id	sid	tid	token	lemma	pos
ejpam-1889	1	1	european	european	PROPN
ejpam-1889	1	2	journal	journal	PROPN
ejpam-1889	1	3	of	of	ADP
ejpam-1889	1	4	pure	pure	ADJ
ejpam-1889	1	5	and	and	CCONJ
ejpam-1889	1	6	applied	apply	VERB
ejpam-1889	1	7	mathematics	mathematic	NOUN
ejpam-1889	1	8	vol	vol	NOUN
ejpam-1889	1	9	.	.	PUNCT
ejpam-1889	2	1	7	7	NUM
ejpam-1889	2	2	,	,	PUNCT
ejpam-1889	2	3	no	no	INTJ
ejpam-1889	2	4	.	.	NOUN
ejpam-1889	2	5	2	2	NUM
ejpam-1889	2	6	,	,	PUNCT
ejpam-1889	2	7	2014	2014	NUM
ejpam-1889	2	8	,	,	PUNCT
ejpam-1889	2	9	140	140	NUM
ejpam-1889	2	10	-	-	SYM
ejpam-1889	2	11	155	155	NUM
ejpam-1889	2	12	issn	issn	PROPN
ejpam-1889	2	13	1307	1307	NUM
ejpam-1889	2	14	-	-	SYM
ejpam-1889	2	15	5543	5543	NUM
ejpam-1889	2	16	–	–	PUNCT
ejpam-1889	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1889	2	18	affine	affine	VERB
ejpam-1889	2	19	subspaces	subspace	NOUN
ejpam-1889	2	20	of	of	ADP
ejpam-1889	2	21	the	the	DET
ejpam-1889	2	22	lie	lie	NOUN
ejpam-1889	2	23	algebra	algebra	PROPN
ejpam-1889	2	24	se(1	se(1	PROPN
ejpam-1889	2	25	,	,	PUNCT
ejpam-1889	2	26	1	1	NUM
ejpam-1889	2	27	)	)	PUNCT
ejpam-1889	2	28	dennis	dennis	PROPN
ejpam-1889	2	29	i.	i.	PROPN
ejpam-1889	2	30	barrett	barrett	PROPN
ejpam-1889	2	31	,	,	PUNCT
ejpam-1889	2	32	rory	rory	PROPN
ejpam-1889	2	33	biggs	biggs	PROPN
ejpam-1889	2	34	,	,	PUNCT
ejpam-1889	2	35	claudiu	claudiu	ADJ
ejpam-1889	2	36	c.	c.	PROPN
ejpam-1889	2	37	remsing∗	remsing∗	NOUN
ejpam-1889	2	38	department	department	PROPN
ejpam-1889	2	39	of	of	ADP
ejpam-1889	2	40	mathematics	mathematics	PROPN
ejpam-1889	2	41	(	(	PUNCT
ejpam-1889	2	42	pure	pure	ADJ
ejpam-1889	2	43	and	and	CCONJ
ejpam-1889	2	44	applied	apply	VERB
ejpam-1889	2	45	)	)	PUNCT
ejpam-1889	2	46	,	,	PUNCT
ejpam-1889	2	47	rhodes	rhode	VERB
ejpam-1889	2	48	university	university	PROPN
ejpam-1889	2	49	,	,	PUNCT
ejpam-1889	2	50	grahamstown	grahamstown	ADJ
ejpam-1889	2	51	6140	6140	NUM
ejpam-1889	2	52	,	,	PUNCT
ejpam-1889	2	53	south	south	PROPN
ejpam-1889	2	54	africa	africa	PROPN
ejpam-1889	2	55	abstract	abstract	PROPN
ejpam-1889	2	56	.	.	PUNCT
ejpam-1889	3	1	we	we	PRON
ejpam-1889	3	2	classify	classify	VERB
ejpam-1889	3	3	the	the	DET
ejpam-1889	3	4	full	full	ADJ
ejpam-1889	3	5	-	-	PUNCT
ejpam-1889	3	6	rank	rank	NOUN
ejpam-1889	3	7	affine	affine	NOUN
ejpam-1889	3	8	subspaces	subspace	NOUN
ejpam-1889	3	9	(	(	PUNCT
ejpam-1889	3	10	resp	resp	NOUN
ejpam-1889	3	11	.	.	PUNCT
ejpam-1889	4	1	parametrized	parametrized	ADJ
ejpam-1889	4	2	affine	affine	NOUN
ejpam-1889	4	3	subspaces	subspace	NOUN
ejpam-1889	4	4	)	)	PUNCT
ejpam-1889	4	5	of	of	ADP
ejpam-1889	4	6	the	the	DET
ejpam-1889	4	7	semieuclidean	semieuclidean	ADJ
ejpam-1889	4	8	lie	lie	NOUN
ejpam-1889	4	9	algebra	algebra	PROPN
ejpam-1889	4	10	se(1	se(1	PROPN
ejpam-1889	4	11	,	,	PUNCT
ejpam-1889	4	12	1	1	NUM
ejpam-1889	4	13	)	)	PUNCT
ejpam-1889	4	14	.	.	PUNCT
ejpam-1889	5	1	the	the	DET
ejpam-1889	5	2	equivalence	equivalence	NOUN
ejpam-1889	5	3	relations	relation	NOUN
ejpam-1889	5	4	under	under	ADP
ejpam-1889	5	5	consideration	consideration	NOUN
ejpam-1889	5	6	are	be	AUX
ejpam-1889	5	7	motivated	motivate	VERB
ejpam-1889	5	8	by	by	ADP
ejpam-1889	5	9	the	the	DET
ejpam-1889	5	10	study	study	NOUN
ejpam-1889	5	11	of	of	ADP
ejpam-1889	5	12	invariant	invariant	ADJ
ejpam-1889	5	13	control	control	NOUN
ejpam-1889	5	14	affine	affine	PROPN
ejpam-1889	5	15	systems	system	NOUN
ejpam-1889	5	16	.	.	PUNCT
ejpam-1889	6	1	exhaustive	exhaustive	ADJ
ejpam-1889	6	2	lists	list	NOUN
ejpam-1889	6	3	of	of	ADP
ejpam-1889	6	4	equivalence	equivalence	NOUN
ejpam-1889	6	5	representatives	representative	NOUN
ejpam-1889	6	6	are	be	AUX
ejpam-1889	6	7	obtained	obtain	VERB
ejpam-1889	6	8	,	,	PUNCT
ejpam-1889	6	9	along	along	ADV
ejpam-1889	6	10	with	with	ADP
ejpam-1889	6	11	classifying	classify	VERB
ejpam-1889	6	12	conditions	condition	NOUN
ejpam-1889	6	13	.	.	PUNCT
ejpam-1889	7	1	2010	2010	NUM
ejpam-1889	7	2	mathematics	mathematic	NOUN
ejpam-1889	7	3	subject	subject	NOUN
ejpam-1889	7	4	classifications	classification	NOUN
ejpam-1889	7	5	:	:	PUNCT
ejpam-1889	7	6	22e60	22e60	NUM
ejpam-1889	7	7	,	,	PUNCT
ejpam-1889	7	8	93b27	93b27	NUM
ejpam-1889	7	9	key	key	ADJ
ejpam-1889	7	10	words	word	NOUN
ejpam-1889	7	11	and	and	CCONJ
ejpam-1889	7	12	phrases	phrase	NOUN
ejpam-1889	7	13	:	:	PUNCT
ejpam-1889	7	14	lie	lie	NOUN
ejpam-1889	7	15	algebra	algebra	NOUN
ejpam-1889	7	16	,	,	PUNCT
ejpam-1889	7	17	affine	affine	NOUN
ejpam-1889	7	18	subspace	subspace	NOUN
ejpam-1889	7	19	,	,	PUNCT
ejpam-1889	7	20	equivalence	equivalence	NOUN
ejpam-1889	7	21	1	1	NUM
ejpam-1889	7	22	.	.	PUNCT
ejpam-1889	7	23	introduction	introduction	NOUN
ejpam-1889	7	24	a	a	DET
ejpam-1889	7	25	left	left	ADJ
ejpam-1889	7	26	-	-	PUNCT
ejpam-1889	7	27	invariant	invariant	ADJ
ejpam-1889	7	28	control	control	NOUN
ejpam-1889	7	29	affine	affine	NOUN
ejpam-1889	7	30	system	system	NOUN
ejpam-1889	7	31	,	,	PUNCT
ejpam-1889	7	32	evolving	evolve	VERB
ejpam-1889	7	33	on	on	ADP
ejpam-1889	7	34	a	a	DET
ejpam-1889	7	35	(	(	PUNCT
ejpam-1889	7	36	real	real	ADJ
ejpam-1889	7	37	,	,	PUNCT
ejpam-1889	7	38	finite	finite	ADJ
ejpam-1889	7	39	-	-	ADJ
ejpam-1889	7	40	dimensional	dimensional	ADJ
ejpam-1889	7	41	)	)	PUNCT
ejpam-1889	7	42	lie	lie	NOUN
ejpam-1889	7	43	group	group	NOUN
ejpam-1889	7	44	,	,	PUNCT
ejpam-1889	7	45	consists	consist	VERB
ejpam-1889	7	46	of	of	ADP
ejpam-1889	7	47	a	a	DET
ejpam-1889	7	48	family	family	NOUN
ejpam-1889	7	49	of	of	ADP
ejpam-1889	7	50	left	left	ADJ
ejpam-1889	7	51	-	-	PUNCT
ejpam-1889	7	52	invariant	invariant	ADJ
ejpam-1889	7	53	vector	vector	NOUN
ejpam-1889	7	54	fields	field	NOUN
ejpam-1889	7	55	and	and	CCONJ
ejpam-1889	7	56	a	a	DET
ejpam-1889	7	57	class	class	NOUN
ejpam-1889	7	58	of	of	ADP
ejpam-1889	7	59	“	"	PUNCT
ejpam-1889	7	60	admissible	admissible	ADJ
ejpam-1889	7	61	controls	control	NOUN
ejpam-1889	7	62	”	"	PUNCT
ejpam-1889	7	63	.	.	PUNCT
ejpam-1889	8	1	the	the	DET
ejpam-1889	8	2	family	family	NOUN
ejpam-1889	8	3	of	of	ADP
ejpam-1889	8	4	vector	vector	NOUN
ejpam-1889	8	5	fields	field	NOUN
ejpam-1889	8	6	is	be	AUX
ejpam-1889	8	7	affinely	affinely	ADV
ejpam-1889	8	8	parametrized	parametrize	VERB
ejpam-1889	8	9	by	by	ADP
ejpam-1889	8	10	the	the	DET
ejpam-1889	8	11	control	control	NOUN
ejpam-1889	8	12	values	value	NOUN
ejpam-1889	8	13	.	.	PUNCT
ejpam-1889	9	1	a	a	DET
ejpam-1889	9	2	(	(	PUNCT
ejpam-1889	9	3	typical	typical	ADJ
ejpam-1889	9	4	)	)	PUNCT
ejpam-1889	9	5	control	control	NOUN
ejpam-1889	9	6	is	be	AUX
ejpam-1889	9	7	a	a	DET
ejpam-1889	9	8	piecewise	piecewise	NOUN
ejpam-1889	9	9	continuous	continuous	ADJ
ejpam-1889	9	10	curve	curve	NOUN
ejpam-1889	9	11	u	u	NOUN
ejpam-1889	9	12	(	(	PUNCT
ejpam-1889	9	13	·	·	PUNCT
ejpam-1889	9	14	)	)	PUNCT
ejpam-1889	9	15	in	in	ADP
ejpam-1889	9	16	some	some	DET
ejpam-1889	9	17	control	control	NOUN
ejpam-1889	9	18	set	set	VERB
ejpam-1889	9	19	r	r	NOUN
ejpam-1889	9	20	`	`	PUNCT
ejpam-1889	9	21	.	.	PUNCT
ejpam-1889	10	1	such	such	DET
ejpam-1889	10	2	a	a	DET
ejpam-1889	10	3	control	control	NOUN
ejpam-1889	10	4	system	system	NOUN
ejpam-1889	10	5	on	on	ADP
ejpam-1889	10	6	a	a	DET
ejpam-1889	10	7	(	(	PUNCT
ejpam-1889	10	8	matrix	matrix	NOUN
ejpam-1889	10	9	)	)	PUNCT
ejpam-1889	10	10	lie	lie	NOUN
ejpam-1889	10	11	group	group	NOUN
ejpam-1889	10	12	g	g	PROPN
ejpam-1889	10	13	is	be	AUX
ejpam-1889	10	14	written	write	VERB
ejpam-1889	10	15	,	,	PUNCT
ejpam-1889	10	16	in	in	ADP
ejpam-1889	10	17	classical	classical	ADJ
ejpam-1889	10	18	notation	notation	NOUN
ejpam-1889	10	19	,	,	PUNCT
ejpam-1889	10	20	as	as	ADP
ejpam-1889	10	21	(	(	PUNCT
ejpam-1889	10	22	cf	cf	NOUN
ejpam-1889	10	23	.	.	PUNCT
ejpam-1889	11	1	[	[	X
ejpam-1889	11	2	11	11	NUM
ejpam-1889	11	3	,	,	PUNCT
ejpam-1889	11	4	16	16	NUM
ejpam-1889	11	5	]	]	PUNCT
ejpam-1889	11	6	)	)	PUNCT
ejpam-1889	11	7	ġ	ġ	NOUN
ejpam-1889	11	8	=	=	PUNCT
ejpam-1889	11	9	g(a+	g(a+	NOUN
ejpam-1889	12	1	u1b1	u1b1	X
ejpam-1889	13	1	+	+	CCONJ
ejpam-1889	13	2	u2b2	u2b2	ADJ
ejpam-1889	13	3	+	+	X
ejpam-1889	13	4	·	·	PUNCT
ejpam-1889	13	5	·	·	PUNCT
ejpam-1889	13	6	·	·	PUNCT
ejpam-1889	13	7	+	+	NUM
ejpam-1889	13	8	u`b	u`b	PROPN
ejpam-1889	13	9	`	`	PUNCT
ejpam-1889	13	10	)	)	PUNCT
ejpam-1889	13	11	,	,	PUNCT
ejpam-1889	13	12	g	g	PROPN
ejpam-1889	13	13	∈	∈	PROPN
ejpam-1889	13	14	g	g	PROPN
ejpam-1889	13	15	,	,	PUNCT
ejpam-1889	13	16	u	u	NOUN
ejpam-1889	13	17	∈	∈	PROPN
ejpam-1889	13	18	r	r	NOUN
ejpam-1889	13	19	`	`	PUNCT
ejpam-1889	13	20	.	.	PUNCT
ejpam-1889	14	1	(	(	PUNCT
ejpam-1889	14	2	1	1	X
ejpam-1889	14	3	)	)	PUNCT
ejpam-1889	14	4	here	here	ADV
ejpam-1889	14	5	a	a	PRON
ejpam-1889	14	6	,	,	PUNCT
ejpam-1889	14	7	b1	b1	NOUN
ejpam-1889	14	8	,	,	PUNCT
ejpam-1889	14	9	.	.	PUNCT
ejpam-1889	14	10	.	.	PUNCT
ejpam-1889	15	1	.	.	PUNCT
ejpam-1889	16	1	,	,	PUNCT
ejpam-1889	16	2	b	b	X
ejpam-1889	16	3	`	`	PUNCT
ejpam-1889	16	4	are	be	AUX
ejpam-1889	16	5	elements	element	NOUN
ejpam-1889	16	6	of	of	ADP
ejpam-1889	16	7	the	the	DET
ejpam-1889	16	8	lie	lie	NOUN
ejpam-1889	16	9	algebra	algebra	NOUN
ejpam-1889	16	10	g.	g.	VERB
ejpam-1889	16	11	these	these	DET
ejpam-1889	16	12	systems	system	NOUN
ejpam-1889	16	13	provide	provide	VERB
ejpam-1889	16	14	a	a	DET
ejpam-1889	16	15	fertile	fertile	ADJ
ejpam-1889	16	16	geometric	geometric	ADJ
ejpam-1889	16	17	setting	setting	NOUN
ejpam-1889	16	18	for	for	ADP
ejpam-1889	16	19	various	various	ADJ
ejpam-1889	16	20	problems	problem	NOUN
ejpam-1889	16	21	in	in	ADP
ejpam-1889	16	22	mathematical	mathematical	ADJ
ejpam-1889	16	23	physics	physics	NOUN
ejpam-1889	16	24	,	,	PUNCT
ejpam-1889	16	25	mechanics	mechanic	NOUN
ejpam-1889	16	26	,	,	PUNCT
ejpam-1889	16	27	elasticity	elasticity	NOUN
ejpam-1889	16	28	,	,	PUNCT
ejpam-1889	16	29	and	and	CCONJ
ejpam-1889	16	30	differential	differential	ADJ
ejpam-1889	16	31	geometry	geometry	NOUN
ejpam-1889	16	32	[	[	X
ejpam-1889	16	33	3	3	NUM
ejpam-1889	16	34	,	,	PUNCT
ejpam-1889	16	35	8	8	NUM
ejpam-1889	16	36	,	,	PUNCT
ejpam-1889	16	37	10	10	NUM
ejpam-1889	16	38	]	]	PUNCT
ejpam-1889	16	39	.	.	PUNCT
ejpam-1889	17	1	there	there	PRON
ejpam-1889	17	2	are	be	VERB
ejpam-1889	17	3	two	two	NUM
ejpam-1889	17	4	natural	natural	ADJ
ejpam-1889	17	5	equivalence	equivalence	NOUN
ejpam-1889	17	6	relations	relation	NOUN
ejpam-1889	17	7	for	for	ADP
ejpam-1889	17	8	left	left	ADJ
ejpam-1889	17	9	-	-	PUNCT
ejpam-1889	17	10	invariant	invariant	ADJ
ejpam-1889	17	11	control	control	NOUN
ejpam-1889	17	12	affine	affine	NOUN
ejpam-1889	17	13	systems	system	NOUN
ejpam-1889	17	14	,	,	PUNCT
ejpam-1889	17	15	namely	namely	ADV
ejpam-1889	17	16	state	state	NOUN
ejpam-1889	17	17	space	space	NOUN
ejpam-1889	17	18	equivalence	equivalence	NOUN
ejpam-1889	17	19	and	and	CCONJ
ejpam-1889	17	20	detached	detach	VERB
ejpam-1889	17	21	feedback	feedback	NOUN
ejpam-1889	17	22	equivalence	equivalence	NOUN
ejpam-1889	17	23	(	(	PUNCT
ejpam-1889	17	24	cf	cf	NOUN
ejpam-1889	17	25	.	.	PUNCT
ejpam-1889	18	1	[	[	X
ejpam-1889	18	2	9	9	NUM
ejpam-1889	18	3	,	,	PUNCT
ejpam-1889	18	4	15	15	NUM
ejpam-1889	18	5	]	]	NUM
ejpam-1889	18	6	)	)	PUNCT
ejpam-1889	18	7	.	.	PUNCT
ejpam-1889	19	1	these	these	DET
ejpam-1889	19	2	equivalence	equivalence	NOUN
ejpam-1889	19	3	relations	relation	NOUN
ejpam-1889	19	4	are	be	AUX
ejpam-1889	19	5	significant	significant	ADJ
ejpam-1889	19	6	in	in	SCONJ
ejpam-1889	19	7	that	that	SCONJ
ejpam-1889	19	8	they	they	PRON
ejpam-1889	19	9	establish	establish	VERB
ejpam-1889	19	10	a	a	DET
ejpam-1889	19	11	one	one	NUM
ejpam-1889	19	12	-	-	PUNCT
ejpam-1889	19	13	to	to	ADP
ejpam-1889	19	14	-	-	PUNCT
ejpam-1889	19	15	one	one	NUM
ejpam-1889	19	16	correspondence	correspondence	NOUN
ejpam-1889	19	17	between	between	ADP
ejpam-1889	19	18	the	the	DET
ejpam-1889	19	19	trajectories	trajectory	NOUN
ejpam-1889	19	20	of	of	ADP
ejpam-1889	19	21	equivalent	equivalent	ADJ
ejpam-1889	19	22	systems	system	NOUN
ejpam-1889	19	23	.	.	PUNCT
ejpam-1889	20	1	two	two	NUM
ejpam-1889	20	2	systems	system	NOUN
ejpam-1889	20	3	are	be	AUX
ejpam-1889	20	4	state	state	NOUN
ejpam-1889	20	5	space	space	NOUN
ejpam-1889	20	6	equivalent	equivalent	ADJ
ejpam-1889	20	7	if	if	SCONJ
ejpam-1889	20	8	one	one	PRON
ejpam-1889	20	9	can	can	AUX
ejpam-1889	20	10	smoothly	smoothly	ADV
ejpam-1889	20	11	transform	transform	VERB
ejpam-1889	20	12	one	one	NUM
ejpam-1889	20	13	system	system	NOUN
ejpam-1889	20	14	into	into	ADP
ejpam-1889	20	15	the	the	DET
ejpam-1889	20	16	other	other	ADJ
ejpam-1889	20	17	,	,	PUNCT
ejpam-1889	20	18	while	while	SCONJ
ejpam-1889	20	19	keeping	keep	VERB
ejpam-1889	20	20	the	the	DET
ejpam-1889	20	21	controls	control	NOUN
ejpam-1889	20	22	fixed	fix	VERB
ejpam-1889	20	23	.	.	PUNCT
ejpam-1889	21	1	for	for	ADP
ejpam-1889	21	2	detached	detach	VERB
ejpam-1889	21	3	feedback	feedback	NOUN
ejpam-1889	21	4	equivalence	equivalence	NOUN
ejpam-1889	21	5	(	(	PUNCT
ejpam-1889	21	6	a	a	DET
ejpam-1889	21	7	weaker	weak	ADJ
ejpam-1889	21	8	equivalence	equivalence	NOUN
ejpam-1889	21	9	relation	relation	NOUN
ejpam-1889	21	10	)	)	PUNCT
ejpam-1889	21	11	,	,	PUNCT
ejpam-1889	21	12	invariant	invariant	ADJ
ejpam-1889	21	13	feedback	feedback	NOUN
ejpam-1889	21	14	transformations	transformation	NOUN
ejpam-1889	21	15	of	of	ADP
ejpam-1889	21	16	the	the	DET
ejpam-1889	21	17	∗corresponding	∗corresponde	VERB
ejpam-1889	21	18	author	author	NOUN
ejpam-1889	21	19	.	.	PUNCT
ejpam-1889	22	1	email	email	NOUN
ejpam-1889	22	2	addresses	address	NOUN
ejpam-1889	22	3	:	:	PUNCT
ejpam-1889	22	4	dbarrett6@gmail.com	dbarrett6@gmail.com	X
ejpam-1889	22	5	(	(	PUNCT
ejpam-1889	22	6	d.	d.	PROPN
ejpam-1889	22	7	barrett	barrett	PROPN
ejpam-1889	22	8	)	)	PUNCT
ejpam-1889	22	9	,	,	PUNCT
ejpam-1889	22	10	rorybiggs@gmail.com	rorybiggs@gmail.com	PROPN
ejpam-1889	22	11	(	(	PUNCT
ejpam-1889	22	12	r.	r.	PROPN
ejpam-1889	22	13	biggs	biggs	PROPN
ejpam-1889	22	14	)	)	PUNCT
ejpam-1889	22	15	,	,	PUNCT
ejpam-1889	22	16	c.c.remsing@ru.ac.za	c.c.remsing@ru.ac.za	NOUN
ejpam-1889	22	17	(	(	PUNCT
ejpam-1889	22	18	c.	c.	NOUN
ejpam-1889	22	19	remsing	remsing	NOUN
ejpam-1889	22	20	)	)	PUNCT
ejpam-1889	22	21	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1889	23	1	140	140	NUM
ejpam-1889	23	2	c	c	X
ejpam-1889	23	3	©	©	NOUN
ejpam-1889	23	4	2014	2014	NUM
ejpam-1889	23	5	ejpam	ejpam	NOUN
ejpam-1889	23	6	all	all	DET
ejpam-1889	23	7	rights	right	NOUN
ejpam-1889	23	8	reserved	reserve	VERB
ejpam-1889	23	9	.	.	PUNCT
ejpam-1889	24	1	d.	d.	PROPN
ejpam-1889	24	2	barrett	barrett	PROPN
ejpam-1889	24	3	,	,	PUNCT
ejpam-1889	24	4	r.	r.	PROPN
ejpam-1889	24	5	biggs	biggs	PROPN
ejpam-1889	24	6	,	,	PUNCT
ejpam-1889	24	7	c.	c.	PROPN
ejpam-1889	24	8	remsing	remsing	NOUN
ejpam-1889	24	9	/	/	SYM
ejpam-1889	24	10	eur	eur	NOUN
ejpam-1889	24	11	.	.	PUNCT
ejpam-1889	25	1	j.	j.	PROPN
ejpam-1889	25	2	pure	pure	PROPN
ejpam-1889	25	3	appl	appl	PROPN
ejpam-1889	25	4	.	.	PROPN
ejpam-1889	25	5	math	math	PROPN
ejpam-1889	25	6	,	,	PUNCT
ejpam-1889	25	7	7	7	NUM
ejpam-1889	25	8	(	(	PUNCT
ejpam-1889	25	9	2014	2014	NUM
ejpam-1889	25	10	)	)	PUNCT
ejpam-1889	25	11	,	,	PUNCT
ejpam-1889	25	12	140	140	NUM
ejpam-1889	25	13	-	-	SYM
ejpam-1889	25	14	155	155	NUM
ejpam-1889	25	15	141	141	NUM
ejpam-1889	25	16	controls	control	NOUN
ejpam-1889	25	17	are	be	AUX
ejpam-1889	25	18	also	also	ADV
ejpam-1889	25	19	permitted	permit	VERB
ejpam-1889	25	20	.	.	PUNCT
ejpam-1889	26	1	it	it	PRON
ejpam-1889	26	2	turns	turn	VERB
ejpam-1889	26	3	out	out	ADP
ejpam-1889	26	4	that	that	SCONJ
ejpam-1889	26	5	these	these	DET
ejpam-1889	26	6	two	two	NUM
ejpam-1889	26	7	equivalence	equivalence	NOUN
ejpam-1889	26	8	relations	relation	NOUN
ejpam-1889	26	9	can	can	AUX
ejpam-1889	26	10	be	be	AUX
ejpam-1889	26	11	entirely	entirely	ADV
ejpam-1889	26	12	characterized	characterize	VERB
ejpam-1889	26	13	at	at	ADP
ejpam-1889	26	14	the	the	DET
ejpam-1889	26	15	level	level	NOUN
ejpam-1889	26	16	of	of	ADP
ejpam-1889	26	17	lie	lie	NOUN
ejpam-1889	26	18	algebras	algebra	NOUN
ejpam-1889	26	19	[	[	X
ejpam-1889	26	20	4	4	NUM
ejpam-1889	26	21	]	]	PUNCT
ejpam-1889	26	22	.	.	PUNCT
ejpam-1889	27	1	more	more	ADV
ejpam-1889	27	2	precisely	precisely	ADV
ejpam-1889	27	3	,	,	PUNCT
ejpam-1889	27	4	two	two	NUM
ejpam-1889	27	5	systems	system	NOUN
ejpam-1889	27	6	are	be	AUX
ejpam-1889	27	7	state	state	NOUN
ejpam-1889	27	8	space	space	NOUN
ejpam-1889	27	9	equivalent	equivalent	NOUN
ejpam-1889	27	10	(	(	PUNCT
ejpam-1889	27	11	resp	resp	NOUN
ejpam-1889	27	12	.	.	PUNCT
ejpam-1889	28	1	detached	detach	VERB
ejpam-1889	28	2	feedback	feedback	NOUN
ejpam-1889	28	3	equivalent	equivalent	ADJ
ejpam-1889	28	4	)	)	PUNCT
ejpam-1889	29	1	if	if	SCONJ
ejpam-1889	29	2	and	and	CCONJ
ejpam-1889	29	3	only	only	ADV
ejpam-1889	29	4	if	if	SCONJ
ejpam-1889	29	5	the	the	DET
ejpam-1889	29	6	associated	associated	ADJ
ejpam-1889	29	7	parametrized	parametrized	ADJ
ejpam-1889	29	8	affine	affine	NOUN
ejpam-1889	29	9	subspaces	subspace	NOUN
ejpam-1889	29	10	(	(	PUNCT
ejpam-1889	29	11	resp	resp	NOUN
ejpam-1889	29	12	.	.	PUNCT
ejpam-1889	30	1	affine	affine	PROPN
ejpam-1889	30	2	subspaces	subspace	NOUN
ejpam-1889	30	3	)	)	PUNCT
ejpam-1889	30	4	are	be	AUX
ejpam-1889	30	5	related	relate	VERB
ejpam-1889	30	6	by	by	ADP
ejpam-1889	30	7	a	a	DET
ejpam-1889	30	8	lie	lie	NOUN
ejpam-1889	30	9	algebra	algebra	NOUN
ejpam-1889	30	10	isomorphism	isomorphism	NOUN
ejpam-1889	30	11	.	.	PUNCT
ejpam-1889	31	1	(	(	PUNCT
ejpam-1889	31	2	for	for	ADP
ejpam-1889	31	3	a	a	DET
ejpam-1889	31	4	system	system	NOUN
ejpam-1889	31	5	(	(	PUNCT
ejpam-1889	31	6	1	1	NUM
ejpam-1889	31	7	)	)	PUNCT
ejpam-1889	31	8	,	,	PUNCT
ejpam-1889	31	9	the	the	DET
ejpam-1889	31	10	associated	associated	ADJ
ejpam-1889	31	11	parametrized	parametrized	ADJ
ejpam-1889	31	12	affine	affine	NOUN
ejpam-1889	31	13	subspace	subspace	NOUN
ejpam-1889	31	14	is	be	AUX
ejpam-1889	31	15	given	give	VERB
ejpam-1889	31	16	by	by	ADP
ejpam-1889	31	17	π	π	PROPN
ejpam-1889	31	18	:	:	PUNCT
ejpam-1889	31	19	u	u	PROPN
ejpam-1889	31	20	7→	7→	NUM
ejpam-1889	31	21	a+	a+	PUNCT
ejpam-1889	31	22	u1b1	u1b1	PROPN
ejpam-1889	31	23	+	+	CCONJ
ejpam-1889	31	24	·	·	PUNCT
ejpam-1889	31	25	·	·	PUNCT
ejpam-1889	31	26	·	·	PUNCT
ejpam-1889	32	1	+	+	CCONJ
ejpam-1889	32	2	u`b	u`b	ADJ
ejpam-1889	32	3	`	`	PUNCT
ejpam-1889	32	4	,	,	PUNCT
ejpam-1889	32	5	whereas	whereas	SCONJ
ejpam-1889	32	6	the	the	DET
ejpam-1889	32	7	associated	associate	VERB
ejpam-1889	32	8	affine	affine	NOUN
ejpam-1889	32	9	subspace	subspace	NOUN
ejpam-1889	32	10	is	be	AUX
ejpam-1889	32	11	given	give	VERB
ejpam-1889	32	12	by	by	ADP
ejpam-1889	32	13	γ	γ	X
ejpam-1889	32	14	=	=	SYM
ejpam-1889	32	15	a+	a+	PUNCT
ejpam-1889	32	16	〈	〈	NOUN
ejpam-1889	32	17	b1	b1	NOUN
ejpam-1889	32	18	,	,	PUNCT
ejpam-1889	32	19	.	.	PUNCT
ejpam-1889	32	20	.	.	PUNCT
ejpam-1889	32	21	.	.	PUNCT
ejpam-1889	33	1	,	,	PUNCT
ejpam-1889	33	2	b	b	X
ejpam-1889	33	3	`	`	PUNCT
ejpam-1889	33	4	〉	〉	NOUN
ejpam-1889	33	5	.	.	PUNCT
ejpam-1889	33	6	)	)	PUNCT
ejpam-1889	34	1	several	several	ADJ
ejpam-1889	34	2	classes	class	NOUN
ejpam-1889	34	3	of	of	ADP
ejpam-1889	34	4	systems	system	NOUN
ejpam-1889	34	5	have	have	AUX
ejpam-1889	34	6	recently	recently	ADV
ejpam-1889	34	7	been	be	AUX
ejpam-1889	34	8	classified	classify	VERB
ejpam-1889	34	9	under	under	ADP
ejpam-1889	34	10	these	these	DET
ejpam-1889	34	11	equivalence	equivalence	NOUN
ejpam-1889	34	12	relations	relation	NOUN
ejpam-1889	34	13	[	[	X
ejpam-1889	34	14	1	1	NUM
ejpam-1889	34	15	,	,	PUNCT
ejpam-1889	34	16	2	2	NUM
ejpam-1889	34	17	,	,	PUNCT
ejpam-1889	34	18	5–7	5–7	NOUN
ejpam-1889	34	19	]	]	PUNCT
ejpam-1889	34	20	.	.	PUNCT
ejpam-1889	35	1	in	in	ADP
ejpam-1889	35	2	this	this	DET
ejpam-1889	35	3	paper	paper	NOUN
ejpam-1889	35	4	we	we	PRON
ejpam-1889	35	5	classify	classify	VERB
ejpam-1889	35	6	,	,	PUNCT
ejpam-1889	35	7	under	under	ADP
ejpam-1889	35	8	the	the	DET
ejpam-1889	35	9	aforementioned	aforementioned	ADJ
ejpam-1889	35	10	equivalence	equivalence	NOUN
ejpam-1889	35	11	relations	relation	NOUN
ejpam-1889	35	12	,	,	PUNCT
ejpam-1889	35	13	the	the	DET
ejpam-1889	35	14	parametrized	parametrized	ADJ
ejpam-1889	35	15	affine	affine	NOUN
ejpam-1889	35	16	subspaces	subspace	NOUN
ejpam-1889	35	17	(	(	PUNCT
ejpam-1889	35	18	resp	resp	NOUN
ejpam-1889	35	19	.	.	PUNCT
ejpam-1889	36	1	affine	affine	PROPN
ejpam-1889	36	2	subspaces	subspace	NOUN
ejpam-1889	36	3	)	)	PUNCT
ejpam-1889	36	4	of	of	ADP
ejpam-1889	36	5	the	the	DET
ejpam-1889	36	6	semi	semi	ADJ
ejpam-1889	36	7	-	-	ADJ
ejpam-1889	36	8	euclidean	euclidean	ADJ
ejpam-1889	36	9	lie	lie	NOUN
ejpam-1889	36	10	algebra	algebra	PROPN
ejpam-1889	36	11	se(1,1	se(1,1	PROPN
ejpam-1889	36	12	)	)	PUNCT
ejpam-1889	36	13	.	.	PUNCT
ejpam-1889	37	1	we	we	PRON
ejpam-1889	37	2	classify	classify	VERB
ejpam-1889	37	3	first	first	ADV
ejpam-1889	37	4	the	the	DET
ejpam-1889	37	5	affine	affine	NOUN
ejpam-1889	37	6	subspaces	subspace	NOUN
ejpam-1889	37	7	of	of	ADP
ejpam-1889	37	8	se(1,1	se(1,1	NOUN
ejpam-1889	37	9	)	)	PUNCT
ejpam-1889	37	10	.	.	PUNCT
ejpam-1889	38	1	using	use	VERB
ejpam-1889	38	2	these	these	DET
ejpam-1889	38	3	results	result	NOUN
ejpam-1889	38	4	,	,	PUNCT
ejpam-1889	38	5	we	we	PRON
ejpam-1889	38	6	then	then	ADV
ejpam-1889	38	7	classify	classify	VERB
ejpam-1889	38	8	the	the	DET
ejpam-1889	38	9	parametrized	parametrized	ADJ
ejpam-1889	38	10	affine	affine	NOUN
ejpam-1889	38	11	subspaces	subspace	NOUN
ejpam-1889	38	12	.	.	PUNCT
ejpam-1889	39	1	both	both	DET
ejpam-1889	39	2	classifications	classification	NOUN
ejpam-1889	39	3	are	be	AUX
ejpam-1889	39	4	organized	organize	VERB
ejpam-1889	39	5	by	by	ADP
ejpam-1889	39	6	distinguishing	distinguish	VERB
ejpam-1889	39	7	between	between	ADP
ejpam-1889	39	8	the	the	DET
ejpam-1889	39	9	homogeneity	homogeneity	NOUN
ejpam-1889	39	10	and	and	CCONJ
ejpam-1889	39	11	dimension	dimension	NOUN
ejpam-1889	39	12	of	of	ADP
ejpam-1889	39	13	the	the	DET
ejpam-1889	39	14	affine	affine	NOUN
ejpam-1889	39	15	subspaces	subspace	NOUN
ejpam-1889	39	16	involved	involve	VERB
ejpam-1889	39	17	.	.	PUNCT
ejpam-1889	40	1	exhaustive	exhaustive	ADJ
ejpam-1889	40	2	lists	list	NOUN
ejpam-1889	40	3	of	of	ADP
ejpam-1889	40	4	class	class	NOUN
ejpam-1889	40	5	representatives	representative	NOUN
ejpam-1889	40	6	are	be	AUX
ejpam-1889	40	7	obtained	obtain	VERB
ejpam-1889	40	8	,	,	PUNCT
ejpam-1889	40	9	along	along	ADP
ejpam-1889	40	10	with	with	ADP
ejpam-1889	40	11	associated	associate	VERB
ejpam-1889	40	12	classifying	classify	VERB
ejpam-1889	40	13	conditions	condition	NOUN
ejpam-1889	40	14	.	.	PUNCT
ejpam-1889	41	1	a	a	DET
ejpam-1889	41	2	tabulation	tabulation	NOUN
ejpam-1889	41	3	of	of	ADP
ejpam-1889	41	4	the	the	DET
ejpam-1889	41	5	main	main	ADJ
ejpam-1889	41	6	results	result	NOUN
ejpam-1889	41	7	is	be	AUX
ejpam-1889	41	8	appended	append	VERB
ejpam-1889	41	9	.	.	PUNCT
ejpam-1889	42	1	2	2	X
ejpam-1889	42	2	.	.	X
ejpam-1889	42	3	affine	affine	NOUN
ejpam-1889	42	4	subspaces	subspace	NOUN
ejpam-1889	42	5	and	and	CCONJ
ejpam-1889	42	6	equivalence	equivalence	NOUN
ejpam-1889	42	7	an	an	DET
ejpam-1889	42	8	`	`	PUNCT
ejpam-1889	42	9	-dimensional	-dimensional	ADJ
ejpam-1889	42	10	affine	affine	NOUN
ejpam-1889	42	11	subspace	subspace	NOUN
ejpam-1889	42	12	of	of	ADP
ejpam-1889	42	13	a	a	DET
ejpam-1889	42	14	lie	lie	NOUN
ejpam-1889	42	15	algebra	algebra	NOUN
ejpam-1889	42	16	g	g	NOUN
ejpam-1889	42	17	is	be	AUX
ejpam-1889	42	18	written	write	VERB
ejpam-1889	42	19	as	as	ADP
ejpam-1889	42	20	γ	γ	X
ejpam-1889	42	21	=	=	SYM
ejpam-1889	42	22	a+γ0	a+γ0	NOUN
ejpam-1889	42	23	=	=	SYM
ejpam-1889	42	24	a+	a+	PUNCT
ejpam-1889	42	25	〈	〈	NOUN
ejpam-1889	42	26	b1	b1	NOUN
ejpam-1889	42	27	,	,	PUNCT
ejpam-1889	42	28	.	.	PUNCT
ejpam-1889	42	29	.	.	PUNCT
ejpam-1889	43	1	.	.	PUNCT
ejpam-1889	44	1	,	,	PUNCT
ejpam-1889	44	2	b	b	X
ejpam-1889	44	3	`	`	PUNCT
ejpam-1889	44	4	〉	〉	NOUN
ejpam-1889	44	5	(	(	PUNCT
ejpam-1889	44	6	2	2	NUM
ejpam-1889	44	7	)	)	PUNCT
ejpam-1889	44	8	where	where	SCONJ
ejpam-1889	44	9	a	a	PRON
ejpam-1889	44	10	,	,	PUNCT
ejpam-1889	44	11	b1	b1	NOUN
ejpam-1889	44	12	,	,	PUNCT
ejpam-1889	44	13	.	.	PUNCT
ejpam-1889	44	14	.	.	PUNCT
ejpam-1889	44	15	.	.	PUNCT
ejpam-1889	45	1	,	,	PUNCT
ejpam-1889	45	2	b	b	X
ejpam-1889	45	3	`	`	PUNCT
ejpam-1889	45	4	∈	∈	PROPN
ejpam-1889	45	5	g	g	NOUN
ejpam-1889	45	6	and	and	CCONJ
ejpam-1889	45	7	b1	b1	PROPN
ejpam-1889	45	8	,	,	PUNCT
ejpam-1889	45	9	.	.	PUNCT
ejpam-1889	45	10	.	.	PUNCT
ejpam-1889	46	1	.	.	PUNCT
ejpam-1889	47	1	,	,	PUNCT
ejpam-1889	47	2	b	b	X
ejpam-1889	47	3	`	`	PUNCT
ejpam-1889	47	4	are	be	AUX
ejpam-1889	47	5	linearly	linearly	ADV
ejpam-1889	47	6	independent	independent	ADJ
ejpam-1889	47	7	.	.	PUNCT
ejpam-1889	48	1	if	if	SCONJ
ejpam-1889	48	2	a	a	DET
ejpam-1889	48	3	∈	∈	PROPN
ejpam-1889	48	4	γ0	γ0	NOUN
ejpam-1889	48	5	,	,	PUNCT
ejpam-1889	48	6	we	we	PRON
ejpam-1889	48	7	say	say	VERB
ejpam-1889	48	8	that	that	SCONJ
ejpam-1889	48	9	γ	γ	PROPN
ejpam-1889	48	10	is	be	AUX
ejpam-1889	48	11	homogeneous	homogeneous	ADJ
ejpam-1889	48	12	;	;	PUNCT
ejpam-1889	48	13	otherwise	otherwise	ADV
ejpam-1889	48	14	,	,	PUNCT
ejpam-1889	48	15	it	it	PRON
ejpam-1889	48	16	is	be	AUX
ejpam-1889	48	17	inhomogeneous	inhomogeneous	ADJ
ejpam-1889	48	18	.	.	PUNCT
ejpam-1889	49	1	γ	γ	PROPN
ejpam-1889	49	2	is	be	AUX
ejpam-1889	49	3	referred	refer	VERB
ejpam-1889	49	4	to	to	ADP
ejpam-1889	49	5	as	as	ADP
ejpam-1889	49	6	an	an	DET
ejpam-1889	49	7	(	(	PUNCT
ejpam-1889	49	8	`	`	PUNCT
ejpam-1889	49	9	,	,	PUNCT
ejpam-1889	49	10	0)-affine	0)-affine	NUM
ejpam-1889	49	11	subspace	subspace	NOUN
ejpam-1889	49	12	if	if	SCONJ
ejpam-1889	49	13	it	it	PRON
ejpam-1889	49	14	is	be	AUX
ejpam-1889	49	15	homogeneous	homogeneous	ADJ
ejpam-1889	49	16	,	,	PUNCT
ejpam-1889	49	17	and	and	CCONJ
ejpam-1889	49	18	as	as	ADP
ejpam-1889	49	19	an	an	DET
ejpam-1889	49	20	(	(	PUNCT
ejpam-1889	49	21	`	`	PUNCT
ejpam-1889	49	22	,	,	PUNCT
ejpam-1889	49	23	1)-affine	1)-affine	NUM
ejpam-1889	49	24	subspace	subspace	NOUN
ejpam-1889	49	25	,	,	PUNCT
ejpam-1889	49	26	otherwise	otherwise	ADV
ejpam-1889	49	27	.	.	PUNCT
ejpam-1889	50	1	we	we	PRON
ejpam-1889	50	2	say	say	VERB
ejpam-1889	50	3	that	that	SCONJ
ejpam-1889	50	4	two	two	NUM
ejpam-1889	50	5	affine	affine	NOUN
ejpam-1889	50	6	subspaces	subspace	VERB
ejpam-1889	50	7	γ	γ	NOUN
ejpam-1889	50	8	and	and	CCONJ
ejpam-1889	50	9	γ′	γ′	NOUN
ejpam-1889	50	10	are	be	AUX
ejpam-1889	50	11	l	l	NOUN
ejpam-1889	50	12	-	-	NOUN
ejpam-1889	50	13	equivalent	equivalent	ADJ
ejpam-1889	50	14	if	if	SCONJ
ejpam-1889	50	15	there	there	PRON
ejpam-1889	50	16	exists	exist	VERB
ejpam-1889	50	17	a	a	DET
ejpam-1889	50	18	lie	lie	NOUN
ejpam-1889	50	19	algebra	algebra	NOUN
ejpam-1889	50	20	automorphismψ	automorphismψ	VERB
ejpam-1889	50	21	such	such	ADJ
ejpam-1889	50	22	thatψ·γ	thatψ·γ	NOUN
ejpam-1889	50	23	=	=	SYM
ejpam-1889	50	24	γ′.	γ′.	PROPN
ejpam-1889	50	25	note	note	NOUN
ejpam-1889	50	26	that	that	SCONJ
ejpam-1889	50	27	γ	γ	AUX
ejpam-1889	50	28	=	=	SYM
ejpam-1889	50	29	a+γ0	a+γ0	PROPN
ejpam-1889	50	30	and	and	CCONJ
ejpam-1889	50	31	γ′	γ′	NOUN
ejpam-1889	50	32	=	=	NOUN
ejpam-1889	50	33	a′	a′	PROPN
ejpam-1889	50	34	+	+	SYM
ejpam-1889	50	35	γ′0	γ′0	NOUN
ejpam-1889	50	36	are	be	AUX
ejpam-1889	50	37	l	l	NOUN
ejpam-1889	50	38	-	-	ADJ
ejpam-1889	50	39	equivalent	equivalent	ADJ
ejpam-1889	50	40	if	if	SCONJ
ejpam-1889	50	41	and	and	CCONJ
ejpam-1889	50	42	only	only	ADV
ejpam-1889	50	43	if	if	SCONJ
ejpam-1889	50	44	there	there	PRON
ejpam-1889	50	45	exists	exist	VERB
ejpam-1889	50	46	an	an	DET
ejpam-1889	50	47	automorphism	automorphism	NOUN
ejpam-1889	50	48	ψ	ψ	ADP
ejpam-1889	50	49	such	such	ADJ
ejpam-1889	50	50	that	that	SCONJ
ejpam-1889	50	51	ψ	ψ	X
ejpam-1889	50	52	·	·	PUNCT
ejpam-1889	50	53	γ0	γ0	NOUN
ejpam-1889	50	54	=	=	SYM
ejpam-1889	50	55	γ′0	γ′0	NOUN
ejpam-1889	50	56	and	and	CCONJ
ejpam-1889	50	57	ψ	ψ	X
ejpam-1889	50	58	·	·	PUNCT
ejpam-1889	50	59	a∈	a∈	PROPN
ejpam-1889	50	60	γ′.	γ′.	VERB
ejpam-1889	50	61	a	a	DET
ejpam-1889	50	62	related	related	ADJ
ejpam-1889	50	63	concept	concept	NOUN
ejpam-1889	50	64	is	be	AUX
ejpam-1889	50	65	that	that	PRON
ejpam-1889	50	66	of	of	ADP
ejpam-1889	50	67	a	a	DET
ejpam-1889	50	68	parametrized	parametrized	ADJ
ejpam-1889	50	69	affine	affine	NOUN
ejpam-1889	50	70	subspace	subspace	NOUN
ejpam-1889	50	71	,	,	PUNCT
ejpam-1889	50	72	i.e.	i.e.	X
ejpam-1889	50	73	,	,	PUNCT
ejpam-1889	50	74	an	an	DET
ejpam-1889	50	75	(	(	PUNCT
ejpam-1889	50	76	injective	injective	ADJ
ejpam-1889	50	77	)	)	PUNCT
ejpam-1889	50	78	affine	affine	NOUN
ejpam-1889	50	79	gvalued	gvalue	VERB
ejpam-1889	50	80	map	map	NOUN
ejpam-1889	50	81	.	.	PUNCT
ejpam-1889	51	1	more	more	ADV
ejpam-1889	51	2	precisely	precisely	ADV
ejpam-1889	51	3	,	,	PUNCT
ejpam-1889	51	4	an	an	DET
ejpam-1889	51	5	`	`	PUNCT
ejpam-1889	51	6	-dimensional	-dimensional	ADJ
ejpam-1889	51	7	parametrized	parametrized	ADJ
ejpam-1889	51	8	affine	affine	NOUN
ejpam-1889	51	9	subspace	subspace	NOUN
ejpam-1889	51	10	is	be	AUX
ejpam-1889	51	11	a	a	DET
ejpam-1889	51	12	map	map	NOUN
ejpam-1889	51	13	π	π	NOUN
ejpam-1889	51	14	:	:	PUNCT
ejpam-1889	51	15	r`→	r`→	NOUN
ejpam-1889	51	16	g	g	NOUN
ejpam-1889	51	17	,	,	PUNCT
ejpam-1889	51	18	(	(	PUNCT
ejpam-1889	51	19	u1	u1	NOUN
ejpam-1889	51	20	,	,	PUNCT
ejpam-1889	51	21	.	.	PUNCT
ejpam-1889	51	22	.	.	PUNCT
ejpam-1889	52	1	.	.	PUNCT
ejpam-1889	53	1	,	,	PUNCT
ejpam-1889	53	2	u	u	NOUN
ejpam-1889	53	3	`	`	PUNCT
ejpam-1889	53	4	)	)	PUNCT
ejpam-1889	53	5	7→	7→	NUM
ejpam-1889	53	6	a+	a+	PUNCT
ejpam-1889	53	7	u1b1	u1b1	X
ejpam-1889	53	8	+	+	CCONJ
ejpam-1889	53	9	·	·	PUNCT
ejpam-1889	53	10	·	·	PUNCT
ejpam-1889	53	11	·	·	PUNCT
ejpam-1889	53	12	+	+	NUM
ejpam-1889	53	13	u`b	u`b	PROPN
ejpam-1889	53	14	`	`	PUNCT
ejpam-1889	53	15	where	where	SCONJ
ejpam-1889	53	16	b1	b1	NOUN
ejpam-1889	53	17	,	,	PUNCT
ejpam-1889	53	18	.	.	PUNCT
ejpam-1889	53	19	.	.	PUNCT
ejpam-1889	54	1	.	.	PUNCT
ejpam-1889	55	1	,	,	PUNCT
ejpam-1889	55	2	b	b	X
ejpam-1889	55	3	`	`	PUNCT
ejpam-1889	55	4	are	be	AUX
ejpam-1889	55	5	linearly	linearly	ADV
ejpam-1889	55	6	independent	independent	ADJ
ejpam-1889	55	7	.	.	PUNCT
ejpam-1889	56	1	whenever	whenever	SCONJ
ejpam-1889	56	2	convenient	convenient	ADJ
ejpam-1889	56	3	,	,	PUNCT
ejpam-1889	56	4	we	we	PRON
ejpam-1889	56	5	shall	shall	AUX
ejpam-1889	56	6	specify	specify	VERB
ejpam-1889	56	7	π	π	PROPN
ejpam-1889	56	8	by	by	ADP
ejpam-1889	56	9	simply	simply	ADV
ejpam-1889	56	10	writing	write	VERB
ejpam-1889	56	11	π	π	PROPN
ejpam-1889	56	12	:	:	PUNCT
ejpam-1889	56	13	a+	a+	PUNCT
ejpam-1889	56	14	u1b1	u1b1	X
ejpam-1889	56	15	+	+	CCONJ
ejpam-1889	56	16	·	·	PUNCT
ejpam-1889	56	17	·	·	PUNCT
ejpam-1889	56	18	·	·	PUNCT
