id	sid	tid	token	lemma	pos
ejpam-6733	1	1	european	european	PROPN
ejpam-6733	1	2	journal	journal	PROPN
ejpam-6733	1	3	of	of	ADP
ejpam-6733	1	4	pure	pure	ADJ
ejpam-6733	1	5	and	and	CCONJ
ejpam-6733	1	6	applied	applied	ADJ
ejpam-6733	1	7	mathematics	mathematic	NOUN
ejpam-6733	1	8	2025	2025	NUM
ejpam-6733	1	9	,	,	PUNCT
ejpam-6733	1	10	vol	vol	NOUN
ejpam-6733	1	11	.	.	PROPN
ejpam-6733	1	12	18	18	NUM
ejpam-6733	1	13	,	,	PUNCT
ejpam-6733	1	14	issue	issue	NOUN
ejpam-6733	1	15	4	4	NUM
ejpam-6733	1	16	,	,	PUNCT
ejpam-6733	1	17	article	article	NOUN
ejpam-6733	1	18	number	number	NOUN
ejpam-6733	1	19	6733	6733	NUM
ejpam-6733	1	20	issn	issn	VERB
ejpam-6733	1	21	1307	1307	NUM
ejpam-6733	1	22	-	-	SYM
ejpam-6733	1	23	5543	5543	NUM
ejpam-6733	1	24	–	–	PUNCT
ejpam-6733	1	25	ejpam.com	ejpam.com	X
ejpam-6733	1	26	published	publish	VERB
ejpam-6733	1	27	by	by	ADP
ejpam-6733	1	28	new	new	PROPN
ejpam-6733	1	29	york	york	PROPN
ejpam-6733	1	30	business	business	PROPN
ejpam-6733	1	31	global	global	ADJ
ejpam-6733	1	32	matrix	matrix	NOUN
ejpam-6733	1	33	representations	representation	NOUN
ejpam-6733	1	34	of	of	ADP
ejpam-6733	1	35	the	the	DET
ejpam-6733	1	36	two	two	NUM
ejpam-6733	1	37	-	-	PUNCT
ejpam-6733	1	38	parameter	parameter	NOUN
ejpam-6733	1	39	deformed	deform	VERB
ejpam-6733	1	40	oscillator	oscillator	NOUN
ejpam-6733	1	41	algebra	algebra	NOUN
ejpam-6733	1	42	latif	latif	PROPN
ejpam-6733	1	43	a	a	DET
ejpam-6733	1	44	-	-	PUNCT
ejpam-6733	1	45	m.	m.	NOUN
ejpam-6733	1	46	hanna1,∗	hanna1,∗	NOUN
ejpam-6733	1	47	,	,	PUNCT
ejpam-6733	1	48	shoukry	shoukry	PROPN
ejpam-6733	1	49	s.	s.	PROPN
ejpam-6733	1	50	hassan2	hassan2	PROPN
ejpam-6733	1	51	,	,	PUNCT
ejpam-6733	1	52	maali	maali	ADJ
ejpam-6733	1	53	almutairi1	almutairi1	PROPN
ejpam-6733	1	54	1	1	NUM
ejpam-6733	1	55	department	department	NOUN
ejpam-6733	1	56	of	of	ADP
ejpam-6733	1	57	mathematics	mathematic	NOUN
ejpam-6733	1	58	,	,	PUNCT
ejpam-6733	1	59	faculty	faculty	NOUN
ejpam-6733	1	60	of	of	ADP
ejpam-6733	1	61	science	science	NOUN
ejpam-6733	1	62	,	,	PUNCT
ejpam-6733	1	63	kuwait	kuwait	PROPN
ejpam-6733	1	64	university	university	PROPN
ejpam-6733	1	65	,	,	PUNCT
ejpam-6733	1	66	p.o	p.o	PROPN
ejpam-6733	1	67	.	.	PROPN
ejpam-6733	1	68	box	box	PROPN
ejpam-6733	1	69	5969	5969	NUM
ejpam-6733	1	70	,	,	PUNCT
ejpam-6733	1	71	safat	safat	NOUN
ejpam-6733	1	72	13060	13060	NUM
ejpam-6733	1	73	,	,	PUNCT
ejpam-6733	1	74	kuwait	kuwait	PROPN
ejpam-6733	1	75	city	city	PROPN
ejpam-6733	1	76	,	,	PUNCT
ejpam-6733	1	77	kuwait	kuwait	PROPN
ejpam-6733	1	78	2	2	NUM
ejpam-6733	1	79	independent	independent	ADJ
ejpam-6733	1	80	researcher	researcher	NOUN
ejpam-6733	1	81	,	,	PUNCT
ejpam-6733	1	82	237	237	NUM
ejpam-6733	1	83	banafseg	banafseg	VERB
ejpam-6733	1	84	7	7	NUM
ejpam-6733	1	85	,	,	PUNCT
ejpam-6733	1	86	new	new	ADJ
ejpam-6733	1	87	cairo	cairo	PROPN
ejpam-6733	1	88	,	,	PUNCT
ejpam-6733	1	89	egypt	egypt	PROPN
ejpam-6733	1	90	abstract	abstract	PROPN
ejpam-6733	1	91	.	.	PUNCT
ejpam-6733	2	1	faithful	faithful	ADJ
ejpam-6733	2	2	matrix	matrix	NOUN
ejpam-6733	2	3	representations	representation	NOUN
ejpam-6733	2	4	are	be	AUX
ejpam-6733	2	5	presented	present	VERB
ejpam-6733	2	6	for	for	ADP
ejpam-6733	2	7	polynomially	polynomially	ADV
ejpam-6733	2	8	(	(	PUNCT
ejpam-6733	2	9	p	p	X
ejpam-6733	2	10	,	,	PUNCT
ejpam-6733	2	11	q)-deformed	q)-deformed	ADJ
ejpam-6733	2	12	lie	lie	NOUN
ejpam-6733	2	13	algebra	algebra	NOUN
ejpam-6733	2	14	lp	lp	NOUN
ejpam-6733	2	15	,	,	PUNCT
ejpam-6733	2	16	q	q	NOUN
ejpam-6733	2	17	:	:	PUNCT
ejpam-6733	2	18	[	[	X
ejpam-6733	2	19	k0,k+]p	k0,k+]p	PROPN
ejpam-6733	2	20	,	,	PUNCT
ejpam-6733	2	21	q	q	NOUN
ejpam-6733	2	22	=	=	SYM
ejpam-6733	2	23	rk+	rk+	NOUN
ejpam-6733	2	24	,	,	PUNCT
ejpam-6733	2	25	[	[	X
ejpam-6733	2	26	k−,k0]p	k−,k0]p	NOUN
ejpam-6733	2	27	,	,	PUNCT
ejpam-6733	2	28	q	q	NOUN
ejpam-6733	2	29	=	=	SYM
ejpam-6733	2	30	rk−,[k+,k−]p	rk−,[k+,k−]p	NUM
ejpam-6733	2	31	,	,	PUNCT
ejpam-6733	2	32	q	q	NOUN
ejpam-6733	2	33	=	=	SYM
ejpam-6733	2	34	f	f	X
ejpam-6733	2	35	(	(	PUNCT
ejpam-6733	2	36	k0	k0	PROPN
ejpam-6733	2	37	)	)	PUNCT
ejpam-6733	2	38	,	,	PUNCT
ejpam-6733	2	39	where	where	SCONJ
ejpam-6733	2	40	f	f	PROPN
ejpam-6733	2	41	is	be	AUX
ejpam-6733	2	42	a	a	DET
ejpam-6733	2	43	real	real	ADJ
ejpam-6733	2	44	polynomial	polynomial	ADJ
ejpam-6733	2	45	function	function	NOUN
ejpam-6733	2	46	,	,	PUNCT
ejpam-6733	2	47	and	and	CCONJ
ejpam-6733	2	48	p	p	X
ejpam-6733	2	49	,	,	PUNCT
ejpam-6733	2	50	q	q	INTJ
ejpam-6733	2	51	,	,	PUNCT
ejpam-6733	2	52	r	r	NOUN
ejpam-6733	2	53	∈	∈	PROPN
ejpam-6733	2	54	r∗	r∗	PROPN
ejpam-6733	2	55	,	,	PUNCT
ejpam-6733	2	56	(	(	PUNCT
ejpam-6733	2	57	r∗	r∗	PROPN
ejpam-6733	2	58	is	be	AUX
ejpam-6733	2	59	the	the	DET
ejpam-6733	2	60	set	set	NOUN
ejpam-6733	2	61	of	of	ADP
ejpam-6733	2	62	nonzero	nonzero	ADJ
ejpam-6733	2	63	real	real	ADJ
ejpam-6733	2	64	numbers	number	NOUN
ejpam-6733	2	65	)	)	PUNCT
ejpam-6733	2	66	.	.	PUNCT
ejpam-6733	3	1	conditions	condition	NOUN
ejpam-6733	3	2	are	be	AUX
ejpam-6733	3	3	set	set	VERB
ejpam-6733	3	4	for	for	ADP
ejpam-6733	3	5	f	f	PROPN
ejpam-6733	3	6	and	and	CCONJ
ejpam-6733	3	7	the	the	DET
ejpam-6733	3	8	(	(	PUNCT
ejpam-6733	3	9	p	p	NOUN
ejpam-6733	3	10	,	,	PUNCT
ejpam-6733	3	11	q)-parameters	q)-parameter	NOUN
ejpam-6733	3	12	,	,	PUNCT
ejpam-6733	3	13	where	where	SCONJ
ejpam-6733	3	14	the	the	DET
ejpam-6733	3	15	operators	operator	NOUN
ejpam-6733	3	16	k+,k−	k+,k−	PROPN
ejpam-6733	3	17	,	,	PUNCT
ejpam-6733	3	18	and	and	CCONJ
ejpam-6733	3	19	k0	k0	PROPN
ejpam-6733	3	20	,	,	PUNCT
ejpam-6733	3	21	satisfy	satisfy	VERB
ejpam-6733	3	22	certain	certain	ADJ
ejpam-6733	3	23	physical	physical	ADJ
ejpam-6733	3	24	properties	property	NOUN
ejpam-6733	3	25	.	.	PUNCT
ejpam-6733	4	1	2020	2020	NUM
ejpam-6733	4	2	mathematics	mathematic	NOUN
ejpam-6733	4	3	subject	subject	NOUN
ejpam-6733	4	4	classifications	classification	NOUN
ejpam-6733	4	5	:	:	PUNCT
ejpam-6733	4	6	17b10	17b10	NUM
ejpam-6733	4	7	,	,	PUNCT
ejpam-6733	4	8	17b81	17b81	NUM
ejpam-6733	4	9	,	,	PUNCT
ejpam-6733	4	10	35q40	35q40	NUM
ejpam-6733	4	11	,	,	PUNCT
ejpam-6733	4	12	81v80	81v80	NUM
ejpam-6733	4	13	key	key	ADJ
ejpam-6733	4	14	words	word	NOUN
ejpam-6733	4	15	and	and	CCONJ
ejpam-6733	4	16	phrases	phrase	NOUN
ejpam-6733	4	17	:	:	PUNCT
ejpam-6733	4	18	faithful	faithful	ADJ
ejpam-6733	4	19	matrix	matrix	NOUN
ejpam-6733	4	20	representation	representation	NOUN
ejpam-6733	4	21	of	of	ADP
ejpam-6733	4	22	lie	lie	NOUN
ejpam-6733	4	23	algebras	algebra	NOUN
ejpam-6733	4	24	,	,	PUNCT
ejpam-6733	4	25	deformed	deform	VERB
ejpam-6733	4	26	lie	lie	NOUN
ejpam-6733	4	27	algebra	algebra	NOUN
ejpam-6733	4	28	,	,	PUNCT
ejpam-6733	4	29	(	(	PUNCT
ejpam-6733	4	30	p	p	X
ejpam-6733	4	31	,	,	PUNCT
ejpam-6733	4	32	q)-algebraic	q)-algebraic	ADJ
ejpam-6733	4	33	deformation	deformation	NOUN
ejpam-6733	4	34	1	1	NUM
ejpam-6733	4	35	.	.	PUNCT
ejpam-6733	4	36	introduction	introduction	NOUN
ejpam-6733	4	37	in	in	ADP
ejpam-6733	4	38	many	many	ADJ
ejpam-6733	4	39	physical	physical	ADJ
ejpam-6733	4	40	contexts	context	NOUN
ejpam-6733	4	41	,	,	PUNCT
ejpam-6733	4	42	such	such	ADJ
ejpam-6733	4	43	as	as	ADP
ejpam-6733	4	44	quantum	quantum	ADJ
ejpam-6733	4	45	optical	optical	ADJ
ejpam-6733	4	46	systems	system	NOUN
ejpam-6733	4	47	,	,	PUNCT
ejpam-6733	4	48	non	non	ADJ
ejpam-6733	4	49	-	-	ADJ
ejpam-6733	4	50	linear	linear	ADJ
ejpam-6733	4	51	quantum	quantum	ADJ
ejpam-6733	4	52	hamiltonians	hamiltonian	NOUN
ejpam-6733	4	53	of	of	ADP
ejpam-6733	4	54	order	order	NOUN
ejpam-6733	4	55	higher	high	ADJ
ejpam-6733	4	56	than	than	ADP
ejpam-6733	4	57	quadratic	quadratic	ADJ
ejpam-6733	4	58	or	or	CCONJ
ejpam-6733	4	59	bilinear	bilinear	NOUN
ejpam-6733	4	60	forms	form	NOUN
ejpam-6733	4	61	appear	appear	VERB
ejpam-6733	4	62	in	in	ADP
ejpam-6733	4	63	modelling	modelling	NOUN
ejpam-6733	4	64	and	and	CCONJ
ejpam-6733	4	65	investigations	investigation	NOUN
ejpam-6733	4	66	of	of	ADP
ejpam-6733	4	67	many	many	ADJ
ejpam-6733	4	68	phenomena	phenomenon	NOUN
ejpam-6733	4	69	.	.	PUNCT
ejpam-6733	5	1	few	few	ADJ
ejpam-6733	5	2	examples	example	NOUN
ejpam-6733	5	3	are	be	AUX
ejpam-6733	5	4	:	:	PUNCT
ejpam-6733	5	5	many	many	ADJ
ejpam-6733	5	6	-	-	PUNCT
ejpam-6733	5	7	body	body	NOUN
ejpam-6733	5	8	systems	system	NOUN
ejpam-6733	5	9	and	and	CCONJ
ejpam-6733	5	10	multiphoton	multiphoton	NOUN
ejpam-6733	5	11	processes	process	NOUN
ejpam-6733	5	12	[	[	X
ejpam-6733	5	13	1	1	NUM
ejpam-6733	5	14	]	]	PUNCT
ejpam-6733	5	15	,	,	PUNCT
ejpam-6733	5	16	[	[	X
ejpam-6733	5	17	2	2	NUM
ejpam-6733	5	18	]	]	PUNCT
ejpam-6733	5	19	,	,	PUNCT
ejpam-6733	5	20	particles	particle	NOUN
ejpam-6733	5	21	that	that	PRON
ejpam-6733	5	22	interpolate	interpolate	VERB
ejpam-6733	5	23	between	between	ADP
ejpam-6733	5	24	bosons	boson	NOUN
ejpam-6733	5	25	and	and	CCONJ
ejpam-6733	5	26	fermions	fermion	NOUN
ejpam-6733	5	27	[	[	X
ejpam-6733	5	28	3	3	NUM
ejpam-6733	5	29	]	]	PUNCT
ejpam-6733	5	30	,	,	PUNCT
ejpam-6733	5	31	[	[	X
ejpam-6733	5	32	4	4	NUM
ejpam-6733	5	33	]	]	PUNCT
ejpam-6733	5	34	,	,	PUNCT
ejpam-6733	5	35	[	[	X
ejpam-6733	5	36	5	5	NUM
ejpam-6733	5	37	]	]	PUNCT
ejpam-6733	5	38	,	,	PUNCT
ejpam-6733	5	39	and	and	CCONJ
ejpam-6733	5	40	quantum	quantum	NOUN
ejpam-6733	5	41	deformed	deform	VERB
ejpam-6733	5	42	(	(	PUNCT
ejpam-6733	5	43	q	q	ADJ
ejpam-6733	5	44	-	-	PUNCT
ejpam-6733	5	45	deformed	deformed	ADJ
ejpam-6733	5	46	)	)	PUNCT
ejpam-6733	5	47	oscillators	oscillator	NOUN
ejpam-6733	5	48	.	.	PUNCT
ejpam-6733	6	1	such	such	ADJ
ejpam-6733	6	2	higher	high	ADJ
ejpam-6733	6	3	orders	order	NOUN
ejpam-6733	6	4	of	of	ADP
ejpam-6733	6	5	non	non	ADJ
ejpam-6733	6	6	-	-	ADJ
ejpam-6733	6	7	linear	linear	ADJ
ejpam-6733	6	8	hamiltonian	hamiltonian	ADJ
ejpam-6733	6	9	models	model	NOUN
ejpam-6733	6	10	are	be	AUX
ejpam-6733	6	11	usually	usually	ADV
ejpam-6733	6	12	associated	associate	VERB
ejpam-6733	6	13	with	with	ADP
ejpam-6733	6	14	two	two	NUM
ejpam-6733	6	15	types	type	NOUN
ejpam-6733	6	16	of	of	ADP
ejpam-6733	6	17	non	non	ADJ
ejpam-6733	6	18	-	-	ADJ
ejpam-6733	6	19	linear	linear	ADJ
ejpam-6733	6	20	q	q	ADJ
ejpam-6733	6	21	-	-	PUNCT
ejpam-6733	6	22	deformed	deform	VERB
ejpam-6733	6	23	algebra	algebra	NOUN
ejpam-6733	6	24	,	,	PUNCT
ejpam-6733	6	25	namely	namely	ADV
ejpam-6733	6	26	,	,	PUNCT
ejpam-6733	6	27	the	the	DET
ejpam-6733	6	28	q	q	ADV
ejpam-6733	6	29	-	-	PUNCT
ejpam-6733	6	30	deformed	deform	VERB
ejpam-6733	6	31	lie	lie	NOUN
ejpam-6733	6	32	brackets	bracket	NOUN
ejpam-6733	6	33	and	and	CCONJ
ejpam-6733	6	34	the	the	DET
ejpam-6733	6	35	polynomially	polynomially	ADV
ejpam-6733	6	36	deformed	deform	VERB
ejpam-6733	6	37	lie	lie	NOUN
ejpam-6733	6	38	algebra	algebra	NOUN
ejpam-6733	6	39	supd	supd	NOUN
ejpam-6733	6	40	(	(	PUNCT
ejpam-6733	6	41	2	2	NUM
ejpam-6733	6	42	)	)	PUNCT
ejpam-6733	6	43	,	,	PUNCT
ejpam-6733	7	1	[	[	X
ejpam-6733	7	2	6	6	NUM
ejpam-6733	7	3	]	]	PUNCT
ejpam-6733	7	4	.	.	PUNCT
ejpam-6733	8	1	generally	generally	ADV
ejpam-6733	8	2	speaking	speak	VERB
ejpam-6733	8	3	,	,	PUNCT
ejpam-6733	8	4	within	within	ADP
ejpam-6733	8	5	the	the	DET
ejpam-6733	8	6	quantum	quantum	ADJ
ejpam-6733	8	7	mechanical	mechanical	ADJ
ejpam-6733	8	8	context	context	NOUN
ejpam-6733	8	9	,	,	PUNCT
ejpam-6733	8	10	generalization	generalization	NOUN
ejpam-6733	8	11	of	of	ADP
ejpam-6733	8	12	the	the	DET
ejpam-6733	8	13	harmonic	harmonic	ADJ
ejpam-6733	8	14	oscillator	oscillator	NOUN
ejpam-6733	8	15	(	(	PUNCT
ejpam-6733	8	16	ho	ho	ADJ
ejpam-6733	8	17	)	)	PUNCT
ejpam-6733	8	18	algebraic	algebraic	ADJ
ejpam-6733	8	19	commutation	commutation	NOUN
ejpam-6733	8	20	relations	relation	NOUN
ejpam-6733	8	21	,	,	PUNCT
ejpam-6733	8	22	called	call	VERB
ejpam-6733	8	23	q	q	ADV
ejpam-6733	8	24	-	-	PUNCT
ejpam-6733	8	25	deformed	deform	VERB
ejpam-6733	8	26	ho	ho	NOUN
ejpam-6733	8	27	,	,	PUNCT
ejpam-6733	8	28	is	be	AUX
ejpam-6733	8	29	due	due	ADJ
ejpam-6733	8	30	to	to	ADP
ejpam-6733	8	31	basically	basically	ADV
ejpam-6733	8	32	the	the	DET
ejpam-6733	8	33	mathematical	mathematical	ADJ
ejpam-6733	8	34	non	non	ADJ
ejpam-6733	8	35	-	-	ADJ
ejpam-6733	8	36	linearity	linearity	ADJ
ejpam-6733	8	37	/	/	SYM
ejpam-6733	8	38	non	non	ADJ
ejpam-6733	8	39	-	-	ADJ
ejpam-6733	8	40	ideal	ideal	ADJ
ejpam-6733	8	41	nature	nature	NOUN
ejpam-6733	8	42	of	of	ADP
ejpam-6733	8	43	the	the	DET
ejpam-6733	8	44	concerned	concerned	ADJ
ejpam-6733	8	45	quantum	quantum	NOUN
ejpam-6733	8	46	complex	complex	ADJ
ejpam-6733	8	47	system	system	NOUN
ejpam-6733	9	1	[	[	X
ejpam-6733	9	2	[	[	X
ejpam-6733	9	3	7	7	NUM
ejpam-6733	9	4	]	]	PUNCT
ejpam-6733	9	5	,	,	PUNCT
ejpam-6733	9	6	and	and	CCONJ
ejpam-6733	9	7	refs	ref	NOUN
ejpam-6733	9	8	.	.	PUNCT
ejpam-6733	10	1	therein	therein	ADV
ejpam-6733	10	2	]	]	PUNCT
ejpam-6733	10	3	.	.	PUNCT
ejpam-6733	11	1	two	two	NUM
ejpam-6733	11	2	particular	particular	ADJ
ejpam-6733	11	3	physical	physical	ADJ
ejpam-6733	11	4	applications	application	NOUN
ejpam-6733	11	5	of	of	ADP
ejpam-6733	11	6	the	the	DET
ejpam-6733	11	7	deformation	deformation	NOUN
ejpam-6733	11	8	algebra	algebra	NOUN
ejpam-6733	11	9	,	,	PUNCT
ejpam-6733	11	10	namely	namely	ADV
ejpam-6733	11	11	:	:	PUNCT
ejpam-6733	11	12	(	(	PUNCT
ejpam-6733	11	13	i	i	NOUN
ejpam-6733	11	14	)	)	PUNCT
ejpam-6733	11	15	the	the	DET
ejpam-6733	11	16	one	one	NUM
ejpam-6733	11	17	q	q	ADJ
ejpam-6733	11	18	-	-	PUNCT
ejpam-6733	11	19	deformation	deformation	NOUN
ejpam-6733	11	20	parameter	parameter	NOUN
ejpam-6733	11	21	is	be	AUX
ejpam-6733	11	22	an	an	DET
ejpam-6733	11	23	indicator	indicator	NOUN
ejpam-6733	11	24	of	of	ADP
ejpam-6733	11	25	information	information	NOUN
ejpam-6733	11	26	of	of	ADP
ejpam-6733	11	27	∗corresponding	∗corresponde	VERB
ejpam-6733	11	28	author	author	NOUN
ejpam-6733	11	29	.	.	PUNCT
ejpam-6733	12	1	doi	doi	NOUN
ejpam-6733	12	2	:	:	PUNCT
ejpam-6733	12	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6733	https://doi.org/10.29020/nybg.ejpam.v18i4.6733	NOUN
ejpam-6733	12	4	email	email	NOUN
ejpam-6733	12	5	addresses	address	NOUN
ejpam-6733	12	6	:	:	PUNCT
ejpam-6733	12	7	latif.hanna@ku.edu.kw	latif.hanna@ku.edu.kw	ADJ
ejpam-6733	12	8	(	(	PUNCT
ejpam-6733	12	9	l.	l.	PROPN
ejpam-6733	12	10	a	a	PROPN
ejpam-6733	12	11	-	-	PUNCT
ejpam-6733	12	12	m.	m.	NOUN
ejpam-6733	12	13	hanna	hanna	NOUN
ejpam-6733	12	14	)	)	PUNCT
ejpam-6733	12	15	,	,	PUNCT
ejpam-6733	12	16	shoukryhassan@hotmail.com	shoukryhassan@hotmail.com	X
ejpam-6733	12	17	(	(	PUNCT
ejpam-6733	12	18	s.	s.	PROPN
ejpam-6733	12	19	s.	s.	PROPN
ejpam-6733	12	20	hassan	hassan	PROPN
ejpam-6733	12	21	)	)	PUNCT
ejpam-6733	12	22	,	,	PUNCT
ejpam-6733	12	23	maali.almutairi@ku.edu.kw	maali.almutairi@ku.edu.kw	NOUN
ejpam-6733	12	24	(	(	PUNCT
ejpam-6733	12	25	m.	m.	NOUN
ejpam-6733	12	26	almutairi	almutairi	PROPN
ejpam-6733	12	27	)	)	PUNCT
ejpam-6733	12	28	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6733	13	1	1	1	NUM
ejpam-6733	13	2	copyright	copyright	NOUN
ejpam-6733	13	3	:	:	PUNCT
ejpam-6733	13	4	©	©	PROPN
ejpam-6733	13	5	2025	2025	NUM
ejpam-6733	13	6	the	the	DET
ejpam-6733	13	7	author(s	author(s	NOUN
ejpam-6733	13	8	)	)	PUNCT
ejpam-6733	13	9	.	.	PUNCT
ejpam-6733	14	1	(	(	PUNCT
ejpam-6733	14	2	cc	cc	NOUN
ejpam-6733	14	3	by	by	ADP
ejpam-6733	14	4	-	-	PUNCT
ejpam-6733	14	5	nc	nc	PROPN
ejpam-6733	14	6	4.0	4.0	NUM
ejpam-6733	14	7	)	)	PUNCT
ejpam-6733	14	8	l.	l.	PROPN
ejpam-6733	14	9	a	a	PROPN
ejpam-6733	14	10	-	-	PUNCT
ejpam-6733	14	11	m.	m.	NOUN
ejpam-6733	14	12	hanna	hanna	NOUN
ejpam-6733	14	13	,	,	PUNCT
ejpam-6733	14	14	s.	s.	PROPN
ejpam-6733	14	15	s.	s.	PROPN
ejpam-6733	14	16	hassan	hassan	PROPN
ejpam-6733	14	17	,	,	PUNCT
ejpam-6733	14	18	m.	m.	NOUN
ejpam-6733	14	19	almutairi	almutairi	PROPN
ejpam-6733	14	20	/	/	SYM
ejpam-6733	14	21	eur	eur	PROPN
ejpam-6733	14	22	.	.	PUNCT
ejpam-6733	15	1	j.	j.	PROPN
ejpam-6733	15	2	pure	pure	PROPN
ejpam-6733	15	3	appl	appl	PROPN
ejpam-6733	15	4	.	.	PROPN
ejpam-6733	15	5	math	math	PROPN
ejpam-6733	15	6	,	,	PUNCT
ejpam-6733	15	7	18	18	NUM
ejpam-6733	15	8	(	(	PUNCT
ejpam-6733	15	9	4	4	NUM
ejpam-6733	15	10	)	)	PUNCT
ejpam-6733	15	11	(	(	PUNCT
ejpam-6733	15	12	2025	2025	NUM
ejpam-6733	15	13	)	)	PUNCT
ejpam-6733	15	14	,	,	PUNCT
ejpam-6733	15	15	6733	6733	NUM
ejpam-6733	15	16	2	2	NUM
ejpam-6733	15	17	of	of	ADP
ejpam-6733	15	18	12	12	NUM
ejpam-6733	15	19	quantum	quantum	NOUN
ejpam-6733	15	20	impurities	impurity	NOUN
ejpam-6733	15	21	in	in	ADP
ejpam-6733	15	22	many	many	ADJ
ejpam-6733	15	23	-	-	PUNCT
ejpam-6733	15	24	particle	particle	NOUN
ejpam-6733	15	25	interactions	interaction	NOUN
ejpam-6733	15	26	in	in	ADP
ejpam-6733	15	27	a	a	DET
ejpam-6733	15	28	condensed	condense	VERB
ejpam-6733	15	29	matter	matter	NOUN
ejpam-6733	15	30	system	system	NOUN
ejpam-6733	15	31	[	[	X
ejpam-6733	15	32	8	8	NUM
ejpam-6733	15	33	]	]	PUNCT
ejpam-6733	15	34	,	,	PUNCT
ejpam-6733	15	35	(	(	PUNCT
ejpam-6733	15	36	ii	ii	NOUN
ejpam-6733	15	37	)	)	PUNCT
ejpam-6733	15	38	the	the	DET
ejpam-6733	15	39	two	two	NUM
ejpam-6733	15	40	(	(	PUNCT
ejpam-6733	15	41	p	p	NOUN
ejpam-6733	15	42	,	,	PUNCT
ejpam-6733	15	43	q)-deformation	q)-deformation	ADJ
ejpam-6733	15	44	parameters	parameter	NOUN
ejpam-6733	15	45	of	of	ADP
ejpam-6733	15	46	the	the	DET
ejpam-6733	15	47	bosonic	bosonic	PROPN
ejpam-6733	15	48	fibonacci	fibonacci	PROPN
ejpam-6733	15	49	oscillator	oscillator	PROPN
ejpam-6733	15	50	algebra	algebra	PROPN
ejpam-6733	15	51	[	[	X
ejpam-6733	15	52	9	9	NUM
ejpam-6733	15	53	]	]	X
ejpam-6733	15	54	mimic	mimic	VERB
ejpam-6733	15	55	the	the	DET
ejpam-6733	15	56	defects	defect	NOUN
ejpam-6733	15	57	and	and	CCONJ
ejpam-6733	15	58	impurities	impurity	NOUN
ejpam-6733	15	59	in	in	ADP
ejpam-6733	15	60	crystalline	crystalline	ADJ
ejpam-6733	15	61	lattice	lattice	NOUN
ejpam-6733	15	62	structure	structure	NOUN
ejpam-6733	15	63	.	.	PUNCT
ejpam-6733	16	1	investigations	investigation	NOUN
ejpam-6733	16	2	of	of	ADP
ejpam-6733	16	3	appropriate	appropriate	ADJ
ejpam-6733	16	4	time	time	NOUN
ejpam-6733	16	5	evolution	evolution	NOUN
ejpam-6733	16	6	operators	operator	NOUN
ejpam-6733	16	7	for	for	ADP
ejpam-6733	16	8	such	such	ADJ
ejpam-6733	16	9	nonlinear	nonlinear	ADJ
ejpam-6733	16	10	hamiltonian	hamiltonian	ADJ
ejpam-6733	16	11	systems	system	NOUN
ejpam-6733	16	12	are	be	AUX
ejpam-6733	16	13	generally	generally	ADV
ejpam-6733	16	14	complicated	complicated	ADJ
ejpam-6733	16	15	to	to	PART
ejpam-6733	16	16	handle	handle	VERB
ejpam-6733	16	17	.	.	PUNCT
ejpam-6733	17	1	the	the	DET
ejpam-6733	17	2	alternative	alternative	ADJ
ejpam-6733	17	3	lie	lie	VERB
ejpam-6733	17	4	algebraic	algebraic	ADJ
ejpam-6733	17	5	decomposition	decomposition	NOUN
ejpam-6733	17	6	approach	approach	NOUN
ejpam-6733	17	7	and	and	CCONJ
ejpam-6733	17	8	its	its	PRON
ejpam-6733	17	9	faithful	faithful	ADJ
ejpam-6733	17	10	matrix	matrix	NOUN
ejpam-6733	17	11	representation	representation	NOUN
ejpam-6733	17	12	(	(	PUNCT
ejpam-6733	17	13	once	once	ADV
ejpam-6733	17	14	found	find	VERB
ejpam-6733	17	15	!	!	PUNCT
ejpam-6733	17	16	)	)	PUNCT
ejpam-6733	18	1	for	for	ADP
ejpam-6733	18	2	the	the	DET
ejpam-6733	18	3	generators	generator	NOUN
ejpam-6733	18	4	of	of	ADP
ejpam-6733	18	5	such	such	ADJ
ejpam-6733	18	6	deformed	deformed	ADJ
ejpam-6733	18	7	lie	lie	NOUN
ejpam-6733	18	8	algebra	algebra	NOUN
ejpam-6733	18	9	is	be	AUX
ejpam-6733	18	10	relatively	relatively	ADV
ejpam-6733	18	11	less	less	ADV
ejpam-6733	18	12	tedious	tedious	ADJ
ejpam-6733	18	13	than	than	ADP
ejpam-6733	18	14	dealing	deal	VERB
ejpam-6733	18	15	with	with	ADP
ejpam-6733	18	16	the	the	DET
ejpam-6733	18	17	direct	direct	ADJ
ejpam-6733	18	18	method	method	NOUN
ejpam-6733	18	19	of	of	ADP
ejpam-6733	18	20	solving	solve	VERB
ejpam-6733	18	21	schrödinger	schrödinger	NOUN
ejpam-6733	18	22	’s	’s	PART
ejpam-6733	18	23	wave	wave	NOUN
ejpam-6733	18	24	equations	equation	NOUN
ejpam-6733	18	25	,	,	PUNCT
ejpam-6733	18	26	e.g.	e.g.	ADV
ejpam-6733	18	27	,	,	PUNCT
ejpam-6733	18	28	[	[	X
ejpam-6733	18	29	10	10	NUM
ejpam-6733	18	30	]	]	PUNCT
ejpam-6733	18	31	.	.	PUNCT
ejpam-6733	19	1	on	on	ADP
ejpam-6733	19	2	the	the	DET
ejpam-6733	19	3	other	other	ADJ
ejpam-6733	19	4	hand	hand	NOUN
ejpam-6733	19	5	,	,	PUNCT
ejpam-6733	19	6	the	the	DET
ejpam-6733	19	7	q	q	ADV
ejpam-6733	19	8	-	-	PUNCT
ejpam-6733	19	9	deformed	deform	VERB
ejpam-6733	19	10	virasoro	virasoro	NOUN
ejpam-6733	19	11	algebras	algebra	NOUN
ejpam-6733	19	12	[	[	X
ejpam-6733	19	13	11	11	NUM
ejpam-6733	19	14	]	]	PUNCT
ejpam-6733	19	15	are	be	AUX
ejpam-6733	19	16	ideal	ideal	ADJ
ejpam-6733	19	17	physical	physical	ADJ
ejpam-6733	19	18	applications	application	NOUN
ejpam-6733	19	19	of	of	ADP
ejpam-6733	19	20	quantum	quantum	ADJ
ejpam-6733	19	21	groups	group	NOUN
ejpam-6733	19	22	[	[	X
ejpam-6733	19	23	12	12	NUM
ejpam-6733	19	24	]	]	PUNCT
ejpam-6733	19	25	,	,	PUNCT
ejpam-6733	19	26	which	which	PRON
ejpam-6733	19	27	are	be	AUX
ejpam-6733	19	28	non	non	ADJ
ejpam-6733	19	29	-	-	ADJ
ejpam-6733	19	30	commutative	commutative	ADJ
ejpam-6733	19	31	and	and	CCONJ
ejpam-6733	19	32	co	co	ADJ
ejpam-6733	19	33	-	-	ADJ
ejpam-6733	19	34	commutative	commutative	ADJ
ejpam-6733	19	35	hopf	hopf	NOUN
ejpam-6733	19	36	algebras	algebras	PROPN
ejpam-6733	19	37	.	.	PUNCT
ejpam-6733	20	1	a	a	DET
ejpam-6733	20	2	two	two	NUM
ejpam-6733	20	3	-	-	PUNCT
ejpam-6733	20	4	parameter	parameter	NOUN
ejpam-6733	20	5	quantum	quantum	ADJ
ejpam-6733	20	6	deformation	deformation	NOUN
ejpam-6733	20	7	of	of	ADP
ejpam-6733	20	8	lie	lie	NOUN
ejpam-6733	20	9	super	super	ADJ
ejpam-6733	20	10	algebras	algebra	NOUN
ejpam-6733	20	11	in	in	ADP
ejpam-6733	20	12	the	the	DET
ejpam-6733	20	13	non	non	ADJ
ejpam-6733	20	14	-	-	ADJ
ejpam-6733	20	15	standard	standard	ADJ
ejpam-6733	20	16	simple	simple	ADJ
ejpam-6733	20	17	root	root	NOUN
ejpam-6733	20	18	system	system	NOUN
ejpam-6733	20	19	with	with	ADP
ejpam-6733	20	20	two	two	NUM
ejpam-6733	20	21	odd	odd	ADJ
ejpam-6733	20	22	simple	simple	ADJ
ejpam-6733	20	23	roots	root	NOUN
ejpam-6733	20	24	is	be	AUX
ejpam-6733	20	25	examined	examine	VERB
ejpam-6733	20	26	in	in	ADP
ejpam-6733	20	27	[	[	X
ejpam-6733	20	28	13	13	NUM
ejpam-6733	20	29	]	]	PUNCT
ejpam-6733	20	30	.	.	PUNCT
ejpam-6733	21	1	in	in	ADP
ejpam-6733	21	2	the	the	DET
ejpam-6733	21	3	present	present	ADJ
ejpam-6733	21	4	work	work	NOUN
ejpam-6733	21	5	,	,	PUNCT
ejpam-6733	21	6	we	we	PRON
ejpam-6733	21	7	search	search	VERB
ejpam-6733	21	8	for	for	ADP
ejpam-6733	21	9	faithful	faithful	ADJ
ejpam-6733	21	10	matrix	matrix	NOUN
ejpam-6733	21	11	representations	representation	NOUN
ejpam-6733	21	12	of	of	ADP
ejpam-6733	21	13	the	the	DET
ejpam-6733	21	14	generators	generator	NOUN
ejpam-6733	21	15	of	of	ADP
ejpam-6733	21	16	two	two	NUM
ejpam-6733	21	17	-	-	PUNCT
ejpam-6733	21	18	parameter	parameter	NOUN
ejpam-6733	21	19	(	(	PUNCT
ejpam-6733	21	20	p	p	X
ejpam-6733	21	21	,	,	PUNCT
ejpam-6733	21	22	q)-deformed	q)-deformed	ADJ
ejpam-6733	21	23	algebraic	algebraic	ADJ
ejpam-6733	21	24	structure	structure	NOUN
ejpam-6733	21	25	,	,	PUNCT
ejpam-6733	21	26	namely	namely	ADV
ejpam-6733	21	27	,	,	PUNCT
ejpam-6733	21	28	the	the	DET
ejpam-6733	21	29	qand	qand	NOUN
ejpam-6733	21	30	the	the	DET
ejpam-6733	21	31	polynomiallydeformed	polynomiallydeforme	VERB
ejpam-6733	21	32	lie	lie	NOUN
ejpam-6733	21	33	algebra	algebra	NOUN
ejpam-6733	21	34	,	,	PUNCT
ejpam-6733	21	35	associated	associate	VERB
ejpam-6733	21	36	with	with	ADP
ejpam-6733	21	37	the	the	DET
ejpam-6733	21	38	generalized	generalized	ADJ
ejpam-6733	21	39	algebra	algebra	NOUN
ejpam-6733	21	40	,	,	PUNCT
ejpam-6733	21	41	lp	lp	PROPN
ejpam-6733	21	42	,	,	PUNCT
ejpam-6733	21	43	q	q	NOUN
ejpam-6733	21	44	,	,	PUNCT
ejpam-6733	21	45	mentioned	mention	VERB
ejpam-6733	21	46	next	next	ADV
ejpam-6733	21	47	in	in	ADP
ejpam-6733	21	48	section	section	NOUN
ejpam-6733	21	49	2	2	NUM
ejpam-6733	21	50	.	.	NOUN
ejpam-6733	21	51	2	2	NUM
ejpam-6733	21	52	.	.	NOUN
ejpam-6733	21	53	preliminaries	preliminary	NOUN
ejpam-6733	21	54	in	in	ADP
ejpam-6733	21	55	[	[	X
ejpam-6733	21	56	12	12	NUM
ejpam-6733	21	57	]	]	PUNCT
ejpam-6733	21	58	,	,	PUNCT
ejpam-6733	21	59	the	the	DET
ejpam-6733	21	60	(	(	PUNCT
ejpam-6733	21	61	p	p	X
ejpam-6733	21	62	,	,	PUNCT
ejpam-6733	21	63	q)-deformed	q)-deforme	VERB
ejpam-6733	21	64	lie	lie	VERB
ejpam-6733	21	65	bracket	bracket	NOUN
ejpam-6733	21	66	is	be	AUX
ejpam-6733	21	67	given	give	VERB
ejpam-6733	21	68	as	as	SCONJ
ejpam-6733	21	69	follows	follow	VERB
ejpam-6733	21	70	.	.	PUNCT
ejpam-6733	22	1	definition	definition	NOUN
ejpam-6733	22	2	1	1	NUM
ejpam-6733	22	3	.	.	PUNCT
ejpam-6733	23	1	let	let	VERB
ejpam-6733	23	2	p	p	NOUN
ejpam-6733	23	3	and	and	CCONJ
ejpam-6733	23	4	q	q	NOUN
ejpam-6733	23	5	be	be	AUX
ejpam-6733	23	6	real	real	ADJ
ejpam-6733	23	7	numbers	number	NOUN
ejpam-6733	23	8	.	.	PUNCT
ejpam-6733	24	1	if	if	SCONJ
ejpam-6733	24	2	x	x	PRON
ejpam-6733	24	3	and	and	CCONJ
ejpam-6733	24	4	y	y	PROPN
ejpam-6733	24	5	are	be	AUX
ejpam-6733	24	6	square	square	ADJ
ejpam-6733	24	7	matrices	matrix	NOUN
ejpam-6733	24	8	of	of	ADP
ejpam-6733	24	9	order	order	NOUN
ejpam-6733	24	10	n	n	CCONJ
ejpam-6733	24	11	,	,	PUNCT
ejpam-6733	24	12	then	then	ADV
ejpam-6733	24	13	the	the	DET
ejpam-6733	24	14	(	(	PUNCT
ejpam-6733	24	15	p	p	X
ejpam-6733	24	16	,	,	PUNCT
ejpam-6733	24	17	q)-deformed	q)-deformed	ADJ
ejpam-6733	24	18	lie	lie	VERB
ejpam-6733	24	19	bracket	bracket	NOUN
ejpam-6733	24	20	of	of	ADP
ejpam-6733	24	21	x	x	X
ejpam-6733	24	22	and	and	CCONJ
ejpam-6733	24	23	y	y	PROPN
ejpam-6733	24	24	,	,	PUNCT
ejpam-6733	24	25	namely	namely	ADV
ejpam-6733	24	26	[	[	X
ejpam-6733	24	27	x	x	X
ejpam-6733	24	28	,	,	PUNCT
ejpam-6733	24	29	y	y	PROPN
ejpam-6733	24	30	]	]	X
ejpam-6733	24	31	p	p	X
ejpam-6733	24	32	,	,	PUNCT
ejpam-6733	24	33	q	q	NOUN
ejpam-6733	24	34	,	,	PUNCT
ejpam-6733	24	35	is	be	AUX
ejpam-6733	24	36	defined	define	VERB
ejpam-6733	24	37	as	as	ADP
ejpam-6733	24	38	,	,	PUNCT
ejpam-6733	24	39	[	[	X
ejpam-6733	24	40	x	x	X
ejpam-6733	24	41	,	,	PUNCT
ejpam-6733	24	42	y	y	PROPN
ejpam-6733	24	43	]	]	X
ejpam-6733	24	44	p	p	X
ejpam-6733	24	45	,	,	PUNCT
ejpam-6733	24	46	q	q	NOUN
ejpam-6733	24	47	=	=	PUNCT
ejpam-6733	24	48	pxy	pxy	PROPN
ejpam-6733	24	49	−	−	PROPN
ejpam-6733	24	50	qy	qy	NOUN
ejpam-6733	24	51	x.	x.	NOUN
ejpam-6733	24	52	(	(	PUNCT
ejpam-6733	24	53	1	1	NUM
ejpam-6733	24	54	)	)	PUNCT
ejpam-6733	24	55	for	for	ADP
ejpam-6733	24	56	the	the	DET
ejpam-6733	24	57	two	two	NUM
ejpam-6733	24	58	particular	particular	ADJ
ejpam-6733	24	59	cases	case	NOUN
ejpam-6733	24	60	,	,	PUNCT
ejpam-6733	24	61	namely	namely	ADV
ejpam-6733	24	62	,	,	PUNCT
ejpam-6733	24	63	p	p	NOUN
ejpam-6733	24	64	=	=	NOUN
ejpam-6733	24	65	1	1	NUM
ejpam-6733	24	66	,	,	PUNCT
ejpam-6733	24	67	q	q	NOUN
ejpam-6733	24	68	=	=	SYM
ejpam-6733	24	69	0	0	NUM
ejpam-6733	24	70	and	and	CCONJ
ejpam-6733	24	71	p	p	X
ejpam-6733	24	72	=	=	NOUN
ejpam-6733	24	73	0	0	NUM
ejpam-6733	24	74	,	,	PUNCT
ejpam-6733	24	75	q	q	NOUN
ejpam-6733	24	76	=	=	SYM
ejpam-6733	24	77	−1	−1	NOUN
ejpam-6733	24	78	,	,	PUNCT
ejpam-6733	24	79	we	we	PRON
ejpam-6733	24	80	have	have	VERB
ejpam-6733	24	81	the	the	DET
ejpam-6733	24	82	usual	usual	ADJ
ejpam-6733	24	83	matrix	matrix	NOUN
ejpam-6733	24	84	multiplication	multiplication	NOUN
ejpam-6733	24	85	of	of	ADP
ejpam-6733	24	86	x	x	PROPN
ejpam-6733	24	87	and	and	CCONJ
ejpam-6733	24	88	y	y	PROPN
ejpam-6733	24	89	.	.	PUNCT
ejpam-6733	25	1	so	so	ADV
ejpam-6733	25	2	we	we	PRON
ejpam-6733	25	3	always	always	ADV
ejpam-6733	25	4	consider	consider	VERB
ejpam-6733	25	5	that	that	PRON
ejpam-6733	25	6	here	here	ADV
ejpam-6733	25	7	,	,	PUNCT
ejpam-6733	25	8	p	p	NOUN
ejpam-6733	25	9	and	and	CCONJ
ejpam-6733	25	10	q	q	NOUN
ejpam-6733	25	11	are	be	AUX
ejpam-6733	25	12	supposed	suppose	VERB
ejpam-6733	25	13	to	to	PART
ejpam-6733	25	14	be	be	AUX
ejpam-6733	25	15	nonzero	nonzero	ADJ
ejpam-6733	25	16	real	real	ADJ
ejpam-6733	25	17	numbers	number	NOUN
ejpam-6733	25	18	,	,	PUNCT
ejpam-6733	25	19	i.e.	i.e.	X
ejpam-6733	25	20	,	,	PUNCT
ejpam-6733	25	21	pq	pq	INTJ
ejpam-6733	25	22	6=	6=	PROPN
ejpam-6733	25	23	0	0	NUM
ejpam-6733	25	24	.	.	PUNCT
ejpam-6733	26	1	for	for	ADP
ejpam-6733	26	2	instance	instance	NOUN
ejpam-6733	26	3	,	,	PUNCT
ejpam-6733	26	4	in	in	ADP
ejpam-6733	26	5	[	[	X
ejpam-6733	26	6	3	3	NUM
ejpam-6733	26	7	]	]	PUNCT
ejpam-6733	26	8	,	,	PUNCT
ejpam-6733	26	9	the	the	DET
ejpam-6733	26	10	model	model	NOUN
ejpam-6733	26	11	of	of	ADP
ejpam-6733	26	12	fermion	fermion	NOUN
ejpam-6733	26	13	oscillators	oscillator	NOUN
ejpam-6733	26	14	has	have	VERB
ejpam-6733	26	15	p	p	NOUN
ejpam-6733	26	16	=	=	SYM
ejpam-6733	26	17	1	1	NUM
ejpam-6733	26	18	and	and	CCONJ
ejpam-6733	26	19	0	0	NUM
ejpam-6733	26	20	≤	≤	NUM
ejpam-6733	26	21	q	q	PROPN
ejpam-6733	26	22	≤	≤	NUM
ejpam-6733	26	23	1	1	NUM
ejpam-6733	26	24	.	.	PUNCT
ejpam-6733	27	1	it	it	PRON
