id	sid	tid	token	lemma	pos
ejpam-5546	1	1	european	european	PROPN
ejpam-5546	1	2	journal	journal	PROPN
ejpam-5546	1	3	of	of	ADP
ejpam-5546	1	4	pure	pure	ADJ
ejpam-5546	1	5	and	and	CCONJ
ejpam-5546	1	6	applied	applied	ADJ
ejpam-5546	1	7	mathematics	mathematic	NOUN
ejpam-5546	1	8	2025	2025	NUM
ejpam-5546	1	9	,	,	PUNCT
ejpam-5546	1	10	vol	vol	NOUN
ejpam-5546	1	11	.	.	PROPN
ejpam-5546	1	12	18	18	NUM
ejpam-5546	1	13	,	,	PUNCT
ejpam-5546	1	14	issue	issue	NOUN
ejpam-5546	1	15	1	1	NUM
ejpam-5546	1	16	,	,	PUNCT
ejpam-5546	1	17	article	article	NOUN
ejpam-5546	1	18	number	number	NOUN
ejpam-5546	1	19	5546	5546	NUM
ejpam-5546	1	20	issn	issn	PROPN
ejpam-5546	1	21	1307	1307	NUM
ejpam-5546	1	22	-	-	SYM
ejpam-5546	1	23	5543	5543	NUM
ejpam-5546	1	24	–	–	PUNCT
ejpam-5546	1	25	ejpam.com	ejpam.com	X
ejpam-5546	1	26	published	publish	VERB
ejpam-5546	1	27	by	by	ADP
ejpam-5546	1	28	new	new	PROPN
ejpam-5546	1	29	york	york	PROPN
ejpam-5546	1	30	business	business	PROPN
ejpam-5546	1	31	global	global	PROPN
ejpam-5546	1	32	on	on	ADP
ejpam-5546	1	33	leonard	leonard	PROPN
ejpam-5546	1	34	pairs	pair	NOUN
ejpam-5546	1	35	and	and	CCONJ
ejpam-5546	1	36	q	q	ADJ
ejpam-5546	1	37	-	-	PUNCT
ejpam-5546	1	38	tetrahedron	tetrahedron	NOUN
ejpam-5546	1	39	algebra	algebra	PROPN
ejpam-5546	1	40	⊠q	⊠q	PROPN
ejpam-5546	1	41	hasan	hasan	PROPN
ejpam-5546	1	42	alnajjar	alnajjar	PROPN
ejpam-5546	1	43	department	department	PROPN
ejpam-5546	1	44	of	of	ADP
ejpam-5546	1	45	mathematics	mathematics	PROPN
ejpam-5546	1	46	,	,	PUNCT
ejpam-5546	1	47	the	the	DET
ejpam-5546	1	48	university	university	PROPN
ejpam-5546	1	49	of	of	ADP
ejpam-5546	1	50	jordan	jordan	PROPN
ejpam-5546	1	51	,	,	PUNCT
ejpam-5546	1	52	amman	amman	PROPN
ejpam-5546	1	53	11942	11942	NUM
ejpam-5546	1	54	,	,	PUNCT
ejpam-5546	1	55	jordan	jordan	PROPN
ejpam-5546	1	56	abstract	abstract	PROPN
ejpam-5546	1	57	.	.	PUNCT
ejpam-5546	2	1	let	let	VERB
ejpam-5546	2	2	f	f	PRON
ejpam-5546	2	3	denote	denote	VERB
ejpam-5546	2	4	an	an	DET
ejpam-5546	2	5	algebraically	algebraically	ADV
ejpam-5546	2	6	closed	closed	ADJ
ejpam-5546	2	7	field	field	NOUN
ejpam-5546	2	8	of	of	ADP
ejpam-5546	2	9	characteristic	characteristic	ADJ
ejpam-5546	2	10	zero	zero	NUM
ejpam-5546	2	11	,	,	PUNCT
ejpam-5546	2	12	fix	fix	VERB
ejpam-5546	2	13	a	a	DET
ejpam-5546	2	14	nonzero	nonzero	NOUN
ejpam-5546	2	15	scalar	scalar	ADJ
ejpam-5546	2	16	q	q	PROPN
ejpam-5546	2	17	∈	∈	PROPN
ejpam-5546	2	18	f	f	X
ejpam-5546	2	19	that	that	PRON
ejpam-5546	2	20	is	be	AUX
ejpam-5546	2	21	not	not	PART
ejpam-5546	2	22	a	a	DET
ejpam-5546	2	23	root	root	NOUN
ejpam-5546	2	24	of	of	ADP
ejpam-5546	2	25	unity	unity	NOUN
ejpam-5546	2	26	.	.	PUNCT
ejpam-5546	3	1	consider	consider	VERB
ejpam-5546	3	2	the	the	DET
ejpam-5546	3	3	q	q	ADJ
ejpam-5546	3	4	-	-	PUNCT
ejpam-5546	3	5	tetrahedron	tetrahedron	NOUN
ejpam-5546	3	6	algebra	algebra	NOUN
ejpam-5546	3	7	⊠q	⊠q	NOUN
ejpam-5546	3	8	over	over	ADP
ejpam-5546	3	9	f	f	PROPN
ejpam-5546	3	10	with	with	ADP
ejpam-5546	3	11	standard	standard	ADJ
ejpam-5546	3	12	generators	generator	NOUN
ejpam-5546	3	13	{	{	PUNCT
ejpam-5546	3	14	xij	xij	NOUN
ejpam-5546	3	15	:	:	PUNCT
ejpam-5546	3	16	i	i	PRON
ejpam-5546	3	17	,	,	PUNCT
ejpam-5546	3	18	j	j	PROPN
ejpam-5546	3	19	∈	∈	PROPN
ejpam-5546	3	20	z4	z4	PROPN
ejpam-5546	3	21	,	,	PUNCT
ejpam-5546	3	22	j	j	PROPN
ejpam-5546	3	23	−	−	NOUN
ejpam-5546	4	1	i	i	PRON
ejpam-5546	4	2	=	=	NOUN
ejpam-5546	4	3	1	1	NUM
ejpam-5546	4	4	or	or	CCONJ
ejpam-5546	4	5	j	j	ADJ
ejpam-5546	5	1	−	−	NOUN
ejpam-5546	6	1	i	i	PRON
ejpam-5546	6	2	=	=	NOUN
ejpam-5546	6	3	2	2	NUM
ejpam-5546	6	4	}	}	PUNCT
ejpam-5546	6	5	.	.	PUNCT
ejpam-5546	7	1	let	let	VERB
ejpam-5546	7	2	v	v	PART
ejpam-5546	7	3	denote	denote	VERB
ejpam-5546	7	4	finite	finite	ADJ
ejpam-5546	7	5	dimensional	dimensional	ADJ
ejpam-5546	7	6	evaluation	evaluation	NOUN
ejpam-5546	7	7	module	module	NOUN
ejpam-5546	7	8	for	for	ADP
ejpam-5546	7	9	⊠q	⊠q	PROPN
ejpam-5546	7	10	.	.	PUNCT
ejpam-5546	8	1	in	in	ADP
ejpam-5546	8	2	this	this	DET
ejpam-5546	8	3	article	article	NOUN
ejpam-5546	8	4	for	for	ADP
ejpam-5546	8	5	each	each	DET
ejpam-5546	8	6	r	r	NOUN
ejpam-5546	8	7	∈	∈	PROPN
ejpam-5546	8	8	z4	z4	PROPN
ejpam-5546	8	9	and	and	CCONJ
ejpam-5546	8	10	xr+2,r	xr+2,r	PROPN
ejpam-5546	8	11	∈	∈	PROPN
ejpam-5546	8	12	⊠q	⊠q	NOUN
ejpam-5546	8	13	we	we	PRON
ejpam-5546	8	14	find	find	VERB
ejpam-5546	8	15	a	a	DET
ejpam-5546	8	16	∈	∈	PROPN
ejpam-5546	8	17	⊠q	⊠q	NOUN
ejpam-5546	8	18	such	such	ADJ
ejpam-5546	8	19	that	that	SCONJ
ejpam-5546	8	20	the	the	DET
ejpam-5546	8	21	pairs	pair	NOUN
ejpam-5546	8	22	a	a	PRON
ejpam-5546	8	23	,	,	PUNCT
ejpam-5546	8	24	xr+2,r	xr+2,r	PROPN
ejpam-5546	8	25	,	,	PUNCT
ejpam-5546	8	26	a	a	PRON
ejpam-5546	8	27	,	,	PUNCT
ejpam-5546	8	28	xr+2,r+3	xr+2,r+3	NUM
ejpam-5546	8	29	,	,	PUNCT
ejpam-5546	8	30	and	and	CCONJ
ejpam-5546	8	31	a	a	DET
ejpam-5546	8	32	,	,	PUNCT
ejpam-5546	8	33	xr+3,r	xr+3,r	PROPN
ejpam-5546	8	34	act	act	NOUN
ejpam-5546	8	35	on	on	ADP
ejpam-5546	8	36	v	v	NOUN
ejpam-5546	8	37	as	as	ADP
ejpam-5546	8	38	leonard	leonard	NOUN
ejpam-5546	8	39	pairs	pair	NOUN
ejpam-5546	8	40	.	.	PUNCT
ejpam-5546	9	1	indeed	indeed	ADV
ejpam-5546	9	2	we	we	PRON
ejpam-5546	9	3	will	will	AUX
ejpam-5546	9	4	show	show	VERB
ejpam-5546	9	5	that	that	SCONJ
ejpam-5546	9	6	a	a	PRON
ejpam-5546	9	7	is	be	AUX
ejpam-5546	9	8	a	a	DET
ejpam-5546	9	9	linear	linear	ADJ
ejpam-5546	9	10	combination	combination	NOUN
ejpam-5546	9	11	of	of	ADP
ejpam-5546	9	12	xr	xr	PROPN
ejpam-5546	9	13	,	,	PUNCT
ejpam-5546	9	14	r+1	r+1	PROPN
ejpam-5546	9	15	and	and	CCONJ
ejpam-5546	9	16	xr+1,r+2	xr+1,r+2	X
ejpam-5546	9	17	.	.	NOUN
ejpam-5546	10	1	1	1	X
ejpam-5546	10	2	.	.	X
ejpam-5546	10	3	introduction	introduction	NOUN
ejpam-5546	10	4	leonard	leonard	PROPN
ejpam-5546	10	5	pairs	pair	NOUN
ejpam-5546	10	6	were	be	AUX
ejpam-5546	10	7	introduced	introduce	VERB
ejpam-5546	10	8	by	by	ADP
ejpam-5546	10	9	p.	p.	PROPN
ejpam-5546	10	10	terwilliger	terwilliger	NOUN
ejpam-5546	11	1	[	[	X
ejpam-5546	11	2	6	6	NUM
ejpam-5546	11	3	]	]	PUNCT
ejpam-5546	11	4	to	to	PART
ejpam-5546	11	5	study	study	VERB
ejpam-5546	11	6	the	the	DET
ejpam-5546	11	7	sequences	sequence	NOUN
ejpam-5546	11	8	of	of	ADP
ejpam-5546	11	9	orthogonal	orthogonal	ADJ
ejpam-5546	11	10	polynomials	polynomial	NOUN
ejpam-5546	11	11	with	with	ADP
ejpam-5546	11	12	discrete	discrete	ADJ
ejpam-5546	11	13	support	support	NOUN
ejpam-5546	11	14	for	for	ADP
ejpam-5546	11	15	which	which	PRON
ejpam-5546	11	16	there	there	PRON
ejpam-5546	11	17	is	be	VERB
ejpam-5546	11	18	a	a	DET
ejpam-5546	11	19	dual	dual	ADJ
ejpam-5546	11	20	sequence	sequence	NOUN
ejpam-5546	11	21	of	of	ADP
ejpam-5546	11	22	orthogonal	orthogonal	ADJ
ejpam-5546	11	23	polynomials	polynomial	NOUN
ejpam-5546	11	24	.	.	PUNCT
ejpam-5546	12	1	because	because	SCONJ
ejpam-5546	12	2	these	these	DET
ejpam-5546	12	3	polynomials	polynomial	NOUN
ejpam-5546	12	4	frequently	frequently	ADV
ejpam-5546	12	5	arise	arise	VERB
ejpam-5546	12	6	in	in	ADP
ejpam-5546	12	7	connection	connection	NOUN
ejpam-5546	12	8	with	with	ADP
ejpam-5546	12	9	the	the	DET
ejpam-5546	12	10	finite	finite	ADJ
ejpam-5546	12	11	-	-	ADJ
ejpam-5546	12	12	dimensional	dimensional	ADJ
ejpam-5546	12	13	representations	representation	NOUN
ejpam-5546	12	14	of	of	ADP
ejpam-5546	12	15	nice	nice	ADJ
ejpam-5546	12	16	algebras	algebra	NOUN
ejpam-5546	12	17	and	and	CCONJ
ejpam-5546	12	18	quantum	quantum	NOUN
ejpam-5546	12	19	groups	group	NOUN
ejpam-5546	12	20	,	,	PUNCT
ejpam-5546	12	21	it	it	PRON
ejpam-5546	12	22	is	be	AUX
ejpam-5546	12	23	natural	natural	ADJ
ejpam-5546	12	24	to	to	PART
ejpam-5546	12	25	find	find	VERB
ejpam-5546	12	26	leonard	leonard	NOUN
ejpam-5546	12	27	pairs	pair	NOUN
ejpam-5546	12	28	associated	associate	VERB
ejpam-5546	12	29	with	with	ADP
ejpam-5546	12	30	these	these	DET
ejpam-5546	12	31	algebraic	algebraic	ADJ
ejpam-5546	12	32	objects	object	NOUN
ejpam-5546	12	33	.	.	PUNCT
ejpam-5546	13	1	in	in	ADP
ejpam-5546	13	2	[	[	X
ejpam-5546	13	3	1	1	NUM
ejpam-5546	13	4	]	]	PUNCT
ejpam-5546	13	5	and	and	CCONJ
ejpam-5546	13	6	[	[	X
ejpam-5546	13	7	3	3	NUM
ejpam-5546	13	8	]	]	PUNCT
ejpam-5546	13	9	,	,	PUNCT
ejpam-5546	13	10	the	the	DET
ejpam-5546	13	11	author	author	NOUN
ejpam-5546	13	12	constructed	construct	VERB
ejpam-5546	13	13	a	a	DET
ejpam-5546	13	14	family	family	NOUN
ejpam-5546	13	15	of	of	ADP
ejpam-5546	13	16	leonard	leonard	PROPN
ejpam-5546	13	17	pairs	pair	NOUN
ejpam-5546	13	18	from	from	ADP
ejpam-5546	13	19	the	the	DET
ejpam-5546	13	20	equitable	equitable	ADJ
ejpam-5546	13	21	basis	basis	NOUN
ejpam-5546	13	22	of	of	ADP
ejpam-5546	13	23	sl2	sl2	PROPN
ejpam-5546	13	24	and	and	CCONJ
ejpam-5546	13	25	the	the	DET
ejpam-5546	13	26	equitable	equitable	ADJ
ejpam-5546	13	27	generators	generator	NOUN
ejpam-5546	13	28	of	of	ADP
ejpam-5546	13	29	uq(sl2	uq(sl2	PROPN
ejpam-5546	13	30	)	)	PUNCT
ejpam-5546	13	31	.	.	PUNCT
ejpam-5546	14	1	in	in	ADP
ejpam-5546	14	2	this	this	DET
ejpam-5546	14	3	article	article	NOUN
ejpam-5546	14	4	we	we	PRON
ejpam-5546	14	5	will	will	AUX
ejpam-5546	14	6	use	use	VERB
ejpam-5546	14	7	the	the	DET
ejpam-5546	14	8	standard	standard	ADJ
ejpam-5546	14	9	generators	generator	NOUN
ejpam-5546	14	10	of	of	ADP
ejpam-5546	14	11	the	the	DET
ejpam-5546	14	12	q	q	ADJ
ejpam-5546	14	13	-	-	PUNCT
ejpam-5546	14	14	tetrahedron	tetrahedron	NOUN
ejpam-5546	14	15	algebra	algebra	NOUN
ejpam-5546	14	16	⊠q	⊠q	PROPN
ejpam-5546	14	17	to	to	PART
ejpam-5546	14	18	construct	construct	VERB
ejpam-5546	14	19	a	a	DET
ejpam-5546	14	20	family	family	NOUN
ejpam-5546	14	21	of	of	ADP
ejpam-5546	14	22	leonard	leonard	PROPN
ejpam-5546	14	23	pairs	pair	NOUN
ejpam-5546	14	24	.	.	PUNCT
ejpam-5546	15	1	the	the	DET
ejpam-5546	15	2	the	the	DET
ejpam-5546	15	3	q	q	ADJ
ejpam-5546	15	4	-	-	PUNCT
ejpam-5546	15	5	tetrahedron	tetrahedron	NOUN
ejpam-5546	15	6	algebra	algebra	NOUN
ejpam-5546	15	7	⊠q	⊠q	PROPN
ejpam-5546	15	8	is	be	AUX
ejpam-5546	15	9	associative	associative	ADJ
ejpam-5546	15	10	,	,	PUNCT
ejpam-5546	15	11	non	non	ADJ
ejpam-5546	15	12	-	-	ADJ
ejpam-5546	15	13	commutative	commutative	ADJ
ejpam-5546	15	14	algebra	algebra	NOUN
ejpam-5546	15	15	,	,	PUNCT
ejpam-5546	15	16	this	this	DET
ejpam-5546	15	17	algebra	algebra	NOUN
ejpam-5546	15	18	was	be	AUX
ejpam-5546	15	19	introduced	introduce	VERB
ejpam-5546	15	20	by	by	ADP
ejpam-5546	15	21	p.	p.	PROPN
ejpam-5546	15	22	terwilliger	terwilliger	NOUN
ejpam-5546	15	23	and	and	CCONJ
ejpam-5546	15	24	t.	t.	PROPN
ejpam-5546	15	25	ito	ito	PROPN
ejpam-5546	16	1	[	[	X
ejpam-5546	16	2	5	5	NUM
ejpam-5546	16	3	]	]	PUNCT
ejpam-5546	16	4	.	.	PUNCT
ejpam-5546	17	1	the	the	DET
ejpam-5546	17	2	⊠q	⊠q	PROPN
ejpam-5546	17	3	has	have	VERB
ejpam-5546	17	4	eight	eight	NUM
ejpam-5546	17	5	generators	generator	NOUN
ejpam-5546	17	6	{	{	PUNCT
ejpam-5546	17	7	xij	xij	NOUN
ejpam-5546	17	8	:	:	PUNCT
ejpam-5546	17	9	i	i	PRON
ejpam-5546	17	10	,	,	PUNCT
ejpam-5546	17	11	j	j	PROPN
ejpam-5546	17	12	∈	∈	PROPN
ejpam-5546	17	13	z4	z4	PROPN
ejpam-5546	17	14	,	,	PUNCT
ejpam-5546	17	15	j	j	PROPN
ejpam-5546	17	16	−	−	NOUN
ejpam-5546	18	1	i	i	PRON
ejpam-5546	18	2	=	=	NOUN
ejpam-5546	18	3	1	1	NUM
ejpam-5546	18	4	or	or	CCONJ
ejpam-5546	18	5	j	j	ADJ
ejpam-5546	19	1	−	−	NOUN
ejpam-5546	20	1	i	i	PRON
ejpam-5546	20	2	=	=	NOUN
ejpam-5546	20	3	2	2	NUM
ejpam-5546	20	4	}	}	PUNCT
ejpam-5546	20	5	.	.	PUNCT
ejpam-5546	21	1	we	we	PRON
ejpam-5546	21	2	can	can	AUX
ejpam-5546	21	3	view	view	VERB
ejpam-5546	21	4	the	the	DET
ejpam-5546	21	5	algebra	algebra	NOUN
ejpam-5546	21	6	⊠q	⊠q	PROPN
ejpam-5546	21	7	as	as	SCONJ
ejpam-5546	21	8	follows	follow	VERB
ejpam-5546	21	9	:	:	PUNCT
ejpam-5546	21	10	the	the	DET
ejpam-5546	21	11	elements	element	NOUN
ejpam-5546	21	12	of	of	ADP
ejpam-5546	21	13	z4	z4	PROPN
ejpam-5546	21	14	represent	represent	VERB
ejpam-5546	21	15	the	the	DET
ejpam-5546	21	16	vertices	vertex	NOUN
ejpam-5546	21	17	of	of	ADP
ejpam-5546	21	18	the	the	DET
ejpam-5546	21	19	tetrahedron	tetrahedron	NOUN
ejpam-5546	21	20	and	and	CCONJ
ejpam-5546	21	21	for	for	ADP
ejpam-5546	21	22	each	each	DET
ejpam-5546	21	23	distinct	distinct	PROPN
ejpam-5546	21	24	i	i	PROPN
ejpam-5546	21	25	,	,	PUNCT
ejpam-5546	21	26	j	j	PROPN
ejpam-5546	21	27	∈	∈	PROPN
ejpam-5546	21	28	z4	z4	PROPN
ejpam-5546	21	29	,	,	PUNCT
ejpam-5546	21	30	the	the	DET
ejpam-5546	21	31	standard	standard	ADJ
ejpam-5546	21	32	generator	generator	NOUN
ejpam-5546	21	33	xij	xij	PROPN
ejpam-5546	21	34	of	of	ADP
ejpam-5546	21	35	⊠q	⊠q	PROPN
ejpam-5546	21	36	represents	represent	VERB
ejpam-5546	21	37	the	the	DET
ejpam-5546	21	38	edge	edge	NOUN
ejpam-5546	21	39	of	of	ADP
ejpam-5546	21	40	the	the	DET
ejpam-5546	21	41	tetrahedron	tetrahedron	NOUN
ejpam-5546	21	42	oriented	orient	VERB
ejpam-5546	21	43	from	from	ADP
ejpam-5546	21	44	i	i	PRON
ejpam-5546	21	45	to	to	ADP
ejpam-5546	21	46	j.	j.	PROPN
ejpam-5546	22	1	so	so	ADV
ejpam-5546	22	2	,	,	PUNCT
ejpam-5546	22	3	the	the	DET
ejpam-5546	22	4	generators	generator	NOUN
ejpam-5546	22	5	x20	x20	NOUN
ejpam-5546	22	6	,	,	PUNCT
ejpam-5546	22	7	x02	x02	PROPN
ejpam-5546	22	8	represent	represent	VERB
ejpam-5546	22	9	the	the	DET
ejpam-5546	22	10	same	same	ADJ
ejpam-5546	22	11	edge	edge	NOUN
ejpam-5546	22	12	but	but	CCONJ
ejpam-5546	22	13	opposite	opposite	ADJ
ejpam-5546	22	14	direction	direction	NOUN
ejpam-5546	22	15	,	,	PUNCT
ejpam-5546	22	16	similarly	similarly	ADV
ejpam-5546	22	17	the	the	DET
ejpam-5546	22	18	generators	generator	NOUN
ejpam-5546	22	19	x31	x31	NUM
ejpam-5546	22	20	,	,	PUNCT
ejpam-5546	22	21	x13	x13	PROPN
ejpam-5546	22	22	,	,	PUNCT
ejpam-5546	22	23	the	the	DET
ejpam-5546	22	24	other	other	ADJ
ejpam-5546	22	25	generators	generator	NOUN
ejpam-5546	22	26	x01	x01	PROPN
ejpam-5546	22	27	,	,	PUNCT
ejpam-5546	22	28	x12	x12	NUM
ejpam-5546	22	29	,	,	PUNCT
ejpam-5546	22	30	x23	x23	NUM
ejpam-5546	22	31	,	,	PUNCT
ejpam-5546	22	32	x30	x30	PROPN
ejpam-5546	22	33	represent	represent	VERB
ejpam-5546	22	34	the	the	DET
ejpam-5546	22	35	other	other	ADJ
ejpam-5546	22	36	edges	edge	NOUN
ejpam-5546	22	37	but	but	CCONJ
ejpam-5546	22	38	oriented	orient	VERB
ejpam-5546	22	39	in	in	ADP
ejpam-5546	22	40	one	one	NUM
ejpam-5546	22	41	direction	direction	NOUN
ejpam-5546	22	42	.	.	PUNCT
ejpam-5546	23	1	throughout	throughout	ADP
ejpam-5546	23	2	this	this	DET
ejpam-5546	23	3	paper	paper	NOUN
ejpam-5546	23	4	f	f	PROPN
ejpam-5546	23	5	denotes	denote	VERB
ejpam-5546	23	6	an	an	DET
ejpam-5546	23	7	algebraically	algebraically	ADV
ejpam-5546	23	8	closed	closed	ADJ
ejpam-5546	23	9	field	field	NOUN
ejpam-5546	23	10	with	with	ADP
ejpam-5546	23	11	characteristic	characteristic	ADJ
ejpam-5546	23	12	zero	zero	NUM
ejpam-5546	23	13	,	,	PUNCT
ejpam-5546	23	14	d	d	PRON
ejpam-5546	23	15	is	be	AUX
ejpam-5546	23	16	a	a	DET
ejpam-5546	23	17	nonnegative	nonnegative	ADJ
ejpam-5546	23	18	integer	integer	NOUN
ejpam-5546	23	19	,	,	PUNCT
ejpam-5546	23	20	and	and	CCONJ
ejpam-5546	23	21	q	q	PROPN
ejpam-5546	23	22	∈	∈	PROPN
ejpam-5546	23	23	f	f	NOUN
ejpam-5546	23	24	is	be	AUX
ejpam-5546	23	25	a	a	DET
ejpam-5546	23	26	nonzero	nonzero	NOUN
ejpam-5546	23	27	scalar	scalar	NOUN
ejpam-5546	23	28	which	which	PRON
ejpam-5546	23	29	is	be	AUX
ejpam-5546	23	30	not	not	PART
ejpam-5546	23	31	a	a	DET
ejpam-5546	23	32	root	root	NOUN
ejpam-5546	23	33	of	of	ADP
ejpam-5546	23	34	unity	unity	NOUN
ejpam-5546	23	35	.	.	PUNCT
ejpam-5546	24	1	also	also	ADV
ejpam-5546	24	2	,	,	PUNCT
ejpam-5546	24	3	let	let	VERB
ejpam-5546	24	4	matd+1(f	matd+1(f	VERB
ejpam-5546	24	5	)	)	PUNCT
ejpam-5546	24	6	represents	represent	VERB
ejpam-5546	24	7	the	the	DET
ejpam-5546	24	8	f	f	NOUN
ejpam-5546	24	9	-	-	PUNCT
ejpam-5546	24	10	algebra	algebra	NOUN
ejpam-5546	24	11	of	of	ADP
ejpam-5546	24	12	(	(	PUNCT
ejpam-5546	24	13	d+	d+	NOUN
ejpam-5546	24	14	1)×	1)×	NUM
ejpam-5546	24	15	(	(	PUNCT
ejpam-5546	24	16	d+	d+	NOUN
ejpam-5546	24	17	1	1	NUM
ejpam-5546	24	18	)	)	PUNCT
ejpam-5546	24	19	matrices	matrix	NOUN
ejpam-5546	24	20	.	.	PUNCT
ejpam-5546	25	1	the	the	DET
ejpam-5546	25	2	article	article	NOUN
ejpam-5546	25	3	is	be	AUX
ejpam-5546	25	4	organized	organize	VERB
ejpam-5546	25	5	as	as	SCONJ
ejpam-5546	25	6	follows	follow	VERB
ejpam-5546	25	7	.	.	PUNCT
ejpam-5546	26	1	in	in	ADP
ejpam-5546	26	2	section	section	NOUN
ejpam-5546	26	3	2	2	NUM
ejpam-5546	26	4	we	we	PRON
ejpam-5546	26	5	recall	recall	VERB
ejpam-5546	26	6	the	the	DET
ejpam-5546	26	7	definitions	definition	NOUN
ejpam-5546	26	8	of	of	ADP
ejpam-5546	26	9	leonard	leonard	NOUN
ejpam-5546	26	10	pairs	pair	NOUN
ejpam-5546	26	11	and	and	CCONJ
ejpam-5546	26	12	parameters	parameter	NOUN
ejpam-5546	26	13	array	array	VERB
ejpam-5546	26	14	,	,	PUNCT
ejpam-5546	26	15	and	and	CCONJ
ejpam-5546	26	16	state	state	NOUN
ejpam-5546	26	17	some	some	DET
ejpam-5546	26	18	facts	fact	NOUN
ejpam-5546	26	19	related	relate	VERB
ejpam-5546	26	20	to	to	ADP
ejpam-5546	26	21	leonard	leonard	PROPN
ejpam-5546	26	22	pairs	pair	NOUN
ejpam-5546	26	23	.	.	PUNCT
ejpam-5546	27	1	in	in	ADP
ejpam-5546	27	2	section	section	NOUN
ejpam-5546	27	3	3	3	NUM
ejpam-5546	27	4	we	we	PRON
ejpam-5546	27	5	doi	doi	VERB
ejpam-5546	27	6	:	:	PUNCT
ejpam-5546	27	7	https://doi.org/10.29020/nybg.ejpam.v18i1.5546	https://doi.org/10.29020/nybg.ejpam.v18i1.5546	NUM
ejpam-5546	27	8	email	email	NOUN
ejpam-5546	27	9	address	address	NOUN
ejpam-5546	27	10	:	:	PUNCT
ejpam-5546	27	11	h.najjar@ju.edu.jo	h.najjar@ju.edu.jo	PROPN
ejpam-5546	27	12	(	(	PUNCT
ejpam-5546	27	13	h.	h.	PROPN
ejpam-5546	27	14	alnajjar	alnajjar	PROPN
ejpam-5546	27	15	)	)	PUNCT
ejpam-5546	27	16	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5546	28	1	1	1	NUM
ejpam-5546	28	2	copyright	copyright	NOUN
ejpam-5546	28	3	:	:	PUNCT
ejpam-5546	28	4	©	©	PROPN
ejpam-5546	28	5	2025	2025	NUM
ejpam-5546	28	6	the	the	DET
ejpam-5546	28	7	author(s	author(s	NOUN
ejpam-5546	28	8	)	)	PUNCT
ejpam-5546	28	9	.	.	PUNCT
ejpam-5546	29	1	(	(	PUNCT
ejpam-5546	29	2	cc	cc	NOUN
ejpam-5546	29	3	by	by	ADP
ejpam-5546	29	4	-	-	PUNCT
ejpam-5546	29	5	nc	nc	PROPN
ejpam-5546	29	6	4.0	4.0	NUM
ejpam-5546	29	7	)	)	PUNCT
ejpam-5546	29	8	h.	h.	PROPN
ejpam-5546	29	9	alnajjar	alnajjar	PROPN
ejpam-5546	29	10	/	/	SYM
ejpam-5546	29	11	eur	eur	PROPN
ejpam-5546	29	12	.	.	PUNCT
ejpam-5546	30	1	j.	j.	PROPN
ejpam-5546	30	2	pure	pure	PROPN
ejpam-5546	30	3	appl	appl	PROPN
ejpam-5546	30	4	.	.	PROPN
ejpam-5546	30	5	math	math	PROPN
ejpam-5546	30	6	,	,	PUNCT
ejpam-5546	30	7	18	18	NUM
ejpam-5546	30	8	(	(	PUNCT
ejpam-5546	30	9	1	1	NUM
ejpam-5546	30	10	)	)	PUNCT
ejpam-5546	30	11	(	(	PUNCT
ejpam-5546	30	12	2025	2025	NUM
ejpam-5546	30	13	)	)	PUNCT
ejpam-5546	30	14	,	,	PUNCT
ejpam-5546	30	15	5546	5546	NUM
ejpam-5546	30	16	2	2	NUM
ejpam-5546	30	17	of	of	ADP
ejpam-5546	30	18	14	14	NUM
ejpam-5546	30	19	recall	recall	VERB
ejpam-5546	30	20	the	the	DET
ejpam-5546	30	21	definition	definition	NOUN
ejpam-5546	30	22	of	of	ADP
ejpam-5546	30	23	the	the	DET
ejpam-5546	30	24	q	q	ADJ
ejpam-5546	30	25	-	-	PUNCT
ejpam-5546	30	26	tetrahedron	tetrahedron	NOUN
ejpam-5546	30	27	algebra	algebra	NOUN
ejpam-5546	30	28	⊠q	⊠q	PROPN
ejpam-5546	30	29	and	and	CCONJ
ejpam-5546	30	30	we	we	PRON
ejpam-5546	30	31	give	give	VERB
ejpam-5546	30	32	explanation	explanation	NOUN
ejpam-5546	30	33	for	for	ADP
ejpam-5546	30	34	family	family	NOUN
ejpam-5546	30	35	of	of	ADP
ejpam-5546	30	36	bases	basis	NOUN
ejpam-5546	30	37	described	describe	VERB
ejpam-5546	30	38	by	by	ADP
ejpam-5546	30	39	authors	author	NOUN
ejpam-5546	30	40	in	in	ADP
ejpam-5546	30	41	[	[	X
ejpam-5546	30	42	5	5	NUM
ejpam-5546	30	43	]	]	PUNCT
ejpam-5546	30	44	for	for	ADP
ejpam-5546	30	45	finite	finite	ADJ
ejpam-5546	30	46	dimensional	dimensional	ADJ
ejpam-5546	30	47	evaluation	evaluation	NOUN
ejpam-5546	30	48	module	module	NOUN
ejpam-5546	30	49	of	of	ADP
ejpam-5546	30	50	⊠q	⊠q	PROPN
ejpam-5546	30	51	.	.	PUNCT
ejpam-5546	31	1	in	in	ADP
ejpam-5546	31	2	sections	section	NOUN
ejpam-5546	31	3	4	4	NUM
ejpam-5546	31	4	,	,	PUNCT
ejpam-5546	31	5	5	5	NUM
ejpam-5546	31	6	,	,	PUNCT
ejpam-5546	31	7	and	and	CCONJ
ejpam-5546	31	8	6	6	NUM
ejpam-5546	31	9	we	we	PRON
ejpam-5546	31	10	prove	prove	VERB
ejpam-5546	31	11	the	the	DET
ejpam-5546	31	12	result	result	NOUN
ejpam-5546	31	13	of	of	ADP
ejpam-5546	31	14	this	this	DET
ejpam-5546	31	15	article	article	NOUN
ejpam-5546	31	16	,	,	PUNCT
ejpam-5546	31	17	we	we	PRON
ejpam-5546	31	18	will	will	AUX
ejpam-5546	31	19	show	show	VERB
ejpam-5546	31	20	that	that	SCONJ
ejpam-5546	31	21	if	if	SCONJ
ejpam-5546	31	22	v	v	NOUN
ejpam-5546	31	23	is	be	AUX
ejpam-5546	31	24	finite	finite	ADJ
ejpam-5546	31	25	dimensional	dimensional	ADJ
ejpam-5546	31	26	evaluation	evaluation	NOUN
ejpam-5546	31	27	module	module	NOUN
ejpam-5546	31	28	for	for	ADP
ejpam-5546	31	29	⊠q	⊠q	PROPN
ejpam-5546	31	30	,	,	PUNCT
ejpam-5546	31	31	then	then	ADV
ejpam-5546	31	32	for	for	ADP
ejpam-5546	31	33	each	each	DET
ejpam-5546	31	34	r	r	NOUN
ejpam-5546	31	35	∈	∈	PROPN
ejpam-5546	31	36	z4	z4	PROPN
ejpam-5546	31	37	and	and	CCONJ
ejpam-5546	31	38	xr+2,r	xr+2,r	PROPN
ejpam-5546	31	39	∈	∈	PROPN
ejpam-5546	31	40	⊠q	⊠q	NOUN
ejpam-5546	31	41	we	we	PRON
ejpam-5546	31	42	can	can	AUX
ejpam-5546	31	43	find	find	VERB
ejpam-5546	31	44	a	a	DET
ejpam-5546	31	45	∈	∈	PROPN
ejpam-5546	31	46	⊠q	⊠q	NOUN
ejpam-5546	31	47	such	such	ADJ
ejpam-5546	31	48	that	that	SCONJ
ejpam-5546	31	49	the	the	DET
ejpam-5546	31	50	pairs	pair	NOUN
ejpam-5546	31	51	a	a	PRON
ejpam-5546	31	52	,	,	PUNCT
ejpam-5546	31	53	xr+2,r	xr+2,r	PROPN
ejpam-5546	31	54	,	,	PUNCT
ejpam-5546	31	55	a	a	PRON
ejpam-5546	31	56	,	,	PUNCT
ejpam-5546	31	57	xr+2,r+3	xr+2,r+3	NUM
ejpam-5546	31	58	,	,	PUNCT
ejpam-5546	31	59	and	and	CCONJ
ejpam-5546	31	60	a	a	DET
ejpam-5546	31	61	,	,	PUNCT
ejpam-5546	31	62	xr+3,r	xr+3,r	PROPN
ejpam-5546	31	63	act	act	NOUN
ejpam-5546	31	64	on	on	ADP
ejpam-5546	31	65	v	v	NOUN
ejpam-5546	31	66	as	as	ADP
ejpam-5546	31	67	leonard	leonard	PROPN
ejpam-5546	31	68	pairs	pair	NOUN
ejpam-5546	31	69	.	.	PUNCT
ejpam-5546	32	1	also	also	ADV
ejpam-5546	32	2	we	we	PRON
ejpam-5546	32	3	will	will	AUX
ejpam-5546	32	4	show	show	VERB
ejpam-5546	32	5	that	that	SCONJ
ejpam-5546	32	6	a	a	PRON
ejpam-5546	32	7	is	be	AUX
ejpam-5546	32	8	a	a	DET
ejpam-5546	32	9	linear	linear	ADJ
ejpam-5546	32	10	combination	combination	NOUN
ejpam-5546	32	11	of	of	ADP
ejpam-5546	32	12	xr	xr	PROPN
ejpam-5546	32	13	,	,	PUNCT
ejpam-5546	32	14	r+1	r+1	PROPN
ejpam-5546	32	15	and	and	CCONJ
ejpam-5546	32	16	xr+1,r+2	xr+1,r+2	X
ejpam-5546	32	17	.	.	NOUN
ejpam-5546	33	1	2	2	X
ejpam-5546	33	2	.	.	X
ejpam-5546	33	3	leonard	leonard	NOUN
ejpam-5546	33	4	pairs	pair	NOUN
ejpam-5546	33	5	in	in	ADP
ejpam-5546	33	6	this	this	DET
ejpam-5546	33	7	section	section	NOUN
ejpam-5546	33	8	we	we	PRON
ejpam-5546	33	9	recall	recall	VERB
ejpam-5546	33	10	the	the	DET
ejpam-5546	33	11	definitions	definition	NOUN
ejpam-5546	33	12	of	of	ADP
ejpam-5546	33	13	leonard	leonard	NOUN
ejpam-5546	33	14	pairs	pair	NOUN
ejpam-5546	33	15	and	and	CCONJ
ejpam-5546	33	16	parameter	parameter	NOUN
ejpam-5546	33	17	arrays	array	NOUN
ejpam-5546	33	18	and	and	CCONJ
ejpam-5546	33	19	some	some	DET
ejpam-5546	33	20	facts	fact	NOUN
ejpam-5546	33	21	concerning	concern	VERB
ejpam-5546	33	22	them	they	PRON
ejpam-5546	33	23	that	that	SCONJ
ejpam-5546	33	24	we	we	PRON
ejpam-5546	33	25	will	will	AUX
ejpam-5546	33	26	use	use	VERB
ejpam-5546	33	27	later	later	ADV
ejpam-5546	33	28	in	in	ADP
ejpam-5546	33	29	this	this	DET
ejpam-5546	33	30	article	article	NOUN
ejpam-5546	33	31	,	,	PUNCT
ejpam-5546	33	32	before	before	SCONJ
ejpam-5546	33	33	we	we	PRON
ejpam-5546	33	34	state	state	VERB
ejpam-5546	33	35	these	these	DET
ejpam-5546	33	36	definitions	definition	NOUN
ejpam-5546	33	37	we	we	PRON
ejpam-5546	33	38	review	review	VERB
ejpam-5546	33	39	some	some	DET
ejpam-5546	33	40	concepts	concept	NOUN
ejpam-5546	33	41	.	.	PUNCT
ejpam-5546	34	1	by	by	ADP
ejpam-5546	34	2	tridiagonal	tridiagonal	ADJ
ejpam-5546	34	3	matrix	matrix	NOUN
ejpam-5546	34	4	we	we	PRON
ejpam-5546	34	5	mean	mean	VERB
ejpam-5546	34	6	a	a	DET
ejpam-5546	34	7	square	square	ADJ
ejpam-5546	34	8	matrix	matrix	NOUN
ejpam-5546	34	9	in	in	ADP
ejpam-5546	34	10	which	which	PRON
ejpam-5546	34	11	nonzero	nonzero	NOUN
ejpam-5546	34	12	entry	entry	NOUN
ejpam-5546	34	13	presents	present	NOUN
ejpam-5546	34	14	only	only	ADV
ejpam-5546	34	15	on	on	ADV
ejpam-5546	34	16	,	,	PUNCT
ejpam-5546	34	17	immediately	immediately	ADV
ejpam-5546	34	18	below	below	ADV
ejpam-5546	34	19	or	or	CCONJ
ejpam-5546	34	20	immediately	immediately	ADV
ejpam-5546	34	21	above	above	ADP
ejpam-5546	34	22	the	the	DET
ejpam-5546	34	23	main	main	ADJ
ejpam-5546	34	24	diagonal	diagonal	NOUN
ejpam-5546	34	25	.	.	PUNCT
ejpam-5546	35	1	a	a	DET
ejpam-5546	35	2	tridiagonal	tridiagonal	ADJ
ejpam-5546	35	3	matrix	matrix	NOUN
ejpam-5546	35	4	is	be	AUX
ejpam-5546	35	5	called	call	VERB
ejpam-5546	35	6	irreducible	irreducible	ADJ
ejpam-5546	35	7	if	if	SCONJ
ejpam-5546	35	8	all	all	DET
ejpam-5546	35	9	entries	entry	NOUN
ejpam-5546	35	10	present	present	VERB
ejpam-5546	35	11	immediately	immediately	ADV
ejpam-5546	35	12	below	below	ADV
ejpam-5546	35	13	or	or	CCONJ
ejpam-5546	35	14	immediately	immediately	ADV
ejpam-5546	35	15	above	above	ADP
ejpam-5546	35	16	the	the	DET
ejpam-5546	35	17	main	main	ADJ
ejpam-5546	35	18	diagonal	diagonal	NOUN
ejpam-5546	35	19	are	be	AUX
ejpam-5546	35	20	nonzeros	nonzero	NOUN
ejpam-5546	35	21	.	.	PUNCT
ejpam-5546	36	1	a	a	DET
ejpam-5546	36	2	square	square	ADJ
ejpam-5546	36	3	matrix	matrix	NOUN
ejpam-5546	36	4	is	be	AUX
ejpam-5546	36	5	called	call	VERB
ejpam-5546	36	6	upper	upper	ADJ
ejpam-5546	36	7	bidiagonal	bidiagonal	NOUN
ejpam-5546	36	8	if	if	SCONJ
ejpam-5546	36	9	nonzero	nonzero	PROPN
ejpam-5546	36	10	entry	entry	NOUN
ejpam-5546	36	11	presents	present	NOUN
ejpam-5546	36	12	on	on	ADP
ejpam-5546	36	13	or	or	CCONJ
ejpam-5546	36	14	immediately	immediately	ADV
ejpam-5546	36	15	above	above	ADP
ejpam-5546	36	16	the	the	DET
ejpam-5546	36	17	main	main	ADJ
ejpam-5546	36	18	diagonal	diagonal	NOUN
ejpam-5546	36	19	,	,	PUNCT
ejpam-5546	36	20	and	and	CCONJ
ejpam-5546	36	21	is	be	AUX
ejpam-5546	36	22	called	call	VERB
ejpam-5546	36	23	lower	low	ADJ
ejpam-5546	36	24	bidiagonal	bidiagonal	ADJ
ejpam-5546	36	25	if	if	SCONJ
ejpam-5546	36	26	nonzero	nonzero	PROPN
ejpam-5546	36	27	entry	entry	NOUN
ejpam-5546	36	28	presents	present	NOUN
ejpam-5546	36	29	on	on	ADP
ejpam-5546	36	30	or	or	CCONJ
ejpam-5546	36	31	immediately	immediately	ADV
ejpam-5546	36	32	below	below	ADP
ejpam-5546	36	33	the	the	DET
ejpam-5546	36	34	main	main	ADJ
ejpam-5546	36	35	diagonal	diagonal	NOUN
ejpam-5546	36	36	.	.	PUNCT
ejpam-5546	37	1	definition	definition	NOUN
ejpam-5546	37	2	1	1	NUM
ejpam-5546	37	3	.	.	PUNCT
ejpam-5546	38	1	[	[	X
ejpam-5546	38	2	6	6	NUM
ejpam-5546	38	3	]	]	PUNCT
ejpam-5546	38	4	let	let	VERB
ejpam-5546	38	5	v	v	PART
ejpam-5546	38	6	denote	denote	VERB
ejpam-5546	38	7	a	a	DET
ejpam-5546	38	8	vector	vector	NOUN
ejpam-5546	38	9	space	space	NOUN
ejpam-5546	38	10	over	over	ADP
ejpam-5546	38	11	f	f	PROPN
ejpam-5546	38	12	with	with	ADP
ejpam-5546	38	13	finite	finite	ADJ
ejpam-5546	38	14	positive	positive	ADJ
ejpam-5546	38	15	dimension	dimension	NOUN
ejpam-5546	38	16	.	.	PUNCT
ejpam-5546	39	1	by	by	ADP
ejpam-5546	39	2	a	a	DET
ejpam-5546	39	3	leonard	leonard	PROPN
ejpam-5546	39	4	pair	pair	NOUN
ejpam-5546	39	5	on	on	ADP
ejpam-5546	39	6	v	v	NUM
ejpam-5546	39	7	,	,	PUNCT
ejpam-5546	39	8	we	we	PRON
ejpam-5546	39	9	mean	mean	VERB
ejpam-5546	39	10	an	an	DET
ejpam-5546	39	11	ordered	order	VERB
ejpam-5546	39	12	pair	pair	NOUN
ejpam-5546	39	13	a	a	PRON
ejpam-5546	39	14	,	,	PUNCT
ejpam-5546	39	15	a∗	a∗	PROPN
ejpam-5546	39	16	,	,	PUNCT
ejpam-5546	39	17	where	where	SCONJ
ejpam-5546	39	18	a	a	DET
ejpam-5546	39	19	:	:	PUNCT
ejpam-5546	39	20	v	v	NOUN
ejpam-5546	39	21	→	→	SYM
ejpam-5546	39	22	v	v	NOUN
ejpam-5546	39	23	and	and	CCONJ
ejpam-5546	39	24	a∗	a∗	ADJ
ejpam-5546	39	25	:	:	PUNCT
ejpam-5546	39	26	v	v	NOUN
ejpam-5546	39	27	→	→	SYM
ejpam-5546	39	28	v	v	NUM
ejpam-5546	39	29	are	be	AUX
ejpam-5546	39	30	linear	linear	ADJ
ejpam-5546	39	31	transformations	transformation	NOUN
ejpam-5546	39	32	that	that	PRON
ejpam-5546	39	33	satisfy	satisfy	VERB
ejpam-5546	39	34	both	both	PRON
ejpam-5546	39	35	(	(	PUNCT
ejpam-5546	39	36	i	i	NOUN
ejpam-5546	39	37	)	)	PUNCT
ejpam-5546	39	38	and	and	CCONJ
ejpam-5546	39	39	(	(	PUNCT
ejpam-5546	39	40	ii	ii	NOUN
ejpam-5546	39	41	)	)	PUNCT
ejpam-5546	39	42	below	below	ADV
ejpam-5546	39	43	.	.	PUNCT
ejpam-5546	40	1	(	(	PUNCT
ejpam-5546	40	2	i	i	NOUN
ejpam-5546	40	3	)	)	PUNCT
ejpam-5546	40	4	there	there	PRON
ejpam-5546	40	5	exists	exist	VERB
ejpam-5546	40	6	a	a	DET
ejpam-5546	40	7	basis	basis	NOUN
ejpam-5546	40	8	for	for	ADP
ejpam-5546	40	9	v	v	NOUN
ejpam-5546	40	10	with	with	ADP
ejpam-5546	40	11	respect	respect	NOUN
ejpam-5546	40	12	to	to	ADP
ejpam-5546	40	13	which	which	PRON
ejpam-5546	40	14	the	the	DET
ejpam-5546	40	15	matrix	matrix	NOUN
ejpam-5546	40	16	representing	represent	VERB
ejpam-5546	40	17	a∗	a∗	NOUN
ejpam-5546	40	18	is	be	AUX
ejpam-5546	40	19	diagonal	diagonal	ADJ
ejpam-5546	40	20	and	and	CCONJ
ejpam-5546	40	21	the	the	DET
ejpam-5546	40	22	matrix	matrix	NOUN
ejpam-5546	40	23	representing	represent	VERB
ejpam-5546	40	24	a	a	PRON
ejpam-5546	40	25	is	be	AUX
ejpam-5546	40	26	irreducible	irreducible	ADJ
ejpam-5546	40	27	tridiagonal	tridiagonal	ADJ
ejpam-5546	40	28	.	.	PUNCT
ejpam-5546	41	1	(	(	PUNCT
ejpam-5546	41	2	ii	ii	NOUN
ejpam-5546	41	3	)	)	PUNCT
ejpam-5546	41	4	there	there	PRON
ejpam-5546	41	5	exists	exist	VERB
ejpam-5546	41	6	a	a	DET
ejpam-5546	41	7	basis	basis	NOUN
ejpam-5546	41	8	for	for	ADP
ejpam-5546	41	9	v	v	NOUN
ejpam-5546	41	10	with	with	ADP
ejpam-5546	41	11	respect	respect	NOUN
ejpam-5546	41	12	to	to	ADP
ejpam-5546	41	13	which	which	PRON
ejpam-5546	41	14	the	the	DET
ejpam-5546	41	15	matrix	matrix	NOUN
ejpam-5546	41	16	representing	represent	VERB
ejpam-5546	41	17	a	a	PRON
ejpam-5546	41	18	is	be	AUX
ejpam-5546	41	19	diagonal	diagonal	ADJ
ejpam-5546	41	20	and	and	CCONJ
ejpam-5546	41	21	the	the	DET
ejpam-5546	41	22	matrix	matrix	NOUN
ejpam-5546	41	23	representing	represent	VERB
ejpam-5546	41	24	a∗	a∗	NOUN
ejpam-5546	41	25	is	be	AUX
ejpam-5546	41	26	irreducible	irreducible	ADJ
ejpam-5546	41	27	tridiagonal	tridiagonal	ADJ
