id	sid	tid	token	lemma	pos
ap-3265	1	1	acta	acta	PROPN
ap-3265	1	2	polytechnica	polytechnica	PROPN
ap-3265	1	3	doi:10.14311	doi:10.14311	PROPN
ap-3265	1	4	/	/	SYM
ap-3265	1	5	ap.2016.56.0214	ap.2016.56.0214	PROPN
ap-3265	1	6	acta	acta	PROPN
ap-3265	1	7	polytechnica	polytechnica	PROPN
ap-3265	1	8	56(3):214–223	56(3):214–223	PROPN
ap-3265	1	9	,	,	PUNCT
ap-3265	1	10	2016	2016	NUM
ap-3265	1	11	©	©	PROPN
ap-3265	1	12	czech	czech	PROPN
ap-3265	1	13	technical	technical	PROPN
ap-3265	1	14	university	university	PROPN
ap-3265	1	15	in	in	ADP
ap-3265	1	16	prague	prague	PROPN
ap-3265	1	17	,	,	PUNCT
ap-3265	1	18	2016	2016	NUM
ap-3265	1	19	available	available	ADJ
ap-3265	1	20	online	online	ADV
ap-3265	1	21	at	at	ADP
ap-3265	1	22	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3265	1	23	laplace	laplace	NOUN
ap-3265	1	24	equations	equation	NOUN
ap-3265	1	25	,	,	PUNCT
ap-3265	1	26	conformal	conformal	ADJ
ap-3265	1	27	superintegrability	superintegrability	NOUN
ap-3265	1	28	and	and	CCONJ
ap-3265	1	29	bôcher	bôcher	PROPN
ap-3265	1	30	contractions	contraction	NOUN
ap-3265	1	31	ernest	ernest	PROPN
ap-3265	1	32	kalninsa	kalninsa	PROPN
ap-3265	1	33	,	,	PUNCT
ap-3265	1	34	willard	willard	PROPN
ap-3265	1	35	miller	miller	PROPN
ap-3265	1	36	,	,	PUNCT
ap-3265	1	37	jr.b,∗	jr.b,∗	PROPN
ap-3265	1	38	,	,	PUNCT
ap-3265	1	39	eyal	eyal	PROPN
ap-3265	1	40	subagc	subagc	PROPN
ap-3265	1	41	a	a	DET
ap-3265	1	42	department	department	NOUN
ap-3265	1	43	of	of	ADP
ap-3265	1	44	mathematics	mathematics	PROPN
ap-3265	1	45	,	,	PUNCT
ap-3265	1	46	university	university	NOUN
ap-3265	1	47	of	of	ADP
ap-3265	1	48	waikato	waikato	PROPN
ap-3265	1	49	,	,	PUNCT
ap-3265	1	50	hamilton	hamilton	PROPN
ap-3265	1	51	,	,	PUNCT
ap-3265	1	52	new	new	PROPN
ap-3265	1	53	zealand	zealand	PROPN
ap-3265	1	54	b	b	PROPN
ap-3265	1	55	school	school	NOUN
ap-3265	1	56	of	of	ADP
ap-3265	1	57	mathematics	mathematic	NOUN
ap-3265	1	58	,	,	PUNCT
ap-3265	1	59	university	university	PROPN
ap-3265	1	60	of	of	ADP
ap-3265	1	61	minnesota	minnesota	PROPN
ap-3265	1	62	,	,	PUNCT
ap-3265	1	63	minneapolis	minneapolis	PROPN
ap-3265	1	64	,	,	PUNCT
ap-3265	1	65	minnesota	minnesota	PROPN
ap-3265	1	66	55455	55455	NUM
ap-3265	1	67	,	,	PUNCT
ap-3265	1	68	usa	usa	PROPN
ap-3265	1	69	c	c	PROPN
ap-3265	1	70	department	department	PROPN
ap-3265	1	71	of	of	ADP
ap-3265	1	72	mathematics	mathematics	PROPN
ap-3265	1	73	,	,	PUNCT
ap-3265	1	74	pennsylvania	pennsylvania	PROPN
ap-3265	1	75	state	state	PROPN
ap-3265	1	76	university	university	PROPN
ap-3265	1	77	,	,	PUNCT
ap-3265	1	78	state	state	NOUN
ap-3265	1	79	college	college	NOUN
ap-3265	1	80	16802	16802	NUM
ap-3265	1	81	,	,	PUNCT
ap-3265	1	82	pennsylvania	pennsylvania	PROPN
ap-3265	1	83	usa	usa	PROPN
ap-3265	1	84	∗	∗	PROPN
ap-3265	1	85	corresponding	correspond	VERB
ap-3265	1	86	author	author	NOUN
ap-3265	1	87	:	:	PUNCT
ap-3265	1	88	miller@ima.umn.edu	miller@ima.umn.edu	X
ap-3265	1	89	abstract	abstract	ADJ
ap-3265	1	90	.	.	PUNCT
ap-3265	2	1	quantum	quantum	PROPN
ap-3265	2	2	superintegrable	superintegrable	ADJ
ap-3265	2	3	systems	system	NOUN
ap-3265	2	4	are	be	AUX
ap-3265	2	5	solvable	solvable	ADJ
ap-3265	2	6	eigenvalue	eigenvalue	NOUN
ap-3265	2	7	problems	problem	NOUN
ap-3265	2	8	.	.	PUNCT
ap-3265	3	1	their	their	PRON
ap-3265	3	2	solvability	solvability	NOUN
ap-3265	3	3	is	be	AUX
ap-3265	3	4	due	due	ADJ
ap-3265	3	5	to	to	ADP
ap-3265	3	6	symmetry	symmetry	NOUN
ap-3265	3	7	,	,	PUNCT
ap-3265	3	8	but	but	CCONJ
ap-3265	3	9	the	the	DET
ap-3265	3	10	symmetry	symmetry	NOUN
ap-3265	3	11	is	be	AUX
ap-3265	3	12	often	often	ADV
ap-3265	3	13	“	"	PUNCT
ap-3265	3	14	hidden	hide	VERB
ap-3265	3	15	”	"	PUNCT
ap-3265	3	16	.	.	PUNCT
ap-3265	4	1	the	the	DET
ap-3265	4	2	symmetry	symmetry	NOUN
ap-3265	4	3	generators	generator	NOUN
ap-3265	4	4	of	of	ADP
ap-3265	4	5	2nd	2nd	ADJ
ap-3265	4	6	order	order	NOUN
ap-3265	4	7	superintegrable	superintegrable	ADJ
ap-3265	4	8	systems	system	NOUN
ap-3265	4	9	in	in	ADP
ap-3265	4	10	2	2	NUM
ap-3265	4	11	dimensions	dimension	NOUN
ap-3265	4	12	close	close	ADJ
ap-3265	4	13	under	under	ADP
ap-3265	4	14	commutation	commutation	NOUN
ap-3265	4	15	to	to	PART
ap-3265	4	16	define	define	VERB
ap-3265	4	17	quadratic	quadratic	ADJ
ap-3265	4	18	algebras	algebra	NOUN
ap-3265	4	19	,	,	PUNCT
ap-3265	4	20	a	a	DET
ap-3265	4	21	generalization	generalization	NOUN
ap-3265	4	22	of	of	ADP
ap-3265	4	23	lie	lie	NOUN
ap-3265	4	24	algebras	algebra	NOUN
ap-3265	4	25	.	.	PUNCT
ap-3265	5	1	distinct	distinct	ADJ
ap-3265	5	2	systems	system	NOUN
ap-3265	5	3	and	and	CCONJ
ap-3265	5	4	their	their	PRON
ap-3265	5	5	algebras	algebra	NOUN
ap-3265	5	6	are	be	AUX
ap-3265	5	7	related	relate	VERB
ap-3265	5	8	by	by	ADP
ap-3265	5	9	geometric	geometric	ADJ
ap-3265	5	10	limits	limit	NOUN
ap-3265	5	11	,	,	PUNCT
ap-3265	5	12	induced	induce	VERB
ap-3265	5	13	by	by	ADP
ap-3265	5	14	generalized	generalized	ADJ
ap-3265	5	15	inönü	inönü	NOUN
ap-3265	5	16	-	-	PUNCT
ap-3265	5	17	wigner	wigner	NOUN
ap-3265	5	18	lie	lie	NOUN
ap-3265	5	19	algebra	algebra	NOUN
ap-3265	5	20	contractions	contraction	NOUN
ap-3265	5	21	of	of	ADP
ap-3265	5	22	the	the	DET
ap-3265	5	23	symmetry	symmetry	NOUN
ap-3265	5	24	algebras	algebra	NOUN
ap-3265	5	25	of	of	ADP
ap-3265	5	26	the	the	DET
ap-3265	5	27	underlying	underlying	ADJ
ap-3265	5	28	spaces	space	NOUN
ap-3265	5	29	.	.	PUNCT
ap-3265	6	1	these	these	PRON
ap-3265	6	2	have	have	VERB
ap-3265	6	3	physical	physical	ADJ
ap-3265	6	4	/	/	SYM
ap-3265	6	5	geometric	geometric	ADJ
ap-3265	6	6	implications	implication	NOUN
ap-3265	6	7	,	,	PUNCT
ap-3265	6	8	such	such	ADJ
ap-3265	6	9	as	as	ADP
ap-3265	6	10	the	the	DET
ap-3265	6	11	askey	askey	ADJ
ap-3265	6	12	scheme	scheme	NOUN
ap-3265	6	13	for	for	ADP
ap-3265	6	14	hypergeometric	hypergeometric	ADJ
ap-3265	6	15	orthogonal	orthogonal	ADJ
ap-3265	6	16	polynomials	polynomial	NOUN
ap-3265	6	17	.	.	PUNCT
ap-3265	7	1	the	the	DET
ap-3265	7	2	systems	system	NOUN
ap-3265	7	3	can	can	AUX
ap-3265	7	4	be	be	AUX
ap-3265	7	5	best	well	ADV
ap-3265	7	6	understood	understand	VERB
ap-3265	7	7	by	by	ADP
ap-3265	7	8	transforming	transform	VERB
ap-3265	7	9	them	they	PRON
ap-3265	7	10	to	to	ADP
ap-3265	7	11	laplace	laplace	NOUN
ap-3265	7	12	conformally	conformally	ADV
ap-3265	7	13	superintegrable	superintegrable	ADJ
ap-3265	7	14	systems	system	NOUN
ap-3265	7	15	and	and	CCONJ
ap-3265	7	16	using	use	VERB
ap-3265	7	17	ideas	idea	NOUN
ap-3265	7	18	introduced	introduce	VERB
ap-3265	7	19	in	in	ADP
ap-3265	7	20	the	the	DET
ap-3265	7	21	1894	1894	NUM
ap-3265	7	22	thesis	thesis	NOUN
ap-3265	7	23	of	of	ADP
ap-3265	7	24	bôcher	bôcher	NOUN
ap-3265	7	25	to	to	PART
ap-3265	7	26	study	study	VERB
ap-3265	7	27	separable	separable	ADJ
ap-3265	7	28	solutions	solution	NOUN
ap-3265	7	29	of	of	ADP
ap-3265	7	30	the	the	DET
ap-3265	7	31	wave	wave	NOUN
ap-3265	7	32	equation	equation	NOUN
ap-3265	7	33	.	.	PUNCT
ap-3265	8	1	the	the	DET
ap-3265	8	2	contractions	contraction	NOUN
ap-3265	8	3	can	can	AUX
ap-3265	8	4	be	be	AUX
ap-3265	8	5	subsumed	subsume	VERB
ap-3265	8	6	into	into	ADP
ap-3265	8	7	contractions	contraction	NOUN
ap-3265	8	8	of	of	ADP
ap-3265	8	9	the	the	DET
ap-3265	8	10	conformal	conformal	ADJ
ap-3265	8	11	algebra	algebra	NOUN
ap-3265	8	12	so(4,c	so(4,c	NOUN
ap-3265	8	13	)	)	PUNCT
ap-3265	8	14	to	to	ADP
ap-3265	8	15	itself	itself	PRON
ap-3265	8	16	.	.	PUNCT
ap-3265	9	1	here	here	ADV
ap-3265	9	2	we	we	PRON
ap-3265	9	3	announce	announce	VERB
ap-3265	9	4	main	main	ADJ
ap-3265	9	5	findings	finding	NOUN
ap-3265	9	6	,	,	PUNCT
ap-3265	9	7	with	with	ADP
ap-3265	9	8	detailed	detailed	ADJ
ap-3265	9	9	classifications	classification	NOUN
ap-3265	9	10	in	in	ADP
ap-3265	9	11	papers	paper	NOUN
ap-3265	9	12	submitted	submit	VERB
ap-3265	9	13	and	and	CCONJ
ap-3265	9	14	under	under	ADP
ap-3265	9	15	preparation	preparation	NOUN
ap-3265	9	16	.	.	PUNCT
ap-3265	10	1	keywords	keyword	NOUN
ap-3265	10	2	:	:	PUNCT
ap-3265	10	3	conformal	conformal	ADJ
ap-3265	10	4	superintegrability	superintegrability	NOUN
ap-3265	10	5	;	;	PUNCT
ap-3265	10	6	contractions	contraction	NOUN
ap-3265	10	7	;	;	PUNCT
ap-3265	10	8	laplace	laplace	NOUN
ap-3265	10	9	equations	equation	NOUN
ap-3265	10	10	.	.	PUNCT
ap-3265	11	1	1	1	X
ap-3265	11	2	.	.	X
ap-3265	11	3	introduction	introduction	NOUN
ap-3265	11	4	a	a	DET
ap-3265	11	5	quantum	quantum	ADJ
ap-3265	11	6	superintegrable	superintegrable	ADJ
ap-3265	11	7	system	system	NOUN
ap-3265	11	8	is	be	AUX
ap-3265	11	9	an	an	DET
ap-3265	11	10	integrable	integrable	ADJ
ap-3265	11	11	hamiltonian	hamiltonian	ADJ
ap-3265	11	12	system	system	NOUN
ap-3265	11	13	on	on	ADP
ap-3265	11	14	an	an	DET
ap-3265	11	15	n	n	ADV
ap-3265	11	16	-	-	PUNCT
ap-3265	11	17	dimensional	dimensional	ADJ
ap-3265	11	18	riemannian	riemannian	ADJ
ap-3265	11	19	/	/	SYM
ap-3265	11	20	pseudo	pseudo	NOUN
ap-3265	11	21	-	-	ADJ
ap-3265	11	22	riemannian	riemannian	ADJ
ap-3265	11	23	manifold	manifold	NOUN
ap-3265	11	24	with	with	ADP
ap-3265	11	25	potential	potential	NOUN
ap-3265	11	26	:	:	PUNCT
ap-3265	11	27	h	h	NOUN
ap-3265	11	28	=	=	SYM
ap-3265	11	29	∆n	∆n	PROPN
ap-3265	11	30	+	+	CCONJ
ap-3265	11	31	v	v	NOUN
ap-3265	11	32	that	that	PRON
ap-3265	11	33	admits	admit	VERB
ap-3265	11	34	2n−	2n−	PROPN
ap-3265	11	35	1	1	NUM
ap-3265	11	36	algebraically	algebraically	ADV
ap-3265	11	37	independent	independent	ADJ
ap-3265	11	38	partial	partial	ADJ
ap-3265	11	39	differential	differential	NOUN
ap-3265	11	40	operators	operator	NOUN
ap-3265	11	41	lj	lj	VERB
ap-3265	11	42	commuting	commute	VERB
ap-3265	11	43	with	with	ADP
ap-3265	11	44	h	h	NOUN
ap-3265	11	45	,	,	PUNCT
ap-3265	11	46	the	the	DET
ap-3265	11	47	maximum	maximum	ADJ
ap-3265	11	48	possible	possible	ADJ
ap-3265	11	49	.	.	PUNCT
ap-3265	12	1	[	[	X
ap-3265	12	2	h	h	NOUN
ap-3265	12	3	,	,	PUNCT
ap-3265	12	4	lj	lj	INTJ
ap-3265	12	5	]	]	PUNCT
ap-3265	12	6	=	=	SYM
ap-3265	12	7	0	0	NUM
ap-3265	12	8	,	,	PUNCT
ap-3265	12	9	j	j	PROPN
ap-3265	12	10	=	=	SYM
ap-3265	12	11	1	1	NUM
ap-3265	12	12	,	,	PUNCT
ap-3265	12	13	2	2	NUM
ap-3265	12	14	,	,	PUNCT
ap-3265	12	15	·	·	PUNCT
ap-3265	12	16	·	·	PUNCT
ap-3265	12	17	·	·	PUNCT
ap-3265	12	18	,	,	PUNCT
ap-3265	12	19	2n−	2n−	PROPN
ap-3265	12	20	1	1	NUM
ap-3265	12	21	.	.	PUNCT
ap-3265	12	22	superintegrability	superintegrability	NOUN
ap-3265	12	23	captures	capture	VERB
ap-3265	12	24	the	the	DET
ap-3265	12	25	properties	property	NOUN
ap-3265	12	26	of	of	ADP
ap-3265	12	27	quantum	quantum	ADJ
ap-3265	12	28	hamiltonian	hamiltonian	NOUN
ap-3265	12	29	systems	system	NOUN
ap-3265	12	30	that	that	PRON
ap-3265	12	31	allow	allow	VERB
ap-3265	12	32	the	the	DET
ap-3265	12	33	schrödinger	schrödinger	PROPN
ap-3265	12	34	eigenvalue	eigenvalue	PROPN
ap-3265	12	35	problem	problem	NOUN
ap-3265	12	36	(	(	PUNCT
ap-3265	12	37	or	or	CCONJ
ap-3265	12	38	helmholtz	helmholtz	NOUN
ap-3265	12	39	equation	equation	NOUN
ap-3265	12	40	)	)	PUNCT
ap-3265	12	41	hψ	hψ	NOUN
ap-3265	13	1	=	=	SYM
ap-3265	13	2	eψ	eψ	NOUN
ap-3265	13	3	to	to	PART
ap-3265	13	4	be	be	AUX
ap-3265	13	5	solved	solve	VERB
ap-3265	13	6	exactly	exactly	ADV
ap-3265	13	7	,	,	PUNCT
ap-3265	13	8	analytically	analytically	ADV
ap-3265	13	9	and	and	CCONJ
ap-3265	13	10	algebraically	algebraically	ADV
ap-3265	13	11	[	[	X
ap-3265	13	12	1–5	1–5	X
ap-3265	13	13	]	]	X
ap-3265	13	14	.	.	PUNCT
ap-3265	14	1	a	a	DET
ap-3265	14	2	system	system	NOUN
ap-3265	14	3	is	be	AUX
ap-3265	14	4	of	of	ADP
ap-3265	14	5	order	order	NOUN
ap-3265	15	1	k	k	NOUN
ap-3265	16	1	if	if	SCONJ
ap-3265	16	2	the	the	DET
ap-3265	16	3	maximum	maximum	ADJ
ap-3265	16	4	order	order	NOUN
ap-3265	16	5	of	of	ADP
ap-3265	16	6	the	the	DET
ap-3265	16	7	symmetry	symmetry	NOUN
ap-3265	16	8	operators	operator	NOUN
ap-3265	16	9	,	,	PUNCT
ap-3265	16	10	other	other	ADJ
ap-3265	16	11	than	than	ADP
ap-3265	16	12	h	h	NOUN
ap-3265	16	13	,	,	PUNCT
ap-3265	16	14	is	be	AUX
ap-3265	16	15	k.	k.	PROPN
ap-3265	16	16	for	for	ADP
ap-3265	16	17	n	n	PROPN
ap-3265	16	18	=	=	SYM
ap-3265	16	19	2	2	NUM
ap-3265	16	20	,	,	PUNCT
ap-3265	16	21	k	k	NOUN
ap-3265	16	22	=	=	SYM
ap-3265	16	23	1	1	NUM
ap-3265	16	24	,	,	PUNCT
ap-3265	16	25	2	2	NUM
ap-3265	16	26	all	all	DET
ap-3265	16	27	systems	system	NOUN
ap-3265	16	28	are	be	AUX
ap-3265	16	29	known	know	VERB
ap-3265	16	30	,	,	PUNCT
ap-3265	16	31	see	see	VERB
ap-3265	16	32	,	,	PUNCT
ap-3265	16	33	e.g.	e.g.	ADV
ap-3265	16	34	,	,	PUNCT
ap-3265	16	35	[	[	X
ap-3265	16	36	6	6	NUM
ap-3265	16	37	,	,	PUNCT
ap-3265	16	38	7	7	NUM
ap-3265	16	39	]	]	PUNCT
ap-3265	16	40	we	we	PRON
ap-3265	16	41	review	review	VERB
ap-3265	16	42	quickly	quickly	ADV
ap-3265	16	43	the	the	DET
ap-3265	16	44	facts	fact	NOUN
ap-3265	16	45	for	for	ADP
ap-3265	16	46	free	free	ADJ
ap-3265	16	47	2nd	2nd	ADJ
ap-3265	16	48	order	order	NOUN
ap-3265	16	49	superintegrable	superintegrable	ADJ
ap-3265	16	50	systems	system	NOUN
ap-3265	16	51	,	,	PUNCT
ap-3265	16	52	(	(	PUNCT
ap-3265	16	53	i.e.	i.e.	X
ap-3265	16	54	,	,	PUNCT
ap-3265	16	55	no	no	DET
ap-3265	16	56	potential	potential	NOUN
ap-3265	16	57	,	,	PUNCT
ap-3265	16	58	k	k	PROPN
ap-3265	16	59	=	=	SYM
ap-3265	16	60	2	2	NUM
ap-3265	16	61	)	)	PUNCT
ap-3265	16	62	in	in	ADP
ap-3265	16	63	the	the	DET
ap-3265	16	64	case	case	NOUN
ap-3265	16	65	n	n	NOUN
ap-3265	16	66	=	=	SYM
ap-3265	16	67	2	2	NUM
ap-3265	16	68	,	,	PUNCT
ap-3265	16	69	2n	2n	NUM
ap-3265	16	70	−	−	NOUN
ap-3265	16	71	1	1	NUM
ap-3265	16	72	=	=	SYM
ap-3265	16	73	3	3	X
ap-3265	16	74	.	.	PUNCT
ap-3265	17	1	the	the	DET
ap-3265	17	2	complex	complex	ADJ
ap-3265	17	3	spaces	space	NOUN
ap-3265	17	4	with	with	ADP
ap-3265	17	5	laplace	laplace	NOUN
ap-3265	17	6	-	-	PUNCT
ap-3265	17	7	beltrami	beltrami	ADJ
ap-3265	17	8	operators	operator	NOUN
ap-3265	17	9	admitting	admit	VERB
ap-3265	17	10	at	at	ADV
ap-3265	17	11	least	least	ADV
ap-3265	17	12	three	three	NUM
ap-3265	17	13	2nd	2nd	ADJ
ap-3265	17	14	order	order	NOUN
ap-3265	17	15	symmetries	symmetry	NOUN
ap-3265	17	16	were	be	AUX
ap-3265	17	17	classified	classify	VERB
ap-3265	17	18	by	by	ADP
ap-3265	17	19	koenigs	koenig	NOUN
ap-3265	17	20	in	in	ADP
ap-3265	17	21	1896	1896	NUM
ap-3265	17	22	[	[	X
ap-3265	17	23	8	8	NUM
ap-3265	17	24	]	]	PUNCT
ap-3265	17	25	.	.	PUNCT
ap-3265	18	1	they	they	PRON
ap-3265	18	2	are	be	AUX
ap-3265	18	3	:	:	PUNCT
ap-3265	18	4	•	•	ADP
ap-3265	18	5	the	the	DET
ap-3265	18	6	two	two	NUM
ap-3265	18	7	constant	constant	ADJ
ap-3265	18	8	curvature	curvature	NOUN
ap-3265	18	9	spaces	space	NOUN
ap-3265	18	10	(	(	PUNCT
ap-3265	18	11	flat	flat	ADJ
ap-3265	18	12	space	space	NOUN
ap-3265	18	13	and	and	CCONJ
ap-3265	18	14	the	the	DET
ap-3265	18	15	complex	complex	ADJ
ap-3265	18	16	sphere	sphere	NOUN
ap-3265	18	17	)	)	PUNCT
ap-3265	18	18	,	,	PUNCT
ap-3265	18	19	six	six	NUM
ap-3265	18	20	linearly	linearly	ADV
ap-3265	18	21	independent	independent	ADJ
ap-3265	18	22	2nd	2nd	ADJ
ap-3265	18	23	order	order	NOUN
ap-3265	18	24	symmetries	symmetry	NOUN
ap-3265	18	25	and	and	CCONJ
ap-3265	18	26	three	three	NUM
ap-3265	18	27	1st	1st	ADJ
ap-3265	18	28	order	order	NOUN
ap-3265	18	29	symmetries	symmetry	NOUN
ap-3265	18	30	,	,	PUNCT
ap-3265	18	31	•	•	ADP
ap-3265	18	32	the	the	DET
ap-3265	18	33	four	four	NUM
ap-3265	18	34	darboux	darboux	ADJ
ap-3265	18	35	spaces	space	NOUN
ap-3265	18	36	(	(	PUNCT
ap-3265	18	37	one	one	NUM
ap-3265	18	38	with	with	ADP
ap-3265	18	39	a	a	DET
ap-3265	18	40	parameter	parameter	NOUN
ap-3265	18	41	)	)	PUNCT
ap-3265	18	42	,	,	PUNCT
ap-3265	18	43	four	four	NUM
ap-3265	18	44	2nd	2nd	ADJ
ap-3265	18	45	order	order	NOUN
ap-3265	18	46	symmetries	symmetry	NOUN
ap-3265	18	47	and	and	CCONJ
ap-3265	18	48	one	one	NUM
ap-3265	18	49	1st	1st	ADJ
ap-3265	18	50	order	order	NOUN
ap-3265	18	51	symmetry	symmetry	NOUN
ap-3265	19	1	[	[	X
ap-3265	19	2	9	9	NUM
ap-3265	19	3	]	]	PUNCT
ap-3265	19	4	,	,	PUNCT
ap-3265	19	5	ds2	ds2	PROPN
ap-3265	19	6	=	=	SYM
ap-3265	19	7	4x(dx2	4x(dx2	PROPN
ap-3265	19	8	+	+	NUM
ap-3265	19	9	dy2	dy2	PROPN
ap-3265	19	10	)	)	PUNCT
ap-3265	19	11	,	,	PUNCT
ap-3265	20	1	ds2	ds2	PROPN
ap-3265	20	2	=	=	SYM
ap-3265	20	3	x2	x2	PROPN
ap-3265	21	1	+	+	CCONJ
ap-3265	21	2	1	1	NUM
ap-3265	21	3	x2	x2	NOUN
ap-3265	21	4	(	(	PUNCT
ap-3265	21	5	dx2	dx2	PROPN
ap-3265	21	6	+	+	PROPN
ap-3265	21	7	dy2	dy2	PROPN
ap-3265	21	8	)	)	PUNCT
ap-3265	21	9	,	,	PUNCT
ap-3265	21	10	ds2	ds2	PROPN
ap-3265	21	11	=	=	PUNCT
ap-3265	21	12	ex	ex	X
ap-3265	22	1	+	+	NOUN
ap-3265	22	2	1	1	NUM
ap-3265	22	3	e2x	e2x	X
ap-3265	22	4	(	(	PUNCT
ap-3265	22	5	dx2	dx2	PROPN
ap-3265	22	6	+	+	PROPN
ap-3265	22	7	dy2	dy2	PROPN
ap-3265	22	8	)	)	PUNCT
ap-3265	22	9	,	,	PUNCT
ap-3265	22	10	ds2	ds2	PROPN
ap-3265	22	11	=	=	SYM
ap-3265	22	12	2	2	X
ap-3265	22	13	cos	cos	NOUN
ap-3265	22	14	2x+	2x+	NUM
ap-3265	22	15	b	b	PROPN
ap-3265	22	16	sin2	sin2	NOUN
ap-3265	22	17	2x	2x	NUM
ap-3265	22	18	(	(	PUNCT
ap-3265	22	19	dx2	dx2	PROPN
ap-3265	22	20	+	+	PROPN
ap-3265	22	21	dy2	dy2	PROPN
ap-3265	22	22	)	)	PUNCT
ap-3265	22	23	.	.	PUNCT
ap-3265	23	1	•	•	NUM
ap-3265	23	2	eleven	eleven	NUM
ap-3265	23	3	4	4	NUM
ap-3265	23	4	-	-	PUNCT
ap-3265	23	5	parameter	parameter	NOUN
ap-3265	23	6	koenigs	koenig	NOUN
ap-3265	23	7	spaces	space	VERB
ap-3265	23	8	.	.	PUNCT
ap-3265	24	1	no	no	DET
ap-3265	24	2	1st	1st	ADJ
ap-3265	24	3	order	order	NOUN
ap-3265	24	4	symmetries	symmetry	NOUN
ap-3265	24	5	.	.	PUNCT
ap-3265	25	1	an	an	DET
ap-3265	25	2	example	example	NOUN
ap-3265	25	3	is	be	AUX
ap-3265	25	4	ds2	ds2	PROPN
ap-3265	25	5	=	=	PUNCT
ap-3265	25	6	(	(	PUNCT
ap-3265	25	7	c1	c1	PROPN
ap-3265	25	8	x2	x2	PROPN
ap-3265	26	1	+	+	CCONJ
ap-3265	26	2	y2	y2	PROPN
ap-3265	27	1	+	+	CCONJ
ap-3265	27	2	c2	c2	PROPN
ap-3265	27	3	x2	x2	PROPN
ap-3265	28	1	+	+	CCONJ
ap-3265	28	2	c3	c3	PROPN
ap-3265	28	3	y2	y2	PROPN
ap-3265	28	4	+	+	CCONJ
ap-3265	28	5	c4	c4	NOUN
ap-3265	28	6	)	)	PUNCT
ap-3265	28	7	(	(	PUNCT
ap-3265	28	8	dx2	dx2	PROPN
ap-3265	28	9	+	+	PROPN
ap-3265	28	10	dy2	dy2	PROPN
ap-3265	28	11	)	)	PUNCT
ap-3265	28	12	.	.	PUNCT
ap-3265	29	1	for	for	ADP
ap-3265	29	2	2nd	2nd	ADJ
ap-3265	29	3	order	order	NOUN
ap-3265	29	4	systems	system	NOUN
ap-3265	29	5	with	with	ADP
ap-3265	29	6	non	non	ADJ
ap-3265	29	7	-	-	ADJ
ap-3265	29	8	constant	constant	ADJ
ap-3265	29	9	potential	potential	NOUN
ap-3265	29	10	,	,	PUNCT
ap-3265	29	11	k	k	PROPN
ap-3265	29	12	=	=	SYM
ap-3265	29	13	2	2	NUM
ap-3265	29	14	,	,	PUNCT
ap-3265	29	15	the	the	DET
ap-3265	29	16	following	follow	VERB
ap-3265	29	17	is	be	AUX
ap-3265	29	18	true	true	ADJ
ap-3265	29	19	[	[	X
ap-3265	29	20	6	6	NUM
ap-3265	29	21	,	,	PUNCT
ap-3265	29	22	7	7	NUM
ap-3265	29	23	,	,	PUNCT
ap-3265	29	24	10–12	10–12	NUM
ap-3265	29	25	]	]	PUNCT
ap-3265	29	26	.	.	PUNCT
ap-3265	30	1	•	•	NUM
ap-3265	30	2	the	the	DET
ap-3265	30	3	symmetry	symmetry	NOUN
ap-3265	30	4	operators	operator	NOUN
ap-3265	30	5	of	of	ADP
ap-3265	30	6	each	each	DET
ap-3265	30	7	system	system	NOUN
ap-3265	30	8	close	close	ADJ
ap-3265	30	9	under	under	ADP
ap-3265	30	10	commutation	commutation	NOUN
ap-3265	30	11	to	to	PART
ap-3265	30	12	generate	generate	VERB
ap-3265	30	13	a	a	DET
ap-3265	30	14	quadratic	quadratic	ADJ
ap-3265	30	15	algebra	algebra	NOUN
ap-3265	30	16	,	,	PUNCT
ap-3265	30	17	and	and	CCONJ
ap-3265	30	18	the	the	DET
ap-3265	30	19	irreducible	irreducible	ADJ
ap-3265	30	20	representations	representation	NOUN
ap-3265	30	21	of	of	ADP
ap-3265	30	22	this	this	DET
ap-3265	30	23	algebra	algebra	NOUN
ap-3265	30	24	determine	determine	VERB
ap-3265	30	25	the	the	DET
ap-3265	30	26	eigenvalues	eigenvalue	NOUN
ap-3265	30	27	of	of	ADP
ap-3265	30	28	h	h	NOUN
ap-3265	30	29	and	and	CCONJ
ap-3265	30	30	their	their	PRON
ap-3265	30	31	multiplicity	multiplicity	NOUN
ap-3265	30	32	.	.	PUNCT
ap-3265	31	1	•	•	NUM
ap-3265	31	2	all	all	DET
ap-3265	31	3	the	the	DET
ap-3265	31	4	2nd	2nd	ADJ
ap-3265	31	5	order	order	NOUN
ap-3265	31	6	superintegrable	superintegrable	ADJ
ap-3265	31	7	systems	system	NOUN
ap-3265	31	8	are	be	AUX
ap-3265	31	9	limiting	limit	VERB
ap-3265	31	10	cases	case	NOUN
ap-3265	31	11	of	of	ADP
ap-3265	31	12	a	a	DET
ap-3265	31	13	single	single	ADJ
ap-3265	31	14	system	system	NOUN
ap-3265	31	15	:	:	PUNCT
ap-3265	31	16	the	the	DET
ap-3265	31	17	generic	generic	ADJ
ap-3265	31	18	3	3	NUM
ap-3265	31	19	-	-	PUNCT
ap-3265	31	20	parameter	parameter	NOUN
ap-3265	31	21	potential	potential	NOUN
ap-3265	31	22	on	on	ADP
ap-3265	31	23	the	the	DET
ap-3265	31	24	2	2	NUM
ap-3265	31	25	-	-	PUNCT
ap-3265	31	26	sphere	sphere	NOUN
ap-3265	31	27	,	,	PUNCT
ap-3265	31	28	s9	s9	VERB
ap-3265	31	29	in	in	ADP
ap-3265	31	30	our	our	PRON
ap-3265	31	31	listing	list	VERB
ap-3265	31	32	[	[	X
ap-3265	31	33	13	13	NUM
ap-3265	31	34	]	]	PUNCT
ap-3265	31	35	,	,	PUNCT
ap-3265	31	36	or	or	CCONJ
ap-3265	31	37	are	be	AUX
ap-3265	31	38	obtained	obtain	VERB
ap-3265	31	39	from	from	ADP
ap-3265	31	40	these	these	DET
ap-3265	31	41	limits	limit	NOUN
ap-3265	31	42	by	by	ADP
ap-3265	31	43	a	a	DET
ap-3265	31	44	stäckel	stäckel	NOUN
ap-3265	31	45	transform	transform	NOUN
ap-3265	31	46	(	(	PUNCT
ap-3265	31	47	an	an	DET
ap-3265	31	48	invertible	invertible	ADJ
ap-3265	31	49	structure	structure	NOUN
ap-3265	31	50	preserving	preserve	VERB
ap-3265	31	51	mapping	mapping	NOUN
ap-3265	31	52	of	of	ADP
ap-3265	31	53	superintegrable	superintegrable	ADJ
ap-3265	31	54	systems	system	NOUN
ap-3265	32	1	[	[	X
ap-3265	32	2	6	6	NUM
ap-3265	32	3	]	]	NUM
ap-3265	32	4	)	)	PUNCT
ap-3265	32	5	.	.	PUNCT
ap-3265	33	1	analogously	analogously	ADV
ap-3265	33	2	all	all	DET
ap-3265	33	3	quadratic	quadratic	ADJ
ap-3265	33	4	symmetry	symmetry	NOUN
ap-3265	33	5	algebras	algebra	NOUN
ap-3265	33	6	of	of	ADP
ap-3265	33	7	these	these	DET
ap-3265	33	8	systems	system	NOUN
ap-3265	33	9	are	be	AUX
ap-3265	33	10	limits	limit	NOUN
ap-3265	33	11	of	of	ADP
ap-3265	33	12	that	that	PRON
ap-3265	33	13	of	of	ADP
ap-3265	33	14	s9	s9	NOUN
ap-3265	33	15	.	.	PUNCT
ap-3265	34	1	s9	s9	NOUN
ap-3265	34	2	:	:	PUNCT
ap-3265	35	1	h	h	NOUN
ap-3265	35	2	=	=	PUNCT
ap-3265	35	3	∆2	∆2	PROPN
ap-3265	36	1	+	+	CCONJ
ap-3265	36	2	a1	a1	NOUN
ap-3265	36	3	s2	s2	NOUN
ap-3265	36	4	1	1	NUM
ap-3265	36	5	+	+	NUM
ap-3265	36	6	a2	a2	PROPN
ap-3265	36	7	s2	s2	NOUN
ap-3265	36	8	2	2	NUM
ap-3265	36	9	+	+	NUM
ap-3265	36	10	a3	a3	NOUN
ap-3265	36	11	s2	s2	NOUN
ap-3265	36	12	3	3	NUM
ap-3265	36	13	,	,	PUNCT
ap-3265	36	14	s2	s2	VERB
ap-3265	36	15	1	1	NUM
ap-3265	36	16	+	+	NOUN
ap-3265	36	17	s2	s2	VERB
ap-3265	36	18	2	2	NUM
ap-3265	36	19	+	+	CCONJ
ap-3265	36	20	s2	s2	VERB
ap-3265	36	21	3	3	NUM
ap-3265	36	22	=	=	SYM
ap-3265	36	23	1	1	NUM
ap-3265	36	24	,	,	PUNCT
ap-3265	36	25	l1	l1	PROPN
ap-3265	36	26	=	=	SYM
ap-3265	36	27	(	(	PUNCT
ap-3265	36	28	s2∂s3	s2∂s3	VERB
ap-3265	36	29	−	−	PROPN
ap-3265	36	30	s3∂s2)2	s3∂s2)2	PROPN
ap-3265	36	31	+	+	CCONJ
ap-3265	36	32	a3s	a3s	NOUN
ap-3265	36	33	2	2	NUM
ap-3265	36	34	2	2	NUM
ap-3265	36	35	s2	s2	NOUN
ap-3265	36	36	3	3	NUM
ap-3265	36	37	+	+	CCONJ
ap-3265	36	38	a2s	a2s	NOUN
ap-3265	36	39	2	2	NUM
ap-3265	36	40	3	3	NUM
ap-3265	36	41	s2	s2	NOUN
ap-3265	36	42	2	2	NUM
ap-3265	36	43	,	,	PUNCT
ap-3265	36	44	l2	l2	NOUN
ap-3265	36	45	,	,	PUNCT
ap-3265	36	46	l3	l3	PROPN
ap-3265	36	47	,	,	PUNCT
ap-3265	36	48	•	•	NUM
ap-3265	36	49	2nd	2nd	ADJ
ap-3265	36	50	order	order	NOUN
ap-3265	36	51	superintegrable	superintegrable	ADJ
ap-3265	36	52	systems	system	NOUN
ap-3265	36	53	are	be	AUX
ap-3265	36	54	multiseparable	multiseparable	ADJ
ap-3265	36	55	.	.	PUNCT
ap-3265	37	1	214	214	NUM
ap-3265	37	2	http://dx.doi.org/10.14311/ap.2016.56.0214	http://dx.doi.org/10.14311/ap.2016.56.0214	NOUN
ap-3265	37	3	http://ojs.cvut.cz/ojs/index.php/ap	http://ojs.cvut.cz/ojs/index.php/ap	PROPN
ap-3265	37	4	vol	vol	NOUN
ap-3265	37	5	.	.	PUNCT
ap-3265	38	1	56	56	NUM
ap-3265	38	2	no	no	NOUN
ap-3265	38	3	.	.	PUNCT
ap-3265	39	1	3/2016	3/2016	NUM
ap-3265	39	2	laplace	laplace	NOUN
ap-3265	39	3	equations	equation	NOUN
ap-3265	39	4	,	,	PUNCT
ap-3265	39	5	conformal	conformal	ADJ
ap-3265	39	6	superintegrability	superintegrability	NOUN
ap-3265	39	7	and	and	CCONJ
ap-3265	39	8	bôcher	bôcher	NOUN
ap-3265	39	9	contractions	contraction	NOUN
ap-3265	39	10	here	here	ADV
ap-3265	39	11	we	we	PRON
ap-3265	39	12	consider	consider	VERB
ap-3265	39	13	only	only	ADV
ap-3265	39	14	the	the	DET
ap-3265	39	15	nondegenerate	nondegenerate	ADJ
ap-3265	39	16	superintegrable	superintegrable	ADJ
ap-3265	39	17	systems	system	NOUN
ap-3265	39	18	:	:	PUNCT
ap-3265	39	19	those	those	PRON
ap-3265	39	20	with	with	ADP
ap-3265	39	21	4	4	NUM
ap-3265	39	22	-	-	PUNCT
ap-3265	39	23	parameter	parameter	NOUN
ap-3265	39	24	potentials	potential	NOUN
ap-3265	39	25	(	(	PUNCT
ap-3265	39	26	the	the	DET
ap-3265	39	27	maximum	maximum	ADJ
ap-3265	39	28	possible	possible	ADJ
ap-3265	39	29	):	):	PUNCT
ap-3265	39	30	v	v	X
ap-3265	39	31	(	(	PUNCT
ap-3265	39	32	x	x	NOUN
ap-3265	39	33	)	)	PUNCT
ap-3265	39	34	=	=	SYM
ap-3265	39	35	a1v(1)(x	a1v(1)(x	NOUN
ap-3265	39	36	)	)	PUNCT
ap-3265	39	37	+	+	PUNCT
ap-3265	39	38	a2v(2)(x	a2v(2)(x	PROPN
ap-3265	39	39	)	)	PUNCT
ap-3265	39	40	+	+	ADJ
ap-3265	39	41	a3v(3)(x	a3v(3)(x	NOUN
ap-3265	39	42	)	)	PUNCT
ap-3265	39	43	+	+	CCONJ
ap-3265	39	44	a4	a4	NOUN
ap-3265	39	45	,	,	PUNCT
ap-3265	39	46	where	where	SCONJ
ap-3265	39	47	{	{	PUNCT
ap-3265	39	48	v(1)(x	v(1)(x	NOUN
ap-3265	39	49	)	)	PUNCT
ap-3265	39	50	,	,	PUNCT
ap-3265	39	51	v(2)(x	v(2)(x	NOUN
ap-3265	39	52	)	)	PUNCT
ap-3265	39	53	,	,	PUNCT
ap-3265	39	54	v(3)(x	v(3)(x	NOUN
ap-3265	39	55	)	)	PUNCT
ap-3265	39	56	,	,	PUNCT
ap-3265	39	57	1	1	X
ap-3265	39	58	}	}	PUNCT
ap-3265	39	59	is	be	AUX
ap-3265	39	60	a	a	DET
ap-3265	39	61	linearly	linearly	ADV
ap-3265	39	62	independent	independent	ADJ
ap-3265	39	63	set	set	NOUN
ap-3265	39	64	.	.	PUNCT
ap-3265	40	1	for	for	ADP
ap-3265	40	2	these	these	DET
ap-3265	40	3	the	the	DET
ap-3265	40	4	symmetry	symmetry	NOUN
ap-3265	40	5	algebra	algebra	NOUN
ap-3265	40	6	generated	generate	VERB
ap-3265	40	7	by	by	ADP
ap-3265	40	8	h	h	PROPN
ap-3265	40	9	,	,	PUNCT
ap-3265	40	10	l1	l1	PROPN
ap-3265	40	11	,	,	PUNCT
ap-3265	40	12	l2	l2	NOUN
ap-3265	40	13	always	always	ADV
ap-3265	40	14	closes	close	VERB
ap-3265	40	15	under	under	ADP
ap-3265	40	16	commutation	commutation	NOUN
ap-3265	40	17	and	and	CCONJ
ap-3265	40	18	gives	give	VERB
ap-3265	40	19	the	the	DET
ap-3265	40	20	following	follow	VERB
ap-3265	40	21	quadratic	quadratic	ADJ
ap-3265	40	22	algebra	algebra	NOUN
ap-3265	40	23	structure	structure	NOUN
ap-3265	40	24	:	:	PUNCT
ap-3265	40	25	define	define	VERB
ap-3265	40	26	3rd	3rd	ADJ
ap-3265	40	27	order	order	NOUN
ap-3265	40	28	commutator	commutator	NOUN
ap-3265	40	29	r	r	NOUN
ap-3265	40	30	by	by	ADP
ap-3265	40	31	r	r	NOUN
ap-3265	40	32	=	=	PUNCT
ap-3265	41	1	[	[	X
ap-3265	41	2	l1	l1	PROPN
ap-3265	41	3	,	,	PUNCT
ap-3265	41	4	l2	l2	NOUN
ap-3265	41	5	]	]	PUNCT
ap-3265	41	6	.	.	PUNCT
ap-3265	42	1	then	then	ADV
ap-3265	42	2	[	[	X
ap-3265	42	3	lj	lj	INTJ
ap-3265	42	4	,	,	PUNCT
ap-3265	42	5	r	r	X
ap-3265	42	6	]	]	X
ap-3265	42	7	=	=	SYM
ap-3265	42	8	a	a	PRON
ap-3265	42	9	(	(	PUNCT
ap-3265	42	10	j	j	NOUN
ap-3265	42	11	)	)	PUNCT
ap-3265	42	12	1	1	NUM
ap-3265	42	13	l2	l2	NOUN
ap-3265	42	14	1	1	NUM
ap-3265	42	15	+	+	NOUN
ap-3265	42	16	a	a	DET
ap-3265	42	17	(	(	PUNCT
ap-3265	42	18	j	j	NOUN
ap-3265	42	19	)	)	PUNCT
ap-3265	42	20	2	2	NUM
ap-3265	42	21	l2	l2	NOUN
ap-3265	42	22	2	2	NUM
ap-3265	42	23	+	+	NOUN
ap-3265	42	24	a	a	DET
ap-3265	42	25	(	(	PUNCT
ap-3265	42	26	j	j	NOUN
ap-3265	42	27	)	)	PUNCT
ap-3265	42	28	3	3	NUM
ap-3265	42	29	h2	h2	NOUN
ap-3265	42	30	+	+	NOUN
ap-3265	42	31	a	a	DET
ap-3265	42	32	(	(	PUNCT
ap-3265	42	33	j	j	NOUN
ap-3265	42	34	)	)	PUNCT
ap-3265	42	35	4	4	NUM
ap-3265	42	36	{	{	PUNCT
ap-3265	42	37	l1	l1	PROPN
ap-3265	42	38	,	,	PUNCT
ap-3265	42	39	l2}+a	l2}+a	X
ap-3265	42	40	(	(	PUNCT
ap-3265	42	41	j	j	NOUN
ap-3265	42	42	)	)	PUNCT
ap-3265	42	43	5	5	NUM
ap-3265	42	44	hl1	hl1	PROPN
ap-3265	42	45	+	+	PROPN
ap-3265	42	46	a	a	DET
ap-3265	42	47	(	(	PUNCT
ap-3265	42	48	j	j	NOUN
ap-3265	42	49	)	)	PUNCT
ap-3265	42	50	6	6	NUM
ap-3265	42	51	hl2	hl2	NOUN
ap-3265	42	52	+	+	ADP
ap-3265	42	53	a	a	DET
ap-3265	42	54	(	(	PUNCT
ap-3265	42	55	j	j	NOUN
ap-3265	42	56	)	)	PUNCT
ap-3265	42	57	7	7	NUM
ap-3265	42	58	l1	l1	PROPN
ap-3265	42	59	+	+	PROPN
ap-3265	42	60	a	a	DET
ap-3265	42	61	(	(	PUNCT
ap-3265	42	62	j	j	NOUN
ap-3265	42	63	)	)	PUNCT
ap-3265	42	64	8	8	NUM
ap-3265	42	65	l2	l2	NOUN
ap-3265	42	66	+	+	ADV
ap-3265	42	67	a	a	DET
ap-3265	42	68	(	(	PUNCT
ap-3265	42	69	j	j	NOUN
ap-3265	42	70	)	)	PUNCT
ap-3265	42	71	9	9	NUM
ap-3265	42	72	h	h	NOUN
ap-3265	43	1	+	+	NOUN
ap-3265	43	2	a	a	DET
ap-3265	43	3	(	(	PUNCT
ap-3265	43	4	j	j	NOUN
ap-3265	43	5	)	)	PUNCT
ap-3265	43	6	10	10	NUM
ap-3265	43	7	,	,	PUNCT
ap-3265	43	8	r2	r2	PROPN
ap-3265	43	9	=	=	PUNCT
ap-3265	43	10	b1l	b1l	PROPN
ap-3265	43	11	3	3	NUM
ap-3265	43	12	1	1	NUM
ap-3265	43	13	+	+	ADJ
ap-3265	43	14	b2l	b2l	PROPN
ap-3265	43	15	3	3	NUM
ap-3265	43	16	2	2	NUM
ap-3265	43	17	+	+	NOUN
ap-3265	43	18	b3h	b3h	NOUN
ap-3265	43	19	3	3	NUM
ap-3265	44	1	+	+	NOUN
ap-3265	44	2	b4{l2	b4{l2	PROPN
ap-3265	44	3	1	1	NUM
ap-3265	44	4	,	,	PUNCT
ap-3265	44	5	l2}+b5{l1	l2}+b5{l1	NOUN
ap-3265	44	6	,	,	PUNCT
ap-3265	44	7	l	l	NOUN
ap-3265	44	8	2	2	NUM
ap-3265	44	9	2	2	NUM
ap-3265	44	10	}	}	PUNCT
ap-3265	44	11	+	+	CCONJ
ap-3265	44	12	b6l1l2l1	b6l1l2l1	NOUN
ap-3265	44	13	+	+	CCONJ
ap-3265	44	14	b7l2l1l2	b7l2l1l2	PROPN
ap-3265	44	15	+	+	CCONJ
ap-3265	44	16	b8h{l1	b8h{l1	NOUN
ap-3265	44	17	,	,	PUNCT
ap-3265	44	18	l2}+	l2}+	X
ap-3265	44	19	b9hl	b9hl	X
ap-3265	44	20	2	2	NUM
ap-3265	44	21	1	1	NUM
ap-3265	44	22	+	+	CCONJ
ap-3265	44	23	b10hl	b10hl	VERB
ap-3265	44	24	2	2	NUM
ap-3265	44	25	2	2	NUM
ap-3265	44	26	+	+	NUM
ap-3265	44	27	b11h	b11h	NOUN
ap-3265	44	28	2l1	2l1	NUM
ap-3265	44	29	+	+	CCONJ
ap-3265	44	30	b12h	b12h	NUM
ap-3265	44	31	2l2	2l2	NUM
ap-3265	45	1	+	+	CCONJ
ap-3265	45	2	b13l	b13l	NOUN
ap-3265	45	3	2	2	NUM
ap-3265	45	4	1	1	NUM
ap-3265	45	5	+	+	CCONJ
ap-3265	45	6	b14l	b14l	SYM
ap-3265	45	7	2	2	NUM
ap-3265	45	8	2	2	NUM
ap-3265	45	9	+	+	CCONJ
ap-3265	45	10	b15{l1	b15{l1	VERB
ap-3265	45	11	,	,	PUNCT
ap-3265	45	12	l2}+	l2}+	ADV