ejpam-6733	27	2	should	should	AUX
ejpam-6733	27	3	be	be	AUX
ejpam-6733	27	4	noted	note	VERB
ejpam-6733	27	5	that	that	SCONJ
ejpam-6733	27	6	the	the	DET
ejpam-6733	27	7	case	case	NOUN
ejpam-6733	27	8	when	when	SCONJ
ejpam-6733	27	9	p	p	PROPN
ejpam-6733	27	10	=	=	NOUN
ejpam-6733	27	11	1	1	NUM
ejpam-6733	27	12	,	,	PUNCT
ejpam-6733	27	13	q	q	NOUN
ejpam-6733	27	14	=	=	SYM
ejpam-6733	27	15	1	1	NUM
ejpam-6733	27	16	is	be	AUX
ejpam-6733	27	17	the	the	DET
ejpam-6733	27	18	ordinary	ordinary	ADJ
ejpam-6733	27	19	lie	lie	NOUN
ejpam-6733	27	20	bracket	bracket	NOUN
ejpam-6733	27	21	.	.	PUNCT
ejpam-6733	28	1	thus	thus	ADV
ejpam-6733	28	2	,	,	PUNCT
ejpam-6733	28	3	we	we	PRON
ejpam-6733	28	4	may	may	AUX
ejpam-6733	28	5	write	write	VERB
ejpam-6733	28	6	[	[	X
ejpam-6733	28	7	x	x	X
ejpam-6733	28	8	,	,	PUNCT
ejpam-6733	28	9	y	y	PROPN
ejpam-6733	28	10	]	]	PUNCT
ejpam-6733	28	11	1,1	1,1	NUM
ejpam-6733	28	12	as	as	ADP
ejpam-6733	28	13	[	[	X
ejpam-6733	28	14	x	x	X
ejpam-6733	28	15	,	,	PUNCT
ejpam-6733	28	16	y	y	PROPN
ejpam-6733	28	17	]	]	PUNCT
ejpam-6733	28	18	.	.	PUNCT
ejpam-6733	29	1	faithful	faithful	ADJ
ejpam-6733	29	2	matrix	matrix	NOUN
ejpam-6733	29	3	representations	representation	NOUN
ejpam-6733	29	4	of	of	ADP
ejpam-6733	29	5	the	the	DET
ejpam-6733	29	6	least	least	ADJ
ejpam-6733	29	7	degree	degree	NOUN
ejpam-6733	29	8	of	of	ADP
ejpam-6733	29	9	the	the	DET
ejpam-6733	29	10	lie	lie	NOUN
ejpam-6733	29	11	algebra	algebra	NOUN
ejpam-6733	29	12	l	l	NOUN
ejpam-6733	29	13	were	be	AUX
ejpam-6733	29	14	considered	consider	VERB
ejpam-6733	29	15	in	in	ADP
ejpam-6733	29	16	[	[	X
ejpam-6733	29	17	10]-[14	10]-[14	PROPN
ejpam-6733	29	18	]	]	X
ejpam-6733	29	19	,	,	PUNCT
ejpam-6733	29	20	[	[	X
ejpam-6733	29	21	1]-[15	1]-[15	X
ejpam-6733	29	22	]	]	PUNCT
ejpam-6733	29	23	where	where	SCONJ
ejpam-6733	29	24	,	,	PUNCT
ejpam-6733	29	25	l	l	NOUN
ejpam-6733	29	26	:	:	PUNCT
ejpam-6733	30	1	[	[	X
ejpam-6733	30	2	k0,k±	k0,k±	X
ejpam-6733	30	3	]	]	X
ejpam-6733	30	4	=	=	SYM
ejpam-6733	30	5	±rk±	±rk±	NOUN
ejpam-6733	30	6	and	and	CCONJ
ejpam-6733	30	7	[	[	X
ejpam-6733	30	8	k+,k−	k+,k−	X
ejpam-6733	30	9	]	]	X
ejpam-6733	30	10	=	=	SYM
ejpam-6733	30	11	f	f	X
ejpam-6733	30	12	(	(	PUNCT
ejpam-6733	30	13	k0	k0	PROPN
ejpam-6733	30	14	)	)	PUNCT
ejpam-6733	30	15	,	,	PUNCT
ejpam-6733	30	16	(	(	PUNCT
ejpam-6733	30	17	2	2	X
ejpam-6733	30	18	)	)	PUNCT
ejpam-6733	30	19	with	with	ADP
ejpam-6733	30	20	f	f	PROPN
ejpam-6733	30	21	is	be	AUX
ejpam-6733	30	22	a	a	DET
ejpam-6733	30	23	real	real	ADJ
ejpam-6733	30	24	polynomial	polynomial	ADJ
ejpam-6733	30	25	function	function	NOUN
ejpam-6733	30	26	and	and	CCONJ
ejpam-6733	30	27	r	r	NOUN
ejpam-6733	30	28	∈	∈	PROPN
ejpam-6733	30	29	r∗	r∗	NOUN
ejpam-6733	30	30	(	(	PUNCT
ejpam-6733	30	31	r∗	r∗	PROPN
ejpam-6733	30	32	,	,	PUNCT
ejpam-6733	30	33	is	be	AUX
ejpam-6733	30	34	the	the	DET
ejpam-6733	30	35	set	set	NOUN
ejpam-6733	30	36	of	of	ADP
ejpam-6733	30	37	nonzero	nonzero	ADJ
ejpam-6733	30	38	real	real	ADJ
ejpam-6733	30	39	numbers	number	NOUN
ejpam-6733	30	40	)	)	PUNCT
ejpam-6733	30	41	,	,	PUNCT
ejpam-6733	30	42	subject	subject	ADJ
ejpam-6733	30	43	to	to	ADP
ejpam-6733	30	44	the	the	DET
ejpam-6733	30	45	physical	physical	ADJ
ejpam-6733	30	46	properties	property	NOUN
ejpam-6733	30	47	,	,	PUNCT
ejpam-6733	30	48	namely	namely	ADV
ejpam-6733	30	49	,	,	PUNCT
ejpam-6733	30	50	k0	k0	PROPN
ejpam-6733	30	51	is	be	AUX
ejpam-6733	30	52	a	a	DET
ejpam-6733	30	53	real	real	ADJ
ejpam-6733	30	54	diagonal	diagonal	ADJ
ejpam-6733	30	55	operator	operator	NOUN
ejpam-6733	30	56	and	and	CCONJ
ejpam-6733	30	57	k−	k−	PROPN
ejpam-6733	30	58	=	=	PUNCT
ejpam-6733	31	1	k†	k†	PROPN
ejpam-6733	31	2	+	+	ADV
ejpam-6733	31	3	,	,	PUNCT
ejpam-6733	31	4	(	(	PUNCT
ejpam-6733	31	5	†	†	PROPN
ejpam-6733	31	6	is	be	AUX
ejpam-6733	31	7	for	for	ADP
ejpam-6733	31	8	hermitian	hermitian	ADJ
ejpam-6733	31	9	conjugation	conjugation	NOUN
ejpam-6733	31	10	)	)	PUNCT
ejpam-6733	31	11	.	.	PUNCT
ejpam-6733	32	1	the	the	DET
ejpam-6733	32	2	nonzero	nonzero	PROPN
ejpam-6733	32	3	parameter	parameter	PROPN
ejpam-6733	32	4	r	r	NOUN
ejpam-6733	32	5	is	be	AUX
ejpam-6733	32	6	a	a	DET
ejpam-6733	32	7	proportionality	proportionality	NOUN
ejpam-6733	32	8	factor	factor	NOUN
ejpam-6733	32	9	relating	relate	VERB
ejpam-6733	32	10	the	the	DET
ejpam-6733	32	11	ho	ho	PROPN
ejpam-6733	32	12	operators	operator	NOUN
ejpam-6733	32	13	k±	k±	PROPN
ejpam-6733	32	14	to	to	ADP
ejpam-6733	32	15	the	the	DET
ejpam-6733	32	16	corresponding	corresponding	ADJ
ejpam-6733	32	17	atomic	atomic	ADJ
ejpam-6733	32	18	spin	spin	NOUN
ejpam-6733	32	19	-	-	PUNCT
ejpam-6733	32	20	up	up	NOUN
ejpam-6733	32	21	and	and	CCONJ
ejpam-6733	32	22	-down	-down	ADJ
ejpam-6733	32	23	operators	operator	NOUN
ejpam-6733	32	24	s±	s±	X
ejpam-6733	32	25	(	(	PUNCT
ejpam-6733	32	26	e.g.	e.g.	ADV
ejpam-6733	32	27	,	,	PUNCT
ejpam-6733	32	28	[	[	X
ejpam-6733	32	29	16	16	NUM
ejpam-6733	32	30	]	]	PUNCT
ejpam-6733	32	31	)	)	PUNCT
ejpam-6733	32	32	in	in	ADP
ejpam-6733	32	33	the	the	DET
ejpam-6733	32	34	present	present	ADJ
ejpam-6733	32	35	work	work	NOUN
ejpam-6733	32	36	,	,	PUNCT
ejpam-6733	32	37	we	we	PRON
ejpam-6733	32	38	consider	consider	VERB
ejpam-6733	32	39	the	the	DET
ejpam-6733	32	40	hamiltonian	hamiltonian	ADJ
ejpam-6733	32	41	h	h	NOUN
ejpam-6733	32	42	of	of	ADP
ejpam-6733	32	43	two	two	NUM
ejpam-6733	32	44	coupled	couple	VERB
ejpam-6733	32	45	harmonic	harmonic	ADJ
ejpam-6733	32	46	oscillators	oscillator	NOUN
ejpam-6733	32	47	in	in	ADP
ejpam-6733	32	48	an	an	DET
ejpam-6733	32	49	optical	optical	ADJ
ejpam-6733	32	50	cavity	cavity	NOUN
ejpam-6733	32	51	,	,	PUNCT
ejpam-6733	32	52	representing	represent	VERB
ejpam-6733	32	53	’	'	PUNCT
ejpam-6733	32	54	optical	optical	ADJ
ejpam-6733	32	55	2	2	NUM
ejpam-6733	32	56	-	-	PUNCT
ejpam-6733	32	57	level	level	NOUN
ejpam-6733	32	58	atom	atom	NOUN
ejpam-6733	32	59	’	'	PUNCT
ejpam-6733	32	60	in	in	ADP
ejpam-6733	32	61	the	the	DET
ejpam-6733	32	62	form	form	NOUN
ejpam-6733	32	63	[	[	X
ejpam-6733	32	64	16	16	NUM
ejpam-6733	32	65	]	]	PUNCT
ejpam-6733	32	66	(	(	PUNCT
ejpam-6733	32	67	we	we	PRON
ejpam-6733	32	68	take	take	VERB
ejpam-6733	32	69	the	the	DET
ejpam-6733	32	70	reduced	reduce	VERB
ejpam-6733	32	71	planck	planck	NOUN
ejpam-6733	32	72	constant	constant	ADJ
ejpam-6733	32	73	h=	h=	NOUN
ejpam-6733	32	74	1	1	NUM
ejpam-6733	32	75	)	)	PUNCT
ejpam-6733	32	76	,	,	PUNCT
ejpam-6733	32	77	l.	l.	PROPN
ejpam-6733	32	78	a	a	PROPN
ejpam-6733	32	79	-	-	PUNCT
ejpam-6733	32	80	m.	m.	NOUN
ejpam-6733	32	81	hanna	hanna	NOUN
ejpam-6733	32	82	,	,	PUNCT
ejpam-6733	32	83	s.	s.	PROPN
ejpam-6733	32	84	s.	s.	PROPN
ejpam-6733	32	85	hassan	hassan	PROPN
ejpam-6733	32	86	,	,	PUNCT
ejpam-6733	32	87	m.	m.	NOUN
ejpam-6733	32	88	almutairi	almutairi	PROPN
ejpam-6733	32	89	/	/	SYM
ejpam-6733	32	90	eur	eur	PROPN
ejpam-6733	32	91	.	.	PUNCT
ejpam-6733	33	1	j.	j.	PROPN
ejpam-6733	33	2	pure	pure	PROPN
ejpam-6733	33	3	appl	appl	PROPN
ejpam-6733	33	4	.	.	PROPN
ejpam-6733	33	5	math	math	PROPN
ejpam-6733	33	6	,	,	PUNCT
ejpam-6733	33	7	18	18	NUM
ejpam-6733	33	8	(	(	PUNCT
ejpam-6733	33	9	4	4	NUM
ejpam-6733	33	10	)	)	PUNCT
ejpam-6733	33	11	(	(	PUNCT
ejpam-6733	33	12	2025	2025	NUM
ejpam-6733	33	13	)	)	PUNCT
ejpam-6733	33	14	,	,	PUNCT
ejpam-6733	33	15	6733	6733	NUM
ejpam-6733	33	16	3	3	NUM
ejpam-6733	33	17	of	of	ADP
ejpam-6733	33	18	12	12	NUM
ejpam-6733	33	19	h	h	NOUN
ejpam-6733	33	20	=	=	NOUN
ejpam-6733	33	21	ωk0	ωk0	NOUN
ejpam-6733	34	1	+	+	CCONJ
ejpam-6733	34	2	λ	λ	PROPN
ejpam-6733	34	3	(	(	PUNCT
ejpam-6733	34	4	t	t	PROPN
ejpam-6733	34	5	)	)	PUNCT
ejpam-6733	34	6	(	(	PUNCT
ejpam-6733	34	7	k+	k+	X
ejpam-6733	34	8	+	+	ADJ
ejpam-6733	34	9	k−	k−	PROPN
ejpam-6733	34	10	)	)	PUNCT
ejpam-6733	35	1	=	=	SYM
ejpam-6733	35	2	h†.	h†.	PROPN
ejpam-6733	35	3	(	(	PUNCT
ejpam-6733	35	4	3	3	NUM
ejpam-6733	35	5	)	)	PUNCT
ejpam-6733	35	6	note	note	NOUN
ejpam-6733	35	7	that	that	SCONJ
ejpam-6733	35	8	,	,	PUNCT
ejpam-6733	35	9	the	the	DET
ejpam-6733	35	10	total	total	ADJ
ejpam-6733	35	11	hamiltonian	hamiltonian	ADJ
ejpam-6733	35	12	operator	operator	NOUN
ejpam-6733	35	13	h	h	NOUN
ejpam-6733	35	14	in	in	ADP
ejpam-6733	35	15	(	(	PUNCT
ejpam-6733	35	16	3	3	NUM
ejpam-6733	35	17	)	)	PUNCT
ejpam-6733	35	18	represents	represent	VERB
ejpam-6733	35	19	the	the	DET
ejpam-6733	35	20	total	total	ADJ
ejpam-6733	35	21	quantum	quantum	ADJ
ejpam-6733	35	22	energy	energy	NOUN
ejpam-6733	35	23	operator	operator	NOUN
ejpam-6733	35	24	of	of	ADP
ejpam-6733	35	25	the	the	DET
ejpam-6733	35	26	considered	consider	VERB
ejpam-6733	35	27	system	system	NOUN
ejpam-6733	35	28	(	(	PUNCT
ejpam-6733	35	29	coupled	couple	VERB
ejpam-6733	35	30	quantized	quantize	VERB
ejpam-6733	35	31	optical	optical	ADJ
ejpam-6733	35	32	atoms	atom	NOUN
ejpam-6733	35	33	)	)	PUNCT
ejpam-6733	35	34	.	.	PUNCT
ejpam-6733	36	1	for	for	ADP
ejpam-6733	36	2	physical	physical	ADJ
ejpam-6733	36	3	requirements	requirement	NOUN
ejpam-6733	36	4	,	,	PUNCT
ejpam-6733	36	5	h	h	NOUN
ejpam-6733	36	6	must	must	AUX
ejpam-6733	36	7	be	be	AUX
ejpam-6733	36	8	a	a	DET
ejpam-6733	36	9	hermitian	hermitian	ADJ
ejpam-6733	36	10	operator	operator	NOUN
ejpam-6733	36	11	,	,	PUNCT
ejpam-6733	36	12	and	and	CCONJ
ejpam-6733	36	13	so	so	ADV
ejpam-6733	36	14	,	,	PUNCT
ejpam-6733	36	15	its	its	PRON
ejpam-6733	36	16	observed	observed	ADJ
ejpam-6733	36	17	energy	energy	NOUN
ejpam-6733	36	18	eigenvalues	eigenvalue	NOUN
ejpam-6733	36	19	must	must	AUX
ejpam-6733	36	20	be	be	AUX
ejpam-6733	36	21	real	real	ADJ
ejpam-6733	36	22	,	,	PUNCT
ejpam-6733	36	23	and	and	CCONJ
ejpam-6733	36	24	in	in	ADP
ejpam-6733	36	25	turn	turn	NOUN
ejpam-6733	36	26	,	,	PUNCT
ejpam-6733	36	27	its	its	PRON
ejpam-6733	36	28	constituent	constituent	NOUN
ejpam-6733	36	29	operators	operator	NOUN
ejpam-6733	36	30	k0	k0	PROPN
ejpam-6733	36	31	,	,	PUNCT
ejpam-6733	36	32	a	a	DET
ejpam-6733	36	33	real	real	ADJ
ejpam-6733	36	34	diagonal	diagonal	ADJ
ejpam-6733	36	35	operator	operator	NOUN
ejpam-6733	36	36	,	,	PUNCT
ejpam-6733	36	37	and	and	CCONJ
ejpam-6733	36	38	k−	k−	PROPN
ejpam-6733	36	39	=	=	PUNCT
ejpam-6733	37	1	k†	k†	PROPN
ejpam-6733	37	2	+	+	PRON
ejpam-6733	37	3	are	be	AUX
ejpam-6733	37	4	two	two	NUM
ejpam-6733	37	5	hermitian	hermitian	ADJ
ejpam-6733	37	6	conjugate	conjugate	ADJ
ejpam-6733	37	7	operators	operator	NOUN
ejpam-6733	37	8	.	.	PUNCT
ejpam-6733	38	1	here	here	ADV
ejpam-6733	38	2	,	,	PUNCT
ejpam-6733	38	3	we	we	PRON
ejpam-6733	38	4	examine	examine	VERB
ejpam-6733	38	5	the	the	DET
ejpam-6733	38	6	faithful	faithful	ADJ
ejpam-6733	38	7	matrix	matrix	NOUN
ejpam-6733	38	8	representations	representation	NOUN
ejpam-6733	38	9	of	of	ADP
ejpam-6733	38	10	the	the	DET
ejpam-6733	38	11	generalized	generalized	ADJ
ejpam-6733	38	12	lie	lie	NOUN
ejpam-6733	38	13	algebra	algebra	PROPN
ejpam-6733	38	14	lp	lp	PROPN
ejpam-6733	38	15	,	,	PUNCT
ejpam-6733	38	16	q	q	X
ejpam-6733	38	17	(	(	PUNCT
ejpam-6733	38	18	cf	cf	X
ejpam-6733	39	1	[	[	X
ejpam-6733	39	2	13	13	NUM
ejpam-6733	39	3	]	]	NUM
ejpam-6733	39	4	)	)	PUNCT
ejpam-6733	39	5	,	,	PUNCT
ejpam-6733	39	6	[	[	X
ejpam-6733	39	7	k0,k+]p	k0,k+]p	PROPN
ejpam-6733	39	8	,	,	PUNCT
ejpam-6733	39	9	q	q	NOUN
ejpam-6733	39	10	=	=	SYM
ejpam-6733	39	11	rk+	rk+	NOUN
ejpam-6733	39	12	,	,	PUNCT
ejpam-6733	39	13	(	(	PUNCT
ejpam-6733	39	14	4	4	X
ejpam-6733	39	15	)	)	PUNCT
ejpam-6733	40	1	[	[	X
ejpam-6733	40	2	k−,k0]p	k−,k0]p	NOUN
ejpam-6733	40	3	,	,	PUNCT
ejpam-6733	40	4	q	q	X
ejpam-6733	40	5	=	=	SYM
ejpam-6733	40	6	rk−	rk−	NOUN
ejpam-6733	40	7	,	,	PUNCT
ejpam-6733	40	8	(	(	PUNCT
ejpam-6733	40	9	5	5	NUM
ejpam-6733	40	10	)	)	PUNCT
ejpam-6733	40	11	[	[	X
ejpam-6733	40	12	k+,k−]p	k+,k−]p	X
ejpam-6733	40	13	,	,	PUNCT
ejpam-6733	40	14	q	q	PROPN
ejpam-6733	40	15	=	=	SYM
ejpam-6733	40	16	f	f	X
ejpam-6733	40	17	(	(	PUNCT
ejpam-6733	40	18	k0	k0	PROPN
ejpam-6733	40	19	)	)	PUNCT
ejpam-6733	40	20	,	,	PUNCT
ejpam-6733	40	21	(	(	PUNCT
ejpam-6733	40	22	6	6	X
ejpam-6733	40	23	)	)	PUNCT
ejpam-6733	40	24	subject	subject	NOUN
ejpam-6733	40	25	to	to	ADP
ejpam-6733	40	26	the	the	DET
ejpam-6733	40	27	physical	physical	ADJ
ejpam-6733	40	28	properties	property	NOUN
ejpam-6733	40	29	mentioned	mention	VERB
ejpam-6733	40	30	below	below	ADV
ejpam-6733	40	31	(	(	PUNCT
ejpam-6733	40	32	3	3	NUM
ejpam-6733	40	33	)	)	PUNCT
ejpam-6733	40	34	.	.	PUNCT
ejpam-6733	41	1	note	note	VERB
ejpam-6733	41	2	that	that	SCONJ
ejpam-6733	41	3	,	,	PUNCT
ejpam-6733	41	4	for	for	ADP
ejpam-6733	41	5	p	p	NOUN
ejpam-6733	41	6	=	=	NOUN
ejpam-6733	41	7	q	q	NOUN
ejpam-6733	41	8	=	=	SYM
ejpam-6733	41	9	1	1	NUM
ejpam-6733	41	10	,	,	PUNCT
ejpam-6733	41	11	equations	equation	NOUN
ejpam-6733	41	12	(	(	PUNCT
ejpam-6733	41	13	4)-(6	4)-(6	NOUN
ejpam-6733	41	14	)	)	PUNCT
ejpam-6733	41	15	are	be	AUX
ejpam-6733	41	16	reduced	reduce	VERB
ejpam-6733	41	17	to	to	ADP
ejpam-6733	41	18	the	the	DET
ejpam-6733	41	19	lie	lie	NOUN
ejpam-6733	41	20	algebra	algebra	NOUN
ejpam-6733	41	21	l1,1	l1,1	PROPN
ejpam-6733	41	22	=	=	PUNCT
ejpam-6733	41	23	l	l	NOUN
ejpam-6733	41	24	in	in	ADP
ejpam-6733	41	25	(	(	PUNCT
ejpam-6733	41	26	2	2	NUM
ejpam-6733	41	27	)	)	PUNCT
ejpam-6733	41	28	,	,	PUNCT
ejpam-6733	42	1	[	[	X
ejpam-6733	42	2	14	14	NUM
ejpam-6733	42	3	]	]	PUNCT
ejpam-6733	42	4	,	,	PUNCT
ejpam-6733	42	5	[	[	X
ejpam-6733	42	6	15	15	NUM
ejpam-6733	42	7	]	]	PUNCT
ejpam-6733	42	8	.	.	PUNCT
ejpam-6733	43	1	3	3	X
ejpam-6733	43	2	.	.	X
ejpam-6733	43	3	basic	basic	ADJ
ejpam-6733	43	4	properties	property	NOUN
ejpam-6733	43	5	of	of	ADP
ejpam-6733	43	6	the	the	DET
ejpam-6733	43	7	(	(	PUNCT
ejpam-6733	43	8	p	p	X
ejpam-6733	43	9	,	,	PUNCT
ejpam-6733	43	10	q)-deformed	q)-deforme	VERB
ejpam-6733	43	11	lie	lie	VERB
ejpam-6733	43	12	bracket	bracket	NOUN
ejpam-6733	43	13	here	here	ADV
ejpam-6733	43	14	,	,	PUNCT
ejpam-6733	43	15	we	we	PRON
ejpam-6733	43	16	list	list	VERB
ejpam-6733	43	17	some	some	DET
ejpam-6733	43	18	properties	property	NOUN
ejpam-6733	43	19	of	of	ADP
ejpam-6733	43	20	the	the	DET
ejpam-6733	43	21	(	(	PUNCT
ejpam-6733	43	22	p	p	X
ejpam-6733	43	23	,	,	PUNCT
ejpam-6733	43	24	q)-deformed	q)-deforme	VERB
ejpam-6733	43	25	lie	lie	VERB
ejpam-6733	43	26	bracket	bracket	NOUN
ejpam-6733	43	27	in	in	ADP
ejpam-6733	43	28	the	the	DET
ejpam-6733	43	29	following	follow	VERB
ejpam-6733	43	30	theorem	theorem	PROPN
ejpam-6733	43	31	.	.	PUNCT
ejpam-6733	43	32	theorem	theorem	NOUN
ejpam-6733	43	33	1	1	NUM
ejpam-6733	43	34	.	.	PUNCT
ejpam-6733	44	1	let	let	VERB
ejpam-6733	44	2	x	x	PRON
ejpam-6733	44	3	,	,	PUNCT
ejpam-6733	44	4	y	y	PROPN
ejpam-6733	44	5	and	and	CCONJ
ejpam-6733	44	6	z	z	PROPN
ejpam-6733	44	7	be	be	AUX
ejpam-6733	44	8	n×	n×	PROPN
ejpam-6733	44	9	n	n	PRON
ejpam-6733	44	10	matrices	matrix	NOUN
ejpam-6733	44	11	,	,	PUNCT
ejpam-6733	44	12	and	and	CCONJ
ejpam-6733	44	13	p	p	X
ejpam-6733	44	14	,	,	PUNCT
ejpam-6733	44	15	q	q	PROPN
ejpam-6733	44	16	∈	∈	PROPN
ejpam-6733	44	17	r∗	r∗	PROPN
ejpam-6733	44	18	,	,	PUNCT
ejpam-6733	44	19	and	and	CCONJ
ejpam-6733	44	20	α	α	X
ejpam-6733	44	21	,	,	PUNCT
ejpam-6733	44	22	β	β	PROPN
ejpam-6733	44	23	∈	∈	PROPN
ejpam-6733	44	24	r.	r.	PROPN
ejpam-6733	44	25	then	then	ADV
ejpam-6733	44	26	1	1	X
ejpam-6733	44	27	.	.	PUNCT
ejpam-6733	45	1	tr	tr	VERB
ejpam-6733	45	2	(	(	PUNCT
ejpam-6733	45	3	[	[	X
ejpam-6733	45	4	x	x	X
ejpam-6733	45	5	,	,	PUNCT
ejpam-6733	45	6	y	y	PROPN
ejpam-6733	45	7	]	]	X
ejpam-6733	45	8	p	p	X
ejpam-6733	45	9	,	,	PUNCT
ejpam-6733	45	10	q	q	NOUN
ejpam-6733	45	11	)	)	PUNCT
ejpam-6733	45	12	=	=	PUNCT
ejpam-6733	45	13	tr	tr	VERB
ejpam-6733	45	14	(	(	PUNCT
ejpam-6733	45	15	[	[	X
ejpam-6733	45	16	y	y	NOUN
ejpam-6733	45	17	,	,	PUNCT
ejpam-6733	45	18	x]p	x]p	NOUN
ejpam-6733	45	19	,	,	PUNCT
ejpam-6733	45	20	q	q	NOUN
ejpam-6733	45	21	)	)	PUNCT
ejpam-6733	45	22	=	=	SYM
ejpam-6733	45	23	(	(	PUNCT
ejpam-6733	45	24	p−	p−	NOUN
ejpam-6733	45	25	q	q	NOUN
ejpam-6733	45	26	)	)	PUNCT
ejpam-6733	45	27	tr	tr	VERB
ejpam-6733	45	28	(	(	PUNCT
ejpam-6733	45	29	xy	xy	PROPN
ejpam-6733	45	30	)	)	PUNCT
ejpam-6733	45	31	=	=	PUNCT
ejpam-6733	46	1	(	(	PUNCT
ejpam-6733	46	2	p−	p−	NOUN
ejpam-6733	46	3	q	q	NOUN
ejpam-6733	46	4	)	)	PUNCT
ejpam-6733	46	5	tr	tr	VERB
ejpam-6733	46	6	(	(	PUNCT
ejpam-6733	46	7	y	y	NOUN
ejpam-6733	46	8	x	x	PROPN
ejpam-6733	46	9	)	)	PUNCT
ejpam-6733	46	10	.	.	PUNCT
ejpam-6733	47	1	2	2	X
ejpam-6733	47	2	.	.	X
ejpam-6733	48	1	[	[	X
ejpam-6733	48	2	x	x	X
ejpam-6733	48	3	,	,	PUNCT
ejpam-6733	48	4	y	y	PROPN
ejpam-6733	48	5	]	]	X
ejpam-6733	48	6	†p	†p	NUM
ejpam-6733	48	7	,	,	PUNCT
ejpam-6733	48	8	q	q	NOUN
ejpam-6733	48	9	=	=	PUNCT
ejpam-6733	48	10	[	[	PUNCT
ejpam-6733	48	11	y	y	PROPN
ejpam-6733	48	12	†	†	PROPN
ejpam-6733	48	13	,	,	PUNCT
ejpam-6733	49	1	x†	x†	X
ejpam-6733	49	2	]	]	X
ejpam-6733	50	1	p	p	X
ejpam-6733	50	2	,	,	PUNCT
ejpam-6733	50	3	q	q	NOUN
ejpam-6733	50	4	.	.	PUNCT
ejpam-6733	51	1	3	3	X
ejpam-6733	51	2	.	.	X
ejpam-6733	52	1	(	(	PUNCT
ejpam-6733	52	2	[	[	PUNCT
ejpam-6733	52	3	x	x	X
ejpam-6733	52	4	,	,	PUNCT
ejpam-6733	52	5	x†	x†	ADJ
ejpam-6733	52	6	]	]	X
ejpam-6733	53	1	p	p	X
ejpam-6733	53	2	,	,	PUNCT
ejpam-6733	53	3	q	q	NOUN
ejpam-6733	53	4	)	)	PUNCT
ejpam-6733	53	5	ij	ij	NOUN
ejpam-6733	53	6	=	=	PUNCT
ejpam-6733	53	7	(	(	PUNCT
ejpam-6733	53	8	[	[	X
ejpam-6733	53	9	x	x	X
ejpam-6733	53	10	,	,	PUNCT
ejpam-6733	53	11	x†]p	x†]p	PROPN
ejpam-6733	53	12	,	,	PUNCT
ejpam-6733	53	13	q	q	NOUN
ejpam-6733	53	14	)	)	PUNCT
ejpam-6733	53	15	ji	ji	PROPN
ejpam-6733	53	16	for	for	ADP
ejpam-6733	53	17	i	i	PROPN
ejpam-6733	53	18	6=	6=	PROPN
ejpam-6733	53	19	j.	j.	PROPN
ejpam-6733	53	20	4	4	NUM
ejpam-6733	53	21	.	.	PUNCT
ejpam-6733	54	1	[	[	X
ejpam-6733	54	2	x	x	X
ejpam-6733	54	3	,	,	PUNCT
ejpam-6733	54	4	y	y	PROPN
ejpam-6733	54	5	+	+	PROPN
ejpam-6733	54	6	z]p	z]p	PROPN
ejpam-6733	54	7	,	,	PUNCT
ejpam-6733	54	8	q	q	NOUN
ejpam-6733	54	9	=	=	PUNCT
ejpam-6733	55	1	[	[	X
ejpam-6733	55	2	x	x	X
ejpam-6733	55	3	,	,	PUNCT
ejpam-6733	55	4	y	y	PROPN
ejpam-6733	55	5	]	]	X
ejpam-6733	55	6	p	p	X
ejpam-6733	55	7	,	,	PUNCT
ejpam-6733	55	8	q	q	X
ejpam-6733	56	1	+	+	X
ejpam-6733	57	1	[	[	X
ejpam-6733	57	2	x	x	X
ejpam-6733	57	3	,	,	PUNCT
ejpam-6733	57	4	z]p	z]p	PROPN
ejpam-6733	57	5	,	,	PUNCT
ejpam-6733	57	6	q	q	X
ejpam-6733	57	7	.	.	PUNCT
ejpam-6733	58	1	5	5	X
ejpam-6733	58	2	.	.	PUNCT
ejpam-6733	59	1	[	[	X
ejpam-6733	59	2	x	x	X
ejpam-6733	59	3	+	+	NUM
ejpam-6733	59	4	y	y	PROPN
ejpam-6733	59	5	,	,	PUNCT
ejpam-6733	59	6	z]p	z]p	PROPN
ejpam-6733	59	7	,	,	PUNCT
ejpam-6733	59	8	q	q	X
ejpam-6733	59	9	=	=	PUNCT
ejpam-6733	60	1	[	[	X
ejpam-6733	60	2	x	x	X
ejpam-6733	60	3	,	,	PUNCT
ejpam-6733	60	4	z]p	z]p	PROPN
ejpam-6733	60	5	,	,	PUNCT
ejpam-6733	60	6	q	q	X
ejpam-6733	61	1	+	+	PROPN
ejpam-6733	61	2	[	[	X
ejpam-6733	61	3	y	y	PROPN
ejpam-6733	61	4	,	,	PUNCT
ejpam-6733	61	5	z]p	z]p	PROPN
ejpam-6733	61	6	,	,	PUNCT
ejpam-6733	61	7	q	q	NOUN
ejpam-6733	61	8	.	.	PUNCT
ejpam-6733	62	1	6	6	X
ejpam-6733	62	2	.	.	PUNCT
ejpam-6733	63	1	[	[	X
ejpam-6733	63	2	αx	αx	X
ejpam-6733	63	3	,	,	PUNCT
ejpam-6733	63	4	βy	βy	X
ejpam-6733	63	5	]	]	X
ejpam-6733	63	6	p	p	X
ejpam-6733	63	7	,	,	PUNCT
ejpam-6733	63	8	q	q	NOUN
ejpam-6733	63	9	=	=	PUNCT
ejpam-6733	63	10	αβ	αβ	PRON
ejpam-6733	64	1	[	[	X
ejpam-6733	64	2	x	x	X
ejpam-6733	64	3	,	,	PUNCT
ejpam-6733	64	4	y	y	PROPN
ejpam-6733	64	5	]	]	X
ejpam-6733	64	6	p	p	X
ejpam-6733	64	7	,	,	PUNCT
ejpam-6733	64	8	q	q	NOUN
ejpam-6733	64	9	.	.	PUNCT
ejpam-6733	65	1	7	7	X
ejpam-6733	65	2	.	.	X
ejpam-6733	65	3	[	[	PUNCT
ejpam-6733	65	4	x	x	X
ejpam-6733	65	5	,	,	PUNCT
ejpam-6733	65	6	[	[	X
ejpam-6733	65	7	y	y	PROPN
ejpam-6733	65	8	,	,	PUNCT
ejpam-6733	65	9	z]p	z]p	PROPN
ejpam-6733	65	10	,	,	PUNCT
ejpam-6733	65	11	q	q	X
ejpam-6733	65	12	]	]	X
ejpam-6733	65	13	p	p	X
ejpam-6733	65	14	,	,	PUNCT
ejpam-6733	65	15	q	q	NOUN
ejpam-6733	65	16	=	=	SYM
ejpam-6733	65	17	p2xy	p2xy	PUNCT
ejpam-6733	65	18	z	z	NOUN
ejpam-6733	65	19	−	−	PROPN
ejpam-6733	65	20	pqy	pqy	NOUN
ejpam-6733	65	21	zx	zx	NUM
ejpam-6733	65	22	−	−	PROPN
ejpam-6733	65	23	pqxzy	pqxzy	NOUN
ejpam-6733	65	24	+	+	CCONJ
ejpam-6733	65	25	q2zy	q2zy	ADJ
ejpam-6733	65	26	x.	x.	NOUN
ejpam-6733	65	27	8	8	NUM
ejpam-6733	65	28	.	.	PUNCT
ejpam-6733	66	1	[	[	PUNCT
ejpam-6733	66	2	[	[	X
ejpam-6733	66	3	x	x	X
ejpam-6733	66	4	,	,	PUNCT
ejpam-6733	66	5	y	y	PROPN
ejpam-6733	66	6	]	]	X
ejpam-6733	66	7	p	p	X
ejpam-6733	66	8	,	,	PUNCT
ejpam-6733	66	9	q	q	NOUN
ejpam-6733	66	10	,	,	PUNCT
ejpam-6733	66	11	z	z	NOUN
ejpam-6733	66	12	]	]	X
ejpam-6733	66	13	p	p	X
ejpam-6733	66	14	,	,	PUNCT
ejpam-6733	66	15	q	q	NOUN
ejpam-6733	66	16	=	=	SYM
ejpam-6733	66	17	p2xy	p2xy	PUNCT
ejpam-6733	66	18	z	z	NOUN
ejpam-6733	66	19	−	−	PROPN
ejpam-6733	66	20	pqy	pqy	NOUN
ejpam-6733	66	21	xz	xz	PROPN
ejpam-6733	66	22	−	−	PROPN
ejpam-6733	66	23	pqzxy	pqzxy	NOUN
ejpam-6733	66	24	+	+	CCONJ
ejpam-6733	66	25	q2zy	q2zy	ADJ
ejpam-6733	66	26	x.	x.	NOUN
ejpam-6733	66	27	9	9	NUM
ejpam-6733	66	28	.	.	PUNCT
ejpam-6733	67	1	[	[	PUNCT
ejpam-6733	67	2	x	x	X
ejpam-6733	67	3	,	,	PUNCT
ejpam-6733	67	4	[	[	X
ejpam-6733	67	5	y	y	PROPN
ejpam-6733	67	6	,	,	PUNCT
ejpam-6733	67	7	z]p	z]p	PROPN
ejpam-6733	67	8	,	,	PUNCT
ejpam-6733	67	9	q	q	X
ejpam-6733	67	10	]	]	X
ejpam-6733	67	11	p	p	X
ejpam-6733	67	12	,	,	PUNCT
ejpam-6733	67	13	q	q	X
ejpam-6733	67	14	+	+	PUNCT
ejpam-6733	67	15	[	[	PUNCT
ejpam-6733	67	16	y	y	NOUN
ejpam-6733	67	17	,	,	PUNCT
ejpam-6733	67	18	[	[	X
ejpam-6733	67	19	z	z	X
ejpam-6733	67	20	,	,	PUNCT
ejpam-6733	67	21	x]p	x]p	PROPN
ejpam-6733	67	22	,	,	PUNCT
ejpam-6733	67	23	q	q	X
ejpam-6733	67	24	]	]	X
ejpam-6733	67	25	p	p	X
ejpam-6733	67	26	,	,	PUNCT
ejpam-6733	67	27	q	q	X
ejpam-6733	68	1	+	+	PUNCT
ejpam-6733	68	2	[	[	PUNCT
ejpam-6733	68	3	z	z	NOUN
ejpam-6733	68	4	,	,	PUNCT
ejpam-6733	68	5	[	[	X
ejpam-6733	68	6	x	x	X
ejpam-6733	68	7	,	,	PUNCT
ejpam-6733	68	8	y	y	PROPN
ejpam-6733	68	9	]	]	X
ejpam-6733	68	10	p	p	X
ejpam-6733	68	11	,	,	PUNCT
ejpam-6733	68	12	q	q	X
ejpam-6733	68	13	]	]	X
ejpam-6733	68	14	p	p	X
ejpam-6733	68	15	,	,	PUNCT
ejpam-6733	68	16	q	q	NOUN
ejpam-6733	68	17	=	=	X
ejpam-6733	68	18	(	(	PUNCT
ejpam-6733	68	19	p−	p−	NOUN
ejpam-6733	68	20	q	q	NOUN
ejpam-6733	68	21	)	)	PUNCT
ejpam-6733	69	1	[	[	X
ejpam-6733	69	2	p	p	X
ejpam-6733	69	3	(	(	PUNCT
ejpam-6733	69	4	xy	xy	PROPN
ejpam-6733	69	5	z	z	PROPN
ejpam-6733	69	6	+	+	CCONJ
ejpam-6733	69	7	y	y	PROPN
ejpam-6733	69	8	zx	zx	PROPN
ejpam-6733	69	9	+	+	CCONJ
ejpam-6733	69	10	zxy	zxy	X
ejpam-6733	69	11	)	)	PUNCT
ejpam-6733	69	12	−	−	PROPN
ejpam-6733	70	1	q	q	PROPN
ejpam-6733	70	2	(	(	PUNCT
ejpam-6733	70	3	xzy	xzy	PROPN
ejpam-6733	71	1	+	+	CCONJ
ejpam-6733	71	2	y	y	PROPN
ejpam-6733	71	3	xz	xz	PROPN
ejpam-6733	72	1	+	+	CCONJ
ejpam-6733	72	2	zy	zy	PROPN
ejpam-6733	72	3	x	x	PROPN
ejpam-6733	72	4	)	)	PUNCT
ejpam-6733	72	5	]	]	PUNCT
ejpam-6733	72	6	.	.	PUNCT
ejpam-6733	73	1	l.	l.	PROPN
ejpam-6733	73	2	a	a	DET
ejpam-6733	73	3	-	-	PUNCT
ejpam-6733	73	4	m.	m.	NOUN
ejpam-6733	73	5	hanna	hanna	NOUN
ejpam-6733	73	6	,	,	PUNCT
ejpam-6733	73	7	s.	s.	PROPN
ejpam-6733	73	8	s.	s.	PROPN
ejpam-6733	73	9	hassan	hassan	PROPN
ejpam-6733	73	10	,	,	PUNCT
ejpam-6733	73	11	m.	m.	NOUN
ejpam-6733	73	12	almutairi	almutairi	PROPN
ejpam-6733	73	13	/	/	SYM
ejpam-6733	73	14	eur	eur	PROPN
ejpam-6733	73	15	.	.	PUNCT
ejpam-6733	74	1	j.	j.	PROPN
ejpam-6733	74	2	pure	pure	PROPN
ejpam-6733	74	3	appl	appl	PROPN
ejpam-6733	74	4	.	.	PROPN
ejpam-6733	74	5	math	math	PROPN
ejpam-6733	74	6	,	,	PUNCT
ejpam-6733	74	7	18	18	NUM
ejpam-6733	74	8	(	(	PUNCT
ejpam-6733	74	9	4	4	NUM
ejpam-6733	74	10	)	)	PUNCT
ejpam-6733	74	11	(	(	PUNCT
ejpam-6733	74	12	2025	2025	NUM
ejpam-6733	74	13	)	)	PUNCT
ejpam-6733	74	14	,	,	PUNCT
ejpam-6733	74	15	6733	6733	NUM
ejpam-6733	74	16	4	4	NUM
ejpam-6733	74	17	of	of	ADP
ejpam-6733	74	18	12	12	NUM
ejpam-6733	74	19	proof	proof	NOUN
ejpam-6733	74	20	.	.	PUNCT
ejpam-6733	75	1	the	the	DET
ejpam-6733	75	2	proof	proof	NOUN
ejpam-6733	75	3	of	of	ADP
ejpam-6733	75	4	parts	part	NOUN
ejpam-6733	75	5	(	(	PUNCT
ejpam-6733	75	6	1	1	NUM
ejpam-6733	75	7	)	)	PUNCT
ejpam-6733	75	8	(	(	PUNCT
ejpam-6733	75	9	6	6	NUM
ejpam-6733	75	10	)	)	PUNCT
ejpam-6733	75	11	is	be	AUX
ejpam-6733	75	12	simple	simple	ADJ
ejpam-6733	75	13	and	and	CCONJ
ejpam-6733	75	14	deduced	deduce	VERB
ejpam-6733	75	15	directly	directly	ADV
ejpam-6733	75	16	from	from	ADP
ejpam-6733	75	17	the	the	DET
ejpam-6733	75	18	definition	definition	NOUN
ejpam-6733	75	19	in	in	ADP
ejpam-6733	75	20	(	(	PUNCT
ejpam-6733	75	21	1	1	NUM
ejpam-6733	75	22	)	)	PUNCT
ejpam-6733	75	23	.	.	PUNCT
ejpam-6733	76	1	so	so	ADV
ejpam-6733	76	2	,	,	PUNCT
ejpam-6733	76	3	we	we	PRON
ejpam-6733	76	4	prove	prove	VERB
ejpam-6733	76	5	parts	part	NOUN
ejpam-6733	76	6	(	(	PUNCT
ejpam-6733	76	7	7	7	NUM
ejpam-6733	76	8	)	)	PUNCT
ejpam-6733	76	9	(	(	PUNCT
ejpam-6733	76	10	9	9	NUM
ejpam-6733	76	11	)	)	PUNCT
ejpam-6733	76	12	.	.	PUNCT
ejpam-6733	77	1	for	for	ADP
ejpam-6733	77	2	the	the	DET
ejpam-6733	77	3	proof	proof	NOUN
ejpam-6733	77	4	of	of	ADP
ejpam-6733	77	5	part	part	NOUN
ejpam-6733	77	6	(	(	PUNCT
ejpam-6733	77	7	7	7	NUM
ejpam-6733	77	8	)	)	PUNCT
ejpam-6733	77	9	,	,	PUNCT
ejpam-6733	77	10	we	we	PRON
ejpam-6733	77	11	have	have	VERB
ejpam-6733	77	12	[	[	PUNCT
ejpam-6733	77	13	x	x	SYM
ejpam-6733	77	14	,	,	PUNCT
ejpam-6733	77	15	[	[	X
ejpam-6733	77	16	y	y	PROPN
ejpam-6733	77	17	,	,	PUNCT
ejpam-6733	77	18	z]p	z]p	PROPN
ejpam-6733	77	19	,	,	PUNCT
ejpam-6733	77	20	q	q	X
ejpam-6733	77	21	]	]	X
ejpam-6733	77	22	p	p	X
ejpam-6733	77	23	,	,	PUNCT
ejpam-6733	77	24	q	q	NOUN
ejpam-6733	77	25	=	=	PUNCT
ejpam-6733	78	1	[	[	X
ejpam-6733	78	2	x	x	X
ejpam-6733	78	3	,	,	PUNCT
ejpam-6733	78	4	(	(	PUNCT
ejpam-6733	78	5	py	py	INTJ
ejpam-6733	78	6	z	z	PROPN
ejpam-6733	78	7	−	−	PROPN
ejpam-6733	78	8	qzy	qzy	NOUN
ejpam-6733	78	9	)	)	PUNCT
ejpam-6733	79	1	]	]	X
ejpam-6733	79	2	p	p	X
ejpam-6733	79	3	,	,	PUNCT
ejpam-6733	79	4	q	q	NOUN
ejpam-6733	79	5	=	=	SYM
ejpam-6733	79	6	px	px	X
ejpam-6733	79	7	(	(	PUNCT
ejpam-6733	79	8	py	py	PROPN
ejpam-6733	79	9	z	z	PROPN
ejpam-6733	79	10	−	−	PROPN
ejpam-6733	79	11	qzy	qzy	NOUN
ejpam-6733	79	12	)	)	PUNCT
ejpam-6733	79	13	−	−	PROPN
ejpam-6733	80	1	q	q	NOUN
ejpam-6733	80	2	(	(	PUNCT
ejpam-6733	80	3	py	py	INTJ
ejpam-6733	80	4	z	z	PROPN
ejpam-6733	80	5	−	−	PROPN
ejpam-6733	80	6	qzy	qzy	NOUN
ejpam-6733	80	7	)	)	PUNCT
ejpam-6733	80	8	x	x	X
ejpam-6733	81	1	=	=	PUNCT
ejpam-6733	81	2	p2xy	p2xy	PUNCT
ejpam-6733	81	3	z	z	NOUN
ejpam-6733	81	4	−	−	PROPN
ejpam-6733	81	5	pqxzy	pqxzy	NOUN
ejpam-6733	81	6	−	−	PROPN
ejpam-6733	81	7	pqy	pqy	PROPN
ejpam-6733	81	8	zx	zx	PROPN
ejpam-6733	81	9	+	+	CCONJ
ejpam-6733	81	10	q2zy	q2zy	PROPN
ejpam-6733	81	11	x.	x.	NOUN
ejpam-6733	81	12	similarly	similarly	ADV
ejpam-6733	81	13	,	,	PUNCT
ejpam-6733	81	14	for	for	ADP
ejpam-6733	81	15	the	the	DET
ejpam-6733	81	16	proof	proof	NOUN
ejpam-6733	81	17	of	of	ADP
ejpam-6733	81	18	part	part	NOUN
ejpam-6733	81	19	(	(	PUNCT
ejpam-6733	81	20	8)	8)	NUM
ejpam-6733	81	21	,	,	PUNCT
ejpam-6733	81	22	we	we	PRON
ejpam-6733	81	23	have	have	VERB
ejpam-6733	81	24	[	[	PUNCT
ejpam-6733	81	25	[	[	X
ejpam-6733	81	26	x	x	X
ejpam-6733	81	27	,	,	PUNCT
ejpam-6733	81	28	y	y	PROPN
ejpam-6733	81	29	]	]	X
ejpam-6733	81	30	p	p	X
ejpam-6733	81	31	,	,	PUNCT
ejpam-6733	81	32	q	q	NOUN
ejpam-6733	81	33	,	,	PUNCT
ejpam-6733	81	34	z	z	NOUN
ejpam-6733	81	35	]	]	X
ejpam-6733	82	1	p	p	X
ejpam-6733	82	2	,	,	PUNCT
ejpam-6733	82	3	q	q	NOUN
ejpam-6733	82	4	=	=	PUNCT
ejpam-6733	83	1	[	[	X
ejpam-6733	83	2	(	(	PUNCT
ejpam-6733	83	3	pxy	pxy	PROPN
ejpam-6733	83	4	−	−	PROPN
ejpam-6733	83	5	qy	qy	PROPN
ejpam-6733	83	6	x	x	PROPN
ejpam-6733	83	7	)	)	PUNCT
ejpam-6733	83	8	,	,	PUNCT
ejpam-6733	83	9	z]p	z]p	PROPN
ejpam-6733	83	10	,	,	PUNCT
ejpam-6733	83	11	q	q	PROPN
ejpam-6733	83	12	=	=	SYM
ejpam-6733	83	13	p	p	X
ejpam-6733	83	14	(	(	PUNCT
ejpam-6733	83	15	pxy	pxy	PROPN
ejpam-6733	83	16	−	−	PROPN
ejpam-6733	83	17	qy	qy	NOUN
ejpam-6733	83	18	x)z	x)z	PUNCT
ejpam-6733	83	19	−	−	PROPN
ejpam-6733	83	20	qz	qz	PROPN
ejpam-6733	83	21	(	(	PUNCT
ejpam-6733	83	22	pxy	pxy	PROPN
ejpam-6733	83	23	−	−	PROPN
ejpam-6733	83	24	qy	qy	PROPN
ejpam-6733	83	25	x	x	NOUN
ejpam-6733	83	26	)	)	PUNCT
ejpam-6733	83	27	=	=	SYM
ejpam-6733	83	28	p2xy	p2xy	PUNCT
ejpam-6733	83	29	z	z	X
ejpam-6733	83	30	−	−	PROPN
ejpam-6733	83	31	pqy	pqy	NOUN
ejpam-6733	83	32	xz	xz	PROPN
ejpam-6733	83	33	−	−	PROPN
ejpam-6733	83	34	pqzxy	pqzxy	NOUN
ejpam-6733	83	35	+	+	CCONJ
ejpam-6733	83	36	q2zy	q2zy	ADJ
ejpam-6733	83	37	x.	x.	NOUN
ejpam-6733	83	38	(	(	PUNCT
ejpam-6733	83	39	iii	iii	NOUN
ejpam-6733	83	40	)	)	PUNCT
ejpam-6733	83	41	now	now	ADV
ejpam-6733	83	42	,	,	PUNCT
ejpam-6733	83	43	for	for	ADP
ejpam-6733	83	44	part	part	NOUN
ejpam-6733	83	45	(	(	PUNCT
ejpam-6733	83	46	9	9	NUM
ejpam-6733	83	47	)	)	PUNCT
ejpam-6733	83	48	,	,	PUNCT
ejpam-6733	83	49	we	we	PRON
ejpam-6733	83	50	have	have	VERB
