id	sid	tid	token	lemma	pos
ejpam-2101	1	1	european	european	PROPN
ejpam-2101	1	2	journal	journal	PROPN
ejpam-2101	1	3	of	of	ADP
ejpam-2101	1	4	pure	pure	ADJ
ejpam-2101	1	5	and	and	CCONJ
ejpam-2101	1	6	applied	apply	VERB
ejpam-2101	1	7	mathematics	mathematic	NOUN
ejpam-2101	1	8	vol	vol	NOUN
ejpam-2101	1	9	.	.	PUNCT
ejpam-2101	2	1	7	7	NUM
ejpam-2101	2	2	,	,	PUNCT
ejpam-2101	2	3	no	no	INTJ
ejpam-2101	2	4	.	.	NOUN
ejpam-2101	2	5	2	2	NUM
ejpam-2101	2	6	,	,	PUNCT
ejpam-2101	2	7	2014	2014	NUM
ejpam-2101	2	8	,	,	PUNCT
ejpam-2101	2	9	191	191	NUM
ejpam-2101	2	10	-	-	SYM
ejpam-2101	2	11	200	200	NUM
ejpam-2101	2	12	issn	issn	PROPN
ejpam-2101	2	13	1307	1307	NUM
ejpam-2101	2	14	-	-	SYM
ejpam-2101	2	15	5543	5543	NUM
ejpam-2101	2	16	–	–	PUNCT
ejpam-2101	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-2101	2	18	intersections	intersection	NOUN
ejpam-2101	2	19	of	of	ADP
ejpam-2101	2	20	rational	rational	ADJ
ejpam-2101	2	21	parametrized	parametrized	ADJ
ejpam-2101	2	22	plane	plane	NOUN
ejpam-2101	2	23	curves	curve	NOUN
ejpam-2101	2	24	mohammed	mohammed	PROPN
ejpam-2101	2	25	tesemma	tesemma	PROPN
ejpam-2101	2	26	1	1	NUM
ejpam-2101	2	27	,	,	PUNCT
ejpam-2101	2	28	haohao	haohao	PROPN
ejpam-2101	2	29	wang	wang	PROPN
ejpam-2101	2	30	2,∗	2,∗	NUM
ejpam-2101	2	31	1	1	NUM
ejpam-2101	2	32	department	department	NOUN
ejpam-2101	2	33	of	of	ADP
ejpam-2101	2	34	mathematics	mathematics	PROPN
ejpam-2101	2	35	,	,	PUNCT
ejpam-2101	2	36	spelman	spelman	PROPN
ejpam-2101	2	37	college	college	PROPN
ejpam-2101	2	38	,	,	PUNCT
ejpam-2101	2	39	atlanta	atlanta	PROPN
ejpam-2101	2	40	,	,	PUNCT
ejpam-2101	2	41	ga	ga	PROPN
ejpam-2101	2	42	30314	30314	NUM
ejpam-2101	2	43	2	2	NUM
ejpam-2101	2	44	department	department	NOUN
ejpam-2101	2	45	of	of	ADP
ejpam-2101	2	46	mathematics	mathematic	NOUN
ejpam-2101	2	47	,	,	PUNCT
ejpam-2101	2	48	southeast	southeast	PROPN
ejpam-2101	2	49	missouri	missouri	PROPN
ejpam-2101	2	50	state	state	PROPN
ejpam-2101	2	51	university	university	PROPN
ejpam-2101	2	52	,	,	PUNCT
ejpam-2101	2	53	cape	cape	PROPN
ejpam-2101	2	54	girardeau	girardeau	PROPN
ejpam-2101	2	55	,	,	PUNCT
ejpam-2101	2	56	mo	mo	PROPN
ejpam-2101	2	57	,	,	PUNCT
ejpam-2101	2	58	usa	usa	PROPN
ejpam-2101	2	59	abstract	abstract	NOUN
ejpam-2101	2	60	.	.	PUNCT
ejpam-2101	3	1	in	in	ADP
ejpam-2101	3	2	this	this	DET
ejpam-2101	3	3	paper	paper	NOUN
ejpam-2101	3	4	,	,	PUNCT
ejpam-2101	3	5	we	we	PRON
ejpam-2101	3	6	introduce	introduce	VERB
ejpam-2101	3	7	and	and	CCONJ
ejpam-2101	3	8	compare	compare	VERB
ejpam-2101	3	9	three	three	NUM
ejpam-2101	3	10	different	different	ADJ
ejpam-2101	3	11	methods	method	NOUN
ejpam-2101	3	12	of	of	ADP
ejpam-2101	3	13	computing	compute	VERB
ejpam-2101	3	14	the	the	DET
ejpam-2101	3	15	intersections	intersection	NOUN
ejpam-2101	3	16	of	of	ADP
ejpam-2101	3	17	rational	rational	ADJ
ejpam-2101	3	18	parametrized	parametrized	ADJ
ejpam-2101	3	19	plane	plane	NOUN
ejpam-2101	3	20	curves	curve	NOUN
ejpam-2101	3	21	.	.	PUNCT
ejpam-2101	4	1	the	the	DET
ejpam-2101	4	2	common	common	ADJ
ejpam-2101	4	3	approach	approach	NOUN
ejpam-2101	4	4	of	of	ADP
ejpam-2101	4	5	these	these	DET
ejpam-2101	4	6	methods	method	NOUN
ejpam-2101	4	7	is	be	AUX
ejpam-2101	4	8	to	to	PART
ejpam-2101	4	9	apply	apply	VERB
ejpam-2101	4	10	the	the	DET
ejpam-2101	4	11	µ-basis	µ-basis	NOUN
ejpam-2101	4	12	of	of	ADP
ejpam-2101	4	13	the	the	DET
ejpam-2101	4	14	plane	plane	NOUN
ejpam-2101	4	15	curves	curve	NOUN
ejpam-2101	4	16	,	,	PUNCT
ejpam-2101	4	17	and	and	CCONJ
ejpam-2101	4	18	avoid	avoid	VERB
ejpam-2101	4	19	of	of	ADP
ejpam-2101	4	20	computing	compute	VERB
ejpam-2101	4	21	the	the	DET
ejpam-2101	4	22	implicit	implicit	ADJ
ejpam-2101	4	23	equations	equation	NOUN
ejpam-2101	4	24	of	of	ADP
ejpam-2101	4	25	the	the	DET
ejpam-2101	4	26	curves	curve	NOUN
ejpam-2101	4	27	,	,	PUNCT
ejpam-2101	4	28	which	which	PRON
ejpam-2101	4	29	increase	increase	VERB
ejpam-2101	4	30	the	the	DET
ejpam-2101	4	31	computation	computation	NOUN
ejpam-2101	4	32	efficiency	efficiency	NOUN
ejpam-2101	4	33	.	.	PUNCT
ejpam-2101	5	1	2010	2010	NUM
ejpam-2101	5	2	mathematics	mathematic	NOUN
ejpam-2101	5	3	subject	subject	NOUN
ejpam-2101	5	4	classifications	classification	NOUN
ejpam-2101	5	5	:	:	PUNCT
ejpam-2101	5	6	14q05	14q05	NUM
ejpam-2101	5	7	,	,	PUNCT
ejpam-2101	5	8	13d02	13d02	NUM
ejpam-2101	5	9	key	key	ADJ
ejpam-2101	5	10	words	word	NOUN
ejpam-2101	5	11	and	and	CCONJ
ejpam-2101	5	12	phrases	phrase	NOUN
ejpam-2101	5	13	:	:	PUNCT
ejpam-2101	5	14	syzygy	syzygy	NOUN
ejpam-2101	5	15	,	,	PUNCT
ejpam-2101	5	16	smith	smith	PROPN
ejpam-2101	5	17	normal	normal	ADJ
ejpam-2101	5	18	form	form	NOUN
ejpam-2101	5	19	,	,	PUNCT
ejpam-2101	5	20	resultants	resultant	NOUN
ejpam-2101	5	21	,	,	PUNCT
ejpam-2101	5	22	curves	curve	NOUN
ejpam-2101	5	23	1	1	NUM
ejpam-2101	5	24	.	.	PUNCT
ejpam-2101	6	1	introduction	introduction	NOUN
ejpam-2101	6	2	through	through	ADP
ejpam-2101	6	3	this	this	DET
ejpam-2101	6	4	paper	paper	NOUN
ejpam-2101	6	5	,	,	PUNCT
ejpam-2101	6	6	we	we	PRON
ejpam-2101	6	7	shall	shall	AUX
ejpam-2101	6	8	consider	consider	VERB
ejpam-2101	6	9	two	two	NUM
ejpam-2101	6	10	rational	rational	ADJ
ejpam-2101	6	11	plane	plane	NOUN
ejpam-2101	6	12	curves	curve	NOUN
ejpam-2101	6	13	c1	c1	NOUN
ejpam-2101	6	14	and	and	CCONJ
ejpam-2101	6	15	c2	c2	PROPN
ejpam-2101	6	16	in	in	ADP
ejpam-2101	6	17	the	the	DET
ejpam-2101	6	18	complex	complex	ADJ
ejpam-2101	6	19	projective	projective	ADJ
ejpam-2101	6	20	two	two	NUM
ejpam-2101	6	21	-	-	PUNCT
ejpam-2101	6	22	space	space	NOUN
ejpam-2101	6	23	given	give	VERB
ejpam-2101	6	24	as	as	ADP
ejpam-2101	6	25	the	the	DET
ejpam-2101	6	26	image	image	NOUN
ejpam-2101	6	27	of	of	ADP
ejpam-2101	6	28	generic	generic	ADJ
ejpam-2101	6	29	one	one	NUM
ejpam-2101	6	30	-	-	PUNCT
ejpam-2101	6	31	to	to	ADP
ejpam-2101	6	32	-	-	PUNCT
ejpam-2101	6	33	one	one	NUM
ejpam-2101	6	34	rational	rational	ADJ
ejpam-2101	6	35	parametrizations	parametrization	NOUN
ejpam-2101	6	36	:	:	PUNCT
ejpam-2101	6	37	f(s	f(s	PROPN
ejpam-2101	6	38	,	,	PUNCT
ejpam-2101	6	39	t	t	PROPN
ejpam-2101	6	40	)	)	PUNCT
ejpam-2101	6	41	=	=	SYM
ejpam-2101	6	42	(	(	PUNCT
ejpam-2101	6	43	f0(s	f0(s	PROPN
ejpam-2101	6	44	,	,	PUNCT
ejpam-2101	6	45	t	t	PROPN
ejpam-2101	6	46	)	)	PUNCT
ejpam-2101	6	47	,	,	PUNCT
ejpam-2101	6	48	f1(s	f1(s	PROPN
ejpam-2101	6	49	,	,	PUNCT
ejpam-2101	6	50	t	t	PROPN
ejpam-2101	6	51	)	)	PUNCT
ejpam-2101	6	52	,	,	PUNCT
ejpam-2101	6	53	f2(s	f2(s	PROPN
ejpam-2101	6	54	,	,	PUNCT
ejpam-2101	6	55	t	t	PROPN
ejpam-2101	6	56	)	)	PUNCT
ejpam-2101	6	57	)	)	PUNCT
ejpam-2101	6	58	,	,	PUNCT
ejpam-2101	6	59	(	(	PUNCT
ejpam-2101	6	60	s	s	X
ejpam-2101	6	61	,	,	PUNCT
ejpam-2101	6	62	t	t	PROPN
ejpam-2101	6	63	)	)	PUNCT
ejpam-2101	6	64	6=	6=	ADP
ejpam-2101	6	65	(	(	PUNCT
ejpam-2101	6	66	0	0	NUM
ejpam-2101	6	67	,	,	PUNCT
ejpam-2101	6	68	0	0	NUM
ejpam-2101	6	69	)	)	PUNCT
ejpam-2101	6	70	,	,	PUNCT
ejpam-2101	6	71	(	(	PUNCT
ejpam-2101	6	72	1	1	X
ejpam-2101	6	73	)	)	PUNCT
ejpam-2101	6	74	and	and	CCONJ
ejpam-2101	6	75	g(u	g(u	PROPN
ejpam-2101	6	76	,	,	PUNCT
ejpam-2101	6	77	v	v	NOUN
ejpam-2101	6	78	)	)	PUNCT
ejpam-2101	6	79	=	=	SYM
ejpam-2101	6	80	(	(	PUNCT
ejpam-2101	6	81	g0(u	g0(u	ADP
ejpam-2101	6	82	,	,	PUNCT
ejpam-2101	6	83	v	v	NOUN
ejpam-2101	6	84	)	)	PUNCT
ejpam-2101	6	85	,	,	PUNCT
ejpam-2101	6	86	g1(u	g1(u	PROPN
ejpam-2101	6	87	,	,	PUNCT
ejpam-2101	6	88	v	v	NOUN
ejpam-2101	6	89	)	)	PUNCT
ejpam-2101	6	90	,	,	PUNCT
ejpam-2101	6	91	g2(u	g2(u	PROPN
ejpam-2101	6	92	,	,	PUNCT
ejpam-2101	6	93	v	v	NOUN
ejpam-2101	6	94	)	)	PUNCT
ejpam-2101	6	95	)	)	PUNCT
ejpam-2101	6	96	,	,	PUNCT
ejpam-2101	6	97	(	(	PUNCT
ejpam-2101	6	98	u	u	NOUN
ejpam-2101	6	99	,	,	PUNCT
ejpam-2101	6	100	v	v	NOUN
ejpam-2101	6	101	)	)	PUNCT
ejpam-2101	6	102	6=	6=	X
ejpam-2101	6	103	(	(	PUNCT
ejpam-2101	6	104	0	0	NUM
ejpam-2101	6	105	,	,	PUNCT
ejpam-2101	6	106	0	0	NUM
ejpam-2101	6	107	)	)	PUNCT
ejpam-2101	6	108	,	,	PUNCT
ejpam-2101	6	109	(	(	PUNCT
ejpam-2101	6	110	2	2	X
ejpam-2101	6	111	)	)	PUNCT
ejpam-2101	6	112	where	where	SCONJ
ejpam-2101	6	113	f0	f0	PROPN
ejpam-2101	6	114	,	,	PUNCT
ejpam-2101	6	115	f1	f1	NOUN
ejpam-2101	6	116	,	,	PUNCT
ejpam-2101	6	117	f2	f2	PROPN
ejpam-2101	6	118	(	(	PUNCT
ejpam-2101	6	119	respectively	respectively	ADV
ejpam-2101	6	120	,	,	PUNCT
ejpam-2101	6	121	g0	g0	PROPN
ejpam-2101	6	122	,	,	PUNCT
ejpam-2101	6	123	g1	g1	NOUN
ejpam-2101	6	124	,	,	PUNCT
ejpam-2101	6	125	g2	g2	PROPN
ejpam-2101	6	126	)	)	PUNCT
ejpam-2101	6	127	are	be	AUX
ejpam-2101	6	128	linearly	linearly	ADV
ejpam-2101	6	129	independent	independent	ADJ
ejpam-2101	6	130	homogeneous	homogeneous	ADJ
ejpam-2101	6	131	polynomials	polynomial	NOUN
ejpam-2101	6	132	of	of	ADP
ejpam-2101	6	133	the	the	DET
ejpam-2101	6	134	same	same	ADJ
ejpam-2101	6	135	degree	degree	NOUN
ejpam-2101	6	136	d	d	X
ejpam-2101	6	137	≥	≥	NUM
ejpam-2101	6	138	2	2	NUM
ejpam-2101	6	139	(	(	PUNCT
ejpam-2101	6	140	respectively	respectively	ADV
ejpam-2101	6	141	,	,	PUNCT
ejpam-2101	6	142	d	d	PROPN
ejpam-2101	6	143	′	′	NUM
ejpam-2101	6	144	≥	≥	NOUN
ejpam-2101	6	145	2	2	NUM
ejpam-2101	6	146	)	)	PUNCT
ejpam-2101	6	147	,	,	PUNCT
ejpam-2101	6	148	and	and	CCONJ
ejpam-2101	6	149	gcd	gcd	PROPN
ejpam-2101	6	150	(	(	PUNCT
ejpam-2101	6	151	f0	f0	PROPN
ejpam-2101	6	152	,	,	PUNCT
ejpam-2101	6	153	f1	f1	NOUN
ejpam-2101	6	154	,	,	PUNCT
ejpam-2101	6	155	f2	f2	PROPN
ejpam-2101	6	156	)	)	PUNCT
ejpam-2101	6	157	=	=	SYM
ejpam-2101	6	158	1	1	NUM
ejpam-2101	6	159	(	(	PUNCT
ejpam-2101	6	160	respectively	respectively	ADV
ejpam-2101	6	161	,	,	PUNCT
ejpam-2101	6	162	gcd(g0	gcd(g0	PROPN
ejpam-2101	6	163	,	,	PUNCT
ejpam-2101	6	164	g1	g1	NOUN
ejpam-2101	6	165	,	,	PUNCT
ejpam-2101	6	166	g2	g2	PROPN
ejpam-2101	6	167	)	)	PUNCT
ejpam-2101	6	168	=	=	SYM
ejpam-2101	6	169	1	1	NUM
ejpam-2101	6	170	)	)	PUNCT
ejpam-2101	6	171	.	.	PUNCT
ejpam-2101	7	1	the	the	DET
ejpam-2101	7	2	implicit	implicit	ADJ
ejpam-2101	7	3	equation	equation	NOUN
ejpam-2101	7	4	of	of	ADP
ejpam-2101	7	5	a	a	DET
ejpam-2101	7	6	parametric	parametric	ADJ
ejpam-2101	7	7	curve	curve	NOUN
ejpam-2101	7	8	is	be	AUX
ejpam-2101	7	9	a	a	DET
ejpam-2101	7	10	polynomial	polynomial	ADJ
ejpam-2101	7	11	f	f	NOUN
ejpam-2101	7	12	in	in	ADP
ejpam-2101	7	13	the	the	DET
ejpam-2101	7	14	polynomial	polynomial	ADJ
ejpam-2101	7	15	ring	ring	NOUN
ejpam-2101	7	16	c[x0	c[x0	X
ejpam-2101	7	17	,	,	PUNCT
ejpam-2101	7	18	x1	x1	PROPN
ejpam-2101	7	19	,	,	PUNCT
ejpam-2101	7	20	x2	x2	PROPN
ejpam-2101	7	21	]	]	PUNCT
ejpam-2101	8	1	such	such	ADJ
ejpam-2101	8	2	that	that	SCONJ
ejpam-2101	8	3	f	f	PROPN
ejpam-2101	8	4	(	(	PUNCT
ejpam-2101	8	5	a0	a0	PROPN
ejpam-2101	8	6	,	,	PUNCT
ejpam-2101	8	7	a1	a1	PROPN
ejpam-2101	8	8	,	,	PUNCT
ejpam-2101	8	9	a2	a2	NOUN
ejpam-2101	8	10	)	)	PUNCT
ejpam-2101	8	11	=	=	SYM
ejpam-2101	8	12	0	0	PUNCT
ejpam-2101	9	1	whenever	whenever	SCONJ
ejpam-2101	9	2	[	[	X
ejpam-2101	9	3	a0	a0	NOUN
ejpam-2101	9	4	,	,	PUNCT
ejpam-2101	9	5	a1	a1	PROPN
ejpam-2101	9	6	,	,	PUNCT
ejpam-2101	9	7	a2	a2	PROPN
ejpam-2101	9	8	]	]	PUNCT
ejpam-2101	9	9	is	be	AUX
ejpam-2101	9	10	a	a	DET
ejpam-2101	9	11	point	point	NOUN
ejpam-2101	9	12	on	on	ADP
ejpam-2101	9	13	the	the	DET
ejpam-2101	9	14	parametrized	parametrized	ADJ
ejpam-2101	9	15	curve	curve	NOUN
ejpam-2101	9	16	,	,	PUNCT
ejpam-2101	9	17	and	and	CCONJ
ejpam-2101	9	18	f	f	PROPN
ejpam-2101	9	19	is	be	AUX
ejpam-2101	9	20	irreducible	irreducible	ADJ
ejpam-2101	9	21	.	.	PUNCT
ejpam-2101	10	1	without	without	ADP
ejpam-2101	10	2	loss	loss	NOUN
ejpam-2101	10	3	of	of	ADP
ejpam-2101	10	4	generality	generality	NOUN
ejpam-2101	10	5	,	,	PUNCT
ejpam-2101	10	6	we	we	PRON
ejpam-2101	10	7	let	let	VERB
ejpam-2101	10	8	f(x	f(x	PROPN
ejpam-2101	10	9	,	,	PUNCT
ejpam-2101	10	10	y	y	PROPN
ejpam-2101	10	11	,	,	PUNCT
ejpam-2101	10	12	z	z	NOUN
ejpam-2101	10	13	)	)	PUNCT
ejpam-2101	10	14	=	=	SYM
ejpam-2101	10	15	0	0	NUM
ejpam-2101	10	16	and	and	CCONJ
ejpam-2101	10	17	g(x	g(x	PROPN
ejpam-2101	10	18	,	,	PUNCT
ejpam-2101	10	19	y	y	PROPN
ejpam-2101	10	20	,	,	PUNCT
ejpam-2101	10	21	z	z	NOUN
ejpam-2101	10	22	)	)	PUNCT
ejpam-2101	10	23	=	=	SYM
ejpam-2101	10	24	0	0	NUM
ejpam-2101	10	25	be	be	AUX
ejpam-2101	10	26	the	the	DET
ejpam-2101	10	27	implicit	implicit	ADJ
ejpam-2101	10	28	equation	equation	NOUN
ejpam-2101	10	29	of	of	ADP
ejpam-2101	10	30	the	the	DET
ejpam-2101	10	31	parametrized	parametrized	ADJ
ejpam-2101	10	32	curves	curve	NOUN
ejpam-2101	10	33	f(s	f(s	PROPN
ejpam-2101	10	34	,	,	PUNCT
ejpam-2101	10	35	t	t	PROPN
ejpam-2101	10	36	)	)	PUNCT
ejpam-2101	10	37	and	and	CCONJ
ejpam-2101	10	38	g(u	g(u	PROPN
ejpam-2101	10	39	,	,	PUNCT
ejpam-2101	10	40	v	v	NOUN
ejpam-2101	10	41	)	)	PUNCT
ejpam-2101	10	42	respectively	respectively	ADV
ejpam-2101	10	43	.	.	PUNCT
ejpam-2101	11	1	it	it	PRON
ejpam-2101	11	2	is	be	AUX
ejpam-2101	11	3	known	know	VERB
ejpam-2101	11	4	that	that	SCONJ
ejpam-2101	11	5	the	the	DET
ejpam-2101	11	6	intersection	intersection	NOUN
ejpam-2101	11	7	number	number	NOUN
ejpam-2101	11	8	of	of	ADP
ejpam-2101	11	9	c1	c1	PROPN
ejpam-2101	11	10	and	and	CCONJ
ejpam-2101	11	11	c2	c2	PROPN
ejpam-2101	11	12	is	be	AUX
ejpam-2101	11	13	dd	dd	NOUN
ejpam-2101	11	14	′	′	NUM
ejpam-2101	11	15	counting	count	VERB
ejpam-2101	11	16	the	the	DET
ejpam-2101	11	17	intersection	intersection	NOUN
ejpam-2101	11	18	multiplicity	multiplicity	NOUN
ejpam-2101	11	19	.	.	PUNCT
ejpam-2101	12	1	in	in	ADP
ejpam-2101	12	2	general	general	ADJ
ejpam-2101	12	3	,	,	PUNCT
ejpam-2101	12	4	one	one	PRON
ejpam-2101	12	5	can	can	AUX
ejpam-2101	12	6	obtain	obtain	VERB
ejpam-2101	12	7	this	this	DET
ejpam-2101	12	8	information	information	NOUN
ejpam-2101	12	9	by	by	ADP
ejpam-2101	12	10	computing	compute	VERB
ejpam-2101	12	11	the	the	DET
ejpam-2101	12	12	implicit	implicit	ADJ
ejpam-2101	12	13	equation	equation	NOUN
ejpam-2101	12	14	g(x	g(x	PROPN
ejpam-2101	12	15	,	,	PUNCT
ejpam-2101	12	16	y	y	PROPN
ejpam-2101	12	17	,	,	PUNCT
ejpam-2101	12	18	z	z	NOUN
ejpam-2101	12	19	)	)	PUNCT
ejpam-2101	12	20	=	=	SYM
ejpam-2101	12	21	0	0	NUM
ejpam-2101	12	22	of	of	ADP
ejpam-2101	12	23	the	the	DET
ejpam-2101	12	24	curvec2	curvec2	NOUN
ejpam-2101	12	25	,	,	PUNCT
ejpam-2101	12	26	then	then	ADV
ejpam-2101	12	27	solve	solve	VERB
ejpam-2101	12	28	the	the	DET
ejpam-2101	12	29	equation	equation	NOUN
ejpam-2101	12	30	g	g	PROPN
ejpam-2101	12	31	(	(	PUNCT
ejpam-2101	12	32	f0(s	f0(s	PROPN
ejpam-2101	12	33	,	,	PUNCT
ejpam-2101	12	34	t	t	PROPN
ejpam-2101	12	35	)	)	PUNCT
ejpam-2101	12	36	,	,	PUNCT
ejpam-2101	12	37	f1(s	f1(s	PROPN
ejpam-2101	12	38	,	,	PUNCT
ejpam-2101	12	39	t	t	PROPN
ejpam-2101	12	40	)	)	PUNCT
ejpam-2101	12	41	,	,	PUNCT
ejpam-2101	12	42	f2(s	f2(s	PROPN
ejpam-2101	12	43	,	,	PUNCT
ejpam-2101	12	44	t	t	PROPN
ejpam-2101	12	45	)	)	PUNCT
ejpam-2101	12	46	)	)	PUNCT
ejpam-2101	13	1	=	=	SYM
ejpam-2101	13	2	0	0	NUM
ejpam-2101	14	1	for	for	ADP
ejpam-2101	14	2	(	(	PUNCT
ejpam-2101	14	3	s	s	PROPN
ejpam-2101	14	4	,	,	PUNCT
ejpam-2101	14	5	t	t	PROPN
ejpam-2101	14	6	)	)	PUNCT
ejpam-2101	14	7	.	.	PUNCT
ejpam-2101	15	1	∗corresponding	∗corresponde	VERB
ejpam-2101	15	2	author	author	NOUN
ejpam-2101	15	3	.	.	PUNCT
ejpam-2101	16	1	email	email	NOUN
ejpam-2101	16	2	addresses	address	NOUN
ejpam-2101	16	3	:	:	PUNCT
ejpam-2101	16	4	mtesemma@spelman.edu	mtesemma@spelman.edu	PROPN
ejpam-2101	16	5	(	(	PUNCT
ejpam-2101	16	6	m.	m.	NOUN
ejpam-2101	16	7	tesemma	tesemma	PROPN
ejpam-2101	16	8	)	)	PUNCT
ejpam-2101	16	9	,	,	PUNCT
ejpam-2101	16	10	hwang@semo.edu	hwang@semo.edu	PROPN
ejpam-2101	17	1	(	(	PUNCT
ejpam-2101	17	2	h.	h.	PROPN
ejpam-2101	17	3	wang	wang	PROPN
ejpam-2101	17	4	)	)	PUNCT
ejpam-2101	17	5	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-2101	18	1	191	191	NUM
ejpam-2101	18	2	c	c	X
ejpam-2101	18	3	©	©	NOUN
ejpam-2101	18	4	2014	2014	NUM
ejpam-2101	18	5	ejpam	ejpam	NOUN
ejpam-2101	18	6	all	all	DET
ejpam-2101	18	7	rights	right	NOUN
ejpam-2101	18	8	reserved	reserve	VERB
ejpam-2101	18	9	.	.	PUNCT
ejpam-2101	19	1	m.	m.	PROPN
ejpam-2101	19	2	tesemma	tesemma	PROPN
ejpam-2101	19	3	,	,	PUNCT
ejpam-2101	19	4	h.	h.	PROPN
ejpam-2101	19	5	wang	wang	PROPN
ejpam-2101	19	6	,	,	PUNCT
ejpam-2101	19	7	/	/	SYM
ejpam-2101	19	8	eur	eur	NOUN
ejpam-2101	19	9	.	.	PUNCT
ejpam-2101	20	1	j.	j.	PROPN
ejpam-2101	20	2	pure	pure	PROPN
ejpam-2101	20	3	appl	appl	PROPN
ejpam-2101	20	4	.	.	PROPN
ejpam-2101	20	5	math	math	PROPN
ejpam-2101	20	6	,	,	PUNCT
ejpam-2101	20	7	7	7	NUM
ejpam-2101	20	8	(	(	PUNCT
ejpam-2101	20	9	2014	2014	NUM
ejpam-2101	20	10	)	)	PUNCT
ejpam-2101	20	11	,	,	PUNCT
ejpam-2101	20	12	191	191	NUM
ejpam-2101	20	13	-	-	SYM
ejpam-2101	20	14	200	200	NUM
ejpam-2101	20	15	192	192	NUM
ejpam-2101	20	16	(	(	PUNCT
ejpam-2101	20	17	or	or	CCONJ
ejpam-2101	20	18	computing	compute	VERB
ejpam-2101	20	19	the	the	DET
ejpam-2101	20	20	implicit	implicit	ADJ
ejpam-2101	20	21	equation	equation	NOUN
ejpam-2101	20	22	f(x	f(x	PROPN
ejpam-2101	20	23	,	,	PUNCT
ejpam-2101	20	24	y	y	PROPN
ejpam-2101	20	25	,	,	PUNCT
ejpam-2101	20	26	z	z	NOUN
ejpam-2101	20	27	)	)	PUNCT
ejpam-2101	20	28	=	=	SYM
ejpam-2101	20	29	0	0	NUM
ejpam-2101	20	30	of	of	ADP
ejpam-2101	20	31	the	the	DET
ejpam-2101	20	32	curve	curve	NOUN
ejpam-2101	20	33	c1	c1	NOUN
ejpam-2101	20	34	,	,	PUNCT
ejpam-2101	20	35	then	then	ADV
ejpam-2101	20	36	solve	solve	VERB
ejpam-2101	20	37	the	the	DET
ejpam-2101	20	38	equation	equation	NOUN
ejpam-2101	20	39	f(g0(u	f(g0(u	PROPN
ejpam-2101	20	40	,	,	PUNCT
ejpam-2101	20	41	v	v	NOUN
ejpam-2101	20	42	)	)	PUNCT
ejpam-2101	20	43	,	,	PUNCT
ejpam-2101	20	44	g1(u	g1(u	PROPN
ejpam-2101	20	45	,	,	PUNCT
ejpam-2101	20	46	v	v	NOUN
ejpam-2101	20	47	)	)	PUNCT
ejpam-2101	20	48	,	,	PUNCT
ejpam-2101	20	49	g2(u	g2(u	PROPN
ejpam-2101	20	50	,	,	PUNCT
ejpam-2101	20	51	v	v	NOUN
ejpam-2101	20	52	)	)	PUNCT
ejpam-2101	20	53	)	)	PUNCT
ejpam-2101	21	1	=	=	SYM
ejpam-2101	21	2	0	0	NUM
ejpam-2101	22	1	for	for	ADP
ejpam-2101	22	2	(	(	PUNCT
ejpam-2101	22	3	u	u	NOUN
ejpam-2101	22	4	,	,	PUNCT
ejpam-2101	22	5	v	v	NOUN
ejpam-2101	22	6	)	)	PUNCT
ejpam-2101	22	7	.	.	PUNCT
ejpam-2101	22	8	)	)	PUNCT
ejpam-2101	23	1	the	the	DET
ejpam-2101	23	2	aim	aim	NOUN
ejpam-2101	23	3	of	of	ADP
ejpam-2101	23	4	this	this	DET
ejpam-2101	23	5	paper	paper	NOUN
ejpam-2101	23	6	is	be	AUX
ejpam-2101	23	7	to	to	PART
ejpam-2101	23	8	find	find	VERB
ejpam-2101	23	9	the	the	DET
ejpam-2101	23	10	intersection	intersection	NOUN
ejpam-2101	23	11	of	of	ADP
ejpam-2101	23	12	the	the	DET
ejpam-2101	23	13	curve	curve	NOUN
ejpam-2101	23	14	c1	c1	PROPN
ejpam-2101	23	15	and	and	CCONJ
ejpam-2101	23	16	the	the	DET
ejpam-2101	23	17	curve	curve	NOUN
ejpam-2101	23	18	c2	c2	PROPN
ejpam-2101	23	19	only	only	ADV
ejpam-2101	23	20	use	use	VERB
ejpam-2101	23	21	the	the	DET
ejpam-2101	23	22	parametrizations	parametrization	NOUN
ejpam-2101	23	23	of	of	ADP
ejpam-2101	23	24	the	the	DET
ejpam-2101	23	25	curves	curve	NOUN
ejpam-2101	23	26	without	without	ADP
ejpam-2101	23	27	computing	compute	VERB
ejpam-2101	23	28	the	the	DET
ejpam-2101	23	29	implicit	implicit	ADJ
ejpam-2101	23	30	equation	equation	NOUN
ejpam-2101	23	31	of	of	ADP
ejpam-2101	23	32	the	the	DET
ejpam-2101	23	33	curves	curve	NOUN
ejpam-2101	23	34	.	.	PUNCT
ejpam-2101	24	1	we	we	PRON
ejpam-2101	24	2	will	will	AUX
ejpam-2101	24	3	accomplish	accomplish	VERB
ejpam-2101	24	4	this	this	PRON
ejpam-2101	24	5	by	by	ADP
ejpam-2101	24	6	using	use	VERB
ejpam-2101	24	7	the	the	DET
ejpam-2101	24	8	µ-basis	µ-basis	NOUN
ejpam-2101	24	9	of	of	ADP
ejpam-2101	24	10	the	the	DET
ejpam-2101	24	11	syzygies	syzygy	NOUN
ejpam-2101	24	12	of	of	ADP
ejpam-2101	24	13	the	the	DET
ejpam-2101	24	14	curve	curve	NOUN
ejpam-2101	24	15	.	.	PUNCT
ejpam-2101	25	1	moving	move	VERB
ejpam-2101	25	2	lines	line	NOUN
ejpam-2101	25	3	and	and	CCONJ
ejpam-2101	25	4	moving	move	VERB
ejpam-2101	25	5	planes	plane	NOUN
ejpam-2101	25	6	(	(	PUNCT
ejpam-2101	25	7	syzygies	syzygy	NOUN
ejpam-2101	25	8	)	)	PUNCT
ejpam-2101	25	9	were	be	AUX
ejpam-2101	25	10	introduced	introduce	VERB
ejpam-2101	25	11	into	into	ADP
ejpam-2101	25	12	computer	computer	NOUN
ejpam-2101	25	13	aided	aid	VERB
ejpam-2101	25	14	geometric	geometric	ADJ
ejpam-2101	25	15	design	design	NOUN
ejpam-2101	25	16	by	by	ADP
ejpam-2101	25	17	sederberg	sederberg	PROPN
ejpam-2101	25	18	,	,	PUNCT
ejpam-2101	25	19	cox	cox	PROPN
ejpam-2101	25	20	and	and	CCONJ
ejpam-2101	25	21	their	their	PRON
ejpam-2101	25	22	collaborators	collaborator	NOUN
ejpam-2101	25	23	in	in	ADP
ejpam-2101	25	24	order	order	NOUN
ejpam-2101	25	25	to	to	PART
ejpam-2101	25	26	develop	develop	VERB
ejpam-2101	25	27	robust	robust	ADJ
ejpam-2101	25	28	,	,	PUNCT
ejpam-2101	25	29	efficient	efficient	ADJ
ejpam-2101	25	30	algorithms	algorithm	NOUN
ejpam-2101	25	31	for	for	ADP
ejpam-2101	25	32	implicitizing	implicitize	VERB
ejpam-2101	25	33	rational	rational	ADJ
ejpam-2101	25	34	curves	curve	NOUN
ejpam-2101	25	35	and	and	CCONJ
ejpam-2101	25	36	surfaces	surface	NOUN
ejpam-2101	25	37	[	[	X
ejpam-2101	25	38	5	5	NUM
ejpam-2101	25	39	,	,	PUNCT
ejpam-2101	25	40	7–9	7–9	NOUN
ejpam-2101	25	41	]	]	X
ejpam-2101	25	42	.	.	PUNCT
ejpam-2101	26	1	their	their	PRON
ejpam-2101	26	2	success	success	NOUN
ejpam-2101	26	3	motivated	motivate	VERB
ejpam-2101	26	4	people	people	NOUN
ejpam-2101	26	5	to	to	PART
ejpam-2101	26	6	develop	develop	VERB
ejpam-2101	26	7	fast	fast	ADJ
ejpam-2101	26	8	algorithms	algorithm	NOUN
ejpam-2101	26	9	for	for	ADP
ejpam-2101	26	10	computing	compute	VERB
ejpam-2101	26	11	special	special	ADJ
ejpam-2101	26	12	bases	basis	NOUN
ejpam-2101	26	13	,	,	PUNCT
ejpam-2101	26	14	called	call	VERB
ejpam-2101	26	15	µ-bases	µ-base	NOUN
ejpam-2101	26	16	,	,	PUNCT
ejpam-2101	26	17	for	for	ADP
ejpam-2101	26	18	moving	move	VERB
ejpam-2101	26	19	lines	line	NOUN
ejpam-2101	26	20	and	and	CCONJ
ejpam-2101	26	21	moving	move	VERB
ejpam-2101	26	22	planes	plane	NOUN
ejpam-2101	27	1	[	[	X
ejpam-2101	27	2	1–3	1–3	NOUN
ejpam-2101	27	3	,	,	PUNCT
