id	sid	tid	token	lemma	pos
uva.x030312957	1	1	828	828	NUM
uva.x030312957	1	2	.s5	.s5	PROPN
uva.x030312957	1	3	1916	1916	NUM
uva.x030312957	2	1	sei	sei	PROPN
uva.x030312957	2	2	/	/	SYM
uva.x030312957	2	3	tech	tech	NOUN
uva.x030312957	2	4	.	.	PUNCT
uva.x030312957	3	1	university	university	PROPN
uva.x030312957	3	2	of	of	ADP
uva.x030312957	3	3	virginia	virginia	PROPN
uva.x030312957	3	4	library	library	PROPN
uva.x030312957	3	5	x030312957	x030312957	PROPN
uva.x030312957	3	6	solution	solution	NOUN
uva.x030312957	3	7	of	of	ADP
uva.x030312957	3	8	the	the	DET
uva.x030312957	3	9	equation	equation	NOUN
uva.x030312957	3	10	of	of	ADP
uva.x030312957	3	11	secular	secular	ADJ
uva.x030312957	3	12	variation	variation	NOUN
uva.x030312957	3	13	by	by	ADP
uva.x030312957	3	14	a	a	DET
uva.x030312957	3	15	method	method	NOUN
uva.x030312957	3	16	due	due	ADP
uva.x030312957	3	17	to	to	ADP
uva.x030312957	3	18	hermite	hermite	NOUN
uva.x030312957	3	19	3547	3547	NUM
uva.x030312957	3	20	:	:	PUNCT
uva.x030312957	3	21	48	48	NUM
uva.x030312957	3	22	dissertation	dissertation	NOUN
uva.x030312957	3	23	presented	present	VERB
uva.x030312957	3	24	to	to	ADP
uva.x030312957	3	25	the	the	DET
uva.x030312957	3	26	faculty	faculty	NOUN
uva.x030312957	3	27	of	of	ADP
uva.x030312957	3	28	the	the	DET
uva.x030312957	3	29	university	university	PROPN
uva.x030312957	3	30	of	of	ADP
uva.x030312957	3	31	virginia	virginia	PROPN
uva.x030312957	3	32	by	by	ADP
uva.x030312957	3	33	edward	edward	PROPN
uva.x030312957	3	34	staples	staples	PROPN
uva.x030312957	3	35	smith	smith	PROPN
uva.x030312957	3	36	press	press	PROPN
uva.x030312957	3	37	of	of	ADP
uva.x030312957	3	38	the	the	DET
uva.x030312957	3	39	new	new	ADJ
uva.x030312957	3	40	era	era	NOUN
uva.x030312957	3	41	painting	paint	VERB
uva.x030312957	3	42	company	company	NOUN
uva.x030312957	3	43	lancaster	lancaster	PROPN
uva.x030312957	3	44	,	,	PUNCT
uva.x030312957	3	45	pa	pa	PROPN
uva.x030312957	3	46	.	.	PROPN
uva.x030312957	3	47	1916	1916	NUM
uva.x030312957	3	48	1	1	NUM
uva.x030312957	3	49	solution	solution	NOUN
uva.x030312957	3	50	of	of	ADP
uva.x030312957	3	51	the	the	DET
uva.x030312957	3	52	equation	equation	NOUN
uva.x030312957	3	53	of	of	ADP
uva.x030312957	3	54	secular	secular	ADJ
uva.x030312957	3	55	variation	variation	NOUN
uva.x030312957	3	56	by	by	ADP
uva.x030312957	3	57	a	a	DET
uva.x030312957	3	58	method	method	NOUN
uva.x030312957	3	59	due	due	ADP
uva.x030312957	3	60	to	to	ADP
uva.x030312957	3	61	hermite	hermite	NOUN
uva.x030312957	3	62	dissertation	dissertation	NOUN
uva.x030312957	3	63	presented	present	VERB
uva.x030312957	3	64	to	to	ADP
uva.x030312957	3	65	the	the	DET
uva.x030312957	3	66	faculty	faculty	NOUN
uva.x030312957	3	67	of	of	ADP
uva.x030312957	3	68	the	the	DET
uva.x030312957	3	69	university	university	PROPN
uva.x030312957	3	70	of	of	ADP
uva.x030312957	3	71	virginia	virginia	PROPN
uva.x030312957	3	72	by	by	ADP
uva.x030312957	3	73	edward	edward	PROPN
uva.x030312957	3	74	staples	staples	PROPN
uva.x030312957	3	75	smith	smith	PROPN
uva.x030312957	3	76	ensin	ensin	PROPN
uva.x030312957	3	77	ary	ary	PROPN
uva.x030312957	4	1	1819	1819	NUM
uva.x030312957	4	2	press	press	NOUN
uva.x030312957	4	3	of	of	ADP
uva.x030312957	4	4	the	the	DET
uva.x030312957	4	5	new	new	ADJ
uva.x030312957	4	6	era	era	NOUN
uva.x030312957	4	7	printing	print	VERB
uva.x030312957	4	8	company	company	NOUN
uva.x030312957	4	9	lancaster	lancaster	PROPN
uva.x030312957	4	10	,	,	PUNCT
uva.x030312957	4	11	pa	pa	PROPN
uva.x030312957	4	12	.	.	PROPN
uva.x030312957	4	13	1916	1916	NUM
uva.x030312957	4	14	gift	gift	NOUN
uva.x030312957	4	15	jul	jul	PROPN
uva.x030312957	4	16	17	17	NUM
uva.x030312957	4	17	34	34	NUM
uva.x030312957	4	18	binding	bind	VERB
uva.x030312957	4	19	nov	nov	PROPN
uva.x030312957	4	20	30	30	NUM
uva.x030312957	4	21	49	49	NUM
uva.x030312957	4	22	virginiana	virginiana	PROPN
uva.x030312957	4	23	qc	qc	PROPN
uva.x030312957	4	24	€	€	SYM
uva.x030312957	4	25	28	28	NUM
uva.x030312957	4	26	,	,	PUNCT
uva.x030312957	4	27	55	55	NUM
uva.x030312957	4	28	1916	1916	NUM
uva.x030312957	4	29	1178016	1178016	NUM
uva.x030312957	4	30	preface	preface	NOUN
uva.x030312957	4	31	رو	رو	ADP
uva.x030312957	4	32	the	the	DET
uva.x030312957	4	33	“	"	PUNCT
uva.x030312957	4	34	equation	equation	NOUN
uva.x030312957	4	35	of	of	ADP
uva.x030312957	4	36	secular	secular	ADJ
uva.x030312957	4	37	variations	variation	NOUN
uva.x030312957	4	38	"	"	PUNCT
uva.x030312957	4	39	plays	play	VERB
uva.x030312957	4	40	such	such	DET
uva.x030312957	4	41	an	an	DET
uva.x030312957	4	42	important	important	ADJ
uva.x030312957	4	43	rôle	rôle	NOUN
uva.x030312957	4	44	in	in	ADP
uva.x030312957	4	45	many	many	ADJ
uva.x030312957	4	46	analytical	analytical	ADJ
uva.x030312957	4	47	investigations	investigation	NOUN
uva.x030312957	4	48	,	,	PUNCT
uva.x030312957	4	49	particularly	particularly	ADV
uva.x030312957	4	50	in	in	ADP
uva.x030312957	4	51	the	the	DET
uva.x030312957	4	52	determination	determination	NOUN
uva.x030312957	4	53	of	of	ADP
uva.x030312957	4	54	the	the	DET
uva.x030312957	4	55	secular	secular	ADJ
uva.x030312957	4	56	variations	variation	NOUN
uva.x030312957	4	57	of	of	ADP
uva.x030312957	4	58	the	the	DET
uva.x030312957	4	59	planets	planet	NOUN
uva.x030312957	4	60	,	,	PUNCT
uva.x030312957	4	61	and	and	CCONJ
uva.x030312957	4	62	in	in	ADP
uva.x030312957	4	63	fixing	fix	VERB
uva.x030312957	4	64	the	the	DET
uva.x030312957	4	65	principal	principal	ADJ
uva.x030312957	4	66	axes	axis	NOUN
uva.x030312957	4	67	of	of	ADP
uva.x030312957	4	68	surfaces	surface	NOUN
uva.x030312957	4	69	of	of	ADP
uva.x030312957	4	70	the	the	DET
uva.x030312957	4	71	second	second	ADJ
uva.x030312957	4	72	degree	degree	NOUN
uva.x030312957	4	73	,	,	PUNCT
uva.x030312957	4	74	that	that	SCONJ
uva.x030312957	4	75	dr	dr	PROPN
uva.x030312957	4	76	.	.	PROPN
uva.x030312957	4	77	hancock	hancock	PROPN
uva.x030312957	4	78	suggested	suggest	VERB
uva.x030312957	4	79	i	i	PRON
uva.x030312957	4	80	undertake	undertake	VERB
uva.x030312957	4	81	its	its	PRON
uva.x030312957	4	82	solution	solution	NOUN
uva.x030312957	4	83	by	by	ADP
uva.x030312957	4	84	“	"	PUNCT
uva.x030312957	4	85	hermite	hermite	PROPN
uva.x030312957	4	86	's	's	PART
uva.x030312957	4	87	method	method	NOUN
uva.x030312957	4	88	.	.	PUNCT
uva.x030312957	4	89	"	"	PUNCT
uva.x030312957	5	1	this	this	PRON
uva.x030312957	5	2	is	be	AUX
uva.x030312957	5	3	done	do	VERB
uva.x030312957	5	4	in	in	ADP
uva.x030312957	5	5	the	the	DET
uva.x030312957	5	6	present	present	ADJ
uva.x030312957	5	7	paper	paper	NOUN
uva.x030312957	5	8	,	,	PUNCT
uva.x030312957	5	9	which	which	PRON
uva.x030312957	5	10	has	have	AUX
uva.x030312957	5	11	been	be	AUX
uva.x030312957	5	12	developed	develop	VERB
uva.x030312957	5	13	in	in	ADP
uva.x030312957	5	14	three	three	NUM
uva.x030312957	5	15	distinct	distinct	ADJ
uva.x030312957	5	16	parts	part	NOUN
uva.x030312957	5	17	,	,	PUNCT
uva.x030312957	5	18	as	as	SCONJ
uva.x030312957	5	19	follows	follow	VERB
uva.x030312957	5	20	:	:	PUNCT
uva.x030312957	5	21	i.	i.	PROPN
uva.x030312957	5	22	a	a	DET
uva.x030312957	5	23	history	history	NOUN
uva.x030312957	5	24	of	of	ADP
uva.x030312957	5	25	the	the	DET
uva.x030312957	5	26	secular	secular	ADJ
uva.x030312957	5	27	variations	variation	NOUN
uva.x030312957	5	28	of	of	ADP
uva.x030312957	5	29	the	the	DET
uva.x030312957	5	30	planets	planet	NOUN
uva.x030312957	5	31	,	,	PUNCT
uva.x030312957	5	32	introducing	introduce	VERB
uva.x030312957	5	33	the	the	DET
uva.x030312957	5	34	secular	secular	ADJ
uva.x030312957	5	35	equation	equation	NOUN
uva.x030312957	5	36	.	.	PUNCT
uva.x030312957	6	1	ii	ii	PROPN
uva.x030312957	6	2	.	.	PUNCT
uva.x030312957	7	1	the	the	DET
uva.x030312957	7	2	development	development	NOUN
uva.x030312957	7	3	of	of	ADP
uva.x030312957	7	4	“	"	PUNCT
uva.x030312957	7	5	hermite	hermite	PROPN
uva.x030312957	7	6	's	's	PART
uva.x030312957	7	7	method	method	NOUN
uva.x030312957	7	8	.	.	PUNCT
uva.x030312957	7	9	”	"	PUNCT
uva.x030312957	7	10	iii	iii	PROPN
uva.x030312957	7	11	.	.	PUNCT
uva.x030312957	8	1	the	the	DET
uva.x030312957	8	2	solution	solution	NOUN
uva.x030312957	8	3	of	of	ADP
uva.x030312957	8	4	the	the	DET
uva.x030312957	8	5	equation	equation	NOUN
uva.x030312957	8	6	of	of	ADP
uva.x030312957	8	7	secular	secular	ADJ
uva.x030312957	8	8	variations	variation	NOUN
uva.x030312957	8	9	and	and	CCONJ
uva.x030312957	8	10	applications	application	NOUN
uva.x030312957	8	11	.	.	PUNCT
uva.x030312957	9	1	the	the	DET
uva.x030312957	9	2	history	history	NOUN
uva.x030312957	9	3	has	have	AUX
uva.x030312957	9	4	been	be	AUX
uva.x030312957	9	5	obtained	obtain	VERB
uva.x030312957	9	6	largely	largely	ADV
uva.x030312957	9	7	from	from	ADP
uva.x030312957	9	8	die	die	ADJ
uva.x030312957	9	9	mathematischen	mathematischen	PROPN
uva.x030312957	9	10	theorien	theorien	PROPN
uva.x030312957	9	11	der	der	PROPN
uva.x030312957	9	12	planeten	planeten	PROPN
uva.x030312957	9	13	-	-	PUNCT
uva.x030312957	9	14	bewegungen	bewegungen	PROPN
uva.x030312957	9	15	,	,	PUNCT
uva.x030312957	9	16	von	von	PROPN
uva.x030312957	9	17	dr	dr	PROPN
uva.x030312957	9	18	.	.	PROPN
uva.x030312957	9	19	otto	otto	PROPN
uva.x030312957	9	20	dziobek	dziobek	PROPN
uva.x030312957	9	21	,	,	PUNCT
uva.x030312957	9	22	from	from	ADP
uva.x030312957	9	23	laplace	laplace	PROPN
uva.x030312957	9	24	's	's	PART
uva.x030312957	9	25	collected	collect	VERB
uva.x030312957	9	26	works	work	NOUN
uva.x030312957	9	27	,	,	PUNCT
uva.x030312957	9	28	vol	vol	NOUN
uva.x030312957	9	29	.	.	PUNCT
uva.x030312957	10	1	xi	xi	PROPN
uva.x030312957	10	2	,	,	PUNCT
uva.x030312957	10	3	page	page	NOUN
uva.x030312957	10	4	49	49	NUM
uva.x030312957	10	5	,	,	PUNCT
uva.x030312957	10	6	and	and	CCONJ
uva.x030312957	10	7	from	from	ADP
uva.x030312957	10	8	moulton	moulton	PROPN
uva.x030312957	10	9	's	's	PART
uva.x030312957	10	10	celestial	celestial	ADJ
uva.x030312957	10	11	mechanics	mechanic	NOUN
uva.x030312957	10	12	.	.	PUNCT
uva.x030312957	11	1	no	no	DET
uva.x030312957	11	2	special	special	ADJ
uva.x030312957	11	3	reference	reference	NOUN
uva.x030312957	11	4	is	be	AUX
uva.x030312957	11	5	given	give	VERB
uva.x030312957	11	6	in	in	ADP
uva.x030312957	11	7	the	the	DET
uva.x030312957	11	8	history	history	NOUN
uva.x030312957	11	9	to	to	ADP
uva.x030312957	11	10	the	the	DET
uva.x030312957	11	11	one	one	NUM
uva.x030312957	11	12	of	of	ADP
uva.x030312957	11	13	the	the	DET
uva.x030312957	11	14	three	three	NUM
uva.x030312957	11	15	authors	author	NOUN
uva.x030312957	11	16	from	from	ADP
uva.x030312957	11	17	whom	whom	PRON
uva.x030312957	11	18	the	the	DET
uva.x030312957	11	19	material	material	NOUN
uva.x030312957	11	20	was	be	AUX
uva.x030312957	11	21	obtained	obtain	VERB
uva.x030312957	11	22	,	,	PUNCT
uva.x030312957	11	23	as	as	SCONJ
uva.x030312957	11	24	they	they	PRON
uva.x030312957	11	25	were	be	AUX
uva.x030312957	11	26	all	all	PRON
uva.x030312957	11	27	used	use	VERB
uva.x030312957	11	28	throughout	throughout	ADP
uva.x030312957	11	29	.	.	PUNCT
uva.x030312957	12	1	the	the	DET
uva.x030312957	12	2	history	history	NOUN
uva.x030312957	12	3	necessarily	necessarily	ADV
uva.x030312957	12	4	deals	deal	VERB
uva.x030312957	12	5	with	with	ADP
uva.x030312957	12	6	the	the	DET
uva.x030312957	12	7	other	other	ADJ
uva.x030312957	12	8	perturbations	perturbation	NOUN
uva.x030312957	12	9	as	as	ADV
uva.x030312957	12	10	well	well	ADV
uva.x030312957	12	11	as	as	ADP
uva.x030312957	12	12	the	the	DET
uva.x030312957	12	13	secular	secular	ADJ
uva.x030312957	12	14	terms	term	NOUN
uva.x030312957	12	15	,	,	PUNCT
uva.x030312957	12	16	but	but	CCONJ
uva.x030312957	12	17	i	i	PRON
uva.x030312957	12	18	have	have	AUX
uva.x030312957	12	19	attempted	attempt	VERB
uva.x030312957	12	20	to	to	PART
uva.x030312957	12	21	lay	lay	VERB
uva.x030312957	12	22	special	special	ADJ
uva.x030312957	12	23	stress	stress	NOUN
uva.x030312957	12	24	on	on	ADP
uva.x030312957	12	25	the	the	DET
uva.x030312957	12	26	history	history	NOUN
uva.x030312957	12	27	of	of	ADP
uva.x030312957	12	28	the	the	DET
uva.x030312957	12	29	secular	secular	ADJ
uva.x030312957	12	30	,	,	PUNCT
uva.x030312957	12	31	rather	rather	ADV
uva.x030312957	12	32	than	than	ADP
uva.x030312957	12	33	the	the	DET
uva.x030312957	12	34	periodic	periodic	ADJ
uva.x030312957	12	35	,	,	PUNCT
uva.x030312957	12	36	terms	term	NOUN
uva.x030312957	12	37	.	.	PUNCT
uva.x030312957	13	1	in	in	ADP
uva.x030312957	13	2	the	the	DET
uva.x030312957	13	3	development	development	NOUN
uva.x030312957	13	4	of	of	ADP
uva.x030312957	13	5	the	the	DET
uva.x030312957	13	6	form	form	NOUN
uva.x030312957	13	7	of	of	ADP
uva.x030312957	13	8	sturm	sturm	PROPN
uva.x030312957	13	9	's	's	PART
uva.x030312957	13	10	theorem	theorem	NOUN
uva.x030312957	13	11	known	know	VERB
uva.x030312957	13	12	as	as	ADP
uva.x030312957	13	13	“	"	PUNCT
uva.x030312957	13	14	hermite	hermite	PROPN
uva.x030312957	13	15	's	's	PART
uva.x030312957	13	16	method	method	NOUN
uva.x030312957	13	17	of	of	ADP
uva.x030312957	13	18	solving	solve	VERB
uva.x030312957	13	19	sturm	sturm	PROPN
uva.x030312957	13	20	's	's	PART
uva.x030312957	13	21	theorem	theorem	NOUN
uva.x030312957	13	22	”	"	PUNCT
uva.x030312957	13	23	weber	weber	PROPN
uva.x030312957	13	24	's	's	PART
uva.x030312957	13	25	algebra	algebra	NOUN
uva.x030312957	13	26	has	have	AUX
uva.x030312957	13	27	been	be	AUX
uva.x030312957	13	28	closely	closely	ADV
uva.x030312957	13	29	followed	follow	VERB
uva.x030312957	13	30	.	.	PUNCT
uva.x030312957	14	1	in	in	ADP
uva.x030312957	14	2	order	order	NOUN
uva.x030312957	14	3	to	to	PART
uva.x030312957	14	4	have	have	AUX
uva.x030312957	14	5	the	the	DET
uva.x030312957	14	6	method	method	NOUN
uva.x030312957	14	7	before	before	ADP
uva.x030312957	14	8	me	i	PRON
uva.x030312957	14	9	in	in	ADP
uva.x030312957	14	10	concise	concise	ADJ
uva.x030312957	14	11	form	form	NOUN
uva.x030312957	14	12	for	for	ADP
uva.x030312957	14	13	ready	ready	ADJ
uva.x030312957	14	14	reference	reference	NOUN
uva.x030312957	14	15	,	,	PUNCT
uva.x030312957	14	16	and	and	CCONJ
uva.x030312957	14	17	to	to	PART
uva.x030312957	14	18	develop	develop	VERB
uva.x030312957	14	19	the	the	DET
uva.x030312957	14	20	method	method	NOUN
uva.x030312957	14	21	in	in	ADP
uva.x030312957	14	22	logical	logical	ADJ
uva.x030312957	14	23	order	order	NOUN
uva.x030312957	14	24	,	,	PUNCT
uva.x030312957	14	25	i	i	PRON
uva.x030312957	14	26	have	have	AUX
uva.x030312957	14	27	tabulated	tabulate	VERB
uva.x030312957	14	28	in	in	ADP
uva.x030312957	14	29	full	full	ADJ
uva.x030312957	14	30	the	the	DET
uva.x030312957	14	31	material	material	NOUN
uva.x030312957	14	32	needed	need	VERB
uva.x030312957	14	33	to	to	PART
uva.x030312957	14	34	derive	derive	VERB
uva.x030312957	14	35	the	the	DET
uva.x030312957	14	36	method	method	NOUN
uva.x030312957	14	37	.	.	PUNCT
uva.x030312957	15	1	in	in	ADP
uva.x030312957	15	2	the	the	DET
uva.x030312957	15	3	third	third	ADJ
uva.x030312957	15	4	chapter	chapter	NOUN
uva.x030312957	15	5	,	,	PUNCT
uva.x030312957	15	6	application	application	NOUN
uva.x030312957	15	7	is	be	AUX
uva.x030312957	15	8	made	make	VERB
uva.x030312957	15	9	of	of	ADP
uva.x030312957	15	10	the	the	DET
uva.x030312957	15	11	method	method	NOUN
uva.x030312957	15	12	set	set	VERB
uva.x030312957	15	13	forth	forth	ADP
uva.x030312957	15	14	in	in	ADP
uva.x030312957	15	15	chapter	chapter	PROPN
uva.x030312957	15	16	ii	ii	PROPN
uva.x030312957	15	17	,	,	PUNCT
uva.x030312957	15	18	and	and	CCONJ
uva.x030312957	15	19	the	the	DET
uva.x030312957	15	20	equation	equation	NOUN
uva.x030312957	15	21	is	be	AUX
uva.x030312957	15	22	solved	solve	VERB
uva.x030312957	15	23	independently	independently	ADV
uva.x030312957	15	24	of	of	ADP
uva.x030312957	15	25	any	any	DET
uva.x030312957	15	26	previous	previous	ADJ
uva.x030312957	15	27	solution	solution	NOUN
uva.x030312957	15	28	.	.	PUNCT
uva.x030312957	16	1	the	the	DET
uva.x030312957	16	2	solution	solution	NOUN
uva.x030312957	16	3	is	be	AUX
uva.x030312957	16	4	then	then	ADV
uva.x030312957	16	5	followed	follow	VERB
uva.x030312957	16	6	by	by	ADP
uva.x030312957	16	7	a	a	DET
uva.x030312957	16	8	few	few	ADJ
uva.x030312957	16	9	important	important	ADJ
uva.x030312957	16	10	applications	application	NOUN
uva.x030312957	16	11	.	.	PUNCT
uva.x030312957	17	1	besides	besides	SCONJ
uva.x030312957	17	2	the	the	DET
uva.x030312957	17	3	general	general	ADJ
uva.x030312957	17	4	credit	credit	NOUN
uva.x030312957	17	5	given	give	VERB
uva.x030312957	17	6	above	above	ADV
uva.x030312957	17	7	for	for	ADP
uva.x030312957	17	8	the	the	DET
uva.x030312957	17	9	source	source	NOUN
uva.x030312957	17	10	of	of	ADP
uva.x030312957	17	11	my	my	PRON
uva.x030312957	17	12	material	material	NOUN
uva.x030312957	17	13	,	,	PUNCT
uva.x030312957	17	14	an	an	DET
uva.x030312957	17	15	attempt	attempt	NOUN
uva.x030312957	17	16	has	have	AUX
uva.x030312957	17	17	been	be	AUX
uva.x030312957	17	18	made	make	VERB
uva.x030312957	17	19	to	to	PART
uva.x030312957	17	20	give	give	VERB
uva.x030312957	17	21	due	due	ADJ
uva.x030312957	17	22	credit	credit	NOUN
uva.x030312957	17	23	in	in	ADP
uva.x030312957	17	24	footnotes	footnote	NOUN
uva.x030312957	17	25	.	.	PUNCT
uva.x030312957	18	1	i	i	PRON
uva.x030312957	18	2	wish	wish	VERB
uva.x030312957	18	3	to	to	PART
uva.x030312957	18	4	acknowledge	acknowledge	VERB
uva.x030312957	18	5	here	here	ADV
uva.x030312957	18	6	my	my	PRON
uva.x030312957	18	7	indebtedness	indebtedness	NOUN
uva.x030312957	18	8	to	to	PART
uva.x030312957	18	9	professor	professor	PROPN
uva.x030312957	18	10	w.	w.	PROPN
uva.x030312957	18	11	h.	h.	PROPN
uva.x030312957	18	12	echols	echols	PROPN
uva.x030312957	18	13	,	,	PUNCT
uva.x030312957	18	14	and	and	CCONJ
uva.x030312957	18	15	dr	dr	PROPN
uva.x030312957	18	16	.	.	PROPN
uva.x030312957	18	17	j.	j.	PROPN
uva.x030312957	18	18	m.	m.	PROPN
uva.x030312957	18	19	page	page	PROPN
uva.x030312957	18	20	,	,	PUNCT
uva.x030312957	18	21	who	who	PRON
uva.x030312957	18	22	labored	labor	VERB
uva.x030312957	18	23	with	with	ADP
uva.x030312957	18	24	me	i	PRON
uva.x030312957	18	25	as	as	ADP
uva.x030312957	18	26	a	a	DET
uva.x030312957	18	27	student	student	NOUN
uva.x030312957	18	28	at	at	ADP
uva.x030312957	18	29	the	the	DET
uva.x030312957	18	30	university	university	PROPN
uva.x030312957	18	31	of	of	ADP
uva.x030312957	18	32	virginia	virginia	PROPN
uva.x030312957	18	33	to	to	PART
uva.x030312957	18	34	make	make	VERB
uva.x030312957	18	35	it	it	PRON
uva.x030312957	18	36	possible	possible	ADJ
uva.x030312957	18	37	for	for	SCONJ
uva.x030312957	18	38	me	i	PRON
uva.x030312957	18	39	to	to	PART
uva.x030312957	18	40	pursue	pursue	VERB
uva.x030312957	18	41	further	further	ADJ
uva.x030312957	18	42	investigations	investigation	NOUN
uva.x030312957	18	43	,	,	PUNCT
uva.x030312957	18	44	and	and	CCONJ
uva.x030312957	18	45	also	also	ADV
uva.x030312957	18	46	to	to	PART
uva.x030312957	18	47	thank	thank	VERB
uva.x030312957	18	48	dr	dr	PROPN
uva.x030312957	18	49	.	.	PROPN
uva.x030312957	18	50	harris	harris	PROPN
uva.x030312957	18	51	hancock	hancock	PROPN
uva.x030312957	18	52	for	for	ADP
uva.x030312957	18	53	suggesting	suggest	VERB
uva.x030312957	18	54	the	the	DET
uva.x030312957	18	55	problem	problem	NOUN
uva.x030312957	18	56	.	.	PUNCT
uva.x030312957	19	1	university	university	PROPN
uva.x030312957	19	2	of	of	ADP
uva.x030312957	19	3	cincinnati	cincinnati	PROPN
uva.x030312957	19	4	,	,	PUNCT
uva.x030312957	19	5	march	march	PROPN
uva.x030312957	19	6	15	15	NUM
uva.x030312957	19	7	,	,	PUNCT
uva.x030312957	19	8	1916	1916	NUM
uva.x030312957	19	9	.	.	PUNCT
uva.x030312957	20	1	iii	iii	NUM
uva.x030312957	20	2	chapter	chapter	NOUN
uva.x030312957	20	3	i	i	PRON
uva.x030312957	20	4	a	a	DET
uva.x030312957	20	5	short	short	ADJ
uva.x030312957	20	6	history	history	NOUN
uva.x030312957	20	7	of	of	ADP
uva.x030312957	20	8	the	the	DET
uva.x030312957	20	9	perturbations	perturbation	NOUN
uva.x030312957	20	10	of	of	ADP
uva.x030312957	20	11	the	the	DET
uva.x030312957	20	12	planets	planet	NOUN
uva.x030312957	20	13	,	,	PUNCT
uva.x030312957	20	14	with	with	ADP
uva.x030312957	20	15	particular	particular	ADJ
uva.x030312957	20	16	attention	attention	NOUN
uva.x030312957	20	17	to	to	ADP
uva.x030312957	20	18	the	the	DET
uva.x030312957	20	19	secular	secular	ADJ
uva.x030312957	20	20	terms	term	NOUN
uva.x030312957	20	21	the	the	DET
uva.x030312957	20	22	equation	equation	NOUN
uva.x030312957	20	23	of	of	ADP
uva.x030312957	20	24	secular	secular	ADJ
uva.x030312957	20	25	variations	variation	NOUN
uva.x030312957	20	26	,	,	PUNCT
uva.x030312957	20	27	the	the	DET
uva.x030312957	20	28	solution	solution	NOUN
uva.x030312957	20	29	of	of	ADP
uva.x030312957	20	30	which	which	PRON
uva.x030312957	20	31	is	be	AUX
uva.x030312957	20	32	the	the	DET
uva.x030312957	20	33	object	object	NOUN
uva.x030312957	20	34	of	of	ADP
uva.x030312957	20	35	this	this	DET
uva.x030312957	20	36	treatise	treatise	NOUN
uva.x030312957	20	37	,	,	PUNCT
uva.x030312957	20	38	is	be	AUX
uva.x030312957	20	39	so	so	ADV
uva.x030312957	20	40	named	name	VERB
uva.x030312957	20	41	because	because	SCONJ
uva.x030312957	20	42	of	of	ADP
uva.x030312957	20	43	its	its	PRON
uva.x030312957	20	44	part	part	NOUN
uva.x030312957	20	45	in	in	ADP
uva.x030312957	20	46	establishing	establish	VERB
uva.x030312957	20	47	the	the	DET
uva.x030312957	20	48	secular	secular	ADJ
uva.x030312957	20	49	terms	term	NOUN
uva.x030312957	20	50	in	in	ADP
uva.x030312957	20	51	the	the	DET
uva.x030312957	20	52	perturbations	perturbation	NOUN
uva.x030312957	20	53	of	of	ADP
uva.x030312957	20	54	three	three	NUM
uva.x030312957	20	55	or	or	CCONJ
uva.x030312957	20	56	more	more	ADJ
uva.x030312957	20	57	planets	planet	NOUN
uva.x030312957	20	58	.	.	PUNCT
uva.x030312957	21	1	according	accord	VERB
uva.x030312957	21	2	to	to	ADP
uva.x030312957	21	3	laplace	laplace	NOUN
uva.x030312957	21	4	,	,	PUNCT
uva.x030312957	21	5	*	*	PUNCT
uva.x030312957	21	6	the	the	DET
uva.x030312957	21	7	planetary	planetary	ADJ
uva.x030312957	21	8	perturbations	perturbation	NOUN
uva.x030312957	21	9	divide	divide	VERB
uva.x030312957	21	10	themselves	themselves	PRON
uva.x030312957	21	11	into	into	ADP
uva.x030312957	21	12	two	two	NUM
uva.x030312957	21	13	classes	class	NOUN
uva.x030312957	21	14	,	,	PUNCT
uva.x030312957	21	15	the	the	DET
uva.x030312957	21	16	periodic	periodic	NOUN
uva.x030312957	21	17	and	and	CCONJ
uva.x030312957	21	18	the	the	DET
uva.x030312957	21	19	secular	secular	ADJ
uva.x030312957	21	20	.	.	PUNCT
uva.x030312957	22	1	the	the	DET
uva.x030312957	22	2	periodic	periodic	ADJ
uva.x030312957	22	3	are	be	AUX
uva.x030312957	22	4	,	,	PUNCT
uva.x030312957	22	5	for	for	ADP
uva.x030312957	22	6	the	the	DET
uva.x030312957	22	7	most	most	ADJ
uva.x030312957	22	8	part	part	NOUN
uva.x030312957	22	9	,	,	PUNCT
uva.x030312957	22	10	very	very	ADV
uva.x030312957	22	11	small	small	ADJ
uva.x030312957	22	12	,	,	PUNCT
uva.x030312957	22	13	depend	depend	VERB
uva.x030312957	22	14	on	on	ADP
uva.x030312957	22	15	the	the	DET
uva.x030312957	22	16	positions	position	NOUN
uva.x030312957	22	17	of	of	ADP
uva.x030312957	22	18	the	the	DET
uva.x030312957	22	19	planets	planet	NOUN
uva.x030312957	22	20	in	in	ADP
uva.x030312957	22	21	their	their	PRON
uva.x030312957	22	22	orbits	orbit	NOUN
uva.x030312957	22	23	,	,	PUNCT
uva.x030312957	22	24	and	and	CCONJ
uva.x030312957	22	25	usually	usually	ADV
uva.x030312957	22	26	run	run	VERB
uva.x030312957	22	27	their	their	PRON
uva.x030312957	22	28	course	course	NOUN
uva.x030312957	22	29	in	in	ADP
uva.x030312957	22	30	a	a	DET
uva.x030312957	22	31	few	few	ADJ
uva.x030312957	22	32	revolutions	revolution	NOUN
uva.x030312957	22	33	of	of	ADP
uva.x030312957	22	34	the	the	DET
uva.x030312957	22	35	planet	planet	NOUN
uva.x030312957	22	36	in	in	ADP
uva.x030312957	22	37	question	question	NOUN
uva.x030312957	22	38	.	.	PUNCT
uva.x030312957	23	1	in	in	ADP
uva.x030312957	23	2	the	the	DET
uva.x030312957	23	3	earlier	early	ADJ
uva.x030312957	23	4	investigations	investigation	NOUN
uva.x030312957	23	5	the	the	DET
uva.x030312957	23	6	secular	secular	ADJ
uva.x030312957	23	7	inequalities	inequality	NOUN
uva.x030312957	23	8	were	be	AUX
uva.x030312957	23	9	not	not	PART
uva.x030312957	23	10	considered	consider	VERB
uva.x030312957	23	11	,	,	PUNCT
uva.x030312957	23	12	as	as	SCONJ
uva.x030312957	23	13	their	their	PRON
uva.x030312957	23	14	influence	influence	NOUN
uva.x030312957	23	15	is	be	AUX
uva.x030312957	23	16	negligible	negligible	ADJ
uva.x030312957	23	17	unless	unless	SCONJ
uva.x030312957	23	18	exerted	exert	VERB
uva.x030312957	23	19	over	over	ADP
uva.x030312957	23	20	a	a	DET
uva.x030312957	23	21	very	very	ADV
uva.x030312957	23	22	great	great	ADJ
uva.x030312957	23	23	period	period	NOUN
uva.x030312957	23	24	,	,	PUNCT
uva.x030312957	23	25	and	and	CCONJ
uva.x030312957	23	26	they	they	PRON
uva.x030312957	23	27	were	be	AUX
uva.x030312957	23	28	not	not	PART
uva.x030312957	23	29	considered	consider	VERB
uva.x030312957	23	30	until	until	SCONJ
uva.x030312957	23	31	it	it	PRON
uva.x030312957	23	32	was	be	AUX
uva.x030312957	23	33	demonstrated	demonstrate	VERB
uva.x030312957	23	34	that	that	SCONJ
uva.x030312957	23	35	over	over	ADP
uva.x030312957	23	36	cycles	cycle	NOUN
uva.x030312957	23	37	of	of	ADP
uva.x030312957	23	38	centuries	century	NOUN
uva.x030312957	23	39	their	their	PRON
uva.x030312957	23	40	influence	influence	NOUN
uva.x030312957	23	41	is	be	AUX
uva.x030312957	23	42	enormous	enormous	ADJ
uva.x030312957	23	43	.	.	PUNCT
uva.x030312957	24	1	these	these	DET
uva.x030312957	24	2	inequalities	inequality	NOUN
uva.x030312957	24	3	are	be	AUX
uva.x030312957	24	4	not	not	PART
uva.x030312957	24	5	dependent	dependent	ADJ
uva.x030312957	24	6	on	on	ADP
uva.x030312957	24	7	the	the	DET
uva.x030312957	24	8	position	position	NOUN
uva.x030312957	24	9	of	of	ADP
uva.x030312957	24	10	the	the	DET
uva.x030312957	24	11	planets	planet	NOUN
uva.x030312957	24	12	in	in	ADP
uva.x030312957	24	13	their	their	PRON
uva.x030312957	24	14	orbits	orbit	NOUN
uva.x030312957	24	15	,	,	PUNCT
uva.x030312957	24	16	but	but	CCONJ
uva.x030312957	24	17	on	on	ADP
uva.x030312957	24	18	the	the	DET
uva.x030312957	24	19	relative	relative	ADJ
uva.x030312957	24	20	positions	position	NOUN
uva.x030312957	24	21	of	of	ADP
uva.x030312957	24	22	the	the	DET
uva.x030312957	24	23	orbits	orbit	NOUN
uva.x030312957	24	24	themselves	themselves	PRON
uva.x030312957	24	25	.	.	PUNCT
uva.x030312957	25	1	the	the	DET
uva.x030312957	25	2	history	history	NOUN
uva.x030312957	25	3	of	of	ADP
uva.x030312957	25	4	the	the	DET
uva.x030312957	25	5	disturbance	disturbance	NOUN
uva.x030312957	25	6	theories	theory	NOUN
uva.x030312957	25	7	begins	begin	VERB
uva.x030312957	25	8	with	with	ADP
uva.x030312957	25	9	newton	newton	PROPN
uva.x030312957	25	10	,	,	PUNCT
uva.x030312957	25	11	who	who	PRON
uva.x030312957	25	12	explained	explain	VERB
uva.x030312957	25	13	the	the	DET
uva.x030312957	25	14	principal	principal	ADJ
uva.x030312957	25	15	irregularities	irregularity	NOUN
uva.x030312957	25	16	in	in	ADP
uva.x030312957	25	17	the	the	DET
uva.x030312957	25	18	movement	movement	NOUN
uva.x030312957	25	19	of	of	ADP
uva.x030312957	25	20	the	the	DET
uva.x030312957	25	21	moon	moon	NOUN
uva.x030312957	25	22	in	in	ADP
uva.x030312957	25	23	the	the	DET
uva.x030312957	25	24	third	third	ADJ
uva.x030312957	25	25	book	book	NOUN
uva.x030312957	25	26	of	of	ADP
uva.x030312957	25	27	his	his	PRON
uva.x030312957	25	28	principia	principia	NOUN
uva.x030312957	25	29	.	.	PUNCT
uva.x030312957	26	1	he	he	PRON
uva.x030312957	26	2	developed	develop	VERB
uva.x030312957	26	3	the	the	DET
uva.x030312957	26	4	theory	theory	NOUN
uva.x030312957	26	5	of	of	ADP
uva.x030312957	26	6	perturbations	perturbation	NOUN
uva.x030312957	26	7	as	as	SCONJ
uva.x030312957	26	8	applied	apply	VERB
uva.x030312957	26	9	to	to	ADP
uva.x030312957	26	10	the	the	DET
uva.x030312957	26	11	lunar	lunar	ADJ
uva.x030312957	26	12	theory	theory	NOUN
uva.x030312957	26	13	by	by	ADP
uva.x030312957	26	14	the	the	DET
uva.x030312957	26	15	methods	method	NOUN
uva.x030312957	26	16	of	of	ADP
uva.x030312957	26	17	geometry	geometry	NOUN
uva.x030312957	26	18	.	.	PUNCT
uva.x030312957	27	1	clairaut	clairaut	PROPN
uva.x030312957	27	2	and	and	CCONJ
uva.x030312957	27	3	d'alembert	d'alembert	NOUN
uva.x030312957	27	4	made	make	VERB
uva.x030312957	27	5	further	further	ADJ
uva.x030312957	27	6	progress	progress	NOUN
uva.x030312957	27	7	in	in	ADP
uva.x030312957	27	8	their	their	PRON
uva.x030312957	27	9	memoirs	memoir	NOUN
uva.x030312957	27	10	of	of	ADP
uva.x030312957	27	11	1747	1747	NUM
uva.x030312957	27	12	,	,	PUNCT
uva.x030312957	27	13	presented	present	VERB
uva.x030312957	27	14	to	to	ADP
uva.x030312957	27	15	the	the	DET
uva.x030312957	27	16	french	french	ADJ
uva.x030312957	27	17	academy	academy	NOUN
uva.x030312957	27	18	of	of	ADP
uva.x030312957	27	19	sciences	sciences	PROPN
uva.x030312957	27	20	on	on	ADP
uva.x030312957	27	21	the	the	DET
uva.x030312957	27	22	same	same	ADJ
uva.x030312957	27	23	day	day	NOUN
uva.x030312957	27	24	,	,	PUNCT
uva.x030312957	27	25	in	in	ADP
uva.x030312957	27	26	which	which	PRON
uva.x030312957	27	27	they	they	PRON
uva.x030312957	27	28	solved	solve	VERB
uva.x030312957	27	29	the	the	DET
uva.x030312957	27	30	problem	problem	NOUN
uva.x030312957	27	31	of	of	ADP
uva.x030312957	27	32	three	three	NUM
uva.x030312957	27	33	bodies	body	NOUN
uva.x030312957	27	34	when	when	SCONJ
uva.x030312957	27	35	the	the	DET
uva.x030312957	27	36	central	central	ADJ
uva.x030312957	27	37	force	force	NOUN
uva.x030312957	27	38	outweighs	outweigh	VERB
uva.x030312957	27	39	the	the	DET
uva.x030312957	27	40	remaining	remain	VERB
uva.x030312957	27	41	in	in	ADP
uva.x030312957	27	42	importance	importance	NOUN
uva.x030312957	27	43	.	.	PUNCT
uva.x030312957	28	1	their	their	PRON
uva.x030312957	28	2	solution	solution	NOUN
uva.x030312957	28	3	depended	depend	VERB
uva.x030312957	28	4	on	on	ADP
uva.x030312957	28	5	the	the	DET
uva.x030312957	28	6	integration	integration	NOUN
uva.x030312957	28	7	of	of	ADP
uva.x030312957	28	8	the	the	DET
uva.x030312957	28	9	differential	differential	ADJ
uva.x030312957	28	10	equation	equation	NOUN
uva.x030312957	28	11	of	of	ADP
uva.x030312957	28	12	motion	motion	NOUN
uva.x030312957	28	13	in	in	ADP
uva.x030312957	28	14	series	series	PROPN
uva.x030312957	28	15	.	.	PUNCT
uva.x030312957	29	1	clairaut	clairaut	PROPN
uva.x030312957	29	2	soon	soon	ADV
uva.x030312957	29	3	made	make	VERB
uva.x030312957	29	4	a	a	DET
uva.x030312957	29	5	forceful	forceful	ADJ
uva.x030312957	29	6	application	application	NOUN
uva.x030312957	29	7	of	of	ADP
uva.x030312957	29	8	his	his	PRON
uva.x030312957	29	9	brilliant	brilliant	ADJ
uva.x030312957	29	10	theory	theory	NOUN
uva.x030312957	29	11	,	,	PUNCT
uva.x030312957	29	12	by	by	ADP
uva.x030312957	29	13	studying	study	VERB
uva.x030312957	29	14	the	the	DET
uva.x030312957	29	15	perturbations	perturbation	NOUN
uva.x030312957	29	16	of	of	ADP
uva.x030312957	29	17	halley	halley	PROPN
uva.x030312957	29	18	's	's	PART
uva.x030312957	29	19	comet	comet	NOUN
uva.x030312957	29	20	.	.	PUNCT
uva.x030312957	30	1	this	this	DET
uva.x030312957	30	2	comet	comet	NOUN
uva.x030312957	30	3	had	have	AUX
uva.x030312957	30	4	been	be	AUX
uva.x030312957	30	5	observed	observe	VERB
uva.x030312957	30	6	in	in	ADP
uva.x030312957	30	7	1531	1531	NUM
uva.x030312957	30	8	,	,	PUNCT
uva.x030312957	30	9	1607	1607	NUM
uva.x030312957	30	10	and	and	CCONJ
uva.x030312957	30	11	1682	1682	NUM
uva.x030312957	30	12	and	and	CCONJ
uva.x030312957	30	13	its	its	PRON
uva.x030312957	30	14	period	period	NOUN
uva.x030312957	30	15	fixed	fix	VERB
uva.x030312957	30	16	as	as	ADP
uva.x030312957	30	17	about	about	ADV
uva.x030312957	30	18	seventy	seventy	NUM
uva.x030312957	30	19	-	-	PUNCT
uva.x030312957	30	20	five	five	NUM
uva.x030312957	30	21	years	year	NOUN
uva.x030312957	30	22	.	.	PUNCT
uva.x030312957	31	1	its	its	PRON
uva.x030312957	31	2	return	return	NOUN
uva.x030312957	31	3	was	be	AUX
uva.x030312957	31	4	therefore	therefore	ADV
uva.x030312957	31	5	expected	expect	VERB
uva.x030312957	31	6	at	at	ADP
uva.x030312957	31	7	the	the	DET
uva.x030312957	31	8	latest	late	ADJ
uva.x030312957	31	9	toward	toward	ADP
uva.x030312957	31	10	the	the	DET
uva.x030312957	31	11	end	end	NOUN
uva.x030312957	31	12	of	of	ADP
uva.x030312957	31	13	the	the	DET
uva.x030312957	31	14	year	year	NOUN
uva.x030312957	31	15	1758	1758	NUM
uva.x030312957	31	16	.	.	PUNCT
uva.x030312957	32	1	clairaut	clairaut	PROPN
uva.x030312957	32	2	calculated	calculate	VERB
uva.x030312957	32	3	the	the	DET
uva.x030312957	32	4	influence	influence	NOUN
uva.x030312957	32	5	which	which	PRON
uva.x030312957	32	6	the	the	DET
uva.x030312957	32	7	then	then	ADV
uva.x030312957	32	8	known	know	VERB
uva.x030312957	32	9	planets	planet	NOUN
uva.x030312957	32	10	would	would	AUX
uva.x030312957	32	11	exercise	exercise	VERB
uva.x030312957	32	12	on	on	ADP
uva.x030312957	32	13	it	it	PRON
uva.x030312957	32	14	,	,	PUNCT
uva.x030312957	32	15	and	and	CCONJ
uva.x030312957	32	16	reported	report	VERB
uva.x030312957	32	17	to	to	ADP
uva.x030312957	32	18	the	the	DET
uva.x030312957	32	19	academy	academy	NOUN
uva.x030312957	32	20	of	of	ADP
uva.x030312957	32	21	sciences	sciences	PROPN
uva.x030312957	32	22	that	that	PRON
uva.x030312957	32	23	the	the	DET
uva.x030312957	32	24	disturbance	disturbance	NOUN
uva.x030312957	32	25	caused	cause	VERB
uva.x030312957	32	26	by	by	ADP
uva.x030312957	32	27	them	they	PRON
uva.x030312957	32	28	would	would	AUX
uva.x030312957	32	29	delay	delay	VERB
uva.x030312957	32	30	its	its	PRON
uva.x030312957	32	31	return	return	NOUN
uva.x030312957	32	32	until	until	ADP
uva.x030312957	32	33	the	the	DET
uva.x030312957	32	34	middle	middle	NOUN
uva.x030312957	32	35	of	of	ADP
uva.x030312957	32	36	april	april	PROPN
uva.x030312957	32	37	,	,	PUNCT
uva.x030312957	32	38	1759	1759	NUM
uva.x030312957	32	39	.	.	PUNCT
uva.x030312957	33	1	he	he	PRON
uva.x030312957	33	2	later	later	ADV
uva.x030312957	33	3	added	add	VERB
uva.x030312957	33	4	this	this	PRON
uva.x030312957	33	5	might	might	AUX
uva.x030312957	33	6	vary	vary	VERB
uva.x030312957	33	7	about	about	ADV
uva.x030312957	33	8	a	a	PRON
uva.x030312957	33	9	month	month	NOUN
uva.x030312957	33	10	due	due	ADP
uva.x030312957	33	11	to	to	ADP
uva.x030312957	33	12	small	small	ADJ
uva.x030312957	33	13	influences	influence	NOUN
uva.x030312957	33	14	he	he	PRON
uva.x030312957	33	15	had	have	AUX
uva.x030312957	33	16	neglected	neglect	VERB
uva.x030312957	33	17	.	.	PUNCT
uva.x030312957	34	1	while	while	SCONJ
uva.x030312957	34	2	the	the	DET
uva.x030312957	34	3	comet	comet	NOUN
uva.x030312957	34	4	reappeared	reappear	VERB
uva.x030312957	34	5	within	within	ADP
uva.x030312957	34	6	the	the	DET
uva.x030312957	34	7	limit	limit	NOUN
uva.x030312957	34	8	given	give	VERB
uva.x030312957	34	9	by	by	ADP
uva.x030312957	34	10	him	he	PRON
uva.x030312957	34	11	,	,	PUNCT
uva.x030312957	34	12	being	be	AUX
uva.x030312957	34	13	first	first	ADV
uva.x030312957	34	14	seen	see	VERB
uva.x030312957	34	15	on	on	ADP
uva.x030312957	34	16	march	march	PROPN
uva.x030312957	34	17	12	12	NUM
uva.x030312957	34	18	,	,	PUNCT
uva.x030312957	34	19	1759	1759	NUM
uva.x030312957	34	20	,	,	PUNCT
uva.x030312957	34	21	still	still	ADV
uva.x030312957	34	22	there	there	PRON
uva.x030312957	34	23	was	be	VERB
uva.x030312957	34	24	a	a	DET
uva.x030312957	34	25	greater	great	ADJ
uva.x030312957	34	26	see	see	NOUN
uva.x030312957	34	27	laplace	laplace	NOUN
uva.x030312957	34	28	's	's	PART
uva.x030312957	34	29	collected	collect	VERB
uva.x030312957	34	30	works	work	NOUN
uva.x030312957	34	31	.	.	PUNCT
uva.x030312957	35	1	1	1	NUM
uva.x030312957	35	2	2	2	NUM
uva.x030312957	35	3	solution	solution	NOUN
uva.x030312957	35	4	of	of	ADP
uva.x030312957	35	5	the	the	DET
uva.x030312957	35	6	equation	equation	NOUN
uva.x030312957	35	7	of	of	ADP
uva.x030312957	35	8	secular	secular	ADJ
uva.x030312957	35	9	variation	variation	NOUN
uva.x030312957	35	10	difference	difference	NOUN
uva.x030312957	35	11	between	between	ADP
uva.x030312957	35	12	his	his	PRON
uva.x030312957	35	13	calculation	calculation	NOUN
uva.x030312957	35	14	and	and	CCONJ
uva.x030312957	35	15	the	the	DET
uva.x030312957	35	16	actual	actual	ADJ
uva.x030312957	35	17	occurrence	occurrence	NOUN
uva.x030312957	35	18	than	than	SCONJ
uva.x030312957	35	19	there	there	PRON
uva.x030312957	35	20	would	would	AUX
uva.x030312957	35	21	have	have	AUX
uva.x030312957	35	22	been	be	AUX
uva.x030312957	35	23	had	have	VERB
uva.x030312957	35	24	the	the	DET
uva.x030312957	35	25	mass	mass	NOUN
uva.x030312957	35	26	of	of	ADP
uva.x030312957	35	27	saturn	saturn	NOUN
uva.x030312957	35	28	been	be	AUX
uva.x030312957	35	29	more	more	ADV
uva.x030312957	35	30	correctly	correctly	ADV
uva.x030312957	35	31	known	know	VERB
uva.x030312957	35	32	.	.	PUNCT
uva.x030312957	36	1	the	the	DET
uva.x030312957	36	2	methods	method	NOUN
uva.x030312957	36	3	of	of	ADP
uva.x030312957	36	4	geometry	geometry	NOUN
uva.x030312957	36	5	were	be	AUX
uva.x030312957	36	6	succeeded	succeed	VERB
uva.x030312957	36	7	by	by	ADP
uva.x030312957	36	8	the	the	DET
uva.x030312957	36	9	more	more	ADV
uva.x030312957	36	10	powerful	powerful	ADJ
uva.x030312957	36	11	methods	method	NOUN
uva.x030312957	36	12	of	of	ADP
uva.x030312957	36	13	analysis	analysis	NOUN
uva.x030312957	36	14	,	,	PUNCT
uva.x030312957	36	15	and	and	CCONJ
uva.x030312957	36	16	were	be	AUX
uva.x030312957	36	17	developed	develop	VERB
uva.x030312957	36	18	largely	largely	ADV
uva.x030312957	36	19	by	by	ADP
uva.x030312957	36	20	fuler	fuler	PROPN
uva.x030312957	36	21	,	,	PUNCT
uva.x030312957	36	22	clairaut	clairaut	PROPN
uva.x030312957	36	23	,	,	PUNCT
uva.x030312957	36	24	d'alembert	d'alembert	PROPN
uva.x030312957	36	25	,	,	PUNCT
uva.x030312957	36	26	lagrange	lagrange	NOUN
uva.x030312957	36	27	and	and	CCONJ
uva.x030312957	36	28	laplace	laplace	PROPN
uva.x030312957	36	29	.	.	PUNCT
uva.x030312957	37	1	euler	euler	PROPN
uva.x030312957	37	2	(	(	PUNCT
uva.x030312957	37	3	1707	1707	NUM
uva.x030312957	37	4	-	-	SYM
uva.x030312957	37	5	1783	1783	NUM
uva.x030312957	37	6	)	)	PUNCT
uva.x030312957	37	7	was	be	AUX
uva.x030312957	37	8	the	the	DET
uva.x030312957	37	9	pioneer	pioneer	NOUN
uva.x030312957	37	10	in	in	ADP
uva.x030312957	37	11	the	the	DET
uva.x030312957	37	12	applications	application	NOUN
uva.x030312957	37	13	of	of	ADP
uva.x030312957	37	14	analysis	analysis	NOUN
uva.x030312957	37	15	to	to	ADP
uva.x030312957	37	16	the	the	DET
uva.x030312957	37	17	perturbations	perturbation	NOUN
uva.x030312957	37	18	,	,	PUNCT
uva.x030312957	37	19	having	have	VERB
uva.x030312957	37	20	to	to	PART
uva.x030312957	37	21	develop	develop	VERB
uva.x030312957	37	22	the	the	DET
uva.x030312957	37	23	methods	method	NOUN
uva.x030312957	37	24	which	which	PRON
uva.x030312957	37	25	he	he	PRON
uva.x030312957	37	26	used	use	VERB
uva.x030312957	37	27	in	in	ADP
uva.x030312957	37	28	attacking	attack	VERB
uva.x030312957	37	29	the	the	DET
uva.x030312957	37	30	problem	problem	NOUN
uva.x030312957	37	31	.	.	PUNCT
uva.x030312957	38	1	he	he	PRON
uva.x030312957	38	2	presented	present	VERB
uva.x030312957	38	3	three	three	NUM
uva.x030312957	38	4	memoirs	memoir	NOUN
uva.x030312957	38	5	on	on	ADP
uva.x030312957	38	6	the	the	DET
uva.x030312957	38	7	perturbations	perturbation	NOUN
uva.x030312957	38	8	of	of	ADP
uva.x030312957	38	9	the	the	DET
uva.x030312957	38	10	planets	planet	NOUN
uva.x030312957	38	11	,	,	PUNCT
uva.x030312957	38	12	treating	treat	VERB
uva.x030312957	38	13	primarily	primarily	ADV
uva.x030312957	38	14	the	the	DET
uva.x030312957	38	15	mutual	mutual	ADJ
uva.x030312957	38	16	perturbations	perturbation	NOUN
uva.x030312957	38	17	of	of	ADP
uva.x030312957	38	18	jupiter	jupiter	PROPN
uva.x030312957	38	19	and	and	CCONJ
uva.x030312957	38	20	saturn	saturn	NOUN
uva.x030312957	38	21	,	,	PUNCT
uva.x030312957	38	22	which	which	PRON
uva.x030312957	38	23	gained	gain	VERB
uva.x030312957	38	24	for	for	ADP
uva.x030312957	38	25	him	he	PRON
uva.x030312957	38	26	the	the	DET
uva.x030312957	38	27	prizes	prize	NOUN
uva.x030312957	38	28	of	of	ADP
uva.x030312957	38	29	the	the	DET
uva.x030312957	38	30	paris	paris	PROPN
uva.x030312957	38	31	academy	academy	PROPN
uva.x030312957	38	32	of	of	ADP
uva.x030312957	38	33	sciences	sciences	PROPN
uva.x030312957	38	34	in	in	ADP
uva.x030312957	38	35	the	the	DET
uva.x030312957	38	36	years	year	NOUN
uva.x030312957	38	37	1748	1748	NUM
uva.x030312957	38	38	,	,	PUNCT
uva.x030312957	38	39	1752	1752	NUM
uva.x030312957	38	40	and	and	CCONJ
uva.x030312957	38	41	1756	1756	NUM
uva.x030312957	38	42	.	.	PUNCT
uva.x030312957	39	1	in	in	ADP
uva.x030312957	39	2	these	these	DET
uva.x030312957	39	3	memoirs	memoir	NOUN
uva.x030312957	39	4	he	he	PRON
uva.x030312957	39	5	gave	give	VERB
uva.x030312957	39	6	the	the	DET
uva.x030312957	39	7	first	first	ADJ
uva.x030312957	39	8	analytical	analytical	ADJ
uva.x030312957	39	9	development	development	NOUN
uva.x030312957	39	10	of	of	ADP
uva.x030312957	39	11	the	the	DET
uva.x030312957	39	12	method	method	NOUN
uva.x030312957	39	13	of	of	ADP
uva.x030312957	39	14	the	the	DET
uva.x030312957	39	15	variations	variation	NOUN
uva.x030312957	39	16	of	of	ADP
uva.x030312957	39	17	parameters	parameter	NOUN
uva.x030312957	39	18	.	.	PUNCT
uva.x030312957	40	1	his	his	PRON
uva.x030312957	40	2	formulas	formula	NOUN
uva.x030312957	40	3	were	be	AUX
uva.x030312957	40	4	not	not	PART
uva.x030312957	40	5	entirely	entirely	ADV
uva.x030312957	40	6	general	general	ADJ
uva.x030312957	40	7	because	because	SCONJ
uva.x030312957	40	8	he	he	PRON
uva.x030312957	40	9	did	do	AUX
uva.x030312957	40	10	not	not	PART
uva.x030312957	40	11	vary	vary	VERB
uva.x030312957	40	12	many	many	ADJ
uva.x030312957	40	13	of	of	ADP
uva.x030312957	40	14	the	the	DET
uva.x030312957	40	15	constants	constant	NOUN
uva.x030312957	40	16	simultaneously	simultaneously	ADV
uva.x030312957	40	17	.	.	PUNCT
uva.x030312957	41	1	still	still	ADV
uva.x030312957	41	2	,	,	PUNCT
uva.x030312957	41	3	in	in	ADP
uva.x030312957	41	4	the	the	DET
uva.x030312957	41	5	case	case	NOUN
uva.x030312957	41	6	of	of	ADP
uva.x030312957	41	7	two	two	NUM
uva.x030312957	41	8	planets	planet	NOUN
uva.x030312957	41	9	he	he	PRON
uva.x030312957	41	10	arrived	arrive	VERB
uva.x030312957	41	11	at	at	ADP
uva.x030312957	41	12	the	the	DET
uva.x030312957	41	13	proof	proof	NOUN
uva.x030312957	41	14	of	of	ADP
uva.x030312957	41	15	the	the	DET
uva.x030312957	41	16	existence	existence	NOUN
uva.x030312957	41	17	of	of	ADP
uva.x030312957	41	18	the	the	DET
uva.x030312957	41	19	secular	secular	ADJ
uva.x030312957	41	20	variations	variation	NOUN
uva.x030312957	41	21	of	of	ADP
uva.x030312957	41	22	the	the	DET
uva.x030312957	41	23	eccentricity	eccentricity	NOUN
uva.x030312957	41	24	,	,	PUNCT
uva.x030312957	41	25	inclination	inclination	NOUN
uva.x030312957	41	26	,	,	PUNCT
uva.x030312957	41	27	perihelion	perihelion	NOUN
uva.x030312957	41	28	,	,	PUNCT
uva.x030312957	41	29	and	and	CCONJ
uva.x030312957	41	30	node	node	PROPN
uva.x030312957	41	31	.	.	PUNCT
uva.x030312957	42	1	unfortunately	unfortunately	ADV
uva.x030312957	42	2	many	many	ADJ
uva.x030312957	42	3	mistakes	mistake	NOUN
uva.x030312957	42	4	appeared	appear	VERB
uva.x030312957	42	5	in	in	ADP
uva.x030312957	42	6	the	the	DET
uva.x030312957	42	7	numerical	numerical	ADJ
uva.x030312957	42	8	calculations	calculation	NOUN
uva.x030312957	42	9	,	,	PUNCT
uva.x030312957	42	10	but	but	CCONJ
uva.x030312957	42	11	the	the	DET
uva.x030312957	42	12	results	result	NOUN
uva.x030312957	42	13	were	be	AUX
uva.x030312957	42	14	later	later	ADV
uva.x030312957	42	15	correctly	correctly	ADV
uva.x030312957	42	16	obtained	obtain	VERB
uva.x030312957	42	17	by	by	ADP
uva.x030312957	42	18	lagrange	lagrange	PROPN
uva.x030312957	42	19	.	.	PUNCT
uva.x030312957	43	1	lagrange	lagrange	PROPN
uva.x030312957	43	2	(	(	PUNCT
uva.x030312957	43	3	1736	1736	NUM
uva.x030312957	43	4	-	-	SYM
uva.x030312957	43	5	1813	1813	NUM
uva.x030312957	43	6	)	)	PUNCT
uva.x030312957	43	7	pursued	pursue	VERB
uva.x030312957	43	8	the	the	DET
uva.x030312957	43	9	ideas	idea	NOUN
uva.x030312957	43	10	of	of	ADP
uva.x030312957	43	11	euler	euler	PROPN
uva.x030312957	43	12	,	,	PUNCT
uva.x030312957	43	13	and	and	CCONJ
uva.x030312957	43	14	developed	develop	VERB
uva.x030312957	43	15	still	still	ADV
uva.x030312957	43	16	further	far	ADV
uva.x030312957	43	17	the	the	DET
uva.x030312957	43	18	method	method	NOUN
uva.x030312957	43	19	of	of	ADP
uva.x030312957	43	20	the	the	DET
uva.x030312957	43	21	variation	variation	NOUN
uva.x030312957	43	22	of	of	ADP
uva.x030312957	43	23	parameters	parameter	NOUN
uva.x030312957	43	24	.	.	PUNCT
uva.x030312957	44	1	his	his	PRON
uva.x030312957	44	2	contributions	contribution	NOUN
uva.x030312957	44	3	to	to	ADP
uva.x030312957	44	4	celestial	celestial	ADJ
uva.x030312957	44	5	mechanics	mechanic	NOUN
uva.x030312957	44	6	were	be	AUX
uva.x030312957	44	7	exceptionally	exceptionally	ADV
uva.x030312957	44	8	valuable	valuable	ADJ
uva.x030312957	44	9	,	,	PUNCT
uva.x030312957	44	10	and	and	CCONJ
uva.x030312957	44	11	should	should	AUX
uva.x030312957	44	12	insure	insure	VERB
uva.x030312957	44	13	him	he	PRON
uva.x030312957	44	14	a	a	DET
uva.x030312957	44	15	permanent	permanent	ADJ
uva.x030312957	44	16	monument	monument	NOUN
uva.x030312957	44	17	in	in	ADP
uva.x030312957	44	18	all	all	DET
uva.x030312957	44	19	works	work	NOUN
uva.x030312957	44	20	on	on	ADP
uva.x030312957	44	21	astronomy	astronomy	NOUN
uva.x030312957	44	22	.	.	PUNCT
uva.x030312957	45	1	his	his	PRON
uva.x030312957	45	2	first	first	ADJ
uva.x030312957	45	3	work	work	NOUN
uva.x030312957	45	4	appeared	appear	VERB
uva.x030312957	45	5	in	in	ADP
uva.x030312957	45	6	the	the	DET
uva.x030312957	45	7	mélanges	mélanges	PROPN
uva.x030312957	45	8	de	de	PROPN
uva.x030312957	45	9	la	la	X
uva.x030312957	45	10	société	société	PROPN
uva.x030312957	45	11	de	de	ADP
uva.x030312957	45	12	turin	turin	PROPN
uva.x030312957	45	13	,	,	PUNCT
uva.x030312957	45	14	tome	tome	PROPN
uva.x030312957	45	15	iii	iii	PROPN
uva.x030312957	45	16	,	,	PUNCT
uva.x030312957	45	17	1766	1766	NUM
uva.x030312957	45	18	.	.	PUNCT
uva.x030312957	46	1	in	in	ADP
uva.x030312957	46	2	this	this	PRON
uva.x030312957	46	3	he	he	PRON
uva.x030312957	46	4	applied	apply	VERB
uva.x030312957	46	5	the	the	DET
uva.x030312957	46	6	methods	method	NOUN
uva.x030312957	46	7	of	of	ADP
uva.x030312957	46	8	the	the	DET
uva.x030312957	46	9	variations	variation	NOUN
uva.x030312957	46	10	of	of	ADP
uva.x030312957	46	11	parameters	parameter	NOUN
uva.x030312957	46	12	to	to	ADP
uva.x030312957	46	13	the	the	DET
uva.x030312957	46	14	perturbations	perturbation	NOUN
uva.x030312957	46	15	of	of	ADP
uva.x030312957	46	16	jupiter	jupiter	PROPN
uva.x030312957	46	17	and	and	CCONJ
uva.x030312957	46	18	saturn	saturn	NOUN
uva.x030312957	46	19	,	,	PUNCT
uva.x030312957	46	20	but	but	CCONJ
uva.x030312957	46	21	his	his	PRON
uva.x030312957	46	22	procedure	procedure	NOUN
uva.x030312957	46	23	was	be	AUX
uva.x030312957	46	24	not	not	PART
uva.x030312957	46	25	precise	precise	ADJ
uva.x030312957	46	26	because	because	SCONJ
uva.x030312957	46	27	he	he	PRON
uva.x030312957	46	28	regarded	regard	VERB
uva.x030312957	46	29	the	the	DET
uva.x030312957	46	30	major	major	ADJ
uva.x030312957	46	31	axes	axis	NOUN
uva.x030312957	46	32	and	and	CCONJ
uva.x030312957	46	33	the	the	DET
uva.x030312957	46	34	epochs	epochs	NOUN
uva.x030312957	46	35	of	of	ADP
uva.x030312957	46	36	the	the	DET
uva.x030312957	46	37	perihelion	perihelion	NOUN
uva.x030312957	46	38	passages	passage	NOUN
uva.x030312957	46	39	as	as	ADP
uva.x030312957	46	40	constants	constant	NOUN
uva.x030312957	46	41	.	.	PUNCT
uva.x030312957	47	1	however	however	ADV
uva.x030312957	47	2	,	,	PUNCT
uva.x030312957	47	3	limiting	limit	VERB
uva.x030312957	47	4	himself	himself	PRON
uva.x030312957	47	5	to	to	ADP
uva.x030312957	47	6	two	two	NUM
uva.x030312957	47	7	planets	planet	NOUN
uva.x030312957	47	8	,	,	PUNCT
uva.x030312957	47	9	he	he	PRON
uva.x030312957	47	10	obtained	obtain	VERB
uva.x030312957	47	11	the	the	DET
uva.x030312957	47	12	right	right	ADJ
uva.x030312957	47	13	final	final	ADJ
uva.x030312957	47	14	equation	equation	NOUN
uva.x030312957	47	15	for	for	ADP
uva.x030312957	47	16	the	the	DET
uva.x030312957	47	17	consideration	consideration	NOUN
uva.x030312957	47	18	of	of	ADP
uva.x030312957	47	19	the	the	DET
uva.x030312957	47	20	secular	secular	ADJ
uva.x030312957	47	21	periods	period	NOUN
uva.x030312957	47	22	.	.	PUNCT
uva.x030312957	48	1	this	this	PRON
uva.x030312957	48	2	had	have	AUX
uva.x030312957	48	3	been	be	AUX
uva.x030312957	48	4	given	give	VERB
uva.x030312957	48	5	incorrectly	incorrectly	ADV
uva.x030312957	48	6	by	by	ADP
uva.x030312957	48	7	euler	euler	PROPN
uva.x030312957	48	8	.	.	PUNCT
uva.x030312957	49	1	for	for	ADP
uva.x030312957	49	2	the	the	DET
uva.x030312957	49	3	inclinations	inclination	NOUN
uva.x030312957	49	4	and	and	CCONJ
uva.x030312957	49	5	nodes	node	NOUN
uva.x030312957	49	6	he	he	PRON
uva.x030312957	49	7	obtained	obtain	VERB
uva.x030312957	49	8	correct	correct	ADJ
uva.x030312957	49	9	formulas	formula	NOUN
uva.x030312957	49	10	,	,	PUNCT
uva.x030312957	49	11	so	so	SCONJ
uva.x030312957	49	12	that	that	SCONJ
uva.x030312957	49	13	his	his	PRON
uva.x030312957	49	14	numerical	numerical	ADJ
uva.x030312957	49	15	results	result	NOUN
uva.x030312957	49	16	,	,	PUNCT
uva.x030312957	49	17	by	by	ADP
uva.x030312957	49	18	the	the	DET
uva.x030312957	49	19	use	use	NOUN
uva.x030312957	49	20	of	of	ADP
uva.x030312957	49	21	the	the	DET
uva.x030312957	49	22	theory	theory	NOUN
uva.x030312957	49	23	of	of	ADP
uva.x030312957	49	24	the	the	DET
uva.x030312957	49	25	greatest	great	ADJ
uva.x030312957	49	26	planetsjupiter	planetsjupiter	NOUN
uva.x030312957	49	27	and	and	CCONJ
uva.x030312957	49	28	saturnare	saturnare	NOUN
uva.x030312957	49	29	passably	passably	ADV
uva.x030312957	49	30	correct	correct	ADJ
uva.x030312957	49	31	.	.	PUNCT
uva.x030312957	50	1	in	in	ADP
uva.x030312957	50	2	the	the	DET
uva.x030312957	50	3	year	year	NOUN
uva.x030312957	50	4	1773	1773	NUM
uva.x030312957	50	5	laplace	laplace	NOUN
uva.x030312957	50	6	(	(	PUNCT
uva.x030312957	50	7	1749–1827	1749–1827	NUM
uva.x030312957	50	8	)	)	PUNCT
uva.x030312957	50	9	presented	present	VERB
uva.x030312957	50	10	to	to	ADP
uva.x030312957	50	11	the	the	DET
uva.x030312957	50	12	academy	academy	NOUN
uva.x030312957	50	13	of	of	ADP
uva.x030312957	50	14	sciences	sciences	PROPN
uva.x030312957	50	15	his	his	PRON
uva.x030312957	50	16	first	first	ADJ
uva.x030312957	50	17	work	work	NOUN
uva.x030312957	50	18	on	on	ADP
uva.x030312957	50	19	the	the	DET
uva.x030312957	50	20	theory	theory	NOUN
uva.x030312957	50	21	of	of	ADP
uva.x030312957	50	22	the	the	DET
uva.x030312957	50	23	planetary	planetary	ADJ
uva.x030312957	50	24	system	system	NOUN
uva.x030312957	50	25	,	,	PUNCT
uva.x030312957	50	26	which	which	PRON
uva.x030312957	50	27	appeared	appear	VERB
uva.x030312957	50	28	in	in	ADP
uva.x030312957	50	29	the	the	DET
uva.x030312957	50	30	year	year	NOUN
uva.x030312957	50	31	1776	1776	NUM
uva.x030312957	50	32	in	in	ADP