ap-3265	45	13	b16hl1	b16hl1	PROPN
ap-3265	45	14	+	+	CCONJ
ap-3265	45	15	b17hl2	b17hl2	PROPN
ap-3265	45	16	+	+	CCONJ
ap-3265	45	17	b18h	b18h	NOUN
ap-3265	45	18	2	2	NUM
ap-3265	45	19	+	+	NUM
ap-3265	45	20	b19l1	b19l1	NOUN
ap-3265	45	21	+	+	X
ap-3265	45	22	b20l2	b20l2	NOUN
ap-3265	45	23	+	+	CCONJ
ap-3265	45	24	b21h	b21h	PROPN
ap-3265	45	25	+	+	CCONJ
ap-3265	45	26	b22	b22	PROPN
ap-3265	45	27	,	,	PUNCT
ap-3265	45	28	where	where	SCONJ
ap-3265	45	29	{	{	PUNCT
ap-3265	45	30	l1	l1	PROPN
ap-3265	45	31	,	,	PUNCT
ap-3265	45	32	l2	l2	NOUN
ap-3265	45	33	}	}	PUNCT
ap-3265	45	34	=	=	SYM
ap-3265	46	1	l1l2	l1l2	PROPN
ap-3265	46	2	+	+	CCONJ
ap-3265	46	3	l2l1	l2l1	X
ap-3265	46	4	and	and	CCONJ
ap-3265	46	5	a(j	a(j	PROPN
ap-3265	46	6	)	)	PUNCT
ap-3265	47	1	i	i	PRON
ap-3265	47	2	,	,	PUNCT
ap-3265	47	3	bk	bk	NOUN
ap-3265	47	4	are	be	AUX
ap-3265	47	5	constants	constant	NOUN
ap-3265	47	6	.	.	PUNCT
ap-3265	48	1	all	all	DET
ap-3265	48	2	2nd	2nd	ADJ
ap-3265	48	3	order	order	NOUN
ap-3265	48	4	2d	2d	NUM
ap-3265	48	5	superintegrable	superintegrable	ADJ
ap-3265	48	6	systems	system	NOUN
ap-3265	48	7	with	with	ADP
ap-3265	48	8	potential	potential	NOUN
ap-3265	48	9	and	and	CCONJ
ap-3265	48	10	their	their	PRON
ap-3265	48	11	quadratic	quadratic	ADJ
ap-3265	48	12	algebras	algebra	NOUN
ap-3265	48	13	are	be	AUX
ap-3265	48	14	known	know	VERB
ap-3265	48	15	.	.	PUNCT
ap-3265	49	1	there	there	PRON
ap-3265	49	2	are	be	VERB
ap-3265	49	3	44	44	NUM
ap-3265	49	4	nondegenerate	nondegenerate	ADJ
ap-3265	49	5	systems	system	NOUN
ap-3265	49	6	,	,	PUNCT
ap-3265	49	7	on	on	ADP
ap-3265	49	8	a	a	DET
ap-3265	49	9	variety	variety	NOUN
ap-3265	49	10	of	of	ADP
ap-3265	49	11	manifolds	manifold	NOUN
ap-3265	49	12	(	(	PUNCT
ap-3265	49	13	just	just	ADV
ap-3265	49	14	the	the	DET
ap-3265	49	15	manifolds	manifold	NOUN
ap-3265	49	16	classified	classify	VERB
ap-3265	49	17	by	by	ADP
ap-3265	49	18	koenigs	koenig	NOUN
ap-3265	49	19	)	)	PUNCT
ap-3265	49	20	,	,	PUNCT
ap-3265	49	21	but	but	CCONJ
ap-3265	49	22	under	under	ADP
ap-3265	49	23	the	the	DET
ap-3265	49	24	stäckel	stäckel	NOUN
ap-3265	49	25	transform	transform	NOUN
ap-3265	49	26	they	they	PRON
ap-3265	49	27	divide	divide	VERB
ap-3265	49	28	into	into	ADP
ap-3265	49	29	6	6	NUM
ap-3265	49	30	equivalence	equivalence	NOUN
ap-3265	49	31	classes	class	NOUN
ap-3265	49	32	with	with	ADP
ap-3265	49	33	representatives	representative	NOUN
ap-3265	49	34	on	on	ADP
ap-3265	49	35	flat	flat	ADJ
ap-3265	49	36	space	space	NOUN
ap-3265	49	37	and	and	CCONJ
ap-3265	49	38	the	the	DET
ap-3265	49	39	2	2	NUM
ap-3265	49	40	-	-	PUNCT
ap-3265	49	41	sphere	sphere	NOUN
ap-3265	49	42	[	[	X
ap-3265	49	43	14	14	NUM
ap-3265	49	44	]	]	PUNCT
ap-3265	49	45	.	.	PUNCT
ap-3265	50	1	every	every	DET
ap-3265	50	2	2nd	2nd	ADJ
ap-3265	50	3	order	order	NOUN
ap-3265	50	4	symmetry	symmetry	NOUN
ap-3265	50	5	operator	operator	NOUN
ap-3265	50	6	on	on	ADP
ap-3265	50	7	a	a	DET
ap-3265	50	8	constant	constant	ADJ
ap-3265	50	9	curvature	curvature	NOUN
ap-3265	50	10	space	space	NOUN
ap-3265	50	11	takes	take	VERB
ap-3265	50	12	the	the	DET
ap-3265	50	13	form	form	NOUN
ap-3265	50	14	l	l	NOUN
ap-3265	50	15	=	=	PUNCT
ap-3265	51	1	k	k	PROPN
ap-3265	51	2	+	+	PROPN
ap-3265	51	3	w	w	PROPN
ap-3265	51	4	(	(	PUNCT
ap-3265	51	5	x	x	NOUN
ap-3265	51	6	)	)	PUNCT
ap-3265	51	7	,	,	PUNCT
ap-3265	51	8	where	where	SCONJ
ap-3265	51	9	k	k	PROPN
ap-3265	51	10	is	be	AUX
ap-3265	51	11	a	a	DET
ap-3265	51	12	2nd	2nd	ADJ
ap-3265	51	13	order	order	NOUN
ap-3265	51	14	element	element	NOUN
ap-3265	51	15	in	in	ADP
ap-3265	51	16	the	the	DET
ap-3265	51	17	enveloping	enveloping	NOUN
ap-3265	51	18	algebra	algebra	NOUN
ap-3265	51	19	of	of	ADP
ap-3265	51	20	o(3,c	o(3,c	NUM
ap-3265	51	21	)	)	PUNCT
ap-3265	51	22	or	or	CCONJ
ap-3265	51	23	e(2,c	e(2,c	NUM
ap-3265	51	24	)	)	PUNCT
ap-3265	51	25	.	.	PUNCT
ap-3265	52	1	an	an	DET
ap-3265	52	2	example	example	NOUN
ap-3265	52	3	is	be	AUX
ap-3265	52	4	s9	s9	NOUN
ap-3265	52	5	where	where	SCONJ
ap-3265	52	6	h	h	NOUN
ap-3265	52	7	=	=	SYM
ap-3265	52	8	j2	j2	PROPN
ap-3265	52	9	1	1	NUM
ap-3265	52	10	+	+	CCONJ
ap-3265	52	11	j2	j2	PROPN
ap-3265	52	12	2	2	NUM
ap-3265	52	13	+	+	CCONJ
ap-3265	52	14	j2	j2	PROPN
ap-3265	52	15	3	3	NUM
ap-3265	52	16	+	+	CCONJ
ap-3265	52	17	a1	a1	NOUN
ap-3265	52	18	s2	s2	NOUN
ap-3265	52	19	1	1	NUM
ap-3265	52	20	+	+	NUM
ap-3265	52	21	a2	a2	PROPN
ap-3265	52	22	s2	s2	NOUN
ap-3265	52	23	2	2	NUM
ap-3265	52	24	+	+	NUM
ap-3265	52	25	a3	a3	NOUN
ap-3265	52	26	s2	s2	NOUN
ap-3265	52	27	3	3	NUM
ap-3265	52	28	,	,	PUNCT
ap-3265	52	29	where	where	SCONJ
ap-3265	52	30	j3	j3	PROPN
ap-3265	52	31	=	=	SYM
ap-3265	52	32	s1∂s2	s1∂s2	PROPN
ap-3265	52	33	−	−	PROPN
ap-3265	52	34	s2∂s1	s2∂s1	PROPN
ap-3265	52	35	and	and	CCONJ
ap-3265	52	36	j2	j2	PROPN
ap-3265	52	37	,	,	PUNCT
ap-3265	52	38	j3	j3	PROPN
ap-3265	52	39	are	be	AUX
ap-3265	52	40	obtained	obtain	VERB
ap-3265	52	41	by	by	ADP
ap-3265	52	42	cyclic	cyclic	ADJ
ap-3265	52	43	permutations	permutation	NOUN
ap-3265	52	44	of	of	ADP
ap-3265	52	45	indices	index	NOUN
ap-3265	52	46	.	.	PUNCT
ap-3265	53	1	basis	basis	NOUN
ap-3265	53	2	symmetries	symmetry	NOUN
ap-3265	53	3	are	be	AUX
ap-3265	53	4	(	(	PUNCT
ap-3265	53	5	j3	j3	PROPN
ap-3265	53	6	=	=	PUNCT
ap-3265	53	7	s2∂s1	s2∂s1	PROPN
ap-3265	53	8	−	−	PROPN
ap-3265	53	9	s1∂s2	s1∂s2	NOUN
ap-3265	53	10	,	,	PUNCT
ap-3265	53	11	.	.	PUNCT
ap-3265	53	12	.	.	PUNCT
ap-3265	53	13	.	.	PUNCT
ap-3265	53	14	)	)	PUNCT
ap-3265	54	1	l1	l1	PROPN
ap-3265	54	2	=	=	PROPN
ap-3265	54	3	j2	j2	PROPN
ap-3265	54	4	1	1	NUM
ap-3265	54	5	+	+	CCONJ
ap-3265	54	6	a3s	a3s	NOUN
ap-3265	54	7	2	2	NUM
ap-3265	54	8	2	2	NUM
ap-3265	54	9	s2	s2	NOUN
ap-3265	54	10	3	3	NUM
ap-3265	54	11	+	+	CCONJ
ap-3265	54	12	a2s	a2s	NOUN
ap-3265	54	13	2	2	NUM
ap-3265	54	14	3	3	NUM
ap-3265	54	15	s2	s2	NOUN
ap-3265	54	16	2	2	NUM
ap-3265	54	17	,	,	PUNCT
ap-3265	54	18	l2	l2	NOUN
ap-3265	54	19	=	=	SYM
ap-3265	54	20	j2	j2	NOUN
ap-3265	54	21	2	2	NUM
ap-3265	54	22	+	+	CCONJ
ap-3265	54	23	a1s	a1s	PROPN
ap-3265	54	24	2	2	NUM
ap-3265	54	25	3	3	NUM
ap-3265	54	26	s2	s2	NOUN
ap-3265	54	27	1	1	NUM
ap-3265	54	28	+	+	CCONJ
ap-3265	54	29	a3s	a3s	NOUN
ap-3265	54	30	2	2	NUM
ap-3265	54	31	1	1	NUM
ap-3265	54	32	s2	s2	NOUN
ap-3265	54	33	3	3	NUM
ap-3265	54	34	,	,	PUNCT
ap-3265	54	35	l3	l3	PROPN
ap-3265	54	36	=	=	PROPN
ap-3265	54	37	j2	j2	PROPN
ap-3265	54	38	3	3	NUM
ap-3265	54	39	+	+	CCONJ
ap-3265	54	40	a2s	a2s	NOUN
ap-3265	54	41	2	2	NUM
ap-3265	54	42	1	1	NUM
ap-3265	54	43	s2	s2	NOUN
ap-3265	54	44	2	2	NUM
ap-3265	54	45	+	+	CCONJ
ap-3265	54	46	a1s	a1s	PROPN
ap-3265	54	47	2	2	NUM
ap-3265	54	48	2	2	NUM
ap-3265	54	49	s2	s2	NOUN
ap-3265	54	50	1	1	NUM
ap-3265	54	51	.	.	PUNCT
ap-3265	55	1	theorem	theorem	NOUN
ap-3265	55	2	1	1	NUM
ap-3265	55	3	.	.	PUNCT
ap-3265	56	1	there	there	PRON
ap-3265	56	2	is	be	VERB
ap-3265	56	3	a	a	DET
ap-3265	56	4	bijection	bijection	NOUN
ap-3265	56	5	between	between	ADP
ap-3265	56	6	quadratic	quadratic	ADJ
ap-3265	56	7	algebras	algebra	NOUN
ap-3265	56	8	generated	generate	VERB
ap-3265	56	9	by	by	ADP
ap-3265	56	10	2nd	2nd	ADJ
ap-3265	56	11	order	order	NOUN
ap-3265	56	12	elements	element	NOUN
ap-3265	56	13	in	in	ADP
ap-3265	56	14	the	the	DET
ap-3265	56	15	enveloping	enveloping	NOUN
ap-3265	56	16	algebra	algebra	NOUN
ap-3265	56	17	of	of	ADP
ap-3265	56	18	o(3,c	o(3,c	NUM
ap-3265	56	19	)	)	PUNCT
ap-3265	56	20	,	,	PUNCT
ap-3265	56	21	called	call	VERB
ap-3265	56	22	free	free	ADJ
ap-3265	56	23	,	,	PUNCT
ap-3265	56	24	and	and	CCONJ
ap-3265	56	25	2nd	2nd	ADJ
ap-3265	56	26	order	order	NOUN
ap-3265	56	27	nondegenerate	nondegenerate	ADJ
ap-3265	56	28	superintegrable	superintegrable	ADJ
ap-3265	56	29	systems	system	NOUN
ap-3265	56	30	on	on	ADP
ap-3265	56	31	the	the	DET
ap-3265	56	32	complex	complex	ADJ
ap-3265	56	33	2	2	NUM
ap-3265	56	34	-	-	PUNCT
ap-3265	56	35	sphere	sphere	NOUN
ap-3265	56	36	.	.	PUNCT
ap-3265	57	1	similarly	similarly	ADV
ap-3265	57	2	,	,	PUNCT
ap-3265	57	3	there	there	PRON
ap-3265	57	4	is	be	VERB
ap-3265	57	5	a	a	DET
ap-3265	57	6	bijection	bijection	NOUN
ap-3265	57	7	between	between	ADP
ap-3265	57	8	quadratic	quadratic	ADJ
ap-3265	57	9	algebras	algebra	NOUN
ap-3265	57	10	generated	generate	VERB
ap-3265	57	11	by	by	ADP
ap-3265	57	12	2nd	2nd	ADJ
ap-3265	57	13	order	order	NOUN
ap-3265	57	14	elements	element	NOUN
ap-3265	57	15	in	in	ADP
ap-3265	57	16	the	the	DET
ap-3265	57	17	enveloping	enveloping	NOUN
ap-3265	57	18	algebra	algebra	NOUN
ap-3265	57	19	of	of	ADP
ap-3265	57	20	e(2,c	e(2,c	NUM
ap-3265	57	21	)	)	PUNCT
ap-3265	57	22	and	and	CCONJ
ap-3265	57	23	2nd	2nd	ADJ
ap-3265	57	24	order	order	NOUN
ap-3265	57	25	nondegenerate	nondegenerate	ADJ
ap-3265	57	26	superintegrable	superintegrable	ADJ
ap-3265	57	27	systems	system	NOUN
ap-3265	57	28	on	on	ADP
ap-3265	57	29	the	the	DET
ap-3265	57	30	2d	2d	NUM
ap-3265	57	31	complex	complex	ADJ
ap-3265	57	32	flat	flat	ADJ
ap-3265	57	33	space	space	NOUN
ap-3265	57	34	.	.	PUNCT
ap-3265	58	1	remark	remark	PROPN
ap-3265	58	2	.	.	PUNCT
ap-3265	59	1	this	this	DET
ap-3265	59	2	theorem	theorem	NOUN
ap-3265	59	3	is	be	AUX
ap-3265	59	4	constructive	constructive	ADJ
ap-3265	59	5	[	[	X
ap-3265	59	6	15	15	NUM
ap-3265	59	7	]	]	PUNCT
ap-3265	59	8	.	.	PUNCT
ap-3265	60	1	given	give	VERB
ap-3265	60	2	a	a	DET
ap-3265	60	3	free	free	ADJ
ap-3265	60	4	quadratic	quadratic	ADJ
ap-3265	60	5	algebra	algebra	NOUN
ap-3265	60	6	q̃	q̃	PROPN
ap-3265	60	7	one	one	NUM
ap-3265	60	8	can	can	AUX
ap-3265	60	9	compute	compute	VERB
ap-3265	60	10	the	the	DET
ap-3265	60	11	potential	potential	ADJ
ap-3265	60	12	v	v	NOUN
ap-3265	60	13	and	and	CCONJ
ap-3265	60	14	the	the	DET
ap-3265	60	15	symmetries	symmetry	NOUN
ap-3265	60	16	of	of	ADP
ap-3265	60	17	the	the	DET
ap-3265	60	18	quadratic	quadratic	ADJ
ap-3265	60	19	algebra	algebra	NOUN
ap-3265	60	20	q	q	PROPN
ap-3265	60	21	of	of	ADP
ap-3265	60	22	the	the	DET
ap-3265	60	23	nondegenerate	nondegenerate	ADJ
ap-3265	60	24	superintegrable	superintegrable	ADJ
ap-3265	60	25	system	system	NOUN
ap-3265	60	26	.	.	PUNCT
ap-3265	61	1	special	special	ADJ
ap-3265	61	2	functions	function	NOUN
ap-3265	61	3	arise	arise	VERB
ap-3265	61	4	from	from	ADP
ap-3265	61	5	these	these	DET
ap-3265	61	6	systems	system	NOUN
ap-3265	61	7	in	in	ADP
ap-3265	61	8	two	two	NUM
ap-3265	61	9	distinct	distinct	ADJ
ap-3265	61	10	ways	way	NOUN
ap-3265	61	11	:	:	PUNCT
ap-3265	61	12	1	1	NUM
ap-3265	61	13	)	)	PUNCT
ap-3265	61	14	as	as	ADP
ap-3265	61	15	separable	separable	ADJ
ap-3265	61	16	eigenfunctions	eigenfunction	NOUN
ap-3265	61	17	of	of	ADP
ap-3265	61	18	the	the	DET
ap-3265	61	19	quantum	quantum	ADJ
ap-3265	61	20	hamiltonian	hamiltonian	NOUN
ap-3265	61	21	.	.	PUNCT
ap-3265	62	1	second	second	ADJ
ap-3265	62	2	order	order	NOUN
ap-3265	62	3	superintegrable	superintegrable	ADJ
ap-3265	62	4	systems	system	NOUN
ap-3265	62	5	are	be	AUX
ap-3265	62	6	multiseparable	multiseparable	ADJ
ap-3265	62	7	[	[	X
ap-3265	62	8	6	6	NUM
ap-3265	62	9	]	]	SYM
ap-3265	62	10	.	.	PUNCT
ap-3265	63	1	2	2	NUM
ap-3265	63	2	)	)	PUNCT
ap-3265	63	3	as	as	ADP
ap-3265	63	4	interbasis	interbasis	NOUN
ap-3265	63	5	expansion	expansion	NOUN
ap-3265	63	6	coefficients	coefficient	NOUN
ap-3265	63	7	relating	relate	VERB
ap-3265	63	8	distinct	distinct	ADJ
ap-3265	63	9	separable	separable	ADJ
ap-3265	63	10	coordinate	coordinate	NOUN
ap-3265	63	11	eigenbases	eigenbase	NOUN
ap-3265	64	1	[	[	X
ap-3265	64	2	16	16	NUM
ap-3265	64	3	,	,	PUNCT
ap-3265	64	4	17	17	NUM
ap-3265	64	5	,	,	PUNCT
ap-3265	64	6	19	19	NUM
ap-3265	64	7	,	,	PUNCT
ap-3265	64	8	20	20	NUM
ap-3265	64	9	]	]	PUNCT
ap-3265	64	10	.	.	PUNCT
ap-3265	65	1	most	most	ADJ
ap-3265	65	2	of	of	ADP
ap-3265	65	3	the	the	DET
ap-3265	65	4	classical	classical	ADJ
ap-3265	65	5	special	special	ADJ
ap-3265	65	6	functions	function	NOUN
ap-3265	65	7	in	in	ADP
ap-3265	65	8	the	the	DET
ap-3265	65	9	digital	digital	ADJ
ap-3265	65	10	library	library	NOUN
ap-3265	65	11	of	of	ADP
ap-3265	65	12	mathematical	mathematical	ADJ
ap-3265	65	13	functions	function	NOUN
ap-3265	65	14	,	,	PUNCT
ap-3265	65	15	as	as	ADV
ap-3265	65	16	well	well	ADV
ap-3265	65	17	as	as	ADP
ap-3265	65	18	wilson	wilson	PROPN
ap-3265	65	19	polynomials	polynomial	NOUN
ap-3265	65	20	,	,	PUNCT
ap-3265	65	21	appear	appear	VERB
ap-3265	65	22	in	in	ADP
ap-3265	65	23	these	these	DET
ap-3265	65	24	ways	way	NOUN
ap-3265	65	25	[	[	X
ap-3265	65	26	21	21	NUM
ap-3265	65	27	]	]	PUNCT
ap-3265	65	28	.	.	PUNCT
ap-3265	66	1	1.1	1.1	NUM
ap-3265	66	2	.	.	PUNCT
ap-3265	67	1	the	the	DET
ap-3265	67	2	big	big	ADJ
ap-3265	67	3	picture	picture	NOUN
ap-3265	67	4	:	:	PUNCT
ap-3265	67	5	contractions	contraction	NOUN
ap-3265	67	6	and	and	CCONJ
ap-3265	67	7	special	special	ADJ
ap-3265	67	8	functions	function	NOUN
ap-3265	67	9	•	•	ADV
ap-3265	67	10	taking	take	VERB
ap-3265	67	11	coordinate	coordinate	NOUN
ap-3265	67	12	limits	limit	NOUN
ap-3265	67	13	starting	start	VERB
ap-3265	67	14	from	from	ADP
ap-3265	67	15	quantum	quantum	ADJ
ap-3265	67	16	system	system	NOUN
ap-3265	67	17	s9	s9	NOUN
ap-3265	67	18	we	we	PRON
ap-3265	67	19	can	can	AUX
ap-3265	67	20	obtain	obtain	VERB
ap-3265	67	21	other	other	ADJ
ap-3265	67	22	superintegrable	superintegrable	ADJ
ap-3265	67	23	systems	system	NOUN
ap-3265	67	24	.	.	PUNCT
ap-3265	68	1	•	•	NOUN
ap-3265	68	2	these	these	DET
ap-3265	68	3	coordinate	coordinate	NOUN
ap-3265	68	4	limits	limit	NOUN
ap-3265	68	5	induce	induce	VERB
ap-3265	68	6	limit	limit	NOUN
ap-3265	68	7	relations	relation	NOUN
ap-3265	68	8	between	between	ADP
ap-3265	68	9	the	the	DET
ap-3265	68	10	special	special	ADJ
ap-3265	68	11	functions	function	NOUN
ap-3265	68	12	associated	associate	VERB
ap-3265	68	13	as	as	ADP
ap-3265	68	14	eigenfunctions	eigenfunction	NOUN
ap-3265	68	15	of	of	ADP
ap-3265	68	16	the	the	DET
ap-3265	68	17	superintegrable	superintegrable	ADJ
ap-3265	68	18	systems	system	NOUN
ap-3265	68	19	.	.	PUNCT
ap-3265	69	1	•	•	NUM
ap-3265	69	2	the	the	DET
ap-3265	69	3	limits	limit	NOUN
ap-3265	69	4	induce	induce	VERB
ap-3265	69	5	contractions	contraction	NOUN
ap-3265	69	6	of	of	ADP
ap-3265	69	7	the	the	DET
ap-3265	69	8	associated	associated	ADJ
ap-3265	69	9	quadratic	quadratic	ADJ
ap-3265	69	10	algebras	algebra	NOUN
ap-3265	69	11	,	,	PUNCT
ap-3265	69	12	and	and	CCONJ
ap-3265	69	13	via	via	ADP
ap-3265	69	14	the	the	DET
ap-3265	69	15	models	model	NOUN
ap-3265	69	16	,	,	PUNCT
ap-3265	69	17	limit	limit	VERB
ap-3265	69	18	relations	relation	NOUN
ap-3265	69	19	between	between	ADP
ap-3265	69	20	the	the	DET
ap-3265	69	21	associated	associated	ADJ
ap-3265	69	22	special	special	ADJ
ap-3265	69	23	functions	function	NOUN
ap-3265	69	24	.	.	PUNCT
ap-3265	70	1	•	•	NUM
ap-3265	70	2	for	for	ADP
ap-3265	70	3	constant	constant	ADJ
ap-3265	70	4	curvature	curvature	NOUN
ap-3265	70	5	systems	system	NOUN
ap-3265	70	6	the	the	DET
ap-3265	70	7	required	require	VERB
ap-3265	70	8	limits	limit	NOUN
ap-3265	70	9	are	be	AUX
ap-3265	70	10	all	all	PRON
ap-3265	70	11	induced	induce	VERB
ap-3265	70	12	by	by	ADP
ap-3265	70	13	inönü	inönü	NOUN
ap-3265	70	14	-	-	PUNCT
ap-3265	70	15	wigner	wigner	NOUN
ap-3265	70	16	-	-	PUNCT
ap-3265	70	17	type	type	NOUN
ap-3265	70	18	lie	lie	NOUN
ap-3265	70	19	algebra	algebra	NOUN
ap-3265	70	20	contractions	contraction	NOUN
ap-3265	70	21	of	of	ADP
ap-3265	70	22	o(3,c	o(3,c	NUM
ap-3265	70	23	)	)	PUNCT
ap-3265	70	24	and	and	CCONJ
ap-3265	70	25	e(2,c	e(2,c	NUM
ap-3265	70	26	)	)	PUNCT
ap-3265	71	1	[	[	X
ap-3265	71	2	22–24	22–24	NUM
ap-3265	71	3	]	]	PUNCT
ap-3265	71	4	•	•	NUM
ap-3265	71	5	the	the	DET
ap-3265	71	6	askey	askey	ADJ
ap-3265	71	7	scheme	scheme	NOUN
ap-3265	71	8	for	for	ADP
ap-3265	71	9	orthogonal	orthogonal	ADJ
ap-3265	71	10	functions	function	NOUN
ap-3265	71	11	of	of	ADP
ap-3265	71	12	hypergeometric	hypergeometric	ADJ
ap-3265	71	13	type	type	NOUN
ap-3265	71	14	fits	fit	VERB
ap-3265	71	15	nicely	nicely	ADV
ap-3265	71	16	into	into	ADP
ap-3265	71	17	this	this	DET
ap-3265	71	18	picture	picture	NOUN
ap-3265	71	19	[	[	X
ap-3265	71	20	25	25	NUM
ap-3265	71	21	]	]	PUNCT
ap-3265	71	22	.	.	PUNCT
ap-3265	72	1	lie	lie	PROPN
ap-3265	72	2	algebra	algebra	NOUN
ap-3265	72	3	contractions	contraction	NOUN
ap-3265	72	4	.	.	PUNCT
ap-3265	73	1	let	let	VERB
ap-3265	73	2	(	(	PUNCT
ap-3265	73	3	a	a	PRON
ap-3265	73	4	;	;	PUNCT
ap-3265	73	5	[	[	X
ap-3265	73	6	;	;	PUNCT
ap-3265	73	7	]	]	X
ap-3265	73	8	a	a	X
ap-3265	73	9	)	)	PUNCT
ap-3265	73	10	,	,	PUNCT
ap-3265	73	11	(	(	PUNCT
ap-3265	73	12	b	b	X
ap-3265	73	13	;	;	PUNCT
ap-3265	73	14	[	[	X
ap-3265	73	15	;	;	PUNCT
ap-3265	73	16	]	]	SYM
ap-3265	73	17	b	b	X
ap-3265	73	18	)	)	PUNCT
ap-3265	73	19	be	be	VERB
ap-3265	73	20	two	two	NUM
ap-3265	73	21	complex	complex	ADJ
ap-3265	73	22	lie	lie	NOUN
ap-3265	73	23	algebras	algebra	NOUN
ap-3265	73	24	.	.	PUNCT
ap-3265	74	1	we	we	PRON
ap-3265	74	2	say	say	VERB
ap-3265	74	3	that	that	SCONJ
ap-3265	74	4	b	b	PROPN
ap-3265	74	5	is	be	AUX
ap-3265	74	6	a	a	DET
ap-3265	74	7	contraction	contraction	NOUN
ap-3265	74	8	of	of	ADP
ap-3265	74	9	a	a	DET
ap-3265	74	10	if	if	NOUN
ap-3265	74	11	for	for	ADP
ap-3265	74	12	every	every	DET
ap-3265	74	13	ε	ε	PROPN
ap-3265	74	14	∈	∈	PROPN
ap-3265	74	15	(	(	PUNCT
ap-3265	74	16	0	0	NUM
ap-3265	74	17	;	;	PUNCT
ap-3265	74	18	1	1	X
ap-3265	74	19	]	]	PUNCT
ap-3265	74	20	there	there	PRON
ap-3265	74	21	exists	exist	VERB
ap-3265	74	22	a	a	DET
ap-3265	74	23	linear	linear	PROPN
ap-3265	74	24	invertible	invertible	ADJ
ap-3265	74	25	map	map	NOUN
ap-3265	74	26	tε	tε	ADP
ap-3265	74	27	:	:	PUNCT
ap-3265	74	28	b	b	X
ap-3265	74	29	→	→	PUNCT
ap-3265	74	30	a	a	DET
ap-3265	74	31	such	such	ADJ
ap-3265	74	32	that	that	PRON
ap-3265	74	33	for	for	ADP
ap-3265	74	34	every	every	DET
ap-3265	74	35	x	x	NOUN
ap-3265	74	36	,	,	PUNCT
ap-3265	74	37	y	y	PROPN
ap-3265	74	38	∈	∈	PROPN
ap-3265	74	39	b	b	PROPN
ap-3265	74	40	,	,	PUNCT
ap-3265	74	41	limε→0	limε→0	PROPN
ap-3265	74	42	t	t	NOUN
ap-3265	74	43	−1	−1	NOUN
ap-3265	74	44	ε	ε	PROPN
ap-3265	75	1	[	[	X
ap-3265	75	2	tεx	tεx	NOUN
ap-3265	75	3	,	,	PUNCT
ap-3265	75	4	tεy	tεy	ADP
ap-3265	75	5	]	]	X
ap-3265	75	6	a	a	PRON
ap-3265	75	7	=	=	X
ap-3265	76	1	[	[	X
ap-3265	76	2	x	x	X
ap-3265	76	3	,	,	PUNCT
ap-3265	76	4	y	y	PROPN
ap-3265	76	5	]	]	X
ap-3265	76	6	b	b	X
ap-3265	76	7	.	.	PUNCT
ap-3265	77	1	thus	thus	ADV
ap-3265	77	2	,	,	PUNCT
ap-3265	77	3	as	as	SCONJ
ap-3265	77	4	ε→	ε→	X
ap-3265	77	5	0	0	NUM
ap-3265	77	6	the	the	DET
ap-3265	77	7	1	1	NUM
ap-3265	77	8	-	-	PUNCT
ap-3265	77	9	parameter	parameter	NOUN
ap-3265	77	10	family	family	NOUN
ap-3265	77	11	of	of	ADP
ap-3265	77	12	basis	basis	NOUN
ap-3265	77	13	transformations	transformation	NOUN
ap-3265	77	14	can	can	AUX
ap-3265	77	15	become	become	VERB
ap-3265	77	16	nonsingular	nonsingular	ADJ
ap-3265	77	17	but	but	CCONJ
ap-3265	77	18	the	the	DET
ap-3265	77	19	structure	structure	NOUN
ap-3265	77	20	constants	constant	NOUN
ap-3265	77	21	go	go	VERB
ap-3265	77	22	to	to	ADP
ap-3265	77	23	a	a	DET
ap-3265	77	24	finite	finite	ADJ
ap-3265	77	25	limit	limit	NOUN
ap-3265	77	26	.	.	PUNCT
ap-3265	78	1	contractions	contraction	NOUN
ap-3265	78	2	of	of	ADP
ap-3265	78	3	e(2,c	e(2,c	NOUN
ap-3265	78	4	)	)	PUNCT
ap-3265	78	5	and	and	CCONJ
ap-3265	78	6	o(3,c	o(3,c	NUM
ap-3265	78	7	)	)	PUNCT
ap-3265	78	8	.	.	PUNCT
ap-3265	79	1	these	these	PRON
ap-3265	79	2	are	be	AUX
ap-3265	79	3	the	the	DET
ap-3265	79	4	symmetry	symmetry	NOUN
ap-3265	79	5	lie	lie	VERB
ap-3265	79	6	algebras	algebra	NOUN
ap-3265	79	7	of	of	ADP
ap-3265	79	8	free	free	ADJ
ap-3265	79	9	(	(	PUNCT
ap-3265	79	10	zero	zero	NUM
ap-3265	79	11	potential	potential	ADJ
ap-3265	79	12	)	)	PUNCT
ap-3265	79	13	systems	system	NOUN
ap-3265	79	14	on	on	ADP
ap-3265	79	15	constant	constant	ADJ
ap-3265	79	16	curvature	curvature	NOUN
ap-3265	79	17	spaces	space	NOUN
ap-3265	79	18	.	.	PUNCT
ap-3265	80	1	their	their	PRON
ap-3265	80	2	contractions	contraction	NOUN
ap-3265	80	3	have	have	AUX
ap-3265	80	4	long	long	ADV
ap-3265	80	5	since	since	ADV
ap-3265	80	6	been	be	AUX
ap-3265	80	7	classified	classify	VERB
ap-3265	80	8	[	[	PUNCT
ap-3265	80	9	15	15	NUM
ap-3265	80	10	]	]	PUNCT
ap-3265	80	11	.	.	PUNCT
ap-3265	81	1	there	there	PRON
ap-3265	81	2	are	be	VERB
ap-3265	81	3	6	6	NUM
ap-3265	81	4	nontrivial	nontrivial	ADJ
ap-3265	81	5	contractions	contraction	NOUN
ap-3265	81	6	of	of	ADP
ap-3265	81	7	e(2,c	e(2,c	NOUN
ap-3265	81	8	)	)	PUNCT
ap-3265	81	9	and	and	CCONJ
ap-3265	81	10	4	4	NUM
ap-3265	81	11	of	of	ADP
ap-3265	81	12	o(3,c	o(3,c	NUM
ap-3265	81	13	)	)	PUNCT
ap-3265	81	14	.	.	PUNCT
ap-3265	82	1	they	they	PRON
ap-3265	82	2	are	be	AUX
ap-3265	82	3	each	each	PRON
ap-3265	82	4	induced	induce	VERB
ap-3265	82	5	by	by	ADP
ap-3265	82	6	coordinate	coordinate	NOUN
ap-3265	82	7	limits	limit	NOUN
ap-3265	82	8	.	.	PUNCT
ap-3265	83	1	example	example	NOUN
ap-3265	83	2	—	—	PUNCT
ap-3265	83	3	an	an	DET
ap-3265	83	4	inönü	inönü	NOUN
ap-3265	83	5	-	-	PUNCT
ap-3265	83	6	wignercontraction	wignercontraction	NOUN
ap-3265	83	7	of	of	ADP
ap-3265	83	8	o(3,c	o(3,c	NUM
ap-3265	83	9	)	)	PUNCT
ap-3265	83	10	.	.	PUNCT
ap-3265	84	1	we	we	PRON
ap-3265	84	2	use	use	VERB
ap-3265	84	3	the	the	DET
ap-3265	84	4	classical	classical	ADJ
ap-3265	84	5	realization	realization	NOUN
ap-3265	84	6	for	for	ADP
ap-3265	84	7	o(3,c	o(3,c	NOUN
ap-3265	84	8	)	)	PUNCT
ap-3265	84	9	acting	act	VERB
ap-3265	84	10	on	on	ADP
ap-3265	84	11	the	the	DET
ap-3265	84	12	2	2	NUM
ap-3265	84	13	-	-	PUNCT
ap-3265	84	14	sphere	sphere	NOUN
ap-3265	84	15	,	,	PUNCT
ap-3265	84	16	with	with	ADP
ap-3265	84	17	basis	basis	NOUN
ap-3265	84	18	j1	j1	NOUN
ap-3265	84	19	=	=	PUNCT
ap-3265	84	20	s2∂s3	s2∂s3	NOUN
ap-3265	84	21	−	−	PROPN
ap-3265	84	22	s3∂s2	s3∂s2	PROPN
ap-3265	84	23	,	,	PUNCT
ap-3265	84	24	j2	j2	PROPN
ap-3265	84	25	=	=	SYM
ap-3265	84	26	s3∂s1	s3∂s1	PROPN
ap-3265	84	27	−	−	PROPN
ap-3265	84	28	s1∂s3	s1∂s3	NOUN
ap-3265	84	29	,	,	PUNCT
ap-3265	84	30	j3	j3	PROPN
ap-3265	84	31	=	=	PUNCT
ap-3265	84	32	s1∂s2	s1∂s2	PROPN
ap-3265	84	33	−	−	PROPN
ap-3265	84	34	s2∂s1	s2∂s1	NOUN
ap-3265	84	35	,	,	PUNCT
ap-3265	84	36	commutation	commutation	NOUN
ap-3265	84	37	relations	relation	NOUN
ap-3265	85	1	[	[	X
ap-3265	85	2	j2	j2	PROPN
ap-3265	85	3	,	,	PUNCT
ap-3265	85	4	j1	j1	PROPN
ap-3265	85	5	]	]	PUNCT
ap-3265	85	6	=	=	SYM
ap-3265	85	7	j3	j3	PROPN
ap-3265	85	8	,	,	PUNCT
ap-3265	85	9	[	[	X
ap-3265	85	10	j3	j3	PROPN
ap-3265	85	11	,	,	PUNCT
ap-3265	85	12	j2	j2	PROPN
ap-3265	85	13	]	]	X
ap-3265	85	14	=	=	SYM
ap-3265	85	15	j1	j1	PROPN
ap-3265	85	16	,	,	PUNCT
ap-3265	85	17	[	[	X
ap-3265	85	18	j1	j1	PROPN
ap-3265	85	19	,	,	PUNCT
ap-3265	85	20	j3	j3	PROPN
ap-3265	85	21	]	]	PUNCT
ap-3265	85	22	=	=	SYM
ap-3265	85	23	j2	j2	PROPN
ap-3265	85	24	,	,	PUNCT
ap-3265	85	25	and	and	CCONJ
ap-3265	85	26	hamiltonianh	hamiltonianh	NOUN
ap-3265	85	27	=	=	PROPN
ap-3265	85	28	j2	j2	PROPN
ap-3265	85	29	1	1	NUM
ap-3265	85	30	+	+	NOUN
ap-3265	85	31	j2	j2	PROPN
ap-3265	85	32	2	2	NUM
ap-3265	85	33	+	+	NOUN
ap-3265	85	34	j2	j2	PROPN
ap-3265	85	35	3	3	NUM
ap-3265	85	36	.	.	PUNCT
ap-3265	86	1	here	here	ADV
ap-3265	86	2	s2	s2	PROPN
ap-3265	86	3	1+s2	1+s2	NUM
ap-3265	86	4	2+s2	2+s2	NUM
ap-3265	86	5	3	3	NUM
ap-3265	86	6	=	=	SYM
ap-3265	86	7	1	1	NUM
ap-3265	86	8	.	.	X
ap-3265	87	1	we	we	PRON
ap-3265	87	2	introduce	introduce	VERB
ap-3265	87	3	the	the	DET
ap-3265	87	4	basis	basis	NOUN
ap-3265	87	5	change	change	NOUN
ap-3265	87	6	:	:	PUNCT
ap-3265	87	7	{	{	PUNCT
ap-3265	87	8	j	j	PROPN
ap-3265	87	9	′1	′1	PROPN
ap-3265	87	10	,	,	PUNCT
ap-3265	87	11	j	j	PROPN
ap-3265	87	12	′2	′2	PROPN
ap-3265	87	13	,	,	PUNCT
ap-3265	87	14	j	j	PROPN
ap-3265	87	15	′3	′3	NOUN
ap-3265	87	16	}	}	PUNCT
ap-3265	87	17	=	=	SYM
ap-3265	87	18	{	{	PUNCT
ap-3265	87	19	εj1	εj1	PROPN
ap-3265	87	20	,	,	PUNCT
ap-3265	87	21	εj2	εj2	PROPN
ap-3265	87	22	,	,	PUNCT
ap-3265	87	23	j3	j3	PROPN
ap-3265	87	24	}	}	PUNCT
ap-3265	87	25	,	,	PUNCT
ap-3265	87	26	0	0	NUM
ap-3265	87	27	<	<	X
ap-3265	87	28	ε	ε	PROPN
ap-3265	87	29	≤	≤	NUM
ap-3265	87	30	1	1	NUM
ap-3265	87	31	,	,	PUNCT
ap-3265	87	32	with	with	ADP
ap-3265	87	33	coordinate	coordinate	NOUN
ap-3265	87	34	implementation	implementation	NOUN
ap-3265	87	35	x	x	PUNCT
ap-3265	87	36	=	=	SYM
ap-3265	87	37	s1	s1	PROPN
ap-3265	87	38	ε	ε	PROPN
ap-3265	87	39	,	,	PUNCT
ap-3265	87	40	y	y	PROPN
ap-3265	87	41	=	=	SYM
ap-3265	87	42	s2	s2	PROPN
ap-3265	87	43	ε	ε	PROPN
ap-3265	87	44	,	,	PUNCT
ap-3265	87	45	s3	s3	PROPN
ap-3265	87	46	≈	≈	PROPN
ap-3265	87	47	1	1	NUM
ap-3265	87	48	.	.	PUNCT
ap-3265	88	1	the	the	DET
ap-3265	88	2	structure	structure	NOUN
ap-3265	88	3	relations	relation	NOUN
ap-3265	88	4	become	become	VERB
ap-3265	88	5	[	[	X
ap-3265	88	6	j	j	NOUN
ap-3265	88	7	′2	′2	PROPN
ap-3265	88	8	,	,	PUNCT
ap-3265	88	9	j	j	PROPN
ap-3265	88	10	′1	′1	SYM
ap-3265	88	11	]	]	X
ap-3265	88	12	=	=	X
ap-3265	88	13	ε2j	ε2j	X
ap-3265	88	14	′3	′3	NOUN
ap-3265	88	15	,	,	PUNCT
ap-3265	88	16	[	[	X
ap-3265	88	17	j	j	PROPN
ap-3265	88	18	′3	′3	PROPN
ap-3265	88	19	,	,	PUNCT
ap-3265	88	20	j	j	PROPN
ap-3265	88	21	′2	′2	X
ap-3265	88	22	]	]	PUNCT
ap-3265	88	23	=	=	SYM
ap-3265	88	24	j	j	PROPN
ap-3265	88	25	′1	′1	SYM
ap-3265	88	26	,	,	PUNCT
ap-3265	88	27	[	[	X
ap-3265	88	28	j	j	X
ap-3265	88	29	′1	′1	PROPN
ap-3265	88	30	,	,	PUNCT
ap-3265	88	31	j	j	PROPN
ap-3265	88	32	′3	′3	NOUN
ap-3265	88	33	]	]	X
ap-3265	88	34	=	=	SYM
ap-3265	88	35	j	j	PROPN
ap-3265	88	36	′2	′2	PROPN
ap-3265	88	37	,	,	PUNCT
ap-3265	88	38	215	215	NUM
ap-3265	88	39	e.	e.	PROPN
ap-3265	88	40	kalnins	kalnins	PROPN
ap-3265	88	41	,	,	PUNCT
ap-3265	88	42	w.	w.	PROPN
ap-3265	88	43	miller	miller	PROPN
ap-3265	88	44	,	,	PUNCT
ap-3265	88	45	e.	e.	PROPN
ap-3265	88	46	subag	subag	PROPN
ap-3265	88	47	acta	acta	PROPN
ap-3265	88	48	polytechnica	polytechnica	PROPN
ap-3265	88	49	as	as	ADP
ap-3265	88	50	ε→	ε→	X
ap-3265	88	51	0	0	NUM
ap-3265	88	52	these	these	PRON
ap-3265	88	53	converge	converge	VERB
ap-3265	88	54	to	to	ADP
ap-3265	88	55	[	[	X
ap-3265	88	56	j	j	PROPN
ap-3265	88	57	′2	′2	PROPN
ap-3265	88	58	,	,	PUNCT
ap-3265	88	59	j	j	PROPN
ap-3265	88	60	′1	′1	SYM
ap-3265	88	61	]	]	X
ap-3265	88	62	=	=	SYM
ap-3265	88	63	0	0	NUM
ap-3265	88	64	,	,	PUNCT
ap-3265	88	65	[	[	X
ap-3265	88	66	j	j	NOUN
ap-3265	88	67	′3	′3	PROPN
ap-3265	88	68	,	,	PUNCT
ap-3265	88	69	j	j	PROPN
ap-3265	88	70	′2	′2	X
ap-3265	88	71	]	]	PUNCT
ap-3265	88	72	=	=	SYM
ap-3265	88	73	j	j	PROPN
ap-3265	88	74	′1	′1	SYM
ap-3265	88	75	,	,	PUNCT
ap-3265	88	76	[	[	X
ap-3265	88	77	j	j	X
ap-3265	88	78	′1	′1	PROPN
ap-3265	88	79	,	,	PUNCT
ap-3265	88	80	j	j	PROPN
ap-3265	88	81	′3	′3	NOUN
ap-3265	88	82	]	]	X
ap-3265	88	83	=	=	SYM
ap-3265	88	84	j	j	PROPN
ap-3265	88	85	′2	′2	PROPN
ap-3265	88	86	,	,	PUNCT
ap-3265	88	87	the	the	DET
ap-3265	88	88	lie	lie	NOUN
ap-3265	88	89	algebra	algebra	NOUN
ap-3265	88	90	e(2,c	e(2,c	NUM
ap-3265	88	91	)	)	PUNCT
ap-3265	88	92	.	.	PUNCT
ap-3265	89	1	contractions	contraction	NOUN
ap-3265	89	2	of	of	ADP
ap-3265	89	3	quadratic	quadratic	ADJ
ap-3265	89	4	algebras	algebra	NOUN
ap-3265	89	5	.	.	PUNCT
ap-3265	90	1	just	just	ADV
ap-3265	90	2	as	as	ADP
ap-3265	90	3	for	for	ADP
ap-3265	90	4	lie	lie	NOUN
ap-3265	90	5	algebras	algebra	NOUN
ap-3265	90	6	we	we	PRON
ap-3265	90	7	can	can	AUX
ap-3265	90	8	define	define	VERB
ap-3265	90	9	a	a	DET
ap-3265	90	10	contraction	contraction	NOUN
ap-3265	90	11	of	of	ADP
ap-3265	90	12	a	a	DET
ap-3265	90	13	quadratic	quadratic	ADJ
ap-3265	90	14	algebra	algebra	NOUN
ap-3265	90	15	in	in	ADP
ap-3265	90	16	terms	term	NOUN
ap-3265	90	17	of	of	ADP
ap-3265	90	18	1	1	NUM
ap-3265	90	19	-	-	PUNCT
ap-3265	90	20	parameter	parameter	NOUN
ap-3265	90	21	families	family	NOUN
ap-3265	90	22	of	of	ADP
ap-3265	90	23	basis	basis	NOUN
ap-3265	90	24	changes	change	NOUN
ap-3265	90	25	in	in	ADP
ap-3265	90	26	the	the	DET
ap-3265	90	27	algebra	algebra	NOUN
ap-3265	90	28	:	:	PUNCT
ap-3265	90	29	as	as	SCONJ
ap-3265	90	30	ε→	ε→	X
ap-3265	90	31	0	0	NUM
ap-3265	90	32	the	the	DET
ap-3265	90	33	1	1	NUM
ap-3265	90	34	-	-	PUNCT
ap-3265	90	35	parameter	parameter	NOUN
ap-3265	90	36	family	family	NOUN
ap-3265	90	37	of	of	ADP
ap-3265	90	38	basis	basis	NOUN
ap-3265	90	39	transformations	transformation	NOUN
ap-3265	90	40	becomes	become	VERB
ap-3265	90	41	singular	singular	ADJ
ap-3265	90	42	but	but	CCONJ
ap-3265	90	43	the	the	DET
ap-3265	90	44	structure	structure	NOUN
ap-3265	90	45	constants	constant	NOUN
ap-3265	90	46	go	go	VERB
ap-3265	90	47	to	to	ADP
ap-3265	90	48	a	a	DET
ap-3265	90	49	finite	finite	ADJ
ap-3265	90	50	limit	limit	NOUN
ap-3265	90	51	[	[	X
ap-3265	90	52	15	15	NUM
ap-3265	90	53	]	]	PUNCT
ap-3265	90	54	.	.	PUNCT
ap-3265	91	1	motivating	motivate	VERB
ap-3265	91	2	idea	idea	NOUN
ap-3265	91	3	—	—	PUNCT
ap-3265	91	4	lie	lie	VERB
ap-3265	91	5	algebra	algebra	NOUN
ap-3265	91	6	contractions	contraction	NOUN
ap-3265	91	7	induce	induce	VERB
ap-3265	91	8	quadratic	quadratic	ADJ
ap-3265	91	9	algebra	algebra	NOUN
ap-3265	91	10	contractions	contraction	NOUN
ap-3265	91	11	.	.	PUNCT
ap-3265	92	1	for	for	ADP
ap-3265	92	2	constant	constant	ADJ
ap-3265	92	3	curvature	curvature	NOUN
ap-3265	92	4	spaces	space	NOUN
ap-3265	92	5	we	we	PRON
ap-3265	92	6	have	have	VERB
ap-3265	92	7	the	the	DET
ap-3265	92	8	following	follow	VERB
ap-3265	92	9	theorem	theorem	VERB
ap-3265	92	10	.	.	PUNCT
ap-3265	92	11	theorem	theorem	ADJ
ap-3265	92	12	2	2	NUM
ap-3265	92	13	[	[	X
ap-3265	92	14	15	15	NUM
ap-3265	92	15	]	]	PUNCT
ap-3265	92	16	.	.	PUNCT
ap-3265	93	1	every	every	DET
ap-3265	93	2	lie	lie	NOUN
ap-3265	93	3	algebra	algebra	NOUN
ap-3265	93	4	contraction	contraction	NOUN
ap-3265	93	5	of	of	ADP
ap-3265	93	6	a	a	DET
ap-3265	93	7	=	=	SYM
ap-3265	93	8	e(2,c	e(2,c	NUM
ap-3265	93	9	)	)	PUNCT
ap-3265	93	10	or	or	CCONJ
ap-3265	93	11	a	a	DET
ap-3265	93	12	=	=	SYM
ap-3265	93	13	o(3,c	o(3,c	NOUN
ap-3265	93	14	)	)	PUNCT
ap-3265	93	15	induces	induce	VERB
ap-3265	93	16	a	a	DET
ap-3265	93	17	contraction	contraction	NOUN
ap-3265	93	18	of	of	ADP
ap-3265	93	19	a	a	DET
ap-3265	93	20	free	free	ADJ
ap-3265	93	21	(	(	PUNCT
ap-3265	93	22	zero	zero	NUM
ap-3265	93	23	potential	potential	ADJ
ap-3265	93	24	)	)	PUNCT
ap-3265	93	25	quadratic	quadratic	ADJ