ejpam-2101	27	4	10	10	NUM
ejpam-2101	27	5	]	]	PUNCT
ejpam-2101	27	6	.	.	PUNCT
ejpam-2101	28	1	we	we	PRON
ejpam-2101	28	2	begin	begin	VERB
ejpam-2101	28	3	in	in	ADP
ejpam-2101	28	4	section	section	NOUN
ejpam-2101	28	5	2	2	NUM
ejpam-2101	28	6	with	with	ADP
ejpam-2101	28	7	a	a	DET
ejpam-2101	28	8	brief	brief	ADJ
ejpam-2101	28	9	review	review	NOUN
ejpam-2101	28	10	of	of	ADP
ejpam-2101	28	11	moving	move	VERB
ejpam-2101	28	12	lines	line	NOUN
ejpam-2101	28	13	and	and	CCONJ
ejpam-2101	28	14	µ-basis	µ-basis	NOUN
ejpam-2101	28	15	of	of	ADP
ejpam-2101	28	16	the	the	DET
ejpam-2101	28	17	moving	move	VERB
ejpam-2101	28	18	lines	line	NOUN
ejpam-2101	28	19	or	or	CCONJ
ejpam-2101	28	20	rational	rational	ADJ
ejpam-2101	28	21	parametrized	parametrized	ADJ
ejpam-2101	28	22	plane	plane	NOUN
ejpam-2101	28	23	curves	curve	NOUN
ejpam-2101	28	24	.	.	PUNCT
ejpam-2101	29	1	in	in	ADP
ejpam-2101	29	2	sections	section	NOUN
ejpam-2101	29	3	3	3	NUM
ejpam-2101	29	4	,	,	PUNCT
ejpam-2101	29	5	we	we	PRON
ejpam-2101	29	6	describe	describe	VERB
ejpam-2101	29	7	three	three	NUM
ejpam-2101	29	8	different	different	ADJ
ejpam-2101	29	9	different	different	ADJ
ejpam-2101	29	10	methods	method	NOUN
ejpam-2101	29	11	of	of	ADP
ejpam-2101	29	12	computing	compute	VERB
ejpam-2101	29	13	the	the	DET
ejpam-2101	29	14	intersections	intersection	NOUN
ejpam-2101	29	15	of	of	ADP
ejpam-2101	29	16	two	two	NUM
ejpam-2101	29	17	parametric	parametric	ADJ
ejpam-2101	29	18	curves	curve	NOUN
ejpam-2101	29	19	.	.	PUNCT
ejpam-2101	30	1	for	for	ADP
ejpam-2101	30	2	each	each	DET
ejpam-2101	30	3	method	method	NOUN
ejpam-2101	30	4	,	,	PUNCT
ejpam-2101	30	5	we	we	PRON
ejpam-2101	30	6	first	first	ADV
ejpam-2101	30	7	provide	provide	VERB
ejpam-2101	30	8	the	the	DET
ejpam-2101	30	9	theoretical	theoretical	ADJ
ejpam-2101	30	10	background	background	NOUN
ejpam-2101	30	11	behind	behind	ADP
ejpam-2101	30	12	the	the	DET
ejpam-2101	30	13	algorithm	algorithm	NOUN
ejpam-2101	30	14	,	,	PUNCT
ejpam-2101	30	15	then	then	ADV
ejpam-2101	30	16	we	we	PRON
ejpam-2101	30	17	give	give	VERB
ejpam-2101	30	18	the	the	DET
ejpam-2101	30	19	specific	specific	ADJ
ejpam-2101	30	20	algorithm	algorithm	NOUN
ejpam-2101	30	21	,	,	PUNCT
ejpam-2101	30	22	and	and	CCONJ
ejpam-2101	30	23	then	then	ADV
ejpam-2101	30	24	we	we	PRON
ejpam-2101	30	25	illustrate	illustrate	VERB
ejpam-2101	30	26	the	the	DET
ejpam-2101	30	27	algorithm	algorithm	NOUN
ejpam-2101	30	28	via	via	ADP
ejpam-2101	30	29	an	an	DET
ejpam-2101	30	30	example	example	NOUN
ejpam-2101	30	31	.	.	PUNCT
ejpam-2101	31	1	in	in	ADP
ejpam-2101	31	2	section	section	NOUN
ejpam-2101	31	3	4	4	NUM
ejpam-2101	31	4	,	,	PUNCT
ejpam-2101	31	5	we	we	PRON
ejpam-2101	31	6	provide	provide	VERB
ejpam-2101	31	7	a	a	DET
ejpam-2101	31	8	brief	brief	ADJ
ejpam-2101	31	9	summary	summary	NOUN
ejpam-2101	31	10	of	of	ADP
ejpam-2101	31	11	the	the	DET
ejpam-2101	31	12	paper	paper	NOUN
ejpam-2101	31	13	,	,	PUNCT
ejpam-2101	31	14	and	and	CCONJ
ejpam-2101	31	15	a	a	DET
ejpam-2101	31	16	open	open	ADJ
ejpam-2101	31	17	questions	question	NOUN
ejpam-2101	31	18	for	for	ADP
ejpam-2101	31	19	future	future	ADJ
ejpam-2101	31	20	study	study	NOUN
ejpam-2101	31	21	.	.	PUNCT
ejpam-2101	32	1	2	2	X
ejpam-2101	32	2	.	.	X
ejpam-2101	32	3	moving	move	VERB
ejpam-2101	32	4	lines	line	NOUN
ejpam-2101	32	5	a	a	DET
ejpam-2101	32	6	moving	move	VERB
ejpam-2101	32	7	line	line	NOUN
ejpam-2101	32	8	is	be	AUX
ejpam-2101	32	9	a	a	DET
ejpam-2101	32	10	family	family	NOUN
ejpam-2101	32	11	of	of	ADP
ejpam-2101	32	12	lines	line	NOUN
ejpam-2101	32	13	with	with	ADP
ejpam-2101	32	14	each	each	DET
ejpam-2101	32	15	pair	pair	NOUN
ejpam-2101	32	16	of	of	ADP
ejpam-2101	32	17	parameters	parameter	NOUN
ejpam-2101	32	18	(	(	PUNCT
ejpam-2101	32	19	s	s	PROPN
ejpam-2101	32	20	,	,	PUNCT
ejpam-2101	32	21	t	t	NOUN
ejpam-2101	32	22	)	)	PUNCT
ejpam-2101	32	23	corresponding	correspond	VERB
ejpam-2101	32	24	to	to	ADP
ejpam-2101	32	25	a	a	DET
ejpam-2101	32	26	line	line	NOUN
ejpam-2101	32	27	:	:	PUNCT
ejpam-2101	32	28	l(x0	l(x0	PROPN
ejpam-2101	32	29	,	,	PUNCT
ejpam-2101	32	30	x1	x1	PROPN
ejpam-2101	32	31	,	,	PUNCT
ejpam-2101	32	32	x2	x2	PROPN
ejpam-2101	32	33	;	;	PUNCT
ejpam-2101	32	34	s	s	PROPN
ejpam-2101	32	35	,	,	PUNCT
ejpam-2101	32	36	t	t	PROPN
ejpam-2101	32	37	)	)	PUNCT
ejpam-2101	32	38	=	=	SYM
ejpam-2101	32	39	2	2	NUM
ejpam-2101	32	40	∑	∑	PUNCT
ejpam-2101	32	41	i=0	i=0	PROPN
ejpam-2101	32	42	ai(s	ai(s	NUM
ejpam-2101	32	43	,	,	PUNCT
ejpam-2101	32	44	t)x	t)x	PUNCT
ejpam-2101	32	45	i	i	PROPN
ejpam-2101	32	46	=	=	SYM
ejpam-2101	32	47	a0	a0	PROPN
ejpam-2101	32	48	x0	x0	PROPN
ejpam-2101	33	1	+	+	CCONJ
ejpam-2101	33	2	a1	a1	NOUN
ejpam-2101	33	3	x1	x1	PROPN
ejpam-2101	33	4	+	+	PROPN
ejpam-2101	33	5	a2	a2	PROPN
ejpam-2101	33	6	x2	x2	PROPN
ejpam-2101	33	7	,	,	PUNCT
ejpam-2101	33	8	(	(	PUNCT
ejpam-2101	33	9	3	3	X
ejpam-2101	33	10	)	)	PUNCT
ejpam-2101	33	11	where	where	SCONJ
ejpam-2101	33	12	a0	a0	PROPN
ejpam-2101	33	13	,	,	PUNCT
ejpam-2101	33	14	a1	a1	PROPN
ejpam-2101	33	15	,	,	PUNCT
ejpam-2101	33	16	a2	a2	PROPN
ejpam-2101	33	17	are	be	AUX
ejpam-2101	33	18	homogeneous	homogeneous	ADJ
ejpam-2101	33	19	polynomials	polynomial	NOUN
ejpam-2101	33	20	in	in	ADP
ejpam-2101	33	21	s	s	PROPN
ejpam-2101	33	22	,	,	PUNCT
ejpam-2101	33	23	t	t	PROPN
ejpam-2101	33	24	of	of	ADP
ejpam-2101	33	25	the	the	DET
ejpam-2101	33	26	same	same	ADJ
ejpam-2101	33	27	degree	degree	NOUN
ejpam-2101	33	28	.	.	PUNCT
ejpam-2101	34	1	for	for	ADP
ejpam-2101	34	2	simplicity	simplicity	NOUN
ejpam-2101	34	3	,	,	PUNCT
ejpam-2101	34	4	sometimes	sometimes	ADV
ejpam-2101	34	5	we	we	PRON
ejpam-2101	34	6	write	write	VERB
ejpam-2101	34	7	a	a	DET
ejpam-2101	34	8	moving	move	VERB
ejpam-2101	34	9	plane	plane	NOUN
ejpam-2101	34	10	as	as	ADP
ejpam-2101	34	11	l	l	NOUN
ejpam-2101	34	12	=	=	SYM
ejpam-2101	34	13	(	(	PUNCT
ejpam-2101	34	14	a0	a0	PROPN
ejpam-2101	34	15	,	,	PUNCT
ejpam-2101	34	16	a1	a1	NOUN
ejpam-2101	34	17	,	,	PUNCT
ejpam-2101	34	18	a2	a2	PROPN
ejpam-2101	34	19	)	)	PUNCT
ejpam-2101	34	20	.	.	PUNCT
ejpam-2101	35	1	the	the	DET
ejpam-2101	35	2	moving	move	VERB
ejpam-2101	35	3	plane	plane	NOUN
ejpam-2101	35	4	(	(	PUNCT
ejpam-2101	35	5	3	3	X
ejpam-2101	35	6	)	)	PUNCT
ejpam-2101	35	7	follows	follow	VERB
ejpam-2101	35	8	the	the	DET
ejpam-2101	35	9	parametrization	parametrization	NOUN
ejpam-2101	35	10	(	(	PUNCT
ejpam-2101	35	11	1	1	X
ejpam-2101	35	12	)	)	PUNCT
ejpam-2101	35	13	if	if	SCONJ
ejpam-2101	35	14	l	l	NOUN
ejpam-2101	35	15	·	·	PUNCT
ejpam-2101	35	16	f=	f=	ADJ
ejpam-2101	35	17	2	2	NUM
ejpam-2101	35	18	∑	∑	ADP
ejpam-2101	35	19	i=0	i=0	PROPN
ejpam-2101	35	20	ai(s	ai(s	NUM
ejpam-2101	35	21	,	,	PUNCT
ejpam-2101	35	22	t	t	PROPN
ejpam-2101	35	23	)	)	PUNCT
ejpam-2101	35	24	fi(s	fi(s	NUM
ejpam-2101	35	25	,	,	PUNCT
ejpam-2101	35	26	t	t	PROPN
ejpam-2101	35	27	)	)	PUNCT
ejpam-2101	35	28	=	=	PROPN
ejpam-2101	35	29	a0	a0	PROPN
ejpam-2101	35	30	f0	f0	PROPN
ejpam-2101	35	31	+	+	CCONJ
ejpam-2101	35	32	a1	a1	NOUN
ejpam-2101	35	33	f1	f1	NOUN
ejpam-2101	35	34	+	+	CCONJ
ejpam-2101	35	35	a2	a2	PROPN
ejpam-2101	35	36	f2	f2	PROPN
ejpam-2101	35	37	≡	≡	PROPN
ejpam-2101	35	38	0	0	NUM
ejpam-2101	35	39	,	,	PUNCT
ejpam-2101	35	40	(	(	PUNCT
ejpam-2101	35	41	4	4	X
ejpam-2101	35	42	)	)	PUNCT
ejpam-2101	35	43	that	that	PRON
ejpam-2101	35	44	is	be	AUX
ejpam-2101	35	45	,	,	PUNCT
ejpam-2101	35	46	if	if	SCONJ
ejpam-2101	35	47	the	the	DET
ejpam-2101	35	48	point	point	NOUN
ejpam-2101	35	49	on	on	ADP
ejpam-2101	35	50	the	the	DET
ejpam-2101	35	51	curve	curve	NOUN
ejpam-2101	35	52	at	at	ADP
ejpam-2101	35	53	the	the	DET
ejpam-2101	35	54	parameter	parameter	NOUN
ejpam-2101	35	55	(	(	PUNCT
ejpam-2101	35	56	s	s	PROPN
ejpam-2101	35	57	,	,	PUNCT
ejpam-2101	35	58	t	t	PROPN
ejpam-2101	35	59	)	)	PUNCT
ejpam-2101	35	60	lies	lie	VERB
ejpam-2101	35	61	on	on	ADP
ejpam-2101	35	62	the	the	DET
ejpam-2101	35	63	plane	plane	NOUN
ejpam-2101	35	64	at	at	ADP
ejpam-2101	35	65	the	the	DET
ejpam-2101	35	66	parameter	parameter	NOUN
ejpam-2101	35	67	(	(	PUNCT
ejpam-2101	35	68	s	s	PROPN
ejpam-2101	35	69	,	,	PUNCT
ejpam-2101	35	70	t	t	PROPN
ejpam-2101	35	71	)	)	PUNCT
ejpam-2101	35	72	.	.	PUNCT
ejpam-2101	36	1	definition	definition	NOUN
ejpam-2101	36	2	1	1	NUM
ejpam-2101	36	3	.	.	X
ejpam-2101	37	1	two	two	NUM
ejpam-2101	37	2	moving	move	VERB
ejpam-2101	37	3	lines	line	NOUN
ejpam-2101	37	4	p(s	p(s	NOUN
ejpam-2101	37	5	,	,	PUNCT
ejpam-2101	37	6	t),q(s	t),q(s	NUM
ejpam-2101	37	7	,	,	PUNCT
ejpam-2101	37	8	t	t	PROPN
ejpam-2101	37	9	)	)	PUNCT
ejpam-2101	37	10	are	be	AUX
ejpam-2101	37	11	called	call	VERB
ejpam-2101	37	12	a	a	DET
ejpam-2101	37	13	µ-basis	µ-basis	NOUN
ejpam-2101	37	14	of	of	ADP
ejpam-2101	37	15	the	the	DET
ejpam-2101	37	16	rational	rational	ADJ
ejpam-2101	37	17	plane	plane	NOUN
ejpam-2101	37	18	curve	curve	NOUN
ejpam-2101	37	19	f(s	f(s	PROPN
ejpam-2101	37	20	,	,	PUNCT
ejpam-2101	37	21	t	t	PROPN
ejpam-2101	37	22	)	)	PUNCT
ejpam-2101	37	23	if	if	SCONJ
ejpam-2101	37	24	p	p	X
ejpam-2101	37	25	,	,	PUNCT
ejpam-2101	37	26	q	q	X
ejpam-2101	37	27	are	be	AUX
ejpam-2101	37	28	moving	move	VERB
ejpam-2101	37	29	lines	line	NOUN
ejpam-2101	37	30	that	that	PRON
ejpam-2101	37	31	follow	follow	VERB
ejpam-2101	37	32	f(s	f(s	PROPN
ejpam-2101	37	33	,	,	PUNCT
ejpam-2101	37	34	t	t	PROPN
ejpam-2101	37	35	)	)	PUNCT
ejpam-2101	37	36	and	and	CCONJ
ejpam-2101	37	37	satisfy	satisfy	VERB
ejpam-2101	37	38	the	the	DET
ejpam-2101	37	39	following	follow	VERB
ejpam-2101	37	40	two	two	NUM
ejpam-2101	37	41	conditions	condition	NOUN
ejpam-2101	37	42	:	:	PUNCT
ejpam-2101	38	1	1	1	X
ejpam-2101	38	2	.	.	PUNCT
ejpam-2101	39	1	[	[	X
ejpam-2101	39	2	p	p	X
ejpam-2101	39	3	,	,	PUNCT
ejpam-2101	39	4	q	q	X
ejpam-2101	39	5	]	]	X
ejpam-2101	39	6	=	=	X
ejpam-2101	39	7	κf(s	κf(s	X
ejpam-2101	39	8	,	,	PUNCT
ejpam-2101	39	9	t	t	PROPN
ejpam-2101	39	10	)	)	PUNCT
ejpam-2101	39	11	,	,	PUNCT
ejpam-2101	39	12	2	2	X
ejpam-2101	39	13	.	.	X
ejpam-2101	39	14	deg(p	deg(p	NUM
ejpam-2101	39	15	)	)	PUNCT
ejpam-2101	40	1	+	+	PUNCT
ejpam-2101	41	1	deg(q	deg(q	NOUN
ejpam-2101	41	2	)	)	PUNCT
ejpam-2101	41	3	)	)	PUNCT
ejpam-2101	42	1	=	=	SYM
ejpam-2101	42	2	deg(f	deg(f	PROPN
ejpam-2101	42	3	)	)	PUNCT
ejpam-2101	42	4	,	,	PUNCT
ejpam-2101	42	5	where	where	SCONJ
ejpam-2101	42	6	κ	κ	NOUN
ejpam-2101	42	7	is	be	AUX
ejpam-2101	42	8	some	some	DET
ejpam-2101	42	9	nonzero	nonzero	NOUN
ejpam-2101	42	10	constant	constant	ADJ
ejpam-2101	42	11	and	and	CCONJ
ejpam-2101	42	12	[	[	X
ejpam-2101	42	13	p	p	X
ejpam-2101	42	14	,	,	PUNCT
ejpam-2101	42	15	q	q	X
ejpam-2101	42	16	]	]	X
ejpam-2101	42	17	is	be	AUX
ejpam-2101	42	18	the	the	DET
ejpam-2101	42	19	outer	outer	ADJ
ejpam-2101	42	20	product	product	NOUN
ejpam-2101	42	21	of	of	ADP
ejpam-2101	42	22	p	p	PROPN
ejpam-2101	42	23	,	,	PUNCT
ejpam-2101	42	24	q.	q.	VERB
ejpam-2101	42	25	the	the	DET
ejpam-2101	42	26	notation	notation	NOUN
ejpam-2101	42	27	of	of	ADP
ejpam-2101	42	28	a	a	DET
ejpam-2101	42	29	µ-basis	µ-basis	NOUN
ejpam-2101	42	30	for	for	ADP
ejpam-2101	42	31	rational	rational	ADJ
ejpam-2101	42	32	space	space	NOUN
ejpam-2101	42	33	curves	curve	NOUN
ejpam-2101	42	34	can	can	AUX
ejpam-2101	42	35	be	be	AUX
ejpam-2101	42	36	generalized	generalize	VERB
ejpam-2101	42	37	in	in	ADP
ejpam-2101	42	38	an	an	DET
ejpam-2101	42	39	obvious	obvious	ADJ
ejpam-2101	42	40	way	way	NOUN
ejpam-2101	42	41	to	to	ADP
ejpam-2101	42	42	rational	rational	ADJ
ejpam-2101	42	43	curves	curve	NOUN
ejpam-2101	42	44	of	of	ADP
ejpam-2101	42	45	arbitrary	arbitrary	ADJ
ejpam-2101	42	46	dimension	dimension	NOUN
ejpam-2101	42	47	.	.	PUNCT
ejpam-2101	43	1	the	the	DET
ejpam-2101	43	2	existence	existence	NOUN
ejpam-2101	43	3	of	of	ADP
ejpam-2101	43	4	a	a	DET
ejpam-2101	43	5	µ-basis	µ-basis	NOUN
ejpam-2101	43	6	for	for	ADP
ejpam-2101	43	7	a	a	DET
ejpam-2101	43	8	rational	rational	ADJ
ejpam-2101	43	9	curve	curve	NOUN
ejpam-2101	43	10	in	in	ADP
ejpam-2101	43	11	any	any	DET
ejpam-2101	43	12	dimension	dimension	NOUN
ejpam-2101	43	13	follows	follow	VERB
ejpam-2101	43	14	directly	directly	ADV
ejpam-2101	43	15	from	from	ADP
ejpam-2101	43	16	the	the	DET
ejpam-2101	43	17	hilbert	hilbert	PROPN
ejpam-2101	43	18	-	-	PUNCT
ejpam-2101	43	19	burch	burch	PROPN
ejpam-2101	43	20	theorem	theorem	NOUN
ejpam-2101	43	21	[	[	PUNCT
ejpam-2101	43	22	theorem	theorem	ADJ
ejpam-2101	43	23	20.15	20.15	NUM
ejpam-2101	43	24	,	,	PUNCT
ejpam-2101	43	25	6	6	NUM
ejpam-2101	43	26	]	]	PUNCT
ejpam-2101	43	27	.	.	PUNCT
ejpam-2101	44	1	in	in	ADP
ejpam-2101	44	2	particular	particular	ADJ
ejpam-2101	44	3	,	,	PUNCT
ejpam-2101	44	4	m.	m.	NOUN
ejpam-2101	44	5	tesemma	tesemma	PROPN
ejpam-2101	44	6	,	,	PUNCT
ejpam-2101	44	7	h.	h.	PROPN
ejpam-2101	44	8	wang	wang	PROPN
ejpam-2101	44	9	,	,	PUNCT
ejpam-2101	44	10	/	/	SYM
ejpam-2101	44	11	eur	eur	NOUN
ejpam-2101	44	12	.	.	PUNCT
ejpam-2101	45	1	j.	j.	PROPN
ejpam-2101	45	2	pure	pure	PROPN
ejpam-2101	45	3	appl	appl	PROPN
ejpam-2101	45	4	.	.	PROPN
ejpam-2101	45	5	math	math	PROPN
ejpam-2101	45	6	,	,	PUNCT
ejpam-2101	45	7	7	7	NUM
ejpam-2101	45	8	(	(	PUNCT
ejpam-2101	45	9	2014	2014	NUM
ejpam-2101	45	10	)	)	PUNCT
ejpam-2101	45	11	,	,	PUNCT
ejpam-2101	45	12	191	191	NUM
ejpam-2101	45	13	-	-	SYM
ejpam-2101	45	14	200	200	NUM
ejpam-2101	45	15	193	193	NUM
ejpam-2101	45	16	the	the	DET
ejpam-2101	45	17	proof	proof	NOUN
ejpam-2101	45	18	of	of	ADP
ejpam-2101	45	19	the	the	DET
ejpam-2101	45	20	existence	existence	NOUN
ejpam-2101	45	21	of	of	ADP
ejpam-2101	45	22	a	a	DET
ejpam-2101	45	23	µ-basis	µ-basis	NOUN
ejpam-2101	45	24	for	for	ADP
ejpam-2101	45	25	a	a	DET
ejpam-2101	45	26	rational	rational	ADJ
ejpam-2101	45	27	curve	curve	NOUN
ejpam-2101	45	28	in	in	ADP
ejpam-2101	45	29	an	an	DET
ejpam-2101	45	30	affine	affine	NOUN
ejpam-2101	45	31	n	n	CCONJ
ejpam-2101	45	32	-	-	PUNCT
ejpam-2101	45	33	space	space	NOUN
ejpam-2101	45	34	is	be	AUX
ejpam-2101	45	35	given	give	VERB
ejpam-2101	45	36	in	in	ADP
ejpam-2101	45	37	[	[	PUNCT
ejpam-2101	45	38	exercise	exercise	NOUN
ejpam-2101	45	39	17	17	NUM
ejpam-2101	45	40	,	,	PUNCT
ejpam-2101	45	41	page	page	NOUN
ejpam-2101	45	42	286	286	NUM
ejpam-2101	45	43	,	,	PUNCT
ejpam-2101	45	44	4	4	NUM
ejpam-2101	45	45	]	]	PUNCT
ejpam-2101	45	46	.	.	PUNCT
ejpam-2101	46	1	an	an	DET
ejpam-2101	46	2	alternative	alternative	ADJ
ejpam-2101	46	3	existence	existence	NOUN
ejpam-2101	46	4	proof	proof	NOUN
ejpam-2101	46	5	as	as	ADV
ejpam-2101	46	6	well	well	ADV
ejpam-2101	46	7	as	as	ADP
ejpam-2101	46	8	a	a	DET
ejpam-2101	46	9	simple	simple	ADJ
ejpam-2101	46	10	algorithm	algorithm	NOUN
ejpam-2101	46	11	to	to	PART
ejpam-2101	46	12	compute	compute	VERB
ejpam-2101	46	13	a	a	DET
ejpam-2101	46	14	µ-basis	µ-basis	NOUN
ejpam-2101	46	15	based	base	VERB
ejpam-2101	46	16	solely	solely	ADV
ejpam-2101	46	17	on	on	ADP
ejpam-2101	46	18	gaussian	gaussian	ADJ
ejpam-2101	46	19	elimination	elimination	NOUN
ejpam-2101	46	20	is	be	AUX
ejpam-2101	46	21	presented	present	VERB
ejpam-2101	46	22	in	in	ADP
ejpam-2101	46	23	[	[	X
ejpam-2101	46	24	10	10	NUM
ejpam-2101	46	25	]	]	PUNCT
ejpam-2101	46	26	.	.	PUNCT
ejpam-2101	47	1	the	the	DET
ejpam-2101	47	2	µ-basis	µ-basis	NOUN
ejpam-2101	47	3	elements	element	NOUN
ejpam-2101	47	4	p	p	X
ejpam-2101	47	5	,	,	PUNCT
ejpam-2101	47	6	q	q	NOUN
ejpam-2101	47	7	for	for	ADP
ejpam-2101	47	8	a	a	DET
ejpam-2101	47	9	rational	rational	ADJ
ejpam-2101	47	10	plane	plane	NOUN
ejpam-2101	47	11	curve	curve	NOUN
ejpam-2101	47	12	are	be	AUX
ejpam-2101	47	13	not	not	PART
ejpam-2101	47	14	unique	unique	ADJ
ejpam-2101	47	15	.	.	PUNCT
ejpam-2101	48	1	but	but	CCONJ
ejpam-2101	48	2	the	the	DET
ejpam-2101	48	3	degrees	degree	NOUN
ejpam-2101	48	4	of	of	ADP
ejpam-2101	48	5	the	the	DET
ejpam-2101	48	6	µ-basis	µ-basis	NOUN
ejpam-2101	48	7	elements	element	NOUN
ejpam-2101	48	8	µ1	µ1	NOUN
ejpam-2101	48	9	=	=	SYM
ejpam-2101	48	10	deg(p	deg(p	PROPN
ejpam-2101	48	11	)	)	PUNCT
ejpam-2101	48	12	,	,	PUNCT
ejpam-2101	48	13	µ2	µ2	PROPN
ejpam-2101	48	14	=	=	SYM
ejpam-2101	48	15	deg(q	deg(q	PROPN
ejpam-2101	48	16	)	)	PUNCT
ejpam-2101	48	17	for	for	ADP
ejpam-2101	48	18	a	a	DET
ejpam-2101	48	19	rational	rational	ADJ
ejpam-2101	48	20	plane	plane	NOUN
ejpam-2101	48	21	curve	curve	NOUN
ejpam-2101	48	22	are	be	AUX
ejpam-2101	48	23	unique	unique	ADJ
ejpam-2101	48	24	.	.	PUNCT
ejpam-2101	49	1	songgoldman	songgoldman	VERB
ejpam-2101	50	1	[	[	X
ejpam-2101	50	2	10	10	NUM
ejpam-2101	50	3	]	]	PUNCT
ejpam-2101	50	4	proved	prove	VERB
ejpam-2101	50	5	this	this	DET
ejpam-2101	50	6	result	result	NOUN
ejpam-2101	50	7	and	and	CCONJ
ejpam-2101	50	8	the	the	DET
ejpam-2101	50	9	following	follow	VERB
ejpam-2101	50	10	proposition	proposition	NOUN
ejpam-2101	50	11	for	for	ADP
ejpam-2101	50	12	rational	rational	ADJ
ejpam-2101	50	13	space	space	NOUN
ejpam-2101	50	14	curves	curve	NOUN
ejpam-2101	50	15	.	.	PUNCT
ejpam-2101	51	1	for	for	ADP
ejpam-2101	51	2	the	the	DET
ejpam-2101	51	3	convenience	convenience	NOUN
ejpam-2101	51	4	of	of	ADP
ejpam-2101	51	5	the	the	DET
ejpam-2101	51	6	reader	reader	NOUN
ejpam-2101	51	7	,	,	PUNCT
ejpam-2101	51	8	we	we	PRON
ejpam-2101	51	9	will	will	AUX
ejpam-2101	51	10	focus	focus	VERB
ejpam-2101	51	11	our	our	PRON
ejpam-2101	51	12	attention	attention	NOUN
ejpam-2101	51	13	to	to	ADP
ejpam-2101	51	14	plane	plane	NOUN
ejpam-2101	51	15	curves	curve	NOUN
ejpam-2101	51	16	,	,	PUNCT
ejpam-2101	51	17	and	and	CCONJ
ejpam-2101	51	18	below	below	ADV
ejpam-2101	51	19	is	be	AUX
ejpam-2101	51	20	the	the	DET
ejpam-2101	51	21	statement	statement	NOUN
ejpam-2101	51	22	of	of	ADP
ejpam-2101	51	23	their	their	PRON
ejpam-2101	51	24	result	result	NOUN
ejpam-2101	51	25	for	for	ADP
ejpam-2101	51	26	plane	plane	NOUN
ejpam-2101	51	27	curves	curve	NOUN
ejpam-2101	51	28	.	.	PUNCT
ejpam-2101	52	1	proposition	proposition	NOUN
ejpam-2101	52	2	1	1	NUM
ejpam-2101	52	3	.	.	PUNCT
ejpam-2101	52	4	suppose	suppose	VERB
ejpam-2101	52	5	p(s	p(s	PROPN
ejpam-2101	52	6	,	,	PUNCT
ejpam-2101	52	7	t	t	PROPN
ejpam-2101	52	8	)	)	PUNCT
ejpam-2101	52	9	,	,	PUNCT
ejpam-2101	52	10	q(s	q(s	PROPN
ejpam-2101	52	11	,	,	PUNCT
ejpam-2101	52	12	t	t	PROPN
ejpam-2101	52	13	)	)	PUNCT
ejpam-2101	52	14	are	be	AUX
ejpam-2101	52	15	a	a	DET
ejpam-2101	52	16	µ-basis	µ-basis	NOUN
ejpam-2101	52	17	of	of	ADP
ejpam-2101	52	18	degrees	degree	NOUN
ejpam-2101	52	19	µ1,µ2	µ1,µ2	PROPN
ejpam-2101	52	20	for	for	ADP
ejpam-2101	52	21	the	the	DET
ejpam-2101	52	22	rational	rational	ADJ
ejpam-2101	52	23	plane	plane	NOUN
ejpam-2101	52	24	curve	curve	NOUN
ejpam-2101	52	25	f(s	f(s	PROPN
ejpam-2101	52	26	,	,	PUNCT
ejpam-2101	52	27	t	t	PROPN
ejpam-2101	52	28	)	)	PUNCT
ejpam-2101	52	29	and	and	CCONJ
ejpam-2101	52	30	let	let	VERB
ejpam-2101	52	31	l(s	l(s	PROPN
ejpam-2101	52	32	,	,	PUNCT
ejpam-2101	52	33	t	t	PROPN
ejpam-2101	52	34	)	)	PUNCT
ejpam-2101	52	35	be	be	AUX
ejpam-2101	52	36	a	a	DET
ejpam-2101	52	37	moving	move	VERB
ejpam-2101	52	38	curve	curve	NOUN
ejpam-2101	52	39	of	of	ADP
ejpam-2101	52	40	degree	degree	NOUN
ejpam-2101	52	41	m	m	NOUN
ejpam-2101	52	42	that	that	PRON
ejpam-2101	52	43	follows	follow	VERB
ejpam-2101	52	44	the	the	DET
ejpam-2101	52	45	curve	curve	NOUN
ejpam-2101	52	46	.	.	PUNCT
ejpam-2101	53	1	then	then	ADV
ejpam-2101	53	2	there	there	PRON
ejpam-2101	53	3	exist	exist	VERB
ejpam-2101	53	4	polynomials	polynomial	NOUN
ejpam-2101	53	5	α(s	α(s	PROPN
ejpam-2101	53	6	,	,	PUNCT
ejpam-2101	53	7	t	t	PROPN
ejpam-2101	53	8	)	)	PUNCT
ejpam-2101	53	9	,	,	PUNCT
ejpam-2101	53	10	β(s	β(s	PROPN
ejpam-2101	53	11	,	,	PUNCT
ejpam-2101	53	12	t	t	PROPN
ejpam-2101	53	13	)	)	PUNCT
ejpam-2101	53	14	such	such	ADJ
ejpam-2101	53	15	that	that	SCONJ
ejpam-2101	53	16	l=	l=	ADJ
ejpam-2101	53	17	αp+	αp+	NOUN
ejpam-2101	53	18	βq	βq	VERB
ejpam-2101	53	19	,	,	PUNCT
ejpam-2101	53	20	where	where	SCONJ
ejpam-2101	53	21	deg(α	deg(α	NOUN
ejpam-2101	53	22	)	)	PUNCT
ejpam-2101	53	23	=	=	SYM
ejpam-2101	53	24	m−µ1	m−µ1	NOUN
ejpam-2101	53	25	,	,	PUNCT
ejpam-2101	53	26	deg(β	deg(β	PROPN
ejpam-2101	53	27	)	)	PUNCT
ejpam-2101	53	28	=	=	SYM
ejpam-2101	53	29	m−µ2	m−µ2	NOUN
ejpam-2101	53	30	.	.	NOUN
ejpam-2101	54	1	3	3	X
ejpam-2101	54	2	.	.	X
ejpam-2101	54	3	comparison	comparison	NOUN
ejpam-2101	54	4	of	of	ADP
ejpam-2101	54	5	computational	computational	ADJ
ejpam-2101	54	6	methods	method	NOUN
ejpam-2101	54	7	in	in	ADP
ejpam-2101	54	8	this	this	DET
ejpam-2101	54	9	section	section	NOUN
ejpam-2101	54	10	,	,	PUNCT
ejpam-2101	54	11	we	we	PRON
ejpam-2101	54	12	will	will	AUX
ejpam-2101	54	13	introduce	introduce	VERB
ejpam-2101	54	14	three	three	NUM
ejpam-2101	54	15	different	different	ADJ
ejpam-2101	54	16	methods	method	NOUN
ejpam-2101	54	17	,	,	PUNCT
ejpam-2101	54	18	gcd	gcd	NOUN
ejpam-2101	54	19	method	method	NOUN
ejpam-2101	54	20	,	,	PUNCT
ejpam-2101	54	21	resultant	resultant	NOUN
ejpam-2101	54	22	matrix	matrix	NOUN
ejpam-2101	54	23	method	method	NOUN
ejpam-2101	54	24	,	,	PUNCT
ejpam-2101	54	25	and	and	CCONJ
ejpam-2101	54	26	smith	smith	PROPN
ejpam-2101	54	27	normal	normal	ADJ
ejpam-2101	54	28	form	form	NOUN
ejpam-2101	54	29	method	method	NOUN
ejpam-2101	54	30	,	,	PUNCT
ejpam-2101	54	31	to	to	PART
ejpam-2101	54	32	compute	compute	VERB
ejpam-2101	54	33	the	the	DET
ejpam-2101	54	34	intersection	intersection	NOUN
ejpam-2101	54	35	of	of	ADP
ejpam-2101	54	36	two	two	NUM
ejpam-2101	54	37	parametrized	parametrized	ADJ
ejpam-2101	54	38	curves	curve	NOUN
ejpam-2101	54	39	c1	c1	NOUN
ejpam-2101	54	40	and	and	CCONJ
ejpam-2101	54	41	c2	c2	PROPN
ejpam-2101	54	42	,	,	PUNCT
ejpam-2101	54	43	where	where	SCONJ
ejpam-2101	54	44	c1	c1	PROPN
ejpam-2101	54	45	and	and	CCONJ
ejpam-2101	54	46	c2	c2	PROPN
ejpam-2101	54	47	are	be	AUX
ejpam-2101	54	48	given	give	VERB
ejpam-2101	54	49	as	as	ADP
ejpam-2101	54	50	the	the	DET
ejpam-2101	54	51	image	image	NOUN
ejpam-2101	54	52	of	of	ADP
ejpam-2101	54	53	generic	generic	ADJ
ejpam-2101	54	54	one	one	NUM
ejpam-2101	54	55	-	-	PUNCT
ejpam-2101	54	56	to	to	ADP