ejpam-1889	57	1	+	+	CCONJ
ejpam-1889	57	2	u`b	u`b	ADJ
ejpam-1889	57	3	`	`	PUNCT
ejpam-1889	57	4	.	.	PUNCT
ejpam-1889	58	1	we	we	PRON
ejpam-1889	58	2	say	say	VERB
ejpam-1889	58	3	that	that	SCONJ
ejpam-1889	58	4	two	two	NUM
ejpam-1889	58	5	parametrized	parametrized	ADJ
ejpam-1889	58	6	affine	affine	NOUN
ejpam-1889	58	7	subspaces	subspace	NOUN
ejpam-1889	58	8	π	π	NOUN
ejpam-1889	58	9	and	and	CCONJ
ejpam-1889	58	10	π′	π′	NOUN
ejpam-1889	58	11	are	be	AUX
ejpam-1889	58	12	p	p	NOUN
ejpam-1889	58	13	-	-	PUNCT
ejpam-1889	58	14	equivalent	equivalent	ADJ
ejpam-1889	58	15	if	if	SCONJ
ejpam-1889	58	16	there	there	PRON
ejpam-1889	58	17	exists	exist	VERB
ejpam-1889	58	18	an	an	DET
ejpam-1889	58	19	automorphism	automorphism	NOUN
ejpam-1889	58	20	ψ	ψ	X
ejpam-1889	58	21	∈	∈	PROPN
ejpam-1889	58	22	aut(g	aut(g	PROPN
ejpam-1889	58	23	)	)	PUNCT
ejpam-1889	58	24	such	such	ADJ
ejpam-1889	58	25	that	that	SCONJ
ejpam-1889	58	26	ψ	ψ	ADP
ejpam-1889	58	27	◦	◦	NOUN
ejpam-1889	58	28	π	π	NOUN
ejpam-1889	58	29	=	=	X
ejpam-1889	58	30	π′.	π′.	X
ejpam-1889	58	31	clearly	clearly	ADV
ejpam-1889	58	32	π	π	X
ejpam-1889	58	33	:	:	PUNCT
ejpam-1889	59	1	a+u1b1	a+u1b1	X
ejpam-1889	59	2	+	+	NUM
ejpam-1889	59	3	·	·	PUNCT
ejpam-1889	59	4	·	·	PUNCT
ejpam-1889	59	5	·	·	PUNCT
ejpam-1889	59	6	+	+	PROPN
ejpam-1889	59	7	u`b	u`b	PROPN
ejpam-1889	59	8	`	`	PUNCT
ejpam-1889	59	9	is	be	AUX
ejpam-1889	59	10	p	p	NOUN
ejpam-1889	59	11	-	-	PUNCT
ejpam-1889	59	12	equivalent	equivalent	ADJ
ejpam-1889	59	13	to	to	ADP
ejpam-1889	59	14	π′	π′	NUM
ejpam-1889	59	15	:	:	PUNCT
ejpam-1889	59	16	a′+u1b′1	a′+u1b′1	X
ejpam-1889	59	17	+	+	X
ejpam-1889	59	18	·	·	PUNCT
ejpam-1889	59	19	·	·	PUNCT
ejpam-1889	59	20	·	·	PUNCT
ejpam-1889	60	1	+	+	PROPN
ejpam-1889	60	2	u`b	u`b	ADJ
ejpam-1889	60	3	′	′	NOUN
ejpam-1889	61	1	`	`	PUNCT
ejpam-1889	62	1	if	if	SCONJ
ejpam-1889	62	2	and	and	CCONJ
ejpam-1889	62	3	only	only	ADV
ejpam-1889	62	4	if	if	SCONJ
ejpam-1889	62	5	there	there	PRON
ejpam-1889	62	6	exists	exist	VERB
ejpam-1889	62	7	an	an	DET
ejpam-1889	62	8	automorphism	automorphism	NOUN
ejpam-1889	62	9	ψ	ψ	ADP
ejpam-1889	62	10	such	such	ADJ
ejpam-1889	62	11	that	that	SCONJ
ejpam-1889	62	12	ψ	ψ	PART
ejpam-1889	62	13	·	·	PUNCT
ejpam-1889	62	14	a=	a=	VERB
ejpam-1889	62	15	a′	a′	PROPN
ejpam-1889	62	16	and	and	CCONJ
ejpam-1889	62	17	ψ	ψ	PROPN
ejpam-1889	62	18	·	·	PUNCT
ejpam-1889	62	19	bi	bi	NOUN
ejpam-1889	62	20	=	=	PROPN
ejpam-1889	62	21	b′i	b′i	PROPN
ejpam-1889	62	22	.	.	PUNCT
ejpam-1889	63	1	an	an	DET
ejpam-1889	63	2	affine	affine	NOUN
ejpam-1889	63	3	subspace	subspace	NOUN
ejpam-1889	63	4	is	be	AUX
ejpam-1889	63	5	said	say	VERB
ejpam-1889	63	6	to	to	PART
ejpam-1889	63	7	have	have	VERB
ejpam-1889	63	8	full	full	ADJ
ejpam-1889	63	9	rank	rank	NOUN
ejpam-1889	63	10	if	if	SCONJ
ejpam-1889	63	11	it	it	PRON
ejpam-1889	63	12	generates	generate	VERB
ejpam-1889	63	13	the	the	DET
ejpam-1889	63	14	entire	entire	ADJ
ejpam-1889	63	15	lie	lie	NOUN
ejpam-1889	63	16	algebra	algebra	NOUN
ejpam-1889	63	17	.	.	PUNCT
ejpam-1889	64	1	(	(	PUNCT
ejpam-1889	64	2	for	for	ADP
ejpam-1889	64	3	control	control	NOUN
ejpam-1889	64	4	systems	system	NOUN
ejpam-1889	64	5	on	on	ADP
ejpam-1889	64	6	lie	lie	NOUN
ejpam-1889	64	7	groups	group	NOUN
ejpam-1889	64	8	,	,	PUNCT
ejpam-1889	64	9	the	the	DET
ejpam-1889	64	10	full	full	ADJ
ejpam-1889	64	11	-	-	PUNCT
ejpam-1889	64	12	rank	rank	NOUN
ejpam-1889	64	13	condition	condition	NOUN
ejpam-1889	64	14	is	be	AUX
ejpam-1889	64	15	necessary	necessary	ADJ
ejpam-1889	64	16	for	for	ADP
ejpam-1889	64	17	controllability	controllability	NOUN
ejpam-1889	64	18	)	)	PUNCT
ejpam-1889	64	19	.	.	PUNCT
ejpam-1889	65	1	similarly	similarly	ADV
ejpam-1889	65	2	,	,	PUNCT
ejpam-1889	65	3	a	a	DET
ejpam-1889	65	4	parametrized	parametrized	ADJ
ejpam-1889	65	5	affine	affine	NOUN
ejpam-1889	65	6	subspace	subspace	NOUN
ejpam-1889	65	7	has	have	VERB
ejpam-1889	65	8	full	full	ADJ
ejpam-1889	65	9	rank	rank	NOUN
ejpam-1889	65	10	if	if	SCONJ
ejpam-1889	65	11	its	its	PRON
ejpam-1889	65	12	image	image	NOUN
ejpam-1889	65	13	has	have	VERB
ejpam-1889	65	14	full	full	ADJ
ejpam-1889	65	15	rank	rank	NOUN
ejpam-1889	65	16	.	.	PUNCT
ejpam-1889	66	1	the	the	DET
ejpam-1889	66	2	full	full	ADJ
ejpam-1889	66	3	-	-	PUNCT
ejpam-1889	66	4	rank	rank	NOUN
ejpam-1889	66	5	property	property	NOUN
ejpam-1889	66	6	is	be	AUX
ejpam-1889	66	7	invariant	invariant	ADJ
ejpam-1889	66	8	under	under	ADP
ejpam-1889	66	9	both	both	CCONJ
ejpam-1889	66	10	l	l	NOUN
ejpam-1889	66	11	-	-	NOUN
ejpam-1889	66	12	equivalence	equivalence	NOUN
ejpam-1889	66	13	and	and	CCONJ
ejpam-1889	66	14	p	p	NOUN
ejpam-1889	66	15	-	-	PUNCT
ejpam-1889	66	16	equivalence	equivalence	NOUN
ejpam-1889	66	17	.	.	PUNCT
ejpam-1889	67	1	throughout	throughout	ADP
ejpam-1889	67	2	,	,	PUNCT
ejpam-1889	67	3	we	we	PRON
ejpam-1889	67	4	assume	assume	VERB
ejpam-1889	67	5	that	that	SCONJ
ejpam-1889	67	6	all	all	DET
ejpam-1889	67	7	affine	affine	NOUN
ejpam-1889	67	8	subspaces	subspace	NOUN
ejpam-1889	67	9	(	(	PUNCT
ejpam-1889	67	10	resp	resp	NOUN
ejpam-1889	67	11	.	.	PUNCT
ejpam-1889	68	1	parametrized	parametrized	ADJ
ejpam-1889	68	2	affine	affine	NOUN
ejpam-1889	68	3	subspaces	subspace	NOUN
ejpam-1889	68	4	)	)	PUNCT
ejpam-1889	68	5	under	under	ADP
ejpam-1889	68	6	consideration	consideration	NOUN
ejpam-1889	68	7	have	have	VERB
ejpam-1889	68	8	full	full	ADJ
ejpam-1889	68	9	rank	rank	NOUN
ejpam-1889	68	10	.	.	PUNCT
ejpam-1889	69	1	d.	d.	PROPN
ejpam-1889	69	2	barrett	barrett	PROPN
ejpam-1889	69	3	,	,	PUNCT
ejpam-1889	69	4	r.	r.	PROPN
ejpam-1889	69	5	biggs	biggs	PROPN
ejpam-1889	69	6	,	,	PUNCT
ejpam-1889	69	7	c.	c.	PROPN
ejpam-1889	69	8	remsing	remsing	NOUN
ejpam-1889	69	9	/	/	SYM
ejpam-1889	69	10	eur	eur	NOUN
ejpam-1889	69	11	.	.	PUNCT
ejpam-1889	70	1	j.	j.	PROPN
ejpam-1889	70	2	pure	pure	PROPN
ejpam-1889	70	3	appl	appl	PROPN
ejpam-1889	70	4	.	.	PROPN
ejpam-1889	70	5	math	math	PROPN
ejpam-1889	70	6	,	,	PUNCT
ejpam-1889	70	7	7	7	NUM
ejpam-1889	70	8	(	(	PUNCT
ejpam-1889	70	9	2014	2014	NUM
ejpam-1889	70	10	)	)	PUNCT
ejpam-1889	70	11	,	,	PUNCT
ejpam-1889	70	12	140	140	NUM
ejpam-1889	70	13	-	-	SYM
ejpam-1889	70	14	155	155	NUM
ejpam-1889	70	15	142	142	NUM
ejpam-1889	70	16	3	3	NUM
ejpam-1889	70	17	.	.	PUNCT
ejpam-1889	71	1	classification	classification	VERB
ejpam-1889	71	2	the	the	DET
ejpam-1889	71	3	(	(	PUNCT
ejpam-1889	71	4	real	real	ADJ
ejpam-1889	71	5	)	)	PUNCT
ejpam-1889	71	6	three	three	NUM
ejpam-1889	71	7	-	-	PUNCT
ejpam-1889	71	8	dimensional	dimensional	ADJ
ejpam-1889	71	9	semi	semi	ADJ
ejpam-1889	71	10	-	-	ADJ
ejpam-1889	71	11	euclidean	euclidean	ADJ
ejpam-1889	71	12	lie	lie	NOUN
ejpam-1889	71	13	algebra	algebra	PROPN
ejpam-1889	71	14	se(1	se(1	PROPN
ejpam-1889	71	15	,	,	PUNCT
ejpam-1889	71	16	1	1	NUM
ejpam-1889	71	17	)	)	PUNCT
ejpam-1889	71	18	=	=	PUNCT
ejpam-1889	72	1			PROPN
ejpam-1889	72	2			ADP
ejpam-1889	72	3			ADJ
ejpam-1889	72	4			PROPN
ejpam-1889	72	5			NOUN
ejpam-1889	72	6	0	0	NUM
ejpam-1889	72	7	0	0	NUM
ejpam-1889	72	8	0	0	NUM
ejpam-1889	73	1	x1	x1	NOUN
ejpam-1889	73	2	0	0	NUM
ejpam-1889	74	1	x3	x3	ADJ
ejpam-1889	74	2	x2	x2	NOUN
ejpam-1889	74	3	x3	x3	ADJ
ejpam-1889	74	4	0	0	PUNCT
ejpam-1889	75	1			PROPN
ejpam-1889	75	2			PROPN
ejpam-1889	75	3	:	:	PUNCT
ejpam-1889	75	4	x1	x1	NUM
ejpam-1889	75	5	,	,	PUNCT
ejpam-1889	75	6	x2	x2	PROPN
ejpam-1889	75	7	,	,	PUNCT
ejpam-1889	75	8	x3	x3	PROPN
ejpam-1889	75	9	∈	∈	PROPN
ejpam-1889	75	10	r	r	NOUN
ejpam-1889	75	11			PROPN
ejpam-1889	75	12			PROPN
ejpam-1889	75	13			NOUN
ejpam-1889	75	14	has	have	VERB
ejpam-1889	75	15	standard	standard	ADJ
ejpam-1889	75	16	basis	basis	NOUN
ejpam-1889	75	17	e1	e1	NOUN
ejpam-1889	75	18	=	=	PUNCT
ejpam-1889	75	19			PROPN
ejpam-1889	75	20			NOUN
ejpam-1889	75	21	0	0	NUM
ejpam-1889	76	1	0	0	NUM
ejpam-1889	76	2	0	0	NUM
ejpam-1889	76	3	1	1	NUM
ejpam-1889	76	4	0	0	NUM
ejpam-1889	76	5	0	0	NUM
ejpam-1889	76	6	0	0	NUM
ejpam-1889	76	7	0	0	NUM
ejpam-1889	76	8	0	0	NUM
ejpam-1889	76	9			PROPN
ejpam-1889	76	10			PROPN
ejpam-1889	76	11	,	,	PUNCT
ejpam-1889	76	12	e2	e2	NOUN
ejpam-1889	76	13	=	=	PUNCT
ejpam-1889	76	14			PROPN
ejpam-1889	76	15			NOUN
ejpam-1889	76	16	0	0	NUM
ejpam-1889	76	17	0	0	NUM
ejpam-1889	76	18	0	0	NUM
ejpam-1889	76	19	0	0	NUM
ejpam-1889	76	20	0	0	NUM
ejpam-1889	76	21	0	0	NUM
ejpam-1889	76	22	1	1	NUM
ejpam-1889	76	23	0	0	NUM
ejpam-1889	76	24	0	0	NUM
ejpam-1889	76	25			PROPN
ejpam-1889	76	26			PROPN
ejpam-1889	76	27	,	,	PUNCT
ejpam-1889	76	28	e3	e3	NOUN
ejpam-1889	76	29	=	=	SYM
ejpam-1889	76	30			NOUN
ejpam-1889	76	31			NOUN
ejpam-1889	76	32	0	0	NUM
ejpam-1889	76	33	0	0	NUM
ejpam-1889	76	34	0	0	NUM
ejpam-1889	76	35	0	0	NUM
ejpam-1889	76	36	0	0	NUM
ejpam-1889	76	37	1	1	NUM
ejpam-1889	76	38	0	0	NUM
ejpam-1889	76	39	1	1	NUM
ejpam-1889	76	40	0	0	NUM
ejpam-1889	76	41			PROPN
ejpam-1889	76	42			PROPN
ejpam-1889	76	43	.	.	PUNCT
ejpam-1889	77	1	the	the	DET
ejpam-1889	77	2	commutator	commutator	NOUN
ejpam-1889	77	3	relations	relation	NOUN
ejpam-1889	77	4	are	be	AUX
ejpam-1889	77	5	given	give	VERB
ejpam-1889	77	6	by	by	ADP
ejpam-1889	77	7	[	[	X
ejpam-1889	77	8	e2	e2	PROPN
ejpam-1889	77	9	,	,	PUNCT
ejpam-1889	77	10	e3	e3	NOUN
ejpam-1889	77	11	]	]	X
ejpam-1889	77	12	=	=	SYM
ejpam-1889	77	13	−e1	−e1	PROPN
ejpam-1889	77	14	,	,	PUNCT
ejpam-1889	77	15	[	[	X
ejpam-1889	77	16	e3	e3	NOUN
ejpam-1889	77	17	,	,	PUNCT
ejpam-1889	77	18	e1	e1	NOUN
ejpam-1889	77	19	]	]	PUNCT
ejpam-1889	77	20	=	=	SYM
ejpam-1889	77	21	e2	e2	PROPN
ejpam-1889	77	22	,	,	PUNCT
ejpam-1889	77	23	[	[	X
ejpam-1889	77	24	e1	e1	NOUN
ejpam-1889	77	25	,	,	PUNCT
ejpam-1889	77	26	e2	e2	X
ejpam-1889	77	27	]	]	PUNCT
ejpam-1889	77	28	=	=	SYM
ejpam-1889	78	1	0	0	X
ejpam-1889	78	2	.	.	PUNCT
ejpam-1889	78	3	remark	remark	PROPN
ejpam-1889	78	4	.	.	PUNCT
ejpam-1889	79	1	se(1,1	se(1,1	NOUN
ejpam-1889	79	2	)	)	PUNCT
ejpam-1889	79	3	is	be	AUX
ejpam-1889	79	4	the	the	DET
ejpam-1889	79	5	lie	lie	NOUN
ejpam-1889	79	6	algebra	algebra	NOUN
ejpam-1889	79	7	of	of	ADP
ejpam-1889	79	8	the	the	DET
ejpam-1889	79	9	semi	semi	ADJ
ejpam-1889	79	10	-	-	ADJ
ejpam-1889	79	11	euclidean	euclidean	ADJ
ejpam-1889	79	12	group	group	NOUN
ejpam-1889	79	13	.	.	PUNCT
ejpam-1889	80	1	this	this	DET
ejpam-1889	80	2	matrix	matrix	NOUN
ejpam-1889	80	3	lie	lie	NOUN
ejpam-1889	80	4	group	group	NOUN
ejpam-1889	80	5	is	be	AUX
ejpam-1889	80	6	the	the	DET
ejpam-1889	80	7	group	group	NOUN
ejpam-1889	80	8	of	of	ADP
ejpam-1889	80	9	motions	motion	NOUN
ejpam-1889	80	10	of	of	ADP
ejpam-1889	80	11	the	the	DET
ejpam-1889	80	12	minkowski	minkowski	ADJ
ejpam-1889	80	13	plane	plane	NOUN
ejpam-1889	80	14	r1,1	r1,1	NOUN
ejpam-1889	80	15	.	.	PUNCT
ejpam-1889	81	1	the	the	DET
ejpam-1889	81	2	signature	signature	NOUN
ejpam-1889	81	3	(	(	PUNCT
ejpam-1889	81	4	−1	−1	NOUN
ejpam-1889	81	5	,	,	PUNCT
ejpam-1889	81	6	1	1	NUM
ejpam-1889	81	7	)	)	PUNCT
ejpam-1889	81	8	for	for	ADP
ejpam-1889	81	9	the	the	DET
ejpam-1889	81	10	lorentz	lorentz	PROPN
ejpam-1889	81	11	metric	metric	ADJ
ejpam-1889	81	12	corresponds	correspond	NOUN
ejpam-1889	81	13	to	to	ADP
ejpam-1889	81	14	the	the	DET
ejpam-1889	81	15	standard	standard	ADJ
ejpam-1889	81	16	basis	basis	NOUN
ejpam-1889	81	17	(	(	PUNCT
ejpam-1889	81	18	e1	e1	PROPN
ejpam-1889	81	19	,	,	PUNCT
ejpam-1889	81	20	e2	e2	PROPN
ejpam-1889	81	21	,	,	PUNCT
ejpam-1889	81	22	e3	e3	NOUN
ejpam-1889	81	23	)	)	PUNCT
ejpam-1889	81	24	,	,	PUNCT
ejpam-1889	81	25	whereas	whereas	SCONJ
ejpam-1889	81	26	the	the	DET
ejpam-1889	81	27	signature	signature	NOUN
ejpam-1889	81	28	(	(	PUNCT
ejpam-1889	81	29	1,−1	1,−1	NUM
ejpam-1889	81	30	)	)	PUNCT
ejpam-1889	81	31	corresponds	correspond	VERB
ejpam-1889	81	32	to	to	ADP
ejpam-1889	81	33	the	the	DET
ejpam-1889	81	34	(	(	PUNCT
ejpam-1889	81	35	bianchi	bianchi	NOUN
ejpam-1889	81	36	-	-	PUNCT
ejpam-1889	81	37	behr	behr	NOUN
ejpam-1889	81	38	)	)	PUNCT
ejpam-1889	81	39	basis	basis	NOUN
ejpam-1889	81	40	(	(	PUNCT
ejpam-1889	81	41	e1	e1	NOUN
ejpam-1889	81	42	,	,	PUNCT
ejpam-1889	81	43	e2,−e3	e2,−e3	NUM
ejpam-1889	81	44	)	)	PUNCT
ejpam-1889	82	1	[	[	X
ejpam-1889	82	2	12–14	12–14	NUM
ejpam-1889	82	3	]	]	X
ejpam-1889	82	4	.	.	PUNCT
ejpam-1889	83	1	with	with	ADP
ejpam-1889	83	2	respect	respect	NOUN
ejpam-1889	83	3	to	to	ADP
ejpam-1889	83	4	the	the	DET
ejpam-1889	83	5	standard	standard	ADJ
ejpam-1889	83	6	basis	basis	NOUN
ejpam-1889	83	7	(	(	PUNCT
ejpam-1889	83	8	e1	e1	PROPN
ejpam-1889	83	9	,	,	PUNCT
ejpam-1889	83	10	e2	e2	PROPN
ejpam-1889	83	11	,	,	PUNCT
ejpam-1889	83	12	e3	e3	NOUN
ejpam-1889	83	13	)	)	PUNCT
ejpam-1889	83	14	,	,	PUNCT
ejpam-1889	83	15	the	the	DET
ejpam-1889	83	16	group	group	NOUN
ejpam-1889	83	17	of	of	ADP
ejpam-1889	83	18	automorphisms	automorphisms	PROPN
ejpam-1889	83	19	aut	aut	PROPN
ejpam-1889	83	20	(	(	PUNCT
ejpam-1889	83	21	se(1	se(1	PROPN
ejpam-1889	83	22	,	,	PUNCT
ejpam-1889	83	23	1	1	NUM
ejpam-1889	83	24	)	)	PUNCT
ejpam-1889	83	25	)	)	PUNCT
ejpam-1889	83	26	takes	take	VERB
ejpam-1889	83	27	the	the	DET
ejpam-1889	83	28	form	form	NOUN
ejpam-1889	83	29			NOUN
ejpam-1889	83	30			ADJ
ejpam-1889	83	31			ADJ
ejpam-1889	83	32			NOUN
ejpam-1889	83	33			NOUN
ejpam-1889	83	34	x	x	PUNCT
ejpam-1889	84	1	y	y	NOUN
ejpam-1889	84	2	v	v	INTJ
ejpam-1889	84	3	ςy	ςy	INTJ
ejpam-1889	84	4	ςx	ςx	INTJ
ejpam-1889	84	5	w	w	NOUN
ejpam-1889	84	6	0	0	NUM
ejpam-1889	84	7	0	0	NUM
ejpam-1889	84	8	ς	ς	PROPN
ejpam-1889	84	9			PROPN
ejpam-1889	84	10			PROPN
ejpam-1889	84	11	:	:	PUNCT
ejpam-1889	84	12	v	v	NOUN
ejpam-1889	84	13	,	,	PUNCT
ejpam-1889	84	14	w	w	PROPN
ejpam-1889	84	15	,	,	PUNCT
ejpam-1889	84	16	x	x	INTJ
ejpam-1889	84	17	,	,	PUNCT
ejpam-1889	84	18	y	y	PROPN
ejpam-1889	84	19	∈	∈	PROPN
ejpam-1889	84	20	r	r	NOUN
ejpam-1889	84	21	,	,	PUNCT
ejpam-1889	84	22	ς	ς	PROPN
ejpam-1889	84	23	∈	∈	PROPN
ejpam-1889	84	24	{	{	PUNCT
ejpam-1889	84	25	−1	−1	NOUN
ejpam-1889	84	26	,	,	PUNCT
ejpam-1889	84	27	1	1	NUM
ejpam-1889	84	28	}	}	PUNCT
ejpam-1889	84	29	,	,	PUNCT
ejpam-1889	84	30	x2	x2	PROPN
ejpam-1889	84	31	6=	6=	NUM
ejpam-1889	85	1	y2	y2	PROPN
ejpam-1889	85	2			PROPN
ejpam-1889	85	3			PROPN
ejpam-1889	85	4			NOUN
ejpam-1889	85	5	.	.	PUNCT
ejpam-1889	86	1	the	the	DET
ejpam-1889	86	2	subsets	subset	NOUN
ejpam-1889	86	3	〈	〈	PROPN
ejpam-1889	86	4	e1	e1	PROPN
ejpam-1889	86	5	,	,	PUNCT
ejpam-1889	86	6	e2	e2	NOUN
ejpam-1889	86	7	〉	〉	NOUN
ejpam-1889	86	8	and	and	CCONJ
ejpam-1889	86	9	〈	〈	NOUN
ejpam-1889	86	10	e1	e1	PROPN
ejpam-1889	86	11	+	+	CCONJ
ejpam-1889	86	12	e2	e2	X
ejpam-1889	86	13	〉	〉	NOUN
ejpam-1889	86	14	∪	∪	X
ejpam-1889	86	15	〈	〈	NOUN
ejpam-1889	86	16	e1	e1	PROPN
ejpam-1889	86	17	−	−	PROPN
ejpam-1889	86	18	e2	e2	PROPN
ejpam-1889	86	19	〉	〉	NOUN
ejpam-1889	86	20	are	be	AUX
ejpam-1889	86	21	invariant	invariant	ADJ
ejpam-1889	86	22	.	.	PUNCT
ejpam-1889	87	1	we	we	PRON
ejpam-1889	87	2	now	now	ADV
ejpam-1889	87	3	classify	classify	VERB
ejpam-1889	87	4	,	,	PUNCT
ejpam-1889	87	5	under	under	ADP
ejpam-1889	87	6	l	l	NOUN
ejpam-1889	87	7	-	-	NOUN
ejpam-1889	87	8	equivalence	equivalence	NOUN
ejpam-1889	87	9	(	(	PUNCT
ejpam-1889	87	10	resp	resp	NOUN
ejpam-1889	87	11	.	.	PUNCT
ejpam-1889	88	1	p	p	X
ejpam-1889	88	2	-	-	PUNCT
ejpam-1889	88	3	equivalence	equivalence	NOUN
ejpam-1889	88	4	)	)	PUNCT
ejpam-1889	88	5	,	,	PUNCT
ejpam-1889	88	6	all	all	DET
ejpam-1889	88	7	full	full	ADJ
ejpam-1889	88	8	-	-	PUNCT
ejpam-1889	88	9	rank	rank	NOUN
ejpam-1889	88	10	affine	affine	NOUN
ejpam-1889	88	11	subspaces	subspace	NOUN
ejpam-1889	88	12	(	(	PUNCT
ejpam-1889	88	13	resp	resp	NOUN
ejpam-1889	88	14	.	.	PUNCT
ejpam-1889	89	1	parametrized	parametrized	ADJ
ejpam-1889	89	2	affine	affine	NOUN
ejpam-1889	89	3	subspaces	subspace	NOUN
ejpam-1889	89	4	)	)	PUNCT
ejpam-1889	89	5	of	of	ADP
ejpam-1889	89	6	se(1	se(1	PROPN
ejpam-1889	89	7	,	,	PUNCT
ejpam-1889	89	8	1	1	NUM
ejpam-1889	89	9	)	)	PUNCT
ejpam-1889	89	10	.	.	PUNCT
ejpam-1889	90	1	we	we	PRON
ejpam-1889	90	2	outline	outline	VERB
ejpam-1889	90	3	the	the	DET
ejpam-1889	90	4	approach	approach	NOUN
ejpam-1889	90	5	followed	follow	VERB
ejpam-1889	90	6	in	in	ADP
ejpam-1889	90	7	classifying	classify	VERB
ejpam-1889	90	8	these	these	DET
ejpam-1889	90	9	objects	object	NOUN
ejpam-1889	90	10	.	.	PUNCT
ejpam-1889	91	1	first	first	ADV
ejpam-1889	91	2	,	,	PUNCT
ejpam-1889	91	3	we	we	PRON
ejpam-1889	91	4	distinguish	distinguish	VERB
ejpam-1889	91	5	between	between	ADP
ejpam-1889	91	6	the	the	DET
ejpam-1889	91	7	dimension	dimension	NOUN
ejpam-1889	91	8	and	and	CCONJ
ejpam-1889	91	9	the	the	DET
ejpam-1889	91	10	homogeneity	homogeneity	NOUN
ejpam-1889	91	11	of	of	ADP
ejpam-1889	91	12	the	the	DET
ejpam-1889	91	13	affine	affine	NOUN
ejpam-1889	91	14	subspaces	subspace	NOUN
ejpam-1889	91	15	;	;	PUNCT
ejpam-1889	91	16	this	this	PRON
ejpam-1889	91	17	yields	yield	VERB
ejpam-1889	91	18	four	four	NUM
ejpam-1889	91	19	types	type	NOUN
ejpam-1889	91	20	of	of	ADP
ejpam-1889	91	21	affine	affine	NOUN
ejpam-1889	91	22	subspaces	subspace	NOUN
ejpam-1889	91	23	.	.	PUNCT
ejpam-1889	92	1	the	the	DET
ejpam-1889	92	2	invariant	invariant	ADJ
ejpam-1889	92	3	subsets	subset	NOUN
ejpam-1889	92	4	allow	allow	VERB
ejpam-1889	92	5	us	we	PRON
ejpam-1889	92	6	to	to	PART
ejpam-1889	92	7	distinguish	distinguish	VERB
ejpam-1889	92	8	between	between	ADP
ejpam-1889	92	9	various	various	ADJ
ejpam-1889	92	10	(	(	PUNCT
ejpam-1889	92	11	families	family	NOUN
ejpam-1889	92	12	of	of	ADP
ejpam-1889	92	13	)	)	PUNCT
ejpam-1889	92	14	equivalence	equivalence	NOUN
ejpam-1889	92	15	classes	class	NOUN
ejpam-1889	92	16	.	.	PUNCT
ejpam-1889	93	1	in	in	ADP
ejpam-1889	93	2	each	each	DET
ejpam-1889	93	3	case	case	NOUN
ejpam-1889	93	4	,	,	PUNCT
ejpam-1889	93	5	we	we	PRON
ejpam-1889	93	6	simplify	simplify	VERB
ejpam-1889	93	7	an	an	DET
ejpam-1889	93	8	arbitrary	arbitrary	ADJ
ejpam-1889	93	9	affine	affine	NOUN
ejpam-1889	93	10	subspace	subspace	NOUN
ejpam-1889	93	11	(	(	PUNCT
ejpam-1889	93	12	resp	resp	NOUN
ejpam-1889	93	13	.	.	PUNCT
ejpam-1889	94	1	parametrized	parametrized	ADJ
ejpam-1889	94	2	affine	affine	NOUN
ejpam-1889	94	3	subspace	subspace	NOUN
ejpam-1889	94	4	)	)	PUNCT
ejpam-1889	94	5	by	by	ADP
ejpam-1889	94	6	successively	successively	ADV
ejpam-1889	94	7	applying	apply	VERB
ejpam-1889	94	8	automorphisms	automorphism	NOUN
ejpam-1889	94	9	.	.	PUNCT
ejpam-1889	95	1	finally	finally	ADV
ejpam-1889	95	2	,	,	PUNCT
ejpam-1889	95	3	we	we	PRON
ejpam-1889	95	4	verify	verify	VERB
ejpam-1889	95	5	that	that	SCONJ
ejpam-1889	95	6	all	all	DET
ejpam-1889	95	7	the	the	DET
ejpam-1889	95	8	candidates	candidate	NOUN
ejpam-1889	95	9	for	for	ADP
ejpam-1889	95	10	class	class	NOUN
ejpam-1889	95	11	representatives	representative	NOUN
ejpam-1889	95	12	are	be	AUX
ejpam-1889	95	13	distinct	distinct	ADJ
ejpam-1889	95	14	and	and	CCONJ
ejpam-1889	95	15	not	not	PART
ejpam-1889	95	16	equivalent	equivalent	ADJ
ejpam-1889	95	17	.	.	PUNCT
ejpam-1889	96	1	families	family	NOUN
ejpam-1889	96	2	of	of	ADP
ejpam-1889	96	3	representatives	representative	NOUN
ejpam-1889	96	4	are	be	AUX
ejpam-1889	96	5	typically	typically	ADV
ejpam-1889	96	6	parametrized	parametrize	VERB
ejpam-1889	96	7	by	by	ADP
ejpam-1889	96	8	constants	constant	NOUN
ejpam-1889	96	9	α	α	PROPN
ejpam-1889	96	10	>	>	X
ejpam-1889	96	11	0	0	PROPN
ejpam-1889	96	12	,	,	PUNCT
ejpam-1889	96	13	β	β	X
ejpam-1889	96	14	=	=	SYM
ejpam-1889	96	15	(	(	PUNCT
ejpam-1889	96	16	βi	βi	NOUN
ejpam-1889	96	17	)	)	PUNCT
ejpam-1889	96	18	and	and	CCONJ
ejpam-1889	96	19	γ=	γ=	PROPN
ejpam-1889	96	20	(	(	PUNCT
ejpam-1889	96	21	γi	γi	INTJ
ejpam-1889	96	22	)	)	PUNCT
ejpam-1889	96	23	,	,	PUNCT
ejpam-1889	96	24	where	where	SCONJ
ejpam-1889	96	25	βi	βi	X
ejpam-1889	96	26	6=	6=	NUM
ejpam-1889	96	27	0	0	NUM
ejpam-1889	96	28	,	,	PUNCT
ejpam-1889	96	29	γi	γi	PROPN
ejpam-1889	96	30	∈	∈	PROPN
ejpam-1889	96	31	r.	r.	PROPN
ejpam-1889	96	32	remark	remark	PROPN
ejpam-1889	96	33	.	.	PUNCT
ejpam-1889	97	1	on	on	ADP
ejpam-1889	97	2	se(1,1	se(1,1	NOUN
ejpam-1889	97	3	)	)	PUNCT
ejpam-1889	97	4	(	(	PUNCT
ejpam-1889	97	5	in	in	ADP
ejpam-1889	97	6	fact	fact	NOUN
ejpam-1889	97	7	,	,	PUNCT
ejpam-1889	97	8	on	on	ADP
ejpam-1889	97	9	any	any	DET
ejpam-1889	97	10	three	three	NUM
ejpam-1889	97	11	-	-	PUNCT
ejpam-1889	97	12	dimensional	dimensional	ADJ
ejpam-1889	97	13	lie	lie	NOUN
ejpam-1889	97	14	algebra	algebra	NOUN
ejpam-1889	97	15	)	)	PUNCT
ejpam-1889	97	16	,	,	PUNCT
ejpam-1889	97	17	the	the	DET
ejpam-1889	97	18	full	full	ADJ
ejpam-1889	97	19	-	-	PUNCT
ejpam-1889	97	20	rank	rank	NOUN
ejpam-1889	97	21	condition	condition	NOUN
ejpam-1889	97	22	for	for	ADP
ejpam-1889	97	23	an	an	DET
ejpam-1889	97	24	affine	affine	NOUN
ejpam-1889	97	25	subspace	subspace	NOUN
ejpam-1889	97	26	(	(	PUNCT
ejpam-1889	97	27	2	2	X
ejpam-1889	97	28	)	)	PUNCT
ejpam-1889	97	29	can	can	AUX
ejpam-1889	97	30	be	be	AUX
ejpam-1889	97	31	characterized	characterize	VERB
ejpam-1889	97	32	as	as	SCONJ
ejpam-1889	97	33	follows	follow	VERB
ejpam-1889	97	34	.	.	PUNCT
ejpam-1889	98	1	no	no	DET
ejpam-1889	98	2	(	(	PUNCT
ejpam-1889	98	3	1	1	NUM
ejpam-1889	98	4	,	,	PUNCT
ejpam-1889	98	5	0)-affine	0)-affine	NUM
ejpam-1889	98	6	subspace	subspace	NOUN
ejpam-1889	98	7	has	have	VERB
ejpam-1889	98	8	full	full	ADJ
ejpam-1889	98	9	rank	rank	NOUN
ejpam-1889	98	10	.	.	PUNCT
ejpam-1889	99	1	a	a	DET
ejpam-1889	99	2	(	(	PUNCT
ejpam-1889	99	3	1,1)-affine	1,1)-affine	NUM
ejpam-1889	99	4	subspace	subspace	NOUN
ejpam-1889	99	5	has	have	VERB
ejpam-1889	99	6	full	full	ADJ
ejpam-1889	99	7	rank	rank	NOUN
ejpam-1889	99	8	if	if	SCONJ
ejpam-1889	100	1	and	and	CCONJ
ejpam-1889	100	2	only	only	ADV
ejpam-1889	100	3	if	if	SCONJ
ejpam-1889	100	4	a	a	PRON
ejpam-1889	100	5	,	,	PUNCT
ejpam-1889	100	6	b1	b1	NOUN
ejpam-1889	100	7	and	and	CCONJ
ejpam-1889	100	8	[	[	X
ejpam-1889	100	9	a	a	X
ejpam-1889	100	10	,	,	PUNCT
ejpam-1889	100	11	b1	b1	PROPN
ejpam-1889	100	12	]	]	PUNCT
ejpam-1889	100	13	are	be	AUX
ejpam-1889	100	14	linearly	linearly	ADV
ejpam-1889	100	15	independent	independent	ADJ
ejpam-1889	100	16	,	,	PUNCT
ejpam-1889	100	17	whereas	whereas	SCONJ
ejpam-1889	100	18	a	a	DET
ejpam-1889	100	19	(	(	PUNCT
ejpam-1889	100	20	2,0)-affine	2,0)-affine	NUM
ejpam-1889	100	21	subspace	subspace	NOUN
ejpam-1889	100	22	has	have	VERB
ejpam-1889	100	23	full	full	ADJ
ejpam-1889	100	24	rank	rank	NOUN
ejpam-1889	101	1	if	if	SCONJ
ejpam-1889	101	2	and	and	CCONJ
ejpam-1889	101	3	only	only	ADV
ejpam-1889	101	4	if	if	SCONJ
ejpam-1889	101	5	b1	b1	NOUN
ejpam-1889	101	6	,	,	PUNCT
ejpam-1889	101	7	b2	b2	NOUN
ejpam-1889	101	8	and	and	CCONJ
ejpam-1889	101	9	[	[	X
ejpam-1889	101	10	b1	b1	NOUN
ejpam-1889	101	11	,	,	PUNCT
ejpam-1889	101	12	b2	b2	NOUN
ejpam-1889	101	13	]	]	PUNCT
ejpam-1889	101	14	are	be	AUX
ejpam-1889	101	15	linearly	linearly	ADV
ejpam-1889	101	16	independent	independent	ADJ
ejpam-1889	101	17	.	.	PUNCT
ejpam-1889	102	1	also	also	ADV
ejpam-1889	102	2	,	,	PUNCT
ejpam-1889	102	3	it	it	PRON
ejpam-1889	102	4	is	be	AUX
ejpam-1889	102	5	clear	clear	ADJ
ejpam-1889	102	6	that	that	SCONJ
ejpam-1889	102	7	any	any	DET
ejpam-1889	102	8	(	(	PUNCT
ejpam-1889	102	9	2,1)-affine	2,1)-affine	NUM
ejpam-1889	102	10	subspace	subspace	NOUN
ejpam-1889	102	11	or	or	CCONJ
ejpam-1889	102	12	(	(	PUNCT
ejpam-1889	102	13	3	3	NUM
ejpam-1889	102	14	,	,	PUNCT
ejpam-1889	102	15	0)-affine	0)-affine	NUM
ejpam-1889	102	16	subspace	subspace	NOUN
ejpam-1889	102	17	has	have	VERB
ejpam-1889	102	18	full	full	ADJ
ejpam-1889	102	19	rank	rank	NOUN
ejpam-1889	102	20	.	.	PUNCT
ejpam-1889	103	1	d.	d.	PROPN
ejpam-1889	103	2	barrett	barrett	PROPN
ejpam-1889	103	3	,	,	PUNCT
ejpam-1889	103	4	r.	r.	PROPN
ejpam-1889	103	5	biggs	biggs	PROPN
ejpam-1889	103	6	,	,	PUNCT
ejpam-1889	103	7	c.	c.	PROPN
ejpam-1889	103	8	remsing	remsing	NOUN
ejpam-1889	103	9	/	/	SYM
ejpam-1889	103	10	eur	eur	NOUN
ejpam-1889	103	11	.	.	PUNCT
ejpam-1889	104	1	j.	j.	PROPN
ejpam-1889	104	2	pure	pure	PROPN
ejpam-1889	104	3	appl	appl	PROPN
ejpam-1889	104	4	.	.	PROPN
ejpam-1889	104	5	math	math	PROPN
ejpam-1889	104	6	,	,	PUNCT
ejpam-1889	104	7	7	7	NUM
ejpam-1889	104	8	(	(	PUNCT
ejpam-1889	104	9	2014	2014	NUM
ejpam-1889	104	10	)	)	PUNCT
ejpam-1889	104	11	,	,	PUNCT
ejpam-1889	104	12	140	140	NUM
ejpam-1889	104	13	-	-	SYM
ejpam-1889	104	14	155	155	NUM
ejpam-1889	104	15	143	143	NUM
ejpam-1889	104	16	3.1	3.1	NUM
ejpam-1889	104	17	.	.	PUNCT
ejpam-1889	104	18	affine	affine	NOUN
ejpam-1889	104	19	subspaces	subspace	NOUN
ejpam-1889	104	20	we	we	PRON
ejpam-1889	104	21	begin	begin	VERB
ejpam-1889	104	22	by	by	ADP
ejpam-1889	104	23	classifying	classify	VERB
ejpam-1889	104	24	the	the	DET
ejpam-1889	104	25	affine	affine	NOUN
ejpam-1889	104	26	subspaces	subspace	NOUN
ejpam-1889	104	27	of	of	ADP
ejpam-1889	104	28	se(1,1	se(1,1	NOUN
ejpam-1889	104	29	)	)	PUNCT
ejpam-1889	104	30	.	.	PUNCT
ejpam-1889	105	1	such	such	DET
ejpam-1889	105	2	a	a	DET
ejpam-1889	105	3	classification	classification	NOUN
ejpam-1889	105	4	has	have	AUX
ejpam-1889	105	5	been	be	AUX
ejpam-1889	105	6	obtained	obtain	VERB
ejpam-1889	105	7	elsewhere	elsewhere	ADV
ejpam-1889	105	8	[	[	X
ejpam-1889	105	9	7	7	NUM
ejpam-1889	105	10	]	]	PUNCT
ejpam-1889	105	11	.	.	PUNCT
ejpam-1889	106	1	however	however	ADV
ejpam-1889	106	2	,	,	PUNCT
ejpam-1889	106	3	for	for	ADP
ejpam-1889	106	4	the	the	DET
ejpam-1889	106	5	sake	sake	NOUN
ejpam-1889	106	6	of	of	ADP
ejpam-1889	106	7	completeness	completeness	NOUN
ejpam-1889	106	8	,	,	PUNCT
ejpam-1889	106	9	we	we	PRON
ejpam-1889	106	10	include	include	VERB
ejpam-1889	106	11	full	full	ADJ
ejpam-1889	106	12	proofs	proof	NOUN
ejpam-1889	106	13	here	here	ADV
ejpam-1889	106	14	.	.	PUNCT
ejpam-1889	107	1	we	we	PRON
ejpam-1889	107	2	denote	denote	VERB
ejpam-1889	107	3	by	by	ADP
ejpam-1889	107	4	e∗3	e∗3	NOUN
ejpam-1889	107	5	the	the	DET
ejpam-1889	107	6	corresponding	correspond	VERB
ejpam-1889	107	7	element	element	NOUN
ejpam-1889	107	8	of	of	ADP
ejpam-1889	107	9	the	the	DET
ejpam-1889	107	10	dual	dual	ADJ
ejpam-1889	107	11	basis	basis	NOUN
ejpam-1889	107	12	.	.	PUNCT
ejpam-1889	108	1	theorem	theorem	NOUN
ejpam-1889	108	2	1	1	NUM
ejpam-1889	108	3	.	.	PUNCT
ejpam-1889	109	1	any	any	DET
ejpam-1889	109	2	(	(	PUNCT
ejpam-1889	109	3	1	1	NUM
ejpam-1889	109	4	,	,	PUNCT
ejpam-1889	109	5	1)-affine	1)-affine	NUM
ejpam-1889	109	6	subspace	subspace	NOUN
ejpam-1889	109	7	γ	γ	X
ejpam-1889	109	8	=	=	PUNCT
ejpam-1889	109	9	a+γ0	a+γ0	PROPN
ejpam-1889	109	10	is	be	AUX
ejpam-1889	109	11	l	l	NOUN
ejpam-1889	109	12	-	-	NOUN
ejpam-1889	109	13	equivalent	equivalent	ADJ
ejpam-1889	109	14	to	to	ADP
ejpam-1889	109	15	exactly	exactly	ADV
ejpam-1889	109	16	one	one	NUM
ejpam-1889	109	17	of	of	ADP
ejpam-1889	109	18	the	the	DET
ejpam-1889	109	19	following	follow	VERB
ejpam-1889	109	20	affine	affine	NOUN
ejpam-1889	109	21	subspaces	subspace	NOUN
ejpam-1889	109	22	¨	¨	NOUN
ejpam-1889	109	23	γ(1,1	γ(1,1	NOUN
ejpam-1889	109	24	)	)	PUNCT
ejpam-1889	109	25	1	1	NUM
ejpam-1889	109	26	=	=	NOUN
ejpam-1889	109	27	e1	e1	PROPN
ejpam-1889	109	28	+	+	CCONJ
ejpam-1889	109	29	〈	〈	NOUN
ejpam-1889	109	30	e3	e3	NOUN
ejpam-1889	109	31	〉	〉	NOUN
ejpam-1889	109	32	e∗3(γ	e∗3(γ	PROPN
ejpam-1889	109	33	0	0	NUM
ejpam-1889	109	34	)	)	PUNCT
ejpam-1889	109	35	6=	6=	ADP
ejpam-1889	109	36	{	{	PUNCT
ejpam-1889	109	37	0	0	NUM
ejpam-1889	109	38	}	}	PUNCT
ejpam-1889	109	39	γ(1,1	γ(1,1	NOUN
ejpam-1889	109	40	)	)	PUNCT
ejpam-1889	109	41	2,α	2,α	NOUN
ejpam-1889	109	42	=	=	SYM
ejpam-1889	109	43	αe3	αe3	NOUN
ejpam-1889	109	44	+	+	CCONJ
ejpam-1889	109	45	〈	〈	NOUN
ejpam-1889	109	46	e1	e1	NOUN
ejpam-1889	109	47	〉	〉	NOUN
ejpam-1889	109	48	e∗3(γ	e∗3(γ	PROPN
ejpam-1889	109	49	0	0	NUM
ejpam-1889	109	50	)	)	PUNCT
ejpam-1889	109	51	=	=	PRON
ejpam-1889	109	52	{	{	PUNCT
ejpam-1889	109	53	0	0	NUM
ejpam-1889	109	54	}	}	PUNCT
ejpam-1889	109	55	.	.	PUNCT
ejpam-1889	110	1	here	here	ADV
ejpam-1889	110	2	α	α	X
ejpam-1889	110	3	>	>	X
ejpam-1889	110	4	0	0	NUM
ejpam-1889	110	5	,	,	PUNCT
ejpam-1889	110	6	with	with	ADP
ejpam-1889	110	7	different	different	ADJ
ejpam-1889	110	8	values	value	NOUN
ejpam-1889	110	9	of	of	ADP
ejpam-1889	110	10	the	the	DET
ejpam-1889	110	11	parameter	parameter	NOUN
ejpam-1889	110	12	yielding	yield	VERB
ejpam-1889	110	13	distinct	distinct	ADJ
ejpam-1889	110	14	(	(	PUNCT
ejpam-1889	110	15	non	non	ADJ
ejpam-1889	110	16	-	-	ADJ
ejpam-1889	110	17	equivalent	equivalent	ADJ
ejpam-1889	110	18	)	)	PUNCT
ejpam-1889	110	19	class	class	NOUN
ejpam-1889	110	20	representatives	representative	NOUN
ejpam-1889	110	21	.	.	PUNCT
ejpam-1889	111	1	proof	proof	NOUN
ejpam-1889	111	2	.	.	PUNCT
ejpam-1889	112	1	suppose	suppose	VERB
ejpam-1889	112	2	that	that	SCONJ
ejpam-1889	112	3	e∗3(γ	e∗3(γ	PROPN
ejpam-1889	112	4	0	0	NUM
ejpam-1889	112	5	)	)	PUNCT
ejpam-1889	112	6	6=	6=	ADP
ejpam-1889	112	7	{	{	PUNCT
ejpam-1889	112	8	0	0	NUM
ejpam-1889	112	9	}	}	PUNCT
ejpam-1889	112	10	.	.	PUNCT
ejpam-1889	113	1	then	then	ADV
ejpam-1889	113	2	γ	γ	X
ejpam-1889	113	3	=	=	SYM
ejpam-1889	113	4	a1e1	a1e1	PROPN
ejpam-1889	113	5	+	+	CCONJ
ejpam-1889	113	6	a2e2	a2e2	PROPN
ejpam-1889	113	7	+	+	NUM
ejpam-1889	113	8	〈	〈	PROPN
ejpam-1889	113	9	b1e1	b1e1	NOUN
ejpam-1889	113	10	+	+	CCONJ
ejpam-1889	113	11	b2e2	b2e2	PROPN
ejpam-1889	113	12	+	+	NOUN
ejpam-1889	113	13	e3	e3	VERB
ejpam-1889	113	14	〉	〉	NOUN
ejpam-1889	113	15	and	and	CCONJ
ejpam-1889	113	16			NOUN
ejpam-1889	113	17			PROPN
ejpam-1889	113	18			NUM
ejpam-1889	113	19	a1	a1	NOUN
ejpam-1889	113	20	a2	a2	PROPN
ejpam-1889	113	21	1−a2	1−a2	NUM
ejpam-1889	113	22	2	2	NUM
ejpam-1889	113	23	−	−	PROPN
ejpam-1889	113	24	a2	a2	PROPN
ejpam-1889	113	25	a2	a2	PROPN
ejpam-1889	113	26	1−a2	1−a2	NUM
ejpam-1889	113	27	2	2	NUM
ejpam-1889	113	28	0	0	NUM
ejpam-1889	113	29	−	−	PROPN
ejpam-1889	113	30	a2	a2	PROPN
ejpam-1889	113	31	a2	a2	PROPN
ejpam-1889	113	32	1−a2	1−a2	NUM
ejpam-1889	113	33	2	2	NUM
ejpam-1889	113	34	a1	a1	NOUN
ejpam-1889	113	35	a2	a2	PROPN
ejpam-1889	113	36	1−a2	1−a2	NUM
ejpam-1889	113	37	2	2	NUM
ejpam-1889	113	38	0	0	NUM
ejpam-1889	113	39	0	0	NUM
ejpam-1889	113	40	0	0	NUM
ejpam-1889	113	41	1	1	NUM
ejpam-1889	113	42			PROPN
ejpam-1889	113	43			PROPN
ejpam-1889	113	44			PROPN
ejpam-1889	113	45			NOUN
ejpam-1889	113	46			VERB
ejpam-1889	113	47	1	1	NUM
ejpam-1889	113	48	0	0	NUM
ejpam-1889	113	49	−b1	−b1	NOUN
ejpam-1889	113	50	0	0	NUM
ejpam-1889	113	51	1	1	NUM
ejpam-1889	113	52	−b2	−b2	NUM
ejpam-1889	113	53	0	0	NUM
ejpam-1889	113	54	0	0	NUM
ejpam-1889	113	55	1	1	NUM
ejpam-1889	113	56			PROPN
ejpam-1889	113	57			PROPN
ejpam-1889	113	58	·	·	PUNCT
ejpam-1889	113	59	γ	γ	X
ejpam-1889	113	60	=	=	SYM
ejpam-1889	113	61	e1	e1	PROPN
ejpam-1889	113	62	+	+	CCONJ
ejpam-1889	113	63	〈	〈	PROPN
ejpam-1889	113	64	e3〉=	e3〉=	PROPN