ejpam-5546	41	28	.	.	PUNCT
ejpam-5546	42	1	for	for	ADP
ejpam-5546	42	2	more	more	ADJ
ejpam-5546	42	3	details	detail	NOUN
ejpam-5546	42	4	about	about	ADP
ejpam-5546	42	5	leonard	leonard	NOUN
ejpam-5546	42	6	pairs	pair	NOUN
ejpam-5546	42	7	see	see	VERB
ejpam-5546	42	8	[	[	X
ejpam-5546	42	9	2	2	NUM
ejpam-5546	42	10	,	,	PUNCT
ejpam-5546	42	11	8–11	8–11	NOUN
ejpam-5546	42	12	]	]	PUNCT
ejpam-5546	42	13	.	.	PUNCT
ejpam-5546	43	1	in	in	ADP
ejpam-5546	43	2	[	[	X
ejpam-5546	43	3	7	7	NUM
ejpam-5546	43	4	]	]	PUNCT
ejpam-5546	43	5	,	,	PUNCT
ejpam-5546	43	6	terwilliger	terwilliger	NOUN
ejpam-5546	43	7	showed	show	VERB
ejpam-5546	43	8	that	that	SCONJ
ejpam-5546	43	9	for	for	SCONJ
ejpam-5546	43	10	each	each	DET
ejpam-5546	43	11	leonard	leonard	PROPN
ejpam-5546	43	12	pair	pair	NOUN
ejpam-5546	43	13	there	there	ADV
ejpam-5546	43	14	exists	exist	VERB
ejpam-5546	43	15	corresponding	correspond	VERB
ejpam-5546	43	16	sequence	sequence	NOUN
ejpam-5546	43	17	of	of	ADP
ejpam-5546	43	18	scalars	scalar	NOUN
ejpam-5546	43	19	called	call	VERB
ejpam-5546	43	20	parameter	parameter	NOUN
ejpam-5546	43	21	array	array	NOUN
ejpam-5546	43	22	,	,	PUNCT
ejpam-5546	43	23	the	the	DET
ejpam-5546	43	24	scalars	scalar	NOUN
ejpam-5546	43	25	that	that	PRON
ejpam-5546	43	26	appear	appear	VERB
ejpam-5546	43	27	in	in	ADP
ejpam-5546	43	28	this	this	DET
ejpam-5546	43	29	parameter	parameter	NOUN
ejpam-5546	43	30	array	array	NOUN
ejpam-5546	43	31	depend	depend	VERB
ejpam-5546	43	32	on	on	ADP
ejpam-5546	43	33	the	the	DET
ejpam-5546	43	34	eigenvalues	eigenvalue	NOUN
ejpam-5546	43	35	of	of	ADP
ejpam-5546	43	36	the	the	DET
ejpam-5546	43	37	leonard	leonard	PROPN
ejpam-5546	43	38	pair	pair	PROPN
ejpam-5546	43	39	.	.	PUNCT
ejpam-5546	44	1	we	we	PRON
ejpam-5546	44	2	now	now	ADV
ejpam-5546	44	3	recall	recall	VERB
ejpam-5546	44	4	the	the	DET
ejpam-5546	44	5	definition	definition	NOUN
ejpam-5546	44	6	of	of	ADP
ejpam-5546	44	7	the	the	DET
ejpam-5546	44	8	parameter	parameter	NOUN
ejpam-5546	44	9	array	array	NOUN
ejpam-5546	44	10	.	.	PUNCT
ejpam-5546	45	1	definition	definition	NOUN
ejpam-5546	45	2	2	2	NUM
ejpam-5546	45	3	.	.	PUNCT
ejpam-5546	46	1	[	[	X
ejpam-5546	46	2	7	7	X
ejpam-5546	46	3	]	]	X
ejpam-5546	46	4	let	let	VERB
ejpam-5546	46	5	d	d	PART
ejpam-5546	46	6	denote	denote	VERB
ejpam-5546	46	7	a	a	DET
ejpam-5546	46	8	non	non	ADJ
ejpam-5546	46	9	negative	negative	ADJ
ejpam-5546	46	10	integer	integer	NOUN
ejpam-5546	46	11	.	.	PUNCT
ejpam-5546	47	1	by	by	ADP
ejpam-5546	47	2	a	a	DET
ejpam-5546	47	3	parameter	parameter	NOUN
ejpam-5546	47	4	array	array	NOUN
ejpam-5546	47	5	over	over	ADP
ejpam-5546	47	6	f	f	PROPN
ejpam-5546	47	7	of	of	ADP
ejpam-5546	47	8	diameter	diameter	NOUN
ejpam-5546	47	9	d	d	NOUN
ejpam-5546	47	10	,	,	PUNCT
ejpam-5546	47	11	we	we	PRON
ejpam-5546	47	12	mean	mean	VERB
ejpam-5546	47	13	a	a	DET
ejpam-5546	47	14	sequence	sequence	NOUN
ejpam-5546	47	15	of	of	ADP
ejpam-5546	47	16	scalars	scalar	NOUN
ejpam-5546	47	17	(	(	PUNCT
ejpam-5546	47	18	{	{	PUNCT
ejpam-5546	47	19	θi}di=0	θi}di=0	PROPN
ejpam-5546	47	20	,	,	PUNCT
ejpam-5546	47	21	{	{	PUNCT
ejpam-5546	47	22	θ∗i	θ∗i	X
ejpam-5546	47	23	}	}	PUNCT
ejpam-5546	47	24	di=0	di=0	NOUN
ejpam-5546	47	25	;	;	PUNCT
ejpam-5546	47	26	{	{	PUNCT
ejpam-5546	47	27	φj}dj=1	φj}dj=1	NOUN
ejpam-5546	47	28	,	,	PUNCT
ejpam-5546	47	29	{	{	PUNCT
ejpam-5546	47	30	ϕj}dj=1	ϕj}dj=1	NOUN
ejpam-5546	47	31	)	)	PUNCT
ejpam-5546	47	32	taken	take	VERB
ejpam-5546	47	33	from	from	ADP
ejpam-5546	47	34	f	f	PROPN
ejpam-5546	47	35	that	that	PRON
ejpam-5546	47	36	satisfy	satisfy	VERB
ejpam-5546	47	37	the	the	DET
ejpam-5546	47	38	following	following	ADJ
ejpam-5546	47	39	conditions	condition	NOUN
ejpam-5546	47	40	.	.	PUNCT
ejpam-5546	48	1	θi	θi	ADP
ejpam-5546	48	2	̸=	̸=	PROPN
ejpam-5546	48	3	θj	θj	ADV
ejpam-5546	48	4	(	(	PUNCT
ejpam-5546	48	5	0	0	NUM
ejpam-5546	48	6	≤	≤	NUM
ejpam-5546	49	1	i	i	PRON
ejpam-5546	49	2	<	<	X
ejpam-5546	49	3	j	j	PROPN
ejpam-5546	49	4	≤	≤	NUM
ejpam-5546	49	5	d	d	NOUN
ejpam-5546	49	6	)	)	PUNCT
ejpam-5546	49	7	,	,	PUNCT
ejpam-5546	49	8	(	(	PUNCT
ejpam-5546	49	9	1	1	X
ejpam-5546	49	10	)	)	PUNCT
ejpam-5546	49	11	θ∗i	θ∗i	PROPN
ejpam-5546	49	12	̸=	̸=	PROPN
ejpam-5546	49	13	θ∗j	θ∗j	NUM
ejpam-5546	49	14	(	(	PUNCT
ejpam-5546	49	15	0	0	NUM
ejpam-5546	49	16	≤	≤	PUNCT
ejpam-5546	50	1	i	i	PRON
ejpam-5546	50	2	<	<	X
ejpam-5546	50	3	j	j	PROPN
ejpam-5546	50	4	≤	≤	NUM
ejpam-5546	50	5	d	d	NOUN
ejpam-5546	50	6	)	)	PUNCT
ejpam-5546	50	7	,	,	PUNCT
ejpam-5546	50	8	(	(	PUNCT
ejpam-5546	50	9	2	2	X
ejpam-5546	50	10	)	)	PUNCT
ejpam-5546	50	11	φi	φi	ADP
ejpam-5546	50	12	̸=	̸=	PROPN
ejpam-5546	50	13	0	0	NUM
ejpam-5546	50	14	(	(	PUNCT
ejpam-5546	50	15	1	1	NUM
ejpam-5546	50	16	≤	≤	NUM
ejpam-5546	50	17	i	i	X
ejpam-5546	50	18	≤	≤	NUM
ejpam-5546	51	1	d	d	X
ejpam-5546	51	2	)	)	PUNCT
ejpam-5546	51	3	,	,	PUNCT
ejpam-5546	51	4	(	(	PUNCT
ejpam-5546	51	5	3	3	X
ejpam-5546	51	6	)	)	PUNCT
ejpam-5546	51	7	ϕi	ϕi	ADP
ejpam-5546	51	8	̸=	̸=	PROPN
ejpam-5546	51	9	0	0	NUM
ejpam-5546	51	10	(	(	PUNCT
ejpam-5546	51	11	1	1	NUM
ejpam-5546	51	12	≤	≤	NUM
ejpam-5546	51	13	i	i	X
ejpam-5546	51	14	≤	≤	NUM
ejpam-5546	52	1	d	d	X
ejpam-5546	52	2	)	)	PUNCT
ejpam-5546	52	3	,	,	PUNCT
ejpam-5546	52	4	(	(	PUNCT
ejpam-5546	52	5	4	4	X
ejpam-5546	52	6	)	)	PUNCT
ejpam-5546	52	7	φi	φi	NOUN
ejpam-5546	52	8	=	=	PUNCT
ejpam-5546	52	9	ϕ1	ϕ1	NOUN
ejpam-5546	52	10	i−1∑	i−1∑	NUM
ejpam-5546	52	11	h=0	h=0	PROPN
ejpam-5546	52	12	θh	θh	NOUN
ejpam-5546	53	1	−	−	PROPN
ejpam-5546	53	2	θd−h	θd−h	PROPN
ejpam-5546	53	3	θ0	θ0	PROPN
ejpam-5546	53	4	−	−	PROPN
ejpam-5546	54	1	θd	θd	PROPN
ejpam-5546	54	2	+	+	CCONJ
ejpam-5546	54	3	(	(	PUNCT
ejpam-5546	54	4	θ∗i	θ∗i	NUM
ejpam-5546	54	5	−	−	PROPN
ejpam-5546	54	6	θ∗0)(θi−1	θ∗0)(θi−1	NOUN
ejpam-5546	54	7	−	−	NOUN
ejpam-5546	54	8	θd	θd	NOUN
ejpam-5546	54	9	)	)	PUNCT
ejpam-5546	54	10	(	(	PUNCT
ejpam-5546	54	11	1	1	NUM
ejpam-5546	54	12	≤	≤	NUM
ejpam-5546	54	13	i	i	X
ejpam-5546	54	14	≤	≤	NUM
ejpam-5546	54	15	d	d	X
ejpam-5546	54	16	)	)	PUNCT
ejpam-5546	54	17	,	,	PUNCT
ejpam-5546	54	18	(	(	PUNCT
ejpam-5546	54	19	5	5	X
ejpam-5546	54	20	)	)	PUNCT
ejpam-5546	54	21	h.	h.	NOUN
ejpam-5546	54	22	alnajjar	alnajjar	PROPN
ejpam-5546	54	23	/	/	SYM
ejpam-5546	54	24	eur	eur	PROPN
ejpam-5546	54	25	.	.	PUNCT
ejpam-5546	55	1	j.	j.	PROPN
ejpam-5546	55	2	pure	pure	PROPN
ejpam-5546	55	3	appl	appl	PROPN
ejpam-5546	55	4	.	.	PROPN
ejpam-5546	55	5	math	math	PROPN
ejpam-5546	55	6	,	,	PUNCT
ejpam-5546	55	7	18	18	NUM
ejpam-5546	55	8	(	(	PUNCT
ejpam-5546	55	9	1	1	NUM
ejpam-5546	55	10	)	)	PUNCT
ejpam-5546	55	11	(	(	PUNCT
ejpam-5546	55	12	2025	2025	NUM
ejpam-5546	55	13	)	)	PUNCT
ejpam-5546	55	14	,	,	PUNCT
ejpam-5546	55	15	5546	5546	NUM
ejpam-5546	55	16	3	3	NUM
ejpam-5546	55	17	of	of	ADP
ejpam-5546	55	18	14	14	NUM
ejpam-5546	55	19	ϕi	ϕi	ADP
ejpam-5546	55	20	=	=	PUNCT
ejpam-5546	55	21	φ1	φ1	PROPN
ejpam-5546	55	22	i−1∑	i−1∑	NOUN
ejpam-5546	55	23	h=0	h=0	PROPN
ejpam-5546	55	24	θh	θh	NOUN
ejpam-5546	55	25	−	−	PROPN
ejpam-5546	55	26	θd−h	θd−h	PROPN
ejpam-5546	55	27	θ0	θ0	PROPN
ejpam-5546	55	28	−	−	PROPN
ejpam-5546	56	1	θd	θd	PROPN
ejpam-5546	56	2	+	+	CCONJ
ejpam-5546	56	3	(	(	PUNCT
ejpam-5546	56	4	θ∗i	θ∗i	NUM
ejpam-5546	56	5	−	−	NUM
ejpam-5546	56	6	θ∗0)(θd−i+1	θ∗0)(θd−i+1	SYM
ejpam-5546	56	7	−	−	PROPN
ejpam-5546	56	8	θ0	θ0	PROPN
ejpam-5546	56	9	)	)	PUNCT
ejpam-5546	56	10	(	(	PUNCT
ejpam-5546	56	11	1	1	NUM
ejpam-5546	56	12	≤	≤	NUM
ejpam-5546	56	13	i	i	X
ejpam-5546	56	14	≤	≤	NUM
ejpam-5546	57	1	d	d	X
ejpam-5546	57	2	)	)	PUNCT
ejpam-5546	57	3	,	,	PUNCT
ejpam-5546	57	4	(	(	PUNCT
ejpam-5546	57	5	6	6	X
ejpam-5546	57	6	)	)	PUNCT
ejpam-5546	57	7	θi−2	θi−2	NOUN
ejpam-5546	57	8	−	−	PROPN
ejpam-5546	57	9	θi+1	θi+1	NUM
ejpam-5546	57	10	θi−1	θi−1	PROPN
ejpam-5546	57	11	−	−	PROPN
ejpam-5546	57	12	θi	θi	NOUN
ejpam-5546	57	13	=	=	SYM
ejpam-5546	57	14	θ∗j−2	θ∗j−2	PROPN
ejpam-5546	57	15	−	−	NOUN
ejpam-5546	57	16	θ∗j+1	θ∗j+1	NOUN
ejpam-5546	57	17	θ∗j−1	θ∗j−1	NOUN
ejpam-5546	57	18	−	−	NOUN
ejpam-5546	57	19	θ∗j	θ∗j	NUM
ejpam-5546	57	20	(	(	PUNCT
ejpam-5546	57	21	2	2	NUM
ejpam-5546	57	22	≤	≤	NUM
ejpam-5546	57	23	i	i	PRON
ejpam-5546	57	24	,	,	PUNCT
ejpam-5546	57	25	j	j	PROPN
ejpam-5546	57	26	≤	≤	PUNCT
ejpam-5546	57	27	d−	d−	PROPN
ejpam-5546	57	28	1	1	NUM
ejpam-5546	57	29	)	)	PUNCT
ejpam-5546	57	30	.	.	PUNCT
ejpam-5546	58	1	(	(	PUNCT
ejpam-5546	58	2	7	7	X
ejpam-5546	58	3	)	)	PUNCT
ejpam-5546	58	4	the	the	DET
ejpam-5546	58	5	common	common	ADJ
ejpam-5546	58	6	value	value	NOUN
ejpam-5546	58	7	of	of	ADP
ejpam-5546	58	8	(	(	PUNCT
ejpam-5546	58	9	7	7	NUM
ejpam-5546	58	10	)	)	PUNCT
ejpam-5546	58	11	minus	minus	CCONJ
ejpam-5546	58	12	one	one	NUM
ejpam-5546	58	13	is	be	AUX
ejpam-5546	58	14	called	call	VERB
ejpam-5546	58	15	the	the	DET
ejpam-5546	58	16	fundamental	fundamental	ADJ
ejpam-5546	58	17	parameter	parameter	NOUN
ejpam-5546	58	18	of	of	ADP
ejpam-5546	58	19	the	the	DET
ejpam-5546	58	20	leonard	leonard	PROPN
ejpam-5546	58	21	pair	pair	PROPN
ejpam-5546	58	22	,	,	PUNCT
ejpam-5546	58	23	the	the	DET
ejpam-5546	58	24	fundamental	fundamental	ADJ
ejpam-5546	58	25	parameter	parameter	NOUN
ejpam-5546	58	26	of	of	ADP
ejpam-5546	58	27	the	the	DET
ejpam-5546	58	28	leonard	leonard	PROPN
ejpam-5546	58	29	pairs	pair	NOUN
ejpam-5546	58	30	appear	appear	VERB
ejpam-5546	58	31	through	through	ADP
ejpam-5546	58	32	this	this	DET
ejpam-5546	58	33	article	article	NOUN
ejpam-5546	58	34	is	be	AUX
ejpam-5546	58	35	equal	equal	ADJ
ejpam-5546	58	36	q2	q2	NOUN
ejpam-5546	58	37	+	+	X
ejpam-5546	59	1	q−2	q−2	PROPN
ejpam-5546	59	2	.	.	PUNCT
ejpam-5546	60	1	in	in	ADP
ejpam-5546	60	2	definition	definition	NOUN
ejpam-5546	60	3	1	1	NUM
ejpam-5546	60	4	,	,	PUNCT
ejpam-5546	60	5	the	the	DET
ejpam-5546	60	6	leonard	leonard	PROPN
ejpam-5546	60	7	pair	pair	NOUN
ejpam-5546	60	8	is	be	AUX
ejpam-5546	60	9	described	describe	VERB
ejpam-5546	60	10	as	as	ADP
ejpam-5546	60	11	diagonal	diagonal	ADJ
ejpam-5546	60	12	and	and	CCONJ
ejpam-5546	60	13	irreducible	irreducible	ADJ
ejpam-5546	60	14	tridiagonal	tridiagonal	ADJ
ejpam-5546	60	15	matrices	matrix	NOUN
ejpam-5546	60	16	.	.	PUNCT
ejpam-5546	61	1	in	in	ADP
ejpam-5546	61	2	[	[	X
ejpam-5546	61	3	12	12	NUM
ejpam-5546	61	4	]	]	PUNCT
ejpam-5546	61	5	,	,	PUNCT
ejpam-5546	61	6	terwilliger	terwilliger	NOUN
ejpam-5546	61	7	showed	show	VERB
ejpam-5546	61	8	that	that	SCONJ
ejpam-5546	61	9	the	the	DET
ejpam-5546	61	10	leonard	leonard	PROPN
ejpam-5546	61	11	pair	pair	NOUN
ejpam-5546	61	12	can	can	AUX
ejpam-5546	61	13	also	also	ADV
ejpam-5546	61	14	be	be	AUX
ejpam-5546	61	15	described	describe	VERB
ejpam-5546	61	16	as	as	ADP
ejpam-5546	61	17	upper	upper	ADJ
ejpam-5546	61	18	bidiagonal	bidiagonal	ADJ
ejpam-5546	61	19	and	and	CCONJ
ejpam-5546	61	20	lower	low	ADJ
ejpam-5546	61	21	bidiagonal	bidiagonal	ADJ
ejpam-5546	61	22	matrices	matrix	NOUN
ejpam-5546	61	23	using	use	VERB
ejpam-5546	61	24	the	the	DET
ejpam-5546	61	25	parameter	parameter	NOUN
ejpam-5546	61	26	array	array	NOUN
ejpam-5546	61	27	associated	associate	VERB
ejpam-5546	61	28	with	with	ADP
ejpam-5546	61	29	the	the	DET
ejpam-5546	61	30	leonard	leonard	PROPN
ejpam-5546	61	31	pair	pair	NOUN
ejpam-5546	61	32	as	as	SCONJ
ejpam-5546	61	33	it	it	PRON
ejpam-5546	61	34	appears	appear	VERB
ejpam-5546	61	35	in	in	ADP
ejpam-5546	61	36	the	the	DET
ejpam-5546	61	37	following	follow	VERB
ejpam-5546	61	38	theorem	theorem	PROPN
ejpam-5546	61	39	.	.	PUNCT
ejpam-5546	61	40	theorem	theorem	NOUN
ejpam-5546	61	41	1	1	NUM
ejpam-5546	61	42	.	.	PUNCT
ejpam-5546	62	1	[	[	X
ejpam-5546	62	2	12	12	NUM
ejpam-5546	62	3	]	]	PUNCT
ejpam-5546	62	4	let	let	VERB
ejpam-5546	62	5	d	d	PART
ejpam-5546	62	6	denote	denote	VERB
ejpam-5546	62	7	a	a	DET
ejpam-5546	62	8	nonnegative	nonnegative	ADJ
ejpam-5546	62	9	integer	integer	NOUN
ejpam-5546	62	10	,	,	PUNCT
ejpam-5546	62	11	let	let	VERB
ejpam-5546	62	12	b	b	NOUN
ejpam-5546	62	13	and	and	CCONJ
ejpam-5546	62	14	b∗	b∗	ADJ
ejpam-5546	62	15	denote	denote	VERB
ejpam-5546	62	16	matrices	matrix	NOUN
ejpam-5546	62	17	in	in	ADP
ejpam-5546	62	18	matd+1(f	matd+1(f	NOUN
ejpam-5546	62	19	)	)	PUNCT
ejpam-5546	62	20	.	.	PUNCT
ejpam-5546	63	1	assume	assume	VERB
ejpam-5546	63	2	b	b	NOUN
ejpam-5546	63	3	is	be	AUX
ejpam-5546	63	4	lower	low	ADJ
ejpam-5546	63	5	bidiagonal	bidiagonal	ADJ
ejpam-5546	63	6	and	and	CCONJ
ejpam-5546	63	7	b∗	b∗	ADJ
ejpam-5546	63	8	is	be	AUX
ejpam-5546	63	9	upper	upper	ADJ
ejpam-5546	63	10	bidiagonal	bidiagonal	NOUN
ejpam-5546	63	11	.	.	PUNCT
ejpam-5546	64	1	then	then	ADV
ejpam-5546	64	2	the	the	DET
ejpam-5546	64	3	following	following	NOUN
ejpam-5546	64	4	are	be	AUX
ejpam-5546	64	5	equivalent	equivalent	ADJ
ejpam-5546	64	6	.	.	PUNCT
ejpam-5546	65	1	(	(	PUNCT
ejpam-5546	65	2	i	i	NOUN
ejpam-5546	65	3	)	)	PUNCT
ejpam-5546	65	4	the	the	DET
ejpam-5546	65	5	pair	pair	NOUN
ejpam-5546	65	6	b	b	NOUN
ejpam-5546	65	7	,	,	PUNCT
ejpam-5546	65	8	b∗	b∗	ADV
ejpam-5546	65	9	is	be	AUX
ejpam-5546	65	10	a	a	DET
ejpam-5546	65	11	leonard	leonard	NOUN
ejpam-5546	65	12	pair	pair	NOUN
ejpam-5546	65	13	in	in	ADP
ejpam-5546	65	14	matd+1(f	matd+1(f	PROPN
ejpam-5546	65	15	)	)	PUNCT
ejpam-5546	65	16	.	.	PUNCT
ejpam-5546	66	1	(	(	PUNCT
ejpam-5546	66	2	ii	ii	X
ejpam-5546	66	3	)	)	PUNCT
ejpam-5546	66	4	there	there	PRON
ejpam-5546	66	5	exists	exist	VERB
ejpam-5546	66	6	a	a	DET
ejpam-5546	66	7	parameter	parameter	NOUN
ejpam-5546	66	8	array	array	NOUN
ejpam-5546	66	9	(	(	PUNCT
ejpam-5546	66	10	{	{	PUNCT
ejpam-5546	66	11	θi}di=0	θi}di=0	VERB
ejpam-5546	66	12	,	,	PUNCT
ejpam-5546	66	13	{	{	PUNCT
ejpam-5546	66	14	θ∗i	θ∗i	X
ejpam-5546	66	15	}	}	PUNCT
ejpam-5546	66	16	di=0	di=0	NOUN
ejpam-5546	66	17	;	;	PUNCT
ejpam-5546	66	18	{	{	PUNCT
ejpam-5546	66	19	φj}dj=1	φj}dj=1	NOUN
ejpam-5546	66	20	,	,	PUNCT
ejpam-5546	66	21	{	{	PUNCT
ejpam-5546	66	22	ϕj}dj=1	ϕj}dj=1	PROPN
ejpam-5546	66	23	)	)	PUNCT
ejpam-5546	66	24	over	over	ADP
ejpam-5546	66	25	f	f	PROPN
ejpam-5546	66	26	such	such	ADJ
ejpam-5546	67	1	that	that	SCONJ
ejpam-5546	67	2	b(i	b(i	NOUN
ejpam-5546	67	3	,	,	PUNCT
ejpam-5546	67	4	i	i	NOUN
ejpam-5546	67	5	)	)	PUNCT
ejpam-5546	67	6	=	=	SYM
ejpam-5546	67	7	θi	θi	X
ejpam-5546	67	8	,	,	PUNCT
ejpam-5546	67	9	b∗(i	b∗(i	PROPN
ejpam-5546	67	10	,	,	PUNCT
ejpam-5546	67	11	i	i	NOUN
ejpam-5546	67	12	)	)	PUNCT
ejpam-5546	67	13	=	=	SYM
ejpam-5546	67	14	θ∗i	θ∗i	X
ejpam-5546	67	15	(	(	PUNCT
ejpam-5546	67	16	0	0	NUM
ejpam-5546	67	17	≤	≤	NUM
ejpam-5546	67	18	i	i	NOUN
ejpam-5546	67	19	≤	≤	NUM
ejpam-5546	67	20	d	d	NOUN
ejpam-5546	67	21	)	)	PUNCT
ejpam-5546	67	22	,	,	PUNCT
ejpam-5546	67	23	b(j	b(j	PROPN
ejpam-5546	67	24	,	,	PUNCT
ejpam-5546	67	25	j	j	PROPN
ejpam-5546	67	26	−	−	PROPN
ejpam-5546	67	27	1)b∗(j	1)b∗(j	PROPN
ejpam-5546	67	28	−	−	PROPN
ejpam-5546	67	29	1	1	NUM
ejpam-5546	67	30	,	,	PUNCT
ejpam-5546	67	31	j	j	NOUN
ejpam-5546	67	32	)	)	PUNCT
ejpam-5546	67	33	=	=	SYM
ejpam-5546	67	34	φj	φj	PROPN
ejpam-5546	67	35	(	(	PUNCT
ejpam-5546	67	36	1	1	NUM
ejpam-5546	67	37	≤	≤	NUM
ejpam-5546	67	38	j	j	PROPN
ejpam-5546	67	39	≤	≤	NUM
ejpam-5546	67	40	d	d	NOUN
ejpam-5546	67	41	)	)	PUNCT
ejpam-5546	67	42	.	.	PUNCT
ejpam-5546	68	1	suppose	suppose	VERB
ejpam-5546	68	2	(	(	PUNCT
ejpam-5546	68	3	i	i	NOUN
ejpam-5546	68	4	)	)	PUNCT
ejpam-5546	68	5	,	,	PUNCT
ejpam-5546	68	6	(	(	PUNCT
ejpam-5546	68	7	ii	ii	NOUN
ejpam-5546	68	8	)	)	PUNCT
ejpam-5546	68	9	hold	hold	VERB
ejpam-5546	68	10	.	.	PUNCT
ejpam-5546	69	1	then	then	ADV
ejpam-5546	69	2	the	the	DET
ejpam-5546	69	3	parameter	parameter	NOUN
ejpam-5546	69	4	array	array	NOUN
ejpam-5546	69	5	in	in	ADP
ejpam-5546	69	6	(	(	PUNCT
ejpam-5546	69	7	ii	ii	NOUN
ejpam-5546	69	8	)	)	PUNCT
ejpam-5546	69	9	is	be	AUX
ejpam-5546	69	10	uniquely	uniquely	ADV
ejpam-5546	69	11	determined	determine	VERB
ejpam-5546	69	12	by	by	ADP
ejpam-5546	69	13	b	b	NUM
ejpam-5546	69	14	,	,	PUNCT
ejpam-5546	69	15	b∗.	b∗.	NOUN
ejpam-5546	69	16	indeed	indeed	ADV
ejpam-5546	69	17	to	to	PART
ejpam-5546	69	18	prove	prove	VERB
ejpam-5546	69	19	the	the	DET
ejpam-5546	69	20	result	result	NOUN
ejpam-5546	69	21	of	of	ADP
ejpam-5546	69	22	this	this	DET
ejpam-5546	69	23	article	article	NOUN
ejpam-5546	69	24	we	we	PRON
ejpam-5546	69	25	will	will	AUX
ejpam-5546	69	26	describe	describe	VERB
ejpam-5546	69	27	the	the	DET
ejpam-5546	69	28	leonard	leonard	NOUN
ejpam-5546	69	29	pairs	pair	NOUN
ejpam-5546	69	30	that	that	PRON
ejpam-5546	69	31	appear	appear	VERB
ejpam-5546	69	32	in	in	ADP
ejpam-5546	69	33	sections	section	NOUN
ejpam-5546	69	34	4	4	NUM
ejpam-5546	69	35	,	,	PUNCT
ejpam-5546	69	36	5	5	NUM
ejpam-5546	69	37	and	and	CCONJ
ejpam-5546	69	38	6	6	NUM
ejpam-5546	69	39	as	as	ADP
ejpam-5546	69	40	upper	upper	ADJ
ejpam-5546	69	41	bidiagonal	bidiagonal	ADJ
ejpam-5546	69	42	and	and	CCONJ
ejpam-5546	69	43	lower	low	ADJ
ejpam-5546	69	44	bidiagonal	bidiagonal	ADJ
ejpam-5546	69	45	matrices	matrix	NOUN
ejpam-5546	69	46	and	and	CCONJ
ejpam-5546	69	47	use	use	NOUN
ejpam-5546	69	48	theorem	theorem	NOUN
ejpam-5546	69	49	1	1	NUM
ejpam-5546	69	50	to	to	PART
ejpam-5546	69	51	obtain	obtain	VERB
ejpam-5546	69	52	our	our	PRON
ejpam-5546	69	53	result	result	NOUN
ejpam-5546	69	54	.	.	PUNCT
ejpam-5546	70	1	3	3	X
ejpam-5546	70	2	.	.	X
ejpam-5546	70	3	the	the	DET
ejpam-5546	70	4	q	q	ADJ
ejpam-5546	70	5	-	-	PUNCT
ejpam-5546	70	6	tetrahedron	tetrahedron	NOUN
ejpam-5546	70	7	algebra	algebra	NOUN
ejpam-5546	70	8	⊠q	⊠q	NOUN
ejpam-5546	70	9	in	in	ADP
ejpam-5546	70	10	this	this	DET
ejpam-5546	70	11	section	section	NOUN
ejpam-5546	70	12	we	we	PRON
ejpam-5546	70	13	recall	recall	VERB
ejpam-5546	70	14	the	the	DET
ejpam-5546	70	15	definitions	definition	NOUN
ejpam-5546	70	16	of	of	ADP
ejpam-5546	70	17	⊠q	⊠q	PROPN
ejpam-5546	70	18	algebra	algebra	PROPN
ejpam-5546	70	19	and	and	CCONJ
ejpam-5546	70	20	its	its	PRON
ejpam-5546	70	21	evaluation	evaluation	NOUN
ejpam-5546	70	22	module	module	NOUN
ejpam-5546	70	23	,	,	PUNCT
ejpam-5546	70	24	also	also	ADV
ejpam-5546	70	25	we	we	PRON
ejpam-5546	70	26	state	state	VERB
ejpam-5546	70	27	some	some	DET
ejpam-5546	70	28	facts	fact	NOUN
ejpam-5546	70	29	about	about	ADP
ejpam-5546	70	30	this	this	DET
ejpam-5546	70	31	algebra	algebra	NOUN
ejpam-5546	70	32	that	that	PRON
ejpam-5546	70	33	we	we	PRON
ejpam-5546	70	34	will	will	AUX
ejpam-5546	70	35	use	use	VERB
ejpam-5546	70	36	later	later	ADV
ejpam-5546	70	37	in	in	ADP
ejpam-5546	70	38	this	this	DET
ejpam-5546	70	39	article	article	NOUN
ejpam-5546	70	40	.	.	PUNCT
ejpam-5546	71	1	the	the	DET
ejpam-5546	71	2	material	material	NOUN
ejpam-5546	71	3	in	in	ADP
ejpam-5546	71	4	this	this	DET
ejpam-5546	71	5	section	section	NOUN
ejpam-5546	71	6	can	can	AUX
ejpam-5546	71	7	be	be	AUX
ejpam-5546	71	8	found	find	VERB
ejpam-5546	71	9	in	in	ADP
ejpam-5546	71	10	[	[	X
ejpam-5546	71	11	4	4	NUM
ejpam-5546	71	12	]	]	PUNCT
ejpam-5546	71	13	and	and	CCONJ
ejpam-5546	71	14	[	[	X
ejpam-5546	71	15	5	5	NUM
ejpam-5546	71	16	]	]	PUNCT
ejpam-5546	71	17	.	.	PUNCT
ejpam-5546	72	1	definition	definition	NOUN
ejpam-5546	72	2	3	3	NUM
ejpam-5546	72	3	.	.	PUNCT
ejpam-5546	73	1	[	[	X
ejpam-5546	73	2	5	5	NUM
ejpam-5546	73	3	]	]	PUNCT
ejpam-5546	73	4	let	let	AUX
ejpam-5546	73	5	⊠q	⊠q	PROPN
ejpam-5546	73	6	denote	denote	VERB
ejpam-5546	73	7	the	the	DET
ejpam-5546	73	8	unital	unital	ADJ
ejpam-5546	73	9	associative	associative	NOUN
ejpam-5546	73	10	f	f	NOUN
ejpam-5546	73	11	-	-	PUNCT
ejpam-5546	73	12	algebra	algebra	NOUN
ejpam-5546	73	13	that	that	PRON
ejpam-5546	73	14	has	have	VERB
ejpam-5546	73	15	generators	generator	NOUN
ejpam-5546	73	16	{	{	PUNCT
ejpam-5546	73	17	xij	xij	NOUN
ejpam-5546	73	18	:	:	PUNCT
ejpam-5546	73	19	i	i	PRON
ejpam-5546	73	20	,	,	PUNCT
ejpam-5546	73	21	j	j	PROPN
ejpam-5546	73	22	∈	∈	PROPN
ejpam-5546	73	23	z4	z4	PROPN
ejpam-5546	73	24	,	,	PUNCT
ejpam-5546	73	25	j	j	PROPN
ejpam-5546	73	26	−	−	NOUN
ejpam-5546	74	1	i	i	PRON
ejpam-5546	74	2	=	=	NOUN
ejpam-5546	74	3	1	1	NUM
ejpam-5546	74	4	or	or	CCONJ
ejpam-5546	74	5	j	j	ADJ
ejpam-5546	75	1	−	−	NOUN
ejpam-5546	76	1	i	i	PRON
ejpam-5546	76	2	=	=	NOUN
ejpam-5546	76	3	2	2	NUM
ejpam-5546	76	4	}	}	PUNCT
ejpam-5546	76	5	.	.	PUNCT
ejpam-5546	77	1	and	and	CCONJ
ejpam-5546	77	2	the	the	DET
ejpam-5546	77	3	following	follow	VERB
ejpam-5546	77	4	relations	relation	NOUN
ejpam-5546	77	5	:	:	PUNCT
ejpam-5546	77	6	(	(	PUNCT
ejpam-5546	77	7	i	i	NOUN
ejpam-5546	77	8	)	)	PUNCT
ejpam-5546	77	9	for	for	ADP
ejpam-5546	77	10	i	i	PRON
ejpam-5546	77	11	,	,	PUNCT
ejpam-5546	77	12	j	j	PROPN
ejpam-5546	77	13	∈	∈	PROPN
ejpam-5546	77	14	z4	z4	PROPN
ejpam-5546	78	1	such	such	ADJ
ejpam-5546	78	2	that	that	SCONJ
ejpam-5546	78	3	j	j	PROPN
ejpam-5546	78	4	−	−	NOUN
ejpam-5546	79	1	i	i	PRON
ejpam-5546	79	2	=	=	NOUN
ejpam-5546	79	3	2	2	NUM
ejpam-5546	79	4	,	,	PUNCT
ejpam-5546	79	5	xijxji	xijxji	PROPN
ejpam-5546	80	1	=	=	NOUN
ejpam-5546	80	2	1	1	X
ejpam-5546	80	3	.	.	PUNCT
ejpam-5546	80	4	h.	h.	PROPN
ejpam-5546	80	5	alnajjar	alnajjar	PROPN
ejpam-5546	80	6	/	/	SYM
ejpam-5546	80	7	eur	eur	PROPN
ejpam-5546	80	8	.	.	PUNCT
ejpam-5546	81	1	j.	j.	PROPN
ejpam-5546	81	2	pure	pure	PROPN
ejpam-5546	81	3	appl	appl	PROPN
ejpam-5546	81	4	.	.	PROPN
ejpam-5546	81	5	math	math	PROPN
ejpam-5546	81	6	,	,	PUNCT
ejpam-5546	81	7	18	18	NUM
ejpam-5546	81	8	(	(	PUNCT
ejpam-5546	81	9	1	1	NUM
ejpam-5546	81	10	)	)	PUNCT
ejpam-5546	81	11	(	(	PUNCT
ejpam-5546	81	12	2025	2025	NUM
ejpam-5546	81	13	)	)	PUNCT
ejpam-5546	81	14	,	,	PUNCT
ejpam-5546	81	15	5546	5546	NUM
ejpam-5546	81	16	4	4	NUM
ejpam-5546	81	17	of	of	ADP
ejpam-5546	81	18	14	14	NUM
ejpam-5546	81	19	(	(	PUNCT
ejpam-5546	81	20	ii	ii	NOUN
ejpam-5546	81	21	)	)	PUNCT
ejpam-5546	81	22	for	for	ADP
ejpam-5546	81	23	h	h	NOUN
ejpam-5546	81	24	,	,	PUNCT
ejpam-5546	81	25	i	i	PRON
ejpam-5546	81	26	,	,	PUNCT
ejpam-5546	81	27	j	j	PROPN
ejpam-5546	81	28	∈	∈	PROPN
ejpam-5546	81	29	z4	z4	PROPN
ejpam-5546	81	30	such	such	ADJ
ejpam-5546	81	31	that	that	SCONJ
ejpam-5546	81	32	the	the	DET
ejpam-5546	81	33	the	the	DET
ejpam-5546	81	34	pair	pair	NOUN
ejpam-5546	81	35	(	(	PUNCT
ejpam-5546	81	36	i−	i−	PROPN
ejpam-5546	81	37	h	h	PROPN
ejpam-5546	81	38	,	,	PUNCT
ejpam-5546	81	39	j	j	PROPN
ejpam-5546	81	40	−	−	PROPN
ejpam-5546	81	41	i	i	PROPN
ejpam-5546	81	42	)	)	PUNCT
ejpam-5546	81	43	is	be	AUX
ejpam-5546	81	44	one	one	NUM
ejpam-5546	81	45	of	of	ADP
ejpam-5546	81	46	(	(	PUNCT
ejpam-5546	81	47	1	1	NUM
ejpam-5546	81	48	,	,	PUNCT
ejpam-5546	81	49	1	1	NUM
ejpam-5546	81	50	)	)	PUNCT
ejpam-5546	81	51	,	,	PUNCT
ejpam-5546	81	52	(	(	PUNCT
ejpam-5546	81	53	1	1	NUM
ejpam-5546	81	54	,	,	PUNCT
ejpam-5546	81	55	2	2	NUM
ejpam-5546	81	56	)	)	PUNCT
ejpam-5546	81	57	,	,	PUNCT
ejpam-5546	81	58	(	(	PUNCT
ejpam-5546	81	59	2	2	NUM
ejpam-5546	81	60	,	,	PUNCT
ejpam-5546	81	61	1	1	NUM
ejpam-5546	81	62	)	)	PUNCT
ejpam-5546	81	63	,	,	PUNCT
ejpam-5546	82	1	qxhixij	qxhixij	NOUN
ejpam-5546	82	2	−	−	PROPN
ejpam-5546	82	3	q−1xijxhi	q−1xijxhi	NOUN
ejpam-5546	82	4	q	q	NOUN
ejpam-5546	83	1	−	−	PROPN
ejpam-5546	83	2	q−1	q−1	PROPN
ejpam-5546	83	3	=	=	NOUN
ejpam-5546	83	4	1	1	X
ejpam-5546	83	5	.	.	PUNCT
ejpam-5546	83	6	(	(	PUNCT
ejpam-5546	83	7	iii	iii	NOUN
ejpam-5546	83	8	)	)	PUNCT
ejpam-5546	83	9	for	for	ADP
ejpam-5546	83	10	h	h	NOUN
ejpam-5546	83	11	,	,	PUNCT
ejpam-5546	83	12	i	i	PRON
ejpam-5546	83	13	,	,	PUNCT
ejpam-5546	83	14	j	j	PROPN
ejpam-5546	83	15	,	,	PUNCT
ejpam-5546	83	16	k	k	PROPN
ejpam-5546	83	17	∈	∈	PROPN
ejpam-5546	83	18	z4	z4	NOUN
ejpam-5546	83	19	such	such	ADJ
ejpam-5546	83	20	that	that	SCONJ
ejpam-5546	83	21	i−	i−	PROPN
ejpam-5546	83	22	h	h	NOUN
ejpam-5546	84	1	=	=	SYM
ejpam-5546	84	2	j	j	PROPN
ejpam-5546	85	1	−	−	PUNCT
ejpam-5546	85	2	i	i	PRON
ejpam-5546	85	3	=	=	PUNCT
ejpam-5546	86	1	k	k	PROPN
ejpam-5546	87	1	−	−	PROPN
ejpam-5546	88	1	j	j	NOUN
ejpam-5546	89	1	=	=	SYM
ejpam-5546	90	1	1	1	NUM
ejpam-5546	90	2	,	,	PUNCT
ejpam-5546	90	3	x3	x3	VERB
ejpam-5546	90	4	hixjk	hixjk	ADJ
ejpam-5546	91	1	−	−	PROPN
ejpam-5546	92	1	[	[	X
ejpam-5546	92	2	3]qx	3]qx	NUM
ejpam-5546	92	3	2	2	NUM
ejpam-5546	92	4	hixjkxhi	hixjkxhi	NOUN
ejpam-5546	92	5	+	+	X
ejpam-5546	93	1	[	[	X
ejpam-5546	93	2	3]qxhixjkx	3]qxhixjkx	NUM
ejpam-5546	93	3	2	2	NUM
ejpam-5546	93	4	hi	hi	INTJ
ejpam-5546	93	5	−xjkx	−xjkx	NUM
ejpam-5546	93	6	3	3	NUM
ejpam-5546	93	7	hi	hi	INTJ
ejpam-5546	93	8	=	=	NOUN
ejpam-5546	93	9	0	0	X
ejpam-5546	93	10	.	.	PUNCT
ejpam-5546	94	1	we	we	PRON
ejpam-5546	94	2	call	call	VERB
ejpam-5546	94	3	⊠q	⊠q	ADV
ejpam-5546	94	4	the	the	DET
ejpam-5546	94	5	q	q	ADJ
ejpam-5546	94	6	-	-	PUNCT
ejpam-5546	94	7	tetrahedron	tetrahedron	NOUN
ejpam-5546	94	8	algebra	algebra	NOUN
ejpam-5546	94	9	.	.	PUNCT
ejpam-5546	95	1	to	to	PART
ejpam-5546	95	2	prove	prove	VERB
ejpam-5546	95	3	the	the	DET
ejpam-5546	95	4	result	result	NOUN
ejpam-5546	95	5	of	of	ADP
ejpam-5546	95	6	this	this	DET
ejpam-5546	95	7	article	article	NOUN
ejpam-5546	95	8	in	in	ADP
ejpam-5546	95	9	sections	section	NOUN
ejpam-5546	95	10	4	4	NUM
ejpam-5546	95	11	,	,	PUNCT
ejpam-5546	95	12	5	5	NUM
ejpam-5546	95	13	and	and	CCONJ
ejpam-5546	95	14	6	6	NUM
ejpam-5546	95	15	,	,	PUNCT
ejpam-5546	95	16	we	we	PRON
ejpam-5546	95	17	will	will	AUX
ejpam-5546	95	18	describe	describe	VERB
ejpam-5546	95	19	the	the	DET
ejpam-5546	95	20	action	action	NOUN
ejpam-5546	95	21	of	of	ADP
ejpam-5546	95	22	the	the	DET
ejpam-5546	95	23	generators	generator	NOUN
ejpam-5546	95	24	of	of	ADP
ejpam-5546	95	25	⊠q	⊠q	PROPN
ejpam-5546	95	26	on	on	ADP
ejpam-5546	95	27	different	different	ADJ
ejpam-5546	95	28	bases	basis	NOUN
ejpam-5546	95	29	of	of	ADP
ejpam-5546	95	30	an	an	DET
ejpam-5546	95	31	evaluation	evaluation	NOUN
ejpam-5546	95	32	module	module	NOUN
ejpam-5546	95	33	of	of	ADP
ejpam-5546	95	34	⊠q	⊠q	PROPN
ejpam-5546	95	35	.	.	PUNCT
ejpam-5546	96	1	so	so	ADV
ejpam-5546	96	2	,	,	PUNCT
ejpam-5546	96	3	we	we	PRON
ejpam-5546	96	4	now	now	ADV
ejpam-5546	96	5	recall	recall	VERB
ejpam-5546	96	6	the	the	DET
ejpam-5546	96	7	definition	definition	NOUN
ejpam-5546	96	8	of	of	ADP
ejpam-5546	96	9	an	an	DET
ejpam-5546	96	10	evaluation	evaluation	NOUN
ejpam-5546	96	11	module	module	NOUN
ejpam-5546	96	12	of	of	ADP
ejpam-5546	96	13	⊠q	⊠q	PROPN
ejpam-5546	96	14	.	.	PUNCT
ejpam-5546	97	1	the	the	DET
ejpam-5546	97	2	authors	author	NOUN
ejpam-5546	97	3	in	in	ADP
ejpam-5546	97	4	[	[	X
ejpam-5546	97	5	5	5	NUM
ejpam-5546	97	6	]	]	PUNCT
ejpam-5546	97	7	gave	give	VERB
ejpam-5546	97	8	definition	definition	NOUN
ejpam-5546	97	9	for	for	ADP
ejpam-5546	97	10	the	the	DET
ejpam-5546	97	11	evaluation	evaluation	NOUN
ejpam-5546	97	12	module	module	NOUN
ejpam-5546	97	13	of	of	ADP
ejpam-5546	97	14	⊠q	⊠q	PROPN
ejpam-5546	97	15	,	,	PUNCT
ejpam-5546	97	16	and	and	CCONJ
ejpam-5546	97	17	the	the	DET
ejpam-5546	97	18	authors	author	NOUN
ejpam-5546	97	19	in	in	ADP
ejpam-5546	97	20	[	[	X
ejpam-5546	97	21	4	4	NUM
ejpam-5546	97	22	]	]	PUNCT
ejpam-5546	97	23	described	describe	VERB
ejpam-5546	97	24	24	24	NUM
ejpam-5546	97	25	bases	basis	NOUN
ejpam-5546	97	26	for	for	ADP
ejpam-5546	97	27	it	it	PRON
ejpam-5546	97	28	.	.	PUNCT
ejpam-5546	98	1	we	we	PRON
ejpam-5546	98	2	can	can	AUX
ejpam-5546	98	3	summarize	summarize	VERB
ejpam-5546	98	4	their	their	PRON
ejpam-5546	98	5	work	work	NOUN
ejpam-5546	98	6	as	as	SCONJ
ejpam-5546	98	7	follows	follow	VERB
ejpam-5546	98	8	:	:	PUNCT
ejpam-5546	98	9	let	let	VERB
ejpam-5546	98	10	v	v	PART
ejpam-5546	98	11	be	be	AUX
ejpam-5546	98	12	a	a	DET
ejpam-5546	98	13	vector	vector	NOUN
ejpam-5546	98	14	space	space	NOUN
ejpam-5546	98	15	over	over	ADP
ejpam-5546	98	16	f	f	PROPN
ejpam-5546	98	17	with	with	ADP
ejpam-5546	98	18	finite	finite	ADJ
ejpam-5546	98	19	positive	positive	ADJ
ejpam-5546	98	20	dimension	dimension	NOUN
ejpam-5546	98	21	.	.	PUNCT
ejpam-5546	99	1	let	let	VERB
ejpam-5546	99	2	{	{	PUNCT
ejpam-5546	99	3	si}di=0	si}di=0	VERB
ejpam-5546	99	4	denote	denote	VERB
ejpam-5546	99	5	a	a	DET
ejpam-5546	99	6	sequence	sequence	NOUN
ejpam-5546	99	7	of	of	ADP
ejpam-5546	99	8	positive	positive	ADJ
ejpam-5546	99	9	integers	integer	NOUN
ejpam-5546	99	10	whose	whose	DET
ejpam-5546	99	11	sum	sum	NOUN
ejpam-5546	99	12	is	be	AUX
ejpam-5546	99	13	equal	equal	ADJ
ejpam-5546	99	14	the	the	DET
ejpam-5546	99	15	dimension	dimension	NOUN
ejpam-5546	99	16	of	of	ADP
ejpam-5546	99	17	vector	vector	NOUN
ejpam-5546	99	18	space	space	NOUN
ejpam-5546	99	19	v	v	NOUN
ejpam-5546	99	20	.	.	PUNCT
ejpam-5546	100	1	a	a	DET
ejpam-5546	100	2	decomposition	decomposition	NOUN
ejpam-5546	100	3	of	of	ADP
ejpam-5546	100	4	v	v	NOUN
ejpam-5546	100	5	of	of	ADP
ejpam-5546	100	6	shape	shape	NOUN
ejpam-5546	100	7	{	{	PUNCT
ejpam-5546	100	8	si}di=0	si}di=0	NOUN
ejpam-5546	100	9	is	be	AUX
ejpam-5546	100	10	a	a	DET
ejpam-5546	100	11	sequence	sequence	NOUN
ejpam-5546	100	12	of	of	ADP
ejpam-5546	100	13	subspaces	subspace	NOUN
ejpam-5546	100	14	{	{	PUNCT
ejpam-5546	100	15	wi}di=0	wi}di=0	NOUN
ejpam-5546	100	16	of	of	ADP
ejpam-5546	100	17	vector	vector	NOUN
ejpam-5546	100	18	space	space	NOUN
ejpam-5546	100	19	v	v	ADP
ejpam-5546	100	20	such	such	ADJ
ejpam-5546	100	21	that	that	SCONJ
ejpam-5546	100	22	the	the	DET
ejpam-5546	100	23	dimension	dimension	NOUN
ejpam-5546	100	24	of	of	ADP
ejpam-5546	100	25	wi	wi	PROPN
ejpam-5546	100	26	is	be	AUX
ejpam-5546	100	27	si	si	PROPN
ejpam-5546	100	28	(	(	PUNCT
ejpam-5546	100	29	0	0	NUM
ejpam-5546	100	30	≤	≤	NUM
ejpam-5546	100	31	i	i	NOUN
ejpam-5546	101	1	≤	≤	NUM
ejpam-5546	101	2	d	d	NOUN
ejpam-5546	101	3	)	)	PUNCT
ejpam-5546	101	4	,	,	PUNCT
ejpam-5546	101	5	and	and	CCONJ
ejpam-5546	101	6	v	v	X
ejpam-5546	101	7	=	=	SYM
ejpam-5546	101	8	∑d	∑d	X
ejpam-5546	101	9	i=0wi	i=0wi	X
ejpam-5546	101	10	(	(	PUNCT
ejpam-5546	101	11	direct	direct	ADJ
ejpam-5546	101	12	sum	sum	NOUN
ejpam-5546	101	13	)	)	PUNCT
ejpam-5546	101	14	.	.	PUNCT
ejpam-5546	102	1	we	we	PRON
ejpam-5546	102	2	call	call	VERB
ejpam-5546	102	3	d	d	VERB
ejpam-5546	102	4	the	the	DET
ejpam-5546	102	5	diameter	diameter	NOUN
ejpam-5546	102	6	of	of	ADP
ejpam-5546	102	7	v	v	PROPN
ejpam-5546	102	8	.	.	PUNCT
ejpam-5546	103	1	definition	definition	NOUN
ejpam-5546	103	2	4	4	NUM
ejpam-5546	103	3	.	.	PUNCT
ejpam-5546	104	1	[	[	X
ejpam-5546	104	2	5	5	NUM
ejpam-5546	104	3	]	]	PUNCT
ejpam-5546	104	4	an	an	DET
ejpam-5546	104	5	evaluation	evaluation	NOUN
ejpam-5546	104	6	module	module	NOUN
ejpam-5546	104	7	for	for	ADP
ejpam-5546	104	8	q	q	ADJ
ejpam-5546	104	9	-	-	PUNCT
ejpam-5546	104	10	tetrahedron	tetrahedron	NOUN