uva.x030312957	50	33	the	the	DET
uva.x030312957	50	34	mémoires	mémoires	X
uva.x030312957	50	35	des	des	X
uva.x030312957	50	36	savants	savant	NOUN
uva.x030312957	50	37	étrangers	étranger	NOUN
uva.x030312957	50	38	.	.	PUNCT
uva.x030312957	51	1	he	he	PRON
uva.x030312957	51	2	fixed	fix	VERB
uva.x030312957	51	3	with	with	ADP
uva.x030312957	51	4	full	full	ADJ
uva.x030312957	51	5	accuracy	accuracy	NOUN
uva.x030312957	51	6	the	the	DET
uva.x030312957	51	7	formula	formula	NOUN
uva.x030312957	51	8	for	for	ADP
uva.x030312957	51	9	the	the	DET
uva.x030312957	51	10	differential	differential	ADJ
uva.x030312957	51	11	quotient	quotient	NOUN
uva.x030312957	51	12	of	of	ADP
uva.x030312957	51	13	the	the	DET
uva.x030312957	51	14	elements	element	NOUN
uva.x030312957	51	15	,	,	PUNCT
uva.x030312957	51	16	though	though	SCONJ
uva.x030312957	51	17	this	this	PRON
uva.x030312957	51	18	did	do	AUX
uva.x030312957	51	19	not	not	PART
uva.x030312957	51	20	at	at	ADP
uva.x030312957	51	21	first	first	ADV
uva.x030312957	51	22	possess	possess	VERB
uva.x030312957	51	23	its	its	PRON
uva.x030312957	51	24	later	later	ADV
uva.x030312957	51	25	elegant	elegant	ADJ
uva.x030312957	51	26	form	form	NOUN
uva.x030312957	51	27	.	.	PUNCT
uva.x030312957	52	1	in	in	ADP
uva.x030312957	52	2	this	this	DET
uva.x030312957	52	3	memoir	memoir	NOUN
uva.x030312957	52	4	he	he	PRON
uva.x030312957	52	5	proved	prove	VERB
uva.x030312957	52	6	his	his	PRON
uva.x030312957	52	7	celebrated	celebrated	ADJ
uva.x030312957	52	8	theorem	theorem	NOUN
uva.x030312957	52	9	that	that	PRON
uva.x030312957	52	10	,	,	PUNCT
uva.x030312957	52	11	up	up	ADP
uva.x030312957	52	12	to	to	ADP
uva.x030312957	52	13	the	the	DET
uva.x030312957	52	14	second	second	ADJ
uva.x030312957	52	15	powers	power	NOUN
uva.x030312957	52	16	of	of	ADP
uva.x030312957	52	17	the	the	DET
uva.x030312957	52	18	eccentricities	eccentricity	NOUN
uva.x030312957	52	19	and	and	CCONJ
uva.x030312957	52	20	the	the	DET
uva.x030312957	52	21	inclinations	inclination	NOUN
uva.x030312957	52	22	,	,	PUNCT
uva.x030312957	52	23	the	the	DET
uva.x030312957	52	24	major	major	ADJ
uva.x030312957	52	25	axes	axis	NOUN
uva.x030312957	52	26	have	have	AUX
uva.x030312957	52	27	no	no	DET
uva.x030312957	52	28	secular	secular	ADJ
uva.x030312957	52	29	terms	term	NOUN
uva.x030312957	52	30	.	.	PUNCT
uva.x030312957	53	1	the	the	DET
uva.x030312957	53	2	theory	theory	NOUN
uva.x030312957	53	3	of	of	ADP
uva.x030312957	53	4	the	the	DET
uva.x030312957	53	5	secular	secular	ADJ
uva.x030312957	53	6	variations	variation	NOUN
uva.x030312957	53	7	of	of	ADP
uva.x030312957	53	8	the	the	DET
uva.x030312957	53	9	elements	element	NOUN
uva.x030312957	53	10	arose	arise	VERB
uva.x030312957	53	11	because	because	SCONJ
uva.x030312957	53	12	in	in	ADP
uva.x030312957	53	13	the	the	DET
uva.x030312957	53	14	customary	customary	ADJ
uva.x030312957	53	15	procedure	procedure	NOUN
uva.x030312957	53	16	of	of	ADP
uva.x030312957	53	17	the	the	DET
uva.x030312957	53	18	integration	integration	NOUN
uva.x030312957	53	19	through	through	ADP
uva.x030312957	53	20	series	series	NOUN
uva.x030312957	53	21	,	,	PUNCT
uva.x030312957	53	22	terms	term	NOUN
uva.x030312957	53	23	were	be	AUX
uva.x030312957	53	24	produced	produce	VERB
uva.x030312957	53	25	which	which	PRON
uva.x030312957	53	26	were	be	AUX
uva.x030312957	53	27	proportional	proportional	ADJ
uva.x030312957	53	28	to	to	ADP
uva.x030312957	53	29	the	the	DET
uva.x030312957	53	30	time	time	NOUN
uva.x030312957	53	31	.	.	PUNCT
uva.x030312957	54	1	euler	euler	PROPN
uva.x030312957	54	2	,	,	PUNCT
uva.x030312957	54	3	lagrange	lagrange	PROPN
uva.x030312957	54	4	and	and	CCONJ
uva.x030312957	54	5	laplace	laplace	NOUN
uva.x030312957	54	6	now	now	ADV
uva.x030312957	54	7	concentrated	concentrate	VERB
uva.x030312957	54	8	their	their	PRON
uva.x030312957	54	9	reflections	reflection	NOUN
uva.x030312957	54	10	on	on	ADP
uva.x030312957	54	11	the	the	DET
uva.x030312957	54	12	effort	effort	NOUN
uva.x030312957	54	13	to	to	PART
uva.x030312957	54	14	remove	remove	VERB
uva.x030312957	54	15	these	these	DET
uva.x030312957	54	16	terms	term	NOUN
uva.x030312957	54	17	.	.	PUNCT
uva.x030312957	55	1	soon	soon	ADV
uva.x030312957	55	2	the	the	PRON
uva.x030312957	55	3	by	by	ADP
uva.x030312957	55	4	a	a	DET
uva.x030312957	55	5	method	method	NOUN
uva.x030312957	55	6	due	due	ADP
uva.x030312957	55	7	to	to	ADP
uva.x030312957	55	8	hermite	hermite	NOUN
uva.x030312957	55	9	3	3	NUM
uva.x030312957	55	10	self	self	NOUN
uva.x030312957	55	11	-	-	PUNCT
uva.x030312957	55	12	evident	evident	ADJ
uva.x030312957	55	13	fact	fact	NOUN
uva.x030312957	55	14	that	that	SCONJ
uva.x030312957	55	15	the	the	DET
uva.x030312957	55	16	theory	theory	NOUN
uva.x030312957	55	17	of	of	ADP
uva.x030312957	55	18	absolute	absolute	ADJ
uva.x030312957	55	19	disturbances	disturbance	NOUN
uva.x030312957	55	20	of	of	ADP
uva.x030312957	55	21	the	the	DET
uva.x030312957	55	22	planetary	planetary	ADJ
uva.x030312957	55	23	system	system	NOUN
uva.x030312957	55	24	was	be	AUX
uva.x030312957	55	25	not	not	PART
uva.x030312957	55	26	the	the	DET
uva.x030312957	55	27	most	most	ADV
uva.x030312957	55	28	suitable	suitable	ADJ
uva.x030312957	55	29	,	,	PUNCT
uva.x030312957	55	30	caused	cause	VERB
uva.x030312957	55	31	the	the	DET
uva.x030312957	55	32	theory	theory	NOUN
uva.x030312957	55	33	of	of	ADP
uva.x030312957	55	34	the	the	DET
uva.x030312957	55	35	variations	variation	NOUN
uva.x030312957	55	36	of	of	ADP
uva.x030312957	55	37	the	the	DET
uva.x030312957	55	38	constants	constant	NOUN
uva.x030312957	55	39	to	to	PART
uva.x030312957	55	40	be	be	AUX
uva.x030312957	55	41	introduced	introduce	VERB
uva.x030312957	55	42	,	,	PUNCT
uva.x030312957	55	43	not	not	PART
uva.x030312957	55	44	at	at	ADP
uva.x030312957	55	45	first	first	ADV
uva.x030312957	55	46	fully	fully	ADV
uva.x030312957	55	47	clear	clear	ADJ
uva.x030312957	55	48	,	,	PUNCT
uva.x030312957	55	49	but	but	CCONJ
uva.x030312957	55	50	mixed	mix	VERB
uva.x030312957	55	51	with	with	ADP
uva.x030312957	55	52	the	the	DET
uva.x030312957	55	53	former	former	ADJ
uva.x030312957	55	54	theory	theory	NOUN
uva.x030312957	55	55	.	.	PUNCT
uva.x030312957	56	1	it	it	PRON
uva.x030312957	56	2	was	be	AUX
uva.x030312957	56	3	evident	evident	ADJ
uva.x030312957	56	4	that	that	SCONJ
uva.x030312957	56	5	the	the	DET
uva.x030312957	56	6	secular	secular	ADJ
uva.x030312957	56	7	terms	term	NOUN
uva.x030312957	56	8	must	must	AUX
uva.x030312957	56	9	endure	endure	VERB
uva.x030312957	56	10	,	,	PUNCT
uva.x030312957	56	11	but	but	CCONJ
uva.x030312957	56	12	instead	instead	ADV
uva.x030312957	56	13	of	of	ADP
uva.x030312957	56	14	determining	determine	VERB
uva.x030312957	56	15	it	it	PRON
uva.x030312957	56	16	directly	directly	ADV
uva.x030312957	56	17	it	it	PRON
uva.x030312957	56	18	was	be	AUX
uva.x030312957	56	19	grasped	grasp	VERB
uva.x030312957	56	20	in	in	ADP
uva.x030312957	56	21	a	a	DET
uva.x030312957	56	22	roundabout	roundabout	ADJ
uva.x030312957	56	23	way	way	NOUN
uva.x030312957	56	24	.	.	PUNCT
uva.x030312957	57	1	this	this	PRON
uva.x030312957	57	2	was	be	AUX
uva.x030312957	57	3	clearly	clearly	ADV
uva.x030312957	57	4	seen	see	VERB
uva.x030312957	57	5	in	in	ADP
uva.x030312957	57	6	laplace	laplace	PROPN
uva.x030312957	57	7	's	's	PART
uva.x030312957	57	8	mécanique	mécanique	ADJ
uva.x030312957	57	9	céleste	céleste	NOUN
uva.x030312957	57	10	where	where	SCONJ
uva.x030312957	57	11	,	,	PUNCT
uva.x030312957	57	12	in	in	ADP
uva.x030312957	57	13	the	the	DET
uva.x030312957	57	14	expression	expression	NOUN
uva.x030312957	57	15	for	for	ADP
uva.x030312957	57	16	the	the	DET
uva.x030312957	57	17	absolute	absolute	ADJ
uva.x030312957	57	18	disturbance	disturbance	NOUN
uva.x030312957	57	19	of	of	ADP
uva.x030312957	57	20	the	the	DET
uva.x030312957	57	21	coördinates	coördinate	NOUN
uva.x030312957	57	22	,	,	PUNCT
uva.x030312957	57	23	he	he	PRON
uva.x030312957	57	24	ingeniously	ingeniously	ADV
uva.x030312957	57	25	withdrew	withdraw	VERB
uva.x030312957	57	26	the	the	DET
uva.x030312957	57	27	terms	term	NOUN
uva.x030312957	57	28	which	which	PRON
uva.x030312957	57	29	were	be	AUX
uva.x030312957	57	30	proportional	proportional	ADJ
uva.x030312957	57	31	to	to	ADP
uva.x030312957	57	32	the	the	DET
uva.x030312957	57	33	time	time	NOUN
uva.x030312957	57	34	,	,	PUNCT
uva.x030312957	57	35	and	and	CCONJ
uva.x030312957	57	36	then	then	ADV
uva.x030312957	57	37	after	after	ADP
uva.x030312957	57	38	the	the	DET
uva.x030312957	57	39	introduction	introduction	NOUN
uva.x030312957	57	40	of	of	ADP
uva.x030312957	57	41	the	the	DET
uva.x030312957	57	42	full	full	ADJ
uva.x030312957	57	43	theory	theory	NOUN
uva.x030312957	57	44	of	of	ADP
uva.x030312957	57	45	the	the	DET
uva.x030312957	57	46	variation	variation	NOUN
uva.x030312957	57	47	of	of	ADP
uva.x030312957	57	48	the	the	DET
uva.x030312957	57	49	constants	constant	NOUN
uva.x030312957	57	50	to	to	ADP
uva.x030312957	57	51	the	the	DET
uva.x030312957	57	52	integration	integration	NOUN
uva.x030312957	57	53	he	he	PRON
uva.x030312957	57	54	found	find	VERB
uva.x030312957	57	55	the	the	DET
uva.x030312957	57	56	secular	secular	ADJ
uva.x030312957	57	57	terms	term	NOUN
uva.x030312957	57	58	of	of	ADP
uva.x030312957	57	59	the	the	DET
uva.x030312957	57	60	disturbance	disturbance	NOUN
uva.x030312957	57	61	theorem	theorem	NOUN
uva.x030312957	57	62	retained	retain	VERB
uva.x030312957	57	63	.	.	PUNCT
uva.x030312957	58	1	poisson	poisson	PROPN
uva.x030312957	58	2	proved	prove	VERB
uva.x030312957	58	3	in	in	ADP
uva.x030312957	58	4	1809	1809	NUM
uva.x030312957	58	5	,	,	PUNCT
uva.x030312957	58	6	in	in	ADP
uva.x030312957	58	7	the	the	DET
uva.x030312957	58	8	treatise	treatise	NOUN
uva.x030312957	58	9	“	"	PUNCT
uva.x030312957	58	10	sur	sur	X
uva.x030312957	58	11	les	les	X
uva.x030312957	58	12	inégalités	inégalités	X
uva.x030312957	58	13	séculaires	séculaire	NOUN
uva.x030312957	58	14	des	des	X
uva.x030312957	58	15	moyens	moyens	X
uva.x030312957	58	16	movements	movement	NOUN
uva.x030312957	58	17	des	des	X
uva.x030312957	58	18	planètes	planète	NOUN
uva.x030312957	58	19	”	"	PUNCT
uva.x030312957	58	20	(	(	PUNCT
uva.x030312957	58	21	journal	journal	PROPN
uva.x030312957	58	22	de	de	PROPN
uva.x030312957	58	23	l'école	l'école	PROPN
uva.x030312957	58	24	polytechnique	polytechnique	NOUN
uva.x030312957	58	25	)	)	PUNCT
uva.x030312957	58	26	,	,	PUNCT
uva.x030312957	58	27	that	that	SCONJ
uva.x030312957	58	28	the	the	DET
uva.x030312957	58	29	major	major	ADJ
uva.x030312957	58	30	axes	axis	NOUN
uva.x030312957	58	31	have	have	VERB
uva.x030312957	58	32	no	no	DET
uva.x030312957	58	33	purely	purely	ADV
uva.x030312957	58	34	secular	secular	ADJ
uva.x030312957	58	35	terms	term	NOUN
uva.x030312957	58	36	in	in	ADP
uva.x030312957	58	37	the	the	DET
uva.x030312957	58	38	perturbations	perturbation	NOUN
uva.x030312957	58	39	of	of	ADP
uva.x030312957	58	40	the	the	DET
uva.x030312957	58	41	second	second	ADJ
uva.x030312957	58	42	order	order	NOUN
uva.x030312957	58	43	with	with	ADP
uva.x030312957	58	44	respect	respect	NOUN
uva.x030312957	58	45	to	to	ADP
uva.x030312957	58	46	the	the	DET
uva.x030312957	58	47	masses	masse	NOUN
uva.x030312957	58	48	.	.	PUNCT
uva.x030312957	59	1	he	he	PRON
uva.x030312957	59	2	arrived	arrive	VERB
uva.x030312957	59	3	at	at	ADP
uva.x030312957	59	4	his	his	PRON
uva.x030312957	59	5	results	result	NOUN
uva.x030312957	59	6	by	by	ADP
uva.x030312957	59	7	a	a	DET
uva.x030312957	59	8	peculiar	peculiar	ADJ
uva.x030312957	59	9	application	application	NOUN
uva.x030312957	59	10	of	of	ADP
uva.x030312957	59	11	the	the	DET
uva.x030312957	59	12	theorem	theorem	NOUN
uva.x030312957	59	13	of	of	ADP
uva.x030312957	59	14	active	active	ADJ
uva.x030312957	59	15	forces	force	NOUN
uva.x030312957	59	16	.	.	PUNCT
uva.x030312957	60	1	laplace	laplace	PROPN
uva.x030312957	60	2	,	,	PUNCT
uva.x030312957	60	3	in	in	ADP
uva.x030312957	60	4	his	his	PRON
uva.x030312957	60	5	mécanique	mécanique	ADJ
uva.x030312957	60	6	céleste	céleste	NOUN
uva.x030312957	60	7	,	,	PUNCT
uva.x030312957	60	8	livre	livre	PROPN
uva.x030312957	60	9	vi	vi	PROPN
uva.x030312957	60	10	,	,	PUNCT
uva.x030312957	60	11	gave	give	VERB
uva.x030312957	60	12	another	another	DET
uva.x030312957	60	13	proof	proof	NOUN
uva.x030312957	60	14	,	,	PUNCT
uva.x030312957	60	15	and	and	CCONJ
uva.x030312957	60	16	lagrange	lagrange	PROPN
uva.x030312957	60	17	had	have	AUX
uva.x030312957	60	18	sought	seek	VERB
uva.x030312957	60	19	to	to	PART
uva.x030312957	60	20	furnish	furnish	VERB
uva.x030312957	60	21	this	this	DET
uva.x030312957	60	22	proof	proof	NOUN
uva.x030312957	60	23	but	but	CCONJ
uva.x030312957	60	24	serret	serret	ADJ
uva.x030312957	60	25	has	have	AUX
uva.x030312957	60	26	shown	show	VERB
uva.x030312957	60	27	that	that	SCONJ
uva.x030312957	60	28	his	his	PRON
uva.x030312957	60	29	procedure	procedure	NOUN
uva.x030312957	60	30	suffered	suffer	VERB
uva.x030312957	60	31	a	a	DET
uva.x030312957	60	32	slight	slight	ADJ
uva.x030312957	60	33	mistake	mistake	NOUN
uva.x030312957	60	34	in	in	ADP
uva.x030312957	60	35	sign	sign	NOUN
uva.x030312957	60	36	.	.	PUNCT
uva.x030312957	61	1	it	it	PRON
uva.x030312957	61	2	was	be	AUX
uva.x030312957	61	3	sought	seek	VERB
uva.x030312957	61	4	to	to	PART
uva.x030312957	61	5	extend	extend	VERB
uva.x030312957	61	6	this	this	DET
uva.x030312957	61	7	result	result	NOUN
uva.x030312957	61	8	to	to	ADP
uva.x030312957	61	9	the	the	DET
uva.x030312957	61	10	third	third	ADJ
uva.x030312957	61	11	power	power	NOUN
uva.x030312957	61	12	of	of	ADP
uva.x030312957	61	13	the	the	DET
uva.x030312957	61	14	disturbing	disturbing	ADJ
uva.x030312957	61	15	masses	masse	NOUN
uva.x030312957	61	16	.	.	PUNCT
uva.x030312957	62	1	thus	thus	ADV
uva.x030312957	62	2	mathiew	mathiew	NOUN
uva.x030312957	62	3	,	,	PUNCT
uva.x030312957	62	4	in	in	ADP
uva.x030312957	62	5	his	his	PRON
uva.x030312957	62	6	“	"	PUNCT
uva.x030312957	62	7	memoire	memoire	PROPN
uva.x030312957	62	8	sur	sur	X
uva.x030312957	62	9	les	les	X
uva.x030312957	62	10	inégalités	inégalités	X
uva.x030312957	62	11	séculaires	séculaire	NOUN
uva.x030312957	62	12	des	des	X
uva.x030312957	62	13	grands	grand	VERB
uva.x030312957	62	14	axes	axis	NOUN
uva.x030312957	62	15	des	des	X
uva.x030312957	62	16	orbits	orbit	NOUN
uva.x030312957	62	17	des	des	X
uva.x030312957	62	18	planètes	planète	NOUN
uva.x030312957	62	19	”	"	PUNCT
uva.x030312957	62	20	(	(	PUNCT
uva.x030312957	62	21	journal	journal	PROPN
uva.x030312957	62	22	von	von	PROPN
uva.x030312957	62	23	crelle	crelle	PROPN
uva.x030312957	62	24	,	,	PUNCT
uva.x030312957	62	25	1875	1875	NUM
uva.x030312957	62	26	)	)	PUNCT
uva.x030312957	62	27	,	,	PUNCT
uva.x030312957	62	28	began	begin	VERB
uva.x030312957	62	29	investigations	investigation	NOUN
uva.x030312957	62	30	from	from	ADP
uva.x030312957	62	31	which	which	PRON
uva.x030312957	62	32	he	he	PRON
uva.x030312957	62	33	concluded	conclude	VERB
uva.x030312957	62	34	that	that	SCONJ
uva.x030312957	62	35	the	the	DET
uva.x030312957	62	36	secular	secular	ADJ
uva.x030312957	62	37	terms	term	NOUN
uva.x030312957	62	38	did	do	AUX
uva.x030312957	62	39	not	not	PART
uva.x030312957	62	40	appear	appear	VERB
uva.x030312957	62	41	even	even	ADV
uva.x030312957	62	42	in	in	ADP
uva.x030312957	62	43	the	the	DET
uva.x030312957	62	44	consideration	consideration	NOUN
uva.x030312957	62	45	of	of	ADP
uva.x030312957	62	46	the	the	DET
uva.x030312957	62	47	third	third	ADJ
uva.x030312957	62	48	powers	power	NOUN
uva.x030312957	62	49	.	.	PUNCT
uva.x030312957	63	1	but	but	CCONJ
uva.x030312957	63	2	finally	finally	ADV
uva.x030312957	63	3	,	,	PUNCT
uva.x030312957	63	4	harétu	harétu	NOUN
uva.x030312957	63	5	proved	prove	VERB
uva.x030312957	63	6	,	,	PUNCT
uva.x030312957	63	7	in	in	ADP
uva.x030312957	63	8	his	his	PRON
uva.x030312957	63	9	dissertation	dissertation	NOUN
uva.x030312957	63	10	at	at	ADP
uva.x030312957	63	11	sorbonne	sorbonne	NOUN
uva.x030312957	63	12	in	in	ADP
uva.x030312957	63	13	1878	1878	NUM
uva.x030312957	63	14	,	,	PUNCT
uva.x030312957	63	15	that	that	SCONJ
uva.x030312957	63	16	there	there	PRON
uva.x030312957	63	17	are	be	VERB
uva.x030312957	63	18	secular	secular	ADJ
uva.x030312957	63	19	variations	variation	NOUN
uva.x030312957	63	20	in	in	ADP
uva.x030312957	63	21	the	the	DET
uva.x030312957	63	22	expressions	expression	NOUN
uva.x030312957	63	23	for	for	ADP
uva.x030312957	63	24	the	the	DET
uva.x030312957	63	25	major	major	ADJ
uva.x030312957	63	26	axes	axis	NOUN
uva.x030312957	63	27	in	in	ADP
uva.x030312957	63	28	the	the	DET
uva.x030312957	63	29	terms	term	NOUN
uva.x030312957	63	30	of	of	ADP
uva.x030312957	63	31	the	the	DET
uva.x030312957	63	32	third	third	ADJ
uva.x030312957	63	33	order	order	NOUN
uva.x030312957	63	34	with	with	ADP
uva.x030312957	63	35	respect	respect	VERB
uva.x030312957	63	36	the	the	DET
uva.x030312957	63	37	masses	masse	NOUN
uva.x030312957	63	38	.	.	PUNCT
uva.x030312957	64	1	the	the	DET
uva.x030312957	64	2	analytical	analytical	ADJ
uva.x030312957	64	3	and	and	CCONJ
uva.x030312957	64	4	numerical	numerical	ADJ
uva.x030312957	64	5	development	development	NOUN
uva.x030312957	64	6	of	of	ADP
uva.x030312957	64	7	the	the	DET
uva.x030312957	64	8	disturbance	disturbance	NOUN
uva.x030312957	64	9	functions	function	NOUN
uva.x030312957	64	10	,	,	PUNCT
uva.x030312957	64	11	when	when	SCONJ
uva.x030312957	64	12	considering	consider	VERB
uva.x030312957	64	13	higher	high	ADJ
uva.x030312957	64	14	powers	power	NOUN
uva.x030312957	64	15	of	of	ADP
uva.x030312957	64	16	the	the	DET
uva.x030312957	64	17	eccentricity	eccentricity	NOUN
uva.x030312957	64	18	and	and	CCONJ
uva.x030312957	64	19	inclination	inclination	NOUN
uva.x030312957	64	20	,	,	PUNCT
uva.x030312957	64	21	led	lead	VERB
uva.x030312957	64	22	to	to	ADP
uva.x030312957	64	23	such	such	ADJ
uva.x030312957	64	24	interesting	interesting	ADJ
uva.x030312957	64	25	and	and	CCONJ
uva.x030312957	64	26	important	important	ADJ
uva.x030312957	64	27	computations	computation	NOUN
uva.x030312957	64	28	that	that	SCONJ
uva.x030312957	64	29	the	the	DET
uva.x030312957	64	30	majority	majority	NOUN
uva.x030312957	64	31	of	of	ADP
uva.x030312957	64	32	the	the	DET
uva.x030312957	64	33	important	important	ADJ
uva.x030312957	64	34	mathematicians	mathematician	NOUN
uva.x030312957	64	35	have	have	AUX
uva.x030312957	64	36	taken	take	VERB
uva.x030312957	64	37	pains	pain	NOUN
uva.x030312957	64	38	with	with	ADP
uva.x030312957	64	39	it	it	PRON
uva.x030312957	64	40	and	and	CCONJ
uva.x030312957	64	41	advanced	advance	VERB
uva.x030312957	64	42	it	it	PRON
uva.x030312957	64	43	.	.	PUNCT
uva.x030312957	65	1	among	among	ADP
uva.x030312957	65	2	these	these	PRON
uva.x030312957	65	3	we	we	PRON
uva.x030312957	65	4	find	find	VERB
uva.x030312957	65	5	cauchy	cauchy	ADJ
uva.x030312957	65	6	,	,	PUNCT
uva.x030312957	65	7	bessel	bessel	PROPN
uva.x030312957	65	8	,	,	PUNCT
uva.x030312957	65	9	lubback	lubback	PROPN
uva.x030312957	65	10	,	,	PUNCT
uva.x030312957	65	11	hansen	hansen	PROPN
uva.x030312957	65	12	,	,	PUNCT
uva.x030312957	65	13	glyden	glyden	PROPN
uva.x030312957	65	14	,	,	PUNCT
uva.x030312957	65	15	newcomb	newcomb	PROPN
uva.x030312957	65	16	and	and	CCONJ
uva.x030312957	65	17	others	other	NOUN
uva.x030312957	65	18	.	.	PUNCT
uva.x030312957	66	1	gauss	gauss	PROPN
uva.x030312957	66	2	,	,	PUNCT
uva.x030312957	66	3	airy	airy	PROPN
uva.x030312957	66	4	,	,	PUNCT
uva.x030312957	66	5	adams	adams	PROPN
uva.x030312957	66	6	,	,	PUNCT
uva.x030312957	66	7	leverrier	leverrier	X
uva.x030312957	66	8	and	and	CCONJ
uva.x030312957	66	9	many	many	ADJ
uva.x030312957	66	10	others	other	NOUN
uva.x030312957	66	11	have	have	AUX
uva.x030312957	66	12	made	make	VERB
uva.x030312957	66	13	important	important	ADJ
uva.x030312957	66	14	contributions	contribution	NOUN
uva.x030312957	66	15	to	to	ADP
uva.x030312957	66	16	the	the	DET
uva.x030312957	66	17	planetary	planetary	ADJ
uva.x030312957	66	18	theory	theory	NOUN
uva.x030312957	66	19	in	in	ADP
uva.x030312957	66	20	some	some	PRON
uva.x030312957	66	21	of	of	ADP
uva.x030312957	66	22	its	its	PRON
uva.x030312957	66	23	many	many	ADJ
uva.x030312957	66	24	aspects	aspect	NOUN
uva.x030312957	66	25	.	.	PUNCT
uva.x030312957	67	1	adams	adam	NOUN
uva.x030312957	67	2	and	and	CCONJ
uva.x030312957	67	3	leverrier	leverrier	NOUN
uva.x030312957	67	4	obtained	obtain	VERB
uva.x030312957	67	5	particular	particular	ADJ
uva.x030312957	67	6	prominence	prominence	NOUN
uva.x030312957	67	7	by	by	ADP
uva.x030312957	67	8	demonstrating	demonstrate	VERB
uva.x030312957	67	9	the	the	DET
uva.x030312957	67	10	existence	existence	NOUN
uva.x030312957	67	11	of	of	ADP
uva.x030312957	67	12	neptune	neptune	NOUN
uva.x030312957	67	13	and	and	CCONJ
uva.x030312957	67	14	calculating	calculate	VERB
uva.x030312957	67	15	its	its	PRON
uva.x030312957	67	16	apparent	apparent	ADJ
uva.x030312957	67	17	position	position	NOUN
uva.x030312957	67	18	from	from	ADP
uva.x030312957	67	19	the	the	DET
uva.x030312957	67	20	unexplained	unexplained	ADJ
uva.x030312957	67	21	irregularities	irregularity	NOUN
uva.x030312957	67	22	in	in	ADP
uva.x030312957	67	23	the	the	DET
uva.x030312957	67	24	motion	motion	NOUN
uva.x030312957	67	25	of	of	ADP
uva.x030312957	67	26	uranus	uranus	NOUN
uva.x030312957	67	27	.	.	PUNCT
uva.x030312957	68	1	the	the	DET
uva.x030312957	68	2	secular	secular	ADJ
uva.x030312957	68	3	value	value	NOUN
uva.x030312957	68	4	of	of	ADP
uva.x030312957	68	5	the	the	DET
uva.x030312957	68	6	elements	element	NOUN
uva.x030312957	68	7	had	have	AUX
uva.x030312957	68	8	been	be	AUX
uva.x030312957	68	9	developed	develop	VERB
uva.x030312957	68	10	by	by	ADP
uva.x030312957	68	11	laplace	laplace	NOUN
uva.x030312957	68	12	and	and	CCONJ
uva.x030312957	68	13	lagrange	lagrange	PROPN
uva.x030312957	68	14	,	,	PUNCT
uva.x030312957	68	15	limiting	limit	VERB
uva.x030312957	68	16	their	their	PRON
uva.x030312957	68	17	discussion	discussion	NOUN
uva.x030312957	68	18	to	to	ADP
uva.x030312957	68	19	the	the	DET
uva.x030312957	68	20	second	second	ADJ
uva.x030312957	68	21	power	power	NOUN
uva.x030312957	68	22	of	of	ADP
uva.x030312957	68	23	the	the	DET
uva.x030312957	68	24	eccentricity	eccentricity	NOUN
uva.x030312957	68	25	and	and	CCONJ
uva.x030312957	68	26	inclination	inclination	NOUN
uva.x030312957	68	27	.	.	PUNCT
uva.x030312957	69	1	according	accord	VERB
uva.x030312957	69	2	to	to	ADP
uva.x030312957	69	3	dziobek	dziobek	NOUN
uva.x030312957	69	4	it	it	PRON
uva.x030312957	69	5	was	be	AUX
uva.x030312957	69	6	leverrier	leverri	ADJ
uva.x030312957	69	7	who	who	PRON
uva.x030312957	69	8	first	first	ADV
uva.x030312957	69	9	attempted	attempt	VERB
uva.x030312957	69	10	to	to	PART
uva.x030312957	69	11	consider	consider	VERB
uva.x030312957	69	12	the	the	DET
uva.x030312957	69	13	influence	influence	NOUN
uva.x030312957	69	14	of	of	ADP
uva.x030312957	69	15	the	the	DET
uva.x030312957	69	16	neglected	neglect	VERB
uva.x030312957	69	17	terms	term	NOUN
uva.x030312957	69	18	.	.	PUNCT
uva.x030312957	70	1	later	later	ADV
uva.x030312957	70	2	his	his	PRON
uva.x030312957	70	3	investigations	investigation	NOUN
uva.x030312957	70	4	were	be	AUX
uva.x030312957	70	5	carried	carry	VERB
uva.x030312957	70	6	further	far	ADV
uva.x030312957	70	7	by	by	ADP
uva.x030312957	70	8	the	the	DET
uva.x030312957	70	9	astronomer	astronomer	PROPN
uva.x030312957	70	10	lehmann	lehmann	PROPN
uva.x030312957	70	11	,	,	PUNCT
uva.x030312957	70	12	who	who	PRON
uva.x030312957	70	13	,	,	PUNCT
uva.x030312957	70	14	however	however	ADV
uva.x030312957	70	15	,	,	PUNCT
uva.x030312957	70	16	died	die	VERB
uva.x030312957	70	17	before	before	ADP
uva.x030312957	70	18	com4	com4	PROPN
uva.x030312957	70	19	solution	solution	NOUN
uva.x030312957	70	20	of	of	ADP
uva.x030312957	70	21	the	the	DET
uva.x030312957	70	22	equation	equation	NOUN
uva.x030312957	70	23	of	of	ADP
uva.x030312957	70	24	secular	secular	ADJ
uva.x030312957	70	25	variation	variation	NOUN
uva.x030312957	70	26	pleting	plete	VERB
uva.x030312957	70	27	his	his	PRON
uva.x030312957	70	28	numerical	numerical	ADJ
uva.x030312957	70	29	investigation	investigation	NOUN
uva.x030312957	70	30	.	.	PUNCT
uva.x030312957	71	1	it	it	PRON
uva.x030312957	71	2	was	be	AUX
uva.x030312957	71	3	the	the	DET
uva.x030312957	71	4	opinion	opinion	NOUN
uva.x030312957	71	5	of	of	ADP
uva.x030312957	71	6	leverrier	leverrier	NOUN
uva.x030312957	71	7	and	and	CCONJ
uva.x030312957	71	8	lehmann	lehmann	PROPN
uva.x030312957	71	9	that	that	SCONJ
uva.x030312957	71	10	the	the	DET
uva.x030312957	71	11	influence	influence	NOUN
uva.x030312957	71	12	of	of	ADP
uva.x030312957	71	13	these	these	DET
uva.x030312957	71	14	terms	term	NOUN
uva.x030312957	71	15	is	be	AUX
uva.x030312957	71	16	greater	great	ADJ
uva.x030312957	71	17	than	than	SCONJ
uva.x030312957	71	18	was	be	AUX
uva.x030312957	71	19	earlier	early	ADV
uva.x030312957	71	20	supposed	suppose	VERB
uva.x030312957	71	21	,	,	PUNCT
uva.x030312957	71	22	and	and	CCONJ
uva.x030312957	71	23	would	would	AUX
uva.x030312957	71	24	possibly	possibly	ADV
uva.x030312957	71	25	bring	bring	VERB
uva.x030312957	71	26	great	great	ADJ
uva.x030312957	71	27	improvement	improvement	NOUN
uva.x030312957	71	28	on	on	ADP
uva.x030312957	71	29	the	the	DET
uva.x030312957	71	30	secular	secular	ADJ
uva.x030312957	71	31	periods	period	NOUN
uva.x030312957	71	32	,	,	PUNCT
uva.x030312957	71	33	as	as	SCONJ
uva.x030312957	71	34	they	they	PRON
uva.x030312957	71	35	would	would	AUX
uva.x030312957	71	36	be	be	AUX
uva.x030312957	71	37	fixed	fix	VERB
uva.x030312957	71	38	through	through	ADP
uva.x030312957	71	39	the	the	DET
uva.x030312957	71	40	roots	root	NOUN
uva.x030312957	71	41	of	of	ADP
uva.x030312957	71	42	the	the	DET
uva.x030312957	71	43	secular	secular	ADJ
uva.x030312957	71	44	equation	equation	NOUN
uva.x030312957	71	45	.	.	PUNCT
uva.x030312957	72	1	the	the	DET
uva.x030312957	72	2	secular	secular	ADJ
uva.x030312957	72	3	equation	equation	NOUN
uva.x030312957	72	4	the	the	DET
uva.x030312957	72	5	way	way	NOUN
uva.x030312957	72	6	the	the	DET
uva.x030312957	72	7	secular	secular	ADJ
uva.x030312957	72	8	equation	equation	NOUN
uva.x030312957	72	9	enters	enter	NOUN
uva.x030312957	72	10	is	be	AUX
uva.x030312957	72	11	shown	show	VERB
uva.x030312957	72	12	by	by	ADP
uva.x030312957	72	13	the	the	DET
uva.x030312957	72	14	following	follow	VERB
uva.x030312957	72	15	treatment	treatment	NOUN
uva.x030312957	72	16	taken	take	VERB
uva.x030312957	72	17	from	from	ADP
uva.x030312957	72	18	dziobek	dziobek	PROPN
uva.x030312957	72	19	.	.	PUNCT
uva.x030312957	72	20	*	*	PUNCT
uva.x030312957	73	1	the	the	DET
uva.x030312957	73	2	secular	secular	ADJ
uva.x030312957	73	3	part	part	NOUN
uva.x030312957	73	4	of	of	ADP
uva.x030312957	73	5	the	the	DET
uva.x030312957	73	6	disturbance	disturbance	NOUN
uva.x030312957	73	7	functions	function	NOUN
uva.x030312957	73	8	depends	depend	VERB
uva.x030312957	73	9	on	on	ADP
uva.x030312957	73	10	the	the	DET
uva.x030312957	73	11	quantity	quantity	NOUN
uva.x030312957	73	12	w	w	ADP
uva.x030312957	73	13	т	т	PROPN
uva.x030312957	73	14	,	,	PUNCT
uva.x030312957	73	15	т	т	PROPN
uva.x030312957	73	16	σ	σ	PROPN
uva.x030312957	73	17	γλμ	γλμ	PROPN
uva.x030312957	73	18	when	when	SCONJ
uva.x030312957	73	19	limiting	limit	VERB
uva.x030312957	73	20	the	the	DET
uva.x030312957	73	21	secular	secular	ADJ
uva.x030312957	73	22	part	part	NOUN
uva.x030312957	73	23	,	,	PUNCT
uva.x030312957	73	24	w	w	PROPN
uva.x030312957	73	25	,	,	PUNCT
uva.x030312957	73	26	of	of	ADP
uva.x030312957	73	27	the	the	DET
uva.x030312957	73	28	disturbance	disturbance	NOUN
uva.x030312957	73	29	function	function	NOUN
uva.x030312957	73	30	to	to	ADP
uva.x030312957	73	31	the	the	DET
uva.x030312957	73	32	terms	term	NOUN
uva.x030312957	73	33	of	of	ADP
uva.x030312957	73	34	second	second	ADJ
uva.x030312957	73	35	degree	degree	NOUN
uva.x030312957	73	36	of	of	ADP
uva.x030312957	73	37	the	the	DET
uva.x030312957	73	38	eccentricity	eccentricity	NOUN
uva.x030312957	73	39	and	and	CCONJ
uva.x030312957	73	40	inclination	inclination	NOUN
uva.x030312957	73	41	,	,	PUNCT
uva.x030312957	73	42	w	w	NOUN
uva.x030312957	73	43	reduces	reduce	VERB
uva.x030312957	73	44	to	to	ADP
uva.x030312957	73	45	tw	tw	X
uva.x030312957	73	46	em	em	PROPN
uva.x030312957	73	47	,	,	PUNCT
uva.x030312957	73	48	m.lil	m.lil	PROPN
uva.x030312957	73	49	,	,	PUNCT
uva.x030312957	73	50	+	+	PROPN
uva.x030312957	73	51	ziii	ziii	PROPN
uva.x030312957	73	52	:	:	PUNCT
uva.x030312957	73	53	{	{	PUNCT
uva.x030312957	73	54	hi	hi	INTJ
uva.x030312957	73	55	+	+	CCONJ
uva.x030312957	73	56	h	h	NOUN
uva.x030312957	74	1	+	+	NOUN
uva.x030312957	74	2	1	1	NUM
uva.x030312957	74	3	+	+	NUM
uva.x030312957	74	4	1	1	NUM
uva.x030312957	75	1	(	(	PUNCT
uva.x030312957	75	2	px	px	PROPN
uva.x030312957	75	3	–	–	PUNCT
uva.x030312957	75	4	pu	pu	PROPN
uva.x030312957	75	5	)	)	PUNCT
uva.x030312957	75	6	?	?	PUNCT
uva.x030312957	76	1	(	(	PUNCT
uva.x030312957	76	2	@a	@a	PROPN
uva.x030312957	76	3	)	)	PUNCT
uva.x030312957	76	4	}	}	PUNCT
uva.x030312957	76	5	{	{	PUNCT
uva.x030312957	76	6	iii	iii	X
uva.x030312957	76	7	(	(	PUNCT
uva.x030312957	76	8	h	h	PROPN
uva.x030312957	76	9	,	,	PUNCT
uva.x030312957	76	10	hy	hy	PROPN
uva.x030312957	76	11	+	+	PROPN
uva.x030312957	76	12	14	14	NUM
uva.x030312957	76	13	)	)	PUNCT
uva.x030312957	76	14	]	]	PUNCT
uva.x030312957	76	15	.	.	PUNCT
uva.x030312957	77	1	the	the	DET
uva.x030312957	77	2	differential	differential	ADJ
uva.x030312957	77	3	equations	equation	NOUN
uva.x030312957	77	4	of	of	ADP
uva.x030312957	77	5	motion	motion	NOUN
uva.x030312957	77	6	then	then	ADV
uva.x030312957	77	7	become	become	VERB
uva.x030312957	77	8	dh	dh	PROPN
uva.x030312957	77	9	,	,	PUNCT
uva.x030312957	77	10	1	1	NUM
uva.x030312957	77	11	mx	mx	X
uva.x030312957	77	12	dt	dt	X
uva.x030312957	77	13	aw	aw	INTJ
uva.x030312957	77	14	'	'	PUNCT
uva.x030312957	77	15	ala	ala	PROPN
uva.x030312957	77	16	'	'	PART
uva.x030312957	77	17	jux	jux	PROPN
uva.x030312957	77	18	ax	ax	PROPN
uva.x030312957	77	19	1	1	NUM
uva.x030312957	78	1	aw	aw	INTJ
uva.x030312957	78	2	dla	dla	NOUN
uva.x030312957	78	3	та	та	X
uva.x030312957	78	4	dt	dt	PROPN
uva.x030312957	78	5	vuxa	vuxa	PROPN
uva.x030312957	78	6	,	,	PUNCT
uva.x030312957	78	7	ah	ah	INTJ
uva.x030312957	78	8	,	,	PUNCT
uva.x030312957	78	9	:	:	PUNCT
uva.x030312957	78	10	(	(	PUNCT
uva.x030312957	78	11	1	1	NUM
uva.x030312957	78	12	=	=	SYM
uva.x030312957	78	13	1,2,	1,2,	PROPN
uva.x030312957	78	14	...	...	PUNCT
uva.x030312957	78	15	,n	,n	PUNCT
uva.x030312957	78	16	)	)	PUNCT
uva.x030312957	78	17	.	.	PUNCT
uva.x030312957	79	1	dpx	dpx	PROPN
uva.x030312957	79	2	ma	ma	PROPN
uva.x030312957	79	3	dt	dt	PROPN
uva.x030312957	79	4	1	1	NUM
uva.x030312957	79	5	alt	alt	PROPN
uva.x030312957	79	6	aga	aga	PROPN
uva.x030312957	79	7	>	>	X
uva.x030312957	79	8	vux	vux	PROPN
uva.x030312957	79	9	ax	ax	PROPN
uva.x030312957	79	10	1	1	NUM
uva.x030312957	79	11	aw	aw	INTJ
uva.x030312957	79	12	mx	mx	PROPN
uva.x030312957	79	13	da	da	PROPN
uva.x030312957	79	14	,	,	PUNCT
uva.x030312957	79	15	dt	dt	PROPN
uva.x030312957	79	16	mx	mx	PROPN
uva.x030312957	79	17	a	a	DET
uva.x030312957	79	18	apa	apa	PROPN
uva.x030312957	79	19	.	.	PUNCT
uva.x030312957	80	1	substitute	substitute	VERB
uva.x030312957	80	2	the	the	DET
uva.x030312957	80	3	value	value	NOUN
uva.x030312957	80	4	of	of	ADP
uva.x030312957	80	5	w	w	X
uva.x030312957	80	6	in	in	ADP
uva.x030312957	80	7	(	(	PUNCT
uva.x030312957	80	8	2	2	NUM
uva.x030312957	80	9	)	)	PUNCT
uva.x030312957	80	10	in	in	ADP
uva.x030312957	80	11	these	these	DET
uva.x030312957	80	12	differential	differential	ADJ
uva.x030312957	80	13	equations	equation	NOUN
uva.x030312957	80	14	,	,	PUNCT
uva.x030312957	80	15	limiting	limit	VERB
uva.x030312957	80	16	to	to	ADP
uva.x030312957	80	17	terms	term	NOUN
uva.x030312957	80	18	in	in	ADP
uva.x030312957	80	19	h	h	PROPN
uva.x030312957	80	20	and	and	CCONJ
uva.x030312957	80	21	l	l	NOUN
uva.x030312957	80	22	,	,	PUNCT
uva.x030312957	80	23	and	and	CCONJ
uva.x030312957	80	24	the	the	DET
uva.x030312957	80	25	result	result	NOUN
uva.x030312957	80	26	can	can	AUX
uva.x030312957	80	27	be	be	AUX
uva.x030312957	80	28	expressed	express	VERB
uva.x030312957	80	29	in	in	ADP
uva.x030312957	80	30	two	two	NUM
uva.x030312957	80	31	groups	group	NOUN
uva.x030312957	80	32	,	,	PUNCT
uva.x030312957	80	33	those	those	PRON
uva.x030312957	80	34	containing	contain	VERB
uva.x030312957	80	35	only	only	ADV
uva.x030312957	80	36	h	h	NOUN
uva.x030312957	80	37	,	,	PUNCT
uva.x030312957	80	38	and	and	CCONJ
uva.x030312957	80	39	those	those	PRON
uva.x030312957	80	40	containing	contain	VERB
uva.x030312957	80	41	only	only	ADV
uva.x030312957	80	42	l.	l.	PROPN
uva.x030312957	81	1	the	the	DET
uva.x030312957	81	2	two	two	NUM
uva.x030312957	81	3	groups	group	NOUN
uva.x030312957	81	4	are	be	AUX
uva.x030312957	81	5	brought	bring	VERB
uva.x030312957	81	6	down	down	ADP
uva.x030312957	81	7	in	in	ADP
uva.x030312957	81	8	final	final	ADJ
uva.x030312957	81	9	form	form	NOUN
uva.x030312957	81	10	to	to	ADP
uva.x030312957	81	11	a	a	DET
uva.x030312957	81	12	quadratic	quadratic	ADJ
uva.x030312957	81	13	form	form	NOUN
uva.x030312957	81	14	in	in	ADP
uva.x030312957	81	15	h.	h.	NOUN
uva.x030312957	81	16	and	and	CCONJ
uva.x030312957	81	17	l.	l.	NOUN
uva.x030312957	81	18	(	(	PUNCT
uva.x030312957	81	19	defined	define	VERB
uva.x030312957	81	20	in	in	ADP
uva.x030312957	81	21	(	(	PUNCT
uva.x030312957	81	22	8)	8)	NUM
uva.x030312957	81	23	,	,	PUNCT
uva.x030312957	81	24	page	page	NOUN
uva.x030312957	81	25	225	225	NUM
uva.x030312957	81	26	)	)	PUNCT
uva.x030312957	81	27	.	.	PUNCT
uva.x030312957	82	1	these	these	DET
uva.x030312957	82	2	quadratic	quadratic	ADJ
uva.x030312957	82	3	forms	form	NOUN
uva.x030312957	82	4	when	when	SCONJ
uva.x030312957	82	5	transformed	transform	VERB
uva.x030312957	82	6	by	by	ADP
uva.x030312957	82	7	linear	linear	ADJ
uva.x030312957	82	8	substitutions	substitution	NOUN
uva.x030312957	82	9	into	into	ADP
uva.x030312957	82	10	a	a	DET
uva.x030312957	82	11	sum	sum	NOUN
uva.x030312957	82	12	of	of	ADP
uva.x030312957	82	13	squares	square	NOUN
uva.x030312957	82	14	,	,	PUNCT
uva.x030312957	82	15	finally	finally	ADV
uva.x030312957	82	16	reduce	reduce	VERB
uva.x030312957	82	17	to	to	ADP
uva.x030312957	82	18	the	the	DET
uva.x030312957	82	19	set	set	NOUN
uva.x030312957	82	20	of	of	ADP
uva.x030312957	82	21	equations	equation	NOUN
uva.x030312957	82	22	,	,	PUNCT
uva.x030312957	82	23	*	*	PUNCT
uva.x030312957	82	24	dziobek	dziobek	ADJ
uva.x030312957	82	25	,	,	PUNCT
uva.x030312957	82	26	planeten	planeten	VERB
uva.x030312957	82	27	-	-	PUNCT
uva.x030312957	82	28	bewegungen	bewegungen	PROPN
uva.x030312957	82	29	,	,	PUNCT
uva.x030312957	82	30	pages	page	VERB
uva.x030312957	82	31	221	221	NUM
uva.x030312957	82	32	to	to	ADP
uva.x030312957	82	33	227	227	NUM
uva.x030312957	82	34	.	.	PUNCT
uva.x030312957	83	1	†	†	PROPN
uva.x030312957	83	2	(	(	PUNCT
uva.x030312957	83	3	2	2	NUM
uva.x030312957	83	4	)	)	PUNCT
uva.x030312957	83	5	,	,	PUNCT
uva.x030312957	83	6	$	$	SYM
uva.x030312957	83	7	31	31	NUM
uva.x030312957	83	8	,	,	PUNCT
uva.x030312957	83	9	page	page	NOUN
uva.x030312957	83	10	224	224	NUM
uva.x030312957	83	11	.	.	PUNCT
uva.x030312957	84	1	(	(	PUNCT
uva.x030312957	84	2	20	20	NUM
uva.x030312957	84	3	)	)	PUNCT
uva.x030312957	84	4	,	,	PUNCT
uva.x030312957	84	5	page	page	NOUN
uva.x030312957	84	6	227	227	NUM
uva.x030312957	84	7	.	.	PUNCT
uva.x030312957	85	1	by	by	ADP
uva.x030312957	85	2	a	a	DET
uva.x030312957	85	3	method	method	NOUN
uva.x030312957	85	4	due	due	ADP
uva.x030312957	85	5	to	to	ADP
uva.x030312957	85	6	hermite	hermite	NOUN
uva.x030312957	85	7	5	5	NUM
uva.x030312957	85	8	+	+	CCONJ
uva.x030312957	85	9	an	an	PRON
uva.x030312957	85	10	,	,	PUNCT
uva.x030312957	85	11	1	1	NUM
uva.x030312957	86	1	[	[	X
uva.x030312957	86	2	n	n	X
uva.x030312957	86	3	,	,	PUNCT
uva.x030312957	86	4	1	1	NUM
uva.x030312957	86	5	]	]	SYM
uva.x030312957	86	6	0	0	NUM
uva.x030312957	86	7	=	=	SYM
uva.x030312957	86	8	q1	q1	PROPN
uva.x030312957	86	9	,	,	PUNCT
uva.x030312957	86	10	1([1,1	1([1,1	NUM
uva.x030312957	86	11	]	]	PUNCT
uva.x030312957	86	12	–	–	PUNCT
uva.x030312957	86	13	91	91	NUM
uva.x030312957	86	14	)	)	PUNCT
uva.x030312957	86	15	+	+	CCONJ
uva.x030312957	86	16	q2	q2	PROPN
uva.x030312957	86	17	,	,	PUNCT
uva.x030312957	86	18	112	112	NUM
uva.x030312957	86	19	,	,	PUNCT
uva.x030312957	86	20	1	1	NUM
uva.x030312957	86	21	]	]	PUNCT
uva.x030312957	86	22	+	+	NUM
uva.x030312957	86	23	23	23	NUM
uva.x030312957	86	24	,	,	PUNCT
uva.x030312957	86	25	113	113	NUM
uva.x030312957	86	26	,	,	PUNCT
uva.x030312957	86	27	1	1	NUM
uva.x030312957	86	28	]	]	PUNCT
uva.x030312957	86	29	+	+	NUM
uva.x030312957	86	30	0	0	NUM
uva.x030312957	86	31	=	=	SYM
uva.x030312957	86	32	21	21	NUM
uva.x030312957	86	33	,	,	PUNCT
uva.x030312957	86	34	1[1	1[1	NUM
uva.x030312957	86	35	,	,	PUNCT
uva.x030312957	86	36	2	2	NUM
uva.x030312957	86	37	]	]	X
uva.x030312957	86	38	+	+	NUM
uva.x030312957	86	39	x2	x2	PROPN
uva.x030312957	86	40	,	,	PUNCT
uva.x030312957	86	41	1([2	1([2	NUM
uva.x030312957	86	42	,	,	PUNCT
uva.x030312957	86	43	2	2	NUM
uva.x030312957	86	44	]	]	PUNCT
uva.x030312957	86	45	–	–	PUNCT
uva.x030312957	86	46	gı	gı	NOUN
uva.x030312957	86	47	)	)	PUNCT
uva.x030312957	86	48	+	+	CCONJ
uva.x030312957	86	49	23	23	NUM
uva.x030312957	86	50	,	,	PUNCT
uva.x030312957	86	51	113,2	113,2	NUM
uva.x030312957	86	52	]	]	X
uva.x030312957	87	1	+	+	PUNCT
uva.x030312957	87	2	...	...	PUNCT
uva.x030312957	87	3	0	0	NUM
uva.x030312957	88	1	ai	ai	VERB
uva.x030312957	88	2	,	,	PUNCT
uva.x030312957	88	3	1[1	1[1	NUM
uva.x030312957	88	4	,	,	PUNCT
uva.x030312957	88	5	3	3	NUM
uva.x030312957	88	6	]	]	PUNCT
uva.x030312957	88	7	+	+	NUM
uva.x030312957	88	8	22	22	NUM
uva.x030312957	88	9	,	,	PUNCT
uva.x030312957	88	10	1[2	1[2	NUM
uva.x030312957	88	11	,	,	PUNCT
uva.x030312957	88	12	3	3	NUM
uva.x030312957	88	13	]	]	PUNCT
uva.x030312957	89	1	+	+	NUM
uva.x030312957	89	2	23	23	NUM
uva.x030312957	89	3	,	,	PUNCT
uva.x030312957	89	4	1([3,3	1([3,3	NUM
uva.x030312957	89	5	]	]	PUNCT
uva.x030312957	89	6	)	)	PUNCT
uva.x030312957	89	7	+	+	CCONJ
uva.x030312957	89	8	+	+	CCONJ
uva.x030312957	89	9	an	an	DET
uva.x030312957	89	10	,	,	PUNCT
uva.x030312957	89	11	i[n	i[n	PROPN
uva.x030312957	89	12	,	,	PUNCT
uva.x030312957	89	13	2	2	NUM
uva.x030312957	89	14	]	]	X
uva.x030312957	89	15	+	+	CCONJ
uva.x030312957	89	16	an	an	DET
uva.x030312957	89	17	,	,	PUNCT
uva.x030312957	89	18	1[n	1[n	NUM
uva.x030312957	89	19	,	,	PUNCT
uva.x030312957	89	20	3	3	NUM
uva.x030312957	89	21	]	]	SYM
uva.x030312957	89	22	0	0	NUM
uva.x030312957	89	23	=	=	NUM
uva.x030312957	89	24	21,1[1	21,1[1	NUM
uva.x030312957	89	25	,	,	PUNCT
uva.x030312957	89	26	n	n	NOUN
uva.x030312957	89	27	]	]	X
uva.x030312957	89	28	+	+	NUM
uva.x030312957	89	29	22	22	NUM
uva.x030312957	89	30	,	,	PUNCT
uva.x030312957	89	31	1[2,n	1[2,n	NUM
uva.x030312957	89	32	]	]	PUNCT
uva.x030312957	89	33	+	+	CCONJ
uva.x030312957	89	34	23	23	NUM
uva.x030312957	89	35	,	,	PUNCT
uva.x030312957	89	36	113	113	NUM
uva.x030312957	89	37	,	,	PUNCT
uva.x030312957	89	38	n	n	CCONJ
uva.x030312957	89	39	]	]	X
uva.x030312957	89	40	+	+	PUNCT
uva.x030312957	89	41	...	...	PUNCT
uva.x030312957	90	1	+	+	CCONJ
uva.x030312957	90	2	an	an	DET
uva.x030312957	90	3	,	,	PUNCT
uva.x030312957	90	4	1([n	1([n	NUM
uva.x030312957	90	5	,	,	PUNCT
uva.x030312957	90	6	n	n	NOUN
uva.x030312957	90	7	)	)	PUNCT
uva.x030312957	90	8	91	91	NUM
uva.x030312957	90	9	)	)	PUNCT
uva.x030312957	90	10	.	.	PUNCT
uva.x030312957	91	1	the	the	DET
uva.x030312957	91	2	gå	gå	PROPN
uva.x030312957	91	3	in	in	ADP
uva.x030312957	91	4	these	these	DET
uva.x030312957	91	5	equations	equation	NOUN
uva.x030312957	91	6	give	give	VERB
uva.x030312957	91	7	the	the	DET
uva.x030312957	91	8	coefficients	coefficient	NOUN
uva.x030312957	91	9	of	of	ADP
uva.x030312957	91	10	the	the	DET
uva.x030312957	91	11	square	square	ADJ
uva.x030312957	91	12	terms	term	NOUN
uva.x030312957	91	13	when	when	SCONJ
uva.x030312957	91	14	expressed	express	VERB
uva.x030312957	91	15	as	as	ADP
uva.x030312957	91	16	sums	sum	NOUN
uva.x030312957	91	17	of	of	ADP
uva.x030312957	91	18	squares	square	NOUN
uva.x030312957	91	19	.	.	PUNCT
uva.x030312957	92	1	the	the	PRON
uva.x030312957	92	2	n	n	PROPN
uva.x030312957	92	3	g	g	PROPN
uva.x030312957	92	4	's	be	AUX
uva.x030312957	92	5	are	be	AUX
uva.x030312957	92	6	obtained	obtain	VERB
uva.x030312957	92	7	by	by	ADP
uva.x030312957	92	8	eliminating	eliminate	VERB
uva.x030312957	92	9	from	from	ADP
uva.x030312957	92	10	the	the	DET
uva.x030312957	92	11	equations	equation	NOUN
uva.x030312957	92	12	(	(	PUNCT
uva.x030312957	92	13	20	20	NUM
uva.x030312957	92	14	)	)	PUNCT
uva.x030312957	92	15	the	the	DET
uva.x030312957	92	16	unknown	unknown	ADJ
uva.x030312957	92	17	ai	ai	NOUN
uva.x030312957	92	18	,	,	PUNCT
uva.x030312957	92	19	1	1	NUM
uva.x030312957	92	20	,	,	PUNCT
uva.x030312957	92	21	02	02	NUM
uva.x030312957	92	22	,	,	PUNCT
uva.x030312957	92	23	1	1	NUM
uva.x030312957	92	24	,	,	PUNCT
uva.x030312957	92	25	63	63	NUM
uva.x030312957	92	26	,	,	PUNCT
uva.x030312957	92	27	1	1	NUM
uva.x030312957	92	28	,	,	PUNCT
uva.x030312957	92	29	an	an	PRON
uva.x030312957	92	30	,	,	PUNCT
uva.x030312957	92	31	1	1	NUM
uva.x030312957	92	32	,	,	PUNCT
uva.x030312957	92	33	when	when	SCONJ
uva.x030312957	92	34	there	there	PRON
uva.x030312957	92	35	results	result	VERB
uva.x030312957	92	36	(	(	PUNCT
uva.x030312957	92	37	n,1	n,1	X
uva.x030312957	92	38	]	]	X
uva.x030312957	93	1	[	[	X
uva.x030312957	93	2	1,1	1,1	X
uva.x030312957	93	3	]	]	PUNCT
uva.x030312957	93	4	9	9	NUM
uva.x030312957	93	5	,	,	PUNCT
uva.x030312957	93	6	12,1	12,1	NUM
uva.x030312957	93	7	]	]	PUNCT
uva.x030312957	93	8	,	,	PUNCT
uva.x030312957	93	9	[	[	PUNCT
uva.x030312957	93	10	3,1	3,1	X
uva.x030312957	93	11	]	]	PUNCT
uva.x030312957	93	12	,	,	PUNCT
uva.x030312957	93	13	[	[	X
uva.x030312957	93	14	1	1	NUM
uva.x030312957	93	15	,	,	PUNCT
uva.x030312957	93	16	2	2	NUM
uva.x030312957	93	17	]	]	PUNCT
uva.x030312957	93	18	,	,	PUNCT
uva.x030312957	93	19	(	(	PUNCT
uva.x030312957	93	20	2	2	NUM
uva.x030312957	93	21	,	,	PUNCT
uva.x030312957	93	22	2	2	NUM
uva.x030312957	93	23	]	]	SYM
uva.x030312957	93	24	9	9	NUM
uva.x030312957	93	25	,	,	PUNCT
uva.x030312957	93	26	13,2	13,2	NUM
uva.x030312957	93	27	]	]	PUNCT
uva.x030312957	93	28	,	,	PUNCT
uva.x030312957	93	29	(	(	PUNCT
uva.x030312957	93	30	1,3	1,3	X
uva.x030312957	93	31	)	)	PUNCT
uva.x030312957	93	32	,	,	PUNCT
uva.x030312957	93	33	[	[	PUNCT
uva.x030312957	93	34	2,3	2,3	NUM
uva.x030312957	93	35	]	]	PUNCT
uva.x030312957	93	36	,	,	PUNCT
uva.x030312957	93	37	(	(	PUNCT
uva.x030312957	93	38	3	3	NUM
uva.x030312957	93	39	,	,	PUNCT
uva.x030312957	93	40	3	3	NUM
uva.x030312957	93	41	)	)	PUNCT
uva.x030312957	93	42	–	–	PUNCT
uva.x030312957	93	43	9	9	X
uva.x030312957	93	44	,	,	PUNCT
uva.x030312957	93	45	[	[	X
uva.x030312957	93	46	n	n	X
uva.x030312957	93	47	,	,	PUNCT
uva.x030312957	93	48	2	2	NUM
uva.x030312957	93	49	]	]	SYM
uva.x030312957	93	50	0	0	NUM
uva.x030312957	93	51	=	=	NOUN
uva.x030312957	93	52	in	in	ADP
uva.x030312957	93	53	,	,	PUNCT
uva.x030312957	93	54	3	3	NUM
uva.x030312957	93	55	]	]	X
uva.x030312957	93	56	[	[	X
uva.x030312957	93	57	3	3	NUM
uva.x030312957	93	58	,	,	PUNCT
uva.x030312957	93	59	n	n	NOUN
uva.x030312957	93	60	)	)	PUNCT
uva.x030312957	93	61	,	,	PUNCT
uva.x030312957	93	62	in	in	ADP
uva.x030312957	93	63	,	,	PUNCT
uva.x030312957	93	64	n	n	CCONJ
uva.x030312957	93	65	]	]	X
uva.x030312957	93	66	9	9	NUM
uva.x030312957	93	67	[	[	X
uva.x030312957	93	68	1	1	NUM
uva.x030312957	93	69	,	,	PUNCT
uva.x030312957	93	70	n	n	NOUN
uva.x030312957	93	71	)	)	PUNCT
uva.x030312957	93	72	,	,	PUNCT
uva.x030312957	93	73	[	[	X
uva.x030312957	93	74	2,n	2,n	NUM
uva.x030312957	93	75	)	)	PUNCT
uva.x030312957	93	76	,	,	PUNCT
uva.x030312957	93	77	the	the	DET
uva.x030312957	93	78	roots	root	NOUN
uva.x030312957	93	79	of	of	ADP
uva.x030312957	93	80	which	which	PRON
uva.x030312957	93	81	give	give	VERB
uva.x030312957	93	82	us	we	PRON
uva.x030312957	93	83	the	the	DET
uva.x030312957	93	84	g	g	PROPN
uva.x030312957	93	85	's	's	PART
uva.x030312957	93	86	.	.	PUNCT
uva.x030312957	94	1	chapter	chapter	PROPN
uva.x030312957	94	2	ii	ii	PROPN
uva.x030312957	94	3	hermite	hermite	PROPN
uva.x030312957	94	4	's	's	PART
uva.x030312957	94	5	method	method	NOUN
uva.x030312957	94	6	of	of	ADP
uva.x030312957	94	7	solving	solve	VERB
uva.x030312957	94	8	sturm	sturm	PROPN
uva.x030312957	94	9	's	's	PART
uva.x030312957	94	10	theorem	theorem	NOUN
uva.x030312957	94	11	§	§	PROPN
uva.x030312957	94	12	1	1	NUM
uva.x030312957	94	13	.	.	PUNCT
uva.x030312957	94	14	before	before	ADP
uva.x030312957	94	15	passing	pass	VERB
uva.x030312957	94	16	to	to	ADP
uva.x030312957	94	17	the	the	DET
uva.x030312957	94	18	solution	solution	NOUN
uva.x030312957	94	19	of	of	ADP
uva.x030312957	94	20	our	our	PRON
uva.x030312957	94	21	particular	particular	ADJ
uva.x030312957	94	22	problem	problem	NOUN
uva.x030312957	94	23	we	we	PRON
uva.x030312957	94	24	shall	shall	AUX
uva.x030312957	94	25	develop	develop	VERB
uva.x030312957	94	26	or	or	CCONJ
uva.x030312957	94	27	tabulate	tabulate	VERB
uva.x030312957	94	28	,	,	PUNCT
uva.x030312957	94	29	for	for	ADP
uva.x030312957	94	30	convenience	convenience	NOUN
uva.x030312957	94	31	of	of	ADP
uva.x030312957	94	32	reference	reference	NOUN
uva.x030312957	94	33	,	,	PUNCT
uva.x030312957	94	34	the	the	DET
uva.x030312957	94	35	method	method	NOUN
uva.x030312957	94	36	known	know	VERB
uva.x030312957	94	37	as	as	ADP
uva.x030312957	94	38	“	"	PUNCT
uva.x030312957	94	39	hermite	hermite	PROPN
uva.x030312957	94	40	's	's	PART
uva.x030312957	94	41	solution	solution	NOUN
uva.x030312957	94	42	of	of	ADP
uva.x030312957	94	43	sturm	sturm	PROPN
uva.x030312957	94	44	's	's	PART
uva.x030312957	94	45	theorem	theorem	NOUN
uva.x030312957	94	46	.	.	PUNCT
uva.x030312957	94	47	”	"	PUNCT
uva.x030312957	95	1	*	*	PUNCT
uva.x030312957	95	2	this	this	DET
uva.x030312957	95	3	method	method	NOUN
uva.x030312957	95	4	leads	lead	VERB
uva.x030312957	95	5	frequently	frequently	ADV
uva.x030312957	95	6	to	to	ADP
uva.x030312957	95	7	a	a	DET
uva.x030312957	95	8	simpler	simple	ADJ
uva.x030312957	95	9	result	result	NOUN
uva.x030312957	95	10	than	than	SCONJ
uva.x030312957	95	11	is	be	AUX
uva.x030312957	95	12	obtained	obtain	VERB
uva.x030312957	95	13	by	by	ADP
uva.x030312957	95	14	direct	direct	ADJ
uva.x030312957	95	15	application	application	NOUN
uva.x030312957	95	16	of	of	ADP
uva.x030312957	95	17	sturm	sturm	PROPN
uva.x030312957	95	18	's	's	PART
uva.x030312957	95	19	theorem	theorem	NOUN
uva.x030312957	95	20	,	,	PUNCT
uva.x030312957	95	21	and	and	CCONJ
uva.x030312957	95	22	is	be	AUX
uva.x030312957	95	23	closely	closely	ADV
uva.x030312957	95	24	related	related	ADJ
uva.x030312957	95	25	to	to	ADP
uva.x030312957	95	26	hermite	hermite	PROPN
uva.x030312957	95	27	's	's	PART
uva.x030312957	95	28	work	work	NOUN
uva.x030312957	95	29	with	with	ADP
uva.x030312957	95	30	the	the	DET
uva.x030312957	95	31	tschirnhausen	tschirnhausen	NOUN
uva.x030312957	95	32	's	's	PART
uva.x030312957	95	33	transformations	transformation	NOUN
uva.x030312957	95	34	.	.	PUNCT
uva.x030312957	96	1	it	it	PRON
uva.x030312957	96	2	also	also	ADV
uva.x030312957	96	3	depends	depend	VERB
uva.x030312957	96	4	on	on	ADP
uva.x030312957	96	5	the	the	DET
uva.x030312957	96	6	theorem	theorem	NOUN
uva.x030312957	96	7	in	in	ADP
uva.x030312957	96	8	quadratic	quadratic	ADJ
uva.x030312957	96	9	forms	form	NOUN
uva.x030312957	96	10	called	call	VERB
uva.x030312957	96	11	by	by	ADP
uva.x030312957	96	12	sylvesterſ	sylvesterſ	NOUN
uva.x030312957	96	13	“	"	PUNCT
uva.x030312957	96	14	the	the	DET
uva.x030312957	96	15	law	law	NOUN
uva.x030312957	96	16	of	of	ADP
uva.x030312957	96	17	inertia	inertia	NOUN
uva.x030312957	96	18	of	of	ADP
uva.x030312957	96	19	quadratic	quadratic	ADJ
uva.x030312957	96	20	forms	form	NOUN
uva.x030312957	96	21	”	"	PUNCT
uva.x030312957	96	22	which	which	PRON
uva.x030312957	96	23	states	state	VERB
uva.x030312957	96	24	:	:	PUNCT
uva.x030312957	96	25	“	"	PUNCT
uva.x030312957	96	26	if	if	SCONJ
uva.x030312957	96	27	we	we	PRON
uva.x030312957	96	28	express	express	VERB
uva.x030312957	96	29	a	a	DET
uva.x030312957	96	30	real	real	ADJ
uva.x030312957	96	31	quadratic	quadratic	ADJ
uva.x030312957	96	32	form	form	NOUN
uva.x030312957	96	33	y(x	y(x	SPACE
uva.x030312957	96	34	)	)	PUNCT
uva.x030312957	96	35	as	as	ADP
uva.x030312957	96	36	a	a	DET
uva.x030312957	96	37	sum	sum	NOUN
uva.x030312957	96	38	of	of	ADP
uva.x030312957	96	39	positive	positive	ADJ
uva.x030312957	96	40	and	and	CCONJ
uva.x030312957	96	41	negative	negative	ADJ
uva.x030312957	96	42	squares	square	NOUN
uva.x030312957	96	43	of	of	ADP
uva.x030312957	96	44	linear	linear	ADJ
uva.x030312957	96	45	functions	function	NOUN
uva.x030312957	96	46	(	(	PUNCT
uva.x030312957	96	47	which	which	PRON
uva.x030312957	96	48	may	may	AUX
uva.x030312957	96	49	be	be	AUX
uva.x030312957	96	50	done	do	VERB
uva.x030312957	96	51	in	in	ADP
uva.x030312957	96	52	an	an	DET
uva.x030312957	96	53	infinite	infinite	ADJ
uva.x030312957	96	54	number	number	NOUN
uva.x030312957	96	55	of	of	ADP
uva.x030312957	96	56	ways	way	NOUN
uva.x030312957	96	57	)	)	PUNCT
uva.x030312957	96	58	then	then	ADV
uva.x030312957	96	59	the	the	DET
uva.x030312957	96	60	number	number	NOUN
uva.x030312957	96	61	of	of	ADP
uva.x030312957	96	62	positive	positive	ADJ
uva.x030312957	96	63	and	and	CCONJ
uva.x030312957	96	64	of	of	ADP
uva.x030312957	96	65	negative	negative	ADJ
uva.x030312957	96	66	squares	square	NOUN
uva.x030312957	96	67	,	,	PUNCT
uva.x030312957	96	68	as	as	ADP
uva.x030312957	96	69	also	also	ADV
uva.x030312957	96	70	of	of	ADP
uva.x030312957	96	71	their	their	PRON
uva.x030312957	96	72	sum	sum	NOUN
uva.x030312957	96	73	,	,	PUNCT
uva.x030312957	96	74	will	will	AUX
uva.x030312957	96	75	always	always	ADV
uva.x030312957	96	76	be	be	AUX
uva.x030312957	96	77	the	the	DET
uva.x030312957	96	78	same	same	ADJ
uva.x030312957	96	79	,	,	PUNCT
uva.x030312957	96	80	provided	provide	VERB
uva.x030312957	96	81	there	there	PRON
uva.x030312957	96	82	is	be	VERB
uva.x030312957	96	83	no	no	DET
uva.x030312957	96	84	linear	linear	ADJ
uva.x030312957	96	85	relation	relation	NOUN
uva.x030312957	96	86	between	between	ADP
uva.x030312957	96	87	the	the	DET
uva.x030312957	96	88	functions	function	NOUN
uva.x030312957	96	89	.	.	PUNCT
uva.x030312957	96	90	"	"	PUNCT
uva.x030312957	97	1	1	1	X
uva.x030312957	97	2	)	)	PUNCT
uva.x030312957	97	3	§	§	PROPN
uva.x030312957	97	4	2	2	NUM
uva.x030312957	97	5	.	.	PUNCT
uva.x030312957	98	1	the	the	DET
uva.x030312957	98	2	quadratic	quadratic	ADJ
uva.x030312957	98	3	form	form	NOUN
uva.x030312957	98	4	hg	hg	PROPN
uva.x030312957	98	5	.	.	PUNCT
uva.x030312957	98	6	consider	consider	VERB
uva.x030312957	98	7	the	the	DET
uva.x030312957	98	8	equation	equation	NOUN
uva.x030312957	98	9	(	(	PUNCT
uva.x030312957	98	10	1	1	NUM
uva.x030312957	98	11	)	)	PUNCT
uva.x030312957	98	12	f(x	f(x	PROPN
uva.x030312957	98	13	)	)	PUNCT
uva.x030312957	98	14	=	=	PUNCT
uva.x030312957	98	15	do	do	VERB
uva.x030312957	98	16	x	x	PUNCT
uva.x030312957	98	17	"	"	PUNCT