ejpam-1889	113	65	γ	γ	X
ejpam-1889	113	66	(	(	PUNCT
ejpam-1889	113	67	1,1	1,1	NUM
ejpam-1889	113	68	)	)	PUNCT
ejpam-1889	113	69	1	1	NUM
ejpam-1889	113	70	;	;	PUNCT
ejpam-1889	113	71	as	as	SCONJ
ejpam-1889	113	72	γ	γ	PROPN
ejpam-1889	113	73	has	have	VERB
ejpam-1889	113	74	full	full	ADJ
ejpam-1889	113	75	rank	rank	NOUN
ejpam-1889	113	76	,	,	PUNCT
ejpam-1889	113	77	we	we	PRON
ejpam-1889	113	78	have	have	VERB
ejpam-1889	113	79	a2	a2	PROPN
ejpam-1889	113	80	1	1	NUM
ejpam-1889	113	81	6=	6=	NUM
ejpam-1889	113	82	a2	a2	PROPN
ejpam-1889	113	83	2	2	NUM
ejpam-1889	113	84	.	.	PUNCT
ejpam-1889	114	1	thus	thus	ADV
ejpam-1889	114	2	γ	γ	X
ejpam-1889	114	3	is	be	AUX
ejpam-1889	114	4	l	l	NOUN
ejpam-1889	114	5	-	-	ADJ
ejpam-1889	114	6	equivalent	equivalent	ADJ
ejpam-1889	114	7	to	to	ADP
ejpam-1889	114	8	γ(1,1	γ(1,1	VERB
ejpam-1889	114	9	)	)	PUNCT
ejpam-1889	114	10	1	1	NUM
ejpam-1889	114	11	.	.	PUNCT
ejpam-1889	115	1	suppose	suppose	VERB
ejpam-1889	115	2	e∗3(γ	e∗3(γ	PROPN
ejpam-1889	115	3	0	0	NUM
ejpam-1889	115	4	)	)	PUNCT
ejpam-1889	115	5	=	=	PRON
ejpam-1889	115	6	{	{	PUNCT
ejpam-1889	115	7	0	0	NUM
ejpam-1889	115	8	}	}	PUNCT
ejpam-1889	115	9	.	.	PUNCT
ejpam-1889	116	1	then	then	ADV
ejpam-1889	116	2	γ	γ	X
ejpam-1889	116	3	=	=	SYM
ejpam-1889	116	4	a1e1	a1e1	PROPN
ejpam-1889	116	5	+	+	PROPN
ejpam-1889	116	6	a2e2	a2e2	PROPN
ejpam-1889	117	1	+	+	NUM
ejpam-1889	117	2	a3e3	a3e3	PROPN
ejpam-1889	117	3	+	+	CCONJ
ejpam-1889	117	4	〈	〈	ADJ
ejpam-1889	117	5	b1e1	b1e1	NOUN
ejpam-1889	117	6	+	+	CCONJ
ejpam-1889	117	7	b2e2	b2e2	PROPN
ejpam-1889	117	8	〉	〉	NOUN
ejpam-1889	117	9	and	and	CCONJ
ejpam-1889	117	10			NOUN
ejpam-1889	117	11			PROPN
ejpam-1889	117	12			NUM
ejpam-1889	117	13	b1	b1	NOUN
ejpam-1889	117	14	b2	b2	NOUN
ejpam-1889	117	15	1−b2	1−b2	NUM
ejpam-1889	117	16	2	2	NUM
ejpam-1889	117	17	−	−	NOUN
ejpam-1889	117	18	b2	b2	NOUN
ejpam-1889	117	19	b2	b2	NOUN
ejpam-1889	117	20	1−b2	1−b2	NUM
ejpam-1889	117	21	2	2	NUM
ejpam-1889	117	22	0	0	NUM
ejpam-1889	117	23	−	−	PROPN
ejpam-1889	117	24	sgn(a3)b2	sgn(a3)b2	NOUN
ejpam-1889	117	25	b2	b2	NOUN
ejpam-1889	117	26	1−b2	1−b2	NUM
ejpam-1889	117	27	2	2	NUM
ejpam-1889	117	28	sgn(a3)b1	sgn(a3)b1	NOUN
ejpam-1889	117	29	b2	b2	NOUN
ejpam-1889	117	30	1−b2	1−b2	NUM
ejpam-1889	117	31	2	2	NUM
ejpam-1889	117	32	0	0	NUM
ejpam-1889	117	33	0	0	NUM
ejpam-1889	117	34	0	0	NUM
ejpam-1889	117	35	sgn(a3	sgn(a3	NOUN
ejpam-1889	117	36	)	)	PUNCT
ejpam-1889	117	37			PROPN
ejpam-1889	117	38			PROPN
ejpam-1889	117	39			PROPN
ejpam-1889	117	40			NOUN
ejpam-1889	117	41			VERB
ejpam-1889	117	42	1	1	NUM
ejpam-1889	117	43	0	0	NUM
ejpam-1889	117	44	−	−	NOUN
ejpam-1889	117	45	a1	a1	NOUN
ejpam-1889	117	46	a3	a3	NOUN
ejpam-1889	117	47	0	0	NUM
ejpam-1889	117	48	1	1	NUM
ejpam-1889	117	49	−	−	PROPN
ejpam-1889	117	50	a2	a2	PROPN
ejpam-1889	117	51	a3	a3	VERB
ejpam-1889	117	52	0	0	NUM
ejpam-1889	117	53	0	0	NUM
ejpam-1889	117	54	1	1	NUM
ejpam-1889	117	55			PROPN
ejpam-1889	117	56			PROPN
ejpam-1889	117	57	·	·	PUNCT
ejpam-1889	117	58	γ	γ	NOUN
ejpam-1889	117	59	=	=	PUNCT
ejpam-1889	117	60	|a3|e3	|a3|e3	NOUN
ejpam-1889	117	61	+	+	CCONJ
ejpam-1889	117	62	〈	〈	PROPN
ejpam-1889	117	63	e1〉=	e1〉=	PROPN
ejpam-1889	117	64	γ	γ	X
ejpam-1889	117	65	(	(	PUNCT
ejpam-1889	117	66	1,1	1,1	NUM
ejpam-1889	117	67	)	)	PUNCT
ejpam-1889	117	68	2,α	2,α	X
ejpam-1889	117	69	whereα=	whereα=	ADP
ejpam-1889	117	70	|a3|	|a3|	VERB
ejpam-1889	117	71	>	>	X
ejpam-1889	117	72	0	0	PUNCT
ejpam-1889	117	73	.	.	PUNCT
ejpam-1889	118	1	due	due	ADP
ejpam-1889	118	2	to	to	ADP
ejpam-1889	118	3	the	the	DET
ejpam-1889	118	4	full	full	ADJ
ejpam-1889	118	5	-	-	PUNCT
ejpam-1889	118	6	rank	rank	NOUN
ejpam-1889	118	7	assumption	assumption	NOUN
ejpam-1889	118	8	,	,	PUNCT
ejpam-1889	118	9	we	we	PRON
ejpam-1889	118	10	have	have	AUX
ejpam-1889	118	11	b2	b2	NOUN
ejpam-1889	118	12	1	1	NUM
ejpam-1889	118	13	6=	6=	NUM
ejpam-1889	118	14	b2	b2	NOUN
ejpam-1889	118	15	2	2	NUM
ejpam-1889	118	16	.	.	PUNCT
ejpam-1889	119	1	hence	hence	ADV
ejpam-1889	119	2	γ	γ	X
ejpam-1889	119	3	isl	isl	PROPN
ejpam-1889	119	4	-	-	PUNCT
ejpam-1889	119	5	equivalent	equivalent	NOUN
ejpam-1889	119	6	to	to	ADP
ejpam-1889	119	7	γ(1,1	γ(1,1	NOUN
ejpam-1889	119	8	)	)	PUNCT
ejpam-1889	119	9	2,α	2,α	NUM
ejpam-1889	119	10	.	.	PUNCT
ejpam-1889	120	1	as	as	ADP
ejpam-1889	120	2	〈	〈	PROPN
ejpam-1889	120	3	e1	e1	NOUN
ejpam-1889	120	4	,	,	PUNCT
ejpam-1889	120	5	e2	e2	PROPN
ejpam-1889	120	6	〉	〉	NOUN
ejpam-1889	120	7	is	be	AUX
ejpam-1889	120	8	an	an	DET
ejpam-1889	120	9	invariant	invariant	ADJ
ejpam-1889	120	10	subspace	subspace	NOUN
ejpam-1889	120	11	,	,	PUNCT
ejpam-1889	120	12	γ(1,1	γ(1,1	VERB
ejpam-1889	120	13	)	)	PUNCT
ejpam-1889	120	14	1	1	NUM
ejpam-1889	120	15	can	can	AUX
ejpam-1889	120	16	not	not	PART
ejpam-1889	120	17	be	be	AUX
ejpam-1889	120	18	l	l	NOUN
ejpam-1889	120	19	-	-	ADJ
ejpam-1889	120	20	equivalent	equivalent	ADJ
ejpam-1889	120	21	to	to	ADP
ejpam-1889	120	22	γ(1,1	γ(1,1	NOUN
ejpam-1889	120	23	)	)	PUNCT
ejpam-1889	120	24	2,α	2,α	NUM
ejpam-1889	120	25	.	.	PUNCT
ejpam-1889	121	1	it	it	PRON
ejpam-1889	121	2	is	be	AUX
ejpam-1889	121	3	easy	easy	ADJ
ejpam-1889	121	4	to	to	PART
ejpam-1889	121	5	show	show	VERB
ejpam-1889	121	6	that	that	SCONJ
ejpam-1889	121	7	γ(1,1	γ(1,1	NOUN
ejpam-1889	121	8	)	)	PUNCT
ejpam-1889	121	9	2,α	2,α	NOUN
ejpam-1889	121	10	and	and	CCONJ
ejpam-1889	121	11	γ(1,1	γ(1,1	NOUN
ejpam-1889	121	12	)	)	PUNCT
ejpam-1889	121	13	2,α′	2,α′	NUM
ejpam-1889	121	14	are	be	AUX
ejpam-1889	121	15	l	l	NOUN
ejpam-1889	121	16	-	-	NOUN
ejpam-1889	121	17	equivalent	equivalent	ADJ
ejpam-1889	121	18	only	only	ADV
ejpam-1889	121	19	if	if	SCONJ
ejpam-1889	121	20	α=	α=	NUM
ejpam-1889	121	21	α′.	α′.	NOUN
ejpam-1889	121	22	if	if	SCONJ
ejpam-1889	121	23	γ	γ	X
ejpam-1889	121	24	=	=	VERB
ejpam-1889	121	25	〈	〈	PROPN
ejpam-1889	121	26	a	a	NOUN
ejpam-1889	121	27	,	,	PUNCT
ejpam-1889	121	28	b	b	X
ejpam-1889	121	29	〉	〉	NOUN
ejpam-1889	121	30	is	be	AUX
ejpam-1889	121	31	a	a	DET
ejpam-1889	121	32	(	(	PUNCT
ejpam-1889	121	33	2	2	NUM
ejpam-1889	121	34	,	,	PUNCT
ejpam-1889	121	35	0)-affine	0)-affine	NUM
ejpam-1889	121	36	subspace	subspace	NOUN
ejpam-1889	121	37	,	,	PUNCT
ejpam-1889	121	38	then	then	ADV
ejpam-1889	121	39	a+	a+	PUNCT
ejpam-1889	121	40	〈	〈	PROPN
ejpam-1889	121	41	b	b	NOUN
ejpam-1889	121	42	〉	〉	NOUN
ejpam-1889	121	43	is	be	AUX
ejpam-1889	121	44	a	a	DET
ejpam-1889	121	45	(	(	PUNCT
ejpam-1889	121	46	1,1)-affine	1,1)-affine	NUM
ejpam-1889	121	47	subspace	subspace	NOUN
ejpam-1889	121	48	and	and	CCONJ
ejpam-1889	121	49	hence	hence	ADV
ejpam-1889	121	50	is	be	AUX
ejpam-1889	121	51	l	l	NOUN
ejpam-1889	121	52	-	-	ADJ
ejpam-1889	121	53	equivalent	equivalent	ADJ
ejpam-1889	121	54	to	to	ADP
ejpam-1889	121	55	either	either	DET
ejpam-1889	121	56	γ(1,1	γ(1,1	VERB
ejpam-1889	121	57	)	)	PUNCT
ejpam-1889	121	58	1	1	NUM
ejpam-1889	121	59	or	or	CCONJ
ejpam-1889	121	60	γ(1,1	γ(1,1	NOUN
ejpam-1889	121	61	)	)	PUNCT
ejpam-1889	121	62	2,α	2,α	NOUN
ejpam-1889	121	63	.	.	PUNCT
ejpam-1889	122	1	thus	thus	ADV
ejpam-1889	122	2	γ	γ	X
ejpam-1889	122	3	is	be	AUX
ejpam-1889	122	4	l	l	NOUN
ejpam-1889	122	5	-	-	ADJ
ejpam-1889	122	6	equivalent	equivalent	ADJ
ejpam-1889	122	7	to	to	ADP
ejpam-1889	122	8	γ(1,1	γ(1,1	VERB
ejpam-1889	122	9	)	)	PUNCT
ejpam-1889	122	10	1	1	NUM
ejpam-1889	122	11	�	�	NOUN
ejpam-1889	122	12	or	or	CCONJ
ejpam-1889	122	13	γ(1,1	γ(1,1	NOUN
ejpam-1889	122	14	)	)	PUNCT
ejpam-1889	122	15	2,α	2,α	PROPN
ejpam-1889	122	16	�	�	PROPN
ejpam-1889	122	17	.	.	PUNCT
ejpam-1889	123	1	accordingly	accordingly	ADV
ejpam-1889	123	2	,	,	PUNCT
ejpam-1889	123	3	we	we	PRON
ejpam-1889	123	4	get	get	VERB
ejpam-1889	123	5	the	the	DET
ejpam-1889	123	6	following	follow	VERB
ejpam-1889	123	7	classification	classification	NOUN
ejpam-1889	123	8	of	of	ADP
ejpam-1889	123	9	(	(	PUNCT
ejpam-1889	123	10	2	2	NUM
ejpam-1889	123	11	,	,	PUNCT
ejpam-1889	123	12	0)-affine	0)-affine	NUM
ejpam-1889	123	13	subspaces	subspace	NOUN
ejpam-1889	123	14	.	.	PUNCT
ejpam-1889	124	1	corollary	corollary	ADJ
ejpam-1889	124	2	1	1	NUM
ejpam-1889	124	3	.	.	PUNCT
ejpam-1889	125	1	any	any	PRON
ejpam-1889	125	2	(	(	PUNCT
ejpam-1889	125	3	2,0)-affine	2,0)-affine	NUM
ejpam-1889	125	4	subspace	subspace	NOUN
ejpam-1889	125	5	is	be	AUX
ejpam-1889	125	6	l	l	NOUN
ejpam-1889	125	7	-	-	ADJ
ejpam-1889	125	8	equivalent	equivalent	ADJ
ejpam-1889	125	9	to	to	PART
ejpam-1889	125	10	γ(2,0	γ(2,0	NOUN
ejpam-1889	125	11	)	)	PUNCT
ejpam-1889	125	12	=	=	PUNCT
ejpam-1889	126	1	〈	〈	NOUN
ejpam-1889	126	2	e1	e1	PROPN
ejpam-1889	126	3	,	,	PUNCT
ejpam-1889	126	4	e3	e3	NOUN
ejpam-1889	126	5	〉	〉	NOUN
ejpam-1889	126	6	.	.	PUNCT
ejpam-1889	126	7	theorem	theorem	VERB
ejpam-1889	126	8	2	2	NUM
ejpam-1889	126	9	.	.	PUNCT
ejpam-1889	127	1	any	any	DET
ejpam-1889	127	2	(	(	PUNCT
ejpam-1889	127	3	2	2	NUM
ejpam-1889	127	4	,	,	PUNCT
ejpam-1889	127	5	1)-affine	1)-affine	NUM
ejpam-1889	127	6	subspace	subspace	NOUN
ejpam-1889	127	7	γ	γ	X
ejpam-1889	127	8	=	=	PUNCT
ejpam-1889	127	9	a+γ0	a+γ0	PROPN
ejpam-1889	127	10	is	be	AUX
ejpam-1889	127	11	l	l	NOUN
ejpam-1889	127	12	-	-	NOUN
ejpam-1889	127	13	equivalent	equivalent	ADJ
ejpam-1889	127	14	to	to	ADP
ejpam-1889	127	15	exactly	exactly	ADV
ejpam-1889	127	16	one	one	NUM
ejpam-1889	127	17	of	of	ADP
ejpam-1889	127	18	the	the	DET
ejpam-1889	127	19	following	follow	VERB
ejpam-1889	127	20	affine	affine	NOUN
ejpam-1889	127	21	subspaces	subspace	NOUN
ejpam-1889	127	22			VERB
ejpam-1889	127	23			ADV
ejpam-1889	127	24			PRON
ejpam-1889	127	25			ADJ
ejpam-1889	127	26			PROPN
ejpam-1889	127	27	γ(2,1	γ(2,1	NOUN
ejpam-1889	127	28	)	)	PUNCT
ejpam-1889	127	29	1	1	NUM
ejpam-1889	127	30	=	=	SYM
ejpam-1889	127	31	e2	e2	PROPN
ejpam-1889	127	32	+	+	CCONJ
ejpam-1889	127	33	〈	〈	PROPN
ejpam-1889	127	34	e1	e1	NOUN
ejpam-1889	127	35	,	,	PUNCT
ejpam-1889	127	36	e3	e3	NOUN
ejpam-1889	127	37	〉	〉	NOUN
ejpam-1889	127	38	e∗3(γ	e∗3(γ	PROPN
ejpam-1889	127	39	0	0	NUM
ejpam-1889	127	40	)	)	PUNCT
ejpam-1889	127	41	6=	6=	ADP
ejpam-1889	127	42	{	{	PUNCT
ejpam-1889	127	43	0	0	NUM
ejpam-1889	127	44	}	}	PUNCT
ejpam-1889	127	45	,	,	PUNCT
ejpam-1889	127	46	e1	e1	PROPN
ejpam-1889	127	47	+	+	CCONJ
ejpam-1889	127	48	e2	e2	PROPN
ejpam-1889	127	49	/∈	/∈	PUNCT
ejpam-1889	128	1	γ0	γ0	NOUN
ejpam-1889	128	2	and	and	CCONJ
ejpam-1889	128	3	e1	e1	PROPN
ejpam-1889	128	4	−	−	PROPN
ejpam-1889	128	5	e2	e2	PROPN
ejpam-1889	128	6	/∈	/∈	PUNCT
ejpam-1889	129	1	γ0	γ0	PROPN
ejpam-1889	129	2	γ(2,1	γ(2,1	NOUN
ejpam-1889	129	3	)	)	PUNCT
ejpam-1889	129	4	2	2	NUM
ejpam-1889	129	5	=	=	NOUN
ejpam-1889	129	6	e1	e1	PROPN
ejpam-1889	129	7	+	+	CCONJ
ejpam-1889	129	8	〈	〈	PROPN
ejpam-1889	129	9	e1	e1	PROPN
ejpam-1889	129	10	+	+	CCONJ
ejpam-1889	129	11	e2	e2	NOUN
ejpam-1889	129	12	,	,	PUNCT
ejpam-1889	129	13	e3	e3	NOUN
ejpam-1889	129	14	〉	〉	NOUN
ejpam-1889	129	15	e∗3(γ	e∗3(γ	PROPN
ejpam-1889	129	16	0	0	NUM
ejpam-1889	129	17	)	)	PUNCT
ejpam-1889	130	1	6=	6=	ADP
ejpam-1889	130	2	{	{	PUNCT
ejpam-1889	130	3	0	0	NUM
ejpam-1889	130	4	}	}	PUNCT
ejpam-1889	130	5	,	,	PUNCT
ejpam-1889	130	6	e1	e1	PROPN
ejpam-1889	130	7	+	+	CCONJ
ejpam-1889	130	8	e2	e2	PROPN
ejpam-1889	130	9	∈	∈	PROPN
ejpam-1889	130	10	γ0	γ0	NOUN
ejpam-1889	130	11	or	or	CCONJ
ejpam-1889	130	12	e1	e1	PROPN
ejpam-1889	130	13	−	−	PROPN
ejpam-1889	130	14	e2	e2	PROPN
ejpam-1889	130	15	∈	∈	PROPN
ejpam-1889	130	16	γ0	γ0	PROPN
ejpam-1889	130	17	γ(2,1	γ(2,1	NOUN
ejpam-1889	130	18	)	)	PUNCT
ejpam-1889	130	19	3,α	3,α	NUM
ejpam-1889	130	20	=	=	SYM
ejpam-1889	130	21	αe3	αe3	NOUN
ejpam-1889	130	22	+	+	CCONJ
ejpam-1889	130	23	〈	〈	PROPN
ejpam-1889	130	24	e1	e1	NOUN
ejpam-1889	130	25	,	,	PUNCT
ejpam-1889	130	26	e2	e2	NOUN
ejpam-1889	130	27	〉	〉	NOUN
ejpam-1889	130	28	e∗3(γ	e∗3(γ	PROPN
ejpam-1889	130	29	0	0	NUM
ejpam-1889	130	30	)	)	PUNCT
ejpam-1889	130	31	=	=	PRON
ejpam-1889	130	32	{	{	PUNCT
ejpam-1889	130	33	0	0	NUM
ejpam-1889	130	34	}	}	PUNCT
ejpam-1889	130	35	.	.	PUNCT
ejpam-1889	131	1	here	here	ADV
ejpam-1889	131	2	α	α	X
ejpam-1889	131	3	>	>	X
ejpam-1889	131	4	0	0	NUM
ejpam-1889	131	5	,	,	PUNCT
ejpam-1889	131	6	with	with	ADP
ejpam-1889	131	7	different	different	ADJ
ejpam-1889	131	8	values	value	NOUN
ejpam-1889	131	9	of	of	ADP
ejpam-1889	131	10	the	the	DET
ejpam-1889	131	11	parameter	parameter	NOUN
ejpam-1889	131	12	yielding	yield	VERB
ejpam-1889	131	13	distinct	distinct	ADJ
ejpam-1889	131	14	(	(	PUNCT
ejpam-1889	131	15	non	non	ADJ
ejpam-1889	131	16	-	-	ADJ
ejpam-1889	131	17	equivalent	equivalent	ADJ
ejpam-1889	131	18	)	)	PUNCT
ejpam-1889	131	19	class	class	NOUN
ejpam-1889	131	20	representatives	representative	NOUN
ejpam-1889	131	21	.	.	PUNCT
ejpam-1889	132	1	d.	d.	PROPN
ejpam-1889	132	2	barrett	barrett	PROPN
ejpam-1889	132	3	,	,	PUNCT
ejpam-1889	132	4	r.	r.	PROPN
ejpam-1889	132	5	biggs	biggs	PROPN
ejpam-1889	132	6	,	,	PUNCT
ejpam-1889	132	7	c.	c.	PROPN
ejpam-1889	132	8	remsing	remsing	NOUN
ejpam-1889	132	9	/	/	SYM
ejpam-1889	132	10	eur	eur	NOUN
ejpam-1889	132	11	.	.	PUNCT
ejpam-1889	133	1	j.	j.	PROPN
ejpam-1889	133	2	pure	pure	PROPN
ejpam-1889	133	3	appl	appl	PROPN
ejpam-1889	133	4	.	.	PROPN
ejpam-1889	133	5	math	math	PROPN
ejpam-1889	133	6	,	,	PUNCT
ejpam-1889	133	7	7	7	NUM
ejpam-1889	133	8	(	(	PUNCT
ejpam-1889	133	9	2014	2014	NUM
ejpam-1889	133	10	)	)	PUNCT
ejpam-1889	133	11	,	,	PUNCT
ejpam-1889	133	12	140	140	NUM
ejpam-1889	133	13	-	-	SYM
ejpam-1889	133	14	155	155	NUM
ejpam-1889	133	15	144	144	NUM
ejpam-1889	133	16	proof	proof	NOUN
ejpam-1889	133	17	.	.	PUNCT
ejpam-1889	133	18	suppose	suppose	VERB
ejpam-1889	133	19	that	that	SCONJ
ejpam-1889	133	20	e∗3(γ	e∗3(γ	PROPN
ejpam-1889	133	21	0	0	NUM
ejpam-1889	133	22	)	)	PUNCT
ejpam-1889	133	23	6=	6=	ADP
ejpam-1889	133	24	{	{	PUNCT
ejpam-1889	133	25	0	0	NUM
ejpam-1889	133	26	}	}	PUNCT
ejpam-1889	133	27	,	,	PUNCT
ejpam-1889	133	28	e1	e1	PROPN
ejpam-1889	133	29	+	+	CCONJ
ejpam-1889	133	30	e2	e2	PROPN
ejpam-1889	133	31	/∈	/∈	PUNCT
ejpam-1889	134	1	γ0	γ0	NOUN
ejpam-1889	134	2	and	and	CCONJ
ejpam-1889	134	3	e1	e1	PROPN
ejpam-1889	134	4	−	−	PROPN
ejpam-1889	134	5	e2	e2	PROPN
ejpam-1889	134	6	/∈	/∈	PUNCT
ejpam-1889	134	7	γ0	γ0	PROPN
ejpam-1889	134	8	.	.	PUNCT
ejpam-1889	135	1	then	then	ADV
ejpam-1889	135	2	γ	γ	X
ejpam-1889	135	3	=	=	SYM
ejpam-1889	135	4	a1e1	a1e1	AUX
ejpam-1889	135	5	+	+	CCONJ
ejpam-1889	135	6	a2e2	a2e2	PROPN
ejpam-1889	135	7	+	+	NUM
ejpam-1889	135	8	〈	〈	PROPN
ejpam-1889	135	9	b1e1	b1e1	PROPN
ejpam-1889	135	10	+	+	CCONJ
ejpam-1889	135	11	b2e2	b2e2	PROPN
ejpam-1889	135	12	,	,	PUNCT
ejpam-1889	135	13	c1e1	c1e1	PROPN
ejpam-1889	135	14	+	+	CCONJ
ejpam-1889	135	15	c2e2	c2e2	PROPN
ejpam-1889	135	16	+	+	NOUN
ejpam-1889	135	17	e3	e3	VERB
ejpam-1889	135	18	〉	〉	NOUN
ejpam-1889	135	19	with	with	ADP
ejpam-1889	135	20	b2	b2	NOUN
ejpam-1889	135	21	1	1	NUM
ejpam-1889	135	22	6=	6=	NUM
ejpam-1889	135	23	b2	b2	NOUN
ejpam-1889	135	24	2	2	NUM
ejpam-1889	135	25	.	.	PUNCT
ejpam-1889	135	26	hence	hence	ADV
ejpam-1889	135	27	γ′	γ′	NOUN
ejpam-1889	135	28	=	=	PUNCT
ejpam-1889	135	29			PROPN
ejpam-1889	135	30			VERB
ejpam-1889	135	31	1	1	NUM
ejpam-1889	135	32	0	0	NUM
ejpam-1889	135	33	−c1	−c1	NOUN
ejpam-1889	135	34	0	0	NUM
ejpam-1889	135	35	1	1	NUM
ejpam-1889	135	36	−c2	−c2	NOUN
ejpam-1889	135	37	0	0	NUM
ejpam-1889	135	38	0	0	NUM
ejpam-1889	135	39	1	1	NUM
ejpam-1889	135	40			PROPN
ejpam-1889	135	41			PROPN
ejpam-1889	135	42	·	·	PUNCT
ejpam-1889	135	43	γ	γ	X
ejpam-1889	135	44	=	=	SYM
ejpam-1889	135	45	a1e1	a1e1	PROPN
ejpam-1889	135	46	+	+	CCONJ
ejpam-1889	135	47	a2e2	a2e2	PROPN
ejpam-1889	135	48	+	+	NUM
ejpam-1889	135	49	〈	〈	PROPN
ejpam-1889	135	50	b1e1	b1e1	NOUN
ejpam-1889	135	51	+	+	CCONJ
ejpam-1889	135	52	b2e2	b2e2	PROPN
ejpam-1889	135	53	,	,	PUNCT
ejpam-1889	135	54	e3	e3	VERB
ejpam-1889	135	55	〉	〉	NOUN
ejpam-1889	135	56	where	where	SCONJ
ejpam-1889	135	57	b1a2	b1a2	X
ejpam-1889	135	58	−	−	NOUN
ejpam-1889	135	59	a1	a1	NOUN
ejpam-1889	135	60	b2	b2	NOUN
ejpam-1889	135	61	6=	6=	ADP
ejpam-1889	135	62	0	0	NUM
ejpam-1889	135	63	(	(	PUNCT
ejpam-1889	135	64	as	as	SCONJ
ejpam-1889	135	65	γ	γ	X
ejpam-1889	135	66	is	be	AUX
ejpam-1889	135	67	inhomogeneous	inhomogeneous	ADJ
ejpam-1889	135	68	)	)	PUNCT
ejpam-1889	135	69	.	.	PUNCT
ejpam-1889	136	1	consequently	consequently	ADV
ejpam-1889	136	2			VERB
ejpam-1889	136	3			PROPN
ejpam-1889	136	4			NUM
ejpam-1889	136	5	b2	b2	NOUN
ejpam-1889	136	6	1−b2	1−b2	NUM
ejpam-1889	136	7	2	2	NUM
ejpam-1889	136	8	b1a2−a1	b1a2−a1	NOUN
ejpam-1889	136	9	b2	b2	NOUN
ejpam-1889	136	10	0	0	NUM
ejpam-1889	136	11	0	0	SYM
ejpam-1889	136	12	0	0	NUM
ejpam-1889	136	13	b2	b2	NOUN
ejpam-1889	136	14	1−b2	1−b2	NUM
ejpam-1889	136	15	2	2	NUM
ejpam-1889	136	16	b1a2−a1	b1a2−a1	NOUN
ejpam-1889	136	17	b2	b2	NOUN
ejpam-1889	136	18	0	0	NUM
ejpam-1889	136	19	0	0	NUM
ejpam-1889	136	20	0	0	NUM
ejpam-1889	136	21	1	1	NUM
ejpam-1889	136	22			PROPN
ejpam-1889	136	23			PROPN
ejpam-1889	136	24			PROPN
ejpam-1889	136	25			NOUN
ejpam-1889	136	26			ADJ
ejpam-1889	136	27			NUM
ejpam-1889	136	28	b1	b1	NOUN
ejpam-1889	136	29	b2	b2	NOUN
ejpam-1889	136	30	1−b2	1−b2	NUM
ejpam-1889	136	31	2	2	NUM
ejpam-1889	136	32	−	−	NOUN
ejpam-1889	136	33	b2	b2	NOUN
ejpam-1889	136	34	b2	b2	NOUN
ejpam-1889	136	35	1−b2	1−b2	NUM
ejpam-1889	136	36	2	2	NUM
ejpam-1889	136	37	0	0	NUM
ejpam-1889	136	38	−	−	NOUN
ejpam-1889	136	39	b2	b2	NOUN
ejpam-1889	136	40	b2	b2	NOUN
ejpam-1889	136	41	1−b2	1−b2	NUM
ejpam-1889	136	42	2	2	NUM
ejpam-1889	136	43	b1	b1	NOUN
ejpam-1889	136	44	b2	b2	NOUN
ejpam-1889	136	45	1−b2	1−b2	NUM
ejpam-1889	136	46	2	2	NUM
ejpam-1889	136	47	0	0	NUM
ejpam-1889	136	48	0	0	NUM
ejpam-1889	136	49	0	0	NUM
ejpam-1889	136	50	1	1	NUM
ejpam-1889	136	51			PROPN
ejpam-1889	136	52			PROPN
ejpam-1889	136	53			PROPN
ejpam-1889	136	54	·	·	PUNCT
ejpam-1889	136	55	γ′	γ′	X
ejpam-1889	136	56	=	=	SYM
ejpam-1889	136	57	a1	a1	NOUN
ejpam-1889	136	58	b2	b2	NOUN
ejpam-1889	136	59	−	−	PROPN
ejpam-1889	136	60	a2	a2	PROPN
ejpam-1889	136	61	b2	b2	NOUN
ejpam-1889	136	62	b1a2	b1a2	ADP
ejpam-1889	136	63	−	−	NOUN
ejpam-1889	136	64	a1	a1	NOUN
ejpam-1889	136	65	b2	b2	NOUN
ejpam-1889	136	66	e1	e1	NOUN
ejpam-1889	136	67	+	+	CCONJ
ejpam-1889	136	68	e2	e2	PROPN
ejpam-1889	136	69	+	+	CCONJ
ejpam-1889	136	70	®	®	NOUN
ejpam-1889	136	71	b2	b2	NOUN
ejpam-1889	136	72	1	1	NUM
ejpam-1889	136	73	−	−	NOUN
ejpam-1889	136	74	b2	b2	NOUN
ejpam-1889	136	75	2	2	NUM
ejpam-1889	136	76	b1a2	b1a2	NOUN
ejpam-1889	136	77	−	−	NOUN
ejpam-1889	136	78	a1	a1	NOUN
ejpam-1889	136	79	b2	b2	NOUN
ejpam-1889	136	80	e1	e1	NOUN
ejpam-1889	136	81	,	,	PUNCT
ejpam-1889	136	82	e3	e3	NOUN
ejpam-1889	136	83	¸	¸	X
ejpam-1889	136	84	=	=	SYM
ejpam-1889	136	85	e2	e2	PROPN
ejpam-1889	136	86	+	+	CCONJ
ejpam-1889	136	87	〈	〈	PROPN
ejpam-1889	136	88	e1	e1	NOUN
ejpam-1889	136	89	,	,	PUNCT
ejpam-1889	136	90	e3〉=	e3〉=	VERB
ejpam-1889	136	91	γ	γ	X
ejpam-1889	136	92	(	(	PUNCT
ejpam-1889	136	93	2,1	2,1	NUM
ejpam-1889	136	94	)	)	PUNCT
ejpam-1889	136	95	1	1	NUM
ejpam-1889	136	96	.	.	PUNCT
ejpam-1889	137	1	thus	thus	ADV
ejpam-1889	137	2	γ	γ	X
ejpam-1889	137	3	is	be	AUX
ejpam-1889	137	4	l	l	NOUN
ejpam-1889	137	5	-	-	ADJ
ejpam-1889	137	6	equivalent	equivalent	ADJ
ejpam-1889	137	7	to	to	ADP
ejpam-1889	137	8	γ(2,1	γ(2,1	PROPN
ejpam-1889	137	9	)	)	PUNCT
ejpam-1889	137	10	1	1	NUM
ejpam-1889	137	11	.	.	PUNCT
ejpam-1889	138	1	on	on	ADP
ejpam-1889	138	2	the	the	DET
ejpam-1889	138	3	other	other	ADJ
ejpam-1889	138	4	hand	hand	NOUN
ejpam-1889	138	5	,	,	PUNCT
ejpam-1889	138	6	suppose	suppose	VERB
ejpam-1889	138	7	that	that	SCONJ
ejpam-1889	138	8	e∗3(γ	e∗3(γ	PROPN
ejpam-1889	138	9	0	0	NUM
ejpam-1889	138	10	)	)	PUNCT
ejpam-1889	138	11	6=	6=	ADP
ejpam-1889	138	12	{	{	PUNCT
ejpam-1889	138	13	0	0	NUM
ejpam-1889	138	14	}	}	PUNCT
ejpam-1889	138	15	and	and	CCONJ
ejpam-1889	138	16	e1	e1	PROPN
ejpam-1889	138	17	±	±	PROPN
ejpam-1889	138	18	e2	e2	PROPN
ejpam-1889	138	19	∈	∈	PROPN
ejpam-1889	138	20	γ0	γ0	NOUN
ejpam-1889	138	21	.	.	PUNCT
ejpam-1889	139	1	then	then	ADV
ejpam-1889	139	2	γ	γ	X
ejpam-1889	139	3	=	=	SYM
ejpam-1889	139	4	a1e1	a1e1	PROPN
ejpam-1889	139	5	+	+	CCONJ
ejpam-1889	139	6	a2e2	a2e2	PROPN
ejpam-1889	139	7	+	+	NUM
ejpam-1889	139	8	〈	〈	PROPN
ejpam-1889	139	9	e1	e1	PROPN
ejpam-1889	139	10	±	±	NUM
ejpam-1889	139	11	e2	e2	PROPN
ejpam-1889	139	12	,	,	PUNCT
ejpam-1889	139	13	b1e1	b1e1	PROPN
ejpam-1889	139	14	+	+	CCONJ
ejpam-1889	139	15	b2e2	b2e2	PROPN
ejpam-1889	139	16	+	+	NOUN
ejpam-1889	139	17	e3	e3	VERB
ejpam-1889	139	18	〉	〉	NOUN
ejpam-1889	139	19	and	and	CCONJ
ejpam-1889	139	20	γ′	γ′	NOUN
ejpam-1889	139	21	=	=	SYM
ejpam-1889	139	22			PROPN
ejpam-1889	139	23			VERB
ejpam-1889	139	24	1	1	NUM
ejpam-1889	139	25	0	0	NUM
ejpam-1889	139	26	−b1	−b1	NOUN
ejpam-1889	139	27	0	0	NUM
ejpam-1889	139	28	1	1	NUM
ejpam-1889	139	29	−b2	−b2	NUM
ejpam-1889	139	30	0	0	NUM
ejpam-1889	139	31	0	0	NUM
ejpam-1889	139	32	1	1	NUM
ejpam-1889	139	33			PROPN
ejpam-1889	139	34			PROPN
ejpam-1889	139	35	·	·	PUNCT
ejpam-1889	139	36	γ	γ	X
ejpam-1889	139	37	=	=	SYM
ejpam-1889	139	38	a1e1	a1e1	PROPN
ejpam-1889	139	39	+	+	CCONJ
ejpam-1889	139	40	a2e2	a2e2	PROPN
ejpam-1889	139	41	+	+	NUM
ejpam-1889	139	42	〈	〈	PROPN
ejpam-1889	139	43	e1	e1	PROPN
ejpam-1889	139	44	±	±	PROPN
ejpam-1889	139	45	e2	e2	PROPN
ejpam-1889	139	46	,	,	PUNCT
ejpam-1889	139	47	e3	e3	NOUN
ejpam-1889	139	48	〉	〉	NOUN
ejpam-1889	139	49	where	where	SCONJ
ejpam-1889	139	50	a1	a1	NOUN
ejpam-1889	139	51	∓	∓	PROPN
ejpam-1889	139	52	a2	a2	PROPN
ejpam-1889	139	53	6=	6=	ADP
ejpam-1889	139	54	0	0	NUM
ejpam-1889	139	55	(	(	PUNCT
ejpam-1889	139	56	as	as	SCONJ
ejpam-1889	139	57	γ	γ	X
ejpam-1889	139	58	is	be	AUX
ejpam-1889	139	59	inhomogeneous	inhomogeneous	ADJ
ejpam-1889	139	60	)	)	PUNCT
ejpam-1889	139	61	.	.	PUNCT
ejpam-1889	140	1	therefore	therefore	ADV
ejpam-1889	140	2			VERB
ejpam-1889	140	3			PROPN
ejpam-1889	140	4			NUM
ejpam-1889	140	5	a1	a1	NOUN
ejpam-1889	140	6	a2	a2	PROPN
ejpam-1889	140	7	1−a2	1−a2	NUM
ejpam-1889	140	8	2	2	NUM
ejpam-1889	140	9	−	−	PROPN
ejpam-1889	140	10	a2	a2	PROPN
ejpam-1889	140	11	a2	a2	PROPN
ejpam-1889	140	12	1−a2	1−a2	NUM
ejpam-1889	140	13	2	2	NUM
ejpam-1889	140	14	0	0	NUM
ejpam-1889	140	15	∓	∓	PROPN
ejpam-1889	140	16	a2	a2	PROPN
ejpam-1889	140	17	a2	a2	PROPN
ejpam-1889	140	18	1−a2	1−a2	NUM
ejpam-1889	140	19	2	2	NUM
ejpam-1889	140	20	±	±	NUM
ejpam-1889	140	21	a1	a1	NOUN
ejpam-1889	140	22	a2	a2	PROPN
ejpam-1889	140	23	1−a2	1−a2	NUM
ejpam-1889	140	24	2	2	NUM
ejpam-1889	140	25	0	0	NUM
ejpam-1889	140	26	0	0	NUM
ejpam-1889	140	27	0	0	NUM
ejpam-1889	140	28	±1	±1	VERB
ejpam-1889	140	29			PROPN
ejpam-1889	140	30			PROPN
ejpam-1889	140	31			PROPN
ejpam-1889	140	32	·	·	PUNCT
ejpam-1889	140	33	γ′	γ′	X
ejpam-1889	141	1	=	=	NOUN
ejpam-1889	141	2	e1	e1	NOUN
ejpam-1889	141	3	+	+	CCONJ
ejpam-1889	141	4	®	®	NOUN
ejpam-1889	141	5	a1	a1	NOUN
ejpam-1889	141	6	∓	∓	PROPN
ejpam-1889	141	7	a2	a2	PROPN
ejpam-1889	141	8	a2	a2	PROPN
ejpam-1889	141	9	1	1	NUM
ejpam-1889	141	10	−	−	PROPN
ejpam-1889	141	11	a2	a2	PROPN
ejpam-1889	141	12	2	2	NUM
ejpam-1889	141	13	(	(	PUNCT
ejpam-1889	141	14	e1	e1	NOUN
ejpam-1889	141	15	+	+	NOUN
ejpam-1889	141	16	e2),±e3	e2),±e3	NOUN
ejpam-1889	141	17	¸	¸	X
ejpam-1889	141	18	=	=	X
ejpam-1889	141	19	e1	e1	PROPN
ejpam-1889	141	20	+	+	CCONJ
ejpam-1889	141	21	〈	〈	NOUN
ejpam-1889	141	22	e1	e1	PROPN
ejpam-1889	141	23	+	+	CCONJ
ejpam-1889	141	24	e2	e2	PROPN
ejpam-1889	141	25	,	,	PUNCT
ejpam-1889	141	26	e3〉=	e3〉=	VERB
ejpam-1889	141	27	γ	γ	X
ejpam-1889	141	28	(	(	PUNCT
ejpam-1889	141	29	2,1	2,1	NUM
ejpam-1889	141	30	)	)	PUNCT
ejpam-1889	141	31	2	2	NUM
ejpam-1889	141	32	.	.	PUNCT
ejpam-1889	142	1	thus	thus	ADV
ejpam-1889	142	2	γ	γ	X
ejpam-1889	142	3	is	be	AUX
ejpam-1889	142	4	l	l	NOUN
ejpam-1889	142	5	-	-	ADJ
ejpam-1889	142	6	equivalent	equivalent	ADJ
ejpam-1889	142	7	to	to	ADP
ejpam-1889	142	8	γ(2,1	γ(2,1	PROPN
ejpam-1889	142	9	)	)	PUNCT
ejpam-1889	142	10	2	2	NUM
ejpam-1889	142	11	.	.	PUNCT
ejpam-1889	143	1	lastly	lastly	ADV
ejpam-1889	143	2	,	,	PUNCT
ejpam-1889	143	3	suppose	suppose	VERB
ejpam-1889	143	4	that	that	SCONJ
ejpam-1889	143	5	e∗3(γ	e∗3(γ	PROPN
ejpam-1889	143	6	0	0	NUM
ejpam-1889	143	7	)	)	PUNCT
ejpam-1889	143	8	=	=	PRON
ejpam-1889	143	9	{	{	PUNCT
ejpam-1889	143	10	0	0	NUM
ejpam-1889	143	11	}	}	PUNCT
ejpam-1889	143	12	.	.	PUNCT
ejpam-1889	144	1	then	then	ADV
ejpam-1889	144	2	γ	γ	X
ejpam-1889	144	3	=	=	SYM
ejpam-1889	144	4	a3e3	a3e3	PROPN
ejpam-1889	144	5	+	+	PROPN
ejpam-1889	144	6	〈	〈	PROPN
ejpam-1889	144	7	e1	e1	NOUN
ejpam-1889	144	8	,	,	PUNCT
ejpam-1889	144	9	e2	e2	NOUN
ejpam-1889	144	10	〉	〉	NOUN
ejpam-1889	144	11	and	and	CCONJ
ejpam-1889	144	12			NOUN
ejpam-1889	144	13			NOUN
ejpam-1889	144	14	1	1	NUM
ejpam-1889	144	15	0	0	NUM
ejpam-1889	144	16	0	0	NUM
ejpam-1889	144	17	0	0	NUM
ejpam-1889	144	18	sgn(a3	sgn(a3	NOUN
ejpam-1889	144	19	)	)	PUNCT
ejpam-1889	144	20	0	0	NUM
ejpam-1889	144	21	0	0	NUM
ejpam-1889	144	22	0	0	NUM
ejpam-1889	144	23	sgn(a3	sgn(a3	NOUN
ejpam-1889	144	24	)	)	PUNCT
ejpam-1889	144	25			PROPN
ejpam-1889	144	26			PROPN
ejpam-1889	144	27	·	·	PUNCT
ejpam-1889	144	28	γ	γ	NOUN
ejpam-1889	144	29	=	=	PUNCT
ejpam-1889	144	30	|a3|e3	|a3|e3	PROPN
ejpam-1889	144	31	+	+	CCONJ
ejpam-1889	144	32	〈	〈	NOUN
ejpam-1889	144	33	e1	e1	NOUN
ejpam-1889	144	34	,	,	PUNCT
ejpam-1889	144	35	sgn(a3)e2〉=	sgn(a3)e2〉=	PROPN
ejpam-1889	144	36	γ	γ	X
ejpam-1889	144	37	(	(	PUNCT
ejpam-1889	144	38	2,1	2,1	NUM
ejpam-1889	144	39	)	)	PUNCT
ejpam-1889	144	40	3,α	3,α	PROPN
ejpam-1889	144	41	d.	d.	PROPN
ejpam-1889	144	42	barrett	barrett	PROPN
ejpam-1889	144	43	,	,	PUNCT
ejpam-1889	144	44	r.	r.	PROPN
ejpam-1889	144	45	biggs	biggs	PROPN
ejpam-1889	144	46	,	,	PUNCT
ejpam-1889	144	47	c.	c.	PROPN
ejpam-1889	144	48	remsing	remsing	NOUN
ejpam-1889	144	49	/	/	SYM
ejpam-1889	144	50	eur	eur	NOUN
ejpam-1889	144	51	.	.	PUNCT
ejpam-1889	145	1	j.	j.	PROPN
ejpam-1889	145	2	pure	pure	PROPN
ejpam-1889	145	3	appl	appl	PROPN
ejpam-1889	145	4	.	.	PROPN
ejpam-1889	145	5	math	math	PROPN
ejpam-1889	145	6	,	,	PUNCT
ejpam-1889	145	7	7	7	NUM
ejpam-1889	145	8	(	(	PUNCT
ejpam-1889	145	9	2014	2014	NUM
ejpam-1889	145	10	)	)	PUNCT
ejpam-1889	145	11	,	,	PUNCT
ejpam-1889	145	12	140	140	NUM
ejpam-1889	145	13	-	-	SYM
ejpam-1889	145	14	155	155	NUM
ejpam-1889	145	15	145	145	NUM
ejpam-1889	145	16	where	where	SCONJ
ejpam-1889	145	17	α=	α=	NOUN
ejpam-1889	145	18	|a3|	|a3|	NOUN
ejpam-1889	145	19	>	>	X
ejpam-1889	145	20	0	0	PROPN
ejpam-1889	145	21	.	.	PUNCT
ejpam-1889	146	1	hence	hence	ADV
ejpam-1889	146	2	γ	γ	PROPN
ejpam-1889	146	3	is	be	AUX
ejpam-1889	146	4	l	l	NOUN
ejpam-1889	146	5	-	-	ADJ
ejpam-1889	146	6	equivalent	equivalent	ADJ
ejpam-1889	146	7	to	to	ADP
ejpam-1889	146	8	γ(2,1	γ(2,1	NUM
ejpam-1889	146	9	)	)	PUNCT
ejpam-1889	146	10	3,α	3,α	NUM
ejpam-1889	146	11	.	.	PUNCT
ejpam-1889	147	1	as	as	ADP
ejpam-1889	147	2	〈	〈	PROPN
ejpam-1889	147	3	e1	e1	NOUN
ejpam-1889	147	4	,	,	PUNCT
ejpam-1889	147	5	e2	e2	NOUN
ejpam-1889	147	6	〉	〉	NOUN
ejpam-1889	147	7	and	and	CCONJ
ejpam-1889	147	8	〈	〈	NOUN
ejpam-1889	147	9	e1	e1	PROPN
ejpam-1889	147	10	+	+	CCONJ
ejpam-1889	147	11	e2	e2	X
ejpam-1889	147	12	〉	〉	NOUN
ejpam-1889	147	13	∪	∪	X
ejpam-1889	147	14	〈	〈	NOUN
ejpam-1889	147	15	e1	e1	PROPN
ejpam-1889	147	16	−	−	PROPN
ejpam-1889	147	17	e2	e2	PROPN
ejpam-1889	147	18	〉	〉	NOUN
ejpam-1889	147	19	are	be	AUX
ejpam-1889	147	20	invariant	invariant	ADJ
ejpam-1889	147	21	subsets	subset	NOUN
ejpam-1889	147	22	,	,	PUNCT
ejpam-1889	147	23	no	no	DET
ejpam-1889	147	24	two	two	NUM
ejpam-1889	147	25	of	of	ADP
ejpam-1889	147	26	γ(2,1	γ(2,1	NOUN
ejpam-1889	147	27	)	)	PUNCT
ejpam-1889	147	28	1	1	NUM
ejpam-1889	147	29	,	,	PUNCT
ejpam-1889	147	30	γ(2,1	γ(2,1	NOUN
ejpam-1889	147	31	)	)	PUNCT
ejpam-1889	147	32	2	2	NUM
ejpam-1889	147	33	and	and	CCONJ
ejpam-1889	147	34	γ(2,1	γ(2,1	NUM
ejpam-1889	147	35	)	)	PUNCT
ejpam-1889	147	36	3,α	3,α	NUM
ejpam-1889	147	37	are	be	AUX
ejpam-1889	147	38	l	l	NOUN
ejpam-1889	147	39	-	-	NOUN
ejpam-1889	147	40	equivalent	equivalent	ADJ
ejpam-1889	147	41	.	.	PUNCT
ejpam-1889	148	1	it	it	PRON
ejpam-1889	148	2	is	be	AUX
ejpam-1889	148	3	a	a	DET
ejpam-1889	148	4	simple	simple	ADJ
ejpam-1889	148	5	matter	matter	NOUN
ejpam-1889	148	6	to	to	PART
ejpam-1889	148	7	show	show	VERB
ejpam-1889	148	8	that	that	PRON
ejpam-1889	148	9	γ(2,1	γ(2,1	NOUN
ejpam-1889	148	10	)	)	PUNCT
ejpam-1889	148	11	3,α	3,α	NUM
ejpam-1889	148	12	is	be	AUX
ejpam-1889	148	13	l	l	NOUN
ejpam-1889	148	14	-	-	ADJ
ejpam-1889	148	15	equivalent	equivalent	ADJ
ejpam-1889	148	16	to	to	ADP
ejpam-1889	148	17	γ(2,1	γ(2,1	NUM
ejpam-1889	148	18	)	)	PUNCT
ejpam-1889	148	19	3,α′	3,α′	NUM
ejpam-1889	148	20	only	only	ADV
ejpam-1889	148	21	if	if	SCONJ
ejpam-1889	148	22	α=	α=	NUM
ejpam-1889	148	23	α′.	α′.	NOUN
ejpam-1889	148	24	remark	remark	VERB
ejpam-1889	148	25	.	.	PUNCT
ejpam-1889	149	1	there	there	PRON
ejpam-1889	149	2	is	be	VERB
ejpam-1889	149	3	only	only	ADV
ejpam-1889	149	4	one	one	NUM
ejpam-1889	149	5	(	(	PUNCT
ejpam-1889	149	6	3,0)-affine	3,0)-affine	NUM
ejpam-1889	149	7	subspace	subspace	NOUN
ejpam-1889	149	8	,	,	PUNCT
ejpam-1889	149	9	namely	namely	ADV
ejpam-1889	149	10	se(1	se(1	NOUN
ejpam-1889	149	11	,	,	PUNCT
ejpam-1889	149	12	1	1	NUM
ejpam-1889	149	13	)	)	PUNCT
ejpam-1889	149	14	itself	itself	PRON
ejpam-1889	149	15	.	.	PUNCT
ejpam-1889	150	1	3.2	3.2	NUM
ejpam-1889	150	2	.	.	PUNCT
ejpam-1889	151	1	parametrized	parametrized	ADJ
ejpam-1889	151	2	affine	affine	NOUN
ejpam-1889	151	3	subspaces	subspace	NOUN
ejpam-1889	151	4	when	when	SCONJ
ejpam-1889	151	5	convenient	convenient	ADJ
ejpam-1889	151	6	,	,	PUNCT
ejpam-1889	151	7	a	a	DET
ejpam-1889	151	8	parametrized	parametrized	ADJ
ejpam-1889	151	9	affine	affine	NOUN
ejpam-1889	151	10	subspace	subspace	NOUN
ejpam-1889	151	11	specified	specify	VERB
ejpam-1889	151	12	by	by	ADP
ejpam-1889	151	13	π	π	PROPN
ejpam-1889	151	14	:	:	PUNCT
ejpam-1889	151	15	3	3	NUM
ejpam-1889	151	16	∑	∑	NOUN
ejpam-1889	151	17	i=1	i=1	PROPN
ejpam-1889	151	18	ai	ai	VERB
ejpam-1889	151	19	ei	ei	NOUN
ejpam-1889	151	20	+	+	NUM
ejpam-1889	151	21	u1	u1	NOUN
ejpam-1889	151	22	3	3	NUM
ejpam-1889	151	23	∑	∑	NOUN
ejpam-1889	151	24	i=1	i=1	PROPN
ejpam-1889	151	25	bi	bi	NOUN
ejpam-1889	151	26	ei	ei	PROPN
ejpam-1889	152	1	+	+	CCONJ
ejpam-1889	152	2	u2	u2	PROPN
ejpam-1889	152	3	3	3	NUM
ejpam-1889	152	4	∑	∑	PROPN
ejpam-1889	152	5	i=1	i=1	PROPN
ejpam-1889	152	6	ci	ci	PROPN
ejpam-1889	152	7	ei	ei	PROPN
ejpam-1889	153	1	+	+	CCONJ
ejpam-1889	153	2	u3	u3	NOUN
ejpam-1889	153	3	3	3	NUM
ejpam-1889	153	4	∑	∑	PROPN
ejpam-1889	153	5	i=1	i=1	PROPN
ejpam-1889	153	6	di	di	NOUN
ejpam-1889	153	7	ei	ei	PROPN
ejpam-1889	153	8	will	will	AUX
