id	sid	tid	token	lemma	pos
6395w66528z	1	1	algorithms	algorithm	NOUN
6395w66528z	1	2	from	from	ADP
6395w66528z	1	3	the	the	DET
6395w66528z	1	4	field	field	NOUN
6395w66528z	1	5	of	of	ADP
6395w66528z	1	6	numerical	numerical	ADJ
6395w66528z	1	7	algebraic	algebraic	ADJ
6395w66528z	1	8	geometry	geometry	NOUN
6395w66528z	1	9	provide	provide	VERB
6395w66528z	1	10	robust	robust	ADJ
6395w66528z	1	11	means	mean	NOUN
6395w66528z	1	12	to	to	PART
6395w66528z	1	13	compute	compute	VERB
6395w66528z	1	14	all	all	DET
6395w66528z	1	15	isolated	isolate	VERB
6395w66528z	1	16	solutions	solution	NOUN
6395w66528z	1	17	of	of	ADP
6395w66528z	1	18	arbitrary	arbitrary	ADJ
6395w66528z	1	19	systems	system	NOUN
6395w66528z	1	20	of	of	ADP
6395w66528z	1	21	polynomials	polynomial	NOUN
6395w66528z	1	22	and	and	CCONJ
6395w66528z	1	23	to	to	PART
6395w66528z	1	24	give	give	VERB
6395w66528z	1	25	a	a	DET
6395w66528z	1	26	thorough	thorough	ADJ
6395w66528z	1	27	numerical	numerical	ADJ
6395w66528z	1	28	description	description	NOUN
6395w66528z	1	29	of	of	ADP
6395w66528z	1	30	positive	positive	ADJ
6395w66528z	1	31	-	-	PUNCT
6395w66528z	1	32	dimensional	dimensional	ADJ
6395w66528z	1	33	solution	solution	NOUN
6395w66528z	1	34	components	component	NOUN
6395w66528z	1	35	.	.	PUNCT
6395w66528z	2	1	however	however	ADV
6395w66528z	2	2	,	,	PUNCT
6395w66528z	2	3	the	the	DET
6395w66528z	2	4	number	number	NOUN
6395w66528z	2	5	of	of	ADP
6395w66528z	2	6	isolated	isolated	ADJ
6395w66528z	2	7	complex	complex	ADJ
6395w66528z	2	8	solutions	solution	NOUN
6395w66528z	2	9	tends	tend	VERB
6395w66528z	2	10	to	to	PART
6395w66528z	2	11	grow	grow	VERB
6395w66528z	2	12	exponentially	exponentially	ADV
6395w66528z	2	13	with	with	ADP
6395w66528z	2	14	respect	respect	NOUN
6395w66528z	2	15	to	to	ADP
6395w66528z	2	16	the	the	DET
6395w66528z	2	17	number	number	NOUN
6395w66528z	2	18	$	$	SYM
6395w66528z	2	19	n$	n$	NOUN
6395w66528z	2	20	of	of	ADP
6395w66528z	2	21	equations	equation	NOUN
6395w66528z	2	22	and	and	CCONJ
6395w66528z	2	23	variables	variable	NOUN
6395w66528z	2	24	,	,	PUNCT
6395w66528z	2	25	limiting	limit	VERB
6395w66528z	2	26	the	the	DET
6395w66528z	2	27	size	size	NOUN
6395w66528z	2	28	of	of	ADP
6395w66528z	2	29	tractable	tractable	ADJ
6395w66528z	2	30	systems	system	NOUN
6395w66528z	2	31	.	.	PUNCT
6395w66528z	3	1	this	this	PRON
6395w66528z	3	2	is	be	AUX
6395w66528z	3	3	a	a	DET
6395w66528z	3	4	particular	particular	ADJ
6395w66528z	3	5	problem	problem	NOUN
6395w66528z	3	6	for	for	ADP
6395w66528z	3	7	systems	system	NOUN
6395w66528z	3	8	arising	arise	VERB
6395w66528z	3	9	from	from	ADP
6395w66528z	3	10	discretizations	discretization	NOUN
