id	sid	tid	token	lemma	pos
ap-3517	1	1	acta	acta	PROPN
ap-3517	1	2	polytechnica	polytechnica	PROPN
ap-3517	1	3	doi:10.14311	doi:10.14311	PROPN
ap-3517	1	4	/	/	SYM
ap-3517	1	5	ap.2016.56.0283	ap.2016.56.0283	PROPN
ap-3517	1	6	acta	acta	PROPN
ap-3517	1	7	polytechnica	polytechnica	PROPN
ap-3517	1	8	56(4):283–290	56(4):283–290	PROPN
ap-3517	1	9	,	,	PUNCT
ap-3517	1	10	2016	2016	NUM
ap-3517	1	11	©	©	PROPN
ap-3517	1	12	czech	czech	PROPN
ap-3517	1	13	technical	technical	PROPN
ap-3517	1	14	university	university	PROPN
ap-3517	1	15	in	in	ADP
ap-3517	1	16	prague	prague	PROPN
ap-3517	1	17	,	,	PUNCT
ap-3517	1	18	2016	2016	NUM
ap-3517	1	19	available	available	ADJ
ap-3517	1	20	online	online	ADV
ap-3517	1	21	at	at	ADP
ap-3517	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3517	1	23	on	on	ADP
ap-3517	1	24	connecting	connect	VERB
ap-3517	1	25	weyl	weyl	VERB
ap-3517	1	26	-	-	PUNCT
ap-3517	1	27	orbit	orbit	NOUN
ap-3517	1	28	functions	function	NOUN
ap-3517	1	29	to	to	ADP
ap-3517	1	30	jacobi	jacobi	PROPN
ap-3517	1	31	polynomials	polynomial	NOUN
ap-3517	1	32	and	and	CCONJ
ap-3517	1	33	multivariate	multivariate	NOUN
ap-3517	1	34	(	(	PUNCT
ap-3517	1	35	anti)symmetric	anti)symmetric	ADJ
ap-3517	1	36	trigonometric	trigonometric	ADJ
ap-3517	1	37	functions	function	NOUN
ap-3517	1	38	jiří	jiří	NOUN
ap-3517	1	39	hrivnák	hrivnák	PROPN
ap-3517	1	40	,	,	PUNCT
ap-3517	1	41	lenka	lenka	PROPN
ap-3517	1	42	motlochová∗	motlochová∗	PROPN
ap-3517	1	43	department	department	PROPN
ap-3517	1	44	of	of	ADP
ap-3517	1	45	physics	physics	PROPN
ap-3517	1	46	,	,	PUNCT
ap-3517	1	47	faculty	faculty	NOUN
ap-3517	1	48	of	of	ADP
ap-3517	1	49	nuclear	nuclear	ADJ
ap-3517	1	50	sciences	science	NOUN
ap-3517	1	51	and	and	CCONJ
ap-3517	1	52	physical	physical	ADJ
ap-3517	1	53	engineering	engineering	NOUN
ap-3517	1	54	,	,	PUNCT
ap-3517	1	55	czech	czech	PROPN
ap-3517	1	56	technical	technical	PROPN
ap-3517	1	57	university	university	PROPN
ap-3517	1	58	in	in	ADP
ap-3517	1	59	prague	prague	PROPN
ap-3517	1	60	,	,	PUNCT
ap-3517	1	61	břehová	břehová	VERB
ap-3517	1	62	7	7	NUM
ap-3517	1	63	,	,	PUNCT
ap-3517	1	64	cz-115	cz-115	PROPN
ap-3517	1	65	19	19	NUM
ap-3517	1	66	prague	prague	NOUN
ap-3517	1	67	,	,	PUNCT
ap-3517	1	68	czech	czech	PROPN
ap-3517	1	69	republic	republic	NOUN
ap-3517	1	70	∗	∗	NOUN
ap-3517	1	71	corresponding	correspond	VERB
ap-3517	1	72	author	author	NOUN
ap-3517	1	73	:	:	PUNCT
ap-3517	1	74	lenka.motlochova@fjfi.cvut.cz	lenka.motlochova@fjfi.cvut.cz	PROPN
ap-3517	1	75	abstract	abstract	NOUN
ap-3517	1	76	.	.	PUNCT
ap-3517	2	1	the	the	DET
ap-3517	2	2	aim	aim	NOUN
ap-3517	2	3	of	of	ADP
ap-3517	2	4	this	this	DET
ap-3517	2	5	paper	paper	NOUN
ap-3517	2	6	is	be	AUX
ap-3517	2	7	to	to	PART
ap-3517	2	8	make	make	VERB
ap-3517	2	9	an	an	DET
ap-3517	2	10	explicit	explicit	ADJ
ap-3517	2	11	link	link	NOUN
ap-3517	2	12	between	between	ADP
ap-3517	2	13	the	the	DET
ap-3517	2	14	weyl	weyl	VERB
ap-3517	2	15	-	-	PUNCT
ap-3517	2	16	orbit	orbit	NOUN
ap-3517	2	17	functions	function	NOUN
ap-3517	2	18	and	and	CCONJ
ap-3517	2	19	the	the	DET
ap-3517	2	20	corresponding	corresponding	ADJ
ap-3517	2	21	polynomials	polynomial	NOUN
ap-3517	2	22	,	,	PUNCT
ap-3517	2	23	on	on	ADP
ap-3517	2	24	the	the	DET
ap-3517	2	25	one	one	NUM
ap-3517	2	26	hand	hand	NOUN
ap-3517	2	27	,	,	PUNCT
ap-3517	2	28	and	and	CCONJ
ap-3517	2	29	to	to	ADP
ap-3517	2	30	several	several	ADJ
ap-3517	2	31	other	other	ADJ
ap-3517	2	32	families	family	NOUN
ap-3517	2	33	of	of	ADP
ap-3517	2	34	special	special	ADJ
ap-3517	2	35	functions	function	NOUN
ap-3517	2	36	and	and	CCONJ
ap-3517	2	37	orthogonal	orthogonal	ADJ
ap-3517	2	38	polynomials	polynomial	NOUN
ap-3517	2	39	on	on	ADP
ap-3517	2	40	the	the	DET
ap-3517	2	41	other	other	ADJ
ap-3517	2	42	.	.	PUNCT
ap-3517	3	1	the	the	DET
ap-3517	3	2	cornerstone	cornerstone	NOUN
ap-3517	3	3	is	be	AUX
ap-3517	3	4	the	the	DET
ap-3517	3	5	connection	connection	NOUN
ap-3517	3	6	that	that	PRON
ap-3517	3	7	is	be	AUX
ap-3517	3	8	made	make	VERB
ap-3517	3	9	between	between	ADP
ap-3517	3	10	the	the	DET
ap-3517	3	11	one	one	NUM
ap-3517	3	12	-	-	PUNCT
ap-3517	3	13	variable	variable	NOUN
ap-3517	3	14	orbit	orbit	NOUN
ap-3517	3	15	functions	function	NOUN
ap-3517	3	16	of	of	ADP
ap-3517	3	17	a1	a1	NOUN
ap-3517	3	18	and	and	CCONJ
ap-3517	3	19	the	the	DET
ap-3517	3	20	four	four	NUM
ap-3517	3	21	kinds	kind	NOUN
ap-3517	3	22	of	of	ADP
ap-3517	3	23	chebyshev	chebyshev	NOUN
ap-3517	3	24	polynomials	polynomial	NOUN
ap-3517	3	25	.	.	PUNCT
ap-3517	4	1	it	it	PRON
ap-3517	4	2	is	be	AUX
ap-3517	4	3	shown	show	VERB
ap-3517	4	4	that	that	SCONJ
ap-3517	4	5	there	there	PRON
ap-3517	4	6	exists	exist	VERB
ap-3517	4	7	a	a	DET
ap-3517	4	8	similar	similar	ADJ
ap-3517	4	9	connection	connection	NOUN
ap-3517	4	10	for	for	ADP
ap-3517	4	11	the	the	DET
ap-3517	4	12	two	two	NUM
ap-3517	4	13	-	-	PUNCT
ap-3517	4	14	variable	variable	NOUN
ap-3517	4	15	orbit	orbit	NOUN
ap-3517	4	16	functions	function	NOUN
ap-3517	4	17	of	of	ADP
ap-3517	4	18	a2	a2	PROPN
ap-3517	4	19	and	and	CCONJ
ap-3517	4	20	a	a	DET
ap-3517	4	21	specific	specific	ADJ
ap-3517	4	22	version	version	NOUN
ap-3517	4	23	of	of	ADP
ap-3517	4	24	two	two	NUM
ap-3517	4	25	variable	variable	ADJ
ap-3517	4	26	jacobi	jacobi	NOUN
ap-3517	4	27	polynomials	polynomial	NOUN
ap-3517	4	28	.	.	PUNCT
ap-3517	5	1	the	the	DET
ap-3517	5	2	connection	connection	NOUN
ap-3517	5	3	with	with	ADP
ap-3517	5	4	recently	recently	ADV
ap-3517	5	5	studied	study	VERB
ap-3517	5	6	g2	g2	PROPN
ap-3517	5	7	-	-	PUNCT
ap-3517	5	8	polynomials	polynomial	NOUN
ap-3517	5	9	is	be	AUX
ap-3517	5	10	established	establish	VERB
ap-3517	5	11	.	.	PUNCT
ap-3517	6	1	formulas	formula	NOUN
ap-3517	6	2	for	for	ADP
ap-3517	6	3	connection	connection	NOUN
ap-3517	6	4	between	between	ADP
ap-3517	6	5	the	the	DET
ap-3517	6	6	four	four	NUM
ap-3517	6	7	types	type	NOUN
ap-3517	6	8	of	of	ADP
ap-3517	6	9	orbit	orbit	NOUN
ap-3517	6	10	functions	function	NOUN
ap-3517	6	11	of	of	ADP
ap-3517	6	12	bn	bn	NOUN
ap-3517	6	13	or	or	CCONJ
ap-3517	6	14	cn	cn	PROPN
ap-3517	6	15	and	and	CCONJ
ap-3517	6	16	the	the	DET
ap-3517	6	17	(	(	PUNCT
ap-3517	6	18	anti)symmetric	anti)symmetric	ADJ
ap-3517	6	19	multivariate	multivariate	NOUN
ap-3517	6	20	cosine	cosine	NOUN
ap-3517	6	21	and	and	CCONJ
ap-3517	6	22	sine	sine	ADJ
ap-3517	6	23	functions	function	NOUN
ap-3517	6	24	are	be	AUX
ap-3517	6	25	explicitly	explicitly	ADV
ap-3517	6	26	derived	derive	VERB
ap-3517	6	27	.	.	PUNCT
ap-3517	7	1	keywords	keyword	NOUN
ap-3517	7	2	:	:	PUNCT
ap-3517	7	3	weyl	weyl	VERB
ap-3517	7	4	-	-	PUNCT
ap-3517	7	5	orbit	orbit	NOUN
ap-3517	7	6	functions	function	NOUN
ap-3517	7	7	,	,	PUNCT
ap-3517	7	8	chebyshev	chebyshev	NOUN
ap-3517	7	9	polynomials	polynomial	NOUN
ap-3517	7	10	,	,	PUNCT
ap-3517	7	11	jacobi	jacobi	PROPN
ap-3517	7	12	polynomials	polynomial	NOUN
ap-3517	7	13	,	,	PUNCT
ap-3517	7	14	(	(	PUNCT
ap-3517	7	15	anti)symmetric	anti)symmetric	ADJ
ap-3517	7	16	trigonometric	trigonometric	ADJ
ap-3517	7	17	functions	function	NOUN
ap-3517	7	18	.	.	PUNCT
ap-3517	8	1	1	1	X
ap-3517	8	2	.	.	X
ap-3517	8	3	introduction	introduction	NOUN
ap-3517	8	4	special	special	ADJ
ap-3517	8	5	functions	function	NOUN
ap-3517	8	6	associated	associate	VERB
ap-3517	8	7	with	with	ADP
ap-3517	8	8	the	the	DET
ap-3517	8	9	root	root	NOUN
ap-3517	8	10	systems	system	NOUN
ap-3517	8	11	of	of	ADP
ap-3517	8	12	simple	simple	ADJ
ap-3517	8	13	lie	lie	NOUN
ap-3517	8	14	algebras	algebra	NOUN
ap-3517	8	15	,	,	PUNCT
ap-3517	8	16	e.g.	e.g.	ADV
ap-3517	8	17	weyl	weyl	VERB
ap-3517	8	18	-	-	PUNCT
ap-3517	8	19	orbit	orbit	NOUN
ap-3517	8	20	functions	function	NOUN
ap-3517	8	21	,	,	PUNCT
ap-3517	8	22	play	play	VERB
ap-3517	8	23	an	an	DET
ap-3517	8	24	important	important	ADJ
ap-3517	8	25	role	role	NOUN
ap-3517	8	26	in	in	ADP
ap-3517	8	27	several	several	ADJ
ap-3517	8	28	domains	domain	NOUN
ap-3517	8	29	of	of	ADP
ap-3517	8	30	mathematics	mathematic	NOUN
ap-3517	8	31	and	and	CCONJ
ap-3517	8	32	theoretical	theoretical	ADJ
ap-3517	8	33	physics	physics	NOUN
ap-3517	8	34	,	,	PUNCT
ap-3517	8	35	in	in	ADP
ap-3517	8	36	particular	particular	ADJ
ap-3517	8	37	in	in	ADP
ap-3517	8	38	representation	representation	NOUN
ap-3517	8	39	theory	theory	NOUN
ap-3517	8	40	,	,	PUNCT
ap-3517	8	41	harmonic	harmonic	ADJ
ap-3517	8	42	analysis	analysis	NOUN
ap-3517	8	43	,	,	PUNCT
ap-3517	8	44	numerical	numerical	ADJ
ap-3517	8	45	integration	integration	NOUN
ap-3517	8	46	and	and	CCONJ
ap-3517	8	47	conformal	conformal	ADJ
ap-3517	8	48	field	field	NOUN
ap-3517	8	49	theory	theory	NOUN
ap-3517	8	50	.	.	PUNCT
ap-3517	9	1	the	the	DET
ap-3517	9	2	purpose	purpose	NOUN
ap-3517	9	3	of	of	ADP
ap-3517	9	4	this	this	DET
ap-3517	9	5	paper	paper	NOUN
ap-3517	9	6	is	be	AUX
ap-3517	9	7	to	to	PART
ap-3517	9	8	link	link	VERB
ap-3517	9	9	weyl	weyl	VERB
ap-3517	9	10	-	-	PUNCT
ap-3517	9	11	orbit	orbit	NOUN
ap-3517	9	12	functions	function	NOUN
ap-3517	9	13	with	with	ADP
ap-3517	9	14	various	various	ADJ
ap-3517	9	15	types	type	NOUN
ap-3517	9	16	of	of	ADP
ap-3517	9	17	orthogonal	orthogonal	ADJ
ap-3517	9	18	polynomials	polynomial	NOUN
ap-3517	9	19	,	,	PUNCT
ap-3517	9	20	namely	namely	ADV
ap-3517	9	21	chebyshev	chebyshev	NOUN
ap-3517	9	22	and	and	CCONJ
ap-3517	9	23	jacobi	jacobi	PROPN
ap-3517	9	24	polynomials	polynomial	NOUN
ap-3517	9	25	and	and	CCONJ
ap-3517	9	26	their	their	PRON
ap-3517	9	27	multivariate	multivariate	NOUN
ap-3517	9	28	generalizations	generalization	NOUN
ap-3517	9	29	,	,	PUNCT
ap-3517	9	30	and	and	CCONJ
ap-3517	9	31	thus	thus	ADV
ap-3517	9	32	to	to	PART
ap-3517	9	33	motivate	motivate	VERB
ap-3517	9	34	further	further	ADJ
ap-3517	9	35	development	development	NOUN
ap-3517	9	36	of	of	ADP
ap-3517	9	37	the	the	DET
ap-3517	9	38	remarkable	remarkable	ADJ
ap-3517	9	39	properties	property	NOUN
ap-3517	9	40	of	of	ADP
ap-3517	9	41	these	these	DET
ap-3517	9	42	polynomials	polynomial	NOUN
ap-3517	9	43	in	in	ADP
ap-3517	9	44	connection	connection	NOUN
ap-3517	9	45	with	with	ADP
ap-3517	9	46	orbit	orbit	NOUN
ap-3517	9	47	functions	function	NOUN
ap-3517	9	48	.	.	PUNCT
ap-3517	10	1	the	the	DET
ap-3517	10	2	collection	collection	NOUN
ap-3517	10	3	of	of	ADP
ap-3517	10	4	weyl	weyl	VERB
ap-3517	10	5	-	-	PUNCT
ap-3517	10	6	orbit	orbit	NOUN
ap-3517	10	7	functions	function	NOUN
ap-3517	10	8	includes	include	VERB
ap-3517	10	9	four	four	NUM
ap-3517	10	10	different	different	ADJ
ap-3517	10	11	families	family	NOUN
ap-3517	10	12	of	of	ADP
ap-3517	10	13	functions	function	NOUN
ap-3517	10	14	called	call	VERB
ap-3517	10	15	c	c	NOUN
ap-3517	10	16	–	–	PUNCT
ap-3517	10	17	,	,	PUNCT
ap-3517	10	18	s	s	X
ap-3517	10	19	–	–	PUNCT
ap-3517	10	20	,	,	PUNCT
ap-3517	10	21	ss	ss	NOUN
ap-3517	10	22	–	–	PUNCT
ap-3517	10	23	and	and	CCONJ
ap-3517	10	24	sl	sl	NOUN
ap-3517	10	25	–	–	PUNCT
ap-3517	10	26	functions	function	NOUN
ap-3517	10	27	[	[	X
ap-3517	10	28	6	6	NUM
ap-3517	10	29	,	,	PUNCT
ap-3517	10	30	15	15	NUM
ap-3517	10	31	,	,	PUNCT
ap-3517	10	32	16	16	NUM
ap-3517	10	33	,	,	PUNCT
ap-3517	10	34	25	25	NUM
ap-3517	10	35	]	]	PUNCT
ap-3517	10	36	.	.	PUNCT
ap-3517	11	1	they	they	PRON
ap-3517	11	2	are	be	AUX
ap-3517	11	3	induced	induce	VERB
ap-3517	11	4	from	from	ADP
ap-3517	11	5	the	the	DET
ap-3517	11	6	sign	sign	NOUN
ap-3517	11	7	homomorphisms	homomorphism	NOUN
ap-3517	11	8	of	of	ADP
ap-3517	11	9	the	the	DET
ap-3517	11	10	weyl	weyl	VERB
ap-3517	11	11	groups	group	NOUN
ap-3517	11	12	of	of	ADP
ap-3517	11	13	geometric	geometric	ADJ
ap-3517	11	14	symmetries	symmetry	NOUN
ap-3517	11	15	related	relate	VERB
ap-3517	11	16	to	to	ADP
ap-3517	11	17	the	the	DET
ap-3517	11	18	underlying	underlie	VERB
ap-3517	11	19	lie	lie	NOUN
ap-3517	11	20	algebras	algebra	VERB
ap-3517	11	21	.	.	PUNCT
ap-3517	12	1	the	the	DET
ap-3517	12	2	symmetric	symmetric	ADJ
ap-3517	12	3	c	c	PROPN
ap-3517	12	4	–	–	PUNCT
ap-3517	12	5	functions	function	NOUN
ap-3517	12	6	and	and	CCONJ
ap-3517	12	7	antisymmetric	antisymmetric	ADJ
ap-3517	12	8	s	s	PROPN
ap-3517	12	9	–	–	PUNCT
ap-3517	12	10	functions	function	NOUN
ap-3517	12	11	also	also	ADV
ap-3517	12	12	appear	appear	VERB
ap-3517	12	13	in	in	ADP
ap-3517	12	14	the	the	DET
ap-3517	12	15	representation	representation	NOUN
ap-3517	12	16	theory	theory	NOUN
ap-3517	12	17	of	of	ADP
ap-3517	12	18	simple	simple	ADJ
ap-3517	12	19	lie	lie	NOUN
ap-3517	12	20	algebras	algebra	NOUN
ap-3517	12	21	[	[	X
ap-3517	12	22	32	32	NUM
ap-3517	12	23	,	,	PUNCT
ap-3517	12	24	34	34	NUM
ap-3517	12	25	]	]	PUNCT
ap-3517	12	26	;	;	PUNCT
ap-3517	12	27	the	the	DET
ap-3517	12	28	s	s	PROPN
ap-3517	12	29	–	–	PUNCT
ap-3517	12	30	functions	function	NOUN
ap-3517	12	31	appear	appear	VERB
ap-3517	12	32	in	in	ADP
ap-3517	12	33	the	the	DET
ap-3517	12	34	weyl	weyl	VERB
ap-3517	12	35	character	character	NOUN
ap-3517	12	36	formula	formula	NOUN
ap-3517	12	37	and	and	CCONJ
ap-3517	12	38	every	every	DET
ap-3517	12	39	character	character	NOUN
ap-3517	12	40	of	of	ADP
ap-3517	12	41	irreducible	irreducible	ADJ
ap-3517	12	42	representations	representation	NOUN
ap-3517	12	43	of	of	ADP
ap-3517	12	44	simple	simple	ADJ
ap-3517	12	45	lie	lie	NOUN
ap-3517	12	46	algebra	algebra	NOUN
ap-3517	12	47	can	can	AUX
ap-3517	12	48	be	be	AUX
ap-3517	12	49	written	write	VERB
ap-3517	12	50	as	as	ADP
ap-3517	12	51	a	a	DET
ap-3517	12	52	linear	linear	ADJ
ap-3517	12	53	combination	combination	NOUN
ap-3517	12	54	of	of	ADP
ap-3517	12	55	c	c	NOUN
ap-3517	12	56	–	–	PUNCT
ap-3517	12	57	functions	function	NOUN
ap-3517	12	58	.	.	PUNCT
ap-3517	13	1	unlike	unlike	ADP
ap-3517	13	2	c	c	PROPN
ap-3517	13	3	–	–	PUNCT
ap-3517	13	4	and	and	CCONJ
ap-3517	13	5	s	s	PROPN
ap-3517	13	6	–	–	PUNCT
ap-3517	13	7	functions	function	NOUN
ap-3517	13	8	,	,	PUNCT
ap-3517	13	9	ss	ss	NOUN
ap-3517	13	10	–	–	PUNCT
ap-3517	13	11	and	and	CCONJ
ap-3517	13	12	sl	sl	NOUN
ap-3517	13	13	–	–	PUNCT
ap-3517	13	14	functions	function	NOUN
ap-3517	13	15	exist	exist	VERB
ap-3517	13	16	only	only	ADV
ap-3517	13	17	in	in	ADP
ap-3517	13	18	the	the	DET
ap-3517	13	19	case	case	NOUN
ap-3517	13	20	of	of	ADP
ap-3517	13	21	simple	simple	ADJ
ap-3517	13	22	lie	lie	NOUN
ap-3517	13	23	algebras	algebra	NOUN
ap-3517	13	24	with	with	ADP
ap-3517	13	25	two	two	NUM
ap-3517	13	26	different	different	ADJ
ap-3517	13	27	lengths	length	NOUN
ap-3517	13	28	of	of	ADP
ap-3517	13	29	roots	root	NOUN
ap-3517	13	30	.	.	PUNCT
ap-3517	14	1	a	a	DET
ap-3517	14	2	review	review	NOUN
ap-3517	14	3	of	of	ADP
ap-3517	14	4	several	several	ADJ
ap-3517	14	5	pertinent	pertinent	ADJ
ap-3517	14	6	properties	property	NOUN
ap-3517	14	7	of	of	ADP
ap-3517	14	8	the	the	DET
ap-3517	14	9	weylorbit	weylorbit	NOUN
ap-3517	14	10	functions	function	NOUN
ap-3517	14	11	is	be	AUX
ap-3517	14	12	contained	contain	VERB
ap-3517	14	13	in	in	ADP
ap-3517	14	14	[	[	X
ap-3517	14	15	8	8	NUM
ap-3517	14	16	,	,	PUNCT
ap-3517	14	17	15	15	NUM
ap-3517	14	18	,	,	PUNCT
ap-3517	14	19	16	16	NUM
ap-3517	14	20	,	,	PUNCT
ap-3517	14	21	25	25	NUM
ap-3517	14	22	]	]	PUNCT
ap-3517	14	23	.	.	PUNCT
ap-3517	15	1	these	these	DET
ap-3517	15	2	functions	function	NOUN
ap-3517	15	3	possess	possess	VERB
ap-3517	15	4	symmetries	symmetry	NOUN
ap-3517	15	5	with	with	ADP
ap-3517	15	6	respect	respect	NOUN
ap-3517	15	7	to	to	ADP
ap-3517	15	8	the	the	DET
ap-3517	15	9	affine	affine	NOUN
ap-3517	15	10	weyl	weyl	VERB
ap-3517	15	11	group	group	NOUN
ap-3517	15	12	–	–	PUNCT
ap-3517	15	13	an	an	DET
ap-3517	15	14	infinite	infinite	ADJ
ap-3517	15	15	extension	extension	NOUN
ap-3517	15	16	of	of	ADP
ap-3517	15	17	the	the	DET
ap-3517	15	18	weyl	weyl	VERB
ap-3517	15	19	group	group	NOUN
ap-3517	15	20	by	by	ADP
ap-3517	15	21	translations	translation	NOUN
ap-3517	15	22	in	in	ADP
ap-3517	15	23	dual	dual	ADJ
ap-3517	15	24	root	root	NOUN
ap-3517	15	25	lattice	lattice	NOUN
ap-3517	15	26	.	.	PUNCT
ap-3517	16	1	therefore	therefore	ADV
ap-3517	16	2	,	,	PUNCT
ap-3517	16	3	we	we	PRON
ap-3517	16	4	consider	consider	VERB
ap-3517	16	5	c	c	NOUN
ap-3517	16	6	–	–	PUNCT
ap-3517	16	7	,	,	PUNCT
ap-3517	16	8	s	s	X
ap-3517	16	9	–	–	PUNCT
ap-3517	16	10	,	,	PUNCT
ap-3517	16	11	ss	ss	NOUN
ap-3517	16	12	–	–	PUNCT
ap-3517	16	13	and	and	CCONJ
ap-3517	16	14	sl	sl	NOUN
ap-3517	16	15	–	–	PUNCT
ap-3517	16	16	functions	function	NOUN
ap-3517	16	17	only	only	ADV
ap-3517	16	18	on	on	ADP
ap-3517	16	19	specific	specific	ADJ
ap-3517	16	20	subsets	subset	NOUN
ap-3517	16	21	of	of	ADP
ap-3517	16	22	the	the	DET
ap-3517	16	23	fundamental	fundamental	ADJ
ap-3517	16	24	domain	domain	NOUN
ap-3517	16	25	f	f	PROPN
ap-3517	16	26	of	of	ADP
ap-3517	16	27	the	the	DET
ap-3517	16	28	affine	affine	NOUN
ap-3517	16	29	weyl	weyl	VERB
ap-3517	16	30	group	group	NOUN
ap-3517	16	31	.	.	PUNCT
ap-3517	17	1	within	within	ADP
ap-3517	17	2	each	each	DET
ap-3517	17	3	family	family	NOUN
ap-3517	17	4	,	,	PUNCT
ap-3517	17	5	the	the	DET
ap-3517	17	6	functions	function	NOUN
ap-3517	17	7	are	be	AUX
ap-3517	17	8	continuously	continuously	ADV
ap-3517	17	9	orthogonal	orthogonal	ADJ
ap-3517	17	10	when	when	SCONJ
ap-3517	17	11	integrated	integrate	VERB
ap-3517	17	12	over	over	ADP
ap-3517	17	13	f	f	PROPN
ap-3517	17	14	and	and	CCONJ
ap-3517	17	15	form	form	VERB
ap-3517	17	16	a	a	DET
ap-3517	17	17	hilbert	hilbert	NOUN
ap-3517	17	18	basis	basis	NOUN
ap-3517	17	19	of	of	ADP
ap-3517	17	20	squared	square	VERB
ap-3517	17	21	integrable	integrable	ADJ
ap-3517	17	22	functions	function	NOUN
ap-3517	17	23	on	on	ADP
ap-3517	17	24	f	f	PROPN
ap-3517	18	1	[	[	X
ap-3517	18	2	25	25	NUM
ap-3517	18	3	,	,	PUNCT
ap-3517	18	4	27	27	NUM
ap-3517	18	5	]	]	PUNCT
ap-3517	18	6	.	.	PUNCT
ap-3517	19	1	they	they	PRON
ap-3517	19	2	also	also	ADV
ap-3517	19	3	satisfy	satisfy	VERB
ap-3517	19	4	discrete	discrete	ADJ
ap-3517	19	5	orthogonality	orthogonality	NOUN
ap-3517	19	6	relations	relation	NOUN
ap-3517	19	7	which	which	PRON
ap-3517	19	8	is	be	AUX
ap-3517	19	9	of	of	ADP
ap-3517	19	10	major	major	ADJ
ap-3517	19	11	importance	importance	NOUN
ap-3517	19	12	for	for	ADP
ap-3517	19	13	the	the	DET
ap-3517	19	14	processing	processing	NOUN
ap-3517	19	15	of	of	ADP
ap-3517	19	16	multidimensional	multidimensional	ADJ
ap-3517	19	17	digital	digital	ADJ
ap-3517	19	18	data	datum	NOUN
ap-3517	19	19	[	[	X
ap-3517	19	20	8	8	NUM
ap-3517	19	21	,	,	PUNCT
ap-3517	19	22	10	10	NUM
ap-3517	19	23	,	,	PUNCT
ap-3517	19	24	27	27	NUM
ap-3517	19	25	]	]	PUNCT
ap-3517	19	26	.	.	PUNCT
ap-3517	20	1	using	use	VERB
ap-3517	20	2	discrete	discrete	ADJ
ap-3517	20	3	fourier	fourier	NOUN
ap-3517	20	4	-	-	PUNCT
ap-3517	20	5	like	like	ADJ
ap-3517	20	6	transforms	transform	NOUN
ap-3517	20	7	arising	arise	VERB
ap-3517	20	8	from	from	ADP
ap-3517	20	9	discrete	discrete	ADJ
ap-3517	20	10	orthogonality	orthogonality	NOUN
ap-3517	20	11	,	,	PUNCT
ap-3517	20	12	digital	digital	ADJ
ap-3517	20	13	data	datum	NOUN
ap-3517	20	14	are	be	AUX
ap-3517	20	15	interpolated	interpolate	VERB
ap-3517	20	16	in	in	ADP
ap-3517	20	17	any	any	DET
ap-3517	20	18	dimension	dimension	NOUN
ap-3517	20	19	and	and	CCONJ
ap-3517	20	20	for	for	ADP
ap-3517	20	21	any	any	DET
ap-3517	20	22	lattice	lattice	NOUN
ap-3517	20	23	symmetry	symmetry	NOUN
ap-3517	20	24	afforded	afford	VERB
ap-3517	20	25	by	by	ADP
ap-3517	20	26	the	the	DET
ap-3517	20	27	underlying	underlie	VERB
ap-3517	20	28	simple	simple	ADJ
ap-3517	20	29	lie	lie	NOUN
ap-3517	20	30	algebra	algebra	NOUN
ap-3517	20	31	.	.	PUNCT
ap-3517	21	1	several	several	ADJ
ap-3517	21	2	special	special	ADJ
ap-3517	21	3	cases	case	NOUN
ap-3517	21	4	of	of	ADP
ap-3517	21	5	simple	simple	ADJ
ap-3517	21	6	lie	lie	NOUN
ap-3517	21	7	algebras	algebra	NOUN
ap-3517	21	8	of	of	ADP
ap-3517	21	9	rank	rank	NOUN
ap-3517	21	10	two	two	NUM
ap-3517	21	11	are	be	AUX
ap-3517	21	12	studied	study	VERB
ap-3517	21	13	in	in	ADP
ap-3517	21	14	[	[	X
ap-3517	21	15	28–30	28–30	NOUN
ap-3517	21	16	]	]	PUNCT
ap-3517	21	17	.	.	PUNCT
ap-3517	22	1	the	the	DET
ap-3517	22	2	properties	property	NOUN
ap-3517	22	3	of	of	ADP
ap-3517	22	4	orbit	orbit	NOUN
ap-3517	22	5	functions	function	NOUN
ap-3517	22	6	also	also	ADV
ap-3517	22	7	lead	lead	VERB
ap-3517	22	8	to	to	ADP
ap-3517	22	9	numerical	numerical	ADJ
ap-3517	22	10	integration	integration	NOUN
ap-3517	22	11	formulas	formula	NOUN
ap-3517	22	12	for	for	ADP
ap-3517	22	13	functions	function	NOUN
ap-3517	22	14	of	of	ADP
ap-3517	22	15	several	several	ADJ
ap-3517	22	16	variables	variable	NOUN
ap-3517	22	17	.	.	PUNCT
ap-3517	23	1	they	they	PRON
ap-3517	23	2	approximate	approximate	VERB
ap-3517	23	3	a	a	DET
ap-3517	23	4	weighted	weight	VERB
ap-3517	23	5	integral	integral	ADJ
ap-3517	23	6	of	of	ADP
ap-3517	23	7	any	any	DET
ap-3517	23	8	function	function	NOUN
ap-3517	23	9	of	of	ADP
ap-3517	23	10	several	several	ADJ
ap-3517	23	11	variables	variable	NOUN
ap-3517	23	12	by	by	ADP
ap-3517	23	13	a	a	DET
ap-3517	23	14	linear	linear	ADJ
ap-3517	23	15	combination	combination	NOUN
ap-3517	23	16	of	of	ADP
ap-3517	23	17	function	function	NOUN
ap-3517	23	18	values	value	NOUN
ap-3517	23	19	at	at	ADP
ap-3517	23	20	points	point	NOUN
ap-3517	23	21	called	call	VERB
ap-3517	23	22	nodes	node	NOUN
ap-3517	23	23	.	.	PUNCT
ap-3517	24	1	in	in	ADP
ap-3517	24	2	general	general	ADJ
ap-3517	24	3	,	,	PUNCT
ap-3517	24	4	such	such	ADJ
ap-3517	24	5	formulas	formula	NOUN
ap-3517	24	6	are	be	AUX
ap-3517	24	7	required	require	VERB
ap-3517	24	8	to	to	PART
ap-3517	24	9	be	be	AUX
ap-3517	24	10	exact	exact	ADJ
ap-3517	24	11	for	for	ADP
ap-3517	24	12	all	all	DET
ap-3517	24	13	polynomial	polynomial	ADJ
ap-3517	24	14	functions	function	NOUN
ap-3517	24	15	up	up	ADP
ap-3517	24	16	to	to	ADP
ap-3517	24	17	a	a	DET
ap-3517	24	18	certain	certain	ADJ
ap-3517	24	19	degree	degree	NOUN
ap-3517	25	1	[	[	X
ap-3517	25	2	3	3	NUM
ap-3517	25	3	]	]	PUNCT
ap-3517	25	4	.	.	PUNCT
ap-3517	26	1	furthermore	furthermore	ADV
ap-3517	26	2	,	,	PUNCT
ap-3517	26	3	the	the	DET
ap-3517	26	4	c	c	NOUN
ap-3517	26	5	–	–	PUNCT
ap-3517	26	6	functions	function	NOUN
ap-3517	26	7	and	and	CCONJ
ap-3517	26	8	s	s	NOUN
ap-3517	26	9	–	–	PUNCT
ap-3517	26	10	functions	function	NOUN
ap-3517	26	11	of	of	ADP
ap-3517	26	12	simple	simple	ADJ
ap-3517	26	13	lie	lie	NOUN
ap-3517	26	14	algebra	algebra	NOUN
ap-3517	26	15	a1	a1	NOUN
ap-3517	26	16	coincide	coincide	NOUN
ap-3517	26	17	,	,	PUNCT
ap-3517	26	18	up	up	ADP
ap-3517	26	19	to	to	ADP
ap-3517	26	20	a	a	DET
ap-3517	26	21	constant	constant	ADJ
ap-3517	26	22	,	,	PUNCT
ap-3517	26	23	with	with	ADP
ap-3517	26	24	the	the	DET
ap-3517	26	25	common	common	ADJ
ap-3517	26	26	cosine	cosine	NOUN
ap-3517	26	27	and	and	CCONJ
ap-3517	26	28	sine	sine	ADJ
ap-3517	26	29	functions	function	NOUN
ap-3517	26	30	respectively	respectively	ADV
ap-3517	26	31	.	.	PUNCT
ap-3517	27	1	they	they	PRON
ap-3517	27	2	,	,	PUNCT
ap-3517	27	3	are	be	AUX
ap-3517	27	4	therefore	therefore	ADV
ap-3517	27	5	,	,	PUNCT
ap-3517	27	6	related	relate	VERB
ap-3517	27	7	to	to	ADP
ap-3517	27	8	the	the	DET
ap-3517	27	9	extensively	extensively	ADV
ap-3517	27	10	studied	study	VERB
ap-3517	27	11	chebyshev	chebyshev	NOUN
ap-3517	27	12	polynomials	polynomial	NOUN
ap-3517	27	13	and	and	CCONJ
ap-3517	27	14	,	,	PUNCT
ap-3517	27	15	consequently	consequently	ADV
ap-3517	27	16	,	,	PUNCT
ap-3517	27	17	to	to	ADP
ap-3517	27	18	the	the	DET
ap-3517	27	19	integration	integration	NOUN
ap-3517	27	20	formulas	formula	NOUN
ap-3517	27	21	,	,	PUNCT
ap-3517	27	22	quadratures	quadrature	NOUN
ap-3517	27	23	,	,	PUNCT
ap-3517	27	24	for	for	ADP
ap-3517	27	25	the	the	DET
ap-3517	27	26	functions	function	NOUN
ap-3517	27	27	of	of	ADP
ap-3517	27	28	one	one	NUM
ap-3517	27	29	variable	variable	NOUN
ap-3517	27	30	[	[	X
ap-3517	27	31	5	5	NUM
ap-3517	27	32	,	,	PUNCT
ap-3517	27	33	31	31	NUM
ap-3517	27	34	]	]	PUNCT
ap-3517	27	35	.	.	PUNCT
ap-3517	28	1	in	in	ADP
ap-3517	28	2	[	[	X
ap-3517	28	3	24	24	NUM
ap-3517	28	4	]	]	PUNCT
ap-3517	28	5	,	,	PUNCT
ap-3517	28	6	it	it	PRON
ap-3517	28	7	is	be	AUX
ap-3517	28	8	shown	show	VERB
ap-3517	28	9	that	that	SCONJ
ap-3517	28	10	there	there	PRON
ap-3517	28	11	are	be	VERB
ap-3517	28	12	analogous	analogous	ADJ
ap-3517	28	13	formulas	formula	NOUN
ap-3517	28	14	for	for	ADP
ap-3517	28	15	numerical	numerical	ADJ
ap-3517	28	16	integration	integration	NOUN
ap-3517	28	17	,	,	PUNCT
ap-3517	28	18	for	for	ADP
ap-3517	28	19	multivariate	multivariate	NOUN
ap-3517	28	20	functions	function	NOUN
ap-3517	28	21	,	,	PUNCT
ap-3517	28	22	that	that	PRON
ap-3517	28	23	depend	depend	VERB
ap-3517	28	24	on	on	ADP
ap-3517	28	25	the	the	DET
ap-3517	28	26	weyl	weyl	VERB
ap-3517	28	27	group	group	NOUN
ap-3517	28	28	of	of	ADP
ap-3517	28	29	the	the	DET
ap-3517	28	30	simple	simple	ADJ
ap-3517	28	31	lie	lie	NOUN
ap-3517	28	32	algebra	algebra	NOUN
ap-3517	28	33	an	an	PRON
ap-3517	28	34	and	and	CCONJ
ap-3517	28	35	the	the	DET
ap-3517	28	36	corresponding	correspond	VERB
ap-3517	28	37	c	c	NOUN
ap-3517	28	38	–	–	PUNCT
ap-3517	28	39	and	and	CCONJ
ap-3517	28	40	s	s	NOUN
ap-3517	28	41	–	–	PUNCT
ap-3517	28	42	functions	function	NOUN
ap-3517	28	43	.	.	PUNCT
ap-3517	29	1	the	the	DET
ap-3517	29	2	resulting	result	VERB
ap-3517	29	3	rules	rule	NOUN
ap-3517	29	4	for	for	ADP
ap-3517	29	5	functions	function	NOUN
ap-3517	29	6	of	of	ADP
ap-3517	29	7	several	several	ADJ
ap-3517	29	8	variables	variable	NOUN
ap-3517	29	9	are	be	AUX
ap-3517	29	10	known	know	VERB
ap-3517	29	11	as	as	ADP
ap-3517	29	12	cubature	cubature	ADJ
ap-3517	29	13	formulas	formula	NOUN
ap-3517	29	14	.	.	PUNCT
ap-3517	30	1	the	the	DET
ap-3517	30	2	idea	idea	NOUN
ap-3517	30	3	of	of	ADP
ap-3517	30	4	[	[	X
ap-3517	30	5	24	24	NUM
ap-3517	30	6	]	]	PUNCT
ap-3517	30	7	is	be	AUX
ap-3517	30	8	extended	extend	VERB
ap-3517	30	9	to	to	ADP
ap-3517	30	10	any	any	DET
ap-3517	30	11	simple	simple	ADJ
ap-3517	30	12	lie	lie	NOUN
ap-3517	30	13	algebra	algebra	NOUN
ap-3517	30	14	in	in	ADP
ap-3517	30	15	[	[	X
ap-3517	30	16	9	9	NUM
ap-3517	30	17	,	,	PUNCT
ap-3517	30	18	25	25	NUM