ap-3265	93	26	algebra	algebra	NOUN
ap-3265	93	27	q̃	q̃	PROPN
ap-3265	93	28	based	base	VERB
ap-3265	93	29	on	on	ADP
ap-3265	93	30	a	a	PRON
ap-3265	93	31	,	,	PUNCT
ap-3265	93	32	which	which	PRON
ap-3265	93	33	in	in	ADP
ap-3265	93	34	turn	turn	NOUN
ap-3265	93	35	induces	induce	VERB
ap-3265	93	36	a	a	DET
ap-3265	93	37	contraction	contraction	NOUN
ap-3265	93	38	of	of	ADP
ap-3265	93	39	the	the	DET
ap-3265	93	40	quadratic	quadratic	ADJ
ap-3265	93	41	algebraq	algebraq	ADV
ap-3265	93	42	with	with	ADP
ap-3265	93	43	potential	potential	NOUN
ap-3265	93	44	.	.	PUNCT
ap-3265	94	1	this	this	PRON
ap-3265	94	2	is	be	AUX
ap-3265	94	3	true	true	ADJ
ap-3265	94	4	for	for	ADP
ap-3265	94	5	both	both	CCONJ
ap-3265	94	6	classical	classical	ADJ
ap-3265	94	7	and	and	CCONJ
ap-3265	94	8	quantum	quantum	NOUN
ap-3265	94	9	algebras	algebra	NOUN
ap-3265	94	10	.	.	PUNCT
ap-3265	95	1	1.2	1.2	NUM
ap-3265	95	2	.	.	PUNCT
ap-3265	96	1	the	the	DET
ap-3265	96	2	problems	problem	NOUN
ap-3265	96	3	and	and	CCONJ
ap-3265	96	4	the	the	DET
ap-3265	96	5	proposed	propose	VERB
ap-3265	96	6	solutions	solution	NOUN
ap-3265	96	7	the	the	DET
ap-3265	96	8	various	various	ADJ
ap-3265	96	9	limits	limit	NOUN
ap-3265	96	10	of	of	ADP
ap-3265	96	11	2nd	2nd	ADJ
ap-3265	96	12	order	order	NOUN
ap-3265	96	13	superintegrable	superintegrable	ADJ
ap-3265	96	14	systems	system	NOUN
ap-3265	96	15	on	on	ADP
ap-3265	96	16	constant	constant	ADJ
ap-3265	96	17	curvature	curvature	NOUN
ap-3265	96	18	spaces	space	NOUN
ap-3265	96	19	and	and	CCONJ
ap-3265	96	20	their	their	PRON
ap-3265	96	21	applications	application	NOUN
ap-3265	96	22	,	,	PUNCT
ap-3265	96	23	such	such	ADJ
ap-3265	96	24	as	as	ADP
ap-3265	96	25	to	to	ADP
ap-3265	96	26	the	the	DET
ap-3265	96	27	askey	askey	ADJ
ap-3265	96	28	-	-	PUNCT
ap-3265	96	29	wilson	wilson	NOUN
ap-3265	96	30	scheme	scheme	NOUN
ap-3265	96	31	,	,	PUNCT
ap-3265	96	32	can	can	AUX
ap-3265	96	33	be	be	AUX
ap-3265	96	34	classified	classify	VERB
ap-3265	96	35	and	and	CCONJ
ap-3265	96	36	understood	understand	VERB
ap-3265	96	37	in	in	ADP
ap-3265	96	38	terms	term	NOUN
ap-3265	96	39	of	of	ADP
ap-3265	96	40	generalized	generalized	ADJ
ap-3265	96	41	inönü	inönü	NOUN
ap-3265	96	42	-	-	PUNCT
ap-3265	96	43	wigner	wigner	NOUN
ap-3265	96	44	contractions	contraction	NOUN
ap-3265	97	1	[	[	X
ap-3265	97	2	15	15	NUM
ap-3265	97	3	]	]	PUNCT
ap-3265	97	4	.	.	PUNCT
ap-3265	98	1	however	however	ADV
ap-3265	98	2	,	,	PUNCT
ap-3265	98	3	there	there	PRON
ap-3265	98	4	are	be	VERB
ap-3265	98	5	complications	complication	NOUN
ap-3265	98	6	for	for	ADP
ap-3265	98	7	spaces	space	NOUN
ap-3265	98	8	not	not	PART
ap-3265	98	9	of	of	ADP
ap-3265	98	10	constant	constant	ADJ
ap-3265	98	11	curvature	curvature	NOUN
ap-3265	98	12	.	.	PUNCT
ap-3265	99	1	for	for	ADP
ap-3265	99	2	darboux	darboux	ADJ
ap-3265	99	3	spaces	space	NOUN
ap-3265	99	4	the	the	DET
ap-3265	99	5	lie	lie	NOUN
ap-3265	99	6	symmetry	symmetry	NOUN
ap-3265	99	7	algebra	algebra	NOUN
ap-3265	99	8	is	be	AUX
ap-3265	99	9	only	only	ADV
ap-3265	99	10	1	1	NUM
ap-3265	99	11	-	-	PUNCT
ap-3265	99	12	dimensional	dimensional	ADJ
ap-3265	99	13	so	so	SCONJ
ap-3265	99	14	limits	limit	NOUN
ap-3265	99	15	must	must	AUX
ap-3265	99	16	be	be	AUX
ap-3265	99	17	determined	determine	VERB
ap-3265	99	18	on	on	ADP
ap-3265	99	19	a	a	DET
ap-3265	99	20	caseby	caseby	ADJ
ap-3265	99	21	-	-	PUNCT
ap-3265	99	22	case	case	NOUN
ap-3265	99	23	basis	basis	NOUN
ap-3265	99	24	.	.	PUNCT
ap-3265	100	1	there	there	PRON
ap-3265	100	2	is	be	VERB
ap-3265	100	3	no	no	DET
ap-3265	100	4	lie	lie	NOUN
ap-3265	100	5	symmetry	symmetry	NOUN
ap-3265	100	6	algebra	algebra	NOUN
ap-3265	100	7	at	at	ADV
ap-3265	100	8	all	all	ADV
ap-3265	100	9	for	for	ADP
ap-3265	100	10	koenigs	koenig	NOUN
ap-3265	100	11	spaces	space	NOUN
ap-3265	100	12	.	.	PUNCT
ap-3265	101	1	furthermore	furthermore	ADV
ap-3265	101	2	,	,	PUNCT
ap-3265	101	3	there	there	PRON
ap-3265	101	4	is	be	VERB
ap-3265	101	5	the	the	DET
ap-3265	101	6	issue	issue	NOUN
ap-3265	101	7	of	of	ADP
ap-3265	101	8	finding	find	VERB
ap-3265	101	9	a	a	DET
ap-3265	101	10	more	more	ADV
ap-3265	101	11	systematic	systematic	ADJ
ap-3265	101	12	way	way	NOUN
ap-3265	101	13	of	of	ADP
ap-3265	101	14	classifying	classify	VERB
ap-3265	101	15	the	the	DET
ap-3265	101	16	44	44	NUM
ap-3265	101	17	distinct	distinct	ADJ
ap-3265	101	18	helmholtz	helmholtz	NOUN
ap-3265	101	19	superintegrable	superintegrable	ADJ
ap-3265	101	20	eigenvalue	eigenvalue	PROPN
ap-3265	101	21	systems	system	NOUN
ap-3265	101	22	on	on	ADP
ap-3265	101	23	different	different	ADJ
ap-3265	101	24	manifolds	manifold	NOUN
ap-3265	101	25	,	,	PUNCT
ap-3265	101	26	and	and	CCONJ
ap-3265	101	27	their	their	PRON
ap-3265	101	28	relations	relation	NOUN
ap-3265	101	29	.	.	PUNCT
ap-3265	102	1	these	these	DET
ap-3265	102	2	issues	issue	NOUN
ap-3265	102	3	can	can	AUX
ap-3265	102	4	be	be	AUX
ap-3265	102	5	clarified	clarify	VERB
ap-3265	102	6	by	by	ADP
ap-3265	102	7	considering	consider	VERB
ap-3265	102	8	the	the	DET
ap-3265	102	9	helmholtz	helmholtz	NOUN
ap-3265	102	10	systems	system	NOUN
ap-3265	102	11	as	as	ADP
ap-3265	102	12	laplace	laplace	NOUN
ap-3265	102	13	equations	equation	NOUN
ap-3265	102	14	(	(	PUNCT
ap-3265	102	15	with	with	ADP
ap-3265	102	16	potential	potential	NOUN
ap-3265	102	17	)	)	PUNCT
ap-3265	102	18	on	on	ADP
ap-3265	102	19	flat	flat	ADJ
ap-3265	102	20	space	space	NOUN
ap-3265	102	21	.	.	PUNCT
ap-3265	103	1	this	this	DET
ap-3265	103	2	point	point	NOUN
ap-3265	103	3	of	of	ADP
ap-3265	103	4	view	view	NOUN
ap-3265	103	5	was	be	AUX
ap-3265	103	6	introduced	introduce	VERB
ap-3265	103	7	in	in	ADP
ap-3265	103	8	the	the	DET
ap-3265	103	9	paper	paper	NOUN
ap-3265	103	10	[	[	X
ap-3265	103	11	26	26	NUM
ap-3265	103	12	]	]	PUNCT
ap-3265	103	13	and	and	CCONJ
ap-3265	103	14	applied	apply	VERB
ap-3265	103	15	in	in	ADP
ap-3265	103	16	[	[	X
ap-3265	103	17	27	27	NUM
ap-3265	103	18	]	]	PUNCT
ap-3265	103	19	to	to	PART
ap-3265	103	20	solve	solve	VERB
ap-3265	103	21	important	important	ADJ
ap-3265	103	22	classification	classification	NOUN
ap-3265	103	23	problems	problem	NOUN
ap-3265	103	24	in	in	ADP
ap-3265	103	25	the	the	DET
ap-3265	103	26	case	case	NOUN
ap-3265	103	27	n	n	NOUN
ap-3265	103	28	=	=	SYM
ap-3265	103	29	3	3	X
ap-3265	103	30	.	.	PUNCT
ap-3265	104	1	it	it	PRON
ap-3265	104	2	is	be	AUX
ap-3265	104	3	the	the	DET
ap-3265	104	4	aim	aim	NOUN
ap-3265	104	5	of	of	ADP
ap-3265	104	6	this	this	DET
ap-3265	104	7	paper	paper	NOUN
ap-3265	104	8	to	to	PART
ap-3265	104	9	describe	describe	VERB
ap-3265	104	10	the	the	DET
ap-3265	104	11	laplace	laplace	NOUN
ap-3265	104	12	equation	equation	NOUN
ap-3265	104	13	mechanism	mechanism	NOUN
ap-3265	104	14	and	and	CCONJ
ap-3265	104	15	how	how	SCONJ
ap-3265	104	16	it	it	PRON
ap-3265	104	17	can	can	AUX
ap-3265	104	18	be	be	AUX
ap-3265	104	19	applied	apply	VERB
ap-3265	104	20	to	to	PART
ap-3265	104	21	systematize	systematize	VERB
ap-3265	104	22	the	the	DET
ap-3265	104	23	classification	classification	NOUN
ap-3265	104	24	of	of	ADP
ap-3265	104	25	helmholtz	helmholtz	NOUN
ap-3265	104	26	superintegrable	superintegrable	ADJ
ap-3265	104	27	systems	system	NOUN
ap-3265	104	28	and	and	CCONJ
ap-3265	104	29	their	their	PRON
ap-3265	104	30	relations	relation	NOUN
ap-3265	104	31	via	via	ADP
ap-3265	104	32	limits	limit	NOUN
ap-3265	104	33	.	.	PUNCT
ap-3265	105	1	the	the	DET
ap-3265	105	2	basic	basic	ADJ
ap-3265	105	3	idea	idea	NOUN
ap-3265	105	4	is	be	AUX
ap-3265	105	5	that	that	SCONJ
ap-3265	105	6	families	family	NOUN
ap-3265	105	7	of	of	ADP
ap-3265	105	8	(	(	PUNCT
ap-3265	105	9	stäckel	stäckel	NOUN
ap-3265	105	10	-	-	PUNCT
ap-3265	105	11	equivalent	equivalent	NOUN
ap-3265	105	12	)	)	PUNCT
ap-3265	105	13	helmholtz	helmholtz	NOUN
ap-3265	105	14	superintegrable	superintegrable	ADJ
ap-3265	105	15	systems	system	NOUN
ap-3265	105	16	on	on	ADP
ap-3265	105	17	a	a	DET
ap-3265	105	18	variety	variety	NOUN
ap-3265	105	19	of	of	ADP
ap-3265	105	20	manifolds	manifold	NOUN
ap-3265	105	21	correspond	correspond	VERB
ap-3265	105	22	to	to	ADP
ap-3265	105	23	a	a	DET
ap-3265	105	24	single	single	ADJ
ap-3265	105	25	conformally	conformally	ADV
ap-3265	105	26	superintegrable	superintegrable	ADJ
ap-3265	105	27	laplace	laplace	NOUN
ap-3265	105	28	equation	equation	NOUN
ap-3265	105	29	on	on	ADP
ap-3265	105	30	flat	flat	ADJ
ap-3265	105	31	space	space	NOUN
ap-3265	105	32	.	.	PUNCT
ap-3265	106	1	we	we	PRON
ap-3265	106	2	exploit	exploit	VERB
ap-3265	106	3	this	this	DET
ap-3265	106	4	relation	relation	NOUN
ap-3265	106	5	in	in	ADP
ap-3265	106	6	the	the	DET
ap-3265	106	7	case	case	NOUN
ap-3265	106	8	n	n	NOUN
ap-3265	106	9	=	=	SYM
ap-3265	106	10	2	2	NUM
ap-3265	106	11	,	,	PUNCT
ap-3265	106	12	but	but	CCONJ
ap-3265	106	13	it	it	PRON
ap-3265	106	14	generalizes	generalize	VERB
ap-3265	106	15	easily	easily	ADV
ap-3265	106	16	to	to	ADP
ap-3265	106	17	all	all	DET
ap-3265	106	18	dimensions	dimension	NOUN
ap-3265	106	19	n	n	PRON
ap-3265	106	20	≥	≥	NOUN
ap-3265	106	21	2	2	NUM
ap-3265	106	22	.	.	PUNCT
ap-3265	107	1	the	the	DET
ap-3265	107	2	conformal	conformal	ADJ
ap-3265	107	3	symmetry	symmetry	NOUN
ap-3265	107	4	algebra	algebra	NOUN
ap-3265	107	5	for	for	ADP
ap-3265	107	6	laplace	laplace	NOUN
ap-3265	107	7	equations	equation	NOUN
ap-3265	107	8	with	with	ADP
ap-3265	107	9	constant	constant	ADJ
ap-3265	107	10	potential	potential	NOUN
ap-3265	107	11	on	on	ADP
ap-3265	107	12	flat	flat	ADJ
ap-3265	107	13	space	space	NOUN
ap-3265	107	14	is	be	AUX
ap-3265	107	15	the	the	DET
ap-3265	107	16	conformal	conformal	ADJ
ap-3265	107	17	algebra	algebra	NOUN
ap-3265	107	18	so(n	so(n	PROPN
ap-3265	107	19	+	+	CCONJ
ap-3265	107	20	2,c	2,c	NUM
ap-3265	107	21	)	)	PUNCT
ap-3265	107	22	.	.	PUNCT
ap-3265	108	1	in	in	ADP
ap-3265	108	2	his	his	PRON
ap-3265	108	3	1894	1894	NUM
ap-3265	108	4	thesis	thesis	NOUN
ap-3265	108	5	[	[	X
ap-3265	108	6	28	28	NUM
ap-3265	108	7	]	]	X
ap-3265	108	8	bôcher	bôcher	NOUN
ap-3265	108	9	introduced	introduce	VERB
ap-3265	108	10	a	a	DET
ap-3265	108	11	limit	limit	NOUN
ap-3265	108	12	procedure	procedure	NOUN
ap-3265	108	13	based	base	VERB
ap-3265	108	14	on	on	ADP
ap-3265	108	15	the	the	DET
ap-3265	108	16	roots	root	NOUN
ap-3265	108	17	of	of	ADP
ap-3265	108	18	quadratic	quadratic	ADJ
ap-3265	108	19	forms	form	NOUN
ap-3265	108	20	to	to	PART
ap-3265	108	21	find	find	VERB
ap-3265	108	22	families	family	NOUN
ap-3265	108	23	of	of	ADP
ap-3265	108	24	rseparable	rseparable	ADJ
ap-3265	108	25	solutions	solution	NOUN
ap-3265	108	26	of	of	ADP
ap-3265	108	27	the	the	DET
ap-3265	108	28	ordinary	ordinary	ADJ
ap-3265	108	29	(	(	PUNCT
ap-3265	108	30	zero	zero	NUM
ap-3265	108	31	potential	potential	NOUN
ap-3265	108	32	)	)	PUNCT
ap-3265	108	33	flat	flat	ADJ
ap-3265	108	34	space	space	NOUN
ap-3265	108	35	laplace	laplace	NOUN
ap-3265	108	36	equation	equation	NOUN
ap-3265	108	37	∆nψ	∆nψ	PUNCT
ap-3265	108	38	=	=	SYM
ap-3265	108	39	0	0	NUM
ap-3265	108	40	in	in	ADP
ap-3265	108	41	n	n	PRON
ap-3265	108	42	dimensions	dimension	NOUN
ap-3265	108	43	.	.	PUNCT
ap-3265	109	1	(	(	PUNCT
ap-3265	109	2	that	that	PRON
ap-3265	109	3	is	is	ADV
ap-3265	109	4	,	,	PUNCT
ap-3265	109	5	he	he	PRON
ap-3265	109	6	constructed	construct	VERB
ap-3265	109	7	separable	separable	ADJ
ap-3265	109	8	solutions	solution	NOUN
ap-3265	109	9	of	of	ADP
ap-3265	109	10	the	the	DET
ap-3265	109	11	form	form	NOUN
ap-3265	109	12	ψ	ψ	X
ap-3265	109	13	=	=	X
ap-3265	109	14	r(u)πn	r(u)πn	PROPN
ap-3265	109	15	j=1ψj(uj	j=1ψj(uj	PROPN
ap-3265	109	16	)	)	PUNCT
ap-3265	109	17	where	where	SCONJ
ap-3265	109	18	r	r	NOUN
ap-3265	109	19	is	be	AUX
ap-3265	109	20	a	a	DET
ap-3265	109	21	fixed	fix	VERB
ap-3265	109	22	gauge	gauge	NOUN
ap-3265	109	23	function	function	NOUN
ap-3265	109	24	and	and	CCONJ
ap-3265	109	25	ψj	ψj	ADV
ap-3265	109	26	depends	depend	VERB
ap-3265	109	27	only	only	ADV
ap-3265	109	28	on	on	ADP
ap-3265	109	29	the	the	DET
ap-3265	109	30	variable	variable	ADJ
ap-3265	109	31	uj	uj	PROPN
ap-3265	109	32	and	and	CCONJ
ap-3265	109	33	the	the	DET
ap-3265	109	34	separation	separation	NOUN
ap-3265	109	35	constants	constant	NOUN
ap-3265	109	36	.	.	PUNCT
ap-3265	109	37	)	)	PUNCT
ap-3265	110	1	we	we	PRON
ap-3265	110	2	show	show	VERB
ap-3265	110	3	that	that	SCONJ
ap-3265	110	4	his	his	PRON
ap-3265	110	5	limit	limit	NOUN
ap-3265	110	6	procedure	procedure	NOUN
ap-3265	110	7	can	can	AUX
ap-3265	110	8	be	be	AUX
ap-3265	110	9	interpreted	interpret	VERB
ap-3265	110	10	as	as	ADP
ap-3265	110	11	constructing	construct	VERB
ap-3265	110	12	generalized	generalized	ADJ
ap-3265	110	13	inönü	inönü	NOUN
ap-3265	110	14	-	-	PUNCT
ap-3265	110	15	wigner	wigner	NOUN
ap-3265	110	16	lie	lie	NOUN
ap-3265	110	17	algebra	algebra	NOUN
ap-3265	110	18	contractions	contraction	NOUN
ap-3265	110	19	of	of	ADP
ap-3265	110	20	so(4,c	so(4,c	NOUN
ap-3265	110	21	)	)	PUNCT
ap-3265	110	22	to	to	ADP
ap-3265	110	23	itself	itself	PRON
ap-3265	110	24	.	.	PUNCT
ap-3265	111	1	we	we	PRON
ap-3265	111	2	call	call	VERB
ap-3265	111	3	these	these	DET
ap-3265	111	4	bôcher	bôcher	ADJ
ap-3265	111	5	contractions	contraction	NOUN
ap-3265	111	6	and	and	CCONJ
ap-3265	111	7	show	show	VERB
ap-3265	111	8	that	that	SCONJ
ap-3265	111	9	all	all	PRON
ap-3265	111	10	of	of	ADP
ap-3265	111	11	the	the	DET
ap-3265	111	12	limits	limit	NOUN
ap-3265	111	13	of	of	ADP
ap-3265	111	14	the	the	DET
ap-3265	111	15	helmholtz	helmholtz	NOUN
ap-3265	111	16	systems	system	NOUN
ap-3265	111	17	classified	classify	VERB
ap-3265	111	18	before	before	ADV
ap-3265	111	19	for	for	ADP
ap-3265	111	20	n	n	NOUN
ap-3265	111	21	=	=	SYM
ap-3265	111	22	2	2	NUM
ap-3265	111	23	[	[	SYM
ap-3265	111	24	15	15	NUM
ap-3265	111	25	]	]	PUNCT
ap-3265	111	26	are	be	AUX
ap-3265	111	27	induced	induce	VERB
ap-3265	111	28	by	by	ADP
ap-3265	111	29	the	the	DET
ap-3265	111	30	larger	large	ADJ
ap-3265	111	31	class	class	NOUN
ap-3265	111	32	of	of	ADP
ap-3265	111	33	bôcher	bôcher	NOUN
ap-3265	111	34	contractions	contraction	NOUN
ap-3265	111	35	.	.	PUNCT
ap-3265	112	1	here	here	ADV
ap-3265	112	2	we	we	PRON
ap-3265	112	3	present	present	VERB
ap-3265	112	4	the	the	DET
ap-3265	112	5	main	main	ADJ
ap-3265	112	6	constructions	construction	NOUN
ap-3265	112	7	and	and	CCONJ
ap-3265	112	8	findings	finding	NOUN
ap-3265	112	9	.	.	PUNCT
ap-3265	113	1	detailed	detailed	ADJ
ap-3265	113	2	proofs	proof	NOUN
ap-3265	113	3	and	and	CCONJ
ap-3265	113	4	the	the	DET
ap-3265	113	5	lengthy	lengthy	ADJ
ap-3265	113	6	classifications	classification	NOUN
ap-3265	113	7	are	be	AUX
ap-3265	113	8	in	in	ADP
ap-3265	113	9	[	[	X
ap-3265	113	10	32	32	NUM
ap-3265	113	11	]	]	PUNCT
ap-3265	113	12	.	.	PUNCT
ap-3265	114	1	2	2	X
ap-3265	114	2	.	.	X
ap-3265	114	3	the	the	DET
ap-3265	114	4	laplace	laplace	NOUN
ap-3265	114	5	equation	equation	NOUN
ap-3265	114	6	systems	system	NOUN
ap-3265	114	7	of	of	ADP
ap-3265	114	8	laplace	laplace	NOUN
ap-3265	114	9	type	type	NOUN
ap-3265	114	10	are	be	AUX
ap-3265	114	11	of	of	ADP
ap-3265	114	12	the	the	DET
ap-3265	114	13	form	form	NOUN
ap-3265	114	14	hψ	hψ	X
ap-3265	114	15	≡	≡	PROPN
ap-3265	114	16	∆nψ	∆nψ	PROPN
ap-3265	115	1	+	+	CCONJ
ap-3265	115	2	vψ	vψ	ADP
ap-3265	115	3	=	=	SYM
ap-3265	115	4	0	0	X
ap-3265	115	5	.	.	PUNCT
ap-3265	116	1	here	here	ADV
ap-3265	116	2	∆n	∆n	PROPN
ap-3265	116	3	is	be	AUX
ap-3265	116	4	the	the	DET
ap-3265	116	5	laplace	laplace	NOUN
ap-3265	116	6	-	-	PUNCT
ap-3265	116	7	beltrami	beltrami	ADJ
ap-3265	116	8	operator	operator	NOUN
ap-3265	116	9	on	on	ADP
ap-3265	116	10	a	a	DET
ap-3265	116	11	conformally	conformally	ADV
ap-3265	116	12	flat	flat	ADJ
ap-3265	116	13	nd	nd	NOUN
ap-3265	116	14	riemannian	riemannian	ADJ
ap-3265	116	15	or	or	CCONJ
ap-3265	116	16	pseudo	pseudo	NOUN
ap-3265	116	17	-	-	ADJ
ap-3265	116	18	riemannian	riemannian	ADJ
ap-3265	116	19	manifold	manifold	NOUN
ap-3265	116	20	.	.	PUNCT
ap-3265	117	1	a	a	DET
ap-3265	117	2	conformal	conformal	ADJ
ap-3265	117	3	symmetry	symmetry	NOUN
ap-3265	117	4	of	of	ADP
ap-3265	117	5	this	this	DET
ap-3265	117	6	equation	equation	NOUN
ap-3265	117	7	is	be	AUX
ap-3265	117	8	a	a	DET
ap-3265	117	9	partial	partial	ADJ
ap-3265	117	10	differential	differential	NOUN
ap-3265	117	11	operator	operator	NOUN
ap-3265	117	12	s	s	VERB
ap-3265	117	13	in	in	ADP
ap-3265	117	14	the	the	DET
ap-3265	117	15	variables	variable	NOUN
ap-3265	117	16	x	x	PUNCT
ap-3265	118	1	=	=	SYM
ap-3265	118	2	(	(	PUNCT
ap-3265	118	3	x1	x1	PROPN
ap-3265	118	4	,	,	PUNCT
ap-3265	118	5	·	·	PUNCT
ap-3265	118	6	·	·	PUNCT
ap-3265	118	7	·	·	PUNCT
ap-3265	118	8	,	,	PUNCT
ap-3265	118	9	xn	xn	X
ap-3265	118	10	)	)	PUNCT
ap-3265	118	11	such	such	ADJ
ap-3265	118	12	that	that	SCONJ
ap-3265	118	13	[	[	X
ap-3265	118	14	s	s	X
ap-3265	118	15	,	,	PUNCT
ap-3265	118	16	h	h	NOUN
ap-3265	118	17	]	]	X
ap-3265	118	18	≡	≡	PROPN
ap-3265	118	19	sh	sh	INTJ
ap-3265	118	20	−hs	−hs	PROPN
ap-3265	118	21	=	=	PUNCT
ap-3265	118	22	rsh	rsh	ADJ
ap-3265	118	23	for	for	ADP
ap-3265	118	24	some	some	DET
ap-3265	118	25	differential	differential	ADJ
ap-3265	118	26	operator	operator	NOUN
ap-3265	118	27	rs	rs	NOUN
ap-3265	118	28	.	.	PUNCT
ap-3265	119	1	the	the	DET
ap-3265	119	2	system	system	NOUN
ap-3265	119	3	is	be	AUX
ap-3265	119	4	maximally	maximally	ADV
ap-3265	119	5	conformally	conformally	ADV
ap-3265	119	6	superintegrable	superintegrable	ADJ
ap-3265	119	7	(	(	PUNCT
ap-3265	119	8	or	or	CCONJ
ap-3265	119	9	laplace	laplace	NOUN
ap-3265	119	10	superintegrable	superintegrable	ADJ
ap-3265	119	11	)	)	PUNCT
ap-3265	119	12	for	for	ADP
ap-3265	119	13	n	n	X
ap-3265	119	14	≥	≥	NUM
ap-3265	119	15	2	2	NUM
ap-3265	119	16	if	if	SCONJ
ap-3265	119	17	there	there	PRON
ap-3265	119	18	are	be	VERB
ap-3265	119	19	2n	2n	NUM
ap-3265	119	20	−	−	ADP
ap-3265	119	21	1	1	NUM
ap-3265	119	22	functionally	functionally	ADV
ap-3265	119	23	independent	independent	ADJ
ap-3265	119	24	conformal	conformal	ADJ
ap-3265	119	25	symmetries	symmetry	NOUN
ap-3265	119	26	,	,	PUNCT
ap-3265	119	27	s1	s1	NOUN
ap-3265	119	28	,	,	PUNCT
ap-3265	119	29	·	·	PUNCT
ap-3265	119	30	·	·	PUNCT
ap-3265	119	31	·	·	PUNCT
ap-3265	119	32	,	,	PUNCT
ap-3265	119	33	s2n−1	s2n−1	VERB
ap-3265	119	34	with	with	ADP
ap-3265	119	35	s1	s1	NOUN
ap-3265	119	36	=	=	PUNCT
ap-3265	119	37	h	h	NOUN
ap-3265	120	1	[	[	X
ap-3265	120	2	26	26	NUM
ap-3265	120	3	]	]	PUNCT
ap-3265	120	4	.	.	PUNCT
ap-3265	121	1	it	it	PRON
ap-3265	121	2	is	be	AUX
ap-3265	121	3	second	second	ADJ
ap-3265	121	4	order	order	NOUN
ap-3265	121	5	conformally	conformally	ADV
ap-3265	121	6	superintegrable	superintegrable	ADJ
ap-3265	121	7	if	if	SCONJ
ap-3265	121	8	each	each	DET
ap-3265	121	9	symmetry	symmetry	NOUN
ap-3265	121	10	si	si	PROPN
ap-3265	121	11	can	can	AUX
ap-3265	121	12	be	be	AUX
ap-3265	121	13	chosen	choose	VERB
ap-3265	121	14	to	to	PART
ap-3265	121	15	be	be	AUX
ap-3265	121	16	a	a	DET
ap-3265	121	17	differential	differential	ADJ
ap-3265	121	18	operator	operator	NOUN
ap-3265	121	19	of	of	ADP
ap-3265	121	20	at	at	ADP
ap-3265	121	21	most	most	ADJ
ap-3265	121	22	second	second	ADJ
ap-3265	121	23	order	order	NOUN
ap-3265	121	24	.	.	PUNCT
ap-3265	122	1	every	every	DET
ap-3265	122	2	2d	2d	NOUN
ap-3265	122	3	riemannian	riemannian	NOUN
ap-3265	122	4	manifold	manifold	NOUN
ap-3265	122	5	is	be	AUX
ap-3265	122	6	conformally	conformally	ADV
ap-3265	122	7	flat	flat	ADJ
ap-3265	122	8	,	,	PUNCT
ap-3265	122	9	so	so	SCONJ
ap-3265	122	10	we	we	PRON
ap-3265	122	11	can	can	AUX
ap-3265	122	12	always	always	ADV
ap-3265	122	13	find	find	VERB
ap-3265	122	14	a	a	DET
ap-3265	122	15	cartesian	cartesian	ADJ
ap-3265	122	16	-	-	PUNCT
ap-3265	122	17	like	like	ADJ
ap-3265	122	18	coordinate	coordinate	NOUN
ap-3265	122	19	system	system	NOUN
ap-3265	122	20	with	with	ADP
ap-3265	122	21	coordinates	coordinate	NOUN
ap-3265	122	22	(	(	PUNCT
ap-3265	122	23	x	x	X
ap-3265	122	24	,	,	PUNCT
ap-3265	122	25	y	y	PROPN
ap-3265	122	26	)	)	PUNCT
ap-3265	122	27	≡	≡	PROPN
ap-3265	122	28	(	(	PUNCT
ap-3265	122	29	x1	x1	PROPN
ap-3265	122	30	,	,	PUNCT
ap-3265	122	31	x2	x2	PROPN
ap-3265	122	32	)	)	PUNCT
ap-3265	122	33	such	such	ADJ
ap-3265	122	34	that	that	SCONJ
ap-3265	122	35	the	the	DET
ap-3265	122	36	helmholtz	helmholtz	NOUN
ap-3265	122	37	eigenvalue	eigenvalue	NOUN
ap-3265	122	38	equation	equation	NOUN
ap-3265	122	39	takes	take	VERB
ap-3265	122	40	the	the	DET
ap-3265	122	41	form	form	NOUN
ap-3265	122	42	h̃ψ	h̃ψ	NOUN
ap-3265	122	43	=	=	SYM
ap-3265	122	44	(	(	PUNCT
ap-3265	122	45	1	1	NUM
ap-3265	122	46	λ(x	λ(x	PROPN
ap-3265	122	47	,	,	PUNCT
ap-3265	122	48	y	y	PROPN
ap-3265	122	49	)	)	PUNCT
ap-3265	122	50	(	(	PUNCT
ap-3265	122	51	∂2	∂2	NOUN
ap-3265	122	52	x	x	X
ap-3265	122	53	+	+	CCONJ
ap-3265	122	54	∂2	∂2	PROPN
ap-3265	122	55	y	y	PROPN
ap-3265	122	56	)	)	PUNCT
ap-3265	123	1	+	+	CCONJ
ap-3265	123	2	ṽ	ṽ	PROPN
ap-3265	123	3	(	(	PUNCT
ap-3265	123	4	x	x	NOUN
ap-3265	123	5	)	)	PUNCT
ap-3265	123	6	)	)	PUNCT
ap-3265	124	1	ψ	ψ	X
ap-3265	124	2	=	=	SYM
ap-3265	124	3	eψ	eψ	PROPN
ap-3265	124	4	.	.	PUNCT
ap-3265	125	1	(	(	PUNCT
ap-3265	125	2	1	1	X
ap-3265	125	3	)	)	PUNCT
ap-3265	125	4	however	however	ADV
ap-3265	125	5	,	,	PUNCT
ap-3265	125	6	this	this	DET
ap-3265	125	7	equation	equation	NOUN
ap-3265	125	8	is	be	AUX
ap-3265	125	9	equivalent	equivalent	ADJ
ap-3265	125	10	to	to	ADP
ap-3265	125	11	the	the	DET
ap-3265	125	12	flat	flat	ADJ
ap-3265	125	13	space	space	NOUN
ap-3265	125	14	laplace	laplace	NOUN
ap-3265	125	15	equation	equation	NOUN
ap-3265	125	16	hψ	hψ	X
ap-3265	125	17	≡	≡	PROPN
ap-3265	125	18	(	(	PUNCT
ap-3265	125	19	∂2	∂2	NUM
ap-3265	125	20	x	x	X
ap-3265	126	1	+	+	CCONJ
ap-3265	127	1	∂2	∂2	PROPN
ap-3265	127	2	y	y	PROPN
ap-3265	127	3	+	+	PROPN
ap-3265	127	4	v	v	PROPN
ap-3265	127	5	(	(	PUNCT
ap-3265	127	6	x	x	NOUN
ap-3265	127	7	)	)	PUNCT
ap-3265	127	8	)	)	PUNCT
ap-3265	128	1	ψ	ψ	X
ap-3265	128	2	=	=	SYM
ap-3265	128	3	0	0	NUM
ap-3265	128	4	,	,	PUNCT
ap-3265	128	5	v	v	NOUN
ap-3265	128	6	(	(	PUNCT
ap-3265	128	7	x	x	NOUN
ap-3265	128	8	)	)	PUNCT
ap-3265	128	9	=	=	SYM
ap-3265	128	10	λ(x)(ṽ	λ(x)(ṽ	PROPN
ap-3265	128	11	(	(	PUNCT
ap-3265	128	12	x)−	x)−	PROPN
ap-3265	128	13	e	e	NOUN
ap-3265	128	14	)	)	PUNCT
ap-3265	128	15	.	.	PUNCT
ap-3265	129	1	(	(	PUNCT
ap-3265	129	2	2	2	X
ap-3265	129	3	)	)	PUNCT
ap-3265	129	4	in	in	ADP
ap-3265	129	5	particular	particular	ADJ
ap-3265	129	6	,	,	PUNCT
ap-3265	129	7	the	the	DET
ap-3265	129	8	symmetries	symmetry	NOUN
ap-3265	129	9	of	of	ADP
ap-3265	129	10	(	(	PUNCT
ap-3265	129	11	1	1	X
ap-3265	129	12	)	)	PUNCT
ap-3265	129	13	correspond	correspond	VERB
ap-3265	129	14	to	to	ADP
ap-3265	129	15	the	the	DET
ap-3265	129	16	conformal	conformal	ADJ
ap-3265	129	17	symmetries	symmetry	NOUN
ap-3265	129	18	of	of	ADP
ap-3265	129	19	(	(	PUNCT
ap-3265	129	20	2	2	NUM
ap-3265	129	21	)	)	PUNCT
ap-3265	129	22	.	.	PUNCT
ap-3265	130	1	indeed	indeed	ADV
ap-3265	130	2	,	,	PUNCT
ap-3265	130	3	if	if	SCONJ
ap-3265	130	4	[	[	X
ap-3265	130	5	s	s	X
ap-3265	130	6	,	,	PUNCT
ap-3265	130	7	h̃	h̃	PROPN
ap-3265	130	8	]	]	X
ap-3265	130	9	=	=	SYM
ap-3265	130	10	0	0	PUNCT
ap-3265	130	11	then	then	ADV
ap-3265	130	12	[	[	X
ap-3265	130	13	s	s	X
ap-3265	130	14	,	,	PUNCT
ap-3265	130	15	h	h	NOUN
ap-3265	130	16	]	]	X
ap-3265	130	17	=	=	PUNCT
ap-3265	131	1	[	[	X
ap-3265	131	2	s	s	X
ap-3265	131	3	,	,	PUNCT
ap-3265	131	4	λ(h̃−e	λ(h̃−e	NOUN
ap-3265	131	5	)	)	PUNCT
ap-3265	131	6	]	]	PUNCT
ap-3265	132	1	=	=	PUNCT
ap-3265	133	1	[	[	X
ap-3265	133	2	s	s	X
ap-3265	133	3	,	,	PUNCT
ap-3265	133	4	λ](h̃−e	λ](h̃−e	NOUN
ap-3265	133	5	)	)	PUNCT
ap-3265	134	1	=	=	PUNCT
ap-3265	135	1	[	[	X
ap-3265	135	2	s	s	X
ap-3265	135	3	,	,	PUNCT
ap-3265	135	4	λ]λ−1h	λ]λ−1h	ADJ
ap-3265	135	5	.	.	PUNCT
ap-3265	136	1	conversely	conversely	ADV
ap-3265	136	2	,	,	PUNCT
ap-3265	136	3	if	if	SCONJ
ap-3265	136	4	s	s	VERB
ap-3265	136	5	is	be	AUX
ap-3265	136	6	an	an	DET
ap-3265	136	7	e	e	ADJ
ap-3265	136	8	-	-	ADJ
ap-3265	136	9	independent	independent	ADJ
ap-3265	136	10	conformal	conformal	ADJ
ap-3265	136	11	symmetry	symmetry	NOUN
ap-3265	136	12	of	of	ADP
ap-3265	136	13	h	h	NOUN
ap-3265	136	14	we	we	PRON
ap-3265	136	15	find	find	VERB
ap-3265	136	16	that	that	SCONJ
ap-3265	136	17	[	[	X
ap-3265	136	18	s	s	X
ap-3265	136	19	,	,	PUNCT
ap-3265	136	20	h̃	h̃	PROPN
ap-3265	136	21	]	]	X
ap-3265	136	22	=	=	SYM
ap-3265	136	23	0	0	X
ap-3265	136	24	.	.	PUNCT
ap-3265	137	1	further	far	ADV
ap-3265	137	2	,	,	PUNCT
ap-3265	137	3	the	the	DET
ap-3265	137	4	conformal	conformal	ADJ
ap-3265	137	5	symmetries	symmetry	NOUN
ap-3265	137	6	of	of	ADP
ap-3265	137	7	the	the	DET
ap-3265	137	8	system	system	NOUN
ap-3265	137	9	(	(	PUNCT
ap-3265	137	10	h̃	h̃	PROPN
ap-3265	137	11	−	−	PROPN
ap-3265	137	12	e)ψ	e)ψ	PUNCT
ap-3265	138	1	=	=	SYM
ap-3265	138	2	0	0	NUM
ap-3265	138	3	are	be	AUX
ap-3265	138	4	identical	identical	ADJ
ap-3265	138	5	with	with	ADP
ap-3265	138	6	the	the	DET
ap-3265	138	7	conformal	conformal	ADJ
ap-3265	138	8	symmetries	symmetry	NOUN
ap-3265	138	9	of	of	ADP
ap-3265	138	10	(	(	PUNCT
ap-3265	138	11	2	2	NUM
ap-3265	138	12	)	)	PUNCT
ap-3265	138	13	.	.	PUNCT
ap-3265	139	1	thus	thus	ADV
ap-3265	139	2	without	without	ADP
ap-3265	139	3	loss	loss	NOUN
ap-3265	139	4	of	of	ADP
ap-3265	139	5	generality	generality	NOUN
ap-3265	139	6	we	we	PRON
ap-3265	139	7	can	can	AUX
ap-3265	139	8	assume	assume	VERB
ap-3265	139	9	the	the	DET
ap-3265	139	10	manifold	manifold	NOUN
ap-3265	139	11	is	be	AUX
ap-3265	139	12	flat	flat	ADJ
ap-3265	139	13	space	space	NOUN
ap-3265	139	14	with	with	ADP
ap-3265	139	15	λ	λ	PROPN
ap-3265	139	16	≡	≡	PROPN
ap-3265	139	17	1	1	NUM
ap-3265	139	18	.	.	PUNCT
ap-3265	140	1	the	the	DET
ap-3265	140	2	conformal	conformal	ADJ
ap-3265	140	3	stäckel	stäckel	NOUN
ap-3265	140	4	transform	transform	NOUN
ap-3265	140	5	.	.	PUNCT
ap-3265	140	6	suppose	suppose	VERB
ap-3265	140	7	we	we	PRON
ap-3265	140	8	have	have	VERB
ap-3265	140	9	a	a	DET
ap-3265	140	10	second	second	ADJ
ap-3265	140	11	order	order	NOUN
ap-3265	140	12	conformal	conformal	ADJ
ap-3265	140	13	superintegrable	superintegrable	ADJ
ap-3265	140	14	system	system	NOUN
ap-3265	140	15	h	h	NOUN
ap-3265	140	16	=	=	SYM
ap-3265	140	17	∂xx	∂xx	PROPN
ap-3265	140	18	+	+	CCONJ
ap-3265	140	19	∂yy	∂yy	PROPN
ap-3265	140	20	+	+	CCONJ
ap-3265	140	21	v	v	NOUN
ap-3265	140	22	(	(	PUNCT
ap-3265	140	23	x	x	NOUN
ap-3265	140	24	,	,	PUNCT
ap-3265	140	25	y	y	NOUN
ap-3265	140	26	)	)	PUNCT
ap-3265	140	27	=	=	SYM
ap-3265	141	1	0	0	NUM
ap-3265	141	2	,	,	PUNCT
ap-3265	141	3	h	h	NOUN
ap-3265	141	4	=	=	PROPN
ap-3265	141	5	h0	h0	PROPN
ap-3265	141	6	+	+	CCONJ
ap-3265	141	7	v	v	NOUN
ap-3265	141	8	,	,	PUNCT
ap-3265	141	9	where	where	SCONJ
ap-3265	141	10	v	v	X
ap-3265	141	11	(	(	PUNCT
ap-3265	141	12	x	x	NOUN
ap-3265	141	13	,	,	PUNCT
ap-3265	141	14	y	y	NOUN
ap-3265	141	15	)	)	PUNCT
ap-3265	142	1	=	=	SYM
ap-3265	142	2	w	w	X
ap-3265	142	3	(	(	PUNCT
ap-3265	142	4	x	x	NOUN
ap-3265	142	5	,	,	PUNCT
ap-3265	142	6	y	y	NOUN
ap-3265	142	7	)	)	PUNCT
ap-3265	142	8	−	−	NOUN
ap-3265	142	9	e	e	NOUN
ap-3265	142	10	u(x	u(x	PROPN
ap-3265	142	11	,	,	PUNCT
ap-3265	142	12	y	y	NOUN
ap-3265	142	13	)	)	PUNCT
ap-3265	142	14	for	for	ADP
ap-3265	142	15	arbitrary	arbitrary	ADJ
ap-3265	142	16	parameter	parameter	NOUN
ap-3265	142	17	e.	e.	PROPN
ap-3265	142	18	216	216	NUM
ap-3265	142	19	vol	vol	NOUN
ap-3265	142	20	.	.	PUNCT
ap-3265	143	1	56	56	NUM
ap-3265	143	2	no	no	NOUN
ap-3265	143	3	.	.	PUNCT
ap-3265	144	1	3/2016	3/2016	NUM
ap-3265	144	2	laplace	laplace	NOUN
ap-3265	144	3	equations	equation	NOUN
ap-3265	144	4	,	,	PUNCT
ap-3265	144	5	conformal	conformal	ADJ
ap-3265	144	6	superintegrability	superintegrability	NOUN
ap-3265	144	7	and	and	CCONJ
ap-3265	144	8	bôcher	bôcher	PROPN
ap-3265	144	9	contractions	contraction	NOUN
ap-3265	144	10	theorem	theorem	VERB
ap-3265	144	11	3	3	NUM
ap-3265	144	12	[	[	X
ap-3265	144	13	26	26	NUM
ap-3265	144	14	]	]	PUNCT
ap-3265	144	15	.	.	PUNCT
ap-3265	145	1	the	the	DET
ap-3265	145	2	transformed	transform	VERB
ap-3265	145	3	(	(	PUNCT
ap-3265	145	4	helmholtz	helmholtz	NOUN
ap-3265	145	5	)	)	PUNCT
ap-3265	145	6	system	system	NOUN
ap-3265	145	7	h̃ψ	h̃ψ	NOUN
ap-3265	145	8	=	=	SYM
ap-3265	145	9	eψ	eψ	PROPN
ap-3265	145	10	,	,	PUNCT
ap-3265	145	11	h̃	h̃	PROPN
ap-3265	145	12	=	=	SYM
ap-3265	145	13	1	1	NUM
ap-3265	145	14	u	u	NOUN
ap-3265	145	15	(	(	PUNCT
ap-3265	145	16	∂xx	∂xx	PROPN
ap-3265	145	17	+	+	CCONJ
ap-3265	145	18	∂yy	∂yy	PROPN
ap-3265	145	19	)	)	PUNCT
ap-3265	145	20	+	+	NUM
ap-3265	146	1	ṽ	ṽ	PROPN
ap-3265	146	2	is	be	AUX
ap-3265	146	3	superintegrable	superintegrable	ADJ
ap-3265	146	4	(	(	PUNCT
ap-3265	146	5	not	not	PART
ap-3265	146	6	just	just	ADV
ap-3265	146	7	conformally	conformally	ADV
ap-3265	146	8	superintegrable	superintegrable	ADJ
ap-3265	146	9	)	)	PUNCT
ap-3265	146	10	,	,	PUNCT
ap-3265	146	11	where	where	SCONJ
ap-3265	146	12	ṽ	ṽ	PROPN
ap-3265	146	13	=	=	SYM
ap-3265	146	14	w	w	PROPN
ap-3265	146	15	u	u	PROPN
ap-3265	146	16	.	.	PUNCT
ap-3265	147	1	there	there	PRON
ap-3265	147	2	is	be	VERB
ap-3265	147	3	a	a	DET
ap-3265	147	4	similar	similar	ADJ
ap-3265	147	5	definition	definition	NOUN
ap-3265	147	6	of	of	ADP
ap-3265	147	7	ordinary	ordinary	ADJ
ap-3265	147	8	stäckel	stäckel	NOUN
ap-3265	147	9	transforms	transform	VERB
ap-3265	147	10	of	of	ADP
ap-3265	147	11	helmholtz	helmholtz	NOUN
ap-3265	147	12	superintegrable	superintegrable	ADJ
ap-3265	147	13	systems	system	NOUN
ap-3265	147	14	hψ	hψ	X
ap-3265	147	15	=	=	SYM
ap-3265	147	16	eψ	eψ	NOUN
ap-3265	147	17	which	which	PRON
ap-3265	147	18	takes	take	VERB
ap-3265	147	19	superintegrable	superintegrable	ADJ
ap-3265	147	20	systems	system	NOUN
ap-3265	147	21	to	to	ADP
ap-3265	147	22	superintegrable	superintegrable	ADJ
ap-3265	147	23	systems	system	NOUN
ap-3265	147	24	,	,	PUNCT
ap-3265	147	25	essentially	essentially	ADV
ap-3265	147	26	preserving	preserve	VERB
ap-3265	147	27	the	the	DET
ap-3265	147	28	quadratic	quadratic	ADJ
ap-3265	147	29	algebra	algebra	NOUN
ap-3265	147	30	structure	structure	NOUN
ap-3265	147	31	[	[	X
ap-3265	147	32	29	29	NUM
ap-3265	147	33	]	]	PUNCT
ap-3265	147	34	.	.	PUNCT
ap-3265	148	1	thus	thus	ADV
