id	sid	tid	token	lemma	pos
5425k932879	1	1	in	in	ADP
5425k932879	1	2	this	this	DET
5425k932879	1	3	thesis	thesis	NOUN
5425k932879	1	4	we	we	PRON
5425k932879	1	5	give	give	VERB
5425k932879	1	6	numerical	numerical	ADJ
5425k932879	1	7	algorithms	algorithm	NOUN
5425k932879	1	8	to	to	PART
5425k932879	1	9	find	find	VERB
5425k932879	1	10	theone	theone	NOUN
5425k932879	1	11	-	-	PUNCT
5425k932879	1	12	dimensional	dimensional	ADJ
5425k932879	1	13	and	and	CCONJ
5425k932879	1	14	two	two	NUM
5425k932879	1	15	-	-	PUNCT
5425k932879	1	16	dimensional	dimensional	ADJ
5425k932879	1	17	parts	part	NOUN
5425k932879	1	18	of	of	ADP
5425k932879	1	19	the	the	DET
5425k932879	1	20	solution	solution	NOUN
5425k932879	1	21	sets	set	VERB
5425k932879	1	22	on$rn$	on$rn$	PROPN
5425k932879	1	23	of	of	ADP
5425k932879	1	24	systemsegin{equation}label{realsystem}f(x):=left[egin{array}{c	systemsegin{equation}label{realsystem}f(x):=left[egin{array}{c	PROPN
5425k932879	1	25	}	}	PUNCT
5425k932879	1	26	f{1}(x{1},ldots	f{1}(x{1},ldots	PROPN
5425k932879	1	27	,	,	PUNCT
5425k932879	1	28	x{n	x{n	X
5425k932879	1	29	}	}	PUNCT
5425k932879	1	30	)	)	PUNCT
5425k932879	1	31	\	\	PROPN
5425k932879	1	32	vdots	vdots	PROPN
5425k932879	1	33	\	\	PROPN
5425k932879	1	34	f{n}(x{1},ldots	f{n}(x{1},ldot	NOUN
5425k932879	1	35	,	,	PUNCT
5425k932879	1	36	x{n	x{n	X
5425k932879	1	37	}	}	PUNCT
5425k932879	1	38	)	)	PUNCT
5425k932879	1	39	end{array}ight]=0end{equation}of	end{array}ight]=0end{equation}of	PROPN
5425k932879	1	40	$	$	SYM
5425k932879	1	41	n$	n$	NOUN
5425k932879	1	42	polynomials	polynomial	NOUN
5425k932879	1	43	on	on	ADP
5425k932879	1	44	$	$	SYM
5425k932879	1	45	rn$.typically	rn$.typically	ADV
5425k932879	1	46	,	,	PUNCT
5425k932879	1	47	we	we	PRON
5425k932879	1	48	want	want	VERB
5425k932879	1	49	to	to	PART
5425k932879	1	50	find	find	VERB
5425k932879	1	51	the	the	DET
5425k932879	1	52	solutions	solution	NOUN
5425k932879	1	53	on	on	ADP
5425k932879	1	54	$	$	SYM
5425k932879	1	55	rn$	rn$	PROPN
5425k932879	1	56	as	as	SCONJ
5425k932879	1	57	opposed	oppose	VERB
5425k932879	1	58	to	to	ADP
5425k932879	1	59	the	the	DET
5425k932879	1	60	solutions	solution	NOUN
5425k932879	1	61	on	on	ADP
5425k932879	1	62	$	$	SYM
5425k932879	1	63	cn$	cn$	NUM
5425k932879	1	64	when	when	SCONJ
5425k932879	1	65	we	we	PRON
5425k932879	1	66	need	need	VERB
5425k932879	1	67	to	to	PART
5425k932879	1	68	solve	solve	VERB
5425k932879	1	69	such	such	DET
5425k932879	1	70	a	a	DET
5425k932879	1	71	system	system	NOUN
5425k932879	1	72	of	of	ADP
5425k932879	1	73	$	$	SYM
5425k932879	1	74	n$polynomials	n$polynomial	NOUN
5425k932879	1	75	.	.	PUNCT
5425k932879	2	1	however	however	ADV
5425k932879	2	2	,	,	PUNCT
5425k932879	2	3	the	the	DET