ejpam-6733	83	51	[	[	PUNCT
ejpam-6733	83	52	x	x	SYM
ejpam-6733	83	53	,	,	PUNCT
ejpam-6733	83	54	[	[	X
ejpam-6733	83	55	y	y	PROPN
ejpam-6733	83	56	,	,	PUNCT
ejpam-6733	83	57	z]p	z]p	PROPN
ejpam-6733	83	58	,	,	PUNCT
ejpam-6733	83	59	q	q	X
ejpam-6733	83	60	]	]	X
ejpam-6733	84	1	p	p	X
ejpam-6733	84	2	,	,	PUNCT
ejpam-6733	84	3	q	q	X
ejpam-6733	85	1	+	+	PUNCT
ejpam-6733	85	2	[	[	PUNCT
ejpam-6733	85	3	y	y	NOUN
ejpam-6733	85	4	,	,	PUNCT
ejpam-6733	85	5	[	[	X
ejpam-6733	85	6	z	z	X
ejpam-6733	85	7	,	,	PUNCT
ejpam-6733	85	8	x]p	x]p	PROPN
ejpam-6733	85	9	,	,	PUNCT
ejpam-6733	85	10	q	q	X
ejpam-6733	85	11	]	]	X
ejpam-6733	85	12	p	p	X
ejpam-6733	85	13	,	,	PUNCT
ejpam-6733	85	14	q	q	X
ejpam-6733	86	1	+	+	PUNCT
ejpam-6733	86	2	[	[	PUNCT
ejpam-6733	86	3	z	z	NOUN
ejpam-6733	86	4	,	,	PUNCT
ejpam-6733	86	5	[	[	X
ejpam-6733	86	6	x	x	X
ejpam-6733	86	7	,	,	PUNCT
ejpam-6733	86	8	y	y	PROPN
ejpam-6733	86	9	]	]	X
ejpam-6733	86	10	p	p	X
ejpam-6733	86	11	,	,	PUNCT
ejpam-6733	86	12	q	q	X
ejpam-6733	86	13	]	]	X
ejpam-6733	86	14	p	p	X
ejpam-6733	86	15	,	,	PUNCT
ejpam-6733	86	16	q	q	NOUN
ejpam-6733	86	17	=	=	PUNCT
ejpam-6733	87	1	[	[	X
ejpam-6733	87	2	x	x	X
ejpam-6733	87	3	,	,	PUNCT
ejpam-6733	87	4	(	(	PUNCT
ejpam-6733	87	5	py	py	INTJ
ejpam-6733	87	6	z	z	PROPN
ejpam-6733	87	7	−	−	PROPN
ejpam-6733	87	8	qzy	qzy	NOUN
ejpam-6733	87	9	)	)	PUNCT
ejpam-6733	88	1	]	]	X
ejpam-6733	88	2	p	p	X
ejpam-6733	88	3	,	,	PUNCT
ejpam-6733	88	4	q	q	X
ejpam-6733	89	1	+	+	PROPN
ejpam-6733	89	2	[	[	X
ejpam-6733	89	3	y	y	X
ejpam-6733	89	4	,	,	PUNCT
ejpam-6733	89	5	(	(	PUNCT
ejpam-6733	89	6	pzx	pzx	PROPN
ejpam-6733	89	7	−	−	PROPN
ejpam-6733	89	8	qxz)]p	qxz)]p	PROPN
ejpam-6733	89	9	,	,	PUNCT
ejpam-6733	89	10	q	q	X
ejpam-6733	90	1	+	+	X
ejpam-6733	91	1	[	[	X
ejpam-6733	91	2	z	z	X
ejpam-6733	91	3	,	,	PUNCT
ejpam-6733	91	4	(	(	PUNCT
ejpam-6733	91	5	pxy	pxy	VERB
ejpam-6733	91	6	−	−	PROPN
ejpam-6733	91	7	qy	qy	NOUN
ejpam-6733	91	8	x)]p	x)]p	PROPN
ejpam-6733	91	9	,	,	PUNCT
ejpam-6733	91	10	q	q	NOUN
ejpam-6733	91	11	=	=	PUNCT
ejpam-6733	91	12	{	{	PUNCT
ejpam-6733	91	13	px	px	X
ejpam-6733	91	14	(	(	PUNCT
ejpam-6733	91	15	py	py	PROPN
ejpam-6733	91	16	z	z	PROPN
ejpam-6733	91	17	−	−	PROPN
ejpam-6733	91	18	qzy	qzy	NOUN
ejpam-6733	91	19	)	)	PUNCT
ejpam-6733	91	20	−	−	PROPN
ejpam-6733	92	1	q	q	NOUN
ejpam-6733	92	2	(	(	PUNCT
ejpam-6733	92	3	py	py	INTJ
ejpam-6733	92	4	z	z	PROPN
ejpam-6733	92	5	−	−	PROPN
ejpam-6733	92	6	qzy	qzy	NOUN
ejpam-6733	92	7	)	)	PUNCT
ejpam-6733	92	8	x}+{py	x}+{py	NOUN
ejpam-6733	92	9	(	(	PUNCT
ejpam-6733	92	10	pzx	pzx	PROPN
ejpam-6733	92	11	−	−	PROPN
ejpam-6733	92	12	qxz)−	qxz)−	PROPN
ejpam-6733	92	13	q	q	PROPN
ejpam-6733	92	14	(	(	PUNCT
ejpam-6733	92	15	pzx	pzx	ADJ
ejpam-6733	92	16	−	−	PROPN
ejpam-6733	92	17	qxz)y	qxz)y	PROPN
ejpam-6733	92	18	}	}	PUNCT
ejpam-6733	92	19	+	+	CCONJ
ejpam-6733	92	20	{	{	PUNCT
ejpam-6733	92	21	pz	pz	NOUN
ejpam-6733	92	22	(	(	PUNCT
ejpam-6733	92	23	pxy	pxy	PROPN
ejpam-6733	92	24	−	−	PROPN
ejpam-6733	92	25	qy	qy	NOUN
ejpam-6733	92	26	x)−	x)−	PROPN
ejpam-6733	92	27	q	q	PROPN
ejpam-6733	93	1	(	(	PUNCT
ejpam-6733	93	2	pxy	pxy	PROPN
ejpam-6733	93	3	−	−	PROPN
ejpam-6733	93	4	qy	qy	NOUN
ejpam-6733	93	5	x)z	x)z	PUNCT
ejpam-6733	93	6	}	}	PUNCT
ejpam-6733	93	7	=	=	PUNCT
ejpam-6733	93	8	p2	p2	X
ejpam-6733	93	9	(	(	PUNCT
ejpam-6733	93	10	xy	xy	NOUN
ejpam-6733	93	11	z	z	PROPN
ejpam-6733	94	1	+	+	CCONJ
ejpam-6733	94	2	y	y	PROPN
ejpam-6733	94	3	zx	zx	PROPN
ejpam-6733	94	4	+	+	CCONJ
ejpam-6733	94	5	zxy	zxy	NOUN
ejpam-6733	94	6	)	)	PUNCT
ejpam-6733	94	7	−pq	−pq	PROPN
ejpam-6733	94	8	(	(	PUNCT
ejpam-6733	94	9	xzy	xzy	PROPN
ejpam-6733	95	1	+	+	CCONJ
ejpam-6733	95	2	y	y	PROPN
ejpam-6733	95	3	zx	zx	PROPN
ejpam-6733	96	1	+	+	CCONJ
ejpam-6733	96	2	y	y	PROPN
ejpam-6733	96	3	xz	xz	PROPN
ejpam-6733	96	4	+	+	CCONJ
ejpam-6733	96	5	zxy	zxy	NOUN
ejpam-6733	97	1	+	+	X
ejpam-6733	97	2	zy	zy	X
ejpam-6733	97	3	x	x	PUNCT
ejpam-6733	97	4	+	+	ADJ
ejpam-6733	97	5	xy	xy	PROPN
ejpam-6733	97	6	z)+	z)+	NUM
ejpam-6733	97	7	q2	q2	NOUN
ejpam-6733	97	8	(	(	PUNCT
ejpam-6733	97	9	zy	zy	NOUN
ejpam-6733	97	10	x	x	PUNCT
ejpam-6733	97	11	+	+	NOUN
ejpam-6733	97	12	xzy	xzy	NOUN
ejpam-6733	97	13	+	+	CCONJ
ejpam-6733	97	14	y	y	PROPN
ejpam-6733	97	15	xz	xz	PROPN
ejpam-6733	97	16	)	)	PUNCT
ejpam-6733	98	1	=	=	NOUN
ejpam-6733	98	2	p2	p2	PROPN
ejpam-6733	98	3	(	(	PUNCT
ejpam-6733	98	4	xy	xy	NOUN
ejpam-6733	98	5	z	z	PROPN
ejpam-6733	99	1	+	+	CCONJ
ejpam-6733	99	2	y	y	PROPN
ejpam-6733	99	3	zx	zx	PROPN
ejpam-6733	99	4	+	+	CCONJ
ejpam-6733	99	5	zxy	zxy	NOUN
ejpam-6733	99	6	)	)	PUNCT
ejpam-6733	99	7	−pq	−pq	PROPN
ejpam-6733	99	8	(	(	PUNCT
ejpam-6733	99	9	xy	xy	NOUN
ejpam-6733	99	10	z	z	PROPN
ejpam-6733	100	1	+	+	CCONJ
ejpam-6733	100	2	y	y	PROPN
ejpam-6733	100	3	zx	zx	PROPN
ejpam-6733	100	4	+	+	CCONJ
ejpam-6733	100	5	zxy	zxy	NOUN
ejpam-6733	101	1	+	+	NOUN
ejpam-6733	101	2	xzy	xzy	NOUN
ejpam-6733	102	1	+	+	CCONJ
ejpam-6733	102	2	y	y	PROPN
ejpam-6733	102	3	xz	xz	PROPN
ejpam-6733	102	4	+	+	CCONJ
ejpam-6733	102	5	zy	zy	PROPN
ejpam-6733	102	6	x)+	x)+	PROPN
ejpam-6733	102	7	q2	q2	PROPN
ejpam-6733	102	8	(	(	PUNCT
ejpam-6733	102	9	xzy	xzy	PROPN
ejpam-6733	103	1	+	+	CCONJ
ejpam-6733	103	2	y	y	PROPN
ejpam-6733	103	3	xz	xz	PROPN
ejpam-6733	104	1	+	+	CCONJ
ejpam-6733	104	2	zy	zy	PROPN
ejpam-6733	104	3	x	x	PROPN
ejpam-6733	104	4	)	)	PUNCT
ejpam-6733	104	5	=	=	SYM
ejpam-6733	104	6	p2	p2	PROPN
ejpam-6733	104	7	(	(	PUNCT
ejpam-6733	104	8	xy	xy	NOUN
ejpam-6733	104	9	z	z	PROPN
ejpam-6733	105	1	+	+	CCONJ
ejpam-6733	105	2	y	y	PROPN
ejpam-6733	105	3	zx	zx	PROPN
ejpam-6733	105	4	+	+	CCONJ
ejpam-6733	105	5	zxy	zxy	NOUN
ejpam-6733	105	6	)	)	PUNCT
ejpam-6733	105	7	−pq	−pq	X
ejpam-6733	105	8	{	{	PUNCT
ejpam-6733	105	9	(	(	PUNCT
ejpam-6733	105	10	xy	xy	NOUN
ejpam-6733	105	11	z	z	PROPN
ejpam-6733	106	1	+	+	CCONJ
ejpam-6733	106	2	y	y	PROPN
ejpam-6733	106	3	zx	zx	PROPN
ejpam-6733	106	4	+	+	CCONJ
ejpam-6733	106	5	zxy	zxy	NOUN
ejpam-6733	106	6	)	)	PUNCT
ejpam-6733	107	1	+	+	CCONJ
ejpam-6733	107	2	(	(	PUNCT
ejpam-6733	107	3	xzy	xzy	PROPN
ejpam-6733	107	4	+	+	CCONJ
ejpam-6733	107	5	y	y	PROPN
ejpam-6733	107	6	xz	xz	PROPN
ejpam-6733	107	7	+	+	CCONJ
ejpam-6733	107	8	zy	zy	X
ejpam-6733	107	9	x)}+	x)}+	DET
ejpam-6733	107	10	q2	q2	NOUN
ejpam-6733	107	11	(	(	PUNCT
ejpam-6733	107	12	xzy	xzy	PROPN
ejpam-6733	108	1	+	+	CCONJ
ejpam-6733	108	2	y	y	PROPN
ejpam-6733	108	3	xz	xz	PROPN
ejpam-6733	109	1	+	+	CCONJ
ejpam-6733	109	2	zy	zy	PROPN
ejpam-6733	109	3	x	x	PROPN
ejpam-6733	109	4	)	)	PUNCT
ejpam-6733	109	5	=	=	SYM
ejpam-6733	109	6	p2	p2	PROPN
ejpam-6733	109	7	(	(	PUNCT
ejpam-6733	109	8	xy	xy	NOUN
ejpam-6733	109	9	z	z	PROPN
ejpam-6733	110	1	+	+	CCONJ
ejpam-6733	110	2	y	y	PROPN
ejpam-6733	110	3	zx	zx	PROPN
ejpam-6733	110	4	+	+	CCONJ
ejpam-6733	110	5	zxy	zxy	NOUN
ejpam-6733	110	6	)	)	PUNCT
ejpam-6733	110	7	−pq	−pq	PROPN
ejpam-6733	110	8	(	(	PUNCT
ejpam-6733	110	9	xy	xy	NOUN
ejpam-6733	110	10	z	z	PROPN
ejpam-6733	111	1	+	+	CCONJ
ejpam-6733	111	2	y	y	PROPN
ejpam-6733	111	3	zx	zx	PROPN
ejpam-6733	111	4	+	+	CCONJ
ejpam-6733	111	5	zxy	zxy	NOUN
ejpam-6733	111	6	)	)	PUNCT
ejpam-6733	111	7	−pq	−pq	PROPN
ejpam-6733	111	8	(	(	PUNCT
ejpam-6733	111	9	xzy	xzy	PROPN
ejpam-6733	112	1	+	+	CCONJ
ejpam-6733	112	2	y	y	PROPN
ejpam-6733	112	3	xz	xz	PROPN
ejpam-6733	112	4	+	+	CCONJ
ejpam-6733	112	5	zy	zy	PROPN
ejpam-6733	112	6	x)+	x)+	PROPN
ejpam-6733	112	7	q2	q2	PROPN
ejpam-6733	112	8	(	(	PUNCT
ejpam-6733	112	9	xzy	xzy	PROPN
ejpam-6733	113	1	+	+	CCONJ
ejpam-6733	113	2	y	y	PROPN
ejpam-6733	113	3	xz	xz	PROPN
ejpam-6733	114	1	+	+	CCONJ
ejpam-6733	114	2	zy	zy	PROPN
ejpam-6733	114	3	x	x	PROPN
ejpam-6733	114	4	)	)	PUNCT
ejpam-6733	114	5	=	=	SYM
ejpam-6733	114	6	(	(	PUNCT
ejpam-6733	114	7	p2	p2	PROPN
ejpam-6733	114	8	−	−	PROPN
ejpam-6733	114	9	pq	pq	NOUN
ejpam-6733	114	10	)	)	PUNCT
ejpam-6733	115	1	(	(	PUNCT
ejpam-6733	115	2	xy	xy	PROPN
ejpam-6733	115	3	z	z	PROPN
ejpam-6733	116	1	+	+	CCONJ
ejpam-6733	116	2	y	y	PROPN
ejpam-6733	116	3	zx	zx	PROPN
ejpam-6733	116	4	+	+	CCONJ
ejpam-6733	116	5	zxy	zxy	NOUN
ejpam-6733	116	6	)	)	PUNCT
ejpam-6733	116	7	−	−	PROPN
ejpam-6733	117	1	(	(	PUNCT
ejpam-6733	117	2	pq	pq	INTJ
ejpam-6733	117	3	−	−	PROPN
ejpam-6733	117	4	q2	q2	NOUN
ejpam-6733	117	5	)	)	PUNCT
ejpam-6733	117	6	(	(	PUNCT
ejpam-6733	117	7	xzy	xzy	X
ejpam-6733	118	1	+	+	CCONJ
ejpam-6733	118	2	y	y	PROPN
ejpam-6733	118	3	xz	xz	PROPN
ejpam-6733	119	1	+	+	CCONJ
ejpam-6733	119	2	zy	zy	PROPN
ejpam-6733	119	3	x	x	PROPN
ejpam-6733	119	4	)	)	PUNCT
ejpam-6733	120	1	=	=	SYM
ejpam-6733	120	2	p	p	NOUN
ejpam-6733	120	3	(	(	PUNCT
ejpam-6733	120	4	p−	p−	NOUN
ejpam-6733	120	5	q	q	NOUN
ejpam-6733	120	6	)	)	PUNCT
ejpam-6733	120	7	(	(	PUNCT
ejpam-6733	120	8	xy	xy	PROPN
ejpam-6733	120	9	z	z	PROPN
ejpam-6733	121	1	+	+	CCONJ
ejpam-6733	121	2	y	y	PROPN
ejpam-6733	121	3	zx	zx	PROPN
ejpam-6733	121	4	+	+	CCONJ
ejpam-6733	121	5	zxy	zxy	X
ejpam-6733	121	6	)	)	PUNCT
ejpam-6733	121	7	−	−	PROPN
ejpam-6733	122	1	q	q	NOUN
ejpam-6733	122	2	(	(	PUNCT
ejpam-6733	122	3	p−	p−	NOUN
ejpam-6733	122	4	q	q	NOUN
ejpam-6733	122	5	)	)	PUNCT
ejpam-6733	122	6	(	(	PUNCT
ejpam-6733	122	7	xzy	xzy	PROPN
ejpam-6733	123	1	+	+	CCONJ
ejpam-6733	123	2	y	y	PROPN
ejpam-6733	123	3	xz	xz	PROPN
ejpam-6733	124	1	+	+	CCONJ
ejpam-6733	124	2	zy	zy	PROPN
ejpam-6733	124	3	x	x	PROPN
ejpam-6733	124	4	)	)	PUNCT
ejpam-6733	125	1	=	=	SYM
ejpam-6733	125	2	(	(	PUNCT
ejpam-6733	125	3	p−	p−	NOUN
ejpam-6733	125	4	q	q	NOUN
ejpam-6733	125	5	)	)	PUNCT
ejpam-6733	126	1	[	[	X
ejpam-6733	126	2	p	p	X
ejpam-6733	126	3	(	(	PUNCT
ejpam-6733	126	4	xy	xy	PROPN
ejpam-6733	126	5	z	z	PROPN
ejpam-6733	126	6	+	+	CCONJ
ejpam-6733	126	7	y	y	PROPN
ejpam-6733	126	8	zx	zx	PROPN
ejpam-6733	126	9	+	+	CCONJ
ejpam-6733	126	10	zxy	zxy	X
ejpam-6733	126	11	)	)	PUNCT
ejpam-6733	126	12	−	−	PROPN
ejpam-6733	127	1	q	q	PROPN
ejpam-6733	127	2	(	(	PUNCT
ejpam-6733	127	3	xzy	xzy	PROPN
ejpam-6733	128	1	+	+	CCONJ
ejpam-6733	128	2	y	y	PROPN
ejpam-6733	128	3	xz	xz	PROPN
ejpam-6733	129	1	+	+	CCONJ
ejpam-6733	129	2	zy	zy	PROPN
ejpam-6733	129	3	x	x	PROPN
ejpam-6733	129	4	)	)	PUNCT
ejpam-6733	129	5	]	]	PUNCT
ejpam-6733	129	6	.	.	PUNCT
ejpam-6733	130	1	part	part	NOUN
ejpam-6733	130	2	(	(	PUNCT
ejpam-6733	130	3	9	9	NUM
ejpam-6733	130	4	)	)	PUNCT
ejpam-6733	130	5	of	of	ADP
ejpam-6733	130	6	theorem	theorem	NOUN
ejpam-6733	130	7	1	1	NUM
ejpam-6733	130	8	is	be	AUX
ejpam-6733	130	9	the	the	DET
ejpam-6733	130	10	jacobi	jacobi	PROPN
ejpam-6733	130	11	identity	identity	NOUN
ejpam-6733	130	12	,	,	PUNCT
ejpam-6733	130	13	where	where	SCONJ
ejpam-6733	130	14	its	its	PRON
ejpam-6733	130	15	right	right	ADJ
ejpam-6733	130	16	-	-	PUNCT
ejpam-6733	130	17	hand	hand	NOUN
ejpam-6733	130	18	side	side	NOUN
ejpam-6733	130	19	should	should	AUX
ejpam-6733	130	20	be	be	AUX
ejpam-6733	130	21	zero	zero	NUM
ejpam-6733	130	22	for	for	ADP
ejpam-6733	130	23	p	p	NOUN
ejpam-6733	130	24	=	=	NOUN
ejpam-6733	130	25	q	q	NOUN
ejpam-6733	130	26	=	=	NOUN
ejpam-6733	130	27	1	1	X
ejpam-6733	130	28	.	.	PUNCT
ejpam-6733	131	1	now	now	ADV
ejpam-6733	131	2	,	,	PUNCT
ejpam-6733	131	3	using	use	VERB
ejpam-6733	131	4	part	part	NOUN
ejpam-6733	131	5	(	(	PUNCT
ejpam-6733	131	6	2	2	NUM
ejpam-6733	131	7	)	)	PUNCT
ejpam-6733	131	8	of	of	ADP
ejpam-6733	131	9	theorem	theorem	NOUN
ejpam-6733	131	10	1	1	NUM
ejpam-6733	131	11	and	and	CCONJ
ejpam-6733	131	12	the	the	DET
ejpam-6733	131	13	fact	fact	NOUN
ejpam-6733	131	14	that	that	SCONJ
ejpam-6733	131	15	k†	k†	X
ejpam-6733	131	16	+	+	CCONJ
ejpam-6733	131	17	=	=	SYM
ejpam-6733	131	18	k−	k−	PROPN
ejpam-6733	131	19	,	,	PUNCT
ejpam-6733	131	20	we	we	PRON
ejpam-6733	131	21	get	get	VERB
ejpam-6733	131	22	the	the	DET
ejpam-6733	131	23	next	next	ADJ
ejpam-6733	131	24	theorem	theorem	PROPN
ejpam-6733	131	25	.	.	PUNCT
ejpam-6733	131	26	theorem	theorem	NOUN
ejpam-6733	131	27	2	2	NUM
ejpam-6733	131	28	.	.	PUNCT
ejpam-6733	132	1	the	the	DET
ejpam-6733	132	2	defining	define	VERB
ejpam-6733	132	3	relations	relation	NOUN
ejpam-6733	132	4	of	of	ADP
ejpam-6733	132	5	lp	lp	NOUN
ejpam-6733	132	6	,	,	PUNCT
ejpam-6733	132	7	q	q	PROPN
ejpam-6733	132	8	can	can	AUX
ejpam-6733	132	9	be	be	AUX
ejpam-6733	132	10	either	either	ADV
ejpam-6733	132	11	:	:	PUNCT
ejpam-6733	133	1	[	[	X
ejpam-6733	133	2	k0,k+]p	k0,k+]p	PROPN
ejpam-6733	133	3	,	,	PUNCT
ejpam-6733	133	4	q	q	NOUN
ejpam-6733	133	5	=	=	SYM
ejpam-6733	133	6	rk+	rk+	NOUN
ejpam-6733	133	7	,	,	PUNCT
ejpam-6733	133	8	and	and	CCONJ
ejpam-6733	133	9	[	[	X
ejpam-6733	133	10	k+,k−]p	k+,k−]p	X
ejpam-6733	133	11	,	,	PUNCT
ejpam-6733	133	12	q	q	PROPN
ejpam-6733	133	13	=	=	SYM
ejpam-6733	133	14	f	f	X
ejpam-6733	133	15	(	(	PUNCT
ejpam-6733	133	16	k0	k0	PROPN
ejpam-6733	133	17	)	)	PUNCT
ejpam-6733	133	18	(	(	PUNCT
ejpam-6733	133	19	7	7	NUM
ejpam-6733	133	20	)	)	PUNCT
ejpam-6733	133	21	or	or	CCONJ
ejpam-6733	133	22	in	in	ADP
ejpam-6733	133	23	its	its	PRON
ejpam-6733	133	24	hermitian	hermitian	ADJ
ejpam-6733	133	25	form	form	NOUN
ejpam-6733	133	26	,	,	PUNCT
ejpam-6733	133	27	[	[	X
ejpam-6733	133	28	k−,k0]p	k−,k0]p	NOUN
ejpam-6733	133	29	,	,	PUNCT
ejpam-6733	133	30	q	q	X
ejpam-6733	133	31	=	=	SYM
ejpam-6733	133	32	rk−	rk−	NOUN
ejpam-6733	133	33	,	,	PUNCT
ejpam-6733	133	34	and	and	CCONJ
ejpam-6733	133	35	[	[	X
ejpam-6733	133	36	k+,k−]p	k+,k−]p	X
ejpam-6733	133	37	,	,	PUNCT
ejpam-6733	133	38	q	q	PROPN
ejpam-6733	133	39	=	=	SYM
ejpam-6733	133	40	f	f	X
ejpam-6733	133	41	(	(	PUNCT
ejpam-6733	133	42	k0	k0	PROPN
ejpam-6733	133	43	)	)	PUNCT
ejpam-6733	133	44	.	.	PUNCT
ejpam-6733	134	1	proof	proof	NOUN
ejpam-6733	134	2	.	.	PUNCT
ejpam-6733	135	1	consider	consider	VERB
ejpam-6733	135	2	the	the	DET
ejpam-6733	135	3	hermitian	hermitian	ADJ
ejpam-6733	135	4	conjugate	conjugate	NOUN
ejpam-6733	135	5	of	of	ADP
ejpam-6733	135	6	(	(	PUNCT
ejpam-6733	135	7	4	4	NUM
ejpam-6733	135	8	)	)	PUNCT
ejpam-6733	135	9	.	.	PUNCT
ejpam-6733	136	1	from	from	ADP
ejpam-6733	136	2	part	part	NOUN
ejpam-6733	136	3	(	(	PUNCT
ejpam-6733	136	4	2	2	NUM
ejpam-6733	136	5	)	)	PUNCT
ejpam-6733	136	6	of	of	ADP
ejpam-6733	136	7	theorem	theorem	NOUN
ejpam-6733	136	8	1	1	NUM
ejpam-6733	136	9	and	and	CCONJ
ejpam-6733	136	10	the	the	DET
ejpam-6733	136	11	facts	fact	NOUN
ejpam-6733	136	12	that	that	SCONJ
ejpam-6733	136	13	k†	k†	X
ejpam-6733	136	14	+	+	CCONJ
ejpam-6733	136	15	=	=	SYM
ejpam-6733	136	16	k−	k−	PROPN
ejpam-6733	136	17	and	and	CCONJ
ejpam-6733	136	18	k†	k†	PROPN
ejpam-6733	136	19	0	0	X
ejpam-6733	136	20	=	=	SYM
ejpam-6733	136	21	k0	k0	PROPN
ejpam-6733	136	22	,	,	PUNCT
ejpam-6733	136	23	we	we	PRON
ejpam-6733	136	24	have	have	VERB
ejpam-6733	136	25	(	(	PUNCT
ejpam-6733	136	26	[	[	X
ejpam-6733	136	27	k0,k+]p	k0,k+]p	PROPN
ejpam-6733	136	28	,	,	PUNCT
ejpam-6733	136	29	q	q	NOUN
ejpam-6733	136	30	)	)	PUNCT
ejpam-6733	136	31	†	†	NOUN
ejpam-6733	136	32	=	=	PUNCT
ejpam-6733	137	1	[	[	PUNCT
ejpam-6733	137	2	k†	k†	X
ejpam-6733	137	3	+	+	PROPN
ejpam-6733	137	4	,	,	PUNCT
ejpam-6733	137	5	k	k	PROPN
ejpam-6733	137	6	†	†	PROPN
ejpam-6733	137	7	0	0	PUNCT
ejpam-6733	137	8	]	]	X
ejpam-6733	138	1	p	p	X
ejpam-6733	138	2	,	,	PUNCT
ejpam-6733	138	3	q	q	NOUN
ejpam-6733	138	4	=	=	PUNCT
ejpam-6733	138	5	[	[	PUNCT
ejpam-6733	138	6	k†	k†	X
ejpam-6733	138	7	−,k0	−,k0	X
ejpam-6733	138	8	]	]	PUNCT
ejpam-6733	139	1	p	p	X
ejpam-6733	139	2	,	,	PUNCT
ejpam-6733	139	3	q	q	NOUN
ejpam-6733	139	4	=	=	PUNCT
ejpam-6733	139	5	(	(	PUNCT
ejpam-6733	139	6	rk+	rk+	NOUN
ejpam-6733	139	7	)	)	PUNCT
ejpam-6733	139	8	†	†	NOUN
ejpam-6733	140	1	=	=	PUNCT
ejpam-6733	140	2	rk−.	rk−.	PROPN
ejpam-6733	141	1	so	so	ADV
ejpam-6733	141	2	,	,	PUNCT
ejpam-6733	141	3	we	we	PRON
ejpam-6733	141	4	have	have	VERB
ejpam-6733	141	5	the	the	DET
ejpam-6733	141	6	second	second	ADJ
ejpam-6733	141	7	defining	define	VERB
ejpam-6733	141	8	relation	relation	NOUN
ejpam-6733	141	9	of	of	ADP
ejpam-6733	141	10	lp	lp	NOUN
ejpam-6733	141	11	,	,	PUNCT
ejpam-6733	141	12	q	q	NOUN
ejpam-6733	141	13	,	,	PUNCT
ejpam-6733	141	14	(	(	PUNCT
ejpam-6733	141	15	5	5	NUM
ejpam-6733	141	16	)	)	PUNCT
ejpam-6733	141	17	.	.	PUNCT
ejpam-6733	142	1	alternatively	alternatively	ADV
ejpam-6733	142	2	,	,	PUNCT
ejpam-6733	142	3	(	(	PUNCT
ejpam-6733	142	4	4	4	X
ejpam-6733	142	5	)	)	PUNCT
ejpam-6733	142	6	is	be	AUX
ejpam-6733	142	7	actually	actually	ADV
ejpam-6733	142	8	the	the	DET
ejpam-6733	142	9	hermitian	hermitian	ADJ
ejpam-6733	142	10	conjugate	conjugate	NOUN
ejpam-6733	142	11	of	of	ADP
ejpam-6733	142	12	(	(	PUNCT
ejpam-6733	142	13	5	5	NUM
ejpam-6733	142	14	)	)	PUNCT
ejpam-6733	142	15	.	.	PUNCT
ejpam-6733	143	1	l.	l.	PROPN
ejpam-6733	143	2	a	a	DET
ejpam-6733	143	3	-	-	PUNCT
ejpam-6733	143	4	m.	m.	NOUN
ejpam-6733	143	5	hanna	hanna	NOUN
ejpam-6733	143	6	,	,	PUNCT
ejpam-6733	143	7	s.	s.	PROPN
ejpam-6733	143	8	s.	s.	PROPN
ejpam-6733	143	9	hassan	hassan	PROPN
ejpam-6733	143	10	,	,	PUNCT
ejpam-6733	143	11	m.	m.	NOUN
ejpam-6733	143	12	almutairi	almutairi	PROPN
ejpam-6733	143	13	/	/	SYM
ejpam-6733	143	14	eur	eur	PROPN
ejpam-6733	143	15	.	.	PUNCT
ejpam-6733	144	1	j.	j.	PROPN
ejpam-6733	144	2	pure	pure	PROPN
ejpam-6733	144	3	appl	appl	PROPN
ejpam-6733	144	4	.	.	PROPN
ejpam-6733	144	5	math	math	PROPN
ejpam-6733	144	6	,	,	PUNCT
ejpam-6733	144	7	18	18	NUM
ejpam-6733	144	8	(	(	PUNCT
ejpam-6733	144	9	4	4	NUM
ejpam-6733	144	10	)	)	PUNCT
ejpam-6733	144	11	(	(	PUNCT
ejpam-6733	144	12	2025	2025	NUM
ejpam-6733	144	13	)	)	PUNCT
ejpam-6733	144	14	,	,	PUNCT
ejpam-6733	144	15	6733	6733	NUM
ejpam-6733	144	16	5	5	NUM
ejpam-6733	144	17	of	of	ADP
ejpam-6733	144	18	12	12	NUM
ejpam-6733	144	19	4	4	NUM
ejpam-6733	144	20	.	.	PUNCT
ejpam-6733	145	1	faithful	faithful	ADJ
ejpam-6733	145	2	representations	representation	NOUN
ejpam-6733	145	3	of	of	ADP
ejpam-6733	145	4	lp	lp	NOUN
ejpam-6733	145	5	,	,	PUNCT
ejpam-6733	145	6	q	q	PUNCT
ejpam-6733	145	7	some	some	DET
ejpam-6733	145	8	basic	basic	ADJ
ejpam-6733	145	9	and	and	CCONJ
ejpam-6733	145	10	necessary	necessary	ADJ
ejpam-6733	145	11	definitions	definition	NOUN
ejpam-6733	145	12	are	be	AUX
ejpam-6733	145	13	presented	present	VERB
ejpam-6733	145	14	at	at	ADP
ejpam-6733	145	15	the	the	DET
ejpam-6733	145	16	beginning	beginning	NOUN
ejpam-6733	145	17	of	of	ADP
ejpam-6733	145	18	this	this	DET
ejpam-6733	145	19	section	section	NOUN
ejpam-6733	145	20	.	.	PUNCT
ejpam-6733	146	1	definition	definition	NOUN
ejpam-6733	146	2	2	2	NUM
ejpam-6733	146	3	.	.	PUNCT
ejpam-6733	147	1	let	let	VERB
ejpam-6733	147	2	k	k	PRON
ejpam-6733	147	3	be	be	AUX
ejpam-6733	147	4	a	a	DET
ejpam-6733	147	5	field	field	NOUN
ejpam-6733	147	6	and	and	CCONJ
ejpam-6733	147	7	mn	mn	PROPN
ejpam-6733	147	8	(	(	PUNCT
ejpam-6733	147	9	k	k	NOUN
ejpam-6733	147	10	)	)	PUNCT
ejpam-6733	147	11	be	be	VERB
ejpam-6733	147	12	the	the	DET
ejpam-6733	147	13	set	set	NOUN
ejpam-6733	147	14	of	of	ADP
ejpam-6733	147	15	all	all	DET
ejpam-6733	147	16	n	n	PRON
ejpam-6733	147	17	×	×	NOUN
ejpam-6733	147	18	n	n	PRON
ejpam-6733	147	19	matrices	matrix	NOUN
ejpam-6733	147	20	of	of	ADP
ejpam-6733	147	21	entries	entry	NOUN
ejpam-6733	147	22	from	from	ADP
ejpam-6733	147	23	k.	k.	PROPN
ejpam-6733	147	24	a	a	DET
ejpam-6733	147	25	matrix	matrix	NOUN
ejpam-6733	147	26	representation	representation	NOUN
ejpam-6733	147	27	of	of	ADP
ejpam-6733	147	28	the	the	DET
ejpam-6733	147	29	degree	degree	NOUN
ejpam-6733	147	30	n	n	PROPN
ejpam-6733	147	31	of	of	ADP
ejpam-6733	147	32	the	the	DET
ejpam-6733	147	33	(	(	PUNCT
ejpam-6733	147	34	p	p	X
ejpam-6733	147	35	,	,	PUNCT
ejpam-6733	147	36	q)-deformed	q)-deformed	ADJ
ejpam-6733	147	37	lie	lie	NOUN
ejpam-6733	147	38	algebra	algebra	NOUN
ejpam-6733	147	39	,	,	PUNCT
ejpam-6733	147	40	lp	lp	PROPN
ejpam-6733	147	41	,	,	PUNCT
ejpam-6733	147	42	q	q	ADJ
ejpam-6733	147	43	,	,	PUNCT
ejpam-6733	147	44	is	be	AUX
ejpam-6733	147	45	a	a	DET
ejpam-6733	147	46	mapping	mapping	NOUN
ejpam-6733	147	47	ρ	ρ	NOUN
ejpam-6733	147	48	:	:	PUNCT
ejpam-6733	148	1	lp	lp	ADJ
ejpam-6733	148	2	,	,	PUNCT
ejpam-6733	148	3	q	q	PROPN
ejpam-6733	148	4	→	→	SYM
ejpam-6733	148	5	mn	mn	PROPN
ejpam-6733	148	6	(	(	PUNCT
ejpam-6733	148	7	k	k	NOUN
ejpam-6733	148	8	)	)	PUNCT
ejpam-6733	148	9	satisfying	satisfy	VERB
ejpam-6733	148	10	the	the	DET
ejpam-6733	148	11	following	follow	VERB
ejpam-6733	148	12	properties	property	NOUN
ejpam-6733	148	13	,	,	PUNCT
ejpam-6733	148	14	for	for	ADP
ejpam-6733	148	15	all	all	DET
ejpam-6733	148	16	u	u	NOUN
ejpam-6733	148	17	and	and	CCONJ
ejpam-6733	148	18	v	v	NOUN
ejpam-6733	148	19	in	in	ADP
ejpam-6733	148	20	lp	lp	NOUN
ejpam-6733	148	21	,	,	PUNCT
ejpam-6733	148	22	q	q	NOUN
ejpam-6733	148	23	and	and	CCONJ
ejpam-6733	148	24	all	all	DET
ejpam-6733	148	25	α	α	NOUN
ejpam-6733	148	26	and	and	CCONJ
ejpam-6733	148	27	β	β	X
ejpam-6733	148	28	in	in	ADP
ejpam-6733	148	29	k	k	NOUN
ejpam-6733	148	30	:	:	PUNCT
ejpam-6733	148	31	(	(	PUNCT
ejpam-6733	148	32	i	i	NOUN
ejpam-6733	148	33	)	)	PUNCT
ejpam-6733	148	34	ρ	ρ	PROPN
ejpam-6733	148	35	(	(	PUNCT
ejpam-6733	148	36	u+	u+	NOUN
ejpam-6733	148	37	v	v	NOUN
ejpam-6733	148	38	)	)	PUNCT
ejpam-6733	148	39	=	=	SYM
ejpam-6733	148	40	ρ	ρ	PROPN
ejpam-6733	148	41	(	(	PUNCT
ejpam-6733	148	42	u	u	NOUN
ejpam-6733	148	43	)	)	PUNCT
ejpam-6733	148	44	+	+	CCONJ
ejpam-6733	148	45	ρ	ρ	PROPN
ejpam-6733	148	46	(	(	PUNCT
ejpam-6733	148	47	v	v	NOUN
ejpam-6733	148	48	)	)	PUNCT
ejpam-6733	148	49	,	,	PUNCT
ejpam-6733	148	50	(	(	PUNCT
ejpam-6733	148	51	ii	ii	NOUN
ejpam-6733	148	52	)	)	PUNCT
ejpam-6733	148	53	ρ	ρ	PROPN
ejpam-6733	148	54	(	(	PUNCT
ejpam-6733	148	55	uv	uv	NOUN
ejpam-6733	148	56	)	)	PUNCT
ejpam-6733	148	57	=	=	SYM
ejpam-6733	148	58	ρ	ρ	PROPN
ejpam-6733	148	59	(	(	PUNCT
ejpam-6733	148	60	u	u	NOUN
ejpam-6733	148	61	)	)	PUNCT
ejpam-6733	148	62	ρ	ρ	PROPN
ejpam-6733	148	63	(	(	PUNCT
ejpam-6733	148	64	v	v	NOUN
ejpam-6733	148	65	)	)	PUNCT
ejpam-6733	148	66	,	,	PUNCT
ejpam-6733	148	67	(	(	PUNCT
ejpam-6733	148	68	iii	iii	X
ejpam-6733	148	69	)	)	PUNCT
ejpam-6733	148	70	ρ	ρ	PROPN
ejpam-6733	148	71	(	(	PUNCT
ejpam-6733	148	72	αu	αu	NOUN
ejpam-6733	148	73	)	)	PUNCT
ejpam-6733	148	74	=	=	SYM
ejpam-6733	148	75	αρ	αρ	PROPN
ejpam-6733	148	76	(	(	PUNCT
ejpam-6733	148	77	v	v	NOUN
ejpam-6733	148	78	)	)	PUNCT
ejpam-6733	148	79	,	,	PUNCT
ejpam-6733	148	80	and	and	CCONJ
ejpam-6733	148	81	(	(	PUNCT
ejpam-6733	148	82	iv	iv	X
ejpam-6733	148	83	)	)	PUNCT
ejpam-6733	148	84	ρ	ρ	NOUN
ejpam-6733	148	85	(	(	PUNCT
ejpam-6733	148	86	[	[	X
ejpam-6733	148	87	u	u	NOUN
ejpam-6733	148	88	,	,	PUNCT
ejpam-6733	148	89	v]p	v]p	NOUN
ejpam-6733	148	90	,	,	PUNCT
ejpam-6733	148	91	q	q	NOUN
ejpam-6733	148	92	)	)	PUNCT
ejpam-6733	148	93	=	=	SYM
ejpam-6733	148	94	pρ	pρ	X
ejpam-6733	148	95	(	(	PUNCT
ejpam-6733	148	96	uv)−	uv)−	NOUN
ejpam-6733	148	97	qρ	qρ	NOUN
ejpam-6733	148	98	(	(	PUNCT
ejpam-6733	148	99	vu	vu	PROPN
ejpam-6733	148	100	)	)	PUNCT
ejpam-6733	148	101	.	.	PUNCT
ejpam-6733	149	1	the	the	DET
ejpam-6733	149	2	matrix	matrix	NOUN
ejpam-6733	149	3	ρ	ρ	PROPN
ejpam-6733	149	4	(	(	PUNCT
ejpam-6733	149	5	u	u	NOUN
ejpam-6733	149	6	)	)	PUNCT
ejpam-6733	149	7	is	be	AUX
ejpam-6733	149	8	called	call	VERB
ejpam-6733	149	9	the	the	DET
ejpam-6733	149	10	representation	representation	NOUN
ejpam-6733	149	11	matrix	matrix	NOUN
ejpam-6733	149	12	of	of	ADP
ejpam-6733	149	13	u	u	PROPN
ejpam-6733	149	14	in	in	ADP
ejpam-6733	149	15	lp	lp	PROPN
ejpam-6733	149	16	,	,	PUNCT
ejpam-6733	149	17	q.	q.	PROPN
ejpam-6733	149	18	if	if	SCONJ
ejpam-6733	149	19	ρ	ρ	PROPN
ejpam-6733	149	20	is	be	AUX
ejpam-6733	149	21	a	a	DET
ejpam-6733	149	22	one	one	NUM
ejpam-6733	149	23	-	-	PUNCT
ejpam-6733	149	24	to	to	ADP
ejpam-6733	149	25	-	-	PUNCT
ejpam-6733	149	26	one	one	NUM
ejpam-6733	149	27	mapping	mapping	NOUN
ejpam-6733	149	28	,	,	PUNCT
ejpam-6733	149	29	then	then	ADV
ejpam-6733	149	30	the	the	DET
ejpam-6733	149	31	representation	representation	NOUN
ejpam-6733	149	32	is	be	AUX
ejpam-6733	149	33	said	say	VERB
ejpam-6733	149	34	to	to	PART
ejpam-6733	149	35	be	be	AUX
ejpam-6733	149	36	faithful	faithful	ADJ
ejpam-6733	149	37	.	.	PUNCT
ejpam-6733	150	1	it	it	PRON
ejpam-6733	150	2	can	can	AUX
ejpam-6733	150	3	be	be	AUX
ejpam-6733	150	4	shown	show	VERB
ejpam-6733	150	5	that	that	SCONJ
ejpam-6733	150	6	the	the	DET
ejpam-6733	150	7	representation	representation	NOUN
ejpam-6733	150	8	matrices	matrix	NOUN
ejpam-6733	150	9	of	of	ADP
ejpam-6733	150	10	a	a	DET
ejpam-6733	150	11	linearly	linearly	ADV
ejpam-6733	150	12	independent	independent	ADJ
ejpam-6733	150	13	set	set	NOUN
ejpam-6733	150	14	of	of	ADP
ejpam-6733	150	15	elements	element	NOUN
ejpam-6733	150	16	in	in	ADP
ejpam-6733	150	17	lp	lp	NOUN
ejpam-6733	150	18	,	,	PUNCT
ejpam-6733	150	19	q	q	PUNCT
ejpam-6733	150	20	are	be	AUX
ejpam-6733	150	21	linearly	linearly	ADV
ejpam-6733	150	22	independent	independent	ADJ
ejpam-6733	150	23	.	.	PUNCT
ejpam-6733	151	1	here	here	ADV
ejpam-6733	151	2	,	,	PUNCT
ejpam-6733	151	3	we	we	PRON
ejpam-6733	151	4	assume	assume	VERB
ejpam-6733	151	5	that	that	SCONJ
ejpam-6733	151	6	a	a	DET
ejpam-6733	151	7	,	,	PUNCT
ejpam-6733	151	8	b	b	NOUN
ejpam-6733	151	9	,	,	PUNCT
ejpam-6733	151	10	and	and	CCONJ
ejpam-6733	151	11	c	c	PROPN
ejpam-6733	151	12	are	be	AUX
ejpam-6733	151	13	representation	representation	NOUN
ejpam-6733	151	14	matrices	matrix	NOUN
ejpam-6733	151	15	for	for	ADP
ejpam-6733	151	16	the	the	DET
ejpam-6733	151	17	generators	generator	NOUN
ejpam-6733	151	18	of	of	ADP
ejpam-6733	151	19	lp	lp	NOUN
ejpam-6733	151	20	,	,	PUNCT
ejpam-6733	151	21	q	q	NOUN
ejpam-6733	151	22	,	,	PUNCT
ejpam-6733	151	23	namely	namely	ADV
ejpam-6733	151	24	,	,	PUNCT
ejpam-6733	151	25	k+,k−	k+,k−	PROPN
ejpam-6733	151	26	,	,	PUNCT
ejpam-6733	151	27	and	and	CCONJ
ejpam-6733	151	28	k0	k0	PROPN
ejpam-6733	151	29	,	,	PUNCT
ejpam-6733	151	30	respectively	respectively	ADV
ejpam-6733	151	31	.	.	PUNCT
ejpam-6733	152	1	all	all	DET
ejpam-6733	152	2	representations	representation	NOUN
ejpam-6733	152	3	under	under	ADP
ejpam-6733	152	4	consideration	consideration	NOUN
ejpam-6733	152	5	are	be	AUX
ejpam-6733	152	6	supposed	suppose	VERB
ejpam-6733	152	7	to	to	PART
ejpam-6733	152	8	satisfy	satisfy	VERB
ejpam-6733	152	9	the	the	DET
ejpam-6733	152	10	physical	physical	ADJ
ejpam-6733	152	11	properties	property	NOUN
ejpam-6733	152	12	:	:	PUNCT
ejpam-6733	152	13	b	b	X
ejpam-6733	152	14	=	=	SYM
ejpam-6733	152	15	a†	a†	PROPN
ejpam-6733	152	16	,	,	PUNCT
ejpam-6733	152	17	and	and	CCONJ
ejpam-6733	152	18	c	c	NOUN
ejpam-6733	152	19	is	be	AUX
ejpam-6733	152	20	a	a	DET
ejpam-6733	152	21	real	real	ADJ
ejpam-6733	152	22	diagonal	diagonal	ADJ
ejpam-6733	152	23	matrix	matrix	NOUN
ejpam-6733	152	24	.	.	PUNCT
ejpam-6733	153	1	also	also	ADV
ejpam-6733	153	2	,	,	PUNCT
ejpam-6733	153	3	p	p	X
ejpam-6733	153	4	,	,	PUNCT
ejpam-6733	153	5	q	q	ADJ
ejpam-6733	153	6	,	,	PUNCT
ejpam-6733	153	7	r	r	NOUN
ejpam-6733	153	8	∈	∈	PROPN
ejpam-6733	153	9	r∗	r∗	NOUN
ejpam-6733	153	10	and	and	CCONJ
ejpam-6733	153	11	f	f	PROPN
ejpam-6733	153	12	(	(	PUNCT
ejpam-6733	153	13	x	x	X
ejpam-6733	153	14	)	)	PUNCT
ejpam-6733	153	15	is	be	AUX
ejpam-6733	153	16	a	a	DET
ejpam-6733	153	17	polynomial	polynomial	ADJ
ejpam-6733	153	18	function	function	NOUN
ejpam-6733	153	19	in	in	ADP
ejpam-6733	153	20	r	r	NOUN
ejpam-6733	153	21	[	[	X
ejpam-6733	153	22	x	x	X
ejpam-6733	153	23	]	]	X
ejpam-6733	153	24	.	.	PUNCT
ejpam-6733	154	1	faithful	faithful	ADJ
ejpam-6733	154	2	matrix	matrix	NOUN
ejpam-6733	154	3	representations	representation	NOUN
ejpam-6733	154	4	of	of	ADP
ejpam-6733	154	5	lp	lp	NOUN
ejpam-6733	154	6	,	,	PUNCT
ejpam-6733	154	7	q	q	NOUN
ejpam-6733	154	8	of	of	ADP
ejpam-6733	154	9	the	the	DET
ejpam-6733	154	10	least	least	ADJ
ejpam-6733	154	11	degree	degree	NOUN
ejpam-6733	154	12	are	be	AUX
ejpam-6733	154	13	the	the	DET
ejpam-6733	154	14	main	main	ADJ
ejpam-6733	154	15	purpose	purpose	NOUN
ejpam-6733	154	16	of	of	ADP
ejpam-6733	154	17	this	this	DET
ejpam-6733	154	18	work	work	NOUN
ejpam-6733	154	19	.	.	PUNCT
ejpam-6733	155	1	mind	mind	NOUN
ejpam-6733	155	2	that	that	SCONJ
ejpam-6733	155	3	the	the	DET
ejpam-6733	155	4	representation	representation	NOUN
ejpam-6733	155	5	matrices	matrice	VERB
ejpam-6733	155	6	a	a	DET
ejpam-6733	155	7	,	,	PUNCT
ejpam-6733	155	8	b	b	NOUN
ejpam-6733	155	9	,	,	PUNCT
ejpam-6733	155	10	and	and	CCONJ
ejpam-6733	155	11	c	c	PROPN
ejpam-6733	155	12	are	be	AUX
ejpam-6733	155	13	supposed	suppose	VERB
ejpam-6733	155	14	to	to	PART
ejpam-6733	155	15	be	be	AUX
ejpam-6733	155	16	linearly	linearly	ADV
ejpam-6733	155	17	independent	independent	ADJ
ejpam-6733	155	18	in	in	ADP
ejpam-6733	155	19	the	the	DET
ejpam-6733	155	20	case	case	NOUN
ejpam-6733	155	21	of	of	ADP
ejpam-6733	155	22	faithful	faithful	ADJ
ejpam-6733	155	23	representations	representation	NOUN
ejpam-6733	155	24	.	.	PUNCT
ejpam-6733	156	1	also	also	ADV
ejpam-6733	156	2	,	,	PUNCT
ejpam-6733	156	3	we	we	PRON
ejpam-6733	156	4	use	use	VERB