ejpam-1889	153	9	be	be	AUX
ejpam-1889	153	10	represented	represent	VERB
ejpam-1889	153	11	(	(	PUNCT
ejpam-1889	153	12	in	in	ADP
ejpam-1889	153	13	matrix	matrix	NOUN
ejpam-1889	153	14	form	form	NOUN
ejpam-1889	153	15	)	)	PUNCT
ejpam-1889	153	16	as	as	SCONJ
ejpam-1889	153	17			NOUN
ejpam-1889	153	18			NUM
ejpam-1889	153	19	a1	a1	NOUN
ejpam-1889	153	20	b1	b1	PROPN
ejpam-1889	153	21	c1	c1	PROPN
ejpam-1889	153	22	d1	d1	PROPN
ejpam-1889	153	23	a2	a2	PROPN
ejpam-1889	153	24	b2	b2	PROPN
ejpam-1889	153	25	c2	c2	PROPN
ejpam-1889	153	26	d2	d2	PROPN
ejpam-1889	153	27	a3	a3	PROPN
ejpam-1889	153	28	b3	b3	PROPN
ejpam-1889	153	29	c3	c3	PROPN
ejpam-1889	153	30	d3	d3	PROPN
ejpam-1889	153	31			PROPN
ejpam-1889	153	32			PROPN
ejpam-1889	153	33	.	.	PUNCT
ejpam-1889	154	1	since	since	SCONJ
ejpam-1889	154	2	any	any	DET
ejpam-1889	154	3	automorphism	automorphism	NOUN
ejpam-1889	154	4	ψ	ψ	NOUN
ejpam-1889	154	5	is	be	AUX
ejpam-1889	154	6	identified	identify	VERB
ejpam-1889	154	7	with	with	ADP
ejpam-1889	154	8	its	its	PRON
ejpam-1889	154	9	matrix	matrix	NOUN
ejpam-1889	154	10	,	,	PUNCT
ejpam-1889	154	11	the	the	DET
ejpam-1889	154	12	composition	composition	NOUN
ejpam-1889	154	13	ψ	ψ	ADP
ejpam-1889	154	14	◦	◦	NOUN
ejpam-1889	154	15	π	π	PROPN
ejpam-1889	154	16	becomes	become	VERB
ejpam-1889	154	17	a	a	DET
ejpam-1889	154	18	matrix	matrix	NOUN
ejpam-1889	154	19	multiplication	multiplication	NOUN
ejpam-1889	154	20	.	.	PUNCT
ejpam-1889	155	1	we	we	PRON
ejpam-1889	155	2	begin	begin	VERB
ejpam-1889	155	3	by	by	ADP
ejpam-1889	155	4	classifying	classify	VERB
ejpam-1889	155	5	the	the	DET
ejpam-1889	155	6	parametrized	parametrized	ADJ
ejpam-1889	155	7	(	(	PUNCT
ejpam-1889	155	8	1	1	NUM
ejpam-1889	155	9	,	,	PUNCT
ejpam-1889	155	10	1)-affine	1)-affine	NUM
ejpam-1889	155	11	subspaces	subspace	NOUN
ejpam-1889	155	12	.	.	PUNCT
ejpam-1889	156	1	theorem	theorem	NOUN
ejpam-1889	156	2	3	3	X
ejpam-1889	156	3	.	.	PUNCT
ejpam-1889	157	1	let	let	VERB
ejpam-1889	157	2	π	π	PRON
ejpam-1889	157	3	be	be	AUX
ejpam-1889	157	4	a	a	DET
ejpam-1889	157	5	parametrization	parametrization	NOUN
ejpam-1889	157	6	of	of	ADP
ejpam-1889	157	7	a	a	DET
ejpam-1889	157	8	(	(	PUNCT
ejpam-1889	157	9	1	1	NUM
ejpam-1889	157	10	,	,	PUNCT
ejpam-1889	157	11	1)-affine	1)-affine	NUM
ejpam-1889	157	12	subspace	subspace	PROPN
ejpam-1889	157	13	γ	γ	PROPN
ejpam-1889	157	14	.	.	PUNCT
ejpam-1889	158	1	(	(	PUNCT
ejpam-1889	158	2	i	i	NOUN
ejpam-1889	158	3	)	)	PUNCT
ejpam-1889	158	4	if	if	SCONJ
ejpam-1889	158	5	γ	γ	X
ejpam-1889	158	6	isl	isl	PROPN
ejpam-1889	158	7	-	-	PUNCT
ejpam-1889	158	8	equivalent	equivalent	NOUN
ejpam-1889	158	9	to	to	ADP
ejpam-1889	158	10	γ(1,1	γ(1,1	VERB
ejpam-1889	158	11	)	)	PUNCT
ejpam-1889	158	12	1	1	NUM
ejpam-1889	158	13	,	,	PUNCT
ejpam-1889	158	14	thenπ	thenπ	NOUN
ejpam-1889	158	15	isp	isp	ADV
ejpam-1889	158	16	-	-	PUNCT
ejpam-1889	158	17	equivalent	equivalent	ADJ
ejpam-1889	158	18	to	to	ADP
ejpam-1889	158	19	exactly	exactly	ADV
ejpam-1889	158	20	one	one	NUM
ejpam-1889	158	21	of	of	ADP
ejpam-1889	158	22	the	the	DET
ejpam-1889	158	23	following	follow	VERB
ejpam-1889	158	24	parametrized	parametrized	ADJ
ejpam-1889	158	25	affine	affine	NOUN
ejpam-1889	158	26	subspaces	subspace	NOUN
ejpam-1889	158	27	π(1,1	π(1,1	NOUN
ejpam-1889	158	28	)	)	PUNCT
ejpam-1889	158	29	1,α	1,α	NOUN
ejpam-1889	158	30	,	,	PUNCT
ejpam-1889	158	31	γ	γ	X
ejpam-1889	158	32	:	:	PUNCT
ejpam-1889	158	33	e1	e1	PROPN
ejpam-1889	158	34	+	+	CCONJ
ejpam-1889	158	35	γ1e3	γ1e3	X
ejpam-1889	158	36	+	+	X
ejpam-1889	158	37	u(αe3	u(αe3	NOUN
ejpam-1889	158	38	)	)	PUNCT
ejpam-1889	158	39	.	.	PUNCT
ejpam-1889	159	1	(	(	PUNCT
ejpam-1889	159	2	ii	ii	NOUN
ejpam-1889	159	3	)	)	PUNCT
ejpam-1889	159	4	if	if	SCONJ
ejpam-1889	159	5	γ	γ	X
ejpam-1889	159	6	isl	isl	PROPN
ejpam-1889	159	7	-	-	PUNCT
ejpam-1889	159	8	equivalent	equivalent	NOUN
ejpam-1889	159	9	to	to	ADP
ejpam-1889	159	10	γ(1,1	γ(1,1	NOUN
ejpam-1889	159	11	)	)	PUNCT
ejpam-1889	159	12	2,α	2,α	NOUN
ejpam-1889	159	13	,	,	PUNCT
ejpam-1889	159	14	thenπ	thenπ	NOUN
ejpam-1889	159	15	isp	isp	ADV
ejpam-1889	159	16	-	-	PUNCT
ejpam-1889	159	17	equivalent	equivalent	ADJ
ejpam-1889	159	18	to	to	ADP
ejpam-1889	159	19	exactly	exactly	ADV
ejpam-1889	159	20	one	one	NUM
ejpam-1889	159	21	of	of	ADP
ejpam-1889	159	22	the	the	DET
ejpam-1889	159	23	following	follow	VERB
ejpam-1889	159	24	parametrized	parametrized	ADJ
ejpam-1889	159	25	affine	affine	NOUN
ejpam-1889	159	26	subspaces	subspace	NOUN
ejpam-1889	159	27	π(1,1	π(1,1	NOUN
ejpam-1889	159	28	)	)	PUNCT
ejpam-1889	159	29	2,α	2,α	NOUN
ejpam-1889	159	30	:	:	PUNCT
ejpam-1889	159	31	αe3	αe3	NOUN
ejpam-1889	159	32	+	+	CCONJ
ejpam-1889	159	33	ue1	ue1	PROPN
ejpam-1889	159	34	.	.	PUNCT
ejpam-1889	160	1	hereα	hereα	VERB
ejpam-1889	160	2	>	>	X
ejpam-1889	160	3	0	0	PUNCT
ejpam-1889	160	4	and	and	CCONJ
ejpam-1889	160	5	γ1	γ1	PROPN
ejpam-1889	160	6	∈	∈	PROPN
ejpam-1889	160	7	r	r	PROPN
ejpam-1889	160	8	,	,	PUNCT
ejpam-1889	160	9	with	with	ADP
ejpam-1889	160	10	different	different	ADJ
ejpam-1889	160	11	values	value	NOUN
ejpam-1889	160	12	of	of	ADP
ejpam-1889	160	13	these	these	DET
ejpam-1889	160	14	parameters	parameter	NOUN
ejpam-1889	160	15	yielding	yield	VERB
ejpam-1889	160	16	distinct	distinct	ADJ
ejpam-1889	160	17	(	(	PUNCT
ejpam-1889	160	18	non	non	ADJ
ejpam-1889	160	19	-	-	ADJ
ejpam-1889	160	20	equivalent	equivalent	ADJ
ejpam-1889	160	21	)	)	PUNCT
ejpam-1889	160	22	class	class	NOUN
ejpam-1889	160	23	representatives	representative	NOUN
ejpam-1889	160	24	.	.	PUNCT
ejpam-1889	161	1	proof	proof	NOUN
ejpam-1889	161	2	.	.	PUNCT
ejpam-1889	162	1	let	let	VERB
ejpam-1889	162	2	π	π	PRON
ejpam-1889	162	3	:	:	PUNCT
ejpam-1889	162	4	∑3	∑3	PROPN
ejpam-1889	163	1	i=1	i=1	PROPN
ejpam-1889	163	2	ai	ai	VERB
ejpam-1889	163	3	ei+u	ei+u	PROPN
ejpam-1889	163	4	∑3	∑3	PROPN
ejpam-1889	163	5	i=1	i=1	PROPN
ejpam-1889	163	6	bi	bi	NOUN
ejpam-1889	163	7	ei	ei	PROPN
ejpam-1889	163	8	.	.	PUNCT
ejpam-1889	164	1	by	by	ADP
ejpam-1889	164	2	theorem	theorem	NOUN
ejpam-1889	164	3	1	1	NUM
ejpam-1889	164	4	,	,	PUNCT
ejpam-1889	164	5	γ	γ	X
ejpam-1889	164	6	is	be	AUX
ejpam-1889	164	7	l	l	NOUN
ejpam-1889	164	8	-	-	ADJ
ejpam-1889	164	9	equivalent	equivalent	ADJ
ejpam-1889	164	10	to	to	ADP
ejpam-1889	164	11	γ(1,1	γ(1,1	VERB
ejpam-1889	164	12	)	)	PUNCT
ejpam-1889	164	13	1	1	NUM
ejpam-1889	164	14	=	=	SYM
ejpam-1889	164	15	e1+〈e3	e1+〈e3	NOUN
ejpam-1889	164	16	〉	〉	NOUN
ejpam-1889	164	17	or	or	CCONJ
ejpam-1889	164	18	γ(1,1	γ(1,1	NOUN
ejpam-1889	164	19	)	)	PUNCT
ejpam-1889	164	20	2,α	2,α	NOUN
ejpam-1889	164	21	=	=	SYM
ejpam-1889	164	22	αe3	αe3	NOUN
ejpam-1889	164	23	+	+	CCONJ
ejpam-1889	164	24	〈	〈	NOUN
ejpam-1889	164	25	e1	e1	NOUN
ejpam-1889	164	26	〉	〉	NOUN
ejpam-1889	164	27	.	.	PUNCT
ejpam-1889	165	1	(	(	PUNCT
ejpam-1889	165	2	i	i	NOUN
ejpam-1889	165	3	)	)	PUNCT
ejpam-1889	165	4	suppose	suppose	VERB
ejpam-1889	165	5	that	that	SCONJ
ejpam-1889	165	6	γ	γ	PROPN
ejpam-1889	165	7	is	be	AUX
ejpam-1889	165	8	l	l	NOUN
ejpam-1889	165	9	-	-	ADJ
ejpam-1889	165	10	equivalent	equivalent	ADJ
ejpam-1889	165	11	to	to	ADP
ejpam-1889	165	12	γ(1,1	γ(1,1	VERB
ejpam-1889	165	13	)	)	PUNCT
ejpam-1889	165	14	1	1	NUM
ejpam-1889	165	15	.	.	PUNCT
ejpam-1889	166	1	then	then	ADV
ejpam-1889	166	2	b3	b3	PROPN
ejpam-1889	166	3	6=	6=	ADP
ejpam-1889	166	4	0	0	NUM
ejpam-1889	166	5	and	and	CCONJ
ejpam-1889	166	6			PROPN
ejpam-1889	166	7			ADJ
ejpam-1889	166	8			NUM
ejpam-1889	166	9	1	1	NUM
ejpam-1889	166	10	0	0	NUM
ejpam-1889	166	11	−	−	PROPN
ejpam-1889	166	12	b1	b1	PROPN
ejpam-1889	166	13	b3	b3	PROPN
ejpam-1889	166	14	0	0	NUM
ejpam-1889	166	15	sgn(b3	sgn(b3	PROPN
ejpam-1889	166	16	)	)	PUNCT
ejpam-1889	166	17	−	−	PROPN
ejpam-1889	166	18	sgn(b3)b2	sgn(b3)b2	PROPN
ejpam-1889	166	19	b3	b3	PROPN
ejpam-1889	166	20	0	0	NUM
ejpam-1889	166	21	0	0	NUM
ejpam-1889	166	22	sgn(b3	sgn(b3	PROPN
ejpam-1889	166	23	)	)	PUNCT
ejpam-1889	166	24			PROPN
ejpam-1889	167	1			PROPN
ejpam-1889	167	2			PROPN
ejpam-1889	167	3			NOUN
ejpam-1889	167	4			NUM
ejpam-1889	167	5	a1	a1	NOUN
ejpam-1889	167	6	b1	b1	PROPN
ejpam-1889	167	7	a2	a2	PROPN
ejpam-1889	167	8	b2	b2	PROPN
ejpam-1889	167	9	a3	a3	NOUN
ejpam-1889	167	10	b3	b3	PROPN
ejpam-1889	167	11			PROPN
ejpam-1889	167	12	=	=	PROPN
ejpam-1889	167	13			NOUN
ejpam-1889	167	14			NOUN
ejpam-1889	167	15	a′1	a′1	PROPN
ejpam-1889	167	16	0	0	PUNCT
ejpam-1889	168	1	a′2	a′2	ADJ
ejpam-1889	168	2	0	0	NUM
ejpam-1889	168	3	a′3	a′3	NOUN
ejpam-1889	168	4	|b3|	|b3|	NOUN
ejpam-1889	168	5			PROPN
ejpam-1889	168	6			PROPN
ejpam-1889	168	7	d.	d.	PROPN
ejpam-1889	168	8	barrett	barrett	PROPN
ejpam-1889	168	9	,	,	PUNCT
ejpam-1889	168	10	r.	r.	PROPN
ejpam-1889	168	11	biggs	biggs	PROPN
ejpam-1889	168	12	,	,	PUNCT
ejpam-1889	168	13	c.	c.	PROPN
ejpam-1889	168	14	remsing	remsing	NOUN
ejpam-1889	168	15	/	/	SYM
ejpam-1889	168	16	eur	eur	NOUN
ejpam-1889	168	17	.	.	PUNCT
ejpam-1889	169	1	j.	j.	PROPN
ejpam-1889	169	2	pure	pure	PROPN
ejpam-1889	169	3	appl	appl	PROPN
ejpam-1889	169	4	.	.	PROPN
ejpam-1889	169	5	math	math	PROPN
ejpam-1889	169	6	,	,	PUNCT
ejpam-1889	169	7	7	7	NUM
ejpam-1889	169	8	(	(	PUNCT
ejpam-1889	169	9	2014	2014	NUM
ejpam-1889	169	10	)	)	PUNCT
ejpam-1889	169	11	,	,	PUNCT
ejpam-1889	169	12	140	140	NUM
ejpam-1889	169	13	-	-	SYM
ejpam-1889	169	14	155	155	NUM
ejpam-1889	169	15	146	146	NUM
ejpam-1889	169	16	(	(	PUNCT
ejpam-1889	169	17	for	for	ADP
ejpam-1889	169	18	some	some	DET
ejpam-1889	169	19	a′1	a′1	PROPN
ejpam-1889	169	20	,	,	PUNCT
ejpam-1889	169	21	a′2	a′2	ADJ
ejpam-1889	169	22	,	,	PUNCT
ejpam-1889	169	23	a′3	a′3	NOUN
ejpam-1889	169	24	∈	∈	PROPN
ejpam-1889	169	25	r	r	NOUN
ejpam-1889	169	26	)	)	PUNCT
ejpam-1889	169	27	.	.	PUNCT
ejpam-1889	170	1	since	since	SCONJ
ejpam-1889	170	2	γ	γ	PROPN
ejpam-1889	170	3	is	be	AUX
ejpam-1889	170	4	l	l	NOUN
ejpam-1889	170	5	-	-	ADJ
ejpam-1889	170	6	equivalent	equivalent	ADJ
ejpam-1889	170	7	to	to	ADP
ejpam-1889	170	8	γ(1,1	γ(1,1	VERB
ejpam-1889	170	9	)	)	PUNCT
ejpam-1889	170	10	1	1	NUM
ejpam-1889	170	11	,	,	PUNCT
ejpam-1889	170	12	we	we	PRON
ejpam-1889	170	13	have	have	VERB
ejpam-1889	170	14	a′1	a′1	PROPN
ejpam-1889	170	15	6=	6=	ADP
ejpam-1889	170	16	0	0	NUM
ejpam-1889	170	17	,	,	PUNCT
ejpam-1889	170	18	a′2	a′2	ADJ
ejpam-1889	170	19	6=	6=	ADP
ejpam-1889	170	20	0	0	NUM
ejpam-1889	171	1	and	and	CCONJ
ejpam-1889	171	2	(	(	PUNCT
ejpam-1889	171	3	a′1	a′1	PROPN
ejpam-1889	171	4	)	)	PUNCT
ejpam-1889	171	5	2	2	NUM
ejpam-1889	171	6	6=	6=	SYM
ejpam-1889	171	7	(	(	PUNCT
ejpam-1889	171	8	a′2	a′2	SYM
ejpam-1889	171	9	)	)	PUNCT
ejpam-1889	171	10	2	2	NUM
ejpam-1889	171	11	.	.	PUNCT
ejpam-1889	171	12	accordingly	accordingly	ADV
ejpam-1889	171	13	,	,	PUNCT
ejpam-1889	171	14			NOUN
ejpam-1889	171	15			ADJ
ejpam-1889	171	16			ADJ
ejpam-1889	171	17			X
ejpam-1889	171	18	a′1	a′1	PROPN
ejpam-1889	171	19	(	(	PUNCT
ejpam-1889	171	20	a′1	a′1	PROPN
ejpam-1889	171	21	)	)	PUNCT
ejpam-1889	171	22	2−(a′2)2	2−(a′2)2	NUM
ejpam-1889	171	23	−	−	NOUN
ejpam-1889	171	24	a′2	a′2	NOUN
ejpam-1889	171	25	(	(	PUNCT
ejpam-1889	171	26	a′1	a′1	PROPN
ejpam-1889	171	27	)	)	PUNCT
ejpam-1889	171	28	2−(a′2)2	2−(a′2)2	NUM
ejpam-1889	171	29	0	0	NUM
ejpam-1889	171	30	−	−	NOUN
ejpam-1889	171	31	a′2	a′2	NOUN
ejpam-1889	171	32	(	(	PUNCT
ejpam-1889	171	33	a′1	a′1	PROPN
ejpam-1889	171	34	)	)	PUNCT
ejpam-1889	171	35	2−(a′2)2	2−(a′2)2	NUM
ejpam-1889	171	36	a′1	a′1	NOUN
ejpam-1889	171	37	(	(	PUNCT
ejpam-1889	171	38	a′1	a′1	PROPN
ejpam-1889	171	39	)	)	PUNCT
ejpam-1889	171	40	2−(a′2)2	2−(a′2)2	NUM
ejpam-1889	171	41	0	0	NUM
ejpam-1889	171	42	0	0	NUM
ejpam-1889	171	43	0	0	NUM
ejpam-1889	171	44	1	1	NUM
ejpam-1889	171	45			PROPN
ejpam-1889	171	46			PROPN
ejpam-1889	171	47			PROPN
ejpam-1889	171	48			PROPN
ejpam-1889	171	49			NOUN
ejpam-1889	171	50			NOUN
ejpam-1889	171	51	a′1	a′1	X
ejpam-1889	171	52	0	0	PUNCT
ejpam-1889	172	1	a′2	a′2	ADJ
ejpam-1889	172	2	0	0	NUM
ejpam-1889	172	3	a′3	a′3	NOUN
ejpam-1889	172	4	|b3|	|b3|	NOUN
ejpam-1889	172	5			PROPN
ejpam-1889	172	6	=	=	PROPN
ejpam-1889	172	7			NOUN
ejpam-1889	172	8			NOUN
ejpam-1889	172	9	1	1	NUM
ejpam-1889	172	10	0	0	NUM
ejpam-1889	172	11	0	0	NUM
ejpam-1889	172	12	0	0	NUM
ejpam-1889	172	13	γ1	γ1	PROPN
ejpam-1889	172	14	α	α	PROPN
ejpam-1889	172	15			PROPN
ejpam-1889	172	16			PROPN
ejpam-1889	172	17	where	where	SCONJ
ejpam-1889	172	18	α=	α=	NOUN
ejpam-1889	172	19	|b3|	|b3|	NOUN
ejpam-1889	172	20	>	>	X
ejpam-1889	172	21	0	0	PUNCT
ejpam-1889	172	22	and	and	CCONJ
ejpam-1889	172	23	γ1	γ1	PROPN
ejpam-1889	172	24	=	=	SYM
ejpam-1889	172	25	a′3	a′3	NOUN
ejpam-1889	172	26	∈	∈	PROPN
ejpam-1889	172	27	r.	r.	PROPN
ejpam-1889	172	28	thus	thus	ADV
ejpam-1889	172	29	π	π	PROPN
ejpam-1889	172	30	is	be	AUX
ejpam-1889	172	31	p	p	NOUN
ejpam-1889	172	32	-	-	PUNCT
ejpam-1889	172	33	equivalent	equivalent	ADJ
ejpam-1889	172	34	to	to	ADP
ejpam-1889	172	35	π(1,1	π(1,1	PROPN
ejpam-1889	172	36	)	)	PUNCT
ejpam-1889	172	37	1,α	1,α	PROPN
ejpam-1889	172	38	,	,	PUNCT
ejpam-1889	172	39	γ	γ	X
ejpam-1889	172	40	.	.	PROPN
ejpam-1889	172	41	(	(	PUNCT
ejpam-1889	172	42	ii	ii	NOUN
ejpam-1889	172	43	)	)	PUNCT
ejpam-1889	172	44	suppose	suppose	VERB
ejpam-1889	172	45	that	that	SCONJ
ejpam-1889	172	46	γ	γ	PROPN
ejpam-1889	172	47	is	be	AUX
ejpam-1889	172	48	l	l	NOUN
ejpam-1889	172	49	-	-	ADJ
ejpam-1889	172	50	equivalent	equivalent	ADJ
ejpam-1889	172	51	to	to	ADP
ejpam-1889	172	52	γ(1,1	γ(1,1	NOUN
ejpam-1889	172	53	)	)	PUNCT
ejpam-1889	172	54	2,α	2,α	NUM
ejpam-1889	172	55	.	.	PUNCT
ejpam-1889	173	1	then	then	ADV
ejpam-1889	173	2	b3	b3	PROPN
ejpam-1889	173	3	=	=	SYM
ejpam-1889	173	4	0	0	NUM
ejpam-1889	173	5	,	,	PUNCT
ejpam-1889	173	6	a3	a3	VERB
ejpam-1889	173	7	6=	6=	ADP
ejpam-1889	173	8	0	0	NUM
ejpam-1889	173	9	,	,	PUNCT
ejpam-1889	173	10	b2	b2	NOUN
ejpam-1889	173	11	1	1	NUM
ejpam-1889	173	12	6=	6=	NUM
ejpam-1889	173	13	b2	b2	NOUN
ejpam-1889	173	14	2	2	NUM
ejpam-1889	173	15	and	and	CCONJ
ejpam-1889	173	16			NOUN
ejpam-1889	173	17			NOUN
ejpam-1889	173	18	1	1	NUM
ejpam-1889	173	19	0	0	NUM
ejpam-1889	173	20	−	−	NOUN
ejpam-1889	173	21	a1	a1	NOUN
ejpam-1889	173	22	a3	a3	NOUN
ejpam-1889	173	23	0	0	SYM
ejpam-1889	173	24	sgn(a3	sgn(a3	NOUN
ejpam-1889	173	25	)	)	PUNCT
ejpam-1889	173	26	−	−	NOUN
ejpam-1889	173	27	sgn(a3)a2	sgn(a3)a2	NOUN
ejpam-1889	173	28	a3	a3	VERB
ejpam-1889	173	29	0	0	NUM
ejpam-1889	173	30	0	0	NUM
ejpam-1889	173	31	sgn(a3	sgn(a3	NOUN
ejpam-1889	173	32	)	)	PUNCT
ejpam-1889	174	1			PROPN
ejpam-1889	174	2			PROPN
ejpam-1889	174	3			NOUN
ejpam-1889	174	4			NUM
ejpam-1889	174	5	a1	a1	NOUN
ejpam-1889	174	6	b1	b1	PROPN
ejpam-1889	174	7	a2	a2	PROPN
ejpam-1889	174	8	b2	b2	PROPN
ejpam-1889	174	9	a3	a3	NOUN
ejpam-1889	174	10	0	0	NUM
ejpam-1889	175	1			PROPN
ejpam-1889	175	2	=	=	VERB
ejpam-1889	175	3			NOUN
ejpam-1889	175	4			NOUN
ejpam-1889	175	5	0	0	NUM
ejpam-1889	175	6	b1	b1	PROPN
ejpam-1889	175	7	0	0	NUM
ejpam-1889	175	8	sgn(a3)b2	sgn(a3)b2	PROPN
ejpam-1889	175	9	|a3|	|a3|	PROPN
ejpam-1889	175	10	0	0	PUNCT
ejpam-1889	176	1			PROPN
ejpam-1889	176	2			PROPN
ejpam-1889	176	3	.	.	PUNCT
ejpam-1889	177	1	furthermore	furthermore	ADV
ejpam-1889	177	2	,	,	PUNCT
ejpam-1889	177	3			NOUN
ejpam-1889	177	4			ADJ
ejpam-1889	177	5			NUM
ejpam-1889	177	6	b1	b1	NOUN
ejpam-1889	177	7	b2	b2	NOUN
ejpam-1889	177	8	1−b2	1−b2	NUM
ejpam-1889	177	9	2	2	NUM
ejpam-1889	177	10	−	−	PROPN
ejpam-1889	177	11	sgn(a3)b2	sgn(a3)b2	NOUN
ejpam-1889	177	12	b2	b2	NOUN
ejpam-1889	177	13	1−b2	1−b2	NUM
ejpam-1889	177	14	2	2	NUM
ejpam-1889	177	15	0	0	NUM
ejpam-1889	177	16	−	−	PROPN
ejpam-1889	177	17	sgn(a3)b2	sgn(a3)b2	NOUN
ejpam-1889	177	18	b2	b2	NOUN
ejpam-1889	177	19	1−b2	1−b2	NUM
ejpam-1889	177	20	2	2	NUM
ejpam-1889	177	21	b1	b1	NOUN
ejpam-1889	177	22	b2	b2	NOUN
ejpam-1889	177	23	1−b2	1−b2	NUM
ejpam-1889	177	24	2	2	NUM
ejpam-1889	177	25	0	0	NUM
ejpam-1889	177	26	0	0	NUM
ejpam-1889	177	27	0	0	NUM
ejpam-1889	177	28	1	1	NUM
ejpam-1889	177	29			PROPN
ejpam-1889	177	30			PROPN
ejpam-1889	177	31			PROPN
ejpam-1889	177	32			NOUN
ejpam-1889	177	33			NOUN
ejpam-1889	177	34	0	0	NUM
ejpam-1889	177	35	b1	b1	PROPN
ejpam-1889	177	36	0	0	NUM
ejpam-1889	177	37	sgn(a3)b2	sgn(a3)b2	PROPN
ejpam-1889	177	38	|a3|	|a3|	PROPN
ejpam-1889	177	39	0	0	NUM
ejpam-1889	178	1			PROPN
ejpam-1889	178	2	=	=	VERB
ejpam-1889	178	3			NOUN
ejpam-1889	178	4			NOUN
ejpam-1889	178	5	0	0	NUM
ejpam-1889	178	6	1	1	NUM
ejpam-1889	178	7	0	0	NUM
ejpam-1889	178	8	0	0	NUM
ejpam-1889	179	1	α	α	NOUN
ejpam-1889	179	2	0	0	PUNCT
ejpam-1889	179	3			PROPN
ejpam-1889	179	4			PROPN
ejpam-1889	179	5	where	where	SCONJ
ejpam-1889	179	6	α=	α=	NOUN
ejpam-1889	179	7	|a3|	|a3|	NOUN
ejpam-1889	179	8	>	>	X
ejpam-1889	179	9	0	0	PROPN
ejpam-1889	179	10	.	.	PUNCT
ejpam-1889	180	1	thus	thus	ADV
ejpam-1889	180	2	π	π	X
ejpam-1889	180	3	is	be	AUX
ejpam-1889	180	4	p	p	NOUN
ejpam-1889	180	5	-	-	PUNCT
ejpam-1889	180	6	equivalent	equivalent	ADJ
ejpam-1889	180	7	to	to	ADP
ejpam-1889	180	8	π(1,1	π(1,1	PROPN
ejpam-1889	180	9	)	)	PUNCT
ejpam-1889	180	10	2,α	2,α	PROPN
ejpam-1889	180	11	.	.	PUNCT
ejpam-1889	181	1	by	by	ADP
ejpam-1889	181	2	theorem	theorem	NOUN
ejpam-1889	181	3	1	1	NUM
ejpam-1889	181	4	,	,	PUNCT
ejpam-1889	181	5	γ(1,1	γ(1,1	NOUN
ejpam-1889	181	6	)	)	PUNCT
ejpam-1889	181	7	1	1	NUM
ejpam-1889	181	8	and	and	CCONJ
ejpam-1889	181	9	γ(1,1	γ(1,1	NOUN
ejpam-1889	181	10	)	)	PUNCT
ejpam-1889	181	11	2,α	2,α	NOUN
ejpam-1889	181	12	are	be	AUX
ejpam-1889	181	13	not	not	PART
ejpam-1889	181	14	l	l	NOUN
ejpam-1889	181	15	-	-	NOUN
ejpam-1889	181	16	equivalent	equivalent	ADJ
ejpam-1889	181	17	.	.	PUNCT
ejpam-1889	182	1	hence	hence	ADV
ejpam-1889	182	2	π(1,1	π(1,1	NUM
ejpam-1889	182	3	)	)	PUNCT
ejpam-1889	182	4	1,α	1,α	NOUN
ejpam-1889	182	5	,	,	PUNCT
ejpam-1889	182	6	γ	γ	X
ejpam-1889	182	7	is	be	AUX
ejpam-1889	182	8	not	not	PART
ejpam-1889	182	9	p	p	NOUN
ejpam-1889	182	10	-	-	PUNCT
ejpam-1889	182	11	equivalent	equivalent	ADJ
ejpam-1889	182	12	to	to	ADP
ejpam-1889	182	13	π(1,1	π(1,1	PROPN
ejpam-1889	182	14	)	)	PUNCT
ejpam-1889	182	15	2,α	2,α	PROPN
ejpam-1889	182	16	.	.	PUNCT
ejpam-1889	183	1	suppose	suppose	VERB
ejpam-1889	183	2	there	there	PRON
ejpam-1889	183	3	exists	exist	VERB
ejpam-1889	183	4	ψ	ψ	X
ejpam-1889	183	5	∈	∈	PROPN
ejpam-1889	183	6	aut	aut	X
ejpam-1889	183	7	(	(	PUNCT
ejpam-1889	183	8	se(1	se(1	PROPN
ejpam-1889	183	9	,	,	PUNCT
ejpam-1889	183	10	1	1	NUM
ejpam-1889	183	11	)	)	PUNCT
ejpam-1889	183	12	)	)	PUNCT
ejpam-1889	183	13	such	such	ADJ
ejpam-1889	183	14	that	that	SCONJ
ejpam-1889	183	15	ψ	ψ	ADP
ejpam-1889	183	16	◦	◦	NOUN
ejpam-1889	183	17	π(1,1	π(1,1	NOUN
ejpam-1889	183	18	)	)	PUNCT
ejpam-1889	183	19	1,α	1,α	NOUN
ejpam-1889	183	20	,	,	PUNCT
ejpam-1889	183	21	γ	γ	X
ejpam-1889	183	22	=	=	SYM
ejpam-1889	183	23	π	π	PROPN
ejpam-1889	183	24	(	(	PUNCT
ejpam-1889	183	25	1,1	1,1	NUM
ejpam-1889	183	26	)	)	PUNCT
ejpam-1889	183	27	1,α′,γ′	1,α′,γ′	PROPN
ejpam-1889	183	28	.	.	PUNCT
ejpam-1889	184	1	then	then	ADV
ejpam-1889	184	2			VERB
ejpam-1889	184	3			NOUN
ejpam-1889	184	4	x	x	PUNCT
ejpam-1889	185	1	+	+	CCONJ
ejpam-1889	185	2	vγ1	vγ1	NOUN
ejpam-1889	185	3	vα	vα	INTJ
ejpam-1889	185	4	ςy	ςy	PRON
ejpam-1889	185	5	+	+	NOUN
ejpam-1889	185	6	wγ1	wγ1	PROPN
ejpam-1889	185	7	wα	wα	NOUN
ejpam-1889	185	8	ςγ1	ςγ1	NOUN
ejpam-1889	185	9	ςα	ςα	ADP
ejpam-1889	185	10			PROPN
ejpam-1889	185	11	=	=	PROPN
ejpam-1889	185	12			NOUN
ejpam-1889	185	13			NOUN
ejpam-1889	185	14	1	1	NUM
ejpam-1889	185	15	0	0	NUM
ejpam-1889	185	16	0	0	NUM
ejpam-1889	185	17	0	0	NUM
ejpam-1889	185	18	γ′1	γ′1	NOUN
ejpam-1889	185	19	ςα′	ςα′	NOUN
ejpam-1889	185	20			PROPN
ejpam-1889	185	21			PROPN
ejpam-1889	185	22	(	(	PUNCT
ejpam-1889	185	23	for	for	ADP
ejpam-1889	185	24	some	some	DET
ejpam-1889	185	25	v	v	NOUN
ejpam-1889	185	26	,	,	PUNCT
ejpam-1889	186	1	w	w	PROPN
ejpam-1889	186	2	∈	∈	PROPN
ejpam-1889	186	3	r	r	NOUN
ejpam-1889	186	4	,	,	PUNCT
ejpam-1889	186	5	x2	x2	PROPN
ejpam-1889	186	6	6=	6=	PROPN
ejpam-1889	186	7	y2	y2	PROPN
ejpam-1889	186	8	and	and	CCONJ
ejpam-1889	186	9	ς	ς	PROPN
ejpam-1889	186	10	∈	∈	PROPN
ejpam-1889	186	11	{	{	PUNCT
ejpam-1889	186	12	−1,1	−1,1	NOUN
ejpam-1889	186	13	}	}	PUNCT
ejpam-1889	186	14	)	)	PUNCT
ejpam-1889	186	15	which	which	PRON
ejpam-1889	186	16	implies	imply	VERB
ejpam-1889	186	17	that	that	SCONJ
ejpam-1889	186	18	α	α	NOUN
ejpam-1889	186	19	=	=	SYM
ejpam-1889	186	20	α′	α′	NUM
ejpam-1889	186	21	,	,	PUNCT
ejpam-1889	186	22	ς	ς	PROPN
ejpam-1889	186	23	=	=	SYM
ejpam-1889	186	24	1	1	NUM
ejpam-1889	186	25	and	and	CCONJ
ejpam-1889	186	26	γ	γ	X
ejpam-1889	186	27	=	=	PUNCT
ejpam-1889	186	28	γ′.	γ′.	VERB
ejpam-1889	186	29	if	if	SCONJ
ejpam-1889	186	30	ψ	ψ	ADP
ejpam-1889	186	31	◦	◦	NOUN
ejpam-1889	186	32	π(1,1	π(1,1	NOUN
ejpam-1889	186	33	)	)	PUNCT
ejpam-1889	187	1	2,α	2,α	NOUN
ejpam-1889	187	2	=	=	SYM
ejpam-1889	187	3	π	π	PROPN
ejpam-1889	187	4	(	(	PUNCT
ejpam-1889	187	5	1,1	1,1	NUM
ejpam-1889	187	6	)	)	PUNCT
ejpam-1889	187	7	2,α′	2,α′	NUM
ejpam-1889	187	8	for	for	ADP
ejpam-1889	187	9	some	some	DET
ejpam-1889	187	10	automorphism	automorphism	NOUN
ejpam-1889	187	11	ψ	ψ	NOUN
ejpam-1889	187	12	,	,	PUNCT
ejpam-1889	187	13	then	then	ADV
ejpam-1889	187	14			VERB
ejpam-1889	187	15			NOUN
ejpam-1889	187	16	vα	vα	ADP
ejpam-1889	187	17	x	x	X
ejpam-1889	187	18	wα	wα	NOUN
ejpam-1889	187	19	ςy	ςy	NOUN
ejpam-1889	187	20	ςα	ςα	PROPN
ejpam-1889	187	21	0	0	NUM
ejpam-1889	187	22			PROPN
ejpam-1889	187	23	=	=	NOUN
ejpam-1889	187	24			NOUN
ejpam-1889	187	25			NOUN
ejpam-1889	187	26	0	0	NUM
ejpam-1889	187	27	1	1	NUM
ejpam-1889	187	28	0	0	NUM
ejpam-1889	187	29	0	0	NUM
ejpam-1889	187	30	α′	α′	NUM
ejpam-1889	187	31	0	0	NUM
ejpam-1889	187	32			PROPN
ejpam-1889	187	33			PROPN
ejpam-1889	187	34	and	and	CCONJ
ejpam-1889	187	35	so	so	ADV
ejpam-1889	187	36	α=	α=	ADJ
ejpam-1889	187	37	α′.	α′.	NOUN
ejpam-1889	187	38	if	if	SCONJ
ejpam-1889	187	39	π	π	X
ejpam-1889	187	40	:	:	PUNCT
ejpam-1889	187	41	a	a	DET
ejpam-1889	187	42	+	+	X
ejpam-1889	187	43	u1b	u1b	X
ejpam-1889	187	44	+	+	CCONJ
ejpam-1889	187	45	u2c	u2c	ADJ
ejpam-1889	187	46	is	be	AUX
ejpam-1889	187	47	a	a	DET
ejpam-1889	187	48	parametrized	parametrized	ADJ
ejpam-1889	187	49	(	(	PUNCT
ejpam-1889	187	50	2,0)-affine	2,0)-affine	NUM
ejpam-1889	187	51	subspace	subspace	NOUN
ejpam-1889	187	52	,	,	PUNCT
ejpam-1889	187	53	then	then	ADV
ejpam-1889	187	54	u	u	PROPN
ejpam-1889	187	55	7→	7→	PROPN
ejpam-1889	187	56	b	b	PROPN
ejpam-1889	187	57	+	+	CCONJ
ejpam-1889	187	58	uc	uc	PROPN
ejpam-1889	187	59	is	be	AUX
ejpam-1889	187	60	a	a	DET
ejpam-1889	187	61	parametrized	parametrized	ADJ
ejpam-1889	187	62	(	(	PUNCT
ejpam-1889	187	63	1,1)-affine	1,1)-affine	NUM
ejpam-1889	187	64	subspace	subspace	NOUN
ejpam-1889	187	65	,	,	PUNCT
ejpam-1889	187	66	and	and	CCONJ
ejpam-1889	187	67	hence	hence	ADV
ejpam-1889	187	68	is	be	AUX
ejpam-1889	187	69	p	p	NOUN
ejpam-1889	187	70	-	-	PUNCT
ejpam-1889	187	71	equivalent	equivalent	ADJ
ejpam-1889	187	72	to	to	ADP
ejpam-1889	187	73	π(1,1	π(1,1	PROPN
ejpam-1889	187	74	)	)	PUNCT
ejpam-1889	187	75	1,α	1,α	NOUN
ejpam-1889	187	76	,	,	PUNCT
ejpam-1889	187	77	γ	γ	NOUN
ejpam-1889	187	78	or	or	CCONJ
ejpam-1889	187	79	π(1,1	π(1,1	NOUN
ejpam-1889	187	80	)	)	PUNCT
ejpam-1889	187	81	2,α	2,α	NOUN
ejpam-1889	187	82	.	.	PUNCT
ejpam-1889	188	1	we	we	PRON
ejpam-1889	188	2	use	use	VERB
ejpam-1889	188	3	this	this	DET
ejpam-1889	188	4	fact	fact	NOUN
ejpam-1889	188	5	to	to	PART
ejpam-1889	188	6	arrive	arrive	VERB
ejpam-1889	188	7	at	at	ADP
ejpam-1889	188	8	the	the	DET
ejpam-1889	188	9	following	follow	VERB
ejpam-1889	188	10	classification	classification	NOUN
ejpam-1889	188	11	of	of	ADP
ejpam-1889	188	12	the	the	DET
ejpam-1889	188	13	parametrized	parametrized	ADJ
ejpam-1889	188	14	(	(	PUNCT
ejpam-1889	188	15	2,0)-affine	2,0)-affine	NUM
ejpam-1889	188	16	subspaces	subspace	NOUN
ejpam-1889	188	17	.	.	PUNCT
ejpam-1889	189	1	these	these	DET
ejpam-1889	189	2	representatives	representative	NOUN
ejpam-1889	189	3	parametrize	parametrize	VERB
ejpam-1889	189	4	γ(2,0	γ(2,0	NOUN
ejpam-1889	189	5	)	)	PUNCT
ejpam-1889	189	6	.	.	PUNCT
ejpam-1889	190	1	d.	d.	PROPN
ejpam-1889	190	2	barrett	barrett	PROPN
ejpam-1889	190	3	,	,	PUNCT
ejpam-1889	190	4	r.	r.	PROPN
ejpam-1889	190	5	biggs	biggs	PROPN
ejpam-1889	190	6	,	,	PUNCT
ejpam-1889	190	7	c.	c.	PROPN
ejpam-1889	190	8	remsing	remsing	NOUN
ejpam-1889	190	9	/	/	SYM
ejpam-1889	190	10	eur	eur	NOUN
ejpam-1889	190	11	.	.	PUNCT
ejpam-1889	191	1	j.	j.	PROPN
ejpam-1889	191	2	pure	pure	PROPN
ejpam-1889	191	3	appl	appl	PROPN
ejpam-1889	191	4	.	.	PROPN
ejpam-1889	191	5	math	math	PROPN
ejpam-1889	191	6	,	,	PUNCT
ejpam-1889	191	7	7	7	NUM
ejpam-1889	191	8	(	(	PUNCT
ejpam-1889	191	9	2014	2014	NUM
ejpam-1889	191	10	)	)	PUNCT
ejpam-1889	191	11	,	,	PUNCT
ejpam-1889	191	12	140	140	NUM
ejpam-1889	191	13	-	-	SYM
ejpam-1889	191	14	155	155	NUM
ejpam-1889	191	15	147	147	NUM
ejpam-1889	191	16	corollary	corollary	ADJ
ejpam-1889	191	17	2	2	NUM
ejpam-1889	191	18	.	.	PUNCT
ejpam-1889	192	1	let	let	VERB
ejpam-1889	192	2	π	π	PRON
ejpam-1889	192	3	:	:	PUNCT
ejpam-1889	192	4	∑3	∑3	PROPN
ejpam-1889	193	1	i=1	i=1	PROPN
ejpam-1889	193	2	ai	ai	VERB
ejpam-1889	193	3	ei	ei	X
ejpam-1889	193	4	+	+	NUM
ejpam-1889	193	5	u1	u1	PROPN
ejpam-1889	193	6	∑3	∑3	PROPN
ejpam-1889	194	1	i=1	i=1	PROPN
ejpam-1889	194	2	bi	bi	NOUN
ejpam-1889	194	3	ei	ei	PROPN
ejpam-1889	195	1	+	+	CCONJ
ejpam-1889	195	2	u2	u2	PROPN
ejpam-1889	195	3	∑3	∑3	PROPN
ejpam-1889	195	4	i=1	i=1	PROPN
ejpam-1889	195	5	ci	ci	NOUN
ejpam-1889	196	1	ei	ei	X
ejpam-1889	196	2	be	be	AUX
ejpam-1889	196	3	a	a	DET
ejpam-1889	196	4	parametrized	parametrized	ADJ
ejpam-1889	196	5	(	(	PUNCT
ejpam-1889	196	6	2	2	NUM
ejpam-1889	196	7	,	,	PUNCT
ejpam-1889	196	8	0)-affine	0)-affine	NUM
ejpam-1889	196	9	subspace	subspace	NOUN
ejpam-1889	196	10	.	.	PUNCT
ejpam-1889	197	1	π	π	PROPN
ejpam-1889	197	2	is	be	AUX
ejpam-1889	197	3	p	p	NOUN
ejpam-1889	197	4	-	-	PUNCT
ejpam-1889	197	5	equivalent	equivalent	ADJ
ejpam-1889	197	6	to	to	ADP
ejpam-1889	197	7	exactly	exactly	ADV
ejpam-1889	197	8	one	one	NUM
ejpam-1889	197	9	of	of	ADP
ejpam-1889	197	10	the	the	DET
ejpam-1889	197	11	following	follow	VERB
ejpam-1889	197	12	parametrized	parametrized	ADJ
ejpam-1889	197	13	affine	affine	NOUN
ejpam-1889	197	14	subspaces	subspace	NOUN
ejpam-1889	197	15	(	(	PUNCT
ejpam-1889	197	16	π(2,0	π(2,0	NOUN
ejpam-1889	197	17	)	)	PUNCT
ejpam-1889	197	18	1,α	1,α	PROPN
ejpam-1889	197	19	,	,	PUNCT
ejpam-1889	197	20	γ	γ	X
ejpam-1889	197	21	:	:	PUNCT
ejpam-1889	197	22	γ1e1	γ1e1	ADP
ejpam-1889	197	23	+	+	NOUN
ejpam-1889	197	24	γ2e3	γ2e3	X
ejpam-1889	197	25	+	+	CCONJ
ejpam-1889	197	26	u1(e1	u1(e1	NOUN
ejpam-1889	197	27	+	+	CCONJ
ejpam-1889	197	28	γ3e3	γ3e3	NOUN
ejpam-1889	197	29	)	)	PUNCT
ejpam-1889	198	1	+	+	CCONJ
ejpam-1889	198	2	u2(αe3	u2(αe3	ADJ
ejpam-1889	198	3	)	)	PUNCT
ejpam-1889	198	4	c3	c3	PROPN
ejpam-1889	198	5	6=	6=	ADP
ejpam-1889	198	6	0	0	NUM
ejpam-1889	198	7	π(2,0	π(2,0	NOUN
ejpam-1889	198	8	)	)	PUNCT
ejpam-1889	198	9	2,α	2,α	PROPN
ejpam-1889	198	10	,	,	PUNCT
ejpam-1889	198	11	γ	γ	X
ejpam-1889	198	12	:	:	PUNCT
ejpam-1889	198	13	γ1e1	γ1e1	ADP
ejpam-1889	198	14	+	+	CCONJ
ejpam-1889	198	15	γ2e3	γ2e3	PROPN
ejpam-1889	198	16	+	+	CCONJ
ejpam-1889	198	17	u1(αe3	u1(αe3	X
ejpam-1889	198	18	)	)	PUNCT
ejpam-1889	199	1	+	+	CCONJ
ejpam-1889	199	2	u2e1	u2e1	X
ejpam-1889	199	3	c3	c3	NOUN
ejpam-1889	199	4	=	=	PUNCT
ejpam-1889	199	5	0	0	X
ejpam-1889	199	6	.	.	PUNCT
ejpam-1889	200	1	here	here	ADV
ejpam-1889	200	2	α	α	X
ejpam-1889	200	3	>	>	X
ejpam-1889	200	4	0	0	PUNCT
ejpam-1889	201	1	and	and	CCONJ
ejpam-1889	201	2	γ1,γ2,γ3	γ1,γ2,γ3	VERB
ejpam-1889	201	3	∈	∈	PROPN
ejpam-1889	201	4	r	r	NOUN
ejpam-1889	201	5	,	,	PUNCT
ejpam-1889	201	6	with	with	ADP
ejpam-1889	201	7	different	different	ADJ
ejpam-1889	201	8	values	value	NOUN
ejpam-1889	201	9	of	of	ADP
ejpam-1889	201	10	these	these	DET
ejpam-1889	201	11	parameters	parameter	NOUN
ejpam-1889	201	12	yielding	yield	VERB
ejpam-1889	201	13	distinct	distinct	ADJ
ejpam-1889	201	14	(	(	PUNCT
ejpam-1889	201	15	nonequivalent	nonequivalent	ADJ
ejpam-1889	201	16	)	)	PUNCT
ejpam-1889	201	17	class	class	NOUN
ejpam-1889	201	18	representatives	representative	NOUN
ejpam-1889	201	19	.	.	PUNCT
ejpam-1889	202	1	we	we	PRON
ejpam-1889	202	2	now	now	ADV
ejpam-1889	202	3	proceed	proceed	VERB
ejpam-1889	202	4	to	to	ADP
ejpam-1889	202	5	the	the	DET
ejpam-1889	202	6	classification	classification	NOUN
ejpam-1889	202	7	of	of	ADP
ejpam-1889	202	8	the	the	DET
ejpam-1889	202	9	parametrized	parametrized	ADJ
ejpam-1889	202	10	(	(	PUNCT
ejpam-1889	202	11	2	2	NUM
ejpam-1889	202	12	,	,	PUNCT
ejpam-1889	202	13	1)-affine	1)-affine	NUM
ejpam-1889	202	14	subspaces	subspace	NOUN
ejpam-1889	202	15	.	.	PUNCT
ejpam-1889	203	1	lemma	lemma	PROPN
ejpam-1889	203	2	1	1	X
ejpam-1889	203	3	.	.	PUNCT
ejpam-1889	204	1	let	let	VERB
ejpam-1889	204	2	x	x	PUNCT
ejpam-1889	204	3	=	=	PRON
ejpam-1889	204	4	∑3	∑3	PROPN
ejpam-1889	204	5	i=1	i=1	X
ejpam-1889	204	6	x	x	VERB
ejpam-1889	205	1	i	i	PRON
ejpam-1889	205	2	ei	ei	X
ejpam-1889	205	3	,	,	PUNCT
ejpam-1889	205	4	y	y	PROPN
ejpam-1889	205	5	=	=	SYM
ejpam-1889	205	6	∑3	∑3	PROPN
ejpam-1889	205	7	i=1	i=1	PROPN
ejpam-1889	205	8	yi	yi	NOUN
ejpam-1889	206	1	ei	ei	NOUN
ejpam-1889	206	2	and	and	CCONJ
ejpam-1889	206	3	z	z	NOUN
ejpam-1889	206	4	=	=	SYM
ejpam-1889	206	5	z3e3	z3e3	NOUN
ejpam-1889	206	6	be	be	AUX
ejpam-1889	206	7	linearly	linearly	ADV
ejpam-1889	206	8	independent	independent	ADJ
ejpam-1889	206	9	elements	element	NOUN
ejpam-1889	206	10	of	of	ADP
ejpam-1889	206	11	se(1,1	se(1,1	NOUN
ejpam-1889	206	12	)	)	PUNCT
ejpam-1889	206	13	and	and	CCONJ
ejpam-1889	206	14	let	let	VERB
ejpam-1889	206	15	σ	σ	X
ejpam-1889	206	16	∈	∈	PROPN
ejpam-1889	206	17	{	{	PUNCT
ejpam-1889	206	18	−1	−1	NOUN
ejpam-1889	206	19	,	,	PUNCT
ejpam-1889	206	20	1	1	NUM
ejpam-1889	206	21	}	}	PUNCT
ejpam-1889	206	22	.	.	PUNCT
ejpam-1889	207	1	(	(	PUNCT
ejpam-1889	207	2	i	i	NOUN
ejpam-1889	207	3	)	)	PUNCT
ejpam-1889	207	4	if	if	SCONJ
ejpam-1889	207	5	y2	y2	PROPN
ejpam-1889	207	6	1	1	NUM
ejpam-1889	207	7	6=	6=	NUM
ejpam-1889	207	8	y2	y2	PROPN
ejpam-1889	207	9	2	2	NUM
ejpam-1889	207	10	,	,	PUNCT
ejpam-1889	207	11	then	then	ADV
ejpam-1889	207	12	there	there	PRON
ejpam-1889	207	13	exists	exist	VERB
ejpam-1889	207	14	ψ	ψ	X
ejpam-1889	207	15	∈	∈	PROPN
ejpam-1889	207	16	aut	aut	X
ejpam-1889	207	17	(	(	PUNCT
ejpam-1889	207	18	se(1	se(1	PROPN
ejpam-1889	207	19	,	,	PUNCT
ejpam-1889	207	20	1	1	NUM
ejpam-1889	207	21	)	)	PUNCT
ejpam-1889	207	22	)	)	PUNCT
ejpam-1889	207	23	such	such	ADJ
ejpam-1889	207	24	that	that	SCONJ
ejpam-1889	207	25	ψ	ψ	X