uva.x030312957	99	1	+	+	PROPN
uva.x030312957	99	2	aj	aj	X
uva.x030312957	99	3	xn-1	xn-1	PUNCT
uva.x030312957	100	1	+	+	CCONJ
uva.x030312957	100	2	az	az	PROPN
uva.x030312957	100	3	x1	x1	PROPN
uva.x030312957	100	4	-	-	PUNCT
uva.x030312957	100	5	2	2	NUM
uva.x030312957	100	6	+	+	CCONJ
uva.x030312957	100	7	+	+	PUNCT
uva.x030312957	100	8	an-1	an-1	PUNCT
uva.x030312957	100	9	x	x	PUNCT
uva.x030312957	101	1	+	+	CCONJ
uva.x030312957	101	2	an	an	DET
uva.x030312957	101	3	=	=	NOUN
uva.x030312957	101	4	0	0	NUM
uva.x030312957	101	5	,	,	PUNCT
uva.x030312957	101	6	whose	whose	DET
uva.x030312957	101	7	roots	root	NOUN
uva.x030312957	101	8	,	,	PUNCT
uva.x030312957	101	9	x1	x1	PROPN
uva.x030312957	101	10	,	,	PUNCT
uva.x030312957	101	11	x2	x2	PROPN
uva.x030312957	101	12	,	,	PUNCT
uva.x030312957	101	13	xn	xn	PROPN
uva.x030312957	101	14	,	,	PUNCT
uva.x030312957	101	15	we	we	PRON
uva.x030312957	101	16	shall	shall	AUX
uva.x030312957	101	17	assume	assume	VERB
uva.x030312957	101	18	are	be	AUX
uva.x030312957	101	19	all	all	ADV
uva.x030312957	101	20	unequal	unequal	ADJ
uva.x030312957	101	21	.	.	PUNCT
uva.x030312957	102	1	if	if	SCONJ
uva.x030312957	102	2	x	x	PUNCT
uva.x030312957	102	3	is	be	AUX
uva.x030312957	102	4	a	a	DET
uva.x030312957	102	5	root	root	NOUN
uva.x030312957	102	6	of	of	ADP
uva.x030312957	102	7	(	(	PUNCT
uva.x030312957	102	8	1	1	X
uva.x030312957	102	9	)	)	PUNCT
uva.x030312957	102	10	we	we	PRON
uva.x030312957	102	11	can	can	AUX
uva.x030312957	102	12	build	build	VERB
uva.x030312957	102	13	the	the	DET
uva.x030312957	102	14	expression	expression	NOUN
uva.x030312957	102	15	f(t	f(t	SPACE
uva.x030312957	102	16	)	)	PUNCT
uva.x030312957	102	17	(	(	PUNCT
uva.x030312957	102	18	2	2	X
uva.x030312957	102	19	)	)	PUNCT
uva.x030312957	102	20	{	{	PUNCT
uva.x030312957	102	21	n-1	n-1	PROPN
uva.x030312957	102	22	fo	fo	X
uva.x030312957	102	23	(	(	PUNCT
uva.x030312957	102	24	x	x	NOUN
uva.x030312957	102	25	)	)	PUNCT
uva.x030312957	102	26	+	+	NUM
uva.x030312957	102	27	tn=2	tn=2	X
uva.x030312957	102	28	f1(a	f1(a	ADV
uva.x030312957	102	29	)	)	PUNCT
uva.x030312957	103	1	+	+	PUNCT
uva.x030312957	103	2	·	·	PUNCT
uva.x030312957	103	3	+	+	CCONJ
uva.x030312957	103	4	tfn-2(x	tfn-2(x	PUNCT
uva.x030312957	103	5	)	)	PUNCT
uva.x030312957	103	6	+	+	CCONJ
uva.x030312957	103	7	fn-1(a	fn-1(a	NUM
uva.x030312957	103	8	)	)	PUNCT
uva.x030312957	103	9	,	,	PUNCT
uva.x030312957	103	10	t	t	PROPN
uva.x030312957	103	11	in	in	ADP
uva.x030312957	103	12	which	which	PRON
uva.x030312957	103	13	t	t	PROPN
uva.x030312957	103	14	is	be	AUX
uva.x030312957	103	15	an	an	DET
uva.x030312957	103	16	undetermined	undetermined	ADJ
uva.x030312957	103	17	quantity	quantity	NOUN
uva.x030312957	103	18	.	.	PUNCT
uva.x030312957	104	1	the	the	DET
uva.x030312957	104	2	coefficients	coefficient	NOUN
uva.x030312957	104	3	of	of	ADP
uva.x030312957	104	4	the	the	DET
uva.x030312957	104	5	powers	power	NOUN
uva.x030312957	104	6	of	of	ADP
uva.x030312957	104	7	t	t	PROPN
uva.x030312957	104	8	are	be	AUX
uva.x030312957	104	9	here	here	ADV
uva.x030312957	104	10	fo(2	fo(2	PROPN
uva.x030312957	104	11	)	)	PUNCT
uva.x030312957	104	12	=	=	PROPN
uva.x030312957	104	13	do	do	VERB
uva.x030312957	104	14	,	,	PUNCT
uva.x030312957	104	15	=	=	PROPN
uva.x030312957	104	16	ao	ao	X
uva.x030312957	104	17	x	x	X
uva.x030312957	104	18	+	+	PUNCT
uva.x030312957	104	19	di	di	PROPN
uva.x030312957	104	20	,	,	PUNCT
uva.x030312957	104	21	fi(x	fi(x	PROPN
uva.x030312957	104	22	)	)	PUNCT
uva.x030312957	104	23	f2	f2	PROPN
uva.x030312957	104	24	(	(	PUNCT
uva.x030312957	104	25	x	x	PROPN
uva.x030312957	104	26	)	)	PUNCT
uva.x030312957	104	27	(	(	PUNCT
uva.x030312957	104	28	3	3	X
uva.x030312957	104	29	)	)	PUNCT
uva.x030312957	104	30	do	do	VERB
uva.x030312957	104	31	x2	x2	PROPN
uva.x030312957	105	1	+	+	CCONJ
uva.x030312957	105	2	212	212	NUM
uva.x030312957	105	3	+	+	NUM
uva.x030312957	105	4	02	02	NUM
uva.x030312957	105	5	,	,	PUNCT
uva.x030312957	105	6	.	.	PUNCT
uva.x030312957	105	7	fr-1(x	fr-1(x	SPACE
uva.x030312957	106	1	)	)	PUNCT
uva.x030312957	106	2	ao	ao	PROPN
uva.x030312957	106	3	xn-1	xn-1	PUNCT
uva.x030312957	107	1	+	+	CCONJ
uva.x030312957	107	2	a₂an-2	a₂an-2	NOUN
uva.x030312957	107	3	+	+	CCONJ
uva.x030312957	107	4	aran-3	aran-3	PROPN
uva.x030312957	107	5	+	+	CCONJ
uva.x030312957	107	6	+	+	PUNCT
uva.x030312957	107	7	an--2x	an--2x	VERB
uva.x030312957	108	1	+	+	PUNCT
uva.x030312957	108	2	an-1	an-1	SPACE
uva.x030312957	108	3	.	.	PUNCT
uva.x030312957	109	1	*	*	PUNCT
uva.x030312957	109	2	hermite	hermite	INTJ
uva.x030312957	109	3	,	,	PUNCT
uva.x030312957	109	4	“	"	PUNCT
uva.x030312957	109	5	remarques	remarque	VERB
uva.x030312957	109	6	sur	sur	PROPN
uva.x030312957	109	7	le	le	X
uva.x030312957	109	8	théorème	théorème	PROPN
uva.x030312957	109	9	de	de	PROPN
uva.x030312957	109	10	m.	m.	NOUN
uva.x030312957	109	11	sturm	sturm	PROPN
uva.x030312957	109	12	,	,	PUNCT
uva.x030312957	109	13	”	"	PUNCT
uva.x030312957	109	14	comptes	comptes	X
uva.x030312957	109	15	rendus	rendus	PROPN
uva.x030312957	109	16	de	de	PROPN
uva.x030312957	109	17	paris	paris	PROPN
uva.x030312957	109	18	akademie	akademie	PROPN
uva.x030312957	109	19	,	,	PUNCT
uva.x030312957	109	20	t.	t.	PROPN
uva.x030312957	109	21	30	30	NUM
uva.x030312957	109	22	(	(	PUNCT
uva.x030312957	109	23	1853	1853	NUM
uva.x030312957	109	24	)	)	PUNCT
uva.x030312957	109	25	.	.	PUNCT
uva.x030312957	110	1	†	†	PRON
uva.x030312957	110	2	see	see	VERB
uva.x030312957	110	3	philosophical	philosophical	ADJ
uva.x030312957	110	4	magazine	magazine	NOUN
uva.x030312957	110	5	,	,	PUNCT
uva.x030312957	110	6	1852	1852	NUM
uva.x030312957	110	7	.	.	PUNCT
uva.x030312957	111	1	6	6	NUM
uva.x030312957	111	2	by	by	ADP
uva.x030312957	111	3	a	a	DET
uva.x030312957	111	4	method	method	NOUN
uva.x030312957	111	5	due	due	ADP
uva.x030312957	111	6	to	to	ADP
uva.x030312957	111	7	hermite	hermite	NOUN
uva.x030312957	111	8	7	7	NUM
uva.x030312957	111	9	now	now	ADV
uva.x030312957	111	10	construct	construct	VERB
uva.x030312957	111	11	the	the	DET
uva.x030312957	111	12	function	function	NOUN
uva.x030312957	111	13	(	(	PUNCT
uva.x030312957	111	14	4	4	NUM
uva.x030312957	111	15	)	)	PUNCT
uva.x030312957	111	16	y	y	PROPN
uva.x030312957	111	17	=	=	PRON
uva.x030312957	111	18	ta	ta	AUX
uva.x030312957	111	19	-	-	PUNCT
uva.x030312957	111	20	fo	fo	NOUN
uva.x030312957	111	21	(	(	PUNCT
uva.x030312957	111	22	2)+	2)+	NUM
uva.x030312957	111	23	–	–	PUNCT
uva.x030312957	111	24	f(x)+	f(x)+	NOUN
uva.x030312957	111	25	...	...	PUNCT
uva.x030312957	112	1	+	+	CCONJ
uva.x030312957	112	2	ti	ti	X
uva.x030312957	112	3	fn-2(x	fn-2(x	SPACE
uva.x030312957	112	4	)	)	PUNCT
uva.x030312957	112	5	+	+	CCONJ
uva.x030312957	112	6	tofn-1(x	tofn-1(x	ADV
uva.x030312957	112	7	)	)	PUNCT
uva.x030312957	112	8	,	,	PUNCT
uva.x030312957	112	9	in	in	ADP
uva.x030312957	112	10	which	which	PRON
uva.x030312957	112	11	to	to	ADP
uva.x030312957	112	12	,	,	PUNCT
uva.x030312957	112	13	ti	ti	PROPN
uva.x030312957	112	14	,	,	PUNCT
uva.x030312957	112	15	...	...	PUNCT
uva.x030312957	112	16	,	,	PUNCT
uva.x030312957	112	17	tn	tn	PROPN
uva.x030312957	112	18	-	-	PUNCT
uva.x030312957	112	19	l	l	NOUN
uva.x030312957	112	20	are	be	AUX
uva.x030312957	112	21	undetermined	undetermined	ADJ
uva.x030312957	112	22	constants	constant	NOUN
uva.x030312957	112	23	,	,	PUNCT
uva.x030312957	112	24	and	and	CCONJ
uva.x030312957	112	25	are	be	AUX
uva.x030312957	112	26	not	not	PART
uva.x030312957	112	27	to	to	PART
uva.x030312957	112	28	be	be	AUX
uva.x030312957	112	29	confused	confuse	VERB
uva.x030312957	112	30	with	with	ADP
uva.x030312957	112	31	powers	power	NOUN
uva.x030312957	112	32	of	of	ADP
uva.x030312957	112	33	t.	t.	PROPN
uva.x030312957	112	34	however	however	ADV
uva.x030312957	112	35	(	(	PUNCT
uva.x030312957	112	36	4	4	X
uva.x030312957	112	37	)	)	PUNCT
uva.x030312957	112	38	goes	go	VERB
uva.x030312957	112	39	into	into	ADP
uva.x030312957	112	40	(	(	PUNCT
uva.x030312957	112	41	2	2	NUM
uva.x030312957	112	42	)	)	PUNCT
uva.x030312957	112	43	if	if	SCONJ
uva.x030312957	112	44	th	th	X
uva.x030312957	112	45	is	be	AUX
uva.x030312957	112	46	changed	change	VERB
uva.x030312957	112	47	to	to	ADP
uva.x030312957	112	48	th	th	PROPN
uva.x030312957	112	49	.	.	PROPN
uva.x030312957	112	50	denoting	denote	VERB
uva.x030312957	112	51	by	by	ADP
uva.x030312957	112	52	yı	yı	PROPN
uva.x030312957	112	53	,	,	PUNCT
uva.x030312957	112	54	y2	y2	PROPN
uva.x030312957	112	55	,	,	PUNCT
uva.x030312957	112	56	y3	y3	PROPN
uva.x030312957	112	57	,	,	PUNCT
uva.x030312957	112	58	the	the	DET
uva.x030312957	112	59	values	value	NOUN
uva.x030312957	112	60	which	which	PRON
uva.x030312957	112	61	y	y	PROPN
uva.x030312957	112	62	takes	take	VERB
uva.x030312957	112	63	for	for	ADP
uva.x030312957	112	64	yn	yn	PROPN
uva.x030312957	112	65	x	x	SYM
uva.x030312957	112	66	=	=	PROPN
uva.x030312957	112	67	x1	x1	PROPN
uva.x030312957	112	68	,	,	PUNCT
uva.x030312957	112	69	x2	x2	PROPN
uva.x030312957	112	70	,	,	PUNCT
uva.x030312957	112	71	x3	x3	PROPN
uva.x030312957	112	72	,	,	PUNCT
uva.x030312957	112	73	xin	xin	PROPN
uva.x030312957	112	74	when	when	SCONJ
uva.x030312957	112	75	x1	x1	PROPN
uva.x030312957	112	76	respectively	respectively	ADV
uva.x030312957	112	77	and	and	CCONJ
uva.x030312957	112	78	taking	take	VERB
uva.x030312957	112	79	a	a	DET
uva.x030312957	112	80	,	,	PUNCT
uva.x030312957	112	81	any	any	DET
uva.x030312957	112	82	fixed	fixed	ADJ
uva.x030312957	112	83	real	real	ADJ
uva.x030312957	112	84	quantity	quantity	NOUN
uva.x030312957	112	85	,	,	PUNCT
uva.x030312957	112	86	we	we	PRON
uva.x030312957	112	87	next	next	ADV
uva.x030312957	112	88	build	build	VERB
uva.x030312957	112	89	the	the	DET
uva.x030312957	112	90	expression	expression	NOUN
uva.x030312957	112	91	(	(	PUNCT
uva.x030312957	112	92	5	5	X
uva.x030312957	112	93	)	)	PUNCT
uva.x030312957	112	94	hq	hq	NOUN
uva.x030312957	112	95	=	=	NOUN
uva.x030312957	113	1	(	(	PUNCT
uva.x030312957	113	2	x1	x1	PROPN
uva.x030312957	113	3	a)yi	a)yi	ADV
uva.x030312957	113	4	+	+	CCONJ
uva.x030312957	113	5	(	(	PUNCT
uva.x030312957	113	6	x2	x2	ADJ
uva.x030312957	113	7	–	–	PUNCT
uva.x030312957	113	8	a	a	X
uva.x030312957	113	9	)	)	PUNCT
uva.x030312957	113	10	yả	yả	PROPN
uva.x030312957	113	11	+	+	CCONJ
uva.x030312957	113	12	+	+	CCONJ
uva.x030312957	114	1	(	(	PUNCT
uva.x030312957	114	2	xn	xn	PROPN
uva.x030312957	114	3	a)ya	a)ya	PROPN
uva.x030312957	114	4	.	.	PUNCT
uva.x030312957	115	1	this	this	PRON
uva.x030312957	115	2	is	be	AUX
uva.x030312957	115	3	a	a	DET
uva.x030312957	115	4	quadratic	quadratic	ADJ
uva.x030312957	115	5	form	form	NOUN
uva.x030312957	115	6	in	in	ADP
uva.x030312957	115	7	the	the	DET
uva.x030312957	115	8	n	n	NOUN
uva.x030312957	115	9	variables	variable	NOUN
uva.x030312957	115	10	ti	ti	NOUN
uva.x030312957	115	11	,	,	PUNCT
uva.x030312957	115	12	and	and	CCONJ
uva.x030312957	115	13	below	below	ADP
uva.x030312957	115	14	it	it	PRON
uva.x030312957	115	15	will	will	AUX
uva.x030312957	115	16	be	be	AUX
uva.x030312957	115	17	shown	show	VERB
uva.x030312957	115	18	that	that	SCONJ
uva.x030312957	115	19	the	the	DET
uva.x030312957	115	20	number	number	NOUN
uva.x030312957	115	21	of	of	ADP
uva.x030312957	115	22	its	its	PRON
uva.x030312957	115	23	negative	negative	ADJ
uva.x030312957	115	24	terms	term	NOUN
uva.x030312957	115	25	,	,	PUNCT
uva.x030312957	115	26	for	for	ADP
uva.x030312957	115	27	a	a	DET
uva.x030312957	115	28	constant	constant	ADJ
uva.x030312957	115	29	a	a	NOUN
uva.x030312957	115	30	,	,	PUNCT
uva.x030312957	115	31	gives	give	VERB
uva.x030312957	115	32	the	the	DET
uva.x030312957	115	33	number	number	NOUN
uva.x030312957	115	34	of	of	ADP
uva.x030312957	115	35	real	real	ADJ
uva.x030312957	115	36	roots	root	NOUN
uva.x030312957	115	37	of	of	ADP
uva.x030312957	115	38	f(x	f(x	NOUN
uva.x030312957	115	39	)	)	PUNCT
uva.x030312957	115	40	=	=	PROPN
uva.x030312957	115	41	0	0	PUNCT
uva.x030312957	115	42	which	which	PRON
uva.x030312957	115	43	are	be	AUX
uva.x030312957	115	44	less	less	ADJ
uva.x030312957	115	45	than	than	ADP
uva.x030312957	115	46	a	a	PRON
uva.x030312957	115	47	,	,	PUNCT
uva.x030312957	115	48	plus	plus	CCONJ
uva.x030312957	115	49	the	the	DET
uva.x030312957	115	50	number	number	NOUN
uva.x030312957	115	51	of	of	ADP
uva.x030312957	115	52	pairs	pair	NOUN
uva.x030312957	115	53	of	of	ADP
uva.x030312957	115	54	imaginary	imaginary	ADJ
uva.x030312957	115	55	roots	root	NOUN
uva.x030312957	115	56	of	of	ADP
uva.x030312957	115	57	f(x	f(x	NOUN
uva.x030312957	115	58	)	)	PUNCT
uva.x030312957	115	59	=	=	PROPN
uva.x030312957	115	60	0	0	X
uva.x030312957	115	61	.	.	PUNCT
uva.x030312957	116	1	if	if	SCONJ
uva.x030312957	116	2	xı	xı	PRON
uva.x030312957	116	3	is	be	AUX
uva.x030312957	116	4	a	a	DET
uva.x030312957	116	5	real	real	ADJ
uva.x030312957	116	6	root	root	NOUN
uva.x030312957	116	7	,	,	PUNCT
uva.x030312957	116	8	then	then	ADV
uva.x030312957	116	9	yı	yı	PRON
uva.x030312957	116	10	is	be	AUX
uva.x030312957	116	11	real	real	ADJ
uva.x030312957	116	12	,	,	PUNCT
uva.x030312957	116	13	and	and	CCONJ
uva.x030312957	116	14	the	the	DET
uva.x030312957	116	15	term	term	NOUN
uva.x030312957	116	16	(	(	PUNCT
uva.x030312957	116	17	x1	x1	PROPN
uva.x030312957	116	18	a	a	X
uva.x030312957	116	19	)	)	PUNCT
uva.x030312957	116	20	yî	yî	X
uva.x030312957	116	21	is	be	AUX
uva.x030312957	116	22	positive	positive	ADJ
uva.x030312957	116	23	or	or	CCONJ
uva.x030312957	116	24	negative	negative	ADJ
uva.x030312957	116	25	according	accord	VERB
uva.x030312957	116	26	as	as	SCONJ
uva.x030312957	116	27	x1	x1	PROPN
uva.x030312957	116	28	is	be	AUX
uva.x030312957	116	29	greater	great	ADJ
uva.x030312957	116	30	or	or	CCONJ
uva.x030312957	116	31	less	less	ADJ
uva.x030312957	116	32	than	than	ADP
uva.x030312957	116	33	a.	a.	NOUN
uva.x030312957	116	34	and	and	CCONJ
uva.x030312957	116	35	x2	x2	PROPN
uva.x030312957	116	36	form	form	VERB
uva.x030312957	116	37	a	a	DET
uva.x030312957	116	38	pair	pair	NOUN
uva.x030312957	116	39	of	of	ADP
uva.x030312957	116	40	conjugate	conjugate	NOUN
uva.x030312957	116	41	imaginaries	imaginary	NOUN
uva.x030312957	116	42	,	,	PUNCT
uva.x030312957	116	43	then	then	ADV
uva.x030312957	116	44	yı	yı	PRON
uva.x030312957	116	45	and	and	CCONJ
uva.x030312957	116	46	y2	y2	PROPN
uva.x030312957	116	47	are	be	AUX
uva.x030312957	116	48	conjugate	conjugate	NOUN
uva.x030312957	116	49	imaginaries	imaginary	NOUN
uva.x030312957	116	50	and	and	CCONJ
uva.x030312957	116	51	(	(	PUNCT
uva.x030312957	116	52	x1	x1	PROPN
uva.x030312957	116	53	a)yi	a)yi	ADV
uva.x030312957	116	54	+	+	CCONJ
uva.x030312957	117	1	(	(	PUNCT
uva.x030312957	117	2	x2	x2	ADJ
uva.x030312957	117	3	–	–	PUNCT
uva.x030312957	117	4	a	a	X
uva.x030312957	117	5	)	)	PUNCT
uva.x030312957	117	6	yž	yž	NOUN
uva.x030312957	117	7	is	be	AUX
uva.x030312957	117	8	composed	compose	VERB
uva.x030312957	117	9	of	of	ADP
uva.x030312957	117	10	a	a	DET
uva.x030312957	117	11	positive	positive	ADJ
uva.x030312957	117	12	and	and	CCONJ
uva.x030312957	117	13	a	a	DET
uva.x030312957	117	14	negative	negative	ADJ
uva.x030312957	117	15	square	square	NOUN
uva.x030312957	117	16	.	.	PUNCT
uva.x030312957	118	1	this	this	PRON
uva.x030312957	118	2	is	be	AUX
uva.x030312957	118	3	easily	easily	ADV
uva.x030312957	118	4	seen	see	VERB
uva.x030312957	118	5	if	if	SCONJ
uva.x030312957	118	6	we	we	PRON
uva.x030312957	118	7	take	take	VERB
uva.x030312957	118	8	yi	yi	PROPN
uva.x030312957	118	9	a	a	DET
uva.x030312957	118	10	=	=	NOUN
uva.x030312957	118	11	u	u	PROPN
uva.x030312957	118	12	+	+	CCONJ
uva.x030312957	118	13	iv	iv	X
uva.x030312957	118	14	,	,	PUNCT
uva.x030312957	118	15	a	a	DET
uva.x030312957	118	16	=	=	NOUN
uva.x030312957	118	17	u	u	PROPN
uva.x030312957	118	18	–	–	PUNCT
uva.x030312957	118	19	iv	iv	X
uva.x030312957	118	20	,	,	PUNCT
uva.x030312957	118	21	whence	whence	NOUN
uva.x030312957	118	22	(	(	PUNCT
uva.x030312957	118	23	x1	x1	PROPN
uva.x030312957	118	24	a)yi	a)yi	ADV
uva.x030312957	119	1	+	+	CCONJ
uva.x030312957	119	2	(	(	PUNCT
uva.x030312957	119	3	x2	x2	ADJ
uva.x030312957	119	4	a	a	X
uva.x030312957	119	5	)	)	PUNCT
uva.x030312957	119	6	yż	yż	PROPN
uva.x030312957	119	7	=	=	PROPN
uva.x030312957	119	8	2u	2u	X
uva.x030312957	119	9	’	'	PUNCT
uva.x030312957	119	10	–	–	PUNCT
uva.x030312957	119	11	202	202	NUM
uva.x030312957	119	12	.	.	PUNCT
uva.x030312957	120	1	from	from	ADP
uva.x030312957	120	2	the	the	DET
uva.x030312957	120	3	foregoing	forego	VERB
uva.x030312957	120	4	it	it	PRON
uva.x030312957	120	5	follows	follow	VERB
uva.x030312957	120	6	that	that	SCONJ
uva.x030312957	120	7	the	the	DET
uva.x030312957	120	8	number	number	NOUN
uva.x030312957	120	9	n	n	CCONJ
uva.x030312957	120	10	,	,	PUNCT
uva.x030312957	120	11	of	of	ADP
uva.x030312957	120	12	the	the	DET
uva.x030312957	120	13	negative	negative	ADJ
uva.x030312957	120	14	squares	square	NOUN
uva.x030312957	120	15	in	in	ADP
uva.x030312957	120	16	h	h	PROPN
uva.x030312957	120	17	,	,	PUNCT
uva.x030312957	120	18	is	be	AUX
uva.x030312957	120	19	equal	equal	ADJ
uva.x030312957	120	20	to	to	ADP
uva.x030312957	120	21	the	the	DET
uva.x030312957	120	22	total	total	ADJ
uva.x030312957	120	23	number	number	NOUN
uva.x030312957	120	24	of	of	ADP
uva.x030312957	120	25	pairs	pair	NOUN
uva.x030312957	120	26	of	of	ADP
uva.x030312957	120	27	imaginary	imaginary	ADJ
uva.x030312957	120	28	roots	root	NOUN
uva.x030312957	120	29	of	of	ADP
uva.x030312957	120	30	f(x	f(x	NOUN
uva.x030312957	120	31	)	)	PUNCT
uva.x030312957	120	32	=	=	PROPN
uva.x030312957	120	33	0	0	NUM
uva.x030312957	120	34	plus	plus	CCONJ
uva.x030312957	120	35	the	the	DET
uva.x030312957	120	36	number	number	NOUN
uva.x030312957	120	37	of	of	ADP
uva.x030312957	120	38	its	its	PRON
uva.x030312957	120	39	real	real	ADJ
uva.x030312957	120	40	roots	root	NOUN
uva.x030312957	120	41	which	which	PRON
uva.x030312957	120	42	are	be	AUX
uva.x030312957	120	43	less	less	ADV
uva.x030312957	120	44	tha	tha	INTJ
uva.x030312957	120	45	take	take	VERB
uva.x030312957	120	46	now	now	ADV
uva.x030312957	120	47	a	a	DET
uva.x030312957	120	48	second	second	ADJ
uva.x030312957	120	49	real	real	ADJ
uva.x030312957	120	50	number	number	NOUN
uva.x030312957	120	51	b	b	X
uva.x030312957	120	52	>	>	X
uva.x030312957	120	53	a	a	PRON
uva.x030312957	120	54	,	,	PUNCT
uva.x030312957	120	55	and	and	CCONJ
uva.x030312957	120	56	form	form	VERB
uva.x030312957	120	57	the	the	DET
uva.x030312957	120	58	function	function	NOUN
uva.x030312957	120	59	h.	h.	NOUN
uva.x030312957	120	60	,	,	PUNCT
uva.x030312957	120	61	representing	represent	VERB
uva.x030312957	120	62	by	by	ADP
uva.x030312957	120	63	n	n	NOUN
uva.x030312957	120	64	,	,	PUNCT
uva.x030312957	120	65	the	the	DET
uva.x030312957	120	66	number	number	NOUN
uva.x030312957	120	67	of	of	ADP
uva.x030312957	120	68	negative	negative	ADJ
uva.x030312957	120	69	squares	square	NOUN
uva.x030312957	120	70	of	of	ADP
uva.x030312957	120	71	hg	hg	PROPN
uva.x030312957	120	72	.	.	PUNCT
uva.x030312957	121	1	then	then	ADV
uva.x030312957	121	2	the	the	DET
uva.x030312957	121	3	difference	difference	NOUN
uva.x030312957	121	4	n.	n.	PROPN
uva.x030312957	121	5	–	–	PUNCT
uva.x030312957	121	6	n.	n.	PROPN
uva.x030312957	121	7	is	be	AUX
uva.x030312957	121	8	equal	equal	ADJ
uva.x030312957	121	9	to	to	ADP
uva.x030312957	121	10	the	the	DET
uva.x030312957	121	11	number	number	NOUN
uva.x030312957	121	12	of	of	ADP
uva.x030312957	121	13	real	real	ADJ
uva.x030312957	121	14	roots	root	NOUN
uva.x030312957	121	15	of	of	ADP
uva.x030312957	121	16	f(x	f(x	NOUN
uva.x030312957	121	17	)	)	PUNCT
uva.x030312957	121	18	=	=	PROPN
uva.x030312957	121	19	0	0	NUM
uva.x030312957	121	20	lying	lie	VERB
uva.x030312957	121	21	between	between	ADP
uva.x030312957	121	22	a	a	PRON
uva.x030312957	121	23	and	and	CCONJ
uva.x030312957	121	24	b.	b.	PROPN
uva.x030312957	121	25	ya	ya	PROPN
uva.x030312957	121	26	vez	vez	VERB
uva.x030312957	121	27	α	α	PROPN
uva.x030312957	121	28	.	.	PUNCT
uva.x030312957	121	29	§	§	PROPN
uva.x030312957	121	30	3	3	NUM
uva.x030312957	121	31	.	.	PUNCT
uva.x030312957	122	1	some	some	DET
uva.x030312957	122	2	relations	relation	NOUN
uva.x030312957	122	3	between	between	ADP
uva.x030312957	122	4	the	the	DET
uva.x030312957	122	5	coefficients	coefficient	NOUN
uva.x030312957	122	6	.	.	PUNCT
uva.x030312957	123	1	we	we	PRON
uva.x030312957	123	2	have	have	VERB
uva.x030312957	123	3	thus	thus	ADV
uva.x030312957	123	4	a	a	DET
uva.x030312957	123	5	means	means	NOUN
uva.x030312957	123	6	of	of	ADP
uva.x030312957	123	7	determining	determine	VERB
uva.x030312957	123	8	the	the	DET
uva.x030312957	123	9	real	real	ADJ
uva.x030312957	123	10	roots	root	NOUN
uva.x030312957	123	11	of	of	ADP
uva.x030312957	123	12	an	an	DET
uva.x030312957	123	13	equation	equation	NOUN
uva.x030312957	123	14	,	,	PUNCT
uva.x030312957	123	15	if	if	SCONJ
uva.x030312957	123	16	we	we	PRON
uva.x030312957	123	17	can	can	AUX
uva.x030312957	123	18	represent	represent	VERB
uva.x030312957	123	19	the	the	DET
uva.x030312957	123	20	coefficients	coefficient	NOUN
uva.x030312957	123	21	of	of	ADP
uva.x030312957	123	22	the	the	DET
uva.x030312957	123	23	tit	tit	NOUN
uva.x030312957	123	24	;	;	PUNCT
uva.x030312957	123	25	in	in	ADP
uva.x030312957	123	26	the	the	DET
uva.x030312957	123	27	function	function	NOUN
uva.x030312957	123	28	h	h	NOUN
uva.x030312957	123	29	,	,	PUNCT
uva.x030312957	123	30	as	as	ADP
uva.x030312957	123	31	functions	function	NOUN
uva.x030312957	123	32	of	of	ADP
uva.x030312957	123	33	a	a	DET
uva.x030312957	123	34	and	and	CCONJ
uva.x030312957	123	35	of	of	ADP
uva.x030312957	123	36	the	the	DET
uva.x030312957	123	37	coefficients	coefficient	NOUN
uva.x030312957	123	38	of	of	ADP
uva.x030312957	123	39	the	the	DET
uva.x030312957	123	40	8	8	NUM
uva.x030312957	123	41	solution	solution	NOUN
uva.x030312957	123	42	of	of	ADP
uva.x030312957	123	43	the	the	DET
uva.x030312957	123	44	equation	equation	NOUN
uva.x030312957	123	45	of	of	ADP
uva.x030312957	123	46	secular	secular	ADJ
uva.x030312957	123	47	variation	variation	NOUN
uva.x030312957	123	48	powers	power	NOUN
uva.x030312957	123	49	of	of	ADP
uva.x030312957	123	50	x	x	PROPN
uva.x030312957	123	51	in	in	ADP
uva.x030312957	123	52	f(x	f(x	PROPN
uva.x030312957	123	53	)	)	PUNCT
uva.x030312957	123	54	.	.	PUNCT
uva.x030312957	124	1	after	after	ADP
uva.x030312957	124	2	a	a	DET
uva.x030312957	124	3	few	few	ADJ
uva.x030312957	124	4	expressions	expression	NOUN
uva.x030312957	124	5	,	,	PUNCT
uva.x030312957	124	6	which	which	PRON
uva.x030312957	124	7	are	be	AUX
uva.x030312957	124	8	used	use	VERB
uva.x030312957	124	9	in	in	ADP
uva.x030312957	124	10	developing	develop	VERB
uva.x030312957	124	11	the	the	DET
uva.x030312957	124	12	process	process	NOUN
uva.x030312957	124	13	or	or	CCONJ
uva.x030312957	124	14	in	in	ADP
uva.x030312957	124	15	its	its	PRON
uva.x030312957	124	16	application	application	NOUN
uva.x030312957	124	17	,	,	PUNCT
uva.x030312957	124	18	are	be	AUX
uva.x030312957	124	19	derived	derive	VERB
uva.x030312957	124	20	,	,	PUNCT
uva.x030312957	124	21	then	then	ADV
uva.x030312957	124	22	we	we	PRON
uva.x030312957	124	23	shall	shall	AUX
uva.x030312957	124	24	proceed	proceed	VERB
uva.x030312957	124	25	to	to	PART
uva.x030312957	124	26	determine	determine	VERB
uva.x030312957	124	27	these	these	DET
uva.x030312957	124	28	coefficients	coefficient	NOUN
uva.x030312957	124	29	.	.	PUNCT
uva.x030312957	125	1	the	the	DET
uva.x030312957	125	2	symbol	symbol	NOUN
uva.x030312957	125	3	s	s	VERB
uva.x030312957	125	4	in	in	ADP
uva.x030312957	125	5	front	front	NOUN
uva.x030312957	125	6	of	of	ADP
uva.x030312957	125	7	an	an	DET
uva.x030312957	125	8	expression	expression	NOUN
uva.x030312957	125	9	is	be	AUX
uva.x030312957	125	10	used	use	VERB
uva.x030312957	125	11	here	here	ADV
uva.x030312957	125	12	to	to	PART
uva.x030312957	125	13	indicate	indicate	VERB
uva.x030312957	125	14	the	the	DET
uva.x030312957	125	15	expression	expression	NOUN
uva.x030312957	125	16	is	be	AUX
uva.x030312957	125	17	to	to	PART
uva.x030312957	125	18	be	be	AUX
uva.x030312957	125	19	summed	sum	VERB
uva.x030312957	125	20	over	over	ADP
uva.x030312957	125	21	all	all	DET
uva.x030312957	125	22	the	the	DET
uva.x030312957	125	23	roots	root	NOUN
uva.x030312957	125	24	of	of	ADP
uva.x030312957	125	25	f(x	f(x	NOUN
uva.x030312957	125	26	)	)	PUNCT
uva.x030312957	125	27	=	=	PROPN
uva.x030312957	125	28	0	0	NUM
uva.x030312957	125	29	.	.	PUNCT
uva.x030312957	126	1	thus	thus	ADV
uva.x030312957	126	2	s(x	s(x	PROPN
uva.x030312957	126	3	)	)	PUNCT
uva.x030312957	126	4	=	=	X
uva.x030312957	126	5	x1	x1	PROPN
uva.x030312957	127	1	+	+	CCONJ
uva.x030312957	127	2	x2	x2	ADJ
uva.x030312957	128	1	+	+	ADJ
uva.x030312957	128	2	!	!	PUNCT
uva.x030312957	129	1	tan	tan	PROPN
uva.x030312957	129	2	,	,	PUNCT
uva.x030312957	129	3	s(y	s(y	PROPN
uva.x030312957	129	4	)	)	PUNCT
uva.x030312957	129	5	=	=	PROPN
uva.x030312957	129	6	yı	yı	PROPN
uva.x030312957	130	1	+	+	PROPN
uva.x030312957	130	2	y2	y2	PROPN
uva.x030312957	131	1	+	+	PUNCT
uva.x030312957	131	2	+	+	PUNCT
uva.x030312957	131	3	yn	yn	X
uva.x030312957	131	4	:	:	PUNCT
uva.x030312957	131	5	summing	sum	VERB
uva.x030312957	131	6	both	both	DET
uva.x030312957	131	7	sides	side	NOUN
uva.x030312957	131	8	of	of	ADP
uva.x030312957	131	9	(	(	PUNCT
uva.x030312957	131	10	2	2	NUM
uva.x030312957	131	11	)	)	PUNCT
uva.x030312957	131	12	over	over	ADP
uva.x030312957	131	13	the	the	DET
uva.x030312957	131	14	roots	root	NOUN
uva.x030312957	131	15	of	of	ADP
uva.x030312957	131	16	f(x	f(x	NOUN
uva.x030312957	131	17	)	)	PUNCT
uva.x030312957	131	18	=	=	PROPN
uva.x030312957	131	19	(	(	PUNCT
uva.x030312957	131	20	0	0	X
uva.x030312957	131	21	)	)	PUNCT
uva.x030312957	131	22	there	there	PRON
uva.x030312957	131	23	results	result	VERB
uva.x030312957	131	24	the	the	DET
uva.x030312957	131	25	expressions	expression	NOUN
uva.x030312957	131	26	,	,	PUNCT
uva.x030312957	131	27	s[fo(x	s[fo(x	PROPN
uva.x030312957	131	28	)	)	PUNCT
uva.x030312957	131	29	]	]	PUNCT
uva.x030312957	132	1	ndo	ndo	PROPN
uva.x030312957	132	2	,	,	PUNCT
uva.x030312957	132	3	s[f1(x	s[f1(x	PROPN
uva.x030312957	132	4	)	)	PUNCT
uva.x030312957	132	5	]	]	PUNCT
uva.x030312957	132	6	=	=	PUNCT
uva.x030312957	132	7	(	(	PUNCT
uva.x030312957	132	8	n	n	CCONJ
uva.x030312957	132	9	−	−	PROPN
uva.x030312957	132	10	1)ai	1)ai	PROPN
uva.x030312957	132	11	,	,	PUNCT
uva.x030312957	132	12	(	(	PUNCT
uva.x030312957	132	13	6	6	X
uva.x030312957	132	14	)	)	PUNCT
uva.x030312957	132	15	s[f2	s[f2	NOUN
uva.x030312957	132	16	(	(	PUNCT
uva.x030312957	132	17	x	x	PROPN
uva.x030312957	132	18	)	)	PUNCT
uva.x030312957	132	19	]	]	PUNCT
uva.x030312957	132	20	=	=	PUNCT
uva.x030312957	132	21	(	(	PUNCT
uva.x030312957	132	22	n	n	CCONJ
uva.x030312957	132	23	2	2	X
uva.x030312957	132	24	)	)	PUNCT
uva.x030312957	132	25	az	az	PROPN
uva.x030312957	132	26	,	,	PUNCT
uva.x030312957	132	27	s[fr-1(x	s[fr-1(x	PROPN
uva.x030312957	132	28	)	)	PUNCT
uva.x030312957	132	29	]	]	PUNCT
uva.x030312957	133	1	=	=	PUNCT
uva.x030312957	133	2	an-1	an-1	SPACE
uva.x030312957	133	3	.	.	PUNCT
uva.x030312957	134	1	the	the	DET
uva.x030312957	134	2	left	left	ADJ
uva.x030312957	134	3	side	side	NOUN
uva.x030312957	134	4	of	of	ADP
uva.x030312957	134	5	(	(	PUNCT
uva.x030312957	134	6	2	2	X
uva.x030312957	134	7	)	)	PUNCT
uva.x030312957	134	8	gives	give	VERB
uva.x030312957	134	9	f(t	f(t	PROPN
uva.x030312957	134	10	)	)	PUNCT
uva.x030312957	134	11	f(t	f(t	PROPN
uva.x030312957	134	12	)	)	PUNCT
uva.x030312957	134	13	+	+	CCONJ
uva.x030312957	135	1	+	+	CCONJ
uva.x030312957	135	2	t	t	X
uva.x030312957	135	3	x2	x2	PROPN
uva.x030312957	136	1	+	+	CCONJ
uva.x030312957	136	2	t	t	X
uva.x030312957	136	3	xn	xn	PROPN
uva.x030312957	136	4	(	(	PUNCT
uva.x030312957	136	5	7	7	X
uva.x030312957	136	6	)	)	PUNCT
uva.x030312957	136	7	=	=	PROPN
uva.x030312957	136	8	(	(	PUNCT
uva.x030312957	136	9	dtf(t	dtf(t	PROPN
uva.x030312957	136	10	)	)	PUNCT
uva.x030312957	136	11	=	=	PROPN
uva.x030312957	137	1	na	na	ADP
uva.x030312957	137	2	,	,	PUNCT
uva.x030312957	137	3	th–1	th–1	PROPN
uva.x030312957	137	4	+	+	PROPN
uva.x030312957	137	5	(	(	PUNCT
uva.x030312957	137	6	n	n	CCONJ
uva.x030312957	137	7	1	1	X
uva.x030312957	137	8	)	)	PUNCT
uva.x030312957	137	9	a	a	PRON
uva.x030312957	137	10	,	,	PUNCT
uva.x030312957	137	11	tn-2	tn-2	NOUN
uva.x030312957	137	12	+	+	PUNCT
uva.x030312957	137	13	...	...	PUNCT
uva.x030312957	138	1	+	+	PUNCT
uva.x030312957	138	2	an-1	an-1	PUNCT
uva.x030312957	138	3	and	and	CCONJ
uva.x030312957	138	4	the	the	DET
uva.x030312957	138	5	right	right	ADJ
uva.x030312957	138	6	side	side	NOUN
uva.x030312957	138	7	of	of	ADP
uva.x030312957	138	8	(	(	PUNCT
uva.x030312957	138	9	2	2	NUM
uva.x030312957	138	10	)	)	PUNCT
uva.x030312957	138	11	summed	sum	VERB
uva.x030312957	138	12	gives	gives	PROPN
uva.x030312957	138	13	(	(	PUNCT
uva.x030312957	138	14	8)	8)	NUM
uva.x030312957	138	15	s	s	PART
uva.x030312957	138	16	s(:-	s(:-	PROPN
uva.x030312957	138	17	)	)	PUNCT
uva.x030312957	138	18	f(t	f(t	PROPN
uva.x030312957	138	19	)	)	PUNCT
uva.x030312957	138	20	t	t	PROPN
uva.x030312957	138	21	=	=	PROPN
uva.x030312957	138	22	fn-1	fn-1	PUNCT
uva.x030312957	138	23	s	s	PROPN
uva.x030312957	138	24	(	(	PUNCT
uva.x030312957	138	25	fo(x	fo(x	SPACE
uva.x030312957	138	26	)	)	PUNCT
uva.x030312957	138	27	]	]	PUNCT
uva.x030312957	139	1	+	+	CCONJ
uva.x030312957	139	2	tn	tn	PROPN
uva.x030312957	139	3	-	-	PUNCT
uva.x030312957	139	4	sifi(x	sifi(x	NOUN
uva.x030312957	139	5	)	)	PUNCT
uva.x030312957	139	6	]	]	PUNCT
uva.x030312957	140	1	+	+	PUNCT
uva.x030312957	140	2	...	...	PUNCT
uva.x030312957	141	1	+	+	CCONJ
uva.x030312957	141	2	s[fr-1(x	s[fr-1(x	NOUN
uva.x030312957	141	3	)	)	PUNCT
uva.x030312957	141	4	]	]	PUNCT
uva.x030312957	141	5	.	.	PUNCT
uva.x030312957	142	1	comparing	compare	VERB
uva.x030312957	142	2	coefficients	coefficient	NOUN
uva.x030312957	142	3	in	in	ADP
uva.x030312957	142	4	(	(	PUNCT
uva.x030312957	142	5	7	7	NUM
uva.x030312957	142	6	)	)	PUNCT
uva.x030312957	142	7	and	and	CCONJ
uva.x030312957	142	8	(	(	PUNCT
uva.x030312957	142	9	8)	8)	NUM
uva.x030312957	142	10	the	the	DET
uva.x030312957	142	11	expressions	expression	NOUN
uva.x030312957	142	12	in	in	ADP
uva.x030312957	142	13	(	(	PUNCT
uva.x030312957	142	14	6	6	NUM
uva.x030312957	142	15	)	)	PUNCT
uva.x030312957	142	16	are	be	AUX
uva.x030312957	142	17	found	find	VERB
uva.x030312957	142	18	.	.	PUNCT
uva.x030312957	143	1	84	84	NUM
uva.x030312957	143	2	.	.	PUNCT
uva.x030312957	144	1	determination	determination	NOUN
uva.x030312957	144	2	of	of	ADP
uva.x030312957	144	3	hermite	hermite	PROPN
uva.x030312957	144	4	's	's	PART
uva.x030312957	144	5	form	form	NOUN
uva.x030312957	144	6	h.	h.	NOUN
uva.x030312957	144	7	represent	represent	VERB
uva.x030312957	144	8	the	the	DET
uva.x030312957	144	9	product	product	NOUN
uva.x030312957	144	10	of	of	ADP
uva.x030312957	144	11	yf	yf	PROPN
uva.x030312957	144	12	,	,	PUNCT
uva.x030312957	144	13	by	by	ADP
uva.x030312957	144	14	(	(	PUNCT
uva.x030312957	144	15	9	9	NUM
uva.x030312957	144	16	)	)	PUNCT
uva.x030312957	144	17	yf	yf	PROPN
uva.x030312957	144	18	.	.	PUNCT
uva.x030312957	144	19	eo	eo	PROPN
uva.x030312957	144	20	,	,	PUNCT
uva.x030312957	144	21	o	o	X
uva.x030312957	144	22	fo	fo	NOUN
uva.x030312957	144	23	+	+	CCONJ
uva.x030312957	144	24	e1	e1	PROPN
uva.x030312957	144	25	,	,	PUNCT
uva.x030312957	144	26	o	o	X
uva.x030312957	144	27	f1	f1	PROPN
uva.x030312957	144	28	+	+	CCONJ
uva.x030312957	144	29	e2	e2	PROPN
uva.x030312957	144	30	,	,	PUNCT
uva.x030312957	144	31	o	o	X
uva.x030312957	144	32	f2	f2	PROPN
uva.x030312957	145	1	+	+	CCONJ
uva.x030312957	145	2	+	+	CCONJ
uva.x030312957	145	3	en-1	en-1	X
uva.x030312957	145	4	,	,	PUNCT
uva.x030312957	145	5	o	o	NOUN
uva.x030312957	145	6	fn-1	fn-1	PUNCT
uva.x030312957	145	7	s	s	PROPN
uva.x030312957	145	8	=	=	NOUN
uva.x030312957	145	9	0	0	NUM
uva.x030312957	145	10	,	,	PUNCT
uva.x030312957	145	11	1	1	NUM
uva.x030312957	145	12	,	,	PUNCT
uva.x030312957	145	13	2	2	NUM
uva.x030312957	145	14	,	,	PUNCT
uva.x030312957	145	15	...	...	PUNCT
uva.x030312957	145	16	,	,	PUNCT
uva.x030312957	145	17	n	n	PROPN
uva.x030312957	145	18	1	1	X
uva.x030312957	145	19	.	.	PUNCT
uva.x030312957	146	1	when	when	SCONJ
uva.x030312957	146	2	8	8	NUM
uva.x030312957	146	3	=	=	SYM
uva.x030312957	146	4	0	0	NUM
uva.x030312957	146	5	,	,	PUNCT
uva.x030312957	146	6	comparing	compare	VERB
uva.x030312957	146	7	coefficients	coefficient	NOUN
uva.x030312957	146	8	in	in	ADP
uva.x030312957	146	9	(	(	PUNCT
uva.x030312957	146	10	9	9	NUM
uva.x030312957	146	11	)	)	PUNCT
uva.x030312957	146	12	and	and	CCONJ
uva.x030312957	146	13	yf	yf	PROPN
uva.x030312957	146	14	,	,	PUNCT
uva.x030312957	146	15	obtained	obtain	VERB
uva.x030312957	146	16	from	from	ADP
uva.x030312957	146	17	(	(	PUNCT
uva.x030312957	146	18	4	4	NUM
uva.x030312957	146	19	)	)	PUNCT
uva.x030312957	146	20	,	,	PUNCT
uva.x030312957	146	21	the	the	DET
uva.x030312957	146	22	set	set	NOUN
uva.x030312957	146	23	of	of	ADP
uva.x030312957	146	24	ei	ei	PROPN
uva.x030312957	146	25	,	,	PUNCT
uva.x030312957	146	26	.	.	PUNCT
uva.x030312957	147	1	for	for	ADP
uva.x030312957	147	2	s	s	NOUN
uva.x030312957	147	3	=	=	SYM
uva.x030312957	147	4	0	0	NUM
uva.x030312957	147	5	are	be	AUX
uva.x030312957	147	6	found	find	VERB
uva.x030312957	147	7	to	to	PART
uva.x030312957	147	8	be	be	AUX
uva.x030312957	147	9	,	,	PUNCT
uva.x030312957	147	10	since	since	SCONJ
uva.x030312957	147	11	fo(x	fo(x	SPACE
uva.x030312957	147	12	)	)	PUNCT
uva.x030312957	147	13	=	=	PUNCT
uva.x030312957	147	14	do	do	VERB
uva.x030312957	147	15	,	,	PUNCT
uva.x030312957	147	16	(	(	PUNCT
uva.x030312957	147	17	10	10	X
uva.x030312957	147	18	)	)	PUNCT
uva.x030312957	147	19	e.	e.	NOUN
uva.x030312957	147	20	0	0	PUNCT
uva.x030312957	147	21	=	=	PUNCT
uva.x030312957	147	22	do	do	VERB
uva.x030312957	147	23	in-1	in-1	PROPN
uva.x030312957	147	24	,	,	PUNCT
uva.x030312957	147	25	e1	e1	PROPN
uva.x030312957	147	26	,	,	PUNCT
uva.x030312957	147	27	o	o	NOUN
uva.x030312957	147	28	=	=	PUNCT
uva.x030312957	147	29	do	do	AUX
uva.x030312957	147	30	tn-2	tn-2	SPACE
uva.x030312957	147	31	,	,	PUNCT
uva.x030312957	147	32	en-1	en-1	PROPN
uva.x030312957	147	33	,	,	PUNCT
uva.x030312957	147	34	a	a	PRON
uva.x030312957	147	35	=	=	NOUN
uva.x030312957	147	36	do	do	AUX
uva.x030312957	147	37	to	to	PART
uva.x030312957	147	38	.	.	PUNCT
uva.x030312957	148	1	9	9	NUM
uva.x030312957	149	1	the	the	DET
uva.x030312957	149	2	remaining	remain	VERB
uva.x030312957	149	3	e	e	NOUN
uva.x030312957	149	4	;	;	PUNCT
uva.x030312957	149	5	,	,	PUNCT
uva.x030312957	149	6	;	;	PUNCT
uva.x030312957	149	7	functions	function	NOUN
uva.x030312957	149	8	are	be	AUX
uva.x030312957	149	9	determined	determine	VERB
uva.x030312957	149	10	from	from	ADP
uva.x030312957	149	11	the	the	DET
uva.x030312957	149	12	following	follow	VERB
uva.x030312957	149	13	relations	relation	NOUN
uva.x030312957	149	14	,	,	PUNCT
uva.x030312957	149	15	which	which	PRON
uva.x030312957	149	16	are	be	AUX
uva.x030312957	149	17	true	true	ADJ
uva.x030312957	149	18	in	in	ADP
uva.x030312957	149	19	virtue	virtue	NOUN
uva.x030312957	149	20	of	of	ADP
uva.x030312957	149	21	(	(	PUNCT
uva.x030312957	149	22	3	3	NUM
uva.x030312957	149	23	)	)	PUNCT
uva.x030312957	149	24	.	.	PUNCT
uva.x030312957	150	1	by	by	ADP
uva.x030312957	150	2	a	a	DET
uva.x030312957	150	3	method	method	NOUN
uva.x030312957	150	4	due	due	ADP
uva.x030312957	150	5	to	to	ADP
uva.x030312957	150	6	hermite	hermite	NOUN
uva.x030312957	150	7	9	9	NUM
uva.x030312957	150	8	æf	æf	PROPN
uva.x030312957	150	9	.	.	PUNCT
uva.x030312957	150	10	=	=	PROPN
uva.x030312957	150	11	ac	ac	X
uva.x030312957	150	12	x	x	X
uva.x030312957	150	13	=	=	X
uva.x030312957	150	14	fı	fı	PROPN
uva.x030312957	150	15	–	–	PUNCT
uva.x030312957	150	16	01	01	NUM
uva.x030312957	150	17	,	,	PUNCT
uva.x030312957	150	18	xfı	xfı	PROPN
uva.x030312957	150	19	=	=	PROPN
uva.x030312957	150	20	f2	f2	PROPN
uva.x030312957	150	21	–	–	PUNCT
uva.x030312957	150	22	02	02	NUM
uva.x030312957	150	23	,	,	PUNCT
uva.x030312957	150	24	xf2	xf2	PROPN
uva.x030312957	150	25	=	=	PUNCT
uva.x030312957	150	26	f3	f3	PROPN
uva.x030312957	150	27	–	–	PUNCT
uva.x030312957	150	28	03	03	NUM
uva.x030312957	150	29	,	,	PUNCT
uva.x030312957	150	30	(	(	PUNCT
uva.x030312957	150	31	11	11	NUM
uva.x030312957	150	32	)	)	PUNCT
uva.x030312957	150	33	afn–2	afn–2	PROPN
uva.x030312957	150	34	=	=	PUNCT
uva.x030312957	150	35	fr-1	fr-1	PUNCT
uva.x030312957	150	36	an-1	an-1	SPACE
uva.x030312957	150	37	,	,	PUNCT
uva.x030312957	150	38	xfn-1	xfn-1	PUNCT
uva.x030312957	150	39	=	=	PROPN
uva.x030312957	150	40	f	f	X
uva.x030312957	150	41	on	on	ADP
uva.x030312957	150	42	,	,	PUNCT
uva.x030312957	150	43	an	an	PRON
uva.x030312957	150	44	since	since	SCONJ
uva.x030312957	150	45	f	f	PROPN
uva.x030312957	150	46	(	(	PUNCT
uva.x030312957	150	47	x	x	SYM
uva.x030312957	150	48	)	)	PUNCT
uva.x030312957	150	49	=	=	SYM
uva.x030312957	150	50	0	0	NUM
uva.x030312957	150	51	.	.	PUNCT
uva.x030312957	150	52	from	from	ADP
uva.x030312957	150	53	(	(	PUNCT
uva.x030312957	150	54	9	9	NUM
uva.x030312957	150	55	)	)	PUNCT
uva.x030312957	150	56	and	and	CCONJ
uva.x030312957	150	57	(	(	PUNCT
uva.x030312957	150	58	11	11	X
uva.x030312957	150	59	)	)	PUNCT
uva.x030312957	150	60	we	we	PRON
uva.x030312957	150	61	have	have	VERB
uva.x030312957	150	62	,	,	PUNCT
uva.x030312957	150	63	xyf	xyf	PROPN
uva.x030312957	150	64	.	.	PUNCT
uva.x030312957	151	1	eo	eo	PROPN
uva.x030312957	151	2	,	,	PUNCT
uva.x030312957	151	3	&	&	CCONJ
uva.x030312957	151	4	fi	fi	PROPN
uva.x030312957	151	5	+	+	PROPN
uva.x030312957	151	6	e1	e1	PROPN
uva.x030312957	151	7	,	,	PUNCT
uva.x030312957	151	8	&	&	CCONJ
uva.x030312957	151	9	f2	f2	PROPN
uva.x030312957	151	10	+	+	PUNCT
uva.x030312957	151	11	...	...	PUNCT
uva.x030312957	152	1	+	+	CCONJ
uva.x030312957	152	2	en-2	en-2	SPACE
uva.x030312957	152	3	,	,	PUNCT
uva.x030312957	152	4	ofn-1	ofn-1	ADP
uva.x030312957	152	5	(	(	PUNCT
uva.x030312957	152	6	12	12	NUM
uva.x030312957	152	7	)	)	PUNCT
uva.x030312957	152	8	a	a	DET
uva.x030312957	152	9	,	,	PUNCT
uva.x030312957	152	10	e.	e.	PROPN
uva.x030312957	152	11	,	,	PUNCT
uva.x030312957	152	12	o	o	NOUN
uva.x030312957	152	13	22	22	NUM
uva.x030312957	152	14	e1	e1	PROPN
uva.x030312957	152	15	,	,	PUNCT
uva.x030312957	152	16	an-1	an-1	PUNCT
uva.x030312957	152	17	en-2,8	en-2,8	PROPN
uva.x030312957	152	18	an	an	DET
uva.x030312957	152	19	en-1	en-1	PROPN
uva.x030312957	152	20	,	,	PUNCT
uva.x030312957	152	21	now	now	ADV
uva.x030312957	152	22	define	define	VERB
uva.x030312957	152	23	e-1	e-1	SPACE
uva.x030312957	152	24	,	,	PUNCT
uva.x030312957	152	25	,	,	PUNCT
uva.x030312957	152	26	by	by	ADP
uva.x030312957	152	27	8	8	NUM
uva.x030312957	152	28	8	8	NUM
uva.x030312957	152	29	(	(	PUNCT
uva.x030312957	152	30	13	13	NUM
uva.x030312957	152	31	)	)	PUNCT
uva.x030312957	152	32	do	do	VERB
uva.x030312957	152	33	e-1	e-1	PROPN
uva.x030312957	152	34	,	,	PUNCT
uva.x030312957	152	35	s	s	VERB
uva.x030312957	152	36	+	+	PROPN
uva.x030312957	152	37	di	di	X
uva.x030312957	152	38	eo	eo	X
uva.x030312957	152	39	,	,	PUNCT
uva.x030312957	152	40	s	s	PART
uva.x030312957	152	41	+	+	PROPN
uva.x030312957	152	42	02	02	NUM
uva.x030312957	152	43	e1	e1	PROPN
uva.x030312957	152	44	,	,	PUNCT
uva.x030312957	152	45	8	8	NUM
uva.x030312957	152	46	+	+	CCONJ
uva.x030312957	152	47	+	+	NUM
uva.x030312957	152	48	an	an	DET
uva.x030312957	152	49	en-1	en-1	NOUN
uva.x030312957	152	50	,	,	PUNCT
uva.x030312957	152	51	=	=	SYM
uva.x030312957	152	52	0	0	NUM
uva.x030312957	152	53	.	.	PUNCT
uva.x030312957	153	1	multiply	multiply	PROPN
uva.x030312957	153	2	(	(	PUNCT
uva.x030312957	153	3	9	9	NUM
uva.x030312957	153	4	)	)	PUNCT
uva.x030312957	153	5	by	by	ADP
uva.x030312957	153	6	a	a	PRON
uva.x030312957	153	7	and	and	CCONJ
uva.x030312957	153	8	subtract	subtract	NOUN
uva.x030312957	153	9	from	from	ADP
uva.x030312957	153	10	(	(	PUNCT
uva.x030312957	153	11	12	12	NUM
uva.x030312957	153	12	)	)	PUNCT
uva.x030312957	153	13	using	use	VERB
uva.x030312957	153	14	(	(	PUNCT
uva.x030312957	153	15	13	13	NUM
uva.x030312957	153	16	)	)	PUNCT
uva.x030312957	153	17	and	and	CCONJ
uva.x030312957	153	18	we	we	PRON
uva.x030312957	153	19	get	get	VERB
uva.x030312957	153	20	(	(	PUNCT
uva.x030312957	153	21	x	x	PUNCT
uva.x030312957	153	22	–	–	PUNCT
uva.x030312957	153	23	a)yf	a)yf	PROPN
uva.x030312957	153	24	,	,	PUNCT
uva.x030312957	153	25	=	=	PUNCT
uva.x030312957	153	26	(	(	PUNCT
uva.x030312957	153	27	e_1	e_1	PROPN
uva.x030312957	153	28	,	,	PUNCT
uva.x030312957	153	29	a	a	DET
uva.x030312957	153	30	eo	eo	X
uva.x030312957	153	31	,	,	PUNCT
uva.x030312957	153	32	e)fo	e)fo	PROPN
uva.x030312957	154	1	+	+	PROPN
uva.x030312957	154	2	(	(	PUNCT
uva.x030312957	154	3	eo	eo	PROPN
uva.x030312957	154	4	,	,	PUNCT
uva.x030312957	154	5	.	.	PUNCT
uva.x030312957	155	1	ae1	ae1	PROPN
uva.x030312957	155	2	,	,	PUNCT
uva.x030312957	155	3	.)fi	.)fi	PUNCT
uva.x030312957	156	1	+	+	CCONJ
uva.x030312957	156	2	...	...	PUNCT
uva.x030312957	156	3	(	(	PUNCT
uva.x030312957	156	4	14	14	NUM
uva.x030312957	156	5	)	)	PUNCT
uva.x030312957	156	6	+	+	NUM
uva.x030312957	156	7	(	(	PUNCT
uva.x030312957	156	8	en-2	en-2	SPACE
uva.x030312957	156	9	,	,	PUNCT
uva.x030312957	156	10	.	.	PUNCT
uva.x030312957	156	11	aem-1	aem-1	SPACE
uva.x030312957	156	12	,	,	PUNCT
uva.x030312957	156	13	2	2	X
uva.x030312957	156	14	)	)	PUNCT
uva.x030312957	156	15	fn-1	fn-1	SPACE
uva.x030312957	156	16	.	.	PROPN
uva.x030312957	156	17	e_1	e_1	PROPN
uva.x030312957	156	18	,	,	PUNCT
uva.x030312957	156	19	o	o	X
uva.x030312957	156	20	may	may	AUX
uva.x030312957	156	21	be	be	AUX
uva.x030312957	156	22	expressed	express	VERB
uva.x030312957	156	23	from	from	ADP
uva.x030312957	156	24	the	the	DET
uva.x030312957	156	25	equation	equation	NOUN
uva.x030312957	156	26	(	(	PUNCT
uva.x030312957	156	27	15	15	NUM
uva.x030312957	156	28	)	)	PUNCT
uva.x030312957	156	29	ao	ao	NOUN
uva.x030312957	156	30	into	into	ADP
uva.x030312957	156	31	tai	tai	PROPN
uva.x030312957	156	32	int8	int8	PROPN
uva.x030312957	156	33	-	-	PUNCT
uva.x030312957	156	34	1	1	NUM
uva.x030312957	156	35	+	+	CCONJ
uva.x030312957	156	36	+	+	ADV
uva.x030312957	156	37	ant	ant	ADJ
uva.x030312957	156	38	,	,	PUNCT
uva.x030312957	156	39	=	=	NOUN
uva.x030312957	156	40	0	0	NUM
uva.x030312957	156	41	,	,	PUNCT
uva.x030312957	156	42	which	which	PRON
uva.x030312957	156	43	is	be	AUX
uva.x030312957	156	44	obtained	obtain	VERB
uva.x030312957	156	45	by	by	ADP
uva.x030312957	156	46	introducing	introduce	VERB
uva.x030312957	156	47	,	,	PUNCT
uva.x030312957	156	48	11	11	NUM
uva.x030312957	156	49	,	,	PUNCT
uva.x030312957	156	50	112	112	NUM
uva.x030312957	156	51	,	,	PUNCT
uva.x030312957	156	52	through	through	ADP
uva.x030312957	156	53	the	the	DET
uva.x030312957	156	54	following	follow	VERB
uva.x030312957	156	55	equations	equation	NOUN
uva.x030312957	156	56	ao	ao	ADP
uva.x030312957	156	57	tn	tn	PROPN
uva.x030312957	156	58	+	+	CCONJ
uva.x030312957	156	59	ai	ai	VERB
uva.x030312957	156	60	tn-1	tn-1	PRON
uva.x030312957	157	1	+	+	CCONJ
uva.x030312957	157	2	a2	a2	PROPN
uva.x030312957	157	3	tn-2	tn-2	X
uva.x030312957	157	4	+	+	SYM
uva.x030312957	157	5	+	+	SYM
uva.x030312957	157	6	anto	anto	PROPN
uva.x030312957	157	7	=	=	PROPN
uva.x030312957	157	8	0	0	NUM
uva.x030312957	157	9	,	,	PUNCT
uva.x030312957	157	10	(	(	PUNCT
uva.x030312957	157	11	16	16	NUM
uva.x030312957	157	12	)	)	PUNCT
uva.x030312957	157	13	ao	ao	ADP
uva.x030312957	157	14	n+1	n+1	X
uva.x030312957	158	1	+	+	CCONJ
uva.x030312957	158	2	a	a	DET
uva.x030312957	158	3	n	n	NOUN
uva.x030312957	158	4	+	+	CCONJ
uva.x030312957	158	5	a2	a2	PROPN
uva.x030312957	158	6	tn-1	tn-1	PROPN
uva.x030312957	159	1	+	+	PUNCT
uva.x030312957	159	2	+	+	NUM
uva.x030312957	159	3	an	an	DET
uva.x030312957	159	4	ti	ti	NOUN
uva.x030312957	159	5	0	0	NUM
uva.x030312957	159	6	,	,	PUNCT
uva.x030312957	159	7	0	0	NUM
uva.x030312957	159	8	,	,	PUNCT
uva.x030312957	159	9	do	do	VERB
uva.x030312957	159	10	tn+2	tn+2	ADV
uva.x030312957	160	1	+	+	PUNCT
uva.x030312957	160	2	atn+1	atn+1	VERB
uva.x030312957	160	3	+	+	CCONJ
uva.x030312957	160	4	a2	a2	PROPN
uva.x030312957	160	5	tn	tn	PROPN
uva.x030312957	160	6	+	+	PROPN
uva.x030312957	160	7	+	+	CCONJ
uva.x030312957	160	8	antz	antz	ADJ
uva.x030312957	160	9	multiply	multiply	ADJ
uva.x030312957	160	10	equations	equation	NOUN
uva.x030312957	160	11	(	(	PUNCT
uva.x030312957	160	12	11	11	NUM
uva.x030312957	160	13	)	)	PUNCT
uva.x030312957	160	14	through	through	ADP
uva.x030312957	160	15	,	,	PUNCT
uva.x030312957	160	16	in	in	ADP
uva.x030312957	160	17	order	order	NOUN
uva.x030312957	160	18	,	,	PUNCT
uva.x030312957	160	19	by	by	ADP
uva.x030312957	160	20	tn-1	tn-1	SPACE
uva.x030312957	160	21	,	,	PUNCT
uva.x030312957	160	22	in-2	in-2	SPACE
uva.x030312957	160	23	,	,	PUNCT
uva.x030312957	160	24	...	...	PUNCT
uva.x030312957	160	25	,	,	PUNCT
uva.x030312957	160	26	to	to	PART
uva.x030312957	160	27	and	and	CCONJ
uva.x030312957	160	28	add	add	VERB
uva.x030312957	160	29	,	,	PUNCT
uva.x030312957	160	30	whence	whence	NOUN
uva.x030312957	160	31	(	(	PUNCT
uva.x030312957	160	32	17	17	NUM
uva.x030312957	160	33	)	)	PUNCT
uva.x030312957	161	1	xy	xy	X
uva.x030312957	161	2	=	=	PROPN
uva.x030312957	161	3	info	info	NOUN
uva.x030312957	161	4	+	+	CCONJ
uva.x030312957	161	5	tn	tn	NOUN
uva.x030312957	161	6	-	-	PUNCT
uva.x030312957	161	7	l	l	NOUN
uva.x030312957	161	8	fi	fi	NOUN
uva.x030312957	162	1	+	+	PUNCT
uva.x030312957	162	2	...	...	PUNCT
uva.x030312957	163	1	+	+	PUNCT
uva.x030312957	163	2	ti	ti	X
uva.x030312957	163	3	fn-1	fn-1	SPACE
uva.x030312957	163	4	.	.	PUNCT
uva.x030312957	164	1	similarly	similarly	ADV
uva.x030312957	164	2	multiply	multiply	ADJ
uva.x030312957	164	3	equations	equation	NOUN
uva.x030312957	164	4	(	(	PUNCT
uva.x030312957	164	5	11	11	NUM
uva.x030312957	164	6	)	)	PUNCT
uva.x030312957	164	7	through	through	ADP
uva.x030312957	164	8	,	,	PUNCT
uva.x030312957	164	9	in	in	ADP
uva.x030312957	164	10	order	order	NOUN
uva.x030312957	164	11	,	,	PUNCT
uva.x030312957	164	12	by	by	ADP
uva.x030312957	164	13	ta	ta	NOUN
uva.x030312957	164	14	,	,	PUNCT
uva.x030312957	164	15	ta-1	ta-1	SPACE
uva.x030312957	164	16	,	,	PUNCT
uva.x030312957	164	17	,	,	PUNCT
uva.x030312957	164	18	ti	ti	PROPN
uva.x030312957	164	19	,	,	PUNCT
uva.x030312957	164	20	add	add	VERB
uva.x030312957	164	21	and	and	CCONJ
uva.x030312957	164	22	use	use	NOUN
uva.x030312957	164	23	(	(	PUNCT
uva.x030312957	164	24	16	16	NUM
uva.x030312957	164	25	)	)	PUNCT
uva.x030312957	164	26	and	and	CCONJ
uva.x030312957	164	27	(	(	PUNCT
uva.x030312957	164	28	17	17	NUM
uva.x030312957	164	29	)	)	PUNCT
uva.x030312957	164	30	,	,	PUNCT
uva.x030312957	164	31	and	and	CCONJ
uva.x030312957	164	32	we	we	PRON
uva.x030312957	164	33	have	have	VERB
uva.x030312957	164	34	,	,	PUNCT
uva.x030312957	164	35	10	10	NUM
uva.x030312957	164	36	solution	solution	NOUN
uva.x030312957	164	37	of	of	ADP
uva.x030312957	164	38	the	the	DET
uva.x030312957	164	39	equation	equation	NOUN
uva.x030312957	164	40	of	of	ADP
uva.x030312957	164	41	secular	secular	ADJ
uva.x030312957	164	42	variation	variation	NOUN
uva.x030312957	164	43	22	22	NUM
uva.x030312957	164	44	y	y	PROPN
uva.x030312957	164	45	(	(	PUNCT
uva.x030312957	164	46	18	18	NUM
uva.x030312957	164	47	)	)	PUNCT
uva.x030312957	164	48	=	=	VERB
uva.x030312957	165	1	tnt1	tnt1	ADV
uva.x030312957	165	2	fo	fo	PROPN
uva.x030312957	165	3	+	+	X
uva.x030312957	165	4	tn	tn	ADJ
uva.x030312957	165	5	fi	fi	NOUN
uva.x030312957	166	1	+	+	PUNCT
uva.x030312957	166	2	...	...	PUNCT
uva.x030312957	167	1	+	+	PUNCT
uva.x030312957	167	2	t2	t2	PROPN
uva.x030312957	167	3	fn–1	fn–1	PROPN
uva.x030312957	167	4	.	.	PUNCT
uva.x030312957	168	1	continuing	continue	VERB
uva.x030312957	168	2	this	this	DET
uva.x030312957	168	3	process	process	NOUN
uva.x030312957	168	4	the	the	DET
uva.x030312957	168	5	following	following	ADJ
uva.x030312957	168	6	system	system	NOUN
uva.x030312957	168	7	is	be	AUX
uva.x030312957	168	8	obtained	obtain	VERB
uva.x030312957	168	9	:	:	PUNCT
uva.x030312957	169	1	y	y	PROPN
uva.x030312957	169	2	=	=	PUNCT
uva.x030312957	169	3	tn-1	tn-1	ADJ
uva.x030312957	169	4	fo	fo	NOUN
uva.x030312957	169	5	+	+	NOUN
uva.x030312957	169	6	tn-2	tn-2	SYM
uva.x030312957	169	7	f1	f1	NOUN
uva.x030312957	169	8	+	+	CCONJ
uva.x030312957	169	9	tn–3f2	tn–3f2	VERB
uva.x030312957	169	10	+	+	NUM
uva.x030312957	169	11	+	+	NUM
uva.x030312957	169	12	to	to	ADP
uva.x030312957	169	13	fn-1	fn-1	SPACE
uva.x030312957	169	14	,	,	PUNCT
uva.x030312957	169	15	xy	xy	PROPN
uva.x030312957	169	16	=	=	NOUN
uva.x030312957	169	17	tn	tn	PROPN
uva.x030312957	169	18	fo	fo	PROPN
uva.x030312957	169	19	+	+	ADJ
uva.x030312957	169	20	tn–1fi	tn–1fi	INTJ
uva.x030312957	169	21	+	+	CCONJ
uva.x030312957	169	22	tn-2f2	tn-2f2	ADJ
uva.x030312957	170	1	+	+	PUNCT
uva.x030312957	170	2	+	+	PUNCT
uva.x030312957	170	3	ti	ti	X
uva.x030312957	170	4	fn-1	fn-1	SPACE
uva.x030312957	170	5	,	,	PUNCT
uva.x030312957	170	6	tn+1	tn+1	PRON
uva.x030312957	170	7	fo	fo	NOUN
uva.x030312957	170	8	+	+	CCONJ
uva.x030312957	170	9	in	in	ADP
uva.x030312957	170	10	fi	fi	NOUN
uva.x030312957	170	11	+	+	CCONJ
uva.x030312957	170	12	tn-1f2	tn-1f2	PROPN
uva.x030312957	170	13	+	+	CCONJ
uva.x030312957	170	14	...	...	PUNCT
uva.x030312957	171	1	+	+	CCONJ
uva.x030312957	171	2	tz	tz	PROPN
uva.x030312957	171	3	fn-1	fn-1	SPACE
uva.x030312957	171	4	,	,	PUNCT
uva.x030312957	171	5	(	(	PUNCT
uva.x030312957	171	6	19	19	NUM
uva.x030312957	171	7	)	)	PUNCT
uva.x030312957	171	8	in+2	in+2	PUNCT
uva.x030312957	171	9	fo	fo	NOUN
uva.x030312957	171	10	+	+	NUM
uva.x030312957	171	11	in+1	in+1	NOUN
uva.x030312957	171	12	fi	fi	NOUN
uva.x030312957	171	13	+	+	CCONJ
uva.x030312957	171	14	tnf2	tnf2	ADJ
uva.x030312957	172	1	+	+	CCONJ
uva.x030312957	172	2	...	...	PUNCT
uva.x030312957	173	1	+	+	CCONJ
uva.x030312957	173	2	tz	tz	PROPN
uva.x030312957	173	3	fn-1	fn-1	SPACE
uva.x030312957	173	4	,	,	PUNCT
uva.x030312957	173	5	y	y	PROPN
uva.x030312957	173	6	=	=	PROPN
uva.x030312957	174	1	22	22	NUM
uva.x030312957	174	2	y	y	X
uva.x030312957	174	3	x	x	PUNCT
uva.x030312957	174	4	y	y	PROPN
uva.x030312957	174	5	=	=	X
uva.x030312957	174	6	tnts-1	tnts-1	NUM
uva.x030312957	174	7	fo	fo	ADP
uva.x030312957	174	8	+	+	CCONJ
uva.x030312957	174	9	int8	int8	PROPN
uva.x030312957	174	10	-	-	PUNCT
uva.x030312957	174	11	2	2	NUM
uva.x030312957	174	12	f1	f1	PROPN
uva.x030312957	174	13	+	+	CCONJ
uva.x030312957	174	14	int8	int8	X
uva.x030312957	174	15	-	-	PUNCT
uva.x030312957	174	16	3f2	3f2	NUM
uva.x030312957	174	17	+	+	PUNCT
uva.x030312957	174	18	...	...	PUNCT
uva.x030312957	175	1	+	+	CCONJ
uva.x030312957	176	1	tofn-1	tofn-1	VERB
uva.x030312957	176	2	.	.	PUNCT
uva.x030312957	177	1	these	these	DET
uva.x030312957	177	2	relations	relation	NOUN
uva.x030312957	177	3	multiplied	multiply	VERB
uva.x030312957	177	4	through	through	ADP
uva.x030312957	177	5	,	,	PUNCT
uva.x030312957	177	6	in	in	ADP
uva.x030312957	177	7	order	order	NOUN
uva.x030312957	177	8	,	,	PUNCT
uva.x030312957	177	9	by	by	ADP
uva.x030312957	177	10	as	as	ADP
uva.x030312957	177	11	,	,	PUNCT
uva.x030312957	177	12	28	28	NUM
uva.x030312957	177	13	-	-	SYM
uva.x030312957	177	14	1	1	NUM
uva.x030312957	177	15	,	,	PUNCT
uva.x030312957	177	16	ag-2	ag-2	SPACE