ejpam-2101	54	57	-	-	PUNCT
ejpam-2101	54	58	one	one	NUM
ejpam-2101	54	59	rational	rational	ADJ
ejpam-2101	54	60	parametrizations	parametrization	NOUN
ejpam-2101	54	61	:	:	PUNCT
ejpam-2101	54	62	f(s	f(s	PROPN
ejpam-2101	54	63	,	,	PUNCT
ejpam-2101	54	64	t	t	PROPN
ejpam-2101	54	65	)	)	PUNCT
ejpam-2101	54	66	=	=	SYM
ejpam-2101	54	67	(	(	PUNCT
ejpam-2101	54	68	f0(s	f0(s	PROPN
ejpam-2101	54	69	,	,	PUNCT
ejpam-2101	54	70	t	t	PROPN
ejpam-2101	54	71	)	)	PUNCT
ejpam-2101	54	72	,	,	PUNCT
ejpam-2101	54	73	f1(s	f1(s	PROPN
ejpam-2101	54	74	,	,	PUNCT
ejpam-2101	54	75	t	t	PROPN
ejpam-2101	54	76	)	)	PUNCT
ejpam-2101	54	77	,	,	PUNCT
ejpam-2101	54	78	f2(s	f2(s	PROPN
ejpam-2101	54	79	,	,	PUNCT
ejpam-2101	54	80	t	t	PROPN
ejpam-2101	54	81	)	)	PUNCT
ejpam-2101	54	82	)	)	PUNCT
ejpam-2101	54	83	,	,	PUNCT
ejpam-2101	54	84	(	(	PUNCT
ejpam-2101	54	85	s	s	X
ejpam-2101	54	86	,	,	PUNCT
ejpam-2101	54	87	t	t	PROPN
ejpam-2101	54	88	)	)	PUNCT
ejpam-2101	54	89	6=	6=	ADP
ejpam-2101	55	1	(	(	PUNCT
ejpam-2101	55	2	0	0	NUM
ejpam-2101	55	3	,	,	PUNCT
ejpam-2101	55	4	0	0	NUM
ejpam-2101	55	5	)	)	PUNCT
ejpam-2101	55	6	,	,	PUNCT
ejpam-2101	55	7	and	and	CCONJ
ejpam-2101	55	8	g(u	g(u	PROPN
ejpam-2101	55	9	,	,	PUNCT
ejpam-2101	55	10	v	v	NOUN
ejpam-2101	55	11	)	)	PUNCT
ejpam-2101	55	12	=	=	SYM
ejpam-2101	55	13	(	(	PUNCT
ejpam-2101	55	14	g0(u	g0(u	ADP
ejpam-2101	55	15	,	,	PUNCT
ejpam-2101	55	16	v	v	NOUN
ejpam-2101	55	17	)	)	PUNCT
ejpam-2101	55	18	,	,	PUNCT
ejpam-2101	55	19	g1(u	g1(u	PROPN
ejpam-2101	55	20	,	,	PUNCT
ejpam-2101	55	21	v	v	NOUN
ejpam-2101	55	22	)	)	PUNCT
ejpam-2101	55	23	,	,	PUNCT
ejpam-2101	55	24	g2(u	g2(u	PROPN
ejpam-2101	55	25	,	,	PUNCT
ejpam-2101	55	26	v	v	NOUN
ejpam-2101	55	27	)	)	PUNCT
ejpam-2101	55	28	)	)	PUNCT
ejpam-2101	55	29	,	,	PUNCT
ejpam-2101	55	30	(	(	PUNCT
ejpam-2101	55	31	u	u	NOUN
ejpam-2101	55	32	,	,	PUNCT
ejpam-2101	55	33	v	v	NOUN
ejpam-2101	55	34	)	)	PUNCT
ejpam-2101	55	35	6=	6=	X
ejpam-2101	55	36	(	(	PUNCT
ejpam-2101	55	37	0	0	NUM
ejpam-2101	55	38	,	,	PUNCT
ejpam-2101	55	39	0	0	NUM
ejpam-2101	55	40	)	)	PUNCT
ejpam-2101	55	41	,	,	PUNCT
ejpam-2101	55	42	where	where	SCONJ
ejpam-2101	55	43	f0	f0	PROPN
ejpam-2101	55	44	,	,	PUNCT
ejpam-2101	55	45	f1	f1	NOUN
ejpam-2101	55	46	,	,	PUNCT
ejpam-2101	55	47	f2	f2	PROPN
ejpam-2101	55	48	(	(	PUNCT
ejpam-2101	55	49	respectively	respectively	ADV
ejpam-2101	55	50	,	,	PUNCT
ejpam-2101	55	51	g0	g0	PROPN
ejpam-2101	55	52	,	,	PUNCT
ejpam-2101	55	53	g1	g1	NOUN
ejpam-2101	55	54	,	,	PUNCT
ejpam-2101	55	55	g2	g2	PROPN
ejpam-2101	55	56	)	)	PUNCT
ejpam-2101	55	57	are	be	AUX
ejpam-2101	55	58	linearly	linearly	ADV
ejpam-2101	55	59	independent	independent	ADJ
ejpam-2101	55	60	homogeneous	homogeneous	ADJ
ejpam-2101	55	61	polynomials	polynomial	NOUN
ejpam-2101	55	62	of	of	ADP
ejpam-2101	55	63	the	the	DET
ejpam-2101	55	64	same	same	ADJ
ejpam-2101	55	65	degree	degree	NOUN
ejpam-2101	55	66	d	d	X
ejpam-2101	55	67	≥	≥	NUM
ejpam-2101	55	68	2	2	NUM
ejpam-2101	55	69	(	(	PUNCT
ejpam-2101	55	70	respectively	respectively	ADV
ejpam-2101	55	71	,	,	PUNCT
ejpam-2101	56	1	d	d	PROPN
ejpam-2101	56	2	′	′	NUM
ejpam-2101	56	3	≥	≥	NOUN
ejpam-2101	56	4	2	2	NUM
ejpam-2101	56	5	)	)	PUNCT
ejpam-2101	56	6	,	,	PUNCT
ejpam-2101	56	7	and	and	CCONJ
ejpam-2101	56	8	gcd	gcd	PROPN
ejpam-2101	56	9	(	(	PUNCT
ejpam-2101	56	10	f0	f0	PROPN
ejpam-2101	56	11	,	,	PUNCT
ejpam-2101	56	12	f1	f1	NOUN
ejpam-2101	56	13	,	,	PUNCT
ejpam-2101	56	14	f2	f2	PROPN
ejpam-2101	56	15	)	)	PUNCT
ejpam-2101	56	16	=	=	SYM
ejpam-2101	56	17	1	1	NUM
ejpam-2101	56	18	(	(	PUNCT
ejpam-2101	56	19	respectively	respectively	ADV
ejpam-2101	56	20	,	,	PUNCT
ejpam-2101	56	21	gcd(g0	gcd(g0	PROPN
ejpam-2101	56	22	,	,	PUNCT
ejpam-2101	56	23	g1	g1	NOUN
ejpam-2101	56	24	,	,	PUNCT
ejpam-2101	56	25	g2	g2	PROPN
ejpam-2101	56	26	)	)	PUNCT
ejpam-2101	56	27	=	=	SYM
ejpam-2101	56	28	1	1	NUM
ejpam-2101	56	29	)	)	PUNCT
ejpam-2101	56	30	.	.	PUNCT
ejpam-2101	57	1	these	these	DET
ejpam-2101	57	2	three	three	NUM
ejpam-2101	57	3	methods	method	NOUN
ejpam-2101	57	4	only	only	ADV
ejpam-2101	57	5	use	use	VERB
ejpam-2101	57	6	the	the	DET
ejpam-2101	57	7	parametrizations	parametrization	NOUN
ejpam-2101	57	8	of	of	ADP
ejpam-2101	57	9	the	the	DET
ejpam-2101	57	10	curves	curve	NOUN
ejpam-2101	57	11	without	without	ADP
ejpam-2101	57	12	computing	compute	VERB
ejpam-2101	57	13	the	the	DET
ejpam-2101	57	14	implicit	implicit	ADJ
ejpam-2101	57	15	equation	equation	NOUN
ejpam-2101	57	16	of	of	ADP
ejpam-2101	57	17	the	the	DET
ejpam-2101	57	18	curves	curve	NOUN
ejpam-2101	57	19	.	.	PUNCT
ejpam-2101	58	1	we	we	PRON
ejpam-2101	58	2	will	will	AUX
ejpam-2101	58	3	accomplish	accomplish	VERB
ejpam-2101	58	4	this	this	PRON
ejpam-2101	58	5	by	by	ADP
ejpam-2101	58	6	using	use	VERB
ejpam-2101	58	7	the	the	DET
ejpam-2101	58	8	µ-basis	µ-basis	NOUN
ejpam-2101	58	9	of	of	ADP
ejpam-2101	58	10	the	the	DET
ejpam-2101	58	11	syzygies	syzygy	NOUN
ejpam-2101	58	12	of	of	ADP
ejpam-2101	58	13	the	the	DET
ejpam-2101	58	14	curve	curve	NOUN
ejpam-2101	58	15	.	.	PUNCT
ejpam-2101	59	1	for	for	ADP
ejpam-2101	59	2	each	each	PRON
ejpam-2101	59	3	of	of	ADP
ejpam-2101	59	4	the	the	DET
ejpam-2101	59	5	method	method	NOUN
ejpam-2101	59	6	,	,	PUNCT
ejpam-2101	59	7	we	we	PRON
ejpam-2101	59	8	will	will	AUX
ejpam-2101	59	9	first	first	ADV
ejpam-2101	59	10	prove	prove	VERB
ejpam-2101	59	11	the	the	DET
ejpam-2101	59	12	validity	validity	NOUN
ejpam-2101	59	13	of	of	ADP
ejpam-2101	59	14	the	the	DET
ejpam-2101	59	15	method	method	NOUN
ejpam-2101	59	16	,	,	PUNCT
ejpam-2101	59	17	and	and	CCONJ
ejpam-2101	59	18	then	then	ADV
ejpam-2101	59	19	provide	provide	VERB
ejpam-2101	59	20	the	the	DET
ejpam-2101	59	21	computational	computational	ADJ
ejpam-2101	59	22	algorithm	algorithm	NOUN
ejpam-2101	59	23	for	for	ADP
ejpam-2101	59	24	each	each	PRON
ejpam-2101	59	25	of	of	ADP
ejpam-2101	59	26	the	the	DET
ejpam-2101	59	27	method	method	NOUN
ejpam-2101	59	28	.	.	PUNCT
ejpam-2101	60	1	3.1	3.1	NUM
ejpam-2101	60	2	.	.	PUNCT
ejpam-2101	60	3	gcd	gcd	PROPN
ejpam-2101	60	4	method	method	NOUN
ejpam-2101	60	5	first	first	ADV
ejpam-2101	60	6	,	,	PUNCT
ejpam-2101	60	7	we	we	PRON
ejpam-2101	60	8	will	will	AUX
ejpam-2101	60	9	study	study	VERB
ejpam-2101	60	10	the	the	DET
ejpam-2101	60	11	gcd	gcd	NOUN
ejpam-2101	60	12	method	method	NOUN
ejpam-2101	60	13	.	.	PUNCT
ejpam-2101	61	1	theorem	theorem	NOUN
ejpam-2101	61	2	1	1	NUM
ejpam-2101	61	3	.	.	PUNCT
ejpam-2101	61	4	with	with	ADP
ejpam-2101	61	5	about	about	ADP
ejpam-2101	61	6	notation	notation	NOUN
ejpam-2101	61	7	,	,	PUNCT
ejpam-2101	61	8	if	if	SCONJ
ejpam-2101	61	9	p(s	p(s	PROPN
ejpam-2101	61	10	,	,	PUNCT
ejpam-2101	61	11	t	t	PROPN
ejpam-2101	61	12	)	)	PUNCT
ejpam-2101	61	13	and	and	CCONJ
ejpam-2101	61	14	p(s	p(s	PROPN
ejpam-2101	61	15	,	,	PUNCT
ejpam-2101	61	16	t	t	PROPN
ejpam-2101	61	17	)	)	PUNCT
ejpam-2101	61	18	are	be	AUX
ejpam-2101	61	19	the	the	DET
ejpam-2101	61	20	µ-basis	µ-basis	NOUN
ejpam-2101	61	21	for	for	ADP
ejpam-2101	61	22	the	the	DET
ejpam-2101	61	23	rational	rational	ADJ
ejpam-2101	61	24	plan	plan	NOUN
ejpam-2101	61	25	curve	curve	NOUN
ejpam-2101	61	26	f(s	f(s	PROPN
ejpam-2101	61	27	,	,	PUNCT
ejpam-2101	61	28	t	t	PROPN
ejpam-2101	61	29	)	)	PUNCT
ejpam-2101	61	30	,	,	PUNCT
ejpam-2101	61	31	then	then	ADV
ejpam-2101	61	32	{	{	PUNCT
ejpam-2101	61	33	(	(	PUNCT
ejpam-2101	61	34	u0	u0	PROPN
ejpam-2101	61	35	,	,	PUNCT
ejpam-2101	61	36	v0	v0	PROPN
ejpam-2101	61	37	)	)	PUNCT
ejpam-2101	62	1	6=	6=	ADP
ejpam-2101	62	2	(	(	PUNCT
ejpam-2101	62	3	0,0	0,0	NOUN
ejpam-2101	62	4	)	)	PUNCT
ejpam-2101	62	5	|	|	ADV
ejpam-2101	62	6	p(s	p(s	NOUN
ejpam-2101	62	7	,	,	PUNCT
ejpam-2101	62	8	t	t	PROPN
ejpam-2101	62	9	)	)	PUNCT
ejpam-2101	62	10	·	·	PUNCT
ejpam-2101	62	11	g(u0	g(u0	NOUN
ejpam-2101	62	12	,	,	PUNCT
ejpam-2101	62	13	v0	v0	NOUN
ejpam-2101	62	14	)	)	PUNCT
ejpam-2101	62	15	=	=	SYM
ejpam-2101	63	1	q(s	q(s	PROPN
ejpam-2101	63	2	,	,	PUNCT
ejpam-2101	63	3	t	t	PROPN
ejpam-2101	63	4	)	)	PUNCT
ejpam-2101	63	5	·	·	PUNCT
ejpam-2101	63	6	g(u0	g(u0	NOUN
ejpam-2101	63	7	,	,	PUNCT
ejpam-2101	63	8	v0	v0	NOUN
ejpam-2101	63	9	)	)	PUNCT
ejpam-2101	63	10	=	=	SYM
ejpam-2101	63	11	0	0	X
ejpam-2101	63	12	}	}	PUNCT
ejpam-2101	63	13	=	=	SYM
ejpam-2101	63	14	{	{	PUNCT
ejpam-2101	63	15	(	(	PUNCT
ejpam-2101	63	16	u0	u0	PROPN
ejpam-2101	63	17	,	,	PUNCT
ejpam-2101	63	18	v0	v0	PROPN
ejpam-2101	63	19	)	)	PUNCT
ejpam-2101	63	20	6=	6=	ADP
ejpam-2101	63	21	(	(	PUNCT
ejpam-2101	63	22	0,0	0,0	NOUN
ejpam-2101	63	23	)	)	PUNCT
ejpam-2101	63	24	|	|	ADV
ejpam-2101	63	25	gcd(ress(p(s	gcd(ress(p(s	VERB
ejpam-2101	63	26	,	,	PUNCT
ejpam-2101	63	27	t	t	PROPN
ejpam-2101	63	28	)	)	PUNCT
ejpam-2101	63	29	·	·	PUNCT
ejpam-2101	63	30	g(u0	g(u0	NOUN
ejpam-2101	63	31	,	,	PUNCT
ejpam-2101	63	32	v0),q(s	v0),q(s	PROPN
ejpam-2101	63	33	,	,	PUNCT
ejpam-2101	63	34	t	t	PROPN
ejpam-2101	63	35	)	)	PUNCT
ejpam-2101	63	36	·	·	PUNCT
ejpam-2101	63	37	g(u0	g(u0	NOUN
ejpam-2101	63	38	,	,	PUNCT
ejpam-2101	63	39	v0	v0	NOUN
ejpam-2101	63	40	)	)	PUNCT
ejpam-2101	63	41	)	)	PUNCT
ejpam-2101	63	42	,	,	PUNCT
ejpam-2101	63	43	rest(p(s	rest(p(s	PROPN
ejpam-2101	63	44	,	,	PUNCT
ejpam-2101	63	45	t	t	PROPN
ejpam-2101	63	46	)	)	PUNCT
ejpam-2101	63	47	·	·	PUNCT
ejpam-2101	63	48	g(u0	g(u0	NOUN
ejpam-2101	63	49	,	,	PUNCT
ejpam-2101	63	50	v0),q(s	v0),q(s	PROPN
ejpam-2101	63	51	,	,	PUNCT
ejpam-2101	63	52	t	t	PROPN
ejpam-2101	63	53	)	)	PUNCT
ejpam-2101	63	54	·	·	PUNCT
ejpam-2101	63	55	g(u0	g(u0	NOUN
ejpam-2101	63	56	,	,	PUNCT
ejpam-2101	63	57	v0	v0	NOUN
ejpam-2101	63	58	)	)	PUNCT
ejpam-2101	63	59	)	)	PUNCT
ejpam-2101	63	60	)	)	PUNCT
ejpam-2101	64	1	=	=	PUNCT
ejpam-2101	64	2	0	0	NUM
ejpam-2101	64	3	}	}	PUNCT
ejpam-2101	64	4	⇔g(u0	⇔g(u0	PROPN
ejpam-2101	64	5	,	,	PUNCT
ejpam-2101	64	6	v0	v0	NOUN
ejpam-2101	64	7	)	)	PUNCT
ejpam-2101	64	8	∈	∈	PROPN
ejpam-2101	64	9	c1	c1	PROPN
ejpam-2101	64	10	∩c2	∩c2	PROPN
ejpam-2101	64	11	.	.	PROPN
ejpam-2101	65	1	m.	m.	PROPN
ejpam-2101	65	2	tesemma	tesemma	PROPN
ejpam-2101	65	3	,	,	PUNCT
ejpam-2101	65	4	h.	h.	PROPN
ejpam-2101	65	5	wang	wang	PROPN
ejpam-2101	65	6	,	,	PUNCT
ejpam-2101	65	7	/	/	SYM
ejpam-2101	65	8	eur	eur	NOUN
ejpam-2101	65	9	.	.	PUNCT
ejpam-2101	66	1	j.	j.	PROPN
ejpam-2101	66	2	pure	pure	PROPN
ejpam-2101	66	3	appl	appl	PROPN
ejpam-2101	66	4	.	.	PROPN
ejpam-2101	66	5	math	math	PROPN
ejpam-2101	66	6	,	,	PUNCT
ejpam-2101	66	7	7	7	NUM
ejpam-2101	66	8	(	(	PUNCT
ejpam-2101	66	9	2014	2014	NUM
ejpam-2101	66	10	)	)	PUNCT
ejpam-2101	66	11	,	,	PUNCT
ejpam-2101	66	12	191	191	NUM
ejpam-2101	66	13	-	-	SYM
ejpam-2101	66	14	200	200	NUM
ejpam-2101	66	15	194	194	NUM
ejpam-2101	66	16	proof	proof	NOUN
ejpam-2101	66	17	.	.	PUNCT
ejpam-2101	67	1	first	first	ADV
ejpam-2101	67	2	,	,	PUNCT
ejpam-2101	67	3	we	we	PRON
ejpam-2101	67	4	will	will	AUX
ejpam-2101	67	5	show	show	VERB
ejpam-2101	67	6	that	that	SCONJ
ejpam-2101	67	7	{	{	PUNCT
ejpam-2101	67	8	(	(	PUNCT
ejpam-2101	67	9	u0	u0	PROPN
ejpam-2101	67	10	,	,	PUNCT
ejpam-2101	67	11	v0	v0	PROPN
ejpam-2101	67	12	)	)	PUNCT
ejpam-2101	67	13	6=	6=	ADP
ejpam-2101	67	14	(	(	PUNCT
ejpam-2101	67	15	0,0	0,0	NOUN
ejpam-2101	67	16	)	)	PUNCT
ejpam-2101	67	17	|	|	ADV
ejpam-2101	67	18	p(s	p(s	NOUN
ejpam-2101	67	19	,	,	PUNCT
ejpam-2101	67	20	t	t	PROPN
ejpam-2101	67	21	)	)	PUNCT
ejpam-2101	67	22	·	·	PUNCT
ejpam-2101	67	23	g(u0	g(u0	NOUN
ejpam-2101	67	24	,	,	PUNCT
ejpam-2101	67	25	v0	v0	NOUN
ejpam-2101	67	26	)	)	PUNCT
ejpam-2101	67	27	=	=	SYM
ejpam-2101	68	1	q(s	q(s	PROPN
ejpam-2101	68	2	,	,	PUNCT
ejpam-2101	68	3	t	t	PROPN
ejpam-2101	68	4	)	)	PUNCT
ejpam-2101	68	5	·	·	PUNCT
ejpam-2101	68	6	g(u0	g(u0	NOUN
ejpam-2101	68	7	,	,	PUNCT
ejpam-2101	68	8	v0	v0	NOUN
ejpam-2101	68	9	)	)	PUNCT
ejpam-2101	68	10	=	=	SYM
ejpam-2101	68	11	0	0	X
ejpam-2101	68	12	}	}	PUNCT
ejpam-2101	68	13	⇔	⇔	PROPN
ejpam-2101	68	14	g(u0	g(u0	NOUN
ejpam-2101	68	15	,	,	PUNCT
ejpam-2101	68	16	v0	v0	PROPN
ejpam-2101	68	17	)	)	PUNCT
ejpam-2101	68	18	∈	∈	PROPN
ejpam-2101	68	19	c1	c1	PROPN
ejpam-2101	68	20	∩c2	∩c2	PROPN
ejpam-2101	68	21	.	.	PUNCT
ejpam-2101	69	1	to	to	PART
ejpam-2101	69	2	do	do	VERB
ejpam-2101	69	3	so	so	ADV
ejpam-2101	69	4	,	,	PUNCT
ejpam-2101	69	5	we	we	PRON
ejpam-2101	69	6	let	let	VERB
ejpam-2101	69	7	(	(	PUNCT
ejpam-2101	69	8	u0	u0	ADJ
ejpam-2101	69	9	,	,	PUNCT
ejpam-2101	69	10	v0	v0	PROPN
ejpam-2101	69	11	)	)	PUNCT
ejpam-2101	69	12	6=	6=	ADP
ejpam-2101	70	1	(	(	PUNCT
ejpam-2101	70	2	0	0	NUM
ejpam-2101	70	3	,	,	PUNCT
ejpam-2101	70	4	0	0	NUM
ejpam-2101	70	5	)	)	PUNCT
ejpam-2101	70	6	be	be	AUX
ejpam-2101	70	7	such	such	ADJ
ejpam-2101	70	8	that	that	SCONJ
ejpam-2101	70	9	p(s	p(s	NOUN
ejpam-2101	70	10	,	,	PUNCT
ejpam-2101	70	11	t	t	PROPN
ejpam-2101	70	12	)	)	PUNCT
ejpam-2101	70	13	·	·	PUNCT
ejpam-2101	70	14	g(u0	g(u0	NOUN
ejpam-2101	70	15	,	,	PUNCT
ejpam-2101	70	16	v0	v0	NOUN
ejpam-2101	70	17	)	)	PUNCT
ejpam-2101	70	18	=	=	SYM
ejpam-2101	71	1	q(s	q(s	PROPN
ejpam-2101	71	2	,	,	PUNCT
ejpam-2101	71	3	t	t	PROPN
ejpam-2101	71	4	)	)	PUNCT
ejpam-2101	71	5	·	·	PUNCT
ejpam-2101	71	6	g(u0	g(u0	NOUN
ejpam-2101	71	7	,	,	PUNCT
ejpam-2101	71	8	v0	v0	PROPN
ejpam-2101	71	9	)	)	PUNCT
ejpam-2101	71	10	=	=	SYM
ejpam-2101	72	1	0	0	X
ejpam-2101	72	2	.	.	PUNCT
ejpam-2101	73	1	this	this	PRON
ejpam-2101	73	2	means	mean	VERB
ejpam-2101	73	3	that	that	SCONJ
ejpam-2101	73	4	g(u0	g(u0	NOUN
ejpam-2101	73	5	,	,	PUNCT
ejpam-2101	73	6	v0	v0	PROPN
ejpam-2101	73	7	)	)	PUNCT
ejpam-2101	73	8	‖	‖	PROPN
ejpam-2101	74	1	[	[	X
ejpam-2101	74	2	p(s	p(s	NUM
ejpam-2101	74	3	,	,	PUNCT
ejpam-2101	74	4	t	t	PROPN
ejpam-2101	74	5	)	)	PUNCT
ejpam-2101	74	6	q(s	q(s	PROPN
ejpam-2101	74	7	,	,	PUNCT
ejpam-2101	74	8	t	t	PROPN
ejpam-2101	74	9	)	)	PUNCT
ejpam-2101	74	10	]	]	PUNCT
ejpam-2101	74	11	.	.	PUNCT
ejpam-2101	75	1	hence	hence	ADV
ejpam-2101	75	2	,	,	PUNCT
ejpam-2101	75	3	g(u0	g(u0	NOUN
ejpam-2101	75	4	,	,	PUNCT
ejpam-2101	75	5	v0	v0	PROPN
ejpam-2101	75	6	)	)	PUNCT
ejpam-2101	75	7	=	=	SYM
ejpam-2101	76	1	kf(s	kf(s	X
ejpam-2101	76	2	,	,	PUNCT
ejpam-2101	76	3	t	t	PROPN
ejpam-2101	76	4	)	)	PUNCT
ejpam-2101	76	5	,	,	PUNCT
ejpam-2101	76	6	and	and	CCONJ
ejpam-2101	76	7	g(u0	g(u0	NOUN
ejpam-2101	76	8	,	,	PUNCT
ejpam-2101	76	9	v0	v0	PROPN
ejpam-2101	76	10	)	)	PUNCT
ejpam-2101	76	11	∈	∈	PROPN
ejpam-2101	76	12	c1	c1	PROPN
ejpam-2101	76	13	∩c2	∩c2	PROPN
ejpam-2101	76	14	.	.	PUNCT
ejpam-2101	77	1	on	on	ADP
ejpam-2101	77	2	the	the	DET
ejpam-2101	77	3	other	other	ADJ
ejpam-2101	77	4	hand	hand	NOUN
ejpam-2101	77	5	,	,	PUNCT
ejpam-2101	77	6	if	if	SCONJ
ejpam-2101	77	7	g(u0	g(u0	NOUN
ejpam-2101	77	8	,	,	PUNCT
ejpam-2101	77	9	v0	v0	PROPN
ejpam-2101	77	10	)	)	PUNCT
ejpam-2101	77	11	∈	∈	PROPN
ejpam-2101	77	12	c1	c1	PROPN
ejpam-2101	77	13	∩c2	∩c2	PROPN
ejpam-2101	77	14	,	,	PUNCT
ejpam-2101	77	15	then	then	ADV
ejpam-2101	77	16	g(u0	g(u0	NOUN
ejpam-2101	77	17	,	,	PUNCT
ejpam-2101	77	18	v0	v0	PROPN
ejpam-2101	77	19	)	)	PUNCT
ejpam-2101	77	20	=	=	SYM
ejpam-2101	77	21	f(s0	f(s0	X
ejpam-2101	77	22	,	,	PUNCT
ejpam-2101	77	23	t0	t0	PROPN
ejpam-2101	77	24	)	)	PUNCT
ejpam-2101	77	25	for	for	ADP
ejpam-2101	77	26	some	some	PRON
ejpam-2101	77	27	(	(	PUNCT
ejpam-2101	77	28	s0	s0	PROPN
ejpam-2101	77	29	,	,	PUNCT
ejpam-2101	77	30	t0	t0	PROPN
ejpam-2101	77	31	)	)	PUNCT
ejpam-2101	77	32	6=	6=	ADP
ejpam-2101	77	33	(	(	PUNCT
ejpam-2101	77	34	0,0	0,0	NOUN
ejpam-2101	77	35	)	)	PUNCT
ejpam-2101	77	36	.	.	PUNCT
ejpam-2101	78	1	thus	thus	ADV
ejpam-2101	78	2	,	,	PUNCT
ejpam-2101	78	3	definition	definition	NOUN
ejpam-2101	78	4	1	1	NUM
ejpam-2101	78	5	yields	yield	NOUN
ejpam-2101	78	6	that	that	PRON
ejpam-2101	78	7	p(s	p(s	NOUN
ejpam-2101	78	8	,	,	PUNCT
ejpam-2101	78	9	t	t	PROPN
ejpam-2101	78	10	)	)	PUNCT
ejpam-2101	78	11	·	·	PUNCT
ejpam-2101	78	12	g(u0	g(u0	NOUN
ejpam-2101	78	13	,	,	PUNCT
ejpam-2101	78	14	v0	v0	NOUN
ejpam-2101	78	15	)	)	PUNCT
ejpam-2101	78	16	=	=	SYM
ejpam-2101	79	1	q(s	q(s	PROPN
ejpam-2101	79	2	,	,	PUNCT
ejpam-2101	79	3	t	t	PROPN
ejpam-2101	79	4	)	)	PUNCT
ejpam-2101	79	5	·	·	PUNCT
ejpam-2101	79	6	g(u0	g(u0	NOUN
ejpam-2101	79	7	,	,	PUNCT
ejpam-2101	79	8	v0	v0	NOUN
ejpam-2101	79	9	)	)	PUNCT
ejpam-2101	79	10	=	=	SYM
ejpam-2101	80	1	0	0	X
ejpam-2101	80	2	.	.	PUNCT
ejpam-2101	81	1	therefore	therefore	ADV
ejpam-2101	81	2	,	,	PUNCT
ejpam-2101	81	3	the	the	DET
ejpam-2101	81	4	claim	claim	NOUN
ejpam-2101	81	5	is	be	AUX
ejpam-2101	81	6	proved	prove	VERB
ejpam-2101	81	7	.	.	PUNCT
ejpam-2101	82	1	now	now	ADV
ejpam-2101	82	2	,	,	PUNCT
ejpam-2101	82	3	we	we	PRON
ejpam-2101	82	4	will	will	AUX
ejpam-2101	82	5	show	show	VERB
ejpam-2101	82	6	that	that	SCONJ
ejpam-2101	82	7	{	{	PUNCT
ejpam-2101	82	8	(	(	PUNCT
ejpam-2101	82	9	u0	u0	PROPN
ejpam-2101	82	10	,	,	PUNCT
ejpam-2101	82	11	v0	v0	PROPN
ejpam-2101	82	12	)	)	PUNCT
ejpam-2101	82	13	6=	6=	ADP
ejpam-2101	82	14	(	(	PUNCT
ejpam-2101	82	15	0,0	0,0	NOUN
ejpam-2101	82	16	)	)	PUNCT
ejpam-2101	82	17	|	|	ADV
ejpam-2101	82	18	p(s	p(s	NOUN
ejpam-2101	82	19	,	,	PUNCT
ejpam-2101	82	20	t	t	PROPN
ejpam-2101	82	21	)	)	PUNCT
ejpam-2101	82	22	·	·	PUNCT
ejpam-2101	82	23	g(u0	g(u0	NOUN
ejpam-2101	82	24	,	,	PUNCT
ejpam-2101	82	25	v0	v0	NOUN
ejpam-2101	82	26	)	)	PUNCT
ejpam-2101	82	27	=	=	SYM
ejpam-2101	83	1	q(s	q(s	PROPN
ejpam-2101	83	2	,	,	PUNCT
ejpam-2101	83	3	t	t	PROPN
ejpam-2101	83	4	)	)	PUNCT
ejpam-2101	83	5	·	·	PUNCT
ejpam-2101	83	6	g(u0	g(u0	NOUN
ejpam-2101	83	7	,	,	PUNCT
ejpam-2101	83	8	v0	v0	NOUN
ejpam-2101	83	9	)	)	PUNCT
ejpam-2101	83	10	=	=	SYM
ejpam-2101	83	11	0	0	X
ejpam-2101	83	12	}	}	PUNCT
ejpam-2101	83	13	=	=	SYM
ejpam-2101	83	14	{	{	PUNCT
ejpam-2101	83	15	(	(	PUNCT
ejpam-2101	83	16	u0	u0	PROPN
ejpam-2101	83	17	,	,	PUNCT
ejpam-2101	83	18	v0	v0	PROPN
ejpam-2101	83	19	)	)	PUNCT
ejpam-2101	83	20	6=	6=	ADP
ejpam-2101	83	21	(	(	PUNCT
ejpam-2101	83	22	0,0	0,0	NOUN
ejpam-2101	83	23	)	)	PUNCT
ejpam-2101	83	24	|	|	ADV
ejpam-2101	83	25	gcd(ress(p(s	gcd(ress(p(s	VERB
ejpam-2101	83	26	,	,	PUNCT
ejpam-2101	83	27	t	t	PROPN
ejpam-2101	83	28	)	)	PUNCT
ejpam-2101	83	29	·	·	PUNCT
ejpam-2101	83	30	g(u0	g(u0	NOUN
ejpam-2101	83	31	,	,	PUNCT
ejpam-2101	83	32	v0),q(s	v0),q(s	PROPN
ejpam-2101	83	33	,	,	PUNCT
ejpam-2101	83	34	t	t	PROPN
ejpam-2101	83	35	)	)	PUNCT
ejpam-2101	83	36	·	·	PUNCT
ejpam-2101	83	37	g(u0	g(u0	NOUN
ejpam-2101	83	38	,	,	PUNCT
ejpam-2101	83	39	v0	v0	NOUN
ejpam-2101	83	40	)	)	PUNCT
ejpam-2101	83	41	)	)	PUNCT
ejpam-2101	83	42	,	,	PUNCT
ejpam-2101	83	43	rest(p(s	rest(p(s	PROPN
ejpam-2101	83	44	,	,	PUNCT
ejpam-2101	83	45	t	t	PROPN
ejpam-2101	83	46	)	)	PUNCT
ejpam-2101	83	47	·	·	PUNCT
ejpam-2101	83	48	g(u0	g(u0	NOUN
ejpam-2101	83	49	,	,	PUNCT
ejpam-2101	83	50	v0),q(s	v0),q(s	PROPN
ejpam-2101	83	51	,	,	PUNCT
ejpam-2101	83	52	t	t	PROPN
ejpam-2101	83	53	)	)	PUNCT
ejpam-2101	83	54	·	·	PUNCT
ejpam-2101	83	55	g(u0	g(u0	NOUN
ejpam-2101	83	56	,	,	PUNCT
ejpam-2101	83	57	v0	v0	NOUN
ejpam-2101	83	58	)	)	PUNCT
ejpam-2101	83	59	)	)	PUNCT
ejpam-2101	83	60	)	)	PUNCT
ejpam-2101	84	1	=	=	PUNCT
ejpam-2101	84	2	0	0	NUM
ejpam-2101	84	3	}	}	PUNCT
ejpam-2101	84	4	.	.	PUNCT
ejpam-2101	85	1	let	let	VERB
ejpam-2101	85	2	gp	gp	NOUN
ejpam-2101	85	3	=	=	VERB
ejpam-2101	85	4	p(s	p(s	PROPN
ejpam-2101	85	5	,	,	PUNCT
ejpam-2101	85	6	t	t	PROPN
ejpam-2101	85	7	)	)	PUNCT
ejpam-2101	85	8	·	·	PUNCT
ejpam-2101	85	9	g(u	g(u	X
ejpam-2101	85	10	,	,	PUNCT
ejpam-2101	85	11	v	v	NOUN
ejpam-2101	85	12	)	)	PUNCT
ejpam-2101	85	13	and	and	CCONJ
ejpam-2101	85	14	gq	gq	NOUN
ejpam-2101	85	15	=	=	SYM
ejpam-2101	85	16	q(s	q(s	PROPN
ejpam-2101	85	17	,	,	PUNCT
ejpam-2101	85	18	t	t	PROPN
ejpam-2101	85	19	)	)	PUNCT
ejpam-2101	85	20	·	·	PUNCT
ejpam-2101	85	21	g(u	g(u	X
ejpam-2101	85	22	,	,	PUNCT
ejpam-2101	85	23	v	v	NOUN
ejpam-2101	85	24	)	)	PUNCT
ejpam-2101	85	25	be	be	AUX
ejpam-2101	85	26	polynomials	polynomial	NOUN
ejpam-2101	85	27	in	in	ADP
ejpam-2101	85	28	variables	variable	NOUN
ejpam-2101	85	29	s	s	PROPN
ejpam-2101	85	30	,	,	PUNCT
ejpam-2101	85	31	t	t	PROPN
ejpam-2101	85	32	,	,	PUNCT
ejpam-2101	85	33	u	u	NOUN
ejpam-2101	85	34	,	,	PUNCT
ejpam-2101	86	1	v.	v.	CCONJ
ejpam-2101	86	2	then	then	ADV
ejpam-2101	86	3	f	f	PROPN
ejpam-2101	86	4	=	=	SYM
ejpam-2101	86	5	ress(gp	ress(gp	PROPN
ejpam-2101	86	6	,	,	PUNCT
ejpam-2101	86	7	gq	gq	PROPN
ejpam-2101	86	8	)	)	PUNCT
ejpam-2101	86	9	is	be	AUX
ejpam-2101	86	10	a	a	DET
ejpam-2101	86	11	polynomial	polynomial	NOUN
ejpam-2101	86	12	in	in	ADP
ejpam-2101	86	13	t	t	PROPN
ejpam-2101	86	14	,	,	PUNCT
ejpam-2101	86	15	u	u	NOUN
ejpam-2101	86	16	,	,	PUNCT
ejpam-2101	86	17	v	v	NOUN
ejpam-2101	86	18	and	and	CCONJ
ejpam-2101	86	19	g	g	NOUN
ejpam-2101	86	20	=	=	PUNCT
ejpam-2101	86	21	rest(gp	rest(gp	PROPN
ejpam-2101	86	22	,	,	PUNCT
ejpam-2101	86	23	gq	gq	PROPN
ejpam-2101	86	24	)	)	PUNCT
ejpam-2101	86	25	is	be	AUX
ejpam-2101	86	26	a	a	DET
ejpam-2101	86	27	polynomial	polynomial	NOUN
ejpam-2101	86	28	in	in	ADP
ejpam-2101	86	29	s	s	PROPN
ejpam-2101	86	30	,	,	PUNCT
ejpam-2101	86	31	u	u	NOUN
ejpam-2101	86	32	,	,	PUNCT
ejpam-2101	87	1	v.	v.	CCONJ
ejpam-2101	87	2	moreover	moreover	ADV
ejpam-2101	87	3	,	,	PUNCT
ejpam-2101	87	4	gcd	gcd	PROPN
ejpam-2101	87	5	(	(	PUNCT
ejpam-2101	87	6	f	f	PROPN
ejpam-2101	87	7	,	,	PUNCT
ejpam-2101	87	8	g	g	PROPN
ejpam-2101	87	9	)	)	PUNCT
ejpam-2101	87	10	is	be	AUX
ejpam-2101	87	11	a	a	DET
ejpam-2101	87	12	polynomial	polynomial	NOUN
ejpam-2101	87	13	in	in	ADP
ejpam-2101	87	14	u	u	PROPN
ejpam-2101	87	15	,	,	PUNCT
ejpam-2101	87	16	v	v	NOUN
ejpam-2101	87	17	,	,	PUNCT
ejpam-2101	87	18	and	and	CCONJ
ejpam-2101	87	19	the	the	DET
ejpam-2101	87	20	solution	solution	NOUN
ejpam-2101	87	21	set	set	VERB
ejpam-2101	87	22	{	{	PUNCT
ejpam-2101	87	23	(	(	PUNCT
ejpam-2101	87	24	u0	u0	PROPN
ejpam-2101	87	25	,	,	PUNCT
ejpam-2101	87	26	v0	v0	PROPN
ejpam-2101	87	27	)	)	PUNCT
ejpam-2101	87	28	6=	6=	ADP
ejpam-2101	87	29	(	(	PUNCT
ejpam-2101	87	30	0,0	0,0	NOUN
ejpam-2101	87	31	)	)	PUNCT
ejpam-2101	87	32	|	|	ADV
ejpam-2101	87	33	gcd	gcd	VERB
