403	15	(	(	PUNCT
ejpam-6458	403	16	h2	h2	NOUN
ejpam-6458	403	17	+	+	CCONJ
ejpam-6458	403	18	h1	h1	X
ejpam-6458	403	19	+	+	CCONJ
ejpam-6458	403	20	2)c4	2)c4	NUM
ejpam-6458	403	21	+	+	CCONJ
ejpam-6458	403	22	c3c4	c3c4	ADJ
ejpam-6458	403	23	−	−	NOUN
ejpam-6458	403	24	h2c3	h2c3	INTJ
ejpam-6458	403	25	−	−	X
ejpam-6458	403	26	c2c3	c2c3	PUNCT
ejpam-6458	404	1	+	+	CCONJ
ejpam-6458	404	2	c1c3	c1c3	NOUN
ejpam-6458	404	3	,	,	PUNCT
ejpam-6458	404	4	(	(	PUNCT
ejpam-6458	404	5	4.9	4.9	NUM
ejpam-6458	404	6	)	)	PUNCT
ejpam-6458	404	7	c5c3	c5c3	NOUN
ejpam-6458	404	8	=	=	SYM
ejpam-6458	404	9	(	(	PUNCT
ejpam-6458	404	10	h2	h2	NOUN
ejpam-6458	404	11	+	+	CCONJ
ejpam-6458	404	12	h1)c5	h1)c5	NOUN
ejpam-6458	405	1	+	+	CCONJ
ejpam-6458	405	2	c3c5	c3c5	NOUN
ejpam-6458	405	3	+	+	X
ejpam-6458	405	4	h2c3	h2c3	PROPN
ejpam-6458	405	5	+	+	CCONJ
ejpam-6458	405	6	c2c3	c2c3	NOUN
ejpam-6458	405	7	−	−	NOUN
ejpam-6458	405	8	c1c3	c1c3	NOUN
ejpam-6458	405	9	,	,	PUNCT
ejpam-6458	405	10	(	(	PUNCT
ejpam-6458	405	11	4.10	4.10	NUM
ejpam-6458	405	12	)	)	PUNCT
ejpam-6458	405	13	c5c4	c5c4	NOUN
ejpam-6458	406	1	=	=	PUNCT
ejpam-6458	406	2	−(2h2	−(2h2	NOUN
ejpam-6458	407	1	+	+	CCONJ
ejpam-6458	407	2	h1)c5	h1)c5	NOUN
ejpam-6458	407	3	−	−	NOUN
ejpam-6458	407	4	c3c5	c3c5	NOUN
ejpam-6458	407	5	−	−	PROPN
ejpam-6458	407	6	2h2c3	2h2c3	NOUN
ejpam-6458	407	7	+	+	CCONJ
ejpam-6458	408	1	c2c5	c2c5	ADP
ejpam-6458	408	2	−	−	PROPN
ejpam-6458	408	3	2c2c3	2c2c3	NUM
ejpam-6458	408	4	−	−	NOUN
ejpam-6458	408	5	c1c5	c1c5	VERB
ejpam-6458	408	6	+	+	X
ejpam-6458	408	7	c1c2c3	c1c2c3	NOUN
ejpam-6458	408	8	+	+	CCONJ
ejpam-6458	408	9	(	(	PUNCT
ejpam-6458	408	10	h2	h2	NOUN
ejpam-6458	408	11	+	+	CCONJ
ejpam-6458	408	12	h1	h1	NOUN
ejpam-6458	408	13	+	+	CCONJ
ejpam-6458	408	14	2)c1c2	2)c1c2	NOUN
ejpam-6458	408	15	,	,	PUNCT
ejpam-6458	408	16	(	(	PUNCT
ejpam-6458	408	17	4.11	4.11	NUM
ejpam-6458	408	18	)	)	PUNCT
ejpam-6458	408	19	c4c5	c4c5	NOUN
ejpam-6458	409	1	=	=	PUNCT
ejpam-6458	409	2	−h1c5	−h1c5	NUM
ejpam-6458	409	3	−	−	NOUN
ejpam-6458	409	4	c3c5	c3c5	NOUN
ejpam-6458	409	5	+	+	CCONJ
ejpam-6458	410	1	h1h2c3	h1h2c3	ADJ
ejpam-6458	410	2	+	+	NOUN
ejpam-6458	410	3	c2c5	c2c5	PROPN
ejpam-6458	410	4	+	+	CCONJ
ejpam-6458	410	5	h1c2c3	h1c2c3	ADJ
ejpam-6458	410	6	−	−	NOUN
ejpam-6458	410	7	c1c5	c1c5	X
ejpam-6458	410	8	+	+	CCONJ
ejpam-6458	410	9	h2c1c3	h2c1c3	NOUN
ejpam-6458	410	10	+	+	CCONJ
ejpam-6458	410	11	c1c2c3	c1c2c3	NOUN
ejpam-6458	410	12	.	.	PUNCT
ejpam-6458	411	1	(	(	PUNCT
ejpam-6458	411	2	4.12	4.12	NUM
ejpam-6458	411	3	)	)	PUNCT
ejpam-6458	411	4	the	the	DET
ejpam-6458	411	5	following	follow	VERB
ejpam-6458	411	6	casimir	casimir	NOUN
ejpam-6458	411	7	elements	element	NOUN
ejpam-6458	411	8	generate	generate	VERB
ejpam-6458	411	9	the	the	DET
ejpam-6458	411	10	center	center	NOUN
ejpam-6458	411	11	of	of	ADP
ejpam-6458	411	12	the	the	DET
ejpam-6458	411	13	universal	universal	ADJ
ejpam-6458	411	14	enveloping	enveloping	NOUN
ejpam-6458	411	15	algebra	algebra	NOUN
ejpam-6458	411	16	[	[	X
ejpam-6458	411	17	14	14	NUM
ejpam-6458	411	18	]	]	SYM
ejpam-6458	411	19	:	:	PUNCT
ejpam-6458	411	20	z1	z1	PROPN
ejpam-6458	411	21	=	=	SYM
ejpam-6458	411	22	c3	c3	PROPN
ejpam-6458	411	23	+	+	CCONJ
ejpam-6458	411	24	c2	c2	PROPN
ejpam-6458	411	25	+	+	CCONJ
ejpam-6458	411	26	c1	c1	PROPN
ejpam-6458	411	27	+	+	CCONJ
ejpam-6458	411	28	1	1	NUM
ejpam-6458	411	29	3	3	NUM
ejpam-6458	411	30	(	(	PUNCT
ejpam-6458	411	31	h22	h22	X
ejpam-6458	411	32	+	+	CCONJ
ejpam-6458	411	33	3h2	3h2	NUM
ejpam-6458	411	34	+	+	CCONJ
ejpam-6458	411	35	h21	h21	NOUN
ejpam-6458	411	36	+	+	CCONJ
ejpam-6458	411	37	3h1	3h1	NUM
ejpam-6458	411	38	+	+	CCONJ
ejpam-6458	411	39	h2h1	h2h1	NOUN
ejpam-6458	411	40	)	)	PUNCT
ejpam-6458	411	41	(	(	PUNCT
ejpam-6458	411	42	4.13	4.13	X
ejpam-6458	411	43	)	)	PUNCT
ejpam-6458	411	44	m.	m.	NOUN
ejpam-6458	411	45	andelić	andelić	PROPN
ejpam-6458	411	46	et	et	PROPN
ejpam-6458	412	1	al	al	PROPN
ejpam-6458	412	2	.	.	PUNCT
ejpam-6458	412	3	/	/	SYM
ejpam-6458	412	4	eur	eur	PROPN
ejpam-6458	412	5	.	.	PUNCT
ejpam-6458	413	1	j.	j.	PROPN
ejpam-6458	413	2	pure	pure	PROPN
ejpam-6458	413	3	appl	appl	PROPN
ejpam-6458	413	4	.	.	PROPN
ejpam-6458	413	5	math	math	PROPN
ejpam-6458	413	6	,	,	PUNCT
ejpam-6458	413	7	18	18	NUM
ejpam-6458	413	8	(	(	PUNCT
ejpam-6458	413	9	3	3	NUM
ejpam-6458	413	10	)	)	PUNCT
ejpam-6458	413	11	(	(	PUNCT
ejpam-6458	413	12	2025	2025	NUM
ejpam-6458	413	13	)	)	PUNCT
ejpam-6458	413	14	,	,	PUNCT
ejpam-6458	413	15	6458	6458	NUM
ejpam-6458	413	16	10	10	NUM
ejpam-6458	413	17	of	of	ADP
ejpam-6458	413	18	21	21	NUM
ejpam-6458	413	19	z2	z2	NOUN
ejpam-6458	413	20	=	=	SYM
ejpam-6458	413	21	c5	c5	PROPN
ejpam-6458	413	22	+	+	CCONJ
ejpam-6458	413	23	c4	c4	NOUN
ejpam-6458	413	24	+	+	CCONJ
ejpam-6458	413	25	1	1	NUM
ejpam-6458	413	26	3	3	NUM
ejpam-6458	413	27	(	(	PUNCT
ejpam-6458	413	28	h1	h1	PROPN
ejpam-6458	413	29	−	−	PROPN
ejpam-6458	413	30	h2)c3	h2)c3	NOUN
ejpam-6458	413	31	−	−	PROPN
ejpam-6458	413	32	1	1	NUM
ejpam-6458	413	33	3	3	NUM
ejpam-6458	413	34	(	(	PUNCT
ejpam-6458	413	35	6	6	NUM
ejpam-6458	413	36	+	+	NUM
ejpam-6458	413	37	2h1	2h1	NUM
ejpam-6458	413	38	+	+	CCONJ
ejpam-6458	413	39	h2)c2	h2)c2	PROPN
ejpam-6458	414	1	+	+	CCONJ
ejpam-6458	414	2	1	1	NUM
ejpam-6458	414	3	3	3	NUM
ejpam-6458	414	4	(	(	PUNCT
ejpam-6458	414	5	h1	h1	PROPN
ejpam-6458	414	6	+	+	CCONJ
ejpam-6458	415	1	2h2)c1	2h2)c1	NUM
ejpam-6458	415	2	+	+	NUM
ejpam-6458	415	3	1	1	NUM
ejpam-6458	415	4	27	27	NUM
ejpam-6458	415	5	(	(	PUNCT
ejpam-6458	415	6	−h2	−h2	VERB
ejpam-6458	415	7	−	−	PROPN
ejpam-6458	415	8	3	3	NUM
ejpam-6458	415	9	+	+	CCONJ
ejpam-6458	415	10	h1)(6	h1)(6	PROPN
ejpam-6458	415	11	+	+	CCONJ
ejpam-6458	415	12	2h1	2h1	NUM
ejpam-6458	415	13	+	+	CCONJ
ejpam-6458	415	14	h2)(h1	h2)(h1	NUM
ejpam-6458	415	15	+	+	CCONJ
ejpam-6458	415	16	2h2	2h2	NUM
ejpam-6458	415	17	)	)	PUNCT
ejpam-6458	415	18	(	(	PUNCT
ejpam-6458	415	19	4.14	4.14	NUM
ejpam-6458	415	20	)	)	PUNCT
ejpam-6458	415	21	using	use	VERB
ejpam-6458	415	22	the	the	DET
ejpam-6458	415	23	relations	relation	NOUN
ejpam-6458	415	24	(	(	PUNCT
ejpam-6458	415	25	4.1)-(4.14	4.1)-(4.14	NOUN
ejpam-6458	415	26	)	)	PUNCT
ejpam-6458	416	1	,	,	PUNCT
ejpam-6458	416	2	we	we	PRON
ejpam-6458	416	3	can	can	AUX
ejpam-6458	416	4	reduce	reduce	VERB
ejpam-6458	416	5	the	the	DET
ejpam-6458	416	6	number	number	NOUN
ejpam-6458	416	7	of	of	ADP
ejpam-6458	416	8	generators	generator	NOUN
ejpam-6458	416	9	of	of	ADP
ejpam-6458	416	10	u0(g	u0(g	NOUN
ejpam-6458	416	11	):	):	PUNCT
ejpam-6458	416	12	applying	apply	VERB
ejpam-6458	416	13	(	(	PUNCT
ejpam-6458	416	14	4.2	4.2	NUM
ejpam-6458	416	15	)	)	PUNCT
ejpam-6458	416	16	,	,	PUNCT
ejpam-6458	416	17	(	(	PUNCT
ejpam-6458	416	18	4.13	4.13	NUM
ejpam-6458	416	19	)	)	PUNCT
ejpam-6458	416	20	,	,	PUNCT
ejpam-6458	416	21	and	and	CCONJ
ejpam-6458	416	22	(	(	PUNCT
ejpam-6458	416	23	4.14	4.14	NUM
ejpam-6458	416	24	)	)	PUNCT
ejpam-6458	416	25	we	we	PRON
ejpam-6458	416	26	can	can	AUX
ejpam-6458	416	27	exclude	exclude	VERB
ejpam-6458	416	28	c3	c3	PROPN
ejpam-6458	416	29	,	,	PUNCT
ejpam-6458	416	30	c4	c4	NOUN
ejpam-6458	416	31	,	,	PUNCT
ejpam-6458	416	32	c5	c5	PROPN
ejpam-6458	416	33	from	from	ADP
ejpam-6458	416	34	all	all	DET
ejpam-6458	416	35	other	other	ADJ
ejpam-6458	416	36	relations	relation	NOUN
ejpam-6458	416	37	.	.	PUNCT
ejpam-6458	417	1	as	as	ADP
ejpam-6458	417	2	a	a	DET
ejpam-6458	417	3	result	result	NOUN
ejpam-6458	417	4	we	we	PRON
ejpam-6458	417	5	will	will	AUX
ejpam-6458	417	6	get	get	VERB
ejpam-6458	417	7	a	a	DET
ejpam-6458	417	8	generating	generate	VERB
ejpam-6458	417	9	set	set	NOUN
ejpam-6458	417	10	s	s	PART
ejpam-6458	417	11	=	=	X
ejpam-6458	417	12	{	{	PUNCT
ejpam-6458	417	13	h1	h1	PROPN
ejpam-6458	417	14	,	,	PUNCT
ejpam-6458	417	15	h2	h2	PROPN
ejpam-6458	417	16	,	,	PUNCT
ejpam-6458	417	17	z1	z1	PROPN
ejpam-6458	417	18	,	,	PUNCT
ejpam-6458	417	19	z2	z2	PROPN
ejpam-6458	417	20	,	,	PUNCT
ejpam-6458	417	21	c1	c1	PROPN
ejpam-6458	417	22	,	,	PUNCT
ejpam-6458	417	23	c2	c2	PROPN
ejpam-6458	417	24	}	}	PUNCT
ejpam-6458	417	25	of	of	ADP
ejpam-6458	417	26	u0(g	u0(g	NOUN
ejpam-6458	417	27	)	)	PUNCT
ejpam-6458	417	28	with	with	ADP
ejpam-6458	417	29	the	the	DET
ejpam-6458	417	30	following	follow	VERB
ejpam-6458	417	31	decomposition	decomposition	NOUN
ejpam-6458	417	32	:	:	PUNCT
ejpam-6458	417	33	s1	s1	NOUN
ejpam-6458	417	34	=	=	PUNCT
ejpam-6458	417	35	{	{	PUNCT
ejpam-6458	417	36	h1	h1	PROPN
ejpam-6458	417	37	,	,	PUNCT
ejpam-6458	417	38	h2	h2	PROPN
ejpam-6458	417	39	,	,	PUNCT
ejpam-6458	417	40	z1	z1	PROPN
ejpam-6458	417	41	,	,	PUNCT
ejpam-6458	417	42	z2	z2	PROPN
ejpam-6458	417	43	}	}	PUNCT
ejpam-6458	417	44	,	,	PUNCT
ejpam-6458	417	45	s2	s2	X
ejpam-6458	417	46	=	=	SYM
ejpam-6458	417	47	{	{	PUNCT
ejpam-6458	417	48	c1	c1	NOUN
ejpam-6458	417	49	}	}	PUNCT
ejpam-6458	417	50	,	,	PUNCT
ejpam-6458	417	51	s3	s3	PROPN
ejpam-6458	417	52	=	=	SYM
ejpam-6458	417	53	{	{	PUNCT
ejpam-6458	417	54	c2	c2	PROPN
ejpam-6458	417	55	}	}	PUNCT
ejpam-6458	417	56	.	.	PUNCT
ejpam-6458	418	1	for	for	ADP
ejpam-6458	418	2	the	the	DET
ejpam-6458	418	3	set	set	NOUN
ejpam-6458	418	4	of	of	ADP
ejpam-6458	418	5	relations	relation	NOUN
ejpam-6458	418	6	we	we	PRON
ejpam-6458	418	7	have	have	VERB
ejpam-6458	418	8	r	r	NOUN
ejpam-6458	418	9	=	=	SYM
ejpam-6458	418	10	r1	r1	PROPN
ejpam-6458	418	11	∪	∪	ADJ
ejpam-6458	418	12	r2	r2	PROPN
ejpam-6458	418	13	,	,	PUNCT
ejpam-6458	418	14	where	where	SCONJ
ejpam-6458	418	15	r1	r1	PROPN
ejpam-6458	418	16	consist	consist	NOUN
ejpam-6458	418	17	of	of	ADP
ejpam-6458	418	18	the	the	DET
ejpam-6458	418	19	relations	relation	NOUN
ejpam-6458	418	20	obtained	obtain	VERB
ejpam-6458	418	21	from	from	ADP
ejpam-6458	418	22	(	(	PUNCT
ejpam-6458	418	23	4.1)-(4.5	4.1)-(4.5	NUM
ejpam-6458	418	24	)	)	PUNCT
ejpam-6458	418	25	,	,	PUNCT
ejpam-6458	418	26	and	and	CCONJ
ejpam-6458	418	27	r2	r2	PROPN
ejpam-6458	418	28	consists	consist	VERB
ejpam-6458	418	29	of	of	ADP
ejpam-6458	418	30	the	the	DET
ejpam-6458	418	31	relations	relation	NOUN
ejpam-6458	418	32	obtained	obtain	VERB
ejpam-6458	418	33	from	from	ADP
ejpam-6458	418	34	(	(	PUNCT
ejpam-6458	418	35	4.6)-(4.12	4.6)-(4.12	NUM
ejpam-6458	418	36	)	)	PUNCT
ejpam-6458	418	37	.	.	PUNCT
ejpam-6458	419	1	4.2	4.2	NUM
ejpam-6458	419	2	.	.	PUNCT
ejpam-6458	420	1	generic	generic	ADJ
ejpam-6458	420	2	torsion	torsion	NOUN
ejpam-6458	420	3	free	free	PROPN
ejpam-6458	420	4	a2	a2	NOUN
ejpam-6458	420	5	-	-	PUNCT
ejpam-6458	420	6	modules	module	NOUN
ejpam-6458	420	7	let	let	VERB
ejpam-6458	420	8	γ	γ	NOUN
ejpam-6458	420	9	be	be	AUX
ejpam-6458	420	10	the	the	DET
ejpam-6458	420	11	commutative	commutative	ADJ
ejpam-6458	420	12	subalgebra	subalgebra	NOUN
ejpam-6458	420	13	of	of	ADP
ejpam-6458	420	14	u0(g	u0(g	NOUN
ejpam-6458	420	15	)	)	PUNCT
ejpam-6458	420	16	generated	generate	VERB
ejpam-6458	420	17	by	by	ADP
ejpam-6458	420	18	the	the	DET
ejpam-6458	420	19	elements	element	NOUN
ejpam-6458	420	20	h1	h1	PROPN
ejpam-6458	420	21	,	,	PUNCT
ejpam-6458	420	22	h2	h2	NOUN
ejpam-6458	420	23	,	,	PUNCT
ejpam-6458	420	24	z1	z1	PROPN
ejpam-6458	420	25	,	,	PUNCT
ejpam-6458	420	26	z2	z2	PROPN
ejpam-6458	420	27	,	,	PUNCT
ejpam-6458	420	28	c1	c1	PROPN
ejpam-6458	420	29	.	.	PUNCT
ejpam-6458	421	1	this	this	PRON
ejpam-6458	421	2	is	be	AUX
ejpam-6458	421	3	a	a	DET
ejpam-6458	421	4	gelfand	gelfand	ADJ
ejpam-6458	421	5	-	-	PUNCT
ejpam-6458	421	6	tsetlin	tsetlin	ADJ
ejpam-6458	421	7	subalgebra	subalgebra	NOUN
ejpam-6458	421	8	of	of	ADP
ejpam-6458	421	9	sl(3	sl(3	PROPN
ejpam-6458	421	10	)	)	PUNCT
ejpam-6458	421	11	.	.	PUNCT
ejpam-6458	422	1	we	we	PRON
ejpam-6458	422	2	give	give	VERB
ejpam-6458	422	3	a	a	DET
ejpam-6458	422	4	construction	construction	NOUN
ejpam-6458	422	5	of	of	ADP
ejpam-6458	422	6	a	a	DET
ejpam-6458	422	7	family	family	NOUN
ejpam-6458	422	8	of	of	ADP
ejpam-6458	422	9	γ	γ	PROPN
ejpam-6458	422	10	-	-	PUNCT
ejpam-6458	422	11	pointed	point	VERB
ejpam-6458	422	12	modules	module	NOUN
ejpam-6458	422	13	v	v	NOUN
ejpam-6458	422	14	(	(	PUNCT
ejpam-6458	422	15	a1	a1	PROPN
ejpam-6458	422	16	,	,	PUNCT
ejpam-6458	422	17	a2	a2	PROPN
ejpam-6458	422	18	,	,	PUNCT
ejpam-6458	422	19	a3	a3	NOUN
ejpam-6458	422	20	,	,	PUNCT
ejpam-6458	422	21	ξ	ξ	PROPN
ejpam-6458	422	22	,	,	PUNCT
ejpam-6458	422	23	µ	µ	NOUN
ejpam-6458	422	24	)	)	PUNCT
ejpam-6458	422	25	which	which	PRON
ejpam-6458	422	26	depend	depend	VERB
ejpam-6458	422	27	on	on	ADP
ejpam-6458	422	28	five	five	NUM
ejpam-6458	422	29	complex	complex	ADJ
ejpam-6458	422	30	parameters	parameter	NOUN
ejpam-6458	422	31	with	with	ADP
ejpam-6458	422	32	the	the	DET
ejpam-6458	422	33	restriction	restriction	NOUN
ejpam-6458	422	34	a3	a3	NOUN
ejpam-6458	422	35	/∈	/∈	PUNCT
ejpam-6458	423	1	z.	z.	PROPN
ejpam-6458	424	1	these	these	PRON
ejpam-6458	424	2	are	be	AUX
ejpam-6458	424	3	essentially	essentially	ADV
ejpam-6458	424	4	the	the	DET
ejpam-6458	424	5	universal	universal	ADJ
ejpam-6458	424	6	generic	generic	PROPN
ejpam-6458	424	7	gelfand	gelfand	PROPN
ejpam-6458	424	8	-	-	PUNCT
ejpam-6458	424	9	tsetlin	tsetlin	PROPN
ejpam-6458	424	10	modules	module	NOUN
ejpam-6458	424	11	initially	initially	ADV
ejpam-6458	424	12	constructed	construct	VERB
ejpam-6458	424	13	in	in	ADP
ejpam-6458	424	14	[	[	X
ejpam-6458	424	15	17	17	NUM
ejpam-6458	424	16	]	]	PUNCT
ejpam-6458	424	17	and	and	CCONJ
ejpam-6458	424	18	[	[	X
ejpam-6458	424	19	7	7	X
ejpam-6458	424	20	]	]	PUNCT
ejpam-6458	424	21	using	use	VERB
ejpam-6458	424	22	a	a	DET
ejpam-6458	424	23	gelfand	gelfand	ADJ
ejpam-6458	424	24	-	-	PUNCT
ejpam-6458	424	25	tsetlin	tsetlin	PROPN
ejpam-6458	424	26	basis	basis	NOUN
ejpam-6458	424	27	[	[	X
ejpam-6458	424	28	19	19	NUM
ejpam-6458	424	29	]	]	PUNCT
ejpam-6458	424	30	.	.	PUNCT
ejpam-6458	425	1	fix	fix	VERB
ejpam-6458	425	2	arbitrary	arbitrary	ADJ
ejpam-6458	425	3	a1	a1	NOUN
ejpam-6458	425	4	,	,	PUNCT
ejpam-6458	425	5	a2	a2	PROPN
ejpam-6458	425	6	,	,	PUNCT
ejpam-6458	425	7	a3	a3	NOUN
ejpam-6458	425	8	,	,	PUNCT
ejpam-6458	425	9	ξ	ξ	PROPN
ejpam-6458	425	10	,	,	PUNCT
ejpam-6458	425	11	µ	µ	X
ejpam-6458	425	12	∈	∈	NOUN
ejpam-6458	425	13	c	c	NOUN
ejpam-6458	425	14	such	such	ADJ
ejpam-6458	425	15	that	that	DET
ejpam-6458	425	16	a3	a3	NOUN
ejpam-6458	425	17	/∈	/∈	PUNCT
ejpam-6458	426	1	z.	z.	PROPN
ejpam-6458	427	1	to	to	PART
ejpam-6458	427	2	simplify	simplify	VERB
ejpam-6458	427	3	formulas	formula	NOUN
ejpam-6458	427	4	we	we	PRON
ejpam-6458	427	5	define	define	VERB
ejpam-6458	427	6	the	the	DET
ejpam-6458	427	7	following	follow	VERB
ejpam-6458	427	8	set	set	NOUN
ejpam-6458	427	9	of	of	ADP
ejpam-6458	427	10	indexed	indexed	ADJ
ejpam-6458	427	11	variables	variable	NOUN
ejpam-6458	427	12	:	:	PUNCT
ejpam-6458	427	13	h	h	NOUN
ejpam-6458	427	14	(	(	PUNCT
ejpam-6458	427	15	1	1	NUM
ejpam-6458	427	16	)	)	PUNCT
ejpam-6458	427	17	ij	ij	NOUN
ejpam-6458	427	18	=	=	NOUN
ejpam-6458	427	19	a1	a1	NOUN
ejpam-6458	427	20	+	+	CCONJ
ejpam-6458	427	21	2i−	2i−	NUM
ejpam-6458	427	22	j	j	PROPN
ejpam-6458	427	23	,	,	PUNCT
ejpam-6458	427	24	h	h	PROPN
ejpam-6458	427	25	(	(	PUNCT
ejpam-6458	427	26	2	2	NUM
ejpam-6458	427	27	)	)	PUNCT
ejpam-6458	427	28	ij	ij	NOUN
ejpam-6458	427	29	=	=	PROPN
ejpam-6458	427	30	a2	a2	PROPN
ejpam-6458	427	31	−	−	PROPN
ejpam-6458	427	32	i+	i+	NUM
ejpam-6458	427	33	2j	2j	NOUN
ejpam-6458	427	34	,	,	PUNCT
ejpam-6458	427	35	sj	sj	INTJ
ejpam-6458	427	36	,	,	PUNCT
ejpam-6458	427	37	k	k	NOUN
ejpam-6458	427	38	=	=	PROPN
ejpam-6458	427	39	a3	a3	PROPN
ejpam-6458	427	40	−	−	PROPN
ejpam-6458	427	41	j	j	PROPN
ejpam-6458	427	42	+	+	CCONJ
ejpam-6458	427	43	2k	2k	NOUN
ejpam-6458	427	44	−	−	NOUN
ejpam-6458	427	45	1	1	NUM
ejpam-6458	427	46	,	,	PUNCT
ejpam-6458	427	47	s+	s+	X
ejpam-6458	427	48	ijk	ijk	PROPN
ejpam-6458	427	49	=	=	PROPN
ejpam-6458	427	50	1	1	NUM
ejpam-6458	427	51	2	2	NUM
ejpam-6458	427	52	(	(	PUNCT
ejpam-6458	427	53	sj	sj	PROPN
ejpam-6458	427	54	,	,	PUNCT
ejpam-6458	427	55	k	k	PROPN
ejpam-6458	428	1	+	+	NUM
ejpam-6458	428	2	h	h	NOUN
ejpam-6458	428	3	(	(	PUNCT
ejpam-6458	428	4	1	1	X
ejpam-6458	428	5	)	)	PUNCT
ejpam-6458	428	6	i	i	PRON
ejpam-6458	428	7	,	,	PUNCT
ejpam-6458	428	8	j	j	PROPN
ejpam-6458	428	9	)	)	PUNCT
ejpam-6458	428	10	=	=	SYM
ejpam-6458	428	11	1	1	NUM
ejpam-6458	428	12	2	2	NUM
ejpam-6458	428	13	(	(	PUNCT
ejpam-6458	428	14	a1	a1	NOUN
ejpam-6458	428	15	+	+	CCONJ
ejpam-6458	428	16	a3	a3	NOUN
ejpam-6458	428	17	−	−	PROPN
ejpam-6458	428	18	1	1	NUM
ejpam-6458	428	19	)	)	PUNCT
ejpam-6458	428	20	+	+	CCONJ
ejpam-6458	428	21	i−	i−	PROPN
ejpam-6458	428	22	j	j	PROPN
ejpam-6458	428	23	+	+	CCONJ
ejpam-6458	428	24	k	k	PROPN
ejpam-6458	428	25	,	,	PUNCT
ejpam-6458	428	26	s−	s−	PROPN
ejpam-6458	428	27	ik	ik	PROPN
ejpam-6458	428	28	=	=	SYM
ejpam-6458	428	29	1	1	NUM
ejpam-6458	428	30	2	2	NUM
ejpam-6458	428	31	(	(	PUNCT
ejpam-6458	428	32	s0,k	s0,k	PROPN
ejpam-6458	428	33	−	−	NOUN
ejpam-6458	428	34	h	h	NOUN
ejpam-6458	428	35	(	(	PUNCT
ejpam-6458	428	36	1	1	NUM
ejpam-6458	428	37	)	)	PUNCT
ejpam-6458	428	38	i,0	i,0	X
ejpam-6458	428	39	)	)	PUNCT
ejpam-6458	429	1	=	=	SYM
ejpam-6458	429	2	1	1	NUM
ejpam-6458	429	3	2	2	NUM
ejpam-6458	429	4	(	(	PUNCT
ejpam-6458	429	5	−a1	−a1	PROPN
ejpam-6458	429	6	+	+	NUM
ejpam-6458	429	7	a3	a3	NOUN
ejpam-6458	430	1	−	−	PROPN
ejpam-6458	430	2	1)−	1)−	PROPN
ejpam-6458	430	3	i+	i+	NUM
ejpam-6458	430	4	k	k	NOUN
ejpam-6458	430	5	,	,	PUNCT
ejpam-6458	431	1	t+	t+	X
ejpam-6458	431	2	k	k	X
ejpam-6458	431	3	=	=	SYM
ejpam-6458	431	4	1	1	NUM
ejpam-6458	431	5	2	2	NUM
ejpam-6458	431	6	(	(	PUNCT
ejpam-6458	431	7	s0,k	s0,k	PROPN
ejpam-6458	431	8	+	+	ADP
ejpam-6458	431	9	1	1	NUM
ejpam-6458	431	10	3	3	NUM
ejpam-6458	431	11	(	(	PUNCT
ejpam-6458	431	12	h	h	NOUN
ejpam-6458	431	13	(	(	PUNCT
ejpam-6458	431	14	1	1	NUM
ejpam-6458	431	15	)	)	PUNCT
ejpam-6458	431	16	0,0	0,0	NOUN
ejpam-6458	431	17	+	+	NUM
ejpam-6458	431	18	2h	2h	NUM
ejpam-6458	431	19	(	(	PUNCT
ejpam-6458	431	20	2	2	NUM
ejpam-6458	431	21	)	)	PUNCT
ejpam-6458	431	22	0,0	0,0	NOUN
ejpam-6458	431	23	)	)	PUNCT
ejpam-6458	431	24	)	)	PUNCT
ejpam-6458	432	1	=	=	SYM
ejpam-6458	432	2	1	1	NUM
ejpam-6458	432	3	6	6	NUM
ejpam-6458	432	4	(	(	PUNCT
ejpam-6458	432	5	a1	a1	NOUN
ejpam-6458	432	6	+	+	CCONJ
ejpam-6458	432	7	2a2	2a2	NUM
ejpam-6458	432	8	+	+	NUM
ejpam-6458	432	9	3a3	3a3	NUM
ejpam-6458	432	10	)	)	PUNCT
ejpam-6458	433	1	+	+	CCONJ
ejpam-6458	433	2	k	k	X
ejpam-6458	433	3	−	−	PROPN
ejpam-6458	433	4	1	1	NUM
ejpam-6458	433	5	2	2	NUM
ejpam-6458	433	6	,	,	PUNCT
ejpam-6458	433	7	t−	t−	PROPN
ejpam-6458	433	8	jk	jk	NOUN
ejpam-6458	433	9	=	=	SYM
ejpam-6458	433	10	1	1	NUM
ejpam-6458	433	11	2	2	NUM
ejpam-6458	433	12	(	(	PUNCT
ejpam-6458	433	13	sj	sj	INTJ
ejpam-6458	433	14	,	,	PUNCT
ejpam-6458	433	15	k	k	PROPN
ejpam-6458	433	16	−	−	PROPN
ejpam-6458	433	17	1	1	NUM
ejpam-6458	433	18	3	3	NUM
ejpam-6458	433	19	(	(	PUNCT
ejpam-6458	433	20	h	h	NOUN
ejpam-6458	433	21	(	(	PUNCT
ejpam-6458	433	22	1	1	NUM
ejpam-6458	433	23	)	)	PUNCT
ejpam-6458	433	24	0,j	0,j	NOUN
ejpam-6458	434	1	+	+	CCONJ
ejpam-6458	434	2	2h	2h	NUM
ejpam-6458	434	3	(	(	PUNCT
ejpam-6458	434	4	2	2	NUM
ejpam-6458	434	5	)	)	PUNCT
ejpam-6458	434	6	0,j	0,j	NOUN
ejpam-6458	434	7	)	)	PUNCT
ejpam-6458	434	8	)	)	PUNCT
ejpam-6458	435	1	=	=	SYM
ejpam-6458	435	2	1	1	NUM
ejpam-6458	435	3	6	6	NUM
ejpam-6458	435	4	(	(	PUNCT
ejpam-6458	435	5	−a1	−a1	PROPN
ejpam-6458	435	6	−	−	PROPN
ejpam-6458	435	7	2a2	2a2	NUM
ejpam-6458	435	8	+	+	CCONJ
ejpam-6458	435	9	3a3)−	3a3)−	NUM
ejpam-6458	435	10	j	j	PROPN
ejpam-6458	436	1	+	+	CCONJ
ejpam-6458	436	2	k	k	PROPN
ejpam-6458	437	1	−	−	PROPN
ejpam-6458	437	2	1	1	NUM
ejpam-6458	437	3	2	2	NUM
ejpam-6458	437	4	,	,	PUNCT
ejpam-6458	437	5	q−	q−	PROPN
ejpam-6458	437	6	jk	jk	PUNCT
ejpam-6458	438	1	=	=	PUNCT
ejpam-6458	439	1	−µ+	−µ+	PROPN
ejpam-6458	440	1	t−	t−	PROPN
ejpam-6458	440	2	j	j	PROPN
ejpam-6458	440	3	,	,	PUNCT
ejpam-6458	440	4	k−2ξ	k−2ξ	PROPN
ejpam-6458	440	5	−	−	PROPN
ejpam-6458	440	6	t−	t−	PROPN
ejpam-6458	440	7	j	j	PROPN
ejpam-6458	440	8	,	,	PUNCT
ejpam-6458	440	9	kt	kt	PROPN
ejpam-6458	440	10	−	−	PROPN
ejpam-6458	440	11	j	j	PROPN
ejpam-6458	440	12	,	,	PUNCT
ejpam-6458	440	13	k−1	k−1	PROPN
ejpam-6458	440	14	t	t	PROPN
ejpam-6458	440	15	−	−	PROPN
ejpam-6458	440	16	j	j	PROPN
ejpam-6458	440	17	,	,	PUNCT
ejpam-6458	440	18	k−2	k−2	PROPN
ejpam-6458	440	19	=	=	PROPN
ejpam-6458	440	20	−(t−	−(t−	PROPN
ejpam-6458	440	21	j	j	PROPN
ejpam-6458	440	22	,	,	PUNCT
ejpam-6458	440	23	k−1	k−1	PROPN
ejpam-6458	440	24	−	−	PROPN
ejpam-6458	441	1	t1)(t	t1)(t	PROPN
ejpam-6458	441	2	−	−	PROPN
ejpam-6458	442	1	j	j	PROPN
ejpam-6458	442	2	,	,	PUNCT
ejpam-6458	442	3	k−1	k−1	PROPN
ejpam-6458	442	4	−	−	PROPN
ejpam-6458	443	1	t2)(t	t2)(t	PROPN
ejpam-6458	443	2	−	−	PROPN
ejpam-6458	443	3	j	j	PROPN
ejpam-6458	443	4	,	,	PUNCT
ejpam-6458	443	5	k−1	k−1	PROPN
ejpam-6458	443	6	−	−	PROPN
ejpam-6458	443	7	t3	t3	PROPN
ejpam-6458	443	8	)	)	PUNCT
ejpam-6458	443	9	,	,	PUNCT
ejpam-6458	443	10	q+	q+	NOUN
ejpam-6458	443	11	k	k	X
ejpam-6458	443	12	=	=	PUNCT
ejpam-6458	443	13	µ+	µ+	PUNCT
ejpam-6458	443	14	t+	t+	NOUN
ejpam-6458	443	15	k	k	PROPN
ejpam-6458	443	16	ξ	ξ	X
ejpam-6458	443	17	−	−	PROPN
ejpam-6458	443	18	t+	t+	NOUN
ejpam-6458	443	19	k	k	PROPN
ejpam-6458	443	20	t	t	PROPN
ejpam-6458	443	21	+	+	CCONJ
ejpam-6458	443	22	k−1	k−1	PROPN
ejpam-6458	443	23	t	t	PROPN
ejpam-6458	443	24	+	+	NUM
ejpam-6458	443	25	k−2	k−2	PROPN
ejpam-6458	443	26	=	=	PUNCT
ejpam-6458	443	27	(	(	PUNCT
ejpam-6458	443	28	t+	t+	PUNCT
ejpam-6458	443	29	k−1	k−1	PROPN
ejpam-6458	443	30	+	+	CCONJ
ejpam-6458	443	31	t1)(t	t1)(t	PROPN
ejpam-6458	443	32	+	+	CCONJ
ejpam-6458	443	33	k−1	k−1	PROPN
ejpam-6458	443	34	+	+	CCONJ
ejpam-6458	443	35	t2)(t	t2)(t	PROPN
ejpam-6458	443	36	+	+	CCONJ
ejpam-6458	443	37	k−1	k−1	PROPN
ejpam-6458	443	38	+	+	CCONJ
ejpam-6458	443	39	t3	t3	PROPN
ejpam-6458	443	40	)	)	PUNCT
ejpam-6458	443	41	.	.	PUNCT
ejpam-6458	444	1	where	where	SCONJ
ejpam-6458	444	2	t1	t1	NOUN
ejpam-6458	444	3	,	,	PUNCT
ejpam-6458	444	4	t2	t2	NOUN
ejpam-6458	444	5	,	,	PUNCT
ejpam-6458	444	6	t3	t3	PROPN
ejpam-6458	444	7	are	be	AUX
ejpam-6458	444	8	three	three	NUM
ejpam-6458	444	9	roots	root	NOUN
ejpam-6458	444	10	of	of	ADP
ejpam-6458	444	11	the	the	DET
ejpam-6458	444	12	equation	equation	NOUN
ejpam-6458	444	13	t	t	PROPN
ejpam-6458	444	14	3	3	NUM
ejpam-6458	444	15	−	−	PROPN
ejpam-6458	444	16	t(ξ	t(ξ	PROPN
ejpam-6458	445	1	+	+	CCONJ
ejpam-6458	445	2	1	1	NUM
ejpam-6458	445	3	)	)	PUNCT
ejpam-6458	445	4	+	+	CCONJ
ejpam-6458	445	5	µ+	µ+	X
ejpam-6458	445	6	ξ	ξ	X
ejpam-6458	445	7	=	=	SYM
ejpam-6458	445	8	0	0	NUM
ejpam-6458	445	9	(	(	PUNCT
ejpam-6458	445	10	4.15	4.15	NUM
ejpam-6458	445	11	)	)	PUNCT
ejpam-6458	445	12	define	define	VERB
ejpam-6458	445	13	an	an	DET
ejpam-6458	445	14	action	action	NOUN
ejpam-6458	445	15	of	of	ADP
ejpam-6458	445	16	the	the	DET
ejpam-6458	445	17	lie	lie	NOUN
ejpam-6458	445	18	algebra	algebra	VERB
ejpam-6458	445	19	g	g	NOUN
ejpam-6458	445	20	on	on	ADP
ejpam-6458	445	21	the	the	DET
ejpam-6458	445	22	vector	vector	NOUN
ejpam-6458	445	23	space	space	NOUN
ejpam-6458	445	24	v	v	NOUN
ejpam-6458	445	25	(	(	PUNCT
ejpam-6458	445	26	a1	a1	PROPN
ejpam-6458	445	27	,	,	PUNCT
ejpam-6458	445	28	a2	a2	PROPN
ejpam-6458	445	29	,	,	PUNCT
ejpam-6458	445	30	a3	a3	NOUN
ejpam-6458	445	31	,	,	PUNCT
ejpam-6458	445	32	ξ	ξ	PROPN
ejpam-6458	445	33	,	,	PUNCT
ejpam-6458	445	34	µ	µ	NOUN
ejpam-6458	445	35	)	)	PUNCT
ejpam-6458	446	1	=	=	SYM
ejpam-6458	446	2	spanc{vijk	spanc{vijk	X
ejpam-6458	447	1	|	|	ADV
ejpam-6458	447	2	i	i	PROPN
ejpam-6458	447	3	,	,	PUNCT
ejpam-6458	447	4	j	j	PROPN
ejpam-6458	447	5	,	,	PUNCT
ejpam-6458	447	6	k	k	PROPN
ejpam-6458	447	7	∈	∈	PROPN
ejpam-6458	448	1	z	z	X
ejpam-6458	448	2	}	}	PUNCT
ejpam-6458	448	3	as	as	SCONJ
ejpam-6458	448	4	follows	follow	VERB
ejpam-6458	448	5	:	:	PUNCT
ejpam-6458	448	6	z1(vijk	z1(vijk	NOUN
ejpam-6458	448	7	)	)	PUNCT
ejpam-6458	449	1	=	=	SYM
ejpam-6458	449	2	ξvijk	ξvijk	NOUN
ejpam-6458	449	3	,	,	PUNCT
ejpam-6458	449	4	z2(vijk	z2(vijk	NOUN
ejpam-6458	449	5	)	)	PUNCT
ejpam-6458	449	6	=	=	SYM
ejpam-6458	449	7	µvijk	µvijk	X
ejpam-6458	449	8	,	,	PUNCT
ejpam-6458	449	9	h01(vijk	h01(vijk	NOUN
ejpam-6458	449	10	)	)	PUNCT
ejpam-6458	449	11	=	=	SYM
ejpam-6458	449	12	h	h	NOUN
ejpam-6458	449	13	(	(	PUNCT
ejpam-6458	449	14	1	1	NUM
ejpam-6458	449	15	)	)	PUNCT
ejpam-6458	449	16	ij	ij	NOUN
ejpam-6458	449	17	vijk	vijk	NOUN
ejpam-6458	449	18	,	,	PUNCT
ejpam-6458	449	19	h10(vijk	h10(vijk	X
ejpam-6458	449	20	)	)	PUNCT
ejpam-6458	449	21	=	=	SYM
ejpam-6458	449	22	h	h	NOUN
ejpam-6458	449	23	(	(	PUNCT
ejpam-6458	449	24	2	2	NUM
ejpam-6458	449	25	)	)	PUNCT
ejpam-6458	449	26	ij	ij	NOUN
ejpam-6458	449	27	vijk	vijk	NOUN
ejpam-6458	449	28	,	,	PUNCT
ejpam-6458	449	29	e01(vijk	e01(vijk	NOUN
ejpam-6458	449	30	)	)	PUNCT
ejpam-6458	449	31	=	=	PUNCT
ejpam-6458	449	32	s+	s+	PUNCT
ejpam-6458	449	33	ijkvi+1,j	ijkvi+1,j	PROPN
ejpam-6458	449	34	,	,	PUNCT
ejpam-6458	449	35	k	k	PROPN
ejpam-6458	449	36	,	,	PUNCT
ejpam-6458	449	37	f01(vijk	f01(vijk	NOUN
ejpam-6458	449	38	)	)	PUNCT
ejpam-6458	449	39	=	=	SYM
ejpam-6458	449	40	s−	s−	PROPN
ejpam-6458	449	41	ikvi−1,j	ikvi−1,j	NOUN
ejpam-6458	449	42	,	,	PUNCT
ejpam-6458	449	43	k	k	PROPN
ejpam-6458	449	44	,	,	PUNCT
ejpam-6458	449	45	e10(vijk	e10(vijk	NOUN
ejpam-6458	449	46	)	)	PUNCT
ejpam-6458	449	47	=	=	SYM
ejpam-6458	449	48	q−	q−	PROPN
ejpam-6458	449	49	jkvi	jkvi	PROPN
ejpam-6458	449	50	,	,	PUNCT
ejpam-6458	449	51	j+1,k	j+1,k	PROPN
ejpam-6458	449	52	+	+	CCONJ
ejpam-6458	449	53	s−	s−	PROPN
ejpam-6458	449	54	i	i	PRON
ejpam-6458	449	55	,	,	PUNCT
ejpam-6458	449	56	k	k	PROPN
ejpam-6458	449	57	sj+1,ksjk	sj+1,ksjk	PROPN
ejpam-6458	449	58	vi	vi	PROPN
ejpam-6458	449	59	,	,	PUNCT
ejpam-6458	449	60	j+1,k+1	j+1,k+1	NOUN
ejpam-6458	449	61	,	,	PUNCT
ejpam-6458	449	62	f10(vijk	f10(vijk	NUM
ejpam-6458	449	63	)	)	PUNCT
ejpam-6458	449	64	=	=	PUNCT
ejpam-6458	449	65	q+	q+	PROPN
ejpam-6458	449	66	k	k	PROPN
ejpam-6458	449	67	vi	vi	PROPN
ejpam-6458	449	68	,	,	PUNCT
ejpam-6458	449	69	j−1,k−1	j−1,k−1	X
ejpam-6458	450	1	+	+	CCONJ
ejpam-6458	450	2	s+	s+	X
ejpam-6458	450	3	i	i	PRON
ejpam-6458	450	4	,	,	PUNCT
ejpam-6458	450	5	j	j	PROPN
ejpam-6458	450	6	,	,	PUNCT
ejpam-6458	450	7	k	k	PROPN
ejpam-6458	450	8	sj+1,ksjk	sj+1,ksjk	PROPN
ejpam-6458	450	9	vi	vi	PROPN
ejpam-6458	450	10	,	,	PUNCT
ejpam-6458	450	11	j−1,k	j−1,k	PROPN
ejpam-6458	450	12	.	.	PUNCT
ejpam-6458	451	1	(	(	PUNCT
ejpam-6458	451	2	4.16	4.16	NUM
ejpam-6458	451	3	)	)	PUNCT
ejpam-6458	451	4	we	we	PRON
ejpam-6458	451	5	have	have	VERB
ejpam-6458	451	6	the	the	DET
ejpam-6458	451	7	following	follow	VERB
ejpam-6458	451	8	statement	statement	NOUN
ejpam-6458	451	9	(	(	PUNCT
ejpam-6458	451	10	cf	cf	NOUN
ejpam-6458	451	11	.	.	PUNCT
ejpam-6458	452	1	[	[	X
ejpam-6458	452	2	7	7	NUM
ejpam-6458	452	3	,	,	PUNCT
ejpam-6458	452	4	14	14	NUM
ejpam-6458	452	5	]	]	PUNCT
ejpam-6458	452	6	)	)	PUNCT
ejpam-6458	452	7	.	.	PUNCT
ejpam-6458	453	1	theorem	theorem	VERB
ejpam-6458	453	2	4.2	4.2	NUM
ejpam-6458	453	3	.	.	PUNCT
ejpam-6458	454	1	let	let	VERB
ejpam-6458	454	2	a1	a1	NOUN
ejpam-6458	454	3	,	,	PUNCT
ejpam-6458	454	4	a2	a2	PROPN
ejpam-6458	454	5	,	,	PUNCT
ejpam-6458	454	6	a3	a3	NOUN
ejpam-6458	454	7	,	,	PUNCT
ejpam-6458	454	8	ξ	ξ	PROPN
ejpam-6458	454	9	,	,	PUNCT
ejpam-6458	454	10	µ	µ	X
ejpam-6458	454	11	∈	∈	PROPN
ejpam-6458	454	12	c	c	X
ejpam-6458	454	13	and	and	CCONJ
ejpam-6458	454	14	a3	a3	PROPN
ejpam-6458	454	15	/∈	/∈	PUNCT
ejpam-6458	455	1	z.	z.	PROPN
ejpam-6458	455	2	then	then	ADV
ejpam-6458	455	3	m.	m.	PROPN
ejpam-6458	455	4	andelić	andelić	PROPN
ejpam-6458	455	5	et	et	PROPN
ejpam-6458	455	6	al	al	PROPN
ejpam-6458	455	7	.	.	PUNCT
ejpam-6458	455	8	/	/	SYM
ejpam-6458	455	9	eur	eur	PROPN
ejpam-6458	455	10	.	.	PUNCT
ejpam-6458	456	1	j.	j.	PROPN
ejpam-6458	456	2	pure	pure	PROPN
ejpam-6458	456	3	appl	appl	PROPN
ejpam-6458	456	4	.	.	PROPN
ejpam-6458	456	5	math	math	PROPN
ejpam-6458	456	6	,	,	PUNCT
ejpam-6458	456	7	18	18	NUM
ejpam-6458	456	8	(	(	PUNCT
ejpam-6458	456	9	3	3	NUM
ejpam-6458	456	10	)	)	PUNCT
ejpam-6458	456	11	(	(	PUNCT
ejpam-6458	456	12	2025	2025	NUM
ejpam-6458	456	13	)	)	PUNCT
ejpam-6458	456	14	,	,	PUNCT
ejpam-6458	456	15	6458	6458	NUM
ejpam-6458	456	16	11	11	NUM
ejpam-6458	456	17	of	of	ADP
ejpam-6458	456	18	21	21	NUM
ejpam-6458	456	19	1	1	NUM
ejpam-6458	456	20	.	.	PUNCT
ejpam-6458	457	1	the	the	DET
ejpam-6458	457	2	space	space	NOUN
ejpam-6458	457	3	v	v	NOUN
ejpam-6458	457	4	(	(	PUNCT
ejpam-6458	457	5	a1	a1	PROPN
ejpam-6458	457	6	,	,	PUNCT
ejpam-6458	457	7	a2	a2	PROPN
ejpam-6458	457	8	,	,	PUNCT
ejpam-6458	457	9	a3	a3	NOUN
ejpam-6458	457	10	,	,	PUNCT
ejpam-6458	457	11	ξ	ξ	PROPN
ejpam-6458	457	12	,	,	PUNCT
ejpam-6458	457	13	µ	µ	NOUN
ejpam-6458	457	14	)	)	PUNCT
ejpam-6458	457	15	is	be	AUX
ejpam-6458	457	16	a	a	DET
ejpam-6458	457	17	torsion	torsion	NOUN
ejpam-6458	457	18	free	free	ADJ
ejpam-6458	457	19	γ	γ	X
ejpam-6458	457	20	-	-	ADJ
ejpam-6458	457	21	pointed	point	VERB
ejpam-6458	457	22	g	g	NOUN
ejpam-6458	457	23	-	-	PUNCT
ejpam-6458	457	24	module	module	NOUN
ejpam-6458	457	25	if	if	SCONJ
ejpam-6458	457	26	and	and	CCONJ
ejpam-6458	457	27	only	only	ADV
ejpam-6458	457	28	if	if	SCONJ
ejpam-6458	457	29	s+	s+	ADV
ejpam-6458	457	30	ijk	ijk	PROPN
ejpam-6458	457	31	and	and	CCONJ
ejpam-6458	457	32	s−	s−	PROPN
ejpam-6458	457	33	ik	ik	PROPN
ejpam-6458	457	34	are	be	AUX
ejpam-6458	457	35	non	non	ADJ
ejpam-6458	457	36	-	-	ADJ
ejpam-6458	457	37	zero	zero	NUM
ejpam-6458	457	38	,	,	PUNCT
ejpam-6458	457	39	for	for	ADP
ejpam-6458	457	40	all	all	DET
ejpam-6458	457	41	i	i	PROPN
ejpam-6458	457	42	,	,	PUNCT
ejpam-6458	457	43	j	j	PROPN
ejpam-6458	457	44	,	,	PUNCT
ejpam-6458	457	45	k	k	PROPN
ejpam-6458	457	46	∈	∈	PROPN
ejpam-6458	457	47	z.	z.	PROPN
ejpam-6458	457	48	2	2	NUM
ejpam-6458	457	49	.	.	PUNCT
ejpam-6458	458	1	the	the	DET
ejpam-6458	458	2	module	module	NOUN
ejpam-6458	458	3	v	v	NOUN
ejpam-6458	458	4	(	(	PUNCT
ejpam-6458	458	5	a1	a1	PROPN
ejpam-6458	458	6	,	,	PUNCT
ejpam-6458	458	7	a2	a2	PROPN
ejpam-6458	458	8	,	,	PUNCT
ejpam-6458	458	9	a3	a3	NOUN
ejpam-6458	458	10	,	,	PUNCT
ejpam-6458	458	11	ξ	ξ	PROPN
ejpam-6458	458	12	,	,	PUNCT
ejpam-6458	458	13	µ	µ	NOUN
ejpam-6458	458	14	)	)	PUNCT
ejpam-6458	458	15	is	be	AUX
ejpam-6458	458	16	simple	simple	ADJ
ejpam-6458	458	17	if	if	SCONJ
ejpam-6458	458	18	and	and	CCONJ
ejpam-6458	458	19	only	only	ADV
ejpam-6458	458	20	if	if	SCONJ
ejpam-6458	458	21	s	s	X
ejpam-6458	458	22	+	+	X
ejpam-6458	458	23	ijk	ijk	X
ejpam-6458	458	24	,	,	PUNCT
ejpam-6458	458	25	s	s	PART
ejpam-6458	458	26	−	−	NOUN
ejpam-6458	458	27	ik	ik	NOUN
ejpam-6458	458	28	,	,	PUNCT
ejpam-6458	458	29	q	q	NOUN
ejpam-6458	458	30	−	−	PROPN
ejpam-6458	458	31	jk	jk	PROPN
ejpam-6458	458	32	,	,	PUNCT
ejpam-6458	458	33	q	q	PROPN
ejpam-6458	459	1	+	+	CCONJ
ejpam-6458	459	2	k	k	X
ejpam-6458	459	3	are	be	AUX
ejpam-6458	459	4	non	non	ADJ
ejpam-6458	459	5	-	-	ADJ
ejpam-6458	459	6	zero	zero	NUM
ejpam-6458	459	7	,	,	PUNCT
ejpam-6458	459	8	for	for	ADP
ejpam-6458	459	9	all	all	DET
ejpam-6458	459	10	i	i	PROPN
ejpam-6458	459	11	,	,	PUNCT
ejpam-6458	459	12	j	j	PROPN
ejpam-6458	459	13	,	,	PUNCT
ejpam-6458	459	14	k	k	PROPN
ejpam-6458	459	15	∈	∈	PROPN
ejpam-6458	459	16	z.	z.	PROPN
ejpam-6458	459	17	proof	proof	NOUN
ejpam-6458	459	18	.	.	PUNCT
ejpam-6458	460	1	the	the	DET
ejpam-6458	460	2	fact	fact	NOUN
ejpam-6458	460	3	that	that	SCONJ
ejpam-6458	460	4	v	v	X
ejpam-6458	460	5	(	(	PUNCT
ejpam-6458	460	6	a1	a1	PROPN
ejpam-6458	460	7	,	,	PUNCT
ejpam-6458	460	8	a2	a2	PROPN
ejpam-6458	460	9	,	,	PUNCT
ejpam-6458	460	10	a3	a3	NOUN
ejpam-6458	460	11	,	,	PUNCT
ejpam-6458	460	12	ξ	ξ	PROPN
ejpam-6458	460	13	,	,	PUNCT
ejpam-6458	460	14	µ	µ	NOUN
ejpam-6458	460	15	)	)	PUNCT
ejpam-6458	460	16	is	be	AUX
ejpam-6458	460	17	a	a	DET
ejpam-6458	460	18	g	g	NOUN
ejpam-6458	460	19	-	-	PUNCT
ejpam-6458	460	20	module	module	NOUN
ejpam-6458	460	21	was	be	AUX
ejpam-6458	460	22	shown	show	VERB
ejpam-6458	460	23	in	in	ADP
ejpam-6458	460	24	[	[	X
ejpam-6458	460	25	14	14	NUM
ejpam-6458	460	26	]	]	PUNCT
ejpam-6458	460	27	and	and	CCONJ
ejpam-6458	460	28	[	[	X
ejpam-6458	460	29	7	7	NUM
ejpam-6458	460	30	]	]	PUNCT
ejpam-6458	460	31	.	.	PUNCT
ejpam-6458	461	1	it	it	PRON
ejpam-6458	461	2	is	be	AUX
ejpam-6458	461	3	γpointed	γpointe	VERB
ejpam-6458	461	4	as	as	SCONJ
ejpam-6458	461	5	γ	γ	PROPN
ejpam-6458	461	6	separates	separate	VERB
ejpam-6458	461	7	the	the	DET
ejpam-6458	461	8	basis	basis	NOUN
ejpam-6458	461	9	elements	element	NOUN
ejpam-6458	461	10	.	.	PUNCT
ejpam-6458	462	1	it	it	PRON
ejpam-6458	462	2	follows	follow	VERB
ejpam-6458	462	3	from	from	ADP
ejpam-6458	462	4	formulas	formula	NOUN
ejpam-6458	462	5	above	above	ADP
ejpam-6458	462	6	that	that	SCONJ
ejpam-6458	462	7	the	the	DET
ejpam-6458	462	8	module	module	NOUN
ejpam-6458	462	9	v	v	NOUN
ejpam-6458	462	10	(	(	PUNCT
ejpam-6458	462	11	a1	a1	PROPN
ejpam-6458	462	12	,	,	PUNCT
ejpam-6458	462	13	a2	a2	PROPN
ejpam-6458	462	14	,	,	PUNCT
ejpam-6458	462	15	a3	a3	NOUN
ejpam-6458	462	16	,	,	PUNCT
ejpam-6458	462	17	ξ	ξ	PROPN
ejpam-6458	462	18	,	,	PUNCT
ejpam-6458	462	19	µ	µ	NOUN
ejpam-6458	462	20	)	)	PUNCT
ejpam-6458	462	21	is	be	AUX
ejpam-6458	462	22	torsion	torsion	NOUN
ejpam-6458	462	23	free	free	ADJ
ejpam-6458	463	1	if	if	SCONJ
ejpam-6458	463	2	and	and	CCONJ
ejpam-6458	463	3	only	only	ADV
ejpam-6458	463	4	if	if	SCONJ
ejpam-6458	463	5	s	s	X
ejpam-6458	463	6	+	+	CCONJ
ejpam-6458	463	7	ijk	ijk	PROPN
ejpam-6458	463	8	and	and	CCONJ
ejpam-6458	463	9	s	s	PROPN
ejpam-6458	463	10	−	−	PROPN
ejpam-6458	463	11	ik	ik	PROPN
ejpam-6458	463	12	are	be	AUX
ejpam-6458	463	13	different	different	ADJ
ejpam-6458	463	14	from	from	ADP
ejpam-6458	463	15	zero	zero	NUM
ejpam-6458	463	16	for	for	ADP
ejpam-6458	463	17	all	all	DET
ejpam-6458	463	18	i	i	PROPN
ejpam-6458	463	19	,	,	PUNCT
ejpam-6458	463	20	j	j	PROPN
ejpam-6458	463	21	,	,	PUNCT
ejpam-6458	463	22	k	k	PROPN
ejpam-6458	463	23	∈	∈	PROPN
ejpam-6458	463	24	z.	z.	PROPN
ejpam-6458	463	25	note	note	VERB
ejpam-6458	463	26	that	that	SCONJ
ejpam-6458	463	27	for	for	ADP
ejpam-6458	463	28	every	every	DET
ejpam-6458	463	29	h	h	NOUN
ejpam-6458	463	30	-	-	PUNCT
ejpam-6458	463	31	weight	weight	NOUN
ejpam-6458	463	32	λ	λ	PROPN
ejpam-6458	463	33	of	of	ADP
ejpam-6458	463	34	v	v	PROPN
ejpam-6458	463	35	(	(	PUNCT
ejpam-6458	463	36	a1	a1	PROPN
ejpam-6458	463	37	,	,	PUNCT
ejpam-6458	463	38	a2	a2	PROPN
ejpam-6458	463	39	,	,	PUNCT
ejpam-6458	463	40	a3	a3	NOUN
ejpam-6458	463	41	,	,	PUNCT
ejpam-6458	463	42	ξ	ξ	PROPN
ejpam-6458	463	43	,	,	PUNCT
ejpam-6458	463	44	µ	µ	NOUN
ejpam-6458	463	45	)	)	PUNCT
ejpam-6458	463	46	,	,	PUNCT
ejpam-6458	463	47	the	the	DET
ejpam-6458	463	48	λ	λ	NOUN
ejpam-6458	463	49	-	-	PUNCT
ejpam-6458	463	50	weight	weight	ADJ
ejpam-6458	463	51	subspace	subspace	NOUN
ejpam-6458	463	52	is	be	AUX
ejpam-6458	463	53	infinite	infinite	ADJ
ejpam-6458	463	54	-	-	PUNCT
ejpam-6458	463	55	dimensional	dimensional	ADJ
ejpam-6458	463	56	with	with	ADP
ejpam-6458	463	57	basis	basis	NOUN
ejpam-6458	463	58	vijk	vijk	NOUN
ejpam-6458	463	59	,	,	PUNCT
ejpam-6458	463	60	where	where	SCONJ
ejpam-6458	463	61	i	i	PRON
ejpam-6458	463	62	,	,	PUNCT
ejpam-6458	463	63	j	j	PROPN
ejpam-6458	463	64	are	be	AUX
ejpam-6458	463	65	determined	determine	VERB
ejpam-6458	463	66	by	by	ADP
ejpam-6458	463	67	λ	λ	PROPN
ejpam-6458	463	68	and	and	CCONJ
ejpam-6458	463	69	k	k	PROPN
ejpam-6458	463	70	runs	run	VERB
ejpam-6458	463	71	through	through	ADP
ejpam-6458	463	72	z.	z.	PROPN
ejpam-6458	463	73	in	in	ADP
ejpam-6458	463	74	this	this	DET
ejpam-6458	463	75	basis	basis	NOUN
ejpam-6458	463	76	the	the	DET
ejpam-6458	463	77	operator	operator	NOUN
ejpam-6458	463	78	c1	c1	NOUN
ejpam-6458	463	79	is	be	AUX
ejpam-6458	463	80	presented	present	VERB
ejpam-6458	463	81	by	by	ADP
ejpam-6458	463	82	an	an	DET
ejpam-6458	463	83	infinite	infinite	ADJ
ejpam-6458	463	84	diagonal	diagonal	ADJ
ejpam-6458	463	85	matrix	matrix	NOUN
