id	sid	tid	token	lemma	pos
ap-926	1	1	ap07_2-3.vp	ap07_2-3.vp	SYM
ap-926	1	2	1	1	NUM
ap-926	1	3	introduction	introduction	NOUN
ap-926	1	4	let	let	VERB
ap-926	1	5	g	g	PRON
ap-926	1	6	be	be	AUX
ap-926	1	7	a	a	DET
ap-926	1	8	finite	finite	ADJ
ap-926	1	9	dimensional	dimensional	ADJ
ap-926	1	10	complex	complex	ADJ
ap-926	1	11	semisimple	semisimple	NOUN
ap-926	1	12	lie	lie	NOUN
ap-926	1	13	algebra	algebra	NOUN
ap-926	1	14	and	and	CCONJ
ap-926	1	15	u	u	NOUN
ap-926	1	16	g	g	PROPN
ap-926	1	17	u	u	PROPN
ap-926	1	18	(	(	PUNCT
ap-926	1	19	)	)	PUNCT
ap-926	1	20	�	�	PROPN
ap-926	1	21	its	its	PRON
ap-926	1	22	corresponding	correspond	VERB
ap-926	1	23	enveloping	enveloping	NOUN
ap-926	1	24	algebra	algebra	NOUN
ap-926	1	25	.	.	PUNCT
ap-926	2	1	if	if	SCONJ
ap-926	2	2	we	we	PRON
ap-926	2	3	want	want	VERB
ap-926	2	4	to	to	PART
ap-926	2	5	study	study	VERB
ap-926	2	6	all	all	DET
ap-926	2	7	two	two	NUM
ap-926	2	8	-	-	PUNCT
ap-926	2	9	sided	sided	ADJ
ap-926	2	10	ideals	ideal	NOUN
ap-926	2	11	of	of	ADP
ap-926	2	12	the	the	DET
ap-926	2	13	associative	associative	ADJ
ap-926	2	14	algebra	algebra	NOUN
ap-926	2	15	u	u	NOUN
ap-926	2	16	(	(	PUNCT
ap-926	2	17	see	see	VERB
ap-926	2	18	[	[	X
ap-926	2	19	1	1	X
ap-926	2	20	]	]	PUNCT
ap-926	2	21	chapters	chapter	NOUN
ap-926	2	22	6–10	6–10	NOUN
ap-926	2	23	)	)	PUNCT
ap-926	2	24	,	,	PUNCT
ap-926	2	25	i.e.	i.e.	X
ap-926	2	26	to	to	PART
ap-926	2	27	find	find	VERB
ap-926	2	28	all	all	DET
ap-926	2	29	the	the	DET
ap-926	2	30	vector	vector	NOUN
ap-926	2	31	spaces	space	NOUN
ap-926	2	32	i	i	PRON
ap-926	2	33	u	u	VERB
ap-926	2	34	�	�	PROPN
ap-926	2	35	which	which	PRON
ap-926	2	36	satisfy	satisfy	VERB
ap-926	2	37	for	for	ADP
ap-926	2	38	all	all	DET
ap-926	2	39	a	a	DET
ap-926	2	40	b	b	X
ap-926	2	41	u	u	X
ap-926	2	42	aib	aib	PROPN
ap-926	2	43	i	i	PRON
ap-926	2	44	,	,	PUNCT
ap-926	2	45	:	:	PUNCT
ap-926	2	46	�	�	PROPN
ap-926	2	47	�	�	PROPN
ap-926	2	48	we	we	PRON
ap-926	2	49	can	can	AUX
ap-926	2	50	easily	easily	ADV
ap-926	2	51	see	see	VERB
ap-926	2	52	that	that	SCONJ
ap-926	2	53	such	such	DET
ap-926	2	54	a	a	DET
ap-926	2	55	two	two	NUM
ap-926	2	56	-	-	PUNCT
ap-926	2	57	sided	sided	ADJ
ap-926	2	58	ideal	ideal	NOUN
ap-926	2	59	is	be	AUX
ap-926	2	60	invariant	invariant	ADJ
ap-926	2	61	with	with	ADP
ap-926	2	62	respect	respect	NOUN
ap-926	2	63	to	to	ADP
ap-926	2	64	adjoint	adjoint	NOUN
ap-926	2	65	action	action	NOUN
ap-926	2	66	of	of	ADP
ap-926	2	67	u	u	NOUN
ap-926	2	68	:	:	PUNCT
ap-926	2	69	if	if	SCONJ
ap-926	2	70	we	we	PRON
ap-926	2	71	take	take	VERB
ap-926	2	72	adjoint	adjoint	NOUN
ap-926	2	73	action	action	NOUN
ap-926	2	74	�	�	PROPN
ap-926	2	75	:	:	PUNCT
ap-926	2	76	(	(	PUNCT
ap-926	2	77	)	)	PUNCT
ap-926	2	78	g	g	NOUN
ap-926	2	79	l	l	X
ap-926	2	80	u	u	NOUN
ap-926	2	81	�	�	PROPN
ap-926	2	82	,	,	PUNCT
ap-926	2	83	i.e.	i.e.	X
ap-926	2	84	�	�	PROPN
ap-926	2	85	(	(	PUNCT
ap-926	2	86	)	)	PUNCT
ap-926	2	87	[	[	PUNCT
ap-926	2	88	,	,	PUNCT
ap-926	2	89	]	]	X
ap-926	2	90	x	x	X
ap-926	2	91	a	a	DET
ap-926	2	92	x	x	X
ap-926	2	93	a	a	DET
ap-926	2	94	�	�	PROPN
ap-926	2	95	for	for	ADP
ap-926	2	96	x	x	SYM
ap-926	2	97	g	g	PROPN
ap-926	2	98	�	�	PROPN
ap-926	2	99	and	and	CCONJ
ap-926	2	100	a	a	DET
ap-926	2	101	u	u	NOUN
ap-926	2	102	�	�	NOUN
ap-926	2	103	and	and	CCONJ
ap-926	2	104	extend	extend	VERB
ap-926	2	105	this	this	DET
ap-926	2	106	definition	definition	NOUN
ap-926	2	107	to	to	ADP
ap-926	2	108	all	all	DET
ap-926	2	109	u	u	NOUN
ap-926	2	110	by	by	ADP
ap-926	2	111	�	�	PROPN
ap-926	2	112	�	�	PROPN
ap-926	2	113	�	�	PROPN
ap-926	2	114	�	�	PROPN
ap-926	2	115	�	�	PROPN
ap-926	2	116	�	�	PROPN
ap-926	2	117	�	�	PROPN
ap-926	2	118	(	(	PUNCT
ap-926	2	119	)	)	PUNCT
ap-926	2	120	(	(	PUNCT
ap-926	2	121	)	)	PUNCT
ap-926	2	122	(	(	PUNCT
ap-926	2	123	)	)	PUNCT
ap-926	2	124	,	,	PUNCT
ap-926	2	125	,	,	PUNCT
ap-926	2	126	[	[	PUNCT
ap-926	2	127	,	,	PUNCT
ap-926	2	128	]	]	X
ap-926	2	129	u	u	NOUN
ap-926	2	130	x	x	NOUN
ap-926	2	131	x	x	PUNCT
ap-926	2	132	x	x	SYM
ap-926	2	133	x	x	X
ap-926	2	134	an	an	DET
ap-926	2	135	n	n	CCONJ
ap-926	2	136	�	�	PROPN
ap-926	2	137	�	�	PROPN
ap-926	2	138	1	1	NUM
ap-926	2	139	1	1	NUM
ap-926	2	140	�	�	PROPN
ap-926	2	141	�	�	PROPN
ap-926	2	142	�	�	PROPN
ap-926	2	143	for	for	ADP
ap-926	2	144	all	all	DET
ap-926	2	145	u	u	NOUN
ap-926	2	146	x	x	NOUN
ap-926	2	147	x	x	SYM
ap-926	2	148	x	x	PUNCT
ap-926	2	149	gn	gn	PROPN
ap-926	2	150	i	i	PRON
ap-926	2	151	�	�	PROPN
ap-926	2	152	�	�	PROPN
ap-926	2	153	1	1	NUM
ap-926	2	154	�	�	PROPN
ap-926	2	155	,	,	PUNCT
ap-926	2	156	we	we	PRON
ap-926	2	157	see	see	VERB
ap-926	2	158	that	that	DET
ap-926	2	159	�	�	PROPN
ap-926	2	160	(	(	PUNCT
ap-926	2	161	)	)	PUNCT
ap-926	2	162	u	u	NOUN
ap-926	2	163	i	i	PROPN
ap-926	2	164	i	i	PROPN
ap-926	2	165	�	�	PROPN
ap-926	2	166	.	.	PUNCT
ap-926	3	1	it	it	PRON
ap-926	3	2	is	be	AUX
ap-926	3	3	well	well	ADV
ap-926	3	4	known	know	VERB
ap-926	3	5	that	that	SCONJ
ap-926	3	6	such	such	ADJ
ap-926	3	7	adjoint	adjoint	NOUN
ap-926	3	8	action	action	NOUN
ap-926	3	9	�	�	PROPN
ap-926	3	10	is	be	AUX
ap-926	3	11	completely	completely	ADV
ap-926	3	12	reducible	reducible	ADJ
ap-926	3	13	for	for	ADP
ap-926	3	14	g	g	PROPN
ap-926	3	15	semisimple	semisimple	NOUN
ap-926	3	16	:	:	PUNCT
ap-926	3	17	it	it	PRON
ap-926	3	18	is	be	AUX
ap-926	3	19	possible	possible	ADJ
ap-926	3	20	to	to	PART
ap-926	3	21	cut	cut	VERB
ap-926	3	22	the	the	DET
ap-926	3	23	enveloping	enveloping	NOUN
ap-926	3	24	algebra	algebra	NOUN
ap-926	3	25	u	u	NOUN
ap-926	3	26	into	into	ADP
ap-926	3	27	pieces	piece	NOUN
ap-926	3	28	u	u	NOUN
ap-926	3	29	k	k	X
ap-926	3	30	�	�	PROPN
ap-926	3	31	such	such	ADJ
ap-926	3	32	that	that	SCONJ
ap-926	3	33	u	u	PRON
ap-926	3	34	u	u	NOUN
ap-926	3	35	k	k	PROPN
ap-926	3	36	k	k	PROPN
ap-926	3	37	�	�	PROPN
ap-926	3	38	�	�	PROPN
ap-926	3	39	�	�	PROPN
ap-926	3	40	0	0	NUM
ap-926	3	41	�	�	PROPN
ap-926	3	42	and	and	CCONJ
ap-926	3	43	each	each	DET
ap-926	3	44	piece	piece	NOUN
ap-926	3	45	u	u	PROPN
ap-926	3	46	k	k	X
ap-926	3	47	�	�	PROPN
ap-926	3	48	is	be	AUX
ap-926	3	49	an	an	DET
ap-926	3	50	invariant	invariant	ADJ
ap-926	3	51	subspace	subspace	NOUN
ap-926	3	52	(	(	PUNCT
ap-926	3	53	corresponding	correspond	VERB
ap-926	3	54	to	to	ADP
ap-926	3	55	an	an	DET
ap-926	3	56	irreducible	irreducible	ADJ
ap-926	3	57	representation	representation	NOUN
ap-926	3	58	(	(	PUNCT
ap-926	3	59	component	component	NOUN
ap-926	3	60	)	)	PUNCT
ap-926	3	61	of	of	ADP
ap-926	3	62	�	�	PROPN
ap-926	3	63	)	)	PUNCT
ap-926	3	64	generated	generate	VERB
ap-926	3	65	by	by	ADP
ap-926	3	66	its	its	PRON
ap-926	3	67	highest	high	ADJ
ap-926	3	68	weight	weight	NOUN
ap-926	3	69	vector	vector	NOUN
ap-926	3	70	�	�	PROPN
ap-926	3	71	k	k	NOUN
ap-926	3	72	:	:	PUNCT
ap-926	3	73	�	�	PROPN
ap-926	3	74	(	(	PUNCT
ap-926	3	75	)	)	PUNCT
ap-926	3	76	u	u	PROPN
ap-926	3	77	uk	uk	PROPN
ap-926	3	78	k	k	PROPN
ap-926	3	79	�	�	PROPN
ap-926	3	80	�	�	PROPN
ap-926	3	81	�	�	PROPN
ap-926	3	82	now	now	ADV
ap-926	3	83	if	if	SCONJ
ap-926	3	84	we	we	PRON
ap-926	3	85	take	take	VERB
ap-926	3	86	any	any	DET
ap-926	3	87	ideal	ideal	NOUN
ap-926	3	88	i	i	PRON
ap-926	3	89	u	u	VERB
ap-926	3	90	�	�	PROPN
ap-926	3	91	and	and	CCONJ
ap-926	3	92	find	find	VERB
ap-926	3	93	any	any	DET
ap-926	3	94	highest	high	ADJ
ap-926	3	95	weight	weight	NOUN
ap-926	3	96	vector	vector	NOUN
ap-926	3	97	�	�	PROPN
ap-926	3	98	k	k	PROPN
ap-926	3	99	i	i	PROPN
ap-926	3	100	�	�	PROPN
ap-926	3	101	,	,	PUNCT
ap-926	3	102	we	we	PRON
ap-926	3	103	automatically	automatically	ADV
ap-926	3	104	know	know	VERB
ap-926	3	105	that	that	DET
ap-926	3	106	�	�	PROPN
ap-926	3	107	(	(	PUNCT
ap-926	3	108	)	)	PUNCT
ap-926	3	109	u	u	NOUN
ap-926	3	110	u	u	PROPN
ap-926	3	111	ik	ik	PROPN
ap-926	3	112	k	k	PROPN
ap-926	3	113	�	�	PROPN
ap-926	3	114	�	�	PROPN
ap-926	3	115	�	�	PROPN
ap-926	3	116	�	�	PROPN
ap-926	3	117	,	,	PUNCT
ap-926	3	118	i.e.	i.e.	X
ap-926	3	119	we	we	PRON
ap-926	3	120	know	know	VERB
ap-926	3	121	a	a	DET
ap-926	3	122	large	large	ADJ
ap-926	3	123	set	set	NOUN
ap-926	3	124	of	of	ADP
ap-926	3	125	vectors	vector	NOUN
ap-926	3	126	which	which	PRON
ap-926	3	127	must	must	AUX
ap-926	3	128	be	be	AUX
ap-926	3	129	contained	contain	VERB
ap-926	3	130	also	also	ADV
ap-926	3	131	in	in	ADP
ap-926	3	132	the	the	DET
ap-926	3	133	ideal	ideal	ADJ
ap-926	3	134	i.	i.	NOUN
ap-926	3	135	this	this	PRON
ap-926	3	136	can	can	AUX
ap-926	3	137	help	help	VERB
ap-926	3	138	considerably	considerably	ADV
ap-926	3	139	in	in	ADP
ap-926	3	140	the	the	DET
ap-926	3	141	classification	classification	NOUN
ap-926	3	142	of	of	ADP
ap-926	3	143	all	all	DET
ap-926	3	144	ideals	ideal	NOUN
ap-926	3	145	of	of	ADP
ap-926	3	146	u.	u.	NOUN
ap-926	3	147	the	the	DET
ap-926	3	148	main	main	ADJ
ap-926	3	149	aim	aim	NOUN
ap-926	3	150	of	of	ADP
ap-926	3	151	this	this	DET
ap-926	3	152	paper	paper	NOUN
ap-926	3	153	is	be	AUX
ap-926	3	154	to	to	PART
ap-926	3	155	give	give	VERB
ap-926	3	156	an	an	DET
ap-926	3	157	explicit	explicit	ADJ
ap-926	3	158	decomposition	decomposition	NOUN
ap-926	3	159	�	�	X
ap-926	3	160	�	�	PROPN
ap-926	3	161	k	k	PROPN
ap-926	3	162	u	u	PROPN
ap-926	3	163	k0	k0	PROPN
ap-926	3	164	�	�	PROPN
ap-926	3	165	,	,	PUNCT
ap-926	3	166	i.e.	i.e.	X
ap-926	3	167	to	to	PART
ap-926	3	168	give	give	VERB
ap-926	3	169	a	a	DET
ap-926	3	170	list	list	NOUN
ap-926	3	171	of	of	ADP
ap-926	3	172	highest	high	ADJ
ap-926	3	173	weight	weight	NOUN
ap-926	3	174	vectors	vector	NOUN
ap-926	3	175	�	�	PROPN
ap-926	3	176	k	k	PROPN
ap-926	3	177	,	,	PUNCT
ap-926	3	178	k	k	PROPN
ap-926	3	179	�	�	PROPN
ap-926	3	180	0	0	NUM
ap-926	3	181	1	1	NUM
ap-926	3	182	,	,	PUNCT
ap-926	3	183	,	,	PUNCT
ap-926	3	184	�	�	PROPN
ap-926	3	185	for	for	ADP
ap-926	3	186	the	the	DET
ap-926	3	187	simplest	simple	ADJ
ap-926	3	188	cases	case	NOUN
ap-926	3	189	of	of	ADP
ap-926	3	190	lie	lie	NOUN
ap-926	3	191	algebras	algebra	NOUN
ap-926	3	192	and	and	CCONJ
ap-926	3	193	to	to	PART
ap-926	3	194	show	show	VERB
ap-926	3	195	that	that	SCONJ
ap-926	3	196	even	even	ADV
ap-926	3	197	in	in	ADP
ap-926	3	198	more	more	ADV
ap-926	3	199	complicated	complicated	ADJ
ap-926	3	200	examples	example	NOUN
ap-926	3	201	the	the	DET
ap-926	3	202	decomposition	decomposition	NOUN
ap-926	3	203	does	do	AUX
ap-926	3	204	not	not	PART
ap-926	3	205	look	look	VERB
ap-926	3	206	too	too	ADV
ap-926	3	207	weird	weird	ADJ
ap-926	3	208	and	and	CCONJ
ap-926	3	209	is	be	AUX
ap-926	3	210	relatively	relatively	ADV
ap-926	3	211	easyli	easyli	NOUN
ap-926	3	212	obtained	obtain	VERB
ap-926	3	213	by	by	ADP
ap-926	3	214	a	a	DET
ap-926	3	215	generally	generally	ADV
ap-926	3	216	described	describe	VERB
ap-926	3	217	procedure	procedure	NOUN
ap-926	3	218	.	.	PUNCT
ap-926	4	1	2	2	NUM
ap-926	4	2	the	the	DET
ap-926	4	3	simplest	simple	ADJ
ap-926	4	4	example	example	NOUN
ap-926	4	5	–	–	PUNCT
ap-926	4	6	algebra	algebra	NOUN
ap-926	4	7	sl(2	sl(2	PROPN
ap-926	4	8	)	)	PUNCT
ap-926	4	9	let	let	VERB
ap-926	4	10	us	we	PRON
ap-926	4	11	have	have	VERB
ap-926	4	12	algebra	algebra	PROPN
ap-926	4	13	sl(2	sl(2	PROPN
ap-926	4	14	)	)	PUNCT
ap-926	4	15	which	which	PRON
ap-926	4	16	is	be	AUX
ap-926	4	17	a	a	DET
ap-926	4	18	complex	complex	ADJ
ap-926	4	19	linear	linear	ADJ
ap-926	4	20	span	span	NOUN
ap-926	4	21	of	of	ADP
ap-926	4	22	three	three	NUM
ap-926	4	23	vectors	vector	NOUN
ap-926	4	24	e	e	NOUN
ap-926	4	25	e	e	NOUN
ap-926	4	26	h	h	NOUN
ap-926	4	27	e	e	NOUN
ap-926	4	28	e12	e12	NOUN
ap-926	4	29	21	21	NUM
ap-926	4	30	1	1	NUM
ap-926	4	31	11	11	NUM
ap-926	4	32	22	22	NUM
ap-926	4	33	,	,	PUNCT
ap-926	4	34	,	,	PUNCT
ap-926	4	35	�	�	PROPN
ap-926	4	36	�	�	PROPN
ap-926	4	37	,	,	PUNCT
ap-926	4	38	where	where	SCONJ
ap-926	4	39	by	by	ADP
ap-926	4	40	eij	eij	PROPN
ap-926	4	41	we	we	PRON
ap-926	4	42	denote	denote	VERB
ap-926	4	43	the	the	DET
ap-926	4	44	matrix	matrix	NOUN
ap-926	4	45	having	have	VERB
ap-926	4	46	1	1	NUM
ap-926	4	47	in	in	ADP
ap-926	4	48	position	position	NOUN
ap-926	4	49	(	(	PUNCT
ap-926	4	50	i	i	PROPN
ap-926	4	51	,	,	PUNCT
ap-926	4	52	j	j	PROPN
ap-926	4	53	)	)	PUNCT
ap-926	4	54	and	and	CCONJ
ap-926	4	55	0s	0	NOUN
ap-926	4	56	elsewhere	elsewhere	ADV
ap-926	4	57	.	.	PUNCT
ap-926	5	1	if	if	SCONJ
ap-926	5	2	we	we	PRON
ap-926	5	3	compute	compute	VERB
ap-926	5	4	the	the	DET
ap-926	5	5	commutation	commutation	NOUN
ap-926	5	6	relations	relation	NOUN
ap-926	5	7	of	of	ADP
ap-926	5	8	these	these	DET
ap-926	5	9	elements	element	NOUN
ap-926	5	10	we	we	PRON
ap-926	5	11	obtain	obtain	VERB
ap-926	5	12	[	[	PUNCT
ap-926	5	13	,	,	PUNCT
ap-926	5	14	]	]	PUNCT
ap-926	5	15	,	,	PUNCT
ap-926	5	16	[	[	PUNCT
ap-926	5	17	,	,	PUNCT
ap-926	5	18	]	]	PUNCT
ap-926	5	19	,	,	PUNCT
ap-926	5	20	[	[	PUNCT
ap-926	5	21	,	,	PUNCT
ap-926	5	22	]	]	X
ap-926	5	23	e	e	X
ap-926	5	24	e	e	NOUN
ap-926	5	25	h	h	NOUN
ap-926	5	26	h	h	NOUN
ap-926	5	27	e	e	NOUN
ap-926	5	28	e	e	NOUN
ap-926	5	29	h	h	NOUN
ap-926	5	30	e	e	PROPN
ap-926	5	31	e12	e12	NOUN
ap-926	5	32	21	21	NUM
ap-926	5	33	1	1	NUM
ap-926	5	34	1	1	NUM
ap-926	5	35	12	12	NUM
ap-926	5	36	12	12	NUM
ap-926	5	37	1	1	NUM
ap-926	5	38	21	21	NUM
ap-926	5	39	212	212	NUM
ap-926	5	40	2	2	NUM
ap-926	5	41	�	�	PROPN
ap-926	5	42	�	�	PROPN
ap-926	5	43	�	�	PROPN
ap-926	5	44	�	�	PROPN
ap-926	5	45	.	.	PUNCT
ap-926	6	1	the	the	DET
ap-926	6	2	enveloping	enveloping	NOUN
ap-926	6	3	algebra	algebra	NOUN
ap-926	6	4	u	u	NOUN
ap-926	6	5	u	u	NOUN
ap-926	6	6	sl	sl	PRON
ap-926	6	7	�	�	PROPN
ap-926	6	8	(	(	PUNCT
ap-926	6	9	(	(	PUNCT
ap-926	6	10	)	)	PUNCT
ap-926	6	11	)	)	PUNCT
ap-926	6	12	2	2	NUM
ap-926	6	13	fulfils	fulfil	VERB
ap-926	6	14	the	the	DET
ap-926	6	15	poincare	poincare	PROPN
ap-926	6	16	-	-	PUNCT
ap-926	6	17	birkhoff	birkhoff	NOUN
ap-926	6	18	-	-	PUNCT
ap-926	6	19	witt	witt	NOUN
ap-926	6	20	theorem	theorem	NOUN
ap-926	6	21	and	and	CCONJ
ap-926	6	22	consists	consist	VERB
ap-926	6	23	of	of	ADP
ap-926	6	24	all	all	DET
ap-926	6	25	complex	complex	ADJ
ap-926	6	26	linear	linear	ADJ
ap-926	6	27	combinations	combination	NOUN
ap-926	6	28	of	of	ADP
ap-926	6	29	monomials	monomial	NOUN
ap-926	6	30	e	e	PROPN
ap-926	6	31	e	e	X
ap-926	6	32	h12	h12	NOUN
ap-926	6	33	21	21	NUM
ap-926	6	34	1	1	NUM
ap-926	6	35	0	0	NUM
ap-926	6	36	�	�	PROPN
ap-926	6	37	�	�	PROPN
ap-926	6	38	�	�	PROPN
ap-926	6	39	�	�	PROPN
ap-926	6	40	�	�	PROPN
ap-926	6	41	�	�	PROPN
ap-926	6	42	,	,	PUNCT
ap-926	6	43	,	,	PUNCT
ap-926	6	44	,	,	PUNCT
ap-926	6	45	�	�	PROPN
ap-926	6	46	.	.	PUNCT
ap-926	7	1	it	it	PRON
ap-926	7	2	has	have	VERB
ap-926	7	3	a	a	DET
ap-926	7	4	natural	natural	ADJ
ap-926	7	5	filtration	filtration	NOUN
ap-926	7	6	un	un	NOUN
ap-926	7	7	,	,	PUNCT
ap-926	7	8	n	n	PRON
ap-926	7	9	�	�	PROPN
ap-926	7	10	0given	0given	NUM
ap-926	7	11	by	by	ADP
ap-926	7	12	the	the	DET
ap-926	7	13	degree	degree	NOUN
ap-926	7	14	n	n	PROPN
ap-926	7	15	of	of	ADP
ap-926	7	16	the	the	DET
ap-926	7	17	elements	element	NOUN
ap-926	7	18	in	in	ADP
ap-926	7	19	un	un	PROPN
ap-926	7	20	.	.	PUNCT
ap-926	8	1	it	it	PRON
ap-926	8	2	is	be	AUX
ap-926	8	3	easily	easily	ADV
ap-926	8	4	seen	see	VERB
ap-926	8	5	that	that	SCONJ
ap-926	8	6	the	the	DET
ap-926	8	7	adjoint	adjoint	NOUN
ap-926	8	8	action	action	NOUN
ap-926	8	9	has	have	AUX
ap-926	8	10	un	un	PROPN
ap-926	8	11	as	as	ADP
ap-926	8	12	its	its	PRON
ap-926	8	13	invariant	invariant	ADJ
ap-926	8	14	subspace	subspace	NOUN
ap-926	8	15	(	(	PUNCT
ap-926	8	16	by	by	ADP
ap-926	8	17	applying	apply	VERB
ap-926	8	18	a	a	DET
ap-926	8	19	commutator	commutator	NOUN
ap-926	8	20	we	we	PRON
ap-926	8	21	can	can	AUX
ap-926	8	22	not	not	PART
ap-926	8	23	obtain	obtain	VERB
ap-926	8	24	an	an	DET
ap-926	8	25	element	element	NOUN
ap-926	8	26	of	of	ADP
ap-926	8	27	higher	high	ADJ
ap-926	8	28	degree	degree	NOUN
ap-926	8	29	)	)	PUNCT
ap-926	8	30	.	.	PUNCT
ap-926	9	1	therefore	therefore	ADV
ap-926	9	2	it	it	PRON
ap-926	9	3	is	be	AUX
ap-926	9	4	completely	completely	ADV
ap-926	9	5	reducible	reducible	ADJ
ap-926	9	6	on	on	ADP
ap-926	9	7	each	each	DET
ap-926	9	8	un	un	PROPN
ap-926	9	9	,	,	PUNCT
ap-926	9	10	i.e.	i.e.	X
ap-926	9	11	we	we	PRON
ap-926	9	12	can	can	AUX
ap-926	9	13	see	see	VERB
ap-926	9	14	un	un	PROPN
ap-926	9	15	as	as	ADP
ap-926	9	16	a	a	DET
ap-926	9	17	direct	direct	ADJ
ap-926	9	18	sum	sum	NOUN
ap-926	9	19	of	of	ADP
ap-926	9	20	invariant	invariant	ADJ
ap-926	9	21	subspaces	subspace	NOUN
ap-926	9	22	generated	generate	VERB
ap-926	9	23	by	by	ADP
ap-926	9	24	certain	certain	ADJ
ap-926	9	25	highest	high	ADJ
ap-926	9	26	weight	weight	NOUN
ap-926	9	27	vectors	vector	NOUN
ap-926	9	28	.	.	PUNCT
ap-926	10	1	the	the	DET
ap-926	10	2	highest	high	ADJ
ap-926	10	3	weight	weight	NOUN
ap-926	10	4	vector	vector	NOUN
ap-926	10	5	v	v	NOUN
ap-926	10	6	of	of	ADP
ap-926	10	7	weight	weight	NOUN
ap-926	10	8	m	m	VERB
ap-926	10	9	satisfies	satisfy	VERB
ap-926	10	10	the	the	DET
ap-926	10	11	relations	relation	NOUN
ap-926	10	12	[	[	PUNCT
ap-926	10	13	,	,	PUNCT
ap-926	10	14	]	]	PUNCT
ap-926	10	15	,	,	PUNCT
ap-926	10	16	[	[	PUNCT
ap-926	10	17	,	,	PUNCT
ap-926	10	18	]	]	X
ap-926	10	19	e	e	X
ap-926	10	20	v	v	NUM
ap-926	10	21	h	h	NOUN
ap-926	10	22	v	v	ADP
ap-926	10	23	mv12	mv12	PROPN
ap-926	10	24	10	10	NUM
ap-926	10	25	2	2	NUM
ap-926	10	26	�	�	PROPN
ap-926	10	27	�	�	PROPN
ap-926	10	28	.	.	PUNCT
ap-926	11	1	from	from	ADP
ap-926	11	2	this	this	PRON
ap-926	11	3	we	we	PRON
ap-926	11	4	can	can	AUX
ap-926	11	5	directly	directly	ADV
ap-926	11	6	find	find	VERB
ap-926	11	7	that	that	SCONJ
ap-926	11	8	all	all	DET
ap-926	11	9	highest	high	ADJ
ap-926	11	10	weight	weight	NOUN
ap-926	11	11	vectors	vector	NOUN
ap-926	11	12	of	of	ADP
ap-926	11	13	small	small	ADJ
ap-926	11	14	degree	degree	NOUN
ap-926	11	15	:	:	PUNCT
ap-926	11	16	degree	degree	NOUN
ap-926	11	17	0	0	NUM
ap-926	11	18	1	1	NUM
ap-926	11	19	degree	degree	NOUN
ap-926	11	20	1	1	NUM
ap-926	11	21	e12	e12	NOUN
ap-926	11	22	degree	degree	NOUN
ap-926	11	23	2	2	NUM
ap-926	11	24	e	e	NOUN
ap-926	11	25	c12	c12	NOUN
ap-926	11	26	2	2	NUM
ap-926	11	27	1	1	NUM
ap-926	11	28	,	,	PUNCT
ap-926	11	29	degree	degree	NOUN
ap-926	11	30	3	3	NUM
ap-926	11	31	e	e	NOUN
ap-926	11	32	c	c	PROPN
ap-926	11	33	e12	e12	PROPN
ap-926	11	34	3	3	NUM
ap-926	11	35	1	1	NUM
ap-926	11	36	12	12	NUM
ap-926	11	37	,	,	PUNCT
ap-926	11	38	…	…	PUNCT
ap-926	11	39	…	…	PUNCT
ap-926	11	40	here	here	ADV
ap-926	11	41	c	c	NOUN
ap-926	11	42	h	h	NOUN
ap-926	12	1	e	e	NOUN
ap-926	13	1	e	e	NOUN
ap-926	13	2	h1	h1	VERB
ap-926	13	3	1	1	NUM
ap-926	13	4	2	2	NUM
ap-926	13	5	12	12	NUM
ap-926	13	6	21	21	NUM
ap-926	13	7	14	14	NUM
ap-926	13	8	2	2	NUM