uva.x030312957	177	17	,	,	PUNCT
uva.x030312957	177	18	do	do	VERB
uva.x030312957	177	19	9	9	NUM
uva.x030312957	177	20	and	and	CCONJ
uva.x030312957	177	21	added	add	VERB
uva.x030312957	177	22	give	give	VERB
uva.x030312957	178	1	the	the	DET
uva.x030312957	178	2	equation	equation	PROPN
uva.x030312957	178	3	yf	yf	PROPN
uva.x030312957	178	4	.	.	PUNCT
uva.x030312957	178	5	eo	eo	PROPN
uva.x030312957	178	6	,	,	PUNCT
uva.x030312957	178	7	ofo	ofo	PROPN
uva.x030312957	178	8	+	+	CCONJ
uva.x030312957	178	9	ei	ei	PROPN
uva.x030312957	178	10	,	,	PUNCT
uva.x030312957	178	11	s	s	VERB
uva.x030312957	178	12	fi	fi	NOUN
uva.x030312957	178	13	+	+	CCONJ
uva.x030312957	178	14	in	in	ADP
uva.x030312957	178	15	which	which	PRON
uva.x030312957	178	16	the	the	DET
uva.x030312957	178	17	ei	ei	PROPN
uva.x030312957	178	18	,	,	PUNCT
uva.x030312957	178	19	are	be	AUX
uva.x030312957	178	20	defined	define	VERB
uva.x030312957	178	21	by	by	ADP
uva.x030312957	178	22	(	(	PUNCT
uva.x030312957	178	23	9	9	NUM
uva.x030312957	178	24	)	)	PUNCT
uva.x030312957	179	1	+	+	NUM
uva.x030312957	179	2	en-1	en-1	PROPN
uva.x030312957	179	3	,	,	PUNCT
uva.x030312957	179	4	o	o	NOUN
uva.x030312957	179	5	fn-1	fn-1	SPACE
uva.x030312957	179	6	,	,	PUNCT
uva.x030312957	179	7	e_1	e_1	PROPN
uva.x030312957	179	8	,	,	PUNCT
uva.x030312957	179	9	8	8	NUM
uva.x030312957	179	10	=	=	SYM
uva.x030312957	179	11	ao	ao	INTJ
uva.x030312957	179	12	ints	int	NOUN
uva.x030312957	180	1	+	+	PUNCT
uva.x030312957	181	1	ay	ay	PROPN
uva.x030312957	181	2	tnt8	tnt8	PROPN
uva.x030312957	181	3	-	-	PUNCT
uva.x030312957	181	4	1	1	NUM
uva.x030312957	181	5	+	+	ADP
uva.x030312957	181	6	ta	ta	NOUN
uva.x030312957	181	7	,	,	PUNCT
uva.x030312957	181	8	tn	tn	PROPN
uva.x030312957	181	9	asti	asti	PROPN
uva.x030312957	181	10	tn-1	tn-1	SPACE
uva.x030312957	181	11	anto	anto	PROPN
uva.x030312957	181	12	,	,	PUNCT
uva.x030312957	181	13	eo	eo	PROPN
uva.x030312957	181	14	,	,	PUNCT
uva.x030312957	181	15	,	,	PUNCT
uva.x030312957	181	16	=	=	PRON
uva.x030312957	181	17	do	do	VERB
uva.x030312957	181	18	tn	tn	PROPN
uva.x030312957	181	19	3	3	NUM
uva.x030312957	181	20	-	-	SYM
uva.x030312957	181	21	1	1	NUM
uva.x030312957	181	22	+	+	NOUN
uva.x030312957	181	23	ai	ai	VERB
uva.x030312957	181	24	tn	tn	PROPN
uva.x030312957	181	25	3	3	NUM
uva.x030312957	181	26	-	-	SYM
uva.x030312957	181	27	2	2	NUM
uva.x030312957	181	28	+	+	NUM
uva.x030312957	181	29	...	...	PUNCT
uva.x030312957	182	1	+	+	CCONJ
uva.x030312957	182	2	a	a	DET
uva.x030312957	182	3	,	,	PUNCT
uva.x030312957	182	4	tn-1	tn-1	DET
uva.x030312957	182	5	28	28	NUM
uva.x030312957	182	6	+	+	NUM
uva.x030312957	182	7	1	1	NUM
uva.x030312957	182	8	tn-2	tn-2	ADJ
uva.x030312957	182	9	ants-1	ants-1	PROPN
uva.x030312957	182	10	,	,	PUNCT
uva.x030312957	182	11	e1	e1	PROPN
uva.x030312957	182	12	,	,	PUNCT
uva.x030312957	182	13	o	o	X
uva.x030312957	182	14	=	=	X
uva.x030312957	182	15	ao	ao	ADP
uva.x030312957	182	16	tn+8	tn+8	PROPN
uva.x030312957	182	17	-	-	PUNCT
uva.x030312957	182	18	2	2	NUM
uva.x030312957	182	19	+	+	PROPN
uva.x030312957	182	20	az	az	PROPN
uva.x030312957	182	21	int3	int3	PROPN
uva.x030312957	182	22	-	-	PUNCT
uva.x030312957	182	23	-3	-3	PROPN
uva.x030312957	182	24	+	+	CCONJ
uva.x030312957	182	25	...	...	PUNCT
uva.x030312957	183	1	+	+	CCONJ
uva.x030312957	183	2	a	a	DET
uva.x030312957	183	3	,	,	PUNCT
uva.x030312957	183	4	tn-2	tn-2	NUM
uva.x030312957	183	5	0.t1tn-3	0.t1tn-3	NUM
uva.x030312957	183	6	an	an	PRON
uva.x030312957	183	7	ts-2	ts-2	SPACE
uva.x030312957	183	8	,	,	PUNCT
uva.x030312957	183	9	e2	e2	PROPN
uva.x030312957	183	10	,	,	PUNCT
uva.x030312957	183	11	.	.	PUNCT
uva.x030312957	184	1	=	=	PUNCT
uva.x030312957	184	2	do	do	VERB
uva.x030312957	184	3	tn	tn	PROPN
uva.x030312957	184	4	18	18	NUM
uva.x030312957	184	5	-	-	SYM
uva.x030312957	184	6	3	3	NUM
uva.x030312957	184	7	+	+	CCONJ
uva.x030312957	184	8	az	az	X
uva.x030312957	184	9	in+84	in+84	NOUN
uva.x030312957	185	1	+	+	PUNCT
uva.x030312957	185	2	+	+	CCONJ
uva.x030312957	185	3	a	a	DET
uva.x030312957	185	4	,	,	PUNCT
uva.x030312957	185	5	tn-3	tn-3	X
uva.x030312957	185	6	ast1	ast1	VERB
uva.x030312957	185	7	tnt	tnt	PROPN
uva.x030312957	185	8	antz	antz	PROPN
uva.x030312957	185	9	-	-	PUNCT
uva.x030312957	185	10	s	s	PROPN
uva.x030312957	185	11	,	,	PUNCT
uva.x030312957	185	12	(	(	PUNCT
uva.x030312957	185	13	20	20	NUM
uva.x030312957	185	14	)	)	PUNCT
uva.x030312957	185	15	e3	e3	PROPN
uva.x030312957	185	16	-	-	PROPN
uva.x030312957	185	17	1	1	NUM
uva.x030312957	185	18	,	,	PUNCT
uva.x030312957	185	19	8	8	NUM
uva.x030312957	185	20	=	=	NOUN
uva.x030312957	185	21	do	do	VERB
uva.x030312957	185	22	tn	tn	PROPN
uva.x030312957	185	23	+	+	NOUN
uva.x030312957	185	24	aiin-1	aiin-1	NUM
uva.x030312957	185	25	+	+	CCONJ
uva.x030312957	185	26	t	t	NOUN
uva.x030312957	185	27	as	as	ADP
uva.x030312957	185	28	tn	tn	PROPN
uva.x030312957	185	29	-	-	PUNCT
uva.x030312957	185	30	s	s	PROPN
uva.x030312957	185	31	ag+1	ag+1	PRON
uva.x030312957	185	32	-1	-1	NOUN
uva.x030312957	185	33	an	an	PRON
uva.x030312957	185	34	to	to	PART
uva.x030312957	185	35	,	,	PUNCT
uva.x030312957	185	36	e.	e.	PROPN
uva.x030312957	185	37	,	,	PUNCT
uva.x030312957	185	38	=	=	PROPN
uva.x030312957	185	39	ao	ao	ADP
uva.x030312957	185	40	tn-1	tn-1	PRON
uva.x030312957	186	1	+	+	ADJ
uva.x030312957	186	2	ai	ai	VERB
uva.x030312957	186	3	tn–2	tn–2	PROPN
uva.x030312957	186	4	+	+	PROPN
uva.x030312957	186	5	+	+	NUM
uva.x030312957	186	6	ag	ag	PROPN
uva.x030312957	186	7	tn-8	tn-8	SPACE
uva.x030312957	186	8	-	-	PUNCT
uva.x030312957	186	9	1	1	NUM
uva.x030312957	186	10	,	,	PUNCT
uva.x030312957	186	11	es+1	es+1	ADV
uva.x030312957	186	12	,	,	PUNCT
uva.x030312957	186	13	ao	ao	INTJ
uva.x030312957	186	14	tầ2	tầ2	NOUN
uva.x030312957	186	15	+	+	CCONJ
uva.x030312957	186	16	a	a	DET
uva.x030312957	186	17	n–3	n–3	NOUN
uva.x030312957	186	18	+	+	PROPN
uva.x030312957	186	19	8	8	NUM
uva.x030312957	186	20	+	+	CCONJ
uva.x030312957	186	21	a	a	DET
uva.x030312957	186	22	,	,	PUNCT
uva.x030312957	186	23	tn--2	tn--2	SPACE
uva.x030312957	186	24	,	,	PUNCT
uva.x030312957	186	25	en-1	en-1	PROPN
uva.x030312957	186	26	,	,	PUNCT
uva.x030312957	186	27	s	s	NOUN
uva.x030312957	186	28	=	=	NOUN
uva.x030312957	186	29	dots	dot	NOUN
uva.x030312957	186	30	+	+	CCONJ
uva.x030312957	186	31	ajts-1	ajts-1	NUM
uva.x030312957	186	32	+	+	PUNCT
uva.x030312957	186	33	...	...	PUNCT
uva.x030312957	187	1	+	+	CCONJ
uva.x030312957	187	2	a	a	DET
uva.x030312957	187	3	,	,	PUNCT
uva.x030312957	187	4	to	to	PART
uva.x030312957	187	5	.	.	PUNCT
uva.x030312957	188	1	next	next	ADV
uva.x030312957	188	2	introduce	introduce	VERB
uva.x030312957	188	3	a	a	DET
uva.x030312957	188	4	second	second	ADJ
uva.x030312957	188	5	system	system	NOUN
uva.x030312957	188	6	of	of	ADP
uva.x030312957	188	7	variables	variable	NOUN
uva.x030312957	188	8	7	7	NUM
uva.x030312957	188	9	through	through	ADP
uva.x030312957	188	10	(	(	PUNCT
uva.x030312957	188	11	21	21	NUM
uva.x030312957	188	12	)	)	PUNCT
uva.x030312957	189	1	z	z	NOUN
uva.x030312957	189	2	=	=	PUNCT
uva.x030312957	189	3	tn-1fo	tn-1fo	INTJ
uva.x030312957	190	1	+	+	PUNCT
uva.x030312957	190	2	t-2	t-2	NUM
uva.x030312957	190	3	f1	f1	PROPN
uva.x030312957	191	1	+	+	CCONJ
uva.x030312957	191	2	...	...	PUNCT
uva.x030312957	192	1	+	+	CCONJ
uva.x030312957	192	2	tofn-1	tofn-1	ADP
uva.x030312957	192	3	,	,	PUNCT
uva.x030312957	192	4	by	by	ADP
uva.x030312957	192	5	a	a	DET
uva.x030312957	192	6	method	method	NOUN
uva.x030312957	192	7	due	due	ADP
uva.x030312957	192	8	to	to	ADP
uva.x030312957	192	9	hermite	hermite	NOUN
uva.x030312957	192	10	11	11	NUM
uva.x030312957	192	11	from	from	ADP
uva.x030312957	192	12	which	which	PRON
uva.x030312957	192	13	we	we	PRON
uva.x030312957	192	14	have	have	VERB
uva.x030312957	192	15	,	,	PUNCT
uva.x030312957	192	16	since	since	SCONJ
uva.x030312957	192	17	by	by	ADP
uva.x030312957	192	18	(	(	PUNCT
uva.x030312957	192	19	6	6	NUM
uva.x030312957	192	20	)	)	PUNCT
uva.x030312957	192	21	s	s	X
uva.x030312957	192	22	(	(	PUNCT
uva.x030312957	192	23	f	f	X
uva.x030312957	192	24	:)	:)	X
uva.x030312957	192	25	(	(	PUNCT
uva.x030312957	192	26	n	n	X
uva.x030312957	192	27	$	$	SYM
uva.x030312957	192	28	)	)	PUNCT
uva.x030312957	192	29	as	as	ADP
uva.x030312957	192	30	,	,	PUNCT
uva.x030312957	192	31	s[(x	s[(x	NOUN
uva.x030312957	192	32	–	–	PUNCT
uva.x030312957	192	33	a	a	X
uva.x030312957	192	34	)	)	PUNCT
uva.x030312957	192	35	yz	yz	NOUN
uva.x030312957	192	36	)	)	PUNCT
uva.x030312957	192	37	=	=	PUNCT
uva.x030312957	192	38	s[(x	s[(x	PROPN
uva.x030312957	192	39	a)y{tn-1	a)y{tn-1	ADJ
uva.x030312957	192	40	fo	fo	NOUN
uva.x030312957	192	41	+	+	X
uva.x030312957	192	42	tn-2f1	tn-2f1	NOUN
uva.x030312957	193	1	+	+	CCONJ
uva.x030312957	193	2	...	...	PUNCT
uva.x030312957	194	1	y	y	X
uva.x030312957	194	2	–	–	PUNCT
uva.x030312957	194	3	+	+	CCONJ
uva.x030312957	194	4	to	to	ADP
uva.x030312957	194	5	fn-1	fn-1	SPACE
uva.x030312957	194	6	}	}	PUNCT
uva.x030312957	194	7	]	]	PUNCT
uva.x030312957	194	8	s[tn-1	s[tn-1	VERB
uva.x030312957	194	9	(	(	PUNCT
uva.x030312957	194	10	x	x	PUNCT
uva.x030312957	194	11	–	–	PUNCT
uva.x030312957	194	12	a	a	X
uva.x030312957	194	13	)	)	PUNCT
uva.x030312957	194	14	yfo	yfo	NOUN
uva.x030312957	194	15	+	+	CCONJ
uva.x030312957	194	16	tn-2	tn-2	SYM
uva.x030312957	194	17	(	(	PUNCT
uva.x030312957	194	18	x	x	PUNCT
uva.x030312957	194	19	–	–	PUNCT
uva.x030312957	194	20	a	a	X
uva.x030312957	194	21	)	)	PUNCT
uva.x030312957	194	22	yfi	yfi	PROPN
uva.x030312957	195	1	+	+	PUNCT
uva.x030312957	195	2	...	...	PUNCT
uva.x030312957	196	1	+	+	PUNCT
uva.x030312957	196	2	to(x	to(x	PUNCT
uva.x030312957	196	3	–	–	PUNCT
uva.x030312957	196	4	a	a	X
uva.x030312957	196	5	)	)	PUNCT
uva.x030312957	196	6	yfn-1	yfn-1	SPACE
uva.x030312957	196	7	}	}	PUNCT
uva.x030312957	196	8	]	]	X
uva.x030312957	196	9	(	(	PUNCT
uva.x030312957	196	10	22	22	NUM
uva.x030312957	196	11	)	)	PUNCT
uva.x030312957	196	12	σ	σ	PROPN
uva.x030312957	196	13	(	(	PUNCT
uva.x030312957	196	14	ε-	ε-	SPACE
uva.x030312957	196	15	..	..	PUNCT
uva.x030312957	196	16	αεο	αεο	ADJ
uva.x030312957	196	17	,	,	PUNCT
uva.x030312957	196	18	.	.	PUNCT
uva.x030312957	196	19	)	)	PUNCT
uva.x030312957	197	1	τη--1	τη--1	X
uva.x030312957	198	1	+	+	CCONJ
uva.x030312957	198	2	(	(	PUNCT
uva.x030312957	198	3	n	n	CCONJ
uva.x030312957	198	4	−	−	VERB
uva.x030312957	198	5	1)a	1)a	PROPN
uva.x030312957	198	6	σ	σ	NOUN
uva.x030312957	198	7	(	(	PUNCT
uva.x030312957	198	8	eo	eo	PROPN
uva.x030312957	198	9	,	,	PUNCT
uva.x030312957	198	10	ae1	ae1	PROPN
uva.x030312957	198	11	,	,	PUNCT
uva.x030312957	198	12	8)	8)	NUM
uva.x030312957	198	13	77	77	NUM
uva.x030312957	198	14	-	-	SYM
uva.x030312957	198	15	8	8	NUM
uva.x030312957	198	16	-	-	SYM
uva.x030312957	198	17	1	1	NUM
uva.x030312957	198	18	=	=	NOUN
uva.x030312957	198	19	ndo	ndo	NOUN
uva.x030312957	198	20	0	0	NUM
uva.x030312957	198	21	,	,	PUNCT
uva.x030312957	198	22	n-1	n-1	NUM
uva.x030312957	198	23	8	8	NUM
uva.x030312957	198	24	0	0	NUM
uva.x030312957	198	25	,	,	PUNCT
uva.x030312957	198	26	n-1	n-1	X
uva.x030312957	198	27	+	+	CCONJ
uva.x030312957	199	1	an-1	an-1	PUNCT
uva.x030312957	199	2	é	é	X
uva.x030312957	199	3	(	(	PUNCT
uva.x030312957	199	4	em-2	em-2	SPACE
uva.x030312957	199	5	,	,	PUNCT
uva.x030312957	199	6	–	–	PUNCT
uva.x030312957	199	7	«	«	PUNCT
uva.x030312957	199	8	en-1	en-1	X
uva.x030312957	199	9	,	,	PUNCT
uva.x030312957	199	10	8)	8)	NUM
uva.x030312957	199	11	in	in	ADP
uva.x030312957	199	12	-	-	PUNCT
uva.x030312957	199	13	o-1	o-1	PROPN
uva.x030312957	199	14	.	.	PUNCT
uva.x030312957	199	15	0	0	NUM
uva.x030312957	199	16	,	,	PUNCT
uva.x030312957	199	17	n-1	n-1	NOUN
uva.x030312957	199	18	on	on	ADP
uva.x030312957	199	19	making	make	VERB
uva.x030312957	199	20	r	r	NOUN
uva.x030312957	199	21	=	=	NOUN
uva.x030312957	199	22	t	t	PROPN
uva.x030312957	199	23	(	(	PUNCT
uva.x030312957	199	24	22	22	NUM
uva.x030312957	199	25	)	)	PUNCT
uva.x030312957	199	26	will	will	AUX
uva.x030312957	199	27	take	take	VERB
uva.x030312957	199	28	the	the	DET
uva.x030312957	199	29	value	value	NOUN
uva.x030312957	199	30	of	of	ADP
uva.x030312957	199	31	h	h	NOUN
uva.x030312957	199	32	,	,	PUNCT
uva.x030312957	199	33	in	in	ADP
uva.x030312957	199	34	(	(	PUNCT
uva.x030312957	199	35	5	5	X
uva.x030312957	199	36	)	)	PUNCT
uva.x030312957	199	37	being	be	AUX
uva.x030312957	199	38	expressed	express	VERB
uva.x030312957	199	39	in	in	ADP
uva.x030312957	199	40	terms	term	NOUN
uva.x030312957	199	41	of	of	ADP
uva.x030312957	199	42	the	the	DET
uva.x030312957	199	43	coefficients	coefficient	NOUN
uva.x030312957	199	44	of	of	ADP
uva.x030312957	199	45	f	f	PROPN
uva.x030312957	199	46	(	(	PUNCT
uva.x030312957	199	47	x	x	PROPN
uva.x030312957	199	48	)	)	PUNCT
uva.x030312957	199	49	and	and	CCONJ
uva.x030312957	199	50	of	of	ADP
uva.x030312957	199	51	a.	a.	NOUN
uva.x030312957	199	52	$	$	SYM
uva.x030312957	199	53	5	5	NUM
uva.x030312957	199	54	.	.	PUNCT
uva.x030312957	199	55	illustrative	illustrative	ADJ
uva.x030312957	199	56	example	example	NOUN
uva.x030312957	199	57	.	.	PUNCT
uva.x030312957	200	1	for	for	ADP
uva.x030312957	200	2	an	an	DET
uva.x030312957	200	3	example	example	NOUN
uva.x030312957	200	4	take	take	VERB
uva.x030312957	200	5	the	the	DET
uva.x030312957	200	6	case	case	NOUN
uva.x030312957	200	7	n	n	ADP
uva.x030312957	200	8	=	=	X
uva.x030312957	200	9	4	4	NUM
uva.x030312957	200	10	,	,	PUNCT
uva.x030312957	200	11	for	for	ADP
uva.x030312957	200	12	which	which	PRON
uva.x030312957	200	13	we	we	PRON
uva.x030312957	200	14	find	find	VERB
uva.x030312957	200	15	.	.	PUNCT
uva.x030312957	201	1	e_1,0	e_1,0	ADJ
uva.x030312957	201	2	as	as	ADP
uva.x030312957	201	3	to	to	ADP
uva.x030312957	201	4	,	,	PUNCT
uva.x030312957	201	5	e-1	e-1	SPACE
uva.x030312957	201	6	,	,	PUNCT
uva.x030312957	201	7	1	1	NUM
uva.x030312957	201	8	=	=	NOUN
uva.x030312957	201	9	–	–	PUNCT
uva.x030312957	201	10	az	az	PROPN
uva.x030312957	201	11	tz	tz	PROPN
uva.x030312957	201	12	–	–	PUNCT
uva.x030312957	201	13	az	az	PROPN
uva.x030312957	201	14	tz	tz	PROPN
uva.x030312957	201	15	04ti	04ti	PROPN
uva.x030312957	201	16	,	,	PUNCT
uva.x030312957	201	17	e_1	e_1	PROPN
uva.x030312957	201	18	.	.	PUNCT
uva.x030312957	202	1	2	2	NUM
uva.x030312957	202	2	=	=	X
uva.x030312957	202	3	az	az	PROPN
uva.x030312957	202	4	tz	tz	PROPN
uva.x030312957	202	5	–	–	PUNCT
uva.x030312957	202	6	ay	ay	PROPN
uva.x030312957	202	7	ta	ta	PROPN
uva.x030312957	202	8	,	,	PUNCT
uva.x030312957	202	9	e-1	e-1	PROPN
uva.x030312957	202	10	,	,	PUNCT
uva.x030312957	202	11	3	3	NUM
uva.x030312957	202	12	=	=	NOUN
uva.x030312957	202	13	–	–	PUNCT
uva.x030312957	202	14	04	04	NUM
uva.x030312957	202	15	13	13	NUM
uva.x030312957	202	16	,	,	PUNCT
uva.x030312957	202	17	aitz	aitz	PROPN
uva.x030312957	202	18	az	az	PROPN
uva.x030312957	202	19	tz	tz	PROPN
uva.x030312957	202	20	az	az	PROPN
uva.x030312957	202	21	tı	tı	PROPN
uva.x030312957	202	22	eo	eo	PROPN
uva.x030312957	202	23	,	,	PUNCT
uva.x030312957	203	1	1	1	NUM
uva.x030312957	203	2	az	az	X
uva.x030312957	203	3	tı	tı	ADJ
uva.x030312957	203	4	ad	ad	NOUN
uva.x030312957	203	5	to	to	ADP
uva.x030312957	203	6	,	,	PUNCT
uva.x030312957	203	7	eo	eo	PROPN
uva.x030312957	203	8	,	,	PUNCT
uva.x030312957	203	9	o	o	X
uva.x030312957	203	10	=	=	X
uva.x030312957	203	11	ao	ao	INTJ
uva.x030312957	203	12	tz	tz	PROPN
uva.x030312957	203	13	,	,	PUNCT
uva.x030312957	203	14	dz	dz	PROPN
uva.x030312957	203	15	to	to	ADP
uva.x030312957	203	16	e.	e.	PROPN
uva.x030312957	203	17	,	,	PUNCT
uva.x030312957	203	18	2	2	NUM
uva.x030312957	203	19	=	=	NOUN
uva.x030312957	203	20	–	–	PUNCT
uva.x030312957	203	21	az	az	PROPN
uva.x030312957	203	22	tz	tz	PROPN
uva.x030312957	203	23	–	–	PUNCT
uva.x030312957	203	24	04	04	NUM
uva.x030312957	203	25	ti	ti	PROPN
uva.x030312957	203	26	,	,	PUNCT
uva.x030312957	203	27	eo	eo	PROPN
uva.x030312957	203	28	.	.	PROPN
uva.x030312957	203	29	3	3	NUM
uva.x030312957	203	30	=	=	NUM
uva.x030312957	203	31	–	–	PUNCT
uva.x030312957	203	32	04	04	NUM
uva.x030312957	203	33	ta	ta	NOUN
uva.x030312957	203	34	,	,	PUNCT
uva.x030312957	203	35	el	el	PROPN
uva.x030312957	203	36	.	.	PUNCT
uva.x030312957	204	1	o	o	SYM
uva.x030312957	204	2	=	=	PUNCT
uva.x030312957	205	1	a	a	DET
uva.x030312957	205	2	,	,	PUNCT
uva.x030312957	205	3	t2	t2	PROPN
uva.x030312957	205	4	,	,	PUNCT
uva.x030312957	205	5	e1	e1	PROPN
uva.x030312957	205	6	,	,	PUNCT
uva.x030312957	205	7	1	1	NUM
uva.x030312957	205	8	=	=	NOUN
uva.x030312957	205	9	a	a	PRON
uva.x030312957	205	10	,	,	PUNCT
uva.x030312957	205	11	tz	tz	PROPN
uva.x030312957	205	12	+	+	NOUN
uva.x030312957	205	13	ai	ai	VERB
uva.x030312957	205	14	ta	ta	PROPN
uva.x030312957	205	15	,	,	PUNCT
uva.x030312957	205	16	e1	e1	PROPN
uva.x030312957	205	17	,	,	PUNCT
uva.x030312957	205	18	2	2	NUM
uva.x030312957	205	19	=	=	NOUN
uva.x030312957	205	20	–	–	PUNCT
uva.x030312957	205	21	az	az	PROPN
uva.x030312957	205	22	tı	tı	X
uva.x030312957	205	23	–	–	PUNCT
uva.x030312957	205	24	ad	ad	NOUN
uva.x030312957	205	25	to	to	ADP
uva.x030312957	205	26	,	,	PUNCT
uva.x030312957	205	27	e1	e1	PROPN
uva.x030312957	205	28	,	,	PUNCT
uva.x030312957	205	29	3	3	NUM
uva.x030312957	205	30	=	=	SYM
uva.x030312957	205	31	anti	anti	PROPN
uva.x030312957	205	32	,	,	PUNCT
uva.x030312957	205	33	e2	e2	PROPN
uva.x030312957	205	34	,	,	PUNCT
uva.x030312957	205	35	o	o	X
uva.x030312957	205	36	=	=	ADP
uva.x030312957	205	37	ao	ao	INTJ
uva.x030312957	205	38	ti	ti	PROPN
uva.x030312957	205	39	,	,	PUNCT
uva.x030312957	205	40	e2	e2	PROPN
uva.x030312957	205	41	,	,	PUNCT
uva.x030312957	205	42	1	1	NUM
uva.x030312957	205	43	=	=	NOUN
uva.x030312957	205	44	a	a	DET
uva.x030312957	205	45	,	,	PUNCT
uva.x030312957	205	46	tz	tz	PROPN
uva.x030312957	205	47	+	+	CCONJ
uva.x030312957	205	48	a	a	PRON
uva.x030312957	205	49	,	,	PUNCT
uva.x030312957	205	50	ti	ti	X
uva.x030312957	205	51	,	,	PUNCT
uva.x030312957	205	52	e2	e2	PROPN
uva.x030312957	205	53	,	,	PUNCT
uva.x030312957	205	54	2	2	NUM
uva.x030312957	205	55	=	=	NOUN
uva.x030312957	205	56	a	a	DET
uva.x030312957	205	57	,	,	PUNCT
uva.x030312957	205	58	tz	tz	PROPN
uva.x030312957	205	59	+	+	CCONJ
uva.x030312957	205	60	ata	ata	PROPN
uva.x030312957	205	61	+	+	CCONJ
uva.x030312957	205	62	ayti	ayti	PROPN
uva.x030312957	205	63	,	,	PUNCT
uva.x030312957	205	64	e2	e2	PROPN
uva.x030312957	205	65	,	,	PUNCT
uva.x030312957	205	66	3	3	NUM
uva.x030312957	205	67	=	=	SYM
uva.x030312957	205	68	to	to	ADP
uva.x030312957	205	69	,	,	PUNCT
uva.x030312957	205	70	e3	e3	PROPN
uva.x030312957	205	71	,	,	PUNCT
uva.x030312957	205	72	o	o	NOUN
uva.x030312957	205	73	=	=	PRON
uva.x030312957	205	74	do	do	VERB
uva.x030312957	205	75	to	to	ADP
uva.x030312957	205	76	,	,	PUNCT
uva.x030312957	205	77	e3	e3	PROPN
uva.x030312957	205	78	.	.	PUNCT
uva.x030312957	205	79	1	1	NUM
uva.x030312957	205	80	=	=	NOUN
uva.x030312957	205	81	do	do	VERB
uva.x030312957	205	82	ti	ti	PROPN
uva.x030312957	206	1	+	+	CCONJ
uva.x030312957	206	2	ai	ai	VERB
uva.x030312957	206	3	to	to	PART
uva.x030312957	206	4	,	,	PUNCT
uva.x030312957	206	5	e3	e3	PROPN
uva.x030312957	206	6	,	,	PUNCT
uva.x030312957	206	7	2	2	NUM
uva.x030312957	206	8	=	=	NOUN
uva.x030312957	206	9	ao	ao	INTJ
uva.x030312957	206	10	tz	tz	PROPN
uva.x030312957	206	11	+	+	CCONJ
uva.x030312957	206	12	ai	ai	VERB
uva.x030312957	206	13	ti	ti	PROPN
uva.x030312957	207	1	+	+	CCONJ
uva.x030312957	207	2	az	az	NOUN
uva.x030312957	207	3	to	to	PART
uva.x030312957	207	4	,	,	PUNCT
uva.x030312957	207	5	ez	ez	PROPN
uva.x030312957	207	6	,	,	PUNCT
uva.x030312957	207	7	a	a	DET
uva.x030312957	207	8	=	=	NOUN
uva.x030312957	207	9	do	do	VERB
uva.x030312957	207	10	tz	tz	PROPN
uva.x030312957	207	11	+	+	CCONJ
uva.x030312957	207	12	a	a	PRON
uva.x030312957	207	13	,	,	PUNCT
uva.x030312957	207	14	tz	tz	PROPN
uva.x030312957	207	15	+	+	CCONJ
uva.x030312957	207	16	az	az	PROPN
uva.x030312957	207	17	ti	ti	PROPN
uva.x030312957	208	1	+	+	CCONJ
uva.x030312957	208	2	az	az	NOUN
uva.x030312957	208	3	to	to	PART
uva.x030312957	208	4	.	.	PUNCT
uva.x030312957	209	1	12	12	NUM
uva.x030312957	209	2	solution	solution	NOUN
uva.x030312957	209	3	of	of	ADP
uva.x030312957	209	4	the	the	DET
uva.x030312957	209	5	equation	equation	NOUN
uva.x030312957	209	6	of	of	ADP
uva.x030312957	209	7	secular	secular	ADJ
uva.x030312957	209	8	variation	variation	NOUN
uva.x030312957	209	9	these	these	DET
uva.x030312957	209	10	values	value	NOUN
uva.x030312957	209	11	of	of	ADP
uva.x030312957	209	12	ei	ei	PROPN
uva.x030312957	209	13	,	,	PUNCT
uva.x030312957	209	14	;	;	PUNCT
uva.x030312957	209	15	substituted	substitute	VERB
uva.x030312957	209	16	in	in	ADP
uva.x030312957	209	17	(	(	PUNCT
uva.x030312957	209	18	22	22	NUM
uva.x030312957	209	19	)	)	PUNCT
uva.x030312957	209	20	give	give	VERB
uva.x030312957	209	21	s[(x	s[(x	NOUN
uva.x030312957	209	22	–	–	PUNCT
uva.x030312957	209	23	a	a	X
uva.x030312957	209	24	)	)	PUNCT
uva.x030312957	209	25	yz	yz	X
uva.x030312957	209	26	]	]	X
uva.x030312957	209	27	=	=	PROPN
uva.x030312957	209	28	t3	t3	PROPN
uva.x030312957	209	29	t3	t3	PROPN
uva.x030312957	209	30	h3	h3	PROPN
uva.x030312957	209	31	,	,	PUNCT
uva.x030312957	209	32	3	3	NUM
uva.x030312957	209	33	+	+	CCONJ
uva.x030312957	209	34	t3	t3	PROPN
uva.x030312957	209	35	t2	t2	PROPN
uva.x030312957	209	36	h3	h3	PROPN
uva.x030312957	209	37	,	,	PUNCT
uva.x030312957	210	1	2	2	NUM
uva.x030312957	210	2	+	+	CCONJ
uva.x030312957	210	3	tz	tz	PROPN
uva.x030312957	210	4	t	t	PROPN
uva.x030312957	210	5	,	,	PUNCT
uva.x030312957	210	6	h3	h3	PROPN
uva.x030312957	210	7	,	,	PUNCT
uva.x030312957	210	8	1	1	NUM
uva.x030312957	210	9	+	+	CCONJ
uva.x030312957	210	10	tz	tz	NOUN
uva.x030312957	210	11	to	to	ADP
uva.x030312957	210	12	h3	h3	PROPN
uva.x030312957	210	13	,	,	PUNCT
uva.x030312957	210	14	o	o	PROPN
uva.x030312957	210	15	+	+	CCONJ
uva.x030312957	210	16	t2	t2	PROPN
uva.x030312957	210	17	t3	t3	PROPN
uva.x030312957	210	18	h2	h2	PROPN
uva.x030312957	210	19	,	,	PUNCT
uva.x030312957	210	20	3	3	NUM
uva.x030312957	210	21	to	to	PART
uva.x030312957	210	22	ta	ta	PART
uva.x030312957	210	23	t2	t2	PROPN
uva.x030312957	210	24	h2	h2	PROPN
uva.x030312957	210	25	,	,	PUNCT
uva.x030312957	210	26	2	2	NUM
uva.x030312957	210	27	+	+	CCONJ
uva.x030312957	210	28	t2	t2	PROPN
uva.x030312957	210	29	t1	t1	X
uva.x030312957	210	30	h2,1	h2,1	PROPN
uva.x030312957	210	31	+	+	CCONJ
uva.x030312957	210	32	t2	t2	PROPN
uva.x030312957	210	33	to	to	ADP
uva.x030312957	210	34	h2	h2	PROPN
uva.x030312957	210	35	,	,	PUNCT
uva.x030312957	210	36	o	o	NOUN
uva.x030312957	210	37	+	+	CCONJ
uva.x030312957	210	38	tı	tı	INTJ
uva.x030312957	210	39	73	73	NUM
uva.x030312957	211	1	h1,3	h1,3	NOUN
uva.x030312957	211	2	t	t	PROPN
uva.x030312957	211	3	ti	ti	PROPN
uva.x030312957	211	4	t2	t2	PROPN
uva.x030312957	211	5	h1	h1	PROPN
uva.x030312957	211	6	,	,	PUNCT
uva.x030312957	211	7	2	2	NUM
uva.x030312957	211	8	+	+	NUM
uva.x030312957	211	9	ti	ti	X
uva.x030312957	211	10	t1	t1	X
uva.x030312957	212	1	h1,1	h1,1	X
uva.x030312957	213	1	+	+	CCONJ
uva.x030312957	213	2	ti	ti	X
uva.x030312957	213	3	to	to	PART
uva.x030312957	213	4	h1	h1	PROPN
uva.x030312957	213	5	,	,	PUNCT
uva.x030312957	214	1	o	o	X
uva.x030312957	214	2	+	+	CCONJ
uva.x030312957	214	3	to	to	ADP
uva.x030312957	214	4	t3	t3	PROPN
uva.x030312957	214	5	h0	h0	PROPN
uva.x030312957	214	6	,	,	PUNCT
uva.x030312957	214	7	3	3	NUM
uva.x030312957	214	8	+	+	NUM
uva.x030312957	214	9	to	to	ADP
uva.x030312957	214	10	t2	t2	PROPN
uva.x030312957	214	11	h.	h.	PROPN
uva.x030312957	214	12	,	,	PUNCT
uva.x030312957	214	13	2	2	NUM
uva.x030312957	214	14	+	+	NUM
uva.x030312957	214	15	to	to	ADP
uva.x030312957	214	16	t1	t1	X
uva.x030312957	215	1	h0,1	h0,1	PROPN
uva.x030312957	216	1	+	+	CCONJ
uva.x030312957	216	2	to	to	ADP
uva.x030312957	216	3	to	to	PART
uva.x030312957	216	4	h0	h0	PROPN
uva.x030312957	216	5	,	,	PUNCT
uva.x030312957	216	6	0	0	NUM
uva.x030312957	216	7	.	.	PUNCT
uva.x030312957	217	1	if	if	SCONJ
uva.x030312957	217	2	7	7	NUM
uva.x030312957	217	3	=	=	SYM
uva.x030312957	217	4	t	t	NOUN
uva.x030312957	217	5	this	this	PRON
uva.x030312957	217	6	goes	go	VERB
uva.x030312957	217	7	into	into	ADP
uva.x030312957	217	8	he	he	PRON
uva.x030312957	217	9	=	=	VERB
uva.x030312957	217	10	t	t	PROPN
uva.x030312957	217	11	;	;	PUNCT
uva.x030312957	217	12	h3	h3	PROPN
uva.x030312957	217	13	,	,	PUNCT
uva.x030312957	217	14	3	3	NUM
uva.x030312957	217	15	+	+	CCONJ
uva.x030312957	217	16	tz	tz	X
uva.x030312957	217	17	to	to	ADP
uva.x030312957	217	18	h3	h3	PROPN
uva.x030312957	217	19	,	,	PUNCT
uva.x030312957	218	1	2	2	NUM
uva.x030312957	218	2	+	+	CCONJ
uva.x030312957	218	3	tz	tz	X
uva.x030312957	218	4	tı	tı	INTJ
uva.x030312957	218	5	h3	h3	PROPN
uva.x030312957	218	6	,	,	PUNCT
uva.x030312957	218	7	1	1	NUM
uva.x030312957	218	8	+	+	CCONJ
uva.x030312957	218	9	tz	tz	NOUN
uva.x030312957	218	10	to	to	ADP
uva.x030312957	218	11	h3	h3	PROPN
uva.x030312957	218	12	,	,	PUNCT
uva.x030312957	218	13	0	0	PUNCT
uva.x030312957	219	1	+	+	CCONJ
uva.x030312957	219	2	tz	tz	PROPN
uva.x030312957	219	3	tz	tz	PROPN
uva.x030312957	219	4	h2	h2	PROPN
uva.x030312957	219	5	,	,	PUNCT
uva.x030312957	219	6	3	3	NUM
uva.x030312957	219	7	+	+	NUM
uva.x030312957	219	8	tź	tź	INTJ
uva.x030312957	219	9	h2	h2	PROPN
uva.x030312957	219	10	,	,	PUNCT
uva.x030312957	219	11	2	2	NUM
uva.x030312957	220	1	+	+	CCONJ
uva.x030312957	220	2	tz	tz	ADP
uva.x030312957	220	3	tı	tı	INTJ
uva.x030312957	220	4	h2	h2	PROPN
uva.x030312957	220	5	,	,	PUNCT
uva.x030312957	220	6	1	1	NUM
uva.x030312957	220	7	+	+	CCONJ
uva.x030312957	220	8	tz	tz	NOUN
uva.x030312957	220	9	to	to	ADP
uva.x030312957	220	10	h2	h2	PROPN
uva.x030312957	220	11	,	,	PUNCT
uva.x030312957	220	12	0	0	PUNCT
uva.x030312957	221	1	+	+	CCONJ
uva.x030312957	221	2	ti	ti	X
uva.x030312957	221	3	tz	tz	PROPN
uva.x030312957	221	4	h1	h1	PROPN
uva.x030312957	221	5	,	,	PUNCT
uva.x030312957	221	6	3	3	NUM
uva.x030312957	222	1	+	+	NUM
uva.x030312957	222	2	ti	ti	X
uva.x030312957	222	3	tz	tz	PROPN
uva.x030312957	222	4	h1	h1	PROPN
uva.x030312957	222	5	,	,	PUNCT
uva.x030312957	222	6	2	2	NUM
uva.x030312957	222	7	+	+	NUM
uva.x030312957	222	8	ti	ti	X
uva.x030312957	222	9	h1	h1	PROPN
uva.x030312957	222	10	,	,	PUNCT
uva.x030312957	222	11	1	1	NUM
uva.x030312957	222	12	+	+	NOUN
uva.x030312957	222	13	ti	ti	NOUN
uva.x030312957	222	14	to	to	PART
uva.x030312957	222	15	h1	h1	PROPN
uva.x030312957	222	16	,	,	PUNCT
uva.x030312957	222	17	o	o	NOUN
uva.x030312957	223	1	+	+	CCONJ
uva.x030312957	223	2	to	to	ADP
uva.x030312957	223	3	tz	tz	PROPN
uva.x030312957	223	4	h.	h.	PROPN
uva.x030312957	223	5	,	,	PUNCT
uva.x030312957	223	6	3	3	NUM
uva.x030312957	223	7	+	+	NUM
uva.x030312957	223	8	to	to	ADP
uva.x030312957	223	9	tz	tz	PROPN
uva.x030312957	223	10	ho	ho	PROPN
uva.x030312957	223	11	,	,	PUNCT
uva.x030312957	223	12	2	2	NUM
uva.x030312957	223	13	+	+	NUM
uva.x030312957	223	14	to	to	ADP
uva.x030312957	223	15	ti	ti	X
uva.x030312957	223	16	ho	ho	PROPN
uva.x030312957	223	17	,	,	PUNCT
uva.x030312957	223	18	1	1	NUM
uva.x030312957	223	19	t	t	PROPN
uva.x030312957	223	20	t.	t.	PROPN
uva.x030312957	223	21	ho	ho	PROPN
uva.x030312957	223	22	,	,	PUNCT
uva.x030312957	223	23	o.	o.	PROPN
uva.x030312957	223	24	1	1	NUM
uva.x030312957	223	25	where	where	SCONJ
uva.x030312957	223	26	the	the	DET
uva.x030312957	223	27	hi	hi	PROPN
uva.x030312957	223	28	,	,	PUNCT
uva.x030312957	223	29	;	;	PUNCT
uva.x030312957	223	30	are	be	AUX
uva.x030312957	223	31	given	give	VERB
uva.x030312957	223	32	by	by	ADP
uva.x030312957	223	33	h3	h3	NOUN
uva.x030312957	223	34	,	,	PUNCT
uva.x030312957	223	35	3	3	NUM
uva.x030312957	223	36	do	do	VERB
uva.x030312957	223	37	(	(	PUNCT
uva.x030312957	223	38	a1	a1	PROPN
uva.x030312957	223	39	+	+	CCONJ
uva.x030312957	223	40	400	400	NUM
uva.x030312957	223	41	a	a	PRON
uva.x030312957	223	42	)	)	PUNCT
uva.x030312957	223	43	,	,	PUNCT
uva.x030312957	223	44	3a	3a	PROPN
uva.x030312957	223	45	,	,	PUNCT
uva.x030312957	223	46	az	az	PROPN
uva.x030312957	223	47	qı	qı	PROPN
uva.x030312957	223	48	az	az	PROPN
uva.x030312957	223	49	a	a	DET
uva.x030312957	223	50	(	(	PUNCT
uva.x030312957	223	51	3aí	3aí	ADJ
uva.x030312957	223	52	2do	2do	NOUN
uva.x030312957	223	53	az	az	PROPN
uva.x030312957	223	54	)	)	PUNCT
uva.x030312957	223	55	,	,	PUNCT
uva.x030312957	223	56	3aa4	3aa4	NUM
uva.x030312957	223	57	–	–	PUNCT
uva.x030312957	223	58	02	02	NUM
uva.x030312957	223	59	03	03	NUM
uva.x030312957	223	60	–	–	PUNCT
uva.x030312957	223	61	2a	2a	NUM
uva.x030312957	223	62	(	(	PUNCT
uva.x030312957	223	63	až	až	X
uva.x030312957	223	64	–	–	PUNCT
uva.x030312957	223	65	21	21	NUM
uva.x030312957	223	66	23	23	NUM
uva.x030312957	223	67	–	–	PUNCT
uva.x030312957	223	68	2a	2a	NUM
uva.x030312957	223	69	,	,	PUNCT
uva.x030312957	223	70	as	as	ADP
uva.x030312957	223	71	)	)	PUNCT
uva.x030312957	223	72	,	,	PUNCT
uva.x030312957	223	73	h.	h.	PROPN
uva.x030312957	223	74	,	,	PUNCT
uva.x030312957	223	75	o	o	NOUN
uva.x030312957	223	76	=	=	PUNCT
uva.x030312957	223	77	–	–	PUNCT
uva.x030312957	223	78	az	az	PROPN
uva.x030312957	223	79	24	24	NUM
uva.x030312957	223	80	a(až	a(až	PROPN
uva.x030312957	223	81	–	–	PUNCT
uva.x030312957	223	82	2a	2a	NUM
uva.x030312957	223	83	,	,	PUNCT
uva.x030312957	223	84	an	an	PRON
uva.x030312957	223	85	)	)	PUNCT
uva.x030312957	223	86	,	,	PUNCT
uva.x030312957	223	87	h2	h2	PROPN
uva.x030312957	223	88	,	,	PUNCT
uva.x030312957	223	89	2	2	NUM
uva.x030312957	223	90	h1,1	h1,1	X
uva.x030312957	223	91	h3,2	h3,2	X
uva.x030312957	223	92	h2	h2	NOUN
uva.x030312957	223	93	,	,	PUNCT
uva.x030312957	223	94	=	=	PROPN
uva.x030312957	223	95	2ao	2ao	PROPN
uva.x030312957	223	96	d2	d2	PROPN
uva.x030312957	223	97	3α	3α	PROPN
uva.x030312957	223	98	,	,	PUNCT
uva.x030312957	223	99	α	α	NOUN
uva.x030312957	223	100	,	,	PUNCT
uva.x030312957	223	101	α	α	NOUN
uva.x030312957	223	102	,	,	PUNCT
uva.x030312957	223	103	3	3	NUM
uva.x030312957	223	104	h3	h3	NOUN
uva.x030312957	223	105	,	,	PUNCT
uva.x030312957	223	106	1	1	NUM
uva.x030312957	223	107	h1,3	h1,3	NOUN
uva.x030312957	223	108	зао	зао	PROPN
uva.x030312957	223	109	аз	аз	ADV
uva.x030312957	223	110	2ας	2ας	NOUN
uva.x030312957	223	111	α2	α2	PROPN
uva.x030312957	223	112	α	α	PROPN
uva.x030312957	223	113	,	,	PUNCT
uva.x030312957	223	114	h3	h3	PROPN
uva.x030312957	223	115	.	.	PUNCT
uva.x030312957	223	116	0	0	NUM
uva.x030312957	224	1	ho	ho	PROPN
uva.x030312957	224	2	,	,	PUNCT
uva.x030312957	224	3	3	3	NUM
uva.x030312957	224	4	h1,2	h1,2	PROPN
uva.x030312957	224	5	h2	h2	NOUN
uva.x030312957	224	6	,	,	PUNCT
uva.x030312957	224	7	1	1	NUM
uva.x030312957	224	8	h2,0	h2,0	NOUN
uva.x030312957	224	9	400	400	NUM
uva.x030312957	224	10	24	24	NUM
uva.x030312957	224	11	do	do	VERB
uva.x030312957	224	12	dz	dz	PROPN
uva.x030312957	224	13	a	a	DET
uva.x030312957	224	14	,	,	PUNCT
uva.x030312957	224	15	4a	4a	NUM
uva.x030312957	224	16	,	,	PUNCT
uva.x030312957	224	17	04	04	NUM
uva.x030312957	224	18	–	–	PUNCT
uva.x030312957	224	19	2a	2a	NUM
uva.x030312957	224	20	,	,	PUNCT
uva.x030312957	224	21	az	az	PROPN
uva.x030312957	224	22	–	–	PUNCT
uva.x030312957	224	23	a	a	PRON
uva.x030312957	224	24	(	(	PUNCT
uva.x030312957	224	25	2a1	2a1	NUM
uva.x030312957	224	26	az	az	PROPN
uva.x030312957	224	27	3a	3a	PROPN
uva.x030312957	224	28	,	,	PUNCT
uva.x030312957	224	29	az	az	PROPN
uva.x030312957	224	30	)	)	PUNCT
uva.x030312957	224	31	,	,	PUNCT
uva.x030312957	224	32	h.	h.	NOUN
uva.x030312957	224	33	2	2	NUM
uva.x030312957	224	34	=	=	SYM
uva.x030312957	224	35	3a	3a	NUM
uva.x030312957	224	36	,	,	PUNCT
uva.x030312957	224	37	04	04	NUM
uva.x030312957	224	38	a	a	PRON
uva.x030312957	224	39	(	(	PUNCT
uva.x030312957	224	40	a	a	PRON
uva.x030312957	224	41	,	,	PUNCT
uva.x030312957	224	42	az	az	PROPN
uva.x030312957	224	43	–	–	PUNCT
uva.x030312957	224	44	4a	4a	PROPN
uva.x030312957	224	45	,	,	PUNCT
uva.x030312957	224	46	24	24	NUM
uva.x030312957	224	47	)	)	PUNCT
uva.x030312957	224	48	,	,	PUNCT
uva.x030312957	224	49	h1,0	h1,0	VERB
uva.x030312957	224	50	=	=	PROPN
uva.x030312957	224	51	h.	h.	NOUN
uva.x030312957	224	52	,	,	PUNCT
uva.x030312957	224	53	1	1	NUM
uva.x030312957	224	54	=	=	NOUN
uva.x030312957	224	55	–	–	PUNCT
uva.x030312957	224	56	2a	2a	NUM
uva.x030312957	224	57	,	,	PUNCT
uva.x030312957	224	58	04	04	NUM
uva.x030312957	224	59	a	a	NOUN
uva.x030312957	224	60	(	(	PUNCT
uva.x030312957	224	61	az	az	PROPN
uva.x030312957	224	62	az	az	PROPN
uva.x030312957	224	63	–	–	PUNCT
uva.x030312957	224	64	3a1	3a1	NUM
uva.x030312957	224	65	au	au	PROPN
uva.x030312957	224	66	)	)	PUNCT
uva.x030312957	224	67	.	.	PUNCT
uva.x030312957	225	1	to	to	PART
uva.x030312957	225	2	help	help	VERB
uva.x030312957	225	3	in	in	ADP
uva.x030312957	225	4	the	the	DET
uva.x030312957	225	5	determination	determination	NOUN
uva.x030312957	225	6	of	of	ADP
uva.x030312957	225	7	the	the	DET
uva.x030312957	225	8	number	number	NOUN
uva.x030312957	225	9	of	of	ADP
uva.x030312957	225	10	negative	negative	ADJ
uva.x030312957	225	11	terms	term	NOUN
uva.x030312957	225	12	in	in	ADP
uva.x030312957	225	13	ha	ha	INTJ
uva.x030312957	225	14	,	,	PUNCT
uva.x030312957	225	15	we	we	PRON
uva.x030312957	225	16	shall	shall	AUX
uva.x030312957	225	17	use	use	VERB
uva.x030312957	225	18	the	the	DET
uva.x030312957	225	19	determinant	determinant	NOUN
uva.x030312957	225	20	of	of	ADP
uva.x030312957	225	21	the	the	DET
uva.x030312957	225	22	hi	hi	NOUN
uva.x030312957	225	23	,	,	PUNCT
uva.x030312957	225	24	;	;	PUNCT
uva.x030312957	225	25	,	,	PUNCT
uva.x030312957	225	26	which	which	DET
uva.x030312957	225	27	determinant	determinant	NOUN
uva.x030312957	225	28	we	we	PRON
uva.x030312957	225	29	shall	shall	AUX
uva.x030312957	225	30	now	now	ADV
uva.x030312957	225	31	develop	develop	VERB
uva.x030312957	225	32	.	.	PUNCT
uva.x030312957	226	1	$	$	SYM
uva.x030312957	226	2	6	6	NUM
uva.x030312957	226	3	.	.	PUNCT
uva.x030312957	227	1	the	the	DET
uva.x030312957	227	2	determinant	determinant	NOUN
uva.x030312957	227	3	of	of	ADP
uva.x030312957	227	4	hermite	hermite	PROPN
uva.x030312957	227	5	's	's	PART
uva.x030312957	227	6	form	form	NOUN
uva.x030312957	227	7	.	.	PUNCT
uva.x030312957	228	1	let	let	VERB
uva.x030312957	228	2	us	we	PRON
uva.x030312957	228	3	now	now	ADV
uva.x030312957	228	4	set	set	VERB
uva.x030312957	228	5	(	(	PUNCT
uva.x030312957	228	6	23	23	NUM
uva.x030312957	228	7	)	)	PUNCT
uva.x030312957	228	8	h	h	PROPN
uva.x030312957	228	9	σσης	σσης	PROPN
uva.x030312957	228	10	,	,	PUNCT
uva.x030312957	228	11	jt	jt	PROPN
uva.x030312957	228	12	,	,	PUNCT
uva.x030312957	228	13	t	t	PROPN
uva.x030312957	228	14	;	;	PUNCT
uva.x030312957	228	15	.	.	PUNCT
uva.x030312957	229	1	ti	ti	PROPN
uva.x030312957	229	2	.	.	PUNCT
uva.x030312957	230	1	0	0	NUM
uva.x030312957	230	2	1	1	NUM
uva.x030312957	230	3	-	-	SYM
uva.x030312957	230	4	1	1	NUM
uva.x030312957	230	5	since	since	SCONJ
uva.x030312957	230	6	hi	hi	INTJ
uva.x030312957	230	7	,	,	PUNCT
uva.x030312957	230	8	;	;	PUNCT
uva.x030312957	230	9	is	be	AUX
uva.x030312957	230	10	the	the	DET
uva.x030312957	230	11	coefficient	coefficient	NOUN
uva.x030312957	230	12	of	of	ADP
uva.x030312957	230	13	tit	tit	PROPN
uva.x030312957	230	14	;	;	PUNCT
uva.x030312957	230	15	we	we	PRON
uva.x030312957	230	16	see	see	VERB
uva.x030312957	230	17	by	by	ADP
uva.x030312957	230	18	(	(	PUNCT
uva.x030312957	230	19	21	21	NUM
uva.x030312957	230	20	)	)	PUNCT
uva.x030312957	230	21	and	and	CCONJ
uva.x030312957	230	22	(	(	PUNCT
uva.x030312957	230	23	22	22	X
uva.x030312957	230	24	)	)	PUNCT
uva.x030312957	230	25	it	it	PRON
uva.x030312957	230	26	is	be	AUX
uva.x030312957	230	27	given	give	VERB
uva.x030312957	230	28	by	by	ADP
uva.x030312957	230	29	(	(	PUNCT
uva.x030312957	230	30	24	24	NUM
uva.x030312957	230	31	)	)	PUNCT
uva.x030312957	230	32	hi	hi	PROPN
uva.x030312957	230	33	,	,	PUNCT
uva.x030312957	230	34	i	i	PRON
uva.x030312957	230	35	s(x	s(x	PROPN
uva.x030312957	230	36	–	–	PUNCT
uva.x030312957	230	37	a	a	X
uva.x030312957	230	38	)	)	PUNCT
uva.x030312957	230	39	fn	fn	NOUN
uva.x030312957	230	40	-	-	PUNCT
uva.x030312957	230	41	i-1	i-1	NOUN
uva.x030312957	230	42	fr–;-1	fr–;-1	PROPN
uva.x030312957	230	43	.	.	PUNCT
uva.x030312957	231	1	using	use	VERB
uva.x030312957	231	2	this	this	DET
uva.x030312957	231	3	relation	relation	NOUN
uva.x030312957	231	4	we	we	PRON
uva.x030312957	231	5	see	see	VERB
uva.x030312957	231	6	that	that	SCONJ
uva.x030312957	231	7	the	the	DET
uva.x030312957	231	8	determinant	determinant	NOUN
uva.x030312957	231	9	a	a	PRON
uva.x030312957	231	10	'	'	PUNCT
uva.x030312957	231	11	of	of	ADP
uva.x030312957	231	12	the	the	DET
uva.x030312957	231	13	nạ	nạ	ADJ
uva.x030312957	231	14	quantities	quantity	NOUN
uva.x030312957	231	15	hi	hi	INTJ
uva.x030312957	231	16	,	,	PUNCT
uva.x030312957	231	17	,	,	PUNCT
uva.x030312957	231	18	,	,	PUNCT
uva.x030312957	231	19	by	by	ADP
uva.x030312957	231	20	a	a	DET
uva.x030312957	231	21	method	method	NOUN
uva.x030312957	231	22	due	due	ADP
uva.x030312957	231	23	to	to	ADP
uva.x030312957	231	24	hermite	hermite	NOUN
uva.x030312957	231	25	13	13	NUM
uva.x030312957	231	26	that	that	PRON
uva.x030312957	231	27	is	be	AUX
uva.x030312957	231	28	the	the	DET
uva.x030312957	231	29	determinant	determinant	NOUN
uva.x030312957	231	30	of	of	ADP
uva.x030312957	231	31	the	the	DET
uva.x030312957	231	32	quadratic	quadratic	ADJ
uva.x030312957	231	33	form	form	NOUN
uva.x030312957	231	34	h	h	NOUN
uva.x030312957	231	35	,	,	PUNCT
uva.x030312957	231	36	is	be	AUX
uva.x030312957	231	37	the	the	DET
uva.x030312957	231	38	determinant	determinant	NOUN
uva.x030312957	231	39	obtained	obtain	VERB
uva.x030312957	231	40	by	by	ADP
uva.x030312957	231	41	multiplying	multiply	VERB
uva.x030312957	231	42	the	the	DET
uva.x030312957	231	43	two	two	NUM
uva.x030312957	231	44	determinants	determinant	NOUN
uva.x030312957	231	45	below	below	ADV
uva.x030312957	231	46	by	by	ADP
uva.x030312957	231	47	columns	column	NOUN
uva.x030312957	231	48	,	,	PUNCT
uva.x030312957	231	49	(	(	PUNCT
uva.x030312957	231	50	x1	x1	PROPN
uva.x030312957	231	51	alfo(x1	alfo(x1	ADJ
uva.x030312957	231	52	)	)	PUNCT
uva.x030312957	231	53	,	,	PUNCT
uva.x030312957	231	54	(	(	PUNCT
uva.x030312957	231	55	x1	x1	PROPN
uva.x030312957	231	56	alfı(ai	alfı(ai	PROPN
uva.x030312957	231	57	)	)	PUNCT
uva.x030312957	231	58	,	,	PUNCT
uva.x030312957	231	59	(	(	PUNCT
uva.x030312957	231	60	x1	x1	PROPN
uva.x030312957	231	61	alfn-1(x1	alfn-1(x1	PROPN
uva.x030312957	231	62	)	)	PUNCT
uva.x030312957	231	63	an(a	an(a	PUNCT
uva.x030312957	231	64	)	)	PUNCT
uva.x030312957	231	65	(	(	PUNCT
uva.x030312957	231	66	x2	x2	PROPN
uva.x030312957	231	67	–	–	PUNCT
uva.x030312957	231	68	a	a	X
uva.x030312957	231	69	)	)	PUNCT
uva.x030312957	231	70	fo	fo	NOUN
uva.x030312957	231	71	(	(	PUNCT
uva.x030312957	231	72	x2	x2	PROPN
uva.x030312957	231	73	)	)	PUNCT
uva.x030312957	231	74	,	,	PUNCT
uva.x030312957	231	75	(	(	PUNCT
uva.x030312957	231	76	x2	x2	ADJ
uva.x030312957	231	77	–	–	PUNCT
uva.x030312957	231	78	a)fı(x2	a)fı(x2	NOUN
uva.x030312957	231	79	)	)	PUNCT
uva.x030312957	231	80	,	,	PUNCT
uva.x030312957	231	81	...	...	PUNCT
uva.x030312957	231	82	,	,	PUNCT
uva.x030312957	231	83	(	(	PUNCT
uva.x030312957	231	84	x2	x2	PROPN
uva.x030312957	231	85	–	–	PUNCT
uva.x030312957	231	86	a)fn-1(x2	a)fn-1(x2	PROPN
uva.x030312957	231	87	)	)	PUNCT
uva.x030312957	231	88	.	.	PUNCT
uva.x030312957	232	1	a-	a-	X
uva.x030312957	232	2	,	,	PUNCT
uva.x030312957	233	1	х	х	NOUN
uva.x030312957	233	2	(	(	PUNCT
uva.x030312957	233	3	2	2	X
uva.x030312957	233	4	)	)	PUNCT
uva.x030312957	233	5	ہو	ہو	PROPN
uva.x030312957	233	6	گی	گی	ADP
uva.x030312957	233	7	...	...	PUNCT
uva.x030312957	234	1	(	(	PUNCT
uva.x030312957	234	2	xn	xn	PROPN
uva.x030312957	234	3	a	a	X
uva.x030312957	234	4	)	)	PUNCT
uva.x030312957	234	5	f.	f.	NOUN
uva.x030312957	234	6	(	(	PUNCT
uva.x030312957	234	7	xn	xn	PROPN
uva.x030312957	234	8	)	)	PUNCT
uva.x030312957	234	9	,	,	PUNCT
uva.x030312957	234	10	(	(	PUNCT
uva.x030312957	234	11	xn	xn	PROPN
uva.x030312957	234	12	–	–	PUNCT
uva.x030312957	234	13	a)fı(xn	a)fı(xn	NOUN
uva.x030312957	234	14	)	)	PUNCT
uva.x030312957	234	15	,	,	PUNCT
uva.x030312957	234	16	...	...	PUNCT
uva.x030312957	234	17	,	,	PUNCT
uva.x030312957	234	18	(	(	PUNCT
uva.x030312957	234	19	xn	xn	PROPN
uva.x030312957	234	20	–	–	PUNCT
uva.x030312957	234	21	a	a	X
uva.x030312957	234	22	)	)	PUNCT
uva.x030312957	234	23	fn-1	fn-1	X
uva.x030312957	235	1	(	(	PUNCT
uva.x030312957	235	2	xn	xn	PROPN
uva.x030312957	235	3	)	)	PUNCT
uva.x030312957	235	4	(	(	PUNCT
uva.x030312957	235	5	25	25	NUM
uva.x030312957	235	6	)	)	PUNCT
uva.x030312957	235	7	fo(x1	fo(x1	PROPN
uva.x030312957	235	8	)	)	PUNCT
uva.x030312957	235	9	,	,	PUNCT
uva.x030312957	235	10	fi(xi	fi(xi	NOUN
uva.x030312957	235	11	)	)	PUNCT
uva.x030312957	235	12	,	,	PUNCT
uva.x030312957	235	13	..	..	PROPN
uva.x030312957	235	14	,	,	PUNCT
uva.x030312957	235	15	fn-1(x1	fn-1(x1	SPACE
uva.x030312957	235	16	)	)	PUNCT
uva.x030312957	235	17	fo	fo	X
uva.x030312957	235	18	(	(	PUNCT
uva.x030312957	235	19	x2	x2	PROPN
uva.x030312957	235	20	)	)	PUNCT
uva.x030312957	235	21	,	,	PUNCT
uva.x030312957	235	22	fı(x2	fı(x2	PROPN
uva.x030312957	235	23	)	)	PUNCT
uva.x030312957	235	24	,	,	PUNCT
uva.x030312957	235	25	fr-1	fr-1	PRON
uva.x030312957	235	26	(	(	PUNCT
uva.x030312957	235	27	x2	x2	NOUN
uva.x030312957	235	28	)	)	PUNCT
uva.x030312957	235	29	fo(an	fo(an	NOUN
uva.x030312957	235	30	)	)	PUNCT
uva.x030312957	235	31	,	,	PUNCT
uva.x030312957	235	32	f1(xn	f1(xn	SPACE
uva.x030312957	235	33	)	)	PUNCT
uva.x030312957	235	34	,	,	PUNCT
uva.x030312957	235	35	...	...	PUNCT
uva.x030312957	235	36	,	,	PUNCT
uva.x030312957	235	37	fn-1	fn-1	X
uva.x030312957	235	38	(	(	PUNCT
uva.x030312957	235	39	zn	zn	X
uva.x030312957	235	40	)	)	PUNCT
uva.x030312957	235	41	>	>	PUNCT
uva.x030312957	236	1	z	z	PROPN
uva.x030312957	236	2	since	since	SCONJ
uva.x030312957	236	3	ao(x1	ao(x1	PROPN
uva.x030312957	236	4	a	a	PRON
uva.x030312957	236	5	)	)	PUNCT
uva.x030312957	236	6	(	(	PUNCT
uva.x030312957	236	7	x2	x2	PROPN
uva.x030312957	236	8	a	a	X
uva.x030312957	236	9	)	)	PUNCT
uva.x030312957	236	10	(	(	PUNCT
uva.x030312957	236	11	x3	x3	PROPN
uva.x030312957	236	12	a	a	X
uva.x030312957	236	13	)	)	PUNCT
uva.x030312957	236	14	...	...	PUNCT
uva.x030312957	237	1	(	(	PUNCT
uva.x030312957	237	2	xn	xn	PROPN
uva.x030312957	237	3	–	–	PUNCT
uva.x030312957	237	4	a	a	X
uva.x030312957	237	5	)	)	PUNCT
uva.x030312957	237	6	=	=	NOUN
uva.x030312957	237	7	(	(	PUNCT
uva.x030312957	237	8	-1	-1	X
uva.x030312957	237	9	)	)	PUNCT
uva.x030312957	237	10	"	"	PUNCT
uva.x030312957	237	11	f(a	f(a	PROPN
uva.x030312957	237	12	)	)	PUNCT
uva.x030312957	237	13	,	,	PUNCT
uva.x030312957	237	14	an(a	an(a	AUX
uva.x030312957	237	15	)	)	PUNCT
uva.x030312957	237	16	reduces	reduce	VERB
uva.x030312957	237	17	to	to	ADP
uva.x030312957	237	18	fo(xi	fo(xi	SPACE
uva.x030312957	237	19	)	)	PUNCT
uva.x030312957	237	20	,	,	PUNCT
uva.x030312957	237	21	f1(xi	f1(xi	NUM
uva.x030312957	237	22	)	)	PUNCT
uva.x030312957	237	23	,	,	PUNCT
uva.x030312957	237	24	fr-1(xi	fr-1(xi	SPACE
uva.x030312957	237	25	)	)	PUNCT
uva.x030312957	237	26	(	(	PUNCT
uva.x030312957	237	27	-1)"f(a	-1)"f(a	PROPN
uva.x030312957	237	28	)	)	PUNCT
uva.x030312957	237	29	fo(x2	fo(x2	PROPN
uva.x030312957	237	30	)	)	PUNCT
uva.x030312957	237	31	,	,	PUNCT
uva.x030312957	237	32	f1(x2	f1(x2	PROPN
uva.x030312957	237	33	)	)	PUNCT
uva.x030312957	237	34	,	,	PUNCT
uva.x030312957	237	35	(	(	PUNCT
uva.x030312957	237	36	26	26	NUM
uva.x030312957	237	37	)	)	PUNCT
uva.x030312957	237	38	al(a	al(a	PROPN
uva.x030312957	237	39	)	)	PUNCT
uva.x030312957	237	40	:	:	PUNCT
uva.x030312957	237	41	;	;	PUNCT
uva.x030312957	237	42	fn-1(x2	fn-1(x2	X
uva.x030312957	237	43	)	)	PUNCT
uva.x030312957	237	44	do	do	AUX
uva.x030312957	237	45	fo(an	fo(an	PROPN
uva.x030312957	237	46	)	)	PUNCT
uva.x030312957	237	47	,	,	PUNCT
uva.x030312957	237	48	fi(zn	fi(zn	PROPN
uva.x030312957	237	49	)	)	PUNCT
uva.x030312957	237	50	,	,	PUNCT
uva.x030312957	237	51	...	...	PUNCT
uva.x030312957	237	52	,	,	PUNCT
uva.x030312957	237	53	fr-1(2n	fr-1(2n	X
uva.x030312957	237	54	)	)	PUNCT
uva.x030312957	237	55	this	this	DET
uva.x030312957	237	56	last	last	ADJ
uva.x030312957	237	57	determinant	determinant	NOUN
uva.x030312957	237	58	may	may	AUX
uva.x030312957	237	59	be	be	AUX
uva.x030312957	237	60	expressed	express	VERB
uva.x030312957	237	61	as	as	ADP
uva.x030312957	237	62	the	the	DET
uva.x030312957	237	63	product	product	NOUN
uva.x030312957	237	64	of	of	ADP
uva.x030312957	237	65	two	two	NUM
uva.x030312957	237	66	determinants	determinant	NOUN
uva.x030312957	237	67	,	,	PUNCT
uva.x030312957	237	68	thus	thus	ADV
uva.x030312957	237	69	fo	fo	PROPN
uva.x030312957	237	70	(	(	PUNCT
uva.x030312957	237	71	21	21	NUM
uva.x030312957	237	72	)	)	PUNCT
uva.x030312957	237	73	,	,	PUNCT
uva.x030312957	237	74	f1(xi	f1(xi	NUM
uva.x030312957	237	75	)	)	PUNCT
uva.x030312957	237	76	,	,	PUNCT
uva.x030312957	237	77	f2(xi	f2(xi	SPACE
uva.x030312957	237	78	)	)	PUNCT
uva.x030312957	237	79	,	,	PUNCT
uva.x030312957	237	80	fr-1(x1	fr-1(x1	PROPN
uva.x030312957	237	81	)	)	PUNCT
uva.x030312957	237	82	fo(22	fo(22	PROPN
uva.x030312957	237	83	)	)	PUNCT
uva.x030312957	237	84	,	,	PUNCT
uva.x030312957	237	85	f1(x2	f1(x2	PROPN
uva.x030312957	237	86	)	)	PUNCT
uva.x030312957	237	87	,	,	PUNCT
uva.x030312957	237	88	f2(x2	f2(x2	NOUN
uva.x030312957	237	89	)	)	PUNCT
uva.x030312957	237	90	,	,	PUNCT
uva.x030312957	237	91	fr-1	fr-1	PRON
uva.x030312957	237	92	(	(	PUNCT
uva.x030312957	237	93	x2	x2	NOUN
uva.x030312957	237	94	)	)	PUNCT
uva.x030312957	237	95	2	2	NUM
uva.x030312957	237	96	=	=	NOUN
uva.x030312957	237	97	iforam	iforam	PROPN
uva.x030312957	237	98	..	..	PUNCT
uva.x030312957	237	99	,	,	PUNCT
uva.x030312957	237	100	fo(an	fo(an	PROPN
uva.x030312957	237	101	)	)	PUNCT
uva.x030312957	237	102	,	,	PUNCT
uva.x030312957	237	103	fi(xn	fi(xn	PROPN
uva.x030312957	237	104	)	)	PUNCT
uva.x030312957	237	105	,	,	PUNCT
uva.x030312957	237	106	f2(xn	f2(xn	SPACE
uva.x030312957	237	107	)	)	PUNCT
uva.x030312957	237	108	,	,	PUNCT
uva.x030312957	237	109	fn-1	fn-1	X
uva.x030312957	237	110	(	(	PUNCT
uva.x030312957	237	111	xn	xn	PROPN
uva.x030312957	237	112	)	)	PUNCT
uva.x030312957	237	113	0	0	NUM
uva.x030312957	237	114	1	1	NUM
uva.x030312957	237	115	,	,	PUNCT
uva.x030312957	237	116	x1	x1	PROPN
uva.x030312957	237	117	,	,	PUNCT
uva.x030312957	237	118	xi	xi	PROPN
uva.x030312957	237	119	,	,	PUNCT
uva.x030312957	237	120	(	(	PUNCT
uva.x030312957	237	121	27	27	NUM
uva.x030312957	237	122	)	)	PUNCT
uva.x030312957	237	123	do	do	AUX
uva.x030312957	237	124	,	,	PUNCT
uva.x030312957	237	125	0	0	NUM
uva.x030312957	237	126	,	,	PUNCT
uva.x030312957	237	127	0	0	NUM
uva.x030312957	237	128	,	,	PUNCT
uva.x030312957	237	129	...	...	PUNCT
uva.x030312957	237	130	,	,	PUNCT
uva.x030312957	237	131	22	22	NUM
uva.x030312957	237	132	di	di	NOUN
uva.x030312957	237	133	,	,	PUNCT
uva.x030312957	237	134	do	do	AUX
uva.x030312957	237	135	,	,	PUNCT
uva.x030312957	237	136	0	0	NUM
uva.x030312957	237	137	,	,	PUNCT
uva.x030312957	237	138	in-1	in-1	NOUN
uva.x030312957	237	139	0	0	NUM
uva.x030312957	237	140	ܕܐ	ܕܐ	ADP
uva.x030312957	237	141	x2	x2	PROPN
uva.x030312957	237	142	,	,	PUNCT
uva.x030312957	237	143	x3	x3	PROPN
uva.x030312957	237	144	,	,	PUNCT
uva.x030312957	237	145	x3	x3	PROPN
uva.x030312957	237	146	,	,	PUNCT
uva.x030312957	237	147	x3	x3	PROPN
uva.x030312957	237	148	,	,	PUNCT
uva.x030312957	237	149	x11	x11	PROPN
uva.x030312957	237	150	,	,	PUNCT
uva.x030312957	237	151	n-1	n-1	NUM
uva.x030312957	237	152	02	02	NUM
uva.x030312957	237	153	,	,	PUNCT
uva.x030312957	237	154	di	di	PROPN
uva.x030312957	237	155	,	,	PUNCT
uva.x030312957	237	156	do	do	AUX
uva.x030312957	237	157	,	,	PUNCT
uva.x030312957	237	158	0	0	PUNCT
uva.x030312957	237	159	.	.	PUNCT
uva.x030312957	237	160	an-1	an-1	SPACE
uva.x030312957	237	161	,	,	PUNCT
uva.x030312957	237	162	an-2	an-2	SPACE
uva.x030312957	237	163	,	,	PUNCT
uva.x030312957	237	164	an-3	an-3	SPACE
uva.x030312957	237	165	,	,	PUNCT
uva.x030312957	237	166	do	do	AUX
uva.x030312957	237	167	1	1	NUM
uva.x030312957	237	168	,	,	PUNCT
uva.x030312957	237	169	2	2	NUM
uva.x030312957	237	170	,	,	PUNCT
uva.x030312957	237	171	3	3	NUM
uva.x030312957	237	172	,	,	PUNCT
uva.x030312957	237	173	x	x	NOUN
uva.x030312957	237	174	the	the	DET
uva.x030312957	237	175	square	square	NOUN
uva.x030312957	237	176	of	of	ADP
uva.x030312957	237	177	this	this	DET
uva.x030312957	237	178	product	product	NOUN
uva.x030312957	237	179	is	be	AUX
uva.x030312957	237	180	equal	equal	ADJ
uva.x030312957	237	181	to	to	ADP
uva.x030312957	237	182	a	a	PRON
uva.x030312957	237	183	;	;	PUNCT
uva.x030312957	237	184	d	d	X
uva.x030312957	237	185	,	,	PUNCT
uva.x030312957	237	186	*	*	PUNCT
uva.x030312957	237	187	where	where	SCONJ
uva.x030312957	237	188	d	d	NOUN
uva.x030312957	237	189	is	be	AUX
uva.x030312957	237	190	the	the	DET
uva.x030312957	237	191	discriminant	discriminant	NOUN
uva.x030312957	237	192	of	of	ADP
uva.x030312957	237	193	the	the	DET
uva.x030312957	237	194	function	function	NOUN
uva.x030312957	237	195	f(x	f(x	PROPN
uva.x030312957	237	196	)	)	PUNCT
uva.x030312957	237	197	.	.	PUNCT
uva.x030312957	238	1	we	we	PRON
uva.x030312957	238	2	see	see	VERB
uva.x030312957	238	3	then	then	ADV
uva.x030312957	238	4	that	that	SCONJ
uva.x030312957	238	5	(	(	PUNCT
uva.x030312957	238	6	28	28	NUM
uva.x030312957	238	7	)	)	PUNCT
uva.x030312957	238	8	al(a	al(a	PROPN
uva.x030312957	238	9	)	)	PUNCT
uva.x030312957	238	10	=	=	PROPN
uva.x030312957	238	11	(	(	PUNCT
uva.x030312957	238	12	-1	-1	X
uva.x030312957	238	13	)	)	PUNCT
uva.x030312957	238	14	"	"	PUNCT
uva.x030312957	238	15	aof	aof	PROPN
uva.x030312957	238	16	(	(	PUNCT
uva.x030312957	238	17	a)d	a)d	PROPN
uva.x030312957	238	18	.	.	PUNCT
uva.x030312957	239	1	since	since	SCONJ
uva.x030312957	239	2	,	,	PUNCT
uva.x030312957	239	3	by	by	ADP
uva.x030312957	239	4	hypothesis	hypothesis	NOUN
uva.x030312957	239	5	,	,	PUNCT
uva.x030312957	239	6	d	d	NOUN
uva.x030312957	239	7	is	be	AUX
uva.x030312957	239	8	different	different	ADJ
uva.x030312957	239	9	from	from	ADP
uva.x030312957	239	10	zero	zero	NUM
uva.x030312957	239	11	,	,	PUNCT
uva.x030312957	239	12	an(a	an(a	AUX
uva.x030312957	239	13	)	)	PUNCT
uva.x030312957	239	14	can	can	AUX
uva.x030312957	239	15	only	only	ADV
uva.x030312957	239	16	vanish	vanish	VERB
uva.x030312957	239	17	when	when	SCONJ
uva.x030312957	239	18	we	we	PRON
uva.x030312957	239	19	substitute	substitute	VERB
uva.x030312957	239	20	one	one	NUM
uva.x030312957	239	21	of	of	ADP
uva.x030312957	239	22	the	the	DET
uva.x030312957	239	23	roots	root	NOUN
uva.x030312957	239	24	of	of	ADP
uva.x030312957	239	25	f	f	PROPN
uva.x030312957	239	26	(	(	PUNCT
uva.x030312957	239	27	x	x	SYM
uva.x030312957	239	28	)	)	PUNCT
uva.x030312957	239	29	since	since	SCONJ
uva.x030312957	239	30	an(a	an(a	NOUN
uva.x030312957	239	31	)	)	PUNCT
uva.x030312957	239	32	is	be	AUX
uva.x030312957	239	33	the	the	DET
uva.x030312957	239	34	determinant	determinant	NOUN
uva.x030312957	239	35	of	of	ADP
uva.x030312957	239	36	the	the	DET
uva.x030312957	239	37	quadratic	quadratic	ADJ
uva.x030312957	239	38	form	form	NOUN
uva.x030312957	239	39	h	h	NOUN
uva.x030312957	239	40	,	,	PUNCT
uva.x030312957	239	41	we	we	PRON
uva.x030312957	239	42	can	can	AUX
uva.x030312957	239	43	fix	fix	VERB
uva.x030312957	239	44	the	the	DET