ap-3265	148	2	any	any	DET
ap-3265	148	3	second	second	ADJ
ap-3265	148	4	order	order	NOUN
ap-3265	148	5	conformal	conformal	ADJ
ap-3265	148	6	laplace	laplace	NOUN
ap-3265	148	7	superintegrable	superintegrable	ADJ
ap-3265	148	8	system	system	NOUN
ap-3265	148	9	admitting	admit	VERB
ap-3265	148	10	a	a	DET
ap-3265	148	11	nonconstant	nonconstant	ADJ
ap-3265	148	12	potential	potential	ADJ
ap-3265	148	13	u	u	NOUN
ap-3265	148	14	can	can	AUX
ap-3265	148	15	be	be	AUX
ap-3265	148	16	stäckel	stäckel	NOUN
ap-3265	148	17	transformed	transform	VERB
ap-3265	148	18	to	to	ADP
ap-3265	148	19	a	a	DET
ap-3265	148	20	helmholtz	helmholtz	NOUN
ap-3265	148	21	superintegrable	superintegrable	ADJ
ap-3265	148	22	system	system	NOUN
ap-3265	148	23	.	.	PUNCT
ap-3265	149	1	by	by	ADP
ap-3265	149	2	choosing	choose	VERB
ap-3265	149	3	all	all	DET
ap-3265	149	4	possible	possible	ADJ
ap-3265	149	5	special	special	ADJ
ap-3265	149	6	potentials	potential	NOUN
ap-3265	149	7	u	u	PRON
ap-3265	149	8	associated	associate	VERB
ap-3265	149	9	with	with	ADP
ap-3265	149	10	the	the	DET
ap-3265	149	11	fixed	fix	VERB
ap-3265	149	12	laplace	laplace	NOUN
ap-3265	149	13	system	system	NOUN
ap-3265	149	14	we	we	PRON
ap-3265	149	15	generate	generate	VERB
ap-3265	149	16	the	the	DET
ap-3265	149	17	equivalence	equivalence	NOUN
ap-3265	149	18	class	class	NOUN
ap-3265	149	19	of	of	ADP
ap-3265	149	20	all	all	DET
ap-3265	149	21	helmholtz	helmholtz	ADJ
ap-3265	149	22	superintegrable	superintegrable	ADJ
ap-3265	149	23	systems	system	NOUN
ap-3265	149	24	obtainable	obtainable	ADJ
ap-3265	149	25	through	through	ADP
ap-3265	149	26	this	this	DET
ap-3265	149	27	process	process	NOUN
ap-3265	149	28	.	.	PUNCT
ap-3265	150	1	theorem	theorem	ADJ
ap-3265	150	2	4	4	NUM
ap-3265	150	3	.	.	PUNCT
ap-3265	151	1	there	there	PRON
ap-3265	151	2	is	be	VERB
ap-3265	151	3	a	a	DET
ap-3265	151	4	one	one	NUM
ap-3265	151	5	-	-	PUNCT
ap-3265	151	6	to	to	ADP
ap-3265	151	7	-	-	PUNCT
ap-3265	151	8	one	one	NUM
ap-3265	151	9	relationship	relationship	NOUN
ap-3265	151	10	between	between	ADP
ap-3265	151	11	flat	flat	ADJ
ap-3265	151	12	space	space	NOUN
ap-3265	151	13	conformally	conformally	ADV
ap-3265	151	14	superintegrable	superintegrable	ADJ
ap-3265	151	15	laplace	laplace	NOUN
ap-3265	151	16	systems	system	NOUN
ap-3265	151	17	with	with	ADP
ap-3265	151	18	nondegenerate	nondegenerate	ADJ
ap-3265	151	19	potential	potential	NOUN
ap-3265	151	20	and	and	CCONJ
ap-3265	151	21	stäckel	stäckel	NOUN
ap-3265	151	22	equivalence	equivalence	NOUN
ap-3265	151	23	classes	class	NOUN
ap-3265	151	24	of	of	ADP
ap-3265	151	25	superintegrable	superintegrable	ADJ
ap-3265	151	26	helmholtz	helmholtz	NOUN
ap-3265	151	27	systems	system	NOUN
ap-3265	151	28	with	with	ADP
ap-3265	151	29	nondegenerate	nondegenerate	ADJ
ap-3265	151	30	potential	potential	NOUN
ap-3265	151	31	.	.	PUNCT
ap-3265	152	1	indeed	indeed	ADV
ap-3265	152	2	,	,	PUNCT
ap-3265	152	3	for	for	ADP
ap-3265	152	4	a	a	DET
ap-3265	152	5	stäckel	stäckel	NOUN
ap-3265	152	6	transform	transform	NOUN
ap-3265	152	7	induced	induce	VERB
ap-3265	152	8	by	by	ADP
ap-3265	152	9	the	the	DET
ap-3265	152	10	function	function	NOUN
ap-3265	152	11	u	u	NOUN
ap-3265	152	12	(	(	PUNCT
ap-3265	152	13	1	1	NUM
ap-3265	152	14	)	)	PUNCT
ap-3265	152	15	,	,	PUNCT
ap-3265	152	16	we	we	PRON
ap-3265	152	17	can	can	AUX
ap-3265	152	18	take	take	VERB
ap-3265	152	19	the	the	DET
ap-3265	152	20	original	original	ADJ
ap-3265	152	21	helmholtz	helmholtz	NOUN
ap-3265	152	22	system	system	NOUN
ap-3265	152	23	to	to	PART
ap-3265	152	24	have	have	VERB
ap-3265	152	25	hamiltonian	hamiltonian	ADJ
ap-3265	152	26	h	h	NOUN
ap-3265	152	27	=	=	PROPN
ap-3265	152	28	h0	h0	PROPN
ap-3265	152	29	+	+	CCONJ
ap-3265	152	30	v	v	NOUN
ap-3265	152	31	=	=	SYM
ap-3265	152	32	h0	h0	PROPN
ap-3265	152	33	+	+	CCONJ
ap-3265	152	34	u	u	PROPN
ap-3265	152	35	(	(	PUNCT
ap-3265	152	36	1)α1	1)α1	NUM
ap-3265	153	1	+	+	NUM
ap-3265	153	2	u	u	SYM
ap-3265	153	3	(	(	PUNCT
ap-3265	153	4	2)α2	2)α2	NUM
ap-3265	153	5	+	+	CCONJ
ap-3265	153	6	u	u	SYM
ap-3265	153	7	(	(	PUNCT
ap-3265	153	8	3)α3	3)α3	PROPN
ap-3265	153	9	+	+	NUM
ap-3265	153	10	α4	α4	NOUN
ap-3265	153	11	,	,	PUNCT
ap-3265	153	12	(	(	PUNCT
ap-3265	153	13	3	3	X
ap-3265	153	14	)	)	PUNCT
ap-3265	153	15	where	where	SCONJ
ap-3265	153	16	{	{	PUNCT
ap-3265	153	17	u	u	NOUN
ap-3265	153	18	(	(	PUNCT
ap-3265	153	19	1	1	NUM
ap-3265	153	20	)	)	PUNCT
ap-3265	153	21	,	,	PUNCT
ap-3265	153	22	u	u	NOUN
ap-3265	153	23	(	(	PUNCT
ap-3265	153	24	2	2	NUM
ap-3265	153	25	)	)	PUNCT
ap-3265	153	26	,	,	PUNCT
ap-3265	153	27	u	u	NOUN
ap-3265	153	28	(	(	PUNCT
ap-3265	153	29	3	3	NUM
ap-3265	153	30	)	)	PUNCT
ap-3265	153	31	,	,	PUNCT
ap-3265	153	32	1	1	X
ap-3265	153	33	}	}	PUNCT
ap-3265	153	34	is	be	AUX
ap-3265	153	35	a	a	DET
ap-3265	153	36	basis	basis	NOUN
ap-3265	153	37	for	for	ADP
ap-3265	153	38	the	the	DET
ap-3265	153	39	4dimensional	4dimensional	ADJ
ap-3265	153	40	potential	potential	ADJ
ap-3265	153	41	space	space	NOUN
ap-3265	153	42	.	.	PUNCT
ap-3265	154	1	a	a	DET
ap-3265	154	2	2nd	2nd	ADJ
ap-3265	154	3	order	order	NOUN
ap-3265	154	4	symmetry	symmetry	NOUN
ap-3265	154	5	s	s	VERB
ap-3265	154	6	would	would	AUX
ap-3265	154	7	have	have	VERB
ap-3265	154	8	the	the	DET
ap-3265	154	9	form	form	NOUN
ap-3265	154	10	s	s	PART
ap-3265	154	11	=	=	SYM
ap-3265	154	12	s0	s0	PROPN
ap-3265	154	13	+	+	PROPN
ap-3265	154	14	w	w	PROPN
ap-3265	154	15	(	(	PUNCT
ap-3265	154	16	1)α1	1)α1	NUM
ap-3265	154	17	+	+	NOUN
ap-3265	154	18	w	w	NOUN
ap-3265	154	19	(	(	PUNCT
ap-3265	154	20	2)α2	2)α2	NUM
ap-3265	155	1	+	+	NOUN
ap-3265	155	2	w	w	PROPN
ap-3265	155	3	(	(	PUNCT
ap-3265	155	4	3)α3	3)α3	PROPN
ap-3265	155	5	,	,	PUNCT
ap-3265	155	6	where	where	SCONJ
ap-3265	155	7	s0	s0	PROPN
ap-3265	155	8	is	be	AUX
ap-3265	155	9	a	a	DET
ap-3265	155	10	symmetry	symmetry	NOUN
ap-3265	155	11	of	of	ADP
ap-3265	155	12	the	the	DET
ap-3265	155	13	potential	potential	ADJ
ap-3265	155	14	free	free	ADJ
ap-3265	155	15	hamiltonian	hamiltonian	NOUN
ap-3265	155	16	,	,	PUNCT
ap-3265	155	17	h0	h0	PROPN
ap-3265	155	18	.	.	PUNCT
ap-3265	156	1	the	the	DET
ap-3265	156	2	stäckel	stäckel	NOUN
ap-3265	156	3	transformed	transform	VERB
ap-3265	156	4	symmetry	symmetry	NOUN
ap-3265	156	5	and	and	CCONJ
ap-3265	156	6	hamiltonian	hamiltonian	NOUN
ap-3265	156	7	take	take	VERB
ap-3265	156	8	the	the	DET
ap-3265	156	9	form	form	NOUN
ap-3265	156	10	s̃	s̃	PROPN
ap-3265	156	11	=	=	SYM
ap-3265	156	12	s	s	PART
ap-3265	156	13	−w	−w	ADV
ap-3265	156	14	(	(	PUNCT
ap-3265	156	15	1)h̃	1)h̃	NUM
ap-3265	156	16	and	and	CCONJ
ap-3265	156	17	h̃	h̃	PROPN
ap-3265	156	18	=	=	SYM
ap-3265	156	19	1	1	NUM
ap-3265	156	20	u	u	NOUN
ap-3265	156	21	(	(	PUNCT
ap-3265	156	22	1)h0	1)h0	PROPN
ap-3265	156	23	+	+	NUM
ap-3265	156	24	u	u	PROPN
ap-3265	156	25	(	(	PUNCT
ap-3265	156	26	1)α1	1)α1	NUM
ap-3265	156	27	+	+	NUM
ap-3265	156	28	u	u	SYM
ap-3265	156	29	(	(	PUNCT
ap-3265	156	30	2)α2	2)α2	NUM
ap-3265	156	31	+	+	CCONJ
ap-3265	156	32	u	u	SYM
ap-3265	156	33	(	(	PUNCT
ap-3265	156	34	3)α3	3)α3	PROPN
ap-3265	156	35	+	+	NUM
ap-3265	156	36	α4	α4	NOUN
ap-3265	156	37	u	u	NOUN
ap-3265	156	38	(	(	PUNCT
ap-3265	156	39	1	1	NUM
ap-3265	156	40	)	)	PUNCT
ap-3265	156	41	.	.	PUNCT
ap-3265	157	1	note	note	VERB
ap-3265	157	2	that	that	SCONJ
ap-3265	157	3	the	the	DET
ap-3265	157	4	parameter	parameter	NOUN
ap-3265	157	5	α1	α1	PROPN
ap-3265	157	6	cancels	cancel	VERB
ap-3265	157	7	out	out	ADP
ap-3265	157	8	of	of	ADP
ap-3265	157	9	the	the	DET
ap-3265	157	10	expression	expression	NOUN
ap-3265	157	11	for	for	ADP
ap-3265	157	12	s̃	s̃	PROPN
ap-3265	157	13	;	;	PUNCT
ap-3265	157	14	it	it	PRON
ap-3265	157	15	is	be	AUX
ap-3265	157	16	replaced	replace	VERB
ap-3265	157	17	by	by	ADP
ap-3265	157	18	a	a	DET
ap-3265	157	19	term	term	NOUN
ap-3265	157	20	−α4w	−α4w	PROPN
ap-3265	157	21	(	(	PUNCT
ap-3265	157	22	1)/u	1)/u	NUM
ap-3265	157	23	(	(	PUNCT
ap-3265	157	24	1	1	NUM
ap-3265	157	25	)	)	PUNCT
ap-3265	157	26	.	.	PUNCT
ap-3265	158	1	now	now	ADV
ap-3265	158	2	suppose	suppose	VERB
ap-3265	158	3	that	that	SCONJ
ap-3265	158	4	ψ	ψ	NOUN
ap-3265	158	5	is	be	AUX
ap-3265	158	6	a	a	DET
ap-3265	158	7	formal	formal	ADJ
ap-3265	158	8	eigenfunction	eigenfunction	NOUN
ap-3265	158	9	of	of	ADP
ap-3265	158	10	h	h	NOUN
ap-3265	158	11	(	(	PUNCT
ap-3265	158	12	not	not	PART
ap-3265	158	13	required	require	VERB
ap-3265	158	14	to	to	PART
ap-3265	158	15	be	be	AUX
ap-3265	158	16	normalizable	normalizable	ADJ
ap-3265	158	17	):	):	PUNCT
ap-3265	158	18	hψ	hψ	X
ap-3265	158	19	=	=	SYM
ap-3265	158	20	eψ	eψ	PROPN
ap-3265	158	21	.	.	PUNCT
ap-3265	158	22	without	without	ADP
ap-3265	158	23	loss	loss	NOUN
ap-3265	158	24	of	of	ADP
ap-3265	158	25	generality	generality	NOUN
ap-3265	158	26	we	we	PRON
ap-3265	158	27	can	can	AUX
ap-3265	158	28	absorb	absorb	VERB
ap-3265	158	29	the	the	DET
ap-3265	158	30	energy	energy	NOUN
ap-3265	158	31	eigenvalue	eigenvalue	NOUN
ap-3265	158	32	into	into	ADP
ap-3265	158	33	α4	α4	NOUN
ap-3265	158	34	so	so	SCONJ
ap-3265	158	35	that	that	SCONJ
ap-3265	158	36	α4	α4	NOUN
ap-3265	158	37	=	=	PRON
ap-3265	158	38	−e	−e	NOUN
ap-3265	158	39	in	in	ADP
ap-3265	158	40	(	(	PUNCT
ap-3265	158	41	3	3	NUM
ap-3265	158	42	)	)	PUNCT
ap-3265	158	43	and	and	CCONJ
ap-3265	158	44	,	,	PUNCT
ap-3265	158	45	in	in	ADP
ap-3265	158	46	terms	term	NOUN
ap-3265	158	47	of	of	ADP
ap-3265	158	48	this	this	DET
ap-3265	158	49	redefined	redefine	VERB
ap-3265	158	50	h	h	NOUN
ap-3265	158	51	,	,	PUNCT
ap-3265	158	52	we	we	PRON
ap-3265	158	53	have	have	VERB
ap-3265	158	54	hψ	hψ	NOUN
ap-3265	158	55	=	=	SYM
ap-3265	158	56	0	0	X
ap-3265	158	57	.	.	PUNCT
ap-3265	159	1	it	it	PRON
ap-3265	159	2	follows	follow	VERB
ap-3265	159	3	immediately	immediately	ADV
ap-3265	159	4	that	that	SCONJ
ap-3265	159	5	s̃ψ	s̃ψ	PROPN
ap-3265	159	6	=	=	SYM
ap-3265	159	7	sψ	sψ	PROPN
ap-3265	159	8	.	.	PUNCT
ap-3265	160	1	thus	thus	ADV
ap-3265	160	2	,	,	PUNCT
ap-3265	160	3	for	for	ADP
ap-3265	160	4	the	the	DET
ap-3265	160	5	3	3	NUM
ap-3265	160	6	-	-	PUNCT
ap-3265	160	7	parameter	parameter	NOUN
ap-3265	160	8	system	system	NOUN
ap-3265	160	9	h	h	NOUN
ap-3265	160	10	′	′	NOUN
ap-3265	160	11	and	and	CCONJ
ap-3265	160	12	the	the	DET
ap-3265	160	13	stäckel	stäckel	NOUN
ap-3265	160	14	transform	transform	VERB
ap-3265	160	15	h̃	h̃	PROPN
ap-3265	160	16	′	′	NOUN
ap-3265	160	17	,	,	PUNCT
ap-3265	160	18	h	h	NOUN
ap-3265	160	19	′	′	NOUN
ap-3265	161	1	=	=	PUNCT
ap-3265	161	2	h0	h0	PROPN
ap-3265	161	3	+	+	CCONJ
ap-3265	161	4	v	v	NOUN
ap-3265	161	5	′	′	NOUN
ap-3265	161	6	=	=	PUNCT
ap-3265	161	7	h0	h0	PROPN
ap-3265	161	8	+	+	CCONJ
ap-3265	161	9	u	u	PROPN
ap-3265	161	10	(	(	PUNCT
ap-3265	161	11	1)α1	1)α1	NUM
ap-3265	161	12	+	+	NUM
ap-3265	161	13	u	u	SYM
ap-3265	161	14	(	(	PUNCT
ap-3265	161	15	2)α2	2)α2	NUM
ap-3265	161	16	+	+	CCONJ
ap-3265	161	17	u	u	SYM
ap-3265	161	18	(	(	PUNCT
ap-3265	161	19	3)α3	3)α3	PROPN
ap-3265	161	20	,	,	PUNCT
ap-3265	161	21	h̃	h̃	PROPN
ap-3265	161	22	′	′	NUM
ap-3265	162	1	=	=	SYM
ap-3265	162	2	1	1	NUM
ap-3265	162	3	u	u	NOUN
ap-3265	162	4	(	(	PUNCT
ap-3265	162	5	1)h0	1)h0	PROPN
ap-3265	162	6	+	+	NUM
ap-3265	162	7	−u	−u	PROPN
ap-3265	162	8	(	(	PUNCT
ap-3265	162	9	1)e	1)e	NUM
ap-3265	162	10	+	+	NUM
ap-3265	162	11	u	u	NOUN
ap-3265	162	12	(	(	PUNCT
ap-3265	162	13	2)α2	2)α2	NUM
ap-3265	162	14	+	+	CCONJ
ap-3265	162	15	u	u	SYM
ap-3265	162	16	(	(	PUNCT
ap-3265	162	17	3)α3	3)α3	PROPN
ap-3265	162	18	u	u	NOUN
ap-3265	162	19	(	(	PUNCT
ap-3265	162	20	1	1	NUM
ap-3265	162	21	)	)	PUNCT
ap-3265	162	22	,	,	PUNCT
ap-3265	162	23	we	we	PRON
ap-3265	162	24	have	have	VERB
ap-3265	162	25	h	h	NOUN
ap-3265	162	26	′ψ	′ψ	VERB
ap-3265	163	1	=	=	PUNCT
ap-3265	163	2	eψ	eψ	NOUN
ap-3265	163	3	and	and	CCONJ
ap-3265	163	4	h̃	h̃	PROPN
ap-3265	163	5	′ψ	′ψ	PROPN
ap-3265	163	6	=	=	PUNCT
ap-3265	163	7	−α1ψ	−α1ψ	PROPN
ap-3265	163	8	.	.	PUNCT
ap-3265	164	1	the	the	DET
ap-3265	164	2	effect	effect	NOUN
ap-3265	164	3	of	of	ADP
ap-3265	164	4	the	the	DET
ap-3265	164	5	stäckel	stäckel	NOUN
ap-3265	164	6	transform	transform	NOUN
ap-3265	164	7	is	be	AUX
ap-3265	164	8	to	to	PART
ap-3265	164	9	replace	replace	VERB
ap-3265	164	10	α1	α1	PROPN
ap-3265	164	11	by	by	ADP
ap-3265	164	12	−e	−e	NOUN
ap-3265	164	13	and	and	CCONJ
ap-3265	164	14	e	e	X
ap-3265	164	15	by	by	ADP
ap-3265	164	16	−α1	−α1	PROPN
ap-3265	164	17	.	.	PUNCT
ap-3265	164	18	further	far	ADV
ap-3265	164	19	,	,	PUNCT
ap-3265	164	20	s	s	PART
ap-3265	164	21	and	and	CCONJ
ap-3265	164	22	s̃	s̃	PROPN
ap-3265	164	23	must	must	AUX
ap-3265	164	24	agree	agree	VERB
ap-3265	164	25	on	on	ADP
ap-3265	164	26	eigenspaces	eigenspace	NOUN
ap-3265	164	27	of	of	ADP
ap-3265	164	28	h	h	NOUN
ap-3265	164	29	′.	′.	NOUN
ap-3265	164	30	we	we	PRON
ap-3265	164	31	know	know	VERB
ap-3265	164	32	that	that	SCONJ
ap-3265	164	33	the	the	DET
ap-3265	164	34	symmetry	symmetry	NOUN
ap-3265	164	35	operators	operator	NOUN
ap-3265	164	36	of	of	ADP
ap-3265	164	37	all	all	DET
ap-3265	164	38	2nd	2nd	ADJ
ap-3265	164	39	order	order	NOUN
ap-3265	164	40	nondegenerate	nondegenerate	ADJ
ap-3265	164	41	superintegrable	superintegrable	ADJ
ap-3265	164	42	systems	system	NOUN
ap-3265	164	43	in	in	ADP
ap-3265	164	44	2d	2d	NUM
ap-3265	164	45	generate	generate	VERB
ap-3265	164	46	a	a	DET
ap-3265	164	47	quadratic	quadratic	ADJ
ap-3265	164	48	algebra	algebra	NOUN
ap-3265	164	49	of	of	ADP
ap-3265	164	50	the	the	DET
ap-3265	164	51	form	form	NOUN
ap-3265	164	52	[	[	X
ap-3265	164	53	r	r	X
ap-3265	164	54	,	,	PUNCT
ap-3265	164	55	sj	sj	INTJ
ap-3265	164	56	]	]	PUNCT
ap-3265	164	57	=	=	SYM
ap-3265	164	58	f	f	X
ap-3265	164	59	(	(	PUNCT
ap-3265	164	60	j)(s1	j)(s1	PROPN
ap-3265	164	61	,	,	PUNCT
ap-3265	164	62	s2	s2	PROPN
ap-3265	164	63	,	,	PUNCT
ap-3265	164	64	α1	α1	PROPN
ap-3265	164	65	,	,	PUNCT
ap-3265	164	66	α2	α2	ADJ
ap-3265	164	67	,	,	PUNCT
ap-3265	164	68	α3	α3	PROPN
ap-3265	164	69	,	,	PUNCT
ap-3265	164	70	h	h	NOUN
ap-3265	164	71	′	′	NUM
ap-3265	164	72	)	)	PUNCT
ap-3265	164	73	,	,	PUNCT
ap-3265	164	74	j	j	PROPN
ap-3265	165	1	=	=	SYM
ap-3265	165	2	1	1	NUM
ap-3265	165	3	,	,	PUNCT
ap-3265	165	4	2	2	NUM
ap-3265	165	5	,	,	PUNCT
ap-3265	165	6	r2	r2	PROPN
ap-3265	165	7	=	=	SYM
ap-3265	165	8	f	f	PROPN
ap-3265	165	9	(	(	PUNCT
ap-3265	165	10	3)(s1	3)(s1	PROPN
ap-3265	165	11	,	,	PUNCT
ap-3265	165	12	s2	s2	PROPN
ap-3265	165	13	,	,	PUNCT
ap-3265	165	14	α1	α1	PROPN
ap-3265	165	15	,	,	PUNCT
ap-3265	165	16	α2	α2	ADJ
ap-3265	165	17	,	,	PUNCT
ap-3265	165	18	α3	α3	PROPN
ap-3265	165	19	,	,	PUNCT
ap-3265	165	20	h	h	NOUN
ap-3265	165	21	′	′	NUM
ap-3265	165	22	)	)	PUNCT
ap-3265	165	23	,	,	PUNCT
ap-3265	165	24	(	(	PUNCT
ap-3265	165	25	4	4	X
ap-3265	165	26	)	)	PUNCT
ap-3265	165	27	where	where	SCONJ
ap-3265	165	28	{	{	PUNCT
ap-3265	165	29	s1	s1	NOUN
ap-3265	165	30	,	,	PUNCT
ap-3265	165	31	s2	s2	PROPN
ap-3265	165	32	,	,	PUNCT
ap-3265	165	33	h	h	NOUN
ap-3265	165	34	}	}	PUNCT
ap-3265	165	35	is	be	AUX
ap-3265	165	36	a	a	DET
ap-3265	165	37	basis	basis	NOUN
ap-3265	165	38	for	for	ADP
ap-3265	165	39	the	the	DET
ap-3265	165	40	2nd	2nd	ADJ
ap-3265	165	41	order	order	NOUN
ap-3265	165	42	symmetries	symmetry	NOUN
ap-3265	165	43	and	and	CCONJ
ap-3265	165	44	α1	α1	PROPN
ap-3265	165	45	,	,	PUNCT
ap-3265	165	46	α2	α2	ADJ
ap-3265	165	47	,	,	PUNCT
ap-3265	165	48	α3	α3	PROPN
ap-3265	165	49	are	be	AUX
ap-3265	165	50	the	the	DET
ap-3265	165	51	parameters	parameter	NOUN
ap-3265	165	52	for	for	ADP
ap-3265	165	53	the	the	DET
ap-3265	165	54	potential	potential	NOUN
ap-3265	165	55	[	[	X
ap-3265	165	56	6	6	NUM
ap-3265	165	57	]	]	PUNCT
ap-3265	165	58	.	.	PUNCT
ap-3265	166	1	it	it	PRON
ap-3265	166	2	follows	follow	VERB
ap-3265	166	3	from	from	ADP
ap-3265	166	4	the	the	DET
ap-3265	166	5	above	above	ADJ
ap-3265	166	6	considerations	consideration	NOUN
ap-3265	166	7	that	that	SCONJ
ap-3265	166	8	the	the	DET
ap-3265	166	9	effect	effect	NOUN
ap-3265	166	10	of	of	ADP
ap-3265	166	11	a	a	DET
ap-3265	166	12	stäckel	stäckel	NOUN
ap-3265	166	13	transform	transform	NOUN
ap-3265	166	14	generated	generate	VERB
ap-3265	166	15	by	by	ADP
ap-3265	166	16	the	the	DET
ap-3265	166	17	potential	potential	ADJ
ap-3265	166	18	function	function	NOUN
ap-3265	166	19	u	u	NOUN
ap-3265	166	20	(	(	PUNCT
ap-3265	166	21	1	1	NUM
ap-3265	166	22	)	)	PUNCT
ap-3265	166	23	is	be	AUX
ap-3265	166	24	to	to	PART
ap-3265	166	25	determine	determine	VERB
ap-3265	166	26	a	a	DET
ap-3265	166	27	new	new	ADJ
ap-3265	166	28	superintegrable	superintegrable	ADJ
ap-3265	166	29	system	system	NOUN
ap-3265	166	30	with	with	ADP
ap-3265	166	31	structure	structure	NOUN
ap-3265	166	32	[	[	X
ap-3265	166	33	r̃	r̃	PROPN
ap-3265	166	34	,	,	PUNCT
ap-3265	166	35	s̃j	s̃j	VERB
ap-3265	166	36	]	]	PUNCT
ap-3265	166	37	=	=	SYM
ap-3265	166	38	f	f	X
ap-3265	166	39	(	(	PUNCT
ap-3265	166	40	j)(s̃1	j)(s̃1	NOUN
ap-3265	166	41	,	,	PUNCT
ap-3265	166	42	s̃2,−h̃	s̃2,−h̃	PROPN
ap-3265	166	43	′	′	NUM
ap-3265	166	44	,	,	PUNCT
ap-3265	166	45	α2	α2	ADJ
ap-3265	166	46	,	,	PUNCT
ap-3265	166	47	α3,−α1	α3,−α1	NUM
ap-3265	166	48	)	)	PUNCT
ap-3265	166	49	,	,	PUNCT
ap-3265	166	50	j	j	PROPN
ap-3265	167	1	=	=	SYM
ap-3265	167	2	1	1	NUM
ap-3265	167	3	,	,	PUNCT
ap-3265	167	4	2	2	NUM
ap-3265	167	5	,	,	PUNCT
ap-3265	167	6	r2	r2	PROPN
ap-3265	167	7	=	=	SYM
ap-3265	167	8	f	f	PROPN
ap-3265	167	9	(	(	PUNCT
ap-3265	167	10	3)(s̃1	3)(s̃1	NOUN
ap-3265	167	11	,	,	PUNCT
ap-3265	167	12	s̃2,−h̃	s̃2,−h̃	PROPN
ap-3265	167	13	′	′	NUM
ap-3265	167	14	,	,	PUNCT
ap-3265	167	15	α2	α2	ADJ
ap-3265	167	16	,	,	PUNCT
ap-3265	167	17	α3,−α1	α3,−α1	NUM
ap-3265	167	18	)	)	PUNCT
ap-3265	167	19	,	,	PUNCT
ap-3265	167	20	(	(	PUNCT
ap-3265	167	21	5	5	X
ap-3265	167	22	)	)	PUNCT
ap-3265	167	23	of	of	ADP
ap-3265	167	24	course	course	NOUN
ap-3265	167	25	,	,	PUNCT
ap-3265	167	26	the	the	DET
ap-3265	167	27	switch	switch	NOUN
ap-3265	167	28	of	of	ADP
ap-3265	167	29	α1	α1	PROPN
ap-3265	167	30	and	and	CCONJ
ap-3265	167	31	h	h	NOUN
ap-3265	167	32	′	′	NOUN
ap-3265	167	33	is	be	AUX
ap-3265	167	34	only	only	ADV
ap-3265	167	35	for	for	ADP
ap-3265	167	36	illustration	illustration	NOUN
ap-3265	167	37	;	;	PUNCT
ap-3265	167	38	there	there	PRON
ap-3265	167	39	is	be	VERB
ap-3265	167	40	a	a	DET
ap-3265	167	41	stäckel	stäckel	NOUN
ap-3265	167	42	transform	transform	NOUN
ap-3265	167	43	that	that	PRON
ap-3265	167	44	replaces	replace	VERB
ap-3265	167	45	any	any	DET
ap-3265	167	46	αj	αj	NOUN
ap-3265	167	47	by	by	ADP
ap-3265	167	48	−h	−h	ADJ
ap-3265	167	49	′	′	NOUN
ap-3265	168	1	and	and	CCONJ
ap-3265	168	2	h	h	NOUN
ap-3265	168	3	′	′	NUM
ap-3265	168	4	by	by	ADP
ap-3265	168	5	−αj	−αj	PROPN
ap-3265	168	6	and	and	CCONJ
ap-3265	168	7	similar	similar	ADJ
ap-3265	168	8	transforms	transform	NOUN
ap-3265	168	9	that	that	PRON
ap-3265	168	10	apply	apply	VERB
ap-3265	168	11	to	to	ADP
ap-3265	168	12	any	any	DET
ap-3265	168	13	basis	basis	NOUN
ap-3265	168	14	that	that	SCONJ
ap-3265	168	15	we	we	PRON
ap-3265	168	16	choose	choose	VERB
ap-3265	168	17	for	for	ADP
ap-3265	168	18	the	the	DET
ap-3265	168	19	potential	potential	ADJ
ap-3265	168	20	space	space	NOUN
ap-3265	168	21	.	.	PUNCT
ap-3265	169	1	formulas	formula	NOUN
ap-3265	169	2	(	(	PUNCT
ap-3265	169	3	4	4	NUM
ap-3265	169	4	)	)	PUNCT
ap-3265	169	5	and	and	CCONJ
ap-3265	169	6	(	(	PUNCT
ap-3265	169	7	5	5	X
ap-3265	169	8	)	)	PUNCT
ap-3265	169	9	are	be	AUX
ap-3265	169	10	just	just	ADV
ap-3265	169	11	instances	instance	NOUN
ap-3265	169	12	of	of	ADP
ap-3265	169	13	the	the	DET
ap-3265	169	14	quadratic	quadratic	ADJ
ap-3265	169	15	algebras	algebra	NOUN
ap-3265	169	16	of	of	ADP
ap-3265	169	17	the	the	DET
ap-3265	169	18	superintegrable	superintegrable	ADJ
ap-3265	169	19	systems	system	NOUN
ap-3265	169	20	belonging	belong	VERB
ap-3265	169	21	to	to	ADP
ap-3265	169	22	the	the	DET
ap-3265	169	23	equivalence	equivalence	NOUN
ap-3265	169	24	class	class	NOUN
ap-3265	169	25	of	of	ADP
ap-3265	169	26	a	a	DET
ap-3265	169	27	single	single	ADJ
ap-3265	169	28	nondegenerate	nondegenerate	NOUN
ap-3265	169	29	conformally	conformally	ADV
ap-3265	169	30	superintegrable	superintegrable	ADJ
ap-3265	169	31	hamiltonian	hamiltonian	NOUN
ap-3265	169	32	ĥ	ĥ	PROPN
ap-3265	169	33	=	=	SYM
ap-3265	169	34	∂xx	∂xx	PROPN
ap-3265	169	35	+	+	CCONJ
ap-3265	169	36	∂yy	∂yy	PROPN
ap-3265	169	37	+	+	CCONJ
ap-3265	169	38	4∑	4∑	NUM
ap-3265	169	39	j=1	j=1	NOUN
ap-3265	169	40	αjv	αjv	NOUN
ap-3265	169	41	(	(	PUNCT
ap-3265	169	42	j)(x	j)(x	PROPN
ap-3265	169	43	,	,	PUNCT
ap-3265	169	44	y	y	PROPN
ap-3265	169	45	)	)	PUNCT
ap-3265	169	46	.	.	PUNCT
ap-3265	170	1	(	(	PUNCT
ap-3265	170	2	6	6	X
ap-3265	170	3	)	)	PUNCT
ap-3265	170	4	let	let	VERB
ap-3265	170	5	ŝ1	ŝ1	PROPN
ap-3265	170	6	,	,	PUNCT
ap-3265	170	7	ŝ2	ŝ2	PROPN
ap-3265	170	8	,	,	PUNCT
ap-3265	170	9	ĥ	ĥ	X
ap-3265	170	10	be	be	AUX
ap-3265	170	11	a	a	DET
ap-3265	170	12	basis	basis	NOUN
ap-3265	170	13	of	of	ADP
ap-3265	170	14	2nd	2nd	ADJ
ap-3265	170	15	order	order	NOUN
ap-3265	170	16	conformal	conformal	ADJ
ap-3265	170	17	symmetries	symmetry	NOUN
ap-3265	170	18	of	of	ADP
ap-3265	170	19	ĥ.	ĥ.	NOUN
ap-3265	170	20	from	from	ADP
ap-3265	170	21	the	the	DET
ap-3265	170	22	above	above	ADJ
ap-3265	170	23	discussion	discussion	NOUN
ap-3265	170	24	we	we	PRON
ap-3265	170	25	can	can	AUX
ap-3265	170	26	conclude	conclude	VERB
ap-3265	170	27	the	the	DET
ap-3265	170	28	following	following	NOUN
ap-3265	170	29	.	.	PUNCT
ap-3265	171	1	theorem	theorem	NOUN
ap-3265	171	2	5	5	NUM
ap-3265	171	3	.	.	PUNCT
ap-3265	172	1	the	the	DET
ap-3265	172	2	symmetries	symmetry	NOUN
ap-3265	172	3	of	of	ADP
ap-3265	172	4	the	the	DET
ap-3265	172	5	2d	2d	NUM
ap-3265	172	6	nondegenerate	nondegenerate	PROPN
ap-3265	172	7	conformal	conformal	ADJ
ap-3265	172	8	superintegrable	superintegrable	ADJ
ap-3265	172	9	hamiltonian	hamiltonian	NOUN
ap-3265	172	10	ĥ	ĥ	PUNCT
ap-3265	172	11	generate	generate	VERB
ap-3265	172	12	a	a	DET
ap-3265	172	13	quadratic	quadratic	ADJ
ap-3265	172	14	algebra	algebra	NOUN
ap-3265	172	15	[	[	X
ap-3265	172	16	r̂	r̂	NOUN
ap-3265	172	17	,	,	PUNCT
ap-3265	172	18	ŝ1	ŝ1	PROPN
ap-3265	172	19	]	]	X
ap-3265	172	20	=	=	SYM
ap-3265	172	21	f	f	X
ap-3265	172	22	(	(	PUNCT
ap-3265	172	23	1)(ŝ1	1)(ŝ1	NUM
ap-3265	172	24	,	,	PUNCT
ap-3265	172	25	ŝ2	ŝ2	PROPN
ap-3265	172	26	,	,	PUNCT
ap-3265	172	27	α1	α1	PROPN
ap-3265	172	28	,	,	PUNCT
ap-3265	172	29	α2	α2	ADJ
ap-3265	172	30	,	,	PUNCT
ap-3265	172	31	α3	α3	NOUN
ap-3265	172	32	,	,	PUNCT
ap-3265	172	33	α4	α4	NOUN
ap-3265	172	34	)	)	PUNCT
ap-3265	172	35	,	,	PUNCT
ap-3265	173	1	[	[	X
ap-3265	173	2	r̂	r̂	NOUN
ap-3265	173	3	,	,	PUNCT
ap-3265	173	4	ŝ2	ŝ2	PROPN
ap-3265	173	5	]	]	PUNCT
ap-3265	173	6	=	=	SYM
ap-3265	173	7	f	f	PROPN
ap-3265	173	8	(	(	PUNCT
ap-3265	173	9	2)(ŝ1	2)(ŝ1	NUM
ap-3265	173	10	,	,	PUNCT
ap-3265	173	11	ŝ2	ŝ2	PROPN
ap-3265	173	12	,	,	PUNCT
ap-3265	173	13	α1	α1	PROPN
ap-3265	173	14	,	,	PUNCT
ap-3265	173	15	α2	α2	ADJ
ap-3265	173	16	,	,	PUNCT
ap-3265	173	17	α3	α3	NOUN
ap-3265	173	18	,	,	PUNCT
ap-3265	173	19	α4	α4	NOUN
ap-3265	173	20	)	)	PUNCT
ap-3265	173	21	,	,	PUNCT
ap-3265	173	22	r̂2	r̂2	PROPN
ap-3265	173	23	=	=	SYM
ap-3265	173	24	f	f	PROPN
ap-3265	173	25	(	(	PUNCT
ap-3265	173	26	3)(ŝ1	3)(ŝ1	NUM
ap-3265	173	27	,	,	PUNCT
ap-3265	173	28	ŝ2	ŝ2	PROPN
ap-3265	173	29	,	,	PUNCT
ap-3265	173	30	α1	α1	PROPN
ap-3265	173	31	,	,	PUNCT
ap-3265	173	32	α2	α2	ADJ
ap-3265	173	33	,	,	PUNCT
ap-3265	173	34	α3	α3	NOUN
ap-3265	173	35	,	,	PUNCT
ap-3265	173	36	α4	α4	NOUN
ap-3265	173	37	)	)	PUNCT
ap-3265	173	38	,	,	PUNCT
ap-3265	173	39	(	(	PUNCT
ap-3265	173	40	7	7	X
ap-3265	173	41	)	)	PUNCT
ap-3265	173	42	where	where	SCONJ
ap-3265	173	43	r̂	r̂	NOUN
ap-3265	173	44	=	=	PUNCT
ap-3265	174	1	[	[	X
ap-3265	174	2	ŝ1	ŝ1	PROPN
ap-3265	174	3	,	,	PUNCT
ap-3265	174	4	ŝ2	ŝ2	PROPN
ap-3265	174	5	]	]	PUNCT
ap-3265	174	6	and	and	CCONJ
ap-3265	174	7	all	all	DET
ap-3265	174	8	identities	identity	NOUN
ap-3265	174	9	hold	hold	VERB
ap-3265	174	10	mod(ĥ	mod(ĥ	PROPN
ap-3265	174	11	)	)	PUNCT
ap-3265	174	12	.	.	PUNCT
ap-3265	175	1	a	a	DET
ap-3265	175	2	conformal	conformal	ADJ
ap-3265	175	3	stäckel	stäckel	NOUN
ap-3265	175	4	transform	transform	NOUN
ap-3265	175	5	generated	generate	VERB
ap-3265	175	6	by	by	ADP
ap-3265	175	7	the	the	DET
ap-3265	175	8	potential	potential	ADJ
ap-3265	175	9	v	v	NOUN
ap-3265	175	10	(	(	PUNCT
ap-3265	175	11	j)(x	j)(x	PROPN
ap-3265	175	12	,	,	PUNCT
ap-3265	175	13	y	y	PROPN
ap-3265	175	14	)	)	PUNCT
ap-3265	175	15	yields	yield	VERB
ap-3265	175	16	a	a	DET
ap-3265	175	17	nondegenerate	nondegenerate	ADJ
ap-3265	175	18	helmholtz	helmholtz	NOUN
ap-3265	175	19	superintegrable	superintegrable	ADJ
ap-3265	175	20	hamiltonian	hamiltonian	NOUN
ap-3265	175	21	h̃	h̃	PROPN
ap-3265	175	22	with	with	ADP
ap-3265	175	23	quadratic	quadratic	ADJ
ap-3265	175	24	algebra	algebra	NOUN
ap-3265	175	25	relations	relation	NOUN
ap-3265	175	26	identical	identical	ADJ
ap-3265	175	27	to	to	ADP
ap-3265	175	28	(	(	PUNCT
ap-3265	175	29	7	7	NUM
ap-3265	175	30	)	)	PUNCT
ap-3265	175	31	,	,	PUNCT
ap-3265	175	32	except	except	SCONJ
ap-3265	175	33	that	that	SCONJ
ap-3265	175	34	we	we	PRON
ap-3265	175	35	make	make	VERB
ap-3265	175	36	the	the	DET
ap-3265	175	37	replacements	replacement	NOUN
ap-3265	175	38	ŝ	ŝ	NOUN
ap-3265	175	39	`	`	PUNCT
ap-3265	175	40	→	→	SYM
ap-3265	175	41	s̃	s̃	PROPN
ap-3265	175	42	`	`	PUNCT
ap-3265	175	43	for	for	ADP
ap-3265	175	44	`	`	PUNCT
ap-3265	175	45	=	=	SYM
ap-3265	175	46	1	1	NUM
ap-3265	175	47	,	,	PUNCT
ap-3265	175	48	2	2	NUM
ap-3265	175	49	and	and	CCONJ
ap-3265	175	50	αj	αj	NOUN
ap-3265	175	51	→	→	SYM
ap-3265	175	52	−h̃.	−h̃.	PROPN
ap-3265	175	53	these	these	DET
ap-3265	175	54	modified	modify	VERB
ap-3265	175	55	relations	relation	NOUN
ap-3265	175	56	(	(	PUNCT
ap-3265	175	57	6	6	NUM
ap-3265	175	58	)	)	PUNCT
ap-3265	175	59	are	be	AUX
ap-3265	175	60	now	now	ADV
ap-3265	175	61	true	true	ADJ
ap-3265	175	62	identities	identity	NOUN
ap-3265	175	63	,	,	PUNCT
ap-3265	175	64	not	not	PART
ap-3265	175	65	mod(ĥ	mod(ĥ	ADJ
ap-3265	175	66	)	)	PUNCT
ap-3265	175	67	.	.	PUNCT
ap-3265	176	1	every	every	DET
ap-3265	176	2	2nd	2nd	ADJ
ap-3265	176	3	order	order	NOUN
ap-3265	176	4	conformal	conformal	NOUN
ap-3265	176	5	symmetry	symmetry	NOUN
ap-3265	176	6	is	be	AUX
ap-3265	176	7	of	of	ADP
ap-3265	176	8	the	the	DET
ap-3265	176	9	form	form	NOUN
ap-3265	176	10	s	s	PART
ap-3265	176	11	=	=	NOUN
ap-3265	176	12	s0	s0	PROPN
ap-3265	177	1	+	+	PROPN
ap-3265	177	2	w	w	PROPN
ap-3265	177	3	where	where	SCONJ
ap-3265	177	4	s0	s0	NOUN
ap-3265	177	5	is	be	AUX
ap-3265	177	6	a	a	DET
ap-3265	177	7	2nd	2nd	ADJ
ap-3265	177	8	order	order	NOUN
ap-3265	177	9	element	element	NOUN
ap-3265	177	10	of	of	ADP
ap-3265	177	11	the	the	DET
ap-3265	177	12	enveloping	enveloping	NOUN
ap-3265	177	13	algebra	algebra	NOUN
ap-3265	177	14	of	of	ADP
ap-3265	177	15	so(4,c	so(4,c	NOUN
ap-3265	177	16	)	)	PUNCT
ap-3265	177	17	.	.	PUNCT
ap-3265	178	1	the	the	DET
ap-3265	178	2	dimension	dimension	NOUN
ap-3265	178	3	of	of	ADP
ap-3265	178	4	this	this	DET
ap-3265	178	5	space	space	NOUN
ap-3265	178	6	of	of	ADP
ap-3265	178	7	2nd	2nd	ADJ
ap-3265	178	8	order	order	NOUN
ap-3265	178	9	elements	element	NOUN
ap-3265	178	10	is	be	AUX
ap-3265	178	11	21	21	NUM
ap-3265	178	12	but	but	CCONJ
ap-3265	178	13	there	there	PRON
ap-3265	178	14	is	be	VERB
ap-3265	178	15	an	an	DET
ap-3265	178	16	11dimensional	11dimensional	ADJ
ap-3265	178	17	subspace	subspace	NOUN
ap-3265	178	18	of	of	ADP
ap-3265	178	19	symmetries	symmetry	NOUN
ap-3265	178	20	congruent	congruent	ADJ
ap-3265	178	21	to	to	ADP
ap-3265	178	22	0	0	NUM
ap-3265	178	23	mod(h0	mod(h0	NOUN
ap-3265	178	24	)	)	PUNCT
ap-3265	178	25	where	where	SCONJ
ap-3265	178	26	h0	h0	NOUN
ap-3265	178	27	=	=	PROPN
ap-3265	178	28	p	p	NOUN
ap-3265	178	29	2	2	NUM
ap-3265	178	30	1	1	NUM
ap-3265	178	31	+	+	CCONJ
ap-3265	178	32	p	p	NOUN
ap-3265	178	33	2	2	NUM
ap-3265	178	34	2	2	NUM
ap-3265	178	35	.	.	PUNCT
ap-3265	179	1	thus	thus	ADV
ap-3265	179	2	mod(h0	mod(h0	X
ap-3265	179	3	)	)	PUNCT
ap-3265	179	4	the	the	DET
ap-3265	179	5	space	space	NOUN
ap-3265	179	6	of	of	ADP
ap-3265	179	7	2nd	2nd	ADJ
ap-3265	179	8	order	order	NOUN
ap-3265	179	9	symmetries	symmetry	NOUN
ap-3265	179	10	is	be	AUX
ap-3265	179	11	10	10	NUM
ap-3265	179	12	-	-	PUNCT
ap-3265	179	13	dimensional	dimensional	ADJ
ap-3265	179	14	.	.	PUNCT
ap-3265	180	1	217	217	NUM
ap-3265	180	2	e.	e.	PROPN
ap-3265	180	3	kalnins	kalnins	PROPN
ap-3265	180	4	,	,	PUNCT
ap-3265	180	5	w.	w.	PROPN
ap-3265	180	6	miller	miller	PROPN
ap-3265	180	7	,	,	PUNCT
ap-3265	180	8	e.	e.	PROPN
ap-3265	180	9	subag	subag	PROPN
ap-3265	180	10	acta	acta	PROPN
ap-3265	180	11	polytechnica	polytechnica	PROPN
ap-3265	180	12	3	3	NUM
ap-3265	180	13	.	.	PUNCT
ap-3265	181	1	the	the	DET
ap-3265	181	2	bôcher	bôcher	NOUN
ap-3265	181	3	method	method	NOUN
ap-3265	181	4	in	in	ADP
ap-3265	181	5	his	his	PRON
ap-3265	181	6	1894	1894	NUM
ap-3265	181	7	thesis	thesis	NOUN
ap-3265	181	8	bôcher	bôcher	NOUN
ap-3265	181	9	[	[	X
ap-3265	181	10	28	28	NUM
ap-3265	181	11	]	]	PUNCT
ap-3265	181	12	,	,	PUNCT
ap-3265	181	13	developed	develop	VERB
ap-3265	181	14	a	a	DET
ap-3265	181	15	geometrical	geometrical	ADJ
ap-3265	181	16	method	method	NOUN
ap-3265	181	17	for	for	ADP
ap-3265	181	18	finding	find	VERB
ap-3265	181	19	and	and	CCONJ
ap-3265	181	20	classifying	classify	VERB
ap-3265	181	21	the	the	DET
ap-3265	181	22	r	r	NOUN
ap-3265	181	23	-	-	PUNCT
ap-3265	181	24	separable	separable	ADJ
ap-3265	181	25	orthogonal	orthogonal	ADJ
ap-3265	181	26	coordinate	coordinate	NOUN
ap-3265	181	27	systems	system	NOUN
ap-3265	181	28	for	for	ADP
ap-3265	181	29	the	the	DET
ap-3265	181	30	flat	flat	ADJ
ap-3265	181	31	space	space	NOUN
ap-3265	181	32	laplace	laplace	NOUN
ap-3265	181	33	equation	equation	NOUN
ap-3265	181	34	∆nψ	∆nψ	PUNCT
ap-3265	181	35	=	=	SYM
ap-3265	181	36	0	0	NUM
ap-3265	181	37	in	in	ADP
ap-3265	181	38	n	n	PRON
ap-3265	181	39	dimensions	dimension	NOUN
ap-3265	181	40	.	.	PUNCT
ap-3265	182	1	it	it	PRON
ap-3265	182	2	was	be	AUX
ap-3265	182	3	based	base	VERB
ap-3265	182	4	on	on	ADP
ap-3265	182	5	the	the	DET
ap-3265	182	6	conformal	conformal	ADJ
ap-3265	182	7	symmetry	symmetry	NOUN