ejpam-5546	104	11	algebra	algebra	NOUN
ejpam-5546	104	12	⊠q	⊠q	PROPN
ejpam-5546	104	13	is	be	AUX
ejpam-5546	104	14	a	a	DET
ejpam-5546	104	15	finite	finite	ADJ
ejpam-5546	104	16	dimensional	dimensional	ADJ
ejpam-5546	104	17	,	,	PUNCT
ejpam-5546	104	18	nontrivial	nontrivial	ADJ
ejpam-5546	104	19	irreducible	irreducible	ADJ
ejpam-5546	104	20	⊠q	⊠q	NOUN
ejpam-5546	104	21	-	-	NOUN
ejpam-5546	104	22	module	module	NOUN
ejpam-5546	104	23	with	with	ADP
ejpam-5546	104	24	shape	shape	NOUN
ejpam-5546	104	25	(	(	PUNCT
ejpam-5546	104	26	1	1	NUM
ejpam-5546	104	27	,	,	PUNCT
ejpam-5546	104	28	1	1	NUM
ejpam-5546	104	29	,	,	PUNCT
ejpam-5546	104	30	...	...	PUNCT
ejpam-5546	104	31	,	,	PUNCT
ejpam-5546	104	32	1	1	NUM
ejpam-5546	104	33	)	)	PUNCT
ejpam-5546	104	34	.	.	PUNCT
ejpam-5546	105	1	a	a	DET
ejpam-5546	105	2	flag	flag	NOUN
ejpam-5546	105	3	on	on	ADP
ejpam-5546	105	4	vector	vector	NOUN
ejpam-5546	105	5	space	space	NOUN
ejpam-5546	105	6	v	v	ADP
ejpam-5546	105	7	of	of	ADP
ejpam-5546	105	8	shape	shape	NOUN
ejpam-5546	105	9	{	{	PUNCT
ejpam-5546	105	10	si}di=0	si}di=0	NOUN
ejpam-5546	105	11	is	be	AUX
ejpam-5546	105	12	a	a	DET
ejpam-5546	105	13	sequence	sequence	NOUN
ejpam-5546	105	14	of	of	ADP
ejpam-5546	105	15	subspaces	subspace	NOUN
ejpam-5546	105	16	{	{	PUNCT
ejpam-5546	105	17	wi}di=0	wi}di=0	NOUN
ejpam-5546	105	18	of	of	ADP
ejpam-5546	105	19	v	v	NOUN
ejpam-5546	105	20	such	such	ADJ
ejpam-5546	105	21	that	that	DET
ejpam-5546	105	22	wi−1	wi−1	PROPN
ejpam-5546	105	23	⊆	⊆	NUM
ejpam-5546	105	24	wi	wi	PROPN
ejpam-5546	105	25	,	,	PUNCT
ejpam-5546	105	26	and	and	CCONJ
ejpam-5546	105	27	the	the	DET
ejpam-5546	105	28	dimension	dimension	NOUN
ejpam-5546	105	29	of	of	ADP
ejpam-5546	105	30	wi	wi	PROPN
ejpam-5546	105	31	is	be	AUX
ejpam-5546	105	32	equal	equal	ADJ
ejpam-5546	105	33	s0	s0	NOUN
ejpam-5546	105	34	+	+	CCONJ
ejpam-5546	105	35	s1	s1	PROPN
ejpam-5546	105	36	+	+	CCONJ
ejpam-5546	105	37	...	...	PUNCT
ejpam-5546	105	38	+	+	X
ejpam-5546	105	39	si	si	X
ejpam-5546	105	40	for	for	ADP
ejpam-5546	105	41	0	0	NUM
ejpam-5546	105	42	≤	≤	NUM
ejpam-5546	105	43	i	i	PRON
ejpam-5546	105	44	≤	≤	PROPN
ejpam-5546	105	45	d.	d.	PROPN
ejpam-5546	105	46	let	let	VERB
ejpam-5546	105	47	v	v	PART
ejpam-5546	105	48	denote	denote	VERB
ejpam-5546	105	49	finite	finite	ADJ
ejpam-5546	105	50	dimensional	dimensional	ADJ
ejpam-5546	105	51	irreducible	irreducible	ADJ
ejpam-5546	105	52	module	module	NOUN
ejpam-5546	105	53	for	for	ADP
ejpam-5546	105	54	⊠q	⊠q	PROPN
ejpam-5546	105	55	with	with	ADP
ejpam-5546	105	56	diameter	diameter	PROPN
ejpam-5546	105	57	d.	d.	PROPN
ejpam-5546	105	58	for	for	ADP
ejpam-5546	105	59	distinct	distinct	PROPN
ejpam-5546	105	60	i	i	PROPN
ejpam-5546	105	61	,	,	PUNCT
ejpam-5546	105	62	j	j	PROPN
ejpam-5546	105	63	in	in	ADP
ejpam-5546	105	64	z4	z4	PROPN
ejpam-5546	106	1	such	such	ADJ
ejpam-5546	106	2	that	that	SCONJ
ejpam-5546	106	3	j	j	PROPN
ejpam-5546	107	1	−	−	NOUN
ejpam-5546	108	1	i	i	PRON
ejpam-5546	108	2	=	=	NOUN
ejpam-5546	108	3	1	1	NUM
ejpam-5546	108	4	or	or	CCONJ
ejpam-5546	108	5	j	j	ADJ
ejpam-5546	109	1	−	−	NOUN
ejpam-5546	110	1	i	i	PRON
ejpam-5546	110	2	=	=	NOUN
ejpam-5546	110	3	2	2	NUM
ejpam-5546	110	4	we	we	PRON
ejpam-5546	110	5	define	define	VERB
ejpam-5546	110	6	a	a	DET
ejpam-5546	110	7	decomposition	decomposition	NOUN
ejpam-5546	110	8	of	of	ADP
ejpam-5546	110	9	the	the	DET
ejpam-5546	110	10	vector	vector	NOUN
ejpam-5546	110	11	space	space	NOUN
ejpam-5546	110	12	v	v	NOUN
ejpam-5546	110	13	called	call	VERB
ejpam-5546	111	1	[	[	X
ejpam-5546	111	2	i	i	PROPN
ejpam-5546	111	3	,	,	PUNCT
ejpam-5546	111	4	j	j	PROPN
ejpam-5546	111	5	]	]	X
ejpam-5546	111	6	.	.	PUNCT
ejpam-5546	112	1	the	the	DET
ejpam-5546	112	2	decomposition	decomposition	NOUN
ejpam-5546	112	3	[	[	X
ejpam-5546	112	4	i	i	X
ejpam-5546	112	5	,	,	PUNCT
ejpam-5546	112	6	j	j	PROPN
ejpam-5546	112	7	]	]	X
ejpam-5546	112	8	has	have	VERB
ejpam-5546	112	9	diameter	diameter	NOUN
ejpam-5546	112	10	d	d	NOUN
ejpam-5546	112	11	,	,	PUNCT
ejpam-5546	112	12	and	and	CCONJ
ejpam-5546	112	13	the	the	DET
ejpam-5546	112	14	nth	nth	NOUN
ejpam-5546	112	15	component	component	NOUN
ejpam-5546	112	16	of	of	ADP
ejpam-5546	112	17	[	[	X
ejpam-5546	112	18	i	i	PROPN
ejpam-5546	112	19	,	,	PUNCT
ejpam-5546	112	20	j	j	PROPN
ejpam-5546	112	21	]	]	X
ejpam-5546	112	22	is	be	AUX
ejpam-5546	112	23	the	the	DET
ejpam-5546	112	24	eigenspace	eigenspace	NOUN
ejpam-5546	112	25	of	of	ADP
ejpam-5546	112	26	xij	xij	PROPN
ejpam-5546	112	27	with	with	ADP
ejpam-5546	112	28	eigenvalue	eigenvalue	PROPN
ejpam-5546	112	29	qd−2n	qd−2n	PROPN
ejpam-5546	112	30	for	for	ADP
ejpam-5546	112	31	0	0	NUM
ejpam-5546	112	32	≤	≤	NUM
ejpam-5546	113	1	n	n	DET
ejpam-5546	113	2	≤	≤	PROPN
ejpam-5546	113	3	d.	d.	NOUN
ejpam-5546	113	4	there	there	PRON
ejpam-5546	113	5	exists	exist	VERB
ejpam-5546	113	6	a	a	DET
ejpam-5546	113	7	collection	collection	NOUN
ejpam-5546	113	8	of	of	ADP
ejpam-5546	113	9	flags	flag	NOUN
ejpam-5546	113	10	on	on	ADP
ejpam-5546	113	11	vector	vector	NOUN
ejpam-5546	113	12	spaces	space	NOUN
ejpam-5546	113	13	v	v	NUM
ejpam-5546	113	14	,	,	PUNCT
ejpam-5546	113	15	denoted	denote	VERB
ejpam-5546	113	16	[	[	X
ejpam-5546	113	17	i	i	X
ejpam-5546	113	18	]	]	X
ejpam-5546	113	19	,	,	PUNCT
ejpam-5546	113	20	i	i	PRON
ejpam-5546	113	21	∈	∈	PROPN
ejpam-5546	113	22	z4	z4	PROPN
ejpam-5546	113	23	,	,	PUNCT
ejpam-5546	113	24	such	such	ADJ
ejpam-5546	113	25	that	that	PRON
ejpam-5546	113	26	for	for	ADP
ejpam-5546	113	27	distinct	distinct	ADJ
ejpam-5546	113	28	i	i	PROPN
ejpam-5546	113	29	,	,	PUNCT
ejpam-5546	113	30	j	j	PROPN
ejpam-5546	113	31	∈	∈	PROPN
ejpam-5546	113	32	z4	z4	VERB
ejpam-5546	113	33	the	the	DET
ejpam-5546	113	34	decomposition	decomposition	NOUN
ejpam-5546	113	35	[	[	X
ejpam-5546	113	36	i	i	X
ejpam-5546	113	37	,	,	PUNCT
ejpam-5546	113	38	j	j	PROPN
ejpam-5546	113	39	]	]	PUNCT
ejpam-5546	113	40	induces	induce	VERB
ejpam-5546	113	41	the	the	DET
ejpam-5546	113	42	flag	flag	NOUN
ejpam-5546	114	1	[	[	X
ejpam-5546	114	2	i	i	X
ejpam-5546	114	3	]	]	X
ejpam-5546	114	4	.	.	PUNCT
ejpam-5546	115	1	by	by	ADP
ejpam-5546	115	2	construction	construction	NOUN
ejpam-5546	115	3	,	,	PUNCT
ejpam-5546	115	4	the	the	DET
ejpam-5546	115	5	shape	shape	NOUN
ejpam-5546	115	6	of	of	ADP
ejpam-5546	115	7	the	the	DET
ejpam-5546	115	8	flag	flag	NOUN
ejpam-5546	115	9	[	[	X
ejpam-5546	115	10	i	i	X
ejpam-5546	115	11	]	]	X
ejpam-5546	115	12	coincides	coincide	VERB
ejpam-5546	115	13	with	with	ADP
ejpam-5546	115	14	the	the	DET
ejpam-5546	115	15	shape	shape	NOUN
ejpam-5546	115	16	of	of	ADP
ejpam-5546	115	17	v	v	NOUN
ejpam-5546	115	18	.	.	PUNCT
ejpam-5546	116	1	definition	definition	NOUN
ejpam-5546	116	2	5	5	NUM
ejpam-5546	116	3	.	.	PUNCT
ejpam-5546	117	1	[	[	X
ejpam-5546	117	2	4	4	X
ejpam-5546	117	3	]	]	PUNCT
ejpam-5546	117	4	let	let	VERB
ejpam-5546	117	5	v	v	PART
ejpam-5546	117	6	denote	denote	VERB
ejpam-5546	117	7	an	an	DET
ejpam-5546	117	8	evaluation	evaluation	NOUN
ejpam-5546	117	9	module	module	NOUN
ejpam-5546	117	10	for	for	ADP
ejpam-5546	117	11	⊠q	⊠q	PROPN
ejpam-5546	117	12	that	that	PRON
ejpam-5546	117	13	has	have	VERB
ejpam-5546	117	14	diameter	diameter	NOUN
ejpam-5546	117	15	d.	d.	PROPN
ejpam-5546	117	16	pick	pick	VERB
ejpam-5546	117	17	mutually	mutually	ADV
ejpam-5546	117	18	distinct	distinct	ADJ
ejpam-5546	118	1	i	i	PRON
ejpam-5546	118	2	,	,	PUNCT
ejpam-5546	118	3	j	j	PROPN
ejpam-5546	118	4	,	,	PUNCT
ejpam-5546	118	5	k	k	PROPN
ejpam-5546	118	6	,	,	PUNCT
ejpam-5546	118	7	l	l	PROPN
ejpam-5546	118	8	∈	∈	PROPN
ejpam-5546	118	9	z4	z4	PROPN
ejpam-5546	118	10	.	.	PUNCT
ejpam-5546	119	1	a	a	DET
ejpam-5546	119	2	basis	basis	NOUN
ejpam-5546	119	3	{	{	PUNCT
ejpam-5546	119	4	vn}dn=0	vn}dn=0	VERB
ejpam-5546	119	5	for	for	ADP
ejpam-5546	119	6	v	v	NOUN
ejpam-5546	119	7	is	be	AUX
ejpam-5546	119	8	called	call	VERB
ejpam-5546	119	9	an	an	DET
ejpam-5546	119	10	[	[	X
ejpam-5546	119	11	i	i	PROPN
ejpam-5546	119	12	,	,	PUNCT
ejpam-5546	119	13	j	j	PROPN
ejpam-5546	119	14	,	,	PUNCT
ejpam-5546	119	15	k	k	NOUN
ejpam-5546	119	16	,	,	PUNCT
ejpam-5546	119	17	l]-basis	l]-basis	VERB
ejpam-5546	119	18	whenever	whenever	ADV
ejpam-5546	119	19	:	:	PUNCT
ejpam-5546	119	20	(	(	PUNCT
ejpam-5546	119	21	i	i	NOUN
ejpam-5546	119	22	)	)	PUNCT
ejpam-5546	119	23	for	for	ADP
ejpam-5546	119	24	0	0	NUM
ejpam-5546	119	25	≤	≤	NOUN
ejpam-5546	119	26	n	n	PRON
ejpam-5546	119	27	≤	≤	NOUN
ejpam-5546	119	28	d	d	SCONJ
ejpam-5546	119	29	the	the	DET
ejpam-5546	119	30	vector	vector	NOUN
ejpam-5546	119	31	vn	vn	PROPN
ejpam-5546	119	32	is	be	AUX
ejpam-5546	119	33	contained	contain	VERB
ejpam-5546	119	34	in	in	ADP
ejpam-5546	119	35	the	the	DET
ejpam-5546	119	36	component	component	NOUN
ejpam-5546	119	37	n	n	PROPN
ejpam-5546	119	38	of	of	ADP
ejpam-5546	119	39	the	the	DET
ejpam-5546	119	40	decomposition	decomposition	NOUN
ejpam-5546	119	41	[	[	X
ejpam-5546	119	42	k	k	X
ejpam-5546	119	43	,	,	PUNCT
ejpam-5546	119	44	l	l	NOUN
ejpam-5546	119	45	]	]	PUNCT
ejpam-5546	119	46	of	of	ADP
ejpam-5546	119	47	v	v	NOUN
ejpam-5546	119	48	;	;	PUNCT
ejpam-5546	119	49	(	(	PUNCT
ejpam-5546	119	50	ii	ii	NOUN
ejpam-5546	119	51	)	)	PUNCT
ejpam-5546	119	52	∑d	∑d	PROPN
ejpam-5546	120	1	n=0	n=0	NUM
ejpam-5546	120	2	vn	vn	NOUN
ejpam-5546	120	3	is	be	AUX
ejpam-5546	120	4	contained	contain	VERB
ejpam-5546	120	5	in	in	ADP
ejpam-5546	120	6	component	component	NOUN
ejpam-5546	120	7	0	0	NUM
ejpam-5546	120	8	of	of	ADP
ejpam-5546	120	9	the	the	DET
ejpam-5546	120	10	flag	flag	NOUN
ejpam-5546	121	1	[	[	X
ejpam-5546	121	2	j	j	X
ejpam-5546	121	3	]	]	X
ejpam-5546	121	4	on	on	ADP
ejpam-5546	121	5	v	v	NUM
ejpam-5546	121	6	.	.	PUNCT
ejpam-5546	122	1	lemma	lemma	PROPN
ejpam-5546	122	2	1	1	NUM
ejpam-5546	122	3	.	.	PUNCT
ejpam-5546	123	1	[	[	X
ejpam-5546	123	2	4	4	X
ejpam-5546	123	3	]	]	PUNCT
ejpam-5546	123	4	let	let	VERB
ejpam-5546	123	5	v	v	PART
ejpam-5546	123	6	denote	denote	VERB
ejpam-5546	123	7	an	an	DET
ejpam-5546	123	8	evaluation	evaluation	NOUN
ejpam-5546	123	9	module	module	NOUN
ejpam-5546	123	10	for	for	ADP
ejpam-5546	123	11	⊠q	⊠q	PROPN
ejpam-5546	123	12	,	,	PUNCT
ejpam-5546	123	13	and	and	CCONJ
ejpam-5546	123	14	pick	pick	VERB
ejpam-5546	123	15	mutually	mutually	ADV
ejpam-5546	123	16	distinct	distinct	ADJ
ejpam-5546	124	1	i	i	PRON
ejpam-5546	124	2	,	,	PUNCT
ejpam-5546	124	3	j	j	PROPN
ejpam-5546	124	4	,	,	PUNCT
ejpam-5546	124	5	k	k	PROPN
ejpam-5546	124	6	,	,	PUNCT
ejpam-5546	124	7	l	l	PROPN
ejpam-5546	124	8	∈	∈	PROPN
ejpam-5546	124	9	z4	z4	X
ejpam-5546	124	10	.	.	PUNCT
ejpam-5546	125	1	then	then	ADV
ejpam-5546	125	2	there	there	PRON
ejpam-5546	125	3	exists	exist	VERB
ejpam-5546	125	4	an	an	DET
ejpam-5546	125	5	[	[	X
ejpam-5546	125	6	i	i	PROPN
ejpam-5546	125	7	,	,	PUNCT
ejpam-5546	125	8	j	j	PROPN
ejpam-5546	125	9	,	,	PUNCT
ejpam-5546	125	10	k	k	NOUN
ejpam-5546	125	11	,	,	PUNCT
ejpam-5546	125	12	l]-basis	l]-basis	NOUN
ejpam-5546	125	13	for	for	ADP
ejpam-5546	125	14	v	v	NOUN
ejpam-5546	125	15	.	.	PUNCT
ejpam-5546	126	1	h.	h.	PROPN
ejpam-5546	126	2	alnajjar	alnajjar	PROPN
ejpam-5546	126	3	/	/	SYM
ejpam-5546	126	4	eur	eur	PROPN
ejpam-5546	126	5	.	.	PUNCT
ejpam-5546	127	1	j.	j.	PROPN
ejpam-5546	127	2	pure	pure	PROPN
ejpam-5546	127	3	appl	appl	PROPN
ejpam-5546	127	4	.	.	PROPN
ejpam-5546	127	5	math	math	PROPN
ejpam-5546	127	6	,	,	PUNCT
ejpam-5546	127	7	18	18	NUM
ejpam-5546	127	8	(	(	PUNCT
ejpam-5546	127	9	1	1	NUM
ejpam-5546	127	10	)	)	PUNCT
ejpam-5546	127	11	(	(	PUNCT
ejpam-5546	127	12	2025	2025	NUM
ejpam-5546	127	13	)	)	PUNCT
ejpam-5546	127	14	,	,	PUNCT
ejpam-5546	127	15	5546	5546	NUM
ejpam-5546	127	16	5	5	NUM
ejpam-5546	127	17	of	of	ADP
ejpam-5546	127	18	14	14	NUM
ejpam-5546	127	19	let	let	VERB
ejpam-5546	127	20	v	v	PART
ejpam-5546	127	21	denote	denote	VERB
ejpam-5546	127	22	an	an	DET
ejpam-5546	127	23	evaluation	evaluation	NOUN
ejpam-5546	127	24	module	module	NOUN
ejpam-5546	127	25	for	for	ADP
ejpam-5546	127	26	⊠q	⊠q	PROPN
ejpam-5546	127	27	.	.	PUNCT
ejpam-5546	128	1	in	in	ADP
ejpam-5546	128	2	definition	definition	NOUN
ejpam-5546	128	3	5	5	NUM
ejpam-5546	128	4	and	and	CCONJ
ejpam-5546	128	5	lemma	lemma	PROPN
ejpam-5546	128	6	1	1	NUM
ejpam-5546	128	7	we	we	PRON
ejpam-5546	128	8	can	can	AUX
ejpam-5546	128	9	recognize	recognize	VERB
ejpam-5546	128	10	24	24	NUM
ejpam-5546	128	11	bases	basis	NOUN
ejpam-5546	128	12	for	for	ADP
ejpam-5546	128	13	v	v	NOUN
ejpam-5546	128	14	.	.	PUNCT
ejpam-5546	129	1	the	the	DET
ejpam-5546	129	2	action	action	NOUN
ejpam-5546	129	3	of	of	ADP
ejpam-5546	129	4	standard	standard	ADJ
ejpam-5546	129	5	generators	generator	NOUN
ejpam-5546	129	6	of	of	ADP
ejpam-5546	129	7	⊠q	⊠q	PROPN
ejpam-5546	129	8	on	on	ADP
ejpam-5546	129	9	these	these	DET
ejpam-5546	129	10	24	24	NUM
ejpam-5546	129	11	bases	basis	NOUN
ejpam-5546	129	12	is	be	AUX
ejpam-5546	129	13	described	describe	VERB
ejpam-5546	129	14	in	in	ADP
ejpam-5546	129	15	theorem	theorem	NOUN
ejpam-5546	129	16	11.1	11.1	NUM
ejpam-5546	129	17	in	in	ADP
ejpam-5546	129	18	[	[	X
ejpam-5546	129	19	4	4	NUM
ejpam-5546	129	20	]	]	PUNCT
ejpam-5546	129	21	,	,	PUNCT
ejpam-5546	129	22	the	the	DET
ejpam-5546	129	23	authors	author	NOUN
ejpam-5546	129	24	used	use	VERB
ejpam-5546	129	25	special	special	ADJ
ejpam-5546	129	26	matrices	matrix	NOUN
ejpam-5546	129	27	z	z	PROPN
ejpam-5546	129	28	,	,	PUNCT
ejpam-5546	129	29	kq	kq	PROPN
ejpam-5546	129	30	,	,	PUNCT
ejpam-5546	129	31	eq	eq	NOUN
ejpam-5546	129	32	,	,	PUNCT
ejpam-5546	129	33	and	and	CCONJ
ejpam-5546	129	34	gq(t	gq(t	VERB
ejpam-5546	129	35	)	)	PUNCT
ejpam-5546	129	36	to	to	PART
ejpam-5546	129	37	describe	describe	VERB
ejpam-5546	129	38	the	the	DET
ejpam-5546	129	39	action	action	NOUN
ejpam-5546	129	40	of	of	ADP
ejpam-5546	129	41	the	the	DET
ejpam-5546	129	42	standard	standard	ADJ
ejpam-5546	129	43	generators	generator	NOUN
ejpam-5546	129	44	of	of	ADP
ejpam-5546	129	45	⊠q	⊠q	PROPN
ejpam-5546	129	46	on	on	ADP
ejpam-5546	129	47	these	these	DET
ejpam-5546	129	48	24	24	NUM
ejpam-5546	129	49	bases	basis	NOUN
ejpam-5546	129	50	,	,	PUNCT
ejpam-5546	129	51	these	these	DET
ejpam-5546	129	52	matrices	matrix	NOUN
ejpam-5546	129	53	are	be	AUX
ejpam-5546	129	54	described	describe	VERB
ejpam-5546	129	55	in	in	ADP
ejpam-5546	129	56	the	the	DET
ejpam-5546	129	57	following	follow	VERB
ejpam-5546	129	58	definition	definition	NOUN
ejpam-5546	129	59	.	.	PUNCT
ejpam-5546	130	1	definition	definition	NOUN
ejpam-5546	130	2	6	6	NUM
ejpam-5546	130	3	.	.	PUNCT
ejpam-5546	131	1	let	let	VERB
ejpam-5546	131	2	z	z	NOUN
ejpam-5546	131	3	,	,	PUNCT
ejpam-5546	131	4	kq	kq	PROPN
ejpam-5546	131	5	,	,	PUNCT
ejpam-5546	131	6	eq	eq	NOUN
ejpam-5546	131	7	,	,	PUNCT
ejpam-5546	131	8	and	and	CCONJ
ejpam-5546	131	9	gq(t	gq(t	X
ejpam-5546	131	10	)	)	PUNCT
ejpam-5546	131	11	denote	denote	VERB
ejpam-5546	131	12	the	the	DET
ejpam-5546	131	13	matrices	matrix	NOUN
ejpam-5546	131	14	in	in	ADP
ejpam-5546	131	15	matd+1(f	matd+1(f	NOUN
ejpam-5546	131	16	)	)	PUNCT
ejpam-5546	131	17	such	such	ADJ
ejpam-5546	131	18	that	that	SCONJ
ejpam-5546	131	19	z(i	z(i	PROPN
ejpam-5546	131	20	,	,	PUNCT
ejpam-5546	131	21	j	j	NOUN
ejpam-5546	131	22	)	)	PUNCT
ejpam-5546	131	23	=	=	SYM
ejpam-5546	131	24	δi+j	δi+j	PROPN
ejpam-5546	131	25	,	,	PUNCT
ejpam-5546	131	26	d	d	NOUN
ejpam-5546	131	27	for	for	ADP
ejpam-5546	131	28	0	0	NUM
ejpam-5546	131	29	≤	≤	NOUN
ejpam-5546	132	1	i	i	PRON
ejpam-5546	132	2	,	,	PUNCT
ejpam-5546	132	3	j	j	PROPN
ejpam-5546	132	4	≤	≤	PROPN
ejpam-5546	132	5	d	d	PROPN
ejpam-5546	132	6	,	,	PUNCT
ejpam-5546	132	7	the	the	DET
ejpam-5546	132	8	matrix	matrix	NOUN
ejpam-5546	132	9	kq	kq	PROPN
ejpam-5546	132	10	is	be	AUX
ejpam-5546	132	11	diagonal	diagonal	ADJ
ejpam-5546	132	12	with	with	ADP
ejpam-5546	132	13	kq(i	kq(i	NUM
ejpam-5546	132	14	,	,	PUNCT
ejpam-5546	132	15	i	i	NOUN
ejpam-5546	132	16	)	)	PUNCT
ejpam-5546	132	17	=	=	PUNCT
ejpam-5546	133	1	qd−2i	qd−2i	NOUN
ejpam-5546	133	2	for	for	ADP
ejpam-5546	133	3	0	0	NUM
ejpam-5546	133	4	≤	≤	NUM
ejpam-5546	133	5	i	i	PRON
ejpam-5546	134	1	≤	≤	PROPN
ejpam-5546	134	2	d	d	X
ejpam-5546	134	3	,	,	PUNCT
ejpam-5546	134	4	the	the	DET
ejpam-5546	134	5	matrix	matrix	NOUN
ejpam-5546	134	6	eq	eq	ADP
ejpam-5546	134	7	is	be	AUX
ejpam-5546	134	8	upper	upper	ADJ
ejpam-5546	134	9	bidiagonal	bidiagonal	NOUN
ejpam-5546	134	10	with	with	ADP
ejpam-5546	134	11	eq(i	eq(i	NOUN
ejpam-5546	134	12	,	,	PUNCT
ejpam-5546	134	13	i	i	NOUN
ejpam-5546	134	14	)	)	PUNCT
ejpam-5546	135	1	=	=	PUNCT
ejpam-5546	135	2	q2i−d	q2i−d	NOUN
ejpam-5546	135	3	for	for	ADP
ejpam-5546	135	4	0	0	NUM
ejpam-5546	135	5	≤	≤	NUM
ejpam-5546	136	1	i	i	PRON
ejpam-5546	136	2	≤	≤	NOUN
ejpam-5546	136	3	d	d	ADP
ejpam-5546	136	4	,	,	PUNCT
ejpam-5546	136	5	and	and	CCONJ
ejpam-5546	136	6	eq(i	eq(i	PUNCT
ejpam-5546	136	7	−	−	PROPN
ejpam-5546	136	8	1	1	NUM
ejpam-5546	136	9	,	,	PUNCT
ejpam-5546	136	10	i	i	NOUN
ejpam-5546	136	11	)	)	PUNCT
ejpam-5546	136	12	=	=	SYM
ejpam-5546	136	13	qd	qd	NOUN
ejpam-5546	136	14	−	−	NOUN
ejpam-5546	136	15	q2i−d−2	q2i−d−2	NOUN
ejpam-5546	136	16	for	for	ADP
ejpam-5546	136	17	1	1	NUM
ejpam-5546	136	18	≤	≤	NUM
ejpam-5546	136	19	i	i	PRON
ejpam-5546	137	1	≤	≤	PROPN
ejpam-5546	137	2	d	d	ADP
ejpam-5546	137	3	,	,	PUNCT
ejpam-5546	137	4	and	and	CCONJ
ejpam-5546	137	5	the	the	DET
ejpam-5546	137	6	matrix	matrix	NOUN
ejpam-5546	137	7	gq(t	gq(t	NOUN
ejpam-5546	137	8	)	)	PUNCT
ejpam-5546	137	9	is	be	AUX
ejpam-5546	137	10	upper	upper	ADJ
ejpam-5546	137	11	bidiagonal	bidiagonal	NOUN
ejpam-5546	137	12	with	with	ADP
ejpam-5546	137	13	gq(t)(i	gq(t)(i	PROPN
ejpam-5546	137	14	,	,	PUNCT
ejpam-5546	137	15	i	i	NOUN
ejpam-5546	137	16	)	)	PUNCT
ejpam-5546	138	1	=	=	PUNCT
ejpam-5546	138	2	q2i−d	q2i−d	NOUN
ejpam-5546	138	3	for	for	ADP
ejpam-5546	138	4	0	0	NUM
ejpam-5546	138	5	≤	≤	NUM
ejpam-5546	139	1	i	i	PRON
ejpam-5546	139	2	≤	≤	NOUN
ejpam-5546	139	3	d	d	ADP
ejpam-5546	139	4	,	,	PUNCT
ejpam-5546	139	5	and	and	CCONJ
ejpam-5546	139	6	gq(t)(i	gq(t)(i	NOUN
ejpam-5546	139	7	−	−	NOUN
ejpam-5546	139	8	1	1	NUM
ejpam-5546	139	9	,	,	PUNCT
ejpam-5546	139	10	i	i	NOUN
ejpam-5546	139	11	)	)	PUNCT
ejpam-5546	139	12	=	=	PUNCT
ejpam-5546	139	13	(	(	PUNCT
ejpam-5546	139	14	qd	qd	NOUN
ejpam-5546	139	15	−	−	NOUN
ejpam-5546	139	16	q2i−d−2)(1	q2i−d−2)(1	PRON
ejpam-5546	139	17	−	−	PROPN
ejpam-5546	139	18	tqd−2i+1	tqd−2i+1	PUNCT
ejpam-5546	139	19	)	)	PUNCT
ejpam-5546	139	20	for	for	ADP
ejpam-5546	139	21	1	1	NUM
ejpam-5546	139	22	≤	≤	NUM
ejpam-5546	140	1	i	i	PRON
ejpam-5546	140	2	≤	≤	ADJ
ejpam-5546	140	3	d.	d.	NOUN
ejpam-5546	140	4	we	we	PRON
ejpam-5546	140	5	remark	remark	VERB
ejpam-5546	140	6	here	here	ADV
ejpam-5546	140	7	that	that	SCONJ
ejpam-5546	140	8	we	we	PRON
ejpam-5546	140	9	will	will	AUX
ejpam-5546	140	10	use	use	VERB
ejpam-5546	140	11	the	the	DET
ejpam-5546	140	12	notations	notation	NOUN
ejpam-5546	140	13	in	in	ADP
ejpam-5546	140	14	definition	definition	NOUN
ejpam-5546	140	15	6	6	NUM
ejpam-5546	140	16	in	in	ADP
ejpam-5546	140	17	our	our	PRON
ejpam-5546	140	18	work	work	NOUN
ejpam-5546	140	19	in	in	ADP
ejpam-5546	140	20	the	the	DET
ejpam-5546	140	21	next	next	ADJ
ejpam-5546	140	22	sections	section	NOUN
ejpam-5546	140	23	.	.	PUNCT
ejpam-5546	141	1	4	4	X
ejpam-5546	141	2	.	.	X
ejpam-5546	141	3	the	the	DET
ejpam-5546	141	4	leonard	leonard	PROPN
ejpam-5546	141	5	pair	pair	NOUN
ejpam-5546	141	6	a	a	PRON
ejpam-5546	141	7	,	,	PUNCT
ejpam-5546	141	8	x20	x20	NOUN
ejpam-5546	141	9	the	the	DET
ejpam-5546	141	10	q	q	ADJ
ejpam-5546	141	11	-	-	PUNCT
ejpam-5546	141	12	tetrahedron	tetrahedron	NOUN
ejpam-5546	141	13	algebra	algebra	NOUN
ejpam-5546	141	14	has	have	VERB
ejpam-5546	141	15	eight	eight	NUM
ejpam-5546	141	16	generators	generator	NOUN
ejpam-5546	141	17	{	{	PUNCT
ejpam-5546	141	18	x20	x20	PROPN
ejpam-5546	141	19	,	,	PUNCT
ejpam-5546	141	20	x02	x02	PROPN
ejpam-5546	141	21	,	,	PUNCT
ejpam-5546	141	22	x13	x13	PROPN
ejpam-5546	141	23	,	,	PUNCT
ejpam-5546	141	24	x31	x31	PROPN
ejpam-5546	141	25	,	,	PUNCT
ejpam-5546	141	26	x01	x01	PROPN
ejpam-5546	141	27	,	,	PUNCT
ejpam-5546	141	28	x30	x30	PROPN
ejpam-5546	141	29	,	,	PUNCT
ejpam-5546	141	30	x12	x12	NUM
ejpam-5546	141	31	,	,	PUNCT
ejpam-5546	141	32	x23	x23	NUM
ejpam-5546	141	33	}	}	PUNCT
ejpam-5546	141	34	with	with	ADP
ejpam-5546	141	35	relations	relation	NOUN
ejpam-5546	141	36	as	as	ADP
ejpam-5546	141	37	in	in	ADP
ejpam-5546	141	38	definition	definition	NOUN
ejpam-5546	141	39	3	3	NUM
ejpam-5546	141	40	.	.	PUNCT
ejpam-5546	142	1	let	let	VERB
ejpam-5546	142	2	s	s	PRON
ejpam-5546	142	3	=	=	SYM
ejpam-5546	142	4	{	{	PUNCT
ejpam-5546	142	5	x20	x20	PROPN
ejpam-5546	142	6	,	,	PUNCT
ejpam-5546	142	7	x02	x02	PROPN
ejpam-5546	142	8	,	,	PUNCT
ejpam-5546	142	9	x13	x13	PROPN
ejpam-5546	142	10	,	,	PUNCT
ejpam-5546	142	11	x31	x31	PROPN
ejpam-5546	142	12	}	}	PUNCT
ejpam-5546	142	13	,	,	PUNCT
ejpam-5546	142	14	and	and	CCONJ
ejpam-5546	142	15	let	let	VERB
ejpam-5546	142	16	{	{	PUNCT
ejpam-5546	142	17	a1	a1	PROPN
ejpam-5546	142	18	,	,	PUNCT
ejpam-5546	142	19	a2	a2	PROPN
ejpam-5546	142	20	,	,	PUNCT
ejpam-5546	142	21	a3	a3	NOUN
ejpam-5546	142	22	,	,	PUNCT
ejpam-5546	142	23	a4	a4	NOUN
ejpam-5546	142	24	}	}	PUNCT
ejpam-5546	142	25	=	=	SYM
ejpam-5546	142	26	{	{	PUNCT
ejpam-5546	142	27	x01	x01	PROPN
ejpam-5546	142	28	,	,	PUNCT
ejpam-5546	142	29	x30	x30	PROPN
ejpam-5546	142	30	,	,	PUNCT
ejpam-5546	142	31	x12	x12	NUM
ejpam-5546	142	32	,	,	PUNCT
ejpam-5546	142	33	x23	x23	NUM
ejpam-5546	142	34	}	}	PUNCT
ejpam-5546	142	35	.	.	PUNCT
ejpam-5546	143	1	in	in	ADP
ejpam-5546	143	2	this	this	DET
ejpam-5546	143	3	paper	paper	NOUN
ejpam-5546	143	4	we	we	PRON
ejpam-5546	143	5	show	show	VERB
ejpam-5546	143	6	that	that	SCONJ
ejpam-5546	143	7	for	for	ADP
ejpam-5546	143	8	each	each	DET
ejpam-5546	143	9	b	b	PROPN
ejpam-5546	143	10	∈	∈	PROPN
ejpam-5546	143	11	s	s	PART
ejpam-5546	143	12	,	,	PUNCT
ejpam-5546	143	13	we	we	PRON
ejpam-5546	143	14	can	can	AUX
ejpam-5546	143	15	find	find	VERB
ejpam-5546	143	16	a	a	DET
ejpam-5546	143	17	=	=	SYM
ejpam-5546	143	18	aa1	aa1	PROPN
ejpam-5546	143	19	+	+	X
ejpam-5546	143	20	ba2	ba2	PROPN
ejpam-5546	143	21	such	such	ADJ
ejpam-5546	143	22	that	that	SCONJ
ejpam-5546	143	23	the	the	DET
ejpam-5546	143	24	pairs	pair	NOUN
ejpam-5546	143	25	a	a	DET
ejpam-5546	143	26	,	,	PUNCT
ejpam-5546	143	27	b	b	NOUN
ejpam-5546	143	28	,	,	PUNCT
ejpam-5546	143	29	a	a	DET
ejpam-5546	143	30	,	,	PUNCT
ejpam-5546	143	31	a3	a3	NOUN
ejpam-5546	143	32	,	,	PUNCT
ejpam-5546	143	33	and	and	CCONJ
ejpam-5546	143	34	a	a	DET
ejpam-5546	143	35	,	,	PUNCT
ejpam-5546	143	36	a4	a4	NOUN
ejpam-5546	143	37	are	be	AUX
ejpam-5546	143	38	leonard	leonard	NOUN
ejpam-5546	143	39	pairs	pair	NOUN
ejpam-5546	143	40	.	.	PUNCT
ejpam-5546	144	1	before	before	SCONJ
ejpam-5546	144	2	we	we	PRON
ejpam-5546	144	3	start	start	VERB
ejpam-5546	144	4	proving	prove	VERB
ejpam-5546	144	5	our	our	PRON
ejpam-5546	144	6	result	result	NOUN
ejpam-5546	144	7	,	,	PUNCT
ejpam-5546	144	8	we	we	PRON
ejpam-5546	144	9	recall	recall	VERB
ejpam-5546	144	10	the	the	DET
ejpam-5546	144	11	following	following	ADJ
ejpam-5546	144	12	lemmas	lemma	NOUN
ejpam-5546	144	13	which	which	PRON
ejpam-5546	144	14	will	will	AUX
ejpam-5546	144	15	help	help	VERB
ejpam-5546	144	16	us	we	PRON
ejpam-5546	144	17	in	in	ADP
ejpam-5546	144	18	our	our	PRON
ejpam-5546	144	19	work	work	NOUN
ejpam-5546	144	20	.	.	PUNCT
ejpam-5546	145	1	lemma	lemma	PROPN
ejpam-5546	145	2	2	2	NUM
ejpam-5546	145	3	.	.	PUNCT
ejpam-5546	146	1	[	[	X
ejpam-5546	146	2	4	4	X
ejpam-5546	146	3	]	]	PUNCT
ejpam-5546	146	4	pick	pick	VERB
ejpam-5546	146	5	an	an	DET
ejpam-5546	146	6	integer	integer	NOUN
ejpam-5546	146	7	d	d	NOUN
ejpam-5546	146	8	⩾	⩾	PROPN
ejpam-5546	146	9	1	1	NUM
ejpam-5546	146	10	and	and	CCONJ
ejpam-5546	146	11	a	a	DET
ejpam-5546	146	12	nonzero	nonzero	NOUN
ejpam-5546	146	13	t	t	PROPN
ejpam-5546	146	14	∈	∈	PROPN
ejpam-5546	146	15	f	f	PROPN
ejpam-5546	146	16	that	that	PRON
ejpam-5546	146	17	is	be	AUX
ejpam-5546	146	18	not	not	PART
ejpam-5546	146	19	among	among	ADP
ejpam-5546	146	20	{	{	PUNCT
ejpam-5546	146	21	qd−2n+1}dn=1	qd−2n+1}dn=1	PROPN
ejpam-5546	146	22	.	.	PUNCT
ejpam-5546	147	1	then	then	ADV
ejpam-5546	147	2	there	there	PRON
ejpam-5546	147	3	exists	exist	VERB
ejpam-5546	147	4	an	an	DET
ejpam-5546	147	5	evaluation	evaluation	NOUN
ejpam-5546	147	6	module	module	NOUN
ejpam-5546	147	7	vd(t	vd(t	NUM
ejpam-5546	147	8	)	)	PUNCT
ejpam-5546	147	9	for	for	ADP
ejpam-5546	147	10	⊠q	⊠q	NUM
ejpam-5546	147	11	such	such	ADJ
ejpam-5546	147	12	that	that	PRON
ejpam-5546	147	13	vd(t	vd(t	NUM
ejpam-5546	147	14	)	)	PUNCT
ejpam-5546	147	15	has	have	VERB
ejpam-5546	147	16	a	a	DET
ejpam-5546	147	17	basis	basis	NOUN
ejpam-5546	147	18	s	s	PART
ejpam-5546	147	19	=	=	PUNCT
ejpam-5546	148	1	[	[	X
ejpam-5546	148	2	3	3	NUM
ejpam-5546	148	3	,	,	PUNCT
ejpam-5546	148	4	2	2	NUM
ejpam-5546	148	5	,	,	PUNCT
ejpam-5546	148	6	0	0	NUM
ejpam-5546	148	7	,	,	PUNCT
ejpam-5546	148	8	1	1	NUM
ejpam-5546	148	9	]	]	PUNCT
ejpam-5546	148	10	for	for	ADP
ejpam-5546	148	11	which	which	PRON
ejpam-5546	148	12	the	the	DET
ejpam-5546	148	13	matrices	matrix	NOUN
ejpam-5546	148	14	represent	represent	VERB
ejpam-5546	148	15	x20	x20	NOUN
ejpam-5546	148	16	,	,	PUNCT
ejpam-5546	148	17	x01	x01	PROPN
ejpam-5546	148	18	,	,	PUNCT
ejpam-5546	148	19	x12	x12	NUM
ejpam-5546	148	20	,	,	PUNCT
ejpam-5546	148	21	and	and	CCONJ
ejpam-5546	148	22	x30	x30	NUM
ejpam-5546	148	23	are	be	AUX
ejpam-5546	148	24	eq	eq	ADP
ejpam-5546	148	25	,	,	PUNCT
ejpam-5546	148	26	kq	kq	PROPN
ejpam-5546	148	27	,	,	PUNCT
ejpam-5546	148	28	zeq−1z	zeq−1z	PROPN
ejpam-5546	148	29	,	,	PUNCT
ejpam-5546	148	30	and	and	CCONJ
ejpam-5546	148	31	gq(t	gq(t	X
ejpam-5546	148	32	)	)	PUNCT
ejpam-5546	148	33	respectively	respectively	ADV
ejpam-5546	148	34	.	.	PUNCT
ejpam-5546	149	1	the	the	DET
ejpam-5546	149	2	entries	entry	NOUN
ejpam-5546	149	3	of	of	ADP
ejpam-5546	149	4	the	the	DET
ejpam-5546	149	5	matrix	matrix	NOUN
ejpam-5546	149	6	eq−1	eq−1	NOUN
ejpam-5546	149	7	is	be	AUX
ejpam-5546	149	8	given	give	VERB
ejpam-5546	149	9	in	in	ADP
ejpam-5546	149	10	definition	definition	NOUN
ejpam-5546	149	11	6	6	NUM
ejpam-5546	149	12	,	,	PUNCT
ejpam-5546	149	13	the	the	DET
ejpam-5546	149	14	entries	entry	NOUN
ejpam-5546	149	15	of	of	ADP
ejpam-5546	149	16	zeq−1z	zeq−1z	NOUN
ejpam-5546	149	17	can	can	AUX
ejpam-5546	149	18	be	be	AUX
ejpam-5546	149	19	found	find	VERB
ejpam-5546	149	20	using	use	VERB
ejpam-5546	149	21	the	the	DET
ejpam-5546	149	22	following	follow	VERB
ejpam-5546	149	23	lemma	lemma	PROPN
ejpam-5546	149	24	.	.	PUNCT
ejpam-5546	150	1	lemma	lemma	PROPN
ejpam-5546	150	2	3	3	NUM
ejpam-5546	150	3	.	.	PUNCT
ejpam-5546	151	1	[	[	X
ejpam-5546	151	2	4	4	X
ejpam-5546	151	3	]	]	PUNCT
ejpam-5546	151	4	for	for	ADP
ejpam-5546	151	5	c	c	PROPN
ejpam-5546	151	6	∈	∈	PROPN
ejpam-5546	151	7	matd+1(f	matd+1(f	PROPN
ejpam-5546	151	8	)	)	PUNCT
ejpam-5546	151	9	and	and	CCONJ
ejpam-5546	151	10	0	0	NUM
ejpam-5546	151	11	⩽	⩽	PROPN
ejpam-5546	151	12	i	i	PROPN
ejpam-5546	151	13	,	,	PUNCT
ejpam-5546	151	14	j	j	PROPN
ejpam-5546	151	15	⩽	⩽	PROPN
ejpam-5546	152	1	d	d	PROPN
ejpam-5546	152	2	the	the	DET
ejpam-5546	152	3	following	follow	VERB
ejpam-5546	152	4	coincide	coincide	NOUN
ejpam-5546	152	5	(	(	PUNCT
ejpam-5546	152	6	i	i	NOUN
ejpam-5546	152	7	)	)	PUNCT
ejpam-5546	152	8	the	the	DET
ejpam-5546	152	9	entry	entry	NOUN
ejpam-5546	152	10	(	(	PUNCT
ejpam-5546	152	11	i	i	PROPN
ejpam-5546	152	12	,	,	PUNCT
ejpam-5546	152	13	j	j	PROPN
ejpam-5546	152	14	)	)	PUNCT
ejpam-5546	152	15	of	of	ADP
ejpam-5546	152	16	zcz	zcz	PROPN
ejpam-5546	152	17	,	,	PUNCT
ejpam-5546	152	18	(	(	PUNCT
ejpam-5546	152	19	ii	ii	NOUN
ejpam-5546	152	20	)	)	PUNCT
ejpam-5546	152	21	the	the	DET
ejpam-5546	152	22	entry	entry	NOUN
ejpam-5546	152	23	(	(	PUNCT
ejpam-5546	152	24	d−	d−	PROPN
ejpam-5546	152	25	i	i	PROPN
ejpam-5546	152	26	,	,	PUNCT
ejpam-5546	152	27	d−	d−	PROPN
ejpam-5546	152	28	j	j	PROPN
ejpam-5546	152	29	)	)	PUNCT
ejpam-5546	152	30	of	of	ADP
ejpam-5546	152	31	c.	c.	PROPN
ejpam-5546	152	32	lemma	lemma	PROPN
ejpam-5546	153	1	4	4	NUM
ejpam-5546	153	2	.	.	PUNCT
ejpam-5546	154	1	[	[	X
ejpam-5546	154	2	4	4	X
ejpam-5546	154	3	]	]	PUNCT
ejpam-5546	154	4	let	let	VERB
ejpam-5546	154	5	v	v	PART
ejpam-5546	154	6	denote	denote	VERB
ejpam-5546	154	7	an	an	DET
ejpam-5546	154	8	evaluation	evaluation	NOUN
ejpam-5546	154	9	module	module	NOUN
ejpam-5546	154	10	for	for	ADP
ejpam-5546	154	11	⊠q	⊠q	PROPN
ejpam-5546	154	12	that	that	PRON
ejpam-5546	154	13	has	have	VERB
ejpam-5546	154	14	diameter	diameter	NOUN
ejpam-5546	154	15	d.	d.	PROPN
ejpam-5546	154	16	then	then	ADV
ejpam-5546	154	17	there	there	PRON
ejpam-5546	154	18	exists	exist	VERB
ejpam-5546	154	19	a	a	DET
ejpam-5546	154	20	unique	unique	ADJ
ejpam-5546	154	21	t	t	NOUN
ejpam-5546	154	22	∈	∈	NOUN
ejpam-5546	154	23	f	f	PROPN
ejpam-5546	154	24	such	such	ADJ
ejpam-5546	154	25	that	that	PRON
ejpam-5546	154	26	:	:	PUNCT
ejpam-5546	154	27	(	(	PUNCT
ejpam-5546	154	28	i	i	NOUN
ejpam-5546	154	29	)	)	PUNCT
ejpam-5546	154	30	t	t	PROPN
ejpam-5546	154	31	is	be	AUX
ejpam-5546	154	32	a	a	DET
ejpam-5546	154	33	nonzero	nonzero	NOUN
ejpam-5546	154	34	and	and	CCONJ
ejpam-5546	154	35	not	not	PART
ejpam-5546	154	36	among	among	ADP
ejpam-5546	154	37	{	{	PUNCT
ejpam-5546	154	38	qd−2n+1}dn=1	qd−2n+1}dn=1	PROPN
ejpam-5546	154	39	.	.	PUNCT
ejpam-5546	155	1	(	(	PUNCT
ejpam-5546	155	2	ii	ii	NOUN
ejpam-5546	155	3	)	)	PUNCT
ejpam-5546	155	4	the	the	DET
ejpam-5546	155	5	⊠q	⊠q	NOUN
ejpam-5546	155	6	-	-	PUNCT
ejpam-5546	155	7	module	module	NOUN
ejpam-5546	155	8	v	v	NOUN
ejpam-5546	155	9	is	be	AUX
ejpam-5546	155	10	isomorphic	isomorphic	ADJ
ejpam-5546	155	11	to	to	ADP
ejpam-5546	155	12	vd(t	vd(t	NUM
ejpam-5546	155	13	)	)	PUNCT
ejpam-5546	155	14	.	.	PUNCT
ejpam-5546	156	1	h.	h.	PROPN
ejpam-5546	156	2	alnajjar	alnajjar	PROPN
ejpam-5546	156	3	/	/	SYM
ejpam-5546	156	4	eur	eur	PROPN
ejpam-5546	156	5	.	.	PUNCT
ejpam-5546	157	1	j.	j.	PROPN
ejpam-5546	157	2	pure	pure	PROPN
ejpam-5546	157	3	appl	appl	PROPN
ejpam-5546	157	4	.	.	PROPN
ejpam-5546	157	5	math	math	PROPN
ejpam-5546	157	6	,	,	PUNCT
ejpam-5546	157	7	18	18	NUM
ejpam-5546	157	8	(	(	PUNCT
ejpam-5546	157	9	1	1	NUM
ejpam-5546	157	10	)	)	PUNCT
ejpam-5546	157	11	(	(	PUNCT
ejpam-5546	157	12	2025	2025	NUM
ejpam-5546	157	13	)	)	PUNCT
ejpam-5546	157	14	,	,	PUNCT
ejpam-5546	157	15	5546	5546	NUM