uva.x030312957	239	45	number	number	NOUN
uva.x030312957	239	46	of	of	ADP
uva.x030312957	239	47	negative	negative	ADJ
uva.x030312957	239	48	squares	square	NOUN
uva.x030312957	239	49	in	in	ADP
uva.x030312957	239	50	h	h	PROPN
uva.x030312957	239	51	,	,	PUNCT
uva.x030312957	239	52	if	if	SCONJ
uva.x030312957	239	53	expressed	express	VERB
uva.x030312957	239	54	as	as	ADP
uva.x030312957	239	55	the	the	DET
uva.x030312957	239	56	sum	sum	NOUN
uva.x030312957	239	57	of	of	ADP
uva.x030312957	239	58	squares	square	NOUN
uva.x030312957	239	59	of	of	ADP
uva.x030312957	239	60	linear	linear	ADJ
uva.x030312957	239	61	terms	term	NOUN
uva.x030312957	239	62	,	,	PUNCT
uva.x030312957	239	63	by	by	ADP
uva.x030312957	239	64	the	the	DET
uva.x030312957	239	65	number	number	NOUN
uva.x030312957	239	66	of	of	ADP
uva.x030312957	239	67	variations	variation	NOUN
uva.x030312957	239	68	in	in	ADP
uva.x030312957	239	69	the	the	DET
uva.x030312957	239	70	chain	chain	NOUN
uva.x030312957	239	71	of	of	ADP
uva.x030312957	239	72	principal	principal	ADJ
uva.x030312957	239	73	minors	minor	NOUN
uva.x030312957	239	74	of	of	ADP
uva.x030312957	239	75	ah	ah	INTJ
uva.x030312957	239	76	(	(	PUNCT
uva.x030312957	239	77	a	a	NOUN
uva.x030312957	239	78	)	)	PUNCT
uva.x030312957	239	79	.	.	PUNCT
uva.x030312957	240	1	*	*	PUNCT
uva.x030312957	240	2	see	see	VERB
uva.x030312957	240	3	(	(	PUNCT
uva.x030312957	240	4	7	7	NUM
uva.x030312957	240	5	)	)	PUNCT
uva.x030312957	240	6	$	$	SYM
uva.x030312957	240	7	50	50	NUM
uva.x030312957	240	8	,	,	PUNCT
uva.x030312957	240	9	vol	vol	NOUN
uva.x030312957	240	10	.	.	PUNCT
uva.x030312957	241	1	i	i	PROPN
uva.x030312957	241	2	,	,	PUNCT
uva.x030312957	241	3	weber	weber	PROPN
uva.x030312957	241	4	.	.	PUNCT
uva.x030312957	241	5	†	†	PROPN
uva.x030312957	241	6	see	see	VERB
uva.x030312957	241	7	v	v	PROPN
uva.x030312957	241	8	,	,	PUNCT
uva.x030312957	241	9	8	8	NUM
uva.x030312957	241	10	89	89	NUM
uva.x030312957	241	11	,	,	PUNCT
uva.x030312957	241	12	vol	vol	NOUN
uva.x030312957	241	13	.	.	PUNCT
uva.x030312957	242	1	i	i	PROPN
uva.x030312957	242	2	,	,	PUNCT
uva.x030312957	242	3	weber	weber	PROPN
uva.x030312957	242	4	.	.	PROPN
uva.x030312957	242	5	0	0	PROPN
uva.x030312957	242	6	for	for	ADP
uva.x030312957	242	7	a.	a.	NOUN
uva.x030312957	242	8	14	14	NUM
uva.x030312957	242	9	solution	solution	NOUN
uva.x030312957	242	10	of	of	ADP
uva.x030312957	242	11	the	the	DET
uva.x030312957	242	12	equation	equation	NOUN
uva.x030312957	242	13	of	of	ADP
uva.x030312957	242	14	secular	secular	ADJ
uva.x030312957	242	15	variation	variation	NOUN
uva.x030312957	242	16	by	by	ADP
uva.x030312957	242	17	the	the	DET
uva.x030312957	242	18	principal	principal	ADJ
uva.x030312957	242	19	minors	minor	NOUN
uva.x030312957	242	20	of	of	ADP
uva.x030312957	242	21	4(a	4(a	NUM
uva.x030312957	242	22	)	)	PUNCT
uva.x030312957	242	23	we	we	PRON
uva.x030312957	242	24	mean	mean	VERB
uva.x030312957	242	25	determinants	determinant	NOUN
uva.x030312957	242	26	formed	form	VERB
uva.x030312957	242	27	in	in	ADP
uva.x030312957	242	28	succession	succession	NOUN
uva.x030312957	242	29	by	by	ADP
uva.x030312957	242	30	starting	start	VERB
uva.x030312957	242	31	with	with	ADP
uva.x030312957	242	32	an	an	DET
uva.x030312957	242	33	(	(	PUNCT
uva.x030312957	242	34	a	a	NOUN
uva.x030312957	242	35	)	)	PUNCT
uva.x030312957	242	36	and	and	CCONJ
uva.x030312957	242	37	leaving	leave	VERB
uva.x030312957	242	38	off	off	ADP
uva.x030312957	242	39	the	the	DET
uva.x030312957	242	40	last	last	ADJ
uva.x030312957	242	41	row	row	NOUN
uva.x030312957	242	42	and	and	CCONJ
uva.x030312957	242	43	last	last	ADJ
uva.x030312957	242	44	column	column	NOUN
uva.x030312957	242	45	,	,	PUNCT
uva.x030312957	242	46	then	then	ADV
uva.x030312957	242	47	leave	leave	VERB
uva.x030312957	242	48	off	off	ADP
uva.x030312957	242	49	the	the	DET
uva.x030312957	242	50	last	last	ADJ
uva.x030312957	242	51	row	row	NOUN
uva.x030312957	242	52	and	and	CCONJ
uva.x030312957	242	53	column	column	NOUN
uva.x030312957	242	54	of	of	ADP
uva.x030312957	242	55	this	this	PRON
uva.x030312957	242	56	,	,	PUNCT
uva.x030312957	242	57	and	and	CCONJ
uva.x030312957	242	58	so	so	ADV
uva.x030312957	242	59	on	on	ADV
uva.x030312957	242	60	down	down	ADP
uva.x030312957	242	61	to	to	ADP
uva.x030312957	242	62	the	the	DET
uva.x030312957	242	63	last	last	ADJ
uva.x030312957	242	64	.	.	PUNCT
uva.x030312957	243	1	the	the	DET
uva.x030312957	243	2	chain	chain	NOUN
uva.x030312957	243	3	of	of	ADP
uva.x030312957	243	4	these	these	DET
uva.x030312957	243	5	principal	principal	ADJ
uva.x030312957	243	6	minors	minor	NOUN
uva.x030312957	243	7	would	would	AUX
uva.x030312957	243	8	then	then	ADV
uva.x030312957	243	9	appear	appear	VERB
uva.x030312957	243	10	as	as	ADP
uva.x030312957	243	11	41(a	41(a	NUM
uva.x030312957	243	12	)	)	PUNCT
uva.x030312957	243	13	,	,	PUNCT
uva.x030312957	243	14	4	4	NUM
uva.x030312957	243	15	.	.	PUNCT
uva.x030312957	244	1	(	(	PUNCT
uva.x030312957	244	2	a	a	X
uva.x030312957	244	3	)	)	PUNCT
uva.x030312957	244	4	,	,	PUNCT
uva.x030312957	244	5	a	a	DET
uva.x030312957	244	6	's	's	NOUN
uva.x030312957	244	7	(	(	PUNCT
uva.x030312957	244	8	a	a	NOUN
uva.x030312957	244	9	)	)	PUNCT
uva.x030312957	244	10	,	,	PUNCT
uva.x030312957	244	11	...	...	PUNCT
uva.x030312957	244	12	,	,	PUNCT
uva.x030312957	244	13	41(a	41(a	NUM
uva.x030312957	244	14	)	)	PUNCT
uva.x030312957	244	15	,	,	PUNCT
uva.x030312957	244	16	when	when	SCONJ
uva.x030312957	244	17	arranged	arrange	VERB
uva.x030312957	244	18	in	in	ADP
uva.x030312957	244	19	reverse	reverse	ADJ
uva.x030312957	244	20	order	order	NOUN
uva.x030312957	244	21	.	.	PUNCT
uva.x030312957	245	1	the	the	DET
uva.x030312957	245	2	number	number	NOUN
uva.x030312957	245	3	of	of	ADP
uva.x030312957	245	4	negative	negative	ADJ
uva.x030312957	245	5	squares	square	NOUN
uva.x030312957	245	6	in	in	ADP
uva.x030312957	245	7	h	h	PROPN
uva.x030312957	245	8	will	will	AUX
uva.x030312957	245	9	then	then	ADV
uva.x030312957	245	10	be	be	AUX
uva.x030312957	245	11	equal	equal	ADJ
uva.x030312957	245	12	to	to	ADP
uva.x030312957	245	13	the	the	DET
uva.x030312957	245	14	number	number	NOUN
uva.x030312957	245	15	of	of	ADP
uva.x030312957	245	16	variations	variation	NOUN
uva.x030312957	245	17	in	in	ADP
uva.x030312957	245	18	sign	sign	NOUN
uva.x030312957	245	19	between	between	ADP
uva.x030312957	245	20	the	the	DET
uva.x030312957	245	21	functions	function	NOUN
uva.x030312957	245	22	(	(	PUNCT
uva.x030312957	245	23	29	29	NUM
uva.x030312957	245	24	)	)	PUNCT
uva.x030312957	245	25	1	1	NUM
uva.x030312957	245	26	,	,	PUNCT
uva.x030312957	245	27	ai(a	ai(a	ADJ
uva.x030312957	245	28	)	)	PUNCT
uva.x030312957	245	29	,	,	PUNCT
uva.x030312957	245	30	42	42	NUM
uva.x030312957	245	31	(	(	PUNCT
uva.x030312957	245	32	a	a	NOUN
uva.x030312957	245	33	)	)	PUNCT
uva.x030312957	245	34	,	,	PUNCT
uva.x030312957	245	35	ag	ag	PROPN
uva.x030312957	245	36	(	(	PUNCT
uva.x030312957	245	37	a	a	PROPN
uva.x030312957	245	38	)	)	PUNCT
uva.x030312957	245	39	,	,	PUNCT
uva.x030312957	245	40	:	:	PUNCT
uva.x030312957	245	41	...	...	PUNCT
uva.x030312957	245	42	,	,	PUNCT
uva.x030312957	245	43	4(a	4(a	NUM
uva.x030312957	245	44	)	)	PUNCT
uva.x030312957	245	45	.	.	PUNCT
uva.x030312957	246	1	since	since	SCONJ
uva.x030312957	246	2	this	this	DET
uva.x030312957	246	3	h	h	NOUN
uva.x030312957	246	4	,	,	PUNCT
uva.x030312957	246	5	as	as	SCONJ
uva.x030312957	246	6	given	give	VERB
uva.x030312957	246	7	in	in	ADP
uva.x030312957	246	8	(	(	PUNCT
uva.x030312957	246	9	23	23	NUM
uva.x030312957	246	10	)	)	PUNCT
uva.x030312957	246	11	,	,	PUNCT
uva.x030312957	246	12	is	be	AUX
uva.x030312957	246	13	the	the	DET
uva.x030312957	246	14	same	same	ADJ
uva.x030312957	246	15	as	as	ADP
uva.x030312957	246	16	our	our	PRON
uva.x030312957	246	17	hin	hin	X
uva.x030312957	246	18	(	(	PUNCT
uva.x030312957	246	19	5	5	NUM
uva.x030312957	246	20	)	)	PUNCT
uva.x030312957	246	21	with	with	ADP
uva.x030312957	246	22	the	the	DET
uva.x030312957	246	23	y	y	PROPN
uva.x030312957	246	24	's	be	AUX
uva.x030312957	246	25	expressed	express	VERB
uva.x030312957	246	26	in	in	ADP
uva.x030312957	246	27	terms	term	NOUN
uva.x030312957	246	28	of	of	ADP
uva.x030312957	246	29	the	the	DET
uva.x030312957	246	30	t	t	PROPN
uva.x030312957	246	31	's	's	PART
uva.x030312957	246	32	,	,	PUNCT
uva.x030312957	246	33	the	the	DET
uva.x030312957	246	34	number	number	NOUN
uva.x030312957	246	35	of	of	ADP
uva.x030312957	246	36	negative	negative	ADJ
uva.x030312957	246	37	squares	square	NOUN
uva.x030312957	246	38	in	in	ADP
uva.x030312957	246	39	h	h	PROPN
uva.x030312957	246	40	,	,	PUNCT
uva.x030312957	246	41	is	be	AUX
uva.x030312957	246	42	obtained	obtain	VERB
uva.x030312957	246	43	from	from	ADP
uva.x030312957	246	44	the	the	DET
uva.x030312957	246	45	variations	variation	NOUN
uva.x030312957	246	46	in	in	ADP
uva.x030312957	246	47	the	the	DET
uva.x030312957	246	48	signs	sign	NOUN
uva.x030312957	246	49	between	between	ADP
uva.x030312957	246	50	the	the	DET
uva.x030312957	246	51	functions	function	NOUN
uva.x030312957	246	52	in	in	ADP
uva.x030312957	246	53	(	(	PUNCT
uva.x030312957	246	54	29	29	NUM
uva.x030312957	246	55	)	)	PUNCT
uva.x030312957	246	56	.	.	PUNCT
uva.x030312957	247	1	call	call	VERB
uva.x030312957	247	2	this	this	DET
uva.x030312957	247	3	number	number	NOUN
uva.x030312957	247	4	na	na	ADP
uva.x030312957	247	5	,	,	PUNCT
uva.x030312957	247	6	and	and	CCONJ
uva.x030312957	247	7	denote	denote	ADJ
uva.x030312957	247	8	by	by	ADP
uva.x030312957	247	9	ng	ng	PROPN
uva.x030312957	247	10	the	the	DET
uva.x030312957	247	11	corresponding	corresponding	ADJ
uva.x030312957	247	12	number	number	NOUN
uva.x030312957	247	13	of	of	ADP
uva.x030312957	247	14	variations	variation	NOUN
uva.x030312957	247	15	in	in	ADP
uva.x030312957	247	16	the	the	DET
uva.x030312957	247	17	chain	chain	NOUN
uva.x030312957	247	18	where	where	SCONJ
uva.x030312957	247	19	ß	ß	NOUN
uva.x030312957	247	20	replaces	replace	VERB
uva.x030312957	247	21	a	a	DET
uva.x030312957	247	22	,	,	PUNCT
uva.x030312957	247	23	ß	ß	NOUN
uva.x030312957	247	24	>	>	PUNCT
uva.x030312957	247	25	a.	a.	NOUN
uva.x030312957	247	26	that	that	PRON
uva.x030312957	247	27	is	be	AUX
uva.x030312957	247	28	no	no	PRON
uva.x030312957	247	29	is	be	AUX
uva.x030312957	247	30	the	the	DET
uva.x030312957	247	31	number	number	NOUN
uva.x030312957	247	32	of	of	ADP
uva.x030312957	247	33	variations	variation	NOUN
uva.x030312957	247	34	in	in	ADP
uva.x030312957	247	35	1	1	NUM
uva.x030312957	247	36	,	,	PUNCT
uva.x030312957	247	37	δ	δ	PROPN
uva.x030312957	247	38	,	,	PUNCT
uva.x030312957	247	39	(	(	PUNCT
uva.x030312957	247	40	β	β	PROPN
uva.x030312957	247	41	)	)	PUNCT
uva.x030312957	247	42	,	,	PUNCT
uva.x030312957	247	43	δ	δ	PROPN
uva.x030312957	247	44	,	,	PUNCT
uva.x030312957	247	45	(	(	PUNCT
uva.x030312957	247	46	β	β	PROPN
uva.x030312957	247	47	)	)	PUNCT
uva.x030312957	247	48	,	,	PUNCT
uva.x030312957	247	49	δ	δ	PROPN
uva.x030312957	247	50	,	,	PUNCT
uva.x030312957	247	51	(	(	PUNCT
uva.x030312957	247	52	β	β	PROPN
uva.x030312957	247	53	)	)	PUNCT
uva.x030312957	247	54	,	,	PUNCT
uva.x030312957	247	55	a(b	a(b	PROPN
uva.x030312957	247	56	)	)	PUNCT
uva.x030312957	247	57	.	.	PUNCT
uva.x030312957	248	1	then	then	ADV
uva.x030312957	248	2	na	na	ADP
uva.x030312957	248	3	n	n	PROPN
uva.x030312957	248	4	,	,	PUNCT
uva.x030312957	248	5	will	will	AUX
uva.x030312957	248	6	give	give	VERB
uva.x030312957	248	7	us	we	PRON
uva.x030312957	248	8	the	the	DET
uva.x030312957	248	9	number	number	NOUN
uva.x030312957	248	10	of	of	ADP
uva.x030312957	248	11	real	real	ADJ
uva.x030312957	248	12	roots	root	NOUN
uva.x030312957	248	13	of	of	ADP
uva.x030312957	248	14	f(x	f(x	NOUN
uva.x030312957	248	15	)	)	PUNCT
uva.x030312957	248	16	=	=	PROPN
uva.x030312957	248	17	0	0	NUM
uva.x030312957	248	18	lying	lie	VERB
uva.x030312957	248	19	between	between	ADP
uva.x030312957	248	20	a	a	PRON
uva.x030312957	248	21	and	and	CCONJ
uva.x030312957	248	22	b.	b.	PROPN
uva.x030312957	248	23	chapter	chapter	PROPN
uva.x030312957	248	24	iii	iii	PROPN
uva.x030312957	248	25	the	the	DET
uva.x030312957	248	26	solution	solution	NOUN
uva.x030312957	248	27	of	of	ADP
uva.x030312957	248	28	the	the	DET
uva.x030312957	248	29	equation	equation	NOUN
uva.x030312957	248	30	of	of	ADP
uva.x030312957	248	31	secular	secular	ADJ
uva.x030312957	248	32	variations	variation	NOUN
uva.x030312957	248	33	and	and	CCONJ
uva.x030312957	248	34	applications	application	NOUN
uva.x030312957	248	35	$	$	SYM
uva.x030312957	248	36	1	1	NUM
uva.x030312957	248	37	.	.	PUNCT
uva.x030312957	249	1	the	the	DET
uva.x030312957	249	2	quadratic	quadratic	ADJ
uva.x030312957	249	3	form	form	NOUN
uva.x030312957	249	4	o'.-we	o'.-we	NOUN
uva.x030312957	249	5	shall	shall	AUX
uva.x030312957	249	6	now	now	ADV
uva.x030312957	249	7	apply	apply	VERB
uva.x030312957	249	8	hermite	hermite	NOUN
uva.x030312957	249	9	's	's	PART
uva.x030312957	249	10	method	method	NOUN
uva.x030312957	249	11	,	,	PUNCT
uva.x030312957	249	12	as	as	SCONJ
uva.x030312957	249	13	outlined	outline	VERB
uva.x030312957	249	14	above	above	ADV
uva.x030312957	249	15	,	,	PUNCT
uva.x030312957	249	16	to	to	ADP
uva.x030312957	249	17	the	the	DET
uva.x030312957	249	18	solution	solution	NOUN
uva.x030312957	249	19	of	of	ADP
uva.x030312957	249	20	the	the	DET
uva.x030312957	249	21	equation	equation	NOUN
uva.x030312957	249	22	of	of	ADP
uva.x030312957	249	23	secular	secular	ADJ
uva.x030312957	249	24	variations	variation	NOUN
uva.x030312957	249	25	,	,	PUNCT
uva.x030312957	249	26	which	which	PRON
uva.x030312957	249	27	we	we	PRON
uva.x030312957	249	28	take	take	VERB
uva.x030312957	249	29	in	in	ADP
uva.x030312957	249	30	the	the	DET
uva.x030312957	249	31	form	form	NOUN
uva.x030312957	249	32	:	:	PUNCT
uva.x030312957	249	33	di	di	PROPN
uva.x030312957	249	34	,	,	PUNCT
uva.x030312957	249	35	1	1	NUM
uva.x030312957	249	36	de	de	X
uva.x030312957	249	37	,	,	PUNCT
uva.x030312957	249	38	a	a	DET
uva.x030312957	249	39	1	1	NUM
uva.x030312957	249	40	,	,	PUNCT
uva.x030312957	249	41	2	2	NUM
uva.x030312957	249	42	,	,	PUNCT
uva.x030312957	249	43	01	01	NUM
uva.x030312957	249	44	,	,	PUNCT
uva.x030312957	249	45	3	3	NUM
uva.x030312957	249	46	,	,	PUNCT
uva.x030312957	249	47	di	di	NOUN
uva.x030312957	249	48	,	,	PUNCT
uva.x030312957	249	49	n	n	CCONJ
uva.x030312957	249	50	9	9	NUM
uva.x030312957	249	51	02	02	NUM
uva.x030312957	249	52	,	,	PUNCT
uva.x030312957	249	53	1	1	NUM
uva.x030312957	249	54	,	,	PUNCT
uva.x030312957	249	55	02	02	NUM
uva.x030312957	249	56	,	,	PUNCT
uva.x030312957	249	57	2	2	NUM
uva.x030312957	249	58	x	x	NUM
uva.x030312957	249	59	,	,	PUNCT
uva.x030312957	249	60	a2	a2	PROPN
uva.x030312957	249	61	,	,	PUNCT
uva.x030312957	249	62	3	3	NUM
uva.x030312957	249	63	,	,	PUNCT
uva.x030312957	249	64	02	02	NUM
uva.x030312957	249	65	.	.	PUNCT
uva.x030312957	250	1	n	n	PROPN
uva.x030312957	250	2	(	(	PUNCT
uva.x030312957	250	3	30	30	NUM
uva.x030312957	250	4	)	)	PUNCT
uva.x030312957	250	5	an	an	PRON
uva.x030312957	250	6	(	(	PUNCT
uva.x030312957	250	7	x	x	NOUN
uva.x030312957	250	8	)	)	PUNCT
uva.x030312957	250	9	=	=	PUNCT
uva.x030312957	250	10	=	=	PUNCT
uva.x030312957	250	11	0	0	NUM
uva.x030312957	250	12	.	.	PUNCT
uva.x030312957	250	13	(	(	PUNCT
uva.x030312957	250	14	3	3	NUM
uva.x030312957	250	15	,	,	PUNCT
uva.x030312957	250	16	1	1	NUM
uva.x030312957	250	17	,	,	PUNCT
uva.x030312957	250	18	03	03	NUM
uva.x030312957	250	19	,	,	PUNCT
uva.x030312957	250	20	2	2	NUM
uva.x030312957	250	21	,	,	PUNCT
uva.x030312957	250	22	03	03	NUM
uva.x030312957	250	23	,	,	PUNCT
uva.x030312957	250	24	3	3	NUM
uva.x030312957	250	25	x	x	NUM
uva.x030312957	250	26	,	,	PUNCT
uva.x030312957	250	27	(	(	PUNCT
uva.x030312957	250	28	3	3	NUM
uva.x030312957	250	29	,	,	PUNCT
uva.x030312957	250	30	no	no	DET
uva.x030312957	250	31	an	an	PRON
uva.x030312957	250	32	,	,	PUNCT
uva.x030312957	250	33	1	1	NUM
uva.x030312957	250	34	,	,	PUNCT
uva.x030312957	250	35	an	an	DET
uva.x030312957	250	36	,	,	PUNCT
uva.x030312957	250	37	2	2	NUM
uva.x030312957	250	38	on	on	ADP
uva.x030312957	250	39	,	,	PUNCT
uva.x030312957	250	40	31	31	NUM
uva.x030312957	250	41	an	an	PRON
uva.x030312957	250	42	,	,	PUNCT
uva.x030312957	250	43	n	n	X
uva.x030312957	250	44	2	2	NUM
uva.x030312957	250	45	in	in	ADP
uva.x030312957	250	46	this	this	PRON
uva.x030312957	250	47	we	we	PRON
uva.x030312957	250	48	take	take	VERB
uva.x030312957	250	49	the	the	DET
uva.x030312957	250	50	ai	ai	NOUN
uva.x030312957	250	51	,	,	PUNCT
uva.x030312957	250	52	j	j	PROPN
uva.x030312957	250	53	as	as	ADP
uva.x030312957	250	54	real	real	ADJ
uva.x030312957	250	55	quantities	quantity	NOUN
uva.x030312957	250	56	,	,	PUNCT
uva.x030312957	250	57	and	and	CCONJ
uva.x030312957	250	58	further	further	ADJ
uva.x030312957	250	59	ai	ai	VERB
uva.x030312957	250	60	,	,	PUNCT
uva.x030312957	250	61	i	i	PROPN
uva.x030312957	250	62	aj	aj	PROPN
uva.x030312957	250	63	,	,	PUNCT
uva.x030312957	250	64	i	i	PRON
uva.x030312957	250	65	,	,	PUNCT
uva.x030312957	250	66	i=1	i=1	PROPN
uva.x030312957	250	67	,	,	PUNCT
uva.x030312957	250	68	2	2	NUM
uva.x030312957	250	69	,	,	PUNCT
uva.x030312957	250	70	...	...	PUNCT
uva.x030312957	250	71	,	,	PUNCT
uva.x030312957	250	72	n.	n.	PROPN
uva.x030312957	250	73	j=1	j=1	PROPN
uva.x030312957	250	74	,	,	PUNCT
uva.x030312957	250	75	2	2	NUM
uva.x030312957	250	76	,	,	PUNCT
uva.x030312957	250	77	...	...	PUNCT
uva.x030312957	250	78	,	,	PUNCT
uva.x030312957	250	79	n.	n.	PROPN
uva.x030312957	250	80	if	if	SCONJ
uva.x030312957	250	81	this	this	DET
uva.x030312957	250	82	determinant	determinant	NOUN
uva.x030312957	250	83	is	be	AUX
uva.x030312957	250	84	expanded	expand	VERB
uva.x030312957	250	85	,	,	PUNCT
uva.x030312957	250	86	we	we	PRON
uva.x030312957	250	87	obtain	obtain	VERB
uva.x030312957	250	88	a	a	DET
uva.x030312957	250	89	polynomial	polynomial	NOUN
uva.x030312957	250	90	of	of	ADP
uva.x030312957	250	91	the	the	DET
uva.x030312957	250	92	nth	nth	NOUN
uva.x030312957	250	93	degree	degree	NOUN
uva.x030312957	250	94	in	in	ADP
uva.x030312957	250	95	x	x	PROPN
uva.x030312957	250	96	,	,	PUNCT
uva.x030312957	250	97	the	the	DET
uva.x030312957	250	98	coefficient	coefficient	NOUN
uva.x030312957	250	99	of	of	ADP
uva.x030312957	250	100	xn	xn	PROPN
uva.x030312957	250	101	being	be	AUX
uva.x030312957	250	102	(	(	PUNCT
uva.x030312957	250	103	1	1	X
uva.x030312957	250	104	)	)	PUNCT
uva.x030312957	250	105	"	"	PUNCT
uva.x030312957	250	106	.	.	PUNCT
uva.x030312957	251	1	represent	represent	VERB
uva.x030312957	251	2	this	this	DET
uva.x030312957	251	3	polynomial	polynomial	NOUN
uva.x030312957	251	4	as	as	ADP
uva.x030312957	251	5	(	(	PUNCT
uva.x030312957	251	6	31	31	NUM
uva.x030312957	251	7	)	)	PUNCT
uva.x030312957	251	8	f(x	f(x	PROPN
uva.x030312957	251	9	)	)	PUNCT
uva.x030312957	251	10	=	=	X
uva.x030312957	251	11	ao	ao	INTJ
uva.x030312957	251	12	x	x	X
uva.x030312957	251	13	"	"	PUNCT
uva.x030312957	251	14	+	+	CCONJ
uva.x030312957	251	15	aix"-1	aix"-1	ADJ
uva.x030312957	251	16	+	+	CCONJ
uva.x030312957	251	17	a2	a2	PROPN
uva.x030312957	251	18	21–2	21–2	NOUN
uva.x030312957	251	19	+	+	NUM
uva.x030312957	251	20	+	+	CCONJ
uva.x030312957	251	21	an	an	PRON
uva.x030312957	251	22	,	,	PUNCT
uva.x030312957	251	23	ao	ao	X
uva.x030312957	251	24	=	=	PROPN
uva.x030312957	251	25	(	(	PUNCT
uva.x030312957	251	26	-1	-1	X
uva.x030312957	251	27	)	)	PUNCT
uva.x030312957	251	28	"	"	PUNCT
uva.x030312957	251	29	and	and	CCONJ
uva.x030312957	251	30	then	then	ADV
uva.x030312957	251	31	find	find	VERB
uva.x030312957	251	32	the	the	DET
uva.x030312957	251	33	number	number	NOUN
uva.x030312957	251	34	of	of	ADP
uva.x030312957	251	35	roots	root	NOUN
uva.x030312957	251	36	of	of	ADP
uva.x030312957	251	37	(	(	PUNCT
uva.x030312957	251	38	32	32	NUM
uva.x030312957	251	39	)	)	PUNCT
uva.x030312957	251	40	f(x	f(x	PROPN
uva.x030312957	251	41	)	)	PUNCT
uva.x030312957	251	42	=	=	PROPN
uva.x030312957	251	43	0	0	NUM
uva.x030312957	251	44	.	.	PUNCT
uva.x030312957	251	45	from	from	ADP
uva.x030312957	251	46	(	(	PUNCT
uva.x030312957	251	47	32	32	NUM
uva.x030312957	251	48	)	)	PUNCT
uva.x030312957	251	49	form	form	VERB
uva.x030312957	251	50	the	the	DET
uva.x030312957	251	51	function	function	NOUN
uva.x030312957	251	52	h	h	NOUN
uva.x030312957	251	53	,	,	PUNCT
uva.x030312957	251	54	as	as	SCONJ
uva.x030312957	251	55	shown	show	VERB
uva.x030312957	251	56	in	in	ADP
uva.x030312957	251	57	(	(	PUNCT
uva.x030312957	251	58	5	5	NUM
uva.x030312957	251	59	)	)	PUNCT
uva.x030312957	251	60	,	,	PUNCT
uva.x030312957	251	61	(	(	PUNCT
uva.x030312957	251	62	5	5	X
uva.x030312957	251	63	)	)	PUNCT
uva.x030312957	251	64	hq	hq	NOUN
uva.x030312957	251	65	=	=	NOUN
uva.x030312957	251	66	(	(	PUNCT
uva.x030312957	251	67	x1	x1	PROPN
uva.x030312957	251	68	a)yi	a)yi	ADV
uva.x030312957	251	69	+	+	CCONJ
uva.x030312957	252	1	(	(	PUNCT
uva.x030312957	252	2	x2	x2	ADJ
uva.x030312957	252	3	a	a	X
uva.x030312957	252	4	)	)	PUNCT
uva.x030312957	252	5	yż	yż	PROPN
uva.x030312957	253	1	+	+	PUNCT
uva.x030312957	253	2	...	...	PUNCT
uva.x030312957	254	1	+	+	CCONJ
uva.x030312957	254	2	(	(	PUNCT
uva.x030312957	254	3	c	c	PROPN
uva.x030312957	254	4	a	a	X
uva.x030312957	254	5	)	)	PUNCT
uva.x030312957	254	6	gỉ	gỉ	PROPN
uva.x030312957	254	7	.	.	PUNCT
uva.x030312957	255	1	then	then	ADV
uva.x030312957	255	2	the	the	DET
uva.x030312957	255	3	number	number	NOUN
uva.x030312957	255	4	,	,	PUNCT
uva.x030312957	255	5	na	na	ADV
uva.x030312957	255	6	,	,	PUNCT
uva.x030312957	255	7	of	of	ADP
uva.x030312957	255	8	negative	negative	ADJ
uva.x030312957	255	9	squares	square	NOUN
uva.x030312957	255	10	in	in	ADP
uva.x030312957	255	11	this	this	DET
uva.x030312957	255	12	function	function	NOUN
uva.x030312957	255	13	will	will	AUX
uva.x030312957	255	14	give	give	VERB
uva.x030312957	255	15	the	the	DET
uva.x030312957	255	16	number	number	NOUN
uva.x030312957	255	17	of	of	ADP
uva.x030312957	255	18	real	real	ADJ
uva.x030312957	255	19	roots	root	NOUN
uva.x030312957	255	20	of	of	ADP
uva.x030312957	255	21	f(x	f(x	NOUN
uva.x030312957	255	22	)	)	PUNCT
uva.x030312957	255	23	=	=	PROPN
uva.x030312957	255	24	0	0	NUM
uva.x030312957	255	25	,	,	PUNCT
uva.x030312957	255	26	or	or	CCONJ
uva.x030312957	255	27	of	of	ADP
uva.x030312957	255	28	an	an	PRON
uva.x030312957	255	29	(	(	PUNCT
uva.x030312957	255	30	x	x	NOUN
uva.x030312957	255	31	)	)	PUNCT
uva.x030312957	255	32	=	=	PUNCT
uva.x030312957	255	33	0	0	NUM
uva.x030312957	255	34	,	,	PUNCT
uva.x030312957	255	35	which	which	PRON
uva.x030312957	255	36	are	be	AUX
uva.x030312957	255	37	less	less	ADJ
uva.x030312957	255	38	than	than	ADP
uva.x030312957	255	39	a	a	PRON
uva.x030312957	255	40	,	,	PUNCT
uva.x030312957	255	41	plus	plus	CCONJ
uva.x030312957	255	42	the	the	DET
uva.x030312957	255	43	number	number	NOUN
uva.x030312957	255	44	of	of	ADP
uva.x030312957	255	45	pairs	pair	NOUN
uva.x030312957	255	46	of	of	ADP
uva.x030312957	255	47	imaginary	imaginary	ADJ
uva.x030312957	255	48	roots	root	NOUN
uva.x030312957	255	49	of	of	ADP
uva.x030312957	255	50	this	this	DET
uva.x030312957	255	51	equation	equation	NOUN
uva.x030312957	255	52	.	.	PUNCT
uva.x030312957	256	1	to	to	PART
uva.x030312957	256	2	enable	enable	VERB
uva.x030312957	256	3	us	we	PRON
uva.x030312957	256	4	to	to	PART
uva.x030312957	256	5	find	find	VERB
uva.x030312957	256	6	this	this	DET
uva.x030312957	256	7	quantity	quantity	NOUN
uva.x030312957	256	8	na	na	ADP
uva.x030312957	256	9	,	,	PUNCT
uva.x030312957	256	10	we	we	PRON
uva.x030312957	256	11	shall	shall	AUX
uva.x030312957	256	12	study	study	VERB
uva.x030312957	256	13	with	with	ADP
uva.x030312957	256	14	the	the	DET
uva.x030312957	256	15	quadratic	quadratic	ADJ
uva.x030312957	256	16	form	form	NOUN
uva.x030312957	256	17	hą	hą	PROPN
uva.x030312957	256	18	,	,	PUNCT
uva.x030312957	256	19	another	another	DET
uva.x030312957	256	20	quadratic	quadratic	ADJ
uva.x030312957	256	21	form	form	NOUN
uva.x030312957	256	22	whose	whose	DET
uva.x030312957	256	23	determinant	determinant	NOUN
uva.x030312957	256	24	is	be	AUX
uva.x030312957	256	25	an	an	DET
uva.x030312957	256	26	(	(	PUNCT
uva.x030312957	256	27	a	a	NOUN
uva.x030312957	256	28	)	)	PUNCT
uva.x030312957	256	29	.	.	PUNCT
uva.x030312957	257	1	consider	consider	VERB
uva.x030312957	257	2	the	the	DET
uva.x030312957	257	3	quadratic	quadratic	ADJ
uva.x030312957	257	4	form	form	NOUN
uva.x030312957	257	5	(	(	PUNCT
uva.x030312957	257	6	33	33	NUM
uva.x030312957	257	7	)	)	PUNCT
uva.x030312957	257	8	$	$	SYM
uva.x030312957	257	9	(	(	PUNCT
uva.x030312957	257	10	ti	ti	PROPN
uva.x030312957	257	11	,	,	PUNCT
uva.x030312957	257	12	t2	t2	PROPN
uva.x030312957	257	13	,	,	PUNCT
uva.x030312957	257	14	...	...	PUNCT
uva.x030312957	257	15	,	,	PUNCT
uva.x030312957	257	16	tn	tn	PROPN
uva.x030312957	257	17	)	)	PUNCT
uva.x030312957	257	18	σ	σ	PROPN
uva.x030312957	257	19	αι	αι	PROPN
uva.x030312957	257	20	,	,	PUNCT
uva.x030312957	257	21	jt	jt	PROPN
uva.x030312957	257	22	,	,	PUNCT
uva.x030312957	257	23	t	t	PROPN
uva.x030312957	257	24	,	,	PUNCT
uva.x030312957	257	25	di	di	PROPN
uva.x030312957	257	26	,	,	PUNCT
uva.x030312957	257	27	i	i	PRON
uva.x030312957	257	28	=	=	X
uva.x030312957	257	29	aj	aj	INTJ
uva.x030312957	257	30	,	,	PUNCT
uva.x030312957	257	31	i	i	PRON
uva.x030312957	257	32	,	,	PUNCT
uva.x030312957	257	33	i=1	i=1	PROPN
uva.x030312957	257	34	,	,	PUNCT
uva.x030312957	257	35	2	2	NUM
uva.x030312957	257	36	,	,	PUNCT
uva.x030312957	257	37	...	...	PUNCT
uva.x030312957	257	38	,	,	PUNCT
uva.x030312957	257	39	no	no	DET
uva.x030312957	257	40	j=1	j=1	PROPN
uva.x030312957	257	41	,	,	PUNCT
uva.x030312957	257	42	2	2	NUM
uva.x030312957	257	43	,	,	PUNCT
uva.x030312957	257	44	...	...	PUNCT
uva.x030312957	257	45	,	,	PUNCT
uva.x030312957	257	46	91	91	NUM
uva.x030312957	257	47	15	15	NUM
uva.x030312957	257	48	16	16	NUM
uva.x030312957	257	49	solution	solution	NOUN
uva.x030312957	257	50	of	of	ADP
uva.x030312957	257	51	the	the	DET
uva.x030312957	257	52	equation	equation	NOUN
uva.x030312957	257	53	of	of	ADP
uva.x030312957	257	54	secular	secular	ADJ
uva.x030312957	257	55	variation	variation	NOUN
uva.x030312957	257	56	whose	whose	DET
uva.x030312957	257	57	determinant	determinant	NOUN
uva.x030312957	257	58	is	be	AUX
uva.x030312957	257	59	(	(	PUNCT
uva.x030312957	257	60	1	1	NUM
uva.x030312957	257	61	,	,	PUNCT
uva.x030312957	257	62	1	1	NUM
uva.x030312957	257	63	,	,	PUNCT
uva.x030312957	257	64	01	01	NUM
uva.x030312957	257	65	,	,	PUNCT
uva.x030312957	257	66	2	2	NUM
uva.x030312957	257	67	,	,	PUNCT
uva.x030312957	257	68	ai	ai	VERB
uva.x030312957	257	69	,	,	PUNCT
uva.x030312957	257	70	n	n	NOUN
uva.x030312957	257	71	(	(	PUNCT
uva.x030312957	257	72	2	2	NUM
uva.x030312957	257	73	,	,	PUNCT
uva.x030312957	257	74	1	1	NUM
uva.x030312957	257	75	,	,	PUNCT
uva.x030312957	257	76	a2	a2	PROPN
uva.x030312957	257	77	,	,	PUNCT
uva.x030312957	257	78	2	2	NUM
uva.x030312957	257	79	,	,	PUNCT
uva.x030312957	257	80	02	02	NUM
uva.x030312957	257	81	,	,	PUNCT
uva.x030312957	257	82	n	n	NOUN
uva.x030312957	257	83	(	(	PUNCT
uva.x030312957	257	84	34	34	NUM
uva.x030312957	257	85	)	)	PUNCT
uva.x030312957	257	86	an	an	DET
uva.x030312957	257	87	,	,	PUNCT
uva.x030312957	257	88	1	1	NUM
uva.x030312957	257	89	,	,	PUNCT
uva.x030312957	257	90	an	an	DET
uva.x030312957	257	91	,	,	PUNCT
uva.x030312957	257	92	2	2	NUM
uva.x030312957	257	93	,	,	PUNCT
uva.x030312957	257	94	an	an	PRON
uva.x030312957	257	95	,	,	PUNCT
uva.x030312957	257	96	in	in	ADP
uva.x030312957	257	97	>	>	X
uva.x030312957	257	98	with	with	ADP
uva.x030312957	257	99	this	this	DET
uva.x030312957	257	100	form	form	NOUN
uva.x030312957	257	101	y	y	PROPN
uva.x030312957	257	102	build	build	VERB
uva.x030312957	257	103	the	the	DET
uva.x030312957	257	104	quadratic	quadratic	ADJ
uva.x030312957	257	105	form	form	NOUN
uva.x030312957	257	106	,	,	PUNCT
uva.x030312957	258	1	(	(	PUNCT
uva.x030312957	258	2	35	35	NUM
uva.x030312957	258	3	)	)	PUNCT
uva.x030312957	258	4	ø	ø	PROPN
uva.x030312957	258	5	a(ti	a(ti	PROPN
uva.x030312957	258	6	+	+	SYM
uva.x030312957	258	7	t.	t.	PROPN
uva.x030312957	258	8	+	+	SYM
uva.x030312957	258	9	+	+	NUM
uva.x030312957	258	10	tä	tä	PROPN
uva.x030312957	258	11	)	)	PUNCT
uva.x030312957	258	12	,	,	PUNCT
uva.x030312957	258	13	the	the	DET
uva.x030312957	258	14	determinant	determinant	NOUN
uva.x030312957	258	15	for	for	ADP
uva.x030312957	258	16	which	which	PRON
uva.x030312957	258	17	is	be	AUX
uva.x030312957	258	18	di	di	PROPN
uva.x030312957	258	19	,	,	PUNCT
uva.x030312957	258	20	1	1	NUM
uva.x030312957	258	21	a	a	PRON
uva.x030312957	258	22	,	,	PUNCT
uva.x030312957	258	23	01	01	NUM
uva.x030312957	258	24	,	,	PUNCT
uva.x030312957	258	25	2	2	NUM
uva.x030312957	258	26	,	,	PUNCT
uva.x030312957	258	27	di	di	NOUN
uva.x030312957	258	28	,	,	PUNCT
uva.x030312957	258	29	n	n	NOUN
uva.x030312957	258	30	02	02	NUM
uva.x030312957	258	31	,	,	PUNCT
uva.x030312957	258	32	1	1	NUM
uva.x030312957	258	33	a2	a2	NUM
uva.x030312957	258	34	,	,	PUNCT
uva.x030312957	258	35	2	2	NUM
uva.x030312957	258	36	-α	-α	SPACE
uva.x030312957	258	37	,	,	PUNCT
uva.x030312957	258	38	d2	d2	PROPN
uva.x030312957	258	39	,	,	PUNCT
uva.x030312957	258	40	n	n	NOUN
uva.x030312957	258	41	(	(	PUNCT
uva.x030312957	258	42	36	36	NUM
uva.x030312957	258	43	)	)	PUNCT
uva.x030312957	258	44	an	an	DET
uva.x030312957	258	45	(	(	PUNCT
uva.x030312957	258	46	a	a	X
uva.x030312957	258	47	)	)	PUNCT
uva.x030312957	258	48	=	=	X
uva.x030312957	258	49	an	an	DET
uva.x030312957	258	50	,	,	PUNCT
uva.x030312957	258	51	1	1	NUM
uva.x030312957	258	52	,	,	PUNCT
uva.x030312957	258	53	an	an	DET
uva.x030312957	258	54	,	,	PUNCT
uva.x030312957	258	55	2	2	NUM
uva.x030312957	258	56	,	,	PUNCT
uva.x030312957	258	57	on	on	ADP
uva.x030312957	258	58	,	,	PUNCT
uva.x030312957	258	59	no	no	DET
uva.x030312957	258	60	a	a	PRON
uva.x030312957	258	61	the	the	DET
uva.x030312957	258	62	variations	variation	NOUN
uva.x030312957	258	63	in	in	ADP
uva.x030312957	258	64	sign	sign	NOUN
uva.x030312957	258	65	between	between	ADP
uva.x030312957	258	66	the	the	DET
uva.x030312957	258	67	terms	term	NOUN
uva.x030312957	258	68	in	in	ADP
uva.x030312957	258	69	the	the	DET
uva.x030312957	258	70	chain	chain	NOUN
uva.x030312957	258	71	(	(	PUNCT
uva.x030312957	258	72	37	37	NUM
uva.x030312957	258	73	)	)	PUNCT
uva.x030312957	258	74	1	1	NUM
uva.x030312957	258	75	,	,	PUNCT
uva.x030312957	258	76	δ	δ	PROPN
uva.x030312957	258	77	,	,	PUNCT
uva.x030312957	258	78	(	(	PUNCT
uva.x030312957	258	79	α	α	NOUN
uva.x030312957	258	80	)	)	PUNCT
uva.x030312957	258	81	,	,	PUNCT
uva.x030312957	258	82	δ	δ	PROPN
uva.x030312957	258	83	.	.	PROPN
uva.x030312957	258	84	(	(	PUNCT
uva.x030312957	258	85	α	α	PROPN
uva.x030312957	258	86	)	)	PUNCT
uva.x030312957	258	87	,	,	PUNCT
uva.x030312957	258	88	...	...	PUNCT
uva.x030312957	258	89	,	,	PUNCT
uva.x030312957	258	90	δ	δ	PROPN
uva.x030312957	258	91	.	.	PUNCT
uva.x030312957	258	92	(	(	PUNCT
uva.x030312957	258	93	α	α	NOUN
uva.x030312957	258	94	)	)	PUNCT
uva.x030312957	258	95	will	will	AUX
uva.x030312957	258	96	give	give	VERB
uva.x030312957	258	97	the	the	DET
uva.x030312957	258	98	number	number	NOUN
uva.x030312957	258	99	of	of	ADP
uva.x030312957	258	100	negative	negative	ADJ
uva.x030312957	258	101	terms	term	NOUN
uva.x030312957	258	102	of	of	ADP
uva.x030312957	258	103	''	''	PUNCT
uva.x030312957	258	104	,	,	PUNCT
uva.x030312957	258	105	when	when	SCONJ
uva.x030312957	258	106	expressed	express	VERB
uva.x030312957	258	107	as	as	ADP
uva.x030312957	258	108	the	the	DET
uva.x030312957	258	109	sum	sum	NOUN
uva.x030312957	258	110	of	of	ADP
uva.x030312957	258	111	squares	square	NOUN
uva.x030312957	258	112	of	of	ADP
uva.x030312957	258	113	linear	linear	ADJ
uva.x030312957	258	114	functions	function	NOUN
uva.x030312957	258	115	.	.	PUNCT
uva.x030312957	259	1	in	in	ADP
uva.x030312957	259	2	what	what	PRON
uva.x030312957	259	3	follows	follow	VERB
uva.x030312957	259	4	we	we	PRON
uva.x030312957	259	5	shall	shall	AUX
uva.x030312957	259	6	assume	assume	VERB
uva.x030312957	259	7	that	that	SCONJ
uva.x030312957	259	8	no	no	DET
uva.x030312957	259	9	two	two	NUM
uva.x030312957	259	10	consecutive	consecutive	ADJ
uva.x030312957	259	11	terms	term	NOUN
uva.x030312957	259	12	of	of	ADP
uva.x030312957	259	13	this	this	DET
uva.x030312957	259	14	chain	chain	NOUN
uva.x030312957	259	15	(	(	PUNCT
uva.x030312957	259	16	37	37	NUM
uva.x030312957	259	17	)	)	PUNCT
uva.x030312957	259	18	vanish	vanish	VERB
uva.x030312957	259	19	for	for	ADP
uva.x030312957	259	20	the	the	DET
uva.x030312957	259	21	same	same	ADJ
uva.x030312957	259	22	value	value	NOUN
uva.x030312957	259	23	of	of	ADP
uva.x030312957	259	24	x	x	SYM
uva.x030312957	259	25	,	,	PUNCT
uva.x030312957	259	26	and	and	CCONJ
uva.x030312957	259	27	shall	shall	AUX
uva.x030312957	259	28	later	later	ADV
uva.x030312957	259	29	show	show	VERB
uva.x030312957	259	30	we	we	PRON
uva.x030312957	259	31	are	be	AUX
uva.x030312957	259	32	justified	justify	VERB
uva.x030312957	259	33	in	in	ADP
uva.x030312957	259	34	making	make	VERB
uva.x030312957	259	35	this	this	DET
uva.x030312957	259	36	assumption	assumption	NOUN
uva.x030312957	259	37	.	.	PUNCT
uva.x030312957	260	1	the	the	DET
uva.x030312957	260	2	relation	relation	NOUN
uva.x030312957	260	3	(	(	PUNCT
uva.x030312957	260	4	38	38	NUM
uva.x030312957	260	5	)	)	PUNCT
uva.x030312957	260	6	below	below	ADV
uva.x030312957	260	7	will	will	AUX
uva.x030312957	260	8	help	help	VERB
uva.x030312957	260	9	us	we	PRON
uva.x030312957	260	10	in	in	ADP
uva.x030312957	260	11	determining	determine	VERB
uva.x030312957	260	12	the	the	DET
uva.x030312957	260	13	number	number	NOUN
uva.x030312957	260	14	of	of	ADP
uva.x030312957	260	15	negative	negative	ADJ
uva.x030312957	260	16	terms	term	NOUN
uva.x030312957	260	17	in	in	ADP
uva.x030312957	260	18	h	h	PROPN
uva.x030312957	260	19	,	,	PUNCT
uva.x030312957	260	20	from	from	ADP
uva.x030312957	260	21	those	those	PRON
uva.x030312957	260	22	of	of	ADP
uva.x030312957	260	23	the	the	DET
uva.x030312957	260	24	quadratic	quadratic	ADJ
uva.x030312957	260	25	form	form	NOUN
uva.x030312957	260	26	''	''	PUNCT
uva.x030312957	260	27	,	,	PUNCT
uva.x030312957	260	28	(	(	PUNCT
uva.x030312957	260	29	38	38	NUM
uva.x030312957	260	30	)	)	PUNCT
uva.x030312957	260	31	ax(a	ax(a	X
uva.x030312957	260	32	)	)	PUNCT
uva.x030312957	260	33	sx	sx	PROPN
uva.x030312957	260	34	–	–	PUNCT
uva.x030312957	260	35	t	t	PROPN
uva.x030312957	260	36	ax-1(a	ax-1(a	SPACE
uva.x030312957	260	37	)	)	PUNCT
uva.x030312957	260	38	ak+1(a	ak+1(a	PROPN
uva.x030312957	260	39	)	)	PUNCT
uva.x030312957	260	40	.	.	PUNCT
uva.x030312957	261	1	*	*	PUNCT
uva.x030312957	262	1	in	in	ADP
uva.x030312957	262	2	(	(	PUNCT
uva.x030312957	262	3	38	38	NUM
uva.x030312957	262	4	)	)	PUNCT
uva.x030312957	262	5	sk	sk	PROPN
uva.x030312957	262	6	and	and	CCONJ
uva.x030312957	262	7	tk	tk	PRON
uva.x030312957	262	8	are	be	AUX
uva.x030312957	262	9	rational	rational	ADJ
uva.x030312957	262	10	integral	integral	ADJ
uva.x030312957	262	11	functions	function	NOUN
uva.x030312957	262	12	of	of	ADP
uva.x030312957	262	13	x	x	PRON
uva.x030312957	262	14	,	,	PUNCT
uva.x030312957	262	15	and	and	CCONJ
uva.x030312957	262	16	ak(a	ak(a	NOUN
uva.x030312957	262	17	)	)	PUNCT
uva.x030312957	262	18	,	,	PUNCT
uva.x030312957	262	19	ak-1	ak-1	PUNCT
uva.x030312957	262	20	(	(	PUNCT
uva.x030312957	262	21	a	a	X
uva.x030312957	262	22	)	)	PUNCT
uva.x030312957	262	23	and	and	CCONJ
uva.x030312957	262	24	akti	akti	PROPN
uva.x030312957	262	25	(	(	PUNCT
uva.x030312957	262	26	a	a	X
uva.x030312957	262	27	)	)	PUNCT
uva.x030312957	262	28	have	have	VERB
uva.x030312957	262	29	the	the	DET
uva.x030312957	262	30	same	same	ADJ
uva.x030312957	262	31	meaning	meaning	NOUN
uva.x030312957	262	32	as	as	ADP
uva.x030312957	262	33	in	in	ADP
uva.x030312957	262	34	the	the	DET
uva.x030312957	262	35	chain	chain	NOUN
uva.x030312957	262	36	above	above	ADV
uva.x030312957	262	37	.	.	PUNCT
uva.x030312957	263	1	it	it	PRON
uva.x030312957	263	2	is	be	AUX
uva.x030312957	263	3	evident	evident	ADJ
uva.x030312957	263	4	from	from	ADP
uva.x030312957	263	5	(	(	PUNCT
uva.x030312957	263	6	38	38	NUM
uva.x030312957	263	7	)	)	PUNCT
uva.x030312957	263	8	that	that	SCONJ
uva.x030312957	263	9	if	if	SCONJ
uva.x030312957	263	10	ax	ax	ADJ
uva.x030312957	263	11	(	(	PUNCT
uva.x030312957	263	12	a	a	X
uva.x030312957	263	13	)	)	PUNCT
uva.x030312957	263	14	=	=	PROPN
uva.x030312957	263	15	0	0	NUM
uva.x030312957	263	16	,	,	PUNCT
uva.x030312957	263	17	ak-1(a	ak-1(a	NUM
uva.x030312957	263	18	)	)	PUNCT
uva.x030312957	263	19	and	and	CCONJ
uva.x030312957	263	20	akti(a	akti(a	PROPN
uva.x030312957	263	21	)	)	PUNCT
uva.x030312957	263	22	will	will	AUX
uva.x030312957	263	23	have	have	VERB
uva.x030312957	263	24	opposite	opposite	ADJ
uva.x030312957	263	25	signs	sign	NOUN
uva.x030312957	263	26	.	.	PUNCT
uva.x030312957	264	1	=	=	PROPN
uva.x030312957	264	2	§	§	PROPN
uva.x030312957	264	3	2	2	NUM
uva.x030312957	264	4	.	.	PUNCT
uva.x030312957	265	1	relation	relation	NOUN
uva.x030312957	265	2	between	between	ADP
uva.x030312957	265	3	the	the	DET
uva.x030312957	265	4	negative	negative	ADJ
uva.x030312957	265	5	squares	square	NOUN
uva.x030312957	265	6	of	of	ADP
uva.x030312957	265	7	h	h	NOUN
uva.x030312957	265	8	,	,	PUNCT
uva.x030312957	265	9	and	and	CCONJ
uva.x030312957	265	10	o	o	VERB
uva.x030312957	265	11	'	'	PUNCT
uva.x030312957	265	12	.	.	PUNCT
uva.x030312957	266	1	now	now	ADV
uva.x030312957	266	2	let	let	VERB
uva.x030312957	266	3	x	x	PUNCT
uva.x030312957	266	4	pass	pass	VERB
uva.x030312957	266	5	through	through	ADP
uva.x030312957	266	6	a	a	DET
uva.x030312957	266	7	real	real	ADJ
uva.x030312957	266	8	root	root	NOUN
uva.x030312957	266	9	of	of	ADP
uva.x030312957	266	10	an	an	PRON
uva.x030312957	266	11	(	(	PUNCT
uva.x030312957	266	12	x	x	NOUN
uva.x030312957	266	13	)	)	PUNCT
uva.x030312957	266	14	=	=	SYM
uva.x030312957	266	15	0	0	NUM
uva.x030312957	266	16	,	,	PUNCT
uva.x030312957	266	17	say	say	VERB
uva.x030312957	266	18	xr	xr	PROPN
uva.x030312957	266	19	.	.	PROPN
uva.x030312957	267	1	then	then	ADV
uva.x030312957	267	2	take	take	VERB
uva.x030312957	267	3	a	a	DET
uva.x030312957	267	4	small	small	ADJ
uva.x030312957	267	5	quantity	quantity	NOUN
uva.x030312957	267	6	,	,	PUNCT
uva.x030312957	267	7	h	h	NOUN
uva.x030312957	267	8	,	,	PUNCT
uva.x030312957	267	9	so	so	ADV
uva.x030312957	267	10	small	small	ADJ
uva.x030312957	267	11	that	that	SCONJ
uva.x030312957	267	12	no	no	DET
uva.x030312957	267	13	root	root	NOUN
uva.x030312957	267	14	of	of	ADP
uva.x030312957	267	15	an	an	PRON
uva.x030312957	267	16	(	(	PUNCT
uva.x030312957	267	17	x	x	NOUN
uva.x030312957	267	18	)	)	PUNCT
uva.x030312957	267	19	=	=	SYM
uva.x030312957	267	20	0	0	NUM
uva.x030312957	267	21	,	,	PUNCT
uva.x030312957	267	22	excepting	except	VERB
uva.x030312957	267	23	xr	xr	PROPN
uva.x030312957	267	24	,	,	PUNCT
uva.x030312957	267	25	lies	lie	VERB
uva.x030312957	267	26	in	in	ADP
uva.x030312957	267	27	the	the	DET
uva.x030312957	267	28	interval	interval	NOUN
uva.x030312957	267	29	xr	xr	PROPN
uva.x030312957	267	30	h	h	NOUN
uva.x030312957	267	31	to	to	ADP
uva.x030312957	267	32	xr	xr	PROPN
uva.x030312957	268	1	+	+	PROPN
uva.x030312957	268	2	h	h	NOUN
uva.x030312957	268	3	,	,	PUNCT
uva.x030312957	268	4	and	and	CCONJ
uva.x030312957	268	5	let	let	VERB
uva.x030312957	268	6	xr	xr	PROPN
uva.x030312957	269	1	–	–	PUNCT
uva.x030312957	269	2	h	h	PROPN
uva.x030312957	269	3	=	=	X
uva.x030312957	269	4	y	y	PROPN
uva.x030312957	269	5	and	and	CCONJ
uva.x030312957	269	6	x	x	PROPN
uva.x030312957	269	7	,	,	PUNCT
uva.x030312957	269	8	+	+	NUM
uva.x030312957	269	9	h	h	NOUN
uva.x030312957	269	10	=	=	SYM
uva.x030312957	269	11	8	8	NUM
uva.x030312957	269	12	.	.	PUNCT
uva.x030312957	270	1	since	since	SCONJ
uva.x030312957	270	2	x	x	PUNCT
uva.x030312957	270	3	passes	pass	VERB
uva.x030312957	270	4	through	through	ADP
uva.x030312957	270	5	a	a	DET
uva.x030312957	270	6	root	root	NOUN
uva.x030312957	270	7	of	of	ADP
uva.x030312957	270	8	an	an	PRON
uva.x030312957	270	9	(	(	PUNCT
uva.x030312957	270	10	x	x	NOUN
uva.x030312957	270	11	)	)	PUNCT
uva.x030312957	270	12	=	=	PUNCT
uva.x030312957	270	13	0	0	PUNCT
uva.x030312957	270	14	in	in	ADP
uva.x030312957	270	15	going	go	VERB
uva.x030312957	270	16	from	from	ADP
uva.x030312957	270	17	y	y	PROPN
uva.x030312957	270	18	to	to	PROPN
uva.x030312957	270	19	&	&	CCONJ
uva.x030312957	270	20	there	there	PRON
uva.x030312957	270	21	will	will	AUX
uva.x030312957	270	22	be	be	AUX
uva.x030312957	270	23	one	one	NUM
uva.x030312957	270	24	more	more	ADV
uva.x030312957	270	25	negative	negative	ADJ
uva.x030312957	270	26	square	square	NOUN
uva.x030312957	270	27	in	in	ADP
uva.x030312957	270	28	iis	iis	PROPN
uva.x030312957	270	29	than	than	ADP
uva.x030312957	270	30	in	in	ADP
uva.x030312957	270	31	h	h	PROPN
uva.x030312957	270	32	,	,	PUNCT
uva.x030312957	270	33	.	.	PUNCT
uva.x030312957	271	1	hg	hg	PRON
uva.x030312957	271	2	and	and	CCONJ
uva.x030312957	271	3	h	h	PROPN
uva.x030312957	271	4	,	,	PUNCT
uva.x030312957	271	5	are	be	AUX
uva.x030312957	271	6	used	use	VERB
uva.x030312957	271	7	here	here	ADV
uva.x030312957	271	8	,	,	PUNCT
uva.x030312957	271	9	as	as	SCONJ
uva.x030312957	271	10	other	other	ADJ
uva.x030312957	271	11	subscripts	subscript	NOUN
uva.x030312957	271	12	will	will	AUX
uva.x030312957	271	13	be	be	AUX
uva.x030312957	271	14	used	use	VERB
uva.x030312957	271	15	,	,	PUNCT
uva.x030312957	271	16	to	to	PART
uva.x030312957	271	17	denote	denote	VERB
uva.x030312957	271	18	the	the	DET
uva.x030312957	271	19	value	value	NOUN
uva.x030312957	271	20	of	of	ADP
uva.x030312957	271	21	h	h	NOUN
uva.x030312957	271	22	,	,	PUNCT
uva.x030312957	271	23	in	in	ADP
uva.x030312957	271	24	(	(	PUNCT
uva.x030312957	271	25	5	5	NUM
uva.x030312957	271	26	)	)	PUNCT
uva.x030312957	271	27	when	when	SCONJ
uva.x030312957	271	28	a	a	PRON
uva.x030312957	271	29	is	be	AUX
uva.x030312957	271	30	made	make	VERB
uva.x030312957	271	31	equal	equal	ADJ
uva.x030312957	271	32	to	to	ADP
uva.x030312957	271	33	ô	ô	PROPN
uva.x030312957	271	34	and	and	CCONJ
uva.x030312957	271	35	y	y	PROPN
uva.x030312957	271	36	respectively	respectively	ADV
uva.x030312957	271	37	.	.	PUNCT
uva.x030312957	272	1	correspondingly	correspondingly	ADV
uva.x030312957	272	2	if	if	SCONJ
uva.x030312957	272	3	,	,	PUNCT
uva.x030312957	272	4	in	in	ADP
uva.x030312957	272	5	the	the	DET
uva.x030312957	272	6	chain	chain	NOUN
uva.x030312957	272	7	of	of	ADP
uva.x030312957	272	8	functions	function	NOUN
uva.x030312957	272	9	(	(	PUNCT
uva.x030312957	272	10	37	37	NUM
uva.x030312957	272	11	)	)	PUNCT
uva.x030312957	272	12	,	,	PUNCT
uva.x030312957	272	13	we	we	PRON
uva.x030312957	272	14	let	let	VERB
uva.x030312957	272	15	x	x	PUNCT
uva.x030312957	272	16	pass	pass	VERB
uva.x030312957	272	17	through	through	ADP
uva.x030312957	272	18	the	the	DET
uva.x030312957	272	19	root	root	NOUN
uva.x030312957	272	20	xr	xr	PROPN
uva.x030312957	272	21	,	,	PUNCT
uva.x030312957	272	22	there	there	PRON
uva.x030312957	272	23	will	will	AUX
uva.x030312957	272	24	be	be	AUX
uva.x030312957	272	25	one	one	NUM
uva.x030312957	272	26	more	more	ADJ
uva.x030312957	272	27	variation	variation	NOUN
uva.x030312957	272	28	in	in	ADP
uva.x030312957	272	29	sign	sign	NOUN
uva.x030312957	272	30	between	between	ADP
uva.x030312957	272	31	the	the	DET
uva.x030312957	272	32	functions	function	NOUN
uva.x030312957	272	33	of	of	ADP
uva.x030312957	272	34	the	the	DET
uva.x030312957	272	35	chain	chain	NOUN
uva.x030312957	272	36	for	for	ADP
uva.x030312957	272	37	x	x	PUNCT
uva.x030312957	272	38	slightly	slightly	ADV
uva.x030312957	272	39	larger	large	ADJ
uva.x030312957	272	40	than	than	ADP
uva.x030312957	272	41	xr	xr	PROPN
uva.x030312957	272	42	,	,	PUNCT
uva.x030312957	272	43	than	than	SCONJ
uva.x030312957	272	44	there	there	PRON
uva.x030312957	272	45	is	be	VERB
uva.x030312957	272	46	in	in	ADP
uva.x030312957	272	47	the	the	DET
uva.x030312957	272	48	chain	chain	NOUN
uva.x030312957	272	49	for	for	ADP
uva.x030312957	272	50	x	x	PUNCT
uva.x030312957	272	51	slightly	slightly	ADV
uva.x030312957	272	52	*	*	PUNCT
uva.x030312957	272	53	see	see	VERB
uva.x030312957	272	54	$	$	SYM
uva.x030312957	272	55	88	88	NUM
uva.x030312957	272	56	,	,	PUNCT
uva.x030312957	272	57	page	page	NOUN
uva.x030312957	272	58	291	291	NUM
uva.x030312957	272	59	,	,	PUNCT
uva.x030312957	272	60	weber	weber	PROPN
uva.x030312957	272	61	,	,	PUNCT
uva.x030312957	272	62	vol	vol	NOUN
uva.x030312957	272	63	.	.	PUNCT
uva.x030312957	273	1	i.	i.	PROPN
uva.x030312957	273	2	by	by	ADP
uva.x030312957	273	3	a	a	DET
uva.x030312957	273	4	method	method	NOUN
uva.x030312957	273	5	due	due	ADP
uva.x030312957	273	6	to	to	ADP
uva.x030312957	273	7	hermite	hermite	NOUN
uva.x030312957	273	8	17	17	NUM
uva.x030312957	273	9	less	less	ADJ
uva.x030312957	273	10	than	than	ADP
uva.x030312957	273	11	xr	xr	PROPN
uva.x030312957	273	12	.	.	PROPN
uva.x030312957	274	1	that	that	PRON
uva.x030312957	274	2	is	be	AUX
uva.x030312957	274	3	in	in	ADP
uva.x030312957	274	4	1	1	NUM
uva.x030312957	274	5	,	,	PUNCT
uva.x030312957	274	6	41(8	41(8	NUM
uva.x030312957	274	7	)	)	PUNCT
uva.x030312957	274	8	,	,	PUNCT
uva.x030312957	274	9	a2	a2	X
uva.x030312957	274	10	(	(	PUNCT
uva.x030312957	274	11	8)	8)	NUM
uva.x030312957	274	12	,	,	PUNCT
uva.x030312957	274	13	...	...	PUNCT
uva.x030312957	274	14	,	,	PUNCT
uva.x030312957	274	15	an	an	DET
uva.x030312957	274	16	(	(	PUNCT
uva.x030312957	274	17	8)	8)	NUM
uva.x030312957	274	18	there	there	PRON
uva.x030312957	274	19	is	be	VERB
uva.x030312957	274	20	one	one	NUM
uva.x030312957	274	21	more	more	ADJ
uva.x030312957	274	22	variation	variation	NOUN
uva.x030312957	274	23	in	in	ADP
uva.x030312957	274	24	sign	sign	NOUN
uva.x030312957	274	25	than	than	SCONJ
uva.x030312957	274	26	there	there	PRON
uva.x030312957	274	27	in	in	ADP
uva.x030312957	274	28	is	be	AUX
uva.x030312957	274	29	the	the	DET
uva.x030312957	274	30	chain	chain	NOUN
uva.x030312957	274	31	1	1	NUM
uva.x030312957	274	32	,	,	PUNCT
uva.x030312957	274	33	41(y	41(y	NUM
uva.x030312957	274	34	)	)	PUNCT
uva.x030312957	274	35	,	,	PUNCT
uva.x030312957	274	36	12(7	12(7	NUM
uva.x030312957	274	37	)	)	PUNCT
uva.x030312957	274	38	,	,	PUNCT
uva.x030312957	274	39	...	...	PUNCT
uva.x030312957	274	40	,	,	PUNCT
uva.x030312957	274	41	an(7	an(7	PROPN
uva.x030312957	274	42	)	)	PUNCT
uva.x030312957	274	43	.	.	PUNCT
uva.x030312957	275	1	the	the	DET
uva.x030312957	275	2	fact	fact	NOUN
uva.x030312957	275	3	just	just	ADV
uva.x030312957	275	4	stated	state	VERB
uva.x030312957	275	5	is	be	AUX
uva.x030312957	275	6	true	true	ADJ
uva.x030312957	275	7	because	because	SCONJ
uva.x030312957	275	8	as	as	SCONJ
uva.x030312957	275	9	x	x	SYM
uva.x030312957	275	10	passes	pass	VERB
uva.x030312957	275	11	through	through	ADP
uva.x030312957	275	12	xr	xr	PROPN
uva.x030312957	275	13	an	an	PRON
uva.x030312957	275	14	(	(	PUNCT
uva.x030312957	275	15	x	x	SYM
uva.x030312957	275	16	)	)	PUNCT
uva.x030312957	275	17	changes	change	VERB
uva.x030312957	275	18	sign	sign	NOUN
uva.x030312957	275	19	,	,	PUNCT
uva.x030312957	275	20	while	while	SCONJ
uva.x030312957	275	21	an-1(a	an-1(a	SPACE
uva.x030312957	275	22	)	)	PUNCT
uva.x030312957	275	23	does	do	VERB
uva.x030312957	275	24	not	not	PART
uva.x030312957	275	25	,	,	PUNCT
uva.x030312957	275	26	and	and	CCONJ
uva.x030312957	275	27	there	there	PRON
uva.x030312957	275	28	will	will	AUX
uva.x030312957	275	29	be	be	AUX
uva.x030312957	275	30	a	a	DET
uva.x030312957	275	31	variation	variation	NOUN
uva.x030312957	275	32	introduced	introduce	VERB
uva.x030312957	275	33	between	between	ADP
uva.x030312957	275	34	these	these	DET
uva.x030312957	275	35	two	two	NUM
uva.x030312957	275	36	terms	term	NOUN
uva.x030312957	275	37	in	in	ADP
uva.x030312957	275	38	our	our	PRON
uva.x030312957	275	39	chain	chain	NOUN
uva.x030312957	275	40	.	.	PUNCT
uva.x030312957	276	1	at	at	ADP
uva.x030312957	276	2	the	the	DET
uva.x030312957	276	3	same	same	ADJ
uva.x030312957	276	4	time	time	NOUN
uva.x030312957	276	5	there	there	PRON
uva.x030312957	276	6	will	will	AUX
uva.x030312957	276	7	be	be	AUX
uva.x030312957	276	8	no	no	DET
uva.x030312957	276	9	other	other	ADJ
uva.x030312957	276	10	variation	variation	NOUN
uva.x030312957	276	11	introduced	introduce	VERB
uva.x030312957	276	12	in	in	ADP
uva.x030312957	276	13	the	the	DET
uva.x030312957	276	14	chain	chain	NOUN
uva.x030312957	276	15	of	of	ADP
uva.x030312957	276	16	functions	function	NOUN
uva.x030312957	276	17	.	.	PUNCT
uva.x030312957	277	1	if	if	SCONJ
uva.x030312957	277	2	there	there	PRON
uva.x030312957	277	3	could	could	AUX
uva.x030312957	277	4	be	be	AUX
uva.x030312957	277	5	another	another	DET
uva.x030312957	277	6	variation	variation	NOUN
uva.x030312957	277	7	introduced	introduce	VERB
uva.x030312957	277	8	one	one	NUM
uva.x030312957	277	9	of	of	ADP
uva.x030312957	277	10	the	the	DET
uva.x030312957	277	11	terms	term	NOUN
uva.x030312957	277	12	,	,	PUNCT
uva.x030312957	277	13	say	say	VERB
uva.x030312957	277	14	ap(x	ap(x	PROPN
uva.x030312957	277	15	)	)	PUNCT
uva.x030312957	277	16	,	,	PUNCT
uva.x030312957	277	17	would	would	AUX
uva.x030312957	277	18	have	have	VERB
uva.x030312957	277	19	to	to	PART
uva.x030312957	277	20	change	change	VERB
uva.x030312957	277	21	sign	sign	NOUN
uva.x030312957	277	22	,	,	PUNCT
uva.x030312957	277	23	and	and	CCONJ
uva.x030312957	277	24	hence	hence	ADV
uva.x030312957	277	25	would	would	AUX
uva.x030312957	277	26	have	have	VERB
uva.x030312957	277	27	to	to	PART
uva.x030312957	277	28	pass	pass	VERB
uva.x030312957	277	29	through	through	ADP
uva.x030312957	277	30	zero	zero	NUM
uva.x030312957	277	31	.	.	PUNCT
uva.x030312957	278	1	but	but	CCONJ
uva.x030312957	278	2	as	as	ADP
uva.x030312957	278	3	ap(x	ap(x	SPACE
uva.x030312957	278	4	)	)	PUNCT
uva.x030312957	278	5	passes	pass	VERB
uva.x030312957	278	6	through	through	ADP
uva.x030312957	278	7	zero	zero	NUM
uva.x030312957	278	8	no	no	DET
uva.x030312957	278	9	variation	variation	NOUN
uva.x030312957	278	10	in	in	ADP
uva.x030312957	278	11	sign	sign	NOUN
uva.x030312957	278	12	is	be	AUX
uva.x030312957	278	13	introduced	introduce	VERB
uva.x030312957	278	14	since	since	SCONJ
uva.x030312957	278	15	by	by	ADP
uva.x030312957	278	16	(	(	PUNCT
uva.x030312957	278	17	38	38	NUM
uva.x030312957	278	18	)	)	PUNCT
uva.x030312957	279	1	when	when	SCONJ
uva.x030312957	279	2	ap(x	ap(x	SPACE
uva.x030312957	279	3	)	)	PUNCT
uva.x030312957	279	4	=	=	PROPN
uva.x030312957	279	5	0	0	NUM
uva.x030312957	279	6	,	,	PUNCT
uva.x030312957	279	7	ap-1	ap-1	PUNCT
uva.x030312957	279	8	(	(	PUNCT
uva.x030312957	279	9	x	x	NOUN
uva.x030312957	279	10	)	)	PUNCT
uva.x030312957	279	11	and	and	CCONJ
uva.x030312957	279	12	ap+1	ap+1	VERB
uva.x030312957	279	13	(	(	PUNCT
uva.x030312957	279	14	x	x	SYM
uva.x030312957	279	15	)	)	PUNCT
uva.x030312957	279	16	have	have	VERB
uva.x030312957	279	17	opposite	opposite	ADJ
uva.x030312957	279	18	signs	sign	NOUN
uva.x030312957	279	19	.	.	PUNCT
uva.x030312957	280	1	ap	ap	PROPN
uva.x030312957	280	2	(	(	PUNCT
uva.x030312957	280	3	a	a	X
uva.x030312957	280	4	)	)	PUNCT
uva.x030312957	280	5	will	will	AUX
uva.x030312957	280	6	then	then	ADV
uva.x030312957	280	7	have	have	VERB
uva.x030312957	280	8	the	the	DET
uva.x030312957	280	9	same	same	ADJ
uva.x030312957	280	10	sign	sign	NOUN