ejpam-6458	463	86	and	and	CCONJ
ejpam-6458	463	87	the	the	DET
ejpam-6458	463	88	operator	operator	NOUN
ejpam-6458	463	89	c2	c2	PROPN
ejpam-6458	463	90	is	be	AUX
ejpam-6458	463	91	presented	present	VERB
ejpam-6458	463	92	by	by	ADP
ejpam-6458	463	93	a	a	DET
ejpam-6458	463	94	3	3	NUM
ejpam-6458	463	95	-	-	PUNCT
ejpam-6458	463	96	diagonal	diagonal	ADJ
ejpam-6458	463	97	matrix	matrix	NOUN
ejpam-6458	463	98	(	(	PUNCT
ejpam-6458	463	99	bst	bst	PROPN
ejpam-6458	463	100	)	)	PUNCT
ejpam-6458	463	101	,	,	PUNCT
ejpam-6458	463	102	with	with	ADP
ejpam-6458	463	103	bst	bst	PROPN
ejpam-6458	463	104	=	=	SYM
ejpam-6458	463	105	0	0	PROPN
ejpam-6458	463	106	,	,	PUNCT
ejpam-6458	463	107	for	for	ADP
ejpam-6458	463	108	all	all	DET
ejpam-6458	463	109	s	s	PROPN
ejpam-6458	463	110	,	,	PUNCT
ejpam-6458	463	111	t	t	VERB
ejpam-6458	463	112	such	such	ADJ
ejpam-6458	463	113	that	that	DET
ejpam-6458	463	114	|s−	|s−	ADJ
ejpam-6458	463	115	t|	t|	NOUN
ejpam-6458	463	116	>	>	X
ejpam-6458	463	117	1	1	X
ejpam-6458	463	118	.	.	PUNCT
ejpam-6458	464	1	this	this	PRON
ejpam-6458	464	2	is	be	AUX
ejpam-6458	464	3	a	a	DET
ejpam-6458	464	4	consequence	consequence	NOUN
ejpam-6458	464	5	of	of	ADP
ejpam-6458	464	6	relations	relation	NOUN
ejpam-6458	464	7	above	above	ADV
ejpam-6458	464	8	.	.	PUNCT
ejpam-6458	465	1	the	the	DET
ejpam-6458	465	2	simplicity	simplicity	NOUN
ejpam-6458	465	3	of	of	ADP
ejpam-6458	465	4	v	v	NOUN
ejpam-6458	465	5	(	(	PUNCT
ejpam-6458	465	6	a1	a1	PROPN
ejpam-6458	465	7	,	,	PUNCT
ejpam-6458	465	8	a2	a2	PROPN
ejpam-6458	465	9	,	,	PUNCT
ejpam-6458	465	10	a3	a3	NOUN
ejpam-6458	465	11	,	,	PUNCT
ejpam-6458	465	12	ξ	ξ	PROPN
ejpam-6458	465	13	,	,	PUNCT
ejpam-6458	465	14	µ	µ	NOUN
ejpam-6458	465	15	)	)	PUNCT
ejpam-6458	465	16	results	result	NOUN
ejpam-6458	465	17	in	in	ADP
ejpam-6458	465	18	the	the	DET
ejpam-6458	465	19	simplicity	simplicity	NOUN
ejpam-6458	465	20	of	of	ADP
ejpam-6458	465	21	each	each	DET
ejpam-6458	465	22	λ	λ	NOUN
ejpam-6458	465	23	-	-	ADJ
ejpam-6458	465	24	weight	weight	ADJ
ejpam-6458	465	25	subspace	subspace	NOUN
ejpam-6458	465	26	as	as	ADP
ejpam-6458	465	27	u0(g)-module	u0(g)-module	PROPN
ejpam-6458	465	28	.	.	PUNCT
ejpam-6458	466	1	this	this	PRON
ejpam-6458	466	2	implies	imply	VERB
ejpam-6458	466	3	the	the	DET
ejpam-6458	466	4	required	require	VERB
ejpam-6458	466	5	conditions	condition	NOUN
ejpam-6458	466	6	in	in	ADP
ejpam-6458	466	7	item	item	NOUN
ejpam-6458	466	8	2	2	NUM
ejpam-6458	466	9	.	.	PUNCT
ejpam-6458	467	1	□	□	PUNCT
ejpam-6458	467	2	simple	simple	ADJ
ejpam-6458	467	3	subquotients	subquotient	NOUN
ejpam-6458	467	4	of	of	ADP
ejpam-6458	467	5	the	the	DET
ejpam-6458	467	6	module	module	NOUN
ejpam-6458	467	7	v	v	NOUN
ejpam-6458	467	8	(	(	PUNCT
ejpam-6458	467	9	a1	a1	PROPN
ejpam-6458	467	10	,	,	PUNCT
ejpam-6458	467	11	a2	a2	PROPN
ejpam-6458	467	12	,	,	PUNCT
ejpam-6458	467	13	a3	a3	NOUN
ejpam-6458	467	14	,	,	PUNCT
ejpam-6458	467	15	ξ	ξ	PROPN
ejpam-6458	467	16	,	,	PUNCT
ejpam-6458	467	17	µ	µ	NOUN
ejpam-6458	467	18	)	)	PUNCT
ejpam-6458	467	19	give	give	VERB
ejpam-6458	467	20	all	all	DET
ejpam-6458	467	21	simple	simple	ADJ
ejpam-6458	467	22	generic	generic	ADJ
ejpam-6458	467	23	gelfand	gelfand	PROPN
ejpam-6458	467	24	-	-	PUNCT
ejpam-6458	467	25	tsetlin	tsetlin	PROPN
ejpam-6458	467	26	g	g	NOUN
ejpam-6458	467	27	-	-	PUNCT
ejpam-6458	467	28	modules	module	NOUN
ejpam-6458	467	29	with	with	ADP
ejpam-6458	467	30	finite	finite	NOUN
ejpam-6458	467	31	or	or	CCONJ
ejpam-6458	467	32	infinite	infinite	ADJ
ejpam-6458	467	33	weight	weight	NOUN
ejpam-6458	467	34	multiplicities	multiplicity	NOUN
ejpam-6458	468	1	[	[	X
ejpam-6458	468	2	20	20	NUM
ejpam-6458	468	3	]	]	PUNCT
ejpam-6458	468	4	.	.	PUNCT
ejpam-6458	469	1	moreover	moreover	ADV
ejpam-6458	469	2	,	,	PUNCT
ejpam-6458	469	3	since	since	SCONJ
ejpam-6458	469	4	any	any	DET
ejpam-6458	469	5	simple	simple	ADJ
ejpam-6458	469	6	subquotient	subquotient	NOUN
ejpam-6458	469	7	v	v	ADP
ejpam-6458	469	8	′	′	NUM
ejpam-6458	469	9	of	of	ADP
ejpam-6458	469	10	v	v	PROPN
ejpam-6458	469	11	(	(	PUNCT
ejpam-6458	469	12	a1	a1	PROPN
ejpam-6458	469	13	,	,	PUNCT
ejpam-6458	469	14	a2	a2	PROPN
ejpam-6458	469	15	,	,	PUNCT
ejpam-6458	469	16	a3	a3	NOUN
ejpam-6458	469	17	,	,	PUNCT
ejpam-6458	469	18	ξ	ξ	PROPN
ejpam-6458	469	19	,	,	PUNCT
ejpam-6458	469	20	µ	µ	NOUN
ejpam-6458	469	21	)	)	PUNCT
ejpam-6458	469	22	is	be	AUX
ejpam-6458	469	23	torsion	torsion	NOUN
ejpam-6458	469	24	free	free	ADJ
ejpam-6458	469	25	and	and	CCONJ
ejpam-6458	469	26	we	we	PRON
ejpam-6458	469	27	can	can	AUX
ejpam-6458	469	28	choose	choose	VERB
ejpam-6458	469	29	any	any	DET
ejpam-6458	469	30	weight	weight	NOUN
ejpam-6458	469	31	from	from	ADP
ejpam-6458	469	32	the	the	DET
ejpam-6458	469	33	weight	weight	NOUN
ejpam-6458	469	34	lattice	lattice	NOUN
ejpam-6458	469	35	as	as	ADP
ejpam-6458	469	36	part	part	NOUN
ejpam-6458	469	37	of	of	ADP
ejpam-6458	469	38	the	the	DET
ejpam-6458	469	39	parameter	parameter	NOUN
ejpam-6458	469	40	set	set	NOUN
ejpam-6458	469	41	,	,	PUNCT
ejpam-6458	469	42	we	we	PRON
ejpam-6458	469	43	have	have	VERB
ejpam-6458	469	44	corollary	corollary	NOUN
ejpam-6458	469	45	4.3	4.3	NUM
ejpam-6458	469	46	.	.	PUNCT
ejpam-6458	470	1	if	if	SCONJ
ejpam-6458	470	2	v	v	NOUN
ejpam-6458	470	3	′	′	NOUN
ejpam-6458	470	4	is	be	AUX
ejpam-6458	470	5	a	a	DET
ejpam-6458	470	6	simple	simple	ADJ
ejpam-6458	470	7	generic	generic	ADJ
ejpam-6458	470	8	gelfand	gelfand	PROPN
ejpam-6458	470	9	-	-	PUNCT
ejpam-6458	470	10	tsetlin	tsetlin	PROPN
ejpam-6458	470	11	g	g	NOUN
ejpam-6458	470	12	-	-	PUNCT
ejpam-6458	470	13	module	module	NOUN
ejpam-6458	470	14	,	,	PUNCT
ejpam-6458	470	15	then	then	ADV
ejpam-6458	470	16	it	it	PRON
ejpam-6458	470	17	is	be	AUX
ejpam-6458	470	18	isomorphic	isomorphic	ADJ
ejpam-6458	470	19	to	to	ADP
ejpam-6458	470	20	a	a	DET
ejpam-6458	470	21	subquotient	subquotient	NOUN
ejpam-6458	470	22	of	of	ADP
ejpam-6458	470	23	v	v	PROPN
ejpam-6458	470	24	(	(	PUNCT
ejpam-6458	470	25	a1	a1	PROPN
ejpam-6458	470	26	,	,	PUNCT
ejpam-6458	470	27	a2	a2	PROPN
ejpam-6458	470	28	,	,	PUNCT
ejpam-6458	470	29	a3	a3	NOUN
ejpam-6458	470	30	,	,	PUNCT
ejpam-6458	470	31	ξ	ξ	PROPN
ejpam-6458	470	32	,	,	PUNCT
ejpam-6458	470	33	µ	µ	NOUN
ejpam-6458	470	34	)	)	PUNCT
ejpam-6458	470	35	for	for	ADP
ejpam-6458	470	36	some	some	DET
ejpam-6458	470	37	suitable	suitable	ADJ
ejpam-6458	470	38	parameters	parameter	NOUN
ejpam-6458	470	39	such	such	ADJ
ejpam-6458	470	40	that	that	SCONJ
ejpam-6458	470	41	0	0	NUM
ejpam-6458	470	42	≤	≤	NUM
ejpam-6458	470	43	rea1	rea1	NOUN
ejpam-6458	470	44	<	<	X
ejpam-6458	470	45	1	1	NUM
ejpam-6458	470	46	,	,	PUNCT
ejpam-6458	470	47	0	0	NUM
ejpam-6458	470	48	≤	≤	NUM
ejpam-6458	470	49	rea2	rea2	NOUN
ejpam-6458	470	50	<	<	X
ejpam-6458	470	51	3	3	NUM
ejpam-6458	470	52	,	,	PUNCT
ejpam-6458	470	53	0	0	NUM
ejpam-6458	470	54	<	<	X
ejpam-6458	470	55	rea3	rea3	PROPN
ejpam-6458	470	56	<	<	X
ejpam-6458	470	57	2	2	NUM
ejpam-6458	470	58	,	,	PUNCT
ejpam-6458	470	59	a3	a3	NOUN
ejpam-6458	470	60	̸=	̸=	PROPN
ejpam-6458	470	61	1	1	NUM
ejpam-6458	470	62	,	,	PUNCT
ejpam-6458	470	63	where	where	SCONJ
ejpam-6458	470	64	rea	rea	PROPN
ejpam-6458	470	65	stands	stand	VERB
ejpam-6458	470	66	for	for	ADP
ejpam-6458	470	67	the	the	DET
ejpam-6458	470	68	real	real	ADJ
ejpam-6458	470	69	part	part	NOUN
ejpam-6458	470	70	of	of	ADP
ejpam-6458	470	71	a.	a.	NOUN
ejpam-6458	470	72	4.3	4.3	NUM
ejpam-6458	470	73	.	.	PUNCT
ejpam-6458	471	1	subquotients	subquotient	NOUN
ejpam-6458	471	2	of	of	ADP
ejpam-6458	471	3	v	v	NOUN
ejpam-6458	471	4	(	(	PUNCT
ejpam-6458	471	5	a1	a1	PROPN
ejpam-6458	471	6	,	,	PUNCT
ejpam-6458	471	7	a2	a2	PROPN
ejpam-6458	471	8	,	,	PUNCT
ejpam-6458	471	9	a3	a3	NOUN
ejpam-6458	471	10	,	,	PUNCT
ejpam-6458	471	11	ξ	ξ	PROPN
ejpam-6458	471	12	,	,	PUNCT
ejpam-6458	471	13	µ	µ	NOUN
ejpam-6458	471	14	)	)	PUNCT
ejpam-6458	471	15	as	as	SCONJ
ejpam-6458	471	16	we	we	PRON
ejpam-6458	471	17	saw	see	VERB
ejpam-6458	471	18	in	in	ADP
ejpam-6458	471	19	the	the	DET
ejpam-6458	471	20	previous	previous	ADJ
ejpam-6458	471	21	section	section	NOUN
ejpam-6458	471	22	,	,	PUNCT
ejpam-6458	471	23	the	the	DET
ejpam-6458	471	24	γ	γ	PROPN
ejpam-6458	471	25	-	-	PUNCT
ejpam-6458	471	26	pointed	point	VERB
ejpam-6458	471	27	module	module	NOUN
ejpam-6458	471	28	v	v	NOUN
ejpam-6458	471	29	(	(	PUNCT
ejpam-6458	471	30	a1	a1	PROPN
ejpam-6458	471	31	,	,	PUNCT
ejpam-6458	471	32	a2	a2	PROPN
ejpam-6458	471	33	,	,	PUNCT
ejpam-6458	471	34	a3	a3	NOUN
ejpam-6458	471	35	,	,	PUNCT
ejpam-6458	471	36	ξ	ξ	PROPN
ejpam-6458	471	37	,	,	PUNCT
ejpam-6458	471	38	µ	µ	NOUN
ejpam-6458	471	39	)	)	PUNCT
ejpam-6458	471	40	is	be	AUX
ejpam-6458	471	41	simple	simple	ADJ
ejpam-6458	471	42	when	when	SCONJ
ejpam-6458	471	43	s+	s+	PUNCT
ejpam-6458	471	44	ijk	ijk	PROPN
ejpam-6458	471	45	,	,	PUNCT
ejpam-6458	471	46	s	s	PART
ejpam-6458	471	47	−	−	NOUN
ejpam-6458	471	48	ik	ik	NOUN
ejpam-6458	471	49	,	,	PUNCT
ejpam-6458	471	50	q	q	NOUN
ejpam-6458	471	51	−	−	PROPN
ejpam-6458	471	52	jk	jk	PROPN
ejpam-6458	471	53	,	,	PUNCT
ejpam-6458	471	54	q	q	PROPN
ejpam-6458	472	1	+	+	CCONJ
ejpam-6458	472	2	k	k	X
ejpam-6458	472	3	are	be	AUX
ejpam-6458	472	4	non	non	ADJ
ejpam-6458	472	5	-	-	ADJ
ejpam-6458	472	6	zero	zero	NUM
ejpam-6458	472	7	,	,	PUNCT
ejpam-6458	472	8	for	for	ADP
ejpam-6458	472	9	all	all	DET
ejpam-6458	472	10	i	i	PROPN
ejpam-6458	472	11	,	,	PUNCT
ejpam-6458	472	12	j	j	PROPN
ejpam-6458	472	13	,	,	PUNCT
ejpam-6458	472	14	k	k	PROPN
ejpam-6458	472	15	∈	∈	PROPN
ejpam-6458	472	16	z.	z.	PROPN
ejpam-6458	473	1	if	if	SCONJ
ejpam-6458	473	2	one	one	NUM
ejpam-6458	473	3	or	or	CCONJ
ejpam-6458	473	4	more	more	ADJ
ejpam-6458	473	5	these	these	DET
ejpam-6458	473	6	coefficients	coefficient	NOUN
ejpam-6458	473	7	are	be	AUX
ejpam-6458	473	8	equal	equal	ADJ
ejpam-6458	473	9	to	to	ADP
ejpam-6458	473	10	zero	zero	NUM
ejpam-6458	473	11	,	,	PUNCT
ejpam-6458	473	12	then	then	ADV
ejpam-6458	473	13	a	a	DET
ejpam-6458	473	14	system	system	NOUN
ejpam-6458	473	15	of	of	ADP
ejpam-6458	473	16	sub	sub	NOUN
ejpam-6458	473	17	modules	module	NOUN
ejpam-6458	473	18	arises	arise	VERB
ejpam-6458	473	19	.	.	PUNCT
ejpam-6458	474	1	below	below	ADV
ejpam-6458	474	2	,	,	PUNCT
ejpam-6458	474	3	we	we	PRON
ejpam-6458	474	4	present	present	VERB
ejpam-6458	474	5	two	two	NUM
ejpam-6458	474	6	examples	example	NOUN
ejpam-6458	474	7	of	of	ADP
ejpam-6458	474	8	such	such	ADJ
ejpam-6458	474	9	sub	sub	NOUN
ejpam-6458	474	10	modules	module	NOUN
ejpam-6458	474	11	.	.	PUNCT
ejpam-6458	475	1	let	let	VERB
ejpam-6458	475	2	i	i	PRON
ejpam-6458	475	3	=	=	SYM
ejpam-6458	475	4	z3	z3	PROPN
ejpam-6458	475	5	⊂	⊂	PROPN
ejpam-6458	475	6	r3	r3	PROPN
ejpam-6458	475	7	be	be	AUX
ejpam-6458	475	8	the	the	DET
ejpam-6458	475	9	weight	weight	NOUN
ejpam-6458	475	10	lattice	lattice	NOUN
ejpam-6458	475	11	(	(	PUNCT
ejpam-6458	475	12	the	the	DET
ejpam-6458	475	13	lattice	lattice	NOUN
ejpam-6458	475	14	of	of	ADP
ejpam-6458	475	15	indices	index	NOUN
ejpam-6458	475	16	)	)	PUNCT
ejpam-6458	475	17	of	of	ADP
ejpam-6458	475	18	the	the	DET
ejpam-6458	475	19	module	module	NOUN
ejpam-6458	475	20	v	v	NOUN
ejpam-6458	475	21	(	(	PUNCT
ejpam-6458	475	22	a1	a1	PROPN
ejpam-6458	475	23	,	,	PUNCT
ejpam-6458	475	24	a2	a2	PROPN
ejpam-6458	475	25	,	,	PUNCT
ejpam-6458	475	26	a3	a3	NOUN
ejpam-6458	475	27	,	,	PUNCT
ejpam-6458	475	28	ξ	ξ	PROPN
ejpam-6458	475	29	,	,	PUNCT
ejpam-6458	475	30	µ	µ	NOUN
ejpam-6458	475	31	)	)	PUNCT
ejpam-6458	475	32	.	.	PUNCT
ejpam-6458	476	1	case	case	NOUN
ejpam-6458	476	2	1	1	X
ejpam-6458	476	3	.	.	X
ejpam-6458	476	4	assume	assume	VERB
ejpam-6458	476	5	that	that	SCONJ
ejpam-6458	476	6	s+	s+	PUNCT
ejpam-6458	476	7	i0,j0,k0	i0,j0,k0	PROPN
ejpam-6458	476	8	=	=	NOUN
ejpam-6458	476	9	0	0	NUM
ejpam-6458	476	10	for	for	ADP
ejpam-6458	476	11	some	some	DET
ejpam-6458	476	12	i0	i0	PROPN
ejpam-6458	476	13	,	,	PUNCT
ejpam-6458	476	14	j0	j0	PROPN
ejpam-6458	476	15	,	,	PUNCT
ejpam-6458	476	16	k0	k0	PROPN
ejpam-6458	476	17	∈	∈	PROPN
ejpam-6458	476	18	z.	z.	PROPN
ejpam-6458	476	19	then	then	ADV
ejpam-6458	476	20	,	,	PUNCT
ejpam-6458	476	21	it	it	PRON
ejpam-6458	476	22	follows	follow	VERB
ejpam-6458	476	23	that	that	SCONJ
ejpam-6458	476	24	a1	a1	NOUN
ejpam-6458	476	25	+	+	CCONJ
ejpam-6458	476	26	a3	a3	NOUN
ejpam-6458	476	27	∈	∈	PROPN
ejpam-6458	476	28	2z+1	2z+1	PROPN
ejpam-6458	476	29	.	.	PUNCT
ejpam-6458	477	1	consider	consider	VERB
ejpam-6458	477	2	the	the	DET
ejpam-6458	477	3	function	function	NOUN
ejpam-6458	477	4	f	f	X
ejpam-6458	477	5	(	(	PUNCT
ejpam-6458	477	6	i	i	PROPN
ejpam-6458	477	7	,	,	PUNCT
ejpam-6458	477	8	j	j	PROPN
ejpam-6458	477	9	,	,	PUNCT
ejpam-6458	477	10	k	k	NOUN
ejpam-6458	477	11	)	)	PUNCT
ejpam-6458	477	12	=	=	PUNCT
ejpam-6458	477	13	s+	s+	PUNCT
ejpam-6458	478	1	ijk	ijk	PROPN
ejpam-6458	478	2	defined	define	VERB
ejpam-6458	478	3	on	on	ADP
ejpam-6458	478	4	the	the	DET
ejpam-6458	478	5	set	set	NOUN
ejpam-6458	478	6	i.	i.	NOUN
ejpam-6458	478	7	the	the	DET
ejpam-6458	478	8	subset	subset	NOUN
ejpam-6458	478	9	of	of	ADP
ejpam-6458	478	10	zero	zero	NUM
ejpam-6458	478	11	points	point	NOUN
ejpam-6458	478	12	p	p	X
ejpam-6458	478	13	(	(	PUNCT
ejpam-6458	478	14	f	f	PROPN
ejpam-6458	478	15	)	)	PUNCT
ejpam-6458	478	16	=	=	PRON
ejpam-6458	479	1	{	{	PUNCT
ejpam-6458	479	2	(	(	PUNCT
ejpam-6458	479	3	i	i	PROPN
ejpam-6458	479	4	,	,	PUNCT
ejpam-6458	479	5	j	j	PROPN
ejpam-6458	479	6	,	,	PUNCT
ejpam-6458	479	7	k	k	PROPN
ejpam-6458	479	8	)	)	PUNCT
ejpam-6458	479	9	|f	|f	PROPN
ejpam-6458	480	1	(	(	PUNCT
ejpam-6458	480	2	i	i	PROPN
ejpam-6458	480	3	,	,	PUNCT
ejpam-6458	480	4	j	j	PROPN
ejpam-6458	480	5	,	,	PUNCT
ejpam-6458	480	6	k	k	PROPN
ejpam-6458	480	7	)	)	PUNCT
ejpam-6458	480	8	=	=	SYM
ejpam-6458	480	9	0	0	X
ejpam-6458	480	10	}	}	PUNCT
ejpam-6458	480	11	is	be	AUX
ejpam-6458	480	12	called	call	VERB
ejpam-6458	480	13	the	the	DET
ejpam-6458	480	14	splitting	splitting	NOUN
ejpam-6458	480	15	hyperplane	hyperplane	NOUN
ejpam-6458	480	16	of	of	ADP
ejpam-6458	480	17	the	the	DET
ejpam-6458	480	18	function	function	NOUN
ejpam-6458	480	19	f	f	PROPN
ejpam-6458	480	20	.	.	PUNCT
ejpam-6458	481	1	the	the	DET
ejpam-6458	481	2	splitting	splitting	NOUN
ejpam-6458	481	3	hyperplane	hyperplane	NOUN
ejpam-6458	481	4	f	f	X
ejpam-6458	481	5	(	(	PUNCT
ejpam-6458	481	6	i	i	PROPN
ejpam-6458	481	7	,	,	PUNCT
ejpam-6458	481	8	j	j	PROPN
ejpam-6458	481	9	,	,	PUNCT
ejpam-6458	481	10	k	k	NOUN
ejpam-6458	481	11	)	)	PUNCT
ejpam-6458	481	12	divides	divide	VERB
ejpam-6458	481	13	the	the	DET
ejpam-6458	481	14	set	set	NOUN
ejpam-6458	481	15	i	i	PRON
ejpam-6458	481	16	into	into	ADP
ejpam-6458	481	17	two	two	NUM
ejpam-6458	481	18	subsets	subset	NOUN
ejpam-6458	481	19	,	,	PUNCT
ejpam-6458	481	20	called	call	VERB
ejpam-6458	481	21	the	the	DET
ejpam-6458	481	22	positive	positive	ADJ
ejpam-6458	481	23	and	and	CCONJ
ejpam-6458	481	24	the	the	DET
ejpam-6458	481	25	negative	negative	ADJ
ejpam-6458	481	26	components	component	NOUN
ejpam-6458	481	27	,	,	PUNCT
ejpam-6458	481	28	given	give	VERB
ejpam-6458	481	29	by	by	ADP
ejpam-6458	481	30	i+f	i+f	PROPN
ejpam-6458	481	31	=	=	SYM
ejpam-6458	481	32	{	{	PUNCT
ejpam-6458	481	33	(	(	PUNCT
ejpam-6458	481	34	i	i	PROPN
ejpam-6458	481	35	,	,	PUNCT
ejpam-6458	481	36	j	j	PROPN
ejpam-6458	481	37	,	,	PUNCT
ejpam-6458	481	38	k	k	PROPN
ejpam-6458	481	39	)	)	PUNCT
ejpam-6458	481	40	|f	|f	PROPN
ejpam-6458	482	1	(	(	PUNCT
ejpam-6458	482	2	i	i	PROPN
ejpam-6458	482	3	,	,	PUNCT
ejpam-6458	482	4	j	j	PROPN
ejpam-6458	482	5	,	,	PUNCT
ejpam-6458	482	6	k	k	PROPN
ejpam-6458	482	7	)	)	PUNCT
ejpam-6458	482	8	>	>	X
ejpam-6458	482	9	0	0	NUM
ejpam-6458	482	10	}	}	PUNCT
ejpam-6458	482	11	and	and	CCONJ
ejpam-6458	482	12	i−f	i−f	NOUN
ejpam-6458	482	13	=	=	PUNCT
ejpam-6458	482	14	{	{	PUNCT
ejpam-6458	482	15	(	(	PUNCT
ejpam-6458	482	16	i	i	PROPN
ejpam-6458	482	17	,	,	PUNCT
ejpam-6458	482	18	j	j	PROPN
ejpam-6458	482	19	,	,	PUNCT
ejpam-6458	482	20	k	k	PROPN
ejpam-6458	482	21	)	)	PUNCT
ejpam-6458	482	22	|f	|f	PROPN
ejpam-6458	482	23	(	(	PUNCT
ejpam-6458	482	24	i	i	PROPN
ejpam-6458	482	25	,	,	PUNCT
ejpam-6458	482	26	j	j	PROPN
ejpam-6458	482	27	,	,	PUNCT
ejpam-6458	482	28	k	k	NOUN
ejpam-6458	482	29	)	)	PUNCT
ejpam-6458	482	30	≤	≤	NOUN
ejpam-6458	482	31	0	0	NUM
ejpam-6458	482	32	}	}	PUNCT
ejpam-6458	482	33	.	.	PUNCT
ejpam-6458	483	1	using	use	VERB
ejpam-6458	483	2	(	(	PUNCT
ejpam-6458	483	3	4.16	4.16	NUM
ejpam-6458	483	4	)	)	PUNCT
ejpam-6458	483	5	,	,	PUNCT
ejpam-6458	483	6	we	we	PRON
ejpam-6458	483	7	observe	observe	VERB
ejpam-6458	483	8	that	that	SCONJ
ejpam-6458	483	9	,	,	PUNCT
ejpam-6458	483	10	for	for	ADP
ejpam-6458	483	11	any	any	DET
ejpam-6458	483	12	(	(	PUNCT
ejpam-6458	483	13	i	i	PROPN
ejpam-6458	483	14	,	,	PUNCT
ejpam-6458	483	15	j	j	PROPN
ejpam-6458	483	16	,	,	PUNCT
ejpam-6458	483	17	k	k	PROPN
ejpam-6458	483	18	)	)	PUNCT
ejpam-6458	483	19	∈	∈	PROPN
ejpam-6458	483	20	i−f	i−f	NOUN
ejpam-6458	483	21	,	,	PUNCT
ejpam-6458	483	22	the	the	DET
ejpam-6458	483	23	action	action	NOUN
ejpam-6458	483	24	of	of	ADP
ejpam-6458	483	25	the	the	DET
ejpam-6458	483	26	elements	element	NOUN
ejpam-6458	483	27	e01	e01	X
ejpam-6458	483	28	,	,	PUNCT
ejpam-6458	483	29	f01	f01	NOUN
ejpam-6458	483	30	,	,	PUNCT
ejpam-6458	483	31	e10	e10	PROPN
ejpam-6458	483	32	,	,	PUNCT
ejpam-6458	483	33	f10	f10	NOUN
ejpam-6458	483	34	on	on	ADP
ejpam-6458	483	35	vijk	vijk	PROPN
ejpam-6458	483	36	results	result	NOUN
ejpam-6458	483	37	in	in	ADP
ejpam-6458	483	38	elements	element	NOUN
ejpam-6458	483	39	that	that	PRON
ejpam-6458	483	40	remain	remain	VERB
ejpam-6458	483	41	in	in	ADP
ejpam-6458	483	42	the	the	DET
ejpam-6458	483	43	subspace	subspace	NOUN
ejpam-6458	483	44	v	v	ADP
ejpam-6458	483	45	′	′	NUM
ejpam-6458	484	1	=	=	PUNCT
ejpam-6458	484	2	spanc{vijk	spanc{vijk	X
ejpam-6458	485	1	|	|	ADV
ejpam-6458	485	2	(	(	PUNCT
ejpam-6458	485	3	i	i	PROPN
ejpam-6458	485	4	,	,	PUNCT
ejpam-6458	485	5	j	j	PROPN
ejpam-6458	485	6	,	,	PUNCT
ejpam-6458	485	7	k	k	PROPN
ejpam-6458	485	8	)	)	PUNCT
ejpam-6458	485	9	∈	∈	PROPN
ejpam-6458	485	10	i−f	i−f	NOUN
ejpam-6458	485	11	}	}	PUNCT
ejpam-6458	485	12	⊂	⊂	PROPN
ejpam-6458	485	13	v	v	NOUN
ejpam-6458	485	14	.	.	PUNCT
ejpam-6458	486	1	thus	thus	ADV
ejpam-6458	486	2	v	v	X
ejpam-6458	486	3	′	′	NUM
ejpam-6458	486	4	forms	form	NOUN
ejpam-6458	486	5	a	a	DET
ejpam-6458	486	6	submodule	submodule	NOUN
ejpam-6458	486	7	of	of	ADP
ejpam-6458	486	8	v	v	NOUN
ejpam-6458	486	9	.	.	PUNCT
ejpam-6458	487	1	it	it	PRON
ejpam-6458	487	2	is	be	AUX
ejpam-6458	487	3	simple	simple	ADJ
ejpam-6458	487	4	if	if	SCONJ
ejpam-6458	487	5	none	none	NOUN
ejpam-6458	487	6	of	of	ADP
ejpam-6458	487	7	s−	s−	PROPN
ejpam-6458	487	8	ik	ik	PROPN
ejpam-6458	487	9	,	,	PUNCT
ejpam-6458	487	10	q	q	PROPN
ejpam-6458	488	1	+	+	CCONJ
ejpam-6458	488	2	jk	jk	NOUN
ejpam-6458	488	3	or	or	CCONJ
ejpam-6458	488	4	q	q	PROPN
ejpam-6458	489	1	−	−	PROPN
ejpam-6458	489	2	jk	jk	PROPN
ejpam-6458	489	3	vanish	vanish	VERB
ejpam-6458	489	4	for	for	ADP
ejpam-6458	489	5	any	any	DET
ejpam-6458	489	6	choice	choice	NOUN
ejpam-6458	489	7	of	of	ADP
ejpam-6458	489	8	indices	index	NOUN
ejpam-6458	489	9	.	.	PUNCT
ejpam-6458	490	1	case	case	NOUN
ejpam-6458	490	2	2	2	NUM
ejpam-6458	490	3	.	.	X
ejpam-6458	490	4	assume	assume	VERB
ejpam-6458	490	5	that	that	SCONJ
ejpam-6458	490	6	q+	q+	ADP
ejpam-6458	490	7	k	k	X
ejpam-6458	490	8	=	=	PUNCT
ejpam-6458	490	9	0	0	PROPN
ejpam-6458	490	10	for	for	ADP
ejpam-6458	490	11	some	some	DET
ejpam-6458	490	12	k	k	PROPN
ejpam-6458	490	13	∈	∈	PROPN
ejpam-6458	490	14	z.	z.	PROPN
ejpam-6458	490	15	as	as	SCONJ
ejpam-6458	490	16	we	we	PRON
ejpam-6458	490	17	can	can	AUX
ejpam-6458	490	18	see	see	VERB
ejpam-6458	490	19	,	,	PUNCT
ejpam-6458	490	20	q+	q+	ADV
ejpam-6458	490	21	k	k	PROPN
ejpam-6458	490	22	is	be	AUX
ejpam-6458	490	23	the	the	DET
ejpam-6458	490	24	product	product	NOUN
ejpam-6458	490	25	of	of	ADP
ejpam-6458	490	26	three	three	NUM
ejpam-6458	490	27	first	first	ADJ
ejpam-6458	490	28	degree	degree	NOUN
ejpam-6458	490	29	polynomials	polynomial	NOUN
ejpam-6458	490	30	fm(i	fm(i	ADV
ejpam-6458	490	31	,	,	PUNCT
ejpam-6458	490	32	j	j	PROPN
ejpam-6458	490	33	,	,	PUNCT
ejpam-6458	490	34	k	k	PROPN
ejpam-6458	490	35	)	)	PUNCT
ejpam-6458	490	36	=	=	SYM
ejpam-6458	491	1	(	(	PUNCT
ejpam-6458	491	2	t+	t+	NOUN
ejpam-6458	491	3	k	k	PROPN
ejpam-6458	491	4	+	+	CCONJ
ejpam-6458	491	5	tm	tm	NOUN
ejpam-6458	491	6	)	)	PUNCT
ejpam-6458	491	7	,	,	PUNCT
ejpam-6458	491	8	with	with	ADP
ejpam-6458	491	9	m	m	PROPN
ejpam-6458	491	10	=	=	SYM
ejpam-6458	491	11	1	1	NUM
ejpam-6458	491	12	,	,	PUNCT
ejpam-6458	491	13	2	2	NUM
ejpam-6458	491	14	,	,	PUNCT
ejpam-6458	491	15	3	3	NUM
ejpam-6458	491	16	,	,	PUNCT
ejpam-6458	491	17	in	in	ADP
ejpam-6458	491	18	the	the	DET
ejpam-6458	491	19	variable	variable	NOUN
ejpam-6458	491	20	k.	k.	PROPN
ejpam-6458	491	21	let	let	VERB
ejpam-6458	491	22	us	we	PRON
ejpam-6458	491	23	m.	m.	VERB
ejpam-6458	491	24	andelić	andelić	ADV
ejpam-6458	491	25	et	et	PROPN
ejpam-6458	491	26	al	al	PROPN
ejpam-6458	491	27	.	.	PUNCT
ejpam-6458	491	28	/	/	SYM
ejpam-6458	491	29	eur	eur	PROPN
ejpam-6458	491	30	.	.	PUNCT
ejpam-6458	492	1	j.	j.	PROPN
ejpam-6458	492	2	pure	pure	PROPN
ejpam-6458	492	3	appl	appl	PROPN
ejpam-6458	492	4	.	.	PROPN
ejpam-6458	492	5	math	math	PROPN
ejpam-6458	492	6	,	,	PUNCT
ejpam-6458	492	7	18	18	NUM
ejpam-6458	492	8	(	(	PUNCT
ejpam-6458	492	9	3	3	NUM
ejpam-6458	492	10	)	)	PUNCT
ejpam-6458	492	11	(	(	PUNCT
ejpam-6458	492	12	2025	2025	NUM
ejpam-6458	492	13	)	)	PUNCT
ejpam-6458	492	14	,	,	PUNCT
ejpam-6458	492	15	6458	6458	NUM
ejpam-6458	492	16	12	12	NUM
ejpam-6458	492	17	of	of	ADP
ejpam-6458	492	18	21	21	NUM
ejpam-6458	492	19	consider	consider	VERB
ejpam-6458	492	20	the	the	DET
ejpam-6458	492	21	case	case	NOUN
ejpam-6458	492	22	when	when	SCONJ
ejpam-6458	492	23	q+	q+	ADV
ejpam-6458	492	24	k	k	X
ejpam-6458	492	25	=	=	SYM
ejpam-6458	492	26	0	0	PROPN
ejpam-6458	492	27	has	have	VERB
ejpam-6458	492	28	three	three	NUM
ejpam-6458	492	29	distinct	distinct	ADJ
ejpam-6458	492	30	roots	root	NOUN
ejpam-6458	492	31	.	.	PUNCT
ejpam-6458	493	1	we	we	PRON
ejpam-6458	493	2	need	need	VERB
ejpam-6458	493	3	to	to	PART
ejpam-6458	493	4	find	find	VERB
ejpam-6458	493	5	possible	possible	ADJ
ejpam-6458	493	6	values	value	NOUN
ejpam-6458	493	7	of	of	ADP
ejpam-6458	493	8	the	the	DET
ejpam-6458	493	9	parameters	parameter	NOUN
ejpam-6458	493	10	a1	a1	PROPN
ejpam-6458	493	11	,	,	PUNCT
ejpam-6458	493	12	a2	a2	PROPN
ejpam-6458	493	13	,	,	PUNCT
ejpam-6458	493	14	a3	a3	NOUN
ejpam-6458	493	15	,	,	PUNCT
ejpam-6458	493	16	t1	t1	NOUN
ejpam-6458	493	17	,	,	PUNCT
ejpam-6458	493	18	t2	t2	NOUN
ejpam-6458	493	19	,	,	PUNCT
ejpam-6458	493	20	t3	t3	NOUN
ejpam-6458	493	21	such	such	ADJ
ejpam-6458	493	22	that	that	SCONJ
ejpam-6458	493	23	the	the	DET
ejpam-6458	493	24	system	system	NOUN
ejpam-6458	493	25	of	of	ADP
ejpam-6458	493	26	three	three	NUM
ejpam-6458	493	27	equations	equation	NOUN
ejpam-6458	493	28	:	:	PUNCT
ejpam-6458	493	29	fm(i	fm(i	PROPN
ejpam-6458	493	30	,	,	PUNCT
ejpam-6458	493	31	j	j	PROPN
ejpam-6458	493	32	,	,	PUNCT
ejpam-6458	493	33	km	km	PROPN
ejpam-6458	493	34	)	)	PUNCT
ejpam-6458	493	35	=	=	SYM
ejpam-6458	493	36	0	0	NUM
ejpam-6458	493	37	,	,	PUNCT
ejpam-6458	493	38	m	m	VERB
ejpam-6458	493	39	=	=	NOUN
ejpam-6458	493	40	1	1	NUM
ejpam-6458	493	41	,	,	PUNCT
ejpam-6458	493	42	2	2	NUM
ejpam-6458	493	43	,	,	PUNCT
ejpam-6458	493	44	3	3	NUM
ejpam-6458	493	45	has	have	VERB
ejpam-6458	493	46	integer	integer	NOUN
ejpam-6458	493	47	solutions	solution	NOUN
ejpam-6458	493	48	for	for	ADP
ejpam-6458	493	49	the	the	DET
ejpam-6458	493	50	variables	variable	NOUN
ejpam-6458	493	51	km	km	PROPN
ejpam-6458	493	52	.	.	PUNCT
ejpam-6458	494	1	we	we	PRON
ejpam-6458	494	2	find	find	VERB
ejpam-6458	494	3	that	that	SCONJ
ejpam-6458	494	4	q	q	PROPN
ejpam-6458	495	1	+	+	NUM
ejpam-6458	495	2	k	k	X
ejpam-6458	495	3	=	=	SYM
ejpam-6458	495	4	0	0	NUM
ejpam-6458	495	5	,	,	PUNCT
ejpam-6458	495	6	for	for	ADP
ejpam-6458	495	7	k	k	PROPN
ejpam-6458	495	8	=	=	SYM
ejpam-6458	495	9	k1	k1	PROPN
ejpam-6458	495	10	,	,	PUNCT
ejpam-6458	495	11	k2	k2	NOUN
ejpam-6458	495	12	,	,	PUNCT
ejpam-6458	495	13	k3	k3	VERB
ejpam-6458	495	14	∈	∈	PROPN
ejpam-6458	495	15	z	z	NOUN
ejpam-6458	495	16	if	if	SCONJ
ejpam-6458	495	17	the	the	DET
ejpam-6458	495	18	following	follow	VERB
ejpam-6458	495	19	conditions	condition	NOUN
ejpam-6458	495	20	hold	hold	VERB
ejpam-6458	495	21	:	:	PUNCT
ejpam-6458	495	22	tm	tm	PROPN
ejpam-6458	495	23	=	=	PROPN
ejpam-6458	495	24	1	1	NUM
ejpam-6458	495	25	3(k1	3(k1	NUM
ejpam-6458	495	26	+	+	CCONJ
ejpam-6458	495	27	k2	k2	ADJ
ejpam-6458	495	28	+	+	CCONJ
ejpam-6458	495	29	k3	k3	ADJ
ejpam-6458	495	30	)	)	PUNCT
ejpam-6458	495	31	−	−	PROPN
ejpam-6458	495	32	km	km	PROPN
ejpam-6458	495	33	,	,	PUNCT
ejpam-6458	495	34	m	m	VERB
ejpam-6458	495	35	=	=	NOUN
ejpam-6458	495	36	1	1	NUM
ejpam-6458	495	37	,	,	PUNCT
ejpam-6458	495	38	2	2	NUM
ejpam-6458	495	39	,	,	PUNCT
ejpam-6458	495	40	3	3	NUM
ejpam-6458	495	41	and	and	CCONJ
ejpam-6458	495	42	a3	a3	NOUN
ejpam-6458	495	43	=	=	NOUN
ejpam-6458	495	44	3	3	NUM
ejpam-6458	495	45	−	−	NOUN
ejpam-6458	495	46	1	1	NUM
ejpam-6458	495	47	3(2k1	3(2k1	NOUN
ejpam-6458	495	48	+	+	CCONJ
ejpam-6458	495	49	2k2	2k2	NUM
ejpam-6458	495	50	+	+	CCONJ
ejpam-6458	495	51	2k3	2k3	NUM
ejpam-6458	495	52	+	+	CCONJ
ejpam-6458	495	53	a1	a1	NOUN
ejpam-6458	495	54	+	+	CCONJ
ejpam-6458	495	55	2a2	2a2	NUM
ejpam-6458	495	56	)	)	PUNCT
ejpam-6458	495	57	.	.	PUNCT
ejpam-6458	496	1	suppose	suppose	VERB
ejpam-6458	496	2	that	that	SCONJ
ejpam-6458	496	3	k1	k1	PROPN
ejpam-6458	496	4	>	>	X
ejpam-6458	496	5	k2	k2	PROPN
ejpam-6458	496	6	>	>	X
ejpam-6458	496	7	k3	k3	PROPN
ejpam-6458	496	8	.	.	PUNCT
ejpam-6458	497	1	then	then	ADV
ejpam-6458	497	2	we	we	PRON
ejpam-6458	497	3	have	have	VERB
ejpam-6458	497	4	three	three	NUM
ejpam-6458	497	5	splitting	splitting	NOUN
ejpam-6458	497	6	hyperplanes	hyperplane	NOUN
ejpam-6458	497	7	pm	pm	NOUN
ejpam-6458	497	8	=	=	SYM
ejpam-6458	497	9	{	{	PUNCT
ejpam-6458	497	10	(	(	PUNCT
ejpam-6458	497	11	i	i	PROPN
ejpam-6458	497	12	,	,	PUNCT
ejpam-6458	497	13	j	j	PROPN
ejpam-6458	497	14	,	,	PUNCT
ejpam-6458	497	15	k	k	PROPN
ejpam-6458	497	16	)	)	PUNCT
ejpam-6458	498	1	|fm(i	|fm(i	PROPN
ejpam-6458	498	2	,	,	PUNCT
ejpam-6458	498	3	j	j	PROPN
ejpam-6458	498	4	,	,	PUNCT
ejpam-6458	498	5	k	k	PROPN
ejpam-6458	498	6	)	)	PUNCT
ejpam-6458	498	7	=	=	SYM
ejpam-6458	498	8	0	0	X
ejpam-6458	498	9	}	}	PUNCT
ejpam-6458	498	10	and	and	CCONJ
ejpam-6458	498	11	i	i	PRON
ejpam-6458	498	12	=	=	SYM
ejpam-6458	498	13	i+fm	i+fm	NOUN
ejpam-6458	498	14	∪	∪	VERB
ejpam-6458	498	15	i−fm	i−fm	NOUN
ejpam-6458	498	16	,	,	PUNCT
ejpam-6458	498	17	where	where	SCONJ
ejpam-6458	498	18	i+fm	i+fm	NOUN
ejpam-6458	498	19	=	=	PRON
ejpam-6458	498	20	{	{	PUNCT
ejpam-6458	498	21	(	(	PUNCT
ejpam-6458	498	22	i	i	PROPN
ejpam-6458	498	23	,	,	PUNCT
ejpam-6458	498	24	j	j	PROPN
ejpam-6458	498	25	,	,	PUNCT
ejpam-6458	498	26	k	k	PROPN
ejpam-6458	498	27	)	)	PUNCT
ejpam-6458	498	28	|fm(i	|fm(i	PROPN
ejpam-6458	498	29	,	,	PUNCT
ejpam-6458	498	30	j	j	PROPN
ejpam-6458	498	31	,	,	PUNCT
ejpam-6458	498	32	k	k	PROPN
ejpam-6458	498	33	)	)	PUNCT
ejpam-6458	498	34	≥	≥	NOUN
ejpam-6458	498	35	0	0	NUM
ejpam-6458	498	36	}	}	PUNCT
ejpam-6458	498	37	,	,	PUNCT
ejpam-6458	498	38	i−fm	i−fm	NOUN
ejpam-6458	498	39	=	=	SYM
ejpam-6458	498	40	{	{	PUNCT
ejpam-6458	498	41	(	(	PUNCT
ejpam-6458	498	42	i	i	PROPN
ejpam-6458	498	43	,	,	PUNCT
ejpam-6458	498	44	j	j	PROPN
ejpam-6458	498	45	,	,	PUNCT
ejpam-6458	498	46	k	k	PROPN
ejpam-6458	498	47	)	)	PUNCT
ejpam-6458	498	48	|fm(i	|fm(i	PROPN
ejpam-6458	498	49	,	,	PUNCT
ejpam-6458	498	50	j	j	PROPN
ejpam-6458	498	51	,	,	PUNCT
ejpam-6458	498	52	k	k	PROPN
ejpam-6458	498	53	)	)	PUNCT
ejpam-6458	498	54	<	<	X
ejpam-6458	498	55	0	0	NUM
ejpam-6458	498	56	}	}	PUNCT
ejpam-6458	498	57	,	,	PUNCT
ejpam-6458	498	58	for	for	ADP
ejpam-6458	498	59	m	m	PROPN
ejpam-6458	498	60	=	=	SYM
ejpam-6458	498	61	1	1	NUM
ejpam-6458	498	62	,	,	PUNCT
ejpam-6458	498	63	2	2	NUM
ejpam-6458	498	64	,	,	PUNCT
ejpam-6458	498	65	3	3	NUM
ejpam-6458	498	66	.	.	PUNCT
ejpam-6458	498	67	again	again	ADV
ejpam-6458	498	68	,	,	PUNCT
ejpam-6458	498	69	using	use	VERB
ejpam-6458	498	70	(	(	PUNCT
ejpam-6458	498	71	4.16	4.16	NUM
ejpam-6458	498	72	)	)	PUNCT
ejpam-6458	498	73	we	we	PRON
ejpam-6458	498	74	immediately	immediately	ADV
ejpam-6458	498	75	obtain	obtain	VERB
ejpam-6458	498	76	proposition	proposition	NOUN
ejpam-6458	498	77	4.4	4.4	NUM
ejpam-6458	498	78	.	.	PUNCT
ejpam-6458	499	1	the	the	DET
ejpam-6458	499	2	subspaces	subspace	NOUN
ejpam-6458	499	3	v	v	VERB
ejpam-6458	499	4	′	′	NUM
ejpam-6458	499	5	m	m	NOUN
ejpam-6458	499	6	=	=	SYM
ejpam-6458	499	7	spanc{vijk	spanc{vijk	X
ejpam-6458	500	1	|	|	ADV
ejpam-6458	500	2	(	(	PUNCT
ejpam-6458	500	3	i	i	PROPN
ejpam-6458	500	4	,	,	PUNCT
ejpam-6458	500	5	j	j	PROPN
ejpam-6458	500	6	,	,	PUNCT
ejpam-6458	500	7	k	k	NOUN
ejpam-6458	500	8	)	)	PUNCT
ejpam-6458	500	9	∈	∈	PROPN
ejpam-6458	500	10	i+fm	i+fm	NOUN
ejpam-6458	500	11	}	}	PUNCT
ejpam-6458	500	12	⊂	⊂	PROPN
ejpam-6458	500	13	v	v	X
ejpam-6458	500	14	(	(	PUNCT
ejpam-6458	500	15	a1	a1	PROPN
ejpam-6458	500	16	,	,	PUNCT
ejpam-6458	500	17	a2	a2	PROPN
ejpam-6458	500	18	,	,	PUNCT
ejpam-6458	500	19	a3	a3	NOUN
ejpam-6458	500	20	,	,	PUNCT
ejpam-6458	500	21	ξ	ξ	PROPN
ejpam-6458	500	22	,	,	PUNCT
ejpam-6458	500	23	µ	µ	NOUN
ejpam-6458	500	24	)	)	PUNCT
ejpam-6458	500	25	are	be	AUX
ejpam-6458	500	26	submodules	submodule	NOUN
ejpam-6458	500	27	of	of	ADP
ejpam-6458	500	28	v	v	NOUN
ejpam-6458	500	29	(	(	PUNCT
ejpam-6458	500	30	a1	a1	PROPN
ejpam-6458	500	31	,	,	PUNCT
ejpam-6458	500	32	a2	a2	PROPN
ejpam-6458	500	33	,	,	PUNCT
ejpam-6458	500	34	a3	a3	NOUN
ejpam-6458	500	35	,	,	PUNCT
ejpam-6458	500	36	ξ	ξ	PROPN
ejpam-6458	500	37	,	,	PUNCT
ejpam-6458	500	38	µ	µ	NOUN
ejpam-6458	500	39	)	)	PUNCT
ejpam-6458	500	40	satisfying	satisfy	VERB
ejpam-6458	500	41	the	the	DET
ejpam-6458	500	42	inclusion	inclusion	NOUN
ejpam-6458	500	43	v	v	ADP
ejpam-6458	500	44	′	′	NUM
ejpam-6458	500	45	1	1	NUM
ejpam-6458	501	1	⊂	⊂	NOUN
ejpam-6458	501	2	v	v	NOUN
ejpam-6458	501	3	′	′	NUM
ejpam-6458	501	4	2	2	NUM
ejpam-6458	501	5	⊂	⊂	NOUN
ejpam-6458	501	6	v	v	ADP
ejpam-6458	501	7	′	′	NUM
ejpam-6458	501	8	3	3	NUM
ejpam-6458	501	9	.	.	PUNCT
ejpam-6458	502	1	if	if	SCONJ
ejpam-6458	502	2	none	none	NOUN
ejpam-6458	502	3	of	of	ADP
ejpam-6458	502	4	s+	s+	PUNCT
ejpam-6458	502	5	ijk	ijk	PROPN
ejpam-6458	502	6	or	or	CCONJ
ejpam-6458	502	7	s	s	PROPN
ejpam-6458	502	8	−	−	PROPN
ejpam-6458	502	9	ik	ik	PROPN
ejpam-6458	502	10	or	or	CCONJ
ejpam-6458	502	11	q	q	PROPN
ejpam-6458	502	12	−	−	PROPN
ejpam-6458	502	13	jk	jk	PROPN
ejpam-6458	502	14	are	be	AUX
ejpam-6458	502	15	zero	zero	NUM
ejpam-6458	502	16	for	for	ADP
ejpam-6458	502	17	all	all	DET
ejpam-6458	502	18	choices	choice	NOUN
ejpam-6458	502	19	of	of	ADP
ejpam-6458	502	20	indices	index	NOUN
ejpam-6458	502	21	,	,	PUNCT
ejpam-6458	502	22	then	then	ADV
ejpam-6458	502	23	v	v	X
ejpam-6458	502	24	′	′	NUM
ejpam-6458	502	25	1	1	NUM
ejpam-6458	502	26	and	and	CCONJ
ejpam-6458	502	27	v	v	NUM
ejpam-6458	502	28	′	′	NUM
ejpam-6458	502	29	2	2	NUM
ejpam-6458	502	30	/	/	SYM
ejpam-6458	502	31	v	v	NOUN
ejpam-6458	502	32	′	′	NUM
ejpam-6458	502	33	1	1	NUM
ejpam-6458	502	34	and	and	CCONJ
ejpam-6458	502	35	v	v	NUM
ejpam-6458	502	36	′	′	NUM
ejpam-6458	502	37	3	3	NUM
ejpam-6458	502	38	/	/	SYM
ejpam-6458	502	39	v	v	NOUN
ejpam-6458	502	40	′	′	NUM
ejpam-6458	502	41	2	2	NUM
ejpam-6458	502	42	and	and	CCONJ
ejpam-6458	502	43	v	v	NOUN
ejpam-6458	502	44	(	(	PUNCT
ejpam-6458	502	45	a1	a1	PROPN
ejpam-6458	502	46	,	,	PUNCT
ejpam-6458	502	47	a2	a2	PROPN
ejpam-6458	502	48	,	,	PUNCT
ejpam-6458	502	49	a3	a3	NOUN
ejpam-6458	502	50	,	,	PUNCT
ejpam-6458	502	51	ξ	ξ	PROPN
ejpam-6458	502	52	,	,	PUNCT
ejpam-6458	502	53	µ)/v	µ)/v	PROPN
ejpam-6458	502	54	′	′	NUM
ejpam-6458	502	55	3	3	NUM
ejpam-6458	502	56	are	be	AUX
ejpam-6458	502	57	simple	simple	ADJ
ejpam-6458	502	58	,	,	PUNCT
ejpam-6458	502	59	torsion	torsion	NOUN
ejpam-6458	502	60	-	-	PUNCT
ejpam-6458	502	61	free	free	ADJ
ejpam-6458	502	62	modules	module	NOUN
ejpam-6458	502	63	.	.	PUNCT
ejpam-6458	503	1	all	all	DET
ejpam-6458	503	2	non	non	ADJ
ejpam-6458	503	3	-	-	ADJ
ejpam-6458	503	4	zero	zero	NUM
ejpam-6458	503	5	weight	weight	NOUN
ejpam-6458	503	6	spaces	space	NOUN
ejpam-6458	503	7	of	of	ADP
ejpam-6458	503	8	these	these	DET
ejpam-6458	503	9	modules	module	NOUN
ejpam-6458	503	10	have	have	VERB
ejpam-6458	503	11	dimensions	dimension	NOUN
ejpam-6458	503	12	respectively	respectively	ADV
ejpam-6458	503	13	:	:	PUNCT
ejpam-6458	503	14	∞	∞	PROPN
ejpam-6458	503	15	for	for	ADP
ejpam-6458	503	16	v	v	NUM
ejpam-6458	503	17	′	′	NUM
ejpam-6458	503	18	1	1	NUM
ejpam-6458	503	19	and	and	CCONJ
ejpam-6458	503	20	v	v	NOUN
ejpam-6458	503	21	(	(	PUNCT
ejpam-6458	503	22	a1	a1	PROPN
ejpam-6458	503	23	,	,	PUNCT
ejpam-6458	503	24	a2	a2	PROPN
ejpam-6458	503	25	,	,	PUNCT
ejpam-6458	503	26	a3	a3	NOUN
ejpam-6458	503	27	,	,	PUNCT
ejpam-6458	503	28	ξ	ξ	PROPN
ejpam-6458	503	29	,	,	PUNCT
ejpam-6458	503	30	µ)/v	µ)/v	PROPN
ejpam-6458	503	31	′	′	NUM
ejpam-6458	503	32	3	3	NUM
ejpam-6458	503	33	,	,	PUNCT
ejpam-6458	503	34	k1	k1	NOUN
ejpam-6458	503	35	−	−	PROPN
ejpam-6458	503	36	k2	k2	PROPN
ejpam-6458	503	37	for	for	ADP
ejpam-6458	503	38	v	v	NUM
ejpam-6458	503	39	′	′	NUM
ejpam-6458	503	40	2	2	NUM
ejpam-6458	503	41	/	/	SYM
ejpam-6458	503	42	v	v	NOUN
ejpam-6458	503	43	′	′	NUM
ejpam-6458	503	44	1	1	NUM
ejpam-6458	503	45	,	,	PUNCT
ejpam-6458	503	46	and	and	CCONJ
ejpam-6458	503	47	k2	k2	ADJ
ejpam-6458	503	48	−	−	PROPN
ejpam-6458	503	49	k3	k3	VERB
ejpam-6458	503	50	for	for	ADP
ejpam-6458	503	51	v	v	NUM
ejpam-6458	503	52	′	′	NUM
ejpam-6458	503	53	3	3	NUM
ejpam-6458	503	54	/	/	SYM
ejpam-6458	503	55	v	v	NOUN
ejpam-6458	503	56	′	′	NUM
ejpam-6458	503	57	2	2	NUM
ejpam-6458	503	58	.	.	PUNCT
ejpam-6458	504	1	a	a	DET
ejpam-6458	504	2	similar	similar	ADJ
ejpam-6458	504	3	construction	construction	NOUN
ejpam-6458	504	4	of	of	ADP
ejpam-6458	504	5	a	a	DET
ejpam-6458	504	6	family	family	NOUN
ejpam-6458	504	7	of	of	ADP
ejpam-6458	504	8	torsion	torsion	NOUN
ejpam-6458	504	9	-	-	PUNCT
ejpam-6458	504	10	free	free	ADJ
ejpam-6458	504	11	submodules	submodule	NOUN
ejpam-6458	504	12	can	can	AUX
ejpam-6458	504	13	be	be	AUX
ejpam-6458	504	14	obtained	obtain	VERB
ejpam-6458	504	15	in	in	ADP
ejpam-6458	504	16	the	the	DET
ejpam-6458	504	17	case	case	NOUN
ejpam-6458	504	18	when	when	SCONJ
ejpam-6458	504	19	q−	q−	PROPN
ejpam-6458	504	20	j	j	PROPN
ejpam-6458	504	21	,	,	PUNCT
ejpam-6458	504	22	k	k	PROPN
ejpam-6458	505	1	=	=	NOUN
ejpam-6458	505	2	0	0	X
ejpam-6458	505	3	.	.	PUNCT
ejpam-6458	506	1	combining	combine	VERB
ejpam-6458	506	2	the	the	DET
ejpam-6458	506	3	conditions	condition	NOUN
ejpam-6458	506	4	under	under	ADP
ejpam-6458	506	5	which	which	PRON
ejpam-6458	506	6	one	one	NUM
ejpam-6458	506	7	or	or	CCONJ
ejpam-6458	506	8	more	more	ADJ
ejpam-6458	506	9	coefficients	coefficient	NOUN
ejpam-6458	506	10	are	be	AUX
ejpam-6458	506	11	equal	equal	ADJ
ejpam-6458	506	12	to	to	ADP
ejpam-6458	506	13	zero	zero	NUM
ejpam-6458	506	14	we	we	PRON
ejpam-6458	506	15	can	can	AUX
ejpam-6458	506	16	obtain	obtain	VERB
ejpam-6458	506	17	various	various	ADJ
ejpam-6458	506	18	distinct	distinct	ADJ
ejpam-6458	506	19	modules	module	NOUN
ejpam-6458	506	20	.	.	PUNCT
ejpam-6458	507	1	the	the	DET
ejpam-6458	507	2	full	full	ADJ
ejpam-6458	507	3	classification	classification	NOUN
ejpam-6458	507	4	of	of	ADP
ejpam-6458	507	5	sl(3	sl(3	PROPN
ejpam-6458	507	6	)	)	PUNCT
ejpam-6458	507	7	modules	module	NOUN
ejpam-6458	507	8	was	be	AUX
ejpam-6458	507	9	obtained	obtain	VERB
ejpam-6458	507	10	in	in	ADP
ejpam-6458	507	11	[	[	X
ejpam-6458	507	12	7	7	NUM
ejpam-6458	507	13	]	]	PUNCT
ejpam-6458	507	14	using	use	VERB
ejpam-6458	507	15	the	the	DET