ejpam-5546	157	16	6	6	NUM
ejpam-5546	157	17	of	of	ADP
ejpam-5546	157	18	14	14	NUM
ejpam-5546	157	19	for	for	ADP
ejpam-5546	157	20	the	the	DET
ejpam-5546	157	21	rest	rest	NOUN
ejpam-5546	157	22	of	of	ADP
ejpam-5546	157	23	the	the	DET
ejpam-5546	157	24	paper	paper	NOUN
ejpam-5546	157	25	we	we	PRON
ejpam-5546	157	26	use	use	VERB
ejpam-5546	157	27	v	v	NOUN
ejpam-5546	157	28	to	to	AUX
ejpam-5546	157	29	represents	represent	VERB
ejpam-5546	157	30	vd(t	vd(t	NOUN
ejpam-5546	157	31	)	)	PUNCT
ejpam-5546	157	32	,	,	PUNCT
ejpam-5546	157	33	and	and	CCONJ
ejpam-5546	157	34	t	t	PROPN
ejpam-5546	157	35	will	will	AUX
ejpam-5546	157	36	be	be	AUX
ejpam-5546	157	37	a	a	DET
ejpam-5546	157	38	nonzero	nonzero	NOUN
ejpam-5546	157	39	and	and	CCONJ
ejpam-5546	157	40	not	not	PART
ejpam-5546	157	41	among	among	ADP
ejpam-5546	157	42	{	{	PUNCT
ejpam-5546	157	43	qd−2n+1}dn=1	qd−2n+1}dn=1	NOUN
ejpam-5546	157	44	scalar	scalar	ADV
ejpam-5546	157	45	in	in	ADP
ejpam-5546	157	46	f	f	PROPN
ejpam-5546	157	47	.	.	PUNCT
ejpam-5546	158	1	we	we	PRON
ejpam-5546	158	2	now	now	ADV
ejpam-5546	158	3	start	start	VERB
ejpam-5546	158	4	proving	prove	VERB
ejpam-5546	158	5	the	the	DET
ejpam-5546	158	6	our	our	PRON
ejpam-5546	158	7	result	result	NOUN
ejpam-5546	158	8	.	.	PUNCT
ejpam-5546	159	1	definition	definition	NOUN
ejpam-5546	159	2	7	7	NUM
ejpam-5546	159	3	.	.	PUNCT
ejpam-5546	160	1	let	let	VERB
ejpam-5546	160	2	a	a	DET
ejpam-5546	160	3	∈	∈	PROPN
ejpam-5546	160	4	⊠q	⊠q	PROPN
ejpam-5546	160	5	denote	denote	VERB
ejpam-5546	160	6	a	a	DET
ejpam-5546	160	7	linear	linear	ADJ
ejpam-5546	160	8	combination	combination	NOUN
ejpam-5546	160	9	of	of	ADP
ejpam-5546	160	10	x01	x01	PROPN
ejpam-5546	160	11	,	,	PUNCT
ejpam-5546	160	12	x12	x12	PROPN
ejpam-5546	160	13	.	.	PUNCT
ejpam-5546	161	1	write	write	VERB
ejpam-5546	161	2	a	a	DET
ejpam-5546	161	3	=	=	SYM
ejpam-5546	161	4	ax01	ax01	PROPN
ejpam-5546	161	5	+	+	CCONJ
ejpam-5546	161	6	bx12	bx12	PROPN
ejpam-5546	161	7	.	.	PROPN
ejpam-5546	162	1	for	for	ADP
ejpam-5546	162	2	the	the	DET
ejpam-5546	162	3	rest	rest	NOUN
ejpam-5546	162	4	of	of	ADP
ejpam-5546	162	5	the	the	DET
ejpam-5546	162	6	article	article	NOUN
ejpam-5546	162	7	,	,	PUNCT
ejpam-5546	162	8	by	by	ADP
ejpam-5546	162	9	the	the	DET
ejpam-5546	162	10	notation	notation	NOUN
ejpam-5546	162	11	[	[	X
ejpam-5546	162	12	t	t	X
ejpam-5546	162	13	]	]	X
ejpam-5546	162	14	s	s	X
ejpam-5546	162	15	we	we	PRON
ejpam-5546	162	16	mean	mean	VERB
ejpam-5546	162	17	the	the	DET
ejpam-5546	162	18	matrix	matrix	NOUN
ejpam-5546	162	19	that	that	PRON
ejpam-5546	162	20	represents	represent	VERB
ejpam-5546	162	21	the	the	DET
ejpam-5546	162	22	linear	linear	ADJ
ejpam-5546	162	23	map	map	NOUN
ejpam-5546	162	24	t	t	NOUN
ejpam-5546	162	25	:	:	PUNCT
ejpam-5546	162	26	v	v	PROPN
ejpam-5546	162	27	→	→	SYM
ejpam-5546	162	28	v	v	NOUN
ejpam-5546	162	29	with	with	ADP
ejpam-5546	162	30	respect	respect	NOUN
ejpam-5546	162	31	to	to	ADP
ejpam-5546	162	32	the	the	DET
ejpam-5546	162	33	basis	basis	NOUN
ejpam-5546	162	34	s	s	NOUN
ejpam-5546	162	35	of	of	ADP
ejpam-5546	162	36	v	v	NOUN
ejpam-5546	162	37	.	.	PUNCT
ejpam-5546	163	1	lemma	lemma	PROPN
ejpam-5546	163	2	5	5	NUM
ejpam-5546	163	3	.	.	PUNCT
ejpam-5546	164	1	with	with	ADP
ejpam-5546	164	2	reference	reference	NOUN
ejpam-5546	164	3	to	to	ADP
ejpam-5546	164	4	lemma	lemma	PROPN
ejpam-5546	164	5	2	2	NUM
ejpam-5546	164	6	and	and	CCONJ
ejpam-5546	164	7	definition	definition	NOUN
ejpam-5546	164	8	7	7	NUM
ejpam-5546	164	9	,	,	PUNCT
ejpam-5546	164	10	let	let	VERB
ejpam-5546	164	11	b1	b1	NOUN
ejpam-5546	164	12	=	=	SYM
ejpam-5546	164	13	x20	x20	PROPN
ejpam-5546	164	14	.	.	PUNCT
ejpam-5546	165	1	then	then	ADV
ejpam-5546	165	2	the	the	DET
ejpam-5546	165	3	matrices	matrix	NOUN
ejpam-5546	165	4	represent	represent	VERB
ejpam-5546	165	5	a	a	PRON
ejpam-5546	165	6	and	and	CCONJ
ejpam-5546	165	7	b1	b1	VERB
ejpam-5546	165	8	with	with	ADP
ejpam-5546	165	9	respect	respect	NOUN
ejpam-5546	165	10	to	to	ADP
ejpam-5546	165	11	the	the	DET
ejpam-5546	165	12	basis	basis	NOUN
ejpam-5546	165	13	s	s	NOUN
ejpam-5546	165	14	are	be	AUX
ejpam-5546	165	15	lower	low	ADJ
ejpam-5546	165	16	bidiagonal	bidiagonal	ADJ
ejpam-5546	165	17	and	and	CCONJ
ejpam-5546	165	18	upper	upper	ADJ
ejpam-5546	165	19	bidiagonal	bidiagonal	NOUN
ejpam-5546	165	20	respectively	respectively	ADV
ejpam-5546	165	21	with	with	ADP
ejpam-5546	165	22	entries	entry	NOUN
ejpam-5546	165	23	:	:	PUNCT
ejpam-5546	165	24	[	[	X
ejpam-5546	165	25	a]s(i	a]s(i	NOUN
ejpam-5546	165	26	,	,	PUNCT
ejpam-5546	165	27	i	i	NOUN
ejpam-5546	165	28	)	)	PUNCT
ejpam-5546	165	29	=	=	PUNCT
ejpam-5546	166	1	aqd−2i	aqd−2i	NOUN
ejpam-5546	167	1	+	+	CCONJ
ejpam-5546	167	2	bq2i−d	bq2i−d	NOUN
ejpam-5546	167	3	(	(	PUNCT
ejpam-5546	167	4	0	0	NUM
ejpam-5546	167	5	≤	≤	NUM
ejpam-5546	167	6	i	i	NOUN
ejpam-5546	167	7	≤	≤	NUM
ejpam-5546	168	1	d	d	X
ejpam-5546	168	2	)	)	PUNCT
ejpam-5546	168	3	,	,	PUNCT
ejpam-5546	169	1	[	[	X
ejpam-5546	169	2	b1]s(i	b1]s(i	PROPN
ejpam-5546	169	3	,	,	PUNCT
ejpam-5546	169	4	i	i	NOUN
ejpam-5546	169	5	)	)	PUNCT
ejpam-5546	169	6	=	=	PUNCT
ejpam-5546	169	7	q2i−d	q2i−d	PROPN
ejpam-5546	169	8	(	(	PUNCT
ejpam-5546	169	9	0	0	NUM
ejpam-5546	169	10	≤	≤	NUM
ejpam-5546	170	1	i	i	NOUN
ejpam-5546	170	2	≤	≤	NUM
ejpam-5546	171	1	d	d	X
ejpam-5546	171	2	)	)	PUNCT
ejpam-5546	171	3	,	,	PUNCT
ejpam-5546	172	1	[	[	X
ejpam-5546	172	2	a]s(i	a]s(i	NOUN
ejpam-5546	172	3	,	,	PUNCT
ejpam-5546	172	4	i−	i−	PROPN
ejpam-5546	172	5	1	1	NUM
ejpam-5546	172	6	)	)	PUNCT
ejpam-5546	172	7	=	=	PUNCT
ejpam-5546	172	8	bq−d(1−	bq−d(1−	PROPN
ejpam-5546	172	9	q2i	q2i	PROPN
ejpam-5546	172	10	)	)	PUNCT
ejpam-5546	172	11	(	(	PUNCT
ejpam-5546	172	12	1	1	NUM
ejpam-5546	172	13	≤	≤	NUM
ejpam-5546	172	14	i	i	X
ejpam-5546	172	15	≤	≤	NUM
ejpam-5546	173	1	d	d	X
ejpam-5546	173	2	)	)	PUNCT
ejpam-5546	173	3	,	,	PUNCT
ejpam-5546	173	4	[	[	X
ejpam-5546	173	5	b1]s(i−	b1]s(i−	NOUN
ejpam-5546	173	6	1	1	NUM
ejpam-5546	173	7	,	,	PUNCT
ejpam-5546	173	8	i	i	NOUN
ejpam-5546	173	9	)	)	PUNCT
ejpam-5546	174	1	=	=	SYM
ejpam-5546	174	2	qd(1−	qd(1−	ADJ
ejpam-5546	174	3	q2i−2d−2	q2i−2d−2	NOUN
ejpam-5546	174	4	)	)	PUNCT
ejpam-5546	174	5	(	(	PUNCT
ejpam-5546	174	6	1	1	NUM
ejpam-5546	174	7	≤	≤	NUM
ejpam-5546	174	8	i	i	X
ejpam-5546	174	9	≤	≤	NUM
ejpam-5546	175	1	d	d	X
ejpam-5546	175	2	)	)	PUNCT
ejpam-5546	175	3	.	.	PUNCT
ejpam-5546	176	1	proof	proof	NOUN
ejpam-5546	176	2	.	.	PUNCT
ejpam-5546	177	1	the	the	DET
ejpam-5546	177	2	matrices	matrix	NOUN
ejpam-5546	177	3	that	that	PRON
ejpam-5546	177	4	represent	represent	VERB
ejpam-5546	177	5	the	the	DET
ejpam-5546	177	6	action	action	NOUN
ejpam-5546	177	7	of	of	ADP
ejpam-5546	177	8	x01	x01	PROPN
ejpam-5546	177	9	,	,	PUNCT
ejpam-5546	177	10	x12	x12	NUM
ejpam-5546	177	11	and	and	CCONJ
ejpam-5546	177	12	x20	x20	NOUN
ejpam-5546	177	13	are	be	AUX
ejpam-5546	177	14	given	give	VERB
ejpam-5546	177	15	in	in	ADP
ejpam-5546	177	16	lemma	lemma	PROPN
ejpam-5546	177	17	2	2	NUM
ejpam-5546	177	18	,	,	PUNCT
ejpam-5546	177	19	and	and	CCONJ
ejpam-5546	177	20	the	the	DET
ejpam-5546	177	21	entries	entry	NOUN
ejpam-5546	177	22	of	of	ADP
ejpam-5546	177	23	these	these	DET
ejpam-5546	177	24	matrices	matrix	NOUN
ejpam-5546	177	25	are	be	AUX
ejpam-5546	177	26	given	give	VERB
ejpam-5546	177	27	in	in	ADP
ejpam-5546	177	28	definition	definition	NOUN
ejpam-5546	177	29	6	6	NUM
ejpam-5546	177	30	.	.	PUNCT
ejpam-5546	178	1	definition	definition	NOUN
ejpam-5546	178	2	8	8	NUM
ejpam-5546	178	3	.	.	PUNCT
ejpam-5546	179	1	with	with	ADP
ejpam-5546	179	2	reference	reference	NOUN
ejpam-5546	179	3	to	to	ADP
ejpam-5546	179	4	lemma	lemma	PROPN
ejpam-5546	179	5	5	5	NUM
ejpam-5546	179	6	,	,	PUNCT
ejpam-5546	179	7	define	define	VERB
ejpam-5546	179	8	αi	αi	NOUN
ejpam-5546	179	9	=	=	PUNCT
ejpam-5546	180	1	aqd−2i	aqd−2i	PRON
ejpam-5546	181	1	+	+	CCONJ
ejpam-5546	181	2	bq2i−d	bq2i−d	NOUN
ejpam-5546	181	3	(	(	PUNCT
ejpam-5546	181	4	0	0	NUM
ejpam-5546	181	5	≤	≤	NUM
ejpam-5546	181	6	i	i	NOUN
ejpam-5546	181	7	≤	≤	NUM
ejpam-5546	182	1	d	d	X
ejpam-5546	182	2	)	)	PUNCT
ejpam-5546	182	3	,	,	PUNCT
ejpam-5546	182	4	α∗	α∗	VERB
ejpam-5546	182	5	i	i	PRON
ejpam-5546	182	6	=	=	PUNCT
ejpam-5546	183	1	q2i−d	q2i−d	PROPN
ejpam-5546	183	2	(	(	PUNCT
ejpam-5546	183	3	0	0	NUM
ejpam-5546	183	4	≤	≤	NUM
ejpam-5546	183	5	i	i	NOUN
ejpam-5546	184	1	≤	≤	NUM
ejpam-5546	184	2	d	d	X
ejpam-5546	184	3	)	)	PUNCT
ejpam-5546	184	4	,	,	PUNCT
ejpam-5546	184	5	φi	φi	ADP
ejpam-5546	184	6	=	=	PUNCT
ejpam-5546	184	7	b(q2i	b(q2i	NOUN
ejpam-5546	184	8	−	−	PROPN
ejpam-5546	184	9	1)(q2i−2d−2	1)(q2i−2d−2	NUM
ejpam-5546	184	10	−	−	NOUN
ejpam-5546	184	11	1	1	NUM
ejpam-5546	184	12	)	)	PUNCT
ejpam-5546	184	13	(	(	PUNCT
ejpam-5546	184	14	1	1	NUM
ejpam-5546	184	15	≤	≤	NUM
ejpam-5546	184	16	i	i	X
ejpam-5546	185	1	≤	≤	NUM
ejpam-5546	185	2	d	d	X
ejpam-5546	185	3	)	)	PUNCT
ejpam-5546	185	4	,	,	PUNCT
ejpam-5546	185	5	ϕi	ϕi	ADP
ejpam-5546	185	6	=	=	PUNCT
ejpam-5546	185	7	a(q2i	a(q2i	NOUN
ejpam-5546	185	8	−	−	PROPN
ejpam-5546	185	9	1)(q2i−2d−2	1)(q2i−2d−2	NUM
ejpam-5546	185	10	−	−	NOUN
ejpam-5546	185	11	1	1	NUM
ejpam-5546	185	12	)	)	PUNCT
ejpam-5546	185	13	(	(	PUNCT
ejpam-5546	185	14	1	1	NUM
ejpam-5546	185	15	≤	≤	NUM
ejpam-5546	185	16	i	i	X
ejpam-5546	185	17	≤	≤	NUM
ejpam-5546	185	18	d	d	X
ejpam-5546	185	19	)	)	PUNCT
ejpam-5546	185	20	note	note	NOUN
ejpam-5546	185	21	that	that	SCONJ
ejpam-5546	185	22	αi	αi	VERB
ejpam-5546	185	23	=	=	PUNCT
ejpam-5546	186	1	[	[	X
ejpam-5546	186	2	a]s(i	a]s(i	PRON
ejpam-5546	186	3	,	,	PUNCT
ejpam-5546	186	4	i	i	PROPN
ejpam-5546	186	5	)	)	PUNCT
ejpam-5546	186	6	,	,	PUNCT
ejpam-5546	186	7	α	α	NOUN
ejpam-5546	186	8	∗	∗	NOUN
ejpam-5546	186	9	i	i	PRON
ejpam-5546	186	10	=	=	PUNCT
ejpam-5546	187	1	[	[	X
ejpam-5546	187	2	b1]s(i	b1]s(i	PROPN
ejpam-5546	187	3	,	,	PUNCT
ejpam-5546	187	4	i	i	PROPN
ejpam-5546	187	5	)	)	PUNCT
ejpam-5546	187	6	for	for	ADP
ejpam-5546	187	7	(	(	PUNCT
ejpam-5546	187	8	0	0	NUM
ejpam-5546	187	9	≤	≤	NUM
ejpam-5546	188	1	i	i	NOUN
ejpam-5546	188	2	≤	≤	NUM
ejpam-5546	189	1	d	d	NOUN
ejpam-5546	189	2	)	)	PUNCT
ejpam-5546	189	3	,	,	PUNCT
ejpam-5546	189	4	and	and	CCONJ
ejpam-5546	189	5	φi	φi	ADP
ejpam-5546	189	6	=	=	X
ejpam-5546	190	1	[	[	X
ejpam-5546	190	2	a]s(i	a]s(i	NOUN
ejpam-5546	190	3	,	,	PUNCT
ejpam-5546	190	4	i−1)[b1]s(i−	i−1)[b1]s(i−	VERB
ejpam-5546	190	5	1	1	NUM
ejpam-5546	190	6	,	,	PUNCT
ejpam-5546	190	7	i	i	NOUN
ejpam-5546	190	8	)	)	PUNCT
ejpam-5546	190	9	for	for	ADP
ejpam-5546	190	10	(	(	PUNCT
ejpam-5546	190	11	1	1	NUM
ejpam-5546	190	12	≤	≤	NUM
ejpam-5546	190	13	i	i	X
ejpam-5546	190	14	≤	≤	NUM
ejpam-5546	191	1	d	d	X
ejpam-5546	191	2	)	)	PUNCT
ejpam-5546	191	3	.	.	PUNCT
ejpam-5546	192	1	now	now	ADV
ejpam-5546	192	2	,	,	PUNCT
ejpam-5546	192	3	by	by	ADP
ejpam-5546	192	4	theorem	theorem	NOUN
ejpam-5546	192	5	1	1	NUM
ejpam-5546	192	6	,	,	PUNCT
ejpam-5546	192	7	if	if	SCONJ
ejpam-5546	192	8	we	we	PRON
ejpam-5546	192	9	find	find	VERB
ejpam-5546	192	10	the	the	DET
ejpam-5546	192	11	conditions	condition	NOUN
ejpam-5546	192	12	on	on	ADP
ejpam-5546	192	13	the	the	DET
ejpam-5546	192	14	sequence	sequence	NOUN
ejpam-5546	192	15	of	of	ADP
ejpam-5546	192	16	scalars	scalar	NOUN
ejpam-5546	192	17	(	(	PUNCT
ejpam-5546	192	18	{	{	PUNCT
ejpam-5546	192	19	αi}di=0	αi}di=0	NOUN
ejpam-5546	192	20	,	,	PUNCT
ejpam-5546	192	21	{	{	PUNCT
ejpam-5546	192	22	α∗	α∗	NOUN
ejpam-5546	192	23	i	i	PRON
ejpam-5546	192	24	}	}	PUNCT
ejpam-5546	192	25	di=0	di=0	PROPN
ejpam-5546	192	26	;	;	PUNCT
ejpam-5546	192	27	{	{	PUNCT
ejpam-5546	192	28	φj}dj=1	φj}dj=1	NOUN
ejpam-5546	192	29	,	,	PUNCT
ejpam-5546	192	30	{	{	PUNCT
ejpam-5546	192	31	ϕj}dj=1	ϕj}dj=1	PROPN
ejpam-5546	192	32	)	)	PUNCT
ejpam-5546	192	33	in	in	ADP
ejpam-5546	192	34	which	which	PRON
ejpam-5546	192	35	the	the	DET
ejpam-5546	192	36	sequence	sequence	NOUN
ejpam-5546	192	37	is	be	AUX
ejpam-5546	192	38	a	a	DET
ejpam-5546	192	39	parameter	parameter	NOUN
ejpam-5546	192	40	array	array	NOUN
ejpam-5546	192	41	,	,	PUNCT
ejpam-5546	192	42	then	then	ADV
ejpam-5546	192	43	these	these	DET
ejpam-5546	192	44	conditions	condition	NOUN
ejpam-5546	192	45	imply	imply	VERB
ejpam-5546	192	46	that	that	SCONJ
ejpam-5546	192	47	the	the	DET
ejpam-5546	192	48	pair	pair	NOUN
ejpam-5546	192	49	a	a	X
ejpam-5546	192	50	,	,	PUNCT
ejpam-5546	192	51	b1	b1	PROPN
ejpam-5546	192	52	is	be	AUX
ejpam-5546	192	53	a	a	DET
ejpam-5546	192	54	leonard	leonard	NOUN
ejpam-5546	192	55	pair	pair	NOUN
ejpam-5546	192	56	.	.	PUNCT
ejpam-5546	193	1	so	so	ADV
ejpam-5546	193	2	,	,	PUNCT
ejpam-5546	193	3	in	in	ADP
ejpam-5546	193	4	the	the	DET
ejpam-5546	193	5	next	next	ADJ
ejpam-5546	193	6	work	work	NOUN
ejpam-5546	193	7	we	we	PRON
ejpam-5546	193	8	will	will	AUX
ejpam-5546	193	9	find	find	VERB
ejpam-5546	193	10	when	when	SCONJ
ejpam-5546	193	11	the	the	DET
ejpam-5546	193	12	sequence	sequence	NOUN
ejpam-5546	193	13	(	(	PUNCT
ejpam-5546	193	14	{	{	PUNCT
ejpam-5546	193	15	αi}di=0	αi}di=0	NOUN
ejpam-5546	193	16	,	,	PUNCT
ejpam-5546	193	17	{	{	PUNCT
ejpam-5546	193	18	α∗	α∗	NOUN
ejpam-5546	193	19	i	i	PRON
ejpam-5546	193	20	}	}	PUNCT
ejpam-5546	193	21	di=0	di=0	PROPN
ejpam-5546	193	22	;	;	PUNCT
ejpam-5546	193	23	{	{	PUNCT
ejpam-5546	193	24	φj}dj=1	φj}dj=1	NOUN
ejpam-5546	193	25	,	,	PUNCT
ejpam-5546	193	26	{	{	PUNCT
ejpam-5546	193	27	ϕj}dj=1	ϕj}dj=1	NOUN
ejpam-5546	193	28	)	)	PUNCT
ejpam-5546	193	29	satisfies	satisfy	VERB
ejpam-5546	193	30	the	the	DET
ejpam-5546	193	31	conditions	condition	NOUN
ejpam-5546	193	32	1−	1−	NUM
ejpam-5546	193	33	7	7	NUM
ejpam-5546	193	34	in	in	ADP
ejpam-5546	193	35	definition	definition	NOUN
ejpam-5546	193	36	2	2	NUM
ejpam-5546	193	37	.	.	PUNCT
ejpam-5546	194	1	lemma	lemma	PROPN
ejpam-5546	194	2	6	6	NUM
ejpam-5546	194	3	.	.	PUNCT
ejpam-5546	195	1	with	with	ADP
ejpam-5546	195	2	reference	reference	NOUN
ejpam-5546	195	3	to	to	ADP
ejpam-5546	195	4	definition	definition	NOUN
ejpam-5546	195	5	8	8	NUM
ejpam-5546	195	6	,	,	PUNCT
ejpam-5546	195	7	αk	αk	CCONJ
ejpam-5546	195	8	̸=	̸=	PROPN
ejpam-5546	195	9	αi	αi	VERB
ejpam-5546	195	10	for	for	ADP
ejpam-5546	195	11	k	k	PROPN
ejpam-5546	195	12	̸=	̸=	PROPN
ejpam-5546	195	13	i	i	PRON
ejpam-5546	195	14	(	(	PUNCT
ejpam-5546	195	15	0	0	NUM
ejpam-5546	195	16	≤	≤	NOUN
ejpam-5546	195	17	i	i	PRON
ejpam-5546	195	18	,	,	PUNCT
ejpam-5546	196	1	k	k	PROPN
ejpam-5546	196	2	≤	≤	PROPN
ejpam-5546	196	3	d	d	X
ejpam-5546	196	4	)	)	PUNCT
ejpam-5546	196	5	if	if	SCONJ
ejpam-5546	196	6	and	and	CCONJ
ejpam-5546	196	7	only	only	ADV
ejpam-5546	196	8	if	if	SCONJ
ejpam-5546	196	9	a−	a−	PROPN
ejpam-5546	196	10	bq2(h−d	bq2(h−d	NOUN
ejpam-5546	196	11	)	)	PUNCT
ejpam-5546	197	1	̸=	̸=	PROPN
ejpam-5546	197	2	0	0	NUM
ejpam-5546	197	3	for	for	ADP
ejpam-5546	197	4	0	0	NUM
ejpam-5546	197	5	<	<	X
ejpam-5546	197	6	h	h	X
ejpam-5546	197	7	<	<	X
ejpam-5546	197	8	2d	2d	NOUN
ejpam-5546	197	9	.	.	PUNCT
ejpam-5546	198	1	proof	proof	NOUN
ejpam-5546	198	2	.	.	PUNCT
ejpam-5546	199	1	αk	αk	AUX
ejpam-5546	199	2	−	−	PROPN
ejpam-5546	199	3	αi	αi	NOUN
ejpam-5546	199	4	=	=	SYM
ejpam-5546	199	5	a(qd−2k	a(qd−2k	NOUN
ejpam-5546	199	6	−	−	PROPN
ejpam-5546	199	7	qd−2i	qd−2i	NUM
ejpam-5546	199	8	)	)	PUNCT
ejpam-5546	199	9	+	+	CCONJ
ejpam-5546	199	10	b(q2k−d	b(q2k−d	ADV
ejpam-5546	199	11	−	−	NOUN
ejpam-5546	199	12	q2i−d	q2i−d	NOUN
ejpam-5546	199	13	)	)	PUNCT
ejpam-5546	199	14	=	=	PUNCT
ejpam-5546	199	15	aqd−2k(1−	aqd−2k(1−	PROPN
ejpam-5546	199	16	q2(k−i	q2(k−i	PROPN
ejpam-5546	199	17	)	)	PUNCT
ejpam-5546	199	18	)	)	PUNCT
ejpam-5546	200	1	+	+	CCONJ
ejpam-5546	200	2	bq2i−d(q2(k−i	bq2i−d(q2(k−i	NOUN
ejpam-5546	200	3	)	)	PUNCT
ejpam-5546	200	4	−	−	PROPN
ejpam-5546	200	5	1	1	NUM
ejpam-5546	200	6	)	)	PUNCT
ejpam-5546	200	7	=	=	SYM
ejpam-5546	200	8	(	(	PUNCT
ejpam-5546	200	9	1−	1−	NUM
ejpam-5546	200	10	q2(k−i))(aqd−2k	q2(k−i))(aqd−2k	ADJ
ejpam-5546	200	11	−	−	NOUN
ejpam-5546	200	12	bq2i−d	bq2i−d	NOUN
ejpam-5546	200	13	)	)	PUNCT
ejpam-5546	200	14	=	=	PUNCT
ejpam-5546	200	15	qd−2k(1−	qd−2k(1−	VERB
ejpam-5546	200	16	q2(k−i))(a−	q2(k−i))(a−	NOUN
ejpam-5546	200	17	bq2(i+k−d	bq2(i+k−d	NOUN
ejpam-5546	200	18	)	)	PUNCT
ejpam-5546	200	19	)	)	PUNCT
ejpam-5546	201	1	h.	h.	PROPN
ejpam-5546	201	2	alnajjar	alnajjar	PROPN
ejpam-5546	201	3	/	/	SYM
ejpam-5546	201	4	eur	eur	PROPN
ejpam-5546	201	5	.	.	PUNCT
ejpam-5546	202	1	j.	j.	PROPN
ejpam-5546	202	2	pure	pure	PROPN
ejpam-5546	202	3	appl	appl	PROPN
ejpam-5546	202	4	.	.	PROPN
ejpam-5546	202	5	math	math	PROPN
ejpam-5546	202	6	,	,	PUNCT
ejpam-5546	202	7	18	18	NUM
ejpam-5546	202	8	(	(	PUNCT
ejpam-5546	202	9	1	1	NUM
ejpam-5546	202	10	)	)	PUNCT
ejpam-5546	202	11	(	(	PUNCT
ejpam-5546	202	12	2025	2025	NUM
ejpam-5546	202	13	)	)	PUNCT
ejpam-5546	202	14	,	,	PUNCT
ejpam-5546	202	15	5546	5546	NUM
ejpam-5546	202	16	7	7	NUM
ejpam-5546	202	17	of	of	ADP
ejpam-5546	202	18	14	14	NUM
ejpam-5546	202	19	=	=	SYM
ejpam-5546	202	20	qd−2k(1−	qd−2k(1−	VERB
ejpam-5546	202	21	q2(k−i))(a−	q2(k−i))(a−	PROPN
ejpam-5546	202	22	bq2(h−d	bq2(h−d	NOUN
ejpam-5546	202	23	)	)	PUNCT
ejpam-5546	202	24	)	)	PUNCT
ejpam-5546	202	25	,	,	PUNCT
ejpam-5546	202	26	where	where	SCONJ
ejpam-5546	202	27	h	h	NOUN
ejpam-5546	203	1	=	=	SYM
ejpam-5546	203	2	k	k	PROPN
ejpam-5546	203	3	+	+	PROPN
ejpam-5546	203	4	i.	i.	NOUN
ejpam-5546	203	5	note	note	VERB
ejpam-5546	203	6	that	that	SCONJ
ejpam-5546	203	7	0	0	PUNCT
ejpam-5546	203	8	<	<	X
ejpam-5546	203	9	h	h	X
ejpam-5546	203	10	<	<	X
ejpam-5546	203	11	2d	2d	PROPN
ejpam-5546	203	12	,	,	PUNCT
ejpam-5546	203	13	its	its	PRON
ejpam-5546	203	14	clear	clear	ADJ
ejpam-5546	203	15	that	that	SCONJ
ejpam-5546	203	16	αk	αk	AUX
ejpam-5546	203	17	=	=	NOUN
ejpam-5546	203	18	αi	αi	VERB
ejpam-5546	203	19	if	if	SCONJ
ejpam-5546	203	20	and	and	CCONJ
ejpam-5546	203	21	only	only	ADV
ejpam-5546	203	22	if	if	SCONJ
ejpam-5546	203	23	qd−2k(1	qd−2k(1	PROPN
ejpam-5546	203	24	−	−	PROPN
ejpam-5546	203	25	q2(k−i))(a	q2(k−i))(a	NOUN
ejpam-5546	203	26	−	−	PROPN
ejpam-5546	203	27	bq2(h−d	bq2(h−d	NOUN
ejpam-5546	203	28	)	)	PUNCT
ejpam-5546	203	29	)	)	PUNCT
ejpam-5546	204	1	=	=	PUNCT
ejpam-5546	204	2	0	0	NUM
ejpam-5546	204	3	,	,	PUNCT
ejpam-5546	204	4	but	but	CCONJ
ejpam-5546	204	5	1	1	NUM
ejpam-5546	204	6	−	−	NOUN
ejpam-5546	204	7	q2(k−i	q2(k−i	PROPN
ejpam-5546	204	8	)	)	PUNCT
ejpam-5546	204	9	̸=	̸=	PROPN
ejpam-5546	204	10	0	0	NUM
ejpam-5546	204	11	because	because	SCONJ
ejpam-5546	204	12	q	q	NOUN
ejpam-5546	204	13	is	be	AUX
ejpam-5546	204	14	not	not	PART
ejpam-5546	204	15	a	a	DET
ejpam-5546	204	16	root	root	NOUN
ejpam-5546	204	17	of	of	ADP
ejpam-5546	204	18	unity	unity	NOUN
ejpam-5546	204	19	,	,	PUNCT
ejpam-5546	204	20	hence	hence	ADV
ejpam-5546	204	21	,	,	PUNCT
ejpam-5546	204	22	αk	αk	CCONJ
ejpam-5546	204	23	̸=	̸=	PROPN
ejpam-5546	204	24	αi	αi	VERB
ejpam-5546	204	25	if	if	SCONJ
ejpam-5546	204	26	and	and	CCONJ
ejpam-5546	204	27	only	only	ADV
ejpam-5546	204	28	if	if	SCONJ
ejpam-5546	204	29	a−	a−	PROPN
ejpam-5546	204	30	bq2(h−d	bq2(h−d	NOUN
ejpam-5546	204	31	)	)	PUNCT
ejpam-5546	204	32	̸=	̸=	PROPN
ejpam-5546	204	33	0	0	NUM
ejpam-5546	204	34	for	for	ADP
ejpam-5546	204	35	0	0	NUM
ejpam-5546	204	36	<	<	X
ejpam-5546	204	37	h	h	X
ejpam-5546	204	38	<	<	X
ejpam-5546	204	39	2d	2d	PROPN
ejpam-5546	204	40	.	.	PUNCT
ejpam-5546	205	1	lemma	lemma	PROPN
ejpam-5546	205	2	7	7	NUM
ejpam-5546	205	3	.	.	PUNCT
ejpam-5546	205	4	with	with	ADP
ejpam-5546	205	5	reference	reference	NOUN
ejpam-5546	205	6	to	to	ADP
ejpam-5546	205	7	definition	definition	NOUN
ejpam-5546	205	8	8	8	NUM
ejpam-5546	205	9	,	,	PUNCT
ejpam-5546	205	10	α∗	α∗	VERB
ejpam-5546	205	11	k	k	PROPN
ejpam-5546	205	12	̸=	̸=	PROPN
ejpam-5546	205	13	α∗	α∗	VERB
ejpam-5546	205	14	i	i	PRON
ejpam-5546	205	15	for	for	ADP
ejpam-5546	205	16	k	k	PROPN
ejpam-5546	205	17	̸=	̸=	PROPN
ejpam-5546	205	18	i	i	PRON
ejpam-5546	205	19	(	(	PUNCT
ejpam-5546	205	20	0	0	NUM
ejpam-5546	205	21	≤	≤	NOUN
ejpam-5546	205	22	i	i	PRON
ejpam-5546	205	23	,	,	PUNCT
ejpam-5546	205	24	k	k	PROPN
ejpam-5546	205	25	≤	≤	PROPN
ejpam-5546	206	1	d	d	NOUN
ejpam-5546	206	2	)	)	PUNCT
ejpam-5546	206	3	.	.	PUNCT
ejpam-5546	207	1	proof	proof	NOUN
ejpam-5546	207	2	.	.	PUNCT
ejpam-5546	208	1	α∗	α∗	NOUN
ejpam-5546	208	2	k−α∗	k−α∗	VERB
ejpam-5546	209	1	i	i	PRON
ejpam-5546	209	2	=	=	NOUN
ejpam-5546	209	3	0	0	PUNCT
ejpam-5546	210	1	if	if	SCONJ
ejpam-5546	210	2	and	and	CCONJ
ejpam-5546	210	3	only	only	ADV
ejpam-5546	210	4	if	if	SCONJ
ejpam-5546	210	5	q2k−d−	q2k−d−	PROPN
ejpam-5546	210	6	q2i−d	q2i−d	NOUN
ejpam-5546	211	1	=	=	NOUN
ejpam-5546	211	2	0	0	PUNCT
ejpam-5546	212	1	if	if	SCONJ
ejpam-5546	212	2	and	and	CCONJ
ejpam-5546	212	3	only	only	ADV
ejpam-5546	212	4	if	if	SCONJ
ejpam-5546	212	5	q2k−d(1−	q2k−d(1−	PUNCT
ejpam-5546	212	6	q2(i−k	q2(i−k	PROPN
ejpam-5546	212	7	)	)	PUNCT
ejpam-5546	212	8	)	)	PUNCT
ejpam-5546	213	1	=	=	PUNCT
ejpam-5546	213	2	0	0	NUM
ejpam-5546	213	3	,	,	PUNCT
ejpam-5546	213	4	but	but	CCONJ
ejpam-5546	213	5	q	q	NOUN
ejpam-5546	213	6	is	be	AUX
ejpam-5546	213	7	not	not	PART
ejpam-5546	213	8	a	a	DET
ejpam-5546	213	9	root	root	NOUN
ejpam-5546	213	10	of	of	ADP
ejpam-5546	213	11	unity	unity	NOUN
ejpam-5546	213	12	.	.	PUNCT
ejpam-5546	214	1	hence	hence	ADV
ejpam-5546	214	2	the	the	DET
ejpam-5546	214	3	result	result	NOUN
ejpam-5546	214	4	hold	hold	NOUN
ejpam-5546	214	5	.	.	PUNCT
ejpam-5546	215	1	lemma	lemma	PROPN
ejpam-5546	215	2	8	8	NUM
ejpam-5546	215	3	.	.	PUNCT
ejpam-5546	216	1	with	with	ADP
ejpam-5546	216	2	reference	reference	NOUN
ejpam-5546	216	3	to	to	ADP
ejpam-5546	216	4	definition	definition	NOUN
ejpam-5546	216	5	8	8	NUM
ejpam-5546	216	6	,	,	PUNCT
ejpam-5546	216	7	φi	φi	ADP
ejpam-5546	216	8	̸=	̸=	PROPN
ejpam-5546	216	9	0	0	PUNCT
ejpam-5546	217	1	if	if	SCONJ
ejpam-5546	217	2	and	and	CCONJ
ejpam-5546	217	3	only	only	ADV
ejpam-5546	217	4	if	if	SCONJ
ejpam-5546	217	5	b	b	PROPN
ejpam-5546	217	6	̸=	̸=	PROPN
ejpam-5546	217	7	0	0	NUM
ejpam-5546	217	8	,	,	PUNCT
ejpam-5546	217	9	and	and	CCONJ
ejpam-5546	217	10	ϕi	ϕi	ADP
ejpam-5546	217	11	̸=	̸=	PROPN
ejpam-5546	217	12	0	0	PUNCT
ejpam-5546	217	13	if	if	SCONJ
ejpam-5546	217	14	and	and	CCONJ
ejpam-5546	217	15	only	only	ADV
ejpam-5546	217	16	if	if	SCONJ
ejpam-5546	217	17	a	a	DET
ejpam-5546	217	18	̸=	̸=	PROPN
ejpam-5546	217	19	0	0	NUM
ejpam-5546	217	20	for	for	ADP
ejpam-5546	217	21	1	1	NUM
ejpam-5546	217	22	≤	≤	NUM
ejpam-5546	217	23	i	i	PRON
ejpam-5546	217	24	≤	≤	ADJ
ejpam-5546	217	25	d.	d.	NOUN
ejpam-5546	217	26	proof	proof	NOUN
ejpam-5546	217	27	.	.	PUNCT
ejpam-5546	218	1	clear	clear	ADJ
ejpam-5546	218	2	,	,	PUNCT
ejpam-5546	218	3	since	since	SCONJ
ejpam-5546	218	4	q	q	NOUN
ejpam-5546	218	5	is	be	AUX
ejpam-5546	218	6	not	not	PART
ejpam-5546	218	7	a	a	DET
ejpam-5546	218	8	root	root	NOUN
ejpam-5546	218	9	of	of	ADP
ejpam-5546	218	10	unity	unity	NOUN
ejpam-5546	218	11	.	.	PUNCT
ejpam-5546	219	1	lemma	lemma	PROPN
ejpam-5546	219	2	9	9	NUM
ejpam-5546	219	3	.	.	PUNCT
ejpam-5546	220	1	with	with	ADP
ejpam-5546	220	2	reference	reference	NOUN
ejpam-5546	220	3	to	to	ADP
ejpam-5546	220	4	definition	definition	NOUN
ejpam-5546	220	5	8	8	NUM
ejpam-5546	220	6	,	,	PUNCT
ejpam-5546	220	7	φi	φi	ADP
ejpam-5546	220	8	=	=	PUNCT
ejpam-5546	220	9	ϕ1	ϕ1	NOUN
ejpam-5546	220	10	i−1∑	i−1∑	NUM
ejpam-5546	220	11	k=0	k=0	PROPN
ejpam-5546	220	12	αk	αk	AUX
ejpam-5546	220	13	−	−	NOUN
ejpam-5546	220	14	αd−k	αd−k	NOUN
ejpam-5546	220	15	α0	α0	ADJ
ejpam-5546	220	16	−	−	PROPN
ejpam-5546	220	17	αd	αd	NOUN
ejpam-5546	221	1	+	+	CCONJ
ejpam-5546	221	2	(	(	PUNCT
ejpam-5546	221	3	α∗	α∗	NOUN
ejpam-5546	221	4	i	i	PRON
ejpam-5546	221	5	−	−	VERB
ejpam-5546	221	6	α∗	α∗	VERB
ejpam-5546	221	7	0)(αi−1	0)(αi−1	NUM
ejpam-5546	221	8	−	−	NUM
ejpam-5546	221	9	αd	αd	PROPN
ejpam-5546	221	10	)	)	PUNCT
ejpam-5546	221	11	(	(	PUNCT
ejpam-5546	221	12	1	1	NUM
ejpam-5546	221	13	≤	≤	NUM
ejpam-5546	221	14	i	i	X
ejpam-5546	221	15	≤	≤	NUM
ejpam-5546	221	16	d	d	X
ejpam-5546	221	17	)	)	PUNCT
ejpam-5546	221	18	.	.	PUNCT
ejpam-5546	222	1	proof	proof	NOUN
ejpam-5546	222	2	.	.	PUNCT
ejpam-5546	223	1	note	note	VERB
ejpam-5546	223	2	that	that	SCONJ
ejpam-5546	223	3	αk	αk	AUX
ejpam-5546	223	4	−	−	NOUN
ejpam-5546	223	5	αd−k	αd−k	NOUN
ejpam-5546	223	6	=	=	PUNCT
ejpam-5546	223	7	(	(	PUNCT
ejpam-5546	224	1	aqd−2k	aqd−2k	NOUN
ejpam-5546	224	2	+	+	CCONJ
ejpam-5546	224	3	bq2k−d)−	bq2k−d)−	PROPN
ejpam-5546	224	4	(	(	PUNCT
ejpam-5546	224	5	aq2k−d	aq2k−d	NOUN
ejpam-5546	224	6	+	+	PUNCT
ejpam-5546	224	7	bqd−2k	bqd−2k	NOUN
ejpam-5546	224	8	)	)	PUNCT
ejpam-5546	224	9	=	=	PUNCT
ejpam-5546	224	10	(	(	PUNCT
ejpam-5546	224	11	a−	a−	NOUN
ejpam-5546	224	12	b)(qd−2k	b)(qd−2k	NOUN
ejpam-5546	224	13	−	−	NOUN
ejpam-5546	224	14	q2k−d	q2k−d	NOUN
ejpam-5546	224	15	)	)	PUNCT
ejpam-5546	224	16	,	,	PUNCT
ejpam-5546	224	17	and	and	CCONJ
ejpam-5546	224	18	α0	α0	ADJ
ejpam-5546	224	19	−	−	PROPN
ejpam-5546	224	20	αd	αd	PROPN
ejpam-5546	224	21	=	=	SYM
ejpam-5546	224	22	(	(	PUNCT
ejpam-5546	224	23	aqd	aqd	NOUN
ejpam-5546	224	24	+	+	X
ejpam-5546	224	25	bq−d)−	bq−d)−	PROPN
ejpam-5546	224	26	(	(	PUNCT
ejpam-5546	224	27	aq−d	aq−d	NOUN
ejpam-5546	224	28	+	+	CCONJ
ejpam-5546	224	29	bqd	bqd	NOUN
ejpam-5546	224	30	)	)	PUNCT
ejpam-5546	224	31	=	=	PUNCT
ejpam-5546	224	32	(	(	PUNCT
ejpam-5546	224	33	a−	a−	PROPN
ejpam-5546	224	34	b)(qd	b)(qd	VERB
ejpam-5546	224	35	−	−	PROPN
ejpam-5546	224	36	q−d	q−d	NOUN
ejpam-5546	224	37	)	)	PUNCT
ejpam-5546	224	38	.	.	PUNCT
ejpam-5546	225	1	so	so	ADV
ejpam-5546	225	2	,	,	PUNCT
ejpam-5546	225	3	i−1∑	i−1∑	NUM
ejpam-5546	225	4	k=0	k=0	PROPN
ejpam-5546	225	5	αk	αk	AUX
ejpam-5546	225	6	−	−	NOUN
ejpam-5546	225	7	αd−k	αd−k	NOUN
ejpam-5546	225	8	α0	α0	ADJ
ejpam-5546	225	9	−	−	PROPN
ejpam-5546	225	10	αd	αd	NOUN
ejpam-5546	225	11	=	=	PUNCT
ejpam-5546	225	12	i−1∑	i−1∑	NOUN
ejpam-5546	225	13	k=0	k=0	PROPN
ejpam-5546	225	14	qd−2k	qd−2k	ADP
ejpam-5546	225	15	−	−	ADP
ejpam-5546	225	16	q2k−d	q2k−d	NOUN
ejpam-5546	225	17	qd	qd	ADP
ejpam-5546	225	18	−	−	NOUN
ejpam-5546	225	19	q−d	q−d	PROPN
ejpam-5546	225	20	=	=	SYM
ejpam-5546	225	21	(	(	PUNCT
ejpam-5546	225	22	q2(d−i+1	q2(d−i+1	NOUN
ejpam-5546	225	23	)	)	PUNCT
ejpam-5546	225	24	−	−	PROPN
ejpam-5546	225	25	1)(q2i	1)(q2i	NUM
ejpam-5546	225	26	−	−	PROPN
ejpam-5546	225	27	1	1	NUM
ejpam-5546	225	28	)	)	PUNCT
ejpam-5546	225	29	(	(	PUNCT
ejpam-5546	225	30	q2d	q2d	ADJ
ejpam-5546	225	31	−	−	PROPN
ejpam-5546	225	32	1)(q2	1)(q2	NUM
ejpam-5546	225	33	−	−	PROPN
ejpam-5546	225	34	1	1	NUM
ejpam-5546	225	35	)	)	PUNCT
ejpam-5546	225	36	.	.	PUNCT
ejpam-5546	226	1	and	and	CCONJ
ejpam-5546	226	2	,	,	PUNCT
ejpam-5546	226	3	α∗	α∗	VERB
ejpam-5546	226	4	i	i	PRON
ejpam-5546	226	5	−	−	NOUN
ejpam-5546	226	6	α∗	α∗	VERB
ejpam-5546	226	7	0	0	NUM
ejpam-5546	227	1	=	=	SYM
ejpam-5546	227	2	q2i−d	q2i−d	NOUN
ejpam-5546	227	3	−	−	NOUN
ejpam-5546	227	4	q−d	q−d	PROPN
ejpam-5546	227	5	=	=	PUNCT
ejpam-5546	227	6	q−d(q2i	q−d(q2i	NOUN
ejpam-5546	227	7	−	−	NOUN
ejpam-5546	227	8	1	1	NUM
ejpam-5546	227	9	)	)	PUNCT
ejpam-5546	227	10	,	,	PUNCT
ejpam-5546	227	11	αi−1−αd	αi−1−αd	NOUN
ejpam-5546	227	12	=	=	SYM
ejpam-5546	227	13	(	(	PUNCT
ejpam-5546	227	14	aqd−2i+2+bq2i−d−2)−	aqd−2i+2+bq2i−d−2)−	PROPN
ejpam-5546	227	15	(	(	PUNCT
ejpam-5546	227	16	aq−d+bqd	aq−d+bqd	NOUN
ejpam-5546	227	17	)	)	PUNCT
ejpam-5546	227	18	=	=	SYM
ejpam-5546	227	19	aq−d(q2(d−i+1)−1)+bqd(q2(i−d−1)−1	aq−d(q2(d−i+1)−1)+bqd(q2(i−d−1)−1	PROPN
ejpam-5546	227	20	)	)	PUNCT
ejpam-5546	227	21	,	,	PUNCT
ejpam-5546	227	22	ϕ1	ϕ1	NOUN
ejpam-5546	227	23	=	=	SYM
ejpam-5546	227	24	aq−2d(q2	aq−2d(q2	X
ejpam-5546	227	25	−	−	PROPN
ejpam-5546	227	26	1)(1−	1)(1−	NUM
ejpam-5546	227	27	q2d	q2d	NOUN
ejpam-5546	227	28	)	)	PUNCT
ejpam-5546	227	29	.	.	PUNCT
ejpam-5546	228	1	now	now	ADV
ejpam-5546	228	2	,	,	PUNCT
ejpam-5546	228	3	simplify	simplify	VERB
ejpam-5546	228	4	to	to	PART
ejpam-5546	228	5	get	get	VERB
ejpam-5546	228	6	the	the	DET
ejpam-5546	228	7	result	result	NOUN
ejpam-5546	228	8	.	.	PUNCT
ejpam-5546	229	1	lemma	lemma	PROPN
ejpam-5546	229	2	10	10	NUM
ejpam-5546	229	3	.	.	PUNCT
ejpam-5546	230	1	with	with	ADP
ejpam-5546	230	2	reference	reference	NOUN
ejpam-5546	230	3	to	to	ADP
ejpam-5546	230	4	definition	definition	NOUN
ejpam-5546	230	5	8	8	NUM
ejpam-5546	230	6	,	,	PUNCT
ejpam-5546	230	7	ϕi	ϕi	ADP
ejpam-5546	230	8	=	=	ADJ
ejpam-5546	230	9	φ1	φ1	NOUN
ejpam-5546	230	10	i−1∑	i−1∑	NUM
ejpam-5546	230	11	k=0	k=0	PROPN
ejpam-5546	230	12	αk	αk	AUX
ejpam-5546	230	13	−	−	NOUN
ejpam-5546	230	14	αd−k	αd−k	NOUN
ejpam-5546	230	15	α0	α0	ADJ
ejpam-5546	230	16	−	−	PROPN
ejpam-5546	230	17	αd	αd	NOUN
ejpam-5546	230	18	+	+	CCONJ
ejpam-5546	230	19	(	(	PUNCT
ejpam-5546	230	20	α∗	α∗	NOUN
ejpam-5546	230	21	i	i	PRON
ejpam-5546	230	22	−	−	NOUN
ejpam-5546	230	23	α∗	α∗	VERB
ejpam-5546	230	24	0)(αd−i+1	0)(αd−i+1	NOUN
ejpam-5546	230	25	−	−	PROPN
ejpam-5546	230	26	α0	α0	ADJ
ejpam-5546	230	27	)	)	PUNCT
ejpam-5546	230	28	(	(	PUNCT
ejpam-5546	230	29	1	1	NUM
ejpam-5546	230	30	≤	≤	NUM
ejpam-5546	230	31	i	i	X
ejpam-5546	230	32	≤	≤	NUM
ejpam-5546	231	1	d	d	X
ejpam-5546	231	2	)	)	PUNCT
ejpam-5546	231	3	.	.	PUNCT
ejpam-5546	232	1	h.	h.	PROPN
ejpam-5546	232	2	alnajjar	alnajjar	PROPN
ejpam-5546	232	3	/	/	SYM
ejpam-5546	232	4	eur	eur	PROPN
ejpam-5546	232	5	.	.	PUNCT
ejpam-5546	233	1	j.	j.	PROPN
ejpam-5546	233	2	pure	pure	PROPN
ejpam-5546	233	3	appl	appl	PROPN
ejpam-5546	233	4	.	.	PROPN
ejpam-5546	233	5	math	math	PROPN
ejpam-5546	233	6	,	,	PUNCT
ejpam-5546	233	7	18	18	NUM
ejpam-5546	233	8	(	(	PUNCT
ejpam-5546	233	9	1	1	NUM
ejpam-5546	233	10	)	)	PUNCT
ejpam-5546	233	11	(	(	PUNCT
ejpam-5546	233	12	2025	2025	NUM
ejpam-5546	233	13	)	)	PUNCT
ejpam-5546	233	14	,	,	PUNCT
ejpam-5546	233	15	5546	5546	NUM
ejpam-5546	233	16	8	8	NUM
ejpam-5546	233	17	of	of	ADP
ejpam-5546	233	18	14	14	NUM
ejpam-5546	233	19	proof	proof	NOUN
ejpam-5546	233	20	.	.	PUNCT
ejpam-5546	234	1	similar	similar	ADJ
ejpam-5546	234	2	to	to	ADP
ejpam-5546	234	3	proof	proof	NOUN
ejpam-5546	234	4	of	of	ADP
ejpam-5546	234	5	lemma	lemma	PROPN
ejpam-5546	234	6	9	9	NUM
ejpam-5546	234	7	.	.	PUNCT
ejpam-5546	235	1	lemma	lemma	PROPN
ejpam-5546	235	2	11	11	NUM
ejpam-5546	235	3	.	.	PUNCT
ejpam-5546	236	1	with	with	ADP
ejpam-5546	236	2	reference	reference	NOUN
ejpam-5546	236	3	to	to	ADP
ejpam-5546	236	4	definition	definition	NOUN
ejpam-5546	236	5	8	8	NUM
ejpam-5546	236	6	,	,	PUNCT
ejpam-5546	236	7	αh−2	αh−2	NOUN
ejpam-5546	236	8	−	−	PROPN
ejpam-5546	236	9	αh+1	αh+1	PROPN