ap-926	13	9	�	�	PROPN
ap-926	13	10	�	�	PROPN
ap-926	13	11	is	be	AUX
ap-926	13	12	a	a	DET
ap-926	13	13	casimir	casimir	NOUN
ap-926	13	14	element	element	NOUN
ap-926	13	15	from	from	ADP
ap-926	13	16	the	the	DET
ap-926	13	17	center	center	NOUN
ap-926	13	18	of	of	ADP
ap-926	13	19	u.	u.	NOUN
ap-926	13	20	by	by	ADP
ap-926	13	21	commuting	commute	VERB
ap-926	13	22	these	these	DET
ap-926	13	23	vectors	vector	NOUN
ap-926	13	24	we	we	PRON
ap-926	13	25	see	see	VERB
ap-926	13	26	that	that	SCONJ
ap-926	13	27	©	©	PROPN
ap-926	13	28	czech	czech	PROPN
ap-926	13	29	technical	technical	PROPN
ap-926	13	30	university	university	PROPN
ap-926	13	31	publishing	publishing	NOUN
ap-926	13	32	house	house	NOUN
ap-926	13	33	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-926	13	34	25	25	NUM
ap-926	13	35	acta	acta	PROPN
ap-926	13	36	polytechnica	polytechnica	PROPN
ap-926	13	37	vol	vol	NOUN
ap-926	13	38	.	.	PUNCT
ap-926	14	1	47	47	NUM
ap-926	14	2	no	no	NOUN
ap-926	14	3	.	.	PUNCT
ap-926	15	1	2–3/2007	2–3/2007	NUM
ap-926	15	2	structure	structure	NOUN
ap-926	15	3	of	of	ADP
ap-926	15	4	the	the	DET
ap-926	15	5	enveloping	enveloping	NOUN
ap-926	15	6	algebras	algebras	PROPN
ap-926	15	7	č	č	PROPN
ap-926	15	8	.	.	PUNCT
ap-926	15	9	burdík	burdík	PROPN
ap-926	15	10	,	,	PUNCT
ap-926	15	11	o.	o.	PROPN
ap-926	15	12	navrátil	navrátil	PROPN
ap-926	15	13	,	,	PUNCT
ap-926	15	14	s.	s.	PROPN
ap-926	15	15	pošta	pošta	PROPN
ap-926	15	16	the	the	DET
ap-926	15	17	adjoint	adjoint	NOUN
ap-926	15	18	representations	representation	NOUN
ap-926	15	19	of	of	ADP
ap-926	15	20	several	several	ADJ
ap-926	15	21	small	small	ADJ
ap-926	15	22	dimensional	dimensional	ADJ
ap-926	15	23	lie	lie	NOUN
ap-926	15	24	algebras	algebra	NOUN
ap-926	15	25	on	on	ADP
ap-926	15	26	their	their	PRON
ap-926	15	27	universal	universal	ADJ
ap-926	15	28	enveloping	enveloping	NOUN
ap-926	15	29	algebras	algebra	NOUN
ap-926	15	30	are	be	AUX
ap-926	15	31	explicitly	explicitly	ADV
ap-926	15	32	decomposed	decompose	VERB
ap-926	15	33	.	.	PUNCT
ap-926	16	1	it	it	PRON
ap-926	16	2	is	be	AUX
ap-926	16	3	shown	show	VERB
ap-926	16	4	that	that	SCONJ
ap-926	16	5	commutants	commutant	NOUN
ap-926	16	6	of	of	ADP
ap-926	16	7	raising	raise	VERB
ap-926	16	8	operators	operator	NOUN
ap-926	16	9	are	be	AUX
ap-926	16	10	generated	generate	VERB
ap-926	16	11	as	as	ADP
ap-926	16	12	polynomials	polynomial	NOUN
ap-926	16	13	in	in	ADP
ap-926	16	14	several	several	ADJ
ap-926	16	15	basic	basic	ADJ
ap-926	16	16	elements	element	NOUN
ap-926	16	17	.	.	PUNCT
ap-926	17	1	the	the	DET
ap-926	17	2	explicit	explicit	ADJ
ap-926	17	3	form	form	NOUN
ap-926	17	4	of	of	ADP
ap-926	17	5	these	these	DET
ap-926	17	6	elements	element	NOUN
ap-926	17	7	is	be	AUX
ap-926	17	8	given	give	VERB
ap-926	17	9	and	and	CCONJ
ap-926	17	10	the	the	DET
ap-926	17	11	general	general	ADJ
ap-926	17	12	method	method	NOUN
ap-926	17	13	for	for	ADP
ap-926	17	14	obtaining	obtain	VERB
ap-926	17	15	these	these	DET
ap-926	17	16	elements	element	NOUN
ap-926	17	17	is	be	AUX
ap-926	17	18	described	describe	VERB
ap-926	17	19	.	.	PUNCT
ap-926	18	1	keywords	keyword	NOUN
ap-926	18	2	:	:	PUNCT
ap-926	18	3	adjoint	adjoint	NOUN
ap-926	18	4	representation	representation	NOUN
ap-926	18	5	,	,	PUNCT
ap-926	18	6	enveloping	envelop	VERB
ap-926	18	7	algebra	algebra	NOUN
ap-926	18	8	,	,	PUNCT
ap-926	18	9	lie	lie	NOUN
ap-926	18	10	algebra	algebra	NOUN
ap-926	18	11	.	.	PUNCT
ap-926	19	1	u	u	PRON
ap-926	19	2	u	u	X
ap-926	19	3	u	u	X
ap-926	19	4	u	u	X
ap-926	19	5	e	e	X
ap-926	19	6	u	u	NOUN
ap-926	19	7	u	u	X
ap-926	19	8	u	u	NOUN
ap-926	19	9	e	e	X
ap-926	19	10	u	u	NOUN
ap-926	19	11	c	c	PROPN
ap-926	19	12	u	u	NOUN
ap-926	19	13	0	0	NUM
ap-926	19	14	1	1	NUM
ap-926	19	15	12	12	NUM
ap-926	19	16	0	0	NUM
ap-926	19	17	2	2	NUM
ap-926	19	18	12	12	NUM
ap-926	19	19	2	2	NUM
ap-926	19	20	1	1	NUM
ap-926	19	21	1	1	NUM
ap-926	19	22	1	1	NUM
ap-926	19	23	�	�	PROPN
ap-926	19	24	�	�	PROPN
ap-926	19	25	�	�	PROPN
ap-926	19	26	�	�	PROPN
ap-926	19	27	�	�	PROPN
ap-926	19	28	�	�	PROPN
ap-926	19	29	�	�	PROPN
ap-926	19	30	�	�	PROPN
ap-926	19	31	�	�	PROPN
ap-926	19	32	�	�	PROPN
ap-926	19	33	(	(	PUNCT
ap-926	19	34	)	)	PUNCT
ap-926	19	35	,	,	PUNCT
ap-926	19	36	(	(	PUNCT
ap-926	19	37	)	)	PUNCT
ap-926	19	38	,	,	PUNCT
ap-926	19	39	(	(	PUNCT
ap-926	19	40	)	)	PUNCT
ap-926	19	41	(	(	PUNCT
ap-926	19	42	)	)	PUNCT
ap-926	19	43	,	,	PUNCT
ap-926	19	44	�	�	PROPN
ap-926	19	45	from	from	ADP
ap-926	19	46	this	this	PRON
ap-926	19	47	we	we	PRON
ap-926	19	48	can	can	AUX
ap-926	19	49	claim	claim	VERB
ap-926	19	50	that	that	SCONJ
ap-926	19	51	for	for	ADP
ap-926	19	52	any	any	DET
ap-926	19	53	n	n	PRON
ap-926	19	54	�	�	PROPN
ap-926	19	55	0	0	NUM
ap-926	19	56	u	u	PROPN
ap-926	19	57	u	u	X
ap-926	19	58	c	c	PROPN
ap-926	19	59	en	en	X
ap-926	19	60	k	k	PROPN
ap-926	19	61	m	m	VERB
ap-926	19	62	k	k	PROPN
ap-926	19	63	m	m	VERB
ap-926	19	64	n	n	PROPN
ap-926	19	65	k	k	PROPN
ap-926	19	66	m	m	PROPN
ap-926	19	67	�	�	PROPN
ap-926	19	68	�	�	PROPN
ap-926	19	69	�	�	PROPN
ap-926	19	70	,	,	PUNCT
ap-926	19	71	(	(	PUNCT
ap-926	19	72	)	)	PUNCT
ap-926	19	73	0	0	NUM
ap-926	19	74	2	2	NUM
ap-926	19	75	1	1	NUM
ap-926	19	76	12	12	NUM
ap-926	19	77	�	�	PROPN
ap-926	19	78	(	(	PUNCT
ap-926	19	79	1	1	NUM
ap-926	19	80	)	)	PUNCT
ap-926	19	81	the	the	DET
ap-926	19	82	proof	proof	NOUN
ap-926	19	83	of	of	ADP
ap-926	19	84	this	this	DET
ap-926	19	85	general	general	ADJ
ap-926	19	86	formula	formula	NOUN
ap-926	19	87	is	be	AUX
ap-926	19	88	based	base	VERB
ap-926	19	89	on	on	ADP
ap-926	19	90	a	a	DET
ap-926	19	91	dimensional	dimensional	ADJ
ap-926	19	92	check	check	NOUN
ap-926	19	93	:	:	PUNCT
ap-926	19	94	first	first	ADV
ap-926	19	95	we	we	PRON
ap-926	19	96	see	see	VERB
ap-926	19	97	that	that	SCONJ
ap-926	19	98	the	the	DET
ap-926	19	99	sum	sum	NOUN
ap-926	19	100	�	�	PROPN
ap-926	19	101	�	�	PROPN
ap-926	19	102	(	(	PUNCT
ap-926	19	103	)	)	PUNCT
ap-926	19	104	(	(	PUNCT
ap-926	19	105	)	)	PUNCT
ap-926	19	106	u	u	NOUN
ap-926	19	107	v	v	NUM
ap-926	19	108	u	u	NOUN
ap-926	19	109	v1	v1	NOUN
ap-926	19	110	2	2	NUM
ap-926	19	111	,	,	PUNCT
ap-926	19	112	where	where	SCONJ
ap-926	19	113	v1	v1	NOUN
ap-926	19	114	,	,	PUNCT
ap-926	19	115	v2	v2	PROPN
ap-926	19	116	are	be	AUX
ap-926	19	117	highest	high	ADJ
ap-926	19	118	weight	weight	NOUN
ap-926	19	119	vectors	vector	NOUN
ap-926	19	120	,	,	PUNCT
ap-926	19	121	is	be	AUX
ap-926	19	122	direct	direct	ADJ
ap-926	19	123	if	if	SCONJ
ap-926	19	124	and	and	CCONJ
ap-926	19	125	only	only	ADV
ap-926	19	126	if	if	SCONJ
ap-926	19	127	v1	v1	NOUN
ap-926	19	128	,	,	PUNCT
ap-926	19	129	v2	v2	PROPN
ap-926	19	130	are	be	AUX
ap-926	19	131	linear	linear	ADJ
ap-926	19	132	independent	independent	ADJ
ap-926	19	133	.	.	PUNCT
ap-926	20	1	thus	thus	ADV
ap-926	20	2	in	in	ADP
ap-926	20	3	our	our	PRON
ap-926	20	4	example	example	NOUN
ap-926	20	5	we	we	PRON
ap-926	20	6	must	must	AUX
ap-926	20	7	check	check	VERB
ap-926	20	8	that	that	SCONJ
ap-926	20	9	the	the	DET
ap-926	20	10	vectors	vector	NOUN
ap-926	20	11	c	c	PROPN
ap-926	20	12	ek	ek	PROPN
ap-926	20	13	m	m	VERB
ap-926	20	14	1	1	NUM
ap-926	20	15	12	12	NUM
ap-926	20	16	are	be	AUX
ap-926	20	17	linear	linear	ADJ
ap-926	20	18	independent	independent	ADJ
ap-926	20	19	for	for	ADP
ap-926	20	20	different	different	ADJ
ap-926	20	21	k	k	NOUN
ap-926	20	22	,	,	PUNCT
ap-926	20	23	m.	m.	NOUN
ap-926	20	24	but	but	CCONJ
ap-926	20	25	this	this	PRON
ap-926	20	26	is	be	AUX
ap-926	20	27	easily	easily	ADV
ap-926	20	28	seen	see	VERB
ap-926	20	29	from	from	ADP
ap-926	20	30	the	the	DET
ap-926	20	31	definition	definition	NOUN
ap-926	20	32	,	,	PUNCT
ap-926	20	33	since	since	SCONJ
ap-926	20	34	c	c	X
ap-926	20	35	e	e	PROPN
ap-926	20	36	e	e	PROPN
ap-926	20	37	hk	hk	PROPN
ap-926	20	38	m	m	PROPN
ap-926	20	39	m	m	VERB
ap-926	20	40	k	k	ADJ
ap-926	20	41	1	1	NUM
ap-926	20	42	12	12	NUM
ap-926	20	43	12	12	NUM
ap-926	20	44	1	1	NUM
ap-926	20	45	2	2	NUM
ap-926	20	46	�	�	NOUN
ap-926	20	47	lower	low	ADJ
ap-926	20	48	terms	term	NOUN
ap-926	20	49	where	where	SCONJ
ap-926	20	50	“	"	PUNCT
ap-926	20	51	lower	low	ADJ
ap-926	20	52	terms	term	NOUN
ap-926	20	53	“	"	PUNCT
ap-926	20	54	contain	contain	VERB
ap-926	20	55	monomials	monomial	NOUN
ap-926	20	56	with	with	ADP
ap-926	20	57	h	h	NOUN
ap-926	20	58	k	k	NOUN
ap-926	20	59	1	1	NUM
ap-926	20	60	2	2	NUM
ap-926	20	61	1	1	NUM
ap-926	20	62	�	�	NOUN
ap-926	20	63	and	and	CCONJ
ap-926	20	64	lower	low	ADJ
ap-926	20	65	.	.	PUNCT
ap-926	21	1	next	next	ADV
ap-926	21	2	it	it	PRON
ap-926	21	3	is	be	AUX
ap-926	21	4	well	well	ADV
ap-926	21	5	known	know	VERB
ap-926	21	6	from	from	ADP
ap-926	21	7	representation	representation	NOUN
ap-926	21	8	theory	theory	NOUN
ap-926	21	9	that	that	SCONJ
ap-926	21	10	the	the	DET
ap-926	21	11	dimension	dimension	NOUN
ap-926	21	12	of	of	ADP
ap-926	21	13	the	the	DET
ap-926	21	14	irreducible	irreducible	ADJ
ap-926	21	15	representation	representation	NOUN
ap-926	21	16	with	with	ADP
ap-926	21	17	highest	high	ADJ
ap-926	21	18	weight	weight	NOUN
ap-926	21	19	m	m	NOUN
ap-926	21	20	is	be	AUX
ap-926	21	21	2	2	NUM
ap-926	21	22	1	1	NUM
ap-926	21	23	m	m	NOUN
ap-926	21	24	.	.	PUNCT
ap-926	22	1	on	on	ADP
ap-926	22	2	the	the	DET
ap-926	22	3	other	other	ADJ
ap-926	22	4	hand	hand	NOUN
ap-926	22	5	the	the	DET
ap-926	22	6	dimension	dimension	NOUN
ap-926	22	7	of	of	ADP
ap-926	22	8	un	un	PROPN
ap-926	22	9	is	be	AUX
ap-926	22	10	also	also	ADV
ap-926	22	11	easy	easy	ADJ
ap-926	22	12	to	to	PART
ap-926	22	13	determine	determine	VERB
ap-926	22	14	,	,	PUNCT
ap-926	22	15	because	because	SCONJ
ap-926	22	16	it	it	PRON
ap-926	22	17	is	be	AUX
ap-926	22	18	well	well	ADV
ap-926	22	19	known	know	VERB
ap-926	22	20	that	that	SCONJ
ap-926	22	21	it	it	PRON
ap-926	22	22	is	be	AUX
ap-926	22	23	isomorphic	isomorphic	ADJ
ap-926	22	24	(	(	PUNCT
ap-926	22	25	as	as	ADP
ap-926	22	26	a	a	DET
ap-926	22	27	vector	vector	NOUN
ap-926	22	28	space	space	NOUN
ap-926	22	29	)	)	PUNCT
ap-926	22	30	to	to	ADP
ap-926	22	31	the	the	DET
ap-926	22	32	direct	direct	ADJ
ap-926	22	33	sum	sum	NOUN
ap-926	22	34	�	�	PROPN
ap-926	22	35	�	�	PROPN
ap-926	22	36	k	k	PROPN
ap-926	22	37	n	n	PROPN
ap-926	22	38	ks	ks	NOUN
ap-926	22	39	g	g	PROPN
ap-926	22	40	0	0	NUM
ap-926	22	41	(	(	PUNCT
ap-926	22	42	)	)	PUNCT
ap-926	22	43	of	of	ADP
ap-926	22	44	the	the	DET
ap-926	22	45	k	k	PROPN
ap-926	22	46	-	-	PUNCT
ap-926	22	47	th	th	VERB
ap-926	22	48	symmetric	symmetric	ADJ
ap-926	22	49	powers	power	NOUN
ap-926	22	50	of	of	ADP
ap-926	22	51	lie	lie	NOUN
ap-926	22	52	algebra	algebra	NOUN
ap-926	22	53	g.	g.	NOUN
ap-926	23	1	we	we	PRON
ap-926	23	2	can	can	AUX
ap-926	23	3	construct	construct	VERB
ap-926	23	4	the	the	DET
ap-926	23	5	symmetric	symmetric	ADJ
ap-926	23	6	algebra	algebra	PROPN
ap-926	23	7	s(g	s(g	PROPN
ap-926	23	8	)	)	PUNCT
ap-926	23	9	from	from	ADP
ap-926	23	10	the	the	DET
ap-926	23	11	tensor	tensor	NOUN
ap-926	23	12	algebra	algebra	NOUN
ap-926	23	13	t(g	t(g	PRON
ap-926	23	14	)	)	PUNCT
ap-926	23	15	by	by	ADP
ap-926	23	16	taking	take	VERB
ap-926	23	17	the	the	DET
ap-926	23	18	quotient	quotient	NOUN
ap-926	23	19	algebra	algebra	NOUN
ap-926	23	20	of	of	ADP
ap-926	23	21	t(g	t(g	NOUN
ap-926	23	22	)	)	PUNCT
ap-926	23	23	by	by	ADP
ap-926	23	24	the	the	DET
ap-926	23	25	ideal	ideal	NOUN
ap-926	23	26	generated	generate	VERB
ap-926	23	27	by	by	ADP
ap-926	23	28	all	all	DET
ap-926	23	29	differences	difference	NOUN
ap-926	23	30	of	of	ADP
ap-926	23	31	products	product	NOUN
ap-926	23	32	v	v	ADP
ap-926	23	33	w	w	PROPN
ap-926	23	34	w	w	PROPN
ap-926	23	35	v	v	PRON
ap-926	23	36	�	�	PROPN
ap-926	23	37	�	�	PROPN
ap-926	23	38	�	�	PROPN
ap-926	23	39	for	for	ADP
ap-926	23	40	v	v	PROPN
ap-926	23	41	w	w	NOUN
ap-926	23	42	g	g	NOUN
ap-926	23	43	,	,	PUNCT
ap-926	23	44	�	�	PROPN
ap-926	23	45	;	;	VERB
ap-926	23	46	then	then	ADV
ap-926	23	47	there	there	PRON
ap-926	23	48	is	be	VERB
ap-926	23	49	a	a	DET
ap-926	23	50	direct	direct	ADJ
ap-926	23	51	sum	sum	NOUN
ap-926	23	52	decomposition	decomposition	NOUN
ap-926	23	53	of	of	ADP
ap-926	23	54	s(g	s(g	PROPN
ap-926	23	55	)	)	PUNCT
ap-926	23	56	as	as	ADP
ap-926	23	57	a	a	DET
ap-926	23	58	graded	grade	VERB
ap-926	23	59	algebra	algebra	NOUN
ap-926	23	60	into	into	ADP
ap-926	23	61	the	the	DET
ap-926	23	62	summands	summand	NOUN
ap-926	23	63	sk(g	sk(g	NOUN
ap-926	23	64	)	)	PUNCT
ap-926	23	65	which	which	PRON
ap-926	23	66	consist	consist	VERB
ap-926	23	67	of	of	ADP
ap-926	23	68	the	the	DET
ap-926	23	69	linear	linear	ADJ
ap-926	23	70	span	span	NOUN
ap-926	23	71	of	of	ADP
ap-926	23	72	the	the	DET
ap-926	23	73	monomials	monomial	NOUN
ap-926	23	74	in	in	ADP
ap-926	23	75	vectors	vector	NOUN
ap-926	23	76	of	of	ADP
ap-926	23	77	g	g	NOUN
ap-926	23	78	of	of	ADP
ap-926	23	79	degree	degree	NOUN
ap-926	23	80	k.	k.	PROPN
ap-926	24	1	the	the	DET
ap-926	24	2	symmetric	symmetric	ADJ
ap-926	24	3	algebra	algebra	PROPN
ap-926	24	4	s(g	s(g	PROPN
ap-926	24	5	)	)	PUNCT
ap-926	24	6	is	be	AUX
ap-926	24	7	in	in	ADP
ap-926	24	8	effect	effect	NOUN
ap-926	24	9	the	the	DET
ap-926	24	10	same	same	ADJ
ap-926	24	11	as	as	ADP
ap-926	24	12	the	the	DET
ap-926	24	13	polynomial	polynomial	ADJ
ap-926	24	14	ring	ring	NOUN
ap-926	24	15	in	in	ADP
ap-926	24	16	the	the	DET
ap-926	24	17	indeterminates	indeterminate	NOUN
ap-926	24	18	that	that	PRON
ap-926	24	19	are	be	AUX
ap-926	24	20	basis	basis	NOUN
ap-926	24	21	vectors	vector	NOUN
ap-926	24	22	for	for	ADP
ap-926	24	23	g.	g.	PROPN
ap-926	24	24	therefore	therefore	ADV
ap-926	24	25	we	we	PRON
ap-926	24	26	see	see	VERB
ap-926	24	27	that	that	DET
ap-926	24	28	dim	dim	NOUN
ap-926	24	29	(	(	PUNCT
ap-926	24	30	)	)	PUNCT
ap-926	24	31	dim	dim	PROPN
ap-926	24	32	s	s	NOUN
ap-926	24	33	g	g	NOUN
ap-926	24	34	g	g	PROPN
ap-926	24	35	k	k	PROPN
ap-926	24	36	k	k	PROPN
ap-926	24	37	k	k	PROPN
ap-926	24	38	�	�	PROPN
ap-926	24	39	�	�	PROPN
ap-926	24	40	�	�	PROPN
ap-926	24	41	�	�	PROPN
ap-926	24	42	�	�	PROPN
ap-926	24	43	�	�	PROPN
ap-926	24	44	�	�	PROPN
ap-926	24	45	�	�	PROPN
ap-926	24	46	1	1	NUM
ap-926	24	47	and	and	CCONJ
ap-926	25	1	from	from	ADP
ap-926	25	2	this	this	PRON
ap-926	25	3	we	we	PRON
ap-926	25	4	have	have	AUX
ap-926	25	5	dim	dim	ADJ
ap-926	25	6	dim	dim	ADJ
ap-926	25	7	dim	dim	ADJ
ap-926	25	8	dim	dim	NOUN
ap-926	25	9	u	u	NOUN
ap-926	25	10	g	g	PROPN
ap-926	25	11	k	k	PROPN
ap-926	25	12	k	k	PROPN
ap-926	25	13	n	n	CCONJ
ap-926	25	14	g	g	PROPN
ap-926	25	15	gn	gn	PROPN
ap-926	25	16	k	k	PROPN
ap-926	25	17	n	n	PROPN
ap-926	25	18	�	�	PROPN
ap-926	25	19	�	�	PROPN
ap-926	25	20	�	�	PROPN
ap-926	25	21	�	�	PROPN
ap-926	25	22	�	�	PROPN
ap-926	25	23	�	�	PROPN
ap-926	25	24	�	�	PROPN
ap-926	25	25	�	�	PROPN
ap-926	25	26	�	�	PROPN
ap-926	25	27	�	�	PROPN
ap-926	25	28	�	�	PROPN
ap-926	25	29	�	�	PROPN
ap-926	25	30	�	�	PROPN
ap-926	25	31	�	�	PROPN
ap-926	25	32	�	�	PROPN
ap-926	25	33	�	�	PROPN
ap-926	25	34	�	�	PROPN
ap-926	25	35	1	1	NUM
ap-926	25	36	0	0	NUM
ap-926	25	37	,	,	PUNCT
ap-926	25	38	thus	thus	ADV
ap-926	25	39	in	in	ADP
ap-926	25	40	our	our	PRON
ap-926	25	41	example	example	NOUN
ap-926	25	42	dim	dim	ADJ
ap-926	25	43	u	u	NOUN
ap-926	25	44	n	n	CCONJ
ap-926	25	45	n	n	CCONJ
ap-926	25	46	�	�	PROPN
ap-926	25	47	�	�	PROPN
ap-926	25	48	�	�	PROPN
ap-926	25	49	�	�	PROPN
ap-926	25	50	�	�	PROPN
ap-926	25	51	�	�	PROPN
ap-926	25	52	�	�	PROPN
ap-926	25	53	3	3	NUM
ap-926	25	54	3	3	NUM
ap-926	25	55	.	.	PUNCT
ap-926	26	1	now	now	ADV
ap-926	26	2	it	it	PRON
ap-926	26	3	is	be	AUX
ap-926	26	4	sufficent	sufficent	NOUN
ap-926	26	5	to	to	PART
ap-926	26	6	prove	prove	VERB
ap-926	26	7	that	that	SCONJ
ap-926	26	8	the	the	DET
ap-926	26	9	dimensions	dimension	NOUN
ap-926	26	10	of	of	ADP
ap-926	26	11	two	two	NUM
ap-926	26	12	spaces	space	NOUN
ap-926	26	13	on	on	ADP
ap-926	26	14	both	both	DET
ap-926	26	15	sides	side	NOUN
ap-926	26	16	(	(	PUNCT
ap-926	26	17	1	1	X
ap-926	26	18	)	)	PUNCT
ap-926	26	19	are	be	AUX
ap-926	26	20	equal	equal	ADJ
ap-926	26	21	,	,	PUNCT
ap-926	27	1	i.e.	i.e.	X
ap-926	27	2	that	that	SCONJ
ap-926	27	3	n	n	NUM
ap-926	27	4	m	m	VERB
ap-926	27	5	k	k	NOUN
ap-926	27	6	m	m	VERB
ap-926	27	7	k	k	PROPN
ap-926	27	8	m	m	VERB
ap-926	27	9	n	n	PRON
ap-926	27	10	�	�	PROPN
ap-926	27	11	�	�	PROPN
ap-926	27	12	�	�	PROPN
ap-926	27	13	�	�	PROPN
ap-926	27	14	�	�	PROPN
ap-926	27	15	�	�	PROPN
ap-926	27	16	�	�	PROPN
ap-926	27	17	�	�	PROPN
ap-926	27	18	�	�	PROPN
ap-926	27	19	3	3	NUM
ap-926	27	20	3	3	NUM
ap-926	27	21	2	2	NUM
ap-926	27	22	1	1	NUM
ap-926	27	23	0	0	NUM
ap-926	27	24	2	2	NUM
ap-926	27	25	(	(	PUNCT
ap-926	27	26	)	)	PUNCT
ap-926	27	27	,	,	PUNCT
ap-926	27	28	.	.	PUNCT
ap-926	28	1	we	we	PRON
ap-926	28	2	have	have	VERB
ap-926	28	3	(	(	PUNCT
ap-926	28	4	)	)	PUNCT
ap-926	28	5	(	(	PUNCT
ap-926	28	6	)	)	PUNCT
ap-926	28	7	(	(	PUNCT
ap-926	28	8	)	)	PUNCT
ap-926	28	9	,	,	PUNCT
ap-926	28	10	2	2	NUM
ap-926	28	11	1	1	NUM
ap-926	28	12	2	2	NUM
ap-926	28	13	1	1	NUM
ap-926	28	14	2	2	NUM
ap-926	28	15	1	1	NUM
ap-926	28	16	0	0	NUM
ap-926	28	17	2	2	NUM
ap-926	28	18	0	0	NUM
ap-926	28	19	2	2	NUM
ap-926	28	20	0	0	NUM
ap-926	28	21	0	0	NUM
ap-926	28	22	m	m	VERB
ap-926	28	23	m	m	VERB
ap-926	28	24	m	m	VERB
ap-926	28	25	k	k	X
ap-926	28	26	m	m	VERB
ap-926	28	27	k	k	NOUN
ap-926	28	28	m	m	VERB
ap-926	28	29	n	n	VERB
ap-926	28	30	m	m	VERB
ap-926	28	31	n	n	ADJ
ap-926	28	32	k	k	X
ap-926	28	33	k	k	PROPN
ap-926	28	34	m	m	VERB
ap-926	28	35	n	n	PRON
ap-926	28	36	�	�	PROPN
ap-926	28	37	�	�	PROPN
ap-926	28	38	�	�	PROPN
ap-926	28	39	�	�	PROPN
ap-926	28	40	�	�	PROPN
ap-926	28	41	�	�	PROPN
ap-926	28	42	�	�	PROPN
ap-926	28	43	�	�	PROPN
ap-926	28	44	�	�	PROPN
ap-926	28	45	�	�	PROPN
ap-926	28	46	�	�	PROPN
ap-926	28	47	�	�	PROPN
ap-926	28	48	�	�	PROPN
ap-926	28	49	�	�	PROPN
ap-926	28	50	�	�	PROPN
ap-926	28	51	�	�	PROPN
ap-926	28	52	�	�	PROPN
ap-926	28	53	�	�	PROPN
ap-926	28	54	�	�	PROPN
ap-926	28	55	�	�	PROPN
ap-926	28	56	�	�	PROPN
ap-926	28	57	�	�	PROPN
ap-926	28	58	�	�	PROPN
ap-926	28	59	�	�	PROPN
ap-926	28	60	�	�	PROPN
ap-926	28	61	�	�	PROPN
ap-926	28	62	2	2	NUM
ap-926	28	63	0	0	NUM
ap-926	28	64	2	2	NUM
ap-926	28	65	2	2	NUM
ap-926	28	66	2	2	NUM
ap-926	28	67	1	1	NUM
ap-926	28	68	1	1	NUM
ap-926	28	69	6	6	NUM
ap-926	28	70	1	1	NUM
ap-926	28	71	2	2	NUM
ap-926	28	72	3	3	NUM
ap-926	28	73	3	3	NUM
ap-926	28	74	3	3	NUM
ap-926	28	75	k	k	NOUN
ap-926	28	76	k	k	PROPN
ap-926	28	77	k	k	PROPN
ap-926	28	78	n	n	CCONJ
ap-926	28	79	n	n	CCONJ
ap-926	28	80	k	k	PROPN
ap-926	28	81	n	n	CCONJ
ap-926	28	82	n	n	CCONJ
ap-926	28	83	n	n	CCONJ
ap-926	28	84	n	n	PROPN
