id	sid	tid	token	lemma	pos
ap-768	1	1	ap05_5.vp	ap05_5.vp	NOUN
ap-768	1	2	1	1	NUM
ap-768	1	3	introduction	introduction	NOUN
ap-768	1	4	the	the	DET
ap-768	1	5	important	important	ADJ
ap-768	1	6	role	role	NOUN
ap-768	1	7	of	of	ADP
ap-768	1	8	symmetries	symmetry	NOUN
ap-768	1	9	in	in	ADP
ap-768	1	10	classical	classical	ADJ
ap-768	1	11	and	and	CCONJ
ap-768	1	12	quantum	quantum	NOUN
ap-768	1	13	physics	physics	NOUN
ap-768	1	14	is	be	AUX
ap-768	1	15	well	well	ADV
ap-768	1	16	known	known	ADJ
ap-768	1	17	.	.	PUNCT
ap-768	2	1	we	we	PRON
ap-768	2	2	focus	focus	VERB
ap-768	2	3	on	on	ADP
ap-768	2	4	so	so	ADV
ap-768	2	5	called	call	VERB
ap-768	2	6	discrete	discrete	ADJ
ap-768	2	7	quantum	quantum	NOUN
ap-768	2	8	physics	physic	NOUN
ap-768	2	9	;	;	PUNCT
ap-768	2	10	this	this	PRON
ap-768	2	11	means	mean	VERB
ap-768	2	12	that	that	SCONJ
ap-768	2	13	the	the	DET
ap-768	2	14	corresponding	correspond	VERB
ap-768	2	15	hilbert	hilbert	NOUN
ap-768	2	16	space	space	NOUN
ap-768	2	17	is	be	AUX
ap-768	2	18	finite	finite	ADJ
ap-768	2	19	dimensional	dimensional	ADJ
ap-768	2	20	[	[	X
ap-768	2	21	1	1	NUM
ap-768	2	22	,	,	PUNCT
ap-768	2	23	2	2	NUM
ap-768	2	24	]	]	PUNCT
ap-768	2	25	.	.	PUNCT
ap-768	3	1	well	well	INTJ
ap-768	3	2	known	know	VERB
ap-768	3	3	are	be	AUX
ap-768	3	4	also	also	ADV
ap-768	3	5	2×2	2×2	NUM
ap-768	3	6	pauli	pauli	PROPN
ap-768	3	7	matrices	matrix	NOUN
ap-768	3	8	.	.	PUNCT
ap-768	4	1	besides	besides	SCONJ
ap-768	4	2	spanning	span	VERB
ap-768	4	3	real	real	ADJ
ap-768	4	4	lie	lie	NOUN
ap-768	4	5	algebra	algebra	PROPN
ap-768	4	6	su(2	su(2	NOUN
ap-768	4	7	)	)	PUNCT
ap-768	4	8	,	,	PUNCT
ap-768	4	9	they	they	PRON
ap-768	4	10	form	form	VERB
ap-768	4	11	a	a	DET
ap-768	4	12	fine	fine	ADJ
ap-768	4	13	grading	grading	NOUN
ap-768	4	14	of	of	ADP
ap-768	4	15	sl(2	sl(2	PROPN
ap-768	4	16	,	,	PUNCT
ap-768	4	17	c	c	NOUN
ap-768	4	18	)	)	PUNCT
ap-768	4	19	.	.	PUNCT
ap-768	5	1	the	the	DET
ap-768	5	2	fine	fine	ADJ
ap-768	5	3	gradings	grading	NOUN
ap-768	5	4	of	of	ADP
ap-768	5	5	a	a	DET
ap-768	5	6	given	give	VERB
ap-768	5	7	lie	lie	NOUN
ap-768	5	8	algebra	algebra	NOUN
ap-768	5	9	are	be	AUX
ap-768	5	10	preferred	prefer	VERB
ap-768	5	11	bases	basis	NOUN
ap-768	5	12	which	which	PRON
ap-768	5	13	yield	yield	VERB
ap-768	5	14	quantum	quantum	ADJ
ap-768	5	15	observables	observable	NOUN
ap-768	5	16	with	with	ADP
ap-768	5	17	additive	additive	ADJ
ap-768	5	18	quantum	quantum	NOUN
ap-768	5	19	numbers	number	NOUN
ap-768	5	20	.	.	PUNCT
ap-768	6	1	the	the	DET
ap-768	6	2	generalized	generalize	VERB
ap-768	6	3	n×n	n×n	PROPN
ap-768	6	4	pauli	pauli	NOUN
ap-768	6	5	matrices	matrix	NOUN
ap-768	6	6	were	be	AUX
ap-768	6	7	described	describe	VERB
ap-768	6	8	in	in	ADP
ap-768	6	9	[	[	X
ap-768	6	10	3	3	NUM
ap-768	6	11	]	]	PUNCT
ap-768	6	12	.	.	PUNCT
ap-768	7	1	for	for	ADP
ap-768	7	2	n	n	PRON
ap-768	7	3	�	�	PROPN
ap-768	7	4	3	3	NUM
ap-768	7	5	these	these	DET
ap-768	7	6	3×3	3×3	NUM
ap-768	7	7	pauli	pauli	PROPN
ap-768	7	8	matrices	matrix	NOUN
ap-768	7	9	form	form	VERB
ap-768	7	10	one	one	NUM
ap-768	7	11	of	of	ADP
ap-768	7	12	four	four	NUM
ap-768	7	13	non	non	ADJ
ap-768	7	14	-	-	ADJ
ap-768	7	15	equivalent	equivalent	ADJ
ap-768	7	16	gradings	grading	NOUN
ap-768	7	17	of	of	ADP
ap-768	7	18	sl(3,c	sl(3,c	ADJ
ap-768	7	19	)	)	PUNCT
ap-768	7	20	.	.	PUNCT
ap-768	8	1	other	other	ADJ
ap-768	8	2	fine	fine	ADJ
ap-768	8	3	gradings	grading	NOUN
ap-768	8	4	are	be	AUX
ap-768	8	5	cartan	cartan	ADJ
ap-768	8	6	decomposition	decomposition	NOUN
ap-768	8	7	and	and	CCONJ
ap-768	8	8	the	the	DET
ap-768	8	9	grading	grading	NOUN
ap-768	8	10	which	which	PRON
ap-768	8	11	corresponds	correspond	VERB
ap-768	8	12	to	to	ADP
ap-768	8	13	gell	gell	NOUN
ap-768	8	14	-	-	PUNCT
ap-768	8	15	mann	mann	NOUN
ap-768	8	16	matrices	matrix	NOUN
ap-768	8	17	[	[	X
ap-768	8	18	4	4	NUM
ap-768	8	19	,	,	PUNCT
ap-768	8	20	5	5	NUM
ap-768	8	21	]	]	PUNCT
ap-768	8	22	.	.	PUNCT
ap-768	9	1	the	the	DET
ap-768	9	2	symmetries	symmetry	NOUN
ap-768	9	3	of	of	ADP
ap-768	9	4	the	the	DET
ap-768	9	5	fine	fine	ADJ
ap-768	9	6	grading	grading	NOUN
ap-768	9	7	of	of	ADP
ap-768	9	8	sl(n	sl(n	ADJ
ap-768	9	9	,	,	PUNCT
ap-768	9	10	c	c	X
ap-768	9	11	)	)	PUNCT
ap-768	9	12	associated	associate	VERB
ap-768	9	13	with	with	ADP
ap-768	9	14	these	these	DET
ap-768	9	15	generalized	generalize	VERB
ap-768	9	16	pauli	pauli	PROPN
ap-768	9	17	matrices	matrix	NOUN
ap-768	9	18	were	be	AUX
ap-768	9	19	studied	study	VERB
ap-768	9	20	only	only	ADV
ap-768	9	21	recently	recently	ADV
ap-768	9	22	in	in	ADP
ap-768	9	23	[	[	X
ap-768	9	24	6	6	NUM
ap-768	9	25	]	]	PUNCT
ap-768	9	26	.	.	PUNCT
ap-768	10	1	this	this	DET
ap-768	10	2	work	work	NOUN
ap-768	10	3	pointed	point	VERB
ap-768	10	4	out	out	ADP
ap-768	10	5	the	the	DET
ap-768	10	6	importance	importance	NOUN
ap-768	10	7	of	of	ADP
ap-768	10	8	the	the	DET
ap-768	10	9	finite	finite	PROPN
ap-768	10	10	group	group	NOUN
ap-768	10	11	sl(2	sl(2	PROPN
ap-768	10	12	,	,	PUNCT
ap-768	10	13	zn	zn	PROPN
ap-768	10	14	)	)	PUNCT
ap-768	10	15	as	as	ADP
ap-768	10	16	the	the	DET
ap-768	10	17	group	group	NOUN
ap-768	10	18	of	of	ADP
ap-768	10	19	symmetry	symmetry	NOUN
ap-768	10	20	of	of	ADP
ap-768	10	21	the	the	DET
ap-768	10	22	pauli	pauli	PROPN
ap-768	10	23	gradings	grading	NOUN
ap-768	10	24	.	.	PUNCT
ap-768	11	1	the	the	DET
ap-768	11	2	additive	additive	ADJ
ap-768	11	3	quantum	quantum	NOUN
ap-768	11	4	numbers	number	NOUN
ap-768	11	5	,	,	PUNCT
ap-768	11	6	mentioned	mention	VERB
ap-768	11	7	above	above	ADV
ap-768	11	8	,	,	PUNCT
ap-768	11	9	form	form	NOUN
ap-768	11	10	in	in	ADP
ap-768	11	11	this	this	DET
ap-768	11	12	case	case	NOUN
ap-768	11	13	the	the	DET
ap-768	11	14	finite	finite	ADJ
ap-768	11	15	associative	associative	ADJ
ap-768	11	16	additive	additive	ADJ
ap-768	11	17	ring	ring	NOUN
ap-768	11	18	zn×zn	zn×zn	PROPN
ap-768	11	19	.	.	PUNCT
ap-768	12	1	the	the	DET
ap-768	12	2	action	action	NOUN
ap-768	12	3	of	of	ADP
ap-768	12	4	sl(2	sl(2	PROPN
ap-768	12	5	,	,	PUNCT
ap-768	12	6	zn	zn	PROPN
ap-768	12	7	)	)	PUNCT
ap-768	12	8	on	on	ADP
ap-768	12	9	zn×zn	zn×zn	PROPN
ap-768	12	10	then	then	ADV
ap-768	12	11	represents	represent	VERB
ap-768	12	12	the	the	DET
ap-768	12	13	symmetry	symmetry	NOUN
ap-768	12	14	transformations	transformation	NOUN
ap-768	12	15	of	of	ADP
ap-768	12	16	pauli	pauli	PROPN
ap-768	12	17	gradings	grading	NOUN
ap-768	12	18	of	of	ADP
ap-768	12	19	sl(n	sl(n	ADJ
ap-768	12	20	,	,	PUNCT
ap-768	12	21	c	c	NOUN
ap-768	12	22	)	)	PUNCT
ap-768	12	23	.	.	PUNCT
ap-768	13	1	the	the	DET
ap-768	13	2	orbits	orbit	NOUN
ap-768	13	3	of	of	ADP
ap-768	13	4	this	this	DET
ap-768	13	5	action	action	NOUN
ap-768	13	6	form	form	NOUN
ap-768	13	7	such	such	ADJ
ap-768	13	8	points	point	NOUN
ap-768	13	9	in	in	ADP
ap-768	13	10	zn×zn	zn×zn	PROPN
ap-768	13	11	which	which	PRON
ap-768	13	12	can	can	AUX
ap-768	13	13	be	be	AUX
ap-768	13	14	reached	reach	VERB
ap-768	13	15	by	by	ADP
ap-768	13	16	symmetries	symmetry	NOUN
ap-768	13	17	.	.	PUNCT
ap-768	14	1	for	for	ADP
ap-768	14	2	the	the	DET
ap-768	14	3	purpose	purpose	NOUN
ap-768	14	4	of	of	ADP
ap-768	14	5	so	so	ADV
ap-768	14	6	called	call	VERB
ap-768	14	7	graded	grade	VERB
ap-768	14	8	contractions	contraction	NOUN
ap-768	14	9	[	[	X
ap-768	14	10	7	7	NUM
ap-768	14	11	]	]	PUNCT
ap-768	14	12	,	,	PUNCT
ap-768	14	13	it	it	PRON
ap-768	14	14	became	become	VERB
ap-768	14	15	convenient	convenient	ADJ
ap-768	14	16	to	to	PART
ap-768	14	17	study	study	VERB
ap-768	14	18	the	the	DET
ap-768	14	19	action	action	NOUN
ap-768	14	20	of	of	ADP
ap-768	14	21	sl(2	sl(2	PROPN
ap-768	14	22	,	,	PUNCT
ap-768	14	23	zn	zn	PROPN
ap-768	14	24	)	)	PUNCT
ap-768	14	25	on	on	ADP
ap-768	14	26	various	various	ADJ
ap-768	14	27	types	type	NOUN
ap-768	14	28	of	of	ADP
ap-768	14	29	cartesian	cartesian	ADJ
ap-768	14	30	products	product	NOUN
ap-768	14	31	of	of	ADP
ap-768	14	32	zn	zn	PROPN
ap-768	15	1	[	[	X
ap-768	15	2	8	8	NUM
ap-768	15	3	]	]	PUNCT
ap-768	15	4	.	.	PUNCT
ap-768	16	1	note	note	VERB
ap-768	16	2	that	that	SCONJ
ap-768	16	3	the	the	DET
ap-768	16	4	orbits	orbit	NOUN
ap-768	16	5	of	of	ADP
ap-768	16	6	sl(2	sl(2	PROPN
ap-768	16	7	,	,	PUNCT
ap-768	16	8	zp	zp	PROPN
ap-768	16	9	)	)	PUNCT
ap-768	16	10	on	on	ADP
ap-768	16	11	z	z	PROPN
ap-768	16	12	p	p	NOUN
ap-768	16	13	2	2	NUM
ap-768	16	14	,	,	PUNCT
ap-768	16	15	where	where	SCONJ
ap-768	16	16	p	p	NOUN
ap-768	16	17	is	be	AUX
ap-768	16	18	a	a	DET
ap-768	16	19	prime	prime	ADJ
ap-768	16	20	number	number	NOUN
ap-768	16	21	were	be	AUX
ap-768	16	22	,	,	PUNCT
ap-768	16	23	considered	consider	VERB
ap-768	16	24	in	in	ADP
ap-768	16	25	[	[	X
ap-768	16	26	9	9	NUM
ap-768	16	27	]	]	PUNCT
ap-768	16	28	§	§	NOUN
ap-768	16	29	16.3	16.3	NUM
ap-768	16	30	.	.	PUNCT
ap-768	17	1	the	the	DET
ap-768	17	2	purpose	purpose	NOUN
ap-768	17	3	of	of	ADP
ap-768	17	4	this	this	DET
ap-768	17	5	paper	paper	NOUN
ap-768	17	6	is	be	AUX
ap-768	17	7	to	to	PART
ap-768	17	8	generalize	generalize	VERB
ap-768	17	9	this	this	DET
ap-768	17	10	result	result	NOUN
ap-768	17	11	to	to	ADP
ap-768	17	12	orbits	orbit	NOUN
ap-768	17	13	of	of	ADP
ap-768	17	14	sl(m	sl(m	PROPN
ap-768	17	15	,	,	PUNCT
ap-768	17	16	zn	zn	PROPN
ap-768	17	17	)	)	PUNCT
ap-768	17	18	on	on	ADP
ap-768	17	19	zn	zn	X
ap-768	17	20	m	m	VERB
ap-768	17	21	where	where	SCONJ
ap-768	17	22	m	m	VERB
ap-768	17	23	,	,	PUNCT
ap-768	17	24	n	n	PRON
ap-768	17	25	are	be	AUX
ap-768	17	26	arbitrary	arbitrary	ADJ
ap-768	17	27	natural	natural	ADJ
ap-768	17	28	numbers	number	NOUN
ap-768	17	29	.	.	PUNCT
ap-768	18	1	2	2	NUM
ap-768	18	2	action	action	NOUN
ap-768	18	3	of	of	ADP
ap-768	18	4	the	the	DET
ap-768	18	5	group	group	NOUN
ap-768	18	6	sl(m	sl(m	PROPN
ap-768	18	7	,	,	PUNCT
ap-768	18	8	zn	zn	NOUN
ap-768	18	9	)	)	PUNCT
ap-768	18	10	throughout	throughout	ADP
ap-768	18	11	the	the	DET
ap-768	18	12	paper	paper	NOUN
ap-768	18	13	we	we	PRON
ap-768	18	14	shall	shall	AUX
ap-768	18	15	use	use	VERB
ap-768	18	16	the	the	DET
ap-768	18	17	following	following	ADJ
ap-768	18	18	notation	notation	NOUN
ap-768	18	19	:	:	PUNCT
ap-768	18	20	n:	n:	PROPN
ap-768	18	21	�	�	PROPN
ap-768	18	22	{1	{1	NOUN
ap-768	18	23	,	,	PUNCT
ap-768	18	24	2	2	NUM
ap-768	18	25	,	,	PUNCT
ap-768	18	26	3	3	NUM
ap-768	18	27	,	,	PUNCT
ap-768	18	28	…	…	PUNCT
ap-768	18	29	}	}	PUNCT
ap-768	18	30	denotes	denote	VERB
ap-768	18	31	the	the	DET
ap-768	18	32	set	set	NOUN
ap-768	18	33	of	of	ADP
ap-768	18	34	all	all	DET
ap-768	18	35	natural	natural	ADJ
ap-768	18	36	numbers	number	NOUN
ap-768	18	37	and	and	CCONJ
ap-768	18	38	p:	p:	NOUN
ap-768	18	39	�	�	NOUN
ap-768	18	40	{2	{2	NOUN
ap-768	18	41	,	,	PUNCT
ap-768	18	42	3	3	NUM
ap-768	18	43	,	,	PUNCT
ap-768	18	44	5	5	NUM
ap-768	18	45	,	,	PUNCT
ap-768	18	46	…	…	PUNCT
ap-768	18	47	}	}	PUNCT
ap-768	18	48	denotes	denote	VERB
ap-768	18	49	the	the	DET
ap-768	18	50	set	set	NOUN
ap-768	18	51	of	of	ADP
ap-768	18	52	all	all	DET
ap-768	18	53	prime	prime	ADJ
ap-768	18	54	numbers	number	NOUN
ap-768	18	55	.	.	PUNCT
ap-768	19	1	let	let	VERB
ap-768	19	2	n	n	PRON
ap-768	19	3	be	be	AUX
ap-768	19	4	a	a	DET
ap-768	19	5	natural	natural	ADJ
ap-768	19	6	number	number	NOUN
ap-768	19	7	,	,	PUNCT
ap-768	19	8	then	then	ADV
ap-768	19	9	the	the	DET
ap-768	19	10	set	set	NOUN
ap-768	19	11	{	{	PUNCT
ap-768	19	12	0	0	NUM
ap-768	19	13	,	,	PUNCT
ap-768	19	14	1	1	NUM
ap-768	19	15	,	,	PUNCT
ap-768	19	16	…	…	PUNCT
ap-768	19	17	,	,	PUNCT
ap-768	19	18	n	n	X
ap-768	19	19	�	�	PROPN
ap-768	19	20	1	1	NUM
ap-768	19	21	}	}	PUNCT
ap-768	19	22	forms	form	NOUN
ap-768	19	23	,	,	PUNCT
ap-768	19	24	together	together	ADV
ap-768	19	25	with	with	ADP
ap-768	19	26	operations	operation	NOUN
ap-768	19	27	�	�	PROPN
ap-768	19	28	mod	mod	PROPN
ap-768	19	29	n	n	PROPN
ap-768	19	30	,	,	PUNCT
ap-768	19	31	×mod	×mod	NUM
ap-768	19	32	n	n	CCONJ
ap-768	19	33	,	,	PUNCT
ap-768	19	34	an	an	DET
ap-768	19	35	associative	associative	ADJ
ap-768	19	36	commutative	commutative	ADJ
ap-768	19	37	ring	ring	NOUN
ap-768	19	38	with	with	ADP
ap-768	19	39	unity	unity	NOUN
ap-768	19	40	.	.	PUNCT
ap-768	20	1	we	we	PRON
ap-768	20	2	will	will	AUX
ap-768	20	3	denote	denote	VERB
ap-768	20	4	this	this	DET
ap-768	20	5	ring	ring	NOUN
ap-768	20	6	,	,	PUNCT
ap-768	20	7	as	as	ADP
ap-768	20	8	usual	usual	ADJ
ap-768	20	9	,	,	PUNCT
ap-768	20	10	by	by	ADP
ap-768	20	11	zn	zn	PROPN
ap-768	20	12	.	.	PUNCT
ap-768	21	1	it	it	PRON
ap-768	21	2	is	be	AUX
ap-768	21	3	well	well	ADV
ap-768	21	4	known	know	VERB
ap-768	21	5	that	that	SCONJ
ap-768	21	6	for	for	ADP
ap-768	21	7	n	n	PRON
ap-768	21	8	prime	prime	NOUN
ap-768	21	9	the	the	DET
ap-768	21	10	ring	ring	NOUN
ap-768	21	11	zn	zn	PROPN
ap-768	21	12	is	be	AUX
ap-768	21	13	a	a	DET
ap-768	21	14	field	field	NOUN
ap-768	21	15	.	.	PUNCT
ap-768	22	1	let	let	VERB
ap-768	22	2	us	we	PRON
ap-768	22	3	consider	consider	VERB
ap-768	22	4	m	m	PRON
ap-768	22	5	,	,	PUNCT
ap-768	22	6	n	n	CCONJ
ap-768	22	7	to	to	PART
ap-768	22	8	be	be	AUX
ap-768	22	9	arbitrary	arbitrary	ADJ
ap-768	22	10	natural	natural	ADJ
ap-768	22	11	numbers	number	NOUN
ap-768	22	12	.	.	PUNCT
ap-768	23	1	we	we	PRON
ap-768	23	2	denote	denote	VERB
ap-768	23	3	by	by	ADP
ap-768	23	4	z	z	PROPN
ap-768	23	5	z	z	PROPN
ap-768	23	6	z	z	PROPN
ap-768	23	7	zn	zn	NUM
ap-768	23	8	m	m	VERB
ap-768	23	9	n	n	ADP
ap-768	23	10	n	n	CCONJ
ap-768	23	11	n	n	PRON
ap-768	23	12	m	m	PROPN
ap-768	23	13	�	�	PROPN
ap-768	23	14	�	�	PROPN
ap-768	23	15	�	�	PROPN
ap-768	23	16	�	�	PROPN
ap-768	23	17	�	�	PROPN
ap-768	23	18	�	�	PROPN
ap-768	23	19	�	�	PROPN
ap-768	23	20	�	�	PROPN
ap-768	23	21	�	�	PROPN
ap-768	23	22	�	�	PROPN
ap-768	23	23	�	�	PROPN
ap-768	23	24	�	�	PROPN
ap-768	23	25	the	the	DET
ap-768	23	26	cartesian	cartesian	ADJ
ap-768	23	27	product	product	NOUN
ap-768	23	28	of	of	ADP
ap-768	23	29	m	m	PROPN
ap-768	23	30	rings	ring	NOUN
ap-768	23	31	zn	zn	PROPN
ap-768	23	32	.	.	PUNCT
ap-768	24	1	it	it	PRON
ap-768	24	2	is	be	AUX
ap-768	24	3	clear	clear	ADJ
ap-768	24	4	that	that	SCONJ
ap-768	24	5	zn	zn	PROPN
ap-768	24	6	m	m	VERB
ap-768	24	7	with	with	ADP
ap-768	24	8	operations	operation	NOUN
ap-768	24	9	�	�	PROPN
ap-768	24	10	mod	mod	PROPN
ap-768	24	11	n	n	PROPN
ap-768	24	12	,	,	PUNCT
ap-768	24	13	×mod	×mod	DET
ap-768	24	14	n	n	ADV
ap-768	24	15	defined	define	VERB
ap-768	24	16	elementwise	elementwise	NOUN
ap-768	24	17	is	be	AUX
ap-768	24	18	an	an	DET
ap-768	24	19	associative	associative	ADJ
ap-768	24	20	commutative	commutative	ADJ
ap-768	24	21	ring	ring	NOUN
ap-768	24	22	with	with	ADP
ap-768	24	23	unity	unity	NOUN
ap-768	24	24	again	again	ADV
ap-768	24	25	.	.	PUNCT
ap-768	25	1	it	it	PRON
ap-768	25	2	contains	contain	VERB
ap-768	25	3	divisors	divisor	NOUN
ap-768	25	4	of	of	ADP
ap-768	25	5	zero	zero	NUM
ap-768	25	6	and	and	CCONJ
ap-768	25	7	we	we	PRON
ap-768	25	8	call	call	VERB
ap-768	25	9	its	its	PRON
ap-768	25	10	elements	element	NOUN
ap-768	25	11	row	row	NOUN
ap-768	25	12	vectors	vector	NOUN
ap-768	25	13	or	or	CCONJ
ap-768	25	14	points	point	NOUN
ap-768	25	15	.	.	PUNCT
ap-768	26	1	furthermore	furthermore	ADV
ap-768	26	2	we	we	PRON
ap-768	26	3	call	call	VERB
ap-768	26	4	the	the	DET
ap-768	26	5	zero	zero	NUM
ap-768	26	6	element	element	NOUN
ap-768	26	7	(	(	PUNCT
ap-768	26	8	0	0	NUM
ap-768	26	9	,	,	PUNCT
ap-768	26	10	…	…	PUNCT
ap-768	26	11	,	,	PUNCT
ap-768	26	12	0	0	NUM
ap-768	26	13	)	)	PUNCT
ap-768	26	14	zero	zero	NUM
ap-768	26	15	vector	vector	NOUN
ap-768	26	16	and	and	CCONJ
ap-768	26	17	denote	denote	VERB
ap-768	26	18	it	it	PRON
ap-768	26	19	simply	simply	ADV
ap-768	26	20	by	by	ADP
ap-768	26	21	0	0	PROPN
ap-768	26	22	.	.	PUNCT
ap-768	27	1	we	we	PRON
ap-768	27	2	denote	denote	VERB
ap-768	27	3	by	by	ADP
ap-768	27	4	zn	zn	PROPN
ap-768	27	5	m	m	VERB
ap-768	27	6	m	m	PROPN
ap-768	27	7	,	,	PUNCT
ap-768	27	8	the	the	DET
ap-768	27	9	set	set	NOUN
ap-768	27	10	of	of	ADP
ap-768	27	11	all	all	DET
ap-768	27	12	m×m	m×m	ADJ
ap-768	27	13	matrices	matrix	NOUN
ap-768	27	14	with	with	ADP
ap-768	27	15	elements	element	NOUN
ap-768	27	16	in	in	ADP
ap-768	27	17	the	the	DET
ap-768	27	18	ring	ring	NOUN
ap-768	27	19	zn	zn	PROPN
ap-768	27	20	.	.	PUNCT
ap-768	28	1	for	for	ADP
ap-768	28	2	k	k	PROPN
ap-768	28	3	�	�	PROPN
ap-768	28	4	n	n	PROPN
ap-768	28	5	and	and	CCONJ
ap-768	28	6	a	a	DET
ap-768	28	7	z	z	PROPN
ap-768	28	8	�	�	PROPN
ap-768	28	9	n	n	CCONJ
ap-768	28	10	m	m	NOUN
ap-768	28	11	m	m	VERB
ap-768	28	12	,	,	PUNCT
ap-768	28	13	we	we	PRON
ap-768	28	14	will	will	AUX
ap-768	28	15	denote	denote	VERB
ap-768	28	16	by	by	ADP
ap-768	28	17	(	(	PUNCT
ap-768	28	18	a)mod	a)mod	PROPN
ap-768	28	19	k	k	PROPN
ap-768	28	20	a	a	DET
ap-768	28	21	matrix	matrix	NOUN
ap-768	28	22	which	which	PRON
ap-768	28	23	arose	arise	VERB
ap-768	28	24	from	from	ADP
ap-768	28	25	matrix	matrix	NOUN
ap-768	28	26	a	a	DET
ap-768	28	27	after	after	ADP
ap-768	28	28	application	application	NOUN
ap-768	28	29	of	of	ADP
ap-768	28	30	operation	operation	NOUN
ap-768	28	31	modulo	modulo	PROPN
ap-768	28	32	k	k	X
ap-768	28	33	on	on	ADP
ap-768	28	34	its	its	PRON
ap-768	28	35	elements	element	NOUN
ap-768	28	36	.	.	PUNCT
ap-768	29	1	in	in	ADP
ap-768	29	2	the	the	DET
ap-768	29	3	following	following	NOUN
ap-768	29	4	we	we	PRON
ap-768	29	5	shall	shall	AUX
ap-768	29	6	frequently	frequently	ADV
ap-768	29	7	use	use	VERB
ap-768	29	8	a	a	DET
ap-768	29	9	product	product	NOUN
ap-768	29	10	on	on	ADP
ap-768	29	11	the	the	DET
ap-768	29	12	set	set	NOUN
ap-768	29	13	zn	zn	PROPN
ap-768	29	14	m	m	VERB
ap-768	29	15	m	m	PROPN
ap-768	29	16	,	,	PUNCT
ap-768	29	17	defined	define	VERB
ap-768	29	18	as	as	ADP
ap-768	29	19	matrix	matrix	NOUN
ap-768	29	20	multiplication	multiplication	NOUN
ap-768	29	21	together	together	ADV
ap-768	29	22	with	with	ADP
ap-768	29	23	operation	operation	NOUN
ap-768	29	24	modulo	modulo	PROPN
ap-768	29	25	n	n	CCONJ
ap-768	29	26	,	,	PUNCT
ap-768	29	27	i.e.	i.e.	X
ap-768	29	28	a	a	DET
ap-768	29	29	,	,	PUNCT
ap-768	29	30	b	b	PROPN
ap-768	29	31	z	z	PROPN
ap-768	29	32	ab	ab	PROPN
ap-768	29	33	)	)	PUNCT
ap-768	29	34	�	�	PROPN
ap-768	29	35	�	�	PROPN
ap-768	29	36	n	n	PRON
ap-768	29	37	m	m	NOUN
ap-768	29	38	m	m	VERB
ap-768	29	39	n	n	PRON
ap-768	29	40	,	,	PUNCT
ap-768	29	41	mod	mod	PROPN
ap-768	29	42	(	(	PUNCT
ap-768	29	43	.	.	PUNCT
ap-768	30	1	(	(	PUNCT
ap-768	30	2	2.1	2.1	NUM
ap-768	30	3	)	)	PUNCT
ap-768	30	4	this	this	DET
ap-768	30	5	product	product	NOUN
ap-768	30	6	is	be	AUX
ap-768	30	7	,	,	PUNCT
ap-768	30	8	due	due	ADP
ap-768	30	9	to	to	ADP
ap-768	30	10	the	the	DET
ap-768	30	11	associativity	associativity	NOUN
ap-768	30	12	of	of	ADP
ap-768	30	13	matrix	matrix	NOUN
ap-768	30	14	multiplication	multiplication	NOUN
ap-768	30	15	,	,	PUNCT
ap-768	30	16	associative	associative	ADJ
ap-768	30	17	again	again	ADV
ap-768	30	18	and	and	CCONJ
ap-768	30	19	the	the	DET
ap-768	30	20	set	set	NOUN
ap-768	30	21	zn	zn	PROPN
ap-768	30	22	m	m	VERB
ap-768	30	23	m	m	PROPN
ap-768	30	24	,	,	PUNCT
ap-768	30	25	equipped	equip	VERB
ap-768	30	26	with	with	ADP
ap-768	30	27	this	this	DET
ap-768	30	28	product	product	NOUN
ap-768	30	29	forms	form	VERB
ap-768	30	30	a	a	DET
ap-768	30	31	semigroup	semigroup	NOUN
ap-768	30	32	.	.	PUNCT
ap-768	31	1	if	if	SCONJ
ap-768	31	2	we	we	PRON
ap-768	31	3	take	take	VERB
ap-768	31	4	matrices	matrix	NOUN
ap-768	31	5	a	a	PRON
ap-768	31	6	,	,	PUNCT
ap-768	31	7	b	b	PROPN
ap-768	31	8	z	z	PROPN
ap-768	31	9	�	�	PROPN
ap-768	31	10	n	n	CCONJ
ap-768	31	11	m	m	NOUN
ap-768	31	12	m	m	ADJ
ap-768	31	13	,	,	PUNCT
ap-768	31	14	,	,	PUNCT
ap-768	31	15	such	such	ADJ
ap-768	31	16	that	that	DET
ap-768	31	17	det(a	det(a	PROPN
ap-768	31	18	)	)	PUNCT
ap-768	31	19	�	�	PROPN
ap-768	31	20	det(b	det(b	PROPN
ap-768	31	21	)	)	PUNCT
ap-768	31	22	�	�	PROPN
ap-768	31	23	1	1	NUM
ap-768	31	24	(	(	PUNCT
ap-768	31	25	mod	mod	NOUN
ap-768	31	26	n	n	CCONJ
ap-768	31	27	)	)	PUNCT
ap-768	31	28	,	,	PUNCT
ap-768	31	29	then	then	ADV
ap-768	31	30	det((ab)mod	det((ab)mod	PROPN
ap-768	31	31	n	n	CCONJ
ap-768	31	32	)	)	PUNCT
ap-768	31	33	�	�	PROPN
ap-768	31	34	1	1	NUM
ap-768	31	35	(	(	PUNCT
ap-768	31	36	mod	mod	NOUN
ap-768	31	37	n	n	CCONJ
ap-768	31	38	)	)	PUNCT
ap-768	31	39	holds	hold	NOUN
ap-768	31	40	.	.	PUNCT
ap-768	32	1	it	it	PRON
ap-768	32	2	follows	follow	VERB
ap-768	32	3	that	that	SCONJ
ap-768	32	4	the	the	DET
ap-768	32	5	subset	subset	NOUN
ap-768	32	6	of	of	ADP
ap-768	32	7	zn	zn	PROPN
ap-768	32	8	m	m	VERB
ap-768	32	9	m	m	PROPN
ap-768	32	10	,	,	PUNCT
ap-768	32	11	formed	form	VERB
ap-768	32	12	by	by	ADP
ap-768	32	13	all	all	DET
ap-768	32	14	matrices	matrix	NOUN
ap-768	32	15	with	with	ADP
ap-768	32	16	the	the	DET
ap-768	32	17	determinant	determinant	ADJ
ap-768	32	18	equal	equal	ADJ
ap-768	32	19	to	to	ADP