ejpam-1889	207	26	·	·	PUNCT
ejpam-1889	207	27	x	x	SYM
ejpam-1889	208	1	=	=	SYM
ejpam-1889	208	2			NOUN
ejpam-1889	208	3			NUM
ejpam-1889	208	4	x	x	SYM
ejpam-1889	208	5	′1	′1	SYM
ejpam-1889	208	6	σx	σx	ADP
ejpam-1889	208	7	′2	′2	PROPN
ejpam-1889	208	8	σx3	σx3	NOUN
ejpam-1889	208	9			PROPN
ejpam-1889	208	10			PROPN
ejpam-1889	208	11	,	,	PUNCT
ejpam-1889	208	12	ψ	ψ	NOUN
ejpam-1889	208	13	·	·	PUNCT
ejpam-1889	208	14	y	y	NOUN
ejpam-1889	208	15	=	=	SYM
ejpam-1889	208	16			PROPN
ejpam-1889	208	17			NOUN
ejpam-1889	208	18	1	1	NUM
ejpam-1889	208	19	0	0	NUM
ejpam-1889	208	20	σy3	σy3	PROPN
ejpam-1889	208	21			PROPN
ejpam-1889	208	22			PROPN
ejpam-1889	208	23	,	,	PUNCT
ejpam-1889	208	24	ψ	ψ	NOUN
ejpam-1889	208	25	·	·	PUNCT
ejpam-1889	208	26	z	z	X
ejpam-1889	208	27	=	=	SYM
ejpam-1889	208	28			PROPN
ejpam-1889	208	29			NOUN
ejpam-1889	208	30	0	0	NUM
ejpam-1889	208	31	0	0	NUM
ejpam-1889	208	32	σz3	σz3	PROPN
ejpam-1889	208	33			PROPN
ejpam-1889	208	34			PROPN
ejpam-1889	208	35	for	for	ADP
ejpam-1889	208	36	some	some	DET
ejpam-1889	208	37	x	x	PUNCT
ejpam-1889	208	38	′1	′1	NOUN
ejpam-1889	208	39	,	,	PUNCT
ejpam-1889	208	40	x	x	X
ejpam-1889	208	41	′2	′2	PROPN
ejpam-1889	208	42	∈	∈	PROPN
ejpam-1889	208	43	r.	r.	PROPN
ejpam-1889	208	44	(	(	PUNCT
ejpam-1889	208	45	ii	ii	PROPN
ejpam-1889	208	46	)	)	PUNCT
ejpam-1889	208	47	if	if	SCONJ
ejpam-1889	208	48	y2	y2	PROPN
ejpam-1889	208	49	1	1	NUM
ejpam-1889	208	50	=	=	SYM
ejpam-1889	208	51	y2	y2	NOUN
ejpam-1889	208	52	2	2	NUM
ejpam-1889	208	53	and	and	CCONJ
ejpam-1889	208	54	x2	x2	NOUN
ejpam-1889	208	55	1	1	X
ejpam-1889	208	56	6=	6=	NUM
ejpam-1889	208	57	x2	x2	PROPN
ejpam-1889	208	58	2	2	NUM
ejpam-1889	208	59	,	,	PUNCT
ejpam-1889	208	60	then	then	ADV
ejpam-1889	208	61	there	there	PRON
ejpam-1889	208	62	exists	exist	VERB
ejpam-1889	208	63	%	%	NOUN
ejpam-1889	208	64	∈	∈	PROPN
ejpam-1889	208	65	{	{	PUNCT
ejpam-1889	208	66	−1,1	−1,1	NOUN
ejpam-1889	208	67	}	}	PUNCT
ejpam-1889	208	68	and	and	CCONJ
ejpam-1889	208	69	ψ	ψ	X
ejpam-1889	208	70	∈	∈	PROPN
ejpam-1889	208	71	aut	aut	X
ejpam-1889	208	72	(	(	PUNCT
ejpam-1889	208	73	se(1	se(1	PROPN
ejpam-1889	208	74	,	,	PUNCT
ejpam-1889	208	75	1	1	NUM
ejpam-1889	208	76	)	)	PUNCT
ejpam-1889	208	77	)	)	PUNCT
ejpam-1889	208	78	such	such	ADJ
ejpam-1889	208	79	that	that	SCONJ
ejpam-1889	208	80	ψ	ψ	X
ejpam-1889	208	81	·	·	PUNCT
ejpam-1889	208	82	x	x	SYM
ejpam-1889	209	1	=	=	SYM
ejpam-1889	209	2			NOUN
ejpam-1889	209	3			NUM
ejpam-1889	209	4	x	x	SYM
ejpam-1889	209	5	′1	′1	SYM
ejpam-1889	209	6	0	0	NUM
ejpam-1889	209	7	σx3	σx3	NOUN
ejpam-1889	209	8			PROPN
ejpam-1889	209	9			PROPN
ejpam-1889	209	10	,	,	PUNCT
ejpam-1889	209	11	ψ	ψ	NOUN
ejpam-1889	209	12	·	·	PUNCT
ejpam-1889	209	13	y	y	NOUN
ejpam-1889	209	14	=	=	SYM
ejpam-1889	209	15			PROPN
ejpam-1889	209	16			VERB
ejpam-1889	209	17	1	1	NUM
ejpam-1889	209	18	%	%	NOUN
ejpam-1889	209	19	σ	σ	X
ejpam-1889	209	20	σy3	σy3	PROPN
ejpam-1889	209	21			PROPN
ejpam-1889	209	22			PROPN
ejpam-1889	209	23	,	,	PUNCT
ejpam-1889	209	24	ψ	ψ	NOUN
ejpam-1889	209	25	·	·	PUNCT
ejpam-1889	209	26	z	z	X
ejpam-1889	209	27	=	=	SYM
ejpam-1889	209	28			PROPN
ejpam-1889	209	29			NOUN
ejpam-1889	209	30	0	0	NUM
ejpam-1889	209	31	0	0	NUM
ejpam-1889	210	1	σz3	σz3	PROPN
ejpam-1889	210	2			PROPN
ejpam-1889	210	3			PROPN
ejpam-1889	210	4	for	for	ADP
ejpam-1889	210	5	some	some	DET
ejpam-1889	210	6	x	x	SYM
ejpam-1889	210	7	′1	′1	PROPN
ejpam-1889	210	8	∈	∈	PROPN
ejpam-1889	210	9	r.	r.	X
ejpam-1889	210	10	(	(	PUNCT
ejpam-1889	210	11	iii	iii	NOUN
ejpam-1889	210	12	)	)	PUNCT
ejpam-1889	210	13	if	if	SCONJ
ejpam-1889	210	14	y2	y2	PROPN
ejpam-1889	210	15	1	1	NUM
ejpam-1889	210	16	=	=	SYM
ejpam-1889	210	17	y2	y2	NOUN
ejpam-1889	210	18	2	2	NUM
ejpam-1889	210	19	and	and	CCONJ
ejpam-1889	210	20	x2	x2	PROPN
ejpam-1889	210	21	1	1	X
ejpam-1889	211	1	=	=	SYM
ejpam-1889	211	2	x2	x2	NOUN
ejpam-1889	211	3	2	2	NUM
ejpam-1889	211	4	,	,	PUNCT
ejpam-1889	211	5	then	then	ADV
ejpam-1889	211	6	there	there	PRON
ejpam-1889	211	7	exists	exist	VERB
ejpam-1889	211	8	%	%	NOUN
ejpam-1889	211	9	∈	∈	PROPN
ejpam-1889	211	10	{	{	PUNCT
ejpam-1889	211	11	−1,1	−1,1	NOUN
ejpam-1889	211	12	}	}	PUNCT
ejpam-1889	211	13	and	and	CCONJ
ejpam-1889	211	14	ψ	ψ	X
ejpam-1889	211	15	∈	∈	PROPN
ejpam-1889	211	16	aut	aut	X
ejpam-1889	211	17	(	(	PUNCT
ejpam-1889	211	18	se(1	se(1	PROPN
ejpam-1889	211	19	,	,	PUNCT
ejpam-1889	211	20	1	1	NUM
ejpam-1889	211	21	)	)	PUNCT
ejpam-1889	211	22	)	)	PUNCT
ejpam-1889	211	23	such	such	ADJ
ejpam-1889	211	24	that	that	SCONJ
ejpam-1889	211	25	ψ	ψ	X
ejpam-1889	211	26	·	·	PUNCT
ejpam-1889	211	27	x	x	SYM
ejpam-1889	211	28	=	=	PUNCT
ejpam-1889	211	29			PROPN
ejpam-1889	211	30			NUM
ejpam-1889	211	31	1	1	NUM
ejpam-1889	211	32	−σ	−σ	NOUN
ejpam-1889	211	33	σ%x3	σ%x3	VERB
ejpam-1889	211	34			PROPN
ejpam-1889	211	35			PROPN
ejpam-1889	211	36	,	,	PUNCT
ejpam-1889	211	37	ψ	ψ	NOUN
ejpam-1889	211	38	·	·	PUNCT
ejpam-1889	211	39	y	y	NOUN
ejpam-1889	211	40	=	=	SYM
ejpam-1889	211	41			PROPN
ejpam-1889	211	42			NUM
ejpam-1889	211	43	1	1	NUM
ejpam-1889	211	44	σ	σ	PROPN
ejpam-1889	211	45	σ%	σ%	PUNCT
ejpam-1889	211	46	y3	y3	NOUN
ejpam-1889	211	47			PROPN
ejpam-1889	211	48			PROPN
ejpam-1889	211	49	,	,	PUNCT
ejpam-1889	211	50	ψ	ψ	NOUN
ejpam-1889	211	51	·	·	PUNCT
ejpam-1889	211	52	z	z	X
ejpam-1889	211	53	=	=	SYM
ejpam-1889	211	54			PROPN
ejpam-1889	211	55			NOUN
ejpam-1889	211	56	0	0	NUM
ejpam-1889	211	57	0	0	NUM
ejpam-1889	212	1	σ%z3	σ%z3	NOUN
ejpam-1889	212	2			PROPN
ejpam-1889	212	3			PROPN
ejpam-1889	212	4	.	.	PUNCT
ejpam-1889	212	5	proof	proof	NOUN
ejpam-1889	212	6	.	.	PUNCT
ejpam-1889	213	1	(	(	PUNCT
ejpam-1889	213	2	i	i	NOUN
ejpam-1889	213	3	)	)	PUNCT
ejpam-1889	213	4	suppose	suppose	VERB
ejpam-1889	213	5	that	that	SCONJ
ejpam-1889	213	6	y2	y2	PROPN
ejpam-1889	213	7	1	1	NUM
ejpam-1889	213	8	6=	6=	NUM
ejpam-1889	213	9	y2	y2	PROPN
ejpam-1889	213	10	2	2	NUM
ejpam-1889	213	11	.	.	PUNCT
ejpam-1889	214	1	then	then	ADV
ejpam-1889	214	2			VERB
ejpam-1889	214	3			PROPN
ejpam-1889	214	4			NUM
ejpam-1889	214	5	y1	y1	NOUN
ejpam-1889	214	6	y2	y2	NOUN
ejpam-1889	214	7	1−y2	1−y2	NUM
ejpam-1889	214	8	2	2	NUM
ejpam-1889	214	9	−	−	NOUN
ejpam-1889	214	10	y2	y2	NOUN
ejpam-1889	214	11	y2	y2	NOUN
ejpam-1889	215	1	1−y2	1−y2	NUM
ejpam-1889	215	2	2	2	NUM
ejpam-1889	215	3	0	0	NUM
ejpam-1889	215	4	−	−	NOUN
ejpam-1889	215	5	σy2	σy2	NOUN
ejpam-1889	215	6	y2	y2	NOUN
ejpam-1889	215	7	1−y2	1−y2	NUM
ejpam-1889	215	8	2	2	NUM
ejpam-1889	215	9	σy1	σy1	NOUN
ejpam-1889	215	10	y2	y2	NOUN
ejpam-1889	215	11	1−y2	1−y2	NUM
ejpam-1889	215	12	2	2	NUM
ejpam-1889	215	13	0	0	NUM
ejpam-1889	215	14	0	0	NUM
ejpam-1889	215	15	0	0	NUM
ejpam-1889	215	16	σ	σ	PROPN
ejpam-1889	215	17			PROPN
ejpam-1889	215	18			PROPN
ejpam-1889	215	19			PROPN
ejpam-1889	215	20			NOUN
ejpam-1889	215	21			NOUN
ejpam-1889	215	22	x1	x1	NOUN
ejpam-1889	216	1	y1	y1	NOUN
ejpam-1889	216	2	0	0	NUM
ejpam-1889	217	1	x2	x2	NOUN
ejpam-1889	217	2	y2	y2	NOUN
ejpam-1889	217	3	0	0	NUM
ejpam-1889	218	1	x3	x3	ADJ
ejpam-1889	218	2	y3	y3	PROPN
ejpam-1889	218	3	z3	z3	PROPN
ejpam-1889	218	4			PROPN
ejpam-1889	218	5	=	=	PROPN
ejpam-1889	218	6			NOUN
ejpam-1889	218	7			NOUN
ejpam-1889	218	8	x	x	SYM
ejpam-1889	218	9	′1	′1	SYM
ejpam-1889	218	10	1	1	NUM
ejpam-1889	218	11	0	0	NUM
ejpam-1889	218	12	σx	σx	ADP
ejpam-1889	218	13	′2	′2	PROPN
ejpam-1889	218	14	0	0	NUM
ejpam-1889	218	15	0	0	NUM
ejpam-1889	218	16	σx3	σx3	NOUN
ejpam-1889	218	17	σy3	σy3	PROPN
ejpam-1889	218	18	σz3	σz3	PROPN
ejpam-1889	218	19			PROPN
ejpam-1889	218	20			PROPN
ejpam-1889	218	21	.	.	PUNCT
ejpam-1889	219	1	(	(	PUNCT
ejpam-1889	219	2	ii	ii	NOUN
ejpam-1889	219	3	)	)	PUNCT
ejpam-1889	219	4	suppose	suppose	VERB
ejpam-1889	219	5	that	that	SCONJ
ejpam-1889	219	6	y2	y2	PROPN
ejpam-1889	219	7	1	1	NUM
ejpam-1889	219	8	=	=	SYM
ejpam-1889	219	9	y2	y2	NOUN
ejpam-1889	219	10	2	2	NUM
ejpam-1889	219	11	and	and	CCONJ
ejpam-1889	219	12	x2	x2	NOUN
ejpam-1889	219	13	1	1	X
ejpam-1889	219	14	6=	6=	NUM
ejpam-1889	219	15	x2	x2	PROPN
ejpam-1889	219	16	2	2	NUM
ejpam-1889	219	17	.	.	PUNCT
ejpam-1889	220	1	let	let	VERB
ejpam-1889	220	2	y0	y0	PRON
ejpam-1889	220	3	=	=	SYM
ejpam-1889	220	4	y1	y1	PROPN
ejpam-1889	220	5	6=	6=	ADP
ejpam-1889	220	6	0	0	NUM
ejpam-1889	220	7	.	.	PUNCT
ejpam-1889	221	1	then	then	ADV
ejpam-1889	221	2	y2	y2	PROPN
ejpam-1889	221	3	=	=	SYM
ejpam-1889	221	4	±y0	±y0	NOUN
ejpam-1889	221	5	and	and	CCONJ
ejpam-1889	221	6			NOUN
ejpam-1889	221	7			ADJ
ejpam-1889	221	8			NOUN
ejpam-1889	222	1	x1	x1	NUM
ejpam-1889	222	2	x2	x2	NOUN
ejpam-1889	222	3	1−x2	1−x2	NUM
ejpam-1889	222	4	2	2	NUM
ejpam-1889	222	5	−	−	NOUN
ejpam-1889	222	6	x2	x2	NOUN
ejpam-1889	222	7	x2	x2	PROPN
ejpam-1889	222	8	1−x2	1−x2	NUM
ejpam-1889	222	9	2	2	NUM
ejpam-1889	222	10	0	0	NUM
ejpam-1889	222	11	∓	∓	NOUN
ejpam-1889	223	1	x2	x2	NOUN
ejpam-1889	223	2	x2	x2	PROPN
ejpam-1889	223	3	1−x2	1−x2	NUM
ejpam-1889	223	4	2	2	NUM
ejpam-1889	223	5	±	±	NUM
ejpam-1889	223	6	x1	x1	NOUN
ejpam-1889	224	1	x2	x2	NOUN
ejpam-1889	224	2	1−x2	1−x2	NUM
ejpam-1889	224	3	2	2	NUM
ejpam-1889	224	4	0	0	NUM
ejpam-1889	224	5	0	0	NUM
ejpam-1889	224	6	0	0	NUM
ejpam-1889	224	7	±1	±1	VERB
ejpam-1889	224	8			PROPN
ejpam-1889	224	9			PROPN
ejpam-1889	224	10			PROPN
ejpam-1889	224	11			NOUN
ejpam-1889	224	12			NOUN
ejpam-1889	225	1	x1	x1	NUM
ejpam-1889	225	2	y0	y0	NOUN
ejpam-1889	225	3	0	0	NUM
ejpam-1889	226	1	x2	x2	PROPN
ejpam-1889	226	2	±y0	±y0	NOUN
ejpam-1889	226	3	0	0	NUM
ejpam-1889	227	1	x3	x3	ADJ
ejpam-1889	227	2	y3	y3	PROPN
ejpam-1889	227	3	z3	z3	PROPN
ejpam-1889	227	4			PROPN
ejpam-1889	227	5	=	=	PROPN
ejpam-1889	227	6			NOUN
ejpam-1889	227	7			NUM
ejpam-1889	227	8	1	1	NUM
ejpam-1889	227	9	y	y	PROPN
ejpam-1889	227	10	′0	′0	PROPN
ejpam-1889	227	11	0	0	NUM
ejpam-1889	227	12	0	0	NUM
ejpam-1889	227	13	y	y	PROPN
ejpam-1889	227	14	′0	′0	NOUN
ejpam-1889	227	15	0	0	NUM
ejpam-1889	227	16	±x3	±x3	NOUN
ejpam-1889	227	17	±y3	±y3	X
ejpam-1889	227	18	±z3	±z3	NOUN
ejpam-1889	227	19			PROPN
ejpam-1889	227	20			PROPN
ejpam-1889	227	21	.	.	PUNCT
ejpam-1889	227	22	d.	d.	PROPN
ejpam-1889	227	23	barrett	barrett	PROPN
ejpam-1889	227	24	,	,	PUNCT
ejpam-1889	227	25	r.	r.	PROPN
ejpam-1889	227	26	biggs	biggs	PROPN
ejpam-1889	227	27	,	,	PUNCT
ejpam-1889	227	28	c.	c.	PROPN
ejpam-1889	227	29	remsing	remsing	NOUN
ejpam-1889	227	30	/	/	SYM
ejpam-1889	227	31	eur	eur	NOUN
ejpam-1889	227	32	.	.	PUNCT
ejpam-1889	228	1	j.	j.	PROPN
ejpam-1889	228	2	pure	pure	PROPN
ejpam-1889	228	3	appl	appl	PROPN
ejpam-1889	228	4	.	.	PROPN
ejpam-1889	228	5	math	math	PROPN
ejpam-1889	228	6	,	,	PUNCT
ejpam-1889	228	7	7	7	NUM
ejpam-1889	228	8	(	(	PUNCT
ejpam-1889	228	9	2014	2014	NUM
ejpam-1889	228	10	)	)	PUNCT
ejpam-1889	228	11	,	,	PUNCT
ejpam-1889	228	12	140	140	NUM
ejpam-1889	228	13	-	-	SYM
ejpam-1889	228	14	155	155	NUM
ejpam-1889	228	15	148	148	NUM
ejpam-1889	228	16	furthermore	furthermore	ADV
ejpam-1889	228	17	,	,	PUNCT
ejpam-1889	228	18			NOUN
ejpam-1889	228	19			ADJ
ejpam-1889	228	20			NUM
ejpam-1889	228	21	1	1	NUM
ejpam-1889	228	22	y	y	PROPN
ejpam-1889	228	23	′0	′0	NOUN
ejpam-1889	228	24	0	0	NUM
ejpam-1889	228	25	0	0	NUM
ejpam-1889	228	26	0	0	NUM
ejpam-1889	228	27	±	±	NUM
ejpam-1889	228	28	σy	σy	NOUN
ejpam-1889	228	29	′0	′0	PROPN
ejpam-1889	228	30	0	0	NUM
ejpam-1889	228	31	0	0	NUM
ejpam-1889	228	32	0	0	NUM
ejpam-1889	228	33	±σ	±σ	PROPN
ejpam-1889	228	34			PROPN
ejpam-1889	228	35			PROPN
ejpam-1889	228	36			PROPN
ejpam-1889	228	37			NOUN
ejpam-1889	228	38			VERB
ejpam-1889	228	39	1	1	NUM
ejpam-1889	228	40	y	y	PROPN
ejpam-1889	228	41	′0	′0	PROPN
ejpam-1889	228	42	0	0	NUM
ejpam-1889	228	43	0	0	NUM
ejpam-1889	229	1	y	y	PROPN
ejpam-1889	229	2	′0	′0	NOUN
ejpam-1889	229	3	0	0	NUM
ejpam-1889	229	4	±x3	±x3	NOUN
ejpam-1889	229	5	±y3	±y3	PUNCT
ejpam-1889	229	6	±z3	±z3	NOUN
ejpam-1889	229	7			NUM
ejpam-1889	229	8	=	=	NOUN
ejpam-1889	229	9			NOUN
ejpam-1889	229	10			NOUN
ejpam-1889	229	11	x	x	SYM
ejpam-1889	229	12	′′1	′′1	NOUN
ejpam-1889	229	13	1	1	NUM
ejpam-1889	229	14	0	0	NUM
ejpam-1889	229	15	0	0	NUM
ejpam-1889	229	16	%	%	NOUN
ejpam-1889	229	17	σ	σ	NOUN
ejpam-1889	229	18	0	0	NUM
ejpam-1889	229	19	σx3	σx3	NOUN
ejpam-1889	229	20	σy3	σy3	PROPN
ejpam-1889	229	21	σz3	σz3	PROPN
ejpam-1889	229	22			PROPN
ejpam-1889	229	23			PROPN
ejpam-1889	229	24	where	where	SCONJ
ejpam-1889	229	25	%	%	NOUN
ejpam-1889	229	26	=	=	SYM
ejpam-1889	229	27	±1	±1	VERB
ejpam-1889	229	28	.	.	PUNCT
ejpam-1889	230	1	(	(	PUNCT
ejpam-1889	230	2	the	the	DET
ejpam-1889	230	3	composition	composition	NOUN
ejpam-1889	230	4	of	of	ADP
ejpam-1889	230	5	these	these	DET
ejpam-1889	230	6	two	two	NUM
ejpam-1889	230	7	automorphisms	automorphisms	PROPN
ejpam-1889	230	8	yields	yield	VERB
ejpam-1889	230	9	ψ	ψ	NOUN
ejpam-1889	230	10	.	.	PUNCT
ejpam-1889	230	11	)	)	PUNCT
ejpam-1889	231	1	(	(	PUNCT
ejpam-1889	231	2	iii	iii	X
ejpam-1889	231	3	)	)	PUNCT
ejpam-1889	231	4	suppose	suppose	VERB
ejpam-1889	231	5	that	that	SCONJ
ejpam-1889	231	6	y2	y2	PROPN
ejpam-1889	231	7	1	1	NUM
ejpam-1889	231	8	=	=	SYM
ejpam-1889	231	9	y2	y2	NOUN
ejpam-1889	231	10	2	2	NUM
ejpam-1889	231	11	and	and	CCONJ
ejpam-1889	231	12	x2	x2	PROPN
ejpam-1889	231	13	1	1	X
ejpam-1889	231	14	=	=	SYM
ejpam-1889	231	15	x2	x2	NOUN
ejpam-1889	231	16	2	2	X
ejpam-1889	231	17	.	.	PUNCT
ejpam-1889	232	1	let	let	VERB
ejpam-1889	232	2	y0	y0	PRON
ejpam-1889	232	3	=	=	SYM
ejpam-1889	232	4	y1	y1	PROPN
ejpam-1889	232	5	6=	6=	ADP
ejpam-1889	232	6	0	0	NUM
ejpam-1889	233	1	and	and	CCONJ
ejpam-1889	233	2	x0	x0	PROPN
ejpam-1889	233	3	=	=	PUNCT
ejpam-1889	234	1	x1	x1	PROPN
ejpam-1889	234	2	6=	6=	ADP
ejpam-1889	234	3	0	0	NUM
ejpam-1889	234	4	.	.	PUNCT
ejpam-1889	235	1	then	then	ADV
ejpam-1889	235	2	(	(	PUNCT
ejpam-1889	235	3	since	since	SCONJ
ejpam-1889	235	4	x	x	PROPN
ejpam-1889	235	5	and	and	CCONJ
ejpam-1889	235	6	y	y	PROPN
ejpam-1889	235	7	are	be	AUX
ejpam-1889	235	8	linearly	linearly	ADV
ejpam-1889	235	9	independent	independent	ADJ
ejpam-1889	235	10	)	)	PUNCT
ejpam-1889	236	1	y2	y2	NOUN
ejpam-1889	236	2	=	=	SYM
ejpam-1889	237	1	±y0	±y0	NOUN
ejpam-1889	237	2	and	and	CCONJ
ejpam-1889	237	3	x2	x2	NOUN
ejpam-1889	237	4	=	=	PUNCT
ejpam-1889	238	1	∓x0	∓x0	ADJ
ejpam-1889	238	2	.	.	PUNCT
ejpam-1889	239	1	we	we	PRON
ejpam-1889	239	2	have	have	VERB
ejpam-1889	239	3			NOUN
ejpam-1889	239	4			NOUN
ejpam-1889	239	5	1	1	NUM
ejpam-1889	239	6	y0	y0	NOUN
ejpam-1889	239	7	0	0	NUM
ejpam-1889	239	8	0	0	NUM
ejpam-1889	239	9	0	0	NUM
ejpam-1889	239	10	±	±	NUM
ejpam-1889	239	11	1	1	NUM
ejpam-1889	239	12	y0	y0	NOUN
ejpam-1889	239	13	0	0	NUM
ejpam-1889	239	14	0	0	SYM
ejpam-1889	239	15	0	0	NUM
ejpam-1889	239	16	±1	±1	VERB
ejpam-1889	239	17			PROPN
ejpam-1889	239	18			PROPN
ejpam-1889	239	19			NOUN
ejpam-1889	239	20			NOUN
ejpam-1889	239	21	x0	x0	NUM
ejpam-1889	239	22	y0	y0	NOUN
ejpam-1889	239	23	0	0	PUNCT
ejpam-1889	240	1	∓x0	∓x0	PUNCT
ejpam-1889	240	2	±y0	±y0	NOUN
ejpam-1889	240	3	0	0	NUM
ejpam-1889	240	4	x3	x3	ADJ
ejpam-1889	240	5	y3	y3	PROPN
ejpam-1889	240	6	z3	z3	PROPN
ejpam-1889	240	7			PROPN
ejpam-1889	240	8	=	=	PROPN
ejpam-1889	241	1			NOUN
ejpam-1889	241	2			NOUN
ejpam-1889	241	3	x	x	SYM
ejpam-1889	241	4	′0	′0	NOUN
ejpam-1889	241	5	1	1	NUM
ejpam-1889	241	6	0	0	NUM
ejpam-1889	241	7	−x	−x	NUM
ejpam-1889	241	8	′0	′0	NOUN
ejpam-1889	241	9	1	1	NUM
ejpam-1889	241	10	0	0	NUM
ejpam-1889	241	11	±x3	±x3	NOUN
ejpam-1889	241	12	±y3	±y3	X
ejpam-1889	241	13	±z3	±z3	NOUN
ejpam-1889	241	14			PROPN
ejpam-1889	241	15			PROPN
ejpam-1889	241	16	.	.	PUNCT
ejpam-1889	242	1	moreover	moreover	ADV
ejpam-1889	242	2	,	,	PUNCT
ejpam-1889	242	3			NOUN
ejpam-1889	242	4			ADJ
ejpam-1889	242	5			ADJ
ejpam-1889	242	6			NOUN
ejpam-1889	242	7	x	x	X
ejpam-1889	242	8	′0	′0	X
ejpam-1889	242	9	+	+	ADJ
ejpam-1889	242	10	1	1	NUM
ejpam-1889	242	11	2x	2x	NUM
ejpam-1889	242	12	′0	′0	NOUN
ejpam-1889	242	13	x	x	SYM
ejpam-1889	242	14	′0−1	′0−1	VERB
ejpam-1889	242	15	2x	2x	NUM
ejpam-1889	242	16	′0	′0	NOUN
ejpam-1889	242	17	0	0	NUM
ejpam-1889	242	18	σ(x	σ(x	PROPN
ejpam-1889	242	19	′0−1	′0−1	NUM
ejpam-1889	242	20	)	)	PUNCT
ejpam-1889	242	21	2x	2x	NUM
ejpam-1889	242	22	′0	′0	NOUN
ejpam-1889	242	23	σ(x	σ(x	PROPN
ejpam-1889	242	24	′0	′0	NOUN
ejpam-1889	242	25	+	+	ADJ
ejpam-1889	242	26	1	1	NUM
ejpam-1889	242	27	)	)	PUNCT
ejpam-1889	242	28	2x	2x	NUM
ejpam-1889	243	1	′0	′0	NOUN
ejpam-1889	243	2	0	0	NUM
ejpam-1889	243	3	0	0	NUM
ejpam-1889	243	4	0	0	NUM
ejpam-1889	243	5	σ	σ	NOUN
ejpam-1889	243	6			PROPN
ejpam-1889	243	7			PROPN
ejpam-1889	243	8			PROPN
ejpam-1889	243	9			PROPN
ejpam-1889	243	10			NOUN
ejpam-1889	243	11			NOUN
ejpam-1889	243	12	x	x	SYM
ejpam-1889	243	13	′0	′0	NOUN
ejpam-1889	243	14	1	1	NUM
ejpam-1889	243	15	0	0	NUM
ejpam-1889	243	16	−x	−x	NUM
ejpam-1889	243	17	′0	′0	NOUN
ejpam-1889	243	18	1	1	NUM
ejpam-1889	243	19	0	0	NUM
ejpam-1889	243	20	±x3	±x3	NOUN
ejpam-1889	243	21	±y3	±y3	PUNCT
ejpam-1889	243	22	±z3	±z3	NOUN
ejpam-1889	243	23			NUM
ejpam-1889	243	24	=	=	VERB
ejpam-1889	243	25			NOUN
ejpam-1889	243	26			NOUN
ejpam-1889	243	27	1	1	NUM
ejpam-1889	243	28	1	1	NUM
ejpam-1889	243	29	0	0	NUM
ejpam-1889	243	30	−σ	−σ	NOUN
ejpam-1889	243	31	σ	σ	PROPN
ejpam-1889	243	32	0	0	NUM
ejpam-1889	243	33	σ%x3	σ%x3	NOUN
ejpam-1889	243	34	σ%	σ%	ADV
ejpam-1889	243	35	y3	y3	NOUN
ejpam-1889	243	36	σ%z3	σ%z3	NOUN
ejpam-1889	243	37			PROPN
ejpam-1889	243	38			PROPN
ejpam-1889	243	39	where	where	SCONJ
ejpam-1889	243	40	%	%	NOUN
ejpam-1889	243	41	=	=	SYM
ejpam-1889	243	42	±1	±1	VERB
ejpam-1889	243	43	.	.	PUNCT
ejpam-1889	244	1	theorem	theorem	NOUN
ejpam-1889	244	2	4	4	NUM
ejpam-1889	244	3	.	.	PUNCT
ejpam-1889	245	1	let	let	VERB
ejpam-1889	245	2	π	π	PRON
ejpam-1889	245	3	:	:	PUNCT
ejpam-1889	245	4	∑3	∑3	PROPN
ejpam-1889	246	1	i=1	i=1	PROPN
ejpam-1889	246	2	ai	ai	VERB
ejpam-1889	246	3	ei	ei	X
ejpam-1889	246	4	+	+	NUM
ejpam-1889	246	5	u1	u1	PROPN
ejpam-1889	246	6	∑3	∑3	PROPN
ejpam-1889	247	1	i=1	i=1	PROPN
ejpam-1889	247	2	bi	bi	NOUN
ejpam-1889	247	3	ei	ei	PROPN
ejpam-1889	248	1	+	+	CCONJ
ejpam-1889	248	2	u2	u2	PROPN
ejpam-1889	248	3	∑3	∑3	PROPN
ejpam-1889	248	4	i=1	i=1	PROPN
ejpam-1889	248	5	ci	ci	NOUN
ejpam-1889	249	1	ei	ei	AUX
ejpam-1889	249	2	be	be	AUX
ejpam-1889	249	3	a	a	DET
ejpam-1889	249	4	parametrization	parametrization	NOUN
ejpam-1889	249	5	of	of	ADP
ejpam-1889	249	6	a	a	DET
ejpam-1889	249	7	(	(	PUNCT
ejpam-1889	249	8	2	2	NUM
ejpam-1889	249	9	,	,	PUNCT
ejpam-1889	249	10	1)affine	1)affine	NUM
ejpam-1889	249	11	subspace	subspace	PROPN
ejpam-1889	249	12	γ	γ	PROPN
ejpam-1889	249	13	.	.	PUNCT
ejpam-1889	250	1	(	(	PUNCT
ejpam-1889	250	2	i	i	NOUN
ejpam-1889	250	3	)	)	PUNCT
ejpam-1889	250	4	if	if	SCONJ
ejpam-1889	250	5	γ	γ	X
ejpam-1889	250	6	isl	isl	PROPN
ejpam-1889	250	7	-	-	PUNCT
ejpam-1889	250	8	equivalent	equivalent	ADJ
ejpam-1889	250	9	to	to	ADP
ejpam-1889	250	10	γ(2,1	γ(2,1	PROPN
ejpam-1889	250	11	)	)	PUNCT
ejpam-1889	250	12	1	1	NUM
ejpam-1889	250	13	,	,	PUNCT
ejpam-1889	250	14	thenπ	thenπ	NOUN
ejpam-1889	250	15	isp	isp	ADV
ejpam-1889	250	16	-	-	PUNCT
ejpam-1889	250	17	equivalent	equivalent	ADJ
ejpam-1889	250	18	to	to	ADP
ejpam-1889	250	19	exactly	exactly	ADV
ejpam-1889	250	20	one	one	NUM
ejpam-1889	250	21	of	of	ADP
ejpam-1889	250	22	the	the	DET
ejpam-1889	250	23	following	follow	VERB
ejpam-1889	250	24	parametrized	parametrized	ADJ
ejpam-1889	250	25	affine	affine	NOUN
ejpam-1889	250	26	subspaces	subspace	NOUN
ejpam-1889	250	27	(	(	PUNCT
ejpam-1889	250	28	π(2,1	π(2,1	NOUN
ejpam-1889	250	29	)	)	PUNCT
ejpam-1889	250	30	1,α	1,α	NOUN
ejpam-1889	250	31	,	,	PUNCT
ejpam-1889	250	32	β	β	X
ejpam-1889	250	33	,	,	PUNCT
ejpam-1889	250	34	γ	γ	X
ejpam-1889	250	35	:	:	PUNCT
ejpam-1889	250	36	γ1e1	γ1e1	ADP
ejpam-1889	250	37	+	+	X
ejpam-1889	250	38	β1e2	β1e2	PUNCT
ejpam-1889	251	1	+	+	NUM
ejpam-1889	251	2	γ2e3	γ2e3	X
ejpam-1889	251	3	+	+	CCONJ
ejpam-1889	251	4	u1(e1	u1(e1	NOUN
ejpam-1889	251	5	+	+	CCONJ
ejpam-1889	251	6	γ3e3	γ3e3	NOUN
ejpam-1889	251	7	)	)	PUNCT
ejpam-1889	251	8	+	+	CCONJ
ejpam-1889	251	9	u2(αe3	u2(αe3	ADJ
ejpam-1889	251	10	)	)	PUNCT
ejpam-1889	251	11	c3	c3	PROPN
ejpam-1889	251	12	6=	6=	ADP
ejpam-1889	251	13	0	0	NUM
ejpam-1889	251	14	π(2,1	π(2,1	NOUN
ejpam-1889	251	15	)	)	PUNCT
ejpam-1889	251	16	2,α	2,α	PROPN
ejpam-1889	251	17	,	,	PUNCT
ejpam-1889	251	18	β	β	X
ejpam-1889	251	19	,	,	PUNCT
ejpam-1889	251	20	γ	γ	X
ejpam-1889	251	21	:	:	PUNCT
ejpam-1889	251	22	γ1e1	γ1e1	ADP
ejpam-1889	251	23	+	+	X
ejpam-1889	251	24	β1e2	β1e2	PUNCT
ejpam-1889	251	25	+	+	NUM
ejpam-1889	251	26	γ2e3	γ2e3	X
ejpam-1889	251	27	+	+	CCONJ
ejpam-1889	251	28	u1(αe3	u1(αe3	X
ejpam-1889	251	29	)	)	PUNCT
ejpam-1889	252	1	+	+	CCONJ
ejpam-1889	252	2	u2e1	u2e1	X
ejpam-1889	252	3	c3	c3	X
ejpam-1889	252	4	=	=	PROPN
ejpam-1889	252	5	0	0	PROPN
ejpam-1889	252	6	.	.	PUNCT
ejpam-1889	252	7	(	(	PUNCT
ejpam-1889	252	8	ii	ii	NOUN
ejpam-1889	252	9	)	)	PUNCT
ejpam-1889	252	10	if	if	SCONJ
ejpam-1889	252	11	γ	γ	X
ejpam-1889	252	12	isl	isl	PROPN
ejpam-1889	252	13	-	-	PUNCT
ejpam-1889	252	14	equivalent	equivalent	ADJ
ejpam-1889	252	15	to	to	ADP
ejpam-1889	252	16	γ(2,1	γ(2,1	PROPN
ejpam-1889	252	17	)	)	PUNCT
ejpam-1889	252	18	2	2	NUM
ejpam-1889	252	19	,	,	PUNCT
ejpam-1889	252	20	thenπ	thenπ	NOUN
ejpam-1889	252	21	isp	isp	ADV
ejpam-1889	252	22	-	-	PUNCT
ejpam-1889	252	23	equivalent	equivalent	ADJ
ejpam-1889	252	24	to	to	ADP
ejpam-1889	252	25	exactly	exactly	ADV
ejpam-1889	252	26	one	one	NUM
ejpam-1889	252	27	of	of	ADP
ejpam-1889	252	28	the	the	DET
ejpam-1889	252	29	following	follow	VERB
ejpam-1889	252	30	parametrized	parametrized	ADJ
ejpam-1889	252	31	affine	affine	NOUN
ejpam-1889	252	32	subspaces	subspace	NOUN
ejpam-1889	252	33			PRON
ejpam-1889	252	34			ADJ
ejpam-1889	252	35			PROPN
ejpam-1889	252	36			PROPN
ejpam-1889	252	37			PROPN
ejpam-1889	252	38			NOUN
ejpam-1889	252	39			PROPN
ejpam-1889	252	40			PROPN
ejpam-1889	252	41			PROPN
ejpam-1889	252	42			PROPN
ejpam-1889	252	43			PROPN
ejpam-1889	252	44	π(2,1	π(2,1	PROPN
ejpam-1889	252	45	)	)	PUNCT
ejpam-1889	252	46	3,β	3,β	NUM
ejpam-1889	252	47	,	,	PUNCT
ejpam-1889	252	48	γ	γ	X
ejpam-1889	252	49	:	:	PUNCT
ejpam-1889	252	50	β1e1	β1e1	SYM
ejpam-1889	252	51	+	+	CCONJ
ejpam-1889	252	52	γ1e3	γ1e3	X
ejpam-1889	252	53	+	+	CCONJ
ejpam-1889	252	54	u1(e1	u1(e1	NOUN
ejpam-1889	252	55	+	+	CCONJ
ejpam-1889	252	56	e2	e2	PROPN
ejpam-1889	252	57	+	+	CCONJ
ejpam-1889	252	58	γ2e3	γ2e3	X
ejpam-1889	252	59	)	)	PUNCT
ejpam-1889	253	1	+	+	CCONJ
ejpam-1889	253	2	u2(β2e3	u2(β2e3	X
ejpam-1889	253	3	)	)	PUNCT
ejpam-1889	253	4	c3	c3	PROPN
ejpam-1889	253	5	6=	6=	ADP
ejpam-1889	253	6	0	0	NUM
ejpam-1889	253	7	,	,	PUNCT
ejpam-1889	253	8	�	�	PROPN
ejpam-1889	253	9	a1c3−a3c1	a1c3−a3c1	PROPN
ejpam-1889	253	10	c3	c3	PROPN
ejpam-1889	253	11	�	�	PROPN
ejpam-1889	253	12	2	2	NUM
ejpam-1889	253	13	6=	6=	NUM
ejpam-1889	253	14	�	�	PROPN
ejpam-1889	253	15	a2c3−a3c2	a2c3−a3c2	PROPN
ejpam-1889	253	16	c3	c3	PROPN
ejpam-1889	253	17	�	�	PROPN
ejpam-1889	253	18	2	2	NUM
ejpam-1889	253	19	π(2,1	π(2,1	NOUN
ejpam-1889	253	20	)	)	PUNCT
ejpam-1889	253	21	4,β	4,β	NOUN
ejpam-1889	253	22	,	,	PUNCT
ejpam-1889	253	23	γ	γ	X
ejpam-1889	253	24	:	:	PUNCT
ejpam-1889	253	25	e1	e1	VERB
ejpam-1889	253	26	−	−	PROPN
ejpam-1889	253	27	e2	e2	PROPN
ejpam-1889	253	28	+	+	CCONJ
ejpam-1889	253	29	γ1e3	γ1e3	X
ejpam-1889	253	30	+	+	CCONJ
ejpam-1889	253	31	u1(e1	u1(e1	NOUN
ejpam-1889	253	32	+	+	CCONJ
ejpam-1889	253	33	e2	e2	PROPN
ejpam-1889	253	34	+	+	CCONJ
ejpam-1889	253	35	γ2e3	γ2e3	X
ejpam-1889	253	36	)	)	PUNCT
ejpam-1889	254	1	+	+	CCONJ
ejpam-1889	254	2	u2(β1e3	u2(β1e3	PROPN
ejpam-1889	254	3	)	)	PUNCT
ejpam-1889	254	4	c3	c3	PROPN
ejpam-1889	254	5	6=	6=	PROPN
ejpam-1889	254	6	0	0	NUM
ejpam-1889	254	7	,	,	PUNCT
ejpam-1889	254	8	�	�	PROPN
ejpam-1889	254	9	a1c3−a3c1	a1c3−a3c1	PROPN
ejpam-1889	254	10	c3	c3	PROPN
ejpam-1889	254	11	�	�	PROPN
ejpam-1889	254	12	2	2	NUM
ejpam-1889	254	13	=	=	SYM
ejpam-1889	254	14	�	�	PROPN
ejpam-1889	254	15	a2c3−a3c2	a2c3−a3c2	PROPN
ejpam-1889	254	16	c3	c3	PROPN
ejpam-1889	254	17	�	�	PROPN
ejpam-1889	254	18	2	2	NUM
ejpam-1889	254	19	π(2,1	π(2,1	NOUN
ejpam-1889	254	20	)	)	PUNCT
ejpam-1889	254	21	5,β	5,β	NUM
ejpam-1889	254	22	,	,	PUNCT
ejpam-1889	254	23	γ	γ	X
ejpam-1889	254	24	:	:	PUNCT
ejpam-1889	254	25	β1e1	β1e1	SYM
ejpam-1889	254	26	+	+	CCONJ
ejpam-1889	254	27	γ1e3	γ1e3	X
ejpam-1889	254	28	+	+	CCONJ
ejpam-1889	254	29	u1(β2e3	u1(β2e3	NOUN
ejpam-1889	254	30	)	)	PUNCT
ejpam-1889	254	31	+	+	CCONJ
ejpam-1889	254	32	u2(e1	u2(e1	NOUN
ejpam-1889	254	33	+	+	CCONJ
ejpam-1889	254	34	e2	e2	PROPN
ejpam-1889	254	35	)	)	PUNCT
ejpam-1889	254	36	c3	c3	NOUN
ejpam-1889	254	37	=	=	SYM
ejpam-1889	254	38	0	0	NUM
ejpam-1889	254	39	,	,	PUNCT
ejpam-1889	254	40	�	�	PROPN
ejpam-1889	254	41	a1	a1	NOUN
ejpam-1889	254	42	b3−a3	b3−a3	PROPN
ejpam-1889	254	43	b1	b1	PROPN
ejpam-1889	254	44	b3	b3	PROPN
ejpam-1889	254	45	�	�	PROPN
ejpam-1889	254	46	2	2	NUM
ejpam-1889	254	47	6=	6=	NUM
ejpam-1889	254	48	�	�	PROPN
ejpam-1889	254	49	a2	a2	PROPN
ejpam-1889	254	50	b3−a3	b3−a3	PROPN
ejpam-1889	254	51	b2	b2	NOUN
ejpam-1889	254	52	b3	b3	PROPN
ejpam-1889	254	53	�	�	PROPN
ejpam-1889	254	54	2	2	NUM
ejpam-1889	254	55	π(2,1	π(2,1	NOUN
ejpam-1889	254	56	)	)	PUNCT
ejpam-1889	254	57	6,β	6,β	NOUN
ejpam-1889	254	58	,	,	PUNCT
ejpam-1889	254	59	γ	γ	X
ejpam-1889	254	60	:	:	PUNCT
ejpam-1889	254	61	e1	e1	VERB
ejpam-1889	254	62	−	−	PROPN
ejpam-1889	254	63	e2	e2	PROPN
ejpam-1889	254	64	+	+	CCONJ
ejpam-1889	254	65	γ1e3	γ1e3	PROPN
ejpam-1889	254	66	+	+	CCONJ
ejpam-1889	254	67	u1(β1e3	u1(β1e3	ADJ
ejpam-1889	254	68	)	)	PUNCT
ejpam-1889	255	1	+	+	CCONJ
ejpam-1889	255	2	u2(e1	u2(e1	NOUN
ejpam-1889	255	3	+	+	CCONJ
ejpam-1889	255	4	e2	e2	PROPN
ejpam-1889	255	5	)	)	PUNCT
ejpam-1889	255	6	c3	c3	NOUN
ejpam-1889	255	7	=	=	SYM
ejpam-1889	255	8	0	0	NUM
ejpam-1889	255	9	,	,	PUNCT
ejpam-1889	255	10	�	�	PROPN
ejpam-1889	255	11	a1	a1	NOUN
ejpam-1889	255	12	b3−a3	b3−a3	PROPN
ejpam-1889	255	13	b1	b1	PROPN
ejpam-1889	255	14	b3	b3	PROPN
ejpam-1889	255	15	�	�	PROPN
ejpam-1889	255	16	2	2	NUM
ejpam-1889	255	17	=	=	SYM
ejpam-1889	255	18	�	�	PROPN
ejpam-1889	255	19	a2	a2	PROPN
ejpam-1889	255	20	b3−a3	b3−a3	PROPN
ejpam-1889	255	21	b2	b2	NOUN
ejpam-1889	255	22	b3	b3	PROPN
ejpam-1889	255	23	�	�	PROPN
ejpam-1889	255	24	2	2	NUM
ejpam-1889	255	25	.	.	PUNCT
ejpam-1889	256	1	(	(	PUNCT
ejpam-1889	256	2	iii	iii	X
ejpam-1889	256	3	)	)	PUNCT
ejpam-1889	256	4	if	if	SCONJ
ejpam-1889	256	5	γ	γ	X
ejpam-1889	256	6	isl	isl	PROPN
ejpam-1889	256	7	-	-	PUNCT
ejpam-1889	256	8	equivalent	equivalent	ADJ
ejpam-1889	256	9	to	to	ADP
ejpam-1889	256	10	γ(2,1	γ(2,1	NUM
ejpam-1889	256	11	)	)	PUNCT
ejpam-1889	256	12	3,α	3,α	NUM
ejpam-1889	256	13	,	,	PUNCT
ejpam-1889	256	14	thenπ	thenπ	NOUN
ejpam-1889	256	15	isp	isp	ADV
ejpam-1889	256	16	-	-	PUNCT
ejpam-1889	256	17	equivalent	equivalent	ADJ
ejpam-1889	256	18	to	to	ADP
ejpam-1889	256	19	exactly	exactly	ADV
ejpam-1889	256	20	one	one	NUM
ejpam-1889	256	21	of	of	ADP
ejpam-1889	256	22	the	the	DET
ejpam-1889	256	23	following	follow	VERB
ejpam-1889	256	24	parametrized	parametrized	ADJ
ejpam-1889	256	25	affine	affine	NOUN
ejpam-1889	256	26	subspaces	subspace	NOUN
ejpam-1889	256	27			VERB
ejpam-1889	256	28			ADV
ejpam-1889	256	29			DET
ejpam-1889	256	30			PROPN
ejpam-1889	256	31			PROPN
ejpam-1889	256	32	π(2,1	π(2,1	PROPN
ejpam-1889	256	33	)	)	PUNCT
ejpam-1889	256	34	7,α	7,α	PROPN
ejpam-1889	256	35	,	,	PUNCT
ejpam-1889	256	36	β	β	X
ejpam-1889	256	37	,	,	PUNCT
ejpam-1889	256	38	γ	γ	X
ejpam-1889	256	39	:	:	PUNCT
ejpam-1889	256	40	β1e3	β1e3	PUNCT
ejpam-1889	256	41	+	+	CCONJ
ejpam-1889	256	42	u1(γ1e1	u1(γ1e1	NOUN
ejpam-1889	256	43	+	+	NOUN
ejpam-1889	256	44	αe2	αe2	NOUN
ejpam-1889	256	45	)	)	PUNCT
ejpam-1889	257	1	+	+	CCONJ
ejpam-1889	258	1	u2e1	u2e1	INTJ
ejpam-1889	258	2	c2	c2	PROPN
ejpam-1889	258	3	1	1	NUM
ejpam-1889	258	4	6=	6=	NUM
ejpam-1889	258	5	c2	c2	PROPN
ejpam-1889	258	6	2	2	NUM
ejpam-1889	258	7	π(2,1	π(2,1	NOUN
ejpam-1889	258	8	)	)	PUNCT
ejpam-1889	258	9	8,β	8,β	NUM
ejpam-1889	258	10	:	:	PUNCT
ejpam-1889	258	11	β1e3	β1e3	PUNCT
ejpam-1889	259	1	+	+	CCONJ
ejpam-1889	259	2	u1(β2e1	u1(β2e1	ADJ
ejpam-1889	259	3	)	)	PUNCT
ejpam-1889	259	4	+	+	CCONJ
ejpam-1889	259	5	u2(e1	u2(e1	NOUN
ejpam-1889	259	6	+	+	CCONJ
ejpam-1889	259	7	e2	e2	PROPN
ejpam-1889	259	8	)	)	PUNCT
ejpam-1889	259	9	c2	c2	PROPN
ejpam-1889	259	10	1	1	NUM
ejpam-1889	259	11	=	=	SYM
ejpam-1889	259	12	c2	c2	PROPN
ejpam-1889	259	13	2	2	NUM
ejpam-1889	259	14	,	,	PUNCT
ejpam-1889	259	15	b2	b2	NOUN
ejpam-1889	259	16	1	1	NUM
ejpam-1889	259	17	6=	6=	NUM
ejpam-1889	259	18	b2	b2	NOUN
ejpam-1889	259	19	2	2	NUM
ejpam-1889	259	20	π(2,1	π(2,1	NOUN
ejpam-1889	259	21	)	)	PUNCT
ejpam-1889	259	22	9,β	9,β	NOUN
ejpam-1889	259	23	:	:	PUNCT
ejpam-1889	259	24	β1e3	β1e3	PUNCT
ejpam-1889	259	25	+	+	X
ejpam-1889	259	26	u1(e1	u1(e1	NOUN
ejpam-1889	259	27	−	−	PROPN
ejpam-1889	259	28	e2	e2	PROPN
ejpam-1889	259	29	)	)	PUNCT
ejpam-1889	260	1	+	+	CCONJ
ejpam-1889	260	2	u2(e1	u2(e1	NOUN
ejpam-1889	260	3	+	+	CCONJ
ejpam-1889	260	4	e2	e2	PROPN
ejpam-1889	260	5	)	)	PUNCT
ejpam-1889	260	6	c2	c2	PROPN
ejpam-1889	260	7	1	1	NUM
ejpam-1889	260	8	=	=	SYM
ejpam-1889	260	9	c2	c2	PROPN
ejpam-1889	260	10	2	2	NUM
ejpam-1889	260	11	,	,	PUNCT
ejpam-1889	260	12	b2	b2	NOUN
ejpam-1889	260	13	1	1	NUM
ejpam-1889	260	14	=	=	SYM
ejpam-1889	260	15	b2	b2	NOUN
ejpam-1889	260	16	2	2	NUM
ejpam-1889	260	17	.	.	PUNCT
ejpam-1889	260	18	d.	d.	PROPN
ejpam-1889	260	19	barrett	barrett	PROPN
ejpam-1889	260	20	,	,	PUNCT
ejpam-1889	260	21	r.	r.	PROPN
ejpam-1889	260	22	biggs	biggs	PROPN
ejpam-1889	260	23	,	,	PUNCT
ejpam-1889	260	24	c.	c.	PROPN
ejpam-1889	260	25	remsing	remsing	NOUN
ejpam-1889	260	26	/	/	SYM
ejpam-1889	260	27	eur	eur	NOUN
ejpam-1889	260	28	.	.	PUNCT
ejpam-1889	261	1	j.	j.	PROPN
ejpam-1889	261	2	pure	pure	PROPN
ejpam-1889	261	3	appl	appl	PROPN
ejpam-1889	261	4	.	.	PROPN
ejpam-1889	261	5	math	math	PROPN
ejpam-1889	261	6	,	,	PUNCT
ejpam-1889	261	7	7	7	NUM
ejpam-1889	261	8	(	(	PUNCT
ejpam-1889	261	9	2014	2014	NUM
ejpam-1889	261	10	)	)	PUNCT
ejpam-1889	261	11	,	,	PUNCT
ejpam-1889	261	12	140	140	NUM
ejpam-1889	261	13	-	-	SYM
ejpam-1889	261	14	155	155	NUM
ejpam-1889	261	15	149	149	NUM
ejpam-1889	261	16	here	here	ADV
ejpam-1889	261	17	α	α	PROPN
ejpam-1889	261	18	>	>	X
ejpam-1889	261	19	0	0	NUM
ejpam-1889	261	20	,	,	PUNCT
ejpam-1889	261	21	βi	βi	PROPN
ejpam-1889	261	22	6=	6=	ADP
ejpam-1889	261	23	0	0	NUM
ejpam-1889	262	1	and	and	CCONJ
ejpam-1889	262	2	γi	γi	ADP
ejpam-1889	262	3	∈	∈	PROPN
ejpam-1889	262	4	r	r	NOUN
ejpam-1889	262	5	,	,	PUNCT
ejpam-1889	262	6	with	with	ADP
ejpam-1889	262	7	different	different	ADJ
