id	sid	tid	token	lemma	pos
jd472v26s89	1	1	homotopy	homotopy	NOUN
jd472v26s89	1	2	continuation	continuation	NOUN
jd472v26s89	1	3	is	be	AUX
jd472v26s89	1	4	the	the	DET
jd472v26s89	1	5	fundamental	fundamental	ADJ
jd472v26s89	1	6	method	method	NOUN
jd472v26s89	1	7	,	,	PUNCT
jd472v26s89	1	8	or	or	CCONJ
jd472v26s89	1	9	family	family	NOUN
jd472v26s89	1	10	of	of	ADP
jd472v26s89	1	11	methods	method	NOUN
jd472v26s89	1	12	,	,	PUNCT
jd472v26s89	1	13	of	of	ADP
jd472v26s89	1	14	numerical	numerical	ADJ
jd472v26s89	1	15	algebraic	algebraic	ADJ
jd472v26s89	1	16	geometry	geometry	NOUN
jd472v26s89	1	17	.	.	PUNCT
jd472v26s89	2	1	using	use	VERB
jd472v26s89	2	2	homotopies	homotopie	NOUN
jd472v26s89	2	3	,	,	PUNCT
jd472v26s89	2	4	we	we	PRON
jd472v26s89	2	5	compute	compute	VERB
jd472v26s89	2	6	solution	solution	NOUN
jd472v26s89	2	7	sets	set	NOUN
jd472v26s89	2	8	for	for	ADP
jd472v26s89	2	9	systems	system	NOUN
jd472v26s89	2	10	of	of	ADP
jd472v26s89	2	11	polynomial	polynomial	ADJ
jd472v26s89	2	12	equations	equation	NOUN
jd472v26s89	2	13	.	.	PUNCT
jd472v26s89	3	1	we	we	PRON
jd472v26s89	3	2	focus	focus	VERB
jd472v26s89	3	3	on	on	ADP
jd472v26s89	3	4	a	a	DET
jd472v26s89	3	5	particular	particular	ADJ
jd472v26s89	3	6	class	class	NOUN
jd472v26s89	3	7	of	of	ADP
jd472v26s89	3	8	homotopy	homotopy	NOUN
jd472v26s89	3	9	,	,	PUNCT
jd472v26s89	3	10	namely	namely	ADV
jd472v26s89	3	11	,	,	PUNCT
jd472v26s89	3	12	the	the	DET
jd472v26s89	3	13	newton	newton	PROPN
jd472v26s89	3	14	homotopy	homotopy	PROPN
jd472v26s89	3	15	,	,	PUNCT
jd472v26s89	3	16	which	which	PRON
jd472v26s89	3	17	is	be	AUX
jd472v26s89	3	18	a	a	DET
jd472v26s89	3	19	homotopy	homotopy	NOUN
jd472v26s89	3	20	for	for	ADP
jd472v26s89	3	21	which	which	PRON
jd472v26s89	3	22	only	only	ADV
jd472v26s89	3	23	the	the	DET
jd472v26s89	3	24	constant	constant	ADJ
jd472v26s89	3	25	terms	term	NOUN
jd472v26s89	3	26	are	be	AUX
jd472v26s89	3	27	changed	change	VERB
jd472v26s89	3	28	.	.	PUNCT
jd472v26s89	4	1	newton	newton	PROPN
jd472v26s89	4	2	homotopies	homotopie	NOUN
jd472v26s89	4	3	arise	arise	VERB
jd472v26s89	4	4	naturally	naturally	ADV
jd472v26s89	4	5	when	when	SCONJ
jd472v26s89	4	6	performing	perform	VERB
jd472v26s89	4	7	monodromy	monodromy	NOUN
jd472v26s89	4	8	loops	loop	NOUN
jd472v26s89	4	9	,	,	PUNCT
jd472v26s89	4	10	moving	move	VERB
jd472v26s89	4	11	end	end	NOUN
jd472v26s89	4	12	effectors	effector	NOUN
jd472v26s89	4	13	of	of	ADP
jd472v26s89	4	14	robots	robot	NOUN
jd472v26s89	4	15	,	,	PUNCT
jd472v26s89	4	16	or	or	CCONJ
jd472v26s89	4	17	simply	simply	ADV
jd472v26s89	4	18	when	when	SCONJ
jd472v26s89	4	19	trying	try	VERB
jd472v26s89	4	20	to	to	PART
jd472v26s89	4	21	compute	compute	VERB
jd472v26s89	4	22	a	a	DET
jd472v26s89	4	23	solution	solution	NOUN
jd472v26s89	4	24	to	to	ADP
jd472v26s89	4	25	a	a	DET
jd472v26s89	4	26	square	square	ADJ
jd472v26s89	4	27	system	system	NOUN
jd472v26s89	4	28	of	of	ADP
jd472v26s89	4	29	equations	equation	NOUN
jd472v26s89	4	30	.	.	PUNCT
jd472v26s89	5	1	in	in	ADP
jd472v26s89	5	2	this	this	DET
jd472v26s89	5	3	thesis	thesis	NOUN
jd472v26s89	5	4	,	,	PUNCT
jd472v26s89	5	5	we	we	PRON
jd472v26s89	5	6	present	present	VERB
jd472v26s89	5	7	an	an	DET
jd472v26s89	5	8	a	a	DET
jd472v26s89	5	9	posteriori	posteriori	NOUN
jd472v26s89	5	10	certification	certification	NOUN
jd472v26s89	5	11	scheme	scheme	NOUN
jd472v26s89	5	12	which	which	PRON
jd472v26s89	5	13	uses	use	VERB
jd472v26s89	5	14	the	the	DET
jd472v26s89	5	15	result	result	NOUN
jd472v26s89	5	16	of	of	ADP