ejpam-6458	507	16	gelfand	gelfand	PROPN
ejpam-6458	507	17	-	-	PUNCT
ejpam-6458	507	18	tsetlin	tsetlin	PROPN
ejpam-6458	507	19	tableaux	tableaux	ADJ
ejpam-6458	507	20	technique	technique	NOUN
ejpam-6458	507	21	.	.	PUNCT
ejpam-6458	508	1	5	5	X
ejpam-6458	508	2	.	.	X
ejpam-6458	508	3	construction	construction	NOUN
ejpam-6458	508	4	of	of	ADP
ejpam-6458	508	5	simple	simple	ADJ
ejpam-6458	508	6	weight	weight	NOUN
ejpam-6458	508	7	c2	c2	PROPN
ejpam-6458	508	8	-	-	PUNCT
ejpam-6458	508	9	modules	module	NOUN
ejpam-6458	508	10	in	in	ADP
ejpam-6458	508	11	this	this	DET
ejpam-6458	508	12	section	section	NOUN
ejpam-6458	508	13	we	we	PRON
ejpam-6458	508	14	use	use	VERB
ejpam-6458	508	15	the	the	DET
ejpam-6458	508	16	technique	technique	NOUN
ejpam-6458	508	17	developed	develop	VERB
ejpam-6458	508	18	in	in	ADP
ejpam-6458	508	19	the	the	DET
ejpam-6458	508	20	previous	previous	ADJ
ejpam-6458	508	21	section	section	NOUN
ejpam-6458	508	22	to	to	PART
ejpam-6458	508	23	construct	construct	VERB
ejpam-6458	508	24	simple	simple	ADJ
ejpam-6458	508	25	gelfand	gelfand	PROPN
ejpam-6458	508	26	-	-	PUNCT
ejpam-6458	508	27	tsetlin	tsetlin	PROPN
ejpam-6458	508	28	modules	module	NOUN
ejpam-6458	508	29	for	for	ADP
ejpam-6458	508	30	the	the	DET
ejpam-6458	508	31	lie	lie	NOUN
ejpam-6458	508	32	algebra	algebra	NOUN
ejpam-6458	508	33	of	of	ADP
ejpam-6458	508	34	type	type	NOUN
ejpam-6458	508	35	c2	c2	PROPN
ejpam-6458	508	36	.	.	PUNCT
ejpam-6458	509	1	5.1	5.1	NUM
ejpam-6458	509	2	.	.	PUNCT
ejpam-6458	510	1	the	the	DET
ejpam-6458	510	2	centralizer	centralizer	NOUN
ejpam-6458	510	3	for	for	ADP
ejpam-6458	510	4	c2	c2	PROPN
ejpam-6458	510	5	consider	consider	VERB
ejpam-6458	510	6	the	the	DET
ejpam-6458	510	7	root	root	NOUN
ejpam-6458	510	8	system	system	NOUN
ejpam-6458	510	9	of	of	ADP
ejpam-6458	510	10	c2	c2	PROPN
ejpam-6458	510	11	:	:	PUNCT
ejpam-6458	510	12	∆	∆	PROPN
ejpam-6458	510	13	=	=	SYM
ejpam-6458	510	14	{	{	PUNCT
ejpam-6458	510	15	α1	α1	PROPN
ejpam-6458	510	16	,	,	PUNCT
ejpam-6458	510	17	α2	α2	ADJ
ejpam-6458	510	18	,	,	PUNCT
ejpam-6458	510	19	α3	α3	NOUN
ejpam-6458	510	20	=	=	SYM
ejpam-6458	510	21	α1	α1	PROPN
ejpam-6458	510	22	+	+	CCONJ
ejpam-6458	510	23	α2	α2	ADJ
ejpam-6458	510	24	,	,	PUNCT
ejpam-6458	510	25	α4	α4	NOUN
ejpam-6458	510	26	=	=	SYM
ejpam-6458	510	27	2α1	2α1	NUM
ejpam-6458	510	28	+	+	CCONJ
ejpam-6458	510	29	α2	α2	ADJ
ejpam-6458	510	30	,	,	PUNCT
ejpam-6458	510	31	α5	α5	NOUN
ejpam-6458	510	32	=	=	SYM
ejpam-6458	510	33	−α4	−α4	PROPN
ejpam-6458	510	34	,	,	PUNCT
ejpam-6458	510	35	α6	α6	NOUN
ejpam-6458	510	36	=	=	SYM
ejpam-6458	510	37	−α3	−α3	PROPN
ejpam-6458	510	38	,	,	PUNCT
ejpam-6458	510	39	α7	α7	NOUN
ejpam-6458	510	40	=	=	SYM
ejpam-6458	510	41	−α2	−α2	PROPN
ejpam-6458	510	42	,	,	PUNCT
ejpam-6458	510	43	α8	α8	PROPN
ejpam-6458	510	44	=	=	SYM
ejpam-6458	510	45	−α1	−α1	PROPN
ejpam-6458	510	46	}	}	PUNCT
ejpam-6458	510	47	and	and	CCONJ
ejpam-6458	510	48	the	the	DET
ejpam-6458	510	49	chevalley	chevalley	PROPN
ejpam-6458	510	50	basis	basis	NOUN
ejpam-6458	510	51	:	:	PUNCT
ejpam-6458	510	52	e10	e10	PROPN
ejpam-6458	510	53	=	=	SYM
ejpam-6458	510	54	e12	e12	NOUN
ejpam-6458	510	55	−	−	PROPN
ejpam-6458	510	56	e43	e43	NOUN
ejpam-6458	510	57	,	,	PUNCT
ejpam-6458	510	58	f10	f10	NOUN
ejpam-6458	510	59	=	=	SYM
ejpam-6458	510	60	e21	e21	PROPN
ejpam-6458	510	61	−	−	PROPN
ejpam-6458	510	62	e34	e34	NOUN
ejpam-6458	510	63	,	,	PUNCT
ejpam-6458	510	64	e01	e01	PROPN
ejpam-6458	510	65	=	=	SYM
ejpam-6458	510	66	e31	e31	PROPN
ejpam-6458	510	67	,	,	PUNCT
ejpam-6458	510	68	f01	f01	PROPN
ejpam-6458	510	69	=	=	PUNCT
ejpam-6458	510	70	e13	e13	PROPN
ejpam-6458	510	71	,	,	PUNCT
ejpam-6458	510	72	h10	h10	NOUN
ejpam-6458	510	73	=	=	SYM
ejpam-6458	510	74	(	(	PUNCT
ejpam-6458	510	75	e11−e22−e33+e44	e11−e22−e33+e44	PROPN
ejpam-6458	510	76	)	)	PUNCT
ejpam-6458	510	77	,	,	PUNCT
ejpam-6458	510	78	h01	h01	NOUN
ejpam-6458	510	79	=	=	SYM
ejpam-6458	511	1	−e11+e33	−e11+e33	PROPN
ejpam-6458	511	2	,	,	PUNCT
ejpam-6458	511	3	e11	e11	NOUN
ejpam-6458	511	4	=	=	SYM
ejpam-6458	511	5	−e32−e41	−e32−e41	PROPN
ejpam-6458	511	6	,	,	PUNCT
ejpam-6458	511	7	e21	e21	PROPN
ejpam-6458	511	8	=	=	SYM
ejpam-6458	511	9	2e42	2e42	NUM
ejpam-6458	511	10	,	,	PUNCT
ejpam-6458	511	11	f11	f11	X
ejpam-6458	511	12	=	=	SYM
ejpam-6458	511	13	−e14−e23	−e14−e23	PROPN
ejpam-6458	511	14	,	,	PUNCT
ejpam-6458	511	15	f21	f21	NOUN
ejpam-6458	511	16	=	=	PUNCT
ejpam-6458	511	17	2e24	2e24	NUM
ejpam-6458	511	18	with	with	ADP
ejpam-6458	511	19	the	the	DET
ejpam-6458	511	20	order	order	NOUN
ejpam-6458	511	21	h10	h10	NOUN
ejpam-6458	511	22	<	<	X
ejpam-6458	511	23	h01	h01	PROPN
ejpam-6458	511	24	<	<	X
ejpam-6458	511	25	f10	f10	X
ejpam-6458	511	26	<	<	X
ejpam-6458	511	27	f01	f01	PROPN
ejpam-6458	511	28	<	<	X
ejpam-6458	511	29	f11	f11	PROPN
ejpam-6458	511	30	<	<	X
ejpam-6458	511	31	f21	f21	PROPN
ejpam-6458	511	32	<	<	X
ejpam-6458	511	33	e21	e21	PROPN
ejpam-6458	511	34	<	<	X
ejpam-6458	511	35	e11	e11	X
ejpam-6458	511	36	<	<	X
ejpam-6458	511	37	e01	e01	X
ejpam-6458	511	38	<	<	X
ejpam-6458	511	39	e10	e10	NUM
ejpam-6458	511	40	.	.	PUNCT
ejpam-6458	512	1	the	the	DET
ejpam-6458	512	2	following	follow	VERB
ejpam-6458	512	3	is	be	AUX
ejpam-6458	512	4	a	a	DET
ejpam-6458	512	5	complete	complete	ADJ
ejpam-6458	512	6	set	set	NOUN
ejpam-6458	512	7	of	of	ADP
ejpam-6458	512	8	indecomposable	indecomposable	ADJ
ejpam-6458	512	9	lists	list	NOUN
ejpam-6458	512	10	of	of	ADP
ejpam-6458	512	11	roots	root	NOUN
ejpam-6458	512	12	:	:	PUNCT
ejpam-6458	512	13	{	{	PUNCT
ejpam-6458	512	14	α1	α1	PROPN
ejpam-6458	512	15	,	,	PUNCT
ejpam-6458	512	16	α8	α8	NOUN
ejpam-6458	512	17	}	}	PUNCT
ejpam-6458	512	18	,	,	PUNCT
ejpam-6458	512	19	{	{	PUNCT
ejpam-6458	512	20	α2	α2	ADJ
ejpam-6458	512	21	,	,	PUNCT
ejpam-6458	512	22	α7	α7	NOUN
ejpam-6458	512	23	}	}	PUNCT
ejpam-6458	512	24	,	,	PUNCT
ejpam-6458	512	25	{	{	PUNCT
ejpam-6458	512	26	α3	α3	NOUN
ejpam-6458	512	27	,	,	PUNCT
ejpam-6458	512	28	α6	α6	NOUN
ejpam-6458	512	29	}	}	PUNCT
ejpam-6458	512	30	,	,	PUNCT
ejpam-6458	512	31	{	{	PUNCT
ejpam-6458	512	32	α4	α4	NOUN
ejpam-6458	512	33	,	,	PUNCT
ejpam-6458	512	34	α5	α5	NOUN
ejpam-6458	512	35	}	}	PUNCT
ejpam-6458	512	36	,	,	PUNCT
ejpam-6458	512	37	{	{	PUNCT
ejpam-6458	512	38	α1	α1	PROPN
ejpam-6458	512	39	,	,	PUNCT
ejpam-6458	512	40	α2	α2	PROPN
ejpam-6458	512	41	,	,	PUNCT
ejpam-6458	512	42	α6	α6	NOUN
ejpam-6458	512	43	}	}	PUNCT
ejpam-6458	512	44	,	,	PUNCT
ejpam-6458	512	45	{	{	PUNCT
ejpam-6458	512	46	α3	α3	NOUN
ejpam-6458	512	47	,	,	PUNCT
ejpam-6458	512	48	α7	α7	NOUN
ejpam-6458	512	49	,	,	PUNCT
ejpam-6458	512	50	α8	α8	NOUN
ejpam-6458	512	51	}	}	PUNCT
ejpam-6458	512	52	,	,	PUNCT
ejpam-6458	512	53	{	{	PUNCT
ejpam-6458	512	54	α1	α1	PROPN
ejpam-6458	512	55	,	,	PUNCT
ejpam-6458	512	56	α3	α3	PROPN
ejpam-6458	512	57	,	,	PUNCT
ejpam-6458	512	58	α5	α5	NOUN
ejpam-6458	512	59	}	}	PUNCT
ejpam-6458	512	60	,	,	PUNCT
ejpam-6458	512	61	{	{	PUNCT
ejpam-6458	512	62	α4	α4	NOUN
ejpam-6458	512	63	,	,	PUNCT
ejpam-6458	512	64	α6	α6	NOUN
ejpam-6458	512	65	,	,	PUNCT
ejpam-6458	512	66	α8	α8	NOUN
ejpam-6458	512	67	}	}	PUNCT
ejpam-6458	512	68	,	,	PUNCT
ejpam-6458	512	69	{	{	PUNCT
ejpam-6458	512	70	α1	α1	PROPN
ejpam-6458	512	71	,	,	PUNCT
ejpam-6458	512	72	α1	α1	PROPN
ejpam-6458	512	73	,	,	PUNCT
ejpam-6458	512	74	α2	α2	ADJ
ejpam-6458	512	75	,	,	PUNCT
ejpam-6458	512	76	α5	α5	NOUN
ejpam-6458	512	77	}	}	PUNCT
ejpam-6458	512	78	,	,	PUNCT
ejpam-6458	512	79	{	{	PUNCT
ejpam-6458	512	80	α4	α4	NOUN
ejpam-6458	512	81	,	,	PUNCT
ejpam-6458	512	82	α7	α7	NOUN
ejpam-6458	512	83	,	,	PUNCT
ejpam-6458	512	84	α8	α8	NOUN
ejpam-6458	512	85	,	,	PUNCT
ejpam-6458	512	86	α8	α8	NOUN
ejpam-6458	512	87	}	}	PUNCT
ejpam-6458	512	88	,	,	PUNCT
ejpam-6458	512	89	{	{	PUNCT
ejpam-6458	512	90	α3	α3	NOUN
ejpam-6458	512	91	,	,	PUNCT
ejpam-6458	512	92	α3	α3	PROPN
ejpam-6458	512	93	,	,	PUNCT
ejpam-6458	512	94	α5	α5	NOUN
ejpam-6458	512	95	,	,	PUNCT
ejpam-6458	512	96	α7	α7	NOUN
ejpam-6458	512	97	}	}	PUNCT
ejpam-6458	512	98	,	,	PUNCT
ejpam-6458	512	99	{	{	PUNCT
ejpam-6458	512	100	α2	α2	ADJ
ejpam-6458	512	101	,	,	PUNCT
ejpam-6458	512	102	α4	α4	NOUN
ejpam-6458	512	103	,	,	PUNCT
ejpam-6458	512	104	α6	α6	NOUN
ejpam-6458	512	105	,	,	PUNCT
ejpam-6458	512	106	α6	α6	NOUN
ejpam-6458	512	107	}	}	PUNCT
ejpam-6458	512	108	.	.	PUNCT
ejpam-6458	513	1	let	let	VERB
ejpam-6458	513	2	us	we	PRON
ejpam-6458	513	3	choose	choose	VERB
ejpam-6458	513	4	the	the	DET
ejpam-6458	513	5	following	follow	VERB
ejpam-6458	513	6	generators	generator	NOUN
ejpam-6458	513	7	of	of	ADP
ejpam-6458	513	8	u0	u0	ADJ
ejpam-6458	513	9	=	=	SYM
ejpam-6458	513	10	u0(c2	u0(c2	PROPN
ejpam-6458	513	11	):	):	PUNCT
ejpam-6458	513	12	h1	h1	PROPN
ejpam-6458	513	13	=	=	PUNCT
ejpam-6458	513	14	h01	h01	PROPN
ejpam-6458	513	15	,	,	PUNCT
ejpam-6458	513	16	h2	h2	NOUN
ejpam-6458	513	17	=	=	SYM
ejpam-6458	513	18	h10	h10	PROPN
ejpam-6458	513	19	,	,	PUNCT
ejpam-6458	513	20	c1	c1	PROPN
ejpam-6458	513	21	=	=	PUNCT
ejpam-6458	513	22	f01e01	f01e01	PROPN
ejpam-6458	513	23	,	,	PUNCT
ejpam-6458	513	24	c2	c2	PROPN
ejpam-6458	513	25	=	=	PUNCT
ejpam-6458	513	26	f21e21	f21e21	PROPN
ejpam-6458	513	27	,	,	PUNCT
ejpam-6458	513	28	c3	c3	PROPN
ejpam-6458	513	29	=	=	SYM
ejpam-6458	513	30	f10e10	f10e10	PROPN
ejpam-6458	513	31	,	,	PUNCT
ejpam-6458	513	32	c4	c4	NOUN
ejpam-6458	513	33	=	=	SYM
ejpam-6458	513	34	f11e11	f11e11	PROPN
ejpam-6458	513	35	,	,	PUNCT
ejpam-6458	513	36	c5	c5	PROPN
ejpam-6458	513	37	=	=	SYM
ejpam-6458	513	38	f11e01e10	f11e01e10	PROPN
ejpam-6458	513	39	,	,	PUNCT
ejpam-6458	513	40	c6	c6	NOUN
ejpam-6458	513	41	=	=	SYM
ejpam-6458	513	42	f10f01e11	f10f01e11	PROPN
ejpam-6458	513	43	,	,	PUNCT
ejpam-6458	513	44	c7	c7	PROPN
ejpam-6458	513	45	=	=	SYM
ejpam-6458	513	46	f21e11e10	f21e11e10	PROPN
ejpam-6458	513	47	,	,	PUNCT
ejpam-6458	513	48	c8	c8	PROPN
ejpam-6458	513	49	=	=	SYM
ejpam-6458	513	50	f10f11e21	f10f11e21	PROPN
ejpam-6458	513	51	,	,	PUNCT
ejpam-6458	513	52	c9	c9	NOUN
ejpam-6458	513	53	=	=	PUNCT
ejpam-6458	513	54	f21e01e10e10	f21e01e10e10	PROPN
ejpam-6458	513	55	,	,	PUNCT
ejpam-6458	513	56	c10	c10	NOUN
ejpam-6458	513	57	=	=	SYM
ejpam-6458	513	58	f10f10f01e21	f10f10f01e21	PROPN
ejpam-6458	513	59	,	,	PUNCT
ejpam-6458	513	60	c11	c11	NOUN
ejpam-6458	513	61	=	=	SYM
ejpam-6458	513	62	f01f21e11e11	f01f21e11e11	PROPN
ejpam-6458	513	63	,	,	PUNCT
ejpam-6458	513	64	c12	c12	NOUN
ejpam-6458	513	65	=	=	SYM
ejpam-6458	513	66	f11f11e21e01	f11f11e21e01	ADJ
ejpam-6458	513	67	.	.	PUNCT
ejpam-6458	514	1	order	order	VERB
ejpam-6458	514	2	the	the	DET
ejpam-6458	514	3	set	set	NOUN
ejpam-6458	514	4	of	of	ADP
ejpam-6458	514	5	perfect	perfect	ADJ
ejpam-6458	514	6	monomials	monomial	NOUN
ejpam-6458	514	7	as	as	SCONJ
ejpam-6458	514	8	follows	follow	VERB
ejpam-6458	514	9	:	:	PUNCT
ejpam-6458	514	10	h1	h1	VERB
ejpam-6458	514	11	<	<	X
ejpam-6458	514	12	h2	h2	PROPN
ejpam-6458	514	13	<	<	X
ejpam-6458	514	14	c1	c1	PROPN
ejpam-6458	514	15	<	<	X
ejpam-6458	514	16	c2	c2	PROPN
ejpam-6458	514	17	<	<	X
ejpam-6458	514	18	c3	c3	PROPN
ejpam-6458	514	19	<	<	X
ejpam-6458	514	20	c4	c4	PROPN
ejpam-6458	514	21	<	<	X
ejpam-6458	514	22	c5	c5	PROPN
ejpam-6458	514	23	<	<	X
ejpam-6458	514	24	c6	c6	PROPN
ejpam-6458	514	25	<	<	X
ejpam-6458	514	26	c7	c7	PROPN
ejpam-6458	514	27	<	<	X
ejpam-6458	514	28	c8	c8	PROPN
ejpam-6458	514	29	<	<	X
ejpam-6458	514	30	c9	c9	PROPN
ejpam-6458	514	31	<	<	X
ejpam-6458	514	32	c10	c10	VERB
ejpam-6458	514	33	<	<	X
ejpam-6458	514	34	c11	c11	PROPN
ejpam-6458	514	35	<	<	X
ejpam-6458	514	36	c12	c12	PROPN
ejpam-6458	514	37	.	.	PUNCT
ejpam-6458	515	1	(	(	PUNCT
ejpam-6458	515	2	5.1	5.1	NUM
ejpam-6458	515	3	)	)	PUNCT
ejpam-6458	515	4	as	as	ADP
ejpam-6458	515	5	in	in	ADP
ejpam-6458	515	6	type	type	NOUN
ejpam-6458	515	7	a2	a2	PROPN
ejpam-6458	515	8	we	we	PRON
ejpam-6458	515	9	have	have	VERB
ejpam-6458	515	10	proposition	proposition	NOUN
ejpam-6458	515	11	5.1	5.1	NUM
ejpam-6458	515	12	.	.	PUNCT
ejpam-6458	516	1	m.	m.	NOUN
ejpam-6458	516	2	andelić	andelić	PROPN
ejpam-6458	516	3	et	et	PROPN
ejpam-6458	516	4	al	al	PROPN
ejpam-6458	516	5	.	.	PUNCT
ejpam-6458	516	6	/	/	SYM
ejpam-6458	516	7	eur	eur	PROPN
ejpam-6458	516	8	.	.	PUNCT
ejpam-6458	517	1	j.	j.	PROPN
ejpam-6458	517	2	pure	pure	PROPN
ejpam-6458	517	3	appl	appl	PROPN
ejpam-6458	517	4	.	.	PROPN
ejpam-6458	517	5	math	math	PROPN
ejpam-6458	517	6	,	,	PUNCT
ejpam-6458	517	7	18	18	NUM
ejpam-6458	517	8	(	(	PUNCT
ejpam-6458	517	9	3	3	NUM
ejpam-6458	517	10	)	)	PUNCT
ejpam-6458	517	11	(	(	PUNCT
ejpam-6458	517	12	2025	2025	NUM
ejpam-6458	517	13	)	)	PUNCT
ejpam-6458	517	14	,	,	PUNCT
ejpam-6458	517	15	6458	6458	NUM
ejpam-6458	517	16	13	13	NUM
ejpam-6458	517	17	of	of	ADP
ejpam-6458	517	18	21	21	NUM
ejpam-6458	517	19	1	1	NUM
ejpam-6458	517	20	)	)	PUNCT
ejpam-6458	517	21	the	the	DET
ejpam-6458	517	22	following	follow	VERB
ejpam-6458	517	23	set	set	NOUN
ejpam-6458	517	24	of	of	ADP
ejpam-6458	517	25	monomials	monomial	NOUN
ejpam-6458	517	26	is	be	AUX
ejpam-6458	517	27	a	a	DET
ejpam-6458	517	28	basis	basis	NOUN
ejpam-6458	517	29	of	of	ADP
ejpam-6458	517	30	u0	u0	ADJ
ejpam-6458	517	31	:	:	PUNCT
ejpam-6458	517	32	p	p	X
ejpam-6458	517	33	=	=	NOUN
ejpam-6458	517	34	{	{	PUNCT
ejpam-6458	517	35	hs11	hs11	PROPN
ejpam-6458	517	36	h	h	NOUN
ejpam-6458	517	37	s2	s2	VERB
ejpam-6458	517	38	2	2	NUM
ejpam-6458	517	39	c	c	NOUN
ejpam-6458	517	40	s3	s3	PROPN
ejpam-6458	517	41	1	1	NUM
ejpam-6458	517	42	c	c	NOUN
ejpam-6458	517	43	s4	s4	PROPN
ejpam-6458	517	44	2	2	PROPN
ejpam-6458	517	45	c	c	NOUN
ejpam-6458	517	46	s5	s5	X
ejpam-6458	517	47	3	3	NUM
ejpam-6458	517	48	c	c	PROPN
ejpam-6458	517	49	s6	s6	PROPN
ejpam-6458	517	50	4	4	NUM
ejpam-6458	517	51	c	c	NOUN
ejpam-6458	517	52	sm	sm	PROPN
ejpam-6458	517	53	m	m	VERB
ejpam-6458	517	54	csnn	csnn	ADJ
ejpam-6458	517	55	|	|	CCONJ
ejpam-6458	517	56	s1	s1	NOUN
ejpam-6458	517	57	,	,	PUNCT
ejpam-6458	517	58	s2	s2	NOUN
ejpam-6458	517	59	,	,	PUNCT
ejpam-6458	517	60	.	.	PUNCT
ejpam-6458	517	61	.	.	PUNCT
ejpam-6458	518	1	.	.	PUNCT
ejpam-6458	519	1	,	,	PUNCT
ejpam-6458	519	2	s6	s6	PROPN
ejpam-6458	519	3	,	,	PUNCT
ejpam-6458	519	4	sm	sm	PROPN
ejpam-6458	519	5	,	,	PUNCT
ejpam-6458	519	6	sn	sn	PROPN
ejpam-6458	519	7	∈	∈	PROPN
ejpam-6458	519	8	n	n	PROPN
ejpam-6458	519	9	and	and	CCONJ
ejpam-6458	519	10	(	(	PUNCT
ejpam-6458	519	11	m	m	PROPN
ejpam-6458	519	12	,	,	PUNCT
ejpam-6458	519	13	n	n	CCONJ
ejpam-6458	519	14	)	)	PUNCT
ejpam-6458	519	15	∈	∈	NOUN
ejpam-6458	519	16	{	{	PUNCT
ejpam-6458	519	17	(	(	PUNCT
ejpam-6458	519	18	5	5	NUM
ejpam-6458	519	19	,	,	PUNCT
ejpam-6458	519	20	9	9	NUM
ejpam-6458	519	21	)	)	PUNCT
ejpam-6458	519	22	,	,	PUNCT
ejpam-6458	519	23	(	(	PUNCT
ejpam-6458	519	24	5	5	NUM
ejpam-6458	519	25	,	,	PUNCT
ejpam-6458	519	26	12	12	NUM
ejpam-6458	519	27	)	)	PUNCT
ejpam-6458	519	28	,	,	PUNCT
ejpam-6458	519	29	(	(	PUNCT
ejpam-6458	519	30	6	6	NUM
ejpam-6458	519	31	,	,	PUNCT
ejpam-6458	519	32	10	10	NUM
ejpam-6458	519	33	)	)	PUNCT
ejpam-6458	519	34	,	,	PUNCT
ejpam-6458	519	35	(	(	PUNCT
ejpam-6458	519	36	6	6	NUM
ejpam-6458	519	37	,	,	PUNCT
ejpam-6458	519	38	11	11	NUM
ejpam-6458	519	39	)	)	PUNCT
ejpam-6458	519	40	,	,	PUNCT
ejpam-6458	519	41	(	(	PUNCT
ejpam-6458	519	42	7	7	NUM
ejpam-6458	519	43	,	,	PUNCT
ejpam-6458	519	44	9	9	NUM
ejpam-6458	519	45	)	)	PUNCT
ejpam-6458	519	46	,	,	PUNCT
ejpam-6458	519	47	(	(	PUNCT
ejpam-6458	519	48	7	7	NUM
ejpam-6458	519	49	,	,	PUNCT
ejpam-6458	519	50	11	11	NUM
ejpam-6458	519	51	)	)	PUNCT
ejpam-6458	519	52	,	,	PUNCT
ejpam-6458	519	53	(	(	PUNCT
ejpam-6458	519	54	8	8	NUM
ejpam-6458	519	55	,	,	PUNCT
ejpam-6458	519	56	10	10	NUM
ejpam-6458	519	57	)	)	PUNCT
ejpam-6458	519	58	,	,	PUNCT
ejpam-6458	519	59	(	(	PUNCT
ejpam-6458	519	60	8	8	NUM
ejpam-6458	519	61	,	,	PUNCT
ejpam-6458	519	62	12	12	NUM
ejpam-6458	519	63	)	)	PUNCT
ejpam-6458	519	64	}	}	PUNCT
ejpam-6458	519	65	}	}	PUNCT
ejpam-6458	519	66	.	.	PUNCT
ejpam-6458	520	1	(	(	PUNCT
ejpam-6458	520	2	5.2	5.2	NUM
ejpam-6458	520	3	)	)	PUNCT
ejpam-6458	520	4	2	2	NUM
ejpam-6458	520	5	)	)	PUNCT
ejpam-6458	520	6	the	the	DET
ejpam-6458	520	7	set	set	NOUN
ejpam-6458	520	8	k̃	k̃	PROPN
ejpam-6458	520	9	=	=	PRON
ejpam-6458	520	10	{	{	PUNCT
ejpam-6458	520	11	x|x	x|x	PROPN
ejpam-6458	520	12	∈	∈	PROPN
ejpam-6458	520	13	k	k	PROPN
ejpam-6458	520	14	′,len(x	′,len(x	PROPN
ejpam-6458	520	15	)	)	PUNCT
ejpam-6458	520	16	=	=	SYM
ejpam-6458	520	17	2	2	X
ejpam-6458	520	18	}	}	PUNCT
ejpam-6458	520	19	is	be	AUX
ejpam-6458	520	20	a	a	DET
ejpam-6458	520	21	generating	generate	VERB
ejpam-6458	520	22	set	set	NOUN
ejpam-6458	520	23	of	of	ADP
ejpam-6458	520	24	the	the	DET
ejpam-6458	520	25	ideal	ideal	NOUN
ejpam-6458	520	26	of	of	ADP
ejpam-6458	520	27	relations	relation	NOUN
ejpam-6458	520	28	k.	k.	PROPN
ejpam-6458	520	29	proof	proof	PROPN
ejpam-6458	520	30	.	.	PUNCT
ejpam-6458	521	1	let	let	VERB
ejpam-6458	521	2	x	x	PUNCT
ejpam-6458	521	3	=	=	PUNCT
ejpam-6458	521	4	cmcnck	cmcnck	NOUN
ejpam-6458	521	5	∈	∈	PROPN
ejpam-6458	521	6	q0(c2	q0(c2	NOUN
ejpam-6458	521	7	)	)	PUNCT
ejpam-6458	521	8	,	,	PUNCT
ejpam-6458	521	9	where	where	SCONJ
ejpam-6458	521	10	4	4	NUM
ejpam-6458	521	11	<	<	X
ejpam-6458	521	12	m	m	X
ejpam-6458	521	13	<	<	X
ejpam-6458	521	14	n	n	X
ejpam-6458	521	15	<	<	X
ejpam-6458	521	16	k	k	X
ejpam-6458	521	17	≤	≤	NUM
ejpam-6458	521	18	12	12	NUM
ejpam-6458	521	19	be	be	AUX
ejpam-6458	521	20	a	a	DET
ejpam-6458	521	21	monomial	monomial	ADJ
ejpam-6458	521	22	.	.	PUNCT
ejpam-6458	522	1	manual	manual	ADJ
ejpam-6458	522	2	calculation	calculation	NOUN
ejpam-6458	522	3	shows	show	VERB
ejpam-6458	522	4	that	that	SCONJ
ejpam-6458	522	5	for	for	ADP
ejpam-6458	522	6	any	any	DET
ejpam-6458	522	7	triple	triple	ADJ
ejpam-6458	522	8	m	m	NOUN
ejpam-6458	522	9	,	,	PUNCT
ejpam-6458	522	10	n	n	CCONJ
ejpam-6458	522	11	,	,	PUNCT
ejpam-6458	522	12	k	k	PROPN
ejpam-6458	522	13	satisfying	satisfying	NOUN
ejpam-6458	522	14	above	above	ADP
ejpam-6458	522	15	condition	condition	NOUN
ejpam-6458	522	16	there	there	PRON
ejpam-6458	522	17	is	be	VERB
ejpam-6458	522	18	1	1	NUM
ejpam-6458	522	19	≤	≤	NOUN
ejpam-6458	522	20	p	p	NOUN
ejpam-6458	522	21	≤	≤	NUM
ejpam-6458	522	22	4	4	NUM
ejpam-6458	522	23	such	such	ADJ
ejpam-6458	522	24	that	that	SCONJ
ejpam-6458	522	25	l1(cp	l1(cp	PROPN
ejpam-6458	522	26	)	)	PUNCT
ejpam-6458	522	27	is	be	AUX
ejpam-6458	522	28	sublist	sublist	NOUN
ejpam-6458	522	29	of	of	ADP
ejpam-6458	522	30	l1(x	l1(x	NOUN
ejpam-6458	522	31	)	)	PUNCT
ejpam-6458	522	32	.	.	PUNCT
ejpam-6458	523	1	for	for	ADP
ejpam-6458	523	2	example	example	NOUN
ejpam-6458	523	3	,	,	PUNCT
ejpam-6458	523	4	if	if	SCONJ
ejpam-6458	523	5	(	(	PUNCT
ejpam-6458	523	6	m	m	NOUN
ejpam-6458	523	7	,	,	PUNCT
ejpam-6458	523	8	n	n	CCONJ
ejpam-6458	523	9	,	,	PUNCT
ejpam-6458	523	10	k	k	NOUN
ejpam-6458	523	11	)	)	PUNCT
ejpam-6458	523	12	=	=	SYM
ejpam-6458	523	13	(	(	PUNCT
ejpam-6458	523	14	5	5	NUM
ejpam-6458	523	15	,	,	PUNCT
ejpam-6458	523	16	6	6	NUM
ejpam-6458	523	17	,	,	PUNCT
ejpam-6458	523	18	7	7	NUM
ejpam-6458	523	19	)	)	PUNCT
ejpam-6458	523	20	,	,	PUNCT
ejpam-6458	523	21	then	then	ADV
ejpam-6458	523	22	l1(c1	l1(c1	PROPN
ejpam-6458	523	23	)	)	PUNCT
ejpam-6458	523	24	⊏	⊏	PROPN
ejpam-6458	523	25	l1(x	l1(x	NUM
ejpam-6458	523	26	)	)	PUNCT
ejpam-6458	523	27	.	.	PUNCT
ejpam-6458	524	1	this	this	PRON
ejpam-6458	524	2	means	mean	VERB
ejpam-6458	524	3	that	that	SCONJ
ejpam-6458	524	4	no	no	DET
ejpam-6458	524	5	semi	semi	ADJ
ejpam-6458	524	6	-	-	ADJ
ejpam-6458	524	7	perfect	perfect	ADJ
ejpam-6458	524	8	element	element	NOUN
ejpam-6458	524	9	can	can	AUX
ejpam-6458	524	10	contain	contain	VERB
ejpam-6458	524	11	above	above	ADP
ejpam-6458	524	12	three	three	NUM
ejpam-6458	524	13	perfect	perfect	ADJ
ejpam-6458	524	14	monomials	monomial	NOUN
ejpam-6458	524	15	.	.	PUNCT
ejpam-6458	525	1	now	now	ADV
ejpam-6458	525	2	,	,	PUNCT
ejpam-6458	525	3	let	let	VERB
ejpam-6458	525	4	x	x	SYM
ejpam-6458	525	5	=	=	PUNCT
ejpam-6458	525	6	cmcn	cmcn	PROPN
ejpam-6458	525	7	∈	∈	PROPN
ejpam-6458	525	8	q0(c2	q0(c2	PROPN
ejpam-6458	525	9	)	)	PUNCT
ejpam-6458	525	10	,	,	PUNCT
ejpam-6458	525	11	where	where	SCONJ
ejpam-6458	525	12	4	4	NUM
ejpam-6458	525	13	<	<	X
ejpam-6458	525	14	m	m	X
ejpam-6458	525	15	<	<	X
ejpam-6458	525	16	n	n	CCONJ
ejpam-6458	525	17	≤	≤	NUM
ejpam-6458	525	18	12	12	NUM
ejpam-6458	525	19	be	be	AUX
ejpam-6458	525	20	a	a	DET
ejpam-6458	525	21	monomial	monomial	NOUN
ejpam-6458	525	22	.	.	PUNCT
ejpam-6458	526	1	one	one	PRON
ejpam-6458	526	2	can	can	AUX
ejpam-6458	526	3	easily	easily	ADV
ejpam-6458	526	4	see	see	VERB
ejpam-6458	526	5	that	that	PRON
ejpam-6458	526	6	for	for	ADP
ejpam-6458	526	7	any	any	DET
ejpam-6458	526	8	pair	pair	NOUN
ejpam-6458	526	9	m	m	NOUN
ejpam-6458	526	10	,	,	PUNCT
ejpam-6458	526	11	n	n	CCONJ
ejpam-6458	526	12	which	which	PRON
ejpam-6458	526	13	is	be	AUX
ejpam-6458	526	14	not	not	PART
ejpam-6458	526	15	in	in	ADP
ejpam-6458	526	16	the	the	DET
ejpam-6458	526	17	(	(	PUNCT
ejpam-6458	526	18	5.2	5.2	NUM
ejpam-6458	526	19	)	)	PUNCT
ejpam-6458	526	20	,	,	PUNCT
ejpam-6458	526	21	there	there	PRON
ejpam-6458	526	22	exists	exist	VERB
ejpam-6458	526	23	1	1	NUM
ejpam-6458	526	24	≤	≤	NOUN
ejpam-6458	526	25	p	p	NOUN
ejpam-6458	526	26	≤	≤	NUM
ejpam-6458	526	27	4	4	NUM
ejpam-6458	526	28	such	such	ADJ
ejpam-6458	526	29	that	that	SCONJ
ejpam-6458	526	30	l1(cp	l1(cp	PROPN
ejpam-6458	526	31	)	)	PUNCT
ejpam-6458	526	32	is	be	AUX
ejpam-6458	526	33	a	a	DET
ejpam-6458	526	34	sublist	sublist	NOUN
ejpam-6458	526	35	of	of	ADP
ejpam-6458	526	36	l1(x	l1(x	NOUN
ejpam-6458	526	37	)	)	PUNCT
ejpam-6458	526	38	.	.	PUNCT
ejpam-6458	527	1	for	for	ADP
ejpam-6458	527	2	example	example	NOUN
ejpam-6458	527	3	,	,	PUNCT
ejpam-6458	527	4	if	if	SCONJ
ejpam-6458	527	5	(	(	PUNCT
ejpam-6458	527	6	m	m	NOUN
ejpam-6458	527	7	,	,	PUNCT
ejpam-6458	527	8	n	n	CCONJ
ejpam-6458	527	9	)	)	PUNCT
ejpam-6458	527	10	=	=	NOUN
ejpam-6458	527	11	(	(	PUNCT
ejpam-6458	527	12	9	9	NUM
ejpam-6458	527	13	,	,	PUNCT
ejpam-6458	527	14	12	12	NUM
ejpam-6458	527	15	)	)	PUNCT
ejpam-6458	527	16	,	,	PUNCT
ejpam-6458	527	17	then	then	ADV
ejpam-6458	527	18	l1(c2	l1(c2	NOUN
ejpam-6458	527	19	)	)	PUNCT
ejpam-6458	527	20	⊏	⊏	PROPN
ejpam-6458	527	21	l1(x	l1(x	NUM
ejpam-6458	527	22	)	)	PUNCT
ejpam-6458	527	23	.	.	PUNCT
ejpam-6458	528	1	it	it	PRON
ejpam-6458	528	2	follows	follow	VERB
ejpam-6458	528	3	that	that	SCONJ
ejpam-6458	528	4	the	the	DET
ejpam-6458	528	5	only	only	ADJ
ejpam-6458	528	6	possible	possible	ADJ
ejpam-6458	528	7	perfect	perfect	ADJ
ejpam-6458	528	8	monomials	monomial	NOUN
ejpam-6458	528	9	in	in	ADP
ejpam-6458	528	10	semi	semi	ADJ
ejpam-6458	528	11	-	-	ADJ
ejpam-6458	528	12	perfect	perfect	ADJ
ejpam-6458	528	13	monomials	monomial	NOUN
ejpam-6458	528	14	are	be	AUX
ejpam-6458	528	15	the	the	DET
ejpam-6458	528	16	ones	one	NOUN
ejpam-6458	528	17	given	give	VERB
ejpam-6458	528	18	above	above	ADV
ejpam-6458	528	19	,	,	PUNCT
ejpam-6458	528	20	proving	prove	VERB
ejpam-6458	528	21	1	1	NUM
ejpam-6458	528	22	.	.	PUNCT
ejpam-6458	529	1	in	in	ADP
ejpam-6458	529	2	particular	particular	ADJ
ejpam-6458	529	3	this	this	PRON
ejpam-6458	529	4	means	mean	VERB
ejpam-6458	529	5	that	that	SCONJ
ejpam-6458	529	6	we	we	PRON
ejpam-6458	529	7	can	can	AUX
ejpam-6458	529	8	take	take	VERB
ejpam-6458	529	9	d0	d0	NOUN
ejpam-6458	529	10	=	=	SYM
ejpam-6458	529	11	2	2	NUM
ejpam-6458	529	12	in	in	ADP
ejpam-6458	529	13	the	the	DET
ejpam-6458	529	14	definition	definition	NOUN
ejpam-6458	529	15	of	of	ADP
ejpam-6458	529	16	k	k	PROPN
ejpam-6458	529	17	′	′	NUM
ejpam-6458	529	18	(	(	PUNCT
ejpam-6458	529	19	cf	cf	NOUN
ejpam-6458	529	20	.	.	PUNCT
ejpam-6458	530	1	(	(	PUNCT
ejpam-6458	530	2	2.4	2.4	NUM
ejpam-6458	530	3	)	)	PUNCT
ejpam-6458	530	4	)	)	PUNCT
ejpam-6458	530	5	and	and	CCONJ
ejpam-6458	530	6	in	in	ADP
ejpam-6458	530	7	theorem	theorem	NOUN
ejpam-6458	530	8	2.5	2.5	NUM
ejpam-6458	530	9	with	with	ADP
ejpam-6458	530	10	sort	sort	ADJ
ejpam-6458	530	11	order	order	NOUN
ejpam-6458	530	12	defined	define	VERB
ejpam-6458	530	13	in	in	ADP
ejpam-6458	530	14	(	(	PUNCT
ejpam-6458	530	15	5.1	5.1	NUM
ejpam-6458	530	16	)	)	PUNCT
ejpam-6458	530	17	.	.	PUNCT
ejpam-6458	531	1	□	□	PUNCT
ejpam-6458	531	2	denote	denote	NOUN
ejpam-6458	531	3	h3	h3	NOUN
ejpam-6458	531	4	=	=	SYM
ejpam-6458	531	5	h1	h1	PROPN
ejpam-6458	531	6	+	+	CCONJ
ejpam-6458	531	7	h2	h2	NOUN
ejpam-6458	531	8	and	and	CCONJ
ejpam-6458	531	9	let	let	VERB
ejpam-6458	531	10	u	u	PRON
ejpam-6458	531	11	′	′	NOUN
ejpam-6458	531	12	0	0	X
ejpam-6458	532	1	=	=	PUNCT
ejpam-6458	532	2	u0[h	u0[h	ADP
ejpam-6458	532	3	−1	−1	NOUN
ejpam-6458	532	4	1	1	NUM
ejpam-6458	532	5	,	,	PUNCT
ejpam-6458	532	6	h−1	h−1	PROPN
ejpam-6458	532	7	3	3	NUM
ejpam-6458	532	8	]	]	PUNCT
ejpam-6458	532	9	.	.	PUNCT
ejpam-6458	533	1	it	it	PRON
ejpam-6458	533	2	will	will	AUX
ejpam-6458	533	3	be	be	AUX
ejpam-6458	533	4	convenient	convenient	ADJ
ejpam-6458	533	5	for	for	SCONJ
ejpam-6458	533	6	us	we	PRON
ejpam-6458	533	7	to	to	PART
ejpam-6458	533	8	work	work	VERB
ejpam-6458	533	9	with	with	ADP
ejpam-6458	533	10	u	u	NOUN
ejpam-6458	533	11	′	′	NUM
ejpam-6458	533	12	0	0	NUM
ejpam-6458	533	13	.	.	PUNCT
ejpam-6458	534	1	the	the	DET
ejpam-6458	534	2	list	list	NOUN
ejpam-6458	534	3	of	of	ADP
ejpam-6458	534	4	all	all	DET
ejpam-6458	534	5	relations	relation	NOUN
ejpam-6458	534	6	is	be	AUX
ejpam-6458	534	7	rather	rather	ADV
ejpam-6458	534	8	big	big	ADJ
ejpam-6458	534	9	,	,	PUNCT
ejpam-6458	534	10	so	so	SCONJ
ejpam-6458	534	11	we	we	PRON
ejpam-6458	534	12	will	will	AUX
ejpam-6458	534	13	give	give	VERB
ejpam-6458	534	14	only	only	ADV
ejpam-6458	534	15	those	those	PRON
ejpam-6458	534	16	of	of	ADP
ejpam-6458	534	17	them	they	PRON
ejpam-6458	534	18	that	that	PRON
ejpam-6458	534	19	are	be	AUX
ejpam-6458	534	20	used	use	VERB
ejpam-6458	534	21	in	in	ADP
ejpam-6458	534	22	our	our	PRON
ejpam-6458	534	23	calculations	calculation	NOUN
ejpam-6458	534	24	.	.	PUNCT
ejpam-6458	535	1	the	the	DET
ejpam-6458	535	2	following	follow	VERB
ejpam-6458	535	3	list	list	NOUN
ejpam-6458	535	4	of	of	ADP
ejpam-6458	535	5	relations	relation	NOUN
ejpam-6458	535	6	is	be	AUX
ejpam-6458	535	7	used	use	VERB
ejpam-6458	535	8	to	to	PART
ejpam-6458	535	9	express	express	VERB
ejpam-6458	535	10	c12	c12	NOUN
ejpam-6458	535	11	,	,	PUNCT
ejpam-6458	535	12	.	.	PUNCT
ejpam-6458	535	13	.	.	PUNCT
ejpam-6458	536	1	.	.	PUNCT
ejpam-6458	537	1	,	,	PUNCT
ejpam-6458	537	2	c5	c5	PROPN
ejpam-6458	537	3	via	via	ADP
ejpam-6458	537	4	c4	c4	PROPN
ejpam-6458	537	5	,	,	PUNCT
ejpam-6458	537	6	c3	c3	PROPN
ejpam-6458	537	7	,	,	PUNCT
ejpam-6458	537	8	c2	c2	PROPN
ejpam-6458	537	9	,	,	PUNCT
ejpam-6458	537	10	c1	c1	PROPN
ejpam-6458	537	11	,	,	PUNCT
ejpam-6458	537	12	h1	h1	PROPN
ejpam-6458	537	13	,	,	PUNCT
ejpam-6458	537	14	h3	h3	NOUN
ejpam-6458	537	15	,	,	PUNCT
ejpam-6458	537	16	z1	z1	PROPN
ejpam-6458	537	17	in	in	ADP
ejpam-6458	537	18	u	u	NOUN
ejpam-6458	537	19	′	′	NUM
ejpam-6458	537	20	0	0	NUM
ejpam-6458	537	21	:	:	PUNCT
ejpam-6458	537	22	c12	c12	PROPN
ejpam-6458	537	23	=	=	PROPN
ejpam-6458	537	24	−	−	PROPN
ejpam-6458	537	25	c10	c10	VERB
ejpam-6458	537	26	−	−	PROPN
ejpam-6458	537	27	c2	c2	PROPN
ejpam-6458	537	28	−	−	PROPN
ejpam-6458	537	29	2c8	2c8	NUM
ejpam-6458	538	1	+	+	CCONJ
ejpam-6458	539	1	[	[	X
ejpam-6458	539	2	c1	c1	NOUN
ejpam-6458	539	3	,	,	PUNCT
ejpam-6458	539	4	c8	c8	PROPN
ejpam-6458	539	5	]	]	PUNCT
ejpam-6458	539	6	,	,	PUNCT
ejpam-6458	539	7	(	(	PUNCT
ejpam-6458	539	8	5.3	5.3	NUM
ejpam-6458	539	9	)	)	PUNCT
ejpam-6458	539	10	c11	c11	NOUN
ejpam-6458	539	11	=	=	CCONJ
ejpam-6458	539	12	−	−	PROPN
ejpam-6458	539	13	c9	c9	NOUN
ejpam-6458	539	14	−	−	PROPN
ejpam-6458	539	15	2c7	2c7	X
ejpam-6458	539	16	+	+	CCONJ
ejpam-6458	539	17	c2	c2	PROPN
ejpam-6458	539	18	−	−	PROPN
ejpam-6458	540	1	[	[	X
ejpam-6458	540	2	c1	c1	PROPN
ejpam-6458	540	3	,	,	PUNCT
ejpam-6458	540	4	c7	c7	PROPN
ejpam-6458	540	5	]	]	PUNCT
ejpam-6458	540	6	,	,	PUNCT
ejpam-6458	540	7	(	(	PUNCT
ejpam-6458	540	8	5.4	5.4	NUM
ejpam-6458	540	9	)	)	PUNCT
ejpam-6458	540	10	c10	c10	NOUN
ejpam-6458	540	11	=	=	PROPN
ejpam-6458	540	12	c9	c9	PROPN
ejpam-6458	540	13	−	−	PROPN
ejpam-6458	540	14	c8	c8	PROPN
ejpam-6458	540	15	+	+	CCONJ
ejpam-6458	540	16	c7	c7	PROPN
ejpam-6458	540	17	+	+	CCONJ
ejpam-6458	540	18	1	1	NUM
ejpam-6458	540	19	2	2	NUM
ejpam-6458	540	20	[	[	X
ejpam-6458	540	21	c5	c5	PROPN
ejpam-6458	540	22	,	,	PUNCT
ejpam-6458	540	23	c2	c2	PROPN
ejpam-6458	540	24	]	]	PUNCT
ejpam-6458	540	25	+	+	PROPN
ejpam-6458	541	1	[	[	X
ejpam-6458	541	2	c1	c1	NOUN
ejpam-6458	541	3	,	,	PUNCT
ejpam-6458	541	4	c8	c8	PROPN
ejpam-6458	541	5	]	]	PUNCT
ejpam-6458	541	6	(	(	PUNCT
ejpam-6458	541	7	5.5	5.5	NUM
ejpam-6458	541	8	)	)	PUNCT
ejpam-6458	541	9	c9	c9	NOUN
ejpam-6458	541	10	=	=	NOUN
ejpam-6458	541	11	1	1	NUM
ejpam-6458	541	12	2h1	2h1	NUM
ejpam-6458	541	13	(	(	PUNCT
ejpam-6458	541	14	[	[	X
ejpam-6458	541	15	c1	c1	NOUN
ejpam-6458	541	16	,	,	PUNCT
ejpam-6458	541	17	[	[	X
ejpam-6458	541	18	c1	c1	NOUN
ejpam-6458	541	19	,	,	PUNCT
ejpam-6458	541	20	c7]]−	c7]]−	NOUN
ejpam-6458	541	21	2c1c2	2c1c2	NUM
ejpam-6458	541	22	−	−	NOUN
ejpam-6458	541	23	2c7c1	2c7c1	NUM
ejpam-6458	541	24	−	−	NOUN
ejpam-6458	541	25	2c1c7	2c1c7	NUM
ejpam-6458	541	26	)	)	PUNCT
ejpam-6458	542	1	+	+	CCONJ
ejpam-6458	542	2	1	1	NUM
ejpam-6458	542	3	2	2	NUM
ejpam-6458	542	4	[	[	X
ejpam-6458	542	5	c7	c7	PROPN
ejpam-6458	542	6	,	,	PUNCT
ejpam-6458	542	7	c1]−	c1]−	VERB
ejpam-6458	542	8	2c7	2c7	NUM
ejpam-6458	542	9	−	−	PROPN
ejpam-6458	542	10	c2	c2	PROPN
ejpam-6458	542	11	,	,	PUNCT
ejpam-6458	542	12	(	(	PUNCT
ejpam-6458	542	13	5.6	5.6	NUM
ejpam-6458	542	14	)	)	PUNCT
ejpam-6458	542	15	c8	c8	PROPN
ejpam-6458	542	16	=	=	PROPN
ejpam-6458	542	17	c7	c7	PROPN
ejpam-6458	542	18	+	+	CCONJ
ejpam-6458	542	19	1	1	NUM
ejpam-6458	542	20	2	2	NUM
ejpam-6458	542	21	[	[	X
ejpam-6458	542	22	c2	c2	PROPN
ejpam-6458	542	23	,	,	PUNCT
ejpam-6458	542	24	c3	c3	PROPN
ejpam-6458	542	25	]	]	PUNCT
ejpam-6458	542	26	(	(	PUNCT
ejpam-6458	542	27	5.7	5.7	NUM
ejpam-6458	542	28	)	)	PUNCT
ejpam-6458	543	1	c7	c7	PROPN
ejpam-6458	543	2	=	=	SYM
ejpam-6458	543	3	1	1	NUM
ejpam-6458	543	4	16h3	16h3	NUM
ejpam-6458	543	5	(	(	PUNCT
ejpam-6458	543	6	−[c2	−[c2	X
ejpam-6458	543	7	,	,	PUNCT
ejpam-6458	543	8	[	[	X
ejpam-6458	543	9	c2	c2	PROPN
ejpam-6458	543	10	,	,	PUNCT
ejpam-6458	543	11	c3	c3	PROPN
ejpam-6458	543	12	]	]	X
ejpam-6458	543	13	]	]	X
ejpam-6458	543	14	+	+	NUM
ejpam-6458	543	15	8c3c2	8c3c2	NUM
ejpam-6458	543	16	−	−	PROPN
ejpam-6458	543	17	8c2c4	8c2c4	NUM
ejpam-6458	543	18	−	−	PROPN
ejpam-6458	543	19	8h1c2	8h1c2	NUM
ejpam-6458	543	20	)	)	PUNCT
ejpam-6458	543	21	+	+	CCONJ
ejpam-6458	543	22	1	1	NUM
ejpam-6458	543	23	4	4	NUM
ejpam-6458	543	24	[	[	X
ejpam-6458	543	25	c3	c3	NOUN
ejpam-6458	543	26	,	,	PUNCT
ejpam-6458	543	27	c2]−	c2]−	VERB
ejpam-6458	543	28	1	1	NUM
ejpam-6458	543	29	2	2	NUM
ejpam-6458	543	30	c2	c2	PROPN
ejpam-6458	543	31	,	,	PUNCT
ejpam-6458	543	32	(	(	PUNCT
ejpam-6458	543	33	5.8	5.8	NUM
ejpam-6458	543	34	)	)	PUNCT
ejpam-6458	543	35	c6	c6	NOUN
ejpam-6458	544	1	=	=	PROPN
ejpam-6458	544	2	c5	c5	PROPN
ejpam-6458	544	3	+	+	PROPN
ejpam-6458	545	1	[	[	X
ejpam-6458	545	2	c3	c3	PROPN
ejpam-6458	545	3	,	,	PUNCT
ejpam-6458	545	4	c1	c1	PROPN
ejpam-6458	545	5	]	]	PUNCT
ejpam-6458	545	6	(	(	PUNCT
ejpam-6458	545	7	5.9	5.9	NUM
ejpam-6458	545	8	)	)	PUNCT
ejpam-6458	545	9	c5	c5	PROPN
ejpam-6458	545	10	=	=	SYM
ejpam-6458	545	11	−	−	PROPN
ejpam-6458	545	12	c4	c4	NOUN
ejpam-6458	545	13	+	+	CCONJ
ejpam-6458	545	14	c1c3	c1c3	X
ejpam-6458	545	15	+	+	CCONJ
ejpam-6458	545	16	1	1	NUM
ejpam-6458	545	17	2h1	2h1	NUM
ejpam-6458	545	18	(	(	PUNCT
ejpam-6458	545	19	−[c1	−[c1	NUM
ejpam-6458	545	20	,	,	PUNCT
ejpam-6458	545	21	c1	c1	NOUN
ejpam-6458	545	22	,	,	PUNCT
ejpam-6458	545	23	c3]−	c3]−	VERB
ejpam-6458	545	24	c3c1(h1	c3c1(h1	NOUN
ejpam-6458	545	25	−	−	PROPN
ejpam-6458	545	26	2)−	2)−	NUM
ejpam-6458	545	27	2c1c4	2c1c4	NUM
ejpam-6458	545	28	)	)	PUNCT
ejpam-6458	545	29	.	.	PUNCT
ejpam-6458	546	1	(	(	PUNCT
ejpam-6458	546	2	5.10	5.10	NUM
ejpam-6458	546	3	)	)	PUNCT
ejpam-6458	546	4	the	the	DET
ejpam-6458	546	5	following	follow	VERB
ejpam-6458	546	6	relations	relation	NOUN
ejpam-6458	546	7	are	be	AUX
ejpam-6458	546	8	used	use	VERB
ejpam-6458	546	9	to	to	PART
ejpam-6458	546	10	find	find	VERB
ejpam-6458	546	11	relations	relation	NOUN
ejpam-6458	546	12	between	between	ADP
ejpam-6458	546	13	the	the	DET
ejpam-6458	546	14	elements	element	NOUN
ejpam-6458	546	15	c4	c4	NOUN
ejpam-6458	546	16	,	,	PUNCT
ejpam-6458	546	17	c3	c3	PROPN
ejpam-6458	546	18	,	,	PUNCT
ejpam-6458	546	19	c2	c2	PROPN
ejpam-6458	546	20	,	,	PUNCT
ejpam-6458	546	21	c1	c1	PROPN
ejpam-6458	546	22	,	,	PUNCT
ejpam-6458	546	23	h1	h1	PROPN
ejpam-6458	546	24	,	,	PUNCT
ejpam-6458	546	25	h3	h3	NOUN
ejpam-6458	546	26	,	,	PUNCT
ejpam-6458	546	27	z1	z1	PROPN
ejpam-6458	546	28	.	.	PUNCT
ejpam-6458	547	1	c5c1	c5c1	NOUN
ejpam-6458	547	2	=	=	PUNCT
ejpam-6458	548	1	−c6	−c6	ADJ
ejpam-6458	548	2	+	+	CCONJ
ejpam-6458	548	3	(	(	PUNCT
ejpam-6458	548	4	h1	h1	X
ejpam-6458	548	5	+	+	CCONJ
ejpam-6458	548	6	1)c5	1)c5	NUM
ejpam-6458	548	7	+	+	CCONJ
ejpam-6458	548	8	h1c4	h1c4	VERB
ejpam-6458	548	9	+	+	CCONJ
ejpam-6458	548	10	c1c5	c1c5	X
ejpam-6458	548	11	+	+	CCONJ
ejpam-6458	548	12	c1c4	c1c4	VERB
ejpam-6458	548	13	−	−	NOUN
ejpam-6458	548	14	c1c3	c1c3	NOUN
ejpam-6458	548	15	(	(	PUNCT
ejpam-6458	548	16	5.11	5.11	NUM
ejpam-6458	548	17	)	)	PUNCT
ejpam-6458	548	18	c7c2	c7c2	NOUN
ejpam-6458	548	19	=	=	NOUN
ejpam-6458	548	20	−4h3c7	−4h3c7	PROPN
ejpam-6458	548	21	+	+	CCONJ
ejpam-6458	548	22	c2c7	c2c7	NOUN
ejpam-6458	548	23	−	−	NOUN
ejpam-6458	548	24	2c2c4	2c2c4	NUM
ejpam-6458	549	1	+	+	CCONJ
ejpam-6458	549	2	2c2c3	2c2c3	NUM
ejpam-6458	549	3	+	+	CCONJ
ejpam-6458	549	4	(	(	PUNCT
ejpam-6458	549	5	−2h3	−2h3	NUM
ejpam-6458	549	6	−	−	NOUN
ejpam-6458	549	7	2h1)c2	2h1)c2	NUM
ejpam-6458	549	8	(	(	PUNCT
ejpam-6458	549	9	5.12	5.12	NUM
ejpam-6458	549	10	)	)	PUNCT
ejpam-6458	549	11	c5c3	c5c3	NOUN
ejpam-6458	549	12	=	=	SYM
ejpam-6458	549	13	c9	c9	PROPN
ejpam-6458	549	14	+	+	CCONJ
ejpam-6458	549	15	c8	c8	PROPN
ejpam-6458	549	16	−	−	PROPN
ejpam-6458	549	17	2c6	2c6	NUM
ejpam-6458	549	18	+	+	CCONJ
ejpam-6458	549	19	(	(	PUNCT
ejpam-6458	549	20	h3	h3	NOUN
ejpam-6458	549	21	−	−	NOUN
ejpam-6458	549	22	h1)c5	h1)c5	NOUN
ejpam-6458	549	23	+	+	CCONJ
ejpam-6458	549	24	c3c5	c3c5	ADP
ejpam-6458	549	25	−	−	PROPN
ejpam-6458	549	26	c3c4	c3c4	PROPN
ejpam-6458	549	27	+	+	PROPN
ejpam-6458	549	28	2c1c3	2c1c3	NUM
ejpam-6458	549	29	(	(	PUNCT
ejpam-6458	549	30	5.13	5.13	NUM
ejpam-6458	549	31	)	)	PUNCT
ejpam-6458	549	32	m.	m.	NOUN
ejpam-6458	549	33	andelić	andelić	PROPN
ejpam-6458	549	34	et	et	PROPN
ejpam-6458	549	35	al	al	PROPN
ejpam-6458	549	36	.	.	PUNCT
ejpam-6458	549	37	/	/	SYM
ejpam-6458	549	38	eur	eur	PROPN
ejpam-6458	549	39	.	.	PUNCT
ejpam-6458	550	1	j.	j.	PROPN
ejpam-6458	550	2	pure	pure	PROPN
ejpam-6458	550	3	appl	appl	PROPN
ejpam-6458	550	4	.	.	PROPN
ejpam-6458	550	5	math	math	PROPN
ejpam-6458	550	6	,	,	PUNCT
ejpam-6458	550	7	18	18	NUM
ejpam-6458	550	8	(	(	PUNCT
ejpam-6458	550	9	3	3	NUM
ejpam-6458	550	10	)	)	PUNCT
ejpam-6458	550	11	(	(	PUNCT
ejpam-6458	550	12	2025	2025	NUM
ejpam-6458	550	13	)	)	PUNCT
ejpam-6458	550	14	,	,	PUNCT
ejpam-6458	550	15	6458	6458	NUM
ejpam-6458	550	16	14	14	NUM
ejpam-6458	550	17	of	of	ADP
ejpam-6458	550	18	21	21	NUM
ejpam-6458	550	19	c7c3	c7c3	NOUN
ejpam-6458	550	20	=	=	PUNCT
ejpam-6458	550	21	−2c9	−2c9	NUM
ejpam-6458	550	22	−	−	NOUN
ejpam-6458	550	23	2c8	2c8	NUM
ejpam-6458	551	1	+	+	CCONJ
ejpam-6458	551	2	(	(	PUNCT
ejpam-6458	551	3	h3	h3	NOUN
ejpam-6458	551	4	−	−	NOUN
ejpam-6458	551	5	h1)c7	h1)c7	NOUN
ejpam-6458	551	6	+	+	CCONJ
ejpam-6458	551	7	4c6	4c6	NUM
ejpam-6458	552	1	+	+	CCONJ
ejpam-6458	552	2	c3c7	c3c7	X
ejpam-6458	552	3	+	+	CCONJ
ejpam-6458	552	4	2c3c4	2c3c4	NUM
ejpam-6458	552	5	−	−	NOUN
ejpam-6458	553	1	c2c3	c2c3	INTJ
ejpam-6458	553	2	(	(	PUNCT
ejpam-6458	553	3	5.14	5.14	NUM