ap-768	32	20	unity	unity	NOUN
ap-768	32	21	modulo	modulo	NOUN
ap-768	32	22	n	n	PRON
ap-768	32	23	is	be	AUX
ap-768	32	24	a	a	DET
ap-768	32	25	semigroup	semigroup	NOUN
ap-768	32	26	.	.	PUNCT
ap-768	33	1	definition	definition	NOUN
ap-768	33	2	2.1	2.1	NUM
ap-768	33	3	:	:	PUNCT
ap-768	33	4	for	for	ADP
ap-768	33	5	m	m	PROPN
ap-768	33	6	n	n	SYM
ap-768	33	7	,	,	PUNCT
ap-768	33	8	�	�	PROPN
ap-768	33	9	n	n	CCONJ
ap-768	33	10	,	,	PUNCT
ap-768	33	11	n	n	X
ap-768	33	12	�	�	PROPN
ap-768	33	13	2	2	NUM
ap-768	33	14	we	we	PRON
ap-768	33	15	define	define	VERB
ap-768	33	16	sl	sl	INTJ
ap-768	33	17	m	m	VERB
ap-768	33	18	nn	nn	PROPN
ap-768	33	19	n	n	PROPN
ap-768	33	20	m	m	NOUN
ap-768	33	21	m	m	PROPN
ap-768	33	22	(	(	PUNCT
ap-768	33	23	,	,	PUNCT
ap-768	33	24	):	):	PUNCT
ap-768	33	25	{	{	PUNCT
ap-768	33	26	|det	|det	NOUN
ap-768	33	27	(	(	PUNCT
ap-768	33	28	mod	mod	NOUN
ap-768	33	29	)	)	PUNCT
ap-768	33	30	}	}	PUNCT
ap-768	33	31	,	,	PUNCT
ap-768	33	32	z	z	NOUN
ap-768	33	33	a	a	DET
ap-768	33	34	z	z	NOUN
ap-768	33	35	a	a	DET
ap-768	33	36	�	�	PROPN
ap-768	33	37	�	�	PROPN
ap-768	33	38	�	�	PROPN
ap-768	33	39	1	1	NUM
ap-768	33	40	.	.	PUNCT
ap-768	34	1	now	now	ADV
ap-768	34	2	we	we	PRON
ap-768	34	3	show	show	VERB
ap-768	34	4	that	that	SCONJ
ap-768	34	5	sl(m	sl(m	PROPN
ap-768	34	6	,	,	PUNCT
ap-768	34	7	zn	zn	PROPN
ap-768	34	8	)	)	PUNCT
ap-768	34	9	with	with	ADP
ap-768	34	10	operation	operation	NOUN
ap-768	34	11	(	(	PUNCT
ap-768	34	12	2.1	2.1	NUM
ap-768	34	13	)	)	PUNCT
ap-768	34	14	forms	form	VERB
ap-768	34	15	a	a	DET
ap-768	34	16	group	group	NOUN
ap-768	34	17	.	.	PUNCT
ap-768	35	1	because	because	SCONJ
ap-768	35	2	sl(m	sl(m	PROPN
ap-768	35	3	,	,	PUNCT
ap-768	35	4	zn	zn	PROPN
ap-768	35	5	)	)	PUNCT
ap-768	35	6	is	be	AUX
ap-768	35	7	a	a	DET
ap-768	35	8	semigroup	semigroup	NOUN
ap-768	35	9	,	,	PUNCT
ap-768	35	10	it	it	PRON
ap-768	35	11	is	be	AUX
ap-768	35	12	sufficient	sufficient	ADJ
ap-768	35	13	to	to	PART
ap-768	35	14	show	show	VERB
ap-768	35	15	that	that	SCONJ
ap-768	35	16	there	there	PRON
ap-768	35	17	exists	exist	VERB
ap-768	35	18	a	a	DET
ap-768	35	19	unit	unit	NOUN
ap-768	35	20	element	element	NOUN
ap-768	35	21	and	and	CCONJ
ap-768	35	22	a	a	DET
ap-768	35	23	right	right	ADJ
ap-768	35	24	inverse	inverse	NOUN
ap-768	35	25	element	element	NOUN
ap-768	35	26	.	.	PUNCT
ap-768	36	1	unit	unit	NOUN
ap-768	36	2	matrix	matrix	NOUN
ap-768	36	3	is	be	AUX
ap-768	36	4	clearly	clearly	ADV
ap-768	36	5	the	the	DET
ap-768	36	6	unit	unit	NOUN
ap-768	36	7	element	element	NOUN
ap-768	36	8	.	.	PUNCT
ap-768	37	1	in	in	ADP
ap-768	37	2	order	order	NOUN
ap-768	37	3	to	to	PART
ap-768	37	4	find	find	VERB
ap-768	37	5	a	a	DET
ap-768	37	6	right	right	ADJ
ap-768	37	7	inverse	inverse	NOUN
ap-768	37	8	element	element	NOUN
ap-768	37	9	consider	consider	VERB
ap-768	37	10	the	the	DET
ap-768	37	11	following	follow	VERB
ap-768	37	12	equation	equation	NOUN
ap-768	37	13	aa	aa	NOUN
ap-768	37	14	a)iadj	a)iadj	PROPN
ap-768	37	15	�	�	PROPN
ap-768	37	16	det	det	PROPN
ap-768	37	17	(	(	PUNCT
ap-768	37	18	.	.	PUNCT
ap-768	38	1	(	(	PUNCT
ap-768	38	2	2.2	2.2	NUM
ap-768	38	3	)	)	PUNCT
ap-768	38	4	the	the	DET
ap-768	38	5	symbol	symbol	NOUN
ap-768	38	6	aadj	aadj	NOUN
ap-768	38	7	denotes	denote	VERB
ap-768	38	8	the	the	DET
ap-768	38	9	adjoint	adjoint	PROPN
ap-768	38	10	matrix	matrix	NOUN
ap-768	38	11	defined	define	VERB
ap-768	38	12	by	by	ADP
ap-768	38	13	(	(	PUNCT
ap-768	38	14	a	a	DET
ap-768	38	15	a	a	X
ap-768	38	16	(	(	PUNCT
ap-768	38	17	,	,	PUNCT
ap-768	38	18	)	)	PUNCT
ap-768	38	19	adj	adj	NOUN
ap-768	38	20	)	)	PUNCT
ap-768	38	21	:	:	PUNCT
ap-768	38	22	(	(	PUNCT
ap-768	38	23	)	)	PUNCT
ap-768	38	24	det	det	PROPN
ap-768	38	25	,	,	PUNCT
ap-768	38	26	i	i	PRON
ap-768	39	1	j	j	VERB
ap-768	40	1	i	i	PRON
ap-768	40	2	j	j	PROPN
ap-768	41	1	j	j	PROPN
ap-768	41	2	i	i	PRON
ap-768	41	3	�	�	PROPN
ap-768	41	4	�	�	PROPN
ap-768	41	5	�	�	PROPN
ap-768	41	6	1	1	NUM
ap-768	41	7	,	,	PUNCT
ap-768	41	8	where	where	SCONJ
ap-768	41	9	a	a	PRON
ap-768	41	10	(	(	PUNCT
ap-768	41	11	,	,	PUNCT
ap-768	41	12	)	)	PUNCT
ap-768	41	13	j	j	PROPN
ap-768	42	1	i	i	PRON
ap-768	42	2	is	be	AUX
ap-768	42	3	the	the	DET
ap-768	42	4	matrix	matrix	NOUN
ap-768	42	5	obtained	obtain	VERB
ap-768	42	6	from	from	ADP
ap-768	42	7	matrix	matrix	NOUN
ap-768	42	8	a	a	PRON
ap-768	42	9	by	by	ADP
ap-768	42	10	omitting	omit	VERB
ap-768	42	11	the	the	DET
ap-768	42	12	j	j	PROPN
ap-768	42	13	-	-	PUNCT
ap-768	42	14	th	th	X
ap-768	42	15	row	row	NOUN
ap-768	42	16	and	and	CCONJ
ap-768	42	17	the	the	DET
ap-768	42	18	i	i	PROPN
ap-768	42	19	-	-	PUNCT
ap-768	42	20	th	th	X
ap-768	42	21	column	column	NOUN
ap-768	42	22	.	.	PUNCT
ap-768	43	1	the	the	DET
ap-768	43	2	equation	equation	NOUN
ap-768	43	3	(	(	PUNCT
ap-768	43	4	2.2	2.2	NUM
ap-768	43	5	)	)	PUNCT
ap-768	43	6	holds	hold	VERB
ap-768	43	7	for	for	ADP
ap-768	43	8	an	an	DET
ap-768	43	9	arbitrary	arbitrary	ADJ
ap-768	43	10	matrix	matrix	NOUN
ap-768	43	11	,	,	PUNCT
ap-768	43	12	hence	hence	ADV
ap-768	43	13	it	it	PRON
ap-768	43	14	holds	hold	VERB
ap-768	43	15	for	for	ADP
ap-768	43	16	matrices	matrix	NOUN
ap-768	43	17	from	from	ADP
ap-768	43	18	sl(m	sl(m	PROPN
ap-768	43	19	,	,	PUNCT
ap-768	43	20	zn	zn	PROPN
ap-768	43	21	)	)	PUNCT
ap-768	43	22	,	,	PUNCT
ap-768	43	23	and	and	CCONJ
ap-768	43	24	evidently	evidently	ADV
ap-768	43	25	holds	hold	VERB
ap-768	43	26	after	after	ADP
ap-768	43	27	application	application	NOUN
ap-768	43	28	of	of	ADP
ap-768	43	29	operation	operation	NOUN
ap-768	43	30	modulo	modulo	PROPN
ap-768	43	31	n	n	X
ap-768	43	32	on	on	ADP
ap-768	43	33	both	both	DET
ap-768	43	34	sides	side	NOUN
ap-768	43	35	.	.	PUNCT
ap-768	44	1	consequently	consequently	ADV
ap-768	44	2	,	,	PUNCT
ap-768	44	3	for	for	ADP
ap-768	44	4	a	a	DET
ap-768	44	5	z	z	PROPN
ap-768	44	6	�	�	PROPN
ap-768	44	7	sl	sl	NOUN
ap-768	44	8	m	m	VERB
ap-768	44	9	n	n	CCONJ
ap-768	44	10	(	(	PUNCT
ap-768	44	11	,	,	PUNCT
ap-768	44	12	)	)	PUNCT
ap-768	44	13	,	,	PUNCT
ap-768	44	14	we	we	PRON
ap-768	44	15	have	have	VERB
ap-768	44	16	aa	aa	PROPN
ap-768	44	17	iadj	iadj	PROPN
ap-768	44	18	�	�	PROPN
ap-768	44	19	(	(	PUNCT
ap-768	44	20	mod	mod	PROPN
ap-768	44	21	)	)	PUNCT
ap-768	44	22	n	n	CCONJ
ap-768	44	23	,	,	PUNCT
ap-768	44	24	i.e.	i.e.	X
ap-768	44	25	(	(	PUNCT
ap-768	44	26	aa	aa	PROPN
ap-768	44	27	iadj)mod	iadj)mod	PROPN
ap-768	44	28	n	n	PROPN
ap-768	44	29	�	�	PROPN
ap-768	44	30	.	.	PUNCT
ap-768	45	1	therefore	therefore	ADV
ap-768	45	2	aadj	aadj	NOUN
ap-768	45	3	is	be	AUX
ap-768	45	4	the	the	DET
ap-768	45	5	right	right	ADJ
ap-768	45	6	inverse	inverse	NOUN
ap-768	45	7	element	element	NOUN
ap-768	45	8	corresponding	correspond	VERB
ap-768	45	9	to	to	PART
ap-768	45	10	matrix	matrix	VERB
ap-768	45	11	a	a	PRON
ap-768	45	12	,	,	PUNCT
ap-768	45	13	and	and	CCONJ
ap-768	45	14	consequently	consequently	ADV
ap-768	45	15	sl(m	sl(m	PROPN
ap-768	45	16	,	,	PUNCT
ap-768	45	17	zn	zn	X
ap-768	45	18	)	)	PUNCT
ap-768	45	19	is	be	AUX
ap-768	45	20	a	a	DET
ap-768	45	21	group	group	NOUN
ap-768	45	22	.	.	PUNCT
ap-768	46	1	©	©	PROPN
ap-768	46	2	czech	czech	PROPN
ap-768	46	3	technical	technical	PROPN
ap-768	46	4	university	university	PROPN
ap-768	46	5	publishing	publishing	NOUN
ap-768	46	6	house	house	NOUN
ap-768	46	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-768	46	8	39	39	NUM
ap-768	46	9	czech	czech	PROPN
ap-768	46	10	technical	technical	PROPN
ap-768	46	11	university	university	PROPN
ap-768	46	12	in	in	ADP
ap-768	46	13	prague	prague	PROPN
ap-768	46	14	acta	acta	PROPN
ap-768	46	15	polytechnica	polytechnica	PROPN
ap-768	46	16	vol	vol	NOUN
ap-768	46	17	.	.	PROPN
ap-768	47	1	45	45	NUM
ap-768	47	2	no	no	NOUN
ap-768	47	3	.	.	PUNCT
ap-768	48	1	5/2005	5/2005	NUM
ap-768	48	2	on	on	ADP
ap-768	48	3	orbits	orbit	NOUN
ap-768	48	4	of	of	ADP
ap-768	48	5	the	the	DET
ap-768	48	6	ring	ring	NOUN
ap-768	48	7	zn	zn	PROPN
ap-768	48	8	m	m	VERB
ap-768	48	9	under	under	ADP
ap-768	48	10	action	action	NOUN
ap-768	48	11	of	of	ADP
ap-768	48	12	the	the	DET
ap-768	48	13	group	group	NOUN
ap-768	48	14	sl(m	sl(m	PROPN
ap-768	48	15	,	,	PUNCT
ap-768	48	16	zn	zn	X
ap-768	48	17	)	)	PUNCT
ap-768	48	18	p.	p.	PROPN
ap-768	48	19	novotný	novotný	PROPN
ap-768	48	20	,	,	PUNCT
ap-768	48	21	j.	j.	PROPN
ap-768	48	22	hrivnák	hrivnák	PROPN
ap-768	48	23	we	we	PRON
ap-768	48	24	consider	consider	VERB
ap-768	48	25	the	the	DET
ap-768	48	26	action	action	NOUN
ap-768	48	27	of	of	ADP
ap-768	48	28	the	the	DET
ap-768	48	29	finite	finite	PROPN
ap-768	48	30	matrix	matrix	NOUN
ap-768	48	31	group	group	PROPN
ap-768	48	32	sl(m	sl(m	PROPN
ap-768	48	33	,	,	PUNCT
ap-768	48	34	zn	zn	PROPN
ap-768	48	35	)	)	PUNCT
ap-768	48	36	on	on	ADP
ap-768	48	37	the	the	DET
ap-768	48	38	ring	ring	NOUN
ap-768	48	39	zn	zn	PROPN
ap-768	48	40	m.	m.	NOUN
ap-768	48	41	we	we	PRON
ap-768	48	42	determine	determine	VERB
ap-768	48	43	orbits	orbit	NOUN
ap-768	48	44	of	of	ADP
ap-768	48	45	this	this	DET
ap-768	48	46	action	action	NOUN
ap-768	48	47	for	for	ADP
ap-768	48	48	n	n	CCONJ
ap-768	48	49	arbitrary	arbitrary	ADJ
ap-768	48	50	natural	natural	ADJ
ap-768	48	51	number	number	NOUN
ap-768	48	52	.	.	PUNCT
ap-768	49	1	it	it	PRON
ap-768	49	2	is	be	AUX
ap-768	49	3	a	a	DET
ap-768	49	4	generalization	generalization	NOUN
ap-768	49	5	of	of	ADP
ap-768	49	6	the	the	DET
ap-768	49	7	task	task	NOUN
ap-768	49	8	which	which	PRON
ap-768	49	9	was	be	AUX
ap-768	49	10	studied	study	VERB
ap-768	49	11	by	by	ADP
ap-768	49	12	a.	a.	PROPN
ap-768	49	13	a.	a.	NOUN
ap-768	49	14	kirillov	kirillov	PROPN
ap-768	49	15	for	for	ADP
ap-768	49	16	m	m	PROPN
ap-768	49	17	�	�	PROPN
ap-768	49	18	2	2	NUM
ap-768	49	19	and	and	CCONJ
ap-768	49	20	n	n	CCONJ
ap-768	49	21	prime	prime	ADJ
ap-768	49	22	number	number	NOUN
ap-768	49	23	.	.	PUNCT
ap-768	50	1	keywords	keyword	NOUN
ap-768	50	2	:	:	PUNCT
ap-768	50	3	ring	ring	NOUN
ap-768	50	4	,	,	PUNCT
ap-768	50	5	finite	finite	PROPN
ap-768	50	6	group	group	NOUN
ap-768	50	7	.	.	PUNCT
ap-768	51	1	the	the	DET
ap-768	51	2	group	group	PROPN
ap-768	51	3	sl(m	sl(m	PROPN
ap-768	51	4	,	,	PUNCT
ap-768	51	5	zn	zn	X
ap-768	51	6	)	)	PUNCT
ap-768	51	7	is	be	AUX
ap-768	51	8	finite	finite	ADJ
ap-768	51	9	and	and	CCONJ
ap-768	51	10	its	its	PRON
ap-768	51	11	order	order	NOUN
ap-768	51	12	was	be	AUX
ap-768	51	13	computed	compute	VERB
ap-768	51	14	by	by	ADP
ap-768	51	15	you	you	PRON
ap-768	51	16	hong	hong	PROPN
ap-768	51	17	and	and	CCONJ
ap-768	51	18	gao	gao	VERB
ap-768	51	19	you	you	PRON
ap-768	51	20	in	in	ADP
ap-768	51	21	[	[	X
ap-768	51	22	10	10	NUM
ap-768	51	23	]	]	PUNCT
ap-768	51	24	(	(	PUNCT
ap-768	51	25	see	see	VERB
ap-768	51	26	also	also	ADV
ap-768	51	27	[	[	X
ap-768	51	28	11	11	NUM
ap-768	51	29	]	]	PUNCT
ap-768	51	30	,	,	PUNCT
ap-768	51	31	p.	p.	NOUN
ap-768	51	32	86	86	NUM
ap-768	51	33	)	)	PUNCT
ap-768	51	34	.	.	PUNCT
ap-768	52	1	if	if	SCONJ
ap-768	52	2	n	n	PRON
ap-768	52	3	n	n	CCONJ
ap-768	52	4	�	�	PROPN
ap-768	52	5	�	�	PROPN
ap-768	52	6	n	n	NUM
ap-768	52	7	,	,	PUNCT
ap-768	52	8	2	2	NUM
ap-768	52	9	is	be	AUX
ap-768	52	10	written	write	VERB
ap-768	52	11	in	in	ADP
ap-768	52	12	the	the	DET
ap-768	52	13	form	form	NOUN
ap-768	53	1	n	n	DET
ap-768	53	2	pi	pi	NOUN
ap-768	54	1	k	k	INTJ
ap-768	55	1	i	i	PRON
ap-768	55	2	r	r	VERB
ap-768	55	3	i	i	PRON
ap-768	55	4	�	�	PROPN
ap-768	55	5	�	�	PROPN
ap-768	55	6	1	1	NUM
ap-768	55	7	,	,	PUNCT
ap-768	55	8	where	where	SCONJ
ap-768	55	9	pi	pi	NOUN
ap-768	55	10	are	be	AUX
ap-768	55	11	distinct	distinct	ADJ
ap-768	55	12	primes	prime	NOUN
ap-768	55	13	,	,	PUNCT
ap-768	55	14	then	then	ADV
ap-768	55	15	according	accord	VERB
ap-768	55	16	to	to	ADP
ap-768	55	17	[	[	X
ap-768	55	18	10	10	NUM
ap-768	55	19	]	]	PUNCT
ap-768	55	20	,	,	PUNCT
ap-768	55	21	the	the	DET
ap-768	55	22	order	order	NOUN
ap-768	55	23	of	of	ADP
ap-768	55	24	sl(m	sl(m	PROPN
ap-768	55	25	,	,	PUNCT
ap-768	55	26	zn	zn	X
ap-768	55	27	)	)	PUNCT
ap-768	55	28	is	be	AUX
ap-768	55	29	sl	sl	INTJ
ap-768	55	30	m	m	PROPN
ap-768	55	31	n	n	ADP
ap-768	55	32	p	p	NOUN
ap-768	56	1	n	n	INTJ
ap-768	56	2	m	m	VERB
ap-768	56	3	i	i	PRON
ap-768	56	4	j	j	PROPN
ap-768	57	1	j	j	NOUN
ap-768	57	2	m	m	VERB
ap-768	58	1	i	i	VERB
ap-768	58	2	r	r	NOUN
ap-768	58	3	(	(	PUNCT
ap-768	58	4	,	,	PUNCT
ap-768	58	5	)	)	PUNCT
ap-768	58	6	z	z	PROPN
ap-768	58	7	�	�	PROPN
ap-768	58	8	�	�	PROPN
ap-768	58	9	�	�	PROPN
ap-768	58	10	�	�	PROPN
ap-768	58	11	�	�	PROPN
ap-768	58	12	�	�	PROPN
ap-768	58	13	�	�	PROPN
ap-768	58	14	�	�	PROPN
ap-768	58	15	�	�	PROPN
ap-768	58	16	�	�	PROPN
ap-768	58	17	�	�	PROPN
ap-768	58	18	2	2	NUM
ap-768	58	19	1	1	NUM
ap-768	58	20	21	21	NUM
ap-768	58	21	1	1	NUM
ap-768	58	22	1	1	NUM
ap-768	58	23	.	.	PUNCT
ap-768	59	1	(	(	PUNCT
ap-768	59	2	2.3	2.3	NUM
ap-768	59	3	)	)	PUNCT
ap-768	59	4	let	let	VERB
ap-768	59	5	g	g	NOUN
ap-768	59	6	be	be	AUX
ap-768	59	7	a	a	DET
ap-768	59	8	group	group	NOUN
ap-768	59	9	and	and	CCONJ
ap-768	59	10	x	x	PART
ap-768	59	11	�	�	PROPN
ap-768	59	12	0	0	NUM
ap-768	59	13	a	a	DET
ap-768	59	14	set	set	NOUN
ap-768	59	15	.	.	PUNCT
ap-768	60	1	recall	recall	VERB
ap-768	60	2	that	that	SCONJ
ap-768	60	3	a	a	DET
ap-768	60	4	mapping	mapping	NOUN
ap-768	60	5	�	�	NOUN
ap-768	60	6	:	:	PUNCT
ap-768	60	7	g	g	PROPN
ap-768	60	8	�	�	PROPN
ap-768	60	9	�	�	PROPN
ap-768	60	10	x	x	VERB
ap-768	60	11	x	x	NOUN
ap-768	60	12	is	be	AUX
ap-768	60	13	called	call	VERB
ap-768	60	14	a	a	DET
ap-768	60	15	right	right	ADJ
ap-768	60	16	action	action	NOUN
ap-768	60	17	of	of	ADP
ap-768	60	18	the	the	DET
ap-768	60	19	group	group	NOUN
ap-768	60	20	g	g	PROPN
ap-768	60	21	on	on	ADP
ap-768	60	22	the	the	DET
ap-768	60	23	set	set	NOUN
ap-768	60	24	x	x	PUNCT
ap-768	60	25	if	if	SCONJ
ap-768	60	26	the	the	DET
ap-768	60	27	following	follow	VERB
ap-768	60	28	conditions	condition	NOUN
ap-768	60	29	hold	hold	VERB
ap-768	60	30	for	for	ADP
ap-768	60	31	all	all	DET
ap-768	60	32	elements	element	NOUN
ap-768	60	33	x	x	SYM
ap-768	60	34	�	�	PROPN
ap-768	60	35	x	x	NOUN
ap-768	60	36	:	:	PUNCT
ap-768	60	37	1	1	X
ap-768	60	38	.	.	X
ap-768	60	39	�	�	PROPN
ap-768	60	40	�	�	PROPN
ap-768	60	41	�	�	PROPN
ap-768	60	42	(	(	PUNCT
ap-768	60	43	,	,	PUNCT
ap-768	60	44	)	)	PUNCT
ap-768	60	45	(	(	PUNCT
ap-768	60	46	,	,	PUNCT
ap-768	60	47	(	(	PUNCT
ap-768	60	48	,	,	PUNCT
ap-768	60	49	)	)	PUNCT
ap-768	60	50	)	)	PUNCT
ap-768	61	1	gh	gh	PROPN
ap-768	61	2	x	x	X
ap-768	62	1	g	g	PROPN
ap-768	62	2	h	h	NOUN
ap-768	62	3	x	x	NOUN
ap-768	62	4	�	�	PROPN
ap-768	62	5	for	for	ADP
ap-768	62	6	all	all	DET
ap-768	62	7	h	h	NOUN
ap-768	62	8	g	g	PROPN
ap-768	62	9	g	g	PROPN
ap-768	62	10	,	,	PUNCT
ap-768	62	11	�	�	PROPN
ap-768	62	12	.	.	PUNCT
ap-768	63	1	2	2	X
ap-768	63	2	.	.	X
ap-768	63	3	�	�	PROPN
ap-768	63	4	(	(	PUNCT
ap-768	63	5	,	,	PUNCT
ap-768	63	6	)	)	PUNCT
ap-768	63	7	e	e	NOUN
ap-768	63	8	x	x	SYM
ap-768	63	9	x	x	X
ap-768	63	10	�	�	PROPN
ap-768	63	11	,	,	PUNCT
ap-768	63	12	where	where	SCONJ
ap-768	63	13	e	e	NOUN
ap-768	63	14	is	be	AUX
ap-768	63	15	the	the	DET
ap-768	63	16	unit	unit	NOUN
ap-768	63	17	element	element	NOUN
ap-768	63	18	of	of	ADP
ap-768	63	19	g.	g.	PROPN
ap-768	63	20	let	let	VERB
ap-768	63	21	�	�	PROPN
ap-768	63	22	be	be	AUX
ap-768	63	23	an	an	DET
ap-768	63	24	action	action	NOUN
ap-768	63	25	of	of	ADP
ap-768	63	26	a	a	DET
ap-768	63	27	group	group	NOUN
ap-768	63	28	g	g	NOUN
ap-768	63	29	on	on	ADP
ap-768	63	30	a	a	DET
ap-768	63	31	set	set	NOUN
ap-768	63	32	x.	x.	NOUN
ap-768	63	33	a	a	DET
ap-768	63	34	subset	subset	NOUN
ap-768	63	35	of	of	ADP
ap-768	63	36	g	g	NOUN
ap-768	63	37	,	,	PUNCT
ap-768	63	38	{	{	PUNCT
ap-768	63	39	|	|	ADV
ap-768	63	40	(	(	PUNCT
ap-768	63	41	,	,	PUNCT
ap-768	63	42	)	)	PUNCT
ap-768	63	43	}	}	PUNCT
ap-768	63	44	g	g	NOUN
ap-768	63	45	g	g	PROPN
ap-768	63	46	g	g	PROPN
ap-768	63	47	a	a	DET
ap-768	63	48	a	a	DET
ap-768	63	49	�	�	PROPN
ap-768	63	50	�	�	PROPN
ap-768	63	51	�	�	PROPN
ap-768	63	52	is	be	AUX
ap-768	63	53	called	call	VERB
ap-768	63	54	a	a	DET
ap-768	63	55	stability	stability	NOUN
ap-768	63	56	subgroup	subgroup	NOUN
ap-768	63	57	of	of	ADP
ap-768	63	58	the	the	DET
ap-768	63	59	element	element	NOUN
ap-768	63	60	a	a	DET
ap-768	63	61	�	�	PROPN
ap-768	63	62	x.	x.	NOUN
ap-768	63	63	a	a	DET
ap-768	63	64	subset	subset	NOUN
ap-768	63	65	of	of	ADP
ap-768	63	66	x	x	X
ap-768	63	67	,	,	PUNCT
ap-768	63	68	{	{	PUNCT
ap-768	63	69	|	|	ADV
ap-768	63	70	,	,	PUNCT
ap-768	63	71	(	(	PUNCT
ap-768	63	72	,	,	PUNCT
ap-768	63	73	)	)	PUNCT
ap-768	63	74	}	}	PUNCT
ap-768	63	75	b	b	X
ap-768	63	76	x	x	SYM
ap-768	63	77	g	g	PROPN
ap-768	63	78	g	g	PROPN
ap-768	63	79	b	b	PROPN
ap-768	63	80	g	g	PROPN
ap-768	63	81	a	a	DET
ap-768	63	82	�	�	PROPN
ap-768	63	83	�	�	PROPN
ap-768	63	84	�	�	PROPN
ap-768	63	85	�	�	PROPN
ap-768	63	86	�	�	PROPN
ap-768	63	87	is	be	AUX
ap-768	63	88	called	call	VERB
ap-768	63	89	an	an	DET
ap-768	63	90	orbit	orbit	NOUN
ap-768	63	91	of	of	ADP
ap-768	63	92	the	the	DET
ap-768	63	93	element	element	NOUN
ap-768	63	94	a	a	DET
ap-768	63	95	�	�	NOUN
ap-768	63	96	x	x	PUNCT
ap-768	63	97	with	with	ADP
ap-768	63	98	respect	respect	NOUN
ap-768	63	99	to	to	ADP
ap-768	63	100	the	the	DET
ap-768	63	101	action	action	NOUN
ap-768	63	102	�	�	PROPN
ap-768	63	103	of	of	ADP
ap-768	63	104	group	group	PROPN
ap-768	63	105	g.	g.	PROPN
ap-768	63	106	let	let	VERB
ap-768	63	107	us	we	PRON
ap-768	63	108	note	note	VERB
ap-768	63	109	that	that	SCONJ
ap-768	63	110	if	if	SCONJ
ap-768	63	111	�	�	PROPN
ap-768	63	112	is	be	AUX
ap-768	63	113	an	an	DET
ap-768	63	114	action	action	NOUN
ap-768	63	115	of	of	ADP
ap-768	63	116	a	a	DET
ap-768	63	117	group	group	NOUN
ap-768	63	118	g	g	NOUN
ap-768	63	119	on	on	ADP
ap-768	63	120	a	a	DET
ap-768	63	121	set	set	NOUN
ap-768	63	122	x	x	PUNCT
ap-768	63	123	then	then	ADV
ap-768	63	124	relation	relation	NOUN
ap-768	63	125	~	~	PUNCT
ap-768	63	126	defined	define	VERB
ap-768	63	127	by	by	ADP
ap-768	63	128	formula	formula	NOUN
ap-768	63	129	a	a	DET
ap-768	63	130	b	b	NOUN
ap-768	63	131	a	a	DET
ap-768	63	132	b	b	NOUN
ap-768	63	133	g	g	NOUN
ap-768	63	134	g	g	PROPN
ap-768	63	135	g	g	PROPN
ap-768	63	136	a	a	DET
ap-768	63	137	b	b	NOUN
ap-768	63	138	,	,	PUNCT
ap-768	63	139	,	,	PUNCT
ap-768	63	140	~	~	PUNCT
ap-768	63	141	,	,	PUNCT
ap-768	63	142	(	(	PUNCT
ap-768	63	143	,	,	PUNCT
ap-768	63	144	)	)	PUNCT
ap-768	63	145	�	�	PROPN
ap-768	63	146	�	�	PROPN
ap-768	63	147	�	�	PROPN
ap-768	63	148	�	�	PROPN
ap-768	63	149	�	�	PROPN
ap-768	63	150	x	x	PROPN
ap-768	63	151	�	�	PROPN
ap-768	63	152	(	(	PUNCT
ap-768	63	153	2.4	2.4	NUM
ap-768	63	154	)	)	PUNCT
ap-768	63	155	is	be	AUX
ap-768	63	156	an	an	DET
ap-768	63	157	equivalence	equivalence	NOUN
ap-768	63	158	on	on	ADP
ap-768	63	159	the	the	DET
ap-768	63	160	set	set	NOUN
ap-768	63	161	x	x	PUNCT
ap-768	63	162	and	and	CCONJ
ap-768	63	163	the	the	DET
ap-768	63	164	corresponding	corresponding	ADJ
ap-768	63	165	equivalence	equivalence	NOUN
ap-768	63	166	classes	class	NOUN
ap-768	63	167	are	be	AUX
ap-768	63	168	orbits	orbit	NOUN
ap-768	63	169	.	.	PUNCT
ap-768	64	1	definition	definition	NOUN
ap-768	64	2	2.2	2.2	NUM
ap-768	64	3	:	:	PUNCT
ap-768	64	4	for	for	ADP
ap-768	64	5	m	m	PROPN
ap-768	64	6	n	n	SYM
ap-768	64	7	,	,	PUNCT
ap-768	64	8	�	�	PROPN
ap-768	64	9	n	n	CCONJ
ap-768	64	10	,	,	PUNCT
ap-768	64	11	n	n	X
ap-768	64	12	�	�	PROPN
ap-768	64	13	2	2	NUM
ap-768	64	14	we	we	PRON
ap-768	64	15	define	define	VERB
ap-768	64	16	a	a	DET
ap-768	64	17	right	right	ADJ
ap-768	64	18	action	action	NOUN
ap-768	64	19	�	�	PROPN
ap-768	64	20	of	of	ADP
ap-768	64	21	the	the	DET
ap-768	64	22	group	group	PROPN
ap-768	64	23	sl(m	sl(m	PROPN
ap-768	64	24	,	,	PUNCT
ap-768	64	25	zn	zn	PROPN
ap-768	64	26	)	)	PUNCT
ap-768	64	27	on	on	ADP
ap-768	64	28	the	the	DET
ap-768	64	29	set	set	NOUN
ap-768	64	30	zn	zn	PROPN
ap-768	64	31	m	m	NOUN
ap-768	64	32	as	as	ADP
ap-768	64	33	right	right	ADJ
ap-768	64	34	multiplication	multiplication	NOUN
ap-768	64	35	of	of	ADP
ap-768	64	36	the	the	DET
ap-768	64	37	row	row	NOUN
ap-768	64	38	vector	vector	NOUN
ap-768	64	39	a	a	DET
ap-768	64	40	n	n	PRON
ap-768	64	41	m	m	NOUN
ap-768	64	42	�	�	PROPN
ap-768	64	43	z	z	PROPN
ap-768	64	44	by	by	ADP
ap-768	64	45	the	the	DET
ap-768	64	46	matrix	matrix	NOUN
ap-768	64	47	a	a	DET
ap-768	64	48	z	z	X
ap-768	64	49	�	�	PROPN
ap-768	64	50	sl	sl	NOUN
ap-768	64	51	m	m	VERB
ap-768	64	52	n	n	CCONJ
ap-768	64	53	(	(	PUNCT
ap-768	64	54	,	,	PUNCT
ap-768	64	55	)	)	PUNCT
ap-768	64	56	modulo	modulo	PROPN
ap-768	64	57	n	n	CCONJ
ap-768	64	58	:	:	PUNCT
ap-768	64	59	�	�	PROPN
ap-768	64	60	(	(	PUNCT
ap-768	64	61	,	,	PUNCT
ap-768	64	62	):	):	PUNCT
ap-768	64	63	(	(	PUNCT
ap-768	64	64	)	)	PUNCT
ap-768	64	65	moda	moda	PROPN