ap-3517	30	19	,	,	PUNCT
ap-3517	30	20	26	26	NUM
ap-3517	30	21	]	]	PUNCT
ap-3517	30	22	.	.	PUNCT
ap-3517	31	1	optimal	optimal	ADJ
ap-3517	31	2	cubature	cubature	ADJ
ap-3517	31	3	formulas	formula	NOUN
ap-3517	31	4	in	in	ADP
ap-3517	31	5	the	the	DET
ap-3517	31	6	sense	sense	NOUN
ap-3517	31	7	of	of	ADP
ap-3517	31	8	the	the	DET
ap-3517	31	9	nodal	nodal	NOUN
ap-3517	31	10	points	point	NOUN
ap-3517	31	11	that	that	PRON
ap-3517	31	12	are	be	AUX
ap-3517	31	13	required	require	VERB
ap-3517	31	14	are	be	AUX
ap-3517	31	15	known	know	VERB
ap-3517	31	16	only	only	ADV
ap-3517	31	17	for	for	ADP
ap-3517	31	18	s	s	PROPN
ap-3517	31	19	–	–	PUNCT
ap-3517	31	20	and	and	CCONJ
ap-3517	31	21	ss	ss	ADJ
ap-3517	31	22	–	–	NOUN
ap-3517	31	23	functions	function	NOUN
ap-3517	31	24	.	.	PUNCT
ap-3517	32	1	283	283	NUM
ap-3517	32	2	http://dx.doi.org/10.14311/ap.2016.56.0283	http://dx.doi.org/10.14311/ap.2016.56.0283	PRON
ap-3517	32	3	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3517	32	4	jiří	jiří	NOUN
ap-3517	32	5	hrivnák	hrivnák	NOUN
ap-3517	32	6	,	,	PUNCT
ap-3517	32	7	lenka	lenka	PROPN
ap-3517	32	8	motlochová	motlochová	PROPN
ap-3517	32	9	acta	acta	PROPN
ap-3517	32	10	polytechnica	polytechnica	PROPN
ap-3517	32	11	besides	besides	SCONJ
ap-3517	32	12	the	the	DET
ap-3517	32	13	chebyshev	chebyshev	NOUN
ap-3517	32	14	polynomials	polynomial	NOUN
ap-3517	32	15	,	,	PUNCT
ap-3517	32	16	the	the	DET
ap-3517	32	17	weyl	weyl	VERB
ap-3517	32	18	-	-	PUNCT
ap-3517	32	19	orbit	orbit	NOUN
ap-3517	32	20	functions	function	NOUN
ap-3517	32	21	are	be	AUX
ap-3517	32	22	related	relate	VERB
ap-3517	32	23	to	to	ADP
ap-3517	32	24	other	other	ADJ
ap-3517	32	25	orthogonal	orthogonal	ADJ
ap-3517	32	26	polynomials	polynomial	NOUN
ap-3517	32	27	.	.	PUNCT
ap-3517	33	1	for	for	ADP
ap-3517	33	2	example	example	NOUN
ap-3517	33	3	,	,	PUNCT
ap-3517	33	4	orbit	orbit	NOUN
ap-3517	33	5	functions	function	NOUN
ap-3517	33	6	of	of	ADP
ap-3517	33	7	a2	a2	PROPN
ap-3517	33	8	and	and	CCONJ
ap-3517	33	9	c2	c2	PROPN
ap-3517	33	10	coincide	coincide	VERB
ap-3517	33	11	with	with	ADP
ap-3517	33	12	two	two	NUM
ap-3517	33	13	-	-	PUNCT
ap-3517	33	14	variable	variable	ADJ
ap-3517	33	15	analogues	analogue	NOUN
ap-3517	33	16	of	of	ADP
ap-3517	33	17	jacobi	jacobi	PROPN
ap-3517	33	18	polynomials	polynomial	VERB
ap-3517	33	19	[	[	X
ap-3517	33	20	21	21	NUM
ap-3517	33	21	]	]	PUNCT
ap-3517	33	22	.	.	PUNCT
ap-3517	34	1	it	it	PRON
ap-3517	34	2	can	can	AUX
ap-3517	34	3	also	also	ADV
ap-3517	34	4	be	be	AUX
ap-3517	34	5	shown	show	VERB
ap-3517	34	6	that	that	SCONJ
ap-3517	34	7	the	the	DET
ap-3517	34	8	c	c	NOUN
ap-3517	34	9	–	–	PUNCT
ap-3517	34	10	,	,	PUNCT
ap-3517	34	11	s	s	X
ap-3517	34	12	–	–	PUNCT
ap-3517	34	13	,	,	PUNCT
ap-3517	34	14	ss	ss	NOUN
ap-3517	34	15	–	–	PUNCT
ap-3517	34	16	and	and	CCONJ
ap-3517	34	17	sl	sl	NOUN
ap-3517	34	18	–	–	PUNCT
ap-3517	34	19	functions	function	NOUN
ap-3517	34	20	arising	arise	VERB
ap-3517	34	21	in	in	ADP
ap-3517	34	22	connection	connection	NOUN
ap-3517	34	23	with	with	ADP
ap-3517	34	24	simple	simple	ADJ
ap-3517	34	25	lie	lie	NOUN
ap-3517	34	26	algebras	algebras	PROPN
ap-3517	34	27	bn	bn	PROPN
ap-3517	34	28	and	and	CCONJ
ap-3517	34	29	cn	cn	PROPN
ap-3517	34	30	become	become	VERB
ap-3517	34	31	,	,	PUNCT
ap-3517	34	32	up	up	ADP
ap-3517	34	33	to	to	ADP
ap-3517	34	34	a	a	DET
ap-3517	34	35	constant	constant	ADJ
ap-3517	34	36	,	,	PUNCT
ap-3517	34	37	(	(	PUNCT
ap-3517	34	38	anti)symmetric	anti)symmetric	ADJ
ap-3517	34	39	multivariate	multivariate	NOUN
ap-3517	34	40	cosine	cosine	NOUN
ap-3517	34	41	functions	function	NOUN
ap-3517	34	42	and	and	CCONJ
ap-3517	34	43	(	(	PUNCT
ap-3517	34	44	anti)symmetric	anti)symmetric	ADJ
ap-3517	34	45	multivariate	multivariate	NOUN
ap-3517	34	46	sine	sine	NOUN
ap-3517	34	47	functions	function	NOUN
ap-3517	34	48	[	[	X
ap-3517	34	49	17	17	NUM
ap-3517	34	50	]	]	PUNCT
ap-3517	34	51	.	.	PUNCT
ap-3517	35	1	note	note	VERB
ap-3517	35	2	that	that	SCONJ
ap-3517	35	3	these	these	DET
ap-3517	35	4	generalizations	generalization	NOUN
ap-3517	35	5	lead	lead	VERB
ap-3517	35	6	to	to	PART
ap-3517	35	7	multivariate	multivariate	VERB
ap-3517	35	8	analogues	analogue	NOUN
ap-3517	35	9	of	of	ADP
ap-3517	35	10	chebyshev	chebyshev	NOUN
ap-3517	35	11	polynomials	polynomial	NOUN
ap-3517	35	12	and	and	CCONJ
ap-3517	35	13	are	be	AUX
ap-3517	35	14	used	use	VERB
ap-3517	35	15	to	to	PART
ap-3517	35	16	derive	derive	VERB
ap-3517	35	17	optimal	optimal	ADJ
ap-3517	35	18	cubature	cubature	NOUN
ap-3517	35	19	formulas	formula	NOUN
ap-3517	35	20	.	.	PUNCT
ap-3517	36	1	therefore	therefore	ADV
ap-3517	36	2	,	,	PUNCT
ap-3517	36	3	this	this	DET
ap-3517	36	4	fact	fact	NOUN
ap-3517	36	5	indicates	indicate	VERB
ap-3517	36	6	that	that	SCONJ
ap-3517	36	7	it	it	PRON
ap-3517	36	8	might	might	AUX
ap-3517	36	9	be	be	AUX
ap-3517	36	10	possible	possible	ADJ
ap-3517	36	11	to	to	PART
ap-3517	36	12	obtain	obtain	VERB
ap-3517	36	13	such	such	ADJ
ap-3517	36	14	formulas	formula	NOUN
ap-3517	36	15	for	for	ADP
ap-3517	36	16	all	all	DET
ap-3517	36	17	families	family	NOUN
ap-3517	36	18	of	of	ADP
ap-3517	36	19	orbit	orbit	NOUN
ap-3517	36	20	functions	function	NOUN
ap-3517	36	21	.	.	PUNCT
ap-3517	37	1	as	as	ADP
ap-3517	37	2	for	for	ADP
ap-3517	37	3	chebyshev	chebyshev	NOUN
ap-3517	37	4	polynomials	polynomial	NOUN
ap-3517	37	5	,	,	PUNCT
ap-3517	37	6	it	it	PRON
ap-3517	37	7	is	be	AUX
ap-3517	37	8	of	of	ADP
ap-3517	37	9	interest	interest	NOUN
ap-3517	37	10	to	to	PART
ap-3517	37	11	study	study	VERB
ap-3517	37	12	the	the	DET
ap-3517	37	13	accuracy	accuracy	NOUN
ap-3517	37	14	of	of	ADP
ap-3517	37	15	approximations	approximation	NOUN
ap-3517	37	16	and	and	CCONJ
ap-3517	37	17	interpolations	interpolation	NOUN
ap-3517	37	18	using	use	VERB
ap-3517	37	19	cubature	cubature	ADJ
ap-3517	37	20	formulas	formula	NOUN
ap-3517	37	21	.	.	PUNCT
ap-3517	38	1	this	this	DET
ap-3517	38	2	paper	paper	NOUN
ap-3517	38	3	starts	start	VERB
ap-3517	38	4	with	with	ADP
ap-3517	38	5	a	a	DET
ap-3517	38	6	brief	brief	ADJ
ap-3517	38	7	introduction	introduction	NOUN
ap-3517	38	8	to	to	ADP
ap-3517	38	9	weyl	weyl	VERB
ap-3517	38	10	groups	group	NOUN
ap-3517	38	11	in	in	ADP
ap-3517	38	12	section	section	NOUN
ap-3517	38	13	2	2	NUM
ap-3517	38	14	.	.	PUNCT
ap-3517	39	1	then	then	ADV
ap-3517	39	2	there	there	PRON
ap-3517	39	3	is	be	VERB
ap-3517	39	4	a	a	DET
ap-3517	39	5	review	review	NOUN
ap-3517	39	6	of	of	ADP
ap-3517	39	7	the	the	DET
ap-3517	39	8	relations	relation	NOUN
ap-3517	39	9	of	of	ADP
ap-3517	39	10	the	the	DET
ap-3517	39	11	weyl	weyl	VERB
ap-3517	39	12	-	-	PUNCT
ap-3517	39	13	orbit	orbit	NOUN
ap-3517	39	14	functions	function	NOUN
ap-3517	39	15	with	with	ADP
ap-3517	39	16	other	other	ADJ
ap-3517	39	17	special	special	ADJ
ap-3517	39	18	functions	function	NOUN
ap-3517	39	19	which	which	PRON
ap-3517	39	20	are	be	AUX
ap-3517	39	21	associated	associate	VERB
ap-3517	39	22	with	with	ADP
ap-3517	39	23	the	the	DET
ap-3517	39	24	weyl	weyl	VERB
ap-3517	39	25	groups	group	NOUN
ap-3517	39	26	.	.	PUNCT
ap-3517	40	1	in	in	ADP
ap-3517	40	2	section	section	NOUN
ap-3517	40	3	3.1	3.1	NUM
ap-3517	40	4	,	,	PUNCT
ap-3517	40	5	the	the	DET
ap-3517	40	6	connection	connection	NOUN
ap-3517	40	7	of	of	ADP
ap-3517	40	8	the	the	DET
ap-3517	40	9	c	c	NOUN
ap-3517	40	10	–	–	PUNCT
ap-3517	40	11	and	and	CCONJ
ap-3517	40	12	s	s	PROPN
ap-3517	40	13	–	–	PUNCT
ap-3517	40	14	functions	function	NOUN
ap-3517	40	15	of	of	ADP
ap-3517	40	16	one	one	NUM
ap-3517	40	17	variable	variable	NOUN
ap-3517	40	18	with	with	ADP
ap-3517	40	19	chebyshev	chebyshev	NOUN
ap-3517	40	20	polynomials	polynomial	NOUN
ap-3517	40	21	is	be	AUX
ap-3517	40	22	recalled	recall	VERB
ap-3517	40	23	.	.	PUNCT
ap-3517	41	1	in	in	ADP
ap-3517	41	2	sections	section	NOUN
ap-3517	41	3	3.2	3.2	NUM
ap-3517	41	4	and	and	CCONJ
ap-3517	41	5	3.4	3.4	NUM
ap-3517	41	6	,	,	PUNCT
ap-3517	41	7	we	we	PRON
ap-3517	41	8	show	show	VERB
ap-3517	41	9	that	that	SCONJ
ap-3517	41	10	each	each	DET
ap-3517	41	11	family	family	NOUN
ap-3517	41	12	of	of	ADP
ap-3517	41	13	weyl	weyl	VERB
ap-3517	41	14	-	-	PUNCT
ap-3517	41	15	orbit	orbit	NOUN
ap-3517	41	16	functions	function	NOUN
ap-3517	41	17	corresponding	correspond	VERB
ap-3517	41	18	to	to	ADP
ap-3517	41	19	a2	a2	PROPN
ap-3517	41	20	and	and	CCONJ
ap-3517	41	21	c2	c2	PROPN
ap-3517	41	22	can	can	AUX
ap-3517	41	23	be	be	AUX
ap-3517	41	24	viewed	view	VERB
ap-3517	41	25	as	as	ADP
ap-3517	41	26	a	a	DET
ap-3517	41	27	two	two	NUM
ap-3517	41	28	-	-	PUNCT
ap-3517	41	29	variable	variable	NOUN
ap-3517	41	30	analogue	analogue	NOUN
ap-3517	41	31	of	of	ADP
ap-3517	41	32	jacobi	jacobi	PROPN
ap-3517	41	33	polynomials	polynomial	VERB
ap-3517	41	34	[	[	X
ap-3517	41	35	21	21	NUM
ap-3517	41	36	]	]	PUNCT
ap-3517	41	37	.	.	PUNCT
ap-3517	42	1	in	in	ADP
ap-3517	42	2	section	section	NOUN
ap-3517	42	3	3.4	3.4	NUM
ap-3517	42	4	,	,	PUNCT
ap-3517	42	5	we	we	PRON
ap-3517	42	6	also	also	ADV
ap-3517	42	7	provide	provide	VERB
ap-3517	42	8	the	the	DET
ap-3517	42	9	exact	exact	ADJ
ap-3517	42	10	connection	connection	NOUN
ap-3517	42	11	with	with	ADP
ap-3517	42	12	generalizations	generalization	NOUN
ap-3517	42	13	of	of	ADP
ap-3517	42	14	trigonometric	trigonometric	ADJ
ap-3517	42	15	functions	function	NOUN
ap-3517	42	16	[	[	X
ap-3517	42	17	34	34	NUM
ap-3517	42	18	]	]	PUNCT
ap-3517	42	19	.	.	PUNCT
ap-3517	43	1	2	2	X
ap-3517	43	2	.	.	X
ap-3517	43	3	weyl	weyl	VERB
ap-3517	43	4	groups	group	NOUN
ap-3517	43	5	of	of	ADP
ap-3517	43	6	simple	simple	ADJ
ap-3517	43	7	lie	lie	NOUN
ap-3517	43	8	algebras	algebra	NOUN
ap-3517	43	9	in	in	ADP
ap-3517	43	10	this	this	DET
ap-3517	43	11	section	section	NOUN
ap-3517	43	12	,	,	PUNCT
ap-3517	43	13	we	we	PRON
ap-3517	43	14	summarize	summarize	VERB
ap-3517	43	15	the	the	DET
ap-3517	43	16	properties	property	NOUN
ap-3517	43	17	of	of	ADP
ap-3517	43	18	the	the	DET
ap-3517	43	19	weyl	weyl	VERB
ap-3517	43	20	groups	group	NOUN
ap-3517	43	21	that	that	PRON
ap-3517	43	22	are	be	AUX
ap-3517	43	23	neeeded	neeede	VERB
ap-3517	43	24	for	for	ADP
ap-3517	43	25	definition	definition	NOUN
ap-3517	43	26	of	of	ADP
ap-3517	43	27	orbit	orbit	NOUN
ap-3517	43	28	functions	function	NOUN
ap-3517	43	29	.	.	PUNCT
ap-3517	44	1	there	there	PRON
ap-3517	44	2	are	be	VERB
ap-3517	44	3	four	four	NUM
ap-3517	44	4	series	series	NOUN
ap-3517	44	5	of	of	ADP
ap-3517	44	6	simple	simple	ADJ
ap-3517	44	7	lie	lie	NOUN
ap-3517	44	8	algebras	algebras	PROPN
ap-3517	44	9	an(n	an(n	PROPN
ap-3517	44	10	≥	≥	PROPN
ap-3517	44	11	1	1	NUM
ap-3517	44	12	)	)	PUNCT
ap-3517	44	13	,	,	PUNCT
ap-3517	44	14	bn(n	bn(n	PUNCT
ap-3517	44	15	≥	≥	NOUN
ap-3517	44	16	3	3	NUM
ap-3517	44	17	)	)	PUNCT
ap-3517	44	18	,	,	PUNCT
ap-3517	44	19	cn(n	cn(n	X
ap-3517	44	20	≥	≥	NOUN
ap-3517	44	21	2	2	NUM
ap-3517	44	22	)	)	PUNCT
ap-3517	44	23	,	,	PUNCT
ap-3517	44	24	dn(n	dn(n	X
ap-3517	44	25	≥	≥	X
ap-3517	44	26	4	4	NUM
ap-3517	44	27	)	)	PUNCT
ap-3517	44	28	and	and	CCONJ
ap-3517	44	29	five	five	NUM
ap-3517	44	30	exceptional	exceptional	ADJ
ap-3517	44	31	simple	simple	ADJ
ap-3517	44	32	lie	lie	NOUN
ap-3517	44	33	algebras	algebras	PROPN
ap-3517	44	34	e6	e6	PROPN
ap-3517	44	35	,	,	PUNCT
ap-3517	44	36	e7	e7	PROPN
ap-3517	44	37	,	,	PUNCT
ap-3517	44	38	e8	e8	PROPN
ap-3517	44	39	,	,	PUNCT
ap-3517	44	40	f4	f4	PROPN
ap-3517	44	41	and	and	CCONJ
ap-3517	44	42	g2	g2	PROPN
ap-3517	44	43	.	.	PUNCT
ap-3517	45	1	each	each	PRON
ap-3517	45	2	of	of	ADP
ap-3517	45	3	these	these	DET
ap-3517	45	4	algebras	algebra	NOUN
ap-3517	45	5	is	be	AUX
ap-3517	45	6	connected	connect	VERB
ap-3517	45	7	with	with	ADP
ap-3517	45	8	its	its	PRON
ap-3517	45	9	corresponding	corresponding	ADJ
ap-3517	45	10	weyl	weyl	VERB
ap-3517	45	11	group	group	NOUN
ap-3517	46	1	[	[	X
ap-3517	46	2	1	1	NUM
ap-3517	46	3	,	,	PUNCT
ap-3517	46	4	12	12	NUM
ap-3517	46	5	,	,	PUNCT
ap-3517	46	6	13	13	NUM
ap-3517	46	7	,	,	PUNCT
ap-3517	46	8	18	18	NUM
ap-3517	46	9	,	,	PUNCT
ap-3517	46	10	34	34	NUM
ap-3517	46	11	]	]	PUNCT
ap-3517	46	12	.	.	PUNCT
ap-3517	47	1	they	they	PRON
ap-3517	47	2	are	be	AUX
ap-3517	47	3	completely	completely	ADV
ap-3517	47	4	classified	classify	VERB
ap-3517	47	5	by	by	ADP
ap-3517	47	6	dynkin	dynkin	ADJ
ap-3517	47	7	diagrams	diagram	NOUN
ap-3517	47	8	(	(	PUNCT
ap-3517	47	9	see	see	VERB
ap-3517	47	10	e.g.	e.g.	ADV
ap-3517	47	11	figure	figure	NOUN
ap-3517	47	12	in	in	ADP
ap-3517	47	13	[	[	X
ap-3517	47	14	15	15	NUM
ap-3517	47	15	]	]	NUM
ap-3517	47	16	)	)	PUNCT
ap-3517	47	17	.	.	PUNCT
ap-3517	48	1	a	a	DET
ap-3517	48	2	dynkin	dynkin	ADJ
ap-3517	48	3	diagram	diagram	NOUN
ap-3517	48	4	characterizes	characterize	VERB
ap-3517	48	5	a	a	DET
ap-3517	48	6	set	set	ADJ
ap-3517	48	7	∆	∆	PROPN
ap-3517	48	8	of	of	ADP
ap-3517	48	9	simple	simple	ADJ
ap-3517	48	10	roots	root	NOUN
ap-3517	48	11	α1	α1	NOUN
ap-3517	48	12	,	,	PUNCT
ap-3517	48	13	.	.	PUNCT
ap-3517	48	14	.	.	PUNCT
ap-3517	49	1	.	.	PUNCT
ap-3517	50	1	,	,	PUNCT
ap-3517	50	2	αn	αn	NOUN
ap-3517	50	3	generating	generate	VERB
ap-3517	50	4	an	an	DET
ap-3517	50	5	euclidean	euclidean	ADJ
ap-3517	50	6	space	space	NOUN
ap-3517	50	7	isomorphic	isomorphic	ADJ
ap-3517	50	8	to	to	ADP
ap-3517	50	9	rn	rn	PROPN
ap-3517	50	10	with	with	ADP
ap-3517	50	11	the	the	DET
ap-3517	50	12	scalar	scalar	ADJ
ap-3517	50	13	product	product	NOUN
ap-3517	50	14	denoted	denote	VERB
ap-3517	50	15	by	by	ADP
ap-3517	50	16	〈	〈	PROPN
ap-3517	50	17	·	·	PROPN
ap-3517	50	18	,	,	PUNCT
ap-3517	50	19	·	·	PUNCT
ap-3517	50	20	〉	〉	NUM
ap-3517	50	21	.	.	PUNCT
ap-3517	51	1	each	each	DET
ap-3517	51	2	node	node	NOUN
ap-3517	51	3	of	of	ADP
ap-3517	51	4	the	the	DET
ap-3517	51	5	dynkin	dynkin	ADJ
ap-3517	51	6	diagram	diagram	NOUN
ap-3517	51	7	represents	represent	VERB
ap-3517	51	8	one	one	NUM
ap-3517	51	9	simple	simple	ADJ
ap-3517	51	10	root	root	NOUN
ap-3517	51	11	αi	αi	NOUN
ap-3517	51	12	.	.	PUNCT
ap-3517	52	1	the	the	DET
ap-3517	52	2	number	number	NOUN
ap-3517	52	3	of	of	ADP
ap-3517	52	4	links	link	NOUN
ap-3517	52	5	between	between	ADP
ap-3517	52	6	two	two	NUM
ap-3517	52	7	nodes	node	NOUN
ap-3517	52	8	corresponding	correspond	VERB
ap-3517	52	9	to	to	ADP
ap-3517	52	10	αi	αi	PRON
ap-3517	52	11	and	and	CCONJ
ap-3517	52	12	αj	αj	NOUN
ap-3517	52	13	respectively	respectively	ADV
ap-3517	52	14	is	be	AUX
ap-3517	52	15	equal	equal	ADJ
ap-3517	52	16	to	to	ADP
ap-3517	52	17	〈	〈	VERB
ap-3517	52	18	αi	αi	PART
ap-3517	52	19	,	,	PUNCT
ap-3517	52	20	α∨j	α∨j	PROPN
ap-3517	52	21	〉	〉	PROPN
ap-3517	52	22	〈	〈	PROPN
ap-3517	52	23	αj	αj	PROPN
ap-3517	52	24	,	,	PUNCT
ap-3517	52	25	α∨i	α∨i	PROPN
ap-3517	52	26	〉	〉	PROPN
ap-3517	52	27	,	,	PUNCT
ap-3517	52	28	where	where	SCONJ
ap-3517	52	29	α∨i	α∨i	PROPN
ap-3517	52	30	≡	≡	PROPN
ap-3517	52	31	2αi	2αi	PROPN
ap-3517	53	1	〈	〈	PROPN
ap-3517	53	2	αi	αi	PART
ap-3517	53	3	,	,	PUNCT
ap-3517	53	4	αi	αi	PROPN
ap-3517	53	5	〉	〉	NOUN
ap-3517	53	6	.	.	PUNCT
ap-3517	54	1	note	note	VERB
ap-3517	54	2	that	that	SCONJ
ap-3517	54	3	we	we	PRON
ap-3517	54	4	use	use	VERB
ap-3517	54	5	the	the	DET
ap-3517	54	6	standard	standard	ADJ
ap-3517	54	7	normalization	normalization	NOUN
ap-3517	54	8	for	for	ADP
ap-3517	54	9	the	the	DET
ap-3517	54	10	lengths	length	NOUN
ap-3517	54	11	of	of	ADP
ap-3517	54	12	roots	root	NOUN
ap-3517	54	13	,	,	PUNCT
ap-3517	54	14	namely	namely	ADV
ap-3517	54	15	〈	〈	PROPN
ap-3517	54	16	αi	αi	NOUN
ap-3517	54	17	,	,	PUNCT
ap-3517	54	18	αi	αi	PROPN
ap-3517	54	19	〉	〉	NOUN
ap-3517	54	20	=	=	SYM
ap-3517	54	21	2	2	NUM
ap-3517	54	22	if	if	SCONJ
ap-3517	54	23	αi	αi	PRON
ap-3517	54	24	is	be	AUX
ap-3517	54	25	a	a	DET
ap-3517	54	26	long	long	ADJ
ap-3517	54	27	simple	simple	ADJ
ap-3517	54	28	root	root	NOUN
ap-3517	54	29	.	.	PUNCT
ap-3517	55	1	in	in	ADP
ap-3517	55	2	addition	addition	NOUN
ap-3517	55	3	to	to	ADP
ap-3517	55	4	the	the	DET
ap-3517	55	5	basis	basis	NOUN
ap-3517	55	6	of	of	ADP
ap-3517	55	7	rn	rn	PROPN
ap-3517	55	8	consisting	consist	VERB
ap-3517	55	9	of	of	ADP
ap-3517	55	10	the	the	DET
ap-3517	55	11	simple	simple	ADJ
ap-3517	55	12	roots	root	NOUN
ap-3517	55	13	αi	αi	VERB
ap-3517	55	14	,	,	PUNCT
ap-3517	55	15	it	it	PRON
ap-3517	55	16	is	be	AUX
ap-3517	55	17	convenient	convenient	ADJ
ap-3517	55	18	for	for	SCONJ
ap-3517	55	19	our	our	PRON
ap-3517	55	20	purposes	purpose	NOUN
ap-3517	55	21	to	to	PART
ap-3517	55	22	introduce	introduce	VERB
ap-3517	55	23	the	the	DET
ap-3517	55	24	basis	basis	NOUN
ap-3517	55	25	of	of	ADP
ap-3517	55	26	fundamental	fundamental	ADJ
ap-3517	55	27	weights	weight	NOUN
ap-3517	55	28	ωj	ωj	ADP
ap-3517	55	29	given	give	VERB
ap-3517	55	30	by	by	ADP
ap-3517	55	31	〈	〈	PROPN
ap-3517	55	32	ωj	ωj	ADP
ap-3517	55	33	,	,	PUNCT
ap-3517	55	34	α∨i	α∨i	PROPN
ap-3517	55	35	〉	〉	PROPN
ap-3517	55	36	=	=	SYM
ap-3517	55	37	δij	δij	NOUN
ap-3517	55	38	.	.	PUNCT
ap-3517	56	1	this	this	PRON
ap-3517	56	2	allows	allow	VERB
ap-3517	56	3	us	we	PRON
ap-3517	56	4	to	to	PART
ap-3517	56	5	express	express	VERB
ap-3517	56	6	the	the	DET
ap-3517	56	7	weight	weight	NOUN
ap-3517	56	8	lattice	lattice	NOUN
ap-3517	56	9	p	p	PROPN
ap-3517	56	10	defined	define	VERB
ap-3517	56	11	by	by	ADP
ap-3517	56	12	p	p	PROPN
ap-3517	56	13	≡	≡	PROPN
ap-3517	56	14	{	{	PUNCT
ap-3517	56	15	λ	λ	X
ap-3517	56	16	∈	∈	PROPN
ap-3517	56	17	rn	rn	PROPN
ap-3517	56	18	|	|	ADV
ap-3517	56	19	〈	〈	PROPN
ap-3517	56	20	λ	λ	PROPN
ap-3517	56	21	,	,	PUNCT
ap-3517	56	22	α∨i	α∨i	NOUN
ap-3517	56	23	〉	〉	PROPN
ap-3517	56	24	∈	∈	PROPN
ap-3517	57	1	z	z	NOUN
ap-3517	57	2	,	,	PUNCT
ap-3517	57	3	i	i	PRON
ap-3517	57	4	=	=	NOUN
ap-3517	57	5	1	1	NUM
ap-3517	57	6	,	,	PUNCT
ap-3517	57	7	.	.	PUNCT
ap-3517	57	8	.	.	PUNCT
ap-3517	57	9	.	.	PUNCT
ap-3517	57	10	,	,	PUNCT
ap-3517	57	11	n	n	CCONJ
ap-3517	57	12	}	}	PUNCT
ap-3517	57	13	as	as	ADP
ap-3517	57	14	z	z	NOUN
ap-3517	57	15	-	-	PUNCT
ap-3517	57	16	linear	linear	NOUN
ap-3517	57	17	combinations	combination	NOUN
ap-3517	57	18	of	of	ADP
ap-3517	57	19	ωj	ωj	NOUN
ap-3517	57	20	.	.	PUNCT
ap-3517	58	1	the	the	DET
ap-3517	58	2	subset	subset	NOUN
ap-3517	58	3	of	of	ADP
ap-3517	58	4	dominant	dominant	ADJ
ap-3517	58	5	weights	weight	NOUN
ap-3517	58	6	p+	p+	NOUN
ap-3517	58	7	is	be	AUX
ap-3517	58	8	standardly	standardly	ADV
ap-3517	58	9	given	give	VERB
ap-3517	58	10	as	as	ADP
ap-3517	58	11	p+	p+	PROPN
ap-3517	58	12	≡	≡	PROPN
ap-3517	58	13	z≥0ω1	z≥0ω1	NOUN
ap-3517	58	14	+	+	CCONJ
ap-3517	58	15	·	·	PUNCT
ap-3517	58	16	·	·	PUNCT
ap-3517	58	17	·	·	PUNCT
ap-3517	59	1	+	+	PUNCT
ap-3517	60	1	z≥0ωn	z≥0ωn	NOUN
ap-3517	60	2	.	.	PUNCT
ap-3517	61	1	we	we	PRON
ap-3517	61	2	consider	consider	VERB
ap-3517	61	3	the	the	DET
ap-3517	61	4	usual	usual	ADJ
ap-3517	61	5	partial	partial	ADJ
ap-3517	61	6	ordering	ordering	NOUN
ap-3517	61	7	on	on	ADP
ap-3517	61	8	p	p	NOUN
ap-3517	61	9	given	give	VERB
ap-3517	61	10	by	by	ADP
ap-3517	61	11	µ	µ	PRON
ap-3517	61	12	�	�	PROPN
ap-3517	61	13	λ	λ	PROPN
ap-3517	61	14	if	if	SCONJ
ap-3517	62	1	and	and	CCONJ
ap-3517	62	2	only	only	ADV
ap-3517	63	1	if	if	SCONJ
ap-3517	63	2	λ	λ	PROPN
ap-3517	63	3	−	−	PROPN
ap-3517	63	4	µ	µ	PROPN
ap-3517	63	5	is	be	AUX
ap-3517	63	6	a	a	DET
ap-3517	63	7	sum	sum	NOUN
ap-3517	63	8	of	of	ADP
ap-3517	63	9	simple	simple	ADJ
ap-3517	63	10	roots	root	NOUN
ap-3517	63	11	with	with	ADP
ap-3517	63	12	non	non	ADJ
ap-3517	63	13	-	-	ADJ
ap-3517	63	14	negative	negative	ADJ
ap-3517	63	15	integer	integer	NOUN
ap-3517	63	16	coefficients	coefficient	NOUN
ap-3517	63	17	.	.	PUNCT
ap-3517	64	1	to	to	ADP
ap-3517	64	2	each	each	DET
ap-3517	64	3	simple	simple	ADJ
ap-3517	64	4	root	root	NOUN
ap-3517	64	5	αi	αi	NOUN
ap-3517	64	6	there	there	PRON
ap-3517	64	7	is	be	VERB
ap-3517	64	8	a	a	DET
ap-3517	64	9	corresponding	corresponding	ADJ
ap-3517	64	10	reflection	reflection	NOUN
ap-3517	64	11	ri	ri	NOUN
ap-3517	64	12	with	with	ADP
ap-3517	64	13	respect	respect	NOUN
ap-3517	64	14	to	to	ADP
ap-3517	64	15	the	the	DET
ap-3517	64	16	hyperplane	hyperplane	PROPN
ap-3517	64	17	orthogonal	orthogonal	NOUN
ap-3517	64	18	to	to	ADP
ap-3517	64	19	αi	αi	NOUN
ap-3517	64	20	,	,	PUNCT
ap-3517	64	21	ri(a	ri(a	X
ap-3517	65	1	)	)	PUNCT
ap-3517	65	2	≡	≡	PROPN
ap-3517	65	3	rαi(a	rαi(a	PROPN
ap-3517	65	4	)	)	PUNCT
ap-3517	65	5	=	=	SYM
ap-3517	65	6	a−	a−	NOUN
ap-3517	65	7	2〈a	2〈a	NUM
ap-3517	65	8	,	,	PUNCT
ap-3517	65	9	αi	αi	PROPN
ap-3517	65	10	〉	〉	PROPN
ap-3517	65	11	〈	〈	PROPN
ap-3517	65	12	αi	αi	PART
ap-3517	65	13	,	,	PUNCT
ap-3517	65	14	αi	αi	PROPN
ap-3517	65	15	〉	〉	PROPN
ap-3517	65	16	αi	αi	PROPN
ap-3517	65	17	,	,	PUNCT
ap-3517	65	18	for	for	ADP
ap-3517	65	19	a	a	DET
ap-3517	65	20	∈	∈	PROPN
ap-3517	65	21	rn	rn	PROPN
ap-3517	65	22	.	.	PUNCT
ap-3517	66	1	the	the	DET
ap-3517	66	2	finite	finite	PROPN
ap-3517	66	3	group	group	PROPN
ap-3517	66	4	w	w	PROPN
ap-3517	66	5	generated	generate	VERB
ap-3517	66	6	by	by	ADP
ap-3517	66	7	such	such	ADJ
ap-3517	66	8	reflections	reflection	NOUN
ap-3517	66	9	ri	ri	NOUN
ap-3517	66	10	,	,	PUNCT
ap-3517	66	11	i	i	PRON
ap-3517	66	12	=	=	NOUN
ap-3517	66	13	1	1	NUM
ap-3517	66	14	,	,	PUNCT
ap-3517	66	15	.	.	PUNCT
ap-3517	66	16	.	.	PUNCT
ap-3517	67	1	.	.	PUNCT
ap-3517	68	1	,	,	PUNCT
ap-3517	68	2	n	n	PRON
ap-3517	68	3	is	be	AUX
ap-3517	68	4	called	call	VERB
ap-3517	68	5	the	the	DET
ap-3517	68	6	weyl	weyl	VERB
ap-3517	68	7	group	group	NOUN
ap-3517	68	8	.	.	PUNCT
ap-3517	69	1	for	for	ADP
ap-3517	69	2	the	the	DET
ap-3517	69	3	properties	property	NOUN
ap-3517	69	4	of	of	ADP
ap-3517	69	5	the	the	DET
ap-3517	69	6	weyl	weyl	VERB
ap-3517	69	7	groups	group	NOUN
ap-3517	69	8	see	see	VERB
ap-3517	69	9	e.g.	e.g.	ADV
ap-3517	69	10	[	[	X
ap-3517	69	11	12	12	NUM
ap-3517	69	12	,	,	PUNCT
ap-3517	69	13	14	14	NUM
ap-3517	69	14	]	]	PUNCT
ap-3517	69	15	.	.	PUNCT
ap-3517	70	1	in	in	ADP
ap-3517	70	2	the	the	DET
ap-3517	70	3	case	case	NOUN
ap-3517	70	4	of	of	ADP
ap-3517	70	5	simple	simple	ADJ
ap-3517	70	6	lie	lie	NOUN
ap-3517	70	7	algebras	algebra	NOUN
ap-3517	70	8	with	with	ADP
ap-3517	70	9	two	two	NUM
ap-3517	70	10	different	different	ADJ
ap-3517	70	11	lengths	length	NOUN
ap-3517	70	12	of	of	ADP
ap-3517	70	13	the	the	DET
ap-3517	70	14	roots	root	NOUN
ap-3517	70	15	,	,	PUNCT
ap-3517	70	16	we	we	PRON
ap-3517	70	17	need	need	VERB
ap-3517	70	18	to	to	PART
ap-3517	70	19	distinguish	distinguish	VERB
ap-3517	70	20	between	between	ADP
ap-3517	70	21	short	short	ADJ
ap-3517	70	22	and	and	CCONJ
ap-3517	70	23	long	long	ADJ
ap-3517	70	24	simple	simple	ADJ
ap-3517	70	25	roots	root	NOUN
ap-3517	70	26	.	.	PUNCT
ap-3517	71	1	therefore	therefore	ADV
ap-3517	71	2	,	,	PUNCT
ap-3517	71	3	we	we	PRON
ap-3517	71	4	denote	denote	VERB
ap-3517	71	5	by	by	ADP
ap-3517	71	6	∆s	∆s	PROPN
ap-3517	71	7	the	the	DET
ap-3517	71	8	set	set	NOUN
ap-3517	71	9	of	of	ADP
ap-3517	71	10	simple	simple	ADJ
ap-3517	71	11	roots	root	NOUN
ap-3517	71	12	containing	contain	VERB
ap-3517	71	13	only	only	ADV
ap-3517	71	14	short	short	ADJ
ap-3517	71	15	simple	simple	ADJ
ap-3517	71	16	roots	root	NOUN
ap-3517	71	17	and	and	CCONJ
ap-3517	71	18	we	we	PRON
ap-3517	71	19	denote	denote	VERB
ap-3517	71	20	by	by	ADP
ap-3517	71	21	∆l	∆l	PROPN
ap-3517	71	22	the	the	DET
ap-3517	71	23	set	set	NOUN
ap-3517	71	24	of	of	ADP
ap-3517	71	25	long	long	ADJ
ap-3517	71	26	simple	simple	ADJ
ap-3517	71	27	roots	root	NOUN
ap-3517	71	28	.	.	PUNCT
ap-3517	72	1	we	we	PRON
ap-3517	72	2	also	also	ADV
ap-3517	72	3	define	define	VERB
ap-3517	72	4	the	the	DET
ap-3517	72	5	following	follow	VERB
ap-3517	72	6	vectors	vector	NOUN
ap-3517	72	7	:	:	PUNCT
ap-3517	72	8	%	%	INTJ
ap-3517	72	9	≡	≡	PROPN
ap-3517	72	10	n∑	n∑	PROPN
ap-3517	72	11	i=1	i=1	PROPN
ap-3517	72	12	ωi	ωi	PROPN
ap-3517	72	13	,	,	PUNCT
ap-3517	72	14	%	%	NOUN
ap-3517	72	15	s	s	X
ap-3517	72	16	≡	≡	PROPN
ap-3517	72	17	∑	∑	PROPN
ap-3517	72	18	αi∈∆s	αi∈∆s	NUM
ap-3517	72	19	ωi	ωi	NOUN
ap-3517	72	20	,	,	PUNCT
ap-3517	72	21	%	%	NOUN
ap-3517	72	22	l	l	PROPN
ap-3517	72	23	≡	≡	PROPN
ap-3517	72	24	∑	∑	PUNCT
ap-3517	72	25	αi∈∆l	αi∈∆l	NUM
ap-3517	72	26	ωi	ωi	NOUN
ap-3517	72	27	.	.	PUNCT
ap-3517	72	28	(	(	PUNCT
ap-3517	72	29	1	1	NUM
ap-3517	72	30	)	)	PUNCT
ap-3517	72	31	3	3	NUM
ap-3517	72	32	.	.	PUNCT
ap-3517	72	33	weyl	weyl	VERB
ap-3517	72	34	-	-	PUNCT
ap-3517	72	35	orbit	orbit	NOUN
ap-3517	72	36	functions	function	NOUN
ap-3517	72	37	each	each	DET
ap-3517	72	38	type	type	NOUN
ap-3517	72	39	of	of	ADP
ap-3517	72	40	weyl	weyl	VERB
ap-3517	72	41	-	-	PUNCT
ap-3517	72	42	orbit	orbit	NOUN
ap-3517	72	43	function	function	NOUN
ap-3517	72	44	arises	arise	VERB
ap-3517	72	45	from	from	ADP
ap-3517	72	46	the	the	DET
ap-3517	72	47	sign	sign	NOUN
ap-3517	72	48	homomorphism	homomorphism	PROPN
ap-3517	72	49	of	of	ADP
ap-3517	72	50	weyl	weyl	VERB
ap-3517	72	51	groups	group	NOUN
ap-3517	72	52	σ	σ	NOUN
ap-3517	72	53	:	:	PUNCT
ap-3517	72	54	w	w	X
ap-3517	72	55	→	→	PUNCT
ap-3517	72	56	{	{	PUNCT
ap-3517	72	57	±1	±1	NOUN
ap-3517	72	58	}	}	PUNCT
ap-3517	72	59	.	.	PUNCT
ap-3517	73	1	there	there	PRON
ap-3517	73	2	exist	exist	VERB
ap-3517	73	3	only	only	ADV
ap-3517	73	4	two	two	NUM
ap-3517	73	5	different	different	ADJ
ap-3517	73	6	sign	sign	NOUN
ap-3517	73	7	homomorphisms	homomorphism	NOUN
ap-3517	73	8	on	on	ADP
ap-3517	73	9	w	w	ADP
ap-3517	73	10	connected	connect	VERB
ap-3517	73	11	to	to	ADP
ap-3517	73	12	simple	simple	ADJ
ap-3517	73	13	lie	lie	NOUN
ap-3517	73	14	algebras	algebra	NOUN
ap-3517	73	15	with	with	ADP
ap-3517	73	16	one	one	NUM
ap-3517	73	17	length	length	NOUN
ap-3517	73	18	of	of	ADP
ap-3517	73	19	the	the	DET
ap-3517	73	20	roots	root	NOUN
ap-3517	73	21	:	:	PUNCT
ap-3517	73	22	identity	identity	NOUN
ap-3517	73	23	,	,	PUNCT
ap-3517	73	24	denoted	denote	VERB
ap-3517	73	25	by	by	ADP
ap-3517	73	26	1	1	NUM
ap-3517	73	27	,	,	PUNCT
ap-3517	73	28	and	and	CCONJ
ap-3517	73	29	the	the	DET
ap-3517	73	30	determinant	determinant	ADJ
ap-3517	73	31	[	[	X
ap-3517	73	32	8	8	NUM
ap-3517	73	33	,	,	PUNCT
ap-3517	73	34	25	25	NUM
ap-3517	73	35	]	]	PUNCT
ap-3517	73	36	.	.	PUNCT
ap-3517	74	1	they	they	PRON
ap-3517	74	2	are	be	AUX