ejpam-5546	236	10	αh−1	αh−1	PROPN
ejpam-5546	236	11	−	−	NOUN
ejpam-5546	237	1	αh	αh	NOUN
ejpam-5546	237	2	=	=	NOUN
ejpam-5546	237	3	α∗	α∗	VERB
ejpam-5546	237	4	k−2	k−2	PROPN
ejpam-5546	237	5	−	−	PROPN
ejpam-5546	237	6	α∗	α∗	VERB
ejpam-5546	237	7	k+1	k+1	NOUN
ejpam-5546	237	8	α∗	α∗	VERB
ejpam-5546	237	9	k−1	k−1	PROPN
ejpam-5546	237	10	−	−	PROPN
ejpam-5546	237	11	α∗	α∗	VERB
ejpam-5546	237	12	k	k	NOUN
ejpam-5546	237	13	=	=	PUNCT
ejpam-5546	237	14	q2	q2	PROPN
ejpam-5546	237	15	+	+	CCONJ
ejpam-5546	237	16	q−2	q−2	PROPN
ejpam-5546	238	1	+	+	NOUN
ejpam-5546	238	2	1	1	NUM
ejpam-5546	238	3	(	(	PUNCT
ejpam-5546	238	4	2	2	NUM
ejpam-5546	238	5	≤	≤	NUM
ejpam-5546	238	6	h	h	NOUN
ejpam-5546	238	7	,	,	PUNCT
ejpam-5546	238	8	k	k	PROPN
ejpam-5546	238	9	≤	≤	NUM
ejpam-5546	238	10	d−	d−	PROPN
ejpam-5546	238	11	1	1	NUM
ejpam-5546	238	12	)	)	PUNCT
ejpam-5546	238	13	.	.	PUNCT
ejpam-5546	239	1	proof	proof	NOUN
ejpam-5546	239	2	.	.	PUNCT
ejpam-5546	240	1	α∗	α∗	VERB
ejpam-5546	240	2	k−2	k−2	PROPN
ejpam-5546	240	3	−	−	PROPN
ejpam-5546	240	4	α∗	α∗	VERB
ejpam-5546	240	5	k+1	k+1	X
ejpam-5546	240	6	=	=	PUNCT
ejpam-5546	240	7	q2(k−2)−d	q2(k−2)−d	NOUN
ejpam-5546	240	8	−	−	PROPN
ejpam-5546	240	9	q2(k+1)−d	q2(k+1)−d	NOUN
ejpam-5546	240	10	=	=	SYM
ejpam-5546	240	11	q2k−d−4(1−	q2k−d−4(1−	PROPN
ejpam-5546	240	12	q6	q6	PROPN
ejpam-5546	240	13	)	)	PUNCT
ejpam-5546	240	14	,	,	PUNCT
ejpam-5546	240	15	and	and	CCONJ
ejpam-5546	240	16	α∗	α∗	VERB
ejpam-5546	240	17	k−1	k−1	PROPN
ejpam-5546	240	18	−	−	PROPN
ejpam-5546	240	19	α∗	α∗	VERB
ejpam-5546	240	20	k	k	NOUN
ejpam-5546	241	1	=	=	PUNCT
ejpam-5546	241	2	q2(k−1)−d	q2(k−1)−d	NUM
ejpam-5546	241	3	−	−	PROPN
ejpam-5546	241	4	q2(k)−d	q2(k)−d	PROPN
ejpam-5546	241	5	=	=	PROPN
ejpam-5546	241	6	q2k−d−2(1−	q2k−d−2(1−	PROPN
ejpam-5546	241	7	q2	q2	PROPN
ejpam-5546	241	8	)	)	PUNCT
ejpam-5546	241	9	.	.	PUNCT
ejpam-5546	242	1	hence	hence	ADV
ejpam-5546	242	2	,	,	PUNCT
ejpam-5546	242	3	α∗	α∗	VERB
ejpam-5546	242	4	k−2	k−2	PROPN
ejpam-5546	242	5	−	−	PROPN
ejpam-5546	242	6	α∗	α∗	VERB
ejpam-5546	242	7	k+1	k+1	NOUN
ejpam-5546	242	8	α∗	α∗	VERB
ejpam-5546	242	9	k−1	k−1	PROPN
ejpam-5546	242	10	−	−	PROPN
ejpam-5546	242	11	α∗	α∗	VERB
ejpam-5546	242	12	k	k	NOUN
ejpam-5546	243	1	=	=	SYM
ejpam-5546	243	2	q−2	q−2	PROPN
ejpam-5546	243	3	1−	1−	NUM
ejpam-5546	243	4	q6	q6	PROPN
ejpam-5546	243	5	1−	1−	NUM
ejpam-5546	243	6	q2	q2	NOUN
ejpam-5546	243	7	=	=	SYM
ejpam-5546	243	8	q2	q2	PROPN
ejpam-5546	243	9	+	+	CCONJ
ejpam-5546	243	10	q−2	q−2	PROPN
ejpam-5546	243	11	+	+	NOUN
ejpam-5546	243	12	1	1	NUM
ejpam-5546	243	13	(	(	PUNCT
ejpam-5546	243	14	2	2	NUM
ejpam-5546	243	15	≤	≤	NUM
ejpam-5546	243	16	k	k	X
ejpam-5546	243	17	≤	≤	NUM
ejpam-5546	243	18	d−	d−	PROPN
ejpam-5546	243	19	1	1	NUM
ejpam-5546	243	20	)	)	PUNCT
ejpam-5546	243	21	.	.	PUNCT
ejpam-5546	244	1	similar	similar	ADJ
ejpam-5546	244	2	proof	proof	NOUN
ejpam-5546	244	3	for	for	ADP
ejpam-5546	244	4	α	α	PROPN
ejpam-5546	244	5	.	.	PUNCT
ejpam-5546	245	1	lemma	lemma	PROPN
ejpam-5546	245	2	12	12	NUM
ejpam-5546	245	3	.	.	PUNCT
ejpam-5546	246	1	with	with	ADP
ejpam-5546	246	2	reference	reference	NOUN
ejpam-5546	246	3	to	to	ADP
ejpam-5546	246	4	definition	definition	NOUN
ejpam-5546	246	5	8	8	NUM
ejpam-5546	246	6	,	,	PUNCT
ejpam-5546	246	7	let	let	VERB
ejpam-5546	246	8	a	a	PRON
ejpam-5546	246	9	and	and	CCONJ
ejpam-5546	246	10	b	b	NOUN
ejpam-5546	246	11	be	be	AUX
ejpam-5546	246	12	scalars	scalar	NOUN
ejpam-5546	246	13	in	in	ADP
ejpam-5546	246	14	f	f	PROPN
ejpam-5546	246	15	.	.	PUNCT
ejpam-5546	247	1	then	then	ADV
ejpam-5546	247	2	the	the	DET
ejpam-5546	247	3	sequence	sequence	NOUN
ejpam-5546	247	4	of	of	ADP
ejpam-5546	247	5	scalars	scalar	NOUN
ejpam-5546	247	6	(	(	PUNCT
ejpam-5546	247	7	{	{	PUNCT
ejpam-5546	247	8	αi}di=0	αi}di=0	NOUN
ejpam-5546	247	9	,	,	PUNCT
ejpam-5546	247	10	{	{	PUNCT
ejpam-5546	247	11	α∗	α∗	NOUN
ejpam-5546	247	12	i	i	PRON
ejpam-5546	247	13	}	}	PUNCT
ejpam-5546	247	14	di=0	di=0	PROPN
ejpam-5546	247	15	;	;	PUNCT
ejpam-5546	247	16	{	{	PUNCT
ejpam-5546	247	17	φj}dj=1	φj}dj=1	NOUN
ejpam-5546	247	18	,	,	PUNCT
ejpam-5546	247	19	{	{	PUNCT
ejpam-5546	247	20	ϕj}dj=1	ϕj}dj=1	PROPN
ejpam-5546	247	21	)	)	PUNCT
ejpam-5546	247	22	is	be	AUX
ejpam-5546	247	23	a	a	DET
ejpam-5546	247	24	parameter	parameter	NOUN
ejpam-5546	247	25	array	array	NOUN
ejpam-5546	247	26	if	if	SCONJ
ejpam-5546	248	1	and	and	CCONJ
ejpam-5546	248	2	only	only	ADV
ejpam-5546	248	3	if	if	SCONJ
ejpam-5546	248	4	a	a	DET
ejpam-5546	248	5	̸=	̸=	PROPN
ejpam-5546	248	6	0	0	NUM
ejpam-5546	248	7	,	,	PUNCT
ejpam-5546	248	8	b	b	X
ejpam-5546	248	9	̸=	̸=	PROPN
ejpam-5546	248	10	0	0	NUM
ejpam-5546	248	11	and	and	CCONJ
ejpam-5546	248	12	a−	a−	PROPN
ejpam-5546	248	13	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	248	14	)	)	PUNCT
ejpam-5546	249	1	̸=	̸=	NOUN
ejpam-5546	249	2	0	0	NUM
ejpam-5546	249	3	for	for	ADP
ejpam-5546	249	4	1	1	NUM
ejpam-5546	249	5	≤	≤	NUM
ejpam-5546	249	6	i	i	PRON
ejpam-5546	249	7	≤	≤	NOUN
ejpam-5546	250	1	2d−	2d−	PROPN
ejpam-5546	250	2	1	1	NUM
ejpam-5546	250	3	.	.	PUNCT
ejpam-5546	251	1	proof	proof	NOUN
ejpam-5546	251	2	.	.	PUNCT
ejpam-5546	252	1	note	note	VERB
ejpam-5546	252	2	that	that	SCONJ
ejpam-5546	252	3	the	the	DET
ejpam-5546	252	4	conditions	condition	NOUN
ejpam-5546	252	5	1−7	1−7	NUM
ejpam-5546	252	6	of	of	ADP
ejpam-5546	252	7	the	the	DET
ejpam-5546	252	8	parameter	parameter	NOUN
ejpam-5546	252	9	array	array	NOUN
ejpam-5546	252	10	in	in	ADP
ejpam-5546	252	11	definition	definition	NOUN
ejpam-5546	252	12	2	2	NUM
ejpam-5546	252	13	hold	hold	VERB
ejpam-5546	252	14	for	for	ADP
ejpam-5546	252	15	the	the	DET
ejpam-5546	252	16	sequence	sequence	NOUN
ejpam-5546	252	17	(	(	PUNCT
ejpam-5546	252	18	{	{	PUNCT
ejpam-5546	252	19	αi}di=0	αi}di=0	NOUN
ejpam-5546	252	20	,	,	PUNCT
ejpam-5546	252	21	{	{	PUNCT
ejpam-5546	252	22	α∗	α∗	NOUN
ejpam-5546	252	23	i	i	PRON
ejpam-5546	252	24	}	}	PUNCT
ejpam-5546	252	25	di=0	di=0	PROPN
ejpam-5546	252	26	;	;	PUNCT
ejpam-5546	252	27	{	{	PUNCT
ejpam-5546	252	28	φj}dj=1	φj}dj=1	NOUN
ejpam-5546	252	29	,	,	PUNCT
ejpam-5546	252	30	{	{	PUNCT
ejpam-5546	252	31	ϕj}dj=1	ϕj}dj=1	PROPN
ejpam-5546	252	32	)	)	PUNCT
ejpam-5546	252	33	from	from	ADP
ejpam-5546	252	34	lemmas	lemmas	PROPN
ejpam-5546	252	35	6	6	NUM
ejpam-5546	252	36	,	,	PUNCT
ejpam-5546	252	37	7	7	NUM
ejpam-5546	252	38	,	,	PUNCT
ejpam-5546	252	39	8	8	NUM
ejpam-5546	252	40	,	,	PUNCT
ejpam-5546	252	41	9	9	NUM
ejpam-5546	252	42	,	,	PUNCT
ejpam-5546	252	43	10	10	NUM
ejpam-5546	252	44	,	,	PUNCT
ejpam-5546	252	45	11	11	NUM
ejpam-5546	252	46	respectively	respectively	ADV
ejpam-5546	252	47	if	if	SCONJ
ejpam-5546	252	48	and	and	CCONJ
ejpam-5546	252	49	only	only	ADV
ejpam-5546	252	50	if	if	SCONJ
ejpam-5546	252	51	a	a	DET
ejpam-5546	252	52	̸=	̸=	PROPN
ejpam-5546	252	53	0	0	NUM
ejpam-5546	252	54	,	,	PUNCT
ejpam-5546	252	55	b	b	X
ejpam-5546	252	56	̸=	̸=	PROPN
ejpam-5546	252	57	0	0	NUM
ejpam-5546	252	58	and	and	CCONJ
ejpam-5546	252	59	a−	a−	PROPN
ejpam-5546	252	60	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	252	61	)	)	PUNCT
ejpam-5546	252	62	̸=	̸=	NOUN
ejpam-5546	252	63	0	0	NUM
ejpam-5546	252	64	for	for	ADP
ejpam-5546	252	65	1	1	NUM
ejpam-5546	252	66	≤	≤	NUM
ejpam-5546	252	67	i	i	PRON
ejpam-5546	252	68	≤	≤	NOUN
ejpam-5546	253	1	2d−	2d−	NUM
ejpam-5546	253	2	1	1	NUM
ejpam-5546	253	3	.	.	PUNCT
ejpam-5546	254	1	theorem	theorem	NOUN
ejpam-5546	254	2	2	2	NUM
ejpam-5546	254	3	.	.	X
ejpam-5546	254	4	assume	assume	VERB
ejpam-5546	254	5	d	d	X
ejpam-5546	254	6	≥	≥	NUM
ejpam-5546	254	7	2	2	NUM
ejpam-5546	254	8	,	,	PUNCT
ejpam-5546	254	9	let	let	VERB
ejpam-5546	254	10	v	v	PART
ejpam-5546	254	11	denote	denote	VERB
ejpam-5546	254	12	an	an	DET
ejpam-5546	254	13	evaluation	evaluation	NOUN
ejpam-5546	254	14	module	module	NOUN
ejpam-5546	254	15	for	for	ADP
ejpam-5546	254	16	⊠q	⊠q	PROPN
ejpam-5546	254	17	with	with	ADP
ejpam-5546	254	18	dimension	dimension	NOUN
ejpam-5546	254	19	d	d	PROPN
ejpam-5546	255	1	+	+	NOUN
ejpam-5546	255	2	1	1	X
ejpam-5546	255	3	.	.	PUNCT
ejpam-5546	255	4	let	let	VERB
ejpam-5546	255	5	a	a	DET
ejpam-5546	255	6	∈	∈	PROPN
ejpam-5546	255	7	⊠q	⊠q	PROPN
ejpam-5546	255	8	denote	denote	VERB
ejpam-5546	255	9	an	an	DET
ejpam-5546	255	10	arbitrary	arbitrary	ADJ
ejpam-5546	255	11	linear	linear	ADJ
ejpam-5546	255	12	combination	combination	NOUN
ejpam-5546	255	13	of	of	ADP
ejpam-5546	255	14	x01	x01	PROPN
ejpam-5546	255	15	and	and	CCONJ
ejpam-5546	255	16	x12	x12	NUM
ejpam-5546	255	17	,	,	PUNCT
ejpam-5546	255	18	let	let	VERB
ejpam-5546	255	19	b1	b1	NOUN
ejpam-5546	255	20	∈	∈	PROPN
ejpam-5546	255	21	⊠q	⊠q	NOUN
ejpam-5546	255	22	such	such	ADJ
ejpam-5546	255	23	that	that	DET
ejpam-5546	255	24	b1	b1	NOUN
ejpam-5546	255	25	=	=	SYM
ejpam-5546	255	26	x20	x20	PROPN
ejpam-5546	255	27	,	,	PUNCT
ejpam-5546	255	28	let	let	VERB
ejpam-5546	255	29	a	a	PRON
ejpam-5546	255	30	and	and	CCONJ
ejpam-5546	255	31	b	b	NOUN
ejpam-5546	255	32	be	be	AUX
ejpam-5546	255	33	scalars	scalar	NOUN
ejpam-5546	255	34	in	in	ADP
ejpam-5546	255	35	f	f	PROPN
ejpam-5546	255	36	.	.	PUNCT
ejpam-5546	256	1	write	write	VERB
ejpam-5546	256	2	a	a	DET
ejpam-5546	256	3	=	=	SYM
ejpam-5546	256	4	ax01	ax01	PROPN
ejpam-5546	256	5	+	+	CCONJ
ejpam-5546	256	6	bx12	bx12	PROPN
ejpam-5546	256	7	.	.	PUNCT
ejpam-5546	257	1	then	then	ADV
ejpam-5546	257	2	the	the	DET
ejpam-5546	257	3	pair	pair	NOUN
ejpam-5546	257	4	a	a	X
ejpam-5546	257	5	,	,	PUNCT
ejpam-5546	257	6	b1	b1	NOUN
ejpam-5546	257	7	acts	act	VERB
ejpam-5546	257	8	on	on	ADP
ejpam-5546	257	9	v	v	NOUN
ejpam-5546	257	10	as	as	ADP
ejpam-5546	257	11	a	a	DET
ejpam-5546	257	12	leonard	leonard	NOUN
ejpam-5546	257	13	pair	pair	NOUN
ejpam-5546	257	14	if	if	SCONJ
ejpam-5546	257	15	and	and	CCONJ
ejpam-5546	257	16	only	only	ADV
ejpam-5546	257	17	if	if	SCONJ
ejpam-5546	257	18	a	a	DET
ejpam-5546	257	19	̸=	̸=	PROPN
ejpam-5546	257	20	0	0	NUM
ejpam-5546	257	21	,	,	PUNCT
ejpam-5546	257	22	b	b	X
ejpam-5546	257	23	̸=	̸=	PROPN
ejpam-5546	257	24	0	0	NUM
ejpam-5546	257	25	and	and	CCONJ
ejpam-5546	257	26	a	a	DET
ejpam-5546	257	27	−	−	PROPN
ejpam-5546	257	28	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	257	29	)	)	PUNCT
ejpam-5546	258	1	̸=	̸=	PROPN
ejpam-5546	258	2	0	0	NUM
ejpam-5546	258	3	for	for	ADP
ejpam-5546	258	4	1	1	NUM
ejpam-5546	258	5	≤	≤	NUM
ejpam-5546	258	6	i	i	PRON
ejpam-5546	258	7	≤	≤	NOUN
ejpam-5546	259	1	2d−	2d−	PROPN
ejpam-5546	259	2	1	1	NUM
ejpam-5546	259	3	.	.	PUNCT
ejpam-5546	260	1	proof	proof	NOUN
ejpam-5546	260	2	.	.	PUNCT
ejpam-5546	261	1	the	the	DET
ejpam-5546	261	2	action	action	NOUN
ejpam-5546	261	3	of	of	ADP
ejpam-5546	261	4	the	the	DET
ejpam-5546	261	5	pair	pair	NOUN
ejpam-5546	261	6	a	a	X
ejpam-5546	261	7	,	,	PUNCT
ejpam-5546	261	8	b1	b1	NOUN
ejpam-5546	261	9	on	on	ADP
ejpam-5546	261	10	the	the	DET
ejpam-5546	261	11	basis	basis	NOUN
ejpam-5546	261	12	s	s	NOUN
ejpam-5546	261	13	is	be	AUX
ejpam-5546	261	14	described	describe	VERB
ejpam-5546	261	15	in	in	ADP
ejpam-5546	261	16	lemma	lemma	PROPN
ejpam-5546	261	17	5	5	NUM
ejpam-5546	261	18	,	,	PUNCT
ejpam-5546	261	19	the	the	DET
ejpam-5546	261	20	matrices	matrix	NOUN
ejpam-5546	261	21	represent	represent	VERB
ejpam-5546	261	22	a	a	PRON
ejpam-5546	261	23	and	and	CCONJ
ejpam-5546	261	24	b1	b1	VERB
ejpam-5546	261	25	with	with	ADP
ejpam-5546	261	26	respect	respect	NOUN
ejpam-5546	261	27	to	to	ADP
ejpam-5546	261	28	the	the	DET
ejpam-5546	261	29	basis	basis	NOUN
ejpam-5546	261	30	s	s	NOUN
ejpam-5546	261	31	are	be	AUX
ejpam-5546	261	32	lower	low	ADJ
ejpam-5546	261	33	bidiagonal	bidiagonal	ADJ
ejpam-5546	261	34	and	and	CCONJ
ejpam-5546	261	35	upper	upper	ADJ
ejpam-5546	261	36	bidiagonal	bidiagonal	NOUN
ejpam-5546	261	37	respectively	respectively	ADV
ejpam-5546	261	38	in	in	ADP
ejpam-5546	261	39	which	which	PRON
ejpam-5546	261	40	αi	αi	X
ejpam-5546	261	41	=	=	PUNCT
ejpam-5546	262	1	[	[	X
ejpam-5546	262	2	a]s(i	a]s(i	PRON
ejpam-5546	262	3	,	,	PUNCT
ejpam-5546	262	4	i	i	PROPN
ejpam-5546	262	5	)	)	PUNCT
ejpam-5546	262	6	,	,	PUNCT
ejpam-5546	262	7	α	α	NOUN
ejpam-5546	262	8	∗	∗	NOUN
ejpam-5546	262	9	i	i	PRON
ejpam-5546	262	10	=	=	PUNCT
ejpam-5546	263	1	[	[	X
ejpam-5546	263	2	b1]s(i	b1]s(i	PROPN
ejpam-5546	263	3	,	,	PUNCT
ejpam-5546	263	4	i	i	PROPN
ejpam-5546	263	5	)	)	PUNCT
ejpam-5546	263	6	,	,	PUNCT
ejpam-5546	263	7	and	and	CCONJ
ejpam-5546	263	8	φi	φi	ADP
ejpam-5546	263	9	=	=	X
ejpam-5546	263	10	[	[	X
ejpam-5546	263	11	a]s(i	a]s(i	NOUN
ejpam-5546	263	12	,	,	PUNCT
ejpam-5546	263	13	i−	i−	ADJ
ejpam-5546	263	14	1)[b1]s(i−	1)[b1]s(i−	NUM
ejpam-5546	263	15	1	1	NUM
ejpam-5546	263	16	,	,	PUNCT
ejpam-5546	263	17	i	i	NOUN
ejpam-5546	263	18	)	)	PUNCT
ejpam-5546	263	19	.	.	PUNCT
ejpam-5546	264	1	in	in	ADP
ejpam-5546	264	2	lemma	lemma	PROPN
ejpam-5546	264	3	12	12	NUM
ejpam-5546	264	4	we	we	PRON
ejpam-5546	264	5	show	show	VERB
ejpam-5546	264	6	that	that	SCONJ
ejpam-5546	264	7	the	the	DET
ejpam-5546	264	8	sequence	sequence	NOUN
ejpam-5546	264	9	of	of	ADP
ejpam-5546	264	10	scalars	scalar	NOUN
ejpam-5546	264	11	(	(	PUNCT
ejpam-5546	264	12	{	{	PUNCT
ejpam-5546	264	13	αi}di=0	αi}di=0	NOUN
ejpam-5546	264	14	,	,	PUNCT
ejpam-5546	264	15	{	{	PUNCT
ejpam-5546	264	16	α∗	α∗	NOUN
ejpam-5546	264	17	i	i	PRON
ejpam-5546	264	18	}	}	PUNCT
ejpam-5546	264	19	di=0	di=0	PROPN
ejpam-5546	264	20	;	;	PUNCT
ejpam-5546	264	21	{	{	PUNCT
ejpam-5546	264	22	φj}dj=1	φj}dj=1	NOUN
ejpam-5546	264	23	,	,	PUNCT
ejpam-5546	264	24	{	{	PUNCT
ejpam-5546	264	25	ϕj}dj=1	ϕj}dj=1	PROPN
ejpam-5546	264	26	)	)	PUNCT
ejpam-5546	264	27	is	be	AUX
ejpam-5546	264	28	a	a	DET
ejpam-5546	264	29	parameter	parameter	NOUN
ejpam-5546	264	30	array	array	NOUN
ejpam-5546	264	31	if	if	SCONJ
ejpam-5546	264	32	and	and	CCONJ
ejpam-5546	264	33	only	only	ADV
ejpam-5546	264	34	if	if	SCONJ
ejpam-5546	264	35	a	a	DET
ejpam-5546	264	36	̸=	̸=	PROPN
ejpam-5546	264	37	0	0	NUM
ejpam-5546	264	38	,	,	PUNCT
ejpam-5546	264	39	b	b	X
ejpam-5546	264	40	̸=	̸=	PROPN
ejpam-5546	264	41	0	0	NUM
ejpam-5546	264	42	and	and	CCONJ
ejpam-5546	264	43	a	a	DET
ejpam-5546	264	44	−	−	PROPN
ejpam-5546	264	45	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	264	46	)	)	PUNCT
ejpam-5546	264	47	̸=	̸=	PROPN
ejpam-5546	264	48	0	0	NUM
ejpam-5546	264	49	for	for	ADP
ejpam-5546	264	50	1	1	NUM
ejpam-5546	264	51	≤	≤	NUM
ejpam-5546	264	52	i	i	PRON
ejpam-5546	264	53	≤	≤	ADJ
ejpam-5546	264	54	2d	2d	NOUN
ejpam-5546	264	55	−	−	NOUN
ejpam-5546	264	56	1	1	NUM
ejpam-5546	264	57	.	.	PUNCT
ejpam-5546	265	1	hence	hence	ADV
ejpam-5546	265	2	,	,	PUNCT
ejpam-5546	265	3	the	the	DET
ejpam-5546	265	4	result	result	NOUN
ejpam-5546	265	5	hold	hold	NOUN
ejpam-5546	265	6	by	by	ADP
ejpam-5546	265	7	theorem	theorem	NOUN
ejpam-5546	265	8	1	1	NUM
ejpam-5546	265	9	.	.	PUNCT
ejpam-5546	265	10	h.	h.	PROPN
ejpam-5546	265	11	alnajjar	alnajjar	PROPN
ejpam-5546	265	12	/	/	SYM
ejpam-5546	265	13	eur	eur	PROPN
ejpam-5546	265	14	.	.	PUNCT
ejpam-5546	266	1	j.	j.	PROPN
ejpam-5546	266	2	pure	pure	PROPN
ejpam-5546	266	3	appl	appl	PROPN
ejpam-5546	266	4	.	.	PROPN
ejpam-5546	266	5	math	math	PROPN
ejpam-5546	266	6	,	,	PUNCT
ejpam-5546	266	7	18	18	NUM
ejpam-5546	266	8	(	(	PUNCT
ejpam-5546	266	9	1	1	NUM
ejpam-5546	266	10	)	)	PUNCT
ejpam-5546	266	11	(	(	PUNCT
ejpam-5546	266	12	2025	2025	NUM
ejpam-5546	266	13	)	)	PUNCT
ejpam-5546	266	14	,	,	PUNCT
ejpam-5546	266	15	5546	5546	NUM
ejpam-5546	266	16	9	9	NUM
ejpam-5546	266	17	of	of	ADP
ejpam-5546	266	18	14	14	NUM
ejpam-5546	266	19	5	5	NUM
ejpam-5546	266	20	.	.	PUNCT
ejpam-5546	267	1	the	the	DET
ejpam-5546	267	2	leonard	leonard	PROPN
ejpam-5546	267	3	pair	pair	NOUN
ejpam-5546	267	4	a	a	PRON
ejpam-5546	267	5	,	,	PUNCT
ejpam-5546	267	6	x30	x30	PROPN
ejpam-5546	267	7	lemma	lemma	PROPN
ejpam-5546	267	8	13	13	NUM
ejpam-5546	267	9	.	.	PUNCT
ejpam-5546	268	1	with	with	ADP
ejpam-5546	268	2	reference	reference	NOUN
ejpam-5546	268	3	to	to	ADP
ejpam-5546	268	4	lemma	lemma	PROPN
ejpam-5546	268	5	2	2	NUM
ejpam-5546	268	6	and	and	CCONJ
ejpam-5546	268	7	definition	definition	NOUN
ejpam-5546	268	8	7	7	NUM
ejpam-5546	268	9	,	,	PUNCT
ejpam-5546	268	10	let	let	VERB
ejpam-5546	268	11	b2	b2	NOUN
ejpam-5546	268	12	=	=	PUNCT
ejpam-5546	268	13	x30	x30	PROPN
ejpam-5546	268	14	.	.	PUNCT
ejpam-5546	269	1	then	then	ADV
ejpam-5546	269	2	the	the	DET
ejpam-5546	269	3	matrices	matrix	NOUN
ejpam-5546	269	4	represent	represent	VERB
ejpam-5546	269	5	a	a	PRON
ejpam-5546	269	6	and	and	CCONJ
ejpam-5546	269	7	b2	b2	VERB
ejpam-5546	269	8	with	with	ADP
ejpam-5546	269	9	respect	respect	NOUN
ejpam-5546	269	10	to	to	ADP
ejpam-5546	269	11	the	the	DET
ejpam-5546	269	12	basis	basis	NOUN
ejpam-5546	269	13	s	s	NOUN
ejpam-5546	269	14	are	be	AUX
ejpam-5546	269	15	lower	low	ADJ
ejpam-5546	269	16	bidiagonal	bidiagonal	ADJ
ejpam-5546	269	17	and	and	CCONJ
ejpam-5546	269	18	upper	upper	ADJ
ejpam-5546	269	19	bidiagonal	bidiagonal	NOUN
ejpam-5546	269	20	respectively	respectively	ADV
ejpam-5546	269	21	with	with	ADP
ejpam-5546	269	22	entries	entry	NOUN
ejpam-5546	269	23	:	:	PUNCT
ejpam-5546	269	24	[	[	X
ejpam-5546	269	25	a]s(i	a]s(i	NOUN
ejpam-5546	269	26	,	,	PUNCT
ejpam-5546	269	27	i	i	NOUN
ejpam-5546	269	28	)	)	PUNCT
ejpam-5546	269	29	=	=	PUNCT
ejpam-5546	270	1	aqd−2i	aqd−2i	NOUN
ejpam-5546	271	1	+	+	CCONJ
ejpam-5546	271	2	bq2i−d	bq2i−d	NOUN
ejpam-5546	271	3	(	(	PUNCT
ejpam-5546	271	4	0	0	NUM
ejpam-5546	271	5	≤	≤	NUM
ejpam-5546	271	6	i	i	NOUN
ejpam-5546	271	7	≤	≤	NUM
ejpam-5546	272	1	d	d	X
ejpam-5546	272	2	)	)	PUNCT
ejpam-5546	272	3	,	,	PUNCT
ejpam-5546	273	1	[	[	X
ejpam-5546	273	2	b2]s(i	b2]s(i	NOUN
ejpam-5546	273	3	,	,	PUNCT
ejpam-5546	273	4	i	i	NOUN
ejpam-5546	273	5	)	)	PUNCT
ejpam-5546	274	1	=	=	PUNCT
ejpam-5546	274	2	q2i−d	q2i−d	PROPN
ejpam-5546	274	3	(	(	PUNCT
ejpam-5546	274	4	0	0	NUM
ejpam-5546	274	5	≤	≤	NUM
ejpam-5546	275	1	i	i	NOUN
ejpam-5546	275	2	≤	≤	NUM
ejpam-5546	276	1	d	d	X
ejpam-5546	276	2	)	)	PUNCT
ejpam-5546	276	3	,	,	PUNCT
ejpam-5546	277	1	[	[	X
ejpam-5546	277	2	a]s(i	a]s(i	NOUN
ejpam-5546	277	3	,	,	PUNCT
ejpam-5546	277	4	i−	i−	PROPN
ejpam-5546	277	5	1	1	NUM
ejpam-5546	277	6	)	)	PUNCT
ejpam-5546	277	7	=	=	PUNCT
ejpam-5546	277	8	bq−d(1−	bq−d(1−	PROPN
ejpam-5546	277	9	q2i	q2i	PROPN
ejpam-5546	277	10	)	)	PUNCT
ejpam-5546	277	11	(	(	PUNCT
ejpam-5546	277	12	1	1	NUM
ejpam-5546	277	13	≤	≤	NUM
ejpam-5546	277	14	i	i	X
ejpam-5546	277	15	≤	≤	NUM
ejpam-5546	278	1	d	d	X
ejpam-5546	278	2	)	)	PUNCT
ejpam-5546	278	3	,	,	PUNCT
ejpam-5546	278	4	[	[	X
ejpam-5546	278	5	b2]s(i−	b2]s(i−	NOUN
ejpam-5546	278	6	1	1	NUM
ejpam-5546	278	7	,	,	PUNCT
ejpam-5546	278	8	i	i	NOUN
ejpam-5546	278	9	)	)	PUNCT
ejpam-5546	278	10	=	=	PUNCT
ejpam-5546	278	11	qd(1−	qd(1−	PROPN
ejpam-5546	278	12	q2i−2d−2)(1−	q2i−2d−2)(1−	PROPN
ejpam-5546	278	13	tqd−2i+1	tqd−2i+1	PRON
ejpam-5546	278	14	)	)	PUNCT
ejpam-5546	278	15	(	(	PUNCT
ejpam-5546	278	16	1	1	NUM
ejpam-5546	278	17	≤	≤	NUM
ejpam-5546	278	18	i	i	X
ejpam-5546	278	19	≤	≤	NUM
ejpam-5546	278	20	d	d	X
ejpam-5546	278	21	)	)	PUNCT
ejpam-5546	278	22	.	.	PUNCT
ejpam-5546	279	1	proof	proof	NOUN
ejpam-5546	279	2	.	.	PUNCT
ejpam-5546	280	1	the	the	DET
ejpam-5546	280	2	matrices	matrix	NOUN
ejpam-5546	280	3	that	that	PRON
ejpam-5546	280	4	represent	represent	VERB
ejpam-5546	280	5	the	the	DET
ejpam-5546	280	6	action	action	NOUN
ejpam-5546	280	7	of	of	ADP
ejpam-5546	280	8	x01	x01	PROPN
ejpam-5546	280	9	,	,	PUNCT
ejpam-5546	280	10	x12	x12	NUM
ejpam-5546	280	11	and	and	CCONJ
ejpam-5546	280	12	x30	x30	NUM
ejpam-5546	280	13	are	be	AUX
ejpam-5546	280	14	given	give	VERB
ejpam-5546	280	15	in	in	ADP
ejpam-5546	280	16	lemma	lemma	PROPN
ejpam-5546	280	17	2	2	NUM
ejpam-5546	280	18	,	,	PUNCT
ejpam-5546	280	19	and	and	CCONJ
ejpam-5546	280	20	the	the	DET
ejpam-5546	280	21	entries	entry	NOUN
ejpam-5546	280	22	of	of	ADP
ejpam-5546	280	23	these	these	DET
ejpam-5546	280	24	matrices	matrix	NOUN
ejpam-5546	280	25	are	be	AUX
ejpam-5546	280	26	given	give	VERB
ejpam-5546	280	27	in	in	ADP
ejpam-5546	280	28	definition	definition	NOUN
ejpam-5546	280	29	6	6	NUM
ejpam-5546	280	30	.	.	PUNCT
ejpam-5546	281	1	definition	definition	NOUN
ejpam-5546	281	2	9	9	NUM
ejpam-5546	281	3	.	.	PUNCT
ejpam-5546	282	1	with	with	ADP
ejpam-5546	282	2	reference	reference	NOUN
ejpam-5546	282	3	to	to	ADP
ejpam-5546	282	4	lemma	lemma	PROPN
ejpam-5546	282	5	13	13	NUM
ejpam-5546	282	6	,	,	PUNCT
ejpam-5546	282	7	define	define	VERB
ejpam-5546	282	8	ψi	ψi	ADP
ejpam-5546	282	9	=	=	SYM
ejpam-5546	282	10	b(1−	b(1−	X
ejpam-5546	282	11	q2i−d)(1−	q2i−d)(1−	PROPN
ejpam-5546	282	12	q2i−2d−2)(1−	q2i−2d−2)(1−	PROPN
ejpam-5546	282	13	tqd−2i+1	tqd−2i+1	PRON
ejpam-5546	282	14	)	)	PUNCT
ejpam-5546	282	15	(	(	PUNCT
ejpam-5546	282	16	1	1	NUM
ejpam-5546	282	17	≤	≤	NUM
ejpam-5546	282	18	i	i	X
ejpam-5546	282	19	≤	≤	NUM
ejpam-5546	283	1	d	d	X
ejpam-5546	283	2	)	)	PUNCT
ejpam-5546	283	3	,	,	PUNCT
ejpam-5546	283	4	λi	λi	ADP
ejpam-5546	283	5	=	=	PRON
ejpam-5546	283	6	q−d−1(q2d−2i+2	q−d−1(q2d−2i+2	VERB
ejpam-5546	283	7	−	−	PROPN
ejpam-5546	283	8	1)(q2i	1)(q2i	NUM
ejpam-5546	283	9	−	−	PROPN
ejpam-5546	283	10	1)(bt−	1)(bt−	PROPN
ejpam-5546	283	11	aq2i−d−1	aq2i−d−1	NUM
ejpam-5546	283	12	)	)	PUNCT
ejpam-5546	283	13	(	(	PUNCT
ejpam-5546	283	14	1	1	NUM
ejpam-5546	283	15	≤	≤	NUM
ejpam-5546	283	16	i	i	X
ejpam-5546	284	1	≤	≤	NUM
ejpam-5546	284	2	d	d	X
ejpam-5546	284	3	)	)	PUNCT
ejpam-5546	284	4	note	note	NOUN
ejpam-5546	284	5	that	that	SCONJ
ejpam-5546	284	6	αi	αi	VERB
ejpam-5546	284	7	=	=	PUNCT
ejpam-5546	285	1	[	[	X
ejpam-5546	285	2	a]s(i	a]s(i	PRON
ejpam-5546	285	3	,	,	PUNCT
ejpam-5546	285	4	i	i	PROPN
ejpam-5546	285	5	)	)	PUNCT
ejpam-5546	285	6	,	,	PUNCT
ejpam-5546	285	7	α	α	NOUN
ejpam-5546	285	8	∗	∗	NOUN
ejpam-5546	285	9	i	i	PRON
ejpam-5546	286	1	=	=	PUNCT
ejpam-5546	287	1	[	[	X
ejpam-5546	287	2	b2]s(i	b2]s(i	NOUN
ejpam-5546	287	3	,	,	PUNCT
ejpam-5546	287	4	i	i	NOUN
ejpam-5546	287	5	)	)	PUNCT
ejpam-5546	287	6	for	for	ADP
ejpam-5546	287	7	(	(	PUNCT
ejpam-5546	287	8	0	0	NUM
ejpam-5546	287	9	≤	≤	NUM
ejpam-5546	287	10	i	i	NOUN
ejpam-5546	287	11	≤	≤	NUM
ejpam-5546	287	12	d	d	X
ejpam-5546	287	13	)	)	PUNCT
ejpam-5546	287	14	,	,	PUNCT
ejpam-5546	287	15	where	where	SCONJ
ejpam-5546	287	16	αi	αi	PRON
ejpam-5546	287	17	and	and	CCONJ
ejpam-5546	287	18	α∗	α∗	NOUN
ejpam-5546	287	19	i	i	PRON
ejpam-5546	287	20	appear	appear	VERB
ejpam-5546	287	21	in	in	ADP
ejpam-5546	287	22	definition	definition	NOUN
ejpam-5546	287	23	8	8	NUM
ejpam-5546	287	24	.	.	PUNCT
ejpam-5546	287	25	and	and	CCONJ
ejpam-5546	287	26	ψi	ψi	ADP
ejpam-5546	287	27	=	=	PUNCT
ejpam-5546	288	1	[	[	X
ejpam-5546	288	2	a]s(i	a]s(i	NOUN
ejpam-5546	288	3	,	,	PUNCT
ejpam-5546	288	4	i−	i−	ADJ
ejpam-5546	288	5	1)[b2]s(i−	1)[b2]s(i−	NUM
ejpam-5546	288	6	1	1	NUM
ejpam-5546	288	7	,	,	PUNCT
ejpam-5546	288	8	i	i	NOUN
ejpam-5546	288	9	)	)	PUNCT
ejpam-5546	288	10	for	for	ADP
ejpam-5546	288	11	(	(	PUNCT
ejpam-5546	288	12	1	1	NUM
ejpam-5546	288	13	≤	≤	NUM
ejpam-5546	288	14	i	i	X
ejpam-5546	289	1	≤	≤	NUM
ejpam-5546	289	2	d	d	X
ejpam-5546	289	3	)	)	PUNCT
ejpam-5546	289	4	.	.	PUNCT
ejpam-5546	290	1	now	now	ADV
ejpam-5546	290	2	,	,	PUNCT
ejpam-5546	290	3	by	by	ADP
ejpam-5546	290	4	theorem	theorem	NOUN
ejpam-5546	290	5	1	1	NUM
ejpam-5546	290	6	,	,	PUNCT
ejpam-5546	290	7	if	if	SCONJ
ejpam-5546	290	8	we	we	PRON
ejpam-5546	290	9	find	find	VERB
ejpam-5546	290	10	the	the	DET
ejpam-5546	290	11	conditions	condition	NOUN
ejpam-5546	290	12	on	on	ADP
ejpam-5546	290	13	the	the	DET
ejpam-5546	290	14	sequence	sequence	NOUN
ejpam-5546	290	15	of	of	ADP
ejpam-5546	290	16	scalars	scalar	NOUN
ejpam-5546	290	17	(	(	PUNCT
ejpam-5546	290	18	{	{	PUNCT
ejpam-5546	290	19	αi}di=0	αi}di=0	NOUN
ejpam-5546	290	20	,	,	PUNCT
ejpam-5546	290	21	{	{	PUNCT
ejpam-5546	290	22	α∗	α∗	NOUN
ejpam-5546	290	23	i	i	PRON
ejpam-5546	290	24	}	}	PUNCT
ejpam-5546	290	25	di=0	di=0	PROPN
ejpam-5546	290	26	;	;	PUNCT
ejpam-5546	290	27	{	{	PUNCT
ejpam-5546	290	28	ψj}dj=1	ψj}dj=1	PROPN
ejpam-5546	290	29	,	,	PUNCT
ejpam-5546	290	30	{	{	PUNCT
ejpam-5546	290	31	λj}dj=1	λj}dj=1	PROPN
ejpam-5546	290	32	)	)	PUNCT
ejpam-5546	290	33	in	in	ADP
ejpam-5546	290	34	which	which	PRON
ejpam-5546	290	35	the	the	DET
ejpam-5546	290	36	sequence	sequence	NOUN
ejpam-5546	290	37	is	be	AUX
ejpam-5546	290	38	a	a	DET
ejpam-5546	290	39	parameter	parameter	NOUN
ejpam-5546	290	40	array	array	NOUN
ejpam-5546	290	41	,	,	PUNCT
ejpam-5546	290	42	then	then	ADV
ejpam-5546	290	43	these	these	DET
ejpam-5546	290	44	conditions	condition	NOUN
ejpam-5546	290	45	imply	imply	VERB
ejpam-5546	290	46	that	that	SCONJ
ejpam-5546	290	47	the	the	DET
ejpam-5546	290	48	pair	pair	NOUN
ejpam-5546	290	49	a	a	DET
ejpam-5546	290	50	,	,	PUNCT
ejpam-5546	290	51	b2	b2	NOUN
ejpam-5546	290	52	is	be	AUX
ejpam-5546	290	53	a	a	DET
ejpam-5546	290	54	leonard	leonard	NOUN
ejpam-5546	290	55	pair	pair	NOUN
ejpam-5546	290	56	.	.	PUNCT
ejpam-5546	291	1	so	so	ADV
ejpam-5546	291	2	,	,	PUNCT
ejpam-5546	291	3	we	we	PRON
ejpam-5546	291	4	now	now	ADV
ejpam-5546	291	5	need	need	VERB
ejpam-5546	291	6	to	to	PART
ejpam-5546	291	7	find	find	VERB
ejpam-5546	291	8	when	when	SCONJ
ejpam-5546	291	9	the	the	DET
ejpam-5546	291	10	sequence	sequence	NOUN
ejpam-5546	291	11	(	(	PUNCT
ejpam-5546	291	12	{	{	PUNCT
ejpam-5546	291	13	αi}di=0	αi}di=0	NOUN
ejpam-5546	291	14	,	,	PUNCT
ejpam-5546	291	15	{	{	PUNCT
ejpam-5546	291	16	α∗	α∗	NOUN
ejpam-5546	291	17	i	i	PRON
ejpam-5546	291	18	}	}	PUNCT
ejpam-5546	291	19	di=0	di=0	PROPN
ejpam-5546	291	20	;	;	PUNCT
ejpam-5546	291	21	{	{	PUNCT
ejpam-5546	291	22	ψj}dj=1	ψj}dj=1	PROPN
ejpam-5546	291	23	,	,	PUNCT
ejpam-5546	291	24	{	{	PUNCT
ejpam-5546	291	25	λj}dj=1	λj}dj=1	NOUN
ejpam-5546	291	26	)	)	PUNCT
ejpam-5546	291	27	satisfies	satisfy	VERB
ejpam-5546	291	28	the	the	DET
ejpam-5546	291	29	seven	seven	NUM
ejpam-5546	291	30	conditions	condition	NOUN
ejpam-5546	291	31	of	of	ADP
ejpam-5546	291	32	the	the	DET
ejpam-5546	291	33	parameter	parameter	NOUN
ejpam-5546	291	34	array	array	NOUN
ejpam-5546	291	35	in	in	ADP
ejpam-5546	291	36	definition	definition	NOUN
ejpam-5546	291	37	2	2	NUM
ejpam-5546	291	38	.	.	PUNCT
ejpam-5546	291	39	from	from	ADP
ejpam-5546	291	40	lemmas	lemmas	PROPN
ejpam-5546	291	41	6	6	NUM
ejpam-5546	291	42	,	,	PUNCT
ejpam-5546	291	43	7	7	NUM
ejpam-5546	291	44	,	,	PUNCT
ejpam-5546	291	45	and	and	CCONJ
ejpam-5546	291	46	11	11	NUM
ejpam-5546	291	47	we	we	PRON
ejpam-5546	291	48	know	know	VERB
ejpam-5546	291	49	when	when	SCONJ
ejpam-5546	291	50	the	the	DET
ejpam-5546	291	51	conditions	condition	NOUN
ejpam-5546	291	52	1	1	NUM
ejpam-5546	291	53	,	,	PUNCT
ejpam-5546	291	54	2	2	NUM
ejpam-5546	291	55	,	,	PUNCT
ejpam-5546	291	56	and	and	CCONJ
ejpam-5546	291	57	7	7	NUM
ejpam-5546	291	58	hold	hold	NOUN
ejpam-5546	291	59	.	.	PUNCT
ejpam-5546	292	1	in	in	ADP
ejpam-5546	292	2	the	the	DET
ejpam-5546	292	3	next	next	ADJ
ejpam-5546	292	4	work	work	NOUN
ejpam-5546	292	5	we	we	PRON
ejpam-5546	292	6	will	will	AUX
ejpam-5546	292	7	find	find	VERB
ejpam-5546	292	8	when	when	SCONJ
ejpam-5546	292	9	the	the	DET
ejpam-5546	292	10	conditions	condition	NOUN
ejpam-5546	292	11	3−	3−	NUM
ejpam-5546	292	12	6	6	NUM
ejpam-5546	292	13	of	of	ADP
ejpam-5546	292	14	definition	definition	NOUN
ejpam-5546	292	15	2	2	NUM
ejpam-5546	292	16	hold	hold	NOUN
ejpam-5546	292	17	.	.	PUNCT
ejpam-5546	293	1	lemma	lemma	PROPN
ejpam-5546	293	2	14	14	NUM
ejpam-5546	293	3	.	.	PUNCT
ejpam-5546	294	1	with	with	ADP
ejpam-5546	294	2	reference	reference	NOUN
ejpam-5546	294	3	to	to	ADP
ejpam-5546	294	4	definitions	definition	NOUN
ejpam-5546	294	5	9	9	NUM
ejpam-5546	294	6	,	,	PUNCT
ejpam-5546	294	7	ψi	ψi	ADP
ejpam-5546	294	8	̸=	̸=	PROPN
ejpam-5546	294	9	0	0	PUNCT
ejpam-5546	294	10	if	if	SCONJ
ejpam-5546	294	11	and	and	CCONJ
ejpam-5546	294	12	only	only	ADV
ejpam-5546	294	13	if	if	SCONJ
ejpam-5546	294	14	b	b	PROPN
ejpam-5546	294	15	̸=	̸=	PROPN
ejpam-5546	294	16	0	0	NUM
ejpam-5546	294	17	and	and	CCONJ
ejpam-5546	294	18	t	t	PROPN
ejpam-5546	294	19	̸=	̸=	PROPN
ejpam-5546	294	20	q2i−d−1	q2i−d−1	NOUN
ejpam-5546	294	21	for	for	ADP
ejpam-5546	294	22	1	1	NUM
ejpam-5546	294	23	≤	≤	NUM
ejpam-5546	294	24	i	i	PRON
ejpam-5546	294	25	≤	≤	PROPN
ejpam-5546	294	26	d.	d.	PROPN
ejpam-5546	294	27	and	and	CCONJ
ejpam-5546	294	28	λi	λi	X
ejpam-5546	294	29	̸=	̸=	PROPN
ejpam-5546	294	30	0	0	PUNCT
ejpam-5546	295	1	if	if	SCONJ
ejpam-5546	295	2	and	and	CCONJ
ejpam-5546	295	3	only	only	ADV
ejpam-5546	295	4	if	if	SCONJ
ejpam-5546	295	5	bt	bt	PROPN
ejpam-5546	295	6	̸=	̸=	PROPN
ejpam-5546	295	7	aq2i−d−1	aq2i−d−1	X
ejpam-5546	295	8	for	for	ADP
ejpam-5546	295	9	1	1	NUM
ejpam-5546	295	10	≤	≤	NUM
ejpam-5546	295	11	i	i	PRON
ejpam-5546	295	12	≤	≤	ADJ
ejpam-5546	295	13	d.	d.	NOUN
ejpam-5546	295	14	proof	proof	NOUN
ejpam-5546	295	15	.	.	PUNCT
ejpam-5546	296	1	since	since	SCONJ
ejpam-5546	296	2	q	q	PROPN
ejpam-5546	296	3	is	be	AUX
ejpam-5546	296	4	not	not	PART
ejpam-5546	296	5	a	a	DET
ejpam-5546	296	6	root	root	NOUN
ejpam-5546	296	7	of	of	ADP
ejpam-5546	296	8	unity	unity	NOUN
ejpam-5546	296	9	,	,	PUNCT
ejpam-5546	296	10	this	this	PRON
ejpam-5546	296	11	implies	imply	VERB
ejpam-5546	296	12	that	that	SCONJ
ejpam-5546	296	13	ψi	ψi	ADP
ejpam-5546	296	14	=	=	SYM
ejpam-5546	296	15	0	0	PUNCT
ejpam-5546	297	1	if	if	SCONJ
ejpam-5546	297	2	and	and	CCONJ
ejpam-5546	297	3	only	only	ADV
ejpam-5546	297	4	if	if	SCONJ
ejpam-5546	297	5	b	b	X
ejpam-5546	297	6	=	=	SYM
ejpam-5546	297	7	0	0	NUM
ejpam-5546	297	8	or	or	CCONJ
ejpam-5546	297	9	1−	1−	NUM
ejpam-5546	297	10	tqd−2i+1	tqd−2i+1	PUNCT
ejpam-5546	297	11	=	=	NOUN
ejpam-5546	297	12	0	0	NUM
ejpam-5546	297	13	,	,	PUNCT
ejpam-5546	297	14	solve	solve	VERB
ejpam-5546	297	15	for	for	ADP
ejpam-5546	297	16	t	t	PROPN
ejpam-5546	297	17	to	to	PART
ejpam-5546	297	18	get	get	VERB
ejpam-5546	297	19	the	the	DET
ejpam-5546	297	20	result	result	NOUN
ejpam-5546	297	21	for	for	ADP
ejpam-5546	297	22	ψi	ψi	NOUN
ejpam-5546	297	23	.	.	PUNCT
ejpam-5546	297	24	similar	similar	ADJ
ejpam-5546	297	25	work	work	NOUN
ejpam-5546	297	26	for	for	ADP
ejpam-5546	297	27	λi	λi	PROPN
ejpam-5546	297	28	.	.	PUNCT
ejpam-5546	297	29	lemma	lemma	PROPN
ejpam-5546	297	30	15	15	NUM
ejpam-5546	297	31	.	.	PUNCT
ejpam-5546	298	1	with	with	ADP
ejpam-5546	298	2	reference	reference	NOUN
ejpam-5546	298	3	to	to	ADP
ejpam-5546	298	4	definitions	definition	NOUN
ejpam-5546	298	5	8	8	NUM
ejpam-5546	298	6	and	and	CCONJ
ejpam-5546	298	7	9	9	NUM