6395w66528z	3	11	of	of	ADP
6395w66528z	3	12	ordinary	ordinary	ADJ
6395w66528z	3	13	differential	differential	ADJ
6395w66528z	3	14	equations	equation	NOUN
6395w66528z	3	15	because	because	SCONJ
6395w66528z	3	16	$	$	SYM
6395w66528z	3	17	n$	n$	NOUN
6395w66528z	3	18	is	be	AUX
6395w66528z	3	19	directly	directly	ADV
6395w66528z	3	20	related	relate	VERB
6395w66528z	3	21	to	to	ADP
6395w66528z	3	22	mesh	mesh	NOUN
6395w66528z	3	23	size	size	NOUN
6395w66528z	3	24	,	,	PUNCT
6395w66528z	3	25	and	and	CCONJ
6395w66528z	3	26	finer	fine	ADJ
6395w66528z	3	27	meshes	mesh	NOUN
6395w66528z	3	28	are	be	AUX
6395w66528z	3	29	generally	generally	ADV
6395w66528z	3	30	more	more	ADV
6395w66528z	3	31	desirable	desirable	ADJ
6395w66528z	3	32	.	.	PUNCT
6395w66528z	4	1	on	on	ADP
6395w66528z	4	2	the	the	DET
6395w66528z	4	3	other	other	ADJ
6395w66528z	4	4	hand	hand	NOUN
6395w66528z	4	5	,	,	PUNCT
6395w66528z	4	6	the	the	DET
6395w66528z	4	7	number	number	NOUN
6395w66528z	4	8	of	of	ADP
6395w66528z	4	9	interesting	interesting	ADJ
6395w66528z	4	10	solutions	solution	NOUN
6395w66528z	4	11	is	be	AUX
6395w66528z	4	12	often	often	ADV
6395w66528z	4	13	far	far	ADV
6395w66528z	4	14	smaller	small	ADJ
6395w66528z	4	15	than	than	ADP
6395w66528z	4	16	the	the	DET
6395w66528z	4	17	total	total	ADJ
6395w66528z	4	18	count	count	NOUN
6395w66528z	4	19	,	,	PUNCT
6395w66528z	4	20	and	and	CCONJ
6395w66528z	4	21	much	much	ADJ
6395w66528z	4	22	effort	effort	NOUN
6395w66528z	4	23	is	be	AUX
6395w66528z	4	24	wasted	waste	VERB
6395w66528z	4	25	on	on	ADP
6395w66528z	4	26	complex	complex	ADJ
6395w66528z	4	27	solutions	solution	NOUN
6395w66528z	4	28	with	with	ADP
6395w66528z	4	29	no	no	DET
6395w66528z	4	30	physical	physical	NOUN
6395w66528z	4	31	interpretation.in	interpretation.in	X
6395w66528z	4	32	the	the	DET
6395w66528z	4	33	first	first	ADJ
6395w66528z	4	34	part	part	NOUN
6395w66528z	4	35	of	of	ADP
6395w66528z	4	36	this	this	DET
6395w66528z	4	37	thesis	thesis	NOUN
6395w66528z	4	38	,	,	PUNCT
6395w66528z	4	39	a	a	DET
6395w66528z	4	40	general	general	ADJ
6395w66528z	4	41	method	method	NOUN
6395w66528z	4	42	is	be	AUX
6395w66528z	4	43	given	give	VERB
6395w66528z	4	44	for	for	ADP
6395w66528z	4	45	constructing	construct	VERB
6395w66528z	4	46	a	a	DET
6395w66528z	4	47	homotopy	homotopy	NOUN
6395w66528z	4	48	that	that	PRON
6395w66528z	4	49	directly	directly	ADV
6395w66528z	4	50	relates	relate	VERB
6395w66528z	4	51	solutions	solution	NOUN
6395w66528z	4	52	on	on	ADP
6395w66528z	4	53	grids	grid	NOUN
6395w66528z	4	54	of	of	ADP
6395w66528z	4	55	different	different	ADJ
6395w66528z	4	56	resolutions	resolution	NOUN