ejpam-6733	156	5	0	0	NUM
ejpam-6733	156	6	for	for	ADP
ejpam-6733	156	7	the	the	DET
ejpam-6733	156	8	zero	zero	NUM
ejpam-6733	156	9	matrix	matrix	NOUN
ejpam-6733	156	10	of	of	ADP
ejpam-6733	156	11	appropriate	appropriate	ADJ
ejpam-6733	156	12	size	size	NOUN
ejpam-6733	156	13	,	,	PUNCT
ejpam-6733	156	14	and	and	CCONJ
ejpam-6733	156	15	o	o	X
ejpam-6733	156	16	for	for	ADP
ejpam-6733	156	17	the	the	DET
ejpam-6733	156	18	zero	zero	NUM
ejpam-6733	156	19	element	element	NOUN
ejpam-6733	156	20	of	of	ADP
ejpam-6733	156	21	lp	lp	NOUN
ejpam-6733	156	22	,	,	PUNCT
ejpam-6733	156	23	q.	q.	NOUN
ejpam-6733	156	24	for	for	ADP
ejpam-6733	156	25	a	a	DET
ejpam-6733	156	26	representation	representation	NOUN
ejpam-6733	156	27	of	of	ADP
ejpam-6733	156	28	degree	degree	NOUN
ejpam-6733	156	29	n	n	CCONJ
ejpam-6733	156	30	,	,	PUNCT
ejpam-6733	156	31	the	the	DET
ejpam-6733	156	32	following	follow	VERB
ejpam-6733	156	33	equations	equation	NOUN
ejpam-6733	156	34	(	(	PUNCT
ejpam-6733	156	35	8)-(12	8)-(12	NUM
ejpam-6733	156	36	)	)	PUNCT
ejpam-6733	156	37	are	be	AUX
ejpam-6733	156	38	necessary	necessary	ADJ
ejpam-6733	156	39	relations	relation	NOUN
ejpam-6733	156	40	for	for	ADP
ejpam-6733	156	41	a	a	DET
ejpam-6733	156	42	,	,	PUNCT
ejpam-6733	156	43	b	b	NOUN
ejpam-6733	156	44	,	,	PUNCT
ejpam-6733	156	45	and	and	CCONJ
ejpam-6733	156	46	c	c	X
ejpam-6733	156	47	,	,	PUNCT
ejpam-6733	156	48	which	which	PRON
ejpam-6733	156	49	are	be	AUX
ejpam-6733	156	50	obtained	obtain	VERB
ejpam-6733	156	51	from	from	ADP
ejpam-6733	156	52	(	(	PUNCT
ejpam-6733	156	53	4	4	NUM
ejpam-6733	156	54	)	)	PUNCT
ejpam-6733	156	55	and	and	CCONJ
ejpam-6733	156	56	(	(	PUNCT
ejpam-6733	156	57	6	6	NUM
ejpam-6733	156	58	)	)	PUNCT
ejpam-6733	156	59	,	,	PUNCT
ejpam-6733	156	60	respectively	respectively	ADV
ejpam-6733	156	61	.	.	PUNCT
ejpam-6733	157	1	for	for	ADP
ejpam-6733	157	2	i	i	PROPN
ejpam-6733	157	3	,	,	PUNCT
ejpam-6733	157	4	j	j	PROPN
ejpam-6733	157	5	=	=	SYM
ejpam-6733	157	6	1	1	NUM
ejpam-6733	157	7	,	,	PUNCT
ejpam-6733	157	8	2	2	NUM
ejpam-6733	157	9	,	,	PUNCT
ejpam-6733	157	10	...	...	PUNCT
ejpam-6733	157	11	,	,	PUNCT
ejpam-6733	157	12	n	n	CCONJ
ejpam-6733	157	13	,	,	PUNCT
ejpam-6733	157	14	we	we	PRON
ejpam-6733	157	15	have	have	VERB
ejpam-6733	157	16	[	[	X
ejpam-6733	157	17	r	r	X
ejpam-6733	157	18	−	−	PROPN
ejpam-6733	157	19	(	(	PUNCT
ejpam-6733	157	20	pcii	pcii	ADJ
ejpam-6733	157	21	−	−	PROPN
ejpam-6733	157	22	qcjj	qcjj	NOUN
ejpam-6733	157	23	)	)	PUNCT
ejpam-6733	157	24	]	]	PUNCT
ejpam-6733	157	25	aij	aij	PROPN
ejpam-6733	157	26	=	=	SYM
ejpam-6733	157	27	0	0	PROPN
ejpam-6733	157	28	for	for	ADP
ejpam-6733	157	29	i	i	PROPN
ejpam-6733	157	30	6=	6=	PROPN
ejpam-6733	157	31	j	j	PROPN
ejpam-6733	157	32	,	,	PUNCT
ejpam-6733	157	33	(	(	PUNCT
ejpam-6733	157	34	8)	8)	NUM
ejpam-6733	157	35	aii	aii	NOUN
ejpam-6733	158	1	[	[	X
ejpam-6733	158	2	r	r	NOUN
ejpam-6733	158	3	−	−	PROPN
ejpam-6733	158	4	(	(	PUNCT
ejpam-6733	158	5	p−	p−	NOUN
ejpam-6733	158	6	q	q	NOUN
ejpam-6733	158	7	)	)	PUNCT
ejpam-6733	158	8	cii	cii	X
ejpam-6733	158	9	]	]	X
ejpam-6733	158	10	=	=	SYM
ejpam-6733	158	11	0	0	NUM
ejpam-6733	158	12	,	,	PUNCT
ejpam-6733	158	13	(	(	PUNCT
ejpam-6733	158	14	9	9	NUM
ejpam-6733	158	15	)	)	PUNCT
ejpam-6733	158	16	and	and	CCONJ
ejpam-6733	158	17	∑n	∑n	PROPN
ejpam-6733	158	18	t=1	t=1	PROPN
ejpam-6733	158	19	(	(	PUNCT
ejpam-6733	158	20	paitājt	paitājt	ADP
ejpam-6733	158	21	−	−	PROPN
ejpam-6733	158	22	qatj	qatj	PROPN
ejpam-6733	158	23	āti	āti	PROPN
ejpam-6733	158	24	)	)	PUNCT
ejpam-6733	159	1	=	=	PUNCT
ejpam-6733	159	2	0	0	PUNCT
ejpam-6733	160	1	for	for	ADP
ejpam-6733	160	2	i	i	PROPN
ejpam-6733	160	3	6=	6=	PROPN
ejpam-6733	160	4	j	j	PROPN
ejpam-6733	160	5	,	,	PUNCT
ejpam-6733	160	6	(	(	PUNCT
ejpam-6733	160	7	10)∑n	10)∑n	NUM
ejpam-6733	160	8	t=1	t=1	ADV
ejpam-6733	160	9	(	(	PUNCT
ejpam-6733	160	10	p	p	X
ejpam-6733	160	11	|ait|2	|ait|2	X
ejpam-6733	160	12	−	−	PROPN
ejpam-6733	160	13	q	q	NOUN
ejpam-6733	160	14	|ati|2	|ati|2	NOUN
ejpam-6733	160	15	)	)	PUNCT
ejpam-6733	161	1	=	=	SYM
ejpam-6733	161	2	f	f	PROPN
ejpam-6733	161	3	(	(	PUNCT
ejpam-6733	161	4	cii	cii	PROPN
ejpam-6733	161	5	)	)	PUNCT
ejpam-6733	161	6	,	,	PUNCT
ejpam-6733	161	7	(	(	PUNCT
ejpam-6733	161	8	11	11	NUM
ejpam-6733	161	9	)	)	PUNCT
ejpam-6733	161	10	(	(	PUNCT
ejpam-6733	161	11	p−	p−	NOUN
ejpam-6733	161	12	q	q	NOUN
ejpam-6733	161	13	)	)	PUNCT
ejpam-6733	161	14	∑n	∑n	PROPN
ejpam-6733	161	15	i=1	i=1	PROPN
ejpam-6733	161	16	∑n	∑n	PROPN
ejpam-6733	161	17	t=1	t=1	ADV
ejpam-6733	161	18	|ait|2	|ait|2	X
ejpam-6733	161	19	=	=	PUNCT
ejpam-6733	162	1	∑n	∑n	PROPN
ejpam-6733	162	2	i=1	i=1	PROPN
ejpam-6733	162	3	f	f	PROPN
ejpam-6733	162	4	(	(	PUNCT
ejpam-6733	162	5	cii	cii	PROPN
ejpam-6733	162	6	)	)	PUNCT
ejpam-6733	162	7	.	.	PUNCT
ejpam-6733	163	1	(	(	PUNCT
ejpam-6733	163	2	12	12	NUM
ejpam-6733	163	3	)	)	PUNCT
ejpam-6733	163	4	l.	l.	PROPN
ejpam-6733	163	5	a	a	PROPN
ejpam-6733	163	6	-	-	PUNCT
ejpam-6733	163	7	m.	m.	NOUN
ejpam-6733	163	8	hanna	hanna	NOUN
ejpam-6733	163	9	,	,	PUNCT
ejpam-6733	163	10	s.	s.	PROPN
ejpam-6733	163	11	s.	s.	PROPN
ejpam-6733	163	12	hassan	hassan	PROPN
ejpam-6733	163	13	,	,	PUNCT
ejpam-6733	163	14	m.	m.	NOUN
ejpam-6733	163	15	almutairi	almutairi	PROPN
ejpam-6733	163	16	/	/	SYM
ejpam-6733	163	17	eur	eur	PROPN
ejpam-6733	163	18	.	.	PUNCT
ejpam-6733	164	1	j.	j.	PROPN
ejpam-6733	164	2	pure	pure	PROPN
ejpam-6733	164	3	appl	appl	PROPN
ejpam-6733	164	4	.	.	PROPN
ejpam-6733	164	5	math	math	PROPN
ejpam-6733	164	6	,	,	PUNCT
ejpam-6733	164	7	18	18	NUM
ejpam-6733	164	8	(	(	PUNCT
ejpam-6733	164	9	4	4	NUM
ejpam-6733	164	10	)	)	PUNCT
ejpam-6733	164	11	(	(	PUNCT
ejpam-6733	164	12	2025	2025	NUM
ejpam-6733	164	13	)	)	PUNCT
ejpam-6733	164	14	,	,	PUNCT
ejpam-6733	164	15	6733	6733	NUM
ejpam-6733	164	16	6	6	NUM
ejpam-6733	164	17	of	of	ADP
ejpam-6733	164	18	12	12	NUM
ejpam-6733	164	19	5	5	NUM
ejpam-6733	164	20	.	.	PUNCT
ejpam-6733	165	1	faithful	faithful	ADJ
ejpam-6733	165	2	matrix	matrix	NOUN
ejpam-6733	165	3	representations	representation	NOUN
ejpam-6733	165	4	of	of	ADP
ejpam-6733	165	5	lp	lp	NOUN
ejpam-6733	165	6	,	,	PUNCT
ejpam-6733	165	7	q	q	NOUN
ejpam-6733	165	8	since	since	SCONJ
ejpam-6733	165	9	lp	lp	NOUN
ejpam-6733	165	10	,	,	PUNCT
ejpam-6733	165	11	q	q	PUNCT
ejpam-6733	165	12	is	be	AUX
ejpam-6733	165	13	generated	generate	VERB
ejpam-6733	165	14	by	by	ADP
ejpam-6733	165	15	3	3	NUM
ejpam-6733	165	16	generators	generator	NOUN
ejpam-6733	165	17	,	,	PUNCT
ejpam-6733	165	18	namely	namely	ADV
ejpam-6733	165	19	,	,	PUNCT
ejpam-6733	165	20	k±	k±	PROPN
ejpam-6733	165	21	and	and	CCONJ
ejpam-6733	165	22	k0	k0	PROPN
ejpam-6733	165	23	,	,	PUNCT
ejpam-6733	165	24	then	then	ADV
ejpam-6733	165	25	the	the	DET
ejpam-6733	165	26	least	least	ADV
ejpam-6733	165	27	possible	possible	ADJ
ejpam-6733	165	28	degree	degree	NOUN
ejpam-6733	165	29	of	of	ADP
ejpam-6733	165	30	a	a	DET
ejpam-6733	165	31	faithful	faithful	ADJ
ejpam-6733	165	32	matrix	matrix	NOUN
ejpam-6733	165	33	representation	representation	NOUN
ejpam-6733	165	34	is	be	AUX
ejpam-6733	165	35	2	2	NUM
ejpam-6733	165	36	.	.	PUNCT
ejpam-6733	166	1	so	so	ADV
ejpam-6733	166	2	,	,	PUNCT
ejpam-6733	166	3	let	let	VERB
ejpam-6733	166	4	a	a	PRON
ejpam-6733	166	5	=	=	PUNCT
ejpam-6733	166	6	[	[	PUNCT
ejpam-6733	166	7	a	a	PRON
ejpam-6733	166	8	b	b	NOUN
ejpam-6733	166	9	c	c	NOUN
ejpam-6733	166	10	d	d	X
ejpam-6733	166	11	]	]	X
ejpam-6733	166	12	,	,	PUNCT
ejpam-6733	166	13	b	b	X
ejpam-6733	166	14	=	=	SYM
ejpam-6733	166	15	a†	a†	NOUN
ejpam-6733	166	16	and	and	CCONJ
ejpam-6733	166	17	c	c	NOUN
ejpam-6733	166	18	=	=	SYM
ejpam-6733	166	19	diag	diag	PROPN
ejpam-6733	166	20	(	(	PUNCT
ejpam-6733	166	21	c1	c1	PROPN
ejpam-6733	166	22	,	,	PUNCT
ejpam-6733	166	23	c2	c2	PROPN
ejpam-6733	166	24	)	)	PUNCT
ejpam-6733	166	25	,	,	PUNCT
ejpam-6733	166	26	where	where	SCONJ
ejpam-6733	166	27	c1	c1	PROPN
ejpam-6733	166	28	,	,	PUNCT
ejpam-6733	166	29	c2	c2	PROPN
ejpam-6733	166	30	∈	∈	PROPN
ejpam-6733	166	31	r	r	NOUN
ejpam-6733	166	32	,	,	PUNCT
ejpam-6733	166	33	while	while	SCONJ
ejpam-6733	166	34	a	a	DET
ejpam-6733	166	35	,	,	PUNCT
ejpam-6733	166	36	b	b	NOUN
ejpam-6733	166	37	,	,	PUNCT
ejpam-6733	166	38	c	c	NOUN
ejpam-6733	166	39	,	,	PUNCT
ejpam-6733	166	40	d	d	PROPN
ejpam-6733	166	41	∈	∈	PROPN
ejpam-6733	166	42	c	c	X
ejpam-6733	166	43	(	(	PUNCT
ejpam-6733	166	44	13	13	NUM
ejpam-6733	166	45	)	)	PUNCT
ejpam-6733	166	46	be	be	AUX
ejpam-6733	166	47	linearly	linearly	ADV
ejpam-6733	166	48	independent	independent	ADJ
ejpam-6733	166	49	2×	2×	NUM
ejpam-6733	166	50	2	2	NUM
ejpam-6733	166	51	matrices	matrix	NOUN
ejpam-6733	166	52	.	.	PUNCT
ejpam-6733	167	1	thus	thus	ADV
ejpam-6733	167	2	,	,	PUNCT
ejpam-6733	167	3	from	from	ADP
ejpam-6733	167	4	(	(	PUNCT
ejpam-6733	167	5	13	13	NUM
ejpam-6733	167	6	)	)	PUNCT
ejpam-6733	167	7	in	in	ADP
ejpam-6733	167	8	(	(	PUNCT
ejpam-6733	167	9	6	6	NUM
ejpam-6733	167	10	)	)	PUNCT
ejpam-6733	167	11	,	,	PUNCT
ejpam-6733	167	12	we	we	PRON
ejpam-6733	167	13	have	have	VERB
ejpam-6733	167	14	,	,	PUNCT
ejpam-6733	167	15	[	[	X
ejpam-6733	167	16	a	a	DET
ejpam-6733	167	17	,	,	PUNCT
ejpam-6733	167	18	b]p	b]p	X
ejpam-6733	167	19	,	,	PUNCT
ejpam-6733	167	20	q	q	NOUN
ejpam-6733	167	21	=	=	SYM
ejpam-6733	167	22	paa†	paa†	NOUN
ejpam-6733	167	23	−	−	NOUN
ejpam-6733	167	24	qa†a	qa†a	NOUN
ejpam-6733	167	25	=	=	SYM
ejpam-6733	168	1	p	p	X
ejpam-6733	168	2	[	[	PUNCT
ejpam-6733	168	3	a	a	PRON
ejpam-6733	168	4	b	b	NOUN
ejpam-6733	168	5	c	c	NOUN
ejpam-6733	168	6	d	d	X
ejpam-6733	168	7	]	]	X
ejpam-6733	168	8	[	[	PUNCT
ejpam-6733	168	9	ā	ā	X
ejpam-6733	168	10	c̄	c̄	PROPN
ejpam-6733	168	11	b̄	b̄	NOUN
ejpam-6733	168	12	d̄	d̄	NOUN
ejpam-6733	168	13	]	]	PUNCT
ejpam-6733	169	1	−	−	PROPN
ejpam-6733	169	2	q	q	X
ejpam-6733	170	1	[	[	PUNCT
ejpam-6733	170	2	ā	ā	ADJ
ejpam-6733	170	3	c̄	c̄	PROPN
ejpam-6733	170	4	b̄	b̄	NOUN
ejpam-6733	170	5	d̄	d̄	NOUN
ejpam-6733	170	6	]	]	X
ejpam-6733	171	1	[	[	PUNCT
ejpam-6733	171	2	a	a	PRON
ejpam-6733	171	3	b	b	NOUN
ejpam-6733	171	4	c	c	NOUN
ejpam-6733	171	5	d	d	X
ejpam-6733	171	6	]	]	X
ejpam-6733	171	7	=	=	PUNCT
ejpam-6733	171	8	p	p	X
ejpam-6733	171	9	[	[	PUNCT
ejpam-6733	171	10	|a|2	|a|2	PROPN
ejpam-6733	171	11	+	+	CCONJ
ejpam-6733	171	12	|b|2	|b|2	PROPN
ejpam-6733	171	13	ac̄+	ac̄+	PROPN
ejpam-6733	171	14	bd̄	bd̄	X
ejpam-6733	171	15	āc+	āc+	PROPN
ejpam-6733	171	16	b̄d	b̄d	PROPN
ejpam-6733	171	17	|c|2	|c|2	PROPN
ejpam-6733	171	18	+	+	NUM
ejpam-6733	171	19	|d|2	|d|2	NOUN
ejpam-6733	171	20	]	]	PUNCT
ejpam-6733	171	21	−	−	PROPN
ejpam-6733	171	22	q	q	X
ejpam-6733	171	23	[	[	PUNCT
ejpam-6733	171	24	|a|2	|a|2	PROPN
ejpam-6733	171	25	+	+	CCONJ
ejpam-6733	171	26	|c|2	|c|2	PROPN
ejpam-6733	171	27	āb+	āb+	X
ejpam-6733	171	28	c̄d	c̄d	PROPN
ejpam-6733	171	29	ab̄+	ab̄+	VERB
ejpam-6733	171	30	cd̄	cd̄	X
ejpam-6733	171	31	|b|2	|b|2	PROPN
ejpam-6733	171	32	+	+	CCONJ
ejpam-6733	171	33	|d|2	|d|2	NOUN
ejpam-6733	171	34	]	]	PUNCT
ejpam-6733	171	35	=	=	PUNCT
ejpam-6733	171	36			PROPN
ejpam-6733	171	37	(	(	PUNCT
ejpam-6733	171	38	p−	p−	NOUN
ejpam-6733	171	39	q	q	NOUN
ejpam-6733	171	40	)	)	PUNCT
ejpam-6733	171	41	|a|2	|a|2	PROPN
ejpam-6733	171	42	+	+	PROPN
ejpam-6733	171	43	p	p	PROPN
ejpam-6733	171	44	|b|2	|b|2	ADJ
ejpam-6733	171	45	−	−	NOUN
ejpam-6733	171	46	q	q	PROPN
ejpam-6733	171	47	|c|2	|c|2	PROPN
ejpam-6733	171	48	p	p	NOUN
ejpam-6733	171	49	(	(	PUNCT
ejpam-6733	171	50	ac̄+	ac̄+	PROPN
ejpam-6733	171	51	bd̄	bd̄	X
ejpam-6733	171	52	)	)	PUNCT
ejpam-6733	172	1	−	−	PROPN
ejpam-6733	172	2	q	q	X
ejpam-6733	172	3	(	(	PUNCT
ejpam-6733	172	4	āb+	āb+	NOUN
ejpam-6733	172	5	c̄d	c̄d	X
ejpam-6733	172	6	)	)	PUNCT
ejpam-6733	173	1	p	p	NOUN
ejpam-6733	173	2	(	(	PUNCT
ejpam-6733	173	3	ac̄+	ac̄+	PROPN
ejpam-6733	173	4	bd̄	bd̄	X
ejpam-6733	173	5	)	)	PUNCT
ejpam-6733	173	6	−	−	PROPN
ejpam-6733	173	7	q	q	X
ejpam-6733	173	8	(	(	PUNCT
ejpam-6733	173	9	āb+	āb+	NOUN
ejpam-6733	173	10	c̄d	c̄d	X
ejpam-6733	173	11	)	)	PUNCT
ejpam-6733	173	12	p	p	X
ejpam-6733	173	13	|c|2	|c|2	PROPN
ejpam-6733	173	14	−	−	NOUN
ejpam-6733	173	15	q	q	PROPN
ejpam-6733	174	1	|b|2	|b|2	PROPN
ejpam-6733	174	2	+	+	PUNCT
ejpam-6733	174	3	(	(	PUNCT
ejpam-6733	174	4	p−	p−	NOUN
ejpam-6733	174	5	q	q	NOUN
ejpam-6733	174	6	)	)	PUNCT
ejpam-6733	174	7	|d|2	|d|2	NOUN
ejpam-6733	174	8			NOUN
ejpam-6733	174	9	=	=	SYM
ejpam-6733	174	10	f	f	X
ejpam-6733	174	11	(	(	PUNCT
ejpam-6733	174	12	c	c	NOUN
ejpam-6733	174	13	)	)	PUNCT
ejpam-6733	174	14	.	.	PUNCT
ejpam-6733	175	1	thus	thus	ADV
ejpam-6733	175	2	,	,	PUNCT
ejpam-6733	175	3	we	we	PRON
ejpam-6733	175	4	have	have	VERB
ejpam-6733	175	5	[	[	X
ejpam-6733	175	6	a	a	DET
ejpam-6733	175	7	,	,	PUNCT
ejpam-6733	175	8	b]p	b]p	X
ejpam-6733	175	9	,	,	PUNCT
ejpam-6733	175	10	q	q	PUNCT
ejpam-6733	175	11	=	=	SYM
ejpam-6733	175	12			PROPN
ejpam-6733	175	13	(	(	PUNCT
ejpam-6733	175	14	p−	p−	NOUN
ejpam-6733	175	15	q	q	NOUN
ejpam-6733	175	16	)	)	PUNCT
ejpam-6733	175	17	|a|2	|a|2	PROPN
ejpam-6733	175	18	+	+	PROPN
ejpam-6733	175	19	p	p	PROPN
ejpam-6733	175	20	|b|2	|b|2	ADJ
ejpam-6733	175	21	−	−	NOUN
ejpam-6733	175	22	q	q	PROPN
ejpam-6733	175	23	|c|2	|c|2	PROPN
ejpam-6733	175	24	p	p	NOUN
ejpam-6733	175	25	(	(	PUNCT
ejpam-6733	175	26	ac̄+	ac̄+	PROPN
ejpam-6733	175	27	bd̄	bd̄	X
ejpam-6733	175	28	)	)	PUNCT
ejpam-6733	176	1	−	−	PROPN
ejpam-6733	177	1	q	q	X
ejpam-6733	178	1	(	(	PUNCT
ejpam-6733	178	2	āb+	āb+	NOUN
ejpam-6733	178	3	c̄d	c̄d	X
ejpam-6733	178	4	)	)	PUNCT
ejpam-6733	179	1	p	p	NOUN
ejpam-6733	179	2	(	(	PUNCT
ejpam-6733	179	3	ac̄+	ac̄+	PROPN
ejpam-6733	179	4	bd̄	bd̄	X
ejpam-6733	179	5	)	)	PUNCT
ejpam-6733	179	6	−	−	PROPN
ejpam-6733	179	7	q	q	X
ejpam-6733	179	8	(	(	PUNCT
ejpam-6733	179	9	āb+	āb+	NOUN
ejpam-6733	179	10	c̄d	c̄d	X
ejpam-6733	179	11	)	)	PUNCT
ejpam-6733	179	12	p	p	X
ejpam-6733	179	13	|c|2	|c|2	PROPN
ejpam-6733	179	14	−	−	NOUN
ejpam-6733	179	15	q	q	PROPN
ejpam-6733	180	1	|b|2	|b|2	PROPN
ejpam-6733	180	2	+	+	PUNCT
ejpam-6733	180	3	(	(	PUNCT
ejpam-6733	180	4	p−	p−	NOUN
ejpam-6733	180	5	q	q	NOUN
ejpam-6733	180	6	)	)	PUNCT
ejpam-6733	180	7	|d|2	|d|2	NOUN
ejpam-6733	180	8			NOUN
ejpam-6733	180	9	=	=	SYM
ejpam-6733	180	10	diag	diag	NOUN
ejpam-6733	180	11	(	(	PUNCT
ejpam-6733	180	12	f	f	PROPN
ejpam-6733	180	13	(	(	PUNCT
ejpam-6733	180	14	c1	c1	PROPN
ejpam-6733	180	15	)	)	PUNCT
ejpam-6733	180	16	,	,	PUNCT
ejpam-6733	180	17	f	f	PROPN
ejpam-6733	180	18	(	(	PUNCT
ejpam-6733	180	19	c2	c2	PROPN
ejpam-6733	180	20	)	)	PUNCT
ejpam-6733	180	21	)	)	PUNCT
ejpam-6733	180	22	.	.	PUNCT
ejpam-6733	181	1	(	(	PUNCT
ejpam-6733	181	2	14	14	NUM
ejpam-6733	181	3	)	)	PUNCT
ejpam-6733	181	4	similarly	similarly	ADV
ejpam-6733	181	5	,	,	PUNCT
ejpam-6733	181	6	using	use	VERB
ejpam-6733	181	7	(	(	PUNCT
ejpam-6733	181	8	13	13	NUM
ejpam-6733	181	9	)	)	PUNCT
ejpam-6733	181	10	in	in	ADP
ejpam-6733	181	11	(	(	PUNCT
ejpam-6733	181	12	4	4	NUM
ejpam-6733	181	13	)	)	PUNCT
ejpam-6733	181	14	,	,	PUNCT
ejpam-6733	181	15	we	we	PRON
ejpam-6733	181	16	have	have	VERB
ejpam-6733	181	17	,	,	PUNCT
ejpam-6733	181	18	[	[	X
ejpam-6733	181	19	c	c	X
ejpam-6733	181	20	,	,	PUNCT
ejpam-6733	181	21	a]p	a]p	NOUN
ejpam-6733	181	22	,	,	PUNCT
ejpam-6733	181	23	q	q	NOUN
ejpam-6733	182	1	=	=	SYM
ejpam-6733	182	2	p	p	X
ejpam-6733	182	3	[	[	PUNCT
ejpam-6733	182	4	c1	c1	NOUN
ejpam-6733	182	5	0	0	NUM
ejpam-6733	182	6	0	0	NUM
ejpam-6733	182	7	c2	c2	PROPN
ejpam-6733	182	8	]	]	PUNCT
ejpam-6733	182	9	[	[	PUNCT
ejpam-6733	182	10	a	a	PRON
ejpam-6733	182	11	b	b	NOUN
ejpam-6733	182	12	c	c	NOUN
ejpam-6733	182	13	d	d	X
ejpam-6733	182	14	]	]	X
ejpam-6733	182	15	−	−	PROPN
ejpam-6733	182	16	q	q	X
ejpam-6733	183	1	[	[	PUNCT
ejpam-6733	183	2	a	a	PRON
ejpam-6733	183	3	b	b	NOUN
ejpam-6733	183	4	c	c	NOUN
ejpam-6733	183	5	d	d	NOUN
ejpam-6733	183	6	]	]	X
ejpam-6733	183	7	[	[	PUNCT
ejpam-6733	183	8	c1	c1	NOUN
ejpam-6733	183	9	0	0	NUM
ejpam-6733	183	10	0	0	NUM
ejpam-6733	183	11	c2	c2	PROPN
ejpam-6733	183	12	]	]	PUNCT
ejpam-6733	184	1	=	=	PUNCT
ejpam-6733	184	2	ra	ra	PROPN
ejpam-6733	184	3	.	.	PUNCT
ejpam-6733	185	1	so	so	ADV
ejpam-6733	185	2	,	,	PUNCT
ejpam-6733	185	3	we	we	PRON
ejpam-6733	185	4	have	have	VERB
ejpam-6733	185	5	,	,	PUNCT
ejpam-6733	185	6	[	[	X
ejpam-6733	185	7	c	c	X
ejpam-6733	185	8	,	,	PUNCT
ejpam-6733	185	9	a]p	a]p	ADJ
ejpam-6733	185	10	,	,	PUNCT
ejpam-6733	185	11	q	q	NOUN
ejpam-6733	185	12	=	=	SYM
ejpam-6733	185	13			PROPN
ejpam-6733	185	14	(	(	PUNCT
ejpam-6733	185	15	p−	p−	NOUN
ejpam-6733	185	16	q	q	NOUN
ejpam-6733	185	17	)	)	PUNCT
ejpam-6733	185	18	c1a	c1a	X
ejpam-6733	185	19	(	(	PUNCT
ejpam-6733	185	20	pc1	pc1	PROPN
ejpam-6733	185	21	−	−	PROPN
ejpam-6733	185	22	qc2	qc2	PROPN
ejpam-6733	185	23	)	)	PUNCT
ejpam-6733	185	24	b	b	PROPN
ejpam-6733	185	25	(	(	PUNCT
ejpam-6733	185	26	pc2	pc2	NOUN
ejpam-6733	185	27	−	−	PROPN
ejpam-6733	185	28	qc1	qc1	NOUN
ejpam-6733	185	29	)	)	PUNCT
ejpam-6733	185	30	c	c	NOUN
ejpam-6733	185	31	(	(	PUNCT
ejpam-6733	185	32	p−	p−	NOUN
ejpam-6733	185	33	q	q	NOUN
ejpam-6733	185	34	)	)	PUNCT
ejpam-6733	185	35	c2d	c2d	NOUN
ejpam-6733	185	36			NOUN
ejpam-6733	185	37	=	=	SYM
ejpam-6733	185	38	ra	ra	PROPN
ejpam-6733	185	39	.	.	PUNCT
ejpam-6733	186	1	(	(	PUNCT
ejpam-6733	186	2	15	15	NUM
ejpam-6733	186	3	)	)	PUNCT
ejpam-6733	186	4	from	from	ADP
ejpam-6733	186	5	(	(	PUNCT
ejpam-6733	186	6	14	14	NUM
ejpam-6733	186	7	)	)	PUNCT
ejpam-6733	186	8	,	,	PUNCT
ejpam-6733	186	9	as	as	SCONJ
ejpam-6733	186	10	tr	tr	ADJ
ejpam-6733	186	11	(	(	PUNCT
ejpam-6733	186	12	[	[	X
ejpam-6733	186	13	a	a	X
ejpam-6733	186	14	,	,	PUNCT
ejpam-6733	186	15	b]p	b]p	X
ejpam-6733	186	16	,	,	PUNCT
ejpam-6733	186	17	q	q	NOUN
ejpam-6733	186	18	)	)	PUNCT
ejpam-6733	187	1	=	=	SYM
ejpam-6733	187	2	f	f	PROPN
ejpam-6733	187	3	(	(	PUNCT
ejpam-6733	187	4	c1	c1	PROPN
ejpam-6733	187	5	)	)	PUNCT
ejpam-6733	188	1	+	+	CCONJ
ejpam-6733	188	2	f	f	X
ejpam-6733	188	3	(	(	PUNCT
ejpam-6733	188	4	c2	c2	PROPN
ejpam-6733	188	5	)	)	PUNCT
ejpam-6733	188	6	.	.	PUNCT
ejpam-6733	189	1	thus	thus	ADV
ejpam-6733	189	2	,	,	PUNCT
ejpam-6733	189	3	we	we	PRON
ejpam-6733	189	4	have	have	VERB
ejpam-6733	189	5	,	,	PUNCT
ejpam-6733	189	6	(	(	PUNCT
ejpam-6733	189	7	p−	p−	NOUN
ejpam-6733	189	8	q	q	NOUN
ejpam-6733	189	9	)	)	PUNCT
ejpam-6733	189	10	(	(	PUNCT
ejpam-6733	189	11	|a|2	|a|2	PROPN
ejpam-6733	189	12	+	+	CCONJ
ejpam-6733	189	13	|b|2	|b|2	PROPN
ejpam-6733	189	14	+	+	CCONJ
ejpam-6733	189	15	|c|2	|c|2	PROPN
ejpam-6733	189	16	+	+	NUM
ejpam-6733	189	17	|d|2	|d|2	NOUN
ejpam-6733	189	18	)	)	PUNCT
ejpam-6733	190	1	=	=	SYM
ejpam-6733	190	2	f	f	PROPN
ejpam-6733	190	3	(	(	PUNCT
ejpam-6733	190	4	c1	c1	PROPN
ejpam-6733	190	5	)	)	PUNCT
ejpam-6733	191	1	+	+	CCONJ
ejpam-6733	191	2	f	f	X
ejpam-6733	191	3	(	(	PUNCT
ejpam-6733	191	4	c2	c2	PROPN
ejpam-6733	191	5	)	)	PUNCT
ejpam-6733	191	6	.	.	PUNCT
ejpam-6733	192	1	(	(	PUNCT
ejpam-6733	192	2	16	16	NUM
ejpam-6733	192	3	)	)	PUNCT
ejpam-6733	192	4	similarly	similarly	ADV
ejpam-6733	192	5	,	,	PUNCT
ejpam-6733	192	6	from	from	ADP
ejpam-6733	192	7	(	(	PUNCT
ejpam-6733	192	8	15	15	NUM
ejpam-6733	192	9	)	)	PUNCT
ejpam-6733	192	10	,	,	PUNCT
ejpam-6733	192	11	we	we	PRON
ejpam-6733	192	12	have	have	VERB
ejpam-6733	192	13	,	,	PUNCT
ejpam-6733	192	14	tr	tr	VERB
ejpam-6733	192	15	(	(	PUNCT
ejpam-6733	192	16	[	[	X
ejpam-6733	192	17	c	c	X
ejpam-6733	192	18	,	,	PUNCT
ejpam-6733	192	19	a]p	a]p	NOUN
ejpam-6733	192	20	,	,	PUNCT
ejpam-6733	192	21	q	q	NOUN
ejpam-6733	192	22	)	)	PUNCT
ejpam-6733	192	23	=	=	SYM
ejpam-6733	192	24	ra+	ra+	PROPN
ejpam-6733	192	25	rd	rd	PROPN
ejpam-6733	192	26	.	.	PUNCT
ejpam-6733	193	1	so	so	ADV
ejpam-6733	193	2	,	,	PUNCT
ejpam-6733	193	3	(	(	PUNCT
ejpam-6733	193	4	p−	p−	NOUN
ejpam-6733	193	5	q	q	NOUN
ejpam-6733	193	6	)	)	PUNCT
ejpam-6733	193	7	(	(	PUNCT
ejpam-6733	193	8	ac1	ac1	PROPN
ejpam-6733	193	9	+	+	CCONJ
ejpam-6733	193	10	dc2	dc2	PROPN
ejpam-6733	193	11	)	)	PUNCT
ejpam-6733	194	1	=	=	SYM
ejpam-6733	194	2	r	r	NOUN
ejpam-6733	194	3	(	(	PUNCT
ejpam-6733	194	4	a+	a+	NOUN
ejpam-6733	194	5	d	d	NOUN
ejpam-6733	194	6	)	)	PUNCT
ejpam-6733	194	7	.	.	PUNCT
ejpam-6733	195	1	(	(	PUNCT
ejpam-6733	195	2	17	17	NUM
ejpam-6733	195	3	)	)	PUNCT
ejpam-6733	195	4	l.	l.	PROPN
ejpam-6733	195	5	a	a	PROPN
ejpam-6733	195	6	-	-	PUNCT
ejpam-6733	195	7	m.	m.	NOUN
ejpam-6733	195	8	hanna	hanna	NOUN
ejpam-6733	195	9	,	,	PUNCT
ejpam-6733	195	10	s.	s.	PROPN
ejpam-6733	195	11	s.	s.	PROPN
ejpam-6733	195	12	hassan	hassan	PROPN
ejpam-6733	195	13	,	,	PUNCT
ejpam-6733	195	14	m.	m.	NOUN
ejpam-6733	195	15	almutairi	almutairi	PROPN
ejpam-6733	195	16	/	/	SYM
ejpam-6733	195	17	eur	eur	PROPN
ejpam-6733	195	18	.	.	PUNCT
ejpam-6733	196	1	j.	j.	PROPN
ejpam-6733	196	2	pure	pure	PROPN
ejpam-6733	196	3	appl	appl	PROPN
ejpam-6733	196	4	.	.	PROPN
ejpam-6733	196	5	math	math	PROPN
ejpam-6733	196	6	,	,	PUNCT
ejpam-6733	196	7	18	18	NUM
ejpam-6733	196	8	(	(	PUNCT
ejpam-6733	196	9	4	4	NUM
ejpam-6733	196	10	)	)	PUNCT
ejpam-6733	196	11	(	(	PUNCT
ejpam-6733	196	12	2025	2025	NUM
ejpam-6733	196	13	)	)	PUNCT
ejpam-6733	196	14	,	,	PUNCT
ejpam-6733	196	15	6733	6733	NUM
ejpam-6733	196	16	7	7	NUM
ejpam-6733	196	17	of	of	ADP
ejpam-6733	196	18	12	12	NUM
ejpam-6733	196	19	lemma	lemma	PROPN
ejpam-6733	196	20	1	1	NUM
ejpam-6733	196	21	.	.	PUNCT
ejpam-6733	197	1	if	if	SCONJ
ejpam-6733	197	2	c	c	PROPN
ejpam-6733	197	3	=	=	SYM
ejpam-6733	197	4	ki2	ki2	PROPN
ejpam-6733	197	5	,	,	PUNCT
ejpam-6733	197	6	a	a	DET
ejpam-6733	197	7	scalar	scalar	ADJ
ejpam-6733	197	8	matrix	matrix	NOUN
ejpam-6733	197	9	and	and	CCONJ
ejpam-6733	197	10	p	p	NOUN
ejpam-6733	197	11	6=	6=	PROPN
ejpam-6733	197	12	q	q	PROPN
ejpam-6733	197	13	,	,	PUNCT
ejpam-6733	197	14	then	then	ADV
ejpam-6733	197	15	k	k	PROPN
ejpam-6733	197	16	=	=	SYM
ejpam-6733	197	17	r	r	NOUN
ejpam-6733	197	18	p−q	p−q	NOUN
ejpam-6733	197	19	.	.	PUNCT
ejpam-6733	198	1	proof	proof	NOUN
ejpam-6733	198	2	.	.	PUNCT
ejpam-6733	199	1	since	since	SCONJ
ejpam-6733	199	2	[	[	X
ejpam-6733	199	3	c	c	X
ejpam-6733	199	4	,	,	PUNCT
ejpam-6733	199	5	a]p	a]p	NOUN
ejpam-6733	199	6	,	,	PUNCT
ejpam-6733	199	7	q	q	NOUN
ejpam-6733	199	8	=	=	X
ejpam-6733	199	9	(	(	PUNCT
ejpam-6733	199	10	p−	p−	NOUN
ejpam-6733	199	11	q	q	NOUN
ejpam-6733	199	12	)	)	PUNCT
ejpam-6733	199	13	ka	ka	PROPN
ejpam-6733	199	14	=	=	PROPN
ejpam-6733	199	15	ra	ra	PROPN
ejpam-6733	199	16	.	.	PUNCT
ejpam-6733	199	17	since	since	SCONJ
ejpam-6733	199	18	a	a	PRON
ejpam-6733	199	19	6=	6=	NUM
ejpam-6733	199	20	0	0	NUM
ejpam-6733	199	21	,	,	PUNCT
ejpam-6733	199	22	then	then	ADV
ejpam-6733	199	23	k	k	PROPN
ejpam-6733	199	24	=	=	SYM
ejpam-6733	199	25	r	r	NOUN
ejpam-6733	199	26	p−q	p−q	NOUN
ejpam-6733	199	27	.	.	PUNCT
ejpam-6733	200	1	5.1	5.1	NUM
ejpam-6733	200	2	.	.	PUNCT
ejpam-6733	201	1	representation	representation	NOUN
ejpam-6733	201	2	matrices	matrix	NOUN
ejpam-6733	201	3	of	of	ADP
ejpam-6733	201	4	degree	degree	NOUN
ejpam-6733	201	5	2	2	NUM
ejpam-6733	201	6	of	of	ADP
ejpam-6733	201	7	lq	lq	NOUN
ejpam-6733	201	8	,	,	PUNCT
ejpam-6733	201	9	q	q	NOUN
ejpam-6733	201	10	in	in	ADP
ejpam-6733	201	11	this	this	DET
ejpam-6733	201	12	subsection	subsection	NOUN
ejpam-6733	201	13	,	,	PUNCT
ejpam-6733	201	14	we	we	PRON
ejpam-6733	201	15	consider	consider	VERB
ejpam-6733	201	16	the	the	DET
ejpam-6733	201	17	special	special	ADJ
ejpam-6733	201	18	case	case	NOUN
ejpam-6733	201	19	when	when	SCONJ
ejpam-6733	201	20	p	p	PROPN
ejpam-6733	201	21	=	=	PROPN
ejpam-6733	201	22	q.	q.	PROPN
ejpam-6733	201	23	theorem	theorem	VERB
ejpam-6733	201	24	3	3	NUM
ejpam-6733	201	25	.	.	PUNCT
ejpam-6733	202	1	lp	lp	NOUN
ejpam-6733	202	2	,	,	PUNCT
ejpam-6733	202	3	q	q	PUNCT
ejpam-6733	202	4	is	be	AUX
ejpam-6733	202	5	a	a	DET
ejpam-6733	202	6	lie	lie	NOUN
ejpam-6733	202	7	algebra	algebra	NOUN
ejpam-6733	202	8	iff	iff	PROPN
ejpam-6733	202	9	p	p	NOUN
ejpam-6733	202	10	=	=	PROPN
ejpam-6733	202	11	q.	q.	NOUN
ejpam-6733	202	12	proof	proof	NOUN
ejpam-6733	202	13	.	.	PUNCT
ejpam-6733	203	1	let	let	VERB
ejpam-6733	203	2	x	x	PRON
ejpam-6733	203	3	,	,	PUNCT
ejpam-6733	203	4	y	y	PROPN
ejpam-6733	203	5	∈	∈	PROPN
ejpam-6733	203	6	lq	lq	NOUN
ejpam-6733	203	7	,	,	PUNCT
ejpam-6733	203	8	q	q	NOUN
ejpam-6733	203	9	,	,	PUNCT
ejpam-6733	203	10	then	then	ADV
ejpam-6733	203	11	from	from	ADP
ejpam-6733	203	12	definition	definition	NOUN
ejpam-6733	203	13	(	(	PUNCT
ejpam-6733	203	14	1	1	NUM
ejpam-6733	203	15	)	)	PUNCT
ejpam-6733	203	16	,	,	PUNCT
ejpam-6733	203	17	we	we	PRON
ejpam-6733	203	18	have	have	VERB
ejpam-6733	203	19	[	[	X
ejpam-6733	203	20	x	x	NOUN
ejpam-6733	203	21	,	,	PUNCT
ejpam-6733	203	22	y]q	y]q	NOUN
ejpam-6733	203	23	,	,	PUNCT
ejpam-6733	203	24	q	q	NOUN
ejpam-6733	203	25	=	=	PUNCT
ejpam-6733	204	1	−	−	PROPN
ejpam-6733	205	1	[	[	X
ejpam-6733	205	2	y	y	NOUN
ejpam-6733	205	3	,	,	PUNCT
ejpam-6733	205	4	x]q	x]q	ADJ
ejpam-6733	205	5	,	,	PUNCT
ejpam-6733	205	6	q	q	NOUN
ejpam-6733	205	7	and	and	CCONJ
ejpam-6733	205	8	[	[	X
ejpam-6733	205	9	x	x	X
ejpam-6733	205	10	,	,	PUNCT
ejpam-6733	205	11	x]q	x]q	ADJ
ejpam-6733	205	12	,	,	PUNCT
ejpam-6733	205	13	q	q	X
ejpam-6733	205	14	=	=	PUNCT
ejpam-6733	205	15	o.	o.	NOUN
ejpam-6733	205	16	from	from	ADP
ejpam-6733	205	17	parts	part	NOUN
ejpam-6733	205	18	(	(	PUNCT
ejpam-6733	205	19	4	4	NUM
ejpam-6733	205	20	)	)	PUNCT
ejpam-6733	205	21	and	and	CCONJ
ejpam-6733	205	22	(	(	PUNCT
ejpam-6733	205	23	5	5	NUM
ejpam-6733	205	24	)	)	PUNCT
ejpam-6733	205	25	,	,	PUNCT
ejpam-6733	205	26	the	the	DET
ejpam-6733	205	27	bilinearity	bilinearity	NOUN
ejpam-6733	205	28	is	be	AUX
ejpam-6733	205	29	satisfied	satisfied	ADJ
ejpam-6733	205	30	,	,	PUNCT
ejpam-6733	205	31	while	while	SCONJ
ejpam-6733	205	32	the	the	DET
ejpam-6733	205	33	jacobi	jacobi	PROPN
ejpam-6733	205	34	identity	identity	NOUN
ejpam-6733	205	35	is	be	AUX
ejpam-6733	205	36	satisfied	satisfied	ADJ
ejpam-6733	205	37	from	from	ADP
ejpam-6733	205	38	part	part	NOUN
ejpam-6733	205	39	(	(	PUNCT
ejpam-6733	205	40	9	9	NUM
ejpam-6733	205	41	)	)	PUNCT
ejpam-6733	205	42	of	of	ADP
ejpam-6733	205	43	theorem	theorem	ADJ
ejpam-6733	205	44	1	1	NUM
ejpam-6733	205	45	,	,	PUNCT
ejpam-6733	205	46	respectively	respectively	ADV
ejpam-6733	205	47	.	.	PUNCT
ejpam-6733	206	1	conversely	conversely	ADV
ejpam-6733	206	2	,	,	PUNCT
ejpam-6733	206	3	from	from	ADP
ejpam-6733	206	4	definition	definition	NOUN
ejpam-6733	206	5	(	(	PUNCT
ejpam-6733	206	6	1	1	NUM
ejpam-6733	206	7	)	)	PUNCT
ejpam-6733	206	8	,	,	PUNCT
ejpam-6733	206	9	∀x	∀x	VERB
ejpam-6733	206	10	∈	∈	PROPN
ejpam-6733	206	11	lp	lp	NOUN
ejpam-6733	206	12	,	,	PUNCT
ejpam-6733	206	13	q	q	INTJ
ejpam-6733	206	14	,	,	PUNCT
ejpam-6733	206	15	we	we	PRON
ejpam-6733	206	16	have	have	VERB
ejpam-6733	206	17	[	[	X
ejpam-6733	206	18	x	x	X
ejpam-6733	206	19	,	,	PUNCT
ejpam-6733	206	20	x]p	x]p	NOUN
ejpam-6733	206	21	,	,	PUNCT
ejpam-6733	206	22	q	q	X
ejpam-6733	207	1	=	=	X
ejpam-6733	207	2	(	(	PUNCT
ejpam-6733	207	3	p−	p−	NOUN
ejpam-6733	207	4	q)x2	q)x2	NOUN
ejpam-6733	207	5	=	=	PUNCT
ejpam-6733	207	6	o	o	NOUN
ejpam-6733	207	7	,	,	PUNCT
ejpam-6733	207	8	only	only	ADV
ejpam-6733	207	9	if	if	SCONJ
ejpam-6733	207	10	p	p	X
ejpam-6733	207	11	=	=	X
ejpam-6733	207	12	q	q	X
ejpam-6733	207	13	or	or	CCONJ
ejpam-6733	207	14	x2	x2	NOUN
ejpam-6733	207	15	=	=	SYM
ejpam-6733	207	16	o	o	NOUN
ejpam-6733	207	17	,	,	PUNCT
ejpam-6733	207	18	∀x	∀x	X
ejpam-6733	207	19	∈lp	∈lp	NOUN
ejpam-6733	207	20	,	,	PUNCT
ejpam-6733	207	21	q.	q.	PROPN
ejpam-6733	207	22	since	since	SCONJ
ejpam-6733	207	23	c	c	PROPN
ejpam-6733	207	24	is	be	AUX
ejpam-6733	207	25	a	a	DET
ejpam-6733	207	26	diagonal	diagonal	ADJ
ejpam-6733	207	27	matrix	matrix	NOUN
ejpam-6733	207	28	,	,	PUNCT
ejpam-6733	207	29	then	then	ADV
ejpam-6733	207	30	c2	c2	PROPN
ejpam-6733	207	31	=	=	SYM
ejpam-6733	207	32	0	0	PROPN
ejpam-6733	207	33	,	,	PUNCT
ejpam-6733	207	34	if	if	SCONJ
ejpam-6733	207	35	and	and	CCONJ
ejpam-6733	207	36	only	only	ADV
ejpam-6733	207	37	if	if	SCONJ
ejpam-6733	207	38	,	,	PUNCT
ejpam-6733	207	39	c	c	NOUN
ejpam-6733	207	40	=	=	SYM
ejpam-6733	207	41	0	0	PROPN
ejpam-6733	207	42	,	,	PUNCT
ejpam-6733	207	43	which	which	PRON
ejpam-6733	207	44	is	be	AUX
ejpam-6733	207	45	impossible	impossible	ADJ
ejpam-6733	207	46	since	since	SCONJ
ejpam-6733	207	47	c	c	PROPN
ejpam-6733	207	48	is	be	AUX
ejpam-6733	207	49	a	a	DET
ejpam-6733	207	50	representation	representation	NOUN
ejpam-6733	207	51	matrix	matrix	NOUN
ejpam-6733	207	52	of	of	ADP
ejpam-6733	207	53	a	a	DET
ejpam-6733	207	54	basis	basis	NOUN
ejpam-6733	207	55	element	element	NOUN
ejpam-6733	207	56	of	of	ADP
ejpam-6733	207	57	lp	lp	PROPN
ejpam-6733	207	58	,	,	PUNCT
ejpam-6733	207	59	q.	q.	PROPN
ejpam-6733	207	60	as	as	SCONJ
ejpam-6733	207	61	lq.q	lq.q	NOUN
ejpam-6733	207	62	is	be	AUX
ejpam-6733	207	63	a	a	DET
ejpam-6733	207	64	lie	lie	NOUN
ejpam-6733	207	65	algebra	algebra	NOUN
ejpam-6733	207	66	,	,	PUNCT
ejpam-6733	207	67	we	we	PRON