ap-926	28	85	(	(	PUNCT
ap-926	28	86	)	)	PUNCT
ap-926	28	87	(	(	PUNCT
ap-926	28	88	)	)	PUNCT
ap-926	28	89	(	(	PUNCT
ap-926	28	90	(	(	PUNCT
ap-926	28	91	(	(	PUNCT
ap-926	28	92	)	)	PUNCT
ap-926	28	93	�	�	PROPN
ap-926	28	94	�	�	PROPN
ap-926	28	95	�	�	PROPN
ap-926	28	96	�	�	PROPN
ap-926	28	97	0	0	NUM
ap-926	28	98	2	2	NUM
ap-926	28	99	n	n	NOUN
ap-926	28	100	.	.	PUNCT
ap-926	29	1	3	3	NUM
ap-926	29	2	moving	move	VERB
ap-926	29	3	to	to	ADP
ap-926	29	4	the	the	DET
ap-926	29	5	commutative	commutative	ADJ
ap-926	29	6	case	case	NOUN
ap-926	29	7	there	there	PRON
ap-926	29	8	is	be	VERB
ap-926	29	9	an	an	DET
ap-926	29	10	alternative	alternative	ADJ
ap-926	29	11	approach	approach	NOUN
ap-926	29	12	to	to	PART
ap-926	29	13	obtain	obtain	VERB
ap-926	29	14	this	this	DET
ap-926	29	15	decomposition	decomposition	NOUN
ap-926	29	16	–	–	PUNCT
ap-926	29	17	move	move	VERB
ap-926	29	18	to	to	ADP
ap-926	29	19	the	the	DET
ap-926	29	20	commutative	commutative	ADJ
ap-926	29	21	case	case	NOUN
ap-926	29	22	:	:	PUNCT
ap-926	29	23	it	it	PRON
ap-926	29	24	is	be	AUX
ap-926	29	25	a	a	DET
ap-926	29	26	well	well	ADV
ap-926	29	27	-	-	PUNCT
ap-926	29	28	known	know	VERB
ap-926	29	29	fact	fact	NOUN
ap-926	29	30	(	(	PUNCT
ap-926	29	31	see	see	VERB
ap-926	29	32	[	[	X
ap-926	29	33	2	2	NUM
ap-926	29	34	]	]	PUNCT
ap-926	29	35	)	)	PUNCT
ap-926	29	36	that	that	SCONJ
ap-926	29	37	the	the	DET
ap-926	29	38	mapping	mapping	NOUN
ap-926	29	39	e	e	NOUN
ap-926	29	40	c	c	NOUN
ap-926	29	41	x	x	SYM
ap-926	29	42	xi	xi	NUM
ap-926	29	43	ij	ij	INTJ
ap-926	29	44	k	k	PROPN
ap-926	29	45	k	k	PROPN
ap-926	29	46	jj	jj	PROPN
ap-926	29	47	k	k	PROPN
ap-926	29	48	n	n	PROPN
ap-926	29	49	�	�	PROPN
ap-926	29	50	�	�	PROPN
ap-926	29	51	�	�	PROPN
ap-926	29	52	�	�	PROPN
ap-926	29	53	�	�	PROPN
ap-926	29	54	,	,	PUNCT
ap-926	29	55	1	1	NUM
ap-926	29	56	is	be	AUX
ap-926	29	57	a	a	DET
ap-926	29	58	representation	representation	NOUN
ap-926	29	59	of	of	ADP
ap-926	29	60	an	an	DET
ap-926	29	61	n	n	ADV
ap-926	29	62	-	-	PUNCT
ap-926	29	63	dimensional	dimensional	ADJ
ap-926	29	64	lie	lie	NOUN
ap-926	29	65	algebra	algebra	NOUN
ap-926	29	66	with	with	ADP
ap-926	29	67	basis	basis	NOUN
ap-926	29	68	ei	ei	NOUN
ap-926	29	69	,	,	PUNCT
ap-926	29	70	i	i	PROPN
ap-926	29	71	n	n	CCONJ
ap-926	29	72	�	�	PROPN
ap-926	29	73	1	1	NUM
ap-926	29	74	,	,	PUNCT
ap-926	29	75	,	,	PUNCT
ap-926	29	76	�	�	PROPN
ap-926	29	77	on	on	ADP
ap-926	29	78	a	a	DET
ap-926	29	79	space	space	NOUN
ap-926	29	80	of	of	ADP
ap-926	29	81	polynomials	polynomial	NOUN
ap-926	29	82	of	of	ADP
ap-926	29	83	the	the	DET
ap-926	29	84	variables	variable	NOUN
ap-926	29	85	xi	xi	PROPN
ap-926	29	86	,	,	PUNCT
ap-926	29	87	i	i	PROPN
ap-926	29	88	n	n	CCONJ
ap-926	29	89	�	�	PROPN
ap-926	29	90	1	1	NUM
ap-926	29	91	,	,	PUNCT
ap-926	29	92	,	,	PUNCT
ap-926	29	93	�	�	PROPN
ap-926	29	94	;	;	PUNCT
ap-926	29	95	if	if	SCONJ
ap-926	29	96	we	we	PRON
ap-926	29	97	view	view	VERB
ap-926	29	98	s(g	s(g	PROPN
ap-926	29	99	)	)	PUNCT
ap-926	29	100	as	as	ADP
ap-926	29	101	the	the	DET
ap-926	29	102	polynomial	polynomial	ADJ
ap-926	29	103	ring	ring	NOUN
ap-926	29	104	,	,	PUNCT
ap-926	29	105	this	this	DET
ap-926	29	106	representation	representation	NOUN
ap-926	29	107	is	be	AUX
ap-926	29	108	equivalent	equivalent	ADJ
ap-926	29	109	as	as	ADP
ap-926	29	110	a	a	DET
ap-926	29	111	representation	representation	NOUN
ap-926	29	112	of	of	ADP
ap-926	29	113	the	the	DET
ap-926	29	114	enveloping	enveloping	NOUN
ap-926	29	115	algebra	algebra	NOUN
ap-926	29	116	to	to	ADP
ap-926	29	117	the	the	DET
ap-926	29	118	adjoint	adjoint	PROPN
ap-926	29	119	representation	representation	NOUN
ap-926	29	120	via	via	ADP
ap-926	29	121	canonical	canonical	ADJ
ap-926	29	122	isomorphism	isomorphism	NOUN
ap-926	29	123	u	u	NOUN
ap-926	29	124	g	g	PROPN
ap-926	29	125	s	s	PROPN
ap-926	29	126	g	g	NOUN
ap-926	29	127	(	(	PUNCT
ap-926	29	128	)	)	PUNCT
ap-926	29	129	(	(	PUNCT
ap-926	29	130	)	)	PUNCT
ap-926	29	131	�	�	PROPN
ap-926	29	132	.	.	PUNCT
ap-926	30	1	therefore	therefore	ADV
ap-926	30	2	if	if	SCONJ
ap-926	30	3	we	we	PRON
ap-926	30	4	return	return	VERB
ap-926	30	5	to	to	ADP
ap-926	30	6	our	our	PRON
ap-926	30	7	example	example	NOUN
ap-926	30	8	and	and	CCONJ
ap-926	30	9	represent	represent	VERB
ap-926	30	10	the	the	DET
ap-926	30	11	basis	basis	NOUN
ap-926	30	12	vectors	vector	NOUN
ap-926	30	13	of	of	ADP
ap-926	30	14	the	the	DET
ap-926	30	15	lie	lie	NOUN
ap-926	30	16	algebra	algebra	PROPN
ap-926	30	17	sl(2	sl(2	PROPN
ap-926	30	18	)	)	PUNCT
ap-926	30	19	by	by	ADP
ap-926	30	20	operators	operator	NOUN
ap-926	30	21	e	e	X
ap-926	30	22	e	e	X
ap-926	30	23	e	e	X
ap-926	30	24	h	h	NOUN
ap-926	30	25	e	e	NOUN
ap-926	30	26	e	e	X
ap-926	30	27	e	e	X
ap-926	30	28	h	h	NOUN
ap-926	30	29	h	h	NOUN
ap-926	30	30	e	e	NOUN
ap-926	30	31	e	e	X
ap-926	30	32	12	12	NUM
ap-926	30	33	21	21	NUM
ap-926	30	34	12	12	NUM
ap-926	30	35	1	1	NUM
ap-926	30	36	21	21	NUM
ap-926	30	37	12	12	NUM
ap-926	30	38	21	21	NUM
ap-926	30	39	1	1	NUM
ap-926	30	40	1	1	NUM
ap-926	30	41	12	12	NUM
ap-926	30	42	12	12	NUM
ap-926	30	43	2	2	NUM
ap-926	30	44	2	2	NUM
ap-926	30	45	2	2	NUM
ap-926	30	46	2	2	NUM
ap-926	30	47	�	�	PROPN
ap-926	30	48	�	�	PROPN
ap-926	30	49	�	�	PROPN
ap-926	30	50	�	�	PROPN
ap-926	30	51	�	�	PROPN
ap-926	30	52	�	�	PROPN
ap-926	30	53	�	�	PROPN
ap-926	30	54	�	�	PROPN
ap-926	30	55	�	�	PROPN
ap-926	30	56	�	�	PROPN
ap-926	30	57	�	�	PROPN
ap-926	30	58	�	�	PROPN
ap-926	30	59	�	�	PROPN
ap-926	30	60	�	�	PROPN
ap-926	30	61	�	�	PROPN
ap-926	30	62	�	�	PROPN
ap-926	30	63	e	e	PROPN
ap-926	30	64	e21	e21	NUM
ap-926	30	65	21	21	NUM
ap-926	30	66	�	�	PROPN
ap-926	30	67	�	�	PROPN
ap-926	30	68	acting	act	VERB
ap-926	30	69	on	on	ADP
ap-926	30	70	the	the	DET
ap-926	30	71	space	space	NOUN
ap-926	30	72	of	of	ADP
ap-926	30	73	polynomials	polynomial	NOUN
ap-926	30	74	in	in	ADP
ap-926	30	75	three	three	NUM
ap-926	30	76	variables	variable	NOUN
ap-926	30	77	e12	e12	NOUN
ap-926	30	78	,	,	PUNCT
ap-926	30	79	e21	e21	PROPN
ap-926	30	80	,	,	PUNCT
ap-926	30	81	h1	h1	PROPN
ap-926	30	82	,	,	PUNCT
ap-926	30	83	we	we	PRON
ap-926	30	84	can	can	AUX
ap-926	30	85	find	find	VERB
ap-926	30	86	all	all	DET
ap-926	30	87	highest	high	ADJ
ap-926	30	88	weight	weight	NOUN
ap-926	30	89	vectors	vector	NOUN
ap-926	30	90	by	by	ADP
ap-926	30	91	solving	solve	VERB
ap-926	30	92	this	this	DET
ap-926	30	93	system	system	NOUN
ap-926	30	94	of	of	ADP
ap-926	30	95	differential	differential	ADJ
ap-926	30	96	equations	equation	NOUN
ap-926	30	97	:	:	PUNCT
ap-926	31	1	h	h	NOUN
ap-926	31	2	f	f	NOUN
ap-926	31	3	e	e	PROPN
ap-926	31	4	e	e	X
ap-926	31	5	f	f	PROPN
ap-926	31	6	h	h	NOUN
ap-926	31	7	e	e	NOUN
ap-926	31	8	f	f	PROPN
ap-926	31	9	e	e	X
ap-926	31	10	e	e	X
ap-926	31	11	f	f	PROPN
ap-926	31	12	e	e	X
ap-926	31	13	mf	mf	VERB
ap-926	31	14	1	1	NUM
ap-926	31	15	21	21	NUM
ap-926	31	16	12	12	NUM
ap-926	31	17	1	1	NUM
ap-926	31	18	12	12	NUM
ap-926	31	19	12	12	NUM
ap-926	31	20	21	21	NUM
ap-926	31	21	21	21	NUM
ap-926	31	22	2	2	NUM
ap-926	31	23	0	0	NUM
ap-926	31	24	2	2	NUM
ap-926	31	25	2	2	NUM
ap-926	31	26	2	2	NUM
ap-926	31	27	�	�	PROPN
ap-926	31	28	�	�	PROPN
ap-926	31	29	�	�	PROPN
ap-926	31	30	�	�	PROPN
ap-926	31	31	�	�	PROPN
ap-926	31	32	�	�	PROPN
ap-926	31	33	�	�	PROPN
ap-926	31	34	�	�	PROPN
ap-926	31	35	�	�	PROPN
ap-926	31	36	�	�	PROPN
ap-926	31	37	�	�	PROPN
ap-926	31	38	�	�	PROPN
ap-926	31	39	,	,	PUNCT
ap-926	31	40	.	.	PUNCT
ap-926	32	1	this	this	DET
ap-926	32	2	system	system	NOUN
ap-926	32	3	can	can	AUX
ap-926	32	4	be	be	AUX
ap-926	32	5	easily	easily	ADV
ap-926	32	6	solved	solve	VERB
ap-926	32	7	,	,	PUNCT
ap-926	32	8	and	and	CCONJ
ap-926	32	9	the	the	DET
ap-926	32	10	general	general	ADJ
ap-926	32	11	solution	solution	NOUN
ap-926	32	12	is	be	AUX
ap-926	32	13	f	f	X
ap-926	32	14	e	e	X
ap-926	32	15	e	e	X
ap-926	32	16	h	h	NOUN
ap-926	32	17	e	e	PROPN
ap-926	32	18	f	f	PROPN
ap-926	32	19	cm	cm	PROPN
ap-926	32	20	(	(	PUNCT
ap-926	32	21	,	,	PUNCT
ap-926	32	22	,	,	PUNCT
ap-926	32	23	)	)	PUNCT
ap-926	32	24	(	(	PUNCT
ap-926	32	25	)	)	PUNCT
ap-926	32	26	12	12	NUM
ap-926	32	27	21	21	NUM
ap-926	32	28	1	1	NUM
ap-926	32	29	12	12	NUM
ap-926	32	30	1	1	NUM
ap-926	32	31	�	�	PROPN
ap-926	32	32	,	,	PUNCT
ap-926	32	33	where	where	SCONJ
ap-926	32	34	f	f	PROPN
ap-926	32	35	is	be	AUX
ap-926	32	36	any	any	DET
ap-926	32	37	differentiable	differentiable	ADJ
ap-926	32	38	function	function	NOUN
ap-926	32	39	of	of	ADP
ap-926	32	40	the	the	DET
ap-926	32	41	variable	variable	NOUN
ap-926	32	42	c	c	NOUN
ap-926	32	43	h	h	NOUN
ap-926	32	44	e	e	NOUN
ap-926	32	45	e1	e1	VERB
ap-926	32	46	1	1	NUM
ap-926	32	47	2	2	NUM
ap-926	32	48	12	12	NUM
ap-926	32	49	214	214	NUM
ap-926	32	50	�	�	PROPN
ap-926	32	51	.	.	PUNCT
ap-926	33	1	we	we	PRON
ap-926	33	2	see	see	VERB
ap-926	33	3	that	that	SCONJ
ap-926	33	4	when	when	SCONJ
ap-926	33	5	f	f	PROPN
ap-926	33	6	x	x	SYM
ap-926	33	7	xk	xk	PROPN
ap-926	33	8	(	(	PUNCT
ap-926	33	9	)	)	PUNCT
ap-926	33	10	�	�	PROPN
ap-926	33	11	,	,	PUNCT
ap-926	33	12	the	the	DET
ap-926	33	13	solution	solution	NOUN
ap-926	33	14	is	be	AUX
ap-926	33	15	polynomial	polynomial	ADJ
ap-926	33	16	and	and	CCONJ
ap-926	33	17	we	we	PRON
ap-926	33	18	can	can	AUX
ap-926	33	19	transfer	transfer	VERB
ap-926	33	20	back	back	ADV
ap-926	33	21	to	to	ADP
ap-926	33	22	the	the	DET
ap-926	33	23	enveloping	enveloping	NOUN
ap-926	33	24	algebra	algebra	NOUN
ap-926	33	25	using	use	VERB
ap-926	33	26	the	the	DET
ap-926	33	27	canonical	canonical	ADJ
ap-926	33	28	isomorphism	isomorphism	NOUN
ap-926	33	29	s	s	VERB
ap-926	33	30	g	g	NOUN
ap-926	33	31	u	u	NOUN
ap-926	33	32	g	g	PROPN
ap-926	33	33	(	(	PUNCT
ap-926	33	34	)	)	PUNCT
ap-926	33	35	(	(	PUNCT
ap-926	33	36	)	)	PUNCT
ap-926	33	37	�	�	PROPN
ap-926	33	38	:	:	PUNCT
ap-926	33	39	if	if	SCONJ
ap-926	33	40	a1	a1	PROPN
ap-926	33	41	,	,	PUNCT
ap-926	33	42	…	…	PUNCT
ap-926	33	43	,	,	PUNCT
ap-926	33	44	a	a	DET
ap-926	33	45	gk	gk	PROPN
ap-926	33	46	�	�	PROPN
ap-926	33	47	,	,	PUNCT
ap-926	33	48	this	this	DET
ap-926	33	49	isomorphism	isomorphism	NOUN
ap-926	33	50	sends	send	VERB
ap-926	33	51	a	a	DET
ap-926	33	52	a	a	DET
ap-926	33	53	k	k	PROPN
ap-926	33	54	a	a	DET
ap-926	33	55	ak	ak	PROPN
ap-926	33	56	k1	k1	PROPN
ap-926	33	57	1	1	NUM
ap-926	33	58	1	1	NUM
ap-926	33	59	�	�	PROPN
ap-926	33	60	�	�	PROPN
ap-926	33	61	�	�	PROPN
ap-926	33	62	�	�	PROPN
ap-926	33	63	!	!	PUNCT
ap-926	34	1	(	(	PUNCT
ap-926	34	2	)	)	PUNCT
ap-926	34	3	(	(	PUNCT
ap-926	34	4	)	)	PUNCT
ap-926	34	5	�	�	PROPN
ap-926	34	6	�	�	PROPN
ap-926	34	7	�	�	PROPN
ap-926	34	8	26	26	NUM
ap-926	34	9	©	©	PROPN
ap-926	34	10	czech	czech	PROPN
ap-926	34	11	technical	technical	PROPN
ap-926	34	12	university	university	PROPN
ap-926	34	13	publishing	publishing	NOUN
ap-926	34	14	house	house	NOUN
ap-926	34	15	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-926	34	16	acta	acta	PROPN
ap-926	34	17	polytechnica	polytechnica	PROPN
ap-926	34	18	vol	vol	NOUN
ap-926	34	19	.	.	PUNCT
ap-926	35	1	47	47	NUM
ap-926	35	2	no	no	NOUN
ap-926	35	3	.	.	PUNCT
ap-926	36	1	2–3/2007	2–3/2007	NUM
ap-926	36	2	(	(	PUNCT
ap-926	36	3	we	we	PRON
ap-926	36	4	sum	sum	VERB
ap-926	36	5	over	over	ADP
ap-926	36	6	all	all	DET
ap-926	36	7	permutations	permutation	NOUN
ap-926	36	8	of	of	ADP
ap-926	36	9	the	the	DET
ap-926	36	10	indices	index	NOUN
ap-926	36	11	1	1	NUM
ap-926	36	12	,	,	PUNCT
ap-926	36	13	…	…	PUNCT
ap-926	36	14	,	,	PUNCT
ap-926	36	15	k	k	NOUN
ap-926	36	16	)	)	PUNCT
ap-926	36	17	.	.	PUNCT
ap-926	37	1	in	in	ADP
ap-926	37	2	our	our	PRON
ap-926	37	3	example	example	NOUN
ap-926	37	4	c	c	NOUN
ap-926	37	5	h	h	NOUN
ap-926	37	6	e	e	X
ap-926	37	7	e	e	X
ap-926	37	8	e	e	X
ap-926	37	9	e	e	X
ap-926	37	10	h	h	NOUN
ap-926	37	11	e	e	NOUN
ap-926	37	12	e	e	NOUN
ap-926	37	13	h	h	NOUN
ap-926	37	14	c	c	NOUN
ap-926	37	15	1	1	NUM
ap-926	37	16	1	1	NUM
ap-926	37	17	2	2	NUM
ap-926	37	18	12	12	NUM
ap-926	37	19	21	21	NUM
ap-926	37	20	21	21	NUM
ap-926	37	21	12	12	NUM
ap-926	37	22	1	1	NUM
ap-926	37	23	2	2	NUM
ap-926	37	24	12	12	NUM
ap-926	37	25	21	21	NUM
ap-926	37	26	1	1	NUM
ap-926	37	27	1	1	NUM
ap-926	37	28	4	4	NUM
ap-926	37	29	1	1	NUM
ap-926	37	30	2	2	NUM
ap-926	37	31	1	1	NUM
ap-926	37	32	2	2	NUM
ap-926	37	33	4	4	NUM
ap-926	37	34	2	2	NUM
ap-926	37	35	�	�	PROPN
ap-926	37	36	�	�	PROPN
ap-926	37	37	�	�	PROPN
ap-926	37	38	�	�	PROPN
ap-926	37	39	�	�	PROPN
ap-926	37	40	�	�	PROPN
ap-926	37	41	�	�	PROPN
ap-926	37	42	�	�	PROPN
ap-926	37	43	�	�	PROPN
ap-926	37	44	�	�	PROPN
ap-926	37	45	.	.	PUNCT
ap-926	38	1	doing	do	VERB
ap-926	38	2	the	the	DET
ap-926	38	3	dimension	dimension	NOUN
ap-926	38	4	check	check	NOUN
ap-926	38	5	as	as	SCONJ
ap-926	38	6	before	before	ADP
ap-926	38	7	the	the	PRON
ap-926	38	8	we	we	PRON
ap-926	38	9	see	see	VERB
ap-926	38	10	that	that	DET
ap-926	38	11	decomposition	decomposition	NOUN
ap-926	38	12	is	be	AUX
ap-926	38	13	complete	complete	ADJ
ap-926	38	14	.	.	PUNCT
ap-926	39	1	4	4	NUM
ap-926	39	2	the	the	DET
ap-926	39	3	algebras	algebras	PROPN
ap-926	39	4	sl(3	sl(3	PROPN
ap-926	39	5	)	)	PUNCT
ap-926	39	6	and	and	CCONJ
ap-926	39	7	gl(3	gl(3	VERB
ap-926	39	8	)	)	PUNCT
ap-926	39	9	the	the	DET
ap-926	39	10	case	case	NOUN
ap-926	39	11	of	of	ADP
ap-926	39	12	algebra	algebra	PROPN
ap-926	39	13	sl(3	sl(3	PROPN
ap-926	39	14	)	)	PUNCT
ap-926	39	15	is	be	AUX
ap-926	39	16	more	more	ADV
ap-926	39	17	complicated	complicated	ADJ
ap-926	39	18	.	.	PUNCT
ap-926	40	1	the	the	DET
ap-926	40	2	decomposition	decomposition	NOUN
ap-926	40	3	of	of	ADP
ap-926	40	4	this	this	DET
ap-926	40	5	case	case	NOUN
ap-926	40	6	is	be	AUX
ap-926	40	7	done	do	VERB
ap-926	40	8	in	in	ADP
ap-926	40	9	[	[	X
ap-926	40	10	3	3	NUM
ap-926	40	11	]	]	PUNCT
ap-926	40	12	.	.	PUNCT
ap-926	41	1	let	let	VERB
ap-926	41	2	us	we	PRON
ap-926	41	3	show	show	VERB
ap-926	41	4	where	where	SCONJ
ap-926	41	5	the	the	DET
ap-926	41	6	complications	complication	NOUN
ap-926	41	7	in	in	ADP
ap-926	41	8	the	the	DET
ap-926	41	9	decomposition	decomposition	NOUN
ap-926	41	10	arise	arise	NOUN
ap-926	41	11	,	,	PUNCT
ap-926	41	12	using	use	VERB
ap-926	41	13	the	the	DET
ap-926	41	14	similar	similar	ADJ
ap-926	41	15	case	case	NOUN
ap-926	41	16	of	of	ADP
ap-926	41	17	lie	lie	NOUN
ap-926	41	18	algebra	algebra	PROPN
ap-926	41	19	gl(3	gl(3	PROPN
ap-926	41	20	)	)	PUNCT
ap-926	41	21	with	with	ADP
ap-926	41	22	the	the	DET
ap-926	41	23	basis	basis	NOUN
ap-926	41	24	eij	eij	PROPN
ap-926	41	25	,	,	PUNCT
ap-926	41	26	i	i	PROPN
ap-926	41	27	j	j	PROPN
ap-926	41	28	,	,	PUNCT
ap-926	41	29	,	,	PUNCT
ap-926	41	30	,	,	PUNCT
ap-926	41	31	�	�	PROPN
ap-926	41	32	1	1	NUM
ap-926	41	33	2	2	NUM
ap-926	41	34	3	3	NUM
ap-926	41	35	and	and	CCONJ
ap-926	41	36	commutation	commutation	NOUN
ap-926	41	37	relations	relation	NOUN
ap-926	41	38	[	[	PUNCT
ap-926	41	39	,	,	PUNCT
ap-926	41	40	]	]	X
ap-926	41	41	e	e	X
ap-926	41	42	e	e	X
ap-926	41	43	e	e	X
ap-926	41	44	eij	eij	PROPN
ap-926	41	45	kl	kl	PROPN
ap-926	41	46	ij	ij	INTJ
ap-926	41	47	jk	jk	PROPN
ap-926	41	48	kj	kj	PROPN
ap-926	41	49	il	il	PROPN
ap-926	41	50	�	�	PROPN
ap-926	41	51	�	�	PROPN
ap-926	41	52	.	.	PUNCT
ap-926	42	1	we	we	PRON
ap-926	42	2	turn	turn	VERB
ap-926	42	3	directly	directly	ADV
ap-926	42	4	into	into	ADP
ap-926	42	5	the	the	DET
ap-926	42	6	commutative	commutative	ADJ
ap-926	42	7	case	case	NOUN
ap-926	42	8	.	.	PUNCT
ap-926	43	1	first	first	ADV
ap-926	43	2	we	we	PRON
ap-926	43	3	set	set	VERB
ap-926	43	4	up	up	ADP
ap-926	43	5	,	,	PUNCT
ap-926	43	6	as	as	ADP
ap-926	43	7	before	before	ADV
ap-926	43	8	,	,	PUNCT
ap-926	43	9	the	the	DET
ap-926	43	10	system	system	NOUN
ap-926	43	11	of	of	ADP
ap-926	43	12	differential	differential	ADJ
ap-926	43	13	equations	equation	NOUN
ap-926	43	14	for	for	ADP
ap-926	43	15	the	the	DET
ap-926	43	16	highest	high	ADJ
ap-926	43	17	weight	weight	NOUN
ap-926	43	18	vectors	vector	NOUN
ap-926	43	19	of	of	ADP
ap-926	43	20	weight	weight	NOUN
ap-926	43	21	(	(	PUNCT
ap-926	43	22	n1	n1	NOUN
ap-926	43	23	,	,	PUNCT
ap-926	43	24	n2	n2	NOUN
ap-926	43	25	,	,	PUNCT
ap-926	43	26	n3	n3	NOUN
ap-926	43	27	):	):	PUNCT
ap-926	43	28	e	e	NOUN
ap-926	43	29	x	x	X
ap-926	43	30	f	f	NOUN
ap-926	43	31	x	x	X
ap-926	43	32	x	x	SYM
ap-926	43	33	f	f	NOUN
ap-926	43	34	x	x	X
ap-926	43	35	f	f	NOUN
ap-926	43	36	x	x	PUNCT
ap-926	43	37	x	x	PUNCT
ap-926	43	38	x	x	SYM
ap-926	43	39	f	f	NOUN
ap-926	43	40	12	12	NUM
ap-926	43	41	13	13	NUM
ap-926	43	42	23	23	NUM
ap-926	43	43	12	12	NUM
ap-926	43	44	11	11	NUM
ap-926	43	45	22	22	NUM
ap-926	43	46	11	11	NUM
ap-926	43	47	22	22	NUM
ap-926	43	48	�	�	PROPN
ap-926	43	49	�	�	PROPN
ap-926	43	50	�	�	PROPN
ap-926	43	51	�	�	PROPN
ap-926	43	52	�	�	PROPN
ap-926	43	53	�	�	PROPN
ap-926	43	54	�	�	PROPN
ap-926	43	55	�	�	PROPN
ap-926	43	56	�	�	PROPN
ap-926	43	57	�	�	PROPN
ap-926	43	58	�	�	PROPN
ap-926	43	59	�	�	PROPN
ap-926	43	60	�	�	PROPN
ap-926	43	61	�	�	PROPN
ap-926	43	62	�	�	PROPN
ap-926	43	63	�	�	PROPN
ap-926	43	64	�	�	PROPN
ap-926	43	65	�	�	PROPN
ap-926	43	66	�	�	PROPN
ap-926	43	67	(	(	PUNCT
ap-926	43	68	)	)	PUNCT
ap-926	43	69	�	�	PROPN
ap-926	43	70	�	�	PROPN
ap-926	43	71	�	�	PROPN
ap-926	43	72	�	�	PROPN
ap-926	43	73	�	�	PROPN
ap-926	43	74	�	�	PROPN
ap-926	43	75	�	�	PROPN
ap-926	43	76	�	�	PROPN
ap-926	43	77	�	�	PROPN
ap-926	43	78	x	x	PUNCT
ap-926	43	79	x	x	SYM
ap-926	43	80	f	f	NOUN
ap-926	43	81	x	x	X
ap-926	43	82	e	e	NOUN
ap-926	43	83	x	x	X
ap-926	43	84	f	f	NOUN
ap-926	43	85	x	x	X
ap-926	43	86	x	x	SYM
ap-926	43	87	f	f	NOUN
ap-926	43	88	x	x	SYM
ap-926	43	89	f	f	NOUN
ap-926	43	90	x	x	SYM
ap-926	43	91	21	21	NUM
ap-926	43	92	32	32	NUM
ap-926	43	93	31	31	NUM
ap-926	43	94	23	23	NUM
ap-926	43	95	13	13	NUM
ap-926	43	96	12	12	NUM
ap-926	43	97	23	23	NUM
ap-926	43	98	22	22	NUM
ap-926	43	99	33	33	NUM
ap-926	43	100	0	0	NUM
ap-926	43	101	�	�	PROPN
ap-926	43	102	�	�	PROPN
ap-926	43	103	�	�	PROPN
ap-926	43	104	�	�	PROPN
ap-926	43	105	�	�	PROPN
ap-926	43	106	�	�	PROPN
ap-926	43	107	�	�	PROPN
ap-926	43	108	�	�	PROPN
ap-926	43	109	�	�	PROPN
ap-926	43	110	�	�	PROPN
ap-926	43	111	�	�	PROPN
ap-926	43	112	�	�	PROPN
ap-926	43	113	�	�	PROPN
ap-926	43	114	�	�	PROPN
ap-926	43	115	�	�	PROPN
ap-926	43	116	�	�	PROPN
ap-926	43	117	�	�	PROPN
ap-926	43	118	�	�	PROPN
ap-926	43	119	�	�	PROPN
ap-926	43	120	(	(	PUNCT
ap-926	43	121	)	)	PUNCT
ap-926	43	122	,	,	PUNCT
ap-926	43	123	x	x	PUNCT
ap-926	43	124	x	x	PUNCT
ap-926	43	125	f	f	X
ap-926	43	126	x	x	PUNCT
ap-926	43	127	x	x	SYM
ap-926	43	128	f	f	NOUN
ap-926	43	129	x	x	X
ap-926	43	130	e	e	NOUN
ap-926	43	131	x	x	PROPN
ap-926	43	132	f	f	NOUN