ap-768	64	66	aa	aa	PROPN
ap-768	64	67	a	a	PRON
ap-768	64	68	n	n	X
ap-768	64	69	�	�	PROPN
ap-768	64	70	.	.	PUNCT
ap-768	65	1	henceforth	henceforth	ADV
ap-768	65	2	we	we	PRON
ap-768	65	3	will	will	AUX
ap-768	65	4	omit	omit	VERB
ap-768	65	5	the	the	DET
ap-768	65	6	symbol	symbol	NOUN
ap-768	65	7	mod	mod	PROPN
ap-768	65	8	n	n	PROPN
ap-768	65	9	and	and	CCONJ
ap-768	65	10	write	write	VERB
ap-768	65	11	this	this	DET
ap-768	65	12	action	action	NOUN
ap-768	65	13	simply	simply	ADV
ap-768	65	14	as	as	ADP
ap-768	65	15	aa	aa	NOUN
ap-768	65	16	.	.	PROPN
ap-768	65	17	3	3	NUM
ap-768	65	18	orbits	orbit	NOUN
ap-768	65	19	for	for	ADP
ap-768	65	20	n	n	PRON
ap-768	65	21	�	�	PROPN
ap-768	65	22	p	p	NOUN
ap-768	65	23	prime	prime	ADJ
ap-768	65	24	number	number	NOUN
ap-768	65	25	the	the	DET
ap-768	65	26	purpose	purpose	NOUN
ap-768	65	27	of	of	ADP
ap-768	65	28	this	this	DET
ap-768	65	29	section	section	NOUN
ap-768	65	30	is	be	AUX
ap-768	65	31	to	to	PART
ap-768	65	32	describe	describe	VERB
ap-768	65	33	orbits	orbit	NOUN
ap-768	65	34	of	of	ADP
ap-768	65	35	the	the	DET
ap-768	65	36	ring	ring	NOUN
ap-768	65	37	z	z	PROPN
ap-768	65	38	p	p	X
ap-768	65	39	m	m	NOUN
ap-768	65	40	under	under	ADP
ap-768	65	41	the	the	DET
ap-768	65	42	action	action	NOUN
ap-768	65	43	of	of	ADP
ap-768	65	44	the	the	DET
ap-768	65	45	group	group	NOUN
ap-768	65	46	sl(m	sl(m	PROPN
ap-768	65	47	,	,	PUNCT
ap-768	65	48	zp	zp	PROPN
ap-768	65	49	)	)	PUNCT
ap-768	65	50	,	,	PUNCT
ap-768	65	51	where	where	SCONJ
ap-768	65	52	p	p	NOUN
ap-768	65	53	is	be	AUX
ap-768	65	54	prime	prime	ADJ
ap-768	65	55	.	.	PUNCT
ap-768	66	1	trivially	trivially	ADV
ap-768	66	2	,	,	PUNCT
ap-768	66	3	for	for	ADP
ap-768	66	4	m	m	PROPN
ap-768	66	5	�	�	PROPN
ap-768	66	6	1	1	NUM
ap-768	66	7	is	be	AUX
ap-768	66	8	sl(1	sl(1	NOUN
ap-768	66	9	,	,	PUNCT
ap-768	66	10	zp	zp	NOUN
ap-768	66	11	)	)	PUNCT
ap-768	66	12	�	�	PROPN
ap-768	66	13	{	{	PUNCT
ap-768	66	14	(	(	PUNCT
ap-768	66	15	1	1	NUM
ap-768	66	16	)	)	PUNCT
ap-768	66	17	}	}	PUNCT
ap-768	66	18	and	and	CCONJ
ap-768	66	19	any	any	DET
ap-768	66	20	orbit	orbit	NOUN
ap-768	66	21	has	have	VERB
ap-768	66	22	the	the	DET
ap-768	66	23	form	form	NOUN
ap-768	66	24	{	{	PUNCT
ap-768	66	25	a	a	NOUN
ap-768	66	26	}	}	PUNCT
ap-768	66	27	for	for	ADP
ap-768	66	28	a	a	DET
ap-768	66	29	p	p	X
ap-768	66	30	�	�	PROPN
ap-768	66	31	z	z	PROPN
ap-768	66	32	.	.	PUNCT
ap-768	67	1	consequently	consequently	ADV
ap-768	67	2	we	we	PRON
ap-768	67	3	will	will	AUX
ap-768	67	4	further	far	ADV
ap-768	67	5	consider	consider	VERB
ap-768	67	6	m	m	NOUN
ap-768	67	7	�	�	PROPN
ap-768	67	8	2	2	NUM
ap-768	67	9	.	.	PUNCT
ap-768	68	1	it	it	PRON
ap-768	68	2	is	be	AUX
ap-768	68	3	clear	clear	ADJ
ap-768	68	4	that	that	SCONJ
ap-768	68	5	the	the	DET
ap-768	68	6	zero	zero	NUM
ap-768	68	7	element	element	NOUN
ap-768	68	8	can	can	AUX
ap-768	68	9	be	be	AUX
ap-768	68	10	transformed	transform	VERB
ap-768	68	11	by	by	ADP
ap-768	68	12	the	the	DET
ap-768	68	13	action	action	NOUN
ap-768	68	14	of	of	ADP
ap-768	68	15	sl(m	sl(m	PROPN
ap-768	68	16	,	,	PUNCT
ap-768	68	17	zp	zp	PROPN
ap-768	68	18	)	)	PUNCT
ap-768	68	19	to	to	ADP
ap-768	68	20	itself	itself	PRON
ap-768	68	21	only	only	ADV
ap-768	68	22	,	,	PUNCT
ap-768	68	23	thus	thus	ADV
ap-768	68	24	it	it	PRON
ap-768	68	25	forms	form	VERB
ap-768	68	26	a	a	DET
ap-768	68	27	one	one	NUM
ap-768	68	28	-	-	PUNCT
ap-768	68	29	point	point	NOUN
ap-768	68	30	orbit	orbit	NOUN
ap-768	68	31	and	and	CCONJ
ap-768	68	32	its	its	PRON
ap-768	68	33	stability	stability	NOUN
ap-768	68	34	subgroup	subgroup	NOUN
ap-768	68	35	is	be	AUX
ap-768	68	36	the	the	DET
ap-768	68	37	whole	whole	ADJ
ap-768	68	38	sl(m	sl(m	PROPN
ap-768	68	39	,	,	PUNCT
ap-768	68	40	zp	zp	PROPN
ap-768	68	41	)	)	PUNCT
ap-768	68	42	.	.	PUNCT
ap-768	69	1	let	let	VERB
ap-768	69	2	us	we	PRON
ap-768	69	3	take	take	VERB
ap-768	69	4	a	a	DET
ap-768	69	5	nonzero	nonzero	NOUN
ap-768	69	6	element	element	NOUN
ap-768	69	7	,	,	PUNCT
ap-768	69	8	for	for	ADP
ap-768	69	9	instance	instance	NOUN
ap-768	69	10	(	(	PUNCT
ap-768	69	11	,	,	PUNCT
ap-768	69	12	,	,	PUNCT
ap-768	69	13	,	,	PUNCT
ap-768	69	14	)	)	PUNCT
ap-768	69	15	0	0	SYM
ap-768	69	16	0	0	NUM
ap-768	69	17	1	1	NUM
ap-768	69	18	�	�	PROPN
ap-768	69	19	�	�	PROPN
ap-768	69	20	z	z	PROPN
ap-768	69	21	p	p	NOUN
ap-768	69	22	m	m	PROPN
ap-768	69	23	,	,	PUNCT
ap-768	69	24	and	and	CCONJ
ap-768	69	25	find	find	VERB
ap-768	69	26	its	its	PRON
ap-768	69	27	orbit	orbit	NOUN
ap-768	69	28	.	.	PUNCT
ap-768	70	1	an	an	DET
ap-768	70	2	arbitrary	arbitrary	ADJ
ap-768	70	3	matrix	matrix	NOUN
ap-768	70	4	a	a	PRON
ap-768	70	5	from	from	ADP
ap-768	70	6	sl(m	sl(m	PROPN
ap-768	70	7	,	,	PUNCT
ap-768	70	8	zp	zp	NOUN
ap-768	70	9	)	)	PUNCT
ap-768	70	10	acts	act	VERB
ap-768	70	11	on	on	ADP
ap-768	70	12	this	this	DET
ap-768	70	13	element	element	NOUN
ap-768	70	14	as	as	SCONJ
ap-768	70	15	follows	follow	VERB
ap-768	70	16	(	(	PUNCT
ap-768	70	17	,	,	PUNCT
ap-768	70	18	,	,	PUNCT
ap-768	70	19	,	,	PUNCT
ap-768	70	20	)	)	PUNCT
ap-768	70	21	,	,	PUNCT
ap-768	70	22	,	,	PUNCT
ap-768	70	23	,	,	PUNCT
ap-768	70	24	,	,	PUNCT
ap-768	70	25	,	,	PUNCT
ap-768	70	26	,	,	PUNCT
ap-768	70	27	,	,	PUNCT
ap-768	70	28	0	0	NUM
ap-768	70	29	0	0	NUM
ap-768	70	30	1	1	NUM
ap-768	70	31	1	1	NUM
ap-768	70	32	1	1	NUM
ap-768	70	33	1	1	NUM
ap-768	70	34	2	2	NUM
ap-768	70	35	1	1	NUM
ap-768	70	36	1	1	NUM
ap-768	70	37	1	1	NUM
ap-768	70	38	1	1	NUM
ap-768	70	39	2	2	NUM
ap-768	70	40	1	1	NUM
ap-768	70	41	1	1	NUM
ap-768	70	42	�	�	PROPN
ap-768	70	43	�	�	PROPN
ap-768	70	44	�	�	PROPN
ap-768	70	45	�	�	PROPN
ap-768	70	46	�	�	PROPN
ap-768	70	47	�	�	PROPN
ap-768	70	48	�	�	PROPN
ap-768	70	49	a	a	DET
ap-768	70	50	a	a	DET
ap-768	70	51	a	a	DET
ap-768	70	52	a	a	DET
ap-768	70	53	a	a	DET
ap-768	70	54	a	a	DET
ap-768	70	55	a	a	DET
ap-768	70	56	a	a	DET
ap-768	70	57	m	m	NOUN
ap-768	70	58	m	m	VERB
ap-768	70	59	m	m	VERB
ap-768	70	60	m	m	VERB
ap-768	70	61	m	m	VERB
ap-768	70	62	m	m	PROPN
ap-768	70	63	�	�	PROPN
ap-768	70	64	�	�	PROPN
ap-768	70	65	�	�	PROPN
ap-768	70	66	m	m	VERB
ap-768	70	67	m	m	VERB
ap-768	70	68	m	m	VERB
ap-768	70	69	m	m	VERB
ap-768	70	70	m	m	VERB
ap-768	70	71	m	m	VERB
ap-768	70	72	m	m	VERB
ap-768	70	73	a	a	DET
ap-768	70	74	a	a	DET
ap-768	70	75	a	a	DET
ap-768	70	76	a	a	DET
ap-768	70	77	p	p	NOUN
ap-768	70	78	,	,	PUNCT
ap-768	70	79	,	,	PUNCT
ap-768	70	80	,	,	PUNCT
ap-768	70	81	,	,	PUNCT
ap-768	70	82	,	,	PUNCT
ap-768	70	83	(	(	PUNCT
ap-768	70	84	,	,	PUNCT
ap-768	70	85	,	,	PUNCT
ap-768	70	86	)	)	PUNCT
ap-768	70	87	(	(	PUNCT
ap-768	70	88	mod	mod	PROPN
ap-768	70	89	)	)	PUNCT
ap-768	70	90	.	.	PUNCT
ap-768	71	1	2	2	NUM
ap-768	71	2	1	1	NUM
ap-768	71	3	2	2	NUM
ap-768	71	4	�	�	PROPN
ap-768	71	5	�	�	PROPN
ap-768	71	6	�	�	PROPN
ap-768	71	7	�	�	PROPN
ap-768	71	8	�	�	PROPN
ap-768	71	9	�	�	PROPN
ap-768	71	10	�	�	PROPN
ap-768	71	11	�	�	PROPN
ap-768	71	12	�	�	PROPN
ap-768	71	13	�	�	PROPN
ap-768	71	14	�	�	PROPN
ap-768	71	15	�	�	PROPN
ap-768	71	16	�	�	PROPN
ap-768	71	17	�	�	PROPN
ap-768	71	18	�	�	PROPN
ap-768	71	19	�	�	PROPN
ap-768	71	20	thus	thus	ADV
ap-768	71	21	the	the	DET
ap-768	71	22	orbit	orbit	NOUN
ap-768	71	23	of	of	ADP
ap-768	71	24	element	element	NOUN
ap-768	71	25	(	(	PUNCT
ap-768	71	26	,	,	PUNCT
ap-768	71	27	,	,	PUNCT
ap-768	71	28	,	,	PUNCT
ap-768	71	29	)	)	PUNCT
ap-768	71	30	0	0	SYM
ap-768	71	31	0	0	NUM
ap-768	71	32	1	1	NUM
ap-768	71	33	�	�	PROPN
ap-768	71	34	contains	contain	VERB
ap-768	71	35	the	the	DET
ap-768	71	36	last	last	ADJ
ap-768	71	37	row	row	NOUN
ap-768	71	38	of	of	ADP
ap-768	71	39	any	any	DET
ap-768	71	40	matrix	matrix	NOUN
ap-768	71	41	from	from	ADP
ap-768	71	42	sl(m	sl(m	PROPN
ap-768	71	43	,	,	PUNCT
ap-768	71	44	zp	zp	PROPN
ap-768	71	45	)	)	PUNCT
ap-768	71	46	.	.	PUNCT
ap-768	72	1	it	it	PRON
ap-768	72	2	follows	follow	VERB
ap-768	72	3	from	from	ADP
ap-768	72	4	det(a	det(a	PROPN
ap-768	72	5	)	)	PUNCT
ap-768	72	6	�	�	PROPN
ap-768	72	7	1	1	NUM
ap-768	72	8	that	that	SCONJ
ap-768	72	9	these	these	DET
ap-768	72	10	rows	row	NOUN
ap-768	72	11	can	can	AUX
ap-768	72	12	not	not	PART
ap-768	72	13	be	be	AUX
ap-768	72	14	zero	zero	NUM
ap-768	72	15	and	and	CCONJ
ap-768	72	16	we	we	PRON
ap-768	72	17	show	show	VERB
ap-768	72	18	that	that	SCONJ
ap-768	72	19	they	they	PRON
ap-768	72	20	can	can	AUX
ap-768	72	21	be	be	AUX
ap-768	72	22	equal	equal	ADJ
ap-768	72	23	to	to	ADP
ap-768	72	24	an	an	DET
ap-768	72	25	arbitrary	arbitrary	ADJ
ap-768	72	26	nonzero	nonzero	NOUN
ap-768	72	27	element	element	NOUN
ap-768	72	28	from	from	ADP
ap-768	72	29	z	z	PROPN
ap-768	72	30	p	p	PROPN
ap-768	72	31	m.	m.	NOUN
ap-768	72	32	let	let	VERB
ap-768	72	33	(	(	PUNCT
ap-768	72	34	,	,	PUNCT
ap-768	72	35	,	,	PUNCT
ap-768	72	36	)	)	PUNCT
ap-768	72	37	,	,	PUNCT
ap-768	72	38	,	,	PUNCT
ap-768	72	39	,	,	PUNCT
ap-768	72	40	a	a	DET
ap-768	72	41	a	a	DET
ap-768	72	42	am	am	NOUN
ap-768	72	43	m	m	VERB
ap-768	72	44	m	m	VERB
ap-768	72	45	m	m	ADJ
ap-768	72	46	p	p	NOUN
ap-768	72	47	m	m	PROPN
ap-768	72	48	1	1	NUM
ap-768	72	49	2	2	NUM
ap-768	72	50	�	�	PROPN
ap-768	72	51	�	�	PROPN
ap-768	72	52	z	z	PROPN
ap-768	72	53	be	be	AUX
ap-768	72	54	a	a	DET
ap-768	72	55	nonzero	nonzero	NOUN
ap-768	72	56	element	element	NOUN
ap-768	72	57	,	,	PUNCT
ap-768	72	58	which	which	PRON
ap-768	72	59	means	mean	VERB
ap-768	72	60	�	�	PROPN
ap-768	72	61	�	�	PROPN
ap-768	72	62	j	j	PROPN
ap-768	72	63	m	m	PRON
ap-768	72	64	{	{	PUNCT
ap-768	72	65	,	,	PUNCT
ap-768	72	66	,	,	PUNCT
ap-768	72	67	,	,	PUNCT
ap-768	72	68	}	}	PUNCT
ap-768	72	69	1	1	NUM
ap-768	72	70	2	2	NUM
ap-768	72	71	�	�	NOUN
ap-768	72	72	such	such	ADJ
ap-768	72	73	that	that	SCONJ
ap-768	72	74	amj	amj	PROPN
ap-768	72	75	�	�	PROPN
ap-768	72	76	0	0	NUM
ap-768	72	77	,	,	PUNCT
ap-768	72	78	then	then	ADV
ap-768	72	79	matrix	matrix	VERB
ap-768	72	80	a	a	PRON
ap-768	72	81	can	can	AUX
ap-768	72	82	be	be	AUX
ap-768	72	83	chosen	choose	VERB
ap-768	72	84	with	with	ADP
ap-768	72	85	the	the	DET
ap-768	72	86	determinant	determinant	ADJ
ap-768	72	87	equal	equal	ADJ
ap-768	72	88	to	to	ADP
ap-768	72	89	1	1	NUM
ap-768	72	90	.	.	PUNCT
ap-768	73	1	without	without	ADP
ap-768	73	2	loss	loss	NOUN
ap-768	73	3	of	of	ADP
ap-768	73	4	generality	generality	NOUN
ap-768	73	5	consider	consider	VERB
ap-768	73	6	j	j	PROPN
ap-768	73	7	�	�	PROPN
ap-768	73	8	1	1	NUM
ap-768	73	9	:	:	PUNCT
ap-768	73	10	a	a	DET
ap-768	73	11	b	b	PROPN
ap-768	73	12	�	�	PROPN
ap-768	73	13	�	�	PROPN
ap-768	73	14	�	�	PROPN
ap-768	73	15	�	�	PROPN
ap-768	73	16	�	�	PROPN
ap-768	73	17	�	�	PROPN
ap-768	73	18	�	�	PROPN
ap-768	73	19	�	�	PROPN
ap-768	73	20	�	�	PROPN
ap-768	73	21	�	�	PROPN
ap-768	73	22	�	�	PROPN
ap-768	73	23	�	�	PROPN
ap-768	73	24	�	�	PROPN
ap-768	73	25	0	0	NUM
ap-768	73	26	0	0	NUM
ap-768	73	27	1	1	NUM
ap-768	73	28	2	2	NUM
ap-768	73	29	�	�	PROPN
ap-768	73	30	�	�	PROPN
ap-768	73	31	a	a	PRON
ap-768	73	32	a	a	DET
ap-768	73	33	am	am	NOUN
ap-768	73	34	m	m	NOUN
ap-768	73	35	m	m	NOUN
ap-768	73	36	m	m	ADJ
ap-768	73	37	,	,	PUNCT
ap-768	73	38	,	,	PUNCT
ap-768	73	39	,	,	PUNCT
ap-768	73	40	,	,	PUNCT
ap-768	73	41	where	where	SCONJ
ap-768	73	42	�	�	PROPN
ap-768	73	43	�	�	PROPN
ap-768	73	44	b	b	PROPN
ap-768	73	45	�	�	PROPN
ap-768	73	46	�	�	PROPN
ap-768	73	47	�	�	PROPN
ap-768	73	48	�	�	PROPN
ap-768	73	49	diag	diag	NOUN
ap-768	73	50	1	1	NUM
ap-768	73	51	1	1	NUM
ap-768	73	52	1	1	NUM
ap-768	73	53	1	1	NUM
ap-768	73	54	1	1	NUM
ap-768	73	55	1	1	NUM
ap-768	73	56	,	,	PUNCT
ap-768	73	57	,	,	PUNCT
ap-768	73	58	,	,	PUNCT
ap-768	73	59	(	(	PUNCT
ap-768	73	60	)	)	PUNCT
ap-768	73	61	(	(	PUNCT
ap-768	73	62	)	)	PUNCT
ap-768	73	63	,	,	PUNCT
ap-768	73	64	�	�	PROPN
ap-768	73	65	m	m	PROPN
ap-768	73	66	ma	ma	PROPN
ap-768	73	67	.	.	PUNCT
ap-768	74	1	here	here	ADV
ap-768	74	2	(	(	PUNCT
ap-768	74	3	am,1)	am,1)	PROPN
ap-768	74	4	�	�	NOUN
ap-768	74	5	1	1	NUM
ap-768	74	6	denotes	denote	VERB
ap-768	74	7	the	the	DET
ap-768	74	8	inverse	inverse	NOUN
ap-768	74	9	element	element	NOUN
ap-768	74	10	to	to	ADP
ap-768	74	11	am,1	am,1	PROPN
ap-768	74	12	in	in	ADP
ap-768	74	13	the	the	DET
ap-768	74	14	field	field	NOUN
ap-768	74	15	zp	zp	X
ap-768	74	16	.	.	PUNCT
ap-768	75	1	we	we	PRON
ap-768	75	2	conclude	conclude	VERB
ap-768	75	3	that	that	SCONJ
ap-768	75	4	in	in	ADP
ap-768	75	5	the	the	DET
ap-768	75	6	case	case	NOUN
ap-768	75	7	of	of	ADP
ap-768	75	8	n	n	PRON
ap-768	75	9	�	�	PROPN
ap-768	75	10	p	p	PROPN
ap-768	75	11	prime	prime	NOUN
ap-768	75	12	there	there	PRON
ap-768	75	13	are	be	VERB
ap-768	75	14	only	only	ADV
ap-768	75	15	two	two	NUM
ap-768	75	16	orbits	orbit	NOUN
ap-768	75	17	:	:	PUNCT
ap-768	75	18	1	1	X
ap-768	75	19	.	.	X
ap-768	75	20	one	one	NUM
ap-768	75	21	-	-	PUNCT
ap-768	75	22	point	point	NOUN
ap-768	75	23	orbit	orbit	NOUN
ap-768	75	24	represented	represent	VERB
ap-768	75	25	by	by	ADP
ap-768	75	26	the	the	DET
ap-768	75	27	zero	zero	NUM
ap-768	75	28	element	element	NOUN
ap-768	75	29	(	(	PUNCT
ap-768	75	30	0	0	NUM
ap-768	75	31	,	,	PUNCT
ap-768	75	32	…	…	PUNCT
ap-768	75	33	,	,	PUNCT
ap-768	75	34	0	0	NUM
ap-768	75	35	,	,	PUNCT
ap-768	75	36	0	0	NUM
ap-768	75	37	)	)	PUNCT
ap-768	75	38	2	2	NUM
ap-768	75	39	.	.	PUNCT
ap-768	76	1	(	(	PUNCT
ap-768	76	2	pm	pm	NOUN
ap-768	76	3	�	�	NOUN
ap-768	76	4	1)-point	1)-point	NUM
ap-768	76	5	orbit	orbit	NOUN
ap-768	76	6	z	z	PROPN
ap-768	76	7	p	p	NOUN
ap-768	76	8	m\{0	m\{0	PROPN
ap-768	76	9	}	}	PUNCT
ap-768	76	10	represented	represent	VERB
ap-768	76	11	by	by	ADP
ap-768	76	12	the	the	DET
ap-768	76	13	element	element	NOUN
ap-768	76	14	(	(	PUNCT
ap-768	76	15	0	0	NUM
ap-768	76	16	,	,	PUNCT
ap-768	76	17	…	…	PUNCT
ap-768	76	18	,	,	PUNCT
ap-768	76	19	0	0	NUM
ap-768	76	20	,	,	PUNCT
ap-768	76	21	1	1	NUM
ap-768	76	22	)	)	PUNCT
ap-768	76	23	4	4	NUM
ap-768	76	24	orbits	orbit	NOUN
ap-768	76	25	for	for	ADP
ap-768	76	26	n	n	CCONJ
ap-768	76	27	natural	natural	ADJ
ap-768	76	28	number	number	NOUN
ap-768	76	29	we	we	PRON
ap-768	76	30	consider	consider	VERB
ap-768	76	31	an	an	DET
ap-768	76	32	arbitrary	arbitrary	ADJ
ap-768	76	33	natural	natural	ADJ
ap-768	76	34	number	number	NOUN
ap-768	76	35	n	n	NUM
ap-768	76	36	of	of	ADP
ap-768	76	37	the	the	DET
ap-768	76	38	form	form	NOUN
ap-768	76	39	n	n	PRON
ap-768	76	40	pi	pi	NOUN
ap-768	77	1	k	k	INTJ
ap-768	78	1	i	i	PRON
ap-768	78	2	r	r	VERB
ap-768	78	3	i	i	PRON
ap-768	78	4	�	�	PROPN
ap-768	78	5	�	�	PROPN
ap-768	78	6	1	1	NUM
ap-768	78	7	,	,	PUNCT
ap-768	78	8	where	where	SCONJ
ap-768	78	9	pi	pi	NOUN
ap-768	78	10	are	be	AUX
ap-768	78	11	distinct	distinct	ADJ
ap-768	78	12	primes	prime	NOUN
ap-768	78	13	and	and	CCONJ
ap-768	78	14	ki	ki	PROPN
ap-768	78	15	are	be	AUX
ap-768	78	16	natural	natural	ADJ
ap-768	78	17	numbers	number	NOUN
ap-768	78	18	.	.	PUNCT
ap-768	79	1	the	the	DET
ap-768	79	2	action	action	NOUN
ap-768	79	3	of	of	ADP
ap-768	79	4	the	the	DET
ap-768	79	5	group	group	NOUN
ap-768	79	6	sl(m	sl(m	PROPN
ap-768	79	7	,	,	PUNCT
ap-768	79	8	zn	zn	PROPN
ap-768	79	9	)	)	PUNCT
ap-768	79	10	on	on	ADP
ap-768	79	11	the	the	DET
ap-768	79	12	ring	ring	NOUN
ap-768	79	13	zn	zn	PROPN
ap-768	79	14	m	m	PROPN
ap-768	79	15	was	be	AUX
ap-768	79	16	established	establish	VERB
ap-768	79	17	in	in	ADP
ap-768	79	18	definition	definition	NOUN
ap-768	79	19	2.2	2.2	NUM
ap-768	79	20	as	as	ADP
ap-768	79	21	a	a	DET
ap-768	79	22	right	right	ADJ
ap-768	79	23	multiplication	multiplication	NOUN
ap-768	79	24	of	of	ADP
ap-768	79	25	a	a	DET
ap-768	79	26	row	row	NOUN
ap-768	79	27	vector	vector	NOUN
ap-768	79	28	from	from	ADP
ap-768	79	29	zn	zn	PROPN
ap-768	79	30	m	m	VERB
ap-768	79	31	by	by	ADP
ap-768	79	32	a	a	DET
ap-768	79	33	matrix	matrix	NOUN
ap-768	79	34	from	from	ADP
ap-768	79	35	sl(m	sl(m	PROPN
ap-768	79	36	,	,	PUNCT
ap-768	79	37	zn	zn	X
ap-768	79	38	)	)	PUNCT
ap-768	79	39	modulo	modulo	PROPN
ap-768	79	40	n.	n.	NOUN
ap-768	79	41	we	we	PRON
ap-768	79	42	define	define	VERB
ap-768	79	43	an	an	DET
ap-768	79	44	equivalence	equivalence	NOUN
ap-768	79	45	induced	induce	VERB
ap-768	79	46	by	by	ADP
ap-768	79	47	this	this	DET
ap-768	79	48	action	action	NOUN
ap-768	79	49	on	on	ADP
ap-768	79	50	the	the	DET
ap-768	79	51	ring	ring	NOUN
ap-768	79	52	zn	zn	PROPN
ap-768	79	53	m	m	VERB
ap-768	79	54	according	accord	VERB
ap-768	79	55	to	to	ADP
ap-768	79	56	(	(	PUNCT
ap-768	79	57	2.4	2.4	NUM
ap-768	79	58	)	)	PUNCT
ap-768	79	59	.	.	PUNCT
ap-768	80	1	elements	element	NOUN
ap-768	80	2	a	a	DET
ap-768	80	3	a	a	DET
ap-768	80	4	a	a	DET
ap-768	80	5	am	am	NOUN
ap-768	80	6	�	�	NOUN
ap-768	80	7	(	(	PUNCT
ap-768	80	8	,	,	PUNCT
ap-768	80	9	,	,	PUNCT
ap-768	80	10	,	,	PUNCT
ap-768	80	11	)	)	PUNCT
ap-768	80	12	1	1	NUM
ap-768	80	13	2	2	NUM
ap-768	80	14	�	�	PROPN
ap-768	80	15	,	,	PUNCT
ap-768	80	16	b	b	PROPN
ap-768	80	17	b	b	PROPN
ap-768	80	18	b	b	X
ap-768	80	19	bm	bm	PROPN
ap-768	80	20	n	n	PROPN
ap-768	80	21	m	m	PROPN
ap-768	80	22	�	�	PROPN
ap-768	80	23	�	�	PROPN
ap-768	80	24	(	(	PUNCT
ap-768	80	25	,	,	PUNCT
ap-768	80	26	,	,	PUNCT
ap-768	80	27	,	,	PUNCT
ap-768	80	28	)	)	PUNCT
ap-768	80	29	1	1	NUM
ap-768	80	30	2	2	NUM
ap-768	80	31	�	�	PROPN
ap-768	80	32	z	z	NOUN
ap-768	80	33	are	be	AUX
ap-768	80	34	equivalent	equivalent	ADJ
ap-768	80	35	a	a	PRON
ap-768	80	36	~	~	NOUN
ap-768	80	37	b	b	NOUN
ap-768	80	38	if	if	SCONJ
ap-768	80	39	and	and	CCONJ
ap-768	80	40	only	only	ADV
ap-768	80	41	if	if	SCONJ
ap-768	80	42	there	there	PRON
ap-768	80	43	exists	exist	VERB
ap-768	80	44	a	a	DET
ap-768	80	45	z	z	PROPN
ap-768	80	46	�	�	PROPN
ap-768	80	47	sl	sl	NOUN
ap-768	80	48	m	m	VERB
ap-768	80	49	n	n	CCONJ
ap-768	80	50	(	(	PUNCT
ap-768	80	51	,	,	PUNCT
ap-768	80	52	)	)	PUNCT
ap-768	81	1	such	such	ADJ
ap-768	81	2	that	that	SCONJ
ap-768	81	3	aa	aa	PROPN
ap-768	81	4	�	�	PROPN
ap-768	81	5	b	b	PROPN
ap-768	81	6	i.e.	i.e.	X
ap-768	81	7	a	a	DET
ap-768	81	8	a	a	DET
ap-768	81	9	b	b	NOUN
ap-768	81	10	n	n	NOUN
ap-768	81	11	i	i	PRON
ap-768	81	12	mj	mj	VERB
ap-768	81	13	i	i	PRON
ap-768	82	1	j	j	PROPN
ap-768	83	1	i	i	PRON
ap-768	83	2	j	j	PROPN
ap-768	83	3	m	m	VERB
ap-768	83	4	,	,	PUNCT
ap-768	83	5	(	(	PUNCT
ap-768	83	6	mod	mod	PROPN
ap-768	83	7	)	)	PUNCT
ap-768	83	8	,	,	PUNCT
ap-768	83	9	{	{	PUNCT
ap-768	83	10	,	,	PUNCT
ap-768	83	11	,	,	PUNCT
ap-768	83	12	,	,	PUNCT
ap-768	83	13	}	}	PUNCT
ap-768	83	14	�	�	PROPN
ap-768	83	15	�	�	PROPN
ap-768	83	16	�	�	PROPN
ap-768	83	17	�	�	PROPN
ap-768	83	18	�	�	PROPN
ap-768	83	19	1	1	NUM
ap-768	83	20	1	1	NUM
ap-768	83	21	2	2	NUM
ap-768	83	22	�	�	NOUN
ap-768	83	23	.	.	PUNCT
ap-768	84	1	(	(	PUNCT
ap-768	84	2	4.1	4.1	NUM
ap-768	84	3	)	)	PUNCT
ap-768	84	4	definition	definition	NOUN
ap-768	84	5	4.1	4.1	NUM
ap-768	84	6	:	:	PUNCT
ap-768	84	7	let	let	VERB
ap-768	84	8	~	~	PUNCT
ap-768	84	9	be	be	AUX
ap-768	84	10	the	the	DET
ap-768	84	11	equivalence	equivalence	NOUN
ap-768	84	12	on	on	ADP
ap-768	84	13	zn	zn	PROPN
ap-768	84	14	m	m	AUX
ap-768	84	15	defined	define	VERB
ap-768	84	16	by	by	ADP
ap-768	84	17	(	(	PUNCT
ap-768	84	18	4.1	4.1	NUM
ap-768	84	19	)	)	PUNCT
ap-768	84	20	.	.	PUNCT
ap-768	85	1	for	for	ADP
ap-768	85	2	any	any	DET
ap-768	85	3	divisor	divisor	NOUN
ap-768	85	4	d	d	PROPN
ap-768	85	5	of	of	ADP
ap-768	85	6	n	n	CCONJ
ap-768	85	7	,	,	PUNCT
ap-768	85	8	we	we	PRON
ap-768	85	9	will	will	AUX
ap-768	85	10	denote	denote	VERB
ap-768	85	11	by	by	ADP
ap-768	85	12	orm	orm	NOUN
ap-768	85	13	,	,	PUNCT
ap-768	85	14	n(d	n(d	PROPN
ap-768	85	15	)	)	PUNCT
ap-768	85	16	the	the	DET
ap-768	85	17	class	class	NOUN
ap-768	85	18	of	of	ADP
ap-768	85	19	equivalence	equivalence	NOUN
ap-768	85	20	(	(	PUNCT
ap-768	85	21	orbit	orbit	NOUN
ap-768	85	22	)	)	PUNCT
ap-768	85	23	containing	contain	VERB
ap-768	85	24	the	the	DET
ap-768	85	25	point	point	NOUN
ap-768	85	26	(	(	PUNCT
ap-768	85	27	0	0	NUM
ap-768	85	28	,	,	PUNCT
ap-768	85	29	…	…	PUNCT
ap-768	85	30	,	,	PUNCT
ap-768	85	31	0	0	NUM
ap-768	85	32	,	,	PUNCT
ap-768	85	33	(	(	PUNCT
ap-768	85	34	d)mod	d)mod	NOUN
ap-768	85	35	n	n	CCONJ
ap-768	85	36	)	)	PUNCT
ap-768	85	37	,	,	PUNCT
ap-768	85	38	i.e.	i.e.	X
ap-768	85	39	or	or	CCONJ
ap-768	85	40	zm	zm	PROPN
ap-768	85	41	n	n	PROPN
ap-768	85	42	n	n	PROPN
ap-768	85	43	m	m	VERB
ap-768	85	44	nd	nd	ADV
ap-768	85	45	a	a	DET
ap-768	85	46	a	a	PROPN
ap-768	85	47	d	d	PROPN
ap-768	85	48	,	,	PUNCT
ap-768	85	49	mod	mod	X
ap-768	85	50	(	(	PUNCT
ap-768	85	51	)	)	PUNCT
ap-768	85	52	{	{	PUNCT
ap-768	86	1	|	|	ADV
ap-768	86	2	~	~	PUNCT
ap-768	86	3	(	(	PUNCT
ap-768	86	4	,	,	PUNCT
ap-768	86	5	,	,	PUNCT
ap-768	86	6	(	(	PUNCT
ap-768	86	7	)	)	PUNCT
ap-768	86	8	)	)	PUNCT
ap-768	86	9	}	}	PUNCT
ap-768	86	10	�	�	PROPN
ap-768	86	11	�	�	PROPN
ap-768	86	12	0	0	NUM
ap-768	86	13	�	�	PROPN
ap-768	86	14	.	.	PUNCT
ap-768	87	1	(	(	PUNCT
ap-768	87	2	4.2	4.2	X
ap-768	87	3	)	)	PUNCT
ap-768	87	4	note	note	VERB