ejpam-6458	553	4	)	)	PUNCT
ejpam-6458	553	5	c6c5	c6c5	NOUN
ejpam-6458	554	1	=	=	PRON
ejpam-6458	554	2	c10	c10	VERB
ejpam-6458	554	3	+	+	CCONJ
ejpam-6458	555	1	2c8	2c8	NUM
ejpam-6458	556	1	−	−	ADP
ejpam-6458	557	1	c7	c7	PROPN
ejpam-6458	558	1	+	+	CCONJ
ejpam-6458	558	2	(	(	PUNCT
ejpam-6458	558	3	h3	h3	NOUN
ejpam-6458	558	4	−	−	PROPN
ejpam-6458	558	5	h1	h1	NOUN
ejpam-6458	558	6	−	−	PROPN
ejpam-6458	558	7	2)c6	2)c6	NUM
ejpam-6458	558	8	−	−	NOUN
ejpam-6458	558	9	c4c5	c4c5	ADP
ejpam-6458	558	10	−	−	NOUN
ejpam-6458	558	11	c3c6	c3c6	ADP
ejpam-6458	558	12	−	−	PROPN
ejpam-6458	558	13	2c3c4	2c3c4	NOUN
ejpam-6458	558	14	−	−	ADP
ejpam-6458	559	1	c1c8	c1c8	NOUN
ejpam-6458	559	2	+	+	NOUN
ejpam-6458	559	3	2c1c6	2c1c6	NUM
ejpam-6458	560	1	+	+	CCONJ
ejpam-6458	560	2	c1c3c4	c1c3c4	X
ejpam-6458	560	3	+	+	CCONJ
ejpam-6458	560	4	(	(	PUNCT
ejpam-6458	560	5	h3	h3	NOUN
ejpam-6458	560	6	+	+	CCONJ
ejpam-6458	560	7	h1	h1	NOUN
ejpam-6458	560	8	+	+	NOUN
ejpam-6458	560	9	2)c1c3	2)c1c3	NUM
ejpam-6458	560	10	.	.	PUNCT
ejpam-6458	561	1	(	(	PUNCT
ejpam-6458	561	2	5.15	5.15	NUM
ejpam-6458	561	3	)	)	PUNCT
ejpam-6458	561	4	the	the	DET
ejpam-6458	561	5	center	center	NOUN
ejpam-6458	561	6	of	of	ADP
ejpam-6458	561	7	the	the	DET
ejpam-6458	561	8	universal	universal	ADJ
ejpam-6458	561	9	enveloping	enveloping	NOUN
ejpam-6458	561	10	algebra	algebra	NOUN
ejpam-6458	561	11	of	of	ADP
ejpam-6458	561	12	g	g	PROPN
ejpam-6458	561	13	is	be	AUX
ejpam-6458	561	14	generated	generate	VERB
ejpam-6458	561	15	by	by	ADP
ejpam-6458	561	16	the	the	DET
ejpam-6458	561	17	following	follow	VERB
ejpam-6458	561	18	casimir	casimir	NOUN
ejpam-6458	561	19	elements	element	NOUN
ejpam-6458	561	20	:	:	PUNCT
ejpam-6458	561	21	z1	z1	NUM
ejpam-6458	561	22	=	=	NOUN
ejpam-6458	561	23	4c1	4c1	NUM
ejpam-6458	562	1	+	+	CCONJ
ejpam-6458	562	2	c2	c2	PROPN
ejpam-6458	562	3	+	+	CCONJ
ejpam-6458	562	4	2c3	2c3	NUM
ejpam-6458	562	5	+	+	CCONJ
ejpam-6458	562	6	2c4	2c4	NUM
ejpam-6458	562	7	+	+	CCONJ
ejpam-6458	562	8	2h21	2h21	NOUN
ejpam-6458	562	9	+	+	CCONJ
ejpam-6458	562	10	2h23	2h23	NUM
ejpam-6458	562	11	+	+	CCONJ
ejpam-6458	562	12	2h1	2h1	NUM
ejpam-6458	562	13	+	+	CCONJ
ejpam-6458	562	14	4h3	4h3	NUM
ejpam-6458	562	15	,	,	PUNCT
ejpam-6458	562	16	(	(	PUNCT
ejpam-6458	562	17	5.16	5.16	NUM
ejpam-6458	562	18	)	)	PUNCT
ejpam-6458	562	19	z2	z2	NOUN
ejpam-6458	562	20	=	=	SYM
ejpam-6458	562	21	2c12	2c12	PROPN
ejpam-6458	562	22	+	+	CCONJ
ejpam-6458	562	23	2c11	2c11	NOUN
ejpam-6458	562	24	−	−	NOUN
ejpam-6458	562	25	2c10	2c10	NUM
ejpam-6458	562	26	−	−	PROPN
ejpam-6458	562	27	2c9	2c9	NUM
ejpam-6458	563	1	+	+	CCONJ
ejpam-6458	563	2	(	(	PUNCT
ejpam-6458	563	3	2h1	2h1	NUM
ejpam-6458	563	4	+	+	CCONJ
ejpam-6458	563	5	1)c8	1)c8	NUM
ejpam-6458	563	6	+	+	CCONJ
ejpam-6458	563	7	(	(	PUNCT
ejpam-6458	563	8	2h1	2h1	NUM
ejpam-6458	563	9	−	−	PROPN
ejpam-6458	563	10	1)c7	1)c7	NUM
ejpam-6458	563	11	+	+	CCONJ
ejpam-6458	563	12	(	(	PUNCT
ejpam-6458	563	13	4h3	4h3	NUM
ejpam-6458	564	1	+	+	CCONJ
ejpam-6458	564	2	6)c6	6)c6	NOUN
ejpam-6458	564	3	+	+	CCONJ
ejpam-6458	564	4	(	(	PUNCT
ejpam-6458	564	5	4h3	4h3	NUM
ejpam-6458	564	6	+	+	CCONJ
ejpam-6458	564	7	10)c5	10)c5	NUM
ejpam-6458	564	8	−	−	PROPN
ejpam-6458	564	9	c24	c24	NOUN
ejpam-6458	564	10	+	+	CCONJ
ejpam-6458	564	11	(	(	PUNCT
ejpam-6458	564	12	−2h1h3	−2h1h3	NOUN
ejpam-6458	564	13	−	−	PROPN
ejpam-6458	564	14	4h1	4h1	NUM
ejpam-6458	565	1	+	+	CCONJ
ejpam-6458	565	2	2h3	2h3	NUM
ejpam-6458	566	1	+	+	CCONJ
ejpam-6458	566	2	6)c4	6)c4	NUM
ejpam-6458	566	3	−	−	PROPN
ejpam-6458	566	4	2c3c4	2c3c4	NUM
ejpam-6458	566	5	−	−	NOUN
ejpam-6458	566	6	c23	c23	PROPN
ejpam-6458	566	7	+	+	CCONJ
ejpam-6458	566	8	(	(	PUNCT
ejpam-6458	566	9	2h1h3	2h1h3	NUM
ejpam-6458	566	10	+	+	CCONJ
ejpam-6458	566	11	4h1	4h1	NUM
ejpam-6458	567	1	+	+	CCONJ
ejpam-6458	567	2	2h3	2h3	NUM
ejpam-6458	568	1	+	+	CCONJ
ejpam-6458	568	2	6)c3	6)c3	NUM
ejpam-6458	568	3	−	−	NOUN
ejpam-6458	568	4	(	(	PUNCT
ejpam-6458	568	5	h1	h1	VERB
ejpam-6458	568	6	−	−	NOUN
ejpam-6458	568	7	1)(h1	1)(h1	NUM
ejpam-6458	569	1	+	+	CCONJ
ejpam-6458	569	2	1)c2	1)c2	NUM
ejpam-6458	569	3	−	−	PROPN
ejpam-6458	569	4	4c1c2	4c1c2	NUM
ejpam-6458	570	1	−	−	NOUN
ejpam-6458	571	1	4(h2	4(h2	NUM
ejpam-6458	571	2	+	+	NOUN
ejpam-6458	571	3	3)(h2	3)(h2	NUM
ejpam-6458	572	1	+	+	CCONJ
ejpam-6458	572	2	1)c1	1)c1	NUM
ejpam-6458	572	3	−	−	PROPN
ejpam-6458	573	1	h1(h3	h1(h3	PRON
ejpam-6458	573	2	+	+	NOUN
ejpam-6458	573	3	3)(h3	3)(h3	NUM
ejpam-6458	573	4	+	+	CCONJ
ejpam-6458	573	5	1)(h1	1)(h1	NUM
ejpam-6458	573	6	+	+	CCONJ
ejpam-6458	573	7	2	2	NUM
ejpam-6458	573	8	)	)	PUNCT
ejpam-6458	573	9	.	.	PUNCT
ejpam-6458	574	1	as	as	ADP
ejpam-6458	574	2	in	in	ADP
ejpam-6458	574	3	type	type	NOUN
ejpam-6458	574	4	a	a	PRON
ejpam-6458	574	5	,	,	PUNCT
ejpam-6458	574	6	our	our	PRON
ejpam-6458	574	7	goal	goal	NOUN
ejpam-6458	574	8	is	be	AUX
ejpam-6458	574	9	to	to	PART
ejpam-6458	574	10	find	find	VERB
ejpam-6458	574	11	the	the	DET
ejpam-6458	574	12	”	"	PUNCT
ejpam-6458	574	13	best	good	ADJ
ejpam-6458	574	14	”	"	PUNCT
ejpam-6458	574	15	choice	choice	NOUN
ejpam-6458	574	16	of	of	ADP
ejpam-6458	574	17	a	a	DET
ejpam-6458	574	18	generating	generate	VERB
ejpam-6458	574	19	set	set	NOUN
ejpam-6458	574	20	s	s	PROPN
ejpam-6458	574	21	of	of	ADP
ejpam-6458	574	22	u0	u0	PROPN
ejpam-6458	574	23	,	,	PUNCT
ejpam-6458	574	24	such	such	ADJ
ejpam-6458	574	25	that	that	SCONJ
ejpam-6458	574	26	the	the	DET
ejpam-6458	574	27	cardinality	cardinality	NOUN
ejpam-6458	574	28	of	of	ADP
ejpam-6458	574	29	the	the	DET
ejpam-6458	574	30	set	set	NOUN
ejpam-6458	574	31	s3	s3	PROPN
ejpam-6458	574	32	is	be	AUX
ejpam-6458	574	33	minimal	minimal	ADJ
ejpam-6458	574	34	.	.	PUNCT
ejpam-6458	575	1	lemma	lemma	PROPN
ejpam-6458	575	2	5.2	5.2	NUM
ejpam-6458	575	3	.	.	NOUN
ejpam-6458	576	1	1	1	NUM
ejpam-6458	576	2	.	.	PUNCT
ejpam-6458	577	1	the	the	DET
ejpam-6458	577	2	set	set	NOUN
ejpam-6458	577	3	s	s	PART
ejpam-6458	577	4	=	=	X
ejpam-6458	577	5	{	{	PUNCT
ejpam-6458	577	6	h1	h1	PROPN
ejpam-6458	577	7	,	,	PUNCT
ejpam-6458	577	8	h2	h2	PROPN
ejpam-6458	577	9	,	,	PUNCT
ejpam-6458	577	10	z1	z1	PROPN
ejpam-6458	577	11	,	,	PUNCT
ejpam-6458	577	12	z2	z2	PROPN
ejpam-6458	577	13	,	,	PUNCT
ejpam-6458	577	14	c1	c1	PROPN
ejpam-6458	577	15	,	,	PUNCT
ejpam-6458	577	16	c2	c2	PROPN
ejpam-6458	577	17	,	,	PUNCT
ejpam-6458	577	18	c3	c3	PROPN
ejpam-6458	577	19	}	}	PUNCT
ejpam-6458	577	20	is	be	AUX
ejpam-6458	577	21	a	a	DET
ejpam-6458	577	22	generating	generate	VERB
ejpam-6458	577	23	set	set	NOUN
ejpam-6458	577	24	of	of	ADP
ejpam-6458	577	25	the	the	DET
ejpam-6458	577	26	centralizer	centralizer	NOUN
ejpam-6458	577	27	u	u	NOUN
ejpam-6458	577	28	′	′	NOUN
ejpam-6458	577	29	0	0	NUM
ejpam-6458	577	30	with	with	ADP
ejpam-6458	577	31	the	the	DET
ejpam-6458	577	32	following	follow	VERB
ejpam-6458	577	33	decomposition	decomposition	NOUN
ejpam-6458	577	34	:	:	PUNCT
ejpam-6458	577	35	s1	s1	NOUN
ejpam-6458	577	36	=	=	PUNCT
ejpam-6458	577	37	{	{	PUNCT
ejpam-6458	577	38	h1	h1	PROPN
ejpam-6458	577	39	,	,	PUNCT
ejpam-6458	577	40	h2	h2	PROPN
ejpam-6458	577	41	,	,	PUNCT
ejpam-6458	577	42	z1	z1	PROPN
ejpam-6458	577	43	,	,	PUNCT
ejpam-6458	577	44	z2	z2	PROPN
ejpam-6458	577	45	}	}	PUNCT
ejpam-6458	577	46	,	,	PUNCT
ejpam-6458	577	47	s2	s2	X
ejpam-6458	577	48	=	=	SYM
ejpam-6458	577	49	{	{	PUNCT
ejpam-6458	577	50	c1	c1	NOUN
ejpam-6458	577	51	,	,	PUNCT
ejpam-6458	577	52	c2	c2	PROPN
ejpam-6458	577	53	}	}	PUNCT
ejpam-6458	577	54	,	,	PUNCT
ejpam-6458	577	55	s3	s3	PROPN
ejpam-6458	577	56	=	=	SYM
ejpam-6458	577	57	{	{	PUNCT
ejpam-6458	577	58	c3	c3	NOUN
ejpam-6458	577	59	}	}	PUNCT
ejpam-6458	577	60	.	.	PUNCT
ejpam-6458	578	1	2	2	X
ejpam-6458	578	2	.	.	X
ejpam-6458	578	3	the	the	DET
ejpam-6458	578	4	decomposition	decomposition	NOUN
ejpam-6458	578	5	of	of	ADP
ejpam-6458	578	6	the	the	DET
ejpam-6458	578	7	set	set	NOUN
ejpam-6458	578	8	of	of	ADP
ejpam-6458	578	9	relations	relation	NOUN
ejpam-6458	578	10	is	be	AUX
ejpam-6458	578	11	the	the	DET
ejpam-6458	578	12	following	follow	VERB
ejpam-6458	578	13	:	:	PUNCT
ejpam-6458	578	14	r	r	NOUN
ejpam-6458	578	15	=	=	SYM
ejpam-6458	578	16	r1	r1	PROPN
ejpam-6458	578	17	∪	∪	ADJ
ejpam-6458	578	18	r2	r2	PROPN
ejpam-6458	578	19	,	,	PUNCT
ejpam-6458	578	20	where	where	SCONJ
ejpam-6458	578	21	r1	r1	PROPN
ejpam-6458	578	22	consists	consist	VERB
ejpam-6458	578	23	of	of	ADP
ejpam-6458	578	24	two	two	NUM
ejpam-6458	578	25	relations	relation	NOUN
ejpam-6458	578	26	obtained	obtain	VERB
ejpam-6458	578	27	from	from	ADP
ejpam-6458	578	28	(	(	PUNCT
ejpam-6458	578	29	5.11	5.11	NUM
ejpam-6458	578	30	)	)	PUNCT
ejpam-6458	578	31	and	and	CCONJ
ejpam-6458	578	32	(	(	PUNCT
ejpam-6458	578	33	5.12	5.12	NUM
ejpam-6458	578	34	)	)	PUNCT
ejpam-6458	578	35	,	,	PUNCT
ejpam-6458	578	36	while	while	SCONJ
ejpam-6458	578	37	r2	r2	PROPN
ejpam-6458	578	38	consists	consist	VERB
ejpam-6458	578	39	of	of	ADP
ejpam-6458	578	40	three	three	NUM
ejpam-6458	578	41	relations	relation	NOUN
ejpam-6458	578	42	obtained	obtain	VERB
ejpam-6458	578	43	from	from	ADP
ejpam-6458	578	44	(	(	PUNCT
ejpam-6458	578	45	5.13	5.13	NUM
ejpam-6458	578	46	)	)	PUNCT
ejpam-6458	578	47	,	,	PUNCT
ejpam-6458	578	48	(	(	PUNCT
ejpam-6458	578	49	5.14	5.14	NUM
ejpam-6458	578	50	)	)	PUNCT
ejpam-6458	578	51	,	,	PUNCT
ejpam-6458	578	52	and	and	CCONJ
ejpam-6458	578	53	(	(	PUNCT
ejpam-6458	578	54	5.15	5.15	NUM
ejpam-6458	578	55	)	)	PUNCT
ejpam-6458	578	56	.	.	PUNCT
ejpam-6458	579	1	proof	proof	NOUN
ejpam-6458	579	2	.	.	PUNCT
ejpam-6458	580	1	using	use	VERB
ejpam-6458	580	2	the	the	DET
ejpam-6458	580	3	(	(	PUNCT
ejpam-6458	580	4	5.3)-(5.10	5.3)-(5.10	NUM
ejpam-6458	580	5	)	)	PUNCT
ejpam-6458	580	6	and	and	CCONJ
ejpam-6458	580	7	(	(	PUNCT
ejpam-6458	580	8	5.16	5.16	NUM
ejpam-6458	580	9	)	)	PUNCT
ejpam-6458	580	10	for	for	ADP
ejpam-6458	580	11	the	the	DET
ejpam-6458	580	12	casimir	casimir	PROPN
ejpam-6458	580	13	element	element	NOUN
ejpam-6458	580	14	z1	z1	NOUN
ejpam-6458	580	15	we	we	PRON
ejpam-6458	580	16	can	can	AUX
ejpam-6458	580	17	exclude	exclude	VERB
ejpam-6458	580	18	the	the	DET
ejpam-6458	580	19	generators	generator	NOUN
ejpam-6458	580	20	c12	c12	PROPN
ejpam-6458	580	21	,	,	PUNCT
ejpam-6458	580	22	.	.	PUNCT
ejpam-6458	580	23	.	.	PUNCT
ejpam-6458	581	1	.	.	PUNCT
ejpam-6458	582	1	,	,	PUNCT
ejpam-6458	582	2	c4	c4	NOUN
ejpam-6458	582	3	from	from	ADP
ejpam-6458	582	4	all	all	DET
ejpam-6458	582	5	other	other	ADJ
ejpam-6458	582	6	relations	relation	NOUN
ejpam-6458	582	7	.	.	PUNCT
ejpam-6458	583	1	as	as	ADP
ejpam-6458	583	2	the	the	DET
ejpam-6458	583	3	result	result	NOUN
ejpam-6458	583	4	,	,	PUNCT
ejpam-6458	583	5	we	we	PRON
ejpam-6458	583	6	will	will	AUX
ejpam-6458	583	7	get	get	VERB
ejpam-6458	583	8	the	the	DET
ejpam-6458	583	9	generating	generate	VERB
ejpam-6458	583	10	set	set	NOUN
ejpam-6458	583	11	s	s	PART
ejpam-6458	583	12	=	=	X
ejpam-6458	583	13	{	{	PUNCT
ejpam-6458	583	14	h1	h1	PROPN
ejpam-6458	583	15	,	,	PUNCT
ejpam-6458	583	16	h2	h2	PROPN
ejpam-6458	583	17	,	,	PUNCT
ejpam-6458	583	18	z1	z1	PROPN
ejpam-6458	583	19	,	,	PUNCT
ejpam-6458	583	20	c1	c1	PROPN
ejpam-6458	583	21	,	,	PUNCT
ejpam-6458	583	22	c2	c2	PROPN
ejpam-6458	583	23	,	,	PUNCT
ejpam-6458	583	24	c3	c3	PROPN
ejpam-6458	583	25	}	}	PUNCT
ejpam-6458	583	26	.	.	PUNCT
ejpam-6458	584	1	the	the	DET
ejpam-6458	584	2	rest	rest	NOUN
ejpam-6458	584	3	can	can	AUX
ejpam-6458	584	4	be	be	AUX
ejpam-6458	584	5	verified	verify	VERB
ejpam-6458	584	6	by	by	ADP
ejpam-6458	584	7	direct	direct	ADJ
ejpam-6458	584	8	computations	computation	NOUN
ejpam-6458	584	9	.	.	PUNCT
ejpam-6458	585	1	□	□	PUNCT
ejpam-6458	585	2	remark	remark	NOUN
ejpam-6458	585	3	.	.	PUNCT
ejpam-6458	586	1	we	we	PRON
ejpam-6458	586	2	can	can	AUX
ejpam-6458	586	3	not	not	PART
ejpam-6458	586	4	claim	claim	VERB
ejpam-6458	586	5	that	that	SCONJ
ejpam-6458	586	6	s	s	VERB
ejpam-6458	586	7	is	be	AUX
ejpam-6458	586	8	a	a	DET
ejpam-6458	586	9	generating	generate	VERB
ejpam-6458	586	10	set	set	NOUN
ejpam-6458	586	11	of	of	ADP
ejpam-6458	586	12	u0	u0	PROPN
ejpam-6458	586	13	.	.	PUNCT
ejpam-6458	587	1	nevertheless	nevertheless	ADV
ejpam-6458	587	2	,	,	PUNCT
ejpam-6458	587	3	any	any	DET
ejpam-6458	587	4	u0	u0	ADJ
ejpam-6458	587	5	-	-	PUNCT
ejpam-6458	587	6	module	module	NOUN
ejpam-6458	587	7	m	m	NOUN
ejpam-6458	587	8	with	with	ADP
ejpam-6458	587	9	a	a	DET
ejpam-6458	587	10	non	non	ADJ
ejpam-6458	587	11	-	-	ADJ
ejpam-6458	587	12	zero	zero	ADJ
ejpam-6458	587	13	scalar	scalar	ADJ
ejpam-6458	587	14	action	action	NOUN
ejpam-6458	587	15	of	of	ADP
ejpam-6458	587	16	h1	h1	PROPN
ejpam-6458	587	17	is	be	AUX
ejpam-6458	587	18	a	a	DET
ejpam-6458	587	19	u	u	NOUN
ejpam-6458	587	20	′	′	NUM
ejpam-6458	587	21	0	0	NUM
ejpam-6458	587	22	-	-	PUNCT
ejpam-6458	587	23	module	module	NOUN
ejpam-6458	587	24	.	.	PUNCT
ejpam-6458	588	1	5.2	5.2	NUM
ejpam-6458	588	2	.	.	PUNCT
ejpam-6458	589	1	construction	construction	NOUN
ejpam-6458	589	2	of	of	ADP
ejpam-6458	589	3	torsion	torsion	NOUN
ejpam-6458	589	4	free	free	ADJ
ejpam-6458	589	5	c2	c2	PROPN
ejpam-6458	589	6	-	-	PUNCT
ejpam-6458	589	7	modules	module	NOUN
ejpam-6458	589	8	let	let	VERB
ejpam-6458	589	9	γ	γ	NOUN
ejpam-6458	589	10	be	be	AUX
ejpam-6458	589	11	the	the	DET
ejpam-6458	589	12	commutative	commutative	ADJ
ejpam-6458	589	13	subalgebra	subalgebra	NOUN
ejpam-6458	589	14	of	of	ADP
ejpam-6458	589	15	u0(c2	u0(c2	NOUN
ejpam-6458	589	16	)	)	PUNCT
ejpam-6458	589	17	generated	generate	VERB
ejpam-6458	589	18	by	by	ADP
ejpam-6458	589	19	the	the	DET
ejpam-6458	589	20	elements	element	NOUN
ejpam-6458	589	21	h1	h1	PROPN
ejpam-6458	589	22	,	,	PUNCT
ejpam-6458	589	23	h2	h2	NOUN
ejpam-6458	589	24	,	,	PUNCT
ejpam-6458	589	25	z1	z1	PROPN
ejpam-6458	589	26	,	,	PUNCT
ejpam-6458	589	27	z2	z2	PROPN
ejpam-6458	589	28	,	,	PUNCT
ejpam-6458	589	29	c1	c1	NOUN
ejpam-6458	589	30	.	.	PUNCT
ejpam-6458	590	1	we	we	PRON
ejpam-6458	590	2	construct	construct	VERB
ejpam-6458	590	3	two	two	NUM
ejpam-6458	590	4	families	family	NOUN
ejpam-6458	590	5	of	of	ADP
ejpam-6458	590	6	γ	γ	PROPN
ejpam-6458	590	7	-	-	PUNCT
ejpam-6458	590	8	pointed	point	VERB
ejpam-6458	590	9	modules	module	NOUN
ejpam-6458	590	10	,	,	PUNCT
ejpam-6458	590	11	each	each	PRON
ejpam-6458	590	12	depending	depend	VERB
ejpam-6458	590	13	on	on	ADP
ejpam-6458	590	14	four	four	NUM
ejpam-6458	590	15	complex	complex	ADJ
ejpam-6458	590	16	parameters	parameter	NOUN
ejpam-6458	590	17	.	.	PUNCT
ejpam-6458	591	1	fix	fix	VERB
ejpam-6458	591	2	arbitrary	arbitrary	ADJ
ejpam-6458	591	3	complex	complex	ADJ
ejpam-6458	591	4	number	number	NOUN
ejpam-6458	591	5	a1	a1	NOUN
ejpam-6458	591	6	,	,	PUNCT
ejpam-6458	591	7	a2	a2	PROPN
ejpam-6458	591	8	,	,	PUNCT
ejpam-6458	591	9	a3	a3	NOUN
ejpam-6458	591	10	,	,	PUNCT
ejpam-6458	591	11	a4	a4	PROPN
ejpam-6458	591	12	,	,	PUNCT
ejpam-6458	591	13	η	η	NOUN
ejpam-6458	591	14	,	,	PUNCT
ejpam-6458	591	15	and	and	CCONJ
ejpam-6458	591	16	define	define	VERB
ejpam-6458	591	17	the	the	DET
ejpam-6458	591	18	following	follow	VERB
ejpam-6458	591	19	set	set	NOUN
ejpam-6458	591	20	of	of	ADP
ejpam-6458	591	21	indexed	indexed	ADJ
ejpam-6458	591	22	variables	variable	NOUN
ejpam-6458	591	23	:	:	PUNCT
ejpam-6458	591	24	h	h	NOUN
ejpam-6458	591	25	(	(	PUNCT
ejpam-6458	591	26	1	1	NUM
ejpam-6458	591	27	)	)	PUNCT
ejpam-6458	591	28	ij	ij	NOUN
ejpam-6458	591	29	=	=	NOUN
ejpam-6458	591	30	a1	a1	NOUN
ejpam-6458	592	1	+	+	CCONJ
ejpam-6458	592	2	2i−	2i−	NUM
ejpam-6458	592	3	j	j	PROPN
ejpam-6458	592	4	,	,	PUNCT
ejpam-6458	592	5	h	h	PROPN
ejpam-6458	592	6	(	(	PUNCT
ejpam-6458	592	7	2	2	NUM
ejpam-6458	592	8	)	)	PUNCT
ejpam-6458	592	9	ij	ij	NOUN
ejpam-6458	592	10	=	=	PROPN
ejpam-6458	592	11	a2	a2	PROPN
ejpam-6458	592	12	−	−	PROPN
ejpam-6458	592	13	2i+	2i+	NUM
ejpam-6458	592	14	2j	2j	NOUN
ejpam-6458	592	15	,	,	PUNCT
ejpam-6458	592	16	sjk	sjk	PROPN
ejpam-6458	592	17	=	=	PROPN
ejpam-6458	592	18	a3	a3	PROPN
ejpam-6458	592	19	−	−	PROPN
ejpam-6458	592	20	j	j	PROPN
ejpam-6458	592	21	+	+	CCONJ
ejpam-6458	592	22	2k	2k	NOUN
ejpam-6458	592	23	−	−	NOUN
ejpam-6458	592	24	1	1	NUM
ejpam-6458	592	25	,	,	PUNCT
ejpam-6458	592	26	q±	q±	ADJ
ejpam-6458	592	27	jk	jk	PROPN
ejpam-6458	592	28	=	=	PROPN
ejpam-6458	592	29	η	η	PROPN
ejpam-6458	592	30	sjk	sjk	PROPN
ejpam-6458	592	31	±	±	PROPN
ejpam-6458	592	32	1	1	NUM
ejpam-6458	592	33	,	,	PUNCT
ejpam-6458	592	34	s+	s+	X
ejpam-6458	592	35	ijk	ijk	PROPN
ejpam-6458	592	36	=	=	NOUN
ejpam-6458	592	37	1	1	NUM
ejpam-6458	592	38	2	2	NUM
ejpam-6458	592	39	(	(	PUNCT
ejpam-6458	592	40	a1	a1	NOUN
ejpam-6458	592	41	+	+	CCONJ
ejpam-6458	592	42	a3	a3	NOUN
ejpam-6458	592	43	+	+	CCONJ
ejpam-6458	592	44	2i−	2i−	NUM
ejpam-6458	592	45	2j	2j	NOUN
ejpam-6458	592	46	+	+	CCONJ
ejpam-6458	592	47	2k	2k	NOUN
ejpam-6458	592	48	−	−	NOUN
ejpam-6458	592	49	1	1	NUM
ejpam-6458	592	50	)	)	PUNCT
ejpam-6458	592	51	,	,	PUNCT
ejpam-6458	592	52	s−	s−	PROPN
ejpam-6458	592	53	ik	ik	PROPN
ejpam-6458	592	54	=	=	SYM
ejpam-6458	592	55	1	1	NUM
ejpam-6458	592	56	2	2	NUM
ejpam-6458	592	57	(	(	PUNCT
ejpam-6458	592	58	−a1	−a1	PROPN
ejpam-6458	592	59	+	+	SYM
ejpam-6458	592	60	a3	a3	NOUN
ejpam-6458	592	61	−	−	PROPN
ejpam-6458	592	62	2i+	2i+	NUM
ejpam-6458	592	63	2k	2k	NOUN
ejpam-6458	592	64	−	−	NOUN
ejpam-6458	592	65	1	1	NUM
ejpam-6458	592	66	)	)	PUNCT
ejpam-6458	592	67	,	,	PUNCT
ejpam-6458	592	68	t+	t+	X
ejpam-6458	592	69	k	k	NOUN
ejpam-6458	592	70	=	=	SYM
ejpam-6458	592	71	1	1	NUM
ejpam-6458	592	72	2	2	NUM
ejpam-6458	592	73	(	(	PUNCT
ejpam-6458	592	74	a1	a1	NOUN
ejpam-6458	592	75	+	+	CCONJ
ejpam-6458	592	76	a2	a2	PROPN
ejpam-6458	592	77	+	+	CCONJ
ejpam-6458	592	78	a4	a4	NOUN
ejpam-6458	592	79	+	+	CCONJ
ejpam-6458	592	80	2k	2k	NOUN
ejpam-6458	592	81	−	−	NOUN
ejpam-6458	592	82	1	1	NUM
ejpam-6458	592	83	)	)	PUNCT
ejpam-6458	592	84	,	,	PUNCT
ejpam-6458	592	85	t−	t−	PROPN
ejpam-6458	592	86	jk	jk	PROPN
ejpam-6458	592	87	=	=	SYM
ejpam-6458	592	88	1	1	NUM
ejpam-6458	592	89	2	2	NUM
ejpam-6458	592	90	(	(	PUNCT
ejpam-6458	592	91	−a1	−a1	PROPN
ejpam-6458	592	92	−	−	PROPN
ejpam-6458	592	93	a2	a2	PROPN
ejpam-6458	592	94	+	+	CCONJ
ejpam-6458	592	95	a4	a4	NOUN
ejpam-6458	592	96	−	−	NOUN
ejpam-6458	592	97	2j	2j	NOUN
ejpam-6458	592	98	+	+	CCONJ
ejpam-6458	592	99	2k	2k	NOUN
ejpam-6458	592	100	−	−	NOUN
ejpam-6458	592	101	1	1	NUM
ejpam-6458	592	102	)	)	PUNCT
ejpam-6458	592	103	,	,	PUNCT
ejpam-6458	592	104	where	where	SCONJ
ejpam-6458	592	105	i	i	PRON
ejpam-6458	592	106	,	,	PUNCT
ejpam-6458	592	107	j	j	PROPN
ejpam-6458	592	108	,	,	PUNCT
ejpam-6458	592	109	k	k	PROPN
ejpam-6458	592	110	∈	∈	PROPN
ejpam-6458	592	111	z.	z.	PROPN
ejpam-6458	592	112	(	(	PUNCT
ejpam-6458	592	113	5.17	5.17	NUM
ejpam-6458	592	114	)	)	PUNCT
ejpam-6458	592	115	m.	m.	NOUN
ejpam-6458	592	116	andelić	andelić	PROPN
ejpam-6458	592	117	et	et	PROPN
ejpam-6458	592	118	al	al	PROPN
ejpam-6458	592	119	.	.	PUNCT
ejpam-6458	592	120	/	/	SYM
ejpam-6458	592	121	eur	eur	PROPN
ejpam-6458	592	122	.	.	PUNCT
ejpam-6458	593	1	j.	j.	PROPN
ejpam-6458	593	2	pure	pure	PROPN
ejpam-6458	593	3	appl	appl	PROPN
ejpam-6458	593	4	.	.	PROPN
ejpam-6458	593	5	math	math	PROPN
ejpam-6458	593	6	,	,	PUNCT
ejpam-6458	593	7	18	18	NUM
ejpam-6458	593	8	(	(	PUNCT
ejpam-6458	593	9	3	3	NUM
ejpam-6458	593	10	)	)	PUNCT
ejpam-6458	593	11	(	(	PUNCT
ejpam-6458	593	12	2025	2025	NUM
ejpam-6458	593	13	)	)	PUNCT
ejpam-6458	593	14	,	,	PUNCT
ejpam-6458	593	15	6458	6458	NUM
ejpam-6458	593	16	15	15	NUM
ejpam-6458	593	17	of	of	ADP
ejpam-6458	593	18	21	21	NUM
ejpam-6458	593	19	consider	consider	VERB
ejpam-6458	593	20	the	the	DET
ejpam-6458	593	21	vector	vector	NOUN
ejpam-6458	593	22	space	space	NOUN
ejpam-6458	593	23	v	v	NOUN
ejpam-6458	593	24	(	(	PUNCT
ejpam-6458	593	25	a1	a1	PROPN
ejpam-6458	593	26	,	,	PUNCT
ejpam-6458	593	27	a2	a2	PROPN
ejpam-6458	593	28	,	,	PUNCT
ejpam-6458	593	29	a3	a3	NOUN
ejpam-6458	593	30	,	,	PUNCT
ejpam-6458	593	31	a4	a4	PROPN
ejpam-6458	593	32	,	,	PUNCT
ejpam-6458	593	33	η	η	NOUN
ejpam-6458	593	34	)	)	PUNCT
ejpam-6458	593	35	=	=	SYM
ejpam-6458	593	36	spanc{vijk	spanc{vijk	X
ejpam-6458	594	1	|	|	ADV
ejpam-6458	594	2	i	i	PROPN
ejpam-6458	594	3	,	,	PUNCT
ejpam-6458	594	4	j	j	PROPN
ejpam-6458	594	5	,	,	PUNCT
ejpam-6458	594	6	k	k	PROPN
ejpam-6458	594	7	∈	∈	PROPN
ejpam-6458	595	1	z	z	X
ejpam-6458	595	2	}	}	PUNCT
ejpam-6458	595	3	and	and	CCONJ
ejpam-6458	595	4	define	define	VERB
ejpam-6458	595	5	the	the	DET
ejpam-6458	595	6	following	follow	VERB
ejpam-6458	595	7	operators	operator	NOUN
ejpam-6458	595	8	on	on	ADP
ejpam-6458	595	9	v	v	PROPN
ejpam-6458	595	10	(	(	PUNCT
ejpam-6458	595	11	a1	a1	PROPN
ejpam-6458	595	12	,	,	PUNCT
ejpam-6458	595	13	a2	a2	PROPN
ejpam-6458	595	14	,	,	PUNCT
ejpam-6458	595	15	a3	a3	NOUN
ejpam-6458	595	16	,	,	PUNCT
ejpam-6458	595	17	a4	a4	PROPN
ejpam-6458	595	18	,	,	PUNCT
ejpam-6458	595	19	η	η	NOUN
ejpam-6458	595	20	)	)	PUNCT
ejpam-6458	595	21	(	(	PUNCT
ejpam-6458	595	22	using	use	VERB
ejpam-6458	595	23	the	the	DET
ejpam-6458	595	24	same	same	ADJ
ejpam-6458	595	25	letters	letter	NOUN
ejpam-6458	595	26	as	as	ADP
ejpam-6458	595	27	for	for	ADP
ejpam-6458	595	28	the	the	DET
ejpam-6458	595	29	generators	generator	NOUN
ejpam-6458	595	30	of	of	ADP
ejpam-6458	595	31	g	g	NOUN
ejpam-6458	595	32	):	):	PUNCT
ejpam-6458	595	33	h1(vijk	h1(vijk	NOUN
ejpam-6458	595	34	)	)	PUNCT
ejpam-6458	596	1	=	=	SYM
ejpam-6458	596	2	h	h	NOUN
ejpam-6458	596	3	(	(	PUNCT
ejpam-6458	596	4	1	1	NUM
ejpam-6458	596	5	)	)	PUNCT
ejpam-6458	596	6	ij	ij	NOUN
ejpam-6458	596	7	vijk	vijk	NOUN
ejpam-6458	596	8	,	,	PUNCT
ejpam-6458	596	9	h2(vijk	h2(vijk	X
ejpam-6458	596	10	)	)	PUNCT
ejpam-6458	596	11	=	=	SYM
ejpam-6458	597	1	h	h	NOUN
ejpam-6458	597	2	(	(	PUNCT
ejpam-6458	597	3	2	2	NUM
ejpam-6458	597	4	)	)	PUNCT
ejpam-6458	597	5	ij	ij	NOUN
ejpam-6458	597	6	vijk	vijk	NOUN
ejpam-6458	597	7	,	,	PUNCT
ejpam-6458	597	8	e01(vijk	e01(vijk	NOUN
ejpam-6458	597	9	)	)	PUNCT
ejpam-6458	597	10	=	=	PUNCT
ejpam-6458	597	11	s+	s+	PUNCT
ejpam-6458	597	12	ijkvi+1,j	ijkvi+1,j	PROPN
ejpam-6458	597	13	,	,	PUNCT
ejpam-6458	597	14	k	k	PROPN
ejpam-6458	597	15	,	,	PUNCT
ejpam-6458	597	16	f01(vijk	f01(vijk	NOUN
ejpam-6458	597	17	)	)	PUNCT
ejpam-6458	597	18	=	=	SYM
ejpam-6458	597	19	s−	s−	PROPN
ejpam-6458	597	20	ikvi−1,j	ikvi−1,j	NOUN
ejpam-6458	597	21	,	,	PUNCT
ejpam-6458	597	22	k	k	PROPN
ejpam-6458	597	23	,	,	PUNCT
ejpam-6458	597	24	e10(vijk	e10(vijk	NOUN
ejpam-6458	597	25	)	)	PUNCT
ejpam-6458	597	26	=	=	SYM
ejpam-6458	597	27	s−	s−	PROPN
ejpam-6458	597	28	ikq	ikq	NOUN
ejpam-6458	597	29	+	+	CCONJ
ejpam-6458	598	1	j+1,kvi	j+1,kvi	PROPN
ejpam-6458	598	2	,	,	PUNCT
ejpam-6458	598	3	j+1,k+1	j+1,k+1	NOUN
ejpam-6458	598	4	+	+	CCONJ
ejpam-6458	598	5	t−	t−	PROPN
ejpam-6458	598	6	j+1,kq	j+1,kq	PROPN
ejpam-6458	598	7	−	−	PROPN
ejpam-6458	598	8	j+1,kvi	j+1,kvi	PROPN
ejpam-6458	598	9	,	,	PUNCT
ejpam-6458	598	10	j+1,k	j+1,k	PROPN
ejpam-6458	598	11	,	,	PUNCT
ejpam-6458	598	12	f10(vijk	f10(vijk	PROPN
ejpam-6458	598	13	)	)	PUNCT
ejpam-6458	598	14	=	=	PUNCT
ejpam-6458	598	15	s+	s+	PUNCT
ejpam-6458	598	16	ijkq	ijkq	NOUN
ejpam-6458	598	17	+	+	CCONJ
ejpam-6458	598	18	j+1,kvi	j+1,kvi	PROPN
ejpam-6458	598	19	,	,	PUNCT
ejpam-6458	598	20	j−1,k	j−1,k	PROPN
ejpam-6458	598	21	+	+	CCONJ
ejpam-6458	598	22	t+	t+	NOUN
ejpam-6458	598	23	k−1q	k−1q	NOUN
ejpam-6458	598	24	−	−	PROPN
ejpam-6458	598	25	j+1,kvi	j+1,kvi	PROPN
ejpam-6458	598	26	,	,	PUNCT
ejpam-6458	598	27	j−1,k−1	j−1,k−1	PART
ejpam-6458	598	28	,	,	PUNCT
ejpam-6458	598	29	e11(vijk	e11(vijk	X
ejpam-6458	598	30	)	)	PUNCT
ejpam-6458	598	31	=	=	SYM
ejpam-6458	598	32	−s+	−s+	ADP
ejpam-6458	598	33	ijkq	ijkq	NOUN
ejpam-6458	598	34	+	+	CCONJ
ejpam-6458	598	35	j+1,kvi+1,j+1,k+1	j+1,kvi+1,j+1,k+1	VERB
ejpam-6458	598	36	+	+	CCONJ
ejpam-6458	598	37	t−	t−	PROPN
ejpam-6458	598	38	j+1,kq	j+1,kq	PROPN
ejpam-6458	598	39	−	−	PROPN
ejpam-6458	598	40	j+1,kvi+1,j+1,k	j+1,kvi+1,j+1,k	PROPN
ejpam-6458	598	41	,	,	PUNCT
ejpam-6458	598	42	f11(vijk	f11(vijk	PROPN
ejpam-6458	598	43	)	)	PUNCT
ejpam-6458	598	44	=	=	SYM
ejpam-6458	599	1	s−	s−	PROPN
ejpam-6458	599	2	i	i	PRON
ejpam-6458	599	3	,	,	PUNCT
ejpam-6458	599	4	kq	kq	PROPN
ejpam-6458	599	5	+	+	CCONJ
ejpam-6458	599	6	j+1,kvi−1,j−1,k	j+1,kvi−1,j−1,k	PROPN
ejpam-6458	599	7	−	−	PROPN
ejpam-6458	599	8	t+	t+	PUNCT
ejpam-6458	599	9	k−1q	k−1q	NOUN
ejpam-6458	599	10	−	−	PROPN
ejpam-6458	599	11	j+1,kvi−1,j−1,k−1	j+1,kvi−1,j−1,k−1	PROPN
ejpam-6458	599	12	,	,	PUNCT
ejpam-6458	599	13	e21(vijk	e21(vijk	NUM
ejpam-6458	599	14	)	)	PUNCT
ejpam-6458	599	15	=	=	NOUN
ejpam-6458	600	1	2t−	2t−	NOUN
ejpam-6458	600	2	j+1,kvi+1,j+2,k+1	j+1,kvi+1,j+2,k+1	ADJ
ejpam-6458	600	3	,	,	PUNCT
ejpam-6458	600	4	f21(vijk	f21(vijk	NOUN
ejpam-6458	600	5	)	)	PUNCT
ejpam-6458	600	6	=	=	SYM
ejpam-6458	600	7	2t+	2t+	NUM
ejpam-6458	600	8	k−1vi−1,j−2,k−1	k−1vi−1,j−2,k−1	PROPN
ejpam-6458	600	9	.	.	PUNCT
ejpam-6458	601	1	(	(	PUNCT
ejpam-6458	601	2	5.18	5.18	NUM
ejpam-6458	601	3	)	)	PUNCT
ejpam-6458	601	4	these	these	DET
ejpam-6458	601	5	formulas	formula	NOUN
ejpam-6458	601	6	define	define	VERB
ejpam-6458	601	7	a	a	DET
ejpam-6458	601	8	γ	γ	NOUN
ejpam-6458	601	9	-	-	PUNCT
ejpam-6458	601	10	module	module	NOUN
ejpam-6458	601	11	structure	structure	NOUN
ejpam-6458	601	12	on	on	ADP
ejpam-6458	601	13	v	v	PROPN
ejpam-6458	601	14	(	(	PUNCT
ejpam-6458	601	15	a1	a1	PROPN
ejpam-6458	601	16	,	,	PUNCT
ejpam-6458	601	17	a2	a2	PROPN
ejpam-6458	601	18	,	,	PUNCT
ejpam-6458	601	19	a3	a3	NOUN
ejpam-6458	601	20	,	,	PUNCT
ejpam-6458	601	21	a4	a4	PROPN
ejpam-6458	601	22	,	,	PUNCT
ejpam-6458	601	23	η	η	NOUN
ejpam-6458	601	24	)	)	PUNCT
ejpam-6458	601	25	,	,	PUNCT
ejpam-6458	601	26	but	but	CCONJ
ejpam-6458	601	27	at	at	ADP
ejpam-6458	601	28	this	this	DET
ejpam-6458	601	29	point	point	NOUN
ejpam-6458	601	30	we	we	PRON
ejpam-6458	601	31	can	can	AUX
ejpam-6458	601	32	not	not	PART
ejpam-6458	601	33	claim	claim	VERB
ejpam-6458	601	34	a	a	DET
ejpam-6458	601	35	g	g	NOUN
ejpam-6458	601	36	-	-	PUNCT
ejpam-6458	601	37	module	module	NOUN
ejpam-6458	601	38	structure	structure	NOUN
ejpam-6458	601	39	.	.	PUNCT
ejpam-6458	602	1	lemma	lemma	PROPN
ejpam-6458	602	2	5.3	5.3	NUM
ejpam-6458	602	3	.	.	PUNCT
ejpam-6458	603	1	the	the	DET
ejpam-6458	603	2	subalgebra	subalgebra	NOUN
ejpam-6458	603	3	γ	γ	PROPN
ejpam-6458	603	4	has	have	VERB
ejpam-6458	603	5	a	a	DET
ejpam-6458	603	6	simple	simple	ADJ
ejpam-6458	603	7	spectrum	spectrum	NOUN
ejpam-6458	603	8	on	on	ADP
ejpam-6458	603	9	v	v	PROPN
ejpam-6458	603	10	(	(	PUNCT
ejpam-6458	603	11	a1	a1	PROPN
ejpam-6458	603	12	,	,	PUNCT
ejpam-6458	603	13	a2	a2	PROPN
ejpam-6458	603	14	,	,	PUNCT
ejpam-6458	603	15	a3	a3	NOUN
ejpam-6458	603	16	,	,	PUNCT
ejpam-6458	603	17	a4	a4	PROPN
ejpam-6458	603	18	,	,	PUNCT
ejpam-6458	603	19	η	η	NOUN
ejpam-6458	603	20	)	)	PUNCT
ejpam-6458	603	21	,	,	PUNCT
ejpam-6458	603	22	and	and	CCONJ
ejpam-6458	603	23	hence	hence	ADV
ejpam-6458	603	24	separates	separate	VERB
ejpam-6458	603	25	the	the	DET
ejpam-6458	603	26	basis	basis	NOUN
ejpam-6458	603	27	elements	element	NOUN
ejpam-6458	603	28	vijk	vijk	ADV
ejpam-6458	603	29	,	,	PUNCT
ejpam-6458	603	30	if	if	SCONJ
ejpam-6458	603	31	and	and	CCONJ
ejpam-6458	603	32	only	only	ADV
ejpam-6458	603	33	if	if	SCONJ
ejpam-6458	603	34	a3	a3	NOUN
ejpam-6458	603	35	/∈	/∈	PUNCT
ejpam-6458	604	1	z.	z.	PROPN
ejpam-6458	604	2	proof	proof	NOUN
ejpam-6458	604	3	.	.	PUNCT
ejpam-6458	605	1	we	we	PRON
ejpam-6458	605	2	need	need	VERB
ejpam-6458	605	3	to	to	PART
ejpam-6458	605	4	show	show	VERB
ejpam-6458	605	5	that	that	SCONJ
ejpam-6458	605	6	γ	γ	PROPN
ejpam-6458	605	7	acts	act	VERB
ejpam-6458	605	8	with	with	ADP
ejpam-6458	605	9	different	different	ADJ
ejpam-6458	605	10	characters	character	NOUN
ejpam-6458	605	11	on	on	ADP
ejpam-6458	605	12	basis	basis	NOUN
ejpam-6458	605	13	elements	element	NOUN
ejpam-6458	605	14	vi	vi	PROPN
ejpam-6458	605	15	,	,	PUNCT
ejpam-6458	605	16	j	j	PROPN
ejpam-6458	605	17	,	,	PUNCT
ejpam-6458	605	18	k.	k.	PROPN
ejpam-6458	606	1	it	it	PRON
ejpam-6458	606	2	is	be	AUX
ejpam-6458	606	3	sufficient	sufficient	ADJ
ejpam-6458	606	4	to	to	PART
ejpam-6458	606	5	consider	consider	VERB
ejpam-6458	606	6	vectors	vector	NOUN
ejpam-6458	606	7	from	from	ADP
ejpam-6458	606	8	the	the	DET
ejpam-6458	606	9	same	same	ADJ
ejpam-6458	606	10	weight	weight	NOUN
ejpam-6458	606	11	space	space	NOUN
ejpam-6458	606	12	.	.	PUNCT
ejpam-6458	607	1	suppose	suppose	VERB
ejpam-6458	607	2	h1(vijk	h1(vijk	NOUN
ejpam-6458	607	3	)	)	PUNCT
ejpam-6458	607	4	=	=	PUNCT
ejpam-6458	608	1	(	(	PUNCT
ejpam-6458	608	2	a1	a1	NOUN
ejpam-6458	608	3	+	+	X
ejpam-6458	608	4	2i−	2i−	NUM
ejpam-6458	608	5	j)vijk	j)vijk	X
ejpam-6458	609	1	=	=	SYM
ejpam-6458	609	2	λvijk	λvijk	X
ejpam-6458	609	3	,	,	PUNCT
ejpam-6458	609	4	h2(vijk	h2(vijk	NOUN
ejpam-6458	609	5	)	)	PUNCT
ejpam-6458	609	6	=	=	SYM
ejpam-6458	609	7	(	(	PUNCT
ejpam-6458	609	8	a2	a2	PROPN
ejpam-6458	609	9	−	−	PROPN
ejpam-6458	609	10	2i+	2i+	NUM
ejpam-6458	609	11	2j)vijk	2j)vijk	NUM
ejpam-6458	609	12	=	=	SYM
ejpam-6458	609	13	µvijk	µvijk	X
ejpam-6458	609	14	,	,	PUNCT
ejpam-6458	609	15	for	for	ADP
ejpam-6458	609	16	some	some	DET
ejpam-6458	609	17	fixed	fix	VERB
ejpam-6458	609	18	λ	λ	PROPN
ejpam-6458	609	19	and	and	CCONJ
ejpam-6458	609	20	µ.	µ.	NOUN
ejpam-6458	609	21	then	then	ADV
ejpam-6458	610	1	i	i	PRON
ejpam-6458	610	2	and	and	CCONJ
ejpam-6458	610	3	j	j	PROPN
ejpam-6458	610	4	are	be	AUX
ejpam-6458	610	5	uniquely	uniquely	ADV
ejpam-6458	610	6	determined	determined	ADJ
ejpam-6458	610	7	:	:	PUNCT
ejpam-6458	610	8	j	j	PROPN
ejpam-6458	610	9	=	=	SYM
ejpam-6458	610	10	λ	λ	PROPN
ejpam-6458	610	11	+	+	CCONJ
ejpam-6458	610	12	µ	µ	PRON
ejpam-6458	610	13	−	−	NOUN
ejpam-6458	610	14	a1	a1	NOUN
ejpam-6458	610	15	−	−	PROPN
ejpam-6458	610	16	a2	a2	PROPN
ejpam-6458	610	17	and	and	CCONJ
ejpam-6458	610	18	i	i	NOUN
ejpam-6458	610	19	=	=	NOUN
ejpam-6458	611	1	1	1	NUM
ejpam-6458	611	2	2(λ	2(λ	NUM
ejpam-6458	612	1	+	+	CCONJ
ejpam-6458	612	2	j	j	PROPN
ejpam-6458	612	3	−	−	PROPN
ejpam-6458	612	4	a1	a1	NOUN
ejpam-6458	612	5	)	)	PUNCT
ejpam-6458	612	6	.	.	PUNCT
ejpam-6458	613	1	hence	hence	ADV
ejpam-6458	613	2	,	,	PUNCT
ejpam-6458	613	3	basis	basis	NOUN
ejpam-6458	613	4	elements	element	NOUN
ejpam-6458	613	5	of	of	ADP
ejpam-6458	613	6	this	this	DET
ejpam-6458	613	7	weight	weight	NOUN
ejpam-6458	613	8	subspace	subspace	NOUN
ejpam-6458	613	9	differ	differ	VERB
ejpam-6458	613	10	by	by	ADP
ejpam-6458	613	11	the	the	DET
ejpam-6458	613	12	third	third	ADJ
ejpam-6458	613	13	index	index	NOUN
ejpam-6458	613	14	.	.	PUNCT
ejpam-6458	614	1	consider	consider	VERB
ejpam-6458	614	2	vijk1	vijk1	NOUN
ejpam-6458	614	3	and	and	CCONJ
ejpam-6458	614	4	vijk2	vijk2	NOUN
ejpam-6458	614	5	for	for	ADP
ejpam-6458	614	6	arbitrary	arbitrary	ADJ
ejpam-6458	614	7	integer	integer	NOUN
ejpam-6458	614	8	i	i	PROPN
ejpam-6458	614	9	,	,	PUNCT
ejpam-6458	614	10	j	j	PROPN
ejpam-6458	614	11	,	,	PUNCT
ejpam-6458	614	12	k1	k1	PROPN
ejpam-6458	614	13	,	,	PUNCT
ejpam-6458	614	14	k2	k2	NOUN
ejpam-6458	614	15	.	.	PUNCT
ejpam-6458	615	1	we	we	PRON
ejpam-6458	615	2	have	have	VERB
ejpam-6458	615	3	c1(vijk	c1(vijk	NOUN
ejpam-6458	615	4	)	)	PUNCT
ejpam-6458	615	5	=	=	PUNCT
ejpam-6458	615	6	f01e01(vijk	f01e01(vijk	X
ejpam-6458	615	7	)	)	PUNCT
ejpam-6458	616	1	=	=	VERB
ejpam-6458	617	1	f01(s	f01(	NOUN
ejpam-6458	618	1	+	+	CCONJ
ejpam-6458	618	2	i	i	PROPN
ejpam-6458	618	3	,	,	PUNCT
ejpam-6458	618	4	j	j	PROPN
ejpam-6458	618	5	,	,	PUNCT
ejpam-6458	618	6	kvi+1jk	kvi+1jk	PROPN
ejpam-6458	618	7	)	)	PUNCT
ejpam-6458	618	8	=	=	SYM
ejpam-6458	618	9	s−	s−	PROPN
ejpam-6458	618	10	i+1,ks	i+1,ks	PROPN
ejpam-6458	619	1	+	+	CCONJ
ejpam-6458	619	2	i	i	PROPN
ejpam-6458	619	3	,	,	PUNCT
ejpam-6458	619	4	j	j	PROPN
ejpam-6458	619	5	,	,	PUNCT
ejpam-6458	619	6	k(vijk	k(vijk	PROPN
ejpam-6458	619	7	)	)	PUNCT
ejpam-6458	619	8	(	(	PUNCT
ejpam-6458	619	9	5.19	5.19	NUM
ejpam-6458	619	10	)	)	PUNCT
ejpam-6458	619	11	suppose	suppose	VERB
ejpam-6458	619	12	that	that	SCONJ
ejpam-6458	619	13	c1	c1	PROPN
ejpam-6458	619	14	has	have	VERB
ejpam-6458	619	15	the	the	DET
ejpam-6458	619	16	same	same	ADJ
ejpam-6458	619	17	value	value	NOUN
ejpam-6458	619	18	on	on	ADP
ejpam-6458	619	19	vijk1	vijk1	NOUN
ejpam-6458	619	20	and	and	CCONJ
ejpam-6458	619	21	vijk2	vijk2	NOUN
ejpam-6458	619	22	.	.	PUNCT
ejpam-6458	620	1	then	then	ADV
ejpam-6458	620	2	we	we	PRON
ejpam-6458	620	3	have	have	VERB
ejpam-6458	620	4	the	the	DET
ejpam-6458	620	5	equation	equation	NOUN
ejpam-6458	620	6	0	0	NUM
ejpam-6458	621	1	=	=	SYM
ejpam-6458	621	2	s−	s−	PROPN
ejpam-6458	621	3	i+1,k1	i+1,k1	ADV
ejpam-6458	621	4	s+	s+	PUNCT
ejpam-6458	621	5	i	i	PRON
ejpam-6458	621	6	,	,	PUNCT
ejpam-6458	621	7	j	j	PROPN
ejpam-6458	621	8	,	,	PUNCT
ejpam-6458	621	9	k1	k1	PROPN
ejpam-6458	621	10	−s−	−s−	PROPN
ejpam-6458	621	11	i+1,k2	i+1,k2	PROPN
ejpam-6458	621	12	s+	s+	PUNCT
ejpam-6458	621	13	i	i	PRON
ejpam-6458	621	14	,	,	PUNCT
ejpam-6458	621	15	j	j	PROPN
ejpam-6458	621	16	,	,	PUNCT
ejpam-6458	621	17	k2	k2	PROPN
ejpam-6458	621	18	which	which	PRON
ejpam-6458	621	19	simplifies	simplify	VERB
ejpam-6458	621	20	to	to	ADP
ejpam-6458	621	21	0	0	NUM
ejpam-6458	621	22	=	=	SYM
ejpam-6458	621	23	1	1	NUM
ejpam-6458	621	24	4(k1−	4(k1−	NUM
ejpam-6458	621	25	k2)(a3−	k2)(a3−	NOUN
ejpam-6458	621	26	j+	j+	NUM
ejpam-6458	621	27	k1	k1	NOUN
ejpam-6458	621	28	+	+	CCONJ
ejpam-6458	621	29	k2−	k2−	PROPN
ejpam-6458	621	30	2	2	NUM
ejpam-6458	621	31	)	)	PUNCT
ejpam-6458	621	32	.	.	PUNCT
ejpam-6458	622	1	since	since	SCONJ
ejpam-6458	622	2	k1	k1	PROPN
ejpam-6458	622	3	̸=	̸=	PROPN
ejpam-6458	622	4	k2	k2	NOUN
ejpam-6458	622	5	,	,	PUNCT
ejpam-6458	622	6	it	it	PRON
ejpam-6458	622	7	follows	follow	VERB
ejpam-6458	622	8	that	that	DET
ejpam-6458	622	9	a3	a3	NOUN
ejpam-6458	622	10	=	=	SYM
ejpam-6458	623	1	j	j	PROPN
ejpam-6458	623	2	−	−	PROPN
ejpam-6458	623	3	k1	k1	PROPN
ejpam-6458	623	4	−	−	PROPN
ejpam-6458	623	5	k2	k2	PROPN
ejpam-6458	623	6	+	+	CCONJ
ejpam-6458	623	7	2	2	NUM
ejpam-6458	623	8	,	,	PUNCT
ejpam-6458	623	9	which	which	PRON
ejpam-6458	623	10	must	must	AUX
ejpam-6458	623	11	be	be	AUX
ejpam-6458	623	12	an	an	DET
ejpam-6458	623	13	integer	integer	NOUN
ejpam-6458	623	14	.	.	PUNCT
ejpam-6458	624	1	□	□	PUNCT
ejpam-6458	624	2	denote	denote	VERB
ejpam-6458	624	3	v1(a1	v1(a1	NOUN
ejpam-6458	624	4	,	,	PUNCT
ejpam-6458	624	5	a2	a2	PROPN
ejpam-6458	624	6	,	,	PUNCT
ejpam-6458	624	7	a3	a3	NOUN
ejpam-6458	624	8	,	,	PUNCT
ejpam-6458	624	9	η	η	NOUN
ejpam-6458	624	10	)	)	PUNCT
ejpam-6458	624	11	=	=	SYM
ejpam-6458	624	12	v	v	X
ejpam-6458	624	13	(	(	PUNCT
ejpam-6458	624	14	a1	a1	PROPN
ejpam-6458	624	15	,	,	PUNCT
ejpam-6458	624	16	a2	a2	PROPN
ejpam-6458	624	17	,	,	PUNCT
ejpam-6458	624	18	a3	a3	NOUN
ejpam-6458	624	19	,	,	PUNCT
ejpam-6458	624	20	a3	a3	NOUN
ejpam-6458	624	21	,	,	PUNCT
ejpam-6458	624	22	η	η	NOUN
ejpam-6458	624	23	)	)	PUNCT
ejpam-6458	624	24	and	and	CCONJ
ejpam-6458	624	25	v2(a1	v2(a1	NOUN
ejpam-6458	624	26	,	,	PUNCT
ejpam-6458	624	27	a2	a2	PROPN
ejpam-6458	624	28	,	,	PUNCT
ejpam-6458	624	29	a3	a3	NOUN
ejpam-6458	624	30	,	,	PUNCT
ejpam-6458	624	31	a4	a4	NOUN
ejpam-6458	624	32	)	)	PUNCT
ejpam-6458	624	33	=	=	SYM
ejpam-6458	624	34	v	v	X
ejpam-6458	624	35	(	(	PUNCT
ejpam-6458	624	36	a1	a1	PROPN
ejpam-6458	624	37	,	,	PUNCT
ejpam-6458	624	38	a2	a2	PROPN
ejpam-6458	624	39	,	,	PUNCT
ejpam-6458	624	40	a3	a3	NOUN
ejpam-6458	624	41	,	,	PUNCT
ejpam-6458	624	42	a4	a4	NOUN
ejpam-6458	624	43	,	,	PUNCT
ejpam-6458	624	44	0	0	NUM
ejpam-6458	624	45	)	)	PUNCT
ejpam-6458	624	46	and	and	CCONJ
ejpam-6458	624	47	ξ	ξ	X
ejpam-6458	624	48	=	=	SYM
ejpam-6458	624	49	2(η	2(η	NUM
ejpam-6458	624	50	+	+	CCONJ
ejpam-6458	624	51	1)(η	1)(η	NUM
ejpam-6458	624	52	−	−	NOUN
ejpam-6458	624	53	2	2	NUM
ejpam-6458	624	54	)	)	PUNCT
ejpam-6458	624	55	.	.	PUNCT
ejpam-6458	625	1	theorem	theorem	VERB
ejpam-6458	625	2	5.4	5.4	NUM
ejpam-6458	625	3	.	.	PUNCT
ejpam-6458	626	1	let	let	VERB
ejpam-6458	626	2	v	v	NOUN
ejpam-6458	626	3	=	=	SYM