uva.x030312957	280	11	as	as	ADP
uva.x030312957	280	12	one	one	NUM
uva.x030312957	280	13	of	of	ADP
uva.x030312957	280	14	them	they	PRON
uva.x030312957	280	15	,	,	PUNCT
uva.x030312957	280	16	say	say	VERB
uva.x030312957	280	17	ap-1	ap-1	PUNCT
uva.x030312957	280	18	(	(	PUNCT
uva.x030312957	280	19	a	a	X
uva.x030312957	280	20	)	)	PUNCT
uva.x030312957	280	21	and	and	CCONJ
uva.x030312957	280	22	the	the	DET
uva.x030312957	280	23	opposite	opposite	ADJ
uva.x030312957	280	24	sign	sign	NOUN
uva.x030312957	280	25	from	from	ADP
uva.x030312957	280	26	the	the	DET
uva.x030312957	280	27	other	other	ADJ
uva.x030312957	280	28	one	one	NUM
uva.x030312957	280	29	ap+1	ap+1	NOUN
uva.x030312957	280	30	(	(	PUNCT
uva.x030312957	280	31	a	a	NOUN
uva.x030312957	280	32	)	)	PUNCT
uva.x030312957	280	33	,	,	PUNCT
uva.x030312957	280	34	before	before	ADP
uva.x030312957	280	35	passing	pass	VERB
uva.x030312957	280	36	through	through	ADP
uva.x030312957	280	37	xr	xr	PROPN
uva.x030312957	280	38	,	,	PUNCT
uva.x030312957	280	39	while	while	SCONJ
uva.x030312957	280	40	after	after	ADP
uva.x030312957	280	41	passing	pass	VERB
uva.x030312957	280	42	through	through	ADP
uva.x030312957	280	43	xr	xr	PROPN
uva.x030312957	280	44	,	,	PUNCT
uva.x030312957	280	45	an	an	PRON
uva.x030312957	280	46	(	(	PUNCT
uva.x030312957	280	47	x	x	NOUN
uva.x030312957	280	48	)	)	PUNCT
uva.x030312957	280	49	will	will	AUX
uva.x030312957	280	50	have	have	VERB
uva.x030312957	280	51	opposite	opposite	ADJ
uva.x030312957	280	52	sign	sign	NOUN
uva.x030312957	280	53	to	to	ADP
uva.x030312957	280	54	ap-1	ap-1	PUNCT
uva.x030312957	280	55	(	(	PUNCT
uva.x030312957	280	56	x	x	PROPN
uva.x030312957	280	57	)	)	PUNCT
uva.x030312957	280	58	,	,	PUNCT
uva.x030312957	280	59	and	and	CCONJ
uva.x030312957	280	60	same	same	ADJ
uva.x030312957	280	61	sign	sign	NOUN
uva.x030312957	280	62	as	as	SCONJ
uva.x030312957	280	63	ap+1	ap+1	ADV
uva.x030312957	280	64	(	(	PUNCT
uva.x030312957	280	65	x	x	NOUN
uva.x030312957	280	66	)	)	PUNCT
uva.x030312957	280	67	and	and	CCONJ
uva.x030312957	280	68	will	will	AUX
uva.x030312957	280	69	,	,	PUNCT
uva.x030312957	280	70	therefore	therefore	ADV
uva.x030312957	280	71	,	,	PUNCT
uva.x030312957	280	72	keep	keep	VERB
uva.x030312957	280	73	the	the	DET
uva.x030312957	280	74	number	number	NOUN
uva.x030312957	280	75	of	of	ADP
uva.x030312957	280	76	variations	variation	NOUN
uva.x030312957	280	77	between	between	ADP
uva.x030312957	280	78	the	the	DET
uva.x030312957	280	79	three	three	NUM
uva.x030312957	280	80	consecutive	consecutive	ADJ
uva.x030312957	280	81	functions	function	NOUN
uva.x030312957	280	82	the	the	DET
uva.x030312957	280	83	same	same	ADJ
uva.x030312957	280	84	.	.	PUNCT
uva.x030312957	281	1	this	this	DET
uva.x030312957	281	2	discussion	discussion	NOUN
uva.x030312957	281	3	also	also	ADV
uva.x030312957	281	4	shows	show	VERB
uva.x030312957	281	5	there	there	PRON
uva.x030312957	281	6	will	will	AUX
uva.x030312957	281	7	be	be	AUX
uva.x030312957	281	8	no	no	DET
uva.x030312957	281	9	variation	variation	NOUN
uva.x030312957	281	10	lost	lose	VERB
uva.x030312957	281	11	in	in	ADP
uva.x030312957	281	12	this	this	DET
uva.x030312957	281	13	interval	interval	NOUN
uva.x030312957	281	14	.	.	PUNCT
uva.x030312957	282	1	there	there	PRON
uva.x030312957	282	2	will	will	AUX
uva.x030312957	282	3	,	,	PUNCT
uva.x030312957	282	4	therefore	therefore	ADV
uva.x030312957	282	5	,	,	PUNCT
uva.x030312957	282	6	be	be	AUX
uva.x030312957	282	7	no	no	DET
uva.x030312957	282	8	variation	variation	NOUN
uva.x030312957	282	9	in	in	ADP
uva.x030312957	282	10	sign	sign	NOUN
uva.x030312957	282	11	introduced	introduce	VERB
uva.x030312957	282	12	or	or	CCONJ
uva.x030312957	282	13	lost	lose	VERB
uva.x030312957	282	14	in	in	ADP
uva.x030312957	282	15	the	the	DET
uva.x030312957	282	16	chain	chain	NOUN
uva.x030312957	282	17	of	of	ADP
uva.x030312957	282	18	functions	function	NOUN
uva.x030312957	282	19	as	as	SCONJ
uva.x030312957	282	20	x	x	PUNCT
uva.x030312957	282	21	passes	pass	VERB
uva.x030312957	282	22	through	through	ADP
uva.x030312957	282	23	the	the	DET
uva.x030312957	282	24	root	root	NOUN
uva.x030312957	282	25	,	,	PUNCT
uva.x030312957	282	26	excepting	except	VERB
uva.x030312957	282	27	one	one	NUM
uva.x030312957	282	28	variation	variation	NOUN
uva.x030312957	282	29	introduced	introduce	VERB
uva.x030312957	282	30	between	between	ADP
uva.x030312957	282	31	an-1(x	an-1(x	SPACE
uva.x030312957	282	32	)	)	PUNCT
uva.x030312957	282	33	and	and	CCONJ
uva.x030312957	282	34	an	an	DET
uva.x030312957	282	35	(	(	PUNCT
uva.x030312957	282	36	x	x	SYM
uva.x030312957	282	37	)	)	PUNCT
uva.x030312957	282	38	.	.	PUNCT
uva.x030312957	283	1	and	and	CCONJ
uva.x030312957	283	2	similarly	similarly	ADV
uva.x030312957	283	3	as	as	SCONJ
uva.x030312957	283	4	x	x	PUNCT
uva.x030312957	283	5	passes	pass	VERB
uva.x030312957	283	6	through	through	ADP
uva.x030312957	283	7	each	each	PRON
uva.x030312957	283	8	of	of	ADP
uva.x030312957	283	9	the	the	DET
uva.x030312957	283	10	roots	root	NOUN
uva.x030312957	283	11	of	of	ADP
uva.x030312957	283	12	an	an	PRON
uva.x030312957	283	13	(	(	PUNCT
uva.x030312957	283	14	x	x	NOUN
uva.x030312957	283	15	)	)	PUNCT
uva.x030312957	283	16	=	=	SYM
uva.x030312957	283	17	0	0	NUM
uva.x030312957	283	18	,	,	PUNCT
uva.x030312957	283	19	there	there	PRON
uva.x030312957	283	20	will	will	AUX
uva.x030312957	283	21	be	be	AUX
uva.x030312957	283	22	one	one	NUM
uva.x030312957	283	23	variation	variation	NOUN
uva.x030312957	283	24	in	in	ADP
uva.x030312957	283	25	sign	sign	NOUN
uva.x030312957	283	26	introduced	introduce	VERB
uva.x030312957	283	27	between	between	ADP
uva.x030312957	283	28	the	the	DET
uva.x030312957	283	29	functions	function	NOUN
uva.x030312957	283	30	of	of	ADP
uva.x030312957	283	31	the	the	DET
uva.x030312957	283	32	chain	chain	NOUN
uva.x030312957	283	33	(	(	PUNCT
uva.x030312957	283	34	37	37	NUM
uva.x030312957	283	35	)	)	PUNCT
uva.x030312957	283	36	.	.	PUNCT
uva.x030312957	284	1	since	since	SCONJ
uva.x030312957	284	2	,	,	PUNCT
uva.x030312957	284	3	at	at	ADP
uva.x030312957	284	4	the	the	DET
uva.x030312957	284	5	same	same	ADJ
uva.x030312957	284	6	time	time	NOUN
uva.x030312957	284	7	,	,	PUNCT
uva.x030312957	284	8	as	as	SCONJ
uva.x030312957	284	9	x	x	SYM
uva.x030312957	284	10	increases	increase	VERB
uva.x030312957	284	11	through	through	ADP
uva.x030312957	284	12	each	each	PRON
uva.x030312957	284	13	of	of	ADP
uva.x030312957	284	14	the	the	DET
uva.x030312957	284	15	roots	root	NOUN
uva.x030312957	284	16	of	of	ADP
uva.x030312957	284	17	an	an	PRON
uva.x030312957	284	18	(	(	PUNCT
uva.x030312957	284	19	x	x	SYM
uva.x030312957	284	20	)	)	PUNCT
uva.x030312957	284	21	=	=	PUNCT
uva.x030312957	284	22	0	0	NUM
uva.x030312957	284	23	,	,	PUNCT
uva.x030312957	284	24	there	there	PRON
uva.x030312957	284	25	is	be	VERB
uva.x030312957	284	26	one	one	NUM
uva.x030312957	284	27	negative	negative	ADJ
uva.x030312957	284	28	square	square	NOUN
uva.x030312957	284	29	introduced	introduce	VERB
uva.x030312957	284	30	in	in	ADP
uva.x030312957	284	31	hą	hą	PROPN
uva.x030312957	284	32	,	,	PUNCT
uva.x030312957	284	33	the	the	DET
uva.x030312957	284	34	number	number	NOUN
uva.x030312957	284	35	of	of	ADP
uva.x030312957	284	36	negative	negative	ADJ
uva.x030312957	284	37	squares	square	NOUN
uva.x030312957	284	38	introduced	introduce	VERB
uva.x030312957	284	39	in	in	ADP
uva.x030312957	284	40	h	h	PROPN
uva.x030312957	284	41	,	,	PUNCT
uva.x030312957	284	42	as	as	ADP
uva.x030312957	284	43	a	a	DET
uva.x030312957	284	44	passes	pass	NOUN
uva.x030312957	284	45	from	from	ADP
uva.x030312957	284	46	a	a	DET
uva.x030312957	284	47	to	to	ADP
uva.x030312957	284	48	ß	ß	PROPN
uva.x030312957	284	49	will	will	AUX
uva.x030312957	284	50	be	be	AUX
uva.x030312957	284	51	the	the	DET
uva.x030312957	284	52	same	same	ADJ
uva.x030312957	284	53	as	as	ADP
uva.x030312957	284	54	the	the	DET
uva.x030312957	284	55	number	number	NOUN
uva.x030312957	284	56	of	of	ADP
uva.x030312957	284	57	variations	variation	NOUN
uva.x030312957	284	58	in	in	ADP
uva.x030312957	284	59	sign	sign	NOUN
uva.x030312957	284	60	introduced	introduce	VERB
uva.x030312957	284	61	in	in	ADP
uva.x030312957	284	62	the	the	DET
uva.x030312957	284	63	chain	chain	NOUN
uva.x030312957	284	64	(	(	PUNCT
uva.x030312957	284	65	37	37	NUM
uva.x030312957	284	66	)	)	PUNCT
uva.x030312957	284	67	as	as	ADP
uva.x030312957	284	68	x	x	SYM
uva.x030312957	284	69	passes	pass	VERB
uva.x030312957	284	70	from	from	ADP
uva.x030312957	284	71	a	a	PRON
uva.x030312957	284	72	to	to	ADP
uva.x030312957	284	73	ß	ß	PROPN
uva.x030312957	284	74	.	.	PUNCT
uva.x030312957	284	75	consequently	consequently	ADV
uva.x030312957	284	76	to	to	PART
uva.x030312957	284	77	count	count	VERB
uva.x030312957	284	78	the	the	DET
uva.x030312957	284	79	difference	difference	NOUN
uva.x030312957	284	80	in	in	ADP
uva.x030312957	284	81	the	the	DET
uva.x030312957	284	82	number	number	NOUN
uva.x030312957	284	83	of	of	ADP
uva.x030312957	284	84	negative	negative	ADJ
uva.x030312957	284	85	squares	square	NOUN
uva.x030312957	284	86	in	in	ADP
uva.x030312957	284	87	hg	hg	PRON
uva.x030312957	284	88	and	and	CCONJ
uva.x030312957	284	89	h	h	PROPN
uva.x030312957	284	90	,	,	PUNCT
uva.x030312957	284	91	we	we	PRON
uva.x030312957	284	92	can	can	AUX
uva.x030312957	284	93	find	find	VERB
uva.x030312957	284	94	the	the	DET
uva.x030312957	284	95	difference	difference	NOUN
uva.x030312957	284	96	in	in	ADP
uva.x030312957	284	97	the	the	DET
uva.x030312957	284	98	number	number	NOUN
uva.x030312957	284	99	of	of	ADP
uva.x030312957	284	100	variations	variation	NOUN
uva.x030312957	284	101	in	in	ADP
uva.x030312957	284	102	the	the	DET
uva.x030312957	284	103	two	two	NUM
uva.x030312957	284	104	chains	chain	NOUN
uva.x030312957	284	105	1	1	NUM
uva.x030312957	284	106	,	,	PUNCT
uva.x030312957	284	107	41(b	41(b	SPACE
uva.x030312957	284	108	)	)	PUNCT
uva.x030312957	284	109	,	,	PUNCT
uva.x030312957	284	110	a2	a2	X
uva.x030312957	284	111	(	(	PUNCT
uva.x030312957	284	112	b	b	NOUN
uva.x030312957	284	113	)	)	PUNCT
uva.x030312957	284	114	,	,	PUNCT
uva.x030312957	284	115	...	...	PUNCT
uva.x030312957	284	116	,	,	PUNCT
uva.x030312957	284	117	an	an	DET
uva.x030312957	284	118	(	(	PUNCT
uva.x030312957	284	119	b	b	NOUN
uva.x030312957	284	120	)	)	PUNCT
uva.x030312957	284	121	and	and	CCONJ
uva.x030312957	284	122	1	1	NUM
uva.x030312957	284	123	,	,	PUNCT
uva.x030312957	284	124	41(a	41(a	NUM
uva.x030312957	284	125	)	)	PUNCT
uva.x030312957	284	126	,	,	PUNCT
uva.x030312957	284	127	a2	a2	X
uva.x030312957	284	128	(	(	PUNCT
uva.x030312957	284	129	a	a	NOUN
uva.x030312957	284	130	)	)	PUNCT
uva.x030312957	284	131	,	,	PUNCT
uva.x030312957	284	132	...	...	PUNCT
uva.x030312957	284	133	,	,	PUNCT
uva.x030312957	284	134	an(a	an(a	NOUN
uva.x030312957	284	135	)	)	PUNCT
uva.x030312957	284	136	b	b	PROPN
uva.x030312957	284	137	>	>	X
uva.x030312957	284	138	a.	a.	PROPN
uva.x030312957	284	139	but	but	CCONJ
uva.x030312957	284	140	this	this	PRON
uva.x030312957	284	141	is	be	AUX
uva.x030312957	284	142	the	the	DET
uva.x030312957	284	143	same	same	ADJ
uva.x030312957	284	144	as	as	ADP
uva.x030312957	284	145	finding	find	VERB
uva.x030312957	284	146	the	the	DET
uva.x030312957	284	147	difference	difference	NOUN
uva.x030312957	284	148	in	in	ADP
uva.x030312957	284	149	the	the	DET
uva.x030312957	284	150	number	number	NOUN
uva.x030312957	284	151	of	of	ADP
uva.x030312957	284	152	negative	negative	ADJ
uva.x030312957	284	153	squares	square	NOUN
uva.x030312957	284	154	of	of	ADP
uva.x030312957	284	155	¢	¢	NOUN
uva.x030312957	284	156	'	'	PUNCT
uva.x030312957	284	157	,	,	PUNCT
uva.x030312957	284	158	when	when	SCONJ
uva.x030312957	284	159	a	a	PRON
uva.x030312957	284	160	is	be	AUX
uva.x030312957	284	161	replaced	replace	VERB
uva.x030312957	284	162	by	by	ADP
uva.x030312957	284	163	b	b	NOUN
uva.x030312957	284	164	,	,	PUNCT
uva.x030312957	284	165	and	and	CCONJ
uva.x030312957	284	166	in	in	ADP
uva.x030312957	284	167	o	o	NOUN
uva.x030312957	284	168	'	'	PUNCT
uva.x030312957	284	169	when	when	SCONJ
uva.x030312957	284	170	a	a	PRON
uva.x030312957	284	171	is	be	AUX
uva.x030312957	284	172	equal	equal	ADJ
uva.x030312957	284	173	to	to	PART
uva.x030312957	284	174	a.	a.	VERB
uva.x030312957	284	175	before	before	SCONJ
uva.x030312957	284	176	we	we	PRON
uva.x030312957	284	177	proceed	proceed	VERB
uva.x030312957	284	178	to	to	PART
uva.x030312957	284	179	use	use	VERB
uva.x030312957	284	180	the	the	DET
uva.x030312957	284	181	quadratic	quadratic	ADJ
uva.x030312957	284	182	form	form	NOUN
uva.x030312957	284	183	to	to	PART
uva.x030312957	284	184	determine	determine	VERB
uva.x030312957	284	185	the	the	DET
uva.x030312957	284	186	quantity	quantity	NOUN
uva.x030312957	284	187	no	no	ADV
uva.x030312957	284	188	na	na	NOUN
uva.x030312957	284	189	,	,	PUNCT
uva.x030312957	284	190	which	which	PRON
uva.x030312957	284	191	gives	give	VERB
uva.x030312957	284	192	us	we	PRON
uva.x030312957	284	193	the	the	DET
uva.x030312957	284	194	number	number	NOUN
uva.x030312957	284	195	of	of	ADP
uva.x030312957	284	196	real	real	ADJ
uva.x030312957	284	197	roots	root	NOUN
uva.x030312957	284	198	of	of	ADP
uva.x030312957	284	199	an	an	PRON
uva.x030312957	284	200	(	(	PUNCT
uva.x030312957	284	201	x	x	NOUN
uva.x030312957	284	202	)	)	PUNCT
uva.x030312957	284	203	=	=	SYM
uva.x030312957	284	204	0	0	NUM
uva.x030312957	284	205	lying	lie	VERB
uva.x030312957	284	206	between	between	ADP
uva.x030312957	284	207	a	a	PRON
uva.x030312957	284	208	and	and	CCONJ
uva.x030312957	284	209	ß	ß	NOUN
uva.x030312957	284	210	,	,	PUNCT
uva.x030312957	284	211	we	we	PRON
uva.x030312957	284	212	shall	shall	AUX
uva.x030312957	284	213	show	show	VERB
uva.x030312957	284	214	we	we	PRON
uva.x030312957	284	215	were	be	AUX
uva.x030312957	284	216	justified	justify	VERB
uva.x030312957	284	217	in	in	ADP
uva.x030312957	284	218	assuming	assume	VERB
uva.x030312957	284	219	no	no	DET
uva.x030312957	284	220	two	two	NUM
uva.x030312957	284	221	terms	term	NOUN
uva.x030312957	284	222	of	of	ADP
uva.x030312957	284	223	the	the	DET
uva.x030312957	284	224	chain	chain	NOUN
uva.x030312957	284	225	(	(	PUNCT
uva.x030312957	284	226	37	37	NUM
uva.x030312957	284	227	)	)	PUNCT
uva.x030312957	284	228	would	would	AUX
uva.x030312957	284	229	vanish	vanish	VERB
uva.x030312957	284	230	for	for	ADP
uva.x030312957	284	231	the	the	DET
uva.x030312957	284	232	same	same	ADJ
uva.x030312957	284	233	value	value	NOUN
uva.x030312957	284	234	of	of	ADP
uva.x030312957	284	235	x.	x.	PROPN
uva.x030312957	284	236	18	18	NUM
uva.x030312957	284	237	solution	solution	NOUN
uva.x030312957	284	238	of	of	ADP
uva.x030312957	284	239	the	the	DET
uva.x030312957	284	240	equation	equation	NOUN
uva.x030312957	284	241	of	of	ADP
uva.x030312957	284	242	secular	secular	ADJ
uva.x030312957	284	243	variation	variation	NOUN
uva.x030312957	284	244	=	=	VERB
uva.x030312957	284	245	first	first	ADV
uva.x030312957	284	246	,	,	PUNCT
uva.x030312957	284	247	it	it	PRON
uva.x030312957	284	248	is	be	AUX
uva.x030312957	284	249	obvious	obvious	ADJ
uva.x030312957	284	250	that	that	SCONJ
uva.x030312957	284	251	if	if	SCONJ
uva.x030312957	284	252	ap-1(a	ap-1(a	SPACE
uva.x030312957	284	253	)	)	PUNCT
uva.x030312957	284	254	,	,	PUNCT
uva.x030312957	284	255	ap	ap	PROPN
uva.x030312957	284	256	(	(	PUNCT
uva.x030312957	284	257	x	x	PROPN
uva.x030312957	284	258	)	)	PUNCT
uva.x030312957	284	259	and	and	CCONJ
uva.x030312957	284	260	ap+1(x	ap+1(x	ADV
uva.x030312957	284	261	)	)	PUNCT
uva.x030312957	284	262	all	all	DET
uva.x030312957	284	263	three	three	NUM
uva.x030312957	284	264	pass	pass	VERB
uva.x030312957	284	265	through	through	ADP
uva.x030312957	284	266	zero	zero	NUM
uva.x030312957	284	267	and	and	CCONJ
uva.x030312957	284	268	change	change	VERB
uva.x030312957	284	269	sign	sign	NOUN
uva.x030312957	284	270	for	for	ADP
uva.x030312957	284	271	the	the	DET
uva.x030312957	284	272	same	same	ADJ
uva.x030312957	284	273	value	value	NOUN
uva.x030312957	284	274	of	of	ADP
uva.x030312957	284	275	x	x	PRON
uva.x030312957	284	276	,	,	PUNCT
uva.x030312957	284	277	there	there	PRON
uva.x030312957	284	278	will	will	AUX
uva.x030312957	284	279	be	be	AUX
uva.x030312957	284	280	no	no	DET
uva.x030312957	284	281	change	change	NOUN
uva.x030312957	284	282	in	in	ADP
uva.x030312957	284	283	the	the	DET
uva.x030312957	284	284	variations	variation	NOUN
uva.x030312957	284	285	or	or	CCONJ
uva.x030312957	284	286	permanences	permanence	NOUN
uva.x030312957	284	287	in	in	ADP
uva.x030312957	284	288	the	the	DET
uva.x030312957	284	289	three	three	NUM
uva.x030312957	284	290	functions	function	NOUN
uva.x030312957	284	291	before	before	ADV
uva.x030312957	284	292	and	and	CCONJ
uva.x030312957	284	293	after	after	ADP
uva.x030312957	284	294	x	x	PUNCT
uva.x030312957	284	295	passes	pass	VERB
uva.x030312957	284	296	through	through	ADP
uva.x030312957	284	297	this	this	DET
uva.x030312957	284	298	value	value	NOUN
uva.x030312957	284	299	.	.	PUNCT
uva.x030312957	285	1	suppose	suppose	VERB
uva.x030312957	285	2	,	,	PUNCT
uva.x030312957	285	3	then	then	ADV
uva.x030312957	285	4	,	,	PUNCT
uva.x030312957	285	5	for	for	ADP
uva.x030312957	285	6	some	some	DET
uva.x030312957	285	7	value	value	NOUN
uva.x030312957	285	8	of	of	ADP
uva.x030312957	285	9	x	x	PUNCT
uva.x030312957	285	10	in	in	ADP
uva.x030312957	285	11	the	the	DET
uva.x030312957	285	12	interval	interval	NOUN
uva.x030312957	285	13	in	in	ADP
uva.x030312957	285	14	question	question	NOUN
uva.x030312957	285	15	ap	ap	PROPN
uva.x030312957	285	16	(	(	PUNCT
uva.x030312957	285	17	.	.	PUNCT
uva.x030312957	285	18	)	)	PUNCT
uva.x030312957	285	19	and	and	CCONJ
uva.x030312957	285	20	ap+1	ap+1	VERB
uva.x030312957	285	21	(	(	PUNCT
uva.x030312957	285	22	x	x	PUNCT
uva.x030312957	285	23	)	)	PUNCT
uva.x030312957	285	24	both	both	PRON
uva.x030312957	285	25	vanish	vanish	VERB
uva.x030312957	285	26	,	,	PUNCT
uva.x030312957	285	27	but	but	CCONJ
uva.x030312957	285	28	ap-1(x	ap-1(x	SPACE
uva.x030312957	285	29	)	)	PUNCT
uva.x030312957	285	30	does	do	VERB
uva.x030312957	285	31	not	not	PART
uva.x030312957	285	32	.	.	PUNCT
uva.x030312957	286	1	in	in	ADP
uva.x030312957	286	2	this	this	DET
uva.x030312957	286	3	case	case	NOUN
uva.x030312957	286	4	we	we	PRON
uva.x030312957	286	5	can	can	AUX
uva.x030312957	286	6	so	so	ADV
uva.x030312957	286	7	choose	choose	VERB
uva.x030312957	286	8	the	the	DET
uva.x030312957	286	9	ap+1	ap+1	NOUN
uva.x030312957	286	10	,	,	PUNCT
uva.x030312957	286	11	in	in	ADP
uva.x030312957	286	12	which	which	PRON
uva.x030312957	286	13	occur	occur	VERB
uva.x030312957	286	14	in	in	ADP
uva.x030312957	286	15	ap+1(x	ap+1(x	PROPN
uva.x030312957	286	16	)	)	PUNCT
uva.x030312957	286	17	,	,	PUNCT
uva.x030312957	286	18	but	but	CCONJ
uva.x030312957	286	19	not	not	PART
uva.x030312957	286	20	in	in	ADP
uva.x030312957	286	21	an	an	DET
uva.x030312957	286	22	(	(	PUNCT
uva.x030312957	286	23	x	x	SYM
uva.x030312957	286	24	)	)	PUNCT
uva.x030312957	286	25	,	,	PUNCT
uva.x030312957	286	26	that	that	SCONJ
uva.x030312957	286	27	ap+1(x	ap+1(x	PROPN
uva.x030312957	286	28	)	)	PUNCT
uva.x030312957	286	29	will	will	AUX
uva.x030312957	286	30	not	not	PART
uva.x030312957	286	31	vanish	vanish	VERB
uva.x030312957	286	32	when	when	SCONJ
uva.x030312957	286	33	a	a	PRON
uva.x030312957	286	34	,	,	PUNCT
uva.x030312957	286	35	(	(	PUNCT
uva.x030312957	286	36	x	x	SYM
uva.x030312957	286	37	)	)	PUNCT
uva.x030312957	286	38	vanishes	vanish	VERB
uva.x030312957	286	39	.	.	PUNCT
uva.x030312957	287	1	this	this	PRON
uva.x030312957	287	2	is	be	AUX
uva.x030312957	287	3	true	true	ADJ
uva.x030312957	287	4	because	because	SCONJ
uva.x030312957	287	5	ap+1	ap+1	ADV
uva.x030312957	287	6	(	(	PUNCT
uva.x030312957	287	7	x	x	PUNCT
uva.x030312957	287	8	)	)	PUNCT
uva.x030312957	287	9	can	can	AUX
uva.x030312957	287	10	not	not	PART
uva.x030312957	287	11	vanish	vanish	VERB
uva.x030312957	287	12	identically	identically	ADV
uva.x030312957	287	13	for	for	ADP
uva.x030312957	287	14	all	all	DET
uva.x030312957	287	15	values	value	NOUN
uva.x030312957	287	16	of	of	ADP
uva.x030312957	287	17	akt1	akt1	PROPN
uva.x030312957	287	18	,	,	PUNCT
uva.x030312957	287	19	i	i	PRON
uva.x030312957	287	20	since	since	SCONJ
uva.x030312957	287	21	it	it	PRON
uva.x030312957	287	22	contains	contain	VERB
uva.x030312957	287	23	the	the	DET
uva.x030312957	287	24	term	term	NOUN
uva.x030312957	287	25	-	-	PUNCT
uva.x030312957	287	26	a3	a3	NOUN
uva.x030312957	287	27	+	+	NUM
uva.x030312957	287	28	1	1	NUM
uva.x030312957	287	29	,	,	PUNCT
uva.x030312957	287	30	ap-1(x	ap-1(x	SPACE
uva.x030312957	287	31	)	)	PUNCT
uva.x030312957	287	32	,	,	PUNCT
uva.x030312957	287	33	*	*	PUNCT
uva.x030312957	287	34	which	which	PRON
uva.x030312957	287	35	can	can	AUX
uva.x030312957	287	36	only	only	ADV
uva.x030312957	287	37	vanish	vanish	VERB
uva.x030312957	287	38	if	if	SCONJ
uva.x030312957	287	39	ap+1	ap+1	SPACE
uva.x030312957	287	40	,	,	PUNCT
uva.x030312957	287	41	p	p	NOUN
uva.x030312957	287	42	=	=	SYM
uva.x030312957	287	43	0	0	NUM
uva.x030312957	287	44	.	.	PUNCT
uva.x030312957	288	1	we	we	PRON
uva.x030312957	288	2	can	can	AUX
uva.x030312957	288	3	then	then	ADV
uva.x030312957	288	4	build	build	VERB
uva.x030312957	288	5	a	a	DET
uva.x030312957	288	6	new	new	ADJ
uva.x030312957	288	7	function	function	NOUN
uva.x030312957	288	8	an	an	DET
uva.x030312957	288	9	(	(	PUNCT
uva.x030312957	288	10	x	x	SYM
uva.x030312957	288	11	)	)	PUNCT
uva.x030312957	288	12	,	,	PUNCT
uva.x030312957	288	13	in	in	ADP
uva.x030312957	288	14	which	which	PRON
uva.x030312957	288	15	the	the	DET
uva.x030312957	288	16	ai	ai	NOUN
uva.x030312957	288	17	,	,	PUNCT
uva.x030312957	288	18	are	be	AUX
uva.x030312957	288	19	chosen	choose	VERB
uva.x030312957	288	20	to	to	PART
uva.x030312957	288	21	differ	differ	VERB
uva.x030312957	288	22	by	by	ADP
uva.x030312957	288	23	less	less	ADJ
uva.x030312957	288	24	than	than	ADP
uva.x030312957	288	25	an	an	DET
uva.x030312957	288	26	arbitrarily	arbitrarily	ADV
uva.x030312957	288	27	small	small	ADJ
uva.x030312957	288	28	amount	amount	NOUN
uva.x030312957	288	29	,	,	PUNCT
uva.x030312957	288	30	e	e	NUM
uva.x030312957	288	31	,	,	PUNCT
uva.x030312957	288	32	from	from	ADP
uva.x030312957	288	33	the	the	DET
uva.x030312957	288	34	corresponding	corresponding	ADJ
uva.x030312957	288	35	ai	ai	NOUN
uva.x030312957	288	36	,	,	PUNCT
uva.x030312957	288	37	i	i	PRON
uva.x030312957	288	38	terms	term	NOUN
uva.x030312957	288	39	of	of	ADP
uva.x030312957	288	40	an	an	DET
uva.x030312957	288	41	(	(	PUNCT
uva.x030312957	288	42	x	x	SYM
uva.x030312957	288	43	)	)	PUNCT
uva.x030312957	288	44	,	,	PUNCT
uva.x030312957	288	45	but	but	CCONJ
uva.x030312957	288	46	so	so	ADV
uva.x030312957	288	47	that	that	SCONJ
uva.x030312957	288	48	no	no	DET
uva.x030312957	288	49	two	two	NUM
uva.x030312957	288	50	consecutive	consecutive	ADJ
uva.x030312957	288	51	terms	term	NOUN
uva.x030312957	288	52	in	in	ADP
uva.x030312957	288	53	the	the	DET
uva.x030312957	288	54	chain	chain	NOUN
uva.x030312957	288	55	of	of	ADP
uva.x030312957	288	56	principal	principal	ADJ
uva.x030312957	288	57	minors	minor	NOUN
uva.x030312957	288	58	of	of	ADP
uva.x030312957	288	59	an	an	PRON
uva.x030312957	288	60	(	(	PUNCT
uva.x030312957	288	61	x	x	SYM
uva.x030312957	288	62	)	)	PUNCT
uva.x030312957	288	63	will	will	AUX
uva.x030312957	288	64	vanish	vanish	VERB
uva.x030312957	288	65	for	for	ADP
uva.x030312957	288	66	the	the	DET
uva.x030312957	288	67	same	same	ADJ
uva.x030312957	288	68	values	value	NOUN
uva.x030312957	288	69	of	of	ADP
uva.x030312957	288	70	x.	x.	PROPN
uva.x030312957	288	71	e	e	NOUN
uva.x030312957	288	72	can	can	AUX
uva.x030312957	288	73	be	be	AUX
uva.x030312957	288	74	made	make	VERB
uva.x030312957	288	75	so	so	ADV
uva.x030312957	288	76	small	small	ADJ
uva.x030312957	288	77	that	that	SCONJ
uva.x030312957	288	78	the	the	DET
uva.x030312957	288	79	roots	root	NOUN
uva.x030312957	288	80	of	of	ADP
uva.x030312957	288	81	an	an	PRON
uva.x030312957	288	82	(	(	PUNCT
uva.x030312957	288	83	x	x	NOUN
uva.x030312957	288	84	)	)	PUNCT
uva.x030312957	288	85	=	=	PUNCT
uva.x030312957	288	86	0	0	NUM
uva.x030312957	288	87	and	and	CCONJ
uva.x030312957	288	88	ān	ān	PROPN
uva.x030312957	288	89	(	(	PUNCT
uva.x030312957	288	90	x	x	X
uva.x030312957	288	91	)	)	PUNCT
uva.x030312957	288	92	=	=	PUNCT
uva.x030312957	288	93	0	0	PUNCT
uva.x030312957	288	94	will	will	AUX
uva.x030312957	288	95	differ	differ	VERB
uva.x030312957	288	96	by	by	ADP
uva.x030312957	288	97	less	less	ADJ
uva.x030312957	288	98	than	than	ADP
uva.x030312957	288	99	any	any	DET
uva.x030312957	288	100	assigned	assign	VERB
uva.x030312957	288	101	arbitrarily	arbitrarily	ADV
uva.x030312957	288	102	small	small	ADJ
uva.x030312957	288	103	quantity	quantity	NOUN
uva.x030312957	288	104	,	,	PUNCT
uva.x030312957	288	105	and	and	CCONJ
uva.x030312957	288	106	consequently	consequently	ADV
uva.x030312957	288	107	a	a	DET
uva.x030312957	288	108	variation	variation	NOUN
uva.x030312957	288	109	will	will	AUX
uva.x030312957	288	110	be	be	AUX
uva.x030312957	288	111	introduced	introduce	VERB
uva.x030312957	288	112	between	between	ADP
uva.x030312957	288	113	an-1	an-1	PROPN
uva.x030312957	288	114	(	(	PUNCT
uva.x030312957	288	115	x	x	PUNCT
uva.x030312957	288	116	)	)	PUNCT
uva.x030312957	288	117	and	and	CCONJ
uva.x030312957	288	118	an	an	DET
uva.x030312957	288	119	(	(	PUNCT
uva.x030312957	288	120	x	x	NOUN
uva.x030312957	288	121	)	)	PUNCT
uva.x030312957	288	122	,	,	PUNCT
uva.x030312957	288	123	and	and	CCONJ
uva.x030312957	288	124	between	between	ADP
uva.x030312957	288	125	an-1	an-1	PRON
uva.x030312957	288	126	(	(	PUNCT
uva.x030312957	288	127	x	x	NOUN
uva.x030312957	288	128	)	)	PUNCT
uva.x030312957	288	129	and	and	CCONJ
uva.x030312957	288	130	ār	ār	PROPN
uva.x030312957	288	131	(	(	PUNCT
uva.x030312957	288	132	x	x	PROPN
uva.x030312957	288	133	)	)	PUNCT
uva.x030312957	288	134	within	within	ADP
uva.x030312957	288	135	the	the	DET
uva.x030312957	288	136	neighborhood	neighborhood	NOUN
uva.x030312957	288	137	of	of	ADP
uva.x030312957	288	138	the	the	DET
uva.x030312957	288	139	same	same	ADJ
uva.x030312957	288	140	quantity	quantity	NOUN
uva.x030312957	288	141	.	.	PUNCT
uva.x030312957	289	1	then	then	ADV
uva.x030312957	289	2	the	the	DET
uva.x030312957	289	3	two	two	NUM
uva.x030312957	289	4	quantities	quantity	NOUN
uva.x030312957	289	5	a	a	PRON
uva.x030312957	289	6	and	and	CCONJ
uva.x030312957	289	7	b	b	NOUN
uva.x030312957	289	8	can	can	AUX
uva.x030312957	289	9	be	be	AUX
uva.x030312957	289	10	so	so	ADV
uva.x030312957	289	11	chosen	choose	VERB
uva.x030312957	289	12	that	that	SCONJ
uva.x030312957	289	13	in	in	ADP
uva.x030312957	289	14	the	the	DET
uva.x030312957	289	15	two	two	NUM
uva.x030312957	289	16	chains	chain	NOUN
uva.x030312957	289	17	(	(	PUNCT
uva.x030312957	289	18	i	i	NOUN
uva.x030312957	289	19	)	)	PUNCT
uva.x030312957	289	20	1	1	NUM
uva.x030312957	289	21	,	,	PUNCT
uva.x030312957	289	22	41(x	41(x	NUM
uva.x030312957	289	23	)	)	PUNCT
uva.x030312957	289	24	,	,	PUNCT
uva.x030312957	289	25	a2	a2	X
uva.x030312957	289	26	(	(	PUNCT
uva.x030312957	289	27	2	2	NUM
uva.x030312957	289	28	)	)	PUNCT
uva.x030312957	289	29	,	,	PUNCT
uva.x030312957	289	30	...	...	PUNCT
uva.x030312957	289	31	,	,	PUNCT
uva.x030312957	289	32	an	an	PRON
uva.x030312957	289	33	(	(	PUNCT
uva.x030312957	289	34	x	x	NOUN
uva.x030312957	289	35	)	)	PUNCT
uva.x030312957	289	36	and	and	CCONJ
uva.x030312957	289	37	(	(	PUNCT
uva.x030312957	289	38	ii	ii	PROPN
uva.x030312957	289	39	)	)	PUNCT
uva.x030312957	289	40	1	1	NUM
uva.x030312957	289	41	,	,	PUNCT
uva.x030312957	289	42	71(x	71(x	NUM
uva.x030312957	289	43	)	)	PUNCT
uva.x030312957	289	44	,	,	PUNCT
uva.x030312957	289	45	ā,(x	ā,(x	PROPN
uva.x030312957	289	46	)	)	PUNCT
uva.x030312957	289	47	,	,	PUNCT
uva.x030312957	289	48	...	...	PUNCT
uva.x030312957	289	49	,	,	PUNCT
uva.x030312957	289	50	ān	ān	PROPN
uva.x030312957	289	51	(	(	PUNCT
uva.x030312957	289	52	x	x	SYM
uva.x030312957	289	53	)	)	PUNCT
uva.x030312957	289	54	none	none	NOUN
uva.x030312957	289	55	of	of	ADP
uva.x030312957	289	56	the	the	DET
uva.x030312957	289	57	terms	term	NOUN
uva.x030312957	289	58	will	will	AUX
uva.x030312957	289	59	vanish	vanish	VERB
uva.x030312957	289	60	for	for	ADP
uva.x030312957	289	61	x	x	PUNCT
uva.x030312957	289	62	=	=	NOUN
uva.x030312957	289	63	a	a	PRON
uva.x030312957	289	64	or	or	CCONJ
uva.x030312957	289	65	for	for	ADP
uva.x030312957	289	66	x	x	PUNCT
uva.x030312957	289	67	=	=	NOUN
uva.x030312957	289	68	ß	ß	PROPN
uva.x030312957	289	69	.	.	PUNCT
uva.x030312957	290	1	the	the	DET
uva.x030312957	290	2	corresponding	correspond	VERB
uva.x030312957	290	3	members	member	NOUN
uva.x030312957	290	4	of	of	ADP
uva.x030312957	290	5	the	the	DET
uva.x030312957	290	6	two	two	NUM
uva.x030312957	290	7	chains	chain	NOUN
uva.x030312957	290	8	will	will	AUX
uva.x030312957	290	9	then	then	ADV
uva.x030312957	290	10	have	have	VERB
uva.x030312957	290	11	the	the	DET
uva.x030312957	290	12	same	same	ADJ
uva.x030312957	290	13	signs	sign	NOUN
uva.x030312957	290	14	.	.	PUNCT
uva.x030312957	291	1	since	since	SCONJ
uva.x030312957	291	2	no	no	DET
uva.x030312957	291	3	two	two	NUM
uva.x030312957	291	4	consecutive	consecutive	ADJ
uva.x030312957	291	5	terms	term	NOUN
uva.x030312957	291	6	of	of	ADP
uva.x030312957	291	7	the	the	DET
uva.x030312957	291	8	chain	chain	NOUN
uva.x030312957	291	9	(	(	PUNCT
uva.x030312957	291	10	ii	ii	PROPN
uva.x030312957	291	11	)	)	PUNCT
uva.x030312957	291	12	vanish	vanish	VERB
uva.x030312957	291	13	for	for	ADP
uva.x030312957	291	14	the	the	DET
uva.x030312957	291	15	same	same	ADJ
uva.x030312957	291	16	value	value	NOUN
uva.x030312957	291	17	of	of	ADP
uva.x030312957	291	18	x	x	PRON
uva.x030312957	291	19	,	,	PUNCT
uva.x030312957	291	20	then	then	ADV
uva.x030312957	291	21	the	the	DET
uva.x030312957	291	22	discussion	discussion	NOUN
uva.x030312957	291	23	above	above	ADV
uva.x030312957	291	24	,	,	PUNCT
uva.x030312957	291	25	regarding	regard	VERB
uva.x030312957	291	26	the	the	DET
uva.x030312957	291	27	variations	variation	NOUN
uva.x030312957	291	28	in	in	ADP
uva.x030312957	291	29	sign	sign	NOUN
uva.x030312957	291	30	introduced	introduce	VERB
uva.x030312957	291	31	as	as	SCONJ
uva.x030312957	291	32	x	x	PUNCT
uva.x030312957	291	33	passes	pass	VERB
uva.x030312957	291	34	through	through	ADP
uva.x030312957	291	35	a	a	DET
uva.x030312957	291	36	root	root	NOUN
uva.x030312957	291	37	of	of	ADP
uva.x030312957	291	38	an	an	PRON
uva.x030312957	291	39	(	(	PUNCT
uva.x030312957	291	40	x	x	NOUN
uva.x030312957	291	41	)	)	PUNCT
uva.x030312957	291	42	=	=	NOUN
uva.x030312957	291	43	0	0	NUM
uva.x030312957	291	44	,	,	PUNCT
uva.x030312957	291	45	holds	hold	VERB
uva.x030312957	291	46	for	for	ADP
uva.x030312957	291	47	this	this	DET
uva.x030312957	291	48	chain	chain	NOUN
uva.x030312957	291	49	.	.	PUNCT
uva.x030312957	292	1	but	but	CCONJ
uva.x030312957	292	2	the	the	DET
uva.x030312957	292	3	difference	difference	NOUN
uva.x030312957	292	4	in	in	ADP
uva.x030312957	292	5	the	the	DET
uva.x030312957	292	6	number	number	NOUN
uva.x030312957	292	7	of	of	ADP
uva.x030312957	292	8	variations	variation	NOUN
uva.x030312957	292	9	in	in	ADP
uva.x030312957	292	10	sign	sign	NOUN
uva.x030312957	292	11	of	of	ADP
uva.x030312957	292	12	the	the	DET
uva.x030312957	292	13	functions	function	NOUN
uva.x030312957	292	14	of	of	ADP
uva.x030312957	292	15	the	the	DET
uva.x030312957	292	16	chains	chain	NOUN
uva.x030312957	292	17	for	for	ADP
uva.x030312957	292	18	x	x	PUNCT
uva.x030312957	292	19	=	=	PROPN
uva.x030312957	292	20	b	b	PROPN
uva.x030312957	292	21	and	and	CCONJ
uva.x030312957	292	22	for	for	ADP
uva.x030312957	292	23	x	x	SYM
uva.x030312957	292	24	=	=	PRON
uva.x030312957	292	25	a	a	PRON
uva.x030312957	292	26	will	will	AUX
uva.x030312957	292	27	be	be	AUX
uva.x030312957	292	28	the	the	DET
uva.x030312957	292	29	same	same	ADJ
uva.x030312957	292	30	for	for	ADP
uva.x030312957	292	31	both	both	DET
uva.x030312957	292	32	chains	chain	NOUN
uva.x030312957	292	33	,	,	PUNCT
uva.x030312957	292	34	and	and	CCONJ
uva.x030312957	292	35	may	may	AUX
uva.x030312957	292	36	be	be	AUX
uva.x030312957	292	37	determined	determine	VERB
uva.x030312957	292	38	from	from	ADP
uva.x030312957	292	39	either	either	ADV
uva.x030312957	292	40	.	.	PUNCT
uva.x030312957	293	1	the	the	DET
uva.x030312957	293	2	assumption	assumption	NOUN
uva.x030312957	293	3	,	,	PUNCT
uva.x030312957	293	4	therefore	therefore	ADV
uva.x030312957	293	5	,	,	PUNCT
uva.x030312957	293	6	that	that	SCONJ
uva.x030312957	293	7	no	no	DET
uva.x030312957	293	8	two	two	NUM
uva.x030312957	293	9	consecutive	consecutive	ADJ
uva.x030312957	293	10	terms	term	NOUN
uva.x030312957	293	11	of	of	ADP
uva.x030312957	293	12	the	the	DET
uva.x030312957	293	13	chain	chain	NOUN
uva.x030312957	293	14	(	(	PUNCT
uva.x030312957	293	15	37	37	NUM
uva.x030312957	293	16	)	)	PUNCT
uva.x030312957	293	17	would	would	AUX
uva.x030312957	293	18	vanish	vanish	VERB
uva.x030312957	293	19	for	for	ADP
uva.x030312957	293	20	the	the	DET
uva.x030312957	293	21	same	same	ADJ
uva.x030312957	293	22	value	value	NOUN
uva.x030312957	293	23	of	of	ADP
uva.x030312957	293	24	x	x	SYM
uva.x030312957	293	25	did	do	AUX
uva.x030312957	293	26	not	not	PART
uva.x030312957	293	27	lead	lead	VERB
uva.x030312957	293	28	to	to	ADP
uva.x030312957	293	29	false	false	ADJ
uva.x030312957	293	30	conclusions	conclusion	NOUN
uva.x030312957	293	31	,	,	PUNCT
uva.x030312957	293	32	and	and	CCONJ
uva.x030312957	293	33	the	the	DET
uva.x030312957	293	34	quantity	quantity	NOUN
uva.x030312957	293	35	no	no	ADV
uva.x030312957	293	36	na	na	NOUN
uva.x030312957	293	37	can	can	AUX
uva.x030312957	293	38	be	be	AUX
uva.x030312957	293	39	found	find	VERB
uva.x030312957	293	40	by	by	ADP
uva.x030312957	293	41	determining	determine	VERB
uva.x030312957	293	42	the	the	DET
uva.x030312957	293	43	number	number	NOUN
uva.x030312957	293	44	of	of	ADP
uva.x030312957	293	45	negative	negative	ADJ
uva.x030312957	293	46	squares	square	NOUN
uva.x030312957	293	47	in	in	ADP
uva.x030312957	293	48	'	'	PUNCT
uva.x030312957	293	49	for	for	ADP
uva.x030312957	293	50	x	x	SYM
uva.x030312957	293	51	=	=	NOUN
uva.x030312957	293	52	a	a	PRON
uva.x030312957	293	53	and	and	CCONJ
uva.x030312957	293	54	x	x	SYM
uva.x030312957	293	55	=	=	PROPN
uva.x030312957	293	56	b.	b.	PROPN
uva.x030312957	293	57	this	this	PRON
uva.x030312957	293	58	is	be	AUX
uva.x030312957	293	59	done	do	VERB
uva.x030312957	293	60	by	by	ADP
uva.x030312957	293	61	determining	determine	VERB
uva.x030312957	293	62	the	the	DET
uva.x030312957	293	63	number	number	NOUN
uva.x030312957	293	64	of	of	ADP
uva.x030312957	293	65	variations	variation	NOUN
uva.x030312957	293	66	in	in	ADP
uva.x030312957	293	67	signs	sign	NOUN
uva.x030312957	293	68	between	between	ADP
uva.x030312957	293	69	the	the	DET
uva.x030312957	293	70	principal	principal	ADJ
uva.x030312957	293	71	minors	minor	NOUN
uva.x030312957	293	72	of	of	ADP
uva.x030312957	293	73	its	its	PRON
uva.x030312957	293	74	determinant	determinant	NOUN
uva.x030312957	293	75	when	when	SCONJ
uva.x030312957	293	76	arranged	arrange	VERB
uva.x030312957	293	77	in	in	ADP
uva.x030312957	293	78	the	the	DET
uva.x030312957	293	79	form	form	NOUN
uva.x030312957	293	80	of	of	ADP
uva.x030312957	293	81	the	the	DET
uva.x030312957	293	82	chain	chain	NOUN
uva.x030312957	293	83	(	(	PUNCT
uva.x030312957	293	84	37	37	NUM
uva.x030312957	293	85	)	)	PUNCT
uva.x030312957	293	86	.	.	PUNCT
uva.x030312957	294	1	since	since	SCONJ
uva.x030312957	294	2	this	this	PRON
uva.x030312957	294	3	at	at	ADP
uva.x030312957	294	4	the	the	DET
uva.x030312957	294	5	same	same	ADJ
uva.x030312957	294	6	time	time	NOUN
uva.x030312957	294	7	gives	give	VERB
uva.x030312957	294	8	the	the	DET
uva.x030312957	294	9	difference	difference	NOUN
uva.x030312957	294	10	in	in	ADP
uva.x030312957	294	11	the	the	DET
uva.x030312957	294	12	number	number	NOUN
uva.x030312957	294	13	of	of	ADP
uva.x030312957	294	14	negative	negative	ADJ
uva.x030312957	294	15	squares	square	NOUN
uva.x030312957	294	16	between	between	ADP
uva.x030312957	294	17	hg	hg	INTJ
uva.x030312957	294	18	and	and	CCONJ
uva.x030312957	294	19	hą	hą	PROPN
uva.x030312957	294	20	,	,	PUNCT
uva.x030312957	294	21	and	and	CCONJ
uva.x030312957	294	22	consequently	consequently	ADV
uva.x030312957	294	23	the	the	DET
uva.x030312957	294	24	number	number	NOUN
uva.x030312957	294	25	of	of	ADP
uva.x030312957	294	26	roots	root	NOUN
uva.x030312957	294	27	of	of	ADP
uva.x030312957	294	28	an	an	PRON
uva.x030312957	294	29	(	(	PUNCT
uva.x030312957	294	30	x	x	NOUN
uva.x030312957	294	31	)	)	PUNCT
uva.x030312957	294	32	=	=	SYM
uva.x030312957	294	33	0	0	PUNCT
uva.x030312957	294	34	.	.	PUNCT
uva.x030312957	295	1	lying	lie	VERB
uva.x030312957	295	2	in	in	ADP
uva.x030312957	295	3	the	the	DET
uva.x030312957	295	4	interval	interval	NOUN
uva.x030312957	295	5	from	from	ADP
uva.x030312957	295	6	a	a	PRON
uva.x030312957	295	7	to	to	ADP
uva.x030312957	295	8	ß	ß	NOUN
uva.x030312957	295	9	,	,	PUNCT
uva.x030312957	295	10	we	we	PRON
uva.x030312957	295	11	shall	shall	AUX
uva.x030312957	295	12	use	use	VERB
uva.x030312957	295	13	it	it	PRON
uva.x030312957	295	14	immediately	immediately	ADV
uva.x030312957	295	15	for	for	ADP
uva.x030312957	295	16	that	that	DET
uva.x030312957	295	17	purpose	purpose	NOUN
uva.x030312957	295	18	.	.	PUNCT
uva.x030312957	296	1	*	*	PUNCT
uva.x030312957	296	2	see	see	VERB
uva.x030312957	296	3	$	$	SYM
uva.x030312957	296	4	62	62	NUM
uva.x030312957	296	5	,	,	PUNCT
uva.x030312957	296	6	“	"	PUNCT
uva.x030312957	296	7	theory	theory	NOUN
uva.x030312957	296	8	of	of	ADP
uva.x030312957	296	9	determinants	determinant	NOUN
uva.x030312957	296	10	,	,	PUNCT
uva.x030312957	296	11	"	"	PUNCT
uva.x030312957	296	12	by	by	ADP
uva.x030312957	296	13	thomas	thomas	PROPN
uva.x030312957	296	14	muir	muir	PROPN
uva.x030312957	296	15	.	.	PUNCT
uva.x030312957	297	1	by	by	ADP
uva.x030312957	297	2	a	a	DET
uva.x030312957	297	3	method	method	NOUN
uva.x030312957	297	4	due	due	ADP
uva.x030312957	297	5	to	to	ADP
uva.x030312957	297	6	hermite	hermite	NOUN
uva.x030312957	297	7	19	19	NUM
uva.x030312957	297	8	$	$	SYM
uva.x030312957	297	9	3	3	NUM
uva.x030312957	297	10	.	.	PUNCT
uva.x030312957	297	11	solution	solution	NOUN
uva.x030312957	297	12	of	of	ADP
uva.x030312957	297	13	the	the	DET
uva.x030312957	297	14	equation	equation	NOUN
uva.x030312957	297	15	.	.	PUNCT
uva.x030312957	298	1	since	since	SCONJ
uva.x030312957	298	2	ap(a	ap(a	SPACE
uva.x030312957	298	3	)	)	PUNCT
uva.x030312957	298	4	=	=	PROPN
uva.x030312957	298	5	(	(	PUNCT
uva.x030312957	298	6	-1	-1	X
uva.x030312957	298	7	)	)	PUNCT
uva.x030312957	298	8	”	"	PUNCT
uva.x030312957	299	1	qp	qp	NOUN
uva.x030312957	299	2	+	+	NOUN
uva.x030312957	299	3	pian	pian	NOUN
uva.x030312957	299	4	!	!	PUNCT
uva.x030312957	300	1	+	+	CCONJ
uva.x030312957	300	2	p2	p2	PROPN
uva.x030312957	300	3	ap	ap	PROPN
uva.x030312957	300	4	?	?	PUNCT
uva.x030312957	301	1	+	+	PUNCT
uva.x030312957	301	2	...	...	PUNCT
uva.x030312957	302	1	+	+	PUNCT
uva.x030312957	302	2	pr	pr	X
uva.x030312957	302	3	(	(	PUNCT
uva.x030312957	302	4	p1	p1	PROPN
uva.x030312957	302	5	,	,	PUNCT
uva.x030312957	302	6	p2	p2	PROPN
uva.x030312957	302	7	,	,	PUNCT
uva.x030312957	302	8	...	...	PUNCT
uva.x030312957	302	9	,	,	PUNCT
uva.x030312957	302	10	pr	pr	X
uva.x030312957	302	11	being	be	AUX
uva.x030312957	302	12	constants	constants	ADJ
uva.x030312957	302	13	)	)	PUNCT
uva.x030312957	303	1	we	we	PRON
uva.x030312957	303	2	note	note	VERB
uva.x030312957	303	3	that	that	SCONJ
uva.x030312957	303	4	for	for	ADP
uva.x030312957	303	5	a	a	DET
uva.x030312957	303	6	sufficiently	sufficiently	ADV
uva.x030312957	303	7	large	large	ADJ
uva.x030312957	303	8	in	in	ADP
uva.x030312957	303	9	absolute	absolute	ADJ
uva.x030312957	303	10	value	value	NOUN
uva.x030312957	303	11	,	,	PUNCT
uva.x030312957	303	12	the	the	DET
uva.x030312957	303	13	sign	sign	NOUN
uva.x030312957	303	14	of	of	ADP
uva.x030312957	303	15	ap	ap	PROPN
uva.x030312957	303	16	(	(	PUNCT
uva.x030312957	303	17	a	a	X
uva.x030312957	303	18	)	)	PUNCT
uva.x030312957	303	19	will	will	AUX
uva.x030312957	303	20	be	be	AUX
uva.x030312957	303	21	the	the	DET
uva.x030312957	303	22	sign	sign	NOUN
uva.x030312957	303	23	of	of	ADP
uva.x030312957	303	24	the	the	DET
uva.x030312957	303	25	leading	lead	VERB
uva.x030312957	303	26	term	term	NOUN
uva.x030312957	303	27	(	(	PUNCT
uva.x030312957	303	28	1)pqp	1)pqp	NUM
uva.x030312957	303	29	.	.	PUNCT
uva.x030312957	304	1	in	in	ADP
uva.x030312957	304	2	the	the	DET
uva.x030312957	304	3	chain	chain	NOUN
uva.x030312957	304	4	(	(	PUNCT
uva.x030312957	304	5	37	37	NUM
uva.x030312957	304	6	)	)	PUNCT
uva.x030312957	304	7	1	1	NUM
uva.x030312957	304	8	,	,	PUNCT
uva.x030312957	304	9	41(a	41(a	NUM
uva.x030312957	304	10	)	)	PUNCT
uva.x030312957	304	11	,	,	PUNCT
uva.x030312957	304	12	42	42	NUM
uva.x030312957	304	13	(	(	PUNCT
uva.x030312957	304	14	a	a	NOUN
uva.x030312957	304	15	)	)	PUNCT
uva.x030312957	304	16	,	,	PUNCT
uva.x030312957	304	17	an	an	DET
uva.x030312957	304	18	(	(	PUNCT
uva.x030312957	304	19	a	a	NOUN
uva.x030312957	304	20	)	)	PUNCT
uva.x030312957	304	21	for	for	ADP
uva.x030312957	304	22	a	a	DET
uva.x030312957	304	23	=	=	NOUN
uva.x030312957	304	24	00	00	PUNCT
uva.x030312957	304	25	each	each	DET
uva.x030312957	304	26	member	member	NOUN
uva.x030312957	304	27	of	of	ADP
uva.x030312957	304	28	the	the	DET
uva.x030312957	304	29	chain	chain	NOUN
uva.x030312957	304	30	is	be	AUX
uva.x030312957	304	31	positive	positive	ADJ
uva.x030312957	304	32	[	[	X
uva.x030312957	304	33	(	(	PUNCT
uva.x030312957	304	34	-1	-1	X
uva.x030312957	304	35	)	)	PUNCT
uva.x030312957	304	36	'	'	PUNCT
uva.x030312957	304	37	(	(	PUNCT
uva.x030312957	304	38	.	.	PUNCT
uva.x030312957	304	39	)	)	PUNCT
uva.x030312957	305	1	being	be	AUX
uva.x030312957	305	2	positive	positive	ADJ
uva.x030312957	305	3	whether	whether	SCONJ
uva.x030312957	305	4	p	p	PROPN
uva.x030312957	305	5	is	be	AUX
uva.x030312957	305	6	even	even	ADV
uva.x030312957	305	7	or	or	CCONJ
uva.x030312957	305	8	odd	odd	ADJ
uva.x030312957	305	9	]	]	PUNCT
uva.x030312957	305	10	,	,	PUNCT
uva.x030312957	305	11	there	there	PRON
uva.x030312957	305	12	are	be	VERB
uva.x030312957	305	13	no	no	DET
uva.x030312957	305	14	variations	variation	NOUN
uva.x030312957	305	15	in	in	ADP
uva.x030312957	305	16	sign	sign	NOUN
uva.x030312957	305	17	between	between	ADP
uva.x030312957	305	18	these	these	DET
uva.x030312957	305	19	members	member	NOUN
uva.x030312957	305	20	and	and	CCONJ
uva.x030312957	305	21	n-=	n-=	PROPN
uva.x030312957	305	22	0	0	NUM
uva.x030312957	305	23	.	.	PUNCT
uva.x030312957	306	1	for	for	ADP
uva.x030312957	306	2	a	a	DET
uva.x030312957	306	3	=	=	NOUN
uva.x030312957	306	4	+	+	NUM
uva.x030312957	306	5	0	0	NUM
uva.x030312957	306	6	,	,	PUNCT
uva.x030312957	306	7	on	on	ADP
uva.x030312957	306	8	the	the	DET
uva.x030312957	306	9	other	other	ADJ
uva.x030312957	306	10	hand	hand	NOUN
uva.x030312957	306	11	,	,	PUNCT
uva.x030312957	306	12	there	there	PRON
uva.x030312957	306	13	is	be	VERB
uva.x030312957	306	14	a	a	DET
uva.x030312957	306	15	variation	variation	NOUN
uva.x030312957	306	16	between	between	ADP
uva.x030312957	306	17	each	each	DET
uva.x030312957	306	18	successive	successive	ADJ
uva.x030312957	306	19	term	term	NOUN
uva.x030312957	306	20	,	,	PUNCT
uva.x030312957	306	21	as	as	ADP
uva.x030312957	306	22	the	the	DET
uva.x030312957	306	23	sign	sign	NOUN
uva.x030312957	306	24	of	of	ADP
uva.x030312957	306	25	each	each	DET
uva.x030312957	306	26	term	term	NOUN
uva.x030312957	306	27	,	,	PUNCT
uva.x030312957	306	28	beginning	begin	VERB
uva.x030312957	306	29	with	with	ADP
uva.x030312957	306	30	the	the	DET
uva.x030312957	306	31	second	second	NOUN
uva.x030312957	306	32	,	,	PUNCT
uva.x030312957	306	33	is	be	AUX
uva.x030312957	306	34	determined	determine	VERB
uva.x030312957	306	35	by	by	ADP
uva.x030312957	306	36	(	(	PUNCT
uva.x030312957	306	37	1	1	NUM
uva.x030312957	306	38	)	)	PUNCT
uva.x030312957	306	39	”	"	PUNCT
uva.x030312957	306	40	,	,	PUNCT
uva.x030312957	306	41	which	which	PRON
uva.x030312957	306	42	makes	make	VERB
uva.x030312957	306	43	a1	a1	PROPN
uva.x030312957	306	44	(	(	PUNCT
uva.x030312957	306	45	+	+	NOUN
uva.x030312957	306	46	)	)	PUNCT
uva.x030312957	306	47	negative	negative	ADJ
uva.x030312957	306	48	and	and	CCONJ
uva.x030312957	306	49	each	each	DET
uva.x030312957	306	50	member	member	NOUN
uva.x030312957	306	51	of	of	ADP
uva.x030312957	306	52	the	the	DET
uva.x030312957	306	53	chain	chain	NOUN
uva.x030312957	306	54	after	after	ADP
uva.x030312957	306	55	that	that	DET
uva.x030312957	306	56	alternately	alternately	ADV
uva.x030312957	306	57	positive	positive	ADJ
uva.x030312957	306	58	and	and	CCONJ
uva.x030312957	306	59	negative	negative	ADJ
uva.x030312957	306	60	.	.	PUNCT
uva.x030312957	307	1	there	there	PRON
uva.x030312957	307	2	are	be	VERB
uva.x030312957	307	3	then	then	ADV
uva.x030312957	307	4	n	n	ADP
uva.x030312957	307	5	variations	variation	NOUN
uva.x030312957	307	6	in	in	ADP
uva.x030312957	307	7	the	the	DET
uva.x030312957	307	8	chain	chain	NOUN
uva.x030312957	307	9	of	of	ADP
uva.x030312957	307	10	functions	function	NOUN
uva.x030312957	307	11	for	for	ADP
uva.x030312957	307	12	a	a	DET
uva.x030312957	307	13	=	=	NOUN
uva.x030312957	308	1	+	+	CCONJ
uva.x030312957	308	2	oor	oor	NOUN
uva.x030312957	308	3	=	=	PRON
uva.x030312957	308	4	n.	n.	PROPN
uva.x030312957	308	5	hence	hence	ADV
uva.x030312957	308	6	we	we	PRON
uva.x030312957	308	7	have	have	VERB
uva.x030312957	308	8	ntoo	ntoo	ADV
uva.x030312957	308	9	nno	nno	ADJ
uva.x030312957	309	1	=	=	ADP
uva.x030312957	309	2	n	n	ADP
uva.x030312957	309	3	and	and	CCONJ
uva.x030312957	309	4	we	we	PRON
uva.x030312957	309	5	see	see	VERB
uva.x030312957	309	6	that	that	SCONJ
uva.x030312957	309	7	all	all	PRON
uva.x030312957	309	8	of	of	ADP
uva.x030312957	309	9	the	the	DET
uva.x030312957	309	10	roots	root	NOUN
uva.x030312957	309	11	of	of	ADP
uva.x030312957	309	12	the	the	DET
uva.x030312957	309	13	equation	equation	NOUN
uva.x030312957	309	14	of	of	ADP
uva.x030312957	309	15	secular	secular	ADJ
uva.x030312957	309	16	variations	variation	NOUN
uva.x030312957	309	17	are	be	AUX
uva.x030312957	309	18	real	real	ADJ
uva.x030312957	309	19	.	.	PUNCT
uva.x030312957	310	1	§	§	PROPN
uva.x030312957	310	2	4	4	NUM
uva.x030312957	310	3	.	.	PUNCT
uva.x030312957	310	4	condition	condition	NOUN
uva.x030312957	310	5	for	for	ADP
uva.x030312957	310	6	all	all	PRON
uva.x030312957	310	7	of	of	ADP
uva.x030312957	310	8	the	the	DET
uva.x030312957	310	9	roots	root	NOUN
uva.x030312957	310	10	to	to	PART
uva.x030312957	310	11	be	be	AUX
uva.x030312957	310	12	positive	positive	ADJ
uva.x030312957	310	13	.	.	PUNCT
uva.x030312957	311	1	in	in	ADP
uva.x030312957	311	2	order	order	NOUN
uva.x030312957	311	3	to	to	PART
uva.x030312957	311	4	fix	fix	VERB
uva.x030312957	311	5	the	the	DET
uva.x030312957	311	6	conditions	condition	NOUN
uva.x030312957	311	7	to	to	PART
uva.x030312957	311	8	be	be	AUX
uva.x030312957	311	9	satisfied	satisfied	ADJ
uva.x030312957	311	10	in	in	ADP
uva.x030312957	311	11	order	order	NOUN
uva.x030312957	311	12	that	that	SCONJ
uva.x030312957	311	13	all	all	DET
uva.x030312957	311	14	the	the	DET
uva.x030312957	311	15	roots	root	NOUN
uva.x030312957	311	16	of	of	ADP
uva.x030312957	311	17	an	an	PRON
uva.x030312957	311	18	(	(	PUNCT
uva.x030312957	311	19	x	x	NOUN
uva.x030312957	311	20	)	)	PUNCT
uva.x030312957	311	21	=	=	PUNCT
uva.x030312957	311	22	0	0	PUNCT
uva.x030312957	311	23	may	may	AUX
uva.x030312957	311	24	be	be	AUX
uva.x030312957	311	25	positive	positive	ADJ
uva.x030312957	311	26	,	,	PUNCT
uva.x030312957	311	27	make	make	VERB
uva.x030312957	311	28	a	a	PRON
uva.x030312957	311	29	take	take	VERB
uva.x030312957	311	30	the	the	DET
uva.x030312957	311	31	value	value	NOUN
uva.x030312957	311	32	8	8	NUM
uva.x030312957	311	33	,	,	PUNCT
uva.x030312957	311	34	where	where	SCONJ
uva.x030312957	311	35	is	be	AUX
uva.x030312957	311	36	a	a	DET
uva.x030312957	311	37	positive	positive	ADJ
uva.x030312957	311	38	quantity	quantity	NOUN
uva.x030312957	311	39	so	so	ADV
uva.x030312957	311	40	small	small	ADJ
uva.x030312957	311	41	that	that	SCONJ
uva.x030312957	311	42	there	there	PRON
uva.x030312957	311	43	are	be	VERB
uva.x030312957	311	44	no	no	DET
uva.x030312957	311	45	positive	positive	ADJ
uva.x030312957	311	46	roots	root	NOUN
uva.x030312957	311	47	of	of	ADP
uva.x030312957	311	48	an	an	DET
uva.x030312957	311	49	(	(	PUNCT
uva.x030312957	311	50	x	x	NOUN
uva.x030312957	311	51	)	)	PUNCT
uva.x030312957	311	52	=	=	SYM
uva.x030312957	311	53	0	0	NUM
uva.x030312957	311	54	that	that	PRON
uva.x030312957	311	55	are	be	AUX
uva.x030312957	311	56	less	less	ADJ
uva.x030312957	311	57	than	than	ADP
uva.x030312957	311	58	8	8	NUM
uva.x030312957	311	59	.	.	PUNCT
uva.x030312957	312	1	since	since	SCONJ
uva.x030312957	312	2	the	the	DET
uva.x030312957	312	3	number	number	NOUN
uva.x030312957	312	4	of	of	ADP
uva.x030312957	312	5	variations	variation	NOUN
uva.x030312957	312	6	in	in	ADP
uva.x030312957	312	7	sign	sign	NOUN
uva.x030312957	312	8	in	in	ADP
uva.x030312957	312	9	the	the	DET
uva.x030312957	312	10	chain	chain	NOUN
uva.x030312957	312	11	of	of	ADP
uva.x030312957	312	12	functions	function	NOUN
uva.x030312957	312	13	a	a	PRON
uva.x030312957	312	14	;	;	PUNCT
uva.x030312957	312	15	(	(	PUNCT
uva.x030312957	312	16	a	a	X
uva.x030312957	312	17	)	)	PUNCT
uva.x030312957	312	18	for	for	ADP
uva.x030312957	312	19	a	a	DET
uva.x030312957	312	20	=	=	NOUN
uva.x030312957	312	21	+	+	SYM
uva.x030312957	312	22	co	co	NOUN
uva.x030312957	312	23	is	be	AUX
uva.x030312957	312	24	n	n	ADV
uva.x030312957	312	25	,	,	PUNCT
uva.x030312957	312	26	in	in	ADP
uva.x030312957	312	27	order	order	NOUN
uva.x030312957	312	28	to	to	PART
uva.x030312957	312	29	have	have	AUX
uva.x030312957	312	30	all	all	DET
uva.x030312957	312	31	the	the	DET
uva.x030312957	312	32	roots	root	NOUN
uva.x030312957	312	33	of	of	ADP
uva.x030312957	312	34	an	an	DET
uva.x030312957	312	35	(	(	PUNCT
uva.x030312957	312	36	x	x	SYM
uva.x030312957	312	37	)	)	PUNCT
uva.x030312957	312	38	=	=	PUNCT
uva.x030312957	312	39	0	0	NUM
uva.x030312957	312	40	positive	positive	ADJ
uva.x030312957	312	41	it	it	PRON
uva.x030312957	312	42	is	be	AUX
uva.x030312957	312	43	necessary	necessary	ADJ
uva.x030312957	312	44	that	that	SCONJ
uva.x030312957	312	45	,	,	PUNCT
uva.x030312957	312	46	when	when	SCONJ
uva.x030312957	312	47	a	a	DET
uva.x030312957	312	48	=	=	NOUN
uva.x030312957	312	49	8	8	NUM
uva.x030312957	312	50	,	,	PUNCT
uva.x030312957	312	51	there	there	PRON
uva.x030312957	312	52	should	should	AUX
uva.x030312957	312	53	be	be	AUX
uva.x030312957	312	54	no	no	DET
uva.x030312957	312	55	variations	variation	NOUN
uva.x030312957	312	56	in	in	ADP
uva.x030312957	312	57	sign	sign	NOUN
uva.x030312957	312	58	in	in	ADP
uva.x030312957	312	59	the	the	DET
uva.x030312957	312	60	functions	function	NOUN
uva.x030312957	312	61	1	1	NUM
uva.x030312957	312	62	,	,	PUNCT
uva.x030312957	312	63	41(8	41(8	NUM
uva.x030312957	312	64	)	)	PUNCT
uva.x030312957	312	65	,	,	PUNCT
uva.x030312957	312	66	a2	a2	X
uva.x030312957	312	67	(	(	PUNCT