ap-926	43	133	x	x	SYM
ap-926	43	134	22	22	NUM
ap-926	43	135	33	33	NUM
ap-926	43	136	32	32	NUM
ap-926	43	137	21	21	NUM
ap-926	43	138	31	31	NUM
ap-926	43	139	13	13	NUM
ap-926	43	140	13	13	NUM
ap-926	43	141	11	11	NUM
ap-926	43	142	0	0	NUM
ap-926	43	143	�	�	PROPN
ap-926	43	144	�	�	PROPN
ap-926	43	145	�	�	PROPN
ap-926	43	146	�	�	PROPN
ap-926	43	147	�	�	PROPN
ap-926	43	148	�	�	PROPN
ap-926	43	149	�	�	PROPN
ap-926	43	150	f	f	PROPN
ap-926	43	151	x	x	NOUN
ap-926	43	152	x	x	X
ap-926	43	153	f	f	NOUN
ap-926	43	154	x	x	PUNCT
ap-926	43	155	x	x	X
ap-926	43	156	f	f	NOUN
ap-926	43	157	x	x	PUNCT
ap-926	43	158	x	x	PUNCT
ap-926	43	159	x	x	X
ap-926	43	160	f	f	X
ap-926	43	161	x	x	SYM
ap-926	43	162	�	�	PROPN
ap-926	43	163	�	�	PROPN
ap-926	43	164	�	�	PROPN
ap-926	43	165	�	�	PROPN
ap-926	43	166	�	�	PROPN
ap-926	43	167	�	�	PROPN
ap-926	43	168	�	�	PROPN
ap-926	43	169	33	33	NUM
ap-926	43	170	23	23	NUM
ap-926	43	171	21	21	NUM
ap-926	43	172	12	12	NUM
ap-926	43	173	32	32	NUM
ap-926	43	174	11	11	NUM
ap-926	43	175	33	33	NUM
ap-926	43	176	31	31	NUM
ap-926	43	177	�	�	PROPN
ap-926	43	178	�	�	PROPN
ap-926	43	179	�	�	PROPN
ap-926	43	180	�	�	PROPN
ap-926	43	181	�	�	PROPN
ap-926	43	182	�	�	PROPN
ap-926	43	183	�	�	PROPN
ap-926	43	184	�	�	PROPN
ap-926	43	185	�	�	PROPN
ap-926	43	186	�	�	PROPN
ap-926	43	187	�	�	PROPN
ap-926	43	188	(	(	PUNCT
ap-926	43	189	)	)	PUNCT
ap-926	43	190	0	0	NUM
ap-926	43	191	11	11	NUM
ap-926	43	192	12	12	NUM
ap-926	43	193	12	12	NUM
ap-926	43	194	13	13	NUM
ap-926	43	195	13	13	NUM
ap-926	43	196	21	21	NUM
ap-926	43	197	21	21	NUM
ap-926	43	198	31	31	NUM
ap-926	43	199	31	31	NUM
ap-926	43	200	1	1	NUM
ap-926	43	201	,	,	PUNCT
ap-926	43	202	,	,	PUNCT
ap-926	43	203	e	e	NOUN
ap-926	43	204	x	x	X
ap-926	43	205	f	f	NOUN
ap-926	43	206	x	x	X
ap-926	43	207	x	x	X
ap-926	43	208	f	f	NOUN
ap-926	43	209	x	x	PUNCT
ap-926	43	210	x	x	X
ap-926	43	211	f	f	NOUN
ap-926	43	212	x	x	PUNCT
ap-926	43	213	x	x	X
ap-926	43	214	f	f	NOUN
ap-926	43	215	x	x	SYM
ap-926	43	216	n	n	PROPN
ap-926	43	217	f	f	X
ap-926	43	218	�	�	PROPN
ap-926	43	219	�	�	PROPN
ap-926	43	220	�	�	PROPN
ap-926	43	221	�	�	PROPN
ap-926	43	222	�	�	PROPN
ap-926	43	223	�	�	PROPN
ap-926	43	224	�	�	PROPN
ap-926	43	225	�	�	PROPN
ap-926	43	226	�	�	PROPN
ap-926	43	227	�	�	PROPN
ap-926	43	228	�	�	PROPN
ap-926	43	229	�	�	PROPN
ap-926	43	230	e	e	X
ap-926	43	231	x	x	PROPN
ap-926	43	232	f	f	NOUN
ap-926	43	233	x	x	X
ap-926	43	234	x	x	X
ap-926	43	235	f	f	NOUN
ap-926	43	236	x	x	PUNCT
ap-926	43	237	x	x	X
ap-926	43	238	f	f	NOUN
ap-926	43	239	x	x	PUNCT
ap-926	43	240	x	x	X
ap-926	43	241	f	f	NOUN
ap-926	43	242	x	x	SYM
ap-926	43	243	n	n	PROPN
ap-926	43	244	f	f	NOUN
ap-926	43	245	e	e	NOUN
ap-926	43	246	22	22	NUM
ap-926	43	247	12	12	NUM
ap-926	43	248	12	12	NUM
ap-926	43	249	23	23	NUM
ap-926	43	250	23	23	NUM
ap-926	43	251	21	21	NUM
ap-926	43	252	21	21	NUM
ap-926	43	253	32	32	NUM
ap-926	43	254	32	32	NUM
ap-926	43	255	2	2	NUM
ap-926	43	256	�	�	PROPN
ap-926	43	257	�	�	PROPN
ap-926	43	258	�	�	PROPN
ap-926	43	259	�	�	PROPN
ap-926	43	260	�	�	PROPN
ap-926	43	261	�	�	PROPN
ap-926	43	262	�	�	PROPN
ap-926	43	263	�	�	PROPN
ap-926	43	264	�	�	PROPN
ap-926	43	265	�	�	PROPN
ap-926	43	266	�	�	PROPN
ap-926	43	267	�	�	PROPN
ap-926	43	268	,	,	PUNCT
ap-926	43	269	33	33	NUM
ap-926	43	270	13	13	NUM
ap-926	43	271	13	13	NUM
ap-926	43	272	23	23	NUM
ap-926	43	273	23	23	NUM
ap-926	43	274	32	32	NUM
ap-926	43	275	32	32	NUM
ap-926	43	276	31	31	NUM
ap-926	43	277	31	31	NUM
ap-926	43	278	3	3	NUM
ap-926	43	279	�	�	PROPN
ap-926	43	280	�	�	PROPN
ap-926	43	281	�	�	PROPN
ap-926	43	282	�	�	PROPN
ap-926	43	283	x	x	PROPN
ap-926	43	284	f	f	NOUN
ap-926	43	285	x	x	PUNCT
ap-926	43	286	x	x	X
ap-926	43	287	f	f	NOUN
ap-926	43	288	x	x	PUNCT
ap-926	43	289	x	x	X
ap-926	43	290	f	f	NOUN
ap-926	43	291	x	x	PUNCT
ap-926	43	292	x	x	X
ap-926	43	293	f	f	X
ap-926	43	294	x	x	SYM
ap-926	43	295	n	n	PROPN
ap-926	43	296	f	f	PROPN
ap-926	43	297	�	�	PROPN
ap-926	43	298	�	�	PROPN
ap-926	43	299	�	�	PROPN
ap-926	43	300	�	�	PROPN
ap-926	43	301	�	�	PROPN
ap-926	43	302	�	�	PROPN
ap-926	43	303	�	�	PROPN
ap-926	43	304	�	�	PROPN
ap-926	43	305	.	.	PUNCT
ap-926	44	1	from	from	ADP
ap-926	44	2	this	this	PRON
ap-926	44	3	immediately	immediately	ADV
ap-926	44	4	follows	follow	VERB
ap-926	44	5	n	n	PRON
ap-926	44	6	n	n	ADV
ap-926	44	7	n1	n1	NOUN
ap-926	44	8	2	2	NUM
ap-926	44	9	3	3	NUM
ap-926	44	10	0	0	NUM
ap-926	44	11	�	�	PROPN
ap-926	44	12	.	.	PUNCT
ap-926	45	1	if	if	SCONJ
ap-926	45	2	we	we	PRON
ap-926	45	3	define	define	VERB
ap-926	45	4	new	new	ADJ
ap-926	45	5	variables	variable	NOUN
ap-926	45	6	x	x	PUNCT
ap-926	45	7	x1	x1	ADJ
ap-926	45	8	13	13	NUM
ap-926	45	9	�	�	NOUN
ap-926	45	10	,	,	PUNCT
ap-926	45	11	x	x	PUNCT
ap-926	45	12	x	x	PUNCT
ap-926	45	13	x	x	PUNCT
ap-926	45	14	x	x	PUNCT
ap-926	45	15	x	x	PUNCT
ap-926	45	16	x	x	SYM
ap-926	45	17	x	x	PUNCT
ap-926	45	18	x	x	SYM
ap-926	45	19	x3	x3	VERB
ap-926	45	20	12	12	NUM
ap-926	45	21	2	2	NUM
ap-926	45	22	23	23	NUM
ap-926	45	23	12	12	NUM
ap-926	45	24	13	13	NUM
ap-926	45	25	33	33	NUM
ap-926	45	26	22	22	NUM
ap-926	45	27	13	13	NUM
ap-926	45	28	2	2	NUM
ap-926	45	29	32	32	NUM
ap-926	45	30	�	�	PROPN
ap-926	45	31	�	�	PROPN
ap-926	45	32	�	�	PROPN
ap-926	45	33	(	(	PUNCT
ap-926	45	34	)	)	PUNCT
ap-926	45	35	then	then	ADV
ap-926	45	36	any	any	DET
ap-926	45	37	solution	solution	NOUN
ap-926	45	38	f	f	PROPN
ap-926	45	39	can	can	AUX
ap-926	45	40	be	be	AUX
ap-926	45	41	written	write	VERB
ap-926	45	42	as	as	ADP
ap-926	45	43	f	f	PROPN
ap-926	45	44	x	x	PROPN
ap-926	45	45	x	x	SYM
ap-926	45	46	x	x	PROPN
ap-926	45	47	fij	fij	PROPN
ap-926	45	48	n	n	CCONJ
ap-926	45	49	n	n	PROPN
ap-926	45	50	n	n	CCONJ
ap-926	45	51	(	(	PUNCT
ap-926	45	52	)	)	PUNCT
ap-926	45	53	�	�	PROPN
ap-926	45	54	�	�	PROPN
ap-926	45	55	�	�	PROPN
ap-926	45	56	1	1	NUM
ap-926	45	57	3	3	NUM
ap-926	45	58	2	2	NUM
ap-926	45	59	3	3	NUM
ap-926	45	60	2	2	NUM
ap-926	45	61	,	,	PUNCT
ap-926	45	62	where	where	SCONJ
ap-926	45	63	the	the	DET
ap-926	45	64	new	new	ADJ
ap-926	45	65	unknown	unknown	ADJ
ap-926	45	66	function	function	NOUN
ap-926	45	67	f	f	PROPN
ap-926	45	68	satisfies	satisfy	VERB
ap-926	45	69	the	the	DET
ap-926	45	70	following	follow	VERB
ap-926	45	71	system	system	NOUN
ap-926	45	72	of	of	ADP
ap-926	45	73	differential	differential	ADJ
ap-926	45	74	equations	equation	NOUN
ap-926	45	75	:	:	PUNCT
ap-926	46	1	x	x	X
ap-926	46	2	f	f	X
ap-926	46	3	x	x	PUNCT
ap-926	46	4	x	x	SYM
ap-926	46	5	f	f	NOUN
ap-926	46	6	x	x	X
ap-926	46	7	f	f	NOUN
ap-926	46	8	x	x	PUNCT
ap-926	46	9	x	x	PUNCT
ap-926	46	10	x	x	SYM
ap-926	46	11	f	f	PROPN
ap-926	46	12	x13	x13	PROPN
ap-926	46	13	23	23	NUM
ap-926	46	14	12	12	NUM
ap-926	46	15	11	11	NUM
ap-926	46	16	22	22	NUM
ap-926	46	17	11	11	NUM
ap-926	46	18	22	22	NUM
ap-926	46	19	21	21	NUM
ap-926	46	20	�	�	PROPN
ap-926	46	21	�	�	PROPN
ap-926	46	22	�	�	PROPN
ap-926	46	23	�	�	PROPN
ap-926	46	24	�	�	PROPN
ap-926	46	25	�	�	PROPN
ap-926	46	26	�	�	PROPN
ap-926	46	27	�	�	PROPN
ap-926	46	28	�	�	PROPN
ap-926	46	29	�	�	PROPN
ap-926	46	30	�	�	PROPN
ap-926	46	31	�	�	PROPN
ap-926	46	32	�	�	PROPN
ap-926	46	33	�	�	PROPN
ap-926	46	34	�	�	PROPN
ap-926	46	35	�	�	PROPN
ap-926	46	36	�	�	PROPN
ap-926	46	37	�	�	PROPN
ap-926	46	38	�	�	PROPN
ap-926	46	39	(	(	PUNCT
ap-926	46	40	)	)	PUNCT
ap-926	46	41	�	�	PROPN
ap-926	46	42	�	�	PROPN
ap-926	46	43	�	�	PROPN
ap-926	46	44	�	�	PROPN
ap-926	46	45	�	�	PROPN
ap-926	46	46	�	�	PROPN
ap-926	46	47	�	�	PROPN
ap-926	46	48	�	�	PROPN
ap-926	46	49	�	�	PROPN
ap-926	46	50	�	�	PROPN
ap-926	46	51	�	�	PROPN
ap-926	46	52	�	�	PROPN
ap-926	46	53	x	x	PUNCT
ap-926	46	54	f	f	NOUN
ap-926	46	55	x	x	PUNCT
ap-926	46	56	x	x	X
ap-926	46	57	f	f	NOUN
ap-926	46	58	x	x	PUNCT
ap-926	46	59	x	x	SYM
ap-926	46	60	f	f	NOUN
ap-926	46	61	x	x	X
ap-926	46	62	f	f	NOUN
ap-926	46	63	x	x	PUNCT
ap-926	46	64	x	x	SYM
ap-926	46	65	32	32	NUM
ap-926	46	66	31	31	NUM
ap-926	46	67	13	13	NUM
ap-926	46	68	12	12	NUM
ap-926	46	69	23	23	NUM
ap-926	46	70	22	22	NUM
ap-926	46	71	33	33	NUM
ap-926	46	72	0	0	NUM
ap-926	46	73	�	�	PROPN
ap-926	46	74	�	�	PROPN
ap-926	46	75	�	�	PROPN
ap-926	46	76	�	�	PROPN
ap-926	46	77	�	�	PROPN
ap-926	46	78	�	�	PROPN
ap-926	46	79	�	�	PROPN
ap-926	46	80	�	�	PROPN
ap-926	46	81	,	,	PUNCT
ap-926	46	82	(	(	PUNCT
ap-926	46	83	22	22	NUM
ap-926	46	84	33	33	NUM
ap-926	46	85	32	32	NUM
ap-926	46	86	21	21	NUM
ap-926	46	87	31	31	NUM
ap-926	46	88	13	13	NUM
ap-926	46	89	11	11	NUM
ap-926	46	90	33	33	NUM
ap-926	46	91	0	0	NUM
ap-926	46	92	�	�	PROPN
ap-926	46	93	�	�	PROPN
ap-926	46	94	�	�	PROPN
ap-926	46	95	�	�	PROPN
ap-926	46	96	�	�	PROPN
ap-926	46	97	�	�	PROPN
ap-926	46	98	�	�	PROPN
ap-926	46	99	�	�	PROPN
ap-926	46	100	�	�	PROPN
ap-926	46	101	�	�	PROPN
ap-926	46	102	�	�	PROPN
ap-926	46	103	�	�	PROPN
ap-926	46	104	x	x	PUNCT
ap-926	46	105	f	f	NOUN
ap-926	46	106	x	x	PUNCT
ap-926	46	107	x	x	X
ap-926	46	108	f	f	NOUN
ap-926	46	109	x	x	PUNCT
ap-926	46	110	x	x	SYM
ap-926	46	111	f	f	PUNCT
ap-926	46	112	x	x	X
ap-926	46	113	f	f	PROPN
ap-926	46	114	x	x	PROPN
ap-926	46	115	)	)	PUNCT
ap-926	46	116	,	,	PUNCT
ap-926	46	117	�	�	PROPN
ap-926	46	118	�	�	PROPN
ap-926	46	119	�	�	PROPN
ap-926	46	120	�	�	PROPN
ap-926	46	121	�	�	PROPN
ap-926	46	122	�	�	PROPN
ap-926	46	123	�	�	PROPN
ap-926	46	124	�	�	PROPN
ap-926	46	125	�	�	PROPN
ap-926	46	126	�	�	PROPN
ap-926	46	127	�	�	PROPN
ap-926	46	128	�	�	PROPN
ap-926	46	129	x	x	PROPN
ap-926	46	130	f	f	NOUN
ap-926	46	131	x	x	PUNCT
ap-926	47	1	x	x	X
ap-926	47	2	f	f	NOUN
ap-926	47	3	x	x	PUNCT
ap-926	47	4	x	x	PUNCT
ap-926	47	5	x	x	SYM
ap-926	47	6	f	f	X
ap-926	47	7	x23	x23	NUM
ap-926	47	8	21	21	NUM
ap-926	47	9	12	12	NUM
ap-926	47	10	32	32	NUM
ap-926	47	11	11	11	NUM
ap-926	47	12	33	33	NUM
ap-926	47	13	31	31	NUM
ap-926	47	14	0	0	NUM
ap-926	47	15	�	�	PROPN
ap-926	47	16	�	�	PROPN
ap-926	47	17	�	�	PROPN
ap-926	47	18	�	�	PROPN
ap-926	47	19	�	�	PROPN
ap-926	47	20	�	�	PROPN
ap-926	47	21	(	(	PUNCT
ap-926	47	22	)	)	PUNCT
ap-926	47	23	,	,	PUNCT
ap-926	47	24	x	x	X
ap-926	48	1	f	f	X
ap-926	48	2	x	x	PUNCT
ap-926	48	3	x	x	X
ap-926	48	4	f	f	NOUN
ap-926	48	5	x	x	PUNCT
ap-926	48	6	x	x	X
ap-926	48	7	f	f	NOUN
ap-926	48	8	x	x	PUNCT
ap-926	48	9	x	x	X
ap-926	48	10	f	f	NOUN
ap-926	48	11	x	x	PUNCT
ap-926	48	12	x	x	SYM
ap-926	48	13	f	f	NOUN
ap-926	48	14	x	x	SYM
ap-926	48	15	12	12	NUM
ap-926	48	16	12	12	NUM
ap-926	48	17	13	13	NUM
ap-926	48	18	13	13	NUM
ap-926	48	19	21	21	NUM
ap-926	48	20	21	21	NUM
ap-926	48	21	31	31	NUM
ap-926	48	22	31	31	NUM
ap-926	48	23	13	13	NUM
ap-926	48	24	1	1	NUM
ap-926	48	25	0	0	NUM
ap-926	48	26	�	�	PROPN
ap-926	48	27	�	�	PROPN
ap-926	48	28	�	�	PROPN
ap-926	48	29	�	�	PROPN
ap-926	48	30	�	�	PROPN
ap-926	48	31	�	�	PROPN
ap-926	48	32	�	�	PROPN
ap-926	48	33	�	�	PROPN
ap-926	48	34	�	�	PROPN
ap-926	48	35	�	�	PROPN
ap-926	48	36	�	�	PROPN
ap-926	48	37	�	�	PROPN
ap-926	48	38	�	�	PROPN
ap-926	48	39	,	,	PUNCT
ap-926	48	40	3	3	NUM
ap-926	48	41	23	23	NUM
ap-926	48	42	23	23	NUM
ap-926	48	43	32	32	NUM
ap-926	48	44	32	32	NUM
ap-926	48	45	31	31	NUM
ap-926	48	46	31	31	NUM
ap-926	48	47	0	0	NUM
ap-926	48	48	�	�	PROPN
ap-926	48	49	�	�	PROPN
ap-926	48	50	�	�	PROPN
ap-926	48	51	x	x	PROPN
ap-926	48	52	f	f	NOUN
ap-926	48	53	x	x	PUNCT
ap-926	48	54	x	x	X
ap-926	48	55	f	f	NOUN
ap-926	48	56	x	x	X
ap-926	48	57	x	x	X
ap-926	48	58	f	f	PROPN
ap-926	48	59	x	x	SYM
ap-926	48	60	�	�	PROPN
ap-926	48	61	�	�	PROPN
ap-926	48	62	�	�	PROPN
ap-926	48	63	�	�	PROPN
ap-926	48	64	�	�	PROPN
ap-926	48	65	�	�	PROPN
ap-926	48	66	.	.	PUNCT
ap-926	49	1	solving	solve	VERB
ap-926	49	2	this	this	DET
ap-926	49	3	system	system	NOUN
ap-926	49	4	,	,	PUNCT
ap-926	49	5	we	we	PRON
ap-926	49	6	obtain	obtain	VERB
ap-926	49	7	that	that	SCONJ
ap-926	49	8	the	the	DET
ap-926	49	9	general	general	ADJ
ap-926	49	10	solution	solution	NOUN
ap-926	49	11	of	of	ADP
ap-926	49	12	the	the	DET
ap-926	49	13	system	system	NOUN
ap-926	49	14	has	have	VERB
ap-926	49	15	the	the	DET
ap-926	49	16	form	form	NOUN
ap-926	49	17	:	:	PUNCT
ap-926	49	18	f	f	X
ap-926	49	19	x	x	PUNCT
ap-926	49	20	x	x	PUNCT
ap-926	49	21	x	x	X
ap-926	49	22	f	f	NOUN
ap-926	49	23	x	x	X
ap-926	49	24	x	x	X
ap-926	49	25	c	c	NOUN
ap-926	49	26	c	c	PROPN
ap-926	49	27	cij	cij	PROPN
ap-926	49	28	n	n	PROPN
ap-926	49	29	n	n	PROPN
ap-926	49	30	n	n	CCONJ
ap-926	49	31	(	(	PUNCT
ap-926	49	32	)	)	PUNCT
ap-926	49	33	,	,	PUNCT
ap-926	49	34	,	,	PUNCT
ap-926	49	35	,	,	PUNCT
ap-926	49	36	�	�	PROPN
ap-926	49	37	�	�	PROPN
ap-926	49	38	�	�	PROPN
ap-926	49	39	�	�	PROPN
ap-926	49	40	�	�	PROPN
ap-926	49	41	�	�	PROPN
ap-926	49	42	�	�	PROPN
ap-926	49	43	�	�	PROPN
ap-926	49	44	�	�	PROPN
ap-926	49	45	�	�	PROPN
ap-926	49	46	�	�	PROPN
ap-926	49	47	1	1	NUM
ap-926	49	48	3	3	NUM
ap-926	49	49	2	2	NUM
ap-926	49	50	1	1	NUM
ap-926	49	51	1	1	NUM
ap-926	49	52	2	2	NUM
ap-926	49	53	3	3	NUM
ap-926	49	54	2	2	NUM
ap-926	49	55	3	3	NUM
ap-926	49	56	2	2	NUM
ap-926	49	57	,	,	PUNCT
ap-926	49	58	where	where	SCONJ
ap-926	49	59	x	x	X
ap-926	49	60	x	x	PROPN
ap-926	49	61	xk	xk	PROPN
ap-926	49	62	k2	k2	PROPN
ap-926	49	63	1	1	NUM
ap-926	49	64	3	3	NUM
ap-926	49	65	�	�	PROPN
ap-926	49	66	,	,	PUNCT
ap-926	49	67	c	c	PROPN
ap-926	49	68	xkk1	xkk1	PROPN
ap-926	49	69	�	�	PROPN
ap-926	49	70	,	,	PUNCT
ap-926	49	71	c	c	PROPN
ap-926	49	72	x	x	SYM
ap-926	49	73	xik	xik	PROPN
ap-926	49	74	ki2	ki2	PROPN
ap-926	49	75	�	�	PROPN
ap-926	49	76	,	,	PUNCT
ap-926	49	77	c	c	NOUN
ap-926	49	78	x	x	SYM
ap-926	49	79	x	x	X
ap-926	49	80	xik	xik	PROPN
ap-926	49	81	kl	kl	PROPN
ap-926	49	82	li3	li3	PROPN
ap-926	49	83	�	�	PROPN
ap-926	49	84	.	.	PUNCT
ap-926	50	1	(	(	PUNCT
ap-926	50	2	we	we	PRON
ap-926	50	3	omit	omit	VERB
ap-926	50	4	the	the	DET
ap-926	50	5	summation	summation	NOUN
ap-926	50	6	of	of	ADP
ap-926	50	7	repeated	repeat	VERB
ap-926	50	8	indices	index	NOUN
ap-926	50	9	going	go	VERB
ap-926	50	10	over	over	ADP
ap-926	50	11	1	1	NUM
ap-926	50	12	,	,	PUNCT
ap-926	50	13	2	2	NUM
ap-926	50	14	,	,	PUNCT
ap-926	50	15	3	3	NUM
ap-926	50	16	)	)	PUNCT
ap-926	50	17	.	.	PUNCT
ap-926	51	1	we	we	PRON
ap-926	51	2	now	now	ADV
ap-926	51	3	encounter	encounter	VERB
ap-926	51	4	the	the	DET
ap-926	51	5	first	first	ADJ
ap-926	51	6	problem	problem	NOUN
ap-926	51	7	which	which	PRON
ap-926	51	8	arises	arise	VERB
ap-926	51	9	in	in	ADP
ap-926	51	10	the	the	DET
ap-926	51	11	process	process	NOUN
ap-926	51	12	of	of	ADP
ap-926	51	13	decomposition	decomposition	NOUN
ap-926	51	14	.	.	PUNCT
ap-926	52	1	although	although	SCONJ
ap-926	52	2	we	we	PRON
ap-926	52	3	know	know	VERB
ap-926	52	4	the	the	DET
ap-926	52	5	general	general	ADJ
ap-926	52	6	solution	solution	NOUN
ap-926	52	7	of	of	ADP
ap-926	52	8	this	this	DET
ap-926	52	9	system	system	NOUN
ap-926	52	10	of	of	ADP
ap-926	52	11	differential	differential	ADJ
ap-926	52	12	equations	equation	NOUN
ap-926	52	13	,	,	PUNCT
ap-926	52	14	an	an	DET
ap-926	52	15	important	important	ADJ
ap-926	52	16	question	question	NOUN
ap-926	52	17	is	be	AUX
ap-926	52	18	how	how	SCONJ
ap-926	52	19	to	to	PART
ap-926	52	20	obtain	obtain	VERB
ap-926	52	21	enough	enough	ADJ
ap-926	52	22	polynomial	polynomial	ADJ
ap-926	52	23	solutions	solution	NOUN
ap-926	52	24	in	in	ADP
ap-926	52	25	variables	variable	NOUN
ap-926	52	26	xij	xij	PROPN
ap-926	52	27	from	from	ADP
ap-926	52	28	this	this	DET
ap-926	52	29	general	general	ADJ
ap-926	52	30	solution	solution	NOUN
ap-926	52	31	.	.	PUNCT
ap-926	53	1	this	this	PRON
ap-926	53	2	can	can	AUX
ap-926	53	3	be	be	AUX
ap-926	53	4	generally	generally	ADV
ap-926	53	5	difficult	difficult	ADJ
ap-926	53	6	.	.	PUNCT
ap-926	54	1	for	for	ADP
ap-926	54	2	example	example	NOUN
ap-926	54	3	,	,	PUNCT
ap-926	54	4	the	the	DET
ap-926	54	5	expression	expression	NOUN
ap-926	54	6	x	x	PUNCT
ap-926	55	1	x	x	PUNCT
ap-926	55	2	x	x	PUNCT
ap-926	55	3	x	x	X
ap-926	55	4	c	c	NOUN
ap-926	55	5	x	x	PUNCT
ap-926	55	6	x	x	X
ap-926	55	7	c	c	NOUN
ap-926	55	8	c	c	NOUN
ap-926	55	9	x	x	PUNCT
ap-926	55	10	x	x	X
ap-926	55	11	c	c	NOUN
ap-926	55	12	c	c	NOUN
ap-926	55	13	4	4	NUM
ap-926	55	14	1	1	NUM
ap-926	55	15	3	3	NUM
ap-926	55	16	2	2	NUM
ap-926	55	17	3	3	NUM
ap-926	55	18	1	1	NUM
ap-926	55	19	3	3	NUM
ap-926	55	20	1	1	NUM
ap-926	55	21	2	2	NUM
ap-926	55	22	2	2	NUM
ap-926	55	23	1	1	NUM
ap-926	55	24	2	2	NUM
ap-926	55	25	1	1	NUM
ap-926	55	26	2	2	NUM
ap-926	55	27	2	2	NUM
ap-926	55	28	2	2	NUM
ap-926	55	29	1	1	NUM
ap-926	55	30	1	1	NUM
ap-926	55	31	3	3	NUM
ap-926	55	32	32	32	NUM
ap-926	55	33	1	1	NUM
ap-926	55	34	2	2	NUM
ap-926	55	35	3	3	NUM
ap-926	55	36	1	1	NUM
ap-926	55	37	3	3	NUM
ap-926	55	38	�	�	PROPN
ap-926	55	39	�	�	PROPN
ap-926	55	40	�	�	PROPN
ap-926	55	41	�	�	PROPN
ap-926	55	42	�	�	PROPN
ap-926	55	43	�	�	PROPN
ap-926	55	44	(	(	PUNCT
ap-926	55	45	)	)	PUNCT
ap-926	55	46	(	(	PUNCT
ap-926	55	47	)	)	PUNCT
ap-926	55	48	�	�	PROPN
ap-926	55	49	�	�	PROPN
ap-926	55	50	�	�	PROPN
ap-926	55	51	�	�	PROPN
ap-926	55	52	�	�	PROPN
ap-926	55	53	�	�	PROPN
ap-926	55	54	�	�	PROPN
ap-926	55	55	�	�	PROPN
ap-926	55	56	�	�	PROPN
ap-926	55	57	�	�	PROPN
ap-926	55	58	x	x	PUNCT
ap-926	55	59	x	x	PUNCT
ap-926	55	60	x	x	PUNCT
ap-926	55	61	x	x	PUNCT
ap-926	55	62	x	x	PUNCT
ap-926	55	63	x	x	PUNCT
ap-926	55	64	x	x	SYM
ap-926	55	65	x	x	SYM
ap-926	55	66	x	x	SYM
ap-926	55	67	3	3	NUM
ap-926	55	68	12	12	NUM
ap-926	55	69	23	23	NUM
ap-926	55	70	2	2	NUM
ap-926	55	71	13	13	NUM
ap-926	55	72	23	23	NUM
ap-926	55	73	11	11	NUM
ap-926	55	74	22	22	NUM
ap-926	55	75	13	13	NUM
ap-926	55	76	2	2	NUM
ap-926	55	77	21	21	NUM
ap-926	55	78	(	(	PUNCT
ap-926	55	79	)	)	PUNCT
ap-926	55	80	although	although	SCONJ
ap-926	55	81	rational	rational	ADJ
ap-926	55	82	in	in	ADP
ap-926	55	83	variables	variable	NOUN
ap-926	55	84	xj	xj	PROPN
ap-926	55	85	,	,	PUNCT
ap-926	55	86	cj	cj	PROPN
ap-926	55	87	is	be	AUX
ap-926	55	88	polynomial	polynomial	ADJ
ap-926	55	89	in	in	ADP
ap-926	55	90	variables	variable	NOUN
ap-926	55	91	xij	xij	PRON
ap-926	55	92	!	!	PUNCT
ap-926	56	1	the	the	DET
ap-926	56	2	second	second	ADJ
ap-926	56	3	question	question	NOUN
ap-926	56	4	which	which	PRON
ap-926	56	5	arises	arise	VERB
ap-926	56	6	is	be	AUX
ap-926	56	7	,	,	PUNCT
ap-926	56	8	in	in	ADP
ap-926	56	9	some	some	DET
ap-926	56	10	sense	sense	NOUN
ap-926	56	11	,	,	PUNCT
ap-926	56	12	the	the	DET
ap-926	56	13	opposite	opposite	ADJ
ap-926	56	14	kind	kind	NOUN
ap-926	56	15	of	of	ADP
ap-926	56	16	problem	problem	NOUN
ap-926	56	17	.	.	PUNCT
ap-926	57	1	we	we	PRON
ap-926	57	2	can	can	AUX
ap-926	57	3	generate	generate	VERB
ap-926	57	4	too	too	ADV
ap-926	57	5	many	many	ADJ
ap-926	57	6	polynomial	polynomial	ADJ