ap-768	87	5	that	that	SCONJ
ap-768	87	6	the	the	DET
ap-768	87	7	orbit	orbit	NOUN
ap-768	87	8	orm	orm	NOUN
ap-768	87	9	,	,	PUNCT
ap-768	87	10	n(n	n(n	NUM
ap-768	87	11	)	)	PUNCT
ap-768	87	12	contains	contain	VERB
ap-768	87	13	only	only	ADV
ap-768	87	14	the	the	DET
ap-768	87	15	zero	zero	NUM
ap-768	87	16	vector	vector	NOUN
ap-768	87	17	,	,	PUNCT
ap-768	87	18	because	because	SCONJ
ap-768	87	19	the	the	DET
ap-768	87	20	zero	zero	NUM
ap-768	87	21	vector	vector	NOUN
ap-768	87	22	can	can	AUX
ap-768	87	23	be	be	AUX
ap-768	87	24	transformed	transform	VERB
ap-768	87	25	by	by	ADP
ap-768	87	26	the	the	DET
ap-768	87	27	action	action	NOUN
ap-768	87	28	of	of	ADP
ap-768	87	29	sl(m	sl(m	PROPN
ap-768	87	30	,	,	PUNCT
ap-768	87	31	zn	zn	PROPN
ap-768	87	32	)	)	PUNCT
ap-768	87	33	only	only	ADV
ap-768	87	34	to	to	ADP
ap-768	87	35	itself	itself	PRON
ap-768	87	36	.	.	PUNCT
ap-768	88	1	we	we	PRON
ap-768	88	2	shall	shall	AUX
ap-768	88	3	see	see	VERB
ap-768	88	4	later	later	ADV
ap-768	88	5	that	that	SCONJ
ap-768	88	6	any	any	DET
ap-768	88	7	orbit	orbit	NOUN
ap-768	88	8	in	in	ADP
ap-768	88	9	zn	zn	PROPN
ap-768	88	10	m	m	VERB
ap-768	88	11	has	have	VERB
ap-768	88	12	the	the	DET
ap-768	88	13	form	form	NOUN
ap-768	88	14	(	(	PUNCT
ap-768	88	15	4.2	4.2	NUM
ap-768	88	16	)	)	PUNCT
ap-768	88	17	.	.	PUNCT
ap-768	89	1	definition	definition	NOUN
ap-768	89	2	4.2	4.2	NUM
ap-768	89	3	:	:	PUNCT
ap-768	89	4	a	a	DET
ap-768	89	5	greatest	great	ADJ
ap-768	89	6	common	common	ADJ
ap-768	89	7	divisor	divisor	NOUN
ap-768	89	8	of	of	ADP
ap-768	89	9	the	the	DET
ap-768	89	10	element	element	NOUN
ap-768	89	11	a	a	DET
ap-768	89	12	a	a	DET
ap-768	89	13	a	a	DET
ap-768	89	14	am	am	NOUN
ap-768	89	15	n	n	PRON
ap-768	89	16	m	m	PROPN
ap-768	89	17	�	�	PROPN
ap-768	89	18	�	�	PROPN
ap-768	89	19	(	(	PUNCT
ap-768	89	20	,	,	PUNCT
ap-768	89	21	,	,	PUNCT
ap-768	89	22	,	,	PUNCT
ap-768	89	23	)	)	PUNCT
ap-768	89	24	1	1	NUM
ap-768	89	25	2	2	NUM
ap-768	89	26	�	�	PROPN
ap-768	89	27	z	z	PROPN
ap-768	89	28	and	and	CCONJ
ap-768	89	29	the	the	DET
ap-768	89	30	number	number	NOUN
ap-768	89	31	n	n	PRON
ap-768	89	32	�	�	NOUN
ap-768	89	33	n	n	PART
ap-768	89	34	is	be	AUX
ap-768	89	35	the	the	DET
ap-768	89	36	greatest	great	ADJ
ap-768	89	37	common	common	ADJ
ap-768	89	38	divisor	divisor	NOUN
ap-768	89	39	of	of	ADP
ap-768	89	40	all	all	DET
ap-768	89	41	components	component	NOUN
ap-768	89	42	of	of	ADP
ap-768	89	43	the	the	DET
ap-768	89	44	element	element	NOUN
ap-768	89	45	a	a	PRON
ap-768	89	46	and	and	CCONJ
ap-768	89	47	the	the	DET
ap-768	89	48	number	number	NOUN
ap-768	89	49	n	n	NOUN
ap-768	89	50	in	in	ADP
ap-768	89	51	the	the	DET
ap-768	89	52	ring	ring	NOUN
ap-768	89	53	of	of	ADP
ap-768	89	54	integers	integer	NOUN
ap-768	89	55	z.	z.	PROPN
ap-768	89	56	we	we	PRON
ap-768	89	57	denote	denote	VERB
ap-768	89	58	it	it	PRON
ap-768	89	59	by	by	ADP
ap-768	89	60	gcd	gcd	PROPN
ap-768	89	61	(	(	PUNCT
ap-768	89	62	,	,	PUNCT
ap-768	89	63	):	):	PUNCT
ap-768	89	64	gcd	gcd	PROPN
ap-768	89	65	(	(	PUNCT
ap-768	89	66	,	,	PUNCT
ap-768	89	67	,	,	PUNCT
ap-768	89	68	,	,	PUNCT
ap-768	89	69	,	,	PUNCT
ap-768	89	70	)	)	PUNCT
ap-768	89	71	a	a	PRON
ap-768	89	72	n	n	ADV
ap-768	89	73	a	a	DET
ap-768	89	74	a	a	DET
ap-768	89	75	a	a	DET
ap-768	89	76	nm	nm	ADJ
ap-768	89	77	�	�	PROPN
ap-768	89	78	1	1	NUM
ap-768	89	79	2	2	NUM
ap-768	89	80	�	�	PROPN
ap-768	89	81	.	.	PUNCT
ap-768	90	1	(	(	PUNCT
ap-768	90	2	4.3	4.3	NUM
ap-768	90	3	)	)	PUNCT
ap-768	90	4	lemma	lemma	PROPN
ap-768	90	5	4.3	4.3	NUM
ap-768	90	6	:	:	PUNCT
ap-768	90	7	the	the	DET
ap-768	90	8	action	action	NOUN
ap-768	90	9	of	of	ADP
ap-768	90	10	the	the	DET
ap-768	90	11	group	group	NOUN
ap-768	90	12	sl(m	sl(m	PROPN
ap-768	90	13	,	,	PUNCT
ap-768	90	14	zn	zn	PROPN
ap-768	90	15	)	)	PUNCT
ap-768	90	16	on	on	ADP
ap-768	90	17	the	the	DET
ap-768	90	18	ring	ring	NOUN
ap-768	90	19	zn	zn	PROPN
ap-768	90	20	m	m	VERB
ap-768	90	21	preserves	preserve	VERB
ap-768	90	22	the	the	DET
ap-768	90	23	greatest	great	ADJ
ap-768	90	24	common	common	ADJ
ap-768	90	25	divisor	divisor	NOUN
ap-768	90	26	of	of	ADP
ap-768	90	27	an	an	DET
ap-768	90	28	arbitrary	arbitrary	ADJ
ap-768	90	29	element	element	NOUN
ap-768	90	30	a	a	DET
ap-768	90	31	n	n	NUM
ap-768	90	32	m	m	NOUN
ap-768	90	33	�	�	PROPN
ap-768	90	34	z	z	PROPN
ap-768	90	35	and	and	CCONJ
ap-768	90	36	the	the	DET
ap-768	90	37	number	number	NOUN
ap-768	90	38	n	n	CCONJ
ap-768	90	39	,	,	PUNCT
ap-768	90	40	i.e.	i.e.	X
ap-768	90	41	40	40	NUM
ap-768	90	42	©	©	PROPN
ap-768	90	43	czech	czech	PROPN
ap-768	90	44	technical	technical	PROPN
ap-768	90	45	university	university	PROPN
ap-768	90	46	publishing	publishing	NOUN
ap-768	90	47	house	house	NOUN
ap-768	90	48	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-768	90	49	acta	acta	PROPN
ap-768	90	50	polytechnica	polytechnica	PROPN
ap-768	90	51	vol	vol	NOUN
ap-768	90	52	.	.	PROPN
ap-768	91	1	45	45	NUM
ap-768	91	2	no	no	NOUN
ap-768	91	3	.	.	PUNCT
ap-768	92	1	5/2005	5/2005	NUM
ap-768	92	2	czech	czech	PROPN
ap-768	92	3	technical	technical	PROPN
ap-768	92	4	university	university	PROPN
ap-768	92	5	in	in	ADP
ap-768	92	6	prague	prague	PROPN
ap-768	92	7	gcd	gcd	PROPN
ap-768	92	8	(	(	PUNCT
ap-768	92	9	,	,	PUNCT
ap-768	92	10	)	)	PUNCT
ap-768	92	11	gcd	gcd	NOUN
ap-768	92	12	(	(	PUNCT
ap-768	92	13	,	,	PUNCT
ap-768	92	14	)	)	PUNCT
ap-768	92	15	,	,	PUNCT
ap-768	92	16	(	(	PUNCT
ap-768	92	17	,	,	PUNCT
ap-768	92	18	)	)	PUNCT
ap-768	92	19	a	a	PRON
ap-768	92	20	n	n	DET
ap-768	92	21	a	a	DET
ap-768	92	22	n	n	NOUN
ap-768	92	23	a	a	PRON
ap-768	93	1	sl	sl	INTJ
ap-768	94	1	mn	mn	NOUN
ap-768	94	2	m	m	NOUN
ap-768	94	3	na	na	ADP
ap-768	94	4	z	z	PROPN
ap-768	94	5	a	a	DET
ap-768	94	6	z	z	PROPN
ap-768	94	7	�	�	PROPN
ap-768	94	8	�	�	PROPN
ap-768	94	9	�	�	PROPN
ap-768	94	10	�	�	PROPN
ap-768	94	11	�	�	PROPN
ap-768	94	12	.	.	PUNCT
ap-768	95	1	proof	proof	NOUN
ap-768	95	2	:	:	PUNCT
ap-768	95	3	it	it	PRON
ap-768	95	4	follows	follow	VERB
ap-768	95	5	from	from	ADP
ap-768	95	6	a	a	DET
ap-768	95	7	a	a	DET
ap-768	95	8	a	a	PRON
ap-768	95	9	a	a	DET
ap-768	95	10	ai	ai	NOUN
ap-768	95	11	ii	ii	NOUN
ap-768	95	12	m	m	INTJ
ap-768	95	13	i	i	PRON
ap-768	95	14	i	i	PRON
ap-768	95	15	mi	mi	PROPN
ap-768	95	16	m	m	PROPN
ap-768	95	17	a	a	DET
ap-768	95	18	�	�	PROPN
ap-768	95	19	�	�	PROPN
ap-768	95	20	�	�	PROPN
ap-768	95	21	�	�	PROPN
ap-768	95	22	�	�	PROPN
ap-768	95	23	�	�	PROPN
ap-768	95	24	�	�	PROPN
ap-768	95	25	�	�	PROPN
ap-768	95	26	�	�	PROPN
ap-768	95	27	,	,	PUNCT
ap-768	95	28	,	,	PUNCT
ap-768	95	29	,	,	PUNCT
ap-768	95	30	,	,	PUNCT
ap-768	95	31	11	11	NUM
ap-768	95	32	1	1	NUM
ap-768	95	33	�	�	PROPN
ap-768	95	34	and	and	CCONJ
ap-768	95	35	gcd	gcd	PROPN
ap-768	95	36	(	(	PUNCT
ap-768	95	37	,	,	PUNCT
ap-768	95	38	)	)	PUNCT
ap-768	96	1	|	|	ADV
ap-768	96	2	,	,	PUNCT
ap-768	96	3	a	a	DET
ap-768	96	4	n	n	NOUN
ap-768	96	5	a	a	DET
ap-768	96	6	ai	ai	VERB
ap-768	97	1	i	i	PRON
ap-768	98	1	ji	ji	PROPN
ap-768	98	2	m	m	PROPN
ap-768	98	3	�	�	PROPN
ap-768	98	4	�	�	PROPN
ap-768	98	5	1	1	NUM
ap-768	98	6	,	,	PUNCT
ap-768	98	7	�	�	PROPN
ap-768	98	8	�	�	PROPN
ap-768	98	9	j	j	PROPN
ap-768	98	10	m	m	PRON
ap-768	98	11	{	{	PUNCT
ap-768	98	12	,	,	PUNCT
ap-768	98	13	,	,	PUNCT
ap-768	98	14	,	,	PUNCT
ap-768	98	15	}	}	PUNCT
ap-768	98	16	1	1	NUM
ap-768	98	17	2	2	NUM
ap-768	98	18	�	�	PROPN
ap-768	98	19	that	that	PRON
ap-768	98	20	gcd	gcd	VERB
ap-768	98	21	(	(	PUNCT
ap-768	98	22	,	,	PUNCT
ap-768	98	23	)	)	PUNCT
ap-768	98	24	|gcd	|gcd	NOUN
ap-768	98	25	(	(	PUNCT
ap-768	98	26	,	,	PUNCT
ap-768	98	27	)	)	PUNCT
ap-768	98	28	a	a	DET
ap-768	98	29	n	n	ADV
ap-768	98	30	a	a	DET
ap-768	98	31	na	na	NOUN
ap-768	98	32	,	,	PUNCT
ap-768	98	33	i.e.	i.e.	X
ap-768	98	34	the	the	DET
ap-768	98	35	greatest	great	ADJ
ap-768	98	36	common	common	ADJ
ap-768	98	37	divisor	divisor	NOUN
ap-768	98	38	can	can	AUX
ap-768	98	39	not	not	PART
ap-768	98	40	decrease	decrease	VERB
ap-768	98	41	during	during	ADP
ap-768	98	42	this	this	DET
ap-768	98	43	action	action	NOUN
ap-768	98	44	.	.	PUNCT
ap-768	99	1	if	if	SCONJ
ap-768	99	2	we	we	PRON
ap-768	99	3	take	take	VERB
ap-768	99	4	an	an	DET
ap-768	99	5	element	element	NOUN
ap-768	99	6	aa	aa	NOUN
ap-768	99	7	and	and	CCONJ
ap-768	99	8	a	a	DET
ap-768	99	9	matrix	matrix	NOUN
ap-768	99	10	a	a	DET
ap-768	99	11	�	�	NOUN
ap-768	99	12	1	1	NUM
ap-768	99	13	we	we	PRON
ap-768	99	14	obtain	obtain	VERB
ap-768	99	15	gcd	gcd	NOUN
ap-768	99	16	(	(	PUNCT
ap-768	99	17	,	,	PUNCT
ap-768	99	18	)	)	PUNCT
ap-768	99	19	|gcd	|gcd	NOUN
ap-768	99	20	(	(	PUNCT
ap-768	99	21	,	,	PUNCT
ap-768	99	22	)	)	PUNCT
ap-768	99	23	gcd	gcd	NOUN
ap-768	99	24	(	(	PUNCT
ap-768	99	25	,	,	PUNCT
ap-768	99	26	)	)	PUNCT
ap-768	99	27	a	a	DET
ap-768	99	28	n	n	DET
ap-768	99	29	a	a	DET
ap-768	99	30	n	n	NOUN
ap-768	99	31	a	a	DET
ap-768	99	32	na	na	INTJ
ap-768	99	33	aa	aa	PROPN
ap-768	99	34	1	1	NUM
ap-768	99	35	�	�	PROPN
ap-768	99	36	�	�	PROPN
ap-768	99	37	and	and	CCONJ
ap-768	99	38	together	together	ADV
ap-768	99	39	with	with	ADP
ap-768	99	40	the	the	DET
ap-768	99	41	first	first	ADJ
ap-768	99	42	condition	condition	NOUN
ap-768	99	43	we	we	PRON
ap-768	99	44	havegcd	havegcd	VERB
ap-768	99	45	(	(	PUNCT
ap-768	99	46	,	,	PUNCT
ap-768	99	47	)	)	PUNCT
ap-768	99	48	gcd	gcd	NOUN
ap-768	99	49	(	(	PUNCT
ap-768	99	50	,	,	PUNCT
ap-768	99	51	)	)	PUNCT
ap-768	99	52	a	a	PRON
ap-768	99	53	n	n	ADV
ap-768	99	54	a	a	DET
ap-768	99	55	na	na	X
ap-768	99	56	�	�	PROPN
ap-768	99	57	.	.	PUNCT
ap-768	100	1	qed	qed	PROPN
ap-768	100	2	corollary	corollary	PROPN
ap-768	100	3	4.4	4.4	NUM
ap-768	100	4	:	:	PUNCT
ap-768	100	5	for	for	ADP
ap-768	100	6	any	any	DET
ap-768	100	7	divisor	divisor	NOUN
ap-768	100	8	d	d	PROPN
ap-768	100	9	of	of	ADP
ap-768	100	10	n	n	PRON
ap-768	100	11	the	the	DET
ap-768	100	12	orbit	orbit	NOUN
ap-768	100	13	orm	orm	NOUN
ap-768	100	14	,	,	PUNCT
ap-768	100	15	n(d	n(d	PROPN
ap-768	100	16	)	)	PUNCT
ap-768	100	17	is	be	AUX
ap-768	100	18	a	a	DET
ap-768	100	19	subset	subset	NOUN
ap-768	100	20	of	of	ADP
ap-768	100	21	{	{	PUNCT
ap-768	100	22	|gcd	|gcd	NOUN
ap-768	100	23	(	(	PUNCT
ap-768	100	24	,	,	PUNCT
ap-768	100	25	)	)	PUNCT
ap-768	100	26	}	}	PUNCT
ap-768	100	27	a	a	DET
ap-768	100	28	a	a	PRON
ap-768	100	29	n	n	ADV
ap-768	100	30	dn	dn	PROPN
ap-768	100	31	m	m	PROPN
ap-768	100	32	�	�	PROPN
ap-768	100	33	�	�	PROPN
ap-768	100	34	z	z	PROPN
ap-768	100	35	.	.	PUNCT
ap-768	101	1	we	we	PRON
ap-768	101	2	will	will	AUX
ap-768	101	3	show	show	VERB
ap-768	101	4	that	that	SCONJ
ap-768	101	5	the	the	DET
ap-768	101	6	orbit	orbit	NOUN
ap-768	101	7	orm	orm	NOUN
ap-768	101	8	,	,	PUNCT
ap-768	101	9	n(1	n(1	PROPN
ap-768	101	10	)	)	PUNCT
ap-768	101	11	is	be	AUX
ap-768	101	12	equal	equal	ADJ
ap-768	101	13	to	to	ADP
ap-768	101	14	the	the	DET
ap-768	101	15	set	set	NOUN
ap-768	101	16	{	{	PUNCT
ap-768	101	17	|gcd	|gcd	NOUN
ap-768	101	18	(	(	PUNCT
ap-768	101	19	,	,	PUNCT
ap-768	101	20	)	)	PUNCT
ap-768	101	21	}	}	PUNCT
ap-768	101	22	a	a	DET
ap-768	101	23	a	a	DET
ap-768	101	24	nn	nn	PROPN
ap-768	101	25	m	m	PROPN
ap-768	101	26	�	�	PROPN
ap-768	101	27	�	�	PROPN
ap-768	101	28	z	z	PROPN
ap-768	101	29	1	1	NUM
ap-768	101	30	.	.	PUNCT
ap-768	102	1	from	from	ADP
ap-768	102	2	corollary	corollary	ADJ
ap-768	102	3	4.4	4.4	NUM
ap-768	102	4	we	we	PRON
ap-768	102	5	know	know	VERB
ap-768	102	6	that	that	DET
ap-768	102	7	orm	orm	NOUN
ap-768	102	8	,	,	PUNCT
ap-768	102	9	n(1	n(1	PROPN
ap-768	102	10	)	)	PUNCT
ap-768	102	11	is	be	AUX
ap-768	102	12	the	the	DET
ap-768	102	13	subset	subset	NOUN
ap-768	102	14	of	of	ADP
ap-768	102	15	{	{	PUNCT
ap-768	102	16	|gcd	|gcd	NOUN
ap-768	102	17	(	(	PUNCT
ap-768	102	18	,	,	PUNCT
ap-768	102	19	)	)	PUNCT
ap-768	102	20	}	}	PUNCT
ap-768	102	21	a	a	DET
ap-768	102	22	a	a	DET
ap-768	102	23	nn	nn	PROPN
ap-768	102	24	m	m	PROPN
ap-768	102	25	�	�	PROPN
ap-768	102	26	�	�	PROPN
ap-768	102	27	z	z	PROPN
ap-768	102	28	1	1	NUM
ap-768	102	29	and	and	CCONJ
ap-768	102	30	we	we	PRON
ap-768	102	31	prove	prove	VERB
ap-768	102	32	that	that	SCONJ
ap-768	102	33	they	they	PRON
ap-768	102	34	have	have	VERB
ap-768	102	35	the	the	DET
ap-768	102	36	same	same	ADJ
ap-768	102	37	number	number	NOUN
ap-768	102	38	of	of	ADP
ap-768	102	39	elements	element	NOUN
ap-768	102	40	.	.	PUNCT
ap-768	103	1	at	at	ADP
ap-768	103	2	first	first	ADV
ap-768	103	3	we	we	PRON
ap-768	103	4	determine	determine	VERB
ap-768	103	5	the	the	DET
ap-768	103	6	number	number	NOUN
ap-768	103	7	of	of	ADP
ap-768	103	8	points	point	NOUN
ap-768	103	9	in	in	ADP
ap-768	103	10	orm	orm	NOUN
ap-768	103	11	,	,	PUNCT
ap-768	103	12	n(1	n(1	NOUN
ap-768	103	13	)	)	PUNCT
ap-768	103	14	.	.	PUNCT
ap-768	104	1	for	for	ADP
ap-768	104	2	this	this	DET
ap-768	104	3	purpose	purpose	NOUN
ap-768	104	4	we	we	PRON
ap-768	104	5	determine	determine	VERB
ap-768	104	6	the	the	DET
ap-768	104	7	stability	stability	NOUN
ap-768	104	8	subgroup	subgroup	NOUN
ap-768	104	9	of	of	ADP
ap-768	104	10	the	the	DET
ap-768	104	11	element	element	NOUN
ap-768	104	12	(	(	PUNCT
ap-768	104	13	0	0	NUM
ap-768	104	14	,	,	PUNCT
ap-768	104	15	…	…	PUNCT
ap-768	104	16	,	,	PUNCT
ap-768	104	17	0	0	NUM
ap-768	104	18	,	,	PUNCT
ap-768	104	19	1	1	NUM
ap-768	104	20	)	)	PUNCT
ap-768	104	21	.	.	PUNCT
ap-768	105	1	it	it	PRON
ap-768	105	2	is	be	AUX
ap-768	105	3	obviously	obviously	ADV
ap-768	105	4	formed	form	VERB
ap-768	105	5	by	by	ADP
ap-768	105	6	matrices	matrix	NOUN
ap-768	105	7	of	of	ADP
ap-768	105	8	the	the	DET
ap-768	105	9	form	form	NOUN
ap-768	105	10	a	a	DET
ap-768	105	11	�	�	PROPN
ap-768	105	12	�	�	PROPN
ap-768	105	13	�	�	PROPN
ap-768	105	14	�	�	PROPN
ap-768	105	15	�	�	PROPN
ap-768	105	16	�	�	PROPN
ap-768	105	17	�	�	PROPN
ap-768	105	18	�	�	PROPN
ap-768	105	19	�	�	PROPN
ap-768	105	20	�	�	PROPN
ap-768	105	21	a	a	DET
ap-768	105	22	a	a	DET
ap-768	105	23	a	a	DET
ap-768	105	24	a	a	DET
ap-768	105	25	a	a	DET
ap-768	105	26	a	a	DET
ap-768	105	27	m	m	NOUN
ap-768	105	28	m	m	VERB
ap-768	105	29	m	m	VERB
ap-768	105	30	m	m	VERB
ap-768	105	31	m	m	VERB
ap-768	105	32	1	1	NUM
ap-768	105	33	1	1	NUM
ap-768	105	34	1	1	NUM
ap-768	105	35	2	2	NUM
ap-768	105	36	1	1	NUM
ap-768	105	37	1	1	NUM
ap-768	105	38	1	1	NUM
ap-768	105	39	1	1	NUM
ap-768	105	40	2	2	NUM
ap-768	105	41	1	1	NUM
ap-768	105	42	0	0	NUM
ap-768	105	43	0	0	NUM
ap-768	105	44	1	1	NUM
ap-768	105	45	,	,	PUNCT
ap-768	105	46	,	,	PUNCT
ap-768	105	47	,	,	PUNCT
ap-768	105	48	,	,	PUNCT
ap-768	105	49	,	,	PUNCT
ap-768	105	50	,	,	PUNCT
ap-768	105	51	�	�	PROPN
ap-768	105	52	�	�	PROPN
ap-768	105	53	�	�	PROPN
ap-768	105	54	�	�	PROPN
ap-768	105	55	�	�	PROPN
ap-768	105	56	�	�	PROPN
ap-768	105	57	�	�	PROPN
ap-768	105	58	�	�	PROPN
ap-768	105	59	�	�	PROPN
ap-768	105	60	�	�	PROPN
ap-768	105	61	�	�	PROPN
ap-768	105	62	�	�	PROPN
ap-768	105	63	,	,	PUNCT
ap-768	105	64	det	det	PROPN
ap-768	105	65	(	(	PUNCT
ap-768	105	66	)	)	PUNCT
ap-768	105	67	(	(	PUNCT
ap-768	105	68	mod	mod	PROPN
ap-768	105	69	)	)	PUNCT
ap-768	105	70	a	a	DET
ap-768	105	71	1	1	NUM
ap-768	105	72	n	n	NOUN
ap-768	105	73	.	.	PUNCT
ap-768	106	1	expansion	expansion	NOUN
ap-768	106	2	of	of	ADP
ap-768	106	3	this	this	DET
ap-768	106	4	determinant	determinant	NOUN
ap-768	106	5	gives	give	VERB
ap-768	106	6	1	1	NUM
ap-768	106	7	1	1	NUM
ap-768	106	8	�	�	PROPN
ap-768	106	9	�	�	PROPN
ap-768	106	10	�	�	PROPN
ap-768	106	11	�	�	PROPN
ap-768	106	12	�	�	PROPN
ap-768	106	13	det	det	PROPN
ap-768	106	14	(	(	PUNCT
ap-768	106	15	)	)	PUNCT
ap-768	106	16	(	(	PUNCT
ap-768	106	17	)	)	PUNCT
ap-768	106	18	det	det	PROPN
ap-768	106	19	(	(	PUNCT
ap-768	106	20	,	,	PUNCT
ap-768	106	21	)	)	PUNCT
ap-768	106	22	det	det	PROPN
ap-768	106	23	(	(	PUNCT
ap-768	106	24	,	,	PUNCT
ap-768	106	25	)	)	PUNCT
ap-768	106	26	(	(	PUNCT
ap-768	106	27	mod	mod	PROPN
ap-768	106	28	)	)	PUNCT
ap-768	106	29	a	a	DET
ap-768	106	30	a	a	DET
ap-768	106	31	am	am	NOUN
ap-768	106	32	m	m	VERB
ap-768	106	33	m	m	VERB
ap-768	106	34	m	m	VERB
ap-768	106	35	m	m	VERB
ap-768	106	36	m	m	VERB
ap-768	106	37	n	n	ADJ
ap-768	106	38	.	.	PUNCT
ap-768	107	1	therefore	therefore	ADV
ap-768	107	2	the	the	DET
ap-768	107	3	stability	stability	NOUN
ap-768	107	4	subgroup	subgroup	NOUN
ap-768	107	5	of	of	ADP
ap-768	107	6	the	the	DET
ap-768	107	7	point	point	NOUN
ap-768	107	8	(	(	PUNCT
ap-768	107	9	0	0	NUM
ap-768	107	10	,	,	PUNCT
ap-768	107	11	…	…	PUNCT
ap-768	107	12	,	,	PUNCT
ap-768	107	13	0	0	NUM
ap-768	107	14	,	,	PUNCT
ap-768	107	15	1	1	NUM
ap-768	107	16	)	)	PUNCT
ap-768	107	17	is	be	AUX
ap-768	107	18	:	:	PUNCT
ap-768	107	19	s	s	VERB
ap-768	107	20	a	a	PRON
ap-768	107	21	a	a	DET
ap-768	107	22	sl	sl	NOUN
ap-768	107	23	m	m	NOUN
ap-768	107	24	sl	sl	NOUN
ap-768	107	25	m	m	VERB
ap-768	107	26	m	m	VERB
ap-768	107	27	m	m	VERB
ap-768	107	28	n	n	NUM
ap-768	107	29	:	:	PUNCT
ap-768	107	30	(	(	PUNCT
ap-768	107	31	,	,	PUNCT
ap-768	107	32	)	)	PUNCT
ap-768	108	1	|	|	ADV
ap-768	108	2	(	(	PUNCT
ap-768	108	3	,	,	PUNCT
ap-768	108	4	,	,	PUNCT
ap-768	108	5	,	,	PUNCT
ap-768	108	6	�	�	PROPN
ap-768	108	7	�	�	PROPN
ap-768	108	8	�	�	PROPN
ap-768	108	9	�	�	PROPN
ap-768	108	10	�	�	PROPN
ap-768	108	11	�	�	PROPN
ap-768	108	12	�	�	PROPN
ap-768	108	13	�	�	PROPN
ap-768	108	14	�	�	PROPN
ap-768	108	15	�	�	PROPN
ap-768	108	16	�	�	PROPN
ap-768	108	17	�	�	PROPN
ap-768	108	18	�	�	PROPN
ap-768	108	19	�	�	PROPN
ap-768	108	20	�	�	PROPN
ap-768	108	21	a	a	DET
ap-768	108	22	b	b	PROPN
ap-768	108	23	z	z	NOUN
ap-768	108	24	b	b	PROPN
ap-768	108	25	1	1	NUM
ap-768	108	26	2	2	NUM
ap-768	108	27	0	0	NUM
ap-768	108	28	0	0	NUM
ap-768	108	29	1	1	NUM
ap-768	108	30	1	1	NUM
ap-768	108	31	�	�	PROPN
ap-768	108	32	�	�	PROPN
ap-768	108	33	zn	zn	PROPN
ap-768	108	34	)	)	PUNCT
ap-768	108	35	�	�	PROPN
ap-768	108	36	�	�	PROPN
ap-768	108	37	�	�	PROPN
ap-768	108	38	�	�	PROPN
ap-768	108	39	�	�	PROPN
ap-768	108	40	�	�	PROPN
ap-768	108	41	�	�	PROPN
ap-768	108	42	�	�	PROPN
ap-768	108	43	�	�	PROPN
ap-768	108	44	�	�	PROPN
ap-768	108	45	�	�	PROPN
ap-768	108	46	�	�	PROPN
ap-768	108	47	�	�	PROPN
ap-768	108	48	�	�	PROPN
ap-768	108	49	,	,	PUNCT
ap-768	108	50	and	and	CCONJ
ap-768	108	51	its	its	PRON
ap-768	108	52	order	order	NOUN
ap-768	108	53	is	be	AUX
ap-768	108	54	s	s	PRON
ap-768	108	55	n	n	PRON
ap-768	108	56	pm	pm	NOUN
ap-768	109	1	m	m	VERB
ap-768	110	1	i	i	PRON
ap-768	110	2	j	j	PROPN
ap-768	111	1	j	j	NOUN
ap-768	111	2	m	m	VERB
ap-768	111	3	i	i	VERB
ap-768	111	4	r	r	VERB
ap-768	111	5	�	�	PROPN
ap-768	111	6	�	�	PROPN
ap-768	111	7	�	�	PROPN
ap-768	111	8	�	�	PROPN
ap-768	111	9	�	�	PROPN
ap-768	111	10	�	�	PROPN
ap-768	111	11	�	�	PROPN
ap-768	111	12	�	�	PROPN
ap-768	111	13	2	2	NUM
ap-768	111	14	1	1	NUM
ap-768	111	15	2	2	NUM
ap-768	111	16	1	1	NUM
ap-768	111	17	1	1	NUM
ap-768	111	18	1	1	NUM
ap-768	111	19	(	(	PUNCT
ap-768	111	20	)	)	PUNCT
ap-768	111	21	.	.	PUNCT
ap-768	112	1	(	(	PUNCT
ap-768	112	2	4.4	4.4	NUM
ap-768	112	3	)	)	PUNCT
ap-768	112	4	according	accord	VERB
ap-768	112	5	to	to	ADP
ap-768	112	6	the	the	DET
ap-768	112	7	lagrange	lagrange	NOUN
ap-768	112	8	theorem	theorem	NOUN
ap-768	112	9	,	,	PUNCT
ap-768	112	10	the	the	DET
ap-768	112	11	product	product	NOUN
ap-768	112	12	of	of	ADP
ap-768	112	13	the	the	DET
ap-768	112	14	order	order	NOUN
ap-768	112	15	and	and	CCONJ
ap-768	112	16	the	the	DET
ap-768	112	17	index	index	NOUN
ap-768	112	18	of	of	ADP
ap-768	112	19	an	an	DET
ap-768	112	20	arbitrary	arbitrary	ADJ
ap-768	112	21	subgroup	subgroup	NOUN
ap-768	112	22	of	of	ADP
ap-768	112	23	a	a	DET
ap-768	112	24	given	give	VERB
ap-768	112	25	finite	finite	ADJ
ap-768	112	26	group	group	NOUN
ap-768	112	27	is	be	AUX
ap-768	112	28	equal	equal	ADJ
ap-768	112	29	to	to	ADP
ap-768	112	30	the	the	DET
ap-768	112	31	order	order	NOUN
ap-768	112	32	of	of	ADP
ap-768	112	33	this	this	DET
ap-768	112	34	group	group	NOUN
ap-768	112	35	.	.	PUNCT
ap-768	113	1	if	if	SCONJ
ap-768	113	2	we	we	PRON
ap-768	113	3	define	define	VERB
ap-768	113	4	on	on	ADP
ap-768	113	5	the	the	DET
ap-768	113	6	group	group	NOUN
ap-768	113	7	sl(m	sl(m	PROPN
ap-768	113	8	,	,	PUNCT
ap-768	113	9	zn	zn	PROPN
ap-768	113	10	)	)	PUNCT
ap-768	113	11	a	a	DET
ap-768	113	12	left	left	ADJ
ap-768	113	13	equivalence	equivalence	NOUN
ap-768	113	14	induced	induce	VERB
ap-768	113	15	by	by	ADP
ap-768	113	16	the	the	DET
ap-768	113	17	stability	stability	NOUN
ap-768	113	18	subgroup	subgroup	NOUN
ap-768	113	19	s	s	VERB
ap-768	113	20	by	by	ADP
ap-768	113	21	formula	formula	NOUN
ap-768	113	22	a	a	PRON
ap-768	113	23	,	,	PUNCT
ap-768	113	24	b	b	PROPN
ap-768	113	25	z	z	PROPN
ap-768	113	26	a	a	PRON
ap-768	113	27	b	b	X
ap-768	113	28	ab	ab	PRON
ap-768	113	29	�	�	PROPN
ap-768	113	30	�	�	PROPN
ap-768	113	31	�	�	PROPN
ap-768	113	32	�	�	PROPN
ap-768	113	33	�	�	PROPN