ejpam-5546	298	8	ψi	ψi	NOUN
ejpam-5546	298	9	=	=	SYM
ejpam-5546	298	10	λ1	λ1	ADJ
ejpam-5546	298	11	i−1∑	i−1∑	NUM
ejpam-5546	298	12	k=0	k=0	PROPN
ejpam-5546	298	13	αk	αk	AUX
ejpam-5546	298	14	−	−	NOUN
ejpam-5546	298	15	αd−k	αd−k	NOUN
ejpam-5546	298	16	α0	α0	ADJ
ejpam-5546	298	17	−	−	PROPN
ejpam-5546	298	18	αd	αd	NOUN
ejpam-5546	299	1	+	+	CCONJ
ejpam-5546	299	2	(	(	PUNCT
ejpam-5546	299	3	α∗	α∗	NOUN
ejpam-5546	299	4	i	i	PRON
ejpam-5546	299	5	−	−	VERB
ejpam-5546	299	6	α∗	α∗	VERB
ejpam-5546	299	7	0)(αi−1	0)(αi−1	NUM
ejpam-5546	299	8	−	−	NUM
ejpam-5546	299	9	αd	αd	PROPN
ejpam-5546	299	10	)	)	PUNCT
ejpam-5546	299	11	(	(	PUNCT
ejpam-5546	299	12	1	1	NUM
ejpam-5546	299	13	≤	≤	NUM
ejpam-5546	299	14	i	i	X
ejpam-5546	299	15	≤	≤	NUM
ejpam-5546	299	16	d	d	X
ejpam-5546	299	17	)	)	PUNCT
ejpam-5546	299	18	.	.	PUNCT
ejpam-5546	300	1	proof	proof	NOUN
ejpam-5546	300	2	.	.	PUNCT
ejpam-5546	301	1	similar	similar	ADJ
ejpam-5546	301	2	to	to	ADP
ejpam-5546	301	3	proof	proof	NOUN
ejpam-5546	301	4	of	of	ADP
ejpam-5546	301	5	lemma	lemma	PROPN
ejpam-5546	301	6	9	9	NUM
ejpam-5546	301	7	.	.	PUNCT
ejpam-5546	302	1	lemma	lemma	PROPN
ejpam-5546	302	2	16	16	NUM
ejpam-5546	302	3	.	.	PUNCT
ejpam-5546	303	1	with	with	ADP
ejpam-5546	303	2	reference	reference	NOUN
ejpam-5546	303	3	to	to	ADP
ejpam-5546	303	4	definitions	definition	NOUN
ejpam-5546	303	5	8	8	NUM
ejpam-5546	303	6	and	and	CCONJ
ejpam-5546	303	7	9	9	NUM
ejpam-5546	303	8	,	,	PUNCT
ejpam-5546	303	9	λi	λi	NOUN
ejpam-5546	303	10	=	=	NOUN
ejpam-5546	303	11	ψ1	ψ1	NOUN
ejpam-5546	303	12	i−1∑	i−1∑	NOUN
ejpam-5546	303	13	h=0	h=0	PROPN
ejpam-5546	303	14	αh	αh	ADP
ejpam-5546	303	15	−	−	NOUN
ejpam-5546	303	16	αd−h	αd−h	PROPN
ejpam-5546	303	17	α0	α0	ADJ
ejpam-5546	303	18	−	−	PROPN
ejpam-5546	303	19	αd	αd	PROPN
ejpam-5546	303	20	+	+	CCONJ
ejpam-5546	303	21	(	(	PUNCT
ejpam-5546	303	22	α∗	α∗	NOUN
ejpam-5546	303	23	i	i	PRON
ejpam-5546	303	24	−	−	NOUN
ejpam-5546	303	25	α∗	α∗	VERB
ejpam-5546	303	26	0)(αd−i+1	0)(αd−i+1	NOUN
ejpam-5546	303	27	−	−	PROPN
ejpam-5546	303	28	α0	α0	ADJ
ejpam-5546	303	29	)	)	PUNCT
ejpam-5546	303	30	(	(	PUNCT
ejpam-5546	303	31	1	1	NUM
ejpam-5546	303	32	≤	≤	NUM
ejpam-5546	303	33	i	i	X
ejpam-5546	303	34	≤	≤	NUM
ejpam-5546	304	1	d	d	X
ejpam-5546	304	2	)	)	PUNCT
ejpam-5546	304	3	.	.	PUNCT
ejpam-5546	305	1	h.	h.	PROPN
ejpam-5546	305	2	alnajjar	alnajjar	PROPN
ejpam-5546	305	3	/	/	SYM
ejpam-5546	305	4	eur	eur	PROPN
ejpam-5546	305	5	.	.	PUNCT
ejpam-5546	306	1	j.	j.	PROPN
ejpam-5546	306	2	pure	pure	PROPN
ejpam-5546	306	3	appl	appl	PROPN
ejpam-5546	306	4	.	.	PROPN
ejpam-5546	306	5	math	math	PROPN
ejpam-5546	306	6	,	,	PUNCT
ejpam-5546	306	7	18	18	NUM
ejpam-5546	306	8	(	(	PUNCT
ejpam-5546	306	9	1	1	NUM
ejpam-5546	306	10	)	)	PUNCT
ejpam-5546	306	11	(	(	PUNCT
ejpam-5546	306	12	2025	2025	NUM
ejpam-5546	306	13	)	)	PUNCT
ejpam-5546	306	14	,	,	PUNCT
ejpam-5546	306	15	5546	5546	NUM
ejpam-5546	306	16	10	10	NUM
ejpam-5546	306	17	of	of	ADP
ejpam-5546	306	18	14	14	NUM
ejpam-5546	306	19	proof	proof	NOUN
ejpam-5546	306	20	.	.	PUNCT
ejpam-5546	307	1	similar	similar	ADJ
ejpam-5546	307	2	to	to	ADP
ejpam-5546	307	3	proof	proof	NOUN
ejpam-5546	307	4	of	of	ADP
ejpam-5546	307	5	lemma	lemma	PROPN
ejpam-5546	307	6	9	9	NUM
ejpam-5546	307	7	.	.	PUNCT
ejpam-5546	308	1	lemma	lemma	PROPN
ejpam-5546	308	2	17	17	NUM
ejpam-5546	308	3	.	.	PUNCT
ejpam-5546	309	1	with	with	ADP
ejpam-5546	309	2	reference	reference	NOUN
ejpam-5546	309	3	to	to	ADP
ejpam-5546	309	4	definitions	definition	NOUN
ejpam-5546	309	5	8	8	NUM
ejpam-5546	309	6	and	and	CCONJ
ejpam-5546	309	7	9	9	NUM
ejpam-5546	309	8	,	,	PUNCT
ejpam-5546	309	9	let	let	VERB
ejpam-5546	309	10	a	a	DET
ejpam-5546	309	11	,	,	PUNCT
ejpam-5546	309	12	b	b	NOUN
ejpam-5546	309	13	and	and	CCONJ
ejpam-5546	309	14	t	t	PROPN
ejpam-5546	309	15	be	be	AUX
ejpam-5546	309	16	scalars	scalar	NOUN
ejpam-5546	309	17	in	in	ADP
ejpam-5546	309	18	f	f	PROPN
ejpam-5546	309	19	.	.	PUNCT
ejpam-5546	310	1	then	then	ADV
ejpam-5546	310	2	the	the	DET
ejpam-5546	310	3	sequence	sequence	NOUN
ejpam-5546	310	4	of	of	ADP
ejpam-5546	310	5	scalars	scalar	NOUN
ejpam-5546	310	6	(	(	PUNCT
ejpam-5546	310	7	{	{	PUNCT
ejpam-5546	310	8	αi}di=0	αi}di=0	NOUN
ejpam-5546	310	9	,	,	PUNCT
ejpam-5546	310	10	{	{	PUNCT
ejpam-5546	310	11	α∗	α∗	NOUN
ejpam-5546	310	12	i	i	PRON
ejpam-5546	310	13	}	}	PUNCT
ejpam-5546	310	14	di=0	di=0	PROPN
ejpam-5546	310	15	;	;	PUNCT
ejpam-5546	310	16	{	{	PUNCT
ejpam-5546	310	17	ψj}dj=1	ψj}dj=1	PROPN
ejpam-5546	310	18	,	,	PUNCT
ejpam-5546	310	19	{	{	PUNCT
ejpam-5546	310	20	λj}dj=1	λj}dj=1	PROPN
ejpam-5546	310	21	)	)	PUNCT
ejpam-5546	310	22	is	be	AUX
ejpam-5546	310	23	a	a	DET
ejpam-5546	310	24	parameter	parameter	NOUN
ejpam-5546	310	25	array	array	NOUN
ejpam-5546	310	26	if	if	SCONJ
ejpam-5546	311	1	and	and	CCONJ
ejpam-5546	311	2	only	only	ADV
ejpam-5546	311	3	if	if	SCONJ
ejpam-5546	311	4	b	b	PROPN
ejpam-5546	311	5	̸=	̸=	PROPN
ejpam-5546	311	6	0	0	NUM
ejpam-5546	311	7	,	,	PUNCT
ejpam-5546	311	8	t	t	PROPN
ejpam-5546	311	9	̸=	̸=	PROPN
ejpam-5546	311	10	q2i−d−1	q2i−d−1	NOUN
ejpam-5546	311	11	,	,	PUNCT
ejpam-5546	311	12	bt	bt	NOUN
ejpam-5546	311	13	̸=	̸=	PROPN
ejpam-5546	311	14	aq2i−d−1	aq2i−d−1	X
ejpam-5546	311	15	for	for	ADP
ejpam-5546	311	16	1	1	NUM
ejpam-5546	311	17	≤	≤	NUM
ejpam-5546	311	18	i	i	PRON
ejpam-5546	311	19	≤	≤	PROPN
ejpam-5546	311	20	d	d	ADP
ejpam-5546	311	21	,	,	PUNCT
ejpam-5546	311	22	and	and	CCONJ
ejpam-5546	311	23	a−	a−	PROPN
ejpam-5546	311	24	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	311	25	)	)	PUNCT
ejpam-5546	312	1	̸=	̸=	NOUN
ejpam-5546	312	2	0	0	NUM
ejpam-5546	312	3	for	for	ADP
ejpam-5546	312	4	1	1	NUM
ejpam-5546	312	5	≤	≤	NUM
ejpam-5546	312	6	i	i	PRON
ejpam-5546	312	7	≤	≤	NOUN
ejpam-5546	313	1	2d−	2d−	PROPN
ejpam-5546	313	2	1	1	NUM
ejpam-5546	313	3	.	.	PUNCT
ejpam-5546	314	1	proof	proof	NOUN
ejpam-5546	314	2	.	.	PUNCT
ejpam-5546	315	1	note	note	VERB
ejpam-5546	315	2	that	that	SCONJ
ejpam-5546	315	3	the	the	DET
ejpam-5546	315	4	conditions	condition	NOUN
ejpam-5546	315	5	1	1	NUM
ejpam-5546	315	6	−	−	NOUN
ejpam-5546	315	7	7	7	NUM
ejpam-5546	315	8	of	of	ADP
ejpam-5546	315	9	the	the	DET
ejpam-5546	315	10	parameter	parameter	NOUN
ejpam-5546	315	11	array	array	NOUN
ejpam-5546	315	12	in	in	ADP
ejpam-5546	315	13	definition	definition	NOUN
ejpam-5546	315	14	2	2	NUM
ejpam-5546	315	15	hold	hold	VERB
ejpam-5546	315	16	for	for	ADP
ejpam-5546	315	17	the	the	DET
ejpam-5546	315	18	sequence	sequence	NOUN
ejpam-5546	315	19	(	(	PUNCT
ejpam-5546	315	20	{	{	PUNCT
ejpam-5546	315	21	αi}di=0	αi}di=0	NOUN
ejpam-5546	315	22	,	,	PUNCT
ejpam-5546	315	23	{	{	PUNCT
ejpam-5546	315	24	α∗	α∗	NOUN
ejpam-5546	315	25	i	i	PRON
ejpam-5546	315	26	}	}	PUNCT
ejpam-5546	315	27	di=0	di=0	PROPN
ejpam-5546	315	28	;	;	PUNCT
ejpam-5546	315	29	{	{	PUNCT
ejpam-5546	315	30	ψj}dj=1	ψj}dj=1	PROPN
ejpam-5546	315	31	,	,	PUNCT
ejpam-5546	315	32	{	{	PUNCT
ejpam-5546	315	33	λj}dj=1	λj}dj=1	PROPN
ejpam-5546	315	34	)	)	PUNCT
ejpam-5546	315	35	from	from	ADP
ejpam-5546	315	36	lemmas	lemmas	PROPN
ejpam-5546	315	37	6	6	NUM
ejpam-5546	315	38	,	,	PUNCT
ejpam-5546	315	39	7	7	NUM
ejpam-5546	315	40	,	,	PUNCT
ejpam-5546	315	41	14	14	NUM
ejpam-5546	315	42	,	,	PUNCT
ejpam-5546	315	43	15	15	NUM
ejpam-5546	315	44	,	,	PUNCT
ejpam-5546	315	45	16	16	NUM
ejpam-5546	315	46	,	,	PUNCT
ejpam-5546	315	47	11	11	NUM
ejpam-5546	315	48	respectively	respectively	ADV
ejpam-5546	315	49	if	if	SCONJ
ejpam-5546	315	50	and	and	CCONJ
ejpam-5546	315	51	only	only	ADV
ejpam-5546	315	52	if	if	SCONJ
ejpam-5546	315	53	b	b	PROPN
ejpam-5546	315	54	̸=	̸=	PROPN
ejpam-5546	315	55	0	0	NUM
ejpam-5546	315	56	,	,	PUNCT
ejpam-5546	315	57	t	t	PROPN
ejpam-5546	315	58	̸=	̸=	PROPN
ejpam-5546	315	59	q2i−d−1	q2i−d−1	NOUN
ejpam-5546	315	60	,	,	PUNCT
ejpam-5546	315	61	bt	bt	NOUN
ejpam-5546	315	62	̸=	̸=	PROPN
ejpam-5546	315	63	aq2i−d−1	aq2i−d−1	X
ejpam-5546	315	64	for	for	ADP
ejpam-5546	315	65	1	1	NUM
ejpam-5546	315	66	≤	≤	NUM
ejpam-5546	315	67	i	i	PRON
ejpam-5546	315	68	≤	≤	PROPN
ejpam-5546	316	1	d	d	ADP
ejpam-5546	316	2	,	,	PUNCT
ejpam-5546	316	3	and	and	CCONJ
ejpam-5546	316	4	a−	a−	PROPN
ejpam-5546	316	5	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	316	6	)	)	PUNCT
ejpam-5546	317	1	̸=	̸=	NOUN
ejpam-5546	317	2	0	0	NUM
ejpam-5546	317	3	for	for	ADP
ejpam-5546	317	4	1	1	NUM
ejpam-5546	317	5	≤	≤	NUM
ejpam-5546	317	6	i	i	PRON
ejpam-5546	317	7	≤	≤	NOUN
ejpam-5546	318	1	2d−	2d−	NUM
ejpam-5546	318	2	1	1	NUM
ejpam-5546	318	3	.	.	PUNCT
ejpam-5546	319	1	theorem	theorem	NOUN
ejpam-5546	319	2	3	3	NUM
ejpam-5546	320	1	.	.	PUNCT
ejpam-5546	320	2	assume	assume	VERB
ejpam-5546	320	3	d	d	X
ejpam-5546	320	4	≥	≥	NUM
ejpam-5546	320	5	2	2	NUM
ejpam-5546	320	6	,	,	PUNCT
ejpam-5546	320	7	let	let	VERB
ejpam-5546	320	8	v	v	PART
ejpam-5546	320	9	denote	denote	VERB
ejpam-5546	320	10	an	an	DET
ejpam-5546	320	11	evaluation	evaluation	NOUN
ejpam-5546	320	12	module	module	NOUN
ejpam-5546	320	13	for	for	ADP
ejpam-5546	320	14	⊠q	⊠q	PROPN
ejpam-5546	320	15	with	with	ADP
ejpam-5546	320	16	dimension	dimension	NOUN
ejpam-5546	320	17	d	d	PROPN
ejpam-5546	321	1	+	+	NOUN
ejpam-5546	321	2	1	1	X
ejpam-5546	321	3	.	.	PUNCT
ejpam-5546	321	4	let	let	VERB
ejpam-5546	321	5	a	a	DET
ejpam-5546	321	6	∈	∈	PROPN
ejpam-5546	321	7	⊠q	⊠q	PROPN
ejpam-5546	321	8	denote	denote	VERB
ejpam-5546	321	9	an	an	DET
ejpam-5546	321	10	arbitrary	arbitrary	ADJ
ejpam-5546	321	11	linear	linear	ADJ
ejpam-5546	321	12	combination	combination	NOUN
ejpam-5546	321	13	of	of	ADP
ejpam-5546	321	14	x01	x01	PROPN
ejpam-5546	321	15	and	and	CCONJ
ejpam-5546	321	16	x12	x12	NUM
ejpam-5546	321	17	,	,	PUNCT
ejpam-5546	321	18	let	let	VERB
ejpam-5546	321	19	b2	b2	NOUN
ejpam-5546	321	20	∈	∈	PROPN
ejpam-5546	321	21	⊠q	⊠q	NOUN
ejpam-5546	321	22	such	such	ADJ
ejpam-5546	321	23	that	that	DET
ejpam-5546	321	24	b2	b2	NOUN
ejpam-5546	321	25	=	=	SYM
ejpam-5546	321	26	x30	x30	PROPN
ejpam-5546	321	27	,	,	PUNCT
ejpam-5546	321	28	let	let	VERB
ejpam-5546	321	29	a	a	DET
ejpam-5546	321	30	,	,	PUNCT
ejpam-5546	321	31	b	b	NOUN
ejpam-5546	321	32	and	and	CCONJ
ejpam-5546	321	33	t	t	PROPN
ejpam-5546	322	1	̸=	̸=	PROPN
ejpam-5546	322	2	0	0	NUM
ejpam-5546	322	3	be	be	AUX
ejpam-5546	322	4	scalars	scalar	NOUN
ejpam-5546	322	5	in	in	ADP
ejpam-5546	322	6	f	f	PROPN
ejpam-5546	322	7	.	.	PUNCT
ejpam-5546	323	1	write	write	VERB
ejpam-5546	323	2	a	a	DET
ejpam-5546	323	3	=	=	SYM
ejpam-5546	323	4	ax01	ax01	PROPN
ejpam-5546	323	5	+	+	CCONJ
ejpam-5546	323	6	bx12	bx12	PROPN
ejpam-5546	323	7	.	.	PUNCT
ejpam-5546	324	1	then	then	ADV
ejpam-5546	324	2	the	the	DET
ejpam-5546	324	3	pair	pair	NOUN
ejpam-5546	324	4	a	a	PRON
ejpam-5546	324	5	,	,	PUNCT
ejpam-5546	324	6	b2	b2	NOUN
ejpam-5546	324	7	acts	act	NOUN
ejpam-5546	324	8	on	on	ADP
ejpam-5546	324	9	v	v	NOUN
ejpam-5546	324	10	as	as	ADP
ejpam-5546	324	11	a	a	DET
ejpam-5546	324	12	leonard	leonard	NOUN
ejpam-5546	324	13	pair	pair	NOUN
ejpam-5546	324	14	if	if	SCONJ
ejpam-5546	324	15	and	and	CCONJ
ejpam-5546	324	16	only	only	ADV
ejpam-5546	324	17	if	if	SCONJ
ejpam-5546	324	18	b	b	PROPN
ejpam-5546	324	19	̸=	̸=	PROPN
ejpam-5546	324	20	0	0	NUM
ejpam-5546	324	21	,	,	PUNCT
ejpam-5546	324	22	t	t	PROPN
ejpam-5546	324	23	̸=	̸=	PROPN
ejpam-5546	324	24	q2i−d−1	q2i−d−1	NOUN
ejpam-5546	324	25	,	,	PUNCT
ejpam-5546	324	26	bt	bt	NOUN
ejpam-5546	324	27	̸=	̸=	PROPN
ejpam-5546	324	28	aq2i−d−1	aq2i−d−1	X
ejpam-5546	324	29	for	for	ADP
ejpam-5546	324	30	1	1	NUM
ejpam-5546	324	31	≤	≤	NUM
ejpam-5546	324	32	i	i	PRON
ejpam-5546	325	1	≤	≤	PROPN
ejpam-5546	325	2	d	d	ADP
ejpam-5546	325	3	,	,	PUNCT
ejpam-5546	325	4	and	and	CCONJ
ejpam-5546	325	5	a−	a−	PROPN
ejpam-5546	325	6	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	325	7	)	)	PUNCT
ejpam-5546	326	1	̸=	̸=	NOUN
ejpam-5546	326	2	0	0	NUM
ejpam-5546	326	3	for	for	ADP
ejpam-5546	326	4	1	1	NUM
ejpam-5546	326	5	≤	≤	NUM
ejpam-5546	326	6	i	i	PRON
ejpam-5546	326	7	≤	≤	NOUN
ejpam-5546	327	1	2d−	2d−	PROPN
ejpam-5546	327	2	1	1	NUM
ejpam-5546	327	3	.	.	PUNCT
ejpam-5546	328	1	proof	proof	NOUN
ejpam-5546	328	2	.	.	PUNCT
ejpam-5546	329	1	the	the	DET
ejpam-5546	329	2	action	action	NOUN
ejpam-5546	329	3	of	of	ADP
ejpam-5546	329	4	the	the	DET
ejpam-5546	329	5	pair	pair	NOUN
ejpam-5546	329	6	a	a	PRON
ejpam-5546	329	7	,	,	PUNCT
ejpam-5546	329	8	b2	b2	NOUN
ejpam-5546	329	9	on	on	ADP
ejpam-5546	329	10	the	the	DET
ejpam-5546	329	11	basis	basis	NOUN
ejpam-5546	329	12	s	s	NOUN
ejpam-5546	329	13	is	be	AUX
ejpam-5546	329	14	described	describe	VERB
ejpam-5546	329	15	in	in	ADP
ejpam-5546	329	16	lemma	lemma	PROPN
ejpam-5546	329	17	13	13	NUM
ejpam-5546	329	18	,	,	PUNCT
ejpam-5546	329	19	the	the	DET
ejpam-5546	329	20	matrices	matrix	NOUN
ejpam-5546	329	21	represent	represent	VERB
ejpam-5546	329	22	a	a	PRON
ejpam-5546	329	23	and	and	CCONJ
ejpam-5546	329	24	b2	b2	VERB
ejpam-5546	329	25	with	with	ADP
ejpam-5546	329	26	respect	respect	NOUN
ejpam-5546	329	27	to	to	ADP
ejpam-5546	329	28	the	the	DET
ejpam-5546	329	29	basis	basis	NOUN
ejpam-5546	329	30	s	s	NOUN
ejpam-5546	329	31	are	be	AUX
ejpam-5546	329	32	lower	low	ADJ
ejpam-5546	329	33	bidiagonal	bidiagonal	ADJ
ejpam-5546	329	34	and	and	CCONJ
ejpam-5546	329	35	upper	upper	ADJ
ejpam-5546	329	36	bidiagonal	bidiagonal	NOUN
ejpam-5546	329	37	respectively	respectively	ADV
ejpam-5546	329	38	in	in	ADP
ejpam-5546	329	39	which	which	PRON
ejpam-5546	329	40	αi	αi	X
ejpam-5546	329	41	=	=	PUNCT
ejpam-5546	330	1	[	[	X
ejpam-5546	330	2	a]s(i	a]s(i	PRON
ejpam-5546	330	3	,	,	PUNCT
ejpam-5546	330	4	i	i	PROPN
ejpam-5546	330	5	)	)	PUNCT
ejpam-5546	330	6	,	,	PUNCT
ejpam-5546	330	7	α∗	α∗	VERB
ejpam-5546	330	8	i	i	PRON
ejpam-5546	330	9	=	=	PUNCT
ejpam-5546	331	1	[	[	X
ejpam-5546	331	2	b2]s(i	b2]s(i	NOUN
ejpam-5546	331	3	,	,	PUNCT
ejpam-5546	331	4	i	i	NOUN
ejpam-5546	331	5	)	)	PUNCT
ejpam-5546	331	6	,	,	PUNCT
ejpam-5546	331	7	and	and	CCONJ
ejpam-5546	331	8	ψi	ψi	ADP
ejpam-5546	331	9	=	=	PUNCT
ejpam-5546	332	1	[	[	X
ejpam-5546	332	2	a]s(i	a]s(i	NOUN
ejpam-5546	332	3	,	,	PUNCT
ejpam-5546	332	4	i	i	PRON
ejpam-5546	332	5	−	−	VERB
ejpam-5546	332	6	1)[b2]s(i	1)[b2]s(i	NUM
ejpam-5546	332	7	−	−	NOUN
ejpam-5546	332	8	1	1	NUM
ejpam-5546	332	9	,	,	PUNCT
ejpam-5546	332	10	i	i	NOUN
ejpam-5546	332	11	)	)	PUNCT
ejpam-5546	332	12	.	.	PUNCT
ejpam-5546	333	1	in	in	ADP
ejpam-5546	333	2	lemma	lemma	PROPN
ejpam-5546	333	3	17	17	NUM
ejpam-5546	333	4	we	we	PRON
ejpam-5546	333	5	show	show	VERB
ejpam-5546	333	6	that	that	SCONJ
ejpam-5546	333	7	the	the	DET
ejpam-5546	333	8	sequence	sequence	NOUN
ejpam-5546	333	9	of	of	ADP
ejpam-5546	333	10	scalars	scalar	NOUN
ejpam-5546	333	11	(	(	PUNCT
ejpam-5546	333	12	{	{	PUNCT
ejpam-5546	333	13	αi}di=0	αi}di=0	NOUN
ejpam-5546	333	14	,	,	PUNCT
ejpam-5546	333	15	{	{	PUNCT
ejpam-5546	333	16	α∗	α∗	NOUN
ejpam-5546	333	17	i	i	PRON
ejpam-5546	333	18	}	}	PUNCT
ejpam-5546	333	19	di=0	di=0	PROPN
ejpam-5546	333	20	;	;	PUNCT
ejpam-5546	333	21	{	{	PUNCT
ejpam-5546	333	22	ψj}dj=1	ψj}dj=1	PROPN
ejpam-5546	333	23	,	,	PUNCT
ejpam-5546	333	24	{	{	PUNCT
ejpam-5546	333	25	λj}dj=1	λj}dj=1	PROPN
ejpam-5546	333	26	)	)	PUNCT
ejpam-5546	333	27	is	be	AUX
ejpam-5546	333	28	a	a	DET
ejpam-5546	333	29	parameter	parameter	NOUN
ejpam-5546	333	30	array	array	NOUN
ejpam-5546	333	31	if	if	SCONJ
ejpam-5546	333	32	and	and	CCONJ
ejpam-5546	333	33	only	only	ADV
ejpam-5546	333	34	if	if	SCONJ
ejpam-5546	333	35	b	b	PROPN
ejpam-5546	333	36	̸=	̸=	PROPN
ejpam-5546	333	37	0	0	NUM
ejpam-5546	333	38	,	,	PUNCT
ejpam-5546	333	39	t	t	PROPN
ejpam-5546	333	40	̸=	̸=	PROPN
ejpam-5546	333	41	q2i−d−1	q2i−d−1	NOUN
ejpam-5546	333	42	,	,	PUNCT
ejpam-5546	333	43	bt	bt	NOUN
ejpam-5546	333	44	̸=	̸=	PROPN
ejpam-5546	333	45	aq2i−d−1	aq2i−d−1	X
ejpam-5546	333	46	for	for	ADP
ejpam-5546	333	47	1	1	NUM
ejpam-5546	333	48	≤	≤	NUM
ejpam-5546	333	49	i	i	PRON
ejpam-5546	334	1	≤	≤	PROPN
ejpam-5546	334	2	d	d	ADP
ejpam-5546	334	3	,	,	PUNCT
ejpam-5546	334	4	and	and	CCONJ
ejpam-5546	334	5	a−	a−	PROPN
ejpam-5546	334	6	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	334	7	)	)	PUNCT
ejpam-5546	335	1	̸=	̸=	NOUN
ejpam-5546	335	2	0	0	NUM
ejpam-5546	335	3	for	for	ADP
ejpam-5546	335	4	1	1	NUM
ejpam-5546	335	5	≤	≤	NUM
ejpam-5546	335	6	i	i	PRON
ejpam-5546	335	7	≤	≤	NOUN
ejpam-5546	336	1	2d−	2d−	PROPN
ejpam-5546	336	2	1	1	NUM
ejpam-5546	336	3	.	.	PUNCT
ejpam-5546	337	1	hence	hence	ADV
ejpam-5546	337	2	,	,	PUNCT
ejpam-5546	337	3	the	the	DET
ejpam-5546	337	4	result	result	NOUN
ejpam-5546	337	5	hold	hold	NOUN
ejpam-5546	337	6	by	by	ADP
ejpam-5546	337	7	theorem	theorem	NOUN
ejpam-5546	337	8	1	1	NUM
ejpam-5546	337	9	.	.	NOUN
ejpam-5546	337	10	6	6	NUM
ejpam-5546	337	11	.	.	PUNCT
ejpam-5546	338	1	the	the	DET
ejpam-5546	338	2	leonard	leonard	PROPN
ejpam-5546	338	3	pair	pair	NOUN
ejpam-5546	338	4	a	a	PRON
ejpam-5546	338	5	,	,	PUNCT
ejpam-5546	338	6	x23	x23	PROPN
ejpam-5546	338	7	lemma	lemma	PROPN
ejpam-5546	338	8	18	18	NUM
ejpam-5546	338	9	.	.	PUNCT
ejpam-5546	339	1	[	[	X
ejpam-5546	339	2	4	4	X
ejpam-5546	339	3	]	]	PUNCT
ejpam-5546	339	4	with	with	ADP
ejpam-5546	339	5	reference	reference	NOUN
ejpam-5546	339	6	to	to	ADP
ejpam-5546	339	7	definition	definition	NOUN
ejpam-5546	339	8	3	3	NUM
ejpam-5546	339	9	and	and	CCONJ
ejpam-5546	339	10	lemma	lemma	PROPN
ejpam-5546	339	11	1	1	NUM
ejpam-5546	339	12	,	,	PUNCT
ejpam-5546	339	13	let	let	VERB
ejpam-5546	339	14	v	v	PART
ejpam-5546	339	15	denote	denote	VERB
ejpam-5546	339	16	an	an	DET
ejpam-5546	339	17	evaluation	evaluation	NOUN
ejpam-5546	339	18	module	module	NOUN
ejpam-5546	339	19	for	for	ADP
ejpam-5546	339	20	⊠q	⊠q	PROPN
ejpam-5546	339	21	.	.	PUNCT
ejpam-5546	340	1	then	then	ADV
ejpam-5546	340	2	for	for	ADP
ejpam-5546	340	3	the	the	DET
ejpam-5546	340	4	basis	basis	NOUN
ejpam-5546	340	5	v	v	NOUN
ejpam-5546	340	6	=	=	PUNCT
ejpam-5546	340	7	[	[	X
ejpam-5546	340	8	3	3	NUM
ejpam-5546	340	9	,	,	PUNCT
ejpam-5546	340	10	0	0	NUM
ejpam-5546	340	11	,	,	PUNCT
ejpam-5546	340	12	2	2	NUM
ejpam-5546	340	13	,	,	PUNCT
ejpam-5546	340	14	1	1	NUM
ejpam-5546	340	15	]	]	PUNCT
ejpam-5546	340	16	of	of	ADP
ejpam-5546	340	17	v	v	ADP
ejpam-5546	340	18	the	the	DET
ejpam-5546	340	19	matrices	matrix	NOUN
ejpam-5546	340	20	represent	represent	VERB
ejpam-5546	340	21	x23	x23	NUM
ejpam-5546	340	22	,	,	PUNCT
ejpam-5546	340	23	x12	x12	NUM
ejpam-5546	340	24	,	,	PUNCT
ejpam-5546	340	25	and	and	CCONJ
ejpam-5546	340	26	x01	x01	PROPN
ejpam-5546	340	27	are	be	AUX
ejpam-5546	340	28	gq−1(t	gq−1(t	PROPN
ejpam-5546	340	29	)	)	PUNCT
ejpam-5546	340	30	,	,	PUNCT
ejpam-5546	340	31	kq−1	kq−1	ADV
ejpam-5546	340	32	,	,	PUNCT
ejpam-5546	340	33	and	and	CCONJ
ejpam-5546	340	34	zeqz	zeqz	NOUN
ejpam-5546	340	35	respectively	respectively	ADV
ejpam-5546	340	36	.	.	PUNCT
ejpam-5546	341	1	lemma	lemma	PROPN
ejpam-5546	341	2	19	19	NUM
ejpam-5546	341	3	.	.	PUNCT
ejpam-5546	342	1	with	with	ADP
ejpam-5546	342	2	reference	reference	NOUN
ejpam-5546	342	3	to	to	ADP
ejpam-5546	342	4	lemma	lemma	PROPN
ejpam-5546	342	5	18	18	NUM
ejpam-5546	342	6	and	and	CCONJ
ejpam-5546	342	7	definition	definition	NOUN
ejpam-5546	342	8	7	7	NUM
ejpam-5546	342	9	,	,	PUNCT
ejpam-5546	342	10	let	let	VERB
ejpam-5546	342	11	b3	b3	PROPN
ejpam-5546	342	12	=	=	SYM
ejpam-5546	342	13	x23	x23	PROPN
ejpam-5546	342	14	.	.	PUNCT
ejpam-5546	343	1	then	then	ADV
ejpam-5546	343	2	the	the	DET
ejpam-5546	343	3	matrices	matrix	NOUN
ejpam-5546	343	4	represent	represent	VERB
ejpam-5546	343	5	a	a	PRON
ejpam-5546	343	6	and	and	CCONJ
ejpam-5546	343	7	b3	b3	PROPN
ejpam-5546	343	8	with	with	ADP
ejpam-5546	343	9	respect	respect	NOUN
ejpam-5546	343	10	to	to	ADP
ejpam-5546	343	11	the	the	DET
ejpam-5546	343	12	basis	basis	NOUN
ejpam-5546	343	13	v	v	NOUN
ejpam-5546	343	14	are	be	AUX
ejpam-5546	343	15	lower	low	ADJ
ejpam-5546	343	16	bidiagonal	bidiagonal	ADJ
ejpam-5546	343	17	and	and	CCONJ
ejpam-5546	343	18	upper	upper	ADJ
ejpam-5546	343	19	bidiagonal	bidiagonal	NOUN
ejpam-5546	343	20	respectively	respectively	ADV
ejpam-5546	343	21	with	with	ADP
ejpam-5546	343	22	entries	entry	NOUN
ejpam-5546	343	23	:	:	PUNCT
ejpam-5546	344	1	[	[	X
ejpam-5546	344	2	a]v(i	a]v(i	NOUN
ejpam-5546	344	3	,	,	PUNCT
ejpam-5546	344	4	i	i	NOUN
ejpam-5546	344	5	)	)	PUNCT
ejpam-5546	344	6	=	=	PUNCT
ejpam-5546	344	7	aqd−2i	aqd−2i	NOUN
ejpam-5546	345	1	+	+	CCONJ
ejpam-5546	345	2	bq2i−d	bq2i−d	NOUN
ejpam-5546	345	3	(	(	PUNCT
ejpam-5546	345	4	0	0	NUM
ejpam-5546	345	5	≤	≤	NUM
ejpam-5546	345	6	i	i	NOUN
ejpam-5546	345	7	≤	≤	NUM
ejpam-5546	346	1	d	d	X
ejpam-5546	346	2	)	)	PUNCT
ejpam-5546	346	3	,	,	PUNCT
ejpam-5546	347	1	[	[	X
ejpam-5546	347	2	b3]v(i	b3]v(i	PROPN
ejpam-5546	347	3	,	,	PUNCT
ejpam-5546	347	4	i	i	NOUN
ejpam-5546	347	5	)	)	PUNCT
ejpam-5546	347	6	=	=	PUNCT
ejpam-5546	347	7	qd−2i	qd−2i	NUM
ejpam-5546	347	8	(	(	PUNCT
ejpam-5546	347	9	0	0	NUM
ejpam-5546	347	10	≤	≤	NUM
ejpam-5546	347	11	i	i	NOUN
ejpam-5546	347	12	≤	≤	NUM
ejpam-5546	347	13	d	d	X
ejpam-5546	347	14	)	)	PUNCT
ejpam-5546	347	15	,	,	PUNCT
ejpam-5546	348	1	[	[	X
ejpam-5546	348	2	a]v(i	a]v(i	NOUN
ejpam-5546	348	3	,	,	PUNCT
ejpam-5546	348	4	i−	i−	PROPN
ejpam-5546	348	5	1	1	NUM
ejpam-5546	348	6	)	)	PUNCT
ejpam-5546	348	7	=	=	PUNCT
ejpam-5546	348	8	aqd(1−	aqd(1−	PROPN
ejpam-5546	348	9	q−2i	q−2i	PROPN
ejpam-5546	348	10	)	)	PUNCT
ejpam-5546	348	11	(	(	PUNCT
ejpam-5546	348	12	1	1	NUM
ejpam-5546	348	13	≤	≤	NUM
ejpam-5546	348	14	i	i	X
ejpam-5546	348	15	≤	≤	NUM
ejpam-5546	349	1	d	d	X
ejpam-5546	349	2	)	)	PUNCT
ejpam-5546	349	3	,	,	PUNCT
ejpam-5546	350	1	[	[	X
ejpam-5546	350	2	b3]v(i−1	b3]v(i−1	X
ejpam-5546	350	3	,	,	PUNCT
ejpam-5546	350	4	i	i	NOUN
ejpam-5546	350	5	)	)	PUNCT
ejpam-5546	350	6	=	=	SYM
ejpam-5546	350	7	q−d(1−q2d−2i+2)(1−tq2i−d−1	q−d(1−q2d−2i+2)(1−tq2i−d−1	X
ejpam-5546	350	8	)	)	PUNCT
ejpam-5546	350	9	(	(	PUNCT
ejpam-5546	350	10	1	1	NUM
ejpam-5546	350	11	≤	≤	NUM
ejpam-5546	350	12	i	i	X
ejpam-5546	350	13	≤	≤	NUM
ejpam-5546	351	1	d	d	X
ejpam-5546	351	2	)	)	PUNCT
ejpam-5546	351	3	.	.	PUNCT
ejpam-5546	352	1	proof	proof	NOUN
ejpam-5546	352	2	.	.	PUNCT
ejpam-5546	353	1	the	the	DET
ejpam-5546	353	2	matrices	matrix	NOUN
ejpam-5546	353	3	that	that	PRON
ejpam-5546	353	4	represent	represent	VERB
ejpam-5546	353	5	the	the	DET
ejpam-5546	353	6	action	action	NOUN
ejpam-5546	353	7	of	of	ADP
ejpam-5546	353	8	x01	x01	PROPN
ejpam-5546	353	9	,	,	PUNCT
ejpam-5546	353	10	x12	x12	NUM
ejpam-5546	353	11	and	and	CCONJ
ejpam-5546	353	12	x23	x23	NUM
ejpam-5546	353	13	are	be	AUX
ejpam-5546	353	14	given	give	VERB
ejpam-5546	353	15	in	in	ADP
ejpam-5546	353	16	lemma	lemma	PROPN
ejpam-5546	353	17	18	18	NUM
ejpam-5546	353	18	,	,	PUNCT
ejpam-5546	353	19	and	and	CCONJ
ejpam-5546	353	20	the	the	DET
ejpam-5546	353	21	entries	entry	NOUN
ejpam-5546	353	22	of	of	ADP
ejpam-5546	353	23	these	these	DET
ejpam-5546	353	24	matrices	matrix	NOUN
ejpam-5546	353	25	are	be	AUX
ejpam-5546	353	26	given	give	VERB
ejpam-5546	353	27	in	in	ADP
ejpam-5546	353	28	definition	definition	NOUN
ejpam-5546	353	29	6	6	NUM
ejpam-5546	353	30	.	.	PUNCT
ejpam-5546	354	1	h.	h.	PROPN
ejpam-5546	354	2	alnajjar	alnajjar	PROPN
ejpam-5546	354	3	/	/	SYM
ejpam-5546	354	4	eur	eur	PROPN
ejpam-5546	354	5	.	.	PUNCT
ejpam-5546	355	1	j.	j.	PROPN
ejpam-5546	355	2	pure	pure	PROPN
ejpam-5546	355	3	appl	appl	PROPN
ejpam-5546	355	4	.	.	PROPN
ejpam-5546	355	5	math	math	PROPN
ejpam-5546	355	6	,	,	PUNCT
ejpam-5546	355	7	18	18	NUM
ejpam-5546	355	8	(	(	PUNCT
ejpam-5546	355	9	1	1	NUM
ejpam-5546	355	10	)	)	PUNCT
ejpam-5546	355	11	(	(	PUNCT
ejpam-5546	355	12	2025	2025	NUM
ejpam-5546	355	13	)	)	PUNCT
ejpam-5546	355	14	,	,	PUNCT
ejpam-5546	355	15	5546	5546	NUM
ejpam-5546	355	16	11	11	NUM
ejpam-5546	355	17	of	of	ADP
ejpam-5546	355	18	14	14	NUM
ejpam-5546	355	19	definition	definition	NOUN
ejpam-5546	355	20	10	10	NUM
ejpam-5546	355	21	.	.	PUNCT
ejpam-5546	356	1	with	with	ADP
ejpam-5546	356	2	reference	reference	NOUN
ejpam-5546	356	3	to	to	ADP
ejpam-5546	356	4	lemma	lemma	PROPN
ejpam-5546	356	5	19	19	NUM
ejpam-5546	356	6	,	,	PUNCT
ejpam-5546	356	7	define	define	VERB
ejpam-5546	356	8	υi	υi	NOUN
ejpam-5546	356	9	=	=	SYM
ejpam-5546	356	10	a(1−	a(1−	NOUN
ejpam-5546	356	11	q2d−2i+2)(1−	q2d−2i+2)(1−	NOUN
ejpam-5546	356	12	q−2i)(1−	q−2i)(1−	PROPN
ejpam-5546	356	13	tq2i−d−1	tq2i−d−1	NUM
ejpam-5546	356	14	)	)	PUNCT
ejpam-5546	356	15	(	(	PUNCT
ejpam-5546	356	16	1	1	NUM
ejpam-5546	356	17	≤	≤	NUM
ejpam-5546	356	18	i	i	X
ejpam-5546	356	19	≤	≤	NUM
ejpam-5546	357	1	d	d	X
ejpam-5546	357	2	)	)	PUNCT
ejpam-5546	357	3	,	,	PUNCT
ejpam-5546	357	4	ωi	ωi	X
ejpam-5546	357	5	=	=	PUNCT
ejpam-5546	357	6	q−d−1(q2d−2i+2	q−d−1(q2d−2i+2	VERB
ejpam-5546	357	7	−	−	PROPN
ejpam-5546	357	8	1)(q2i	1)(q2i	NUM
ejpam-5546	357	9	−	−	PROPN
ejpam-5546	357	10	1)(at−	1)(at−	NUM
ejpam-5546	357	11	bqd−2i+1	bqd−2i+1	NUM
ejpam-5546	357	12	)	)	PUNCT
ejpam-5546	357	13	(	(	PUNCT
ejpam-5546	357	14	1	1	NUM
ejpam-5546	357	15	≤	≤	NUM
ejpam-5546	357	16	i	i	X
ejpam-5546	358	1	≤	≤	NUM
ejpam-5546	358	2	d	d	X
ejpam-5546	358	3	)	)	PUNCT
ejpam-5546	358	4	.	.	PUNCT
ejpam-5546	359	1	note	note	VERB
ejpam-5546	359	2	that	that	SCONJ
ejpam-5546	359	3	αi	αi	VERB
ejpam-5546	359	4	=	=	PUNCT
ejpam-5546	360	1	[	[	X
ejpam-5546	360	2	a]v(i	a]v(i	NOUN
ejpam-5546	360	3	,	,	PUNCT
ejpam-5546	360	4	i	i	PROPN
ejpam-5546	360	5	)	)	PUNCT
ejpam-5546	360	6	,	,	PUNCT
ejpam-5546	360	7	α	α	NOUN
ejpam-5546	360	8	∗	∗	NOUN
ejpam-5546	360	9	i	i	PRON
ejpam-5546	360	10	=	=	PUNCT
ejpam-5546	361	1	[	[	X
ejpam-5546	361	2	b3]v(i	b3]v(i	PROPN
ejpam-5546	361	3	,	,	PUNCT
ejpam-5546	361	4	i	i	PROPN
ejpam-5546	361	5	)	)	PUNCT
ejpam-5546	361	6	for	for	ADP
ejpam-5546	361	7	(	(	PUNCT
ejpam-5546	361	8	0	0	NUM
ejpam-5546	361	9	≤	≤	NUM
ejpam-5546	361	10	i	i	NOUN
ejpam-5546	361	11	≤	≤	NUM
ejpam-5546	361	12	d	d	X
ejpam-5546	361	13	)	)	PUNCT
ejpam-5546	361	14	,	,	PUNCT
ejpam-5546	361	15	where	where	SCONJ
ejpam-5546	361	16	αi	αi	PRON
ejpam-5546	361	17	and	and	CCONJ
ejpam-5546	361	18	α∗	α∗	NOUN
ejpam-5546	361	19	i	i	PRON
ejpam-5546	361	20	appear	appear	VERB
ejpam-5546	361	21	in	in	ADP
ejpam-5546	361	22	definition	definition	NOUN
ejpam-5546	361	23	8	8	NUM
ejpam-5546	361	24	.	.	PUNCT
ejpam-5546	362	1	and	and	CCONJ
ejpam-5546	362	2	υi	υi	NOUN
ejpam-5546	362	3	=	=	PUNCT
ejpam-5546	363	1	[	[	X
ejpam-5546	363	2	a]v(i	a]v(i	NOUN
ejpam-5546	363	3	,	,	PUNCT
ejpam-5546	363	4	i−	i−	PROPN
ejpam-5546	363	5	1)[b3]v(i−	1)[b3]v(i−	NUM
ejpam-5546	363	6	1	1	NUM
ejpam-5546	363	7	,	,	PUNCT
ejpam-5546	363	8	i	i	NOUN
ejpam-5546	363	9	)	)	PUNCT
ejpam-5546	363	10	for	for	ADP
ejpam-5546	363	11	(	(	PUNCT
ejpam-5546	363	12	1	1	NUM
ejpam-5546	363	13	≤	≤	NUM
ejpam-5546	363	14	i	i	X
ejpam-5546	363	15	≤	≤	NUM
ejpam-5546	363	16	d	d	X
ejpam-5546	363	17	)	)	PUNCT
ejpam-5546	363	18	.	.	PUNCT
ejpam-5546	364	1	now	now	ADV
ejpam-5546	364	2	,	,	PUNCT
ejpam-5546	364	3	by	by	ADP
ejpam-5546	364	4	theorem	theorem	NOUN
ejpam-5546	364	5	1	1	NUM
ejpam-5546	364	6	,	,	PUNCT
ejpam-5546	364	7	if	if	SCONJ
ejpam-5546	364	8	we	we	PRON
ejpam-5546	364	9	find	find	VERB
ejpam-5546	364	10	the	the	DET
ejpam-5546	364	11	conditions	condition	NOUN
ejpam-5546	364	12	on	on	ADP
ejpam-5546	364	13	the	the	DET
ejpam-5546	364	14	sequence	sequence	NOUN
ejpam-5546	364	15	of	of	ADP
ejpam-5546	364	16	scalars	scalar	NOUN
ejpam-5546	364	17	(	(	PUNCT
ejpam-5546	364	18	{	{	PUNCT
ejpam-5546	364	19	αi}di=0	αi}di=0	NOUN
ejpam-5546	364	20	,	,	PUNCT
ejpam-5546	364	21	{	{	PUNCT
ejpam-5546	364	22	α∗	α∗	NOUN
ejpam-5546	364	23	i	i	PRON
ejpam-5546	364	24	}	}	PUNCT
ejpam-5546	364	25	di=0	di=0	PROPN
ejpam-5546	364	26	;	;	PUNCT
ejpam-5546	364	27	{	{	PUNCT
ejpam-5546	364	28	υj}dj=1	υj}dj=1	PROPN
ejpam-5546	364	29	,	,	PUNCT
ejpam-5546	364	30	{	{	PUNCT
ejpam-5546	364	31	ωj}dj=1	ωj}dj=1	NOUN
ejpam-5546	364	32	)	)	PUNCT
ejpam-5546	364	33	in	in	ADP
ejpam-5546	364	34	which	which	PRON
ejpam-5546	364	35	the	the	DET
ejpam-5546	364	36	sequence	sequence	NOUN
ejpam-5546	364	37	is	be	AUX
ejpam-5546	364	38	a	a	DET
ejpam-5546	364	39	parameter	parameter	NOUN
ejpam-5546	364	40	array	array	NOUN
ejpam-5546	364	41	,	,	PUNCT
ejpam-5546	364	42	then	then	ADV
ejpam-5546	364	43	these	these	DET
ejpam-5546	364	44	conditions	condition	NOUN
ejpam-5546	364	45	imply	imply	VERB
ejpam-5546	364	46	that	that	SCONJ
ejpam-5546	364	47	the	the	DET
ejpam-5546	364	48	pair	pair	NOUN
ejpam-5546	364	49	a	a	PRON
ejpam-5546	364	50	,	,	PUNCT
ejpam-5546	364	51	b3	b3	PROPN
ejpam-5546	364	52	is	be	AUX
ejpam-5546	364	53	a	a	DET
ejpam-5546	364	54	leonard	leonard	NOUN
ejpam-5546	364	55	pair	pair	NOUN
ejpam-5546	364	56	.	.	PUNCT
ejpam-5546	365	1	so	so	ADV
ejpam-5546	365	2	,	,	PUNCT
ejpam-5546	365	3	we	we	PRON
ejpam-5546	365	4	now	now	ADV
ejpam-5546	365	5	need	need	VERB
ejpam-5546	365	6	to	to	PART
ejpam-5546	365	7	find	find	VERB
ejpam-5546	365	8	when	when	SCONJ
ejpam-5546	365	9	the	the	DET
ejpam-5546	365	10	sequence	sequence	NOUN
ejpam-5546	365	11	(	(	PUNCT
ejpam-5546	365	12	{	{	PUNCT
ejpam-5546	365	13	αi}di=0	αi}di=0	NOUN
ejpam-5546	365	14	,	,	PUNCT
ejpam-5546	365	15	{	{	PUNCT
ejpam-5546	365	16	α∗	α∗	NOUN
ejpam-5546	365	17	i	i	PRON
ejpam-5546	365	18	}	}	PUNCT
ejpam-5546	365	19	di=0	di=0	PROPN
ejpam-5546	365	20	;	;	PUNCT
ejpam-5546	365	21	{	{	PUNCT
ejpam-5546	365	22	υj}dj=1	υj}dj=1	PROPN
ejpam-5546	365	23	,	,	PUNCT
ejpam-5546	365	24	{	{	PUNCT
ejpam-5546	365	25	ωj}dj=1	ωj}dj=1	NOUN
ejpam-5546	365	26	)	)	PUNCT
ejpam-5546	365	27	satisfies	satisfy	VERB
ejpam-5546	365	28	the	the	DET
ejpam-5546	365	29	seven	seven	NUM
ejpam-5546	365	30	conditions	condition	NOUN
ejpam-5546	365	31	of	of	ADP
ejpam-5546	365	32	the	the	DET
ejpam-5546	365	33	parameter	parameter	NOUN
ejpam-5546	365	34	array	array	NOUN
ejpam-5546	365	35	in	in	ADP
ejpam-5546	365	36	definition	definition	NOUN
ejpam-5546	365	37	2	2	NUM
ejpam-5546	365	38	.	.	PUNCT
ejpam-5546	365	39	from	from	ADP
ejpam-5546	365	40	lemmas	lemmas	PROPN
ejpam-5546	365	41	6	6	NUM
ejpam-5546	365	42	,	,	PUNCT
ejpam-5546	365	43	7	7	NUM
ejpam-5546	365	44	,	,	PUNCT
ejpam-5546	365	45	and	and	CCONJ
ejpam-5546	365	46	11	11	NUM
ejpam-5546	365	47	we	we	PRON
ejpam-5546	365	48	know	know	VERB
ejpam-5546	365	49	when	when	SCONJ
ejpam-5546	365	50	the	the	DET
ejpam-5546	365	51	conditions	condition	NOUN
ejpam-5546	365	52	1	1	NUM
ejpam-5546	365	53	,	,	PUNCT
ejpam-5546	365	54	2	2	NUM
ejpam-5546	365	55	,	,	PUNCT
ejpam-5546	365	56	and	and	CCONJ
ejpam-5546	365	57	7	7	NUM
ejpam-5546	365	58	hold	hold	NOUN