ap-3517	74	3	given	give	VERB
ap-3517	74	4	by	by	ADP
ap-3517	74	5	their	their	PRON
ap-3517	74	6	values	value	NOUN
ap-3517	74	7	on	on	ADP
ap-3517	74	8	the	the	DET
ap-3517	74	9	generators	generator	NOUN
ap-3517	74	10	ri	ri	PROPN
ap-3517	74	11	of	of	ADP
ap-3517	74	12	w	w	PROPN
ap-3517	74	13	as	as	ADP
ap-3517	74	14	1(ri	1(ri	NUM
ap-3517	74	15	)	)	PUNCT
ap-3517	74	16	=	=	SYM
ap-3517	74	17	1	1	NUM
ap-3517	74	18	for	for	ADP
ap-3517	74	19	all	all	DET
ap-3517	74	20	αi	αi	PRON
ap-3517	74	21	∈	∈	PROPN
ap-3517	74	22	∆	∆	X
ap-3517	74	23	,	,	PUNCT
ap-3517	74	24	det(ri	det(ri	NOUN
ap-3517	74	25	)	)	PUNCT
ap-3517	74	26	=	=	SYM
ap-3517	74	27	−1	−1	NOUN
ap-3517	74	28	for	for	ADP
ap-3517	74	29	all	all	DET
ap-3517	74	30	αi	αi	PRON
ap-3517	74	31	∈	∈	PROPN
ap-3517	75	1	∆.	∆.	X
ap-3517	75	2	in	in	ADP
ap-3517	75	3	the	the	DET
ap-3517	75	4	case	case	NOUN
ap-3517	75	5	of	of	ADP
ap-3517	75	6	simple	simple	ADJ
ap-3517	75	7	lie	lie	NOUN
ap-3517	75	8	algebras	algebra	NOUN
ap-3517	75	9	with	with	ADP
ap-3517	75	10	two	two	NUM
ap-3517	75	11	different	different	ADJ
ap-3517	75	12	lengths	length	NOUN
ap-3517	75	13	of	of	ADP
ap-3517	75	14	roots	root	NOUN
ap-3517	75	15	,	,	PUNCT
ap-3517	75	16	i.e.	i.e.	X
ap-3517	75	17	bn	bn	X
ap-3517	75	18	,	,	PUNCT
ap-3517	75	19	cn	cn	PROPN
ap-3517	75	20	,	,	PUNCT
ap-3517	75	21	f4	f4	PROPN
ap-3517	75	22	and	and	CCONJ
ap-3517	75	23	g2	g2	PROPN
ap-3517	75	24	,	,	PUNCT
ap-3517	75	25	there	there	PRON
ap-3517	75	26	are	be	VERB
ap-3517	75	27	two	two	NUM
ap-3517	75	28	additional	additional	ADJ
ap-3517	75	29	sign	sign	NOUN
ap-3517	75	30	homomorphisms	homomorphism	NOUN
ap-3517	75	31	denoted	denote	VERB
ap-3517	75	32	by	by	ADP
ap-3517	75	33	σs	σs	ADP
ap-3517	75	34	and	and	CCONJ
ap-3517	75	35	σl	σl	ADV
ap-3517	75	36	and	and	CCONJ
ap-3517	75	37	given	give	VERB
ap-3517	75	38	as	as	ADP
ap-3517	75	39	σs(ri	σs(ri	PROPN
ap-3517	75	40	)	)	PUNCT
ap-3517	76	1	=	=	PRON
ap-3517	76	2	{	{	PUNCT
ap-3517	76	3	−1	−1	NOUN
ap-3517	76	4	if	if	SCONJ
ap-3517	76	5	αi	αi	PRON
ap-3517	76	6	∈	∈	PROPN
ap-3517	76	7	∆s	∆s	PROPN
ap-3517	76	8	,	,	PUNCT
ap-3517	76	9	1	1	NUM
ap-3517	76	10	if	if	SCONJ
ap-3517	76	11	αi	αi	PRON
ap-3517	76	12	∈	∈	PROPN
ap-3517	76	13	∆l	∆l	PROPN
ap-3517	76	14	,	,	PUNCT
ap-3517	76	15	σl(ri	σl(ri	PROPN
ap-3517	76	16	)	)	PUNCT
ap-3517	76	17	=	=	PRON
ap-3517	76	18	{	{	PUNCT
ap-3517	76	19	1	1	NUM
ap-3517	76	20	if	if	SCONJ
ap-3517	76	21	αi	αi	PRON
ap-3517	76	22	∈	∈	PROPN
ap-3517	76	23	∆s	∆s	PROPN
ap-3517	76	24	,	,	PUNCT
ap-3517	76	25	−1	−1	NOUN
ap-3517	76	26	if	if	SCONJ
ap-3517	76	27	αi	αi	PRON
ap-3517	76	28	∈	∈	PROPN
ap-3517	76	29	∆l	∆l	PROPN
ap-3517	76	30	.	.	PROPN
ap-3517	76	31	labelled	label	VERB
ap-3517	76	32	by	by	ADP
ap-3517	76	33	the	the	DET
ap-3517	76	34	parameter	parameter	NOUN
ap-3517	76	35	a	a	DET
ap-3517	76	36	∈	∈	PROPN
ap-3517	76	37	rn	rn	PROPN
ap-3517	76	38	,	,	PUNCT
ap-3517	76	39	the	the	DET
ap-3517	76	40	weyl	weyl	VERB
ap-3517	76	41	-	-	PUNCT
ap-3517	76	42	orbit	orbit	NOUN
ap-3517	76	43	function	function	NOUN
ap-3517	76	44	of	of	ADP
ap-3517	76	45	the	the	DET
ap-3517	76	46	variable	variable	PROPN
ap-3517	76	47	b	b	PROPN
ap-3517	76	48	∈	∈	PROPN
ap-3517	76	49	rn	rn	PROPN
ap-3517	76	50	corresponding	correspond	VERB
ap-3517	76	51	to	to	PART
ap-3517	76	52	sign	sign	VERB
ap-3517	76	53	homomorphism	homomorphism	PROPN
ap-3517	76	54	σ	σ	PROPN
ap-3517	76	55	is	be	AUX
ap-3517	76	56	introduced	introduce	VERB
ap-3517	76	57	via	via	ADP
ap-3517	76	58	the	the	DET
ap-3517	76	59	formula	formula	NOUN
ap-3517	76	60	ϕσa(b	ϕσa(b	PROPN
ap-3517	76	61	)	)	PUNCT
ap-3517	76	62	=	=	PUNCT
ap-3517	77	1	∑	∑	PROPN
ap-3517	77	2	w∈w	w∈w	VERB
ap-3517	77	3	σ(w)e2πi〈w(a),b	σ(w)e2πi〈w(a),b	PROPN
ap-3517	77	4	〉	〉	PROPN
ap-3517	77	5	,	,	PUNCT
ap-3517	77	6	a	a	PRON
ap-3517	77	7	,	,	PUNCT
ap-3517	77	8	b	b	PROPN
ap-3517	77	9	∈	∈	PROPN
ap-3517	77	10	rn	rn	PROPN
ap-3517	77	11	.	.	PROPN
ap-3517	77	12	284	284	NUM
ap-3517	77	13	vol	vol	NOUN
ap-3517	77	14	.	.	PUNCT
ap-3517	78	1	56	56	NUM
ap-3517	78	2	no	no	NOUN
ap-3517	78	3	.	.	PUNCT
ap-3517	79	1	4/2016	4/2016	PROPN
ap-3517	79	2	weyl	weyl	VERB
ap-3517	79	3	orbit	orbit	NOUN
ap-3517	79	4	functions	function	NOUN
ap-3517	79	5	and	and	CCONJ
ap-3517	79	6	(	(	PUNCT
ap-3517	79	7	anti)symmetric	anti)symmetric	ADJ
ap-3517	79	8	trigonometric	trigonometric	ADJ
ap-3517	79	9	functions	function	NOUN
ap-3517	79	10	each	each	DET
ap-3517	79	11	sign	sign	VERB
ap-3517	79	12	homomorphism	homomorphism	NOUN
ap-3517	79	13	1,det	1,det	NUM
ap-3517	79	14	,	,	PUNCT
ap-3517	79	15	σs	σs	ADP
ap-3517	79	16	,	,	PUNCT
ap-3517	79	17	σl	σl	PART
ap-3517	79	18	determines	determine	VERB
ap-3517	79	19	one	one	NUM
ap-3517	79	20	family	family	NOUN
ap-3517	79	21	of	of	ADP
ap-3517	79	22	complex	complex	ADJ
ap-3517	79	23	valued	value	VERB
ap-3517	79	24	weyl	weyl	VERB
ap-3517	79	25	-	-	PUNCT
ap-3517	79	26	orbit	orbit	NOUN
ap-3517	79	27	functions	function	NOUN
ap-3517	79	28	,	,	PUNCT
ap-3517	79	29	called	call	VERB
ap-3517	79	30	c	c	NOUN
ap-3517	79	31	–	–	PUNCT
ap-3517	79	32	,	,	PUNCT
ap-3517	79	33	s	s	X
ap-3517	79	34	–	–	PUNCT
ap-3517	79	35	,	,	PUNCT
ap-3517	79	36	ss	ss	NOUN
ap-3517	79	37	–	–	PUNCT
ap-3517	79	38	and	and	CCONJ
ap-3517	79	39	sl	sl	NOUN
ap-3517	79	40	–	–	PUNCT
ap-3517	79	41	functions	function	NOUN
ap-3517	79	42	respectively	respectively	ADV
ap-3517	79	43	,	,	PUNCT
ap-3517	79	44	and	and	CCONJ
ap-3517	79	45	denoted	denote	VERB
ap-3517	79	46	by	by	ADP
ap-3517	79	47	c	c	NOUN
ap-3517	79	48	–	–	PUNCT
ap-3517	79	49	functions	function	NOUN
ap-3517	79	50	:	:	PUNCT
ap-3517	79	51	σ	σ	PROPN
ap-3517	79	52	≡	≡	PROPN
ap-3517	79	53	1	1	NUM
ap-3517	79	54	,	,	PUNCT
ap-3517	79	55	ϕσ	ϕσ	PROPN
ap-3517	79	56	≡	≡	PROPN
ap-3517	79	57	φ	φ	PROPN
ap-3517	79	58	,	,	PUNCT
ap-3517	79	59	s	s	PROPN
ap-3517	79	60	–	–	PUNCT
ap-3517	79	61	functions	function	NOUN
ap-3517	79	62	:	:	PUNCT
ap-3517	79	63	σ	σ	PROPN
ap-3517	79	64	≡	≡	PROPN
ap-3517	79	65	det	det	PROPN
ap-3517	79	66	,	,	PUNCT
ap-3517	79	67	ϕσ	ϕσ	PROPN
ap-3517	79	68	≡	≡	PROPN
ap-3517	79	69	ϕ	ϕ	PROPN
ap-3517	79	70	,	,	PUNCT
ap-3517	79	71	ss	ss	PROPN
ap-3517	79	72	–	–	NOUN
ap-3517	79	73	functions	function	NOUN
ap-3517	79	74	:	:	PUNCT
ap-3517	79	75	σ	σ	PROPN
ap-3517	79	76	≡	≡	PROPN
ap-3517	79	77	σs	σs	PROPN
ap-3517	79	78	,	,	PUNCT
ap-3517	79	79	ϕσ	ϕσ	PROPN
ap-3517	79	80	≡	≡	PROPN
ap-3517	79	81	ϕs	ϕs	PROPN
ap-3517	79	82	,	,	PUNCT
ap-3517	79	83	sl	sl	INTJ
ap-3517	79	84	–	–	PUNCT
ap-3517	79	85	functions	function	NOUN
ap-3517	79	86	:	:	PUNCT
ap-3517	79	87	σ	σ	PROPN
ap-3517	79	88	≡	≡	PROPN
ap-3517	80	1	σl	σl	PROPN
ap-3517	80	2	,	,	PUNCT
ap-3517	80	3	ϕσ	ϕσ	PROPN
ap-3517	80	4	≡	≡	PROPN
ap-3517	80	5	ϕl	ϕl	PROPN
ap-3517	80	6	.	.	PUNCT
ap-3517	81	1	several	several	ADJ
ap-3517	81	2	remarkable	remarkable	ADJ
ap-3517	81	3	properties	property	NOUN
ap-3517	81	4	of	of	ADP
ap-3517	81	5	weyl	weyl	VERB
ap-3517	81	6	-	-	PUNCT
ap-3517	81	7	orbit	orbit	NOUN
ap-3517	81	8	functions	function	NOUN
ap-3517	81	9	,	,	PUNCT
ap-3517	81	10	such	such	ADJ
ap-3517	81	11	as	as	ADP
ap-3517	81	12	continuous	continuous	ADJ
ap-3517	81	13	and	and	CCONJ
ap-3517	81	14	discrete	discrete	ADJ
ap-3517	81	15	orthogonality	orthogonality	NOUN
ap-3517	81	16	are	be	AUX
ap-3517	81	17	usually	usually	ADV
ap-3517	81	18	achieved	achieve	VERB
ap-3517	81	19	by	by	ADP
ap-3517	81	20	restricting	restrict	VERB
ap-3517	81	21	a	a	PRON
ap-3517	81	22	to	to	ADP
ap-3517	81	23	some	some	DET
ap-3517	81	24	subsets	subset	NOUN
ap-3517	81	25	of	of	ADP
ap-3517	81	26	the	the	DET
ap-3517	81	27	weight	weight	NOUN
ap-3517	81	28	lattice	lattice	NOUN
ap-3517	81	29	p	p	X
ap-3517	81	30	(	(	PUNCT
ap-3517	81	31	see	see	VERB
ap-3517	81	32	for	for	ADP
ap-3517	81	33	example	example	NOUN
ap-3517	81	34	[	[	X
ap-3517	81	35	8	8	NUM
ap-3517	81	36	,	,	PUNCT
ap-3517	81	37	10	10	NUM
ap-3517	81	38	,	,	PUNCT
ap-3517	81	39	15	15	NUM
ap-3517	81	40	,	,	PUNCT
ap-3517	81	41	16	16	NUM
ap-3517	81	42	,	,	PUNCT
ap-3517	81	43	27	27	NUM
ap-3517	81	44	]	]	NUM
ap-3517	81	45	)	)	PUNCT
ap-3517	81	46	.	.	PUNCT
ap-3517	82	1	note	note	VERB
ap-3517	82	2	also	also	ADV
ap-3517	82	3	that	that	SCONJ
ap-3517	82	4	symmetric	symmetric	ADJ
ap-3517	82	5	c	c	NOUN
ap-3517	82	6	–	–	PUNCT
ap-3517	82	7	functions	function	NOUN
ap-3517	82	8	and	and	CCONJ
ap-3517	82	9	antisymmetric	antisymmetric	ADJ
ap-3517	82	10	s	s	NOUN
ap-3517	82	11	–	–	PUNCT
ap-3517	82	12	functions	function	NOUN
ap-3517	82	13	appear	appear	VERB
ap-3517	82	14	in	in	ADP
ap-3517	82	15	the	the	DET
ap-3517	82	16	theory	theory	NOUN
ap-3517	82	17	of	of	ADP
ap-3517	82	18	irreducible	irreducible	ADJ
ap-3517	82	19	representations	representation	NOUN
ap-3517	82	20	of	of	ADP
ap-3517	82	21	simple	simple	ADJ
ap-3517	82	22	lie	lie	NOUN
ap-3517	82	23	algebras	algebra	NOUN
ap-3517	83	1	[	[	X
ap-3517	83	2	32	32	NUM
ap-3517	83	3	,	,	PUNCT
ap-3517	83	4	34	34	NUM
ap-3517	83	5	]	]	PUNCT
ap-3517	83	6	.	.	PUNCT
ap-3517	84	1	it	it	PRON
ap-3517	84	2	is	be	AUX
ap-3517	84	3	also	also	ADV
ap-3517	84	4	convenient	convenient	ADJ
ap-3517	84	5	to	to	PART
ap-3517	84	6	use	use	VERB
ap-3517	84	7	an	an	DET
ap-3517	84	8	alternative	alternative	ADJ
ap-3517	84	9	definition	definition	NOUN
ap-3517	84	10	of	of	ADP
ap-3517	84	11	the	the	DET
ap-3517	84	12	weyl	weyl	VERB
ap-3517	84	13	-	-	PUNCT
ap-3517	84	14	orbit	orbit	NOUN
ap-3517	84	15	functions	function	NOUN
ap-3517	84	16	via	via	ADP
ap-3517	84	17	sums	sum	NOUN
ap-3517	84	18	over	over	ADP
ap-3517	84	19	the	the	DET
ap-3517	84	20	weyl	weyl	PROPN
ap-3517	84	21	group	group	NOUN
ap-3517	84	22	orbits	orbit	NOUN
ap-3517	84	23	[	[	X
ap-3517	84	24	15	15	NUM
ap-3517	84	25	,	,	PUNCT
ap-3517	84	26	16	16	NUM
ap-3517	84	27	,	,	PUNCT
ap-3517	84	28	25	25	NUM
ap-3517	84	29	]	]	PUNCT
ap-3517	84	30	.	.	PUNCT
ap-3517	85	1	these	these	DET
ap-3517	85	2	orbit	orbit	NOUN
ap-3517	85	3	sums	sum	NOUN
ap-3517	85	4	ca	ca	NOUN
ap-3517	85	5	,	,	PUNCT
ap-3517	85	6	sa+%	sa+%	NOUN
ap-3517	85	7	,	,	PUNCT
ap-3517	85	8	ssa+%s	ssa+%s	NOUN
ap-3517	85	9	,	,	PUNCT
ap-3517	85	10	sla+%l	sla+%l	PROPN
ap-3517	85	11	differ	differ	VERB
ap-3517	85	12	from	from	ADP
ap-3517	85	13	φa	φa	ADP
ap-3517	85	14	,	,	PUNCT
ap-3517	85	15	ϕa+%	ϕa+%	PRON
ap-3517	85	16	,	,	PUNCT
ap-3517	85	17	ϕsa+%s	ϕsa+%s	INTJ
ap-3517	85	18	,	,	PUNCT
ap-3517	85	19	ϕla+%l	ϕla+%l	PROPN
ap-3517	85	20	only	only	ADV
ap-3517	85	21	by	by	ADP
ap-3517	85	22	a	a	DET
ap-3517	85	23	constant	constant	ADJ
ap-3517	85	24	ca(b	ca(b	NOUN
ap-3517	85	25	)	)	PUNCT
ap-3517	85	26	=	=	SYM
ap-3517	86	1	φa(b	φa(b	X
ap-3517	86	2	)	)	PUNCT
ap-3517	86	3	|stabw	|stabw	PROPN
ap-3517	86	4	a|	a|	PROPN
ap-3517	86	5	,	,	PUNCT
ap-3517	86	6	sa+%(b	sa+%(b	PROPN
ap-3517	86	7	)	)	PUNCT
ap-3517	87	1	=	=	SYM
ap-3517	87	2	ϕa+%(b	ϕa+%(b	PROPN
ap-3517	87	3	)	)	PUNCT
ap-3517	87	4	,	,	PUNCT
ap-3517	87	5	ssa+%s(b	ssa+%s(b	ADV
ap-3517	87	6	)	)	PUNCT
ap-3517	87	7	=	=	SYM
ap-3517	87	8	ϕsa+%s(b	ϕsa+%s(b	NOUN
ap-3517	87	9	)	)	PUNCT
ap-3517	87	10	|stabw	|stabw	PROPN
ap-3517	87	11	(	(	PUNCT
ap-3517	87	12	a+	a+	PUNCT
ap-3517	87	13	%	%	INTJ
ap-3517	88	1	s)|	s)|	NOUN
ap-3517	88	2	,	,	PUNCT
ap-3517	88	3	sla+%l(b	sla+%l(b	NOUN
ap-3517	88	4	)	)	PUNCT
ap-3517	88	5	=	=	SYM
ap-3517	88	6	ϕla+%l(b	ϕla+%l(b	ADJ
ap-3517	88	7	)	)	PUNCT
ap-3517	88	8	|stabw	|stabw	PROPN
ap-3517	88	9	(	(	PUNCT
ap-3517	88	10	a+	a+	PUNCT
ap-3517	88	11	%	%	INTJ
ap-3517	88	12	l)|	l)|	ADJ
ap-3517	88	13	with	with	ADP
ap-3517	88	14	|stabw	|stabw	PROPN
ap-3517	88	15	c|	c|	PROPN
ap-3517	88	16	denoting	denote	VERB
ap-3517	88	17	the	the	DET
ap-3517	88	18	number	number	NOUN
ap-3517	88	19	of	of	ADP
ap-3517	88	20	elements	element	NOUN
ap-3517	88	21	of	of	ADP
ap-3517	88	22	w	w	ADP
ap-3517	88	23	which	which	PRON
ap-3517	88	24	leave	leave	VERB
ap-3517	88	25	c	c	PROPN
ap-3517	88	26	invariant	invariant	ADJ
ap-3517	88	27	.	.	PUNCT
ap-3517	88	28	3.1	3.1	NUM
ap-3517	88	29	.	.	PUNCT
ap-3517	88	30	case	case	NOUN
ap-3517	88	31	a1	a1	VERB
ap-3517	88	32	the	the	DET
ap-3517	88	33	symmetric	symmetric	ADJ
ap-3517	88	34	c	c	PROPN
ap-3517	88	35	–	–	PUNCT
ap-3517	88	36	functions	function	NOUN
ap-3517	88	37	and	and	CCONJ
ap-3517	88	38	antisymmetric	antisymmetric	ADJ
ap-3517	88	39	s	s	PROPN
ap-3517	88	40	–	–	PUNCT
ap-3517	88	41	functions	function	NOUN
ap-3517	88	42	of	of	ADP
ap-3517	88	43	a1	a1	NOUN
ap-3517	88	44	are	be	AUX
ap-3517	88	45	,	,	PUNCT
ap-3517	88	46	up	up	ADP
ap-3517	88	47	to	to	ADP
ap-3517	88	48	a	a	DET
ap-3517	88	49	constant	constant	ADJ
ap-3517	88	50	,	,	PUNCT
ap-3517	88	51	the	the	DET
ap-3517	88	52	common	common	ADJ
ap-3517	88	53	cosine	cosine	NOUN
ap-3517	88	54	and	and	CCONJ
ap-3517	88	55	sine	sine	ADJ
ap-3517	88	56	functions	function	NOUN
ap-3517	88	57	[	[	X
ap-3517	88	58	15	15	NUM
ap-3517	88	59	,	,	PUNCT
ap-3517	88	60	16	16	NUM
ap-3517	88	61	]	]	PUNCT
ap-3517	88	62	,	,	PUNCT
ap-3517	88	63	ca(b	ca(b	ADJ
ap-3517	88	64	)	)	PUNCT
ap-3517	88	65	=	=	SYM
ap-3517	88	66	2	2	NUM
ap-3517	88	67	cos	cos	X
ap-3517	88	68	(	(	PUNCT
ap-3517	88	69	2πa1b1	2πa1b1	NUM
ap-3517	88	70	)	)	PUNCT
ap-3517	88	71	,	,	PUNCT
ap-3517	88	72	sa(b	sa(b	NUM
ap-3517	88	73	)	)	PUNCT
ap-3517	89	1	=	=	SYM
ap-3517	89	2	2i	2i	NUM
ap-3517	89	3	sin	sin	NOUN
ap-3517	89	4	(	(	PUNCT
ap-3517	89	5	2πa1b1	2πa1b1	NUM
ap-3517	89	6	)	)	PUNCT
ap-3517	89	7	,	,	PUNCT
ap-3517	89	8	where	where	SCONJ
ap-3517	89	9	a	a	DET
ap-3517	89	10	=	=	SYM
ap-3517	89	11	a1ω1	a1ω1	PROPN
ap-3517	89	12	,	,	PUNCT
ap-3517	89	13	b	b	NOUN
ap-3517	89	14	=	=	SYM
ap-3517	89	15	b1α	b1α	NOUN
ap-3517	89	16	∨	∨	NUM
ap-3517	89	17	1	1	NUM
ap-3517	89	18	.	.	PUNCT
ap-3517	90	1	it	it	PRON
ap-3517	90	2	is	be	AUX
ap-3517	90	3	well	well	ADV
ap-3517	90	4	known	know	VERB
ap-3517	90	5	that	that	SCONJ
ap-3517	90	6	such	such	ADJ
ap-3517	90	7	functions	function	NOUN
ap-3517	90	8	appear	appear	VERB
ap-3517	90	9	in	in	ADP
ap-3517	90	10	the	the	DET
ap-3517	90	11	definition	definition	NOUN
ap-3517	90	12	of	of	ADP
ap-3517	90	13	the	the	DET
ap-3517	90	14	extensively	extensively	ADV
ap-3517	90	15	studied	study	VERB
ap-3517	90	16	chebyshev	chebyshev	NOUN
ap-3517	90	17	polynomials	polynomial	NOUN
ap-3517	90	18	[	[	X
ap-3517	90	19	5	5	NUM
ap-3517	90	20	,	,	PUNCT
ap-3517	90	21	31	31	NUM
ap-3517	90	22	]	]	PUNCT
ap-3517	90	23	.	.	PUNCT
ap-3517	91	1	several	several	ADJ
ap-3517	91	2	types	type	NOUN
ap-3517	91	3	of	of	ADP
ap-3517	91	4	chebyshev	chebyshev	NOUN
ap-3517	91	5	polynomials	polynomial	NOUN
ap-3517	91	6	are	be	AUX
ap-3517	91	7	widely	widely	ADV
ap-3517	91	8	used	use	VERB
ap-3517	91	9	in	in	ADP
ap-3517	91	10	mathematical	mathematical	ADJ
ap-3517	91	11	analysis	analysis	NOUN
ap-3517	91	12	,	,	PUNCT
ap-3517	91	13	in	in	ADP
ap-3517	91	14	particular	particular	ADJ
ap-3517	91	15	,	,	PUNCT
ap-3517	91	16	as	as	ADP
ap-3517	91	17	efficient	efficient	ADJ
ap-3517	91	18	tools	tool	NOUN
ap-3517	91	19	for	for	ADP
ap-3517	91	20	numerical	numerical	ADJ
ap-3517	91	21	integration	integration	NOUN
ap-3517	91	22	and	and	CCONJ
ap-3517	91	23	approximations	approximation	NOUN
ap-3517	91	24	.	.	PUNCT
ap-3517	92	1	the	the	DET
ap-3517	92	2	chebyshev	chebyshev	NOUN
ap-3517	92	3	polynomials	polynomial	NOUN
ap-3517	92	4	of	of	ADP
ap-3517	92	5	the	the	DET
ap-3517	92	6	first	first	ADJ
ap-3517	92	7	,	,	PUNCT
ap-3517	92	8	second	second	ADJ
ap-3517	92	9	,	,	PUNCT
ap-3517	92	10	third	third	ADJ
ap-3517	92	11	and	and	CCONJ
ap-3517	92	12	fourth	fourth	ADJ
ap-3517	92	13	kind	kind	NOUN
ap-3517	92	14	are	be	AUX
ap-3517	92	15	denoted	denote	VERB
ap-3517	92	16	by	by	ADP
ap-3517	92	17	tm(x	tm(x	NOUN
ap-3517	92	18	)	)	PUNCT
ap-3517	92	19	,	,	PUNCT
ap-3517	92	20	um(x	um(x	NOUN
ap-3517	92	21	)	)	PUNCT
ap-3517	92	22	,	,	PUNCT
ap-3517	92	23	vm(x	vm(x	NUM
ap-3517	92	24	)	)	PUNCT
ap-3517	92	25	and	and	CCONJ
ap-3517	92	26	wm(x	wm(x	NOUN
ap-3517	92	27	)	)	PUNCT
ap-3517	92	28	,	,	PUNCT
ap-3517	92	29	respectively	respectively	ADV
ap-3517	92	30	.	.	PUNCT
ap-3517	93	1	if	if	SCONJ
ap-3517	93	2	x	x	PROPN
ap-3517	93	3	=	=	PUNCT
ap-3517	93	4	cos(θ	cos(θ	PROPN
ap-3517	93	5	)	)	PUNCT
ap-3517	93	6	,	,	PUNCT
ap-3517	93	7	then	then	ADV
ap-3517	93	8	for	for	ADP
ap-3517	93	9	any	any	DET
ap-3517	93	10	m	m	NOUN
ap-3517	93	11	∈	∈	PROPN
ap-3517	93	12	z≥0	z≥0	NOUN
ap-3517	93	13	it	it	PRON
ap-3517	93	14	holds	hold	VERB
ap-3517	93	15	that	that	DET
ap-3517	93	16	tm(x	tm(x	PUNCT
ap-3517	93	17	)	)	PUNCT
ap-3517	93	18	≡	≡	PROPN
ap-3517	93	19	cos(mθ	cos(mθ	PROPN
ap-3517	93	20	)	)	PUNCT
ap-3517	93	21	,	,	PUNCT
ap-3517	93	22	um(x	um(x	NOUN
ap-3517	93	23	)	)	PUNCT
ap-3517	93	24	≡	≡	PROPN
ap-3517	93	25	sin	sin	NOUN
ap-3517	93	26	(	(	PUNCT
ap-3517	93	27	(	(	PUNCT
ap-3517	93	28	m+	m+	NUM
ap-3517	93	29	1)θ	1)θ	NUM
ap-3517	93	30	)	)	PUNCT
ap-3517	93	31	sin(θ	sin(θ	PROPN
ap-3517	93	32	)	)	PUNCT
ap-3517	93	33	,	,	PUNCT
ap-3517	93	34	vm(x	vm(x	X
ap-3517	93	35	)	)	PUNCT
ap-3517	94	1	≡	≡	PROPN
ap-3517	94	2	cos	cos	PROPN
ap-3517	94	3	(	(	PUNCT
ap-3517	94	4	(	(	PUNCT
ap-3517	94	5	m+	m+	NUM
ap-3517	94	6	1	1	NUM
ap-3517	94	7	2	2	NUM
ap-3517	94	8	)	)	PUNCT
ap-3517	94	9	θ	θ	PROPN
ap-3517	94	10	)	)	PUNCT
ap-3517	94	11	cos	cos	PROPN
ap-3517	94	12	(	(	PUNCT
ap-3517	94	13	1	1	NUM
ap-3517	94	14	2θ	2θ	NUM
ap-3517	94	15	)	)	PUNCT
ap-3517	94	16	,	,	PUNCT
ap-3517	94	17	wm(x	wm(x	X
ap-3517	94	18	)	)	PUNCT
ap-3517	94	19	≡	≡	PROPN
ap-3517	94	20	sin	sin	NOUN
ap-3517	94	21	(	(	PUNCT
ap-3517	94	22	(	(	PUNCT
ap-3517	94	23	m+	m+	NUM
ap-3517	94	24	1	1	NUM
ap-3517	94	25	2	2	NUM
ap-3517	94	26	)	)	PUNCT
ap-3517	94	27	θ	θ	PROPN
ap-3517	94	28	)	)	PUNCT
ap-3517	94	29	sin	sin	NOUN
ap-3517	94	30	(	(	PUNCT
ap-3517	94	31	1	1	NUM
ap-3517	94	32	2θ	2θ	NUM
ap-3517	94	33	)	)	PUNCT
ap-3517	94	34	.	.	PUNCT
ap-3517	95	1	therefore	therefore	ADV
ap-3517	95	2	,	,	PUNCT
ap-3517	95	3	for	for	ADP
ap-3517	95	4	specific	specific	ADJ
ap-3517	95	5	choices	choice	NOUN
ap-3517	95	6	of	of	ADP
ap-3517	95	7	parameter	parameter	NOUN
ap-3517	95	8	a1	a1	NOUN
ap-3517	95	9	and	and	CCONJ
ap-3517	95	10	2πb1	2πb1	NUM
ap-3517	95	11	=	=	SYM
ap-3517	95	12	θ	θ	NOUN
ap-3517	95	13	,	,	PUNCT
ap-3517	95	14	we	we	PRON
ap-3517	95	15	can	can	AUX
ap-3517	95	16	view	view	VERB
ap-3517	95	17	the	the	DET
ap-3517	95	18	weyl	weyl	VERB
ap-3517	95	19	-	-	PUNCT
ap-3517	95	20	orbit	orbit	NOUN
ap-3517	95	21	functions	function	NOUN
ap-3517	95	22	of	of	ADP
ap-3517	95	23	a1	a1	NOUN
ap-3517	95	24	as	as	ADP
ap-3517	95	25	these	these	DET
ap-3517	95	26	chebyshev	chebyshev	NOUN
ap-3517	95	27	polynomials	polynomial	NOUN
ap-3517	95	28	.	.	PUNCT
ap-3517	96	1	recall	recall	PROPN
ap-3517	96	2	also	also	ADV
ap-3517	96	3	that	that	SCONJ
ap-3517	96	4	the	the	DET
ap-3517	96	5	chebyshev	chebyshev	NOUN
ap-3517	96	6	polynomials	polynomial	NOUN
ap-3517	96	7	are	be	AUX
ap-3517	96	8	actually	actually	ADV
ap-3517	96	9	,	,	PUNCT
ap-3517	96	10	up	up	ADP
ap-3517	96	11	to	to	ADP
ap-3517	96	12	a	a	DET
ap-3517	96	13	constant	constant	ADJ
ap-3517	96	14	cα	cα	NOUN
ap-3517	96	15	,	,	PUNCT
ap-3517	96	16	β	β	X
ap-3517	96	17	,	,	PUNCT
ap-3517	96	18	special	special	ADJ
ap-3517	96	19	cases	case	NOUN
ap-3517	96	20	of	of	ADP
ap-3517	96	21	jacobi	jacobi	PROPN
ap-3517	96	22	polynomials	polynomial	VERB
ap-3517	96	23	p	p	PROPN
ap-3517	96	24	(	(	PUNCT
ap-3517	96	25	α	α	X
ap-3517	96	26	,	,	PUNCT
ap-3517	96	27	β	β	NOUN
ap-3517	96	28	)	)	PUNCT
ap-3517	96	29	m	m	VERB
ap-3517	96	30	(	(	PUNCT
ap-3517	96	31	x	x	NOUN
ap-3517	96	32	)	)	PUNCT
ap-3517	96	33	,	,	PUNCT
ap-3517	96	34	m	m	PROPN
ap-3517	96	35	∈	∈	NOUN
ap-3517	96	36	z≥0	z≥0	NOUN
ap-3517	96	37	.	.	PUNCT
ap-3517	97	1	the	the	DET
ap-3517	97	2	jacobi	jacobi	PROPN
ap-3517	97	3	polynomials	polynomial	NOUN
ap-3517	97	4	are	be	AUX
ap-3517	97	5	given	give	VERB
ap-3517	97	6	as	as	ADP
ap-3517	97	7	orthogonal	orthogonal	ADJ
ap-3517	97	8	polynomials	polynomial	NOUN
ap-3517	97	9	with	with	ADP
ap-3517	97	10	respect	respect	NOUN
ap-3517	97	11	to	to	ADP
ap-3517	97	12	the	the	DET
ap-3517	97	13	weight	weight	NOUN
ap-3517	97	14	function	function	NOUN
ap-3517	97	15	(	(	PUNCT
ap-3517	97	16	1−	1−	NUM
ap-3517	97	17	x)α(1	x)α(1	PROPN
ap-3517	97	18	+	+	CCONJ
ap-3517	97	19	x)β	x)β	NOUN
ap-3517	97	20	,	,	PUNCT
ap-3517	97	21	−1	−1	NOUN
ap-3517	97	22	<	<	X
ap-3517	97	23	x	x	X
ap-3517	97	24	<	<	X
ap-3517	97	25	1	1	NUM
ap-3517	97	26	,	,	PUNCT
ap-3517	97	27	where	where	SCONJ
ap-3517	97	28	the	the	DET
ap-3517	97	29	parameters	parameter	NOUN
ap-3517	97	30	α	α	PRON
ap-3517	97	31	,	,	PUNCT
ap-3517	97	32	β	β	X
ap-3517	97	33	are	be	AUX
ap-3517	97	34	subjects	subject	NOUN
ap-3517	97	35	to	to	ADP
ap-3517	97	36	the	the	DET
ap-3517	97	37	condition	condition	NOUN
ap-3517	97	38	α	α	NOUN
ap-3517	97	39	,	,	PUNCT
ap-3517	97	40	β	β	X
ap-3517	97	41	>	>	X
ap-3517	97	42	−1	−1	NOUN
ap-3517	98	1	[	[	X
ap-3517	98	2	4	4	NUM
ap-3517	98	3	,	,	PUNCT
ap-3517	98	4	33	33	NUM
ap-3517	98	5	]	]	PUNCT
ap-3517	98	6	.	.	PUNCT
ap-3517	99	1	in	in	ADP
ap-3517	99	2	particular	particular	ADJ
ap-3517	99	3	,	,	PUNCT
ap-3517	99	4	it	it	PRON
ap-3517	99	5	holds	hold	VERB
ap-3517	99	6	that	that	PRON
ap-3517	99	7	tm(x	tm(x	PUNCT
ap-3517	99	8	)	)	PUNCT
ap-3517	99	9	=	=	SYM
ap-3517	99	10	c−	c−	NOUN
ap-3517	99	11	1	1	NUM
ap-3517	99	12	2	2	NUM
ap-3517	99	13	,	,	PUNCT
ap-3517	99	14	−	−	PROPN
ap-3517	99	15	1	1	NUM
ap-3517	99	16	2	2	NUM
ap-3517	99	17	p	p	NOUN
ap-3517	99	18	(	(	PUNCT
ap-3517	99	19	−	−	PROPN
ap-3517	99	20	1	1	NUM
ap-3517	99	21	2	2	NUM
ap-3517	99	22	,	,	PUNCT
ap-3517	99	23	−	−	PROPN
ap-3517	99	24	1	1	NUM
ap-3517	99	25	2	2	NUM
ap-3517	99	26	)	)	PUNCT
ap-3517	99	27	m	m	VERB
ap-3517	99	28	(	(	PUNCT
ap-3517	99	29	x	x	NOUN
ap-3517	99	30	)	)	PUNCT
ap-3517	99	31	,	,	PUNCT
ap-3517	99	32	um(x	um(x	NOUN
ap-3517	99	33	)	)	PUNCT
ap-3517	99	34	=	=	PUNCT
ap-3517	100	1	c	c	NOUN
ap-3517	100	2	1	1	NUM
ap-3517	100	3	2	2	NUM
ap-3517	100	4	,	,	PUNCT
ap-3517	100	5	1	1	NUM
ap-3517	100	6	2	2	NUM
ap-3517	100	7	p	p	NOUN
ap-3517	100	8	(	(	PUNCT
ap-3517	100	9	1	1	NUM
ap-3517	100	10	2	2	NUM
ap-3517	100	11	,	,	PUNCT
ap-3517	100	12	1	1	NUM
ap-3517	100	13	2	2	NUM
ap-3517	100	14	)	)	PUNCT
ap-3517	100	15	m	m	VERB
ap-3517	100	16	(	(	PUNCT
ap-3517	100	17	x	x	NOUN
ap-3517	100	18	)	)	PUNCT
ap-3517	100	19	,	,	PUNCT
ap-3517	100	20	vm(x	vm(x	PUNCT
ap-3517	100	21	)	)	PUNCT
ap-3517	100	22	=	=	SYM
ap-3517	100	23	c−	c−	NOUN
ap-3517	100	24	1	1	NUM
ap-3517	100	25	2	2	NUM
ap-3517	100	26	,	,	PUNCT
ap-3517	100	27	1	1	NUM
ap-3517	100	28	2	2	NUM
ap-3517	100	29	p	p	NOUN
ap-3517	100	30	(	(	PUNCT
ap-3517	100	31	−	−	PROPN
ap-3517	100	32	1	1	NUM
ap-3517	100	33	2	2	NUM
ap-3517	100	34	,	,	PUNCT
ap-3517	100	35	1	1	NUM
ap-3517	100	36	2	2	NUM
ap-3517	100	37	)	)	PUNCT
ap-3517	100	38	m	m	VERB
ap-3517	100	39	(	(	PUNCT
ap-3517	100	40	x	x	NOUN
ap-3517	100	41	)	)	PUNCT
ap-3517	100	42	,	,	PUNCT
ap-3517	100	43	wm(x	wm(x	X
ap-3517	100	44	)	)	PUNCT
ap-3517	100	45	=	=	PUNCT
ap-3517	101	1	c	c	NOUN
ap-3517	101	2	1	1	NUM
ap-3517	101	3	2	2	NUM
ap-3517	101	4	,	,	PUNCT
ap-3517	101	5	−	−	PROPN
ap-3517	101	6	1	1	NUM
ap-3517	101	7	2	2	NUM
ap-3517	101	8	p	p	NOUN
ap-3517	101	9	(	(	PUNCT
ap-3517	101	10	1	1	NUM
ap-3517	101	11	2	2	NUM
ap-3517	101	12	,	,	PUNCT
ap-3517	101	13	−	−	PROPN
ap-3517	101	14	1	1	NUM
ap-3517	101	15	2	2	NUM
ap-3517	101	16	)	)	PUNCT
ap-3517	101	17	m	m	VERB
ap-3517	101	18	(	(	PUNCT
ap-3517	101	19	x	x	NOUN
ap-3517	101	20	)	)	PUNCT
ap-3517	101	21	.	.	PUNCT
ap-3517	102	1	for	for	ADP
ap-3517	102	2	both	both	DET
ap-3517	102	3	chebyshev	chebyshev	NOUN
ap-3517	102	4	polynomials	polynomial	NOUN
ap-3517	102	5	and	and	CCONJ
ap-3517	102	6	jacobi	jacobi	PROPN
ap-3517	102	7	polynomials	polynomial	NOUN
ap-3517	102	8	,	,	PUNCT
ap-3517	102	9	there	there	PRON
ap-3517	102	10	exist	exist	VERB
ap-3517	102	11	various	various	ADJ
ap-3517	102	12	multivariate	multivariate	NOUN
ap-3517	102	13	generalizations	generalization	NOUN
ap-3517	102	14	,	,	PUNCT
ap-3517	102	15	see	see	VERB
ap-3517	102	16	for	for	ADP
ap-3517	102	17	example	example	NOUN
ap-3517	102	18	[	[	X
ap-3517	102	19	3	3	NUM
ap-3517	102	20	,	,	PUNCT
ap-3517	102	21	21	21	NUM
ap-3517	102	22	,	,	PUNCT
ap-3517	102	23	22	22	NUM
ap-3517	102	24	]	]	PUNCT
ap-3517	102	25	.	.	PUNCT
ap-3517	103	1	in	in	ADP
ap-3517	103	2	sections	section	NOUN
ap-3517	103	3	3.2	3.2	NUM
ap-3517	103	4	,	,	PUNCT
ap-3517	103	5	3.3	3.3	NUM
ap-3517	103	6	and	and	CCONJ
ap-3517	103	7	3.4	3.4	NUM
ap-3517	103	8	,	,	PUNCT
ap-3517	103	9	we	we	PRON
ap-3517	103	10	identify	identify	VERB
ap-3517	103	11	some	some	PRON
ap-3517	103	12	of	of	ADP
ap-3517	103	13	the	the	DET
ap-3517	103	14	two	two	NUM
ap-3517	103	15	-	-	PUNCT
ap-3517	103	16	variable	variable	NOUN
ap-3517	103	17	analogous	analogous	ADJ
ap-3517	103	18	orthogonal	orthogonal	ADJ
ap-3517	103	19	polynomials	polynomial	NOUN
ap-3517	103	20	with	with	ADP
ap-3517	103	21	specific	specific	ADJ
ap-3517	103	22	weyl	weyl	VERB
ap-3517	103	23	-	-	PUNCT
ap-3517	103	24	orbit	orbit	NOUN
ap-3517	103	25	functions	function	NOUN
ap-3517	103	26	.	.	PUNCT
ap-3517	104	1	3.2	3.2	NUM
ap-3517	104	2	.	.	PUNCT
ap-3517	104	3	case	case	NOUN
ap-3517	104	4	a2	a2	PROPN
ap-3517	104	5	since	since	ADV
ap-3517	104	6	,	,	PUNCT
ap-3517	104	7	for	for	ADP
ap-3517	104	8	a2	a2	PROPN
ap-3517	104	9	the	the	DET
ap-3517	104	10	two	two	NUM
ap-3517	104	11	simple	simple	ADJ
ap-3517	104	12	roots	root	NOUN
ap-3517	104	13	are	be	AUX
ap-3517	104	14	of	of	ADP
ap-3517	104	15	the	the	DET
ap-3517	104	16	same	same	ADJ
ap-3517	104	17	length	length	NOUN
ap-3517	104	18	,	,	PUNCT
ap-3517	104	19	there	there	PRON
ap-3517	104	20	are	be	VERB
ap-3517	104	21	only	only	ADV
ap-3517	104	22	two	two	NUM
ap-3517	104	23	corresponding	correspond	VERB
ap-3517	104	24	families	family	NOUN
ap-3517	104	25	of	of	ADP
ap-3517	104	26	weyl	weyl	VERB
ap-3517	104	27	-	-	PUNCT
ap-3517	104	28	orbit	orbit	NOUN
ap-3517	104	29	functions	function	NOUN
ap-3517	104	30	,	,	PUNCT
ap-3517	104	31	c	c	NOUN
ap-3517	104	32	–	–	PUNCT
ap-3517	104	33	and	and	CCONJ
ap-3517	104	34	s	s	NOUN
ap-3517	104	35	–	–	PUNCT
ap-3517	104	36	functions	function	NOUN
ap-3517	104	37	.	.	PUNCT