ap-926	57	7	solutions	solution	NOUN
ap-926	57	8	and	and	CCONJ
ap-926	57	9	their	their	PRON
ap-926	57	10	polynomial	polynomial	ADJ
ap-926	57	11	combinations	combination	NOUN
ap-926	57	12	will	will	AUX
ap-926	57	13	no	no	ADV
ap-926	57	14	longer	long	ADV
ap-926	57	15	be	be	AUX
ap-926	57	16	linear	linear	ADV
ap-926	57	17	independent	independent	ADJ
ap-926	57	18	(	(	PUNCT
ap-926	57	19	or	or	CCONJ
ap-926	57	20	,	,	PUNCT
ap-926	57	21	equivalently	equivalently	ADV
ap-926	57	22	,	,	PUNCT
ap-926	57	23	the	the	DET
ap-926	57	24	polynomial	polynomial	ADJ
ap-926	57	25	solutions	solution	NOUN
ap-926	57	26	will	will	AUX
ap-926	57	27	be	be	AUX
ap-926	57	28	functionally	functionally	ADV
ap-926	57	29	dependent	dependent	ADJ
ap-926	57	30	)	)	PUNCT
ap-926	57	31	.	.	PUNCT
ap-926	58	1	for	for	ADP
ap-926	58	2	example	example	NOUN
ap-926	58	3	,	,	PUNCT
ap-926	58	4	in	in	ADP
ap-926	58	5	our	our	PRON
ap-926	58	6	case	case	NOUN
ap-926	58	7	of	of	ADP
ap-926	58	8	algebra	algebra	NOUN
ap-926	58	9	gl(3	gl(3	NOUN
ap-926	58	10	)	)	PUNCT
ap-926	58	11	we	we	PRON
ap-926	58	12	have	have	VERB
ap-926	58	13	x	x	X
ap-926	58	14	x	x	PUNCT
ap-926	58	15	x	x	X
ap-926	58	16	c	c	NOUN
ap-926	58	17	x	x	PUNCT
ap-926	58	18	x	x	X
ap-926	58	19	c	c	NOUN
ap-926	58	20	c	c	NOUN
ap-926	58	21	x	x	PUNCT
ap-926	58	22	x	x	X
ap-926	58	23	c	c	NOUN
ap-926	58	24	c	c	NOUN
ap-926	58	25	x3	x3	VERB
ap-926	58	26	4	4	NUM
ap-926	58	27	2	2	NUM
ap-926	58	28	3	3	NUM
ap-926	58	29	1	1	NUM
ap-926	58	30	2	2	NUM
ap-926	58	31	2	2	NUM
ap-926	58	32	1	1	NUM
ap-926	58	33	1	1	NUM
ap-926	58	34	2	2	NUM
ap-926	58	35	2	2	NUM
ap-926	58	36	2	2	NUM
ap-926	58	37	1	1	NUM
ap-926	58	38	2	2	NUM
ap-926	58	39	1	1	NUM
ap-926	58	40	3	3	NUM
ap-926	58	41	3	3	NUM
ap-926	58	42	1	1	NUM
ap-926	58	43	32	32	NUM
ap-926	58	44	1	1	NUM
ap-926	58	45	2	2	NUM
ap-926	58	46	3	3	NUM
ap-926	58	47	1	1	NUM
ap-926	58	48	3	3	NUM
ap-926	58	49	�	�	PROPN
ap-926	58	50	�	�	PROPN
ap-926	58	51	�	�	PROPN
ap-926	58	52	�	�	PROPN
ap-926	58	53	�	�	PROPN
ap-926	58	54	(	(	PUNCT
ap-926	58	55	)	)	PUNCT
ap-926	58	56	(	(	PUNCT
ap-926	58	57	)	)	PUNCT
ap-926	58	58	.	.	PUNCT
ap-926	59	1	this	this	DET
ap-926	59	2	dependency	dependency	NOUN
ap-926	59	3	signals	signal	NOUN
ap-926	59	4	that	that	SCONJ
ap-926	59	5	it	it	PRON
ap-926	59	6	is	be	AUX
ap-926	59	7	forbidden	forbid	VERB
ap-926	59	8	to	to	PART
ap-926	59	9	have	have	VERB
ap-926	59	10	product	product	NOUN
ap-926	59	11	x3x4	x3x4	ADP
ap-926	59	12	in	in	ADP
ap-926	59	13	the	the	DET
ap-926	59	14	decomposition	decomposition	NOUN
ap-926	59	15	.	.	PUNCT
ap-926	60	1	luckily	luckily	ADV
ap-926	60	2	,	,	PUNCT
ap-926	60	3	both	both	CCONJ
ap-926	60	4	above	above	ADV
ap-926	60	5	-	-	PUNCT
ap-926	60	6	mentioned	mention	VERB
ap-926	60	7	problems	problem	NOUN
ap-926	60	8	are	be	AUX
ap-926	60	9	easily	easily	ADV
ap-926	60	10	found	find	VERB
ap-926	60	11	out	out	ADP
ap-926	60	12	by	by	ADP
ap-926	60	13	a	a	DET
ap-926	60	14	dimension	dimension	NOUN
ap-926	60	15	check	check	NOUN
ap-926	60	16	.	.	PUNCT
ap-926	61	1	if	if	SCONJ
ap-926	61	2	there	there	PRON
ap-926	61	3	are	be	VERB
ap-926	61	4	not	not	PART
ap-926	61	5	enough	enough	ADJ
ap-926	61	6	solutions	solution	NOUN
ap-926	61	7	we	we	PRON
ap-926	61	8	will	will	AUX
ap-926	61	9	not	not	PART
ap-926	61	10	have	have	VERB
ap-926	61	11	enough	enough	ADJ
ap-926	61	12	linear	linear	ADJ
ap-926	61	13	independent	independent	ADJ
ap-926	61	14	vectors	vector	NOUN
ap-926	61	15	to	to	PART
ap-926	61	16	construct	construct	VERB
ap-926	61	17	the	the	DET
ap-926	61	18	decomposition	decomposition	NOUN
ap-926	61	19	,	,	PUNCT
ap-926	61	20	so	so	SCONJ
ap-926	61	21	that	that	SCONJ
ap-926	61	22	the	the	DET
ap-926	61	23	number	number	NOUN
ap-926	61	24	of	of	ADP
ap-926	61	25	linear	linear	ADJ
ap-926	61	26	independent	independent	ADJ
ap-926	61	27	vectors	vector	NOUN
ap-926	61	28	we	we	PRON
ap-926	61	29	generate	generate	VERB
ap-926	61	30	is	be	AUX
ap-926	61	31	less	less	ADJ
ap-926	61	32	than	than	ADP
ap-926	61	33	the	the	DET
ap-926	61	34	dimension	dimension	NOUN
ap-926	61	35	of	of	ADP
ap-926	61	36	the	the	DET
ap-926	61	37	corresponding	correspond	VERB
ap-926	61	38	filtration	filtration	NOUN
ap-926	61	39	part	part	NOUN
ap-926	61	40	un	un	PROPN
ap-926	61	41	.	.	PROPN
ap-926	62	1	in	in	ADP
ap-926	62	2	the	the	DET
ap-926	62	3	opposite	opposite	ADJ
ap-926	62	4	case	case	NOUN
ap-926	62	5	,	,	PUNCT
ap-926	62	6	if	if	SCONJ
ap-926	62	7	the	the	DET
ap-926	62	8	number	number	NOUN
ap-926	62	9	is	be	AUX
ap-926	62	10	greater	great	ADJ
ap-926	62	11	,	,	PUNCT
ap-926	62	12	it	it	PRON
ap-926	62	13	clearly	clearly	ADV
ap-926	62	14	indicates	indicate	VERB
ap-926	62	15	that	that	SCONJ
ap-926	62	16	there	there	PRON
ap-926	62	17	is	be	VERB
ap-926	62	18	some	some	DET
ap-926	62	19	linear	linear	ADJ
ap-926	62	20	dependency	dependency	NOUN
ap-926	62	21	between	between	ADP
ap-926	62	22	the	the	DET
ap-926	62	23	considered	consider	VERB
ap-926	62	24	vectors	vector	NOUN
ap-926	62	25	.	.	PUNCT
ap-926	63	1	©	©	PROPN
ap-926	63	2	czech	czech	PROPN
ap-926	63	3	technical	technical	PROPN
ap-926	63	4	university	university	PROPN
ap-926	63	5	publishing	publishing	NOUN
ap-926	63	6	house	house	NOUN
ap-926	63	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-926	63	8	27	27	NUM
ap-926	63	9	acta	acta	PROPN
ap-926	63	10	polytechnica	polytechnica	PROPN
ap-926	63	11	vol	vol	NOUN
ap-926	63	12	.	.	PUNCT
ap-926	64	1	47	47	NUM
ap-926	64	2	no	no	NOUN
ap-926	64	3	.	.	PUNCT
ap-926	65	1	2–3/2007	2–3/2007	NUM
ap-926	65	2	summing	sum	VERB
ap-926	65	3	up	up	ADP
ap-926	65	4	these	these	DET
ap-926	65	5	facts	fact	NOUN
ap-926	65	6	,	,	PUNCT
ap-926	65	7	if	if	SCONJ
ap-926	65	8	we	we	PRON
ap-926	65	9	now	now	ADV
ap-926	65	10	anti	anti	VERB
ap-926	65	11	-	-	ADJ
ap-926	65	12	symmetrize	symmetrize	ADJ
ap-926	65	13	xj	xj	NOUN
ap-926	65	14	,	,	PUNCT
ap-926	65	15	cj	cj	VERB
ap-926	65	16	into	into	ADP
ap-926	65	17	elements	element	NOUN
ap-926	65	18	xj	xj	PROPN
ap-926	65	19	,	,	PUNCT
ap-926	65	20	cj	cj	NOUN
ap-926	65	21	of	of	ADP
ap-926	65	22	the	the	DET
ap-926	65	23	enveloping	enveloping	NOUN
ap-926	65	24	algebra	algebra	NOUN
ap-926	65	25	u	u	NOUN
ap-926	65	26	,	,	PUNCT
ap-926	65	27	i.e.	i.e.	X
ap-926	65	28	x	x	SYM
ap-926	65	29	x	x	X
ap-926	65	30	e	e	NOUN
ap-926	65	31	x	x	PUNCT
ap-926	65	32	x	x	X
ap-926	65	33	e	e	X
ap-926	65	34	e	e	X
ap-926	65	35	e	e	X
ap-926	65	36	e	e	X
ap-926	65	37	e	e	X
ap-926	65	38	e	e	X
ap-926	65	39	1	1	NUM
ap-926	65	40	1	1	NUM
ap-926	65	41	13	13	NUM
ap-926	65	42	2	2	NUM
ap-926	65	43	2	2	NUM
ap-926	65	44	12	12	NUM
ap-926	65	45	23	23	NUM
ap-926	65	46	13	13	NUM
ap-926	65	47	11	11	NUM
ap-926	65	48	33	33	NUM
ap-926	65	49	13	13	NUM
ap-926	65	50	1	1	NUM
ap-926	65	51	2	2	NUM
ap-926	65	52	�	�	PROPN
ap-926	65	53	�	�	PROPN
ap-926	65	54	�	�	PROPN
ap-926	65	55	�	�	PROPN
ap-926	65	56	�	�	PROPN
ap-926	65	57	(	(	PUNCT
ap-926	65	58	)	)	PUNCT
ap-926	65	59	etc	etc	X
ap-926	65	60	.	.	X
ap-926	66	1	we	we	PRON
ap-926	66	2	can	can	AUX
ap-926	66	3	construct	construct	VERB
ap-926	66	4	vectors	vector	NOUN
ap-926	66	5	c	c	NOUN
ap-926	66	6	c	c	NOUN
ap-926	66	7	c	c	NOUN
ap-926	66	8	x	x	PUNCT
ap-926	66	9	x	x	PUNCT
ap-926	66	10	x	x	PUNCT
ap-926	66	11	xk	xk	PROPN
ap-926	66	12	k	k	PROPN
ap-926	66	13	k	k	PROPN
ap-926	66	14	n	n	CCONJ
ap-926	66	15	n	n	CCONJ
ap-926	66	16	n	n	CCONJ
ap-926	66	17	n	n	ADV
ap-926	66	18	1	1	NUM
ap-926	66	19	2	2	NUM
ap-926	66	20	3	3	NUM
ap-926	66	21	1	1	NUM
ap-926	66	22	2	2	NUM
ap-926	66	23	3	3	NUM
ap-926	66	24	4	4	NUM
ap-926	66	25	1	1	NUM
ap-926	66	26	2	2	NUM
ap-926	66	27	3	3	NUM
ap-926	66	28	1	1	NUM
ap-926	66	29	2	2	NUM
ap-926	66	30	3	3	NUM
ap-926	66	31	4	4	NUM
ap-926	66	32	,	,	PUNCT
ap-926	66	33	k	k	PROPN
ap-926	66	34	nj	nj	PROPN
ap-926	66	35	j	j	PROPN
ap-926	66	36	,	,	PUNCT
ap-926	66	37	�	�	PROPN
ap-926	66	38	0	0	NUM
ap-926	66	39	,	,	PUNCT
ap-926	66	40	n	n	X
ap-926	66	41	n3	n3	ADJ
ap-926	66	42	4	4	NUM
ap-926	66	43	0	0	NUM
ap-926	66	44	�	�	PROPN
ap-926	66	45	and	and	CCONJ
ap-926	66	46	compute	compute	VERB
ap-926	66	47	their	their	PRON
ap-926	66	48	weights	weight	NOUN
ap-926	66	49	.	.	PUNCT
ap-926	67	1	the	the	DET
ap-926	67	2	weight	weight	NOUN
ap-926	67	3	of	of	ADP
ap-926	67	4	the	the	DET
ap-926	67	5	product	product	NOUN
ap-926	67	6	of	of	ADP
ap-926	67	7	any	any	DET
ap-926	67	8	elements	element	NOUN
ap-926	67	9	is	be	AUX
ap-926	67	10	obtained	obtain	VERB
ap-926	67	11	by	by	ADP
ap-926	67	12	the	the	DET
ap-926	67	13	sum	sum	NOUN
ap-926	67	14	of	of	ADP
ap-926	67	15	the	the	DET
ap-926	67	16	weights	weight	NOUN
ap-926	67	17	of	of	ADP
ap-926	67	18	the	the	DET
ap-926	67	19	corresponding	corresponding	ADJ
ap-926	67	20	elements	element	NOUN
ap-926	67	21	;	;	PUNCT
ap-926	67	22	we	we	PRON
ap-926	67	23	have	have	VERB
ap-926	67	24	element	element	NOUN
ap-926	67	25	weight	weight	NOUN
ap-926	68	1	x1	x1	PROPN
ap-926	69	1	(	(	PUNCT
ap-926	69	2	1,0,	1,0,	NOUN
ap-926	69	3	�	�	PROPN
ap-926	69	4	1	1	NUM
ap-926	69	5	)	)	PUNCT
ap-926	69	6	x2	x2	NOUN
ap-926	69	7	(	(	PUNCT
ap-926	69	8	1,0,	1,0,	NOUN
ap-926	69	9	�	�	PROPN
ap-926	69	10	1	1	NUM
ap-926	69	11	)	)	PUNCT
ap-926	69	12	x3	x3	NOUN
ap-926	69	13	(	(	PUNCT
ap-926	69	14	2,	2,	NUM
ap-926	69	15	�	�	NOUN
ap-926	69	16	1,	1,	NUM
ap-926	69	17	�	�	NOUN
ap-926	69	18	1	1	NUM
ap-926	69	19	)	)	PUNCT
ap-926	69	20	x4	x4	NOUN
ap-926	69	21	(	(	PUNCT
ap-926	69	22	1,1,	1,1,	NUM
ap-926	69	23	�	�	NOUN
ap-926	69	24	2	2	NUM
ap-926	69	25	)	)	PUNCT
ap-926	69	26	c1,2,3	c1,2,3	PROPN
ap-926	69	27	(	(	PUNCT
ap-926	69	28	0,0,0	0,0,0	NOUN
ap-926	69	29	)	)	PUNCT
ap-926	69	30	therefore	therefore	ADV
ap-926	69	31	weight	weight	NOUN
ap-926	69	32	(	(	PUNCT
ap-926	69	33	)	)	PUNCT
ap-926	69	34	(	(	PUNCT
ap-926	69	35	c	c	NOUN
ap-926	69	36	c	c	NOUN
ap-926	69	37	c	c	NOUN
ap-926	69	38	x	x	PUNCT
ap-926	70	1	x	x	PUNCT
ap-926	70	2	x	x	SYM
ap-926	70	3	x	x	SYM
ap-926	70	4	n	n	CCONJ
ap-926	70	5	n	n	CCONJ
ap-926	70	6	n	n	CCONJ
ap-926	70	7	n	n	NOUN
ap-926	70	8	k	k	PROPN
ap-926	70	9	k	k	PROPN
ap-926	70	10	k	k	PROPN
ap-926	70	11	n	n	CCONJ
ap-926	70	12	n	n	CCONJ
ap-926	70	13	n	n	CCONJ
ap-926	70	14	n	n	ADV
ap-926	70	15	1	1	NUM
ap-926	70	16	2	2	NUM
ap-926	70	17	3	3	NUM
ap-926	70	18	1	1	NUM
ap-926	70	19	2	2	NUM
ap-926	70	20	3	3	NUM
ap-926	70	21	4	4	NUM
ap-926	70	22	1	1	NUM
ap-926	70	23	2	2	NUM
ap-926	70	24	3	3	NUM
ap-926	70	25	4	4	NUM
ap-926	70	26	1	1	NUM
ap-926	70	27	2	2	NUM
ap-926	70	28	3	3	NUM
ap-926	70	29	1	1	NUM
ap-926	70	30	2	2	NUM
ap-926	70	31	3	3	NUM
ap-926	70	32	4	4	NUM
ap-926	70	33	2	2	NUM
ap-926	70	34	�	�	NOUN
ap-926	70	35	,	,	PUNCT
ap-926	70	36	,	,	PUNCT
ap-926	70	37	)	)	PUNCT
ap-926	70	38	.n	.n	PROPN
ap-926	70	39	n	n	CCONJ
ap-926	70	40	n	n	CCONJ
ap-926	70	41	n	n	CCONJ
ap-926	70	42	n	n	CCONJ
ap-926	70	43	n4	n4	PROPN
ap-926	70	44	3	3	NUM
ap-926	70	45	1	1	NUM
ap-926	70	46	2	2	NUM
ap-926	70	47	3	3	NUM
ap-926	70	48	42	42	NUM
ap-926	70	49	�	�	PROPN
ap-926	70	50	�	�	PROPN
ap-926	70	51	�	�	PROPN
ap-926	70	52	�	�	PROPN
ap-926	70	53	�	�	PROPN
ap-926	70	54	the	the	DET
ap-926	70	55	degree	degree	NOUN
ap-926	70	56	of	of	ADP
ap-926	70	57	the	the	DET
ap-926	70	58	general	general	ADJ
ap-926	70	59	element	element	NOUN
ap-926	70	60	is	be	AUX
ap-926	70	61	n	n	PRON
ap-926	71	1	k	k	PROPN
ap-926	71	2	k	k	PROPN
ap-926	71	3	k	k	PROPN
ap-926	71	4	n	n	CCONJ
ap-926	71	5	n	n	CCONJ
ap-926	71	6	n	n	CCONJ
ap-926	71	7	n	n	CCONJ
ap-926	71	8	�	�	PROPN
ap-926	71	9	1	1	NUM
ap-926	71	10	2	2	NUM
ap-926	71	11	3	3	NUM
ap-926	71	12	1	1	NUM
ap-926	71	13	2	2	NUM
ap-926	71	14	3	3	NUM
ap-926	71	15	42	42	NUM
ap-926	71	16	3	3	NUM
ap-926	71	17	2	2	NUM
ap-926	71	18	3	3	NUM
ap-926	71	19	3	3	NUM
ap-926	71	20	.	.	PUNCT
ap-926	72	1	now	now	ADV
ap-926	72	2	we	we	PRON
ap-926	72	3	can	can	AUX
ap-926	72	4	perform	perform	VERB
ap-926	72	5	a	a	DET
ap-926	72	6	dimension	dimension	NOUN
ap-926	72	7	check	check	NOUN
ap-926	72	8	to	to	PART
ap-926	72	9	see	see	VERB
ap-926	72	10	if	if	SCONJ
ap-926	72	11	our	our	PRON
ap-926	72	12	hypothesis	hypothesis	NOUN
ap-926	72	13	is	be	AUX
ap-926	72	14	correct	correct	ADJ
ap-926	72	15	:	:	PUNCT
ap-926	72	16	from	from	ADP
ap-926	72	17	representation	representation	NOUN
ap-926	72	18	theory	theory	NOUN
ap-926	72	19	,	,	PUNCT
ap-926	72	20	the	the	DET
ap-926	72	21	dimension	dimension	NOUN
ap-926	72	22	of	of	ADP
ap-926	72	23	the	the	DET
ap-926	72	24	representation	representation	NOUN
ap-926	72	25	with	with	ADP
ap-926	72	26	highest	high	ADJ
ap-926	72	27	weight	weight	NOUN
ap-926	72	28	(	(	PUNCT
ap-926	72	29	n1	n1	NOUN
ap-926	72	30	,	,	PUNCT
ap-926	72	31	n2	n2	NOUN
ap-926	72	32	,	,	PUNCT
ap-926	72	33	n3	n3	NOUN
ap-926	72	34	)	)	PUNCT
ap-926	72	35	is	be	AUX
ap-926	72	36	d	d	PROPN
ap-926	72	37	n	n	CCONJ
ap-926	72	38	n	n	CCONJ
ap-926	72	39	n	n	CCONJ
ap-926	72	40	n	n	CCONJ
ap-926	72	41	n	n	CCONJ
ap-926	72	42	n	n	CCONJ
ap-926	72	43	n	n	CCONJ
ap-926	72	44	n	n	CCONJ
ap-926	72	45	n	n	CCONJ
ap-926	72	46	(	(	PUNCT
ap-926	72	47	,	,	PUNCT
ap-926	72	48	,	,	PUNCT
ap-926	72	49	)	)	PUNCT
ap-926	72	50	(	(	PUNCT
ap-926	72	51	)	)	PUNCT
ap-926	72	52	(	(	PUNCT
ap-926	72	53	)	)	PUNCT
ap-926	72	54	(	(	PUNCT
ap-926	72	55	)	)	SYM
ap-926	72	56	1	1	NUM
ap-926	72	57	2	2	NUM
ap-926	72	58	3	3	NUM
ap-926	72	59	1	1	NUM
ap-926	72	60	2	2	NUM
ap-926	72	61	1	1	NUM
ap-926	72	62	3	3	NUM
ap-926	72	63	2	2	NUM
ap-926	72	64	3	3	NUM
ap-926	72	65	1	1	NUM
ap-926	72	66	2	2	NUM
ap-926	72	67	1	1	NUM
ap-926	72	68	2	2	NUM
ap-926	72	69	1	1	NUM
ap-926	72	70	�	�	PROPN
ap-926	72	71	�	�	PROPN
ap-926	72	72	�	�	PROPN
ap-926	72	73	�	�	PROPN
ap-926	72	74	,	,	PUNCT
ap-926	72	75	hence	hence	ADV
ap-926	72	76	the	the	DET
ap-926	72	77	dimension	dimension	NOUN
ap-926	72	78	of	of	ADP
ap-926	72	79	the	the	DET
ap-926	72	80	representation	representation	NOUN
ap-926	72	81	generated	generate	VERB
ap-926	72	82	by	by	ADP
ap-926	72	83	our	our	PRON
ap-926	72	84	general	general	ADJ
ap-926	72	85	element	element	NOUN
ap-926	72	86	is	be	AUX
ap-926	72	87	~	~	PUNCT
ap-926	72	88	(	(	PUNCT
ap-926	72	89	,	,	PUNCT
ap-926	72	90	,	,	PUNCT
ap-926	72	91	,	,	PUNCT
ap-926	72	92	)	)	PUNCT
ap-926	72	93	(	(	PUNCT
ap-926	72	94	)	)	PUNCT
ap-926	72	95	(	(	PUNCT
ap-926	72	96	)	)	PUNCT
ap-926	73	1	(	(	PUNCT
ap-926	73	2	d	d	NOUN
ap-926	73	3	n	n	CCONJ
ap-926	73	4	n	n	CCONJ
ap-926	73	5	n	n	CCONJ
ap-926	73	6	n	n	CCONJ
ap-926	73	7	n	n	CCONJ
ap-926	73	8	n	n	CCONJ
ap-926	73	9	n	n	CCONJ
ap-926	73	10	n	n	CCONJ
ap-926	73	11	n	n	CCONJ
ap-926	73	12	n	n	CCONJ
ap-926	73	13	n	n	ADV
ap-926	73	14	1	1	NUM
ap-926	73	15	2	2	NUM
ap-926	73	16	3	3	NUM
ap-926	73	17	4	4	NUM
ap-926	73	18	1	1	NUM
ap-926	73	19	2	2	NUM
ap-926	73	20	3	3	NUM
ap-926	73	21	1	1	NUM
ap-926	73	22	2	2	NUM
ap-926	73	23	4	4	NUM
ap-926	73	24	1	1	NUM
ap-926	73	25	1	1	NUM
ap-926	73	26	2	2	NUM
ap-926	73	27	3	3	NUM
ap-926	73	28	1	1	NUM
ap-926	73	29	3	3	NUM
ap-926	73	30	1	1	NUM
ap-926	73	31	2	2	NUM
ap-926	73	32	2	2	NUM
ap-926	73	33	�	�	PROPN
ap-926	73	34	n	n	CCONJ
ap-926	73	35	n	n	NOUN
ap-926	73	36	n2	n2	NOUN
ap-926	73	37	3	3	NUM
ap-926	73	38	43	43	NUM
ap-926	73	39	3	3	NUM
ap-926	73	40	2	2	NUM
ap-926	73	41	)	)	PUNCT
ap-926	73	42	.	.	PUNCT
ap-926	74	1	it	it	PRON
ap-926	74	2	follows	follow	VERB
ap-926	74	3	that	that	SCONJ
ap-926	74	4	we	we	PRON
ap-926	74	5	must	must	AUX
ap-926	74	6	prove	prove	VERB
ap-926	74	7	that	that	SCONJ
ap-926	74	8	~	~	PUNCT
ap-926	74	9	(	(	PUNCT
ap-926	74	10	,	,	PUNCT
ap-926	74	11	,	,	PUNCT
ap-926	74	12	,	,	PUNCT
ap-926	74	13	)	)	PUNCT
ap-926	74	14	,	,	PUNCT
ap-926	74	15	,	,	PUNCT
ap-926	74	16	,	,	PUNCT
ap-926	74	17	,	,	PUNCT
ap-926	74	18	,	,	PUNCT
ap-926	74	19	,	,	PUNCT
ap-926	74	20	d	d	PROPN
ap-926	74	21	n	n	CCONJ
ap-926	74	22	n	n	CCONJ
ap-926	74	23	n	n	CCONJ
ap-926	74	24	n	n	NOUN
ap-926	74	25	k	k	PROPN
ap-926	74	26	k	k	PROPN
ap-926	74	27	k	k	PROPN
ap-926	74	28	n	n	CCONJ
ap-926	74	29	n	n	CCONJ
ap-926	74	30	n	n	CCONJ
ap-926	74	31	n	n	CCONJ
ap-926	74	32	n	n	CCONJ
ap-926	74	33	n	n	NOUN
ap-926	74	34	k	k	NOUN
ap-926	74	35	k	k	NOUN
ap-926	74	36	1	1	NUM
ap-926	74	37	2	2	NUM
ap-926	74	38	3	3	NUM
ap-926	74	39	4	4	NUM
ap-926	74	40	0	0	NUM
ap-926	74	41	0	0	NUM
ap-926	74	42	2	2	NUM
ap-926	74	43	1	1	NUM
ap-926	74	44	2	2	NUM
ap-926	74	45	3	3	NUM
ap-926	74	46	1	1	NUM
ap-926	74	47	2	2	NUM
ap-926	74	48	3	3	NUM
ap-926	74	49	4	4	NUM
ap-926	74	50	3	3	NUM
ap-926	74	51	3	3	NUM
ap-926	74	52	1	1	NUM
ap-926	74	53	2	2	NUM
ap-926	74	54	�	�	PROPN
ap-926	74	55	�	�	PROPN
ap-926	74	56	3	3	NUM
ap-926	74	57	2	2	NUM
ap-926	74	58	3	3	NUM
ap-926	74	59	33	33	NUM
ap-926	74	60	1	1	NUM
ap-926	74	61	2	2	NUM
ap-926	74	62	3	3	NUM
ap-926	74	63	4	4	NUM
ap-926	74	64	9	9	NUM
ap-926	74	65	k	k	NOUN
ap-926	74	66	n	n	CCONJ
ap-926	74	67	n	n	CCONJ
ap-926	74	68	n	n	CCONJ
ap-926	74	69	n	n	CCONJ
ap-926	74	70	n	n	CCONJ
ap-926	74	71	n	n	CCONJ
ap-926	74	72	n	n	CCONJ
ap-926	74	73	�	�	PROPN
ap-926	74	74	�	�	PROPN
ap-926	74	75	�	�	PROPN
ap-926	74	76	�	�	PROPN
ap-926	74	77	�	�	PROPN
ap-926	74	78	�	�	PROPN
ap-926	74	79	�	�	PROPN
ap-926	74	80	�	�	PROPN
ap-926	74	81	.	.	PUNCT
ap-926	75	1	the	the	DET
ap-926	75	2	first	first	ADJ
ap-926	75	3	look	look	NOUN
ap-926	75	4	leads	lead	VERB
ap-926	75	5	us	we	PRON
ap-926	75	6	of	of	ADP
ap-926	75	7	course	course	NOUN
ap-926	75	8	to	to	PART
ap-926	75	9	check	check	VERB
ap-926	75	10	if	if	SCONJ
ap-926	75	11	it	it	PRON
ap-926	75	12	is	be	AUX
ap-926	75	13	correct	correct	ADJ
ap-926	75	14	for	for	ADP
ap-926	75	15	small	small	ADJ
ap-926	75	16	n	n	CCONJ
ap-926	75	17	:	:	PUNCT
ap-926	75	18	we	we	PRON
ap-926	75	19	make	make	VERB
ap-926	75	20	a	a	DET
ap-926	75	21	table	table	NOUN
ap-926	75	22	n	n	DET
ap-926	75	23	sum	sum	NOUN
ap-926	75	24	on	on	ADP
ap-926	75	25	the	the	DET
ap-926	75	26	left	left	ADJ
ap-926	75	27	side	side	NOUN
ap-926	75	28	n	n	CCONJ
ap-926	75	29	�	�	PROPN
ap-926	75	30	�	�	PROPN
ap-926	75	31	�	�	PROPN
ap-926	75	32	�	�	PROPN
ap-926	75	33	�	�	PROPN
ap-926	75	34	�	�	PROPN
ap-926	75	35	9	9	NUM
ap-926	75	36	9	9	NUM
ap-926	75	37	1	1	NUM
ap-926	75	38	10	10	NUM
ap-926	75	39	10	10	NUM
ap-926	75	40	2	2	NUM
ap-926	75	41	55	55	NUM
ap-926	75	42	55	55	NUM
ap-926	75	43	3	3	NUM
ap-926	75	44	220	220	NUM
ap-926	75	45	220	220	NUM
ap-926	75	46	4	4	NUM
ap-926	75	47	715	715	NUM
ap-926	75	48	715	715	NUM
ap-926	75	49	…	…	PUNCT
ap-926	75	50	…	…	PUNCT
ap-926	75	51	from	from	ADP
ap-926	75	52	which	which	PRON
ap-926	75	53	we	we	PRON
ap-926	75	54	see	see	VERB
ap-926	75	55	that	that	SCONJ
ap-926	75	56	it	it	PRON
ap-926	75	57	should	should	AUX
ap-926	75	58	work	work	VERB
ap-926	75	59	.	.	PUNCT
ap-926	76	1	a	a	DET
ap-926	76	2	general	general	ADJ