ap-3265	182	8	of	of	ADP
ap-3265	182	9	these	these	DET
ap-3265	182	10	equations	equation	NOUN
ap-3265	182	11	.	.	PUNCT
ap-3265	183	1	the	the	DET
ap-3265	183	2	conformal	conformal	ADJ
ap-3265	183	3	lie	lie	NOUN
ap-3265	183	4	symmetry	symmetry	NOUN
ap-3265	183	5	algebra	algebra	NOUN
ap-3265	183	6	of	of	ADP
ap-3265	183	7	the	the	DET
ap-3265	183	8	flat	flat	ADJ
ap-3265	183	9	space	space	NOUN
ap-3265	183	10	complex	complex	NOUN
ap-3265	183	11	laplacian	laplacian	NOUN
ap-3265	183	12	is	be	AUX
ap-3265	183	13	so(n	so(n	NOUN
ap-3265	183	14	+	+	CCONJ
ap-3265	184	1	2,c	2,c	NUM
ap-3265	184	2	)	)	PUNCT
ap-3265	184	3	.	.	PUNCT
ap-3265	185	1	we	we	PRON
ap-3265	185	2	will	will	AUX
ap-3265	185	3	use	use	VERB
ap-3265	185	4	his	his	PRON
ap-3265	185	5	ideas	idea	NOUN
ap-3265	185	6	for	for	ADP
ap-3265	185	7	n	n	NOUN
ap-3265	185	8	=	=	SYM
ap-3265	185	9	2	2	NUM
ap-3265	185	10	,	,	PUNCT
ap-3265	185	11	but	but	CCONJ
ap-3265	185	12	applied	apply	VERB
ap-3265	185	13	to	to	ADP
ap-3265	185	14	the	the	DET
ap-3265	185	15	laplace	laplace	NOUN
ap-3265	185	16	equation	equation	NOUN
ap-3265	185	17	with	with	ADP
ap-3265	185	18	potentialhψ	potentialhψ	PROPN
ap-3265	185	19	≡	≡	PROPN
ap-3265	185	20	(	(	PUNCT
ap-3265	185	21	∂2	∂2	PROPN
ap-3265	185	22	x+∂2	x+∂2	X
ap-3265	185	23	y+v	y+v	PROPN
ap-3265	185	24	)	)	PUNCT
ap-3265	185	25	ψ	ψ	NOUN
ap-3265	185	26	=	=	NOUN
ap-3265	185	27	0	0	NUM
ap-3265	185	28	.	.	PUNCT
ap-3265	186	1	the	the	DET
ap-3265	186	2	so(4,c	so(4,c	NOUN
ap-3265	186	3	)	)	PUNCT
ap-3265	186	4	conformal	conformal	NOUN
ap-3265	186	5	symmetry	symmetry	NOUN
ap-3265	186	6	algebra	algebra	NOUN
ap-3265	186	7	in	in	ADP
ap-3265	186	8	the	the	DET
ap-3265	186	9	case	case	NOUN
ap-3265	186	10	n	n	NOUN
ap-3265	186	11	=	=	SYM
ap-3265	186	12	2	2	NUM
ap-3265	186	13	has	have	VERB
ap-3265	186	14	the	the	DET
ap-3265	186	15	basis	basis	NOUN
ap-3265	186	16	p1	p1	NOUN
ap-3265	186	17	=	=	SYM
ap-3265	186	18	∂x	∂x	PROPN
ap-3265	186	19	,	,	PUNCT
ap-3265	186	20	p2	p2	X
ap-3265	186	21	=	=	SYM
ap-3265	186	22	∂y	∂y	PROPN
ap-3265	186	23	,	,	PUNCT
ap-3265	186	24	j	j	PROPN
ap-3265	187	1	=	=	SYM
ap-3265	188	1	x∂y	x∂y	PROPN
ap-3265	189	1	−	−	PROPN
ap-3265	189	2	y∂x	y∂x	NOUN
ap-3265	189	3	,	,	PUNCT
ap-3265	189	4	d	d	PROPN
ap-3265	189	5	=	=	PUNCT
ap-3265	189	6	x∂x	x∂x	PROPN
ap-3265	190	1	+	+	CCONJ
ap-3265	190	2	y∂y	y∂y	ADJ
ap-3265	190	3	,	,	PUNCT
ap-3265	190	4	k1	k1	NOUN
ap-3265	190	5	=	=	SYM
ap-3265	190	6	(	(	PUNCT
ap-3265	190	7	x2	x2	INTJ
ap-3265	190	8	−	−	PROPN
ap-3265	190	9	y2)∂x	y2)∂x	VERB
ap-3265	190	10	+	+	CCONJ
ap-3265	190	11	2xy∂y	2xy∂y	NOUN
ap-3265	190	12	,	,	PUNCT
ap-3265	190	13	k2	k2	NOUN
ap-3265	190	14	=	=	SYM
ap-3265	190	15	(	(	PUNCT
ap-3265	190	16	y2	y2	INTJ
ap-3265	190	17	−	−	PROPN
ap-3265	190	18	x2)∂y	x2)∂y	ADJ
ap-3265	191	1	+	+	CCONJ
ap-3265	191	2	2xy∂x	2xy∂x	NUM
ap-3265	191	3	.	.	PUNCT
ap-3265	192	1	bôcher	bôcher	PROPN
ap-3265	192	2	linearizes	linearize	VERB
ap-3265	192	3	this	this	DET
ap-3265	192	4	action	action	NOUN
ap-3265	192	5	by	by	ADP
ap-3265	192	6	introducing	introduce	VERB
ap-3265	192	7	tetraspherical	tetraspherical	ADJ
ap-3265	192	8	coordinates	coordinate	NOUN
ap-3265	192	9	.	.	PUNCT
ap-3265	193	1	these	these	PRON
ap-3265	193	2	are	be	AUX
ap-3265	193	3	4	4	NUM
ap-3265	193	4	projective	projective	ADJ
ap-3265	193	5	complex	complex	ADJ
ap-3265	193	6	coordinates	coordinate	NOUN
ap-3265	193	7	(	(	PUNCT
ap-3265	193	8	x1	x1	PROPN
ap-3265	193	9	,	,	PUNCT
ap-3265	193	10	x2	x2	PROPN
ap-3265	193	11	,	,	PUNCT
ap-3265	193	12	x3	x3	PROPN
ap-3265	193	13	,	,	PUNCT
ap-3265	193	14	x4	x4	PROPN
ap-3265	193	15	)	)	PUNCT
ap-3265	193	16	confined	confine	VERB
ap-3265	193	17	to	to	ADP
ap-3265	193	18	the	the	DET
ap-3265	193	19	null	null	ADJ
ap-3265	193	20	cone	cone	NOUN
ap-3265	193	21	x2	x2	NOUN
ap-3265	193	22	1	1	NUM
ap-3265	194	1	+	+	NUM
ap-3265	194	2	x2	x2	PROPN
ap-3265	194	3	2	2	NUM
ap-3265	194	4	+	+	NUM
ap-3265	194	5	x2	x2	PROPN
ap-3265	194	6	3	3	NUM
ap-3265	195	1	+	+	NUM
ap-3265	195	2	x2	x2	PROPN
ap-3265	195	3	4	4	NUM
ap-3265	195	4	=	=	SYM
ap-3265	195	5	0	0	NUM
ap-3265	195	6	.	.	PUNCT
ap-3265	196	1	they	they	PRON
ap-3265	196	2	are	be	AUX
ap-3265	196	3	related	relate	VERB
ap-3265	196	4	to	to	ADP
ap-3265	196	5	complex	complex	ADJ
ap-3265	196	6	cartesian	cartesian	ADJ
ap-3265	196	7	coordinates	coordinate	NOUN
ap-3265	196	8	(	(	PUNCT
ap-3265	196	9	x	x	X
ap-3265	196	10	,	,	PUNCT
ap-3265	196	11	y	y	NOUN
ap-3265	196	12	)	)	PUNCT
ap-3265	196	13	via	via	ADP
ap-3265	196	14	x	x	X
ap-3265	197	1	=	=	PUNCT
ap-3265	197	2	−	−	PROPN
ap-3265	197	3	x1	x1	NUM
ap-3265	197	4	x3	x3	PROPN
ap-3265	197	5	+	+	CCONJ
ap-3265	197	6	ix4	ix4	VERB
ap-3265	197	7	,	,	PUNCT
ap-3265	197	8	y	y	PROPN
ap-3265	197	9	=	=	PUNCT
ap-3265	197	10	−	−	PROPN
ap-3265	198	1	x2	x2	INTJ
ap-3265	198	2	x3	x3	PROPN
ap-3265	198	3	+	+	CCONJ
ap-3265	198	4	ix4	ix4	VERB
ap-3265	198	5	,	,	PUNCT
ap-3265	198	6	h	h	NOUN
ap-3265	198	7	=	=	SYM
ap-3265	198	8	∂xx	∂xx	PROPN
ap-3265	198	9	+	+	CCONJ
ap-3265	198	10	∂yy	∂yy	PROPN
ap-3265	198	11	+	+	CCONJ
ap-3265	198	12	ṽ	ṽ	PROPN
ap-3265	198	13	=	=	SYM
ap-3265	198	14	(	(	PUNCT
ap-3265	198	15	x3	x3	PROPN
ap-3265	198	16	+	+	CCONJ
ap-3265	198	17	ix4)2	ix4)2	PROPN
ap-3265	198	18	(	(	PUNCT
ap-3265	198	19	4∑	4∑	NOUN
ap-3265	198	20	k=1	k=1	NOUN
ap-3265	198	21	∂2	∂2	PROPN
ap-3265	198	22	xk	xk	PROPN
ap-3265	199	1	+	+	CCONJ
ap-3265	199	2	v	v	NOUN
ap-3265	199	3	)	)	PUNCT
ap-3265	199	4	,	,	PUNCT
ap-3265	200	1	where	where	SCONJ
ap-3265	200	2	ṽ	ṽ	PROPN
ap-3265	200	3	=	=	SYM
ap-3265	200	4	(	(	PUNCT
ap-3265	200	5	x3	x3	VERB
ap-3265	200	6	+	+	CCONJ
ap-3265	200	7	ix4)2v	ix4)2v	NOUN
ap-3265	200	8	.	.	PUNCT
ap-3265	201	1	we	we	PRON
ap-3265	201	2	define	define	VERB
ap-3265	201	3	ljk	ljk	PROPN
ap-3265	201	4	=	=	PUNCT
ap-3265	201	5	xj∂xk	xj∂xk	PROPN
ap-3265	202	1	−	−	PROPN
ap-3265	202	2	xk∂xj	xk∂xj	NOUN
ap-3265	202	3	,	,	PUNCT
ap-3265	202	4	1	1	NUM
ap-3265	202	5	≤	≤	NUM
ap-3265	202	6	j	j	PROPN
ap-3265	202	7	,	,	PUNCT
ap-3265	202	8	k	k	PROPN
ap-3265	202	9	≤	≤	PROPN
ap-3265	202	10	4	4	NUM
ap-3265	202	11	,	,	PUNCT
ap-3265	202	12	j	j	PROPN
ap-3265	202	13	6=	6=	PROPN
ap-3265	202	14	k	k	PROPN
ap-3265	202	15	,	,	PUNCT
ap-3265	202	16	where	where	SCONJ
ap-3265	202	17	ljk	ljk	ADJ
ap-3265	202	18	=	=	SYM
ap-3265	202	19	−lkj	−lkj	NOUN
ap-3265	202	20	.	.	PUNCT
ap-3265	203	1	these	these	DET
ap-3265	203	2	operators	operator	NOUN
ap-3265	203	3	are	be	AUX
ap-3265	203	4	clearly	clearly	ADV
ap-3265	203	5	a	a	DET
ap-3265	203	6	basis	basis	NOUN
ap-3265	203	7	for	for	ADP
ap-3265	203	8	so(4,c	so(4,c	NOUN
ap-3265	203	9	)	)	PUNCT
ap-3265	203	10	.	.	PUNCT
ap-3265	204	1	the	the	DET
ap-3265	204	2	generators	generator	NOUN
ap-3265	204	3	for	for	ADP
ap-3265	204	4	flat	flat	ADJ
ap-3265	204	5	space	space	NOUN
ap-3265	204	6	conformal	conformal	NOUN
ap-3265	204	7	symmetries	symmetry	NOUN
ap-3265	204	8	are	be	AUX
ap-3265	204	9	related	relate	VERB
ap-3265	204	10	to	to	ADP
ap-3265	204	11	these	these	PRON
ap-3265	204	12	via	via	ADP
ap-3265	204	13	p1	p1	NOUN
ap-3265	204	14	=	=	SYM
ap-3265	204	15	∂x	∂x	PROPN
ap-3265	204	16	=	=	SYM
ap-3265	204	17	l13	l13	PROPN
ap-3265	204	18	+	+	CCONJ
ap-3265	204	19	il14	il14	PROPN
ap-3265	204	20	,	,	PUNCT
ap-3265	204	21	p2	p2	X
ap-3265	204	22	=	=	SYM
ap-3265	204	23	∂y	∂y	SYM
ap-3265	204	24	=	=	SYM
ap-3265	204	25	l23	l23	NOUN
ap-3265	204	26	+	+	CCONJ
ap-3265	204	27	il24	il24	PROPN
ap-3265	204	28	,	,	PUNCT
ap-3265	205	1	d	d	NOUN
ap-3265	205	2	=	=	SYM
ap-3265	205	3	il34	il34	PROPN
ap-3265	205	4	,	,	PUNCT
ap-3265	205	5	j	j	NOUN
ap-3265	205	6	=	=	SYM
ap-3265	205	7	l12	l12	PROPN
ap-3265	205	8	,	,	PUNCT
ap-3265	205	9	k1	k1	NOUN
ap-3265	205	10	=	=	SYM
ap-3265	205	11	l13	l13	ADJ
ap-3265	205	12	−	−	PROPN
ap-3265	205	13	il14	il14	PROPN
ap-3265	205	14	,	,	PUNCT
ap-3265	205	15	k2	k2	NOUN
ap-3265	205	16	=	=	PUNCT
ap-3265	205	17	l23	l23	NOUN
ap-3265	205	18	−	−	PROPN
ap-3265	205	19	il24	il24	PROPN
ap-3265	205	20	.	.	PROPN
ap-3265	206	1	3.1	3.1	NUM
ap-3265	206	2	.	.	PUNCT
ap-3265	206	3	relation	relation	NOUN
ap-3265	206	4	to	to	ADP
ap-3265	206	5	separation	separation	NOUN
ap-3265	206	6	of	of	ADP
ap-3265	206	7	variables	variable	NOUN
ap-3265	206	8	bôcher	bôcher	PROPN
ap-3265	206	9	uses	use	VERB
ap-3265	206	10	symbols	symbol	NOUN
ap-3265	206	11	of	of	ADP
ap-3265	206	12	the	the	DET
ap-3265	206	13	form	form	NOUN
ap-3265	206	14	[	[	X
ap-3265	206	15	n1	n1	NOUN
ap-3265	206	16	,	,	PUNCT
ap-3265	206	17	n2	n2	NOUN
ap-3265	206	18	,	,	PUNCT
ap-3265	206	19	..	..	PUNCT
ap-3265	206	20	,	,	PUNCT
ap-3265	206	21	np	np	INTJ
ap-3265	206	22	]	]	X
ap-3265	206	23	where	where	SCONJ
ap-3265	206	24	n1	n1	PROPN
ap-3265	206	25	+	+	CCONJ
ap-3265	206	26	...	...	PUNCT
ap-3265	207	1	+	+	CCONJ
ap-3265	207	2	np	np	X
ap-3265	207	3	=	=	SYM
ap-3265	207	4	4	4	NUM
ap-3265	207	5	,	,	PUNCT
ap-3265	207	6	to	to	PART
ap-3265	207	7	define	define	VERB
ap-3265	207	8	coordinate	coordinate	NOUN
ap-3265	207	9	surfaces	surface	NOUN
ap-3265	207	10	as	as	SCONJ
ap-3265	207	11	follows	follow	VERB
ap-3265	207	12	.	.	PUNCT
ap-3265	208	1	consider	consider	VERB
ap-3265	208	2	the	the	DET
ap-3265	208	3	quadratic	quadratic	ADJ
ap-3265	208	4	forms	form	NOUN
ap-3265	208	5	ω	ω	NOUN
ap-3265	209	1	=	=	SYM
ap-3265	209	2	x2	x2	NOUN
ap-3265	209	3	1	1	NUM
ap-3265	210	1	+	+	NUM
ap-3265	210	2	x2	x2	PROPN
ap-3265	210	3	2	2	NUM
ap-3265	211	1	+	+	NUM
ap-3265	211	2	x2	x2	PROPN
ap-3265	211	3	3	3	NUM
ap-3265	212	1	+	+	NUM
ap-3265	212	2	x2	x2	PROPN
ap-3265	212	3	4	4	NUM
ap-3265	212	4	=	=	SYM
ap-3265	212	5	0	0	NUM
ap-3265	212	6	,	,	PUNCT
ap-3265	212	7	φ	φ	NOUN
ap-3265	212	8	=	=	SYM
ap-3265	212	9	x2	x2	PROPN
ap-3265	212	10	1	1	NUM
ap-3265	212	11	λ−	λ−	PROPN
ap-3265	212	12	e1	e1	PROPN
ap-3265	212	13	+	+	CCONJ
ap-3265	212	14	x2	x2	PROPN
ap-3265	212	15	2	2	NUM
ap-3265	212	16	λ−	λ−	PROPN
ap-3265	212	17	e2	e2	PROPN
ap-3265	212	18	+	+	CCONJ
ap-3265	212	19	x2	x2	PROPN
ap-3265	212	20	3	3	NUM
ap-3265	212	21	λ−	λ−	PROPN
ap-3265	212	22	e3	e3	VERB
ap-3265	213	1	+	+	CCONJ
ap-3265	213	2	x2	x2	PROPN
ap-3265	213	3	4	4	NUM
ap-3265	213	4	λ−	λ−	PROPN
ap-3265	213	5	e4	e4	PROPN
ap-3265	213	6	.	.	PUNCT
ap-3265	214	1	if	if	SCONJ
ap-3265	214	2	the	the	DET
ap-3265	214	3	parameters	parameter	NOUN
ap-3265	214	4	ej	ej	X
ap-3265	214	5	are	be	AUX
ap-3265	214	6	pairwise	pairwise	NOUN
ap-3265	214	7	distinct	distinct	ADJ
ap-3265	214	8	,	,	PUNCT
ap-3265	214	9	the	the	DET
ap-3265	214	10	elementary	elementary	ADJ
ap-3265	214	11	divisors	divisor	NOUN
ap-3265	214	12	of	of	ADP
ap-3265	214	13	these	these	DET
ap-3265	214	14	two	two	NUM
ap-3265	214	15	forms	form	NOUN
ap-3265	214	16	are	be	AUX
ap-3265	214	17	denoted	denote	VERB
ap-3265	214	18	by	by	ADP
ap-3265	214	19	[	[	X
ap-3265	214	20	1	1	NUM
ap-3265	214	21	,	,	PUNCT
ap-3265	214	22	1	1	NUM
ap-3265	214	23	,	,	PUNCT
ap-3265	214	24	1	1	NUM
ap-3265	214	25	,	,	PUNCT
ap-3265	214	26	1	1	NUM
ap-3265	214	27	]	]	PUNCT
ap-3265	214	28	.	.	PUNCT
ap-3265	215	1	given	give	VERB
ap-3265	215	2	a	a	DET
ap-3265	215	3	point	point	NOUN
ap-3265	215	4	in	in	ADP
ap-3265	215	5	2d	2d	NOUN
ap-3265	215	6	flat	flat	ADJ
ap-3265	215	7	space	space	NOUN
ap-3265	215	8	with	with	ADP
ap-3265	215	9	cartesian	cartesian	ADJ
ap-3265	215	10	coordinates	coordinate	NOUN
ap-3265	215	11	(	(	PUNCT
ap-3265	215	12	x0	x0	PROPN
ap-3265	215	13	,	,	PUNCT
ap-3265	215	14	y0	y0	PROPN
ap-3265	215	15	)	)	PUNCT
ap-3265	215	16	,	,	PUNCT
ap-3265	215	17	there	there	PRON
ap-3265	215	18	corresponds	correspond	VERB
ap-3265	215	19	a	a	DET
ap-3265	215	20	set	set	NOUN
ap-3265	215	21	of	of	ADP
ap-3265	215	22	tetraspherical	tetraspherical	ADJ
ap-3265	215	23	coordinates	coordinate	NOUN
ap-3265	215	24	(	(	PUNCT
ap-3265	215	25	x0	x0	PROPN
ap-3265	215	26	1	1	NUM
ap-3265	215	27	,	,	PUNCT
ap-3265	215	28	x	x	NOUN
ap-3265	215	29	0	0	NUM
ap-3265	215	30	2	2	NUM
ap-3265	215	31	,	,	PUNCT
ap-3265	215	32	x	x	NOUN
ap-3265	215	33	0	0	NUM
ap-3265	215	34	3	3	NUM
ap-3265	215	35	,	,	PUNCT
ap-3265	215	36	x	x	NOUN
ap-3265	215	37	0	0	NUM
ap-3265	215	38	4	4	NUM
ap-3265	215	39	)	)	PUNCT
ap-3265	215	40	,	,	PUNCT
ap-3265	215	41	unique	unique	ADJ
ap-3265	215	42	up	up	ADP
ap-3265	215	43	to	to	ADP
ap-3265	215	44	multiplication	multiplication	NOUN
ap-3265	215	45	by	by	ADP
ap-3265	215	46	a	a	DET
ap-3265	215	47	nonzero	nonzero	NOUN
ap-3265	215	48	constant	constant	ADJ
ap-3265	215	49	.	.	PUNCT
ap-3265	216	1	if	if	SCONJ
ap-3265	216	2	we	we	PRON
ap-3265	216	3	substitute	substitute	VERB
ap-3265	216	4	into	into	ADP
ap-3265	216	5	φ	φ	PROPN
ap-3265	216	6	we	we	PRON
ap-3265	216	7	see	see	VERB
ap-3265	216	8	that	that	SCONJ
ap-3265	216	9	there	there	PRON
ap-3265	216	10	are	be	VERB
ap-3265	216	11	exactly	exactly	ADV
ap-3265	216	12	2	2	NUM
ap-3265	216	13	roots	root	NOUN
ap-3265	216	14	λ	λ	X
ap-3265	216	15	=	=	SYM
ap-3265	216	16	ρ	ρ	PROPN
ap-3265	216	17	,	,	PUNCT
ap-3265	216	18	µ	µ	NOUN
ap-3265	216	19	such	such	ADJ
ap-3265	216	20	that	that	SCONJ
ap-3265	216	21	φ	φ	PROPN
ap-3265	216	22	=	=	SYM
ap-3265	216	23	0	0	PROPN
ap-3265	216	24	.	.	PUNCT
ap-3265	217	1	(	(	PUNCT
ap-3265	217	2	if	if	SCONJ
ap-3265	217	3	e4	e4	PROPN
ap-3265	217	4	→	→	SYM
ap-3265	217	5	∞	∞	NUM
ap-3265	217	6	these	these	PRON
ap-3265	217	7	correspond	correspond	VERB
ap-3265	217	8	to	to	ADP
ap-3265	217	9	elliptic	elliptic	ADJ
ap-3265	217	10	coordinates	coordinate	NOUN
ap-3265	217	11	on	on	ADP
ap-3265	217	12	the	the	DET
ap-3265	217	13	2sphere	2sphere	NUM
ap-3265	217	14	.	.	PUNCT
ap-3265	217	15	)	)	PUNCT
ap-3265	218	1	they	they	PRON
ap-3265	218	2	are	be	AUX
ap-3265	218	3	orthogonal	orthogonal	ADJ
ap-3265	218	4	with	with	ADP
ap-3265	218	5	respect	respect	NOUN
ap-3265	218	6	to	to	ADP
ap-3265	218	7	the	the	DET
ap-3265	218	8	metric	metric	ADJ
ap-3265	218	9	ds2	ds2	PROPN
ap-3265	218	10	=	=	SYM
ap-3265	218	11	dx2	dx2	PROPN
ap-3265	218	12	+	+	CCONJ
ap-3265	218	13	dy2	dy2	PROPN
ap-3265	218	14	and	and	CCONJ
ap-3265	218	15	are	be	AUX
ap-3265	218	16	r	r	NOUN
ap-3265	218	17	-	-	PUNCT
ap-3265	218	18	separable	separable	NOUN
ap-3265	218	19	for	for	ADP
ap-3265	218	20	the	the	DET
ap-3265	218	21	laplace	laplace	NOUN
ap-3265	218	22	equations	equation	NOUN
ap-3265	218	23	(	(	PUNCT
ap-3265	218	24	∂2	∂2	PROPN
ap-3265	218	25	x+∂2	x+∂2	NUM
ap-3265	218	26	y)θ	y)θ	NUM
ap-3265	219	1	=	=	SYM
ap-3265	219	2	0	0	NUM
ap-3265	219	3	or	or	CCONJ
ap-3265	219	4	(	(	PUNCT
ap-3265	219	5	∑4	∑4	PROPN
ap-3265	219	6	j−1	j−1	PROPN
ap-3265	219	7	∂	∂	NUM
ap-3265	219	8	2	2	NUM
ap-3265	219	9	xj	xj	NOUN
ap-3265	219	10	)	)	PUNCT
ap-3265	219	11	θ	θ	X
ap-3265	219	12	=	=	PUNCT
ap-3265	219	13	0	0	X
ap-3265	219	14	.	.	PUNCT
ap-3265	219	15	example	example	NOUN
ap-3265	219	16	.	.	PUNCT
ap-3265	220	1	consider	consider	VERB
ap-3265	220	2	the	the	DET
ap-3265	220	3	potential	potential	ADJ
ap-3265	220	4	v[1,1,1,1	v[1,1,1,1	NOUN
ap-3265	220	5	]	]	PUNCT
ap-3265	221	1	=	=	SYM
ap-3265	221	2	a1	a1	NOUN
ap-3265	221	3	x2	x2	NOUN
ap-3265	221	4	1	1	NUM
ap-3265	221	5	+	+	NUM
ap-3265	221	6	a2	a2	PROPN
ap-3265	221	7	x2	x2	NOUN
ap-3265	221	8	2	2	NUM
ap-3265	221	9	+	+	NUM
ap-3265	221	10	a3	a3	NOUN
ap-3265	221	11	x2	x2	NOUN
ap-3265	221	12	3	3	NUM
ap-3265	221	13	+	+	NUM
ap-3265	221	14	a4	a4	NOUN
ap-3265	221	15	x2	x2	NOUN
ap-3265	221	16	4	4	NUM
ap-3265	221	17	.	.	PUNCT
ap-3265	222	1	it	it	PRON
ap-3265	222	2	is	be	AUX
ap-3265	222	3	the	the	DET
ap-3265	222	4	only	only	ADJ
ap-3265	222	5	potential	potential	NOUN
ap-3265	222	6	v	v	ADP
ap-3265	222	7	such	such	ADJ
ap-3265	222	8	that	that	DET
ap-3265	222	9	equation	equation	NOUN
ap-3265	222	10	(	(	PUNCT
ap-3265	222	11	∑4	∑4	PROPN
ap-3265	222	12	j−1	j−1	PROPN
ap-3265	222	13	∂	∂	NUM
ap-3265	222	14	2	2	NUM
ap-3265	222	15	xj	xj	PROPN
ap-3265	222	16	+	+	X
ap-3265	222	17	v	v	NOUN
ap-3265	222	18	)	)	PUNCT
ap-3265	222	19	θ	θ	NOUN
ap-3265	223	1	=	=	SYM
ap-3265	223	2	0	0	NUM
ap-3265	223	3	is	be	AUX
ap-3265	223	4	r	r	NOUN
ap-3265	223	5	-	-	PUNCT
ap-3265	223	6	separable	separable	NOUN
ap-3265	223	7	in	in	ADP
ap-3265	223	8	elliptic	elliptic	ADJ
ap-3265	223	9	coordinates	coordinate	NOUN
ap-3265	223	10	for	for	ADP
ap-3265	223	11	all	all	DET
ap-3265	223	12	choices	choice	NOUN
ap-3265	223	13	of	of	ADP
ap-3265	223	14	the	the	DET
ap-3265	223	15	parameters	parameter	NOUN
ap-3265	223	16	ej	ej	X
ap-3265	223	17	.	.	PUNCT
ap-3265	224	1	the	the	DET
ap-3265	224	2	separation	separation	NOUN
ap-3265	224	3	is	be	AUX
ap-3265	224	4	characterized	characterize	VERB
ap-3265	224	5	by	by	ADP
ap-3265	224	6	2nd	2nd	ADJ
ap-3265	224	7	order	order	NOUN
ap-3265	224	8	conformal	conformal	NOUN
ap-3265	224	9	symmetry	symmetry	NOUN
ap-3265	224	10	operators	operator	NOUN
ap-3265	224	11	that	that	PRON
ap-3265	224	12	are	be	AUX
ap-3265	224	13	linear	linear	ADJ
ap-3265	224	14	in	in	ADP
ap-3265	224	15	the	the	DET
ap-3265	224	16	parameters	parameter	NOUN
ap-3265	224	17	ej	ej	X
ap-3265	224	18	.	.	PUNCT
ap-3265	225	1	in	in	ADP
ap-3265	225	2	particular	particular	ADJ
ap-3265	225	3	the	the	DET
ap-3265	225	4	symmetries	symmetry	NOUN
ap-3265	225	5	span	span	VERB
ap-3265	225	6	a	a	DET
ap-3265	225	7	3	3	NUM
ap-3265	225	8	-	-	PUNCT
ap-3265	225	9	dimensional	dimensional	ADJ
ap-3265	225	10	subspace	subspace	NOUN
ap-3265	225	11	of	of	ADP
ap-3265	225	12	symmetries	symmetry	NOUN
ap-3265	225	13	,	,	PUNCT
ap-3265	225	14	so	so	ADV
ap-3265	225	15	the	the	DET
ap-3265	225	16	system	system	NOUN
ap-3265	225	17	hθ	hθ	NOUN
ap-3265	225	18	=	=	PUNCT
ap-3265	225	19	(	(	PUNCT
ap-3265	225	20	∑4	∑4	NOUN
ap-3265	225	21	j=1	j=1	PROPN
ap-3265	225	22	∂	∂	NUM
ap-3265	225	23	2	2	NUM
ap-3265	225	24	xj	xj	PROPN
ap-3265	225	25	+	+	CCONJ
ap-3265	225	26	v[1,1,1,1])θ	v[1,1,1,1])θ	PROPN
ap-3265	225	27	=	=	NOUN
ap-3265	225	28	0	0	NUM
ap-3265	225	29	must	must	AUX
ap-3265	225	30	be	be	AUX
ap-3265	225	31	conformally	conformally	ADV
ap-3265	225	32	superintegrable	superintegrable	ADJ
ap-3265	225	33	.	.	PUNCT
ap-3265	226	1	3.2	3.2	NUM
ap-3265	226	2	.	.	PUNCT
ap-3265	227	1	bôcher	bôcher	PROPN
ap-3265	227	2	limits	limit	NOUN
ap-3265	227	3	suppose	suppose	VERB
ap-3265	227	4	some	some	PRON
ap-3265	227	5	of	of	ADP
ap-3265	227	6	the	the	DET
ap-3265	227	7	ei	ei	NOUN
ap-3265	227	8	become	become	VERB
ap-3265	227	9	equal	equal	ADJ
ap-3265	227	10	.	.	PUNCT
ap-3265	228	1	to	to	PART
ap-3265	228	2	obtain	obtain	VERB
ap-3265	228	3	separable	separable	ADJ
ap-3265	228	4	coordinates	coordinate	NOUN
ap-3265	228	5	we	we	PRON
ap-3265	228	6	can	can	AUX
ap-3265	228	7	not	not	PART
ap-3265	228	8	just	just	ADV
ap-3265	228	9	set	set	VERB
ap-3265	228	10	them	they	PRON
ap-3265	228	11	equal	equal	ADJ
ap-3265	228	12	in	in	ADP
ap-3265	228	13	ω	ω	PROPN
ap-3265	228	14	,	,	PUNCT
ap-3265	228	15	φ	φ	PROPN
ap-3265	228	16	but	but	CCONJ
ap-3265	228	17	must	must	AUX
ap-3265	228	18	take	take	VERB
ap-3265	228	19	limits	limit	NOUN
ap-3265	228	20	,	,	PUNCT
ap-3265	228	21	bôcher	bôcher	NOUN
ap-3265	228	22	develops	develop	VERB
ap-3265	228	23	a	a	DET
ap-3265	228	24	calculus	calculus	NOUN
ap-3265	228	25	to	to	PART
ap-3265	228	26	describe	describe	VERB
ap-3265	228	27	this	this	PRON
ap-3265	228	28	.	.	PUNCT
ap-3265	229	1	thus	thus	ADV
ap-3265	229	2	the	the	DET
ap-3265	229	3	process	process	NOUN
ap-3265	229	4	of	of	ADP
ap-3265	229	5	making	make	VERB
ap-3265	229	6	e1	e1	PROPN
ap-3265	229	7	→	→	SYM
ap-3265	229	8	e2	e2	PROPN
ap-3265	229	9	is	be	AUX
ap-3265	229	10	described	describe	VERB
ap-3265	229	11	by	by	ADP
ap-3265	229	12	the	the	DET
ap-3265	229	13	mapping	mapping	NOUN
ap-3265	229	14	,	,	PUNCT
ap-3265	229	15	which	which	PRON
ap-3265	229	16	in	in	ADP
ap-3265	229	17	the	the	DET
ap-3265	229	18	limit	limit	NOUN
ap-3265	229	19	as	as	ADP
ap-3265	229	20	ε→	ε→	NUM
ap-3265	229	21	0	0	NUM
ap-3265	229	22	takes	take	VERB
ap-3265	229	23	the	the	DET
ap-3265	229	24	null	null	ADJ
ap-3265	229	25	cone	cone	NOUN
ap-3265	229	26	to	to	ADP
ap-3265	229	27	the	the	DET
ap-3265	229	28	null	null	ADJ
ap-3265	229	29	cone	cone	NOUN
ap-3265	229	30	:	:	PUNCT
ap-3265	229	31	e1	e1	PROPN
ap-3265	229	32	=	=	PROPN
ap-3265	229	33	e2	e2	PROPN
ap-3265	229	34	+	+	CCONJ
ap-3265	229	35	ε2	ε2	ADJ
ap-3265	229	36	,	,	PUNCT
ap-3265	229	37	x1	x1	PROPN
ap-3265	229	38	→	→	SYM
ap-3265	229	39	i(x′1	i(x′1	X
ap-3265	229	40	+	+	X
ap-3265	229	41	ix′2)√	ix′2)√	PROPN
ap-3265	229	42	2ε	2ε	NOUN
ap-3265	229	43	,	,	PUNCT
ap-3265	229	44	x2	x2	PROPN
ap-3265	229	45	→	→	PUNCT
ap-3265	229	46	(	(	PUNCT
ap-3265	229	47	x′1	x′1	NOUN
ap-3265	230	1	+	+	CCONJ
ap-3265	230	2	ix′2)√	ix′2)√	PROPN
ap-3265	230	3	2ε	2ε	NOUN
ap-3265	230	4	+	+	CCONJ
ap-3265	230	5	ε	ε	PROPN
ap-3265	230	6	(	(	PUNCT
ap-3265	230	7	x′1	x′1	NOUN
ap-3265	230	8	−	−	PROPN
ap-3265	230	9	ix′2)√	ix′2)√	PROPN
ap-3265	230	10	2	2	NUM
ap-3265	230	11	,	,	PUNCT
ap-3265	230	12	x3	x3	PROPN
ap-3265	230	13	→	→	SYM
ap-3265	230	14	x′3	x′3	PROPN
ap-3265	230	15	,	,	PUNCT
ap-3265	230	16	x4	x4	PROPN
ap-3265	230	17	→	→	PROPN
ap-3265	230	18	x′4	x′4	PROPN
ap-3265	230	19	,	,	PUNCT
ap-3265	230	20	in	in	ADP
ap-3265	230	21	the	the	DET
ap-3265	230	22	limit	limit	NOUN
ap-3265	230	23	we	we	PRON
ap-3265	230	24	have	have	VERB
ap-3265	230	25	ω	ω	NOUN
ap-3265	230	26	=	=	SYM
ap-3265	230	27	x′1	x′1	PROPN
ap-3265	230	28	2	2	NUM
ap-3265	231	1	+	+	CCONJ
ap-3265	231	2	x′2	x′2	ADP
ap-3265	231	3	2	2	NUM
ap-3265	231	4	+	+	CCONJ
ap-3265	231	5	x′3	x′3	NOUN
ap-3265	231	6	2	2	NUM
ap-3265	232	1	+	+	CCONJ
ap-3265	232	2	x′4	x′4	X
ap-3265	232	3	2	2	NUM
ap-3265	232	4	=	=	SYM
ap-3265	232	5	0	0	NUM
ap-3265	232	6	,	,	PUNCT
ap-3265	232	7	φ	φ	NOUN
ap-3265	232	8	=	=	SYM
ap-3265	232	9	(	(	PUNCT
ap-3265	232	10	x′1	x′1	PROPN
ap-3265	233	1	+	+	CCONJ
ap-3265	233	2	ix′2)2	ix′2)2	VERB
ap-3265	233	3	2(λ−	2(λ−	NUM
ap-3265	233	4	e2)2	e2)2	NOUN
ap-3265	234	1	+	+	NUM
ap-3265	234	2	x′1	x′1	NOUN
ap-3265	234	3	2	2	NUM
ap-3265	235	1	+	+	CCONJ
ap-3265	235	2	x′2	x′2	NOUN
ap-3265	235	3	2	2	NUM
ap-3265	235	4	λ−	λ−	PROPN
ap-3265	235	5	e2	e2	PROPN
ap-3265	235	6	+	+	CCONJ
ap-3265	235	7	x′3	x′3	PROPN
ap-3265	235	8	2	2	NUM
ap-3265	235	9	λ−	λ−	PROPN
ap-3265	235	10	e3	e3	VERB
ap-3265	235	11	+	+	CCONJ
ap-3265	235	12	x′4	x′4	X
ap-3265	235	13	2	2	NUM
ap-3265	235	14	λ−	λ−	PROPN
ap-3265	235	15	e4	e4	PROPN
ap-3265	235	16	,	,	PUNCT
ap-3265	235	17	which	which	PRON
ap-3265	235	18	has	have	VERB
ap-3265	235	19	elementary	elementary	ADJ
ap-3265	235	20	divisors	divisor	NOUN
ap-3265	235	21	[	[	X
ap-3265	235	22	2	2	NUM
ap-3265	235	23	,	,	PUNCT
ap-3265	235	24	1	1	NUM
ap-3265	235	25	,	,	PUNCT
ap-3265	235	26	1	1	NUM
ap-3265	235	27	]	]	PUNCT
ap-3265	235	28	,	,	PUNCT
ap-3265	235	29	see	see	VERB
ap-3265	235	30	[	[	X
ap-3265	235	31	30	30	NUM
ap-3265	235	32	,	,	PUNCT
ap-3265	235	33	31	31	NUM
ap-3265	235	34	]	]	PUNCT
ap-3265	235	35	.	.	PUNCT
ap-3265	236	1	in	in	ADP
ap-3265	236	2	the	the	DET
ap-3265	236	3	same	same	ADJ
ap-3265	236	4	way	way	NOUN
ap-3265	236	5	as	as	ADP
ap-3265	236	6	for	for	ADP
ap-3265	236	7	[	[	X
ap-3265	236	8	1	1	NUM
ap-3265	236	9	,	,	PUNCT
ap-3265	236	10	1	1	NUM
ap-3265	236	11	,	,	PUNCT
ap-3265	236	12	1	1	NUM
ap-3265	236	13	,	,	PUNCT
ap-3265	236	14	1	1	NUM
ap-3265	236	15	]	]	PUNCT
ap-3265	236	16	,	,	PUNCT
ap-3265	236	17	these	these	DET
ap-3265	236	18	forms	form	NOUN
ap-3265	236	19	define	define	VERB
ap-3265	236	20	a	a	DET
ap-3265	236	21	new	new	ADJ
ap-3265	236	22	set	set	NOUN
ap-3265	236	23	of	of	ADP
ap-3265	236	24	orthogonal	orthogonal	ADJ
ap-3265	236	25	coordinates	coordinate	NOUN
ap-3265	236	26	r	r	NOUN
ap-3265	236	27	-	-	PUNCT
ap-3265	236	28	separable	separable	NOUN
ap-3265	236	29	for	for	ADP
ap-3265	236	30	the	the	DET
ap-3265	236	31	laplace	laplace	NOUN
ap-3265	236	32	equations	equation	NOUN
ap-3265	236	33	.	.	PUNCT
ap-3265	237	1	we	we	PRON
ap-3265	237	2	can	can	AUX
ap-3265	237	3	show	show	VERB
ap-3265	237	4	that	that	SCONJ
ap-3265	237	5	the	the	DET
ap-3265	237	6	coordinate	coordinate	NOUN
ap-3265	237	7	limit	limit	NOUN
ap-3265	237	8	induces	induce	VERB
ap-3265	237	9	a	a	DET
ap-3265	237	10	contraction	contraction	NOUN
ap-3265	237	11	of	of	ADP
ap-3265	237	12	so(4,c	so(4,c	NOUN
ap-3265	237	13	)	)	PUNCT
ap-3265	237	14	to	to	ADP
ap-3265	237	15	itself	itself	PRON
ap-3265	237	16	:	:	PUNCT
ap-3265	237	17	l′12	l′12	X
ap-3265	237	18	=	=	SYM
ap-3265	237	19	l12	l12	NOUN
ap-3265	237	20	,	,	PUNCT
ap-3265	237	21	l	l	NOUN
ap-3265	237	22	′	′	NOUN
ap-3265	238	1	13	13	NUM
ap-3265	238	2	=	=	SYM
ap-3265	238	3	−	−	NOUN
ap-3265	238	4	i√	i√	PROPN
ap-3265	238	5	2	2	NUM
ap-3265	238	6	ε	ε	X
ap-3265	238	7	(	(	PUNCT
ap-3265	238	8	l13	l13	ADJ
ap-3265	238	9	−	−	PROPN
ap-3265	238	10	il23)−	il23)−	NOUN
ap-3265	239	1	i	i	PRON
ap-3265	239	2	ε√	ε√	NOUN
ap-3265	239	3	2	2	NUM
ap-3265	239	4	l13	l13	PROPN
ap-3265	239	5	,	,	PUNCT
ap-3265	239	6	l′23	l′23	ADJ
ap-3265	239	7	=	=	SYM
ap-3265	239	8	−	−	NOUN
ap-3265	239	9	i√	i√	ADJ
ap-3265	239	10	2	2	NUM
ap-3265	239	11	ε	ε	X
ap-3265	239	12	(	(	PUNCT
ap-3265	239	13	l13	l13	ADJ
ap-3265	239	14	−	−	PROPN
ap-3265	239	15	il23)−	il23)−	NOUN
ap-3265	239	16	ε√	ε√	PROPN
ap-3265	239	17	2	2	NUM
ap-3265	239	18	l13	l13	PROPN
ap-3265	239	19	,	,	PUNCT
ap-3265	239	20	l	l	NOUN
ap-3265	239	21	′	′	NOUN
ap-3265	240	1	34	34	NUM
ap-3265	240	2	=	=	NOUN
ap-3265	240	3	l34	l34	PROPN
ap-3265	240	4	,	,	PUNCT
ap-3265	240	5	l′14	l′14	NOUN
ap-3265	240	6	=	=	SYM
ap-3265	240	7	−	−	PROPN
ap-3265	240	8	i√	i√	PROPN
ap-3265	240	9	2	2	NUM
ap-3265	240	10	ε	ε	X
ap-3265	240	11	(	(	PUNCT
ap-3265	240	12	l14	l14	PROPN
ap-3265	240	13	−	−	PROPN
ap-3265	240	14	il24)−	il24)−	VERB
ap-3265	240	15	i	i	PROPN
ap-3265	240	16	ε√	ε√	PROPN
ap-3265	240	17	2	2	NUM
ap-3265	240	18	l14	l14	NOUN
ap-3265	240	19	,	,	PUNCT
ap-3265	240	20	l′24	l′24	X
ap-3265	240	21	=	=	PUNCT
ap-3265	240	22	−	−	PROPN
ap-3265	240	23	i√	i√	PROPN
ap-3265	240	24	2	2	NUM
ap-3265	240	25	ε	ε	X
ap-3265	240	26	(	(	PUNCT
ap-3265	240	27	l14	l14	PROPN
ap-3265	240	28	−	−	PROPN
ap-3265	240	29	il24)−	il24)−	NOUN
ap-3265	240	30	ε√	ε√	PROPN
ap-3265	240	31	2	2	NUM
ap-3265	240	32	l14	l14	NOUN
ap-3265	240	33	.	.	PUNCT
ap-3265	241	1	we	we	PRON
ap-3265	241	2	call	call	VERB
ap-3265	241	3	this	this	PRON
ap-3265	241	4	the	the	DET
ap-3265	241	5	bôcher	bôcher	NOUN
ap-3265	241	6	contraction	contraction	NOUN
ap-3265	242	1	[	[	X
ap-3265	242	2	1	1	NUM
ap-3265	242	3	,	,	PUNCT
ap-3265	242	4	1	1	NUM
ap-3265	242	5	,	,	PUNCT
ap-3265	242	6	1	1	NUM
ap-3265	242	7	,	,	PUNCT
ap-3265	242	8	1	1	NUM
ap-3265	242	9	]	]	PUNCT
ap-3265	242	10	→	→	PUNCT
ap-3265	242	11	[	[	X
ap-3265	242	12	2	2	NUM
ap-3265	242	13	,	,	PUNCT
ap-3265	242	14	1	1	NUM
ap-3265	242	15	,	,	PUNCT
ap-3265	242	16	1	1	NUM
ap-3265	242	17	]	]	PUNCT
ap-3265	242	18	.	.	PUNCT
ap-3265	243	1	there	there	PRON
ap-3265	243	2	are	be	VERB
ap-3265	243	3	analogous	analogous	ADJ
ap-3265	243	4	bôcher	bôcher	NOUN
ap-3265	243	5	contractions	contraction	NOUN
ap-3265	243	6	of	of	ADP
ap-3265	243	7	so(4,c	so(4,c	NOUN
ap-3265	243	8	)	)	PUNCT
ap-3265	243	9	to	to	ADP
ap-3265	243	10	itself	itself	PRON
ap-3265	243	11	corresponding	correspond	VERB
ap-3265	243	12	to	to	ADP
ap-3265	243	13	limits	limit	NOUN
ap-3265	243	14	from	from	ADP
ap-3265	243	15	[	[	X
ap-3265	243	16	1	1	NUM
ap-3265	243	17	,	,	PUNCT
ap-3265	243	18	1	1	NUM
ap-3265	243	19	,	,	PUNCT
ap-3265	243	20	1	1	NUM
ap-3265	243	21	,	,	PUNCT
ap-3265	243	22	1	1	NUM
ap-3265	243	23	]	]	PUNCT
ap-3265	243	24	to	to	ADP
ap-3265	243	25	[	[	X
ap-3265	243	26	2	2	NUM
ap-3265	243	27	,	,	PUNCT
ap-3265	243	28	2	2	NUM
ap-3265	243	29	]	]	PUNCT
ap-3265	243	30	,	,	PUNCT
ap-3265	243	31	[	[	X
ap-3265	243	32	3	3	NUM
ap-3265	243	33	,	,	PUNCT
ap-3265	243	34	1	1	NUM
ap-3265	243	35	]	]	PUNCT
ap-3265	243	36	,	,	PUNCT
ap-3265	243	37	[	[	X
ap-3265	243	38	4	4	NUM
ap-3265	243	39	]	]	PUNCT
ap-3265	243	40	.	.	PUNCT
ap-3265	244	1	similarly	similarly	ADV
ap-3265	244	2	,	,	PUNCT
ap-3265	244	3	there	there	PRON
ap-3265	244	4	are	be	VERB
ap-3265	244	5	bôcher	bôcher	ADJ
ap-3265	244	6	contractions	contraction	NOUN
ap-3265	245	1	[	[	X
ap-3265	245	2	2	2	NUM
ap-3265	245	3	,	,	PUNCT
ap-3265	245	4	1	1	NUM
ap-3265	245	5	,	,	PUNCT
ap-3265	245	6	1]→	1]→	NOUN
ap-3265	246	1	[	[	X
ap-3265	246	2	2	2	NUM
ap-3265	246	3	,	,	PUNCT
ap-3265	246	4	2	2	NUM
ap-3265	246	5	]	]	PUNCT
ap-3265	246	6	,	,	PUNCT
ap-3265	246	7	etc	etc	X
ap-3265	246	8	.	.	X
ap-3265	247	1	if	if	SCONJ
ap-3265	247	2	we	we	PRON
ap-3265	247	3	apply	apply	VERB
ap-3265	247	4	the	the	DET
ap-3265	247	5	contraction	contraction	NOUN
ap-3265	247	6	[	[	X
ap-3265	247	7	1	1	NUM
ap-3265	247	8	,	,	PUNCT
ap-3265	247	9	1	1	NUM
ap-3265	247	10	,	,	PUNCT
ap-3265	247	11	1	1	NUM
ap-3265	247	12	,	,	PUNCT
ap-3265	247	13	1]→	1]→	NOUN
ap-3265	247	14	[	[	X
ap-3265	247	15	2	2	NUM
ap-3265	247	16	,	,	PUNCT
ap-3265	247	17	1	1	NUM
ap-3265	247	18	,	,	PUNCT
ap-3265	247	19	1	1	NUM
ap-3265	247	20	]	]	PUNCT
ap-3265	247	21	to	to	ADP
ap-3265	247	22	the	the	DET
ap-3265	247	23	potential	potential	ADJ
ap-3265	247	24	v[1,1,1,1	v[1,1,1,1	NOUN
ap-3265	247	25	]	]	PUNCT
ap-3265	247	26	we	we	PRON
ap-3265	247	27	get	get	VERB
ap-3265	247	28	a	a	DET
ap-3265	247	29	finite	finite	ADJ
ap-3265	247	30	limit	limit	NOUN
ap-3265	247	31	v[2,1,1	v[2,1,1	ADP
ap-3265	247	32	]	]	X
ap-3265	247	33	=	=	SYM
ap-3265	247	34	b1	b1	PROPN
ap-3265	247	35	(	(	PUNCT
ap-3265	247	36	x′1	x′1	PROPN
ap-3265	247	37	+	+	CCONJ
ap-3265	247	38	ix′2)2	ix′2)2	PROPN
ap-3265	247	39	+	+	NOUN
ap-3265	247	40	b2(x′1	b2(x′1	NOUN
ap-3265	247	41	−	−	PROPN
ap-3265	247	42	ix′2	ix′2	NOUN
ap-3265	247	43	)	)	PUNCT
ap-3265	247	44	(	(	PUNCT
ap-3265	247	45	x′1	x′1	NOUN
ap-3265	248	1	+	+	CCONJ
ap-3265	248	2	ix′2)3	ix′2)3	PROPN
ap-3265	248	3	+	+	X
ap-3265	248	4	b3	b3	NOUN
ap-3265	248	5	x′3	x′3	NOUN
ap-3265	248	6	2	2	NUM
ap-3265	249	1	+	+	NUM
ap-3265	249	2	b4	b4	NOUN
ap-3265	249	3	x′4	x′4	NOUN
ap-3265	249	4	2	2	NUM
ap-3265	249	5	,	,	PUNCT
ap-3265	249	6	(	(	PUNCT
ap-3265	249	7	8)	8)	NUM
ap-3265	249	8	provided	provide	VERB
ap-3265	249	9	the	the	DET
ap-3265	249	10	parameters	parameter	NOUN
ap-3265	249	11	transform	transform	VERB
ap-3265	249	12	as	as	ADP
ap-3265	249	13	a1	a1	NOUN
ap-3265	249	14	=	=	NOUN
ap-3265	249	15	−1	−1	NOUN
ap-3265	249	16	2	2	NUM
ap-3265	249	17	(	(	PUNCT
ap-3265	249	18	b1	b1	NOUN
ap-3265	249	19	ε2	ε2	NOUN
ap-3265	249	20	+	+	CCONJ
ap-3265	249	21	b2	b2	NOUN
ap-3265	249	22	2ε4	2ε4	NUM