ap-3517	105	1	for	for	ADP
ap-3517	105	2	a	a	DET
ap-3517	105	3	=	=	SYM
ap-3517	105	4	a1ω1	a1ω1	PROPN
ap-3517	105	5	+	+	ADJ
ap-3517	105	6	a2ω2	a2ω2	NOUN
ap-3517	105	7	and	and	CCONJ
ap-3517	105	8	b	b	NOUN
ap-3517	105	9	=	=	SYM
ap-3517	105	10	b1α	b1α	NOUN
ap-3517	105	11	∨	∨	NUM
ap-3517	105	12	1	1	NUM
ap-3517	105	13	+	+	NOUN
ap-3517	105	14	b2α∨2	b2α∨2	NOUN
ap-3517	105	15	the	the	DET
ap-3517	105	16	explicit	explicit	ADJ
ap-3517	105	17	formulas	formula	NOUN
ap-3517	105	18	of	of	ADP
ap-3517	105	19	c	c	NOUN
ap-3517	105	20	–	–	PUNCT
ap-3517	105	21	functions	function	NOUN
ap-3517	105	22	and	and	CCONJ
ap-3517	105	23	s	s	NOUN
ap-3517	105	24	–	–	PUNCT
ap-3517	105	25	functions	function	NOUN
ap-3517	105	26	are	be	AUX
ap-3517	105	27	given	give	VERB
ap-3517	105	28	by	by	ADP
ap-3517	105	29	ca(b	ca(b	ADJ
ap-3517	105	30	)	)	PUNCT
ap-3517	105	31	=	=	SYM
ap-3517	105	32	1	1	NUM
ap-3517	105	33	|stabw	|stabw	NOUN
ap-3517	105	34	a|	a|	PROPN
ap-3517	105	35	(	(	PUNCT
ap-3517	105	36	e2πi(a1b1+a2b2	e2πi(a1b1+a2b2	NOUN
ap-3517	105	37	)	)	PUNCT
ap-3517	105	38	+	+	CCONJ
ap-3517	105	39	e2πi(−a1b1+(a1+a2)b2	e2πi(−a1b1+(a1+a2)b2	NOUN
ap-3517	105	40	)	)	PUNCT
ap-3517	105	41	+	+	CCONJ
ap-3517	105	42	e2πi((a1+a2)b1−a2b2	e2πi((a1+a2)b1−a2b2	NUM
ap-3517	105	43	)	)	PUNCT
ap-3517	106	1	+	+	CCONJ
ap-3517	106	2	e2πi(a2b1−(a1+a2)b2	e2πi(a2b1−(a1+a2)b2	NOUN
ap-3517	106	3	)	)	PUNCT
ap-3517	107	1	+	+	PUNCT
ap-3517	107	2	e2πi((−a1−a2)b1+a1b2	e2πi((−a1−a2)b1+a1b2	VERB
ap-3517	107	3	)	)	PUNCT
ap-3517	108	1	+	+	CCONJ
ap-3517	108	2	e2πi(−a2b1−a1b2	e2πi(−a2b1−a1b2	NOUN
ap-3517	108	3	)	)	PUNCT
ap-3517	108	4	)	)	PUNCT
ap-3517	108	5	,	,	PUNCT
ap-3517	108	6	sa(b	sa(b	NUM
ap-3517	108	7	)	)	PUNCT
ap-3517	108	8	=	=	SYM
ap-3517	108	9	e2πi(a1b1+a2b2	e2πi(a1b1+a2b2	PROPN
ap-3517	108	10	)	)	PUNCT
ap-3517	108	11	−	−	ADP
ap-3517	108	12	e2πi(−a1b1+(a1+a2)b2	e2πi(−a1b1+(a1+a2)b2	NOUN
ap-3517	108	13	)	)	PUNCT
ap-3517	108	14	−	−	NUM
ap-3517	108	15	e2πi((a1+a2)b1−a2b2	e2πi((a1+a2)b1−a2b2	NUM
ap-3517	108	16	)	)	PUNCT
ap-3517	109	1	+	+	CCONJ
ap-3517	109	2	e2πi(a2b1−(a1+a2)b2	e2πi(a2b1−(a1+a2)b2	NOUN
ap-3517	109	3	)	)	PUNCT
ap-3517	110	1	+	+	SYM
ap-3517	110	2	e2πi((−a1−a2)b1+a1b2	e2πi((−a1−a2)b1+a1b2	NOUN
ap-3517	110	3	)	)	PUNCT
ap-3517	110	4	−	−	PROPN
ap-3517	110	5	e2πi(−a2b1−a1b2	e2πi(−a2b1−a1b2	NOUN
ap-3517	110	6	)	)	PUNCT
ap-3517	110	7	with	with	ADP
ap-3517	110	8	the	the	DET
ap-3517	110	9	values	value	NOUN
ap-3517	110	10	|stabw	|stabw	VERB
ap-3517	110	11	a|	a|	PROPN
ap-3517	110	12	given	give	VERB
ap-3517	110	13	in	in	ADP
ap-3517	110	14	table	table	NOUN
ap-3517	110	15	1	1	NUM
ap-3517	110	16	of	of	ADP
ap-3517	110	17	[	[	X
ap-3517	110	18	9	9	NUM
ap-3517	110	19	]	]	PUNCT
ap-3517	110	20	.	.	PUNCT
ap-3517	111	1	they	they	PRON
ap-3517	111	2	are	be	AUX
ap-3517	111	3	related	relate	VERB
ap-3517	111	4	to	to	ADP
ap-3517	111	5	the	the	DET
ap-3517	111	6	generalized	generalized	ADJ
ap-3517	111	7	cosine	cosine	NOUN
ap-3517	111	8	and	and	CCONJ
ap-3517	111	9	sine	sine	ADJ
ap-3517	111	10	functions	function	NOUN
ap-3517	111	11	tck	tck	PROPN
ap-3517	111	12	and	and	CCONJ
ap-3517	111	13	tsk	tsk	PROPN
ap-3517	111	14	studied	study	VERB
ap-3517	111	15	in	in	ADP
ap-3517	111	16	[	[	X
ap-3517	111	17	23	23	NUM
ap-3517	111	18	]	]	PUNCT
ap-3517	111	19	and	and	CCONJ
ap-3517	111	20	defined	define	VERB
ap-3517	111	21	as	as	ADP
ap-3517	111	22	tck(t	tck(t	NOUN
ap-3517	111	23	)	)	PUNCT
ap-3517	111	24	=	=	SYM
ap-3517	111	25	1	1	NUM
ap-3517	111	26	3	3	NUM
ap-3517	111	27	(	(	PUNCT
ap-3517	111	28	e	e	X
ap-3517	111	29	iπ	iπ	ADJ
ap-3517	111	30	3	3	NUM
ap-3517	111	31	(	(	PUNCT
ap-3517	111	32	k2−k3)(t2−t3	k2−k3)(t2−t3	PROPN
ap-3517	111	33	)	)	PUNCT
ap-3517	111	34	cos	cos	ADP
ap-3517	111	35	k1πt1	k1πt1	PROPN
ap-3517	112	1	+	+	CCONJ
ap-3517	112	2	e	e	X
ap-3517	112	3	iπ	iπ	ADV
ap-3517	112	4	3	3	NUM
ap-3517	112	5	(	(	PUNCT
ap-3517	112	6	k2−k3)(t3−t1	k2−k3)(t3−t1	PROPN
ap-3517	112	7	)	)	PUNCT
ap-3517	112	8	cos	cos	ADP
ap-3517	112	9	k1πt2	k1πt2	PROPN
ap-3517	112	10	+	+	CCONJ
ap-3517	112	11	e	e	X
ap-3517	112	12	iπ	iπ	ADV
ap-3517	112	13	3	3	NUM
ap-3517	112	14	(	(	PUNCT
ap-3517	112	15	k2−k3)(t1−t2	k2−k3)(t1−t2	PROPN
ap-3517	112	16	)	)	PUNCT
ap-3517	112	17	cos	cos	ADP
ap-3517	112	18	k1πt3	k1πt3	PROPN
ap-3517	112	19	)	)	PUNCT
ap-3517	112	20	,	,	PUNCT
ap-3517	112	21	tsk(t	tsk(t	NUM
ap-3517	112	22	)	)	PUNCT
ap-3517	112	23	=	=	SYM
ap-3517	112	24	1	1	NUM
ap-3517	112	25	3	3	NUM
ap-3517	112	26	(	(	PUNCT
ap-3517	112	27	e	e	X
ap-3517	112	28	iπ	iπ	ADJ
ap-3517	112	29	3	3	NUM
ap-3517	112	30	(	(	PUNCT
ap-3517	112	31	k2−k3)(t2−t3	k2−k3)(t2−t3	PROPN
ap-3517	112	32	)	)	PUNCT
ap-3517	112	33	sin	sin	NOUN
ap-3517	112	34	k1πt1	k1πt1	NOUN
ap-3517	112	35	+	+	CCONJ
ap-3517	112	36	e	e	X
ap-3517	112	37	iπ	iπ	ADV
ap-3517	112	38	3	3	NUM
ap-3517	112	39	(	(	PUNCT
ap-3517	112	40	k2−k3)(t3−t1	k2−k3)(t3−t1	ADV
ap-3517	112	41	)	)	PUNCT
ap-3517	112	42	sin	sin	NOUN
ap-3517	112	43	k1πt2	k1πt2	NOUN
ap-3517	112	44	+	+	CCONJ
ap-3517	112	45	e	e	X
ap-3517	112	46	iπ	iπ	ADV
ap-3517	112	47	3	3	NUM
ap-3517	112	48	(	(	PUNCT
ap-3517	112	49	k2−k3)(t1−t2	k2−k3)(t1−t2	PROPN
ap-3517	112	50	)	)	PUNCT
ap-3517	112	51	sin	sin	NOUN
ap-3517	112	52	k1πt3	k1πt3	PROPN
ap-3517	112	53	)	)	PUNCT
ap-3517	112	54	,	,	PUNCT
ap-3517	112	55	285	285	NUM
ap-3517	112	56	jiří	jiří	NOUN
ap-3517	112	57	hrivnák	hrivnák	NOUN
ap-3517	112	58	,	,	PUNCT
ap-3517	112	59	lenka	lenka	PROPN
ap-3517	112	60	motlochová	motlochová	PROPN
ap-3517	112	61	acta	acta	PROPN
ap-3517	112	62	polytechnica	polytechnica	PROPN
ap-3517	112	63	figure	figure	NOUN
ap-3517	112	64	1	1	NUM
ap-3517	112	65	.	.	PUNCT
ap-3517	113	1	the	the	DET
ap-3517	113	2	region	region	NOUN
ap-3517	113	3	of	of	ADP
ap-3517	113	4	orthogonality	orthogonality	NOUN
ap-3517	113	5	bounded	bound	VERB
ap-3517	113	6	by	by	ADP
ap-3517	113	7	the	the	DET
ap-3517	113	8	three	three	NUM
ap-3517	113	9	-	-	PUNCT
ap-3517	113	10	cusped	cuspe	VERB
ap-3517	113	11	deltoid	deltoid	NOUN
ap-3517	113	12	.	.	PUNCT
ap-3517	114	1	where	where	SCONJ
ap-3517	114	2	t	t	NOUN
ap-3517	114	3	=	=	SYM
ap-3517	114	4	(	(	PUNCT
ap-3517	114	5	t1	t1	PROPN
ap-3517	114	6	,	,	PUNCT
ap-3517	114	7	t2	t2	NOUN
ap-3517	114	8	,	,	PUNCT
ap-3517	114	9	t3	t3	PROPN
ap-3517	114	10	)	)	PUNCT
ap-3517	114	11	∈	∈	PROPN
ap-3517	114	12	r3	r3	PROPN
ap-3517	114	13	with	with	ADP
ap-3517	114	14	t1	t1	NOUN
ap-3517	114	15	+	+	CCONJ
ap-3517	114	16	t2	t2	PROPN
ap-3517	114	17	+	+	CCONJ
ap-3517	114	18	t3	t3	PROPN
ap-3517	114	19	=	=	SYM
ap-3517	114	20	0	0	PROPN
ap-3517	114	21	and	and	CCONJ
ap-3517	114	22	k	k	PROPN
ap-3517	114	23	=	=	SYM
ap-3517	114	24	(	(	PUNCT
ap-3517	114	25	k1	k1	PROPN
ap-3517	114	26	,	,	PUNCT
ap-3517	114	27	k2	k2	NOUN
ap-3517	114	28	,	,	PUNCT
ap-3517	114	29	k3	k3	ADJ
ap-3517	114	30	)	)	PUNCT
ap-3517	114	31	∈	∈	PROPN
ap-3517	114	32	z3	z3	PROPN
ap-3517	114	33	with	with	ADP
ap-3517	114	34	k1	k1	PROPN
ap-3517	114	35	+	+	CCONJ
ap-3517	114	36	k2	k2	ADJ
ap-3517	114	37	+	+	CCONJ
ap-3517	114	38	k3	k3	ADJ
ap-3517	114	39	=	=	NOUN
ap-3517	114	40	0	0	NUM
ap-3517	114	41	.	.	PUNCT
ap-3517	115	1	the	the	DET
ap-3517	115	2	explicit	explicit	ADJ
ap-3517	115	3	correspondence	correspondence	NOUN
ap-3517	115	4	ca	ca	NOUN
ap-3517	115	5	=	=	SYM
ap-3517	115	6	6	6	NUM
ap-3517	115	7	|stabw	|stabw	PROPN
ap-3517	115	8	a|	a|	PROPN
ap-3517	115	9	tck	tck	PROPN
ap-3517	115	10	,	,	PUNCT
ap-3517	115	11	sa	sa	X
ap-3517	115	12	=	=	PUNCT
ap-3517	116	1	6tsk	6tsk	PROPN
ap-3517	116	2	is	be	AUX
ap-3517	116	3	obtained	obtain	VERB
ap-3517	116	4	by	by	ADP
ap-3517	116	5	the	the	DET
ap-3517	116	6	following	follow	VERB
ap-3517	116	7	change	change	NOUN
ap-3517	116	8	of	of	ADP
ap-3517	116	9	variables	variable	NOUN
ap-3517	116	10	and	and	CCONJ
ap-3517	116	11	parameters	parameter	NOUN
ap-3517	116	12	,	,	PUNCT
ap-3517	116	13	k1	k1	NOUN
ap-3517	116	14	=	=	SYM
ap-3517	116	15	a1	a1	PROPN
ap-3517	116	16	,	,	PUNCT
ap-3517	116	17	k2	k2	NOUN
ap-3517	116	18	=	=	PROPN
ap-3517	116	19	a2	a2	PROPN
ap-3517	116	20	,	,	PUNCT
ap-3517	116	21	k3	k3	X
ap-3517	116	22	=	=	PUNCT
ap-3517	116	23	−a1	−a1	PROPN
ap-3517	116	24	−	−	PROPN
ap-3517	116	25	a2	a2	PROPN
ap-3517	116	26	,	,	PUNCT
ap-3517	116	27	t1	t1	NOUN
ap-3517	116	28	=	=	SYM
ap-3517	116	29	2b1	2b1	NUM
ap-3517	116	30	−	−	NOUN
ap-3517	116	31	b2	b2	NOUN
ap-3517	116	32	,	,	PUNCT
ap-3517	116	33	t2	t2	NOUN
ap-3517	116	34	=	=	SYM
ap-3517	116	35	−b1	−b1	PROPN
ap-3517	116	36	+	+	CCONJ
ap-3517	116	37	2b2	2b2	NUM
ap-3517	116	38	,	,	PUNCT
ap-3517	116	39	t3	t3	PROPN
ap-3517	116	40	=	=	PROPN
ap-3517	116	41	−b1	−b1	PROPN
ap-3517	116	42	−	−	PROPN
ap-3517	116	43	b2	b2	NOUN
ap-3517	116	44	.	.	PUNCT
ap-3517	117	1	it	it	PRON
ap-3517	117	2	is	be	AUX
ap-3517	117	3	possible	possible	ADJ
ap-3517	117	4	to	to	PART
ap-3517	117	5	express	express	VERB
ap-3517	117	6	ca	ca	NOUN
ap-3517	117	7	and	and	CCONJ
ap-3517	117	8	sa+%/s%	sa+%/s%	PUNCT
ap-3517	117	9	with	with	ADP
ap-3517	117	10	a	a	DET
ap-3517	117	11	∈	∈	PROPN
ap-3517	117	12	p+	p+	NOUN
ap-3517	117	13	as	as	ADP
ap-3517	117	14	polynomials	polynomial	NOUN
ap-3517	117	15	in	in	ADP
ap-3517	117	16	cω1	cω1	NOUN
ap-3517	117	17	and	and	CCONJ
ap-3517	117	18	cω2	cω2	VERB
ap-3517	117	19	[	[	X
ap-3517	117	20	1	1	NUM
ap-3517	117	21	]	]	PUNCT
ap-3517	117	22	.	.	PUNCT
ap-3517	118	1	taking	take	VERB
ap-3517	118	2	into	into	ADP
ap-3517	118	3	account	account	NOUN
ap-3517	118	4	that	that	SCONJ
ap-3517	118	5	cω1	cω1	PRON
ap-3517	118	6	=	=	PUNCT
ap-3517	118	7	cω2	cω2	NOUN
ap-3517	118	8	,	,	PUNCT
ap-3517	118	9	one	one	PRON
ap-3517	118	10	can	can	AUX
ap-3517	118	11	pass	pass	VERB
ap-3517	118	12	to	to	ADP
ap-3517	118	13	real	real	ADJ
ap-3517	118	14	variables	variable	NOUN
ap-3517	118	15	by	by	ADP
ap-3517	118	16	making	make	VERB
ap-3517	118	17	a	a	DET
ap-3517	118	18	natural	natural	ADJ
ap-3517	118	19	change	change	NOUN
ap-3517	118	20	of	of	ADP
ap-3517	118	21	variables	variable	NOUN
ap-3517	118	22	,	,	PUNCT
ap-3517	118	23	these	these	PRON
ap-3517	118	24	x	x	X
ap-3517	118	25	=	=	SYM
ap-3517	118	26	cω1	cω1	NOUN
ap-3517	118	27	+	+	CCONJ
ap-3517	118	28	cω2	cω2	NOUN
ap-3517	118	29	2	2	NUM
ap-3517	118	30	=	=	SYM
ap-3517	118	31	cos	cos	X
ap-3517	118	32	2πb1	2πb1	PROPN
ap-3517	118	33	+	+	CCONJ
ap-3517	118	34	cos	cos	PROPN
ap-3517	118	35	2πb2	2πb2	NUM
ap-3517	118	36	+	+	NUM
ap-3517	118	37	cos	cos	PROPN
ap-3517	118	38	2π(b1	2π(b1	NUM
ap-3517	118	39	−	−	PROPN
ap-3517	118	40	b2	b2	NOUN
ap-3517	118	41	)	)	PUNCT
ap-3517	118	42	,	,	PUNCT
ap-3517	118	43	y	y	NOUN
ap-3517	118	44	=	=	PUNCT
ap-3517	118	45	cω1	cω1	ADV
ap-3517	118	46	−	−	NOUN
ap-3517	118	47	cω2	cω2	NOUN
ap-3517	118	48	2i	2i	NOUN
ap-3517	118	49	=	=	PUNCT
ap-3517	118	50	sin	sin	VERB
ap-3517	118	51	2πb1	2πb1	NUM
ap-3517	118	52	−	−	PROPN
ap-3517	118	53	sin	sin	NOUN
ap-3517	119	1	2πb2	2πb2	NUM
ap-3517	119	2	−	−	NOUN
ap-3517	119	3	sin	sin	NOUN
ap-3517	119	4	2π(b1	2π(b1	NUM
ap-3517	119	5	−	−	PROPN
ap-3517	119	6	b2	b2	NOUN
ap-3517	119	7	)	)	PUNCT
ap-3517	119	8	.	.	PUNCT
ap-3517	120	1	since	since	SCONJ
ap-3517	120	2	c	c	NOUN
ap-3517	120	3	–	–	PUNCT
ap-3517	120	4	functions	function	NOUN
ap-3517	120	5	and	and	CCONJ
ap-3517	120	6	s	s	NOUN
ap-3517	120	7	–	–	PUNCT
ap-3517	120	8	functions	function	NOUN
ap-3517	120	9	are	be	AUX
ap-3517	120	10	continuously	continuously	ADV
ap-3517	120	11	orthogonal	orthogonal	ADJ
ap-3517	120	12	,	,	PUNCT
ap-3517	120	13	their	their	PRON
ap-3517	120	14	polynomial	polynomial	ADJ
ap-3517	120	15	versions	version	NOUN
ap-3517	120	16	inherit	inherit	VERB
ap-3517	120	17	the	the	DET
ap-3517	120	18	orthogonality	orthogonality	NOUN
ap-3517	120	19	property	property	NOUN
ap-3517	120	20	.	.	PUNCT
ap-3517	121	1	one	one	PRON
ap-3517	121	2	can	can	AUX
ap-3517	121	3	verify	verify	VERB
ap-3517	121	4	that	that	SCONJ
ap-3517	121	5	the	the	DET
ap-3517	121	6	corresponding	corresponding	ADJ
ap-3517	121	7	polynomials	polynomial	NOUN
ap-3517	121	8	are	be	AUX
ap-3517	121	9	special	special	ADJ
ap-3517	121	10	cases	case	NOUN
ap-3517	121	11	of	of	ADP
ap-3517	121	12	twodimensional	twodimensional	ADJ
ap-3517	121	13	analogues	analogue	NOUN
ap-3517	121	14	of	of	ADP
ap-3517	121	15	jacobi	jacobi	PROPN
ap-3517	121	16	polynomials	polynomials	PROPN
ap-3517	121	17	orthogonal	orthogonal	ADJ
ap-3517	121	18	with	with	ADP
ap-3517	121	19	respect	respect	NOUN
ap-3517	121	20	to	to	ADP
ap-3517	121	21	the	the	DET
ap-3517	121	22	weight	weight	NOUN
ap-3517	121	23	function	function	NOUN
ap-3517	121	24	wα(x	wα(x	PROPN
ap-3517	121	25	,	,	PUNCT
ap-3517	121	26	y	y	NOUN
ap-3517	121	27	)	)	PUNCT
ap-3517	121	28	=	=	PUNCT
ap-3517	122	1	(	(	PUNCT
ap-3517	122	2	−(x2	−(x2	X
ap-3517	122	3	+	+	CCONJ
ap-3517	123	1	y2	y2	PROPN
ap-3517	124	1	+	+	CCONJ
ap-3517	125	1	9)2	9)2	NUM
ap-3517	126	1	+	+	CCONJ
ap-3517	126	2	8(x3	8(x3	NUM
ap-3517	126	3	−	−	NOUN
ap-3517	126	4	3xy2	3xy2	NUM
ap-3517	126	5	)	)	PUNCT
ap-3517	127	1	+	+	CCONJ
ap-3517	127	2	108	108	NUM
ap-3517	127	3	)	)	PUNCT
ap-3517	127	4	α	α	NOUN
ap-3517	127	5	on	on	ADP
ap-3517	127	6	the	the	DET
ap-3517	127	7	region	region	NOUN
ap-3517	127	8	bounded	bound	VERB
ap-3517	127	9	by	by	ADP
ap-3517	127	10	the	the	DET
ap-3517	127	11	three	three	NUM
ap-3517	127	12	-	-	PUNCT
ap-3517	127	13	cusped	cuspe	VERB
ap-3517	127	14	deltoid	deltoid	NOUN
ap-3517	127	15	called	call	VERB
ap-3517	127	16	steiner	steiner	PROPN
ap-3517	127	17	’s	’s	PART
ap-3517	127	18	hypocycloid	hypocycloid	NOUN
ap-3517	128	1	[	[	X
ap-3517	128	2	21	21	NUM
ap-3517	128	3	]	]	PUNCT
ap-3517	128	4	with	with	ADP
ap-3517	128	5	the	the	DET
ap-3517	128	6	boundary	boundary	NOUN
ap-3517	128	7	given	give	VERB
ap-3517	128	8	by	by	ADP
ap-3517	128	9	−(x2	−(x2	NOUN
ap-3517	128	10	+	+	NOUN
ap-3517	128	11	y2	y2	PROPN
ap-3517	129	1	+	+	CCONJ
ap-3517	129	2	9)2	9)2	NUM
ap-3517	129	3	+	+	CCONJ
ap-3517	129	4	8(x3	8(x3	NUM
ap-3517	129	5	−	−	NOUN
ap-3517	129	6	3xy2	3xy2	NUM
ap-3517	129	7	)	)	PUNCT
ap-3517	130	1	+	+	CCONJ
ap-3517	130	2	108	108	NUM
ap-3517	130	3	=	=	SYM
ap-3517	130	4	0	0	NUM
ap-3517	130	5	,	,	PUNCT
ap-3517	130	6	see	see	VERB
ap-3517	130	7	fig	fig	NOUN
ap-3517	130	8	.	.	PUNCT
ap-3517	131	1	1	1	NUM
ap-3517	131	2	.	.	X
ap-3517	131	3	more	more	ADV
ap-3517	131	4	precisely	precisely	ADV
ap-3517	131	5	,	,	PUNCT
ap-3517	131	6	the	the	DET
ap-3517	131	7	polynomials	polynomial	NOUN
ap-3517	131	8	ca	can	AUX
ap-3517	131	9	and	and	CCONJ
ap-3517	131	10	sa+%/s%	sa+%/s%	PROPN
ap-3517	131	11	correspond	correspond	VERB
ap-3517	131	12	to	to	ADP
ap-3517	131	13	the	the	DET
ap-3517	131	14	choices	choice	NOUN
ap-3517	131	15	α	α	NOUN
ap-3517	131	16	=	=	SYM
ap-3517	132	1	−	−	PROPN
ap-3517	132	2	1	1	NUM
ap-3517	132	3	2	2	NUM
ap-3517	132	4	and	and	CCONJ
ap-3517	132	5	α	α	NOUN
ap-3517	132	6	=	=	SYM
ap-3517	132	7	1	1	NUM
ap-3517	132	8	2	2	NUM
ap-3517	132	9	respectively	respectively	ADV
ap-3517	132	10	.	.	PUNCT
ap-3517	133	1	3.3	3.3	NUM
ap-3517	133	2	.	.	PUNCT
ap-3517	134	1	case	case	NOUN
ap-3517	134	2	g2	g2	PROPN
ap-3517	134	3	since	since	ADV
ap-3517	134	4	,	,	PUNCT
ap-3517	134	5	for	for	ADP
ap-3517	134	6	g2	g2	PROPN
ap-3517	134	7	its	its	PRON
ap-3517	134	8	two	two	NUM
ap-3517	134	9	simple	simple	ADJ
ap-3517	134	10	roots	root	NOUN
ap-3517	134	11	are	be	AUX
ap-3517	134	12	of	of	ADP
ap-3517	134	13	different	different	ADJ
ap-3517	134	14	lengths	length	NOUN
ap-3517	134	15	,	,	PUNCT
ap-3517	134	16	all	all	DET
ap-3517	134	17	four	four	NUM
ap-3517	134	18	families	family	NOUN
ap-3517	134	19	of	of	ADP
ap-3517	134	20	c	c	NOUN
ap-3517	134	21	–	–	PUNCT
ap-3517	134	22	,	,	PUNCT
ap-3517	134	23	s	s	X
ap-3517	134	24	–	–	PUNCT
ap-3517	134	25	,	,	PUNCT
ap-3517	134	26	ss	ss	NOUN
ap-3517	134	27	and	and	CCONJ
ap-3517	134	28	sl	sl	NOUN
ap-3517	134	29	–	–	PUNCT
ap-3517	134	30	functions	function	NOUN
ap-3517	134	31	are	be	AUX
ap-3517	134	32	obtained	obtain	VERB
ap-3517	134	33	[	[	X
ap-3517	134	34	15	15	NUM
ap-3517	134	35	,	,	PUNCT
ap-3517	134	36	16	16	NUM
ap-3517	134	37	,	,	PUNCT
ap-3517	134	38	25	25	NUM
ap-3517	134	39	]	]	PUNCT
ap-3517	134	40	.	.	PUNCT
ap-3517	135	1	the	the	DET
ap-3517	135	2	symmetric	symmetric	ADJ
ap-3517	135	3	and	and	CCONJ
ap-3517	135	4	antisymmetric	antisymmetric	ADJ
ap-3517	135	5	orbit	orbit	NOUN
ap-3517	135	6	functions	function	NOUN
ap-3517	135	7	are	be	AUX
ap-3517	135	8	given	give	VERB
ap-3517	135	9	by	by	ADP
ap-3517	135	10	the	the	DET
ap-3517	135	11	following	follow	VERB
ap-3517	135	12	formulas	formula	NOUN
ap-3517	135	13	for	for	ADP
ap-3517	135	14	a	a	DET
ap-3517	135	15	=	=	SYM
ap-3517	135	16	a1ω1	a1ω1	PROPN
ap-3517	135	17	+	+	ADJ
ap-3517	135	18	a2ω2	a2ω2	NOUN
ap-3517	135	19	and	and	CCONJ
ap-3517	135	20	b	b	NOUN
ap-3517	135	21	=	=	SYM
ap-3517	135	22	b1α	b1α	NOUN
ap-3517	135	23	∨	∨	NUM
ap-3517	135	24	1	1	NUM
ap-3517	135	25	+	+	NOUN
ap-3517	135	26	b2α∨2	b2α∨2	NOUN
ap-3517	135	27	,	,	PUNCT
ap-3517	135	28	ca(b	ca(b	ADJ
ap-3517	135	29	)	)	PUNCT
ap-3517	135	30	=	=	SYM
ap-3517	135	31	2	2	NUM
ap-3517	135	32	|stabw	|stabw	NOUN
ap-3517	135	33	a|	a|	PROPN
ap-3517	135	34	(	(	PUNCT
ap-3517	135	35	cos	cos	PROPN
ap-3517	135	36	2π(a1b1	2π(a1b1	PROPN
ap-3517	135	37	+	+	NUM
ap-3517	135	38	a2b2	a2b2	PUNCT
ap-3517	135	39	)	)	PUNCT
ap-3517	135	40	+	+	CCONJ
ap-3517	135	41	cos	cos	PROPN
ap-3517	135	42	2π(−a1b1	2π(−a1b1	NUM
ap-3517	135	43	+	+	CCONJ
ap-3517	135	44	(	(	PUNCT
ap-3517	135	45	3a1	3a1	NUM
ap-3517	135	46	+	+	CCONJ
ap-3517	135	47	a2)b2	a2)b2	NOUN
ap-3517	135	48	)	)	PUNCT
ap-3517	136	1	+	+	CCONJ
ap-3517	136	2	cos	cos	ADJ
ap-3517	136	3	2π((a1	2π((a1	NUM
ap-3517	136	4	+	+	CCONJ
ap-3517	136	5	a2)b1	a2)b1	NOUN
ap-3517	136	6	−	−	NOUN
ap-3517	136	7	a2b2	a2b2	PUNCT
ap-3517	136	8	)	)	PUNCT
ap-3517	136	9	+	+	CCONJ
ap-3517	136	10	cos	cos	PROPN
ap-3517	136	11	2π((2a1	2π((2a1	PROPN
ap-3517	136	12	+	+	CCONJ
ap-3517	136	13	a2)b1	a2)b1	NOUN
ap-3517	136	14	−	−	PROPN
ap-3517	136	15	(	(	PUNCT
ap-3517	136	16	3a1	3a1	NUM
ap-3517	136	17	+	+	CCONJ
ap-3517	136	18	a2)b2	a2)b2	NOUN
ap-3517	136	19	)	)	PUNCT
ap-3517	137	1	+	+	SYM
ap-3517	137	2	cos	cos	ADP
ap-3517	137	3	2π((−a1	2π((−a1	NUM
ap-3517	137	4	−	−	NOUN
ap-3517	137	5	a2)b1	a2)b1	NOUN
ap-3517	137	6	+	+	CCONJ
ap-3517	137	7	(	(	PUNCT
ap-3517	137	8	3a1	3a1	NUM
ap-3517	137	9	+	+	CCONJ
ap-3517	137	10	2a2)b2	2a2)b2	NUM
ap-3517	137	11	)	)	PUNCT
ap-3517	138	1	+	+	CCONJ
ap-3517	138	2	cos	cos	X
ap-3517	138	3	2π((−2a1	2π((−2a1	NUM
ap-3517	138	4	−	−	NOUN
ap-3517	138	5	a2)b1	a2)b1	NOUN
ap-3517	138	6	+	+	CCONJ
ap-3517	138	7	(	(	PUNCT
ap-3517	138	8	3a1	3a1	NUM
ap-3517	138	9	+	+	CCONJ
ap-3517	138	10	2a2)b2	2a2)b2	NUM
ap-3517	138	11	)	)	PUNCT
ap-3517	138	12	)	)	PUNCT
ap-3517	138	13	,	,	PUNCT
ap-3517	138	14	sa(b	sa(b	NUM
ap-3517	138	15	)	)	PUNCT
ap-3517	138	16	=	=	SYM
ap-3517	138	17	2	2	NUM
ap-3517	138	18	(	(	PUNCT
ap-3517	138	19	cos	cos	PROPN
ap-3517	138	20	2π(a1b1	2π(a1b1	PROPN
ap-3517	138	21	+	+	NUM
ap-3517	138	22	a2b2	a2b2	PROPN
ap-3517	138	23	)	)	PUNCT
ap-3517	138	24	−	−	PROPN
ap-3517	138	25	cos	cos	PROPN
ap-3517	138	26	2π(−a1b1	2π(−a1b1	PROPN
ap-3517	138	27	+	+	CCONJ
ap-3517	138	28	(	(	PUNCT
ap-3517	138	29	3a1	3a1	NUM
ap-3517	138	30	+	+	CCONJ
ap-3517	138	31	a2)b2	a2)b2	NOUN
ap-3517	138	32	)	)	PUNCT
ap-3517	138	33	−	−	PROPN
ap-3517	139	1	cos	cos	PROPN
ap-3517	139	2	2π((a1	2π((a1	NUM
ap-3517	139	3	+	+	CCONJ
ap-3517	139	4	a2)b1	a2)b1	NOUN
ap-3517	139	5	−	−	NOUN
ap-3517	139	6	a2b2	a2b2	PUNCT
ap-3517	139	7	)	)	PUNCT
ap-3517	139	8	+	+	CCONJ
ap-3517	139	9	cos	cos	PROPN
ap-3517	139	10	2π((2a1	2π((2a1	PROPN
ap-3517	139	11	+	+	CCONJ
ap-3517	139	12	a2)b1	a2)b1	NOUN
ap-3517	139	13	−	−	PROPN
ap-3517	139	14	(	(	PUNCT
ap-3517	139	15	3a1	3a1	NUM
ap-3517	139	16	+	+	CCONJ
ap-3517	139	17	a2)b2	a2)b2	NOUN
ap-3517	139	18	)	)	PUNCT
ap-3517	140	1	+	+	SYM
ap-3517	140	2	cos	cos	ADP
ap-3517	140	3	2π((−a1	2π((−a1	NUM
ap-3517	140	4	−	−	NOUN
ap-3517	140	5	a2)b1	a2)b1	NOUN
ap-3517	140	6	+	+	CCONJ
ap-3517	140	7	(	(	PUNCT
ap-3517	140	8	3a1	3a1	NUM
ap-3517	140	9	+	+	CCONJ
ap-3517	140	10	2a2)b2	2a2)b2	NUM
ap-3517	140	11	)	)	PUNCT
ap-3517	140	12	−	−	PROPN
ap-3517	141	1	cos	cos	PROPN
ap-3517	141	2	2π((−2a1	2π((−2a1	NUM
ap-3517	141	3	−	−	NOUN
ap-3517	141	4	a2)b1	a2)b1	NOUN
ap-3517	141	5	+	+	CCONJ
ap-3517	141	6	(	(	PUNCT
ap-3517	141	7	3a1	3a1	NUM
ap-3517	141	8	+	+	CCONJ
ap-3517	141	9	2a2)b2	2a2)b2	NUM
ap-3517	141	10	)	)	PUNCT
ap-3517	141	11	)	)	PUNCT
ap-3517	141	12	.	.	PUNCT
ap-3517	142	1	the	the	DET
ap-3517	142	2	hybrid	hybrid	ADJ
ap-3517	142	3	cases	case	NOUN
ap-3517	142	4	can	can	AUX
ap-3517	142	5	be	be	AUX
ap-3517	142	6	expressed	express	VERB
ap-3517	142	7	as	as	ADP
ap-3517	142	8	ssa(b	ssa(b	PROPN
ap-3517	142	9	)	)	PUNCT
ap-3517	143	1	=	=	SYM
ap-3517	143	2	2i	2i	NUM
ap-3517	143	3	|stabw	|stabw	PROPN
ap-3517	143	4	a|	a|	PROPN
ap-3517	143	5	(	(	PUNCT
ap-3517	143	6	sin	sin	NOUN
ap-3517	143	7	2π(a1b1	2π(a1b1	NUM
ap-3517	143	8	+	+	CCONJ
ap-3517	143	9	a2b2	a2b2	PUNCT
ap-3517	143	10	)	)	PUNCT
ap-3517	143	11	+	+	CCONJ
ap-3517	143	12	sin	sin	NOUN
ap-3517	143	13	2π(−a1b1	2π(−a1b1	NUM
ap-3517	143	14	+	+	CCONJ
ap-3517	143	15	(	(	PUNCT
ap-3517	143	16	3a1	3a1	NUM
ap-3517	143	17	+	+	CCONJ
ap-3517	143	18	a2)b2	a2)b2	NOUN
ap-3517	143	19	)	)	PUNCT
ap-3517	143	20	−	−	NOUN
ap-3517	143	21	sin	sin	VERB
ap-3517	143	22	2π((a1	2π((a1	NUM
ap-3517	143	23	+	+	CCONJ
ap-3517	143	24	a2)b1	a2)b1	VERB
ap-3517	143	25	−	−	NOUN
ap-3517	143	26	a2b2	a2b2	PUNCT
ap-3517	143	27	)	)	PUNCT
ap-3517	143	28	−	−	NOUN
ap-3517	143	29	sin	sin	NOUN
ap-3517	143	30	2π((2a1	2π((2a1	PUNCT
ap-3517	144	1	+	+	CCONJ
ap-3517	144	2	a2)b1	a2)b1	NOUN
ap-3517	144	3	−	−	PROPN
ap-3517	144	4	(	(	PUNCT
ap-3517	144	5	3a1	3a1	NUM
ap-3517	144	6	+	+	CCONJ
ap-3517	144	7	a2)b2	a2)b2	NOUN
ap-3517	144	8	)	)	PUNCT
ap-3517	144	9	−	−	NOUN
ap-3517	144	10	sin	sin	NOUN
ap-3517	144	11	2π((−a1	2π((−a1	NUM
ap-3517	144	12	−	−	NOUN
ap-3517	144	13	a2)b1	a2)b1	NOUN
ap-3517	144	14	+	+	CCONJ
ap-3517	144	15	(	(	PUNCT
ap-3517	144	16	3a1	3a1	NUM
ap-3517	144	17	+	+	CCONJ
ap-3517	144	18	2a2)b2	2a2)b2	NUM
ap-3517	144	19	)	)	PUNCT
ap-3517	144	20	−	−	NOUN
ap-3517	144	21	sin	sin	NOUN
ap-3517	144	22	2π((−2a1	2π((−2a1	NUM
ap-3517	144	23	−	−	NOUN
ap-3517	145	1	a2)b1	a2)b1	NOUN
ap-3517	145	2	+	+	CCONJ
ap-3517	145	3	(	(	PUNCT
ap-3517	145	4	3a1	3a1	NUM
ap-3517	145	5	+	+	CCONJ
ap-3517	145	6	2a2)b2	2a2)b2	NUM
ap-3517	145	7	)	)	PUNCT
ap-3517	145	8	)	)	PUNCT
ap-3517	145	9	,	,	PUNCT
ap-3517	145	10	sla(b	sla(b	PROPN
ap-3517	145	11	)	)	PUNCT
ap-3517	145	12	=	=	SYM
ap-3517	145	13	2	2	NUM
ap-3517	145	14	(	(	PUNCT
ap-3517	145	15	sin	sin	NOUN
ap-3517	145	16	2π(a1b1	2π(a1b1	NUM
ap-3517	145	17	+	+	CCONJ
ap-3517	145	18	a2b2	a2b2	PUNCT
ap-3517	145	19	)	)	PUNCT
ap-3517	145	20	−	−	NOUN
ap-3517	145	21	sin	sin	NOUN
ap-3517	145	22	2π(−a1b1	2π(−a1b1	NUM
ap-3517	146	1	+	+	CCONJ
ap-3517	146	2	(	(	PUNCT
ap-3517	146	3	3a1	3a1	NUM
ap-3517	146	4	+	+	CCONJ
ap-3517	146	5	a2)b2	a2)b2	NOUN
ap-3517	146	6	)	)	PUNCT
ap-3517	146	7	+	+	NUM
ap-3517	146	8	sin	sin	NOUN
ap-3517	146	9	2π((a1	2π((a1	NUM
ap-3517	146	10	+	+	CCONJ
ap-3517	146	11	a2)b1	a2)b1	VERB
ap-3517	146	12	−	−	NOUN
ap-3517	146	13	a2b2	a2b2	PUNCT
ap-3517	146	14	)	)	PUNCT
ap-3517	146	15	−	−	NOUN
ap-3517	146	16	sin	sin	NOUN
ap-3517	146	17	2π((2a1	2π((2a1	PUNCT
ap-3517	147	1	+	+	CCONJ
ap-3517	147	2	a2)b1	a2)b1	NOUN
ap-3517	147	3	−	−	PROPN
ap-3517	147	4	(	(	PUNCT
ap-3517	147	5	3a1	3a1	NUM
ap-3517	147	6	+	+	CCONJ
ap-3517	147	7	a2)b2	a2)b2	NOUN
ap-3517	147	8	)	)	PUNCT
ap-3517	147	9	−	−	NOUN
ap-3517	147	10	sin	sin	NOUN
ap-3517	147	11	2π((−a1	2π((−a1	NUM
ap-3517	147	12	−	−	NOUN
ap-3517	147	13	a2)b1	a2)b1	NOUN
ap-3517	147	14	+	+	CCONJ
ap-3517	147	15	(	(	PUNCT
ap-3517	147	16	3a1	3a1	NUM
ap-3517	147	17	+	+	CCONJ
ap-3517	147	18	2a2)b2	2a2)b2	NUM
ap-3517	147	19	)	)	PUNCT
ap-3517	147	20	+	+	CCONJ
ap-3517	147	21	sin	sin	NOUN
ap-3517	147	22	2π((−2a1	2π((−2a1	NUM
ap-3517	147	23	−	−	NOUN
ap-3517	147	24	a2)b1	a2)b1	NOUN
ap-3517	147	25	+	+	CCONJ
ap-3517	147	26	(	(	PUNCT
ap-3517	147	27	3a1	3a1	NUM
ap-3517	147	28	+	+	CCONJ
ap-3517	147	29	2a2)b2	2a2)b2	NUM
ap-3517	147	30	)	)	PUNCT
ap-3517	147	31	)	)	PUNCT
ap-3517	147	32	.	.	PUNCT
ap-3517	148	1	these	these	DET
ap-3517	148	2	functions	function	NOUN
ap-3517	148	3	have	have	AUX
ap-3517	148	4	been	be	AUX
ap-3517	148	5	studied	study	VERB
ap-3517	148	6	in	in	ADP
ap-3517	148	7	[	[	X
ap-3517	148	8	22	22	NUM
ap-3517	148	9	]	]	PUNCT
ap-3517	148	10	,	,	PUNCT
ap-3517	148	11	under	under	ADP
ap-3517	148	12	the	the	DET
ap-3517	148	13	notation	notation	NOUN
ap-3517	148	14	cck	cck	NOUN
ap-3517	148	15	,	,	PUNCT
ap-3517	148	16	ssk	ssk	PROPN
ap-3517	148	17	,	,	PUNCT
ap-3517	148	18	sck	sck	PROPN
ap-3517	148	19	and	and	CCONJ
ap-3517	148	20	csk	csk	NOUN
ap-3517	148	21	with	with	ADP
ap-3517	148	22	cck(t	cck(t	PROPN
ap-3517	148	23	)	)	PUNCT
ap-3517	148	24	=	=	SYM
ap-3517	148	25	1	1	NUM
ap-3517	148	26	3	3	NUM
ap-3517	148	27	(	(	PUNCT
ap-3517	148	28	cos	cos	ADP
ap-3517	148	29	π(k1	π(k1	PROPN
ap-3517	148	30	−	−	PROPN
ap-3517	148	31	k3)(t1	k3)(t1	NOUN
ap-3517	148	32	−	−	PROPN
ap-3517	148	33	t3	t3	PROPN
ap-3517	148	34	)	)	PUNCT
ap-3517	148	35	3	3	NUM
ap-3517	148	36	cosπk2t2	cosπk2t2	NUM
ap-3517	148	37	+	+	X
ap-3517	148	38	cos	cos	PROPN
ap-3517	148	39	π(k1	π(k1	ADJ
ap-3517	148	40	−	−	PROPN
ap-3517	148	41	k3)(t2	k3)(t2	PROPN
ap-3517	148	42	−	−	PROPN
ap-3517	148	43	t1	t1	NOUN
ap-3517	148	44	)	)	PUNCT
ap-3517	148	45	3	3	NUM
ap-3517	148	46	cosπk2t3	cosπk2t3	NOUN
ap-3517	148	47	+	+	NOUN
ap-3517	148	48	cos	cos	ADP
ap-3517	148	49	π(k1	π(k1	PROPN
ap-3517	148	50	−	−	PROPN
ap-3517	148	51	k3)(t3	k3)(t3	VERB
ap-3517	148	52	−	−	PROPN
ap-3517	148	53	t2	t2	PROPN
ap-3517	148	54	)	)	PUNCT
ap-3517	148	55	3	3	NUM
ap-3517	148	56	cosπk2t1	cosπk2t1	NOUN
ap-3517	148	57	)	)	PUNCT
ap-3517	148	58	,	,	PUNCT
ap-3517	148	59	ssk(t	ssk(t	NOUN
ap-3517	148	60	)	)	PUNCT
ap-3517	148	61	=	=	SYM
ap-3517	148	62	1	1	NUM
ap-3517	148	63	3	3	NUM
ap-3517	148	64	(	(	PUNCT
ap-3517	148	65	sin	sin	NOUN
ap-3517	148	66	π(k1	π(k1	ADP
ap-3517	148	67	−	−	PROPN