ap-926	76	3	proof	proof	NOUN
ap-926	76	4	of	of	ADP
ap-926	76	5	the	the	DET
ap-926	76	6	formula	formula	NOUN
ap-926	76	7	can	can	AUX
ap-926	76	8	be	be	AUX
ap-926	76	9	performed	perform	VERB
ap-926	76	10	for	for	ADP
ap-926	76	11	example	example	NOUN
ap-926	76	12	using	use	VERB
ap-926	76	13	generating	generating	NOUN
ap-926	76	14	functions	function	NOUN
ap-926	76	15	:	:	PUNCT
ap-926	76	16	because	because	SCONJ
ap-926	76	17	n	n	CCONJ
ap-926	76	18	n	n	CCONJ
ap-926	76	19	n	n	CCONJ
ap-926	76	20	�	�	PROPN
ap-926	76	21	�	�	PROPN
ap-926	76	22	�	�	PROPN
ap-926	76	23	�	�	PROPN
ap-926	76	24	�	�	PROPN
ap-926	76	25	�	�	PROPN
ap-926	76	26	�	�	PROPN
ap-926	76	27	�	�	PROPN
ap-926	76	28	�	�	PROPN
ap-926	76	29	�	�	PROPN
ap-926	76	30	�	�	PROPN
ap-926	76	31	�	�	PROPN
ap-926	76	32	�	�	PROPN
ap-926	76	33	�	�	PROPN
ap-926	76	34	�	�	PROPN
ap-926	76	35	�	�	PROPN
ap-926	76	36	�	�	PROPN
ap-926	76	37	�	�	PROPN
ap-926	76	38	�	�	PROPN
ap-926	76	39	�	�	PROPN
ap-926	76	40	�	�	PROPN
ap-926	76	41	9	9	NUM
ap-926	76	42	9	9	NUM
ap-926	76	43	1	1	NUM
ap-926	76	44	9	9	NUM
ap-926	76	45	9	9	NUM
ap-926	76	46	8	8	NUM
ap-926	76	47	8	8	NUM
ap-926	76	48	(	(	PUNCT
ap-926	76	49	)	)	PUNCT
ap-926	76	50	it	it	PRON
ap-926	76	51	is	be	AUX
ap-926	76	52	sufficient	sufficient	ADJ
ap-926	76	53	to	to	PART
ap-926	76	54	show	show	VERB
ap-926	76	55	~	~	PROPN
ap-926	76	56	(	(	PUNCT
ap-926	76	57	,	,	PUNCT
ap-926	76	58	,	,	PUNCT
ap-926	76	59	,	,	PUNCT
ap-926	76	60	)	)	PUNCT
ap-926	76	61	,	,	PUNCT
ap-926	76	62	,	,	PUNCT
ap-926	76	63	,	,	PUNCT
ap-926	76	64	,	,	PUNCT
ap-926	76	65	,	,	PUNCT
ap-926	76	66	,	,	PUNCT
ap-926	76	67	d	d	PROPN
ap-926	76	68	n	n	CCONJ
ap-926	76	69	n	n	CCONJ
ap-926	76	70	n	n	CCONJ
ap-926	76	71	n	n	NOUN
ap-926	76	72	k	k	PROPN
ap-926	76	73	k	k	PROPN
ap-926	76	74	k	k	PROPN
ap-926	76	75	n	n	CCONJ
ap-926	76	76	n	n	CCONJ
ap-926	76	77	n	n	CCONJ
ap-926	76	78	n	n	CCONJ
ap-926	76	79	n	n	CCONJ
ap-926	76	80	n	n	NOUN
ap-926	76	81	k	k	NOUN
ap-926	76	82	k	k	NOUN
ap-926	76	83	1	1	NUM
ap-926	76	84	2	2	NUM
ap-926	76	85	3	3	NUM
ap-926	76	86	4	4	NUM
ap-926	76	87	0	0	NUM
ap-926	76	88	0	0	NUM
ap-926	76	89	2	2	NUM
ap-926	76	90	1	1	NUM
ap-926	76	91	2	2	NUM
ap-926	76	92	3	3	NUM
ap-926	76	93	1	1	NUM
ap-926	76	94	2	2	NUM
ap-926	76	95	3	3	NUM
ap-926	76	96	4	4	NUM
ap-926	76	97	3	3	NUM
ap-926	76	98	4	4	NUM
ap-926	76	99	1	1	NUM
ap-926	76	100	2	2	NUM
ap-926	76	101	�	�	PROPN
ap-926	76	102	�	�	PROPN
ap-926	76	103	3	3	NUM
ap-926	76	104	2	2	NUM
ap-926	76	105	3	3	NUM
ap-926	76	106	33	33	NUM
ap-926	76	107	1	1	NUM
ap-926	76	108	2	2	NUM
ap-926	76	109	3	3	NUM
ap-926	76	110	4	4	NUM
ap-926	76	111	8	8	NUM
ap-926	76	112	8	8	NUM
ap-926	76	113	k	k	NOUN
ap-926	76	114	n	n	CCONJ
ap-926	76	115	n	n	CCONJ
ap-926	76	116	n	n	CCONJ
ap-926	76	117	n	n	CCONJ
ap-926	76	118	n	n	CCONJ
ap-926	76	119	n	n	CCONJ
ap-926	76	120	�	�	PROPN
ap-926	76	121	�	�	PROPN
ap-926	76	122	�	�	PROPN
ap-926	76	123	�	�	PROPN
ap-926	76	124	�	�	PROPN
ap-926	76	125	�	�	PROPN
ap-926	76	126	�	�	PROPN
ap-926	76	127	�	�	PROPN
ap-926	76	128	�	�	PROPN
ap-926	76	129	or	or	CCONJ
ap-926	76	130	,	,	PUNCT
ap-926	76	131	equivalently	equivalently	ADV
ap-926	76	132	,	,	PUNCT
ap-926	76	133	~	~	PUNCT
ap-926	76	134	(	(	PUNCT
ap-926	76	135	,	,	PUNCT
ap-926	76	136	,	,	PUNCT
ap-926	76	137	,	,	PUNCT
ap-926	76	138	)	)	PUNCT
ap-926	76	139	,	,	PUNCT
ap-926	76	140	,	,	PUNCT
ap-926	76	141	,	,	PUNCT
ap-926	76	142	,	,	PUNCT
ap-926	76	143	,	,	PUNCT
ap-926	76	144	,	,	PUNCT
ap-926	76	145	d	d	PROPN
ap-926	76	146	n	n	CCONJ
ap-926	76	147	n	n	CCONJ
ap-926	76	148	n	n	CCONJ
ap-926	76	149	n	n	NOUN
ap-926	76	150	xn	xn	PROPN
ap-926	77	1	k	k	PROPN
ap-926	77	2	k	k	PROPN
ap-926	77	3	k	k	PROPN
ap-926	77	4	n	n	CCONJ
ap-926	77	5	n	n	CCONJ
ap-926	77	6	n	n	CCONJ
ap-926	77	7	n	n	CCONJ
ap-926	77	8	n	n	CCONJ
ap-926	77	9	n	n	NOUN
ap-926	77	10	k	k	NOUN
ap-926	77	11	k	k	NOUN
ap-926	77	12	1	1	NUM
ap-926	77	13	2	2	NUM
ap-926	77	14	3	3	NUM
ap-926	77	15	4	4	NUM
ap-926	77	16	0	0	NUM
ap-926	77	17	0	0	NUM
ap-926	77	18	2	2	NUM
ap-926	77	19	1	1	NUM
ap-926	77	20	2	2	NUM
ap-926	77	21	3	3	NUM
ap-926	77	22	1	1	NUM
ap-926	77	23	2	2	NUM
ap-926	77	24	3	3	NUM
ap-926	77	25	4	4	NUM
ap-926	77	26	3	3	NUM
ap-926	77	27	4	4	NUM
ap-926	77	28	1	1	NUM
ap-926	77	29	�	�	PROPN
ap-926	77	30	�	�	PROPN
ap-926	77	31	2	2	NUM
ap-926	77	32	3	3	NUM
ap-926	77	33	1	1	NUM
ap-926	77	34	2	2	NUM
ap-926	77	35	3	3	NUM
ap-926	77	36	43	43	NUM
ap-926	77	37	2	2	NUM
ap-926	77	38	3	3	NUM
ap-926	77	39	3	3	NUM
ap-926	77	40	0	0	NUM
ap-926	77	41	0	0	NUM
ap-926	77	42	8	8	NUM
ap-926	77	43	8	8	NUM
ap-926	77	44	�	�	PROPN
ap-926	77	45	�	�	PROPN
ap-926	77	46	�	�	PROPN
ap-926	77	47	�	�	PROPN
ap-926	77	48	�	�	PROPN
ap-926	77	49	�	�	PROPN
ap-926	77	50	�	�	PROPN
ap-926	77	51	�	�	PROPN
ap-926	77	52	�	�	PROPN
ap-926	77	53	�	�	PROPN
ap-926	77	54	�	�	PROPN
ap-926	77	55	�	�	PROPN
ap-926	77	56	�	�	PROPN
ap-926	77	57	k	k	PROPN
ap-926	77	58	n	n	CCONJ
ap-926	77	59	n	n	CCONJ
ap-926	77	60	n	n	CCONJ
ap-926	77	61	n	n	CCONJ
ap-926	77	62	n	n	CCONJ
ap-926	77	63	n	n	CCONJ
ap-926	77	64	n	n	CCONJ
ap-926	77	65	n	n	CCONJ
ap-926	77	66	n	n	NOUN
ap-926	77	67	x	x	NOUN
ap-926	77	68	.	.	PUNCT
ap-926	78	1	this	this	PRON
ap-926	78	2	is	be	AUX
ap-926	78	3	easily	easily	ADV
ap-926	78	4	done	do	VERB
ap-926	78	5	with	with	ADP
ap-926	78	6	the	the	DET
ap-926	78	7	help	help	NOUN
ap-926	78	8	of	of	ADP
ap-926	78	9	the	the	DET
ap-926	78	10	sum	sum	NOUN
ap-926	78	11	of	of	ADP
ap-926	78	12	the	the	DET
ap-926	78	13	geometric	geometric	ADJ
ap-926	78	14	series	series	NOUN
ap-926	78	15	,	,	PUNCT
ap-926	78	16	namely	namely	ADV
ap-926	78	17	1	1	NUM
ap-926	78	18	1	1	NUM
ap-926	78	19	0	0	NUM
ap-926	78	20	�	�	PROPN
ap-926	78	21	�	�	PROPN
ap-926	78	22	�	�	PROPN
ap-926	78	23	�	�	PROPN
ap-926	78	24	x	x	PROPN
ap-926	78	25	xn	xn	PROPN
ap-926	78	26	n	n	NUM
ap-926	78	27	which	which	PRON
ap-926	78	28	can	can	AUX
ap-926	78	29	be	be	AUX
ap-926	78	30	differentiated	differentiate	VERB
ap-926	78	31	several	several	ADJ
ap-926	78	32	times	time	NOUN
ap-926	78	33	to	to	PART
ap-926	78	34	get	get	VERB
ap-926	78	35	1	1	NUM
ap-926	78	36	1	1	NUM
ap-926	78	37	2	2	NUM
ap-926	78	38	0	0	NUM
ap-926	78	39	(	(	PUNCT
ap-926	78	40	)	)	PUNCT
ap-926	78	41	�	�	PROPN
ap-926	78	42	�	�	PROPN
ap-926	78	43	�	�	PROPN
ap-926	78	44	�	�	PROPN
ap-926	78	45	x	x	PROPN
ap-926	78	46	n	n	PROPN
ap-926	78	47	xn	xn	PROPN
ap-926	78	48	n	n	PROPN
ap-926	78	49	,	,	PUNCT
ap-926	78	50	x	x	PUNCT
ap-926	78	51	x	x	PUNCT
ap-926	78	52	x	x	SYM
ap-926	78	53	n	n	PROPN
ap-926	78	54	xn	xn	PROPN
ap-926	78	55	n	n	PROPN
ap-926	78	56	(	(	PUNCT
ap-926	78	57	)	)	PUNCT
ap-926	78	58	(	(	PUNCT
ap-926	78	59	)	)	PUNCT
ap-926	78	60	�	�	PROPN
ap-926	78	61	�	�	PROPN
ap-926	78	62	�	�	PROPN
ap-926	78	63	�	�	PROPN
ap-926	78	64	1	1	NUM
ap-926	78	65	1	1	NUM
ap-926	78	66	3	3	NUM
ap-926	78	67	2	2	NUM
ap-926	78	68	0	0	NUM
ap-926	78	69	,	,	PUNCT
ap-926	78	70	…	…	PUNCT
ap-926	78	71	etc	etc	X
ap-926	78	72	.	.	X
ap-926	79	1	this	this	DET
ap-926	79	2	way	way	NOUN
ap-926	79	3	,	,	PUNCT
ap-926	79	4	after	after	ADP
ap-926	79	5	expanding	expand	VERB
ap-926	79	6	the	the	DET
ap-926	79	7	right	right	ADJ
ap-926	79	8	hand	hand	NOUN
ap-926	79	9	side	side	NOUN
ap-926	79	10	we	we	PRON
ap-926	79	11	get	get	VERB
ap-926	79	12	n	n	PRON
ap-926	79	13	x	x	SYM
ap-926	79	14	x	x	SYM
ap-926	79	15	n	n	CCONJ
ap-926	79	16	n	n	CCONJ
ap-926	79	17	�	�	PROPN
ap-926	79	18	�	�	PROPN
ap-926	79	19	�	�	PROPN
ap-926	79	20	�	�	PROPN
ap-926	79	21	�	�	PROPN
ap-926	79	22	�	�	PROPN
ap-926	79	23	�	�	PROPN
ap-926	79	24	�	�	PROPN
ap-926	79	25	�	�	PROPN
ap-926	79	26	�	�	PROPN
ap-926	79	27	8	8	NUM
ap-926	79	28	8	8	NUM
ap-926	79	29	1	1	NUM
ap-926	79	30	10	10	NUM
ap-926	79	31	9	9	NUM
ap-926	79	32	(	(	PUNCT
ap-926	79	33	)	)	PUNCT
ap-926	79	34	.	.	PUNCT
ap-926	80	1	28	28	NUM
ap-926	81	1	©	©	PROPN
ap-926	81	2	czech	czech	PROPN
ap-926	81	3	technical	technical	PROPN
ap-926	81	4	university	university	PROPN
ap-926	81	5	publishing	publishing	NOUN
ap-926	81	6	house	house	NOUN
ap-926	81	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-926	81	8	acta	acta	PROPN
ap-926	81	9	polytechnica	polytechnica	PROPN
ap-926	81	10	vol	vol	NOUN
ap-926	81	11	.	.	PUNCT
ap-926	82	1	47	47	NUM
ap-926	82	2	no	no	NOUN
ap-926	82	3	.	.	PUNCT
ap-926	83	1	2–3/2007	2–3/2007	NUM
ap-926	83	2	to	to	PART
ap-926	83	3	remove	remove	VERB
ap-926	83	4	the	the	DET
ap-926	83	5	unwanted	unwanted	ADJ
ap-926	83	6	condition	condition	NOUN
ap-926	83	7	n	n	NOUN
ap-926	83	8	n3	n3	NOUN
ap-926	83	9	4	4	NUM
ap-926	83	10	0	0	NUM
ap-926	83	11	�	�	NOUN
ap-926	83	12	we	we	PRON
ap-926	83	13	can	can	AUX
ap-926	83	14	rewrite	rewrite	VERB
ap-926	83	15	the	the	DET
ap-926	83	16	inner	inner	ADJ
ap-926	83	17	sum	sum	NOUN
ap-926	83	18	as	as	ADP
ap-926	83	19	~	~	PROPN
ap-926	83	20	(	(	PUNCT
ap-926	83	21	,	,	PUNCT
ap-926	83	22	,	,	PUNCT
ap-926	83	23	,	,	PUNCT
ap-926	83	24	)	)	PUNCT
ap-926	83	25	,	,	PUNCT
ap-926	83	26	,	,	PUNCT
ap-926	83	27	,	,	PUNCT
ap-926	83	28	,	,	PUNCT
ap-926	83	29	,	,	PUNCT
ap-926	83	30	,	,	PUNCT
ap-926	83	31	d	d	PROPN
ap-926	83	32	n	n	CCONJ
ap-926	83	33	n	n	CCONJ
ap-926	83	34	n	n	CCONJ
ap-926	83	35	n	n	NOUN
ap-926	83	36	k	k	PROPN
ap-926	83	37	k	k	PROPN
ap-926	83	38	k	k	PROPN
ap-926	83	39	n	n	CCONJ
ap-926	83	40	n	n	CCONJ
ap-926	83	41	n	n	CCONJ
ap-926	83	42	n	n	CCONJ
ap-926	83	43	n	n	CCONJ
ap-926	83	44	n	n	NOUN
ap-926	84	1	k	k	NOUN
ap-926	84	2	k	k	NOUN
ap-926	84	3	1	1	NUM
ap-926	84	4	2	2	NUM
ap-926	84	5	3	3	NUM
ap-926	84	6	4	4	NUM
ap-926	84	7	0	0	NUM
ap-926	84	8	0	0	NUM
ap-926	84	9	2	2	NUM
ap-926	84	10	1	1	NUM
ap-926	84	11	2	2	NUM
ap-926	84	12	3	3	NUM
ap-926	84	13	1	1	NUM
ap-926	84	14	2	2	NUM
ap-926	84	15	3	3	NUM
ap-926	84	16	4	4	NUM
ap-926	84	17	3	3	NUM
ap-926	84	18	4	4	NUM
ap-926	84	19	1	1	NUM
ap-926	84	20	2	2	NUM
ap-926	84	21	�	�	PROPN
ap-926	84	22	�	�	PROPN
ap-926	84	23	3	3	NUM
ap-926	84	24	2	2	NUM
ap-926	84	25	3	3	NUM
ap-926	84	26	3	3	NUM
ap-926	84	27	1	1	NUM
ap-926	84	28	2	2	NUM
ap-926	84	29	3	3	NUM
ap-926	84	30	3	3	NUM
ap-926	84	31	1	1	NUM
ap-926	84	32	2	2	NUM
ap-926	84	33	3	3	NUM
ap-926	84	34	4	4	NUM
ap-926	84	35	1	1	NUM
ap-926	84	36	2	2	NUM
ap-926	84	37	3	3	NUM
ap-926	84	38	1	1	NUM
ap-926	84	39	2	2	NUM
ap-926	84	40	0	0	NUM
ap-926	84	41	k	k	PROPN
ap-926	84	42	n	n	CCONJ
ap-926	84	43	n	n	CCONJ
ap-926	84	44	n	n	CCONJ
ap-926	84	45	n	n	CCONJ
ap-926	84	46	n	n	NOUN
ap-926	84	47	k	k	PROPN
ap-926	84	48	k	k	PROPN
ap-926	84	49	k	k	PROPN
ap-926	84	50	n	n	CCONJ
ap-926	84	51	n	n	PROPN
ap-926	84	52	d	d	PROPN
ap-926	84	53	n	n	CCONJ
ap-926	84	54	n	n	CCONJ
ap-926	84	55	n	n	CCONJ
ap-926	84	56	�	�	PROPN
ap-926	84	57	�	�	PROPN
ap-926	84	58	�	�	PROPN
ap-926	84	59	~	~	PUNCT
ap-926	84	60	(	(	PUNCT
ap-926	84	61	,	,	PUNCT
ap-926	84	62	,	,	PUNCT
ap-926	84	63	,	,	PUNCT
ap-926	84	64	)	)	PUNCT
ap-926	84	65	,	,	PUNCT
ap-926	84	66	,	,	PUNCT
ap-926	84	67	,	,	PUNCT
ap-926	84	68	,	,	PUNCT
ap-926	84	69	,	,	PUNCT
ap-926	84	70	,	,	PUNCT
ap-926	84	71	~	~	PUNCT
ap-926	84	72	(	(	PUNCT
ap-926	84	73	,	,	PUNCT
ap-926	84	74	,	,	PUNCT
ap-926	84	75	,	,	PUNCT
ap-926	84	76	n	n	CCONJ
ap-926	84	77	n	n	CCONJ
ap-926	84	78	k	k	NOUN
ap-926	84	79	k	k	PROPN
ap-926	84	80	k	k	PROPN
ap-926	84	81	n	n	CCONJ
ap-926	84	82	n	n	CCONJ
ap-926	84	83	n	n	CCONJ
ap-926	84	84	n	n	CCONJ
ap-926	84	85	n	n	NOUN
ap-926	84	86	d	d	PROPN
ap-926	84	87	n	n	CCONJ
ap-926	84	88	n	n	CCONJ
ap-926	84	89	n	n	ADV
ap-926	84	90	3	3	NUM
ap-926	84	91	4	4	NUM
ap-926	84	92	1	1	NUM
ap-926	84	93	2	2	NUM
ap-926	84	94	3	3	NUM
ap-926	84	95	1	1	NUM
ap-926	84	96	2	2	NUM
ap-926	84	97	3	3	NUM
ap-926	84	98	4	4	NUM
ap-926	84	99	0	0	NUM
ap-926	84	100	2	2	NUM
ap-926	84	101	3	3	NUM
ap-926	84	102	2	2	NUM
ap-926	84	103	3	3	NUM
ap-926	84	104	3	3	NUM
ap-926	84	105	1	1	NUM
ap-926	84	106	2	2	NUM
ap-926	84	107	40	40	NUM
ap-926	84	108	�	�	PROPN
ap-926	84	109	�	�	PROPN
ap-926	84	110	�	�	PROPN
ap-926	84	111	)	)	PUNCT
ap-926	84	112	,	,	PUNCT
ap-926	84	113	,	,	PUNCT
ap-926	84	114	,	,	PUNCT
ap-926	84	115	,	,	PUNCT
ap-926	84	116	,	,	PUNCT
ap-926	84	117	,	,	PUNCT
ap-926	84	118	k	k	PROPN
ap-926	84	119	k	k	PROPN
ap-926	84	120	k	k	PROPN
ap-926	84	121	n	n	CCONJ
ap-926	84	122	n	n	CCONJ
ap-926	84	123	n	n	CCONJ
ap-926	84	124	n	n	NOUN
ap-926	84	125	k	k	PROPN
ap-926	84	126	k	k	PROPN
ap-926	84	127	k	k	PROPN
ap-926	84	128	n	n	CCONJ
ap-926	84	129	n	n	CCONJ
ap-926	84	130	n	n	CCONJ
ap-926	84	131	n	n	CCONJ
ap-926	84	132	n	n	ADV
ap-926	85	1	1	1	NUM
ap-926	85	2	2	2	NUM
ap-926	85	3	3	3	NUM
ap-926	85	4	1	1	NUM
ap-926	85	5	2	2	NUM
ap-926	85	6	3	3	NUM
ap-926	85	7	4	4	NUM
ap-926	85	8	1	1	NUM
ap-926	85	9	2	2	NUM
ap-926	85	10	3	3	NUM
ap-926	85	11	1	1	NUM
ap-926	85	12	2	2	NUM
ap-926	85	13	3	3	NUM
ap-926	85	14	4	4	NUM
ap-926	85	15	0	0	NUM
ap-926	85	16	2	2	NUM
ap-926	85	17	3	3	NUM
ap-926	85	18	2	2	NUM
ap-926	85	19	3	3	NUM
ap-926	85	20	3	3	NUM
ap-926	85	21	�	�	PROPN
ap-926	85	22	�	�	PROPN
ap-926	85	23	�	�	PROPN
ap-926	85	24	�	�	PROPN
ap-926	85	25	�	�	PROPN
ap-926	85	26	~	~	PUNCT
ap-926	85	27	(	(	PUNCT
ap-926	85	28	,	,	PUNCT
ap-926	85	29	,	,	PUNCT
ap-926	85	30	,	,	PUNCT
ap-926	85	31	)	)	PUNCT
ap-926	85	32	,	,	PUNCT
ap-926	85	33	,	,	PUNCT
ap-926	85	34	,	,	PUNCT
ap-926	85	35	,	,	PUNCT
ap-926	85	36	,	,	PUNCT
ap-926	85	37	,	,	PUNCT
ap-926	85	38	d	d	PROPN
ap-926	85	39	n	n	CCONJ
ap-926	85	40	n	n	PROPN
ap-926	85	41	k	k	PROPN
ap-926	85	42	k	k	PROPN
ap-926	85	43	k	k	PROPN
ap-926	85	44	n	n	CCONJ
ap-926	85	45	n	n	CCONJ
ap-926	85	46	n	n	CCONJ
ap-926	85	47	n	n	NOUN
ap-926	86	1	k	k	PROPN
ap-926	86	2	k	k	PROPN
ap-926	86	3	k	k	PROPN
ap-926	86	4	n	n	PROPN
ap-926	86	5	1	1	NUM
ap-926	86	6	2	2	NUM
ap-926	86	7	0	0	NUM
ap-926	86	8	2	2	NUM
ap-926	86	9	3	3	NUM
ap-926	86	10	0	0	NUM
ap-926	86	11	0	0	NUM
ap-926	86	12	1	1	NUM
ap-926	86	13	2	2	NUM
ap-926	86	14	3	3	NUM
ap-926	86	15	1	1	NUM
ap-926	86	16	2	2	NUM
ap-926	86	17	3	3	NUM
ap-926	86	18	4	4	NUM
ap-926	86	19	1	1	NUM
ap-926	86	20	2	2	NUM
ap-926	86	21	3	3	NUM
ap-926	86	22	1	1	NUM
ap-926	86	23	�	�	PROPN
ap-926	86	24	�	�	PROPN
ap-926	86	25	2	2	NUM
ap-926	86	26	3	3	NUM
ap-926	86	27	32	32	NUM
ap-926	86	28	3	3	NUM
ap-926	86	29	4n	4n	X
ap-926	86	30	n	n	CCONJ
ap-926	86	31	n	n	CCONJ
ap-926	86	32	n	n	CCONJ
ap-926	86	33	©	©	PROPN
ap-926	86	34	czech	czech	PROPN
ap-926	86	35	technical	technical	PROPN
ap-926	86	36	university	university	PROPN
ap-926	86	37	publishing	publishing	NOUN
ap-926	86	38	house	house	NOUN
ap-926	86	39	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-926	86	40	29	29	NUM
ap-926	86	41	acta	acta	PROPN
ap-926	86	42	polytechnica	polytechnica	PROPN
ap-926	86	43	vol	vol	NOUN
ap-926	86	44	.	.	PUNCT
ap-926	87	1	47	47	NUM
ap-926	87	2	no	no	NOUN
ap-926	87	3	.	.	PUNCT
ap-926	88	1	2–3/2007	2–3/2007	NUM
ap-926	89	1	and	and	CCONJ
ap-926	89	2	sum	sum	VERB
ap-926	89	3	each	each	PRON
ap-926	89	4	of	of	ADP
ap-926	89	5	the	the	DET
ap-926	89	6	summands	summand	NOUN
ap-926	89	7	separately	separately	ADV
ap-926	89	8	.	.	PUNCT
ap-926	90	1	for	for	ADP
ap-926	90	2	the	the	DET
ap-926	90	3	first	first	ADJ
ap-926	90	4	one	one	NOUN
ap-926	90	5	we	we	PRON
ap-926	90	6	have	have	VERB
ap-926	90	7	~	~	PUNCT
ap-926	90	8	(	(	PUNCT
ap-926	90	9	,	,	PUNCT
ap-926	90	10	,	,	PUNCT
ap-926	90	11	,	,	PUNCT
ap-926	90	12	)	)	PUNCT
ap-926	90	13	,	,	PUNCT
ap-926	90	14	,	,	PUNCT
ap-926	90	15	,	,	PUNCT
ap-926	90	16	,	,	PUNCT
ap-926	90	17	,	,	PUNCT
ap-926	90	18	d	d	PROPN
ap-926	90	19	n	n	CCONJ
ap-926	90	20	n	n	CCONJ
ap-926	90	21	n	n	NOUN
ap-926	90	22	xn	xn	PROPN
ap-926	90	23	k	k	PROPN
ap-926	90	24	k	k	PROPN
ap-926	90	25	k	k	PROPN
ap-926	90	26	n	n	CCONJ
ap-926	90	27	n	n	CCONJ
ap-926	90	28	n	n	NOUN
ap-926	90	29	k	k	PROPN
ap-926	90	30	k	k	PROPN
ap-926	90	31	k	k	PROPN
ap-926	90	32	n	n	PROPN
ap-926	90	33	1	1	NUM
ap-926	90	34	2	2	NUM
ap-926	90	35	3	3	NUM
ap-926	90	36	0	0	NUM
ap-926	90	37	2	2	NUM
ap-926	90	38	3	3	NUM
ap-926	90	39	2	2	NUM
ap-926	90	40	0	0	NUM
ap-926	90	41	1	1	NUM
ap-926	90	42	2	2	NUM
ap-926	90	43	3	3	NUM
ap-926	90	44	1	1	NUM
ap-926	90	45	2	2	NUM
ap-926	90	46	3	3	NUM
ap-926	90	47	1	1	NUM
ap-926	90	48	2	2	NUM
ap-926	90	49	3	3	NUM
ap-926	90	50	1	1	NUM
ap-926	90	51	�	�	PROPN
ap-926	90	52	n	n	CCONJ
ap-926	90	53	n	n	CCONJ
ap-926	90	54	n	n	CCONJ
ap-926	90	55	n	n	CCONJ
ap-926	90	56	n	n	CCONJ
ap-926	90	57	n	n	CCONJ
ap-926	90	58	n	n	CCONJ
ap-926	90	59	n	n	CCONJ
ap-926	90	60	n	n	CCONJ
ap-926	90	61	n	n	CCONJ
ap-926	90	62	n	n	ADV
ap-926	90	63	2	2	NUM
ap-926	90	64	33	33	NUM
ap-926	90	65	0	0	NUM
ap-926	90	66	1	1	NUM
ap-926	90	67	2	2	NUM
ap-926	90	68	1	1	NUM
ap-926	90	69	2	2	NUM
ap-926	90	70	3	3	NUM
ap-926	90	71	1	1	NUM
ap-926	90	72	2	2	NUM
ap-926	90	73	1	1	NUM
ap-926	90	74	2	2	NUM
ap-926	90	75	1	1	NUM
ap-926	90	76	3	3	NUM
ap-926	90	77	1	1	NUM
ap-926	90	78	2	2	NUM
ap-926	90	79	2	2	NUM
ap-926	90	80	3	3	NUM
ap-926	90	81	�	�	PROPN
ap-926	90	82	�	�	PROPN
ap-926	90	83	�	�	PROPN
ap-926	90	84	�	�	PROPN
ap-926	90	85	�	�	PROPN
ap-926	90	86	(	(	PUNCT
ap-926	90	87	)	)	PUNCT
ap-926	90	88	(	(	PUNCT
ap-926	90	89	)	)	PUNCT
ap-926	90	90	(	(	PUNCT
ap-926	90	91	n	n	X
ap-926	90	92	xk	xk	PROPN
ap-926	90	93	k	k	PROPN
ap-926	90	94	k	k	PROPN
ap-926	90	95	n	n	CCONJ
ap-926	90	96	n	n	CCONJ
ap-926	90	97	n	n	NOUN
ap-926	90	98	k	k	PROPN
ap-926	90	99	k	k	PROPN
ap-926	90	100	k	k	PROPN
ap-926	90	101	n	n	CCONJ
ap-926	90	102	n	n	CCONJ
ap-926	90	103	n	n	ADV
ap-926	90	104	3	3	NUM
ap-926	90	105	2	2	NUM
ap-926	90	106	3	3	NUM
ap-926	90	107	2	2	NUM
ap-926	90	108	3	3	NUM
ap-926	90	109	0	0	NUM
ap-926	90	110	2	2	NUM
ap-926	90	111	1	1	NUM
ap-926	90	112	2	2	NUM
ap-926	90	113	3	3	NUM
ap-926	90	114	1	1	NUM
ap-926	90	115	2	2	NUM
ap-926	90	116	3	3	NUM
ap-926	90	117	1	1	NUM
ap-926	90	118	2	2	NUM
ap-926	90	119	3	3	NUM
ap-926	90	120	1	1	NUM
ap-926	90	121	2	2	NUM
ap-926	90	122	3	3	NUM
ap-926	90	123	�	�	PROPN
ap-926	90	124	�	�	PROPN
ap-926	90	125	�	�	PROPN
ap-926	90	126	)	)	PUNCT
ap-926	90	127	,	,	PUNCT
ap-926	90	128	,	,	PUNCT
ap-926	90	129	,	,	PUNCT
ap-926	90	130	,	,	PUNCT
ap-926	90	131	,	,	PUNCT
ap-926	90	132	10	10	NUM
ap-926	90	133	5	5	NUM
ap-926	90	134	1	1	NUM
ap-926	90	135	1	1	NUM
ap-926	90	136	1	1	NUM
ap-926	90	137	2	2	NUM
ap-926	90	138	9	9	NUM
ap-926	90	139	5	5	NUM
ap-926	90	140	x	x	SYM
ap-926	90	141	x	x	SYM
ap-926	90	142	x	x	SYM
ap-926	90	143	x	x	SYM
ap-926	90	144	�	�	PROPN
ap-926	90	145	(	(	PUNCT
ap-926	90	146	)	)	PUNCT
ap-926	90	147	(	(	PUNCT
ap-926	90	148	)	)	PUNCT
ap-926	90	149	the	the	DET
ap-926	90	150	second	second	ADJ
ap-926	90	151	term	term	NOUN
ap-926	90	152	is	be	AUX
ap-926	90	153	obviously	obviously	ADV
ap-926	90	154	equal	equal	ADJ