uva.x030312957	312	68	8)	8)	NUM
uva.x030312957	312	69	,	,	PUNCT
uva.x030312957	312	70	a3	a3	PROPN
uva.x030312957	312	71	(	(	PUNCT
uva.x030312957	312	72	8)	8)	NUM
uva.x030312957	312	73	,	,	PUNCT
uva.x030312957	312	74	...	...	PUNCT
uva.x030312957	312	75	,	,	PUNCT
uva.x030312957	312	76	an	an	DET
uva.x030312957	312	77	(	(	PUNCT
uva.x030312957	312	78	8)	8)	NUM
uva.x030312957	312	79	,	,	PUNCT
uva.x030312957	312	80	that	that	ADV
uva.x030312957	312	81	is	is	ADV
uva.x030312957	312	82	,	,	PUNCT
uva.x030312957	312	83	they	they	PRON
uva.x030312957	312	84	must	must	AUX
uva.x030312957	312	85	all	all	ADV
uva.x030312957	312	86	be	be	AUX
uva.x030312957	312	87	positive	positive	ADJ
uva.x030312957	312	88	.	.	PUNCT
uva.x030312957	313	1	by	by	ADP
uva.x030312957	313	2	taking	take	VERB
uva.x030312957	313	3	d	d	NOUN
uva.x030312957	313	4	sufficiently	sufficiently	ADV
uva.x030312957	313	5	small	small	ADJ
uva.x030312957	313	6	the	the	DET
uva.x030312957	313	7	sign	sign	NOUN
uva.x030312957	313	8	of	of	ADP
uva.x030312957	313	9	these	these	DET
uva.x030312957	313	10	functions	function	NOUN
uva.x030312957	313	11	will	will	AUX
uva.x030312957	313	12	be	be	AUX
uva.x030312957	313	13	the	the	DET
uva.x030312957	313	14	same	same	ADJ
uva.x030312957	313	15	as	as	ADP
uva.x030312957	313	16	the	the	DET
uva.x030312957	313	17	corresponding	corresponding	ADJ
uva.x030312957	313	18	principal	principal	ADJ
uva.x030312957	313	19	minors	minor	NOUN
uva.x030312957	313	20	of	of	ADP
uva.x030312957	313	21	canla	canla	PROPN
uva.x030312957	313	22	di	di	PROPN
uva.x030312957	313	23	,	,	PUNCT
uva.x030312957	313	24	1	1	NUM
uva.x030312957	313	25	,	,	PUNCT
uva.x030312957	313	26	01	01	NUM
uva.x030312957	313	27	,	,	PUNCT
uva.x030312957	313	28	2	2	NUM
uva.x030312957	313	29	,	,	PUNCT
uva.x030312957	313	30	>	>	X
uva.x030312957	313	31	ai	ai	INTJ
uva.x030312957	313	32	,	,	PUNCT
uva.x030312957	313	33	n	n	CCONJ
uva.x030312957	313	34	amino	amino	NOUN
uva.x030312957	313	35	1	1	NUM
uva.x030312957	313	36	02	02	NUM
uva.x030312957	313	37	,	,	PUNCT
uva.x030312957	313	38	1	1	NUM
uva.x030312957	313	39	,	,	PUNCT
uva.x030312957	313	40	a2	a2	PROPN
uva.x030312957	313	41	,	,	PUNCT
uva.x030312957	313	42	2	2	NUM
uva.x030312957	313	43	,	,	PUNCT
uva.x030312957	313	44	a2	a2	PROPN
uva.x030312957	313	45	,	,	PUNCT
uva.x030312957	313	46	n	n	CCONJ
uva.x030312957	313	47	an	an	DET
uva.x030312957	313	48	ry	ry	NOUN
uva.x030312957	313	49	1819	1819	NUM
uva.x030312957	313	50	an	an	PRON
uva.x030312957	313	51	,	,	PUNCT
uva.x030312957	313	52	1	1	NUM
uva.x030312957	313	53	,	,	PUNCT
uva.x030312957	313	54	an	an	PRON
uva.x030312957	313	55	,	,	PUNCT
uva.x030312957	313	56	?	?	PUNCT
uva.x030312957	313	57	,	,	PUNCT
uva.x030312957	313	58	an	an	PRON
uva.x030312957	313	59	,	,	PUNCT
uva.x030312957	313	60	or	or	CCONJ
uva.x030312957	313	61	of	of	ADP
uva.x030312957	313	62	1	1	NUM
uva.x030312957	313	63	,	,	PUNCT
uva.x030312957	313	64	a1	a1	PROPN
uva.x030312957	313	65	,	,	PUNCT
uva.x030312957	313	66	a2	a2	X
uva.x030312957	313	67	,	,	PUNCT
uva.x030312957	313	68	a3	a3	PROPN
uva.x030312957	313	69	,	,	PUNCT
uva.x030312957	313	70	...	...	PUNCT
uva.x030312957	313	71	,	,	PUNCT
uva.x030312957	313	72	an	an	DET
uva.x030312957	313	73	20	20	NUM
uva.x030312957	313	74	solution	solution	NOUN
uva.x030312957	313	75	of	of	ADP
uva.x030312957	313	76	the	the	DET
uva.x030312957	313	77	equation	equation	NOUN
uva.x030312957	313	78	of	of	ADP
uva.x030312957	313	79	secular	secular	ADJ
uva.x030312957	313	80	variation	variation	NOUN
uva.x030312957	313	81	where	where	SCONJ
uva.x030312957	313	82	di	di	PROPN
uva.x030312957	313	83	,	,	PUNCT
uva.x030312957	313	84	1	1	NUM
uva.x030312957	313	85	,	,	PUNCT
uva.x030312957	313	86	ai	ai	VERB
uva.x030312957	313	87	,	,	PUNCT
uva.x030312957	313	88	2	2	NUM
uva.x030312957	313	89	a1	a1	NOUN
uva.x030312957	313	90	ai	ai	VERB
uva.x030312957	313	91	,	,	PUNCT
uva.x030312957	313	92	1	1	NUM
uva.x030312957	313	93	,	,	PUNCT
uva.x030312957	313	94	δ	δ	PROPN
uva.x030312957	313	95	,	,	PUNCT
uva.x030312957	313	96	etc	etc	X
uva.x030312957	313	97	.	.	X
uva.x030312957	313	98	02	02	NUM
uva.x030312957	313	99	,	,	PUNCT
uva.x030312957	313	100	1	1	NUM
uva.x030312957	313	101	,	,	PUNCT
uva.x030312957	313	102	02	02	NUM
uva.x030312957	313	103	,	,	PUNCT
uva.x030312957	313	104	2	2	NUM
uva.x030312957	313	105	0	0	NUM
uva.x030312957	313	106	are	be	AUX
uva.x030312957	313	107	all	all	PRON
uva.x030312957	313	108	to	to	PART
uva.x030312957	313	109	be	be	AUX
uva.x030312957	313	110	positive	positive	ADJ
uva.x030312957	313	111	then	then	ADV
uva.x030312957	313	112	hence	hence	ADV
uva.x030312957	313	113	if	if	SCONJ
uva.x030312957	313	114	the	the	DET
uva.x030312957	313	115	roots	root	NOUN
uva.x030312957	313	116	of	of	ADP
uva.x030312957	313	117	the	the	DET
uva.x030312957	313	118	given	give	VERB
uva.x030312957	313	119	equation	equation	NOUN
uva.x030312957	313	120	an	an	DET
uva.x030312957	313	121	(	(	PUNCT
uva.x030312957	313	122	x	x	SYM
uva.x030312957	313	123	)	)	PUNCT
uva.x030312957	313	124	a1	a1	PROPN
uva.x030312957	313	125	,	,	PUNCT
uva.x030312957	313	126	a2	a2	X
uva.x030312957	313	127	,	,	PUNCT
uva.x030312957	313	128	...	...	PUNCT
uva.x030312957	313	129	,	,	PUNCT
uva.x030312957	313	130	an	an	PRON
uva.x030312957	313	131	must	must	AUX
uva.x030312957	313	132	all	all	PRON
uva.x030312957	313	133	be	be	AUX
uva.x030312957	313	134	positive	positive	ADJ
uva.x030312957	313	135	.	.	PUNCT
uva.x030312957	314	1	$	$	SYM
uva.x030312957	314	2	5	5	NUM
uva.x030312957	314	3	.	.	PUNCT
uva.x030312957	314	4	principal	principal	ADJ
uva.x030312957	314	5	planes	plane	NOUN
uva.x030312957	314	6	of	of	ADP
uva.x030312957	314	7	surfaces	surface	NOUN
uva.x030312957	314	8	of	of	ADP
uva.x030312957	314	9	second	second	ADJ
uva.x030312957	314	10	degree	degree	NOUN
uva.x030312957	314	11	.	.	PUNCT
uva.x030312957	315	1	as	as	ADP
uva.x030312957	315	2	a	a	DET
uva.x030312957	315	3	particular	particular	ADJ
uva.x030312957	315	4	application	application	NOUN
uva.x030312957	315	5	we	we	PRON
uva.x030312957	315	6	shall	shall	AUX
uva.x030312957	315	7	consider	consider	VERB
uva.x030312957	315	8	an	an	DET
uva.x030312957	315	9	equation	equation	NOUN
uva.x030312957	315	10	used	use	VERB
uva.x030312957	315	11	in	in	ADP
uva.x030312957	315	12	finding	find	VERB
uva.x030312957	315	13	the	the	DET
uva.x030312957	315	14	principal	principal	ADJ
uva.x030312957	315	15	planes	plane	NOUN
uva.x030312957	315	16	of	of	ADP
uva.x030312957	315	17	surfaces	surface	NOUN
uva.x030312957	315	18	of	of	ADP
uva.x030312957	315	19	the	the	DET
uva.x030312957	315	20	second	second	ADJ
uva.x030312957	315	21	degree	degree	NOUN
uva.x030312957	315	22	.	.	PUNCT
uva.x030312957	316	1	the	the	DET
uva.x030312957	316	2	equations	equation	NOUN
uva.x030312957	316	3	of	of	ADP
uva.x030312957	316	4	these	these	DET
uva.x030312957	316	5	principal	principal	ADJ
uva.x030312957	316	6	planes	plane	NOUN
uva.x030312957	316	7	depend	depend	VERB
uva.x030312957	316	8	on	on	ADP
uva.x030312957	316	9	the	the	DET
uva.x030312957	316	10	solutions	solution	NOUN
uva.x030312957	316	11	of	of	ADP
uva.x030312957	316	12	the	the	DET
uva.x030312957	316	13	equation	equation	NOUN
uva.x030312957	316	14	*	*	PUNCT
uva.x030312957	316	15	a	a	X
uva.x030312957	316	16	-	-	PUNCT
uva.x030312957	316	17	x	x	NOUN
uva.x030312957	316	18	,	,	PUNCT
uva.x030312957	316	19	h	h	PROPN
uva.x030312957	316	20	,	,	PUNCT
uva.x030312957	316	21	9	9	NUM
uva.x030312957	316	22	h	h	NOUN
uva.x030312957	316	23	,	,	PUNCT
uva.x030312957	316	24	b\	b\	PROPN
uva.x030312957	316	25	,	,	PUNCT
uva.x030312957	316	26	f	f	PROPN
uva.x030312957	316	27	=	=	SYM
uva.x030312957	316	28	0	0	NUM
uva.x030312957	316	29	.	.	PROPN
uva.x030312957	316	30	9	9	NUM
uva.x030312957	316	31	,	,	PUNCT
uva.x030312957	316	32	f	f	PROPN
uva.x030312957	316	33	,	,	PUNCT
uva.x030312957	316	34	c	c	PROPN
uva.x030312957	316	35	-	-	PUNCT
uva.x030312957	316	36	x	x	NOUN
uva.x030312957	316	37	we	we	PRON
uva.x030312957	316	38	see	see	VERB
uva.x030312957	316	39	this	this	PRON
uva.x030312957	316	40	is	be	AUX
uva.x030312957	316	41	the	the	DET
uva.x030312957	316	42	equation	equation	NOUN
uva.x030312957	316	43	an	an	PRON
uva.x030312957	316	44	(	(	PUNCT
uva.x030312957	316	45	x	x	NOUN
uva.x030312957	316	46	)	)	PUNCT
uva.x030312957	316	47	=	=	SYM
uva.x030312957	316	48	0	0	NUM
uva.x030312957	316	49	)	)	PUNCT
uva.x030312957	316	50	with	with	ADP
uva.x030312957	316	51	n	n	NOUN
uva.x030312957	316	52	=	=	SYM
uva.x030312957	316	53	3	3	NUM
uva.x030312957	316	54	,	,	PUNCT
uva.x030312957	316	55	and	and	CCONJ
uva.x030312957	316	56	it	it	PRON
uva.x030312957	316	57	follows	follow	VERB
uva.x030312957	316	58	,	,	PUNCT
uva.x030312957	316	59	therefore	therefore	ADV
uva.x030312957	316	60	,	,	PUNCT
uva.x030312957	316	61	that	that	SCONJ
uva.x030312957	316	62	its	its	PRON
uva.x030312957	316	63	roots	root	NOUN
uva.x030312957	316	64	are	be	AUX
uva.x030312957	316	65	all	all	ADV
uva.x030312957	316	66	real	real	ADJ
uva.x030312957	316	67	.	.	PUNCT
uva.x030312957	317	1	§	§	PROPN
uva.x030312957	317	2	6	6	NUM
uva.x030312957	317	3	.	.	PUNCT
uva.x030312957	318	1	relation	relation	NOUN
uva.x030312957	318	2	between	between	ADP
uva.x030312957	318	3	the	the	DET
uva.x030312957	318	4	roots	root	NOUN
uva.x030312957	318	5	of	of	ADP
uva.x030312957	318	6	an	an	DET
uva.x030312957	318	7	(	(	PUNCT
uva.x030312957	318	8	x	x	NOUN
uva.x030312957	318	9	)	)	PUNCT
uva.x030312957	318	10	=	=	PUNCT
uva.x030312957	318	11	0	0	NUM
uva.x030312957	318	12	and	and	CCONJ
uva.x030312957	318	13	an+1(x	an+1(x	NOUN
uva.x030312957	318	14	)	)	PUNCT
uva.x030312957	318	15	=	=	PROPN
uva.x030312957	318	16	0	0	X
uva.x030312957	318	17	.	.	PUNCT
uva.x030312957	318	18	let	let	VERB
uva.x030312957	318	19	us	we	PRON
uva.x030312957	318	20	locate	locate	VERB
uva.x030312957	318	21	the	the	DET
uva.x030312957	318	22	roots	root	NOUN
uva.x030312957	318	23	of	of	ADP
uva.x030312957	318	24	anti(x	anti(x	NOUN
uva.x030312957	318	25	)	)	PUNCT
uva.x030312957	318	26	=	=	PROPN
uva.x030312957	318	27	0	0	NUM
uva.x030312957	318	28	in	in	ADP
uva.x030312957	318	29	relation	relation	NOUN
uva.x030312957	318	30	to	to	ADP
uva.x030312957	318	31	those	those	PRON
uva.x030312957	318	32	of	of	ADP
uva.x030312957	318	33	an	an	PRON
uva.x030312957	318	34	(	(	PUNCT
uva.x030312957	318	35	x	x	NOUN
uva.x030312957	318	36	)	)	PUNCT
uva.x030312957	318	37	=	=	SYM
uva.x030312957	318	38	0	0	NUM
uva.x030312957	318	39	.	.	PUNCT
uva.x030312957	319	1	note	note	VERB
uva.x030312957	319	2	that	that	SCONJ
uva.x030312957	319	3	,	,	PUNCT
uva.x030312957	319	4	since	since	SCONJ
uva.x030312957	319	5	all	all	DET
uva.x030312957	319	6	the	the	DET
uva.x030312957	319	7	roots	root	NOUN
uva.x030312957	319	8	of	of	ADP
uva.x030312957	319	9	an	an	PRON
uva.x030312957	319	10	(	(	PUNCT
uva.x030312957	319	11	x	x	NOUN
uva.x030312957	319	12	)	)	PUNCT
uva.x030312957	319	13	=	=	PUNCT
uva.x030312957	319	14	0	0	NUM
uva.x030312957	319	15	are	be	AUX
uva.x030312957	319	16	real	real	ADJ
uva.x030312957	319	17	,	,	PUNCT
uva.x030312957	319	18	and	and	CCONJ
uva.x030312957	319	19	there	there	PRON
uva.x030312957	319	20	are	be	VERB
uva.x030312957	319	21	no	no	DET
uva.x030312957	319	22	variations	variation	NOUN
uva.x030312957	319	23	in	in	ADP
uva.x030312957	319	24	sign	sign	NOUN
uva.x030312957	319	25	in	in	ADP
uva.x030312957	319	26	the	the	DET
uva.x030312957	319	27	chain	chain	NOUN
uva.x030312957	319	28	(	(	PUNCT
uva.x030312957	319	29	37	37	NUM
uva.x030312957	319	30	)	)	PUNCT
uva.x030312957	319	31	for	for	ADP
uva.x030312957	319	32	a	a	DET
uva.x030312957	319	33	=	=	NOUN
uva.x030312957	319	34	–	–	PUNCT
uva.x030312957	319	35	0	0	NUM
uva.x030312957	319	36	the	the	DET
uva.x030312957	319	37	number	number	NOUN
uva.x030312957	319	38	of	of	ADP
uva.x030312957	319	39	variations	variation	NOUN
uva.x030312957	319	40	in	in	ADP
uva.x030312957	319	41	sign	sign	NOUN
uva.x030312957	319	42	of	of	ADP
uva.x030312957	319	43	the	the	DET
uva.x030312957	319	44	chain	chain	NOUN
uva.x030312957	319	45	(	(	PUNCT
uva.x030312957	319	46	37	37	NUM
uva.x030312957	319	47	)	)	PUNCT
uva.x030312957	319	48	will	will	AUX
uva.x030312957	319	49	give	give	VERB
uva.x030312957	319	50	the	the	DET
uva.x030312957	319	51	number	number	NOUN
uva.x030312957	319	52	of	of	ADP
uva.x030312957	319	53	roots	root	NOUN
uva.x030312957	319	54	of	of	ADP
uva.x030312957	319	55	an(x	an(x	ADV
uva.x030312957	319	56	)	)	PUNCT
uva.x030312957	319	57	=	=	X
uva.x030312957	319	58	(	(	PUNCT
uva.x030312957	319	59	that	that	PRON
uva.x030312957	319	60	are	be	AUX
uva.x030312957	319	61	less	less	ADJ
uva.x030312957	319	62	than	than	ADP
uva.x030312957	319	63	a.	a.	NOUN
uva.x030312957	319	64	take	take	VERB
uva.x030312957	319	65	for	for	ADP
uva.x030312957	319	66	a	a	DET
uva.x030312957	319	67	general	general	ADJ
uva.x030312957	319	68	investigation	investigation	NOUN
uva.x030312957	319	69	n	n	CCONJ
uva.x030312957	319	70	=	=	PROPN
uva.x030312957	319	71	r.	r.	PROPN
uva.x030312957	319	72	let	let	VERB
uva.x030312957	319	73	the	the	DET
uva.x030312957	319	74	roots	root	NOUN
uva.x030312957	319	75	of	of	ADP
uva.x030312957	319	76	a	a	PRON
uva.x030312957	319	77	,	,	PUNCT
uva.x030312957	319	78	(	(	PUNCT
uva.x030312957	319	79	x	x	SYM
uva.x030312957	319	80	)	)	PUNCT
uva.x030312957	319	81	=	=	SYM
uva.x030312957	319	82	0	0	NUM
uva.x030312957	319	83	,	,	PUNCT
uva.x030312957	319	84	arranged	arrange	VERB
uva.x030312957	319	85	in	in	ADP
uva.x030312957	319	86	order	order	NOUN
uva.x030312957	319	87	of	of	ADP
uva.x030312957	319	88	magnitude	magnitude	NOUN
uva.x030312957	319	89	,	,	PUNCT
uva.x030312957	319	90	beginning	begin	VERB
uva.x030312957	319	91	with	with	ADP
uva.x030312957	319	92	the	the	DET
uva.x030312957	319	93	smallest	small	ADJ
uva.x030312957	319	94	,	,	PUNCT
uva.x030312957	319	95	be	be	AUX
uva.x030312957	319	96	or-1	or-1	SPACE
uva.x030312957	319	97	,	,	PUNCT
uva.x030312957	319	98	ar	ar	PROPN
uva.x030312957	319	99	,	,	PUNCT
uva.x030312957	319	100	ai	ai	VERB
uva.x030312957	319	101	,	,	PUNCT
uva.x030312957	319	102	a2	a2	PROPN
uva.x030312957	319	103	,	,	PUNCT
uva.x030312957	319	104	a3	a3	NOUN
uva.x030312957	319	105	,	,	PUNCT
uva.x030312957	319	106	and	and	CCONJ
uva.x030312957	319	107	examine	examine	VERB
uva.x030312957	319	108	the	the	DET
uva.x030312957	319	109	chains	chain	NOUN
uva.x030312957	319	110	of	of	ADP
uva.x030312957	319	111	principal	principal	ADJ
uva.x030312957	319	112	minors	minor	NOUN
uva.x030312957	319	113	of	of	ADP
uva.x030312957	319	114	δ	δ	PROPN
uva.x030312957	319	115	,	,	PUNCT
uva.x030312957	319	116	(	(	PUNCT
uva.x030312957	319	117	r	r	NOUN
uva.x030312957	319	118	)	)	PUNCT
uva.x030312957	319	119	and	and	CCONJ
uva.x030312957	319	120	ar+1(x	ar+1(x	NOUN
uva.x030312957	319	121	)	)	PUNCT
uva.x030312957	319	122	.	.	PUNCT
uva.x030312957	320	1	in	in	ADP
uva.x030312957	320	2	the	the	DET
uva.x030312957	320	3	chain	chain	NOUN
uva.x030312957	320	4	of	of	ADP
uva.x030312957	320	5	principal	principal	ADJ
uva.x030312957	320	6	minors	minor	NOUN
uva.x030312957	320	7	1	1	NUM
uva.x030312957	320	8	,	,	PUNCT
uva.x030312957	320	9	41	41	NUM
uva.x030312957	320	10	(	(	PUNCT
uva.x030312957	320	11	ar	ar	PROPN
uva.x030312957	320	12	)	)	PUNCT
uva.x030312957	320	13	,	,	PUNCT
uva.x030312957	320	14	a.	a.	PROPN
uva.x030312957	320	15	(	(	PUNCT
uva.x030312957	320	16	ar	ar	PROPN
uva.x030312957	320	17	)	)	PUNCT
uva.x030312957	320	18	,	,	PUNCT
uva.x030312957	320	19	...	...	PUNCT
uva.x030312957	320	20	,	,	PUNCT
uva.x030312957	320	21	4.-1(ar	4.-1(ar	NUM
uva.x030312957	320	22	)	)	PUNCT
uva.x030312957	320	23	,	,	PUNCT
uva.x030312957	320	24	a.	a.	PROPN
uva.x030312957	320	25	(	(	PUNCT
uva.x030312957	320	26	ar	ar	PROPN
uva.x030312957	320	27	)	)	PUNCT
uva.x030312957	320	28	,	,	PUNCT
uva.x030312957	320	29	arti(ar	arti(ar	PROPN
uva.x030312957	320	30	)	)	PUNCT
uva.x030312957	320	31	since	since	SCONJ
uva.x030312957	320	32	a	a	DET
uva.x030312957	320	33	,	,	PUNCT
uva.x030312957	320	34	(	(	PUNCT
uva.x030312957	320	35	ar	ar	PROPN
uva.x030312957	320	36	)	)	PUNCT
uva.x030312957	320	37	=	=	PROPN
uva.x030312957	320	38	0	0	NUM
uva.x030312957	320	39	,	,	PUNCT
uva.x030312957	320	40	then	then	ADV
uva.x030312957	320	41	ar-1(ar	ar-1(ar	SPACE
uva.x030312957	320	42	)	)	PUNCT
uva.x030312957	320	43	and	and	CCONJ
uva.x030312957	320	44	ar+1	ar+1	VERB
uva.x030312957	320	45	(	(	PUNCT
uva.x030312957	320	46	ar	ar	PROPN
uva.x030312957	320	47	)	)	PUNCT
uva.x030312957	320	48	have	have	VERB
uva.x030312957	320	49	opposite	opposite	ADJ
uva.x030312957	320	50	signs	sign	NOUN
uva.x030312957	320	51	,	,	PUNCT
uva.x030312957	320	52	by	by	ADP
uva.x030312957	320	53	(	(	PUNCT
uva.x030312957	320	54	38	38	NUM
uva.x030312957	320	55	)	)	PUNCT
uva.x030312957	320	56	.	.	PUNCT
uva.x030312957	321	1	increase	increase	VERB
uva.x030312957	321	2	ay	ay	PROPN
uva.x030312957	321	3	by	by	ADP
uva.x030312957	321	4	a	a	DET
uva.x030312957	321	5	small	small	ADJ
uva.x030312957	321	6	amount	amount	NOUN
uva.x030312957	321	7	h	h	NOUN
uva.x030312957	321	8	,	,	PUNCT
uva.x030312957	321	9	where	where	SCONJ
uva.x030312957	321	10	,	,	PUNCT
uva.x030312957	321	11	as	as	SCONJ
uva.x030312957	321	12	previously	previously	ADV
uva.x030312957	321	13	used	use	VERB
uva.x030312957	321	14	,	,	PUNCT
uva.x030312957	321	15	h	h	NOUN
uva.x030312957	321	16	is	be	AUX
uva.x030312957	321	17	a	a	DET
uva.x030312957	321	18	small	small	ADJ
uva.x030312957	321	19	positive	positive	ADJ
uva.x030312957	321	20	quantity	quantity	NOUN
uva.x030312957	321	21	,	,	PUNCT
uva.x030312957	321	22	so	so	ADV
uva.x030312957	321	23	small	small	ADJ
uva.x030312957	321	24	that	that	SCONJ
uva.x030312957	321	25	none	none	NOUN
uva.x030312957	321	26	of	of	ADP
uva.x030312957	321	27	the	the	DET
uva.x030312957	321	28	functions	function	NOUN
uva.x030312957	321	29	ai(a	ai(a	ADV
uva.x030312957	321	30	)	)	PUNCT
uva.x030312957	321	31	will	will	AUX
uva.x030312957	321	32	change	change	VERB
uva.x030312957	321	33	sign	sign	NOUN
uva.x030312957	321	34	in	in	ADP
uva.x030312957	321	35	the	the	DET
uva.x030312957	321	36	interval	interval	NOUN
uva.x030312957	321	37	qr	qr	NOUN
uva.x030312957	321	38	–	–	PUNCT
uva.x030312957	321	39	h	h	NOUN
uva.x030312957	321	40	to	to	ADP
uva.x030312957	321	41	ar	ar	PROPN
uva.x030312957	321	42	+	+	PROPN
uva.x030312957	321	43	h	h	NOUN
uva.x030312957	321	44	,	,	PUNCT
uva.x030312957	321	45	excepting	except	VERB
uva.x030312957	321	46	δ	δ	PROPN
uva.x030312957	321	47	,	,	PUNCT
uva.x030312957	321	48	(	(	PUNCT
uva.x030312957	321	49	α	α	NOUN
uva.x030312957	321	50	)	)	PUNCT
uva.x030312957	321	51	.	.	PUNCT
uva.x030312957	322	1	*	*	PUNCT
uva.x030312957	322	2	see	see	VERB
uva.x030312957	322	3	echols	echol	NOUN
uva.x030312957	322	4	'	'	PART
uva.x030312957	322	5	calculus	calculus	NOUN
uva.x030312957	322	6	,	,	PUNCT
uva.x030312957	322	7	page	page	NOUN
uva.x030312957	322	8	361	361	NUM
uva.x030312957	322	9	.	.	PUNCT
uva.x030312957	323	1	by	by	ADP
uva.x030312957	323	2	a	a	DET
uva.x030312957	323	3	method	method	NOUN
uva.x030312957	323	4	due	due	ADP
uva.x030312957	323	5	to	to	ADP
uva.x030312957	323	6	hermite	hermite	NOUN
uva.x030312957	323	7	21	21	NUM
uva.x030312957	323	8	in	in	ADP
uva.x030312957	323	9	the	the	DET
uva.x030312957	323	10	two	two	NUM
uva.x030312957	323	11	chains	chain	NOUN
uva.x030312957	323	12	of	of	ADP
uva.x030312957	323	13	principal	principal	ADJ
uva.x030312957	323	14	minors	minor	NOUN
uva.x030312957	323	15	(	(	PUNCT
uva.x030312957	323	16	i	i	NOUN
uva.x030312957	323	17	)	)	PUNCT
uva.x030312957	323	18	1	1	NUM
uva.x030312957	323	19	,	,	PUNCT
uva.x030312957	323	20	41(ar	41(ar	NUM
uva.x030312957	323	21	)	)	PUNCT
uva.x030312957	323	22	,	,	PUNCT
uva.x030312957	323	23	a2	a2	X
uva.x030312957	323	24	(	(	PUNCT
uva.x030312957	323	25	qr	qr	PROPN
uva.x030312957	323	26	)	)	PUNCT
uva.x030312957	323	27	,	,	PUNCT
uva.x030312957	323	28	...	...	PUNCT
uva.x030312957	323	29	,	,	PUNCT
uva.x030312957	323	30	ar-1	ar-1	ADP
uva.x030312957	323	31	(	(	PUNCT
uva.x030312957	323	32	ar	ar	PROPN
uva.x030312957	323	33	)	)	PUNCT
uva.x030312957	323	34	,	,	PUNCT
uva.x030312957	323	35	ar	ar	PROPN
uva.x030312957	323	36	(	(	PUNCT
uva.x030312957	323	37	ar	ar	PROPN
uva.x030312957	323	38	)	)	PUNCT
uva.x030312957	323	39	and	and	CCONJ
uva.x030312957	323	40	(	(	PUNCT
uva.x030312957	323	41	ii	ii	PROPN
uva.x030312957	323	42	)	)	PUNCT
uva.x030312957	323	43	1	1	NUM
uva.x030312957	323	44	,	,	PUNCT
uva.x030312957	323	45	41(ar	41(ar	NUM
uva.x030312957	323	46	+	+	CCONJ
uva.x030312957	323	47	h	h	PROPN
uva.x030312957	323	48	)	)	PUNCT
uva.x030312957	323	49	,	,	PUNCT
uva.x030312957	323	50	a2	a2	X
uva.x030312957	323	51	(	(	PUNCT
uva.x030312957	323	52	ar	ar	PROPN
uva.x030312957	323	53	+	+	NOUN
uva.x030312957	323	54	h	h	NOUN
uva.x030312957	323	55	)	)	PUNCT
uva.x030312957	323	56	,	,	PUNCT
uva.x030312957	323	57	.	.	PUNCT
uva.x030312957	323	58	,	,	PUNCT
uva.x030312957	323	59	ar-1(qr	ar-1(qr	ADJ
uva.x030312957	324	1	+	+	CCONJ
uva.x030312957	324	2	h	h	PROPN
uva.x030312957	324	3	)	)	PUNCT
uva.x030312957	324	4	,	,	PUNCT
uva.x030312957	324	5	ar	ar	PROPN
uva.x030312957	324	6	(	(	PUNCT
uva.x030312957	324	7	qr	qr	NOUN
uva.x030312957	324	8	+	+	PRON
uva.x030312957	324	9	h	h	NOUN
uva.x030312957	324	10	)	)	PUNCT
uva.x030312957	324	11	all	all	PRON
uva.x030312957	324	12	of	of	ADP
uva.x030312957	324	13	the	the	DET
uva.x030312957	324	14	corresponding	correspond	VERB
uva.x030312957	324	15	functions	function	NOUN
uva.x030312957	324	16	will	will	AUX
uva.x030312957	324	17	have	have	VERB
uva.x030312957	324	18	the	the	DET
uva.x030312957	324	19	same	same	ADJ
uva.x030312957	324	20	sign	sign	NOUN
uva.x030312957	324	21	excepting	except	VERB
uva.x030312957	324	22	the	the	DET
uva.x030312957	324	23	last	last	ADJ
uva.x030312957	324	24	one	one	NOUN
uva.x030312957	324	25	,	,	PUNCT
uva.x030312957	324	26	which	which	PRON
uva.x030312957	324	27	in	in	ADP
uva.x030312957	324	28	the	the	DET
uva.x030312957	324	29	first	first	ADJ
uva.x030312957	324	30	chain	chain	NOUN
uva.x030312957	324	31	is	be	AUX
uva.x030312957	324	32	zero	zero	NUM
uva.x030312957	324	33	,	,	PUNCT
uva.x030312957	324	34	but	but	CCONJ
uva.x030312957	324	35	in	in	ADP
uva.x030312957	324	36	the	the	DET
uva.x030312957	324	37	second	second	ADJ
uva.x030312957	324	38	chain	chain	NOUN
uva.x030312957	324	39	may	may	AUX
uva.x030312957	324	40	be	be	AUX
uva.x030312957	324	41	either	either	CCONJ
uva.x030312957	324	42	positive	positive	ADJ
uva.x030312957	324	43	or	or	CCONJ
uva.x030312957	324	44	negative	negative	ADJ
uva.x030312957	324	45	.	.	PUNCT
uva.x030312957	325	1	the	the	DET
uva.x030312957	325	2	second	second	ADJ
uva.x030312957	325	3	chain	chain	NOUN
uva.x030312957	325	4	(	(	PUNCT
uva.x030312957	325	5	ii	ii	PROPN
uva.x030312957	325	6	)	)	PUNCT
uva.x030312957	325	7	will	will	AUX
uva.x030312957	325	8	have	have	VERB
uva.x030312957	325	9	r	r	NOUN
uva.x030312957	325	10	variations	variation	NOUN
uva.x030312957	325	11	,	,	PUNCT
uva.x030312957	325	12	since	since	SCONJ
uva.x030312957	325	13	all	all	PRON
uva.x030312957	325	14	of	of	ADP
uva.x030312957	325	15	the	the	DET
uva.x030312957	325	16	roots	root	NOUN
uva.x030312957	325	17	of	of	ADP
uva.x030312957	325	18	a	a	PRON
uva.x030312957	325	19	,	,	PUNCT
uva.x030312957	325	20	(	(	PUNCT
uva.x030312957	325	21	x	x	SYM
uva.x030312957	325	22	)	)	PUNCT
uva.x030312957	325	23	=	=	PUNCT
uva.x030312957	325	24	0	0	NUM
uva.x030312957	325	25	are	be	AUX
uva.x030312957	325	26	less	less	ADJ
uva.x030312957	325	27	than	than	ADP
uva.x030312957	325	28	an	an	DET
uva.x030312957	325	29	+	+	ADJ
uva.x030312957	325	30	h	h	NOUN
uva.x030312957	325	31	,	,	PUNCT
uva.x030312957	325	32	having	having	AUX
uva.x030312957	325	33	taken	take	VERB
uva.x030312957	325	34	ar	ar	PROPN
uva.x030312957	325	35	as	as	ADP
uva.x030312957	325	36	the	the	DET
uva.x030312957	325	37	greatest	great	ADJ
uva.x030312957	325	38	root	root	NOUN
uva.x030312957	325	39	.	.	PUNCT
uva.x030312957	326	1	having	have	VERB
uva.x030312957	326	2	r	r	NOUN
uva.x030312957	326	3	variations	variation	NOUN
uva.x030312957	326	4	there	there	PRON
uva.x030312957	326	5	will	will	AUX
uva.x030312957	326	6	be	be	AUX
uva.x030312957	326	7	a	a	DET
uva.x030312957	326	8	variation	variation	NOUN
uva.x030312957	326	9	between	between	ADP
uva.x030312957	326	10	each	each	DET
uva.x030312957	326	11	pair	pair	NOUN
uva.x030312957	326	12	of	of	ADP
uva.x030312957	326	13	successive	successive	ADJ
uva.x030312957	326	14	functions	function	NOUN
uva.x030312957	326	15	,	,	PUNCT
uva.x030312957	326	16	and	and	CCONJ
uva.x030312957	326	17	consequently	consequently	ADV
uva.x030312957	326	18	a	a	DET
uva.x030312957	326	19	variation	variation	NOUN
uva.x030312957	326	20	between	between	ADP
uva.x030312957	326	21	an-1	an-1	PROPN
uva.x030312957	326	22	(	(	PUNCT
uva.x030312957	326	23	ar	ar	PROPN
uva.x030312957	326	24	+	+	NOUN
uva.x030312957	326	25	h	h	PROPN
uva.x030312957	326	26	)	)	PUNCT
uva.x030312957	326	27	and	and	CCONJ
uva.x030312957	326	28	ar	ar	PROPN
uva.x030312957	326	29	(	(	PUNCT
uva.x030312957	326	30	qr	qr	NOUN
uva.x030312957	326	31	+	+	PRON
uva.x030312957	326	32	h	h	NOUN
uva.x030312957	326	33	)	)	PUNCT
uva.x030312957	326	34	.	.	PUNCT
uva.x030312957	327	1	since	since	SCONJ
uva.x030312957	327	2	ar-1(ar	ar-1(ar	SPACE
uva.x030312957	327	3	)	)	PUNCT
uva.x030312957	327	4	and	and	CCONJ
uva.x030312957	327	5	art1	art1	VERB
uva.x030312957	327	6	(	(	PUNCT
uva.x030312957	327	7	ar	ar	PROPN
uva.x030312957	327	8	)	)	PUNCT
uva.x030312957	327	9	have	have	VERB
uva.x030312957	327	10	opposite	opposite	ADJ
uva.x030312957	327	11	signs	sign	NOUN
uva.x030312957	327	12	so	so	SCONJ
uva.x030312957	327	13	will	will	AUX
uva.x030312957	327	14	ar-1	ar-1	VERB
uva.x030312957	327	15	(	(	PUNCT
uva.x030312957	327	16	ar	ar	PROPN
uva.x030312957	327	17	+	+	NOUN
uva.x030312957	327	18	h	h	PROPN
uva.x030312957	327	19	)	)	PUNCT
uva.x030312957	327	20	and	and	CCONJ
uva.x030312957	327	21	ar+1	ar+1	VERB
uva.x030312957	327	22	(	(	PUNCT
uva.x030312957	327	23	ar	ar	PROPN
uva.x030312957	327	24	+	+	NOUN
uva.x030312957	327	25	h	h	NOUN
uva.x030312957	327	26	)	)	PUNCT
uva.x030312957	327	27	have	have	VERB
uva.x030312957	327	28	opposite	opposite	ADJ
uva.x030312957	327	29	signs	sign	NOUN
uva.x030312957	327	30	and	and	CCONJ
uva.x030312957	327	31	from	from	ADP
uva.x030312957	327	32	above	above	ADP
uva.x030312957	327	33	ar	ar	PROPN
uva.x030312957	327	34	(	(	PUNCT
uva.x030312957	327	35	ar	ar	PROPN
uva.x030312957	327	36	+	+	NOUN
uva.x030312957	327	37	h	h	PROPN
uva.x030312957	327	38	)	)	PUNCT
uva.x030312957	327	39	and	and	CCONJ
uva.x030312957	327	40	ar+1	ar+1	VERB
uva.x030312957	327	41	(	(	PUNCT
uva.x030312957	327	42	qr	qr	NOUN
uva.x030312957	327	43	+	+	PRON
uva.x030312957	327	44	h	h	NOUN
uva.x030312957	327	45	)	)	PUNCT
uva.x030312957	327	46	will	will	AUX
uva.x030312957	327	47	have	have	VERB
uva.x030312957	327	48	the	the	DET
uva.x030312957	327	49	same	same	ADJ
uva.x030312957	327	50	sign	sign	NOUN
uva.x030312957	327	51	.	.	PUNCT
uva.x030312957	328	1	then	then	ADV
uva.x030312957	328	2	the	the	DET
uva.x030312957	328	3	chain	chain	NOUN
uva.x030312957	328	4	(	(	PUNCT
uva.x030312957	328	5	iii	iii	NOUN
uva.x030312957	328	6	)	)	PUNCT
uva.x030312957	328	7	1	1	NUM
uva.x030312957	328	8	,	,	PUNCT
uva.x030312957	328	9	41(ar	41(ar	NUM
uva.x030312957	328	10	+	+	CCONJ
uva.x030312957	328	11	h	h	PROPN
uva.x030312957	328	12	)	)	PUNCT
uva.x030312957	328	13	,	,	PUNCT
uva.x030312957	328	14	a2	a2	X
uva.x030312957	328	15	(	(	PUNCT
uva.x030312957	328	16	ar	ar	PROPN
uva.x030312957	328	17	+	+	NOUN
uva.x030312957	328	18	h	h	PROPN
uva.x030312957	328	19	)	)	PUNCT
uva.x030312957	328	20	,	,	PUNCT
uva.x030312957	328	21	·	·	PUNCT
uva.x030312957	328	22	,	,	PUNCT
uva.x030312957	328	23	ar-1	ar-1	ADP
uva.x030312957	328	24	(	(	PUNCT
uva.x030312957	328	25	ar	ar	PROPN
uva.x030312957	328	26	+	+	NOUN
uva.x030312957	328	27	h	h	PROPN
uva.x030312957	328	28	)	)	PUNCT
uva.x030312957	328	29	,	,	PUNCT
uva.x030312957	328	30	a.	a.	PROPN
uva.x030312957	328	31	(	(	PUNCT
uva.x030312957	328	32	qr	qr	NOUN
uva.x030312957	328	33	+	+	CCONJ
uva.x030312957	328	34	h	h	NOUN
uva.x030312957	328	35	)	)	PUNCT
uva.x030312957	328	36	,	,	PUNCT
uva.x030312957	328	37	ar+1	ar+1	INTJ
uva.x030312957	328	38	(	(	PUNCT
uva.x030312957	328	39	qr	qr	NOUN
uva.x030312957	328	40	+	+	CCONJ
uva.x030312957	328	41	h	h	NOUN
uva.x030312957	328	42	)	)	PUNCT
uva.x030312957	328	43	will	will	AUX
uva.x030312957	328	44	have	have	VERB
uva.x030312957	328	45	only	only	ADV
uva.x030312957	328	46	r	r	NOUN
uva.x030312957	328	47	variations	variation	NOUN
uva.x030312957	328	48	,	,	PUNCT
uva.x030312957	328	49	the	the	DET
uva.x030312957	328	50	same	same	ADJ
uva.x030312957	328	51	as	as	ADP
uva.x030312957	328	52	in	in	ADP
uva.x030312957	328	53	(	(	PUNCT
uva.x030312957	328	54	ii	ii	PROPN
uva.x030312957	328	55	)	)	PUNCT
uva.x030312957	328	56	.	.	PUNCT
uva.x030312957	329	1	hence	hence	ADV
uva.x030312957	329	2	there	there	PRON
uva.x030312957	329	3	are	be	VERB
uva.x030312957	329	4	r	r	NOUN
uva.x030312957	329	5	roots	root	NOUN
uva.x030312957	329	6	of	of	ADP
uva.x030312957	329	7	4	4	NUM
uva.x030312957	329	8	+	+	NUM
uva.x030312957	329	9	1(x	1(x	NUM
uva.x030312957	329	10	)	)	PUNCT
uva.x030312957	329	11	=	=	PUNCT
uva.x030312957	329	12	0	0	NUM
uva.x030312957	329	13	less	less	ADJ
uva.x030312957	329	14	than	than	ADP
uva.x030312957	329	15	ax	ax	NOUN
uva.x030312957	329	16	+	+	NOUN
uva.x030312957	329	17	h	h	NOUN
uva.x030312957	329	18	,	,	PUNCT
uva.x030312957	329	19	and	and	CCONJ
uva.x030312957	329	20	since	since	SCONJ
uva.x030312957	329	21	art1	art1	NOUN
uva.x030312957	329	22	(	(	PUNCT
uva.x030312957	329	23	x	x	NOUN
uva.x030312957	329	24	)	)	PUNCT
uva.x030312957	329	25	=	=	PUNCT
uva.x030312957	329	26	0	0	PUNCT
uva.x030312957	329	27	has	have	VERB
uva.x030312957	329	28	r	r	NOUN
uva.x030312957	329	29	+1	+1	NOUN
uva.x030312957	329	30	roots	root	NOUN
uva.x030312957	329	31	there	there	PRON
uva.x030312957	329	32	is	be	VERB
uva.x030312957	329	33	one	one	NUM
uva.x030312957	329	34	root	root	NOUN
uva.x030312957	329	35	of	of	ADP
uva.x030312957	329	36	arti	arti	NOUN
uva.x030312957	329	37	(	(	PUNCT
uva.x030312957	329	38	a	a	X
uva.x030312957	329	39	)	)	PUNCT
uva.x030312957	329	40	=	=	PROPN
uva.x030312957	329	41	0	0	X
uva.x030312957	329	42	)	)	PUNCT
uva.x030312957	329	43	which	which	PRON
uva.x030312957	329	44	is	be	AUX
uva.x030312957	329	45	greater	great	ADJ
uva.x030312957	329	46	than	than	ADP
uva.x030312957	329	47	ax	ax	NOUN
uva.x030312957	330	1	+	+	NOUN
uva.x030312957	330	2	h.	h.	NOUN
uva.x030312957	330	3	that	that	PRON
uva.x030312957	330	4	is	is	ADV
uva.x030312957	330	5	,	,	PUNCT
uva.x030312957	330	6	there	there	PRON
uva.x030312957	330	7	is	be	VERB
uva.x030312957	330	8	one	one	NUM
uva.x030312957	330	9	,	,	PUNCT
uva.x030312957	330	10	and	and	CCONJ
uva.x030312957	330	11	only	only	ADV
uva.x030312957	330	12	one	one	NUM
uva.x030312957	330	13	,	,	PUNCT
uva.x030312957	330	14	root	root	NOUN
uva.x030312957	330	15	of	of	ADP
uva.x030312957	330	16	ar+1	ar+1	NOUN
uva.x030312957	330	17	(	(	PUNCT
uva.x030312957	330	18	2	2	NUM
uva.x030312957	330	19	)	)	PUNCT
uva.x030312957	330	20	=	=	SYM
uva.x030312957	330	21	0	0	X
uva.x030312957	330	22	greater	great	ADJ
uva.x030312957	330	23	than	than	ADP
uva.x030312957	330	24	the	the	DET
uva.x030312957	330	25	greatest	great	ADJ
uva.x030312957	330	26	root	root	NOUN
uva.x030312957	330	27	of	of	ADP
uva.x030312957	330	28	a	a	PRON
uva.x030312957	330	29	,	,	PUNCT
uva.x030312957	330	30	(	(	PUNCT
uva.x030312957	330	31	x	x	NOUN
uva.x030312957	330	32	)	)	PUNCT
uva.x030312957	330	33	=	=	SYM
uva.x030312957	330	34	0	0	NUM
uva.x030312957	330	35	.	.	PUNCT
uva.x030312957	331	1	next	next	ADV
uva.x030312957	331	2	consider	consider	VERB
uva.x030312957	331	3	the	the	DET
uva.x030312957	331	4	root	root	NOUN
uva.x030312957	331	5	op-1	op-1	SPACE
uva.x030312957	331	6	,	,	PUNCT
uva.x030312957	331	7	which	which	PRON
uva.x030312957	331	8	is	be	AUX
uva.x030312957	331	9	the	the	DET
uva.x030312957	331	10	second	second	ADV
uva.x030312957	331	11	largest	large	ADJ
uva.x030312957	331	12	root	root	NOUN
uva.x030312957	331	13	of	of	ADP
uva.x030312957	331	14	af(x	af(x	SPACE
uva.x030312957	331	15	)	)	PUNCT
uva.x030312957	331	16	=	=	PROPN
uva.x030312957	331	17	0	0	NUM
uva.x030312957	331	18	.	.	PUNCT
uva.x030312957	332	1	in	in	ADP
uva.x030312957	332	2	the	the	DET
uva.x030312957	332	3	chain	chain	NOUN
uva.x030312957	332	4	1	1	NUM
uva.x030312957	332	5	,	,	PUNCT
uva.x030312957	332	6	41(ar-1	41(ar-1	NUM
uva.x030312957	332	7	)	)	PUNCT
uva.x030312957	332	8	,	,	PUNCT
uva.x030312957	332	9	42	42	NUM
uva.x030312957	332	10	(	(	PUNCT
uva.x030312957	332	11	ar-1	ar-1	PROPN
uva.x030312957	332	12	)	)	PUNCT
uva.x030312957	332	13	,	,	PUNCT
uva.x030312957	332	14	...	...	PUNCT
uva.x030312957	332	15	,	,	PUNCT
uva.x030312957	332	16	ar-1(ar-1	ar-1(ar-1	ADJ
uva.x030312957	332	17	)	)	PUNCT
uva.x030312957	332	18	,	,	PUNCT
uva.x030312957	332	19	a.	a.	PROPN
uva.x030312957	332	20	(	(	PUNCT
uva.x030312957	332	21	ar-1	ar-1	PROPN
uva.x030312957	332	22	)	)	PUNCT
uva.x030312957	332	23	,	,	PUNCT
uva.x030312957	332	24	arti(ar-1	arti(ar-1	PROPN
uva.x030312957	332	25	)	)	PUNCT
uva.x030312957	332	26	,	,	PUNCT
uva.x030312957	332	27	since	since	SCONJ
uva.x030312957	332	28	a	a	PRON
uva.x030312957	332	29	,	,	PUNCT
uva.x030312957	332	30	(	(	PUNCT
uva.x030312957	332	31	ar-1	ar-1	SPACE
uva.x030312957	332	32	)	)	PUNCT
uva.x030312957	332	33	=	=	PROPN
uva.x030312957	332	34	0	0	NUM
uva.x030312957	332	35	,	,	PUNCT
uva.x030312957	332	36	then	then	ADV
uva.x030312957	332	37	by	by	ADP
uva.x030312957	332	38	(	(	PUNCT
uva.x030312957	332	39	38	38	NUM
uva.x030312957	332	40	)	)	PUNCT
uva.x030312957	332	41	ar-1	ar-1	ADP
uva.x030312957	332	42	(	(	PUNCT
uva.x030312957	332	43	ar-1	ar-1	NOUN
uva.x030312957	332	44	)	)	PUNCT
uva.x030312957	332	45	and	and	CCONJ
uva.x030312957	332	46	art1	art1	VERB
uva.x030312957	332	47	(	(	PUNCT
uva.x030312957	332	48	ar-1	ar-1	NOUN
uva.x030312957	332	49	)	)	PUNCT
uva.x030312957	332	50	have	have	VERB
uva.x030312957	332	51	opposite	opposite	ADJ
uva.x030312957	332	52	signs	sign	NOUN
uva.x030312957	332	53	.	.	PUNCT
uva.x030312957	333	1	from	from	ADP
uva.x030312957	333	2	this	this	PRON
uva.x030312957	333	3	it	it	PRON
uva.x030312957	333	4	follows	follow	VERB
uva.x030312957	333	5	that	that	SCONJ
uva.x030312957	333	6	(	(	PUNCT
uva.x030312957	333	7	a	a	X
uva.x030312957	333	8	)	)	PUNCT
uva.x030312957	333	9	ar-1	ar-1	NOUN
uva.x030312957	333	10	(	(	PUNCT
uva.x030312957	333	11	ar-1	ar-1	ADP
uva.x030312957	333	12	+	+	NOUN
uva.x030312957	333	13	h	h	NOUN
uva.x030312957	333	14	)	)	PUNCT
uva.x030312957	333	15	and	and	CCONJ
uva.x030312957	333	16	ar+1	ar+1	VERB
uva.x030312957	333	17	(	(	PUNCT
uva.x030312957	333	18	ar-1	ar-1	ADP
uva.x030312957	333	19	+	+	PRON
uva.x030312957	333	20	h	h	NOUN
uva.x030312957	333	21	)	)	PUNCT
uva.x030312957	333	22	have	have	VERB
uva.x030312957	333	23	opposite	opposite	ADJ
uva.x030312957	333	24	signs	sign	NOUN
uva.x030312957	333	25	,	,	PUNCT
uva.x030312957	333	26	as	as	SCONJ
uva.x030312957	333	27	they	they	PRON
uva.x030312957	333	28	have	have	VERB
uva.x030312957	333	29	the	the	DET
uva.x030312957	333	30	same	same	ADJ
uva.x030312957	333	31	sign	sign	NOUN
uva.x030312957	333	32	as	as	ADP
uva.x030312957	333	33	ar-1	ar-1	ADP
uva.x030312957	333	34	(	(	PUNCT
uva.x030312957	333	35	ar-1	ar-1	NOUN
uva.x030312957	333	36	)	)	PUNCT
uva.x030312957	333	37	and	and	CCONJ
uva.x030312957	333	38	ar+1	ar+1	VERB
uva.x030312957	333	39	(	(	PUNCT
uva.x030312957	333	40	-1	-1	X
uva.x030312957	333	41	)	)	PUNCT
uva.x030312957	333	42	respectively	respectively	ADV
uva.x030312957	333	43	.	.	PUNCT
uva.x030312957	334	1	the	the	DET
uva.x030312957	334	2	chain	chain	NOUN
uva.x030312957	334	3	(	(	PUNCT
uva.x030312957	334	4	iv	iv	X
uva.x030312957	334	5	)	)	PUNCT
uva.x030312957	334	6	1	1	NUM
uva.x030312957	334	7	,	,	PUNCT
uva.x030312957	334	8	41(ar-1	41(ar-1	NUM
uva.x030312957	334	9	+	+	NUM
uva.x030312957	334	10	h	h	NOUN
uva.x030312957	334	11	)	)	PUNCT
uva.x030312957	334	12	,	,	PUNCT
uva.x030312957	334	13	a2	a2	X
uva.x030312957	334	14	(	(	PUNCT
uva.x030312957	334	15	ar-1	ar-1	ADP
uva.x030312957	334	16	+	+	PRON
uva.x030312957	334	17	h	h	NOUN
uva.x030312957	334	18	)	)	PUNCT
uva.x030312957	334	19	,	,	PUNCT
uva.x030312957	334	20	...	...	PUNCT
uva.x030312957	334	21	,	,	PUNCT
uva.x030312957	334	22	ar-1	ar-1	ADP
uva.x030312957	334	23	(	(	PUNCT
uva.x030312957	334	24	ar-1	ar-1	ADP
uva.x030312957	334	25	+	+	PRON
uva.x030312957	334	26	h	h	NOUN
uva.x030312957	334	27	)	)	PUNCT
uva.x030312957	334	28	,	,	PUNCT
uva.x030312957	334	29	ar	ar	PROPN
uva.x030312957	334	30	(	(	PUNCT
uva.x030312957	334	31	ar-1	ar-1	ADP
uva.x030312957	334	32	+	+	PRON
uva.x030312957	334	33	h	h	NOUN
uva.x030312957	334	34	)	)	PUNCT
uva.x030312957	334	35	will	will	AUX
uva.x030312957	334	36	haver	haver	VERB
uva.x030312957	334	37	–	–	PUNCT
uva.x030312957	334	38	1	1	NUM
uva.x030312957	334	39	variations	variation	NOUN
uva.x030312957	334	40	,	,	PUNCT
uva.x030312957	334	41	since	since	SCONJ
uva.x030312957	334	42	there	there	PRON
uva.x030312957	334	43	are	be	VERB
uva.x030312957	334	44	r	r	NOUN
uva.x030312957	334	45	–	–	PUNCT
uva.x030312957	334	46	1	1	NUM
uva.x030312957	334	47	roots	root	NOUN
uva.x030312957	334	48	of	of	ADP
uva.x030312957	334	49	a	a	PRON
uva.x030312957	334	50	,	,	PUNCT
uva.x030312957	334	51	(	(	PUNCT
uva.x030312957	334	52	x	x	SYM
uva.x030312957	334	53	)	)	PUNCT
uva.x030312957	334	54	=	=	PUNCT
uva.x030312957	334	55	0	0	NUM
uva.x030312957	334	56	less	less	ADJ
uva.x030312957	334	57	than	than	ADP
uva.x030312957	334	58	ar–1	ar–1	ADJ
uva.x030312957	335	1	+	+	NOUN
uva.x030312957	335	2	h.	h.	NOUN
uva.x030312957	335	3	on	on	ADP
uva.x030312957	335	4	the	the	DET
uva.x030312957	335	5	other	other	ADJ
uva.x030312957	335	6	hand	hand	NOUN
uva.x030312957	335	7	there	there	PRON
uva.x030312957	335	8	will	will	AUX
uva.x030312957	335	9	be	be	AUX
uva.x030312957	335	10	only	only	ADV
uva.x030312957	335	11	r	r	NOUN
uva.x030312957	335	12	–	–	PUNCT
uva.x030312957	335	13	2	2	NUM
uva.x030312957	335	14	variations	variation	NOUN
uva.x030312957	335	15	in	in	ADP
uva.x030312957	335	16	(	(	PUNCT
uva.x030312957	335	17	v	v	NOUN
uva.x030312957	335	18	)	)	PUNCT
uva.x030312957	335	19	1	1	NUM
uva.x030312957	335	20	,	,	PUNCT
uva.x030312957	335	21	41(ar-1	41(ar-1	NUM
uva.x030312957	335	22	–	–	PUNCT
uva.x030312957	335	23	h	h	NOUN
uva.x030312957	335	24	)	)	PUNCT
uva.x030312957	335	25	,	,	PUNCT
uva.x030312957	335	26	a2	a2	X
uva.x030312957	335	27	(	(	PUNCT
uva.x030312957	335	28	ar-1	ar-1	ADP
uva.x030312957	335	29	–	–	PUNCT
uva.x030312957	335	30	h	h	PROPN
uva.x030312957	335	31	)	)	PUNCT
uva.x030312957	335	32	,	,	PUNCT
uva.x030312957	335	33	h	h	PROPN
uva.x030312957	335	34	)	)	PUNCT
uva.x030312957	335	35	,	,	PUNCT
uva.x030312957	335	36	...	...	PUNCT
uva.x030312957	335	37	,	,	PUNCT
uva.x030312957	335	38	4.-1	4.-1	NUM
uva.x030312957	335	39	(	(	PUNCT
uva.x030312957	335	40	07	07	NUM
uva.x030312957	335	41	-	-	SYM
uva.x030312957	335	42	1	1	NUM
uva.x030312957	335	43	h	h	NOUN
uva.x030312957	335	44	)	)	PUNCT
uva.x030312957	335	45	,	,	PUNCT
uva.x030312957	335	46	a	a	PRON
uva.x030312957	335	47	,	,	PUNCT
uva.x030312957	335	48	(	(	PUNCT
uva.x030312957	335	49	ar-1	ar-1	NOUN
uva.x030312957	335	50	-	-	PUNCT
uva.x030312957	335	51	h	h	NOUN
uva.x030312957	335	52	)	)	PUNCT
uva.x030312957	335	53	.	.	PUNCT
uva.x030312957	336	1	as	as	SCONJ
uva.x030312957	336	2	there	there	PRON
uva.x030312957	336	3	is	be	VERB
uva.x030312957	336	4	a	a	DET
uva.x030312957	336	5	variation	variation	NOUN
uva.x030312957	336	6	gained	gain	VERB
uva.x030312957	336	7	in	in	ADP
uva.x030312957	336	8	(	(	PUNCT
uva.x030312957	336	9	iv	iv	X
uva.x030312957	336	10	)	)	PUNCT
uva.x030312957	336	11	over	over	ADP
uva.x030312957	336	12	(	(	PUNCT
uva.x030312957	336	13	v	v	NOUN
uva.x030312957	336	14	)	)	PUNCT
uva.x030312957	336	15	and	and	CCONJ
uva.x030312957	336	16	is	be	AUX
uva.x030312957	336	17	gained	gain	VERB
uva.x030312957	336	18	by	by	ADP
uva.x030312957	336	19	the	the	DET
uva.x030312957	336	20	last	last	ADJ
uva.x030312957	336	21	function	function	NOUN
uva.x030312957	336	22	22	22	NUM
uva.x030312957	336	23	solution	solution	NOUN
uva.x030312957	336	24	of	of	ADP
uva.x030312957	336	25	the	the	DET
uva.x030312957	336	26	equation	equation	NOUN
uva.x030312957	336	27	of	of	ADP
uva.x030312957	336	28	secular	secular	ADJ
uva.x030312957	336	29	variation	variation	NOUN
uva.x030312957	336	30	1	1	NUM
uva.x030312957	336	31	of	of	ADP
uva.x030312957	336	32	the	the	DET
uva.x030312957	336	33	chain	chain	NOUN
uva.x030312957	336	34	,	,	PUNCT
uva.x030312957	336	35	a.	a.	PROPN
uva.x030312957	336	36	(	(	PUNCT
uva.x030312957	336	37	a	a	NOUN
uva.x030312957	336	38	)	)	PUNCT
uva.x030312957	336	39	,	,	PUNCT
uva.x030312957	336	40	changing	change	VERB
uva.x030312957	336	41	sign	sign	NOUN
uva.x030312957	336	42	on	on	ADP
uva.x030312957	336	43	passing	pass	VERB
uva.x030312957	336	44	through	through	ADP
uva.x030312957	336	45	the	the	DET
uva.x030312957	336	46	root	root	NOUN
uva.x030312957	336	47	on-1	on-1	NUM
uva.x030312957	336	48	,	,	PUNCT
uva.x030312957	336	49	then	then	ADV
uva.x030312957	336	50	in	in	ADP
uva.x030312957	336	51	(	(	PUNCT
uva.x030312957	336	52	v	v	NOUN
uva.x030312957	336	53	)	)	PUNCT
uva.x030312957	336	54	the	the	DET
uva.x030312957	336	55	last	last	ADJ
uva.x030312957	336	56	two	two	NUM
uva.x030312957	336	57	functions	function	NOUN
uva.x030312957	336	58	have	have	VERB
uva.x030312957	336	59	the	the	DET
uva.x030312957	336	60	same	same	ADJ
uva.x030312957	336	61	sign	sign	NOUN
uva.x030312957	336	62	,	,	PUNCT
uva.x030312957	336	63	but	but	CCONJ
uva.x030312957	336	64	in	in	ADP
uva.x030312957	336	65	(	(	PUNCT
uva.x030312957	336	66	iv	iv	X
uva.x030312957	336	67	)	)	PUNCT
uva.x030312957	336	68	they	they	PRON
uva.x030312957	336	69	must	must	AUX
uva.x030312957	336	70	have	have	VERB
uva.x030312957	336	71	opposite	opposite	ADJ
uva.x030312957	336	72	signs	sign	NOUN
uva.x030312957	336	73	.	.	PUNCT
uva.x030312957	337	1	that	that	PRON
uva.x030312957	337	2	is	is	ADV
uva.x030312957	337	3	(	(	PUNCT
uva.x030312957	337	4	b	b	NOUN
uva.x030312957	337	5	)	)	PUNCT
uva.x030312957	337	6	ar-1(a-1	ar-1(a-1	PROPN
uva.x030312957	337	7	+	+	PROPN
uva.x030312957	337	8	h	h	NOUN
uva.x030312957	337	9	)	)	PUNCT
uva.x030312957	337	10	and	and	CCONJ
uva.x030312957	337	11	a.	a.	NOUN
uva.x030312957	337	12	(	(	PUNCT
uva.x030312957	337	13	ar-1	ar-1	ADP
uva.x030312957	337	14	+	+	PRON
uva.x030312957	337	15	h	h	NOUN
uva.x030312957	337	16	)	)	PUNCT
uva.x030312957	337	17	will	will	AUX
uva.x030312957	337	18	have	have	VERB
uva.x030312957	337	19	opposite	opposite	ADJ
uva.x030312957	337	20	signs	sign	NOUN
uva.x030312957	337	21	.	.	PUNCT
uva.x030312957	338	1	in	in	ADP
uva.x030312957	338	2	the	the	DET
uva.x030312957	338	3	chain	chain	NOUN
uva.x030312957	338	4	(	(	PUNCT
uva.x030312957	338	5	vi	vi	PROPN
uva.x030312957	338	6	)	)	PUNCT
uva.x030312957	338	7	1	1	NUM
uva.x030312957	338	8	,	,	PUNCT
uva.x030312957	338	9	41(ar-1	41(ar-1	NUM
uva.x030312957	338	10	+	+	NUM
uva.x030312957	338	11	h	h	NOUN
uva.x030312957	338	12	)	)	PUNCT
uva.x030312957	338	13	,	,	PUNCT
uva.x030312957	338	14	a	a	PRON
uva.x030312957	338	15	,	,	PUNCT
uva.x030312957	338	16	(	(	PUNCT
uva.x030312957	338	17	qr-1	qr-1	NOUN
uva.x030312957	338	18	+	+	SYM
uva.x030312957	338	19	h	h	NOUN
uva.x030312957	338	20	)	)	PUNCT
uva.x030312957	338	21	,	,	PUNCT
uva.x030312957	338	22	...	...	PUNCT
uva.x030312957	338	23	,	,	PUNCT
uva.x030312957	338	24	ar-1	ar-1	ADP
uva.x030312957	338	25	(	(	PUNCT
uva.x030312957	338	26	ar-1	ar-1	ADP
uva.x030312957	338	27	+	+	PRON
uva.x030312957	338	28	h	h	NOUN
uva.x030312957	338	29	)	)	PUNCT
uva.x030312957	338	30	,	,	PUNCT
uva.x030312957	338	31	a	a	PRON
uva.x030312957	338	32	,	,	PUNCT
uva.x030312957	338	33	(	(	PUNCT
uva.x030312957	338	34	q-1	q-1	NUM
uva.x030312957	338	35	+	+	CCONJ
uva.x030312957	338	36	h	h	NOUN
uva.x030312957	338	37	)	)	PUNCT
uva.x030312957	338	38	,	,	PUNCT
uva.x030312957	338	39	art1	art1	VERB
uva.x030312957	338	40	(	(	PUNCT
uva.x030312957	338	41	ar-1	ar-1	ADP
uva.x030312957	338	42	+	+	PRON
uva.x030312957	338	43	h	h	NOUN
uva.x030312957	338	44	)	)	PUNCT
uva.x030312957	338	45	,	,	PUNCT
uva.x030312957	338	46	the	the	DET
uva.x030312957	338	47	functions	function	NOUN
uva.x030312957	338	48	up	up	ADP
uva.x030312957	338	49	to	to	ADP
uva.x030312957	338	50	and	and	CCONJ
uva.x030312957	338	51	including	include	VERB
uva.x030312957	338	52	a	a	PRON
uva.x030312957	338	53	,	,	PUNCT
uva.x030312957	338	54	(	(	PUNCT
uva.x030312957	338	55	qr-1	qr-1	NOUN
uva.x030312957	338	56	+	+	CCONJ
uva.x030312957	338	57	h	h	NOUN
uva.x030312957	338	58	)	)	PUNCT
uva.x030312957	338	59	are	be	AUX
uva.x030312957	338	60	the	the	DET
uva.x030312957	338	61	same	same	ADJ
uva.x030312957	338	62	as	as	ADP
uva.x030312957	338	63	in	in	ADP
uva.x030312957	338	64	(	(	PUNCT
uva.x030312957	338	65	iv	iv	X
uva.x030312957	338	66	)	)	PUNCT
uva.x030312957	338	67	above	above	ADV
uva.x030312957	338	68	,	,	PUNCT
uva.x030312957	338	69	and	and	CCONJ
uva.x030312957	338	70	hence	hence	ADV
uva.x030312957	338	71	there	there	PRON
uva.x030312957	338	72	are	be	VERB
uva.x030312957	338	73	r	r	NOUN
uva.x030312957	338	74	1	1	NUM
uva.x030312957	338	75	variations	variation	NOUN
uva.x030312957	338	76	in	in	ADP
uva.x030312957	338	77	this	this	DET
uva.x030312957	338	78	part	part	NOUN
uva.x030312957	338	79	of	of	ADP
uva.x030312957	338	80	the	the	DET
uva.x030312957	338	81	chain	chain	NOUN
uva.x030312957	338	82	(	(	PUNCT
uva.x030312957	338	83	vi	vi	NOUN
uva.x030312957	338	84	)	)	PUNCT
uva.x030312957	338	85	and	and	CCONJ
uva.x030312957	338	86	,	,	PUNCT
uva.x030312957	338	87	in	in	ADP
uva.x030312957	338	88	fact	fact	NOUN
uva.x030312957	338	89	,	,	PUNCT
uva.x030312957	338	90	we	we	PRON
uva.x030312957	338	91	shall	shall	AUX
uva.x030312957	338	92	show	show	VERB
uva.x030312957	338	93	there	there	PRON
uva.x030312957	338	94	are	be	VERB
uva.x030312957	338	95	only	only	ADV
uva.x030312957	338	96	r	r	NOUN
uva.x030312957	338	97	1	1	NUM
uva.x030312957	338	98	variations	variation	NOUN
uva.x030312957	338	99	in	in	ADP
uva.x030312957	338	100	the	the	DET
uva.x030312957	338	101	chain	chain	NOUN
uva.x030312957	338	102	(	(	PUNCT
uva.x030312957	338	103	vi	vi	NOUN
uva.x030312957	338	104	)	)	PUNCT
uva.x030312957	338	105	.	.	PUNCT
uva.x030312957	339	1	there	there	PRON
uva.x030312957	339	2	is	be	VERB
uva.x030312957	339	3	no	no	DET
uva.x030312957	339	4	variation	variation	NOUN
uva.x030312957	339	5	between	between	ADP
uva.x030312957	339	6	a	a	PRON
uva.x030312957	339	7	,	,	PUNCT
uva.x030312957	339	8	(	(	PUNCT
uva.x030312957	339	9	qr-1	qr-1	NOUN
uva.x030312957	339	10	+	+	CCONJ
uva.x030312957	339	11	h	h	NOUN
uva.x030312957	339	12	)	)	PUNCT
uva.x030312957	339	13	and	and	CCONJ
uva.x030312957	339	14	art1	art1	VERB
uva.x030312957	339	15	(	(	PUNCT
uva.x030312957	339	16	qr-1	qr-1	ADP
uva.x030312957	339	17	+	+	NUM
uva.x030312957	339	18	h	h	NOUN
uva.x030312957	339	19	)	)	PUNCT
uva.x030312957	339	20	,	,	PUNCT
uva.x030312957	339	21	because	because	SCONJ
uva.x030312957	339	22	by	by	ADP
uva.x030312957	339	23	(	(	PUNCT
uva.x030312957	339	24	a	a	X
uva.x030312957	339	25	)	)	PUNCT
uva.x030312957	339	26	ar-1(ar-1	ar-1(ar-1	ADJ
uva.x030312957	339	27	+	+	PROPN
uva.x030312957	339	28	h	h	PROPN
uva.x030312957	339	29	)	)	PUNCT
uva.x030312957	339	30	and	and	CCONJ
uva.x030312957	339	31	ar+1	ar+1	VERB
uva.x030312957	339	32	(	(	PUNCT
uva.x030312957	339	33	ar-1	ar-1	ADP
uva.x030312957	339	34	+	+	PRON
uva.x030312957	339	35	h	h	NOUN
uva.x030312957	339	36	)	)	PUNCT
uva.x030312957	339	37	have	have	VERB
uva.x030312957	339	38	opposite	opposite	ADJ
uva.x030312957	339	39	signs	sign	NOUN
uva.x030312957	339	40	,	,	PUNCT
uva.x030312957	339	41	and	and	CCONJ
uva.x030312957	339	42	by	by	ADP
uva.x030312957	339	43	(	(	PUNCT
uva.x030312957	339	44	b	b	NOUN
uva.x030312957	339	45	)	)	PUNCT
uva.x030312957	339	46	ar-1(qr-1	ar-1(qr-1	VERB
uva.x030312957	339	47	+	+	PROPN
uva.x030312957	339	48	h	h	NOUN
uva.x030312957	339	49	)	)	PUNCT
uva.x030312957	339	50	and	and	CCONJ
uva.x030312957	339	51	a	a	PRON
uva.x030312957	339	52	,	,	PUNCT
uva.x030312957	339	53	(	(	PUNCT
uva.x030312957	339	54	qr-1	qr-1	NOUN
uva.x030312957	339	55	+	+	CCONJ
uva.x030312957	339	56	h	h	NOUN
uva.x030312957	339	57	)	)	PUNCT
uva.x030312957	339	58	have	have	VERB
uva.x030312957	339	59	opposite	opposite	ADJ
uva.x030312957	339	60	signs	sign	NOUN
uva.x030312957	339	61	,	,	PUNCT
uva.x030312957	339	62	hence	hence	ADV
uva.x030312957	339	63	ar	ar	PROPN
uva.x030312957	339	64	(	(	PUNCT
uva.x030312957	339	65	ar-1	ar-1	ADP
uva.x030312957	339	66	+	+	PRON
uva.x030312957	339	67	h	h	NOUN
uva.x030312957	339	68	)	)	PUNCT
uva.x030312957	339	69	and	and	CCONJ
uva.x030312957	339	70	ar+1(qr-1	ar+1(qr-1	ADJ
uva.x030312957	339	71	+	+	NOUN
uva.x030312957	339	72	h	h	NOUN
uva.x030312957	339	73	)	)	PUNCT
uva.x030312957	339	74	have	have	VERB
uva.x030312957	339	75	same	same	ADJ
uva.x030312957	339	76	sings	sing	NOUN
uva.x030312957	339	77	.	.	PUNCT
uva.x030312957	340	1	therefore	therefore	ADV
uva.x030312957	340	2	there	there	PRON
uva.x030312957	340	3	are	be	VERB
uva.x030312957	340	4	r	r	NOUN
uva.x030312957	340	5	1	1	NUM
uva.x030312957	340	6	variations	variation	NOUN
uva.x030312957	340	7	in	in	ADP
uva.x030312957	340	8	sign	sign	NOUN
uva.x030312957	340	9	in	in	ADP
uva.x030312957	340	10	the	the	DET
uva.x030312957	340	11	chain	chain	NOUN
uva.x030312957	340	12	(	(	PUNCT
uva.x030312957	340	13	vi	vi	NOUN
uva.x030312957	340	14	)	)	PUNCT
uva.x030312957	340	15	,	,	PUNCT
uva.x030312957	340	16	and	and	CCONJ
uva.x030312957	340	17	therefore	therefore	ADV
uva.x030312957	340	18	r	r	X
uva.x030312957	340	19	–	–	PUNCT
uva.x030312957	340	20	1	1	NUM
uva.x030312957	340	21	roots	root	NOUN
uva.x030312957	340	22	of	of	ADP
uva.x030312957	340	23	ar+1(x	ar+1(x	NOUN
uva.x030312957	340	24	)	)	PUNCT
uva.x030312957	340	25	=	=	PROPN
uva.x030312957	340	26	0	0	NUM
uva.x030312957	340	27	less	less	ADJ
uva.x030312957	340	28	than	than	ADP
uva.x030312957	340	29	ar-1	ar-1	ADP
uva.x030312957	340	30	+	+	PROPN
uva.x030312957	340	31	h	h	NOUN
uva.x030312957	340	32	,	,	PUNCT
uva.x030312957	340	33	or	or	CCONJ
uva.x030312957	340	34	less	less	ADJ
uva.x030312957	340	35	than	than	ADP
uva.x030312957	340	36	ar-1	ar-1	VERB
uva.x030312957	340	37	.	.	PUNCT
uva.x030312957	341	1	the	the	DET
uva.x030312957	341	2	remaining	remain	VERB
uva.x030312957	341	3	two	two	NUM
uva.x030312957	341	4	roots	root	NOUN
uva.x030312957	341	5	of	of	ADP
uva.x030312957	341	6	art1(x	art1(x	NOUN
uva.x030312957	341	7	)	)	PUNCT
uva.x030312957	341	8	=	=	NOUN
uva.x030312957	341	9	0	0	NUM
uva.x030312957	341	10	are	be	AUX
uva.x030312957	341	11	then	then	ADV
uva.x030312957	341	12	greater	great	ADJ
uva.x030312957	341	13	than	than	SCONJ
uva.x030312957	341	14	ar-1	ar-1	ADP
uva.x030312957	341	15	and	and	CCONJ
uva.x030312957	341	16	since	since	SCONJ
uva.x030312957	341	17	we	we	PRON
uva.x030312957	341	18	have	have	AUX
uva.x030312957	341	19	shown	show	VERB
uva.x030312957	341	20	that	that	DET
uva.x030312957	341	21	one	one	NOUN