ap-3517	148	68	k3)(t1	k3)(t1	NOUN
ap-3517	148	69	−	−	PROPN
ap-3517	148	70	t3	t3	PROPN
ap-3517	148	71	)	)	PUNCT
ap-3517	148	72	3	3	NUM
ap-3517	148	73	sin	sin	NOUN
ap-3517	148	74	πk2t2	πk2t2	PROPN
ap-3517	148	75	+	+	NUM
ap-3517	148	76	sin	sin	VERB
ap-3517	148	77	π(k1	π(k1	NOUN
ap-3517	148	78	−	−	PROPN
ap-3517	148	79	k3)(t2	k3)(t2	PROPN
ap-3517	148	80	−	−	PROPN
ap-3517	148	81	t1	t1	NOUN
ap-3517	148	82	)	)	PUNCT
ap-3517	148	83	3	3	NUM
ap-3517	148	84	sin	sin	NOUN
ap-3517	148	85	πk2t3	πk2t3	NOUN
ap-3517	148	86	+	+	NUM
ap-3517	148	87	sin	sin	NOUN
ap-3517	148	88	π(k1	π(k1	NOUN
ap-3517	148	89	−	−	PROPN
ap-3517	148	90	k3)(t3	k3)(t3	VERB
ap-3517	148	91	−	−	PROPN
ap-3517	148	92	t2	t2	PROPN
ap-3517	148	93	)	)	PUNCT
ap-3517	148	94	3	3	NUM
ap-3517	148	95	sin	sin	NOUN
ap-3517	148	96	πk2t1	πk2t1	PROPN
ap-3517	148	97	)	)	PUNCT
ap-3517	148	98	,	,	PUNCT
ap-3517	148	99	286	286	NUM
ap-3517	148	100	vol	vol	NOUN
ap-3517	148	101	.	.	PUNCT
ap-3517	149	1	56	56	NUM
ap-3517	149	2	no	no	NOUN
ap-3517	149	3	.	.	PUNCT
ap-3517	150	1	4/2016	4/2016	PROPN
ap-3517	150	2	weyl	weyl	VERB
ap-3517	150	3	orbit	orbit	NOUN
ap-3517	150	4	functions	function	NOUN
ap-3517	150	5	and	and	CCONJ
ap-3517	150	6	(	(	PUNCT
ap-3517	150	7	anti)symmetric	anti)symmetric	ADJ
ap-3517	150	8	trigonometric	trigonometric	ADJ
ap-3517	150	9	functions	function	NOUN
ap-3517	150	10	sck(t	sck(t	X
ap-3517	150	11	)	)	PUNCT
ap-3517	150	12	=	=	SYM
ap-3517	150	13	1	1	NUM
ap-3517	150	14	3	3	NUM
ap-3517	150	15	(	(	PUNCT
ap-3517	150	16	sin	sin	NOUN
ap-3517	150	17	π(k1	π(k1	ADP
ap-3517	150	18	−	−	PROPN
ap-3517	150	19	k3)(t1	k3)(t1	NOUN
ap-3517	150	20	−	−	PROPN
ap-3517	150	21	t3	t3	PROPN
ap-3517	150	22	)	)	PUNCT
ap-3517	150	23	3	3	NUM
ap-3517	150	24	cosπk2t2	cosπk2t2	NUM
ap-3517	150	25	+	+	CCONJ
ap-3517	150	26	sin	sin	NOUN
ap-3517	150	27	π(k1	π(k1	NOUN
ap-3517	150	28	−	−	PROPN
ap-3517	150	29	k3)(t2	k3)(t2	PROPN
ap-3517	150	30	−	−	PROPN
ap-3517	150	31	t1	t1	NOUN
ap-3517	150	32	)	)	PUNCT
ap-3517	150	33	3	3	NUM
ap-3517	150	34	cosπk2t3	cosπk2t3	NOUN
ap-3517	150	35	+	+	NOUN
ap-3517	150	36	sin	sin	NOUN
ap-3517	150	37	π(k1	π(k1	ADV
ap-3517	150	38	−	−	PROPN
ap-3517	150	39	k3)(t3	k3)(t3	VERB
ap-3517	150	40	−	−	PROPN
ap-3517	150	41	t2	t2	PROPN
ap-3517	150	42	)	)	PUNCT
ap-3517	150	43	3	3	NUM
ap-3517	150	44	cosπk2t1	cosπk2t1	NOUN
ap-3517	150	45	)	)	PUNCT
ap-3517	150	46	,	,	PUNCT
ap-3517	150	47	csk(t	csk(t	PROPN
ap-3517	150	48	)	)	PUNCT
ap-3517	150	49	=	=	SYM
ap-3517	150	50	1	1	NUM
ap-3517	150	51	3	3	NUM
ap-3517	150	52	(	(	PUNCT
ap-3517	150	53	cos	cos	ADP
ap-3517	150	54	π(k1	π(k1	PROPN
ap-3517	150	55	−	−	PROPN
ap-3517	150	56	k3)(t1	k3)(t1	NOUN
ap-3517	150	57	−	−	PROPN
ap-3517	150	58	t3	t3	PROPN
ap-3517	150	59	)	)	PUNCT
ap-3517	150	60	3	3	NUM
ap-3517	150	61	sin	sin	NOUN
ap-3517	150	62	πk2t2	πk2t2	PROPN
ap-3517	150	63	+	+	PROPN
ap-3517	150	64	cos	cos	PROPN
ap-3517	150	65	π(k1	π(k1	ADJ
ap-3517	150	66	−	−	PROPN
ap-3517	150	67	k3)(t2	k3)(t2	PROPN
ap-3517	150	68	−	−	PROPN
ap-3517	150	69	t1	t1	NOUN
ap-3517	150	70	)	)	PUNCT
ap-3517	150	71	3	3	NUM
ap-3517	150	72	sin	sin	NOUN
ap-3517	150	73	πk2t3	πk2t3	PROPN
ap-3517	150	74	+	+	PROPN
ap-3517	150	75	cos	cos	PROPN
ap-3517	150	76	π(k1	π(k1	PROPN
ap-3517	150	77	−	−	PROPN
ap-3517	150	78	k3)(t3	k3)(t3	VERB
ap-3517	150	79	−	−	PROPN
ap-3517	150	80	t2	t2	PROPN
ap-3517	150	81	)	)	PUNCT
ap-3517	150	82	3	3	NUM
ap-3517	150	83	sin	sin	NOUN
ap-3517	150	84	πk2t1	πk2t1	PROPN
ap-3517	150	85	)	)	PUNCT
ap-3517	150	86	,	,	PUNCT
ap-3517	150	87	where	where	SCONJ
ap-3517	150	88	the	the	DET
ap-3517	150	89	variable	variable	NOUN
ap-3517	150	90	t	t	NOUN
ap-3517	150	91	=	=	SYM
ap-3517	150	92	(	(	PUNCT
ap-3517	150	93	t1	t1	NOUN
ap-3517	150	94	,	,	PUNCT
ap-3517	150	95	t2	t2	NOUN
ap-3517	150	96	,	,	PUNCT
ap-3517	150	97	t3	t3	PROPN
ap-3517	150	98	)	)	PUNCT
ap-3517	150	99	∈	∈	PROPN
ap-3517	150	100	r3	r3	PROPN
ap-3517	150	101	h	h	NOUN
ap-3517	150	102	=	=	PRON
ap-3517	150	103	{	{	PUNCT
ap-3517	150	104	t	t	PROPN
ap-3517	150	105	∈	∈	PROPN
ap-3517	150	106	r3	r3	PROPN
ap-3517	150	107	|	|	ADV
ap-3517	150	108	t1	t1	NOUN
ap-3517	150	109	+	+	CCONJ
ap-3517	151	1	t2	t2	PROPN
ap-3517	152	1	+	+	CCONJ
ap-3517	152	2	t3	t3	NOUN
ap-3517	152	3	=	=	SYM
ap-3517	152	4	0	0	NUM
ap-3517	152	5	}	}	PUNCT
ap-3517	152	6	and	and	CCONJ
ap-3517	152	7	parameter	parameter	NOUN
ap-3517	152	8	k	k	PROPN
ap-3517	153	1	=	=	PUNCT
ap-3517	153	2	(	(	PUNCT
ap-3517	153	3	k1	k1	PROPN
ap-3517	153	4	,	,	PUNCT
ap-3517	153	5	k2	k2	NOUN
ap-3517	153	6	,	,	PUNCT
ap-3517	153	7	k3	k3	ADJ
ap-3517	153	8	)	)	PUNCT
ap-3517	153	9	∈	∈	PROPN
ap-3517	153	10	z3	z3	PROPN
ap-3517	153	11	∩	∩	PROPN
ap-3517	153	12	r3	r3	PROPN
ap-3517	153	13	h	h	NOUN
ap-3517	153	14	.	.	PUNCT
ap-3517	154	1	indeed	indeed	ADV
ap-3517	154	2	,	,	PUNCT
ap-3517	154	3	performing	perform	VERB
ap-3517	154	4	the	the	DET
ap-3517	154	5	following	follow	VERB
ap-3517	154	6	change	change	NOUN
ap-3517	154	7	of	of	ADP
ap-3517	154	8	variables	variable	NOUN
ap-3517	154	9	and	and	CCONJ
ap-3517	154	10	parameters	parameter	NOUN
ap-3517	154	11	,	,	PUNCT
ap-3517	154	12	t1	t1	NOUN
ap-3517	154	13	=	=	PROPN
ap-3517	154	14	−b1	−b1	PROPN
ap-3517	154	15	+	+	CCONJ
ap-3517	154	16	3b2	3b2	NUM
ap-3517	154	17	,	,	PUNCT
ap-3517	154	18	t2	t2	NOUN
ap-3517	154	19	=	=	SYM
ap-3517	154	20	2b1	2b1	NUM
ap-3517	154	21	−	−	NOUN
ap-3517	154	22	3b2	3b2	NUM
ap-3517	154	23	,	,	PUNCT
ap-3517	154	24	t3	t3	PROPN
ap-3517	154	25	=	=	SYM
ap-3517	154	26	−b1	−b1	PROPN
ap-3517	154	27	,	,	PUNCT
ap-3517	154	28	k1	k1	NOUN
ap-3517	154	29	=	=	SYM
ap-3517	154	30	a1	a1	PROPN
ap-3517	154	31	+	+	CCONJ
ap-3517	154	32	a2	a2	PROPN
ap-3517	154	33	,	,	PUNCT
ap-3517	154	34	k2	k2	NOUN
ap-3517	154	35	=	=	PUNCT
ap-3517	154	36	a1	a1	PROPN
ap-3517	154	37	,	,	PUNCT
ap-3517	154	38	k3	k3	ADJ
ap-3517	154	39	=	=	SYM
ap-3517	154	40	−2a1	−2a1	NUM
ap-3517	154	41	−	−	NOUN
ap-3517	154	42	a2	a2	NOUN
ap-3517	154	43	,	,	PUNCT
ap-3517	154	44	we	we	PRON
ap-3517	154	45	obtain	obtain	VERB
ap-3517	154	46	the	the	DET
ap-3517	154	47	following	follow	VERB
ap-3517	154	48	relations	relation	NOUN
ap-3517	154	49	.	.	PUNCT
ap-3517	155	1	ca	can	AUX
ap-3517	155	2	=	=	NOUN
ap-3517	155	3	12	12	NUM
ap-3517	155	4	|stabw	|stabw	PROPN
ap-3517	155	5	a|	a|	PROPN
ap-3517	155	6	cck	cck	PROPN
ap-3517	155	7	,	,	PUNCT
ap-3517	155	8	sa	sa	NOUN
ap-3517	155	9	=	=	PUNCT
ap-3517	155	10	−12ssk	−12ssk	ADV
ap-3517	155	11	,	,	PUNCT
ap-3517	155	12	ssa	ssa	NOUN
ap-3517	155	13	=	=	PROPN
ap-3517	155	14	12i	12i	NUM
ap-3517	155	15	|stabw	|stabw	PROPN
ap-3517	155	16	a|	a|	PROPN
ap-3517	155	17	sck	sck	PROPN
ap-3517	155	18	,	,	PUNCT
ap-3517	155	19	sla	sla	PROPN
ap-3517	155	20	=	=	PUNCT
ap-3517	155	21	12i	12i	NUM
ap-3517	155	22	|stabw	|stabw	PROPN
ap-3517	155	23	a|	a|	PROPN
ap-3517	155	24	csk	csk	PROPN
ap-3517	155	25	.	.	PUNCT
ap-3517	156	1	in	in	ADP
ap-3517	156	2	[	[	X
ap-3517	156	3	22	22	NUM
ap-3517	156	4	]	]	PUNCT
ap-3517	156	5	,	,	PUNCT
ap-3517	156	6	the	the	DET
ap-3517	156	7	functions	function	NOUN
ap-3517	156	8	ca	can	AUX
ap-3517	156	9	,	,	PUNCT
ap-3517	156	10	sa+%/s%	sa+%/s%	PROPN
ap-3517	156	11	,	,	PUNCT
ap-3517	156	12	s	s	PROPN
ap-3517	156	13	s	s	AUX
ap-3517	156	14	a+%s	a+%s	NOUN
ap-3517	156	15	/	/	SYM
ap-3517	156	16	s	s	PART
ap-3517	156	17	s	s	NOUN
ap-3517	156	18	%	%	NOUN
ap-3517	156	19	s	s	NOUN
ap-3517	156	20	and	and	CCONJ
ap-3517	156	21	sla+%l	sla+%l	NOUN
ap-3517	156	22	/	/	SYM
ap-3517	156	23	s	s	PART
ap-3517	156	24	l	l	NOUN
ap-3517	156	25	%	%	NOUN
ap-3517	156	26	l	l	NOUN
ap-3517	156	27	are	be	AUX
ap-3517	156	28	expressed	express	VERB
ap-3517	156	29	as	as	ADP
ap-3517	156	30	two	two	NUM
ap-3517	156	31	-	-	PUNCT
ap-3517	156	32	variable	variable	NOUN
ap-3517	156	33	polynomials	polynomial	NOUN
ap-3517	156	34	in	in	ADP
ap-3517	156	35	variables	variable	NOUN
ap-3517	156	36	x	x	PUNCT
ap-3517	157	1	=	=	SYM
ap-3517	157	2	1	1	NUM
ap-3517	157	3	6cω2	6cω2	NUM
ap-3517	157	4	=	=	SYM
ap-3517	157	5	1	1	NUM
ap-3517	157	6	3	3	NUM
ap-3517	157	7	(	(	PUNCT
ap-3517	157	8	cos	cos	PROPN
ap-3517	157	9	2πb2	2πb2	NUM
ap-3517	157	10	+	+	NUM
ap-3517	157	11	cos	cos	PROPN
ap-3517	157	12	2π(b1	2π(b1	NUM
ap-3517	157	13	−	−	NOUN
ap-3517	157	14	b2	b2	NOUN
ap-3517	157	15	)	)	PUNCT
ap-3517	157	16	+	+	CCONJ
ap-3517	157	17	cos	cos	PROPN
ap-3517	157	18	2π(−b1	2π(−b1	NUM
ap-3517	157	19	+	+	NUM
ap-3517	157	20	2b2	2b2	NUM
ap-3517	157	21	)	)	PUNCT
ap-3517	157	22	)	)	PUNCT
ap-3517	157	23	,	,	PUNCT
ap-3517	158	1	y	y	NOUN
ap-3517	158	2	=	=	NOUN
ap-3517	158	3	1	1	NUM
ap-3517	158	4	6cω1	6cω1	NUM
ap-3517	158	5	=	=	SYM
ap-3517	158	6	1	1	NUM
ap-3517	158	7	3	3	NUM
ap-3517	158	8	(	(	PUNCT
ap-3517	158	9	cos	cos	PROPN
ap-3517	158	10	2πb1	2πb1	PROPN
ap-3517	158	11	+	+	CCONJ
ap-3517	158	12	cos	cos	PROPN
ap-3517	158	13	2π(−b1	2π(−b1	NUM
ap-3517	158	14	+	+	NUM
ap-3517	158	15	3b2	3b2	NUM
ap-3517	158	16	)	)	PUNCT
ap-3517	159	1	+	+	CCONJ
ap-3517	159	2	cos	cos	PROPN
ap-3517	159	3	2π(2b1	2π(2b1	NUM
ap-3517	159	4	−	−	PROPN
ap-3517	159	5	3b2	3b2	NUM
ap-3517	159	6	)	)	PUNCT
ap-3517	159	7	)	)	PUNCT
ap-3517	160	1	and	and	CCONJ
ap-3517	160	2	it	it	PRON
ap-3517	160	3	is	be	AUX
ap-3517	160	4	shown	show	VERB
ap-3517	160	5	that	that	SCONJ
ap-3517	160	6	they	they	PRON
ap-3517	160	7	are	be	AUX
ap-3517	160	8	orthogonal	orthogonal	ADJ
ap-3517	160	9	within	within	ADP
ap-3517	160	10	each	each	DET
ap-3517	160	11	family	family	NOUN
ap-3517	160	12	with	with	ADP
ap-3517	160	13	respect	respect	NOUN
ap-3517	160	14	to	to	ADP
ap-3517	160	15	a	a	DET
ap-3517	160	16	weighted	weight	VERB
ap-3517	160	17	integral	integral	ADJ
ap-3517	160	18	on	on	ADP
ap-3517	160	19	the	the	DET
ap-3517	160	20	region	region	NOUN
ap-3517	160	21	(	(	PUNCT
ap-3517	160	22	see	see	VERB
ap-3517	160	23	fig	fig	NOUN
ap-3517	160	24	.	.	PUNCT
ap-3517	161	1	2	2	X
ap-3517	161	2	)	)	PUNCT
ap-3517	161	3	containing	contain	VERB
ap-3517	161	4	points	point	NOUN
ap-3517	161	5	(	(	PUNCT
ap-3517	161	6	x	x	X
ap-3517	161	7	,	,	PUNCT
ap-3517	161	8	y	y	NOUN
ap-3517	161	9	)	)	PUNCT
ap-3517	162	1	satisfying	satisfy	VERB
ap-3517	162	2	(	(	PUNCT
ap-3517	162	3	1	1	NUM
ap-3517	162	4	+	+	NUM
ap-3517	162	5	2y	2y	NUM
ap-3517	162	6	−	−	NOUN
ap-3517	162	7	3x2)(24x3	3x2)(24x3	NUM
ap-3517	162	8	−	−	PROPN
ap-3517	163	1	y2	y2	NOUN
ap-3517	163	2	−	−	PROPN
ap-3517	163	3	12xy	12xy	ADJ
ap-3517	163	4	−	−	PROPN
ap-3517	164	1	6x−	6x−	NOUN
ap-3517	164	2	4y	4y	NUM
ap-3517	164	3	−	−	NOUN
ap-3517	164	4	1	1	X
ap-3517	164	5	)	)	PUNCT
ap-3517	164	6	≥	≥	NOUN
ap-3517	164	7	0	0	NUM
ap-3517	164	8	with	with	ADP
ap-3517	164	9	the	the	DET
ap-3517	164	10	weight	weight	NOUN
ap-3517	164	11	function	function	NOUN
ap-3517	164	12	wα	wα	NOUN
ap-3517	164	13	,	,	PUNCT
ap-3517	164	14	β(x	β(x	PROPN
ap-3517	164	15	,	,	PUNCT
ap-3517	164	16	y	y	NOUN
ap-3517	164	17	)	)	PUNCT
ap-3517	164	18	equal	equal	ADJ
ap-3517	164	19	to	to	ADP
ap-3517	164	20	(	(	PUNCT
ap-3517	164	21	1	1	NUM
ap-3517	164	22	+	+	NUM
ap-3517	164	23	2y	2y	NUM
ap-3517	164	24	−	−	ADP
ap-3517	164	25	3x2)α(24x3	3x2)α(24x3	NUM
ap-3517	164	26	−	−	NOUN
ap-3517	164	27	y2	y2	NOUN
ap-3517	164	28	−	−	PROPN
ap-3517	164	29	12xy	12xy	ADJ
ap-3517	165	1	−	−	PROPN
ap-3517	165	2	6x−	6x−	PROPN
ap-3517	165	3	4y	4y	NUM
ap-3517	165	4	−	−	PROPN
ap-3517	165	5	1)β	1)β	NOUN
ap-3517	165	6	with	with	ADP
ap-3517	165	7	parameters	parameter	NOUN
ap-3517	165	8	α	α	NOUN
ap-3517	165	9	=	=	SYM
ap-3517	165	10	β	β	X
ap-3517	165	11	=	=	SYM
ap-3517	165	12	−1	−1	NOUN
ap-3517	165	13	2	2	NUM
ap-3517	165	14	for	for	ADP
ap-3517	165	15	c	c	NOUN
ap-3517	165	16	–	–	PUNCT
ap-3517	165	17	functions	function	NOUN
ap-3517	165	18	,	,	PUNCT
ap-3517	165	19	α	α	NOUN
ap-3517	165	20	=	=	PUNCT
ap-3517	165	21	β	β	X
ap-3517	165	22	=	=	SYM
ap-3517	165	23	1	1	NUM
ap-3517	165	24	2	2	NUM
ap-3517	165	25	for	for	ADP
ap-3517	165	26	s	s	NOUN
ap-3517	165	27	–	–	PUNCT
ap-3517	165	28	functions	function	NOUN
ap-3517	165	29	,	,	PUNCT
ap-3517	165	30	α	α	NOUN
ap-3517	165	31	=	=	SYM
ap-3517	165	32	1	1	NUM
ap-3517	165	33	2	2	NUM
ap-3517	165	34	,	,	PUNCT
ap-3517	165	35	β	β	NOUN
ap-3517	165	36	=	=	SYM
ap-3517	165	37	−1	−1	NOUN
ap-3517	165	38	2	2	NUM
ap-3517	165	39	for	for	ADP
ap-3517	165	40	ss	ss	NOUN
ap-3517	165	41	–	–	NOUN
ap-3517	165	42	functions	function	NOUN
ap-3517	165	43	,	,	PUNCT
ap-3517	165	44	α	α	NOUN
ap-3517	165	45	=	=	SYM
ap-3517	165	46	−1	−1	NOUN
ap-3517	165	47	2	2	NUM
ap-3517	165	48	,	,	PUNCT
ap-3517	165	49	β	β	X
ap-3517	165	50	=	=	NOUN
ap-3517	165	51	1	1	NUM
ap-3517	165	52	2	2	NUM
ap-3517	165	53	for	for	ADP
ap-3517	165	54	sl	sl	NOUN
ap-3517	165	55	–	–	PUNCT
ap-3517	165	56	functions	function	NOUN
ap-3517	165	57	.	.	PUNCT
ap-3517	166	1	figure	figure	NOUN
ap-3517	166	2	2	2	NUM
ap-3517	166	3	.	.	PUNCT
ap-3517	167	1	the	the	DET
ap-3517	167	2	region	region	NOUN
ap-3517	167	3	of	of	ADP
ap-3517	167	4	orthogonality	orthogonality	NOUN
ap-3517	167	5	for	for	ADP
ap-3517	167	6	the	the	DET
ap-3517	167	7	case	case	NOUN
ap-3517	167	8	g2	g2	PROPN
ap-3517	167	9	.	.	PUNCT
ap-3517	168	1	3.4	3.4	NUM
ap-3517	168	2	.	.	PUNCT
ap-3517	168	3	cases	case	NOUN
ap-3517	168	4	bn	bn	VERB
ap-3517	168	5	and	and	CCONJ
ap-3517	168	6	cn	cn	X
ap-3517	168	7	it	it	PRON
ap-3517	168	8	is	be	AUX
ap-3517	168	9	shown	show	VERB
ap-3517	168	10	in	in	ADP
ap-3517	168	11	this	this	DET
ap-3517	168	12	section	section	NOUN
ap-3517	168	13	that	that	SCONJ
ap-3517	168	14	the	the	DET
ap-3517	168	15	c	c	NOUN
ap-3517	168	16	–	–	PUNCT
ap-3517	168	17	,	,	PUNCT
ap-3517	168	18	s	s	X
ap-3517	168	19	–	–	PUNCT
ap-3517	168	20	,	,	PUNCT
ap-3517	168	21	ss	ss	NOUN
ap-3517	168	22	–	–	PUNCT
ap-3517	168	23	and	and	CCONJ
ap-3517	168	24	sl	sl	NOUN
ap-3517	168	25	–	–	PUNCT
ap-3517	168	26	functions	function	NOUN
ap-3517	168	27	arising	arise	VERB
ap-3517	168	28	from	from	ADP
ap-3517	168	29	bn	bn	ADV
ap-3517	168	30	and	and	CCONJ
ap-3517	168	31	cn	cn	PROPN
ap-3517	168	32	are	be	AUX
ap-3517	168	33	related	relate	VERB
ap-3517	168	34	to	to	ADP
ap-3517	168	35	the	the	DET
ap-3517	168	36	symmetric	symmetric	ADJ
ap-3517	168	37	and	and	CCONJ
ap-3517	168	38	antisymmetric	antisymmetric	ADJ
ap-3517	168	39	multivariate	multivariate	NOUN
ap-3517	168	40	generalizations	generalization	NOUN
ap-3517	168	41	of	of	ADP
ap-3517	168	42	trigonometric	trigonometric	ADJ
ap-3517	168	43	functions	function	NOUN
ap-3517	168	44	[	[	X
ap-3517	168	45	17	17	NUM
ap-3517	168	46	]	]	PUNCT
ap-3517	168	47	.	.	PUNCT
ap-3517	169	1	the	the	DET
ap-3517	169	2	symmetric	symmetric	ADJ
ap-3517	169	3	cosine	cosine	NOUN
ap-3517	169	4	functions	function	NOUN
ap-3517	169	5	cos+	cos+	PROPN
ap-3517	169	6	λ	λ	X
ap-3517	169	7	(	(	PUNCT
ap-3517	169	8	x	x	NOUN
ap-3517	169	9	)	)	PUNCT
ap-3517	169	10	and	and	CCONJ
ap-3517	169	11	the	the	DET
ap-3517	169	12	antisymmetric	antisymmetric	ADJ
ap-3517	169	13	cosine	cosine	NOUN
ap-3517	169	14	functions	function	NOUN
ap-3517	169	15	cos−λ	cos−λ	NOUN
ap-3517	169	16	(	(	PUNCT
ap-3517	169	17	x	x	NOUN
ap-3517	169	18	)	)	PUNCT
ap-3517	169	19	of	of	ADP
ap-3517	169	20	the	the	DET
ap-3517	169	21	variable	variable	NOUN
ap-3517	169	22	x	x	PUNCT
ap-3517	169	23	=	=	SYM
ap-3517	169	24	(	(	PUNCT
ap-3517	169	25	x1	x1	PROPN
ap-3517	169	26	,	,	PUNCT
ap-3517	169	27	.	.	PUNCT
ap-3517	169	28	.	.	PUNCT
ap-3517	169	29	.	.	PUNCT
ap-3517	170	1	,	,	PUNCT
ap-3517	170	2	xn	xn	X
ap-3517	170	3	)	)	PUNCT
ap-3517	170	4	∈	∈	PROPN
ap-3517	170	5	rn	rn	PROPN
ap-3517	170	6	are	be	AUX
ap-3517	170	7	labelled	label	VERB
ap-3517	170	8	by	by	ADP
ap-3517	170	9	the	the	DET
ap-3517	170	10	parameter	parameter	NOUN
ap-3517	170	11	λ	λ	PROPN
ap-3517	170	12	=	=	SYM
ap-3517	170	13	(	(	PUNCT
ap-3517	170	14	λ1	λ1	ADJ
ap-3517	170	15	,	,	PUNCT
ap-3517	170	16	.	.	PUNCT
ap-3517	170	17	.	.	PUNCT
ap-3517	171	1	.	.	PUNCT
ap-3517	172	1	,	,	PUNCT
ap-3517	172	2	λn	λn	NOUN
ap-3517	172	3	)	)	PUNCT
ap-3517	172	4	∈	∈	PROPN
ap-3517	172	5	rn	rn	PROPN
ap-3517	172	6	and	and	CCONJ
ap-3517	172	7	are	be	AUX
ap-3517	172	8	given	give	VERB
ap-3517	172	9	by	by	ADP
ap-3517	172	10	the	the	DET
ap-3517	172	11	following	follow	VERB
ap-3517	172	12	explicit	explicit	ADJ
ap-3517	172	13	formulas	formula	NOUN
ap-3517	172	14	,	,	PUNCT
ap-3517	172	15	cos+	cos+	PROPN
ap-3517	172	16	λ	λ	X
ap-3517	172	17	(	(	PUNCT
ap-3517	172	18	x	x	NOUN
ap-3517	172	19	)	)	PUNCT
ap-3517	172	20	≡	≡	PROPN
ap-3517	172	21	∑	∑	PROPN
ap-3517	172	22	σ∈sn	σ∈sn	PROPN
ap-3517	172	23	n∏	n∏	PROPN
ap-3517	172	24	k=1	k=1	PROPN
ap-3517	172	25	cos(πλσ(k)xk	cos(πλσ(k)xk	PROPN
ap-3517	172	26	)	)	PUNCT
ap-3517	172	27	,	,	PUNCT
ap-3517	172	28	cos−λ	cos−λ	X
ap-3517	172	29	(	(	PUNCT
ap-3517	172	30	x	x	X
ap-3517	172	31	)	)	PUNCT
ap-3517	172	32	≡	≡	PROPN
ap-3517	172	33	∑	∑	PROPN
ap-3517	172	34	σ∈sn	σ∈sn	PROPN
ap-3517	172	35	sgn(σ	sgn(σ	PROPN
ap-3517	172	36	)	)	PUNCT
ap-3517	172	37	n∏	n∏	PROPN
ap-3517	172	38	k=1	k=1	PROPN
ap-3517	173	1	cos(πλσ(k)xk	cos(πλσ(k)xk	PROPN
ap-3517	173	2	)	)	PUNCT
ap-3517	173	3	,	,	PUNCT
ap-3517	173	4	where	where	SCONJ
ap-3517	173	5	sn	sn	PROPN
ap-3517	173	6	denotes	denote	VERB
ap-3517	173	7	the	the	DET
ap-3517	173	8	symmetric	symmetric	ADJ
ap-3517	173	9	group	group	NOUN
ap-3517	173	10	consisting	consist	VERB
ap-3517	173	11	of	of	ADP
ap-3517	173	12	all	all	DET
ap-3517	173	13	permutations	permutation	NOUN
ap-3517	173	14	of	of	ADP
ap-3517	173	15	numbers	number	NOUN
ap-3517	173	16	1	1	NUM
ap-3517	173	17	,	,	PUNCT
ap-3517	173	18	.	.	PUNCT
ap-3517	173	19	.	.	PUNCT
ap-3517	174	1	.	.	PUNCT
ap-3517	175	1	,	,	PUNCT
ap-3517	175	2	n	n	CCONJ
ap-3517	175	3	,	,	PUNCT
ap-3517	175	4	and	and	CCONJ
ap-3517	175	5	sgn(σ	sgn(σ	PROPN
ap-3517	175	6	)	)	PUNCT
ap-3517	175	7	is	be	AUX
ap-3517	175	8	the	the	DET
ap-3517	175	9	signature	signature	NOUN
ap-3517	175	10	of	of	ADP
ap-3517	175	11	σ	σ	PROPN
ap-3517	175	12	.	.	PUNCT
ap-3517	176	1	the	the	DET
ap-3517	176	2	symmetric	symmetric	ADJ
ap-3517	176	3	sine	sine	NOUN
ap-3517	176	4	functions	function	NOUN
ap-3517	176	5	sin+	sin+	PROPN
ap-3517	176	6	λ	λ	PROPN
ap-3517	176	7	(	(	PUNCT
ap-3517	176	8	x	x	NOUN
ap-3517	176	9	)	)	PUNCT
ap-3517	176	10	and	and	CCONJ
ap-3517	176	11	the	the	DET
ap-3517	176	12	antisymmetric	antisymmetric	ADJ
ap-3517	176	13	sine	sine	ADJ
ap-3517	176	14	functions	function	NOUN
ap-3517	176	15	sin−λ	sin−λ	PROPN
ap-3517	176	16	(	(	PUNCT
ap-3517	176	17	x	x	X
ap-3517	176	18	)	)	PUNCT
ap-3517	176	19	are	be	AUX
ap-3517	176	20	defined	define	VERB
ap-3517	176	21	similarly	similarly	ADV
ap-3517	176	22	,	,	PUNCT
ap-3517	176	23	sin+	sin+	PROPN
ap-3517	176	24	λ	λ	PROPN
ap-3517	176	25	(	(	PUNCT
ap-3517	176	26	x	x	NOUN
ap-3517	176	27	)	)	PUNCT
ap-3517	176	28	≡	≡	PROPN
ap-3517	176	29	∑	∑	PROPN
ap-3517	176	30	σ∈sn	σ∈sn	PROPN
ap-3517	176	31	n∏	n∏	PROPN
ap-3517	176	32	k=1	k=1	PROPN
ap-3517	176	33	sin(πλσ(k)xk	sin(πλσ(k)xk	PROPN
ap-3517	176	34	)	)	PUNCT
ap-3517	176	35	,	,	PUNCT
ap-3517	176	36	sin−λ	sin−λ	PROPN
ap-3517	176	37	(	(	PUNCT
ap-3517	176	38	x	x	NOUN
ap-3517	176	39	)	)	PUNCT
ap-3517	176	40	≡	≡	PROPN
ap-3517	176	41	∑	∑	PROPN
ap-3517	176	42	σ∈sn	σ∈sn	PROPN
ap-3517	176	43	sgn(σ	sgn(σ	PROPN
ap-3517	176	44	)	)	PUNCT
ap-3517	176	45	n∏	n∏	PROPN
ap-3517	176	46	k=1	k=1	PROPN
ap-3517	176	47	sin(πλσ(k)xk	sin(πλσ(k)xk	PROPN
ap-3517	176	48	)	)	PUNCT
ap-3517	176	49	.	.	PUNCT
ap-3517	177	1	firstly	firstly	ADV
ap-3517	177	2	,	,	PUNCT
ap-3517	177	3	consider	consider	VERB
ap-3517	177	4	the	the	DET
ap-3517	177	5	lie	lie	NOUN
ap-3517	177	6	algebra	algebra	PROPN
ap-3517	177	7	bn	bn	INTJ
ap-3517	177	8	and	and	CCONJ
ap-3517	177	9	an	an	DET
ap-3517	177	10	orthonormal	orthonormal	ADJ
ap-3517	177	11	basis	basis	NOUN
ap-3517	177	12	{	{	PUNCT
ap-3517	177	13	e1	e1	NOUN
ap-3517	177	14	,	,	PUNCT
ap-3517	177	15	.	.	PUNCT
ap-3517	177	16	.	.	PUNCT
ap-3517	178	1	.	.	PUNCT
ap-3517	179	1	,	,	PUNCT
ap-3517	179	2	en	en	ADP
ap-3517	179	3	}	}	PUNCT
ap-3517	179	4	of	of	ADP
ap-3517	179	5	rn	rn	PROPN
ap-3517	179	6	such	such	ADJ
ap-3517	179	7	that	that	SCONJ
ap-3517	179	8	αi	αi	ADV
ap-3517	180	1	=	=	PUNCT
ap-3517	180	2	ei	ei	X
ap-3517	181	1	−	−	NOUN
ap-3517	181	2	ei+1	ei+1	NOUN
ap-3517	181	3	for	for	ADP
ap-3517	181	4	i	i	PRON
ap-3517	181	5	=	=	NOUN
ap-3517	181	6	1	1	NUM
ap-3517	181	7	,	,	PUNCT
ap-3517	181	8	.	.	PUNCT
ap-3517	181	9	.	.	PUNCT
ap-3517	181	10	.	.	PUNCT
ap-3517	182	1	,	,	PUNCT
ap-3517	182	2	n−	n−	NOUN
ap-3517	182	3	1	1	NUM
ap-3517	182	4	and	and	CCONJ
ap-3517	182	5	αn	αn	NOUN
ap-3517	183	1	=	=	SYM
ap-3517	183	2	en	en	X
ap-3517	183	3	.	.	PUNCT
ap-3517	184	1	if	if	SCONJ
ap-3517	184	2	we	we	PRON
ap-3517	184	3	determine	determine	VERB
ap-3517	184	4	any	any	DET
ap-3517	184	5	a	a	DET
ap-3517	184	6	∈	∈	PROPN
ap-3517	184	7	rn	rn	NOUN
ap-3517	184	8	by	by	ADP
ap-3517	184	9	its	its	PRON
ap-3517	184	10	coordinates	coordinate	NOUN
ap-3517	184	11	with	with	ADP
ap-3517	184	12	respect	respect	NOUN
ap-3517	184	13	to	to	ADP
ap-3517	184	14	the	the	DET
ap-3517	184	15	basis	basis	NOUN
ap-3517	184	16	{	{	PUNCT
ap-3517	184	17	e1	e1	NOUN
ap-3517	184	18	,	,	PUNCT
ap-3517	184	19	.	.	PUNCT
ap-3517	184	20	.	.	PUNCT
ap-3517	185	1	.	.	PUNCT
ap-3517	185	2	,	,	PUNCT
ap-3517	185	3	en	en	ADP
ap-3517	185	4	}	}	PUNCT
ap-3517	185	5	,	,	PUNCT
ap-3517	185	6	a	a	DET
ap-3517	185	7	=	=	X
ap-3517	185	8	(	(	PUNCT
ap-3517	185	9	a1	a1	PROPN
ap-3517	185	10	,	,	PUNCT
ap-3517	185	11	.	.	PUNCT
ap-3517	185	12	.	.	PUNCT
ap-3517	186	1	.	.	PUNCT
ap-3517	187	1	,	,	PUNCT
ap-3517	187	2	an	an	X
ap-3517	187	3	)	)	PUNCT
ap-3517	187	4	=	=	SYM
ap-3517	187	5	a1e1	a1e1	PROPN
ap-3517	187	6	+	+	X
ap-3517	187	7	·	·	PUNCT
ap-3517	187	8	·	·	PUNCT
ap-3517	187	9	·	·	PUNCT
ap-3517	188	1	+	+	NUM
ap-3517	188	2	anen	anen	NOUN
ap-3517	188	3	,	,	PUNCT
ap-3517	188	4	then	then	ADV
ap-3517	188	5	it	it	PRON
ap-3517	188	6	holds	hold	VERB
ap-3517	188	7	for	for	ADP
ap-3517	188	8	the	the	DET
ap-3517	188	9	generators	generator	NOUN
ap-3517	188	10	ri	ri	PROPN
ap-3517	188	11	,	,	PUNCT
ap-3517	188	12	i	i	NOUN
ap-3517	188	13	=	=	NOUN
ap-3517	188	14	1	1	NUM
ap-3517	188	15	,	,	PUNCT
ap-3517	188	16	.	.	PUNCT
ap-3517	188	17	.	.	PUNCT
ap-3517	189	1	.	.	PUNCT
ap-3517	190	1	,	,	PUNCT
ap-3517	190	2	n−1	n−1	PROPN
ap-3517	190	3	and	and	CCONJ
ap-3517	190	4	rn	rn	PROPN
ap-3517	190	5	of	of	ADP
ap-3517	190	6	the	the	DET
ap-3517	190	7	weyl	weyl	PROPN
ap-3517	190	8	group	group	NOUN
ap-3517	190	9	w	w	PROPN
ap-3517	190	10	(	(	PUNCT
ap-3517	190	11	bn	bn	NOUN
ap-3517	190	12	)	)	PUNCT
ap-3517	190	13	of	of	ADP
ap-3517	190	14	bn	bn	ADP
ap-3517	190	15	that	that	DET
ap-3517	190	16	ri(a1	ri(a1	NOUN
ap-3517	190	17	,	,	PUNCT
ap-3517	190	18	.	.	PUNCT
ap-3517	190	19	.	.	PUNCT
ap-3517	191	1	.	.	PUNCT
ap-3517	192	1	,	,	PUNCT
ap-3517	192	2	ai	ai	VERB
ap-3517	192	3	,	,	PUNCT
ap-3517	192	4	ai+1	ai+1	PROPN
ap-3517	192	5	,	,	PUNCT
ap-3517	192	6	.	.	PUNCT
ap-3517	192	7	.	.	PUNCT
ap-3517	193	1	.	.	PUNCT
ap-3517	194	1	,	,	PUNCT
ap-3517	194	2	an	an	X
ap-3517	194	3	)	)	PUNCT
ap-3517	194	4	=	=	SYM
ap-3517	194	5	(	(	PUNCT
ap-3517	194	6	a1	a1	PROPN
ap-3517	194	7	,	,	PUNCT
ap-3517	194	8	.	.	PUNCT
ap-3517	194	9	.	.	PUNCT
ap-3517	194	10	.	.	PUNCT
ap-3517	195	1	,	,	PUNCT
ap-3517	195	2	ai+1	ai+1	X
ap-3517	195	3	,	,	PUNCT
ap-3517	195	4	ai	ai	VERB
ap-3517	195	5	,	,	PUNCT
ap-3517	195	6	.	.	PUNCT
ap-3517	195	7	.	.	PUNCT
ap-3517	196	1	.	.	PUNCT
ap-3517	197	1	,	,	PUNCT
ap-3517	197	2	an	an	X
ap-3517	197	3	)	)	PUNCT
ap-3517	197	4	,	,	PUNCT
ap-3517	197	5	rn(a1	rn(a1	NOUN
ap-3517	197	6	,	,	PUNCT
ap-3517	197	7	.	.	PUNCT
ap-3517	197	8	.	.	PUNCT
ap-3517	198	1	.	.	PUNCT
ap-3517	199	1	,	,	PUNCT
ap-3517	199	2	an−1	an−1	ADJ
ap-3517	199	3	,	,	PUNCT
ap-3517	199	4	an	an	PRON
ap-3517	199	5	)	)	PUNCT
ap-3517	199	6	=	=	SYM
ap-3517	199	7	(	(	PUNCT
ap-3517	199	8	a1	a1	PROPN
ap-3517	199	9	,	,	PUNCT
ap-3517	199	10	.	.	PUNCT
ap-3517	199	11	.	.	PUNCT
ap-3517	199	12	.	.	PUNCT
ap-3517	200	1	,	,	PUNCT
ap-3517	200	2	an−1,−an	an−1,−an	PROPN
ap-3517	200	3	)	)	PUNCT
ap-3517	200	4	.	.	PUNCT
ap-3517	201	1	287	287	NUM
ap-3517	201	2	jiří	jiří	NOUN
ap-3517	201	3	hrivnák	hrivnák	NOUN
ap-3517	201	4	,	,	PUNCT
ap-3517	201	5	lenka	lenka	PROPN
ap-3517	201	6	motlochová	motlochová	PROPN
ap-3517	201	7	acta	acta	PROPN
ap-3517	201	8	polytechnica	polytechnica	PROPN
ap-3517	201	9	therefore	therefore	ADV
ap-3517	201	10	,	,	PUNCT
ap-3517	201	11	w	w	PROPN
ap-3517	201	12	(	(	PUNCT
ap-3517	201	13	bn	bn	NOUN
ap-3517	201	14	)	)	PUNCT
ap-3517	201	15	consists	consist	VERB
ap-3517	201	16	of	of	ADP
ap-3517	201	17	all	all	DET
ap-3517	201	18	permutations	permutation	NOUN
ap-3517	201	19	of	of	ADP
ap-3517	201	20	the	the	DET
ap-3517	201	21	coordinates	coordinate	NOUN
ap-3517	201	22	ai	ai	VERB
ap-3517	201	23	with	with	ADP
ap-3517	201	24	possible	possible	ADJ
ap-3517	201	25	sign	sign	NOUN
ap-3517	201	26	alternations	alternation	NOUN
ap-3517	201	27	of	of	ADP
ap-3517	201	28	some	some	PRON
ap-3517	201	29	of	of	ADP
ap-3517	201	30	them	they	PRON
ap-3517	201	31	,	,	PUNCT
ap-3517	201	32	and	and	CCONJ
ap-3517	201	33	we	we	PRON
ap-3517	201	34	actually	actually	ADV
ap-3517	201	35	have	have	VERB
ap-3517	201	36	that	that	DET
ap-3517	201	37	w	w	PROPN
ap-3517	201	38	(	(	PUNCT
ap-3517	201	39	bn	bn	NOUN
ap-3517	201	40	)	)	PUNCT
ap-3517	201	41	is	be	AUX
ap-3517	201	42	isomorphic	isomorphic	ADJ
ap-3517	201	43	to	to	ADP
ap-3517	201	44	(	(	PUNCT
ap-3517	201	45	z/2z)n	z/2z)n	INTJ
ap-3517	202	1	o	o	X
ap-3517	202	2	sn	sn	PROPN
ap-3517	203	1	[	[	X
ap-3517	203	2	12	12	NUM
ap-3517	203	3	]	]	PUNCT
ap-3517	203	4	.	.	PUNCT
ap-3517	204	1	this	this	PRON
ap-3517	204	2	implies	imply	VERB
ap-3517	204	3	that	that	SCONJ
ap-3517	204	4	φa(b	φa(b	PUNCT
ap-3517	204	5	)	)	PUNCT
ap-3517	205	1	=	=	PUNCT
ap-3517	205	2	∑	∑	PUNCT
ap-3517	205	3	w∈w	w∈w	X
ap-3517	205	4	(	(	PUNCT
ap-3517	205	5	bn	bn	NOUN
ap-3517	205	6	)	)	PUNCT
ap-3517	205	7	e2πi〈w(a),b	e2πi〈w(a),b	PROPN
ap-3517	205	8	〉	〉	NOUN
ap-3517	205	9	=	=	SYM
ap-3517	205	10	∑	∑	PUNCT
ap-3517	205	11	σ∈sn	σ∈sn	PROPN
ap-3517	205	12	n∏	n∏	PROPN
ap-3517	205	13	k=1	k=1	PROPN
ap-3517	205	14	∑	∑	PUNCT
ap-3517	205	15	lk=±1	lk=±1	PROPN
ap-3517	205	16	e2πi(lkaσ(k)bk	e2πi(lkaσ(k)bk	X