ap-768	113	34	sl	sl	NOUN
ap-768	113	35	m	m	PROPN
ap-768	113	36	sn	sn	NOUN
ap-768	113	37	s	s	PROPN
ap-768	113	38	(	(	PUNCT
ap-768	113	39	,	,	PUNCT
ap-768	113	40	)	)	PUNCT
ap-768	113	41	1	1	NUM
ap-768	113	42	,	,	PUNCT
ap-768	113	43	then	then	ADV
ap-768	113	44	we	we	PRON
ap-768	113	45	obtain	obtain	VERB
ap-768	113	46	equivalence	equivalence	NOUN
ap-768	113	47	classes	class	NOUN
ap-768	113	48	of	of	ADP
ap-768	113	49	the	the	DET
ap-768	113	50	form	form	NOUN
ap-768	113	51	s	s	PROPN
ap-768	113	52	sb	sb	PROPN
ap-768	113	53	ab	ab	PROPN
ap-768	113	54	a	a	PROPN
ap-768	113	55	�	�	PROPN
ap-768	113	56	�	�	PROPN
ap-768	113	57	{	{	PUNCT
ap-768	113	58	|	|	ADV
ap-768	113	59	}	}	PUNCT
ap-768	113	60	,	,	PUNCT
ap-768	113	61	b	b	PROPN
ap-768	113	62	z	z	PROPN
ap-768	113	63	�	�	PROPN
ap-768	113	64	sl	sl	NOUN
ap-768	113	65	m	m	VERB
ap-768	113	66	n	n	CCONJ
ap-768	113	67	(	(	PUNCT
ap-768	113	68	,	,	PUNCT
ap-768	113	69	)	)	PUNCT
ap-768	113	70	,	,	PUNCT
ap-768	113	71	i.e.	i.e.	X
ap-768	113	72	right	right	ADJ
ap-768	113	73	cosets	coset	NOUN
ap-768	113	74	from	from	ADP
ap-768	113	75	sl(m	sl(m	PROPN
ap-768	113	76	,	,	PUNCT
ap-768	113	77	zn)/s	zn)/s	PROPN
ap-768	113	78	.	.	PUNCT
ap-768	114	1	the	the	DET
ap-768	114	2	number	number	NOUN
ap-768	114	3	of	of	ADP
ap-768	114	4	these	these	DET
ap-768	114	5	cosets	coset	NOUN
ap-768	114	6	is	be	AUX
ap-768	114	7	,	,	PUNCT
ap-768	114	8	by	by	ADP
ap-768	114	9	definition	definition	NOUN
ap-768	114	10	,	,	PUNCT
ap-768	114	11	the	the	DET
ap-768	114	12	index	index	NOUN
ap-768	114	13	of	of	ADP
ap-768	114	14	subgroup	subgroup	PROPN
ap-768	114	15	s.	s.	PROPN
ap-768	115	1	these	these	DET
ap-768	115	2	cosets	coset	NOUN
ap-768	115	3	correspond	correspond	VERB
ap-768	115	4	one	one	NUM
ap-768	115	5	-	-	PUNCT
ap-768	115	6	to	to	ADP
ap-768	115	7	-	-	PUNCT
ap-768	115	8	one	one	NUM
ap-768	115	9	with	with	ADP
ap-768	115	10	the	the	DET
ap-768	115	11	points	point	NOUN
ap-768	115	12	of	of	ADP
ap-768	115	13	the	the	DET
ap-768	115	14	orbit	orbit	NOUN
ap-768	115	15	which	which	PRON
ap-768	115	16	includes	include	VERB
ap-768	115	17	the	the	DET
ap-768	115	18	point	point	NOUN
ap-768	115	19	(	(	PUNCT
ap-768	115	20	0	0	NUM
ap-768	115	21	,	,	PUNCT
ap-768	115	22	…	…	PUNCT
ap-768	115	23	,	,	PUNCT
ap-768	115	24	0	0	NUM
ap-768	115	25	,	,	PUNCT
ap-768	115	26	1	1	NUM
ap-768	115	27	)	)	PUNCT
ap-768	115	28	.	.	PUNCT
ap-768	116	1	therefore	therefore	ADV
ap-768	116	2	the	the	DET
ap-768	116	3	index	index	NOUN
ap-768	116	4	of	of	ADP
ap-768	116	5	the	the	DET
ap-768	116	6	stability	stability	NOUN
ap-768	116	7	subgroup	subgroup	NOUN
ap-768	116	8	s	s	PART
ap-768	116	9	is	be	AUX
ap-768	116	10	equal	equal	ADJ
ap-768	116	11	to	to	ADP
ap-768	116	12	the	the	DET
ap-768	116	13	number	number	NOUN
ap-768	116	14	of	of	ADP
ap-768	116	15	points	point	NOUN
ap-768	116	16	in	in	ADP
ap-768	116	17	this	this	DET
ap-768	116	18	orbit	orbit	NOUN
ap-768	116	19	.	.	PUNCT
ap-768	117	1	a	a	DET
ap-768	117	2	similar	similar	ADJ
ap-768	117	3	calculation	calculation	NOUN
ap-768	117	4	can	can	AUX
ap-768	117	5	be	be	AUX
ap-768	117	6	done	do	VERB
ap-768	117	7	for	for	ADP
ap-768	117	8	an	an	DET
ap-768	117	9	arbitrary	arbitrary	ADJ
ap-768	117	10	point	point	NOUN
ap-768	117	11	in	in	ADP
ap-768	117	12	an	an	DET
ap-768	117	13	arbitrary	arbitrary	ADJ
ap-768	117	14	orbit	orbit	NOUN
ap-768	117	15	.	.	PUNCT
ap-768	118	1	thus	thus	ADV
ap-768	118	2	we	we	PRON
ap-768	118	3	have	have	VERB
ap-768	118	4	the	the	DET
ap-768	118	5	following	follow	VERB
ap-768	118	6	proposition	proposition	NOUN
ap-768	118	7	.	.	PUNCT
ap-768	119	1	proposition	proposition	NOUN
ap-768	119	2	4.5	4.5	NUM
ap-768	119	3	:	:	PUNCT
ap-768	119	4	the	the	DET
ap-768	119	5	number	number	NOUN
ap-768	119	6	of	of	ADP
ap-768	119	7	elements	element	NOUN
ap-768	119	8	in	in	ADP
ap-768	119	9	an	an	DET
ap-768	119	10	orbit	orbit	NOUN
ap-768	119	11	is	be	AUX
ap-768	119	12	equal	equal	ADJ
ap-768	119	13	to	to	ADP
ap-768	119	14	the	the	DET
ap-768	119	15	order	order	NOUN
ap-768	119	16	of	of	ADP
ap-768	119	17	the	the	DET
ap-768	119	18	group	group	NOUN
ap-768	119	19	sl(m	sl(m	PROPN
ap-768	119	20	,	,	PUNCT
ap-768	119	21	zn	zn	NOUN
ap-768	119	22	)	)	PUNCT
ap-768	119	23	divided	divide	VERB
ap-768	119	24	by	by	ADP
ap-768	119	25	the	the	DET
ap-768	119	26	order	order	NOUN
ap-768	119	27	of	of	ADP
ap-768	119	28	the	the	DET
ap-768	119	29	stability	stability	NOUN
ap-768	119	30	subgroup	subgroup	NOUN
ap-768	119	31	of	of	ADP
ap-768	119	32	an	an	DET
ap-768	119	33	arbitrary	arbitrary	ADJ
ap-768	119	34	element	element	NOUN
ap-768	119	35	in	in	ADP
ap-768	119	36	this	this	DET
ap-768	119	37	orbit	orbit	NOUN
ap-768	119	38	.	.	PUNCT
ap-768	120	1	using	use	VERB
ap-768	120	2	(	(	PUNCT
ap-768	120	3	2.3	2.3	NUM
ap-768	120	4	)	)	PUNCT
ap-768	120	5	and	and	CCONJ
ap-768	120	6	(	(	PUNCT
ap-768	120	7	4.4	4.4	NUM
ap-768	120	8	)	)	PUNCT
ap-768	120	9	we	we	PRON
ap-768	120	10	obtain	obtain	VERB
ap-768	120	11	that	that	SCONJ
ap-768	120	12	the	the	DET
ap-768	120	13	number	number	NOUN
ap-768	120	14	of	of	ADP
ap-768	120	15	points	point	NOUN
ap-768	120	16	in	in	ADP
ap-768	120	17	the	the	DET
ap-768	120	18	orbit	orbit	NOUN
ap-768	120	19	orm	orm	NOUN
ap-768	120	20	,	,	PUNCT
ap-768	120	21	n(1	n(1	PROPN
ap-768	120	22	)	)	PUNCT
ap-768	120	23	is	be	AUX
ap-768	120	24	equal	equal	ADJ
ap-768	120	25	to	to	ADP
ap-768	120	26	or	or	CCONJ
ap-768	120	27	=	=	NOUN
ap-768	120	28	m	m	NOUN
ap-768	120	29	n	n	VERB
ap-768	120	30	m	m	VERB
ap-768	121	1	i	i	PRON
ap-768	121	2	m	m	VERB
ap-768	122	1	i	i	VERB
ap-768	122	2	r	r	NOUN
ap-768	122	3	n	n	NOUN
ap-768	122	4	p	p	X
ap-768	122	5	,	,	PUNCT
ap-768	122	6	(	(	PUNCT
ap-768	122	7	)	)	PUNCT
ap-768	122	8	(	(	PUNCT
ap-768	122	9	)	)	SYM
ap-768	122	10	1	1	NUM
ap-768	122	11	1	1	NUM
ap-768	122	12	1	1	NUM
ap-768	122	13	�	�	PROPN
ap-768	122	14	�	�	PROPN
ap-768	122	15	�	�	PROPN
ap-768	122	16	.	.	PUNCT
ap-768	123	1	(	(	PUNCT
ap-768	123	2	4.5	4.5	NUM
ap-768	123	3	)	)	PUNCT
ap-768	123	4	now	now	ADV
ap-768	123	5	we	we	PRON
ap-768	123	6	will	will	AUX
ap-768	123	7	determine	determine	VERB
ap-768	123	8	the	the	DET
ap-768	123	9	number	number	NOUN
ap-768	123	10	of	of	ADP
ap-768	123	11	all	all	DET
ap-768	123	12	elements	element	NOUN
ap-768	123	13	in	in	ADP
ap-768	123	14	zn	zn	PROPN
ap-768	123	15	m	m	VERB
ap-768	123	16	that	that	PRON
ap-768	123	17	have	have	VERB
ap-768	123	18	the	the	DET
ap-768	123	19	greatest	great	ADJ
ap-768	123	20	common	common	ADJ
ap-768	123	21	divisor	divisor	NOUN
ap-768	123	22	with	with	ADP
ap-768	123	23	the	the	DET
ap-768	123	24	number	number	NOUN
ap-768	123	25	n	n	PRON
ap-768	123	26	equal	equal	ADJ
ap-768	123	27	to	to	ADP
ap-768	123	28	unity	unity	NOUN
ap-768	123	29	.	.	PUNCT
ap-768	124	1	this	this	DET
ap-768	124	2	number	number	NOUN
ap-768	124	3	is	be	AUX
ap-768	124	4	equal	equal	ADJ
ap-768	124	5	to	to	ADP
ap-768	124	6	the	the	DET
ap-768	124	7	jordan	jordan	PROPN
ap-768	124	8	function	function	PROPN
ap-768	124	9	.	.	PUNCT
ap-768	125	1	definition	definition	NOUN
ap-768	125	2	4.6	4.6	NUM
ap-768	125	3	:	:	PUNCT
ap-768	125	4	for	for	ADP
ap-768	125	5	m	m	PROPN
ap-768	125	6	�	�	PROPN
ap-768	125	7	n	n	PART
ap-768	125	8	a	a	DET
ap-768	125	9	mapping	mapping	NOUN
ap-768	125	10	�	�	NOUN
ap-768	125	11	m	m	NOUN
ap-768	125	12	:	:	PUNCT
ap-768	125	13	n	n	CCONJ
ap-768	125	14	n	n	CCONJ
ap-768	125	15	�	�	PROPN
ap-768	125	16	defined	define	VERB
ap-768	125	17	by	by	ADP
ap-768	125	18	�	�	PROPN
ap-768	125	19	m	m	PROPN
ap-768	125	20	n	n	NUM
ap-768	125	21	mn	mn	PROPN
ap-768	125	22	a	a	DET
ap-768	125	23	a	a	PRON
ap-768	125	24	n	n	CCONJ
ap-768	125	25	(	(	PUNCT
ap-768	125	26	)	)	PUNCT
ap-768	125	27	{	{	PUNCT
ap-768	125	28	|gcd	|gcd	X
ap-768	125	29	(	(	PUNCT
ap-768	125	30	,	,	PUNCT
ap-768	125	31	)	)	PUNCT
ap-768	125	32	}	}	PUNCT
ap-768	125	33	�	�	PROPN
ap-768	125	34	�	�	PROPN
ap-768	125	35	�	�	PROPN
ap-768	125	36	z	z	PROPN
ap-768	125	37	1	1	NUM
ap-768	125	38	(	(	PUNCT
ap-768	125	39	4.6	4.6	NUM
ap-768	125	40	)	)	PUNCT
ap-768	125	41	is	be	AUX
ap-768	125	42	called	call	VERB
ap-768	125	43	the	the	DET
ap-768	125	44	jordan	jordan	PROPN
ap-768	125	45	function	function	NOUN
ap-768	125	46	of	of	ADP
ap-768	125	47	the	the	DET
ap-768	125	48	order	order	NOUN
ap-768	125	49	m.	m.	NOUN
ap-768	125	50	we	we	PRON
ap-768	125	51	present	present	VERB
ap-768	125	52	,	,	PUNCT
ap-768	125	53	without	without	ADP
ap-768	125	54	proof	proof	NOUN
ap-768	125	55	,	,	PUNCT
ap-768	125	56	some	some	DET
ap-768	125	57	basic	basic	ADJ
ap-768	125	58	properties	property	NOUN
ap-768	125	59	of	of	ADP
ap-768	125	60	the	the	DET
ap-768	125	61	jordan	jordan	PROPN
ap-768	125	62	function	function	NOUN
ap-768	125	63	which	which	PRON
ap-768	125	64	can	can	AUX
ap-768	125	65	be	be	AUX
ap-768	125	66	found	find	VERB
ap-768	125	67	in	in	ADP
ap-768	125	68	[	[	X
ap-768	125	69	12	12	NUM
ap-768	125	70	]	]	PUNCT
ap-768	125	71	.	.	PUNCT
ap-768	126	1	proposition	proposition	NOUN
ap-768	126	2	4.7	4.7	NUM
ap-768	126	3	:	:	PUNCT
ap-768	126	4	for	for	SCONJ
ap-768	126	5	the	the	DET
ap-768	126	6	jordan	jordan	PROPN
ap-768	126	7	function	function	PROPN
ap-768	126	8	�	�	PROPN
ap-768	126	9	m	m	PROPN
ap-768	126	10	of	of	ADP
ap-768	126	11	the	the	DET
ap-768	126	12	order	order	NOUN
ap-768	126	13	m	m	VERB
ap-768	126	14	�	�	NOUN
ap-768	126	15	n	n	NOUN
ap-768	126	16	and	and	CCONJ
ap-768	126	17	for	for	ADP
ap-768	126	18	any	any	DET
ap-768	126	19	n	n	DET
ap-768	126	20	�	�	PROPN
ap-768	126	21	n	n	NOUN
ap-768	126	22	holds	hold	VERB
ap-768	126	23	:	:	PUNCT
ap-768	126	24	1	1	X
ap-768	126	25	.	.	X
ap-768	126	26	�	�	PROPN
ap-768	126	27	m	m	NOUN
ap-768	126	28	m	m	VERB
ap-768	126	29	m	m	VERB
ap-768	126	30	p	p	ADJ
ap-768	126	31	n	n	PRON
ap-768	126	32	p	p	NOUN
ap-768	126	33	n	n	CCONJ
ap-768	126	34	n	n	ADV
ap-768	126	35	p	p	X
ap-768	126	36	(	(	PUNCT
ap-768	126	37	)	)	PUNCT
ap-768	126	38	)	)	PUNCT
ap-768	127	1	|	|	ADV
ap-768	127	2	,	,	PUNCT
ap-768	127	3	�	�	PROPN
ap-768	127	4	�	�	PROPN
ap-768	127	5	�	�	PROPN
ap-768	127	6	�	�	PROPN
ap-768	127	7	(	(	PUNCT
ap-768	127	8	p	p	NOUN
ap-768	127	9	1	1	NUM
ap-768	127	10	(	(	PUNCT
ap-768	127	11	4.7	4.7	NUM
ap-768	127	12	)	)	PUNCT
ap-768	127	13	2	2	NUM
ap-768	127	14	.	.	X
ap-768	127	15	�	�	PROPN
ap-768	127	16	m	m	PROPN
ap-768	127	17	d	d	PROPN
ap-768	127	18	n	n	PROPN
ap-768	127	19	d	d	PROPN
ap-768	127	20	md	md	PROPN
ap-768	127	21	n	n	CCONJ
ap-768	127	22	(	(	PUNCT
ap-768	127	23	)	)	PUNCT
ap-768	127	24	|	|	ADV
ap-768	127	25	,	,	PUNCT
ap-768	127	26	�	�	PROPN
ap-768	127	27	�	�	PROPN
ap-768	127	28	�	�	PROPN
ap-768	127	29	n	n	CCONJ
ap-768	127	30	(	(	PUNCT
ap-768	127	31	4.8	4.8	NUM
ap-768	127	32	)	)	PUNCT
ap-768	127	33	3	3	NUM
ap-768	127	34	.	.	X
ap-768	127	35	�	�	PROPN
ap-768	127	36	m	m	PROPN
ap-768	127	37	n	n	PROPN
ap-768	127	38	d	d	NOUN
ap-768	127	39	m	m	VERB
ap-768	127	40	n	n	ADV
ap-768	127	41	m	m	NOUN
ap-768	127	42	n	n	PROPN
ap-768	127	43	d	d	NOUN
ap-768	127	44	a	a	DET
ap-768	127	45	a	a	PRON
ap-768	127	46	n	n	NOUN
ap-768	127	47	d	d	NOUN
ap-768	127	48	a	a	DET
ap-768	127	49	a	a	PRON
ap-768	127	50	n	n	NOUN
ap-768	127	51	d	d	PROPN
ap-768	127	52	�	�	PROPN
ap-768	127	53	�	�	PROPN
ap-768	127	54	�	�	PROPN
ap-768	127	55	�	�	PROPN
ap-768	127	56	�	�	PROPN
ap-768	127	57	�	�	PROPN
ap-768	127	58	�	�	PROPN
ap-768	127	59	�	�	PROPN
ap-768	127	60	�	�	PROPN
ap-768	127	61	�	�	PROPN
ap-768	127	62	�	�	PROPN
ap-768	127	63	{	{	PUNCT
ap-768	127	64	|gcd	|gcd	PROPN
ap-768	127	65	(	(	PUNCT
ap-768	127	66	,	,	PUNCT
ap-768	127	67	)	)	PUNCT
ap-768	127	68	}	}	PUNCT
ap-768	127	69	{	{	PUNCT
ap-768	127	70	|gcd	|gcd	X
ap-768	127	71	(	(	PUNCT
ap-768	127	72	,	,	PUNCT
ap-768	127	73	)	)	PUNCT
ap-768	127	74	z	z	NOUN
ap-768	127	75	z	z	NOUN
ap-768	127	76	1	1	NUM
ap-768	127	77	}	}	PUNCT
ap-768	127	78	.	.	PUNCT
ap-768	128	1	(	(	PUNCT
ap-768	128	2	4.9	4.9	NUM
ap-768	128	3	)	)	PUNCT
ap-768	128	4	the	the	DET
ap-768	128	5	number	number	NOUN
ap-768	128	6	of	of	ADP
ap-768	128	7	all	all	DET
ap-768	128	8	elements	element	NOUN
ap-768	128	9	in	in	ADP
ap-768	128	10	zn	zn	PROPN
ap-768	128	11	m	m	PROPN
ap-768	128	12	,	,	PUNCT
ap-768	128	13	which	which	PRON
ap-768	128	14	are	be	AUX
ap-768	128	15	co	co	ADJ
ap-768	128	16	-	-	NOUN
ap-768	128	17	prime	prime	ADJ
ap-768	128	18	with	with	ADP
ap-768	128	19	n	n	CCONJ
ap-768	128	20	,	,	PUNCT
ap-768	128	21	given	give	VERB
ap-768	128	22	by	by	ADP
ap-768	128	23	the	the	DET
ap-768	128	24	first	first	ADJ
ap-768	128	25	property	property	NOUN
ap-768	128	26	of	of	ADP
ap-768	128	27	the	the	DET
ap-768	128	28	jordan	jordan	PROPN
ap-768	128	29	function	function	PROPN
ap-768	128	30	�	�	PROPN
ap-768	128	31	m(n	m(n	NOUN
ap-768	128	32	)	)	PUNCT
ap-768	128	33	(	(	PUNCT
ap-768	128	34	4.7	4.7	NUM
ap-768	128	35	)	)	PUNCT
ap-768	128	36	,	,	PUNCT
ap-768	128	37	is	be	AUX
ap-768	128	38	equal	equal	ADJ
ap-768	128	39	to	to	ADP
ap-768	128	40	the	the	DET
ap-768	128	41	number	number	NOUN
ap-768	128	42	of	of	ADP
ap-768	128	43	points	point	NOUN
ap-768	128	44	in	in	ADP
ap-768	128	45	the	the	DET
ap-768	128	46	orbit	orbit	NOUN
ap-768	128	47	orm	orm	NOUN
ap-768	128	48	,	,	PUNCT
ap-768	128	49	n(1	n(1	PROPN
ap-768	128	50	)	)	PUNCT
ap-768	128	51	.	.	PUNCT
ap-768	129	1	therefore	therefore	ADV
ap-768	129	2	the	the	DET
ap-768	129	3	orbit	orbit	NOUN
ap-768	129	4	orm	orm	NOUN
ap-768	129	5	,	,	PUNCT
ap-768	129	6	n(1	n(1	PROPN
ap-768	129	7	)	)	PUNCT
ap-768	129	8	is	be	AUX
ap-768	129	9	formed	form	VERB
ap-768	129	10	by	by	ADP
ap-768	129	11	all	all	DET
ap-768	129	12	elements	element	NOUN
ap-768	129	13	in	in	ADP
ap-768	129	14	zn	zn	PROPN
ap-768	129	15	m	m	VERB
ap-768	129	16	which	which	PRON
ap-768	129	17	are	be	AUX
ap-768	129	18	co	co	ADJ
ap-768	129	19	-	-	NOUN
ap-768	129	20	prime	prime	ADJ
ap-768	129	21	with	with	ADP
ap-768	129	22	n.	n.	NOUN
ap-768	129	23	proposition	proposition	NOUN
ap-768	129	24	4.8	4.8	NUM
ap-768	129	25	:	:	PUNCT
ap-768	129	26	for	for	ADP
ap-768	129	27	m	m	PROPN
ap-768	129	28	n	n	SYM
ap-768	129	29	,	,	PUNCT
ap-768	129	30	�	�	PROPN
ap-768	129	31	n	n	CCONJ
ap-768	129	32	,	,	PUNCT
ap-768	129	33	m	m	VERB
ap-768	129	34	�	�	PROPN
ap-768	129	35	2	2	NUM
ap-768	129	36	holds	hold	VERB
ap-768	129	37	or	or	CCONJ
ap-768	129	38	zm	zm	PROPN
ap-768	129	39	n	n	PROPN
ap-768	129	40	n	n	PROPN
ap-768	129	41	ma	ma	PROPN
ap-768	129	42	a	a	PRON
ap-768	129	43	n	n	X
ap-768	129	44	,	,	PUNCT
ap-768	129	45	(	(	PUNCT
ap-768	129	46	)	)	PUNCT
ap-768	129	47	{	{	PUNCT
ap-768	129	48	|gcd	|gcd	X
ap-768	129	49	(	(	PUNCT
ap-768	129	50	,	,	PUNCT
ap-768	129	51	)	)	PUNCT
ap-768	129	52	}	}	PUNCT
ap-768	129	53	1	1	NUM
ap-768	129	54	1	1	NUM
ap-768	129	55	�	�	PROPN
ap-768	129	56	�	�	PROPN
ap-768	129	57	�	�	PROPN
ap-768	129	58	.	.	PUNCT
ap-768	129	59	4.1	4.1	NUM
ap-768	129	60	orbits	orbit	NOUN
ap-768	129	61	for	for	ADP
ap-768	129	62	n	n	X
ap-768	129	63	�	�	PROPN
ap-768	129	64	pk	pk	NOUN
ap-768	129	65	power	power	NOUN
ap-768	129	66	of	of	ADP
ap-768	129	67	a	a	DET
ap-768	129	68	prime	prime	NOUN
ap-768	129	69	let	let	VERB
ap-768	129	70	us	we	PRON
ap-768	129	71	now	now	ADV
ap-768	129	72	consider	consider	VERB
ap-768	129	73	n	n	PRON
ap-768	129	74	of	of	ADP
ap-768	129	75	the	the	DET
ap-768	129	76	form	form	NOUN
ap-768	129	77	n	n	PROPN
ap-768	129	78	�	�	PROPN
ap-768	129	79	pk	pk	PROPN
ap-768	129	80	,	,	PUNCT
ap-768	129	81	where	where	SCONJ
ap-768	129	82	p	p	NOUN
ap-768	129	83	is	be	AUX
ap-768	129	84	a	a	DET
ap-768	129	85	prime	prime	ADJ
ap-768	129	86	number	number	NOUN
ap-768	129	87	and	and	CCONJ
ap-768	129	88	k	k	PROPN
ap-768	129	89	�	�	PROPN
ap-768	129	90	n	n	NUM
ap-768	129	91	,	,	PUNCT
ap-768	129	92	and	and	CCONJ
ap-768	129	93	determine	determine	VERB
ap-768	129	94	orbits	orbit	NOUN
ap-768	129	95	in	in	ADP
ap-768	129	96	this	this	DET
ap-768	129	97	case	case	NOUN
ap-768	129	98	.	.	PUNCT
ap-768	130	1	definition	definition	NOUN
ap-768	130	2	4.1.1	4.1.1	NUM
ap-768	130	3	:	:	PUNCT
ap-768	130	4	for	for	ADP
ap-768	130	5	j	j	PROPN
ap-768	130	6	j	j	PROPN
ap-768	130	7	k	k	PROPN
ap-768	130	8	�	�	PROPN
ap-768	130	9	�	�	PROPN
ap-768	130	10	n	n	NUM
ap-768	130	11	,	,	PUNCT
ap-768	130	12	,	,	PUNCT
ap-768	130	13	we	we	PRON
ap-768	130	14	define	define	VERB
ap-768	130	15	a	a	DET
ap-768	130	16	mapping	mapping	NOUN
ap-768	130	17	f	f	NOUN
ap-768	130	18	z	z	PROPN
ap-768	130	19	zj	zj	PROPN
ap-768	131	1	p	p	NOUN
ap-768	132	1	m	m	PROPN
ap-768	132	2	p	p	NOUN
ap-768	132	3	m	m	PROPN
ap-768	132	4	k	k	ADJ
ap-768	132	5	k	k	NOUN
ap-768	132	6	:	:	PUNCT
ap-768	132	7	�	�	NOUN
ap-768	132	8	by	by	ADP
ap-768	132	9	the	the	DET
ap-768	132	10	formula	formula	NOUN
ap-768	133	1	f	f	PROPN
ap-768	133	2	j	j	PROPN
ap-768	133	3	j	j	PROPN
ap-768	133	4	p	p	X
ap-768	133	5	a	a	DET
ap-768	133	6	p	p	X
ap-768	133	7	a	a	DET
ap-768	133	8	k	k	X
ap-768	133	9	(	(	PUNCT
ap-768	133	10	)	)	PUNCT
ap-768	133	11	(	(	PUNCT
ap-768	133	12	)	)	PUNCT
ap-768	133	13	mod	mod	PROPN
ap-768	133	14	�	�	PROPN
ap-768	133	15	for	for	ADP
ap-768	133	16	any	any	DET
ap-768	133	17	a	a	DET
ap-768	133	18	p	p	NOUN
ap-768	133	19	m	m	ADJ
ap-768	133	20	k	k	X
ap-768	133	21	�	�	PROPN
ap-768	133	22	z	z	PROPN
ap-768	133	23	.	.	PUNCT
ap-768	134	1	lemma	lemma	PROPN
ap-768	134	2	4.1.2	4.1.2	NUM
ap-768	134	3	:	:	PUNCT
ap-768	134	4	let	let	VERB
ap-768	134	5	a	a	PRON
ap-768	134	6	and	and	CCONJ
ap-768	134	7	b	b	NOUN
ap-768	134	8	be	be	AUX
ap-768	134	9	two	two	NUM
ap-768	134	10	equivalent	equivalent	ADJ
ap-768	134	11	elements	element	NOUN
ap-768	134	12	from	from	ADP
ap-768	134	13	z	z	PROPN
ap-768	134	14	p	p	NOUN
ap-768	134	15	m	m	PROPN
ap-768	134	16	k	k	PROPN
ap-768	134	17	and	and	CCONJ
ap-768	134	18	j	j	PROPN
ap-768	135	1	k	k	PROPN
ap-768	135	2	�	�	PROPN
ap-768	135	3	.	.	PUNCT
ap-768	136	1	then	then	ADV
ap-768	136	2	the	the	DET
ap-768	136	3	elements	element	NOUN
ap-768	136	4	f	f	PROPN
ap-768	136	5	j	j	PROPN
ap-768	136	6	a	a	X
ap-768	136	7	(	(	PUNCT
ap-768	136	8	)	)	PUNCT
ap-768	136	9	and	and	CCONJ
ap-768	136	10	f	f	PROPN
ap-768	136	11	j	j	PROPN
ap-768	136	12	b	b	PROPN
ap-768	136	13	(	(	PUNCT
ap-768	136	14	)	)	PUNCT
ap-768	136	15	are	be	AUX
ap-768	136	16	equivalent	equivalent	ADJ
ap-768	136	17	as	as	ADV
ap-768	136	18	well	well	ADV
ap-768	136	19	.	.	PUNCT
ap-768	137	1	proof	proof	NOUN
ap-768	137	2	:	:	PUNCT
ap-768	137	3	let	let	VERB
ap-768	137	4	a	a	DET
ap-768	137	5	b	b	NOUN
ap-768	137	6	p	p	NOUN
ap-768	137	7	m	m	PROPN
ap-768	137	8	k	k	NOUN
ap-768	137	9	,	,	PUNCT
ap-768	137	10	z	z	PROPN
ap-768	137	11	�	�	PROPN
ap-768	137	12	,	,	PUNCT
ap-768	137	13	a	a	DET
ap-768	137	14	~	~	PROPN
ap-768	137	15	b.	b.	NOUN
ap-768	137	16	it	it	PRON
ap-768	137	17	follows	follow	VERB
ap-768	137	18	from	from	ADP
ap-768	137	19	the	the	DET
ap-768	137	20	definition	definition	NOUN
ap-768	137	21	of	of	ADP
ap-768	137	22	equivalence	equivalence	NOUN
ap-768	137	23	~	~	PUNCT
ap-768	137	24	that	that	SCONJ
ap-768	137	25	there	there	PRON
ap-768	137	26	exists	exist	VERB
ap-768	137	27	a	a	DET
ap-768	137	28	matrix	matrix	NOUN
ap-768	137	29	a	a	DET
ap-768	137	30	z	z	NOUN
ap-768	137	31	�	�	PROPN
ap-768	137	32	sl	sl	NOUN
ap-768	137	33	m	m	PROPN
ap-768	137	34	p	p	NOUN
ap-768	137	35	k	k	X
ap-768	137	36	(	(	PUNCT
ap-768	137	37	,	,	PUNCT
ap-768	137	38	)	)	PUNCT
ap-768	137	39	such	such	ADJ
ap-768	137	40	that	that	SCONJ
ap-768	137	41	aa	aa	PROPN
ap-768	137	42	�	�	PROPN
ap-768	137	43	b.	b.	PROPN
ap-768	138	1	consequently	consequently	ADV
ap-768	138	2	f	f	PROPN
ap-768	139	1	a	a	PRON
ap-768	139	2	fj	fj	INTJ
ap-768	139	3	ja	ja	PROPN
ap-768	139	4	b	b	PROPN
ap-768	139	5	(	(	PUNCT
ap-768	139	6	)	)	PUNCT
ap-768	139	7	(	(	PUNCT
ap-768	139	8	)	)	PUNCT
ap-768	139	9	�	�	PROPN
ap-768	139	10	,	,	PUNCT
ap-768	139	11	where	where	SCONJ
ap-768	139	12	f	f	PROPN
ap-768	139	13	a	a	DET
ap-768	139	14	a	a	NOUN
ap-768	139	15	)	)	PUNCT
ap-768	139	16	)	)	PUNCT
ap-768	139	17	a	a	X
ap-768	139	18	)	)	PUNCT
ap-768	139	19	f	f	PROPN
ap-768	140	1	a	a	DET
ap-768	140	2	mod	mod	PROPN
ap-768	140	3	mod	mod	PROPN
ap-768	140	4	mod	mod	PROPN
ap-768	140	5	j	j	PROPN
ap-768	140	6	j	j	PROPN
ap-768	140	7	p	p	X
ap-768	140	8	j	j	PROPN
ap-768	141	1	p	p	PROPN
ap-768	141	2	p	p	X
ap-768	141	3	ja	ja	PROPN
ap-768	141	4	p	p	PROPN
ap-768	141	5	a	a	DET
ap-768	141	6	p	p	X
ap-768	141	7	a	a	DET
ap-768	141	8	ak	ak	PROPN
ap-768	141	9	k	k	PROPN
ap-768	141	10	k	k	PROPN
ap-768	141	11	(	(	PUNCT
ap-768	141	12	)	)	PUNCT
ap-768	141	13	(	(	PUNCT
ap-768	141	14	(	(	PUNCT
ap-768	141	15	(	(	PUNCT
ap-768	141	16	(	(	PUNCT
ap-768	141	17	)	)	PUNCT
ap-768	141	18	�	�	PROPN
ap-768	141	19	�	�	PROPN
ap-768	141	20	�	�	PROPN
ap-768	141	21	.	.	PUNCT
ap-768	142	1	©	©	PROPN
ap-768	142	2	czech	czech	PROPN
ap-768	142	3	technical	technical	PROPN