uva.x030312957	341	22	,	,	PUNCT
uva.x030312957	341	23	but	but	CCONJ
uva.x030312957	341	24	only	only	ADV
uva.x030312957	341	25	one	one	NUM
uva.x030312957	341	26	,	,	PUNCT
uva.x030312957	341	27	of	of	ADP
uva.x030312957	341	28	these	these	PRON
uva.x030312957	341	29	is	be	AUX
uva.x030312957	341	30	greater	great	ADJ
uva.x030312957	341	31	than	than	ADP
uva.x030312957	341	32	qr	qr	NOUN
uva.x030312957	341	33	,	,	PUNCT
uva.x030312957	341	34	then	then	ADV
uva.x030312957	341	35	the	the	DET
uva.x030312957	341	36	other	other	ADJ
uva.x030312957	341	37	one	one	NOUN
uva.x030312957	341	38	falls	fall	VERB
uva.x030312957	341	39	between	between	ADP
uva.x030312957	341	40	qr-1	qr-1	ADP
uva.x030312957	341	41	and	and	CCONJ
uva.x030312957	341	42	@r	@r	VERB
uva.x030312957	341	43	.	.	PUNCT
uva.x030312957	342	1	continuing	continue	VERB
uva.x030312957	342	2	this	this	DET
uva.x030312957	342	3	process	process	NOUN
uva.x030312957	342	4	it	it	PRON
uva.x030312957	342	5	is	be	AUX
uva.x030312957	342	6	easy	easy	ADJ
uva.x030312957	342	7	to	to	PART
uva.x030312957	342	8	show	show	VERB
uva.x030312957	342	9	that	that	SCONJ
uva.x030312957	342	10	each	each	DET
uva.x030312957	342	11	root	root	NOUN
uva.x030312957	342	12	in	in	ADP
uva.x030312957	342	13	succession	succession	NOUN
uva.x030312957	342	14	of	of	ADP
uva.x030312957	342	15	ar	ar	PROPN
uva.x030312957	342	16	(	(	PUNCT
uva.x030312957	342	17	2	2	NUM
uva.x030312957	342	18	)	)	PUNCT
uva.x030312957	342	19	=	=	SYM
uva.x030312957	342	20	0	0	NUM
uva.x030312957	342	21	falls	fall	VERB
uva.x030312957	342	22	between	between	ADP
uva.x030312957	342	23	successive	successive	ADJ
uva.x030312957	342	24	roots	root	NOUN
uva.x030312957	342	25	of	of	ADP
uva.x030312957	342	26	ar+1(x	ar+1(x	NOUN
uva.x030312957	342	27	)	)	PUNCT
uva.x030312957	342	28	=	=	PROPN
uva.x030312957	342	29	0	0	NUM
uva.x030312957	342	30	,	,	PUNCT
uva.x030312957	342	31	going	go	VERB
uva.x030312957	342	32	down	down	ADP
uva.x030312957	342	33	in	in	ADP
uva.x030312957	342	34	order	order	NOUN
uva.x030312957	342	35	of	of	ADP
uva.x030312957	342	36	magnitude	magnitude	NOUN
uva.x030312957	342	37	.	.	PUNCT
uva.x030312957	343	1	finally	finally	ADV
uva.x030312957	343	2	for	for	ADP
uva.x030312957	343	3	an	an	PRON
uva.x030312957	343	4	,	,	PUNCT
uva.x030312957	343	5	in	in	ADP
uva.x030312957	343	6	the	the	DET
uva.x030312957	343	7	chain	chain	NOUN
uva.x030312957	343	8	1	1	NUM
uva.x030312957	343	9	,	,	PUNCT
uva.x030312957	343	10	41(ai	41(ai	PROPN
uva.x030312957	343	11	)	)	PUNCT
uva.x030312957	343	12	,	,	PUNCT
uva.x030312957	343	13	a2	a2	X
uva.x030312957	343	14	(	(	PUNCT
uva.x030312957	343	15	ai	ai	PROPN
uva.x030312957	343	16	)	)	PUNCT
uva.x030312957	343	17	,	,	PUNCT
uva.x030312957	343	18	...	...	PUNCT
uva.x030312957	343	19	,	,	PUNCT
uva.x030312957	343	20	ar-1(ai	ar-1(ai	ADV
uva.x030312957	343	21	)	)	PUNCT
uva.x030312957	343	22	,	,	PUNCT
uva.x030312957	343	23	a	a	DET
uva.x030312957	343	24	,	,	PUNCT
uva.x030312957	343	25	(	(	PUNCT
uva.x030312957	343	26	qi	qi	PROPN
uva.x030312957	343	27	)	)	PUNCT
uva.x030312957	343	28	,	,	PUNCT
uva.x030312957	343	29	ar+1(ai	ar+1(ai	ADV
uva.x030312957	343	30	)	)	PUNCT
uva.x030312957	343	31	ar-1(qı	ar-1(qı	SPACE
uva.x030312957	343	32	)	)	PUNCT
uva.x030312957	343	33	and	and	CCONJ
uva.x030312957	343	34	ar+1	ar+1	NOUN
uva.x030312957	343	35	(	(	PUNCT
uva.x030312957	343	36	ai	ai	NOUN
uva.x030312957	343	37	)	)	PUNCT
uva.x030312957	343	38	have	have	VERB
uva.x030312957	343	39	opposite	opposite	ADJ
uva.x030312957	343	40	signs	sign	NOUN
uva.x030312957	343	41	,	,	PUNCT
uva.x030312957	343	42	since	since	SCONJ
uva.x030312957	343	43	ar	ar	PROPN
uva.x030312957	343	44	(	(	PUNCT
uva.x030312957	343	45	q1	q1	PROPN
uva.x030312957	343	46	)	)	PUNCT
uva.x030312957	343	47	=	=	PROPN
uva.x030312957	343	48	0	0	X
uva.x030312957	343	49	.	.	PUNCT
uva.x030312957	344	1	this	this	PRON
uva.x030312957	344	2	is	be	AUX
uva.x030312957	344	3	likewise	likewise	ADV
uva.x030312957	344	4	true	true	ADJ
uva.x030312957	344	5	of	of	ADP
uva.x030312957	344	6	ar-1(q1	ar-1(q1	ADV
uva.x030312957	344	7	+	+	NUM
uva.x030312957	344	8	h	h	PROPN
uva.x030312957	344	9	)	)	PUNCT
uva.x030312957	344	10	and	and	CCONJ
uva.x030312957	344	11	arti	arti	NOUN
uva.x030312957	344	12	(	(	PUNCT
uva.x030312957	344	13	ai	ai	VERB
uva.x030312957	344	14	+	+	PRON
uva.x030312957	344	15	h	h	NOUN
uva.x030312957	344	16	)	)	PUNCT
uva.x030312957	344	17	as	as	SCONJ
uva.x030312957	344	18	they	they	PRON
uva.x030312957	344	19	have	have	VERB
uva.x030312957	344	20	the	the	DET
uva.x030312957	344	21	same	same	ADJ
uva.x030312957	344	22	sign	sign	NOUN
uva.x030312957	344	23	as	as	ADP
uva.x030312957	344	24	ar-1(qı	ar-1(qı	SPACE
uva.x030312957	344	25	)	)	PUNCT
uva.x030312957	344	26	and	and	CCONJ
uva.x030312957	344	27	ar+1(q1	ar+1(q1	SPACE
uva.x030312957	344	28	)	)	PUNCT
uva.x030312957	344	29	respectively	respectively	ADV
uva.x030312957	344	30	.	.	PUNCT
uva.x030312957	345	1	in	in	ADP
uva.x030312957	345	2	the	the	DET
uva.x030312957	345	3	chain	chain	NOUN
uva.x030312957	345	4	(	(	PUNCT
uva.x030312957	345	5	vii	vii	PROPN
uva.x030312957	345	6	)	)	PUNCT
uva.x030312957	345	7	1	1	NUM
uva.x030312957	345	8	,	,	PUNCT
uva.x030312957	345	9	41(qi	41(qi	NUM
uva.x030312957	345	10	–	–	PUNCT
uva.x030312957	345	11	h	h	PROPN
uva.x030312957	345	12	)	)	PUNCT
uva.x030312957	345	13	,	,	PUNCT
uva.x030312957	345	14	a2	a2	X
uva.x030312957	345	15	(	(	PUNCT
uva.x030312957	345	16	q1	q1	PROPN
uva.x030312957	345	17	–	–	PUNCT
uva.x030312957	345	18	h	h	NOUN
uva.x030312957	345	19	)	)	PUNCT
uva.x030312957	345	20	,	,	PUNCT
uva.x030312957	345	21	..	..	PROPN
uva.x030312957	345	22	,	,	PUNCT
uva.x030312957	345	23	ar-1(au	ar-1(au	ADJ
uva.x030312957	345	24	h	h	NOUN
uva.x030312957	345	25	)	)	PUNCT
uva.x030312957	345	26	,	,	PUNCT
uva.x030312957	345	27	a	a	DET
uva.x030312957	345	28	,	,	PUNCT
uva.x030312957	345	29	(	(	PUNCT
uva.x030312957	345	30	ai	ai	NOUN
uva.x030312957	345	31	–	–	PUNCT
uva.x030312957	345	32	h	h	NOUN
uva.x030312957	345	33	)	)	PUNCT
uva.x030312957	345	34	there	there	PRON
uva.x030312957	345	35	are	be	VERB
uva.x030312957	345	36	no	no	DET
uva.x030312957	345	37	variations	variation	NOUN
uva.x030312957	345	38	,	,	PUNCT
uva.x030312957	345	39	qu	qu	PROPN
uva.x030312957	345	40	–	–	PUNCT
uva.x030312957	345	41	h	h	PROPN
uva.x030312957	345	42	being	be	AUX
uva.x030312957	345	43	smaller	small	ADJ
uva.x030312957	345	44	than	than	ADP
uva.x030312957	345	45	any	any	DET
uva.x030312957	345	46	root	root	NOUN
uva.x030312957	345	47	of	of	ADP
uva.x030312957	345	48	a	a	PRON
uva.x030312957	345	49	,	,	PUNCT
uva.x030312957	345	50	(	(	PUNCT
uva.x030312957	345	51	x	x	NOUN
uva.x030312957	345	52	)	)	PUNCT
uva.x030312957	345	53	=	=	SYM
uva.x030312957	345	54	0	0	NUM
uva.x030312957	345	55	.	.	PUNCT
uva.x030312957	346	1	however	however	ADV
uva.x030312957	346	2	,	,	PUNCT
uva.x030312957	346	3	in	in	ADP
uva.x030312957	346	4	the	the	DET
uva.x030312957	346	5	chain	chain	NOUN
uva.x030312957	346	6	(	(	PUNCT
uva.x030312957	346	7	viii	viii	PROPN
uva.x030312957	346	8	)	)	PUNCT
uva.x030312957	346	9	1	1	NUM
uva.x030312957	346	10	,	,	PUNCT
uva.x030312957	346	11	41(a1	41(a1	NUM
uva.x030312957	346	12	+	+	NUM
uva.x030312957	346	13	h	h	NOUN
uva.x030312957	346	14	)	)	PUNCT
uva.x030312957	346	15	,	,	PUNCT
uva.x030312957	346	16	a2	a2	X
uva.x030312957	346	17	(	(	PUNCT
uva.x030312957	346	18	a1	a1	PROPN
uva.x030312957	346	19	+	+	CCONJ
uva.x030312957	346	20	h	h	NOUN
uva.x030312957	346	21	)	)	PUNCT
uva.x030312957	346	22	,	,	PUNCT
uva.x030312957	346	23	...	...	PUNCT
uva.x030312957	346	24	,	,	PUNCT
uva.x030312957	346	25	ar-1(a1	ar-1(a1	PROPN
uva.x030312957	346	26	+	+	NUM
uva.x030312957	346	27	h	h	NOUN
uva.x030312957	346	28	)	)	PUNCT
uva.x030312957	346	29	,	,	PUNCT
uva.x030312957	346	30	a.	a.	PROPN
uva.x030312957	346	31	(	(	PUNCT
uva.x030312957	346	32	q1	q1	PROPN
uva.x030312957	346	33	+	+	CCONJ
uva.x030312957	346	34	h	h	PROPN
uva.x030312957	346	35	)	)	PUNCT
uva.x030312957	346	36	there	there	PRON
uva.x030312957	346	37	is	be	VERB
uva.x030312957	346	38	one	one	NUM
uva.x030312957	346	39	variation	variation	NOUN
uva.x030312957	346	40	,	,	PUNCT
uva.x030312957	346	41	one	one	NUM
uva.x030312957	346	42	root	root	NOUN
uva.x030312957	346	43	oi	oi	INTJ
uva.x030312957	346	44	,	,	PUNCT
uva.x030312957	346	45	of	of	ADP
uva.x030312957	346	46	a	a	PRON
uva.x030312957	346	47	,	,	PUNCT
uva.x030312957	346	48	(	(	PUNCT
uva.x030312957	346	49	x	x	SYM
uva.x030312957	346	50	)	)	PUNCT
uva.x030312957	346	51	=	=	PUNCT
uva.x030312957	346	52	0	0	PUNCT
uva.x030312957	346	53	being	be	AUX
uva.x030312957	346	54	less	less	ADJ
uva.x030312957	346	55	than	than	ADP
uva.x030312957	346	56	ai	ai	VERB
uva.x030312957	346	57	th	th	VERB
uva.x030312957	346	58	.	.	PUNCT
uva.x030312957	347	1	being	be	AUX
uva.x030312957	347	2	no	no	DET
uva.x030312957	347	3	variation	variation	NOUN
uva.x030312957	347	4	in	in	ADP
uva.x030312957	347	5	(	(	PUNCT
uva.x030312957	347	6	vii	vii	NOUN
uva.x030312957	347	7	)	)	PUNCT
uva.x030312957	347	8	,	,	PUNCT
uva.x030312957	347	9	while	while	SCONJ
uva.x030312957	347	10	there	there	PRON
uva.x030312957	347	11	is	be	VERB
uva.x030312957	347	12	one	one	NUM
uva.x030312957	347	13	in	in	ADP
uva.x030312957	347	14	(	(	PUNCT
uva.x030312957	347	15	viii	viii	PROPN
uva.x030312957	347	16	)	)	PUNCT
uva.x030312957	347	17	,	,	PUNCT
uva.x030312957	347	18	which	which	PRON
uva.x030312957	347	19	occurs	occur	VERB
uva.x030312957	347	20	between	between	ADP
uva.x030312957	347	21	the	the	DET
uva.x030312957	347	22	last	last	ADJ
uva.x030312957	347	23	two	two	NUM
uva.x030312957	347	24	functions	function	NOUN
uva.x030312957	347	25	,	,	PUNCT
uva.x030312957	347	26	then	then	ADV
uva.x030312957	347	27	ar-1(qi	ar-1(qi	SPACE
uva.x030312957	347	28	–	–	PUNCT
uva.x030312957	347	29	h	h	NOUN
uva.x030312957	347	30	)	)	PUNCT
uva.x030312957	347	31	and	and	CCONJ
uva.x030312957	347	32	a.	a.	NOUN
uva.x030312957	347	33	(	(	PUNCT
uva.x030312957	347	34	qu	qu	PROPN
uva.x030312957	347	35	–	–	PUNCT
uva.x030312957	347	36	h	h	PROPN
uva.x030312957	347	37	)	)	PUNCT
uva.x030312957	347	38	have	have	VERB
uva.x030312957	347	39	the	the	DET
uva.x030312957	347	40	same	same	ADJ
uva.x030312957	347	41	sign	sign	NOUN
uva.x030312957	347	42	,	,	PUNCT
uva.x030312957	347	43	while	while	SCONJ
uva.x030312957	347	44	ar-1(ai	ar-1(ai	ADJ
uva.x030312957	347	45	+	+	CCONJ
uva.x030312957	347	46	h	h	NOUN
uva.x030312957	347	47	)	)	PUNCT
uva.x030312957	347	48	and	and	CCONJ
uva.x030312957	347	49	a	a	PRON
uva.x030312957	347	50	,	,	PUNCT
uva.x030312957	347	51	(	(	PUNCT
uva.x030312957	347	52	a1	a1	PROPN
uva.x030312957	347	53	+	+	CCONJ
uva.x030312957	347	54	h	h	NOUN
uva.x030312957	347	55	)	)	PUNCT
uva.x030312957	347	56	have	have	VERB
uva.x030312957	347	57	opposite	opposite	ADJ
uva.x030312957	347	58	signs	sign	NOUN
uva.x030312957	347	59	.	.	PUNCT
uva.x030312957	348	1	by	by	ADP
uva.x030312957	348	2	a	a	DET
uva.x030312957	348	3	method	method	NOUN
uva.x030312957	348	4	due	due	ADP
uva.x030312957	348	5	to	to	ADP
uva.x030312957	348	6	hermite	hermite	NOUN
uva.x030312957	348	7	23	23	NUM
uva.x030312957	348	8	next	next	ADV
uva.x030312957	348	9	in	in	ADP
uva.x030312957	348	10	the	the	DET
uva.x030312957	348	11	chain	chain	NOUN
uva.x030312957	348	12	1	1	NUM
uva.x030312957	348	13	,	,	PUNCT
uva.x030312957	348	14	41(qi	41(qi	NUM
uva.x030312957	348	15	–	–	PUNCT
uva.x030312957	348	16	h	h	PROPN
uva.x030312957	348	17	)	)	PUNCT
uva.x030312957	348	18	,	,	PUNCT
uva.x030312957	348	19	a2	a2	X
uva.x030312957	348	20	(	(	PUNCT
uva.x030312957	348	21	qi	qi	PROPN
uva.x030312957	348	22	–	–	PUNCT
uva.x030312957	348	23	h	h	PROPN
uva.x030312957	348	24	)	)	PUNCT
uva.x030312957	348	25	,	,	PUNCT
uva.x030312957	348	26	h	h	PROPN
uva.x030312957	348	27	)	)	PUNCT
uva.x030312957	348	28	,	,	PUNCT
uva.x030312957	348	29	...	...	PUNCT
uva.x030312957	348	30	,	,	PUNCT
uva.x030312957	348	31	ar-1(ai	ar-1(ai	ADV
uva.x030312957	348	32	a	a	X
uva.x030312957	348	33	–	–	PUNCT
uva.x030312957	348	34	(	(	PUNCT
uva.x030312957	348	35	a	a	DET
uva.x030312957	348	36	b	b	NOUN
uva.x030312957	348	37	)	)	PUNCT
uva.x030312957	348	38	,	,	PUNCT
uva.x030312957	348	39	a	a	DET
uva.x030312957	348	40	,	,	PUNCT
uva.x030312957	348	41	(	(	PUNCT
uva.x030312957	348	42	a	a	X
uva.x030312957	348	43	)	)	PUNCT
uva.x030312957	348	44	,	,	PUNCT
uva.x030312957	348	45	(	(	PUNCT
uva.x030312957	348	46	ix	ix	NOUN
uva.x030312957	348	47	)	)	PUNCT
uva.x030312957	348	48	arti(qi	arti(qi	PROPN
uva.x030312957	348	49	–	–	PUNCT
uva.x030312957	348	50	h	h	PROPN
uva.x030312957	348	51	)	)	PUNCT
uva.x030312957	348	52	the	the	DET
uva.x030312957	348	53	functions	function	NOUN
uva.x030312957	348	54	up	up	ADP
uva.x030312957	348	55	to	to	ADP
uva.x030312957	348	56	and	and	CCONJ
uva.x030312957	348	57	including	include	VERB
uva.x030312957	348	58	a	a	PRON
uva.x030312957	348	59	,	,	PUNCT
uva.x030312957	348	60	(	(	PUNCT
uva.x030312957	348	61	au	au	X
uva.x030312957	348	62	h	h	PROPN
uva.x030312957	348	63	)	)	PUNCT
uva.x030312957	348	64	are	be	AUX
uva.x030312957	348	65	identical	identical	ADJ
uva.x030312957	348	66	with	with	ADP
uva.x030312957	348	67	those	those	PRON
uva.x030312957	348	68	in	in	ADP
uva.x030312957	348	69	the	the	DET
uva.x030312957	348	70	chain	chain	NOUN
uva.x030312957	348	71	(	(	PUNCT
uva.x030312957	348	72	vii	vii	NOUN
uva.x030312957	348	73	)	)	PUNCT
uva.x030312957	348	74	,	,	PUNCT
uva.x030312957	348	75	and	and	CCONJ
uva.x030312957	348	76	there	there	PRON
uva.x030312957	348	77	will	will	AUX
uva.x030312957	348	78	be	be	AUX
uva.x030312957	348	79	no	no	DET
uva.x030312957	348	80	variations	variation	NOUN
uva.x030312957	348	81	in	in	ADP
uva.x030312957	348	82	that	that	DET
uva.x030312957	348	83	part	part	NOUN
uva.x030312957	348	84	of	of	ADP
uva.x030312957	348	85	the	the	DET
uva.x030312957	348	86	series	series	NOUN
uva.x030312957	348	87	(	(	PUNCT
uva.x030312957	348	88	ix	ix	PROPN
uva.x030312957	348	89	)	)	PUNCT
uva.x030312957	348	90	.	.	PUNCT
uva.x030312957	349	1	however	however	ADV
uva.x030312957	349	2	,	,	PUNCT
uva.x030312957	349	3	since	since	SCONJ
uva.x030312957	349	4	ar-1(qi	ar-1(qi	PROPN
uva.x030312957	349	5	–	–	PUNCT
uva.x030312957	349	6	h	h	NOUN
uva.x030312957	349	7	)	)	PUNCT
uva.x030312957	349	8	and	and	CCONJ
uva.x030312957	349	9	arti	arti	NOUN
uva.x030312957	349	10	(	(	PUNCT
uva.x030312957	349	11	ai	ai	PROPN
uva.x030312957	349	12	–	–	PUNCT
uva.x030312957	349	13	h	h	NOUN
uva.x030312957	349	14	)	)	PUNCT
uva.x030312957	349	15	have	have	VERB
uva.x030312957	349	16	opposite	opposite	ADJ
uva.x030312957	349	17	signs	sign	NOUN
uva.x030312957	349	18	,	,	PUNCT
uva.x030312957	349	19	and	and	CCONJ
uva.x030312957	349	20	ar-1(au	ar-1(au	PRON
uva.x030312957	349	21	–	–	PUNCT
uva.x030312957	349	22	h	h	NOUN
uva.x030312957	349	23	)	)	PUNCT
uva.x030312957	349	24	and	and	CCONJ
uva.x030312957	349	25	a	a	DET
uva.x030312957	349	26	,	,	PUNCT
uva.x030312957	349	27	(	(	PUNCT
uva.x030312957	349	28	ai	ai	PROPN
uva.x030312957	349	29	h	h	PROPN
uva.x030312957	349	30	)	)	PUNCT
uva.x030312957	349	31	have	have	VERB
uva.x030312957	349	32	same	same	ADJ
uva.x030312957	349	33	signs	sign	NOUN
uva.x030312957	349	34	,	,	PUNCT
uva.x030312957	349	35	then	then	ADV
uva.x030312957	349	36	a	a	DET
uva.x030312957	349	37	,	,	PUNCT
uva.x030312957	349	38	(	(	PUNCT
uva.x030312957	349	39	au	au	X
uva.x030312957	349	40	h	h	PROPN
uva.x030312957	349	41	)	)	PUNCT
uva.x030312957	349	42	and	and	CCONJ
uva.x030312957	349	43	ar+1	ar+1	INTJ
uva.x030312957	349	44	(	(	PUNCT
uva.x030312957	349	45	qu	qu	PROPN
uva.x030312957	349	46	–	–	PUNCT
uva.x030312957	349	47	h	h	PROPN
uva.x030312957	349	48	)	)	PUNCT
uva.x030312957	349	49	have	have	VERB
uva.x030312957	349	50	opposite	opposite	ADJ
uva.x030312957	349	51	signs	sign	NOUN
uva.x030312957	349	52	,	,	PUNCT
uva.x030312957	349	53	there	there	PRON
uva.x030312957	349	54	is	be	VERB
uva.x030312957	349	55	one	one	NUM
uva.x030312957	349	56	variation	variation	NOUN
uva.x030312957	349	57	between	between	ADP
uva.x030312957	349	58	the	the	DET
uva.x030312957	349	59	last	last	ADJ
uva.x030312957	349	60	two	two	NUM
uva.x030312957	349	61	functions	function	NOUN
uva.x030312957	349	62	in	in	ADP
uva.x030312957	349	63	(	(	PUNCT
uva.x030312957	349	64	ix	ix	PROPN
uva.x030312957	349	65	)	)	PUNCT
uva.x030312957	349	66	and	and	CCONJ
uva.x030312957	349	67	hence	hence	ADV
uva.x030312957	349	68	one	one	NUM
uva.x030312957	349	69	variation	variation	NOUN
uva.x030312957	349	70	for	for	ADP
uva.x030312957	349	71	the	the	DET
uva.x030312957	349	72	chain	chain	NOUN
uva.x030312957	349	73	.	.	PUNCT
uva.x030312957	350	1	it	it	PRON
uva.x030312957	350	2	follows	follow	VERB
uva.x030312957	350	3	,	,	PUNCT
uva.x030312957	350	4	then	then	ADV
uva.x030312957	350	5	,	,	PUNCT
uva.x030312957	350	6	that	that	DET
uva.x030312957	350	7	one	one	NOUN
uva.x030312957	350	8	,	,	PUNCT
uva.x030312957	350	9	and	and	CCONJ
uva.x030312957	350	10	only	only	ADV
uva.x030312957	350	11	one	one	NUM
uva.x030312957	350	12	,	,	PUNCT
uva.x030312957	350	13	root	root	NOUN
uva.x030312957	350	14	of	of	ADP
uva.x030312957	350	15	ar+1(x	ar+1(x	NOUN
uva.x030312957	350	16	)	)	PUNCT
uva.x030312957	350	17	0	0	NUM
uva.x030312957	350	18	,	,	PUNCT
uva.x030312957	350	19	is	be	AUX
uva.x030312957	350	20	smaller	small	ADJ
uva.x030312957	350	21	than	than	ADP
uva.x030312957	350	22	«	«	VERB
uva.x030312957	350	23	¡	¡	X
uva.x030312957	350	24	the	the	DET
uva.x030312957	350	25	smallest	small	ADJ
uva.x030312957	350	26	root	root	NOUN
uva.x030312957	350	27	of	of	ADP
uva.x030312957	350	28	a	a	PRON
uva.x030312957	350	29	,	,	PUNCT
uva.x030312957	350	30	(	(	PUNCT
uva.x030312957	350	31	x	x	NOUN
uva.x030312957	350	32	)	)	PUNCT
uva.x030312957	350	33	=	=	SYM
uva.x030312957	350	34	0	0	X
uva.x030312957	350	35	.	.	PUNCT
uva.x030312957	351	1	in	in	ADP
uva.x030312957	351	2	the	the	DET
uva.x030312957	351	3	set	set	NOUN
uva.x030312957	351	4	of	of	ADP
uva.x030312957	351	5	equations	equation	NOUN
uva.x030312957	351	6	,	,	PUNCT
uva.x030312957	351	7	41	41	NUM
uva.x030312957	351	8	(	(	PUNCT
uva.x030312957	351	9	x	x	PUNCT
uva.x030312957	351	10	)	)	PUNCT
uva.x030312957	351	11	=	=	PUNCT
uva.x030312957	351	12	0	0	NUM
uva.x030312957	351	13	,	,	PUNCT
uva.x030312957	351	14	42(x	42(x	NUM
uva.x030312957	351	15	)	)	PUNCT
uva.x030312957	351	16	=	=	PROPN
uva.x030312957	351	17	0	0	NUM
uva.x030312957	351	18	,	,	PUNCT
uva.x030312957	351	19	a3	a3	PROPN
uva.x030312957	351	20	(	(	PUNCT
uva.x030312957	351	21	x	x	NOUN
uva.x030312957	351	22	)	)	PUNCT
uva.x030312957	351	23	=	=	PUNCT
uva.x030312957	351	24	0	0	NUM
uva.x030312957	351	25	,	,	PUNCT
uva.x030312957	351	26	ar-1(x	ar-1(x	SPACE
uva.x030312957	351	27	)	)	PUNCT
uva.x030312957	351	28	=	=	PROPN
uva.x030312957	351	29	0	0	NUM
uva.x030312957	351	30	,	,	PUNCT
uva.x030312957	351	31	(	(	PUNCT
uva.x030312957	351	32	c	c	NOUN
uva.x030312957	351	33	)	)	PUNCT
uva.x030312957	351	34	4(x	4(x	NUM
uva.x030312957	351	35	)	)	PUNCT
uva.x030312957	351	36	=	=	PROPN
uva.x030312957	351	37	0	0	NUM
uva.x030312957	351	38	,	,	PUNCT
uva.x030312957	351	39	ar+1(x	ar+1(x	NOUN
uva.x030312957	351	40	)	)	PUNCT
uva.x030312957	351	41	=	=	PROPN
uva.x030312957	351	42	0	0	NUM
uva.x030312957	351	43	,	,	PUNCT
uva.x030312957	351	44	an-1(x	an-1(x	SPACE
uva.x030312957	351	45	)	)	PUNCT
uva.x030312957	351	46	=	=	PROPN
uva.x030312957	351	47	0	0	NUM
uva.x030312957	351	48	,	,	PUNCT
uva.x030312957	351	49	an	an	PRON
uva.x030312957	351	50	(	(	PUNCT
uva.x030312957	351	51	x	x	NOUN
uva.x030312957	351	52	)	)	PUNCT
uva.x030312957	351	53	=	=	SYM
uva.x030312957	351	54	0	0	NUM
uva.x030312957	351	55	,	,	PUNCT
uva.x030312957	351	56	an	an	DET
uva.x030312957	351	57	(	(	PUNCT
uva.x030312957	351	58	x	x	NOUN
uva.x030312957	351	59	)	)	PUNCT
uva.x030312957	351	60	0	0	NUM
uva.x030312957	351	61	is	be	AUX
uva.x030312957	351	62	our	our	PRON
uva.x030312957	351	63	equation	equation	NOUN
uva.x030312957	351	64	of	of	ADP
uva.x030312957	351	65	secular	secular	ADJ
uva.x030312957	351	66	variations	variation	NOUN
uva.x030312957	351	67	shown	show	VERB
uva.x030312957	351	68	in	in	ADP
uva.x030312957	351	69	(	(	PUNCT
uva.x030312957	351	70	30	30	NUM
uva.x030312957	351	71	)	)	PUNCT
uva.x030312957	351	72	,	,	PUNCT
uva.x030312957	351	73	an-1(x	an-1(x	SPACE
uva.x030312957	351	74	)	)	PUNCT
uva.x030312957	351	75	=	=	PUNCT
uva.x030312957	351	76	0	0	NUM
uva.x030312957	351	77	is	be	AUX
uva.x030312957	351	78	found	find	VERB
uva.x030312957	351	79	from	from	ADP
uva.x030312957	351	80	an	an	PRON
uva.x030312957	351	81	(	(	PUNCT
uva.x030312957	351	82	x	x	NOUN
uva.x030312957	351	83	)	)	PUNCT
uva.x030312957	351	84	=	=	PUNCT
uva.x030312957	351	85	0	0	NUM
uva.x030312957	351	86	by	by	ADP
uva.x030312957	351	87	leaving	leave	VERB
uva.x030312957	351	88	off	off	ADP
uva.x030312957	351	89	the	the	DET
uva.x030312957	351	90	last	last	ADJ
uva.x030312957	351	91	row	row	NOUN
uva.x030312957	351	92	and	and	CCONJ
uva.x030312957	351	93	column	column	NOUN
uva.x030312957	351	94	,	,	PUNCT
uva.x030312957	351	95	and	and	CCONJ
uva.x030312957	351	96	so	so	ADV
uva.x030312957	351	97	on	on	ADV
uva.x030312957	351	98	down	down	ADV
uva.x030312957	351	99	for	for	ADP
uva.x030312957	351	100	all	all	PRON
uva.x030312957	351	101	of	of	ADP
uva.x030312957	351	102	the	the	DET
uva.x030312957	351	103	equations	equation	NOUN
uva.x030312957	351	104	to	to	ADP
uva.x030312957	351	105	x	x	PROPN
uva.x030312957	351	106	,	,	PUNCT
uva.x030312957	351	107	01	01	NUM
uva.x030312957	351	108	,	,	PUNCT
uva.x030312957	351	109	2	2	NUM
uva.x030312957	351	110	a2	a2	X
uva.x030312957	351	111	(	(	PUNCT
uva.x030312957	351	112	x	x	NOUN
uva.x030312957	351	113	)	)	PUNCT
uva.x030312957	351	114	=	=	X
uva.x030312957	351	115	di	di	PROPN
uva.x030312957	351	116	,	,	PUNCT
uva.x030312957	351	117	1	1	NUM
uva.x030312957	351	118	02	02	NUM
uva.x030312957	351	119	,	,	PUNCT
uva.x030312957	351	120	1	1	NUM
uva.x030312957	351	121	,	,	PUNCT
uva.x030312957	351	122	0	0	NUM
uva.x030312957	351	123	a2	a2	NUM
uva.x030312957	351	124	,	,	PUNCT
uva.x030312957	351	125	2	2	NUM
uva.x030312957	351	126	and	and	CCONJ
uva.x030312957	351	127	41	41	NUM
uva.x030312957	351	128	(	(	PUNCT
uva.x030312957	351	129	x	x	SYM
uva.x030312957	351	130	)	)	PUNCT
uva.x030312957	351	131	=	=	NOUN
uva.x030312957	351	132	21	21	NUM
uva.x030312957	351	133	,	,	PUNCT
uva.x030312957	351	134	1	1	NUM
uva.x030312957	351	135	x	x	SYM
uva.x030312957	351	136	=	=	SYM
uva.x030312957	351	137	0	0	NUM
uva.x030312957	351	138	,	,	PUNCT
uva.x030312957	351	139	that	that	ADV
uva.x030312957	351	140	is	is	ADV
uva.x030312957	351	141	,	,	PUNCT
uva.x030312957	351	142	the	the	DET
uva.x030312957	351	143	several	several	ADJ
uva.x030312957	351	144	equations	equation	NOUN
uva.x030312957	351	145	are	be	AUX
uva.x030312957	351	146	the	the	DET
uva.x030312957	351	147	principal	principal	ADJ
uva.x030312957	351	148	minors	minor	NOUN
uva.x030312957	351	149	of	of	ADP
uva.x030312957	351	150	an	an	PRON
uva.x030312957	351	151	(	(	PUNCT
uva.x030312957	351	152	x	x	SYM
uva.x030312957	351	153	)	)	PUNCT
uva.x030312957	351	154	equated	equate	VERB
uva.x030312957	351	155	to	to	ADP
uva.x030312957	351	156	zero	zero	NUM
uva.x030312957	351	157	.	.	PUNCT
uva.x030312957	352	1	by	by	ADP
uva.x030312957	352	2	our	our	PRON
uva.x030312957	352	3	work	work	NOUN
uva.x030312957	352	4	above	above	ADV
uva.x030312957	352	5	,	,	PUNCT
uva.x030312957	352	6	the	the	DET
uva.x030312957	352	7	roots	root	NOUN
uva.x030312957	352	8	of	of	ADP
uva.x030312957	352	9	all	all	PRON
uva.x030312957	352	10	of	of	ADP
uva.x030312957	352	11	these	these	DET
uva.x030312957	352	12	equations	equation	NOUN
uva.x030312957	352	13	are	be	AUX
uva.x030312957	352	14	real	real	ADJ
uva.x030312957	352	15	,	,	PUNCT
uva.x030312957	352	16	the	the	DET
uva.x030312957	352	17	roots	root	NOUN
uva.x030312957	352	18	of	of	ADP
uva.x030312957	352	19	an-1(x	an-1(x	SPACE
uva.x030312957	352	20	)	)	PUNCT
uva.x030312957	352	21	=	=	PUNCT
uva.x030312957	352	22	0	0	NUM
uva.x030312957	353	1	lie	lie	VERB
uva.x030312957	353	2	one	one	NUM
uva.x030312957	353	3	by	by	ADP
uva.x030312957	353	4	one	one	NUM
uva.x030312957	353	5	between	between	ADP
uva.x030312957	353	6	successive	successive	ADJ
uva.x030312957	353	7	pairs	pair	NOUN
uva.x030312957	353	8	of	of	ADP
uva.x030312957	353	9	roots	root	NOUN
uva.x030312957	353	10	of	of	ADP
uva.x030312957	353	11	an	an	PRON
uva.x030312957	353	12	(	(	PUNCT
uva.x030312957	353	13	x	x	NOUN
uva.x030312957	353	14	)	)	PUNCT
uva.x030312957	353	15	=	=	SYM
uva.x030312957	353	16	0	0	NUM
uva.x030312957	353	17	,	,	PUNCT
uva.x030312957	353	18	the	the	DET
uva.x030312957	353	19	roots	root	NOUN
uva.x030312957	353	20	of	of	ADP
uva.x030312957	353	21	an-2(x	an-2(x	SPACE
uva.x030312957	353	22	)	)	PUNCT
uva.x030312957	353	23	=	=	X
uva.x030312957	353	24	0	0	X
uva.x030312957	353	25	lie	lie	VERB
uva.x030312957	353	26	similarly	similarly	ADV
uva.x030312957	353	27	between	between	ADP
uva.x030312957	353	28	each	each	DET
uva.x030312957	353	29	adjacent	adjacent	ADJ
uva.x030312957	353	30	pair	pair	NOUN
uva.x030312957	353	31	of	of	ADP
uva.x030312957	353	32	roots	root	NOUN
uva.x030312957	353	33	of	of	ADP
uva.x030312957	353	34	an–1(x	an–1(x	SPACE
uva.x030312957	353	35	)	)	PUNCT
uva.x030312957	353	36	=	=	PROPN
uva.x030312957	353	37	0	0	NUM
uva.x030312957	353	38	,	,	PUNCT
uva.x030312957	353	39	and	and	CCONJ
uva.x030312957	353	40	so	so	ADV
uva.x030312957	353	41	on	on	ADP
uva.x030312957	353	42	down	down	ADV
uva.x030312957	353	43	until	until	ADP
uva.x030312957	353	44	finally	finally	ADV
uva.x030312957	353	45	the	the	DET
uva.x030312957	353	46	root	root	NOUN
uva.x030312957	353	47	of	of	ADP
uva.x030312957	353	48	41	41	NUM
uva.x030312957	353	49	(	(	PUNCT
uva.x030312957	353	50	a	a	X
uva.x030312957	353	51	)	)	PUNCT
uva.x030312957	353	52	=	=	PROPN
uva.x030312957	353	53	0	0	PUNCT
uva.x030312957	353	54	lies	lie	VERB
uva.x030312957	353	55	between	between	ADP
uva.x030312957	353	56	the	the	DET
uva.x030312957	353	57	two	two	NUM
uva.x030312957	353	58	roots	root	NOUN
uva.x030312957	353	59	of	of	ADP
uva.x030312957	353	60	a2	a2	X
uva.x030312957	353	61	(	(	PUNCT
uva.x030312957	353	62	x	x	SYM
uva.x030312957	353	63	)	)	PUNCT
uva.x030312957	353	64	=	=	SYM
uva.x030312957	353	65	0	0	NUM
uva.x030312957	353	66	.	.	PUNCT
uva.x030312957	354	1	in	in	ADP
uva.x030312957	354	2	other	other	ADJ
uva.x030312957	354	3	words	word	NOUN
uva.x030312957	354	4	,	,	PUNCT
uva.x030312957	354	5	the	the	DET
uva.x030312957	354	6	set	set	NOUN
uva.x030312957	354	7	of	of	ADP
uva.x030312957	354	8	equations	equation	NOUN
uva.x030312957	354	9	(	(	PUNCT
uva.x030312957	354	10	c	c	X
uva.x030312957	354	11	)	)	PUNCT
uva.x030312957	354	12	form	form	NOUN
uva.x030312957	354	13	what	what	PRON
uva.x030312957	354	14	is	be	AUX
uva.x030312957	354	15	called	call	VERB
uva.x030312957	354	16	limiting	limit	VERB
uva.x030312957	354	17	equations	equation	NOUN
uva.x030312957	354	18	.	.	PUNCT
uva.x030312957	355	1	*	*	PUNCT
uva.x030312957	356	1	*	*	PUNCT
uva.x030312957	356	2	see	see	VERB
uva.x030312957	356	3	burnside	burnside	NOUN
uva.x030312957	356	4	and	and	CCONJ
uva.x030312957	356	5	panton	panton	PROPN
uva.x030312957	356	6	,	,	PUNCT
uva.x030312957	356	7	1904	1904	NUM
uva.x030312957	356	8	,	,	PUNCT
uva.x030312957	356	9	vol	vol	NOUN
uva.x030312957	356	10	.	.	PUNCT
uva.x030312957	357	1	i	i	PRON
uva.x030312957	357	2	,	,	PUNCT
uva.x030312957	357	3	page	page	NOUN
uva.x030312957	357	4	187	187	NUM
uva.x030312957	357	5	.	.	PUNCT
uva.x030312957	358	1	24	24	NUM
uva.x030312957	358	2	solution	solution	NOUN
uva.x030312957	358	3	of	of	ADP
uva.x030312957	358	4	the	the	DET
uva.x030312957	358	5	equation	equation	NOUN
uva.x030312957	358	6	of	of	ADP
uva.x030312957	358	7	secular	secular	ADJ
uva.x030312957	358	8	variation	variation	NOUN
uva.x030312957	358	9	the	the	DET
uva.x030312957	358	10	roots	root	NOUN
uva.x030312957	358	11	of	of	ADP
uva.x030312957	358	12	the	the	DET
uva.x030312957	358	13	equations	equation	NOUN
uva.x030312957	358	14	(	(	PUNCT
uva.x030312957	358	15	c	c	NOUN
uva.x030312957	358	16	)	)	PUNCT
uva.x030312957	358	17	when	when	SCONJ
uva.x030312957	358	18	indicated	indicate	VERB
uva.x030312957	358	19	by	by	ADP
uva.x030312957	358	20	points	point	NOUN
uva.x030312957	358	21	of	of	ADP
uva.x030312957	358	22	a	a	DET
uva.x030312957	358	23	straight	straight	ADJ
uva.x030312957	358	24	line	line	NOUN
uva.x030312957	358	25	would	would	AUX
uva.x030312957	358	26	be	be	AUX
uva.x030312957	358	27	represented	represent	VERB
uva.x030312957	358	28	by	by	ADP
uva.x030312957	358	29	the	the	DET
uva.x030312957	358	30	following	follow	VERB
uva.x030312957	358	31	scheme	scheme	NOUN
uva.x030312957	358	32	,	,	PUNCT
uva.x030312957	358	33	an	an	DET
uva.x030312957	358	34	(	(	PUNCT
uva.x030312957	358	35	x	x	NOUN
uva.x030312957	358	36	)	)	PUNCT
uva.x030312957	358	37	=	=	PUNCT
uva.x030312957	358	38	0	0	NUM
uva.x030312957	358	39	n	n	CCONJ
uva.x030312957	358	40	roots	root	NOUN
uva.x030312957	358	41	an-1(x	an-1(x	SPACE
uva.x030312957	358	42	)	)	PUNCT
uva.x030312957	358	43	=	=	PUNCT
uva.x030312957	358	44	0	0	NUM
uva.x030312957	358	45	n	n	CCONJ
uva.x030312957	358	46	1	1	NUM
uva.x030312957	358	47	roots	root	NOUN
uva.x030312957	358	48	an-2	an-2	NOUN
uva.x030312957	358	49	(	(	PUNCT
uva.x030312957	358	50	x	x	NOUN
uva.x030312957	358	51	)	)	PUNCT
uva.x030312957	358	52	=	=	PUNCT
uva.x030312957	358	53	0	0	NUM
uva.x030312957	358	54	n	n	CCONJ
uva.x030312957	358	55	2	2	NUM
uva.x030312957	358	56	roots	root	NOUN
uva.x030312957	358	57	44(x	44(x	SPACE
uva.x030312957	358	58	)	)	PUNCT
uva.x030312957	358	59	=	=	PROPN
uva.x030312957	358	60	0	0	NUM
uva.x030312957	358	61	4	4	NUM
uva.x030312957	358	62	roots	root	NOUN
uva.x030312957	358	63	a3	a3	PROPN
uva.x030312957	358	64	(	(	PUNCT
uva.x030312957	358	65	x	x	SYM
uva.x030312957	358	66	)	)	PUNCT
uva.x030312957	358	67	=	=	PUNCT
uva.x030312957	358	68	0	0	NUM
uva.x030312957	358	69	3	3	NUM
uva.x030312957	358	70	roots	root	NOUN
uva.x030312957	358	71	a2	a2	PROPN
uva.x030312957	358	72	(	(	PUNCT
uva.x030312957	358	73	x	x	SYM
uva.x030312957	358	74	)	)	PUNCT
uva.x030312957	358	75	=	=	PUNCT
uva.x030312957	358	76	0	0	NUM
uva.x030312957	358	77	2	2	NUM
uva.x030312957	358	78	roots	root	NOUN
uva.x030312957	358	79	41(a	41(a	NUM
uva.x030312957	358	80	)	)	PUNCT
uva.x030312957	358	81	=	=	PROPN
uva.x030312957	358	82	0	0	NUM
uva.x030312957	358	83	1	1	NUM
uva.x030312957	358	84	root	root	NOUN
uva.x030312957	358	85	we	we	PRON
uva.x030312957	358	86	shall	shall	AUX
uva.x030312957	358	87	conclude	conclude	VERB
uva.x030312957	358	88	by	by	ADP
uva.x030312957	358	89	taking	take	VERB
uva.x030312957	358	90	a	a	DET
uva.x030312957	358	91	specific	specific	ADJ
uva.x030312957	358	92	example	example	NOUN
uva.x030312957	358	93	with	with	ADP
uva.x030312957	358	94	numerical	numerical	ADJ
uva.x030312957	358	95	coefficients	coefficient	NOUN
uva.x030312957	358	96	.	.	PUNCT
uva.x030312957	359	1	ai	ai	VERB
uva.x030312957	359	2	,	,	PUNCT
uva.x030312957	359	3	=	=	SYM
uva.x030312957	359	4	2	2	NUM
uva.x030312957	359	5	,	,	PUNCT
uva.x030312957	359	6	3	3	NUM
uva.x030312957	359	7	,	,	PUNCT
uva.x030312957	359	8	a1	a1	PROPN
uva.x030312957	359	9	,	,	PUNCT
uva.x030312957	359	10	3	3	NUM
uva.x030312957	359	11	=	=	SYM
uva.x030312957	359	12	1	1	NUM
uva.x030312957	359	13	di	di	NOUN
uva.x030312957	359	14	.	.	PUNCT
uva.x030312957	360	1	ܕܐ	ܕܐ	ADP
uva.x030312957	360	2	4	4	NUM
uva.x030312957	360	3	5	5	NUM
uva.x030312957	360	4	,	,	PUNCT
uva.x030312957	360	5	with	with	ADP
uva.x030312957	360	6	the	the	DET
uva.x030312957	360	7	§	§	PROPN
uva.x030312957	360	8	7	7	NUM
uva.x030312957	360	9	.	.	PUNCT
uva.x030312957	360	10	illustrative	illustrative	ADJ
uva.x030312957	360	11	example	example	NOUN
uva.x030312957	360	12	.	.	PUNCT
uva.x030312957	361	1	take	take	VERB
uva.x030312957	361	2	as	as	ADP
uva.x030312957	361	3	illustrative	illustrative	ADJ
uva.x030312957	361	4	example	example	NOUN
uva.x030312957	361	5	n	n	CCONJ
uva.x030312957	361	6	following	follow	VERB
uva.x030312957	361	7	values	value	NOUN
uva.x030312957	361	8	for	for	ADP
uva.x030312957	361	9	ai	ai	NOUN
uva.x030312957	361	10	,	,	PUNCT
uva.x030312957	361	11	;	;	PUNCT
uva.x030312957	361	12	.	.	PUNCT
uva.x030312957	362	1	a1	a1	PROPN
uva.x030312957	362	2	,	,	PUNCT
uva.x030312957	362	3	2	2	NUM
uva.x030312957	362	4	5	5	NUM
uva.x030312957	362	5	,	,	PUNCT
uva.x030312957	362	6	a1	a1	PROPN
uva.x030312957	362	7	,	,	PUNCT
uva.x030312957	362	8	5	5	NUM
uva.x030312957	362	9	a2	a2	NUM
uva.x030312957	362	10	,	,	PUNCT
uva.x030312957	362	11	1	1	NUM
uva.x030312957	362	12	a2	a2	NOUN
uva.x030312957	362	13	,	,	PUNCT
uva.x030312957	362	14	3	3	NUM
uva.x030312957	362	15	a2	a2	NUM
uva.x030312957	362	16	,	,	PUNCT
uva.x030312957	362	17	4	4	NUM
uva.x030312957	362	18	22	22	NUM
uva.x030312957	362	19	,	,	PUNCT
uva.x030312957	362	20	6	6	NUM
uva.x030312957	362	21	=	=	SYM
uva.x030312957	362	22	3	3	NUM
uva.x030312957	362	23	,	,	PUNCT
uva.x030312957	362	24	5	5	NUM
uva.x030312957	362	25	,	,	PUNCT
uva.x030312957	362	26	a3	a3	PROPN
uva.x030312957	362	27	,	,	PUNCT
uva.x030312957	362	28	3	3	NUM
uva.x030312957	362	29	03	03	NUM
uva.x030312957	362	30	,	,	PUNCT
uva.x030312957	362	31	4	4	NUM
uva.x030312957	362	32	a3	a3	NUM
uva.x030312957	362	33	,	,	PUNCT
uva.x030312957	362	34	5	5	NUM
uva.x030312957	362	35	=	=	SYM
uva.x030312957	362	36	1	1	NUM
uva.x030312957	362	37	,	,	PUNCT
uva.x030312957	362	38	04	04	NUM
uva.x030312957	362	39	,	,	PUNCT
uva.x030312957	362	40	1	1	NUM
uva.x030312957	362	41	44	44	NUM
uva.x030312957	362	42	,	,	PUNCT
uva.x030312957	362	43	4	4	NUM
uva.x030312957	362	44	=	=	SYM
uva.x030312957	362	45	4	4	NUM
uva.x030312957	362	46	,	,	PUNCT
uva.x030312957	362	47	–	–	PUNCT
uva.x030312957	362	48	6	6	X
uva.x030312957	362	49	,	,	PUNCT
uva.x030312957	362	50	=	=	SYM
uva.x030312957	362	51	2	2	NUM
uva.x030312957	362	52	,	,	PUNCT
uva.x030312957	362	53	=	=	SYM
uva.x030312957	362	54	3	3	NUM
uva.x030312957	362	55	,	,	PUNCT
uva.x030312957	362	56	71	71	NUM
uva.x030312957	362	57	02	02	NUM
uva.x030312957	362	58	,	,	PUNCT
uva.x030312957	362	59	2	2	NUM
uva.x030312957	362	60	=	=	SYM
uva.x030312957	362	61	3	3	NUM
uva.x030312957	362	62	,	,	PUNCT
uva.x030312957	362	63	23	23	NUM
uva.x030312957	362	64	,	,	PUNCT
uva.x030312957	362	65	2	2	NUM
uva.x030312957	362	66	=	=	SYM
uva.x030312957	362	67	7	7	NUM
uva.x030312957	362	68	,	,	PUNCT
uva.x030312957	362	69	a3	a3	PROPN
uva.x030312957	362	70	,	,	PUNCT
uva.x030312957	362	71	1	1	NUM
uva.x030312957	362	72	=	=	SYM
uva.x030312957	362	73	-5	-5	PROPN
uva.x030312957	362	74	,	,	PUNCT
uva.x030312957	362	75	04	04	NUM
uva.x030312957	362	76	,	,	PUNCT
uva.x030312957	362	77	2	2	NUM
uva.x030312957	362	78	=	=	SYM
uva.x030312957	362	79	2	2	NUM
uva.x030312957	362	80	,	,	PUNCT
uva.x030312957	362	81	04	04	NUM
uva.x030312957	362	82	,	,	PUNCT
uva.x030312957	362	83	1	1	NUM
uva.x030312957	362	84	5	5	NUM
uva.x030312957	362	85	,	,	PUNCT
uva.x030312957	362	86	1	1	NUM
uva.x030312957	362	87	,	,	PUNCT
uva.x030312957	362	88	04	04	NUM
uva.x030312957	362	89	,	,	PUNCT
uva.x030312957	362	90	ܙ	ܙ	PRON
uva.x030312957	362	91	ܘ	ܘ	PROPN
uva.x030312957	362	92	3	3	NUM
uva.x030312957	362	93	6	6	NUM
uva.x030312957	362	94	,	,	PUNCT
uva.x030312957	362	95	1	1	NUM
uva.x030312957	362	96	5	5	NUM
uva.x030312957	362	97	45	45	NUM
uva.x030312957	362	98	,	,	PUNCT
uva.x030312957	362	99	=	=	PRON
uva.x030312957	362	100	25	25	NUM
uva.x030312957	362	101	,	,	PUNCT
uva.x030312957	362	102	2	2	NUM
uva.x030312957	362	103	=	=	SYM
uva.x030312957	362	104	3	3	NUM
uva.x030312957	362	105	,	,	PUNCT
uva.x030312957	362	106	1	1	NUM
uva.x030312957	362	107	05	05	NUM
uva.x030312957	362	108	.	.	NOUN
uva.x030312957	362	109	2	2	NUM
uva.x030312957	362	110	,	,	PUNCT
uva.x030312957	362	111	as	as	ADP
uva.x030312957	362	112	,	,	PUNCT
uva.x030312957	362	113	3	3	NUM
uva.x030312957	362	114	4	4	NUM
uva.x030312957	362	115	25	25	NUM
uva.x030312957	362	116	,	,	PUNCT
uva.x030312957	362	117	5	5	NUM
uva.x030312957	362	118	=	=	SYM
uva.x030312957	362	119	2	2	NUM
uva.x030312957	362	120	.	.	NUM
uva.x030312957	362	121	61	61	NUM
uva.x030312957	362	122	1	1	NUM
uva.x030312957	362	123	this	this	PRON
uva.x030312957	362	124	gives	give	VERB
uva.x030312957	362	125	2	2	NUM
uva.x030312957	362	126	–	–	PUNCT
uva.x030312957	362	127	x	x	SYM
uva.x030312957	362	128	,	,	PUNCT
uva.x030312957	362	129	3	3	NUM
uva.x030312957	362	130	,	,	PUNCT
uva.x030312957	362	131	5	5	NUM
uva.x030312957	362	132	,	,	PUNCT
uva.x030312957	362	133	3	3	NUM
uva.x030312957	362	134	,	,	PUNCT
uva.x030312957	362	135	3	3	NUM
uva.x030312957	362	136	–	–	PUNCT
uva.x030312957	362	137	x	x	SYM
uva.x030312957	362	138	,	,	PUNCT
uva.x030312957	362	139	7	7	NUM
uva.x030312957	362	140	,	,	PUNCT
uva.x030312957	362	141	2	2	NUM
uva.x030312957	362	142	,	,	PUNCT
uva.x030312957	362	143	a	a	NOUN
uva.x030312957	362	144	:	:	PUNCT
uva.x030312957	362	145	(	(	PUNCT
uva.x030312957	362	146	x	x	PUNCT
uva.x030312957	362	147	)	)	PUNCT
uva.x030312957	362	148	=	=	PROPN
uva.x030312957	362	149	5	5	NUM
uva.x030312957	362	150	,	,	PUNCT
uva.x030312957	362	151	7	7	NUM
uva.x030312957	362	152	,	,	PUNCT
uva.x030312957	362	153	1	1	NUM
uva.x030312957	362	154	–	–	PUNCT
uva.x030312957	362	155	x	x	SYM
uva.x030312957	362	156	,	,	PUNCT
uva.x030312957	362	157	5	5	NUM
uva.x030312957	362	158	,	,	PUNCT
uva.x030312957	362	159	5	5	NUM
uva.x030312957	362	160	,	,	PUNCT
uva.x030312957	362	161	3	3	NUM
uva.x030312957	362	162	1	1	NUM
uva.x030312957	362	163	6	6	NUM
uva.x030312957	362	164	,	,	PUNCT
uva.x030312957	362	165	2	2	NUM
uva.x030312957	362	166	,	,	PUNCT
uva.x030312957	362	167	4	4	NUM
uva.x030312957	362	168	x	x	SYM
uva.x030312957	362	169	,	,	PUNCT
uva.x030312957	362	170	2	2	NUM
uva.x030312957	362	171	1	1	NUM
uva.x030312957	362	172	,	,	PUNCT
uva.x030312957	362	173	3	3	NUM
uva.x030312957	362	174	.	.	NUM
uva.x030312957	362	175	1	1	NUM
uva.x030312957	362	176	,	,	PUNCT
uva.x030312957	362	177	2	2	NUM
uva.x030312957	362	178	.	.	NUM
uva.x030312957	362	179	,	,	PUNCT
uva.x030312957	362	180	2	2	NUM
uva.x030312957	362	181	x	x	SYM
uva.x030312957	362	182	from	from	ADP
uva.x030312957	362	183	which	which	PRON
uva.x030312957	362	184	we	we	PRON
uva.x030312957	362	185	see	see	VERB
uva.x030312957	362	186	a5	a5	PROPN
uva.x030312957	362	187	(	(	PUNCT
uva.x030312957	362	188	x	x	SYM
uva.x030312957	362	189	)	)	PUNCT
uva.x030312957	362	190	=	=	X
uva.x030312957	363	1	2db	2db	NOUN
uva.x030312957	363	2	+	+	NUM
uva.x030312957	363	3	1224	1224	NUM
uva.x030312957	363	4	+	+	NUM
uva.x030312957	363	5	108.23	108.23	NUM
uva.x030312957	363	6	215x2	215x2	NUM
uva.x030312957	363	7	993x	993x	NUM
uva.x030312957	363	8	+	+	NUM
uva.x030312957	363	9	1217	1217	NUM
uva.x030312957	363	10	,	,	PUNCT
uva.x030312957	363	11	44(x	44(x	NUM
uva.x030312957	363	12	)	)	PUNCT
uva.x030312957	363	13	10.203	10.203	NUM
uva.x030312957	363	14	113x2	113x2	NUM
uva.x030312957	363	15	+	+	SYM
uva.x030312957	363	16	23x	23x	NOUN
uva.x030312957	363	17	+	+	CCONJ
uva.x030312957	363	18	811	811	NUM
uva.x030312957	363	19	,	,	PUNCT
uva.x030312957	363	20	=	=	PRON
uva.x030312957	363	21	24	24	NUM
uva.x030312957	363	22	a3	a3	PROPN
uva.x030312957	363	23	(	(	PUNCT
uva.x030312957	363	24	x	x	SYM
uva.x030312957	363	25	)	)	PUNCT
uva.x030312957	363	26	=	=	VERB
uva.x030312957	364	1	203	203	NUM
uva.x030312957	364	2	+	+	CCONJ
uva.x030312957	364	3	6x2	6x2	NUM
uva.x030312957	364	4	+	+	NUM
uva.x030312957	364	5	72x	72x	NUM
uva.x030312957	364	6	+	+	CCONJ
uva.x030312957	364	7	34	34	NUM
uva.x030312957	364	8	,	,	PUNCT
uva.x030312957	364	9	a2	a2	X
uva.x030312957	364	10	(	(	PUNCT
uva.x030312957	364	11	2	2	NUM
uva.x030312957	364	12	)	)	PUNCT
uva.x030312957	364	13	=	=	PROPN
uva.x030312957	364	14	22	22	NUM
uva.x030312957	364	15	–	–	PUNCT
uva.x030312957	364	16	5x	5x	NOUN
uva.x030312957	364	17	–	–	PUNCT
uva.x030312957	364	18	3	3	NUM
uva.x030312957	364	19	,	,	PUNCT
uva.x030312957	364	20	41	41	NUM
uva.x030312957	364	21	(	(	PUNCT
uva.x030312957	364	22	x	x	SYM
uva.x030312957	364	23	)	)	PUNCT
uva.x030312957	364	24	=	=	X
uva.x030312957	364	25	2	2	NUM
uva.x030312957	364	26	–	–	SYM
uva.x030312957	364	27	2	2	NUM
uva.x030312957	364	28	.	.	PUNCT
uva.x030312957	364	29	by	by	ADP
uva.x030312957	364	30	a	a	DET
uva.x030312957	364	31	method	method	NOUN
uva.x030312957	364	32	due	due	ADP
uva.x030312957	364	33	to	to	ADP
uva.x030312957	364	34	hermite	hermite	NOUN
uva.x030312957	364	35	25	25	NUM
uva.x030312957	364	36	the	the	DET
uva.x030312957	364	37	roots	root	NOUN
uva.x030312957	364	38	of	of	ADP
uva.x030312957	364	39	the	the	DET
uva.x030312957	364	40	equations	equation	NOUN
uva.x030312957	364	41	formed	form	VERB
uva.x030312957	364	42	by	by	ADP
uva.x030312957	364	43	equating	equate	VERB
uva.x030312957	364	44	each	each	PRON
uva.x030312957	364	45	of	of	ADP
uva.x030312957	364	46	these	these	PRON
uva.x030312957	364	47	to	to	ADP
uva.x030312957	364	48	zero	zero	NUM
uva.x030312957	364	49	are	be	AUX
uva.x030312957	364	50	equation	equation	NOUN
uva.x030312957	364	51	roots	root	NOUN
uva.x030312957	364	52	a1(x	a1(x	SPACE
uva.x030312957	364	53	)	)	PUNCT
uva.x030312957	364	54	=	=	PROPN
uva.x030312957	364	55	0	0	NUM
uva.x030312957	364	56	2	2	NUM
uva.x030312957	364	57	42	42	NUM
uva.x030312957	364	58	(	(	PUNCT
uva.x030312957	364	59	a	a	NOUN
uva.x030312957	364	60	)	)	PUNCT
uva.x030312957	364	61	=	=	PROPN
uva.x030312957	364	62	0	0	NUM
uva.x030312957	364	63	0.54138	0.54138	NUM
uva.x030312957	364	64	+	+	CCONJ
uva.x030312957	364	65	5.54138	5.54138	NUM
uva.x030312957	364	66	a3	a3	NOUN
uva.x030312957	364	67	(	(	PUNCT
uva.x030312957	364	68	x	x	SYM
uva.x030312957	364	69	)	)	PUNCT
uva.x030312957	364	70	=	=	PUNCT
uva.x030312957	364	71	0	0	NUM
uva.x030312957	364	72	5.659	5.659	NUM
uva.x030312957	364	73	0.494	0.494	NUM
uva.x030312957	364	74	+	+	NUM
uva.x030312957	364	75	12.15	12.15	NUM
uva.x030312957	364	76	a.(x	a.(x	SPACE
uva.x030312957	364	77	)	)	PUNCT
uva.x030312957	364	78	=	=	PROPN
uva.x030312957	364	79	0	0	NUM
uva.x030312957	364	80	–	–	PUNCT
uva.x030312957	364	81	5.88	5.88	NUM
uva.x030312957	364	82	3.24	3.24	NUM
uva.x030312957	364	83	+	+	NUM
uva.x030312957	364	84	2.56	2.56	NUM
uva.x030312957	364	85	+	+	NUM
uva.x030312957	364	86	16.56	16.56	NUM
uva.x030312957	364	87	a3	a3	PROPN
uva.x030312957	364	88	(	(	PUNCT
uva.x030312957	364	89	20	20	NUM
uva.x030312957	364	90	)	)	PUNCT
uva.x030312957	364	91	=	=	PUNCT
uva.x030312957	364	92	0	0	NUM
uva.x030312957	364	93	6.14	6.14	NUM
uva.x030312957	364	94	3.35	3.35	NUM
uva.x030312957	364	95	+	+	NUM
uva.x030312957	364	96	1.12	1.12	NUM
uva.x030312957	364	97	+	+	NUM
uva.x030312957	364	98	3.03	3.03	NUM
uva.x030312957	364	99	+	+	NUM
uva.x030312957	364	100	17.32	17.32	NUM
uva.x030312957	364	101	it	it	PRON
uva.x030312957	364	102	is	be	AUX
uva.x030312957	364	103	seen	see	VERB
uva.x030312957	364	104	here	here	ADV
uva.x030312957	364	105	that	that	SCONJ
uva.x030312957	364	106	all	all	DET
uva.x030312957	364	107	the	the	DET
uva.x030312957	364	108	roots	root	NOUN
uva.x030312957	364	109	are	be	AUX
uva.x030312957	364	110	real	real	ADJ
uva.x030312957	364	111	and	and	CCONJ
uva.x030312957	364	112	that	that	SCONJ
uva.x030312957	364	113	the	the	DET
uva.x030312957	364	114	roots	root	NOUN
uva.x030312957	364	115	of	of	ADP
uva.x030312957	364	116	each	each	DET
uva.x030312957	364	117	equation	equation	NOUN
uva.x030312957	364	118	,	,	PUNCT
uva.x030312957	364	119	one	one	NUM
uva.x030312957	364	120	at	at	ADP
uva.x030312957	364	121	a	a	DET
uva.x030312957	364	122	time	time	NOUN
uva.x030312957	364	123	,	,	PUNCT
uva.x030312957	364	124	lie	lie	VERB
uva.x030312957	364	125	between	between	ADP
uva.x030312957	364	126	adjacent	adjacent	ADJ
uva.x030312957	364	127	pair	pair	NOUN
uva.x030312957	364	128	of	of	ADP
uva.x030312957	364	129	roots	root	NOUN
uva.x030312957	364	130	of	of	ADP
uva.x030312957	364	131	the	the	DET
uva.x030312957	364	132	equation	equation	NOUN
uva.x030312957	364	133	which	which	PRON
uva.x030312957	364	134	succeeds	succeed	VERB
uva.x030312957	364	135	it	it	PRON
uva.x030312957	364	136	.	.	PUNCT
uva.x030312957	365	1	this	this	DET
uva.x030312957	365	2	last	last	ADJ
uva.x030312957	365	3	fact	fact	NOUN
uva.x030312957	365	4	is	be	AUX
uva.x030312957	365	5	more	more	ADV
uva.x030312957	365	6	obvious	obvious	ADJ
uva.x030312957	365	7	from	from	ADP
uva.x030312957	365	8	the	the	DET
uva.x030312957	365	9	diagrammatic	diagrammatic	ADJ
uva.x030312957	365	10	representation	representation	NOUN
uva.x030312957	365	11	of	of	ADP
uva.x030312957	365	12	the	the	DET
uva.x030312957	365	13	roots	root	NOUN
uva.x030312957	365	14	shown	show	VERB
uva.x030312957	365	15	below	below	ADV
uva.x030312957	365	16	.	.	PUNCT
uva.x030312957	366	1	in	in	ADP
uva.x030312957	366	2	the	the	DET
uva.x030312957	366	3	diagram	diagram	NOUN
uva.x030312957	366	4	,	,	PUNCT
uva.x030312957	366	5	on	on	ADP
uva.x030312957	366	6	the	the	DET
uva.x030312957	366	7	next	next	ADJ
uva.x030312957	366	8	page	page	NOUN
uva.x030312957	366	9	,	,	PUNCT
uva.x030312957	366	10	the	the	DET
uva.x030312957	366	11	graphs	graph	NOUN
uva.x030312957	366	12	of	of	ADP
uva.x030312957	366	13	the	the	DET
uva.x030312957	366	14	different	different	ADJ
uva.x030312957	366	15	functions	function	NOUN
uva.x030312957	366	16	are	be	AUX
uva.x030312957	366	17	shown	show	VERB
uva.x030312957	366	18	.	.	PUNCT
uva.x030312957	367	1	no	no	DET
uva.x030312957	367	2	attempt	attempt	NOUN
uva.x030312957	367	3	has	have	AUX
uva.x030312957	367	4	been	be	AUX
uva.x030312957	367	5	made	make	VERB
uva.x030312957	367	6	to	to	PART
uva.x030312957	367	7	represent	represent	VERB
uva.x030312957	367	8	the	the	DET
uva.x030312957	367	9	ordinates	ordinate	NOUN
uva.x030312957	367	10	accurately	accurately	ADV
uva.x030312957	367	11	,	,	PUNCT
uva.x030312957	367	12	on	on	ADP
uva.x030312957	367	13	account	account	NOUN
uva.x030312957	367	14	of	of	ADP
uva.x030312957	367	15	the	the	DET
uva.x030312957	367	16	variation	variation	NOUN
uva.x030312957	367	17	in	in	ADP
uva.x030312957	367	18	size	size	NOUN
uva.x030312957	367	19	between	between	ADP
uva.x030312957	367	20	the	the	DET
uva.x030312957	367	21	different	different	ADJ
uva.x030312957	367	22	curves	curve	NOUN
uva.x030312957	367	23	,	,	PUNCT
uva.x030312957	367	24	which	which	PRON
uva.x030312957	367	25	would	would	AUX
uva.x030312957	367	26	necessitate	necessitate	VERB
uva.x030312957	367	27	a	a	DET
uva.x030312957	367	28	different	different	ADJ
uva.x030312957	367	29	vertical	vertical	ADJ
uva.x030312957	367	30	unit	unit	NOUN
uva.x030312957	367	31	for	for	ADP
uva.x030312957	367	32	each	each	DET
uva.x030312957	367	33	curve	curve	NOUN
uva.x030312957	367	34	.	.	PUNCT
uva.x030312957	368	1	the	the	DET
uva.x030312957	368	2	relative	relative	ADJ
uva.x030312957	368	3	size	size	NOUN
uva.x030312957	368	4	of	of	ADP
uva.x030312957	368	5	the	the	DET
uva.x030312957	368	6	ordinates	ordinate	NOUN
uva.x030312957	368	7	are	be	AUX
uva.x030312957	368	8	shown	show	VERB
uva.x030312957	368	9	and	and	CCONJ
uva.x030312957	368	10	the	the	DET
uva.x030312957	368	11	point	point	NOUN
uva.x030312957	368	12	of	of	ADP
uva.x030312957	368	13	crossing	cross	VERB
uva.x030312957	368	14	the	the	DET
uva.x030312957	368	15	axis	axis	NOUN
uva.x030312957	368	16	is	be	AUX
uva.x030312957	368	17	accurately	accurately	ADV
uva.x030312957	368	18	given	give	VERB
uva.x030312957	368	19	.	.	PUNCT
uva.x030312957	369	1	from	from	ADP
uva.x030312957	369	2	these	these	DET
uva.x030312957	369	3	points	point	NOUN
uva.x030312957	369	4	of	of	ADP
uva.x030312957	369	5	intersection	intersection	NOUN
uva.x030312957	369	6	with	with	ADP
uva.x030312957	369	7	the	the	DET
uva.x030312957	369	8	axis	axis	NOUN
uva.x030312957	369	9	of	of	ADP
uva.x030312957	369	10	x	x	PROPN
uva.x030312957	369	11	,	,	PUNCT
uva.x030312957	369	12	we	we	PRON
uva.x030312957	369	13	see	see	VERB
uva.x030312957	369	14	very	very	ADV
uva.x030312957	369	15	clearly	clearly	ADV
uva.x030312957	369	16	that	that	SCONJ
uva.x030312957	369	17	the	the	DET
uva.x030312957	369	18	relation	relation	NOUN
uva.x030312957	369	19	between	between	ADP
uva.x030312957	369	20	the	the	DET
uva.x030312957	369	21	roots	root	NOUN
uva.x030312957	369	22	of	of	ADP
uva.x030312957	369	23	one	one	NUM
uva.x030312957	369	24	equation	equation	NOUN
uva.x030312957	369	25	and	and	CCONJ
uva.x030312957	369	26	those	those	PRON
uva.x030312957	369	27	of	of	ADP
uva.x030312957	369	28	the	the	DET
uva.x030312957	369	29	equation	equation	NOUN
uva.x030312957	369	30	of	of	ADP
uva.x030312957	369	31	next	next	ADJ
uva.x030312957	369	32	higher	high	ADJ
uva.x030312957	369	33	degree	degree	NOUN
uva.x030312957	369	34	is	be	AUX
uva.x030312957	369	35	that	that	PRON
uva.x030312957	369	36	stated	state	VERB
uva.x030312957	369	37	above	above	ADV
uva.x030312957	369	38	.	.	PUNCT
uva.x030312957	370	1	26	26	NUM
uva.x030312957	370	2	solution	solution	NOUN
uva.x030312957	370	3	of	of	ADP
uva.x030312957	370	4	the	the	DET
uva.x030312957	370	5	equation	equation	NOUN
uva.x030312957	370	6	of	of	ADP
uva.x030312957	370	7	secular	secular	ADJ
uva.x030312957	370	8	variation	variation	NOUN
uva.x030312957	370	9	(	(	PUNCT
uva.x030312957	370	10	2	2	NUM
uva.x030312957	370	11	)	)	PUNCT
uva.x030312957	370	12	a.(e	a.(e	PROPN
uva.x030312957	370	13	)	)	PUNCT
uva.x030312957	370	14	ag(s	ag(s	PROPN
uva.x030312957	370	15	)	)	PUNCT
uva.x030312957	370	16	a.(8	a.(8	PROPN
uva.x030312957	370	17	)	)	PUNCT
uva.x030312957	370	18	agar	agar	PROPN
uva.x030312957	370	19	)	)	PUNCT
uva.x030312957	370	20	la(a	la(a	PROPN
uva.x030312957	370	21	)	)	PUNCT
uva.x030312957	370	22	ascenaile	ascenaile	NOUN
uva.x030312957	370	23	)	)	PUNCT
uva.x030312957	370	24	4	4	NUM
uva.x030312957	370	25	-	-	PUNCT
uva.x030312957	370	26	a,(a	a,(a	X
uva.x030312957	370	27	)	)	PUNCT
uva.x030312957	370	28	a(c	a(c	PROPN
uva.x030312957	370	29	)	)	PUNCT
uva.x030312957	370	30	143(8	143(8	NUM
uva.x030312957	370	31	)	)	PUNCT
uva.x030312957	370	32	---4	---4	PROPN
uva.x030312957	370	33	as(ar	as(ar	NOUN
uva.x030312957	370	34	)	)	PUNCT
uva.x030312957	370	35	a(m	a(m	PROPN
uva.x030312957	370	36	)	)	PUNCT
uva.x030312957	370	37	10	10	NUM
uva.x030312957	370	38	11	11	NUM
uva.x030312957	370	39	18	18	NUM
uva.x030312957	370	40	14_15	14_15	NUM
uva.x030312957	370	41	16	16	NUM
uva.x030312957	370	42	ka	ka	PROPN
uva.x030312957	370	43	12	12	NUM
uva.x030312957	370	44	17	17	NUM
uva.x030312957	370	45	(	(	PUNCT
uva.x030312957	370	46	as(c	as(c	NOUN
uva.x030312957	370	47	)	)	PUNCT
uva.x030312957	370	48	मा	मा	ADV
uva.x030312957	370	49	1a,(c	1a,(c	NUM
uva.x030312957	370	50	)	)	PUNCT
uva.x030312957	370	51	/as(8	/as(8	PROPN
uva.x030312957	370	52	)	)	PUNCT
uva.x030312957	371	1	a.(c	a.(c	PROPN
uva.x030312957	371	2	)	)	PUNCT
uva.x030312957	371	3	date	date	NOUN
uva.x030312957	371	4	due	due	ADJ
uva.x030312957	371	5	brodart	brodart	NOUN
uva.x030312957	371	6	,	,	PUNCT
uva.x030312957	371	7	inc	inc	PROPN
uva.x030312957	371	8	cat	cat	PROPN
uva.x030312957	371	9	no	no	PROPN
uva.x030312957	371	10	.	.	PROPN
uva.x030312957	371	11	23	23	NUM
uva.x030312957	371	12	233	233	NUM
uva.x030312957	371	13	printed	print	VERB
uva.x030312957	371	14	in	in	ADP
uva.x030312957	371	15	usa	usa	PROPN
uva.x030312957	371	16	ux3300335	ux3300335	PROPN
uva.x030312957	371	17	41	41	NUM