ejpam-6458	626	4	v	v	PROPN
ejpam-6458	626	5	(	(	PUNCT
ejpam-6458	626	6	a1	a1	PROPN
ejpam-6458	626	7	,	,	PUNCT
ejpam-6458	626	8	a2	a2	PROPN
ejpam-6458	626	9	,	,	PUNCT
ejpam-6458	626	10	a3	a3	NOUN
ejpam-6458	626	11	,	,	PUNCT
ejpam-6458	626	12	a4	a4	PROPN
ejpam-6458	626	13	,	,	PUNCT
ejpam-6458	626	14	η	η	NOUN
ejpam-6458	626	15	)	)	PUNCT
ejpam-6458	626	16	.	.	PUNCT
ejpam-6458	627	1	then	then	ADV
ejpam-6458	627	2	1	1	X
ejpam-6458	627	3	.	.	X
ejpam-6458	627	4	v	v	NOUN
ejpam-6458	627	5	is	be	AUX
ejpam-6458	627	6	a	a	DET
ejpam-6458	627	7	g	g	NOUN
ejpam-6458	627	8	-	-	PUNCT
ejpam-6458	627	9	module	module	NOUN
ejpam-6458	627	10	if	if	SCONJ
ejpam-6458	627	11	and	and	CCONJ
ejpam-6458	627	12	only	only	ADV
ejpam-6458	627	13	if	if	SCONJ
ejpam-6458	627	14	v	v	NOUN
ejpam-6458	627	15	=	=	SYM
ejpam-6458	627	16	v1(a1	v1(a1	NOUN
ejpam-6458	627	17	,	,	PUNCT
ejpam-6458	627	18	a2	a2	PROPN
ejpam-6458	627	19	,	,	PUNCT
ejpam-6458	627	20	a3	a3	NOUN
ejpam-6458	627	21	,	,	PUNCT
ejpam-6458	627	22	η	η	NOUN
ejpam-6458	627	23	)	)	PUNCT
ejpam-6458	627	24	with	with	ADP
ejpam-6458	627	25	a3	a3	NOUN
ejpam-6458	627	26	/∈	/∈	PUNCT
ejpam-6458	628	1	z	z	NOUN
ejpam-6458	628	2	,	,	PUNCT
ejpam-6458	628	3	or	or	CCONJ
ejpam-6458	628	4	v	v	NOUN
ejpam-6458	628	5	=	=	SYM
ejpam-6458	628	6	v2(a1	v2(a1	NOUN
ejpam-6458	628	7	,	,	PUNCT
ejpam-6458	628	8	a2	a2	PROPN
ejpam-6458	628	9	,	,	PUNCT
ejpam-6458	628	10	a3	a3	NOUN
ejpam-6458	628	11	,	,	PUNCT
ejpam-6458	628	12	a4	a4	NOUN
ejpam-6458	628	13	)	)	PUNCT
ejpam-6458	628	14	.	.	PUNCT
ejpam-6458	629	1	2	2	X
ejpam-6458	629	2	.	.	X
ejpam-6458	629	3	the	the	DET
ejpam-6458	629	4	g	g	NOUN
ejpam-6458	629	5	-	-	PUNCT
ejpam-6458	629	6	module	module	NOUN
ejpam-6458	629	7	v	v	NOUN
ejpam-6458	629	8	is	be	AUX
ejpam-6458	629	9	a	a	DET
ejpam-6458	629	10	torsion	torsion	NOUN
ejpam-6458	629	11	free	free	ADJ
ejpam-6458	629	12	γ	γ	X
ejpam-6458	629	13	-	-	ADJ
ejpam-6458	629	14	pointed	point	VERB
ejpam-6458	629	15	g	g	NOUN
ejpam-6458	629	16	-	-	PUNCT
ejpam-6458	629	17	module	module	NOUN
ejpam-6458	629	18	if	if	SCONJ
ejpam-6458	629	19	and	and	CCONJ
ejpam-6458	629	20	only	only	ADV
ejpam-6458	629	21	if	if	SCONJ
ejpam-6458	629	22	s+	s+	PUNCT
ejpam-6458	629	23	ijks	ijks	VERB
ejpam-6458	629	24	−	−	PROPN
ejpam-6458	629	25	ikt	ikt	PROPN
ejpam-6458	629	26	−	−	PROPN
ejpam-6458	629	27	jkt	jkt	NOUN
ejpam-6458	629	28	+	+	CCONJ
ejpam-6458	629	29	k	k	PROPN
ejpam-6458	629	30	̸=	̸=	PROPN
ejpam-6458	629	31	0	0	NUM
ejpam-6458	629	32	for	for	ADP
ejpam-6458	629	33	all	all	DET
ejpam-6458	629	34	i	i	PROPN
ejpam-6458	629	35	,	,	PUNCT
ejpam-6458	629	36	j	j	PROPN
ejpam-6458	629	37	,	,	PUNCT
ejpam-6458	629	38	k	k	PROPN
ejpam-6458	629	39	∈	∈	PROPN
ejpam-6458	629	40	z.	z.	PROPN
ejpam-6458	630	1	3	3	NUM
ejpam-6458	630	2	.	.	PUNCT
ejpam-6458	631	1	the	the	DET
ejpam-6458	631	2	torsion	torsion	NOUN
ejpam-6458	631	3	free	free	ADJ
ejpam-6458	631	4	γ	γ	X
ejpam-6458	631	5	-	-	ADJ
ejpam-6458	631	6	pointed	point	VERB
ejpam-6458	631	7	g	g	NOUN
ejpam-6458	631	8	-	-	PUNCT
ejpam-6458	631	9	module	module	NOUN
ejpam-6458	631	10	v	v	NOUN
ejpam-6458	631	11	is	be	AUX
ejpam-6458	631	12	simple	simple	ADJ
ejpam-6458	631	13	if	if	SCONJ
ejpam-6458	631	14	and	and	CCONJ
ejpam-6458	631	15	only	only	ADV
ejpam-6458	631	16	if	if	SCONJ
ejpam-6458	631	17	q+	q+	ADV
ejpam-6458	631	18	jkq	jkq	NOUN
ejpam-6458	631	19	−	−	PROPN
ejpam-6458	631	20	jk	jk	PROPN
ejpam-6458	631	21	̸=	̸=	PROPN
ejpam-6458	631	22	0	0	NUM
ejpam-6458	631	23	for	for	ADP
ejpam-6458	631	24	all	all	DET
ejpam-6458	631	25	j	j	PROPN
ejpam-6458	631	26	,	,	PUNCT
ejpam-6458	631	27	k	k	PROPN
ejpam-6458	631	28	∈	∈	PROPN
ejpam-6458	631	29	z.	z.	PROPN
ejpam-6458	631	30	4	4	NUM
ejpam-6458	631	31	.	.	PUNCT
ejpam-6458	632	1	if	if	SCONJ
ejpam-6458	632	2	v	v	NOUN
ejpam-6458	632	3	′	′	NOUN
ejpam-6458	632	4	is	be	AUX
ejpam-6458	632	5	a	a	DET
ejpam-6458	632	6	simple	simple	ADJ
ejpam-6458	632	7	torsion	torsion	NOUN
ejpam-6458	632	8	free	free	ADJ
ejpam-6458	632	9	γ	γ	X
ejpam-6458	632	10	-	-	ADJ
ejpam-6458	632	11	pointed	point	VERB
ejpam-6458	632	12	g	g	NOUN
ejpam-6458	632	13	-	-	PUNCT
ejpam-6458	632	14	module	module	NOUN
ejpam-6458	632	15	with	with	ADP
ejpam-6458	632	16	a	a	DET
ejpam-6458	632	17	basis	basis	NOUN
ejpam-6458	632	18	parametrized	parametrize	VERB
ejpam-6458	632	19	by	by	ADP
ejpam-6458	632	20	the	the	DET
ejpam-6458	632	21	lattice	lattice	PROPN
ejpam-6458	632	22	z3	z3	PROPN
ejpam-6458	632	23	and	and	CCONJ
ejpam-6458	632	24	with	with	ADP
ejpam-6458	632	25	separating	separate	VERB
ejpam-6458	632	26	action	action	NOUN
ejpam-6458	632	27	of	of	ADP
ejpam-6458	632	28	γ	γ	NOUN
ejpam-6458	632	29	on	on	ADP
ejpam-6458	632	30	basis	basis	NOUN
ejpam-6458	632	31	elements	element	NOUN
ejpam-6458	632	32	,	,	PUNCT
ejpam-6458	632	33	then	then	ADV
ejpam-6458	632	34	v	v	X
ejpam-6458	632	35	′	′	NUM
ejpam-6458	632	36	≃	≃	NOUN
ejpam-6458	632	37	v	v	NOUN
ejpam-6458	632	38	(	(	PUNCT
ejpam-6458	632	39	a′1	a′1	PROPN
ejpam-6458	632	40	,	,	PUNCT
ejpam-6458	632	41	a	a	DET
ejpam-6458	632	42	′	′	NOUN
ejpam-6458	632	43	2	2	NUM
ejpam-6458	632	44	,	,	PUNCT
ejpam-6458	632	45	a	a	DET
ejpam-6458	632	46	′	′	NOUN
ejpam-6458	632	47	3	3	NUM
ejpam-6458	632	48	,	,	PUNCT
ejpam-6458	632	49	a	a	DET
ejpam-6458	632	50	′	′	NOUN
ejpam-6458	632	51	4	4	NUM
ejpam-6458	632	52	,	,	PUNCT
ejpam-6458	632	53	η	η	NOUN
ejpam-6458	632	54	′	′	NOUN
ejpam-6458	632	55	)	)	PUNCT
ejpam-6458	632	56	for	for	ADP
ejpam-6458	632	57	some	some	DET
ejpam-6458	632	58	suitable	suitable	ADJ
ejpam-6458	632	59	choice	choice	NOUN
ejpam-6458	632	60	of	of	ADP
ejpam-6458	632	61	parameters	parameter	NOUN
ejpam-6458	632	62	such	such	ADJ
ejpam-6458	632	63	that	that	SCONJ
ejpam-6458	632	64	0	0	NUM
ejpam-6458	632	65	≤	≤	NUM
ejpam-6458	632	66	rea′1	rea′1	PROPN
ejpam-6458	632	67	<	<	X
ejpam-6458	632	68	1	1	NUM
ejpam-6458	632	69	,	,	PUNCT
ejpam-6458	632	70	0	0	NUM
ejpam-6458	632	71	≤	≤	NUM
ejpam-6458	632	72	rea′2	rea′2	NOUN
ejpam-6458	632	73	<	<	X
ejpam-6458	632	74	2	2	NUM
ejpam-6458	632	75	,	,	PUNCT
ejpam-6458	632	76	0	0	NUM
ejpam-6458	632	77	<	<	X
ejpam-6458	632	78	rea′3	rea′3	NOUN
ejpam-6458	632	79	<	<	X
ejpam-6458	632	80	2	2	NUM
ejpam-6458	632	81	,	,	PUNCT
ejpam-6458	632	82	where	where	SCONJ
ejpam-6458	632	83	rea	rea	PROPN
ejpam-6458	632	84	denotes	denote	VERB
ejpam-6458	632	85	the	the	DET
ejpam-6458	632	86	real	real	ADJ
ejpam-6458	632	87	part	part	NOUN
ejpam-6458	632	88	of	of	ADP
ejpam-6458	632	89	a.	a.	NOUN
ejpam-6458	632	90	m.	m.	PROPN
ejpam-6458	632	91	andelić	andelić	PROPN
ejpam-6458	632	92	et	et	PROPN
ejpam-6458	633	1	al	al	PROPN
ejpam-6458	633	2	.	.	PUNCT
ejpam-6458	633	3	/	/	SYM
ejpam-6458	633	4	eur	eur	PROPN
ejpam-6458	633	5	.	.	PUNCT
ejpam-6458	634	1	j.	j.	PROPN
ejpam-6458	634	2	pure	pure	PROPN
ejpam-6458	634	3	appl	appl	PROPN
ejpam-6458	634	4	.	.	PROPN
ejpam-6458	634	5	math	math	PROPN
ejpam-6458	634	6	,	,	PUNCT
ejpam-6458	634	7	18	18	NUM
ejpam-6458	634	8	(	(	PUNCT
ejpam-6458	634	9	3	3	NUM
ejpam-6458	634	10	)	)	PUNCT
ejpam-6458	634	11	(	(	PUNCT
ejpam-6458	634	12	2025	2025	NUM
ejpam-6458	634	13	)	)	PUNCT
ejpam-6458	634	14	,	,	PUNCT
ejpam-6458	634	15	6458	6458	NUM
ejpam-6458	634	16	16	16	NUM
ejpam-6458	634	17	of	of	ADP
ejpam-6458	634	18	21	21	NUM
ejpam-6458	634	19	5	5	NUM
ejpam-6458	634	20	.	.	PUNCT
ejpam-6458	635	1	the	the	DET
ejpam-6458	635	2	action	action	NOUN
ejpam-6458	635	3	of	of	ADP
ejpam-6458	635	4	the	the	DET
ejpam-6458	635	5	casimir	casimir	NOUN
ejpam-6458	635	6	elements	element	NOUN
ejpam-6458	635	7	in	in	ADP
ejpam-6458	635	8	the	the	DET
ejpam-6458	635	9	case	case	NOUN
ejpam-6458	635	10	a3	a3	NOUN
ejpam-6458	635	11	=	=	SYM
ejpam-6458	635	12	a4	a4	PROPN
ejpam-6458	635	13	:	:	PUNCT
ejpam-6458	635	14	z1(vijk	z1(vijk	NOUN
ejpam-6458	635	15	)	)	PUNCT
ejpam-6458	635	16	=	=	SYM
ejpam-6458	635	17	ξvijk	ξvijk	NOUN
ejpam-6458	635	18	,	,	PUNCT
ejpam-6458	635	19	z2(vijk	z2(vijk	NOUN
ejpam-6458	635	20	)	)	PUNCT
ejpam-6458	635	21	=	=	SYM
ejpam-6458	635	22	−1	−1	NOUN
ejpam-6458	635	23	4	4	NUM
ejpam-6458	635	24	ξ(ξ	ξ(ξ	NUM
ejpam-6458	635	25	+	+	CCONJ
ejpam-6458	635	26	4)vijk	4)vijk	NUM
ejpam-6458	635	27	and	and	CCONJ
ejpam-6458	635	28	in	in	ADP
ejpam-6458	635	29	the	the	DET
ejpam-6458	635	30	case	case	NOUN
ejpam-6458	635	31	a3	a3	NOUN
ejpam-6458	635	32	̸=	̸=	PROPN
ejpam-6458	635	33	a4	a4	NUM
ejpam-6458	635	34	:	:	PUNCT
ejpam-6458	635	35	z1(vijk	z1(vijk	NOUN
ejpam-6458	635	36	)	)	PUNCT
ejpam-6458	636	1	=	=	SYM
ejpam-6458	636	2	(	(	PUNCT
ejpam-6458	636	3	(	(	PUNCT
ejpam-6458	636	4	a3	a3	NOUN
ejpam-6458	636	5	−	−	PROPN
ejpam-6458	636	6	a4	a4	PROPN
ejpam-6458	636	7	)	)	PUNCT
ejpam-6458	636	8	2	2	NUM
ejpam-6458	636	9	−	−	PROPN
ejpam-6458	636	10	4)vijk	4)vijk	NUM
ejpam-6458	636	11	,	,	PUNCT
ejpam-6458	636	12	z2(vijk	z2(vijk	NOUN
ejpam-6458	636	13	)	)	PUNCT
ejpam-6458	636	14	=	=	SYM
ejpam-6458	637	1	0	0	X
ejpam-6458	637	2	.	.	PUNCT
ejpam-6458	637	3	proof	proof	NOUN
ejpam-6458	637	4	.	.	PUNCT
ejpam-6458	638	1	the	the	DET
ejpam-6458	638	2	formulas	formula	NOUN
ejpam-6458	638	3	(	(	PUNCT
ejpam-6458	638	4	5.17	5.17	NUM
ejpam-6458	638	5	)	)	PUNCT
ejpam-6458	638	6	and	and	CCONJ
ejpam-6458	638	7	(	(	PUNCT
ejpam-6458	638	8	5.18	5.18	NUM
ejpam-6458	638	9	)	)	PUNCT
ejpam-6458	638	10	are	be	AUX
ejpam-6458	638	11	well	well	ADV
ejpam-6458	638	12	defined	define	VERB
ejpam-6458	638	13	if	if	SCONJ
ejpam-6458	638	14	and	and	CCONJ
ejpam-6458	638	15	only	only	ADV
ejpam-6458	638	16	if	if	SCONJ
ejpam-6458	638	17	v	v	NOUN
ejpam-6458	638	18	=	=	SYM
ejpam-6458	638	19	v1(a1	v1(a1	NOUN
ejpam-6458	638	20	,	,	PUNCT
ejpam-6458	638	21	a2	a2	PROPN
ejpam-6458	638	22	,	,	PUNCT
ejpam-6458	638	23	a3	a3	NOUN
ejpam-6458	638	24	,	,	PUNCT
ejpam-6458	638	25	η	η	NOUN
ejpam-6458	638	26	)	)	PUNCT
ejpam-6458	638	27	with	with	ADP
ejpam-6458	638	28	a3	a3	NOUN
ejpam-6458	638	29	/∈	/∈	PUNCT
ejpam-6458	639	1	z	z	NOUN
ejpam-6458	639	2	,	,	PUNCT
ejpam-6458	639	3	or	or	CCONJ
ejpam-6458	639	4	v	v	NOUN
ejpam-6458	639	5	=	=	SYM
ejpam-6458	639	6	v2(a1	v2(a1	NOUN
ejpam-6458	639	7	,	,	PUNCT
ejpam-6458	639	8	a2	a2	PROPN
ejpam-6458	639	9	,	,	PUNCT
ejpam-6458	639	10	a3	a3	NOUN
ejpam-6458	639	11	,	,	PUNCT
ejpam-6458	639	12	a4	a4	NOUN
ejpam-6458	639	13	)	)	PUNCT
ejpam-6458	639	14	.	.	PUNCT
ejpam-6458	640	1	the	the	DET
ejpam-6458	640	2	statement	statement	NOUN
ejpam-6458	640	3	that	that	SCONJ
ejpam-6458	640	4	v	v	NOUN
ejpam-6458	640	5	is	be	AUX
ejpam-6458	640	6	a	a	DET
ejpam-6458	640	7	g	g	NOUN
ejpam-6458	640	8	-	-	PUNCT
ejpam-6458	640	9	module	module	NOUN
ejpam-6458	640	10	follows	follow	VERB
ejpam-6458	640	11	by	by	ADP
ejpam-6458	640	12	checking	check	VERB
ejpam-6458	640	13	all	all	DET
ejpam-6458	640	14	defining	define	VERB
ejpam-6458	640	15	relations	relation	NOUN
ejpam-6458	640	16	of	of	ADP
ejpam-6458	640	17	the	the	DET
ejpam-6458	640	18	lie	lie	NOUN
ejpam-6458	640	19	algebra	algebra	NOUN
ejpam-6458	640	20	.	.	PUNCT
ejpam-6458	641	1	the	the	DET
ejpam-6458	641	2	relations	relation	NOUN
ejpam-6458	641	3	5.11	5.11	NUM
ejpam-6458	641	4	-	-	SYM
ejpam-6458	641	5	5.15	5.15	NUM
ejpam-6458	641	6	give	give	VERB
ejpam-6458	641	7	only	only	ADV
ejpam-6458	641	8	two	two	NUM
ejpam-6458	641	9	alternatives	alternative	NOUN
ejpam-6458	641	10	v1(a1	v1(a1	NOUN
ejpam-6458	641	11	,	,	PUNCT
ejpam-6458	641	12	a2	a2	PROPN
ejpam-6458	641	13	,	,	PUNCT
ejpam-6458	641	14	a3	a3	NOUN
ejpam-6458	641	15	,	,	PUNCT
ejpam-6458	641	16	η	η	NOUN
ejpam-6458	641	17	)	)	PUNCT
ejpam-6458	641	18	and	and	CCONJ
ejpam-6458	641	19	v2(a1	v2(a1	NOUN
ejpam-6458	641	20	,	,	PUNCT
ejpam-6458	641	21	a2	a2	PROPN
ejpam-6458	641	22	,	,	PUNCT
ejpam-6458	641	23	a3	a3	NOUN
ejpam-6458	641	24	,	,	PUNCT
ejpam-6458	641	25	a4	a4	NOUN
ejpam-6458	641	26	)	)	PUNCT
ejpam-6458	641	27	.	.	PUNCT
ejpam-6458	642	1	it	it	PRON
ejpam-6458	642	2	follows	follow	VERB
ejpam-6458	642	3	immediately	immediately	ADV
ejpam-6458	642	4	from	from	ADP
ejpam-6458	642	5	the	the	DET
ejpam-6458	642	6	formulas	formula	NOUN
ejpam-6458	642	7	of	of	ADP
ejpam-6458	642	8	the	the	DET
ejpam-6458	642	9	action	action	NOUN
ejpam-6458	642	10	of	of	ADP
ejpam-6458	642	11	g	g	PROPN
ejpam-6458	642	12	that	that	DET
ejpam-6458	642	13	v	v	NOUN
ejpam-6458	642	14	(	(	PUNCT
ejpam-6458	642	15	a1	a1	PROPN
ejpam-6458	642	16	,	,	PUNCT
ejpam-6458	642	17	a2	a2	PROPN
ejpam-6458	642	18	,	,	PUNCT
ejpam-6458	642	19	a3	a3	NOUN
ejpam-6458	642	20	,	,	PUNCT
ejpam-6458	642	21	a4	a4	PROPN
ejpam-6458	642	22	,	,	PUNCT
ejpam-6458	642	23	η	η	NOUN
ejpam-6458	642	24	)	)	PUNCT
ejpam-6458	642	25	is	be	AUX
ejpam-6458	642	26	a	a	DET
ejpam-6458	642	27	torsion	torsion	NOUN
ejpam-6458	642	28	free	free	ADJ
ejpam-6458	642	29	module	module	NOUN
ejpam-6458	642	30	if	if	SCONJ
ejpam-6458	642	31	and	and	CCONJ
ejpam-6458	642	32	only	only	ADV
ejpam-6458	642	33	if	if	SCONJ
ejpam-6458	642	34	s	s	X
ejpam-6458	642	35	+	+	X
ejpam-6458	642	36	i	i	PROPN
ejpam-6458	642	37	,	,	PUNCT
ejpam-6458	642	38	j	j	PROPN
ejpam-6458	642	39	,	,	PUNCT
ejpam-6458	642	40	k	k	PROPN
ejpam-6458	642	41	,	,	PUNCT
ejpam-6458	642	42	s	s	PART
ejpam-6458	642	43	−	−	PROPN
ejpam-6458	643	1	i	i	PRON
ejpam-6458	643	2	,	,	PUNCT
ejpam-6458	643	3	k	k	PROPN
ejpam-6458	643	4	,	,	PUNCT
ejpam-6458	643	5	t	t	PROPN
ejpam-6458	643	6	−	−	PROPN
ejpam-6458	643	7	jk	jk	PROPN
ejpam-6458	643	8	and	and	CCONJ
ejpam-6458	643	9	t+	t+	PUNCT
ejpam-6458	643	10	k−1	k−1	PROPN
ejpam-6458	643	11	are	be	AUX
ejpam-6458	643	12	different	different	ADJ
ejpam-6458	643	13	from	from	ADP
ejpam-6458	643	14	zero	zero	NUM
ejpam-6458	643	15	,	,	PUNCT
ejpam-6458	643	16	for	for	ADP
ejpam-6458	643	17	all	all	DET
ejpam-6458	643	18	i	i	PROPN
ejpam-6458	643	19	,	,	PUNCT
ejpam-6458	643	20	j	j	PROPN
ejpam-6458	643	21	,	,	PUNCT
ejpam-6458	643	22	k	k	PROPN
ejpam-6458	643	23	∈	∈	PROPN
ejpam-6458	643	24	z.	z.	PROPN
ejpam-6458	643	25	note	note	VERB
ejpam-6458	643	26	that	that	SCONJ
ejpam-6458	643	27	γ	γ	PROPN
ejpam-6458	643	28	has	have	VERB
ejpam-6458	643	29	a	a	DET
ejpam-6458	643	30	simple	simple	ADJ
ejpam-6458	643	31	spectrum	spectrum	NOUN
ejpam-6458	643	32	on	on	ADP
ejpam-6458	643	33	v	v	PROPN
ejpam-6458	643	34	(	(	PUNCT
ejpam-6458	643	35	a1	a1	PROPN
ejpam-6458	643	36	,	,	PUNCT
ejpam-6458	643	37	a2	a2	PROPN
ejpam-6458	643	38	,	,	PUNCT
ejpam-6458	643	39	a3	a3	NOUN
ejpam-6458	643	40	,	,	PUNCT
ejpam-6458	643	41	a4	a4	PROPN
ejpam-6458	643	42	,	,	PUNCT
ejpam-6458	643	43	η	η	NOUN
ejpam-6458	643	44	)	)	PUNCT
ejpam-6458	643	45	and	and	CCONJ
ejpam-6458	643	46	hence	hence	ADV
ejpam-6458	643	47	,	,	PUNCT
ejpam-6458	643	48	the	the	DET
ejpam-6458	643	49	action	action	NOUN
ejpam-6458	643	50	of	of	ADP
ejpam-6458	643	51	γ	γ	PROPN
ejpam-6458	643	52	separates	separate	VERB
ejpam-6458	643	53	the	the	DET
ejpam-6458	643	54	basis	basis	NOUN
ejpam-6458	643	55	elements	element	NOUN
ejpam-6458	643	56	by	by	ADP
ejpam-6458	643	57	lemma	lemma	PROPN
ejpam-6458	643	58	5.3	5.3	NUM
ejpam-6458	643	59	.	.	PUNCT
ejpam-6458	644	1	in	in	ADP
ejpam-6458	644	2	particular	particular	ADJ
ejpam-6458	644	3	,	,	PUNCT
ejpam-6458	644	4	v	v	NOUN
ejpam-6458	644	5	(	(	PUNCT
ejpam-6458	644	6	a1	a1	PROPN
ejpam-6458	644	7	,	,	PUNCT
ejpam-6458	644	8	a2	a2	PROPN
ejpam-6458	644	9	,	,	PUNCT
ejpam-6458	644	10	a3	a3	NOUN
ejpam-6458	644	11	,	,	PUNCT
ejpam-6458	644	12	a4	a4	PROPN
ejpam-6458	644	13	,	,	PUNCT
ejpam-6458	644	14	η	η	NOUN
ejpam-6458	644	15	)	)	PUNCT
ejpam-6458	644	16	is	be	AUX
ejpam-6458	644	17	γ	γ	X
ejpam-6458	644	18	-	-	PUNCT
ejpam-6458	644	19	pointed	pointed	ADJ
ejpam-6458	644	20	.	.	PUNCT
ejpam-6458	645	1	this	this	PRON
ejpam-6458	645	2	implies	imply	VERB
ejpam-6458	645	3	the	the	DET
ejpam-6458	645	4	second	second	ADJ
ejpam-6458	645	5	statement	statement	NOUN
ejpam-6458	645	6	.	.	PUNCT
ejpam-6458	646	1	suppose	suppose	VERB
ejpam-6458	646	2	the	the	DET
ejpam-6458	646	3	module	module	NOUN
ejpam-6458	646	4	v	v	NOUN
ejpam-6458	646	5	(	(	PUNCT
ejpam-6458	646	6	a1	a1	PROPN
ejpam-6458	646	7	,	,	PUNCT
ejpam-6458	646	8	a2	a2	PROPN
ejpam-6458	646	9	,	,	PUNCT
ejpam-6458	646	10	a3	a3	NOUN
ejpam-6458	646	11	,	,	PUNCT
ejpam-6458	646	12	a4	a4	PROPN
ejpam-6458	646	13	,	,	PUNCT
ejpam-6458	646	14	η	η	NOUN
ejpam-6458	646	15	)	)	PUNCT
ejpam-6458	646	16	is	be	AUX
ejpam-6458	646	17	torsion	torsion	NOUN
ejpam-6458	646	18	free	free	ADJ
ejpam-6458	646	19	.	.	PUNCT
ejpam-6458	647	1	similarly	similarly	ADV
ejpam-6458	647	2	to	to	ADP
ejpam-6458	647	3	case	case	NOUN
ejpam-6458	647	4	of	of	ADP
ejpam-6458	647	5	a2	a2	PROPN
ejpam-6458	647	6	,	,	PUNCT
ejpam-6458	647	7	using	use	VERB
ejpam-6458	647	8	the	the	DET
ejpam-6458	647	9	relations	relation	NOUN
ejpam-6458	647	10	in	in	ADP
ejpam-6458	647	11	u0(g	u0(g	NOUN
ejpam-6458	647	12	)	)	PUNCT
ejpam-6458	647	13	we	we	PRON
ejpam-6458	647	14	get	get	VERB
ejpam-6458	647	15	that	that	DET
ejpam-6458	647	16	c1	c1	NOUN
ejpam-6458	647	17	,	,	PUNCT
ejpam-6458	647	18	c2	c2	PROPN
ejpam-6458	647	19	are	be	AUX
ejpam-6458	647	20	presented	present	VERB
ejpam-6458	647	21	by	by	ADP
ejpam-6458	647	22	infinite	infinite	ADJ
ejpam-6458	647	23	diagonal	diagonal	ADJ
ejpam-6458	647	24	matrices	matrix	NOUN
ejpam-6458	647	25	,	,	PUNCT
ejpam-6458	647	26	while	while	SCONJ
ejpam-6458	647	27	the	the	DET
ejpam-6458	647	28	element	element	NOUN
ejpam-6458	647	29	c3	c3	PROPN
ejpam-6458	647	30	is	be	AUX
ejpam-6458	647	31	presented	present	VERB
ejpam-6458	647	32	by	by	ADP
ejpam-6458	647	33	a	a	DET
ejpam-6458	647	34	3	3	NUM
ejpam-6458	647	35	-	-	PUNCT
ejpam-6458	647	36	diagonal	diagonal	ADJ
ejpam-6458	647	37	matrix	matrix	NOUN
ejpam-6458	647	38	on	on	ADP
ejpam-6458	647	39	every	every	DET
ejpam-6458	647	40	weight	weight	NOUN
ejpam-6458	647	41	subspace	subspace	NOUN
ejpam-6458	647	42	of	of	ADP
ejpam-6458	647	43	v	v	PROPN
ejpam-6458	647	44	(	(	PUNCT
ejpam-6458	647	45	a1	a1	PROPN
ejpam-6458	647	46	,	,	PUNCT
ejpam-6458	647	47	a2	a2	PROPN
ejpam-6458	647	48	,	,	PUNCT
ejpam-6458	647	49	a3	a3	NOUN
ejpam-6458	647	50	,	,	PUNCT
ejpam-6458	647	51	a4	a4	PROPN
ejpam-6458	647	52	,	,	PUNCT
ejpam-6458	647	53	η	η	NOUN
ejpam-6458	647	54	)	)	PUNCT
ejpam-6458	647	55	.	.	PUNCT
ejpam-6458	648	1	using	use	VERB
ejpam-6458	648	2	this	this	DET
ejpam-6458	648	3	fact	fact	NOUN
ejpam-6458	648	4	and	and	CCONJ
ejpam-6458	648	5	the	the	DET
ejpam-6458	648	6	separating	separate	VERB
ejpam-6458	648	7	action	action	NOUN
ejpam-6458	648	8	of	of	ADP
ejpam-6458	648	9	γ	γ	NOUN
ejpam-6458	648	10	on	on	ADP
ejpam-6458	648	11	basis	basis	NOUN
ejpam-6458	648	12	elements	element	NOUN
ejpam-6458	648	13	,	,	PUNCT
ejpam-6458	648	14	it	it	PRON
ejpam-6458	648	15	is	be	AUX
ejpam-6458	648	16	easy	easy	ADJ
ejpam-6458	648	17	to	to	PART
ejpam-6458	648	18	see	see	VERB
ejpam-6458	648	19	that	that	SCONJ
ejpam-6458	648	20	conditions	condition	NOUN
ejpam-6458	648	21	q+	q+	PUNCT
ejpam-6458	648	22	jkq	jkq	NOUN
ejpam-6458	648	23	−	−	PROPN
ejpam-6458	648	24	jk	jk	PROPN
ejpam-6458	648	25	=	=	NOUN
ejpam-6458	648	26	̸	̸	NUM
ejpam-6458	648	27	0	0	NUM
ejpam-6458	648	28	,	,	PUNCT
ejpam-6458	648	29	for	for	SCONJ
ejpam-6458	648	30	all	all	DET
ejpam-6458	648	31	i	i	PROPN
ejpam-6458	648	32	,	,	PUNCT
ejpam-6458	648	33	j	j	PROPN
ejpam-6458	648	34	,	,	PUNCT
ejpam-6458	648	35	k	k	PROPN
ejpam-6458	648	36	∈	∈	PROPN
ejpam-6458	648	37	z	z	NOUN
ejpam-6458	648	38	are	be	AUX
ejpam-6458	648	39	necessary	necessary	ADJ
ejpam-6458	648	40	and	and	CCONJ
ejpam-6458	648	41	sufficient	sufficient	ADJ
ejpam-6458	648	42	to	to	PART
ejpam-6458	648	43	guarantee	guarantee	VERB
ejpam-6458	648	44	that	that	SCONJ
ejpam-6458	648	45	any	any	DET
ejpam-6458	648	46	element	element	NOUN
ejpam-6458	648	47	of	of	ADP
ejpam-6458	648	48	v	v	PROPN
ejpam-6458	648	49	(	(	PUNCT
ejpam-6458	648	50	a1	a1	PROPN
ejpam-6458	648	51	,	,	PUNCT
ejpam-6458	648	52	a2	a2	PROPN
ejpam-6458	648	53	,	,	PUNCT
ejpam-6458	648	54	a3	a3	NOUN
ejpam-6458	648	55	,	,	PUNCT
ejpam-6458	648	56	a4	a4	PROPN
ejpam-6458	648	57	,	,	PUNCT
ejpam-6458	648	58	η	η	NOUN
ejpam-6458	648	59	)	)	PUNCT
ejpam-6458	648	60	generates	generate	VERB
ejpam-6458	648	61	the	the	DET
ejpam-6458	648	62	whole	whole	ADJ
ejpam-6458	648	63	module	module	NOUN
ejpam-6458	648	64	,	,	PUNCT
ejpam-6458	648	65	which	which	PRON
ejpam-6458	648	66	is	be	AUX
ejpam-6458	648	67	equivalent	equivalent	ADJ
ejpam-6458	648	68	to	to	ADP
ejpam-6458	648	69	the	the	DET
ejpam-6458	648	70	simplicity	simplicity	NOUN
ejpam-6458	648	71	of	of	ADP
ejpam-6458	648	72	the	the	DET
ejpam-6458	648	73	module	module	NOUN
ejpam-6458	648	74	.	.	PUNCT
ejpam-6458	649	1	this	this	PRON
ejpam-6458	649	2	implies	imply	VERB
ejpam-6458	649	3	the	the	DET
ejpam-6458	649	4	third	third	ADJ
ejpam-6458	649	5	statement	statement	NOUN
ejpam-6458	649	6	.	.	PUNCT
ejpam-6458	650	1	let	let	VERB
ejpam-6458	650	2	v	v	PART
ejpam-6458	650	3	′	′	VERB
ejpam-6458	650	4	be	be	AUX
ejpam-6458	650	5	a	a	DET
ejpam-6458	650	6	simple	simple	ADJ
ejpam-6458	650	7	torsion	torsion	NOUN
ejpam-6458	650	8	free	free	ADJ
ejpam-6458	650	9	γ	γ	X
ejpam-6458	650	10	-	-	PUNCT
ejpam-6458	650	11	pointed	point	VERB
ejpam-6458	650	12	c2module	c2module	NOUN
ejpam-6458	650	13	with	with	ADP
ejpam-6458	650	14	a	a	DET
ejpam-6458	650	15	basis	basis	NOUN
ejpam-6458	650	16	{	{	PUNCT
ejpam-6458	650	17	v′	v′	PROPN
ejpam-6458	650	18	ijk	ijk	PROPN
ejpam-6458	650	19	,	,	PUNCT
ejpam-6458	650	20	i	i	PROPN
ejpam-6458	650	21	,	,	PUNCT
ejpam-6458	650	22	j	j	PROPN
ejpam-6458	650	23	,	,	PUNCT
ejpam-6458	650	24	k	k	PROPN
ejpam-6458	650	25	∈	∈	PROPN
ejpam-6458	651	1	z	z	PROPN
ejpam-6458	651	2	}	}	PUNCT
ejpam-6458	651	3	such	such	ADJ
ejpam-6458	651	4	that	that	SCONJ
ejpam-6458	651	5	γ	γ	PROPN
ejpam-6458	651	6	acts	act	VERB
ejpam-6458	651	7	by	by	ADP
ejpam-6458	651	8	different	different	ADJ
ejpam-6458	651	9	characters	character	NOUN
ejpam-6458	651	10	on	on	ADP
ejpam-6458	651	11	the	the	DET
ejpam-6458	651	12	basis	basis	NOUN
ejpam-6458	651	13	elements	element	NOUN
ejpam-6458	651	14	v′	v′	PROPN
ejpam-6458	651	15	ijk	ijk	X
ejpam-6458	651	16	.	.	PUNCT
ejpam-6458	652	1	fix	fix	VERB
ejpam-6458	652	2	one	one	NUM
ejpam-6458	652	3	basis	basis	NOUN
ejpam-6458	652	4	element	element	NOUN
ejpam-6458	652	5	v	v	ADP
ejpam-6458	652	6	′	′	NUM
ejpam-6458	652	7	ijk	ijk	PROPN
ejpam-6458	652	8	and	and	CCONJ
ejpam-6458	652	9	apply	apply	VERB
ejpam-6458	652	10	the	the	DET
ejpam-6458	652	11	generators	generator	NOUN
ejpam-6458	652	12	of	of	ADP
ejpam-6458	652	13	the	the	DET
ejpam-6458	652	14	centralizer	centralizer	NOUN
ejpam-6458	652	15	u0(g	u0(g	NOUN
ejpam-6458	652	16	)	)	PUNCT
ejpam-6458	652	17	.	.	PUNCT
ejpam-6458	653	1	one	one	PRON
ejpam-6458	653	2	can	can	AUX
ejpam-6458	653	3	see	see	VERB
ejpam-6458	653	4	directly	directly	ADV
ejpam-6458	653	5	from	from	ADP
ejpam-6458	653	6	the	the	DET
ejpam-6458	653	7	action	action	NOUN
ejpam-6458	653	8	that	that	PRON
ejpam-6458	653	9	u0(g)v	u0(g)v	VERB
ejpam-6458	653	10	′	′	NUM
ejpam-6458	653	11	ijk	ijk	PROPN
ejpam-6458	653	12	will	will	AUX
ejpam-6458	653	13	be	be	AUX
ejpam-6458	653	14	equal	equal	ADJ
ejpam-6458	653	15	to	to	ADP
ejpam-6458	653	16	the	the	DET
ejpam-6458	653	17	whole	whole	ADJ
ejpam-6458	653	18	weight	weight	NOUN
ejpam-6458	653	19	space	space	NOUN
ejpam-6458	653	20	of	of	ADP
ejpam-6458	653	21	v	v	NOUN
ejpam-6458	653	22	′	′	NOUN
ejpam-6458	653	23	,	,	PUNCT
ejpam-6458	653	24	which	which	DET
ejpam-6458	653	25	v′	v′	NOUN
ejpam-6458	653	26	ijk	ijk	PROPN
ejpam-6458	653	27	belongs	belong	VERB
ejpam-6458	653	28	to	to	PART
ejpam-6458	653	29	.	.	PUNCT
ejpam-6458	654	1	moreover	moreover	ADV
ejpam-6458	654	2	,	,	PUNCT
ejpam-6458	654	3	the	the	DET
ejpam-6458	654	4	action	action	NOUN
ejpam-6458	654	5	of	of	ADP
ejpam-6458	654	6	the	the	DET
ejpam-6458	654	7	generators	generator	NOUN
ejpam-6458	654	8	of	of	ADP
ejpam-6458	654	9	γ	γ	X
ejpam-6458	654	10	will	will	AUX
ejpam-6458	654	11	determine	determine	VERB
ejpam-6458	654	12	uniquely	uniquely	ADV
ejpam-6458	654	13	the	the	DET
ejpam-6458	654	14	corresponding	correspond	VERB
ejpam-6458	654	15	parameters	parameter	NOUN
ejpam-6458	654	16	a1	a1	PROPN
ejpam-6458	654	17	,	,	PUNCT
ejpam-6458	654	18	a2	a2	PROPN
ejpam-6458	654	19	,	,	PUNCT
ejpam-6458	654	20	a3	a3	NOUN
ejpam-6458	654	21	,	,	PUNCT
ejpam-6458	654	22	a4	a4	PROPN
ejpam-6458	654	23	,	,	PUNCT
ejpam-6458	654	24	η	η	PROPN
ejpam-6458	654	25	.	.	PROPN
ejpam-6458	654	26	hence	hence	ADV
ejpam-6458	654	27	,	,	PUNCT
ejpam-6458	654	28	we	we	PRON
ejpam-6458	654	29	get	get	VERB
ejpam-6458	654	30	a	a	DET
ejpam-6458	654	31	non	non	ADJ
ejpam-6458	654	32	-	-	ADJ
ejpam-6458	654	33	zero	zero	NUM
ejpam-6458	654	34	homomorphism	homomorphism	NOUN
ejpam-6458	654	35	θ	θ	PROPN
ejpam-6458	654	36	of	of	ADP
ejpam-6458	654	37	u0(g)-modules	u0(g)-module	NOUN
ejpam-6458	654	38	u0(g)vijk	u0(g)vijk	X
ejpam-6458	654	39	and	and	CCONJ
ejpam-6458	654	40	u0(g)v	u0(g)v	NOUN
ejpam-6458	654	41	′	′	NUM
ejpam-6458	654	42	ijk	ijk	PROPN
ejpam-6458	654	43	:	:	PUNCT
ejpam-6458	654	44	θ(vijk	θ(vijk	NOUN
ejpam-6458	654	45	)	)	PUNCT
ejpam-6458	654	46	=	=	SYM
ejpam-6458	654	47	v′	v′	PROPN
ejpam-6458	654	48	ijk	ijk	PROPN
ejpam-6458	654	49	.	.	PUNCT
ejpam-6458	655	1	moreover	moreover	ADV
ejpam-6458	655	2	,	,	PUNCT
ejpam-6458	655	3	u0(g)v	u0(g)v	NOUN
ejpam-6458	655	4	′	′	NUM
ejpam-6458	655	5	ijk	ijk	PROPN
ejpam-6458	655	6	is	be	AUX
ejpam-6458	655	7	a	a	DET
ejpam-6458	655	8	simple	simple	ADJ
ejpam-6458	655	9	u0(g)module	u0(g)module	NOUN
ejpam-6458	655	10	as	as	SCONJ
ejpam-6458	655	11	v	v	NOUN
ejpam-6458	655	12	′	′	NOUN
ejpam-6458	655	13	is	be	AUX
ejpam-6458	655	14	simple	simple	ADJ
ejpam-6458	655	15	.	.	PUNCT
ejpam-6458	656	1	hence	hence	ADV
ejpam-6458	656	2	,	,	PUNCT
ejpam-6458	656	3	θ	θ	PROPN
ejpam-6458	656	4	is	be	AUX
ejpam-6458	656	5	surjective	surjective	ADJ
ejpam-6458	656	6	.	.	PUNCT
ejpam-6458	657	1	it	it	PRON
ejpam-6458	657	2	extends	extend	VERB
ejpam-6458	657	3	to	to	ADP
ejpam-6458	657	4	a	a	DET
ejpam-6458	657	5	surjective	surjective	ADJ
ejpam-6458	657	6	homomorphism	homomorphism	NOUN
ejpam-6458	657	7	from	from	ADP
ejpam-6458	657	8	v	v	PRON
ejpam-6458	657	9	(	(	PUNCT
ejpam-6458	657	10	a1	a1	PROPN
ejpam-6458	657	11	,	,	PUNCT
ejpam-6458	657	12	a2	a2	PROPN
ejpam-6458	657	13	,	,	PUNCT
ejpam-6458	657	14	a3	a3	NOUN
ejpam-6458	657	15	,	,	PUNCT
ejpam-6458	657	16	a4	a4	PROPN
ejpam-6458	657	17	,	,	PUNCT
ejpam-6458	657	18	η	η	NOUN
ejpam-6458	657	19	)	)	PUNCT
ejpam-6458	657	20	to	to	AUX
ejpam-6458	657	21	v	v	NOUN
ejpam-6458	657	22	′.	′.	NOUN
ejpam-6458	657	23	comparing	compare	VERB
ejpam-6458	657	24	the	the	DET
ejpam-6458	657	25	bases	basis	NOUN
ejpam-6458	657	26	of	of	ADP
ejpam-6458	657	27	both	both	DET
ejpam-6458	657	28	modules	module	NOUN
ejpam-6458	657	29	we	we	PRON
ejpam-6458	657	30	conclude	conclude	VERB
ejpam-6458	657	31	the	the	DET
ejpam-6458	657	32	isomorphism	isomorphism	NOUN
ejpam-6458	657	33	v	v	ADP
ejpam-6458	657	34	′	′	NUM
ejpam-6458	657	35	≃	≃	NOUN
ejpam-6458	657	36	v	v	NOUN
ejpam-6458	657	37	(	(	PUNCT
ejpam-6458	657	38	a1	a1	PROPN
ejpam-6458	657	39	,	,	PUNCT
ejpam-6458	657	40	a2	a2	PROPN
ejpam-6458	657	41	,	,	PUNCT
ejpam-6458	657	42	a3	a3	NOUN
ejpam-6458	657	43	,	,	PUNCT
ejpam-6458	657	44	a4	a4	PROPN
ejpam-6458	657	45	,	,	PUNCT
ejpam-6458	657	46	η	η	NOUN
ejpam-6458	657	47	)	)	PUNCT
ejpam-6458	657	48	.	.	PUNCT
ejpam-6458	658	1	since	since	SCONJ
ejpam-6458	658	2	v	v	NUM
ejpam-6458	658	3	′	′	NOUN
ejpam-6458	658	4	is	be	AUX
ejpam-6458	658	5	torsion	torsion	NOUN
ejpam-6458	658	6	free	free	ADJ
ejpam-6458	658	7	we	we	PRON
ejpam-6458	658	8	can	can	AUX
ejpam-6458	658	9	choose	choose	VERB
ejpam-6458	658	10	any	any	DET
ejpam-6458	658	11	weight	weight	NOUN
ejpam-6458	658	12	of	of	ADP
ejpam-6458	658	13	the	the	DET
ejpam-6458	658	14	weight	weight	NOUN
ejpam-6458	658	15	lattice	lattice	NOUN
ejpam-6458	658	16	as	as	ADP
ejpam-6458	658	17	part	part	NOUN
ejpam-6458	658	18	of	of	ADP
ejpam-6458	658	19	the	the	DET
ejpam-6458	658	20	parameter	parameter	NOUN
ejpam-6458	658	21	set	set	NOUN
ejpam-6458	658	22	.	.	PUNCT
ejpam-6458	659	1	this	this	PRON
ejpam-6458	659	2	proves	prove	VERB
ejpam-6458	659	3	the	the	DET
ejpam-6458	659	4	fourth	fourth	ADJ
ejpam-6458	659	5	statement	statement	NOUN
ejpam-6458	659	6	.	.	PUNCT
ejpam-6458	660	1	the	the	DET
ejpam-6458	660	2	last	last	ADJ
ejpam-6458	660	3	statement	statement	NOUN
ejpam-6458	660	4	follows	follow	VERB
ejpam-6458	660	5	by	by	ADP
ejpam-6458	660	6	direct	direct	ADJ
ejpam-6458	660	7	computation	computation	NOUN
ejpam-6458	660	8	.	.	PUNCT
ejpam-6458	661	1	□	□	PUNCT
ejpam-6458	661	2	hence	hence	ADV
ejpam-6458	661	3	,	,	PUNCT
ejpam-6458	661	4	theorem	theorem	VERB
ejpam-6458	661	5	5.4	5.4	NUM
ejpam-6458	661	6	provides	provide	VERB
ejpam-6458	661	7	two	two	NUM
ejpam-6458	661	8	4	4	NUM
ejpam-6458	661	9	-	-	PUNCT
ejpam-6458	661	10	parameter	parameter	NOUN
ejpam-6458	661	11	families	family	NOUN
ejpam-6458	661	12	of	of	ADP
ejpam-6458	661	13	simple	simple	ADJ
ejpam-6458	661	14	torsion	torsion	NOUN
ejpam-6458	661	15	free	free	ADJ
ejpam-6458	661	16	γ	γ	X
ejpam-6458	661	17	-	-	ADJ
ejpam-6458	661	18	pointed	point	VERB
ejpam-6458	661	19	g	g	NOUN
ejpam-6458	661	20	-	-	PUNCT
ejpam-6458	661	21	modules	module	NOUN
ejpam-6458	661	22	.	.	PUNCT
ejpam-6458	662	1	if	if	SCONJ
ejpam-6458	662	2	v	v	X
ejpam-6458	662	3	(	(	PUNCT
ejpam-6458	662	4	a1	a1	PROPN
ejpam-6458	662	5	,	,	PUNCT
ejpam-6458	662	6	a2	a2	PROPN
ejpam-6458	662	7	,	,	PUNCT
ejpam-6458	662	8	a3	a3	NOUN
ejpam-6458	662	9	,	,	PUNCT
ejpam-6458	662	10	a4	a4	PROPN
ejpam-6458	662	11	,	,	PUNCT
ejpam-6458	662	12	η	η	NOUN
ejpam-6458	662	13	)	)	PUNCT
ejpam-6458	662	14	is	be	AUX
ejpam-6458	662	15	a	a	DET
ejpam-6458	662	16	torsion	torsion	NOUN
ejpam-6458	662	17	free	free	ADJ
ejpam-6458	662	18	γ	γ	X
ejpam-6458	662	19	-	-	ADJ
ejpam-6458	662	20	pointed	point	VERB
ejpam-6458	662	21	g	g	NOUN
ejpam-6458	662	22	-	-	PUNCT
ejpam-6458	662	23	module	module	NOUN
ejpam-6458	662	24	which	which	PRON
ejpam-6458	662	25	is	be	AUX
ejpam-6458	662	26	not	not	PART
ejpam-6458	662	27	simple	simple	ADJ
ejpam-6458	662	28	,	,	PUNCT
ejpam-6458	662	29	then	then	ADV
ejpam-6458	662	30	all	all	DET
ejpam-6458	662	31	its	its	PRON
ejpam-6458	662	32	simple	simple	ADJ
ejpam-6458	662	33	subquotients	subquotient	NOUN
ejpam-6458	662	34	are	be	AUX
ejpam-6458	662	35	torsion	torsion	NOUN
ejpam-6458	662	36	free	free	ADJ
ejpam-6458	662	37	γ	γ	X
ejpam-6458	662	38	-	-	PUNCT
ejpam-6458	662	39	pointed	point	VERB
ejpam-6458	662	40	modules	module	NOUN
ejpam-6458	662	41	.	.	PUNCT
ejpam-6458	663	1	they	they	PRON
ejpam-6458	663	2	exhaust	exhaust	VERB
ejpam-6458	663	3	all	all	DET
ejpam-6458	663	4	generic	generic	ADJ
ejpam-6458	663	5	simple	simple	ADJ
ejpam-6458	663	6	torsion	torsion	NOUN
ejpam-6458	663	7	free	free	ADJ
ejpam-6458	663	8	γ	γ	X
ejpam-6458	663	9	-	-	ADJ
ejpam-6458	663	10	pointed	point	VERB
ejpam-6458	663	11	g	g	NOUN
ejpam-6458	663	12	-	-	PUNCT
ejpam-6458	663	13	modules	module	NOUN
ejpam-6458	663	14	,	,	PUNCT
ejpam-6458	663	15	which	which	PRON
ejpam-6458	663	16	are	be	AUX
ejpam-6458	663	17	analogs	analog	NOUN
ejpam-6458	663	18	of	of	ADP
ejpam-6458	663	19	generic	generic	ADJ
ejpam-6458	663	20	simple	simple	ADJ
ejpam-6458	663	21	gelfand	gelfand	PROPN
ejpam-6458	663	22	-	-	PUNCT
ejpam-6458	663	23	tsetlin	tsetlin	PROPN
ejpam-6458	663	24	modules	module	NOUN
ejpam-6458	663	25	in	in	ADP
ejpam-6458	663	26	type	type	NOUN
ejpam-6458	663	27	a.	a.	NOUN
ejpam-6458	663	28	6	6	NUM
ejpam-6458	663	29	.	.	PUNCT
ejpam-6458	664	1	gelfand	gelfand	PROPN
ejpam-6458	664	2	-	-	PUNCT
ejpam-6458	664	3	tsetlin	tsetlin	PROPN
ejpam-6458	664	4	modules	module	NOUN
ejpam-6458	664	5	for	for	ADP
ejpam-6458	664	6	g2	g2	PROPN
ejpam-6458	664	7	in	in	ADP
ejpam-6458	664	8	this	this	DET
ejpam-6458	664	9	section	section	NOUN
ejpam-6458	664	10	we	we	PRON
ejpam-6458	664	11	extend	extend	VERB
ejpam-6458	664	12	the	the	DET
ejpam-6458	664	13	results	result	NOUN
ejpam-6458	664	14	of	of	ADP
ejpam-6458	664	15	previous	previous	ADJ
ejpam-6458	664	16	sections	section	NOUN
ejpam-6458	664	17	to	to	ADP
ejpam-6458	664	18	the	the	PRON
ejpam-6458	664	19	of	of	ADP
ejpam-6458	664	20	the	the	DET
ejpam-6458	664	21	lie	lie	NOUN
ejpam-6458	664	22	algebra	algebra	NOUN
ejpam-6458	664	23	of	of	ADP
ejpam-6458	664	24	type	type	NOUN
ejpam-6458	664	25	g2	g2	PROPN
ejpam-6458	664	26	.	.	PUNCT
ejpam-6458	665	1	6.1	6.1	NUM
ejpam-6458	665	2	.	.	PUNCT
ejpam-6458	665	3	construction	construction	NOUN
ejpam-6458	665	4	of	of	ADP
ejpam-6458	665	5	centralizer	centralizer	NOUN
ejpam-6458	665	6	of	of	ADP
ejpam-6458	665	7	g2	g2	PROPN
ejpam-6458	665	8	define	define	VERB
ejpam-6458	665	9	the	the	DET
ejpam-6458	665	10	root	root	NOUN
ejpam-6458	665	11	system	system	NOUN
ejpam-6458	665	12	for	for	ADP
ejpam-6458	665	13	g2	g2	PROPN
ejpam-6458	665	14	(	(	PUNCT
ejpam-6458	665	15	for	for	ADP
ejpam-6458	665	16	convenience	convenience	NOUN
ejpam-6458	665	17	will	will	AUX
ejpam-6458	665	18	use	use	VERB
ejpam-6458	665	19	notation	notation	NOUN
ejpam-6458	665	20	βi	βi	PROPN
ejpam-6458	665	21	,	,	PUNCT
ejpam-6458	665	22	j	j	PROPN
ejpam-6458	665	23	for	for	ADP
ejpam-6458	665	24	α−i,−j	α−i,−j	NOUN
ejpam-6458	665	25	):	):	PUNCT
ejpam-6458	666	1	∆	∆	PROPN
ejpam-6458	666	2	=	=	PRON
ejpam-6458	666	3	{	{	PUNCT
ejpam-6458	666	4	α01	α01	NOUN
ejpam-6458	666	5	,	,	PUNCT
ejpam-6458	666	6	α10	α10	NOUN
ejpam-6458	666	7	,	,	PUNCT
ejpam-6458	666	8	α11	α11	NOUN
ejpam-6458	666	9	,	,	PUNCT
ejpam-6458	666	10	α21	α21	NUM
ejpam-6458	666	11	,	,	PUNCT
ejpam-6458	666	12	α31	α31	NOUN
ejpam-6458	666	13	,	,	PUNCT
ejpam-6458	666	14	α32	α32	NUM
ejpam-6458	666	15	,	,	PUNCT
ejpam-6458	666	16	β32	β32	NOUN
ejpam-6458	666	17	,	,	PUNCT
ejpam-6458	666	18	β31	β31	ADJ
ejpam-6458	666	19	,	,	PUNCT
ejpam-6458	666	20	β21	β21	NOUN
ejpam-6458	666	21	,	,	PUNCT
ejpam-6458	666	22	β11	β11	NOUN
ejpam-6458	666	23	,	,	PUNCT
ejpam-6458	666	24	β10	β10	NOUN
ejpam-6458	666	25	,	,	PUNCT
ejpam-6458	666	26	β01	β01	NOUN
ejpam-6458	666	27	}	}	PUNCT
ejpam-6458	666	28	,	,	PUNCT
ejpam-6458	666	29	m.	m.	NOUN
ejpam-6458	666	30	andelić	andelić	PROPN
ejpam-6458	666	31	et	et	PROPN
ejpam-6458	666	32	al	al	PROPN
ejpam-6458	666	33	.	.	PUNCT
ejpam-6458	666	34	/	/	SYM
ejpam-6458	666	35	eur	eur	PROPN
ejpam-6458	666	36	.	.	PUNCT
ejpam-6458	667	1	j.	j.	PROPN
ejpam-6458	667	2	pure	pure	PROPN
ejpam-6458	667	3	appl	appl	PROPN
ejpam-6458	667	4	.	.	PROPN
ejpam-6458	667	5	math	math	PROPN
ejpam-6458	667	6	,	,	PUNCT
ejpam-6458	667	7	18	18	NUM
ejpam-6458	667	8	(	(	PUNCT
ejpam-6458	667	9	3	3	NUM
ejpam-6458	667	10	)	)	PUNCT
ejpam-6458	667	11	(	(	PUNCT
ejpam-6458	667	12	2025	2025	NUM
ejpam-6458	667	13	)	)	PUNCT
ejpam-6458	667	14	,	,	PUNCT
ejpam-6458	667	15	6458	6458	NUM
ejpam-6458	667	16	17	17	NUM
ejpam-6458	667	17	of	of	ADP
ejpam-6458	667	18	21	21	NUM
ejpam-6458	667	19	where	where	SCONJ
ejpam-6458	667	20	αij	αij	NOUN
ejpam-6458	667	21	=	=	PROPN
ejpam-6458	667	22	iα10	iα10	PROPN
ejpam-6458	667	23	+	+	CCONJ
ejpam-6458	667	24	jα01	jα01	PROPN
ejpam-6458	667	25	.	.	PUNCT
ejpam-6458	668	1	fix	fix	VERB
ejpam-6458	668	2	a	a	DET
ejpam-6458	668	3	chevalley	chevalley	ADJ
ejpam-6458	668	4	basis	basis	NOUN
ejpam-6458	668	5	:	:	PUNCT
ejpam-6458	668	6	e01	e01	PROPN
ejpam-6458	668	7	=	=	SYM
ejpam-6458	668	8	e31	e31	PROPN
ejpam-6458	668	9	+	+	CCONJ
ejpam-6458	668	10	e64	e64	PROPN
ejpam-6458	668	11	,	,	PUNCT
ejpam-6458	668	12	f01	f01	PROPN
ejpam-6458	668	13	=	=	SYM
ejpam-6458	668	14	e13	e13	PROPN
ejpam-6458	668	15	+	+	SYM
ejpam-6458	668	16	e46	e46	X
ejpam-6458	668	17	,	,	PUNCT
ejpam-6458	668	18	e10	e10	NOUN
ejpam-6458	668	19	=	=	SYM
ejpam-6458	668	20	2e17	2e17	NOUN
ejpam-6458	668	21	+	+	CCONJ
ejpam-6458	668	22	e23	e23	NOUN
ejpam-6458	668	23	−	−	PROPN
ejpam-6458	668	24	e45	e45	PROPN
ejpam-6458	668	25	−	−	PROPN
ejpam-6458	668	26	e76	e76	PROPN
ejpam-6458	668	27	,	,	PUNCT
ejpam-6458	668	28	f10	f10	NOUN
ejpam-6458	668	29	=	=	SYM
ejpam-6458	668	30	e32	e32	NOUN
ejpam-6458	668	31	−	−	PROPN
ejpam-6458	668	32	e54	e54	ADJ
ejpam-6458	668	33	−	−	PROPN
ejpam-6458	668	34	2e67	2e67	NOUN
ejpam-6458	668	35	+	+	CCONJ
ejpam-6458	668	36	e71	e71	NOUN