ejpam-2101	87	34	(	(	PUNCT
ejpam-2101	87	35	f	f	PROPN
ejpam-2101	87	36	,	,	PUNCT
ejpam-2101	87	37	g	g	NOUN
ejpam-2101	87	38	)	)	PUNCT
ejpam-2101	87	39	=	=	SYM
ejpam-2101	88	1	0	0	X
ejpam-2101	88	2	}	}	PUNCT
ejpam-2101	88	3	is	be	AUX
ejpam-2101	88	4	exactly	exactly	ADV
ejpam-2101	88	5	the	the	DET
ejpam-2101	88	6	set	set	NOUN
ejpam-2101	88	7	of	of	ADP
ejpam-2101	88	8	{	{	PUNCT
ejpam-2101	88	9	(	(	PUNCT
ejpam-2101	88	10	u0	u0	PROPN
ejpam-2101	88	11	,	,	PUNCT
ejpam-2101	88	12	v0	v0	PROPN
ejpam-2101	88	13	)	)	PUNCT
ejpam-2101	88	14	6=	6=	ADP
ejpam-2101	88	15	(	(	PUNCT
ejpam-2101	88	16	0,0	0,0	NOUN
ejpam-2101	88	17	)	)	PUNCT
ejpam-2101	88	18	|	|	ADV
ejpam-2101	88	19	p(s	p(s	NOUN
ejpam-2101	88	20	,	,	PUNCT
ejpam-2101	88	21	t	t	PROPN
ejpam-2101	88	22	)	)	PUNCT
ejpam-2101	88	23	·	·	PUNCT
ejpam-2101	88	24	g(u0	g(u0	NOUN
ejpam-2101	88	25	,	,	PUNCT
ejpam-2101	88	26	v0	v0	NOUN
ejpam-2101	88	27	)	)	PUNCT
ejpam-2101	88	28	=	=	SYM
ejpam-2101	89	1	q(s	q(s	PROPN
ejpam-2101	89	2	,	,	PUNCT
ejpam-2101	89	3	t	t	PROPN
ejpam-2101	89	4	)	)	PUNCT
ejpam-2101	89	5	·	·	PUNCT
ejpam-2101	89	6	g(u0	g(u0	NOUN
ejpam-2101	89	7	,	,	PUNCT
ejpam-2101	89	8	v0	v0	NOUN
ejpam-2101	89	9	)	)	PUNCT
ejpam-2101	89	10	=	=	SYM
ejpam-2101	89	11	0	0	X
ejpam-2101	89	12	.	.	PUNCT
ejpam-2101	90	1	hence	hence	ADV
ejpam-2101	90	2	,	,	PUNCT
ejpam-2101	90	3	the	the	DET
ejpam-2101	90	4	natural	natural	ADJ
ejpam-2101	90	5	algorithm	algorithm	NOUN
ejpam-2101	90	6	to	to	PART
ejpam-2101	90	7	compute	compute	VERB
ejpam-2101	90	8	the	the	DET
ejpam-2101	90	9	intersection	intersection	NOUN
ejpam-2101	90	10	of	of	ADP
ejpam-2101	90	11	two	two	NUM
ejpam-2101	90	12	plane	plane	NOUN
ejpam-2101	90	13	curves	curve	NOUN
ejpam-2101	90	14	via	via	ADP
ejpam-2101	90	15	gcd	gcd	PROPN
ejpam-2101	90	16	are	be	AUX
ejpam-2101	90	17	stated	state	VERB
ejpam-2101	90	18	below	below	ADV
ejpam-2101	90	19	:	:	PUNCT
ejpam-2101	90	20	gcd	gcd	PROPN
ejpam-2101	90	21	algorithm	algorithm	NOUN
ejpam-2101	90	22	input	input	NOUN
ejpam-2101	90	23	:	:	PUNCT
ejpam-2101	90	24	parametrized	parametrized	ADJ
ejpam-2101	90	25	curves	curve	NOUN
ejpam-2101	90	26	f(s	f(s	PROPN
ejpam-2101	90	27	,	,	PUNCT
ejpam-2101	90	28	t	t	PROPN
ejpam-2101	90	29	)	)	PUNCT
ejpam-2101	90	30	and	and	CCONJ
ejpam-2101	90	31	g(u	g(u	PROPN
ejpam-2101	90	32	,	,	PUNCT
ejpam-2101	90	33	v	v	NOUN
ejpam-2101	90	34	)	)	PUNCT
ejpam-2101	90	35	.	.	PUNCT
ejpam-2101	91	1	output	output	NOUN
ejpam-2101	91	2	:	:	PUNCT
ejpam-2101	91	3	the	the	DET
ejpam-2101	91	4	set	set	NOUN
ejpam-2101	91	5	of	of	ADP
ejpam-2101	91	6	parameters	parameter	NOUN
ejpam-2101	91	7	and	and	CCONJ
ejpam-2101	91	8	their	their	PRON
ejpam-2101	91	9	corresponding	corresponding	ADJ
ejpam-2101	91	10	points	point	NOUN
ejpam-2101	91	11	of	of	ADP
ejpam-2101	91	12	the	the	DET
ejpam-2101	91	13	intersection	intersection	NOUN
ejpam-2101	91	14	of	of	ADP
ejpam-2101	91	15	two	two	NUM
ejpam-2101	91	16	curves	curve	NOUN
ejpam-2101	91	17	given	give	VERB
ejpam-2101	91	18	by	by	ADP
ejpam-2101	91	19	parametrization	parametrization	NOUN
ejpam-2101	91	20	f(s	f(	NOUN
ejpam-2101	91	21	,	,	PUNCT
ejpam-2101	91	22	t	t	PROPN
ejpam-2101	91	23	)	)	PUNCT
ejpam-2101	91	24	and	and	CCONJ
ejpam-2101	91	25	g(u	g(u	PROPN
ejpam-2101	91	26	,	,	PUNCT
ejpam-2101	91	27	v	v	NOUN
ejpam-2101	91	28	)	)	PUNCT
ejpam-2101	91	29	.	.	PUNCT
ejpam-2101	92	1	procedure	procedure	NOUN
ejpam-2101	92	2	:	:	PUNCT
ejpam-2101	92	3	1	1	X
ejpam-2101	92	4	.	.	X
ejpam-2101	92	5	compute	compute	PROPN
ejpam-2101	92	6	p(s	p(s	NOUN
ejpam-2101	92	7	,	,	PUNCT
ejpam-2101	92	8	t),q(s	t),q(s	NUM
ejpam-2101	92	9	,	,	PUNCT
ejpam-2101	92	10	t	t	PROPN
ejpam-2101	92	11	)	)	PUNCT
ejpam-2101	92	12	,	,	PUNCT
ejpam-2101	92	13	the	the	DET
ejpam-2101	92	14	µ-basis	µ-basis	NOUN
ejpam-2101	92	15	for	for	ADP
ejpam-2101	92	16	f(s	f(	NOUN
ejpam-2101	92	17	,	,	PUNCT
ejpam-2101	92	18	t	t	PROPN
ejpam-2101	92	19	)	)	PUNCT
ejpam-2101	92	20	.	.	PUNCT
ejpam-2101	93	1	2	2	X
ejpam-2101	93	2	.	.	X
ejpam-2101	93	3	compute	compute	NOUN
ejpam-2101	93	4	gp	gp	NOUN
ejpam-2101	94	1	=	=	PUNCT
ejpam-2101	94	2	p(s	p(s	PROPN
ejpam-2101	94	3	,	,	PUNCT
ejpam-2101	94	4	t	t	PROPN
ejpam-2101	94	5	)	)	PUNCT
ejpam-2101	94	6	·	·	PUNCT
ejpam-2101	95	1	g(u	g(u	X
ejpam-2101	95	2	,	,	PUNCT
ejpam-2101	95	3	v	v	NOUN
ejpam-2101	95	4	)	)	PUNCT
ejpam-2101	95	5	,	,	PUNCT
ejpam-2101	95	6	and	and	CCONJ
ejpam-2101	95	7	gq	gq	PROPN
ejpam-2101	95	8	=	=	SYM
ejpam-2101	95	9	q(s	q(s	PROPN
ejpam-2101	95	10	,	,	PUNCT
ejpam-2101	95	11	t	t	PROPN
ejpam-2101	95	12	)	)	PUNCT
ejpam-2101	95	13	·	·	PUNCT
ejpam-2101	96	1	g(u	g(u	X
ejpam-2101	96	2	,	,	PUNCT
ejpam-2101	96	3	v	v	NOUN
ejpam-2101	96	4	)	)	PUNCT
ejpam-2101	96	5	.	.	PUNCT
ejpam-2101	97	1	3	3	X
ejpam-2101	97	2	.	.	X
ejpam-2101	97	3	compute	compute	PROPN
ejpam-2101	97	4	f	f	PROPN
ejpam-2101	97	5	=	=	SYM
ejpam-2101	97	6	ress(gp	ress(gp	PROPN
ejpam-2101	97	7	,	,	PUNCT
ejpam-2101	97	8	gq	gq	PROPN
ejpam-2101	97	9	)	)	PUNCT
ejpam-2101	97	10	and	and	CCONJ
ejpam-2101	97	11	g	g	NOUN
ejpam-2101	97	12	=	=	PUNCT
ejpam-2101	97	13	rest(gp	rest(gp	PROPN
ejpam-2101	97	14	,	,	PUNCT
ejpam-2101	97	15	gq	gq	PROPN
ejpam-2101	97	16	)	)	PUNCT
ejpam-2101	97	17	,	,	PUNCT
ejpam-2101	97	18	where	where	SCONJ
ejpam-2101	97	19	ress	ress	PROPN
ejpam-2101	97	20	(	(	PUNCT
ejpam-2101	97	21	f	f	PROPN
ejpam-2101	97	22	,	,	PUNCT
ejpam-2101	97	23	g	g	PROPN
ejpam-2101	97	24	)	)	PUNCT
ejpam-2101	97	25	stands	stand	VERB
ejpam-2101	97	26	for	for	ADP
ejpam-2101	97	27	the	the	DET
ejpam-2101	97	28	resultant	resultant	NOUN
ejpam-2101	97	29	of	of	ADP
ejpam-2101	97	30	polynomial	polynomial	ADJ
ejpam-2101	97	31	f	f	PROPN
ejpam-2101	97	32	,	,	PUNCT
ejpam-2101	97	33	g	g	PROPN
ejpam-2101	97	34	with	with	ADP
ejpam-2101	97	35	respect	respect	NOUN
ejpam-2101	97	36	to	to	ADP
ejpam-2101	97	37	s.	s.	PROPN
ejpam-2101	97	38	4	4	NUM
ejpam-2101	97	39	.	.	PUNCT
ejpam-2101	98	1	the	the	DET
ejpam-2101	98	2	solution	solution	NOUN
ejpam-2101	98	3	to	to	PART
ejpam-2101	98	4	gcd	gcd	VERB
ejpam-2101	98	5	(	(	PUNCT
ejpam-2101	98	6	f	f	PROPN
ejpam-2101	98	7	,	,	PUNCT
ejpam-2101	98	8	g	g	NOUN
ejpam-2101	98	9	)	)	PUNCT
ejpam-2101	98	10	=	=	SYM
ejpam-2101	98	11	0	0	NUM
ejpam-2101	99	1	corresponding	correspond	VERB
ejpam-2101	99	2	the	the	DET
ejpam-2101	99	3	the	the	DET
ejpam-2101	99	4	parameters	parameter	NOUN
ejpam-2101	99	5	(	(	PUNCT
ejpam-2101	99	6	u0	u0	PROPN
ejpam-2101	99	7	,	,	PUNCT
ejpam-2101	99	8	v0	v0	PROPN
ejpam-2101	99	9	)	)	PUNCT
ejpam-2101	99	10	such	such	ADJ
ejpam-2101	99	11	that	that	DET
ejpam-2101	99	12	g(u0	g(u0	NOUN
ejpam-2101	99	13	,	,	PUNCT
ejpam-2101	99	14	v0	v0	PROPN
ejpam-2101	99	15	)	)	PUNCT
ejpam-2101	99	16	are	be	AUX
ejpam-2101	99	17	the	the	DET
ejpam-2101	99	18	intersection	intersection	NOUN
ejpam-2101	99	19	points	point	NOUN
ejpam-2101	99	20	of	of	ADP
ejpam-2101	99	21	the	the	DET
ejpam-2101	99	22	two	two	NUM
ejpam-2101	99	23	curves	curve	NOUN
ejpam-2101	99	24	with	with	ADP
ejpam-2101	99	25	correct	correct	ADJ
ejpam-2101	99	26	multiplicity	multiplicity	NOUN
ejpam-2101	99	27	.	.	PUNCT
ejpam-2101	100	1	example	example	NOUN
ejpam-2101	101	1	1	1	NUM
ejpam-2101	101	2	.	.	PUNCT
ejpam-2101	101	3	below	below	ADV
ejpam-2101	101	4	are	be	AUX
ejpam-2101	101	5	two	two	NUM
ejpam-2101	101	6	rational	rational	ADJ
ejpam-2101	101	7	paramatrized	paramatrize	VERB
ejpam-2101	101	8	plane	plane	NOUN
ejpam-2101	101	9	curves	curve	NOUN
ejpam-2101	101	10	given	give	VERB
ejpam-2101	101	11	by	by	ADP
ejpam-2101	101	12	wang	wang	PROPN
ejpam-2101	101	13	-	-	PUNCT
ejpam-2101	101	14	goldman	goldman	PROPN
ejpam-2101	102	1	[	[	X
ejpam-2101	102	2	11	11	NUM
ejpam-2101	102	3	]	]	SYM
ejpam-2101	102	4	:	:	PUNCT
ejpam-2101	102	5	lemniscate	lemniscate	PROPN
ejpam-2101	102	6	of	of	ADP
ejpam-2101	102	7	bernoulli	bernoulli	PROPN
ejpam-2101	102	8	,	,	PUNCT
ejpam-2101	102	9	a	a	DET
ejpam-2101	102	10	rational	rational	ADJ
ejpam-2101	102	11	quartic	quartic	ADJ
ejpam-2101	102	12	curve	curve	NOUN
ejpam-2101	102	13	f	f	PROPN
ejpam-2101	102	14	and	and	CCONJ
ejpam-2101	102	15	a	a	DET
ejpam-2101	102	16	rational	rational	ADJ
ejpam-2101	102	17	cubic	cubic	ADJ
ejpam-2101	102	18	curve	curve	NOUN
ejpam-2101	102	19	g(u	g(u	PROPN
ejpam-2101	102	20	,	,	PUNCT
ejpam-2101	102	21	v	v	NOUN
ejpam-2101	102	22	)	)	PUNCT
ejpam-2101	102	23	.	.	PUNCT
ejpam-2101	103	1	f(s	f(s	PROPN
ejpam-2101	103	2	,	,	PUNCT
ejpam-2101	103	3	t	t	PROPN
ejpam-2101	103	4	)	)	PUNCT
ejpam-2101	103	5	=(	=(	NOUN
ejpam-2101	103	6	s4	s4	PROPN
ejpam-2101	103	7	−	−	PROPN
ejpam-2101	103	8	t4	t4	PROPN
ejpam-2101	103	9	,	,	PUNCT
ejpam-2101	103	10	−2st(t2	−2st(t2	NOUN
ejpam-2101	103	11	−	−	PROPN
ejpam-2101	103	12	s2	s2	PROPN
ejpam-2101	103	13	)	)	PUNCT
ejpam-2101	103	14	,	,	PUNCT
ejpam-2101	103	15	t4	t4	PROPN
ejpam-2101	103	16	+	+	PROPN
ejpam-2101	103	17	6s2	6s2	NUM
ejpam-2101	103	18	t2	t2	PROPN
ejpam-2101	103	19	+	+	CCONJ
ejpam-2101	103	20	s4	s4	PROPN
ejpam-2101	103	21	)	)	PUNCT
ejpam-2101	103	22	,	,	PUNCT
ejpam-2101	103	23	g(u	g(u	PROPN
ejpam-2101	103	24	,	,	PUNCT
ejpam-2101	103	25	v	v	NOUN
ejpam-2101	103	26	)	)	PUNCT
ejpam-2101	103	27	=(	=(	NOUN
ejpam-2101	103	28	−3v3	−3v3	NUM
ejpam-2101	103	29	−	−	PROPN
ejpam-2101	103	30	2uv2	2uv2	NUM
ejpam-2101	104	1	+	+	CCONJ
ejpam-2101	104	2	4u2v	4u2v	NOUN
ejpam-2101	104	3	+	+	CCONJ
ejpam-2101	104	4	2u3	2u3	NUM
ejpam-2101	104	5	,	,	PUNCT
ejpam-2101	104	6	−v3	−v3	PROPN
ejpam-2101	104	7	+	+	CCONJ
ejpam-2101	104	8	3uv2	3uv2	NUM
ejpam-2101	104	9	−	−	PROPN
ejpam-2101	104	10	u3	u3	NOUN
ejpam-2101	104	11	+	+	CCONJ
ejpam-2101	104	12	2u2v	2u2v	NUM
ejpam-2101	104	13	,	,	PUNCT
ejpam-2101	104	14	2uv2	2uv2	NUM
ejpam-2101	105	1	+	+	CCONJ
ejpam-2101	105	2	2u2v	2u2v	ADJ
ejpam-2101	105	3	+	+	CCONJ
ejpam-2101	105	4	u3	u3	NOUN
ejpam-2101	105	5	)	)	PUNCT
ejpam-2101	105	6	.	.	PUNCT
ejpam-2101	106	1	m.	m.	PROPN
ejpam-2101	106	2	tesemma	tesemma	PROPN
ejpam-2101	106	3	,	,	PUNCT
ejpam-2101	106	4	h.	h.	PROPN
ejpam-2101	106	5	wang	wang	PROPN
ejpam-2101	106	6	,	,	PUNCT
ejpam-2101	106	7	/	/	SYM
ejpam-2101	106	8	eur	eur	NOUN
ejpam-2101	106	9	.	.	PUNCT
ejpam-2101	107	1	j.	j.	PROPN
ejpam-2101	107	2	pure	pure	PROPN
ejpam-2101	107	3	appl	appl	PROPN
ejpam-2101	107	4	.	.	PROPN
ejpam-2101	107	5	math	math	PROPN
ejpam-2101	107	6	,	,	PUNCT
ejpam-2101	107	7	7	7	NUM
ejpam-2101	107	8	(	(	PUNCT
ejpam-2101	107	9	2014	2014	NUM
ejpam-2101	107	10	)	)	PUNCT
ejpam-2101	107	11	,	,	PUNCT
ejpam-2101	107	12	191	191	NUM
ejpam-2101	107	13	-	-	SYM
ejpam-2101	107	14	200	200	NUM
ejpam-2101	107	15	195	195	NUM
ejpam-2101	107	16	gcd	gcd	NOUN
ejpam-2101	107	17	method	method	NOUN
ejpam-2101	107	18	:	:	PUNCT
ejpam-2101	107	19	first	first	ADV
ejpam-2101	107	20	,	,	PUNCT
ejpam-2101	107	21	compute	compute	VERB
ejpam-2101	107	22	a	a	DET
ejpam-2101	107	23	µ-basis	µ-basis	NOUN
ejpam-2101	107	24	for	for	ADP
ejpam-2101	107	25	f(s	f(	NOUN
ejpam-2101	107	26	,	,	PUNCT
ejpam-2101	107	27	t	t	PROPN
ejpam-2101	107	28	):	):	PUNCT
ejpam-2101	107	29	p(s	p(s	PROPN
ejpam-2101	107	30	,	,	PUNCT
ejpam-2101	107	31	t	t	PROPN
ejpam-2101	107	32	)	)	PUNCT
ejpam-2101	107	33	=	=	PUNCT
ejpam-2101	107	34	(	(	PUNCT
ejpam-2101	107	35	−s2	−s2	PROPN
ejpam-2101	107	36	−	−	PROPN
ejpam-2101	107	37	t2	t2	NOUN
ejpam-2101	107	38	,	,	PUNCT
ejpam-2101	107	39	−2st	−2st	NUM
ejpam-2101	107	40	,	,	PUNCT
ejpam-2101	107	41	s2	s2	NOUN
ejpam-2101	107	42	−	−	NOUN
ejpam-2101	107	43	t2	t2	PROPN
ejpam-2101	107	44	)	)	PUNCT
ejpam-2101	107	45	,	,	PUNCT
ejpam-2101	107	46	q(s	q(s	PROPN
ejpam-2101	107	47	,	,	PUNCT
ejpam-2101	107	48	t	t	PROPN
ejpam-2101	107	49	)	)	PUNCT
ejpam-2101	107	50	=	=	SYM
ejpam-2101	107	51	(	(	PUNCT
ejpam-2101	107	52	2st	2st	NOUN
ejpam-2101	107	53	,	,	PUNCT
ejpam-2101	107	54	−s2	−s2	NOUN
ejpam-2101	107	55	−	−	PROPN
ejpam-2101	107	56	t2	t2	NOUN
ejpam-2101	107	57	,	,	PUNCT
ejpam-2101	107	58	0	0	NUM
ejpam-2101	107	59	)	)	PUNCT
ejpam-2101	107	60	.	.	PUNCT
ejpam-2101	108	1	compute	compute	ADJ
ejpam-2101	108	2	gp	gp	NOUN
ejpam-2101	108	3	:	:	PUNCT
ejpam-2101	108	4	=	=	SYM
ejpam-2101	108	5	p(s	p(s	X
ejpam-2101	108	6	,	,	PUNCT
ejpam-2101	108	7	t	t	PROPN
ejpam-2101	108	8	)	)	PUNCT
ejpam-2101	108	9	·	·	PUNCT
ejpam-2101	108	10	g(u	g(u	X
ejpam-2101	108	11	,	,	PUNCT
ejpam-2101	108	12	v	v	NOUN
ejpam-2101	108	13	)	)	PUNCT
ejpam-2101	108	14	=	=	NOUN
ejpam-2101	108	15	−	−	ADP
ejpam-2101	108	16	s2(u3	s2(u3	NUM
ejpam-2101	108	17	+	+	CCONJ
ejpam-2101	108	18	2u2v	2u2v	NUM
ejpam-2101	108	19	−	−	NOUN
ejpam-2101	108	20	4uv2	4uv2	NUM
ejpam-2101	109	1	−	−	NOUN
ejpam-2101	109	2	3v3)−	3v3)−	NOUN
ejpam-2101	109	3	3t2(u3	3t2(u3	NUM
ejpam-2101	110	1	+	+	CCONJ
ejpam-2101	110	2	2u2v	2u2v	ADJ
ejpam-2101	110	3	−	−	PROPN
ejpam-2101	110	4	v3	v3	PROPN
ejpam-2101	110	5	)	)	PUNCT
ejpam-2101	111	1	+	+	CCONJ
ejpam-2101	112	1	2st(u3	2st(u3	NUM
ejpam-2101	112	2	−	−	NUM
ejpam-2101	112	3	2u2v	2u2v	NOUN
ejpam-2101	112	4	−	−	NOUN
ejpam-2101	112	5	3uv2	3uv2	NUM
ejpam-2101	113	1	+	+	CCONJ
ejpam-2101	113	2	v3	v3	PROPN
ejpam-2101	113	3	)	)	PUNCT
ejpam-2101	113	4	,	,	PUNCT
ejpam-2101	113	5	gq	gq	NOUN
ejpam-2101	113	6	:	:	PUNCT
ejpam-2101	113	7	=	=	SYM
ejpam-2101	113	8	q(s	q(s	X
ejpam-2101	113	9	,	,	PUNCT
ejpam-2101	113	10	t	t	PROPN
ejpam-2101	113	11	)	)	PUNCT
ejpam-2101	113	12	·	·	PUNCT
ejpam-2101	113	13	g(u	g(u	X
ejpam-2101	113	14	,	,	PUNCT
ejpam-2101	113	15	v	v	NOUN
ejpam-2101	113	16	)	)	PUNCT
ejpam-2101	113	17	=	=	NOUN
ejpam-2101	113	18	2st(2u3	2st(2u3	NUM
ejpam-2101	114	1	+	+	CCONJ
ejpam-2101	114	2	4u2v	4u2v	NOUN
ejpam-2101	115	1	−	−	NOUN
ejpam-2101	115	2	2uv2	2uv2	NUM
ejpam-2101	115	3	−	−	PROPN
ejpam-2101	115	4	3v3	3v3	NUM
ejpam-2101	115	5	)	)	PUNCT
ejpam-2101	116	1	+	+	CCONJ
ejpam-2101	116	2	s2(u3	s2(u3	NUM
ejpam-2101	116	3	−	−	NOUN
ejpam-2101	116	4	2u2v	2u2v	NOUN
ejpam-2101	116	5	−	−	NOUN
ejpam-2101	116	6	3uv2	3uv2	NUM
ejpam-2101	117	1	+	+	CCONJ
ejpam-2101	117	2	v3	v3	PROPN
ejpam-2101	117	3	)	)	PUNCT
ejpam-2101	118	1	+	+	CCONJ
ejpam-2101	118	2	t2(u3	t2(u3	ADP
ejpam-2101	118	3	−	−	NUM
ejpam-2101	118	4	2u2v	2u2v	NOUN
ejpam-2101	118	5	−	−	PROPN
ejpam-2101	118	6	3uv2	3uv2	NUM
ejpam-2101	119	1	+	+	CCONJ
ejpam-2101	119	2	v3	v3	PROPN
ejpam-2101	119	3	)	)	PUNCT
ejpam-2101	119	4	.	.	PUNCT
ejpam-2101	120	1	and	and	CCONJ
ejpam-2101	120	2	f	f	X
ejpam-2101	120	3	:	:	PUNCT
ejpam-2101	120	4	=	=	SYM
ejpam-2101	120	5	ress(gp	ress(gp	PROPN
ejpam-2101	120	6	,	,	PUNCT
ejpam-2101	120	7	gq	gq	PROPN
ejpam-2101	120	8	)	)	PUNCT
ejpam-2101	121	1	=	=	SYM
ejpam-2101	121	2	4t4(u2	4t4(u2	NOUN
ejpam-2101	122	1	+	+	NUM
ejpam-2101	122	2	2uv	2uv	ADJ
ejpam-2101	122	3	+	+	CCONJ
ejpam-2101	122	4	2v2)2(22u8	2v2)2(22u8	ADJ
ejpam-2101	122	5	−	−	NOUN
ejpam-2101	122	6	86u6v2	86u6v2	NOUN
ejpam-2101	122	7	−	−	PROPN
ejpam-2101	122	8	10u5v3	10u5v3	NUM
ejpam-2101	122	9	+	+	CCONJ
ejpam-2101	122	10	131u4v4	131u4v4	NUM
ejpam-2101	122	11	+	+	CCONJ
ejpam-2101	122	12	34u3v5	34u3v5	PROPN
ejpam-2101	122	13	−	−	PROPN
ejpam-2101	122	14	84u2v6	84u2v6	NOUN
ejpam-2101	122	15	−	−	PROPN
ejpam-2101	122	16	20uv7	20uv7	NOUN
ejpam-2101	122	17	+	+	CCONJ
ejpam-2101	122	18	25v8	25v8	NUM
ejpam-2101	122	19	)	)	PUNCT
ejpam-2101	122	20	,	,	PUNCT
ejpam-2101	122	21	g	g	NOUN
ejpam-2101	122	22	:	:	PUNCT
ejpam-2101	122	23	=	=	SYM
ejpam-2101	122	24	rest(gp	rest(gp	NOUN
ejpam-2101	122	25	,	,	PUNCT
ejpam-2101	122	26	gq	gq	PROPN
ejpam-2101	122	27	)	)	PUNCT
ejpam-2101	123	1	=	=	SYM
ejpam-2101	123	2	4s4(u2	4s4(u2	NOUN
ejpam-2101	123	3	+	+	NUM
ejpam-2101	123	4	2uv	2uv	ADJ
ejpam-2101	123	5	+	+	CCONJ
ejpam-2101	123	6	2v2)2(22u8	2v2)2(22u8	ADJ
ejpam-2101	123	7	−	−	NOUN
ejpam-2101	123	8	86u6v2	86u6v2	NOUN
ejpam-2101	123	9	−	−	PROPN
ejpam-2101	123	10	10u5v3	10u5v3	NUM
ejpam-2101	123	11	+	+	CCONJ
ejpam-2101	123	12	131u4v4	131u4v4	NUM
ejpam-2101	123	13	+	+	CCONJ
ejpam-2101	123	14	34u3v5	34u3v5	PROPN
ejpam-2101	123	15	−	−	PROPN
ejpam-2101	123	16	84u2v6	84u2v6	NOUN
ejpam-2101	123	17	−	−	PROPN
ejpam-2101	123	18	20uv7	20uv7	NOUN
ejpam-2101	123	19	+	+	CCONJ
ejpam-2101	123	20	25v8	25v8	NUM
ejpam-2101	123	21	)	)	PUNCT
ejpam-2101	123	22	.	.	PUNCT
ejpam-2101	124	1	hence	hence	ADV
ejpam-2101	124	2	,	,	PUNCT
ejpam-2101	124	3	the	the	DET
ejpam-2101	124	4	solutions	solution	NOUN
ejpam-2101	124	5	to	to	PART
ejpam-2101	124	6	gcd	gcd	VERB
ejpam-2101	124	7	(	(	PUNCT
ejpam-2101	124	8	f	f	PROPN
ejpam-2101	124	9	,	,	PUNCT
ejpam-2101	124	10	g	g	NOUN
ejpam-2101	124	11	)	)	PUNCT
ejpam-2101	124	12	=	=	SYM
ejpam-2101	124	13	(	(	PUNCT
ejpam-2101	124	14	u2	u2	PROPN
ejpam-2101	124	15	+	+	PROPN
ejpam-2101	124	16	2uv+2v2)2(22u8−86u6v2−10u5v3	2uv+2v2)2(22u8−86u6v2−10u5v3	NOUN
ejpam-2101	124	17	+	+	NOUN
ejpam-2101	124	18	131u4v4	131u4v4	NUM
ejpam-2101	124	19	+	+	SYM
ejpam-2101	124	20	34u3v5−84u2v6−20uv7	34u3v5−84u2v6−20uv7	NUM
ejpam-2101	124	21	+	+	NOUN
ejpam-2101	124	22	25v8	25v8	NUM
ejpam-2101	124	23	)	)	PUNCT
ejpam-2101	124	24	=	=	SYM
ejpam-2101	124	25	0	0	NUM
ejpam-2101	124	26	are	be	AUX
ejpam-2101	124	27	the	the	DET
ejpam-2101	124	28	parameters	parameter	NOUN
ejpam-2101	124	29	(	(	PUNCT
ejpam-2101	124	30	u0	u0	PROPN
ejpam-2101	124	31	,	,	PUNCT
ejpam-2101	124	32	t0	t0	PROPN
ejpam-2101	124	33	)	)	PUNCT
ejpam-2101	124	34	such	such	ADJ
ejpam-2101	124	35	that	that	DET
ejpam-2101	124	36	g(u0	g(u0	NOUN
ejpam-2101	124	37	,	,	PUNCT
ejpam-2101	124	38	v0	v0	PROPN
ejpam-2101	124	39	)	)	PUNCT
ejpam-2101	124	40	are	be	AUX
ejpam-2101	124	41	the	the	DET
ejpam-2101	124	42	intersections	intersection	NOUN
ejpam-2101	124	43	of	of	ADP
ejpam-2101	124	44	the	the	DET
ejpam-2101	124	45	two	two	NUM
ejpam-2101	124	46	curves	curve	NOUN
ejpam-2101	124	47	.	.	PUNCT
ejpam-2101	125	1	the	the	DET
ejpam-2101	125	2	intersections	intersection	NOUN
ejpam-2101	125	3	are	be	AUX
ejpam-2101	125	4	listed	list	VERB
ejpam-2101	125	5	below	below	ADV
ejpam-2101	125	6	:	:	PUNCT
ejpam-2101	125	7	g(−1−	g(−1−	NOUN
ejpam-2101	125	8	1i	1i	NOUN
ejpam-2101	125	9	,	,	PUNCT
ejpam-2101	125	10	1	1	X
ejpam-2101	125	11	)	)	PUNCT
ejpam-2101	125	12	=(	=(	NOUN
ejpam-2101	126	1	3	3	NUM
ejpam-2101	126	2	+	+	NOUN
ejpam-2101	127	1	6i,−6	6i,−6	NUM
ejpam-2101	127	2	+	+	NOUN
ejpam-2101	127	3	3i	3i	NOUN
ejpam-2101	127	4	,	,	PUNCT
ejpam-2101	127	5	0	0	NUM
ejpam-2101	127	6	)	)	PUNCT
ejpam-2101	127	7	double	double	ADJ
ejpam-2101	127	8	points	point	NOUN
ejpam-2101	127	9	,	,	PUNCT
ejpam-2101	127	10	g(−1	g(−1	PROPN
ejpam-2101	127	11	+	+	X
ejpam-2101	127	12	1i	1i	NOUN
ejpam-2101	127	13	,	,	PUNCT
ejpam-2101	127	14	1	1	X
ejpam-2101	127	15	)	)	PUNCT
ejpam-2101	127	16	=(	=(	NOUN
ejpam-2101	127	17	3−	3−	NUM
ejpam-2101	127	18	6i,−6−	6i,−6−	NUM
ejpam-2101	127	19	3i	3i	NOUN
ejpam-2101	127	20	,	,	PUNCT
ejpam-2101	127	21	0	0	NUM
ejpam-2101	127	22	)	)	PUNCT
ejpam-2101	127	23	double	double	ADJ
ejpam-2101	127	24	points	point	NOUN
ejpam-2101	127	25	,	,	PUNCT
ejpam-2101	127	26	g(−1.163−	g(−1.163−	PROPN
ejpam-2101	127	27	0.135i	0.135i	PROPN
ejpam-2101	127	28	,	,	PUNCT
ejpam-2101	127	29	1	1	X
ejpam-2101	127	30	)	)	PUNCT
ejpam-2101	127	31	=(	=(	NOUN
ejpam-2101	127	32	1.645	1.645	NUM
ejpam-2101	127	33	+	+	NUM
ejpam-2101	127	34	0.436i,−0.311	0.436i,−0.311	NUM
ejpam-2101	127	35	+	+	NUM
ejpam-2101	127	36	0.771i,−1.166−	0.771i,−1.166−	NUM
ejpam-2101	127	37	0.187i	0.187i	NUM
ejpam-2101	127	38	)	)	PUNCT
ejpam-2101	127	39	,	,	PUNCT
ejpam-2101	127	40	g(−1.163	g(−1.163	X
ejpam-2101	127	41	+	+	SYM
ejpam-2101	127	42	0.135i	0.135i	ADJ
ejpam-2101	127	43	,	,	PUNCT
ejpam-2101	127	44	1	1	X
ejpam-2101	127	45	)	)	PUNCT
ejpam-2101	127	46	=(	=(	NOUN
ejpam-2101	127	47	1.645−	1.645−	PROPN
ejpam-2101	127	48	0.436i,−0.311−	0.436i,−0.311−	NUM
ejpam-2101	127	49	0.771i,−1.166	0.771i,−1.166	PROPN
ejpam-2101	127	50	+	+	CCONJ
ejpam-2101	127	51	0.187i	0.187i	NUM
ejpam-2101	127	52	)	)	PUNCT
ejpam-2101	127	53	,	,	PUNCT
ejpam-2101	127	54	g(−0.840−	g(−0.840−	NOUN
ejpam-2101	127	55	0.483i	0.483i	ADJ
ejpam-2101	127	56	,	,	PUNCT
ejpam-2101	127	57	1	1	X
ejpam-2101	127	58	)	)	PUNCT
ejpam-2101	127	59	=(	=(	NOUN
ejpam-2101	127	60	0.566	0.566	NUM
ejpam-2101	127	61	+	+	SYM
ejpam-2101	128	1	2.396i,−2.572	2.396i,−2.572	NUM
ejpam-2101	128	2	+	+	SYM
ejpam-2101	128	3	1.089i,−0.739−	1.089i,−0.739−	NUM
ejpam-2101	128	4	0.253i	0.253i	NOUN
ejpam-2101	128	5	)	)	PUNCT
ejpam-2101	128	6	,	,	PUNCT
ejpam-2101	128	7	g(−0.840	g(−0.840	X
ejpam-2101	129	1	+	+	X
ejpam-2101	129	2	0.483i	0.483i	ADJ
ejpam-2101	129	3	,	,	PUNCT
ejpam-2101	129	4	1	1	X
ejpam-2101	129	5	)	)	PUNCT
ejpam-2101	129	6	=(	=(	NOUN
ejpam-2101	129	7	0.566−	0.566−	ADV
ejpam-2101	129	8	2.396i,−2.572−	2.396i,−2.572−	NUM
ejpam-2101	129	9	1.089i,−0.739	1.089i,−0.739	NUM
ejpam-2101	129	10	+	+	SYM
ejpam-2101	129	11	0.253i	0.253i	NOUN
ejpam-2101	129	12	)	)	PUNCT
ejpam-2101	129	13	,	,	PUNCT
ejpam-2101	129	14	g(0.661−	g(0.661−	NOUN
ejpam-2101	129	15	0.145i	0.145i	NOUN
ejpam-2101	129	16	,	,	PUNCT
ejpam-2101	129	17	1	1	NUM
ejpam-2101	129	18	)	)	PUNCT
ejpam-2101	129	19	=(	=(	NOUN
ejpam-2101	129	20	−2.166−	−2.166−	PRON
ejpam-2101	129	21	0.855i	0.855i	NOUN
ejpam-2101	129	22	,	,	PUNCT
ejpam-2101	129	23	1.567−	1.567−	ADV
ejpam-2101	129	24	0.635i	0.635i	ADJ
ejpam-2101	129	25	,	,	PUNCT
ejpam-2101	129	26	2.399−	2.399−	NUM
ejpam-2101	129	27	0.865i	0.865i	NOUN
ejpam-2101	129	28	)	)	PUNCT
ejpam-2101	129	29	,	,	PUNCT
ejpam-2101	129	30	g(0.661	g(0.661	ADV
ejpam-2101	129	31	+	+	X
ejpam-2101	129	32	0.145i	0.145i	ADJ
ejpam-2101	129	33	,	,	PUNCT
ejpam-2101	129	34	1	1	X
ejpam-2101	129	35	)	)	PUNCT
ejpam-2101	129	36	=(	=(	NOUN
ejpam-2101	129	37	−2.166	−2.166	PROPN
ejpam-2101	129	38	+	+	CCONJ
ejpam-2101	129	39	0.855i	0.855i	NOUN
ejpam-2101	129	40	,	,	PUNCT
ejpam-2101	129	41	1.567	1.567	NUM
ejpam-2101	129	42	+	+	CCONJ
ejpam-2101	129	43	0.635i	0.635i	ADJ
ejpam-2101	129	44	,	,	PUNCT
ejpam-2101	129	45	2.399	2.399	NUM
ejpam-2101	129	46	+	+	NOUN
ejpam-2101	129	47	0.865i	0.865i	NOUN
ejpam-2101	129	48	)	)	PUNCT
ejpam-2101	129	49	,	,	PUNCT
ejpam-2101	129	50	g(1.343−	g(1.343−	NOUN
ejpam-2101	129	51	0.343i	0.343i	NOUN
ejpam-2101	129	52	,	,	PUNCT