5425k932879	2	4	real	real	ADJ
5425k932879	2	5	solutions	solution	NOUN
5425k932879	2	6	are	be	AUX
5425k932879	2	7	much	much	ADV
5425k932879	2	8	more	more	ADV
5425k932879	2	9	complicated	complicated	ADJ
5425k932879	2	10	and	and	CCONJ
5425k932879	2	11	expensive	expensive	ADJ
5425k932879	2	12	to	to	PART
5425k932879	2	13	compute	compute	VERB
5425k932879	2	14	than	than	ADP
5425k932879	2	15	the	the	DET
5425k932879	2	16	complex	complex	ADJ
5425k932879	2	17	solutions	solution	NOUN
5425k932879	2	18	.	.	PUNCT
5425k932879	3	1	our	our	PRON
5425k932879	3	2	approach	approach	NOUN
5425k932879	3	3	is	be	AUX
5425k932879	3	4	to	to	PART
5425k932879	3	5	find	find	VERB
5425k932879	3	6	the	the	DET
5425k932879	3	7	real	real	ADJ
5425k932879	3	8	solutions	solution	NOUN
5425k932879	3	9	starting	start	VERB
5425k932879	3	10	with	with	ADP
5425k932879	3	11	the	the	DET
5425k932879	3	12	known	know	VERB
5425k932879	3	13	complex	complex	ADJ
5425k932879	3	14	components	component	NOUN
5425k932879	3	15	.	.	PUNCT
5425k932879	4	1	recently	recently	ADV
5425k932879	4	2	in	in	ADP
5425k932879	4	3	cite{svw1,svw2,svw3	cite{svw1,svw2,svw3	SPACE
5425k932879	4	4	}	}	PUNCT
5425k932879	4	5	,	,	PUNCT
5425k932879	4	6	new	new	ADJ
5425k932879	4	7	techniques	technique	NOUN
5425k932879	4	8	have	have	AUX
5425k932879	4	9	been	be	AUX
5425k932879	4	10	successfully	successfully	ADV
5425k932879	4	11	developed	develop	VERB
5425k932879	4	12	to	to	PART
5425k932879	4	13	numerically	numerically	ADV
5425k932879	4	14	decompose	decompose	VERB
5425k932879	4	15	complex	complex	ADJ
5425k932879	4	16	algebraic	algebraic	ADJ
5425k932879	4	17	sets	set	NOUN
5425k932879	4	18	into	into	ADP
5425k932879	4	19	irreducible	irreducible	ADJ
5425k932879	4	20	components	component	NOUN
5425k932879	4	21	.	.	PUNCT
5425k932879	5	1	with	with	ADP
5425k932879	5	2	the	the	DET
5425k932879	5	3	help	help	NOUN
5425k932879	5	4	of	of	ADP
5425k932879	5	5	this	this	DET
5425k932879	5	6	decomposition	decomposition	NOUN
5425k932879	5	7	and	and	CCONJ
5425k932879	5	8	a	a	DET
5425k932879	5	9	morse	morse	ADJ
5425k932879	5	10	-	-	PUNCT
5425k932879	5	11	theoretic	theoretic	ADJ
5425k932879	5	12	decomposition	decomposition	NOUN
5425k932879	5	13	,	,	PUNCT
5425k932879	5	14	we	we	PRON
5425k932879	5	15	give	give	VERB
5425k932879	5	16	algorithms	algorithm	NOUN
5425k932879	5	17	for	for	ADP
5425k932879	5	18	numerically	numerically	ADV
5425k932879	5	19	computing	compute	VERB
5425k932879	5	20	the	the	DET
5425k932879	5	21	real	real	ADJ
5425k932879	5	22	solution	solution	NOUN
5425k932879	5	23	sets	set	NOUN
5425k932879	5	24	.	.	PUNCT
5425k932879	6	1	the	the	DET
5425k932879	6	2	morse	morse	ADJ
5425k932879	6	3	-	-	PUNCT
5425k932879	6	4	theoretic	theoretic	ADJ