ejpam-6458	668	37	,	,	PUNCT
ejpam-6458	668	38	e11	e11	NOUN
ejpam-6458	668	39	=	=	SYM
ejpam-6458	668	40	−e21	−e21	SYM
ejpam-6458	669	1	+	+	NUM
ejpam-6458	669	2	2e37	2e37	NUM
ejpam-6458	669	3	−	−	PROPN
ejpam-6458	669	4	e65	e65	PROPN
ejpam-6458	669	5	+	+	CCONJ
ejpam-6458	669	6	e74	e74	NOUN
ejpam-6458	669	7	,	,	PUNCT
ejpam-6458	669	8	f11	f11	X
ejpam-6458	669	9	=	=	PUNCT
ejpam-6458	669	10	−e12	−e12	NOUN
ejpam-6458	669	11	+2e47	+2e47	PRON
ejpam-6458	669	12	−e56	−e56	NUM
ejpam-6458	669	13	+	+	NOUN
ejpam-6458	669	14	e73	e73	PROPN
ejpam-6458	669	15	,	,	PUNCT
ejpam-6458	669	16	e21	e21	NUM
ejpam-6458	669	17	=	=	SYM
ejpam-6458	669	18	e14	e14	NOUN
ejpam-6458	669	19	+2e27	+2e27	PROPN
ejpam-6458	669	20	+	+	NOUN
ejpam-6458	669	21	e36	e36	NOUN
ejpam-6458	669	22	+	+	SYM
ejpam-6458	669	23	e75	e75	PROPN
ejpam-6458	669	24	,	,	PUNCT
ejpam-6458	669	25	f21	f21	NOUN
ejpam-6458	669	26	=	=	PUNCT
ejpam-6458	669	27	e41	e41	NOUN
ejpam-6458	669	28	+2e57	+2e57	X
ejpam-6458	669	29	+	+	NOUN
ejpam-6458	669	30	e63	e63	PROPN
ejpam-6458	669	31	+	+	SYM
ejpam-6458	669	32	e72	e72	PROPN
ejpam-6458	669	33	,	,	PUNCT
ejpam-6458	669	34	e31	e31	PROPN
ejpam-6458	669	35	=	=	PROPN
ejpam-6458	669	36	e15	e15	PROPN
ejpam-6458	669	37	+	+	CCONJ
ejpam-6458	669	38	e26	e26	PROPN
ejpam-6458	669	39	,	,	PUNCT
ejpam-6458	669	40	f31	f31	PROPN
ejpam-6458	669	41	=	=	PUNCT
ejpam-6458	669	42	e51	e51	NOUN
ejpam-6458	669	43	+	+	CCONJ
ejpam-6458	669	44	e62	e62	NOUN
ejpam-6458	669	45	,	,	PUNCT
ejpam-6458	669	46	e32	e32	NOUN
ejpam-6458	669	47	=	=	SYM
ejpam-6458	669	48	−e24	−e24	PUNCT
ejpam-6458	669	49	+	+	NUM
ejpam-6458	669	50	e35	e35	NOUN
ejpam-6458	669	51	,	,	PUNCT
ejpam-6458	669	52	f32	f32	NOUN
ejpam-6458	669	53	=	=	SYM
ejpam-6458	669	54	−e42	−e42	NOUN
ejpam-6458	669	55	+	+	X
ejpam-6458	669	56	e53	e53	PROPN
ejpam-6458	669	57	,	,	PUNCT
ejpam-6458	669	58	h01	h01	NOUN
ejpam-6458	669	59	=	=	SYM
ejpam-6458	669	60	−e11	−e11	PUNCT
ejpam-6458	669	61	+	+	CCONJ
ejpam-6458	669	62	e33	e33	PROPN
ejpam-6458	669	63	−	−	PROPN
ejpam-6458	669	64	e44	e44	NOUN
ejpam-6458	669	65	+	+	CCONJ
ejpam-6458	669	66	e66	e66	PROPN
ejpam-6458	669	67	,	,	PUNCT
ejpam-6458	669	68	h10	h10	NOUN
ejpam-6458	669	69	=	=	SYM
ejpam-6458	669	70	2e11	2e11	X
ejpam-6458	669	71	+	+	CCONJ
ejpam-6458	669	72	e22	e22	PROPN
ejpam-6458	669	73	−	−	PROPN
ejpam-6458	669	74	e33	e33	PROPN
ejpam-6458	669	75	+	+	PROPN
ejpam-6458	669	76	e44	e44	PROPN
ejpam-6458	669	77	−	−	PROPN
ejpam-6458	669	78	e55	e55	NOUN
ejpam-6458	670	1	−	−	PROPN
ejpam-6458	670	2	2e66	2e66	NOUN
ejpam-6458	670	3	,	,	PUNCT
ejpam-6458	670	4	h31	h31	NOUN
ejpam-6458	670	5	=	=	SYM
ejpam-6458	670	6	e11	e11	X
ejpam-6458	670	7	+	+	CCONJ
ejpam-6458	670	8	e22	e22	PROPN
ejpam-6458	670	9	−	−	PROPN
ejpam-6458	670	10	e55	e55	NOUN
ejpam-6458	670	11	−	−	PROPN
ejpam-6458	670	12	e66	e66	PROPN
ejpam-6458	670	13	,	,	PUNCT
ejpam-6458	670	14	h21	h21	NOUN
ejpam-6458	670	15	=	=	SYM
ejpam-6458	670	16	e11	e11	X
ejpam-6458	670	17	+	+	NUM
ejpam-6458	670	18	2e22	2e22	NUM
ejpam-6458	670	19	+	+	CCONJ
ejpam-6458	670	20	e33	e33	PROPN
ejpam-6458	670	21	−	−	PROPN
ejpam-6458	670	22	e44	e44	NOUN
ejpam-6458	670	23	−	−	PROPN
ejpam-6458	670	24	2e55	2e55	NOUN
ejpam-6458	671	1	−	−	PROPN
ejpam-6458	671	2	e66	e66	PROPN
ejpam-6458	671	3	.	.	PUNCT
ejpam-6458	672	1	here	here	ADV
ejpam-6458	672	2	we	we	PRON
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ejpam-6458	672	4	using	use	VERB
ejpam-6458	672	5	a	a	DET
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ejpam-6458	672	9	g2	g2	PROPN
ejpam-6458	672	10	with	with	ADP
ejpam-6458	672	11	matrix	matrix	NOUN
ejpam-6458	672	12	units	unit	NOUN
ejpam-6458	672	13	eij	eij	PROPN
ejpam-6458	672	14	.	.	PUNCT
ejpam-6458	673	1	all	all	DET
ejpam-6458	673	2	indecomposable	indecomposable	ADJ
ejpam-6458	673	3	lists	list	NOUN
ejpam-6458	673	4	of	of	ADP
ejpam-6458	673	5	roots	root	NOUN
ejpam-6458	673	6	of	of	ADP
ejpam-6458	673	7	g2	g2	PROPN
ejpam-6458	673	8	can	can	AUX
ejpam-6458	673	9	be	be	AUX
ejpam-6458	673	10	obtained	obtain	VERB
ejpam-6458	673	11	from	from	ADP
ejpam-6458	673	12	primitive	primitive	ADJ
ejpam-6458	673	13	lists	list	NOUN
ejpam-6458	673	14	of	of	ADP
ejpam-6458	673	15	roots	root	NOUN
ejpam-6458	673	16	by	by	ADP
ejpam-6458	673	17	lemma	lemma	PROPN
ejpam-6458	673	18	2.3.2	2.3.2	NUM
ejpam-6458	673	19	.	.	PUNCT
ejpam-6458	674	1	then	then	ADV
ejpam-6458	674	2	we	we	PRON
ejpam-6458	674	3	obtain	obtain	VERB
ejpam-6458	674	4	the	the	DET
ejpam-6458	674	5	following	follow	VERB
ejpam-6458	674	6	description	description	NOUN
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ejpam-6458	674	8	perfect	perfect	ADJ
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ejpam-6458	674	10	(	(	PUNCT
ejpam-6458	674	11	we	we	PRON
ejpam-6458	674	12	omit	omit	VERB
ejpam-6458	674	13	the	the	DET
ejpam-6458	674	14	details	detail	NOUN
ejpam-6458	674	15	)	)	PUNCT
ejpam-6458	674	16	.	.	PUNCT
ejpam-6458	675	1	lemma	lemma	PROPN
ejpam-6458	675	2	6.1	6.1	NUM
ejpam-6458	675	3	.	.	PUNCT
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ejpam-6458	676	2	following	follow	VERB
ejpam-6458	676	3	is	be	AUX
ejpam-6458	676	4	the	the	DET
ejpam-6458	676	5	set	set	NOUN
ejpam-6458	676	6	of	of	ADP
ejpam-6458	676	7	all	all	DET
ejpam-6458	676	8	perfect	perfect	ADJ
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ejpam-6458	676	10	:	:	PUNCT
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ejpam-6458	676	16	=	=	SYM
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ejpam-6458	676	19	c1	c1	PROPN
ejpam-6458	676	20	=	=	PUNCT
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ejpam-6458	676	22	,	,	PUNCT
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ejpam-6458	676	24	=	=	SYM
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ejpam-6458	676	28	=	=	SYM
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ejpam-6458	676	32	=	=	SYM
ejpam-6458	676	33	f11e10e01	f11e10e01	PROPN
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ejpam-6458	676	36	=	=	SYM
ejpam-6458	676	37	f01f10e11	f01f10e11	PROPN
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ejpam-6458	676	40	=	=	SYM
ejpam-6458	676	41	f21e21	f21e21	PROPN
ejpam-6458	676	42	,	,	PUNCT
ejpam-6458	676	43	c7	c7	PROPN
ejpam-6458	676	44	=	=	SYM
ejpam-6458	676	45	f21e11e10	f21e11e10	PROPN
ejpam-6458	676	46	,	,	PUNCT
ejpam-6458	676	47	c8	c8	PROPN
ejpam-6458	676	48	=	=	SYM
ejpam-6458	676	49	f10f11e21	f10f11e21	PROPN
ejpam-6458	676	50	,	,	PUNCT
ejpam-6458	676	51	c9	c9	NOUN
ejpam-6458	676	52	=	=	PUNCT
ejpam-6458	676	53	f21e	f21e	VERB
ejpam-6458	676	54	2	2	NUM
ejpam-6458	676	55	10e01	10e01	NUM
ejpam-6458	676	56	,	,	PUNCT
ejpam-6458	676	57	c10	c10	PROPN
ejpam-6458	676	58	=	=	SYM
ejpam-6458	676	59	f01f	f01f	PROPN
ejpam-6458	676	60	2	2	NUM
ejpam-6458	676	61	10e21	10e21	NUM
ejpam-6458	676	62	,	,	PUNCT
ejpam-6458	676	63	c11	c11	NOUN
ejpam-6458	676	64	=	=	SYM
ejpam-6458	676	65	f211e21e01	f211e21e01	X
ejpam-6458	676	66	,	,	PUNCT
ejpam-6458	676	67	c12	c12	NOUN
ejpam-6458	676	68	=	=	PUNCT
ejpam-6458	676	69	f01f21e	f01f21e	VERB
ejpam-6458	676	70	2	2	NUM
ejpam-6458	676	71	11	11	NUM
ejpam-6458	676	72	,	,	PUNCT
ejpam-6458	676	73	c13	c13	NOUN
ejpam-6458	676	74	=	=	SYM
ejpam-6458	676	75	f31e31	f31e31	PROPN
ejpam-6458	676	76	,	,	PUNCT
ejpam-6458	676	77	c14	c14	NOUN
ejpam-6458	676	78	=	=	SYM
ejpam-6458	676	79	f31e21e10	f31e21e10	PROPN
ejpam-6458	676	80	,	,	PUNCT
ejpam-6458	676	81	c15	c15	NOUN
ejpam-6458	676	82	=	=	SYM
ejpam-6458	676	83	f10f21e31	f10f21e31	PROPN
ejpam-6458	676	84	,	,	PUNCT
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ejpam-6458	676	86	=	=	SYM
ejpam-6458	676	87	f31e11e	f31e11e	NOUN
ejpam-6458	676	88	2	2	NUM
ejpam-6458	676	89	10	10	NUM
ejpam-6458	676	90	,	,	PUNCT
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ejpam-6458	676	92	=	=	SYM
ejpam-6458	676	93	f210f11e31	f210f11e31	PROPN
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ejpam-6458	676	95	c18	c18	NOUN
ejpam-6458	676	96	=	=	SYM
ejpam-6458	676	97	f31e	f31e	NOUN
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ejpam-6458	676	99	10e01	10e01	NUM
ejpam-6458	676	100	,	,	PUNCT
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ejpam-6458	676	102	=	=	SYM
ejpam-6458	676	103	f01f	f01f	PROPN
ejpam-6458	676	104	3	3	NUM
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ejpam-6458	676	108	=	=	PUNCT
ejpam-6458	676	109	f32e32	f32e32	PROPN
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ejpam-6458	676	113	f32e31e01	f32e31e01	PROPN
ejpam-6458	676	114	,	,	PUNCT
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ejpam-6458	676	116	=	=	PROPN
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ejpam-6458	676	120	=	=	SYM
ejpam-6458	676	121	f01f31e32	f01f31e32	PROPN
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ejpam-6458	676	124	=	=	SYM
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ejpam-6458	676	132	=	=	SYM
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ejpam-6458	676	137	f32e	f32e	NUM
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ejpam-6458	676	139	11e10	11e10	NUM
ejpam-6458	676	140	,	,	PUNCT
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ejpam-6458	676	148	,	,	PUNCT
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ejpam-6458	676	151	f10f	f10f	ADP
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ejpam-6458	676	154	,	,	PUNCT
ejpam-6458	676	155	c31	c31	PROPN
ejpam-6458	676	156	=	=	SYM
ejpam-6458	676	157	f32e11e	f32e11e	VERB
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ejpam-6458	676	163	f10f	f10f	ADP
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ejpam-6458	676	166	,	,	PUNCT
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ejpam-6458	676	169	f01f31e	f01f31e	ADJ
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ejpam-6458	676	175	f01f	f01f	X
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ejpam-6458	676	182	3	3	NUM
ejpam-6458	676	183	10e	10e	NOUN
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ejpam-6458	676	187	c36	c36	PROPN
ejpam-6458	676	188	=	=	PUNCT
ejpam-6458	676	189	f201f	f201f	PROPN
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ejpam-6458	676	199	f01f32e	f01f32e	NOUN
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ejpam-6458	676	202	,	,	PUNCT
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ejpam-6458	676	204	=	=	SYM
ejpam-6458	676	205	f311e31e	f311e31e	PROPN
ejpam-6458	676	206	2	2	NUM
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ejpam-6458	676	208	,	,	PUNCT
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ejpam-6458	676	210	=	=	PUNCT
ejpam-6458	677	1	f201f31e	f201f31e	PROPN
ejpam-6458	677	2	3	3	NUM
ejpam-6458	677	3	11	11	NUM
ejpam-6458	677	4	,	,	PUNCT
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ejpam-6458	677	6	=	=	PUNCT
ejpam-6458	677	7	f11f31e32e10	f11f31e32e10	PROPN
ejpam-6458	677	8	,	,	PUNCT
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ejpam-6458	677	10	=	=	SYM
ejpam-6458	677	11	f221e32e10	f221e32e10	NUM
ejpam-6458	677	12	,	,	PUNCT
ejpam-6458	677	13	c43	c43	X
ejpam-6458	677	14	=	=	SYM
ejpam-6458	677	15	f10f32e31e11	f10f32e31e11	ADJ
ejpam-6458	677	16	,	,	PUNCT
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ejpam-6458	677	18	=	=	SYM
ejpam-6458	677	19	f221e31e11	f221e31e11	PROPN
ejpam-6458	677	20	,	,	PUNCT
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ejpam-6458	677	22	=	=	SYM
ejpam-6458	677	23	f10f32e	f10f32e	PROPN
ejpam-6458	677	24	2	2	NUM
ejpam-6458	677	25	21	21	NUM
ejpam-6458	677	26	,	,	PUNCT
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ejpam-6458	677	28	=	=	SYM
ejpam-6458	677	29	f11f31e	f11f31e	PROPN
ejpam-6458	677	30	2	2	NUM
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ejpam-6458	677	32	,	,	PUNCT
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ejpam-6458	677	34	=	=	SYM
ejpam-6458	677	35	f221e31e10e01	f221e31e10e01	NOUN
ejpam-6458	677	36	,	,	PUNCT
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ejpam-6458	677	38	=	=	SYM
ejpam-6458	677	39	f01f10f31e	f01f10f31e	NOUN
ejpam-6458	677	40	2	2	NUM
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ejpam-6458	677	42	,	,	PUNCT
ejpam-6458	677	43	c49	c49	NOUN
ejpam-6458	677	44	=	=	SYM
ejpam-6458	677	45	f11f32e	f11f32e	NUM
ejpam-6458	677	46	2	2	NUM
ejpam-6458	677	47	21e01	21e01	NUM
ejpam-6458	677	48	,	,	PUNCT
ejpam-6458	677	49	c50	c50	NOUN
ejpam-6458	677	50	=	=	SYM
ejpam-6458	677	51	f01f	f01f	PROPN
ejpam-6458	677	52	2	2	NUM
ejpam-6458	677	53	21e32e11	21e32e11	NUM
ejpam-6458	677	54	,	,	PUNCT
ejpam-6458	677	55	c51	c51	NOUN
ejpam-6458	677	56	=	=	SYM
ejpam-6458	677	57	f21f31e32e	f21f31e32e	NOUN
ejpam-6458	677	58	2	2	NUM
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ejpam-6458	677	62	=	=	SYM
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ejpam-6458	677	64	,	,	PUNCT
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ejpam-6458	677	66	=	=	SYM
ejpam-6458	677	67	f21f32e31e	f21f32e31e	NOUN
ejpam-6458	677	68	2	2	NUM
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ejpam-6458	677	70	,	,	PUNCT
ejpam-6458	677	71	c54	c54	NOUN
ejpam-6458	677	72	=	=	SYM
ejpam-6458	677	73	f211f31e32e21	f211f31e32e21	PROPN
ejpam-6458	677	74	,	,	PUNCT
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ejpam-6458	677	76	=	=	SYM
ejpam-6458	677	77	f231e32e	f231e32e	NOUN
ejpam-6458	677	78	3	3	NUM
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ejpam-6458	677	80	,	,	PUNCT
ejpam-6458	677	81	c56	c56	NOUN
ejpam-6458	677	82	=	=	SYM
ejpam-6458	677	83	f310f32e	f310f32e	NOUN
ejpam-6458	677	84	2	2	NUM
ejpam-6458	677	85	31	31	NUM
ejpam-6458	677	86	,	,	PUNCT
ejpam-6458	677	87	c57	c57	NOUN
ejpam-6458	677	88	=	=	PUNCT
ejpam-6458	677	89	f31f32e	f31f32e	PROPN
ejpam-6458	677	90	3	3	NUM
ejpam-6458	677	91	21	21	NUM
ejpam-6458	677	92	,	,	PUNCT
ejpam-6458	677	93	c58	c58	NOUN
ejpam-6458	677	94	=	=	SYM
ejpam-6458	677	95	f32,1e32e31	f32,1e32e31	PROPN
ejpam-6458	677	96	,	,	PUNCT
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ejpam-6458	677	98	=	=	SYM
ejpam-6458	677	99	f321e	f321e	PROPN
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ejpam-6458	677	101	31e01	31e01	NUM
ejpam-6458	677	102	,	,	PUNCT
ejpam-6458	677	103	c60	c60	NOUN
ejpam-6458	677	104	=	=	SYM
ejpam-6458	677	105	f01f	f01f	PROPN
ejpam-6458	677	106	2	2	NUM
ejpam-6458	677	107	31e	31e	NOUN
ejpam-6458	677	108	3	3	NUM
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ejpam-6458	677	110	,	,	PUNCT
ejpam-6458	677	111	c61	c61	PROPN
ejpam-6458	677	112	=	=	SYM
ejpam-6458	677	113	f232e	f232e	PROPN
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ejpam-6458	677	115	21e01	21e01	NUM
ejpam-6458	677	116	,	,	PUNCT
ejpam-6458	677	117	c62	c62	NOUN
ejpam-6458	677	118	=	=	PUNCT
ejpam-6458	677	119	f232e31e	f232e31e	NOUN
ejpam-6458	677	120	3	3	NUM
ejpam-6458	677	121	11	11	NUM
ejpam-6458	677	122	,	,	PUNCT
ejpam-6458	677	123	c63	c63	NOUN
ejpam-6458	677	124	=	=	PUNCT
ejpam-6458	677	125	f311f31e	f311f31e	NOUN
ejpam-6458	677	126	2	2	NUM
ejpam-6458	677	127	32	32	NUM
ejpam-6458	677	128	,	,	PUNCT
ejpam-6458	677	129	c64	c64	X
ejpam-6458	677	130	=	=	SYM
ejpam-6458	677	131	f01f	f01f	PROPN
ejpam-6458	677	132	3	3	NUM
ejpam-6458	677	133	21e	21e	NOUN
ejpam-6458	677	134	2	2	NUM
ejpam-6458	677	135	32	32	NUM
ejpam-6458	677	136	.	.	PUNCT
ejpam-6458	678	1	define	define	VERB
ejpam-6458	678	2	the	the	DET
ejpam-6458	678	3	order	order	NOUN
ejpam-6458	678	4	on	on	ADP
ejpam-6458	678	5	the	the	DET
ejpam-6458	678	6	set	set	NOUN
ejpam-6458	678	7	of	of	ADP
ejpam-6458	678	8	perfect	perfect	ADJ
ejpam-6458	678	9	monomials	monomial	NOUN
ejpam-6458	678	10	as	as	SCONJ
ejpam-6458	678	11	follows	follow	VERB
ejpam-6458	678	12	:	:	PUNCT
ejpam-6458	678	13	h1	h1	VERB
ejpam-6458	678	14	<	<	X
ejpam-6458	678	15	h2	h2	PROPN
ejpam-6458	678	16	<	<	X
ejpam-6458	678	17	c1	c1	PROPN
ejpam-6458	678	18	<	<	X
ejpam-6458	678	19	c2	c2	PROPN
ejpam-6458	678	20	<	<	X
ejpam-6458	678	21	·	·	PUNCT
ejpam-6458	678	22	·	·	PUNCT
ejpam-6458	678	23	·	·	PUNCT
ejpam-6458	679	1	<	<	X
ejpam-6458	679	2	c63	c63	PROPN
ejpam-6458	679	3	<	<	X
ejpam-6458	679	4	c64	c64	PROPN
ejpam-6458	679	5	.	.	PUNCT
ejpam-6458	680	1	the	the	DET
ejpam-6458	680	2	following	follow	VERB
ejpam-6458	680	3	proposition	proposition	NOUN
ejpam-6458	680	4	can	can	AUX
ejpam-6458	680	5	be	be	AUX
ejpam-6458	680	6	easily	easily	ADV
ejpam-6458	680	7	checked	check	VERB
ejpam-6458	680	8	.	.	PUNCT
ejpam-6458	681	1	proposition	proposition	NOUN
ejpam-6458	681	2	6.2	6.2	NUM
ejpam-6458	681	3	.	.	PUNCT
ejpam-6458	682	1	the	the	DET
ejpam-6458	682	2	centralizer	centralizer	NOUN
ejpam-6458	682	3	subalgebra	subalgebra	NOUN
ejpam-6458	682	4	u0(g2	u0(g2	VERB
ejpam-6458	682	5	)	)	PUNCT
ejpam-6458	682	6	is	be	AUX
ejpam-6458	682	7	generated	generate	VERB
ejpam-6458	682	8	by	by	ADP
ejpam-6458	682	9	a	a	DET
ejpam-6458	682	10	finite	finite	ADJ
ejpam-6458	682	11	set	set	NOUN
ejpam-6458	682	12	of	of	ADP
ejpam-6458	682	13	monomials	monomial	NOUN
ejpam-6458	682	14	{	{	PUNCT
ejpam-6458	682	15	h1	h1	PROPN
ejpam-6458	682	16	,	,	PUNCT
ejpam-6458	682	17	h2	h2	PROPN
ejpam-6458	682	18	,	,	PUNCT
ejpam-6458	682	19	c1	c1	PROPN
ejpam-6458	682	20	,	,	PUNCT
ejpam-6458	682	21	.	.	PUNCT
ejpam-6458	682	22	.	.	PUNCT
ejpam-6458	683	1	.	.	PUNCT
ejpam-6458	684	1	,	,	PUNCT
ejpam-6458	684	2	c64	c64	PROPN
ejpam-6458	684	3	}	}	PUNCT
ejpam-6458	684	4	with	with	ADP
ejpam-6458	684	5	a	a	DET
ejpam-6458	684	6	finite	finite	ADJ
ejpam-6458	684	7	number	number	NOUN
ejpam-6458	684	8	of	of	ADP
ejpam-6458	684	9	relations	relation	NOUN
ejpam-6458	684	10	{	{	PUNCT
ejpam-6458	684	11	r1	r1	NOUN
ejpam-6458	684	12	,	,	PUNCT
ejpam-6458	684	13	.	.	PUNCT
ejpam-6458	684	14	.	.	PUNCT
ejpam-6458	685	1	.	.	PUNCT
ejpam-6458	686	1	,	,	PUNCT
ejpam-6458	686	2	rm	rm	PROPN
ejpam-6458	686	3	}	}	PUNCT
ejpam-6458	686	4	,	,	PUNCT
ejpam-6458	686	5	where	where	SCONJ
ejpam-6458	686	6	ri	ri	PROPN
ejpam-6458	686	7	is	be	AUX
ejpam-6458	686	8	a	a	DET
ejpam-6458	686	9	polynomial	polynomial	NOUN
ejpam-6458	686	10	in	in	ADP
ejpam-6458	686	11	h1	h1	PROPN
ejpam-6458	686	12	,	,	PUNCT
ejpam-6458	686	13	h2	h2	PROPN
ejpam-6458	686	14	,	,	PUNCT
ejpam-6458	686	15	c1	c1	PROPN
ejpam-6458	686	16	,	,	PUNCT
ejpam-6458	686	17	.	.	PUNCT
ejpam-6458	686	18	.	.	PUNCT
ejpam-6458	687	1	.	.	PUNCT
ejpam-6458	688	1	,	,	PUNCT
ejpam-6458	688	2	c64	c64	PROPN
ejpam-6458	688	3	of	of	ADP
ejpam-6458	688	4	length	length	NOUN
ejpam-6458	688	5	≤	≤	NUM
ejpam-6458	688	6	4	4	NUM
ejpam-6458	688	7	.	.	PUNCT
ejpam-6458	689	1	we	we	PRON
ejpam-6458	689	2	will	will	AUX
ejpam-6458	689	3	use	use	VERB
ejpam-6458	689	4	the	the	DET
ejpam-6458	689	5	following	follow	VERB
ejpam-6458	689	6	quadratic	quadratic	ADJ
ejpam-6458	689	7	casimir	casimir	NOUN
ejpam-6458	689	8	element	element	NOUN
ejpam-6458	689	9	of	of	ADP
ejpam-6458	689	10	u0(g	u0(g	NOUN
ejpam-6458	689	11	):	):	PUNCT
ejpam-6458	689	12	z1	z1	ADJ
ejpam-6458	689	13	=	=	SYM
ejpam-6458	689	14	3c1	3c1	NUM
ejpam-6458	689	15	+	+	CCONJ
ejpam-6458	689	16	c2	c2	PROPN
ejpam-6458	689	17	+	+	CCONJ
ejpam-6458	689	18	c3	c3	PROPN
ejpam-6458	689	19	+	+	CCONJ
ejpam-6458	689	20	c6	c6	PROPN
ejpam-6458	689	21	+	+	CCONJ
ejpam-6458	689	22	3c13	3c13	NUM
ejpam-6458	689	23	+	+	CCONJ
ejpam-6458	689	24	3c20	3c20	NOUN
ejpam-6458	689	25	+	+	PUNCT
ejpam-6458	689	26	h201	h201	NUM
ejpam-6458	689	27	+	+	CCONJ
ejpam-6458	689	28	h01h10	h01h10	NOUN
ejpam-6458	689	29	+	+	CCONJ
ejpam-6458	689	30	h210	h210	PROPN
ejpam-6458	689	31	+	+	NUM
ejpam-6458	689	32	4h01	4h01	NOUN
ejpam-6458	689	33	+	+	CCONJ
ejpam-6458	689	34	5h10	5h10	NUM
ejpam-6458	689	35	.	.	PUNCT
ejpam-6458	690	1	tedious	tedious	ADJ
ejpam-6458	690	2	computations	computation	NOUN
ejpam-6458	690	3	show	show	VERB
ejpam-6458	690	4	that	that	SCONJ
ejpam-6458	690	5	using	use	VERB
ejpam-6458	690	6	the	the	DET
ejpam-6458	690	7	relations	relation	NOUN
ejpam-6458	690	8	,	,	PUNCT
ejpam-6458	690	9	the	the	DET
ejpam-6458	690	10	elements	element	NOUN
ejpam-6458	690	11	c64	c64	PROPN
ejpam-6458	690	12	,	,	PUNCT
ejpam-6458	690	13	.	.	PUNCT
ejpam-6458	690	14	.	.	PUNCT
ejpam-6458	690	15	.	.	PUNCT
ejpam-6458	691	1	,	,	PUNCT
ejpam-6458	691	2	c5	c5	PROPN
ejpam-6458	691	3	can	can	AUX
ejpam-6458	691	4	be	be	AUX
ejpam-6458	691	5	written	write	VERB
ejpam-6458	691	6	in	in	ADP
ejpam-6458	691	7	terms	term	NOUN
ejpam-6458	691	8	of	of	ADP
ejpam-6458	691	9	c4	c4	NOUN
ejpam-6458	691	10	,	,	PUNCT
ejpam-6458	691	11	c3	c3	PROPN
ejpam-6458	691	12	,	,	PUNCT
ejpam-6458	691	13	c2	c2	PROPN
ejpam-6458	691	14	,	,	PUNCT
ejpam-6458	691	15	c1	c1	PROPN
ejpam-6458	691	16	,	,	PUNCT
ejpam-6458	691	17	h1	h1	PROPN
ejpam-6458	691	18	,	,	PUNCT
ejpam-6458	691	19	h2	h2	PROPN
ejpam-6458	691	20	,	,	PUNCT
ejpam-6458	691	21	z1	z1	PROPN
ejpam-6458	691	22	.	.	PUNCT
ejpam-6458	692	1	the	the	DET
ejpam-6458	692	2	lie	lie	NOUN
ejpam-6458	692	3	algebra	algebra	PROPN
ejpam-6458	692	4	g2	g2	PROPN
ejpam-6458	692	5	contains	contain	VERB
ejpam-6458	692	6	the	the	DET
ejpam-6458	692	7	subalgebra	subalgebra	NOUN
ejpam-6458	692	8	ĝ	ĝ	NOUN
ejpam-6458	692	9	of	of	ADP
ejpam-6458	692	10	type	type	NOUN
ejpam-6458	692	11	a2	a2	PROPN
ejpam-6458	692	12	generated	generate	VERB
ejpam-6458	692	13	by	by	ADP
ejpam-6458	692	14	the	the	DET
ejpam-6458	692	15	following	follow	VERB
ejpam-6458	692	16	elements	element	NOUN
ejpam-6458	692	17	h01	h01	NOUN
ejpam-6458	692	18	,	,	PUNCT
ejpam-6458	692	19	h31	h31	ADJ
ejpam-6458	692	20	,	,	PUNCT
ejpam-6458	692	21	e01	e01	NOUN
ejpam-6458	692	22	,	,	PUNCT
ejpam-6458	692	23	f01	f01	NOUN
ejpam-6458	692	24	,	,	PUNCT
ejpam-6458	692	25	e31	e31	PROPN
ejpam-6458	692	26	,	,	PUNCT
ejpam-6458	692	27	f31	f31	PROPN
ejpam-6458	692	28	,	,	PUNCT
ejpam-6458	692	29	e32	e32	NOUN
ejpam-6458	692	30	,	,	PUNCT
ejpam-6458	692	31	f32	f32	NOUN
ejpam-6458	692	32	.	.	PUNCT
ejpam-6458	693	1	we	we	PRON
ejpam-6458	693	2	will	will	AUX
ejpam-6458	693	3	use	use	VERB
ejpam-6458	693	4	the	the	DET
ejpam-6458	693	5	results	result	NOUN
ejpam-6458	693	6	from	from	ADP
ejpam-6458	693	7	the	the	DET
ejpam-6458	693	8	previous	previous	ADJ
ejpam-6458	693	9	sections	section	NOUN
ejpam-6458	693	10	just	just	ADV
ejpam-6458	693	11	adding	add	VERB
ejpam-6458	693	12	”	"	PUNCT
ejpam-6458	693	13	hat	hat	NOUN
ejpam-6458	693	14	”	"	PUNCT
ejpam-6458	693	15	to	to	ADP
ejpam-6458	693	16	all	all	DET
ejpam-6458	693	17	generators	generator	NOUN
ejpam-6458	693	18	and	and	CCONJ
ejpam-6458	693	19	to	to	ADP
ejpam-6458	693	20	all	all	DET
ejpam-6458	693	21	formulas	formula	NOUN
ejpam-6458	693	22	.	.	PUNCT
ejpam-6458	694	1	consider	consider	VERB
ejpam-6458	694	2	a	a	DET
ejpam-6458	694	3	natural	natural	ADJ
ejpam-6458	694	4	embedding	embed	VERB
ejpam-6458	694	5	φ	φ	NOUN
ejpam-6458	694	6	:	:	PUNCT
ejpam-6458	694	7	ĝ	ĝ	X
ejpam-6458	694	8	→	→	SYM
ejpam-6458	694	9	g	g	NOUN
ejpam-6458	694	10	:	:	PUNCT
ejpam-6458	694	11	φ(ĥ01	φ(ĥ01	NOUN
ejpam-6458	694	12	)	)	PUNCT
ejpam-6458	694	13	=	=	SYM
ejpam-6458	694	14	h01	h01	NOUN
ejpam-6458	694	15	,	,	PUNCT
ejpam-6458	694	16	φ(ĥ10	φ(ĥ10	NUM
ejpam-6458	694	17	)	)	PUNCT
ejpam-6458	694	18	=	=	SYM
ejpam-6458	694	19	h31	h31	ADJ
ejpam-6458	694	20	,	,	PUNCT
ejpam-6458	694	21	φ(ê01	φ(ê01	ADJ
ejpam-6458	694	22	)	)	PUNCT
ejpam-6458	694	23	=	=	SYM
ejpam-6458	694	24	e01	e01	X
ejpam-6458	694	25	,	,	PUNCT
ejpam-6458	694	26	φ(f̂01	φ(f̂01	PROPN
ejpam-6458	694	27	)	)	PUNCT
ejpam-6458	695	1	=	=	SYM
ejpam-6458	695	2	f01	f01	NOUN
ejpam-6458	695	3	,	,	PUNCT
ejpam-6458	695	4	φ(ê10	φ(ê10	NOUN
ejpam-6458	695	5	)	)	PUNCT
ejpam-6458	695	6	=	=	SYM
ejpam-6458	695	7	e31	e31	X
ejpam-6458	695	8	,	,	PUNCT
ejpam-6458	695	9	φ(f̂10	φ(f̂10	NUM
ejpam-6458	695	10	)	)	PUNCT
ejpam-6458	695	11	=	=	SYM
ejpam-6458	695	12	f31	f31	PROPN
ejpam-6458	695	13	,	,	PUNCT
ejpam-6458	695	14	φ(ê11	φ(ê11	PROPN
ejpam-6458	695	15	)	)	PUNCT
ejpam-6458	695	16	=	=	SYM
ejpam-6458	695	17	e32	e32	PROPN
ejpam-6458	695	18	,	,	PUNCT
ejpam-6458	695	19	φ(f̂11	φ(f̂11	ADJ
ejpam-6458	695	20	)	)	PUNCT
ejpam-6458	695	21	=	=	SYM
ejpam-6458	695	22	f32	f32	NOUN
ejpam-6458	695	23	m.	m.	NOUN
ejpam-6458	695	24	andelić	andelić	PROPN
ejpam-6458	695	25	et	et	PROPN
ejpam-6458	695	26	al	al	PROPN
ejpam-6458	695	27	.	.	PUNCT
ejpam-6458	695	28	/	/	SYM
ejpam-6458	695	29	eur	eur	PROPN
ejpam-6458	695	30	.	.	PUNCT
ejpam-6458	696	1	j.	j.	PROPN
ejpam-6458	696	2	pure	pure	PROPN
ejpam-6458	696	3	appl	appl	PROPN
ejpam-6458	696	4	.	.	PROPN
ejpam-6458	696	5	math	math	PROPN
ejpam-6458	696	6	,	,	PUNCT
ejpam-6458	696	7	18	18	NUM
ejpam-6458	696	8	(	(	PUNCT
ejpam-6458	696	9	3	3	NUM
ejpam-6458	696	10	)	)	PUNCT
ejpam-6458	696	11	(	(	PUNCT
ejpam-6458	696	12	2025	2025	NUM
ejpam-6458	696	13	)	)	PUNCT
ejpam-6458	696	14	,	,	PUNCT
ejpam-6458	696	15	6458	6458	NUM
ejpam-6458	696	16	18	18	NUM
ejpam-6458	696	17	of	of	ADP
ejpam-6458	696	18	21	21	NUM
ejpam-6458	696	19	and	and	CCONJ
ejpam-6458	696	20	extend	extend	VERB
ejpam-6458	696	21	it	it	PRON
ejpam-6458	696	22	to	to	ADP
ejpam-6458	696	23	the	the	DET
ejpam-6458	696	24	embedding	embedding	NOUN
ejpam-6458	696	25	of	of	ADP
ejpam-6458	696	26	the	the	DET
ejpam-6458	696	27	universal	universal	ADJ
ejpam-6458	696	28	enveloping	enveloping	NOUN
ejpam-6458	696	29	algebras	algebra	NOUN
ejpam-6458	696	30	.	.	PUNCT
ejpam-6458	697	1	the	the	DET
ejpam-6458	697	2	images	image	NOUN
ejpam-6458	697	3	of	of	ADP
ejpam-6458	697	4	the	the	DET
ejpam-6458	697	5	casimir	casimir	NOUN
ejpam-6458	697	6	elements	element	NOUN
ejpam-6458	697	7	ẑ1	ẑ1	PROPN
ejpam-6458	697	8	,	,	PUNCT
ejpam-6458	697	9	ẑ2	ẑ2	X
ejpam-6458	697	10	of	of	ADP
ejpam-6458	697	11	u(ĝ	u(ĝ	NOUN
ejpam-6458	697	12	)	)	PUNCT
ejpam-6458	697	13	in	in	ADP
ejpam-6458	697	14	u(g	u(g	PROPN
ejpam-6458	697	15	)	)	PUNCT
ejpam-6458	697	16	are	be	AUX
ejpam-6458	697	17	:	:	PUNCT
ejpam-6458	697	18	z1	z1	PROPN
ejpam-6458	697	19	=	=	PUNCT
ejpam-6458	697	20	φ(ẑ1	φ(ẑ1	PROPN
ejpam-6458	697	21	)	)	PUNCT
ejpam-6458	697	22	=	=	SYM
ejpam-6458	697	23	c20	c20	NOUN
ejpam-6458	697	24	+	+	CCONJ
ejpam-6458	697	25	c13	c13	PROPN
ejpam-6458	697	26	+	+	X
ejpam-6458	697	27	c1	c1	PROPN
ejpam-6458	697	28	+	+	CCONJ
ejpam-6458	697	29	1	1	NUM
ejpam-6458	697	30	3	3	NUM
ejpam-6458	697	31	(	(	PUNCT
ejpam-6458	697	32	h231	h231	PROPN
ejpam-6458	697	33	+	+	NUM
ejpam-6458	697	34	3h31	3h31	NUM
ejpam-6458	698	1	+	+	SYM
ejpam-6458	698	2	h201	h201	NUM
ejpam-6458	699	1	+	+	NUM
ejpam-6458	699	2	3h01	3h01	NUM
ejpam-6458	699	3	+	+	CCONJ
ejpam-6458	699	4	h31h01	h31h01	NOUN
ejpam-6458	699	5	)	)	PUNCT
ejpam-6458	699	6	z2	z2	PROPN
ejpam-6458	699	7	=	=	SYM
ejpam-6458	699	8	φ(ẑ2	φ(ẑ2	PROPN
ejpam-6458	699	9	)	)	PUNCT
ejpam-6458	699	10	=	=	SYM
ejpam-6458	699	11	c23	c23	PROPN
ejpam-6458	699	12	+	+	CCONJ
ejpam-6458	699	13	c21	c21	NOUN
ejpam-6458	700	1	+	+	CCONJ
ejpam-6458	700	2	1	1	NUM
ejpam-6458	700	3	3	3	NUM
ejpam-6458	700	4	(	(	PUNCT
ejpam-6458	700	5	h01	h01	PROPN
ejpam-6458	700	6	−	−	PROPN
ejpam-6458	701	1	h31)c20	h31)c20	PROPN
ejpam-6458	702	1	−	−	PROPN
ejpam-6458	703	1	1	1	NUM
ejpam-6458	703	2	3	3	NUM
ejpam-6458	703	3	(	(	PUNCT
ejpam-6458	703	4	6	6	NUM
ejpam-6458	703	5	+	+	NUM
ejpam-6458	703	6	2h01	2h01	NUM
ejpam-6458	703	7	+	+	SYM
ejpam-6458	703	8	h31)c13	h31)c13	NUM
ejpam-6458	704	1	+	+	CCONJ
ejpam-6458	704	2	1	1	NUM
ejpam-6458	704	3	3	3	NUM
ejpam-6458	704	4	(	(	PUNCT
ejpam-6458	704	5	h01	h01	PROPN
ejpam-6458	704	6	+	+	CCONJ
ejpam-6458	704	7	2h31)c1	2h31)c1	PROPN
ejpam-6458	704	8	+	+	CCONJ
ejpam-6458	704	9	1	1	NUM
ejpam-6458	704	10	27	27	NUM
ejpam-6458	704	11	(	(	PUNCT
ejpam-6458	704	12	−h31	−h31	NUM
ejpam-6458	704	13	−	−	NOUN
ejpam-6458	704	14	3	3	NUM
ejpam-6458	704	15	+	+	NUM
ejpam-6458	704	16	h01)(6	h01)(6	NOUN
ejpam-6458	704	17	+	+	NUM
ejpam-6458	704	18	2h01	2h01	NUM
ejpam-6458	704	19	+	+	CCONJ
ejpam-6458	704	20	h31)(h01	h31)(h01	NOUN
ejpam-6458	704	21	+	+	CCONJ
ejpam-6458	704	22	2h31	2h31	NUM
ejpam-6458	704	23	)	)	PUNCT
ejpam-6458	704	24	.	.	PUNCT
ejpam-6458	705	1	6.2	6.2	NUM
ejpam-6458	705	2	.	.	PUNCT
ejpam-6458	706	1	torsion	torsion	NOUN
ejpam-6458	706	2	free	free	ADJ
ejpam-6458	706	3	g2	g2	NOUN
ejpam-6458	706	4	-	-	PUNCT
ejpam-6458	706	5	modules	module	NOUN
ejpam-6458	706	6	let	let	VERB
ejpam-6458	706	7	γ	γ	NOUN
ejpam-6458	706	8	be	be	AUX
ejpam-6458	706	9	commutative	commutative	ADJ
ejpam-6458	706	10	subalgebra	subalgebra	NOUN
ejpam-6458	706	11	of	of	ADP
ejpam-6458	706	12	u0(g2	u0(g2	ADJ
ejpam-6458	706	13	)	)	PUNCT
ejpam-6458	706	14	generated	generate	VERB
ejpam-6458	706	15	by	by	ADP
ejpam-6458	706	16	elements	element	NOUN
ejpam-6458	706	17	h1	h1	PROPN
ejpam-6458	706	18	,	,	PUNCT
ejpam-6458	706	19	h2	h2	PROPN
ejpam-6458	706	20	,	,	PUNCT
ejpam-6458	706	21	z1	z1	PROPN
ejpam-6458	706	22	,	,	PUNCT
ejpam-6458	706	23	c1	c1	PROPN
ejpam-6458	706	24	.	.	PUNCT
ejpam-6458	707	1	this	this	PRON
ejpam-6458	707	2	our	our	PRON
ejpam-6458	707	3	gelfand	gelfand	PROPN
ejpam-6458	707	4	-	-	PUNCT
ejpam-6458	707	5	tsetlin	tsetlin	PROPN
ejpam-6458	707	6	subalgebra	subalgebra	NOUN
ejpam-6458	707	7	for	for	ADP
ejpam-6458	707	8	g2	g2	PROPN
ejpam-6458	707	9	.	.	PUNCT
ejpam-6458	708	1	we	we	PRON
ejpam-6458	708	2	will	will	AUX
ejpam-6458	708	3	give	give	VERB
ejpam-6458	708	4	a	a	DET
ejpam-6458	708	5	construction	construction	NOUN
ejpam-6458	708	6	of	of	ADP
ejpam-6458	708	7	a	a	DET
ejpam-6458	708	8	3	3	NUM
ejpam-6458	708	9	-	-	PUNCT
ejpam-6458	708	10	parameter	parameter	NOUN
ejpam-6458	708	11	family	family	NOUN
ejpam-6458	708	12	of	of	ADP
ejpam-6458	708	13	γ	γ	PROPN
ejpam-6458	708	14	-	-	PUNCT
ejpam-6458	708	15	pointed	point	VERB
ejpam-6458	708	16	modules	module	NOUN
ejpam-6458	708	17	with	with	ADP
ejpam-6458	708	18	separating	separate	VERB
ejpam-6458	708	19	action	action	NOUN
ejpam-6458	708	20	of	of	ADP
ejpam-6458	708	21	γ	γ	NOUN
ejpam-6458	708	22	on	on	ADP
ejpam-6458	708	23	basis	basis	NOUN
ejpam-6458	708	24	elements	element	NOUN
ejpam-6458	708	25	.	.	PUNCT
ejpam-6458	709	1	fix	fix	NOUN
ejpam-6458	709	2	a1	a1	NOUN
ejpam-6458	709	3	,	,	PUNCT
ejpam-6458	709	4	a2	a2	PROPN
ejpam-6458	709	5	,	,	PUNCT
ejpam-6458	709	6	a3	a3	NOUN
ejpam-6458	709	7	∈	∈	PROPN
ejpam-6458	709	8	c	c	PROPN
ejpam-6458	709	9	such	such	ADJ
ejpam-6458	709	10	that	that	DET
ejpam-6458	709	11	a3	a3	NOUN
ejpam-6458	709	12	/∈	/∈	PUNCT
ejpam-6458	710	1	z.	z.	PROPN
ejpam-6458	710	2	define	define	VERB
ejpam-6458	710	3	the	the	DET
ejpam-6458	710	4	following	follow	VERB
ejpam-6458	710	5	set	set	NOUN
ejpam-6458	710	6	of	of	ADP
ejpam-6458	710	7	indexed	indexed	ADJ
ejpam-6458	710	8	variables	variable	NOUN
ejpam-6458	710	9	:	:	PUNCT
ejpam-6458	710	10	h01(i	h01(i	NOUN
ejpam-6458	710	11	,	,	PUNCT
ejpam-6458	710	12	j	j	NOUN
ejpam-6458	710	13	)	)	PUNCT
ejpam-6458	710	14	=	=	SYM
ejpam-6458	710	15	a1	a1	NOUN
ejpam-6458	710	16	+	+	CCONJ
ejpam-6458	710	17	2i−	2i−	NUM
ejpam-6458	710	18	j	j	NOUN
ejpam-6458	710	19	,	,	PUNCT
ejpam-6458	710	20	h10(i	h10(i	ADJ
ejpam-6458	710	21	,	,	PUNCT
ejpam-6458	710	22	j	j	NOUN
ejpam-6458	710	23	)	)	PUNCT
ejpam-6458	711	1	=	=	SYM
ejpam-6458	711	2	1	1	NUM
ejpam-6458	711	3	2	2	NUM
ejpam-6458	711	4	(	(	PUNCT
ejpam-6458	711	5	h21(i	h21(i	PROPN
ejpam-6458	711	6	,	,	PUNCT
ejpam-6458	711	7	j)−	j)−	PROPN
ejpam-6458	711	8	3h01(i	3h01(i	NUM
ejpam-6458	711	9	,	,	PUNCT
ejpam-6458	711	10	j	j	NOUN
ejpam-6458	711	11	)	)	PUNCT
ejpam-6458	711	12	)	)	PUNCT
ejpam-6458	712	1	=	=	SYM
ejpam-6458	712	2	1	1	NUM
ejpam-6458	712	3	2	2	NUM
ejpam-6458	712	4	(	(	PUNCT
ejpam-6458	712	5	a2	a2	PROPN
ejpam-6458	712	6	−	−	PROPN
ejpam-6458	712	7	3a1)−	3a1)−	PROPN
ejpam-6458	712	8	3i+	3i+	NUM
ejpam-6458	712	9	2j	2j	NUM
ejpam-6458	712	10	,	,	PUNCT
ejpam-6458	712	11	h21(i	h21(i	PROPN
ejpam-6458	712	12	,	,	PUNCT
ejpam-6458	712	13	j	j	PROPN
ejpam-6458	712	14	)	)	PUNCT
ejpam-6458	712	15	=	=	SYM
ejpam-6458	712	16	a2	a2	PROPN
ejpam-6458	712	17	+	+	CCONJ
ejpam-6458	712	18	j	j	PROPN
ejpam-6458	712	19	,	,	PUNCT
ejpam-6458	712	20	h11(i	h11(i	PROPN
ejpam-6458	712	21	,	,	PUNCT
ejpam-6458	712	22	j	j	PROPN
ejpam-6458	712	23	)	)	PUNCT
ejpam-6458	712	24	=	=	SYM
ejpam-6458	712	25	1	1	NUM
ejpam-6458	712	26	2	2	NUM
ejpam-6458	712	27	(	(	PUNCT
ejpam-6458	712	28	h21(i	h21(i	PROPN
ejpam-6458	712	29	,	,	PUNCT
ejpam-6458	712	30	j	j	PROPN
ejpam-6458	712	31	)	)	PUNCT
ejpam-6458	712	32	+	+	SYM
ejpam-6458	712	33	3h01(i	3h01(i	NOUN
ejpam-6458	712	34	,	,	PUNCT
ejpam-6458	712	35	j	j	NOUN
ejpam-6458	712	36	)	)	PUNCT
ejpam-6458	712	37	)	)	PUNCT
ejpam-6458	713	1	=	=	SYM
ejpam-6458	713	2	1	1	NUM
ejpam-6458	713	3	2	2	NUM
ejpam-6458	713	4	(	(	PUNCT
ejpam-6458	713	5	a2	a2	PROPN
ejpam-6458	713	6	+	+	NOUN
ejpam-6458	713	7	3a1	3a1	NUM
ejpam-6458	713	8	)	)	PUNCT
ejpam-6458	714	1	+	+	CCONJ
ejpam-6458	714	2	3i−	3i−	NUM
ejpam-6458	714	3	j	j	PROPN
ejpam-6458	714	4	,	,	PUNCT
ejpam-6458	714	5	h31(i	h31(i	PROPN
ejpam-6458	714	6	,	,	PUNCT
ejpam-6458	714	7	j	j	NOUN
ejpam-6458	714	8	)	)	PUNCT
ejpam-6458	714	9	=	=	SYM
ejpam-6458	714	10	1	1	NUM
ejpam-6458	714	11	2	2	NUM
ejpam-6458	714	12	(	(	PUNCT
ejpam-6458	714	13	h21(i	h21(i	PROPN
ejpam-6458	714	14	,	,	PUNCT
ejpam-6458	714	15	j)−	j)−	PROPN
ejpam-6458	714	16	h01(i	h01(i	PROPN
ejpam-6458	714	17	,	,	PUNCT
ejpam-6458	714	18	j	j	NOUN
ejpam-6458	714	19	)	)	PUNCT
ejpam-6458	714	20	)	)	PUNCT
ejpam-6458	715	1	=	=	SYM
ejpam-6458	715	2	1	1	NUM
ejpam-6458	715	3	2	2	NUM
ejpam-6458	715	4	(	(	PUNCT
ejpam-6458	715	5	a2	a2	PROPN
ejpam-6458	715	6	−	−	PROPN
ejpam-6458	715	7	a1)−	a1)−	VERB
ejpam-6458	715	8	i+	i+	PROPN
ejpam-6458	715	9	j	j	PROPN
ejpam-6458	715	10	,	,	PUNCT
ejpam-6458	715	11	h32(i	h32(i	PROPN
ejpam-6458	715	12	,	,	PUNCT
ejpam-6458	715	13	j	j	NOUN
ejpam-6458	715	14	)	)	PUNCT
ejpam-6458	715	15	=	=	SYM
ejpam-6458	715	16	1	1	NUM
ejpam-6458	715	17	2	2	NUM
ejpam-6458	715	18	(	(	PUNCT
ejpam-6458	715	19	h21(i	h21(i	PROPN
ejpam-6458	715	20	,	,	PUNCT
ejpam-6458	715	21	j	j	PROPN
ejpam-6458	715	22	)	)	PUNCT
ejpam-6458	715	23	+	+	CCONJ
ejpam-6458	715	24	h01(i	h01(i	PROPN
ejpam-6458	715	25	,	,	PUNCT
ejpam-6458	715	26	j	j	NOUN
ejpam-6458	715	27	)	)	PUNCT
ejpam-6458	715	28	)	)	PUNCT
ejpam-6458	716	1	=	=	SYM
ejpam-6458	716	2	1	1	NUM
ejpam-6458	716	3	2	2	NUM
ejpam-6458	716	4	(	(	PUNCT
ejpam-6458	716	5	a2	a2	PROPN
ejpam-6458	716	6	+	+	CCONJ
ejpam-6458	716	7	a1	a1	NOUN
ejpam-6458	716	8	)	)	PUNCT
ejpam-6458	717	1	+	+	CCONJ
ejpam-6458	717	2	i	i	PROPN
ejpam-6458	717	3	,	,	PUNCT
ejpam-6458	717	4	sjk	sjk	PROPN
ejpam-6458	717	5	=	=	PROPN
ejpam-6458	717	6	a3	a3	PROPN
ejpam-6458	717	7	−	−	PROPN
ejpam-6458	717	8	j	j	PROPN
ejpam-6458	717	9	+	+	CCONJ
ejpam-6458	717	10	2k	2k	NOUN
ejpam-6458	717	11	−	−	NOUN
ejpam-6458	717	12	1	1	NUM
ejpam-6458	717	13	,	,	PUNCT
ejpam-6458	717	14	s+	s+	X
ejpam-6458	717	15	ijk	ijk	PROPN
ejpam-6458	717	16	=	=	PROPN
ejpam-6458	717	17	1	1	NUM
ejpam-6458	717	18	2	2	NUM
ejpam-6458	717	19	(	(	PUNCT
ejpam-6458	717	20	sjk	sjk	PROPN
ejpam-6458	717	21	+	+	PROPN
ejpam-6458	717	22	h01(i	h01(i	PROPN
ejpam-6458	717	23	,	,	PUNCT
ejpam-6458	717	24	j	j	NOUN
ejpam-6458	717	25	)	)	PUNCT
ejpam-6458	717	26	)	)	PUNCT
ejpam-6458	718	1	=	=	SYM
ejpam-6458	718	2	1	1	NUM
ejpam-6458	718	3	2	2	NUM
ejpam-6458	718	4	(	(	PUNCT
ejpam-6458	718	5	a1	a1	NOUN
ejpam-6458	718	6	+	+	CCONJ
ejpam-6458	718	7	a3	a3	NOUN
ejpam-6458	718	8	+	+	CCONJ
ejpam-6458	718	9	2i−	2i−	NUM
ejpam-6458	718	10	2j	2j	NOUN
ejpam-6458	718	11	+	+	CCONJ
ejpam-6458	718	12	2k	2k	NOUN
ejpam-6458	718	13	−	−	NOUN
ejpam-6458	718	14	1	1	NUM
ejpam-6458	718	15	)	)	PUNCT
ejpam-6458	718	16	,	,	PUNCT
ejpam-6458	718	17	s−	s−	PROPN
ejpam-6458	718	18	ik	ik	PROPN
ejpam-6458	718	19	=	=	SYM
ejpam-6458	718	20	1	1	NUM
ejpam-6458	718	21	2	2	NUM
ejpam-6458	718	22	(	(	PUNCT
ejpam-6458	718	23	s0k	s0k	NOUN
ejpam-6458	718	24	−	−	PROPN
ejpam-6458	718	25	h01(i	h01(i	NOUN
ejpam-6458	718	26	,	,	PUNCT
ejpam-6458	718	27	0	0	NUM
ejpam-6458	718	28	)	)	PUNCT
ejpam-6458	718	29	)	)	PUNCT
ejpam-6458	719	1	=	=	SYM
ejpam-6458	719	2	1	1	NUM
ejpam-6458	719	3	2	2	NUM
ejpam-6458	719	4	(	(	PUNCT
ejpam-6458	719	5	−a1	−a1	PROPN
ejpam-6458	719	6	+	+	SYM
ejpam-6458	719	7	a3	a3	NOUN
ejpam-6458	719	8	−	−	PROPN