ap-926	90	155	to	to	ADP
ap-926	90	156	the	the	DET
ap-926	90	157	first	first	ADJ
ap-926	90	158	term	term	NOUN
ap-926	90	159	.	.	PUNCT
ap-926	91	1	for	for	ADP
ap-926	91	2	the	the	DET
ap-926	91	3	third	third	ADJ
ap-926	91	4	sum	sum	NOUN
ap-926	91	5	we	we	PRON
ap-926	91	6	have	have	VERB
ap-926	91	7	and	and	CCONJ
ap-926	91	8	sum	sum	VERB
ap-926	91	9	each	each	PRON
ap-926	91	10	of	of	ADP
ap-926	91	11	the	the	DET
ap-926	91	12	summands	summand	NOUN
ap-926	91	13	separately	separately	ADV
ap-926	91	14	.	.	PUNCT
ap-926	92	1	for	for	ADP
ap-926	92	2	the	the	DET
ap-926	92	3	first	first	ADJ
ap-926	92	4	one	one	NOUN
ap-926	92	5	we	we	PRON
ap-926	92	6	have	have	VERB
ap-926	92	7	~	~	PUNCT
ap-926	92	8	(	(	PUNCT
ap-926	92	9	,	,	PUNCT
ap-926	92	10	,	,	PUNCT
ap-926	92	11	,	,	PUNCT
ap-926	92	12	)	)	PUNCT
ap-926	92	13	,	,	PUNCT
ap-926	92	14	,	,	PUNCT
ap-926	92	15	,	,	PUNCT
ap-926	92	16	,	,	PUNCT
ap-926	92	17	d	d	PROPN
ap-926	92	18	n	n	CCONJ
ap-926	92	19	n	n	NOUN
ap-926	92	20	xn	xn	PROPN
ap-926	92	21	k	k	PROPN
ap-926	92	22	k	k	PROPN
ap-926	92	23	k	k	PROPN
ap-926	92	24	n	n	CCONJ
ap-926	92	25	n	n	PROPN
ap-926	92	26	k	k	PROPN
ap-926	92	27	k	k	PROPN
ap-926	92	28	k	k	PROPN
ap-926	92	29	n	n	CCONJ
ap-926	92	30	n	n	CCONJ
ap-926	92	31	n	n	ADV
ap-926	93	1	1	1	NUM
ap-926	93	2	2	2	NUM
ap-926	93	3	0	0	NUM
ap-926	93	4	2	2	NUM
ap-926	93	5	3	3	NUM
ap-926	93	6	2	2	NUM
ap-926	93	7	0	0	NUM
ap-926	93	8	0	0	NUM
ap-926	93	9	1	1	NUM
ap-926	93	10	2	2	NUM
ap-926	93	11	3	3	NUM
ap-926	93	12	1	1	NUM
ap-926	93	13	2	2	NUM
ap-926	93	14	1	1	NUM
ap-926	93	15	2	2	NUM
ap-926	93	16	3	3	NUM
ap-926	93	17	1	1	NUM
ap-926	93	18	2	2	NUM
ap-926	93	19	�	�	PROPN
ap-926	93	20	�	�	PROPN
ap-926	93	21	�	�	PROPN
ap-926	93	22	�	�	PROPN
ap-926	93	23	�	�	PROPN
ap-926	93	24	�	�	PROPN
ap-926	93	25	n	n	CCONJ
ap-926	93	26	k	k	PROPN
ap-926	93	27	k	k	PROPN
ap-926	93	28	k	k	PROPN
ap-926	94	1	n	n	CCONJ
ap-926	94	2	n	n	CCONJ
ap-926	94	3	k	k	PROPN
ap-926	94	4	n	n	CCONJ
ap-926	94	5	n	n	CCONJ
ap-926	94	6	n	n	CCONJ
ap-926	94	7	n	n	NOUN
ap-926	94	8	x	x	SYM
ap-926	94	9	0	0	NUM
ap-926	94	10	1	1	NUM
ap-926	94	11	2	2	NUM
ap-926	94	12	2	2	NUM
ap-926	94	13	1	1	NUM
ap-926	94	14	2	2	NUM
ap-926	94	15	2	2	NUM
ap-926	94	16	3	3	NUM
ap-926	94	17	21	21	NUM
ap-926	94	18	2	2	NUM
ap-926	94	19	1	1	NUM
ap-926	94	20	2	2	NUM
ap-926	94	21	2	2	NUM
ap-926	94	22	2	2	NUM
ap-926	94	23	1	1	NUM
ap-926	94	24	2	2	NUM
ap-926	94	25	3	3	NUM
ap-926	94	26	1	1	NUM
ap-926	94	27	2	2	NUM
ap-926	94	28	(	(	PUNCT
ap-926	94	29	)	)	PUNCT
ap-926	94	30	(	(	PUNCT
ap-926	94	31	)	)	PUNCT
ap-926	94	32	1	1	NUM
ap-926	94	33	2	2	NUM
ap-926	94	34	3	3	NUM
ap-926	94	35	1	1	NUM
ap-926	94	36	2	2	NUM
ap-926	94	37	3	3	NUM
ap-926	94	38	0	0	NUM
ap-926	94	39	4	4	NUM
ap-926	94	40	3	3	NUM
ap-926	94	41	2	2	NUM
ap-926	94	42	8	8	NUM
ap-926	94	43	5	5	NUM
ap-926	94	44	6	6	NUM
ap-926	94	45	16	16	NUM
ap-926	94	46	6	6	NUM
ap-926	94	47	1	1	NUM
ap-926	94	48	1	1	NUM
ap-926	94	49	1	1	NUM
ap-926	94	50	,	,	PUNCT
ap-926	94	51	,	,	PUNCT
ap-926	94	52	,	,	PUNCT
ap-926	94	53	,	,	PUNCT
ap-926	94	54	,	,	PUNCT
ap-926	94	55	(	(	PUNCT
ap-926	94	56	)	)	PUNCT
ap-926	94	57	(	(	PUNCT
ap-926	94	58	)	)	PUNCT
ap-926	95	1	k	k	PROPN
ap-926	95	2	k	k	PROPN
ap-926	95	3	n	n	CCONJ
ap-926	95	4	n	n	CCONJ
ap-926	95	5	n	n	NOUN
ap-926	95	6	x	x	NOUN
ap-926	95	7	x	x	PUNCT
ap-926	95	8	x	x	PUNCT
ap-926	95	9	x	x	SYM
ap-926	95	10	x	x	SYM
ap-926	95	11	x	x	PRON
ap-926	95	12	�	�	PROPN
ap-926	95	13	�	�	PROPN
ap-926	95	14	�	�	PROPN
ap-926	95	15	�	�	PROPN
ap-926	95	16	.	.	PUNCT
ap-926	96	1	now	now	ADV
ap-926	96	2	2	2	NUM
ap-926	96	3	10	10	NUM
ap-926	96	4	5	5	NUM
ap-926	96	5	1	1	NUM
ap-926	96	6	1	1	NUM
ap-926	96	7	1	1	NUM
ap-926	96	8	6	6	NUM
ap-926	96	9	16	16	NUM
ap-926	96	10	6	6	NUM
ap-926	96	11	1	1	NUM
ap-926	96	12	1	1	NUM
ap-926	96	13	1	1	NUM
ap-926	96	14	2	2	NUM
ap-926	96	15	9	9	NUM
ap-926	96	16	5	5	NUM
ap-926	96	17	4	4	NUM
ap-926	96	18	3	3	NUM
ap-926	96	19	2	2	NUM
ap-926	96	20	8	8	NUM
ap-926	96	21	x	x	NOUN
ap-926	96	22	x	x	PUNCT
ap-926	96	23	x	x	PUNCT
ap-926	96	24	x	x	PUNCT
ap-926	96	25	x	x	PUNCT
ap-926	96	26	x	x	PUNCT
ap-926	96	27	x	x	PUNCT
ap-926	96	28	x	x	SYM
ap-926	96	29	x	x	SYM
ap-926	96	30	x	x	SYM
ap-926	96	31	�	�	PROPN
ap-926	96	32	�	�	PROPN
ap-926	96	33	�	�	PROPN
ap-926	96	34	(	(	PUNCT
ap-926	96	35	)	)	PUNCT
ap-926	96	36	(	(	PUNCT
ap-926	96	37	)	)	PUNCT
ap-926	96	38	(	(	PUNCT
ap-926	96	39	)	)	PUNCT
ap-926	96	40	(	(	PUNCT
ap-926	96	41	)	)	PUNCT
ap-926	96	42	5	5	NUM
ap-926	96	43	9	9	NUM
ap-926	96	44	1	1	NUM
ap-926	96	45	1	1	NUM
ap-926	96	46	�	�	PROPN
ap-926	96	47	�	�	PROPN
ap-926	96	48	(	(	PUNCT
ap-926	96	49	)	)	PUNCT
ap-926	96	50	x	x	PROPN
ap-926	96	51	and	and	CCONJ
ap-926	96	52	the	the	DET
ap-926	96	53	dimension	dimension	NOUN
ap-926	96	54	check	check	NOUN
ap-926	96	55	succeeds	succeed	VERB
ap-926	96	56	.	.	PUNCT
ap-926	97	1	5	5	NUM
ap-926	97	2	lie	lie	NOUN
ap-926	97	3	algebra	algebra	NOUN
ap-926	97	4	gl(4	gl(4	VERB
ap-926	97	5	)	)	PUNCT
ap-926	97	6	finally	finally	ADV
ap-926	97	7	let	let	VERB
ap-926	97	8	us	we	PRON
ap-926	97	9	demonstrate	demonstrate	VERB
ap-926	97	10	how	how	SCONJ
ap-926	97	11	the	the	DET
ap-926	97	12	procedure	procedure	NOUN
ap-926	97	13	goes	go	VERB
ap-926	97	14	in	in	ADP
ap-926	97	15	the	the	DET
ap-926	97	16	case	case	NOUN
ap-926	97	17	of	of	ADP
ap-926	97	18	lie	lie	NOUN
ap-926	97	19	algebra	algebra	PROPN
ap-926	97	20	gl(4	gl(4	PROPN
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ap-926	97	22	.	.	PUNCT
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ap-926	98	2	the	the	DET
ap-926	98	3	vectors	vector	NOUN
ap-926	98	4	with	with	ADP
ap-926	98	5	highest	high	ADJ
ap-926	98	6	weights	weight	NOUN
ap-926	98	7	(	(	PUNCT
ap-926	98	8	n1	n1	NOUN
ap-926	98	9	,	,	PUNCT
ap-926	98	10	n2	n2	NOUN
ap-926	98	11	,	,	PUNCT
ap-926	98	12	n3	n3	PROPN
ap-926	98	13	,	,	PUNCT
ap-926	98	14	n4	n4	PROPN
ap-926	98	15	)	)	PUNCT
ap-926	98	16	we	we	PRON
ap-926	98	17	obtain	obtain	VERB
ap-926	98	18	the	the	DET
ap-926	98	19	following	follow	VERB
ap-926	98	20	equations	equation	NOUN
ap-926	98	21	e	e	NOUN
ap-926	98	22	x	x	PUNCT
ap-926	98	23	f	f	NOUN
ap-926	98	24	x	x	X
ap-926	99	1	x	x	X
ap-926	99	2	f	f	NOUN
ap-926	99	3	x	x	PUNCT
ap-926	100	1	x	x	X
ap-926	100	2	f	f	NOUN
ap-926	100	3	x	x	PUNCT
ap-926	100	4	x	x	X
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ap-926	100	7	x	x	SYM
ap-926	100	8	f	f	NOUN
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ap-926	100	10	12	12	NUM
ap-926	100	11	12	12	NUM
ap-926	100	12	13	13	NUM
ap-926	100	13	13	13	NUM
ap-926	100	14	14	14	NUM
ap-926	100	15	14	14	NUM
ap-926	100	16	21	21	NUM
ap-926	100	17	21	21	NUM
ap-926	100	18	31	31	NUM
ap-926	100	19	�	�	PROPN
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ap-926	100	32	x	x	X
ap-926	100	33	x	x	NOUN
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ap-926	100	87	x	x	PUNCT
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ap-926	101	23	,	,	PUNCT
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ap-926	114	18	(	(	PUNCT
ap-926	114	19	)	)	PUNCT
ap-926	114	20	2	2	NUM
ap-926	114	21	�	�	NOUN
ap-926	114	22	,	,	PUNCT
ap-926	114	23	e	e	NOUN
ap-926	114	24	x	x	PUNCT
ap-926	114	25	x	x	X
ap-926	114	26	xik	xik	PROPN
ap-926	114	27	in	in	ADP
ap-926	114	28	nm	nm	ADJ
ap-926	114	29	mk	mk	NOUN
ap-926	114	30	(	(	PUNCT
ap-926	114	31	)	)	PUNCT
ap-926	114	32	3	3	NUM
ap-926	114	33	�	�	PROPN
ap-926	114	34	.	.	PUNCT
ap-926	115	1	using	use	VERB
ap-926	115	2	these	these	DET
ap-926	115	3	elements	element	NOUN
ap-926	115	4	we	we	PRON
ap-926	115	5	define	define	VERB
ap-926	115	6	the	the	DET
ap-926	115	7	following	follow	VERB
ap-926	115	8	solutions	solution	NOUN
ap-926	115	9	of	of	ADP
ap-926	115	10	the	the	DET
ap-926	115	11	system	system	NOUN
ap-926	115	12	(	(	PUNCT
ap-926	115	13	summation	summation	NOUN
ap-926	115	14	of	of	ADP
ap-926	115	15	repeated	repeat	VERB
ap-926	115	16	indices	index	NOUN
ap-926	115	17	going	go	VERB
ap-926	115	18	over	over	ADP
ap-926	115	19	1	1	NUM
ap-926	115	20	…	…	SYM
ap-926	115	21	4	4	NUM
ap-926	115	22	):	):	PUNCT
ap-926	115	23	c	c	PROPN
ap-926	115	24	ekk1	ekk1	PROPN
ap-926	115	25	1	1	NUM
ap-926	115	26	�	�	PROPN
ap-926	115	27	(	(	PUNCT
ap-926	115	28	)	)	PUNCT
ap-926	115	29	,	,	PUNCT
ap-926	115	30	c	c	PROPN
ap-926	115	31	ekk2	ekk2	PROPN
ap-926	115	32	2	2	NUM
ap-926	115	33	�	�	PROPN
ap-926	115	34	(	(	PUNCT
ap-926	115	35	)	)	PUNCT
ap-926	115	36	,	,	PUNCT
ap-926	115	37	c	c	PROPN
ap-926	115	38	ekk3	ekk3	PROPN
ap-926	115	39	3	3	NUM
ap-926	115	40	�	�	PROPN
ap-926	115	41	(	(	PUNCT
ap-926	115	42	)	)	PUNCT
ap-926	115	43	,	,	PUNCT
ap-926	115	44	c	c	PROPN
ap-926	115	45	e	e	NOUN
ap-926	115	46	ekl	ekl	PROPN
ap-926	115	47	lk4	lk4	ADV
ap-926	115	48	3	3	NUM
ap-926	115	49	1	1	NUM
ap-926	115	50	�	�	PROPN
ap-926	115	51	(	(	PUNCT
ap-926	115	52	)	)	PUNCT
ap-926	115	53	(	(	PUNCT
ap-926	115	54	)	)	PUNCT
ap-926	115	55	,	,	PUNCT
ap-926	115	56	the	the	DET
ap-926	115	57	highest	high	ADJ
ap-926	115	58	weights	weight	NOUN
ap-926	115	59	of	of	ADP
ap-926	115	60	the	the	DET
ap-926	115	61	corresponding	corresponding	ADJ
ap-926	115	62	elements	element	NOUN
ap-926	115	63	of	of	ADP
ap-926	115	64	the	the	DET
ap-926	115	65	enveloping	enveloping	NOUN
ap-926	115	66	algebra	algebra	NOUN
ap-926	115	67	are	be	AUX
ap-926	115	68	element	element	NOUN
ap-926	115	69	weight	weight	NOUN
ap-926	115	70	ck	ck	PROPN
ap-926	115	71	(	(	PUNCT
ap-926	115	72	0,0,0,0	0,0,0,0	NOUN
ap-926	115	73	)	)	PUNCT
ap-926	115	74	xk	xk	PROPN
ap-926	115	75	(	(	PUNCT
ap-926	115	76	1,0,0,	1,0,0,	NUM
ap-926	115	77	�	�	NOUN
ap-926	115	78	1	1	NUM
ap-926	115	79	)	)	PUNCT
ap-926	115	80	yk	yk	NOUN
ap-926	115	81	(	(	PUNCT
ap-926	115	82	1,1,	1,1,	NUM
ap-926	115	83	�	�	PROPN
ap-926	115	84	1,	1,	NUM
ap-926	115	85	�	�	NOUN
ap-926	115	86	1	1	NUM
ap-926	115	87	)	)	PUNCT
ap-926	115	88	zk	zk	PROPN
ap-926	115	89	(	(	PUNCT
ap-926	115	90	2,0,	2,0,	NUM
ap-926	115	91	�	�	SYM
ap-926	115	92	1,	1,	NUM
ap-926	115	93	�	�	NOUN
ap-926	115	94	1	1	NUM
ap-926	115	95	)	)	PUNCT
ap-926	115	96	zk	zk	PROPN
ap-926	115	97	�	�	PROPN
ap-926	115	98	(	(	PUNCT
ap-926	115	99	1,1,0,	1,1,0,	NUM
ap-926	115	100	�	�	PROPN
ap-926	115	101	2	2	NUM
ap-926	115	102	)	)	PUNCT
ap-926	115	103	w	w	NOUN
ap-926	115	104	(	(	PUNCT
ap-926	115	105	3,	3,	NUM
ap-926	115	106	�	�	NOUN
ap-926	115	107	1,	1,	NUM
ap-926	115	108	�	�	NOUN
ap-926	115	109	1,	1,	NUM
ap-926	115	110	�	�	NOUN
ap-926	115	111	1	1	NUM
ap-926	115	112	)	)	PUNCT
ap-926	116	1	w	w	PROPN
ap-926	116	2	�	�	PROPN
ap-926	116	3	(	(	PUNCT
ap-926	116	4	1,1,1,	1,1,1,	NUM
ap-926	116	5	�	�	NOUN
ap-926	116	6	3	3	NUM
ap-926	116	7	)	)	PUNCT
ap-926	116	8	t	t	NOUN
ap-926	116	9	(	(	PUNCT
ap-926	116	10	2,1,	2,1,	NUM
ap-926	116	11	�	�	PROPN
ap-926	116	12	1,	1,	NUM
ap-926	116	13	�	�	NOUN
ap-926	116	14	2	2	NUM
ap-926	116	15	)	)	PUNCT
ap-926	116	16	the	the	DET
ap-926	116	17	dimension	dimension	NOUN
ap-926	116	18	of	of	ADP
ap-926	116	19	the	the	DET
ap-926	116	20	representation	representation	NOUN
ap-926	116	21	with	with	ADP
ap-926	116	22	highest	high	ADJ
ap-926	116	23	weight	weight	NOUN
ap-926	116	24	(	(	PUNCT
ap-926	116	25	n1	n1	NOUN
ap-926	116	26	,	,	PUNCT
ap-926	116	27	n2	n2	NOUN
ap-926	116	28	,	,	PUNCT
ap-926	116	29	n3	n3	PROPN
ap-926	116	30	,	,	PUNCT
ap-926	116	31	n4	n4	PROPN
ap-926	116	32	)	)	PUNCT
ap-926	116	33	is	be	AUX
ap-926	116	34	d	d	PROPN
ap-926	116	35	n	n	CCONJ
ap-926	116	36	n	n	CCONJ
ap-926	116	37	n	n	CCONJ
ap-926	116	38	n	n	CCONJ
ap-926	116	39	n	n	CCONJ
ap-926	116	40	n	n	CCONJ
ap-926	116	41	n	n	CCONJ
ap-926	116	42	n	n	CCONJ
ap-926	116	43	n	n	CCONJ
ap-926	116	44	n	n	CCONJ
ap-926	116	45	�	�	PROPN
ap-926	116	46	�	�	PROPN
ap-926	116	47	�	�	PROPN
ap-926	116	48	�	�	PROPN
ap-926	116	49	�	�	PROPN
ap-926	116	50	�	�	PROPN
ap-926	116	51	�	�	PROPN
ap-926	116	52	1	1	NUM
ap-926	116	53	12	12	NUM
ap-926	116	54	1	1	NUM
ap-926	116	55	2	2	NUM
ap-926	116	56	3	3	NUM
ap-926	116	57	1	1	NUM
ap-926	116	58	2	2	NUM
ap-926	116	59	1	1	NUM
ap-926	116	60	2	2	NUM
ap-926	116	61	1	1	NUM
ap-926	116	62	3	3	NUM
ap-926	116	63	1	1	NUM
ap-926	116	64	4	4	NUM
ap-926	116	65	2	2	NUM
ap-926	116	66	3	3	NUM
ap-926	116	67	2	2	NUM
ap-926	116	68	4	4	NUM
ap-926	116	69	(	(	PUNCT
ap-926	116	70	)	)	PUNCT
ap-926	116	71	(	(	PUNCT
ap-926	116	72	)	)	PUNCT
ap-926	116	73	(	(	PUNCT
ap-926	116	74	)	)	PUNCT
ap-926	116	75	(	(	PUNCT
ap-926	116	76	)	)	PUNCT
ap-926	116	77	(	(	PUNCT
ap-926	116	78	)	)	PUNCT
ap-926	116	79	(	(	PUNCT
ap-926	116	80	)	)	PUNCT
ap-926	117	1	.n	.n	PROPN
ap-926	117	2	n3	n3	ADJ
ap-926	117	3	4	4	NUM
ap-926	117	4	1	1	NUM
ap-926	117	5	�	�	PROPN
ap-926	117	6	now	now	ADV
ap-926	117	7	we	we	PRON
ap-926	117	8	start	start	VERB
ap-926	117	9	as	as	ADP
ap-926	117	10	in	in	ADP
ap-926	117	11	the	the	DET
ap-926	117	12	case	case	NOUN
ap-926	117	13	of	of	ADP
ap-926	117	14	gl(3	gl(3	PROPN
ap-926	117	15	)	)	PUNCT
ap-926	117	16	to	to	PART
ap-926	117	17	count	count	VERB
ap-926	117	18	the	the	DET
ap-926	117	19	dimensions	dimension	NOUN
ap-926	117	20	of	of	ADP
ap-926	117	21	the	the	DET
ap-926	117	22	filtration	filtration	NOUN
ap-926	117	23	subspaces	subspace	NOUN
ap-926	117	24	to	to	PART
ap-926	117	25	see	see	VERB
ap-926	117	26	the	the	DET
ap-926	117	27	conditions	condition	NOUN
ap-926	117	28	which	which	PRON
ap-926	117	29	arise	arise	VERB
ap-926	117	30	as	as	ADP
ap-926	117	31	the	the	DET
ap-926	117	32	degree	degree	NOUN
ap-926	117	33	of	of	ADP
ap-926	117	34	the	the	DET
ap-926	117	35	elements	element	NOUN
ap-926	117	36	grows	grow	VERB
ap-926	117	37	.	.	PUNCT
ap-926	118	1	elements	element	NOUN
ap-926	118	2	of	of	ADP
ap-926	118	3	degree	degree	NOUN
ap-926	118	4	1	1	NUM
ap-926	118	5	are	be	AUX
ap-926	118	6	element	element	ADJ
ap-926	118	7	dimension	dimension	NOUN
ap-926	118	8	c1	c1	PROPN
ap-926	118	9	1	1	NUM
ap-926	118	10	x1	x1	PROPN
ap-926	118	11	15	15	NUM
ap-926	118	12	total	total	ADJ
ap-926	118	13	�	�	NOUN
ap-926	118	14	16	16	NUM
ap-926	118	15	elements	element	NOUN
ap-926	118	16	of	of	ADP
ap-926	118	17	degree	degree	NOUN
ap-926	118	18	2	2	NUM
ap-926	118	19	are	be	AUX
ap-926	118	20	element	element	ADJ
ap-926	118	21	dimension	dimension	NOUN
ap-926	118	22	c1	c1	PROPN
ap-926	118	23	2	2	NUM
ap-926	118	24	1	1	NUM
ap-926	118	25	c1x1	c1x1	NUM
ap-926	118	26	15	15	NUM
ap-926	119	1	x1	x1	NOUN
ap-926	119	2	2	2	NUM
ap-926	119	3	84	84	NUM
ap-926	119	4	c2	c2	PROPN
ap-926	119	5	1	1	NUM
ap-926	119	6	x2	x2	SYM
ap-926	119	7	15	15	NUM
ap-926	119	8	y1	y1	NOUN
ap-926	119	9	20	20	NUM
ap-926	119	10	total	total	ADJ
ap-926	119	11	�	�	PROPN
ap-926	119	12	136	136	NUM
ap-926	119	13	…	…	PUNCT
ap-926	119	14	etc	etc	X
ap-926	119	15	.	.	X
ap-926	119	16	analyzing	analyze	VERB
ap-926	119	17	degree	degree	NOUN
ap-926	119	18	6	6	NUM
ap-926	119	19	,	,	PUNCT
ap-926	119	20	we	we	PRON
ap-926	119	21	encounter	encounter	VERB
ap-926	119	22	the	the	DET
ap-926	119	23	first	first	ADJ
ap-926	119	24	linear	linear	ADJ
ap-926	119	25	dependency	dependency	NOUN
ap-926	119	26	which	which	PRON
ap-926	119	27	signals	signal	VERB
ap-926	119	28	some	some	DET
ap-926	119	29	polynomial	polynomial	ADJ
ap-926	119	30	relations	relation	NOUN
ap-926	119	31	(	(	PUNCT
ap-926	119	32	syzygies	syzygy	NOUN
ap-926	119	33	)	)	PUNCT
ap-926	119	34	between	between	ADP
ap-926	119	35	the	the	DET
ap-926	119	36	generators	generator	NOUN
ap-926	119	37	.	.	PUNCT
ap-926	120	1	namely	namely	ADV
ap-926	120	2	we	we	PRON
ap-926	120	3	have	have	VERB
ap-926	120	4	z	z	NOUN
ap-926	120	5	z	z	NOUN
ap-926	120	6	x	x	PUNCT
ap-926	120	7	y	y	NOUN
ap-926	120	8	x	x	X
ap-926	120	9	y	y	NOUN
ap-926	120	10	c	c	NOUN
ap-926	120	11	x	x	SYM
ap-926	120	12	x	x	SYM
ap-926	120	13	y1	y1	NOUN
ap-926	120	14	1	1	NUM
ap-926	120	15	1	1	NUM
ap-926	120	16	2	2	NUM
ap-926	120	17	2	2	NUM
ap-926	120	18	2	2	NUM
ap-926	120	19	2	2	NUM
ap-926	120	20	1	1	NUM
ap-926	120	21	1	1	NUM
ap-926	120	22	1	1	NUM
ap-926	120	23	2	2	NUM
ap-926	120	24	1	1	NUM
ap-926	120	25	(	(	PUNCT
ap-926	120	26	)	)	PUNCT
ap-926	120	27	(	(	PUNCT
ap-926	120	28	)	)	PUNCT
ap-926	120	29	�	�	PROPN
ap-926	120	30	�	�	PROPN
ap-926	120	31	�	�	PROPN
ap-926	120	32	,	,	PUNCT
ap-926	120	33	x	x	X
ap-926	120	34	z	z	NOUN
ap-926	120	35	x	x	X
ap-926	120	36	z	z	NOUN
ap-926	120	37	x	x	SYM
ap-926	120	38	z1	z1	NOUN
ap-926	120	39	3	3	NUM
ap-926	120	40	2	2	NUM
ap-926	120	41	2	2	NUM
ap-926	120	42	3	3	NUM
ap-926	120	43	1	1	NUM
ap-926	120	44	0	0	NUM
ap-926	120	45	(	(	PUNCT
ap-926	120	46	)	)	PUNCT
ap-926	120	47	(	(	PUNCT
ap-926	120	48	)	)	PUNCT
ap-926	120	49	(	(	PUNCT
ap-926	120	50	)	)	PUNCT
ap-926	120	51	�	�	PROPN
ap-926	120	52	�	�	PROPN
ap-926	120	53	x	x	PUNCT
ap-926	120	54	z	z	NOUN
ap-926	120	55	x	x	X
ap-926	120	56	z	z	NOUN
ap-926	120	57	x	x	SYM
ap-926	120	58	z1	z1	NOUN
ap-926	120	59	3	3	NUM
ap-926	120	60	2	2	NUM
ap-926	120	61	2	2	NUM
ap-926	120	62	3	3	NUM
ap-926	120	63	1	1	NUM
ap-926	120	64	0	0	NUM
ap-926	120	65	(	(	PUNCT
ap-926	120	66	)	)	PUNCT
ap-926	120	67	(	(	PUNCT
ap-926	120	68	)	)	PUNCT
ap-926	120	69	(	(	PUNCT
ap-926	120	70	)	)	PUNCT
ap-926	120	71	�	�	PROPN
ap-926	120	72	�	�	PROPN
ap-926	120	73	�	�	PROPN
ap-926	120	74	�	�	PROPN
ap-926	120	75	�	�	PROPN
ap-926	120	76	8	8	NUM
ap-926	120	77	4	4	NUM
ap-926	120	78	2	2	NUM
ap-926	120	79	2	2	NUM
ap-926	120	80	03	03	NUM
ap-926	120	81	2	2	NUM
ap-926	120	82	1	1	NUM
ap-926	120	83	2	2	NUM
ap-926	120	84	2	2	NUM
ap-926	120	85	1	1	NUM
ap-926	120	86	4	4	NUM
ap-926	120	87	1	1	NUM
ap-926	120	88	2	2	NUM
ap-926	120	89	2	2	NUM
ap-926	120	90	4	4	NUM
ap-926	120	91	2	2	NUM
ap-926	120	92	2	2	NUM
ap-926	120	93	1y	1y	NOUN
ap-926	120	94	c	c	NOUN
ap-926	120	95	c	c	NOUN
ap-926	120	96	y	y	NOUN
ap-926	120	97	c	c	NOUN
ap-926	120	98	c	c	NOUN
ap-926	120	99	c	c	NOUN
ap-926	120	100	c	c	NOUN
ap-926	120	101	c	c	PROPN
ap-926	120	102	y	y	PROPN
ap-926	120	103	�	�	PROPN
ap-926	120	104	�	�	PROPN
ap-926	120	105	�	�	PROPN
ap-926	120	106	�	�	PROPN
ap-926	120	107	(	(	PUNCT
ap-926	120	108	)	)	PUNCT
ap-926	120	109	(	(	PUNCT
ap-926	120	110	)	)	PUNCT
ap-926	120	111	.	.	PUNCT
ap-926	121	1	higher	high	ADJ
ap-926	121	2	degrees	degree	NOUN
ap-926	121	3	give	give	VERB
ap-926	121	4	us	we	PRON
ap-926	121	5	many	many	ADJ
ap-926	121	6	other	other	ADJ
ap-926	121	7	relations	relation	NOUN
ap-926	121	8	of	of	ADP
ap-926	121	9	this	this	DET
ap-926	121	10	type	type	NOUN
ap-926	121	11	which	which	PRON
ap-926	121	12	lead	lead	VERB
ap-926	121	13	to	to	ADP
ap-926	121	14	the	the	DET
ap-926	121	15	system	system	NOUN
ap-926	121	16	of	of	ADP
ap-926	121	17	conditions	condition	NOUN
ap-926	121	18	that	that	PRON
ap-926	121	19	must	must	AUX