ejpam-2101	129	53	1	1	X
ejpam-2101	129	54	)	)	PUNCT
ejpam-2101	129	55	=(	=(	NOUN
ejpam-2101	129	56	4.954−	4.954−	PROPN
ejpam-2101	129	57	6.630i	6.630i	PROPN
ejpam-2101	129	58	,	,	PUNCT
ejpam-2101	129	59	4.452−	4.452−	NUM
ejpam-2101	129	60	1.056i	1.056i	NUM
ejpam-2101	129	61	,	,	PUNCT
ejpam-2101	129	62	8.006−	8.006−	NOUN
ejpam-2101	129	63	4.344i	4.344i	NUM
ejpam-2101	129	64	)	)	PUNCT
ejpam-2101	129	65	,	,	PUNCT
ejpam-2101	129	66	g(1.343	g(1.343	PROPN
ejpam-2101	129	67	+	+	PROPN
ejpam-2101	129	68	0.3430i	0.3430i	PROPN
ejpam-2101	129	69	,	,	PUNCT
ejpam-2101	129	70	1	1	X
ejpam-2101	129	71	)	)	PUNCT
ejpam-2101	129	72	=(	=(	NOUN
ejpam-2101	129	73	4.954	4.954	NUM
ejpam-2101	129	74	+	+	CCONJ
ejpam-2101	129	75	6.630i	6.630i	NUM
ejpam-2101	129	76	,	,	PUNCT
ejpam-2101	129	77	4.452	4.452	NUM
ejpam-2101	129	78	+	+	SYM
ejpam-2101	129	79	1.056i	1.056i	NUM
ejpam-2101	129	80	,	,	PUNCT
ejpam-2101	129	81	8.006	8.006	NUM
ejpam-2101	129	82	+	+	SYM
ejpam-2101	129	83	4.344i	4.344i	NUM
ejpam-2101	129	84	)	)	PUNCT
ejpam-2101	129	85	.	.	PUNCT
ejpam-2101	130	1	we	we	PRON
ejpam-2101	130	2	may	may	AUX
ejpam-2101	130	3	check	check	VERB
ejpam-2101	130	4	our	our	PRON
ejpam-2101	130	5	solution	solution	NOUN
ejpam-2101	130	6	by	by	ADP
ejpam-2101	130	7	a	a	DET
ejpam-2101	130	8	conventional	conventional	ADJ
ejpam-2101	130	9	computation	computation	NOUN
ejpam-2101	130	10	via	via	ADP
ejpam-2101	130	11	implicit	implicit	ADJ
ejpam-2101	130	12	equation	equation	NOUN
ejpam-2101	130	13	of	of	ADP
ejpam-2101	130	14	f(s	f(s	PROPN
ejpam-2101	130	15	,	,	PUNCT
ejpam-2101	130	16	t	t	PROPN
ejpam-2101	130	17	)	)	PUNCT
ejpam-2101	130	18	.	.	PUNCT
ejpam-2101	131	1	we	we	PRON
ejpam-2101	131	2	note	note	VERB
ejpam-2101	131	3	that	that	SCONJ
ejpam-2101	131	4	the	the	DET
ejpam-2101	131	5	implicit	implicit	ADJ
ejpam-2101	131	6	equation	equation	NOUN
ejpam-2101	131	7	of	of	ADP
ejpam-2101	131	8	f(s	f(s	PROPN
ejpam-2101	131	9	,	,	PUNCT
ejpam-2101	131	10	t	t	PROPN
ejpam-2101	131	11	)	)	PUNCT
ejpam-2101	131	12	is	be	AUX
ejpam-2101	131	13	:	:	PUNCT
ejpam-2101	131	14	f(x	f(x	PROPN
ejpam-2101	131	15	,	,	PUNCT
ejpam-2101	131	16	y	y	PROPN
ejpam-2101	131	17	,	,	PUNCT
ejpam-2101	131	18	z	z	NOUN
ejpam-2101	131	19	)	)	PUNCT
ejpam-2101	132	1	=	=	SYM
ejpam-2101	132	2	4(x2	4(x2	X
ejpam-2101	132	3	+	+	CCONJ
ejpam-2101	132	4	y2)2	y2)2	PUNCT
ejpam-2101	132	5	+	+	NUM
ejpam-2101	132	6	4w2(y2	4w2(y2	NUM
ejpam-2101	132	7	−	−	NOUN
ejpam-2101	132	8	x2	x2	NOUN
ejpam-2101	132	9	)	)	PUNCT
ejpam-2101	132	10	=	=	SYM
ejpam-2101	132	11	0	0	NUM
ejpam-2101	132	12	,	,	PUNCT
ejpam-2101	132	13	and	and	CCONJ
ejpam-2101	132	14	f(g(u	f(g(u	PROPN
ejpam-2101	132	15	,	,	PUNCT
ejpam-2101	132	16	v	v	NOUN
ejpam-2101	132	17	)	)	PUNCT
ejpam-2101	132	18	)	)	PUNCT
ejpam-2101	133	1	=	=	PUNCT
ejpam-2101	134	1	4(u2	4(u2	PUNCT
ejpam-2101	135	1	+	+	NOUN
ejpam-2101	135	2	2uv+2v2)2(22u8−86u6v2−10u5v3	2uv+2v2)2(22u8−86u6v2−10u5v3	NUM
ejpam-2101	135	3	+	+	ADJ
ejpam-2101	135	4	131u4v4	131u4v4	NUM
ejpam-2101	135	5	+	+	SYM
ejpam-2101	135	6	34u3v5−84u2v6−20uv7	34u3v5−84u2v6−20uv7	NUM
ejpam-2101	135	7	+	+	NOUN
ejpam-2101	135	8	25v8	25v8	NUM
ejpam-2101	135	9	)	)	PUNCT
ejpam-2101	135	10	.	.	PUNCT
ejpam-2101	136	1	obviously	obviously	ADV
ejpam-2101	136	2	,	,	PUNCT
ejpam-2101	136	3	gcd	gcd	PROPN
ejpam-2101	136	4	(	(	PUNCT
ejpam-2101	136	5	f	f	PROPN
ejpam-2101	136	6	,	,	PUNCT
ejpam-2101	136	7	g	g	NOUN
ejpam-2101	136	8	)	)	PUNCT
ejpam-2101	136	9	=	=	SYM
ejpam-2101	136	10	f(g(u	f(g(u	PROPN
ejpam-2101	136	11	,	,	PUNCT
ejpam-2101	136	12	v	v	NOUN
ejpam-2101	136	13	)	)	PUNCT
ejpam-2101	136	14	)	)	PUNCT
ejpam-2101	136	15	,	,	PUNCT
ejpam-2101	136	16	hence	hence	ADV
ejpam-2101	136	17	,	,	PUNCT
ejpam-2101	136	18	the	the	DET
ejpam-2101	136	19	solutions	solution	NOUN
ejpam-2101	136	20	to	to	PART
ejpam-2101	136	21	gcd	gcd	VERB
ejpam-2101	136	22	(	(	PUNCT
ejpam-2101	136	23	f	f	PROPN
ejpam-2101	136	24	,	,	PUNCT
ejpam-2101	136	25	g	g	NOUN
ejpam-2101	136	26	)	)	PUNCT
ejpam-2101	136	27	=	=	SYM
ejpam-2101	136	28	0	0	NUM
ejpam-2101	136	29	are	be	AUX
ejpam-2101	136	30	indeed	indeed	ADV
ejpam-2101	136	31	the	the	DET
ejpam-2101	136	32	parameters	parameter	NOUN
ejpam-2101	136	33	of	of	ADP
ejpam-2101	136	34	g(u	g(u	PROPN
ejpam-2101	136	35	,	,	PUNCT
ejpam-2101	136	36	v	v	NOUN
ejpam-2101	136	37	)	)	PUNCT
ejpam-2101	136	38	corresponding	correspond	VERB
ejpam-2101	136	39	to	to	ADP
ejpam-2101	136	40	the	the	DET
ejpam-2101	136	41	intersections	intersection	NOUN
ejpam-2101	136	42	of	of	ADP
ejpam-2101	136	43	the	the	DET
ejpam-2101	136	44	two	two	NUM
ejpam-2101	136	45	curves	curve	NOUN
ejpam-2101	136	46	.	.	PUNCT
ejpam-2101	137	1	m.	m.	NOUN
ejpam-2101	137	2	tesemma	tesemma	PROPN
ejpam-2101	137	3	,	,	PUNCT
ejpam-2101	137	4	h.	h.	PROPN
ejpam-2101	137	5	wang	wang	PROPN
ejpam-2101	137	6	,	,	PUNCT
ejpam-2101	137	7	/	/	SYM
ejpam-2101	137	8	eur	eur	NOUN
ejpam-2101	137	9	.	.	PUNCT
ejpam-2101	138	1	j.	j.	PROPN
ejpam-2101	138	2	pure	pure	PROPN
ejpam-2101	138	3	appl	appl	PROPN
ejpam-2101	138	4	.	.	PROPN
ejpam-2101	138	5	math	math	PROPN
ejpam-2101	138	6	,	,	PUNCT
ejpam-2101	138	7	7	7	NUM
ejpam-2101	138	8	(	(	PUNCT
ejpam-2101	138	9	2014	2014	NUM
ejpam-2101	138	10	)	)	PUNCT
ejpam-2101	138	11	,	,	PUNCT
ejpam-2101	138	12	191	191	NUM
ejpam-2101	138	13	-	-	SYM
ejpam-2101	138	14	200	200	NUM
ejpam-2101	138	15	196	196	NUM
ejpam-2101	138	16	3.2	3.2	NUM
ejpam-2101	138	17	.	.	PUNCT
ejpam-2101	139	1	resultant	resultant	NOUN
ejpam-2101	139	2	matrix	matrix	NOUN
ejpam-2101	139	3	method	method	NOUN
ejpam-2101	139	4	now	now	ADV
ejpam-2101	139	5	,	,	PUNCT
ejpam-2101	139	6	we	we	PRON
ejpam-2101	139	7	will	will	AUX
ejpam-2101	139	8	use	use	VERB
ejpam-2101	139	9	resultant	resultant	NOUN
ejpam-2101	139	10	matrix	matrix	NOUN
ejpam-2101	139	11	to	to	PART
ejpam-2101	139	12	find	find	VERB
ejpam-2101	139	13	the	the	DET
ejpam-2101	139	14	intersection	intersection	NOUN
ejpam-2101	139	15	of	of	ADP
ejpam-2101	139	16	two	two	NUM
ejpam-2101	139	17	parametrized	parametrized	ADJ
ejpam-2101	139	18	curves	curve	NOUN
ejpam-2101	139	19	.	.	PUNCT
ejpam-2101	140	1	first	first	ADV
ejpam-2101	140	2	,	,	PUNCT
ejpam-2101	140	3	we	we	PRON
ejpam-2101	140	4	let	let	VERB
ejpam-2101	140	5	p(x	p(x	PROPN
ejpam-2101	140	6	,	,	PUNCT
ejpam-2101	140	7	y	y	PROPN
ejpam-2101	140	8	,	,	PUNCT
ejpam-2101	140	9	z	z	PROPN
ejpam-2101	140	10	;	;	PUNCT
ejpam-2101	140	11	s	s	X
ejpam-2101	140	12	,	,	PUNCT
ejpam-2101	140	13	t	t	PROPN
ejpam-2101	140	14	)	)	PUNCT
ejpam-2101	140	15	=	=	SYM
ejpam-2101	140	16	p(s	p(s	PROPN
ejpam-2101	140	17	,	,	PUNCT
ejpam-2101	140	18	t	t	PROPN
ejpam-2101	140	19	)	)	PUNCT
ejpam-2101	140	20	·	·	PUNCT
ejpam-2101	141	1	(	(	PUNCT
ejpam-2101	141	2	x	x	X
ejpam-2101	141	3	,	,	PUNCT
ejpam-2101	141	4	y	y	PROPN
ejpam-2101	141	5	,	,	PUNCT
ejpam-2101	141	6	z	z	NOUN
ejpam-2101	141	7	)	)	PUNCT
ejpam-2101	141	8	and	and	CCONJ
ejpam-2101	141	9	q(x	q(x	PROPN
ejpam-2101	141	10	,	,	PUNCT
ejpam-2101	141	11	y	y	PROPN
ejpam-2101	141	12	,	,	PUNCT
ejpam-2101	141	13	z	z	PROPN
ejpam-2101	141	14	;	;	PUNCT
ejpam-2101	141	15	s	s	X
ejpam-2101	141	16	,	,	PUNCT
ejpam-2101	141	17	t	t	PROPN
ejpam-2101	141	18	)	)	PUNCT
ejpam-2101	141	19	=	=	SYM
ejpam-2101	141	20	q(s	q(s	PROPN
ejpam-2101	141	21	,	,	PUNCT
ejpam-2101	141	22	t	t	PROPN
ejpam-2101	141	23	)	)	PUNCT
ejpam-2101	141	24	·	·	PUNCT
ejpam-2101	141	25	(	(	PUNCT
ejpam-2101	141	26	x	x	X
ejpam-2101	141	27	,	,	PUNCT
ejpam-2101	141	28	y	y	PROPN
ejpam-2101	141	29	,	,	PUNCT
ejpam-2101	141	30	z	z	NOUN
ejpam-2101	141	31	)	)	PUNCT
ejpam-2101	141	32	be	be	AUX
ejpam-2101	141	33	a	a	DET
ejpam-2101	141	34	µ-basis	µ-basis	NOUN
ejpam-2101	141	35	of	of	ADP
ejpam-2101	141	36	a	a	DET
ejpam-2101	141	37	rational	rational	ADJ
ejpam-2101	141	38	parametric	parametric	ADJ
ejpam-2101	141	39	plane	plane	NOUN
ejpam-2101	141	40	curve	curve	NOUN
ejpam-2101	141	41	c1	c1	PROPN
ejpam-2101	141	42	of	of	ADP
ejpam-2101	141	43	degree	degree	NOUN
ejpam-2101	141	44	d	d	NOUN
ejpam-2101	141	45	given	give	VERB
ejpam-2101	141	46	by	by	ADP
ejpam-2101	141	47	f(s	f(	NOUN
ejpam-2101	141	48	,	,	PUNCT
ejpam-2101	141	49	t	t	PROPN
ejpam-2101	141	50	)	)	PUNCT
ejpam-2101	141	51	=	=	SYM
ejpam-2101	141	52	(	(	PUNCT
ejpam-2101	141	53	f0(s	f0(s	PROPN
ejpam-2101	141	54	,	,	PUNCT
ejpam-2101	141	55	t	t	PROPN
ejpam-2101	141	56	)	)	PUNCT
ejpam-2101	141	57	,	,	PUNCT
ejpam-2101	141	58	f1(s	f1(s	PROPN
ejpam-2101	141	59	,	,	PUNCT
ejpam-2101	141	60	t	t	PROPN
ejpam-2101	141	61	)	)	PUNCT
ejpam-2101	141	62	,	,	PUNCT
ejpam-2101	141	63	f2(s	f2(s	PROPN
ejpam-2101	141	64	,	,	PUNCT
ejpam-2101	141	65	t	t	PROPN
ejpam-2101	141	66	)	)	PUNCT
ejpam-2101	141	67	)	)	PUNCT
ejpam-2101	141	68	,	,	PUNCT
ejpam-2101	141	69	(	(	PUNCT
ejpam-2101	141	70	s	s	X
ejpam-2101	141	71	,	,	PUNCT
ejpam-2101	141	72	t	t	PROPN
ejpam-2101	141	73	)	)	PUNCT
ejpam-2101	141	74	6=	6=	ADP
ejpam-2101	141	75	(	(	PUNCT
ejpam-2101	141	76	0	0	NUM
ejpam-2101	141	77	,	,	PUNCT
ejpam-2101	141	78	0	0	NUM
ejpam-2101	141	79	)	)	PUNCT
ejpam-2101	141	80	.	.	PUNCT
ejpam-2101	142	1	it	it	PRON
ejpam-2101	142	2	is	be	AUX
ejpam-2101	142	3	know	know	VERB
ejpam-2101	142	4	that	that	SCONJ
ejpam-2101	142	5	the	the	DET
ejpam-2101	142	6	implicit	implicit	ADJ
ejpam-2101	142	7	equation	equation	NOUN
ejpam-2101	142	8	of	of	ADP
ejpam-2101	142	9	the	the	DET
ejpam-2101	142	10	curve	curve	NOUN
ejpam-2101	142	11	is	be	AUX
ejpam-2101	142	12	f(x	f(x	PROPN
ejpam-2101	142	13	,	,	PUNCT
ejpam-2101	142	14	y	y	PROPN
ejpam-2101	142	15	,	,	PUNCT
ejpam-2101	142	16	z	z	NOUN
ejpam-2101	142	17	)	)	PUNCT
ejpam-2101	143	1	=	=	SYM
ejpam-2101	143	2	ress(p(x	ress(p(x	PROPN
ejpam-2101	143	3	,	,	PUNCT
ejpam-2101	143	4	y	y	PROPN
ejpam-2101	143	5	,	,	PUNCT
ejpam-2101	143	6	z	z	PROPN
ejpam-2101	143	7	;	;	PUNCT
ejpam-2101	143	8	s	s	X
ejpam-2101	143	9	,	,	PUNCT
ejpam-2101	143	10	1	1	NUM
ejpam-2101	143	11	)	)	PUNCT
ejpam-2101	143	12	,	,	PUNCT
ejpam-2101	143	13	q(x	q(x	PROPN
ejpam-2101	143	14	,	,	PUNCT
ejpam-2101	143	15	y	y	PROPN
ejpam-2101	143	16	,	,	PUNCT
ejpam-2101	143	17	z	z	PROPN
ejpam-2101	143	18	;	;	PUNCT
ejpam-2101	143	19	s	s	X
ejpam-2101	143	20	,	,	PUNCT
ejpam-2101	143	21	1	1	NUM
ejpam-2101	143	22	)	)	PUNCT
ejpam-2101	143	23	)	)	PUNCT
ejpam-2101	143	24	.	.	PUNCT
ejpam-2101	144	1	let	let	VERB
ejpam-2101	144	2	the	the	DET
ejpam-2101	144	3	resultant	resultant	NOUN
ejpam-2101	144	4	matrix	matrix	NOUN
ejpam-2101	144	5	of	of	ADP
ejpam-2101	144	6	the	the	DET
ejpam-2101	144	7	curve	curve	NOUN
ejpam-2101	144	8	c1	c1	PROPN
ejpam-2101	144	9	be	be	AUX
ejpam-2101	144	10	denoted	denote	VERB
ejpam-2101	144	11	by	by	ADP
ejpam-2101	144	12	m(x	m(x	PROPN
ejpam-2101	144	13	,	,	PUNCT
ejpam-2101	144	14	y	y	PROPN
ejpam-2101	144	15	,	,	PUNCT
ejpam-2101	144	16	z	z	NOUN
ejpam-2101	144	17	)	)	PUNCT
ejpam-2101	144	18	.	.	PUNCT
ejpam-2101	145	1	we	we	PRON
ejpam-2101	145	2	note	note	VERB
ejpam-2101	145	3	that	that	SCONJ
ejpam-2101	145	4	m(x	m(x	PROPN
ejpam-2101	145	5	,	,	PUNCT
ejpam-2101	145	6	y	y	PROPN
ejpam-2101	145	7	,	,	PUNCT
ejpam-2101	145	8	z	z	NOUN
ejpam-2101	145	9	)	)	PUNCT
ejpam-2101	145	10	is	be	AUX
ejpam-2101	145	11	a	a	DET
ejpam-2101	145	12	square	square	ADJ
ejpam-2101	145	13	matrix	matrix	NOUN
ejpam-2101	145	14	of	of	ADP
ejpam-2101	145	15	size	size	NOUN
ejpam-2101	145	16	d	d	X
ejpam-2101	145	17	×	×	PROPN
ejpam-2101	145	18	d	d	NOUN
ejpam-2101	145	19	,	,	PUNCT
ejpam-2101	145	20	and	and	CCONJ
ejpam-2101	145	21	the	the	DET
ejpam-2101	145	22	rank	rank	NOUN
ejpam-2101	145	23	of	of	ADP
ejpam-2101	145	24	the	the	DET
ejpam-2101	145	25	matrix	matrix	NOUN
ejpam-2101	145	26	rankm(x	rankm(x	PROPN
ejpam-2101	145	27	,	,	PUNCT
ejpam-2101	145	28	y	y	PROPN
ejpam-2101	145	29	,	,	PUNCT
ejpam-2101	145	30	z	z	NOUN
ejpam-2101	145	31	)	)	PUNCT
ejpam-2101	145	32	=	=	SYM
ejpam-2101	145	33	d.	d.	PROPN
ejpam-2101	145	34	let	let	VERB
ejpam-2101	145	35	the	the	DET
ejpam-2101	145	36	rational	rational	ADJ
ejpam-2101	145	37	parametric	parametric	ADJ
ejpam-2101	145	38	plane	plane	NOUN
ejpam-2101	145	39	curve	curve	NOUN
ejpam-2101	145	40	c2	c2	PROPN
ejpam-2101	145	41	of	of	ADP
ejpam-2101	145	42	degree	degree	NOUN
ejpam-2101	145	43	d	d	AUX
ejpam-2101	145	44	′	′	NOUN
ejpam-2101	145	45	be	be	AUX
ejpam-2101	145	46	given	give	VERB
ejpam-2101	145	47	by	by	ADP
ejpam-2101	145	48	g(u	g(u	PROPN
ejpam-2101	145	49	,	,	PUNCT
ejpam-2101	145	50	v	v	NOUN
ejpam-2101	145	51	)	)	PUNCT
ejpam-2101	145	52	=	=	SYM
ejpam-2101	145	53	(	(	PUNCT
ejpam-2101	145	54	g0(u	g0(u	ADP
ejpam-2101	145	55	,	,	PUNCT
ejpam-2101	145	56	v	v	NOUN
ejpam-2101	145	57	)	)	PUNCT
ejpam-2101	145	58	,	,	PUNCT
ejpam-2101	145	59	g1(u	g1(u	PROPN
ejpam-2101	145	60	,	,	PUNCT
ejpam-2101	145	61	v	v	NOUN
ejpam-2101	145	62	)	)	PUNCT
ejpam-2101	145	63	,	,	PUNCT
ejpam-2101	145	64	g2(u	g2(u	PROPN
ejpam-2101	145	65	,	,	PUNCT
ejpam-2101	145	66	v	v	NOUN
ejpam-2101	145	67	)	)	PUNCT
ejpam-2101	145	68	)	)	PUNCT
ejpam-2101	145	69	,	,	PUNCT
ejpam-2101	145	70	(	(	PUNCT
ejpam-2101	145	71	u	u	NOUN
ejpam-2101	145	72	,	,	PUNCT
ejpam-2101	145	73	v	v	NOUN
ejpam-2101	145	74	)	)	PUNCT
ejpam-2101	145	75	6=	6=	X
ejpam-2101	145	76	(	(	PUNCT
ejpam-2101	145	77	0	0	NUM
ejpam-2101	145	78	,	,	PUNCT
ejpam-2101	145	79	0	0	NUM
ejpam-2101	145	80	)	)	PUNCT
ejpam-2101	145	81	.	.	PUNCT
ejpam-2101	146	1	by	by	ADP
ejpam-2101	146	2	substituting	substitute	VERB
ejpam-2101	146	3	the	the	DET
ejpam-2101	146	4	variables	variable	NOUN
ejpam-2101	146	5	x	x	SYM
ejpam-2101	146	6	,	,	PUNCT
ejpam-2101	146	7	y	y	PROPN
ejpam-2101	146	8	,	,	PUNCT
ejpam-2101	146	9	z	z	NOUN
ejpam-2101	146	10	in	in	ADP
ejpam-2101	146	11	matrix	matrix	NOUN
ejpam-2101	146	12	m(x	m(x	PROPN
ejpam-2101	146	13	,	,	PUNCT
ejpam-2101	146	14	y	y	PROPN
ejpam-2101	146	15	,	,	PUNCT
ejpam-2101	146	16	z	z	NOUN
ejpam-2101	146	17	)	)	PUNCT
ejpam-2101	146	18	with	with	ADP
ejpam-2101	146	19	(	(	PUNCT
ejpam-2101	146	20	g0(u	g0(u	ADP
ejpam-2101	146	21	,	,	PUNCT
ejpam-2101	146	22	v	v	NOUN
ejpam-2101	146	23	)	)	PUNCT
ejpam-2101	146	24	,	,	PUNCT
ejpam-2101	146	25	g1(u	g1(u	PROPN
ejpam-2101	146	26	,	,	PUNCT
ejpam-2101	146	27	v	v	NOUN
ejpam-2101	146	28	)	)	PUNCT
ejpam-2101	146	29	,	,	PUNCT
ejpam-2101	146	30	g2(u	g2(u	PROPN
ejpam-2101	146	31	,	,	PUNCT
ejpam-2101	146	32	v	v	NOUN
ejpam-2101	146	33	)	)	PUNCT
ejpam-2101	146	34	)	)	PUNCT
ejpam-2101	146	35	,	,	PUNCT
ejpam-2101	146	36	we	we	PRON
ejpam-2101	146	37	obtain	obtain	VERB
ejpam-2101	146	38	a	a	DET
ejpam-2101	146	39	matrix	matrix	NOUN
ejpam-2101	146	40	m(u	m(u	PROPN
ejpam-2101	146	41	,	,	PUNCT
ejpam-2101	146	42	v	v	NOUN
ejpam-2101	146	43	)	)	PUNCT
ejpam-2101	146	44	=	=	SYM
ejpam-2101	147	1	m(g(u	m(g(u	NOUN
ejpam-2101	147	2	,	,	PUNCT
ejpam-2101	147	3	v	v	NOUN
ejpam-2101	147	4	)	)	PUNCT
ejpam-2101	147	5	)	)	PUNCT
ejpam-2101	148	1	=	=	PUNCT
ejpam-2101	148	2	m(g0(u	m(g0(u	PROPN
ejpam-2101	148	3	,	,	PUNCT
ejpam-2101	148	4	v	v	NOUN
ejpam-2101	148	5	)	)	PUNCT
ejpam-2101	148	6	,	,	PUNCT
ejpam-2101	148	7	g1(u	g1(u	PROPN
ejpam-2101	148	8	,	,	PUNCT
ejpam-2101	148	9	v	v	NOUN
ejpam-2101	148	10	)	)	PUNCT
ejpam-2101	148	11	,	,	PUNCT
ejpam-2101	148	12	g2(u	g2(u	PROPN
ejpam-2101	148	13	,	,	PUNCT
ejpam-2101	148	14	v	v	NOUN
ejpam-2101	148	15	)	)	PUNCT
ejpam-2101	148	16	)	)	PUNCT
ejpam-2101	148	17	.	.	PUNCT
ejpam-2101	149	1	we	we	PRON
ejpam-2101	149	2	can	can	AUX
ejpam-2101	149	3	derive	derive	VERB
ejpam-2101	149	4	the	the	DET
ejpam-2101	149	5	following	follow	VERB
ejpam-2101	149	6	relationship	relationship	NOUN
ejpam-2101	149	7	between	between	ADP
ejpam-2101	149	8	the	the	DET
ejpam-2101	149	9	rank	rank	NOUN
ejpam-2101	149	10	of	of	ADP
ejpam-2101	149	11	the	the	DET
ejpam-2101	149	12	matrix	matrix	NOUN
ejpam-2101	149	13	m(u	m(u	PROPN
ejpam-2101	149	14	,	,	PUNCT
ejpam-2101	149	15	v	v	NOUN
ejpam-2101	149	16	)	)	PUNCT
ejpam-2101	149	17	and	and	CCONJ
ejpam-2101	149	18	the	the	DET
ejpam-2101	149	19	intersection	intersection	NOUN
ejpam-2101	149	20	of	of	ADP
ejpam-2101	149	21	the	the	DET
ejpam-2101	149	22	two	two	NUM
ejpam-2101	149	23	curves	curve	NOUN
ejpam-2101	149	24	:	:	PUNCT
ejpam-2101	149	25	theorem	theorem	NOUN
ejpam-2101	149	26	2	2	NUM
ejpam-2101	149	27	.	.	PUNCT
ejpam-2101	149	28	{	{	PUNCT
ejpam-2101	149	29	(	(	PUNCT
ejpam-2101	149	30	u0	u0	PROPN
ejpam-2101	149	31	,	,	PUNCT
ejpam-2101	149	32	v0	v0	PROPN
ejpam-2101	149	33	)	)	PUNCT
ejpam-2101	149	34	6=	6=	ADP
ejpam-2101	149	35	(	(	PUNCT
ejpam-2101	149	36	0	0	NUM
ejpam-2101	149	37	,	,	PUNCT
ejpam-2101	149	38	0	0	NUM
ejpam-2101	149	39	)	)	PUNCT
ejpam-2101	149	40	|	|	ADV
ejpam-2101	149	41	rankm(u0	rankm(u0	NOUN
ejpam-2101	149	42	,	,	PUNCT
ejpam-2101	149	43	v0	v0	PROPN
ejpam-2101	149	44	)	)	PUNCT
ejpam-2101	149	45	<	<	X
ejpam-2101	149	46	d	d	X
ejpam-2101	149	47	}	}	PUNCT
ejpam-2101	149	48	⇔	⇔	PROPN
ejpam-2101	149	49	g(u0	g(u0	NOUN
ejpam-2101	149	50	,	,	PUNCT
ejpam-2101	149	51	v0	v0	PROPN
ejpam-2101	149	52	)	)	PUNCT
ejpam-2101	149	53	∈	∈	PROPN
ejpam-2101	149	54	c1	c1	PROPN
ejpam-2101	149	55	∩c2	∩c2	PROPN
ejpam-2101	149	56	.	.	PUNCT
ejpam-2101	150	1	proof	proof	NOUN
ejpam-2101	150	2	.	.	PUNCT
ejpam-2101	151	1	g(u0	g(u0	NOUN
ejpam-2101	151	2	,	,	PUNCT
ejpam-2101	151	3	v0	v0	PROPN
ejpam-2101	151	4	)	)	PUNCT
ejpam-2101	151	5	∈	∈	PROPN
ejpam-2101	151	6	c1	c1	PROPN
ejpam-2101	151	7	∩c2	∩c2	INTJ
ejpam-2101	152	1	if	if	SCONJ
ejpam-2101	152	2	and	and	CCONJ
ejpam-2101	152	3	only	only	ADV
ejpam-2101	152	4	if	if	SCONJ
ejpam-2101	152	5	g(u0	g(u0	NOUN
ejpam-2101	152	6	,	,	PUNCT
ejpam-2101	152	7	v0	v0	PROPN
ejpam-2101	152	8	)	)	PUNCT
ejpam-2101	152	9	is	be	AUX
ejpam-2101	152	10	such	such	ADJ
ejpam-2101	152	11	that	that	SCONJ
ejpam-2101	152	12	det	det	PROPN
ejpam-2101	152	13	m(g(u0	m(g(u0	PROPN
ejpam-2101	152	14	,	,	PUNCT
ejpam-2101	152	15	v0	v0	NOUN
ejpam-2101	152	16	)	)	PUNCT
ejpam-2101	152	17	)	)	PUNCT
ejpam-2101	153	1	=	=	PUNCT
ejpam-2101	153	2	0	0	NUM
ejpam-2101	153	3	,	,	PUNCT
ejpam-2101	153	4	which	which	PRON
ejpam-2101	153	5	is	be	AUX
ejpam-2101	153	6	equivalent	equivalent	ADJ
ejpam-2101	153	7	to	to	ADP
ejpam-2101	153	8	the	the	DET
ejpam-2101	153	9	condition	condition	NOUN
ejpam-2101	153	10	that	that	SCONJ
ejpam-2101	153	11	rankm(u0	rankm(u0	NOUN
ejpam-2101	153	12	,	,	PUNCT
ejpam-2101	153	13	v0	v0	PROPN
ejpam-2101	153	14	)	)	PUNCT
ejpam-2101	153	15	<	<	X
ejpam-2101	153	16	d.	d.	PROPN
ejpam-2101	153	17	hence	hence	ADV
ejpam-2101	153	18	,	,	PUNCT
ejpam-2101	153	19	the	the	DET
ejpam-2101	153	20	computational	computational	ADJ
ejpam-2101	153	21	algorithm	algorithm	NOUN
ejpam-2101	153	22	follows	follow	VERB
ejpam-2101	153	23	directly	directly	ADV
ejpam-2101	153	24	as	as	ADP
ejpam-2101	153	25	below	below	ADV
ejpam-2101	153	26	:	:	PUNCT
ejpam-2101	153	27	resultant	resultant	NOUN
ejpam-2101	153	28	matrix	matrix	NOUN
ejpam-2101	153	29	algorithm	algorithm	NOUN
ejpam-2101	153	30	input	input	NOUN
ejpam-2101	153	31	:	:	PUNCT
ejpam-2101	154	1	parametrized	parametrized	ADJ
ejpam-2101	154	2	curves	curve	NOUN
ejpam-2101	154	3	f(s	f(s	PROPN
ejpam-2101	154	4	,	,	PUNCT
ejpam-2101	154	5	t	t	PROPN
ejpam-2101	154	6	)	)	PUNCT
ejpam-2101	154	7	and	and	CCONJ
ejpam-2101	154	8	g(u	g(u	PROPN
ejpam-2101	154	9	,	,	PUNCT
ejpam-2101	154	10	v	v	NOUN
ejpam-2101	154	11	)	)	PUNCT
ejpam-2101	154	12	.	.	PUNCT
ejpam-2101	155	1	output	output	NOUN
ejpam-2101	155	2	:	:	PUNCT
ejpam-2101	155	3	the	the	DET
ejpam-2101	155	4	set	set	NOUN
ejpam-2101	155	5	of	of	ADP
ejpam-2101	155	6	parameters	parameter	NOUN
ejpam-2101	155	7	and	and	CCONJ
ejpam-2101	155	8	their	their	PRON
ejpam-2101	155	9	corresponding	corresponding	ADJ
ejpam-2101	155	10	points	point	NOUN
ejpam-2101	155	11	of	of	ADP
ejpam-2101	155	12	the	the	DET
ejpam-2101	155	13	intersection	intersection	NOUN
ejpam-2101	155	14	of	of	ADP
ejpam-2101	155	15	two	two	NUM
ejpam-2101	155	16	curves	curve	NOUN
ejpam-2101	155	17	given	give	VERB
ejpam-2101	155	18	by	by	ADP
ejpam-2101	155	19	parametrization	parametrization	NOUN
ejpam-2101	155	20	f(s	f(	NOUN
ejpam-2101	155	21	,	,	PUNCT
ejpam-2101	155	22	t	t	PROPN
ejpam-2101	155	23	)	)	PUNCT
ejpam-2101	155	24	and	and	CCONJ
ejpam-2101	155	25	g(u	g(u	PROPN
ejpam-2101	155	26	,	,	PUNCT
ejpam-2101	155	27	v	v	NOUN
ejpam-2101	155	28	)	)	PUNCT
ejpam-2101	155	29	.	.	PUNCT
ejpam-2101	156	1	procedure	procedure	NOUN
ejpam-2101	156	2	:	:	PUNCT
ejpam-2101	156	3	1	1	X
ejpam-2101	156	4	.	.	X
ejpam-2101	156	5	compute	compute	PROPN
ejpam-2101	156	6	p(s	p(s	NOUN
ejpam-2101	156	7	,	,	PUNCT
ejpam-2101	156	8	t),q(s	t),q(s	NUM
ejpam-2101	156	9	,	,	PUNCT
ejpam-2101	156	10	t	t	PROPN
ejpam-2101	156	11	)	)	PUNCT
ejpam-2101	156	12	,	,	PUNCT
ejpam-2101	156	13	the	the	DET
ejpam-2101	156	14	µ-basis	µ-basis	NOUN
ejpam-2101	156	15	for	for	ADP
ejpam-2101	156	16	f(s	f(	NOUN
ejpam-2101	156	17	,	,	PUNCT
ejpam-2101	156	18	t	t	PROPN
ejpam-2101	156	19	)	)	PUNCT
ejpam-2101	156	20	.	.	PUNCT
ejpam-2101	157	1	2	2	X
ejpam-2101	157	2	.	.	X
ejpam-2101	157	3	construct	construct	VERB
ejpam-2101	157	4	the	the	DET
ejpam-2101	157	5	resultant	resultant	NOUN
ejpam-2101	157	6	matrix	matrix	NOUN
ejpam-2101	157	7	of	of	ADP
ejpam-2101	157	8	the	the	DET
ejpam-2101	157	9	curve	curve	NOUN
ejpam-2101	157	10	f(s	f(s	PROPN
ejpam-2101	157	11	,	,	PUNCT
ejpam-2101	157	12	t	t	PROPN
ejpam-2101	157	13	)	)	PUNCT
ejpam-2101	157	14	denoted	denote	VERB
ejpam-2101	157	15	by	by	ADP
ejpam-2101	157	16	m(x	m(x	PROPN
ejpam-2101	157	17	,	,	PUNCT
ejpam-2101	157	18	y	y	PROPN
ejpam-2101	157	19	,	,	PUNCT
ejpam-2101	157	20	z	z	NOUN
ejpam-2101	157	21	)	)	PUNCT
ejpam-2101	157	22	using	use	VERB
ejpam-2101	157	23	information	information	NOUN
ejpam-2101	157	24	of	of	ADP
ejpam-2101	157	25	the	the	DET
ejpam-2101	157	26	µ-basis	µ-basis	NOUN
ejpam-2101	157	27	.	.	PUNCT
ejpam-2101	158	1	3	3	X
ejpam-2101	158	2	.	.	X
ejpam-2101	158	3	substituting	substitute	VERB
ejpam-2101	158	4	the	the	DET
ejpam-2101	158	5	variables	variable	NOUN
ejpam-2101	158	6	x	x	X
ejpam-2101	158	7	,	,	PUNCT
ejpam-2101	158	8	y	y	PROPN
ejpam-2101	158	9	,	,	PUNCT