ejpam-6458	719	9	2i+	2i+	NUM
ejpam-6458	719	10	2k	2k	NOUN
ejpam-6458	719	11	−	−	NOUN
ejpam-6458	719	12	1	1	NUM
ejpam-6458	719	13	)	)	PUNCT
ejpam-6458	719	14	,	,	PUNCT
ejpam-6458	719	15	t+	t+	X
ejpam-6458	719	16	jk	jk	NOUN
ejpam-6458	719	17	=	=	SYM
ejpam-6458	719	18	1	1	NUM
ejpam-6458	719	19	2	2	NUM
ejpam-6458	719	20	(	(	PUNCT
ejpam-6458	719	21	sjk	sjk	PROPN
ejpam-6458	719	22	+	+	PROPN
ejpam-6458	719	23	1	1	NUM
ejpam-6458	719	24	3	3	NUM
ejpam-6458	719	25	h2,1(0	h2,1(0	PROPN
ejpam-6458	719	26	,	,	PUNCT
ejpam-6458	719	27	j	j	NOUN
ejpam-6458	719	28	)	)	PUNCT
ejpam-6458	719	29	)	)	PUNCT
ejpam-6458	720	1	=	=	SYM
ejpam-6458	720	2	1	1	NUM
ejpam-6458	720	3	6	6	NUM
ejpam-6458	720	4	(	(	PUNCT
ejpam-6458	720	5	a1	a1	NOUN
ejpam-6458	720	6	+	+	CCONJ
ejpam-6458	720	7	2a2	2a2	NUM
ejpam-6458	720	8	+	+	CCONJ
ejpam-6458	720	9	3a3	3a3	NUM
ejpam-6458	720	10	−	−	NOUN
ejpam-6458	720	11	2j	2j	NOUN
ejpam-6458	721	1	+	+	CCONJ
ejpam-6458	721	2	6k	6k	NOUN
ejpam-6458	721	3	−	−	NOUN
ejpam-6458	721	4	3	3	NUM
ejpam-6458	721	5	)	)	PUNCT
ejpam-6458	721	6	,	,	PUNCT
ejpam-6458	721	7	t−	t−	PROPN
ejpam-6458	721	8	jk	jk	PROPN
ejpam-6458	721	9	=	=	SYM
ejpam-6458	721	10	1	1	NUM
ejpam-6458	721	11	2	2	NUM
ejpam-6458	721	12	(	(	PUNCT
ejpam-6458	721	13	sjk	sjk	PROPN
ejpam-6458	721	14	−	−	PROPN
ejpam-6458	721	15	1	1	NUM
ejpam-6458	721	16	3	3	NUM
ejpam-6458	721	17	h2,1(0	h2,1(0	PROPN
ejpam-6458	721	18	,	,	PUNCT
ejpam-6458	721	19	j	j	NOUN
ejpam-6458	721	20	)	)	PUNCT
ejpam-6458	721	21	)	)	PUNCT
ejpam-6458	722	1	=	=	SYM
ejpam-6458	722	2	1	1	NUM
ejpam-6458	722	3	6	6	NUM
ejpam-6458	722	4	(	(	PUNCT
ejpam-6458	722	5	−a1	−a1	PROPN
ejpam-6458	722	6	−	−	PROPN
ejpam-6458	722	7	2a2	2a2	NUM
ejpam-6458	722	8	+	+	CCONJ
ejpam-6458	722	9	3a3	3a3	NUM
ejpam-6458	722	10	−	−	ADP
ejpam-6458	722	11	4j	4j	NOUN
ejpam-6458	722	12	+	+	CCONJ
ejpam-6458	722	13	6k	6k	NOUN
ejpam-6458	722	14	−	−	PROPN
ejpam-6458	722	15	3	3	NUM
ejpam-6458	722	16	)	)	PUNCT
ejpam-6458	722	17	,	,	PUNCT
ejpam-6458	722	18	a+	a+	PUNCT
ejpam-6458	723	1	jk	jk	PROPN
ejpam-6458	723	2	=	=	PUNCT
ejpam-6458	723	3	t−	t−	PROPN
ejpam-6458	723	4	j−1,k−1	j−1,k−1	PROPN
ejpam-6458	723	5	t	t	PROPN
ejpam-6458	723	6	+	+	NUM
ejpam-6458	723	7	jkt	jkt	PROPN
ejpam-6458	723	8	+	+	CCONJ
ejpam-6458	723	9	j+1,k	j+1,k	PROPN
ejpam-6458	723	10	9sjksj+1,k	9sjksj+1,k	PROPN
ejpam-6458	723	11	,	,	PUNCT
ejpam-6458	723	12	a−	a−	PROPN
ejpam-6458	723	13	jk	jk	PROPN
ejpam-6458	723	14	=	=	PUNCT
ejpam-6458	723	15	t−	t−	PROPN
ejpam-6458	723	16	j−1,k−1	j−1,k−1	PROPN
ejpam-6458	723	17	t	t	PROPN
ejpam-6458	723	18	−	−	PROPN
ejpam-6458	723	19	jkt	jkt	NOUN
ejpam-6458	723	20	+	+	CCONJ
ejpam-6458	723	21	j+1,k	j+1,k	PROPN
ejpam-6458	723	22	9sjksj+1,k	9sjksj+1,k	PROPN
ejpam-6458	723	23	,	,	PUNCT
ejpam-6458	723	24	b+	b+	VERB
ejpam-6458	723	25	jk	jk	X
ejpam-6458	723	26	=	=	PUNCT
ejpam-6458	723	27	t+	t+	PUNCT
ejpam-6458	723	28	j−1,kt	j−1,kt	NOUN
ejpam-6458	723	29	+	+	CCONJ
ejpam-6458	723	30	jkt	jkt	NOUN
ejpam-6458	723	31	+	+	CCONJ
ejpam-6458	723	32	j+1,k	j+1,k	PROPN
ejpam-6458	723	33	27sjksj+1,k	27sjksj+1,k	PROPN
ejpam-6458	723	34	,	,	PUNCT
ejpam-6458	723	35	b−	b−	PROPN
ejpam-6458	723	36	jk	jk	PROPN
ejpam-6458	723	37	=	=	PRON
ejpam-6458	724	1	t−	t−	PROPN
ejpam-6458	724	2	j−1,k−1	j−1,k−1	PROPN
ejpam-6458	724	3	t	t	PROPN
ejpam-6458	724	4	−	−	PROPN
ejpam-6458	724	5	jkt	jkt	NOUN
ejpam-6458	724	6	−	−	PROPN
ejpam-6458	724	7	j+1,k+1	j+1,k+1	NOUN
ejpam-6458	724	8	27sjksj+1,k	27sjksj+1,k	NUM
ejpam-6458	724	9	,	,	PUNCT
ejpam-6458	724	10	i	i	PRON
ejpam-6458	724	11	,	,	PUNCT
ejpam-6458	724	12	j	j	PROPN
ejpam-6458	724	13	,	,	PUNCT
ejpam-6458	724	14	k	k	PROPN
ejpam-6458	724	15	∈	∈	PROPN
ejpam-6458	724	16	z.	z.	PROPN
ejpam-6458	724	17	(	(	PUNCT
ejpam-6458	724	18	6.1	6.1	NUM
ejpam-6458	724	19	)	)	PUNCT
ejpam-6458	724	20	define	define	VERB
ejpam-6458	724	21	the	the	DET
ejpam-6458	724	22	action	action	NOUN
ejpam-6458	724	23	of	of	ADP
ejpam-6458	724	24	the	the	DET
ejpam-6458	724	25	lie	lie	NOUN
ejpam-6458	724	26	algebra	algebra	VERB
ejpam-6458	724	27	g	g	NOUN
ejpam-6458	724	28	on	on	ADP
ejpam-6458	724	29	v	v	NUM
ejpam-6458	724	30	(	(	PUNCT
ejpam-6458	724	31	a1	a1	PROPN
ejpam-6458	724	32	,	,	PUNCT
ejpam-6458	724	33	a2	a2	PROPN
ejpam-6458	724	34	,	,	PUNCT
ejpam-6458	724	35	a3	a3	NOUN
ejpam-6458	724	36	)	)	PUNCT
ejpam-6458	725	1	=	=	PUNCT
ejpam-6458	725	2	spanc{vijk	spanc{vijk	X
ejpam-6458	726	1	|	|	ADV
ejpam-6458	726	2	i	i	PROPN
ejpam-6458	726	3	,	,	PUNCT
ejpam-6458	726	4	j	j	PROPN
ejpam-6458	726	5	,	,	PUNCT
ejpam-6458	726	6	k	k	PROPN
ejpam-6458	726	7	∈	∈	PROPN
ejpam-6458	727	1	z	z	X
ejpam-6458	727	2	}	}	PUNCT
ejpam-6458	727	3	as	as	SCONJ
ejpam-6458	727	4	follows	follow	VERB
ejpam-6458	727	5	:	:	PUNCT
ejpam-6458	727	6	h01(vijk	h01(vijk	X
ejpam-6458	727	7	)	)	PUNCT
ejpam-6458	727	8	=	=	SYM
ejpam-6458	728	1	h01(i	h01(i	NOUN
ejpam-6458	728	2	,	,	PUNCT
ejpam-6458	728	3	j)vijk	j)vijk	PROPN
ejpam-6458	728	4	,	,	PUNCT
ejpam-6458	728	5	h10(vijk	h10(vijk	X
ejpam-6458	728	6	)	)	PUNCT
ejpam-6458	728	7	=	=	SYM
ejpam-6458	728	8	h10(i	h10(i	ADJ
ejpam-6458	728	9	,	,	PUNCT
ejpam-6458	728	10	j)vijk	j)vijk	PROPN
ejpam-6458	728	11	,	,	PUNCT
ejpam-6458	728	12	h11(vijk	h11(vijk	NUM
ejpam-6458	728	13	)	)	PUNCT
ejpam-6458	728	14	=	=	SYM
ejpam-6458	728	15	h11(i	h11(i	PROPN
ejpam-6458	728	16	,	,	PUNCT
ejpam-6458	728	17	j)vijk	j)vijk	PROPN
ejpam-6458	728	18	,	,	PUNCT
ejpam-6458	728	19	h21(vijk	h21(vijk	NUM
ejpam-6458	728	20	)	)	PUNCT
ejpam-6458	728	21	=	=	SYM
ejpam-6458	728	22	h21(i	h21(i	PROPN
ejpam-6458	728	23	,	,	PUNCT
ejpam-6458	728	24	j)vijk	j)vijk	PROPN
ejpam-6458	728	25	,	,	PUNCT
ejpam-6458	728	26	h31(vijk	h31(vijk	X
ejpam-6458	728	27	)	)	PUNCT
ejpam-6458	728	28	=	=	SYM
ejpam-6458	728	29	h31(i	h31(i	PROPN
ejpam-6458	728	30	,	,	PUNCT
ejpam-6458	728	31	j)vijk	j)vijk	PROPN
ejpam-6458	728	32	,	,	PUNCT
ejpam-6458	728	33	h32(vijk	h32(vijk	PROPN
ejpam-6458	728	34	)	)	PUNCT
ejpam-6458	728	35	=	=	SYM
ejpam-6458	728	36	h32(i	h32(i	NOUN
ejpam-6458	728	37	,	,	PUNCT
ejpam-6458	728	38	j)vijk	j)vijk	PROPN
ejpam-6458	728	39	,	,	PUNCT
ejpam-6458	728	40	e01(vijk	e01(vijk	NOUN
ejpam-6458	728	41	)	)	PUNCT
ejpam-6458	728	42	=	=	PUNCT
ejpam-6458	728	43	s+	s+	PUNCT
ejpam-6458	728	44	ijkvi+1,j	ijkvi+1,j	PROPN
ejpam-6458	728	45	,	,	PUNCT
ejpam-6458	728	46	k	k	PROPN
ejpam-6458	728	47	,	,	PUNCT
ejpam-6458	728	48	f01(vijk	f01(vijk	NOUN
ejpam-6458	728	49	)	)	PUNCT
ejpam-6458	728	50	=	=	SYM
ejpam-6458	729	1	s−	s−	PROPN
ejpam-6458	729	2	ikvi−1,j	ikvi−1,j	ADP
ejpam-6458	729	3	,	,	PUNCT
ejpam-6458	729	4	k	k	PROPN
ejpam-6458	729	5	,	,	PUNCT
ejpam-6458	729	6	e21(vijk	e21(vijk	NUM
ejpam-6458	729	7	)	)	PUNCT
ejpam-6458	729	8	=	=	PUNCT
ejpam-6458	729	9	t+	t+	NOUN
ejpam-6458	729	10	j+1,kvi+1,j+2,k+1	j+1,kvi+1,j+2,k+1	ADJ
ejpam-6458	729	11	,	,	PUNCT
ejpam-6458	729	12	f21(vijk	f21(vijk	NOUN
ejpam-6458	729	13	)	)	PUNCT
ejpam-6458	729	14	=	=	SYM
ejpam-6458	729	15	t−	t−	PROPN
ejpam-6458	729	16	j−1,k−1vi−1,j−2,k−1	j−1,k−1vi−1,j−2,k−1	PROPN
ejpam-6458	729	17	,	,	PUNCT
ejpam-6458	729	18	e10(vijk	e10(vijk	NOUN
ejpam-6458	729	19	)	)	PUNCT
ejpam-6458	729	20	=	=	SYM
ejpam-6458	729	21	3vi	3vi	NOUN
ejpam-6458	729	22	,	,	PUNCT
ejpam-6458	729	23	j+1,k	j+1,k	PROPN
ejpam-6458	729	24	+	+	PROPN
ejpam-6458	729	25	a+	a+	PROPN
ejpam-6458	729	26	jks	jks	PROPN
ejpam-6458	729	27	−	−	PROPN
ejpam-6458	729	28	ikvi	ikvi	PROPN
ejpam-6458	729	29	,	,	PUNCT
ejpam-6458	729	30	j+1,k+1	j+1,k+1	NOUN
ejpam-6458	729	31	,	,	PUNCT
ejpam-6458	729	32	f10(vijk	f10(vijk	NUM
ejpam-6458	729	33	)	)	PUNCT
ejpam-6458	729	34	=	=	SYM
ejpam-6458	730	1	−3vi	−3vi	NOUN
ejpam-6458	730	2	,	,	PUNCT
ejpam-6458	730	3	j−1,k−1	j−1,k−1	PART
ejpam-6458	730	4	−a−	−a−	ADJ
ejpam-6458	730	5	jks	jks	NOUN
ejpam-6458	730	6	+	+	CCONJ
ejpam-6458	730	7	ijkvi	ijkvi	PROPN
ejpam-6458	730	8	,	,	PUNCT
ejpam-6458	730	9	j−1,k	j−1,k	PROPN
ejpam-6458	730	10	,	,	PUNCT
ejpam-6458	730	11	e11(vijk	e11(vijk	X
ejpam-6458	730	12	)	)	PUNCT
ejpam-6458	731	1	=	=	SYM
ejpam-6458	731	2	−3vi+1,j+1,k	−3vi+1,j+1,k	PROPN
ejpam-6458	732	1	+	+	PROPN
ejpam-6458	732	2	a+	a+	X
ejpam-6458	732	3	jks	jks	NOUN
ejpam-6458	732	4	+	+	CCONJ
ejpam-6458	732	5	i+1,j+1,kvi+1,j+1,k+1	i+1,j+1,kvi+1,j+1,k+1	NOUN
ejpam-6458	732	6	,	,	PUNCT
ejpam-6458	732	7	f11(vijk	f11(vijk	NOUN
ejpam-6458	732	8	)	)	PUNCT
ejpam-6458	732	9	=	=	NOUN
ejpam-6458	733	1	−3vi−1,j−1,k−1	−3vi−1,j−1,k−1	NUM
ejpam-6458	733	2	+	+	ADJ
ejpam-6458	733	3	a−	a−	PROPN
ejpam-6458	733	4	jks	jks	NOUN
ejpam-6458	733	5	−	−	PROPN
ejpam-6458	734	1	i+1,k+1vi−1,j−1,k	i+1,k+1vi−1,j−1,k	PROPN
ejpam-6458	734	2	,	,	PUNCT
ejpam-6458	734	3	e31(vijk	e31(vijk	PROPN
ejpam-6458	734	4	)	)	PUNCT
ejpam-6458	734	5	=	=	SYM
ejpam-6458	734	6	vi+1,j+3,k+1	vi+1,j+3,k+1	PROPN
ejpam-6458	734	7	−b+	−b+	NOUN
ejpam-6458	734	8	jks	jks	PROPN
ejpam-6458	735	1	−	−	PROPN
ejpam-6458	735	2	i+1,k+1vi+1,j+3,k+2	i+1,k+1vi+1,j+3,k+2	ADJ
ejpam-6458	735	3	,	,	PUNCT
ejpam-6458	735	4	f31(v	f31(v	NOUN
ejpam-6458	735	5	,	,	PUNCT
ejpam-6458	735	6	jk	jk	PROPN
ejpam-6458	735	7	)	)	PUNCT
ejpam-6458	735	8	=	=	VERB
ejpam-6458	736	1	vi−1,j−3,k−2	vi−1,j−3,k−2	PROPN
ejpam-6458	736	2	−b−	−b−	PROPN
ejpam-6458	736	3	jks	jks	PROPN
ejpam-6458	736	4	+	+	CCONJ
ejpam-6458	736	5	i+1,j+1,kvi−1,j−3,k−1	i+1,j+1,kvi−1,j−3,k−1	PROPN
ejpam-6458	736	6	,	,	PUNCT
ejpam-6458	736	7	e32(v	e32(v	PROPN
ejpam-6458	736	8	,	,	PUNCT
ejpam-6458	736	9	jk	jk	PROPN
ejpam-6458	736	10	)	)	PUNCT
ejpam-6458	736	11	=	=	PUNCT
ejpam-6458	737	1	−vi+2,j+3,k+1	−vi+2,j+3,k+1	NUM
ejpam-6458	737	2	−b+	−b+	NOUN
ejpam-6458	737	3	jks	jks	NOUN
ejpam-6458	737	4	+	+	CCONJ
ejpam-6458	737	5	i+1,j+1,kvi+2,j+3,k+2	i+1,j+1,kvi+2,j+3,k+2	NOUN
ejpam-6458	737	6	,	,	PUNCT
ejpam-6458	737	7	f32(vijk	f32(vijk	NOUN
ejpam-6458	737	8	)	)	PUNCT
ejpam-6458	737	9	=	=	PUNCT
ejpam-6458	738	1	vi−2,j−3,k−2	vi−2,j−3,k−2	NOUN
ejpam-6458	739	1	+	+	NOUN
ejpam-6458	739	2	b−	b−	PROPN
ejpam-6458	739	3	jks	jk	VERB
ejpam-6458	739	4	−	−	PROPN
ejpam-6458	740	1	i+1,k+1vi−2,j−3,k−1	i+1,k+1vi−2,j−3,k−1	PROPN
ejpam-6458	740	2	,	,	PUNCT
ejpam-6458	740	3	z1(vijk	z1(vijk	NOUN
ejpam-6458	740	4	)	)	PUNCT
ejpam-6458	741	1	=	=	SYM
ejpam-6458	741	2	14	14	NUM
ejpam-6458	741	3	3	3	NUM
ejpam-6458	741	4	vijk	vijk	NOUN
ejpam-6458	741	5	.	.	PUNCT
ejpam-6458	742	1	m.	m.	PROPN
ejpam-6458	742	2	andelić	andelić	PROPN
ejpam-6458	742	3	et	et	PROPN
ejpam-6458	742	4	al	al	PROPN
ejpam-6458	742	5	.	.	PUNCT
ejpam-6458	742	6	/	/	SYM
ejpam-6458	742	7	eur	eur	PROPN
ejpam-6458	742	8	.	.	PUNCT
ejpam-6458	743	1	j.	j.	PROPN
ejpam-6458	743	2	pure	pure	PROPN
ejpam-6458	743	3	appl	appl	PROPN
ejpam-6458	743	4	.	.	PROPN
ejpam-6458	743	5	math	math	PROPN
ejpam-6458	743	6	,	,	PUNCT
ejpam-6458	743	7	18	18	NUM
ejpam-6458	743	8	(	(	PUNCT
ejpam-6458	743	9	3	3	NUM
ejpam-6458	743	10	)	)	PUNCT
ejpam-6458	743	11	(	(	PUNCT
ejpam-6458	743	12	2025	2025	NUM
ejpam-6458	743	13	)	)	PUNCT
ejpam-6458	743	14	,	,	PUNCT
ejpam-6458	743	15	6458	6458	NUM
ejpam-6458	743	16	19	19	NUM
ejpam-6458	743	17	of	of	ADP
ejpam-6458	743	18	21	21	NUM
ejpam-6458	743	19	lemma	lemma	PROPN
ejpam-6458	743	20	6.3	6.3	NUM
ejpam-6458	743	21	.	.	PUNCT
ejpam-6458	744	1	subalgebra	subalgebra	PROPN
ejpam-6458	744	2	γ	γ	PROPN
ejpam-6458	744	3	has	have	VERB
ejpam-6458	744	4	a	a	DET
ejpam-6458	744	5	simple	simple	ADJ
ejpam-6458	744	6	spectrum	spectrum	NOUN
ejpam-6458	744	7	on	on	ADP
ejpam-6458	744	8	v	v	PROPN
ejpam-6458	744	9	(	(	PUNCT
ejpam-6458	744	10	a1	a1	PROPN
ejpam-6458	744	11	,	,	PUNCT
ejpam-6458	744	12	a2	a2	PROPN
ejpam-6458	744	13	,	,	PUNCT
ejpam-6458	744	14	a3	a3	NOUN
ejpam-6458	744	15	)	)	PUNCT
ejpam-6458	744	16	,	,	PUNCT
ejpam-6458	744	17	and	and	CCONJ
ejpam-6458	744	18	hence	hence	ADV
ejpam-6458	744	19	separates	separate	VERB
ejpam-6458	744	20	the	the	DET
ejpam-6458	744	21	basis	basis	NOUN
ejpam-6458	744	22	elements	element	NOUN
ejpam-6458	744	23	vijk	vijk	ADV
ejpam-6458	744	24	,	,	PUNCT
ejpam-6458	744	25	if	if	SCONJ
ejpam-6458	744	26	and	and	CCONJ
ejpam-6458	744	27	only	only	ADV
ejpam-6458	744	28	if	if	SCONJ
ejpam-6458	744	29	a3	a3	NOUN
ejpam-6458	744	30	/∈	/∈	PUNCT
ejpam-6458	745	1	z.	z.	PROPN
ejpam-6458	745	2	proof	proof	NOUN
ejpam-6458	745	3	.	.	PUNCT
ejpam-6458	746	1	it	it	PRON
ejpam-6458	746	2	is	be	AUX
ejpam-6458	746	3	sufficient	sufficient	ADJ
ejpam-6458	746	4	to	to	PART
ejpam-6458	746	5	consider	consider	VERB
ejpam-6458	746	6	vectors	vector	NOUN
ejpam-6458	746	7	from	from	ADP
ejpam-6458	746	8	the	the	DET
ejpam-6458	746	9	same	same	ADJ
ejpam-6458	746	10	weight	weight	NOUN
ejpam-6458	746	11	space	space	NOUN
ejpam-6458	746	12	.	.	PUNCT
ejpam-6458	747	1	suppose	suppose	VERB
ejpam-6458	747	2	h1(vijk	h1(vijk	NOUN
ejpam-6458	747	3	)	)	PUNCT
ejpam-6458	747	4	=	=	PUNCT
ejpam-6458	748	1	(	(	PUNCT
ejpam-6458	748	2	a1	a1	NOUN
ejpam-6458	748	3	+	+	X
ejpam-6458	748	4	2i−	2i−	NUM
ejpam-6458	748	5	j)vijk	j)vijk	X
ejpam-6458	749	1	=	=	SYM
ejpam-6458	749	2	λvijk	λvijk	X
ejpam-6458	749	3	,	,	PUNCT
ejpam-6458	749	4	h2(vijk	h2(vijk	NOUN
ejpam-6458	749	5	)	)	PUNCT
ejpam-6458	749	6	=	=	SYM
ejpam-6458	749	7	(	(	PUNCT
ejpam-6458	749	8	a2	a2	PROPN
ejpam-6458	749	9	+	+	CCONJ
ejpam-6458	749	10	j)vijk	j)vijk	X
ejpam-6458	749	11	=	=	SYM
ejpam-6458	749	12	µvijk	µvijk	X
ejpam-6458	749	13	,	,	PUNCT
ejpam-6458	749	14	for	for	ADP
ejpam-6458	749	15	some	some	DET
ejpam-6458	749	16	λ	λ	PROPN
ejpam-6458	749	17	and	and	CCONJ
ejpam-6458	749	18	µ.	µ.	NOUN
ejpam-6458	749	19	then	then	ADV
ejpam-6458	749	20	j	j	PROPN
ejpam-6458	750	1	=	=	SYM
ejpam-6458	750	2	µ−	µ−	PROPN
ejpam-6458	750	3	a2	a2	PROPN
ejpam-6458	750	4	and	and	CCONJ
ejpam-6458	750	5	i	i	NOUN
ejpam-6458	750	6	=	=	NOUN
ejpam-6458	750	7	1	1	NUM
ejpam-6458	750	8	2(λ+	2(λ+	NUM
ejpam-6458	750	9	µ−	µ−	PROPN
ejpam-6458	750	10	a1	a1	NOUN
ejpam-6458	750	11	−	−	PROPN
ejpam-6458	750	12	a2	a2	PROPN
ejpam-6458	750	13	)	)	PUNCT
ejpam-6458	750	14	.	.	PUNCT
ejpam-6458	751	1	hence	hence	ADV
ejpam-6458	751	2	,	,	PUNCT
ejpam-6458	751	3	basis	basis	NOUN
ejpam-6458	751	4	elements	element	NOUN
ejpam-6458	751	5	of	of	ADP
ejpam-6458	751	6	this	this	DET
ejpam-6458	751	7	weight	weight	NOUN
ejpam-6458	751	8	subspace	subspace	NOUN
ejpam-6458	751	9	differ	differ	VERB
ejpam-6458	751	10	by	by	ADP
ejpam-6458	751	11	the	the	DET
ejpam-6458	751	12	third	third	ADJ
ejpam-6458	751	13	index	index	NOUN
ejpam-6458	751	14	.	.	PUNCT
ejpam-6458	752	1	consider	consider	VERB
ejpam-6458	752	2	vijk1	vijk1	NOUN
ejpam-6458	752	3	and	and	CCONJ
ejpam-6458	752	4	vijk2	vijk2	NOUN
ejpam-6458	752	5	for	for	ADP
ejpam-6458	752	6	arbitrary	arbitrary	ADJ
ejpam-6458	752	7	integers	integer	NOUN
ejpam-6458	752	8	i	i	PRON
ejpam-6458	752	9	,	,	PUNCT
ejpam-6458	752	10	j	j	PROPN
ejpam-6458	752	11	,	,	PUNCT
ejpam-6458	752	12	k1	k1	PROPN
ejpam-6458	752	13	,	,	PUNCT
ejpam-6458	752	14	k2	k2	NOUN
ejpam-6458	752	15	.	.	PUNCT
ejpam-6458	753	1	we	we	PRON
ejpam-6458	753	2	have	have	VERB
ejpam-6458	753	3	c1(vijk	c1(vijk	NOUN
ejpam-6458	753	4	)	)	PUNCT
ejpam-6458	753	5	=	=	PUNCT
ejpam-6458	753	6	f01e01(vijk	f01e01(vijk	X
ejpam-6458	753	7	)	)	PUNCT
ejpam-6458	754	1	=	=	VERB
ejpam-6458	755	1	f01(s	f01(	NOUN
ejpam-6458	756	1	+	+	CCONJ
ejpam-6458	756	2	i	i	PROPN
ejpam-6458	756	3	,	,	PUNCT
ejpam-6458	756	4	j	j	PROPN
ejpam-6458	756	5	,	,	PUNCT
ejpam-6458	756	6	kvi+1jk	kvi+1jk	PROPN
ejpam-6458	756	7	)	)	PUNCT
ejpam-6458	756	8	=	=	SYM
ejpam-6458	756	9	s−	s−	PROPN
ejpam-6458	756	10	i+1,ks	i+1,ks	PROPN
ejpam-6458	757	1	+	+	CCONJ
ejpam-6458	757	2	i	i	PROPN
ejpam-6458	757	3	,	,	PUNCT
ejpam-6458	757	4	j	j	PROPN
ejpam-6458	757	5	,	,	PUNCT
ejpam-6458	757	6	k(vijk	k(vijk	PROPN
ejpam-6458	757	7	)	)	PUNCT
ejpam-6458	757	8	.	.	PUNCT
ejpam-6458	758	1	since	since	SCONJ
ejpam-6458	758	2	the	the	DET
ejpam-6458	758	3	formulas	formula	NOUN
ejpam-6458	758	4	for	for	ADP
ejpam-6458	758	5	s−	s−	PROPN
ejpam-6458	758	6	i	i	PRON
ejpam-6458	758	7	,	,	PUNCT
ejpam-6458	758	8	k	k	PROPN
ejpam-6458	758	9	and	and	CCONJ
ejpam-6458	758	10	s	s	PROPN
ejpam-6458	758	11	+	+	CCONJ
ejpam-6458	758	12	i	i	PROPN
ejpam-6458	758	13	,	,	PUNCT
ejpam-6458	758	14	j	j	PROPN
ejpam-6458	758	15	,	,	PUNCT
ejpam-6458	758	16	k	k	PROPN
ejpam-6458	758	17	are	be	AUX
ejpam-6458	758	18	the	the	DET
ejpam-6458	758	19	same	same	ADJ
ejpam-6458	758	20	for	for	ADP
ejpam-6458	758	21	c2	c2	PROPN
ejpam-6458	758	22	(	(	PUNCT
ejpam-6458	758	23	5.17	5.17	NUM
ejpam-6458	758	24	)	)	PUNCT
ejpam-6458	758	25	and	and	CCONJ
ejpam-6458	758	26	g2	g2	PROPN
ejpam-6458	758	27	(	(	PUNCT
ejpam-6458	758	28	6.1	6.1	NUM
ejpam-6458	758	29	)	)	PUNCT
ejpam-6458	758	30	,	,	PUNCT
ejpam-6458	758	31	we	we	PRON
ejpam-6458	758	32	obtain	obtain	VERB
ejpam-6458	758	33	similar	similar	ADJ
ejpam-6458	758	34	results	result	NOUN
ejpam-6458	758	35	as	as	ADP
ejpam-6458	758	36	in	in	ADP
ejpam-6458	758	37	(	(	PUNCT
ejpam-6458	758	38	5.19	5.19	NUM
ejpam-6458	758	39	)	)	PUNCT
ejpam-6458	758	40	and	and	CCONJ
ejpam-6458	758	41	conclude	conclude	VERB
ejpam-6458	758	42	that	that	PRON
ejpam-6458	758	43	c1	c1	PROPN
ejpam-6458	758	44	separates	separate	VERB
ejpam-6458	758	45	the	the	DET
ejpam-6458	758	46	basis	basis	NOUN
ejpam-6458	758	47	elements	element	NOUN
ejpam-6458	758	48	vijk1	vijk1	NOUN
ejpam-6458	758	49	and	and	CCONJ
ejpam-6458	758	50	vijk2	vijk2	NOUN
ejpam-6458	758	51	.	.	PUNCT
ejpam-6458	759	1	this	this	PRON
ejpam-6458	759	2	implies	imply	VERB
ejpam-6458	759	3	the	the	DET
ejpam-6458	759	4	statement	statement	NOUN
ejpam-6458	759	5	.	.	PUNCT
ejpam-6458	760	1	□	□	PUNCT
ejpam-6458	760	2	theorem	theorem	VERB
ejpam-6458	760	3	6.4	6.4	NUM
ejpam-6458	760	4	.	.	PUNCT
ejpam-6458	761	1	for	for	ADP
ejpam-6458	761	2	any	any	DET
ejpam-6458	761	3	complex	complex	ADJ
ejpam-6458	761	4	a1	a1	NOUN
ejpam-6458	761	5	,	,	PUNCT
ejpam-6458	761	6	a2	a2	PROPN
ejpam-6458	761	7	,	,	PUNCT
ejpam-6458	761	8	a3	a3	VERB
ejpam-6458	761	9	such	such	ADJ
ejpam-6458	761	10	that	that	DET
ejpam-6458	761	11	a3	a3	NOUN
ejpam-6458	761	12	/∈	/∈	PUNCT
ejpam-6458	762	1	z	z	X
ejpam-6458	762	2	,	,	PUNCT
ejpam-6458	762	3	the	the	DET
ejpam-6458	762	4	above	above	ADJ
ejpam-6458	762	5	formulas	formula	NOUN
ejpam-6458	762	6	define	define	VERB
ejpam-6458	762	7	the	the	DET
ejpam-6458	762	8	g2	g2	NOUN
ejpam-6458	762	9	-	-	PUNCT
ejpam-6458	762	10	module	module	NOUN
ejpam-6458	762	11	structure	structure	NOUN
ejpam-6458	762	12	on	on	ADP
ejpam-6458	762	13	the	the	DET
ejpam-6458	762	14	space	space	NOUN
ejpam-6458	762	15	v	v	NOUN
ejpam-6458	762	16	(	(	PUNCT
ejpam-6458	762	17	a1	a1	PROPN
ejpam-6458	762	18	,	,	PUNCT
ejpam-6458	762	19	a2	a2	PROPN
ejpam-6458	762	20	,	,	PUNCT
ejpam-6458	762	21	a3	a3	NOUN
ejpam-6458	762	22	)	)	PUNCT
ejpam-6458	762	23	.	.	PUNCT
ejpam-6458	763	1	proof	proof	NOUN
ejpam-6458	763	2	.	.	PUNCT
ejpam-6458	764	1	follows	follow	VERB
ejpam-6458	764	2	by	by	ADP
ejpam-6458	764	3	checking	check	VERB
ejpam-6458	764	4	that	that	SCONJ
ejpam-6458	764	5	the	the	DET
ejpam-6458	764	6	defining	define	VERB
ejpam-6458	764	7	relations	relation	NOUN
ejpam-6458	764	8	of	of	ADP
ejpam-6458	764	9	the	the	DET
ejpam-6458	764	10	lie	lie	NOUN
ejpam-6458	764	11	algebra	algebra	PROPN
ejpam-6458	764	12	g2	g2	PROPN
ejpam-6458	764	13	are	be	AUX
ejpam-6458	764	14	satisfied	satisfied	ADJ
ejpam-6458	764	15	on	on	ADP
ejpam-6458	764	16	v	v	NUM
ejpam-6458	764	17	(	(	PUNCT
ejpam-6458	764	18	a1	a1	PROPN
ejpam-6458	764	19	,	,	PUNCT
ejpam-6458	764	20	a2	a2	PROPN
ejpam-6458	764	21	,	,	PUNCT
ejpam-6458	764	22	a3	a3	NOUN
ejpam-6458	764	23	)	)	PUNCT
ejpam-6458	764	24	.	.	PUNCT
ejpam-6458	765	1	we	we	PRON
ejpam-6458	765	2	omit	omit	VERB
ejpam-6458	765	3	the	the	DET
ejpam-6458	765	4	details	detail	NOUN
ejpam-6458	765	5	.	.	PUNCT
ejpam-6458	766	1	□	□	PUNCT
ejpam-6458	766	2	theorem	theorem	VERB
ejpam-6458	766	3	6.5	6.5	NUM
ejpam-6458	766	4	.	.	PUNCT
ejpam-6458	767	1	let	let	VERB
ejpam-6458	767	2	a1	a1	NOUN
ejpam-6458	767	3	,	,	PUNCT
ejpam-6458	767	4	a2	a2	PROPN
ejpam-6458	767	5	,	,	PUNCT
ejpam-6458	767	6	a3	a3	NOUN
ejpam-6458	767	7	∈	∈	PROPN
ejpam-6458	767	8	c	c	PROPN
ejpam-6458	767	9	and	and	CCONJ
ejpam-6458	767	10	a3	a3	PROPN
ejpam-6458	767	11	/∈	/∈	PUNCT
ejpam-6458	768	1	z.	z.	PROPN
ejpam-6458	769	1	then	then	ADV
ejpam-6458	769	2	1	1	NUM
ejpam-6458	769	3	.	.	X
ejpam-6458	769	4	v	v	X
ejpam-6458	769	5	(	(	PUNCT
ejpam-6458	769	6	a1	a1	PROPN
ejpam-6458	769	7	,	,	PUNCT
ejpam-6458	769	8	a2	a2	PROPN
ejpam-6458	769	9	,	,	PUNCT
ejpam-6458	769	10	a3	a3	NOUN
ejpam-6458	769	11	)	)	PUNCT
ejpam-6458	769	12	is	be	AUX
ejpam-6458	769	13	a	a	DET
ejpam-6458	769	14	torsion	torsion	NOUN
ejpam-6458	769	15	free	free	ADJ
ejpam-6458	769	16	simple	simple	ADJ
ejpam-6458	769	17	γ	γ	PROPN
ejpam-6458	769	18	-	-	PUNCT
ejpam-6458	769	19	pointed	point	VERB
ejpam-6458	769	20	g2	g2	NOUN
ejpam-6458	769	21	-	-	PUNCT
ejpam-6458	769	22	module	module	NOUN
ejpam-6458	769	23	if	if	SCONJ
ejpam-6458	769	24	and	and	CCONJ
ejpam-6458	769	25	only	only	ADV
ejpam-6458	769	26	if	if	SCONJ
ejpam-6458	769	27	s	s	X
ejpam-6458	769	28	+	+	CCONJ
ejpam-6458	769	29	ijks	ijk	NOUN
ejpam-6458	769	30	−	−	PROPN
ejpam-6458	769	31	ikt	ikt	PROPN
ejpam-6458	769	32	+	+	PROPN
ejpam-6458	769	33	jkt	jkt	PROPN
ejpam-6458	769	34	−	−	PROPN
ejpam-6458	769	35	jk	jk	PROPN
ejpam-6458	769	36	̸=	̸=	PROPN
ejpam-6458	769	37	0	0	NUM
ejpam-6458	769	38	,	,	PUNCT
ejpam-6458	769	39	for	for	ADP
ejpam-6458	769	40	all	all	DET
ejpam-6458	769	41	i	i	PROPN
ejpam-6458	769	42	,	,	PUNCT
ejpam-6458	769	43	j	j	PROPN
ejpam-6458	769	44	,	,	PUNCT
ejpam-6458	769	45	k	k	PROPN
ejpam-6458	769	46	∈	∈	PROPN
ejpam-6458	769	47	z.	z.	PROPN
ejpam-6458	769	48	2	2	NUM
ejpam-6458	769	49	.	.	PUNCT
ejpam-6458	770	1	if	if	SCONJ
ejpam-6458	770	2	v	v	NOUN
ejpam-6458	770	3	′	′	NOUN
ejpam-6458	770	4	is	be	AUX
ejpam-6458	770	5	a	a	DET
ejpam-6458	770	6	simple	simple	ADJ
ejpam-6458	770	7	torsion	torsion	NOUN
ejpam-6458	770	8	free	free	ADJ
ejpam-6458	770	9	γ	γ	X
ejpam-6458	770	10	-	-	ADJ
ejpam-6458	770	11	pointed	point	VERB
ejpam-6458	770	12	g2	g2	NOUN
ejpam-6458	770	13	-	-	PUNCT
ejpam-6458	770	14	module	module	NOUN
ejpam-6458	770	15	with	with	ADP
ejpam-6458	770	16	a	a	DET
ejpam-6458	770	17	basis	basis	NOUN
ejpam-6458	770	18	parametrized	parametrize	VERB
ejpam-6458	770	19	by	by	ADP
ejpam-6458	770	20	the	the	DET
ejpam-6458	770	21	lattice	lattice	PROPN
ejpam-6458	770	22	z3	z3	PROPN
ejpam-6458	770	23	and	and	CCONJ
ejpam-6458	770	24	with	with	ADP
ejpam-6458	770	25	separating	separate	VERB
ejpam-6458	770	26	action	action	NOUN
ejpam-6458	770	27	of	of	ADP
ejpam-6458	770	28	γ	γ	NOUN
ejpam-6458	770	29	on	on	ADP
ejpam-6458	770	30	basis	basis	NOUN
ejpam-6458	770	31	elements	element	NOUN
ejpam-6458	770	32	,	,	PUNCT
ejpam-6458	770	33	then	then	ADV
ejpam-6458	770	34	it	it	PRON
ejpam-6458	770	35	is	be	AUX
ejpam-6458	770	36	isomorphic	isomorphic	ADJ
ejpam-6458	770	37	to	to	ADP
ejpam-6458	770	38	v	v	PROPN
ejpam-6458	770	39	(	(	PUNCT
ejpam-6458	770	40	a1	a1	PROPN
ejpam-6458	770	41	,	,	PUNCT
ejpam-6458	770	42	a2	a2	PROPN
ejpam-6458	770	43	,	,	PUNCT
ejpam-6458	770	44	a3	a3	NOUN
ejpam-6458	770	45	)	)	PUNCT
ejpam-6458	770	46	for	for	ADP
ejpam-6458	770	47	suitable	suitable	ADJ
ejpam-6458	770	48	parameters	parameter	NOUN
ejpam-6458	770	49	a1	a1	PROPN
ejpam-6458	770	50	,	,	PUNCT
ejpam-6458	770	51	a2	a2	PROPN
ejpam-6458	770	52	,	,	PUNCT
ejpam-6458	770	53	a3	a3	VERB
ejpam-6458	770	54	such	such	ADJ
ejpam-6458	770	55	that	that	SCONJ
ejpam-6458	770	56	0	0	NUM
ejpam-6458	770	57	≤	≤	NUM
ejpam-6458	770	58	rea1	rea1	NOUN
ejpam-6458	770	59	<	<	X
ejpam-6458	770	60	1	1	NUM
ejpam-6458	770	61	,	,	PUNCT
ejpam-6458	770	62	0	0	NUM
ejpam-6458	770	63	≤	≤	NUM
ejpam-6458	770	64	rea2	rea2	NOUN
ejpam-6458	770	65	<	<	X
ejpam-6458	770	66	2	2	NUM
ejpam-6458	770	67	,	,	PUNCT
ejpam-6458	770	68	0	0	NUM
ejpam-6458	770	69	<	<	X
ejpam-6458	770	70	rea3	rea3	PROPN
ejpam-6458	770	71	<	<	X
ejpam-6458	770	72	2	2	NUM
ejpam-6458	770	73	and	and	CCONJ
ejpam-6458	770	74	a3	a3	VERB
ejpam-6458	770	75	̸=	̸=	PROPN
ejpam-6458	770	76	1	1	NUM
ejpam-6458	770	77	.	.	PUNCT
ejpam-6458	771	1	proof	proof	NOUN
ejpam-6458	771	2	.	.	PUNCT
ejpam-6458	772	1	it	it	PRON
ejpam-6458	772	2	follows	follow	VERB
ejpam-6458	772	3	immediately	immediately	ADV
ejpam-6458	772	4	from	from	ADP
ejpam-6458	772	5	the	the	DET
ejpam-6458	772	6	formulas	formula	NOUN
ejpam-6458	772	7	of	of	ADP
ejpam-6458	772	8	the	the	DET
ejpam-6458	772	9	action	action	NOUN
ejpam-6458	772	10	of	of	ADP
ejpam-6458	772	11	g2	g2	PROPN
ejpam-6458	772	12	that	that	SCONJ
ejpam-6458	772	13	v	v	X
ejpam-6458	772	14	(	(	PUNCT
ejpam-6458	772	15	a1	a1	PROPN
ejpam-6458	772	16	,	,	PUNCT
ejpam-6458	772	17	a2	a2	PROPN
ejpam-6458	772	18	,	,	PUNCT
ejpam-6458	772	19	a3	a3	NOUN
ejpam-6458	772	20	)	)	PUNCT
ejpam-6458	772	21	is	be	AUX
ejpam-6458	772	22	a	a	DET
ejpam-6458	772	23	torsion	torsion	NOUN
ejpam-6458	772	24	free	free	ADJ
ejpam-6458	772	25	module	module	NOUN
ejpam-6458	772	26	if	if	SCONJ
ejpam-6458	772	27	and	and	CCONJ
ejpam-6458	772	28	only	only	ADV
ejpam-6458	772	29	if	if	SCONJ
ejpam-6458	772	30	s+	s+	PUNCT
ejpam-6458	772	31	ijk	ijk	PROPN
ejpam-6458	772	32	̸=	̸=	PROPN
ejpam-6458	772	33	0	0	NUM
ejpam-6458	772	34	,	,	PUNCT
ejpam-6458	772	35	s−	s−	PROPN
ejpam-6458	772	36	ik	ik	PROPN
ejpam-6458	772	37	̸=	̸=	PROPN
ejpam-6458	772	38	0	0	NUM
ejpam-6458	772	39	,	,	PUNCT
ejpam-6458	772	40	t+	t+	VERB
ejpam-6458	772	41	jk	jk	PROPN
ejpam-6458	772	42	=	=	NOUN
ejpam-6458	772	43	̸	̸	NUM
ejpam-6458	772	44	0	0	PUNCT
ejpam-6458	773	1	and	and	CCONJ
ejpam-6458	773	2	t−	t−	PROPN
ejpam-6458	773	3	jk	jk	PROPN
ejpam-6458	773	4	̸=	̸=	PROPN
ejpam-6458	773	5	0	0	NUM
ejpam-6458	773	6	,	,	PUNCT
ejpam-6458	773	7	for	for	ADP
ejpam-6458	773	8	all	all	DET
ejpam-6458	773	9	i	i	PROPN
ejpam-6458	773	10	,	,	PUNCT
ejpam-6458	773	11	j	j	PROPN
ejpam-6458	773	12	,	,	PUNCT
ejpam-6458	773	13	k	k	PROPN
ejpam-6458	773	14	∈	∈	PROPN
ejpam-6458	773	15	z.	z.	PROPN
ejpam-6458	773	16	note	note	VERB
ejpam-6458	773	17	that	that	SCONJ
ejpam-6458	773	18	γ	γ	PROPN
ejpam-6458	773	19	has	have	VERB
ejpam-6458	773	20	a	a	DET
ejpam-6458	773	21	simple	simple	ADJ
ejpam-6458	773	22	spectrum	spectrum	NOUN
ejpam-6458	773	23	on	on	ADP
ejpam-6458	773	24	v	v	PROPN
ejpam-6458	773	25	(	(	PUNCT
ejpam-6458	773	26	a1	a1	PROPN
ejpam-6458	773	27	,	,	PUNCT
ejpam-6458	773	28	a2	a2	PROPN
ejpam-6458	773	29	,	,	PUNCT
ejpam-6458	773	30	a3	a3	NOUN
ejpam-6458	773	31	)	)	PUNCT
ejpam-6458	773	32	and	and	CCONJ
ejpam-6458	773	33	hence	hence	ADV
ejpam-6458	773	34	,	,	PUNCT
ejpam-6458	773	35	the	the	DET
ejpam-6458	773	36	action	action	NOUN
ejpam-6458	773	37	of	of	ADP
ejpam-6458	773	38	γ	γ	PROPN
ejpam-6458	773	39	separates	separate	VERB
ejpam-6458	773	40	the	the	DET
ejpam-6458	773	41	basis	basis	NOUN
ejpam-6458	773	42	elements	element	NOUN
ejpam-6458	773	43	by	by	ADP
ejpam-6458	773	44	lemma	lemma	PROPN
ejpam-6458	773	45	6.3	6.3	NUM
ejpam-6458	773	46	.	.	PUNCT
ejpam-6458	774	1	in	in	ADP
ejpam-6458	774	2	particular	particular	ADJ
ejpam-6458	774	3	,	,	PUNCT
ejpam-6458	774	4	v	v	NOUN
ejpam-6458	774	5	(	(	PUNCT
ejpam-6458	774	6	a1	a1	PROPN
ejpam-6458	774	7	,	,	PUNCT
ejpam-6458	774	8	a2	a2	PROPN
ejpam-6458	774	9	,	,	PUNCT
ejpam-6458	774	10	a3	a3	NOUN
ejpam-6458	774	11	)	)	PUNCT
ejpam-6458	774	12	is	be	AUX
ejpam-6458	774	13	γ	γ	X
ejpam-6458	774	14	-	-	PUNCT
ejpam-6458	774	15	pointed	pointed	ADJ
ejpam-6458	774	16	.	.	PUNCT
ejpam-6458	775	1	using	use	VERB
ejpam-6458	775	2	this	this	DET
ejpam-6458	775	3	fact	fact	NOUN
ejpam-6458	775	4	,	,	PUNCT
ejpam-6458	775	5	it	it	PRON
ejpam-6458	775	6	is	be	AUX
ejpam-6458	775	7	easy	easy	ADJ
ejpam-6458	775	8	to	to	PART
ejpam-6458	775	9	see	see	VERB
ejpam-6458	775	10	that	that	SCONJ
ejpam-6458	775	11	conditions	condition	NOUN
ejpam-6458	775	12	s+	s+	PUNCT
ejpam-6458	775	13	ijks	ijks	VERB
ejpam-6458	775	14	−	−	PROPN
ejpam-6458	775	15	ikt	ikt	PROPN
ejpam-6458	775	16	+	+	PROPN
ejpam-6458	775	17	jkt	jkt	NOUN
ejpam-6458	775	18	−	−	PROPN
ejpam-6458	775	19	jk	jk	NOUN
ejpam-6458	775	20	=	=	NOUN
ejpam-6458	775	21	̸	̸	NUM
ejpam-6458	775	22	0	0	NUM
ejpam-6458	775	23	,	,	PUNCT
ejpam-6458	775	24	for	for	ADP
ejpam-6458	775	25	all	all	DET
ejpam-6458	775	26	i	i	PROPN
ejpam-6458	775	27	,	,	PUNCT
ejpam-6458	775	28	j	j	PROPN
ejpam-6458	775	29	,	,	PUNCT
ejpam-6458	775	30	k	k	PROPN
ejpam-6458	775	31	∈	∈	PROPN
ejpam-6458	775	32	z	z	NOUN
ejpam-6458	775	33	are	be	AUX
ejpam-6458	775	34	necessary	necessary	ADJ
ejpam-6458	775	35	and	and	CCONJ
ejpam-6458	775	36	sufficient	sufficient	ADJ
ejpam-6458	775	37	to	to	PART
ejpam-6458	775	38	guarantee	guarantee	VERB
ejpam-6458	775	39	that	that	SCONJ
ejpam-6458	775	40	any	any	DET
ejpam-6458	775	41	element	element	NOUN
ejpam-6458	775	42	of	of	ADP
ejpam-6458	775	43	v	v	PROPN
ejpam-6458	775	44	(	(	PUNCT
ejpam-6458	775	45	a1	a1	PROPN
ejpam-6458	775	46	,	,	PUNCT
ejpam-6458	775	47	a2	a2	PROPN
ejpam-6458	775	48	,	,	PUNCT
ejpam-6458	775	49	a3	a3	NOUN
ejpam-6458	775	50	)	)	PUNCT
ejpam-6458	775	51	generates	generate	VERB
ejpam-6458	775	52	the	the	DET
ejpam-6458	775	53	whole	whole	ADJ
ejpam-6458	775	54	module	module	NOUN
ejpam-6458	775	55	,	,	PUNCT
ejpam-6458	775	56	and	and	CCONJ
ejpam-6458	775	57	hence	hence	ADV
ejpam-6458	775	58	the	the	DET
ejpam-6458	775	59	simplicity	simplicity	NOUN
ejpam-6458	775	60	of	of	ADP
ejpam-6458	775	61	the	the	DET
ejpam-6458	775	62	module	module	NOUN
ejpam-6458	775	63	.	.	PUNCT
ejpam-6458	776	1	suppose	suppose	VERB
ejpam-6458	776	2	that	that	SCONJ
ejpam-6458	776	3	v	v	NOUN
ejpam-6458	776	4	′	′	NOUN
ejpam-6458	776	5	is	be	AUX
ejpam-6458	776	6	a	a	DET
ejpam-6458	776	7	simple	simple	ADJ
ejpam-6458	776	8	torsion	torsion	NOUN
ejpam-6458	776	9	free	free	ADJ
ejpam-6458	776	10	γ	γ	PROPN
ejpam-6458	776	11	-	-	PUNCT
ejpam-6458	776	12	pointedg2	pointedg2	NOUN
ejpam-6458	776	13	-	-	PUNCT
ejpam-6458	776	14	module	module	NOUN
ejpam-6458	776	15	with	with	ADP
ejpam-6458	776	16	a	a	DET
ejpam-6458	776	17	basis	basis	NOUN
ejpam-6458	776	18	{	{	PUNCT
ejpam-6458	776	19	v′ijk	v′ijk	NUM
ejpam-6458	776	20	,	,	PUNCT
ejpam-6458	776	21	i	i	PRON
ejpam-6458	776	22	,	,	PUNCT
ejpam-6458	776	23	j	j	PROPN
ejpam-6458	776	24	,	,	PUNCT
ejpam-6458	776	25	k	k	PROPN
ejpam-6458	776	26	∈	∈	PROPN
ejpam-6458	776	27	z	z	PROPN
ejpam-6458	776	28	}	}	PUNCT
ejpam-6458	776	29	such	such	ADJ
ejpam-6458	776	30	that	that	SCONJ
ejpam-6458	776	31	γ	γ	PROPN
ejpam-6458	776	32	acts	act	VERB
ejpam-6458	776	33	by	by	ADP
ejpam-6458	776	34	different	different	ADJ
ejpam-6458	776	35	characters	character	NOUN
ejpam-6458	776	36	on	on	ADP
ejpam-6458	776	37	the	the	DET
ejpam-6458	776	38	basis	basis	NOUN
ejpam-6458	776	39	elements	element	NOUN
ejpam-6458	776	40	v′ijk	v′ijk	INTJ
ejpam-6458	776	41	.	.	PUNCT
ejpam-6458	777	1	then	then	ADV
ejpam-6458	777	2	the	the	DET
ejpam-6458	777	3	same	same	ADJ
ejpam-6458	777	4	argument	argument	NOUN
ejpam-6458	777	5	as	as	ADP
ejpam-6458	777	6	in	in	ADP
ejpam-6458	777	7	the	the	DET
ejpam-6458	777	8	proof	proof	NOUN
ejpam-6458	777	9	of	of	ADP
ejpam-6458	777	10	theorem	theorem	ADJ
ejpam-6458	777	11	5.4	5.4	NUM
ejpam-6458	777	12	shows	show	VERB
ejpam-6458	777	13	that	that	SCONJ
ejpam-6458	777	14	v	v	X
ejpam-6458	777	15	′	′	NUM
ejpam-6458	777	16	≃	≃	NOUN
ejpam-6458	777	17	v	v	NOUN
ejpam-6458	777	18	(	(	PUNCT
ejpam-6458	777	19	a1	a1	PROPN
ejpam-6458	777	20	,	,	PUNCT
ejpam-6458	777	21	a2	a2	PROPN
ejpam-6458	777	22	,	,	PUNCT
ejpam-6458	777	23	a3	a3	NOUN
ejpam-6458	777	24	)	)	PUNCT
ejpam-6458	777	25	for	for	ADP
ejpam-6458	777	26	some	some	DET
ejpam-6458	777	27	choice	choice	NOUN
ejpam-6458	777	28	of	of	ADP
ejpam-6458	777	29	complex	complex	ADJ
ejpam-6458	777	30	parameters	parameter	NOUN
ejpam-6458	777	31	a1	a1	NOUN
ejpam-6458	777	32	,	,	PUNCT
ejpam-6458	777	33	a2	a2	PROPN
ejpam-6458	777	34	,	,	PUNCT
ejpam-6458	777	35	a3	a3	VERB
ejpam-6458	777	36	with	with	ADP
ejpam-6458	777	37	a3	a3	PROPN
ejpam-6458	777	38	/∈	/∈	PUNCT
ejpam-6458	778	1	z.	z.	PROPN
ejpam-6458	779	1	since	since	SCONJ
ejpam-6458	779	2	module	module	NOUN
ejpam-6458	779	3	v	v	NOUN
ejpam-6458	779	4	′	′	NOUN
ejpam-6458	779	5	is	be	AUX
ejpam-6458	779	6	torsion	torsion	NOUN
ejpam-6458	779	7	free	free	ADJ
ejpam-6458	779	8	,	,	PUNCT
ejpam-6458	779	9	we	we	PRON
ejpam-6458	779	10	can	can	AUX
ejpam-6458	779	11	choose	choose	VERB
ejpam-6458	779	12	any	any	DET
ejpam-6458	779	13	weight	weight	NOUN
ejpam-6458	779	14	of	of	ADP
ejpam-6458	779	15	the	the	DET
ejpam-6458	779	16	weight	weight	NOUN
ejpam-6458	779	17	lattice	lattice	NOUN
ejpam-6458	779	18	and	and	CCONJ
ejpam-6458	779	19	hence	hence	ADV
ejpam-6458	779	20	the	the	DET
ejpam-6458	779	21	parameters	parameter	NOUN
ejpam-6458	779	22	can	can	AUX
ejpam-6458	779	23	be	be	AUX
ejpam-6458	779	24	chosen	choose	VERB
ejpam-6458	779	25	in	in	ADP
ejpam-6458	779	26	such	such	DET
ejpam-6458	779	27	a	a	DET
ejpam-6458	779	28	way	way	NOUN
ejpam-6458	779	29	that	that	PRON
ejpam-6458	779	30	their	their	PRON
ejpam-6458	779	31	real	real	ADJ
ejpam-6458	779	32	parts	part	NOUN
ejpam-6458	779	33	satisfy	satisfy	VERB
ejpam-6458	779	34	the	the	DET
ejpam-6458	779	35	inequalities	inequality	NOUN
ejpam-6458	779	36	0	0	NUM
ejpam-6458	779	37	≤	≤	NUM
ejpam-6458	779	38	rea1	rea1	NOUN
ejpam-6458	779	39	<	<	X
ejpam-6458	779	40	1	1	NUM
ejpam-6458	779	41	,	,	PUNCT
ejpam-6458	779	42	0	0	NUM
ejpam-6458	779	43	≤	≤	NUM
ejpam-6458	779	44	rea2	rea2	NOUN
ejpam-6458	779	45	<	<	X
ejpam-6458	779	46	3	3	NUM
ejpam-6458	779	47	,	,	PUNCT
ejpam-6458	779	48	0	0	NUM
ejpam-6458	779	49	<	<	X
ejpam-6458	779	50	rea3	rea3	PROPN
ejpam-6458	779	51	<	<	X
ejpam-6458	779	52	2	2	X
ejpam-6458	779	53	.	.	PUNCT
ejpam-6458	780	1	this	this	PRON
ejpam-6458	780	2	completes	complete	VERB
ejpam-6458	780	3	the	the	DET
ejpam-6458	780	4	proof	proof	NOUN
ejpam-6458	780	5	.	.	PUNCT
ejpam-6458	781	1	□	□	PUNCT
ejpam-6458	781	2	consider	consider	VERB
ejpam-6458	781	3	the	the	DET
ejpam-6458	781	4	following	follow	VERB
ejpam-6458	781	5	standard	standard	NOUN
ejpam-6458	781	6	embedding	embed	VERB
ejpam-6458	781	7	θ	θ	PROPN
ejpam-6458	781	8	:	:	PUNCT
ejpam-6458	781	9	a2	a2	PROPN
ejpam-6458	781	10	→	→	SYM
ejpam-6458	781	11	g2	g2	PROPN
ejpam-6458	781	12	:	:	PUNCT
ejpam-6458	781	13	θ(ê01	θ(ê01	ADJ
ejpam-6458	781	14	)	)	PUNCT
ejpam-6458	781	15	=	=	SYM
ejpam-6458	781	16	e01	e01	X
ejpam-6458	781	17	,	,	PUNCT
ejpam-6458	781	18	θ(f̂01	θ(f̂01	NOUN
ejpam-6458	781	19	)	)	PUNCT
ejpam-6458	781	20	=	=	SYM
ejpam-6458	781	21	f01	f01	PROPN
ejpam-6458	781	22	,	,	PUNCT
ejpam-6458	781	23	θ(ê10	θ(ê10	ADV
ejpam-6458	781	24	)	)	PUNCT
ejpam-6458	781	25	=	=	SYM
ejpam-6458	781	26	e31	e31	X
ejpam-6458	781	27	,	,	PUNCT
ejpam-6458	781	28	θ(f̂10	θ(f̂10	PROPN
ejpam-6458	781	29	)	)	PUNCT
ejpam-6458	781	30	=	=	SYM
ejpam-6458	781	31	f31	f31	PROPN
ejpam-6458	781	32	,	,	PUNCT
ejpam-6458	781	33	θ(ê11	θ(ê11	NOUN
ejpam-6458	781	34	)	)	PUNCT
ejpam-6458	781	35	=	=	SYM
ejpam-6458	781	36	e32	e32	NOUN
ejpam-6458	781	37	,	,	PUNCT
ejpam-6458	781	38	θ(f̂11	θ(f̂11	NOUN
ejpam-6458	781	39	)	)	PUNCT
ejpam-6458	781	40	=	=	SYM
ejpam-6458	781	41	f32	f32	NOUN
ejpam-6458	781	42	,	,	PUNCT
ejpam-6458	781	43	θ(ĥ01	θ(ĥ01	ADJ
ejpam-6458	781	44	)	)	PUNCT
ejpam-6458	781	45	=	=	SYM
ejpam-6458	781	46	h01	h01	PROPN
ejpam-6458	781	47	,	,	PUNCT
ejpam-6458	781	48	θ(ĥ10	θ(ĥ10	NOUN
ejpam-6458	781	49	)	)	PUNCT
ejpam-6458	781	50	=	=	SYM
ejpam-6458	781	51	h31	h31	ADJ
ejpam-6458	781	52	,	,	PUNCT
ejpam-6458	781	53	and	and	CCONJ
ejpam-6458	781	54	denote	denote	VERB
ejpam-6458	781	55	m.	m.	NOUN
ejpam-6458	781	56	andelić	andelić	PROPN
ejpam-6458	781	57	et	et	PROPN
ejpam-6458	781	58	al	al	PROPN
ejpam-6458	781	59	.	.	PUNCT
ejpam-6458	781	60	/	/	SYM
ejpam-6458	781	61	eur	eur	PROPN
ejpam-6458	781	62	.	.	PUNCT
ejpam-6458	782	1	j.	j.	PROPN
ejpam-6458	782	2	pure	pure	PROPN
ejpam-6458	782	3	appl	appl	PROPN
ejpam-6458	782	4	.	.	PROPN
ejpam-6458	782	5	math	math	PROPN
ejpam-6458	782	6	,	,	PUNCT
ejpam-6458	782	7	18	18	NUM
ejpam-6458	782	8	(	(	PUNCT
ejpam-6458	782	9	3	3	NUM
ejpam-6458	782	10	)	)	PUNCT
ejpam-6458	782	11	(	(	PUNCT
ejpam-6458	782	12	2025	2025	NUM