6395w66528z	4	57	.	.	PUNCT
6395w66528z	5	1	this	this	PRON
6395w66528z	5	2	enables	enable	VERB
6395w66528z	5	3	iterative	iterative	ADJ
6395w66528z	5	4	generation	generation	NOUN
6395w66528z	5	5	of	of	ADP
6395w66528z	5	6	solutions	solution	NOUN
6395w66528z	5	7	on	on	ADP
6395w66528z	5	8	increasingly	increasingly	ADV
6395w66528z	5	9	fine	fine	ADJ
6395w66528z	5	10	meshes	mesh	NOUN
6395w66528z	5	11	,	,	PUNCT
6395w66528z	5	12	and	and	CCONJ
6395w66528z	5	13	makes	make	VERB
6395w66528z	5	14	it	it	PRON
6395w66528z	5	15	possible	possible	ADJ
6395w66528z	5	16	to	to	PART
6395w66528z	5	17	filter	filter	VERB
6395w66528z	5	18	out	out	ADP
6395w66528z	5	19	some	some	DET
6395w66528z	5	20	non	non	ADJ
6395w66528z	5	21	-	-	ADJ
6395w66528z	5	22	physical	physical	ADJ
6395w66528z	5	23	solutions	solution	NOUN
6395w66528z	5	24	to	to	PART
6395w66528z	5	25	substantially	substantially	ADV
6395w66528z	5	26	reduce	reduce	VERB
6395w66528z	5	27	wasted	waste	VERB
6395w66528z	5	28	computation	computation	NOUN
6395w66528z	5	29	time	time	NOUN
6395w66528z	5	30	.	.	PUNCT
6395w66528z	6	1	in	in	ADP
6395w66528z	6	2	the	the	DET
6395w66528z	6	3	second	second	ADJ
6395w66528z	6	4	part	part	NOUN
6395w66528z	6	5	,	,	PUNCT
6395w66528z	6	6	a	a	DET
6395w66528z	6	7	new	new	ADJ
6395w66528z	6	8	algorithm	algorithm	NOUN
6395w66528z	6	9	is	be	AUX
6395w66528z	6	10	given	give	VERB
6395w66528z	6	11	to	to	PART
6395w66528z	6	12	compute	compute	VERB
6395w66528z	6	13	the	the	DET
6395w66528z	6	14	numerical	numerical	ADJ
6395w66528z	6	15	irreducible	irreducible	ADJ
6395w66528z	6	16	decomposition	decomposition	NOUN
6395w66528z	6	17	of	of	ADP
6395w66528z	6	18	a	a	DET
6395w66528z	6	19	general	general	ADJ
6395w66528z	6	20	polynomial	polynomial	ADJ
6395w66528z	6	21	system	system	NOUN
6395w66528z	6	22	over	over	ADP
6395w66528z	6	23	a	a	DET
6395w66528z	6	24	finite	finite	ADJ
6395w66528z	6	25	algebraic	algebraic	ADJ
6395w66528z	6	26	extension	extension	NOUN
6395w66528z	6	27	of	of	ADP
6395w66528z	6	28	$	$	SYM
6395w66528z	6	29	q$	q$	NOUN
6395w66528z	6	30	by	by	ADP
6395w66528z	6	31	projecting	project	VERB
6395w66528z	6	32	the	the	DET
6395w66528z	6	33	solution	solution	NOUN
6395w66528z	6	34	set	set	VERB
6395w66528z	6	35	onto	onto	ADP
6395w66528z	6	36	a	a	DET
6395w66528z	6	37	line	line	NOUN
6395w66528z	6	38	and	and	CCONJ
6395w66528z	6	39	deducing	deduce	VERB
6395w66528z	6	40	the	the	DET
6395w66528z	6	41	exact	exact	ADJ
6395w66528z	6	42	defining	define	VERB
6395w66528z	6	43	polynomial	polynomial	NOUN
6395w66528z	6	44	of	of	ADP
6395w66528z	6	45	the	the	DET
6395w66528z	6	46	projection	projection	NOUN
6395w66528z	6	47	.	.	PUNCT