5425k932879	6	5	decomposition	decomposition	NOUN
5425k932879	6	6	only	only	ADV
5425k932879	6	7	works	work	VERB
5425k932879	6	8	for	for	ADP
5425k932879	6	9	multiplicity	multiplicity	NOUN
5425k932879	6	10	one	one	NUM
5425k932879	6	11	components	component	NOUN
5425k932879	6	12	.	.	PUNCT
5425k932879	7	1	for	for	ADP
5425k932879	7	2	the	the	DET
5425k932879	7	3	components	component	NOUN
5425k932879	7	4	of	of	ADP
5425k932879	7	5	multiplicity	multiplicity	NOUN
5425k932879	7	6	at	at	ADV
5425k932879	7	7	least	least	ADJ
5425k932879	7	8	two	two	NUM
5425k932879	7	9	,	,	PUNCT
5425k932879	7	10	we	we	PRON
5425k932879	7	11	use	use	VERB
5425k932879	7	12	the	the	DET
5425k932879	7	13	technique	technique	NOUN
5425k932879	7	14	of	of	ADP
5425k932879	7	15	deflation	deflation	NOUN
5425k932879	7	16	to	to	PART
5425k932879	7	17	make	make	VERB
5425k932879	7	18	them	they	PRON
5425k932879	7	19	into	into	ADP
5425k932879	7	20	reduced	reduce	VERB
5425k932879	7	21	components	component	NOUN
5425k932879	7	22	in	in	ADP
5425k932879	7	23	a	a	DET
5425k932879	7	24	higher	high	ADJ
5425k932879	7	25	dimensional	dimensional	ADJ
5425k932879	7	26	space	space	NOUN
5425k932879	7	27	.	.	PUNCT
5425k932879	8	1	the	the	DET
5425k932879	8	2	one	one	NUM
5425k932879	8	3	-	-	PUNCT
5425k932879	8	4	dimensional	dimensional	ADJ
5425k932879	8	5	and	and	CCONJ
5425k932879	8	6	two	two	NUM
5425k932879	8	7	-	-	PUNCT
5425k932879	8	8	dimensional	dimensional	ADJ
5425k932879	8	9	real	real	ADJ
5425k932879	8	10	sets	set	NOUN
5425k932879	8	11	are	be	AUX
5425k932879	8	12	the	the	DET
5425k932879	8	13	most	most	ADV
5425k932879	8	14	interesting	interesting	ADJ
5425k932879	8	15	ones	one	NOUN
5425k932879	8	16	in	in	ADP
5425k932879	8	17	applications	application	NOUN
5425k932879	8	18	.	.	PUNCT
5425k932879	9	1	we	we	PRON
5425k932879	9	2	focus	focus	VERB
5425k932879	9	3	on	on	ADP
5425k932879	9	4	these	these	DET
5425k932879	9	5	two	two	NUM
5425k932879	9	6	cases	case	NOUN
5425k932879	9	7	in	in	ADP
5425k932879	9	8	this	this	DET
5425k932879	9	9	thesis	thesis	NOUN
5425k932879	9	10	.	.	PUNCT
5425k932879	10	1	an	an	DET
5425k932879	10	2	application	application	NOUN
5425k932879	10	3	of	of	ADP
5425k932879	10	4	our	our	PRON
5425k932879	10	5	algorithms	algorithm	NOUN
5425k932879	10	6	to	to	ADP
5425k932879	10	7	mechanisms	mechanism	NOUN
5425k932879	10	8	,	,	PUNCT
5425k932879	10	9	specifically	specifically	ADV
5425k932879	10	10	the	the	DET
5425k932879	10	11	stewart	stewart	PROPN
5425k932879	10	12	-	-	PUNCT
5425k932879	10	13	gough	gough	PROPN
5425k932879	10	14	platform	platform	NOUN
5425k932879	10	15	robot	robot	NOUN
5425k932879	10	16	,	,	PUNCT
5425k932879	10	17	is	be	AUX
5425k932879	10	18	presented	present	VERB
5425k932879	10	19	.	.	PUNCT