ejpam-6733	207	68	get	get	VERB
ejpam-6733	207	69	the	the	DET
ejpam-6733	207	70	following	follow	VERB
ejpam-6733	207	71	corollary	corollary	NOUN
ejpam-6733	207	72	.	.	PUNCT
ejpam-6733	208	1	corollary	corollary	ADJ
ejpam-6733	208	2	1	1	NUM
ejpam-6733	208	3	.	.	PUNCT
ejpam-6733	209	1	in	in	ADP
ejpam-6733	209	2	lq	lq	PROPN
ejpam-6733	209	3	,	,	PUNCT
ejpam-6733	209	4	q	q	NOUN
ejpam-6733	209	5	,	,	PUNCT
ejpam-6733	209	6	tr	tr	VERB
ejpam-6733	209	7	(	(	PUNCT
ejpam-6733	209	8	a	a	X
ejpam-6733	209	9	)	)	PUNCT
ejpam-6733	209	10	=	=	PUNCT
ejpam-6733	209	11	tr	tr	VERB
ejpam-6733	209	12	(	(	PUNCT
ejpam-6733	209	13	f	f	X
ejpam-6733	209	14	(	(	PUNCT
ejpam-6733	209	15	c	c	NOUN
ejpam-6733	209	16	)	)	PUNCT
ejpam-6733	209	17	)	)	PUNCT
ejpam-6733	210	1	=	=	PUNCT
ejpam-6733	210	2	0	0	X
ejpam-6733	210	3	.	.	PUNCT
ejpam-6733	211	1	proof	proof	NOUN
ejpam-6733	211	2	.	.	PUNCT
ejpam-6733	212	1	from	from	ADP
ejpam-6733	212	2	part	part	NOUN
ejpam-6733	212	3	(	(	PUNCT
ejpam-6733	212	4	1	1	NUM
ejpam-6733	212	5	)	)	PUNCT
ejpam-6733	212	6	of	of	ADP
ejpam-6733	212	7	theorem	theorem	NOUN
ejpam-6733	212	8	1	1	NUM
ejpam-6733	212	9	,	,	PUNCT
ejpam-6733	212	10	as	as	ADP
ejpam-6733	212	11	p	p	NOUN
ejpam-6733	212	12	=	=	NOUN
ejpam-6733	212	13	q	q	NOUN
ejpam-6733	212	14	,	,	PUNCT
ejpam-6733	212	15	we	we	PRON
ejpam-6733	212	16	have	have	VERB
ejpam-6733	212	17	tr	tr	VERB
ejpam-6733	212	18	(	(	PUNCT
ejpam-6733	212	19	[	[	X
ejpam-6733	212	20	x	x	X
ejpam-6733	212	21	,	,	PUNCT
ejpam-6733	212	22	y	y	PROPN
ejpam-6733	212	23	]	]	PUNCT
ejpam-6733	212	24	)	)	PUNCT
ejpam-6733	213	1	=	=	SYM
ejpam-6733	213	2	0	0	NUM
ejpam-6733	213	3	for	for	SCONJ
ejpam-6733	213	4	every	every	DET
ejpam-6733	213	5	x	x	NOUN
ejpam-6733	213	6	,	,	PUNCT
ejpam-6733	213	7	y	y	PROPN
ejpam-6733	213	8	∈	∈	PROPN
ejpam-6733	213	9	lq	lq	NOUN
ejpam-6733	213	10	,	,	PUNCT
ejpam-6733	213	11	q	q	NOUN
ejpam-6733	213	12	,	,	PUNCT
ejpam-6733	213	13	then	then	ADV
ejpam-6733	213	14	the	the	DET
ejpam-6733	213	15	corollary	corollary	ADJ
ejpam-6733	213	16	results	result	NOUN
ejpam-6733	213	17	from	from	ADP
ejpam-6733	213	18	(	(	PUNCT
ejpam-6733	213	19	14	14	NUM
ejpam-6733	213	20	)	)	PUNCT
ejpam-6733	213	21	and	and	CCONJ
ejpam-6733	213	22	(	(	PUNCT
ejpam-6733	213	23	15	15	NUM
ejpam-6733	213	24	)	)	PUNCT
ejpam-6733	213	25	.	.	PUNCT
ejpam-6733	214	1	lemma	lemma	PROPN
ejpam-6733	214	2	2	2	X
ejpam-6733	214	3	.	.	PUNCT
ejpam-6733	215	1	if	if	SCONJ
ejpam-6733	215	2	c	c	PROPN
ejpam-6733	215	3	is	be	AUX
ejpam-6733	215	4	a	a	DET
ejpam-6733	215	5	scalar	scalar	ADJ
ejpam-6733	215	6	matrix	matrix	NOUN
ejpam-6733	215	7	,	,	PUNCT
ejpam-6733	215	8	then	then	ADV
ejpam-6733	215	9	the	the	DET
ejpam-6733	215	10	matrix	matrix	NOUN
ejpam-6733	215	11	representation	representation	NOUN
ejpam-6733	215	12	of	of	ADP
ejpam-6733	215	13	lq	lq	NOUN
ejpam-6733	215	14	,	,	PUNCT
ejpam-6733	215	15	q	q	X
ejpam-6733	215	16	is	be	AUX
ejpam-6733	215	17	not	not	PART
ejpam-6733	215	18	faithful	faithful	ADJ
ejpam-6733	215	19	.	.	PUNCT
ejpam-6733	216	1	proof	proof	NOUN
ejpam-6733	216	2	.	.	PUNCT
ejpam-6733	217	1	let	let	VERB
ejpam-6733	217	2	c	c	PRON
ejpam-6733	217	3	be	be	AUX
ejpam-6733	217	4	a	a	DET
ejpam-6733	217	5	scalar	scalar	ADJ
ejpam-6733	217	6	matrix	matrix	NOUN
ejpam-6733	217	7	,	,	PUNCT
ejpam-6733	217	8	then	then	ADV
ejpam-6733	217	9	from	from	ADP
ejpam-6733	217	10	(	(	PUNCT
ejpam-6733	217	11	15	15	NUM
ejpam-6733	217	12	)	)	PUNCT
ejpam-6733	217	13	,	,	PUNCT
ejpam-6733	217	14	as	as	ADP
ejpam-6733	217	15	p	p	NOUN
ejpam-6733	217	16	=	=	NOUN
ejpam-6733	217	17	q	q	NOUN
ejpam-6733	217	18	and	and	CCONJ
ejpam-6733	217	19	since	since	SCONJ
ejpam-6733	217	20	r	r	NOUN
ejpam-6733	217	21	6=	6=	NUM
ejpam-6733	217	22	0	0	NUM
ejpam-6733	217	23	,	,	PUNCT
ejpam-6733	217	24	then	then	ADV
ejpam-6733	217	25	a	a	DET
ejpam-6733	217	26	=	=	NOUN
ejpam-6733	217	27	0	0	X
ejpam-6733	217	28	.	.	PUNCT
ejpam-6733	218	1	lemma	lemma	PROPN
ejpam-6733	218	2	3	3	X
ejpam-6733	218	3	.	.	X
ejpam-6733	219	1	for	for	ADP
ejpam-6733	219	2	faithful	faithful	ADJ
ejpam-6733	219	3	representation	representation	NOUN
ejpam-6733	219	4	of	of	ADP
ejpam-6733	219	5	lq	lq	PROPN
ejpam-6733	219	6	,	,	PUNCT
ejpam-6733	219	7	q	q	NOUN
ejpam-6733	219	8	,	,	PUNCT
ejpam-6733	219	9	the	the	DET
ejpam-6733	219	10	representation	representation	NOUN
ejpam-6733	219	11	matrix	matrix	NOUN
ejpam-6733	220	1	a	a	PRON
ejpam-6733	220	2	=	=	X
ejpam-6733	220	3	[	[	PUNCT
ejpam-6733	220	4	0	0	NUM
ejpam-6733	220	5	b	b	NOUN
ejpam-6733	220	6	0	0	NUM
ejpam-6733	220	7	0	0	NUM
ejpam-6733	220	8	]	]	PUNCT
ejpam-6733	220	9	,	,	PUNCT
ejpam-6733	220	10	where	where	SCONJ
ejpam-6733	220	11	b	b	NOUN
ejpam-6733	220	12	is	be	AUX
ejpam-6733	220	13	a	a	DET
ejpam-6733	220	14	nonzero	nonzero	ADJ
ejpam-6733	220	15	complex	complex	ADJ
ejpam-6733	220	16	number	number	NOUN
ejpam-6733	220	17	.	.	PUNCT
ejpam-6733	221	1	proof	proof	NOUN
ejpam-6733	221	2	.	.	PUNCT
ejpam-6733	222	1	from	from	ADP
ejpam-6733	222	2	(	(	PUNCT
ejpam-6733	222	3	9	9	NUM
ejpam-6733	222	4	)	)	PUNCT
ejpam-6733	222	5	,	,	PUNCT
ejpam-6733	222	6	if	if	SCONJ
ejpam-6733	222	7	i	i	PRON
ejpam-6733	222	8	=	=	NOUN
ejpam-6733	222	9	1	1	NUM
ejpam-6733	222	10	,	,	PUNCT
ejpam-6733	222	11	we	we	PRON
ejpam-6733	222	12	have	have	VERB
ejpam-6733	222	13	a	a	PRON
ejpam-6733	222	14	[	[	X
ejpam-6733	222	15	r	r	X
ejpam-6733	222	16	−	−	PROPN
ejpam-6733	222	17	(	(	PUNCT
ejpam-6733	222	18	q	q	NOUN
ejpam-6733	222	19	−	−	PROPN
ejpam-6733	222	20	q	q	NOUN
ejpam-6733	222	21	)	)	PUNCT
ejpam-6733	222	22	c1	c1	NOUN
ejpam-6733	222	23	]	]	PUNCT
ejpam-6733	222	24	=	=	PUNCT
ejpam-6733	223	1	0	0	NUM
ejpam-6733	223	2	,	,	PUNCT
ejpam-6733	223	3	then	then	ADV
ejpam-6733	223	4	a	a	DET
ejpam-6733	223	5	=	=	SYM
ejpam-6733	223	6	0	0	NUM
ejpam-6733	223	7	and	and	CCONJ
ejpam-6733	223	8	similarly	similarly	ADV
ejpam-6733	223	9	,	,	PUNCT
ejpam-6733	223	10	if	if	SCONJ
ejpam-6733	223	11	i	i	PRON
ejpam-6733	223	12	=	=	NOUN
ejpam-6733	223	13	2	2	NUM
ejpam-6733	223	14	,	,	PUNCT
ejpam-6733	223	15	we	we	PRON
ejpam-6733	223	16	have	have	VERB
ejpam-6733	223	17	d	d	NOUN
ejpam-6733	223	18	=	=	SYM
ejpam-6733	223	19	0	0	NUM
ejpam-6733	223	20	.	.	PUNCT
ejpam-6733	224	1	from	from	ADP
ejpam-6733	224	2	(	(	PUNCT
ejpam-6733	224	3	8)	8)	NUM
ejpam-6733	224	4	,	,	PUNCT
ejpam-6733	224	5	if	if	SCONJ
ejpam-6733	224	6	i	i	PRON
ejpam-6733	224	7	=	=	SYM
ejpam-6733	224	8	1	1	NUM
ejpam-6733	224	9	and	and	CCONJ
ejpam-6733	224	10	j	j	NOUN
ejpam-6733	224	11	=	=	SYM
ejpam-6733	224	12	2	2	NUM
ejpam-6733	224	13	,	,	PUNCT
ejpam-6733	224	14	we	we	PRON
ejpam-6733	224	15	have	have	VERB
ejpam-6733	224	16	b	b	NUM
ejpam-6733	225	1	[	[	X
ejpam-6733	225	2	r	r	NOUN
ejpam-6733	225	3	−	−	PROPN
ejpam-6733	225	4	q	q	NOUN
ejpam-6733	225	5	(	(	PUNCT
ejpam-6733	225	6	c1	c1	PROPN
ejpam-6733	225	7	−	−	PROPN
ejpam-6733	225	8	c2	c2	PROPN
ejpam-6733	225	9	)	)	PUNCT
ejpam-6733	225	10	]	]	PUNCT
ejpam-6733	226	1	=	=	PUNCT
ejpam-6733	226	2	0	0	NUM
ejpam-6733	226	3	,	,	PUNCT
ejpam-6733	226	4	and	and	CCONJ
ejpam-6733	226	5	similarly	similarly	ADV
ejpam-6733	226	6	,	,	PUNCT
ejpam-6733	226	7	for	for	ADP
ejpam-6733	226	8	i	i	PROPN
ejpam-6733	226	9	=	=	SYM
ejpam-6733	226	10	2	2	NUM
ejpam-6733	226	11	and	and	CCONJ
ejpam-6733	226	12	j	j	NOUN
ejpam-6733	226	13	=	=	SYM
ejpam-6733	226	14	1	1	NUM
ejpam-6733	226	15	,	,	PUNCT
ejpam-6733	226	16	we	we	PRON
ejpam-6733	226	17	have	have	VERB
ejpam-6733	226	18	c	c	NOUN
ejpam-6733	227	1	[	[	X
ejpam-6733	227	2	r	r	NOUN
ejpam-6733	227	3	−	−	NOUN
ejpam-6733	227	4	q	q	NOUN
ejpam-6733	227	5	(	(	PUNCT
ejpam-6733	227	6	c2	c2	PROPN
ejpam-6733	227	7	−	−	PROPN
ejpam-6733	227	8	c1	c1	PROPN
ejpam-6733	227	9	)	)	PUNCT
ejpam-6733	227	10	]	]	PUNCT
ejpam-6733	228	1	=	=	PUNCT
ejpam-6733	228	2	0	0	X
ejpam-6733	228	3	.	.	PUNCT
ejpam-6733	229	1	thus	thus	ADV
ejpam-6733	229	2	,	,	PUNCT
ejpam-6733	229	3	suppose	suppose	VERB
ejpam-6733	229	4	bc	bc	PROPN
ejpam-6733	229	5	6=	6=	PROPN
ejpam-6733	229	6	0	0	NUM
ejpam-6733	229	7	,	,	PUNCT
ejpam-6733	229	8	then	then	ADV
ejpam-6733	229	9	we	we	PRON
ejpam-6733	229	10	have	have	VERB
ejpam-6733	229	11	q	q	PROPN
ejpam-6733	229	12	(	(	PUNCT
ejpam-6733	229	13	c1	c1	PROPN
ejpam-6733	229	14	−	−	PROPN
ejpam-6733	229	15	c2	c2	PROPN
ejpam-6733	229	16	)	)	PUNCT
ejpam-6733	230	1	=	=	PUNCT
ejpam-6733	230	2	r	r	NOUN
ejpam-6733	230	3	=	=	PUNCT
ejpam-6733	230	4	q	q	X
ejpam-6733	230	5	(	(	PUNCT
ejpam-6733	230	6	c2	c2	PROPN
ejpam-6733	230	7	−	−	PROPN
ejpam-6733	230	8	c1	c1	PROPN
ejpam-6733	230	9	)	)	PUNCT
ejpam-6733	230	10	.	.	PUNCT
ejpam-6733	231	1	as	as	ADP
ejpam-6733	231	2	q	q	PROPN
ejpam-6733	231	3	6=	6=	NUM
ejpam-6733	231	4	0	0	NUM
ejpam-6733	231	5	,	,	PUNCT
ejpam-6733	231	6	one	one	PRON
ejpam-6733	231	7	gets	get	VERB
ejpam-6733	231	8	that	that	DET
ejpam-6733	231	9	c1	c1	PROPN
ejpam-6733	231	10	=	=	PROPN
ejpam-6733	231	11	c2	c2	PROPN
ejpam-6733	231	12	,	,	PUNCT
ejpam-6733	231	13	i.e.	i.e.	X
ejpam-6733	231	14	,	,	PUNCT
ejpam-6733	231	15	c	c	PROPN
ejpam-6733	231	16	is	be	AUX
ejpam-6733	231	17	a	a	DET
ejpam-6733	231	18	scalar	scalar	ADJ
ejpam-6733	231	19	matrix	matrix	NOUN
ejpam-6733	231	20	.	.	PUNCT
ejpam-6733	232	1	from	from	ADP
ejpam-6733	232	2	lemma	lemma	PROPN
ejpam-6733	232	3	2	2	NUM
ejpam-6733	232	4	,	,	PUNCT
ejpam-6733	232	5	the	the	DET
ejpam-6733	232	6	representation	representation	NOUN
ejpam-6733	232	7	is	be	AUX
ejpam-6733	232	8	not	not	PART
ejpam-6733	232	9	faithful	faithful	ADJ
ejpam-6733	232	10	.	.	PUNCT
ejpam-6733	233	1	therefore	therefore	ADV
ejpam-6733	233	2	,	,	PUNCT
ejpam-6733	233	3	bc	bc	PROPN
ejpam-6733	233	4	=	=	PROPN
ejpam-6733	233	5	0	0	PROPN
ejpam-6733	233	6	.	.	PUNCT
ejpam-6733	234	1	the	the	DET
ejpam-6733	234	2	case	case	NOUN
ejpam-6733	234	3	where	where	SCONJ
ejpam-6733	234	4	b	b	X
ejpam-6733	234	5	=	=	SYM
ejpam-6733	234	6	c	c	NOUN
ejpam-6733	234	7	=	=	SYM
ejpam-6733	234	8	0	0	NUM
ejpam-6733	234	9	,	,	PUNCT
ejpam-6733	234	10	implies	imply	VERB
ejpam-6733	234	11	that	that	SCONJ
ejpam-6733	234	12	a	a	DET
ejpam-6733	234	13	=	=	SYM
ejpam-6733	234	14	0	0	NUM
ejpam-6733	234	15	which	which	PRON
ejpam-6733	234	16	is	be	AUX
ejpam-6733	234	17	rejected	reject	VERB
ejpam-6733	234	18	since	since	SCONJ
ejpam-6733	234	19	a	a	PRON
ejpam-6733	234	20	is	be	AUX
ejpam-6733	234	21	a	a	DET
ejpam-6733	234	22	basis	basis	NOUN
ejpam-6733	234	23	element	element	NOUN
ejpam-6733	234	24	.	.	PUNCT
ejpam-6733	235	1	hence	hence	ADV
ejpam-6733	235	2	,	,	PUNCT
ejpam-6733	235	3	the	the	DET
ejpam-6733	235	4	lemma	lemma	PROPN
ejpam-6733	235	5	.	.	PUNCT
ejpam-6733	235	6	theorem	theorem	VERB
ejpam-6733	235	7	4	4	NUM
ejpam-6733	235	8	.	.	PUNCT
ejpam-6733	236	1	the	the	DET
ejpam-6733	236	2	lie	lie	NOUN
ejpam-6733	236	3	algebra	algebra	NOUN
ejpam-6733	236	4	lq	lq	VERB
ejpam-6733	236	5	,	,	PUNCT
ejpam-6733	236	6	q	q	NOUN
ejpam-6733	236	7	,	,	PUNCT
ejpam-6733	236	8	where	where	SCONJ
ejpam-6733	236	9	q	q	PROPN
ejpam-6733	236	10	∈	∈	PROPN
ejpam-6733	236	11	r∗	r∗	PROPN
ejpam-6733	236	12	,	,	PUNCT
ejpam-6733	236	13	has	have	VERB
ejpam-6733	236	14	a	a	DET
ejpam-6733	236	15	faithful	faithful	ADJ
ejpam-6733	236	16	representation	representation	NOUN
ejpam-6733	236	17	of	of	ADP
ejpam-6733	236	18	degree	degree	NOUN
ejpam-6733	236	19	2	2	NUM
ejpam-6733	236	20	as	as	ADP
ejpam-6733	236	21	the	the	DET
ejpam-6733	236	22	least	least	ADJ
ejpam-6733	236	23	degree	degree	NOUN
ejpam-6733	236	24	,	,	PUNCT
ejpam-6733	236	25	if	if	SCONJ
ejpam-6733	236	26	and	and	CCONJ
ejpam-6733	236	27	only	only	ADV
ejpam-6733	236	28	if	if	SCONJ
ejpam-6733	236	29	,	,	PUNCT
ejpam-6733	236	30	there	there	PRON
ejpam-6733	236	31	exists	exist	VERB
ejpam-6733	236	32	t	t	PROPN
ejpam-6733	236	33	∈	∈	PROPN
ejpam-6733	236	34	r	r	NOUN
ejpam-6733	236	35	,	,	PUNCT
ejpam-6733	236	36	such	such	ADJ
ejpam-6733	236	37	that	that	SCONJ
ejpam-6733	236	38	f	f	PROPN
ejpam-6733	236	39	(	(	PUNCT
ejpam-6733	236	40	t	t	PROPN
ejpam-6733	236	41	)	)	PUNCT
ejpam-6733	237	1	=	=	SYM
ejpam-6733	237	2	−f	−f	NOUN
ejpam-6733	237	3	(	(	PUNCT
ejpam-6733	237	4	t−	t−	PROPN
ejpam-6733	237	5	r	r	NOUN
ejpam-6733	237	6	q	q	NOUN
ejpam-6733	237	7	)	)	PUNCT
ejpam-6733	237	8	with	with	ADP
ejpam-6733	237	9	f	f	PROPN
ejpam-6733	237	10	(	(	PUNCT
ejpam-6733	237	11	t	t	PROPN
ejpam-6733	237	12	)	)	PUNCT
ejpam-6733	237	13	q	q	NOUN
ejpam-6733	237	14	>	>	X
ejpam-6733	237	15	0	0	X
ejpam-6733	237	16	.	.	PUNCT
ejpam-6733	238	1	moreover	moreover	ADV
ejpam-6733	238	2	,	,	PUNCT
ejpam-6733	238	3	the	the	DET
ejpam-6733	238	4	representation	representation	NOUN
ejpam-6733	238	5	matrices	matrix	NOUN
ejpam-6733	238	6	of	of	ADP
ejpam-6733	238	7	k+,k−	k+,k−	PROPN
ejpam-6733	238	8	,	,	PUNCT
ejpam-6733	238	9	and	and	CCONJ
ejpam-6733	238	10	k0	k0	PROPN
ejpam-6733	238	11	are	be	AUX
ejpam-6733	238	12	a	a	DET
ejpam-6733	238	13	=	=	X
ejpam-6733	238	14	[	[	PUNCT
ejpam-6733	238	15	0	0	NUM
ejpam-6733	238	16	b	b	NOUN
ejpam-6733	238	17	0	0	NUM
ejpam-6733	238	18	0	0	NUM
ejpam-6733	238	19	]	]	PUNCT
ejpam-6733	238	20	,	,	PUNCT
ejpam-6733	238	21	b	b	X
ejpam-6733	238	22	=	=	SYM
ejpam-6733	238	23	a†	a†	PROPN
ejpam-6733	238	24	,	,	PUNCT
ejpam-6733	238	25	and	and	CCONJ
ejpam-6733	238	26	c	c	NOUN
ejpam-6733	238	27	=	=	SYM
ejpam-6733	238	28	diag	diag	PROPN
ejpam-6733	238	29	(	(	PUNCT
ejpam-6733	238	30	t	t	PROPN
ejpam-6733	238	31	,	,	PUNCT
ejpam-6733	238	32	t−	t−	PROPN
ejpam-6733	238	33	r	r	NOUN
ejpam-6733	238	34	q	q	NOUN
ejpam-6733	238	35	)	)	PUNCT
ejpam-6733	238	36	,	,	PUNCT
ejpam-6733	238	37	respectively	respectively	ADV
ejpam-6733	238	38	,	,	PUNCT
ejpam-6733	238	39	such	such	ADJ
ejpam-6733	238	40	that	that	SCONJ
ejpam-6733	238	41	|b|2	|b|2	PROPN
ejpam-6733	238	42	=	=	PUNCT
ejpam-6733	238	43	f	f	X
ejpam-6733	238	44	(	(	PUNCT
ejpam-6733	238	45	t	t	PROPN
ejpam-6733	238	46	)	)	PUNCT
ejpam-6733	238	47	q	q	NOUN
ejpam-6733	238	48	.	.	PUNCT
ejpam-6733	239	1	l.	l.	PROPN
ejpam-6733	239	2	a	a	DET
ejpam-6733	239	3	-	-	PUNCT
ejpam-6733	239	4	m.	m.	NOUN
ejpam-6733	239	5	hanna	hanna	NOUN
ejpam-6733	239	6	,	,	PUNCT
ejpam-6733	239	7	s.	s.	PROPN
ejpam-6733	239	8	s.	s.	PROPN
ejpam-6733	239	9	hassan	hassan	PROPN
ejpam-6733	239	10	,	,	PUNCT
ejpam-6733	239	11	m.	m.	NOUN
ejpam-6733	239	12	almutairi	almutairi	PROPN
ejpam-6733	239	13	/	/	SYM
ejpam-6733	239	14	eur	eur	PROPN
ejpam-6733	239	15	.	.	PUNCT
ejpam-6733	240	1	j.	j.	PROPN
ejpam-6733	240	2	pure	pure	PROPN
ejpam-6733	240	3	appl	appl	PROPN
ejpam-6733	240	4	.	.	PROPN
ejpam-6733	240	5	math	math	PROPN
ejpam-6733	240	6	,	,	PUNCT
ejpam-6733	240	7	18	18	NUM
ejpam-6733	240	8	(	(	PUNCT
ejpam-6733	240	9	4	4	NUM
ejpam-6733	240	10	)	)	PUNCT
ejpam-6733	240	11	(	(	PUNCT
ejpam-6733	240	12	2025	2025	NUM
ejpam-6733	240	13	)	)	PUNCT
ejpam-6733	240	14	,	,	PUNCT
ejpam-6733	240	15	6733	6733	NUM
ejpam-6733	240	16	8	8	NUM
ejpam-6733	240	17	of	of	ADP
ejpam-6733	240	18	12	12	NUM
ejpam-6733	240	19	proof	proof	NOUN
ejpam-6733	240	20	.	.	PUNCT
ejpam-6733	241	1	from	from	ADP
ejpam-6733	241	2	lemma	lemma	PROPN
ejpam-6733	241	3	3	3	NUM
ejpam-6733	241	4	,	,	PUNCT
ejpam-6733	241	5	a	a	DET
ejpam-6733	241	6	=	=	X
ejpam-6733	241	7	[	[	PUNCT
ejpam-6733	241	8	0	0	NUM
ejpam-6733	241	9	b	b	NOUN
ejpam-6733	241	10	0	0	NUM
ejpam-6733	241	11	0	0	NUM
ejpam-6733	241	12	]	]	PUNCT
ejpam-6733	241	13	,	,	PUNCT
ejpam-6733	241	14	with	with	ADP
ejpam-6733	241	15	b	b	PROPN
ejpam-6733	241	16	6=	6=	NUM
ejpam-6733	241	17	0	0	NUM
ejpam-6733	241	18	,	,	PUNCT
ejpam-6733	241	19	that	that	PRON
ejpam-6733	241	20	is	be	AUX
ejpam-6733	241	21	|b|2	|b|2	PROPN
ejpam-6733	241	22	>	>	X
ejpam-6733	241	23	0	0	X
ejpam-6733	241	24	.	.	PUNCT
ejpam-6733	242	1	from	from	ADP
ejpam-6733	242	2	(	(	PUNCT
ejpam-6733	242	3	15	15	NUM
ejpam-6733	242	4	)	)	PUNCT
ejpam-6733	242	5	,	,	PUNCT
ejpam-6733	242	6	we	we	PRON
ejpam-6733	242	7	have	have	VERB
ejpam-6733	242	8	bq	bq	INTJ
ejpam-6733	242	9	(	(	PUNCT
ejpam-6733	242	10	c1	c1	PROPN
ejpam-6733	242	11	−	−	PROPN
ejpam-6733	242	12	c2	c2	PROPN
ejpam-6733	242	13	)	)	PUNCT
ejpam-6733	242	14	=	=	SYM
ejpam-6733	242	15	rb	rb	PROPN
ejpam-6733	242	16	.	.	PUNCT
ejpam-6733	243	1	thus	thus	ADV
ejpam-6733	243	2	,	,	PUNCT
ejpam-6733	243	3	c2	c2	PROPN
ejpam-6733	243	4	=	=	PROPN
ejpam-6733	243	5	c1	c1	PROPN
ejpam-6733	243	6	−	−	PROPN
ejpam-6733	243	7	r	r	NOUN
ejpam-6733	243	8	q	q	NOUN
ejpam-6733	243	9	,	,	PUNCT
ejpam-6733	243	10	since	since	SCONJ
ejpam-6733	243	11	b	b	PROPN
ejpam-6733	243	12	6=	6=	PROPN
ejpam-6733	243	13	0	0	NUM
ejpam-6733	243	14	.	.	PUNCT
ejpam-6733	244	1	from	from	ADP
ejpam-6733	244	2	(	(	PUNCT
ejpam-6733	244	3	14	14	NUM
ejpam-6733	244	4	)	)	PUNCT
ejpam-6733	244	5	,	,	PUNCT
ejpam-6733	244	6	f	f	PROPN
ejpam-6733	244	7	(	(	PUNCT
ejpam-6733	244	8	c1	c1	PROPN
ejpam-6733	244	9	)	)	PUNCT
ejpam-6733	244	10	=	=	PUNCT
ejpam-6733	244	11	q	q	PUNCT
ejpam-6733	244	12	|b|2	|b|2	PROPN
ejpam-6733	244	13	,	,	PUNCT
ejpam-6733	244	14	and	and	CCONJ
ejpam-6733	244	15	f	f	PROPN
ejpam-6733	244	16	(	(	PUNCT
ejpam-6733	244	17	c2	c2	PROPN
ejpam-6733	244	18	)	)	PUNCT
ejpam-6733	244	19	=	=	VERB
ejpam-6733	244	20	−q	−q	ADJ
ejpam-6733	244	21	|b|2	|b|2	PROPN
ejpam-6733	244	22	=	=	SYM
ejpam-6733	244	23	−f	−f	PROPN
ejpam-6733	244	24	(	(	PUNCT
ejpam-6733	244	25	c1	c1	PROPN
ejpam-6733	244	26	)	)	PUNCT
ejpam-6733	244	27	.	.	PUNCT
ejpam-6733	245	1	thus	thus	ADV
ejpam-6733	245	2	,	,	PUNCT
ejpam-6733	245	3	for	for	ADP
ejpam-6733	245	4	a	a	DET
ejpam-6733	245	5	faithful	faithful	ADJ
ejpam-6733	245	6	representation	representation	NOUN
ejpam-6733	245	7	of	of	ADP
ejpam-6733	245	8	lq	lq	PROPN
ejpam-6733	245	9	,	,	PUNCT
ejpam-6733	245	10	q	q	NOUN
ejpam-6733	245	11	,	,	PUNCT
ejpam-6733	245	12	the	the	DET
ejpam-6733	245	13	polynomial	polynomial	ADJ
ejpam-6733	245	14	function	function	NOUN
ejpam-6733	245	15	f	f	PROPN
ejpam-6733	245	16	should	should	AUX
ejpam-6733	245	17	satisfy	satisfy	VERB
ejpam-6733	245	18	that	that	SCONJ
ejpam-6733	245	19	f	f	PROPN
ejpam-6733	245	20	(	(	PUNCT
ejpam-6733	245	21	t	t	PROPN
ejpam-6733	245	22	)	)	PUNCT
ejpam-6733	246	1	=	=	SYM
ejpam-6733	246	2	−f	−f	NOUN
ejpam-6733	246	3	(	(	PUNCT
ejpam-6733	246	4	t−	t−	PROPN
ejpam-6733	246	5	r	r	NOUN
ejpam-6733	246	6	q	q	NOUN
ejpam-6733	246	7	)	)	PUNCT
ejpam-6733	246	8	for	for	ADP
ejpam-6733	246	9	some	some	DET
ejpam-6733	246	10	real	real	ADJ
ejpam-6733	246	11	number	number	NOUN
ejpam-6733	246	12	t.	t.	PROPN
ejpam-6733	246	13	actually	actually	ADV
ejpam-6733	246	14	,	,	PUNCT
ejpam-6733	246	15	c1	c1	PROPN
ejpam-6733	246	16	=	=	PUNCT
ejpam-6733	246	17	t.	t.	X
ejpam-6733	246	18	thus	thus	ADV
ejpam-6733	246	19	c	c	NOUN
ejpam-6733	246	20	=	=	SYM
ejpam-6733	246	21	diag	diag	X
ejpam-6733	246	22	(	(	PUNCT
ejpam-6733	246	23	t	t	PROPN
ejpam-6733	246	24	,	,	PUNCT
ejpam-6733	246	25	t−	t−	PROPN
ejpam-6733	246	26	r	r	NOUN
ejpam-6733	246	27	q	q	PROPN
ejpam-6733	246	28	)	)	PUNCT
ejpam-6733	246	29	.	.	PUNCT
ejpam-6733	247	1	if	if	SCONJ
ejpam-6733	247	2	there	there	PRON
ejpam-6733	247	3	is	be	VERB
ejpam-6733	247	4	no	no	DET
ejpam-6733	247	5	such	such	ADJ
ejpam-6733	247	6	t	t	PROPN
ejpam-6733	247	7	,	,	PUNCT
ejpam-6733	247	8	then	then	ADV
ejpam-6733	247	9	the	the	DET
ejpam-6733	247	10	representation	representation	NOUN
ejpam-6733	247	11	matrix	matrix	NOUN
ejpam-6733	247	12	c	c	NOUN
ejpam-6733	247	13	can	can	AUX
ejpam-6733	247	14	not	not	PART
ejpam-6733	247	15	be	be	AUX
ejpam-6733	247	16	found	find	VERB
ejpam-6733	247	17	and	and	CCONJ
ejpam-6733	247	18	hence	hence	ADV
ejpam-6733	247	19	,	,	PUNCT
ejpam-6733	247	20	lq	lq	PROPN
ejpam-6733	247	21	,	,	PUNCT
ejpam-6733	247	22	q	q	PROPN
ejpam-6733	247	23	has	have	VERB
ejpam-6733	247	24	no	no	DET
ejpam-6733	247	25	matrix	matrix	NOUN
ejpam-6733	247	26	representation	representation	NOUN
ejpam-6733	247	27	.	.	PUNCT
ejpam-6733	248	1	also	also	ADV
ejpam-6733	248	2	,	,	PUNCT
ejpam-6733	248	3	from	from	ADP
ejpam-6733	248	4	(	(	PUNCT
ejpam-6733	248	5	14	14	NUM
ejpam-6733	248	6	)	)	PUNCT
ejpam-6733	248	7	,	,	PUNCT
ejpam-6733	248	8	we	we	PRON
ejpam-6733	248	9	have	have	VERB
ejpam-6733	248	10	|b|2	|b|2	NOUN
ejpam-6733	248	11	=	=	SYM
ejpam-6733	248	12	f	f	X
ejpam-6733	248	13	(	(	PUNCT
ejpam-6733	248	14	t	t	PROPN
ejpam-6733	248	15	)	)	PUNCT
ejpam-6733	248	16	q	q	NOUN
ejpam-6733	248	17	must	must	AUX
ejpam-6733	248	18	be	be	AUX
ejpam-6733	248	19	positive	positive	ADJ
ejpam-6733	248	20	,	,	PUNCT
ejpam-6733	248	21	because	because	SCONJ
ejpam-6733	248	22	if	if	SCONJ
ejpam-6733	248	23	it	it	PRON
ejpam-6733	248	24	is	be	AUX
ejpam-6733	248	25	negative	negative	ADJ
ejpam-6733	248	26	,	,	PUNCT
ejpam-6733	248	27	a	a	PRON
ejpam-6733	248	28	does	do	AUX
ejpam-6733	248	29	not	not	PART
ejpam-6733	248	30	exist	exist	VERB
ejpam-6733	248	31	,	,	PUNCT
ejpam-6733	248	32	and	and	CCONJ
ejpam-6733	248	33	if	if	SCONJ
ejpam-6733	248	34	it	it	PRON
ejpam-6733	248	35	is	be	AUX
ejpam-6733	248	36	0	0	NUM
ejpam-6733	248	37	,	,	PUNCT
ejpam-6733	248	38	then	then	ADV
ejpam-6733	248	39	a	a	DET
ejpam-6733	248	40	=	=	NOUN
ejpam-6733	248	41	0	0	NUM
ejpam-6733	248	42	,	,	PUNCT
ejpam-6733	248	43	and	and	CCONJ
ejpam-6733	248	44	the	the	DET
ejpam-6733	248	45	representation	representation	NOUN
ejpam-6733	248	46	is	be	AUX
ejpam-6733	248	47	not	not	PART
ejpam-6733	248	48	faithful	faithful	ADJ
ejpam-6733	248	49	.	.	PUNCT
ejpam-6733	249	1	hence	hence	ADV
ejpam-6733	249	2	the	the	DET
ejpam-6733	249	3	theorem	theorem	NOUN
ejpam-6733	249	4	.	.	PUNCT
ejpam-6733	250	1	the	the	DET
ejpam-6733	250	2	following	follow	VERB
ejpam-6733	250	3	examples	example	NOUN
ejpam-6733	250	4	demonstrate	demonstrate	VERB
ejpam-6733	250	5	the	the	DET
ejpam-6733	250	6	method	method	NOUN
ejpam-6733	250	7	for	for	ADP
ejpam-6733	250	8	calculating	calculate	VERB
ejpam-6733	250	9	the	the	DET
ejpam-6733	250	10	representation	representation	NOUN
ejpam-6733	250	11	matrices	matrix	NOUN
ejpam-6733	250	12	.	.	PUNCT
ejpam-6733	251	1	example	example	NOUN
ejpam-6733	251	2	1	1	NUM
ejpam-6733	251	3	.	.	PUNCT
ejpam-6733	252	1	given	give	VERB
ejpam-6733	252	2	that	that	DET
ejpam-6733	252	3	p	p	NOUN
ejpam-6733	252	4	=	=	X
ejpam-6733	252	5	q	q	NOUN
ejpam-6733	252	6	=	=	SYM
ejpam-6733	252	7	2	2	NUM
ejpam-6733	252	8	,	,	PUNCT
ejpam-6733	252	9	r	r	NOUN
ejpam-6733	252	10	=	=	SYM
ejpam-6733	252	11	4	4	NUM
ejpam-6733	252	12	and	and	CCONJ
ejpam-6733	252	13	f	f	PROPN
ejpam-6733	252	14	(	(	PUNCT
ejpam-6733	252	15	x	x	X
ejpam-6733	252	16	)	)	PUNCT
ejpam-6733	252	17	=	=	SYM
ejpam-6733	252	18	x3	x3	PROPN
ejpam-6733	253	1	+	+	CCONJ
ejpam-6733	253	2	x.	x.	NOUN
ejpam-6733	253	3	first	first	ADV
ejpam-6733	253	4	we	we	PRON
ejpam-6733	253	5	consider	consider	VERB
ejpam-6733	253	6	the	the	DET
ejpam-6733	253	7	equation	equation	NOUN
ejpam-6733	253	8	f	f	X
ejpam-6733	253	9	(	(	PUNCT
ejpam-6733	253	10	t−	t−	PROPN
ejpam-6733	253	11	r	r	NOUN
ejpam-6733	253	12	q	q	NOUN
ejpam-6733	253	13	)	)	PUNCT
ejpam-6733	254	1	=	=	SYM
ejpam-6733	254	2	−f	−f	NOUN
ejpam-6733	254	3	(	(	PUNCT
ejpam-6733	254	4	t	t	PROPN
ejpam-6733	254	5	)	)	PUNCT
ejpam-6733	254	6	.	.	PUNCT
ejpam-6733	255	1	thus	thus	ADV
ejpam-6733	255	2	,	,	PUNCT
ejpam-6733	255	3	(	(	PUNCT
ejpam-6733	255	4	t−	t−	PROPN
ejpam-6733	255	5	2)3	2)3	NUM
ejpam-6733	255	6	+	+	NUM
ejpam-6733	255	7	(	(	PUNCT
ejpam-6733	255	8	t−	t−	PROPN
ejpam-6733	255	9	2	2	NUM
ejpam-6733	255	10	)	)	PUNCT
ejpam-6733	255	11	=	=	SYM
ejpam-6733	255	12	−	−	PROPN
ejpam-6733	255	13	(	(	PUNCT
ejpam-6733	255	14	t3	t3	PROPN
ejpam-6733	255	15	+	+	X
ejpam-6733	255	16	t	t	PROPN
ejpam-6733	255	17	)	)	PUNCT
ejpam-6733	255	18	,	,	PUNCT
ejpam-6733	255	19	which	which	PRON
ejpam-6733	255	20	is	be	AUX
ejpam-6733	255	21	2t3	2t3	NUM
ejpam-6733	255	22	−	−	NUM
ejpam-6733	255	23	5t2	5t2	NUM
ejpam-6733	255	24	+	+	CCONJ
ejpam-6733	255	25	13	13	NUM
ejpam-6733	255	26	t	t	NOUN
ejpam-6733	255	27	−	−	NOUN
ejpam-6733	255	28	10	10	NUM
ejpam-6733	255	29	=	=	SYM
ejpam-6733	255	30	0	0	X
ejpam-6733	255	31	.	.	PUNCT
ejpam-6733	256	1	choose	choose	VERB
ejpam-6733	256	2	the	the	DET
ejpam-6733	256	3	real	real	ADJ
ejpam-6733	256	4	solution	solution	NOUN
ejpam-6733	256	5	t	t	NOUN
ejpam-6733	256	6	=	=	SYM
ejpam-6733	256	7	1	1	NUM
ejpam-6733	256	8	,	,	PUNCT
ejpam-6733	256	9	as	as	SCONJ
ejpam-6733	256	10	it	it	PRON
ejpam-6733	256	11	satisfies	satisfy	VERB
ejpam-6733	256	12	that	that	SCONJ
ejpam-6733	256	13	f	f	PROPN
ejpam-6733	256	14	(	(	PUNCT
ejpam-6733	256	15	t	t	PROPN
ejpam-6733	256	16	)	)	PUNCT
ejpam-6733	256	17	q	q	NOUN
ejpam-6733	256	18	>	>	X
ejpam-6733	256	19	0	0	NUM
ejpam-6733	256	20	,	,	PUNCT
ejpam-6733	256	21	since	since	SCONJ
ejpam-6733	256	22	f	f	PROPN
ejpam-6733	256	23	(	(	PUNCT
ejpam-6733	256	24	t	t	PROPN
ejpam-6733	256	25	)	)	PUNCT
ejpam-6733	256	26	q	q	NOUN
ejpam-6733	257	1	=	=	NOUN
ejpam-6733	257	2	13	13	NUM
ejpam-6733	257	3	+	+	NOUN
ejpam-6733	257	4	1	1	NUM
ejpam-6733	257	5	2	2	NUM
ejpam-6733	257	6	=	=	SYM
ejpam-6733	257	7	1	1	NUM
ejpam-6733	257	8	>	>	X
ejpam-6733	257	9	0	0	X
ejpam-6733	257	10	.	.	PUNCT
ejpam-6733	258	1	so	so	ADV
ejpam-6733	258	2	,	,	PUNCT
ejpam-6733	258	3	|b|2	|b|2	PROPN
ejpam-6733	258	4	=	=	SYM
ejpam-6733	258	5	f	f	X
ejpam-6733	258	6	(	(	PUNCT
ejpam-6733	258	7	t	t	PROPN
ejpam-6733	258	8	)	)	PUNCT
ejpam-6733	258	9	q	q	NOUN
ejpam-6733	259	1	=	=	NOUN
ejpam-6733	259	2	1	1	X
ejpam-6733	259	3	.	.	X
ejpam-6733	259	4	take	take	VERB
ejpam-6733	259	5	b	b	NOUN
ejpam-6733	259	6	=	=	SYM
ejpam-6733	259	7	1	1	NUM
ejpam-6733	259	8	.	.	PUNCT
ejpam-6733	260	1	therefore	therefore	ADV
ejpam-6733	260	2	,	,	PUNCT
ejpam-6733	260	3	a	a	PRON
ejpam-6733	260	4	=	=	X
ejpam-6733	260	5	[	[	PUNCT
ejpam-6733	260	6	0	0	NUM
ejpam-6733	260	7	1	1	NUM
ejpam-6733	260	8	0	0	NUM
ejpam-6733	260	9	0	0	NUM
ejpam-6733	260	10	]	]	PUNCT
ejpam-6733	260	11	,	,	PUNCT
ejpam-6733	260	12	b	b	X
ejpam-6733	260	13	=	=	SYM
ejpam-6733	260	14	a†	a†	NOUN
ejpam-6733	260	15	and	and	CCONJ
ejpam-6733	260	16	c	c	NOUN
ejpam-6733	260	17	=	=	SYM
ejpam-6733	260	18	diag	diag	X
ejpam-6733	260	19	(	(	PUNCT
ejpam-6733	260	20	1,−1	1,−1	NUM
ejpam-6733	260	21	)	)	PUNCT
ejpam-6733	260	22	are	be	AUX
ejpam-6733	260	23	representation	representation	NOUN
ejpam-6733	260	24	matrices	matrix	NOUN
ejpam-6733	260	25	of	of	ADP
ejpam-6733	260	26	k+,k−	k+,k−	PROPN
ejpam-6733	260	27	and	and	CCONJ
ejpam-6733	260	28	k0	k0	PROPN
ejpam-6733	260	29	,	,	PUNCT
ejpam-6733	260	30	respectively	respectively	ADV
ejpam-6733	260	31	.	.	PUNCT
ejpam-6733	261	1	since	since	SCONJ
ejpam-6733	261	2	[	[	X
ejpam-6733	261	3	a	a	X
ejpam-6733	261	4	,	,	PUNCT
ejpam-6733	261	5	b]2,2	b]2,2	PROPN
ejpam-6733	261	6	=	=	SYM
ejpam-6733	261	7	2	2	NUM
ejpam-6733	261	8	[	[	PUNCT
ejpam-6733	261	9	0	0	NUM
ejpam-6733	261	10	1	1	NUM
ejpam-6733	261	11	0	0	NUM
ejpam-6733	261	12	0	0	NUM
ejpam-6733	261	13	]	]	PUNCT
ejpam-6733	261	14	[	[	PUNCT
ejpam-6733	261	15	0	0	NUM
ejpam-6733	261	16	0	0	NUM
ejpam-6733	261	17	1	1	NUM
ejpam-6733	261	18	0	0	NUM
ejpam-6733	261	19	]	]	PUNCT
ejpam-6733	261	20	−2	−2	X
ejpam-6733	261	21	[	[	PUNCT
ejpam-6733	261	22	0	0	NUM
ejpam-6733	261	23	0	0	NUM
ejpam-6733	261	24	1	1	NUM
ejpam-6733	261	25	0	0	NUM
ejpam-6733	261	26	]	]	PUNCT
ejpam-6733	261	27	[	[	PUNCT
ejpam-6733	261	28	0	0	NUM
ejpam-6733	261	29	1	1	NUM
ejpam-6733	261	30	0	0	NUM
ejpam-6733	261	31	0	0	NUM
ejpam-6733	261	32	]	]	PUNCT
ejpam-6733	262	1	=	=	PUNCT
ejpam-6733	262	2	[	[	PUNCT
ejpam-6733	262	3	2	2	NUM
ejpam-6733	262	4	0	0	NUM
ejpam-6733	262	5	0	0	NUM
ejpam-6733	262	6	−2	−2	NOUN
ejpam-6733	262	7	]	]	PUNCT
ejpam-6733	263	1	=	=	PUNCT
ejpam-6733	263	2	diag	diag	NOUN
ejpam-6733	263	3	(	(	PUNCT
ejpam-6733	263	4	f	f	X
ejpam-6733	263	5	(	(	PUNCT
ejpam-6733	263	6	1	1	NUM
ejpam-6733	263	7	)	)	PUNCT
ejpam-6733	263	8	,	,	PUNCT
ejpam-6733	263	9	f	f	PROPN
ejpam-6733	263	10	(	(	PUNCT
ejpam-6733	263	11	−1	−1	NOUN
ejpam-6733	263	12	)	)	PUNCT
ejpam-6733	263	13	)	)	PUNCT
ejpam-6733	263	14	.	.	PUNCT
ejpam-6733	264	1	and	and	CCONJ
ejpam-6733	265	1	[	[	X
ejpam-6733	265	2	c	c	X
ejpam-6733	265	3	,	,	PUNCT
ejpam-6733	265	4	a]2,2	a]2,2	PROPN
ejpam-6733	265	5	=	=	SYM
ejpam-6733	265	6	2	2	NUM
ejpam-6733	265	7	[	[	PUNCT
ejpam-6733	265	8	1	1	NUM
ejpam-6733	265	9	0	0	NUM
ejpam-6733	265	10	0	0	NUM
ejpam-6733	265	11	−1	−1	NOUN
ejpam-6733	265	12	]	]	PUNCT
ejpam-6733	266	1	[	[	PUNCT
ejpam-6733	266	2	0	0	NUM
ejpam-6733	266	3	1	1	NUM
ejpam-6733	266	4	0	0	NUM
ejpam-6733	266	5	0	0	NUM
ejpam-6733	266	6	]	]	PUNCT
ejpam-6733	266	7	−	−	PROPN
ejpam-6733	266	8	2	2	NUM
ejpam-6733	266	9	[	[	PUNCT
ejpam-6733	266	10	0	0	NUM
ejpam-6733	266	11	1	1	NUM
ejpam-6733	266	12	0	0	NUM
ejpam-6733	266	13	0	0	NUM
ejpam-6733	266	14	]	]	PUNCT
ejpam-6733	266	15	[	[	PUNCT
ejpam-6733	266	16	1	1	NUM
ejpam-6733	266	17	0	0	NUM
ejpam-6733	266	18	0	0	NUM
ejpam-6733	266	19	−1	−1	NOUN
ejpam-6733	266	20	]	]	PUNCT
ejpam-6733	267	1	=	=	PUNCT
ejpam-6733	267	2	[	[	PUNCT
ejpam-6733	267	3	0	0	NUM
ejpam-6733	267	4	4	4	NUM
ejpam-6733	267	5	0	0	NUM
ejpam-6733	267	6	0	0	NUM
ejpam-6733	267	7	]	]	PUNCT