ap-768	142	4	university	university	PROPN
ap-768	142	5	publishing	publishing	NOUN
ap-768	142	6	house	house	NOUN
ap-768	142	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-768	142	8	41	41	NUM
ap-768	142	9	czech	czech	PROPN
ap-768	142	10	technical	technical	PROPN
ap-768	142	11	university	university	PROPN
ap-768	142	12	in	in	ADP
ap-768	142	13	prague	prague	PROPN
ap-768	142	14	acta	acta	PROPN
ap-768	142	15	polytechnica	polytechnica	PROPN
ap-768	142	16	vol	vol	NOUN
ap-768	142	17	.	.	PROPN
ap-768	143	1	45	45	NUM
ap-768	143	2	no	no	NOUN
ap-768	143	3	.	.	PUNCT
ap-768	144	1	5/2005	5/2005	NUM
ap-768	144	2	since	since	SCONJ
ap-768	144	3	we	we	PRON
ap-768	144	4	have	have	VERB
ap-768	144	5	f	f	PROPN
ap-768	144	6	a	a	DET
ap-768	144	7	fj	fj	INTJ
ap-768	144	8	ja	ja	PROPN
ap-768	144	9	b	b	PROPN
ap-768	144	10	(	(	PUNCT
ap-768	144	11	)	)	PUNCT
ap-768	144	12	(	(	PUNCT
ap-768	144	13	)	)	PUNCT
ap-768	144	14	�	�	PROPN
ap-768	145	1	and	and	CCONJ
ap-768	145	2	therefore	therefore	ADV
ap-768	145	3	f	f	PROPN
ap-768	145	4	fj	fj	INTJ
ap-768	145	5	ja	ja	PROPN
ap-768	145	6	b	b	PROPN
ap-768	145	7	(	(	PUNCT
ap-768	145	8	)	)	PUNCT
ap-768	145	9	~	~	PUNCT
ap-768	145	10	(	(	PUNCT
ap-768	145	11	)	)	PUNCT
ap-768	145	12	.	.	PUNCT
ap-768	146	1	qed	qed	PROPN
ap-768	146	2	proposition	proposition	NOUN
ap-768	146	3	4.1.3	4.1.3	NUM
ap-768	146	4	:	:	PUNCT
ap-768	146	5	any	any	DET
ap-768	146	6	orbit	orbit	NOUN
ap-768	146	7	in	in	ADP
ap-768	146	8	the	the	DET
ap-768	146	9	ring	ring	NOUN
ap-768	147	1	z	z	PROPN
ap-768	147	2	p	p	NOUN
ap-768	147	3	m	m	VERB
ap-768	147	4	k	k	NOUN
ap-768	147	5	has	have	VERB
ap-768	147	6	the	the	DET
ap-768	147	7	form	form	NOUN
ap-768	147	8	or	or	CCONJ
ap-768	147	9	z	z	NOUN
ap-768	147	10	m	m	VERB
ap-768	147	11	p	p	NOUN
ap-768	147	12	j	j	PROPN
ap-768	148	1	p	p	X
ap-768	148	2	m	m	PROPN
ap-768	148	3	k	k	PROPN
ap-768	148	4	j	j	PROPN
ap-768	148	5	k	k	PROPN
ap-768	148	6	kp	kp	PROPN
ap-768	148	7	a	a	DET
ap-768	148	8	a	a	DET
ap-768	148	9	p	p	X
ap-768	148	10	p	p	NOUN
ap-768	148	11	,	,	PUNCT
ap-768	148	12	(	(	PUNCT
ap-768	148	13	)	)	PUNCT
ap-768	148	14	{	{	PUNCT
ap-768	148	15	|gcd	|gcd	X
ap-768	148	16	(	(	PUNCT
ap-768	148	17	,	,	PUNCT
ap-768	148	18	)	)	PUNCT
ap-768	148	19	}	}	PUNCT
ap-768	148	20	�	�	PROPN
ap-768	148	21	�	�	PROPN
ap-768	148	22	�	�	PROPN
ap-768	148	23	,	,	PUNCT
ap-768	148	24	0	0	NUM
ap-768	148	25	�	�	PROPN
ap-768	148	26	�	�	PROPN
ap-768	148	27	j	j	PROPN
ap-768	148	28	k	k	PROPN
ap-768	148	29	,	,	PUNCT
ap-768	148	30	and	and	CCONJ
ap-768	148	31	consists	consist	VERB
ap-768	148	32	of	of	ADP
ap-768	148	33	or	or	CCONJ
ap-768	148	34	m	m	PROPN
ap-768	148	35	p	p	NOUN
ap-768	149	1	j	j	PROPN
ap-768	149	2	m	m	VERB
ap-768	149	3	k	k	PROPN
ap-768	149	4	j	j	PROPN
ap-768	150	1	k	k	PROPN
ap-768	150	2	p	p	PROPN
ap-768	150	3	p	p	X
ap-768	150	4	,	,	PUNCT
ap-768	150	5	(	(	PUNCT
ap-768	150	6	)	)	PUNCT
ap-768	150	7	(	(	PUNCT
ap-768	150	8	)	)	PUNCT
ap-768	150	9	�	�	PROPN
ap-768	150	10	�	�	PROPN
ap-768	150	11	�	�	PROPN
ap-768	150	12	points	point	NOUN
ap-768	150	13	.	.	PUNCT
ap-768	151	1	proof	proof	NOUN
ap-768	151	2	:	:	PUNCT
ap-768	151	3	from	from	ADP
ap-768	151	4	lemma	lemma	PROPN
ap-768	151	5	4.1.2	4.1.2	NUM
ap-768	151	6	it	it	PRON
ap-768	151	7	is	be	AUX
ap-768	151	8	clear	clear	ADJ
ap-768	151	9	that	that	SCONJ
ap-768	151	10	f	f	PROPN
ap-768	151	11	j	j	PROPN
ap-768	151	12	maps	map	VERB
ap-768	151	13	the	the	DET
ap-768	151	14	orbit	orbit	NOUN
ap-768	151	15	or	or	CCONJ
ap-768	151	16	m	m	PROPN
ap-768	151	17	p	p	NOUN
ap-768	151	18	k	k	PROPN
ap-768	151	19	,	,	PUNCT
ap-768	151	20	(	(	PUNCT
ap-768	151	21	)	)	PUNCT
ap-768	151	22	1	1	NUM
ap-768	151	23	into	into	ADP
ap-768	151	24	the	the	DET
ap-768	151	25	orbit	orbit	NOUN
ap-768	151	26	or	or	CCONJ
ap-768	151	27	m	m	PROPN
ap-768	151	28	p	p	NOUN
ap-768	151	29	j	j	PROPN
ap-768	151	30	k	k	PROPN
ap-768	151	31	p	p	PROPN
ap-768	151	32	,	,	PUNCT
ap-768	151	33	(	(	PUNCT
ap-768	151	34	)	)	PUNCT
ap-768	151	35	and	and	CCONJ
ap-768	151	36	from	from	ADP
ap-768	151	37	corollary	corollary	ADJ
ap-768	151	38	4.4	4.4	NUM
ap-768	151	39	we	we	PRON
ap-768	151	40	have	have	VERB
ap-768	151	41	f	f	PROPN
ap-768	151	42	p	p	PROPN
ap-768	151	43	p	p	PROPN
ap-768	151	44	a	a	PRON
ap-768	151	45	a	a	DET
ap-768	151	46	p	p	X
ap-768	151	47	pj	pj	PROPN
ap-768	151	48	m	m	PROPN
ap-768	151	49	p	p	PROPN
ap-768	151	50	j	j	PROPN
ap-768	151	51	m	m	PROPN
ap-768	151	52	p	p	NOUN
ap-768	151	53	j	j	PROPN
ap-768	151	54	p	p	X
ap-768	151	55	m	m	PROPN
ap-768	151	56	k	k	PROPN
ap-768	151	57	j	j	PROPN
ap-768	151	58	k	k	PROPN
ap-768	151	59	k	k	PROPN
ap-768	151	60	k	k	X
ap-768	151	61	(	(	PUNCT
ap-768	151	62	(	(	PUNCT
ap-768	151	63	)	)	PUNCT
ap-768	151	64	)	)	PUNCT
ap-768	151	65	(	(	PUNCT
ap-768	151	66	)	)	PUNCT
ap-768	151	67	{	{	PUNCT
ap-768	151	68	|gcd	|gcd	X
ap-768	151	69	(	(	PUNCT
ap-768	151	70	,	,	PUNCT
ap-768	151	71	)	)	PUNCT
ap-768	151	72	}	}	PUNCT
ap-768	151	73	,	,	PUNCT
ap-768	151	74	,	,	PUNCT
ap-768	151	75	or	or	CCONJ
ap-768	151	76	or	or	CCONJ
ap-768	151	77	z	z	NOUN
ap-768	151	78	!	!	PUNCT
ap-768	151	79	!	!	PUNCT
ap-768	152	1	�	�	PROPN
ap-768	152	2	�	�	PROPN
ap-768	152	3	.	.	PUNCT
ap-768	153	1	conversely	conversely	ADV
ap-768	153	2	,	,	PUNCT
ap-768	153	3	{	{	PUNCT
ap-768	153	4	|gcd	|gcd	X
ap-768	153	5	(	(	PUNCT
ap-768	153	6	,	,	PUNCT
ap-768	153	7	)	)	PUNCT
ap-768	153	8	}	}	PUNCT
ap-768	153	9	{	{	PUNCT
ap-768	153	10	|	|	ADV
ap-768	153	11	,	,	PUNCT
ap-768	153	12	gcd	gcd	NOUN
ap-768	153	13	(	(	PUNCT
ap-768	153	14	,	,	PUNCT
ap-768	153	15	)	)	PUNCT
ap-768	153	16	}	}	PUNCT
ap-768	153	17	a	a	DET
ap-768	153	18	a	a	DET
ap-768	153	19	p	p	X
ap-768	153	20	p	p	X
ap-768	153	21	p	p	X
ap-768	153	22	a	a	PRON
ap-768	153	23	a	a	DET
ap-768	153	24	a	a	DET
ap-768	153	25	p	p	X
ap-768	153	26	p	p	NOUN
ap-768	153	27	m	m	NOUN
ap-768	153	28	k	k	PROPN
ap-768	154	1	j	j	PROPN
ap-768	154	2	j	j	PROPN
ap-768	155	1	p	p	X
ap-768	155	2	m	m	PROPN
ap-768	155	3	k	k	PROPN
ap-768	155	4	j	j	PROPN
ap-768	155	5	k	k	PROPN
ap-768	155	6	k	k	PROPN
ap-768	155	7	j	j	PROPN
ap-768	155	8	�	�	PROPN
ap-768	155	9	�	�	PROPN
ap-768	155	10	�	�	PROPN
ap-768	155	11	�	�	PROPN
ap-768	155	12	�	�	PROPN
ap-768	155	13	�	�	PROPN
ap-768	155	14	�	�	PROPN
ap-768	155	15	z	z	PROPN
ap-768	155	16	z	z	PROPN
ap-768	155	17	1	1	NUM
ap-768	155	18	!	!	PUNCT
ap-768	155	19	�	�	PROPN
ap-768	155	20	�	�	PROPN
ap-768	155	21	�	�	PROPN
ap-768	155	22	{	{	PUNCT
ap-768	155	23	(	(	PUNCT
ap-768	155	24	)	)	PUNCT
ap-768	155	25	|	|	ADV
ap-768	155	26	,	,	PUNCT
ap-768	155	27	gcd	gcd	NOUN
ap-768	155	28	(	(	PUNCT
ap-768	155	29	,	,	PUNCT
ap-768	155	30	)	)	PUNCT
ap-768	155	31	}	}	PUNCT
ap-768	155	32	(	(	PUNCT
ap-768	155	33	(	(	PUNCT
ap-768	155	34	)	)	PUNCT
ap-768	155	35	)	)	PUNCT
ap-768	155	36	.	.	PUNCT
ap-768	156	1	mod	mod	PROPN
ap-768	156	2	,	,	PUNCT
ap-768	156	3	p	p	X
ap-768	156	4	a	a	PRON
ap-768	156	5	a	a	PRON
ap-768	156	6	a	a	DET
ap-768	156	7	pj	pj	PROPN
ap-768	157	1	p	p	PROPN
ap-768	157	2	p	p	PROPN
ap-768	157	3	m	m	PROPN
ap-768	157	4	k	k	PROPN
ap-768	157	5	j	j	PROPN
ap-768	157	6	m	m	PROPN
ap-768	157	7	pk	pk	PROPN
ap-768	157	8	k	k	PROPN
ap-768	157	9	kz	kz	PROPN
ap-768	157	10	f	f	PROPN
ap-768	157	11	or1	or1	PROPN
ap-768	157	12	1	1	NUM
ap-768	157	13	thus	thus	ADV
ap-768	157	14	we	we	PRON
ap-768	157	15	have	have	VERB
ap-768	157	16	f	f	PROPN
ap-768	157	17	or	or	CCONJ
ap-768	157	18	or	or	CCONJ
ap-768	157	19	zj	zj	NOUN
ap-768	157	20	m	m	PROPN
ap-768	157	21	p	p	NOUN
ap-768	157	22	m	m	PROPN
ap-768	157	23	p	p	NOUN
ap-768	157	24	j	j	PROPN
ap-768	158	1	p	p	X
ap-768	158	2	m	m	PROPN
ap-768	158	3	k	k	PROPN
ap-768	158	4	j	j	PROPN
ap-768	158	5	k	k	PROPN
ap-768	158	6	k	k	PROPN
ap-768	158	7	kp	kp	PROPN
ap-768	158	8	a	a	DET
ap-768	158	9	a	a	DET
ap-768	158	10	p	p	X
ap-768	158	11	p	p	X
ap-768	158	12	(	(	PUNCT
ap-768	158	13	(	(	PUNCT
ap-768	158	14	)	)	PUNCT
ap-768	158	15	)	)	PUNCT
ap-768	158	16	(	(	PUNCT
ap-768	158	17	)	)	PUNCT
ap-768	158	18	{	{	PUNCT
ap-768	158	19	|gcd	|gcd	X
ap-768	158	20	(	(	PUNCT
ap-768	158	21	,	,	PUNCT
ap-768	158	22	)	)	PUNCT
ap-768	158	23	}	}	PUNCT
ap-768	158	24	,	,	PUNCT
ap-768	158	25	,	,	PUNCT
ap-768	158	26	1	1	NUM
ap-768	158	27	�	�	PROPN
ap-768	158	28	�	�	PROPN
ap-768	158	29	�	�	PROPN
ap-768	158	30	�	�	PROPN
ap-768	158	31	.	.	PUNCT
ap-768	159	1	qed	qed	PROPN
ap-768	159	2	4.2	4.2	NUM
ap-768	159	3	orbits	orbit	NOUN
ap-768	159	4	for	for	ADP
ap-768	159	5	n	n	PRON
ap-768	159	6	�	�	PROPN
ap-768	159	7	pq	pq	PROPN
ap-768	159	8	,	,	PUNCT
ap-768	159	9	gcd(p	gcd(p	PROPN
ap-768	159	10	,	,	PUNCT
ap-768	159	11	q	q	NOUN
ap-768	159	12	)	)	PUNCT
ap-768	159	13	�	�	PROPN
ap-768	159	14	1	1	NUM
ap-768	159	15	let	let	VERB
ap-768	159	16	us	we	PRON
ap-768	159	17	now	now	ADV
ap-768	159	18	consider	consider	VERB
ap-768	159	19	n	n	PRON
ap-768	159	20	of	of	ADP
ap-768	159	21	the	the	DET
ap-768	159	22	form	form	NOUN
ap-768	159	23	n	n	PROPN
ap-768	159	24	�	�	PROPN
ap-768	159	25	pq	pq	PROPN
ap-768	159	26	,	,	PUNCT
ap-768	159	27	where	where	SCONJ
ap-768	159	28	pq	pq	PROPN
ap-768	159	29	�	�	PROPN
ap-768	159	30	n	n	PART
ap-768	159	31	are	be	AUX
ap-768	159	32	co	co	ADJ
ap-768	159	33	-	-	ADJ
ap-768	159	34	prime	prime	ADJ
ap-768	159	35	numbers	number	NOUN
ap-768	159	36	.	.	PUNCT
ap-768	160	1	in	in	ADP
ap-768	160	2	this	this	DET
ap-768	160	3	case	case	NOUN
ap-768	160	4	it	it	PRON
ap-768	160	5	will	will	AUX
ap-768	160	6	be	be	AUX
ap-768	160	7	very	very	ADV
ap-768	160	8	useful	useful	ADJ
ap-768	160	9	to	to	PART
ap-768	160	10	apply	apply	VERB
ap-768	160	11	the	the	DET
ap-768	160	12	chinese	chinese	ADJ
ap-768	160	13	remainder	remainder	NOUN
ap-768	160	14	theorem	theorem	NOUN
ap-768	160	15	[	[	X
ap-768	160	16	13	13	NUM
ap-768	160	17	]	]	PUNCT
ap-768	160	18	.	.	PUNCT
ap-768	161	1	theorem	theorem	VERB
ap-768	161	2	4.2.1	4.2.1	NUM
ap-768	161	3	:	:	PUNCT
ap-768	161	4	(	(	PUNCT
ap-768	161	5	chinese	chinese	ADJ
ap-768	161	6	remainder	remainder	NOUN
ap-768	161	7	theorem	theorem	VERB
ap-768	161	8	)	)	PUNCT
ap-768	161	9	let	let	VERB
ap-768	161	10	a	a	DET
ap-768	161	11	a1	a1	NOUN
ap-768	161	12	z	z	PROPN
ap-768	161	13	,	,	PUNCT
ap-768	161	14	2	2	NUM
ap-768	161	15	�	�	PROPN
ap-768	161	16	.	.	PUNCT
ap-768	162	1	let	let	VERB
ap-768	162	2	p	p	PROPN
ap-768	162	3	p1	p1	PROPN
ap-768	162	4	n	n	CCONJ
ap-768	162	5	,	,	PUNCT
ap-768	162	6	2	2	NUM
ap-768	162	7	�	�	NOUN
ap-768	162	8	be	be	AUX
ap-768	162	9	co	co	ADJ
ap-768	162	10	-	-	ADJ
ap-768	162	11	prime	prime	ADJ
ap-768	162	12	numbers	number	NOUN
ap-768	162	13	.	.	PUNCT
ap-768	163	1	then	then	ADV
ap-768	163	2	there	there	PRON
ap-768	163	3	exists	exist	VERB
ap-768	163	4	x	x	X
ap-768	163	5	�	�	PROPN
ap-768	163	6	z	z	PROPN
ap-768	163	7	,	,	PUNCT
ap-768	163	8	such	such	ADJ
ap-768	163	9	that	that	SCONJ
ap-768	163	10	x	x	PROPN
ap-768	163	11	a	a	DET
ap-768	163	12	p	p	X
ap-768	163	13	ii	ii	X
ap-768	163	14	i	i	PRON
ap-768	163	15	�	�	PROPN
ap-768	163	16	�	�	PROPN
ap-768	163	17	�	�	PROPN
ap-768	163	18	(	(	PUNCT
ap-768	163	19	mod	mod	PROPN
ap-768	163	20	)	)	PUNCT
ap-768	163	21	,	,	PUNCT
ap-768	163	22	,	,	PUNCT
ap-768	163	23	1	1	NUM
ap-768	163	24	2	2	NUM
ap-768	163	25	.	.	PUNCT
ap-768	164	1	if	if	SCONJ
ap-768	164	2	x	x	PRON
ap-768	164	3	is	be	AUX
ap-768	164	4	a	a	DET
ap-768	164	5	solution	solution	NOUN
ap-768	164	6	,	,	PUNCT
ap-768	164	7	then	then	ADV
ap-768	164	8	y	y	PROPN
ap-768	164	9	is	be	AUX
ap-768	164	10	a	a	DET
ap-768	164	11	solution	solution	NOUN
ap-768	164	12	if	if	SCONJ
ap-768	164	13	and	and	CCONJ
ap-768	164	14	only	only	ADV
ap-768	164	15	if	if	SCONJ
ap-768	164	16	x	x	PROPN
ap-768	164	17	y	y	PROPN
ap-768	164	18	p	p	X
ap-768	164	19	p	p	PROPN
ap-768	164	20	�	�	PROPN
ap-768	164	21	(	(	PUNCT
ap-768	164	22	mod	mod	PROPN
ap-768	164	23	)	)	PUNCT
ap-768	164	24	1	1	NUM
ap-768	164	25	2	2	NUM
ap-768	164	26	.	.	PUNCT
ap-768	165	1	definition	definition	NOUN
ap-768	165	2	4.2.2	4.2.2	NUM
ap-768	165	3	:	:	PUNCT
ap-768	165	4	for	for	ADP
ap-768	165	5	p	p	PROPN
ap-768	165	6	q	q	PROPN
ap-768	165	7	,	,	PUNCT
ap-768	165	8	�	�	PROPN
ap-768	165	9	n	n	CCONJ
ap-768	165	10	,	,	PUNCT
ap-768	165	11	gcd(p	gcd(p	PROPN
ap-768	165	12	,	,	PUNCT
ap-768	165	13	q	q	NOUN
ap-768	165	14	)	)	PUNCT
ap-768	165	15	�	�	PROPN
ap-768	165	16	1	1	NUM
ap-768	165	17	we	we	PRON
ap-768	165	18	define	define	VERB
ap-768	165	19	a	a	DET
ap-768	165	20	mapping	mapping	NOUN
ap-768	165	21	g	g	PROPN
ap-768	165	22	z	z	PROPN
ap-768	165	23	z	z	PROPN
ap-768	166	1	z	z	NOUN
ap-768	166	2	:	:	PUNCT
ap-768	166	3	pq	pq	INTJ
ap-768	166	4	m	m	PROPN
ap-768	166	5	p	p	NOUN
ap-768	166	6	m	m	PROPN
ap-768	166	7	q	q	NOUN
ap-768	166	8	m	m	PROPN
ap-768	166	9	�	�	PROPN
ap-768	166	10	�	�	PROPN
ap-768	166	11	by	by	ADP
ap-768	166	12	the	the	DET
ap-768	166	13	formula	formula	NOUN
ap-768	166	14	�	�	PROPN
ap-768	166	15	�	�	PROPN
ap-768	166	16	g	g	PROPN
ap-768	166	17	(	(	PUNCT
ap-768	166	18	):	):	PUNCT
ap-768	166	19	(	(	PUNCT
ap-768	166	20	)	)	PUNCT
ap-768	166	21	,	,	PUNCT
ap-768	166	22	(	(	PUNCT
ap-768	166	23	)	)	PUNCT
ap-768	166	24	mod	mod	PROPN
ap-768	166	25	moda	moda	PROPN
ap-768	166	26	a	a	DET
ap-768	166	27	ap	ap	PROPN
ap-768	166	28	q	q	PROPN
ap-768	166	29	�	�	PROPN
ap-768	166	30	for	for	ADP
ap-768	166	31	any	any	DET
ap-768	166	32	a	a	DET
ap-768	166	33	pq	pq	NOUN
ap-768	166	34	m	m	NOUN
ap-768	166	35	�	�	PROPN
ap-768	166	36	z	z	PROPN
ap-768	166	37	,	,	PUNCT
ap-768	166	38	and	and	CCONJ
ap-768	166	39	a	a	DET
ap-768	166	40	mapping	mapping	NOUN
ap-768	166	41	g	g	PROPN
ap-768	166	42	z	z	PROPN
ap-768	166	43	z	z	PROPN
ap-768	167	1	z	z	NOUN
ap-768	167	2	:	:	PUNCT
ap-768	167	3	(	(	PUNCT
ap-768	167	4	,	,	PUNCT
ap-768	167	5	)	)	PUNCT
ap-768	167	6	(	(	PUNCT
ap-768	167	7	,	,	PUNCT
ap-768	167	8	)	)	PUNCT
ap-768	167	9	(	(	PUNCT
ap-768	167	10	,	,	PUNCT
ap-768	167	11	)	)	PUNCT
ap-768	167	12	sl	sl	PROPN
ap-768	167	13	m	m	VERB
ap-768	167	14	sl	sl	INTJ
ap-768	167	15	m	m	VERB
ap-768	167	16	sl	sl	INTJ
ap-768	167	17	mpq	mpq	PROPN
ap-768	168	1	p	p	X
ap-768	168	2	q	q	PROPN
ap-768	168	3	�	�	X
ap-768	168	4	�	�	PROPN
ap-768	168	5	by	by	ADP
ap-768	168	6	the	the	DET
ap-768	168	7	formula	formula	NOUN
ap-768	168	8	�	�	PROPN
ap-768	168	9	�	�	PROPN
ap-768	168	10	g	g	PROPN
ap-768	168	11	a	a	DET
ap-768	168	12	a	a	DET
ap-768	168	13	a	a	X
ap-768	168	14	(	(	PUNCT
ap-768	168	15	):	):	PUNCT
ap-768	168	16	(	(	PUNCT
ap-768	168	17	)	)	PUNCT
ap-768	168	18	,	,	PUNCT
ap-768	168	19	(	(	PUNCT
ap-768	168	20	)	)	PUNCT
ap-768	168	21	mod	mod	PROPN
ap-768	168	22	mod	mod	PROPN
ap-768	168	23	�	�	PROPN
ap-768	168	24	p	p	PROPN
ap-768	168	25	q	q	PROPN
ap-768	168	26	for	for	ADP
ap-768	168	27	any	any	DET
ap-768	168	28	a	a	DET
ap-768	168	29	z	z	PROPN
ap-768	168	30	�	�	PROPN
ap-768	168	31	sl	sl	PROPN
ap-768	168	32	m	m	PROPN
ap-768	168	33	pq	pq	NOUN
ap-768	168	34	(	(	PUNCT
ap-768	168	35	,	,	PUNCT
ap-768	168	36	)	)	PUNCT
ap-768	168	37	.	.	PUNCT
ap-768	169	1	it	it	PRON
ap-768	169	2	is	be	AUX
ap-768	169	3	clear	clear	ADJ
ap-768	169	4	from	from	ADP
ap-768	169	5	definition	definition	NOUN
ap-768	169	6	that	that	SCONJ
ap-768	169	7	g	g	NOUN
ap-768	169	8	,	,	PUNCT
ap-768	169	9	g	g	PROPN
ap-768	169	10	are	be	AUX
ap-768	169	11	homomorphisms	homomorphism	NOUN
ap-768	169	12	and	and	CCONJ
ap-768	169	13	the	the	DET
ap-768	169	14	chinese	chinese	ADJ
ap-768	169	15	remainder	remainder	NOUN
ap-768	169	16	theorem	theorem	NOUN
ap-768	169	17	implies	imply	VERB
ap-768	169	18	that	that	SCONJ
ap-768	169	19	g	g	PROPN
ap-768	169	20	,	,	PUNCT
ap-768	169	21	g	g	PROPN
ap-768	169	22	are	be	AUX
ap-768	169	23	one	one	NUM
ap-768	169	24	-	-	PUNCT
ap-768	169	25	to	to	ADP
ap-768	169	26	-	-	PUNCT
ap-768	169	27	one	one	NUM
ap-768	169	28	correspondences	correspondence	NOUN
ap-768	169	29	.	.	PUNCT
ap-768	170	1	thus	thus	ADV
ap-768	170	2	we	we	PRON
ap-768	170	3	have	have	VERB
ap-768	170	4	the	the	DET
ap-768	170	5	following	follow	VERB
ap-768	170	6	proposition	proposition	NOUN
ap-768	170	7	.	.	PUNCT
ap-768	171	1	proposition	proposition	NOUN
ap-768	171	2	4.2.3	4.2.3	NUM
ap-768	171	3	:	:	PUNCT
ap-768	171	4	the	the	DET
ap-768	171	5	mapping	mapping	NOUN
ap-768	171	6	g	g	NOUN
ap-768	171	7	is	be	AUX
ap-768	171	8	an	an	DET
ap-768	171	9	isomorphism	isomorphism	NOUN
ap-768	171	10	of	of	ADP
ap-768	171	11	rings	ring	NOUN
ap-768	171	12	and	and	CCONJ
ap-768	171	13	the	the	DET
ap-768	171	14	mapping	mapping	NOUN
ap-768	171	15	g	g	NOUN
ap-768	171	16	is	be	AUX
ap-768	171	17	an	an	DET
ap-768	171	18	isomorphism	isomorphism	NOUN
ap-768	171	19	of	of	ADP
ap-768	171	20	groups	group	NOUN
ap-768	171	21	.	.	PUNCT
ap-768	172	1	further	far	ADV
ap-768	172	2	we	we	PRON
ap-768	172	3	determine	determine	VERB
ap-768	172	4	orbits	orbit	NOUN
ap-768	172	5	on	on	ADP
ap-768	172	6	the	the	DET
ap-768	172	7	cartesian	cartesian	ADJ
ap-768	172	8	product	product	NOUN
ap-768	172	9	of	of	ADP
ap-768	172	10	rings	ring	NOUN
ap-768	172	11	z	z	PROPN
ap-768	172	12	zp	zp	PROPN
ap-768	172	13	m	m	PROPN
ap-768	172	14	q	q	PROPN
ap-768	172	15	m	m	PROPN
ap-768	172	16	�	�	PROPN
ap-768	172	17	.	.	PUNCT
ap-768	173	1	for	for	ADP
ap-768	173	2	this	this	DET
ap-768	173	3	purpose	purpose	NOUN
ap-768	173	4	we	we	PRON
ap-768	173	5	define	define	VERB
ap-768	173	6	the	the	DET
ap-768	173	7	action	action	NOUN
ap-768	173	8	of	of	ADP
ap-768	173	9	the	the	DET
ap-768	173	10	cartesian	cartesian	ADJ
ap-768	173	11	product	product	NOUN
ap-768	173	12	of	of	ADP
ap-768	173	13	groups	group	NOUN
ap-768	173	14	sl	sl	INTJ
ap-768	173	15	m	m	VERB
ap-768	174	1	sl	sl	INTJ
ap-768	174	2	mp	mp	PROPN
ap-768	174	3	q	q	PROPN
ap-768	174	4	(	(	PUNCT
ap-768	174	5	,	,	PUNCT
ap-768	174	6	)	)	PUNCT
ap-768	174	7	(	(	PUNCT
ap-768	174	8	,	,	PUNCT
ap-768	174	9	)	)	PUNCT
ap-768	174	10	z	z	NOUN
ap-768	175	1	z	z	X
ap-768	175	2	�	�	PROPN
ap-768	175	3	on	on	ADP
ap-768	175	4	ring	ring	NOUN
ap-768	175	5	z	z	PROPN
ap-768	175	6	zp	zp	PROPN
ap-768	175	7	m	m	PROPN
ap-768	175	8	q	q	PROPN
ap-768	175	9	m	m	VERB
ap-768	175	10	�	�	PROPN
ap-768	175	11	by	by	ADP
ap-768	175	12	the	the	DET
ap-768	175	13	formula	formula	NOUN
ap-768	175	14	�	�	PROPN
ap-768	175	15	�	�	PROPN
ap-768	175	16	a	a	PRON
ap-768	175	17	a	a	DET
ap-768	175	18	a	a	PRON
ap-768	175	19	a	a	DET
ap-768	175	20	ap	ap	PROPN
ap-768	175	21	qa	qa	PROPN
ap-768	175	22	a	a	DET
ap-768	175	23	a	a	DET
ap-768	175	24	a	a	DET
ap-768	175	25	a	a	DET
ap-768	175	26	�	�	PROPN
ap-768	175	27	�	�	PROPN
ap-768	175	28	(	(	PUNCT
ap-768	175	29	,	,	PUNCT
ap-768	175	30	)	)	PUNCT
ap-768	175	31	(	(	PUNCT
ap-768	175	32	,	,	PUNCT
ap-768	175	33	)	)	PUNCT
ap-768	175	34	(	(	PUNCT
ap-768	175	35	)	)	PUNCT
ap-768	175	36	,	,	PUNCT
ap-768	175	37	(	(	PUNCT
ap-768	175	38	)	)	PUNCT
ap-768	175	39	mod	mod	PROPN
ap-768	175	40	mod1	mod1	NOUN
ap-768	175	41	2	2	NUM
ap-768	175	42	1	1	NUM
ap-768	175	43	2	2	NUM
ap-768	175	44	1	1	NUM
ap-768	175	45	1	1	NUM
ap-768	175	46	2	2	NUM
ap-768	175	47	2	2	NUM
ap-768	175	48	for	for	ADP
ap-768	175	49	any	any	DET
ap-768	175	50	a	a	DET
ap-768	175	51	a	a	DET
ap-768	175	52	a	a	DET
ap-768	175	53	p	p	NOUN
ap-768	175	54	m	m	PROPN
ap-768	175	55	q	q	PROPN
ap-768	175	56	m	m	PROPN
ap-768	175	57	�	�	PROPN
ap-768	175	58	�	�	PROPN
ap-768	175	59	�	�	PROPN
ap-768	175	60	(	(	PUNCT
ap-768	175	61	,	,	PUNCT
ap-768	175	62	)	)	PUNCT
ap-768	175	63	1	1	NUM
ap-768	175	64	2	2	NUM
ap-768	175	65	z	z	NOUN
ap-768	175	66	z	z	NOUN
ap-768	175	67	and	and	CCONJ
ap-768	175	68	any	any	DET
ap-768	175	69	a	a	DET
ap-768	175	70	a	a	DET
ap-768	175	71	a	a	DET
ap-768	175	72	z	z	NOUN
ap-768	175	73	z	z	PROPN
ap-768	175	74	�	�	PROPN
ap-768	175	75	�	�	PROPN
ap-768	175	76	�	�	PROPN
ap-768	175	77	(	(	PUNCT
ap-768	175	78	,	,	PUNCT
ap-768	175	79	)	)	PUNCT
ap-768	175	80	(	(	PUNCT
ap-768	175	81	,	,	PUNCT
ap-768	175	82	)	)	PUNCT
ap-768	175	83	(	(	PUNCT
ap-768	175	84	,	,	PUNCT
ap-768	175	85	)	)	PUNCT
ap-768	175	86	1	1	NUM
ap-768	175	87	2	2	NUM
ap-768	175	88	sl	sl	NOUN
ap-768	175	89	m	m	NOUN
ap-768	175	90	sl	sl	INTJ
ap-768	175	91	mp	mp	PROPN
ap-768	175	92	q	q	PROPN
ap-768	175	93	.	.	PUNCT
ap-768	176	1	it	it	PRON
ap-768	176	2	follows	follow	VERB
ap-768	176	3	from	from	ADP
ap-768	176	4	the	the	DET
ap-768	176	5	definition	definition	NOUN
ap-768	176	6	of	of	ADP
ap-768	176	7	this	this	DET
ap-768	176	8	action	action	NOUN
ap-768	176	9	that	that	PRON
ap-768	176	10	orbits	orbit	VERB
ap-768	176	11	in	in	ADP
ap-768	176	12	z	z	PROPN
ap-768	176	13	zp	zp	PROPN
ap-768	176	14	m	m	PROPN
ap-768	176	15	q	q	PROPN
ap-768	176	16	m	m	PRON
ap-768	176	17	�	�	PROPN
ap-768	176	18	are	be	AUX
ap-768	176	19	cartesian	cartesian	ADJ
ap-768	176	20	products	product	NOUN
ap-768	176	21	of	of	ADP
ap-768	176	22	orbits	orbit	NOUN
ap-768	176	23	in	in	ADP
ap-768	176	24	z	z	PROPN
ap-768	176	25	p	p	NOUN