ap-3517	205	17	)	)	PUNCT
ap-3517	206	1	=	=	PUNCT
ap-3517	206	2	∑	∑	PUNCT
ap-3517	206	3	σ∈sn	σ∈sn	PROPN
ap-3517	206	4	n∏	n∏	PROPN
ap-3517	207	1	k=1	k=1	PROPN
ap-3517	207	2	(	(	PUNCT
ap-3517	207	3	e2πiaσ(k)bk	e2πiaσ(k)bk	NOUN
ap-3517	207	4	+	+	X
ap-3517	207	5	e−2πiaσ(k)bk	e−2πiaσ(k)bk	X
ap-3517	207	6	)	)	PUNCT
ap-3517	207	7	=	=	SYM
ap-3517	207	8	2n	2n	NUM
ap-3517	207	9	∑	∑	PROPN
ap-3517	207	10	σ∈sn	σ∈sn	PROPN
ap-3517	207	11	n∏	n∏	PROPN
ap-3517	207	12	k=1	k=1	PUNCT
ap-3517	207	13	cos(2πaσ(k)bk	cos(2πaσ(k)bk	PROPN
ap-3517	207	14	)	)	PUNCT
ap-3517	207	15	=	=	SYM
ap-3517	208	1	2n	2n	NUM
ap-3517	208	2	cos+	cos+	PROPN
ap-3517	208	3	a	a	DET
ap-3517	208	4	(	(	PUNCT
ap-3517	208	5	2b	2b	NUM
ap-3517	208	6	)	)	PUNCT
ap-3517	208	7	.	.	PUNCT
ap-3517	209	1	since	since	SCONJ
ap-3517	209	2	det	det	PROPN
ap-3517	209	3	is	be	AUX
ap-3517	209	4	a	a	DET
ap-3517	209	5	homomorphism	homomorphism	NOUN
ap-3517	209	6	on	on	ADP
ap-3517	209	7	w	w	PROPN
ap-3517	209	8	(	(	PUNCT
ap-3517	209	9	bn	bn	NOUN
ap-3517	209	10	)	)	PUNCT
ap-3517	209	11	,	,	PUNCT
ap-3517	209	12	we	we	PRON
ap-3517	209	13	also	also	ADV
ap-3517	209	14	obtain	obtain	VERB
ap-3517	209	15	ϕa(b	ϕa(b	PRON
ap-3517	209	16	)	)	PUNCT
ap-3517	210	1	=	=	PUNCT
ap-3517	210	2	∑	∑	PUNCT
ap-3517	210	3	w∈w	w∈w	X
ap-3517	210	4	(	(	PUNCT
ap-3517	210	5	bn	bn	NOUN
ap-3517	210	6	)	)	PUNCT
ap-3517	210	7	det(w)e2πi〈w(a),b	det(w)e2πi〈w(a),b	PROPN
ap-3517	210	8	〉	〉	NOUN
ap-3517	210	9	=	=	SYM
ap-3517	210	10	∑	∑	PUNCT
ap-3517	210	11	σ∈sn	σ∈sn	PROPN
ap-3517	210	12	det(σ	det(σ	PROPN
ap-3517	210	13	)	)	PUNCT
ap-3517	210	14	n∏	n∏	PROPN
ap-3517	210	15	k=1	k=1	X
ap-3517	210	16	∑	∑	PUNCT
ap-3517	210	17	lk=±1	lk=±1	PROPN
ap-3517	210	18	lke	lke	PROPN
ap-3517	210	19	2πi(lkaσ(k)bk	2πi(lkaσ(k)bk	NUM
ap-3517	210	20	)	)	PUNCT
ap-3517	210	21	=	=	SYM
ap-3517	210	22	∑	∑	PUNCT
ap-3517	210	23	σ∈sn	σ∈sn	PROPN
ap-3517	210	24	det(σ	det(σ	PROPN
ap-3517	210	25	)	)	PUNCT
ap-3517	210	26	n∏	n∏	PROPN
ap-3517	211	1	k=1	k=1	NOUN
ap-3517	211	2	(	(	PUNCT
ap-3517	211	3	e2πiaσ(k)bk	e2πiaσ(k)bk	PROPN
ap-3517	211	4	−	−	PROPN
ap-3517	211	5	e−2πiaσ(k)bk	e−2πiaσ(k)bk	PROPN
ap-3517	211	6	)	)	PUNCT
ap-3517	211	7	=	=	PUNCT
ap-3517	211	8	(	(	PUNCT
ap-3517	211	9	2i)n	2i)n	NUM
ap-3517	211	10	∑	∑	SYM
ap-3517	211	11	σ∈sn	σ∈sn	PROPN
ap-3517	211	12	det(σ	det(σ	PROPN
ap-3517	211	13	)	)	PUNCT
ap-3517	211	14	n∏	n∏	PROPN
ap-3517	211	15	k=1	k=1	PROPN
ap-3517	211	16	sin(2πaσ(k)bk	sin(2πaσ(k)bk	PROPN
ap-3517	211	17	)	)	PUNCT
ap-3517	211	18	=	=	PRON
ap-3517	211	19	(	(	PUNCT
ap-3517	211	20	2i)n	2i)n	NUM
ap-3517	211	21	sin−a	sin−a	NOUN
ap-3517	211	22	(	(	PUNCT
ap-3517	211	23	2b	2b	NUM
ap-3517	211	24	)	)	PUNCT
ap-3517	211	25	.	.	PUNCT
ap-3517	212	1	similar	similar	ADJ
ap-3517	212	2	connections	connection	NOUN
ap-3517	212	3	are	be	AUX
ap-3517	212	4	valid	valid	ADJ
ap-3517	212	5	for	for	ADP
ap-3517	212	6	ss	ss	NOUN
ap-3517	212	7	–	–	PUNCT
ap-3517	212	8	functions	function	NOUN
ap-3517	212	9	and	and	CCONJ
ap-3517	212	10	sl	sl	NOUN
ap-3517	212	11	–	–	PUNCT
ap-3517	212	12	functions	function	NOUN
ap-3517	212	13	,	,	PUNCT
ap-3517	212	14	ϕsa(b	ϕsa(b	PROPN
ap-3517	212	15	)	)	PUNCT
ap-3517	212	16	=	=	PUNCT
ap-3517	213	1	(	(	PUNCT
ap-3517	213	2	2i)n	2i)n	NUM
ap-3517	213	3	sin+	sin+	PROPN
ap-3517	213	4	a	a	PRON
ap-3517	213	5	(	(	PUNCT
ap-3517	213	6	2b	2b	NUM
ap-3517	213	7	)	)	PUNCT
ap-3517	213	8	,	,	PUNCT
ap-3517	213	9	ϕla(b	ϕla(b	PROPN
ap-3517	213	10	)	)	PUNCT
ap-3517	213	11	=	=	SYM
ap-3517	213	12	2n	2n	NUM
ap-3517	213	13	cos−a	cos−a	PROPN
ap-3517	213	14	(	(	PUNCT
ap-3517	213	15	2b	2b	NUM
ap-3517	213	16	)	)	PUNCT
ap-3517	213	17	.	.	PUNCT
ap-3517	214	1	since	since	SCONJ
ap-3517	214	2	lie	lie	NOUN
ap-3517	214	3	algebras	algebras	PROPN
ap-3517	214	4	bn	bn	PROPN
ap-3517	214	5	and	and	CCONJ
ap-3517	214	6	cn	cn	PROPN
ap-3517	214	7	are	be	AUX
ap-3517	214	8	dual	dual	ADJ
ap-3517	214	9	to	to	ADP
ap-3517	214	10	each	each	DET
ap-3517	214	11	other	other	ADJ
ap-3517	215	1	,	,	PUNCT
ap-3517	215	2	we	we	PRON
ap-3517	215	3	can	can	AUX
ap-3517	215	4	deduce	deduce	VERB
ap-3517	215	5	that	that	SCONJ
ap-3517	215	6	the	the	DET
ap-3517	215	7	symmetric	symmetric	ADJ
ap-3517	215	8	and	and	CCONJ
ap-3517	215	9	antisymmetric	antisymmetric	ADJ
ap-3517	215	10	generalizations	generalization	NOUN
ap-3517	215	11	are	be	AUX
ap-3517	215	12	also	also	ADV
ap-3517	215	13	connected	connect	VERB
ap-3517	215	14	to	to	ADP
ap-3517	215	15	the	the	DET
ap-3517	215	16	weyl	weyl	VERB
ap-3517	215	17	-	-	PUNCT
ap-3517	215	18	orbit	orbit	NOUN
ap-3517	215	19	functions	function	NOUN
ap-3517	215	20	of	of	ADP
ap-3517	215	21	cn	cn	PROPN
ap-3517	215	22	.	.	PUNCT
ap-3517	216	1	in	in	ADP
ap-3517	216	2	order	order	NOUN
ap-3517	216	3	to	to	PART
ap-3517	216	4	obtain	obtain	VERB
ap-3517	216	5	explicit	explicit	ADJ
ap-3517	216	6	relations	relation	NOUN
ap-3517	216	7	,	,	PUNCT
ap-3517	216	8	one	one	PRON
ap-3517	216	9	can	can	AUX
ap-3517	216	10	proceed	proceed	VERB
ap-3517	216	11	by	by	ADP
ap-3517	216	12	analogy	analogy	NOUN
ap-3517	216	13	with	with	ADP
ap-3517	216	14	case	case	NOUN
ap-3517	216	15	bn	bn	ADV
ap-3517	216	16	and	and	CCONJ
ap-3517	216	17	introduce	introduce	VERB
ap-3517	216	18	an	an	DET
ap-3517	216	19	orthogonal	orthogonal	ADJ
ap-3517	216	20	basis	basis	NOUN
ap-3517	216	21	{	{	PUNCT
ap-3517	216	22	f1	f1	NOUN
ap-3517	216	23	,	,	PUNCT
ap-3517	216	24	.	.	PUNCT
ap-3517	216	25	.	.	PUNCT
ap-3517	217	1	.	.	PUNCT
ap-3517	218	1	,	,	PUNCT
ap-3517	218	2	fn	fn	X
ap-3517	218	3	}	}	PUNCT
ap-3517	218	4	such	such	ADJ
ap-3517	218	5	that	that	PRON
ap-3517	218	6	for	for	ADP
ap-3517	218	7	i	i	PRON
ap-3517	218	8	=	=	NOUN
ap-3517	218	9	1	1	NUM
ap-3517	218	10	,	,	PUNCT
ap-3517	218	11	.	.	PUNCT
ap-3517	218	12	.	.	PUNCT
ap-3517	219	1	.	.	PUNCT
ap-3517	220	1	,	,	PUNCT
ap-3517	220	2	n−	n−	NOUN
ap-3517	220	3	1	1	NUM
ap-3517	220	4	〈	〈	PROPN
ap-3517	220	5	fi	fi	NOUN
ap-3517	220	6	,	,	PUNCT
ap-3517	220	7	fi	fi	NOUN
ap-3517	220	8	〉	〉	NOUN
ap-3517	220	9	=	=	SYM
ap-3517	220	10	1	1	NUM
ap-3517	220	11	2	2	NUM
ap-3517	220	12	,	,	PUNCT
ap-3517	220	13	αi	αi	NOUN
ap-3517	220	14	=	=	SYM
ap-3517	220	15	fi	fi	NOUN
ap-3517	221	1	−	−	PROPN
ap-3517	221	2	fi+1	fi+1	NOUN
ap-3517	221	3	and	and	CCONJ
ap-3517	221	4	αn	αn	NOUN
ap-3517	222	1	=	=	NOUN
ap-3517	222	2	2fn	2fn	NOUN
ap-3517	222	3	.	.	PUNCT
ap-3517	223	1	we	we	PRON
ap-3517	223	2	denote	denote	VERB
ap-3517	223	3	by	by	ADP
ap-3517	223	4	ãi	ãi	PROPN
ap-3517	223	5	the	the	DET
ap-3517	223	6	coordinates	coordinate	NOUN
ap-3517	223	7	of	of	ADP
ap-3517	223	8	any	any	DET
ap-3517	223	9	point	point	NOUN
ap-3517	223	10	a	a	DET
ap-3517	223	11	∈	∈	PROPN
ap-3517	223	12	rn	rn	NOUN
ap-3517	223	13	with	with	ADP
ap-3517	223	14	respect	respect	NOUN
ap-3517	223	15	to	to	ADP
ap-3517	223	16	the	the	DET
ap-3517	223	17	basis	basis	NOUN
ap-3517	223	18	{	{	PUNCT
ap-3517	223	19	f1	f1	NOUN
ap-3517	223	20	,	,	PUNCT
ap-3517	223	21	.	.	PUNCT
ap-3517	223	22	.	.	PUNCT
ap-3517	223	23	.	.	PUNCT
ap-3517	224	1	,	,	PUNCT
ap-3517	224	2	fn	fn	NOUN
ap-3517	224	3	}	}	PUNCT
ap-3517	224	4	,	,	PUNCT
ap-3517	224	5	i.e.	i.e.	X
ap-3517	224	6	a	a	X
ap-3517	224	7	=	=	SYM
ap-3517	224	8	(	(	PUNCT
ap-3517	224	9	ã1	ã1	PROPN
ap-3517	224	10	,	,	PUNCT
ap-3517	224	11	.	.	PUNCT
ap-3517	224	12	.	.	PUNCT
ap-3517	224	13	.	.	PUNCT
ap-3517	225	1	,	,	PUNCT
ap-3517	225	2	ãn	ãn	VERB
ap-3517	225	3	)	)	PUNCT
ap-3517	225	4	=	=	SYM
ap-3517	225	5	ã1f1	ã1f1	PROPN
ap-3517	225	6	+	+	CCONJ
ap-3517	225	7	·	·	PUNCT
ap-3517	225	8	·	·	PUNCT
ap-3517	225	9	·	·	PUNCT
ap-3517	226	1	+	+	CCONJ
ap-3517	226	2	ãnfn	ãnfn	X
ap-3517	226	3	.	.	PUNCT
ap-3517	227	1	the	the	DET
ap-3517	227	2	generators	generator	NOUN
ap-3517	227	3	ri	ri	PROPN
ap-3517	227	4	,	,	PUNCT
ap-3517	227	5	i	i	NOUN
ap-3517	227	6	=	=	NOUN
ap-3517	227	7	1	1	NUM
ap-3517	227	8	,	,	PUNCT
ap-3517	227	9	.	.	PUNCT
ap-3517	227	10	.	.	PUNCT
ap-3517	227	11	.	.	PUNCT
ap-3517	228	1	,	,	PUNCT
ap-3517	228	2	n−	n−	NOUN
ap-3517	228	3	1	1	NUM
ap-3517	228	4	and	and	CCONJ
ap-3517	228	5	rn	rn	PROPN
ap-3517	228	6	of	of	ADP
ap-3517	228	7	the	the	DET
ap-3517	228	8	weyl	weyl	PROPN
ap-3517	228	9	group	group	NOUN
ap-3517	228	10	w	w	PROPN
ap-3517	228	11	(	(	PUNCT
ap-3517	228	12	cn	cn	PROPN
ap-3517	228	13	)	)	PUNCT
ap-3517	228	14	corresponding	correspond	VERB
ap-3517	228	15	to	to	ADP
ap-3517	228	16	cn	cn	PROPN
ap-3517	228	17	are	be	AUX
ap-3517	228	18	also	also	ADV
ap-3517	228	19	given	give	VERB
ap-3517	228	20	by	by	ADP
ap-3517	228	21	ri(ã1	ri(ã1	NOUN
ap-3517	228	22	,	,	PUNCT
ap-3517	228	23	.	.	PUNCT
ap-3517	228	24	.	.	PUNCT
ap-3517	228	25	.	.	PUNCT
ap-3517	229	1	,	,	PUNCT
ap-3517	229	2	ãi	ãi	PROPN
ap-3517	229	3	,	,	PUNCT
ap-3517	229	4	ãi+1	ãi+1	NOUN
ap-3517	229	5	,	,	PUNCT
ap-3517	229	6	.	.	PUNCT
ap-3517	229	7	.	.	PUNCT
ap-3517	229	8	.	.	PUNCT
ap-3517	230	1	,	,	PUNCT
ap-3517	230	2	ãn	ãn	VERB
ap-3517	230	3	)	)	PUNCT
ap-3517	230	4	=	=	SYM
ap-3517	231	1	(	(	PUNCT
ap-3517	231	2	ã1	ã1	PROPN
ap-3517	231	3	,	,	PUNCT
ap-3517	231	4	.	.	PUNCT
ap-3517	231	5	.	.	PUNCT
ap-3517	232	1	.	.	PUNCT
ap-3517	233	1	,	,	PUNCT
ap-3517	233	2	ãi+1	ãi+1	NOUN
ap-3517	233	3	,	,	PUNCT
ap-3517	233	4	ãi	ãi	PROPN
ap-3517	233	5	,	,	PUNCT
ap-3517	233	6	.	.	PUNCT
ap-3517	233	7	.	.	PUNCT
ap-3517	233	8	.	.	PUNCT
ap-3517	234	1	,	,	PUNCT
ap-3517	234	2	ãn	ãn	PROPN
ap-3517	234	3	)	)	PUNCT
ap-3517	234	4	,	,	PUNCT
ap-3517	234	5	rn(ã1	rn(ã1	NOUN
ap-3517	234	6	,	,	PUNCT
ap-3517	234	7	.	.	PUNCT
ap-3517	234	8	.	.	PUNCT
ap-3517	235	1	.	.	PUNCT
ap-3517	236	1	,	,	PUNCT
ap-3517	236	2	ãn−1	ãn−1	PROPN
ap-3517	236	3	,	,	PUNCT
ap-3517	236	4	ãn	ãn	ADV
ap-3517	236	5	)	)	PUNCT
ap-3517	236	6	=	=	SYM
ap-3517	236	7	(	(	PUNCT
ap-3517	236	8	ã1	ã1	PROPN
ap-3517	236	9	,	,	PUNCT
ap-3517	236	10	.	.	PUNCT
ap-3517	236	11	.	.	PUNCT
ap-3517	236	12	.	.	PUNCT
ap-3517	237	1	,	,	PUNCT
ap-3517	237	2	ãn−1,−ãn	ãn−1,−ãn	NOUN
ap-3517	237	3	)	)	PUNCT
ap-3517	237	4	.	.	PUNCT
ap-3517	238	1	thus	thus	ADV
ap-3517	238	2	,	,	PUNCT
ap-3517	238	3	proceeding	proceed	VERB
ap-3517	238	4	as	as	ADP
ap-3517	238	5	before	before	ADV
ap-3517	238	6	,	,	PUNCT
ap-3517	238	7	we	we	PRON
ap-3517	238	8	derive	derive	VERB
ap-3517	238	9	the	the	DET
ap-3517	238	10	following	following	NOUN
ap-3517	238	11	.	.	PUNCT
ap-3517	239	1	φa(b	φa(b	PUNCT
ap-3517	239	2	)	)	PUNCT
ap-3517	240	1	=	=	SYM
ap-3517	240	2	2n	2n	NUM
ap-3517	240	3	cos+	cos+	PROPN
ap-3517	240	4	a	a	DET
ap-3517	240	5	(	(	PUNCT
ap-3517	240	6	b	b	NOUN
ap-3517	240	7	)	)	PUNCT
ap-3517	240	8	,	,	PUNCT
ap-3517	240	9	ϕa(b	ϕa(b	NUM
ap-3517	240	10	)	)	PUNCT
ap-3517	240	11	=	=	SYM
ap-3517	241	1	(	(	PUNCT
ap-3517	241	2	2i)n	2i)n	NUM
ap-3517	241	3	sin−a	sin−a	NOUN
ap-3517	241	4	(	(	PUNCT
ap-3517	241	5	b	b	NOUN
ap-3517	241	6	)	)	PUNCT
ap-3517	241	7	,	,	PUNCT
ap-3517	241	8	ϕsa(b	ϕsa(b	PROPN
ap-3517	241	9	)	)	PUNCT
ap-3517	242	1	=	=	SYM
ap-3517	242	2	2n	2n	NUM
ap-3517	242	3	cos−a	cos−a	PROPN
ap-3517	242	4	(	(	PUNCT
ap-3517	242	5	b	b	NOUN
ap-3517	242	6	)	)	PUNCT
ap-3517	242	7	,	,	PUNCT
ap-3517	242	8	ϕla(b	ϕla(b	PROPN
ap-3517	242	9	)	)	PUNCT
ap-3517	242	10	=	=	SYM
ap-3517	242	11	(	(	PUNCT
ap-3517	242	12	2i)n	2i)n	NUM
ap-3517	242	13	sin+	sin+	PROPN
ap-3517	242	14	a	a	DET
ap-3517	242	15	(	(	PUNCT
ap-3517	242	16	b	b	NOUN
ap-3517	242	17	)	)	PUNCT
ap-3517	242	18	.	.	PUNCT
ap-3517	243	1	figure	figure	VERB
ap-3517	243	2	3	3	NUM
ap-3517	243	3	.	.	PUNCT
ap-3517	244	1	the	the	DET
ap-3517	244	2	region	region	NOUN
ap-3517	244	3	of	of	ADP
ap-3517	244	4	orthogonality	orthogonality	NOUN
ap-3517	244	5	bounded	bound	VERB
ap-3517	244	6	by	by	ADP
ap-3517	244	7	two	two	NUM
ap-3517	244	8	lines	line	NOUN
ap-3517	244	9	and	and	CCONJ
ap-3517	244	10	parabola	parabola	PROPN
ap-3517	244	11	.	.	PUNCT
ap-3517	244	12	note	note	VERB
ap-3517	244	13	that	that	SCONJ
ap-3517	244	14	the	the	DET
ap-3517	244	15	ss	ss	PROPN
ap-3517	244	16	–	–	PUNCT
ap-3517	244	17	functions	function	NOUN
ap-3517	244	18	are	be	AUX
ap-3517	244	19	related	relate	VERB
ap-3517	244	20	to	to	ADP
ap-3517	244	21	cos−a	cos−a	NOUN
ap-3517	244	22	and	and	CCONJ
ap-3517	244	23	the	the	DET
ap-3517	244	24	sl	sl	NOUN
ap-3517	244	25	–	–	PUNCT
ap-3517	244	26	functions	function	NOUN
ap-3517	244	27	are	be	AUX
ap-3517	244	28	related	relate	VERB
ap-3517	244	29	to	to	ADP
ap-3517	244	30	sin+	sin+	PROPN
ap-3517	244	31	a	a	PRON
ap-3517	244	32	in	in	ADP
ap-3517	244	33	the	the	DET
ap-3517	244	34	case	case	NOUN
ap-3517	244	35	of	of	ADP
ap-3517	244	36	cn	cn	PROPN
ap-3517	244	37	,	,	PUNCT
ap-3517	244	38	whereas	whereas	SCONJ
ap-3517	244	39	the	the	DET
ap-3517	244	40	ss	ss	PROPN
ap-3517	244	41	–	–	PUNCT
ap-3517	244	42	functions	function	NOUN
ap-3517	244	43	correspond	correspond	VERB
ap-3517	244	44	to	to	ADP
ap-3517	244	45	sin+	sin+	PROPN
ap-3517	244	46	a	a	PROPN
ap-3517	244	47	and	and	CCONJ
ap-3517	244	48	the	the	DET
ap-3517	244	49	sl	sl	NOUN
ap-3517	244	50	–	–	PUNCT
ap-3517	244	51	functions	function	NOUN
ap-3517	244	52	correspond	correspond	VERB
ap-3517	244	53	to	to	ADP
ap-3517	244	54	cos−a	cos−a	PROPN
ap-3517	244	55	if	if	SCONJ
ap-3517	244	56	we	we	PRON
ap-3517	244	57	consider	consider	VERB
ap-3517	244	58	the	the	DET
ap-3517	244	59	simple	simple	ADJ
ap-3517	244	60	lie	lie	NOUN
ap-3517	244	61	algebra	algebra	PROPN
ap-3517	244	62	bn	bn	PROPN
ap-3517	244	63	.	.	PUNCT
ap-3517	245	1	this	this	PRON
ap-3517	245	2	follows	follow	VERB
ap-3517	245	3	from	from	ADP
ap-3517	245	4	the	the	DET
ap-3517	245	5	fact	fact	NOUN
ap-3517	245	6	that	that	SCONJ
ap-3517	245	7	the	the	DET
ap-3517	245	8	short	short	ADJ
ap-3517	245	9	(	(	PUNCT
ap-3517	245	10	long	long	ADJ
ap-3517	245	11	)	)	PUNCT
ap-3517	245	12	roots	root	NOUN
ap-3517	245	13	of	of	ADP
ap-3517	245	14	cn	cn	PROPN
ap-3517	245	15	are	be	AUX
ap-3517	245	16	dual	dual	ADJ
ap-3517	245	17	to	to	ADP
ap-3517	245	18	the	the	DET
ap-3517	245	19	long	long	ADJ
ap-3517	245	20	(	(	PUNCT
ap-3517	245	21	short	short	ADJ
ap-3517	245	22	)	)	PUNCT
ap-3517	245	23	roots	root	NOUN
ap-3517	245	24	of	of	ADP
ap-3517	245	25	bn	bn	NOUN
ap-3517	245	26	.	.	PUNCT
ap-3517	246	1	setting	set	VERB
ap-3517	246	2	n	n	NOUN
ap-3517	246	3	=	=	SYM
ap-3517	246	4	2	2	NUM
ap-3517	246	5	,	,	PUNCT
ap-3517	246	6	the	the	DET
ap-3517	246	7	construction	construction	NOUN
ap-3517	246	8	of	of	ADP
ap-3517	246	9	the	the	DET
ap-3517	246	10	polynomials	polynomial	NOUN
ap-3517	246	11	pi,+(k1,k2	pi,+(k1,k2	VERB
ap-3517	246	12	)	)	PUNCT
ap-3517	247	1	≡	≡	PROPN
ap-3517	247	2	cos+	cos+	PROPN
ap-3517	247	3	(	(	PUNCT
ap-3517	247	4	k1,k2	k1,k2	PROPN
ap-3517	247	5	)	)	PUNCT
ap-3517	247	6	,	,	PUNCT
ap-3517	247	7	pi,−(k1,k2	pi,−(k1,k2	PROPN
ap-3517	247	8	)	)	PUNCT
ap-3517	247	9	≡	≡	PROPN
ap-3517	247	10	cos−(k1	cos−(k1	PROPN
ap-3517	247	11	+	+	PROPN
ap-3517	247	12	1,k2	1,k2	NUM
ap-3517	247	13	)	)	PUNCT
ap-3517	247	14	cos−(1,0	cos−(1,0	PROPN
ap-3517	247	15	)	)	PUNCT
ap-3517	247	16	,	,	PUNCT
ap-3517	247	17	piii	piii	X
ap-3517	247	18	,	,	PUNCT
ap-3517	247	19	+	+	CCONJ
ap-3517	247	20	(	(	PUNCT
ap-3517	247	21	k1,k2	k1,k2	PROPN
ap-3517	247	22	)	)	PUNCT
ap-3517	247	23	≡	≡	PROPN
ap-3517	247	24	cos+	cos+	PROPN
ap-3517	247	25	(	(	PUNCT
ap-3517	247	26	k1	k1	NOUN
ap-3517	247	27	+	+	CCONJ
ap-3517	247	28	1	1	NUM
ap-3517	247	29	2	2	NUM
ap-3517	247	30	,	,	PUNCT
ap-3517	247	31	k2	k2	NOUN
ap-3517	247	32	+	+	CCONJ
ap-3517	247	33	1	1	NUM
ap-3517	247	34	2	2	NUM
ap-3517	247	35	)	)	PUNCT
ap-3517	247	36	cos+	cos+	PUNCT
ap-3517	248	1	(	(	PUNCT
ap-3517	248	2	1	1	NUM
ap-3517	248	3	2	2	NUM
ap-3517	248	4	,	,	PUNCT
ap-3517	248	5	1	1	NUM
ap-3517	248	6	2	2	NUM
ap-3517	248	7	)	)	PUNCT
ap-3517	248	8	,	,	PUNCT
ap-3517	248	9	piii	piii	X
ap-3517	248	10	,	,	PUNCT
ap-3517	248	11	−	−	PROPN
ap-3517	248	12	(	(	PUNCT
ap-3517	248	13	k1,k2	k1,k2	PROPN
ap-3517	248	14	)	)	PUNCT
ap-3517	248	15	≡	≡	PROPN
ap-3517	248	16	cos−(k1	cos−(k1	PROPN
ap-3517	249	1	+	+	NUM
ap-3517	249	2	3	3	NUM
ap-3517	249	3	2	2	NUM
ap-3517	249	4	,	,	PUNCT
ap-3517	249	5	k2	k2	NOUN
ap-3517	249	6	+	+	CCONJ
ap-3517	249	7	1	1	NUM
ap-3517	249	8	2	2	NUM
ap-3517	249	9	)	)	PUNCT
ap-3517	249	10	cos−	cos−	PROPN
ap-3517	249	11	(	(	PUNCT
ap-3517	249	12	3	3	NUM
ap-3517	249	13	2	2	NUM
ap-3517	249	14	,	,	PUNCT
ap-3517	249	15	1	1	NUM
ap-3517	249	16	2	2	NUM
ap-3517	249	17	)	)	PUNCT
ap-3517	249	18	labelled	label	VERB
ap-3517	249	19	by	by	ADP
ap-3517	249	20	k1	k1	PROPN
ap-3517	249	21	≥	≥	PROPN
ap-3517	249	22	k2	k2	PROPN
ap-3517	249	23	≥	≥	NOUN
ap-3517	249	24	0	0	NUM
ap-3517	249	25	and	and	CCONJ
ap-3517	249	26	in	in	ADP
ap-3517	249	27	the	the	DET
ap-3517	249	28	variables	variable	NOUN
ap-3517	249	29	x1	x1	PROPN
ap-3517	249	30	≡	≡	PROPN
ap-3517	249	31	cos+	cos+	PROPN
ap-3517	249	32	(	(	PUNCT
ap-3517	249	33	1,0)(x1	1,0)(x1	NUM
ap-3517	249	34	,	,	PUNCT
ap-3517	249	35	x2	x2	PROPN
ap-3517	249	36	)	)	PUNCT
ap-3517	249	37	=	=	SYM
ap-3517	250	1	cos(x1	cos(x1	ADJ
ap-3517	250	2	)	)	PUNCT
ap-3517	250	3	+	+	NUM
ap-3517	250	4	cos(x2	cos(x2	NOUN
ap-3517	250	5	)	)	PUNCT
ap-3517	250	6	,	,	PUNCT
ap-3517	250	7	x2	x2	PROPN
ap-3517	250	8	≡	≡	PROPN
ap-3517	250	9	cos+	cos+	PROPN
ap-3517	250	10	(	(	PUNCT
ap-3517	250	11	1,1)(x1	1,1)(x1	NUM
ap-3517	250	12	,	,	PUNCT
ap-3517	250	13	x2	x2	PROPN
ap-3517	250	14	)	)	PUNCT
ap-3517	250	15	=	=	SYM
ap-3517	250	16	2	2	NUM
ap-3517	250	17	cos(x1	cos(x1	NOUN
ap-3517	250	18	)	)	PUNCT
ap-3517	250	19	cos(x2	cos(x2	NOUN
ap-3517	250	20	)	)	PUNCT
ap-3517	250	21	yields	yield	VERB
ap-3517	250	22	special	special	ADJ
ap-3517	250	23	cases	case	NOUN
ap-3517	250	24	of	of	ADP
ap-3517	250	25	two	two	NUM
ap-3517	250	26	-	-	PUNCT
ap-3517	250	27	variable	variable	NOUN
ap-3517	250	28	polynomials	polynomial	NOUN
ap-3517	250	29	built	build	VERB
ap-3517	250	30	in	in	ADP
ap-3517	250	31	[	[	X
ap-3517	250	32	19–21	19–21	NUM
ap-3517	250	33	]	]	PUNCT
ap-3517	250	34	.	.	PUNCT
ap-3517	251	1	these	these	DET
ap-3517	251	2	polynomials	polynomial	NOUN
ap-3517	251	3	are	be	AUX
ap-3517	251	4	constructed	construct	VERB
ap-3517	251	5	by	by	ADP
ap-3517	251	6	orthogonalization	orthogonalization	NOUN
ap-3517	251	7	of	of	ADP
ap-3517	251	8	monomials	monomial	NOUN
ap-3517	251	9	1	1	NUM
ap-3517	251	10	,	,	PUNCT
ap-3517	251	11	u	u	NOUN
ap-3517	251	12	,	,	PUNCT
ap-3517	251	13	v	v	NOUN
ap-3517	251	14	,	,	PUNCT
ap-3517	251	15	u2	u2	NOUN
ap-3517	251	16	,	,	PUNCT
ap-3517	251	17	uv	uv	NOUN
ap-3517	251	18	,	,	PUNCT
ap-3517	251	19	v2	v2	PROPN
ap-3517	251	20	,	,	PUNCT
ap-3517	251	21	.	.	PUNCT
ap-3517	251	22	.	.	PUNCT
ap-3517	252	1	.	.	PUNCT
ap-3517	253	1	of	of	ADP
ap-3517	253	2	generic	generic	PROPN
ap-3517	253	3	variables	variables	PROPN
ap-3517	253	4	u	u	PROPN
ap-3517	253	5	,	,	PUNCT
ap-3517	253	6	v	v	NOUN
ap-3517	253	7	with	with	ADP
ap-3517	253	8	respect	respect	NOUN
ap-3517	253	9	to	to	ADP
ap-3517	253	10	the	the	DET
ap-3517	253	11	weight	weight	NOUN
ap-3517	253	12	function	function	NOUN
ap-3517	253	13	(	(	PUNCT
ap-3517	253	14	1−	1−	NUM
ap-3517	253	15	u+	u+	NOUN
ap-3517	253	16	v)α(1	v)α(1	PROPN
ap-3517	253	17	+	+	CCONJ
ap-3517	253	18	u+	u+	NOUN
ap-3517	253	19	v)β(u2	v)β(u2	PROPN
ap-3517	253	20	−	−	PROPN
ap-3517	253	21	4v)γ	4v)γ	NUM
ap-3517	253	22	in	in	ADP
ap-3517	253	23	the	the	DET
ap-3517	253	24	domain	domain	NOUN
ap-3517	253	25	bounded	bound	VERB
ap-3517	253	26	by	by	ADP
ap-3517	253	27	the	the	DET
ap-3517	253	28	curves	curve	NOUN
ap-3517	254	1	1−	1−	NUM
ap-3517	254	2	u+	u+	NOUN
ap-3517	254	3	v	v	NOUN
ap-3517	254	4	=	=	SYM
ap-3517	254	5	0	0	NUM
ap-3517	254	6	,	,	PUNCT
ap-3517	254	7	1	1	NUM
ap-3517	254	8	+	+	NUM
ap-3517	254	9	u	u	NOUN
ap-3517	254	10	+	+	X
ap-3517	254	11	v	v	NOUN
ap-3517	254	12	=	=	SYM
ap-3517	254	13	0	0	NUM
ap-3517	254	14	and	and	CCONJ
ap-3517	254	15	u2	u2	PROPN
ap-3517	254	16	−	−	PROPN
ap-3517	254	17	4v	4v	NUM
ap-3517	254	18	=	=	SYM
ap-3517	254	19	0	0	NUM
ap-3517	254	20	,	,	PUNCT
ap-3517	254	21	see	see	VERB
ap-3517	254	22	fig	fig	NOUN
ap-3517	254	23	.	.	PUNCT
ap-3517	255	1	3	3	X
ap-3517	255	2	.	.	X
ap-3517	255	3	the	the	DET
ap-3517	255	4	parameters	parameter	NOUN
ap-3517	255	5	α	α	PRON
ap-3517	255	6	,	,	PUNCT
ap-3517	255	7	β	β	X
ap-3517	255	8	,	,	PUNCT
ap-3517	255	9	γ	γ	NOUN
ap-3517	255	10	are	be	AUX
ap-3517	255	11	required	require	VERB
ap-3517	255	12	to	to	PART
ap-3517	255	13	satisfy	satisfy	VERB
ap-3517	255	14	the	the	DET
ap-3517	255	15	conditions	condition	NOUN
ap-3517	255	16	α	α	NOUN
ap-3517	255	17	,	,	PUNCT
ap-3517	255	18	β	β	X
ap-3517	255	19	,	,	PUNCT
ap-3517	255	20	γ	γ	X
ap-3517	255	21	>	>	X
ap-3517	255	22	−1	−1	NOUN
ap-3517	255	23	,	,	PUNCT
ap-3517	255	24	α+	α+	PUNCT
ap-3517	255	25	γ	γ	X
ap-3517	255	26	+	+	NOUN
ap-3517	255	27	3	3	NUM
ap-3517	255	28	2	2	NUM
ap-3517	255	29	>	>	SYM
ap-3517	255	30	0	0	PUNCT
ap-3517	256	1	and	and	CCONJ
ap-3517	256	2	β	β	X
ap-3517	256	3	+	+	CCONJ
ap-3517	256	4	γ	γ	X
ap-3517	256	5	+	+	X
ap-3517	256	6	3	3	NUM
ap-3517	256	7	2	2	NUM
ap-3517	256	8	>	>	X
ap-3517	256	9	0	0	NUM
ap-3517	256	10	.	.	PUNCT
ap-3517	257	1	the	the	DET
ap-3517	257	2	resulting	result	VERB
ap-3517	257	3	polynomials	polynomial	NOUN
ap-3517	257	4	with	with	ADP
ap-3517	257	5	the	the	DET
ap-3517	257	6	highest	high	ADJ
ap-3517	257	7	term	term	NOUN
ap-3517	257	8	um−kvk	um−kvk	NOUN
ap-3517	257	9	are	be	AUX
ap-3517	257	10	denoted	denote	VERB
ap-3517	257	11	by	by	ADP
ap-3517	257	12	pα	pα	PROPN
ap-3517	257	13	,	,	PUNCT
ap-3517	257	14	β	β	NOUN
ap-3517	257	15	,	,	PUNCT
ap-3517	257	16	γm	γm	X
ap-3517	257	17	,	,	PUNCT
ap-3517	257	18	k	k	PROPN
ap-3517	257	19	(	(	PUNCT
ap-3517	257	20	u	u	NOUN
ap-3517	257	21	,	,	PUNCT
ap-3517	257	22	v	v	NOUN
ap-3517	257	23	)	)	PUNCT
ap-3517	257	24	,	,	PUNCT
ap-3517	257	25	where	where	SCONJ
ap-3517	257	26	m	m	PROPN
ap-3517	257	27	≥	≥	VERB
ap-3517	257	28	k	k	X
ap-3517	257	29	≥	≥	NUM
ap-3517	257	30	0	0	NUM
ap-3517	257	31	.	.	PUNCT
ap-3517	258	1	the	the	DET
ap-3517	258	2	polynomial	polynomial	ADJ
ap-3517	258	3	variables	variable	NOUN
ap-3517	258	4	x1	x1	PROPN
ap-3517	258	5	and	and	CCONJ
ap-3517	258	6	x2	x2	PROPN
ap-3517	258	7	are	be	AUX
ap-3517	258	8	related	relate	VERB
ap-3517	258	9	to	to	ADP
ap-3517	258	10	the	the	DET
ap-3517	258	11	variables	variable	NOUN
ap-3517	258	12	u	u	NOUN
ap-3517	258	13	and	and	CCONJ
ap-3517	258	14	v	v	NOUN
ap-3517	258	15	of	of	ADP
ap-3517	258	16	[	[	X
ap-3517	258	17	19–21	19–21	NUM
ap-3517	258	18	]	]	PUNCT
ap-3517	258	19	by	by	ADP
ap-3517	258	20	x1	x1	PROPN
ap-3517	258	21	=	=	SYM
ap-3517	258	22	u	u	PROPN
ap-3517	258	23	,	,	PUNCT
ap-3517	258	24	x2	x2	PROPN
ap-3517	258	25	=	=	PUNCT
ap-3517	258	26	2v	2v	PROPN
ap-3517	258	27	and	and	CCONJ
ap-3517	258	28	it	it	PRON
ap-3517	258	29	can	can	AUX
ap-3517	258	30	easily	easily	ADV
ap-3517	258	31	be	be	AUX
ap-3517	258	32	shown	show	VERB
ap-3517	258	33	that	that	SCONJ
ap-3517	258	34	•	•	NUM
ap-3517	258	35	pi,+(k1,k2	pi,+(k1,k2	NOUN
ap-3517	258	36	)	)	PUNCT
ap-3517	258	37	coincides	coincide	NOUN
ap-3517	258	38	,	,	PUNCT
ap-3517	258	39	up	up	ADP
ap-3517	258	40	to	to	ADP
ap-3517	258	41	a	a	DET
ap-3517	258	42	constant	constant	ADJ
ap-3517	258	43	,	,	PUNCT
ap-3517	258	44	with	with	ADP
ap-3517	258	45	pα	pα	PROPN
ap-3517	258	46	,	,	PUNCT
ap-3517	258	47	β	β	NOUN
ap-3517	258	48	,	,	PUNCT
ap-3517	258	49	γk1,k2	γk1,k2	NOUN
ap-3517	258	50	(	(	PUNCT
ap-3517	258	51	u	u	NOUN
ap-3517	258	52	,	,	PUNCT
ap-3517	258	53	v	v	NOUN
ap-3517	258	54	)	)	PUNCT
ap-3517	258	55	for	for	ADP
ap-3517	258	56	α	α	NOUN
ap-3517	258	57	=	=	SYM
ap-3517	258	58	β	β	X
ap-3517	258	59	=	=	PUNCT
ap-3517	258	60	γ	γ	X
ap-3517	258	61	=	=	SYM
ap-3517	258	62	−	−	PROPN
ap-3517	258	63	1	1	NUM
ap-3517	258	64	2	2	NUM
ap-3517	258	65	,	,	PUNCT
ap-3517	258	66	•	•	NOUN
ap-3517	258	67	piii	piii	NOUN
ap-3517	258	68	,	,	PUNCT
ap-3517	258	69	+	+	CCONJ
ap-3517	258	70	(	(	PUNCT
ap-3517	258	71	k1,k2	k1,k2	PROPN
ap-3517	258	72	)	)	PUNCT
ap-3517	258	73	coincides	coincide	NOUN
ap-3517	258	74	,	,	PUNCT
ap-3517	258	75	up	up	ADP
ap-3517	258	76	to	to	ADP
ap-3517	258	77	a	a	DET
ap-3517	258	78	constant	constant	ADJ
ap-3517	258	79	,	,	PUNCT
ap-3517	258	80	with	with	ADP
ap-3517	258	81	pα	pα	PROPN
ap-3517	258	82	,	,	PUNCT
ap-3517	258	83	β	β	NOUN
ap-3517	258	84	,	,	PUNCT
ap-3517	258	85	γk1,k2	γk1,k2	NOUN
ap-3517	258	86	(	(	PUNCT
ap-3517	258	87	u	u	NOUN
ap-3517	258	88	,	,	PUNCT
ap-3517	258	89	v	v	NOUN
ap-3517	258	90	)	)	PUNCT
ap-3517	258	91	for	for	ADP
ap-3517	258	92	α	α	NOUN
ap-3517	258	93	=	=	SYM
ap-3517	258	94	γ	γ	X
ap-3517	258	95	=	=	SYM
ap-3517	258	96	−	−	PROPN
ap-3517	258	97	1	1	NUM
ap-3517	258	98	2	2	NUM
ap-3517	258	99	and	and	CCONJ
ap-3517	258	100	β	β	X
ap-3517	258	101	=	=	NOUN
ap-3517	258	102	1	1	NUM
ap-3517	258	103	2	2	NUM
ap-3517	258	104	,	,	PUNCT
ap-3517	258	105	288	288	NUM
ap-3517	258	106	vol	vol	NOUN
ap-3517	258	107	.	.	PUNCT
ap-3517	259	1	56	56	NUM
ap-3517	259	2	no	no	NOUN
ap-3517	259	3	.	.	PUNCT
ap-3517	260	1	4/2016	4/2016	PROPN
ap-3517	260	2	weyl	weyl	VERB
ap-3517	260	3	orbit	orbit	NOUN
ap-3517	260	4	functions	function	NOUN
ap-3517	260	5	and	and	CCONJ
ap-3517	260	6	(	(	PUNCT
ap-3517	260	7	anti)symmetric	anti)symmetric	ADJ
ap-3517	260	8	trigonometric	trigonometric	ADJ
ap-3517	260	9	functions	function	NOUN
ap-3517	260	10	•	•	ADP
ap-3517	260	11	pi,−(k1,k2	pi,−(k1,k2	NOUN
ap-3517	260	12	)	)	PUNCT
ap-3517	260	13	coincides	coincide	NOUN
ap-3517	260	14	,	,	PUNCT
ap-3517	260	15	up	up	ADP
ap-3517	260	16	to	to	ADP
ap-3517	260	17	a	a	DET
ap-3517	260	18	constant	constant	ADJ
ap-3517	260	19	,	,	PUNCT
ap-3517	260	20	with	with	ADP
ap-3517	260	21	pα	pα	PROPN
ap-3517	260	22	,	,	PUNCT
ap-3517	260	23	β	β	NOUN
ap-3517	260	24	,	,	PUNCT
ap-3517	260	25	γk1,k2	γk1,k2	NOUN
ap-3517	260	26	(	(	PUNCT
ap-3517	260	27	u	u	NOUN
ap-3517	260	28	,	,	PUNCT
ap-3517	260	29	v	v	NOUN
ap-3517	260	30	)	)	PUNCT
ap-3517	260	31	for	for	ADP
ap-3517	260	32	α	α	NOUN
ap-3517	260	33	=	=	SYM
ap-3517	260	34	β	β	X
ap-3517	260	35	=	=	PUNCT
ap-3517	260	36	−	−	PROPN
ap-3517	260	37	1	1	NUM
ap-3517	260	38	2	2	NUM
ap-3517	260	39	and	and	CCONJ
ap-3517	260	40	γ	γ	X
ap-3517	260	41	=	=	SYM
ap-3517	260	42	1	1	NUM
ap-3517	260	43	2	2	NUM