ejpam-6733	267	8	=	=	SYM
ejpam-6733	267	9	4a	4a	NUM
ejpam-6733	267	10	.	.	PUNCT
ejpam-6733	268	1	clearly	clearly	ADV
ejpam-6733	268	2	,	,	PUNCT
ejpam-6733	268	3	the	the	DET
ejpam-6733	268	4	representation	representation	NOUN
ejpam-6733	268	5	is	be	AUX
ejpam-6733	268	6	faithful	faithful	ADJ
ejpam-6733	268	7	,	,	PUNCT
ejpam-6733	268	8	because	because	SCONJ
ejpam-6733	268	9	the	the	DET
ejpam-6733	268	10	matrices	matrix	NOUN
ejpam-6733	268	11	a	a	DET
ejpam-6733	268	12	,	,	PUNCT
ejpam-6733	268	13	b	b	NOUN
ejpam-6733	268	14	,	,	PUNCT
ejpam-6733	268	15	and	and	CCONJ
ejpam-6733	268	16	c	c	NOUN
ejpam-6733	268	17	are	be	AUX
ejpam-6733	268	18	linearly	linearly	ADV
ejpam-6733	268	19	independent	independent	ADJ
ejpam-6733	268	20	.	.	PUNCT
ejpam-6733	269	1	another	another	DET
ejpam-6733	269	2	representation	representation	NOUN
ejpam-6733	269	3	matrices	matrix	NOUN
ejpam-6733	269	4	can	can	AUX
ejpam-6733	269	5	be	be	AUX
ejpam-6733	269	6	considered	consider	VERB
ejpam-6733	269	7	as	as	ADP
ejpam-6733	269	8	|b|2	|b|2	PROPN
ejpam-6733	269	9	=	=	SYM
ejpam-6733	269	10	1	1	NUM
ejpam-6733	269	11	,	,	PUNCT
ejpam-6733	269	12	let	let	VERB
ejpam-6733	269	13	a	a	PRON
ejpam-6733	269	14	=	=	X
ejpam-6733	270	1	[	[	PUNCT
ejpam-6733	270	2	0	0	NUM
ejpam-6733	270	3	i	i	NOUN
ejpam-6733	270	4	0	0	NUM
ejpam-6733	270	5	0	0	NUM
ejpam-6733	270	6	]	]	PUNCT
ejpam-6733	270	7	,	,	PUNCT
ejpam-6733	270	8	b	b	X
ejpam-6733	270	9	=	=	SYM
ejpam-6733	270	10	a†	a†	NOUN
ejpam-6733	270	11	and	and	CCONJ
ejpam-6733	270	12	c	c	NOUN
ejpam-6733	270	13	=	=	SYM
ejpam-6733	270	14	diag	diag	X
ejpam-6733	270	15	(	(	PUNCT
ejpam-6733	270	16	1,−1	1,−1	NUM
ejpam-6733	270	17	)	)	PUNCT
ejpam-6733	270	18	.	.	PUNCT
ejpam-6733	271	1	such	such	DET
ejpam-6733	271	2	a	a	DET
ejpam-6733	271	3	representation	representation	NOUN
ejpam-6733	271	4	does	do	AUX
ejpam-6733	271	5	not	not	PART
ejpam-6733	271	6	satisfy	satisfy	VERB
ejpam-6733	271	7	the	the	DET
ejpam-6733	271	8	condition	condition	NOUN
ejpam-6733	271	9	k+	k+	PUNCT
ejpam-6733	271	10	+	+	SYM
ejpam-6733	271	11	k−	k−	PROPN
ejpam-6733	271	12	is	be	AUX
ejpam-6733	271	13	real	real	ADJ
ejpam-6733	271	14	.	.	PUNCT
ejpam-6733	272	1	actually	actually	ADV
ejpam-6733	272	2	,	,	PUNCT
ejpam-6733	272	3	this	this	DET
ejpam-6733	272	4	condition	condition	NOUN
ejpam-6733	272	5	is	be	AUX
ejpam-6733	272	6	only	only	ADV
ejpam-6733	272	7	satisfied	satisfied	ADJ
ejpam-6733	272	8	when	when	SCONJ
ejpam-6733	272	9	a	a	PRON
ejpam-6733	272	10	is	be	AUX
ejpam-6733	272	11	a	a	DET
ejpam-6733	272	12	real	real	ADJ
ejpam-6733	272	13	matrix	matrix	NOUN
ejpam-6733	272	14	.	.	PUNCT
ejpam-6733	273	1	example	example	NOUN
ejpam-6733	274	1	2	2	NUM
ejpam-6733	274	2	.	.	PUNCT
ejpam-6733	274	3	let	let	VERB
ejpam-6733	274	4	f	f	PROPN
ejpam-6733	274	5	(	(	PUNCT
ejpam-6733	274	6	x	x	X
ejpam-6733	274	7	)	)	PUNCT
ejpam-6733	274	8	=	=	SYM
ejpam-6733	274	9	x2+x+1	x2+x+1	PROPN
ejpam-6733	274	10	.	.	PUNCT
ejpam-6733	275	1	then	then	ADV
ejpam-6733	275	2	lq	lq	X
ejpam-6733	275	3	,	,	PUNCT
ejpam-6733	275	4	q	q	PROPN
ejpam-6733	275	5	has	have	VERB
ejpam-6733	275	6	no	no	DET
ejpam-6733	275	7	faithful	faithful	ADJ
ejpam-6733	275	8	representation	representation	NOUN
ejpam-6733	275	9	since	since	SCONJ
ejpam-6733	275	10	f	f	PROPN
ejpam-6733	275	11	(	(	PUNCT
ejpam-6733	275	12	t	t	PROPN
ejpam-6733	275	13	)	)	PUNCT
ejpam-6733	275	14	>	>	X
ejpam-6733	275	15	0	0	PUNCT
ejpam-6733	276	1	for	for	ADP
ejpam-6733	276	2	any	any	DET
ejpam-6733	276	3	t	t	PROPN
ejpam-6733	276	4	∈	∈	PROPN
ejpam-6733	276	5	r.	r.	PROPN
ejpam-6733	276	6	example	example	NOUN
ejpam-6733	276	7	3	3	X
ejpam-6733	276	8	.	.	PUNCT
ejpam-6733	277	1	the	the	DET
ejpam-6733	277	2	model	model	NOUN
ejpam-6733	277	3	of	of	ADP
ejpam-6733	277	4	light	light	ADJ
ejpam-6733	277	5	amplifier	amplifier	NOUN
ejpam-6733	277	6	,	,	PUNCT
ejpam-6733	277	7	namely	namely	ADV
ejpam-6733	277	8	,	,	PUNCT
ejpam-6733	277	9	[	[	X
ejpam-6733	277	10	k+,k−	k+,k−	X
ejpam-6733	277	11	]	]	X
ejpam-6733	277	12	=	=	SYM
ejpam-6733	277	13	−2k0	−2k0	PROPN
ejpam-6733	277	14	,	,	PUNCT
ejpam-6733	277	15	[	[	X
ejpam-6733	277	16	k0,k±	k0,k±	X
ejpam-6733	277	17	]	]	X
ejpam-6733	277	18	=	=	SYM
ejpam-6733	277	19	±k±	±k±	PROPN
ejpam-6733	278	1	[	[	X
ejpam-6733	278	2	17	17	NUM
ejpam-6733	278	3	]	]	PUNCT
ejpam-6733	278	4	,	,	PUNCT
ejpam-6733	278	5	where	where	SCONJ
ejpam-6733	278	6	p	p	NOUN
ejpam-6733	278	7	=	=	X
ejpam-6733	278	8	q	q	NOUN
ejpam-6733	278	9	=	=	NOUN
ejpam-6733	278	10	1	1	NUM
ejpam-6733	278	11	,	,	PUNCT
ejpam-6733	278	12	r	r	NOUN
ejpam-6733	278	13	=	=	SYM
ejpam-6733	278	14	1	1	NUM
ejpam-6733	278	15	and	and	CCONJ
ejpam-6733	278	16	f	f	PROPN
ejpam-6733	278	17	(	(	PUNCT
ejpam-6733	278	18	x	x	X
ejpam-6733	278	19	)	)	PUNCT
ejpam-6733	278	20	=	=	PUNCT
ejpam-6733	279	1	−2x	−2x	NOUN
ejpam-6733	279	2	.	.	PUNCT
ejpam-6733	280	1	solving	solve	VERB
ejpam-6733	280	2	f	f	PROPN
ejpam-6733	280	3	(	(	PUNCT
ejpam-6733	280	4	t	t	PROPN
ejpam-6733	280	5	)	)	PUNCT
ejpam-6733	281	1	=	=	SYM
ejpam-6733	281	2	−f	−f	NOUN
ejpam-6733	281	3	(	(	PUNCT
ejpam-6733	281	4	t−	t−	PROPN
ejpam-6733	281	5	r	r	NOUN
ejpam-6733	281	6	q	q	NOUN
ejpam-6733	281	7	)	)	PUNCT
ejpam-6733	281	8	for	for	ADP
ejpam-6733	281	9	t	t	PROPN
ejpam-6733	281	10	,	,	PUNCT
ejpam-6733	281	11	we	we	PRON
ejpam-6733	281	12	get	get	VERB
ejpam-6733	281	13	t	t	NOUN
ejpam-6733	281	14	=	=	SYM
ejpam-6733	281	15	1	1	NUM
ejpam-6733	281	16	2	2	NUM
ejpam-6733	281	17	is	be	AUX
ejpam-6733	281	18	the	the	DET
ejpam-6733	281	19	only	only	ADJ
ejpam-6733	281	20	real	real	ADJ
ejpam-6733	281	21	solution	solution	NOUN
ejpam-6733	281	22	,	,	PUNCT
ejpam-6733	281	23	but	but	CCONJ
ejpam-6733	281	24	f	f	PROPN
ejpam-6733	281	25	(	(	PUNCT
ejpam-6733	281	26	t	t	PROPN
ejpam-6733	281	27	)	)	PUNCT
ejpam-6733	281	28	q	q	NOUN
ejpam-6733	282	1	=	=	PUNCT
ejpam-6733	282	2	−2	−2	NOUN
ejpam-6733	282	3	(	(	PUNCT
ejpam-6733	282	4	1	1	NUM
ejpam-6733	282	5	2	2	NUM
ejpam-6733	282	6	)	)	PUNCT
ejpam-6733	282	7	1	1	NUM
ejpam-6733	282	8	=	=	SYM
ejpam-6733	282	9	−1	−1	NOUN
ejpam-6733	282	10	not	not	PART
ejpam-6733	282	11	positive	positive	ADJ
ejpam-6733	282	12	,	,	PUNCT
ejpam-6733	282	13	i.e.	i.e.	X
ejpam-6733	282	14	,	,	PUNCT
ejpam-6733	282	15	|b|2	|b|2	ADJ
ejpam-6733	282	16	<	<	X
ejpam-6733	282	17	0	0	NUM
ejpam-6733	282	18	,	,	PUNCT
ejpam-6733	282	19	which	which	PRON
ejpam-6733	282	20	is	be	AUX
ejpam-6733	282	21	impossible	impossible	ADJ
ejpam-6733	282	22	.	.	PUNCT
ejpam-6733	283	1	so	so	ADV
ejpam-6733	283	2	,	,	PUNCT
ejpam-6733	283	3	a	a	PRON
ejpam-6733	283	4	does	do	AUX
ejpam-6733	283	5	not	not	PART
ejpam-6733	283	6	exist	exist	VERB
ejpam-6733	283	7	.	.	PUNCT
ejpam-6733	284	1	so	so	ADV
ejpam-6733	284	2	,	,	PUNCT
ejpam-6733	284	3	the	the	DET
ejpam-6733	284	4	light	light	ADJ
ejpam-6733	284	5	amplifier	amplifier	NOUN
ejpam-6733	284	6	model	model	NOUN
ejpam-6733	284	7	has	have	VERB
ejpam-6733	284	8	no	no	DET
ejpam-6733	284	9	matrix	matrix	NOUN
ejpam-6733	284	10	representation	representation	NOUN
ejpam-6733	284	11	satisfying	satisfy	VERB
ejpam-6733	284	12	the	the	DET
ejpam-6733	284	13	physical	physical	ADJ
ejpam-6733	284	14	conditions	condition	NOUN
ejpam-6733	284	15	,	,	PUNCT
ejpam-6733	284	16	as	as	SCONJ
ejpam-6733	284	17	previously	previously	ADV
ejpam-6733	284	18	proved	prove	VERB
ejpam-6733	284	19	in	in	ADP
ejpam-6733	284	20	[	[	X
ejpam-6733	284	21	17	17	NUM
ejpam-6733	284	22	]	]	PUNCT
ejpam-6733	284	23	.	.	PUNCT
ejpam-6733	285	1	l.	l.	PROPN
ejpam-6733	285	2	a	a	DET
ejpam-6733	285	3	-	-	PUNCT
ejpam-6733	285	4	m.	m.	NOUN
ejpam-6733	285	5	hanna	hanna	NOUN
ejpam-6733	285	6	,	,	PUNCT
ejpam-6733	285	7	s.	s.	PROPN
ejpam-6733	285	8	s.	s.	PROPN
ejpam-6733	285	9	hassan	hassan	PROPN
ejpam-6733	285	10	,	,	PUNCT
ejpam-6733	285	11	m.	m.	NOUN
ejpam-6733	285	12	almutairi	almutairi	PROPN
ejpam-6733	285	13	/	/	SYM
ejpam-6733	285	14	eur	eur	PROPN
ejpam-6733	285	15	.	.	PUNCT
ejpam-6733	286	1	j.	j.	PROPN
ejpam-6733	286	2	pure	pure	PROPN
ejpam-6733	286	3	appl	appl	PROPN
ejpam-6733	286	4	.	.	PROPN
ejpam-6733	286	5	math	math	PROPN
ejpam-6733	286	6	,	,	PUNCT
ejpam-6733	286	7	18	18	NUM
ejpam-6733	286	8	(	(	PUNCT
ejpam-6733	286	9	4	4	NUM
ejpam-6733	286	10	)	)	PUNCT
ejpam-6733	286	11	(	(	PUNCT
ejpam-6733	286	12	2025	2025	NUM
ejpam-6733	286	13	)	)	PUNCT
ejpam-6733	286	14	,	,	PUNCT
ejpam-6733	286	15	6733	6733	NUM
ejpam-6733	286	16	9	9	NUM
ejpam-6733	286	17	of	of	ADP
ejpam-6733	286	18	12	12	NUM
ejpam-6733	286	19	5.2	5.2	NUM
ejpam-6733	286	20	.	.	PUNCT
ejpam-6733	287	1	representation	representation	NOUN
ejpam-6733	287	2	matrices	matrix	NOUN
ejpam-6733	287	3	of	of	ADP
ejpam-6733	287	4	degree	degree	NOUN
ejpam-6733	287	5	2	2	NUM
ejpam-6733	287	6	of	of	ADP
ejpam-6733	287	7	l−q	l−q	PROPN
ejpam-6733	287	8	,	,	PUNCT
ejpam-6733	287	9	q	q	NOUN
ejpam-6733	287	10	in	in	ADP
ejpam-6733	287	11	this	this	DET
ejpam-6733	287	12	subsection	subsection	NOUN
ejpam-6733	287	13	,	,	PUNCT
ejpam-6733	287	14	we	we	PRON
ejpam-6733	287	15	consider	consider	VERB
ejpam-6733	287	16	the	the	DET
ejpam-6733	287	17	special	special	ADJ
ejpam-6733	287	18	case	case	NOUN
ejpam-6733	287	19	when	when	SCONJ
ejpam-6733	287	20	p	p	NOUN
ejpam-6733	287	21	=	=	NOUN
ejpam-6733	287	22	−q	−q	NOUN
ejpam-6733	287	23	.	.	PUNCT
ejpam-6733	288	1	lemma	lemma	PROPN
ejpam-6733	288	2	4	4	NUM
ejpam-6733	288	3	.	.	PUNCT
ejpam-6733	289	1	in	in	ADP
ejpam-6733	289	2	l−q	l−q	PROPN
ejpam-6733	289	3	,	,	PUNCT
ejpam-6733	289	4	q	q	X
ejpam-6733	289	5	,	,	PUNCT
ejpam-6733	289	6	if	if	SCONJ
ejpam-6733	289	7	c	c	PROPN
ejpam-6733	289	8	is	be	AUX
ejpam-6733	289	9	a	a	DET
ejpam-6733	289	10	scalar	scalar	ADJ
ejpam-6733	289	11	matrix	matrix	NOUN
ejpam-6733	289	12	,	,	PUNCT
ejpam-6733	289	13	then	then	ADV
ejpam-6733	289	14	a	a	PRON
ejpam-6733	289	15	is	be	AUX
ejpam-6733	289	16	of	of	ADP
ejpam-6733	289	17	zero	zero	NUM
ejpam-6733	289	18	diagonal	diagonal	ADJ
ejpam-6733	289	19	elements	element	NOUN
ejpam-6733	289	20	.	.	PUNCT
ejpam-6733	290	1	proof	proof	NOUN
ejpam-6733	290	2	.	.	PUNCT
ejpam-6733	291	1	let	let	VERB
ejpam-6733	291	2	a	a	PRON
ejpam-6733	291	3	as	as	ADP
ejpam-6733	291	4	in	in	ADP
ejpam-6733	291	5	(	(	PUNCT
ejpam-6733	291	6	13	13	NUM
ejpam-6733	291	7	)	)	PUNCT
ejpam-6733	291	8	,	,	PUNCT
ejpam-6733	291	9	and	and	CCONJ
ejpam-6733	291	10	c	c	NOUN
ejpam-6733	291	11	is	be	AUX
ejpam-6733	291	12	a	a	DET
ejpam-6733	291	13	scalar	scalar	ADJ
ejpam-6733	291	14	matrix	matrix	NOUN
ejpam-6733	291	15	.	.	PUNCT
ejpam-6733	292	1	so	so	ADV
ejpam-6733	292	2	,	,	PUNCT
ejpam-6733	292	3	let	let	VERB
ejpam-6733	292	4	c	c	NOUN
ejpam-6733	292	5	=	=	SYM
ejpam-6733	292	6	ti2	ti2	PROPN
ejpam-6733	292	7	.	.	PUNCT
ejpam-6733	293	1	for	for	ADP
ejpam-6733	293	2	the	the	DET
ejpam-6733	293	3	linear	linear	ADJ
ejpam-6733	293	4	independence	independence	NOUN
ejpam-6733	293	5	of	of	ADP
ejpam-6733	293	6	the	the	DET
ejpam-6733	293	7	generators	generator	NOUN
ejpam-6733	293	8	,	,	PUNCT
ejpam-6733	293	9	and	and	CCONJ
ejpam-6733	293	10	since	since	SCONJ
ejpam-6733	293	11	t	t	PROPN
ejpam-6733	293	12	is	be	AUX
ejpam-6733	293	13	a	a	DET
ejpam-6733	293	14	scalar	scalar	ADJ
ejpam-6733	293	15	matrix	matrix	NOUN
ejpam-6733	293	16	,	,	PUNCT
ejpam-6733	293	17	we	we	PRON
ejpam-6733	293	18	assume	assume	VERB
ejpam-6733	293	19	that	that	SCONJ
ejpam-6733	293	20	d	d	PROPN
ejpam-6733	293	21	=	=	SYM
ejpam-6733	293	22	0	0	X
ejpam-6733	293	23	.	.	PUNCT
ejpam-6733	293	24	suppose	suppose	VERB
ejpam-6733	293	25	a	a	DET
ejpam-6733	293	26	6=	6=	NUM
ejpam-6733	293	27	0	0	NUM
ejpam-6733	293	28	.	.	PUNCT
ejpam-6733	294	1	we	we	PRON
ejpam-6733	294	2	have	have	VERB
ejpam-6733	294	3	from	from	ADP
ejpam-6733	294	4	(	(	PUNCT
ejpam-6733	294	5	14	14	NUM
ejpam-6733	294	6	)	)	PUNCT
ejpam-6733	294	7	,	,	PUNCT
ejpam-6733	294	8	f	f	PROPN
ejpam-6733	294	9	(	(	PUNCT
ejpam-6733	294	10	t	t	PROPN
ejpam-6733	294	11	)	)	PUNCT
ejpam-6733	294	12	=	=	NOUN
ejpam-6733	295	1	−q	−q	ADJ
ejpam-6733	295	2	(	(	PUNCT
ejpam-6733	295	3	2	2	NUM
ejpam-6733	295	4	|a|2	|a|2	PROPN
ejpam-6733	295	5	+	+	CCONJ
ejpam-6733	295	6	|b|2	|b|2	PROPN
ejpam-6733	295	7	+	+	CCONJ
ejpam-6733	295	8	|c|2	|c|2	PROPN
ejpam-6733	295	9	)	)	PUNCT
ejpam-6733	295	10	and	and	CCONJ
ejpam-6733	295	11	f	f	PROPN
ejpam-6733	295	12	(	(	PUNCT
ejpam-6733	295	13	t	t	PROPN
ejpam-6733	295	14	)	)	PUNCT
ejpam-6733	295	15	=	=	NOUN
ejpam-6733	296	1	−q	−q	ADJ
ejpam-6733	296	2	(	(	PUNCT
ejpam-6733	296	3	|b|2	|b|2	PROPN
ejpam-6733	296	4	+	+	NOUN
ejpam-6733	296	5	|c|2	|c|2	PROPN
ejpam-6733	296	6	)	)	PUNCT
ejpam-6733	296	7	.	.	PUNCT
ejpam-6733	297	1	then	then	ADV
ejpam-6733	297	2	a	a	DET
ejpam-6733	297	3	=	=	NOUN
ejpam-6733	297	4	0	0	PUNCT
ejpam-6733	297	5	as	as	ADP
ejpam-6733	297	6	q	q	PROPN
ejpam-6733	297	7	6=	6=	NUM
ejpam-6733	297	8	0	0	NUM
ejpam-6733	297	9	.	.	PUNCT
ejpam-6733	297	10	theorem	theorem	NOUN
ejpam-6733	297	11	5	5	NUM
ejpam-6733	297	12	.	.	PUNCT
ejpam-6733	298	1	the	the	DET
ejpam-6733	298	2	l−q	l−q	PROPN
ejpam-6733	298	3	,	,	PUNCT
ejpam-6733	298	4	q	q	PROPN
ejpam-6733	298	5	has	have	VERB
ejpam-6733	298	6	faithful	faithful	ADJ
ejpam-6733	298	7	matrix	matrix	NOUN
ejpam-6733	298	8	representation	representation	NOUN
ejpam-6733	298	9	with	with	ADP
ejpam-6733	298	10	c	c	PROPN
ejpam-6733	298	11	a	a	DET
ejpam-6733	298	12	scalar	scalar	ADJ
ejpam-6733	298	13	matrix	matrix	NOUN
ejpam-6733	298	14	,	,	PUNCT
ejpam-6733	298	15	if	if	SCONJ
ejpam-6733	298	16	f	f	PROPN
ejpam-6733	298	17	(	(	PUNCT
ejpam-6733	298	18	x	x	NOUN
ejpam-6733	298	19	)	)	PUNCT
ejpam-6733	298	20	satisfies	satisfie	NOUN
ejpam-6733	298	21	,	,	PUNCT
ejpam-6733	298	22	that	that	DET
ejpam-6733	298	23	−1	−1	NOUN
ejpam-6733	298	24	qf	qf	PROPN
ejpam-6733	298	25	(	(	PUNCT
ejpam-6733	298	26	r	r	NOUN
ejpam-6733	298	27	−2q	−2q	PROPN
ejpam-6733	298	28	)	)	PUNCT
ejpam-6733	298	29	>	>	X
ejpam-6733	298	30	0	0	NUM
ejpam-6733	298	31	,	,	PUNCT
ejpam-6733	298	32	and	and	CCONJ
ejpam-6733	298	33	the	the	DET
ejpam-6733	298	34	representation	representation	NOUN
ejpam-6733	298	35	matrices	matrix	NOUN
ejpam-6733	298	36	of	of	ADP
ejpam-6733	298	37	k+,k−	k+,k−	PROPN
ejpam-6733	298	38	,	,	PUNCT
ejpam-6733	298	39	and	and	CCONJ
ejpam-6733	298	40	k0	k0	PROPN
ejpam-6733	298	41	are	be	AUX
ejpam-6733	298	42	,	,	PUNCT
ejpam-6733	298	43	a	a	DET
ejpam-6733	298	44	,	,	PUNCT
ejpam-6733	298	45	a†	a†	NOUN
ejpam-6733	298	46	,	,	PUNCT
ejpam-6733	298	47	and	and	CCONJ
ejpam-6733	298	48	c	c	NOUN
ejpam-6733	298	49	,	,	PUNCT
ejpam-6733	298	50	respectively	respectively	ADV
ejpam-6733	298	51	,	,	PUNCT
ejpam-6733	298	52	where	where	SCONJ
ejpam-6733	298	53	(	(	PUNCT
ejpam-6733	298	54	i	i	NOUN
ejpam-6733	298	55	)	)	PUNCT
ejpam-6733	298	56	a	a	PRON
ejpam-6733	299	1	=	=	X
ejpam-6733	300	1	[	[	PUNCT
ejpam-6733	300	2	0	0	NUM
ejpam-6733	300	3	b	b	X
ejpam-6733	300	4	c	c	NOUN
ejpam-6733	300	5	0	0	NUM
ejpam-6733	300	6	]	]	PUNCT
ejpam-6733	300	7	,	,	PUNCT
ejpam-6733	300	8	a†	a†	PROPN
ejpam-6733	300	9	,	,	PUNCT
ejpam-6733	300	10	and	and	CCONJ
ejpam-6733	300	11	c	c	X
ejpam-6733	300	12	=	=	SYM
ejpam-6733	301	1	r	r	NOUN
ejpam-6733	301	2	−2q	−2q	PROPN
ejpam-6733	301	3	i2	i2	PROPN
ejpam-6733	301	4	,	,	PUNCT
ejpam-6733	301	5	respectively	respectively	ADV
ejpam-6733	301	6	,	,	PUNCT
ejpam-6733	301	7	where	where	SCONJ
ejpam-6733	301	8	|b|2	|b|2	PROPN
ejpam-6733	301	9	+	+	NOUN
ejpam-6733	301	10	|c|2	|c|2	PROPN
ejpam-6733	301	11	=	=	SYM
ejpam-6733	301	12	−1	−1	NOUN
ejpam-6733	301	13	qf	qf	PROPN
ejpam-6733	301	14	(	(	PUNCT
ejpam-6733	301	15	r	r	NOUN
ejpam-6733	301	16	−2q	−2q	PROPN
ejpam-6733	301	17	)	)	PUNCT
ejpam-6733	301	18	>	>	X
ejpam-6733	301	19	0	0	PUNCT
ejpam-6733	302	1	such	such	ADJ
ejpam-6733	302	2	that	that	SCONJ
ejpam-6733	302	3	|b|2	|b|2	PROPN
ejpam-6733	302	4	6=	6=	ADP
ejpam-6733	302	5	|c|2	|c|2	NOUN
ejpam-6733	302	6	,	,	PUNCT
ejpam-6733	302	7	with	with	ADP
ejpam-6733	302	8	b	b	NOUN
ejpam-6733	302	9	and	and	CCONJ
ejpam-6733	302	10	c	c	NOUN
ejpam-6733	302	11	are	be	AUX
ejpam-6733	302	12	of	of	ADP
ejpam-6733	302	13	equal	equal	ADJ
ejpam-6733	302	14	imaginary	imaginary	ADJ
ejpam-6733	302	15	parts	part	NOUN
ejpam-6733	302	16	to	to	PART
ejpam-6733	302	17	satisfy	satisfy	VERB
ejpam-6733	302	18	that	that	PRON
ejpam-6733	302	19	k++k−	k++k−	PROPN
ejpam-6733	302	20	is	be	AUX
ejpam-6733	302	21	real	real	ADJ
ejpam-6733	302	22	.	.	PUNCT
ejpam-6733	303	1	(	(	PUNCT
ejpam-6733	303	2	ii	ii	NOUN
ejpam-6733	303	3	)	)	PUNCT
ejpam-6733	303	4	a	a	PRON
ejpam-6733	303	5	=	=	X
ejpam-6733	304	1	[	[	PUNCT
ejpam-6733	304	2	0	0	NUM
ejpam-6733	304	3	b	b	NOUN
ejpam-6733	304	4	0	0	NUM
ejpam-6733	304	5	0	0	NUM
ejpam-6733	304	6	]	]	PUNCT
ejpam-6733	304	7	,	,	PUNCT
ejpam-6733	304	8	a†	a†	PROPN
ejpam-6733	304	9	,	,	PUNCT
ejpam-6733	304	10	and	and	CCONJ
ejpam-6733	304	11	c	c	X
ejpam-6733	304	12	=	=	SYM
ejpam-6733	305	1	r	r	NOUN
ejpam-6733	305	2	−2q	−2q	PROPN
ejpam-6733	305	3	i2	i2	PROPN
ejpam-6733	305	4	,	,	PUNCT
ejpam-6733	305	5	respectively	respectively	ADV
ejpam-6733	305	6	,	,	PUNCT
ejpam-6733	305	7	where	where	SCONJ
ejpam-6733	305	8	|b|2	|b|2	PROPN
ejpam-6733	305	9	=	=	SYM
ejpam-6733	305	10	−1	−1	NOUN
ejpam-6733	305	11	qf	qf	PROPN
ejpam-6733	305	12	(	(	PUNCT
ejpam-6733	305	13	r	r	NOUN
ejpam-6733	305	14	−2q	−2q	PROPN
ejpam-6733	305	15	)	)	PUNCT
ejpam-6733	305	16	>	>	X
ejpam-6733	306	1	0	0	X
ejpam-6733	306	2	.	.	PUNCT
ejpam-6733	307	1	in	in	ADP
ejpam-6733	307	2	this	this	DET
ejpam-6733	307	3	representation	representation	NOUN
ejpam-6733	307	4	,	,	PUNCT
ejpam-6733	307	5	the	the	DET
ejpam-6733	307	6	condition	condition	NOUN
ejpam-6733	307	7	k+	k+	NOUN
ejpam-6733	307	8	+	+	CCONJ
ejpam-6733	307	9	k−	k−	PROPN
ejpam-6733	307	10	is	be	AUX
ejpam-6733	307	11	real	real	ADJ
ejpam-6733	307	12	,	,	PUNCT
ejpam-6733	307	13	and	and	CCONJ
ejpam-6733	307	14	will	will	AUX
ejpam-6733	307	15	only	only	ADV
ejpam-6733	307	16	be	be	AUX
ejpam-6733	307	17	satisfied	satisfied	ADJ
ejpam-6733	307	18	for	for	ADP
ejpam-6733	307	19	a	a	DET
ejpam-6733	307	20	real	real	ADJ
ejpam-6733	307	21	matrix	matrix	NOUN
ejpam-6733	307	22	a.	a.	NOUN
ejpam-6733	307	23	proof	proof	NOUN
ejpam-6733	307	24	.	.	PUNCT
ejpam-6733	308	1	let	let	VERB
ejpam-6733	308	2	c	c	NOUN
ejpam-6733	308	3	=	=	PUNCT
ejpam-6733	308	4	ti2	ti2	PROPN
ejpam-6733	308	5	scalar	scalar	ADJ
ejpam-6733	308	6	matrix	matrix	NOUN
ejpam-6733	308	7	and	and	CCONJ
ejpam-6733	308	8	from	from	ADP
ejpam-6733	308	9	lemma	lemma	PROPN
ejpam-6733	308	10	4	4	NUM
ejpam-6733	308	11	,	,	PUNCT
ejpam-6733	308	12	a	a	DET
ejpam-6733	308	13	=	=	SYM
ejpam-6733	308	14	d	d	NOUN
ejpam-6733	308	15	=	=	SYM
ejpam-6733	308	16	0	0	NUM
ejpam-6733	308	17	.	.	PUNCT
ejpam-6733	309	1	thus	thus	ADV
ejpam-6733	309	2	a	a	DET
ejpam-6733	309	3	=	=	X
ejpam-6733	309	4	[	[	PUNCT
ejpam-6733	309	5	0	0	NUM
ejpam-6733	309	6	b	b	X
ejpam-6733	309	7	c	c	NOUN
ejpam-6733	309	8	0	0	NUM
ejpam-6733	309	9	]	]	PUNCT
ejpam-6733	309	10	.	.	PUNCT
ejpam-6733	310	1	from	from	ADP
ejpam-6733	310	2	(	(	PUNCT
ejpam-6733	310	3	14	14	NUM
ejpam-6733	310	4	)	)	PUNCT
ejpam-6733	310	5	,	,	PUNCT
ejpam-6733	310	6	−q	−q	NOUN
ejpam-6733	310	7	(	(	PUNCT
ejpam-6733	310	8	|b|2	|b|2	PROPN
ejpam-6733	310	9	+	+	NOUN
ejpam-6733	310	10	|c|2	|c|2	PROPN
ejpam-6733	310	11	)	)	PUNCT
ejpam-6733	311	1	=	=	SYM
ejpam-6733	311	2	f	f	PROPN
ejpam-6733	311	3	(	(	PUNCT
ejpam-6733	311	4	t	t	PROPN
ejpam-6733	311	5	)	)	PUNCT
ejpam-6733	311	6	.	.	PUNCT
ejpam-6733	312	1	consider	consider	VERB
ejpam-6733	312	2	the	the	DET
ejpam-6733	312	3	two	two	NUM
ejpam-6733	312	4	cases	case	NOUN
ejpam-6733	312	5	.	.	PUNCT
ejpam-6733	313	1	case	case	NOUN
ejpam-6733	313	2	1	1	NUM
ejpam-6733	313	3	:	:	PUNCT
ejpam-6733	313	4	if	if	SCONJ
ejpam-6733	313	5	bc	bc	PROPN
ejpam-6733	313	6	=	=	PROPN
ejpam-6733	313	7	0	0	PROPN
ejpam-6733	313	8	.	.	PUNCT
ejpam-6733	314	1	let	let	VERB
ejpam-6733	314	2	b	b	PROPN
ejpam-6733	314	3	6=	6=	ADP
ejpam-6733	314	4	0	0	NUM
ejpam-6733	314	5	,	,	PUNCT
ejpam-6733	314	6	c	c	NOUN
ejpam-6733	314	7	=	=	SYM
ejpam-6733	315	1	0	0	PROPN
ejpam-6733	315	2	.	.	PUNCT
ejpam-6733	316	1	then	then	ADV
ejpam-6733	316	2	from	from	ADP
ejpam-6733	316	3	(	(	PUNCT
ejpam-6733	316	4	8)	8)	NUM
ejpam-6733	316	5	,	,	PUNCT
ejpam-6733	316	6	(	(	PUNCT
ejpam-6733	316	7	r	r	NOUN
ejpam-6733	316	8	+	+	NOUN
ejpam-6733	316	9	2qt	2qt	X
ejpam-6733	316	10	)	)	PUNCT
ejpam-6733	316	11	=	=	SYM
ejpam-6733	316	12	0	0	X
ejpam-6733	316	13	.	.	PUNCT
ejpam-6733	317	1	hence	hence	ADV
ejpam-6733	317	2	,	,	PUNCT
ejpam-6733	317	3	t	t	PROPN
ejpam-6733	317	4	=	=	SYM
ejpam-6733	317	5	r	r	NOUN
ejpam-6733	317	6	−2q	−2q	PROPN
ejpam-6733	317	7	.	.	PUNCT
ejpam-6733	318	1	then	then	ADV
ejpam-6733	318	2	f	f	PROPN
ejpam-6733	318	3	(	(	PUNCT
ejpam-6733	318	4	r	r	NOUN
ejpam-6733	318	5	−2q	−2q	PROPN
ejpam-6733	318	6	)	)	PUNCT
ejpam-6733	319	1	=	=	PUNCT
ejpam-6733	319	2	−q	−q	ADJ
ejpam-6733	319	3	|b|2	|b|2	PROPN
ejpam-6733	319	4	.	.	PUNCT
ejpam-6733	320	1	therefore	therefore	ADV
ejpam-6733	320	2	,	,	PUNCT
ejpam-6733	320	3	|b|2	|b|2	PROPN
ejpam-6733	320	4	=	=	SYM
ejpam-6733	320	5	−1	−1	NOUN
ejpam-6733	320	6	qf	qf	PROPN
ejpam-6733	320	7	(	(	PUNCT
ejpam-6733	320	8	r	r	NOUN
ejpam-6733	320	9	−2q	−2q	PROPN
ejpam-6733	320	10	)	)	PUNCT
ejpam-6733	320	11	>	>	X
ejpam-6733	320	12	0	0	X
ejpam-6733	320	13	.	.	PUNCT
ejpam-6733	320	14	case	case	NOUN
ejpam-6733	320	15	2	2	NUM
ejpam-6733	320	16	:	:	PUNCT
ejpam-6733	320	17	if	if	SCONJ
ejpam-6733	320	18	bc	bc	PROPN
ejpam-6733	320	19	6=	6=	PROPN
ejpam-6733	320	20	0	0	NUM
ejpam-6733	320	21	,	,	PUNCT
ejpam-6733	320	22	then	then	ADV
ejpam-6733	320	23	from	from	ADP
ejpam-6733	320	24	(	(	PUNCT
ejpam-6733	320	25	8)	8)	NUM
ejpam-6733	320	26	,	,	PUNCT
ejpam-6733	320	27	we	we	PRON
ejpam-6733	320	28	have	have	VERB
ejpam-6733	320	29	b	b	NUM
ejpam-6733	320	30	(	(	PUNCT
ejpam-6733	320	31	r	r	NOUN
ejpam-6733	320	32	+	+	NOUN
ejpam-6733	320	33	2qt	2qt	X
ejpam-6733	320	34	)	)	PUNCT
ejpam-6733	320	35	=	=	SYM
ejpam-6733	320	36	0	0	NUM
ejpam-6733	320	37	and	and	CCONJ
ejpam-6733	320	38	c	c	NOUN
ejpam-6733	320	39	(	(	PUNCT
ejpam-6733	321	1	r	r	NOUN
ejpam-6733	321	2	+	+	X
ejpam-6733	321	3	2qt	2qt	X
ejpam-6733	321	4	)	)	PUNCT
ejpam-6733	321	5	=	=	SYM
ejpam-6733	322	1	0	0	X
ejpam-6733	322	2	.	.	PUNCT
ejpam-6733	323	1	then	then	ADV
ejpam-6733	323	2	t	t	NOUN
ejpam-6733	324	1	=	=	PUNCT
ejpam-6733	324	2	r	r	NOUN
ejpam-6733	324	3	−2q	−2q	PROPN
ejpam-6733	324	4	.	.	PUNCT
ejpam-6733	325	1	then	then	ADV
ejpam-6733	325	2	|b|2	|b|2	PROPN
ejpam-6733	325	3	+	+	CCONJ
ejpam-6733	325	4	|c|2	|c|2	PROPN
ejpam-6733	325	5	=	=	SYM
ejpam-6733	325	6	−1	−1	NOUN
ejpam-6733	325	7	qf	qf	PROPN
ejpam-6733	325	8	(	(	PUNCT
ejpam-6733	325	9	r	r	NOUN
ejpam-6733	325	10	−2q	−2q	PROPN
ejpam-6733	325	11	)	)	PUNCT
ejpam-6733	325	12	>	>	X
ejpam-6733	326	1	0	0	X
ejpam-6733	326	2	.	.	PUNCT
ejpam-6733	326	3	to	to	PART
ejpam-6733	326	4	satisfy	satisfy	VERB
ejpam-6733	326	5	that	that	DET
ejpam-6733	326	6	k+	k+	NOUN
ejpam-6733	327	1	+	+	NOUN
ejpam-6733	327	2	k−	k−	PROPN
ejpam-6733	327	3	is	be	AUX
ejpam-6733	327	4	a	a	DET
ejpam-6733	327	5	real	real	ADJ
ejpam-6733	327	6	operator	operator	NOUN
ejpam-6733	327	7	,	,	PUNCT
ejpam-6733	327	8	one	one	PRON
ejpam-6733	327	9	must	must	AUX
ejpam-6733	327	10	have	have	VERB
ejpam-6733	327	11	,	,	PUNCT
ejpam-6733	327	12	b+	b+	VERB
ejpam-6733	327	13	c̄	c̄	PROPN
ejpam-6733	327	14	∈	∈	PROPN
ejpam-6733	327	15	r.	r.	NOUN
ejpam-6733	327	16	if	if	SCONJ
ejpam-6733	327	17	|b|2	|b|2	PROPN
ejpam-6733	327	18	=	=	SYM
ejpam-6733	327	19	|c|2	|c|2	PROPN
ejpam-6733	327	20	,	,	PUNCT
ejpam-6733	327	21	then	then	ADV
ejpam-6733	327	22	a	a	PRON
ejpam-6733	327	23	and	and	CCONJ
ejpam-6733	327	24	b	b	NOUN
ejpam-6733	327	25	are	be	AUX
ejpam-6733	327	26	linearly	linearly	ADV
ejpam-6733	327	27	dependent	dependent	ADJ
ejpam-6733	327	28	,	,	PUNCT
ejpam-6733	327	29	and	and	CCONJ
ejpam-6733	327	30	hence	hence	ADV
ejpam-6733	327	31	the	the	DET
ejpam-6733	327	32	representation	representation	NOUN
ejpam-6733	327	33	is	be	AUX
ejpam-6733	327	34	not	not	PART
ejpam-6733	327	35	faithful	faithful	ADJ
ejpam-6733	327	36	.	.	PUNCT
ejpam-6733	327	37	example	example	NOUN
ejpam-6733	328	1	4	4	NUM
ejpam-6733	328	2	.	.	X
ejpam-6733	329	1	for	for	ADP
ejpam-6733	329	2	l−2,2	l−2,2	PROPN
ejpam-6733	329	3	,	,	PUNCT
ejpam-6733	329	4	if	if	SCONJ
ejpam-6733	329	5	r	r	NOUN
ejpam-6733	329	6	=	=	SYM
ejpam-6733	329	7	8	8	NUM
ejpam-6733	329	8	and	and	CCONJ
ejpam-6733	329	9	f	f	PROPN
ejpam-6733	329	10	(	(	PUNCT
ejpam-6733	329	11	x	x	X
ejpam-6733	329	12	)	)	PUNCT
ejpam-6733	329	13	=	=	SYM
ejpam-6733	329	14	x−18	x−18	PROPN
ejpam-6733	329	15	,	,	PUNCT
ejpam-6733	329	16	then	then	ADV
ejpam-6733	329	17	c	c	NOUN
ejpam-6733	329	18	=	=	SYM
ejpam-6733	329	19	−2i2	−2i2	NUM
ejpam-6733	329	20	.	.	PUNCT
ejpam-6733	330	1	to	to	PART
ejpam-6733	330	2	get	get	VERB
ejpam-6733	330	3	a	a	DET
ejpam-6733	330	4	representation	representation	NOUN
ejpam-6733	330	5	of	of	ADP
ejpam-6733	330	6	type	type	NOUN
ejpam-6733	330	7	in	in	ADP
ejpam-6733	330	8	1	1	NUM
ejpam-6733	330	9	,	,	PUNCT
ejpam-6733	330	10	we	we	PRON
ejpam-6733	330	11	can	can	AUX
ejpam-6733	330	12	take	take	VERB
ejpam-6733	330	13	,	,	PUNCT
ejpam-6733	330	14	for	for	ADP
ejpam-6733	330	15	instance	instance	NOUN
ejpam-6733	330	16	,	,	PUNCT
ejpam-6733	330	17	b	b	NOUN
ejpam-6733	330	18	=	=	SYM
ejpam-6733	330	19	3	3	NUM
ejpam-6733	330	20	and	and	CCONJ
ejpam-6733	330	21	c	c	NOUN
ejpam-6733	330	22	=	=	SYM
ejpam-6733	330	23	±1	±1	VERB
ejpam-6733	330	24	,	,	PUNCT
ejpam-6733	330	25	since	since	SCONJ
ejpam-6733	330	26	|b|2	|b|2	PROPN
ejpam-6733	330	27	+	+	CCONJ
ejpam-6733	330	28	|c|2	|c|2	NOUN
ejpam-6733	330	29	=	=	SYM
ejpam-6733	330	30	10	10	NUM
ejpam-6733	330	31	.	.	PUNCT
ejpam-6733	331	1	also	also	ADV
ejpam-6733	331	2	,	,	PUNCT
ejpam-6733	331	3	we	we	PRON
ejpam-6733	331	4	can	can	AUX
ejpam-6733	331	5	take	take	VERB
ejpam-6733	331	6	b	b	NOUN
ejpam-6733	331	7	=	=	NOUN
ejpam-6733	331	8	√	√	PROPN
ejpam-6733	331	9	2	2	NUM
ejpam-6733	331	10	+	+	NUM
ejpam-6733	331	11	2i	2i	NUM
ejpam-6733	331	12	and	and	CCONJ
ejpam-6733	331	13	c	c	NOUN
ejpam-6733	331	14	=	=	SYM
ejpam-6733	331	15	2i	2i	NUM
ejpam-6733	331	16	.	.	PUNCT
ejpam-6733	331	17	example	example	NOUN
ejpam-6733	332	1	5	5	NUM
ejpam-6733	332	2	.	.	X
ejpam-6733	333	1	for	for	ADP
ejpam-6733	333	2	l−2,2	l−2,2	PROPN
ejpam-6733	333	3	,	,	PUNCT
ejpam-6733	333	4	if	if	SCONJ
ejpam-6733	333	5	r	r	NOUN
ejpam-6733	333	6	=	=	SYM
ejpam-6733	333	7	8	8	NUM
ejpam-6733	333	8	and	and	CCONJ
ejpam-6733	333	9	f	f	PROPN
ejpam-6733	333	10	(	(	PUNCT
ejpam-6733	333	11	x	x	X
ejpam-6733	333	12	)	)	PUNCT
ejpam-6733	333	13	=	=	SYM
ejpam-6733	333	14	x−	x−	PROPN
ejpam-6733	333	15	18	18	NUM
ejpam-6733	333	16	,	,	PUNCT
ejpam-6733	333	17	then	then	ADV
ejpam-6733	333	18	c	c	NOUN
ejpam-6733	333	19	=	=	SYM
ejpam-6733	333	20	−2i2	−2i2	PUNCT
ejpam-6733	333	21	and	and	CCONJ
ejpam-6733	333	22	take	take	VERB
ejpam-6733	333	23	b	b	NOUN
ejpam-6733	333	24	=	=	SYM
ejpam-6733	333	25	±	±	NOUN
ejpam-6733	333	26	√	√	NUM
ejpam-6733	333	27	10	10	NUM
ejpam-6733	333	28	,	,	PUNCT
ejpam-6733	333	29	for	for	ADP
ejpam-6733	333	30	a	a	DET
ejpam-6733	333	31	representation	representation	NOUN
ejpam-6733	333	32	of	of	ADP
ejpam-6733	333	33	type	type	NOUN
ejpam-6733	333	34	in	in	ADP
ejpam-6733	333	35	2	2	NUM
ejpam-6733	333	36	.	.	PUNCT
ejpam-6733	334	1	l.	l.	PROPN
ejpam-6733	334	2	a	a	DET
ejpam-6733	334	3	-	-	PUNCT
ejpam-6733	334	4	m.	m.	NOUN
ejpam-6733	334	5	hanna	hanna	NOUN
ejpam-6733	334	6	,	,	PUNCT
ejpam-6733	334	7	s.	s.	PROPN
ejpam-6733	334	8	s.	s.	PROPN
ejpam-6733	334	9	hassan	hassan	PROPN
ejpam-6733	334	10	,	,	PUNCT
ejpam-6733	334	11	m.	m.	NOUN
ejpam-6733	334	12	almutairi	almutairi	PROPN
ejpam-6733	334	13	/	/	SYM
ejpam-6733	334	14	eur	eur	PROPN
ejpam-6733	334	15	.	.	PUNCT
ejpam-6733	335	1	j.	j.	PROPN
ejpam-6733	335	2	pure	pure	PROPN
ejpam-6733	335	3	appl	appl	PROPN
ejpam-6733	335	4	.	.	PROPN
ejpam-6733	335	5	math	math	PROPN
ejpam-6733	335	6	,	,	PUNCT
ejpam-6733	335	7	18	18	NUM
ejpam-6733	335	8	(	(	PUNCT
ejpam-6733	335	9	4	4	NUM
ejpam-6733	335	10	)	)	PUNCT
ejpam-6733	335	11	(	(	PUNCT
ejpam-6733	335	12	2025	2025	NUM
ejpam-6733	335	13	)	)	PUNCT
ejpam-6733	335	14	,	,	PUNCT
ejpam-6733	335	15	6733	6733	NUM
ejpam-6733	335	16	10	10	NUM
ejpam-6733	335	17	of	of	ADP
ejpam-6733	335	18	12	12	NUM
ejpam-6733	335	19	now	now	ADV
ejpam-6733	335	20	consider	consider	VERB
ejpam-6733	335	21	the	the	DET
ejpam-6733	335	22	case	case	NOUN
ejpam-6733	335	23	where	where	SCONJ
ejpam-6733	335	24	c	c	NOUN
ejpam-6733	335	25	=	=	SYM
ejpam-6733	335	26	diag	diag	PROPN
ejpam-6733	335	27	(	(	PUNCT
ejpam-6733	335	28	c1	c1	PROPN
ejpam-6733	335	29	,	,	PUNCT
ejpam-6733	335	30	c2	c2	PROPN
ejpam-6733	335	31	)	)	PUNCT
ejpam-6733	335	32	,	,	PUNCT
ejpam-6733	335	33	which	which	PRON
ejpam-6733	335	34	is	be	AUX
ejpam-6733	335	35	not	not	PART
ejpam-6733	335	36	a	a	DET
ejpam-6733	335	37	scalar	scalar	ADJ