ap-3265	249	23	)	)	PUNCT
ap-3265	249	24	,	,	PUNCT
ap-3265	249	25	a2	a2	PROPN
ap-3265	249	26	=	=	SYM
ap-3265	249	27	−	−	PROPN
ap-3265	249	28	b2	b2	PROPN
ap-3265	249	29	4ε4	4ε4	NUM
ap-3265	249	30	,	,	PUNCT
ap-3265	249	31	a3	a3	NOUN
ap-3265	249	32	=	=	SYM
ap-3265	249	33	b3	b3	PROPN
ap-3265	249	34	,	,	PUNCT
ap-3265	249	35	a4	a4	NOUN
ap-3265	249	36	=	=	SYM
ap-3265	249	37	b4	b4	NOUN
ap-3265	249	38	.	.	PUNCT
ap-3265	250	1	218	218	NUM
ap-3265	250	2	vol	vol	NOUN
ap-3265	250	3	.	.	PUNCT
ap-3265	251	1	56	56	NUM
ap-3265	251	2	no	no	NOUN
ap-3265	251	3	.	.	PUNCT
ap-3265	252	1	3/2016	3/2016	NUM
ap-3265	252	2	laplace	laplace	NOUN
ap-3265	252	3	equations	equation	NOUN
ap-3265	252	4	,	,	PUNCT
ap-3265	252	5	conformal	conformal	ADJ
ap-3265	252	6	superintegrability	superintegrability	NOUN
ap-3265	252	7	and	and	CCONJ
ap-3265	252	8	bôcher	bôcher	PROPN
ap-3265	252	9	contractions	contraction	NOUN
ap-3265	252	10	note	note	VERB
ap-3265	252	11	:	:	PUNCT
ap-3265	252	12	we	we	PRON
ap-3265	252	13	know	know	VERB
ap-3265	252	14	from	from	ADP
ap-3265	252	15	theory	theory	NOUN
ap-3265	252	16	that	that	SCONJ
ap-3265	252	17	the	the	DET
ap-3265	252	18	4	4	NUM
ap-3265	252	19	-	-	PUNCT
ap-3265	252	20	dimensional	dimensional	ADJ
ap-3265	252	21	vector	vector	NOUN
ap-3265	252	22	space	space	NOUN
ap-3265	252	23	of	of	ADP
ap-3265	252	24	potentials	potential	NOUN
ap-3265	252	25	v[1,1,1,1	v[1,1,1,1	VERB
ap-3265	252	26	]	]	PUNCT
ap-3265	252	27	maps	map	NOUN
ap-3265	252	28	to	to	ADP
ap-3265	252	29	the	the	DET
ap-3265	252	30	4dimensional	4dimensional	PROPN
ap-3265	252	31	vector	vector	NOUN
ap-3265	252	32	space	space	NOUN
ap-3265	252	33	of	of	ADP
ap-3265	252	34	potentials	potential	NOUN
ap-3265	252	35	v[2,1,1	v[2,1,1	ADJ
ap-3265	252	36	]	]	X
ap-3265	252	37	1	1	NUM
ap-3265	252	38	-	-	SYM
ap-3265	252	39	1	1	NUM
ap-3265	252	40	under	under	ADP
ap-3265	252	41	the	the	DET
ap-3265	252	42	contraction	contraction	NOUN
ap-3265	252	43	[	[	X
ap-3265	252	44	15	15	NUM
ap-3265	252	45	]	]	PUNCT
ap-3265	252	46	.	.	PUNCT
ap-3265	253	1	the	the	DET
ap-3265	253	2	reason	reason	NOUN
ap-3265	253	3	for	for	ADP
ap-3265	253	4	the	the	DET
ap-3265	253	5	εdependence	εdependence	NOUN
ap-3265	253	6	of	of	ADP
ap-3265	253	7	the	the	DET
ap-3265	253	8	parameters	parameter	NOUN
ap-3265	253	9	is	be	AUX
ap-3265	253	10	the	the	DET
ap-3265	253	11	arbitrariness	arbitrariness	NOUN
ap-3265	253	12	of	of	ADP
ap-3265	253	13	choosing	choose	VERB
ap-3265	253	14	a	a	DET
ap-3265	253	15	basis	basis	NOUN
ap-3265	253	16	.	.	PUNCT
ap-3265	254	1	if	if	SCONJ
ap-3265	254	2	we	we	PRON
ap-3265	254	3	had	have	AUX
ap-3265	254	4	chosen	choose	VERB
ap-3265	254	5	a	a	DET
ap-3265	254	6	basis	basis	NOUN
ap-3265	254	7	for	for	ADP
ap-3265	254	8	v[1,1,1,1	v[1,1,1,1	NOUN
ap-3265	254	9	]	]	PUNCT
ap-3265	254	10	specially	specially	ADV
ap-3265	254	11	adapted	adapt	VERB
ap-3265	254	12	to	to	ADP
ap-3265	254	13	this	this	DET
ap-3265	254	14	contraction	contraction	NOUN
ap-3265	254	15	,	,	PUNCT
ap-3265	254	16	we	we	PRON
ap-3265	254	17	could	could	AUX
ap-3265	254	18	have	have	AUX
ap-3265	254	19	achieved	achieve	VERB
ap-3265	254	20	aj	aj	PROPN
ap-3265	254	21	=	=	NOUN
ap-3265	254	22	bj	bj	NOUN
ap-3265	254	23	,	,	PUNCT
ap-3265	254	24	1	1	NUM
ap-3265	254	25	≤	≤	NUM
ap-3265	255	1	j	j	PROPN
ap-3265	255	2	≤	≤	ADV
ap-3265	255	3	4	4	NUM
ap-3265	255	4	.	.	PUNCT
ap-3265	255	5	bôcher	bôcher	PROPN
ap-3265	255	6	contractions	contraction	NOUN
ap-3265	255	7	obey	obey	VERB
ap-3265	255	8	a	a	DET
ap-3265	255	9	composition	composition	NOUN
ap-3265	255	10	law	law	NOUN
ap-3265	255	11	:	:	PUNCT
ap-3265	255	12	theorem	theorem	VERB
ap-3265	255	13	6	6	NUM
ap-3265	255	14	.	.	PUNCT
ap-3265	256	1	let	let	VERB
ap-3265	256	2	a	a	PRON
ap-3265	256	3	:	:	PUNCT
ap-3265	256	4	(	(	PUNCT
ap-3265	256	5	∆x	∆x	PROPN
ap-3265	256	6	+	+	SYM
ap-3265	256	7	va(x))ψ	va(x))ψ	X
ap-3265	256	8	=	=	SYM
ap-3265	256	9	0	0	NUM
ap-3265	256	10	,	,	PUNCT
ap-3265	256	11	b	b	NOUN
ap-3265	256	12	:	:	PUNCT
ap-3265	256	13	(	(	PUNCT
ap-3265	256	14	∆y	∆y	NOUN
ap-3265	256	15	+	+	X
ap-3265	256	16	vb(y))ψ	vb(y))ψ	NOUN
ap-3265	256	17	=	=	SYM
ap-3265	256	18	0	0	PUNCT
ap-3265	256	19	c	c	NOUN
ap-3265	256	20	:	:	PUNCT
ap-3265	256	21	(	(	PUNCT
ap-3265	256	22	∆z	∆z	NOUN
ap-3265	256	23	+	+	NOUN
ap-3265	256	24	vc(z))ψ	vc(z))ψ	X
ap-3265	256	25	=	=	SYM
ap-3265	256	26	0	0	NUM
ap-3265	256	27	,	,	PUNCT
ap-3265	256	28	be	be	AUX
ap-3265	256	29	bôcher	bôch	ADJ
ap-3265	256	30	superintegrable	superintegrable	ADJ
ap-3265	256	31	systems	system	NOUN
ap-3265	256	32	such	such	ADJ
ap-3265	256	33	that	that	SCONJ
ap-3265	256	34	a	a	DET
ap-3265	256	35	bôchercontracts	bôchercontract	NOUN
ap-3265	256	36	to	to	ADP
ap-3265	256	37	b	b	NOUN
ap-3265	256	38	and	and	CCONJ
ap-3265	256	39	b	b	NOUN
ap-3265	256	40	bôcher	bôcher	NOUN
ap-3265	256	41	-	-	PUNCT
ap-3265	256	42	contracts	contract	NOUN
ap-3265	256	43	to	to	ADP
ap-3265	256	44	c.	c.	NOUN
ap-3265	256	45	then	then	ADV
ap-3265	256	46	there	there	PRON
ap-3265	256	47	is	be	VERB
ap-3265	256	48	a	a	DET
ap-3265	256	49	one	one	NUM
ap-3265	256	50	-	-	PUNCT
ap-3265	256	51	parameter	parameter	NOUN
ap-3265	256	52	contraction	contraction	NOUN
ap-3265	256	53	of	of	ADP
ap-3265	256	54	a	a	PRON
ap-3265	256	55	to	to	ADP
ap-3265	256	56	c.	c.	PROPN
ap-3265	256	57	a	a	DET
ap-3265	256	58	fundamental	fundamental	ADJ
ap-3265	256	59	advantage	advantage	NOUN
ap-3265	256	60	in	in	ADP
ap-3265	256	61	recognizing	recognize	VERB
ap-3265	256	62	bôcher	bôcher	NOUN
ap-3265	256	63	’s	’s	PART
ap-3265	256	64	limit	limit	NOUN
ap-3265	256	65	procedure	procedure	NOUN
ap-3265	256	66	as	as	ADP
ap-3265	256	67	contractions	contraction	NOUN
ap-3265	256	68	is	be	AUX
ap-3265	256	69	that	that	SCONJ
ap-3265	256	70	whereas	whereas	SCONJ
ap-3265	256	71	the	the	DET
ap-3265	256	72	bôcher	bôcher	NOUN
ap-3265	256	73	limits	limit	VERB
ap-3265	256	74	had	have	VERB
ap-3265	256	75	a	a	DET
ap-3265	256	76	fixed	fix	VERB
ap-3265	256	77	starting	starting	NOUN
ap-3265	256	78	and	and	CCONJ
ap-3265	256	79	ending	end	VERB
ap-3265	256	80	point	point	NOUN
ap-3265	256	81	,	,	PUNCT
ap-3265	256	82	say	say	VERB
ap-3265	256	83	[	[	X
ap-3265	256	84	1	1	NUM
ap-3265	256	85	,	,	PUNCT
ap-3265	256	86	1	1	NUM
ap-3265	256	87	,	,	PUNCT
ap-3265	256	88	1	1	NUM
ap-3265	256	89	,	,	PUNCT
ap-3265	256	90	1]→	1]→	NOUN
ap-3265	256	91	[	[	X
ap-3265	256	92	2	2	NUM
ap-3265	256	93	,	,	PUNCT
ap-3265	256	94	1	1	NUM
ap-3265	256	95	,	,	PUNCT
ap-3265	256	96	1	1	NUM
ap-3265	256	97	]	]	PUNCT
ap-3265	256	98	,	,	PUNCT
ap-3265	256	99	contractions	contraction	NOUN
ap-3265	256	100	can	can	AUX
ap-3265	256	101	be	be	AUX
ap-3265	256	102	applied	apply	VERB
ap-3265	256	103	to	to	ADP
ap-3265	256	104	any	any	DET
ap-3265	256	105	nondegenerate	nondegenerate	NOUN
ap-3265	256	106	conformally	conformally	ADV
ap-3265	256	107	superintegrable	superintegrable	ADJ
ap-3265	256	108	system	system	NOUN
ap-3265	256	109	and	and	CCONJ
ap-3265	256	110	are	be	AUX
ap-3265	256	111	guaranteed	guarantee	VERB
ap-3265	256	112	to	to	PART
ap-3265	256	113	result	result	VERB
ap-3265	256	114	in	in	ADP
ap-3265	256	115	another	another	DET
ap-3265	256	116	nondegenerate	nondegenerate	ADJ
ap-3265	256	117	conformally	conformally	ADV
ap-3265	256	118	superintegrable	superintegrable	ADJ
ap-3265	256	119	system	system	NOUN
ap-3265	256	120	.	.	PUNCT
ap-3265	257	1	this	this	PRON
ap-3265	257	2	greatly	greatly	ADV
ap-3265	257	3	increases	increase	VERB
ap-3265	257	4	the	the	DET
ap-3265	257	5	range	range	NOUN
ap-3265	257	6	of	of	ADP
ap-3265	257	7	applicability	applicability	NOUN
ap-3265	257	8	of	of	ADP
ap-3265	257	9	the	the	DET
ap-3265	257	10	limits	limit	NOUN
ap-3265	257	11	.	.	PUNCT
ap-3265	258	1	4	4	X
ap-3265	258	2	.	.	X
ap-3265	258	3	the	the	DET
ap-3265	258	4	8	8	NUM
ap-3265	258	5	classes	class	NOUN
ap-3265	258	6	of	of	ADP
ap-3265	258	7	nondegenerate	nondegenerate	NOUN
ap-3265	258	8	conformally	conformally	ADV
ap-3265	258	9	superintegrable	superintegrable	ADJ
ap-3265	258	10	systems	system	NOUN
ap-3265	258	11	the	the	DET
ap-3265	258	12	possible	possible	ADJ
ap-3265	258	13	laplace	laplace	NOUN
ap-3265	258	14	equations	equation	NOUN
ap-3265	258	15	(	(	PUNCT
ap-3265	258	16	in	in	ADP
ap-3265	258	17	tetraspherical	tetraspherical	ADJ
ap-3265	258	18	coordinates	coordinate	NOUN
ap-3265	258	19	)	)	PUNCT
ap-3265	258	20	are	be	AUX
ap-3265	258	21	(	(	PUNCT
ap-3265	258	22	∑4	∑4	PROPN
ap-3265	258	23	j=1	j=1	PROPN
ap-3265	258	24	∂	∂	NUM
ap-3265	258	25	2	2	NUM
ap-3265	258	26	xj	xj	PROPN
ap-3265	258	27	+	+	X
ap-3265	258	28	v	v	NOUN
ap-3265	258	29	)	)	PUNCT
ap-3265	258	30	ψ	ψ	NOUN
ap-3265	258	31	=	=	NOUN
ap-3265	258	32	0	0	NUM
ap-3265	258	33	with	with	ADP
ap-3265	258	34	potentials	potential	NOUN
ap-3265	258	35	:	:	PUNCT
ap-3265	258	36	v[1,1,1,1	v[1,1,1,1	X
ap-3265	258	37	]	]	PUNCT
ap-3265	258	38	=	=	SYM
ap-3265	258	39	4∑	4∑	NUM
ap-3265	258	40	j=1	j=1	PROPN
ap-3265	258	41	aj	aj	PROPN
ap-3265	258	42	x2	x2	PROPN
ap-3265	258	43	j	j	PROPN
ap-3265	258	44	,	,	PUNCT
ap-3265	258	45	(	(	PUNCT
ap-3265	258	46	9	9	X
ap-3265	258	47	)	)	PUNCT
ap-3265	258	48	v[2,1,1	v[2,1,1	NOUN
ap-3265	258	49	]	]	X
ap-3265	258	50	=	=	SYM
ap-3265	258	51	a1	a1	NOUN
ap-3265	258	52	x2	x2	NOUN
ap-3265	258	53	1	1	NUM
ap-3265	258	54	+	+	NUM
ap-3265	258	55	a2	a2	PROPN
ap-3265	258	56	x2	x2	NOUN
ap-3265	258	57	2	2	NUM
ap-3265	258	58	+	+	CCONJ
ap-3265	258	59	a3(x3	a3(x3	ADV
ap-3265	258	60	−	−	PROPN
ap-3265	258	61	ix4	ix4	VERB
ap-3265	258	62	)	)	PUNCT
ap-3265	258	63	(	(	PUNCT
ap-3265	258	64	x3	x3	VERB
ap-3265	258	65	+	+	CCONJ
ap-3265	258	66	ix4)3	ix4)3	NOUN
ap-3265	258	67	+	+	SYM
ap-3265	258	68	a4	a4	NOUN
ap-3265	258	69	(	(	PUNCT
ap-3265	258	70	x3	x3	ADJ
ap-3265	258	71	+	+	CCONJ
ap-3265	258	72	ix4)2	ix4)2	ADV
ap-3265	258	73	,	,	PUNCT
ap-3265	258	74	v[2,2	v[2,2	NOUN
ap-3265	258	75	]	]	X
ap-3265	258	76	=	=	SYM
ap-3265	258	77	a1	a1	NOUN
ap-3265	258	78	(	(	PUNCT
ap-3265	258	79	x1	x1	PROPN
ap-3265	258	80	+	+	PROPN
ap-3265	258	81	ix2)2	ix2)2	NOUN
ap-3265	258	82	+	+	CCONJ
ap-3265	258	83	a2(x1	a2(x1	ADJ
ap-3265	258	84	−	−	PROPN
ap-3265	258	85	ix2	ix2	PROPN
ap-3265	258	86	)	)	PUNCT
ap-3265	258	87	(	(	PUNCT
ap-3265	258	88	x1	x1	PROPN
ap-3265	258	89	+	+	NUM
ap-3265	258	90	ix2)3	ix2)3	PROPN
ap-3265	258	91	+	+	CCONJ
ap-3265	258	92	a3	a3	NOUN
ap-3265	258	93	(	(	PUNCT
ap-3265	258	94	x3	x3	ADJ
ap-3265	258	95	+	+	CCONJ
ap-3265	258	96	ix4)2	ix4)2	SCONJ
ap-3265	259	1	+	+	CCONJ
ap-3265	259	2	a4(x3	a4(x3	PRON
ap-3265	259	3	−	−	NOUN
ap-3265	259	4	ix4	ix4	VERB
ap-3265	259	5	)	)	PUNCT
ap-3265	259	6	(	(	PUNCT
ap-3265	259	7	x3	x3	VERB
ap-3265	259	8	+	+	CCONJ
ap-3265	259	9	ix4)3	ix4)3	NOUN
ap-3265	259	10	,	,	PUNCT
ap-3265	259	11	v[3,1	v[3,1	NOUN
ap-3265	259	12	]	]	X
ap-3265	260	1	=	=	SYM
ap-3265	260	2	a1	a1	NOUN
ap-3265	260	3	(	(	PUNCT
ap-3265	260	4	x3	x3	ADJ
ap-3265	260	5	+	+	CCONJ
ap-3265	260	6	ix4)2	ix4)2	PROPN
ap-3265	260	7	+	+	CCONJ
ap-3265	260	8	a2x1	a2x1	CCONJ
ap-3265	260	9	(	(	PUNCT
ap-3265	260	10	x3	x3	ADJ
ap-3265	260	11	+	+	CCONJ
ap-3265	260	12	ix4)3	ix4)3	NOUN
ap-3265	260	13	+	+	NOUN
ap-3265	260	14	a3(4x1	a3(4x1	NOUN
ap-3265	260	15	2	2	NUM
ap-3265	260	16	+	+	CCONJ
ap-3265	260	17	x2	x2	PROPN
ap-3265	260	18	2	2	NUM
ap-3265	260	19	)	)	PUNCT
ap-3265	260	20	(	(	PUNCT
ap-3265	260	21	x3	x3	VERB
ap-3265	260	22	+	+	CCONJ
ap-3265	260	23	ix4)4	ix4)4	PROPN
ap-3265	260	24	+	+	SYM
ap-3265	260	25	a4	a4	NUM
ap-3265	260	26	x22	x22	NOUN
ap-3265	260	27	,	,	PUNCT
ap-3265	260	28	v[4	v[4	PROPN
ap-3265	260	29	]	]	X
ap-3265	260	30	=	=	SYM
ap-3265	260	31	a1	a1	NOUN
ap-3265	260	32	(	(	PUNCT
ap-3265	260	33	x3	x3	ADJ
ap-3265	260	34	+	+	CCONJ
ap-3265	260	35	ix4)2	ix4)2	PROPN
ap-3265	260	36	+	+	CCONJ
ap-3265	260	37	a2	a2	PROPN
ap-3265	260	38	x1	x1	PROPN
ap-3265	260	39	+	+	PROPN
ap-3265	260	40	ix2	ix2	PROPN
ap-3265	260	41	(	(	PUNCT
ap-3265	260	42	x3	x3	ADJ
ap-3265	260	43	+	+	CCONJ
ap-3265	260	44	ix4)3	ix4)3	PROPN
ap-3265	260	45	+	+	PROPN
ap-3265	260	46	a3	a3	NOUN
ap-3265	260	47	3(x1	3(x1	PROPN
ap-3265	260	48	+	+	CCONJ
ap-3265	260	49	ix2)2	ix2)2	PROPN
ap-3265	260	50	−	−	NUM
ap-3265	260	51	2(x3	2(x3	NUM
ap-3265	260	52	+	+	CCONJ
ap-3265	260	53	ix4)(x1	ix4)(x1	ADP
ap-3265	260	54	−	−	PROPN
ap-3265	260	55	ix2	ix2	PROPN
ap-3265	260	56	)	)	PUNCT
ap-3265	260	57	(	(	PUNCT
ap-3265	260	58	x3	x3	VERB
ap-3265	260	59	+	+	CCONJ
ap-3265	260	60	ix4)4	ix4)4	PROPN
ap-3265	260	61	,	,	PUNCT
ap-3265	260	62	v[0	v[0	PROPN
ap-3265	260	63	]	]	X
ap-3265	260	64	=	=	SYM
ap-3265	260	65	a1	a1	NOUN
ap-3265	260	66	(	(	PUNCT
ap-3265	260	67	x3	x3	ADJ
ap-3265	260	68	+	+	CCONJ
ap-3265	260	69	ix4)2	ix4)2	PROPN
ap-3265	260	70	+	+	CCONJ
ap-3265	260	71	a2x1	a2x1	PUNCT
ap-3265	260	72	+	+	CCONJ
ap-3265	260	73	a3x2	a3x2	ADP
ap-3265	260	74	(	(	PUNCT
ap-3265	260	75	x3	x3	VERB
ap-3265	260	76	+	+	CCONJ
ap-3265	260	77	ix4)3	ix4)3	PROPN
ap-3265	260	78	+	+	SYM
ap-3265	260	79	a4	a4	NOUN
ap-3265	260	80	x2	x2	NOUN
ap-3265	260	81	1	1	NUM
ap-3265	260	82	+	+	NUM
ap-3265	260	83	x2	x2	PROPN
ap-3265	260	84	2	2	NUM
ap-3265	260	85	(	(	PUNCT
ap-3265	260	86	x3	x3	VERB
ap-3265	260	87	+	+	CCONJ
ap-3265	260	88	ix4)4	ix4)4	PROPN
ap-3265	260	89	,	,	PUNCT
ap-3265	260	90	v	v	NOUN
ap-3265	260	91	(	(	PUNCT
ap-3265	260	92	1	1	NUM
ap-3265	260	93	)	)	PUNCT
ap-3265	260	94	=	=	SYM
ap-3265	260	95	a1	a1	NOUN
ap-3265	260	96	1	1	NUM
ap-3265	260	97	(	(	PUNCT
ap-3265	260	98	x1	x1	PROPN
ap-3265	260	99	+	+	PROPN
ap-3265	260	100	ix2)2	ix2)2	PROPN
ap-3265	260	101	+	+	NUM
ap-3265	260	102	a2	a2	PROPN
ap-3265	260	103	1	1	NUM
ap-3265	260	104	(	(	PUNCT
ap-3265	260	105	x3	x3	VERB
ap-3265	260	106	+	+	CCONJ
ap-3265	260	107	ix4)2	ix4)2	PROPN
ap-3265	260	108	+	+	NOUN
ap-3265	260	109	a3	a3	NOUN
ap-3265	260	110	(	(	PUNCT
ap-3265	260	111	x3	x3	VERB
ap-3265	260	112	+	+	CCONJ
ap-3265	260	113	ix4	ix4	VERB
ap-3265	260	114	)	)	PUNCT
ap-3265	260	115	(	(	PUNCT
ap-3265	260	116	x1	x1	PROPN
ap-3265	260	117	+	+	NUM
ap-3265	260	118	ix2)3	ix2)3	PROPN
ap-3265	260	119	+	+	CCONJ
ap-3265	260	120	a4	a4	NOUN
ap-3265	260	121	(	(	PUNCT
ap-3265	260	122	x3	x3	ADJ
ap-3265	260	123	+	+	X
ap-3265	260	124	ix4)2	ix4)2	PROPN
ap-3265	260	125	(	(	PUNCT
ap-3265	260	126	x1	x1	PROPN
ap-3265	260	127	+	+	X
ap-3265	260	128	ix2)4	ix2)4	PROPN
ap-3265	260	129	,	,	PUNCT
ap-3265	260	130	v	v	X
ap-3265	260	131	(	(	PUNCT
ap-3265	260	132	2	2	NUM
ap-3265	260	133	)	)	PUNCT
ap-3265	260	134	=	=	SYM
ap-3265	260	135	a1	a1	NOUN
ap-3265	260	136	1	1	NUM
ap-3265	260	137	(	(	PUNCT
ap-3265	260	138	x3	x3	ADJ
ap-3265	260	139	+	+	CCONJ
ap-3265	260	140	ix4)2	ix4)2	PROPN
ap-3265	260	141	+	+	NUM
ap-3265	260	142	a2	a2	PROPN
ap-3265	260	143	(	(	PUNCT
ap-3265	260	144	x1	x1	PROPN
ap-3265	260	145	+	+	PROPN
ap-3265	260	146	ix2	ix2	PROPN
ap-3265	260	147	)	)	PUNCT
ap-3265	260	148	(	(	PUNCT
ap-3265	260	149	x3	x3	VERB
ap-3265	260	150	+	+	CCONJ
ap-3265	260	151	ix4)3	ix4)3	PROPN
ap-3265	260	152	+	+	PROPN
ap-3265	260	153	a3	a3	NOUN
ap-3265	260	154	(	(	PUNCT
ap-3265	260	155	x1	x1	PROPN
ap-3265	260	156	+	+	X
ap-3265	260	157	ix2)2	ix2)2	PROPN
ap-3265	260	158	(	(	PUNCT
ap-3265	260	159	x3	x3	VERB
ap-3265	260	160	+	+	CCONJ
ap-3265	260	161	ix4)4	ix4)4	X
ap-3265	260	162	+	+	CCONJ
ap-3265	260	163	a4	a4	NOUN
ap-3265	260	164	(	(	PUNCT
ap-3265	260	165	x1	x1	PROPN
ap-3265	260	166	+	+	X
ap-3265	260	167	ix2)3	ix2)3	PROPN
ap-3265	260	168	(	(	PUNCT
ap-3265	260	169	x3	x3	VERB
ap-3265	260	170	+	+	CCONJ
ap-3265	260	171	ix4)5	ix4)5	PROPN
ap-3265	260	172	.	.	PUNCT
ap-3265	261	1	(	(	PUNCT
ap-3265	261	2	the	the	DET
ap-3265	261	3	last	last	ADJ
ap-3265	261	4	3	3	NUM
ap-3265	261	5	systems	system	NOUN
ap-3265	261	6	do	do	AUX
ap-3265	261	7	not	not	PART
ap-3265	261	8	correspond	correspond	VERB
ap-3265	261	9	to	to	ADP
ap-3265	261	10	elementary	elementary	ADJ
ap-3265	261	11	divisors	divisor	NOUN
ap-3265	261	12	;	;	PUNCT
ap-3265	261	13	they	they	PRON
ap-3265	261	14	appear	appear	VERB
ap-3265	261	15	as	as	ADP
ap-3265	261	16	bôcher	bôcher	NOUN
ap-3265	261	17	contractions	contraction	NOUN
ap-3265	261	18	of	of	ADP
ap-3265	261	19	systems	system	NOUN
ap-3265	261	20	that	that	PRON
ap-3265	261	21	do	do	AUX
ap-3265	261	22	correspond	correspond	VERB
ap-3265	261	23	to	to	ADP
ap-3265	261	24	elementary	elementary	ADJ
ap-3265	261	25	divisors	divisor	NOUN
ap-3265	261	26	.	.	PUNCT
ap-3265	261	27	)	)	PUNCT
ap-3265	262	1	each	each	PRON
ap-3265	262	2	of	of	ADP
ap-3265	262	3	the	the	DET
ap-3265	262	4	44	44	NUM
ap-3265	262	5	helmholtz	helmholtz	NOUN
ap-3265	262	6	nondegenerate	nondegenerate	ADJ
ap-3265	262	7	superintegrable	superintegrable	ADJ
ap-3265	262	8	(	(	PUNCT
ap-3265	262	9	i.e.	i.e.	X
ap-3265	262	10	,	,	PUNCT
ap-3265	262	11	3	3	NUM
ap-3265	262	12	-	-	PUNCT
ap-3265	262	13	parameter	parameter	NOUN
ap-3265	262	14	)	)	PUNCT
ap-3265	262	15	eigenvalue	eigenvalue	NOUN
ap-3265	262	16	systems	system	NOUN
ap-3265	262	17	is	be	AUX
ap-3265	262	18	stäckel	stäckel	NOUN
ap-3265	262	19	equivalent	equivalent	ADJ
ap-3265	262	20	to	to	ADP
ap-3265	262	21	exactly	exactly	ADV
ap-3265	262	22	one	one	NUM
ap-3265	262	23	of	of	ADP
ap-3265	262	24	these	these	DET
ap-3265	262	25	systems	system	NOUN
ap-3265	262	26	.	.	PUNCT
ap-3265	263	1	thus	thus	ADV
ap-3265	263	2	,	,	PUNCT
ap-3265	263	3	with	with	ADP
ap-3265	263	4	one	one	NUM
ap-3265	263	5	caveat	caveat	NOUN
ap-3265	263	6	,	,	PUNCT
ap-3265	263	7	there	there	PRON
ap-3265	263	8	are	be	VERB
ap-3265	263	9	exactly	exactly	ADV
ap-3265	263	10	8	8	NUM
ap-3265	263	11	equivalence	equivalence	NOUN
ap-3265	263	12	classes	class	NOUN
ap-3265	263	13	of	of	ADP
ap-3265	263	14	helmholtz	helmholtz	NOUN
ap-3265	263	15	systems	system	NOUN
ap-3265	263	16	.	.	PUNCT
ap-3265	264	1	the	the	DET
ap-3265	264	2	caveat	caveat	NOUN
ap-3265	264	3	is	be	AUX
ap-3265	264	4	the	the	DET
ap-3265	264	5	singular	singular	ADJ
ap-3265	264	6	family	family	NOUN
ap-3265	264	7	of	of	ADP
ap-3265	264	8	systems	system	NOUN
ap-3265	264	9	with	with	ADP
ap-3265	264	10	potentials	potential	NOUN
ap-3265	264	11	vs	vs	ADP
ap-3265	264	12	=	=	PUNCT
ap-3265	264	13	(	(	PUNCT
ap-3265	264	14	x3	x3	VERB
ap-3265	264	15	+	+	ADJ
ap-3265	264	16	ix4)−2h(x1+ix2	ix4)−2h(x1+ix2	PROPN
ap-3265	264	17	x3+ix4	x3+ix4	NUM
ap-3265	264	18	)	)	PUNCT
ap-3265	264	19	where	where	SCONJ
ap-3265	264	20	h	h	NOUN
ap-3265	264	21	is	be	AUX
ap-3265	264	22	an	an	DET
ap-3265	264	23	arbitrary	arbitrary	ADJ
ap-3265	264	24	analytic	analytic	ADJ
ap-3265	264	25	function	function	NOUN
ap-3265	264	26	except	except	SCONJ
ap-3265	264	27	that	that	PRON
ap-3265	264	28	vs	vs	ADP
ap-3265	264	29	6=	6=	NUM
ap-3265	264	30	v	v	NOUN
ap-3265	264	31	(	(	PUNCT
ap-3265	264	32	1	1	NUM
ap-3265	264	33	)	)	PUNCT
ap-3265	264	34	,	,	PUNCT
ap-3265	264	35	v	v	X
ap-3265	264	36	(	(	PUNCT
ap-3265	264	37	2	2	NUM
ap-3265	264	38	)	)	PUNCT
ap-3265	264	39	.	.	PUNCT
ap-3265	265	1	this	this	DET
ap-3265	265	2	family	family	NOUN
ap-3265	265	3	is	be	AUX
ap-3265	265	4	unrelated	unrelated	ADJ
ap-3265	265	5	to	to	ADP
ap-3265	265	6	the	the	DET
ap-3265	265	7	other	other	ADJ
ap-3265	265	8	systems	system	NOUN
ap-3265	265	9	.	.	PUNCT
ap-3265	266	1	expressed	express	VERB
ap-3265	266	2	as	as	ADP
ap-3265	266	3	flat	flat	ADJ
ap-3265	266	4	space	space	NOUN
ap-3265	266	5	laplace	laplace	NOUN
ap-3265	266	6	equations	equation	NOUN
ap-3265	266	7	(	(	PUNCT
ap-3265	266	8	∂2	∂2	PROPN
ap-3265	266	9	x+∂2	x+∂2	X
ap-3265	266	10	y	y	PROPN
ap-3265	266	11	+	+	CCONJ
ap-3265	266	12	ṽ	ṽ	PROPN
ap-3265	266	13	)	)	PUNCT
ap-3265	266	14	ψ	ψ	NOUN
ap-3265	267	1	=	=	NOUN
ap-3265	267	2	0	0	NUM
ap-3265	267	3	in	in	ADP
ap-3265	267	4	cartesian	cartesian	ADJ
ap-3265	267	5	coordinates	coordinate	NOUN
ap-3265	267	6	,	,	PUNCT
ap-3265	267	7	the	the	DET
ap-3265	267	8	potentials	potential	NOUN
ap-3265	267	9	are	be	AUX
ap-3265	267	10	ṽ[1,1,1,1	ṽ[1,1,1,1	ADP
ap-3265	267	11	]	]	PUNCT
ap-3265	267	12	=	=	SYM
ap-3265	267	13	a1	a1	NOUN
ap-3265	267	14	x2	x2	PROPN
ap-3265	267	15	+	+	NUM
ap-3265	267	16	a2	a2	PROPN
ap-3265	267	17	y2	y2	PROPN
ap-3265	268	1	+	+	CCONJ
ap-3265	268	2	4a3	4a3	NUM
ap-3265	269	1	(	(	PUNCT
ap-3265	269	2	x2	x2	NOUN
ap-3265	269	3	+	+	CCONJ
ap-3265	270	1	y2	y2	PROPN
ap-3265	271	1	−	−	PROPN
ap-3265	271	2	1)2	1)2	NUM
ap-3265	271	3	−	−	PROPN
ap-3265	271	4	4a4	4a4	NUM
ap-3265	272	1	(	(	PUNCT
ap-3265	272	2	x2	x2	PROPN
ap-3265	272	3	+	+	CCONJ
ap-3265	273	1	y2	y2	PROPN
ap-3265	274	1	+	+	CCONJ
ap-3265	274	2	1)2	1)2	NUM
ap-3265	274	3	,	,	PUNCT
ap-3265	274	4	ṽ[2,1,1	ṽ[2,1,1	NOUN
ap-3265	274	5	]	]	PUNCT
ap-3265	274	6	=	=	SYM
ap-3265	275	1	a1	a1	NOUN
ap-3265	275	2	x2	x2	PROPN
ap-3265	275	3	+	+	NUM
ap-3265	275	4	a2	a2	PROPN
ap-3265	275	5	y2	y2	NOUN
ap-3265	275	6	−	−	PROPN
ap-3265	275	7	a3(x2	a3(x2	NOUN
ap-3265	275	8	+	+	CCONJ
ap-3265	275	9	y2	y2	PROPN
ap-3265	275	10	)	)	PUNCT
ap-3265	276	1	+	+	NUM
ap-3265	276	2	a4	a4	NOUN
ap-3265	276	3	,	,	PUNCT
ap-3265	276	4	ṽ[2,2	ṽ[2,2	NUM
ap-3265	276	5	]	]	X
ap-3265	276	6	=	=	SYM
ap-3265	276	7	a1	a1	NOUN
ap-3265	276	8	(	(	PUNCT
ap-3265	276	9	x+	x+	ADJ
ap-3265	276	10	iy)2	iy)2	PROPN
ap-3265	276	11	+	+	CCONJ
ap-3265	276	12	a2(x−	a2(x−	X
ap-3265	276	13	iy	iy	PROPN
ap-3265	276	14	)	)	PUNCT
ap-3265	276	15	(	(	PUNCT
ap-3265	276	16	x+	x+	X
ap-3265	276	17	iy)3	iy)3	PROPN
ap-3265	276	18	+	+	PROPN
ap-3265	276	19	a3	a3	NOUN
ap-3265	276	20	−	−	PROPN
ap-3265	276	21	a4(x2	a4(x2	NOUN
ap-3265	276	22	+	+	CCONJ
ap-3265	276	23	y2	y2	PROPN
ap-3265	276	24	)	)	PUNCT
ap-3265	276	25	,	,	PUNCT
ap-3265	276	26	ṽ[3,1	ṽ[3,1	NUM
ap-3265	276	27	]	]	X
ap-3265	276	28	=	=	SYM
ap-3265	276	29	a1	a1	NOUN
ap-3265	276	30	−	−	NOUN
ap-3265	276	31	a2x+	a2x+	ADV
ap-3265	276	32	a3(4x2	a3(4x2	PROPN
ap-3265	276	33	+	+	CCONJ
ap-3265	276	34	y2	y2	NOUN
ap-3265	276	35	)	)	PUNCT
ap-3265	277	1	+	+	NUM
ap-3265	277	2	a4	a4	X
ap-3265	277	3	y2	y2	INTJ
ap-3265	277	4	,	,	PUNCT
ap-3265	277	5	ṽ[4	ṽ[4	X
ap-3265	277	6	]	]	PUNCT
ap-3265	277	7	=	=	PUNCT
ap-3265	277	8	a1	a1	NOUN
ap-3265	277	9	−	−	PROPN
ap-3265	277	10	a2(x+	a2(x+	PROPN
ap-3265	277	11	iy	iy	PROPN
ap-3265	277	12	)	)	PUNCT
ap-3265	278	1	+	+	NUM
ap-3265	278	2	a3	a3	NOUN
ap-3265	278	3	(	(	PUNCT
ap-3265	278	4	3(x+	3(x+	NUM
ap-3265	278	5	iy)2	iy)2	VERB
ap-3265	278	6	+	+	CCONJ
ap-3265	278	7	2(x−	2(x−	NUM
ap-3265	278	8	iy	iy	PROPN
ap-3265	278	9	)	)	PUNCT
ap-3265	278	10	)	)	PUNCT
ap-3265	279	1	−a4	−a4	ADV
ap-3265	279	2	(	(	PUNCT
ap-3265	279	3	4(x2	4(x2	NOUN
ap-3265	279	4	+	+	CCONJ
ap-3265	280	1	y2	y2	NOUN
ap-3265	280	2	)	)	PUNCT
ap-3265	281	1	+	+	CCONJ
ap-3265	281	2	2(x+	2(x+	NUM
ap-3265	281	3	iy)3	iy)3	NOUN
ap-3265	281	4	)	)	PUNCT
ap-3265	281	5	,	,	PUNCT
ap-3265	281	6	ṽ[0	ṽ[0	X
ap-3265	281	7	]	]	PUNCT
ap-3265	281	8	=	=	SYM
ap-3265	281	9	a1	a1	NOUN
ap-3265	281	10	−	−	PROPN
ap-3265	281	11	(	(	PUNCT
ap-3265	281	12	a2x+	a2x+	INTJ
ap-3265	281	13	a3y	a3y	PROPN
ap-3265	281	14	)	)	PUNCT
ap-3265	282	1	+	+	CCONJ
ap-3265	282	2	a4(x2	a4(x2	NOUN
ap-3265	282	3	+	+	CCONJ
ap-3265	282	4	y2	y2	PROPN
ap-3265	282	5	)	)	PUNCT
ap-3265	282	6	,	,	PUNCT
ap-3265	282	7	ṽ	ṽ	PROPN
ap-3265	282	8	(	(	PUNCT
ap-3265	282	9	1	1	NUM
ap-3265	282	10	)	)	PUNCT
ap-3265	282	11	=	=	NOUN
ap-3265	282	12	a1	a1	NOUN
ap-3265	282	13	(	(	PUNCT
ap-3265	282	14	x+	x+	ADJ
ap-3265	282	15	iy)2	iy)2	PROPN
ap-3265	282	16	+	+	CCONJ
ap-3265	282	17	a2	a2	PROPN
ap-3265	282	18	−	−	PROPN
ap-3265	282	19	a3	a3	NOUN
ap-3265	282	20	(	(	PUNCT
ap-3265	282	21	x+	x+	X
ap-3265	282	22	iy)3	iy)3	PROPN
ap-3265	282	23	+	+	CCONJ
ap-3265	282	24	a4	a4	PROPN
ap-3265	282	25	(	(	PUNCT
ap-3265	282	26	x+	x+	ADJ
ap-3265	282	27	iy)4	iy)4	PROPN
ap-3265	282	28	,	,	PUNCT
ap-3265	282	29	ṽ	ṽ	PROPN
ap-3265	282	30	(	(	PUNCT
ap-3265	282	31	2	2	NUM
ap-3265	282	32	)	)	PUNCT
ap-3265	282	33	=	=	NOUN
ap-3265	282	34	a1	a1	NOUN
ap-3265	282	35	+	+	CCONJ
ap-3265	282	36	a2(x+	a2(x+	PROPN
ap-3265	282	37	iy	iy	PROPN
ap-3265	282	38	)	)	PUNCT
ap-3265	282	39	+	+	CCONJ
ap-3265	283	1	a3(x+	a3(x+	PROPN
ap-3265	283	2	iy)2	iy)2	NOUN
ap-3265	283	3	+	+	PROPN
ap-3265	283	4	a4(x+	a4(x+	PROPN
ap-3265	283	5	iy)3	iy)3	PROPN
ap-3265	283	6	.	.	PUNCT
ap-3265	284	1	(	(	PUNCT
ap-3265	284	2	10	10	NUM
ap-3265	284	3	)	)	PUNCT
ap-3265	284	4	4.1	4.1	NUM
ap-3265	284	5	.	.	PUNCT
ap-3265	285	1	summary	summary	NOUN
ap-3265	285	2	of	of	ADP
ap-3265	285	3	bôcher	bôcher	NOUN
ap-3265	285	4	contractions	contraction	NOUN
ap-3265	285	5	of	of	ADP
ap-3265	285	6	laplace	laplace	PROPN
ap-3265	285	7	superintegrable	superintegrable	ADJ
ap-3265	285	8	systems	system	NOUN
ap-3265	285	9	table	table	NOUN
ap-3265	285	10	1	1	NUM
ap-3265	285	11	contains	contain	VERB
ap-3265	285	12	a	a	DET
ap-3265	285	13	partial	partial	ADJ
ap-3265	285	14	list	list	NOUN
ap-3265	285	15	of	of	ADP
ap-3265	285	16	contractions	contraction	NOUN
ap-3265	285	17	.	.	PUNCT
ap-3265	286	1	the	the	DET
ap-3265	286	2	full	full	ADJ
ap-3265	286	3	list	list	NOUN
ap-3265	286	4	is	be	AUX
ap-3265	286	5	presented	present	VERB
ap-3265	286	6	in	in	ADP
ap-3265	286	7	[	[	X
ap-3265	286	8	32	32	NUM
ap-3265	286	9	]	]	PUNCT
ap-3265	286	10	.	.	PUNCT
ap-3265	287	1	we	we	PRON
ap-3265	287	2	have	have	AUX
ap-3265	287	3	omitted	omit	VERB
ap-3265	287	4	some	some	DET
ap-3265	287	5	contractions	contraction	NOUN
ap-3265	287	6	,	,	PUNCT
ap-3265	287	7	such	such	ADJ
ap-3265	287	8	as	as	ADP
ap-3265	287	9	[	[	X
ap-3265	287	10	3	3	NUM
ap-3265	287	11	,	,	PUNCT
ap-3265	287	12	1	1	NUM
ap-3265	287	13	]	]	PUNCT
ap-3265	287	14	→	→	X
ap-3265	288	1	[	[	X
ap-3265	288	2	4	4	NUM
ap-3265	288	3	]	]	PUNCT
ap-3265	288	4	,	,	PUNCT
ap-3265	288	5	because	because	SCONJ
ap-3265	288	6	they	they	PRON
ap-3265	288	7	are	be	AUX
ap-3265	288	8	consequences	consequence	NOUN
ap-3265	288	9	of	of	ADP
ap-3265	288	10	other	other	ADJ
ap-3265	288	11	contractions	contraction	NOUN
ap-3265	288	12	in	in	ADP
ap-3265	288	13	the	the	DET
ap-3265	288	14	table	table	NOUN
ap-3265	288	15	.	.	PUNCT
ap-3265	289	1	5	5	X
ap-3265	289	2	.	.	X
ap-3265	289	3	helmholtz	helmholtz	NOUN
ap-3265	289	4	contractions	contraction	NOUN
ap-3265	289	5	from	from	ADP
ap-3265	289	6	bôcher	bôcher	NOUN
ap-3265	289	7	contractions	contraction	NOUN
ap-3265	289	8	we	we	PRON
ap-3265	289	9	describe	describe	VERB
ap-3265	289	10	how	how	SCONJ
ap-3265	289	11	bôcher	bôch	ADJ
ap-3265	289	12	contractions	contraction	NOUN
ap-3265	289	13	of	of	ADP
ap-3265	289	14	conformal	conformal	ADJ
ap-3265	289	15	superintegrable	superintegrable	ADJ
ap-3265	289	16	systems	system	NOUN
ap-3265	289	17	induce	induce	VERB
ap-3265	289	18	contractions	contraction	NOUN
ap-3265	289	19	of	of	ADP
ap-3265	289	20	helmholtz	helmholtz	NOUN
ap-3265	289	21	superintegrable	superintegrable	ADJ
ap-3265	289	22	systems	system	NOUN
ap-3265	289	23	.	.	PUNCT
ap-3265	290	1	we	we	PRON
ap-3265	290	2	consider	consider	VERB
ap-3265	290	3	the	the	DET
ap-3265	290	4	conformal	conformal	ADJ
ap-3265	290	5	stäckel	stäckel	NOUN
ap-3265	290	6	transforms	transform	VERB
ap-3265	290	7	of	of	ADP
ap-3265	290	8	the	the	DET
ap-3265	290	9	conformal	conformal	ADJ
ap-3265	290	10	system	system	NOUN
ap-3265	290	11	[	[	X
ap-3265	290	12	1	1	NUM
ap-3265	290	13	,	,	PUNCT
ap-3265	290	14	1	1	NUM
ap-3265	290	15	,	,	PUNCT
ap-3265	290	16	1	1	NUM
ap-3265	290	17	,	,	PUNCT
ap-3265	290	18	1	1	NUM
ap-3265	290	19	]	]	PUNCT
ap-3265	290	20	with	with	ADP
ap-3265	290	21	potential	potential	ADJ
ap-3265	290	22	v[1,1,1,1	v[1,1,1,1	NOUN
ap-3265	290	23	]	]	PUNCT
ap-3265	290	24	.	.	PUNCT
ap-3265	291	1	219	219	NUM
ap-3265	291	2	e.	e.	PROPN
ap-3265	291	3	kalnins	kalnins	PROPN
ap-3265	291	4	,	,	PUNCT
ap-3265	291	5	w.	w.	PROPN
ap-3265	291	6	miller	miller	PROPN
ap-3265	291	7	,	,	PUNCT
ap-3265	291	8	e.	e.	PROPN
ap-3265	291	9	subag	subag	PROPN
ap-3265	291	10	acta	acta	PROPN
ap-3265	291	11	polytechnica	polytechnica	PROPN
ap-3265	292	1	[	[	X
ap-3265	292	2	1	1	NUM
ap-3265	292	3	,	,	PUNCT
ap-3265	292	4	1	1	NUM
ap-3265	292	5	,	,	PUNCT
ap-3265	292	6	1	1	NUM
ap-3265	292	7	,	,	PUNCT
ap-3265	292	8	1]→	1]→	NOUN
ap-3265	293	1	[	[	X
ap-3265	293	2	2	2	NUM
ap-3265	293	3	,	,	PUNCT
ap-3265	293	4	1	1	NUM
ap-3265	293	5	,	,	PUNCT
ap-3265	293	6	1	1	NUM
ap-3265	293	7	]	]	SYM
ap-3265	293	8	v[1,1,1,1	v[1,1,1,1	NOUN
ap-3265	293	9	]	]	PUNCT
ap-3265	293	10	↓	↓	NOUN
ap-3265	294	1	v[2,1,1	v[2,1,1	ADP
ap-3265	294	2	]	]	X
ap-3265	295	1	v[2,1,1	v[2,1,1	ADJ
ap-3265	295	2	]	]	X
ap-3265	295	3	↓	↓	NOUN
ap-3265	295	4	v[2,1,1	v[2,1,1	ADP
ap-3265	295	5	]	]	X
ap-3265	295	6	v[2,2	v[2,2	NOUN
ap-3265	295	7	]	]	PUNCT
ap-3265	295	8	↓	↓	PROPN
ap-3265	295	9	v[2,2	v[2,2	PROPN
ap-3265	295	10	]	]	PUNCT
ap-3265	295	11	v[3,1	v[3,1	NOUN
ap-3265	295	12	]	]	PUNCT
ap-3265	295	13	↓	↓	PROPN
ap-3265	296	1	v(1	v(1	PROPN
ap-3265	296	2	)	)	PUNCT
ap-3265	296	3	v[4	v[4	PROPN
ap-3265	296	4	]	]	PUNCT
ap-3265	296	5	↓	↓	PROPN
ap-3265	297	1	v[0	v[0	PROPN
ap-3265	297	2	]	]	X
ap-3265	297	3	v[0	v[0	PROPN
ap-3265	297	4	]	]	X
ap-3265	297	5	↓	↓	PROPN
ap-3265	297	6	v[0	v[0	PROPN
ap-3265	297	7	]	]	X
ap-3265	297	8	v	v	PROPN
ap-3265	297	9	(	(	PUNCT
ap-3265	297	10	1	1	NUM
ap-3265	297	11	)	)	PUNCT
ap-3265	297	12	↓	↓	NOUN
ap-3265	297	13	v	v	ADP
ap-3265	297	14	(	(	PUNCT
ap-3265	297	15	1	1	NUM
ap-3265	297	16	)	)	PUNCT
ap-3265	297	17	v	v	NOUN
ap-3265	297	18	(	(	PUNCT
ap-3265	297	19	2	2	NUM
ap-3265	297	20	)	)	PUNCT
ap-3265	297	21	↓	↓	NOUN
ap-3265	297	22	v	v	X
ap-3265	297	23	(	(	PUNCT
ap-3265	297	24	2	2	NUM
ap-3265	297	25	)	)	PUNCT
ap-3265	298	1	[	[	X
ap-3265	298	2	1	1	NUM
ap-3265	298	3	,	,	PUNCT
ap-3265	298	4	1	1	NUM
ap-3265	298	5	,	,	PUNCT
ap-3265	298	6	1	1	NUM
ap-3265	298	7	,	,	PUNCT
ap-3265	298	8	1]→	1]→	NOUN
ap-3265	298	9	[	[	X
ap-3265	298	10	2	2	NUM
ap-3265	298	11	,	,	PUNCT
ap-3265	298	12	2	2	NUM
ap-3265	298	13	]	]	SYM
ap-3265	298	14	v[1,1,1,1	v[1,1,1,1	NOUN
ap-3265	298	15	]	]	PUNCT
ap-3265	298	16	↓	↓	PROPN
ap-3265	298	17	v[2,2	v[2,2	PROPN
ap-3265	298	18	]	]	PUNCT
ap-3265	299	1	v[2,1,1	v[2,1,1	ADP
ap-3265	299	2	]	]	X
ap-3265	299	3	↓	↓	PROPN
ap-3265	299	4	v[2,2	v[2,2	PROPN
ap-3265	299	5	]	]	PUNCT
ap-3265	299	6	v[2,2	v[2,2	NOUN
ap-3265	299	7	]	]	PUNCT
ap-3265	299	8	↓	↓	PROPN
ap-3265	299	9	v[2,2	v[2,2	PROPN
ap-3265	299	10	]	]	PUNCT
ap-3265	299	11	v[3,1	v[3,1	NOUN
ap-3265	299	12	]	]	PUNCT
ap-3265	299	13	↓	↓	PROPN
ap-3265	299	14	v	v	X
ap-3265	299	15	(	(	PUNCT
ap-3265	299	16	1	1	NUM
ap-3265	299	17	)	)	PUNCT
ap-3265	299	18	v[4	v[4	PROPN