ejpam-2101	158	10	z	z	NOUN
ejpam-2101	158	11	in	in	ADP
ejpam-2101	158	12	matrix	matrix	NOUN
ejpam-2101	158	13	m(x	m(x	PROPN
ejpam-2101	158	14	,	,	PUNCT
ejpam-2101	158	15	y	y	PROPN
ejpam-2101	158	16	,	,	PUNCT
ejpam-2101	158	17	z	z	NOUN
ejpam-2101	158	18	)	)	PUNCT
ejpam-2101	158	19	with	with	ADP
ejpam-2101	158	20	(	(	PUNCT
ejpam-2101	158	21	g0(u	g0(u	ADP
ejpam-2101	158	22	,	,	PUNCT
ejpam-2101	158	23	v	v	NOUN
ejpam-2101	158	24	)	)	PUNCT
ejpam-2101	158	25	,	,	PUNCT
ejpam-2101	158	26	g1(u	g1(u	PROPN
ejpam-2101	158	27	,	,	PUNCT
ejpam-2101	158	28	v	v	NOUN
ejpam-2101	158	29	)	)	PUNCT
ejpam-2101	158	30	,	,	PUNCT
ejpam-2101	158	31	g2(u	g2(u	PROPN
ejpam-2101	158	32	,	,	PUNCT
ejpam-2101	158	33	v	v	NOUN
ejpam-2101	158	34	)	)	PUNCT
ejpam-2101	158	35	)	)	PUNCT
ejpam-2101	158	36	.	.	PUNCT
ejpam-2101	159	1	4	4	X
ejpam-2101	159	2	.	.	X
ejpam-2101	159	3	the	the	DET
ejpam-2101	159	4	solution	solution	NOUN
ejpam-2101	159	5	to	to	ADP
ejpam-2101	159	6	det(m(g0(u	det(m(g0(u	PROPN
ejpam-2101	159	7	,	,	PUNCT
ejpam-2101	159	8	v	v	NOUN
ejpam-2101	159	9	)	)	PUNCT
ejpam-2101	159	10	,	,	PUNCT
ejpam-2101	159	11	g1(u	g1(u	PROPN
ejpam-2101	159	12	,	,	PUNCT
ejpam-2101	159	13	v	v	NOUN
ejpam-2101	159	14	)	)	PUNCT
ejpam-2101	159	15	,	,	PUNCT
ejpam-2101	159	16	g2(u	g2(u	PROPN
ejpam-2101	159	17	,	,	PUNCT
ejpam-2101	159	18	v	v	NOUN
ejpam-2101	159	19	)	)	PUNCT
ejpam-2101	159	20	)	)	PUNCT
ejpam-2101	160	1	=	=	SYM
ejpam-2101	160	2	0	0	NUM
ejpam-2101	160	3	corresponding	correspond	VERB
ejpam-2101	160	4	the	the	DET
ejpam-2101	160	5	the	the	DET
ejpam-2101	160	6	parameters	parameter	NOUN
ejpam-2101	160	7	(	(	PUNCT
ejpam-2101	160	8	u0	u0	PROPN
ejpam-2101	160	9	,	,	PUNCT
ejpam-2101	160	10	v0	v0	PROPN
ejpam-2101	160	11	)	)	PUNCT
ejpam-2101	160	12	such	such	ADJ
ejpam-2101	160	13	that	that	DET
ejpam-2101	160	14	g(u0	g(u0	NOUN
ejpam-2101	160	15	,	,	PUNCT
ejpam-2101	160	16	v0	v0	PROPN
ejpam-2101	160	17	)	)	PUNCT
ejpam-2101	160	18	are	be	AUX
ejpam-2101	160	19	the	the	DET
ejpam-2101	160	20	intersection	intersection	NOUN
ejpam-2101	160	21	points	point	NOUN
ejpam-2101	160	22	of	of	ADP
ejpam-2101	160	23	the	the	DET
ejpam-2101	160	24	two	two	NUM
ejpam-2101	160	25	curves	curve	NOUN
ejpam-2101	160	26	with	with	ADP
ejpam-2101	160	27	correct	correct	ADJ
ejpam-2101	160	28	multiplicity	multiplicity	NOUN
ejpam-2101	160	29	.	.	PUNCT
ejpam-2101	161	1	m.	m.	PROPN
ejpam-2101	161	2	tesemma	tesemma	PROPN
ejpam-2101	161	3	,	,	PUNCT
ejpam-2101	161	4	h.	h.	PROPN
ejpam-2101	161	5	wang	wang	PROPN
ejpam-2101	161	6	,	,	PUNCT
ejpam-2101	161	7	/	/	SYM
ejpam-2101	161	8	eur	eur	NOUN
ejpam-2101	161	9	.	.	PUNCT
ejpam-2101	162	1	j.	j.	PROPN
ejpam-2101	162	2	pure	pure	PROPN
ejpam-2101	162	3	appl	appl	PROPN
ejpam-2101	162	4	.	.	PROPN
ejpam-2101	162	5	math	math	PROPN
ejpam-2101	162	6	,	,	PUNCT
ejpam-2101	162	7	7	7	NUM
ejpam-2101	162	8	(	(	PUNCT
ejpam-2101	162	9	2014	2014	NUM
ejpam-2101	162	10	)	)	PUNCT
ejpam-2101	162	11	,	,	PUNCT
ejpam-2101	162	12	191	191	NUM
ejpam-2101	162	13	-	-	SYM
ejpam-2101	162	14	200	200	NUM
ejpam-2101	162	15	197	197	NUM
ejpam-2101	162	16	example	example	NOUN
ejpam-2101	162	17	2	2	NUM
ejpam-2101	162	18	.	.	PUNCT
ejpam-2101	162	19	to	to	PART
ejpam-2101	162	20	compare	compare	VERB
ejpam-2101	162	21	the	the	DET
ejpam-2101	162	22	algorithm	algorithm	NOUN
ejpam-2101	162	23	,	,	PUNCT
ejpam-2101	162	24	we	we	PRON
ejpam-2101	162	25	will	will	AUX
ejpam-2101	162	26	use	use	VERB
ejpam-2101	162	27	the	the	DET
ejpam-2101	162	28	same	same	ADJ
ejpam-2101	162	29	example	example	NOUN
ejpam-2101	162	30	as	as	ADP
ejpam-2101	162	31	before	before	ADV
ejpam-2101	162	32	,	,	PUNCT
ejpam-2101	162	33	two	two	NUM
ejpam-2101	162	34	rational	rational	ADJ
ejpam-2101	162	35	paramatrized	paramatrize	VERB
ejpam-2101	162	36	plane	plane	NOUN
ejpam-2101	162	37	curves	curve	NOUN
ejpam-2101	162	38	given	give	VERB
ejpam-2101	162	39	by	by	ADP
ejpam-2101	162	40	wang	wang	PROPN
ejpam-2101	162	41	-	-	PUNCT
ejpam-2101	162	42	goldman	goldman	PROPN
ejpam-2101	163	1	[	[	X
ejpam-2101	163	2	11	11	NUM
ejpam-2101	163	3	]	]	SYM
ejpam-2101	163	4	:	:	PUNCT
ejpam-2101	163	5	lemniscate	lemniscate	PROPN
ejpam-2101	163	6	of	of	ADP
ejpam-2101	163	7	bernoulli	bernoulli	PROPN
ejpam-2101	163	8	,	,	PUNCT
ejpam-2101	163	9	a	a	DET
ejpam-2101	163	10	rational	rational	ADJ
ejpam-2101	163	11	quartic	quartic	ADJ
ejpam-2101	163	12	curve	curve	NOUN
ejpam-2101	163	13	f	f	PROPN
ejpam-2101	163	14	and	and	CCONJ
ejpam-2101	163	15	a	a	DET
ejpam-2101	163	16	rational	rational	ADJ
ejpam-2101	163	17	cubic	cubic	ADJ
ejpam-2101	163	18	curve	curve	NOUN
ejpam-2101	163	19	g(u	g(u	PROPN
ejpam-2101	163	20	,	,	PUNCT
ejpam-2101	163	21	v	v	NOUN
ejpam-2101	163	22	)	)	PUNCT
ejpam-2101	163	23	.	.	PUNCT
ejpam-2101	164	1	f(s	f(s	PROPN
ejpam-2101	164	2	,	,	PUNCT
ejpam-2101	164	3	t	t	PROPN
ejpam-2101	164	4	)	)	PUNCT
ejpam-2101	164	5	=(	=(	NOUN
ejpam-2101	164	6	s4	s4	PROPN
ejpam-2101	164	7	−	−	PROPN
ejpam-2101	164	8	t4	t4	PROPN
ejpam-2101	164	9	,	,	PUNCT
ejpam-2101	164	10	−2st(t2	−2st(t2	NOUN
ejpam-2101	164	11	−	−	PROPN
ejpam-2101	164	12	s2	s2	PROPN
ejpam-2101	164	13	)	)	PUNCT
ejpam-2101	164	14	,	,	PUNCT
ejpam-2101	164	15	t4	t4	PROPN
ejpam-2101	164	16	+	+	PROPN
ejpam-2101	164	17	6s2	6s2	NUM
ejpam-2101	164	18	t2	t2	PROPN
ejpam-2101	164	19	+	+	CCONJ
ejpam-2101	164	20	s4	s4	PROPN
ejpam-2101	164	21	)	)	PUNCT
ejpam-2101	164	22	,	,	PUNCT
ejpam-2101	164	23	bg(u	bg(u	X
ejpam-2101	164	24	,	,	PUNCT
ejpam-2101	164	25	v	v	NOUN
ejpam-2101	164	26	)	)	PUNCT
ejpam-2101	164	27	=(	=(	NOUN
ejpam-2101	164	28	−3v3	−3v3	NUM
ejpam-2101	164	29	−	−	PROPN
ejpam-2101	164	30	2uv2	2uv2	NUM
ejpam-2101	165	1	+	+	CCONJ
ejpam-2101	165	2	4u2v	4u2v	NOUN
ejpam-2101	165	3	+	+	CCONJ
ejpam-2101	165	4	2u3	2u3	NUM
ejpam-2101	165	5	,	,	PUNCT
ejpam-2101	165	6	−v3	−v3	PROPN
ejpam-2101	165	7	+	+	CCONJ
ejpam-2101	165	8	3uv2	3uv2	NUM
ejpam-2101	165	9	−	−	PROPN
ejpam-2101	165	10	u3	u3	NOUN
ejpam-2101	165	11	+	+	CCONJ
ejpam-2101	165	12	2u2v	2u2v	NUM
ejpam-2101	165	13	,	,	PUNCT
ejpam-2101	165	14	2uv2	2uv2	NUM
ejpam-2101	166	1	+	+	CCONJ
ejpam-2101	166	2	2u2v	2u2v	ADJ
ejpam-2101	166	3	+	+	CCONJ
ejpam-2101	166	4	u3	u3	NOUN
ejpam-2101	166	5	)	)	PUNCT
ejpam-2101	166	6	.	.	PUNCT
ejpam-2101	167	1	resultant	resultant	NOUN
ejpam-2101	167	2	matrix	matrix	NOUN
ejpam-2101	167	3	method	method	NOUN
ejpam-2101	167	4	:	:	PUNCT
ejpam-2101	167	5	compute	compute	VERB
ejpam-2101	167	6	the	the	DET
ejpam-2101	167	7	µ-basis	µ-basis	NOUN
ejpam-2101	167	8	of	of	ADP
ejpam-2101	167	9	the	the	DET
ejpam-2101	167	10	parametrized	parametrized	ADJ
ejpam-2101	167	11	curve	curve	NOUN
ejpam-2101	167	12	f(s	f(s	PROPN
ejpam-2101	167	13	,	,	PUNCT
ejpam-2101	167	14	t	t	PROPN
ejpam-2101	167	15	)	)	PUNCT
ejpam-2101	167	16	in	in	ADP
ejpam-2101	167	17	terms	term	NOUN
ejpam-2101	167	18	of	of	ADP
ejpam-2101	167	19	the	the	DET
ejpam-2101	167	20	moving	move	VERB
ejpam-2101	167	21	lines	line	NOUN
ejpam-2101	167	22	as	as	ADP
ejpam-2101	167	23	below	below	ADV
ejpam-2101	167	24	:	:	PUNCT
ejpam-2101	167	25	µ-basis	µ-basis	NOUN
ejpam-2101	167	26	:	:	PUNCT
ejpam-2101	167	27	p(s	p(s	NUM
ejpam-2101	167	28	,	,	PUNCT
ejpam-2101	167	29	t	t	PROPN
ejpam-2101	167	30	)	)	PUNCT
ejpam-2101	167	31	=	=	PUNCT
ejpam-2101	167	32	(	(	PUNCT
ejpam-2101	167	33	−s2	−s2	PROPN
ejpam-2101	167	34	−	−	PROPN
ejpam-2101	167	35	t2	t2	NOUN
ejpam-2101	167	36	,	,	PUNCT
ejpam-2101	167	37	−2st	−2st	NUM
ejpam-2101	167	38	,	,	PUNCT
ejpam-2101	167	39	s2	s2	NOUN
ejpam-2101	167	40	−	−	NOUN
ejpam-2101	167	41	t2	t2	PROPN
ejpam-2101	167	42	)	)	PUNCT
ejpam-2101	167	43	,	,	PUNCT
ejpam-2101	167	44	q(s	q(s	PROPN
ejpam-2101	167	45	,	,	PUNCT
ejpam-2101	167	46	t	t	PROPN
ejpam-2101	167	47	)	)	PUNCT
ejpam-2101	167	48	=	=	SYM
ejpam-2101	167	49	(	(	PUNCT
ejpam-2101	167	50	2st	2st	NOUN
ejpam-2101	167	51	,	,	PUNCT
ejpam-2101	167	52	−s2	−s2	NOUN
ejpam-2101	167	53	−	−	PROPN
ejpam-2101	167	54	t2	t2	NOUN
ejpam-2101	167	55	,	,	PUNCT
ejpam-2101	167	56	0	0	NUM
ejpam-2101	167	57	)	)	PUNCT
ejpam-2101	167	58	moving	move	VERB
ejpam-2101	167	59	line	line	NOUN
ejpam-2101	167	60	form	form	NOUN
ejpam-2101	167	61	:	:	PUNCT
ejpam-2101	167	62	p(x	p(x	PROPN
ejpam-2101	167	63	,	,	PUNCT
ejpam-2101	167	64	y	y	PROPN
ejpam-2101	167	65	,	,	PUNCT
ejpam-2101	167	66	z	z	PROPN
ejpam-2101	167	67	;	;	PUNCT
ejpam-2101	167	68	s	s	X
ejpam-2101	167	69	,	,	PUNCT
ejpam-2101	167	70	1	1	NUM
ejpam-2101	167	71	)	)	PUNCT
ejpam-2101	167	72	=	=	SYM
ejpam-2101	168	1	s2(−x	s2(−x	PROPN
ejpam-2101	169	1	+	+	PUNCT
ejpam-2101	170	1	z)−	z)−	NUM
ejpam-2101	170	2	2s	2s	NUM
ejpam-2101	170	3	y	y	X
ejpam-2101	170	4	−	−	PROPN
ejpam-2101	170	5	(	(	PUNCT
ejpam-2101	170	6	x	x	PROPN
ejpam-2101	170	7	+	+	NUM
ejpam-2101	170	8	z	z	NOUN
ejpam-2101	170	9	)	)	PUNCT
ejpam-2101	170	10	,	,	PUNCT
ejpam-2101	170	11	q(x	q(x	PROPN
ejpam-2101	170	12	,	,	PUNCT
ejpam-2101	170	13	y	y	PROPN
ejpam-2101	170	14	,	,	PUNCT
ejpam-2101	170	15	z	z	PROPN
ejpam-2101	170	16	;	;	PUNCT
ejpam-2101	170	17	s	s	X
ejpam-2101	170	18	,	,	PUNCT
ejpam-2101	170	19	1	1	NUM
ejpam-2101	170	20	)	)	PUNCT
ejpam-2101	170	21	=	=	SYM
ejpam-2101	170	22	−s2	−s2	PROPN
ejpam-2101	170	23	y	y	PROPN
ejpam-2101	170	24	+	+	CCONJ
ejpam-2101	170	25	2sx	2sx	ADJ
ejpam-2101	170	26	−	−	NOUN
ejpam-2101	170	27	y.	y.	NOUN
ejpam-2101	170	28	then	then	ADV
ejpam-2101	170	29	,	,	PUNCT
ejpam-2101	170	30	construct	construct	VERB
ejpam-2101	170	31	matrix	matrix	NOUN
ejpam-2101	170	32	m(x	m(x	PROPN
ejpam-2101	170	33	,	,	PUNCT
ejpam-2101	170	34	y	y	PROPN
ejpam-2101	170	35	,	,	PUNCT
ejpam-2101	170	36	z	z	NOUN
ejpam-2101	170	37	)	)	PUNCT
ejpam-2101	170	38	as	as	ADP
ejpam-2101	170	39	m(x	m(x	PROPN
ejpam-2101	170	40	,	,	PUNCT
ejpam-2101	170	41	y	y	PROPN
ejpam-2101	170	42	,	,	PUNCT
ejpam-2101	170	43	z	z	NOUN
ejpam-2101	170	44	)	)	PUNCT
ejpam-2101	171	1	=	=	NOUN
ejpam-2101	171	2			NOUN
ejpam-2101	171	3			ADJ
ejpam-2101	171	4			ADJ
ejpam-2101	171	5			NOUN
ejpam-2101	171	6	−x	−x	NOUN
ejpam-2101	171	7	+	+	CCONJ
ejpam-2101	171	8	z	z	AUX
ejpam-2101	171	9	0	0	NUM
ejpam-2101	171	10	−y	−y	NOUN
ejpam-2101	171	11	0	0	NUM
ejpam-2101	172	1	−2y	−2y	PROPN
ejpam-2101	172	2	−x	−x	NOUN
ejpam-2101	172	3	+	+	CCONJ
ejpam-2101	172	4	z	z	NOUN
ejpam-2101	172	5	2x	2x	NUM
ejpam-2101	172	6	−y	−y	VERB
ejpam-2101	172	7	−(x	−(x	NOUN
ejpam-2101	173	1	+	+	CCONJ
ejpam-2101	173	2	z	z	X
ejpam-2101	173	3	)	)	PUNCT
ejpam-2101	173	4	−2y	−2y	PROPN
ejpam-2101	173	5	−y	−y	VERB
ejpam-2101	174	1	2x	2x	NUM
ejpam-2101	175	1	0	0	PUNCT
ejpam-2101	175	2	−(x	−(x	NOUN
ejpam-2101	175	3	+	+	CCONJ
ejpam-2101	175	4	z	z	NOUN
ejpam-2101	175	5	)	)	PUNCT
ejpam-2101	175	6	0	0	NUM
ejpam-2101	175	7	−y	−y	NOUN
ejpam-2101	175	8			PROPN
ejpam-2101	175	9			PROPN
ejpam-2101	175	10			PROPN
ejpam-2101	175	11			PROPN
ejpam-2101	175	12	.	.	PUNCT
ejpam-2101	176	1	and	and	CCONJ
ejpam-2101	176	2	m(u	m(u	PROPN
ejpam-2101	176	3	,	,	PUNCT
ejpam-2101	176	4	v	v	NOUN
ejpam-2101	176	5	)	)	PUNCT
ejpam-2101	177	1	=	=	NOUN
ejpam-2101	177	2	m(g(u	m(g(u	NOUN
ejpam-2101	177	3	,	,	PUNCT
ejpam-2101	177	4	v	v	NOUN
ejpam-2101	177	5	)	)	PUNCT
ejpam-2101	177	6	)	)	PUNCT
ejpam-2101	178	1	=	=	SYM
ejpam-2101	178	2	4(u2	4(u2	PROPN
ejpam-2101	179	1	+	+	NUM
ejpam-2101	179	2	2uv	2uv	ADJ
ejpam-2101	179	3	+	+	CCONJ
ejpam-2101	179	4	2v2)2(22u8	2v2)2(22u8	ADJ
ejpam-2101	179	5	−	−	NOUN
ejpam-2101	179	6	86u6v2	86u6v2	NOUN
ejpam-2101	179	7	−	−	PROPN
ejpam-2101	179	8	10u5v3	10u5v3	NUM
ejpam-2101	179	9	+	+	CCONJ
ejpam-2101	179	10	131u4v4	131u4v4	NUM
ejpam-2101	179	11	+	+	CCONJ
ejpam-2101	179	12	34u3v5	34u3v5	PROPN
ejpam-2101	179	13	−	−	PROPN
ejpam-2101	179	14	84u2v6	84u2v6	NOUN
ejpam-2101	179	15	−	−	PROPN
ejpam-2101	179	16	20uv7	20uv7	NOUN
ejpam-2101	179	17	+	+	CCONJ
ejpam-2101	179	18	25v8	25v8	NUM
ejpam-2101	179	19	)	)	PUNCT
ejpam-2101	179	20	.	.	PUNCT
ejpam-2101	180	1	since	since	SCONJ
ejpam-2101	180	2	m(u	m(u	PROPN
ejpam-2101	180	3	,	,	PUNCT
ejpam-2101	180	4	v	v	NOUN
ejpam-2101	180	5	)	)	PUNCT
ejpam-2101	180	6	is	be	AUX
ejpam-2101	180	7	exactly	exactly	ADV
ejpam-2101	180	8	the	the	DET
ejpam-2101	180	9	same	same	ADJ
ejpam-2101	180	10	as	as	ADP
ejpam-2101	180	11	f(g(u	f(g(u	PROPN
ejpam-2101	180	12	,	,	PUNCT
ejpam-2101	180	13	v	v	NOUN
ejpam-2101	180	14	)	)	PUNCT
ejpam-2101	180	15	)	)	PUNCT
ejpam-2101	180	16	,	,	PUNCT
ejpam-2101	180	17	the	the	DET
ejpam-2101	180	18	solutions	solution	NOUN
ejpam-2101	180	19	to	to	ADP
ejpam-2101	180	20	m(u	m(u	PROPN
ejpam-2101	180	21	,	,	PUNCT
ejpam-2101	180	22	v	v	NOUN
ejpam-2101	180	23	)	)	PUNCT
ejpam-2101	180	24	=	=	SYM
ejpam-2101	180	25	0	0	NUM
ejpam-2101	180	26	are	be	AUX
ejpam-2101	180	27	indeed	indeed	ADV
ejpam-2101	180	28	the	the	DET
ejpam-2101	180	29	parameters	parameter	NOUN
ejpam-2101	180	30	of	of	ADP
ejpam-2101	180	31	g(u	g(u	PROPN
ejpam-2101	180	32	,	,	PUNCT
ejpam-2101	180	33	v	v	NOUN
ejpam-2101	180	34	)	)	PUNCT
ejpam-2101	180	35	corresponding	correspond	VERB
ejpam-2101	180	36	to	to	ADP
ejpam-2101	180	37	the	the	DET
ejpam-2101	180	38	intersections	intersection	NOUN
ejpam-2101	180	39	of	of	ADP
ejpam-2101	180	40	the	the	DET
ejpam-2101	180	41	two	two	NUM
ejpam-2101	180	42	curves	curve	NOUN
ejpam-2101	180	43	.	.	PUNCT
ejpam-2101	181	1	3.3	3.3	NUM
ejpam-2101	181	2	.	.	PUNCT
ejpam-2101	182	1	smith	smith	PROPN
ejpam-2101	182	2	normal	normal	ADJ
ejpam-2101	182	3	form	form	NOUN
ejpam-2101	182	4	method	method	NOUN
ejpam-2101	182	5	recall	recall	VERB
ejpam-2101	182	6	that	that	SCONJ
ejpam-2101	182	7	for	for	SCONJ
ejpam-2101	182	8	every	every	DET
ejpam-2101	182	9	nonzero	nonzero	PROPN
ejpam-2101	182	10	square	square	ADJ
ejpam-2101	182	11	univariate	univariate	ADJ
ejpam-2101	182	12	polynomial	polynomial	ADJ
ejpam-2101	182	13	matrix	matrix	NOUN
ejpam-2101	182	14	a	a	PRON
ejpam-2101	182	15	(	(	PUNCT
ejpam-2101	182	16	that	that	PRON
ejpam-2101	182	17	is	be	AUX
ejpam-2101	182	18	the	the	DET
ejpam-2101	182	19	entries	entry	NOUN
ejpam-2101	182	20	of	of	ADP
ejpam-2101	182	21	matrix	matrix	NOUN
ejpam-2101	182	22	a	a	PRON
ejpam-2101	182	23	are	be	AUX
ejpam-2101	182	24	polynomials	polynomial	NOUN
ejpam-2101	182	25	in	in	ADP
ejpam-2101	182	26	one	one	NUM
ejpam-2101	182	27	variable	variable	NOUN
ejpam-2101	182	28	)	)	PUNCT
ejpam-2101	182	29	with	with	ADP
ejpam-2101	182	30	rank(a	rank(a	NOUN
ejpam-2101	182	31	)	)	PUNCT
ejpam-2101	182	32	=	=	SYM
ejpam-2101	183	1	r	r	NOUN
ejpam-2101	183	2	,	,	PUNCT
ejpam-2101	183	3	there	there	PRON
ejpam-2101	183	4	exist	exist	VERB
ejpam-2101	183	5	invertible	invertible	ADJ
ejpam-2101	183	6	polynomial	polynomial	ADJ
ejpam-2101	183	7	matrices	matrix	NOUN
ejpam-2101	183	8	p	p	NOUN
ejpam-2101	183	9	,	,	PUNCT
ejpam-2101	183	10	q	q	X
ejpam-2101	183	11	(	(	PUNCT
ejpam-2101	183	12	p	p	NOUN
ejpam-2101	183	13	is	be	AUX
ejpam-2101	183	14	invertible	invertible	ADJ
ejpam-2101	183	15	if	if	SCONJ
ejpam-2101	183	16	det(p	det(p	PROPN
ejpam-2101	183	17	)	)	PUNCT
ejpam-2101	183	18	is	be	AUX
ejpam-2101	183	19	a	a	DET
ejpam-2101	183	20	non	non	ADJ
ejpam-2101	183	21	-	-	ADJ
ejpam-2101	183	22	zero	zero	ADJ
ejpam-2101	183	23	constant	constant	ADJ
ejpam-2101	183	24	)	)	PUNCT
ejpam-2101	183	25	such	such	ADJ
ejpam-2101	183	26	that	that	DET
ejpam-2101	183	27	paq	paq	NOUN
ejpam-2101	183	28	=	=	SYM
ejpam-2101	183	29	diag	diag	PROPN
ejpam-2101	183	30	(	(	PUNCT
ejpam-2101	183	31	f1	f1	NOUN
ejpam-2101	183	32	,	,	PUNCT
ejpam-2101	183	33	f2	f2	PROPN
ejpam-2101	183	34	,	,	PUNCT
ejpam-2101	183	35	.	.	PUNCT
ejpam-2101	183	36	.	.	PUNCT
ejpam-2101	184	1	.	.	PUNCT
ejpam-2101	185	1	,	,	PUNCT
ejpam-2101	185	2	fr	fr	INTJ
ejpam-2101	185	3	,	,	PUNCT
ejpam-2101	185	4	0	0	NUM
ejpam-2101	185	5	,	,	PUNCT
ejpam-2101	185	6	0	0	NUM
ejpam-2101	185	7	,	,	PUNCT
ejpam-2101	185	8	.	.	PUNCT
ejpam-2101	185	9	.	.	PUNCT
ejpam-2101	186	1	.	.	PUNCT
ejpam-2101	187	1	,	,	PUNCT
ejpam-2101	187	2	0	0	X
ejpam-2101	187	3	)	)	PUNCT
ejpam-2101	187	4	where	where	SCONJ
ejpam-2101	187	5	f1	f1	NOUN
ejpam-2101	187	6	,	,	PUNCT
ejpam-2101	187	7	.	.	PUNCT
ejpam-2101	187	8	.	.	PUNCT
ejpam-2101	188	1	.	.	PUNCT
ejpam-2101	189	1	,	,	PUNCT
ejpam-2101	189	2	fr	fr	PROPN
ejpam-2101	189	3	are	be	AUX
ejpam-2101	189	4	non	non	ADJ
ejpam-2101	189	5	-	-	ADJ
ejpam-2101	189	6	zero	zero	NUM
ejpam-2101	189	7	polynomials	polynomial	NOUN
ejpam-2101	189	8	with	with	ADP
ejpam-2101	189	9	fk	fk	INTJ
ejpam-2101	189	10	|	|	ADV
ejpam-2101	189	11	fk+1	fk+1	VERB
ejpam-2101	189	12	for	for	ADP
ejpam-2101	189	13	1	1	NUM
ejpam-2101	189	14	≤	≤	NUM
ejpam-2101	189	15	k	k	NOUN
ejpam-2101	189	16	≤	≤	ADJ
ejpam-2101	189	17	r	r	NOUN
ejpam-2101	189	18	,	,	PUNCT
ejpam-2101	189	19	and	and	CCONJ
ejpam-2101	189	20	diag(a1	diag(a1	NOUN
ejpam-2101	189	21	,	,	PUNCT
ejpam-2101	189	22	.	.	PUNCT
ejpam-2101	189	23	.	.	PUNCT
ejpam-2101	190	1	.	.	PUNCT
ejpam-2101	191	1	,	,	PUNCT
ejpam-2101	191	2	an	an	PRON
ejpam-2101	191	3	)	)	PUNCT
ejpam-2101	191	4	means	mean	VERB
ejpam-2101	191	5	the	the	DET
ejpam-2101	191	6	diagonal	diagonal	ADJ
ejpam-2101	191	7	matrix	matrix	NOUN
ejpam-2101	191	8	with	with	ADP
ejpam-2101	191	9	diagonal	diagonal	ADJ
ejpam-2101	191	10	entries	entry	NOUN
ejpam-2101	191	11	a1	a1	NOUN
ejpam-2101	191	12	,	,	PUNCT
ejpam-2101	191	13	.	.	PUNCT
ejpam-2101	191	14	.	.	PUNCT
ejpam-2101	192	1	.	.	PUNCT
ejpam-2101	193	1	,	,	PUNCT
ejpam-2101	193	2	an	an	X
ejpam-2101	193	3	.	.	PUNCT
ejpam-2101	194	1	the	the	DET
ejpam-2101	194	2	diagonal	diagonal	ADJ
ejpam-2101	194	3	matrix	matrix	NOUN
ejpam-2101	194	4	is	be	AUX
ejpam-2101	194	5	called	call	VERB
ejpam-2101	194	6	the	the	DET
ejpam-2101	194	7	smith	smith	PROPN
ejpam-2101	194	8	normal	normal	ADJ
ejpam-2101	194	9	form	form	NOUN
ejpam-2101	194	10	of	of	ADP
ejpam-2101	194	11	the	the	DET
ejpam-2101	194	12	polynomial	polynomial	ADJ
ejpam-2101	194	13	matrix	matrix	NOUN
ejpam-2101	194	14	a	a	PRON
ejpam-2101	194	15	is	be	AUX
ejpam-2101	194	16	denoted	denote	VERB
ejpam-2101	194	17	by	by	ADP
ejpam-2101	194	18	s(a	s(a	PROPN
ejpam-2101	194	19	)	)	PUNCT
ejpam-2101	194	20	.	.	PUNCT
ejpam-2101	195	1	the	the	DET
ejpam-2101	195	2	polynomials	polynomial	NOUN
ejpam-2101	195	3	fk	fk	INTJ
ejpam-2101	195	4	for	for	ADP
ejpam-2101	195	5	k	k	PROPN
ejpam-2101	195	6	=	=	SYM
ejpam-2101	195	7	1	1	NUM
ejpam-2101	195	8	,	,	PUNCT
ejpam-2101	195	9	.	.	PUNCT
ejpam-2101	195	10	.	.	PUNCT
ejpam-2101	195	11	.	.	PUNCT
ejpam-2101	196	1	,	,	PUNCT
ejpam-2101	196	2	r	r	NOUN
ejpam-2101	196	3	are	be	AUX
ejpam-2101	196	4	called	call	VERB
ejpam-2101	196	5	the	the	DET
ejpam-2101	196	6	k	k	NOUN
ejpam-2101	196	7	-	-	PUNCT
ejpam-2101	196	8	th	th	VERB
ejpam-2101	196	9	invariant	invariant	ADJ
ejpam-2101	196	10	factors	factor	NOUN
ejpam-2101	196	11	of	of	ADP
ejpam-2101	196	12	a	a	PRON
ejpam-2101	196	13	,	,	PUNCT
ejpam-2101	196	14	and	and	CCONJ
ejpam-2101	196	15	dk	dk	X
ejpam-2101	196	16	=	=	X
ejpam-2101	196	17	∏k	∏k	X
ejpam-2101	196	18	i=1	i=1	PROPN
ejpam-2101	196	19	fi	fi	NOUN
ejpam-2101	196	20	are	be	AUX
ejpam-2101	196	21	called	call	VERB
ejpam-2101	196	22	k	k	ADV
ejpam-2101	196	23	-	-	PUNCT
ejpam-2101	196	24	th	th	X
ejpam-2101	196	25	determinant	determinant	ADJ
ejpam-2101	196	26	factors	factor	NOUN
ejpam-2101	196	27	of	of	ADP
ejpam-2101	196	28	the	the	DET
ejpam-2101	196	29	matrix	matrix	NOUN
ejpam-2101	196	30	a.	a.	NOUN
ejpam-2101	196	31	since	since	SCONJ
ejpam-2101	196	32	the	the	DET
ejpam-2101	196	33	implicit	implicit	ADJ
ejpam-2101	196	34	equation	equation	NOUN
ejpam-2101	196	35	of	of	ADP
ejpam-2101	196	36	the	the	DET
ejpam-2101	196	37	curve	curve	NOUN
ejpam-2101	196	38	is	be	AUX
ejpam-2101	196	39	f(x	f(x	PROPN
ejpam-2101	196	40	,	,	PUNCT
ejpam-2101	196	41	y	y	PROPN
ejpam-2101	196	42	,	,	PUNCT
ejpam-2101	196	43	z	z	NOUN
ejpam-2101	196	44	)	)	PUNCT
ejpam-2101	196	45	=	=	SYM
ejpam-2101	196	46	ress(p(x	ress(p(x	PROPN
ejpam-2101	196	47	,	,	PUNCT
ejpam-2101	196	48	y	y	PROPN
ejpam-2101	196	49	,	,	PUNCT
ejpam-2101	196	50	z	z	PROPN
ejpam-2101	196	51	;	;	PUNCT
ejpam-2101	196	52	s	s	X
ejpam-2101	196	53	,	,	PUNCT
ejpam-2101	196	54	1	1	NUM
ejpam-2101	196	55	)	)	PUNCT
ejpam-2101	196	56	,	,	PUNCT
ejpam-2101	196	57	q(x	q(x	PROPN
ejpam-2101	196	58	,	,	PUNCT
ejpam-2101	196	59	y	y	PROPN
ejpam-2101	196	60	,	,	PUNCT
ejpam-2101	196	61	z	z	PROPN
ejpam-2101	196	62	;	;	PUNCT
ejpam-2101	196	63	s	s	X
ejpam-2101	196	64	,	,	PUNCT
ejpam-2101	196	65	1	1	NUM
ejpam-2101	196	66	)	)	PUNCT
ejpam-2101	196	67	)	)	PUNCT
ejpam-2101	196	68	is	be	AUX
ejpam-2101	196	69	obtained	obtain	VERB
ejpam-2101	196	70	by	by	ADP
ejpam-2101	196	71	m(x	m(x	PROPN
ejpam-2101	196	72	,	,	PUNCT
ejpam-2101	196	73	y	y	PROPN
ejpam-2101	196	74	,	,	PUNCT
ejpam-2101	196	75	z	z	PROPN
ejpam-2101	196	76	)	)	PUNCT
ejpam-2101	196	77	,	,	PUNCT
ejpam-2101	196	78	the	the	DET
ejpam-2101	196	79	determinant	determinant	NOUN
ejpam-2101	196	80	of	of	ADP
ejpam-2101	196	81	the	the	DET
ejpam-2101	196	82	resultant	resultant	NOUN
ejpam-2101	196	83	matrix	matrix	NOUN
ejpam-2101	196	84	of	of	ADP
ejpam-2101	196	85	the	the	DET
ejpam-2101	196	86	curvec1	curvec1	NOUN
ejpam-2101	196	87	.	.	PUNCT
ejpam-2101	197	1	in	in	ADP
ejpam-2101	197	2	the	the	DET
ejpam-2101	197	3	previous	previous	ADJ
ejpam-2101	197	4	subsection	subsection	NOUN
ejpam-2101	197	5	,	,	PUNCT
ejpam-2101	197	6	substituting	substitute	VERB
ejpam-2101	197	7	the	the	DET
ejpam-2101	197	8	variables	variable	NOUN
ejpam-2101	197	9	x	x	X
ejpam-2101	197	10	,	,	PUNCT
ejpam-2101	197	11	y	y	PROPN
ejpam-2101	197	12	,	,	PUNCT
ejpam-2101	197	13	z	z	NOUN
ejpam-2101	197	14	in	in	ADP
ejpam-2101	197	15	matrix	matrix	NOUN
ejpam-2101	197	16	m(x	m(x	PROPN
ejpam-2101	197	17	,	,	PUNCT
ejpam-2101	197	18	y	y	PROPN
ejpam-2101	197	19	,	,	PUNCT
ejpam-2101	197	20	z)with	z)with	PROPN
ejpam-2101	197	21	(	(	PUNCT
ejpam-2101	197	22	g0(u	g0(u	ADP
ejpam-2101	197	23	,	,	PUNCT
ejpam-2101	197	24	v	v	NOUN
ejpam-2101	197	25	)	)	PUNCT
ejpam-2101	197	26	,	,	PUNCT
ejpam-2101	197	27	g1(u	g1(u	PROPN
ejpam-2101	197	28	,	,	PUNCT
ejpam-2101	197	29	v	v	NOUN
ejpam-2101	197	30	)	)	PUNCT
ejpam-2101	197	31	,	,	PUNCT