ejpam-6733	335	38	matrix	matrix	NOUN
ejpam-6733	335	39	.	.	PUNCT
ejpam-6733	336	1	from	from	ADP
ejpam-6733	336	2	(	(	PUNCT
ejpam-6733	336	3	14	14	NUM
ejpam-6733	336	4	)	)	PUNCT
ejpam-6733	336	5	and	and	CCONJ
ejpam-6733	336	6	(	(	PUNCT
ejpam-6733	336	7	15	15	NUM
ejpam-6733	336	8	)	)	PUNCT
ejpam-6733	336	9	,	,	PUNCT
ejpam-6733	336	10	we	we	PRON
ejpam-6733	336	11	have	have	VERB
ejpam-6733	336	12	the	the	DET
ejpam-6733	336	13	following	following	NOUN
ejpam-6733	336	14	theorem	theorem	NOUN
ejpam-6733	336	15	as	as	ADP
ejpam-6733	336	16	p	p	NOUN
ejpam-6733	336	17	=	=	NOUN
ejpam-6733	336	18	−q	−q	NOUN
ejpam-6733	336	19	.	.	PUNCT
ejpam-6733	337	1	theorem	theorem	NOUN
ejpam-6733	337	2	6	6	NUM
ejpam-6733	337	3	.	.	PUNCT
ejpam-6733	338	1	let	let	VERB
ejpam-6733	338	2	p	p	NOUN
ejpam-6733	338	3	=	=	NOUN
ejpam-6733	338	4	−q	−q	NOUN
ejpam-6733	338	5	.	.	PUNCT
ejpam-6733	339	1	then	then	ADV
ejpam-6733	339	2	the	the	DET
ejpam-6733	339	3	l−q	l−q	PROPN
ejpam-6733	339	4	,	,	PUNCT
ejpam-6733	339	5	q	q	PROPN
ejpam-6733	339	6	has	have	VERB
ejpam-6733	339	7	faithful	faithful	ADJ
ejpam-6733	339	8	matrix	matrix	NOUN
ejpam-6733	339	9	representations	representation	NOUN
ejpam-6733	339	10	,	,	PUNCT
ejpam-6733	339	11	with	with	ADP
ejpam-6733	339	12	c	c	X
ejpam-6733	339	13	not	not	PART
ejpam-6733	339	14	a	a	DET
ejpam-6733	339	15	scalar	scalar	ADJ
ejpam-6733	339	16	matrix	matrix	NOUN
ejpam-6733	339	17	,	,	PUNCT
ejpam-6733	339	18	namely	namely	ADV
ejpam-6733	339	19	,	,	PUNCT
ejpam-6733	339	20	(	(	PUNCT
ejpam-6733	339	21	i	i	NOUN
ejpam-6733	339	22	)	)	PUNCT
ejpam-6733	339	23	if	if	SCONJ
ejpam-6733	339	24	there	there	PRON
ejpam-6733	339	25	exists	exist	VERB
ejpam-6733	339	26	t	t	PROPN
ejpam-6733	339	27	∈	∈	PROPN
ejpam-6733	339	28	r	r	NOUN
ejpam-6733	339	29	,	,	PUNCT
ejpam-6733	340	1	such	such	ADJ
ejpam-6733	340	2	that	that	SCONJ
ejpam-6733	340	3	f	f	PROPN
ejpam-6733	340	4	(	(	PUNCT
ejpam-6733	340	5	t	t	PROPN
ejpam-6733	340	6	)	)	PUNCT
ejpam-6733	340	7	=	=	NOUN
ejpam-6733	340	8	−q	−q	ADJ
ejpam-6733	340	9	(	(	PUNCT
ejpam-6733	340	10	|b|2	|b|2	PROPN
ejpam-6733	340	11	+	+	NOUN
ejpam-6733	340	12	|c|2	|c|2	PROPN
ejpam-6733	340	13	)	)	PUNCT
ejpam-6733	340	14	and	and	CCONJ
ejpam-6733	340	15	f	f	PROPN
ejpam-6733	340	16	(	(	PUNCT
ejpam-6733	340	17	−qt−r	−qt−r	NOUN
ejpam-6733	340	18	q	q	NOUN
ejpam-6733	340	19	)	)	PUNCT
ejpam-6733	341	1	=	=	SYM
ejpam-6733	341	2	f	f	PROPN
ejpam-6733	341	3	(	(	PUNCT
ejpam-6733	341	4	t	t	PROPN
ejpam-6733	341	5	)	)	PUNCT
ejpam-6733	341	6	where	where	SCONJ
ejpam-6733	341	7	c	c	NOUN
ejpam-6733	341	8	=	=	SYM
ejpam-6733	341	9	diag	diag	NOUN
ejpam-6733	341	10	(	(	PUNCT
ejpam-6733	341	11	t,−	t,−	ADJ
ejpam-6733	341	12	qt+r	qt+r	PROPN
ejpam-6733	341	13	q	q	NOUN
ejpam-6733	341	14	)	)	PUNCT
ejpam-6733	341	15	and	and	CCONJ
ejpam-6733	341	16	a	a	PRON
ejpam-6733	341	17	=	=	X
ejpam-6733	341	18	[	[	PUNCT
ejpam-6733	341	19	0	0	NUM
ejpam-6733	341	20	b	b	X
ejpam-6733	341	21	c	c	NOUN
ejpam-6733	341	22	0	0	NUM
ejpam-6733	341	23	]	]	PUNCT
ejpam-6733	341	24	,	,	PUNCT
ejpam-6733	341	25	where	where	SCONJ
ejpam-6733	341	26	|c|2	|c|2	PROPN
ejpam-6733	341	27	=	=	SYM
ejpam-6733	341	28	−	−	PROPN
ejpam-6733	341	29	q|b|2+f	q|b|2+f	PROPN
ejpam-6733	341	30	(	(	PUNCT
ejpam-6733	341	31	t	t	PROPN
ejpam-6733	341	32	)	)	PUNCT
ejpam-6733	341	33	q	q	NOUN
ejpam-6733	341	34	>	>	X
ejpam-6733	341	35	0	0	NUM
ejpam-6733	341	36	,	,	PUNCT
ejpam-6733	341	37	and	and	CCONJ
ejpam-6733	341	38	for	for	ADP
ejpam-6733	341	39	the	the	DET
ejpam-6733	341	40	special	special	ADJ
ejpam-6733	341	41	case	case	NOUN
ejpam-6733	341	42	,	,	PUNCT
ejpam-6733	341	43	when	when	SCONJ
ejpam-6733	341	44	c	c	NOUN
ejpam-6733	341	45	=	=	SYM
ejpam-6733	341	46	0	0	PROPN
ejpam-6733	341	47	,	,	PUNCT
ejpam-6733	341	48	(	(	PUNCT
ejpam-6733	341	49	ii	ii	NOUN
ejpam-6733	341	50	)	)	PUNCT
ejpam-6733	341	51	if	if	SCONJ
ejpam-6733	341	52	there	there	PRON
ejpam-6733	341	53	exists	exist	VERB
ejpam-6733	341	54	t	t	PROPN
ejpam-6733	341	55	∈	∈	PROPN
ejpam-6733	341	56	r	r	NOUN
ejpam-6733	341	57	,	,	PUNCT
ejpam-6733	341	58	such	such	ADJ
ejpam-6733	341	59	that	that	SCONJ
ejpam-6733	341	60	|b|2	|b|2	PROPN
ejpam-6733	341	61	=	=	SYM
ejpam-6733	341	62	−f	−f	NOUN
ejpam-6733	341	63	(	(	PUNCT
ejpam-6733	341	64	t	t	PROPN
ejpam-6733	341	65	)	)	PUNCT
ejpam-6733	341	66	q	q	NOUN
ejpam-6733	341	67	>	>	X
ejpam-6733	341	68	0	0	PUNCT
ejpam-6733	341	69	and	and	CCONJ
ejpam-6733	341	70	f	f	PROPN
ejpam-6733	341	71	(	(	PUNCT
ejpam-6733	341	72	−	−	PROPN
ejpam-6733	341	73	qt+r	qt+r	PROPN
ejpam-6733	341	74	q	q	NOUN
ejpam-6733	341	75	)	)	PUNCT
ejpam-6733	342	1	=	=	SYM
ejpam-6733	342	2	f	f	PROPN
ejpam-6733	342	3	(	(	PUNCT
ejpam-6733	342	4	t	t	PROPN
ejpam-6733	342	5	)	)	PUNCT
ejpam-6733	342	6	where	where	SCONJ
ejpam-6733	342	7	c	c	NOUN
ejpam-6733	342	8	=	=	SYM
ejpam-6733	342	9	diag	diag	NOUN
ejpam-6733	342	10	(	(	PUNCT
ejpam-6733	342	11	t,−	t,−	ADJ
ejpam-6733	342	12	qt+r	qt+r	PROPN
ejpam-6733	342	13	q	q	NOUN
ejpam-6733	342	14	)	)	PUNCT
ejpam-6733	342	15	and	and	CCONJ
ejpam-6733	342	16	a	a	PRON
ejpam-6733	342	17	=	=	X
ejpam-6733	342	18	[	[	PUNCT
ejpam-6733	342	19	0	0	NUM
ejpam-6733	342	20	b	b	NOUN
ejpam-6733	342	21	0	0	NUM
ejpam-6733	342	22	0	0	NUM
ejpam-6733	342	23	]	]	PUNCT
ejpam-6733	342	24	.	.	PUNCT
ejpam-6733	343	1	proof	proof	NOUN
ejpam-6733	343	2	.	.	PUNCT
ejpam-6733	344	1	let	let	VERB
ejpam-6733	344	2	p	p	NOUN
ejpam-6733	344	3	=	=	NOUN
ejpam-6733	344	4	−q	−q	NOUN
ejpam-6733	344	5	,	,	PUNCT
ejpam-6733	344	6	then	then	ADV
ejpam-6733	344	7	we	we	PRON
ejpam-6733	344	8	have	have	VERB
ejpam-6733	344	9	from	from	ADP
ejpam-6733	344	10	(	(	PUNCT
ejpam-6733	344	11	14	14	NUM
ejpam-6733	344	12	)	)	PUNCT
ejpam-6733	344	13	,	,	PUNCT
ejpam-6733	344	14	with	with	ADP
ejpam-6733	344	15	a	a	DET
ejpam-6733	344	16	=	=	SYM
ejpam-6733	344	17	d	d	NOUN
ejpam-6733	344	18	=	=	SYM
ejpam-6733	344	19	0	0	NUM
ejpam-6733	344	20	,	,	PUNCT
ejpam-6733	344	21	we	we	PRON
ejpam-6733	344	22	get	get	VERB
ejpam-6733	344	23	f	f	PROPN
ejpam-6733	344	24	(	(	PUNCT
ejpam-6733	344	25	c1	c1	PROPN
ejpam-6733	344	26	)	)	PUNCT
ejpam-6733	345	1	=	=	SYM
ejpam-6733	345	2	f	f	PROPN
ejpam-6733	345	3	(	(	PUNCT
ejpam-6733	345	4	c2	c2	PROPN
ejpam-6733	345	5	)	)	PUNCT
ejpam-6733	345	6	=	=	NOUN
ejpam-6733	346	1	−q	−q	ADJ
ejpam-6733	346	2	(	(	PUNCT
ejpam-6733	346	3	|b|2	|b|2	PROPN
ejpam-6733	346	4	+	+	NOUN
ejpam-6733	346	5	|c|2	|c|2	PROPN
ejpam-6733	346	6	)	)	PUNCT
ejpam-6733	346	7	.	.	PUNCT
ejpam-6733	347	1	so	so	ADV
ejpam-6733	347	2	,	,	PUNCT
ejpam-6733	347	3	let	let	VERB
ejpam-6733	348	1	c1	c1	PROPN
ejpam-6733	348	2	=	=	PROPN
ejpam-6733	348	3	t	t	PROPN
ejpam-6733	348	4	,	,	PUNCT
ejpam-6733	348	5	then	then	ADV
ejpam-6733	348	6	|c|2	|c|2	PROPN
ejpam-6733	348	7	=	=	SYM
ejpam-6733	348	8	−	−	PROPN
ejpam-6733	348	9	q|b|2+f	q|b|2+f	PROPN
ejpam-6733	348	10	(	(	PUNCT
ejpam-6733	348	11	t	t	PROPN
ejpam-6733	348	12	)	)	PUNCT
ejpam-6733	348	13	q	q	NOUN
ejpam-6733	348	14	>	>	X
ejpam-6733	348	15	0	0	NUM
ejpam-6733	348	16	,	,	PUNCT
ejpam-6733	348	17	if	if	SCONJ
ejpam-6733	348	18	bc	bc	PROPN
ejpam-6733	348	19	6=	6=	PROPN
ejpam-6733	348	20	0	0	NUM
ejpam-6733	348	21	.	.	PUNCT
ejpam-6733	349	1	from	from	ADP
ejpam-6733	349	2	(	(	PUNCT
ejpam-6733	349	3	15	15	NUM
ejpam-6733	349	4	)	)	PUNCT
ejpam-6733	349	5	,	,	PUNCT
ejpam-6733	349	6	we	we	PRON
ejpam-6733	349	7	have	have	VERB
ejpam-6733	349	8	,	,	PUNCT
ejpam-6733	349	9	(	(	PUNCT
ejpam-6733	349	10	−qt−	−qt−	X
ejpam-6733	349	11	qc2	qc2	NOUN
ejpam-6733	349	12	)	)	PUNCT
ejpam-6733	349	13	b	b	NOUN
ejpam-6733	349	14	=	=	SYM
ejpam-6733	349	15	rb	rb	PROPN
ejpam-6733	349	16	,	,	PUNCT
ejpam-6733	349	17	thus	thus	ADV
ejpam-6733	349	18	,	,	PUNCT
ejpam-6733	349	19	if	if	SCONJ
ejpam-6733	349	20	bc	bc	PROPN
ejpam-6733	349	21	6=	6=	PROPN
ejpam-6733	349	22	0	0	NUM
ejpam-6733	349	23	,	,	PUNCT
ejpam-6733	349	24	then	then	ADV
ejpam-6733	349	25	c2	c2	PROPN
ejpam-6733	349	26	=	=	PUNCT
ejpam-6733	349	27	−	−	PROPN
ejpam-6733	349	28	qt+r	qt+r	PROPN
ejpam-6733	349	29	q	q	NOUN
ejpam-6733	349	30	.	.	PUNCT
ejpam-6733	350	1	5.3	5.3	NUM
ejpam-6733	350	2	.	.	PUNCT
ejpam-6733	351	1	representation	representation	NOUN
ejpam-6733	351	2	matrices	matrix	NOUN
ejpam-6733	351	3	of	of	ADP
ejpam-6733	351	4	degree	degree	NOUN
ejpam-6733	351	5	2	2	NUM
ejpam-6733	351	6	of	of	ADP
ejpam-6733	351	7	lp	lp	NOUN
ejpam-6733	351	8	,	,	PUNCT
ejpam-6733	351	9	q	q	PROPN
ejpam-6733	351	10	where	where	SCONJ
ejpam-6733	351	11	p2	p2	PROPN
ejpam-6733	351	12	6=	6=	NUM
ejpam-6733	351	13	q2	q2	NOUN
ejpam-6733	351	14	in	in	ADP
ejpam-6733	351	15	this	this	DET
ejpam-6733	351	16	subsection	subsection	NOUN
ejpam-6733	351	17	,	,	PUNCT
ejpam-6733	351	18	we	we	PRON
ejpam-6733	351	19	consider	consider	VERB
ejpam-6733	351	20	the	the	DET
ejpam-6733	351	21	case	case	NOUN
ejpam-6733	351	22	where	where	SCONJ
ejpam-6733	351	23	p2	p2	PROPN
ejpam-6733	351	24	6=	6=	SYM
ejpam-6733	351	25	q2	q2	NOUN
ejpam-6733	351	26	,	,	PUNCT
ejpam-6733	351	27	and	and	CCONJ
ejpam-6733	351	28	we	we	PRON
ejpam-6733	351	29	seek	seek	VERB
ejpam-6733	351	30	a	a	DET
ejpam-6733	351	31	faithful	faithful	ADJ
ejpam-6733	351	32	representation	representation	NOUN
ejpam-6733	351	33	for	for	ADP
ejpam-6733	351	34	lp	lp	NOUN
ejpam-6733	351	35	,	,	PUNCT
ejpam-6733	351	36	q	q	NOUN
ejpam-6733	351	37	of	of	ADP
ejpam-6733	351	38	degree	degree	NOUN
ejpam-6733	351	39	2	2	NUM
ejpam-6733	351	40	as	as	ADP
ejpam-6733	351	41	the	the	DET
ejpam-6733	351	42	least	least	ADJ
ejpam-6733	351	43	degree	degree	NOUN
ejpam-6733	351	44	.	.	PUNCT
ejpam-6733	352	1	lemma	lemma	PROPN
ejpam-6733	352	2	5	5	NUM
ejpam-6733	352	3	.	.	PUNCT
ejpam-6733	353	1	if	if	SCONJ
ejpam-6733	353	2	bc	bc	PROPN
ejpam-6733	353	3	6=	6=	PROPN
ejpam-6733	353	4	0	0	NUM
ejpam-6733	353	5	,	,	PUNCT
ejpam-6733	353	6	and	and	CCONJ
ejpam-6733	353	7	p+	p+	PROPN
ejpam-6733	353	8	q	q	PROPN
ejpam-6733	353	9	6=	6=	PROPN
ejpam-6733	353	10	0	0	NUM
ejpam-6733	353	11	,	,	PUNCT
ejpam-6733	353	12	then	then	ADV
ejpam-6733	353	13	c	c	PROPN
ejpam-6733	353	14	is	be	AUX
ejpam-6733	353	15	a	a	DET
ejpam-6733	353	16	scalar	scalar	ADJ
ejpam-6733	353	17	matrix	matrix	NOUN
ejpam-6733	353	18	.	.	PUNCT
ejpam-6733	354	1	proof	proof	NOUN
ejpam-6733	354	2	.	.	PUNCT
ejpam-6733	355	1	comparing	compare	VERB
ejpam-6733	355	2	the	the	DET
ejpam-6733	355	3	elements	element	NOUN
ejpam-6733	355	4	on	on	ADP
ejpam-6733	355	5	both	both	DET
ejpam-6733	355	6	sides	side	NOUN
ejpam-6733	355	7	of	of	ADP
ejpam-6733	355	8	equation	equation	NOUN
ejpam-6733	355	9	(	(	PUNCT
ejpam-6733	355	10	15	15	NUM
ejpam-6733	355	11	)	)	PUNCT
ejpam-6733	355	12	,	,	PUNCT
ejpam-6733	355	13	we	we	PRON
ejpam-6733	355	14	get	get	VERB
ejpam-6733	355	15	:	:	PUNCT
ejpam-6733	355	16	if	if	SCONJ
ejpam-6733	355	17	b	b	PROPN
ejpam-6733	355	18	6=	6=	NUM
ejpam-6733	355	19	0	0	NUM
ejpam-6733	355	20	,	,	PUNCT
ejpam-6733	355	21	then	then	ADV
ejpam-6733	355	22	,	,	PUNCT
ejpam-6733	355	23	r	r	NOUN
ejpam-6733	355	24	=	=	SYM
ejpam-6733	355	25	pc1	pc1	NOUN
ejpam-6733	356	1	−	−	NOUN
ejpam-6733	356	2	qc2	qc2	NOUN
ejpam-6733	356	3	and	and	CCONJ
ejpam-6733	356	4	similarly	similarly	ADV
ejpam-6733	356	5	,	,	PUNCT
ejpam-6733	356	6	when	when	SCONJ
ejpam-6733	356	7	c	c	PROPN
ejpam-6733	356	8	6=	6=	PROPN
ejpam-6733	356	9	0	0	NUM
ejpam-6733	356	10	,	,	PUNCT
ejpam-6733	356	11	then	then	ADV
ejpam-6733	356	12	r	r	NOUN
ejpam-6733	356	13	=	=	PUNCT
ejpam-6733	356	14	pc2	pc2	NOUN
ejpam-6733	356	15	−	−	PROPN
ejpam-6733	356	16	qc1	qc1	NOUN
ejpam-6733	356	17	.	.	PUNCT
ejpam-6733	357	1	thus	thus	ADV
ejpam-6733	357	2	,	,	PUNCT
ejpam-6733	357	3	(	(	PUNCT
ejpam-6733	357	4	p+	p+	NOUN
ejpam-6733	357	5	q	q	X
ejpam-6733	357	6	)	)	PUNCT
ejpam-6733	357	7	(	(	PUNCT
ejpam-6733	357	8	c1	c1	PROPN
ejpam-6733	357	9	−	−	PROPN
ejpam-6733	357	10	c2	c2	PROPN
ejpam-6733	357	11	)	)	PUNCT
ejpam-6733	358	1	=	=	PUNCT
ejpam-6733	358	2	0	0	X
ejpam-6733	358	3	.	.	PUNCT
ejpam-6733	359	1	therefore	therefore	ADV
ejpam-6733	359	2	,	,	PUNCT
ejpam-6733	359	3	c	c	PROPN
ejpam-6733	359	4	is	be	AUX
ejpam-6733	359	5	a	a	DET
ejpam-6733	359	6	scalar	scalar	ADJ
ejpam-6733	359	7	matrix	matrix	NOUN
ejpam-6733	359	8	.	.	PUNCT
ejpam-6733	360	1	theorem	theorem	VERB
ejpam-6733	360	2	7	7	NUM
ejpam-6733	360	3	.	.	PUNCT
ejpam-6733	361	1	if	if	SCONJ
ejpam-6733	361	2	c	c	PROPN
ejpam-6733	361	3	is	be	AUX
ejpam-6733	361	4	a	a	DET
ejpam-6733	361	5	scalar	scalar	ADJ
ejpam-6733	361	6	matrix	matrix	NOUN
ejpam-6733	361	7	and	and	CCONJ
ejpam-6733	361	8	p+	p+	NOUN
ejpam-6733	361	9	q	q	PROPN
ejpam-6733	361	10	6=	6=	PROPN
ejpam-6733	361	11	0	0	NUM
ejpam-6733	361	12	,	,	PUNCT
ejpam-6733	361	13	then	then	ADV
ejpam-6733	361	14	the	the	DET
ejpam-6733	361	15	representation	representation	NOUN
ejpam-6733	361	16	of	of	ADP
ejpam-6733	361	17	lp	lp	NOUN
ejpam-6733	361	18	,	,	PUNCT
ejpam-6733	361	19	q	q	PUNCT
ejpam-6733	361	20	is	be	AUX
ejpam-6733	361	21	not	not	PART
ejpam-6733	361	22	faithful	faithful	ADJ
ejpam-6733	361	23	.	.	PUNCT
ejpam-6733	362	1	proof	proof	NOUN
ejpam-6733	362	2	.	.	PUNCT
ejpam-6733	363	1	for	for	ADP
ejpam-6733	363	2	the	the	DET
ejpam-6733	363	3	linear	linear	ADJ
ejpam-6733	363	4	independence	independence	NOUN
ejpam-6733	363	5	of	of	ADP
ejpam-6733	363	6	the	the	DET
ejpam-6733	363	7	generators	generator	NOUN
ejpam-6733	363	8	,	,	PUNCT
ejpam-6733	363	9	and	and	CCONJ
ejpam-6733	363	10	as	as	SCONJ
ejpam-6733	363	11	c	c	PROPN
ejpam-6733	363	12	is	be	AUX
ejpam-6733	363	13	a	a	DET
ejpam-6733	363	14	scalar	scalar	ADJ
ejpam-6733	363	15	matrix	matrix	NOUN
ejpam-6733	363	16	,	,	PUNCT
ejpam-6733	363	17	we	we	PRON
ejpam-6733	363	18	assume	assume	VERB
ejpam-6733	363	19	that	that	SCONJ
ejpam-6733	363	20	d	d	PROPN
ejpam-6733	363	21	=	=	SYM
ejpam-6733	363	22	0	0	NUM
ejpam-6733	363	23	.	.	PUNCT
ejpam-6733	364	1	so	so	ADV
ejpam-6733	364	2	,	,	PUNCT
ejpam-6733	364	3	from	from	ADP
ejpam-6733	364	4	(	(	PUNCT
ejpam-6733	364	5	14	14	NUM
ejpam-6733	364	6	)	)	PUNCT
ejpam-6733	364	7	,	,	PUNCT
ejpam-6733	364	8	we	we	PRON
ejpam-6733	364	9	have	have	VERB
ejpam-6733	364	10	p	p	NOUN
ejpam-6733	364	11	(	(	PUNCT
ejpam-6733	364	12	ac̄	ac̄	ADJ
ejpam-6733	364	13	)	)	PUNCT
ejpam-6733	364	14	−	−	PROPN
ejpam-6733	365	1	q	q	NOUN
ejpam-6733	366	1	(	(	PUNCT
ejpam-6733	366	2	āb	āb	PROPN
ejpam-6733	366	3	)	)	PUNCT
ejpam-6733	366	4	=	=	SYM
ejpam-6733	366	5	0	0	X
ejpam-6733	366	6	.	.	PUNCT
ejpam-6733	366	7	suppose	suppose	VERB
ejpam-6733	366	8	a	a	DET
ejpam-6733	366	9	6=	6=	NUM
ejpam-6733	366	10	0	0	NUM
ejpam-6733	366	11	,	,	PUNCT
ejpam-6733	366	12	then	then	ADV
ejpam-6733	366	13	b	b	PROPN
ejpam-6733	366	14	=	=	SYM
ejpam-6733	366	15	pc̄a	pc̄a	PROPN
ejpam-6733	366	16	qā	qā	NOUN
ejpam-6733	366	17	and	and	CCONJ
ejpam-6733	366	18	hence	hence	ADV
ejpam-6733	366	19	|b|2	|b|2	PROPN
ejpam-6733	366	20	=	=	PUNCT
ejpam-6733	366	21	p2|c|2	p2|c|2	PROPN
ejpam-6733	366	22	q2	q2	NOUN
ejpam-6733	366	23	.	.	PUNCT
ejpam-6733	367	1	since	since	SCONJ
ejpam-6733	367	2	c	c	PROPN
ejpam-6733	367	3	is	be	AUX
ejpam-6733	367	4	scalar	scalar	ADJ
ejpam-6733	367	5	,	,	PUNCT
ejpam-6733	367	6	then	then	ADV
ejpam-6733	367	7	f	f	PROPN
ejpam-6733	367	8	(	(	PUNCT
ejpam-6733	367	9	c1	c1	PROPN
ejpam-6733	367	10	)	)	PUNCT
ejpam-6733	368	1	=	=	SYM
ejpam-6733	368	2	f	f	PROPN
ejpam-6733	368	3	(	(	PUNCT
ejpam-6733	368	4	c2	c2	PROPN
ejpam-6733	368	5	)	)	PUNCT
ejpam-6733	368	6	,	,	PUNCT
ejpam-6733	368	7	and	and	CCONJ
ejpam-6733	368	8	hence	hence	ADV
ejpam-6733	368	9	from	from	ADP
ejpam-6733	368	10	(	(	PUNCT
ejpam-6733	368	11	14	14	NUM
ejpam-6733	368	12	)	)	PUNCT
ejpam-6733	368	13	,	,	PUNCT
ejpam-6733	368	14	(	(	PUNCT
ejpam-6733	368	15	p−	p−	NOUN
ejpam-6733	368	16	q	q	NOUN
ejpam-6733	368	17	)	)	PUNCT
ejpam-6733	368	18	|a|2	|a|2	PROPN
ejpam-6733	368	19	+	+	PROPN
ejpam-6733	368	20	p	p	PROPN
ejpam-6733	368	21	|b|2	|b|2	ADJ
ejpam-6733	368	22	−	−	NOUN
ejpam-6733	368	23	q	q	NOUN
ejpam-6733	368	24	|c|2	|c|2	PROPN
ejpam-6733	368	25	=	=	SYM
ejpam-6733	368	26	p	p	DET
ejpam-6733	368	27	|c|2	|c|2	PROPN
ejpam-6733	368	28	−	−	PROPN
ejpam-6733	368	29	q	q	PUNCT
ejpam-6733	368	30	|b|2	|b|2	PROPN
ejpam-6733	368	31	.	.	PUNCT
ejpam-6733	369	1	if	if	SCONJ
ejpam-6733	369	2	p	p	PROPN
ejpam-6733	369	3	+	+	NOUN
ejpam-6733	369	4	q	q	X
ejpam-6733	369	5	6=	6=	NUM
ejpam-6733	369	6	0	0	NUM
ejpam-6733	369	7	,	,	PUNCT
ejpam-6733	369	8	we	we	PRON
ejpam-6733	369	9	have	have	VERB
ejpam-6733	369	10	,	,	PUNCT
ejpam-6733	369	11	|c|2	|c|2	PROPN
ejpam-6733	369	12	=	=	SYM
ejpam-6733	369	13	−	−	PROPN
ejpam-6733	369	14	q2|a|2	q2|a|2	PROPN
ejpam-6733	369	15	(	(	PUNCT
ejpam-6733	369	16	p+q)2	p+q)2	PROPN
ejpam-6733	369	17	which	which	PRON
ejpam-6733	369	18	is	be	AUX
ejpam-6733	369	19	impossible	impossible	ADJ
ejpam-6733	369	20	unless	unless	SCONJ
ejpam-6733	369	21	c	c	NOUN
ejpam-6733	369	22	=	=	SYM
ejpam-6733	369	23	0	0	NUM
ejpam-6733	369	24	,	,	PUNCT
ejpam-6733	369	25	and	and	CCONJ
ejpam-6733	369	26	in	in	ADP
ejpam-6733	369	27	such	such	DET
ejpam-6733	369	28	a	a	DET
ejpam-6733	369	29	case	case	NOUN
ejpam-6733	369	30	a	a	DET
ejpam-6733	369	31	=	=	SYM
ejpam-6733	369	32	0	0	NUM
ejpam-6733	369	33	,	,	PUNCT
ejpam-6733	369	34	contradicting	contradict	VERB
ejpam-6733	369	35	with	with	ADP
ejpam-6733	369	36	a	a	DET
ejpam-6733	369	37	6=	6=	NUM
ejpam-6733	369	38	0	0	NUM
ejpam-6733	369	39	.	.	PUNCT
ejpam-6733	370	1	so	so	ADV
ejpam-6733	370	2	,	,	PUNCT
ejpam-6733	370	3	a	a	DET
ejpam-6733	370	4	=	=	NOUN
ejpam-6733	370	5	0	0	NUM
ejpam-6733	370	6	.	.	PUNCT
ejpam-6733	371	1	then	then	ADV
ejpam-6733	371	2	from	from	ADP
ejpam-6733	371	3	(	(	PUNCT
ejpam-6733	371	4	14	14	NUM
ejpam-6733	371	5	)	)	PUNCT
ejpam-6733	371	6	,	,	PUNCT
ejpam-6733	371	7	we	we	PRON
ejpam-6733	371	8	get	get	VERB
ejpam-6733	371	9	f	f	PROPN
ejpam-6733	371	10	(	(	PUNCT
ejpam-6733	371	11	c1	c1	PROPN
ejpam-6733	371	12	)	)	PUNCT
ejpam-6733	371	13	=	=	PUNCT
ejpam-6733	372	1	p	p	X
ejpam-6733	372	2	|b|2	|b|2	ADJ
ejpam-6733	372	3	−	−	NOUN
ejpam-6733	372	4	q	q	NOUN
ejpam-6733	372	5	|c|2	|c|2	PROPN
ejpam-6733	372	6	and	and	CCONJ
ejpam-6733	372	7	similarly	similarly	ADV
ejpam-6733	372	8	,	,	PUNCT
ejpam-6733	372	9	f	f	PROPN
ejpam-6733	372	10	(	(	PUNCT
ejpam-6733	372	11	c2	c2	PROPN
ejpam-6733	372	12	)	)	PUNCT
ejpam-6733	372	13	=	=	PUNCT
ejpam-6733	373	1	p	p	DET
ejpam-6733	373	2	|c|2	|c|2	PROPN
ejpam-6733	373	3	−	−	PROPN
ejpam-6733	373	4	q	q	PUNCT
ejpam-6733	373	5	|b|2	|b|2	PROPN
ejpam-6733	373	6	.	.	PUNCT
ejpam-6733	374	1	therefore	therefore	ADV
ejpam-6733	374	2	,	,	PUNCT
ejpam-6733	374	3	as	as	SCONJ
ejpam-6733	374	4	c	c	PROPN
ejpam-6733	374	5	is	be	AUX
ejpam-6733	374	6	scalar	scalar	ADJ
ejpam-6733	374	7	,	,	PUNCT
ejpam-6733	374	8	we	we	PRON
ejpam-6733	374	9	get	get	VERB
ejpam-6733	374	10	(	(	PUNCT
ejpam-6733	374	11	p+	p+	NOUN
ejpam-6733	374	12	q	q	X
ejpam-6733	374	13	)	)	PUNCT
ejpam-6733	374	14	(	(	PUNCT
ejpam-6733	374	15	|b|2	|b|2	PROPN
ejpam-6733	374	16	−	−	PROPN
ejpam-6733	374	17	|c|2	|c|2	NOUN
ejpam-6733	374	18	)	)	PUNCT
ejpam-6733	374	19	=	=	PUNCT
ejpam-6733	375	1	0	0	X
ejpam-6733	375	2	.	.	PUNCT
ejpam-6733	376	1	then	then	ADV
ejpam-6733	376	2	either	either	CCONJ
ejpam-6733	376	3	a	a	DET
ejpam-6733	376	4	=	=	SYM
ejpam-6733	376	5	0	0	NUM
ejpam-6733	376	6	or	or	CCONJ
ejpam-6733	376	7	|b|2	|b|2	PROPN
ejpam-6733	376	8	=	=	SYM
ejpam-6733	376	9	|c|2	|c|2	PROPN
ejpam-6733	376	10	.	.	PUNCT
ejpam-6733	377	1	in	in	ADP
ejpam-6733	377	2	both	both	DET
ejpam-6733	377	3	cases	case	NOUN
ejpam-6733	377	4	,	,	PUNCT
ejpam-6733	377	5	the	the	DET
ejpam-6733	377	6	representation	representation	NOUN
ejpam-6733	377	7	is	be	AUX
ejpam-6733	377	8	not	not	PART
ejpam-6733	377	9	faithful	faithful	ADJ
ejpam-6733	377	10	,	,	PUNCT
ejpam-6733	377	11	since	since	SCONJ
ejpam-6733	377	12	the	the	DET
ejpam-6733	377	13	generators	generator	NOUN
ejpam-6733	377	14	a	a	DET
ejpam-6733	377	15	,	,	PUNCT
ejpam-6733	377	16	b	b	NOUN
ejpam-6733	377	17	=	=	SYM
ejpam-6733	377	18	a†	a†	PROPN
ejpam-6733	377	19	,	,	PUNCT
ejpam-6733	377	20	and	and	CCONJ
ejpam-6733	377	21	c	c	NOUN
ejpam-6733	377	22	are	be	AUX
ejpam-6733	377	23	linearly	linearly	ADV
ejpam-6733	377	24	independent	independent	ADJ
ejpam-6733	377	25	,	,	PUNCT
ejpam-6733	377	26	and	and	CCONJ
ejpam-6733	377	27	a+b	a+b	NUM
ejpam-6733	377	28	is	be	AUX
ejpam-6733	377	29	a	a	DET
ejpam-6733	377	30	real	real	ADJ
ejpam-6733	377	31	matrix	matrix	NOUN
ejpam-6733	377	32	.	.	PUNCT
ejpam-6733	378	1	l.	l.	PROPN
ejpam-6733	378	2	a	a	DET
ejpam-6733	378	3	-	-	PUNCT
ejpam-6733	378	4	m.	m.	NOUN
ejpam-6733	378	5	hanna	hanna	NOUN
ejpam-6733	378	6	,	,	PUNCT
ejpam-6733	378	7	s.	s.	PROPN
ejpam-6733	378	8	s.	s.	PROPN
ejpam-6733	378	9	hassan	hassan	PROPN
ejpam-6733	378	10	,	,	PUNCT
ejpam-6733	378	11	m.	m.	NOUN
ejpam-6733	378	12	almutairi	almutairi	PROPN
ejpam-6733	378	13	/	/	SYM
ejpam-6733	378	14	eur	eur	PROPN
ejpam-6733	378	15	.	.	PUNCT
ejpam-6733	379	1	j.	j.	PROPN
ejpam-6733	379	2	pure	pure	PROPN
ejpam-6733	379	3	appl	appl	PROPN
ejpam-6733	379	4	.	.	PROPN
ejpam-6733	379	5	math	math	PROPN
ejpam-6733	379	6	,	,	PUNCT
ejpam-6733	379	7	18	18	NUM
ejpam-6733	379	8	(	(	PUNCT
ejpam-6733	379	9	4	4	NUM
ejpam-6733	379	10	)	)	PUNCT
ejpam-6733	379	11	(	(	PUNCT
ejpam-6733	379	12	2025	2025	NUM
ejpam-6733	379	13	)	)	PUNCT
ejpam-6733	379	14	,	,	PUNCT
ejpam-6733	379	15	6733	6733	NUM
ejpam-6733	379	16	11	11	NUM
ejpam-6733	379	17	of	of	ADP
ejpam-6733	379	18	12	12	NUM
ejpam-6733	379	19	theorem	theorem	NOUN
ejpam-6733	379	20	8	8	NUM
ejpam-6733	379	21	.	.	PUNCT
ejpam-6733	380	1	the	the	DET
ejpam-6733	380	2	lie	lie	NOUN
ejpam-6733	380	3	algebra	algebra	VERB
ejpam-6733	380	4	lp	lp	PROPN
ejpam-6733	380	5	,	,	PUNCT
ejpam-6733	380	6	q	q	NOUN
ejpam-6733	380	7	,	,	PUNCT
ejpam-6733	380	8	where	where	SCONJ
ejpam-6733	380	9	p2	p2	PROPN
ejpam-6733	380	10	6=	6=	NUM
ejpam-6733	380	11	q2	q2	NOUN
ejpam-6733	380	12	with	with	ADP
ejpam-6733	380	13	pq	pq	PROPN
ejpam-6733	380	14	6=	6=	ADP
ejpam-6733	380	15	0	0	NUM
ejpam-6733	380	16	,	,	PUNCT
ejpam-6733	380	17	has	have	VERB
ejpam-6733	380	18	a	a	DET
ejpam-6733	380	19	faithful	faithful	ADJ
ejpam-6733	380	20	representation	representation	NOUN
ejpam-6733	380	21	of	of	ADP
ejpam-6733	380	22	degree	degree	NOUN
ejpam-6733	380	23	2	2	NUM
ejpam-6733	380	24	as	as	ADP
ejpam-6733	380	25	the	the	DET
ejpam-6733	380	26	least	least	ADJ
ejpam-6733	380	27	degree	degree	NOUN
ejpam-6733	380	28	,	,	PUNCT
ejpam-6733	380	29	iff	iff	PROPN
ejpam-6733	380	30	there	there	PRON
ejpam-6733	380	31	exists	exist	VERB
ejpam-6733	380	32	t	t	PROPN
ejpam-6733	380	33	∈	∈	PROPN
ejpam-6733	380	34	r	r	NOUN
ejpam-6733	380	35	,	,	PUNCT
ejpam-6733	380	36	such	such	ADJ
ejpam-6733	380	37	that	that	SCONJ
ejpam-6733	380	38	f	f	PROPN
ejpam-6733	380	39	(	(	PUNCT
ejpam-6733	380	40	t	t	PROPN
ejpam-6733	380	41	)	)	PUNCT
ejpam-6733	380	42	p	p	NOUN
ejpam-6733	380	43	>	>	X
ejpam-6733	380	44	0	0	PUNCT
ejpam-6733	381	1	and	and	CCONJ
ejpam-6733	381	2	f	f	PROPN
ejpam-6733	381	3	(	(	PUNCT
ejpam-6733	381	4	pt−r	pt−r	NOUN
ejpam-6733	381	5	q	q	X
ejpam-6733	381	6	)	)	PUNCT
ejpam-6733	381	7	=	=	SYM
ejpam-6733	382	1	−	−	PROPN
ejpam-6733	382	2	q	q	INTJ
ejpam-6733	382	3	pf	pf	PROPN
ejpam-6733	382	4	(	(	PUNCT
ejpam-6733	382	5	t	t	PROPN
ejpam-6733	382	6	)	)	PUNCT
ejpam-6733	382	7	.	.	PUNCT
ejpam-6733	383	1	moreover	moreover	ADV
ejpam-6733	383	2	,	,	PUNCT
ejpam-6733	383	3	the	the	DET
ejpam-6733	383	4	representation	representation	NOUN
ejpam-6733	383	5	matrices	matrix	NOUN
ejpam-6733	383	6	of	of	ADP
ejpam-6733	383	7	the	the	DET
ejpam-6733	383	8	generators	generator	NOUN
ejpam-6733	383	9	k+,k−	k+,k−	PROPN
ejpam-6733	383	10	,	,	PUNCT
ejpam-6733	383	11	and	and	CCONJ
ejpam-6733	383	12	k0	k0	PROPN
ejpam-6733	383	13	are	be	AUX
ejpam-6733	383	14	a	a	DET
ejpam-6733	383	15	,	,	PUNCT
ejpam-6733	383	16	a†	a†	NOUN
ejpam-6733	383	17	,	,	PUNCT
ejpam-6733	383	18	and	and	CCONJ
ejpam-6733	383	19	c	c	NOUN
ejpam-6733	383	20	=	=	SYM
ejpam-6733	383	21	diag	diag	PROPN
ejpam-6733	383	22	(	(	PUNCT
ejpam-6733	383	23	t	t	PROPN
ejpam-6733	383	24	,	,	PUNCT
ejpam-6733	383	25	pt−r	pt−r	PROPN
ejpam-6733	383	26	q	q	X
ejpam-6733	383	27	)	)	PUNCT
ejpam-6733	383	28	,	,	PUNCT
ejpam-6733	383	29	respectively	respectively	ADV
ejpam-6733	383	30	,	,	PUNCT
ejpam-6733	383	31	where	where	SCONJ
ejpam-6733	383	32	a	a	PRON
ejpam-6733	383	33	=	=	X
ejpam-6733	383	34	[	[	PUNCT
ejpam-6733	383	35	0	0	NUM
ejpam-6733	383	36	b	b	NOUN
ejpam-6733	383	37	0	0	NUM
ejpam-6733	383	38	0	0	NUM
ejpam-6733	383	39	]	]	PUNCT
ejpam-6733	383	40	,	,	PUNCT
ejpam-6733	383	41	such	such	ADJ
ejpam-6733	383	42	that	that	SCONJ
ejpam-6733	383	43	|b|2	|b|2	PROPN
ejpam-6733	383	44	=	=	PUNCT
ejpam-6733	383	45	f	f	X
ejpam-6733	383	46	(	(	PUNCT
ejpam-6733	383	47	t	t	PROPN
ejpam-6733	383	48	)	)	PUNCT
ejpam-6733	383	49	p	p	X
ejpam-6733	383	50	>	>	X
ejpam-6733	383	51	0	0	X
ejpam-6733	383	52	.	.	PUNCT
ejpam-6733	384	1	proof	proof	NOUN
ejpam-6733	384	2	.	.	PUNCT
ejpam-6733	385	1	from	from	ADP
ejpam-6733	385	2	lemma	lemma	PROPN
ejpam-6733	385	3	5	5	NUM
ejpam-6733	385	4	and	and	CCONJ
ejpam-6733	385	5	theorem	theorem	VERB
ejpam-6733	385	6	7	7	NUM
ejpam-6733	385	7	,	,	PUNCT
ejpam-6733	385	8	we	we	PRON
ejpam-6733	385	9	must	must	AUX
ejpam-6733	385	10	have	have	VERB
ejpam-6733	385	11	that	that	PRON
ejpam-6733	385	12	bc	bc	PROPN
ejpam-6733	386	1	=	=	SYM
ejpam-6733	387	1	0	0	PROPN
ejpam-6733	387	2	.	.	PUNCT
ejpam-6733	388	1	so	so	ADV
ejpam-6733	388	2	,	,	PUNCT
ejpam-6733	388	3	we	we	PRON
ejpam-6733	388	4	can	can	AUX
ejpam-6733	388	5	choose	choose	VERB
ejpam-6733	388	6	a	a	DET
ejpam-6733	388	7	=	=	PUNCT
ejpam-6733	388	8	[	[	PUNCT
ejpam-6733	388	9	0	0	NUM
ejpam-6733	388	10	b	b	NOUN
ejpam-6733	388	11	0	0	NUM
ejpam-6733	388	12	0	0	NUM
ejpam-6733	388	13	]	]	PUNCT
ejpam-6733	388	14	,	,	PUNCT
ejpam-6733	388	15	with	with	ADP
ejpam-6733	388	16	b	b	PROPN
ejpam-6733	388	17	6=	6=	NUM
ejpam-6733	388	18	0	0	NUM
ejpam-6733	388	19	.	.	PUNCT
ejpam-6733	389	1	thus	thus	ADV
ejpam-6733	389	2	,	,	PUNCT
ejpam-6733	389	3	from	from	ADP
ejpam-6733	389	4	(	(	PUNCT
ejpam-6733	389	5	14	14	NUM
ejpam-6733	389	6	)	)	PUNCT
ejpam-6733	389	7	,	,	PUNCT
ejpam-6733	389	8	we	we	PRON
ejpam-6733	389	9	have	have	VERB
ejpam-6733	389	10	f	f	PROPN
ejpam-6733	389	11	(	(	PUNCT
ejpam-6733	389	12	c1	c1	PROPN
ejpam-6733	389	13	)	)	PUNCT
ejpam-6733	389	14	=	=	PUNCT
ejpam-6733	390	1	p	p	X
ejpam-6733	390	2	|b|2	|b|2	PROPN
ejpam-6733	390	3	and	and	CCONJ
ejpam-6733	390	4	f	f	PROPN
ejpam-6733	390	5	(	(	PUNCT
ejpam-6733	390	6	c2	c2	PROPN
ejpam-6733	390	7	)	)	PUNCT
ejpam-6733	390	8	=	=	NOUN
ejpam-6733	390	9	−q	−q	ADJ
ejpam-6733	390	10	|b|2	|b|2	PROPN
ejpam-6733	390	11	.	.	PUNCT
ejpam-6733	391	1	thus	thus	ADV
ejpam-6733	391	2	,	,	PUNCT
ejpam-6733	391	3	|b|2	|b|2	PROPN
ejpam-6733	391	4	=	=	SYM
ejpam-6733	391	5	f	f	PROPN
ejpam-6733	391	6	(	(	PUNCT
ejpam-6733	391	7	c1	c1	NOUN
ejpam-6733	391	8	)	)	PUNCT
ejpam-6733	392	1	p	p	X
ejpam-6733	393	1	=	=	PUNCT
ejpam-6733	393	2	−f	−f	PROPN
ejpam-6733	393	3	(	(	PUNCT
ejpam-6733	393	4	c2	c2	PROPN
ejpam-6733	393	5	)	)	PUNCT
ejpam-6733	393	6	q	q	PROPN
ejpam-6733	393	7	.	.	PUNCT
ejpam-6733	394	1	from	from	ADP
ejpam-6733	394	2	(	(	PUNCT
ejpam-6733	394	3	15	15	NUM
ejpam-6733	394	4	)	)	PUNCT
ejpam-6733	394	5	,	,	PUNCT
ejpam-6733	394	6	we	we	PRON
ejpam-6733	394	7	have	have	VERB
ejpam-6733	394	8	(	(	PUNCT
ejpam-6733	394	9	pc1	pc1	NOUN
ejpam-6733	394	10	−	−	PROPN
ejpam-6733	394	11	qc2	qc2	NOUN
ejpam-6733	394	12	)	)	PUNCT
ejpam-6733	395	1	=	=	NOUN
ejpam-6733	395	2	r.	r.	PROPN
ejpam-6733	396	1	so	so	ADV
ejpam-6733	396	2	,	,	PUNCT
ejpam-6733	396	3	pc1−	pc1−	NOUN
ejpam-6733	396	4	r	r	NOUN
ejpam-6733	396	5	=	=	SYM
ejpam-6733	396	6	qc2	qc2	NOUN
ejpam-6733	396	7	.	.	PUNCT
ejpam-6733	397	1	thus	thus	ADV
ejpam-6733	397	2	,	,	PUNCT
ejpam-6733	397	3	c2	c2	PROPN
ejpam-6733	397	4	=	=	PUNCT
ejpam-6733	397	5	pc1−r	pc1−r	PROPN
ejpam-6733	397	6	q	q	X
ejpam-6733	397	7	.	.	PUNCT
ejpam-6733	398	1	let	let	VERB
ejpam-6733	399	1	c1	c1	PROPN
ejpam-6733	399	2	=	=	PROPN
ejpam-6733	399	3	t	t	PROPN
ejpam-6733	399	4	a	a	DET
ejpam-6733	399	5	real	real	ADJ
ejpam-6733	399	6	number	number	NOUN
ejpam-6733	399	7	,	,	PUNCT
ejpam-6733	399	8	then	then	ADV
ejpam-6733	399	9	c2	c2	PROPN
ejpam-6733	399	10	=	=	SYM
ejpam-6733	399	11	pt−r	pt−r	PROPN
ejpam-6733	399	12	q	q	X
ejpam-6733	399	13	.	.	PUNCT
ejpam-6733	400	1	thus	thus	ADV
ejpam-6733	400	2	,	,	PUNCT
ejpam-6733	400	3	|b|2	|b|2	PROPN
ejpam-6733	400	4	=	=	PUNCT
ejpam-6733	400	5	f	f	X
ejpam-6733	400	6	(	(	PUNCT
ejpam-6733	400	7	t	t	PROPN
ejpam-6733	400	8	)	)	PUNCT
ejpam-6733	400	9	p	p	NOUN
ejpam-6733	400	10	=	=	PUNCT
ejpam-6733	401	1	−	−	PROPN
ejpam-6733	401	2	f	f	PROPN
ejpam-6733	401	3	(	(	PUNCT
ejpam-6733	401	4	pt−r	pt−r	PROPN
ejpam-6733	401	5	q	q	X
ejpam-6733	401	6	)	)	PUNCT
ejpam-6733	401	7	q	q	X
ejpam-6733	401	8	>	>	X
ejpam-6733	401	9	0	0	X
ejpam-6733	401	10	.	.	PUNCT
ejpam-6733	402	1	therefore	therefore	ADV