ap-3265	299	19	]	]	X
ap-3265	299	20	↓	↓	PROPN
ap-3265	299	21	v	v	X
ap-3265	299	22	(	(	PUNCT
ap-3265	299	23	2	2	NUM
ap-3265	299	24	)	)	PUNCT
ap-3265	299	25	v[0	v[0	PROPN
ap-3265	299	26	]	]	PUNCT
ap-3265	299	27	↓	↓	PROPN
ap-3265	299	28	v[0	v[0	PROPN
ap-3265	299	29	]	]	X
ap-3265	299	30	v	v	PROPN
ap-3265	299	31	(	(	PUNCT
ap-3265	299	32	1	1	NUM
ap-3265	299	33	)	)	PUNCT
ap-3265	299	34	↓	↓	NOUN
ap-3265	299	35	v	v	ADP
ap-3265	299	36	(	(	PUNCT
ap-3265	299	37	1	1	NUM
ap-3265	299	38	)	)	PUNCT
ap-3265	299	39	v	v	NOUN
ap-3265	299	40	(	(	PUNCT
ap-3265	299	41	2	2	NUM
ap-3265	299	42	)	)	PUNCT
ap-3265	299	43	↓	↓	NOUN
ap-3265	299	44	v	v	X
ap-3265	299	45	(	(	PUNCT
ap-3265	299	46	2	2	NUM
ap-3265	299	47	)	)	PUNCT
ap-3265	299	48	[	[	X
ap-3265	299	49	2	2	NUM
ap-3265	299	50	,	,	PUNCT
ap-3265	299	51	1	1	NUM
ap-3265	299	52	,	,	PUNCT
ap-3265	299	53	1]→	1]→	NOUN
ap-3265	299	54	[	[	X
ap-3265	299	55	3	3	NUM
ap-3265	299	56	,	,	PUNCT
ap-3265	299	57	1	1	NUM
ap-3265	299	58	]	]	SYM
ap-3265	299	59	v[1,1,1,1	v[1,1,1,1	PROPN
ap-3265	299	60	]	]	PUNCT
ap-3265	299	61	↓	↓	NOUN
ap-3265	299	62	v[3,1	v[3,1	PROPN
ap-3265	299	63	]	]	PUNCT
ap-3265	300	1	v[2,1,1	v[2,1,1	ADP
ap-3265	300	2	]	]	X
ap-3265	300	3	↓	↓	NOUN
ap-3265	300	4	v[3,1	v[3,1	PROPN
ap-3265	300	5	]	]	PUNCT
ap-3265	300	6	v[2,2	v[2,2	NOUN
ap-3265	300	7	]	]	PUNCT
ap-3265	300	8	↓	↓	PROPN
ap-3265	300	9	v[0	v[0	PROPN
ap-3265	300	10	]	]	X
ap-3265	300	11	v[3,1	v[3,1	PROPN
ap-3265	300	12	]	]	PUNCT
ap-3265	300	13	↓	↓	PROPN
ap-3265	300	14	v[3,1	v[3,1	PROPN
ap-3265	300	15	]	]	X
ap-3265	301	1	v[4	v[4	X
ap-3265	301	2	]	]	X
ap-3265	301	3	↓	↓	PROPN
ap-3265	302	1	v[0	v[0	PROPN
ap-3265	302	2	]	]	X
ap-3265	302	3	v[0	v[0	PROPN
ap-3265	302	4	]	]	X
ap-3265	302	5	↓	↓	PROPN
ap-3265	302	6	v[0	v[0	PROPN
ap-3265	302	7	]	]	X
ap-3265	302	8	v	v	PROPN
ap-3265	302	9	(	(	PUNCT
ap-3265	302	10	1	1	NUM
ap-3265	302	11	)	)	PUNCT
ap-3265	302	12	↓	↓	NOUN
ap-3265	302	13	v	v	ADP
ap-3265	302	14	(	(	PUNCT
ap-3265	302	15	2	2	NUM
ap-3265	302	16	)	)	PUNCT
ap-3265	302	17	v	v	NOUN
ap-3265	302	18	(	(	PUNCT
ap-3265	302	19	2	2	NUM
ap-3265	302	20	)	)	PUNCT
ap-3265	302	21	↓	↓	NOUN
ap-3265	302	22	v	v	X
ap-3265	302	23	(	(	PUNCT
ap-3265	302	24	2	2	NUM
ap-3265	302	25	)	)	PUNCT
ap-3265	302	26	[	[	X
ap-3265	302	27	1	1	NUM
ap-3265	302	28	,	,	PUNCT
ap-3265	302	29	1	1	NUM
ap-3265	302	30	,	,	PUNCT
ap-3265	302	31	1	1	NUM
ap-3265	302	32	,	,	PUNCT
ap-3265	302	33	1]→	1]→	NOUN
ap-3265	302	34	[	[	X
ap-3265	302	35	4	4	NUM
ap-3265	302	36	]	]	SYM
ap-3265	302	37	v[1,1,1,1	v[1,1,1,1	NOUN
ap-3265	302	38	]	]	PUNCT
ap-3265	302	39	↓	↓	PROPN
ap-3265	303	1	v[4	v[4	X
ap-3265	303	2	]	]	X
ap-3265	304	1	v[2,1,1	v[2,1,1	ADJ
ap-3265	304	2	]	]	X
ap-3265	304	3	↓	↓	NOUN
ap-3265	305	1	v[4	v[4	PROPN
ap-3265	305	2	]	]	X
ap-3265	305	3	v[2,2	v[2,2	NOUN
ap-3265	305	4	]	]	PUNCT
ap-3265	305	5	↓	↓	PROPN
ap-3265	305	6	v[0	v[0	PROPN
ap-3265	305	7	]	]	X
ap-3265	305	8	v[3,1	v[3,1	PROPN
ap-3265	305	9	]	]	PUNCT
ap-3265	305	10	↓	↓	PROPN
ap-3265	306	1	v[4	v[4	X
ap-3265	306	2	]	]	X
ap-3265	307	1	v[4	v[4	X
ap-3265	307	2	]	]	X
ap-3265	307	3	↓	↓	PROPN
ap-3265	308	1	v[0	v[0	PROPN
ap-3265	308	2	]	]	X
ap-3265	308	3	v[0	v[0	PROPN
ap-3265	308	4	]	]	X
ap-3265	308	5	↓	↓	PROPN
ap-3265	308	6	v[0	v[0	PROPN
ap-3265	308	7	]	]	X
ap-3265	308	8	v	v	PROPN
ap-3265	308	9	(	(	PUNCT
ap-3265	308	10	1	1	NUM
ap-3265	308	11	)	)	PUNCT
ap-3265	308	12	↓	↓	NOUN
ap-3265	308	13	v	v	ADP
ap-3265	308	14	(	(	PUNCT
ap-3265	308	15	2	2	NUM
ap-3265	308	16	)	)	PUNCT
ap-3265	308	17	v	v	NOUN
ap-3265	308	18	(	(	PUNCT
ap-3265	308	19	2	2	NUM
ap-3265	308	20	)	)	PUNCT
ap-3265	308	21	↓	↓	NOUN
ap-3265	308	22	v	v	X
ap-3265	308	23	(	(	PUNCT
ap-3265	308	24	2	2	NUM
ap-3265	308	25	)	)	PUNCT
ap-3265	308	26	[	[	X
ap-3265	308	27	2	2	NUM
ap-3265	308	28	,	,	PUNCT
ap-3265	308	29	2]→	2]→	NOUN
ap-3265	308	30	[	[	X
ap-3265	308	31	4	4	NUM
ap-3265	308	32	]	]	SYM
ap-3265	308	33	v[1,1,1,1	v[1,1,1,1	NOUN
ap-3265	308	34	]	]	PUNCT
ap-3265	308	35	↓	↓	PROPN
ap-3265	309	1	v[4	v[4	X
ap-3265	309	2	]	]	X
ap-3265	310	1	v[2,1,1	v[2,1,1	ADJ
ap-3265	310	2	]	]	X
ap-3265	310	3	↓	↓	NOUN
ap-3265	311	1	v[4	v[4	PROPN
ap-3265	311	2	]	]	X
ap-3265	311	3	v[2,2	v[2,2	NOUN
ap-3265	311	4	]	]	PUNCT
ap-3265	311	5	↓	↓	PROPN
ap-3265	312	1	v[4	v[4	PROPN
ap-3265	312	2	]	]	PUNCT
ap-3265	312	3	v[3,1	v[3,1	NOUN
ap-3265	312	4	]	]	PUNCT
ap-3265	312	5	↓	↓	PROPN
ap-3265	312	6	v	v	X
ap-3265	312	7	(	(	PUNCT
ap-3265	312	8	2	2	NUM
ap-3265	312	9	)	)	PUNCT
ap-3265	312	10	v[4	v[4	PROPN
ap-3265	312	11	]	]	X
ap-3265	312	12	↓	↓	PROPN
ap-3265	312	13	v	v	X
ap-3265	312	14	(	(	PUNCT
ap-3265	312	15	2	2	NUM
ap-3265	312	16	)	)	PUNCT
ap-3265	312	17	v[0	v[0	PROPN
ap-3265	312	18	]	]	PUNCT
ap-3265	312	19	↓	↓	PROPN
ap-3265	312	20	v[0	v[0	PROPN
ap-3265	312	21	]	]	X
ap-3265	312	22	v	v	PROPN
ap-3265	312	23	(	(	PUNCT
ap-3265	312	24	1	1	NUM
ap-3265	312	25	)	)	PUNCT
ap-3265	312	26	↓	↓	NOUN
ap-3265	312	27	v	v	ADP
ap-3265	312	28	(	(	PUNCT
ap-3265	312	29	2	2	NUM
ap-3265	312	30	)	)	PUNCT
ap-3265	312	31	v	v	NOUN
ap-3265	312	32	(	(	PUNCT
ap-3265	312	33	2	2	NUM
ap-3265	312	34	)	)	PUNCT
ap-3265	312	35	↓	↓	NOUN
ap-3265	312	36	v	v	X
ap-3265	312	37	(	(	PUNCT
ap-3265	312	38	2	2	NUM
ap-3265	312	39	)	)	PUNCT
ap-3265	312	40	.	.	PUNCT
ap-3265	313	1	[	[	X
ap-3265	313	2	1	1	NUM
ap-3265	313	3	,	,	PUNCT
ap-3265	313	4	1	1	NUM
ap-3265	313	5	,	,	PUNCT
ap-3265	313	6	1	1	NUM
ap-3265	313	7	,	,	PUNCT
ap-3265	313	8	1]→	1]→	NOUN
ap-3265	314	1	[	[	X
ap-3265	314	2	3	3	NUM
ap-3265	314	3	,	,	PUNCT
ap-3265	314	4	1	1	NUM
ap-3265	314	5	]	]	SYM
ap-3265	314	6	v[1,1,1,1	v[1,1,1,1	PROPN
ap-3265	314	7	]	]	PUNCT
ap-3265	314	8	↓	↓	NOUN
ap-3265	314	9	v[3,1	v[3,1	PROPN
ap-3265	314	10	]	]	PUNCT
ap-3265	315	1	v[2,1,1	v[2,1,1	ADP
ap-3265	315	2	]	]	X
ap-3265	315	3	↓	↓	NOUN
ap-3265	315	4	v[3,1	v[3,1	PROPN
ap-3265	315	5	]	]	PUNCT
ap-3265	315	6	v[2,2	v[2,2	NOUN
ap-3265	315	7	]	]	PUNCT
ap-3265	315	8	↓	↓	PROPN
ap-3265	315	9	v[0	v[0	PROPN
ap-3265	315	10	]	]	X
ap-3265	315	11	v[3,1	v[3,1	PROPN
ap-3265	315	12	]	]	PUNCT
ap-3265	315	13	↓	↓	PROPN
ap-3265	315	14	v[3,1	v[3,1	PROPN
ap-3265	315	15	]	]	X
ap-3265	316	1	v[4	v[4	X
ap-3265	316	2	]	]	X
ap-3265	316	3	↓	↓	PROPN
ap-3265	317	1	v[0	v[0	PROPN
ap-3265	317	2	]	]	X
ap-3265	317	3	v[0	v[0	PROPN
ap-3265	317	4	]	]	X
ap-3265	317	5	↓	↓	PROPN
ap-3265	317	6	v[0	v[0	PROPN
ap-3265	317	7	]	]	X
ap-3265	317	8	v	v	PROPN
ap-3265	317	9	(	(	PUNCT
ap-3265	317	10	1	1	NUM
ap-3265	317	11	)	)	PUNCT
ap-3265	317	12	↓	↓	NOUN
ap-3265	317	13	v	v	ADP
ap-3265	317	14	(	(	PUNCT
ap-3265	317	15	2	2	NUM
ap-3265	317	16	)	)	PUNCT
ap-3265	317	17	v	v	NOUN
ap-3265	317	18	(	(	PUNCT
ap-3265	317	19	2	2	NUM
ap-3265	317	20	)	)	PUNCT
ap-3265	317	21	↓	↓	NOUN
ap-3265	317	22	v	v	ADP
ap-3265	317	23	(	(	PUNCT
ap-3265	317	24	2	2	NUM
ap-3265	317	25	)	)	PUNCT
ap-3265	317	26	table	table	NOUN
ap-3265	317	27	1	1	NUM
ap-3265	317	28	.	.	PUNCT
ap-3265	318	1	bôcher	bôcher	PROPN
ap-3265	318	2	contractions	contraction	NOUN
ap-3265	318	3	of	of	ADP
ap-3265	318	4	laplace	laplace	NOUN
ap-3265	318	5	superintegrable	superintegrable	ADJ
ap-3265	318	6	systems	system	NOUN
ap-3265	318	7	.	.	PUNCT
ap-3265	319	1	as	as	SCONJ
ap-3265	319	2	we	we	PRON
ap-3265	319	3	show	show	VERB
ap-3265	319	4	explicitly	explicitly	ADV
ap-3265	319	5	in	in	ADP
ap-3265	319	6	[	[	X
ap-3265	319	7	32	32	NUM
ap-3265	319	8	]	]	PUNCT
ap-3265	319	9	,	,	PUNCT
ap-3265	319	10	the	the	DET
ap-3265	319	11	various	various	ADJ
ap-3265	319	12	possibilities	possibility	NOUN
ap-3265	319	13	are	be	AUX
ap-3265	319	14	s9	s9	ADV
ap-3265	319	15	above	above	ADV
ap-3265	319	16	and	and	CCONJ
ap-3265	319	17	2	2	NUM
ap-3265	319	18	more	more	ADJ
ap-3265	319	19	helmholtz	helmholtz	NOUN
ap-3265	319	20	systems	system	NOUN
ap-3265	319	21	on	on	ADP
ap-3265	319	22	the	the	DET
ap-3265	319	23	sphere	sphere	NOUN
ap-3265	319	24	,	,	PUNCT
ap-3265	319	25	s7	s7	NOUN
ap-3265	319	26	and	and	CCONJ
ap-3265	319	27	s8	s8	NOUN
ap-3265	319	28	,	,	PUNCT
ap-3265	319	29	2	2	NUM
ap-3265	319	30	darboux	darboux	NOUN
ap-3265	319	31	systems	system	NOUN
ap-3265	319	32	d4b	d4b	PROPN
ap-3265	319	33	and	and	CCONJ
ap-3265	319	34	d4c	d4c	PROPN
ap-3265	319	35	,	,	PUNCT
ap-3265	319	36	and	and	CCONJ
ap-3265	319	37	a	a	DET
ap-3265	319	38	family	family	NOUN
ap-3265	319	39	of	of	ADP
ap-3265	319	40	koenigs	koenig	NOUN
ap-3265	319	41	systems	system	NOUN
ap-3265	319	42	.	.	PUNCT
ap-3265	319	43	example	example	NOUN
ap-3265	320	1	1	1	NUM
ap-3265	320	2	.	.	PUNCT
ap-3265	320	3	using	use	VERB
ap-3265	320	4	cartesian	cartesian	ADJ
ap-3265	320	5	coordinates	coordinate	NOUN
ap-3265	320	6	x	x	SYM
ap-3265	320	7	,	,	PUNCT
ap-3265	320	8	y	y	PROPN
ap-3265	320	9	,	,	PUNCT
ap-3265	320	10	we	we	PRON
ap-3265	320	11	consider	consider	VERB
ap-3265	320	12	the	the	DET
ap-3265	320	13	[	[	X
ap-3265	320	14	1	1	NUM
ap-3265	320	15	,	,	PUNCT
ap-3265	320	16	1	1	NUM
ap-3265	320	17	,	,	PUNCT
ap-3265	320	18	1	1	NUM
ap-3265	320	19	,	,	PUNCT
ap-3265	320	20	1	1	NUM
ap-3265	320	21	]	]	X
ap-3265	320	22	hamiltonian	hamiltonian	ADJ
ap-3265	320	23	h	h	NOUN
ap-3265	320	24	=	=	SYM
ap-3265	320	25	∂2	∂2	PROPN
ap-3265	320	26	x	x	X
ap-3265	321	1	+	+	CCONJ
ap-3265	321	2	∂2	∂2	PROPN
ap-3265	321	3	y	y	PROPN
ap-3265	321	4	+	+	CCONJ
ap-3265	321	5	a1	a1	NOUN
ap-3265	321	6	x2	x2	PROPN
ap-3265	321	7	+	+	NUM
ap-3265	321	8	a2	a2	PROPN
ap-3265	321	9	y2	y2	PROPN
ap-3265	321	10	+	+	CCONJ
ap-3265	322	1	4a3	4a3	NUM
ap-3265	323	1	(	(	PUNCT
ap-3265	323	2	x2	x2	NOUN
ap-3265	323	3	+	+	CCONJ
ap-3265	324	1	y2	y2	PROPN
ap-3265	325	1	−	−	PROPN
ap-3265	325	2	1)2	1)2	NUM
ap-3265	325	3	+	+	NUM
ap-3265	325	4	4a4	4a4	NUM
ap-3265	325	5	(	(	PUNCT
ap-3265	325	6	x2	x2	PROPN
ap-3265	325	7	+	+	CCONJ
ap-3265	325	8	y2	y2	PROPN
ap-3265	326	1	+	+	PROPN
ap-3265	326	2	1)2	1)2	NUM
ap-3265	326	3	.	.	PUNCT
ap-3265	327	1	dividing	divide	VERB
ap-3265	327	2	on	on	ADP
ap-3265	327	3	the	the	DET
ap-3265	327	4	left	left	NOUN
ap-3265	327	5	by	by	ADP
ap-3265	327	6	1	1	NUM
ap-3265	327	7	/	/	SYM
ap-3265	327	8	x2	x2	NOUN
ap-3265	327	9	we	we	PRON
ap-3265	327	10	obtain	obtain	VERB
ap-3265	327	11	ĥ	ĥ	X
ap-3265	327	12	=	=	PUNCT
ap-3265	327	13	x2(∂2	x2(∂2	X
ap-3265	327	14	x	x	PUNCT
ap-3265	328	1	+	+	CCONJ
ap-3265	328	2	∂2	∂2	PROPN
ap-3265	328	3	y	y	PROPN
ap-3265	328	4	)	)	PUNCT
ap-3265	329	1	+	+	CCONJ
ap-3265	329	2	a1	a1	NOUN
ap-3265	329	3	+	+	CCONJ
ap-3265	329	4	a2	a2	PROPN
ap-3265	329	5	x2	x2	PROPN
ap-3265	329	6	y2	y2	PROPN
ap-3265	330	1	+	+	CCONJ
ap-3265	330	2	4a3	4a3	NUM
ap-3265	330	3	x2	x2	INTJ
ap-3265	331	1	(	(	PUNCT
ap-3265	332	1	x2	x2	PROPN
ap-3265	333	1	+	+	CCONJ
ap-3265	334	1	y2	y2	PROPN
ap-3265	335	1	−	−	PROPN
ap-3265	335	2	1)2	1)2	NUM
ap-3265	335	3	−	−	PROPN
ap-3265	335	4	4a4	4a4	NUM
ap-3265	336	1	x2	x2	NOUN
ap-3265	336	2	(	(	PUNCT
ap-3265	336	3	x2	x2	PROPN
ap-3265	337	1	+	+	CCONJ
ap-3265	337	2	y2	y2	PROPN
ap-3265	338	1	+	+	CCONJ
ap-3265	338	2	1)2	1)2	NUM
ap-3265	338	3	,	,	PUNCT
ap-3265	338	4	the	the	DET
ap-3265	338	5	stäckel	stäckel	NOUN
ap-3265	338	6	transform	transform	VERB
ap-3265	338	7	corresponding	correspond	VERB
ap-3265	338	8	to	to	ADP
ap-3265	338	9	the	the	DET
ap-3265	338	10	case	case	NOUN
ap-3265	338	11	(	(	PUNCT
ap-3265	338	12	a1	a1	NOUN
ap-3265	338	13	,	,	PUNCT
ap-3265	338	14	a2	a2	PROPN
ap-3265	338	15	,	,	PUNCT
ap-3265	338	16	a3	a3	NOUN
ap-3265	338	17	,	,	PUNCT
ap-3265	338	18	a4	a4	NOUN
ap-3265	338	19	)	)	PUNCT
ap-3265	338	20	=	=	SYM
ap-3265	338	21	(	(	PUNCT
ap-3265	338	22	1	1	NUM
ap-3265	338	23	,	,	PUNCT
ap-3265	338	24	0	0	NUM
ap-3265	338	25	,	,	PUNCT
ap-3265	338	26	0	0	NUM
ap-3265	338	27	,	,	PUNCT
ap-3265	338	28	0	0	NUM
ap-3265	338	29	)	)	PUNCT
ap-3265	338	30	.	.	PUNCT
ap-3265	339	1	this	this	PRON
ap-3265	339	2	becomes	become	VERB
ap-3265	339	3	more	more	ADV
ap-3265	339	4	transparent	transparent	ADJ
ap-3265	339	5	if	if	SCONJ
ap-3265	339	6	we	we	PRON
ap-3265	339	7	introduce	introduce	VERB
ap-3265	339	8	variables	variable	NOUN
ap-3265	339	9	x	x	PUNCT
ap-3265	339	10	=	=	SYM
ap-3265	339	11	e−a	e−a	NOUN
ap-3265	339	12	,	,	PUNCT
ap-3265	339	13	y	y	PROPN
ap-3265	339	14	=	=	SYM
ap-3265	339	15	r.	r.	PROPN
ap-3265	339	16	the	the	DET
ap-3265	339	17	hamiltonian	hamiltonian	ADJ
ap-3265	339	18	ĥ	ĥ	X
ap-3265	339	19	can	can	AUX
ap-3265	339	20	be	be	AUX
ap-3265	339	21	written	write	VERB
ap-3265	339	22	ĥ	ĥ	PUNCT
ap-3265	339	23	=	=	SYM
ap-3265	339	24	∂2	∂2	PROPN
ap-3265	339	25	a	a	DET
ap-3265	339	26	+	+	NOUN
ap-3265	339	27	e−2a∂2	e−2a∂2	PROPN
ap-3265	339	28	r	r	NOUN
ap-3265	339	29	+	+	CCONJ
ap-3265	339	30	a1	a1	NOUN
ap-3265	339	31	+	+	CCONJ
ap-3265	339	32	a2	a2	X
ap-3265	339	33	e−2a	e−2a	ADJ
ap-3265	339	34	r2	r2	NOUN
ap-3265	339	35	+	+	CCONJ
ap-3265	339	36	a3	a3	VERB
ap-3265	339	37	4	4	NUM
ap-3265	339	38	(	(	PUNCT
ap-3265	339	39	e−a	e−a	NOUN
ap-3265	339	40	+	+	PUNCT
ap-3265	339	41	ea(r2	ea(r2	NOUN
ap-3265	339	42	−	−	PROPN
ap-3265	339	43	1))2	1))2	NUM
ap-3265	339	44	−	−	NOUN
ap-3265	339	45	a4	a4	NOUN
ap-3265	339	46	4	4	NUM
ap-3265	339	47	(	(	PUNCT
ap-3265	339	48	e−a	e−a	NOUN
ap-3265	339	49	+	+	CCONJ
ap-3265	339	50	ea(r2	ea(r2	NOUN
ap-3265	339	51	+	+	X
ap-3265	339	52	1))2	1))2	NUM
ap-3265	339	53	.	.	PUNCT
ap-3265	340	1	recalling	recall	VERB
ap-3265	340	2	horospherical	horospherical	ADJ
ap-3265	340	3	coordinates	coordinate	NOUN
ap-3265	340	4	on	on	ADP
ap-3265	340	5	the	the	DET
ap-3265	340	6	complex	complex	ADJ
ap-3265	340	7	two	two	NUM
ap-3265	340	8	sphere	sphere	NOUN
ap-3265	340	9	,	,	PUNCT
ap-3265	340	10	viz	viz	NOUN
ap-3265	340	11	.	.	PUNCT
ap-3265	341	1	s1	s1	NOUN
ap-3265	341	2	=	=	PUNCT
ap-3265	342	1	i	i	PRON
ap-3265	342	2	2(e−a	2(e−a	NUM
ap-3265	342	3	+	+	CCONJ
ap-3265	342	4	(	(	PUNCT
ap-3265	342	5	r2	r2	PROPN
ap-3265	342	6	+	+	CCONJ
ap-3265	342	7	1)ea	1)ea	NUM
ap-3265	342	8	)	)	PUNCT
ap-3265	342	9	,	,	PUNCT
ap-3265	342	10	s2	s2	PROPN
ap-3265	342	11	=	=	SYM
ap-3265	342	12	rea	rea	PROPN
ap-3265	342	13	,	,	PUNCT
ap-3265	342	14	s3	s3	PROPN
ap-3265	342	15	=	=	NOUN
ap-3265	342	16	1	1	NUM
ap-3265	342	17	2(e−a	2(e−a	NUM
ap-3265	342	18	+	+	CCONJ
ap-3265	342	19	(	(	PUNCT
ap-3265	342	20	r2	r2	PROPN
ap-3265	342	21	−	−	PROPN
ap-3265	342	22	1)ea	1)ea	NUM
ap-3265	342	23	)	)	PUNCT
ap-3265	342	24	we	we	PRON
ap-3265	342	25	see	see	VERB
ap-3265	342	26	that	that	SCONJ
ap-3265	342	27	the	the	DET
ap-3265	342	28	hamiltonian	hamiltonian	ADJ
ap-3265	342	29	ĥ	ĥ	X
ap-3265	342	30	can	can	AUX
ap-3265	342	31	be	be	AUX
ap-3265	342	32	written	write	VERB
ap-3265	342	33	as	as	ADP
ap-3265	342	34	ĥ	ĥ	X
ap-3265	342	35	=	=	SYM
ap-3265	342	36	∂2	∂2	NOUN
ap-3265	342	37	s1	s1	NOUN
ap-3265	342	38	+	+	CCONJ
ap-3265	342	39	∂2	∂2	PROPN
ap-3265	342	40	s2	s2	NOUN
ap-3265	342	41	+	+	CCONJ
ap-3265	342	42	∂2	∂2	PROPN
ap-3265	342	43	s3	s3	NOUN
ap-3265	342	44	+	+	CCONJ
ap-3265	342	45	a1	a1	NOUN
ap-3265	342	46	+	+	CCONJ
ap-3265	342	47	a2	a2	NOUN
ap-3265	342	48	s2	s2	NOUN
ap-3265	342	49	2	2	NUM
ap-3265	342	50	+	+	NUM
ap-3265	342	51	a3	a3	NOUN
ap-3265	342	52	s2	s2	NOUN
ap-3265	342	53	3	3	NUM
ap-3265	342	54	+	+	NUM
ap-3265	342	55	a4	a4	NOUN
ap-3265	342	56	s2	s2	NOUN
ap-3265	342	57	1	1	NUM
ap-3265	342	58	,	,	PUNCT
ap-3265	342	59	and	and	CCONJ
ap-3265	342	60	this	this	PRON
ap-3265	342	61	is	be	AUX
ap-3265	342	62	explicitly	explicitly	ADV
ap-3265	342	63	the	the	DET
ap-3265	342	64	superintegrable	superintegrable	ADJ
ap-3265	342	65	system	system	NOUN
ap-3265	342	66	s9	s9	NOUN
ap-3265	342	67	.	.	PUNCT
ap-3265	343	1	more	more	ADV
ap-3265	343	2	generally	generally	ADV
ap-3265	343	3	,	,	PUNCT
ap-3265	343	4	let	let	VERB
ap-3265	343	5	h	h	PRON
ap-3265	343	6	be	be	AUX
ap-3265	343	7	the	the	DET
ap-3265	343	8	initial	initial	ADJ
ap-3265	343	9	hamiltonian	hamiltonian	NOUN
ap-3265	343	10	.	.	PUNCT
ap-3265	344	1	in	in	ADP
ap-3265	344	2	terms	term	NOUN
ap-3265	344	3	of	of	ADP
ap-3265	344	4	tetraspherical	tetraspherical	ADJ
ap-3265	344	5	coordinates	coordinate	NOUN
ap-3265	344	6	a	a	DET
ap-3265	344	7	general	general	ADJ
ap-3265	344	8	conformal	conformal	NOUN
ap-3265	344	9	stäckel	stäckel	NOUN
ap-3265	344	10	transformed	transform	VERB
ap-3265	344	11	potential	potential	NOUN
ap-3265	344	12	will	will	AUX
ap-3265	344	13	take	take	VERB
ap-3265	344	14	the	the	DET
ap-3265	344	15	form	form	NOUN
ap-3265	344	16	v	v	NOUN
ap-3265	344	17	=	=	NOUN
ap-3265	344	18	a1	a1	NOUN
ap-3265	344	19	x2	x2	NOUN
ap-3265	344	20	1	1	NUM
ap-3265	344	21	+	+	NUM
ap-3265	344	22	a2	a2	PROPN
ap-3265	344	23	x2	x2	NOUN
ap-3265	344	24	2	2	NUM
ap-3265	344	25	+	+	NUM
ap-3265	344	26	a3	a3	NOUN
ap-3265	344	27	x2	x2	NOUN
ap-3265	344	28	3	3	NUM
ap-3265	344	29	+	+	NUM
ap-3265	344	30	a4	a4	NOUN
ap-3265	344	31	x2	x2	SYM
ap-3265	344	32	4	4	NUM
ap-3265	344	33	a1	a1	NOUN
ap-3265	344	34	x2	x2	NOUN
ap-3265	344	35	1	1	NUM
ap-3265	344	36	+	+	NUM
ap-3265	344	37	a2	a2	PROPN
ap-3265	344	38	x2	x2	NOUN
ap-3265	344	39	2	2	NUM
ap-3265	344	40	+	+	NUM
ap-3265	344	41	a3	a3	NOUN
ap-3265	344	42	x2	x2	NOUN
ap-3265	344	43	3	3	NUM
ap-3265	344	44	+	+	NUM
ap-3265	344	45	a4	a4	NOUN
ap-3265	344	46	x2	x2	NOUN
ap-3265	344	47	4	4	NUM
ap-3265	344	48	=	=	SYM
ap-3265	344	49	v[1,1,1,1	v[1,1,1,1	NOUN
ap-3265	345	1	]	]	X
ap-3265	345	2	f	f	X
ap-3265	345	3	(	(	PUNCT
ap-3265	345	4	x	x	X
ap-3265	345	5	,	,	PUNCT
ap-3265	345	6	a	a	PRON
ap-3265	345	7	)	)	PUNCT
ap-3265	345	8	,	,	PUNCT
ap-3265	345	9	where	where	SCONJ
ap-3265	345	10	f	f	PROPN
ap-3265	345	11	(	(	PUNCT
ap-3265	345	12	x	x	PROPN
ap-3265	345	13	,	,	PUNCT
ap-3265	345	14	a	a	PRON
ap-3265	345	15	)	)	PUNCT
ap-3265	345	16	=	=	SYM
ap-3265	345	17	a1	a1	NOUN
ap-3265	345	18	x2	x2	NOUN
ap-3265	345	19	1	1	NUM
ap-3265	345	20	+	+	NUM
ap-3265	345	21	a2	a2	PROPN
ap-3265	345	22	x2	x2	NOUN
ap-3265	345	23	2	2	NUM
ap-3265	345	24	+	+	NUM
ap-3265	345	25	a3	a3	NOUN
ap-3265	345	26	x2	x2	NOUN
ap-3265	345	27	3	3	NUM
ap-3265	345	28	+	+	NUM
ap-3265	345	29	a4	a4	NOUN
ap-3265	345	30	x2	x2	NOUN
ap-3265	345	31	4	4	NUM
ap-3265	345	32	,	,	PUNCT
ap-3265	345	33	and	and	CCONJ
ap-3265	345	34	the	the	DET
ap-3265	345	35	transformed	transform	VERB
ap-3265	345	36	hamiltonian	hamiltonian	NOUN
ap-3265	345	37	will	will	AUX
ap-3265	345	38	be	be	AUX
ap-3265	345	39	ĥ	ĥ	X
ap-3265	345	40	=	=	SYM
ap-3265	345	41	1	1	NUM
ap-3265	345	42	f	f	X
ap-3265	345	43	(	(	PUNCT
ap-3265	345	44	x	x	X
ap-3265	345	45	,	,	PUNCT
ap-3265	345	46	a)h	a)h	NOUN
ap-3265	345	47	,	,	PUNCT
ap-3265	345	48	where	where	SCONJ
ap-3265	345	49	the	the	DET
ap-3265	345	50	transform	transform	NOUN
ap-3265	345	51	is	be	AUX
ap-3265	345	52	determined	determine	VERB
ap-3265	345	53	by	by	ADP
ap-3265	345	54	the	the	DET
ap-3265	345	55	fixed	fix	VERB
ap-3265	345	56	vector	vector	NOUN
ap-3265	345	57	(	(	PUNCT
ap-3265	345	58	a1	a1	PROPN
ap-3265	345	59	,	,	PUNCT
ap-3265	345	60	a2	a2	PROPN
ap-3265	345	61	,	,	PUNCT
ap-3265	345	62	a3	a3	NOUN
ap-3265	345	63	,	,	PUNCT
ap-3265	345	64	a4	a4	NOUN
ap-3265	345	65	)	)	PUNCT
ap-3265	345	66	.	.	PUNCT
ap-3265	346	1	now	now	ADV
ap-3265	346	2	we	we	PRON
ap-3265	346	3	apply	apply	VERB
ap-3265	346	4	the	the	DET
ap-3265	346	5	bôcher	bôcher	NOUN
ap-3265	346	6	contraction	contraction	NOUN
ap-3265	347	1	[	[	X
ap-3265	347	2	1	1	NUM
ap-3265	347	3	,	,	PUNCT
ap-3265	347	4	1	1	NUM
ap-3265	347	5	,	,	PUNCT
ap-3265	347	6	1	1	NUM
ap-3265	347	7	,	,	PUNCT
ap-3265	347	8	1]→	1]→	NOUN
ap-3265	348	1	[	[	X
ap-3265	348	2	2	2	NUM
ap-3265	348	3	,	,	PUNCT
ap-3265	348	4	1	1	NUM
ap-3265	348	5	,	,	PUNCT
ap-3265	348	6	1	1	NUM
ap-3265	348	7	]	]	PUNCT
ap-3265	348	8	to	to	ADP
ap-3265	348	9	this	this	DET
ap-3265	348	10	system	system	NOUN
ap-3265	348	11	.	.	PUNCT
ap-3265	349	1	in	in	ADP
ap-3265	349	2	the	the	DET
ap-3265	349	3	limit	limit	NOUN
ap-3265	349	4	as	as	ADP
ap-3265	349	5	ε	ε	PROPN
ap-3265	349	6	→	→	SYM
ap-3265	349	7	0	0	NUM
ap-3265	349	8	the	the	DET
ap-3265	349	9	potential	potential	ADJ
ap-3265	349	10	v[1,1,1,1	v[1,1,1,1	NOUN
ap-3265	349	11	]	]	PUNCT
ap-3265	349	12	→	→	PUNCT
ap-3265	349	13	v[2,1,1	v[2,1,1	PROPN
ap-3265	349	14	]	]	X
ap-3265	349	15	,	,	PUNCT
ap-3265	349	16	(	(	PUNCT
ap-3265	349	17	8)	8)	NUM
ap-3265	349	18	,	,	PUNCT
ap-3265	349	19	and	and	CCONJ
ap-3265	349	20	h	h	NOUN
ap-3265	349	21	→	→	SYM
ap-3265	349	22	h	h	NOUN
ap-3265	350	1	′	′	NUM
ap-3265	351	1	the	the	DET
ap-3265	351	2	[	[	X
ap-3265	351	3	2	2	NUM
ap-3265	351	4	,	,	PUNCT
ap-3265	351	5	1	1	NUM
ap-3265	351	6	,	,	PUNCT
ap-3265	351	7	1	1	NUM
ap-3265	351	8	]	]	PUNCT
ap-3265	351	9	system	system	NOUN
ap-3265	351	10	.	.	PUNCT
ap-3265	352	1	now	now	ADV
ap-3265	352	2	consider	consider	VERB
ap-3265	352	3	f	f	PROPN
ap-3265	352	4	(	(	PUNCT
ap-3265	352	5	x(ε),a	x(ε),a	PROPN
ap-3265	352	6	)	)	PUNCT
ap-3265	352	7	=	=	PROPN
ap-3265	352	8	v	v	ADP
ap-3265	352	9	′(x′	′(x′	PROPN
ap-3265	352	10	,	,	PUNCT
ap-3265	352	11	a)εα	a)εα	PROPN
ap-3265	352	12	+	+	PROPN
ap-3265	352	13	o(εα+1	o(εα+1	NOUN
ap-3265	352	14	)	)	PUNCT
ap-3265	352	15	,	,	PUNCT
ap-3265	352	16	where	where	SCONJ
ap-3265	352	17	the	the	DET
ap-3265	352	18	the	the	DET
ap-3265	352	19	integer	integer	NOUN
ap-3265	352	20	exponent	exponent	NOUN
ap-3265	352	21	α	α	PROPN
ap-3265	352	22	depends	depend	VERB
ap-3265	352	23	upon	upon	SCONJ
ap-3265	352	24	our	our	PRON
ap-3265	352	25	choice	choice	NOUN
ap-3265	352	26	of	of	ADP
ap-3265	352	27	a.	a.	NOUN
ap-3265	352	28	we	we	PRON
ap-3265	352	29	will	will	AUX
ap-3265	352	30	provide	provide	VERB
ap-3265	352	31	the	the	DET
ap-3265	352	32	theory	theory	NOUN
ap-3265	352	33	to	to	PART
ap-3265	352	34	show	show	VERB
ap-3265	352	35	that	that	SCONJ
ap-3265	352	36	the	the	DET
ap-3265	352	37	system	system	NOUN
ap-3265	352	38	defined	define	VERB
ap-3265	352	39	by	by	ADP
ap-3265	352	40	hamiltonian	hamiltonian	ADJ
ap-3265	352	41	ĥ	ĥ	X
ap-3265	352	42	′	′	NUM
ap-3265	352	43	=	=	SYM
ap-3265	352	44	lim	lim	PROPN
ap-3265	352	45	ε→0	ε→0	NOUN
ap-3265	352	46	εαĥ(ε	εαĥ(ε	NOUN
ap-3265	352	47	)	)	PUNCT
ap-3265	353	1	=	=	SYM
ap-3265	353	2	1	1	NUM
ap-3265	353	3	v	v	ADP
ap-3265	353	4	′(x′	′(x′	PROPN
ap-3265	353	5	,	,	PUNCT
ap-3265	353	6	a)h	a)h	X
ap-3265	353	7	′	′	NUM
ap-3265	353	8	is	be	AUX
ap-3265	353	9	a	a	DET
ap-3265	353	10	superintegrable	superintegrable	ADJ
ap-3265	353	11	system	system	NOUN
ap-3265	353	12	that	that	PRON
ap-3265	353	13	arises	arise	VERB
ap-3265	353	14	from	from	ADP
ap-3265	353	15	the	the	DET
ap-3265	353	16	system	system	NOUN
ap-3265	353	17	[	[	X
ap-3265	353	18	2	2	NUM
ap-3265	353	19	,	,	PUNCT
ap-3265	353	20	1	1	NUM
ap-3265	353	21	,	,	PUNCT
ap-3265	353	22	1	1	NUM
ap-3265	353	23	]	]	PUNCT
ap-3265	353	24	by	by	ADP
ap-3265	353	25	a	a	DET
ap-3265	353	26	conformal	conformal	ADJ
ap-3265	353	27	stäckel	stäckel	NOUN
ap-3265	353	28	transform	transform	NOUN
ap-3265	353	29	induced	induce	VERB
ap-3265	353	30	by	by	ADP
ap-3265	353	31	the	the	DET
ap-3265	353	32	potential	potential	NOUN
ap-3265	353	33	v	v	ADP
ap-3265	353	34	′(x′	′(x′	PROPN
ap-3265	353	35	,	,	PUNCT
ap-3265	353	36	a	a	PRON
ap-3265	353	37	)	)	PUNCT
ap-3265	353	38	.	.	PUNCT
ap-3265	354	1	thus	thus	ADV
ap-3265	354	2	the	the	DET
ap-3265	354	3	helmholtz	helmholtz	ADJ
ap-3265	354	4	superintegrable	superintegrable	ADJ
ap-3265	354	5	system	system	NOUN
ap-3265	354	6	with	with	ADP
ap-3265	354	7	potential	potential	ADJ
ap-3265	354	8	v	v	NOUN
ap-3265	354	9	=	=	SYM
ap-3265	354	10	v[1,1,1,1]/f	v[1,1,1,1]/f	PROPN
ap-3265	354	11	contracts	contract	NOUN
ap-3265	354	12	to	to	ADP
ap-3265	354	13	the	the	DET
ap-3265	354	14	helmholtz	helmholtz	NOUN
ap-3265	354	15	superintegrable	superintegrable	ADJ
ap-3265	354	16	system	system	NOUN
ap-3265	354	17	with	with	ADP
ap-3265	354	18	potential	potential	ADJ
ap-3265	354	19	v[2,1,1]/v	v[2,1,1]/v	NOUN
ap-3265	354	20	′.	′.	NOUN
ap-3265	354	21	the	the	DET
ap-3265	354	22	contraction	contraction	NOUN
ap-3265	354	23	is	be	AUX
ap-3265	354	24	induced	induce	VERB
ap-3265	354	25	by	by	ADP
ap-3265	354	26	a	a	DET
ap-3265	354	27	generalized	generalize	VERB
ap-3265	354	28	inönü	inönü	NOUN
ap-3265	354	29	-	-	PUNCT
ap-3265	354	30	wigner	wigner	NOUN
ap-3265	354	31	lie	lie	NOUN
ap-3265	354	32	algebra	algebra	NOUN
ap-3265	354	33	contraction	contraction	NOUN
ap-3265	354	34	of	of	ADP
ap-3265	354	35	the	the	DET
ap-3265	354	36	conformal	conformal	ADJ
ap-3265	354	37	algebra	algebra	NOUN
ap-3265	354	38	so(4,c	so(4,c	NOUN
ap-3265	354	39	)	)	PUNCT
ap-3265	354	40	.	.	PUNCT
ap-3265	355	1	always	always	ADV
ap-3265	355	2	the	the	DET
ap-3265	355	3	v	v	NOUN
ap-3265	355	4	′	′	NOUN
ap-3265	355	5	can	can	AUX
ap-3265	355	6	be	be	AUX
ap-3265	355	7	identified	identify	VERB
ap-3265	355	8	with	with	ADP
ap-3265	355	9	a	a	DET
ap-3265	355	10	specialization	specialization	NOUN
ap-3265	355	11	of	of	ADP
ap-3265	355	12	the	the	DET
ap-3265	355	13	[	[	X
ap-3265	355	14	2	2	NUM
ap-3265	355	15	,	,	PUNCT
ap-3265	355	16	1	1	NUM
ap-3265	355	17	,	,	PUNCT
ap-3265	355	18	1	1	NUM
ap-3265	355	19	]	]	X
ap-3265	355	20	potential	potential	NOUN
ap-3265	355	21	.	.	PUNCT
ap-3265	356	1	thus	thus	ADV
ap-3265	356	2	a	a	DET
ap-3265	356	3	conformal	conformal	ADJ
ap-3265	356	4	stäckel	stäckel	NOUN
ap-3265	356	5	transform	transform	NOUN
ap-3265	356	6	of	of	ADP
ap-3265	356	7	[	[	X
ap-3265	356	8	1	1	NUM
ap-3265	356	9	,	,	PUNCT
ap-3265	356	10	1	1	NUM
ap-3265	356	11	,	,	PUNCT
ap-3265	356	12	1	1	NUM
ap-3265	356	13	,	,	PUNCT
ap-3265	356	14	1	1	NUM
ap-3265	356	15	]	]	PUNCT
ap-3265	356	16	has	have	AUX
ap-3265	356	17	been	be	AUX
ap-3265	356	18	contracted	contract	VERB
ap-3265	356	19	to	to	ADP
ap-3265	356	20	a	a	DET
ap-3265	356	21	conformal	conformal	ADJ
ap-3265	356	22	stäckel	stäckel	NOUN
ap-3265	356	23	220	220	NUM
ap-3265	356	24	vol	vol	NOUN
ap-3265	356	25	.	.	PUNCT
ap-3265	357	1	56	56	NUM
ap-3265	357	2	no	no	NOUN
ap-3265	357	3	.	.	PUNCT
ap-3265	358	1	3/2016	3/2016	NUM
ap-3265	358	2	laplace	laplace	NOUN
ap-3265	358	3	equations	equation	NOUN
ap-3265	358	4	,	,	PUNCT
ap-3265	358	5	conformal	conformal	ADJ
ap-3265	358	6	superintegrability	superintegrability	NOUN
ap-3265	358	7	and	and	CCONJ
ap-3265	358	8	bôcher	bôcher	PROPN
ap-3265	358	9	contractions	contraction	NOUN
ap-3265	358	10	figure	figure	VERB
ap-3265	358	11	1	1	NUM
ap-3265	358	12	.	.	PUNCT
ap-3265	358	13	relationship	relationship	NOUN
ap-3265	358	14	between	between	ADP
ap-3265	358	15	conformal	conformal	ADJ
ap-3265	358	16	stäckel	stäckel	NOUN
ap-3265	358	17	transforms	transform	VERB
ap-3265	358	18	and	and	CCONJ
ap-3265	358	19	bôcher	bôcher	NOUN
ap-3265	358	20	contractions	contraction	NOUN
ap-3265	358	21	.	.	PUNCT
ap-3265	359	1	transform	transform	NOUN
ap-3265	359	2	of	of	ADP
ap-3265	359	3	[	[	X
ap-3265	359	4	2	2	NUM
ap-3265	359	5	,	,	PUNCT
ap-3265	359	6	1	1	NUM
ap-3265	359	7	,	,	PUNCT
ap-3265	359	8	1	1	NUM
ap-3265	359	9	]	]	PUNCT
ap-3265	359	10	.	.	PUNCT
ap-3265	360	1	the	the	DET
ap-3265	360	2	results	result	NOUN
ap-3265	360	3	follow	follow	VERB
ap-3265	360	4	and	and	CCONJ
ap-3265	360	5	generalize	generalize	VERB
ap-3265	360	6	to	to	ADP
ap-3265	360	7	all	all	DET
ap-3265	360	8	laplace	laplace	NOUN
ap-3265	360	9	systems	system	NOUN
ap-3265	360	10	.	.	PUNCT
ap-3265	361	1	the	the	DET
ap-3265	361	2	basic	basic	ADJ
ap-3265	361	3	idea	idea	NOUN
ap-3265	361	4	is	be	AUX
ap-3265	361	5	that	that	SCONJ
ap-3265	361	6	the	the	DET
ap-3265	361	7	procedure	procedure	NOUN
ap-3265	361	8	of	of	ADP
ap-3265	361	9	taking	take	VERB
ap-3265	361	10	a	a	DET
ap-3265	361	11	conformal	conformal	ADJ
ap-3265	361	12	stäckel	stäckel	NOUN
ap-3265	361	13	transform	transform	NOUN
ap-3265	361	14	of	of	ADP
ap-3265	361	15	a	a	DET
ap-3265	361	16	conformal	conformal	ADJ
ap-3265	361	17	superintegrable	superintegrable	ADJ
ap-3265	361	18	system	system	NOUN
ap-3265	361	19	,	,	PUNCT
ap-3265	361	20	followed	follow	VERB
ap-3265	361	21	by	by	ADP
ap-3265	361	22	a	a	DET
ap-3265	361	23	helmholtz	helmholtz	NOUN
ap-3265	361	24	contraction	contraction	NOUN
ap-3265	361	25	yields	yield	VERB
ap-3265	361	26	the	the	DET
ap-3265	361	27	same	same	ADJ
ap-3265	361	28	result	result	NOUN
ap-3265	361	29	as	as	ADP
ap-3265	361	30	taking	take	VERB
ap-3265	361	31	a	a	DET
ap-3265	361	32	bôcher	bôcher	NOUN
ap-3265	361	33	contraction	contraction	NOUN
ap-3265	361	34	followed	follow	VERB
ap-3265	361	35	by	by	ADP
ap-3265	361	36	an	an	DET
ap-3265	361	37	ordinary	ordinary	ADJ
ap-3265	361	38	stäckel	stäckel	NOUN
ap-3265	361	39	transform	transform	NOUN
ap-3265	361	40	:	:	PUNCT
ap-3265	361	41	the	the	DET
ap-3265	361	42	diagrams	diagram	NOUN
ap-3265	361	43	commute	commute	NOUN
ap-3265	361	44	.	.	PUNCT
ap-3265	362	1	the	the	DET
ap-3265	362	2	possible	possible	ADJ
ap-3265	362	3	helmholtz	helmholtz	NOUN
ap-3265	362	4	contractions	contraction	NOUN
ap-3265	362	5	obtainable	obtainable	ADJ
ap-3265	362	6	from	from	ADP
ap-3265	362	7	these	these	DET
ap-3265	362	8	bôcher	bôcher	NOUN
ap-3265	362	9	contractions	contraction	NOUN
ap-3265	362	10	number	number	NOUN
ap-3265	362	11	well	well	ADV
ap-3265	362	12	over	over	ADP
ap-3265	362	13	100	100	NUM
ap-3265	362	14	;	;	PUNCT
ap-3265	362	15	they	they	PRON
ap-3265	362	16	will	will	AUX
ap-3265	362	17	be	be	AUX
ap-3265	362	18	classified	classify	VERB
ap-3265	362	19	in	in	ADP
ap-3265	362	20	another	another	DET
ap-3265	362	21	paper	paper	NOUN
ap-3265	362	22	.	.	PUNCT
ap-3265	363	1	all	all	DET
ap-3265	363	2	quadratic	quadratic	ADJ
ap-3265	363	3	algebra	algebra	NOUN
ap-3265	363	4	contractions	contraction	NOUN
ap-3265	363	5	are	be	AUX
ap-3265	363	6	induced	induce	VERB
ap-3265	363	7	by	by	ADP
ap-3265	363	8	lie	lie	NOUN
ap-3265	363	9	algebra	algebra	NOUN
ap-3265	363	10	contractions	contraction	NOUN
ap-3265	363	11	of	of	ADP
ap-3265	363	12	so(4,c	so(4,c	NOUN
ap-3265	363	13	)	)	PUNCT
ap-3265	363	14	,	,	PUNCT
ap-3265	363	15	even	even	ADV
ap-3265	363	16	those	those	PRON
ap-3265	363	17	for	for	ADP
ap-3265	363	18	darboux	darboux	NOUN
ap-3265	363	19	and	and	CCONJ
ap-3265	363	20	koenigs	koenig	NOUN
ap-3265	363	21	spaces	space	NOUN
ap-3265	363	22	.	.	PUNCT
ap-3265	364	1	6	6	X
ap-3265	364	2	.	.	X
ap-3265	364	3	conclusions	conclusion	NOUN
ap-3265	364	4	and	and	CCONJ
ap-3265	364	5	discussion	discussion	NOUN
ap-3265	364	6	we	we	PRON
ap-3265	364	7	have	have	AUX
ap-3265	364	8	pointed	point	VERB
ap-3265	364	9	out	out	ADP
ap-3265	364	10	that	that	SCONJ
ap-3265	364	11	the	the	DET
ap-3265	364	12	use	use	NOUN
ap-3265	364	13	of	of	ADP