ejpam-5546	365	59	.	.	PUNCT
ejpam-5546	366	1	in	in	ADP
ejpam-5546	366	2	the	the	DET
ejpam-5546	366	3	next	next	ADJ
ejpam-5546	366	4	work	work	NOUN
ejpam-5546	366	5	we	we	PRON
ejpam-5546	366	6	will	will	AUX
ejpam-5546	366	7	find	find	VERB
ejpam-5546	366	8	when	when	SCONJ
ejpam-5546	366	9	the	the	DET
ejpam-5546	366	10	conditions	condition	NOUN
ejpam-5546	366	11	3−	3−	NUM
ejpam-5546	366	12	6	6	NUM
ejpam-5546	366	13	of	of	ADP
ejpam-5546	366	14	definition	definition	NOUN
ejpam-5546	366	15	2	2	NUM
ejpam-5546	366	16	hold	hold	NOUN
ejpam-5546	366	17	.	.	PUNCT
ejpam-5546	367	1	lemma	lemma	PROPN
ejpam-5546	367	2	20	20	NUM
ejpam-5546	367	3	.	.	PUNCT
ejpam-5546	368	1	with	with	ADP
ejpam-5546	368	2	reference	reference	NOUN
ejpam-5546	368	3	to	to	ADP
ejpam-5546	368	4	definition	definition	NOUN
ejpam-5546	368	5	10	10	NUM
ejpam-5546	368	6	,	,	PUNCT
ejpam-5546	368	7	υi	υi	DET
ejpam-5546	368	8	̸=	̸=	PROPN
ejpam-5546	368	9	0	0	PUNCT
ejpam-5546	369	1	if	if	SCONJ
ejpam-5546	369	2	and	and	CCONJ
ejpam-5546	369	3	only	only	ADV
ejpam-5546	369	4	if	if	SCONJ
ejpam-5546	369	5	a	a	DET
ejpam-5546	369	6	̸=	̸=	PROPN
ejpam-5546	369	7	0	0	NUM
ejpam-5546	369	8	and	and	CCONJ
ejpam-5546	369	9	t	t	PROPN
ejpam-5546	369	10	̸=	̸=	PROPN
ejpam-5546	369	11	qd−2i+1	qd−2i+1	NOUN
ejpam-5546	369	12	for	for	ADP
ejpam-5546	369	13	1	1	NUM
ejpam-5546	369	14	≤	≤	NUM
ejpam-5546	369	15	i	i	PRON
ejpam-5546	369	16	≤	≤	PROPN
ejpam-5546	369	17	d.	d.	PROPN
ejpam-5546	369	18	and	and	CCONJ
ejpam-5546	369	19	ωi	ωi	NUM
ejpam-5546	369	20	̸=	̸=	PROPN
ejpam-5546	369	21	0	0	PUNCT
ejpam-5546	370	1	if	if	SCONJ
ejpam-5546	370	2	and	and	CCONJ
ejpam-5546	370	3	only	only	ADV
ejpam-5546	370	4	if	if	SCONJ
ejpam-5546	370	5	at	at	ADP
ejpam-5546	370	6	̸=	̸=	PROPN
ejpam-5546	370	7	bqd−2i+1	bqd−2i+1	NUM
ejpam-5546	370	8	for	for	ADP
ejpam-5546	370	9	1	1	NUM
ejpam-5546	370	10	≤	≤	NUM
ejpam-5546	370	11	i	i	PRON
ejpam-5546	370	12	≤	≤	ADJ
ejpam-5546	370	13	d.	d.	NOUN
ejpam-5546	370	14	proof	proof	NOUN
ejpam-5546	370	15	.	.	PUNCT
ejpam-5546	371	1	since	since	SCONJ
ejpam-5546	371	2	q	q	PROPN
ejpam-5546	371	3	is	be	AUX
ejpam-5546	371	4	not	not	PART
ejpam-5546	371	5	a	a	DET
ejpam-5546	371	6	root	root	NOUN
ejpam-5546	371	7	of	of	ADP
ejpam-5546	371	8	unity	unity	NOUN
ejpam-5546	371	9	,	,	PUNCT
ejpam-5546	371	10	this	this	PRON
ejpam-5546	371	11	implies	imply	VERB
ejpam-5546	371	12	that	that	SCONJ
ejpam-5546	371	13	υi	υi	NOUN
ejpam-5546	371	14	=	=	SYM
ejpam-5546	371	15	0	0	PUNCT
ejpam-5546	372	1	if	if	SCONJ
ejpam-5546	372	2	and	and	CCONJ
ejpam-5546	372	3	only	only	ADV
ejpam-5546	372	4	if	if	SCONJ
ejpam-5546	372	5	a	a	DET
ejpam-5546	372	6	=	=	NOUN
ejpam-5546	372	7	0	0	NUM
ejpam-5546	372	8	or	or	CCONJ
ejpam-5546	372	9	1−	1−	NUM
ejpam-5546	372	10	tq2i−d−1	tq2i−d−1	X
ejpam-5546	372	11	=	=	SYM
ejpam-5546	372	12	0	0	NUM
ejpam-5546	372	13	,	,	PUNCT
ejpam-5546	372	14	solve	solve	VERB
ejpam-5546	372	15	for	for	ADP
ejpam-5546	372	16	t	t	PROPN
ejpam-5546	372	17	to	to	PART
ejpam-5546	372	18	get	get	VERB
ejpam-5546	372	19	the	the	DET
ejpam-5546	372	20	result	result	NOUN
ejpam-5546	372	21	for	for	ADP
ejpam-5546	372	22	υi	υi	NOUN
ejpam-5546	372	23	.	.	PROPN
ejpam-5546	372	24	similar	similar	ADJ
ejpam-5546	372	25	work	work	NOUN
ejpam-5546	372	26	for	for	ADP
ejpam-5546	372	27	ωi	ωi	PROPN
ejpam-5546	372	28	.	.	PUNCT
ejpam-5546	372	29	lemma	lemma	PROPN
ejpam-5546	372	30	21	21	NUM
ejpam-5546	372	31	.	.	PUNCT
ejpam-5546	373	1	with	with	ADP
ejpam-5546	373	2	reference	reference	NOUN
ejpam-5546	373	3	to	to	ADP
ejpam-5546	373	4	definitions	definition	NOUN
ejpam-5546	373	5	8	8	NUM
ejpam-5546	373	6	and	and	CCONJ
ejpam-5546	373	7	10	10	NUM
ejpam-5546	373	8	,	,	PUNCT
ejpam-5546	373	9	υi	υi	PRON
ejpam-5546	373	10	=	=	PROPN
ejpam-5546	373	11	ω1	ω1	PROPN
ejpam-5546	373	12	i−1∑	i−1∑	NUM
ejpam-5546	373	13	k=0	k=0	PROPN
ejpam-5546	373	14	αk	αk	AUX
ejpam-5546	373	15	−	−	NOUN
ejpam-5546	373	16	αd−k	αd−k	NOUN
ejpam-5546	373	17	α0	α0	ADJ
ejpam-5546	373	18	−	−	PROPN
ejpam-5546	373	19	αd	αd	NOUN
ejpam-5546	374	1	+	+	CCONJ
ejpam-5546	374	2	(	(	PUNCT
ejpam-5546	374	3	α∗	α∗	NOUN
ejpam-5546	374	4	i	i	PRON
ejpam-5546	374	5	−	−	VERB
ejpam-5546	374	6	α∗	α∗	VERB
ejpam-5546	374	7	0)(αi−1	0)(αi−1	NUM
ejpam-5546	374	8	−	−	NUM
ejpam-5546	374	9	αd	αd	PROPN
ejpam-5546	374	10	)	)	PUNCT
ejpam-5546	374	11	(	(	PUNCT
ejpam-5546	374	12	1	1	NUM
ejpam-5546	374	13	≤	≤	NUM
ejpam-5546	374	14	i	i	X
ejpam-5546	374	15	≤	≤	NUM
ejpam-5546	374	16	d	d	X
ejpam-5546	374	17	)	)	PUNCT
ejpam-5546	374	18	.	.	PUNCT
ejpam-5546	375	1	proof	proof	NOUN
ejpam-5546	375	2	.	.	PUNCT
ejpam-5546	376	1	similar	similar	ADJ
ejpam-5546	376	2	to	to	ADP
ejpam-5546	376	3	proof	proof	NOUN
ejpam-5546	376	4	of	of	ADP
ejpam-5546	376	5	lemma	lemma	PROPN
ejpam-5546	376	6	9	9	NUM
ejpam-5546	376	7	.	.	PUNCT
ejpam-5546	376	8	lemma	lemma	PROPN
ejpam-5546	376	9	22	22	NUM
ejpam-5546	376	10	.	.	PUNCT
ejpam-5546	377	1	with	with	ADP
ejpam-5546	377	2	reference	reference	NOUN
ejpam-5546	377	3	to	to	ADP
ejpam-5546	377	4	definitions	definition	NOUN
ejpam-5546	377	5	8	8	NUM
ejpam-5546	377	6	and	and	CCONJ
ejpam-5546	377	7	10	10	NUM
ejpam-5546	377	8	,	,	PUNCT
ejpam-5546	377	9	ωi	ωi	NUM
ejpam-5546	377	10	=	=	SYM
ejpam-5546	377	11	υ1	υ1	PROPN
ejpam-5546	377	12	i−1∑	i−1∑	NOUN
ejpam-5546	377	13	k=0	k=0	PROPN
ejpam-5546	377	14	αk	αk	ADP
ejpam-5546	377	15	−	−	NOUN
ejpam-5546	377	16	αd−k	αd−k	NOUN
ejpam-5546	377	17	α0	α0	ADJ
ejpam-5546	377	18	−	−	PROPN
ejpam-5546	377	19	αd	αd	NOUN
ejpam-5546	377	20	+	+	CCONJ
ejpam-5546	377	21	(	(	PUNCT
ejpam-5546	377	22	α∗	α∗	NOUN
ejpam-5546	377	23	i	i	PRON
ejpam-5546	377	24	−	−	NOUN
ejpam-5546	377	25	α∗	α∗	VERB
ejpam-5546	377	26	0)(αd−i+1	0)(αd−i+1	NOUN
ejpam-5546	377	27	−	−	PROPN
ejpam-5546	377	28	α0	α0	ADJ
ejpam-5546	377	29	)	)	PUNCT
ejpam-5546	377	30	(	(	PUNCT
ejpam-5546	377	31	1	1	NUM
ejpam-5546	377	32	≤	≤	NUM
ejpam-5546	377	33	i	i	X
ejpam-5546	377	34	≤	≤	NUM
ejpam-5546	378	1	d	d	X
ejpam-5546	378	2	)	)	PUNCT
ejpam-5546	378	3	.	.	PUNCT
ejpam-5546	379	1	proof	proof	NOUN
ejpam-5546	379	2	.	.	PUNCT
ejpam-5546	380	1	similar	similar	ADJ
ejpam-5546	380	2	to	to	ADP
ejpam-5546	380	3	proof	proof	NOUN
ejpam-5546	380	4	of	of	ADP
ejpam-5546	380	5	lemma	lemma	PROPN
ejpam-5546	380	6	9	9	NUM
ejpam-5546	380	7	.	.	PUNCT
ejpam-5546	380	8	lemma	lemma	PROPN
ejpam-5546	380	9	23	23	NUM
ejpam-5546	380	10	.	.	PUNCT
ejpam-5546	381	1	with	with	ADP
ejpam-5546	381	2	reference	reference	NOUN
ejpam-5546	381	3	to	to	ADP
ejpam-5546	381	4	definition	definition	NOUN
ejpam-5546	381	5	8	8	NUM
ejpam-5546	381	6	and	and	CCONJ
ejpam-5546	381	7	10	10	NUM
ejpam-5546	381	8	,	,	PUNCT
ejpam-5546	381	9	let	let	VERB
ejpam-5546	381	10	a	a	DET
ejpam-5546	381	11	,	,	PUNCT
ejpam-5546	381	12	b	b	NOUN
ejpam-5546	381	13	and	and	CCONJ
ejpam-5546	381	14	t	t	PROPN
ejpam-5546	381	15	be	be	AUX
ejpam-5546	381	16	scalars	scalar	NOUN
ejpam-5546	381	17	in	in	ADP
ejpam-5546	381	18	f	f	PROPN
ejpam-5546	381	19	.	.	PUNCT
ejpam-5546	382	1	then	then	ADV
ejpam-5546	382	2	the	the	DET
ejpam-5546	382	3	sequence	sequence	NOUN
ejpam-5546	382	4	of	of	ADP
ejpam-5546	382	5	scalars	scalar	NOUN
ejpam-5546	382	6	(	(	PUNCT
ejpam-5546	382	7	{	{	PUNCT
ejpam-5546	382	8	αi}di=0	αi}di=0	NOUN
ejpam-5546	382	9	,	,	PUNCT
ejpam-5546	382	10	{	{	PUNCT
ejpam-5546	382	11	α∗	α∗	NOUN
ejpam-5546	382	12	i	i	PRON
ejpam-5546	382	13	}	}	PUNCT
ejpam-5546	382	14	di=0	di=0	PROPN
ejpam-5546	382	15	;	;	PUNCT
ejpam-5546	382	16	{	{	PUNCT
ejpam-5546	382	17	υj}dj=1	υj}dj=1	PROPN
ejpam-5546	382	18	,	,	PUNCT
ejpam-5546	382	19	{	{	PUNCT
ejpam-5546	382	20	ωj}dj=1	ωj}dj=1	NOUN
ejpam-5546	382	21	)	)	PUNCT
ejpam-5546	382	22	is	be	AUX
ejpam-5546	382	23	a	a	DET
ejpam-5546	382	24	parameter	parameter	NOUN
ejpam-5546	382	25	array	array	NOUN
ejpam-5546	382	26	if	if	SCONJ
ejpam-5546	383	1	and	and	CCONJ
ejpam-5546	383	2	only	only	ADV
ejpam-5546	383	3	if	if	SCONJ
ejpam-5546	383	4	a	a	DET
ejpam-5546	383	5	̸=	̸=	PROPN
ejpam-5546	383	6	0	0	NUM
ejpam-5546	383	7	and	and	CCONJ
ejpam-5546	383	8	t	t	PROPN
ejpam-5546	383	9	̸=	̸=	PROPN
ejpam-5546	383	10	qd−2i+1	qd−2i+1	ADV
ejpam-5546	383	11	,	,	PUNCT
ejpam-5546	383	12	at	at	ADP
ejpam-5546	383	13	̸=	̸=	PROPN
ejpam-5546	383	14	bqd−2i+1	bqd−2i+1	NUM
ejpam-5546	383	15	for	for	ADP
ejpam-5546	383	16	1	1	NUM
ejpam-5546	383	17	≤	≤	NUM
ejpam-5546	383	18	i	i	PRON
ejpam-5546	383	19	≤	≤	PROPN
ejpam-5546	383	20	d	d	ADP
ejpam-5546	383	21	,	,	PUNCT
ejpam-5546	383	22	and	and	CCONJ
ejpam-5546	383	23	a	a	DET
ejpam-5546	383	24	−	−	PROPN
ejpam-5546	383	25	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	383	26	)	)	PUNCT
ejpam-5546	383	27	̸=	̸=	PROPN
ejpam-5546	383	28	0	0	NUM
ejpam-5546	383	29	for	for	ADP
ejpam-5546	383	30	1	1	NUM
ejpam-5546	383	31	≤	≤	NUM
ejpam-5546	383	32	i	i	PRON
ejpam-5546	383	33	≤	≤	NOUN
ejpam-5546	384	1	2d−	2d−	PROPN
ejpam-5546	384	2	1	1	NUM
ejpam-5546	384	3	.	.	PUNCT
ejpam-5546	385	1	proof	proof	NOUN
ejpam-5546	385	2	.	.	PUNCT
ejpam-5546	386	1	note	note	VERB
ejpam-5546	386	2	that	that	SCONJ
ejpam-5546	386	3	the	the	DET
ejpam-5546	386	4	conditions	condition	NOUN
ejpam-5546	386	5	1	1	NUM
ejpam-5546	386	6	−	−	NOUN
ejpam-5546	386	7	7	7	NUM
ejpam-5546	386	8	of	of	ADP
ejpam-5546	386	9	the	the	DET
ejpam-5546	386	10	parameter	parameter	NOUN
ejpam-5546	386	11	array	array	NOUN
ejpam-5546	386	12	in	in	ADP
ejpam-5546	386	13	definition	definition	NOUN
ejpam-5546	386	14	2	2	NUM
ejpam-5546	386	15	hold	hold	VERB
ejpam-5546	386	16	for	for	ADP
ejpam-5546	386	17	the	the	DET
ejpam-5546	386	18	sequence	sequence	NOUN
ejpam-5546	386	19	(	(	PUNCT
ejpam-5546	386	20	{	{	PUNCT
ejpam-5546	386	21	αi}di=0	αi}di=0	NOUN
ejpam-5546	386	22	,	,	PUNCT
ejpam-5546	386	23	{	{	PUNCT
ejpam-5546	386	24	α∗	α∗	NOUN
ejpam-5546	386	25	i	i	PRON
ejpam-5546	386	26	}	}	PUNCT
ejpam-5546	386	27	di=0	di=0	PROPN
ejpam-5546	386	28	;	;	PUNCT
ejpam-5546	386	29	{	{	PUNCT
ejpam-5546	386	30	υj}dj=1	υj}dj=1	PROPN
ejpam-5546	386	31	,	,	PUNCT
ejpam-5546	386	32	{	{	PUNCT
ejpam-5546	386	33	ωj}dj=1	ωj}dj=1	NOUN
ejpam-5546	386	34	)	)	PUNCT
ejpam-5546	386	35	from	from	ADP
ejpam-5546	386	36	lemmas	lemmas	PROPN
ejpam-5546	386	37	6	6	NUM
ejpam-5546	386	38	,	,	PUNCT
ejpam-5546	386	39	7	7	NUM
ejpam-5546	386	40	,	,	PUNCT
ejpam-5546	386	41	20	20	NUM
ejpam-5546	386	42	,	,	PUNCT
ejpam-5546	386	43	21	21	NUM
ejpam-5546	386	44	,	,	PUNCT
ejpam-5546	386	45	22	22	NUM
ejpam-5546	386	46	,	,	PUNCT
ejpam-5546	386	47	11	11	NUM
ejpam-5546	386	48	respectively	respectively	ADV
ejpam-5546	386	49	if	if	SCONJ
ejpam-5546	386	50	and	and	CCONJ
ejpam-5546	386	51	only	only	ADV
ejpam-5546	386	52	if	if	SCONJ
ejpam-5546	386	53	a	a	DET
ejpam-5546	386	54	̸=	̸=	PROPN
ejpam-5546	386	55	0	0	NUM
ejpam-5546	386	56	and	and	CCONJ
ejpam-5546	386	57	t	t	PROPN
ejpam-5546	386	58	̸=	̸=	PROPN
ejpam-5546	386	59	qd−2i+1	qd−2i+1	ADV
ejpam-5546	386	60	,	,	PUNCT
ejpam-5546	386	61	at	at	ADP
ejpam-5546	386	62	̸=	̸=	PROPN
ejpam-5546	386	63	bqd−2i+1	bqd−2i+1	NUM
ejpam-5546	386	64	for	for	ADP
ejpam-5546	386	65	1	1	NUM
ejpam-5546	386	66	≤	≤	NUM
ejpam-5546	386	67	i	i	PRON
ejpam-5546	387	1	≤	≤	PROPN
ejpam-5546	387	2	d	d	ADP
ejpam-5546	387	3	,	,	PUNCT
ejpam-5546	387	4	and	and	CCONJ
ejpam-5546	387	5	a−	a−	PROPN
ejpam-5546	387	6	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	387	7	)	)	PUNCT
ejpam-5546	388	1	̸=	̸=	NOUN
ejpam-5546	388	2	0	0	NUM
ejpam-5546	388	3	for	for	ADP
ejpam-5546	388	4	1	1	NUM
ejpam-5546	388	5	≤	≤	NUM
ejpam-5546	388	6	i	i	PRON
ejpam-5546	388	7	≤	≤	NOUN
ejpam-5546	389	1	2d−	2d−	NUM
ejpam-5546	389	2	1	1	NUM
ejpam-5546	389	3	.	.	PUNCT
ejpam-5546	389	4	h.	h.	PROPN
ejpam-5546	389	5	alnajjar	alnajjar	PROPN
ejpam-5546	389	6	/	/	SYM
ejpam-5546	389	7	eur	eur	PROPN
ejpam-5546	389	8	.	.	PUNCT
ejpam-5546	390	1	j.	j.	PROPN
ejpam-5546	390	2	pure	pure	PROPN
ejpam-5546	390	3	appl	appl	PROPN
ejpam-5546	390	4	.	.	PROPN
ejpam-5546	390	5	math	math	PROPN
ejpam-5546	390	6	,	,	PUNCT
ejpam-5546	390	7	18	18	NUM
ejpam-5546	390	8	(	(	PUNCT
ejpam-5546	390	9	1	1	NUM
ejpam-5546	390	10	)	)	PUNCT
ejpam-5546	390	11	(	(	PUNCT
ejpam-5546	390	12	2025	2025	NUM
ejpam-5546	390	13	)	)	PUNCT
ejpam-5546	390	14	,	,	PUNCT
ejpam-5546	390	15	5546	5546	NUM
ejpam-5546	390	16	12	12	NUM
ejpam-5546	390	17	of	of	ADP
ejpam-5546	390	18	14	14	NUM
ejpam-5546	390	19	theorem	theorem	NOUN
ejpam-5546	390	20	4	4	NUM
ejpam-5546	390	21	.	.	PUNCT
ejpam-5546	390	22	assume	assume	VERB
ejpam-5546	390	23	d	d	X
ejpam-5546	390	24	≥	≥	NUM
ejpam-5546	390	25	2	2	NUM
ejpam-5546	390	26	,	,	PUNCT
ejpam-5546	390	27	let	let	VERB
ejpam-5546	390	28	v	v	PART
ejpam-5546	390	29	denote	denote	VERB
ejpam-5546	390	30	an	an	DET
ejpam-5546	390	31	evaluation	evaluation	NOUN
ejpam-5546	390	32	module	module	NOUN
ejpam-5546	390	33	for	for	ADP
ejpam-5546	390	34	⊠q	⊠q	PROPN
ejpam-5546	390	35	with	with	ADP
ejpam-5546	390	36	dimension	dimension	NOUN
ejpam-5546	390	37	d	d	PROPN
ejpam-5546	391	1	+	+	NOUN
ejpam-5546	391	2	1	1	X
ejpam-5546	391	3	.	.	PUNCT
ejpam-5546	391	4	let	let	VERB
ejpam-5546	391	5	a	a	DET
ejpam-5546	391	6	∈	∈	PROPN
ejpam-5546	391	7	⊠q	⊠q	PROPN
ejpam-5546	391	8	denote	denote	VERB
ejpam-5546	391	9	an	an	DET
ejpam-5546	391	10	arbitrary	arbitrary	ADJ
ejpam-5546	391	11	linear	linear	ADJ
ejpam-5546	391	12	combination	combination	NOUN
ejpam-5546	391	13	of	of	ADP
ejpam-5546	391	14	x01	x01	PROPN
ejpam-5546	391	15	and	and	CCONJ
ejpam-5546	391	16	x12	x12	NUM
ejpam-5546	391	17	,	,	PUNCT
ejpam-5546	391	18	let	let	VERB
ejpam-5546	391	19	b3	b3	PROPN
ejpam-5546	391	20	∈	∈	PROPN
ejpam-5546	391	21	⊠q	⊠q	NOUN
ejpam-5546	391	22	such	such	ADJ
ejpam-5546	391	23	that	that	DET
ejpam-5546	391	24	b3	b3	PROPN
ejpam-5546	391	25	=	=	SYM
ejpam-5546	391	26	x23	x23	PROPN
ejpam-5546	391	27	,	,	PUNCT
ejpam-5546	391	28	let	let	VERB
ejpam-5546	391	29	a	a	DET
ejpam-5546	391	30	,	,	PUNCT
ejpam-5546	391	31	b	b	NOUN
ejpam-5546	391	32	and	and	CCONJ
ejpam-5546	391	33	t	t	PROPN
ejpam-5546	392	1	̸=	̸=	PROPN
ejpam-5546	392	2	0	0	NUM
ejpam-5546	392	3	be	be	AUX
ejpam-5546	392	4	scalars	scalar	NOUN
ejpam-5546	392	5	in	in	ADP
ejpam-5546	392	6	f	f	PROPN
ejpam-5546	392	7	.	.	PUNCT
ejpam-5546	393	1	write	write	VERB
ejpam-5546	393	2	a	a	DET
ejpam-5546	393	3	=	=	SYM
ejpam-5546	393	4	ax01	ax01	PROPN
ejpam-5546	393	5	+	+	CCONJ
ejpam-5546	393	6	bx12	bx12	PROPN
ejpam-5546	393	7	.	.	PUNCT
ejpam-5546	394	1	then	then	ADV
ejpam-5546	394	2	the	the	DET
ejpam-5546	394	3	pair	pair	NOUN
ejpam-5546	394	4	a	a	PRON
ejpam-5546	394	5	,	,	PUNCT
ejpam-5546	394	6	b3	b3	PROPN
ejpam-5546	394	7	acts	act	VERB
ejpam-5546	394	8	on	on	ADP
ejpam-5546	394	9	v	v	NOUN
ejpam-5546	394	10	as	as	ADP
ejpam-5546	394	11	a	a	DET
ejpam-5546	394	12	leonard	leonard	NOUN
ejpam-5546	394	13	pair	pair	NOUN
ejpam-5546	394	14	if	if	SCONJ
ejpam-5546	394	15	and	and	CCONJ
ejpam-5546	394	16	only	only	ADV
ejpam-5546	394	17	if	if	SCONJ
ejpam-5546	394	18	a	a	DET
ejpam-5546	394	19	̸=	̸=	PROPN
ejpam-5546	394	20	0	0	NUM
ejpam-5546	394	21	and	and	CCONJ
ejpam-5546	394	22	t	t	PROPN
ejpam-5546	394	23	̸=	̸=	PROPN
ejpam-5546	394	24	qd−2i+1	qd−2i+1	ADV
ejpam-5546	394	25	,	,	PUNCT
ejpam-5546	394	26	at	at	ADP
ejpam-5546	394	27	̸=	̸=	PROPN
ejpam-5546	394	28	bqd−2i+1	bqd−2i+1	NUM
ejpam-5546	394	29	for	for	ADP
ejpam-5546	394	30	1	1	NUM
ejpam-5546	394	31	≤	≤	NUM
ejpam-5546	394	32	i	i	PRON
ejpam-5546	395	1	≤	≤	PROPN
ejpam-5546	395	2	d	d	ADP
ejpam-5546	395	3	,	,	PUNCT
ejpam-5546	395	4	and	and	CCONJ
ejpam-5546	395	5	a−	a−	PROPN
ejpam-5546	395	6	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	395	7	)	)	PUNCT
ejpam-5546	396	1	̸=	̸=	NOUN
ejpam-5546	396	2	0	0	NUM
ejpam-5546	396	3	for	for	ADP
ejpam-5546	396	4	1	1	NUM
ejpam-5546	396	5	≤	≤	NUM
ejpam-5546	396	6	i	i	PRON
ejpam-5546	396	7	≤	≤	NOUN
ejpam-5546	397	1	2d−	2d−	PROPN
ejpam-5546	397	2	1	1	NUM
ejpam-5546	397	3	.	.	PUNCT
ejpam-5546	398	1	proof	proof	NOUN
ejpam-5546	398	2	.	.	PUNCT
ejpam-5546	399	1	the	the	DET
ejpam-5546	399	2	action	action	NOUN
ejpam-5546	399	3	of	of	ADP
ejpam-5546	399	4	the	the	DET
ejpam-5546	399	5	pair	pair	NOUN
ejpam-5546	399	6	a	a	PRON
ejpam-5546	399	7	,	,	PUNCT
ejpam-5546	399	8	b3	b3	PROPN
ejpam-5546	399	9	on	on	ADP
ejpam-5546	399	10	the	the	DET
ejpam-5546	399	11	basis	basis	NOUN
ejpam-5546	399	12	v	v	NOUN
ejpam-5546	399	13	is	be	AUX
ejpam-5546	399	14	described	describe	VERB
ejpam-5546	399	15	in	in	ADP
ejpam-5546	399	16	lemma	lemma	PROPN
ejpam-5546	399	17	19	19	NUM
ejpam-5546	399	18	,	,	PUNCT
ejpam-5546	399	19	the	the	DET
ejpam-5546	399	20	matrices	matrix	NOUN
ejpam-5546	399	21	represent	represent	VERB
ejpam-5546	399	22	a	a	PRON
ejpam-5546	399	23	and	and	CCONJ
ejpam-5546	399	24	b3	b3	PROPN
ejpam-5546	399	25	with	with	ADP
ejpam-5546	399	26	respect	respect	NOUN
ejpam-5546	399	27	to	to	ADP
ejpam-5546	399	28	the	the	DET
ejpam-5546	399	29	basis	basis	NOUN
ejpam-5546	399	30	v	v	NOUN
ejpam-5546	399	31	are	be	AUX
ejpam-5546	399	32	lower	low	ADJ
ejpam-5546	399	33	bidiagonal	bidiagonal	ADJ
ejpam-5546	399	34	and	and	CCONJ
ejpam-5546	399	35	upper	upper	ADJ
ejpam-5546	399	36	bidiagonal	bidiagonal	NOUN
ejpam-5546	399	37	respectively	respectively	ADV
ejpam-5546	399	38	in	in	ADP
ejpam-5546	399	39	which	which	PRON
ejpam-5546	399	40	αi	αi	X
ejpam-5546	399	41	=	=	PUNCT
ejpam-5546	400	1	[	[	X
ejpam-5546	400	2	a]v(i	a]v(i	NOUN
ejpam-5546	400	3	,	,	PUNCT
ejpam-5546	400	4	i	i	PROPN
ejpam-5546	400	5	)	)	PUNCT
ejpam-5546	400	6	,	,	PUNCT
ejpam-5546	400	7	α∗	α∗	VERB
ejpam-5546	400	8	i	i	PRON
ejpam-5546	400	9	=	=	PUNCT
ejpam-5546	401	1	[	[	X
ejpam-5546	401	2	b3]v(i	b3]v(i	PROPN
ejpam-5546	401	3	,	,	PUNCT
ejpam-5546	401	4	i	i	PROPN
ejpam-5546	401	5	)	)	PUNCT
ejpam-5546	401	6	,	,	PUNCT
ejpam-5546	401	7	and	and	CCONJ
ejpam-5546	401	8	υi	υi	NOUN
ejpam-5546	401	9	=	=	PUNCT
ejpam-5546	402	1	[	[	X
ejpam-5546	402	2	a]v(i	a]v(i	NOUN
ejpam-5546	402	3	,	,	PUNCT
ejpam-5546	402	4	i	i	PRON
ejpam-5546	402	5	−	−	PROPN
ejpam-5546	402	6	1)[b3]v(i	1)[b3]v(i	NUM
ejpam-5546	402	7	−	−	PROPN
ejpam-5546	402	8	1	1	NUM
ejpam-5546	402	9	,	,	PUNCT
ejpam-5546	402	10	i	i	NOUN
ejpam-5546	402	11	)	)	PUNCT
ejpam-5546	402	12	.	.	PUNCT
ejpam-5546	403	1	in	in	ADP
ejpam-5546	403	2	lemma	lemma	PROPN
ejpam-5546	403	3	23	23	NUM
ejpam-5546	403	4	we	we	PRON
ejpam-5546	403	5	show	show	VERB
ejpam-5546	403	6	that	that	SCONJ
ejpam-5546	403	7	the	the	DET
ejpam-5546	403	8	sequence	sequence	NOUN
ejpam-5546	403	9	of	of	ADP
ejpam-5546	403	10	scalars	scalar	NOUN
ejpam-5546	403	11	(	(	PUNCT
ejpam-5546	403	12	{	{	PUNCT
ejpam-5546	403	13	αi}di=0	αi}di=0	NOUN
ejpam-5546	403	14	,	,	PUNCT
ejpam-5546	403	15	{	{	PUNCT
ejpam-5546	403	16	α∗	α∗	NOUN
ejpam-5546	403	17	i	i	PRON
ejpam-5546	403	18	}	}	PUNCT
ejpam-5546	403	19	di=0	di=0	PROPN
ejpam-5546	403	20	;	;	PUNCT
ejpam-5546	403	21	{	{	PUNCT
ejpam-5546	403	22	υj}dj=1	υj}dj=1	PROPN
ejpam-5546	403	23	,	,	PUNCT
ejpam-5546	403	24	{	{	PUNCT
ejpam-5546	403	25	ωj}dj=1	ωj}dj=1	NOUN
ejpam-5546	403	26	)	)	PUNCT
ejpam-5546	403	27	is	be	AUX
ejpam-5546	403	28	a	a	DET
ejpam-5546	403	29	parameter	parameter	NOUN
ejpam-5546	403	30	array	array	NOUN
ejpam-5546	403	31	if	if	SCONJ
ejpam-5546	403	32	and	and	CCONJ
ejpam-5546	403	33	only	only	ADV
ejpam-5546	403	34	if	if	SCONJ
ejpam-5546	403	35	a	a	DET
ejpam-5546	403	36	̸=	̸=	PROPN
ejpam-5546	403	37	0	0	NUM
ejpam-5546	403	38	and	and	CCONJ
ejpam-5546	403	39	t	t	PROPN
ejpam-5546	403	40	̸=	̸=	PROPN
ejpam-5546	403	41	qd−2i+1	qd−2i+1	ADV
ejpam-5546	403	42	,	,	PUNCT
ejpam-5546	403	43	at	at	ADP
ejpam-5546	403	44	̸=	̸=	PROPN
ejpam-5546	403	45	bqd−2i+1	bqd−2i+1	NUM
ejpam-5546	403	46	for	for	ADP
ejpam-5546	403	47	1	1	NUM
ejpam-5546	403	48	≤	≤	NUM
ejpam-5546	403	49	i	i	PRON
ejpam-5546	404	1	≤	≤	PROPN
ejpam-5546	404	2	d	d	ADP
ejpam-5546	404	3	,	,	PUNCT
ejpam-5546	404	4	and	and	CCONJ
ejpam-5546	404	5	a−	a−	PROPN
ejpam-5546	404	6	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	404	7	)	)	PUNCT
ejpam-5546	405	1	̸=	̸=	NOUN
ejpam-5546	405	2	0	0	NUM
ejpam-5546	405	3	for	for	ADP
ejpam-5546	405	4	1	1	NUM
ejpam-5546	405	5	≤	≤	NUM
ejpam-5546	405	6	i	i	PRON
ejpam-5546	405	7	≤	≤	NOUN
ejpam-5546	406	1	2d−	2d−	PROPN
ejpam-5546	406	2	1	1	NUM
ejpam-5546	406	3	.	.	PUNCT
ejpam-5546	407	1	hence	hence	ADV
ejpam-5546	407	2	,	,	PUNCT
ejpam-5546	407	3	the	the	DET
ejpam-5546	407	4	result	result	NOUN
ejpam-5546	407	5	hold	hold	NOUN
ejpam-5546	407	6	by	by	ADP
ejpam-5546	407	7	theorem	theorem	NOUN
ejpam-5546	407	8	1	1	NUM
ejpam-5546	407	9	.	.	PUNCT
ejpam-5546	407	10	theorem	theorem	NOUN
ejpam-5546	407	11	5	5	NUM
ejpam-5546	407	12	.	.	PUNCT
ejpam-5546	407	13	assume	assume	VERB
ejpam-5546	407	14	d	d	X
ejpam-5546	407	15	≥	≥	NUM
ejpam-5546	407	16	2	2	NUM
ejpam-5546	407	17	,	,	PUNCT
ejpam-5546	407	18	let	let	VERB
ejpam-5546	407	19	v	v	PART
ejpam-5546	407	20	denote	denote	VERB
ejpam-5546	407	21	an	an	DET
ejpam-5546	407	22	evaluation	evaluation	NOUN
ejpam-5546	407	23	module	module	NOUN
ejpam-5546	407	24	for	for	ADP
ejpam-5546	407	25	⊠q	⊠q	PROPN
ejpam-5546	407	26	with	with	ADP
ejpam-5546	407	27	dimension	dimension	NOUN
ejpam-5546	407	28	d+1	d+1	PROPN
ejpam-5546	407	29	.	.	PUNCT
ejpam-5546	408	1	let	let	VERB
ejpam-5546	408	2	a	a	DET
ejpam-5546	408	3	∈	∈	PROPN
ejpam-5546	408	4	⊠q	⊠q	PROPN
ejpam-5546	408	5	denote	denote	VERB
ejpam-5546	408	6	an	an	DET
ejpam-5546	408	7	arbitrary	arbitrary	ADJ
ejpam-5546	408	8	linear	linear	ADJ
ejpam-5546	408	9	combination	combination	NOUN
ejpam-5546	408	10	of	of	ADP
ejpam-5546	408	11	x01	x01	PROPN
ejpam-5546	408	12	and	and	CCONJ
ejpam-5546	408	13	x12	x12	NUM
ejpam-5546	408	14	,	,	PUNCT
ejpam-5546	408	15	let	let	VERB
ejpam-5546	408	16	b1	b1	NOUN
ejpam-5546	408	17	,	,	PUNCT
ejpam-5546	408	18	b2	b2	NOUN
ejpam-5546	408	19	,	,	PUNCT
ejpam-5546	408	20	b3	b3	PROPN
ejpam-5546	408	21	∈	∈	PROPN
ejpam-5546	408	22	⊠q	⊠q	NOUN
ejpam-5546	408	23	such	such	ADJ
ejpam-5546	408	24	that	that	DET
ejpam-5546	408	25	b1	b1	NOUN
ejpam-5546	408	26	=	=	SYM
ejpam-5546	408	27	x20	x20	NOUN
ejpam-5546	408	28	,	,	PUNCT
ejpam-5546	408	29	b2	b2	NOUN
ejpam-5546	408	30	=	=	SYM
ejpam-5546	408	31	x30	x30	PROPN
ejpam-5546	408	32	,	,	PUNCT
ejpam-5546	408	33	and	and	CCONJ
ejpam-5546	408	34	b3	b3	PROPN
ejpam-5546	408	35	=	=	SYM
ejpam-5546	408	36	x23	x23	PROPN
ejpam-5546	408	37	,	,	PUNCT
ejpam-5546	408	38	let	let	VERB
ejpam-5546	408	39	a	a	DET
ejpam-5546	408	40	,	,	PUNCT
ejpam-5546	408	41	b	b	NOUN
ejpam-5546	408	42	and	and	CCONJ
ejpam-5546	408	43	t	t	PROPN
ejpam-5546	409	1	̸=	̸=	PROPN
ejpam-5546	409	2	0	0	NUM
ejpam-5546	409	3	be	be	AUX
ejpam-5546	409	4	scalars	scalar	NOUN
ejpam-5546	409	5	in	in	ADP
ejpam-5546	409	6	f	f	PROPN
ejpam-5546	409	7	.	.	PUNCT
ejpam-5546	410	1	write	write	VERB
ejpam-5546	410	2	a	a	DET
ejpam-5546	410	3	=	=	SYM
ejpam-5546	410	4	ax01	ax01	PROPN
ejpam-5546	410	5	+	+	CCONJ
ejpam-5546	410	6	bx12	bx12	PROPN
ejpam-5546	410	7	.	.	PUNCT
ejpam-5546	411	1	then	then	ADV
ejpam-5546	411	2	the	the	DET
ejpam-5546	411	3	pairs	pair	NOUN
ejpam-5546	411	4	a	a	PRON
ejpam-5546	411	5	,	,	PUNCT
ejpam-5546	411	6	b1	b1	NOUN
ejpam-5546	411	7	,	,	PUNCT
ejpam-5546	411	8	a	a	DET
ejpam-5546	411	9	,	,	PUNCT
ejpam-5546	411	10	b2	b2	NOUN
ejpam-5546	411	11	,	,	PUNCT
ejpam-5546	411	12	and	and	CCONJ
ejpam-5546	411	13	a	a	DET
ejpam-5546	411	14	,	,	PUNCT
ejpam-5546	411	15	b3	b3	PROPN
ejpam-5546	411	16	act	act	NOUN
ejpam-5546	411	17	on	on	ADP
ejpam-5546	411	18	v	v	NOUN
ejpam-5546	411	19	as	as	ADP
ejpam-5546	411	20	leonard	leonard	NOUN
ejpam-5546	411	21	pairs	pair	NOUN
ejpam-5546	411	22	if	if	SCONJ
ejpam-5546	411	23	and	and	CCONJ
ejpam-5546	411	24	only	only	ADV
ejpam-5546	411	25	if	if	SCONJ
ejpam-5546	411	26	a	a	DET
ejpam-5546	411	27	̸=	̸=	PROPN
ejpam-5546	411	28	0	0	NUM
ejpam-5546	411	29	,	,	PUNCT
ejpam-5546	411	30	b	b	X
ejpam-5546	411	31	̸=	̸=	PROPN
ejpam-5546	411	32	0	0	NUM
ejpam-5546	411	33	,	,	PUNCT
ejpam-5546	411	34	t	t	PROPN
ejpam-5546	411	35	̸=	̸=	PROPN
ejpam-5546	411	36	0	0	NUM
ejpam-5546	411	37	,	,	PUNCT
ejpam-5546	411	38	t	t	PROPN
ejpam-5546	411	39	̸=	̸=	PROPN
ejpam-5546	411	40	qd−2i+1	qd−2i+1	ADV
ejpam-5546	411	41	,	,	PUNCT
ejpam-5546	411	42	a−1bt	a−1bt	NOUN
ejpam-5546	411	43	̸=	̸=	PROPN
ejpam-5546	411	44	q2i−d−1	q2i−d−1	NOUN
ejpam-5546	411	45	,	,	PUNCT
ejpam-5546	411	46	b−1at	b−1at	VERB
ejpam-5546	411	47	̸=	̸=	PROPN
ejpam-5546	411	48	qd−2i+1	qd−2i+1	NOUN
ejpam-5546	411	49	for	for	ADP
ejpam-5546	411	50	1	1	NUM
ejpam-5546	411	51	≤	≤	NUM
ejpam-5546	411	52	i	i	PRON
ejpam-5546	412	1	≤	≤	PROPN
ejpam-5546	412	2	d	d	ADP
ejpam-5546	412	3	,	,	PUNCT
ejpam-5546	412	4	and	and	CCONJ
ejpam-5546	412	5	a−	a−	PROPN
ejpam-5546	412	6	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	412	7	)	)	PUNCT
ejpam-5546	413	1	̸=	̸=	NOUN
ejpam-5546	413	2	0	0	NUM
ejpam-5546	413	3	for	for	ADP
ejpam-5546	413	4	1	1	NUM
ejpam-5546	413	5	≤	≤	NUM
ejpam-5546	413	6	i	i	PRON
ejpam-5546	413	7	≤	≤	NOUN
ejpam-5546	414	1	2d−	2d−	PROPN
ejpam-5546	414	2	1	1	NUM
ejpam-5546	414	3	.	.	PUNCT
ejpam-5546	415	1	proof	proof	NOUN
ejpam-5546	415	2	.	.	PUNCT
ejpam-5546	416	1	clear	clear	ADJ
ejpam-5546	416	2	from	from	ADP
ejpam-5546	416	3	theorems	theorem	NOUN
ejpam-5546	416	4	2	2	NUM
ejpam-5546	416	5	,	,	PUNCT
ejpam-5546	416	6	3	3	NUM
ejpam-5546	416	7	,	,	PUNCT
ejpam-5546	416	8	and	and	CCONJ
ejpam-5546	416	9	4	4	X
ejpam-5546	416	10	.	.	X
ejpam-5546	416	11	lemma	lemma	PROPN
ejpam-5546	416	12	24	24	NUM
ejpam-5546	416	13	.	.	PUNCT
ejpam-5546	417	1	[	[	X
ejpam-5546	417	2	4	4	X
ejpam-5546	417	3	]	]	PUNCT
ejpam-5546	417	4	consider	consider	VERB
ejpam-5546	417	5	the	the	DET
ejpam-5546	417	6	⊠q	⊠q	NOUN
ejpam-5546	417	7	-	-	PUNCT
ejpam-5546	417	8	module	module	NOUN
ejpam-5546	417	9	vd(t	vd(t	NOUN
ejpam-5546	417	10	)	)	PUNCT
ejpam-5546	417	11	.	.	PUNCT
ejpam-5546	418	1	pick	pick	VERB
ejpam-5546	418	2	mutually	mutually	ADV
ejpam-5546	418	3	distinct	distinct	ADJ
ejpam-5546	419	1	i	i	PRON
ejpam-5546	419	2	,	,	PUNCT
ejpam-5546	419	3	j	j	PROPN
ejpam-5546	419	4	,	,	PUNCT
ejpam-5546	419	5	k	k	PROPN
ejpam-5546	419	6	,	,	PUNCT
ejpam-5546	419	7	l	l	PROPN
ejpam-5546	419	8	∈	∈	PROPN
ejpam-5546	419	9	z4	z4	PROPN
ejpam-5546	419	10	.	.	PUNCT
ejpam-5546	420	1	then	then	ADV
ejpam-5546	420	2	for	for	ADP
ejpam-5546	420	3	each	each	DET
ejpam-5546	420	4	standard	standard	PROPN
ejpam-5546	420	5	generator	generator	PROPN
ejpam-5546	420	6	xrs	xrs	PROPN
ejpam-5546	420	7	the	the	DET
ejpam-5546	420	8	following	follow	VERB
ejpam-5546	420	9	are	be	AUX
ejpam-5546	420	10	the	the	DET
ejpam-5546	420	11	same	same	ADJ
ejpam-5546	420	12	:	:	PUNCT
ejpam-5546	420	13	(	(	PUNCT
ejpam-5546	420	14	i	i	NOUN
ejpam-5546	420	15	)	)	PUNCT
ejpam-5546	420	16	the	the	DET
ejpam-5546	420	17	matrix	matrix	NOUN
ejpam-5546	420	18	that	that	PRON
ejpam-5546	420	19	represents	represent	VERB
ejpam-5546	420	20	xrs	xrs	PROPN
ejpam-5546	420	21	with	with	ADP
ejpam-5546	420	22	respect	respect	NOUN
ejpam-5546	420	23	to	to	ADP
ejpam-5546	420	24	an	an	DET
ejpam-5546	420	25	[	[	X
ejpam-5546	420	26	i	i	PROPN
ejpam-5546	420	27	,	,	PUNCT
ejpam-5546	420	28	j	j	PROPN
ejpam-5546	420	29	,	,	PUNCT
ejpam-5546	420	30	k	k	NOUN
ejpam-5546	420	31	,	,	PUNCT
ejpam-5546	420	32	l]-basis	l]-basis	NOUN
ejpam-5546	420	33	for	for	ADP
ejpam-5546	420	34	vd(t	vd(t	NUM
ejpam-5546	420	35	)	)	PUNCT
ejpam-5546	420	36	;	;	PUNCT
ejpam-5546	420	37	(	(	PUNCT
ejpam-5546	420	38	ii	ii	NOUN
ejpam-5546	420	39	)	)	PUNCT
ejpam-5546	420	40	the	the	DET
ejpam-5546	420	41	matrix	matrix	NOUN
ejpam-5546	420	42	that	that	PRON
ejpam-5546	420	43	represents	represent	VERB
ejpam-5546	420	44	xr+1,s+1	xr+1,s+1	ADP
ejpam-5546	420	45	with	with	ADP
ejpam-5546	420	46	respect	respect	NOUN
ejpam-5546	420	47	to	to	ADP
ejpam-5546	420	48	an	an	DET
ejpam-5546	420	49	[	[	X
ejpam-5546	420	50	i+	i+	NOUN
ejpam-5546	420	51	1	1	NUM
ejpam-5546	420	52	,	,	PUNCT
ejpam-5546	420	53	j	j	PROPN
ejpam-5546	421	1	+	+	NOUN
ejpam-5546	421	2	1	1	NUM
ejpam-5546	421	3	,	,	PUNCT
ejpam-5546	421	4	k	k	PROPN
ejpam-5546	422	1	+	+	PROPN
ejpam-5546	422	2	1	1	NUM
ejpam-5546	422	3	,	,	PUNCT
ejpam-5546	422	4	l+	l+	X
ejpam-5546	422	5	1]-basis	1]-basis	NUM
ejpam-5546	422	6	for	for	ADP
ejpam-5546	422	7	vd(t	vd(t	NUM
ejpam-5546	422	8	−1	−1	NOUN
ejpam-5546	422	9	)	)	PUNCT
ejpam-5546	422	10	.	.	PUNCT
ejpam-5546	423	1	theorem	theorem	ADJ
ejpam-5546	423	2	6	6	NUM
ejpam-5546	423	3	.	.	PUNCT
ejpam-5546	424	1	assume	assume	VERB
ejpam-5546	424	2	d	d	X
ejpam-5546	424	3	≥	≥	NUM
ejpam-5546	424	4	2	2	NUM
ejpam-5546	424	5	,	,	PUNCT
ejpam-5546	424	6	let	let	VERB
ejpam-5546	424	7	v	v	PART
ejpam-5546	424	8	denote	denote	VERB
ejpam-5546	424	9	an	an	DET
ejpam-5546	424	10	evaluation	evaluation	NOUN
ejpam-5546	424	11	module	module	NOUN
ejpam-5546	424	12	for	for	ADP
ejpam-5546	424	13	⊠q	⊠q	PROPN
ejpam-5546	424	14	with	with	ADP
ejpam-5546	424	15	dimension	dimension	NOUN
ejpam-5546	424	16	d+1	d+1	PROPN
ejpam-5546	424	17	.	.	PUNCT
ejpam-5546	425	1	let	let	VERB
ejpam-5546	425	2	a	a	DET
ejpam-5546	425	3	∈	∈	PROPN
ejpam-5546	425	4	⊠q	⊠q	PROPN
ejpam-5546	425	5	denote	denote	VERB
ejpam-5546	425	6	an	an	DET
ejpam-5546	425	7	arbitrary	arbitrary	ADJ
ejpam-5546	425	8	linear	linear	ADJ
ejpam-5546	425	9	combination	combination	NOUN
ejpam-5546	425	10	of	of	ADP
ejpam-5546	425	11	x12	x12	NUM
ejpam-5546	425	12	and	and	CCONJ
ejpam-5546	425	13	x23	x23	NUM
ejpam-5546	425	14	,	,	PUNCT
ejpam-5546	425	15	let	let	VERB
ejpam-5546	425	16	b1	b1	NOUN
ejpam-5546	425	17	,	,	PUNCT
ejpam-5546	425	18	b2	b2	NOUN
ejpam-5546	425	19	,	,	PUNCT
ejpam-5546	425	20	b3	b3	PROPN
ejpam-5546	425	21	∈	∈	PROPN
ejpam-5546	425	22	⊠q	⊠q	NOUN
ejpam-5546	425	23	such	such	ADJ
ejpam-5546	425	24	that	that	PRON
ejpam-5546	425	25	b1	b1	NOUN
ejpam-5546	425	26	=	=	SYM
ejpam-5546	425	27	x31	x31	PROPN
ejpam-5546	425	28	,	,	PUNCT
ejpam-5546	425	29	b2	b2	NOUN
ejpam-5546	425	30	=	=	SYM
ejpam-5546	425	31	x01	x01	PROPN
ejpam-5546	425	32	,	,	PUNCT
ejpam-5546	425	33	and	and	CCONJ
ejpam-5546	425	34	b3	b3	PROPN
ejpam-5546	425	35	=	=	SYM
ejpam-5546	425	36	x30	x30	PROPN
ejpam-5546	425	37	,	,	PUNCT
ejpam-5546	425	38	let	let	VERB
ejpam-5546	425	39	a	a	DET
ejpam-5546	425	40	,	,	PUNCT
ejpam-5546	425	41	b	b	NOUN
ejpam-5546	425	42	and	and	CCONJ
ejpam-5546	425	43	t	t	PROPN
ejpam-5546	426	1	̸=	̸=	PROPN
ejpam-5546	426	2	0	0	NUM
ejpam-5546	426	3	be	be	AUX
ejpam-5546	426	4	scalars	scalar	NOUN
ejpam-5546	426	5	in	in	ADP
ejpam-5546	426	6	f	f	PROPN
ejpam-5546	426	7	.	.	PUNCT
ejpam-5546	427	1	write	write	VERB
ejpam-5546	427	2	a	a	DET
ejpam-5546	427	3	=	=	SYM