ejpam-6733	402	2	,	,	PUNCT
ejpam-6733	402	3	the	the	DET
ejpam-6733	402	4	function	function	NOUN
ejpam-6733	402	5	f	f	PROPN
ejpam-6733	402	6	should	should	AUX
ejpam-6733	402	7	satisfy	satisfy	VERB
ejpam-6733	402	8	that	that	SCONJ
ejpam-6733	403	1	f	f	PROPN
ejpam-6733	403	2	(	(	PUNCT
ejpam-6733	403	3	pt−r	pt−r	PROPN
ejpam-6733	403	4	q	q	X
ejpam-6733	403	5	)	)	PUNCT
ejpam-6733	403	6	=	=	SYM
ejpam-6733	404	1	−	−	PROPN
ejpam-6733	404	2	q	q	INTJ
ejpam-6733	404	3	pf	pf	PROPN
ejpam-6733	404	4	(	(	PUNCT
ejpam-6733	404	5	t	t	PROPN
ejpam-6733	404	6	)	)	PUNCT
ejpam-6733	404	7	.	.	PUNCT
ejpam-6733	405	1	example	example	NOUN
ejpam-6733	406	1	6	6	NUM
ejpam-6733	406	2	.	.	X
ejpam-6733	407	1	for	for	ADP
ejpam-6733	407	2	l2,3	l2,3	PROPN
ejpam-6733	407	3	,	,	PUNCT
ejpam-6733	407	4	if	if	SCONJ
ejpam-6733	407	5	r	r	NOUN
ejpam-6733	407	6	=	=	SYM
ejpam-6733	407	7	−1	−1	NOUN
ejpam-6733	407	8	and	and	CCONJ
ejpam-6733	407	9	f	f	PROPN
ejpam-6733	407	10	(	(	PUNCT
ejpam-6733	407	11	x	x	X
ejpam-6733	407	12	)	)	PUNCT
ejpam-6733	407	13	=	=	SYM
ejpam-6733	407	14	3x2	3x2	NUM
ejpam-6733	407	15	−	−	NOUN
ejpam-6733	407	16	x	x	SYM
ejpam-6733	407	17	,	,	PUNCT
ejpam-6733	407	18	then	then	ADV
ejpam-6733	407	19	the	the	DET
ejpam-6733	407	20	solutions	solution	NOUN
ejpam-6733	407	21	of	of	ADP
ejpam-6733	407	22	the	the	DET
ejpam-6733	407	23	equation	equation	NOUN
ejpam-6733	407	24	f	f	PROPN
ejpam-6733	407	25	(	(	PUNCT
ejpam-6733	407	26	pt−r	pt−r	NOUN
ejpam-6733	407	27	q	q	X
ejpam-6733	407	28	)	)	PUNCT
ejpam-6733	408	1	=	=	SYM
ejpam-6733	408	2	−	−	PROPN
ejpam-6733	408	3	q	q	INTJ
ejpam-6733	408	4	pf	pf	PROPN
ejpam-6733	408	5	(	(	PUNCT
ejpam-6733	408	6	t	t	PROPN
ejpam-6733	408	7	)	)	PUNCT
ejpam-6733	408	8	,	,	PUNCT
ejpam-6733	408	9	are	be	AUX
ejpam-6733	408	10	t	t	NOUN
ejpam-6733	408	11	=	=	SYM
ejpam-6733	408	12	0	0	NUM
ejpam-6733	408	13	or	or	CCONJ
ejpam-6733	408	14	t	t	X
ejpam-6733	408	15	=	=	SYM
ejpam-6733	408	16	1	1	NUM
ejpam-6733	408	17	7	7	NUM
ejpam-6733	408	18	.	.	PUNCT
ejpam-6733	409	1	for	for	ADP
ejpam-6733	409	2	t	t	NOUN
ejpam-6733	409	3	=	=	SYM
ejpam-6733	409	4	0	0	NUM
ejpam-6733	409	5	,	,	PUNCT
ejpam-6733	409	6	we	we	PRON
ejpam-6733	409	7	have	have	VERB
ejpam-6733	409	8	|b|2	|b|2	NOUN
ejpam-6733	409	9	=	=	SYM
ejpam-6733	409	10	0	0	NUM
ejpam-6733	409	11	,	,	PUNCT
ejpam-6733	409	12	rejected	reject	VERB
ejpam-6733	409	13	.	.	PUNCT
ejpam-6733	410	1	for	for	ADP
ejpam-6733	410	2	t	t	NOUN
ejpam-6733	410	3	=	=	SYM
ejpam-6733	410	4	1	1	NUM
ejpam-6733	410	5	7	7	NUM
ejpam-6733	410	6	,	,	PUNCT
ejpam-6733	410	7	we	we	PRON
ejpam-6733	410	8	have	have	VERB
ejpam-6733	410	9	|b|2	|b|2	NOUN
ejpam-6733	410	10	=	=	SYM
ejpam-6733	411	1	−	−	PROPN
ejpam-6733	411	2	2	2	NUM
ejpam-6733	411	3	49	49	NUM
ejpam-6733	411	4	<	<	X
ejpam-6733	411	5	0	0	NUM
ejpam-6733	411	6	,	,	PUNCT
ejpam-6733	411	7	rejected	reject	VERB
ejpam-6733	411	8	.	.	PUNCT
ejpam-6733	411	9	example	example	NOUN
ejpam-6733	412	1	7	7	NUM
ejpam-6733	412	2	.	.	X
ejpam-6733	412	3	for	for	ADP
ejpam-6733	412	4	l2,3	l2,3	PROPN
ejpam-6733	412	5	,	,	PUNCT
ejpam-6733	413	1	if	if	SCONJ
ejpam-6733	413	2	r	r	NOUN
ejpam-6733	413	3	=	=	SYM
ejpam-6733	413	4	−1	−1	NOUN
ejpam-6733	413	5	and	and	CCONJ
ejpam-6733	413	6	f	f	PROPN
ejpam-6733	413	7	(	(	PUNCT
ejpam-6733	413	8	x	x	X
ejpam-6733	413	9	)	)	PUNCT
ejpam-6733	413	10	=	=	SYM
ejpam-6733	414	1	2x2	2x2	NUM
ejpam-6733	414	2	−	−	NOUN
ejpam-6733	414	3	x	x	NOUN
ejpam-6733	414	4	,	,	PUNCT
ejpam-6733	414	5	then	then	ADV
ejpam-6733	414	6	the	the	DET
ejpam-6733	414	7	solutions	solution	NOUN
ejpam-6733	414	8	of	of	ADP
ejpam-6733	414	9	the	the	DET
ejpam-6733	414	10	equation	equation	NOUN
ejpam-6733	414	11	f	f	PROPN
ejpam-6733	415	1	(	(	PUNCT
ejpam-6733	415	2	pt−r	pt−r	NOUN
ejpam-6733	415	3	q	q	X
ejpam-6733	415	4	)	)	PUNCT
ejpam-6733	416	1	=	=	SYM
ejpam-6733	416	2	−	−	PROPN
ejpam-6733	416	3	q	q	INTJ
ejpam-6733	416	4	pf	pf	PROPN
ejpam-6733	416	5	(	(	PUNCT
ejpam-6733	416	6	t	t	PROPN
ejpam-6733	416	7	)	)	PUNCT
ejpam-6733	416	8	,	,	PUNCT
ejpam-6733	416	9	are	be	AUX
ejpam-6733	416	10	t	t	NOUN
ejpam-6733	416	11	=	=	SYM
ejpam-6733	416	12	2	2	NUM
ejpam-6733	416	13	5	5	NUM
ejpam-6733	416	14	or	or	CCONJ
ejpam-6733	416	15	t	t	NOUN
ejpam-6733	416	16	=	=	SYM
ejpam-6733	417	1	−	−	PROPN
ejpam-6733	417	2	1	1	NUM
ejpam-6733	417	3	14	14	NUM
ejpam-6733	417	4	.	.	PUNCT
ejpam-6733	418	1	for	for	ADP
ejpam-6733	418	2	t	t	NOUN
ejpam-6733	418	3	=	=	SYM
ejpam-6733	418	4	−	−	PROPN
ejpam-6733	418	5	1	1	NUM
ejpam-6733	418	6	14	14	NUM
ejpam-6733	418	7	,	,	PUNCT
ejpam-6733	418	8	|b|	|b|	X
ejpam-6733	418	9	2	2	NUM
ejpam-6733	418	10	=	=	SYM
ejpam-6733	418	11	2	2	NUM
ejpam-6733	418	12	49	49	NUM
ejpam-6733	418	13	>	>	SYM
ejpam-6733	418	14	0	0	PUNCT
ejpam-6733	419	1	and	and	CCONJ
ejpam-6733	419	2	c	c	NOUN
ejpam-6733	419	3	=	=	SYM
ejpam-6733	419	4	diag	diag	NOUN
ejpam-6733	419	5	(	(	PUNCT
ejpam-6733	419	6	−	−	PROPN
ejpam-6733	419	7	1	1	NUM
ejpam-6733	419	8	14	14	NUM
ejpam-6733	419	9	,	,	PUNCT
ejpam-6733	419	10	2	2	NUM
ejpam-6733	419	11	7	7	NUM
ejpam-6733	419	12	)	)	PUNCT
ejpam-6733	419	13	.	.	PUNCT
ejpam-6733	420	1	for	for	ADP
ejpam-6733	420	2	t	t	NOUN
ejpam-6733	420	3	=	=	SYM
ejpam-6733	420	4	2	2	NUM
ejpam-6733	420	5	5	5	NUM
ejpam-6733	420	6	,	,	PUNCT
ejpam-6733	420	7	|b|	|b|	X
ejpam-6733	420	8	2	2	NUM
ejpam-6733	420	9	=	=	SYM
ejpam-6733	420	10	−	−	PROPN
ejpam-6733	420	11	1	1	NUM
ejpam-6733	420	12	25	25	NUM
ejpam-6733	420	13	<	<	X
ejpam-6733	420	14	0	0	NUM
ejpam-6733	420	15	,	,	PUNCT
ejpam-6733	420	16	rejected	reject	VERB
ejpam-6733	420	17	.	.	PUNCT
ejpam-6733	421	1	6	6	X
ejpam-6733	421	2	.	.	X
ejpam-6733	421	3	conclusion	conclusion	VERB
ejpam-6733	421	4	our	our	PRON
ejpam-6733	421	5	main	main	ADJ
ejpam-6733	421	6	purpose	purpose	NOUN
ejpam-6733	421	7	in	in	ADP
ejpam-6733	421	8	this	this	DET
ejpam-6733	421	9	work	work	NOUN
ejpam-6733	421	10	was	be	AUX
ejpam-6733	421	11	to	to	PART
ejpam-6733	421	12	find	find	VERB
ejpam-6733	421	13	faithful	faithful	ADJ
ejpam-6733	421	14	matrix	matrix	NOUN
ejpam-6733	421	15	representations	representation	NOUN
ejpam-6733	421	16	of	of	ADP
ejpam-6733	421	17	the	the	DET
ejpam-6733	421	18	twoparameter	twoparameter	NOUN
ejpam-6733	421	19	(	(	PUNCT
ejpam-6733	421	20	p	p	X
ejpam-6733	421	21	,	,	PUNCT
ejpam-6733	421	22	q)-deformed	q)-deformed	ADJ
ejpam-6733	421	23	lie	lie	NOUN
ejpam-6733	421	24	algebra	algebra	NOUN
ejpam-6733	421	25	lp	lp	NOUN
ejpam-6733	421	26	,	,	PUNCT
ejpam-6733	421	27	q	q	PUNCT
ejpam-6733	421	28	defined	define	VERB
ejpam-6733	421	29	in	in	ADP
ejpam-6733	421	30	(	(	PUNCT
ejpam-6733	421	31	4)-(6	4)-(6	NUM
ejpam-6733	421	32	)	)	PUNCT
ejpam-6733	421	33	with	with	ADP
ejpam-6733	421	34	p	p	NOUN
ejpam-6733	421	35	and	and	CCONJ
ejpam-6733	421	36	q	q	ADJ
ejpam-6733	421	37	being	be	AUX
ejpam-6733	421	38	nonzero	nonzero	ADJ
ejpam-6733	421	39	real	real	ADJ
ejpam-6733	421	40	numbers	number	NOUN
ejpam-6733	421	41	.	.	PUNCT
ejpam-6733	422	1	the	the	DET
ejpam-6733	422	2	derived	derive	VERB
ejpam-6733	422	3	representations	representation	NOUN
ejpam-6733	422	4	associated	associate	VERB
ejpam-6733	422	5	with	with	ADP
ejpam-6733	422	6	the	the	DET
ejpam-6733	422	7	operator	operator	NOUN
ejpam-6733	422	8	generators	generator	NOUN
ejpam-6733	422	9	k±,0	k±,0	PROPN
ejpam-6733	422	10	in	in	ADP
ejpam-6733	422	11	the	the	DET
ejpam-6733	422	12	hamiltonian	hamiltonian	ADJ
ejpam-6733	422	13	model	model	NOUN
ejpam-6733	422	14	(	(	PUNCT
ejpam-6733	422	15	3	3	X
ejpam-6733	422	16	)	)	PUNCT
ejpam-6733	422	17	can	can	AUX
ejpam-6733	422	18	be	be	AUX
ejpam-6733	422	19	utilized	utilize	VERB
ejpam-6733	422	20	to	to	PART
ejpam-6733	422	21	investigate	investigate	VERB
ejpam-6733	422	22	the	the	DET
ejpam-6733	422	23	quantum	quantum	ADJ
ejpam-6733	422	24	state	state	NOUN
ejpam-6733	422	25	evolution	evolution	NOUN
ejpam-6733	422	26	,	,	PUNCT
ejpam-6733	422	27	similar	similar	ADJ
ejpam-6733	422	28	to	to	ADP
ejpam-6733	422	29	our	our	PRON
ejpam-6733	422	30	earlier	early	ADJ
ejpam-6733	422	31	work	work	NOUN
ejpam-6733	422	32	in	in	ADP
ejpam-6733	422	33	the	the	DET
ejpam-6733	422	34	case	case	NOUN
ejpam-6733	422	35	of	of	ADP
ejpam-6733	422	36	ordinary	ordinary	ADJ
ejpam-6733	422	37	lie	lie	NOUN
ejpam-6733	422	38	bracket	bracket	NOUN
ejpam-6733	422	39	,	,	PUNCT
ejpam-6733	422	40	where	where	SCONJ
ejpam-6733	422	41	p	p	NOUN
ejpam-6733	422	42	=	=	X
ejpam-6733	422	43	q	q	NOUN
ejpam-6733	422	44	=	=	SYM
ejpam-6733	422	45	1	1	NUM
ejpam-6733	423	1	[	[	X
ejpam-6733	423	2	10	10	NUM
ejpam-6733	423	3	]	]	PUNCT
ejpam-6733	423	4	.	.	PUNCT
ejpam-6733	424	1	acknowledgements	acknowledgement	NOUN
ejpam-6733	424	2	the	the	DET
ejpam-6733	424	3	authors	author	NOUN
ejpam-6733	424	4	are	be	AUX
ejpam-6733	424	5	grateful	grateful	ADJ
ejpam-6733	424	6	to	to	ADP
ejpam-6733	424	7	kuwait	kuwait	PROPN
ejpam-6733	424	8	university	university	PROPN
ejpam-6733	424	9	.	.	PUNCT
ejpam-6733	425	1	references	reference	NOUN
ejpam-6733	425	2	[	[	X
ejpam-6733	425	3	1	1	NUM
ejpam-6733	425	4	]	]	SYM
ejpam-6733	425	5	v	v	ADP
ejpam-6733	425	6	p	p	PROPN
ejpam-6733	425	7	karassiov	karassiov	PROPN
ejpam-6733	425	8	.	.	PUNCT
ejpam-6733	426	1	new	new	ADJ
ejpam-6733	426	2	lie	lie	NOUN
ejpam-6733	426	3	-	-	PUNCT
ejpam-6733	426	4	algebraic	algebraic	ADJ
ejpam-6733	426	5	structures	structure	NOUN
ejpam-6733	426	6	in	in	ADP
ejpam-6733	426	7	nonlinear	nonlinear	ADJ
ejpam-6733	426	8	problems	problem	NOUN
ejpam-6733	426	9	of	of	ADP
ejpam-6733	426	10	quantum	quantum	NOUN
ejpam-6733	426	11	optics	optic	NOUN
ejpam-6733	426	12	and	and	CCONJ
ejpam-6733	426	13	laser	laser	NOUN
ejpam-6733	426	14	physics	physics	PROPN
ejpam-6733	426	15	.	.	PUNCT
ejpam-6733	427	1	journal	journal	PROPN
ejpam-6733	427	2	of	of	ADP
ejpam-6733	427	3	soviet	soviet	PROPN
ejpam-6733	427	4	laser	laser	NOUN
ejpam-6733	427	5	research	research	NOUN
ejpam-6733	427	6	,	,	PUNCT
ejpam-6733	427	7	13:188–195	13:188–195	NUM
ejpam-6733	427	8	,	,	PUNCT
ejpam-6733	427	9	1992	1992	NUM
ejpam-6733	427	10	.	.	PUNCT
ejpam-6733	428	1	l.	l.	PROPN
ejpam-6733	428	2	a	a	DET
ejpam-6733	428	3	-	-	PUNCT
ejpam-6733	428	4	m.	m.	NOUN
ejpam-6733	428	5	hanna	hanna	NOUN
ejpam-6733	428	6	,	,	PUNCT
ejpam-6733	428	7	s.	s.	PROPN
ejpam-6733	428	8	s.	s.	PROPN
ejpam-6733	428	9	hassan	hassan	PROPN
ejpam-6733	428	10	,	,	PUNCT
ejpam-6733	428	11	m.	m.	NOUN
ejpam-6733	428	12	almutairi	almutairi	PROPN
ejpam-6733	428	13	/	/	SYM
ejpam-6733	428	14	eur	eur	PROPN
ejpam-6733	428	15	.	.	PUNCT
ejpam-6733	429	1	j.	j.	PROPN
ejpam-6733	429	2	pure	pure	PROPN
ejpam-6733	429	3	appl	appl	PROPN
ejpam-6733	429	4	.	.	PROPN
ejpam-6733	429	5	math	math	PROPN
ejpam-6733	429	6	,	,	PUNCT
ejpam-6733	429	7	18	18	NUM
ejpam-6733	429	8	(	(	PUNCT
ejpam-6733	429	9	4	4	NUM
ejpam-6733	429	10	)	)	PUNCT
ejpam-6733	429	11	(	(	PUNCT
ejpam-6733	429	12	2025	2025	NUM
ejpam-6733	429	13	)	)	PUNCT
ejpam-6733	429	14	,	,	PUNCT
ejpam-6733	429	15	6733	6733	NUM
ejpam-6733	429	16	12	12	NUM
ejpam-6733	429	17	of	of	ADP
ejpam-6733	429	18	12	12	NUM
ejpam-6733	430	1	[	[	X
ejpam-6733	430	2	2	2	NUM
ejpam-6733	430	3	]	]	SYM
ejpam-6733	430	4	v	v	ADP
ejpam-6733	430	5	p	p	PROPN
ejpam-6733	430	6	karassiov	karassiov	PROPN
ejpam-6733	430	7	.	.	PUNCT
ejpam-6733	431	1	g	g	NOUN
ejpam-6733	431	2	-	-	PUNCT
ejpam-6733	431	3	invariant	invariant	ADJ
ejpam-6733	431	4	polynomial	polynomial	ADJ
ejpam-6733	431	5	extensions	extension	NOUN
ejpam-6733	431	6	of	of	ADP
ejpam-6733	431	7	lie	lie	NOUN
ejpam-6733	431	8	algebras	algebra	NOUN
ejpam-6733	431	9	in	in	ADP
ejpam-6733	431	10	quantum	quantum	PROPN
ejpam-6733	431	11	manybody	manybody	NOUN
ejpam-6733	431	12	physics	physics	PROPN
ejpam-6733	431	13	.	.	PUNCT
ejpam-6733	432	1	j.	j.	PROPN
ejpam-6733	432	2	phys	phys	PROPN
ejpam-6733	432	3	.	.	PUNCT
ejpam-6733	433	1	a	a	DET
ejpam-6733	433	2	:	:	PUNCT
ejpam-6733	433	3	math	math	NOUN
ejpam-6733	433	4	.	.	PUNCT
ejpam-6733	434	1	gen	gen	PROPN
ejpam-6733	434	2	.	.	PROPN
ejpam-6733	434	3	,	,	PUNCT
ejpam-6733	434	4	27:153–165	27:153–165	NUM
ejpam-6733	434	5	,	,	PUNCT
ejpam-6733	434	6	1994	1994	NUM
ejpam-6733	434	7	.	.	PUNCT
ejpam-6733	435	1	[	[	X
ejpam-6733	435	2	3	3	X
ejpam-6733	435	3	]	]	X
ejpam-6733	435	4	a	a	DET
ejpam-6733	435	5	algin	algin	NOUN
ejpam-6733	435	6	.	.	PUNCT
ejpam-6733	436	1	a	a	DET
ejpam-6733	436	2	comparative	comparative	ADJ
ejpam-6733	436	3	study	study	NOUN
ejpam-6733	436	4	on	on	ADP
ejpam-6733	436	5	q	q	ADJ
ejpam-6733	436	6	-	-	PUNCT
ejpam-6733	436	7	deformed	deform	VERB
ejpam-6733	436	8	fermion	fermion	NOUN
ejpam-6733	436	9	oscillators	oscillator	NOUN
ejpam-6733	436	10	.	.	PUNCT
ejpam-6733	437	1	int	int	NOUN
ejpam-6733	437	2	.	.	PUNCT
ejpam-6733	438	1	j.	j.	PROPN
ejpam-6733	438	2	theor	theor	PROPN
ejpam-6733	438	3	.	.	PUNCT
ejpam-6733	439	1	phys	phy	NOUN
ejpam-6733	439	2	.	.	PUNCT
ejpam-6733	439	3	,	,	PUNCT
ejpam-6733	439	4	50:1554–1568	50:1554–1568	NUM
ejpam-6733	439	5	,	,	PUNCT
ejpam-6733	439	6	2011	2011	NUM
ejpam-6733	439	7	.	.	PUNCT
ejpam-6733	440	1	[	[	X
ejpam-6733	440	2	4	4	X
ejpam-6733	440	3	]	]	X
ejpam-6733	440	4	w	w	PROPN
ejpam-6733	440	5	s	s	PROPN
ejpam-6733	440	6	chung	chung	NOUN
ejpam-6733	440	7	and	and	CCONJ
ejpam-6733	440	8	h	h	NOUN
ejpam-6733	440	9	hassanabadi	hassanabadi	NOUN
ejpam-6733	440	10	.	.	PUNCT
ejpam-6733	441	1	q	q	X
ejpam-6733	441	2	-	-	PUNCT
ejpam-6733	441	3	deformed	deform	VERB
ejpam-6733	441	4	quantum	quantum	ADJ
ejpam-6733	441	5	mechanics	mechanic	NOUN
ejpam-6733	441	6	based	base	VERB
ejpam-6733	441	7	on	on	ADP
ejpam-6733	441	8	the	the	DET
ejpam-6733	441	9	qaddition	qaddition	NOUN
ejpam-6733	441	10	.	.	PUNCT
ejpam-6733	442	1	advanced	advanced	ADJ
ejpam-6733	442	2	science	science	NOUN
ejpam-6733	442	3	news	news	NOUN
ejpam-6733	442	4	,	,	PUNCT
ejpam-6733	442	5	wiley	wiley	PROPN
ejpam-6733	442	6	-	-	PUNCT
ejpam-6733	442	7	vch	vch	PROPN
ejpam-6733	442	8	verlag	verlag	PROPN
ejpam-6733	442	9	gmbh	gmbh	PROPN
ejpam-6733	442	10	&	&	CCONJ
ejpam-6733	442	11	co.	co.	PROPN
ejpam-6733	442	12	kgaa	kgaa	PROPN
ejpam-6733	442	13	,	,	PUNCT
ejpam-6733	442	14	weinheim	weinheim	PROPN
ejpam-6733	442	15	,	,	PUNCT
ejpam-6733	442	16	fortschr	fortschr	NOUN
ejpam-6733	442	17	,	,	PUNCT
ejpam-6733	442	18	phys	phy	NOUN
ejpam-6733	442	19	.	.	PUNCT
ejpam-6733	442	20	,	,	PUNCT
ejpam-6733	442	21	67:1800111	67:1800111	PROPN
ejpam-6733	442	22	,	,	PUNCT
ejpam-6733	442	23	2019	2019	NUM
ejpam-6733	442	24	.	.	PUNCT
ejpam-6733	443	1	[	[	X
ejpam-6733	443	2	5	5	X
ejpam-6733	443	3	]	]	PUNCT
ejpam-6733	443	4	p	p	NOUN
ejpam-6733	443	5	n	n	X
ejpam-6733	443	6	swamy	swamy	NOUN
ejpam-6733	443	7	.	.	PUNCT
ejpam-6733	444	1	q	q	X
ejpam-6733	444	2	-	-	PUNCT
ejpam-6733	444	3	deformed	deform	VERB
ejpam-6733	444	4	fermions	fermion	NOUN
ejpam-6733	444	5	.	.	PUNCT
ejpam-6733	445	1	eur	eur	ADJ
ejpam-6733	445	2	.	.	PUNCT
ejpam-6733	445	3	phys	phy	NOUN
ejpam-6733	445	4	.	.	PUNCT
ejpam-6733	446	1	j.	j.	PROPN
ejpam-6733	446	2	b	b	PROPN
ejpam-6733	446	3	,	,	PUNCT
ejpam-6733	446	4	50:291–294	50:291–294	NUM
ejpam-6733	446	5	,	,	PUNCT
ejpam-6733	446	6	2006	2006	NUM
ejpam-6733	446	7	.	.	PUNCT
ejpam-6733	447	1	[	[	X
ejpam-6733	447	2	6	6	NUM
ejpam-6733	447	3	]	]	SYM
ejpam-6733	447	4	v	v	ADP
ejpam-6733	447	5	p.	p.	NOUN
ejpam-6733	447	6	karassiov	karassiov	PROPN
ejpam-6733	447	7	and	and	CCONJ
ejpam-6733	447	8	a.	a.	PROPN
ejpam-6733	447	9	b.	b.	PROPN
ejpam-6733	447	10	klimov	klimov	PROPN
ejpam-6733	447	11	.	.	PUNCT
ejpam-6733	448	1	an	an	DET
ejpam-6733	448	2	algebraic	algebraic	ADJ
ejpam-6733	448	3	approach	approach	NOUN
ejpam-6733	448	4	to	to	ADP
ejpam-6733	448	5	solving	solve	VERB
ejpam-6733	448	6	evolution	evolution	NOUN
ejpam-6733	448	7	problems	problem	NOUN
ejpam-6733	448	8	in	in	ADP
ejpam-6733	448	9	some	some	DET
ejpam-6733	448	10	nonlinear	nonlinear	ADJ
ejpam-6733	448	11	quantum	quantum	NOUN
ejpam-6733	448	12	models	model	NOUN
ejpam-6733	448	13	.	.	PUNCT
ejpam-6733	449	1	phys	phy	NOUN
ejpam-6733	449	2	.	.	PUNCT
ejpam-6733	450	1	lett	lett	PROPN
ejpam-6733	450	2	.	.	PUNCT
ejpam-6733	451	1	a	a	DET
ejpam-6733	451	2	,	,	PUNCT
ejpam-6733	451	3	189:43–51	189:43–51	NUM
ejpam-6733	451	4	,	,	PUNCT
ejpam-6733	451	5	1994	1994	NUM
ejpam-6733	451	6	.	.	PUNCT
ejpam-6733	452	1	[	[	X
ejpam-6733	452	2	7	7	X
ejpam-6733	452	3	]	]	X
ejpam-6733	452	4	a	a	DET
ejpam-6733	452	5	algin	algin	NOUN
ejpam-6733	452	6	and	and	CCONJ
ejpam-6733	452	7	w	w	PROPN
ejpam-6733	452	8	s	s	PROPN
ejpam-6733	452	9	chung	chung	PROPN
ejpam-6733	452	10	.	.	PUNCT
ejpam-6733	453	1	two	two	NUM
ejpam-6733	453	2	-	-	PUNCT
ejpam-6733	453	3	parameter	parameter	NOUN
ejpam-6733	453	4	deformed	deform	VERB
ejpam-6733	453	5	quantum	quantum	ADJ
ejpam-6733	453	6	mechanics	mechanic	NOUN
ejpam-6733	453	7	based	base	VERB
ejpam-6733	453	8	on	on	ADP
ejpam-6733	453	9	fibonacci	fibonacci	NOUN
ejpam-6733	453	10	calculus	calculus	PROPN
ejpam-6733	453	11	and	and	CCONJ
ejpam-6733	453	12	debye	debye	PROPN
ejpam-6733	453	13	crystal	crystal	NOUN
ejpam-6733	453	14	model	model	NOUN
ejpam-6733	453	15	of	of	ADP
ejpam-6733	453	16	two	two	NUM
ejpam-6733	453	17	-	-	PUNCT
ejpam-6733	453	18	parameter	parameter	NOUN
ejpam-6733	453	19	deformed	deform	VERB
ejpam-6733	453	20	quantum	quantum	ADJ
ejpam-6733	453	21	statistics	statistic	NOUN
ejpam-6733	453	22	.	.	PUNCT
ejpam-6733	454	1	the	the	DET
ejpam-6733	454	2	european	european	PROPN
ejpam-6733	454	3	physical	physical	PROPN
ejpam-6733	454	4	journal	journal	PROPN
ejpam-6733	454	5	plus	plus	CCONJ
ejpam-6733	454	6	,	,	PUNCT
ejpam-6733	454	7	eue	eue	NOUN
ejpam-6733	454	8	.	.	PUNCT
ejpam-6733	455	1	phys	phy	NOUN
ejpam-6733	455	2	.	.	PUNCT
ejpam-6733	456	1	j.	j.	PROPN
ejpam-6733	456	2	plus	plus	PROPN
ejpam-6733	456	3	,	,	PUNCT
ejpam-6733	456	4	139:139–198	139:139–198	NUM
ejpam-6733	456	5	,	,	PUNCT
ejpam-6733	456	6	2024	2024	NUM
ejpam-6733	456	7	.	.	PUNCT
ejpam-6733	457	1	[	[	X
ejpam-6733	457	2	8	8	NUM
ejpam-6733	457	3	]	]	X
ejpam-6733	457	4	e	e	X
ejpam-6733	457	5	yakaboylu	yakaboylu	PROPN
ejpam-6733	457	6	,	,	PUNCT
ejpam-6733	457	7	m	m	NOUN
ejpam-6733	457	8	shkolnikov	shkolnikov	NOUN
ejpam-6733	457	9	,	,	PUNCT
ejpam-6733	457	10	and	and	CCONJ
ejpam-6733	457	11	m	m	PROPN
ejpam-6733	457	12	lemeshko	lemeshko	ADJ
ejpam-6733	457	13	.	.	PUNCT
ejpam-6733	458	1	quantum	quantum	ADJ
ejpam-6733	458	2	groups	group	NOUN
ejpam-6733	458	3	as	as	ADP
ejpam-6733	458	4	hidden	hidden	ADJ
ejpam-6733	458	5	symmetries	symmetry	NOUN
ejpam-6733	458	6	of	of	ADP
ejpam-6733	458	7	quantum	quantum	ADJ
ejpam-6733	458	8	impurities	impurity	NOUN
ejpam-6733	458	9	.	.	PUNCT
ejpam-6733	459	1	phys	phy	NOUN
ejpam-6733	459	2	.	.	PUNCT
ejpam-6733	460	1	rev	rev	PROPN
ejpam-6733	460	2	.	.	PROPN
ejpam-6733	460	3	lett	lett	PROPN
ejpam-6733	460	4	.	.	PROPN
ejpam-6733	460	5	,	,	PUNCT
ejpam-6733	460	6	121:255302	121:255302	PROPN
ejpam-6733	460	7	,	,	PUNCT
ejpam-6733	460	8	2018	2018	NUM
ejpam-6733	460	9	.	.	PUNCT
ejpam-6733	461	1	[	[	X
ejpam-6733	461	2	9	9	NUM
ejpam-6733	461	3	]	]	X
ejpam-6733	461	4	a	a	DET
ejpam-6733	461	5	a	a	DET
ejpam-6733	461	6	marinho	marinho	NOUN
ejpam-6733	461	7	,	,	PUNCT
ejpam-6733	461	8	f	f	PROPN
ejpam-6733	461	9	a	a	DET
ejpam-6733	461	10	brito	brito	PROPN
ejpam-6733	461	11	,	,	PUNCT
ejpam-6733	461	12	and	and	CCONJ
ejpam-6733	461	13	c	c	PROPN
ejpam-6733	461	14	cheaman	cheaman	NOUN
ejpam-6733	461	15	.	.	PUNCT
ejpam-6733	462	1	thermal	thermal	ADJ
ejpam-6733	462	2	and	and	CCONJ
ejpam-6733	462	3	electrical	electrical	ADJ
ejpam-6733	462	4	properties	property	NOUN
ejpam-6733	462	5	of	of	ADP
ejpam-6733	462	6	a	a	DET
ejpam-6733	462	7	solid	solid	ADJ
ejpam-6733	462	8	through	through	ADP
ejpam-6733	462	9	fibonacci	fibonacci	NOUN
ejpam-6733	462	10	oscillators	oscillator	NOUN
ejpam-6733	462	11	.	.	PUNCT
ejpam-6733	463	1	physica	physica	PROPN
ejpam-6733	463	2	a	a	PRON
ejpam-6733	463	3	,	,	PUNCT
ejpam-6733	463	4	443:324–332	443:324–332	NUM
ejpam-6733	463	5	,	,	PUNCT
ejpam-6733	463	6	2016	2016	NUM
ejpam-6733	463	7	.	.	PUNCT
ejpam-6733	464	1	[	[	X
ejpam-6733	464	2	10	10	NUM
ejpam-6733	464	3	]	]	X
ejpam-6733	464	4	l	l	NOUN
ejpam-6733	464	5	hanna	hanna	NOUN
ejpam-6733	464	6	,	,	PUNCT
ejpam-6733	464	7	r	r	NOUN
ejpam-6733	464	8	alharbey	alharbey	NOUN
ejpam-6733	464	9	,	,	PUNCT
ejpam-6733	464	10	s	s	NOUN
ejpam-6733	464	11	abdalla	abdalla	PROPN
ejpam-6733	464	12	,	,	PUNCT
ejpam-6733	464	13	and	and	CCONJ
ejpam-6733	464	14	s	s	VERB
ejpam-6733	464	15	hassan	hassan	PROPN
ejpam-6733	464	16	.	.	PUNCT
ejpam-6733	465	1	algebraic	algebraic	ADJ
ejpam-6733	465	2	method	method	NOUN
ejpam-6733	465	3	of	of	ADP
ejpam-6733	465	4	solution	solution	NOUN
ejpam-6733	465	5	of	of	ADP
ejpam-6733	465	6	schrödinger	schrödinger	NOUN
ejpam-6733	465	7	’s	’s	PART
ejpam-6733	465	8	equation	equation	NOUN
ejpam-6733	465	9	of	of	ADP
ejpam-6733	465	10	a	a	DET
ejpam-6733	465	11	quantum	quantum	ADJ
ejpam-6733	465	12	model	model	NOUN
ejpam-6733	465	13	.	.	PUNCT
ejpam-6733	466	1	wseas	wseas	PROPN
ejpam-6733	466	2	transactions	transaction	NOUN
ejpam-6733	466	3	on	on	ADP
ejpam-6733	466	4	mathematics	mathematic	NOUN
ejpam-6733	466	5	,	,	PUNCT
ejpam-6733	466	6	19:421–429	19:421–429	NUM
ejpam-6733	466	7	,	,	PUNCT
ejpam-6733	466	8	2020	2020	NUM
ejpam-6733	466	9	.	.	PUNCT
ejpam-6733	467	1	[	[	X
ejpam-6733	467	2	11	11	NUM
ejpam-6733	467	3	]	]	X
ejpam-6733	467	4	o	o	X
ejpam-6733	467	5	elchinger	elchinger	NOUN
ejpam-6733	467	6	,	,	PUNCT
ejpam-6733	467	7	k	k	PROPN
ejpam-6733	467	8	lundengard	lundengard	PROPN
ejpam-6733	467	9	,	,	PUNCT
ejpam-6733	467	10	a	a	DET
ejpam-6733	467	11	makhlouf	makhlouf	NOUN
ejpam-6733	467	12	,	,	PUNCT
ejpam-6733	467	13	and	and	CCONJ
ejpam-6733	467	14	s	s	VERB
ejpam-6733	467	15	silvestrov	silvestrov	NOUN
ejpam-6733	467	16	.	.	PUNCT
ejpam-6733	467	17	brackets	bracket	NOUN
ejpam-6733	467	18	with	with	ADP
ejpam-6733	467	19	(	(	PUNCT
ejpam-6733	467	20	τ	τ	PROPN
ejpam-6733	467	21	,	,	PUNCT
ejpam-6733	467	22	σ)derivations	σ)derivations	PROPN
ejpam-6733	467	23	and	and	CCONJ
ejpam-6733	467	24	(	(	PUNCT
ejpam-6733	467	25	p	p	NOUN
ejpam-6733	467	26	,	,	PUNCT
ejpam-6733	467	27	q)-deformations	q)-deformation	NOUN
ejpam-6733	467	28	of	of	ADP
ejpam-6733	467	29	witt	witt	PROPN
ejpam-6733	467	30	and	and	CCONJ
ejpam-6733	467	31	virasoro	virasoro	VERB
ejpam-6733	467	32	algebras[j	algebras[j	PROPN
ejpam-6733	467	33	]	]	PUNCT
ejpam-6733	467	34	.	.	PUNCT
ejpam-6733	468	1	forum	forum	PROPN
ejpam-6733	468	2	mathematicum	mathematicum	PROPN
ejpam-6733	468	3	,	,	PUNCT
ejpam-6733	468	4	28:657–673	28:657–673	PROPN
ejpam-6733	468	5	,	,	PUNCT
ejpam-6733	468	6	2016	2016	NUM
ejpam-6733	468	7	.	.	PUNCT
ejpam-6733	469	1	[	[	X
ejpam-6733	469	2	12	12	NUM
ejpam-6733	469	3	]	]	X
ejpam-6733	469	4	w	w	PROPN
ejpam-6733	469	5	zhou	zhou	PROPN
ejpam-6733	469	6	and	and	CCONJ
ejpam-6733	469	7	y	y	PROPN
ejpam-6733	469	8	cheng	cheng	PROPN
ejpam-6733	469	9	.	.	PUNCT
ejpam-6733	470	1	two	two	NUM
ejpam-6733	470	2	-	-	PUNCT
ejpam-6733	470	3	parameter	parameter	NOUN
ejpam-6733	470	4	quantum	quantum	NOUN
ejpam-6733	470	5	group	group	NOUN
ejpam-6733	470	6	coming	come	VERB
ejpam-6733	470	7	from	from	ADP
ejpam-6733	470	8	two	two	NUM
ejpam-6733	470	9	-	-	PUNCT
ejpam-6733	470	10	parameter	parameter	NOUN
ejpam-6733	470	11	deformed	deform	VERB
ejpam-6733	470	12	virasoro	virasoro	NOUN
ejpam-6733	470	13	algebra	algebra	NOUN
ejpam-6733	470	14	of	of	ADP
ejpam-6733	470	15	hom	hom	NOUN
ejpam-6733	470	16	-	-	PUNCT
ejpam-6733	470	17	type	type	NOUN
ejpam-6733	470	18	.	.	PUNCT
ejpam-6733	471	1	journal	journal	PROPN
ejpam-6733	471	2	of	of	ADP
ejpam-6733	471	3	mathematical	mathematical	ADJ
ejpam-6733	471	4	study	study	NOUN
ejpam-6733	471	5	,	,	PUNCT
ejpam-6733	471	6	57:425–436	57:425–436	PROPN
ejpam-6733	471	7	,	,	PUNCT
ejpam-6733	471	8	2024	2024	NUM
ejpam-6733	471	9	.	.	PUNCT
ejpam-6733	472	1	[	[	X
ejpam-6733	472	2	13	13	NUM
ejpam-6733	472	3	]	]	SYM
ejpam-6733	472	4	a	a	DET
ejpam-6733	472	5	hegazi	hegazi	NOUN
ejpam-6733	472	6	and	and	CCONJ
ejpam-6733	472	7	m	m	PROPN
ejpam-6733	472	8	mansour	mansour	PROPN
ejpam-6733	472	9	.	.	PROPN
ejpam-6733	472	10	two	two	NUM
ejpam-6733	472	11	-	-	PUNCT
ejpam-6733	472	12	parameter	parameter	NOUN
ejpam-6733	472	13	quantum	quantum	ADJ
ejpam-6733	472	14	deformation	deformation	NOUN
ejpam-6733	472	15	of	of	ADP
ejpam-6733	472	16	lie	lie	NOUN
ejpam-6733	472	17	superalgebras	superalgebras	PROPN
ejpam-6733	472	18	.	.	PUNCT
ejpam-6733	473	1	chaos	chaos	NOUN
ejpam-6733	473	2	.	.	PUNCT
ejpam-6733	474	1	solitons	soliton	NOUN
ejpam-6733	474	2	and	and	CCONJ
ejpam-6733	474	3	fractals	fractal	NOUN
ejpam-6733	474	4	,	,	PUNCT
ejpam-6733	474	5	12:445–452	12:445–452	NOUN
ejpam-6733	474	6	,	,	PUNCT
ejpam-6733	474	7	2001	2001	NUM
ejpam-6733	474	8	.	.	PUNCT
ejpam-6733	475	1	[	[	X
ejpam-6733	475	2	14	14	NUM
ejpam-6733	475	3	]	]	X
ejpam-6733	475	4	l	l	NOUN
ejpam-6733	475	5	a	a	PROPN
ejpam-6733	475	6	-	-	PUNCT
ejpam-6733	475	7	m	m	NOUN
ejpam-6733	475	8	hanna	hanna	NOUN
ejpam-6733	475	9	.	.	PUNCT
ejpam-6733	476	1	on	on	ADP
ejpam-6733	476	2	faithful	faithful	ADJ
ejpam-6733	476	3	matrix	matrix	NOUN
ejpam-6733	476	4	representations	representation	NOUN
ejpam-6733	476	5	of	of	ADP
ejpam-6733	476	6	q	q	NOUN
ejpam-6733	476	7	-	-	PUNCT
ejpam-6733	476	8	deformed	deform	VERB
ejpam-6733	476	9	lie	lie	NOUN
ejpam-6733	476	10	algebra	algebra	NOUN
ejpam-6733	476	11	for	for	ADP
ejpam-6733	476	12	coupled	couple	VERB
ejpam-6733	476	13	quantized	quantize	VERB
ejpam-6733	476	14	oscillators	oscillator	NOUN
ejpam-6733	476	15	.	.	PUNCT
ejpam-6733	477	1	international	international	ADJ
ejpam-6733	477	2	journal	journal	NOUN
ejpam-6733	477	3	of	of	ADP
ejpam-6733	477	4	applied	apply	VERB
ejpam-6733	477	5	mathematics	mathematic	NOUN
ejpam-6733	477	6	,	,	PUNCT
ejpam-6733	477	7	ijam	ijam	NOUN
ejpam-6733	477	8	,	,	PUNCT
ejpam-6733	477	9	33(6):1083–1098	33(6):1083–1098	NUM
ejpam-6733	477	10	,	,	PUNCT
ejpam-6733	477	11	2020	2020	NUM
ejpam-6733	477	12	.	.	PUNCT
ejpam-6733	478	1	[	[	X
ejpam-6733	478	2	15	15	NUM
ejpam-6733	478	3	]	]	X
ejpam-6733	478	4	a	a	DET
ejpam-6733	478	5	b	b	PROPN
ejpam-6733	478	6	klimov	klimov	PROPN
ejpam-6733	478	7	and	and	CCONJ
ejpam-6733	478	8	j	j	PROPN
ejpam-6733	478	9	l	l	PROPN
ejpam-6733	478	10	romero	romero	PROPN
ejpam-6733	478	11	.	.	PUNCT
ejpam-6733	479	1	an	an	DET
ejpam-6733	479	2	algebraic	algebraic	ADJ
ejpam-6733	479	3	solution	solution	NOUN
ejpam-6733	479	4	of	of	ADP
ejpam-6733	479	5	lindblad	lindblad	ADJ
ejpam-6733	479	6	-	-	PUNCT
ejpam-6733	479	7	type	type	NOUN
ejpam-6733	479	8	master	master	NOUN
ejpam-6733	479	9	equation	equation	NOUN
ejpam-6733	479	10	.	.	PUNCT
ejpam-6733	480	1	j.	j.	PROPN
ejpam-6733	480	2	opt	opt	PROPN
ejpam-6733	480	3	.	.	PUNCT
ejpam-6733	481	1	b	b	X
ejpam-6733	481	2	:	:	PUNCT
ejpam-6733	481	3	quantum	quantum	ADJ
ejpam-6733	481	4	semiclass	semiclass	NOUN
ejpam-6733	481	5	.	.	PUNCT
ejpam-6733	482	1	opt	opt	PROPN
ejpam-6733	482	2	.	.	PUNCT
ejpam-6733	482	3	,	,	PUNCT
ejpam-6733	482	4	5	5	NUM
ejpam-6733	482	5	:	:	PUNCT
ejpam-6733	482	6	s316	s316	PROPN
ejpam-6733	482	7	–	–	PUNCT
ejpam-6733	482	8	s321	s321	PROPN
ejpam-6733	482	9	,	,	PUNCT
ejpam-6733	482	10	2003	2003	NUM
ejpam-6733	482	11	.	.	PUNCT
ejpam-6733	483	1	[	[	X
ejpam-6733	483	2	16	16	NUM
ejpam-6733	483	3	]	]	X
ejpam-6733	483	4	r	r	NOUN
ejpam-6733	483	5	j	j	PROPN
ejpam-6733	483	6	c	c	PROPN
ejpam-6733	483	7	spreeuw	spreeuw	PROPN
ejpam-6733	483	8	and	and	CCONJ
ejpam-6733	483	9	j	j	PROPN
ejpam-6733	483	10	p	p	PROPN
ejpam-6733	483	11	woerdman	woerdman	NOUN
ejpam-6733	483	12	.	.	PUNCT
ejpam-6733	484	1	v	v	ADP
ejpam-6733	484	2	optical	optical	ADJ
ejpam-6733	484	3	atoms	atom	NOUN
ejpam-6733	484	4	.	.	PUNCT
ejpam-6733	485	1	progress	progress	NOUN
ejpam-6733	485	2	in	in	ADP
ejpam-6733	485	3	optics	optic	NOUN
ejpam-6733	485	4	,	,	PUNCT
ejpam-6733	485	5	31:263–319	31:263–319	PROPN
ejpam-6733	485	6	,	,	PUNCT
ejpam-6733	485	7	1993	1993	NUM
ejpam-6733	485	8	.	.	PUNCT
ejpam-6733	486	1	[	[	X
ejpam-6733	486	2	17	17	NUM
ejpam-6733	486	3	]	]	X
ejpam-6733	486	4	l	l	NOUN
ejpam-6733	486	5	a	a	PROPN
ejpam-6733	486	6	-	-	PUNCT
ejpam-6733	486	7	m	m	NOUN
ejpam-6733	486	8	hanna	hanna	NOUN
ejpam-6733	486	9	.	.	PUNCT
ejpam-6733	487	1	on	on	ADP
ejpam-6733	487	2	matrix	matrix	NOUN
ejpam-6733	487	3	representations	representation	NOUN
ejpam-6733	487	4	of	of	ADP
ejpam-6733	487	5	deformed	deform	VERB
ejpam-6733	487	6	lie	lie	NOUN
ejpam-6733	487	7	algebras	algebra	NOUN
ejpam-6733	487	8	for	for	ADP
ejpam-6733	487	9	quantized	quantize	VERB
ejpam-6733	487	10	hamiltonians	hamiltonian	NOUN
ejpam-6733	487	11	.	.	PUNCT
ejpam-6733	488	1	linear	linear	ADJ
ejpam-6733	488	2	algebra	algebra	PROPN
ejpam-6733	488	3	appl	appl	NOUN
ejpam-6733	488	4	.	.	PROPN
ejpam-6733	488	5	,	,	PUNCT
ejpam-6733	488	6	434:507–513	434:507–513	PROPN
ejpam-6733	488	7	,	,	PUNCT
ejpam-6733	488	8	2011	2011	NUM
ejpam-6733	488	9	.	.	PUNCT