ejpam-1889	262	8	values	value	NOUN
ejpam-1889	262	9	of	of	ADP
ejpam-1889	262	10	these	these	DET
ejpam-1889	262	11	parameters	parameter	NOUN
ejpam-1889	262	12	yielding	yield	VERB
ejpam-1889	262	13	distinct	distinct	ADJ
ejpam-1889	262	14	(	(	PUNCT
ejpam-1889	262	15	nonequivalent	nonequivalent	ADJ
ejpam-1889	262	16	)	)	PUNCT
ejpam-1889	262	17	class	class	NOUN
ejpam-1889	262	18	representatives	representative	NOUN
ejpam-1889	262	19	.	.	PUNCT
ejpam-1889	263	1	proof	proof	NOUN
ejpam-1889	263	2	.	.	PUNCT
ejpam-1889	264	1	by	by	ADP
ejpam-1889	264	2	theorem	theorem	NOUN
ejpam-1889	264	3	2	2	NUM
ejpam-1889	264	4	,	,	PUNCT
ejpam-1889	264	5	we	we	PRON
ejpam-1889	264	6	have	have	VERB
ejpam-1889	264	7	that	that	SCONJ
ejpam-1889	264	8	γ	γ	PROPN
ejpam-1889	264	9	is	be	AUX
ejpam-1889	264	10	l	l	NOUN
ejpam-1889	264	11	-	-	ADJ
ejpam-1889	264	12	equivalent	equivalent	ADJ
ejpam-1889	264	13	to	to	ADP
ejpam-1889	264	14	γ(2,1	γ(2,1	PROPN
ejpam-1889	264	15	)	)	PUNCT
ejpam-1889	264	16	1	1	NUM
ejpam-1889	264	17	=	=	SYM
ejpam-1889	264	18	e2	e2	PROPN
ejpam-1889	264	19	+	+	CCONJ
ejpam-1889	264	20	〈	〈	PROPN
ejpam-1889	264	21	e1	e1	NOUN
ejpam-1889	264	22	,	,	PUNCT
ejpam-1889	264	23	e3	e3	NOUN
ejpam-1889	264	24	〉	〉	NOUN
ejpam-1889	264	25	,	,	PUNCT
ejpam-1889	264	26	γ(2,1	γ(2,1	NOUN
ejpam-1889	264	27	)	)	PUNCT
ejpam-1889	264	28	2	2	NUM
ejpam-1889	264	29	=	=	NOUN
ejpam-1889	264	30	e1	e1	PROPN
ejpam-1889	264	31	+	+	CCONJ
ejpam-1889	264	32	〈	〈	PROPN
ejpam-1889	264	33	e1	e1	PROPN
ejpam-1889	264	34	+	+	CCONJ
ejpam-1889	264	35	e2	e2	NOUN
ejpam-1889	264	36	,	,	PUNCT
ejpam-1889	264	37	e3	e3	NOUN
ejpam-1889	264	38	〉	〉	NOUN
ejpam-1889	264	39	or	or	CCONJ
ejpam-1889	264	40	γ(2,1	γ(2,1	NOUN
ejpam-1889	264	41	)	)	PUNCT
ejpam-1889	264	42	3,α	3,α	NUM
ejpam-1889	264	43	=	=	SYM
ejpam-1889	264	44	αe3	αe3	NOUN
ejpam-1889	264	45	+	+	CCONJ
ejpam-1889	264	46	〈	〈	PROPN
ejpam-1889	264	47	e1	e1	NOUN
ejpam-1889	264	48	,	,	PUNCT
ejpam-1889	264	49	e2	e2	PROPN
ejpam-1889	264	50	〉	〉	NOUN
ejpam-1889	264	51	.	.	PUNCT
ejpam-1889	265	1	(	(	PUNCT
ejpam-1889	265	2	i	i	NOUN
ejpam-1889	265	3	)	)	PUNCT
ejpam-1889	265	4	assume	assume	VERB
ejpam-1889	265	5	γ	γ	PROPN
ejpam-1889	265	6	is	be	AUX
ejpam-1889	265	7	l	l	NOUN
ejpam-1889	265	8	-	-	ADJ
ejpam-1889	265	9	equivalent	equivalent	ADJ
ejpam-1889	265	10	to	to	ADP
ejpam-1889	265	11	γ(2,1	γ(2,1	PROPN
ejpam-1889	265	12	)	)	PUNCT
ejpam-1889	265	13	1	1	NUM
ejpam-1889	265	14	.	.	PUNCT
ejpam-1889	266	1	the	the	DET
ejpam-1889	266	2	affine	affine	NOUN
ejpam-1889	266	3	subspace	subspace	NOUN
ejpam-1889	266	4	∑3	∑3	PROPN
ejpam-1889	266	5	i=1	i=1	PROPN
ejpam-1889	266	6	bi	bi	PROPN
ejpam-1889	266	7	ei+	ei+	NOUN
ejpam-1889	266	8	∑3	∑3	PROPN
ejpam-1889	267	1	i=1	i=1	PROPN
ejpam-1889	267	2	ci	ci	PROPN
ejpam-1889	267	3	ei	ei	PROPN
ejpam-1889	267	4	�	�	PROPN
ejpam-1889	267	5	has	have	VERB
ejpam-1889	267	6	full	full	ADJ
ejpam-1889	267	7	rank	rank	NOUN
ejpam-1889	267	8	(	(	PUNCT
ejpam-1889	267	9	as	as	ADP
ejpam-1889	267	10	〈	〈	PROPN
ejpam-1889	267	11	e1	e1	NOUN
ejpam-1889	267	12	,	,	PUNCT
ejpam-1889	267	13	e3	e3	NOUN
ejpam-1889	267	14	〉	〉	NOUN
ejpam-1889	267	15	has	have	VERB
ejpam-1889	267	16	full	full	ADJ
ejpam-1889	267	17	rank	rank	NOUN
ejpam-1889	267	18	)	)	PUNCT
ejpam-1889	267	19	and	and	CCONJ
ejpam-1889	267	20	so	so	ADV
ejpam-1889	267	21	the	the	DET
ejpam-1889	267	22	parametrized	parametrized	ADJ
ejpam-1889	267	23	affine	affine	NOUN
ejpam-1889	267	24	subspace	subspace	NOUN
ejpam-1889	267	25	u	u	PROPN
ejpam-1889	267	26	7→	7→	NUM
ejpam-1889	267	27	3	3	NUM
ejpam-1889	267	28	∑	∑	PROPN
ejpam-1889	267	29	i=1	i=1	PROPN
ejpam-1889	267	30	bi	bi	NOUN
ejpam-1889	267	31	ei	ei	NOUN
ejpam-1889	268	1	+	+	CCONJ
ejpam-1889	268	2	u	u	NOUN
ejpam-1889	268	3	3	3	NUM
ejpam-1889	268	4	∑	∑	NOUN
ejpam-1889	268	5	i=1	i=1	PROPN
ejpam-1889	268	6	ci	ci	PROPN
ejpam-1889	268	7	ei	ei	PROPN
ejpam-1889	268	8	is	be	AUX
ejpam-1889	268	9	p	p	NOUN
ejpam-1889	268	10	-	-	PUNCT
ejpam-1889	268	11	equivalent	equivalent	ADJ
ejpam-1889	268	12	to	to	ADP
ejpam-1889	268	13	π(1,1	π(1,1	PROPN
ejpam-1889	268	14	)	)	PUNCT
ejpam-1889	268	15	1,α	1,α	NOUN
ejpam-1889	268	16	,	,	PUNCT
ejpam-1889	268	17	γ	γ	NOUN
ejpam-1889	268	18	or	or	CCONJ
ejpam-1889	268	19	π(1,1	π(1,1	NOUN
ejpam-1889	268	20	)	)	PUNCT
ejpam-1889	268	21	2,α	2,α	NUM
ejpam-1889	268	22	,	,	PUNCT
ejpam-1889	268	23	by	by	ADP
ejpam-1889	268	24	theorem	theorem	NOUN
ejpam-1889	268	25	3	3	X
ejpam-1889	268	26	.	.	PUNCT
ejpam-1889	269	1	it	it	PRON
ejpam-1889	269	2	follows	follow	VERB
ejpam-1889	269	3	that	that	SCONJ
ejpam-1889	269	4	π	π	PROPN
ejpam-1889	269	5	is	be	AUX
ejpam-1889	269	6	p	p	NOUN
ejpam-1889	269	7	-	-	PUNCT
ejpam-1889	269	8	equivalent	equivalent	ADJ
ejpam-1889	269	9	to	to	ADP
ejpam-1889	269	10	π(2,1	π(2,1	PROPN
ejpam-1889	269	11	)	)	PUNCT
ejpam-1889	269	12	1,α	1,α	NOUN
ejpam-1889	269	13	,	,	PUNCT
ejpam-1889	269	14	β	β	X
ejpam-1889	269	15	,	,	PUNCT
ejpam-1889	269	16	γ	γ	X
ejpam-1889	269	17	when	when	SCONJ
ejpam-1889	269	18	c3	c3	PROPN
ejpam-1889	269	19	6=	6=	ADP
ejpam-1889	269	20	0	0	NUM
ejpam-1889	270	1	and	and	CCONJ
ejpam-1889	270	2	π	π	PROPN
ejpam-1889	270	3	is	be	AUX
ejpam-1889	270	4	p	p	NOUN
ejpam-1889	270	5	-	-	PUNCT
ejpam-1889	270	6	equivalent	equivalent	ADJ
ejpam-1889	270	7	to	to	ADP
ejpam-1889	270	8	π(2,1	π(2,1	PROPN
ejpam-1889	270	9	)	)	PUNCT
ejpam-1889	270	10	2,α	2,α	PROPN
ejpam-1889	270	11	,	,	PUNCT
ejpam-1889	270	12	β	β	X
ejpam-1889	270	13	,	,	PUNCT
ejpam-1889	270	14	γ	γ	X
ejpam-1889	270	15	when	when	SCONJ
ejpam-1889	270	16	c3	c3	PROPN
ejpam-1889	270	17	=	=	PROPN
ejpam-1889	270	18	0	0	PROPN
ejpam-1889	270	19	.	.	PUNCT
ejpam-1889	271	1	as	as	SCONJ
ejpam-1889	271	2	π	π	PROPN
ejpam-1889	271	3	is	be	AUX
ejpam-1889	271	4	inhomogeneous	inhomogeneous	ADJ
ejpam-1889	271	5	,	,	PUNCT
ejpam-1889	271	6	β1	β1	PROPN
ejpam-1889	271	7	6=	6=	PRON
ejpam-1889	271	8	0	0	NUM
ejpam-1889	271	9	.	.	PUNCT
ejpam-1889	272	1	(	(	PUNCT
ejpam-1889	272	2	ii	ii	NOUN
ejpam-1889	272	3	)	)	PUNCT
ejpam-1889	272	4	assume	assume	VERB
ejpam-1889	272	5	γ	γ	PROPN
ejpam-1889	272	6	is	be	AUX
ejpam-1889	272	7	l	l	NOUN
ejpam-1889	272	8	-	-	ADJ
ejpam-1889	272	9	equivalent	equivalent	ADJ
ejpam-1889	272	10	to	to	ADP
ejpam-1889	272	11	γ(2,1	γ(2,1	PROPN
ejpam-1889	272	12	)	)	PUNCT
ejpam-1889	272	13	2	2	NUM
ejpam-1889	272	14	(	(	PUNCT
ejpam-1889	272	15	in	in	ADP
ejpam-1889	272	16	this	this	DET
ejpam-1889	272	17	case	case	NOUN
ejpam-1889	272	18	b3	b3	PROPN
ejpam-1889	272	19	6=	6=	PRON
ejpam-1889	272	20	0	0	NUM
ejpam-1889	272	21	or	or	CCONJ
ejpam-1889	272	22	c3	c3	PROPN
ejpam-1889	272	23	6=	6=	PROPN
ejpam-1889	272	24	0	0	NUM
ejpam-1889	272	25	)	)	PUNCT
ejpam-1889	272	26	.	.	PUNCT
ejpam-1889	273	1	suppose	suppose	VERB
ejpam-1889	273	2	that	that	SCONJ
ejpam-1889	273	3	c3	c3	PROPN
ejpam-1889	273	4	6=	6=	PROPN
ejpam-1889	273	5	0	0	NUM
ejpam-1889	273	6	.	.	PUNCT
ejpam-1889	274	1	then	then	ADV
ejpam-1889	274	2			VERB
ejpam-1889	274	3			NUM
ejpam-1889	274	4	1	1	NUM
ejpam-1889	274	5	0	0	NUM
ejpam-1889	274	6	−	−	PROPN
ejpam-1889	274	7	c1	c1	PROPN
ejpam-1889	274	8	c3	c3	NOUN
ejpam-1889	274	9	0	0	NUM
ejpam-1889	274	10	1	1	NUM
ejpam-1889	274	11	−	−	PROPN
ejpam-1889	274	12	c2	c2	PROPN
ejpam-1889	274	13	c3	c3	PROPN
ejpam-1889	274	14	0	0	NUM
ejpam-1889	274	15	0	0	NUM
ejpam-1889	274	16	1	1	NUM
ejpam-1889	274	17			PROPN
ejpam-1889	274	18			PROPN
ejpam-1889	274	19			NOUN
ejpam-1889	274	20			NUM
ejpam-1889	274	21	a1	a1	NOUN
ejpam-1889	274	22	b1	b1	PROPN
ejpam-1889	274	23	c1	c1	PROPN
ejpam-1889	274	24	a2	a2	PROPN
ejpam-1889	274	25	b2	b2	PROPN
ejpam-1889	274	26	c2	c2	PROPN
ejpam-1889	274	27	a3	a3	PROPN
ejpam-1889	274	28	b3	b3	PROPN
ejpam-1889	274	29	c3	c3	PROPN
ejpam-1889	274	30			PROPN
ejpam-1889	274	31	=	=	PROPN
ejpam-1889	274	32			NOUN
ejpam-1889	274	33			NOUN
ejpam-1889	274	34	a′1	a′1	PROPN
ejpam-1889	274	35	b′1	b′1	AUX
ejpam-1889	274	36	0	0	NUM
ejpam-1889	274	37	a′2	a′2	PROPN
ejpam-1889	274	38	b′2	b′2	NOUN
ejpam-1889	274	39	0	0	NUM
ejpam-1889	274	40	a3	a3	NOUN
ejpam-1889	274	41	b3	b3	PROPN
ejpam-1889	274	42	c3	c3	PROPN
ejpam-1889	274	43			PROPN
ejpam-1889	274	44			PROPN
ejpam-1889	274	45	where	where	SCONJ
ejpam-1889	274	46	a′1	a′1	PRON
ejpam-1889	274	47	=	=	PUNCT
ejpam-1889	274	48	a1c3−a3c1	a1c3−a3c1	PROPN
ejpam-1889	274	49	c3	c3	NOUN
ejpam-1889	274	50	,	,	PUNCT
ejpam-1889	274	51	a′2	a′2	NOUN
ejpam-1889	274	52	=	=	PUNCT
ejpam-1889	274	53	a2c3−a3c2	a2c3−a3c2	PROPN
ejpam-1889	274	54	c3	c3	PROPN
ejpam-1889	274	55	and	and	CCONJ
ejpam-1889	274	56	b′1	b′1	PROPN
ejpam-1889	274	57	,	,	PUNCT
ejpam-1889	274	58	b′2	b′2	PROPN
ejpam-1889	274	59	∈	∈	PROPN
ejpam-1889	274	60	r.	r.	PROPN
ejpam-1889	274	61	as	as	SCONJ
ejpam-1889	274	62	γ	γ	X
ejpam-1889	274	63	is	be	AUX
ejpam-1889	274	64	l	l	NOUN
ejpam-1889	274	65	-	-	ADJ
ejpam-1889	274	66	equivalent	equivalent	ADJ
ejpam-1889	274	67	to	to	ADP
ejpam-1889	274	68	γ(2,1	γ(2,1	PROPN
ejpam-1889	274	69	)	)	PUNCT
ejpam-1889	274	70	2	2	NUM
ejpam-1889	274	71	,	,	PUNCT
ejpam-1889	274	72	we	we	PRON
ejpam-1889	274	73	have	have	AUX
ejpam-1889	274	74	(	(	PUNCT
ejpam-1889	274	75	b′1	b′1	NOUN
ejpam-1889	274	76	)	)	PUNCT
ejpam-1889	274	77	2	2	NUM
ejpam-1889	274	78	=	=	SYM
ejpam-1889	274	79	(	(	PUNCT
ejpam-1889	274	80	b′2	b′2	NOUN
ejpam-1889	274	81	)	)	PUNCT
ejpam-1889	274	82	2	2	NUM
ejpam-1889	274	83	.	.	PUNCT
ejpam-1889	274	84	suppose	suppose	VERB
ejpam-1889	274	85	(	(	PUNCT
ejpam-1889	274	86	a′1	a′1	SYM
ejpam-1889	274	87	)	)	PUNCT
ejpam-1889	274	88	2	2	NUM
ejpam-1889	274	89	6=	6=	SYM
ejpam-1889	274	90	(	(	PUNCT
ejpam-1889	274	91	a′2	a′2	SYM
ejpam-1889	274	92	)	)	PUNCT
ejpam-1889	274	93	2	2	NUM
ejpam-1889	274	94	.	.	PUNCT
ejpam-1889	275	1	by	by	ADP
ejpam-1889	275	2	the	the	DET
ejpam-1889	275	3	lemma	lemma	PROPN
ejpam-1889	275	4	(	(	PUNCT
ejpam-1889	275	5	with	with	ADP
ejpam-1889	275	6	x	x	SYM
ejpam-1889	275	7	=	=	PUNCT
ejpam-1889	275	8	a′1e1	a′1e1	PROPN
ejpam-1889	275	9	+	+	CCONJ
ejpam-1889	275	10	a′2e2	a′2e2	PROPN
ejpam-1889	275	11	+	+	CCONJ
ejpam-1889	275	12	a3e3	a3e3	PROPN
ejpam-1889	275	13	,	,	PUNCT
ejpam-1889	275	14	y	y	NOUN
ejpam-1889	275	15	=	=	SYM
ejpam-1889	275	16	b′1e1	b′1e1	PROPN
ejpam-1889	275	17	+	+	CCONJ
ejpam-1889	275	18	b′2e2	b′2e2	PROPN
ejpam-1889	275	19	+	+	CCONJ
ejpam-1889	275	20	b3e3	b3e3	X
ejpam-1889	275	21	and	and	CCONJ
ejpam-1889	275	22	z	z	NOUN
ejpam-1889	275	23	=	=	SYM
ejpam-1889	275	24	c3e3	c3e3	NOUN
ejpam-1889	275	25	)	)	PUNCT
ejpam-1889	275	26	there	there	PRON
ejpam-1889	275	27	exists	exist	VERB
ejpam-1889	275	28	ψ	ψ	X
ejpam-1889	275	29	∈	∈	PROPN
ejpam-1889	275	30	aut	aut	X
ejpam-1889	275	31	(	(	PUNCT
ejpam-1889	275	32	se(1	se(1	PROPN
ejpam-1889	275	33	,	,	PUNCT
ejpam-1889	275	34	1	1	NUM
ejpam-1889	275	35	)	)	PUNCT
ejpam-1889	275	36	)	)	PUNCT
ejpam-1889	275	37	such	such	ADJ
ejpam-1889	275	38	that	that	SCONJ
ejpam-1889	275	39	ψ	ψ	ADP
ejpam-1889	275	40	·	·	PUNCT
ejpam-1889	275	41			PROPN
ejpam-1889	275	42			NOUN
ejpam-1889	275	43	a′1	a′1	PROPN
ejpam-1889	275	44	b′1	b′1	AUX
ejpam-1889	275	45	0	0	NUM
ejpam-1889	275	46	a′2	a′2	PROPN
ejpam-1889	275	47	b′2	b′2	NOUN
ejpam-1889	275	48	0	0	NUM
ejpam-1889	275	49	a3	a3	NOUN
ejpam-1889	275	50	b3	b3	PROPN
ejpam-1889	275	51	c3	c3	PROPN
ejpam-1889	275	52			PROPN
ejpam-1889	275	53	=	=	PROPN
ejpam-1889	275	54			NOUN
ejpam-1889	275	55			NOUN
ejpam-1889	275	56	β1	β1	NOUN
ejpam-1889	275	57	1	1	NUM
ejpam-1889	275	58	0	0	NUM
ejpam-1889	275	59	0	0	NUM
ejpam-1889	275	60	1	1	NUM
ejpam-1889	275	61	0	0	NUM
ejpam-1889	275	62	γ1	γ1	PROPN
ejpam-1889	275	63	γ2	γ2	PROPN
ejpam-1889	275	64	β2	β2	PROPN
ejpam-1889	275	65			PROPN
ejpam-1889	275	66			PROPN
ejpam-1889	275	67	for	for	ADP
ejpam-1889	275	68	some	some	DET
ejpam-1889	275	69	β1,β2	β1,β2	PUNCT
ejpam-1889	275	70	6=	6=	ADP
ejpam-1889	275	71	0	0	NUM
ejpam-1889	275	72	and	and	CCONJ
ejpam-1889	275	73	γ1,γ2	γ1,γ2	PROPN
ejpam-1889	275	74	∈	∈	PROPN
ejpam-1889	275	75	r.	r.	PROPN
ejpam-1889	275	76	therefore	therefore	ADV
ejpam-1889	275	77	π	π	PROPN
ejpam-1889	275	78	is	be	AUX
ejpam-1889	275	79	p	p	NOUN
ejpam-1889	275	80	-	-	PUNCT
ejpam-1889	275	81	equivalent	equivalent	ADJ
ejpam-1889	275	82	to	to	ADP
ejpam-1889	275	83	π(2,1	π(2,1	NOUN
ejpam-1889	275	84	)	)	PUNCT
ejpam-1889	275	85	3,β	3,β	NUM
ejpam-1889	275	86	,	,	PUNCT
ejpam-1889	275	87	γ	γ	X
ejpam-1889	275	88	.	.	PROPN
ejpam-1889	275	89	on	on	ADP
ejpam-1889	275	90	the	the	DET
ejpam-1889	275	91	other	other	ADJ
ejpam-1889	275	92	hand	hand	NOUN
ejpam-1889	275	93	,	,	PUNCT
ejpam-1889	275	94	suppose	suppose	VERB
ejpam-1889	275	95	that	that	SCONJ
ejpam-1889	275	96	(	(	PUNCT
ejpam-1889	275	97	a′1	a′1	PROPN
ejpam-1889	275	98	)	)	PUNCT
ejpam-1889	275	99	2	2	NUM
ejpam-1889	275	100	=	=	SYM
ejpam-1889	275	101	(	(	PUNCT
ejpam-1889	275	102	a′2	a′2	X
ejpam-1889	275	103	)	)	PUNCT
ejpam-1889	275	104	2	2	NUM
ejpam-1889	275	105	.	.	PUNCT
ejpam-1889	275	106	by	by	ADP
ejpam-1889	275	107	the	the	DET
ejpam-1889	275	108	lemma	lemma	PROPN
ejpam-1889	275	109	(	(	PUNCT
ejpam-1889	275	110	with	with	ADP
ejpam-1889	275	111	x	x	SYM
ejpam-1889	275	112	,	,	PUNCT
ejpam-1889	275	113	y	y	PROPN
ejpam-1889	275	114	and	and	CCONJ
ejpam-1889	275	115	z	z	PROPN
ejpam-1889	275	116	as	as	ADP
ejpam-1889	275	117	before	before	ADV
ejpam-1889	275	118	)	)	PUNCT
ejpam-1889	275	119	there	there	PRON
ejpam-1889	275	120	exists	exist	VERB
ejpam-1889	275	121	ψ	ψ	X
ejpam-1889	275	122	∈	∈	PROPN
ejpam-1889	275	123	aut	aut	X
ejpam-1889	275	124	(	(	PUNCT
ejpam-1889	275	125	se(1,1	se(1,1	NOUN
ejpam-1889	275	126	)	)	PUNCT
ejpam-1889	275	127	)	)	PUNCT
ejpam-1889	275	128	such	such	ADJ
ejpam-1889	275	129	that	that	SCONJ
ejpam-1889	275	130	ψ	ψ	ADP
ejpam-1889	275	131	·	·	PUNCT
ejpam-1889	275	132			PROPN
ejpam-1889	275	133			NOUN
ejpam-1889	275	134	a′1	a′1	PROPN
ejpam-1889	275	135	b′1	b′1	AUX
ejpam-1889	275	136	0	0	NUM
ejpam-1889	275	137	a′2	a′2	PROPN
ejpam-1889	275	138	b′2	b′2	NOUN
ejpam-1889	275	139	0	0	NUM
ejpam-1889	275	140	a3	a3	NOUN
ejpam-1889	275	141	b3	b3	PROPN
ejpam-1889	275	142	c3	c3	PROPN
ejpam-1889	275	143			PROPN
ejpam-1889	275	144	=	=	PROPN
ejpam-1889	275	145			NOUN
ejpam-1889	275	146			NOUN
ejpam-1889	276	1	1	1	NUM
ejpam-1889	276	2	1	1	NUM
ejpam-1889	276	3	0	0	NUM
ejpam-1889	276	4	−1	−1	NOUN
ejpam-1889	276	5	1	1	NUM
ejpam-1889	276	6	0	0	NUM
ejpam-1889	276	7	γ1	γ1	PROPN
ejpam-1889	276	8	γ2	γ2	PROPN
ejpam-1889	276	9	β1	β1	PROPN
ejpam-1889	276	10			PROPN
ejpam-1889	276	11			PROPN
ejpam-1889	276	12	for	for	ADP
ejpam-1889	276	13	some	some	DET
ejpam-1889	276	14	β1	β1	NOUN
ejpam-1889	276	15	6=	6=	ADP
ejpam-1889	276	16	0	0	NUM
ejpam-1889	276	17	and	and	CCONJ
ejpam-1889	276	18	γ1,γ2	γ1,γ2	PROPN
ejpam-1889	276	19	∈	∈	PROPN
ejpam-1889	276	20	r.	r.	PROPN
ejpam-1889	276	21	hence	hence	ADV
ejpam-1889	276	22	π	π	PROPN
ejpam-1889	276	23	is	be	AUX
ejpam-1889	276	24	p	p	NOUN
ejpam-1889	276	25	-	-	PUNCT
ejpam-1889	276	26	equivalent	equivalent	ADJ
ejpam-1889	276	27	to	to	ADP
ejpam-1889	276	28	π(2,1	π(2,1	PROPN
ejpam-1889	276	29	)	)	PUNCT
ejpam-1889	276	30	4,β	4,β	NOUN
ejpam-1889	276	31	,	,	PUNCT
ejpam-1889	276	32	γ	γ	X
ejpam-1889	276	33	.	.	PROPN
ejpam-1889	276	34	suppose	suppose	VERB
ejpam-1889	276	35	that	that	SCONJ
ejpam-1889	276	36	c3	c3	PROPN
ejpam-1889	276	37	=	=	PROPN
ejpam-1889	276	38	0	0	PROPN
ejpam-1889	276	39	.	.	PUNCT
ejpam-1889	276	40	then	then	ADV
ejpam-1889	276	41	b3	b3	PROPN
ejpam-1889	276	42	6=	6=	ADP
ejpam-1889	276	43	0	0	NUM
ejpam-1889	276	44	and	and	CCONJ
ejpam-1889	276	45			PROPN
ejpam-1889	276	46			ADJ
ejpam-1889	276	47			NUM
ejpam-1889	276	48	1	1	NUM
ejpam-1889	276	49	0	0	NUM
ejpam-1889	276	50	−	−	PROPN
ejpam-1889	276	51	b1	b1	NOUN
ejpam-1889	276	52	b3	b3	PROPN
ejpam-1889	276	53	0	0	NUM
ejpam-1889	276	54	1	1	NUM
ejpam-1889	276	55	−	−	PROPN
ejpam-1889	276	56	b2	b2	NOUN
ejpam-1889	276	57	b3	b3	NOUN
ejpam-1889	276	58	0	0	NUM
ejpam-1889	276	59	0	0	NUM
ejpam-1889	276	60	1	1	NUM
ejpam-1889	276	61			PROPN
ejpam-1889	276	62			PROPN
ejpam-1889	276	63			PROPN
ejpam-1889	276	64			NOUN
ejpam-1889	276	65			NUM
ejpam-1889	276	66	a1	a1	NOUN
ejpam-1889	276	67	b1	b1	PROPN
ejpam-1889	276	68	c1	c1	PROPN
ejpam-1889	276	69	a2	a2	PROPN
ejpam-1889	276	70	b2	b2	PROPN
ejpam-1889	276	71	c2	c2	PROPN
ejpam-1889	276	72	a3	a3	PROPN
ejpam-1889	276	73	b3	b3	PROPN
ejpam-1889	276	74	0	0	NUM
ejpam-1889	276	75			PROPN
ejpam-1889	276	76	=	=	PROPN
ejpam-1889	276	77			NOUN
ejpam-1889	276	78			NOUN
ejpam-1889	276	79	a′1	a′1	X
ejpam-1889	276	80	0	0	NUM
ejpam-1889	277	1	c′1	c′1	VERB
ejpam-1889	277	2	a′2	a′2	ADJ
ejpam-1889	277	3	0	0	NUM
ejpam-1889	277	4	c′2	c′2	NOUN
ejpam-1889	277	5	a3	a3	NOUN
ejpam-1889	277	6	b3	b3	PROPN
ejpam-1889	277	7	0	0	NUM
ejpam-1889	277	8			PROPN
ejpam-1889	277	9			PROPN
ejpam-1889	277	10	d.	d.	PROPN
ejpam-1889	277	11	barrett	barrett	PROPN
ejpam-1889	277	12	,	,	PUNCT
ejpam-1889	277	13	r.	r.	PROPN
ejpam-1889	277	14	biggs	biggs	PROPN
ejpam-1889	277	15	,	,	PUNCT
ejpam-1889	277	16	c.	c.	PROPN
ejpam-1889	277	17	remsing	remsing	NOUN
ejpam-1889	277	18	/	/	SYM
ejpam-1889	277	19	eur	eur	NOUN
ejpam-1889	277	20	.	.	PUNCT
ejpam-1889	278	1	j.	j.	PROPN
ejpam-1889	278	2	pure	pure	PROPN
ejpam-1889	278	3	appl	appl	PROPN
ejpam-1889	278	4	.	.	PROPN
ejpam-1889	278	5	math	math	PROPN
ejpam-1889	278	6	,	,	PUNCT
ejpam-1889	278	7	7	7	NUM
ejpam-1889	278	8	(	(	PUNCT
ejpam-1889	278	9	2014	2014	NUM
ejpam-1889	278	10	)	)	PUNCT
ejpam-1889	278	11	,	,	PUNCT
ejpam-1889	278	12	140	140	NUM
ejpam-1889	278	13	-	-	SYM
ejpam-1889	278	14	155	155	NUM
ejpam-1889	278	15	150	150	NUM
ejpam-1889	278	16	where	where	SCONJ
ejpam-1889	278	17	a′1	a′1	AUX
ejpam-1889	278	18	=	=	PUNCT
ejpam-1889	278	19	a1	a1	NOUN
ejpam-1889	278	20	b3−b1a3	b3−b1a3	NOUN
ejpam-1889	278	21	b3	b3	NOUN
ejpam-1889	278	22	,	,	PUNCT
ejpam-1889	278	23	a′2	a′2	NOUN
ejpam-1889	278	24	=	=	PUNCT
ejpam-1889	278	25	a2	a2	PROPN
ejpam-1889	278	26	b3−b2a3	b3−b2a3	NOUN
ejpam-1889	278	27	b3	b3	PROPN
ejpam-1889	278	28	and	and	CCONJ
ejpam-1889	278	29	c′1	c′1	NOUN
ejpam-1889	278	30	,	,	PUNCT
ejpam-1889	278	31	c′2	c′2	NOUN
ejpam-1889	278	32	∈	∈	PROPN
ejpam-1889	278	33	r.	r.	PROPN
ejpam-1889	278	34	since	since	SCONJ
ejpam-1889	278	35	γ	γ	PROPN
ejpam-1889	278	36	is	be	AUX
ejpam-1889	278	37	l	l	NOUN
ejpam-1889	278	38	-	-	ADJ
ejpam-1889	278	39	equivalent	equivalent	ADJ
ejpam-1889	278	40	to	to	ADP
ejpam-1889	278	41	γ(2,1	γ(2,1	PROPN
ejpam-1889	278	42	)	)	PUNCT
ejpam-1889	278	43	2	2	NUM
ejpam-1889	278	44	,	,	PUNCT
ejpam-1889	278	45	we	we	PRON
ejpam-1889	278	46	have	have	AUX
ejpam-1889	278	47	(	(	PUNCT
ejpam-1889	278	48	c′1	c′1	NOUN
ejpam-1889	278	49	)	)	PUNCT
ejpam-1889	278	50	2	2	NUM
ejpam-1889	278	51	=	=	SYM
ejpam-1889	278	52	(	(	PUNCT
ejpam-1889	278	53	c′2	c′2	NOUN
ejpam-1889	278	54	)	)	PUNCT
ejpam-1889	278	55	2	2	NUM
ejpam-1889	278	56	.	.	PUNCT
ejpam-1889	278	57	suppose	suppose	VERB
ejpam-1889	278	58	that	that	SCONJ
ejpam-1889	278	59	(	(	PUNCT
ejpam-1889	278	60	a′1	a′1	PROPN
ejpam-1889	278	61	)	)	PUNCT
ejpam-1889	278	62	2	2	NUM
ejpam-1889	278	63	6=	6=	SYM
ejpam-1889	278	64	(	(	PUNCT
ejpam-1889	278	65	a′2	a′2	SYM
ejpam-1889	278	66	)	)	PUNCT
ejpam-1889	278	67	2	2	NUM
ejpam-1889	278	68	.	.	PUNCT
ejpam-1889	278	69	by	by	ADP
ejpam-1889	278	70	the	the	DET
ejpam-1889	278	71	lemma	lemma	PROPN
ejpam-1889	278	72	(	(	PUNCT
ejpam-1889	278	73	with	with	ADP
ejpam-1889	278	74	x	x	SYM
ejpam-1889	278	75	=	=	PUNCT
ejpam-1889	278	76	a′1e1	a′1e1	PROPN
ejpam-1889	278	77	+	+	CCONJ
ejpam-1889	278	78	a′2e2	a′2e2	PROPN
ejpam-1889	278	79	+	+	CCONJ
ejpam-1889	278	80	a3e3	a3e3	PROPN
ejpam-1889	278	81	,	,	PUNCT
ejpam-1889	278	82	y	y	NOUN
ejpam-1889	278	83	=	=	SYM
ejpam-1889	278	84	c′1e1	c′1e1	PROPN
ejpam-1889	278	85	+	+	CCONJ
ejpam-1889	278	86	c′2e2	c′2e2	PROPN
ejpam-1889	278	87	and	and	CCONJ
ejpam-1889	278	88	z	z	NOUN
ejpam-1889	278	89	=	=	SYM
ejpam-1889	278	90	b3e3	b3e3	NOUN
ejpam-1889	278	91	)	)	PUNCT
ejpam-1889	278	92	,	,	PUNCT
ejpam-1889	278	93	there	there	PRON
ejpam-1889	278	94	exists	exist	VERB
ejpam-1889	278	95	ψ	ψ	X
ejpam-1889	278	96	∈	∈	PROPN
ejpam-1889	278	97	aut	aut	X
ejpam-1889	278	98	(	(	PUNCT
ejpam-1889	278	99	se(1,1	se(1,1	NOUN
ejpam-1889	278	100	)	)	PUNCT
ejpam-1889	278	101	)	)	PUNCT
ejpam-1889	278	102	such	such	ADJ
ejpam-1889	278	103	that	that	SCONJ
ejpam-1889	278	104	ψ	ψ	ADP
ejpam-1889	278	105	·	·	PUNCT
ejpam-1889	278	106			PROPN
ejpam-1889	278	107			NOUN
ejpam-1889	278	108	a′1	a′1	X
ejpam-1889	278	109	0	0	NUM
ejpam-1889	279	1	c′1	c′1	VERB
ejpam-1889	279	2	a′2	a′2	ADJ
ejpam-1889	279	3	0	0	NUM
ejpam-1889	279	4	c′2	c′2	NOUN
ejpam-1889	279	5	a3	a3	NOUN
ejpam-1889	279	6	b3	b3	PROPN
ejpam-1889	279	7	0	0	NUM
ejpam-1889	279	8			PROPN
ejpam-1889	279	9	=	=	PROPN
ejpam-1889	279	10			NOUN
ejpam-1889	279	11			NOUN
ejpam-1889	279	12	β1	β1	NOUN
ejpam-1889	279	13	0	0	NUM
ejpam-1889	279	14	1	1	NUM
ejpam-1889	279	15	0	0	NUM
ejpam-1889	279	16	0	0	NUM
ejpam-1889	279	17	1	1	NUM
ejpam-1889	279	18	γ1	γ1	NOUN
ejpam-1889	279	19	β2	β2	NOUN
ejpam-1889	279	20	0	0	NUM
ejpam-1889	279	21			PROPN
ejpam-1889	279	22			PROPN
ejpam-1889	279	23	for	for	ADP
ejpam-1889	279	24	some	some	DET
ejpam-1889	279	25	β1,β2	β1,β2	PUNCT
ejpam-1889	279	26	6=	6=	ADP
ejpam-1889	279	27	0	0	NUM
ejpam-1889	279	28	and	and	CCONJ
ejpam-1889	279	29	γ1	γ1	PROPN
ejpam-1889	279	30	∈	∈	PROPN
ejpam-1889	279	31	r.	r.	PROPN
ejpam-1889	279	32	thus	thus	ADV
ejpam-1889	279	33	π	π	PROPN
ejpam-1889	279	34	is	be	AUX
ejpam-1889	279	35	p	p	NOUN
ejpam-1889	279	36	-	-	PUNCT
ejpam-1889	279	37	equivalent	equivalent	ADJ
ejpam-1889	279	38	to	to	ADP
ejpam-1889	279	39	π(2,1	π(2,1	PROPN
ejpam-1889	279	40	)	)	PUNCT
ejpam-1889	279	41	5,β	5,β	NUM
ejpam-1889	279	42	,	,	PUNCT
ejpam-1889	279	43	γ	γ	X
ejpam-1889	279	44	.	.	PROPN
ejpam-1889	280	1	on	on	ADP
ejpam-1889	280	2	the	the	DET
ejpam-1889	280	3	other	other	ADJ
ejpam-1889	280	4	hand	hand	NOUN
ejpam-1889	280	5	,	,	PUNCT
ejpam-1889	280	6	suppose	suppose	VERB
ejpam-1889	280	7	that	that	SCONJ
ejpam-1889	280	8	(	(	PUNCT
ejpam-1889	280	9	a′1	a′1	PROPN
ejpam-1889	280	10	)	)	PUNCT
ejpam-1889	280	11	2	2	NUM
ejpam-1889	280	12	=	=	SYM
ejpam-1889	280	13	(	(	PUNCT
ejpam-1889	280	14	a′2	a′2	X
ejpam-1889	280	15	)	)	PUNCT
ejpam-1889	280	16	2	2	NUM
ejpam-1889	280	17	.	.	PUNCT
ejpam-1889	280	18	by	by	ADP
ejpam-1889	280	19	the	the	DET
ejpam-1889	280	20	lemma	lemma	PROPN
ejpam-1889	280	21	(	(	PUNCT
ejpam-1889	280	22	with	with	ADP
ejpam-1889	280	23	x	x	SYM
ejpam-1889	280	24	,	,	PUNCT
ejpam-1889	280	25	y	y	PROPN
ejpam-1889	280	26	and	and	CCONJ
ejpam-1889	280	27	z	z	NOUN
ejpam-1889	280	28	as	as	ADP
ejpam-1889	280	29	before	before	ADV
ejpam-1889	280	30	)	)	PUNCT
ejpam-1889	280	31	,	,	PUNCT
ejpam-1889	280	32	there	there	PRON
ejpam-1889	280	33	exists	exist	VERB
ejpam-1889	280	34	ψ	ψ	X
ejpam-1889	280	35	∈	∈	PROPN
ejpam-1889	280	36	aut	aut	X
ejpam-1889	280	37	(	(	PUNCT
ejpam-1889	280	38	se(1	se(1	PROPN
ejpam-1889	280	39	,	,	PUNCT
ejpam-1889	280	40	1	1	NUM
ejpam-1889	280	41	)	)	PUNCT
ejpam-1889	280	42	)	)	PUNCT
ejpam-1889	280	43	such	such	ADJ
ejpam-1889	280	44	that	that	SCONJ
ejpam-1889	280	45	ψ	ψ	ADP
ejpam-1889	280	46	·	·	PUNCT
ejpam-1889	280	47			PROPN
ejpam-1889	280	48			NOUN
ejpam-1889	280	49	a′1	a′1	X
ejpam-1889	280	50	0	0	NUM
ejpam-1889	281	1	c′1	c′1	VERB
ejpam-1889	281	2	a′2	a′2	ADJ
ejpam-1889	281	3	0	0	NUM
ejpam-1889	281	4	c′2	c′2	NOUN
ejpam-1889	281	5	a3	a3	NOUN
ejpam-1889	281	6	b3	b3	PROPN
ejpam-1889	281	7	0	0	NUM
ejpam-1889	281	8			PROPN
ejpam-1889	281	9	=	=	PROPN
ejpam-1889	281	10			NOUN
ejpam-1889	281	11			NOUN
ejpam-1889	281	12	1	1	NUM
ejpam-1889	281	13	0	0	NUM
ejpam-1889	281	14	1	1	NUM
ejpam-1889	281	15	−1	−1	NOUN
ejpam-1889	281	16	0	0	NUM
ejpam-1889	281	17	1	1	NUM
ejpam-1889	281	18	γ1	γ1	NOUN
ejpam-1889	281	19	β1	β1	NOUN
ejpam-1889	281	20	0	0	PUNCT
ejpam-1889	281	21			PROPN
ejpam-1889	281	22			PROPN
ejpam-1889	281	23	for	for	ADP
ejpam-1889	281	24	some	some	DET
ejpam-1889	281	25	β1	β1	PROPN
ejpam-1889	281	26	6=	6=	ADP
ejpam-1889	281	27	0	0	NUM
ejpam-1889	281	28	and	and	CCONJ
ejpam-1889	281	29	γ1	γ1	PROPN
ejpam-1889	281	30	∈	∈	PROPN
ejpam-1889	281	31	r.	r.	PROPN
ejpam-1889	281	32	hence	hence	ADV
ejpam-1889	281	33	π	π	PROPN
ejpam-1889	281	34	is	be	AUX
ejpam-1889	281	35	p	p	NOUN
ejpam-1889	281	36	-	-	PUNCT
ejpam-1889	281	37	equivalent	equivalent	ADJ
ejpam-1889	281	38	to	to	ADP
ejpam-1889	281	39	π(2,1	π(2,1	PROPN
ejpam-1889	281	40	)	)	PUNCT
ejpam-1889	281	41	6,β	6,β	NOUN
ejpam-1889	281	42	,	,	PUNCT
ejpam-1889	281	43	γ	γ	X
ejpam-1889	281	44	.	.	PROPN
ejpam-1889	281	45	(	(	PUNCT
ejpam-1889	281	46	iii	iii	NOUN
ejpam-1889	281	47	)	)	PUNCT
ejpam-1889	281	48	assume	assume	VERB
ejpam-1889	281	49	γ	γ	PROPN
ejpam-1889	281	50	is	be	AUX
ejpam-1889	281	51	l	l	NOUN
ejpam-1889	281	52	-	-	ADJ
ejpam-1889	281	53	equivalent	equivalent	ADJ
ejpam-1889	281	54	to	to	ADP
ejpam-1889	281	55	γ(2,1	γ(2,1	NOUN
ejpam-1889	281	56	)	)	PUNCT
ejpam-1889	281	57	3,α	3,α	NUM
ejpam-1889	281	58	(	(	PUNCT
ejpam-1889	281	59	in	in	ADP
ejpam-1889	281	60	this	this	DET
ejpam-1889	281	61	case	case	NOUN
ejpam-1889	281	62	,	,	PUNCT
ejpam-1889	281	63	b3	b3	PROPN
ejpam-1889	281	64	=	=	SYM
ejpam-1889	281	65	c3	c3	PROPN
ejpam-1889	281	66	=	=	SYM
ejpam-1889	281	67	0	0	NUM
ejpam-1889	281	68	and	and	CCONJ
ejpam-1889	281	69	a3	a3	VERB
ejpam-1889	281	70	6=	6=	ADP
ejpam-1889	281	71	0	0	NUM
ejpam-1889	281	72	)	)	PUNCT
ejpam-1889	281	73	.	.	PUNCT
ejpam-1889	282	1	we	we	PRON
ejpam-1889	282	2	have	have	VERB
ejpam-1889	282	3			NOUN
ejpam-1889	282	4			NUM
ejpam-1889	282	5	1	1	NUM
ejpam-1889	282	6	0	0	NUM
ejpam-1889	282	7	−	−	NOUN
ejpam-1889	282	8	a1	a1	NOUN
ejpam-1889	282	9	a3	a3	NOUN
ejpam-1889	282	10	0	0	NUM
ejpam-1889	282	11	1	1	NUM
ejpam-1889	282	12	−	−	PROPN
ejpam-1889	282	13	a2	a2	PROPN
ejpam-1889	282	14	a3	a3	VERB
ejpam-1889	282	15	0	0	NUM
ejpam-1889	282	16	0	0	NUM
ejpam-1889	282	17	1	1	NUM
ejpam-1889	282	18			PROPN
ejpam-1889	282	19			PROPN
ejpam-1889	282	20			NOUN
ejpam-1889	282	21			NUM
ejpam-1889	282	22	a1	a1	NOUN
ejpam-1889	282	23	b1	b1	PROPN
ejpam-1889	282	24	c1	c1	PROPN
ejpam-1889	282	25	a2	a2	PROPN
ejpam-1889	282	26	b2	b2	PROPN
ejpam-1889	282	27	c2	c2	PROPN
ejpam-1889	282	28	a3	a3	VERB
ejpam-1889	282	29	0	0	NUM
ejpam-1889	282	30	0	0	NUM
ejpam-1889	282	31			PROPN
ejpam-1889	282	32	=	=	NOUN
ejpam-1889	282	33			NOUN
ejpam-1889	282	34			NOUN
ejpam-1889	282	35	0	0	NUM
ejpam-1889	282	36	b1	b1	PROPN
ejpam-1889	282	37	c1	c1	PROPN
ejpam-1889	282	38	0	0	NUM
ejpam-1889	282	39	b2	b2	PROPN
ejpam-1889	282	40	c2	c2	PROPN
ejpam-1889	282	41	a3	a3	NOUN
ejpam-1889	282	42	0	0	NUM
ejpam-1889	282	43	0	0	NUM
ejpam-1889	283	1			PROPN
ejpam-1889	283	2			PROPN
ejpam-1889	283	3	.	.	PUNCT
ejpam-1889	283	4	suppose	suppose	VERB
ejpam-1889	283	5	that	that	SCONJ
ejpam-1889	283	6	c2	c2	PROPN
ejpam-1889	283	7	1	1	NUM
ejpam-1889	283	8	6=	6=	NUM
ejpam-1889	283	9	c2	c2	PROPN
ejpam-1889	283	10	2	2	NUM
ejpam-1889	283	11	.	.	PUNCT
ejpam-1889	284	1	by	by	ADP
ejpam-1889	284	2	the	the	DET
ejpam-1889	284	3	lemma	lemma	PROPN
ejpam-1889	284	4	(	(	PUNCT
ejpam-1889	284	5	with	with	ADP
ejpam-1889	284	6	x	x	SYM
ejpam-1889	284	7	=	=	SYM
ejpam-1889	284	8	b1e1	b1e1	NOUN
ejpam-1889	284	9	+	+	CCONJ
ejpam-1889	284	10	b2e2	b2e2	PROPN
ejpam-1889	284	11	,	,	PUNCT
ejpam-1889	284	12	y	y	NOUN
ejpam-1889	284	13	=	=	PUNCT
ejpam-1889	284	14	c1e1	c1e1	PROPN
ejpam-1889	284	15	+	+	CCONJ
ejpam-1889	284	16	c2e2	c2e2	PROPN
ejpam-1889	284	17	and	and	CCONJ
ejpam-1889	284	18	z	z	NOUN
ejpam-1889	284	19	=	=	SYM
ejpam-1889	284	20	a3e3	a3e3	PROPN
ejpam-1889	284	21	)	)	PUNCT
ejpam-1889	284	22	,	,	PUNCT
ejpam-1889	284	23	there	there	PRON
ejpam-1889	284	24	exists	exist	VERB
ejpam-1889	284	25	ψ	ψ	X
ejpam-1889	284	26	∈	∈	PROPN
ejpam-1889	284	27	aut	aut	X
ejpam-1889	284	28	(	(	PUNCT
ejpam-1889	284	29	se(1	se(1	PROPN
ejpam-1889	284	30	,	,	PUNCT
ejpam-1889	284	31	1	1	NUM
ejpam-1889	284	32	)	)	PUNCT
ejpam-1889	284	33	)	)	PUNCT
ejpam-1889	284	34	such	such	ADJ
ejpam-1889	284	35	that	that	SCONJ
ejpam-1889	284	36	ψ	ψ	X
ejpam-1889	284	37	·	·	PUNCT
ejpam-1889	284	38			PROPN
ejpam-1889	284	39			NOUN
ejpam-1889	284	40	0	0	NUM
ejpam-1889	284	41	b1	b1	PROPN
ejpam-1889	284	42	c1	c1	PROPN
ejpam-1889	284	43	0	0	NUM
ejpam-1889	284	44	b2	b2	PROPN
ejpam-1889	284	45	c2	c2	PROPN
ejpam-1889	284	46	a3	a3	NOUN
ejpam-1889	284	47	0	0	NUM
ejpam-1889	284	48	0	0	NUM
ejpam-1889	285	1			PROPN
ejpam-1889	285	2	=	=	NOUN
ejpam-1889	285	3			NOUN
ejpam-1889	285	4			NOUN
ejpam-1889	285	5	0	0	NUM
ejpam-1889	285	6	γ1	γ1	NOUN
ejpam-1889	285	7	1	1	NUM
ejpam-1889	285	8	0	0	NUM
ejpam-1889	285	9	α	α	NOUN
ejpam-1889	285	10	0	0	PUNCT
ejpam-1889	286	1	β1	β1	NOUN
ejpam-1889	286	2	0	0	NUM
ejpam-1889	286	3	0	0	NUM
ejpam-1889	287	1			PROPN
ejpam-1889	287	2			PROPN
ejpam-1889	287	3	for	for	ADP
ejpam-1889	287	4	some	some	DET
ejpam-1889	287	5	α	α	NOUN
ejpam-1889	287	6	>	>	X
ejpam-1889	287	7	0	0	PROPN
ejpam-1889	287	8	,	,	PUNCT
ejpam-1889	287	9	β1	β1	PROPN
ejpam-1889	287	10	6=	6=	ADP
ejpam-1889	287	11	0	0	NUM
ejpam-1889	287	12	and	and	CCONJ
ejpam-1889	287	13	γ1	γ1	PROPN
ejpam-1889	287	14	∈	∈	PROPN
ejpam-1889	287	15	r.	r.	PROPN
ejpam-1889	287	16	therefore	therefore	ADV
ejpam-1889	287	17	π	π	PROPN
ejpam-1889	287	18	is	be	AUX
ejpam-1889	287	19	p	p	NOUN
ejpam-1889	287	20	-	-	PUNCT
ejpam-1889	287	21	equivalent	equivalent	ADJ
ejpam-1889	287	22	to	to	ADP
ejpam-1889	287	23	π(2,1	π(2,1	PROPN
ejpam-1889	287	24	)	)	PUNCT
ejpam-1889	287	25	7,α	7,α	PROPN
ejpam-1889	287	26	,	,	PUNCT
ejpam-1889	287	27	β	β	X
ejpam-1889	287	28	,	,	PUNCT
ejpam-1889	287	29	γ	γ	X
ejpam-1889	287	30	.	.	PROPN
ejpam-1889	287	31	suppose	suppose	VERB
ejpam-1889	287	32	that	that	SCONJ
ejpam-1889	287	33	c2	c2	PROPN
ejpam-1889	287	34	1	1	NUM
ejpam-1889	287	35	=	=	SYM
ejpam-1889	287	36	c2	c2	PROPN
ejpam-1889	287	37	2	2	NUM
ejpam-1889	287	38	and	and	CCONJ
ejpam-1889	287	39	b2	b2	NOUN
ejpam-1889	287	40	1	1	NUM
ejpam-1889	287	41	6=	6=	NUM
ejpam-1889	287	42	b2	b2	NOUN
ejpam-1889	287	43	2	2	NUM
ejpam-1889	287	44	.	.	PUNCT
ejpam-1889	287	45	by	by	ADP
ejpam-1889	287	46	the	the	DET
ejpam-1889	287	47	lemma	lemma	PROPN
ejpam-1889	287	48	(	(	PUNCT
ejpam-1889	287	49	with	with	ADP
ejpam-1889	287	50	x	x	SYM
ejpam-1889	287	51	=	=	SYM
ejpam-1889	287	52	b1e1	b1e1	NOUN
ejpam-1889	287	53	+	+	CCONJ
ejpam-1889	287	54	b2e2	b2e2	PROPN
ejpam-1889	287	55	,	,	PUNCT
ejpam-1889	287	56	y	y	NOUN
ejpam-1889	287	57	=	=	PUNCT
ejpam-1889	288	1	c1e1	c1e1	PROPN
ejpam-1889	288	2	+	+	CCONJ
ejpam-1889	288	3	c2e2	c2e2	PROPN
ejpam-1889	288	4	and	and	CCONJ
ejpam-1889	288	5	z	z	NOUN
ejpam-1889	288	6	=	=	SYM
ejpam-1889	288	7	a3e3	a3e3	PROPN
ejpam-1889	288	8	)	)	PUNCT
ejpam-1889	288	9	,	,	PUNCT
ejpam-1889	288	10	there	there	PRON
ejpam-1889	288	11	exists	exist	VERB