ejpam-5546	427	4	ax12	ax12	PROPN
ejpam-5546	427	5	+	+	CCONJ
ejpam-5546	427	6	bx23	bx23	PROPN
ejpam-5546	427	7	.	.	PUNCT
ejpam-5546	428	1	then	then	ADV
ejpam-5546	428	2	the	the	DET
ejpam-5546	428	3	pairs	pair	NOUN
ejpam-5546	428	4	a	a	PRON
ejpam-5546	428	5	,	,	PUNCT
ejpam-5546	428	6	b1	b1	NOUN
ejpam-5546	428	7	,	,	PUNCT
ejpam-5546	428	8	a	a	DET
ejpam-5546	428	9	,	,	PUNCT
ejpam-5546	428	10	b2	b2	NOUN
ejpam-5546	428	11	,	,	PUNCT
ejpam-5546	428	12	and	and	CCONJ
ejpam-5546	428	13	a	a	DET
ejpam-5546	428	14	,	,	PUNCT
ejpam-5546	428	15	b3	b3	PROPN
ejpam-5546	428	16	act	act	NOUN
ejpam-5546	428	17	on	on	ADP
ejpam-5546	428	18	v	v	NOUN
ejpam-5546	428	19	as	as	ADP
ejpam-5546	428	20	leonard	leonard	NOUN
ejpam-5546	428	21	pairs	pair	NOUN
ejpam-5546	428	22	if	if	SCONJ
ejpam-5546	428	23	and	and	CCONJ
ejpam-5546	428	24	only	only	ADV
ejpam-5546	428	25	if	if	SCONJ
ejpam-5546	428	26	a	a	DET
ejpam-5546	428	27	̸=	̸=	PROPN
ejpam-5546	428	28	0	0	NUM
ejpam-5546	428	29	,	,	PUNCT
ejpam-5546	428	30	b	b	X
ejpam-5546	428	31	̸=	̸=	PROPN
ejpam-5546	428	32	0	0	NUM
ejpam-5546	428	33	,	,	PUNCT
ejpam-5546	428	34	t	t	PROPN
ejpam-5546	428	35	̸=	̸=	PROPN
ejpam-5546	428	36	0	0	NUM
ejpam-5546	428	37	,	,	PUNCT
ejpam-5546	428	38	t−1	t−1	PROPN
ejpam-5546	428	39	̸=	̸=	PROPN
ejpam-5546	428	40	qd−2i+1	qd−2i+1	ADV
ejpam-5546	428	41	,	,	PUNCT
ejpam-5546	428	42	a−1bt−1	a−1bt−1	PROPN
ejpam-5546	428	43	̸=	̸=	PROPN
ejpam-5546	428	44	q2i−d−1	q2i−d−1	NOUN
ejpam-5546	428	45	,	,	PUNCT
ejpam-5546	428	46	b−1at−1	b−1at−1	NOUN
ejpam-5546	428	47	̸=	̸=	PROPN
ejpam-5546	428	48	qd−2i+1	qd−2i+1	NOUN
ejpam-5546	428	49	for	for	ADP
ejpam-5546	428	50	1	1	NUM
ejpam-5546	428	51	≤	≤	NUM
ejpam-5546	428	52	i	i	PRON
ejpam-5546	428	53	≤	≤	PROPN
ejpam-5546	429	1	d	d	ADP
ejpam-5546	429	2	,	,	PUNCT
ejpam-5546	429	3	and	and	CCONJ
ejpam-5546	429	4	a−	a−	PROPN
ejpam-5546	429	5	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	429	6	)	)	PUNCT
ejpam-5546	430	1	̸=	̸=	NOUN
ejpam-5546	430	2	0	0	NUM
ejpam-5546	430	3	for	for	ADP
ejpam-5546	430	4	1	1	NUM
ejpam-5546	430	5	≤	≤	NUM
ejpam-5546	430	6	i	i	PRON
ejpam-5546	430	7	≤	≤	NOUN
ejpam-5546	431	1	2d−	2d−	PROPN
ejpam-5546	431	2	1	1	NUM
ejpam-5546	431	3	.	.	PUNCT
ejpam-5546	432	1	proof	proof	NOUN
ejpam-5546	432	2	.	.	PUNCT
ejpam-5546	433	1	similar	similar	ADJ
ejpam-5546	433	2	to	to	ADP
ejpam-5546	433	3	proof	proof	NOUN
ejpam-5546	433	4	of	of	ADP
ejpam-5546	433	5	theorem	theorem	NOUN
ejpam-5546	433	6	5	5	NUM
ejpam-5546	433	7	but	but	CCONJ
ejpam-5546	433	8	replace	replace	VERB
ejpam-5546	433	9	t	t	NOUN
ejpam-5546	433	10	by	by	ADP
ejpam-5546	433	11	t−1	t−1	PROPN
ejpam-5546	433	12	and	and	CCONJ
ejpam-5546	433	13	replace	replace	VERB
ejpam-5546	433	14	the	the	DET
ejpam-5546	433	15	bases	basis	NOUN
ejpam-5546	433	16	[	[	X
ejpam-5546	433	17	i	i	PRON
ejpam-5546	433	18	,	,	PUNCT
ejpam-5546	433	19	j	j	PROPN
ejpam-5546	433	20	,	,	PUNCT
ejpam-5546	433	21	k	k	PROPN
ejpam-5546	433	22	,	,	PUNCT
ejpam-5546	433	23	l	l	NOUN
ejpam-5546	433	24	]	]	X
ejpam-5546	433	25	that	that	PRON
ejpam-5546	433	26	appear	appear	VERB
ejpam-5546	433	27	in	in	ADP
ejpam-5546	433	28	the	the	DET
ejpam-5546	433	29	proof	proof	NOUN
ejpam-5546	433	30	of	of	ADP
ejpam-5546	433	31	theorem	theorem	NOUN
ejpam-5546	433	32	5	5	NUM
ejpam-5546	433	33	by	by	ADP
ejpam-5546	433	34	the	the	DET
ejpam-5546	433	35	bases	basis	NOUN
ejpam-5546	434	1	[	[	X
ejpam-5546	434	2	i+1	i+1	X
ejpam-5546	434	3	,	,	PUNCT
ejpam-5546	434	4	j+1	j+1	PROPN
ejpam-5546	434	5	,	,	PUNCT
ejpam-5546	434	6	k+1	k+1	NOUN
ejpam-5546	434	7	,	,	PUNCT
ejpam-5546	434	8	l+1	l+1	PROPN
ejpam-5546	434	9	]	]	PUNCT
ejpam-5546	434	10	,	,	PUNCT
ejpam-5546	434	11	and	and	CCONJ
ejpam-5546	434	12	use	use	VERB
ejpam-5546	434	13	lemma	lemma	PROPN
ejpam-5546	434	14	24	24	NUM
ejpam-5546	434	15	to	to	PART
ejpam-5546	434	16	find	find	VERB
ejpam-5546	434	17	the	the	DET
ejpam-5546	434	18	action	action	NOUN
ejpam-5546	434	19	of	of	ADP
ejpam-5546	434	20	the	the	DET
ejpam-5546	434	21	standard	standard	ADJ
ejpam-5546	434	22	generators	generator	NOUN
ejpam-5546	434	23	of	of	ADP
ejpam-5546	434	24	⊠q	⊠q	PROPN
ejpam-5546	434	25	on	on	ADP
ejpam-5546	434	26	the	the	DET
ejpam-5546	434	27	new	new	ADJ
ejpam-5546	434	28	bases	basis	NOUN
ejpam-5546	434	29	.	.	PUNCT
ejpam-5546	435	1	theorem	theorem	ADJ
ejpam-5546	435	2	7	7	NUM
ejpam-5546	435	3	.	.	PUNCT
ejpam-5546	435	4	assume	assume	VERB
ejpam-5546	435	5	d	d	X
ejpam-5546	435	6	≥	≥	NUM
ejpam-5546	435	7	2	2	NUM
ejpam-5546	435	8	,	,	PUNCT
ejpam-5546	435	9	let	let	VERB
ejpam-5546	435	10	v	v	PART
ejpam-5546	435	11	denote	denote	VERB
ejpam-5546	435	12	an	an	DET
ejpam-5546	435	13	evaluation	evaluation	NOUN
ejpam-5546	435	14	module	module	NOUN
ejpam-5546	435	15	for	for	ADP
ejpam-5546	435	16	⊠q	⊠q	PROPN
ejpam-5546	435	17	with	with	ADP
ejpam-5546	435	18	dimension	dimension	NOUN
ejpam-5546	435	19	d+1	d+1	PROPN
ejpam-5546	435	20	.	.	PUNCT
ejpam-5546	436	1	let	let	VERB
ejpam-5546	436	2	a	a	DET
ejpam-5546	436	3	∈	∈	PROPN
ejpam-5546	436	4	⊠q	⊠q	PROPN
ejpam-5546	436	5	denote	denote	VERB
ejpam-5546	436	6	an	an	DET
ejpam-5546	436	7	arbitrary	arbitrary	ADJ
ejpam-5546	436	8	linear	linear	ADJ
ejpam-5546	436	9	combination	combination	NOUN
ejpam-5546	436	10	of	of	ADP
ejpam-5546	436	11	x23	x23	NUM
ejpam-5546	436	12	and	and	CCONJ
ejpam-5546	436	13	x30	x30	NUM
ejpam-5546	436	14	,	,	PUNCT
ejpam-5546	436	15	let	let	VERB
ejpam-5546	436	16	b1	b1	NOUN
ejpam-5546	436	17	,	,	PUNCT
ejpam-5546	436	18	b2	b2	NOUN
ejpam-5546	436	19	,	,	PUNCT
ejpam-5546	436	20	b3	b3	PROPN
ejpam-5546	436	21	∈	∈	PROPN
ejpam-5546	436	22	⊠q	⊠q	NOUN
ejpam-5546	436	23	such	such	ADJ
ejpam-5546	436	24	that	that	PRON
ejpam-5546	436	25	b1	b1	NOUN
ejpam-5546	436	26	=	=	SYM
ejpam-5546	436	27	x02	x02	PROPN
ejpam-5546	436	28	,	,	PUNCT
ejpam-5546	436	29	b2	b2	NOUN
ejpam-5546	436	30	=	=	SYM
ejpam-5546	436	31	x12	x12	NUM
ejpam-5546	436	32	,	,	PUNCT
ejpam-5546	436	33	and	and	CCONJ
ejpam-5546	436	34	b3	b3	PROPN
ejpam-5546	436	35	=	=	SYM
ejpam-5546	436	36	x01	x01	PROPN
ejpam-5546	436	37	,	,	PUNCT
ejpam-5546	436	38	let	let	VERB
ejpam-5546	436	39	a	a	DET
ejpam-5546	436	40	,	,	PUNCT
ejpam-5546	436	41	b	b	NOUN
ejpam-5546	436	42	and	and	CCONJ
ejpam-5546	436	43	t	t	PROPN
ejpam-5546	437	1	̸=	̸=	PROPN
ejpam-5546	437	2	0	0	NUM
ejpam-5546	437	3	be	be	AUX
ejpam-5546	437	4	scalars	scalar	NOUN
ejpam-5546	437	5	in	in	ADP
ejpam-5546	437	6	f	f	PROPN
ejpam-5546	437	7	.	.	PUNCT
ejpam-5546	438	1	h.	h.	PROPN
ejpam-5546	438	2	alnajjar	alnajjar	PROPN
ejpam-5546	438	3	/	/	SYM
ejpam-5546	438	4	eur	eur	PROPN
ejpam-5546	438	5	.	.	PUNCT
ejpam-5546	439	1	j.	j.	PROPN
ejpam-5546	439	2	pure	pure	PROPN
ejpam-5546	439	3	appl	appl	PROPN
ejpam-5546	439	4	.	.	PROPN
ejpam-5546	439	5	math	math	PROPN
ejpam-5546	439	6	,	,	PUNCT
ejpam-5546	439	7	18	18	NUM
ejpam-5546	439	8	(	(	PUNCT
ejpam-5546	439	9	1	1	NUM
ejpam-5546	439	10	)	)	PUNCT
ejpam-5546	439	11	(	(	PUNCT
ejpam-5546	439	12	2025	2025	NUM
ejpam-5546	439	13	)	)	PUNCT
ejpam-5546	439	14	,	,	PUNCT
ejpam-5546	439	15	5546	5546	NUM
ejpam-5546	439	16	13	13	NUM
ejpam-5546	439	17	of	of	ADP
ejpam-5546	439	18	14	14	NUM
ejpam-5546	439	19	write	write	VERB
ejpam-5546	439	20	a	a	DET
ejpam-5546	439	21	=	=	X
ejpam-5546	439	22	ax23	ax23	PROPN
ejpam-5546	439	23	+	+	NUM
ejpam-5546	439	24	bx30	bx30	PROPN
ejpam-5546	439	25	.	.	PUNCT
ejpam-5546	440	1	then	then	ADV
ejpam-5546	440	2	the	the	DET
ejpam-5546	440	3	pairs	pair	NOUN
ejpam-5546	440	4	a	a	PRON
ejpam-5546	440	5	,	,	PUNCT
ejpam-5546	440	6	b1	b1	NOUN
ejpam-5546	440	7	,	,	PUNCT
ejpam-5546	440	8	a	a	DET
ejpam-5546	440	9	,	,	PUNCT
ejpam-5546	440	10	b2	b2	NOUN
ejpam-5546	440	11	,	,	PUNCT
ejpam-5546	440	12	and	and	CCONJ
ejpam-5546	440	13	a	a	DET
ejpam-5546	440	14	,	,	PUNCT
ejpam-5546	440	15	b3	b3	PROPN
ejpam-5546	440	16	act	act	NOUN
ejpam-5546	440	17	on	on	ADP
ejpam-5546	440	18	v	v	NOUN
ejpam-5546	440	19	as	as	ADP
ejpam-5546	440	20	leonard	leonard	NOUN
ejpam-5546	440	21	pairs	pair	NOUN
ejpam-5546	440	22	if	if	SCONJ
ejpam-5546	440	23	and	and	CCONJ
ejpam-5546	440	24	only	only	ADV
ejpam-5546	440	25	if	if	SCONJ
ejpam-5546	440	26	a	a	DET
ejpam-5546	440	27	̸=	̸=	PROPN
ejpam-5546	440	28	0	0	NUM
ejpam-5546	440	29	,	,	PUNCT
ejpam-5546	440	30	b	b	X
ejpam-5546	440	31	̸=	̸=	PROPN
ejpam-5546	440	32	0	0	NUM
ejpam-5546	440	33	,	,	PUNCT
ejpam-5546	440	34	t	t	PROPN
ejpam-5546	440	35	̸=	̸=	PROPN
ejpam-5546	440	36	0	0	NUM
ejpam-5546	440	37	,	,	PUNCT
ejpam-5546	440	38	t	t	PROPN
ejpam-5546	440	39	̸=	̸=	PROPN
ejpam-5546	440	40	qd−2i+1	qd−2i+1	ADV
ejpam-5546	440	41	,	,	PUNCT
ejpam-5546	440	42	a−1bt	a−1bt	NOUN
ejpam-5546	440	43	̸=	̸=	PROPN
ejpam-5546	440	44	q2i−d−1	q2i−d−1	NOUN
ejpam-5546	440	45	,	,	PUNCT
ejpam-5546	440	46	b−1at	b−1at	VERB
ejpam-5546	440	47	̸=	̸=	PROPN
ejpam-5546	440	48	qd−2i+1	qd−2i+1	NOUN
ejpam-5546	440	49	for	for	ADP
ejpam-5546	440	50	1	1	NUM
ejpam-5546	440	51	≤	≤	NUM
ejpam-5546	440	52	i	i	PRON
ejpam-5546	441	1	≤	≤	PROPN
ejpam-5546	441	2	d	d	ADP
ejpam-5546	441	3	,	,	PUNCT
ejpam-5546	441	4	and	and	CCONJ
ejpam-5546	441	5	a−	a−	PROPN
ejpam-5546	441	6	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	441	7	)	)	PUNCT
ejpam-5546	442	1	̸=	̸=	NOUN
ejpam-5546	442	2	0	0	NUM
ejpam-5546	442	3	for	for	ADP
ejpam-5546	442	4	1	1	NUM
ejpam-5546	442	5	≤	≤	NUM
ejpam-5546	442	6	i	i	PRON
ejpam-5546	442	7	≤	≤	NOUN
ejpam-5546	443	1	2d−	2d−	PROPN
ejpam-5546	443	2	1	1	NUM
ejpam-5546	443	3	.	.	PUNCT
ejpam-5546	444	1	proof	proof	NOUN
ejpam-5546	444	2	.	.	PUNCT
ejpam-5546	445	1	similar	similar	ADJ
ejpam-5546	445	2	to	to	ADP
ejpam-5546	445	3	proof	proof	NOUN
ejpam-5546	445	4	of	of	ADP
ejpam-5546	445	5	theorem	theorem	NOUN
ejpam-5546	445	6	5	5	NUM
ejpam-5546	445	7	but	but	CCONJ
ejpam-5546	445	8	replace	replace	VERB
ejpam-5546	445	9	the	the	DET
ejpam-5546	445	10	bases	basis	NOUN
ejpam-5546	446	1	[	[	X
ejpam-5546	446	2	i	i	PRON
ejpam-5546	446	3	,	,	PUNCT
ejpam-5546	446	4	j	j	PROPN
ejpam-5546	446	5	,	,	PUNCT
ejpam-5546	446	6	k	k	PROPN
ejpam-5546	446	7	,	,	PUNCT
ejpam-5546	446	8	l	l	NOUN
ejpam-5546	446	9	]	]	X
ejpam-5546	446	10	that	that	PRON
ejpam-5546	446	11	appear	appear	VERB
ejpam-5546	446	12	in	in	ADP
ejpam-5546	446	13	the	the	DET
ejpam-5546	446	14	proof	proof	NOUN
ejpam-5546	446	15	of	of	ADP
ejpam-5546	446	16	theorem	theorem	NOUN
ejpam-5546	446	17	5	5	NUM
ejpam-5546	446	18	by	by	ADP
ejpam-5546	446	19	the	the	DET
ejpam-5546	446	20	bases	basis	NOUN
ejpam-5546	446	21	[	[	X
ejpam-5546	446	22	i+	i+	NOUN
ejpam-5546	446	23	2	2	NUM
ejpam-5546	446	24	,	,	PUNCT
ejpam-5546	446	25	j	j	PROPN
ejpam-5546	447	1	+	+	PROPN
ejpam-5546	447	2	2	2	NUM
ejpam-5546	447	3	,	,	PUNCT
ejpam-5546	447	4	k	k	PROPN
ejpam-5546	447	5	+	+	PROPN
ejpam-5546	447	6	2	2	NUM
ejpam-5546	447	7	,	,	PUNCT
ejpam-5546	447	8	l	l	NOUN
ejpam-5546	447	9	+	+	NOUN
ejpam-5546	447	10	2	2	NUM
ejpam-5546	447	11	]	]	PUNCT
ejpam-5546	447	12	,	,	PUNCT
ejpam-5546	447	13	and	and	CCONJ
ejpam-5546	447	14	use	use	VERB
ejpam-5546	447	15	lemma	lemma	PROPN
ejpam-5546	447	16	24	24	NUM
ejpam-5546	447	17	to	to	PART
ejpam-5546	447	18	find	find	VERB
ejpam-5546	447	19	the	the	DET
ejpam-5546	447	20	action	action	NOUN
ejpam-5546	447	21	of	of	ADP
ejpam-5546	447	22	the	the	DET
ejpam-5546	447	23	standard	standard	ADJ
ejpam-5546	447	24	generators	generator	NOUN
ejpam-5546	447	25	of	of	ADP
ejpam-5546	447	26	⊠q	⊠q	PROPN
ejpam-5546	447	27	on	on	ADP
ejpam-5546	447	28	the	the	DET
ejpam-5546	447	29	new	new	ADJ
ejpam-5546	447	30	bases	basis	NOUN
ejpam-5546	447	31	.	.	PUNCT
ejpam-5546	448	1	theorem	theorem	ADJ
ejpam-5546	448	2	8	8	NUM
ejpam-5546	448	3	.	.	PUNCT
ejpam-5546	449	1	assume	assume	VERB
ejpam-5546	449	2	d	d	X
ejpam-5546	449	3	≥	≥	NUM
ejpam-5546	449	4	2	2	NUM
ejpam-5546	449	5	,	,	PUNCT
ejpam-5546	449	6	let	let	VERB
ejpam-5546	449	7	v	v	PART
ejpam-5546	449	8	denote	denote	VERB
ejpam-5546	449	9	an	an	DET
ejpam-5546	449	10	evaluation	evaluation	NOUN
ejpam-5546	449	11	module	module	NOUN
ejpam-5546	449	12	for	for	ADP
ejpam-5546	449	13	⊠q	⊠q	PROPN
ejpam-5546	449	14	with	with	ADP
ejpam-5546	449	15	dimension	dimension	NOUN
ejpam-5546	449	16	d+1	d+1	PROPN
ejpam-5546	449	17	.	.	PUNCT
ejpam-5546	450	1	let	let	VERB
ejpam-5546	450	2	a	a	DET
ejpam-5546	450	3	∈	∈	PROPN
ejpam-5546	450	4	⊠q	⊠q	PROPN
ejpam-5546	450	5	denote	denote	VERB
ejpam-5546	450	6	an	an	DET
ejpam-5546	450	7	arbitrary	arbitrary	ADJ
ejpam-5546	450	8	linear	linear	ADJ
ejpam-5546	450	9	combination	combination	NOUN
ejpam-5546	450	10	of	of	ADP
ejpam-5546	450	11	x12	x12	NUM
ejpam-5546	450	12	and	and	CCONJ
ejpam-5546	450	13	x23	x23	NUM
ejpam-5546	450	14	,	,	PUNCT
ejpam-5546	450	15	let	let	VERB
ejpam-5546	450	16	b1	b1	NOUN
ejpam-5546	450	17	,	,	PUNCT
ejpam-5546	450	18	b2	b2	NOUN
ejpam-5546	450	19	,	,	PUNCT
ejpam-5546	450	20	b3	b3	PROPN
ejpam-5546	450	21	∈	∈	PROPN
ejpam-5546	450	22	⊠q	⊠q	NOUN
ejpam-5546	450	23	such	such	ADJ
ejpam-5546	450	24	that	that	PRON
ejpam-5546	450	25	b1	b1	NOUN
ejpam-5546	450	26	=	=	SYM
ejpam-5546	450	27	x31	x31	PROPN
ejpam-5546	450	28	,	,	PUNCT
ejpam-5546	450	29	b2	b2	NOUN
ejpam-5546	450	30	=	=	SYM
ejpam-5546	450	31	x01	x01	PROPN
ejpam-5546	450	32	,	,	PUNCT
ejpam-5546	450	33	and	and	CCONJ
ejpam-5546	450	34	b3	b3	PROPN
ejpam-5546	450	35	=	=	SYM
ejpam-5546	450	36	x30	x30	PROPN
ejpam-5546	450	37	,	,	PUNCT
ejpam-5546	450	38	let	let	VERB
ejpam-5546	450	39	a	a	DET
ejpam-5546	450	40	,	,	PUNCT
ejpam-5546	450	41	b	b	NOUN
ejpam-5546	450	42	and	and	CCONJ
ejpam-5546	450	43	t	t	PROPN
ejpam-5546	451	1	̸=	̸=	PROPN
ejpam-5546	451	2	0	0	NUM
ejpam-5546	451	3	be	be	AUX
ejpam-5546	451	4	scalars	scalar	NOUN
ejpam-5546	451	5	in	in	ADP
ejpam-5546	451	6	f	f	PROPN
ejpam-5546	451	7	.	.	PUNCT
ejpam-5546	452	1	write	write	VERB
ejpam-5546	452	2	a	a	DET
ejpam-5546	452	3	=	=	SYM
ejpam-5546	452	4	ax12	ax12	PROPN
ejpam-5546	452	5	+	+	CCONJ
ejpam-5546	452	6	bx23	bx23	PROPN
ejpam-5546	452	7	.	.	PUNCT
ejpam-5546	453	1	then	then	ADV
ejpam-5546	453	2	the	the	DET
ejpam-5546	453	3	pairs	pair	NOUN
ejpam-5546	453	4	a	a	PRON
ejpam-5546	453	5	,	,	PUNCT
ejpam-5546	453	6	b1	b1	NOUN
ejpam-5546	453	7	,	,	PUNCT
ejpam-5546	453	8	a	a	DET
ejpam-5546	453	9	,	,	PUNCT
ejpam-5546	453	10	b2	b2	NOUN
ejpam-5546	453	11	,	,	PUNCT
ejpam-5546	453	12	and	and	CCONJ
ejpam-5546	453	13	a	a	DET
ejpam-5546	453	14	,	,	PUNCT
ejpam-5546	453	15	b3	b3	PROPN
ejpam-5546	453	16	act	act	NOUN
ejpam-5546	453	17	on	on	ADP
ejpam-5546	453	18	v	v	NOUN
ejpam-5546	453	19	as	as	ADP
ejpam-5546	453	20	leonard	leonard	NOUN
ejpam-5546	453	21	pairs	pair	NOUN
ejpam-5546	453	22	if	if	SCONJ
ejpam-5546	453	23	and	and	CCONJ
ejpam-5546	453	24	only	only	ADV
ejpam-5546	453	25	if	if	SCONJ
ejpam-5546	453	26	a	a	DET
ejpam-5546	453	27	̸=	̸=	PROPN
ejpam-5546	453	28	0	0	NUM
ejpam-5546	453	29	,	,	PUNCT
ejpam-5546	453	30	b	b	X
ejpam-5546	453	31	̸=	̸=	PROPN
ejpam-5546	453	32	0	0	NUM
ejpam-5546	453	33	,	,	PUNCT
ejpam-5546	453	34	t	t	PROPN
ejpam-5546	453	35	̸=	̸=	PROPN
ejpam-5546	453	36	0	0	NUM
ejpam-5546	453	37	,	,	PUNCT
ejpam-5546	453	38	t−1	t−1	PROPN
ejpam-5546	453	39	̸=	̸=	PROPN
ejpam-5546	453	40	qd−2i+1	qd−2i+1	ADV
ejpam-5546	453	41	,	,	PUNCT
ejpam-5546	453	42	a−1bt−1	a−1bt−1	PROPN
ejpam-5546	453	43	̸=	̸=	PROPN
ejpam-5546	453	44	q2i−d−1	q2i−d−1	NOUN
ejpam-5546	453	45	,	,	PUNCT
ejpam-5546	453	46	b−1at−1	b−1at−1	NOUN
ejpam-5546	453	47	̸=	̸=	PROPN
ejpam-5546	453	48	qd−2i+1	qd−2i+1	NOUN
ejpam-5546	453	49	for	for	ADP
ejpam-5546	453	50	1	1	NUM
ejpam-5546	453	51	≤	≤	NUM
ejpam-5546	453	52	i	i	PRON
ejpam-5546	453	53	≤	≤	PROPN
ejpam-5546	454	1	d	d	ADP
ejpam-5546	454	2	,	,	PUNCT
ejpam-5546	454	3	and	and	CCONJ
ejpam-5546	454	4	a−	a−	PROPN
ejpam-5546	454	5	bq2(i−d	bq2(i−d	NOUN
ejpam-5546	454	6	)	)	PUNCT
ejpam-5546	455	1	̸=	̸=	NOUN
ejpam-5546	455	2	0	0	NUM
ejpam-5546	455	3	for	for	ADP
ejpam-5546	455	4	1	1	NUM
ejpam-5546	455	5	≤	≤	NUM
ejpam-5546	455	6	i	i	PRON
ejpam-5546	455	7	≤	≤	NOUN
ejpam-5546	456	1	2d−	2d−	PROPN
ejpam-5546	456	2	1	1	NUM
ejpam-5546	456	3	.	.	PUNCT
ejpam-5546	457	1	proof	proof	NOUN
ejpam-5546	457	2	.	.	PUNCT
ejpam-5546	458	1	similar	similar	ADJ
ejpam-5546	458	2	to	to	ADP
ejpam-5546	458	3	proof	proof	NOUN
ejpam-5546	458	4	of	of	ADP
ejpam-5546	458	5	theorem	theorem	NOUN
ejpam-5546	458	6	5	5	NUM
ejpam-5546	458	7	but	but	CCONJ
ejpam-5546	458	8	replace	replace	VERB
ejpam-5546	458	9	t	t	NOUN
ejpam-5546	458	10	by	by	ADP
ejpam-5546	458	11	t−1	t−1	PROPN
ejpam-5546	458	12	and	and	CCONJ
ejpam-5546	458	13	replace	replace	VERB
ejpam-5546	458	14	the	the	DET
ejpam-5546	458	15	bases	basis	NOUN
ejpam-5546	458	16	[	[	X
ejpam-5546	458	17	i	i	PRON
ejpam-5546	458	18	,	,	PUNCT
ejpam-5546	458	19	j	j	PROPN
ejpam-5546	458	20	,	,	PUNCT
ejpam-5546	458	21	k	k	PROPN
ejpam-5546	458	22	,	,	PUNCT
ejpam-5546	458	23	l	l	NOUN
ejpam-5546	458	24	]	]	X
ejpam-5546	458	25	that	that	PRON
ejpam-5546	458	26	appear	appear	VERB
ejpam-5546	458	27	in	in	ADP
ejpam-5546	458	28	the	the	DET
ejpam-5546	458	29	proof	proof	NOUN
ejpam-5546	458	30	of	of	ADP
ejpam-5546	458	31	theorem	theorem	NOUN
ejpam-5546	458	32	5	5	NUM
ejpam-5546	458	33	by	by	ADP
ejpam-5546	458	34	the	the	DET
ejpam-5546	458	35	bases	basis	NOUN
ejpam-5546	458	36	[	[	X
ejpam-5546	458	37	i+3	i+3	NOUN
ejpam-5546	458	38	,	,	PUNCT
ejpam-5546	458	39	j+3	j+3	PRON
ejpam-5546	458	40	,	,	PUNCT
ejpam-5546	458	41	k+3	k+3	PROPN
ejpam-5546	458	42	,	,	PUNCT
ejpam-5546	458	43	l+3	l+3	X
ejpam-5546	458	44	]	]	X
ejpam-5546	458	45	,	,	PUNCT
ejpam-5546	458	46	and	and	CCONJ
ejpam-5546	458	47	use	use	VERB
ejpam-5546	458	48	lemma	lemma	PROPN
ejpam-5546	458	49	24	24	NUM
ejpam-5546	458	50	to	to	PART
ejpam-5546	458	51	find	find	VERB
ejpam-5546	458	52	the	the	DET
ejpam-5546	458	53	action	action	NOUN
ejpam-5546	458	54	of	of	ADP
ejpam-5546	458	55	the	the	DET
ejpam-5546	458	56	standard	standard	ADJ
ejpam-5546	458	57	generators	generator	NOUN
ejpam-5546	458	58	of	of	ADP
ejpam-5546	458	59	⊠q	⊠q	PROPN
ejpam-5546	458	60	on	on	ADP
ejpam-5546	458	61	the	the	DET
ejpam-5546	458	62	new	new	ADJ
ejpam-5546	458	63	bases	basis	NOUN
ejpam-5546	458	64	.	.	PUNCT
ejpam-5546	459	1	references	reference	NOUN
ejpam-5546	459	2	[	[	X
ejpam-5546	459	3	1	1	NUM
ejpam-5546	459	4	]	]	PUNCT
ejpam-5546	459	5	h.	h.	PROPN
ejpam-5546	459	6	alnajjar	alnajjar	PROPN
ejpam-5546	459	7	.	.	PUNCT
ejpam-5546	460	1	leonard	leonard	PROPN
ejpam-5546	460	2	pairs	pair	NOUN
ejpam-5546	460	3	associated	associate	VERB
ejpam-5546	460	4	with	with	ADP
ejpam-5546	460	5	equitable	equitable	ADJ
ejpam-5546	460	6	generators	generator	NOUN
ejpam-5546	460	7	of	of	ADP
ejpam-5546	460	8	the	the	DET
ejpam-5546	460	9	quantum	quantum	NOUN
ejpam-5546	460	10	algebra	algebra	NOUN
ejpam-5546	460	11	uq(sl2	uq(sl2	PROPN
ejpam-5546	460	12	)	)	PUNCT
ejpam-5546	460	13	.	.	PUNCT
ejpam-5546	461	1	linear	linear	PROPN
ejpam-5546	461	2	and	and	CCONJ
ejpam-5546	461	3	multilinear	multilinear	PROPN
ejpam-5546	461	4	algebra	algebra	PROPN
ejpam-5546	461	5	,	,	PUNCT
ejpam-5546	461	6	59:1127–1142	59:1127–1142	NUM
ejpam-5546	461	7	,	,	PUNCT
ejpam-5546	461	8	2011	2011	NUM
ejpam-5546	461	9	.	.	PUNCT
ejpam-5546	462	1	[	[	X
ejpam-5546	462	2	2	2	X
ejpam-5546	462	3	]	]	PUNCT
ejpam-5546	462	4	h.	h.	PROPN
ejpam-5546	462	5	alnajjar	alnajjar	PROPN
ejpam-5546	462	6	.	.	PUNCT
ejpam-5546	463	1	a	a	DET
ejpam-5546	463	2	linear	linear	ADJ
ejpam-5546	463	3	map	map	NOUN
ejpam-5546	463	4	that	that	PRON
ejpam-5546	463	5	acts	act	VERB
ejpam-5546	463	6	as	as	ADP
ejpam-5546	463	7	a	a	DET
ejpam-5546	463	8	leonard	leonard	NOUN
ejpam-5546	463	9	pair	pair	NOUN
ejpam-5546	463	10	with	with	ADP
ejpam-5546	463	11	each	each	PRON
ejpam-5546	463	12	of	of	ADP
ejpam-5546	463	13	the	the	DET
ejpam-5546	463	14	generators	generator	NOUN
ejpam-5546	463	15	of	of	ADP
ejpam-5546	463	16	u	u	PROPN
ejpam-5546	463	17	(	(	PUNCT
ejpam-5546	463	18	sl2	sl2	PROPN
ejpam-5546	463	19	)	)	PUNCT
ejpam-5546	463	20	.	.	PUNCT
ejpam-5546	464	1	international	international	ADJ
ejpam-5546	464	2	journal	journal	PROPN
ejpam-5546	464	3	of	of	ADP
ejpam-5546	464	4	mathematics	mathematics	PROPN
ejpam-5546	464	5	and	and	CCONJ
ejpam-5546	464	6	mathematical	mathematical	ADJ
ejpam-5546	464	7	science	science	NOUN
ejpam-5546	464	8	,	,	PUNCT
ejpam-5546	464	9	2020	2020	NUM
ejpam-5546	464	10	,	,	PUNCT
ejpam-5546	464	11	2020	2020	NUM
ejpam-5546	464	12	.	.	PUNCT
ejpam-5546	465	1	[	[	X
ejpam-5546	465	2	3	3	X
ejpam-5546	465	3	]	]	X
ejpam-5546	465	4	h.	h.	PROPN
ejpam-5546	465	5	alnajjar	alnajjar	PROPN
ejpam-5546	465	6	and	and	CCONJ
ejpam-5546	465	7	b.	b.	PROPN
ejpam-5546	465	8	curtin	curtin	PROPN
ejpam-5546	465	9	.	.	PUNCT
ejpam-5546	466	1	leonard	leonard	PROPN
ejpam-5546	466	2	pairs	pair	NOUN
ejpam-5546	466	3	from	from	ADP
ejpam-5546	466	4	the	the	DET
ejpam-5546	466	5	equitable	equitable	ADJ
ejpam-5546	466	6	basis	basis	NOUN
ejpam-5546	466	7	of	of	ADP
ejpam-5546	466	8	sl2	sl2	PROPN
ejpam-5546	466	9	.	.	PUNCT
ejpam-5546	467	1	ela	ela	PROPN
ejpam-5546	467	2	,	,	PUNCT
ejpam-5546	467	3	20:490–505	20:490–505	PROPN
ejpam-5546	467	4	,	,	PUNCT
ejpam-5546	467	5	2010	2010	NUM
ejpam-5546	467	6	.	.	PUNCT
ejpam-5546	468	1	[	[	X
ejpam-5546	468	2	4	4	X
ejpam-5546	468	3	]	]	PUNCT
ejpam-5546	468	4	t.	t.	PROPN
ejpam-5546	468	5	ito	ito	PROPN
ejpam-5546	468	6	,	,	PUNCT
ejpam-5546	468	7	h.	h.	PROPN
ejpam-5546	468	8	rosengren	rosengren	PROPN
ejpam-5546	468	9	,	,	PUNCT
ejpam-5546	468	10	and	and	CCONJ
ejpam-5546	468	11	p.	p.	PROPN
ejpam-5546	468	12	terwilliger	terwilliger	NOUN
ejpam-5546	468	13	.	.	PUNCT
ejpam-5546	469	1	evaluation	evaluation	NOUN
ejpam-5546	469	2	modules	module	NOUN
ejpam-5546	469	3	for	for	ADP
ejpam-5546	469	4	the	the	DET
ejpam-5546	469	5	q	q	ADJ
ejpam-5546	469	6	-	-	PUNCT
ejpam-5546	469	7	tetrahedron	tetrahedron	NOUN
ejpam-5546	469	8	algebra	algebra	NOUN
ejpam-5546	469	9	.	.	PUNCT
ejpam-5546	470	1	linear	linear	PROPN
ejpam-5546	470	2	algebra	algebra	PROPN
ejpam-5546	470	3	appl	appl	PROPN
ejpam-5546	470	4	.	.	PROPN
ejpam-5546	470	5	,	,	PUNCT
ejpam-5546	470	6	451:107–168	451:107–168	NUM
ejpam-5546	470	7	,	,	PUNCT
ejpam-5546	470	8	2014	2014	NUM
ejpam-5546	470	9	.	.	PUNCT
ejpam-5546	471	1	[	[	X
ejpam-5546	471	2	5	5	X
ejpam-5546	471	3	]	]	PUNCT
ejpam-5546	471	4	t.	t.	PROPN
ejpam-5546	471	5	ito	ito	PROPN
ejpam-5546	471	6	and	and	CCONJ
ejpam-5546	471	7	p.	p.	PROPN
ejpam-5546	471	8	terwilliger	terwilliger	NOUN
ejpam-5546	471	9	.	.	PUNCT
ejpam-5546	472	1	the	the	DET
ejpam-5546	472	2	q	q	ADJ
ejpam-5546	472	3	-	-	PUNCT
ejpam-5546	472	4	tetrahedron	tetrahedron	NOUN
ejpam-5546	472	5	algebra	algebra	NOUN
ejpam-5546	472	6	and	and	CCONJ
ejpam-5546	472	7	its	its	PRON
ejpam-5546	472	8	finite	finite	ADJ
ejpam-5546	472	9	dimensional	dimensional	ADJ
ejpam-5546	472	10	irreducible	irreducible	ADJ
ejpam-5546	472	11	modules	module	NOUN
ejpam-5546	472	12	.	.	PUNCT
ejpam-5546	473	1	comm	comm	NOUN
ejpam-5546	473	2	.	.	PUNCT
ejpam-5546	474	1	algebra	algebra	PROPN
ejpam-5546	474	2	,	,	PUNCT
ejpam-5546	474	3	35:3415–3439	35:3415–3439	PROPN
ejpam-5546	474	4	,	,	PUNCT
ejpam-5546	474	5	2007	2007	NUM
ejpam-5546	474	6	.	.	PUNCT
ejpam-5546	475	1	[	[	X
ejpam-5546	475	2	6	6	NUM
ejpam-5546	475	3	]	]	PUNCT
ejpam-5546	475	4	p.	p.	NOUN
ejpam-5546	475	5	terwilliger	terwilliger	NOUN
ejpam-5546	475	6	.	.	PUNCT
ejpam-5546	476	1	the	the	DET
ejpam-5546	476	2	subconstituent	subconstituent	NOUN
ejpam-5546	476	3	algebra	algebra	NOUN
ejpam-5546	476	4	of	of	ADP
ejpam-5546	476	5	an	an	DET
ejpam-5546	476	6	association	association	NOUN
ejpam-5546	476	7	scheme	scheme	NOUN
ejpam-5546	476	8	.	.	PUNCT
ejpam-5546	477	1	iii	iii	PROPN
ejpam-5546	477	2	.	.	PUNCT
ejpam-5546	478	1	j.	j.	PROPN
ejpam-5546	478	2	algebraic	algebraic	PROPN
ejpam-5546	478	3	combin	combin	PROPN
ejpam-5546	478	4	.	.	PUNCT
ejpam-5546	478	5	,	,	PUNCT
ejpam-5546	478	6	2(2):177–210	2(2):177–210	NUM
ejpam-5546	478	7	,	,	PUNCT
ejpam-5546	478	8	1993	1993	NUM
ejpam-5546	478	9	.	.	PUNCT
ejpam-5546	479	1	[	[	X
ejpam-5546	479	2	7	7	X
ejpam-5546	479	3	]	]	PUNCT
ejpam-5546	479	4	p.	p.	NOUN
ejpam-5546	479	5	terwilliger	terwilliger	NOUN
ejpam-5546	479	6	.	.	PUNCT
ejpam-5546	480	1	two	two	NUM
ejpam-5546	480	2	linear	linear	ADJ
ejpam-5546	480	3	transformations	transformation	NOUN
ejpam-5546	480	4	each	each	DET
ejpam-5546	480	5	tridiagonal	tridiagonal	NOUN
ejpam-5546	480	6	with	with	ADP
ejpam-5546	480	7	respect	respect	NOUN
ejpam-5546	480	8	to	to	ADP
ejpam-5546	480	9	an	an	DET
ejpam-5546	480	10	eigenbasis	eigenbasis	NOUN
ejpam-5546	480	11	of	of	ADP
ejpam-5546	480	12	the	the	DET
ejpam-5546	480	13	other	other	ADJ
ejpam-5546	480	14	.	.	PUNCT
ejpam-5546	481	1	linear	linear	PROPN
ejpam-5546	481	2	algebra	algebra	PROPN
ejpam-5546	481	3	appl	appl	NOUN
ejpam-5546	481	4	.	.	PROPN
ejpam-5546	481	5	,	,	PUNCT
ejpam-5546	481	6	330:149–203	330:149–203	NUM
ejpam-5546	481	7	,	,	PUNCT
ejpam-5546	481	8	2001	2001	NUM
ejpam-5546	481	9	.	.	PUNCT
ejpam-5546	482	1	[	[	X
ejpam-5546	482	2	8	8	NUM
ejpam-5546	482	3	]	]	PUNCT
ejpam-5546	482	4	p.	p.	NOUN
ejpam-5546	482	5	terwilliger	terwilliger	NOUN
ejpam-5546	482	6	.	.	PUNCT
ejpam-5546	483	1	leonard	leonard	PROPN
ejpam-5546	483	2	pairs	pair	NOUN
ejpam-5546	483	3	from	from	ADP
ejpam-5546	483	4	24	24	NUM
ejpam-5546	483	5	points	point	NOUN
ejpam-5546	483	6	of	of	ADP
ejpam-5546	483	7	view	view	NOUN
ejpam-5546	483	8	.	.	PUNCT
ejpam-5546	484	1	rocky	rocky	ADJ
ejpam-5546	484	2	mountain	mountain	PROPN
ejpam-5546	484	3	j.	j.	PROPN
ejpam-5546	484	4	math	math	PROPN
ejpam-5546	484	5	.	.	PUNCT
ejpam-5546	484	6	,	,	PUNCT
ejpam-5546	484	7	32(2):827–888	32(2):827–888	PROPN
ejpam-5546	484	8	,	,	PUNCT
ejpam-5546	484	9	2002	2002	NUM
ejpam-5546	484	10	.	.	PUNCT
ejpam-5546	485	1	[	[	X
ejpam-5546	485	2	9	9	NUM
ejpam-5546	485	3	]	]	PUNCT
ejpam-5546	485	4	p.	p.	NOUN
ejpam-5546	485	5	terwilliger	terwilliger	NOUN
ejpam-5546	485	6	.	.	PUNCT
ejpam-5546	486	1	introduction	introduction	NOUN
ejpam-5546	486	2	to	to	ADP
ejpam-5546	486	3	leonard	leonard	PROPN
ejpam-5546	486	4	pairs	pair	NOUN
ejpam-5546	486	5	.	.	PUNCT
ejpam-5546	487	1	opsfa	opsfa	PROPN
ejpam-5546	487	2	rome	rome	PROPN
ejpam-5546	487	3	2001	2001	NUM
ejpam-5546	487	4	.	.	PUNCT
ejpam-5546	488	1	j.	j.	PROPN
ejpam-5546	488	2	comput	comput	PROPN
ejpam-5546	488	3	.	.	PUNCT
ejpam-5546	489	1	appl	appl	PROPN
ejpam-5546	489	2	.	.	PROPN
ejpam-5546	489	3	math	math	PROPN
ejpam-5546	489	4	.	.	PUNCT
ejpam-5546	489	5	,	,	PUNCT
ejpam-5546	489	6	153(2):463–475	153(2):463–475	NUM
ejpam-5546	489	7	,	,	PUNCT
ejpam-5546	489	8	2003	2003	NUM
ejpam-5546	489	9	.	.	PUNCT
ejpam-5546	490	1	[	[	X
ejpam-5546	490	2	10	10	NUM
ejpam-5546	490	3	]	]	PUNCT
ejpam-5546	490	4	p.	p.	NOUN
ejpam-5546	490	5	terwilliger	terwilliger	NOUN
ejpam-5546	490	6	.	.	PUNCT
ejpam-5546	491	1	leonard	leonard	PROPN
ejpam-5546	491	2	pairs	pair	NOUN
ejpam-5546	491	3	and	and	CCONJ
ejpam-5546	491	4	the	the	DET
ejpam-5546	491	5	q	q	ADJ
ejpam-5546	491	6	-	-	PUNCT
ejpam-5546	491	7	racah	racah	ADJ
ejpam-5546	491	8	polynomials	polynomial	NOUN
ejpam-5546	491	9	.	.	PUNCT
ejpam-5546	492	1	linear	linear	ADJ
ejpam-5546	492	2	algebra	algebra	PROPN
ejpam-5546	492	3	appl	appl	NOUN
ejpam-5546	492	4	.	.	PROPN
ejpam-5546	492	5	,	,	PUNCT
ejpam-5546	492	6	387:235–276	387:235–276	NUM
ejpam-5546	492	7	,	,	PUNCT
ejpam-5546	492	8	2004	2004	NUM
ejpam-5546	492	9	.	.	PUNCT
ejpam-5546	493	1	[	[	X
ejpam-5546	493	2	11	11	NUM
ejpam-5546	493	3	]	]	PUNCT
ejpam-5546	493	4	p.	p.	NOUN
ejpam-5546	493	5	terwilliger	terwilliger	NOUN
ejpam-5546	493	6	.	.	PUNCT
ejpam-5546	494	1	two	two	NUM
ejpam-5546	494	2	linear	linear	ADJ
ejpam-5546	494	3	transformations	transformation	NOUN
ejpam-5546	494	4	each	each	DET
ejpam-5546	494	5	tridiagonal	tridiagonal	NOUN
ejpam-5546	494	6	with	with	ADP
ejpam-5546	494	7	respect	respect	NOUN
ejpam-5546	494	8	to	to	ADP
ejpam-5546	494	9	an	an	DET
ejpam-5546	494	10	eigenbasis	eigenbasis	NOUN
ejpam-5546	494	11	of	of	ADP
ejpam-5546	494	12	the	the	DET
ejpam-5546	494	13	other	other	ADJ
ejpam-5546	494	14	.	.	PUNCT
ejpam-5546	495	1	comments	comment	NOUN
ejpam-5546	495	2	on	on	ADP
ejpam-5546	495	3	the	the	DET
ejpam-5546	495	4	parameter	parameter	NOUN
ejpam-5546	495	5	array	array	NOUN
ejpam-5546	495	6	.	.	PUNCT
ejpam-5546	496	1	des	des	PROPN
ejpam-5546	496	2	.	.	PROPN
ejpam-5546	496	3	codes	code	NOUN
ejpam-5546	496	4	cryptogr	cryptogr	NOUN
ejpam-5546	496	5	.	.	PUNCT
ejpam-5546	496	6	,	,	PUNCT
ejpam-5546	496	7	34:307–332	34:307–332	PROPN
ejpam-5546	496	8	,	,	PUNCT
ejpam-5546	496	9	2005	2005	NUM
ejpam-5546	496	10	.	.	PUNCT
ejpam-5546	497	1	h.	h.	PROPN
ejpam-5546	497	2	alnajjar	alnajjar	PROPN
ejpam-5546	497	3	/	/	SYM
ejpam-5546	497	4	eur	eur	PROPN
ejpam-5546	497	5	.	.	PUNCT
ejpam-5546	498	1	j.	j.	PROPN
ejpam-5546	498	2	pure	pure	PROPN
ejpam-5546	498	3	appl	appl	PROPN
ejpam-5546	498	4	.	.	PROPN
ejpam-5546	498	5	math	math	PROPN
ejpam-5546	498	6	,	,	PUNCT
ejpam-5546	498	7	18	18	NUM
ejpam-5546	498	8	(	(	PUNCT
ejpam-5546	498	9	1	1	NUM
ejpam-5546	498	10	)	)	PUNCT
ejpam-5546	498	11	(	(	PUNCT
ejpam-5546	498	12	2025	2025	NUM
ejpam-5546	498	13	)	)	PUNCT
ejpam-5546	498	14	,	,	PUNCT
ejpam-5546	498	15	5546	5546	NUM
ejpam-5546	498	16	14	14	NUM
ejpam-5546	498	17	of	of	ADP
ejpam-5546	498	18	14	14	NUM
ejpam-5546	499	1	[	[	X
ejpam-5546	499	2	12	12	NUM
ejpam-5546	499	3	]	]	PUNCT
ejpam-5546	499	4	p.	p.	NOUN
ejpam-5546	499	5	terwilliger	terwilliger	NOUN
ejpam-5546	499	6	.	.	PUNCT
ejpam-5546	500	1	two	two	NUM
ejpam-5546	500	2	linear	linear	ADJ
ejpam-5546	500	3	transformations	transformation	NOUN
ejpam-5546	500	4	each	each	DET
ejpam-5546	500	5	tridiagonal	tridiagonal	NOUN
ejpam-5546	500	6	with	with	ADP
ejpam-5546	500	7	respect	respect	NOUN
ejpam-5546	500	8	to	to	ADP
ejpam-5546	500	9	an	an	DET
ejpam-5546	500	10	eigenbasis	eigenbasis	NOUN
ejpam-5546	500	11	of	of	ADP
ejpam-5546	500	12	the	the	DET
ejpam-5546	500	13	other	other	ADJ
ejpam-5546	500	14	:	:	PUNCT
ejpam-5546	500	15	the	the	DET
ejpam-5546	500	16	td	td	NOUN
ejpam-5546	500	17	-	-	PUNCT
ejpam-5546	500	18	d	d	NOUN
ejpam-5546	500	19	and	and	CCONJ
ejpam-5546	500	20	the	the	DET
ejpam-5546	500	21	lb	lb	ADJ
ejpam-5546	500	22	-	-	PUNCT
ejpam-5546	500	23	ub	ub	ADJ
ejpam-5546	500	24	canonical	canonical	ADJ
ejpam-5546	500	25	form	form	NOUN
ejpam-5546	500	26	.	.	PUNCT
ejpam-5546	501	1	j.	j.	PROPN
ejpam-5546	501	2	algebra	algebra	PROPN
ejpam-5546	501	3	,	,	PUNCT
ejpam-5546	501	4	291(1):1–45	291(1):1–45	NUM
ejpam-5546	501	5	,	,	PUNCT
ejpam-5546	501	6	2005	2005	NUM
ejpam-5546	501	7	.	.	PUNCT