ap-3517	260	44	,	,	PUNCT
ap-3517	260	45	•	•	NOUN
ap-3517	260	46	piii	piii	NOUN
ap-3517	260	47	,	,	PUNCT
ap-3517	260	48	−	−	PROPN
ap-3517	260	49	(	(	PUNCT
ap-3517	260	50	k1,k2	k1,k2	PROPN
ap-3517	260	51	)	)	PUNCT
ap-3517	260	52	coincides	coincide	NOUN
ap-3517	260	53	,	,	PUNCT
ap-3517	260	54	up	up	ADP
ap-3517	260	55	to	to	ADP
ap-3517	260	56	a	a	DET
ap-3517	260	57	constant	constant	ADJ
ap-3517	260	58	,	,	PUNCT
ap-3517	260	59	with	with	ADP
ap-3517	260	60	pα	pα	PROPN
ap-3517	260	61	,	,	PUNCT
ap-3517	260	62	β	β	NOUN
ap-3517	260	63	,	,	PUNCT
ap-3517	260	64	γk1,k2	γk1,k2	NOUN
ap-3517	260	65	(	(	PUNCT
ap-3517	260	66	u	u	NOUN
ap-3517	260	67	,	,	PUNCT
ap-3517	260	68	v	v	NOUN
ap-3517	260	69	)	)	PUNCT
ap-3517	260	70	for	for	ADP
ap-3517	260	71	α	α	NOUN
ap-3517	260	72	=	=	SYM
ap-3517	261	1	−	−	PROPN
ap-3517	261	2	1	1	NUM
ap-3517	261	3	2	2	NUM
ap-3517	261	4	and	and	CCONJ
ap-3517	261	5	β	β	X
ap-3517	261	6	=	=	SYM
ap-3517	261	7	γ	γ	X
ap-3517	261	8	=	=	SYM
ap-3517	261	9	1	1	NUM
ap-3517	261	10	2	2	NUM
ap-3517	261	11	.	.	PUNCT
ap-3517	262	1	4	4	X
ap-3517	262	2	.	.	X
ap-3517	262	3	concluding	conclude	VERB
ap-3517	262	4	remarks	remark	NOUN
ap-3517	262	5	(	(	PUNCT
ap-3517	262	6	1	1	NUM
ap-3517	262	7	.	.	PUNCT
ap-3517	262	8	)	)	PUNCT
ap-3517	263	1	symmetric	symmetric	ADJ
ap-3517	263	2	and	and	CCONJ
ap-3517	263	3	antisymmetric	antisymmetric	ADJ
ap-3517	263	4	cosine	cosine	NOUN
ap-3517	263	5	functions	function	NOUN
ap-3517	263	6	can	can	AUX
ap-3517	263	7	be	be	AUX
ap-3517	263	8	used	use	VERB
ap-3517	263	9	to	to	PART
ap-3517	263	10	construct	construct	VERB
ap-3517	263	11	multivariate	multivariate	NOUN
ap-3517	263	12	orthogonal	orthogonal	ADJ
ap-3517	263	13	polynomials	polynomial	NOUN
ap-3517	263	14	analogous	analogous	ADJ
ap-3517	263	15	to	to	ADP
ap-3517	263	16	the	the	DET
ap-3517	263	17	chebyshev	chebyshev	NOUN
ap-3517	263	18	polynomials	polynomial	NOUN
ap-3517	263	19	of	of	ADP
ap-3517	263	20	the	the	DET
ap-3517	263	21	first	first	ADJ
ap-3517	263	22	and	and	CCONJ
ap-3517	263	23	third	third	ADJ
ap-3517	263	24	kind	kind	NOUN
ap-3517	263	25	.	.	PUNCT
ap-3517	264	1	the	the	DET
ap-3517	264	2	method	method	NOUN
ap-3517	264	3	of	of	ADP
ap-3517	264	4	construction	construction	NOUN
ap-3517	264	5	is	be	AUX
ap-3517	264	6	based	base	VERB
ap-3517	264	7	on	on	ADP
ap-3517	264	8	decomposition	decomposition	NOUN
ap-3517	264	9	of	of	ADP
ap-3517	264	10	the	the	DET
ap-3517	264	11	products	product	NOUN
ap-3517	264	12	of	of	ADP
ap-3517	264	13	these	these	DET
ap-3517	264	14	functions	function	NOUN
ap-3517	264	15	and	and	CCONJ
ap-3517	264	16	is	be	AUX
ap-3517	264	17	fully	fully	ADV
ap-3517	264	18	described	describe	VERB
ap-3517	264	19	in	in	ADP
ap-3517	264	20	[	[	X
ap-3517	264	21	7	7	NUM
ap-3517	264	22	]	]	PUNCT
ap-3517	264	23	.	.	PUNCT
ap-3517	265	1	to	to	PART
ap-3517	265	2	build	build	VERB
ap-3517	265	3	polynomials	polynomial	NOUN
ap-3517	265	4	analogous	analogous	ADJ
ap-3517	265	5	to	to	ADP
ap-3517	265	6	the	the	DET
ap-3517	265	7	chebyshev	chebyshev	NOUN
ap-3517	265	8	polynomials	polynomial	NOUN
ap-3517	265	9	of	of	ADP
ap-3517	265	10	the	the	DET
ap-3517	265	11	second	second	ADJ
ap-3517	265	12	and	and	CCONJ
ap-3517	265	13	fourth	fourth	ADJ
ap-3517	265	14	kind	kind	NOUN
ap-3517	265	15	,	,	PUNCT
ap-3517	265	16	it	it	PRON
ap-3517	265	17	seems	seem	VERB
ap-3517	265	18	that	that	SCONJ
ap-3517	265	19	the	the	DET
ap-3517	265	20	symmetric	symmetric	ADJ
ap-3517	265	21	and	and	CCONJ
ap-3517	265	22	antisymmetric	antisymmetric	ADJ
ap-3517	265	23	generalizations	generalization	NOUN
ap-3517	265	24	of	of	ADP
ap-3517	265	25	sine	sine	ADJ
ap-3517	265	26	functions	function	NOUN
ap-3517	265	27	have	have	VERB
ap-3517	265	28	to	to	PART
ap-3517	265	29	be	be	AUX
ap-3517	265	30	analysed	analyse	VERB
ap-3517	265	31	.	.	PUNCT
ap-3517	266	1	this	this	DET
ap-3517	266	2	hypothesis	hypothesis	NOUN
ap-3517	266	3	is	be	AUX
ap-3517	266	4	supported	support	VERB
ap-3517	266	5	by	by	ADP
ap-3517	266	6	the	the	DET
ap-3517	266	7	decomposition	decomposition	NOUN
ap-3517	266	8	of	of	ADP
ap-3517	266	9	the	the	DET
ap-3517	266	10	products	product	NOUN
ap-3517	266	11	of	of	ADP
ap-3517	266	12	two	two	NUM
ap-3517	266	13	-	-	PUNCT
ap-3517	266	14	dimensional	dimensional	ADJ
ap-3517	266	15	sine	sine	ADJ
ap-3517	266	16	functions	function	NOUN
ap-3517	266	17	which	which	PRON
ap-3517	266	18	can	can	AUX
ap-3517	266	19	be	be	AUX
ap-3517	266	20	found	find	VERB
ap-3517	266	21	in	in	ADP
ap-3517	266	22	[	[	X
ap-3517	266	23	11	11	NUM
ap-3517	266	24	]	]	PUNCT
ap-3517	266	25	.	.	PUNCT
ap-3517	267	1	(	(	PUNCT
ap-3517	267	2	2	2	NUM
ap-3517	267	3	.	.	PUNCT
ap-3517	267	4	)	)	PUNCT
ap-3517	268	1	another	another	DET
ap-3517	268	2	approach	approach	NOUN
ap-3517	268	3	to	to	ADP
ap-3517	268	4	generalization	generalization	NOUN
ap-3517	268	5	of	of	ADP
ap-3517	268	6	the	the	DET
ap-3517	268	7	multivariate	multivariate	NOUN
ap-3517	268	8	polynomials	polynomial	NOUN
ap-3517	268	9	related	relate	VERB
ap-3517	268	10	to	to	ADP
ap-3517	268	11	the	the	DET
ap-3517	268	12	weyl	weyl	VERB
ap-3517	268	13	-	-	PUNCT
ap-3517	268	14	orbit	orbit	NOUN
ap-3517	268	15	functions	function	NOUN
ap-3517	268	16	stems	stem	VERB
ap-3517	268	17	from	from	ADP
ap-3517	268	18	the	the	DET
ap-3517	268	19	shifted	shift	VERB
ap-3517	268	20	orthogonality	orthogonality	NOUN
ap-3517	268	21	of	of	ADP
ap-3517	268	22	the	the	DET
ap-3517	268	23	orbit	orbit	NOUN
ap-3517	268	24	functions	function	NOUN
ap-3517	268	25	developed	develop	VERB
ap-3517	268	26	in	in	ADP
ap-3517	268	27	[	[	X
ap-3517	268	28	2	2	NUM
ap-3517	268	29	]	]	PUNCT
ap-3517	268	30	.	.	PUNCT
ap-3517	269	1	this	this	DET
ap-3517	269	2	generalization	generalization	NOUN
ap-3517	269	3	encompasses	encompass	VERB
ap-3517	269	4	shifts	shift	NOUN
ap-3517	269	5	of	of	ADP
ap-3517	269	6	the	the	DET
ap-3517	269	7	points	point	NOUN
ap-3517	269	8	of	of	ADP
ap-3517	269	9	the	the	DET
ap-3517	269	10	sets	set	NOUN
ap-3517	269	11	over	over	ADP
ap-3517	269	12	which	which	PRON
ap-3517	269	13	the	the	DET
ap-3517	269	14	functions	function	NOUN
ap-3517	269	15	are	be	AUX
ap-3517	269	16	discretely	discretely	ADV
ap-3517	269	17	orthogonal	orthogonal	ADJ
ap-3517	269	18	,	,	PUNCT
ap-3517	269	19	and	and	CCONJ
ap-3517	269	20	also	also	ADV
ap-3517	269	21	shifts	shift	NOUN
ap-3517	269	22	of	of	ADP
ap-3517	269	23	the	the	DET
ap-3517	269	24	labeling	labeling	NOUN
ap-3517	269	25	weights	weight	NOUN
ap-3517	269	26	.	.	PUNCT
ap-3517	270	1	as	as	ADP
ap-3517	270	2	a	a	DET
ap-3517	270	3	special	special	ADJ
ap-3517	270	4	case	case	NOUN
ap-3517	270	5	it	it	PRON
ap-3517	270	6	contains	contain	VERB
ap-3517	270	7	for	for	ADP
ap-3517	270	8	a1	a1	NOUN
ap-3517	270	9	all	all	DET
ap-3517	270	10	four	four	NUM
ap-3517	270	11	kinds	kind	NOUN
ap-3517	270	12	of	of	ADP
ap-3517	270	13	chebyshev	chebyshev	NOUN
ap-3517	270	14	polynomials	polynomial	NOUN
ap-3517	270	15	.	.	PUNCT
ap-3517	271	1	the	the	DET
ap-3517	271	2	existence	existence	NOUN
ap-3517	271	3	of	of	ADP
ap-3517	271	4	analogous	analogous	ADJ
ap-3517	271	5	polynomials	polynomial	NOUN
ap-3517	271	6	obtained	obtain	VERB
ap-3517	271	7	through	through	ADP
ap-3517	271	8	this	this	DET
ap-3517	271	9	approach	approach	NOUN
ap-3517	271	10	and	and	CCONJ
ap-3517	271	11	their	their	PRON
ap-3517	271	12	relations	relation	NOUN
ap-3517	271	13	to	to	PART
ap-3517	271	14	already	already	ADV
ap-3517	271	15	known	know	VERB
ap-3517	271	16	generalizations	generalization	NOUN
ap-3517	271	17	deserves	deserve	VERB
ap-3517	271	18	further	further	ADJ
ap-3517	271	19	study	study	NOUN
ap-3517	271	20	.	.	PUNCT
ap-3517	272	1	(	(	PUNCT
ap-3517	272	2	3	3	NUM
ap-3517	272	3	.	.	PUNCT
ap-3517	272	4	)	)	PUNCT
ap-3517	273	1	besides	besides	SCONJ
ap-3517	273	2	the	the	DET
ap-3517	273	3	methods	method	NOUN
ap-3517	273	4	of	of	ADP
ap-3517	273	5	polynomial	polynomial	ADJ
ap-3517	273	6	interpolation	interpolation	NOUN
ap-3517	273	7	and	and	CCONJ
ap-3517	273	8	numerical	numerical	ADJ
ap-3517	273	9	integration	integration	NOUN
ap-3517	273	10	,	,	PUNCT
ap-3517	273	11	the	the	DET
ap-3517	273	12	chebyshev	chebyshev	NOUN
ap-3517	273	13	polynomials	polynomial	NOUN
ap-3517	273	14	are	be	AUX
ap-3517	273	15	connected	connect	VERB
ap-3517	273	16	to	to	ADP
ap-3517	273	17	other	other	ADJ
ap-3517	273	18	efficient	efficient	ADJ
ap-3517	273	19	methods	method	NOUN
ap-3517	273	20	in	in	ADP
ap-3517	273	21	numerical	numerical	ADJ
ap-3517	273	22	analysis	analysis	NOUN
ap-3517	273	23	such	such	ADJ
ap-3517	273	24	as	as	ADP
ap-3517	273	25	numerical	numerical	ADJ
ap-3517	273	26	solutions	solution	NOUN
ap-3517	273	27	of	of	ADP
ap-3517	273	28	differential	differential	ADJ
ap-3517	273	29	equations	equation	NOUN
ap-3517	273	30	,	,	PUNCT
ap-3517	273	31	solutions	solution	NOUN
ap-3517	273	32	of	of	ADP
ap-3517	273	33	difference	difference	NOUN
ap-3517	273	34	equations	equation	NOUN
ap-3517	273	35	,	,	PUNCT
ap-3517	273	36	fast	fast	ADJ
ap-3517	273	37	transforms	transform	VERB
ap-3517	273	38	and	and	CCONJ
ap-3517	273	39	spectral	spectral	ADJ
ap-3517	273	40	methods	method	NOUN
ap-3517	273	41	.	.	PUNCT
ap-3517	274	1	the	the	DET
ap-3517	274	2	existence	existence	NOUN
ap-3517	274	3	and	and	CCONJ
ap-3517	274	4	the	the	DET
ap-3517	274	5	form	form	NOUN
ap-3517	274	6	of	of	ADP
ap-3517	274	7	these	these	DET
ap-3517	274	8	methods	method	NOUN
ap-3517	274	9	,	,	PUNCT
ap-3517	274	10	connected	connect	VERB
ap-3517	274	11	in	in	ADP
ap-3517	274	12	a	a	DET
ap-3517	274	13	multivariate	multivariate	NOUN
ap-3517	274	14	setting	set	VERB
ap-3517	274	15	to	to	ADP
ap-3517	274	16	weyl	weyl	VERB
ap-3517	274	17	-	-	PUNCT
ap-3517	274	18	orbit	orbit	NOUN
ap-3517	274	19	functions	function	NOUN
ap-3517	274	20	,	,	PUNCT
ap-3517	274	21	are	be	AUX
ap-3517	274	22	open	open	ADJ
ap-3517	274	23	problems	problem	NOUN
ap-3517	274	24	.	.	PUNCT
ap-3517	275	1	acknowledgements	acknowledgement	NOUN
ap-3517	275	2	the	the	DET
ap-3517	275	3	authors	author	NOUN
ap-3517	275	4	gratefully	gratefully	ADV
ap-3517	275	5	acknowledge	acknowledge	VERB
ap-3517	275	6	the	the	DET
ap-3517	275	7	support	support	NOUN
ap-3517	275	8	received	receive	VERB
ap-3517	275	9	for	for	ADP
ap-3517	275	10	this	this	DET
ap-3517	275	11	work	work	NOUN
ap-3517	275	12	from	from	ADP
ap-3517	275	13	rvo68407700	rvo68407700	NOUN
ap-3517	275	14	.	.	PUNCT
ap-3517	276	1	this	this	DET
ap-3517	276	2	work	work	NOUN
ap-3517	276	3	is	be	AUX
ap-3517	276	4	supported	support	VERB
ap-3517	276	5	by	by	ADP
ap-3517	276	6	the	the	DET
ap-3517	276	7	european	european	PROPN
ap-3517	276	8	union	union	PROPN
ap-3517	276	9	through	through	ADP
ap-3517	276	10	the	the	DET
ap-3517	276	11	project	project	NOUN
ap-3517	276	12	support	support	NOUN
ap-3517	276	13	of	of	ADP
ap-3517	276	14	inter	inter	ADJ
ap-3517	276	15	-	-	ADJ
ap-3517	276	16	sectoral	sectoral	ADJ
ap-3517	276	17	mobility	mobility	NOUN
ap-3517	276	18	and	and	CCONJ
ap-3517	276	19	quality	quality	NOUN
ap-3517	276	20	enhancement	enhancement	NOUN
ap-3517	276	21	of	of	ADP
ap-3517	276	22	research	research	NOUN
ap-3517	276	23	teams	team	NOUN
ap-3517	276	24	at	at	ADP
ap-3517	276	25	the	the	DET
ap-3517	276	26	czech	czech	PROPN
ap-3517	276	27	technical	technical	PROPN
ap-3517	276	28	university	university	PROPN
ap-3517	276	29	in	in	ADP
ap-3517	276	30	prague	prague	NOUN
ap-3517	276	31	cz.1.07/2.3.00/30.0034	cz.1.07/2.3.00/30.0034	PROPN
ap-3517	276	32	.	.	PUNCT
ap-3517	277	1	references	reference	NOUN
ap-3517	277	2	[	[	X
ap-3517	277	3	1	1	NUM
ap-3517	277	4	]	]	X
ap-3517	277	5	n.	n.	NOUN
ap-3517	277	6	bourbaki	bourbaki	PROPN
ap-3517	277	7	,	,	PUNCT
ap-3517	277	8	groupes	groupe	NOUN
ap-3517	277	9	et	et	NOUN
ap-3517	277	10	algèbres	algèbre	NOUN
ap-3517	277	11	de	de	ADP
ap-3517	277	12	lie	lie	NOUN
ap-3517	277	13	,	,	PUNCT
ap-3517	277	14	chapiters	chapiter	VERB
ap-3517	277	15	iv	iv	NUM
ap-3517	277	16	,	,	PUNCT
ap-3517	277	17	v	v	NOUN
ap-3517	277	18	,	,	PUNCT
ap-3517	277	19	vi	vi	PROPN
ap-3517	277	20	,	,	PUNCT
ap-3517	277	21	hermann	hermann	PROPN
ap-3517	277	22	,	,	PUNCT
ap-3517	277	23	paris	paris	PROPN
ap-3517	277	24	1968	1968	NUM
ap-3517	277	25	.	.	PUNCT
ap-3517	278	1	[	[	X
ap-3517	278	2	2	2	X
ap-3517	278	3	]	]	PUNCT
ap-3517	278	4	t.	t.	PROPN
ap-3517	278	5	czyżycki	czyżycki	PROPN
ap-3517	278	6	,	,	PUNCT
ap-3517	278	7	j.	j.	PROPN
ap-3517	278	8	hrivnák	hrivnák	PROPN
ap-3517	278	9	,	,	PUNCT
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ap-3517	278	16	affine	affine	NOUN
ap-3517	278	17	weyl	weyl	VERB
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ap-3517	278	19	,	,	PUNCT
ap-3517	278	20	j.	j.	PROPN
ap-3517	278	21	math	math	PROPN
ap-3517	278	22	.	.	PUNCT
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ap-3517	279	2	.	.	PUNCT
ap-3517	280	1	55	55	NUM
ap-3517	280	2	(	(	PUNCT
ap-3517	280	3	2014	2014	NUM
ap-3517	280	4	)	)	PUNCT
ap-3517	280	5	,	,	PUNCT
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ap-3517	280	7	,	,	PUNCT
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ap-3517	280	9	.	.	PUNCT
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ap-3517	281	2	3	3	X
ap-3517	281	3	]	]	X
ap-3517	281	4	c.	c.	PROPN
ap-3517	281	5	f.	f.	PROPN
ap-3517	281	6	dunkl	dunkl	PROPN
ap-3517	281	7	,	,	PUNCT
ap-3517	281	8	y.	y.	PROPN
ap-3517	281	9	xu	xu	PROPN
ap-3517	281	10	,	,	PUNCT
ap-3517	281	11	orthogonal	orthogonal	ADJ
ap-3517	281	12	polynomials	polynomial	NOUN
ap-3517	281	13	of	of	ADP
ap-3517	281	14	several	several	ADJ
ap-3517	281	15	variables	variable	NOUN
ap-3517	281	16	,	,	PUNCT
ap-3517	281	17	cambridge	cambridge	PROPN
ap-3517	281	18	university	university	PROPN
ap-3517	281	19	press	press	PROPN
ap-3517	281	20	,	,	PUNCT
ap-3517	281	21	cambridge	cambridge	PROPN
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ap-3517	281	24	,	,	PUNCT
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ap-3517	281	26	/	/	SYM
ap-3517	281	27	cbo9781107786134	cbo9781107786134	NOUN
ap-3517	281	28	.	.	PUNCT
ap-3517	282	1	[	[	X
ap-3517	282	2	4	4	NUM
ap-3517	282	3	]	]	PUNCT
ap-3517	282	4	a.	a.	NOUN
ap-3517	282	5	erdélyi	erdélyi	PROPN
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ap-3517	282	7	w.	w.	PROPN
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ap-3517	282	9	,	,	PUNCT
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ap-3517	282	12	,	,	PUNCT
ap-3517	282	13	f.	f.	PROPN
ap-3517	282	14	g.	g.	PROPN
ap-3517	282	15	tricomi	tricomi	PROPN
ap-3517	282	16	,	,	PUNCT
ap-3517	282	17	higher	high	ADJ
ap-3517	282	18	transcendental	transcendental	ADJ
ap-3517	282	19	functions	function	NOUN
ap-3517	282	20	.	.	PUNCT
ap-3517	283	1	vol	vol	NOUN
ap-3517	283	2	.	.	PUNCT
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ap-3517	283	4	,	,	PUNCT
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ap-3517	283	8	publishing	publishing	PROPN
ap-3517	283	9	co.	co.	PROPN
ap-3517	283	10	,	,	PUNCT
ap-3517	283	11	inc	inc	PROPN
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ap-3517	283	13	,	,	PUNCT
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ap-3517	283	16	fla	fla	PROPN
ap-3517	283	17	.	.	PROPN
ap-3517	283	18	,	,	PUNCT
ap-3517	283	19	1981	1981	NUM
ap-3517	283	20	.	.	PUNCT
ap-3517	284	1	[	[	X
ap-3517	284	2	5	5	X
ap-3517	284	3	]	]	PUNCT
ap-3517	284	4	d.	d.	PROPN
ap-3517	284	5	c.	c.	PROPN
ap-3517	284	6	handscomb	handscomb	PROPN
ap-3517	284	7	,	,	PUNCT
ap-3517	284	8	j.	j.	PROPN
ap-3517	284	9	c.	c.	PROPN
ap-3517	284	10	mason	mason	PROPN
ap-3517	284	11	,	,	PUNCT
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ap-3517	284	13	polynomials	polynomial	NOUN
ap-3517	284	14	,	,	PUNCT
ap-3517	284	15	chapman&hall	chapman&hall	PROPN
ap-3517	284	16	/	/	SYM
ap-3517	284	17	crc	crc	PROPN
ap-3517	284	18	,	,	PUNCT
ap-3517	284	19	usa	usa	PROPN
ap-3517	284	20	,	,	PUNCT
ap-3517	284	21	2003	2003	NUM
ap-3517	284	22	,	,	PUNCT
ap-3517	284	23	doi:10.1201/9781420036114	doi:10.1201/9781420036114	NOUN
ap-3517	284	24	.	.	PUNCT
ap-3517	285	1	[	[	X
ap-3517	285	2	6	6	NUM
ap-3517	285	3	]	]	X
ap-3517	285	4	l.	l.	PROPN
ap-3517	285	5	háková	háková	PROPN
ap-3517	285	6	,	,	PUNCT
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ap-3517	285	8	hrivnák	hrivnák	PROPN
ap-3517	285	9	,	,	PUNCT
ap-3517	285	10	j.	j.	PROPN
ap-3517	285	11	patera	patera	PROPN
ap-3517	285	12	,	,	PUNCT
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ap-3517	285	17	group	group	NOUN
ap-3517	285	18	orbit	orbit	NOUN
ap-3517	285	19	functions	function	NOUN
ap-3517	285	20	of	of	ADP
ap-3517	285	21	b3	b3	PROPN
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ap-3517	285	23	c3	c3	PROPN
ap-3517	285	24	,	,	PUNCT
ap-3517	285	25	j.	j.	PROPN
ap-3517	285	26	math	math	PROPN
ap-3517	285	27	.	.	PUNCT
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ap-3517	286	2	.	.	PUNCT
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ap-3517	287	2	(	(	PUNCT
ap-3517	287	3	2013	2013	NUM
ap-3517	287	4	)	)	PUNCT
ap-3517	287	5	,	,	PUNCT
ap-3517	287	6	083501	083501	NUM
ap-3517	287	7	,	,	PUNCT
ap-3517	287	8	19	19	NUM
ap-3517	287	9	,	,	PUNCT
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ap-3517	287	11	.	.	PUNCT
ap-3517	288	1	[	[	X
ap-3517	288	2	7	7	X
ap-3517	288	3	]	]	X
ap-3517	288	4	j.	j.	PROPN
ap-3517	288	5	hrivnák	hrivnák	PROPN
ap-3517	288	6	,	,	PUNCT
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ap-3517	288	18	multivariate	multivariate	NOUN
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ap-3517	288	20	functions	function	NOUN
ap-3517	288	21	,	,	PUNCT
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ap-3517	288	23	j.	j.	PROPN
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ap-3517	288	25	.	.	PROPN
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ap-3517	288	27	.	.	PUNCT
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ap-3517	289	2	(	(	PUNCT
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ap-3517	289	4	)	)	PUNCT
ap-3517	289	5	,	,	PUNCT
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ap-3517	289	9	,	,	PUNCT
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ap-3517	289	11	,	,	PUNCT
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ap-3517	289	13	.	.	PUNCT
ap-3517	290	1	[	[	X
ap-3517	290	2	8	8	X
ap-3517	290	3	]	]	X
ap-3517	290	4	j.	j.	PROPN
ap-3517	290	5	hrivnák	hrivnák	PROPN
ap-3517	290	6	,	,	PUNCT
ap-3517	290	7	l.	l.	PROPN
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ap-3517	290	9	,	,	PUNCT
ap-3517	290	10	j.	j.	PROPN
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ap-3517	290	16	tori	tori	NOUN
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ap-3517	290	18	compact	compact	ADJ
ap-3517	290	19	simple	simple	ADJ
ap-3517	290	20	lie	lie	NOUN
ap-3517	290	21	groups	groups	PROPN
ap-3517	290	22	ii	ii	PROPN
ap-3517	290	23	.	.	PROPN
ap-3517	290	24	,	,	PUNCT
ap-3517	290	25	j.	j.	PROPN
ap-3517	290	26	phys	phys	PROPN
ap-3517	290	27	.	.	PUNCT
ap-3517	291	1	a	a	DET
ap-3517	291	2	45	45	NUM
ap-3517	291	3	(	(	PUNCT
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ap-3517	291	5	)	)	PUNCT
ap-3517	291	6	,	,	PUNCT
ap-3517	291	7	255201	255201	NUM
ap-3517	291	8	,	,	PUNCT
ap-3517	291	9	18	18	NUM
ap-3517	291	10	,	,	PUNCT
ap-3517	291	11	doi:10.1088/1751	doi:10.1088/1751	ADV
ap-3517	291	12	-	-	PUNCT
ap-3517	291	13	8113/45/25/255201	8113/45/25/255201	NUM
ap-3517	291	14	.	.	PUNCT
ap-3517	292	1	[	[	X
ap-3517	292	2	9	9	NUM
ap-3517	292	3	]	]	X
ap-3517	292	4	j.	j.	PROPN
ap-3517	292	5	hrivnák	hrivnák	PROPN
ap-3517	292	6	,	,	PUNCT
ap-3517	292	7	l.	l.	PROPN
ap-3517	292	8	motlochová	motlochová	PROPN
ap-3517	292	9	,	,	PUNCT
ap-3517	292	10	j.	j.	PROPN
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ap-3517	292	12	,	,	PUNCT
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ap-3517	292	16	multivariate	multivariate	NOUN
ap-3517	292	17	polynomials	polynomial	NOUN
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ap-3517	292	19	from	from	ADP
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ap-3517	292	21	orbit	orbit	NOUN
ap-3517	292	22	functions	function	NOUN
ap-3517	292	23	,	,	PUNCT
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ap-3517	292	26	(	(	PUNCT
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ap-3517	292	28	)	)	PUNCT
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ap-3517	292	33	,	,	PUNCT
ap-3517	292	34	63	63	NUM
ap-3517	292	35	,	,	PUNCT
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ap-3517	292	37	/	/	SYM
ap-3517	292	38	sym8070063	sym8070063	NOUN
ap-3517	292	39	.	.	PUNCT
ap-3517	293	1	[	[	X
ap-3517	293	2	10	10	NUM
ap-3517	293	3	]	]	X
ap-3517	293	4	j.	j.	PROPN
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ap-3517	293	6	,	,	PUNCT
ap-3517	293	7	j.	j.	PROPN
ap-3517	293	8	patera	patera	PROPN
ap-3517	293	9	,	,	PUNCT
ap-3517	293	10	on	on	ADP
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ap-3517	293	12	of	of	ADP
ap-3517	293	13	tori	tori	NOUN
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ap-3517	293	17	lie	lie	NOUN
ap-3517	293	18	groups	group	NOUN
ap-3517	293	19	,	,	PUNCT
ap-3517	293	20	j.	j.	PROPN
ap-3517	293	21	phys	phys	PROPN
ap-3517	293	22	.	.	PUNCT
ap-3517	294	1	a	a	DET
ap-3517	294	2	:	:	PUNCT
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ap-3517	294	4	.	.	PUNCT
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ap-3517	295	2	.	.	PUNCT
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ap-3517	296	2	(	(	PUNCT
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ap-3517	296	4	)	)	PUNCT
ap-3517	296	5	,	,	PUNCT
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ap-3517	296	7	,	,	PUNCT
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ap-3517	296	9	-	-	PUNCT
ap-3517	296	10	8113/42/38/385208	8113/42/38/385208	NOUN
ap-3517	296	11	.	.	PUNCT
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ap-3517	297	2	11	11	NUM
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ap-3517	297	4	j.	j.	PROPN
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ap-3517	297	8	motlochová	motlochová	PROPN
ap-3517	297	9	,	,	PUNCT
ap-3517	297	10	j.	j.	PROPN
ap-3517	297	11	patera	patera	PROPN
ap-3517	297	12	,	,	PUNCT
ap-3517	297	13	two	two	NUM
ap-3517	297	14	-	-	PUNCT
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ap-3517	298	3	(	(	PUNCT
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ap-3517	298	5	)	)	PUNCT
ap-3517	298	6	,	,	PUNCT
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ap-3517	298	8	,	,	PUNCT
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ap-3517	298	10	,	,	PUNCT
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ap-3517	299	2	12	12	NUM
ap-3517	299	3	]	]	PUNCT
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ap-3517	299	6	humphreys	humphreys	PROPN
ap-3517	299	7	,	,	PUNCT
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ap-3517	299	9	groups	group	NOUN
ap-3517	299	10	and	and	CCONJ
ap-3517	299	11	coxeter	coxet	ADJ
ap-3517	299	12	groups	group	NOUN
ap-3517	299	13	,	,	PUNCT
ap-3517	299	14	cambridge	cambridge	PROPN
ap-3517	299	15	studies	study	NOUN
ap-3517	299	16	in	in	ADP
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ap-3517	299	18	mathematics	mathematic	NOUN
ap-3517	299	19	,	,	PUNCT
ap-3517	299	20	29	29	NUM
ap-3517	299	21	(	(	PUNCT
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ap-3517	299	25	cambridge	cambridge	PROPN
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ap-3517	299	28	,	,	PUNCT
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ap-3517	299	30	,	,	PUNCT
ap-3517	299	31	doi:10.1017	doi:10.1017	NOUN
ap-3517	299	32	/	/	SYM
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ap-3517	300	7	,	,	PUNCT
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ap-3517	300	10	lie	lie	VERB
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ap-3517	300	12	and	and	CCONJ
ap-3517	300	13	representation	representation	NOUN
ap-3517	300	14	theory	theory	NOUN
ap-3517	300	15	,	,	PUNCT
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ap-3517	300	17	-	-	PUNCT
ap-3517	300	18	verlag	verlag	PROPN
ap-3517	300	19	,	,	PUNCT
ap-3517	300	20	new	new	PROPN
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ap-3517	300	22	,	,	PUNCT
ap-3517	300	23	1978	1978	NUM
ap-3517	300	24	,	,	PUNCT
ap-3517	300	25	doi:10.1007/978	doi:10.1007/978	PROPN
ap-3517	300	26	-	-	PUNCT
ap-3517	300	27	1	1	NUM
ap-3517	300	28	-	-	PUNCT
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ap-3517	300	30	-	-	PUNCT
ap-3517	300	31	6398	6398	NUM
ap-3517	300	32	-	-	PUNCT
ap-3517	300	33	2	2	NUM
ap-3517	300	34	.	.	PUNCT
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ap-3517	301	2	14	14	NUM
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ap-3517	301	6	,	,	PUNCT
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ap-3517	301	12	,	,	PUNCT
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ap-3517	301	14	-	-	PUNCT
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ap-3517	301	16	,	,	PUNCT
ap-3517	301	17	new	new	PROPN
ap-3517	301	18	york	york	PROPN
ap-3517	301	19	,	,	PUNCT
ap-3517	301	20	2001	2001	NUM
ap-3517	301	21	,	,	PUNCT
ap-3517	301	22	doi:10.1007/978	doi:10.1007/978	PROPN
ap-3517	301	23	-	-	PUNCT
ap-3517	301	24	1	1	NUM
ap-3517	301	25	-	-	PUNCT
ap-3517	301	26	4757	4757	NUM
ap-3517	301	27	-	-	PUNCT
ap-3517	301	28	3542	3542	NUM
ap-3517	301	29	-	-	PUNCT
ap-3517	301	30	0	0	NUM
ap-3517	301	31	.	.	PUNCT
ap-3517	302	1	[	[	X
ap-3517	302	2	15	15	NUM
ap-3517	302	3	]	]	PUNCT
ap-3517	302	4	a.	a.	NOUN
ap-3517	302	5	u.	u.	PROPN
ap-3517	302	6	klimyk	klimyk	PROPN
ap-3517	302	7	,	,	PUNCT
ap-3517	302	8	j.	j.	PROPN
ap-3517	302	9	patera	patera	PROPN
ap-3517	302	10	,	,	PUNCT
ap-3517	302	11	orbit	orbit	NOUN
ap-3517	302	12	functions	function	NOUN
ap-3517	302	13	,	,	PUNCT
ap-3517	302	14	sigma	sigma	NOUN
ap-3517	302	15	2	2	NUM
ap-3517	302	16	(	(	PUNCT
ap-3517	302	17	2006	2006	NUM
ap-3517	302	18	)	)	PUNCT
ap-3517	302	19	,	,	PUNCT