ejpam-2101	197	32	g2(u	g2(u	PROPN
ejpam-2101	197	33	,	,	PUNCT
ejpam-2101	197	34	v	v	NOUN
ejpam-2101	197	35	)	)	PUNCT
ejpam-2101	197	36	)	)	PUNCT
ejpam-2101	197	37	,	,	PUNCT
ejpam-2101	197	38	we	we	PRON
ejpam-2101	197	39	obtain	obtain	VERB
ejpam-2101	197	40	a	a	DET
ejpam-2101	197	41	matrix	matrix	NOUN
ejpam-2101	197	42	m(u	m(u	PROPN
ejpam-2101	197	43	,	,	PUNCT
ejpam-2101	197	44	v	v	NOUN
ejpam-2101	197	45	)	)	PUNCT
ejpam-2101	197	46	=	=	SYM
ejpam-2101	198	1	m(g(u	m(g(u	NOUN
ejpam-2101	198	2	,	,	PUNCT
ejpam-2101	198	3	v	v	NOUN
ejpam-2101	198	4	)	)	PUNCT
ejpam-2101	198	5	)	)	PUNCT
ejpam-2101	199	1	=	=	PUNCT
ejpam-2101	199	2	m(g0(u	m(g0(u	PROPN
ejpam-2101	199	3	,	,	PUNCT
ejpam-2101	199	4	v	v	NOUN
ejpam-2101	199	5	)	)	PUNCT
ejpam-2101	199	6	,	,	PUNCT
ejpam-2101	199	7	g1(u	g1(u	PROPN
ejpam-2101	199	8	,	,	PUNCT
ejpam-2101	199	9	v	v	NOUN
ejpam-2101	199	10	)	)	PUNCT
ejpam-2101	199	11	,	,	PUNCT
ejpam-2101	199	12	g2(u	g2(u	PROPN
ejpam-2101	199	13	,	,	PUNCT
ejpam-2101	199	14	v	v	NOUN
ejpam-2101	199	15	)	)	PUNCT
ejpam-2101	199	16	)	)	PUNCT
ejpam-2101	199	17	.	.	PUNCT
ejpam-2101	200	1	m.	m.	PROPN
ejpam-2101	200	2	tesemma	tesemma	PROPN
ejpam-2101	200	3	,	,	PUNCT
ejpam-2101	200	4	h.	h.	PROPN
ejpam-2101	200	5	wang	wang	PROPN
ejpam-2101	200	6	,	,	PUNCT
ejpam-2101	200	7	/	/	SYM
ejpam-2101	200	8	eur	eur	NOUN
ejpam-2101	200	9	.	.	PUNCT
ejpam-2101	201	1	j.	j.	PROPN
ejpam-2101	201	2	pure	pure	PROPN
ejpam-2101	201	3	appl	appl	PROPN
ejpam-2101	201	4	.	.	PROPN
ejpam-2101	201	5	math	math	PROPN
ejpam-2101	201	6	,	,	PUNCT
ejpam-2101	201	7	7	7	NUM
ejpam-2101	201	8	(	(	PUNCT
ejpam-2101	201	9	2014	2014	NUM
ejpam-2101	201	10	)	)	PUNCT
ejpam-2101	201	11	,	,	PUNCT
ejpam-2101	201	12	191	191	NUM
ejpam-2101	201	13	-	-	SYM
ejpam-2101	201	14	200	200	NUM
ejpam-2101	201	15	198	198	NUM
ejpam-2101	201	16	theorem	theorem	NOUN
ejpam-2101	201	17	3	3	NUM
ejpam-2101	201	18	.	.	PUNCT
ejpam-2101	202	1	s(m(u	s(m(u	NOUN
ejpam-2101	202	2	,	,	PUNCT
ejpam-2101	202	3	1	1	NUM
ejpam-2101	202	4	)	)	PUNCT
ejpam-2101	202	5	)	)	PUNCT
ejpam-2101	203	1	=	=	SYM
ejpam-2101	203	2	diag	diag	NOUN
ejpam-2101	203	3	(	(	PUNCT
ejpam-2101	203	4	f1(u	f1(u	NOUN
ejpam-2101	203	5	)	)	PUNCT
ejpam-2101	203	6	,	,	PUNCT
ejpam-2101	203	7	.	.	PUNCT
ejpam-2101	203	8	.	.	PUNCT
ejpam-2101	203	9	.	.	PUNCT
ejpam-2101	204	1	,	,	PUNCT
ejpam-2101	204	2	fd(u	fd(u	X
ejpam-2101	204	3	)	)	PUNCT
ejpam-2101	204	4	)	)	PUNCT
ejpam-2101	205	1	and	and	CCONJ
ejpam-2101	205	2	s(m(1	s(m(1	NOUN
ejpam-2101	205	3	,	,	PUNCT
ejpam-2101	205	4	v	v	NOUN
ejpam-2101	205	5	)	)	PUNCT
ejpam-2101	205	6	)	)	PUNCT
ejpam-2101	206	1	=	=	SYM
ejpam-2101	206	2	diag(g1(v	diag(g1(v	NOUN
ejpam-2101	206	3	)	)	PUNCT
ejpam-2101	206	4	,	,	PUNCT
ejpam-2101	206	5	.	.	PUNCT
ejpam-2101	206	6	.	.	PUNCT
ejpam-2101	207	1	.	.	PUNCT
ejpam-2101	208	1	,	,	PUNCT
ejpam-2101	208	2	gd(v	gd(v	NOUN
ejpam-2101	208	3	)	)	PUNCT
ejpam-2101	208	4	)	)	PUNCT
ejpam-2101	208	5	.	.	PUNCT
ejpam-2101	209	1	and	and	CCONJ
ejpam-2101	209	2	{	{	PUNCT
ejpam-2101	209	3	(	(	PUNCT
ejpam-2101	209	4	u0	u0	ADJ
ejpam-2101	209	5	,	,	PUNCT
ejpam-2101	209	6	1	1	NUM
ejpam-2101	209	7	)	)	PUNCT
ejpam-2101	209	8	or	or	CCONJ
ejpam-2101	209	9	(	(	PUNCT
ejpam-2101	209	10	1	1	NUM
ejpam-2101	209	11	,	,	PUNCT
ejpam-2101	209	12	v0	v0	NOUN
ejpam-2101	209	13	)	)	PUNCT
ejpam-2101	209	14	|	|	ADV
ejpam-2101	209	15	fd(u0	fd(u0	NOUN
ejpam-2101	209	16	)	)	PUNCT
ejpam-2101	209	17	=	=	SYM
ejpam-2101	209	18	0	0	NUM
ejpam-2101	209	19	or	or	CCONJ
ejpam-2101	209	20	gd(v0	gd(v0	ADJ
ejpam-2101	209	21	)	)	PUNCT
ejpam-2101	209	22	=	=	SYM
ejpam-2101	209	23	0}⇔	0}⇔	PROPN
ejpam-2101	209	24	g(u0	g(u0	NOUN
ejpam-2101	209	25	,	,	PUNCT
ejpam-2101	209	26	1	1	NUM
ejpam-2101	209	27	)	)	PUNCT
ejpam-2101	209	28	or	or	CCONJ
ejpam-2101	209	29	g(1	g(1	PROPN
ejpam-2101	209	30	,	,	PUNCT
ejpam-2101	209	31	v0	v0	NOUN
ejpam-2101	209	32	)	)	PUNCT
ejpam-2101	209	33	∈	∈	PROPN
ejpam-2101	209	34	c1	c1	PROPN
ejpam-2101	209	35	∩c2	∩c2	PROPN
ejpam-2101	209	36	.	.	PUNCT
ejpam-2101	210	1	proof	proof	NOUN
ejpam-2101	210	2	.	.	PUNCT
ejpam-2101	211	1	since	since	SCONJ
ejpam-2101	211	2	det(m(u	det(m(u	NOUN
ejpam-2101	211	3	,	,	PUNCT
ejpam-2101	211	4	v	v	NOUN
ejpam-2101	211	5	)	)	PUNCT
ejpam-2101	211	6	)	)	PUNCT
ejpam-2101	211	7	is	be	AUX
ejpam-2101	211	8	not	not	PART
ejpam-2101	211	9	identically	identically	ADV
ejpam-2101	211	10	zero	zero	NUM
ejpam-2101	211	11	,	,	PUNCT
ejpam-2101	211	12	rankm(u	rankm(u	NOUN
ejpam-2101	211	13	,	,	PUNCT
ejpam-2101	211	14	v	v	NOUN
ejpam-2101	211	15	)	)	PUNCT
ejpam-2101	211	16	=	=	SYM
ejpam-2101	212	1	d	d	NOUN
ejpam-2101	212	2	,	,	PUNCT
ejpam-2101	212	3	therefore	therefore	ADV
ejpam-2101	212	4	,	,	PUNCT
ejpam-2101	212	5	the	the	DET
ejpam-2101	212	6	smith	smith	PROPN
ejpam-2101	212	7	normal	normal	ADJ
ejpam-2101	212	8	forms	form	NOUN
ejpam-2101	212	9	s(m(u	s(m(u	PROPN
ejpam-2101	212	10	,	,	PUNCT
ejpam-2101	212	11	1	1	NUM
ejpam-2101	212	12	)	)	PUNCT
ejpam-2101	212	13	)	)	PUNCT
ejpam-2101	213	1	=	=	SYM
ejpam-2101	213	2	diag	diag	NOUN
ejpam-2101	213	3	(	(	PUNCT
ejpam-2101	213	4	f1(u	f1(u	NOUN
ejpam-2101	213	5	)	)	PUNCT
ejpam-2101	213	6	,	,	PUNCT
ejpam-2101	213	7	.	.	PUNCT
ejpam-2101	213	8	.	.	PUNCT
ejpam-2101	213	9	.	.	PUNCT
ejpam-2101	214	1	,	,	PUNCT
ejpam-2101	214	2	fd(u	fd(u	X
ejpam-2101	214	3	)	)	PUNCT
ejpam-2101	214	4	)	)	PUNCT
ejpam-2101	215	1	and	and	CCONJ
ejpam-2101	215	2	s(m(1	s(m(1	NOUN
ejpam-2101	215	3	,	,	PUNCT
ejpam-2101	215	4	v	v	NOUN
ejpam-2101	215	5	)	)	PUNCT
ejpam-2101	215	6	)	)	PUNCT
ejpam-2101	216	1	=	=	SYM
ejpam-2101	216	2	diag(g1(v	diag(g1(v	NOUN
ejpam-2101	216	3	)	)	PUNCT
ejpam-2101	216	4	,	,	PUNCT
ejpam-2101	216	5	.	.	PUNCT
ejpam-2101	216	6	.	.	PUNCT
ejpam-2101	217	1	.	.	PUNCT
ejpam-2101	218	1	,	,	PUNCT
ejpam-2101	218	2	gd(v	gd(v	NOUN
ejpam-2101	218	3	)	)	PUNCT
ejpam-2101	218	4	)	)	PUNCT
ejpam-2101	218	5	.	.	PUNCT
ejpam-2101	219	1	by	by	ADP
ejpam-2101	219	2	the	the	DET
ejpam-2101	219	3	property	property	NOUN
ejpam-2101	219	4	of	of	ADP
ejpam-2101	219	5	smith	smith	PROPN
ejpam-2101	219	6	normal	normal	ADJ
ejpam-2101	219	7	form	form	NOUN
ejpam-2101	219	8	,	,	PUNCT
ejpam-2101	219	9	det	det	PROPN
ejpam-2101	219	10	s(m	s(m	PROPN
ejpam-2101	219	11	)	)	PUNCT
ejpam-2101	219	12	=	=	PUNCT
ejpam-2101	219	13	det(pmq	det(pmq	X
ejpam-2101	219	14	)	)	PUNCT
ejpam-2101	219	15	=	=	PUNCT
ejpam-2101	219	16	c	c	NOUN
ejpam-2101	219	17	detm	detm	NOUN
ejpam-2101	219	18	=	=	SYM
ejpam-2101	219	19	0	0	NUM
ejpam-2101	219	20	,	,	PUNCT
ejpam-2101	219	21	and	and	CCONJ
ejpam-2101	219	22	the	the	DET
ejpam-2101	219	23	solutions	solution	NOUN
ejpam-2101	219	24	to	to	ADP
ejpam-2101	219	25	the	the	DET
ejpam-2101	219	26	d	d	PROPN
ejpam-2101	219	27	-	-	PUNCT
ejpam-2101	219	28	th	th	VERB
ejpam-2101	219	29	invariant	invariant	ADJ
ejpam-2101	219	30	factor	factor	NOUN
ejpam-2101	219	31	ofm	ofm	PROPN
ejpam-2101	219	32	is	be	AUX
ejpam-2101	219	33	exactly	exactly	ADV
ejpam-2101	219	34	the	the	DET
ejpam-2101	219	35	solutions	solution	NOUN
ejpam-2101	219	36	to	to	ADP
ejpam-2101	219	37	det	det	PROPN
ejpam-2101	219	38	s(m	s(m	PROPN
ejpam-2101	219	39	)	)	PUNCT
ejpam-2101	220	1	=	=	SYM
ejpam-2101	220	2	0	0	X
ejpam-2101	220	3	.	.	PUNCT
ejpam-2101	221	1	therefore	therefore	ADV
ejpam-2101	221	2	,	,	PUNCT
ejpam-2101	221	3	g(u0	g(u0	NOUN
ejpam-2101	221	4	,	,	PUNCT
ejpam-2101	221	5	v0	v0	PROPN
ejpam-2101	221	6	)	)	PUNCT
ejpam-2101	221	7	∈	∈	PROPN
ejpam-2101	221	8	c1	c1	PROPN
ejpam-2101	221	9	∩c2	∩c2	PROPN
ejpam-2101	222	1	⇔	⇔	PROPN
ejpam-2101	222	2	{	{	PUNCT
ejpam-2101	222	3	(	(	PUNCT
ejpam-2101	222	4	u0	u0	PROPN
ejpam-2101	222	5	,	,	PUNCT
ejpam-2101	222	6	v0	v0	PROPN
ejpam-2101	222	7	)	)	PUNCT
ejpam-2101	222	8	6=	6=	ADP
ejpam-2101	222	9	(	(	PUNCT
ejpam-2101	222	10	0,0	0,0	NOUN
ejpam-2101	222	11	)	)	PUNCT
ejpam-2101	222	12	|	|	ADV
ejpam-2101	222	13	det	det	PROPN
ejpam-2101	222	14	s(m(u0	s(m(u0	PROPN
ejpam-2101	222	15	,	,	PUNCT
ejpam-2101	222	16	v0	v0	NOUN
ejpam-2101	222	17	)	)	PUNCT
ejpam-2101	222	18	)	)	PUNCT
ejpam-2101	223	1	=	=	SYM
ejpam-2101	223	2	0	0	X
ejpam-2101	223	3	}	}	PUNCT
ejpam-2101	223	4	⇔	⇔	X
ejpam-2101	223	5	{	{	PUNCT
ejpam-2101	223	6	(	(	PUNCT
ejpam-2101	223	7	u0	u0	ADJ
ejpam-2101	223	8	,	,	PUNCT
ejpam-2101	223	9	1	1	NUM
ejpam-2101	223	10	)	)	PUNCT
ejpam-2101	223	11	or	or	CCONJ
ejpam-2101	223	12	(	(	PUNCT
ejpam-2101	223	13	1	1	NUM
ejpam-2101	223	14	,	,	PUNCT
ejpam-2101	223	15	v0	v0	NOUN
ejpam-2101	223	16	)	)	PUNCT
ejpam-2101	223	17	|	|	ADV
ejpam-2101	223	18	fd(u0	fd(u0	NOUN
ejpam-2101	223	19	)	)	PUNCT
ejpam-2101	223	20	=	=	SYM
ejpam-2101	223	21	0	0	NUM
ejpam-2101	223	22	or	or	CCONJ
ejpam-2101	223	23	gd(v0	gd(v0	ADJ
ejpam-2101	223	24	)	)	PUNCT
ejpam-2101	223	25	=	=	SYM
ejpam-2101	223	26	0	0	NUM
ejpam-2101	223	27	}	}	PUNCT
ejpam-2101	223	28	.	.	PUNCT
ejpam-2101	224	1	hence	hence	ADV
ejpam-2101	224	2	,	,	PUNCT
ejpam-2101	224	3	the	the	DET
ejpam-2101	224	4	algorithm	algorithm	NOUN
ejpam-2101	224	5	via	via	ADP
ejpam-2101	224	6	smith	smith	PROPN
ejpam-2101	224	7	normal	normal	ADJ
ejpam-2101	224	8	form	form	NOUN
ejpam-2101	224	9	follows	follow	VERB
ejpam-2101	224	10	directly	directly	ADV
ejpam-2101	224	11	as	as	ADP
ejpam-2101	224	12	below	below	ADV
ejpam-2101	224	13	:	:	PUNCT
ejpam-2101	224	14	smith	smith	PROPN
ejpam-2101	224	15	normal	normal	ADJ
ejpam-2101	224	16	form	form	NOUN
ejpam-2101	224	17	algorithm	algorithm	NOUN
ejpam-2101	224	18	input	input	NOUN
ejpam-2101	224	19	:	:	PUNCT
ejpam-2101	224	20	parametrized	parametrized	ADJ
ejpam-2101	224	21	curves	curve	NOUN
ejpam-2101	224	22	f(s	f(s	PROPN
ejpam-2101	224	23	,	,	PUNCT
ejpam-2101	224	24	t	t	PROPN
ejpam-2101	224	25	)	)	PUNCT
ejpam-2101	224	26	and	and	CCONJ
ejpam-2101	224	27	g(u	g(u	PROPN
ejpam-2101	224	28	,	,	PUNCT
ejpam-2101	224	29	v	v	NOUN
ejpam-2101	224	30	)	)	PUNCT
ejpam-2101	224	31	.	.	PUNCT
ejpam-2101	225	1	output	output	NOUN
ejpam-2101	225	2	:	:	PUNCT
ejpam-2101	225	3	the	the	DET
ejpam-2101	225	4	set	set	NOUN
ejpam-2101	225	5	of	of	ADP
ejpam-2101	225	6	parameters	parameter	NOUN
ejpam-2101	225	7	and	and	CCONJ
ejpam-2101	225	8	their	their	PRON
ejpam-2101	225	9	corresponding	corresponding	ADJ
ejpam-2101	225	10	points	point	NOUN
ejpam-2101	225	11	of	of	ADP
ejpam-2101	225	12	the	the	DET
ejpam-2101	225	13	intersection	intersection	NOUN
ejpam-2101	225	14	of	of	ADP
ejpam-2101	225	15	two	two	NUM
ejpam-2101	225	16	curves	curve	NOUN
ejpam-2101	225	17	given	give	VERB
ejpam-2101	225	18	by	by	ADP
ejpam-2101	225	19	parametrization	parametrization	NOUN
ejpam-2101	225	20	f(s	f(	NOUN
ejpam-2101	225	21	,	,	PUNCT
ejpam-2101	225	22	t	t	PROPN
ejpam-2101	225	23	)	)	PUNCT
ejpam-2101	225	24	and	and	CCONJ
ejpam-2101	225	25	g(u	g(u	PROPN
ejpam-2101	225	26	,	,	PUNCT
ejpam-2101	225	27	v	v	NOUN
ejpam-2101	225	28	)	)	PUNCT
ejpam-2101	225	29	.	.	PUNCT
ejpam-2101	226	1	procedure	procedure	NOUN
ejpam-2101	226	2	:	:	PUNCT
ejpam-2101	226	3	i	i	NOUN
ejpam-2101	226	4	)	)	PUNCT
ejpam-2101	226	5	compute	compute	VERB
ejpam-2101	226	6	p(s	p(s	NOUN
ejpam-2101	226	7	,	,	PUNCT
ejpam-2101	226	8	t),q(s	t),q(s	NUM
ejpam-2101	226	9	,	,	PUNCT
ejpam-2101	226	10	t	t	PROPN
ejpam-2101	226	11	)	)	PUNCT
ejpam-2101	226	12	,	,	PUNCT
ejpam-2101	226	13	the	the	DET
ejpam-2101	226	14	µ-basis	µ-basis	NOUN
ejpam-2101	226	15	for	for	ADP
ejpam-2101	226	16	f(s	f(	NOUN
ejpam-2101	226	17	,	,	PUNCT
ejpam-2101	226	18	t	t	PROPN
ejpam-2101	226	19	)	)	PUNCT
ejpam-2101	226	20	.	.	PUNCT
ejpam-2101	227	1	ii	ii	X
ejpam-2101	227	2	)	)	PUNCT
ejpam-2101	227	3	construct	construct	VERB
ejpam-2101	227	4	the	the	DET
ejpam-2101	227	5	resultant	resultant	NOUN
ejpam-2101	227	6	matrix	matrix	NOUN
ejpam-2101	227	7	of	of	ADP
ejpam-2101	227	8	the	the	DET
ejpam-2101	227	9	curve	curve	NOUN
ejpam-2101	227	10	f	f	PROPN
ejpam-2101	227	11	denoted	denote	VERB
ejpam-2101	227	12	by	by	ADP
ejpam-2101	227	13	m(x	m(x	PROPN
ejpam-2101	227	14	,	,	PUNCT
ejpam-2101	227	15	y	y	PROPN
ejpam-2101	227	16	,	,	PUNCT
ejpam-2101	227	17	z	z	NOUN
ejpam-2101	227	18	)	)	PUNCT
ejpam-2101	227	19	using	use	VERB
ejpam-2101	227	20	information	information	NOUN
ejpam-2101	227	21	of	of	ADP
ejpam-2101	227	22	the	the	DET
ejpam-2101	227	23	µ-basis	µ-basis	NOUN
ejpam-2101	227	24	.	.	PUNCT
ejpam-2101	228	1	iii	iii	X
ejpam-2101	228	2	)	)	PUNCT
ejpam-2101	228	3	substituting	substitute	VERB
ejpam-2101	228	4	the	the	DET
ejpam-2101	228	5	variables	variable	NOUN
ejpam-2101	228	6	x	x	X
ejpam-2101	228	7	,	,	PUNCT
ejpam-2101	228	8	y	y	PROPN
ejpam-2101	228	9	,	,	PUNCT
ejpam-2101	228	10	z	z	NOUN
ejpam-2101	228	11	in	in	ADP
ejpam-2101	228	12	matrix	matrix	NOUN
ejpam-2101	228	13	m(x	m(x	PROPN
ejpam-2101	228	14	,	,	PUNCT
ejpam-2101	228	15	y	y	PROPN
ejpam-2101	228	16	,	,	PUNCT
ejpam-2101	228	17	z	z	NOUN
ejpam-2101	228	18	)	)	PUNCT
ejpam-2101	228	19	with	with	ADP
ejpam-2101	228	20	(	(	PUNCT
ejpam-2101	228	21	g0(u	g0(u	ADP
ejpam-2101	228	22	,	,	PUNCT
ejpam-2101	228	23	v	v	NOUN
ejpam-2101	228	24	)	)	PUNCT
ejpam-2101	228	25	,	,	PUNCT
ejpam-2101	228	26	g1(u	g1(u	PROPN
ejpam-2101	228	27	,	,	PUNCT
ejpam-2101	228	28	v	v	NOUN
ejpam-2101	228	29	)	)	PUNCT
ejpam-2101	228	30	,	,	PUNCT
ejpam-2101	228	31	g2(u	g2(u	PROPN
ejpam-2101	228	32	,	,	PUNCT
ejpam-2101	228	33	v	v	NOUN
ejpam-2101	228	34	)	)	PUNCT
ejpam-2101	228	35	)	)	PUNCT
ejpam-2101	228	36	.	.	PUNCT
ejpam-2101	229	1	iv	iv	X
ejpam-2101	229	2	)	)	PUNCT
ejpam-2101	229	3	compute	compute	VERB
ejpam-2101	229	4	the	the	DET
ejpam-2101	229	5	smith	smith	PROPN
ejpam-2101	229	6	normal	normal	ADJ
ejpam-2101	229	7	form	form	NOUN
ejpam-2101	229	8	s(m(u	s(m(u	PROPN
ejpam-2101	229	9	,	,	PUNCT
ejpam-2101	229	10	1	1	NUM
ejpam-2101	229	11	)	)	PUNCT
ejpam-2101	229	12	)	)	PUNCT
ejpam-2101	229	13	and	and	CCONJ
ejpam-2101	229	14	s(m(1	s(m(1	NOUN
ejpam-2101	229	15	,	,	PUNCT
ejpam-2101	229	16	v	v	NOUN
ejpam-2101	229	17	)	)	PUNCT
ejpam-2101	229	18	)	)	PUNCT
ejpam-2101	229	19	.	.	PUNCT
ejpam-2101	230	1	the	the	DET
ejpam-2101	230	2	solution	solution	NOUN
ejpam-2101	230	3	for	for	ADP
ejpam-2101	230	4	fd(u	fd(u	PUNCT
ejpam-2101	230	5	)	)	PUNCT
ejpam-2101	230	6	=	=	SYM
ejpam-2101	230	7	0	0	NUM
ejpam-2101	230	8	and	and	CCONJ
ejpam-2101	230	9	gd(v	gd(v	ADJ
ejpam-2101	230	10	)	)	PUNCT
ejpam-2101	230	11	=	=	SYM
ejpam-2101	230	12	0	0	NUM
ejpam-2101	231	1	corresponding	correspond	VERB
ejpam-2101	231	2	the	the	DET
ejpam-2101	231	3	the	the	DET
ejpam-2101	231	4	parameters	parameter	NOUN
ejpam-2101	231	5	(	(	PUNCT
ejpam-2101	231	6	u0	u0	ADJ
ejpam-2101	231	7	,	,	PUNCT
ejpam-2101	231	8	1	1	NUM
ejpam-2101	231	9	)	)	PUNCT
ejpam-2101	231	10	and	and	CCONJ
ejpam-2101	231	11	(	(	PUNCT
ejpam-2101	231	12	1	1	NUM
ejpam-2101	231	13	,	,	PUNCT
ejpam-2101	231	14	v0	v0	NOUN
ejpam-2101	231	15	)	)	PUNCT
ejpam-2101	231	16	such	such	ADJ
ejpam-2101	231	17	that	that	DET
ejpam-2101	231	18	g(u0	g(u0	NOUN
ejpam-2101	231	19	,	,	PUNCT
ejpam-2101	231	20	1	1	NUM
ejpam-2101	231	21	)	)	PUNCT
ejpam-2101	231	22	and	and	CCONJ
ejpam-2101	231	23	g(1	g(1	PROPN
ejpam-2101	231	24	,	,	PUNCT
ejpam-2101	231	25	v0	v0	PROPN
ejpam-2101	231	26	)	)	PUNCT
ejpam-2101	231	27	are	be	AUX
ejpam-2101	231	28	the	the	DET
ejpam-2101	231	29	intersection	intersection	NOUN
ejpam-2101	231	30	points	point	NOUN
ejpam-2101	231	31	of	of	ADP
ejpam-2101	231	32	the	the	DET
ejpam-2101	231	33	two	two	NUM
ejpam-2101	231	34	curves	curve	NOUN
ejpam-2101	231	35	with	with	ADP
ejpam-2101	231	36	correct	correct	ADJ
ejpam-2101	231	37	multiplicity	multiplicity	NOUN
ejpam-2101	231	38	.	.	PUNCT
ejpam-2101	232	1	example	example	NOUN
ejpam-2101	233	1	3	3	NUM
ejpam-2101	233	2	.	.	PUNCT
ejpam-2101	233	3	to	to	PART
ejpam-2101	233	4	compare	compare	VERB
ejpam-2101	233	5	the	the	DET
ejpam-2101	233	6	algorithm	algorithm	NOUN
ejpam-2101	233	7	,	,	PUNCT
ejpam-2101	233	8	we	we	PRON
ejpam-2101	233	9	will	will	AUX
ejpam-2101	233	10	use	use	VERB
ejpam-2101	233	11	the	the	DET
ejpam-2101	233	12	same	same	ADJ
ejpam-2101	233	13	example	example	NOUN
ejpam-2101	233	14	as	as	ADP
ejpam-2101	233	15	before	before	ADV
ejpam-2101	233	16	,	,	PUNCT
ejpam-2101	233	17	two	two	NUM
ejpam-2101	233	18	rational	rational	ADJ
ejpam-2101	233	19	paramatrized	paramatrize	VERB
ejpam-2101	233	20	plane	plane	NOUN
ejpam-2101	233	21	curves	curve	NOUN
ejpam-2101	233	22	given	give	VERB
ejpam-2101	233	23	by	by	ADP
ejpam-2101	233	24	wang	wang	PROPN
ejpam-2101	233	25	-	-	PUNCT
ejpam-2101	233	26	goldman	goldman	PROPN
ejpam-2101	234	1	[	[	X
ejpam-2101	234	2	11	11	NUM
ejpam-2101	234	3	]	]	SYM
ejpam-2101	234	4	:	:	PUNCT
ejpam-2101	234	5	lemniscate	lemniscate	PROPN
ejpam-2101	234	6	of	of	ADP
ejpam-2101	234	7	bernoulli	bernoulli	PROPN
ejpam-2101	234	8	,	,	PUNCT
ejpam-2101	234	9	a	a	DET
ejpam-2101	234	10	rational	rational	ADJ
ejpam-2101	234	11	quartic	quartic	ADJ
ejpam-2101	234	12	curve	curve	NOUN
ejpam-2101	234	13	f	f	PROPN
ejpam-2101	234	14	and	and	CCONJ
ejpam-2101	234	15	a	a	DET
ejpam-2101	234	16	rational	rational	ADJ
ejpam-2101	234	17	cubic	cubic	ADJ
ejpam-2101	234	18	curve	curve	NOUN
ejpam-2101	234	19	g(u	g(u	PROPN
ejpam-2101	234	20	,	,	PUNCT
ejpam-2101	234	21	v	v	NOUN
ejpam-2101	234	22	)	)	PUNCT
ejpam-2101	234	23	.	.	PUNCT
ejpam-2101	235	1	f(s	f(s	PROPN
ejpam-2101	235	2	,	,	PUNCT
ejpam-2101	235	3	t	t	PROPN
ejpam-2101	235	4	)	)	PUNCT
ejpam-2101	235	5	=(	=(	NOUN
ejpam-2101	235	6	s4	s4	PROPN
ejpam-2101	235	7	−	−	PROPN
ejpam-2101	235	8	t4	t4	PROPN
ejpam-2101	235	9	,	,	PUNCT
ejpam-2101	235	10	−2st(t2	−2st(t2	NOUN
ejpam-2101	235	11	−	−	PROPN
ejpam-2101	235	12	s2	s2	PROPN
ejpam-2101	235	13	)	)	PUNCT
ejpam-2101	235	14	,	,	PUNCT
ejpam-2101	235	15	t4	t4	PROPN
ejpam-2101	235	16	+	+	PROPN
ejpam-2101	235	17	6s2	6s2	NUM
ejpam-2101	235	18	t2	t2	PROPN
ejpam-2101	235	19	+	+	CCONJ
ejpam-2101	235	20	s4	s4	PROPN
ejpam-2101	235	21	)	)	PUNCT
ejpam-2101	235	22	,	,	PUNCT
ejpam-2101	235	23	g(u	g(u	PROPN
ejpam-2101	235	24	,	,	PUNCT
ejpam-2101	235	25	v	v	NOUN
ejpam-2101	235	26	)	)	PUNCT
ejpam-2101	235	27	=(	=(	NOUN
ejpam-2101	235	28	−3v3	−3v3	NUM
ejpam-2101	235	29	−	−	PROPN
ejpam-2101	235	30	2uv2	2uv2	NUM
ejpam-2101	236	1	+	+	CCONJ
ejpam-2101	236	2	4u2v	4u2v	NOUN
ejpam-2101	236	3	+	+	CCONJ
ejpam-2101	236	4	2u3	2u3	NUM
ejpam-2101	236	5	,	,	PUNCT
ejpam-2101	236	6	−v3	−v3	PROPN
ejpam-2101	236	7	+	+	CCONJ
ejpam-2101	236	8	3uv2	3uv2	NUM
ejpam-2101	236	9	−	−	PROPN
ejpam-2101	236	10	u3	u3	NOUN
ejpam-2101	236	11	+	+	CCONJ
ejpam-2101	236	12	2u2v	2u2v	NUM
ejpam-2101	236	13	,	,	PUNCT
ejpam-2101	236	14	2uv2	2uv2	NUM
ejpam-2101	237	1	+	+	CCONJ
ejpam-2101	237	2	2u2v	2u2v	ADJ
ejpam-2101	237	3	+	+	CCONJ
ejpam-2101	237	4	u3	u3	NOUN
ejpam-2101	237	5	)	)	PUNCT
ejpam-2101	237	6	.	.	PUNCT
ejpam-2101	238	1	smith	smith	PROPN
ejpam-2101	238	2	normal	normal	ADJ
ejpam-2101	238	3	form	form	NOUN
ejpam-2101	238	4	method	method	NOUN
ejpam-2101	238	5	:	:	PUNCT
ejpam-2101	238	6	compute	compute	VERB
ejpam-2101	238	7	the	the	DET
ejpam-2101	238	8	µ-basis	µ-basis	NOUN
ejpam-2101	238	9	of	of	ADP
ejpam-2101	238	10	the	the	DET
ejpam-2101	238	11	parametrized	parametrized	ADJ
ejpam-2101	238	12	curve	curve	NOUN
ejpam-2101	238	13	f(s	f(s	PROPN
ejpam-2101	238	14	,	,	PUNCT
ejpam-2101	238	15	t	t	PROPN
ejpam-2101	238	16	)	)	PUNCT
ejpam-2101	238	17	in	in	ADP
ejpam-2101	238	18	terms	term	NOUN
ejpam-2101	238	19	of	of	ADP
ejpam-2101	238	20	the	the	DET
ejpam-2101	238	21	moving	move	VERB
ejpam-2101	238	22	lines	line	NOUN
ejpam-2101	238	23	as	as	ADP
ejpam-2101	238	24	below	below	ADV
ejpam-2101	238	25	:	:	PUNCT
ejpam-2101	238	26	µ-basis	µ-basis	NOUN
ejpam-2101	238	27	:	:	PUNCT
ejpam-2101	238	28	p(s	p(s	NUM
ejpam-2101	238	29	,	,	PUNCT
ejpam-2101	238	30	t	t	PROPN
ejpam-2101	238	31	)	)	PUNCT
ejpam-2101	238	32	=	=	PUNCT
ejpam-2101	238	33	(	(	PUNCT
ejpam-2101	238	34	−s2	−s2	PROPN
ejpam-2101	238	35	−	−	PROPN
ejpam-2101	238	36	t2	t2	NOUN
ejpam-2101	238	37	,	,	PUNCT
ejpam-2101	238	38	−2st	−2st	NUM
ejpam-2101	238	39	,	,	PUNCT
ejpam-2101	238	40	s2	s2	NOUN
ejpam-2101	238	41	−	−	NOUN
ejpam-2101	238	42	t2	t2	PROPN
ejpam-2101	238	43	)	)	PUNCT
ejpam-2101	238	44	,	,	PUNCT
ejpam-2101	238	45	q(s	q(s	PROPN
ejpam-2101	238	46	,	,	PUNCT
ejpam-2101	238	47	t	t	PROPN
ejpam-2101	238	48	)	)	PUNCT
ejpam-2101	238	49	=	=	SYM
ejpam-2101	238	50	(	(	PUNCT
ejpam-2101	238	51	2st	2st	NOUN
ejpam-2101	238	52	,	,	PUNCT
ejpam-2101	238	53	−s2	−s2	NOUN
ejpam-2101	238	54	−	−	PROPN
ejpam-2101	238	55	t2	t2	NOUN
ejpam-2101	238	56	,	,	PUNCT
ejpam-2101	238	57	0	0	NUM
ejpam-2101	238	58	)	)	PUNCT
ejpam-2101	238	59	m.	m.	NOUN
ejpam-2101	238	60	tesemma	tesemma	PROPN
ejpam-2101	238	61	,	,	PUNCT
ejpam-2101	238	62	h.	h.	PROPN
ejpam-2101	238	63	wang	wang	PROPN
ejpam-2101	238	64	,	,	PUNCT
ejpam-2101	238	65	/	/	SYM
ejpam-2101	238	66	eur	eur	NOUN
ejpam-2101	238	67	.	.	PUNCT
ejpam-2101	239	1	j.	j.	PROPN
ejpam-2101	239	2	pure	pure	PROPN
ejpam-2101	239	3	appl	appl	PROPN
ejpam-2101	239	4	.	.	PROPN
ejpam-2101	239	5	math	math	PROPN
ejpam-2101	239	6	,	,	PUNCT
ejpam-2101	239	7	7	7	NUM
ejpam-2101	239	8	(	(	PUNCT
ejpam-2101	239	9	2014	2014	NUM
ejpam-2101	239	10	)	)	PUNCT
ejpam-2101	239	11	,	,	PUNCT
ejpam-2101	239	12	191	191	NUM
ejpam-2101	239	13	-	-	SYM
ejpam-2101	239	14	200	200	NUM
ejpam-2101	239	15	199	199	NUM
ejpam-2101	239	16	moving	move	VERB
ejpam-2101	239	17	line	line	NOUN
ejpam-2101	239	18	form	form	NOUN
ejpam-2101	239	19	:	:	PUNCT
ejpam-2101	239	20	p(x	p(x	PROPN
ejpam-2101	239	21	,	,	PUNCT
ejpam-2101	239	22	y	y	PROPN
ejpam-2101	239	23	,	,	PUNCT
ejpam-2101	239	24	z	z	PROPN
ejpam-2101	239	25	;	;	PUNCT
ejpam-2101	239	26	s	s	X
ejpam-2101	239	27	,	,	PUNCT
ejpam-2101	239	28	1	1	NUM
ejpam-2101	239	29	)	)	PUNCT
ejpam-2101	239	30	=	=	SYM
ejpam-2101	240	1	s2(−x	s2(−x	PROPN
ejpam-2101	241	1	+	+	PUNCT
ejpam-2101	242	1	z)−	z)−	NUM
ejpam-2101	242	2	2s	2s	NUM
ejpam-2101	242	3	y	y	X
ejpam-2101	242	4	−	−	PROPN
ejpam-2101	242	5	(	(	PUNCT
ejpam-2101	242	6	x	x	PROPN
ejpam-2101	242	7	+	+	NUM
ejpam-2101	242	8	z	z	NOUN
ejpam-2101	242	9	)	)	PUNCT
ejpam-2101	242	10	,	,	PUNCT