ejpam-6458	782	13	)	)	PUNCT
ejpam-6458	782	14	,	,	PUNCT
ejpam-6458	782	15	6458	6458	NUM
ejpam-6458	782	16	20	20	NUM
ejpam-6458	782	17	of	of	ADP
ejpam-6458	782	18	21	21	NUM
ejpam-6458	782	19	by	by	ADP
ejpam-6458	782	20	ĝ	ĝ	X
ejpam-6458	782	21	its	its	PRON
ejpam-6458	782	22	image	image	NOUN
ejpam-6458	782	23	.	.	PUNCT
ejpam-6458	783	1	consider	consider	VERB
ejpam-6458	783	2	the	the	DET
ejpam-6458	783	3	restriction	restriction	NOUN
ejpam-6458	783	4	v̂	v̂	PRON
ejpam-6458	783	5	(	(	PUNCT
ejpam-6458	783	6	a1	a1	PROPN
ejpam-6458	783	7	,	,	PUNCT
ejpam-6458	783	8	a2	a2	PROPN
ejpam-6458	783	9	,	,	PUNCT
ejpam-6458	783	10	a3	a3	NOUN
ejpam-6458	783	11	)	)	PUNCT
ejpam-6458	783	12	of	of	ADP
ejpam-6458	783	13	v	v	PROPN
ejpam-6458	783	14	(	(	PUNCT
ejpam-6458	783	15	a1	a1	PROPN
ejpam-6458	783	16	,	,	PUNCT
ejpam-6458	783	17	a2	a2	PROPN
ejpam-6458	783	18	,	,	PUNCT
ejpam-6458	783	19	a3	a3	NOUN
ejpam-6458	783	20	)	)	PUNCT
ejpam-6458	783	21	on	on	ADP
ejpam-6458	783	22	ĝ.	ĝ.	ADV
ejpam-6458	783	23	the	the	DET
ejpam-6458	783	24	images	image	NOUN
ejpam-6458	783	25	z1	z1	NOUN
ejpam-6458	783	26	(	(	PUNCT
ejpam-6458	783	27	respectively	respectively	ADV
ejpam-6458	783	28	z2	z2	NUM
ejpam-6458	783	29	)	)	PUNCT
ejpam-6458	783	30	of	of	ADP
ejpam-6458	783	31	the	the	DET
ejpam-6458	783	32	casimir	casimir	NOUN
ejpam-6458	783	33	elements	element	NOUN
ejpam-6458	783	34	of	of	ADP
ejpam-6458	783	35	a2	a2	PROPN
ejpam-6458	783	36	act	act	VERB
ejpam-6458	783	37	on	on	ADP
ejpam-6458	783	38	v̂	v̂	PRON
ejpam-6458	783	39	(	(	PUNCT
ejpam-6458	783	40	a1	a1	NOUN
ejpam-6458	783	41	,	,	PUNCT
ejpam-6458	783	42	a2	a2	PROPN
ejpam-6458	783	43	,	,	PUNCT
ejpam-6458	783	44	a3	a3	NOUN
ejpam-6458	783	45	)	)	PUNCT
ejpam-6458	783	46	by	by	ADP
ejpam-6458	783	47	−8	−8	PRON
ejpam-6458	783	48	9	9	NUM
ejpam-6458	783	49	(	(	PUNCT
ejpam-6458	783	50	respectively	respectively	ADV
ejpam-6458	783	51	8	8	NUM
ejpam-6458	783	52	9	9	NUM
ejpam-6458	783	53	)	)	PUNCT
ejpam-6458	783	54	.	.	PUNCT
ejpam-6458	784	1	we	we	PRON
ejpam-6458	784	2	have	have	VERB
ejpam-6458	784	3	the	the	DET
ejpam-6458	784	4	following	follow	VERB
ejpam-6458	784	5	decomposition	decomposition	NOUN
ejpam-6458	784	6	of	of	ADP
ejpam-6458	784	7	v̂	v̂	PRON
ejpam-6458	784	8	(	(	PUNCT
ejpam-6458	784	9	a1	a1	NOUN
ejpam-6458	784	10	,	,	PUNCT
ejpam-6458	784	11	a2	a2	PROPN
ejpam-6458	784	12	,	,	PUNCT
ejpam-6458	784	13	a3	a3	NOUN
ejpam-6458	784	14	)	)	PUNCT
ejpam-6458	784	15	.	.	PUNCT
ejpam-6458	785	1	theorem	theorem	VERB
ejpam-6458	785	2	6.6	6.6	NUM
ejpam-6458	785	3	.	.	PUNCT
ejpam-6458	786	1	suppose	suppose	VERB
ejpam-6458	786	2	that	that	SCONJ
ejpam-6458	786	3	v	v	PROPN
ejpam-6458	786	4	(	(	PUNCT
ejpam-6458	786	5	a1	a1	PROPN
ejpam-6458	786	6	,	,	PUNCT
ejpam-6458	786	7	a2	a2	PROPN
ejpam-6458	786	8	,	,	PUNCT
ejpam-6458	786	9	a3	a3	NOUN
ejpam-6458	786	10	)	)	PUNCT
ejpam-6458	786	11	is	be	AUX
ejpam-6458	786	12	torsion	torsion	NOUN
ejpam-6458	786	13	free	free	ADJ
ejpam-6458	786	14	.	.	PUNCT
ejpam-6458	787	1	the	the	DET
ejpam-6458	787	2	a2	a2	NOUN
ejpam-6458	787	3	-	-	PUNCT
ejpam-6458	787	4	module	module	NOUN
ejpam-6458	787	5	v̂	v̂	X
ejpam-6458	787	6	(	(	PUNCT
ejpam-6458	787	7	a1	a1	NOUN
ejpam-6458	787	8	,	,	PUNCT
ejpam-6458	787	9	a2	a2	PROPN
ejpam-6458	787	10	,	,	PUNCT
ejpam-6458	787	11	a3	a3	NOUN
ejpam-6458	787	12	)	)	PUNCT
ejpam-6458	787	13	decomposes	decompose	VERB
ejpam-6458	787	14	into	into	ADP
ejpam-6458	787	15	a	a	DET
ejpam-6458	787	16	direct	direct	ADJ
ejpam-6458	787	17	sum	sum	NOUN
ejpam-6458	787	18	of	of	ADP
ejpam-6458	787	19	three	three	NUM
ejpam-6458	787	20	torsion	torsion	NOUN
ejpam-6458	787	21	free	free	ADJ
ejpam-6458	787	22	submodules	submodule	NOUN
ejpam-6458	787	23	v̂	v̂	PRON
ejpam-6458	787	24	(	(	PUNCT
ejpam-6458	787	25	a1	a1	NOUN
ejpam-6458	787	26	,	,	PUNCT
ejpam-6458	787	27	a2	a2	PROPN
ejpam-6458	787	28	,	,	PUNCT
ejpam-6458	787	29	a3	a3	NOUN
ejpam-6458	787	30	)	)	PUNCT
ejpam-6458	788	1	=	=	NOUN
ejpam-6458	788	2	v̂	v̂	X
ejpam-6458	788	3	(	(	PUNCT
ejpam-6458	788	4	1)⊕	1)⊕	NUM
ejpam-6458	788	5	v̂	v̂	PRON
ejpam-6458	788	6	(	(	PUNCT
ejpam-6458	788	7	2)⊕	2)⊕	NUM
ejpam-6458	788	8	v̂	v̂	NUM
ejpam-6458	788	9	(	(	PUNCT
ejpam-6458	788	10	3	3	NUM
ejpam-6458	788	11	)	)	PUNCT
ejpam-6458	788	12	,	,	PUNCT
ejpam-6458	789	1	where	where	SCONJ
ejpam-6458	789	2	v̂	v̂	PRON
ejpam-6458	789	3	(	(	PUNCT
ejpam-6458	789	4	m	m	NOUN
ejpam-6458	789	5	)	)	PUNCT
ejpam-6458	789	6	=	=	SYM
ejpam-6458	789	7	spanc{vi,3j+m	spanc{vi,3j+m	PROPN
ejpam-6458	789	8	,	,	PUNCT
ejpam-6458	789	9	k	k	PROPN
ejpam-6458	789	10	|	|	ADV
ejpam-6458	789	11	i	i	PRON
ejpam-6458	789	12	,	,	PUNCT
ejpam-6458	789	13	j	j	PROPN
ejpam-6458	789	14	,	,	PUNCT
ejpam-6458	789	15	k	k	PROPN
ejpam-6458	789	16	∈	∈	PROPN
ejpam-6458	789	17	z	z	PROPN
ejpam-6458	789	18	}	}	PUNCT
ejpam-6458	789	19	≃w	≃w	NUM
ejpam-6458	789	20	=	=	SYM
ejpam-6458	789	21	v	v	NOUN
ejpam-6458	789	22	(	(	PUNCT
ejpam-6458	789	23	a	a	PRON
ejpam-6458	789	24	(	(	PUNCT
ejpam-6458	789	25	m	m	NOUN
ejpam-6458	789	26	)	)	PUNCT
ejpam-6458	789	27	1	1	NUM
ejpam-6458	789	28	,	,	PUNCT
ejpam-6458	789	29	a	a	DET
ejpam-6458	789	30	(	(	PUNCT
ejpam-6458	789	31	m	m	NOUN
ejpam-6458	789	32	)	)	PUNCT
ejpam-6458	789	33	2	2	NUM
ejpam-6458	789	34	,	,	PUNCT
ejpam-6458	789	35	a3	a3	NOUN
ejpam-6458	789	36	,	,	PUNCT
ejpam-6458	789	37	−8	−8	ADP
ejpam-6458	789	38	9	9	NUM
ejpam-6458	789	39	,	,	PUNCT
ejpam-6458	789	40	8	8	NUM
ejpam-6458	789	41	9	9	NUM
ejpam-6458	789	42	)	)	PUNCT
ejpam-6458	789	43	,	,	PUNCT
ejpam-6458	789	44	a	a	DET
ejpam-6458	789	45	(	(	PUNCT
ejpam-6458	789	46	m	m	NOUN
ejpam-6458	789	47	)	)	PUNCT
ejpam-6458	789	48	1	1	NUM
ejpam-6458	789	49	=	=	NOUN
ejpam-6458	789	50	a1	a1	NOUN
ejpam-6458	789	51	−m	−m	NOUN
ejpam-6458	789	52	,	,	PUNCT
ejpam-6458	789	53	a(m	a(m	NOUN
ejpam-6458	789	54	)	)	PUNCT
ejpam-6458	789	55	2	2	NUM
ejpam-6458	789	56	=	=	SYM
ejpam-6458	789	57	1	1	NUM
ejpam-6458	789	58	2(a2	2(a2	NUM
ejpam-6458	789	59	−	−	NOUN
ejpam-6458	789	60	a1	a1	NOUN
ejpam-6458	789	61	)	)	PUNCT
ejpam-6458	789	62	+	+	NOUN
ejpam-6458	789	63	m	m	PROPN
ejpam-6458	789	64	,	,	PUNCT
ejpam-6458	789	65	for	for	ADP
ejpam-6458	789	66	m	m	PROPN
ejpam-6458	789	67	=	=	SYM
ejpam-6458	789	68	0	0	NUM
ejpam-6458	789	69	,	,	PUNCT
ejpam-6458	789	70	1	1	NUM
ejpam-6458	789	71	,	,	PUNCT
ejpam-6458	789	72	2	2	NUM
ejpam-6458	789	73	.	.	PUNCT
ejpam-6458	789	74	proof	proof	NOUN
ejpam-6458	789	75	.	.	PUNCT
ejpam-6458	790	1	consider	consider	VERB
ejpam-6458	790	2	the	the	DET
ejpam-6458	790	3	subspace	subspace	NOUN
ejpam-6458	790	4	v̂	v̂	X
ejpam-6458	790	5	(	(	PUNCT
ejpam-6458	790	6	m	m	NOUN
ejpam-6458	790	7	)	)	PUNCT
ejpam-6458	790	8	=	=	SYM
ejpam-6458	790	9	spanc{vi,3j+m	spanc{vi,3j+m	PROPN
ejpam-6458	790	10	,	,	PUNCT
ejpam-6458	790	11	k	k	PROPN
ejpam-6458	791	1	|	|	ADV
ejpam-6458	791	2	i	i	PRON
ejpam-6458	791	3	,	,	PUNCT
ejpam-6458	791	4	j	j	PROPN
ejpam-6458	791	5	,	,	PUNCT
ejpam-6458	791	6	k	k	PROPN
ejpam-6458	791	7	∈	∈	PROPN
ejpam-6458	791	8	z	z	PROPN
ejpam-6458	791	9	}	}	PUNCT
ejpam-6458	791	10	of	of	ADP
ejpam-6458	791	11	v̂	v̂	PRON
ejpam-6458	791	12	(	(	PUNCT
ejpam-6458	791	13	a1	a1	NOUN
ejpam-6458	791	14	,	,	PUNCT
ejpam-6458	791	15	a2	a2	PROPN
ejpam-6458	791	16	,	,	PUNCT
ejpam-6458	791	17	a3	a3	NOUN
ejpam-6458	791	18	)	)	PUNCT
ejpam-6458	791	19	,	,	PUNCT
ejpam-6458	791	20	for	for	ADP
ejpam-6458	791	21	m	m	PROPN
ejpam-6458	791	22	=	=	SYM
ejpam-6458	791	23	0	0	NUM
ejpam-6458	791	24	,	,	PUNCT
ejpam-6458	791	25	1	1	NUM
ejpam-6458	791	26	,	,	PUNCT
ejpam-6458	791	27	2	2	NUM
ejpam-6458	791	28	.	.	PUNCT
ejpam-6458	791	29	clearly	clearly	ADV
ejpam-6458	791	30	,	,	PUNCT
ejpam-6458	791	31	v̂	v̂	PRON
ejpam-6458	791	32	(	(	PUNCT
ejpam-6458	791	33	m	m	X
ejpam-6458	791	34	)	)	PUNCT
ejpam-6458	791	35	is	be	AUX
ejpam-6458	791	36	a	a	DET
ejpam-6458	791	37	ĝ-submodule	ĝ-submodule	PROPN
ejpam-6458	791	38	of	of	ADP
ejpam-6458	791	39	v̂	v̂	PRON
ejpam-6458	791	40	(	(	PUNCT
ejpam-6458	791	41	a1	a1	NOUN
ejpam-6458	791	42	,	,	PUNCT
ejpam-6458	791	43	a2	a2	PROPN
ejpam-6458	791	44	,	,	PUNCT
ejpam-6458	791	45	a3	a3	NOUN
ejpam-6458	791	46	)	)	PUNCT
ejpam-6458	791	47	.	.	PUNCT
ejpam-6458	792	1	the	the	DET
ejpam-6458	792	2	ĝ-modulew	ĝ-modulew	PROPN
ejpam-6458	792	3	=	=	SYM
ejpam-6458	792	4	spanc{wijk	spanc{wijk	X
ejpam-6458	792	5	|	|	ADV
ejpam-6458	792	6	i	i	PROPN
ejpam-6458	792	7	,	,	PUNCT
ejpam-6458	792	8	j	j	PROPN
ejpam-6458	792	9	,	,	PUNCT
ejpam-6458	792	10	k	k	PROPN
ejpam-6458	792	11	∈	∈	PROPN
ejpam-6458	793	1	z	z	AUX
ejpam-6458	793	2	}	}	PUNCT
ejpam-6458	793	3	is	be	AUX
ejpam-6458	793	4	defined	define	VERB
ejpam-6458	793	5	by	by	ADP
ejpam-6458	793	6	the	the	DET
ejpam-6458	793	7	formulas	formula	NOUN
ejpam-6458	793	8	(	(	PUNCT
ejpam-6458	793	9	4.15	4.15	NUM
ejpam-6458	793	10	)	)	PUNCT
ejpam-6458	793	11	,	,	PUNCT
ejpam-6458	793	12	(	(	PUNCT
ejpam-6458	793	13	4.16	4.16	NUM
ejpam-6458	793	14	)	)	PUNCT
ejpam-6458	793	15	,	,	PUNCT
ejpam-6458	793	16	and	and	CCONJ
ejpam-6458	793	17	we	we	PRON
ejpam-6458	793	18	have	have	VERB
ejpam-6458	793	19	a	a	DET
ejpam-6458	793	20	homomorphism	homomorphism	NOUN
ejpam-6458	793	21	of	of	ADP
ejpam-6458	793	22	ĝ-modules	ĝ-module	NOUN
ejpam-6458	793	23	ψm	ψm	PRON
ejpam-6458	794	1	:	:	PUNCT
ejpam-6458	794	2	w	w	X
ejpam-6458	794	3	→	→	X
ejpam-6458	794	4	v̂	v̂	X
ejpam-6458	794	5	(	(	PUNCT
ejpam-6458	794	6	m	m	NOUN
ejpam-6458	794	7	)	)	PUNCT
ejpam-6458	794	8	,	,	PUNCT
ejpam-6458	794	9	such	such	ADJ
ejpam-6458	794	10	that	that	PRON
ejpam-6458	794	11	ψm	ψm	PROPN
ejpam-6458	794	12	:	:	PUNCT
ejpam-6458	794	13	wijk	wijk	PROPN
ejpam-6458	794	14	7→	7→	NUM
ejpam-6458	794	15	vi+j,3j+m	vi+j,3j+m	PROPN
ejpam-6458	794	16	,	,	PUNCT
ejpam-6458	794	17	k+j	k+j	PROPN
ejpam-6458	794	18	,	,	PUNCT
ejpam-6458	794	19	and	and	CCONJ
ejpam-6458	794	20	for	for	ADP
ejpam-6458	794	21	any	any	DET
ejpam-6458	794	22	x	x	SYM
ejpam-6458	794	23	∈	∈	PROPN
ejpam-6458	794	24	ĝ	ĝ	NOUN
ejpam-6458	794	25	holds	hold	VERB
ejpam-6458	794	26	ψm(x(wijk	ψm(x(wijk	NOUN
ejpam-6458	794	27	)	)	PUNCT
ejpam-6458	794	28	)	)	PUNCT
ejpam-6458	795	1	=	=	SYM
ejpam-6458	795	2	θ(x)(ψm(wijk	θ(x)(ψm(wijk	NOUN
ejpam-6458	795	3	)	)	PUNCT
ejpam-6458	795	4	)	)	PUNCT
ejpam-6458	796	1	=	=	PUNCT
ejpam-6458	796	2	θ(x)(vi+j,3j+m	θ(x)(vi+j,3j+m	X
ejpam-6458	796	3	,	,	PUNCT
ejpam-6458	796	4	k+j	k+j	PROPN
ejpam-6458	796	5	)	)	PUNCT
ejpam-6458	796	6	,	,	PUNCT
ejpam-6458	796	7	for	for	ADP
ejpam-6458	796	8	i	i	PROPN
ejpam-6458	796	9	,	,	PUNCT
ejpam-6458	796	10	j	j	PROPN
ejpam-6458	796	11	,	,	PUNCT
ejpam-6458	796	12	k	k	PROPN
ejpam-6458	796	13	∈	∈	PROPN
ejpam-6458	796	14	z	z	PROPN
ejpam-6458	796	15	and	and	CCONJ
ejpam-6458	796	16	m	m	PROPN
ejpam-6458	796	17	=	=	SYM
ejpam-6458	796	18	0	0	NUM
ejpam-6458	796	19	,	,	PUNCT
ejpam-6458	796	20	1	1	NUM
ejpam-6458	796	21	,	,	PUNCT
ejpam-6458	796	22	2	2	NUM
ejpam-6458	796	23	.	.	PUNCT
ejpam-6458	797	1	since	since	SCONJ
ejpam-6458	797	2	ψm	ψm	PROPN
ejpam-6458	797	3	is	be	AUX
ejpam-6458	797	4	a	a	DET
ejpam-6458	797	5	linear	linear	ADJ
ejpam-6458	797	6	isomorphism	isomorphism	NOUN
ejpam-6458	797	7	,	,	PUNCT
ejpam-6458	797	8	the	the	DET
ejpam-6458	797	9	statement	statement	NOUN
ejpam-6458	797	10	follows	follow	VERB
ejpam-6458	797	11	.	.	PUNCT
ejpam-6458	798	1	□	□	PUNCT
ejpam-6458	798	2	7	7	X
ejpam-6458	798	3	.	.	X
ejpam-6458	798	4	conclusion	conclusion	NOUN
ejpam-6458	798	5	for	for	ADP
ejpam-6458	798	6	all	all	DET
ejpam-6458	798	7	simple	simple	ADJ
ejpam-6458	798	8	lie	lie	NOUN
ejpam-6458	798	9	algebras	algebra	NOUN
ejpam-6458	798	10	of	of	ADP
ejpam-6458	798	11	rank	rank	PROPN
ejpam-6458	798	12	2	2	NUM
ejpam-6458	798	13	we	we	PRON
ejpam-6458	798	14	constructed	construct	VERB
ejpam-6458	798	15	families	family	NOUN
ejpam-6458	798	16	of	of	ADP
ejpam-6458	798	17	simple	simple	ADJ
ejpam-6458	798	18	modules	module	NOUN
ejpam-6458	798	19	with	with	ADP
ejpam-6458	798	20	infinite	infinite	ADJ
ejpam-6458	798	21	-	-	PUNCT
ejpam-6458	798	22	dimensional	dimensional	ADJ
ejpam-6458	798	23	weight	weight	NOUN
ejpam-6458	798	24	spaces	space	NOUN
ejpam-6458	798	25	.	.	PUNCT
ejpam-6458	799	1	these	these	DET
ejpam-6458	799	2	modules	module	NOUN
ejpam-6458	799	3	admit	admit	VERB
ejpam-6458	799	4	a	a	DET
ejpam-6458	799	5	diagonalizable	diagonalizable	ADJ
ejpam-6458	799	6	action	action	NOUN
ejpam-6458	799	7	of	of	ADP
ejpam-6458	799	8	a	a	DET
ejpam-6458	799	9	certain	certain	ADJ
ejpam-6458	799	10	commutative	commutative	ADJ
ejpam-6458	799	11	subalgebra	subalgebra	NOUN
ejpam-6458	799	12	with	with	ADP
ejpam-6458	799	13	a	a	DET
ejpam-6458	799	14	simple	simple	ADJ
ejpam-6458	799	15	spectrum	spectrum	NOUN
ejpam-6458	799	16	.	.	PUNCT
ejpam-6458	800	1	in	in	ADP
ejpam-6458	800	2	type	type	NOUN
ejpam-6458	800	3	a2	a2	PROPN
ejpam-6458	800	4	,	,	PUNCT
ejpam-6458	800	5	this	this	DET
ejpam-6458	800	6	commutative	commutative	ADJ
ejpam-6458	800	7	subalgebra	subalgebra	NOUN
ejpam-6458	800	8	is	be	AUX
ejpam-6458	800	9	a	a	DET
ejpam-6458	800	10	famous	famous	ADJ
ejpam-6458	800	11	gelfand	gelfand	ADJ
ejpam-6458	800	12	-	-	PUNCT
ejpam-6458	800	13	tsetlin	tsetlin	PROPN
ejpam-6458	800	14	subalgebra	subalgebra	NOUN
ejpam-6458	800	15	and	and	CCONJ
ejpam-6458	800	16	the	the	DET
ejpam-6458	800	17	corresponding	correspond	VERB
ejpam-6458	800	18	modules	module	NOUN
ejpam-6458	800	19	are	be	AUX
ejpam-6458	800	20	generic	generic	ADJ
ejpam-6458	800	21	gelfandtsetlin	gelfandtsetlin	PROPN
ejpam-6458	800	22	modules	module	NOUN
ejpam-6458	800	23	.	.	PUNCT
ejpam-6458	801	1	in	in	ADP
ejpam-6458	801	2	type	type	NOUN
ejpam-6458	801	3	c2	c2	PROPN
ejpam-6458	801	4	we	we	PRON
ejpam-6458	801	5	construct	construct	VERB
ejpam-6458	801	6	two	two	NUM
ejpam-6458	801	7	4	4	NUM
ejpam-6458	801	8	-	-	PUNCT
ejpam-6458	801	9	parameter	parameter	NOUN
ejpam-6458	801	10	families	family	NOUN
ejpam-6458	801	11	of	of	ADP
ejpam-6458	801	12	simple	simple	ADJ
ejpam-6458	801	13	modules	module	NOUN
ejpam-6458	801	14	which	which	PRON
ejpam-6458	801	15	are	be	AUX
ejpam-6458	801	16	analogs	analog	NOUN
ejpam-6458	801	17	of	of	ADP
ejpam-6458	801	18	generic	generic	ADJ
ejpam-6458	801	19	gelfand	gelfand	PROPN
ejpam-6458	801	20	-	-	PUNCT
ejpam-6458	801	21	tsetlin	tsetlin	PROPN
ejpam-6458	801	22	modules	module	NOUN
ejpam-6458	801	23	,	,	PUNCT
ejpam-6458	801	24	while	while	SCONJ
ejpam-6458	801	25	in	in	ADP
ejpam-6458	801	26	type	type	NOUN
ejpam-6458	801	27	g2	g2	PROPN
ejpam-6458	801	28	we	we	PRON
ejpam-6458	801	29	construct	construct	VERB
ejpam-6458	801	30	a	a	DET
ejpam-6458	801	31	3	3	NUM
ejpam-6458	801	32	-	-	PUNCT
ejpam-6458	801	33	parameter	parameter	NOUN
ejpam-6458	801	34	family	family	NOUN
ejpam-6458	801	35	of	of	ADP
ejpam-6458	801	36	such	such	ADJ
ejpam-6458	801	37	simple	simple	ADJ
ejpam-6458	801	38	modules	module	NOUN
ejpam-6458	801	39	.	.	PUNCT
ejpam-6458	802	1	detailed	detailed	ADJ
ejpam-6458	802	2	computations	computation	NOUN
ejpam-6458	802	3	are	be	AUX
ejpam-6458	802	4	available	available	ADJ
ejpam-6458	802	5	at	at	ADP
ejpam-6458	802	6	https://icm.sustech.edu.cn/en/people/faculty/vyacheslav-futorny-en	https://icm.sustech.edu.cn/en/people/faculty/vyacheslav-futorny-en	PRON
ejpam-6458	802	7	.	.	PUNCT
ejpam-6458	803	1	acknowledgements	acknowledgement	NOUN
ejpam-6458	803	2	this	this	DET
ejpam-6458	803	3	work	work	NOUN
ejpam-6458	803	4	was	be	AUX
ejpam-6458	803	5	supported	support	VERB
ejpam-6458	803	6	by	by	ADP
ejpam-6458	803	7	kuwait	kuwait	PROPN
ejpam-6458	803	8	university	university	PROPN
ejpam-6458	803	9	,	,	PUNCT
ejpam-6458	803	10	research	research	NOUN
ejpam-6458	803	11	grant	grant	NOUN
ejpam-6458	803	12	sm02/22	sm02/22	PROPN
ejpam-6458	803	13	.	.	PROPN
ejpam-6458	804	1	references	reference	NOUN
ejpam-6458	804	2	[	[	X
ejpam-6458	804	3	1	1	NUM
ejpam-6458	804	4	]	]	X
ejpam-6458	804	5	s	s	PART
ejpam-6458	804	6	fernando	fernando	PROPN
ejpam-6458	804	7	.	.	PROPN
ejpam-6458	805	1	lie	lie	PROPN
ejpam-6458	805	2	algebra	algebra	NOUN
ejpam-6458	805	3	modules	module	NOUN
ejpam-6458	805	4	with	with	ADP
ejpam-6458	805	5	finite	finite	ADJ
ejpam-6458	805	6	dimensional	dimensional	ADJ
ejpam-6458	805	7	weight	weight	NOUN
ejpam-6458	805	8	spaces	space	NOUN
ejpam-6458	805	9	i.	i.	NOUN
ejpam-6458	805	10	transactions	transaction	NOUN
ejpam-6458	805	11	of	of	ADP
ejpam-6458	805	12	the	the	DET
ejpam-6458	805	13	american	american	PROPN
ejpam-6458	805	14	mathematical	mathematical	PROPN
ejpam-6458	805	15	society	society	NOUN
ejpam-6458	805	16	,	,	PUNCT
ejpam-6458	805	17	322:757–781	322:757–781	NUM
ejpam-6458	805	18	,	,	PUNCT
ejpam-6458	805	19	1990	1990	NUM
ejpam-6458	805	20	.	.	PUNCT
ejpam-6458	806	1	[	[	X
ejpam-6458	806	2	2	2	NUM
ejpam-6458	806	3	]	]	X
ejpam-6458	806	4	o	o	X
ejpam-6458	806	5	mathieu	mathieu	PROPN
ejpam-6458	806	6	.	.	PUNCT
ejpam-6458	807	1	classification	classification	NOUN
ejpam-6458	807	2	of	of	ADP
ejpam-6458	807	3	irreducible	irreducible	ADJ
ejpam-6458	807	4	weight	weight	NOUN
ejpam-6458	807	5	modules	module	NOUN
ejpam-6458	807	6	.	.	PUNCT
ejpam-6458	808	1	annales	annales	PROPN
ejpam-6458	808	2	de	de	PROPN
ejpam-6458	808	3	l’institut	l’institut	PROPN
ejpam-6458	808	4	fourier	fourier	NOUN
ejpam-6458	808	5	,	,	PUNCT
ejpam-6458	808	6	50:537–592	50:537–592	PROPN
ejpam-6458	808	7	,	,	PUNCT
ejpam-6458	808	8	2000	2000	NUM
ejpam-6458	808	9	.	.	PUNCT
ejpam-6458	809	1	[	[	X
ejpam-6458	809	2	3	3	X
ejpam-6458	809	3	]	]	SYM
ejpam-6458	809	4	v	v	NOUN
ejpam-6458	809	5	futorny	futorny	NOUN
ejpam-6458	809	6	,	,	PUNCT
ejpam-6458	809	7	d	d	NOUN
ejpam-6458	809	8	grantcharov	grantcharov	NOUN
ejpam-6458	809	9	,	,	PUNCT
ejpam-6458	809	10	and	and	CCONJ
ejpam-6458	809	11	l	l	NOUN
ejpam-6458	809	12	e	e	PROPN
ejpam-6458	809	13	ramírez	ramírez	NOUN
ejpam-6458	809	14	.	.	PUNCT
ejpam-6458	810	1	drinfeld	drinfeld	VERB
ejpam-6458	810	2	category	category	NOUN
ejpam-6458	810	3	and	and	CCONJ
ejpam-6458	810	4	the	the	DET
ejpam-6458	810	5	classification	classification	NOUN
ejpam-6458	810	6	of	of	ADP
ejpam-6458	810	7	singular	singular	PROPN
ejpam-6458	810	8	gelfand	gelfand	PROPN
ejpam-6458	810	9	-	-	PUNCT
ejpam-6458	810	10	tsetlin	tsetlin	PROPN
ejpam-6458	810	11	gln	gln	NOUN
ejpam-6458	810	12	-	-	PUNCT
ejpam-6458	810	13	modules	module	NOUN
ejpam-6458	810	14	.	.	PUNCT
ejpam-6458	811	1	international	international	ADJ
ejpam-6458	811	2	mathematics	mathematics	PROPN
ejpam-6458	811	3	research	research	NOUN
ejpam-6458	811	4	notices	notice	NOUN
ejpam-6458	811	5	,	,	PUNCT
ejpam-6458	811	6	2017	2017	NUM
ejpam-6458	811	7	.	.	PUNCT
ejpam-6458	812	1	[	[	X
ejpam-6458	812	2	4	4	NUM
ejpam-6458	812	3	]	]	SYM
ejpam-6458	812	4	l	l	NOUN
ejpam-6458	812	5	e	e	NOUN
ejpam-6458	812	6	ramírez	ramírez	NOUN
ejpam-6458	812	7	and	and	CCONJ
ejpam-6458	812	8	p	p	NOUN
ejpam-6458	812	9	zadunaisky	zadunaisky	NOUN
ejpam-6458	812	10	.	.	PUNCT
ejpam-6458	813	1	gelfand	gelfand	PROPN
ejpam-6458	813	2	-	-	PUNCT
ejpam-6458	813	3	tsetlin	tsetlin	PROPN
ejpam-6458	813	4	modules	module	NOUN
ejpam-6458	813	5	over	over	ADP
ejpam-6458	813	6	gl(n	gl(n	NUM
ejpam-6458	813	7	)	)	PUNCT
ejpam-6458	813	8	with	with	ADP
ejpam-6458	813	9	arbitrary	arbitrary	ADJ
ejpam-6458	813	10	characters	character	NOUN
ejpam-6458	813	11	.	.	PUNCT
ejpam-6458	814	1	journal	journal	NOUN
ejpam-6458	814	2	of	of	ADP
ejpam-6458	814	3	algebra	algebra	PROPN
ejpam-6458	814	4	,	,	PUNCT
ejpam-6458	814	5	502:328–346	502:328–346	NUM
ejpam-6458	814	6	,	,	PUNCT
ejpam-6458	814	7	2018	2018	NUM
ejpam-6458	814	8	.	.	PUNCT
ejpam-6458	815	1	[	[	X
ejpam-6458	815	2	5	5	NUM
ejpam-6458	815	3	]	]	PUNCT
ejpam-6458	815	4	e	e	X
ejpam-6458	815	5	vishnyakova	vishnyakova	X
ejpam-6458	815	6	.	.	PUNCT
ejpam-6458	816	1	geometric	geometric	ADJ
ejpam-6458	816	2	approach	approach	NOUN
ejpam-6458	816	3	to	to	ADP
ejpam-6458	816	4	p	p	NOUN
ejpam-6458	816	5	-	-	PUNCT
ejpam-6458	816	6	singular	singular	NOUN
ejpam-6458	816	7	gelfand	gelfand	PROPN
ejpam-6458	816	8	-	-	PUNCT
ejpam-6458	816	9	tsetlin	tsetlin	PROPN
ejpam-6458	816	10	gln	gln	NOUN
ejpam-6458	816	11	-	-	PUNCT
ejpam-6458	816	12	modules	module	NOUN
ejpam-6458	816	13	.	.	PUNCT
ejpam-6458	817	1	differential	differential	ADJ
ejpam-6458	817	2	geometry	geometry	NOUN
ejpam-6458	817	3	and	and	CCONJ
ejpam-6458	817	4	applications	application	NOUN
ejpam-6458	817	5	,	,	PUNCT
ejpam-6458	817	6	56:155–160	56:155–160	PROPN
ejpam-6458	817	7	,	,	PUNCT
ejpam-6458	817	8	2018	2018	NUM
ejpam-6458	817	9	.	.	PUNCT
ejpam-6458	818	1	[	[	X
ejpam-6458	818	2	6	6	NUM
ejpam-6458	818	3	]	]	SYM
ejpam-6458	818	4	b	b	X
ejpam-6458	818	5	webster	webster	PROPN
ejpam-6458	818	6	.	.	PUNCT
ejpam-6458	819	1	gelfand	gelfand	PROPN
ejpam-6458	819	2	-	-	PUNCT
ejpam-6458	819	3	tsetlin	tsetlin	PROPN
ejpam-6458	819	4	modules	module	NOUN
ejpam-6458	819	5	in	in	ADP
ejpam-6458	819	6	the	the	DET
ejpam-6458	819	7	coulomb	coulomb	NOUN
ejpam-6458	819	8	context	context	NOUN
ejpam-6458	819	9	,	,	PUNCT
ejpam-6458	819	10	2019	2019	NUM
ejpam-6458	819	11	.	.	PUNCT
ejpam-6458	820	1	arxiv:1904.05415	arxiv:1904.05415	NOUN
ejpam-6458	820	2	.	.	PUNCT
ejpam-6458	821	1	m.	m.	NOUN
ejpam-6458	821	2	andelić	andelić	PROPN
ejpam-6458	821	3	et	et	PROPN
ejpam-6458	821	4	al	al	PROPN
ejpam-6458	821	5	.	.	PUNCT
ejpam-6458	821	6	/	/	SYM
ejpam-6458	821	7	eur	eur	PROPN
ejpam-6458	821	8	.	.	PUNCT
ejpam-6458	822	1	j.	j.	PROPN
ejpam-6458	822	2	pure	pure	PROPN
ejpam-6458	822	3	appl	appl	PROPN
ejpam-6458	822	4	.	.	PROPN
ejpam-6458	822	5	math	math	PROPN
ejpam-6458	822	6	,	,	PUNCT
ejpam-6458	822	7	18	18	NUM
ejpam-6458	822	8	(	(	PUNCT
ejpam-6458	822	9	3	3	NUM
ejpam-6458	822	10	)	)	PUNCT
ejpam-6458	822	11	(	(	PUNCT
ejpam-6458	822	12	2025	2025	NUM
ejpam-6458	822	13	)	)	PUNCT
ejpam-6458	822	14	,	,	PUNCT
ejpam-6458	822	15	6458	6458	NUM
ejpam-6458	822	16	21	21	NUM
ejpam-6458	822	17	of	of	ADP
ejpam-6458	822	18	21	21	NUM
ejpam-6458	822	19	[	[	X
ejpam-6458	822	20	7	7	NUM
ejpam-6458	822	21	]	]	SYM
ejpam-6458	822	22	v	v	NOUN
ejpam-6458	822	23	futorny	futorny	NOUN
ejpam-6458	822	24	,	,	PUNCT
ejpam-6458	822	25	d	d	NOUN
ejpam-6458	822	26	grantcharov	grantcharov	NOUN
ejpam-6458	822	27	,	,	PUNCT
ejpam-6458	822	28	and	and	CCONJ
ejpam-6458	822	29	l	l	NOUN
ejpam-6458	822	30	e	e	PROPN
ejpam-6458	822	31	ramírez	ramírez	NOUN
ejpam-6458	822	32	.	.	PUNCT
ejpam-6458	823	1	classification	classification	NOUN
ejpam-6458	823	2	of	of	ADP
ejpam-6458	823	3	simple	simple	ADJ
ejpam-6458	823	4	gelfand	gelfand	PROPN
ejpam-6458	823	5	-	-	PUNCT
ejpam-6458	823	6	tsetlin	tsetlin	PROPN
ejpam-6458	823	7	modules	module	NOUN
ejpam-6458	823	8	of	of	ADP
ejpam-6458	823	9	sl(3	sl(3	PROPN
ejpam-6458	823	10	)	)	PUNCT
ejpam-6458	823	11	.	.	PUNCT
ejpam-6458	824	1	bulletin	bulletin	NOUN
ejpam-6458	824	2	of	of	ADP
ejpam-6458	824	3	mathematical	mathematical	ADJ
ejpam-6458	824	4	sciences	science	NOUN
ejpam-6458	824	5	,	,	PUNCT
ejpam-6458	824	6	pages	page	NOUN
ejpam-6458	824	7	1–109	1–109	NUM
ejpam-6458	824	8	,	,	PUNCT
ejpam-6458	824	9	2021	2021	NUM
ejpam-6458	824	10	.	.	PUNCT
ejpam-6458	825	1	[	[	X
ejpam-6458	825	2	8	8	NUM
ejpam-6458	825	3	]	]	X
ejpam-6458	825	4	d	d	X
ejpam-6458	825	5	britten	britten	PROPN
ejpam-6458	825	6	and	and	CCONJ
ejpam-6458	825	7	f	f	PROPN
ejpam-6458	825	8	lemire	lemire	PROPN
ejpam-6458	825	9	.	.	PUNCT
ejpam-6458	826	1	a	a	DET
ejpam-6458	826	2	classification	classification	NOUN
ejpam-6458	826	3	of	of	ADP
ejpam-6458	826	4	pointed	point	VERB
ejpam-6458	826	5	an	an	DET
ejpam-6458	826	6	-	-	PUNCT
ejpam-6458	826	7	modules	module	NOUN
ejpam-6458	826	8	.	.	PUNCT
ejpam-6458	827	1	in	in	ADP
ejpam-6458	827	2	lecture	lecture	NOUN
ejpam-6458	827	3	notes	note	NOUN
ejpam-6458	827	4	in	in	ADP
ejpam-6458	827	5	mathematics	mathematic	NOUN
ejpam-6458	827	6	,	,	PUNCT
ejpam-6458	827	7	volume	volume	NOUN
ejpam-6458	827	8	933	933	NUM
ejpam-6458	827	9	,	,	PUNCT
ejpam-6458	827	10	pages	page	NOUN
ejpam-6458	827	11	63–70	63–70	NUM
ejpam-6458	827	12	.	.	PUNCT
ejpam-6458	827	13	1982	1982	NUM
ejpam-6458	827	14	.	.	PUNCT
ejpam-6458	828	1	[	[	X
ejpam-6458	828	2	9	9	NUM
ejpam-6458	828	3	]	]	X
ejpam-6458	828	4	d	d	X
ejpam-6458	828	5	britten	britten	PROPN
ejpam-6458	828	6	and	and	CCONJ
ejpam-6458	828	7	f	f	PROPN
ejpam-6458	828	8	lemire	lemire	PROPN
ejpam-6458	828	9	.	.	PUNCT
ejpam-6458	829	1	irreducible	irreducible	ADJ
ejpam-6458	829	2	representations	representation	NOUN
ejpam-6458	829	3	of	of	ADP
ejpam-6458	829	4	an	an	PRON
ejpam-6458	829	5	with	with	ADP
ejpam-6458	829	6	one	one	NUM
ejpam-6458	829	7	-	-	PUNCT
ejpam-6458	829	8	dimensional	dimensional	ADJ
ejpam-6458	829	9	weight	weight	NOUN
ejpam-6458	829	10	space	space	NOUN
ejpam-6458	829	11	.	.	PUNCT
ejpam-6458	830	1	transactions	transaction	NOUN
ejpam-6458	830	2	of	of	ADP
ejpam-6458	830	3	the	the	DET
ejpam-6458	830	4	american	american	PROPN
ejpam-6458	830	5	mathematical	mathematical	PROPN
ejpam-6458	830	6	society	society	NOUN
ejpam-6458	830	7	,	,	PUNCT
ejpam-6458	830	8	273:509–540	273:509–540	NUM
ejpam-6458	830	9	,	,	PUNCT
ejpam-6458	830	10	1982	1982	NUM
ejpam-6458	830	11	.	.	PUNCT
ejpam-6458	831	1	[	[	X
ejpam-6458	831	2	10	10	NUM
ejpam-6458	831	3	]	]	X
ejpam-6458	831	4	d	d	X
ejpam-6458	831	5	britten	britten	PROPN
ejpam-6458	831	6	and	and	CCONJ
ejpam-6458	831	7	f	f	PROPN
ejpam-6458	831	8	lemire	lemire	PROPN
ejpam-6458	831	9	.	.	PUNCT
ejpam-6458	832	1	a	a	DET
ejpam-6458	832	2	classification	classification	NOUN
ejpam-6458	832	3	of	of	ADP
ejpam-6458	832	4	simple	simple	ADJ
ejpam-6458	832	5	lie	lie	NOUN
ejpam-6458	832	6	modules	module	NOUN
ejpam-6458	832	7	having	have	VERB
ejpam-6458	832	8	a	a	DET
ejpam-6458	832	9	one	one	NUM
ejpam-6458	832	10	-	-	PUNCT
ejpam-6458	832	11	dimensional	dimensional	ADJ
ejpam-6458	832	12	weight	weight	NOUN
ejpam-6458	832	13	space	space	NOUN
ejpam-6458	832	14	.	.	PUNCT
ejpam-6458	833	1	transactions	transaction	NOUN
ejpam-6458	833	2	of	of	ADP
ejpam-6458	833	3	the	the	DET
ejpam-6458	833	4	american	american	PROPN
ejpam-6458	833	5	mathematical	mathematical	PROPN
ejpam-6458	833	6	society	society	NOUN
ejpam-6458	833	7	,	,	PUNCT
ejpam-6458	833	8	299:111–121	299:111–121	NUM
ejpam-6458	833	9	,	,	PUNCT
ejpam-6458	833	10	1987	1987	NUM
ejpam-6458	833	11	.	.	PUNCT
ejpam-6458	834	1	[	[	X
ejpam-6458	834	2	11	11	NUM
ejpam-6458	834	3	]	]	X
ejpam-6458	834	4	d	d	X
ejpam-6458	834	5	j	j	PROPN
ejpam-6458	834	6	britten	britten	PROPN
ejpam-6458	834	7	,	,	PUNCT
ejpam-6458	834	8	v	v	NOUN
ejpam-6458	834	9	futorny	futorny	NOUN
ejpam-6458	834	10	,	,	PUNCT
ejpam-6458	834	11	and	and	CCONJ
ejpam-6458	834	12	f	f	PROPN
ejpam-6458	834	13	w	w	PROPN
ejpam-6458	834	14	lemire	lemire	PROPN
ejpam-6458	834	15	.	.	PUNCT
ejpam-6458	835	1	simple	simple	ADJ
ejpam-6458	835	2	a2	a2	PROPN
ejpam-6458	835	3	-	-	PUNCT
ejpam-6458	835	4	modules	module	NOUN
ejpam-6458	835	5	with	with	ADP
ejpam-6458	835	6	a	a	DET
ejpam-6458	835	7	finite	finite	ADJ
ejpam-6458	835	8	dimensional	dimensional	ADJ
ejpam-6458	835	9	weight	weight	NOUN
ejpam-6458	835	10	space	space	NOUN
ejpam-6458	835	11	.	.	PUNCT
ejpam-6458	836	1	communications	communication	NOUN
ejpam-6458	836	2	in	in	ADP
ejpam-6458	836	3	algebra	algebra	NOUN
ejpam-6458	836	4	,	,	PUNCT
ejpam-6458	836	5	23(2):467–510	23(2):467–510	PROPN
ejpam-6458	836	6	,	,	PUNCT
ejpam-6458	836	7	1995	1995	NUM
ejpam-6458	836	8	.	.	PUNCT
ejpam-6458	837	1	[	[	X
ejpam-6458	837	2	12	12	NUM
ejpam-6458	837	3	]	]	X
ejpam-6458	837	4	y	y	PROPN
ejpam-6458	837	5	drozd	drozd	PROPN
ejpam-6458	837	6	,	,	PUNCT
ejpam-6458	837	7	v	v	X
ejpam-6458	837	8	futorny	futorny	NOUN
ejpam-6458	837	9	,	,	PUNCT
ejpam-6458	837	10	and	and	CCONJ
ejpam-6458	837	11	s	s	VERB
ejpam-6458	837	12	ovsienko	ovsienko	ADJ
ejpam-6458	837	13	.	.	PUNCT
ejpam-6458	838	1	irreducible	irreducible	ADJ
ejpam-6458	838	2	weighted	weight	VERB
ejpam-6458	838	3	sl(3)-modules	sl(3)-module	NOUN
ejpam-6458	838	4	.	.	PUNCT
ejpam-6458	839	1	funksionalnyi	funksionalnyi	PROPN
ejpam-6458	839	2	analiz	analiz	PROPN
ejpam-6458	839	3	i	i	PRON
ejpam-6458	839	4	ego	ego	PROPN
ejpam-6458	839	5	prilozheniya	prilozheniya	NOUN
ejpam-6458	839	6	,	,	PUNCT
ejpam-6458	839	7	23:57–58	23:57–58	NUM
ejpam-6458	839	8	,	,	PUNCT
ejpam-6458	839	9	1989	1989	NUM
ejpam-6458	839	10	.	.	PUNCT
ejpam-6458	840	1	[	[	X
ejpam-6458	840	2	13	13	NUM
ejpam-6458	840	3	]	]	X
ejpam-6458	840	4	y	y	PROPN
ejpam-6458	840	5	drozd	drozd	PROPN
ejpam-6458	840	6	,	,	PUNCT
ejpam-6458	840	7	v	v	X
ejpam-6458	840	8	futorny	futorny	NOUN
ejpam-6458	840	9	,	,	PUNCT
ejpam-6458	840	10	and	and	CCONJ
ejpam-6458	840	11	s	s	VERB
ejpam-6458	840	12	ovsienko	ovsienko	PROPN
ejpam-6458	840	13	.	.	PUNCT
ejpam-6458	841	1	gelfand	gelfand	PROPN
ejpam-6458	841	2	-	-	PUNCT
ejpam-6458	841	3	tsetlin	tsetlin	PROPN
ejpam-6458	841	4	modules	module	NOUN
ejpam-6458	841	5	over	over	ADP
ejpam-6458	841	6	lie	lie	NOUN
ejpam-6458	841	7	algebra	algebra	PROPN
ejpam-6458	841	8	sl(3	sl(3	PROPN
ejpam-6458	841	9	)	)	PUNCT
ejpam-6458	841	10	.	.	PUNCT
ejpam-6458	842	1	in	in	ADP
ejpam-6458	842	2	contemporary	contemporary	ADJ
ejpam-6458	842	3	mathematics	mathematic	NOUN
ejpam-6458	842	4	,	,	PUNCT
ejpam-6458	842	5	volume	volume	NOUN
ejpam-6458	842	6	131	131	NUM
ejpam-6458	842	7	,	,	PUNCT
ejpam-6458	842	8	pages	page	NOUN
ejpam-6458	842	9	23–29	23–29	NUM
ejpam-6458	842	10	.	.	PUNCT
ejpam-6458	842	11	1992	1992	NUM
ejpam-6458	842	12	.	.	PUNCT
ejpam-6458	843	1	[	[	X
ejpam-6458	843	2	14	14	NUM
ejpam-6458	843	3	]	]	SYM
ejpam-6458	843	4	v	v	NOUN
ejpam-6458	843	5	futorny	futorny	NOUN
ejpam-6458	843	6	.	.	PUNCT
ejpam-6458	844	1	irreducible	irreducible	ADJ
ejpam-6458	844	2	sl(3)-modules	sl(3)-module	NOUN
ejpam-6458	844	3	with	with	ADP
ejpam-6458	844	4	infinite	infinite	ADJ
ejpam-6458	844	5	-	-	PUNCT
ejpam-6458	844	6	dimensional	dimensional	ADJ
ejpam-6458	844	7	weight	weight	NOUN
ejpam-6458	844	8	subspaces	subspace	NOUN
ejpam-6458	844	9	.	.	PUNCT
ejpam-6458	845	1	ukrainskii	ukrainskii	ADJ
ejpam-6458	845	2	matematicheskii	matematicheskii	PROPN
ejpam-6458	845	3	zhurnal	zhurnal	PROPN
ejpam-6458	845	4	,	,	PUNCT
ejpam-6458	845	5	41:856–859	41:856–859	NUM
ejpam-6458	845	6	,	,	PUNCT
ejpam-6458	845	7	1989	1989	NUM
ejpam-6458	845	8	.	.	PUNCT
ejpam-6458	846	1	[	[	X
ejpam-6458	846	2	15	15	NUM
ejpam-6458	846	3	]	]	SYM
ejpam-6458	846	4	v	v	NOUN
ejpam-6458	846	5	futorny	futorny	NOUN
ejpam-6458	846	6	.	.	PUNCT
ejpam-6458	847	1	weight	weight	NOUN
ejpam-6458	847	2	sl(3)-modules	sl(3)-module	NOUN
ejpam-6458	847	3	generated	generate	VERB
ejpam-6458	847	4	by	by	ADP
ejpam-6458	847	5	semiprimitive	semiprimitive	ADJ
ejpam-6458	847	6	elements	element	NOUN
ejpam-6458	847	7	.	.	PUNCT
ejpam-6458	848	1	ukrainskii	ukrainskii	ADJ
ejpam-6458	848	2	matematicheskii	matematicheskii	PROPN
ejpam-6458	848	3	zhurnal	zhurnal	PROPN
ejpam-6458	848	4	,	,	PUNCT
ejpam-6458	848	5	43:281–285	43:281–285	PROPN
ejpam-6458	848	6	,	,	PUNCT
ejpam-6458	848	7	1991	1991	NUM
ejpam-6458	848	8	.	.	PUNCT
ejpam-6458	849	1	[	[	X
ejpam-6458	849	2	16	16	NUM
ejpam-6458	849	3	]	]	X
ejpam-6458	849	4	j	j	PROPN
ejpam-6458	849	5	dixmier	dixmier	NOUN
ejpam-6458	849	6	.	.	PUNCT
ejpam-6458	850	1	enveloping	envelop	VERB
ejpam-6458	850	2	algebras	algebra	NOUN
ejpam-6458	850	3	,	,	PUNCT
ejpam-6458	850	4	volume	volume	NOUN
ejpam-6458	850	5	11	11	NUM
ejpam-6458	850	6	of	of	ADP
ejpam-6458	850	7	graduate	graduate	ADJ
ejpam-6458	850	8	studies	study	NOUN
ejpam-6458	850	9	in	in	ADP
ejpam-6458	850	10	mathematics	mathematic	NOUN
ejpam-6458	850	11	.	.	PUNCT
ejpam-6458	851	1	american	american	PROPN
ejpam-6458	851	2	mathematical	mathematical	PROPN
ejpam-6458	851	3	society	society	NOUN
ejpam-6458	851	4	,	,	PUNCT
ejpam-6458	851	5	providence	providence	NOUN
ejpam-6458	851	6	,	,	PUNCT
ejpam-6458	851	7	ri	ri	NOUN
ejpam-6458	851	8	,	,	PUNCT
ejpam-6458	851	9	1996	1996	NUM
ejpam-6458	851	10	.	.	PUNCT
ejpam-6458	852	1	[	[	X
ejpam-6458	852	2	17	17	NUM
ejpam-6458	852	3	]	]	X
ejpam-6458	852	4	y	y	PROPN
ejpam-6458	852	5	drozd	drozd	PROPN
ejpam-6458	852	6	,	,	PUNCT
ejpam-6458	852	7	v	v	X
ejpam-6458	852	8	futorny	futorny	NOUN
ejpam-6458	852	9	,	,	PUNCT
ejpam-6458	852	10	and	and	CCONJ
ejpam-6458	852	11	s	s	VERB
ejpam-6458	852	12	ovsienko	ovsienko	PROPN
ejpam-6458	852	13	.	.	PUNCT
ejpam-6458	853	1	harish	harish	PROPN
ejpam-6458	853	2	-	-	PUNCT
ejpam-6458	853	3	chandra	chandra	PROPN
ejpam-6458	853	4	subalgebras	subalgebras	PROPN
ejpam-6458	853	5	and	and	CCONJ
ejpam-6458	853	6	gelfand	gelfand	PROPN
ejpam-6458	853	7	-	-	PUNCT
ejpam-6458	853	8	zetlin	zetlin	PROPN
ejpam-6458	853	9	modules	module	NOUN
ejpam-6458	853	10	.	.	PUNCT
ejpam-6458	854	1	mathematical	mathematical	ADJ
ejpam-6458	854	2	and	and	CCONJ
ejpam-6458	854	3	physical	physical	ADJ
ejpam-6458	854	4	sciences	science	NOUN
ejpam-6458	854	5	,	,	PUNCT
ejpam-6458	854	6	424:72–89	424:72–89	NUM
ejpam-6458	854	7	,	,	PUNCT
ejpam-6458	854	8	1994	1994	NUM
ejpam-6458	854	9	.	.	PUNCT
ejpam-6458	855	1	[	[	X
ejpam-6458	855	2	18	18	NUM
ejpam-6458	855	3	]	]	SYM
ejpam-6458	855	4	v	v	NOUN
ejpam-6458	855	5	futorny	futorny	NOUN
ejpam-6458	855	6	,	,	PUNCT
ejpam-6458	855	7	l	l	PROPN
ejpam-6458	855	8	e.	e.	PROPN
ejpam-6458	855	9	ramírez	ramírez	PROPN
ejpam-6458	855	10	,	,	PUNCT
ejpam-6458	855	11	and	and	CCONJ
ejpam-6458	855	12	j	j	PROPN
ejpam-6458	855	13	zhang	zhang	PROPN
ejpam-6458	855	14	.	.	PUNCT
ejpam-6458	856	1	combinatorial	combinatorial	ADJ
ejpam-6458	856	2	construction	construction	NOUN
ejpam-6458	856	3	of	of	ADP
ejpam-6458	856	4	gelfand	gelfand	PROPN
ejpam-6458	856	5	-	-	PUNCT
ejpam-6458	856	6	tsetlin	tsetlin	PROPN
ejpam-6458	856	7	modules	module	NOUN
ejpam-6458	856	8	for	for	ADP
ejpam-6458	856	9	gln	gln	PROPN
ejpam-6458	856	10	.	.	PUNCT
ejpam-6458	857	1	advances	advance	NOUN
ejpam-6458	857	2	in	in	ADP
ejpam-6458	857	3	mathematics	mathematic	NOUN
ejpam-6458	857	4	,	,	PUNCT
ejpam-6458	857	5	343:681–711	343:681–711	NUM
ejpam-6458	857	6	,	,	PUNCT
ejpam-6458	857	7	2019	2019	NUM
ejpam-6458	857	8	.	.	PUNCT
ejpam-6458	858	1	[	[	X
ejpam-6458	858	2	19	19	NUM
ejpam-6458	858	3	]	]	X
ejpam-6458	858	4	i	i	PRON
ejpam-6458	858	5	gelfand	gelfand	VERB
ejpam-6458	858	6	and	and	CCONJ
ejpam-6458	858	7	m	m	PROPN
ejpam-6458	858	8	tsetlin	tsetlin	PROPN
ejpam-6458	858	9	.	.	PUNCT
ejpam-6458	859	1	finite	finite	ADJ
ejpam-6458	859	2	-	-	ADJ
ejpam-6458	859	3	dimensional	dimensional	ADJ
ejpam-6458	859	4	representations	representation	NOUN
ejpam-6458	859	5	of	of	ADP
ejpam-6458	859	6	the	the	DET
ejpam-6458	859	7	group	group	NOUN
ejpam-6458	859	8	of	of	ADP
ejpam-6458	859	9	unimodular	unimodular	ADJ
ejpam-6458	859	10	matrices	matrix	NOUN
ejpam-6458	859	11	.	.	PUNCT
ejpam-6458	860	1	doklady	doklady	PROPN
ejpam-6458	860	2	akademii	akademii	NOUN
ejpam-6458	860	3	nauk	nauk	NOUN
ejpam-6458	860	4	sssr	sssr	NOUN
ejpam-6458	860	5	(	(	PUNCT
ejpam-6458	860	6	n.s	n.s	PROPN
ejpam-6458	860	7	.	.	PROPN
ejpam-6458	860	8	)	)	PUNCT
ejpam-6458	860	9	,	,	PUNCT
ejpam-6458	860	10	71:825–828	71:825–828	NOUN
ejpam-6458	860	11	,	,	PUNCT
ejpam-6458	860	12	1950	1950	NUM
ejpam-6458	860	13	.	.	PUNCT
ejpam-6458	861	1	[	[	X
ejpam-6458	861	2	20	20	NUM
ejpam-6458	861	3	]	]	SYM
ejpam-6458	861	4	v	v	NOUN
ejpam-6458	861	5	futorny	futorny	NOUN
ejpam-6458	861	6	,	,	PUNCT
ejpam-6458	861	7	d	d	NOUN
ejpam-6458	861	8	grantcharov	grantcharov	NOUN
ejpam-6458	861	9	,	,	PUNCT
ejpam-6458	861	10	and	and	CCONJ
ejpam-6458	861	11	l	l	PROPN
ejpam-6458	861	12	e.	e.	PROPN
ejpam-6458	861	13	ramírez	ramírez	PROPN
ejpam-6458	861	14	.	.	PUNCT
ejpam-6458	862	1	irreducible	irreducible	ADJ
ejpam-6458	862	2	generic	generic	PROPN
ejpam-6458	862	3	gelfand	gelfand	PROPN
ejpam-6458	862	4	-	-	PUNCT
ejpam-6458	862	5	tsetlin	tsetlin	PROPN
ejpam-6458	862	6	modules	module	NOUN
ejpam-6458	862	7	of	of	ADP
ejpam-6458	862	8	gl(n	gl(n	NUM
ejpam-6458	862	9	)	)	PUNCT
ejpam-6458	862	10	.	.	PUNCT
ejpam-6458	863	1	sigma	sigma	PROPN
ejpam-6458	863	2	,	,	PUNCT
ejpam-6458	863	3	11:018	11:018	NUM
ejpam-6458	863	4	,	,	PUNCT
ejpam-6458	863	5	13	13	NUM
ejpam-6458	863	6	,	,	PUNCT
ejpam-6458	863	7	2015	2015	NUM
ejpam-6458	863	8	.	.	PUNCT