ap-3517	302	20	006	006	NUM
ap-3517	302	21	,	,	PUNCT
ap-3517	302	22	60	60	NUM
ap-3517	302	23	,	,	PUNCT
ap-3517	302	24	doi:10.3842	doi:10.3842	NOUN
ap-3517	302	25	/	/	SYM
ap-3517	302	26	sigma.2006.006	sigma.2006.006	NOUN
ap-3517	302	27	.	.	PUNCT
ap-3517	303	1	[	[	X
ap-3517	303	2	16	16	NUM
ap-3517	303	3	]	]	PUNCT
ap-3517	303	4	a.	a.	NOUN
ap-3517	303	5	u.	u.	PROPN
ap-3517	303	6	klimyk	klimyk	PROPN
ap-3517	303	7	,	,	PUNCT
ap-3517	303	8	j.	j.	PROPN
ap-3517	303	9	patera	patera	PROPN
ap-3517	303	10	,	,	PUNCT
ap-3517	303	11	antisymmetric	antisymmetric	PROPN
ap-3517	303	12	orbit	orbit	NOUN
ap-3517	303	13	functions	function	NOUN
ap-3517	303	14	,	,	PUNCT
ap-3517	303	15	sigma	sigma	X
ap-3517	303	16	3	3	NUM
ap-3517	303	17	(	(	PUNCT
ap-3517	303	18	2007	2007	NUM
ap-3517	303	19	)	)	PUNCT
ap-3517	303	20	,	,	PUNCT
ap-3517	303	21	paper	paper	NOUN
ap-3517	303	22	023	023	NUM
ap-3517	303	23	,	,	PUNCT
ap-3517	303	24	83	83	NUM
ap-3517	303	25	,	,	PUNCT
ap-3517	303	26	doi:10.3842	doi:10.3842	NOUN
ap-3517	303	27	/	/	SYM
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ap-3517	303	29	.	.	PUNCT
ap-3517	304	1	[	[	X
ap-3517	304	2	17	17	NUM
ap-3517	304	3	]	]	PUNCT
ap-3517	304	4	a.	a.	NOUN
ap-3517	304	5	klimyk	klimyk	PROPN
ap-3517	304	6	,	,	PUNCT
ap-3517	304	7	j.	j.	PROPN
ap-3517	304	8	patera	patera	PROPN
ap-3517	304	9	,	,	PUNCT
ap-3517	304	10	(	(	PUNCT
ap-3517	304	11	anti)symmetric	anti)symmetric	ADJ
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ap-3517	304	13	trigonometric	trigonometric	NOUN
ap-3517	304	14	functions	function	NOUN
ap-3517	304	15	and	and	CCONJ
ap-3517	304	16	corresponding	corresponding	ADJ
ap-3517	304	17	fourier	fourier	NOUN
ap-3517	304	18	transforms	transform	VERB
ap-3517	304	19	,	,	PUNCT
ap-3517	304	20	j.	j.	PROPN
ap-3517	304	21	math	math	PROPN
ap-3517	304	22	.	.	PUNCT
ap-3517	305	1	phys	phy	NOUN
ap-3517	305	2	.	.	PUNCT
ap-3517	306	1	48	48	NUM
ap-3517	306	2	(	(	PUNCT
ap-3517	306	3	2007	2007	NUM
ap-3517	306	4	)	)	PUNCT
ap-3517	306	5	,	,	PUNCT
ap-3517	306	6	093504	093504	NUM
ap-3517	306	7	,	,	PUNCT
ap-3517	306	8	24	24	NUM
ap-3517	306	9	,	,	PUNCT
ap-3517	306	10	doi:10.1063/1.2779768	doi:10.1063/1.2779768	NOUN
ap-3517	306	11	.	.	PUNCT
ap-3517	307	1	[	[	X
ap-3517	307	2	18	18	NUM
ap-3517	307	3	]	]	PUNCT
ap-3517	307	4	a.	a.	PROPN
ap-3517	307	5	w.	w.	PROPN
ap-3517	307	6	knapp	knapp	PROPN
ap-3517	307	7	,	,	PUNCT
ap-3517	307	8	lie	lie	NOUN
ap-3517	307	9	groups	group	NOUN
ap-3517	307	10	beyond	beyond	ADP
ap-3517	307	11	an	an	DET
ap-3517	307	12	introduction	introduction	NOUN
ap-3517	307	13	,	,	PUNCT
ap-3517	307	14	birkhäuser	birkhäuser	PROPN
ap-3517	307	15	boston	boston	PROPN
ap-3517	307	16	inc	inc	PROPN
ap-3517	307	17	.	.	PROPN
ap-3517	307	18	,	,	PUNCT
ap-3517	307	19	boston	boston	PROPN
ap-3517	307	20	,	,	PUNCT
ap-3517	307	21	ma	ma	PROPN
ap-3517	307	22	,	,	PUNCT
ap-3517	307	23	1996	1996	NUM
ap-3517	307	24	.	.	PUNCT
ap-3517	308	1	[	[	X
ap-3517	308	2	19	19	NUM
ap-3517	308	3	]	]	PUNCT
ap-3517	308	4	t.	t.	PROPN
ap-3517	308	5	h.	h.	PROPN
ap-3517	308	6	koornwinder	koornwinder	PROPN
ap-3517	308	7	,	,	PUNCT
ap-3517	308	8	orthogonal	orthogonal	ADJ
ap-3517	308	9	polynomials	polynomial	NOUN
ap-3517	308	10	in	in	ADP
ap-3517	308	11	two	two	NUM
ap-3517	308	12	variables	variable	NOUN
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ap-3517	308	14	are	be	AUX
ap-3517	308	15	eigenfunctions	eigenfunction	NOUN
ap-3517	308	16	of	of	ADP
ap-3517	308	17	two	two	NUM
ap-3517	308	18	algebraically	algebraically	ADV
ap-3517	308	19	independent	independent	ADJ
ap-3517	308	20	partial	partial	ADJ
ap-3517	308	21	differential	differential	NOUN
ap-3517	308	22	operators	operator	NOUN
ap-3517	308	23	i	i	PROPN
ap-3517	308	24	-	-	PUNCT
ap-3517	308	25	ii	ii	PROPN
ap-3517	308	26	,	,	PUNCT
ap-3517	308	27	kon	kon	PROPN
ap-3517	308	28	.	.	PUNCT
ap-3517	308	29	ned	ned	PROPN
ap-3517	308	30	.	.	PROPN
ap-3517	308	31	akad	akad	PROPN
ap-3517	308	32	.	.	PUNCT
ap-3517	309	1	wet	wet	ADJ
ap-3517	309	2	.	.	PUNCT
ap-3517	309	3	ser	ser	PROPN
ap-3517	309	4	.	.	PUNCT
ap-3517	310	1	a	a	DET
ap-3517	310	2	77	77	NUM
ap-3517	310	3	(	(	PUNCT
ap-3517	310	4	1974	1974	NUM
ap-3517	310	5	)	)	PUNCT
ap-3517	310	6	,	,	PUNCT
ap-3517	310	7	46–66	46–66	NOUN
ap-3517	310	8	.	.	PUNCT
ap-3517	311	1	[	[	X
ap-3517	311	2	20	20	NUM
ap-3517	311	3	]	]	PUNCT
ap-3517	311	4	t.	t.	PROPN
ap-3517	311	5	h.	h.	PROPN
ap-3517	311	6	koornwinder	koornwinder	PROPN
ap-3517	311	7	,	,	PUNCT
ap-3517	311	8	orthogonal	orthogonal	ADJ
ap-3517	311	9	polynomials	polynomial	NOUN
ap-3517	311	10	in	in	ADP
ap-3517	311	11	two	two	NUM
ap-3517	311	12	variables	variable	NOUN
ap-3517	311	13	which	which	PRON
ap-3517	311	14	are	be	AUX
ap-3517	311	15	eigenfunctions	eigenfunction	NOUN
ap-3517	311	16	of	of	ADP
ap-3517	311	17	two	two	NUM
ap-3517	311	18	algebraically	algebraically	ADV
ap-3517	311	19	independent	independent	ADJ
ap-3517	311	20	partial	partial	ADJ
ap-3517	311	21	differential	differential	NOUN
ap-3517	311	22	operators	operator	NOUN
ap-3517	311	23	iii	iii	PROPN
ap-3517	311	24	-	-	PUNCT
ap-3517	311	25	iv	iv	NUM
ap-3517	311	26	,	,	PUNCT
ap-3517	311	27	indag	indag	PROPN
ap-3517	311	28	.	.	PUNCT
ap-3517	311	29	math	math	NOUN
ap-3517	311	30	.	.	PUNCT
ap-3517	312	1	36	36	NUM
ap-3517	312	2	(	(	PUNCT
ap-3517	312	3	1974	1974	NUM
ap-3517	312	4	)	)	PUNCT
ap-3517	312	5	,	,	PUNCT
ap-3517	312	6	357–381	357–381	NUM
ap-3517	312	7	.	.	PUNCT
ap-3517	313	1	289	289	NUM
ap-3517	313	2	http://dx.doi.org/10.1063/1.4901230	http://dx.doi.org/10.1063/1.4901230	NUM
ap-3517	313	3	http://dx.doi.org/10.1017/cbo9781107786134	http://dx.doi.org/10.1017/cbo9781107786134	X
ap-3517	314	1	http://dx.doi.org/10.1201/9781420036114	http://dx.doi.org/10.1201/9781420036114	PROPN
ap-3517	314	2	http://dx.doi.org/10.1063/1.4817340	http://dx.doi.org/10.1063/1.4817340	PROPN
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ap-3517	314	6	http://dx.doi.org/10.1088/1751-8113/42/38/385208	http://dx.doi.org/10.1088/1751-8113/42/38/385208	NOUN
ap-3517	314	7	http://dx.doi.org/10.1063/1.3430567	http://dx.doi.org/10.1063/1.3430567	NOUN
ap-3517	314	8	http://dx.doi.org/10.1017/cbo9780511623646	http://dx.doi.org/10.1017/cbo9780511623646	NOUN
ap-3517	314	9	http://dx.doi.org/10.1007/978-1-4612-6398-2	http://dx.doi.org/10.1007/978-1-4612-6398-2	NOUN
ap-3517	314	10	http://dx.doi.org/10.1007/978-1-4757-3542-0	http://dx.doi.org/10.1007/978-1-4757-3542-0	NOUN
ap-3517	314	11	http://dx.doi.org/10.3842/sigma.2006.006	http://dx.doi.org/10.3842/sigma.2006.006	NOUN
ap-3517	314	12	http://dx.doi.org/10.3842/sigma.2007.023	http://dx.doi.org/10.3842/sigma.2007.023	NUM
ap-3517	314	13	http://dx.doi.org/10.1063/1.2779768	http://dx.doi.org/10.1063/1.2779768	NOUN
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ap-3517	314	15	hrivnák	hrivnák	NOUN
ap-3517	314	16	,	,	PUNCT
ap-3517	314	17	lenka	lenka	PROPN
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ap-3517	314	19	acta	acta	PROPN
ap-3517	314	20	polytechnica	polytechnica	PROPN
ap-3517	315	1	[	[	X
ap-3517	315	2	21	21	NUM
ap-3517	315	3	]	]	PUNCT
ap-3517	315	4	t.	t.	PROPN
ap-3517	315	5	h.	h.	PROPN
ap-3517	315	6	koornwinder	koornwinder	PROPN
ap-3517	315	7	,	,	PUNCT
ap-3517	315	8	two	two	NUM
ap-3517	315	9	-	-	PUNCT
ap-3517	315	10	variable	variable	ADJ
ap-3517	315	11	analogues	analogue	NOUN
ap-3517	315	12	of	of	ADP
ap-3517	315	13	the	the	DET
ap-3517	315	14	classical	classical	ADJ
ap-3517	315	15	orthogonal	orthogonal	ADJ
ap-3517	315	16	polynomials	polynomial	NOUN
ap-3517	315	17	,	,	PUNCT
ap-3517	315	18	theory	theory	NOUN
ap-3517	315	19	and	and	CCONJ
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ap-3517	315	22	special	special	ADJ
ap-3517	315	23	functions	function	NOUN
ap-3517	315	24	,	,	PUNCT
ap-3517	315	25	edited	edit	VERB
ap-3517	315	26	by	by	ADP
ap-3517	315	27	r.	r.	PROPN
ap-3517	315	28	a.	a.	PROPN
ap-3517	315	29	askey	askey	PROPN
ap-3517	315	30	,	,	PUNCT
ap-3517	315	31	academic	academic	ADJ
ap-3517	315	32	press	press	NOUN
ap-3517	315	33	,	,	PUNCT
ap-3517	315	34	new	new	PROPN
ap-3517	315	35	york	york	PROPN
ap-3517	315	36	(	(	PUNCT
ap-3517	315	37	1975	1975	NUM
ap-3517	315	38	)	)	PUNCT
ap-3517	315	39	435–495	435–495	NUM
ap-3517	315	40	,	,	PUNCT
ap-3517	315	41	doi:10.1016	doi:10.1016	PROPN
ap-3517	315	42	/	/	SYM
ap-3517	315	43	b978	b978	PROPN
ap-3517	315	44	-	-	PUNCT
ap-3517	315	45	0	0	NUM
ap-3517	315	46	-	-	PUNCT
ap-3517	315	47	12	12	NUM
ap-3517	315	48	-	-	PUNCT
ap-3517	315	49	064850	064850	NUM
ap-3517	315	50	-	-	PUNCT
ap-3517	315	51	4.50015	4.50015	NUM
ap-3517	315	52	-	-	PUNCT
ap-3517	315	53	x.	x.	NOUN
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ap-3517	316	9	,	,	PUNCT
ap-3517	316	10	y.	y.	PROPN
ap-3517	316	11	xu	xu	PROPN
ap-3517	316	12	,	,	PUNCT
ap-3517	316	13	discrete	discrete	ADJ
ap-3517	316	14	fourier	fourier	NOUN
ap-3517	316	15	analysis	analysis	NOUN
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ap-3517	316	17	chebyshev	chebyshev	NOUN
ap-3517	316	18	polynomials	polynomial	NOUN
ap-3517	316	19	with	with	ADP
ap-3517	316	20	g2	g2	PROPN
ap-3517	316	21	group	group	NOUN
ap-3517	316	22	,	,	PUNCT
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ap-3517	316	24	8	8	NUM
ap-3517	316	25	(	(	PUNCT
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ap-3517	316	27	)	)	PUNCT
ap-3517	316	28	,	,	PUNCT
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ap-3517	316	34	doi:10.3842	doi:10.3842	NOUN
ap-3517	316	35	/	/	SYM
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ap-3517	317	1	[	[	X
ap-3517	317	2	23	23	NUM
ap-3517	317	3	]	]	X
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ap-3517	317	9	,	,	PUNCT
ap-3517	317	10	y.	y.	PROPN
ap-3517	317	11	xu	xu	PROPN
ap-3517	317	12	,	,	PUNCT
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ap-3517	317	14	fourier	fourier	NOUN
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ap-3517	317	16	,	,	PUNCT
ap-3517	317	17	cubature	cubature	NOUN
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ap-3517	317	21	a	a	DET
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ap-3517	317	23	and	and	CCONJ
ap-3517	317	24	a	a	DET
ap-3517	317	25	triangle	triangle	NOUN
ap-3517	317	26	,	,	PUNCT
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ap-3517	317	28	j.	j.	PROPN
ap-3517	317	29	numer	numer	PROPN
ap-3517	317	30	.	.	PUNCT
ap-3517	318	1	anal	anal	PROPN
ap-3517	318	2	.	.	PUNCT
ap-3517	319	1	46	46	NUM
ap-3517	319	2	(	(	PUNCT
ap-3517	319	3	2008	2008	NUM
ap-3517	319	4	)	)	PUNCT
ap-3517	319	5	,	,	PUNCT
ap-3517	319	6	1653	1653	NUM
ap-3517	319	7	-	-	SYM
ap-3517	319	8	1681	1681	NUM
ap-3517	319	9	,	,	PUNCT
ap-3517	319	10	doi:10.1137/060671851	doi:10.1137/060671851	NOUN
ap-3517	319	11	.	.	PUNCT
ap-3517	320	1	[	[	X
ap-3517	320	2	24	24	NUM
ap-3517	320	3	]	]	X
ap-3517	320	4	h.	h.	PROPN
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ap-3517	320	6	,	,	PUNCT
ap-3517	320	7	y.	y.	PROPN
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ap-3517	320	9	,	,	PUNCT
ap-3517	320	10	discrete	discrete	ADJ
ap-3517	320	11	fourier	fourier	NOUN
ap-3517	320	12	analysis	analysis	NOUN
ap-3517	320	13	on	on	ADP
ap-3517	320	14	fundamental	fundamental	ADJ
ap-3517	320	15	domain	domain	NOUN
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ap-3517	320	18	of	of	ADP
ap-3517	320	19	ad	ad	NOUN
ap-3517	320	20	lattice	lattice	NOUN
ap-3517	320	21	in	in	ADP
ap-3517	320	22	d	d	NOUN
ap-3517	320	23	-	-	NOUN
ap-3517	320	24	variables	variable	NOUN
ap-3517	320	25	,	,	PUNCT
ap-3517	320	26	j.	j.	PROPN
ap-3517	320	27	fourier	fourier	PROPN
ap-3517	320	28	anal	anal	PROPN
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ap-3517	321	1	appl	appl	PROPN
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ap-3517	322	1	16	16	NUM
ap-3517	322	2	,	,	PUNCT
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ap-3517	322	4	-	-	SYM
ap-3517	322	5	433	433	NUM
ap-3517	322	6	,	,	PUNCT
ap-3517	322	7	(	(	PUNCT
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ap-3517	322	9	)	)	PUNCT
ap-3517	322	10	,	,	PUNCT
ap-3517	322	11	doi:10.1007	doi:10.1007	VERB
ap-3517	322	12	/	/	SYM
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ap-3517	322	14	-	-	PUNCT
ap-3517	322	15	009	009	NUM
ap-3517	322	16	-	-	PUNCT
ap-3517	322	17	9106	9106	NUM
ap-3517	322	18	-	-	SYM
ap-3517	322	19	9	9	NUM
ap-3517	322	20	.	.	PUNCT
ap-3517	323	1	[	[	X
ap-3517	323	2	25	25	NUM
ap-3517	323	3	]	]	PUNCT
ap-3517	323	4	r.	r.	PROPN
ap-3517	323	5	v.	v.	PROPN
ap-3517	323	6	moody	moody	PROPN
ap-3517	323	7	,	,	PUNCT
ap-3517	323	8	l.	l.	PROPN
ap-3517	323	9	motlochová	motlochová	PROPN
ap-3517	323	10	,	,	PUNCT
ap-3517	323	11	j.	j.	PROPN
ap-3517	323	12	patera	patera	PROPN
ap-3517	323	13	,	,	PUNCT
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ap-3517	323	15	cubature	cubature	NOUN
ap-3517	323	16	arising	arise	VERB
ap-3517	323	17	from	from	ADP
ap-3517	323	18	hybrid	hybrid	ADJ
ap-3517	323	19	characters	character	NOUN
ap-3517	323	20	of	of	ADP
ap-3517	323	21	simple	simple	ADJ
ap-3517	323	22	lie	lie	NOUN
ap-3517	323	23	groups	group	NOUN
ap-3517	323	24	,	,	PUNCT
ap-3517	323	25	j.	j.	PROPN
ap-3517	323	26	fourier	fourier	PROPN
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ap-3517	323	28	.	.	PUNCT
ap-3517	324	1	appl	appl	PROPN
ap-3517	324	2	.	.	PROPN
ap-3517	325	1	20	20	NUM
ap-3517	325	2	(	(	PUNCT
ap-3517	325	3	2014	2014	NUM
ap-3517	325	4	)	)	PUNCT
ap-3517	326	1	,	,	PUNCT
ap-3517	326	2	issue	issue	NOUN
ap-3517	326	3	6	6	NUM
ap-3517	326	4	,	,	PUNCT
ap-3517	326	5	1257–1290	1257–1290	NUM
ap-3517	326	6	,	,	PUNCT
ap-3517	326	7	doi:10.1007	doi:10.1007	NOUN
ap-3517	326	8	/	/	SYM
ap-3517	326	9	s00041	s00041	NOUN
ap-3517	326	10	-	-	PUNCT
ap-3517	326	11	014	014	NUM
ap-3517	326	12	-	-	PUNCT
ap-3517	326	13	9355	9355	NUM
ap-3517	326	14	-	-	SYM
ap-3517	326	15	0	0	NUM
ap-3517	326	16	.	.	PUNCT
ap-3517	327	1	[	[	X
ap-3517	327	2	26	26	NUM
ap-3517	327	3	]	]	X
ap-3517	327	4	r.	r.	PROPN
ap-3517	327	5	v.	v.	PROPN
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ap-3517	327	8	j.	j.	PROPN
ap-3517	327	9	patera	patera	PROPN
ap-3517	327	10	,	,	PUNCT
ap-3517	327	11	cubature	cubature	NOUN
ap-3517	327	12	formulae	formulae	NOUN
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ap-3517	327	14	orthogonal	orthogonal	ADJ
ap-3517	327	15	polynomials	polynomial	NOUN
ap-3517	327	16	in	in	ADP
ap-3517	327	17	terms	term	NOUN
ap-3517	327	18	of	of	ADP
ap-3517	327	19	elements	element	NOUN
ap-3517	327	20	of	of	ADP
ap-3517	327	21	finite	finite	ADJ
ap-3517	327	22	order	order	NOUN
ap-3517	327	23	of	of	ADP
ap-3517	327	24	compact	compact	ADJ
ap-3517	327	25	simple	simple	ADJ
ap-3517	327	26	lie	lie	NOUN
ap-3517	327	27	groups	group	NOUN
ap-3517	327	28	,	,	PUNCT
ap-3517	327	29	advances	advance	NOUN
ap-3517	327	30	in	in	ADP
ap-3517	327	31	applied	apply	VERB
ap-3517	327	32	mathematics	mathematic	NOUN
ap-3517	327	33	47	47	NUM
ap-3517	327	34	(	(	PUNCT
ap-3517	327	35	2011	2011	NUM
ap-3517	327	36	)	)	PUNCT
ap-3517	327	37	509—535	509—535	PROPN
ap-3517	327	38	,	,	PUNCT
ap-3517	327	39	doi:10.1016	doi:10.1016	PROPN
ap-3517	327	40	/	/	SYM
ap-3517	327	41	j.aam.2010.11.005	j.aam.2010.11.005	PROPN
ap-3517	327	42	.	.	PUNCT
ap-3517	328	1	[	[	X
ap-3517	328	2	27	27	NUM
ap-3517	328	3	]	]	X
ap-3517	328	4	r.	r.	PROPN
ap-3517	328	5	v.	v.	CCONJ
ap-3517	328	6	moody	moody	PROPN
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ap-3517	328	8	j.	j.	PROPN
ap-3517	328	9	patera	patera	PROPN
ap-3517	328	10	,	,	PUNCT
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ap-3517	328	13	the	the	DET
ap-3517	328	14	families	family	NOUN
ap-3517	328	15	of	of	ADP
ap-3517	328	16	c	c	PROPN
ap-3517	328	17	–	–	PUNCT
ap-3517	328	18	,	,	PUNCT
ap-3517	328	19	s	s	PART
ap-3517	328	20	–	–	PUNCT
ap-3517	328	21	,	,	PUNCT
ap-3517	328	22	and	and	CCONJ
ap-3517	328	23	e	e	X
ap-3517	328	24	–	–	PUNCT
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ap-3517	328	26	of	of	ADP
ap-3517	328	27	any	any	DET
ap-3517	328	28	compact	compact	ADJ
ap-3517	328	29	semisimple	semisimple	NOUN
ap-3517	328	30	lie	lie	NOUN
ap-3517	328	31	group	group	NOUN
ap-3517	328	32	,	,	PUNCT
ap-3517	328	33	sigma	sigma	NOUN
ap-3517	328	34	2	2	NUM
ap-3517	328	35	(	(	PUNCT
ap-3517	328	36	2006	2006	NUM
ap-3517	328	37	)	)	PUNCT
ap-3517	328	38	076	076	NUM
ap-3517	328	39	,	,	PUNCT
ap-3517	328	40	14	14	NUM
ap-3517	328	41	,	,	PUNCT
ap-3517	328	42	doi:10.3842	doi:10.3842	NOUN
ap-3517	328	43	/	/	SYM
ap-3517	328	44	sigma.2006.076	sigma.2006.076	NOUN
ap-3517	328	45	.	.	PUNCT
ap-3517	329	1	[	[	X
ap-3517	329	2	28	28	NUM
ap-3517	329	3	]	]	X
ap-3517	329	4	j.	j.	PROPN
ap-3517	329	5	patera	patera	PROPN
ap-3517	329	6	,	,	PUNCT
ap-3517	329	7	a.	a.	NOUN
ap-3517	329	8	zaratsyan	zaratsyan	PROPN
ap-3517	329	9	,	,	PUNCT
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ap-3517	329	11	and	and	CCONJ
ap-3517	329	12	continuous	continuous	ADJ
ap-3517	329	13	sine	sine	NOUN
ap-3517	329	14	transform	transform	NOUN
ap-3517	329	15	generalized	generalize	VERB
ap-3517	329	16	to	to	ADP
ap-3517	329	17	semisimple	semisimple	NOUN
ap-3517	329	18	lie	lie	NOUN
ap-3517	329	19	groups	group	NOUN
ap-3517	329	20	of	of	ADP
ap-3517	329	21	rank	rank	PROPN
ap-3517	329	22	two	two	NUM
ap-3517	329	23	,	,	PUNCT
ap-3517	329	24	j.	j.	PROPN
ap-3517	329	25	math	math	PROPN
ap-3517	329	26	.	.	PUNCT
ap-3517	330	1	phys	phy	NOUN
ap-3517	330	2	.	.	PUNCT
ap-3517	331	1	47	47	NUM
ap-3517	331	2	(	(	PUNCT
ap-3517	331	3	2006	2006	NUM
ap-3517	331	4	)	)	PUNCT
ap-3517	331	5	,	,	PUNCT
ap-3517	331	6	043512	043512	NUM
ap-3517	331	7	,	,	PUNCT
ap-3517	331	8	22	22	NUM
ap-3517	331	9	,	,	PUNCT
ap-3517	331	10	doi:10.1063/1.2191361	doi:10.1063/1.2191361	NOUN
ap-3517	331	11	.	.	PUNCT
ap-3517	332	1	[	[	X
ap-3517	332	2	29	29	NUM
ap-3517	332	3	]	]	PUNCT
ap-3517	332	4	j.	j.	PROPN
ap-3517	332	5	patera	patera	PROPN
ap-3517	332	6	,	,	PUNCT
ap-3517	332	7	a.	a.	NOUN
ap-3517	332	8	zaratsyan	zaratsyan	PROPN
ap-3517	332	9	,	,	PUNCT
ap-3517	332	10	discrete	discrete	ADJ
ap-3517	332	11	and	and	CCONJ
ap-3517	332	12	continuous	continuous	ADJ
ap-3517	332	13	cosine	cosine	NOUN
ap-3517	332	14	transform	transform	NOUN
ap-3517	332	15	generalized	generalize	VERB
ap-3517	332	16	to	to	PART
ap-3517	332	17	lie	lie	VERB
ap-3517	332	18	groups	group	NOUN
ap-3517	332	19	su(3	su(3	PROPN
ap-3517	332	20	)	)	PUNCT
ap-3517	332	21	and	and	CCONJ
ap-3517	332	22	g(2	g(2	PROPN
ap-3517	332	23	)	)	PUNCT
ap-3517	332	24	,	,	PUNCT
ap-3517	332	25	j.	j.	PROPN
ap-3517	332	26	math	math	PROPN
ap-3517	332	27	.	.	PUNCT
ap-3517	333	1	phys	phy	NOUN
ap-3517	333	2	.	.	PUNCT
ap-3517	334	1	46	46	NUM
ap-3517	334	2	(	(	PUNCT
ap-3517	334	3	2005	2005	NUM
ap-3517	334	4	)	)	PUNCT
ap-3517	334	5	,	,	PUNCT
ap-3517	334	6	113506	113506	NUM
ap-3517	334	7	,	,	PUNCT
ap-3517	334	8	17	17	NUM
ap-3517	334	9	,	,	PUNCT
ap-3517	334	10	doi:10.1063/1.2109707	doi:10.1063/1.2109707	NOUN
ap-3517	334	11	.	.	PUNCT
ap-3517	335	1	[	[	X
ap-3517	335	2	30	30	NUM
ap-3517	335	3	]	]	X
ap-3517	335	4	j.	j.	PROPN
ap-3517	335	5	patera	patera	PROPN
ap-3517	335	6	,	,	PUNCT
ap-3517	335	7	a.	a.	NOUN
ap-3517	335	8	zaratsyan	zaratsyan	PROPN
ap-3517	335	9	,	,	PUNCT
ap-3517	335	10	discrete	discrete	ADJ
ap-3517	335	11	and	and	CCONJ
ap-3517	335	12	continuous	continuous	ADJ
ap-3517	335	13	cosine	cosine	NOUN
ap-3517	335	14	transform	transform	NOUN
ap-3517	335	15	generalized	generalize	VERB
ap-3517	335	16	to	to	PART
ap-3517	335	17	lie	lie	VERB
ap-3517	335	18	groups	group	NOUN
ap-3517	335	19	su(2	su(2	NOUN
ap-3517	335	20	)	)	PUNCT
ap-3517	335	21	×	×	NOUN
ap-3517	335	22	su(2	su(2	NOUN
ap-3517	335	23	)	)	PUNCT
ap-3517	335	24	and	and	CCONJ
ap-3517	335	25	o(5	o(5	PROPN
ap-3517	335	26	)	)	PUNCT
ap-3517	335	27	,	,	PUNCT
ap-3517	335	28	j.	j.	PROPN
ap-3517	335	29	math	math	PROPN
ap-3517	335	30	.	.	PUNCT
ap-3517	336	1	phys	phy	NOUN
ap-3517	336	2	.	.	PUNCT
ap-3517	337	1	46	46	NUM
ap-3517	337	2	(	(	PUNCT
ap-3517	337	3	2005	2005	NUM
ap-3517	337	4	)	)	PUNCT
ap-3517	337	5	,	,	PUNCT
ap-3517	337	6	053514	053514	NUM
ap-3517	337	7	,	,	PUNCT
ap-3517	337	8	25	25	NUM
ap-3517	337	9	,	,	PUNCT
ap-3517	337	10	doi:10.1063/1.1897143	doi:10.1063/1.1897143	NOUN
ap-3517	337	11	.	.	PUNCT
ap-3517	338	1	[	[	X
ap-3517	338	2	31	31	NUM
ap-3517	338	3	]	]	PUNCT
ap-3517	338	4	t.	t.	PROPN
ap-3517	338	5	j.	j.	PROPN
ap-3517	338	6	rivlin	rivlin	PROPN
ap-3517	338	7	,	,	PUNCT
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ap-3517	338	11	,	,	PUNCT
ap-3517	338	12	wiley	wiley	NOUN
ap-3517	338	13	,	,	PUNCT
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ap-3517	338	16	,	,	PUNCT
ap-3517	338	17	1974	1974	NUM
ap-3517	338	18	.	.	PUNCT
ap-3517	339	1	[	[	X
ap-3517	339	2	32	32	NUM
ap-3517	339	3	]	]	PUNCT
ap-3517	339	4	j.-p	j.-p	PROPN
ap-3517	339	5	.	.	PUNCT
ap-3517	340	1	serre	serre	PROPN
ap-3517	340	2	,	,	PUNCT
ap-3517	340	3	complex	complex	ADJ
ap-3517	340	4	semisimple	semisimple	NOUN
ap-3517	340	5	lie	lie	NOUN
ap-3517	340	6	algebras	algebra	NOUN
ap-3517	340	7	,	,	PUNCT
ap-3517	340	8	springer	springer	NOUN
ap-3517	340	9	monographs	monograph	NOUN
ap-3517	340	10	in	in	ADP
ap-3517	340	11	mathematics	mathematic	NOUN
ap-3517	340	12	,	,	PUNCT
ap-3517	340	13	springer	springer	NOUN
ap-3517	340	14	-	-	PUNCT
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ap-3517	340	16	,	,	PUNCT
ap-3517	340	17	berlin	berlin	PROPN
ap-3517	340	18	,	,	PUNCT
ap-3517	340	19	2001	2001	NUM
ap-3517	340	20	,	,	PUNCT
ap-3517	340	21	doi:10.1007/978	doi:10.1007/978	PROPN
ap-3517	340	22	-	-	PUNCT
ap-3517	340	23	3	3	NUM
ap-3517	340	24	-	-	PUNCT
ap-3517	340	25	642	642	NUM
ap-3517	340	26	-	-	PUNCT
ap-3517	340	27	56884	56884	NUM
ap-3517	340	28	-	-	SYM
ap-3517	340	29	8	8	NUM
ap-3517	340	30	.	.	PUNCT
ap-3517	341	1	[	[	X
ap-3517	341	2	33	33	NUM
ap-3517	341	3	]	]	PUNCT
ap-3517	341	4	g.	g.	PROPN
ap-3517	341	5	szegő	szegő	PROPN
ap-3517	341	6	,	,	PUNCT
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ap-3517	341	8	polynomials	polynomial	NOUN
ap-3517	341	9	,	,	PUNCT
ap-3517	341	10	american	american	PROPN
ap-3517	341	11	mathematical	mathematical	ADJ
ap-3517	341	12	society	society	NOUN
ap-3517	341	13	,	,	PUNCT
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ap-3517	341	15	,	,	PUNCT
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ap-3517	341	17	.	.	PROPN
ap-3517	341	18	,	,	PUNCT
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ap-3517	341	20	.	.	PUNCT
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ap-3517	342	2	34	34	NUM
ap-3517	342	3	]	]	X
ap-3517	342	4	n.	n.	PROPN
ap-3517	342	5	ja	ja	PROPN
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ap-3517	343	2	,	,	PUNCT
ap-3517	343	3	a.	a.	PROPN
ap-3517	343	4	u.	u.	PROPN
ap-3517	343	5	klimyk	klimyk	PROPN
ap-3517	343	6	,	,	PUNCT
ap-3517	343	7	representation	representation	NOUN
ap-3517	343	8	of	of	ADP
ap-3517	343	9	lie	lie	NOUN
ap-3517	343	10	groups	group	NOUN
ap-3517	343	11	and	and	CCONJ
ap-3517	343	12	special	special	ADJ
ap-3517	343	13	functions	function	NOUN
ap-3517	343	14	,	,	PUNCT
ap-3517	343	15	kluwer	kluwer	NOUN
ap-3517	343	16	academic	academic	ADJ
ap-3517	343	17	publishers	publisher	NOUN
ap-3517	343	18	group	group	NOUN
ap-3517	343	19	,	,	PUNCT
ap-3517	343	20	dordrecht	dordrecht	PROPN
ap-3517	343	21	,	,	PUNCT
ap-3517	343	22	1995	1995	NUM
ap-3517	343	23	,	,	PUNCT
ap-3517	343	24	doi:10.1007/978	doi:10.1007/978	PROPN
ap-3517	343	25	-	-	PUNCT
ap-3517	343	26	94	94	NUM
ap-3517	343	27	-	-	PUNCT
ap-3517	343	28	017	017	NUM
ap-3517	343	29	-	-	PUNCT
ap-3517	343	30	2885	2885	NUM
ap-3517	343	31	-	-	SYM
ap-3517	343	32	0	0	NUM
ap-3517	343	33	.	.	NOUN
ap-3517	343	34	290	290	NUM
ap-3517	343	35	http://dx.doi.org/10.1016/b978-0-12-064850-4.50015-x	http://dx.doi.org/10.1016/b978-0-12-064850-4.50015-x	NOUN
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ap-3517	343	39	http://dx.doi.org/10.1007/s00041-014-9355-0	http://dx.doi.org/10.1007/s00041-014-9355-0	NUM
ap-3517	343	40	http://dx.doi.org/10.1016/j.aam.2010.11.005	http://dx.doi.org/10.1016/j.aam.2010.11.005	VERB
ap-3517	343	41	http://dx.doi.org/10.3842/sigma.2006.076	http://dx.doi.org/10.3842/sigma.2006.076	PROPN
ap-3517	343	42	http://dx.doi.org/10.1063/1.2191361	http://dx.doi.org/10.1063/1.2191361	NOUN
ap-3517	343	43	http://dx.doi.org/10.1063/1.2109707	http://dx.doi.org/10.1063/1.2109707	VERB
ap-3517	343	44	http://dx.doi.org/10.1063/1.1897143	http://dx.doi.org/10.1063/1.1897143	PROPN
ap-3517	343	45	http://dx.doi.org/10.1007/978-3-642-56884-8	http://dx.doi.org/10.1007/978-3-642-56884-8	NOUN
ap-3517	343	46	http://dx.doi.org/10.1007/978-94-017-2885-0	http://dx.doi.org/10.1007/978-94-017-2885-0	NOUN
ap-3517	343	47	acta	acta	PROPN
ap-3517	343	48	polytechnica	polytechnica	PROPN
ap-3517	343	49	56(4):283–290	56(4):283–290	PROPN
ap-3517	343	50	,	,	PUNCT
ap-3517	343	51	2016	2016	NUM
ap-3517	343	52	1	1	NUM
ap-3517	343	53	introduction	introduction	NOUN
ap-3517	343	54	2	2	NUM
ap-3517	343	55	weyl	weyl	VERB
ap-3517	343	56	groups	group	NOUN
ap-3517	343	57	of	of	ADP
ap-3517	343	58	simple	simple	ADJ
ap-3517	343	59	lie	lie	NOUN
ap-3517	343	60	algebras	algebras	PROPN
ap-3517	343	61	3	3	NUM
ap-3517	343	62	weyl	weyl	VERB
ap-3517	343	63	-	-	PUNCT
ap-3517	343	64	orbit	orbit	NOUN
ap-3517	343	65	functions	function	NOUN
ap-3517	343	66	3.1	3.1	NUM
ap-3517	343	67	case	case	NOUN
ap-3517	343	68	a1	a1	NOUN
ap-3517	343	69	3.2	3.2	NUM
ap-3517	343	70	case	case	NOUN
ap-3517	343	71	a2	a2	PROPN
ap-3517	343	72	3.3	3.3	NUM
ap-3517	343	73	case	case	NOUN
ap-3517	343	74	g2	g2	PROPN
ap-3517	343	75	3.4	3.4	NUM
ap-3517	343	76	cases	case	NOUN
ap-3517	343	77	bn	bn	VERB
ap-3517	343	78	and	and	CCONJ
ap-3517	343	79	cn	cn	PROPN
ap-3517	343	80	4	4	NUM
ap-3517	343	81	concluding	conclude	VERB
ap-3517	343	82	remarks	remark	VERB
ap-3517	343	83	acknowledgements	acknowledgement	NOUN
ap-3517	343	84	references	reference	NOUN