jd472v26s89	5	17	heuristic	heuristic	ADJ
jd472v26s89	5	18	tracking	tracking	NOUN
jd472v26s89	5	19	methods	method	NOUN
jd472v26s89	5	20	as	as	ADP
jd472v26s89	5	21	input	input	NOUN
jd472v26s89	5	22	,	,	PUNCT
jd472v26s89	5	23	producing	produce	VERB
jd472v26s89	5	24	a	a	DET
jd472v26s89	5	25	certificate	certificate	NOUN
jd472v26s89	5	26	that	that	PRON
jd472v26s89	5	27	solution	solution	NOUN
jd472v26s89	5	28	the	the	DET
jd472v26s89	5	29	path	path	NOUN
jd472v26s89	5	30	was	be	AUX
jd472v26s89	5	31	tracked	track	VERB
jd472v26s89	5	32	correctly	correctly	ADV
jd472v26s89	5	33	.	.	PUNCT
jd472v26s89	6	1	we	we	PRON
jd472v26s89	6	2	also	also	ADV
jd472v26s89	6	3	describe	describe	VERB
jd472v26s89	6	4	certified	certify	VERB
jd472v26s89	6	5	tracking	tracking	NOUN
jd472v26s89	6	6	procedures	procedure	NOUN
jd472v26s89	6	7	wherein	wherein	SCONJ
jd472v26s89	6	8	the	the	DET
jd472v26s89	6	9	predictor	predictor	NOUN
jd472v26s89	6	10	is	be	AUX
jd472v26s89	6	11	guaranteed	guarantee	VERB
jd472v26s89	6	12	to	to	PART
jd472v26s89	6	13	produce	produce	VERB
jd472v26s89	6	14	a	a	DET
jd472v26s89	6	15	point	point	NOUN
jd472v26s89	6	16	in	in	ADP
jd472v26s89	6	17	the	the	DET
jd472v26s89	6	18	quadratic	quadratic	ADJ
jd472v26s89	6	19	convergence	convergence	NOUN
jd472v26s89	6	20	basin	basin	NOUN
jd472v26s89	6	21	of	of	ADP
jd472v26s89	6	22	newton	newton	PROPN
jd472v26s89	6	23	's	's	PART
jd472v26s89	6	24	method	method	NOUN
jd472v26s89	6	25	for	for	ADP
jd472v26s89	6	26	the	the	DET
jd472v26s89	6	27	next	next	ADJ
jd472v26s89	6	28	step	step	NOUN
jd472v26s89	6	29	.	.	PUNCT
jd472v26s89	7	1	finally	finally	ADV
jd472v26s89	7	2	,	,	PUNCT
jd472v26s89	7	3	we	we	PRON
jd472v26s89	7	4	present	present	VERB
jd472v26s89	7	5	an	an	DET
jd472v26s89	7	6	application	application	NOUN
jd472v26s89	7	7	of	of	ADP
jd472v26s89	7	8	newton	newton	PROPN
jd472v26s89	7	9	homotopies	homotopie	NOUN
jd472v26s89	7	10	to	to	ADP
jd472v26s89	7	11	the	the	DET
jd472v26s89	7	12	computation	computation	NOUN
jd472v26s89	7	13	of	of	ADP
jd472v26s89	7	14	saturation	saturation	NOUN
jd472v26s89	7	15	properties	property	NOUN
jd472v26s89	7	16	from	from	ADP
jd472v26s89	7	17	fundamental	fundamental	ADJ
jd472v26s89	7	18	equations	equation	NOUN
jd472v26s89	7	19	of	of	ADP
jd472v26s89	7	20	state	state	NOUN
jd472v26s89	7	21	,	,	PUNCT
jd472v26s89	7	22	determining	determine	VERB
jd472v26s89	7	23	the	the	DET
jd472v26s89	7	24	coexistence	coexistence	NOUN
jd472v26s89	7	25	curve	curve	NOUN
jd472v26s89	7	26	for	for	ADP
jd472v26s89	7	27	all	all	DET
jd472v26s89	7	28	vapor	vapor	NOUN
jd472v26s89	7	29	-	-	PUNCT
jd472v26s89	7	30	liquid	liquid	ADJ
jd472v26s89	7	31	equilibrium	equilibrium	NOUN
jd472v26s89	7	32	conditions	condition	NOUN
jd472v26s89	7	33	between	between	ADP
jd472v26s89	7	34	the	the	DET
jd472v26s89	7	35	triple	triple	ADJ
jd472v26s89	7	36	point	point	NOUN
jd472v26s89	7	37	and	and	CCONJ
jd472v26s89	7	38	critical	critical	ADJ
jd472v26s89	7	39	point	point	NOUN
jd472v26s89	7	40	.	.	PUNCT
jd472v26s89	8	1	examples	example	NOUN
jd472v26s89	8	2	and	and	CCONJ
jd472v26s89	8	3	computational	computational	ADJ
jd472v26s89	8	4	results	result	NOUN
jd472v26s89	8	5	are	be	AUX
jd472v26s89	8	6	presented	present	VERB
jd472v26s89	8	7	for	for	ADP
jd472v26s89	8	8	all	all	DET
jd472v26s89	8	9	three	three	NUM
jd472v26s89	8	10	applications	application	NOUN
jd472v26s89	8	11	of	of	ADP
jd472v26s89	8	12	newton	newton	PROPN
jd472v26s89	8	13	homotopies	homotopies	PROPN
jd472v26s89	8	14	.	.	PUNCT