ejpam-2101	242	11	q(x	q(x	PROPN
ejpam-2101	242	12	,	,	PUNCT
ejpam-2101	242	13	y	y	PROPN
ejpam-2101	242	14	,	,	PUNCT
ejpam-2101	242	15	z	z	PROPN
ejpam-2101	242	16	;	;	PUNCT
ejpam-2101	242	17	s	s	X
ejpam-2101	242	18	,	,	PUNCT
ejpam-2101	242	19	1	1	NUM
ejpam-2101	242	20	)	)	PUNCT
ejpam-2101	242	21	=	=	SYM
ejpam-2101	242	22	−s2	−s2	PROPN
ejpam-2101	242	23	y	y	PROPN
ejpam-2101	242	24	+	+	CCONJ
ejpam-2101	242	25	2sx	2sx	ADJ
ejpam-2101	242	26	−	−	NOUN
ejpam-2101	242	27	y.	y.	NOUN
ejpam-2101	242	28	then	then	ADV
ejpam-2101	242	29	,	,	PUNCT
ejpam-2101	242	30	construct	construct	VERB
ejpam-2101	242	31	matrix	matrix	NOUN
ejpam-2101	242	32	m(x	m(x	PROPN
ejpam-2101	242	33	,	,	PUNCT
ejpam-2101	242	34	y	y	PROPN
ejpam-2101	242	35	,	,	PUNCT
ejpam-2101	242	36	z	z	NOUN
ejpam-2101	242	37	)	)	PUNCT
ejpam-2101	242	38	as	as	ADP
ejpam-2101	242	39	m(x	m(x	PROPN
ejpam-2101	242	40	,	,	PUNCT
ejpam-2101	242	41	y	y	PROPN
ejpam-2101	242	42	,	,	PUNCT
ejpam-2101	242	43	z	z	NOUN
ejpam-2101	242	44	)	)	PUNCT
ejpam-2101	243	1	=	=	NOUN
ejpam-2101	243	2			NOUN
ejpam-2101	243	3			ADJ
ejpam-2101	243	4			ADJ
ejpam-2101	243	5			NOUN
ejpam-2101	243	6	−x	−x	NOUN
ejpam-2101	243	7	+	+	CCONJ
ejpam-2101	243	8	z	z	AUX
ejpam-2101	243	9	0	0	NUM
ejpam-2101	243	10	−y	−y	NOUN
ejpam-2101	243	11	0	0	NUM
ejpam-2101	244	1	−2y	−2y	PROPN
ejpam-2101	244	2	−x	−x	NOUN
ejpam-2101	244	3	+	+	CCONJ
ejpam-2101	244	4	z	z	NOUN
ejpam-2101	244	5	2x	2x	NUM
ejpam-2101	244	6	−y	−y	VERB
ejpam-2101	244	7	−(x	−(x	NOUN
ejpam-2101	245	1	+	+	CCONJ
ejpam-2101	245	2	z	z	X
ejpam-2101	245	3	)	)	PUNCT
ejpam-2101	245	4	−2y	−2y	PROPN
ejpam-2101	245	5	−y	−y	VERB
ejpam-2101	246	1	2x	2x	NUM
ejpam-2101	247	1	0	0	PUNCT
ejpam-2101	247	2	−(x	−(x	NOUN
ejpam-2101	247	3	+	+	CCONJ
ejpam-2101	247	4	z	z	NOUN
ejpam-2101	247	5	)	)	PUNCT
ejpam-2101	247	6	0	0	NUM
ejpam-2101	247	7	−y	−y	NOUN
ejpam-2101	247	8			PROPN
ejpam-2101	247	9			PROPN
ejpam-2101	247	10			PROPN
ejpam-2101	247	11			PROPN
ejpam-2101	247	12	.	.	PUNCT
ejpam-2101	248	1	and	and	CCONJ
ejpam-2101	248	2	m(u	m(u	PROPN
ejpam-2101	248	3	,	,	PUNCT
ejpam-2101	248	4	v	v	NOUN
ejpam-2101	248	5	)	)	PUNCT
ejpam-2101	249	1	=	=	NOUN
ejpam-2101	249	2	m(g(u	m(g(u	NOUN
ejpam-2101	249	3	,	,	PUNCT
ejpam-2101	249	4	v	v	NOUN
ejpam-2101	249	5	)	)	PUNCT
ejpam-2101	249	6	)	)	PUNCT
ejpam-2101	250	1	=	=	SYM
ejpam-2101	250	2	4(u2	4(u2	PROPN
ejpam-2101	251	1	+	+	NUM
ejpam-2101	251	2	2uv	2uv	ADJ
ejpam-2101	251	3	+	+	CCONJ
ejpam-2101	251	4	2v2)2(22u8	2v2)2(22u8	ADJ
ejpam-2101	251	5	−	−	NOUN
ejpam-2101	251	6	86u6v2	86u6v2	NOUN
ejpam-2101	251	7	−	−	PROPN
ejpam-2101	251	8	10u5v3	10u5v3	NUM
ejpam-2101	251	9	+	+	CCONJ
ejpam-2101	251	10	131u4v4	131u4v4	NUM
ejpam-2101	251	11	+	+	CCONJ
ejpam-2101	251	12	34u3v5	34u3v5	PROPN
ejpam-2101	251	13	−	−	PROPN
ejpam-2101	251	14	84u2v6	84u2v6	NOUN
ejpam-2101	251	15	−	−	PROPN
ejpam-2101	251	16	20uv7	20uv7	NOUN
ejpam-2101	251	17	+	+	CCONJ
ejpam-2101	251	18	25v8	25v8	NUM
ejpam-2101	251	19	)	)	PUNCT
ejpam-2101	251	20	.	.	PUNCT
ejpam-2101	252	1	then	then	ADV
ejpam-2101	252	2	,	,	PUNCT
ejpam-2101	252	3	we	we	PRON
ejpam-2101	252	4	compute	compute	VERB
ejpam-2101	252	5	the	the	DET
ejpam-2101	252	6	smith	smith	PROPN
ejpam-2101	252	7	normal	normal	ADJ
ejpam-2101	252	8	form	form	NOUN
ejpam-2101	252	9	ofm(u	ofm(u	PROPN
ejpam-2101	252	10	,	,	PUNCT
ejpam-2101	252	11	1	1	NUM
ejpam-2101	252	12	)	)	PUNCT
ejpam-2101	252	13	s(m(u	s(m(u	NOUN
ejpam-2101	252	14	,	,	PUNCT
ejpam-2101	252	15	1	1	NUM
ejpam-2101	252	16	)	)	PUNCT
ejpam-2101	252	17	)	)	PUNCT
ejpam-2101	253	1	=	=	NOUN
ejpam-2101	253	2			NOUN
ejpam-2101	253	3			ADJ
ejpam-2101	253	4			ADJ
ejpam-2101	253	5			NUM
ejpam-2101	253	6	1	1	NUM
ejpam-2101	253	7	0	0	NUM
ejpam-2101	253	8	0	0	NUM
ejpam-2101	253	9	0	0	NUM
ejpam-2101	253	10	0	0	NUM
ejpam-2101	253	11	1	1	NUM
ejpam-2101	253	12	0	0	NUM
ejpam-2101	253	13	0	0	NUM
ejpam-2101	253	14	0	0	NUM
ejpam-2101	253	15	0	0	NUM
ejpam-2101	253	16	2	2	NUM
ejpam-2101	253	17	+	+	NUM
ejpam-2101	253	18	2u+	2u+	NUM
ejpam-2101	253	19	u2	u2	NOUN
ejpam-2101	253	20	0	0	NUM
ejpam-2101	253	21	0	0	NUM
ejpam-2101	253	22	0	0	NUM
ejpam-2101	253	23	0	0	NUM
ejpam-2101	253	24	1	1	NUM
ejpam-2101	253	25	22(2	22(2	NUM
ejpam-2101	253	26	+	+	NUM
ejpam-2101	253	27	2u+	2u+	NUM
ejpam-2101	253	28	u2)(25−	u2)(25−	NOUN
ejpam-2101	253	29	20u−	20u−	NUM
ejpam-2101	253	30	84u2	84u2	NUM
ejpam-2101	253	31	+	+	SYM
ejpam-2101	253	32	34u3	34u3	NUM
ejpam-2101	253	33	+	+	CCONJ
ejpam-2101	253	34	131u4	131u4	NUM
ejpam-2101	253	35	−	−	PROPN
ejpam-2101	253	36	10u5	10u5	NUM
ejpam-2101	253	37	−	−	NOUN
ejpam-2101	253	38	86u6	86u6	NUM
ejpam-2101	254	1	+	+	CCONJ
ejpam-2101	254	2	22u8	22u8	NUM
ejpam-2101	254	3	)	)	PUNCT
ejpam-2101	254	4			PROPN
ejpam-2101	254	5			PROPN
ejpam-2101	254	6			PROPN
ejpam-2101	254	7			PROPN
ejpam-2101	254	8	.	.	PUNCT
ejpam-2101	255	1	the	the	DET
ejpam-2101	255	2	last	last	ADJ
ejpam-2101	255	3	diagonal	diagonal	ADJ
ejpam-2101	255	4	entry	entry	NOUN
ejpam-2101	255	5	is	be	AUX
ejpam-2101	255	6	the	the	DET
ejpam-2101	255	7	polynomial	polynomial	ADJ
ejpam-2101	255	8	1	1	NUM
ejpam-2101	255	9	22	22	NUM
ejpam-2101	255	10	(	(	PUNCT
ejpam-2101	255	11	2	2	NUM
ejpam-2101	255	12	+	+	NUM
ejpam-2101	255	13	2u+	2u+	NUM
ejpam-2101	255	14	u2)(25−	u2)(25−	NOUN
ejpam-2101	255	15	20u−	20u−	NUM
ejpam-2101	255	16	84u2	84u2	NUM
ejpam-2101	256	1	+	+	SYM
ejpam-2101	256	2	34u3	34u3	NUM
ejpam-2101	256	3	+	+	CCONJ
ejpam-2101	256	4	131u4	131u4	NUM
ejpam-2101	256	5	−	−	PROPN
ejpam-2101	256	6	10u5	10u5	NUM
ejpam-2101	256	7	−	−	NOUN
ejpam-2101	256	8	86u6	86u6	NUM
ejpam-2101	256	9	+	+	CCONJ
ejpam-2101	256	10	22u8	22u8	NUM
ejpam-2101	256	11	)	)	PUNCT
ejpam-2101	256	12	,	,	PUNCT
ejpam-2101	256	13	which	which	PRON
ejpam-2101	256	14	is	be	AUX
ejpam-2101	256	15	exactlym(u	exactlym(u	PROPN
ejpam-2101	256	16	,	,	PUNCT
ejpam-2101	256	17	1	1	NUM
ejpam-2101	256	18	)	)	PUNCT
ejpam-2101	256	19	and	and	CCONJ
ejpam-2101	256	20	f(g(u	f(g(u	PROPN
ejpam-2101	256	21	,	,	PUNCT
ejpam-2101	256	22	1	1	NUM
ejpam-2101	256	23	)	)	PUNCT
ejpam-2101	256	24	)	)	PUNCT
ejpam-2101	256	25	.	.	PUNCT
ejpam-2101	257	1	hence	hence	ADV
ejpam-2101	257	2	the	the	DET
ejpam-2101	257	3	solution	solution	NOUN
ejpam-2101	257	4	to	to	ADP
ejpam-2101	257	5	the	the	DET
ejpam-2101	257	6	equation	equation	NOUN
ejpam-2101	257	7	1	1	NUM
ejpam-2101	257	8	22	22	NUM
ejpam-2101	257	9	(	(	PUNCT
ejpam-2101	257	10	2	2	NUM
ejpam-2101	257	11	+	+	NUM
ejpam-2101	257	12	2u+	2u+	NUM
ejpam-2101	257	13	u2)(25−	u2)(25−	NOUN
ejpam-2101	257	14	20u−	20u−	NUM
ejpam-2101	257	15	84u2	84u2	NUM
ejpam-2101	257	16	+	+	SYM
ejpam-2101	257	17	34u3	34u3	NUM
ejpam-2101	257	18	+	+	CCONJ
ejpam-2101	257	19	131u4	131u4	NUM
ejpam-2101	257	20	−	−	PROPN
ejpam-2101	257	21	10u5	10u5	NUM
ejpam-2101	257	22	−	−	NOUN
ejpam-2101	257	23	86u6	86u6	NUM
ejpam-2101	257	24	+	+	CCONJ
ejpam-2101	257	25	22u8	22u8	NUM
ejpam-2101	257	26	)	)	PUNCT
ejpam-2101	257	27	=	=	SYM
ejpam-2101	257	28	0	0	NUM
ejpam-2101	257	29	are	be	AUX
ejpam-2101	257	30	the	the	DET
ejpam-2101	257	31	parameters	parameter	NOUN
ejpam-2101	257	32	of	of	ADP
ejpam-2101	257	33	g(u	g(u	PROPN
ejpam-2101	257	34	,	,	PUNCT
ejpam-2101	257	35	v	v	NOUN
ejpam-2101	257	36	)	)	PUNCT
ejpam-2101	257	37	corresponding	correspond	VERB
ejpam-2101	257	38	to	to	ADP
ejpam-2101	257	39	the	the	DET
ejpam-2101	257	40	intersection	intersection	NOUN
ejpam-2101	257	41	of	of	ADP
ejpam-2101	257	42	the	the	DET
ejpam-2101	257	43	two	two	NUM
ejpam-2101	257	44	curves	curve	NOUN
ejpam-2101	257	45	.	.	PUNCT
ejpam-2101	258	1	4	4	X
ejpam-2101	258	2	.	.	X
ejpam-2101	258	3	conclusion	conclusion	NOUN
ejpam-2101	258	4	in	in	ADP
ejpam-2101	258	5	this	this	DET
ejpam-2101	258	6	paper	paper	NOUN
ejpam-2101	258	7	,	,	PUNCT
ejpam-2101	258	8	we	we	PRON
ejpam-2101	258	9	compared	compare	VERB
ejpam-2101	258	10	three	three	NUM
ejpam-2101	258	11	different	different	ADJ
ejpam-2101	258	12	methods	method	NOUN
ejpam-2101	258	13	of	of	ADP
ejpam-2101	258	14	finding	find	VERB
ejpam-2101	258	15	the	the	DET
ejpam-2101	258	16	intersections	intersection	NOUN
ejpam-2101	258	17	of	of	ADP
ejpam-2101	258	18	two	two	NUM
ejpam-2101	258	19	rational	rational	ADJ
ejpam-2101	258	20	parametrized	parametrized	ADJ
ejpam-2101	258	21	plane	plane	NOUN
ejpam-2101	258	22	curves	curve	NOUN
ejpam-2101	258	23	.	.	PUNCT
ejpam-2101	259	1	these	these	DET
ejpam-2101	259	2	methods	method	NOUN
ejpam-2101	259	3	only	only	ADV
ejpam-2101	259	4	use	use	VERB
ejpam-2101	259	5	the	the	DET
ejpam-2101	259	6	µ-basis	µ-basis	NOUN
ejpam-2101	259	7	of	of	ADP
ejpam-2101	259	8	one	one	NUM
ejpam-2101	259	9	curve	curve	NOUN
ejpam-2101	259	10	without	without	ADP
ejpam-2101	259	11	finding	find	VERB
ejpam-2101	259	12	the	the	DET
ejpam-2101	259	13	implicit	implicit	ADJ
ejpam-2101	259	14	equations	equation	NOUN
ejpam-2101	259	15	of	of	ADP
ejpam-2101	259	16	the	the	DET
ejpam-2101	259	17	curves	curve	NOUN
ejpam-2101	259	18	.	.	PUNCT
ejpam-2101	260	1	since	since	SCONJ
ejpam-2101	260	2	finding	find	VERB
ejpam-2101	260	3	implicit	implicit	ADJ
ejpam-2101	260	4	equation	equation	NOUN
ejpam-2101	260	5	is	be	AUX
ejpam-2101	260	6	not	not	PART
ejpam-2101	260	7	an	an	DET
ejpam-2101	260	8	easy	easy	ADJ
ejpam-2101	260	9	task	task	NOUN
ejpam-2101	260	10	,	,	PUNCT
ejpam-2101	260	11	these	these	DET
ejpam-2101	260	12	three	three	NUM
ejpam-2101	260	13	algorithms	algorithm	NOUN
ejpam-2101	260	14	increase	increase	VERB
ejpam-2101	260	15	the	the	DET
ejpam-2101	260	16	computation	computation	NOUN
ejpam-2101	260	17	efficiency	efficiency	NOUN
ejpam-2101	260	18	.	.	PUNCT
ejpam-2101	261	1	to	to	ADP
ejpam-2101	261	2	our	our	PRON
ejpam-2101	261	3	knowledge	knowledge	NOUN
ejpam-2101	261	4	,	,	PUNCT
ejpam-2101	261	5	no	no	DET
ejpam-2101	261	6	research	research	NOUN
ejpam-2101	261	7	has	have	AUX
ejpam-2101	261	8	done	do	VERB
ejpam-2101	261	9	to	to	PART
ejpam-2101	261	10	extend	extend	VERB
ejpam-2101	261	11	these	these	DET
ejpam-2101	261	12	three	three	NUM
ejpam-2101	261	13	algorithms	algorithm	NOUN
ejpam-2101	261	14	to	to	ADP
ejpam-2101	261	15	the	the	DET
ejpam-2101	261	16	case	case	NOUN
ejpam-2101	261	17	of	of	ADP
ejpam-2101	261	18	rational	rational	ADJ
ejpam-2101	261	19	parametrized	parametrized	ADJ
ejpam-2101	261	20	space	space	NOUN
ejpam-2101	261	21	curves	curve	NOUN
ejpam-2101	261	22	.	.	PUNCT
ejpam-2101	262	1	the	the	DET
ejpam-2101	262	2	authors	author	NOUN
ejpam-2101	262	3	are	be	AUX
ejpam-2101	262	4	currently	currently	ADV
ejpam-2101	262	5	studying	study	VERB
ejpam-2101	262	6	how	how	SCONJ
ejpam-2101	262	7	to	to	PART
ejpam-2101	262	8	generalize	generalize	VERB
ejpam-2101	262	9	these	these	DET
ejpam-2101	262	10	methods	method	NOUN
ejpam-2101	262	11	to	to	ADP
ejpam-2101	262	12	higher	high	ADJ
ejpam-2101	262	13	dimensions	dimension	NOUN
ejpam-2101	262	14	.	.	PUNCT
ejpam-2101	263	1	references	reference	NOUN
ejpam-2101	263	2	200	200	NUM
ejpam-2101	263	3	references	reference	NOUN
ejpam-2101	263	4	[	[	X
ejpam-2101	263	5	1	1	NUM
ejpam-2101	263	6	]	]	PUNCT
ejpam-2101	263	7	f.	f.	PROPN
ejpam-2101	263	8	chen	chen	PROPN
ejpam-2101	263	9	and	and	CCONJ
ejpam-2101	263	10	w.	w.	PROPN
ejpam-2101	263	11	wang	wang	PROPN
ejpam-2101	263	12	.	.	PUNCT
ejpam-2101	264	1	the	the	DET
ejpam-2101	264	2	µ-basis	µ-basis	NOUN
ejpam-2101	264	3	of	of	ADP
ejpam-2101	264	4	a	a	DET
ejpam-2101	264	5	planar	planar	ADJ
ejpam-2101	264	6	rational	rational	ADJ
ejpam-2101	264	7	curve	curve	NOUN
ejpam-2101	264	8	:	:	PUNCT
ejpam-2101	264	9	properties	property	NOUN
ejpam-2101	264	10	and	and	CCONJ
ejpam-2101	264	11	computation	computation	NOUN
ejpam-2101	264	12	,	,	PUNCT
ejpam-2101	264	13	graphical	graphical	ADJ
ejpam-2101	264	14	models	model	NOUN
ejpam-2101	264	15	,	,	PUNCT
ejpam-2101	264	16	64	64	NUM
ejpam-2101	264	17	,	,	PUNCT
ejpam-2101	264	18	368	368	NUM
ejpam-2101	264	19	-	-	SYM
ejpam-2101	264	20	381	381	NUM
ejpam-2101	264	21	.	.	PUNCT
ejpam-2101	264	22	2002	2002	NUM
ejpam-2101	264	23	.	.	PUNCT
ejpam-2101	265	1	[	[	X
ejpam-2101	265	2	2	2	X
ejpam-2101	265	3	]	]	PUNCT
ejpam-2101	265	4	f.	f.	PROPN
ejpam-2101	265	5	chen	chen	PROPN
ejpam-2101	265	6	and	and	CCONJ
ejpam-2101	265	7	w.	w.	PROPN
ejpam-2101	265	8	wang	wang	PROPN
ejpam-2101	265	9	.	.	PUNCT
ejpam-2101	266	1	revisiting	revisit	VERB
ejpam-2101	266	2	the	the	DET
ejpam-2101	266	3	µ-basis	µ-basis	NOUN
ejpam-2101	266	4	of	of	ADP
ejpam-2101	266	5	a	a	DET
ejpam-2101	266	6	rational	rational	ADJ
ejpam-2101	266	7	ruled	rule	VERB
ejpam-2101	266	8	surface	surface	NOUN
ejpam-2101	266	9	journal	journal	PROPN
ejpam-2101	266	10	of	of	ADP
ejpam-2101	266	11	symbolic	symbolic	ADJ
ejpam-2101	266	12	computation	computation	NOUN
ejpam-2101	266	13	36	36	NUM
ejpam-2101	266	14	(	(	PUNCT
ejpam-2101	266	15	5	5	NUM
ejpam-2101	266	16	)	)	PUNCT
ejpam-2101	266	17	,	,	PUNCT
ejpam-2101	266	18	699	699	NUM
ejpam-2101	266	19	-	-	SYM
ejpam-2101	266	20	716	716	NUM
ejpam-2101	266	21	.	.	NUM
ejpam-2101	266	22	2003	2003	NUM
ejpam-2101	266	23	.	.	PUNCT
ejpam-2101	267	1	[	[	X
ejpam-2101	267	2	3	3	X
ejpam-2101	267	3	]	]	X
ejpam-2101	267	4	d.	d.	PROPN
ejpam-2101	267	5	a.	a.	PROPN
ejpam-2101	267	6	cox	cox	PROPN
ejpam-2101	267	7	,	,	PUNCT
ejpam-2101	267	8	r.	r.	PROPN
ejpam-2101	267	9	goldman	goldman	PROPN
ejpam-2101	267	10	,	,	PUNCT
ejpam-2101	267	11	and	and	CCONJ
ejpam-2101	267	12	m.	m.	PROPN
ejpam-2101	267	13	zhang	zhang	PROPN
ejpam-2101	267	14	.	.	PUNCT
ejpam-2101	268	1	on	on	ADP
ejpam-2101	268	2	the	the	DET
ejpam-2101	268	3	validity	validity	NOUN
ejpam-2101	268	4	of	of	ADP
ejpam-2101	268	5	implicitization	implicitization	NOUN
ejpam-2101	268	6	by	by	ADP
ejpam-2101	268	7	moving	move	VERB
ejpam-2101	268	8	quadrics	quadric	NOUN
ejpam-2101	268	9	for	for	ADP
ejpam-2101	268	10	rational	rational	ADJ
ejpam-2101	268	11	surfaces	surface	NOUN
ejpam-2101	268	12	with	with	ADP
ejpam-2101	268	13	no	no	DET
ejpam-2101	268	14	base	base	NOUN
ejpam-2101	268	15	points	point	NOUN
ejpam-2101	268	16	,	,	PUNCT
ejpam-2101	268	17	journal	journal	NOUN
ejpam-2101	268	18	of	of	ADP
ejpam-2101	268	19	symbolic	symbolic	ADJ
ejpam-2101	268	20	computation	computation	NOUN
ejpam-2101	268	21	,	,	PUNCT
ejpam-2101	268	22	29	29	NUM
ejpam-2101	268	23	,	,	PUNCT
ejpam-2101	268	24	419	419	NUM
ejpam-2101	268	25	-	-	SYM
ejpam-2101	268	26	440	440	NUM
ejpam-2101	268	27	.	.	PUNCT
ejpam-2101	268	28	2000	2000	NUM
ejpam-2101	268	29	.	.	PUNCT
ejpam-2101	269	1	[	[	X
ejpam-2101	269	2	4	4	X
ejpam-2101	269	3	]	]	X
ejpam-2101	269	4	d.	d.	PROPN
ejpam-2101	269	5	a.	a.	PROPN
ejpam-2101	269	6	cox	cox	PROPN
ejpam-2101	269	7	,	,	PUNCT
ejpam-2101	269	8	j.	j.	PROPN
ejpam-2101	269	9	little	little	PROPN
ejpam-2101	269	10	and	and	CCONJ
ejpam-2101	269	11	d.	d.	PROPN
ejpam-2101	269	12	o’shea	o’shea	PROPN
ejpam-2101	269	13	.	.	PUNCT
ejpam-2101	270	1	using	use	VERB
ejpam-2101	270	2	algebraic	algebraic	ADJ
ejpam-2101	270	3	geometry	geometry	NOUN
ejpam-2101	270	4	,	,	PUNCT
ejpam-2101	270	5	springer	springer	NOUN
ejpam-2101	270	6	,	,	PUNCT
ejpam-2101	270	7	1998	1998	NUM
ejpam-2101	270	8	.	.	PUNCT
ejpam-2101	271	1	[	[	X
ejpam-2101	271	2	5	5	X
ejpam-2101	271	3	]	]	PUNCT
ejpam-2101	271	4	d.	d.	PROPN
ejpam-2101	271	5	a.	a.	PROPN
ejpam-2101	271	6	cox	cox	PROPN
ejpam-2101	271	7	,	,	PUNCT
ejpam-2101	271	8	t.	t.	PROPN
ejpam-2101	271	9	sederberg	sederberg	PROPN
ejpam-2101	271	10	,	,	PUNCT
ejpam-2101	271	11	and	and	CCONJ
ejpam-2101	271	12	f.	f.	PROPN
ejpam-2101	271	13	chen	chen	PROPN
ejpam-2101	271	14	.	.	PUNCT
ejpam-2101	272	1	the	the	DET
ejpam-2101	272	2	moving	move	VERB
ejpam-2101	272	3	line	line	NOUN
ejpam-2101	272	4	ideal	ideal	ADJ
ejpam-2101	272	5	basis	basis	NOUN
ejpam-2101	272	6	of	of	ADP
ejpam-2101	272	7	planar	planar	ADJ
ejpam-2101	272	8	rational	rational	ADJ
ejpam-2101	272	9	curves	curve	NOUN
ejpam-2101	272	10	,	,	PUNCT
ejpam-2101	272	11	computer	computer	NOUN
ejpam-2101	272	12	aided	aid	VERB
ejpam-2101	272	13	geometric	geometric	ADJ
ejpam-2101	272	14	design	design	NOUN
ejpam-2101	272	15	15	15	NUM
ejpam-2101	272	16	,	,	PUNCT
ejpam-2101	272	17	803	803	NUM
ejpam-2101	272	18	-	-	SYM
ejpam-2101	272	19	827	827	NUM
ejpam-2101	272	20	.	.	PUNCT
ejpam-2101	272	21	1998	1998	NUM
ejpam-2101	272	22	.	.	PUNCT
ejpam-2101	273	1	[	[	X
ejpam-2101	273	2	6	6	NUM
ejpam-2101	273	3	]	]	PUNCT
ejpam-2101	273	4	d.	d.	PROPN
ejpam-2101	273	5	eisenbud	eisenbud	PROPN
ejpam-2101	273	6	.	.	PUNCT
ejpam-2101	274	1	commutative	commutative	ADJ
ejpam-2101	274	2	algebra	algebra	NOUN
ejpam-2101	274	3	with	with	ADP
ejpam-2101	274	4	a	a	DET
ejpam-2101	274	5	view	view	NOUN
ejpam-2101	274	6	toward	toward	ADP
ejpam-2101	274	7	algebraic	algebraic	ADJ
ejpam-2101	274	8	geometry	geometry	NOUN
ejpam-2101	274	9	,	,	PUNCT
ejpam-2101	274	10	springer	springer	NOUN
ejpam-2101	274	11	,	,	PUNCT
ejpam-2101	274	12	1994	1994	NUM
ejpam-2101	274	13	.	.	PUNCT
ejpam-2101	275	1	[	[	X
ejpam-2101	275	2	7	7	X
ejpam-2101	275	3	]	]	PUNCT
ejpam-2101	275	4	t.	t.	PROPN
ejpam-2101	275	5	w.	w.	PROPN
ejpam-2101	275	6	sederberg	sederberg	PROPN
ejpam-2101	275	7	and	and	CCONJ
ejpam-2101	275	8	f.	f.	PROPN
ejpam-2101	275	9	chen	chen	PROPN
ejpam-2101	275	10	.	.	PUNCT
ejpam-2101	276	1	implicitization	implicitization	NOUN
ejpam-2101	276	2	using	use	VERB
ejpam-2101	276	3	moving	move	VERB
ejpam-2101	276	4	curves	curve	NOUN
ejpam-2101	276	5	and	and	CCONJ
ejpam-2101	276	6	surfaces	surface	NOUN
ejpam-2101	276	7	proceeding	proceeding	NOUN
ejpam-2101	276	8	of	of	ADP
ejpam-2101	276	9	siggraph	siggraph	PROPN
ejpam-2101	276	10	,	,	PUNCT
ejpam-2101	276	11	301	301	NUM
ejpam-2101	276	12	-	-	SYM
ejpam-2101	276	13	308	308	NUM
ejpam-2101	276	14	.	.	PUNCT
ejpam-2101	276	15	1995	1995	NUM
ejpam-2101	276	16	.	.	PUNCT
ejpam-2101	277	1	[	[	X
ejpam-2101	277	2	8	8	X
ejpam-2101	277	3	]	]	PUNCT
ejpam-2101	277	4	t.	t.	PROPN
ejpam-2101	277	5	sederberg	sederberg	PROPN
ejpam-2101	277	6	,	,	PUNCT
ejpam-2101	277	7	r.	r.	PROPN
ejpam-2101	277	8	goldman	goldman	PROPN
ejpam-2101	277	9	,	,	PUNCT
ejpam-2101	277	10	and	and	CCONJ
ejpam-2101	277	11	h.	h.	PROPN
ejpam-2101	277	12	du	du	PROPN
ejpam-2101	277	13	.	.	PUNCT
ejpam-2101	277	14	implicitizing	implicitize	VERB
ejpam-2101	277	15	rational	rational	ADJ
ejpam-2101	277	16	curves	curve	NOUN
ejpam-2101	277	17	by	by	ADP
ejpam-2101	277	18	the	the	DET
ejpam-2101	277	19	method	method	NOUN
ejpam-2101	277	20	of	of	ADP
ejpam-2101	277	21	moving	move	VERB
ejpam-2101	277	22	algebraic	algebraic	ADJ
ejpam-2101	277	23	curves	curve	NOUN
ejpam-2101	277	24	,	,	PUNCT
ejpam-2101	277	25	journal	journal	NOUN
ejpam-2101	277	26	of	of	ADP
ejpam-2101	277	27	symbolic	symbolic	ADJ
ejpam-2101	277	28	computation	computation	NOUN
ejpam-2101	277	29	,	,	PUNCT
ejpam-2101	277	30	23	23	NUM
ejpam-2101	277	31	,	,	PUNCT
ejpam-2101	277	32	153	153	NUM
ejpam-2101	277	33	-	-	SYM
ejpam-2101	277	34	175	175	NUM
ejpam-2101	277	35	.	.	PUNCT
ejpam-2101	277	36	1997	1997	NUM
ejpam-2101	277	37	.	.	PUNCT
ejpam-2101	278	1	[	[	X
ejpam-2101	278	2	9	9	NUM
ejpam-2101	278	3	]	]	PUNCT
ejpam-2101	278	4	t.	t.	PROPN
ejpam-2101	278	5	sederberg	sederberg	PROPN
ejpam-2101	278	6	,	,	PUNCT
ejpam-2101	278	7	t.	t.	PROPN
ejpam-2101	278	8	saito	saito	PROPN
ejpam-2101	278	9	,	,	PUNCT
ejpam-2101	278	10	d.	d.	PROPN
ejpam-2101	278	11	qi	qi	PROPN
ejpam-2101	278	12	,	,	PUNCT
ejpam-2101	278	13	and	and	CCONJ
ejpam-2101	278	14	k.	k.	PROPN
ejpam-2101	278	15	klimaszewski	klimaszewski	PROPN
ejpam-2101	278	16	.	.	PUNCT
ejpam-2101	279	1	curve	curve	NOUN
ejpam-2101	279	2	implicitization	implicitization	NOUN
ejpam-2101	279	3	using	use	VERB
ejpam-2101	279	4	moving	move	VERB
ejpam-2101	279	5	lines	line	NOUN
ejpam-2101	279	6	,	,	PUNCT
ejpam-2101	279	7	computer	computer	NOUN
ejpam-2101	279	8	aided	aid	VERB
ejpam-2101	279	9	geometric	geometric	ADJ
ejpam-2101	279	10	design	design	NOUN
ejpam-2101	279	11	11	11	NUM
ejpam-2101	279	12	,	,	PUNCT
ejpam-2101	279	13	687	687	NUM
ejpam-2101	279	14	-	-	SYM
ejpam-2101	279	15	706	706	NUM
ejpam-2101	279	16	.	.	NUM
ejpam-2101	279	17	1994	1994	NUM
ejpam-2101	279	18	.	.	PUNCT
ejpam-2101	280	1	[	[	X
ejpam-2101	280	2	10	10	NUM
ejpam-2101	280	3	]	]	X
ejpam-2101	280	4	n.	n.	NOUN
ejpam-2101	280	5	song	song	NOUN
ejpam-2101	280	6	and	and	CCONJ
ejpam-2101	280	7	r.	r.	PROPN
ejpam-2101	280	8	goldman	goldman	PROPN
ejpam-2101	280	9	.	.	PUNCT
ejpam-2101	281	1	µ-bases	µ-base	VERB
ejpam-2101	281	2	for	for	ADP
ejpam-2101	281	3	polynomial	polynomial	ADJ
ejpam-2101	281	4	systems	system	NOUN
ejpam-2101	281	5	in	in	ADP
ejpam-2101	281	6	one	one	NUM
ejpam-2101	281	7	variable	variable	NOUN
ejpam-2101	281	8	,	,	PUNCT
ejpam-2101	281	9	computer	computer	NOUN
ejpam-2101	281	10	aided	aid	VERB
ejpam-2101	281	11	geometric	geometric	ADJ
ejpam-2101	281	12	design	design	NOUN
ejpam-2101	281	13	,	,	PUNCT
ejpam-2101	281	14	26(2	26(2	NUM
ejpam-2101	281	15	)	)	PUNCT
ejpam-2101	281	16	,	,	PUNCT
ejpam-2101	281	17	217	217	NUM
ejpam-2101	281	18	-	-	SYM
ejpam-2101	281	19	230	230	NUM
ejpam-2101	281	20	,	,	PUNCT
ejpam-2101	281	21	2009	2009	NUM
ejpam-2101	281	22	.	.	PUNCT
ejpam-2101	282	1	[	[	X
ejpam-2101	282	2	11	11	NUM
ejpam-2101	282	3	]	]	PUNCT
ejpam-2101	282	4	x.	x.	NOUN
ejpam-2101	282	5	wang	wang	PROPN
ejpam-2101	282	6	and	and	CCONJ
ejpam-2101	282	7	r.	r.	PROPN
ejpam-2101	282	8	goldman	goldman	PROPN
ejpam-2101	282	9	.	.	PUNCT
ejpam-2101	283	1	µ-bases	µ-base	VERB
ejpam-2101	283	2	for	for	ADP
ejpam-2101	283	3	complex	complex	ADJ
ejpam-2101	283	4	rational	rational	ADJ
ejpam-2101	283	5	curves	curve	NOUN
ejpam-2101	283	6	,	,	PUNCT
ejpam-2101	283	7	computer	computer	NOUN
ejpam-2101	283	8	aided	aid	VERB
ejpam-2101	283	9	geometric	geometric	ADJ
ejpam-2101	283	10	design	design	NOUN
ejpam-2101	283	11	,	,	PUNCT
ejpam-2101	283	12	30(7	30(7	NUM
ejpam-2101	283	13	)	)	PUNCT
ejpam-2101	283	14	,	,	PUNCT
ejpam-2101	283	15	623	623	NUM
ejpam-2101	283	16	-	-	SYM
ejpam-2101	283	17	635	635	NUM
ejpam-2101	283	18	,	,	PUNCT
ejpam-2101	283	19	2013	2013	NUM
ejpam-2101	283	20	.	.	PUNCT