ap-768	176	26	m	m	PROPN
ap-768	176	27	and	and	CCONJ
ap-768	176	28	zq	zq	PROPN
ap-768	176	29	m.	m.	NOUN
ap-768	176	30	proposition	proposition	NOUN
ap-768	176	31	4.2.4	4.2.4	NUM
ap-768	176	32	:	:	PUNCT
ap-768	176	33	let	let	VERB
ap-768	176	34	p	p	PROPN
ap-768	176	35	q	q	NOUN
ap-768	176	36	,	,	PUNCT
ap-768	176	37	�	�	PROPN
ap-768	176	38	n	n	PART
ap-768	176	39	be	be	VERB
ap-768	176	40	co	co	ADJ
ap-768	176	41	-	-	ADJ
ap-768	176	42	prime	prime	ADJ
ap-768	176	43	numbers	number	NOUN
ap-768	176	44	.	.	PUNCT
ap-768	177	1	then	then	ADV
ap-768	177	2	the	the	DET
ap-768	177	3	mapping	mapping	NOUN
ap-768	177	4	g	g	NOUN
ap-768	177	5	provides	provide	VERB
ap-768	177	6	one	one	NUM
ap-768	177	7	-	-	PUNCT
ap-768	177	8	to	to	ADP
ap-768	177	9	-	-	PUNCT
ap-768	177	10	one	one	NUM
ap-768	177	11	correspondence	correspondence	NOUN
ap-768	177	12	between	between	ADP
ap-768	177	13	the	the	DET
ap-768	177	14	orbits	orbit	NOUN
ap-768	177	15	in	in	ADP
ap-768	177	16	z	z	PROPN
ap-768	177	17	pq	pq	NOUN
ap-768	177	18	m	m	PROPN
ap-768	177	19	and	and	CCONJ
ap-768	177	20	the	the	DET
ap-768	177	21	cartesian	cartesian	ADJ
ap-768	177	22	products	product	NOUN
ap-768	177	23	of	of	ADP
ap-768	177	24	the	the	DET
ap-768	177	25	orbits	orbit	NOUN
ap-768	177	26	in	in	ADP
ap-768	177	27	z	z	PROPN
ap-768	177	28	p	p	NOUN
ap-768	177	29	m	m	PROPN
ap-768	177	30	and	and	CCONJ
ap-768	177	31	zq	zq	PROPN
ap-768	177	32	m.	m.	NOUN
ap-768	177	33	moreover	moreover	ADV
ap-768	177	34	,	,	PUNCT
ap-768	177	35	if	if	SCONJ
ap-768	177	36	p	p	PROPN
ap-768	177	37	p1|	p1|	PROPN
ap-768	177	38	,	,	PUNCT
ap-768	177	39	q	q	PUNCT
ap-768	177	40	q1|	q1|	ADV
ap-768	177	41	and	and	CCONJ
ap-768	177	42	the	the	DET
ap-768	177	43	orbits	orbit	NOUN
ap-768	177	44	orm	orm	NOUN
ap-768	177	45	,	,	PUNCT
ap-768	177	46	p(p1	p(p1	NOUN
ap-768	177	47	)	)	PUNCT
ap-768	177	48	,	,	PUNCT
ap-768	177	49	orm	orm	NOUN
ap-768	177	50	,	,	PUNCT
ap-768	177	51	q(q1	q(q1	NOUN
ap-768	177	52	)	)	PUNCT
ap-768	177	53	are	be	AUX
ap-768	177	54	of	of	ADP
ap-768	177	55	the	the	DET
ap-768	177	56	form	form	NOUN
ap-768	177	57	or	or	CCONJ
ap-768	177	58	z	z	NOUN
ap-768	177	59	or	or	CCONJ
ap-768	177	60	z	z	NOUN
ap-768	177	61	m	m	VERB
ap-768	177	62	p	p	NOUN
ap-768	177	63	p	p	X
ap-768	177	64	m	m	NOUN
ap-768	177	65	m	m	VERB
ap-768	177	66	q	q	NOUN
ap-768	177	67	q	q	X
ap-768	178	1	m	m	VERB
ap-768	178	2	p	p	X
ap-768	178	3	a	a	PRON
ap-768	178	4	a	a	DET
ap-768	178	5	p	p	X
ap-768	178	6	p	p	X
ap-768	178	7	q	q	NOUN
ap-768	178	8	a	a	PRON
ap-768	178	9	,	,	PUNCT
ap-768	178	10	,	,	PUNCT
ap-768	178	11	(	(	PUNCT
ap-768	178	12	)	)	PUNCT
ap-768	178	13	{	{	PUNCT
ap-768	178	14	|gcd	|gcd	X
ap-768	178	15	(	(	PUNCT
ap-768	178	16	,	,	PUNCT
ap-768	178	17	)	)	PUNCT
ap-768	178	18	}	}	PUNCT
ap-768	178	19	,	,	PUNCT
ap-768	178	20	(	(	PUNCT
ap-768	178	21	)	)	PUNCT
ap-768	178	22	{	{	PUNCT
ap-768	178	23	|gcd	|gcd	NUM
ap-768	178	24	1	1	NUM
ap-768	178	25	1	1	NUM
ap-768	178	26	1	1	NUM
ap-768	178	27	�	�	PROPN
ap-768	178	28	�	�	PROPN
ap-768	178	29	�	�	PROPN
ap-768	178	30	�	�	PROPN
ap-768	178	31	�	�	PROPN
ap-768	178	32	(	(	PUNCT
ap-768	178	33	,	,	PUNCT
ap-768	178	34	)	)	PUNCT
ap-768	178	35	}	}	PUNCT
ap-768	178	36	,	,	PUNCT
ap-768	178	37	a	a	DET
ap-768	178	38	q	q	X
ap-768	178	39	q	q	X
ap-768	178	40	�	�	PROPN
ap-768	178	41	1	1	NUM
ap-768	178	42	then	then	ADV
ap-768	178	43	�	�	PROPN
ap-768	178	44	�	�	PROPN
ap-768	178	45	or	or	CCONJ
ap-768	178	46	g	g	PROPN
ap-768	178	47	or	or	CCONJ
ap-768	178	48	or	or	CCONJ
ap-768	178	49	z	z	NOUN
ap-768	178	50	m	m	VERB
ap-768	179	1	pq	pq	INTJ
ap-768	179	2	m	m	PROPN
ap-768	179	3	p	p	NOUN
ap-768	179	4	m	m	PROPN
ap-768	179	5	q	q	PROPN
ap-768	180	1	pq	pq	INTJ
ap-768	180	2	m	m	PROPN
ap-768	180	3	p	p	NOUN
ap-768	180	4	q	q	X
ap-768	180	5	p	p	X
ap-768	180	6	q	q	X
ap-768	180	7	a	a	DET
ap-768	180	8	a	a	X
ap-768	180	9	,	,	PUNCT
ap-768	180	10	,	,	PUNCT
ap-768	180	11	,	,	PUNCT
ap-768	180	12	(	(	PUNCT
ap-768	180	13	)	)	PUNCT
ap-768	180	14	(	(	PUNCT
ap-768	180	15	)	)	PUNCT
ap-768	180	16	(	(	PUNCT
ap-768	180	17	)	)	PUNCT
ap-768	180	18	{	{	PUNCT
ap-768	180	19	|gcd	|gcd	NOUN
ap-768	180	20	(	(	PUNCT
ap-768	180	21	,	,	PUNCT
ap-768	180	22	1	1	NUM
ap-768	180	23	1	1	NUM
ap-768	180	24	1	1	NUM
ap-768	180	25	1	1	NUM
ap-768	180	26	1	1	NUM
ap-768	180	27	�	�	PROPN
ap-768	180	28	�	�	PROPN
ap-768	180	29	�	�	PROPN
ap-768	180	30	�	�	PROPN
ap-768	180	31	�	�	PROPN
ap-768	180	32	pq	pq	PROPN
ap-768	180	33	p	p	NOUN
ap-768	180	34	q	q	PROPN
ap-768	180	35	)	)	PUNCT
ap-768	180	36	}	}	PUNCT
ap-768	180	37	.	.	PUNCT
ap-768	181	1	�	�	PROPN
ap-768	181	2	1	1	NUM
ap-768	181	3	1	1	NUM
ap-768	181	4	proof	proof	NOUN
ap-768	181	5	:	:	PUNCT
ap-768	181	6	first	first	ADV
ap-768	181	7	,	,	PUNCT
ap-768	181	8	we	we	PRON
ap-768	181	9	prove	prove	VERB
ap-768	181	10	that	that	SCONJ
ap-768	181	11	g	g	PROPN
ap-768	181	12	and	and	CCONJ
ap-768	181	13	g	g	PROPN
ap-768	181	14	�	�	NOUN
ap-768	181	15	1	1	NUM
ap-768	181	16	preserve	preserve	NOUN
ap-768	181	17	equivalence	equivalence	NOUN
ap-768	181	18	,	,	PUNCT
ap-768	181	19	i.e.	i.e.	X
ap-768	181	20	a	a	DET
ap-768	181	21	b	b	NOUN
ap-768	181	22	a	a	DET
ap-768	181	23	b~	b~	PROPN
ap-768	181	24	(	(	PUNCT
ap-768	181	25	)	)	PUNCT
ap-768	181	26	~	~	PUNCT
ap-768	181	27	(	(	PUNCT
ap-768	181	28	)	)	PUNCT
ap-768	181	29	�	�	PROPN
ap-768	182	1	g	g	NOUN
ap-768	182	2	g	g	PROPN
ap-768	182	3	for	for	ADP
ap-768	182	4	all	all	DET
ap-768	182	5	a	a	DET
ap-768	182	6	b	b	PROPN
ap-768	182	7	pq	pq	NOUN
ap-768	182	8	m	m	PROPN
ap-768	182	9	,	,	PUNCT
ap-768	182	10	�	�	PROPN
ap-768	182	11	z	z	PROPN
ap-768	182	12	.	.	PUNCT
ap-768	183	1	from	from	ADP
ap-768	183	2	the	the	DET
ap-768	183	3	definition	definition	NOUN
ap-768	183	4	of	of	ADP
ap-768	183	5	equivalence	equivalence	NOUN
ap-768	183	6	we	we	PRON
ap-768	183	7	have	have	VERB
ap-768	183	8	a	a	DET
ap-768	183	9	b	b	NOUN
ap-768	183	10	sl	sl	INTJ
ap-768	183	11	m	m	PROPN
ap-768	183	12	a	a	DET
ap-768	183	13	b	b	NOUN
ap-768	183	14	a	a	DET
ap-768	183	15	bpq~	bpq~	NOUN
ap-768	183	16	(	(	PUNCT
ap-768	183	17	,	,	PUNCT
ap-768	183	18	)	)	PUNCT
ap-768	183	19	,	,	PUNCT
ap-768	183	20	(	(	PUNCT
ap-768	183	21	(	(	PUNCT
ap-768	183	22	)	)	PUNCT
ap-768	183	23	�	�	PROPN
ap-768	183	24	�	�	PROPN
ap-768	183	25	�	�	PROPN
ap-768	183	26	�	�	PROPN
ap-768	183	27	�	�	PROPN
ap-768	183	28	�	�	PROPN
ap-768	183	29	a	a	DET
ap-768	183	30	z	z	NOUN
ap-768	183	31	a	a	DET
ap-768	183	32	g	g	NOUN
ap-768	183	33	a	a	NOUN
ap-768	183	34	)	)	PUNCT
ap-768	183	35	g	g	NOUN
ap-768	183	36	,	,	PUNCT
ap-768	183	37	where	where	SCONJ
ap-768	183	38	�	�	PROPN
ap-768	183	39	�	�	PROPN
ap-768	183	40	�	�	PROPN
ap-768	183	41	�	�	PROPN
ap-768	183	42	g	g	PROPN
ap-768	183	43	a	a	PRON
ap-768	183	44	)	)	PUNCT
ap-768	183	45	a	a	NOUN
ap-768	183	46	)	)	PUNCT
ap-768	183	47	a	a	NOUN
ap-768	183	48	)	)	PUNCT
ap-768	183	49	)	)	PUNCT
ap-768	183	50	)	)	PUNCT
ap-768	184	1	a	a	X
ap-768	184	2	)	)	PUNCT
ap-768	184	3	a	a	X
ap-768	184	4	)	)	PUNCT
ap-768	184	5	mod	mod	PROPN
ap-768	184	6	mod	mod	PROPN
ap-768	184	7	mod	mod	PROPN
ap-768	184	8	mod	mod	PROPN
ap-768	184	9	mod	mod	PROPN
ap-768	184	10	(	(	PUNCT
ap-768	184	11	(	(	PUNCT
ap-768	184	12	,	,	PUNCT
ap-768	184	13	(	(	PUNCT
ap-768	184	14	(	(	PUNCT
ap-768	184	15	,	,	PUNCT
ap-768	184	16	(	(	PUNCT
ap-768	184	17	(	(	PUNCT
ap-768	184	18	,	,	PUNCT
ap-768	184	19	(	(	PUNCT
ap-768	184	20	a	a	DET
ap-768	184	21	a	a	DET
ap-768	184	22	a	a	DET
ap-768	184	23	a	a	DET
ap-768	184	24	a	a	DET
ap-768	184	25	p	p	NOUN
ap-768	184	26	q	q	X
ap-768	184	27	p	p	X
ap-768	184	28	q	q	X
ap-768	184	29	p	p	X
ap-768	184	30	�	�	PROPN
ap-768	184	31	�	�	PROPN
ap-768	184	32	�	�	PROPN
ap-768	184	33	�	�	PROPN
ap-768	184	34	mod	mod	PROPN
ap-768	184	35	g	g	PROPN
ap-768	184	36	)	)	PUNCT
ap-768	184	37	g	g	PROPN
ap-768	184	38	a	a	NOUN
ap-768	184	39	)	)	PUNCT
ap-768	184	40	.	.	PUNCT
ap-768	185	1	q	q	PUNCT
ap-768	185	2	a	a	DET
ap-768	185	3	�	�	PROPN
ap-768	185	4	�	�	PROPN
ap-768	185	5	(	(	PUNCT
ap-768	185	6	(	(	PUNCT
ap-768	185	7	because	because	SCONJ
ap-768	185	8	g	g	PROPN
ap-768	185	9	and	and	CCONJ
ap-768	185	10	g	g	PROPN
ap-768	185	11	are	be	AUX
ap-768	185	12	one	one	NUM
ap-768	185	13	-	-	PUNCT
ap-768	185	14	to	to	ADP
ap-768	185	15	-	-	PUNCT
ap-768	185	16	one	one	NUM
ap-768	185	17	correspondences	correspondence	NOUN
ap-768	185	18	we	we	PRON
ap-768	185	19	obtain	obtain	VERB
ap-768	185	20	a	a	DET
ap-768	185	21	b	b	NOUN
ap-768	185	22	a	a	DET
ap-768	185	23	b	b	NOUN
ap-768	185	24	a	a	DET
ap-768	185	25	b	b	NOUN
ap-768	185	26	a	a	DET
ap-768	185	27	b~	b~	PROPN
ap-768	185	28	(	(	PUNCT
ap-768	185	29	(	(	PUNCT
ap-768	185	30	(	(	PUNCT
ap-768	185	31	)	)	PUNCT
ap-768	185	32	(	(	PUNCT
ap-768	185	33	(	(	PUNCT
ap-768	185	34	)	)	PUNCT
ap-768	185	35	�	�	PROPN
ap-768	185	36	�	�	PROPN
ap-768	185	37	�	�	PROPN
ap-768	185	38	�	�	PROPN
ap-768	185	39	�	�	PROPN
ap-768	185	40	a	a	DET
ap-768	185	41	g	g	NOUN
ap-768	185	42	)	)	PUNCT
ap-768	185	43	g	g	PROPN
ap-768	185	44	a	a	NOUN
ap-768	185	45	)	)	PUNCT
ap-768	185	46	g	g	PROPN
ap-768	185	47	g	g	PROPN
ap-768	185	48	)	)	PUNCT
ap-768	185	49	~	~	PUNCT
ap-768	185	50	g	g	X
ap-768	185	51	.	.	PUNCT
ap-768	186	1	since	since	SCONJ
ap-768	186	2	the	the	DET
ap-768	186	3	mapping	mapping	NOUN
ap-768	186	4	g	g	NOUN
ap-768	186	5	is	be	AUX
ap-768	186	6	an	an	DET
ap-768	186	7	isomorphism	isomorphism	NOUN
ap-768	186	8	and	and	CCONJ
ap-768	186	9	g	g	NOUN
ap-768	186	10	,	,	PUNCT
ap-768	186	11	g	g	PROPN
ap-768	186	12	�	�	NOUN
ap-768	186	13	1	1	NUM
ap-768	186	14	preserve	preserve	NOUN
ap-768	186	15	equivalence	equivalence	NOUN
ap-768	186	16	,	,	PUNCT
ap-768	186	17	the	the	DET
ap-768	186	18	orbits	orbit	NOUN
ap-768	186	19	in	in	ADP
ap-768	186	20	the	the	DET
ap-768	186	21	ring	ring	NOUN
ap-768	186	22	z	z	PROPN
ap-768	186	23	pq	pq	PROPN
ap-768	186	24	m	m	VERB
ap-768	186	25	correspond	correspond	VERB
ap-768	186	26	one	one	NUM
ap-768	186	27	-	-	PUNCT
ap-768	186	28	to	to	ADP
ap-768	186	29	-	-	PUNCT
ap-768	186	30	one	one	NUM
ap-768	186	31	with	with	ADP
ap-768	186	32	the	the	DET
ap-768	186	33	orbits	orbit	NOUN
ap-768	186	34	in	in	ADP
ap-768	186	35	the	the	DET
ap-768	186	36	ring	ring	NOUN
ap-768	186	37	z	z	PROPN
ap-768	186	38	zp	zp	PROPN
ap-768	186	39	m	m	PROPN
ap-768	186	40	q	q	PROPN
ap-768	186	41	m	m	VERB
ap-768	186	42	�	�	PROPN
ap-768	186	43	,	,	PUNCT
ap-768	186	44	and	and	CCONJ
ap-768	186	45	these	these	PRON
ap-768	186	46	are	be	AUX
ap-768	186	47	cartesian	cartesian	ADJ
ap-768	186	48	products	product	NOUN
ap-768	186	49	of	of	ADP
ap-768	186	50	orbits	orbit	NOUN
ap-768	186	51	on	on	ADP
ap-768	186	52	z	z	PROPN
ap-768	186	53	p	p	NOUN
ap-768	187	1	m	m	PROPN
ap-768	187	2	and	and	CCONJ
ap-768	187	3	zq	zq	PROPN
ap-768	187	4	m.	m.	NOUN
ap-768	187	5	now	now	ADV
ap-768	187	6	remain	remain	VERB
ap-768	187	7	to	to	PART
ap-768	187	8	prove	prove	VERB
ap-768	187	9	that	that	SCONJ
ap-768	187	10	the	the	DET
ap-768	187	11	orbit	orbit	NOUN
ap-768	187	12	orm	orm	NOUN
ap-768	187	13	pq	pq	PROPN
ap-768	187	14	p	p	PROPN
ap-768	187	15	q	q	PROPN
ap-768	187	16	,	,	PUNCT
ap-768	187	17	(	(	PUNCT
ap-768	187	18	)	)	SYM
ap-768	187	19	1	1	NUM
ap-768	187	20	1	1	NUM
ap-768	187	21	corresponds	correspond	NOUN
ap-768	187	22	to	to	ADP
ap-768	187	23	the	the	DET
ap-768	187	24	orbitor	orbitor	NOUN
ap-768	187	25	orm	orm	NOUN
ap-768	187	26	p	p	PROPN
ap-768	187	27	m	m	NOUN
ap-768	187	28	qp	qp	ADP
ap-768	187	29	q	q	NOUN
ap-768	187	30	,	,	PUNCT
ap-768	187	31	,	,	PUNCT
ap-768	187	32	(	(	PUNCT
ap-768	187	33	)	)	PUNCT
ap-768	187	34	(	(	PUNCT
ap-768	187	35	)	)	SYM
ap-768	187	36	1	1	NUM
ap-768	187	37	1	1	NUM
ap-768	187	38	�	�	PROPN
ap-768	187	39	.	.	PUNCT
ap-768	188	1	it	it	PRON
ap-768	188	2	follows	follow	VERB
ap-768	188	3	from	from	ADP
ap-768	188	4	the	the	DET
ap-768	188	5	chinese	chinese	ADJ
ap-768	188	6	remainder	remainder	NOUN
ap-768	188	7	theorem	theorem	NOUN
ap-768	188	8	that	that	SCONJ
ap-768	188	9	g	g	PROPN
ap-768	188	10	maps	map	VERB
ap-768	188	11	the	the	DET
ap-768	188	12	set	set	NOUN
ap-768	188	13	{	{	PUNCT
ap-768	188	14	|gcd	|gcd	NOUN
ap-768	188	15	(	(	PUNCT
ap-768	188	16	,	,	PUNCT
ap-768	188	17	)	)	PUNCT
ap-768	188	18	}	}	PUNCT
ap-768	188	19	a	a	DET
ap-768	188	20	a	a	DET
ap-768	188	21	pq	pq	NOUN
ap-768	188	22	p	p	NOUN
ap-768	188	23	qpq	qpq	PROPN
ap-768	188	24	m	m	PROPN
ap-768	188	25	�	�	PROPN
ap-768	188	26	�	�	PROPN
ap-768	188	27	z	z	PROPN
ap-768	188	28	1	1	NUM
ap-768	188	29	1	1	NUM
ap-768	188	30	on	on	ADP
ap-768	188	31	the	the	DET
ap-768	188	32	set	set	NOUN
ap-768	188	33	{	{	PUNCT
ap-768	188	34	(	(	PUNCT
ap-768	188	35	,	,	PUNCT
ap-768	188	36	)	)	PUNCT
ap-768	188	37	|gcd	|gcd	NOUN
ap-768	188	38	(	(	PUNCT
ap-768	188	39	,	,	PUNCT
ap-768	188	40	)	)	PUNCT
ap-768	188	41	,	,	PUNCT
ap-768	188	42	gcd	gcd	NOUN
ap-768	188	43	(	(	PUNCT
ap-768	188	44	,	,	PUNCT
ap-768	188	45	)	)	PUNCT
ap-768	188	46	}	}	PUNCT
ap-768	189	1	a	a	PRON
ap-768	189	2	a	a	DET
ap-768	189	3	a	a	DET
ap-768	189	4	p	p	X
ap-768	189	5	p	p	NOUN
ap-768	189	6	a	a	DET
ap-768	189	7	q	q	NOUN
ap-768	189	8	qp	qp	ADP
ap-768	189	9	m	m	PROPN
ap-768	189	10	q	q	NOUN
ap-768	189	11	m	m	VERB
ap-768	189	12	1	1	NUM
ap-768	189	13	2	2	NUM
ap-768	189	14	1	1	NUM
ap-768	189	15	1	1	NUM
ap-768	189	16	2	2	NUM
ap-768	189	17	1	1	NUM
ap-768	189	18	�	�	PROPN
ap-768	189	19	�	�	PROPN
ap-768	189	20	�	�	PROPN
ap-768	189	21	�	�	PROPN
ap-768	189	22	z	z	PROPN
ap-768	189	23	z	z	PROPN
ap-768	189	24	,	,	PUNCT
ap-768	189	25	which	which	PRON
ap-768	189	26	is	be	AUX
ap-768	189	27	equal	equal	ADJ
ap-768	189	28	to	to	ADP
ap-768	189	29	the	the	DET
ap-768	189	30	orbitor	orbitor	NOUN
ap-768	189	31	orm	orm	NOUN
ap-768	189	32	p	p	PROPN
ap-768	189	33	m	m	NOUN
ap-768	189	34	qp	qp	ADP
ap-768	189	35	q	q	NOUN
ap-768	189	36	,	,	PUNCT
ap-768	189	37	,	,	PUNCT
ap-768	189	38	(	(	PUNCT
ap-768	189	39	)	)	PUNCT
ap-768	189	40	(	(	PUNCT
ap-768	189	41	)	)	SYM
ap-768	189	42	1	1	NUM
ap-768	189	43	1	1	NUM
ap-768	189	44	�	�	PROPN
ap-768	189	45	.	.	PUNCT
ap-768	190	1	therefore	therefore	ADV
ap-768	190	2	the	the	DET
ap-768	190	3	set	set	NOUN
ap-768	190	4	{	{	PUNCT
ap-768	190	5	|gcd	|gcd	X
ap-768	190	6	(	(	PUNCT
ap-768	190	7	,	,	PUNCT
ap-768	190	8	)	)	PUNCT
ap-768	190	9	}	}	PUNCT
ap-768	190	10	a	a	DET
ap-768	190	11	a	a	DET
ap-768	190	12	pq	pq	NOUN
ap-768	190	13	p	p	NOUN
ap-768	190	14	qpq	qpq	PROPN
ap-768	190	15	m	m	PROPN
ap-768	190	16	�	�	PROPN
ap-768	190	17	�	�	PROPN
ap-768	190	18	z	z	PROPN
ap-768	190	19	1	1	NUM
ap-768	190	20	1	1	NUM
ap-768	190	21	forms	form	NOUN
ap-768	190	22	an	an	DET
ap-768	190	23	orbit	orbit	NOUN
ap-768	190	24	and	and	CCONJ
ap-768	190	25	from	from	ADP
ap-768	190	26	corollary	corollary	ADJ
ap-768	190	27	4.4	4.4	NUM
ap-768	190	28	it	it	PRON
ap-768	190	29	follows	follow	VERB
ap-768	190	30	that	that	PRON
ap-768	190	31	or	or	CCONJ
ap-768	190	32	zm	zm	PROPN
ap-768	190	33	pq	pq	PROPN
ap-768	190	34	pq	pq	INTJ
ap-768	190	35	mp	mp	PROPN
ap-768	190	36	q	q	PROPN
ap-768	190	37	a	a	DET
ap-768	190	38	a	a	DET
ap-768	190	39	pq	pq	NOUN
ap-768	190	40	p	p	NOUN
ap-768	190	41	q	q	NOUN
ap-768	190	42	,	,	PUNCT
ap-768	190	43	(	(	PUNCT
ap-768	190	44	)	)	PUNCT
ap-768	190	45	{	{	PUNCT
ap-768	190	46	|gcd	|gcd	X
ap-768	190	47	(	(	PUNCT
ap-768	190	48	,	,	PUNCT
ap-768	190	49	)	)	PUNCT
ap-768	190	50	}	}	PUNCT
ap-768	190	51	1	1	NUM
ap-768	190	52	1	1	NUM
ap-768	190	53	1	1	NUM
ap-768	190	54	1	1	NUM
ap-768	190	55	�	�	PROPN
ap-768	190	56	�	�	PROPN
ap-768	190	57	�	�	PROPN
ap-768	190	58	.	.	PUNCT
ap-768	191	1	qed	qed	PROPN
ap-768	191	2	as	as	ADP
ap-768	191	3	a	a	DET
ap-768	191	4	corollary	corollary	NOUN
ap-768	191	5	of	of	ADP
ap-768	191	6	propositions	proposition	NOUN
ap-768	191	7	4.1.3	4.1.3	NUM
ap-768	191	8	and	and	CCONJ
ap-768	191	9	4.2.4	4.2.4	NUM
ap-768	191	10	we	we	PRON
ap-768	191	11	obtain	obtain	VERB
ap-768	191	12	the	the	DET
ap-768	191	13	following	follow	VERB
ap-768	191	14	theorem	theorem	VERB
ap-768	191	15	.	.	PUNCT
ap-768	192	1	theorem	theorem	NOUN
ap-768	192	2	4.9	4.9	NUM
ap-768	192	3	:	:	PUNCT
ap-768	192	4	consider	consider	VERB
ap-768	192	5	the	the	DET
ap-768	192	6	decomposition	decomposition	NOUN
ap-768	192	7	of	of	ADP
ap-768	192	8	the	the	DET
ap-768	192	9	ring	ring	NOUN
ap-768	192	10	zn	zn	PROPN
ap-768	192	11	m	m	PROPN
ap-768	192	12	,	,	PUNCT
ap-768	192	13	m	m	VERB
ap-768	192	14	�	�	PROPN
ap-768	192	15	2	2	NUM
ap-768	192	16	into	into	ADP
ap-768	192	17	orbits	orbit	NOUN
ap-768	192	18	with	with	ADP
ap-768	192	19	respect	respect	NOUN
ap-768	192	20	to	to	ADP
ap-768	192	21	the	the	DET
ap-768	192	22	action	action	NOUN
ap-768	192	23	of	of	ADP
ap-768	192	24	the	the	DET
ap-768	192	25	group	group	NOUN
ap-768	192	26	sl(m	sl(m	PROPN
ap-768	192	27	,	,	PUNCT
ap-768	192	28	zn	zn	PROPN
ap-768	192	29	)	)	PUNCT
ap-768	192	30	.	.	PUNCT
ap-768	193	1	then	then	ADV
ap-768	193	2	i	i	PRON
ap-768	193	3	)	)	PUNCT
ap-768	193	4	any	any	DET
ap-768	193	5	orbit	orbit	NOUN
ap-768	193	6	is	be	AUX
ap-768	193	7	equal	equal	ADJ
ap-768	193	8	to	to	ADP
ap-768	193	9	the	the	DET
ap-768	193	10	orbit	orbit	NOUN
ap-768	193	11	orm	orm	NOUN
ap-768	193	12	,	,	PUNCT
ap-768	193	13	n(d	n(d	PROPN
ap-768	193	14	)	)	PUNCT
ap-768	193	15	for	for	ADP
ap-768	193	16	some	some	DET
ap-768	193	17	divisor	divisor	NOUN
ap-768	193	18	d	d	PROPN
ap-768	193	19	of	of	ADP
ap-768	193	20	n	n	CCONJ
ap-768	193	21	,	,	PUNCT
ap-768	193	22	i.e.	i.e.	X
ap-768	193	23	z	z	X
ap-768	193	24	orn	orn	PROPN
ap-768	193	25	m	m	VERB
ap-768	193	26	m	m	VERB
ap-768	193	27	n	n	PROPN
ap-768	193	28	d	d	PROPN
ap-768	193	29	n	n	PROPN
ap-768	193	30	d	d	PROPN
ap-768	193	31	�	�	PROPN
ap-768	193	32	,	,	PUNCT
ap-768	193	33	|	|	ADV
ap-768	193	34	(	(	PUNCT
ap-768	193	35	)	)	PUNCT
ap-768	193	36	�	�	PROPN
ap-768	193	37	;	;	PUNCT
ap-768	193	38	42	42	NUM
ap-768	193	39	©	©	PROPN
ap-768	193	40	czech	czech	PROPN
ap-768	193	41	technical	technical	PROPN
ap-768	193	42	university	university	PROPN
ap-768	193	43	publishing	publishing	NOUN
ap-768	193	44	house	house	NOUN
ap-768	193	45	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-768	193	46	acta	acta	PROPN
ap-768	193	47	polytechnica	polytechnica	PROPN
ap-768	193	48	vol	vol	NOUN
ap-768	193	49	.	.	PROPN
ap-768	194	1	45	45	NUM
ap-768	194	2	no	no	NOUN
ap-768	194	3	.	.	PUNCT
ap-768	195	1	5/2005	5/2005	NUM
ap-768	195	2	czech	czech	PROPN
ap-768	195	3	technical	technical	PROPN
ap-768	195	4	university	university	PROPN
ap-768	195	5	in	in	ADP
ap-768	195	6	prague	prague	PROPN
ap-768	195	7	ii	ii	PROPN
ap-768	195	8	)	)	PUNCT
ap-768	195	9	or	or	CCONJ
ap-768	195	10	zm	zm	PROPN
ap-768	195	11	n	n	PROPN
ap-768	195	12	n	n	PROPN
ap-768	195	13	md	md	VERB
ap-768	195	14	a	a	DET
ap-768	195	15	a	a	PRON
ap-768	195	16	n	n	NOUN
ap-768	195	17	d	d	NOUN
ap-768	195	18	,	,	PUNCT
ap-768	195	19	(	(	PUNCT
ap-768	195	20	)	)	PUNCT
ap-768	195	21	{	{	PUNCT
ap-768	195	22	|gcd	|gcd	X
ap-768	195	23	(	(	PUNCT
ap-768	195	24	,	,	PUNCT
ap-768	195	25	)	)	PUNCT
ap-768	195	26	}	}	PUNCT
ap-768	195	27	�	�	PROPN
ap-768	195	28	�	�	PROPN
ap-768	195	29	�	�	PROPN
ap-768	195	30	;	;	PUNCT
ap-768	195	31	iii)the	iii)the	DET
ap-768	195	32	number	number	NOUN
ap-768	195	33	of	of	ADP
ap-768	195	34	points	point	NOUN
ap-768	195	35	orm	orm	NOUN
ap-768	195	36	n	n	X
ap-768	195	37	d	d	NOUN
ap-768	195	38	,	,	PUNCT
ap-768	195	39	(	(	PUNCT
ap-768	195	40	)	)	PUNCT
ap-768	195	41	in	in	ADP
ap-768	195	42	d	d	X
ap-768	195	43	-	-	PUNCT
ap-768	195	44	orbit	orbit	NOUN
ap-768	195	45	is	be	AUX
ap-768	195	46	given	give	VERB
ap-768	195	47	by	by	ADP
ap-768	195	48	the	the	DET
ap-768	195	49	jordan	jordan	PROPN
ap-768	195	50	function	function	PROPN
ap-768	195	51	or	or	CCONJ
ap-768	195	52	p	p	NOUN
ap-768	195	53	m	m	PROPN
ap-768	195	54	n	n	NUM
ap-768	195	55	m	m	NOUN
ap-768	195	56	m	m	VERB
ap-768	195	57	m	m	VERB
ap-768	195	58	pd	pd	PROPN
ap-768	195	59	n	n	PRON
ap-768	195	60	p	p	PROPN
ap-768	195	61	d	d	PROPN
ap-768	195	62	n	n	PROPN
ap-768	195	63	d	d	PROPN
ap-768	195	64	n	n	PROPN
ap-768	195	65	d	d	PROPN
ap-768	195	66	p	p	X
ap-768	195	67	,	,	PUNCT
ap-768	195	68	|	|	ADV
ap-768	195	69	,	,	PUNCT
ap-768	195	70	(	(	PUNCT
ap-768	195	71	)	)	PUNCT
ap-768	195	72	(	(	PUNCT
ap-768	195	73	)	)	PUNCT
ap-768	195	74	�	�	PROPN
ap-768	195	75	�	�	PROPN
ap-768	195	76	�	�	PROPN
ap-768	195	77	�	�	PROPN
ap-768	195	78	�	�	PROPN
ap-768	195	79	�	�	PROPN
ap-768	195	80	�	�	PROPN
ap-768	195	81	�	�	PROPN
ap-768	195	82	�	�	PROPN
ap-768	195	83	�	�	PROPN
ap-768	195	84	�	�	PROPN
ap-768	195	85	�	�	PROPN
ap-768	195	86	�	�	PROPN
ap-768	195	87	�	�	PROPN
ap-768	195	88	1	1	NUM
ap-768	195	89	.	.	PUNCT
ap-768	196	1	5	5	NUM
ap-768	196	2	conclusion	conclusion	NOUN
ap-768	196	3	we	we	PRON
ap-768	196	4	have	have	AUX
ap-768	196	5	stepwise	stepwise	NOUN