ejpam-1889	288	12	ψ	ψ	X
ejpam-1889	288	13	∈	∈	PROPN
ejpam-1889	288	14	aut	aut	X
ejpam-1889	288	15	(	(	PUNCT
ejpam-1889	288	16	se(1,1	se(1,1	NOUN
ejpam-1889	288	17	)	)	PUNCT
ejpam-1889	288	18	)	)	PUNCT
ejpam-1889	288	19	such	such	ADJ
ejpam-1889	288	20	that	that	SCONJ
ejpam-1889	288	21	ψ	ψ	X
ejpam-1889	288	22	·	·	PUNCT
ejpam-1889	288	23			PROPN
ejpam-1889	288	24			NOUN
ejpam-1889	288	25	0	0	NUM
ejpam-1889	288	26	b1	b1	PROPN
ejpam-1889	288	27	c1	c1	PROPN
ejpam-1889	288	28	0	0	NUM
ejpam-1889	288	29	b2	b2	PROPN
ejpam-1889	288	30	c2	c2	PROPN
ejpam-1889	288	31	a3	a3	NOUN
ejpam-1889	288	32	0	0	NUM
ejpam-1889	288	33	0	0	NUM
ejpam-1889	289	1			PROPN
ejpam-1889	289	2	=	=	NOUN
ejpam-1889	289	3			NOUN
ejpam-1889	289	4			NOUN
ejpam-1889	289	5	0	0	PUNCT
ejpam-1889	290	1	β2	β2	VERB
ejpam-1889	290	2	1	1	NUM
ejpam-1889	290	3	0	0	NUM
ejpam-1889	290	4	0	0	NUM
ejpam-1889	290	5	1	1	NUM
ejpam-1889	290	6	β1	β1	NOUN
ejpam-1889	290	7	0	0	NUM
ejpam-1889	290	8	0	0	NUM
ejpam-1889	290	9			PROPN
ejpam-1889	290	10			PROPN
ejpam-1889	290	11	for	for	ADP
ejpam-1889	290	12	some	some	PRON
ejpam-1889	290	13	β1,β2	β1,β2	PUNCT
ejpam-1889	290	14	6=	6=	ADP
ejpam-1889	290	15	0	0	NUM
ejpam-1889	290	16	.	.	PUNCT
ejpam-1889	291	1	thus	thus	ADV
ejpam-1889	291	2	π	π	X
ejpam-1889	291	3	is	be	AUX
ejpam-1889	291	4	p	p	NOUN
ejpam-1889	291	5	-	-	PUNCT
ejpam-1889	291	6	equivalent	equivalent	ADJ
ejpam-1889	291	7	to	to	ADP
ejpam-1889	291	8	π(2,1	π(2,1	NOUN
ejpam-1889	291	9	)	)	PUNCT
ejpam-1889	291	10	8,β	8,β	NUM
ejpam-1889	291	11	.	.	PUNCT
ejpam-1889	292	1	suppose	suppose	VERB
ejpam-1889	292	2	that	that	SCONJ
ejpam-1889	292	3	c2	c2	PROPN
ejpam-1889	292	4	1	1	NUM
ejpam-1889	292	5	=	=	SYM
ejpam-1889	292	6	c2	c2	PROPN
ejpam-1889	292	7	2	2	NUM
ejpam-1889	292	8	and	and	CCONJ
ejpam-1889	292	9	b2	b2	NOUN
ejpam-1889	292	10	1	1	NUM
ejpam-1889	292	11	=	=	SYM
ejpam-1889	292	12	b2	b2	NOUN
ejpam-1889	292	13	2	2	NUM
ejpam-1889	292	14	.	.	PUNCT
ejpam-1889	292	15	by	by	ADP
ejpam-1889	292	16	the	the	DET
ejpam-1889	292	17	lemma	lemma	PROPN
ejpam-1889	292	18	(	(	PUNCT
ejpam-1889	292	19	with	with	ADP
ejpam-1889	292	20	x	x	SYM
ejpam-1889	292	21	=	=	SYM
ejpam-1889	292	22	b1e1	b1e1	NOUN
ejpam-1889	292	23	+	+	CCONJ
ejpam-1889	292	24	b2e2	b2e2	PROPN
ejpam-1889	292	25	,	,	PUNCT
ejpam-1889	292	26	y	y	NOUN
ejpam-1889	292	27	=	=	PUNCT
ejpam-1889	293	1	c1e1	c1e1	PROPN
ejpam-1889	293	2	+	+	CCONJ
ejpam-1889	293	3	c2e2	c2e2	PROPN
ejpam-1889	293	4	and	and	CCONJ
ejpam-1889	293	5	z	z	NOUN
ejpam-1889	293	6	=	=	SYM
ejpam-1889	293	7	a3e3	a3e3	PROPN
ejpam-1889	293	8	)	)	PUNCT
ejpam-1889	293	9	,	,	PUNCT
ejpam-1889	293	10	there	there	PRON
ejpam-1889	293	11	exists	exist	VERB
ejpam-1889	293	12	ψ	ψ	X
ejpam-1889	293	13	∈	∈	PROPN
ejpam-1889	293	14	aut	aut	X
ejpam-1889	293	15	(	(	PUNCT
ejpam-1889	293	16	se(1,1	se(1,1	NOUN
ejpam-1889	293	17	)	)	PUNCT
ejpam-1889	293	18	)	)	PUNCT
ejpam-1889	293	19	such	such	ADJ
ejpam-1889	293	20	that	that	SCONJ
ejpam-1889	293	21	ψ	ψ	X
ejpam-1889	293	22	·	·	PUNCT
ejpam-1889	293	23			PROPN
ejpam-1889	293	24			NOUN
ejpam-1889	293	25	0	0	NUM
ejpam-1889	293	26	b1	b1	PROPN
ejpam-1889	293	27	c1	c1	PROPN
ejpam-1889	293	28	0	0	NUM
ejpam-1889	293	29	b2	b2	PROPN
ejpam-1889	293	30	c2	c2	PROPN
ejpam-1889	293	31	a3	a3	NOUN
ejpam-1889	293	32	0	0	NUM
ejpam-1889	293	33	0	0	NUM
ejpam-1889	294	1			PROPN
ejpam-1889	294	2	=	=	NOUN
ejpam-1889	294	3			NOUN
ejpam-1889	294	4			NOUN
ejpam-1889	294	5	0	0	NUM
ejpam-1889	294	6	1	1	NUM
ejpam-1889	294	7	1	1	NUM
ejpam-1889	294	8	0	0	NUM
ejpam-1889	294	9	−1	−1	NOUN
ejpam-1889	294	10	1	1	NUM
ejpam-1889	294	11	β1	β1	NOUN
ejpam-1889	294	12	0	0	NUM
ejpam-1889	294	13	0	0	NUM
ejpam-1889	294	14			PROPN
ejpam-1889	294	15			PROPN
ejpam-1889	294	16	d.	d.	PROPN
ejpam-1889	294	17	barrett	barrett	PROPN
ejpam-1889	294	18	,	,	PUNCT
ejpam-1889	294	19	r.	r.	PROPN
ejpam-1889	294	20	biggs	biggs	PROPN
ejpam-1889	294	21	,	,	PUNCT
ejpam-1889	294	22	c.	c.	PROPN
ejpam-1889	294	23	remsing	remsing	NOUN
ejpam-1889	294	24	/	/	SYM
ejpam-1889	294	25	eur	eur	NOUN
ejpam-1889	294	26	.	.	PUNCT
ejpam-1889	295	1	j.	j.	PROPN
ejpam-1889	295	2	pure	pure	PROPN
ejpam-1889	295	3	appl	appl	PROPN
ejpam-1889	295	4	.	.	PROPN
ejpam-1889	295	5	math	math	PROPN
ejpam-1889	295	6	,	,	PUNCT
ejpam-1889	295	7	7	7	NUM
ejpam-1889	295	8	(	(	PUNCT
ejpam-1889	295	9	2014	2014	NUM
ejpam-1889	295	10	)	)	PUNCT
ejpam-1889	295	11	,	,	PUNCT
ejpam-1889	295	12	140	140	NUM
ejpam-1889	295	13	-	-	SYM
ejpam-1889	295	14	155	155	NUM
ejpam-1889	295	15	151	151	NUM
ejpam-1889	295	16	for	for	ADP
ejpam-1889	295	17	some	some	DET
ejpam-1889	295	18	β1	β1	PROPN
ejpam-1889	295	19	6=	6=	ADP
ejpam-1889	295	20	0	0	NUM
ejpam-1889	295	21	.	.	PUNCT
ejpam-1889	296	1	hence	hence	ADV
ejpam-1889	296	2	π	π	PROPN
ejpam-1889	296	3	is	be	AUX
ejpam-1889	296	4	p	p	NOUN
ejpam-1889	296	5	-	-	PUNCT
ejpam-1889	296	6	equivalent	equivalent	ADJ
ejpam-1889	296	7	to	to	ADP
ejpam-1889	296	8	π(2,1	π(2,1	PROPN
ejpam-1889	296	9	)	)	PUNCT
ejpam-1889	296	10	9,β	9,β	NOUN
ejpam-1889	296	11	.	.	PUNCT
ejpam-1889	297	1	clearly	clearly	ADV
ejpam-1889	297	2	,	,	PUNCT
ejpam-1889	297	3	parametrized	parametrized	ADJ
ejpam-1889	297	4	affine	affine	NOUN
ejpam-1889	297	5	subspaces	subspace	NOUN
ejpam-1889	297	6	corresponding	correspond	VERB
ejpam-1889	297	7	to	to	ADP
ejpam-1889	297	8	different	different	ADJ
ejpam-1889	297	9	(	(	PUNCT
ejpam-1889	297	10	2	2	NUM
ejpam-1889	297	11	,	,	PUNCT
ejpam-1889	297	12	1)-affine	1)-affine	NUM
ejpam-1889	297	13	subspace	subspace	NOUN
ejpam-1889	297	14	class	class	NOUN
ejpam-1889	297	15	representatives	representative	NOUN
ejpam-1889	297	16	(	(	PUNCT
ejpam-1889	297	17	γ(2,1	γ(2,1	NOUN
ejpam-1889	297	18	)	)	PUNCT
ejpam-1889	297	19	1	1	NUM
ejpam-1889	297	20	,	,	PUNCT
ejpam-1889	297	21	γ(2,1	γ(2,1	NOUN
ejpam-1889	297	22	)	)	PUNCT
ejpam-1889	297	23	2	2	NUM
ejpam-1889	297	24	and	and	CCONJ
ejpam-1889	297	25	γ(2,1	γ(2,1	NOUN
ejpam-1889	297	26	)	)	PUNCT
ejpam-1889	297	27	3,α	3,α	NUM
ejpam-1889	297	28	)	)	PUNCT
ejpam-1889	297	29	can	can	AUX
ejpam-1889	297	30	not	not	PART
ejpam-1889	297	31	be	be	AUX
ejpam-1889	297	32	p	p	NOUN
ejpam-1889	297	33	-	-	PUNCT
ejpam-1889	297	34	equivalent	equivalent	NOUN
ejpam-1889	297	35	.	.	PUNCT
ejpam-1889	298	1	no	no	DET
ejpam-1889	298	2	two	two	NUM
ejpam-1889	298	3	families	family	NOUN
ejpam-1889	298	4	in	in	ADP
ejpam-1889	298	5	case	case	NOUN
ejpam-1889	298	6	(	(	PUNCT
ejpam-1889	298	7	i	i	NOUN
ejpam-1889	298	8	)	)	PUNCT
ejpam-1889	298	9	,	,	PUNCT
ejpam-1889	298	10	case	case	NOUN
ejpam-1889	298	11	(	(	PUNCT
ejpam-1889	298	12	ii	ii	NOUN
ejpam-1889	298	13	)	)	PUNCT
ejpam-1889	298	14	and	and	CCONJ
ejpam-1889	298	15	case	case	NOUN
ejpam-1889	298	16	(	(	PUNCT
ejpam-1889	298	17	iii	iii	X
ejpam-1889	298	18	)	)	PUNCT
ejpam-1889	298	19	are	be	AUX
ejpam-1889	298	20	p	p	NOUN
ejpam-1889	298	21	-	-	PUNCT
ejpam-1889	298	22	equivalent	equivalent	ADJ
ejpam-1889	298	23	,	,	PUNCT
ejpam-1889	298	24	as	as	SCONJ
ejpam-1889	298	25	the	the	DET
ejpam-1889	298	26	subsets	subset	NOUN
ejpam-1889	298	27	〈	〈	PROPN
ejpam-1889	298	28	e1	e1	PROPN
ejpam-1889	298	29	,	,	PUNCT
ejpam-1889	298	30	e2	e2	NOUN
ejpam-1889	298	31	〉	〉	NOUN
ejpam-1889	298	32	and	and	CCONJ
ejpam-1889	298	33	〈	〈	NOUN
ejpam-1889	298	34	e1	e1	PROPN
ejpam-1889	298	35	+	+	CCONJ
ejpam-1889	298	36	e2	e2	X
ejpam-1889	298	37	〉	〉	NOUN
ejpam-1889	298	38	∪	∪	X
ejpam-1889	298	39	〈	〈	NOUN
ejpam-1889	298	40	e1	e1	PROPN
ejpam-1889	298	41	−	−	PROPN
ejpam-1889	298	42	e2	e2	PROPN
ejpam-1889	298	43	〉	〉	NOUN
ejpam-1889	298	44	are	be	AUX
ejpam-1889	298	45	invariant	invariant	ADJ
ejpam-1889	298	46	.	.	PUNCT
ejpam-1889	299	1	for	for	ADP
ejpam-1889	299	2	each	each	DET
ejpam-1889	299	3	family	family	NOUN
ejpam-1889	299	4	,	,	PUNCT
ejpam-1889	299	5	it	it	PRON
ejpam-1889	299	6	is	be	AUX
ejpam-1889	299	7	straightforward	straightforward	ADJ
ejpam-1889	299	8	to	to	PART
ejpam-1889	299	9	verify	verify	VERB
ejpam-1889	299	10	that	that	SCONJ
ejpam-1889	299	11	two	two	NUM
ejpam-1889	299	12	representatives	representative	NOUN
ejpam-1889	299	13	are	be	AUX
ejpam-1889	299	14	pequivalent	pequivalent	NOUN
ejpam-1889	299	15	only	only	ADV
ejpam-1889	299	16	if	if	SCONJ
ejpam-1889	299	17	their	their	PRON
ejpam-1889	299	18	parameters	parameter	NOUN
ejpam-1889	299	19	are	be	AUX
ejpam-1889	299	20	equal	equal	ADJ
ejpam-1889	299	21	.	.	PUNCT
ejpam-1889	300	1	suppose	suppose	VERB
ejpam-1889	300	2	π	π	X
ejpam-1889	300	3	:	:	PUNCT
ejpam-1889	300	4	a+	a+	PUNCT
ejpam-1889	300	5	u1b	u1b	PROPN
ejpam-1889	300	6	+	+	CCONJ
ejpam-1889	300	7	u2c	u2c	PROPN
ejpam-1889	300	8	+	+	NOUN
ejpam-1889	300	9	u3d	u3d	NOUN
ejpam-1889	300	10	is	be	AUX
ejpam-1889	300	11	a	a	DET
ejpam-1889	300	12	parametrization	parametrization	NOUN
ejpam-1889	300	13	of	of	ADP
ejpam-1889	300	14	a	a	DET
ejpam-1889	300	15	(	(	PUNCT
ejpam-1889	300	16	3,0)-affine	3,0)-affine	NUM
ejpam-1889	300	17	subspace	subspace	PROPN
ejpam-1889	300	18	γ	γ	PROPN
ejpam-1889	300	19	.	.	PUNCT
ejpam-1889	301	1	we	we	PRON
ejpam-1889	301	2	shall	shall	AUX
ejpam-1889	301	3	denote	denote	VERB
ejpam-1889	301	4	by	by	ADP
ejpam-1889	301	5	bπ	bπ	ADP
ejpam-1889	301	6	the	the	DET
ejpam-1889	301	7	parametrization	parametrization	NOUN
ejpam-1889	301	8	bπ	bπ	ADP
ejpam-1889	301	9	:	:	PUNCT
ejpam-1889	301	10	b	b	X
ejpam-1889	301	11	+	+	CCONJ
ejpam-1889	301	12	u1c	u1c	ADJ
ejpam-1889	301	13	+	+	CCONJ
ejpam-1889	301	14	u2d	u2d	NOUN
ejpam-1889	301	15	of	of	ADP
ejpam-1889	301	16	the	the	DET
ejpam-1889	301	17	associated	associate	VERB
ejpam-1889	301	18	affine	affine	NOUN
ejpam-1889	301	19	subspace	subspace	NOUN
ejpam-1889	301	20	bγ	bγ	PROPN
ejpam-1889	301	21	=	=	PUNCT
ejpam-1889	301	22	b+	b+	X
ejpam-1889	301	23	〈	〈	PROPN
ejpam-1889	301	24	c	c	NOUN
ejpam-1889	301	25	,	,	PUNCT
ejpam-1889	301	26	d	d	X
ejpam-1889	301	27	〉	〉	NOUN
ejpam-1889	301	28	.	.	PUNCT
ejpam-1889	302	1	as	as	SCONJ
ejpam-1889	302	2	bπ	bπ	PROPN
ejpam-1889	302	3	is	be	AUX
ejpam-1889	302	4	a	a	DET
ejpam-1889	302	5	parametrized	parametrized	ADJ
ejpam-1889	302	6	(	(	PUNCT
ejpam-1889	302	7	2	2	NUM
ejpam-1889	302	8	,	,	PUNCT
ejpam-1889	302	9	1)-affine	1)-affine	NUM
ejpam-1889	302	10	subspace	subspace	NOUN
ejpam-1889	302	11	,	,	PUNCT
ejpam-1889	302	12	it	it	PRON
ejpam-1889	302	13	is	be	AUX
ejpam-1889	302	14	p	p	NOUN
ejpam-1889	302	15	-	-	PUNCT
ejpam-1889	302	16	equivalent	equivalent	ADJ
ejpam-1889	302	17	to	to	ADP
ejpam-1889	302	18	exactly	exactly	ADV
ejpam-1889	302	19	one	one	NUM
ejpam-1889	302	20	of	of	ADP
ejpam-1889	302	21	the	the	DET
ejpam-1889	302	22	representatives	representative	NOUN
ejpam-1889	302	23	listed	list	VERB
ejpam-1889	302	24	in	in	ADP
ejpam-1889	302	25	theorem	theorem	ADJ
ejpam-1889	302	26	4	4	NUM
ejpam-1889	302	27	.	.	PUNCT
ejpam-1889	302	28	accordingly	accordingly	ADV
ejpam-1889	302	29	,	,	PUNCT
ejpam-1889	302	30	we	we	PRON
ejpam-1889	302	31	get	get	VERB
ejpam-1889	302	32	the	the	DET
ejpam-1889	302	33	following	follow	VERB
ejpam-1889	302	34	classification	classification	NOUN
ejpam-1889	302	35	of	of	ADP
ejpam-1889	302	36	parametrized	parametrized	ADJ
ejpam-1889	302	37	(	(	PUNCT
ejpam-1889	302	38	3,0)-affine	3,0)-affine	NUM
ejpam-1889	302	39	subspaces	subspace	NOUN
ejpam-1889	302	40	(	(	PUNCT
ejpam-1889	302	41	we	we	PRON
ejpam-1889	302	42	again	again	ADV
ejpam-1889	302	43	use	use	VERB
ejpam-1889	302	44	theorem	theorem	NOUN
ejpam-1889	302	45	2	2	NUM
ejpam-1889	302	46	,	,	PUNCT
ejpam-1889	302	47	the	the	DET
ejpam-1889	302	48	classification	classification	NOUN
ejpam-1889	302	49	of	of	ADP
ejpam-1889	302	50	(	(	PUNCT
ejpam-1889	302	51	2,1)-affine	2,1)-affine	NUM
ejpam-1889	302	52	subspaces	subspace	NOUN
ejpam-1889	302	53	,	,	PUNCT
ejpam-1889	302	54	to	to	PART
ejpam-1889	302	55	organize	organize	VERB
ejpam-1889	302	56	the	the	DET
ejpam-1889	302	57	results	result	NOUN
ejpam-1889	302	58	)	)	PUNCT
ejpam-1889	302	59	.	.	PUNCT
ejpam-1889	303	1	corollary	corollary	ADJ
ejpam-1889	303	2	3	3	X
ejpam-1889	303	3	.	.	PUNCT
ejpam-1889	304	1	letπ	letπ	VERB
ejpam-1889	304	2	:	:	PUNCT
ejpam-1889	304	3	∑3	∑3	PROPN
ejpam-1889	305	1	i=1	i=1	PROPN
ejpam-1889	305	2	ai	ai	VERB
ejpam-1889	305	3	ei+u1	ei+u1	NOUN
ejpam-1889	305	4	∑3	∑3	PROPN
ejpam-1889	305	5	i=1	i=1	PROPN
ejpam-1889	305	6	bi	bi	NOUN
ejpam-1889	306	1	ei+u2	ei+u2	PROPN
ejpam-1889	306	2	∑3	∑3	PROPN
ejpam-1889	306	3	i=1	i=1	PROPN
ejpam-1889	306	4	ci	ci	PROPN
ejpam-1889	306	5	ei+u3	ei+u3	PROPN
ejpam-1889	306	6	∑3	∑3	PROPN
ejpam-1889	306	7	i=1	i=1	PROPN
ejpam-1889	306	8	di	di	NOUN
ejpam-1889	306	9	ei	ei	X
ejpam-1889	306	10	be	be	AUX
ejpam-1889	306	11	a	a	DET
ejpam-1889	306	12	parametrization	parametrization	NOUN
ejpam-1889	306	13	of	of	ADP
ejpam-1889	306	14	a	a	DET
ejpam-1889	306	15	(	(	PUNCT
ejpam-1889	306	16	3	3	NUM
ejpam-1889	306	17	,	,	PUNCT
ejpam-1889	306	18	0)-affine	0)-affine	NUM
ejpam-1889	306	19	subspace	subspace	PROPN
ejpam-1889	306	20	γ	γ	PROPN
ejpam-1889	306	21	.	.	PUNCT
ejpam-1889	307	1	(	(	PUNCT
ejpam-1889	307	2	i	i	NOUN
ejpam-1889	307	3	)	)	PUNCT
ejpam-1889	307	4	if	if	SCONJ
ejpam-1889	307	5	bγ	bγ	PROPN
ejpam-1889	307	6	isl	isl	VERB
ejpam-1889	307	7	-	-	PUNCT
ejpam-1889	307	8	equivalent	equivalent	ADJ
ejpam-1889	307	9	to	to	ADP
ejpam-1889	307	10	γ(2,1	γ(2,1	PROPN
ejpam-1889	307	11	)	)	PUNCT
ejpam-1889	307	12	1	1	NUM
ejpam-1889	307	13	,	,	PUNCT
ejpam-1889	307	14	thenπ	thenπ	NOUN
ejpam-1889	307	15	isp	isp	ADV
ejpam-1889	307	16	-	-	PUNCT
ejpam-1889	307	17	equivalent	equivalent	ADJ
ejpam-1889	307	18	to	to	ADP
ejpam-1889	307	19	exactly	exactly	ADV
ejpam-1889	307	20	one	one	NUM
ejpam-1889	307	21	of	of	ADP
ejpam-1889	307	22	the	the	DET
ejpam-1889	307	23	following	follow	VERB
ejpam-1889	307	24	parametrized	parametrized	ADJ
ejpam-1889	307	25	subspaces	subspace	NOUN
ejpam-1889	307	26	(	(	PUNCT
ejpam-1889	307	27	π(3,0	π(3,0	PROPN
ejpam-1889	307	28	)	)	PUNCT
ejpam-1889	307	29	1,α	1,α	NOUN
ejpam-1889	307	30	,	,	PUNCT
ejpam-1889	307	31	β	β	X
ejpam-1889	307	32	,	,	PUNCT
ejpam-1889	307	33	γ	γ	X
ejpam-1889	307	34	:	:	PUNCT
ejpam-1889	307	35	∑3	∑3	PROPN
ejpam-1889	307	36	i=1	i=1	PROPN
ejpam-1889	307	37	γi	γi	X
ejpam-1889	308	1	ei	ei	X
ejpam-1889	308	2	+	+	CCONJ
ejpam-1889	308	3	u1(γ4e1	u1(γ4e1	PROPN
ejpam-1889	308	4	+	+	CCONJ
ejpam-1889	308	5	β1e2	β1e2	PUNCT
ejpam-1889	308	6	+	+	NUM
ejpam-1889	308	7	γ5e3	γ5e3	X
ejpam-1889	308	8	)	)	PUNCT
ejpam-1889	308	9	+	+	CCONJ
ejpam-1889	308	10	u2(e1	u2(e1	NOUN
ejpam-1889	308	11	+	+	CCONJ
ejpam-1889	308	12	γ6e2	γ6e2	ADJ
ejpam-1889	308	13	)	)	PUNCT
ejpam-1889	308	14	+	+	CCONJ
ejpam-1889	308	15	u3(αe3	u3(αe3	NOUN
ejpam-1889	308	16	)	)	PUNCT
ejpam-1889	308	17	d3	d3	PROPN
ejpam-1889	308	18	6=	6=	ADP
ejpam-1889	308	19	0	0	NUM
ejpam-1889	308	20	π(3,0	π(3,0	DET
ejpam-1889	308	21	)	)	PUNCT
ejpam-1889	308	22	2,α	2,α	PROPN
ejpam-1889	308	23	,	,	PUNCT
ejpam-1889	308	24	β	β	X
ejpam-1889	308	25	,	,	PUNCT
ejpam-1889	308	26	γ	γ	X
ejpam-1889	308	27	:	:	PUNCT
ejpam-1889	308	28	∑3	∑3	PROPN
ejpam-1889	308	29	i=1	i=1	PROPN
ejpam-1889	308	30	γi	γi	X
ejpam-1889	309	1	ei	ei	X
ejpam-1889	309	2	+	+	CCONJ
ejpam-1889	309	3	u1(γ4e1	u1(γ4e1	PROPN
ejpam-1889	309	4	+	+	CCONJ
ejpam-1889	309	5	β1e2	β1e2	PUNCT
ejpam-1889	309	6	+	+	NUM
ejpam-1889	309	7	γ5e3	γ5e3	X
ejpam-1889	309	8	)	)	PUNCT
ejpam-1889	310	1	+	+	CCONJ
ejpam-1889	310	2	u2(αe3	u2(αe3	ADJ
ejpam-1889	310	3	)	)	PUNCT
ejpam-1889	310	4	+	+	NUM
ejpam-1889	310	5	u3e1	u3e1	PRON
ejpam-1889	310	6	d3	d3	PROPN
ejpam-1889	310	7	=	=	SYM
ejpam-1889	310	8	0	0	PROPN
ejpam-1889	310	9	.	.	PUNCT
ejpam-1889	310	10	(	(	PUNCT
ejpam-1889	310	11	ii	ii	NOUN
ejpam-1889	310	12	)	)	PUNCT
ejpam-1889	310	13	if	if	SCONJ
ejpam-1889	310	14	bγ	bγ	PROPN
ejpam-1889	310	15	isl	isl	VERB
ejpam-1889	310	16	-	-	PUNCT
ejpam-1889	310	17	equivalent	equivalent	ADJ
ejpam-1889	310	18	to	to	ADP
ejpam-1889	310	19	γ(2,1	γ(2,1	PROPN
ejpam-1889	310	20	)	)	PUNCT
ejpam-1889	310	21	2	2	NUM
ejpam-1889	310	22	,	,	PUNCT
ejpam-1889	310	23	thenπ	thenπ	NOUN
ejpam-1889	310	24	isp	isp	ADV
ejpam-1889	310	25	-	-	PUNCT
ejpam-1889	310	26	equivalent	equivalent	ADJ
ejpam-1889	310	27	to	to	ADP
ejpam-1889	310	28	exactly	exactly	ADV
ejpam-1889	310	29	one	one	NUM
ejpam-1889	310	30	of	of	ADP
ejpam-1889	310	31	the	the	DET
ejpam-1889	310	32	following	follow	VERB
ejpam-1889	310	33	parametrized	parametrized	ADJ
ejpam-1889	310	34	subspaces	subspace	NOUN
ejpam-1889	310	35			VERB
ejpam-1889	310	36			ADJ
ejpam-1889	310	37			PROPN
ejpam-1889	310	38			PROPN
ejpam-1889	310	39			PROPN
ejpam-1889	310	40			PROPN
ejpam-1889	310	41			PROPN
ejpam-1889	310	42			PROPN
ejpam-1889	310	43			PROPN
ejpam-1889	310	44			PROPN
ejpam-1889	310	45			PROPN
ejpam-1889	310	46			PROPN
ejpam-1889	310	47			PROPN
ejpam-1889	310	48			PROPN
ejpam-1889	310	49			NOUN
ejpam-1889	310	50			PROPN
ejpam-1889	310	51			PROPN
ejpam-1889	310	52			PROPN
ejpam-1889	310	53			PROPN
ejpam-1889	310	54			PROPN
ejpam-1889	310	55			PROPN
ejpam-1889	310	56			PROPN
ejpam-1889	310	57			PROPN
ejpam-1889	310	58			PROPN
ejpam-1889	310	59			PROPN
ejpam-1889	310	60			PROPN
ejpam-1889	310	61			PROPN
ejpam-1889	310	62			PROPN
ejpam-1889	310	63			PROPN
ejpam-1889	310	64	π(3,0	π(3,0	NOUN
ejpam-1889	310	65	)	)	PUNCT
ejpam-1889	310	66	3,β	3,β	NUM
ejpam-1889	310	67	,	,	PUNCT
ejpam-1889	310	68	γ	γ	X
ejpam-1889	310	69	:	:	PUNCT
ejpam-1889	310	70	∑3	∑3	PROPN
ejpam-1889	310	71	i=1	i=1	PROPN
ejpam-1889	310	72	γi	γi	X
ejpam-1889	311	1	ei	ei	X
ejpam-1889	311	2	+	+	CCONJ
ejpam-1889	311	3	u1(β1e1	u1(β1e1	NOUN
ejpam-1889	311	4	+	+	CCONJ
ejpam-1889	311	5	γ4e3	γ4e3	NOUN
ejpam-1889	311	6	)	)	PUNCT
ejpam-1889	312	1	+	+	CCONJ
ejpam-1889	312	2	u2(e1	u2(e1	NOUN
ejpam-1889	312	3	+	+	CCONJ
ejpam-1889	312	4	e2	e2	PROPN
ejpam-1889	312	5	+	+	CCONJ
ejpam-1889	312	6	γ5e3	γ5e3	PUNCT
ejpam-1889	312	7	)	)	PUNCT
ejpam-1889	313	1	+	+	CCONJ
ejpam-1889	313	2	u3(β2e3	u3(β2e3	PROPN
ejpam-1889	313	3	)	)	PUNCT
ejpam-1889	313	4	d3	d3	PROPN
ejpam-1889	313	5	6=	6=	ADP
ejpam-1889	313	6	0	0	NUM
ejpam-1889	313	7	,	,	PUNCT
ejpam-1889	313	8	�	�	PROPN
ejpam-1889	313	9	b1d3−b3d1	b1d3−b3d1	PROPN
ejpam-1889	313	10	d3	d3	PROPN
ejpam-1889	313	11	�	�	PROPN
ejpam-1889	313	12	2	2	NUM
ejpam-1889	313	13	6=	6=	NUM
ejpam-1889	313	14	�	�	PROPN
ejpam-1889	313	15	b2d3−b3d2	b2d3−b3d2	PROPN
ejpam-1889	313	16	d3	d3	PROPN
ejpam-1889	313	17	�	�	PROPN
ejpam-1889	313	18	2	2	NUM
ejpam-1889	313	19	π(3,0	π(3,0	PRON
ejpam-1889	313	20	)	)	PUNCT
ejpam-1889	313	21	4,β	4,β	NOUN
ejpam-1889	313	22	,	,	PUNCT
ejpam-1889	313	23	γ	γ	X
ejpam-1889	313	24	:	:	PUNCT
ejpam-1889	313	25	∑3	∑3	PROPN
ejpam-1889	313	26	i=1	i=1	PROPN
ejpam-1889	313	27	γi	γi	X
ejpam-1889	314	1	ei	ei	INTJ
ejpam-1889	314	2	+	+	CCONJ
ejpam-1889	314	3	u1(e1	u1(e1	VERB
ejpam-1889	314	4	−	−	PROPN
ejpam-1889	314	5	e2	e2	PROPN
ejpam-1889	314	6	+	+	CCONJ
ejpam-1889	314	7	γ4e3	γ4e3	X
ejpam-1889	314	8	)	)	PUNCT
ejpam-1889	315	1	+	+	CCONJ
ejpam-1889	315	2	u2(e1	u2(e1	NOUN
ejpam-1889	315	3	+	+	CCONJ
ejpam-1889	315	4	e2	e2	PROPN
ejpam-1889	315	5	+	+	CCONJ
ejpam-1889	315	6	γ5e3	γ5e3	X
ejpam-1889	315	7	)	)	PUNCT
ejpam-1889	316	1	+	+	CCONJ
ejpam-1889	316	2	u3(β1e3	u3(β1e3	PROPN
ejpam-1889	316	3	)	)	PUNCT
ejpam-1889	316	4	d3	d3	PROPN
ejpam-1889	316	5	6=	6=	ADP
ejpam-1889	316	6	0	0	NUM
ejpam-1889	316	7	,	,	PUNCT
ejpam-1889	316	8	�	�	PROPN
ejpam-1889	316	9	b1d3−b3d1	b1d3−b3d1	PROPN
ejpam-1889	316	10	d3	d3	PROPN
ejpam-1889	316	11	�	�	PROPN
ejpam-1889	316	12	2	2	NUM
ejpam-1889	316	13	=	=	SYM
ejpam-1889	316	14	�	�	PROPN
ejpam-1889	316	15	b2d3−b3d2	b2d3−b3d2	PROPN
ejpam-1889	316	16	d3	d3	PROPN
ejpam-1889	316	17	�	�	PROPN
ejpam-1889	316	18	2	2	NUM
ejpam-1889	316	19	π(3,0	π(3,0	PRON
ejpam-1889	316	20	)	)	PUNCT
ejpam-1889	316	21	5,β	5,β	PROPN
ejpam-1889	316	22	,	,	PUNCT
ejpam-1889	316	23	γ	γ	X
ejpam-1889	316	24	:	:	PUNCT
ejpam-1889	316	25	∑3	∑3	PROPN
ejpam-1889	316	26	i=1	i=1	PROPN
ejpam-1889	316	27	γi	γi	X
ejpam-1889	317	1	ei	ei	X
ejpam-1889	317	2	+	+	CCONJ
ejpam-1889	317	3	u1(β1e1	u1(β1e1	NOUN
ejpam-1889	317	4	+	+	CCONJ
ejpam-1889	317	5	γ4e3	γ4e3	NOUN
ejpam-1889	317	6	)	)	PUNCT
ejpam-1889	318	1	+	+	CCONJ
ejpam-1889	318	2	u2(β2e3	u2(β2e3	X
ejpam-1889	318	3	)	)	PUNCT
ejpam-1889	319	1	+	+	CCONJ
ejpam-1889	319	2	u3(e1	u3(e1	NOUN
ejpam-1889	319	3	+	+	CCONJ
ejpam-1889	319	4	e2	e2	PROPN
ejpam-1889	319	5	)	)	PUNCT
ejpam-1889	319	6	d3	d3	PROPN
ejpam-1889	319	7	=	=	SYM
ejpam-1889	319	8	0	0	NUM
ejpam-1889	319	9	,	,	PUNCT
ejpam-1889	319	10	�	�	PROPN
ejpam-1889	319	11	b1c3−b3c1	b1c3−b3c1	PROPN
ejpam-1889	319	12	c3	c3	PROPN
ejpam-1889	319	13	�	�	PROPN
ejpam-1889	319	14	2	2	NUM
ejpam-1889	319	15	6=	6=	NUM
ejpam-1889	319	16	�	�	PROPN
ejpam-1889	319	17	b2c3−b3c2	b2c3−b3c2	PROPN
ejpam-1889	319	18	c3	c3	PROPN
ejpam-1889	319	19	�	�	PROPN
ejpam-1889	319	20	2	2	NUM
ejpam-1889	319	21	π(3,0	π(3,0	PRON
ejpam-1889	319	22	)	)	PUNCT
ejpam-1889	319	23	6,β	6,β	NOUN
ejpam-1889	319	24	,	,	PUNCT
ejpam-1889	319	25	γ	γ	X
ejpam-1889	319	26	:	:	PUNCT
ejpam-1889	319	27	∑3	∑3	PROPN
ejpam-1889	319	28	i=1	i=1	PROPN
ejpam-1889	319	29	γi	γi	X
ejpam-1889	320	1	ei	ei	INTJ
ejpam-1889	320	2	+	+	CCONJ
ejpam-1889	320	3	u1(e1	u1(e1	VERB
ejpam-1889	320	4	−	−	PROPN
ejpam-1889	320	5	e2	e2	PROPN
ejpam-1889	320	6	+	+	CCONJ
ejpam-1889	320	7	γ4e3	γ4e3	X
ejpam-1889	320	8	)	)	PUNCT
ejpam-1889	321	1	+	+	CCONJ
ejpam-1889	321	2	u2(β1e3	u2(β1e3	PROPN
ejpam-1889	321	3	)	)	PUNCT
ejpam-1889	321	4	+	+	CCONJ
ejpam-1889	321	5	u3(e1	u3(e1	NOUN
ejpam-1889	321	6	+	+	CCONJ
ejpam-1889	321	7	e2	e2	PROPN
ejpam-1889	321	8	)	)	PUNCT
ejpam-1889	321	9	d3	d3	PROPN
ejpam-1889	321	10	=	=	SYM
ejpam-1889	321	11	0	0	NUM
ejpam-1889	321	12	,	,	PUNCT
ejpam-1889	321	13	�	�	PROPN
ejpam-1889	321	14	b1c3−b3c1	b1c3−b3c1	PROPN
ejpam-1889	321	15	c3	c3	X
ejpam-1889	321	16	�	�	PROPN
ejpam-1889	321	17	2	2	NUM
ejpam-1889	321	18	=	=	SYM
ejpam-1889	321	19	�	�	PROPN
ejpam-1889	321	20	b2c3−b3c2	b2c3−b3c2	PROPN
ejpam-1889	321	21	c3	c3	PROPN
ejpam-1889	321	22	�	�	PROPN
ejpam-1889	321	23	2	2	NUM
ejpam-1889	321	24	.	.	PUNCT
ejpam-1889	322	1	(	(	PUNCT
ejpam-1889	322	2	iii	iii	X
ejpam-1889	322	3	)	)	PUNCT
ejpam-1889	322	4	if	if	SCONJ
ejpam-1889	322	5	bγ	bγ	PROPN
ejpam-1889	322	6	isl	isl	VERB
ejpam-1889	322	7	-	-	PUNCT
ejpam-1889	322	8	equivalent	equivalent	ADJ
ejpam-1889	322	9	to	to	ADP
ejpam-1889	322	10	γ(2,1	γ(2,1	NUM
ejpam-1889	322	11	)	)	PUNCT
ejpam-1889	322	12	3,α	3,α	NUM
ejpam-1889	322	13	,	,	PUNCT
ejpam-1889	322	14	thenπ	thenπ	NOUN
ejpam-1889	322	15	isp	isp	ADV
ejpam-1889	322	16	-	-	PUNCT
ejpam-1889	322	17	equivalent	equivalent	ADJ
ejpam-1889	322	18	to	to	ADP
ejpam-1889	322	19	exactly	exactly	ADV
ejpam-1889	322	20	one	one	NUM
ejpam-1889	322	21	of	of	ADP
ejpam-1889	322	22	the	the	DET
ejpam-1889	322	23	following	follow	VERB
ejpam-1889	322	24	parametrized	parametrized	ADJ
ejpam-1889	322	25	subspaces	subspace	NOUN
ejpam-1889	322	26			VERB
ejpam-1889	322	27			ADV
ejpam-1889	322	28			DET
ejpam-1889	322	29			PROPN
ejpam-1889	322	30			PROPN
ejpam-1889	322	31	π(3,0	π(3,0	PRON
ejpam-1889	322	32	)	)	PUNCT
ejpam-1889	322	33	7,α	7,α	PROPN
ejpam-1889	322	34	,	,	PUNCT
ejpam-1889	322	35	β	β	X
ejpam-1889	322	36	,	,	PUNCT
ejpam-1889	322	37	γ	γ	X
ejpam-1889	322	38	:	:	PUNCT
ejpam-1889	322	39	∑3	∑3	PROPN
ejpam-1889	322	40	i=1	i=1	PROPN
ejpam-1889	322	41	γi	γi	INTJ
ejpam-1889	323	1	ei	ei	X
ejpam-1889	323	2	+	+	CCONJ
ejpam-1889	323	3	u1(β1e3	u1(β1e3	ADJ
ejpam-1889	323	4	)	)	PUNCT
ejpam-1889	324	1	+	+	CCONJ
ejpam-1889	324	2	u2(γ4e1	u2(γ4e1	PROPN
ejpam-1889	324	3	+	+	NOUN
ejpam-1889	324	4	αe2	αe2	NOUN
ejpam-1889	324	5	)	)	PUNCT
ejpam-1889	325	1	+	+	CCONJ
ejpam-1889	325	2	u3e1	u3e1	PRON
ejpam-1889	325	3	d2	d2	PROPN
ejpam-1889	325	4	1	1	NUM
ejpam-1889	325	5	6=	6=	NUM
ejpam-1889	325	6	d2	d2	PROPN
ejpam-1889	325	7	2	2	NUM
ejpam-1889	325	8	π(3,0	π(3,0	PRON
ejpam-1889	325	9	)	)	PUNCT
ejpam-1889	325	10	8,β	8,β	NUM
ejpam-1889	325	11	,	,	PUNCT
ejpam-1889	325	12	γ	γ	X
ejpam-1889	325	13	:	:	PUNCT
ejpam-1889	325	14	∑3	∑3	PROPN
ejpam-1889	325	15	i=1	i=1	PROPN
ejpam-1889	325	16	γi	γi	INTJ
ejpam-1889	325	17	ei	ei	X
ejpam-1889	326	1	+	+	CCONJ
ejpam-1889	326	2	u1(β1e3	u1(β1e3	ADJ
ejpam-1889	326	3	)	)	PUNCT
ejpam-1889	327	1	+	+	CCONJ
ejpam-1889	327	2	u2(β2e1	u2(β2e1	PROPN
ejpam-1889	327	3	)	)	PUNCT
ejpam-1889	328	1	+	+	CCONJ
ejpam-1889	328	2	u3(e1	u3(e1	NOUN
ejpam-1889	328	3	+	+	CCONJ
ejpam-1889	328	4	e2	e2	PROPN
ejpam-1889	328	5	)	)	PUNCT
ejpam-1889	328	6	d2	d2	PROPN
ejpam-1889	328	7	1	1	NUM
ejpam-1889	328	8	=	=	SYM
ejpam-1889	328	9	d2	d2	PROPN
ejpam-1889	328	10	2	2	NUM
ejpam-1889	328	11	,	,	PUNCT
ejpam-1889	328	12	c2	c2	PROPN
ejpam-1889	328	13	1	1	NUM
ejpam-1889	328	14	6=	6=	NUM
ejpam-1889	328	15	c2	c2	PROPN
ejpam-1889	328	16	2	2	NUM
ejpam-1889	328	17	π(3,0	π(3,0	PRON
ejpam-1889	328	18	)	)	PUNCT
ejpam-1889	328	19	9,β	9,β	NOUN
ejpam-1889	328	20	,	,	PUNCT
ejpam-1889	328	21	γ	γ	X
ejpam-1889	328	22	:	:	PUNCT
ejpam-1889	328	23	∑3	∑3	PROPN
ejpam-1889	328	24	i=1	i=1	PROPN
ejpam-1889	328	25	γi	γi	INTJ
ejpam-1889	328	26	ei	ei	X
ejpam-1889	328	27	+	+	CCONJ
ejpam-1889	328	28	u1(β1e3	u1(β1e3	ADJ
ejpam-1889	328	29	)	)	PUNCT
ejpam-1889	329	1	+	+	CCONJ
ejpam-1889	329	2	u2(e1	u2(e1	VERB
ejpam-1889	329	3	−	−	PROPN
ejpam-1889	329	4	e2	e2	PROPN
ejpam-1889	329	5	)	)	PUNCT
ejpam-1889	330	1	+	+	CCONJ
ejpam-1889	330	2	u3(e1	u3(e1	NOUN
ejpam-1889	330	3	+	+	CCONJ
ejpam-1889	330	4	e2	e2	PROPN
ejpam-1889	330	5	)	)	PUNCT
ejpam-1889	330	6	d2	d2	PROPN
ejpam-1889	330	7	1	1	NUM
ejpam-1889	330	8	=	=	SYM
ejpam-1889	330	9	d2	d2	PROPN
ejpam-1889	330	10	2	2	NUM
ejpam-1889	330	11	,	,	PUNCT
ejpam-1889	330	12	c2	c2	PROPN
ejpam-1889	330	13	1	1	NUM
ejpam-1889	330	14	=	=	SYM
ejpam-1889	330	15	c2	c2	PROPN
ejpam-1889	330	16	2	2	NUM
ejpam-1889	330	17	.	.	PUNCT
ejpam-1889	331	1	references	reference	NOUN
ejpam-1889	331	2	152	152	NUM
ejpam-1889	331	3	here	here	ADV
ejpam-1889	331	4	α	α	PROPN
ejpam-1889	331	5	>	>	X
ejpam-1889	331	6	0	0	PROPN
ejpam-1889	331	7	,	,	PUNCT
ejpam-1889	331	8	βi	βi	PROPN
ejpam-1889	331	9	6=	6=	ADP
ejpam-1889	331	10	0	0	NUM
ejpam-1889	332	1	and	and	CCONJ
ejpam-1889	332	2	γi	γi	ADP
ejpam-1889	332	3	∈	∈	PROPN
ejpam-1889	332	4	r	r	NOUN
ejpam-1889	332	5	,	,	PUNCT
ejpam-1889	332	6	with	with	ADP
ejpam-1889	332	7	different	different	ADJ
ejpam-1889	332	8	values	value	NOUN
ejpam-1889	332	9	of	of	ADP
ejpam-1889	332	10	these	these	DET
ejpam-1889	332	11	parameters	parameter	NOUN
ejpam-1889	332	12	yielding	yield	VERB
ejpam-1889	332	13	distinct	distinct	ADJ
ejpam-1889	332	14	(	(	PUNCT
ejpam-1889	332	15	nonequivalent	nonequivalent	ADJ
ejpam-1889	332	16	)	)	PUNCT
ejpam-1889	332	17	class	class	NOUN
ejpam-1889	332	18	representatives	representative	NOUN
ejpam-1889	332	19	.	.	PUNCT
ejpam-1889	333	1	4	4	X
ejpam-1889	333	2	.	.	X
ejpam-1889	333	3	final	final	ADJ
ejpam-1889	333	4	remark	remark	NOUN
ejpam-1889	333	5	in	in	ADP
ejpam-1889	333	6	this	this	DET
ejpam-1889	333	7	paper	paper	NOUN
ejpam-1889	333	8	we	we	PRON
ejpam-1889	333	9	classified	classify	VERB
ejpam-1889	333	10	,	,	PUNCT
ejpam-1889	333	11	under	under	ADP
ejpam-1889	333	12	l	l	NOUN
ejpam-1889	333	13	-	-	NOUN
ejpam-1889	333	14	equivalence	equivalence	NOUN
ejpam-1889	333	15	(	(	PUNCT
ejpam-1889	333	16	resp	resp	NOUN
ejpam-1889	333	17	.	.	PUNCT
ejpam-1889	334	1	p	p	X
ejpam-1889	334	2	-	-	PUNCT
ejpam-1889	334	3	equivalence	equivalence	NOUN
ejpam-1889	334	4	)	)	PUNCT
ejpam-1889	334	5	,	,	PUNCT
ejpam-1889	334	6	the	the	DET
ejpam-1889	334	7	affine	affine	NOUN
ejpam-1889	334	8	subspaces	subspace	NOUN
ejpam-1889	334	9	(	(	PUNCT
ejpam-1889	334	10	resp	resp	NOUN
ejpam-1889	334	11	.	.	PUNCT
ejpam-1889	335	1	parametrized	parametrized	ADJ
ejpam-1889	335	2	affine	affine	NOUN
ejpam-1889	335	3	subspaces	subspace	NOUN
ejpam-1889	335	4	)	)	PUNCT
ejpam-1889	335	5	of	of	ADP
ejpam-1889	335	6	the	the	DET
ejpam-1889	335	7	semi	semi	ADJ
ejpam-1889	335	8	-	-	ADJ
ejpam-1889	335	9	euclidean	euclidean	ADJ
ejpam-1889	335	10	lie	lie	NOUN
ejpam-1889	335	11	algebra	algebra	PROPN
ejpam-1889	335	12	se(1,1	se(1,1	PROPN
ejpam-1889	335	13	)	)	PUNCT
ejpam-1889	335	14	.	.	PUNCT
ejpam-1889	336	1	this	this	PRON
ejpam-1889	336	2	can	can	AUX
ejpam-1889	336	3	be	be	AUX
ejpam-1889	336	4	interpreted	interpret	VERB
ejpam-1889	336	5	as	as	ADP
ejpam-1889	336	6	a	a	DET
ejpam-1889	336	7	classification	classification	NOUN
ejpam-1889	336	8	,	,	PUNCT
ejpam-1889	336	9	under	under	ADP
ejpam-1889	336	10	detached	detach	VERB
ejpam-1889	336	11	feedback	feedback	NOUN
ejpam-1889	336	12	equivalence	equivalence	NOUN
ejpam-1889	336	13	(	(	PUNCT
ejpam-1889	336	14	resp	resp	NOUN
ejpam-1889	336	15	.	.	PUNCT
ejpam-1889	337	1	state	state	NOUN
ejpam-1889	337	2	space	space	NOUN
ejpam-1889	337	3	equivalence	equivalence	NOUN
ejpam-1889	337	4	)	)	PUNCT
ejpam-1889	337	5	,	,	PUNCT
ejpam-1889	337	6	of	of	ADP
ejpam-1889	337	7	left	left	ADJ
ejpam-1889	337	8	-	-	PUNCT
ejpam-1889	337	9	invariant	invariant	ADJ
ejpam-1889	337	10	control	control	NOUN
ejpam-1889	337	11	affine	affine	NOUN
ejpam-1889	337	12	systems	system	NOUN
ejpam-1889	337	13	on	on	ADP
ejpam-1889	337	14	the	the	DET
ejpam-1889	337	15	semi	semi	ADJ
ejpam-1889	337	16	-	-	ADJ
ejpam-1889	337	17	euclidean	euclidean	ADJ
ejpam-1889	337	18	group	group	NOUN
ejpam-1889	337	19	se(1,1	se(1,1	PROPN
ejpam-1889	337	20	)	)	PUNCT
ejpam-1889	337	21	(	(	PUNCT
ejpam-1889	337	22	i.e.	i.e.	X
ejpam-1889	337	23	,	,	PUNCT
ejpam-1889	337	24	the	the	DET
ejpam-1889	337	25	connected	connected	ADJ
ejpam-1889	337	26	matrix	matrix	NOUN
ejpam-1889	337	27	lie	lie	NOUN
ejpam-1889	337	28	group	group	NOUN
ejpam-1889	337	29	with	with	ADP
ejpam-1889	337	30	lie	lie	NOUN
ejpam-1889	337	31	algebra	algebra	PROPN
ejpam-1889	337	32	se(1,1	se(1,1	PROPN
ejpam-1889	337	33	)	)	PUNCT
ejpam-1889	337	34	)	)	PUNCT
ejpam-1889	337	35	.	.	PUNCT
ejpam-1889	338	1	for	for	ADP
ejpam-1889	338	2	instance	instance	NOUN
ejpam-1889	338	3	,	,	PUNCT
ejpam-1889	338	4	by	by	ADP
ejpam-1889	338	5	corollary	corollary	ADJ
ejpam-1889	338	6	1	1	NUM
ejpam-1889	338	7	,	,	PUNCT
ejpam-1889	338	8	any	any	DET
ejpam-1889	338	9	two	two	NUM
ejpam-1889	338	10	-	-	PUNCT
ejpam-1889	338	11	input	input	NOUN
ejpam-1889	338	12	homogeneous	homogeneous	ADJ
ejpam-1889	338	13	system	system	NOUN
ejpam-1889	338	14	(	(	PUNCT
ejpam-1889	338	15	1	1	NUM
ejpam-1889	338	16	)	)	PUNCT
ejpam-1889	338	17	on	on	ADP
ejpam-1889	338	18	se(1	se(1	PROPN
ejpam-1889	338	19	,	,	PUNCT
ejpam-1889	338	20	1	1	NUM
ejpam-1889	338	21	)	)	PUNCT
ejpam-1889	338	22	is	be	AUX
ejpam-1889	338	23	detached	detach	VERB
ejpam-1889	338	24	feedback	feedback	NOUN
ejpam-1889	338	25	equivalent	equivalent	ADJ
ejpam-1889	338	26	to	to	ADP
ejpam-1889	338	27	the	the	DET
ejpam-1889	338	28	system	system	NOUN
ejpam-1889	338	29	ġ	ġ	NOUN
