id	sid	tid	token	lemma	pos
w3763487g2w	1	1	algorithms	algorithm	NOUN
w3763487g2w	1	2	in	in	ADP
w3763487g2w	1	3	the	the	DET
w3763487g2w	1	4	field	field	NOUN
w3763487g2w	1	5	of	of	ADP
w3763487g2w	1	6	numerical	numerical	ADJ
w3763487g2w	1	7	algebraic	algebraic	ADJ
w3763487g2w	1	8	geometry	geometry	NOUN
w3763487g2w	1	9	provide	provide	VERB
w3763487g2w	1	10	numerical	numerical	ADJ
w3763487g2w	1	11	methods	method	NOUN
w3763487g2w	1	12	for	for	ADP
w3763487g2w	1	13	computing	compute	VERB
w3763487g2w	1	14	and	and	CCONJ
w3763487g2w	1	15	manipulating	manipulate	VERB
w3763487g2w	1	16	solution	solution	NOUN
w3763487g2w	1	17	sets	set	NOUN
w3763487g2w	1	18	of	of	ADP
w3763487g2w	1	19	polynomial	polynomial	ADJ
w3763487g2w	1	20	systems	system	NOUN
w3763487g2w	1	21	.	.	PUNCT
w3763487g2w	2	1	one	one	NUM
w3763487g2w	2	2	of	of	ADP
w3763487g2w	2	3	the	the	DET
w3763487g2w	2	4	main	main	ADJ
w3763487g2w	2	5	algorithms	algorithm	NOUN
w3763487g2w	2	6	in	in	ADP
w3763487g2w	2	7	this	this	DET
w3763487g2w	2	8	field	field	NOUN
w3763487g2w	2	9	is	be	AUX
w3763487g2w	2	10	the	the	DET
w3763487g2w	2	11	computation	computation	NOUN
w3763487g2w	2	12	of	of	ADP
w3763487g2w	2	13	the	the	DET
w3763487g2w	2	14	numerical	numerical	ADJ
w3763487g2w	2	15	irreducible	irreducible	ADJ
w3763487g2w	2	16	decomposition	decomposition	NOUN
w3763487g2w	2	17	.	.	PUNCT
w3763487g2w	3	1	this	this	DET
w3763487g2w	3	2	algorithm	algorithm	PROPN
w3763487g2w	3	3	has	have	VERB
w3763487g2w	3	4	three	three	NUM
w3763487g2w	3	5	main	main	ADJ
w3763487g2w	3	6	parts	part	NOUN
w3763487g2w	3	7	:	:	PUNCT
w3763487g2w	3	8	computing	compute	VERB
w3763487g2w	3	9	a	a	DET
w3763487g2w	3	10	witness	witness	NOUN
w3763487g2w	3	11	superset	superset	NOUN
w3763487g2w	3	12	,	,	PUNCT
w3763487g2w	3	13	filtering	filter	VERB
w3763487g2w	3	14	out	out	ADP
w3763487g2w	3	15	the	the	DET
w3763487g2w	3	16	junk	junk	NOUN
w3763487g2w	3	17	points	point	NOUN
w3763487g2w	3	18	to	to	PART
w3763487g2w	3	19	create	create	VERB
w3763487g2w	3	20	a	a	DET
w3763487g2w	3	21	witness	witness	NOUN
w3763487g2w	3	22	set	set	VERB
w3763487g2w	3	23	,	,	PUNCT
w3763487g2w	3	24	and	and	CCONJ
w3763487g2w	3	25	decomposing	decompose	VERB
w3763487g2w	3	26	the	the	DET
w3763487g2w	3	27	witness	witness	NOUN
w3763487g2w	3	28	set	set	VERB
w3763487g2w	3	29	into	into	ADP
w3763487g2w	3	30	irreducible	irreducible	ADJ
w3763487g2w	3	31	components	component	NOUN
w3763487g2w	3	32	.	.	PUNCT
w3763487g2w	4	1	new	new	ADJ
w3763487g2w	4	2	and	and	CCONJ
w3763487g2w	4	3	efficient	efficient	ADJ
w3763487g2w	4	4	algorithms	algorithm	NOUN
w3763487g2w	4	5	are	be	AUX
w3763487g2w	4	6	presented	present	VERB
w3763487g2w	4	7	in	in	ADP
w3763487g2w	4	8	this	this	DET
w3763487g2w	4	9	thesis	thesis	NOUN
w3763487g2w	4	10	to	to	PART
w3763487g2w	4	11	address	address	VERB
w3763487g2w	4	12	the	the	DET
w3763487g2w	4	13	first	first	ADJ
w3763487g2w	4	14	two	two	NUM
w3763487g2w	4	15	parts	part	NOUN
w3763487g2w	4	16	,	,	PUNCT
w3763487g2w	4	17	namely	namely	ADV
w3763487g2w	4	18	regeneration	regeneration	NOUN
w3763487g2w	4	19	and	and	CCONJ
w3763487g2w	4	20	a	a	DET
w3763487g2w	4	21	local	local	ADJ
w3763487g2w	4	22	dimension	dimension	NOUN