ap-768	196	6	determined	determine	VERB
ap-768	196	7	the	the	DET
ap-768	196	8	orbits	orbit	NOUN
ap-768	196	9	on	on	ADP
ap-768	196	10	the	the	DET
ap-768	196	11	ring	ring	NOUN
ap-768	196	12	zn	zn	PROPN
ap-768	196	13	m	m	VERB
ap-768	196	14	with	with	ADP
ap-768	196	15	respect	respect	NOUN
ap-768	196	16	to	to	ADP
ap-768	196	17	the	the	DET
ap-768	196	18	action	action	NOUN
ap-768	196	19	of	of	ADP
ap-768	196	20	the	the	DET
ap-768	196	21	group	group	NOUN
ap-768	196	22	sl(m	sl(m	PROPN
ap-768	196	23	,	,	PUNCT
ap-768	196	24	zn	zn	PROPN
ap-768	196	25	)	)	PUNCT
ap-768	196	26	.	.	PUNCT
ap-768	197	1	first	first	ADV
ap-768	197	2	,	,	PUNCT
ap-768	197	3	we	we	PRON
ap-768	197	4	proceeded	proceed	VERB
ap-768	197	5	in	in	ADP
ap-768	197	6	the	the	DET
ap-768	197	7	same	same	ADJ
ap-768	197	8	way	way	NOUN
ap-768	197	9	as	as	ADP
ap-768	197	10	kirillov	kirillov	NOUN
ap-768	197	11	in	in	ADP
ap-768	197	12	[	[	X
ap-768	197	13	9	9	NUM
ap-768	197	14	]	]	PUNCT
ap-768	197	15	and	and	CCONJ
ap-768	197	16	we	we	PRON
ap-768	197	17	obtained	obtain	VERB
ap-768	197	18	the	the	DET
ap-768	197	19	orbits	orbit	NOUN
ap-768	197	20	in	in	ADP
ap-768	197	21	the	the	DET
ap-768	197	22	case	case	NOUN
ap-768	197	23	of	of	ADP
ap-768	197	24	n	n	CCONJ
ap-768	197	25	prime	prime	ADJ
ap-768	197	26	number	number	NOUN
ap-768	197	27	.	.	PUNCT
ap-768	198	1	in	in	ADP
ap-768	198	2	this	this	DET
ap-768	198	3	case	case	NOUN
ap-768	198	4	there	there	PRON
ap-768	198	5	are	be	VERB
ap-768	198	6	only	only	ADV
ap-768	198	7	two	two	NUM
ap-768	198	8	orbits	orbit	NOUN
ap-768	198	9	,	,	PUNCT
ap-768	198	10	the	the	DET
ap-768	198	11	first	first	ADJ
ap-768	198	12	is	be	AUX
ap-768	198	13	one	one	NUM
ap-768	198	14	-	-	PUNCT
ap-768	198	15	point	point	NOUN
ap-768	198	16	orbit	orbit	NOUN
ap-768	198	17	formed	form	VERB
ap-768	198	18	by	by	ADP
ap-768	198	19	the	the	DET
ap-768	198	20	zero	zero	NUM
ap-768	198	21	element	element	NOUN
ap-768	198	22	and	and	CCONJ
ap-768	198	23	the	the	DET
ap-768	198	24	second	second	ADJ
ap-768	198	25	is	be	AUX
ap-768	198	26	formed	form	VERB
ap-768	198	27	by	by	ADP
ap-768	198	28	all	all	DET
ap-768	198	29	nonzero	nonzero	ADJ
ap-768	198	30	elements	element	NOUN
ap-768	198	31	.	.	PUNCT
ap-768	199	1	the	the	DET
ap-768	199	2	next	next	ADJ
ap-768	199	3	step	step	NOUN
ap-768	199	4	was	be	AUX
ap-768	199	5	the	the	DET
ap-768	199	6	case	case	NOUN
ap-768	199	7	of	of	ADP
ap-768	199	8	n	n	PRON
ap-768	199	9	�	�	PROPN
ap-768	199	10	pk	pk	NOUN
ap-768	199	11	power	power	NOUN
ap-768	199	12	of	of	ADP
ap-768	199	13	prime	prime	NOUN
ap-768	199	14	.	.	PUNCT
ap-768	200	1	there	there	ADV
ap-768	200	2	we	we	PRON
ap-768	200	3	found	find	VERB
ap-768	200	4	k	k	PROPN
ap-768	200	5	�	�	PROPN
ap-768	200	6	1	1	NUM
ap-768	200	7	orbits	orbit	NOUN
ap-768	200	8	characterized	characterize	VERB
ap-768	200	9	by	by	ADP
ap-768	200	10	the	the	DET
ap-768	200	11	greatest	great	ADJ
ap-768	200	12	common	common	ADJ
ap-768	200	13	divisor	divisor	NOUN
ap-768	200	14	of	of	ADP
ap-768	200	15	their	their	PRON
ap-768	200	16	elements	element	NOUN
ap-768	200	17	and	and	CCONJ
ap-768	200	18	number	number	NOUN
ap-768	200	19	n.	n.	NOUN
ap-768	200	20	finally	finally	ADV
ap-768	200	21	the	the	DET
ap-768	200	22	orbits	orbit	NOUN
ap-768	200	23	for	for	ADP
ap-768	200	24	an	an	DET
ap-768	200	25	arbitrary	arbitrary	ADJ
ap-768	200	26	natural	natural	ADJ
ap-768	200	27	number	number	NOUN
ap-768	200	28	n	n	PRON
ap-768	200	29	were	be	AUX
ap-768	200	30	found	find	VERB
ap-768	200	31	.	.	PUNCT
ap-768	201	1	our	our	PRON
ap-768	201	2	results	result	NOUN
ap-768	201	3	are	be	AUX
ap-768	201	4	summarized	summarize	VERB
ap-768	201	5	in	in	ADP
ap-768	201	6	theorem	theorem	NOUN
ap-768	201	7	4.9	4.9	NUM
ap-768	201	8	.	.	NOUN
ap-768	201	9	6	6	NUM
ap-768	201	10	acknowledgments	acknowledgment	NOUN
ap-768	201	11	we	we	PRON
ap-768	201	12	would	would	AUX
ap-768	201	13	like	like	VERB
ap-768	201	14	to	to	PART
ap-768	201	15	thank	thank	VERB
ap-768	201	16	prof	prof	PROPN
ap-768	201	17	.	.	PROPN
ap-768	202	1	jiří	jiří	PROPN
ap-768	202	2	tolar	tolar	PROPN
ap-768	202	3	,	,	PUNCT
ap-768	202	4	prof	prof	PROPN
ap-768	202	5	.	.	PUNCT
ap-768	203	1	miloslav	miloslav	PROPN
ap-768	203	2	havlíček	havlíček	PROPN
ap-768	203	3	and	and	CCONJ
ap-768	203	4	doc	doc	PROPN
ap-768	203	5	.	.	PROPN
ap-768	203	6	edita	edita	PROPN
ap-768	203	7	pelantová	pelantová	NOUN
ap-768	203	8	for	for	ADP
ap-768	203	9	numerous	numerous	ADJ
ap-768	203	10	stimulating	stimulating	ADJ
ap-768	203	11	and	and	CCONJ
ap-768	203	12	inquisitive	inquisitive	ADJ
ap-768	203	13	discussions	discussion	NOUN
ap-768	203	14	.	.	PUNCT
ap-768	204	1	references	reference	NOUN
ap-768	204	2	[	[	X
ap-768	204	3	1	1	NUM
ap-768	204	4	]	]	PUNCT
ap-768	204	5	št’ovíček	št’ovíček	ADJ
ap-768	204	6	,	,	PUNCT
ap-768	204	7	p.	p.	NOUN
ap-768	204	8	,	,	PUNCT
ap-768	204	9	tolar	tolar	PROPN
ap-768	204	10	,	,	PUNCT
ap-768	204	11	j.	j.	PROPN
ap-768	204	12	:	:	PUNCT
ap-768	204	13	“	"	PUNCT
ap-768	204	14	quantum	quantum	ADJ
ap-768	204	15	mechanics	mechanic	NOUN
ap-768	204	16	in	in	ADP
ap-768	204	17	a	a	DET
ap-768	204	18	discrete	discrete	ADJ
ap-768	204	19	space	space	NOUN
ap-768	204	20	-	-	PUNCT
ap-768	204	21	time	time	NOUN
ap-768	204	22	.	.	PUNCT
ap-768	204	23	”	"	PUNCT
ap-768	205	1	rep	rep	PROPN
ap-768	205	2	.	.	PROPN
ap-768	205	3	math	math	NOUN
ap-768	205	4	.	.	PUNCT
ap-768	206	1	phys	phy	NOUN
ap-768	206	2	.	.	PUNCT
ap-768	207	1	vol	vol	NOUN
ap-768	207	2	.	.	PROPN
ap-768	207	3	20	20	NUM
ap-768	207	4	(	(	PUNCT
ap-768	207	5	1984	1984	NUM
ap-768	207	6	)	)	PUNCT
ap-768	207	7	,	,	PUNCT
ap-768	208	1	p.	p.	NOUN
ap-768	208	2	157–170	157–170	NUM
ap-768	208	3	.	.	PUNCT
ap-768	209	1	[	[	X
ap-768	209	2	2	2	NUM
ap-768	209	3	]	]	X
ap-768	209	4	vourdas	vourda	NOUN
ap-768	209	5	,	,	PUNCT
ap-768	209	6	a.	a.	NOUN
ap-768	209	7	:	:	PUNCT
ap-768	209	8	“	"	PUNCT
ap-768	209	9	quantum	quantum	ADJ
ap-768	209	10	systems	system	NOUN
ap-768	209	11	with	with	ADP
ap-768	209	12	finite	finite	ADJ
ap-768	209	13	hilbert	hilbert	PROPN
ap-768	209	14	space	space	NOUN
ap-768	209	15	.	.	PUNCT
ap-768	209	16	”	"	PUNCT
ap-768	210	1	rep	rep	PROPN
ap-768	210	2	.	.	PROPN
ap-768	210	3	progr	progr	NOUN
ap-768	210	4	.	.	PUNCT
ap-768	211	1	phys	phy	NOUN
ap-768	211	2	.	.	PUNCT
ap-768	212	1	vol	vol	NOUN
ap-768	212	2	.	.	PROPN
ap-768	213	1	67	67	NUM
ap-768	213	2	(	(	PUNCT
ap-768	213	3	2004	2004	NUM
ap-768	213	4	)	)	PUNCT
ap-768	213	5	,	,	PUNCT
ap-768	214	1	p.	p.	NOUN
ap-768	214	2	267–320	267–320	NUM
ap-768	214	3	.	.	PUNCT
ap-768	215	1	[	[	X
ap-768	215	2	3	3	NUM
ap-768	215	3	]	]	PUNCT
ap-768	215	4	patera	patera	NOUN
ap-768	215	5	,	,	PUNCT
ap-768	215	6	j.	j.	PROPN
ap-768	215	7	,	,	PUNCT
ap-768	215	8	zassenhaus	zassenhaus	PROPN
ap-768	215	9	,	,	PUNCT
ap-768	215	10	h.	h.	PROPN
ap-768	215	11	:	:	PUNCT
ap-768	215	12	the	the	DET
ap-768	215	13	pauli	pauli	PROPN
ap-768	215	14	matrices	matrice	VERB
ap-768	215	15	in	in	ADP
ap-768	215	16	n	n	ADP
ap-768	215	17	dimensions	dimension	NOUN
ap-768	215	18	and	and	CCONJ
ap-768	215	19	finest	fine	ADJ
ap-768	215	20	gradings	grading	NOUN
ap-768	215	21	of	of	ADP
ap-768	215	22	simple	simple	ADJ
ap-768	215	23	lie	lie	NOUN
ap-768	215	24	algebras	algebra	NOUN
ap-768	215	25	of	of	ADP
ap-768	215	26	type	type	NOUN
ap-768	215	27	an	an	DET
ap-768	215	28	�	�	NOUN
ap-768	215	29	1	1	NUM
ap-768	215	30	.	.	PUNCT
ap-768	215	31	”	"	PUNCT
ap-768	216	1	j.	j.	PROPN
ap-768	216	2	math	math	PROPN
ap-768	216	3	.	.	PUNCT
ap-768	217	1	phys	phy	NOUN
ap-768	217	2	.	.	PUNCT
ap-768	218	1	vol	vol	NOUN
ap-768	218	2	.	.	PROPN
ap-768	218	3	29	29	NUM
ap-768	218	4	(	(	PUNCT
ap-768	218	5	1988	1988	NUM
ap-768	218	6	)	)	PUNCT
ap-768	218	7	,	,	PUNCT
ap-768	218	8	p.	p.	NOUN
ap-768	218	9	665–673	665–673	NUM
ap-768	218	10	.	.	PUNCT
ap-768	219	1	[	[	X
ap-768	219	2	4	4	NUM
ap-768	219	3	]	]	X
ap-768	219	4	gell	gell	NOUN
ap-768	219	5	-	-	PUNCT
ap-768	219	6	mann	mann	NOUN
ap-768	219	7	,	,	PUNCT
ap-768	219	8	m.	m.	NOUN
ap-768	219	9	:	:	PUNCT
ap-768	219	10	“	"	PUNCT
ap-768	219	11	symmetries	symmetry	NOUN
ap-768	219	12	of	of	ADP
ap-768	219	13	baryons	baryon	NOUN
ap-768	219	14	and	and	CCONJ
ap-768	219	15	mesons	meson	NOUN
ap-768	219	16	.	.	PUNCT
ap-768	219	17	”	"	PUNCT
ap-768	219	18	phys	phy	NOUN
ap-768	219	19	.	.	PUNCT
ap-768	220	1	rev	rev	PROPN
ap-768	220	2	.	.	PROPN
ap-768	220	3	vol	vol	NOUN
ap-768	220	4	.	.	PROPN
ap-768	221	1	125	125	NUM
ap-768	221	2	(	(	PUNCT
ap-768	221	3	1962	1962	NUM
ap-768	221	4	)	)	PUNCT
ap-768	221	5	,	,	PUNCT
ap-768	222	1	p.	p.	NOUN
ap-768	222	2	1067	1067	NUM
ap-768	222	3	.	.	PUNCT
ap-768	223	1	[	[	X
ap-768	223	2	5	5	NUM
ap-768	223	3	]	]	X
ap-768	223	4	havlíček	havlíček	NOUN
ap-768	223	5	,	,	PUNCT
ap-768	223	6	m.	m.	NOUN
ap-768	223	7	,	,	PUNCT
ap-768	223	8	patera	patera	NOUN
ap-768	223	9	,	,	PUNCT
ap-768	223	10	j.	j.	PROPN
ap-768	223	11	,	,	PUNCT
ap-768	223	12	pelantová	pelantová	PROPN
ap-768	223	13	,	,	PUNCT
ap-768	223	14	e.	e.	PROPN
ap-768	223	15	,	,	PUNCT
ap-768	223	16	tolar	tolar	PROPN
ap-768	223	17	,	,	PUNCT
ap-768	223	18	j.	j.	PROPN
ap-768	223	19	:	:	PUNCT
ap-768	223	20	“	"	PUNCT
ap-768	223	21	the	the	DET
ap-768	223	22	fine	fine	ADJ
ap-768	223	23	gradings	grading	NOUN
ap-768	223	24	of	of	ADP
ap-768	223	25	sl(3	sl(3	PROPN
ap-768	223	26	,	,	PUNCT
ap-768	223	27	c	c	NOUN
ap-768	223	28	)	)	PUNCT
ap-768	223	29	and	and	CCONJ
ap-768	223	30	their	their	PRON
ap-768	223	31	symmetries	symmetry	NOUN
ap-768	223	32	,	,	PUNCT
ap-768	223	33	”	"	PUNCT
ap-768	223	34	in	in	ADP
ap-768	223	35	proc	proc	NOUN
ap-768	223	36	.	.	PUNCT
ap-768	224	1	of	of	ADP
ap-768	224	2	xxiii	xxiii	PROPN
ap-768	224	3	.	.	PUNCT
ap-768	225	1	international	international	ADJ
ap-768	225	2	colloquium	colloquium	NOUN
ap-768	225	3	on	on	ADP
ap-768	225	4	group	group	NOUN
ap-768	225	5	theoretical	theoretical	ADJ
ap-768	225	6	methods	method	NOUN
ap-768	225	7	in	in	ADP
ap-768	225	8	physics	physics	PROPN
ap-768	225	9	,	,	PUNCT
ap-768	225	10	eds	eds	PROPN
ap-768	225	11	.	.	PUNCT
ap-768	225	12	a.	a.	PROPN
ap-768	225	13	n.	n.	PROPN
ap-768	225	14	sissakian	sissakian	PROPN
ap-768	225	15	,	,	PUNCT
ap-768	225	16	g.	g.	PROPN
ap-768	225	17	s.	s.	PROPN
ap-768	225	18	pogosyan	pogosyan	PROPN
ap-768	225	19	and	and	CCONJ
ap-768	225	20	l.	l.	PROPN
ap-768	225	21	g.	g.	PROPN
ap-768	225	22	mardoyan	mardoyan	PROPN
ap-768	225	23	,	,	PUNCT
ap-768	225	24	jinr	jinr	PROPN
ap-768	225	25	,	,	PUNCT
ap-768	225	26	dubna	dubna	PROPN
ap-768	225	27	,	,	PUNCT
ap-768	225	28	vol	vol	NOUN
ap-768	225	29	.	.	PROPN
ap-768	225	30	1	1	NUM
ap-768	225	31	(	(	PUNCT
ap-768	225	32	2002	2002	NUM
ap-768	225	33	)	)	PUNCT
ap-768	225	34	,	,	PUNCT
ap-768	225	35	p.	p.	NOUN
ap-768	225	36	57–61	57–61	NUM
ap-768	225	37	.	.	PUNCT
ap-768	226	1	[	[	X
ap-768	226	2	6	6	NUM
ap-768	226	3	]	]	X
ap-768	226	4	havlíček	havlíček	NOUN
ap-768	226	5	,	,	PUNCT
ap-768	226	6	m.	m.	NOUN
ap-768	226	7	,	,	PUNCT
ap-768	226	8	patera	patera	NOUN
ap-768	226	9	,	,	PUNCT
ap-768	226	10	j.	j.	PROPN
ap-768	226	11	,	,	PUNCT
ap-768	226	12	pelantová	pelantová	PROPN
ap-768	226	13	,	,	PUNCT
ap-768	226	14	e.	e.	PROPN
ap-768	226	15	,	,	PUNCT
ap-768	226	16	tolar	tolar	PROPN
ap-768	226	17	,	,	PUNCT
ap-768	226	18	j.	j.	PROPN
ap-768	226	19	:	:	PUNCT
ap-768	226	20	“	"	PUNCT
ap-768	226	21	automorphisms	automorphisms	PROPN
ap-768	226	22	of	of	ADP
ap-768	226	23	the	the	DET
ap-768	226	24	fine	fine	ADJ
ap-768	226	25	grading	grading	NOUN
ap-768	226	26	of	of	ADP
ap-768	226	27	sl(n	sl(n	ADJ
ap-768	226	28	,	,	PUNCT
ap-768	226	29	c	c	NOUN
ap-768	226	30	)	)	PUNCT
ap-768	226	31	associated	associate	VERB
ap-768	226	32	with	with	ADP
ap-768	226	33	the	the	DET
ap-768	226	34	generalized	generalize	VERB
ap-768	226	35	pauli	pauli	PROPN
ap-768	226	36	matrices	matrix	NOUN
ap-768	226	37	.	.	PUNCT
ap-768	226	38	”	"	PUNCT
ap-768	227	1	j.	j.	PROPN
ap-768	227	2	math	math	PROPN
ap-768	227	3	.	.	PUNCT
ap-768	228	1	phys	phy	NOUN
ap-768	228	2	.	.	PUNCT
ap-768	229	1	vol	vol	NOUN
ap-768	229	2	.	.	PROPN
ap-768	230	1	43	43	NUM
ap-768	230	2	,	,	PUNCT
ap-768	230	3	2002	2002	NUM
ap-768	230	4	,	,	PUNCT
ap-768	230	5	p.	p.	NOUN
ap-768	230	6	1083–1094	1083–1094	X
ap-768	230	7	.	.	PUNCT
ap-768	231	1	[	[	X
ap-768	231	2	7	7	NUM
ap-768	231	3	]	]	X
ap-768	231	4	de	de	X
ap-768	231	5	montigny	montigny	PROPN
ap-768	231	6	,	,	PUNCT
ap-768	231	7	m.	m.	NOUN
ap-768	231	8	,	,	PUNCT
ap-768	231	9	patera	patera	NOUN
ap-768	231	10	,	,	PUNCT
ap-768	231	11	j.	j.	PROPN
ap-768	231	12	:	:	PUNCT
ap-768	231	13	“	"	PUNCT
ap-768	231	14	discrete	discrete	ADJ
ap-768	231	15	and	and	CCONJ
ap-768	231	16	continuous	continuous	ADJ
ap-768	231	17	graded	grade	VERB
ap-768	231	18	contractions	contraction	NOUN
ap-768	231	19	of	of	ADP
ap-768	231	20	lie	lie	NOUN
ap-768	231	21	algebras	algebra	NOUN
ap-768	231	22	and	and	CCONJ
ap-768	231	23	superalgebras	superalgebras	PROPN
ap-768	231	24	.	.	PUNCT
ap-768	231	25	”	"	PUNCT
ap-768	232	1	j.	j.	PROPN
ap-768	232	2	phys	phys	PROPN
ap-768	232	3	.	.	PUNCT
ap-768	233	1	a	a	DET
ap-768	233	2	:	:	PUNCT
ap-768	233	3	math	math	NOUN
ap-768	233	4	.	.	PUNCT
ap-768	234	1	gen	gen	PROPN
ap-768	234	2	.	.	PROPN
ap-768	234	3	,	,	PUNCT
ap-768	234	4	vol	vol	NOUN
ap-768	234	5	.	.	PROPN
ap-768	234	6	24	24	NUM
ap-768	234	7	(	(	PUNCT
ap-768	234	8	1991	1991	NUM
ap-768	234	9	)	)	PUNCT
ap-768	234	10	,	,	PUNCT
ap-768	235	1	p.	p.	NOUN
ap-768	235	2	525–547	525–547	NUM
ap-768	235	3	.	.	PUNCT
ap-768	236	1	[	[	X
ap-768	236	2	8	8	NUM
ap-768	236	3	]	]	PUNCT
ap-768	236	4	hrivnák	hrivnák	NOUN
ap-768	236	5	,	,	PUNCT
ap-768	236	6	j.	j.	PROPN
ap-768	236	7	:	:	PUNCT
ap-768	236	8	“	"	PUNCT
ap-768	236	9	solution	solution	NOUN
ap-768	236	10	of	of	ADP
ap-768	236	11	contraction	contraction	NOUN
ap-768	236	12	equations	equation	NOUN
ap-768	236	13	for	for	ADP
ap-768	236	14	the	the	DET
ap-768	236	15	pauli	pauli	PROPN
ap-768	236	16	grading	grade	VERB
ap-768	236	17	of	of	ADP
ap-768	236	18	sl(3	sl(3	PROPN
ap-768	236	19	,	,	PUNCT
ap-768	236	20	c	c	NOUN
ap-768	236	21	)	)	PUNCT
ap-768	236	22	.	.	PUNCT
ap-768	236	23	”	"	PUNCT
ap-768	237	1	diploma	diploma	NOUN
ap-768	237	2	thesis	thesis	NOUN
ap-768	237	3	,	,	PUNCT
ap-768	237	4	czech	czech	PROPN
ap-768	237	5	technical	technical	PROPN
ap-768	237	6	university	university	PROPN
ap-768	237	7	,	,	PUNCT
ap-768	237	8	prague	prague	NOUN
ap-768	237	9	2003	2003	NUM
ap-768	237	10	.	.	PUNCT
ap-768	238	1	[	[	X
ap-768	238	2	9	9	NUM
ap-768	238	3	]	]	PUNCT
ap-768	238	4	kirillov	kirillov	NOUN
ap-768	238	5	,	,	PUNCT
ap-768	238	6	a.	a.	NOUN
ap-768	238	7	a.	a.	NOUN
ap-768	238	8	:	:	PUNCT
ap-768	238	9	elements	element	NOUN
ap-768	238	10	of	of	ADP
ap-768	238	11	the	the	DET
ap-768	238	12	theory	theory	NOUN
ap-768	238	13	of	of	ADP
ap-768	238	14	representations	representation	NOUN
ap-768	238	15	,	,	PUNCT
ap-768	238	16	springer	springer	NOUN
ap-768	238	17	,	,	PUNCT
ap-768	238	18	new	new	PROPN
ap-768	238	19	york	york	PROPN
ap-768	238	20	1976	1976	NUM
ap-768	238	21	.	.	PUNCT
ap-768	239	1	[	[	X
ap-768	239	2	10	10	NUM
ap-768	239	3	]	]	X
ap-768	239	4	you	you	PRON
ap-768	239	5	hong	hong	PROPN
ap-768	239	6	,	,	PUNCT
ap-768	239	7	gao	gao	PROPN
ap-768	239	8	you	you	PRON
ap-768	239	9	:	:	PUNCT
ap-768	239	10	“	"	PUNCT
ap-768	239	11	computation	computation	NOUN
ap-768	239	12	of	of	ADP
ap-768	239	13	orders	order	NOUN
ap-768	239	14	of	of	ADP
ap-768	239	15	classical	classical	ADJ
ap-768	239	16	groups	group	NOUN
ap-768	239	17	over	over	ADP
ap-768	239	18	finite	finite	PROPN
ap-768	239	19	commutative	commutative	ADJ
ap-768	239	20	rings	ring	NOUN
ap-768	239	21	.	.	PUNCT
ap-768	239	22	”	"	PUNCT
ap-768	240	1	chinese	chinese	ADJ
ap-768	240	2	science	science	NOUN
ap-768	240	3	bulletin	bulletin	NOUN
ap-768	240	4	,	,	PUNCT
ap-768	240	5	vol	vol	NOUN
ap-768	240	6	.	.	PROPN
ap-768	240	7	39	39	NUM
ap-768	240	8	(	(	PUNCT
ap-768	240	9	1994	1994	NUM
ap-768	240	10	)	)	PUNCT
ap-768	240	11	,	,	PUNCT
ap-768	240	12	no	no	INTJ
ap-768	240	13	.	.	NOUN
ap-768	240	14	14	14	NUM
ap-768	240	15	,	,	PUNCT
ap-768	240	16	p.	p.	NOUN
ap-768	240	17	1150–1154	1150–1154	NUM
ap-768	240	18	.	.	PUNCT
ap-768	241	1	[	[	X
ap-768	241	2	11	11	NUM
ap-768	241	3	]	]	PUNCT
ap-768	241	4	drápal	drápal	NOUN
ap-768	241	5	,	,	PUNCT
ap-768	241	6	a.	a.	NOUN
ap-768	241	7	:	:	PUNCT
ap-768	241	8	group	group	NOUN
ap-768	241	9	theory	theory	NOUN
ap-768	241	10	–	–	PUNCT
ap-768	241	11	fundamental	fundamental	ADJ
ap-768	241	12	aspects	aspect	NOUN
ap-768	241	13	(	(	PUNCT
ap-768	241	14	in	in	ADP
ap-768	241	15	czech	czech	PROPN
ap-768	241	16	)	)	PUNCT
ap-768	241	17	,	,	PUNCT
ap-768	241	18	karolinum	karolinum	PROPN
ap-768	241	19	,	,	PUNCT
ap-768	241	20	praha	praha	PROPN
ap-768	241	21	2000	2000	NUM
ap-768	241	22	.	.	PUNCT
ap-768	242	1	[	[	X
ap-768	242	2	12	12	NUM
ap-768	242	3	]	]	X
ap-768	242	4	schulte	schulte	PROPN
ap-768	242	5	,	,	PUNCT
ap-768	242	6	j.	j.	PROPN
ap-768	242	7	:	:	PUNCT
ap-768	242	8	“	"	PUNCT
ap-768	242	9	über	über	NOUN
ap-768	242	10	die	die	VERB
ap-768	242	11	jordanische	jordanische	PROPN
ap-768	242	12	verallgemeinerung	verallgemeinerung	PROPN
ap-768	242	13	der	der	PROPN
ap-768	242	14	eulerschen	eulerschen	PROPN
ap-768	242	15	funktion	funktion	PROPN
ap-768	242	16	.	.	PUNCT
ap-768	242	17	”	"	PUNCT
ap-768	243	1	resultate	resultate	ADJ
ap-768	243	2	der	der	PROPN
ap-768	243	3	mathematik	mathematik	PROPN
ap-768	243	4	,	,	PUNCT
ap-768	243	5	vol	vol	NOUN
ap-768	243	6	.	.	PROPN
ap-768	243	7	36	36	NUM
ap-768	243	8	(	(	PUNCT
ap-768	243	9	1999	1999	NUM
ap-768	243	10	)	)	PUNCT
ap-768	243	11	,	,	PUNCT
ap-768	243	12	p.	p.	NOUN
ap-768	243	13	354–364	354–364	NUM
ap-768	243	14	.	.	PUNCT
ap-768	244	1	[	[	X
ap-768	244	2	13	13	NUM
ap-768	244	3	]	]	X
ap-768	244	4	graham	graham	PROPN
ap-768	244	5	,	,	PUNCT
ap-768	244	6	r.	r.	PROPN
ap-768	244	7	l.	l.	PROPN
ap-768	244	8	,	,	PUNCT
ap-768	244	9	kmoth	kmoth	PROPN
ap-768	244	10	,	,	PUNCT
ap-768	244	11	d.	d.	PROPN
ap-768	244	12	e.	e.	PROPN
ap-768	244	13	,	,	PUNCT
ap-768	244	14	patashnik	patashnik	X
ap-768	244	15	,	,	PUNCT
ap-768	244	16	o.	o.	INTJ
ap-768	244	17	:	:	PUNCT
ap-768	244	18	concrete	concrete	ADJ
ap-768	244	19	mathematics	mathematic	NOUN
ap-768	244	20	,	,	PUNCT
ap-768	244	21	addison	addison	PROPN
ap-768	244	22	-	-	PUNCT
ap-768	244	23	wesley	wesley	PROPN
ap-768	244	24	,	,	PUNCT
ap-768	244	25	reading	reading	NOUN
ap-768	244	26	,	,	PUNCT
ap-768	244	27	ma	ma	PROPN
ap-768	244	28	,	,	PUNCT
ap-768	244	29	1994	1994	NUM
ap-768	244	30	.	.	PUNCT
ap-768	245	1	ing	ing	PROPN
ap-768	245	2	.	.	PUNCT
ap-768	246	1	petr	petr	PROPN
ap-768	246	2	novotný	novotný	PROPN
ap-768	246	3	phone	phone	PROPN
ap-768	246	4	:	:	PUNCT
ap-768	246	5	+420	+420	NUM
ap-768	246	6	222	222	NUM
ap-768	246	7	311	311	NUM
ap-768	246	8	333	333	NUM
ap-768	246	9	fujtajflik@seznam.cz	fujtajflik@seznam.cz	NOUN
ap-768	246	10	ing	ing	ADJ
ap-768	246	11	.	.	PUNCT
ap-768	247	1	jiří	jiří	PROPN
ap-768	247	2	hrivnák	hrivnák	PROPN
ap-768	247	3	phone	phone	PROPN
ap-768	247	4	:	:	PUNCT
ap-768	247	5	+420	+420	NUM
ap-768	247	6	222	222	NUM
ap-768	247	7	311	311	NUM
ap-768	247	8	333	333	NUM
ap-768	247	9	hrivnak@post.cz	hrivnak@post.cz	NOUN
ap-768	247	10	department	department	NOUN
ap-768	247	11	of	of	ADP
ap-768	247	12	physics	physics	PROPN
ap-768	247	13	czech	czech	PROPN
ap-768	247	14	technical	technical	PROPN
ap-768	247	15	university	university	PROPN
ap-768	247	16	in	in	ADP
ap-768	247	17	prague	prague	PROPN
ap-768	247	18	faculty	faculty	NOUN
ap-768	247	19	of	of	ADP
ap-768	247	20	nuclear	nuclear	ADJ
ap-768	247	21	sciences	science	NOUN
ap-768	247	22	and	and	CCONJ
ap-768	247	23	physical	physical	ADJ
ap-768	247	24	engineering	engineering	NOUN
ap-768	247	25	břehová	břehová	VERB
ap-768	247	26	7	7	NUM
ap-768	247	27	115	115	NUM
ap-768	247	28	19	19	NUM
ap-768	247	29	prague	prague	NOUN
ap-768	247	30	1	1	NUM
ap-768	247	31	,	,	PUNCT
ap-768	247	32	czech	czech	PROPN
ap-768	247	33	republic	republic	NOUN
ap-768	247	34	©	©	PROPN
ap-768	247	35	czech	czech	PROPN
ap-768	247	36	technical	technical	PROPN
ap-768	247	37	university	university	PROPN
ap-768	247	38	publishing	publishing	NOUN
ap-768	247	39	house	house	NOUN
ap-768	247	40	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-768	247	41	43	43	NUM
ap-768	247	42	czech	czech	PROPN
ap-768	247	43	technical	technical	PROPN
ap-768	247	44	university	university	PROPN
ap-768	247	45	in	in	ADP
ap-768	247	46	prague	prague	PROPN
ap-768	247	47	acta	acta	PROPN
ap-768	247	48	polytechnica	polytechnica	PROPN
ap-768	247	49	vol	vol	NOUN
ap-768	247	50	.	.	PROPN
ap-768	248	1	45	45	NUM
ap-768	248	2	no	no	NOUN
ap-768	248	3	.	.	PUNCT
ap-768	249	1	5/2005	5/2005	NUM