ap-926	121	20	be	be	AUX
ap-926	121	21	fulfilled	fulfil	VERB
ap-926	121	22	to	to	PART
ap-926	121	23	keep	keep	VERB
ap-926	121	24	the	the	DET
ap-926	121	25	set	set	NOUN
ap-926	121	26	of	of	ADP
ap-926	121	27	highest	high	ADJ
ap-926	121	28	weight	weight	NOUN
ap-926	121	29	vectors	vector	NOUN
ap-926	121	30	linear	linear	VERB
ap-926	121	31	independent	independent	ADJ
ap-926	121	32	.	.	PUNCT
ap-926	122	1	going	go	VERB
ap-926	122	2	up	up	ADP
ap-926	122	3	to	to	PART
ap-926	122	4	degree	degree	NOUN
ap-926	122	5	12	12	NUM
ap-926	122	6	finishes	finish	NOUN
ap-926	122	7	the	the	DET
ap-926	122	8	analysis	analysis	NOUN
ap-926	122	9	,	,	PUNCT
ap-926	122	10	and	and	CCONJ
ap-926	122	11	we	we	PRON
ap-926	122	12	no	no	ADV
ap-926	122	13	longer	long	ADV
ap-926	122	14	encounter	encounter	VERB
ap-926	122	15	new	new	ADJ
ap-926	122	16	relations	relation	NOUN
ap-926	122	17	.	.	PUNCT
ap-926	123	1	thus	thus	ADV
ap-926	123	2	we	we	PRON
ap-926	123	3	are	be	AUX
ap-926	123	4	ready	ready	ADJ
ap-926	123	5	to	to	PART
ap-926	123	6	formulate	formulate	VERB
ap-926	123	7	the	the	DET
ap-926	123	8	hypothesis	hypothesis	NOUN
ap-926	123	9	and	and	CCONJ
ap-926	123	10	after	after	ADP
ap-926	123	11	a	a	DET
ap-926	123	12	successful	successful	ADJ
ap-926	123	13	dimension	dimension	NOUN
ap-926	123	14	check	check	NOUN
ap-926	123	15	we	we	PRON
ap-926	123	16	can	can	AUX
ap-926	123	17	state	state	VERB
ap-926	123	18	the	the	DET
ap-926	123	19	final	final	ADJ
ap-926	123	20	result	result	NOUN
ap-926	123	21	,	,	PUNCT
ap-926	123	22	which	which	PRON
ap-926	123	23	is	be	AUX
ap-926	123	24	contained	contain	VERB
ap-926	123	25	in	in	ADP
ap-926	123	26	the	the	DET
ap-926	123	27	following	following	NOUN
ap-926	123	28	theorem	theorem	NOUN
ap-926	123	29	:	:	PUNCT
ap-926	123	30	theorem	theorem	VERB
ap-926	123	31	the	the	DET
ap-926	123	32	set	set	NOUN
ap-926	123	33	of	of	ADP
ap-926	123	34	elements	element	NOUN
ap-926	123	35	c	c	NOUN
ap-926	123	36	c	c	NOUN
ap-926	123	37	c	c	NOUN
ap-926	123	38	x	x	PUNCT
ap-926	123	39	x	x	PUNCT
ap-926	123	40	x	x	PUNCT
ap-926	123	41	y	y	NOUN
ap-926	123	42	y	y	PROPN
ap-926	123	43	t	t	PROPN
ap-926	123	44	z	z	NOUN
ap-926	123	45	z	z	PROPN
ap-926	124	1	k	k	PROPN
ap-926	124	2	k	k	PROPN
ap-926	124	3	k	k	PROPN
ap-926	124	4	n	n	CCONJ
ap-926	124	5	n	n	CCONJ
ap-926	124	6	n	n	ADV
ap-926	124	7	m	m	NOUN
ap-926	124	8	m	m	VERB
ap-926	124	9	p	p	NOUN
ap-926	124	10	r	r	NOUN
ap-926	124	11	2	2	NUM
ap-926	124	12	3	3	NUM
ap-926	124	13	4	4	NUM
ap-926	124	14	1	1	NUM
ap-926	124	15	2	2	NUM
ap-926	124	16	3	3	NUM
ap-926	124	17	1	1	NUM
ap-926	124	18	2	2	NUM
ap-926	124	19	1	1	NUM
ap-926	124	20	2	2	NUM
ap-926	124	21	2	2	NUM
ap-926	124	22	3	3	NUM
ap-926	124	23	4	4	NUM
ap-926	124	24	1	1	NUM
ap-926	124	25	2	2	NUM
ap-926	124	26	3	3	NUM
ap-926	124	27	1	1	NUM
ap-926	124	28	2	2	NUM
ap-926	124	29	1	1	NUM
ap-926	124	30	�	�	PROPN
ap-926	124	31	(	(	PUNCT
ap-926	124	32	)	)	PUNCT
ap-926	124	33	(	(	PUNCT
ap-926	124	34	(	(	PUNCT
ap-926	124	35	)	)	PUNCT
ap-926	124	36	(	(	PUNCT
ap-926	124	37	)	)	PUNCT
ap-926	124	38	)	)	PUNCT
ap-926	124	39	(	(	PUNCT
ap-926	124	40	)	)	PUNCT
ap-926	124	41	(	(	PUNCT
ap-926	124	42	)	)	PUNCT
ap-926	124	43	(	(	PUNCT
ap-926	124	44	)	)	PUNCT
ap-926	124	45	(	(	PUNCT
ap-926	124	46	)	)	PUNCT
ap-926	124	47	(	(	PUNCT
ap-926	124	48	)	)	PUNCT
ap-926	124	49	(	(	PUNCT
ap-926	124	50	)	)	PUNCT
ap-926	124	51	(	(	PUNCT
ap-926	124	52	)	)	PUNCT
ap-926	124	53	(	(	PUNCT
ap-926	124	54	)	)	PUNCT
ap-926	124	55	r	r	NOUN
ap-926	124	56	r	r	NOUN
ap-926	124	57	s	s	NOUN
ap-926	124	58	s	s	NOUN
ap-926	124	59	s	s	X
ap-926	124	60	t	t	NOUN
ap-926	124	61	tz	tz	PROPN
ap-926	124	62	z	z	PROPN
ap-926	124	63	z	z	PROPN
ap-926	124	64	z	z	PROPN
ap-926	124	65	w	w	PROPN
ap-926	124	66	w2	w2	NOUN
ap-926	124	67	3	3	NUM
ap-926	124	68	1	1	NUM
ap-926	124	69	2	2	NUM
ap-926	124	70	3	3	NUM
ap-926	124	71	1	1	NUM
ap-926	124	72	2	2	NUM
ap-926	124	73	3	3	NUM
ap-926	124	74	1	1	NUM
ap-926	124	75	2	2	NUM
ap-926	124	76	3	3	NUM
ap-926	124	77	�	�	PROPN
ap-926	124	78	�	�	PROPN
ap-926	124	79	�	�	PROPN
ap-926	124	80	�	�	PROPN
ap-926	124	81	with	with	ADP
ap-926	124	82	conditions	condition	NOUN
ap-926	124	83	r	r	NOUN
ap-926	124	84	n	n	NOUN
ap-926	124	85	r	r	NOUN
ap-926	124	86	s	s	NOUN
ap-926	124	87	r	r	NOUN
ap-926	124	88	s	s	NOUN
ap-926	124	89	r	r	NOUN
ap-926	124	90	s	s	NOUN
ap-926	124	91	r	r	NOUN
ap-926	124	92	p	p	NOUN
ap-926	124	93	r	r	NOUN
ap-926	124	94	t	t	NOUN
ap-926	124	95	s	s	PART
ap-926	124	96	n	n	PRON
ap-926	124	97	s	s	NOUN
ap-926	124	98	r	r	NOUN
ap-926	124	99	s	s	NOUN
ap-926	124	100	r	r	NOUN
ap-926	124	101	s	s	PROPN
ap-926	124	102	p1	p1	NOUN
ap-926	124	103	3	3	NUM
ap-926	124	104	1	1	NUM
ap-926	124	105	1	1	NUM
ap-926	124	106	1	1	NUM
ap-926	124	107	2	2	NUM
ap-926	124	108	1	1	NUM
ap-926	124	109	3	3	NUM
ap-926	124	110	1	1	NUM
ap-926	124	111	1	1	NUM
ap-926	124	112	2	2	NUM
ap-926	124	113	1	1	NUM
ap-926	124	114	3	3	NUM
ap-926	124	115	1	1	NUM
ap-926	124	116	2	2	NUM
ap-926	124	117	1	1	NUM
ap-926	124	118	3	3	NUM
ap-926	124	119	1	1	NUM
ap-926	124	120	0	0	NUM
ap-926	124	121	�	�	PROPN
ap-926	124	122	�	�	PROPN
ap-926	124	123	�	�	PROPN
ap-926	124	124	�	�	PROPN
ap-926	124	125	�	�	PROPN
ap-926	124	126	�	�	PROPN
ap-926	124	127	�	�	PROPN
ap-926	124	128	�	�	PROPN
ap-926	124	129	�	�	PROPN
ap-926	124	130	�	�	PROPN
ap-926	125	1	r	r	NOUN
ap-926	125	2	s	s	NOUN
ap-926	125	3	r	r	NOUN
ap-926	125	4	s	s	NOUN
ap-926	125	5	r	r	NOUN
ap-926	125	6	t	t	NOUN
ap-926	125	7	r	r	NOUN
ap-926	125	8	p	p	X
ap-926	125	9	s	s	NOUN
ap-926	125	10	r	r	NOUN
ap-926	125	11	s	s	PROPN
ap-926	125	12	t	t	NOUN
ap-926	125	13	r	r	NOUN
ap-926	125	14	s	s	NOUN
ap-926	125	15	s	s	X
ap-926	125	16	p	p	X
ap-926	125	17	s	s	NOUN
ap-926	125	18	t2	t2	NOUN
ap-926	125	19	2	2	NUM
ap-926	125	20	2	2	NUM
ap-926	125	21	3	3	NUM
ap-926	125	22	2	2	NUM
ap-926	125	23	2	2	NUM
ap-926	125	24	2	2	NUM
ap-926	125	25	2	2	NUM
ap-926	125	26	3	3	NUM
ap-926	125	27	2	2	NUM
ap-926	125	28	1	1	NUM
ap-926	125	29	3	3	NUM
ap-926	125	30	3	3	NUM
ap-926	125	31	2	2	NUM
ap-926	125	32	1	1	NUM
ap-926	125	33	1	1	NUM
ap-926	125	34	0	0	NUM
ap-926	125	35	�	�	PROPN
ap-926	125	36	�	�	PROPN
ap-926	125	37	�	�	PROPN
ap-926	125	38	�	�	PROPN
ap-926	125	39	�	�	PROPN
ap-926	125	40	�	�	PROPN
ap-926	125	41	�	�	PROPN
ap-926	125	42	�	�	PROPN
ap-926	125	43	�	�	PROPN
ap-926	125	44	,	,	PUNCT
ap-926	125	45	r	r	NOUN
ap-926	125	46	t	t	NOUN
ap-926	125	47	r	r	NOUN
ap-926	125	48	p	p	NOUN
ap-926	125	49	s	s	PROPN
ap-926	125	50	t	t	NOUN
ap-926	125	51	s	s	X
ap-926	125	52	p	p	X
ap-926	125	53	t	t	PROPN
ap-926	125	54	p	p	X
ap-926	125	55	t	t	PROPN
ap-926	125	56	p	p	PROPN
ap-926	125	57	t	t	PROPN
ap-926	125	58	t3	t3	PROPN
ap-926	125	59	2	2	NUM
ap-926	125	60	3	3	NUM
ap-926	125	61	3	3	NUM
ap-926	125	62	1	1	NUM
ap-926	125	63	3	3	NUM
ap-926	125	64	1	1	NUM
ap-926	125	65	2	2	NUM
ap-926	125	66	1	1	NUM
ap-926	125	67	2	2	NUM
ap-926	125	68	0	0	NUM
ap-926	125	69	�	�	PROPN
ap-926	125	70	�	�	PROPN
ap-926	125	71	�	�	PROPN
ap-926	125	72	�	�	PROPN
ap-926	125	73	�	�	PROPN
ap-926	125	74	�	�	PROPN
ap-926	125	75	�	�	PROPN
ap-926	125	76	,	,	PUNCT
ap-926	125	77	r2	r2	PROPN
ap-926	125	78	0	0	NUM
ap-926	125	79	1	1	NUM
ap-926	125	80	�	�	PROPN
ap-926	125	81	,	,	PUNCT
ap-926	125	82	,	,	PUNCT
ap-926	125	83	s2	s2	VERB
ap-926	125	84	0	0	NUM
ap-926	125	85	1	1	NUM
ap-926	125	86	�	�	PROPN
ap-926	125	87	,	,	PUNCT
ap-926	125	88	,	,	PUNCT
ap-926	125	89	r3	r3	PROPN
ap-926	125	90	0	0	NUM
ap-926	125	91	1	1	NUM
ap-926	125	92	�	�	PROPN
ap-926	125	93	,	,	PUNCT
ap-926	125	94	,	,	PUNCT
ap-926	125	95	s3	s3	PROPN
ap-926	125	96	0	0	NUM
ap-926	125	97	1	1	NUM
ap-926	125	98	�	�	PROPN
ap-926	125	99	,	,	PUNCT
ap-926	125	100	,	,	PUNCT
ap-926	125	101	p	p	PROPN
ap-926	125	102	�	�	PROPN
ap-926	125	103	0	0	NUM
ap-926	125	104	1	1	NUM
ap-926	125	105	,	,	PUNCT
ap-926	125	106	form	form	VERB
ap-926	125	107	a	a	DET
ap-926	125	108	desired	desire	VERB
ap-926	125	109	decomposition	decomposition	NOUN
ap-926	125	110	of	of	ADP
ap-926	125	111	the	the	DET
ap-926	125	112	enveloping	enveloping	NOUN
ap-926	125	113	algebra	algebra	NOUN
ap-926	125	114	u(gl(4	u(gl(4	ADJ
ap-926	125	115	)	)	PUNCT
ap-926	125	116	)	)	PUNCT
ap-926	125	117	.	.	PUNCT
ap-926	126	1	6	6	NUM
ap-926	126	2	conclusion	conclusion	NOUN
ap-926	126	3	we	we	PRON
ap-926	126	4	have	have	AUX
ap-926	126	5	studied	study	VERB
ap-926	126	6	the	the	DET
ap-926	126	7	structure	structure	NOUN
ap-926	126	8	of	of	ADP
ap-926	126	9	enveloping	envelop	VERB
ap-926	126	10	algebras	algebras	X
ap-926	126	11	u(g	u(g	PROPN
ap-926	126	12	)	)	PUNCT
ap-926	126	13	where	where	SCONJ
ap-926	126	14	g	g	PROPN
ap-926	126	15	sl	sl	PROPN
ap-926	126	16	gl	gl	PROPN
ap-926	126	17	gl	gl	PROPN
ap-926	126	18	�	�	PROPN
ap-926	126	19	(	(	PUNCT
ap-926	126	20	)	)	PUNCT
ap-926	126	21	,	,	PUNCT
ap-926	126	22	(	(	PUNCT
ap-926	126	23	)	)	PUNCT
ap-926	126	24	,	,	PUNCT
ap-926	126	25	(	(	PUNCT
ap-926	126	26	)	)	PUNCT
ap-926	126	27	2	2	NUM
ap-926	126	28	3	3	NUM
ap-926	126	29	4	4	NUM
ap-926	126	30	and	and	CCONJ
ap-926	126	31	we	we	PRON
ap-926	126	32	have	have	AUX
ap-926	126	33	decomposed	decompose	VERB
ap-926	126	34	the	the	DET
ap-926	126	35	adjoint	adjoint	NOUN
ap-926	126	36	representation	representation	NOUN
ap-926	126	37	into	into	ADP
ap-926	126	38	its	its	PRON
ap-926	126	39	irreducible	irreducible	ADJ
ap-926	126	40	components	component	NOUN
ap-926	126	41	.	.	PUNCT
ap-926	127	1	we	we	PRON
ap-926	127	2	have	have	AUX
ap-926	127	3	found	find	VERB
ap-926	127	4	explicitly	explicitly	ADV
ap-926	127	5	the	the	DET
ap-926	127	6	highest	high	ADJ
ap-926	127	7	weight	weight	NOUN
ap-926	127	8	vector	vector	NOUN
ap-926	127	9	in	in	ADP
ap-926	127	10	any	any	DET
ap-926	127	11	such	such	ADJ
ap-926	127	12	component	component	NOUN
ap-926	127	13	.	.	PUNCT
ap-926	128	1	our	our	PRON
ap-926	128	2	result	result	NOUN
ap-926	128	3	can	can	AUX
ap-926	128	4	be	be	AUX
ap-926	128	5	useful	useful	ADJ
ap-926	128	6	for	for	ADP
ap-926	128	7	a	a	DET
ap-926	128	8	further	further	ADJ
ap-926	128	9	study	study	NOUN
ap-926	128	10	of	of	ADP
ap-926	128	11	the	the	DET
ap-926	128	12	tensor	tensor	NOUN
ap-926	128	13	products	product	NOUN
ap-926	128	14	of	of	ADP
ap-926	128	15	representations	representation	NOUN
ap-926	128	16	and	and	CCONJ
ap-926	128	17	ideals	ideal	NOUN
ap-926	128	18	of	of	ADP
ap-926	128	19	enveloping	envelop	VERB
ap-926	128	20	30	30	NUM
ap-926	128	21	©	©	PROPN
ap-926	128	22	czech	czech	PROPN
ap-926	128	23	technical	technical	PROPN
ap-926	128	24	university	university	PROPN
ap-926	128	25	publishing	publishing	NOUN
ap-926	128	26	house	house	NOUN
ap-926	128	27	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-926	128	28	acta	acta	PROPN
ap-926	128	29	polytechnica	polytechnica	PROPN
ap-926	128	30	vol	vol	NOUN
ap-926	128	31	.	.	PUNCT
ap-926	129	1	47	47	NUM
ap-926	129	2	no	no	INTJ
ap-926	129	3	.	.	PUNCT
ap-926	130	1	2–3/2007	2–3/2007	NUM
ap-926	130	2	y	y	NOUN
ap-926	130	3	e	e	X
ap-926	130	4	e	e	X
ap-926	130	5	e	e	X
ap-926	130	6	e1	e1	VERB
ap-926	130	7	13	13	NUM
ap-926	130	8	1	1	NUM
ap-926	130	9	14	14	NUM
ap-926	130	10	1	1	NUM
ap-926	130	11	23	23	NUM
ap-926	130	12	1	1	NUM
ap-926	130	13	24	24	NUM
ap-926	130	14	1	1	NUM
ap-926	130	15	�	�	PROPN
ap-926	130	16	�	�	PROPN
ap-926	130	17	�	�	PROPN
ap-926	130	18	�	�	PROPN
ap-926	130	19	�	�	PROPN
ap-926	130	20	�	�	PROPN
ap-926	130	21	�	�	PROPN
ap-926	130	22	�	�	PROPN
ap-926	130	23	�	�	PROPN
ap-926	130	24	det	det	PROPN
ap-926	130	25	(	(	PUNCT
ap-926	130	26	)	)	PUNCT
ap-926	130	27	(	(	PUNCT
ap-926	130	28	)	)	PUNCT
ap-926	130	29	(	(	PUNCT
ap-926	130	30	)	)	PUNCT
ap-926	130	31	(	(	PUNCT
ap-926	130	32	)	)	PUNCT
ap-926	130	33	,	,	PUNCT
ap-926	130	34	y	y	PROPN
ap-926	130	35	e	e	X
ap-926	130	36	e	e	X
ap-926	130	37	e	e	PROPN
ap-926	130	38	e2	e2	PROPN
ap-926	130	39	13	13	NUM
ap-926	130	40	2	2	NUM
ap-926	130	41	14	14	NUM
ap-926	130	42	2	2	NUM
ap-926	130	43	23	23	NUM
ap-926	130	44	2	2	NUM
ap-926	130	45	24	24	NUM
ap-926	130	46	2	2	NUM
ap-926	130	47	�	�	PROPN
ap-926	130	48	�	�	PROPN
ap-926	130	49	�	�	PROPN
ap-926	130	50	�	�	PROPN
ap-926	130	51	�	�	PROPN
ap-926	130	52	�	�	PROPN
ap-926	130	53	�	�	PROPN
ap-926	130	54	�	�	PROPN
ap-926	130	55	�	�	PROPN
ap-926	130	56	det	det	PROPN
ap-926	130	57	(	(	PUNCT
ap-926	130	58	)	)	PUNCT
ap-926	130	59	(	(	PUNCT
ap-926	130	60	)	)	PUNCT
ap-926	130	61	(	(	PUNCT
ap-926	130	62	)	)	PUNCT
ap-926	130	63	(	(	PUNCT
ap-926	130	64	)	)	PUNCT
ap-926	130	65	,	,	PUNCT
ap-926	131	1	y	y	PROPN
ap-926	131	2	e	e	X
ap-926	131	3	e	e	X
ap-926	131	4	e	e	AUX
ap-926	131	5	e3	e3	VERB
ap-926	131	6	13	13	NUM
ap-926	131	7	3	3	NUM
ap-926	131	8	14	14	NUM
ap-926	131	9	3	3	NUM
ap-926	131	10	23	23	NUM
ap-926	131	11	3	3	NUM
ap-926	131	12	24	24	NUM
ap-926	131	13	3	3	NUM
ap-926	131	14	�	�	PROPN
ap-926	131	15	�	�	PROPN
ap-926	131	16	�	�	PROPN
ap-926	131	17	�	�	PROPN
ap-926	131	18	�	�	PROPN
ap-926	131	19	�	�	PROPN
ap-926	131	20	�	�	PROPN
ap-926	131	21	�	�	PROPN
ap-926	131	22	�	�	PROPN
ap-926	131	23	det	det	PROPN
ap-926	131	24	(	(	PUNCT
ap-926	131	25	)	)	PUNCT
ap-926	131	26	(	(	PUNCT
ap-926	131	27	)	)	PUNCT
ap-926	131	28	(	(	PUNCT
ap-926	131	29	)	)	PUNCT
ap-926	131	30	(	(	PUNCT
ap-926	131	31	)	)	PUNCT
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ap-926	140	9	of	of	ADP
ap-926	140	10	the	the	DET
ap-926	140	11	enveloping	enveloping	NOUN
ap-926	140	12	algebra	algebra	NOUN
ap-926	140	13	of	of	ADP
ap-926	140	14	sl3	sl3	PROPN
ap-926	140	15	.	.	PUNCT
ap-926	141	1	j.	j.	PROPN
ap-926	141	2	math	math	PROPN
ap-926	141	3	.	.	PUNCT
ap-926	142	1	phys	phy	NOUN
ap-926	142	2	.	.	PUNCT
ap-926	143	1	vol	vol	NOUN
ap-926	143	2	.	.	PROPN
ap-926	143	3	31	31	NUM
ap-926	143	4	(	(	PUNCT
ap-926	143	5	1990	1990	NUM
ap-926	143	6	)	)	PUNCT
ap-926	143	7	,	,	PUNCT
ap-926	143	8	no	no	INTJ
ap-926	143	9	.	.	NOUN
ap-926	143	10	5	5	NUM
ap-926	143	11	,	,	PUNCT
ap-926	143	12	p.	p.	NOUN
ap-926	143	13	1076–1077	1076–1077	NUM
ap-926	143	14	.	.	PUNCT
ap-926	144	1	[	[	X
ap-926	144	2	4	4	NUM
ap-926	144	3	]	]	X
ap-926	144	4	burdík	burdík	PROPN
ap-926	144	5	,	,	PUNCT
ap-926	144	6	č	č	PROPN
ap-926	144	7	.	.	PROPN
ap-926	144	8	,	,	PUNCT
ap-926	144	9	navrátil	navrátil	PROPN
ap-926	144	10	,	,	PUNCT
ap-926	144	11	o.	o.	NOUN
ap-926	144	12	:	:	PUNCT
ap-926	144	13	decomposition	decomposition	NOUN
ap-926	144	14	of	of	ADP
ap-926	144	15	the	the	DET
ap-926	144	16	enveloping	enveloping	NOUN
ap-926	144	17	algebra	algebra	NOUN
ap-926	144	18	so(5	so(5	PROPN
ap-926	144	19	)	)	PUNCT
ap-926	144	20	,	,	PUNCT
ap-926	144	21	submitted	submit	VERB
ap-926	144	22	to	to	ADP
ap-926	144	23	j.	j.	PROPN
ap-926	144	24	gener	gener	PROPN
ap-926	144	25	.	.	PUNCT
ap-926	145	1	lie	lie	PROPN
ap-926	145	2	theory	theory	NOUN
ap-926	145	3	and	and	CCONJ
ap-926	145	4	app	app	PROPN
ap-926	145	5	.	.	PROPN
ap-926	145	6	prof	prof	PROPN
ap-926	145	7	.	.	PUNCT
ap-926	146	1	rndr	rndr	PROPN
ap-926	146	2	.	.	PUNCT
ap-926	147	1	čestmír	čestmír	PROPN
ap-926	147	2	burdík	burdík	PROPN
ap-926	147	3	,	,	PUNCT
ap-926	147	4	drsc	drsc	PROPN
ap-926	147	5	.	.	PUNCT
ap-926	148	1	phone:+420	phone:+420	PRON
ap-926	148	2	224	224	NUM
ap-926	148	3	358	358	NUM
ap-926	149	1	549	549	NUM
ap-926	149	2	e	e	NOUN
ap-926	149	3	-	-	NOUN
ap-926	149	4	mail	mail	NOUN
ap-926	149	5	:	:	PUNCT
ap-926	149	6	burdik@kmlinux.fjfi.cvut.cz	burdik@kmlinux.fjfi.cvut.cz	PROPN
ap-926	149	7	ing	ing	ADJ
ap-926	149	8	.	.	PUNCT
ap-926	150	1	severin	severin	PROPN
ap-926	150	2	pošta	pošta	PROPN
ap-926	150	3	,	,	PUNCT
ap-926	150	4	ph.d	ph.d	PROPN
ap-926	150	5	.	.	PUNCT
ap-926	150	6	phone	phone	NOUN
ap-926	150	7	:	:	PUNCT
ap-926	150	8	+420	+420	PROPN
ap-926	150	9	224	224	NUM
ap-926	150	10	358	358	NUM
ap-926	150	11	562	562	NUM
ap-926	150	12	e	e	NOUN
ap-926	150	13	-	-	NOUN
ap-926	150	14	mail	mail	NOUN
ap-926	150	15	:	:	PUNCT
ap-926	150	16	severin@km1.fjfi.cvut.cz	severin@km1.fjfi.cvut.cz	PROPN
ap-926	150	17	department	department	PROPN
ap-926	150	18	of	of	ADP
ap-926	150	19	mathematics	mathematics	PROPN
ap-926	150	20	czech	czech	PROPN
ap-926	150	21	technical	technical	PROPN
ap-926	150	22	university	university	PROPN
ap-926	150	23	in	in	ADP
ap-926	150	24	prague	prague	PROPN
ap-926	150	25	faculty	faculty	NOUN
ap-926	150	26	of	of	ADP
ap-926	150	27	nuclear	nuclear	ADJ
ap-926	150	28	sciences	science	NOUN
ap-926	150	29	and	and	CCONJ
ap-926	150	30	physical	physical	ADJ
ap-926	150	31	engineering	engineering	NOUN
ap-926	150	32	trojanova	trojanova	ADP
ap-926	150	33	13	13	NUM
ap-926	150	34	120	120	NUM
ap-926	150	35	00	00	NUM
ap-926	150	36	prague	prague	NOUN
ap-926	150	37	2	2	NUM
ap-926	150	38	,	,	PUNCT
ap-926	150	39	czech	czech	PROPN
ap-926	150	40	republic	republic	PROPN
ap-926	150	41	doc	doc	PROPN
ap-926	150	42	.	.	PROPN
ap-926	151	1	rndr	rndr	PROPN
ap-926	151	2	.	.	PUNCT
ap-926	152	1	ondřej	ondřej	PROPN
ap-926	152	2	navrátil	navrátil	PROPN
ap-926	152	3	,	,	PUNCT
ap-926	152	4	ph.d	ph.d	PROPN
ap-926	152	5	.	.	PUNCT
ap-926	152	6	phone	phone	NOUN
ap-926	152	7	:	:	PUNCT
ap-926	152	8	+420	+420	PROPN
ap-926	152	9	224	224	NUM
ap-926	152	10	890	890	NUM
ap-926	152	11	714	714	NUM
ap-926	152	12	e	e	NOUN
ap-926	152	13	-	-	NOUN
ap-926	152	14	mail	mail	NOUN
ap-926	152	15	:	:	PUNCT
ap-926	152	16	navratil@fd.cvut.cz	navratil@fd.cvut.cz	NOUN
ap-926	152	17	department	department	NOUN
ap-926	152	18	of	of	ADP
ap-926	152	19	mathematics	mathematics	PROPN
ap-926	152	20	czech	czech	PROPN
ap-926	152	21	technical	technical	PROPN
ap-926	152	22	university	university	PROPN
ap-926	152	23	in	in	ADP
ap-926	152	24	prague	prague	PROPN
ap-926	152	25	faculty	faculty	NOUN
ap-926	152	26	of	of	ADP
ap-926	152	27	transportation	transportation	NOUN
ap-926	152	28	sciences	science	NOUN
ap-926	152	29	na	na	PART
ap-926	152	30	florenci	florenci	VERB
ap-926	152	31	25	25	NUM
ap-926	152	32	110	110	NUM
ap-926	152	33	00	00	NUM
ap-926	153	1	prague	prague	PROPN
ap-926	153	2	1	1	NUM
ap-926	153	3	,	,	PUNCT
ap-926	153	4	czech	czech	PROPN
ap-926	153	5	republic	republic	NOUN
ap-926	153	6	©	©	PROPN
ap-926	153	7	czech	czech	PROPN
ap-926	153	8	technical	technical	PROPN
ap-926	153	9	university	university	PROPN
ap-926	153	10	publishing	publishing	NOUN
ap-926	153	11	house	house	NOUN
ap-926	153	12	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-926	153	13	31	31	NUM
ap-926	153	14	acta	acta	PROPN
ap-926	153	15	polytechnica	polytechnica	PROPN
ap-926	153	16	vol	vol	NOUN
ap-926	153	17	.	.	PUNCT
ap-926	154	1	47	47	NUM
ap-926	154	2	no	no	INTJ
ap-926	154	3	.	.	PUNCT
ap-926	155	1	2–3/2007	2–3/2007	NUM