w3763487g2w	4	23	test	test	NOUN
w3763487g2w	4	24	.	.	PUNCT
w3763487g2w	5	1	regeneration	regeneration	NOUN
w3763487g2w	5	2	is	be	AUX
w3763487g2w	5	3	an	an	DET
w3763487g2w	5	4	equation	equation	NOUN
w3763487g2w	5	5	-	-	PUNCT
w3763487g2w	5	6	by	by	ADP
w3763487g2w	5	7	-	-	PUNCT
w3763487g2w	5	8	equation	equation	NOUN
w3763487g2w	5	9	solving	solving	NOUN
w3763487g2w	5	10	method	method	NOUN
w3763487g2w	5	11	that	that	PRON
w3763487g2w	5	12	can	can	AUX
w3763487g2w	5	13	be	be	AUX
w3763487g2w	5	14	used	use	VERB
w3763487g2w	5	15	to	to	PART
w3763487g2w	5	16	efficiently	efficiently	ADV
w3763487g2w	5	17	compute	compute	VERB
w3763487g2w	5	18	a	a	DET
w3763487g2w	5	19	witness	witness	NOUN
w3763487g2w	5	20	superset	superset	VERB
w3763487g2w	5	21	for	for	ADP
w3763487g2w	5	22	a	a	DET
w3763487g2w	5	23	polynomial	polynomial	ADJ
w3763487g2w	5	24	system	system	NOUN
w3763487g2w	5	25	.	.	PUNCT
w3763487g2w	6	1	the	the	DET
w3763487g2w	6	2	local	local	ADJ
w3763487g2w	6	3	dimension	dimension	NOUN
w3763487g2w	6	4	test	test	NOUN
w3763487g2w	6	5	algorithm	algorithm	PROPN
w3763487g2w	6	6	presented	present	VERB
w3763487g2w	6	7	in	in	ADP
w3763487g2w	6	8	this	this	DET
w3763487g2w	6	9	thesis	thesis	NOUN
w3763487g2w	6	10	is	be	AUX
w3763487g2w	6	11	a	a	DET
w3763487g2w	6	12	numerical	numerical	ADJ
w3763487g2w	6	13	-	-	PUNCT
w3763487g2w	6	14	symbolic	symbolic	ADJ
w3763487g2w	6	15	method	method	NOUN
w3763487g2w	6	16	that	that	PRON
w3763487g2w	6	17	can	can	AUX
w3763487g2w	6	18	be	be	AUX
w3763487g2w	6	19	used	use	VERB
w3763487g2w	6	20	to	to	PART
w3763487g2w	6	21	compute	compute	VERB
w3763487g2w	6	22	the	the	DET
w3763487g2w	6	23	local	local	ADJ
w3763487g2w	6	24	dimension	dimension	NOUN
w3763487g2w	6	25	at	at	ADP
w3763487g2w	6	26	an	an	DET
w3763487g2w	6	27	approximated	approximated	ADJ
w3763487g2w	6	28	solution	solution	NOUN
w3763487g2w	6	29	to	to	ADP
w3763487g2w	6	30	a	a	DET
w3763487g2w	6	31	polynomial	polynomial	ADJ
w3763487g2w	6	32	system	system	NOUN
w3763487g2w	6	33	.	.	PUNCT
w3763487g2w	7	1	this	this	DET
w3763487g2w	7	2	test	test	NOUN
w3763487g2w	7	3	is	be	AUX
w3763487g2w	7	4	used	use	VERB
w3763487g2w	7	5	to	to	PART
w3763487g2w	7	6	create	create	VERB
w3763487g2w	7	7	an	an	DET
w3763487g2w	7	8	efficient	efficient	ADJ
w3763487g2w	7	9	algorithm	algorithm	NOUN
w3763487g2w	7	10	that	that	PRON
w3763487g2w	7	11	filters	filter	VERB
w3763487g2w	7	12	out	out	ADP
w3763487g2w	7	13	the	the	DET
w3763487g2w	7	14	junk	junk	NOUN
w3763487g2w	7	15	points	point	NOUN
w3763487g2w	7	16	.	.	PUNCT
w3763487g2w	8	1	the	the	DET
w3763487g2w	8	2	algorithms	algorithm	NOUN
w3763487g2w	8	3	presented	present	VERB
w3763487g2w	8	4	in	in	ADP
w3763487g2w	8	5	this	this	DET
w3763487g2w	8	6	thesis	thesis	NOUN
w3763487g2w	8	7	are	be	AUX
w3763487g2w	8	8	applied	apply	VERB
w3763487g2w	8	9	to	to	ADP
w3763487g2w	8	10	problems	problem	NOUN
w3763487g2w	8	11	arising	arise	VERB
w3763487g2w	8	12	in	in	ADP
w3763487g2w	8	13	kinematics	kinematic	NOUN
w3763487g2w	8	14	and	and	CCONJ
w3763487g2w	8	15	partial	partial	ADJ
w3763487g2w	8	16	differential	differential	ADJ
w3763487g2w	8	17	equations	equation	NOUN
w3763487g2w	8	18	.	.	PUNCT