ejpam-1889	338	30	=	=	NOUN
ejpam-1889	338	31	g(u1e1	g(u1e1	NOUN
ejpam-1889	338	32	+	+	CCONJ
ejpam-1889	338	33	u2e3	u2e3	NOUN
ejpam-1889	338	34	)	)	PUNCT
ejpam-1889	338	35	.	.	PUNCT
ejpam-1889	339	1	likewise	likewise	ADV
ejpam-1889	339	2	,	,	PUNCT
ejpam-1889	339	3	by	by	ADP
ejpam-1889	339	4	corollary	corollary	ADJ
ejpam-1889	339	5	2	2	NUM
ejpam-1889	339	6	,	,	PUNCT
ejpam-1889	339	7	any	any	DET
ejpam-1889	339	8	homogeneous	homogeneous	ADJ
ejpam-1889	339	9	two	two	NUM
ejpam-1889	339	10	-	-	PUNCT
ejpam-1889	339	11	input	input	NOUN
ejpam-1889	339	12	system	system	NOUN
ejpam-1889	339	13	on	on	ADP
ejpam-1889	339	14	se(1	se(1	PROPN
ejpam-1889	339	15	,	,	PUNCT
ejpam-1889	339	16	1	1	NUM
ejpam-1889	339	17	)	)	PUNCT
ejpam-1889	339	18	is	be	AUX
ejpam-1889	339	19	state	state	NOUN
ejpam-1889	339	20	space	space	NOUN
ejpam-1889	339	21	equivalent	equivalent	ADJ
ejpam-1889	339	22	to	to	ADP
ejpam-1889	339	23	exactly	exactly	ADV
ejpam-1889	339	24	one	one	NUM
ejpam-1889	339	25	of	of	ADP
ejpam-1889	339	26	the	the	DET
ejpam-1889	339	27	systems	system	NOUN
ejpam-1889	339	28	ġ	ġ	NOUN
ejpam-1889	339	29	=	=	PUNCT
ejpam-1889	339	30	g	g	PROPN
ejpam-1889	339	31	�	�	PROPN
ejpam-1889	339	32	γ1e1	γ1e1	AUX
ejpam-1889	339	33	+	+	NOUN
ejpam-1889	339	34	γ2e3	γ2e3	PROPN
ejpam-1889	339	35	+	+	CCONJ
ejpam-1889	339	36	u1(e1	u1(e1	NOUN
ejpam-1889	339	37	+	+	CCONJ
ejpam-1889	339	38	γ3e3	γ3e3	NOUN
ejpam-1889	339	39	)	)	PUNCT
ejpam-1889	339	40	+	+	CCONJ
ejpam-1889	339	41	u2(αe3	u2(αe3	ADJ
ejpam-1889	339	42	)	)	PUNCT
ejpam-1889	339	43	�	�	PROPN
ejpam-1889	339	44	ġ	ġ	NOUN
ejpam-1889	339	45	=	=	PUNCT
ejpam-1889	339	46	g	g	PROPN
ejpam-1889	339	47	�	�	PROPN
ejpam-1889	339	48	γ1e1	γ1e1	PUNCT
ejpam-1889	339	49	+	+	CCONJ
ejpam-1889	339	50	γ2e3	γ2e3	PROPN
ejpam-1889	339	51	+	+	CCONJ
ejpam-1889	339	52	u1(αe3	u1(αe3	X
ejpam-1889	339	53	)	)	PUNCT
ejpam-1889	340	1	+	+	CCONJ
ejpam-1889	340	2	u2e1	u2e1	X
ejpam-1889	340	3	�	�	PROPN
ejpam-1889	340	4	.	.	PUNCT
ejpam-1889	341	1	references	reference	NOUN
ejpam-1889	341	2	[	[	X
ejpam-1889	341	3	1	1	NUM
ejpam-1889	341	4	]	]	X
ejpam-1889	341	5	r	r	NOUN
ejpam-1889	341	6	adams	adam	NOUN
ejpam-1889	341	7	,	,	PUNCT
ejpam-1889	341	8	r	r	PROPN
ejpam-1889	341	9	biggs	biggs	PROPN
ejpam-1889	341	10	,	,	PUNCT
ejpam-1889	341	11	and	and	CCONJ
ejpam-1889	341	12	c	c	NOUN
ejpam-1889	341	13	remsing	remsing	NOUN
ejpam-1889	341	14	.	.	PUNCT
ejpam-1889	342	1	equivalence	equivalence	NOUN
ejpam-1889	342	2	of	of	ADP
ejpam-1889	342	3	control	control	NOUN
ejpam-1889	342	4	systems	system	NOUN
ejpam-1889	342	5	on	on	ADP
ejpam-1889	342	6	the	the	DET
ejpam-1889	342	7	euclidean	euclidean	ADJ
ejpam-1889	342	8	group	group	NOUN
ejpam-1889	342	9	se(2	se(2	PROPN
ejpam-1889	342	10	)	)	PUNCT
ejpam-1889	342	11	.	.	PUNCT
ejpam-1889	343	1	control	control	NOUN
ejpam-1889	343	2	and	and	CCONJ
ejpam-1889	343	3	cybernetics	cybernetic	NOUN
ejpam-1889	343	4	,	,	PUNCT
ejpam-1889	343	5	41(3):513–524	41(3):513–524	NUM
ejpam-1889	343	6	,	,	PUNCT
ejpam-1889	343	7	2012	2012	NUM
ejpam-1889	343	8	.	.	PUNCT
ejpam-1889	344	1	[	[	X
ejpam-1889	344	2	2	2	NUM
ejpam-1889	344	3	]	]	X
ejpam-1889	344	4	r	r	NOUN
ejpam-1889	344	5	adams	adam	NOUN
ejpam-1889	344	6	,	,	PUNCT
ejpam-1889	344	7	r	r	PROPN
ejpam-1889	344	8	biggs	biggs	PROPN
ejpam-1889	344	9	,	,	PUNCT
ejpam-1889	344	10	and	and	CCONJ
ejpam-1889	344	11	c	c	NOUN
ejpam-1889	344	12	remsing	remsing	NOUN
ejpam-1889	344	13	.	.	PUNCT
ejpam-1889	345	1	control	control	NOUN
ejpam-1889	345	2	systems	system	NOUN
ejpam-1889	345	3	on	on	ADP
ejpam-1889	345	4	the	the	DET
ejpam-1889	345	5	orthogonal	orthogonal	ADJ
ejpam-1889	345	6	group	group	NOUN
ejpam-1889	345	7	so(4	so(4	PROPN
ejpam-1889	345	8	)	)	PUNCT
ejpam-1889	345	9	.	.	PUNCT
ejpam-1889	346	1	communications	communication	NOUN
ejpam-1889	346	2	in	in	ADP
ejpam-1889	346	3	mathematics	mathematic	NOUN
ejpam-1889	346	4	,	,	PUNCT
ejpam-1889	346	5	21(2):107–128	21(2):107–128	NOUN
ejpam-1889	346	6	,	,	PUNCT
ejpam-1889	346	7	2013	2013	NUM
ejpam-1889	346	8	.	.	PUNCT
ejpam-1889	347	1	[	[	X
ejpam-1889	347	2	3	3	X
ejpam-1889	347	3	]	]	PUNCT
ejpam-1889	347	4	a	a	DET
ejpam-1889	347	5	agrachev	agrachev	NOUN
ejpam-1889	347	6	and	and	CCONJ
ejpam-1889	347	7	y	y	PROPN
ejpam-1889	347	8	sachkov	sachkov	PROPN
ejpam-1889	347	9	.	.	PUNCT
ejpam-1889	348	1	control	control	PROPN
ejpam-1889	348	2	theory	theory	NOUN
ejpam-1889	348	3	from	from	ADP
ejpam-1889	348	4	the	the	DET
ejpam-1889	348	5	geometric	geometric	ADJ
ejpam-1889	348	6	viewpoint	viewpoint	NOUN
ejpam-1889	348	7	.	.	PUNCT
ejpam-1889	349	1	springer	springer	NOUN
ejpam-1889	349	2	-	-	PUNCT
ejpam-1889	349	3	verlag	verlag	PROPN
ejpam-1889	349	4	,	,	PUNCT
ejpam-1889	349	5	berlin	berlin	PROPN
ejpam-1889	349	6	,	,	PUNCT
ejpam-1889	349	7	2004	2004	NUM
ejpam-1889	349	8	.	.	PUNCT
ejpam-1889	350	1	[	[	X
ejpam-1889	350	2	4	4	NUM
ejpam-1889	350	3	]	]	X
ejpam-1889	350	4	r	r	NOUN
ejpam-1889	350	5	biggs	biggs	PROPN
ejpam-1889	350	6	and	and	CCONJ
ejpam-1889	350	7	c	c	PROPN
ejpam-1889	350	8	remsing	remsing	NOUN
ejpam-1889	350	9	.	.	PUNCT
ejpam-1889	351	1	a	a	DET
ejpam-1889	351	2	category	category	NOUN
ejpam-1889	351	3	of	of	ADP
ejpam-1889	351	4	control	control	NOUN
ejpam-1889	351	5	systems	system	NOUN
ejpam-1889	351	6	.	.	PUNCT
ejpam-1889	352	1	analele	analele	ADP
ejpam-1889	352	2	ştiinţifice	ştiinţifice	NOUN
ejpam-1889	352	3	ale	ale	NOUN
ejpam-1889	352	4	universită̧tii	universită̧tii	NOUN
ejpam-1889	352	5	“	"	PUNCT
ejpam-1889	352	6	ovidius	ovidius	NOUN
ejpam-1889	352	7	”	"	PUNCT
ejpam-1889	352	8	constanţa	constanţa	NOUN
ejpam-1889	352	9	.	.	PUNCT
ejpam-1889	353	1	seria	seria	PROPN
ejpam-1889	353	2	matematică	matematică	PROPN
ejpam-1889	353	3	,	,	PUNCT
ejpam-1889	353	4	20(1):355–368	20(1):355–368	PROPN
ejpam-1889	353	5	,	,	PUNCT
ejpam-1889	353	6	2012	2012	NUM
ejpam-1889	353	7	.	.	PUNCT
ejpam-1889	354	1	[	[	X
ejpam-1889	354	2	5	5	NUM
ejpam-1889	354	3	]	]	X
ejpam-1889	354	4	r	r	NOUN
ejpam-1889	354	5	biggs	biggs	PROPN
ejpam-1889	354	6	and	and	CCONJ
ejpam-1889	354	7	c	c	PROPN
ejpam-1889	354	8	remsing	remsing	NOUN
ejpam-1889	354	9	.	.	PUNCT
ejpam-1889	355	1	control	control	NOUN
ejpam-1889	355	2	affine	affine	NOUN
ejpam-1889	355	3	systems	system	NOUN
ejpam-1889	355	4	on	on	ADP
ejpam-1889	355	5	semisimple	semisimple	NOUN
ejpam-1889	355	6	three	three	NUM
ejpam-1889	355	7	-	-	PUNCT
ejpam-1889	355	8	dimensional	dimensional	ADJ
ejpam-1889	355	9	lie	lie	NOUN
ejpam-1889	355	10	groups	group	NOUN
ejpam-1889	355	11	.	.	PUNCT
ejpam-1889	356	1	analele	analele	ADP
ejpam-1889	356	2	ştiinţifice	ştiinţifice	NOUN
ejpam-1889	356	3	ale	ale	NOUN
ejpam-1889	356	4	universită̧tii	universită̧tii	NOUN
ejpam-1889	356	5	“	"	PUNCT
ejpam-1889	356	6	al	al	PROPN
ejpam-1889	356	7	.	.	PROPN
ejpam-1889	356	8	i.	i.	PROPN
ejpam-1889	356	9	cuza	cuza	PROPN
ejpam-1889	356	10	”	"	PUNCT
ejpam-1889	356	11	din	din	VERB
ejpam-1889	356	12	iaşi	iaşi	PROPN
ejpam-1889	356	13	.	.	PUNCT
ejpam-1889	357	1	serie	serie	PROPN
ejpam-1889	357	2	nouă.	nouă.	PROPN
ejpam-1889	357	3	matematică	matematică	NOUN
ejpam-1889	357	4	,	,	PUNCT
ejpam-1889	357	5	59(2):399–414	59(2):399–414	PROPN
ejpam-1889	357	6	,	,	PUNCT
ejpam-1889	357	7	2013	2013	NUM
ejpam-1889	357	8	.	.	PUNCT
ejpam-1889	358	1	[	[	X
ejpam-1889	358	2	6	6	NUM
ejpam-1889	358	3	]	]	X
ejpam-1889	358	4	r	r	NOUN
ejpam-1889	358	5	biggs	biggs	PROPN
ejpam-1889	358	6	and	and	CCONJ
ejpam-1889	358	7	c	c	PROPN
ejpam-1889	358	8	remsing	remsing	NOUN
ejpam-1889	358	9	.	.	PUNCT
ejpam-1889	359	1	control	control	NOUN
ejpam-1889	359	2	affine	affine	NOUN
ejpam-1889	359	3	systems	system	NOUN
ejpam-1889	359	4	on	on	ADP
ejpam-1889	359	5	solvable	solvable	ADJ
ejpam-1889	359	6	three	three	NUM
ejpam-1889	359	7	-	-	PUNCT
ejpam-1889	359	8	dimensional	dimensional	ADJ
ejpam-1889	359	9	lie	lie	NOUN
ejpam-1889	359	10	groups	group	NOUN
ejpam-1889	359	11	,	,	PUNCT
ejpam-1889	359	12	i.	i.	PROPN
ejpam-1889	359	13	archivum	archivum	PROPN
ejpam-1889	359	14	mathematicum	mathematicum	PROPN
ejpam-1889	359	15	,	,	PUNCT
ejpam-1889	359	16	49(3):187–197	49(3):187–197	PROPN
ejpam-1889	359	17	,	,	PUNCT
ejpam-1889	359	18	2013	2013	NUM
ejpam-1889	359	19	.	.	PUNCT
ejpam-1889	360	1	[	[	X
ejpam-1889	360	2	7	7	NUM
ejpam-1889	360	3	]	]	X
ejpam-1889	360	4	r	r	NOUN
ejpam-1889	360	5	biggs	biggs	PROPN
ejpam-1889	360	6	and	and	CCONJ
ejpam-1889	360	7	c	c	PROPN
ejpam-1889	360	8	remsing	remsing	NOUN
ejpam-1889	360	9	.	.	PUNCT
ejpam-1889	361	1	control	control	NOUN
ejpam-1889	361	2	affine	affine	NOUN
ejpam-1889	361	3	systems	system	NOUN
ejpam-1889	361	4	on	on	ADP
ejpam-1889	361	5	solvable	solvable	ADJ
ejpam-1889	361	6	three	three	NUM
ejpam-1889	361	7	-	-	PUNCT
ejpam-1889	361	8	dimensional	dimensional	ADJ
ejpam-1889	361	9	lie	lie	NOUN
ejpam-1889	361	10	groups	group	NOUN
ejpam-1889	361	11	,	,	PUNCT
ejpam-1889	361	12	ii	ii	PROPN
ejpam-1889	361	13	.	.	PUNCT
ejpam-1889	362	1	note	note	PROPN
ejpam-1889	362	2	di	di	PROPN
ejpam-1889	362	3	matematica	matematica	PROPN
ejpam-1889	362	4	,	,	PUNCT
ejpam-1889	362	5	33(2):19–31	33(2):19–31	NUM
ejpam-1889	362	6	,	,	PUNCT
ejpam-1889	362	7	2013	2013	NUM
ejpam-1889	362	8	.	.	PUNCT
ejpam-1889	363	1	[	[	X
ejpam-1889	363	2	8	8	NUM
ejpam-1889	363	3	]	]	PUNCT
ejpam-1889	363	4	a	a	DET
ejpam-1889	363	5	bloch	bloch	NOUN
ejpam-1889	363	6	.	.	PUNCT
ejpam-1889	364	1	nonholonomic	nonholonomic	ADJ
ejpam-1889	364	2	mechanics	mechanic	NOUN
ejpam-1889	364	3	and	and	CCONJ
ejpam-1889	364	4	control	control	NOUN
ejpam-1889	364	5	.	.	PUNCT
ejpam-1889	365	1	springer	springer	NOUN
ejpam-1889	365	2	-	-	PUNCT
ejpam-1889	365	3	verlag	verlag	PROPN
ejpam-1889	365	4	,	,	PUNCT
ejpam-1889	365	5	new	new	PROPN
ejpam-1889	365	6	york	york	PROPN
ejpam-1889	365	7	,	,	PUNCT
ejpam-1889	365	8	2003	2003	NUM
ejpam-1889	365	9	.	.	PUNCT
ejpam-1889	366	1	[	[	X
ejpam-1889	366	2	9	9	NUM
ejpam-1889	366	3	]	]	SYM
ejpam-1889	366	4	b	b	X
ejpam-1889	366	5	jakubczyk	jakubczyk	NOUN
ejpam-1889	366	6	.	.	PUNCT
ejpam-1889	366	7	equivalence	equivalence	NOUN
ejpam-1889	366	8	and	and	CCONJ
ejpam-1889	366	9	invariants	invariant	NOUN
ejpam-1889	366	10	of	of	ADP
ejpam-1889	366	11	nonlinear	nonlinear	ADJ
ejpam-1889	366	12	control	control	PROPN
ejpam-1889	366	13	systems	system	NOUN
ejpam-1889	366	14	.	.	PUNCT
ejpam-1889	367	1	in	in	ADP
ejpam-1889	367	2	h	h	PROPN
ejpam-1889	367	3	sussmann	sussmann	PROPN
ejpam-1889	367	4	,	,	PUNCT
ejpam-1889	367	5	editor	editor	NOUN
ejpam-1889	367	6	,	,	PUNCT
ejpam-1889	367	7	nonlinear	nonlinear	ADJ
ejpam-1889	367	8	controllability	controllability	NOUN
ejpam-1889	367	9	and	and	CCONJ
ejpam-1889	367	10	optimal	optimal	ADJ
ejpam-1889	367	11	control	control	NOUN
ejpam-1889	367	12	.	.	PUNCT
ejpam-1889	368	1	marcel	marcel	PROPN
ejpam-1889	368	2	dekker	dekker	PROPN
ejpam-1889	368	3	,	,	PUNCT
ejpam-1889	368	4	new	new	PROPN
ejpam-1889	368	5	york	york	PROPN
ejpam-1889	368	6	,	,	PUNCT
ejpam-1889	368	7	1990	1990	NUM
ejpam-1889	368	8	.	.	PUNCT
ejpam-1889	369	1	references	reference	NOUN
ejpam-1889	369	2	153	153	NUM
ejpam-1889	369	3	[	[	X
ejpam-1889	369	4	10	10	NUM
ejpam-1889	369	5	]	]	SYM
ejpam-1889	369	6	v	v	NOUN
ejpam-1889	369	7	jurdjevic	jurdjevic	PROPN
ejpam-1889	369	8	.	.	PUNCT
ejpam-1889	370	1	geometric	geometric	ADJ
ejpam-1889	370	2	control	control	NOUN
ejpam-1889	370	3	theory	theory	NOUN
ejpam-1889	370	4	.	.	PUNCT
ejpam-1889	371	1	cambridge	cambridge	PROPN
ejpam-1889	371	2	university	university	PROPN
ejpam-1889	371	3	press	press	PROPN
ejpam-1889	371	4	,	,	PUNCT
ejpam-1889	371	5	cambridge	cambridge	PROPN
ejpam-1889	371	6	,	,	PUNCT
ejpam-1889	371	7	1997	1997	NUM
ejpam-1889	371	8	.	.	PUNCT
ejpam-1889	372	1	[	[	X
ejpam-1889	372	2	11	11	NUM
ejpam-1889	372	3	]	]	SYM
ejpam-1889	372	4	v	v	ADP
ejpam-1889	372	5	jurdjevic	jurdjevic	ADJ
ejpam-1889	372	6	and	and	CCONJ
ejpam-1889	372	7	h	h	PROPN
ejpam-1889	372	8	sussmann	sussmann	PROPN
ejpam-1889	372	9	.	.	PUNCT
ejpam-1889	373	1	control	control	NOUN
ejpam-1889	373	2	systems	system	NOUN
ejpam-1889	373	3	on	on	ADP
ejpam-1889	373	4	lie	lie	NOUN
ejpam-1889	373	5	groups	group	NOUN
ejpam-1889	373	6	.	.	PUNCT
ejpam-1889	374	1	journal	journal	PROPN
ejpam-1889	374	2	of	of	ADP
ejpam-1889	374	3	differential	differential	ADJ
ejpam-1889	374	4	equations	equation	NOUN
ejpam-1889	374	5	,	,	PUNCT
ejpam-1889	374	6	12(2):313–329	12(2):313–329	PROPN
ejpam-1889	374	7	,	,	PUNCT
ejpam-1889	374	8	1972	1972	NUM
ejpam-1889	374	9	.	.	PUNCT
ejpam-1889	375	1	[	[	X
ejpam-1889	375	2	12	12	NUM
ejpam-1889	375	3	]	]	PUNCT
ejpam-1889	375	4	a	a	DET
ejpam-1889	375	5	krasiński	krasiński	NOUN
ejpam-1889	375	6	,	,	PUNCT
ejpam-1889	375	7	c	c	NOUN
ejpam-1889	375	8	behr	behr	NOUN
ejpam-1889	375	9	,	,	PUNCT
ejpam-1889	375	10	e	e	PROPN
ejpam-1889	375	11	schücking	schücking	NOUN
ejpam-1889	375	12	,	,	PUNCT
ejpam-1889	375	13	f	f	PROPN
ejpam-1889	375	14	estabrook	estabrook	NOUN
ejpam-1889	375	15	,	,	PUNCT
ejpam-1889	375	16	h	h	NOUN
ejpam-1889	375	17	wahlquist	wahlquist	NOUN
ejpam-1889	375	18	,	,	PUNCT
ejpam-1889	375	19	g	g	PROPN
ejpam-1889	375	20	ellis	ellis	PROPN
ejpam-1889	375	21	,	,	PUNCT
ejpam-1889	375	22	r	r	PROPN
ejpam-1889	375	23	jantzen	jantzen	PROPN
ejpam-1889	375	24	,	,	PUNCT
ejpam-1889	375	25	and	and	CCONJ
ejpam-1889	375	26	w	w	PROPN
ejpam-1889	375	27	kundt	kundt	NOUN
ejpam-1889	375	28	.	.	PUNCT
ejpam-1889	376	1	the	the	DET
ejpam-1889	376	2	bianchi	bianchi	NOUN
ejpam-1889	376	3	classification	classification	NOUN
ejpam-1889	376	4	in	in	ADP
ejpam-1889	376	5	the	the	DET
ejpam-1889	376	6	schücking	schücke	VERB
ejpam-1889	376	7	-	-	PUNCT
ejpam-1889	376	8	behr	behr	NOUN
ejpam-1889	376	9	approach	approach	NOUN
ejpam-1889	376	10	.	.	PUNCT
ejpam-1889	377	1	general	general	ADJ
ejpam-1889	377	2	relativity	relativity	NOUN
ejpam-1889	377	3	and	and	CCONJ
ejpam-1889	377	4	gravitation	gravitation	NOUN
ejpam-1889	377	5	,	,	PUNCT
ejpam-1889	377	6	35(3):475–489	35(3):475–489	PROPN
ejpam-1889	377	7	,	,	PUNCT
ejpam-1889	377	8	2003	2003	NUM
ejpam-1889	377	9	.	.	PUNCT
ejpam-1889	378	1	[	[	X
ejpam-1889	378	2	13	13	NUM
ejpam-1889	378	3	]	]	SYM
ejpam-1889	378	4	m	m	PROPN
ejpam-1889	378	5	maccallum	maccallum	PROPN
ejpam-1889	378	6	.	.	PROPN
ejpam-1889	379	1	on	on	ADP
ejpam-1889	379	2	the	the	DET
ejpam-1889	379	3	classification	classification	NOUN
ejpam-1889	379	4	of	of	ADP
ejpam-1889	379	5	the	the	DET
ejpam-1889	379	6	real	real	ADJ
ejpam-1889	379	7	four	four	NUM
ejpam-1889	379	8	-	-	PUNCT
ejpam-1889	379	9	dimensional	dimensional	ADJ
ejpam-1889	379	10	lie	lie	NOUN
ejpam-1889	379	11	algebras	algebra	NOUN
ejpam-1889	379	12	.	.	PUNCT
ejpam-1889	380	1	in	in	ADP
ejpam-1889	380	2	a	a	DET
ejpam-1889	380	3	harvey	harvey	NOUN
ejpam-1889	380	4	,	,	PUNCT
ejpam-1889	380	5	editor	editor	NOUN
ejpam-1889	380	6	,	,	PUNCT
ejpam-1889	380	7	on	on	ADP
ejpam-1889	380	8	einstein	einstein	PROPN
ejpam-1889	380	9	’s	’s	PART
ejpam-1889	380	10	path	path	NOUN
ejpam-1889	380	11	:	:	PUNCT
ejpam-1889	380	12	essays	essay	NOUN
ejpam-1889	380	13	in	in	ADP
ejpam-1889	380	14	honour	honour	NOUN
ejpam-1889	380	15	of	of	ADP
ejpam-1889	380	16	e.	e.	PROPN
ejpam-1889	380	17	schücking	schücking	PROPN
ejpam-1889	380	18	.	.	PUNCT
ejpam-1889	381	1	springer	springer	NOUN
ejpam-1889	381	2	-	-	PUNCT
ejpam-1889	381	3	verlag	verlag	PROPN
ejpam-1889	381	4	,	,	PUNCT
ejpam-1889	381	5	new	new	PROPN
ejpam-1889	381	6	york	york	PROPN
ejpam-1889	381	7	,	,	PUNCT
ejpam-1889	381	8	1999	1999	NUM
ejpam-1889	381	9	.	.	PUNCT
ejpam-1889	382	1	[	[	X
ejpam-1889	382	2	14	14	NUM
ejpam-1889	382	3	]	]	X
ejpam-1889	382	4	j	j	PROPN
ejpam-1889	382	5	ratcliffe	ratcliffe	PROPN
ejpam-1889	382	6	.	.	PUNCT
ejpam-1889	383	1	foundations	foundation	NOUN
ejpam-1889	383	2	of	of	ADP
ejpam-1889	383	3	hyperbolic	hyperbolic	ADJ
ejpam-1889	383	4	manifolds	manifold	NOUN
ejpam-1889	383	5	.	.	PUNCT
ejpam-1889	383	6	springer	springer	NOUN
ejpam-1889	383	7	-	-	PUNCT
ejpam-1889	383	8	verlag	verlag	PROPN
ejpam-1889	383	9	,	,	PUNCT
ejpam-1889	383	10	new	new	PROPN
ejpam-1889	383	11	york	york	PROPN
ejpam-1889	383	12	,	,	PUNCT
ejpam-1889	383	13	second	second	ADJ
ejpam-1889	383	14	edition	edition	NOUN
ejpam-1889	383	15	,	,	PUNCT
ejpam-1889	383	16	2006	2006	NUM
ejpam-1889	383	17	.	.	PUNCT
ejpam-1889	384	1	[	[	X
ejpam-1889	384	2	15	15	NUM
ejpam-1889	384	3	]	]	X
ejpam-1889	384	4	w	w	NOUN
ejpam-1889	384	5	respondek	respondek	NOUN
ejpam-1889	384	6	and	and	CCONJ
ejpam-1889	384	7	i	i	PRON
ejpam-1889	384	8	tall	tall	VERB
ejpam-1889	384	9	.	.	PUNCT
ejpam-1889	385	1	feedback	feedback	NOUN
ejpam-1889	385	2	equivalence	equivalence	NOUN
ejpam-1889	385	3	of	of	ADP
ejpam-1889	385	4	nonlinear	nonlinear	ADJ
ejpam-1889	385	5	control	control	PROPN
ejpam-1889	385	6	systems	system	NOUN
ejpam-1889	385	7	:	:	PUNCT
ejpam-1889	385	8	a	a	DET
ejpam-1889	385	9	survey	survey	NOUN
ejpam-1889	385	10	on	on	ADP
ejpam-1889	385	11	formal	formal	ADJ
ejpam-1889	385	12	approach	approach	NOUN
ejpam-1889	385	13	.	.	PUNCT
ejpam-1889	386	1	in	in	ADP
ejpam-1889	386	2	j	j	PROPN
ejpam-1889	386	3	-	-	PROPN
ejpam-1889	386	4	p	p	NOUN
ejpam-1889	386	5	barbot	barbot	NOUN
ejpam-1889	386	6	and	and	CCONJ
ejpam-1889	386	7	w	w	PROPN
ejpam-1889	386	8	perruquetti	perruquetti	PROPN
ejpam-1889	386	9	,	,	PUNCT
ejpam-1889	386	10	editors	editor	NOUN
ejpam-1889	386	11	,	,	PUNCT
ejpam-1889	386	12	chaos	chaos	NOUN
ejpam-1889	386	13	in	in	ADP
ejpam-1889	386	14	automatic	automatic	ADJ
ejpam-1889	386	15	control	control	NOUN
ejpam-1889	386	16	.	.	PUNCT
ejpam-1889	387	1	control	control	PROPN
ejpam-1889	387	2	eng	eng	PROPN
ejpam-1889	387	3	.	.	PUNCT
ejpam-1889	388	1	(	(	PUNCT
ejpam-1889	388	2	taylor	taylor	PROPN
ejpam-1889	388	3	&	&	CCONJ
ejpam-1889	388	4	francis	francis	PROPN
ejpam-1889	388	5	)	)	PUNCT
ejpam-1889	388	6	,	,	PUNCT
ejpam-1889	388	7	crc	crc	NOUN
ejpam-1889	388	8	press	press	NOUN
ejpam-1889	388	9	,	,	PUNCT
ejpam-1889	388	10	2006	2006	NUM
ejpam-1889	388	11	.	.	PUNCT
ejpam-1889	389	1	[	[	X
ejpam-1889	389	2	16	16	NUM
ejpam-1889	389	3	]	]	X
ejpam-1889	389	4	y	y	PROPN
ejpam-1889	389	5	sachkov	sachkov	PROPN
ejpam-1889	389	6	.	.	PUNCT
ejpam-1889	390	1	control	control	PROPN
ejpam-1889	390	2	theory	theory	NOUN
ejpam-1889	390	3	on	on	ADP
ejpam-1889	390	4	lie	lie	NOUN
ejpam-1889	390	5	groups	group	NOUN
ejpam-1889	390	6	.	.	PUNCT
ejpam-1889	391	1	journal	journal	PROPN
ejpam-1889	391	2	of	of	ADP
ejpam-1889	391	3	mathematical	mathematical	ADJ
ejpam-1889	391	4	sciences	science	NOUN
ejpam-1889	391	5	,	,	PUNCT
ejpam-1889	391	6	156(3):381	156(3):381	NUM
ejpam-1889	391	7	–	–	PUNCT
ejpam-1889	391	8	439	439	NUM
ejpam-1889	391	9	,	,	PUNCT
ejpam-1889	391	10	2009	2009	NUM
ejpam-1889	391	11	.	.	PUNCT
ejpam-1889	392	1	references	reference	NOUN
ejpam-1889	392	2	154	154	NUM
ejpam-1889	392	3	appendix	appendix	NOUN
ejpam-1889	392	4	table	table	NOUN
ejpam-1889	392	5	1	1	NUM
ejpam-1889	392	6	:	:	PUNCT
ejpam-1889	392	7	classification	classification	NOUN
ejpam-1889	392	8	of	of	ADP
ejpam-1889	392	9	affine	affine	NOUN
ejpam-1889	392	10	subspaces	subspace	NOUN
ejpam-1889	392	11	and	and	CCONJ
ejpam-1889	392	12	parametrized	parametrized	ADJ
ejpam-1889	392	13	affine	affine	NOUN
ejpam-1889	392	14	subspaces	subspace	NOUN
ejpam-1889	392	15	type	type	NOUN
ejpam-1889	392	16	affine	affine	NOUN
ejpam-1889	392	17	subspaces	subspace	VERB
ejpam-1889	392	18	parametrized	parametrized	ADJ
ejpam-1889	392	19	affine	affine	NOUN
ejpam-1889	392	20	subspaces	subspace	NOUN
ejpam-1889	392	21	(	(	PUNCT
ejpam-1889	392	22	1	1	NUM
ejpam-1889	392	23	,	,	PUNCT
ejpam-1889	392	24	1	1	X
ejpam-1889	392	25	)	)	PUNCT
ejpam-1889	392	26	e1	e1	PROPN
ejpam-1889	392	27	+	+	CCONJ
ejpam-1889	392	28	〈	〈	NOUN
ejpam-1889	392	29	e3	e3	NOUN
ejpam-1889	392	30	〉	〉	NOUN
ejpam-1889	392	31			NOUN
ejpam-1889	392	32			NOUN
ejpam-1889	392	33	1	1	NUM
ejpam-1889	392	34	0	0	NUM
ejpam-1889	392	35	0	0	NUM
ejpam-1889	392	36	0	0	NUM
ejpam-1889	392	37	γ1	γ1	PROPN
ejpam-1889	392	38	α	α	X
ejpam-1889	392	39			PROPN
ejpam-1889	392	40			PROPN
ejpam-1889	392	41	αe3	αe3	NOUN
ejpam-1889	392	42	+	+	CCONJ
ejpam-1889	392	43	〈	〈	PROPN
ejpam-1889	392	44	e1	e1	ADJ
ejpam-1889	392	45	〉	〉	NOUN
ejpam-1889	392	46			NOUN
ejpam-1889	392	47			NOUN
ejpam-1889	392	48	0	0	NUM
ejpam-1889	393	1	1	1	NUM
ejpam-1889	393	2	0	0	NUM
ejpam-1889	393	3	0	0	NUM
ejpam-1889	394	1	α	α	NOUN
ejpam-1889	394	2	0	0	PUNCT
ejpam-1889	394	3			PROPN
ejpam-1889	394	4			PROPN
ejpam-1889	394	5	(	(	PUNCT
ejpam-1889	394	6	2	2	NUM
ejpam-1889	394	7	,	,	PUNCT
ejpam-1889	394	8	0	0	NUM
ejpam-1889	394	9	)	)	PUNCT
ejpam-1889	394	10	〈	〈	NOUN
ejpam-1889	394	11	e1	e1	NOUN
ejpam-1889	394	12	,	,	PUNCT
ejpam-1889	394	13	e3	e3	NOUN
ejpam-1889	394	14	〉	〉	NOUN
ejpam-1889	394	15			NOUN
ejpam-1889	394	16			SYM
ejpam-1889	394	17	γ1	γ1	NOUN
ejpam-1889	394	18	1	1	NUM
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ejpam-1889	394	20	0	0	NUM
ejpam-1889	394	21	0	0	NUM
ejpam-1889	394	22	0	0	NUM
ejpam-1889	395	1	γ2	γ2	PROPN
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ejpam-1889	395	3	α	α	PRON
ejpam-1889	395	4			PROPN
ejpam-1889	395	5			PROPN
ejpam-1889	395	6			NOUN
ejpam-1889	395	7			NUM
ejpam-1889	395	8	γ1	γ1	NOUN
ejpam-1889	395	9	0	0	NUM
ejpam-1889	396	1	1	1	NUM
ejpam-1889	396	2	0	0	NUM
ejpam-1889	396	3	0	0	NUM
ejpam-1889	396	4	0	0	NUM
ejpam-1889	396	5	γ2	γ2	NOUN
ejpam-1889	396	6	α	α	NOUN
ejpam-1889	396	7	0	0	PUNCT
ejpam-1889	396	8			PROPN
ejpam-1889	396	9			PROPN
ejpam-1889	396	10	(	(	PUNCT
ejpam-1889	396	11	2	2	NUM
ejpam-1889	396	12	,	,	PUNCT
ejpam-1889	396	13	1	1	NUM
ejpam-1889	396	14	)	)	PUNCT
ejpam-1889	396	15	e2	e2	NOUN
ejpam-1889	396	16	+	+	CCONJ
ejpam-1889	396	17	〈	〈	PROPN
ejpam-1889	396	18	e1	e1	NOUN
ejpam-1889	396	19	,	,	PUNCT
ejpam-1889	396	20	e3	e3	NOUN
ejpam-1889	396	21	〉	〉	NOUN
ejpam-1889	396	22			NOUN
ejpam-1889	396	23			SYM
ejpam-1889	396	24	γ1	γ1	NOUN
ejpam-1889	396	25	1	1	NUM
ejpam-1889	396	26	0	0	X
ejpam-1889	396	27	β1	β1	NOUN
ejpam-1889	396	28	0	0	NUM
ejpam-1889	396	29	0	0	NUM
ejpam-1889	396	30	γ2	γ2	PROPN
ejpam-1889	396	31	γ3	γ3	NOUN
ejpam-1889	396	32	α	α	PRON
ejpam-1889	396	33			PROPN
ejpam-1889	396	34			PROPN
ejpam-1889	396	35			NOUN
ejpam-1889	396	36			NUM
ejpam-1889	396	37	γ1	γ1	NOUN
ejpam-1889	396	38	0	0	NUM
ejpam-1889	396	39	1	1	NUM
ejpam-1889	396	40	β1	β1	NOUN
ejpam-1889	396	41	0	0	NUM
ejpam-1889	396	42	0	0	NUM
ejpam-1889	397	1	γ2	γ2	PROPN
ejpam-1889	397	2	α	α	NOUN
ejpam-1889	397	3	0	0	PUNCT
ejpam-1889	397	4			PROPN
ejpam-1889	397	5			PROPN
ejpam-1889	397	6	e1	e1	NOUN
ejpam-1889	397	7	+	+	CCONJ
ejpam-1889	397	8	〈	〈	PROPN
ejpam-1889	397	9	e1	e1	PROPN
ejpam-1889	397	10	+	+	CCONJ
ejpam-1889	397	11	e2	e2	NOUN
ejpam-1889	397	12	,	,	PUNCT
ejpam-1889	397	13	e3	e3	NOUN
ejpam-1889	397	14	〉	〉	NOUN
ejpam-1889	397	15			NOUN
ejpam-1889	397	16			NOUN
ejpam-1889	397	17	β1	β1	NOUN
ejpam-1889	397	18	1	1	NUM
ejpam-1889	397	19	0	0	NUM
ejpam-1889	397	20	0	0	NUM
ejpam-1889	397	21	1	1	NUM
ejpam-1889	397	22	0	0	NUM
ejpam-1889	397	23	γ1	γ1	PROPN
ejpam-1889	397	24	γ2	γ2	PROPN
ejpam-1889	397	25	β2	β2	PROPN
ejpam-1889	397	26			PROPN
ejpam-1889	397	27			PROPN
ejpam-1889	397	28			NOUN
ejpam-1889	397	29			NOUN
ejpam-1889	397	30	1	1	NUM
ejpam-1889	397	31	1	1	NUM
ejpam-1889	397	32	0	0	NUM
ejpam-1889	397	33	−1	−1	NOUN
ejpam-1889	397	34	1	1	NUM
ejpam-1889	397	35	0	0	NUM
ejpam-1889	397	36	γ1	γ1	PROPN
ejpam-1889	397	37	γ2	γ2	PROPN
ejpam-1889	397	38	β1	β1	PROPN
ejpam-1889	397	39			PROPN
ejpam-1889	397	40			PROPN
ejpam-1889	397	41			NOUN
ejpam-1889	397	42			X
ejpam-1889	397	43	β1	β1	NOUN
ejpam-1889	397	44	0	0	NUM
ejpam-1889	397	45	1	1	NUM
ejpam-1889	397	46	0	0	NUM
ejpam-1889	397	47	0	0	NUM
ejpam-1889	397	48	1	1	NUM
ejpam-1889	397	49	γ1	γ1	NOUN
ejpam-1889	397	50	β2	β2	NOUN
ejpam-1889	397	51	0	0	NUM
ejpam-1889	397	52			PROPN
ejpam-1889	397	53			PROPN
ejpam-1889	397	54			NOUN
ejpam-1889	397	55			NOUN
ejpam-1889	397	56	1	1	NUM
ejpam-1889	397	57	0	0	NUM
ejpam-1889	397	58	1	1	NUM
ejpam-1889	397	59	−1	−1	NOUN
ejpam-1889	397	60	0	0	NUM
ejpam-1889	397	61	1	1	NUM
ejpam-1889	397	62	γ1	γ1	NOUN
ejpam-1889	397	63	β1	β1	NOUN
ejpam-1889	397	64	0	0	PUNCT
ejpam-1889	397	65			PROPN
ejpam-1889	397	66			PROPN
ejpam-1889	397	67	αe3	αe3	NOUN
ejpam-1889	397	68	+	+	CCONJ
ejpam-1889	397	69	〈	〈	PROPN
ejpam-1889	397	70	e1	e1	NOUN
ejpam-1889	397	71	,	,	PUNCT
ejpam-1889	397	72	e2	e2	NOUN
ejpam-1889	397	73	〉	〉	NOUN
ejpam-1889	397	74			PROPN
ejpam-1889	397	75			NOUN
ejpam-1889	397	76	0	0	NUM
ejpam-1889	397	77	γ1	γ1	NOUN
ejpam-1889	397	78	1	1	NUM
ejpam-1889	397	79	0	0	NUM
ejpam-1889	397	80	α	α	NOUN
ejpam-1889	397	81	0	0	PUNCT
ejpam-1889	398	1	β1	β1	NOUN
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ejpam-1889	398	4			PROPN
ejpam-1889	398	5			PROPN
ejpam-1889	398	6			NOUN
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ejpam-1889	398	8	0	0	PUNCT
ejpam-1889	399	1	β2	β2	VERB
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ejpam-1889	399	4	0	0	NUM
ejpam-1889	399	5	1	1	NUM
ejpam-1889	399	6	β1	β1	NOUN
ejpam-1889	399	7	0	0	NUM
ejpam-1889	399	8	0	0	NUM
ejpam-1889	399	9			PROPN
ejpam-1889	399	10			PROPN
ejpam-1889	399	11			NOUN
ejpam-1889	399	12			NOUN
ejpam-1889	399	13	0	0	NUM
ejpam-1889	399	14	1	1	NUM
ejpam-1889	399	15	1	1	NUM
ejpam-1889	399	16	0	0	NUM
ejpam-1889	399	17	−1	−1	NOUN
ejpam-1889	399	18	1	1	NUM
ejpam-1889	399	19	β1	β1	NOUN
ejpam-1889	399	20	0	0	NUM
ejpam-1889	399	21	0	0	NUM
ejpam-1889	399	22			PROPN
ejpam-1889	399	23			PROPN
ejpam-1889	399	24	α	α	NOUN
ejpam-1889	399	25	>	>	X
ejpam-1889	399	26	0	0	PROPN
ejpam-1889	399	27	,	,	PUNCT
ejpam-1889	399	28	βi	βi	PROPN
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ejpam-1889	399	30	0	0	NUM
ejpam-1889	399	31	,	,	PUNCT
ejpam-1889	399	32	γi	γi	X
ejpam-1889	399	33	∈	∈	NOUN
ejpam-1889	399	34	r	r	NOUN
ejpam-1889	399	35	references	reference	NOUN
ejpam-1889	399	36	155	155	NUM
ejpam-1889	399	37	table	table	NOUN
ejpam-1889	399	38	2	2	NUM
ejpam-1889	399	39	:	:	PUNCT
ejpam-1889	399	40	classification	classification	NOUN
ejpam-1889	399	41	of	of	ADP
ejpam-1889	399	42	parametrized	parametrized	ADJ
ejpam-1889	399	43	(	(	PUNCT
ejpam-1889	399	44	3,0)-affine	3,0)-affine	NUM
ejpam-1889	399	45	subspaces	subspace	NOUN
ejpam-1889	399	46	π	π	NOUN
ejpam-1889	399	47	:	:	PUNCT
ejpam-1889	399	48	a+	a+	PUNCT
ejpam-1889	399	49	u1b	u1b	PROPN
ejpam-1889	399	50	+	+	CCONJ
ejpam-1889	399	51	u2c	u2c	PROPN
ejpam-1889	399	52	+	+	CCONJ
ejpam-1889	400	1	u3d	u3d	NOUN
ejpam-1889	401	1	classifying	classify	VERB
ejpam-1889	401	2	conditions	condition	NOUN
ejpam-1889	401	3	parametrized	parametrized	ADJ
ejpam-1889	401	4	affine	affine	NOUN
ejpam-1889	401	5	subspaces	subspace	NOUN
ejpam-1889	401	6	e∗3(〈c	e∗3(〈c	NOUN
ejpam-1889	401	7	,	,	PUNCT
ejpam-1889	401	8	d	d	NOUN
ejpam-1889	401	9	〉	〉	NOUN
ejpam-1889	401	10	)	)	PUNCT
ejpam-1889	401	11	6=	6=	ADP
ejpam-1889	401	12	{	{	PUNCT
ejpam-1889	401	13	0	0	NUM
ejpam-1889	401	14	}	}	PUNCT
ejpam-1889	401	15	e1	e1	PROPN
ejpam-1889	401	16	+	+	CCONJ
ejpam-1889	401	17	e2	e2	NOUN
ejpam-1889	401	18	,	,	PUNCT
ejpam-1889	401	19	e1	e1	PROPN
ejpam-1889	401	20	−	−	PROPN
ejpam-1889	401	21	e2	e2	PROPN
ejpam-1889	401	22	/∈	/∈	PUNCT
ejpam-1889	402	1	〈	〈	PROPN
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ejpam-1889	402	3	,	,	PUNCT
ejpam-1889	402	4	d	d	PROPN
ejpam-1889	402	5	〉	〉	NOUN
ejpam-1889	403	1			PROPN
ejpam-1889	403	2			SYM
ejpam-1889	403	3	γ1	γ1	PROPN
ejpam-1889	403	4	γ4	γ4	NOUN
ejpam-1889	403	5	1	1	NUM
ejpam-1889	403	6	0	0	NUM
ejpam-1889	403	7	γ2	γ2	NOUN
ejpam-1889	403	8	β1	β1	PROPN
ejpam-1889	403	9	0	0	NUM
ejpam-1889	403	10	0	0	NUM
ejpam-1889	404	1	γ3	γ3	NOUN
ejpam-1889	404	2	γ5	γ5	NOUN
ejpam-1889	404	3	γ6	γ6	PROPN
ejpam-1889	404	4	α	α	PROPN
ejpam-1889	404	5			PROPN
ejpam-1889	404	6			PROPN
ejpam-1889	404	7			NOUN
ejpam-1889	404	8			NUM
ejpam-1889	404	9	γ1	γ1	PROPN
ejpam-1889	404	10	γ4	γ4	NOUN
ejpam-1889	404	11	0	0	NUM
ejpam-1889	404	12	1	1	NUM
ejpam-1889	404	13	γ2	γ2	NOUN
ejpam-1889	404	14	β1	β1	PROPN
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ejpam-1889	404	16	0	0	NUM
ejpam-1889	404	17	γ3	γ3	NOUN
ejpam-1889	404	18	γ5	γ5	NOUN
ejpam-1889	404	19	α	α	NOUN
ejpam-1889	404	20	0	0	PUNCT
ejpam-1889	404	21			PROPN
ejpam-1889	404	22			PROPN
ejpam-1889	404	23	e∗3(〈c	e∗3(〈c	NOUN
ejpam-1889	404	24	,	,	PUNCT
ejpam-1889	404	25	d	d	NOUN
ejpam-1889	404	26	〉	〉	NOUN
ejpam-1889	404	27	)	)	PUNCT
ejpam-1889	404	28	6=	6=	ADP
ejpam-1889	404	29	{	{	PUNCT
ejpam-1889	404	30	0	0	NUM
ejpam-1889	404	31	}	}	PUNCT
ejpam-1889	404	32	e1	e1	PROPN
ejpam-1889	404	33	±	±	NUM
ejpam-1889	404	34	e2	e2	PROPN
ejpam-1889	404	35	∈	∈	PROPN
ejpam-1889	404	36	〈	〈	PROPN
ejpam-1889	404	37	c	c	NOUN
ejpam-1889	404	38	,	,	PUNCT
ejpam-1889	404	39	d	d	PROPN
ejpam-1889	404	40	〉	〉	NOUN
ejpam-1889	404	41			PROPN
ejpam-1889	404	42			NUM
ejpam-1889	404	43	γ1	γ1	NOUN
ejpam-1889	404	44	β1	β1	PROPN
ejpam-1889	404	45	1	1	NUM
ejpam-1889	404	46	0	0	NUM
ejpam-1889	404	47	γ2	γ2	NOUN
ejpam-1889	404	48	0	0	NUM
ejpam-1889	404	49	1	1	NUM
ejpam-1889	404	50	0	0	NUM
ejpam-1889	404	51	γ3	γ3	NOUN
ejpam-1889	404	52	γ4	γ4	NOUN
ejpam-1889	404	53	γ5	γ5	PROPN
ejpam-1889	404	54	β2	β2	VERB
ejpam-1889	404	55			NOUN
ejpam-1889	404	56			PROPN
ejpam-1889	404	57			NOUN
ejpam-1889	404	58			NUM
ejpam-1889	404	59	γ1	γ1	NOUN
ejpam-1889	404	60	1	1	NUM
ejpam-1889	404	61	1	1	NUM
ejpam-1889	404	62	0	0	NUM
ejpam-1889	404	63	γ2	γ2	NOUN
ejpam-1889	404	64	−1	−1	NOUN
ejpam-1889	404	65	1	1	NUM
ejpam-1889	404	66	0	0	NUM
ejpam-1889	404	67	γ3	γ3	NOUN
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ejpam-1889	404	69	γ5	γ5	PROPN
ejpam-1889	404	70	β1	β1	PROPN
ejpam-1889	404	71			PROPN
ejpam-1889	404	72			PROPN
ejpam-1889	404	73			NOUN
ejpam-1889	404	74			NUM
ejpam-1889	404	75	γ1	γ1	NOUN
ejpam-1889	404	76	β1	β1	PROPN
ejpam-1889	404	77	0	0	NUM
ejpam-1889	404	78	1	1	NUM
ejpam-1889	404	79	γ2	γ2	NOUN
ejpam-1889	404	80	0	0	NUM
ejpam-1889	404	81	0	0	NUM
ejpam-1889	404	82	1	1	NUM
ejpam-1889	404	83	γ3	γ3	NOUN
ejpam-1889	404	84	γ4	γ4	NOUN
ejpam-1889	404	85	β2	β2	NOUN
ejpam-1889	404	86	0	0	NUM
ejpam-1889	404	87			PROPN
ejpam-1889	404	88			PROPN
ejpam-1889	404	89			NOUN
ejpam-1889	404	90			NUM
ejpam-1889	404	91	γ1	γ1	NOUN
ejpam-1889	404	92	1	1	NUM
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ejpam-1889	404	94	1	1	NUM
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ejpam-1889	404	104			PROPN
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ejpam-1889	404	108	〉	〉	NOUN
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ejpam-1889	406	14			NUM
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ejpam-1889	407	7	βi	βi	PROPN
ejpam-1889	407	8	6=	6=	NUM
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