ap-3265	364	14	lie	lie	NOUN
ap-3265	364	15	algebra	algebra	NOUN
ap-3265	364	16	contractions	contraction	NOUN
ap-3265	364	17	based	base	VERB
ap-3265	364	18	on	on	ADP
ap-3265	364	19	the	the	DET
ap-3265	364	20	symmetry	symmetry	NOUN
ap-3265	364	21	groups	group	NOUN
ap-3265	364	22	of	of	ADP
ap-3265	364	23	constant	constant	ADJ
ap-3265	364	24	curvature	curvature	NOUN
ap-3265	364	25	spaces	space	NOUN
ap-3265	364	26	to	to	PART
ap-3265	364	27	construct	construct	VERB
ap-3265	364	28	quadratic	quadratic	ADJ
ap-3265	364	29	algebra	algebra	NOUN
ap-3265	364	30	contractions	contraction	NOUN
ap-3265	364	31	of	of	ADP
ap-3265	364	32	2nd	2nd	ADJ
ap-3265	364	33	order	order	NOUN
ap-3265	364	34	2d	2d	NUM
ap-3265	364	35	helmholtz	helmholtz	PROPN
ap-3265	364	36	superintegrable	superintegrable	ADJ
ap-3265	364	37	systems	system	NOUN
ap-3265	364	38	is	be	AUX
ap-3265	364	39	incomplete	incomplete	ADJ
ap-3265	364	40	,	,	PUNCT
ap-3265	364	41	because	because	SCONJ
ap-3265	364	42	it	it	PRON
ap-3265	364	43	does	do	AUX
ap-3265	364	44	n’t	not	PART
ap-3265	364	45	satisfactorily	satisfactorily	ADV
ap-3265	364	46	account	account	VERB
ap-3265	364	47	for	for	ADP
ap-3265	364	48	darboux	darboux	ADJ
ap-3265	364	49	and	and	CCONJ
ap-3265	364	50	koenigs	koenig	NOUN
ap-3265	364	51	spaces	space	NOUN
ap-3265	364	52	,	,	PUNCT
ap-3265	364	53	and	and	CCONJ
ap-3265	364	54	because	because	SCONJ
ap-3265	364	55	even	even	ADV
ap-3265	364	56	for	for	ADP
ap-3265	364	57	constant	constant	ADJ
ap-3265	364	58	curvature	curvature	NOUN
ap-3265	364	59	spaces	space	NOUN
ap-3265	364	60	there	there	PRON
ap-3265	364	61	are	be	VERB
ap-3265	364	62	abstract	abstract	ADJ
ap-3265	364	63	quadratic	quadratic	ADJ
ap-3265	364	64	algebra	algebra	NOUN
ap-3265	364	65	contractions	contraction	NOUN
ap-3265	364	66	that	that	PRON
ap-3265	364	67	can	can	AUX
ap-3265	364	68	not	not	PART
ap-3265	364	69	be	be	AUX
ap-3265	364	70	obtained	obtain	VERB
ap-3265	364	71	from	from	ADP
ap-3265	364	72	the	the	DET
ap-3265	364	73	lie	lie	NOUN
ap-3265	364	74	symmetry	symmetry	NOUN
ap-3265	364	75	algebras	algebras	PROPN
ap-3265	364	76	.	.	PUNCT
ap-3265	365	1	however	however	ADV
ap-3265	365	2	,	,	PUNCT
ap-3265	365	3	this	this	DET
ap-3265	365	4	gap	gap	NOUN
ap-3265	365	5	is	be	AUX
ap-3265	365	6	filled	fill	VERB
ap-3265	365	7	in	in	ADP
ap-3265	365	8	when	when	SCONJ
ap-3265	365	9	one	one	PRON
ap-3265	365	10	extends	extend	VERB
ap-3265	365	11	these	these	DET
ap-3265	365	12	systems	system	NOUN
ap-3265	365	13	to	to	ADP
ap-3265	365	14	2nd	2nd	ADJ
ap-3265	365	15	order	order	NOUN
ap-3265	365	16	laplace	laplace	NOUN
ap-3265	365	17	conformally	conformally	ADV
ap-3265	365	18	superintegrable	superintegrable	ADJ
ap-3265	365	19	systems	system	NOUN
ap-3265	365	20	with	with	ADP
ap-3265	365	21	conformal	conformal	ADJ
ap-3265	365	22	symmetry	symmetry	NOUN
ap-3265	365	23	algebra	algebra	NOUN
ap-3265	365	24	.	.	PUNCT
ap-3265	366	1	classes	class	NOUN
ap-3265	366	2	of	of	ADP
ap-3265	366	3	stäckel	stäckel	NOUN
ap-3265	366	4	equivalent	equivalent	ADJ
ap-3265	366	5	helmholtz	helmholtz	NOUN
ap-3265	366	6	superintegrable	superintegrable	ADJ
ap-3265	366	7	systems	system	NOUN
ap-3265	366	8	are	be	AUX
ap-3265	366	9	now	now	ADV
ap-3265	366	10	recognized	recognize	VERB
ap-3265	366	11	as	as	ADP
ap-3265	366	12	corresponding	correspond	VERB
ap-3265	366	13	to	to	ADP
ap-3265	366	14	a	a	DET
ap-3265	366	15	single	single	ADJ
ap-3265	366	16	laplace	laplace	NOUN
ap-3265	366	17	superintegrable	superintegrable	ADJ
ap-3265	366	18	system	system	NOUN
ap-3265	366	19	on	on	ADP
ap-3265	366	20	flat	flat	ADJ
ap-3265	366	21	space	space	NOUN
ap-3265	366	22	with	with	ADP
ap-3265	366	23	underlying	underlie	VERB
ap-3265	366	24	conformal	conformal	ADJ
ap-3265	366	25	symmetry	symmetry	NOUN
ap-3265	366	26	algebra	algebra	NOUN
ap-3265	366	27	so(4,c	so(4,c	NOUN
ap-3265	366	28	)	)	PUNCT
ap-3265	366	29	.	.	PUNCT
ap-3265	367	1	the	the	DET
ap-3265	367	2	conformal	conformal	ADJ
ap-3265	367	3	lie	lie	NOUN
ap-3265	367	4	algebra	algebra	NOUN
ap-3265	367	5	contractions	contraction	NOUN
ap-3265	367	6	are	be	AUX
ap-3265	367	7	induced	induce	VERB
ap-3265	367	8	by	by	ADP
ap-3265	367	9	bôcher	bôcher	NOUN
ap-3265	367	10	limits	limit	NOUN
ap-3265	367	11	associated	associate	VERB
ap-3265	367	12	with	with	ADP
ap-3265	367	13	invariants	invariant	NOUN
ap-3265	367	14	of	of	ADP
ap-3265	367	15	quadratic	quadratic	ADJ
ap-3265	367	16	forms	form	NOUN
ap-3265	367	17	.	.	PUNCT
ap-3265	368	1	they	they	PRON
ap-3265	368	2	generalize	generalize	VERB
ap-3265	368	3	all	all	PRON
ap-3265	368	4	of	of	ADP
ap-3265	368	5	the	the	DET
ap-3265	368	6	helmholtz	helmholtz	NOUN
ap-3265	368	7	contractions	contraction	NOUN
ap-3265	368	8	derived	derive	VERB
ap-3265	368	9	earlier	early	ADV
ap-3265	368	10	.	.	PUNCT
ap-3265	369	1	in	in	ADP
ap-3265	369	2	particular	particular	ADJ
ap-3265	369	3	,	,	PUNCT
ap-3265	369	4	contractions	contraction	NOUN
ap-3265	369	5	of	of	ADP
ap-3265	369	6	darboux	darboux	ADJ
ap-3265	369	7	figure	figure	NOUN
ap-3265	369	8	2	2	NUM
ap-3265	369	9	.	.	PUNCT
ap-3265	370	1	the	the	DET
ap-3265	370	2	bigger	big	ADJ
ap-3265	370	3	picture	picture	NOUN
ap-3265	370	4	.	.	PUNCT
ap-3265	371	1	and	and	CCONJ
ap-3265	371	2	koenigs	koenig	VERB
ap-3265	371	3	systems	system	NOUN
ap-3265	371	4	can	can	AUX
ap-3265	371	5	be	be	AUX
ap-3265	371	6	described	describe	VERB
ap-3265	371	7	easily	easily	ADV
ap-3265	371	8	.	.	PUNCT
ap-3265	372	1	all	all	PRON
ap-3265	372	2	of	of	ADP
ap-3265	372	3	the	the	DET
ap-3265	372	4	concepts	concept	NOUN
ap-3265	372	5	introduced	introduce	VERB
ap-3265	372	6	in	in	ADP
ap-3265	372	7	this	this	DET
ap-3265	372	8	paper	paper	NOUN
ap-3265	372	9	are	be	AUX
ap-3265	372	10	clearly	clearly	ADV
ap-3265	372	11	also	also	ADV
ap-3265	372	12	applicable	applicable	ADJ
ap-3265	372	13	for	for	ADP
ap-3265	372	14	dimensions	dimension	NOUN
ap-3265	372	15	n	n	CCONJ
ap-3265	372	16	≥	≥	NUM
ap-3265	372	17	3	3	NUM
ap-3265	372	18	[	[	X
ap-3265	372	19	33	33	NUM
ap-3265	372	20	]	]	PUNCT
ap-3265	372	21	.	.	PUNCT
ap-3265	373	1	in	in	ADP
ap-3265	373	2	papers	paper	NOUN
ap-3265	373	3	submitted	submit	VERB
ap-3265	373	4	[	[	X
ap-3265	373	5	32	32	NUM
ap-3265	373	6	]	]	PUNCT
ap-3265	373	7	,	,	PUNCT
ap-3265	373	8	and	and	CCONJ
ap-3265	373	9	under	under	ADP
ap-3265	373	10	preparation	preparation	NOUN
ap-3265	373	11	we	we	PRON
ap-3265	373	12	will	will	AUX
ap-3265	373	13	:	:	PUNCT
ap-3265	373	14	(	(	PUNCT
ap-3265	373	15	1	1	X
ap-3265	373	16	.	.	PUNCT
ap-3265	373	17	)	)	PUNCT
ap-3265	373	18	give	give	VERB
ap-3265	373	19	a	a	DET
ap-3265	373	20	complete	complete	ADJ
ap-3265	373	21	detailed	detailed	ADJ
ap-3265	373	22	classification	classification	NOUN
ap-3265	373	23	of	of	ADP
ap-3265	373	24	2d	2d	NUM
ap-3265	373	25	nondegenerate	nondegenerate	ADJ
ap-3265	373	26	2nd	2nd	ADJ
ap-3265	373	27	order	order	NOUN
ap-3265	373	28	conformally	conformally	ADV
ap-3265	373	29	superintegrable	superintegrable	ADJ
ap-3265	373	30	systems	system	NOUN
ap-3265	373	31	and	and	CCONJ
ap-3265	373	32	their	their	PRON
ap-3265	373	33	relation	relation	NOUN
ap-3265	373	34	to	to	PART
ap-3265	373	35	bôcher	bôcher	VERB
ap-3265	373	36	contractions	contraction	NOUN
ap-3265	373	37	;	;	PUNCT
ap-3265	373	38	(	(	PUNCT
ap-3265	373	39	2	2	NUM
ap-3265	373	40	.	.	PUNCT
ap-3265	373	41	)	)	PUNCT
ap-3265	373	42	present	present	VERB
ap-3265	373	43	a	a	DET
ap-3265	373	44	detailed	detailed	ADJ
ap-3265	373	45	classification	classification	NOUN
ap-3265	373	46	of	of	ADP
ap-3265	373	47	all	all	DET
ap-3265	373	48	bôcher	bôcher	ADJ
ap-3265	373	49	contractions	contraction	NOUN
ap-3265	373	50	of	of	ADP
ap-3265	373	51	2d	2d	NUM
ap-3265	373	52	nondegenerate	nondegenerate	ADJ
ap-3265	373	53	2nd	2nd	ADJ
ap-3265	373	54	order	order	NOUN
ap-3265	373	55	conformally	conformally	ADV
ap-3265	373	56	superintegrable	superintegrable	ADJ
ap-3265	373	57	systems	system	NOUN
ap-3265	373	58	;	;	PUNCT
ap-3265	373	59	(	(	PUNCT
ap-3265	373	60	3	3	NUM
ap-3265	373	61	.	.	PUNCT
ap-3265	373	62	)	)	PUNCT
ap-3265	373	63	present	present	ADJ
ap-3265	373	64	tables	table	NOUN
ap-3265	373	65	describing	describe	VERB
ap-3265	373	66	the	the	DET
ap-3265	373	67	contractions	contraction	NOUN
ap-3265	373	68	of	of	ADP
ap-3265	373	69	nondegenerate	nondegenerate	ADJ
ap-3265	373	70	2nd	2nd	ADJ
ap-3265	373	71	order	order	NOUN
ap-3265	373	72	helmholtz	helmholtz	NOUN
ap-3265	373	73	superintegrable	superintegrable	ADJ
ap-3265	373	74	systems	system	NOUN
ap-3265	373	75	and	and	CCONJ
ap-3265	373	76	how	how	SCONJ
ap-3265	373	77	they	they	PRON
ap-3265	373	78	are	be	AUX
ap-3265	373	79	induced	induce	VERB
ap-3265	373	80	by	by	ADP
ap-3265	373	81	bôcher	bôcher	NOUN
ap-3265	373	82	contractions	contraction	NOUN
ap-3265	373	83	;	;	PUNCT
ap-3265	373	84	(	(	PUNCT
ap-3265	373	85	4	4	NUM
ap-3265	373	86	.	.	PUNCT
ap-3265	373	87	)	)	PUNCT
ap-3265	373	88	introduce	introduce	VERB
ap-3265	373	89	so(4,c	so(4,c	NOUN
ap-3265	373	90	)	)	PUNCT
ap-3265	373	91	→	→	SYM
ap-3265	373	92	e(3,c	e(3,c	ADJ
ap-3265	373	93	)	)	PUNCT
ap-3265	373	94	contractions	contraction	NOUN
ap-3265	373	95	of	of	ADP
ap-3265	373	96	laplace	laplace	NOUN
ap-3265	373	97	systems	system	NOUN
ap-3265	373	98	and	and	CCONJ
ap-3265	373	99	show	show	VERB
ap-3265	373	100	how	how	SCONJ
ap-3265	373	101	they	they	PRON
ap-3265	373	102	produce	produce	VERB
ap-3265	373	103	conformally	conformally	ADV
ap-3265	373	104	2nd	2nd	ADJ
ap-3265	373	105	order	order	NOUN
ap-3265	373	106	superintegrable	superintegrable	ADJ
ap-3265	373	107	2d	2d	NUM
ap-3265	373	108	time	time	NOUN
ap-3265	373	109	-	-	PUNCT
ap-3265	373	110	dependent	dependent	ADJ
ap-3265	373	111	schrödinger	schrödinger	ADJ
ap-3265	373	112	equations	equation	NOUN
ap-3265	373	113	.	.	PUNCT
ap-3265	374	1	from	from	ADP
ap-3265	374	2	theorem	theorem	NOUN
ap-3265	374	3	1	1	NUM
ap-3265	374	4	we	we	PRON
ap-3265	374	5	know	know	VERB
ap-3265	374	6	that	that	SCONJ
ap-3265	374	7	the	the	DET
ap-3265	374	8	potentials	potential	NOUN
ap-3265	374	9	of	of	ADP
ap-3265	374	10	all	all	DET
ap-3265	374	11	helmholtz	helmholtz	ADJ
ap-3265	374	12	superintegrable	superintegrable	ADJ
ap-3265	374	13	systems	system	NOUN
ap-3265	374	14	are	be	AUX
ap-3265	374	15	completely	completely	ADV
ap-3265	374	16	determined	determine	VERB
ap-3265	374	17	by	by	ADP
ap-3265	374	18	their	their	PRON
ap-3265	374	19	free	free	ADJ
ap-3265	374	20	quadratic	quadratic	ADJ
ap-3265	374	21	algebras	algebra	NOUN
ap-3265	374	22	,	,	PUNCT
ap-3265	374	23	i.e.	i.e.	X
ap-3265	374	24	,	,	PUNCT
ap-3265	374	25	the	the	DET
ap-3265	374	26	symmetry	symmetry	NOUN
ap-3265	374	27	algebra	algebra	NOUN
ap-3265	374	28	that	that	PRON
ap-3265	374	29	remains	remain	VERB
ap-3265	374	30	when	when	SCONJ
ap-3265	374	31	the	the	DET
ap-3265	374	32	parameters	parameter	NOUN
ap-3265	374	33	in	in	ADP
ap-3265	374	34	the	the	DET
ap-3265	374	35	potential	potential	NOUN
ap-3265	374	36	are	be	AUX
ap-3265	374	37	set	set	VERB
ap-3265	374	38	equal	equal	ADJ
ap-3265	374	39	to	to	ADP
ap-3265	374	40	0	0	NUM
ap-3265	374	41	.	.	PUNCT
ap-3265	375	1	thus	thus	ADV
ap-3265	375	2	for	for	ADP
ap-3265	375	3	classification	classification	NOUN
ap-3265	375	4	purposes	purpose	NOUN
ap-3265	375	5	it	it	PRON
ap-3265	375	6	is	be	AUX
ap-3265	375	7	enough	enough	ADJ
ap-3265	375	8	to	to	PART
ap-3265	375	9	classify	classify	VERB
ap-3265	375	10	free	free	ADJ
ap-3265	375	11	abstract	abstract	ADJ
ap-3265	375	12	quadratic	quadratic	ADJ
ap-3265	375	13	algebras	algebra	NOUN
ap-3265	375	14	.	.	PUNCT
ap-3265	376	1	in	in	ADP
ap-3265	376	2	a	a	DET
ap-3265	376	3	second	second	ADJ
ap-3265	376	4	paper	paper	NOUN
ap-3265	376	5	under	under	ADP
ap-3265	376	6	preparation	preparation	NOUN
ap-3265	376	7	we	we	PRON
ap-3265	376	8	will	will	AUX
ap-3265	376	9	:	:	PUNCT
ap-3265	376	10	(	(	PUNCT
ap-3265	376	11	1	1	X
ap-3265	376	12	.	.	PUNCT
ap-3265	376	13	)	)	PUNCT
ap-3265	376	14	apply	apply	VERB
ap-3265	376	15	the	the	DET
ap-3265	376	16	bôcher	bôcher	NOUN
ap-3265	376	17	construction	construction	NOUN
ap-3265	376	18	to	to	PART
ap-3265	376	19	degenerate	degenerate	VERB
ap-3265	376	20	221	221	NUM
ap-3265	376	21	e.	e.	PROPN
ap-3265	376	22	kalnins	kalnins	PROPN
ap-3265	376	23	,	,	PUNCT
ap-3265	376	24	w.	w.	PROPN
ap-3265	376	25	miller	miller	PROPN
ap-3265	376	26	,	,	PUNCT
ap-3265	376	27	e.	e.	PROPN
ap-3265	376	28	subag	subag	PROPN
ap-3265	376	29	acta	acta	PROPN
ap-3265	376	30	polytechnica	polytechnica	PROPN
ap-3265	376	31	(	(	PUNCT
ap-3265	376	32	1	1	NUM
ap-3265	376	33	-	-	PUNCT
ap-3265	376	34	parameter	parameter	NOUN
ap-3265	376	35	)	)	PUNCT
ap-3265	376	36	helmholtz	helmholtz	NOUN
ap-3265	376	37	superintegrable	superintegrable	ADJ
ap-3265	376	38	systems	system	NOUN
ap-3265	376	39	(	(	PUNCT
ap-3265	376	40	which	which	PRON
ap-3265	376	41	admit	admit	VERB
ap-3265	376	42	a	a	DET
ap-3265	376	43	1st	1st	ADJ
ap-3265	376	44	order	order	NOUN
ap-3265	376	45	symmetry	symmetry	NOUN
ap-3265	376	46	)	)	PUNCT
ap-3265	376	47	;	;	PUNCT
ap-3265	376	48	(	(	PUNCT
ap-3265	376	49	2	2	NUM
ap-3265	376	50	.	.	PUNCT
ap-3265	376	51	)	)	PUNCT
ap-3265	376	52	give	give	VERB
ap-3265	376	53	a	a	DET
ap-3265	376	54	classification	classification	NOUN
ap-3265	376	55	of	of	ADP
ap-3265	376	56	free	free	ADJ
ap-3265	376	57	abstract	abstract	ADJ
ap-3265	376	58	degenerate	degenerate	ADJ
ap-3265	376	59	quadratic	quadratic	ADJ
ap-3265	376	60	algebras	algebra	NOUN
ap-3265	376	61	and	and	CCONJ
ap-3265	376	62	identify	identify	VERB
ap-3265	376	63	which	which	PRON
ap-3265	376	64	of	of	ADP
ap-3265	376	65	those	those	PRON
ap-3265	376	66	correspond	correspond	VERB
ap-3265	376	67	free	free	ADJ
ap-3265	376	68	2nd	2nd	ADJ
ap-3265	376	69	order	order	NOUN
ap-3265	376	70	superintegrable	superintegrable	ADJ
ap-3265	376	71	systems	system	NOUN
ap-3265	376	72	;	;	PUNCT
ap-3265	376	73	(	(	PUNCT
ap-3265	376	74	3	3	NUM
ap-3265	376	75	.	.	PUNCT
ap-3265	376	76	)	)	PUNCT
ap-3265	376	77	classify	classify	VERB
ap-3265	376	78	abstract	abstract	ADJ
ap-3265	376	79	contractions	contraction	NOUN
ap-3265	376	80	of	of	ADP
ap-3265	376	81	degenerate	degenerate	ADJ
ap-3265	376	82	quadratic	quadratic	ADJ
ap-3265	376	83	algebras	algebra	NOUN
ap-3265	376	84	and	and	CCONJ
ap-3265	376	85	identify	identify	VERB
ap-3265	376	86	which	which	PRON
ap-3265	376	87	of	of	ADP
ap-3265	376	88	those	those	PRON
ap-3265	376	89	correspond	correspond	VERB
ap-3265	376	90	to	to	ADP
ap-3265	376	91	geometric	geometric	ADJ
ap-3265	376	92	contractions	contraction	NOUN
ap-3265	376	93	of	of	ADP
ap-3265	376	94	helmholtz	helmholtz	PROPN
ap-3265	376	95	superintegrable	superintegrable	ADJ
ap-3265	376	96	systems	system	NOUN
ap-3265	376	97	;	;	PUNCT
ap-3265	376	98	(	(	PUNCT
ap-3265	376	99	4	4	NUM
ap-3265	376	100	.	.	PUNCT
ap-3265	376	101	)	)	PUNCT
ap-3265	376	102	classify	classify	VERB
ap-3265	376	103	free	free	ADJ
ap-3265	376	104	abstract	abstract	ADJ
ap-3265	376	105	nondegenerate	nondegenerate	ADJ
ap-3265	376	106	quadratic	quadratic	ADJ
ap-3265	376	107	algebras	algebra	NOUN
ap-3265	376	108	and	and	CCONJ
ap-3265	376	109	identify	identify	VERB
ap-3265	376	110	those	those	PRON
ap-3265	376	111	corresponding	correspond	VERB
ap-3265	376	112	to	to	AUX
ap-3265	376	113	free	free	VERB
ap-3265	376	114	nondegenerate	nondegenerate	ADJ
ap-3265	376	115	helmholtz	helmholtz	NOUN
ap-3265	376	116	2nd	2nd	ADJ
ap-3265	376	117	order	order	NOUN
ap-3265	376	118	superintegrable	superintegrable	ADJ
ap-3265	376	119	systems	system	NOUN
ap-3265	376	120	;	;	PUNCT
ap-3265	376	121	(	(	PUNCT
ap-3265	376	122	5	5	NUM
ap-3265	376	123	.	.	PUNCT
ap-3265	376	124	)	)	PUNCT
ap-3265	377	1	classify	classify	VERB
ap-3265	377	2	the	the	DET
ap-3265	377	3	abstract	abstract	ADJ
ap-3265	377	4	contractions	contraction	NOUN
ap-3265	377	5	of	of	ADP
ap-3265	377	6	nondegenerate	nondegenerate	ADJ
ap-3265	377	7	quadratic	quadratic	ADJ
ap-3265	377	8	algebras	algebra	NOUN
ap-3265	377	9	.	.	PUNCT
ap-3265	378	1	we	we	PRON
ap-3265	378	2	note	note	VERB
ap-3265	378	3	that	that	SCONJ
ap-3265	378	4	by	by	ADP
ap-3265	378	5	taking	take	VERB
ap-3265	378	6	contractions	contraction	NOUN
ap-3265	378	7	step	step	NOUN
ap-3265	378	8	-	-	PUNCT
ap-3265	378	9	by	by	ADP
ap-3265	378	10	-	-	PUNCT
ap-3265	378	11	step	step	NOUN
ap-3265	378	12	from	from	ADP
ap-3265	378	13	a	a	DET
ap-3265	378	14	model	model	NOUN
ap-3265	378	15	of	of	ADP
ap-3265	378	16	the	the	DET
ap-3265	378	17	s9	s9	ADJ
ap-3265	378	18	quadratic	quadratic	ADJ
ap-3265	378	19	algebra	algebra	NOUN
ap-3265	378	20	we	we	PRON
ap-3265	378	21	can	can	AUX
ap-3265	378	22	recover	recover	VERB
ap-3265	378	23	the	the	DET
ap-3265	378	24	askey	askey	ADJ
ap-3265	378	25	scheme	scheme	NOUN
ap-3265	378	26	[	[	X
ap-3265	378	27	25	25	NUM
ap-3265	378	28	]	]	PUNCT
ap-3265	378	29	.	.	PUNCT
ap-3265	379	1	however	however	ADV
ap-3265	379	2	,	,	PUNCT
ap-3265	379	3	the	the	DET
ap-3265	379	4	contraction	contraction	NOUN
ap-3265	379	5	method	method	NOUN
ap-3265	379	6	is	be	AUX
ap-3265	379	7	more	more	ADV
ap-3265	379	8	general	general	ADJ
ap-3265	379	9	.	.	PUNCT
ap-3265	380	1	it	it	PRON
ap-3265	380	2	applies	apply	VERB
ap-3265	380	3	to	to	ADP
ap-3265	380	4	all	all	DET
ap-3265	380	5	special	special	ADJ
ap-3265	380	6	functions	function	NOUN
ap-3265	380	7	that	that	PRON
ap-3265	380	8	arise	arise	VERB
ap-3265	380	9	from	from	ADP
ap-3265	380	10	the	the	DET
ap-3265	380	11	quantum	quantum	NOUN
ap-3265	380	12	systems	system	NOUN
ap-3265	380	13	via	via	ADP
ap-3265	380	14	separation	separation	NOUN
ap-3265	380	15	of	of	ADP
ap-3265	380	16	variables	variable	NOUN
ap-3265	380	17	,	,	PUNCT
ap-3265	380	18	not	not	PART
ap-3265	380	19	just	just	ADV
ap-3265	380	20	polynomials	polynomial	NOUN
ap-3265	380	21	of	of	ADP
ap-3265	380	22	hypergeometric	hypergeometric	ADJ
ap-3265	380	23	type	type	NOUN
ap-3265	380	24	,	,	PUNCT
ap-3265	380	25	and	and	CCONJ
ap-3265	380	26	it	it	PRON
ap-3265	380	27	extends	extend	VERB
ap-3265	380	28	to	to	ADP
ap-3265	380	29	higher	high	ADJ
ap-3265	380	30	dimensions	dimension	NOUN
ap-3265	380	31	.	.	PUNCT
ap-3265	381	1	the	the	DET
ap-3265	381	2	functions	function	NOUN
ap-3265	381	3	in	in	ADP
ap-3265	381	4	the	the	DET
ap-3265	381	5	askey	askey	ADJ
ap-3265	381	6	scheme	scheme	NOUN
ap-3265	381	7	are	be	AUX
ap-3265	381	8	just	just	ADV
ap-3265	381	9	those	those	DET
ap-3265	381	10	hypergeometric	hypergeometric	ADJ
ap-3265	381	11	polynomials	polynomial	NOUN
ap-3265	381	12	that	that	PRON
ap-3265	381	13	arise	arise	VERB
ap-3265	381	14	as	as	ADP
ap-3265	381	15	the	the	DET
ap-3265	381	16	expansion	expansion	NOUN
ap-3265	381	17	coefficients	coefficient	NOUN
ap-3265	381	18	relating	relate	VERB
ap-3265	381	19	two	two	NUM
ap-3265	381	20	separable	separable	ADJ
ap-3265	381	21	eigenbases	eigenbase	NOUN
ap-3265	381	22	that	that	PRON
ap-3265	381	23	are	be	AUX
ap-3265	381	24	both	both	PRON
ap-3265	381	25	of	of	ADP
ap-3265	381	26	hypergeometric	hypergeometric	ADJ
ap-3265	381	27	type	type	NOUN
ap-3265	381	28	.	.	PUNCT
ap-3265	382	1	thus	thus	ADV
ap-3265	382	2	,	,	PUNCT
ap-3265	382	3	there	there	PRON
ap-3265	382	4	are	be	VERB
ap-3265	382	5	some	some	DET
ap-3265	382	6	contractions	contraction	NOUN
ap-3265	382	7	which	which	PRON
ap-3265	382	8	do	do	AUX
ap-3265	382	9	not	not	PART
ap-3265	382	10	fit	fit	VERB
ap-3265	382	11	in	in	ADP
ap-3265	382	12	the	the	DET
ap-3265	382	13	askey	askey	ADJ
ap-3265	382	14	scheme	scheme	NOUN
ap-3265	382	15	since	since	SCONJ
ap-3265	382	16	the	the	DET
ap-3265	382	17	physical	physical	ADJ
ap-3265	382	18	system	system	NOUN
ap-3265	382	19	fails	fail	VERB
ap-3265	382	20	to	to	PART
ap-3265	382	21	have	have	VERB
ap-3265	382	22	such	such	DET
ap-3265	382	23	a	a	DET
ap-3265	382	24	pair	pair	NOUN
ap-3265	382	25	of	of	ADP
ap-3265	382	26	separable	separable	ADJ
ap-3265	382	27	eigenbases	eigenbase	NOUN
ap-3265	382	28	.	.	PUNCT
ap-3265	383	1	in	in	ADP
ap-3265	383	2	a	a	DET
ap-3265	383	3	third	third	ADJ
ap-3265	383	4	paper	paper	NOUN
ap-3265	383	5	under	under	ADP
ap-3265	383	6	preparation	preparation	NOUN
ap-3265	383	7	we	we	PRON
ap-3265	383	8	will	will	AUX
ap-3265	383	9	analyze	analyze	VERB
ap-3265	383	10	the	the	DET
ap-3265	383	11	laplace	laplace	NOUN
ap-3265	383	12	2nd	2nd	ADJ
ap-3265	383	13	order	order	NOUN
ap-3265	383	14	conformally	conformally	ADV
ap-3265	383	15	superintegrable	superintegrable	ADJ
ap-3265	383	16	systems	system	NOUN
ap-3265	383	17	,	,	PUNCT
ap-3265	383	18	determine	determine	VERB
ap-3265	383	19	which	which	PRON
ap-3265	383	20	of	of	ADP
ap-3265	383	21	them	they	PRON
ap-3265	383	22	is	be	AUX
ap-3265	383	23	exactly	exactly	ADV
ap-3265	383	24	solvable	solvable	ADJ
ap-3265	383	25	or	or	CCONJ
ap-3265	383	26	quasi	quasi	ADJ
ap-3265	383	27	-	-	ADJ
ap-3265	383	28	exactly	exactly	ADV
ap-3265	383	29	solvable	solvable	ADJ
ap-3265	383	30	and	and	CCONJ
ap-3265	383	31	identify	identify	VERB
ap-3265	383	32	the	the	DET
ap-3265	383	33	spaces	space	NOUN
ap-3265	383	34	of	of	ADP
ap-3265	383	35	polynomials	polynomial	NOUN
ap-3265	383	36	that	that	PRON
ap-3265	383	37	arise	arise	VERB
ap-3265	383	38	.	.	PUNCT
ap-3265	384	1	again	again	ADV
ap-3265	384	2	,	,	PUNCT
ap-3265	384	3	multiple	multiple	ADJ
ap-3265	384	4	helmholtz	helmholtz	NOUN
ap-3265	384	5	superintegrable	superintegrable	ADJ
ap-3265	384	6	systems	system	NOUN
ap-3265	384	7	will	will	AUX
ap-3265	384	8	correspond	correspond	VERB
ap-3265	384	9	to	to	ADP
ap-3265	384	10	a	a	DET
ap-3265	384	11	single	single	ADJ
ap-3265	384	12	laplace	laplace	NOUN
ap-3265	384	13	system	system	NOUN
ap-3265	384	14	.	.	PUNCT
ap-3265	385	1	this	this	PRON
ap-3265	385	2	will	will	AUX
ap-3265	385	3	enable	enable	VERB
ap-3265	385	4	us	we	PRON
ap-3265	385	5	to	to	PART
ap-3265	385	6	apply	apply	VERB
ap-3265	385	7	our	our	PRON
ap-3265	385	8	results	result	NOUN
ap-3265	385	9	to	to	PART
ap-3265	385	10	characterize	characterize	VERB
ap-3265	385	11	polynomial	polynomial	ADJ
ap-3265	385	12	eigenfunctions	eigenfunction	NOUN
ap-3265	385	13	not	not	PART
ap-3265	385	14	of	of	ADP
ap-3265	385	15	askey	askey	ADJ
ap-3265	385	16	type	type	NOUN
ap-3265	385	17	and	and	CCONJ
ap-3265	385	18	their	their	PRON
ap-3265	385	19	limits	limit	NOUN
ap-3265	385	20	.	.	PUNCT
ap-3265	386	1	acknowledgements	acknowledgement	NOUN
ap-3265	386	2	this	this	DET
ap-3265	386	3	work	work	NOUN
ap-3265	386	4	was	be	AUX
ap-3265	386	5	partially	partially	ADV
ap-3265	386	6	supported	support	VERB
ap-3265	386	7	by	by	ADP
ap-3265	386	8	a	a	DET
ap-3265	386	9	grant	grant	NOUN
ap-3265	386	10	from	from	ADP
ap-3265	386	11	the	the	DET
ap-3265	386	12	simons	simons	PROPN
ap-3265	386	13	foundation	foundation	PROPN
ap-3265	386	14	(	(	PUNCT
ap-3265	386	15	#	#	NOUN
ap-3265	386	16	208754	208754	NUM
ap-3265	386	17	to	to	ADP
ap-3265	386	18	willard	willard	PROPN
ap-3265	386	19	miller	miller	PROPN
ap-3265	386	20	,	,	PUNCT
ap-3265	386	21	jr	jr	PROPN
ap-3265	386	22	)	)	PUNCT
ap-3265	386	23	.	.	PUNCT
ap-3265	387	1	references	reference	NOUN
ap-3265	387	2	[	[	X
ap-3265	387	3	1	1	X
ap-3265	387	4	]	]	X
ap-3265	387	5	evans	evans	PROPN
ap-3265	387	6	n.w	n.w	PROPN
ap-3265	387	7	.	.	PROPN
ap-3265	387	8	,	,	PUNCT
ap-3265	387	9	super	super	NOUN
ap-3265	387	10	-	-	NOUN
ap-3265	387	11	integrability	integrability	NOUN
ap-3265	387	12	of	of	ADP
ap-3265	387	13	the	the	DET
ap-3265	387	14	winternitz	winternitz	NOUN
ap-3265	387	15	system	system	NOUN
ap-3265	387	16	;	;	PUNCT
ap-3265	387	17	phys	phy	NOUN
ap-3265	387	18	.	.	PUNCT
ap-3265	388	1	lett	lett	PROPN
ap-3265	388	2	.	.	PUNCT
ap-3265	389	1	v.a	v.a	PROPN
ap-3265	389	2	147	147	NUM
ap-3265	389	3	,	,	PUNCT
ap-3265	389	4	483–486	483–486	NUM
ap-3265	389	5	,	,	PUNCT
ap-3265	389	6	(	(	PUNCT
ap-3265	389	7	1990	1990	NUM
ap-3265	389	8	)	)	PUNCT
ap-3265	389	9	,	,	PUNCT
ap-3265	389	10	doi:10.1016/0375	doi:10.1016/0375	VERB
ap-3265	389	11	-	-	PUNCT
ap-3265	389	12	9601(90)90611	9601(90)90611	NOUN
ap-3265	389	13	-	-	PUNCT
ap-3265	389	14	q	q	NOUN
ap-3265	390	1	[	[	X
ap-3265	390	2	2	2	NUM
ap-3265	390	3	]	]	X
ap-3265	390	4	tempesta	tempesta	PROPN
ap-3265	390	5	p.	p.	PROPN
ap-3265	390	6	,	,	PUNCT
ap-3265	390	7	turbiner	turbiner	NOUN
ap-3265	390	8	a.	a.	NOUN
ap-3265	390	9	and	and	CCONJ
ap-3265	390	10	winternitz	winternitz	PROPN
ap-3265	390	11	p.	p.	PROPN
ap-3265	390	12	,	,	PUNCT
ap-3265	390	13	exact	exact	ADJ
ap-3265	390	14	solvability	solvability	NOUN
ap-3265	390	15	of	of	ADP
ap-3265	390	16	superintegrable	superintegrable	ADJ
ap-3265	390	17	systems	system	NOUN
ap-3265	390	18	,	,	PUNCT
ap-3265	390	19	j.	j.	PROPN
ap-3265	390	20	math	math	PROPN
ap-3265	390	21	.	.	PUNCT
ap-3265	391	1	phys	phy	NOUN
ap-3265	391	2	.	.	PUNCT
ap-3265	391	3	,	,	PUNCT
ap-3265	391	4	42	42	NUM
ap-3265	391	5	,	,	PUNCT
ap-3265	391	6	4248–4257	4248–4257	NUM
ap-3265	391	7	(	(	PUNCT
ap-3265	391	8	2001	2001	NUM
ap-3265	391	9	)	)	PUNCT
ap-3265	391	10	,	,	PUNCT
ap-3265	391	11	doi:10.1063/1.1386927	doi:10.1063/1.1386927	PROPN
ap-3265	391	12	[	[	X
ap-3265	391	13	3	3	X
ap-3265	391	14	]	]	PUNCT
ap-3265	391	15	superintegrability	superintegrability	NOUN
ap-3265	391	16	in	in	ADP
ap-3265	391	17	classical	classical	ADJ
ap-3265	391	18	and	and	CCONJ
ap-3265	391	19	quantum	quantum	NOUN
ap-3265	391	20	systems	system	NOUN
ap-3265	391	21	,	,	PUNCT
ap-3265	391	22	tempesta	tempesta	PROPN
ap-3265	391	23	p.	p.	PROPN
ap-3265	391	24	,	,	PUNCT
ap-3265	391	25	winternitz	winternitz	PROPN
ap-3265	391	26	p.	p.	PROPN
ap-3265	391	27	,	,	PUNCT
ap-3265	391	28	miller	miller	PROPN
ap-3265	391	29	w.	w.	PROPN
ap-3265	391	30	,	,	PUNCT
ap-3265	391	31	pogosyan	pogosyan	PROPN
ap-3265	391	32	g.	g.	PROPN
ap-3265	391	33	,	,	PUNCT
ap-3265	391	34	editors	editor	NOUN
ap-3265	391	35	,	,	PUNCT
ap-3265	391	36	ams	am	NOUN
ap-3265	391	37	,	,	PUNCT
ap-3265	391	38	vol	vol	NOUN
ap-3265	391	39	.	.	PROPN
ap-3265	391	40	37	37	NUM
ap-3265	391	41	,	,	PUNCT
ap-3265	391	42	2005	2005	NUM
ap-3265	391	43	,	,	PUNCT
ap-3265	391	44	isbn-10	isbn-10	PROPN
ap-3265	391	45	:	:	PUNCT
ap-3265	391	46	0	0	NUM
ap-3265	391	47	-	-	PUNCT
ap-3265	391	48	8218	8218	NUM
ap-3265	391	49	-	-	PUNCT
ap-3265	391	50	3329	3329	NUM
ap-3265	391	51	-	-	SYM
ap-3265	391	52	4	4	NUM
ap-3265	391	53	,	,	PUNCT
ap-3265	391	54	isbn-13	isbn-13	PROPN
ap-3265	391	55	:	:	PUNCT
ap-3265	391	56	978	978	NUM
ap-3265	391	57	-	-	SYM
ap-3265	391	58	0	0	NUM
ap-3265	391	59	-	-	PUNCT
ap-3265	391	60	8218	8218	NUM
ap-3265	391	61	-	-	PUNCT
ap-3265	391	62	3329	3329	NUM
ap-3265	391	63	-	-	SYM
ap-3265	391	64	2	2	NUM
ap-3265	392	1	[	[	SYM
ap-3265	392	2	4	4	NUM
ap-3265	392	3	]	]	X
ap-3265	392	4	fordy	fordy	ADJ
ap-3265	392	5	a.	a.	NOUN
ap-3265	392	6	p.	p.	PROPN
ap-3265	392	7	,	,	PUNCT
ap-3265	392	8	quantum	quantum	ADJ
ap-3265	392	9	super	super	ADJ
ap-3265	392	10	-	-	ADJ
ap-3265	392	11	integrable	integrable	ADJ
ap-3265	392	12	systems	system	NOUN
ap-3265	392	13	as	as	ADP
ap-3265	392	14	exactly	exactly	ADV
ap-3265	392	15	solvable	solvable	ADJ
ap-3265	392	16	models	model	NOUN
ap-3265	392	17	,	,	PUNCT
ap-3265	392	18	sigma	sigma	PROPN
ap-3265	392	19	3	3	NUM
ap-3265	392	20	025	025	NUM
ap-3265	392	21	,	,	PUNCT
ap-3265	392	22	(	(	PUNCT
ap-3265	392	23	2007	2007	NUM
ap-3265	392	24	)	)	PUNCT
ap-3265	392	25	,	,	PUNCT
ap-3265	392	26	doi:10.3842	doi:10.3842	NOUN
ap-3265	392	27	/	/	SYM
ap-3265	393	1	sigma.2007.025	sigma.2007.025	NOUN
ap-3265	393	2	[	[	X
ap-3265	393	3	5	5	NUM
ap-3265	393	4	]	]	X
ap-3265	393	5	miller	miller	PROPN
ap-3265	393	6	w.	w.	PROPN
ap-3265	393	7	jr	jr	PROPN
ap-3265	393	8	.	.	PROPN
ap-3265	393	9	,	,	PUNCT
ap-3265	393	10	post	post	VERB
ap-3265	393	11	s.	s.	PROPN
ap-3265	393	12	and	and	CCONJ
ap-3265	393	13	winternitz	winternitz	PROPN
ap-3265	393	14	p	p	X
ap-3265	393	15	..	..	PUNCT
ap-3265	393	16	classical	classical	ADJ
ap-3265	393	17	and	and	CCONJ
ap-3265	393	18	quantum	quantum	ADJ
ap-3265	393	19	superintegrability	superintegrability	NOUN
ap-3265	393	20	with	with	ADP
ap-3265	393	21	applications	application	NOUN
ap-3265	393	22	,	,	PUNCT
ap-3265	393	23	j.	j.	PROPN
ap-3265	393	24	phys	phys	PROPN
ap-3265	393	25	.	.	PUNCT
ap-3265	394	1	a	a	DET
ap-3265	394	2	:	:	PUNCT
ap-3265	394	3	math	math	NOUN
ap-3265	394	4	.	.	PUNCT
ap-3265	395	1	theor	theor	PROPN
ap-3265	395	2	.	.	PROPN
ap-3265	395	3	,	,	PUNCT
ap-3265	395	4	46	46	NUM
ap-3265	395	5	,	,	PUNCT
ap-3265	395	6	423001	423001	NUM
ap-3265	395	7	,	,	PUNCT
ap-3265	395	8	(	(	PUNCT
ap-3265	395	9	2013	2013	NUM
ap-3265	395	10	)	)	PUNCT
ap-3265	396	1	[	[	X
ap-3265	396	2	6	6	NUM
ap-3265	396	3	]	]	PUNCT
ap-3265	396	4	kalnins	kalnin	NOUN
ap-3265	396	5	e.	e.	PROPN
ap-3265	396	6	g.	g.	PROPN
ap-3265	396	7	,	,	PUNCT
ap-3265	396	8	kress	kress	PROPN
ap-3265	396	9	j	j	PROPN
ap-3265	396	10	.m	.m	PROPN
ap-3265	396	11	,	,	PUNCT
ap-3265	396	12	and	and	CCONJ
ap-3265	396	13	miller	miller	PROPN
ap-3265	396	14	w.	w.	PROPN
ap-3265	396	15	jr	jr	PROPN
ap-3265	396	16	.	.	PROPN
ap-3265	396	17	,	,	PUNCT
ap-3265	396	18	second	second	ADJ
ap-3265	396	19	order	order	NOUN
ap-3265	396	20	superintegrable	superintegrable	ADJ
ap-3265	396	21	systems	system	NOUN
ap-3265	396	22	in	in	ADP
ap-3265	396	23	conformally	conformally	ADV
ap-3265	396	24	flat	flat	ADJ
ap-3265	396	25	spaces	space	NOUN
ap-3265	396	26	.	.	PUNCT
ap-3265	397	1	i	i	PRON
ap-3265	397	2	:	:	PUNCT
ap-3265	397	3	2d	2d	NUM
ap-3265	397	4	classical	classical	ADJ
ap-3265	397	5	structure	structure	NOUN
ap-3265	397	6	theory	theory	NOUN
ap-3265	397	7	.	.	PUNCT
ap-3265	398	1	j.	j.	PROPN
ap-3265	398	2	math	math	PROPN
ap-3265	398	3	.	.	PUNCT
ap-3265	399	1	phys	phy	NOUN
ap-3265	399	2	.	.	PUNCT
ap-3265	399	3	,	,	PUNCT
ap-3265	399	4	46	46	NUM
ap-3265	399	5	,	,	PUNCT
ap-3265	399	6	053509	053509	NUM
ap-3265	399	7	,	,	PUNCT
ap-3265	399	8	(	(	PUNCT
ap-3265	399	9	2005	2005	NUM
ap-3265	399	10	)	)	PUNCT
ap-3265	399	11	;	;	PUNCT
ap-3265	400	1	ii	ii	X
ap-3265	400	2	:	:	PUNCT
ap-3265	400	3	the	the	DET
ap-3265	400	4	classical	classical	ADJ
ap-3265	400	5	2d	2d	NUM
ap-3265	400	6	stäckel	stäckel	NOUN
ap-3265	400	7	transform	transform	NOUN
ap-3265	400	8	.	.	PUNCT
ap-3265	401	1	j.	j.	PROPN
ap-3265	401	2	math	math	PROPN
ap-3265	401	3	.	.	PUNCT
ap-3265	402	1	phys	phy	NOUN
ap-3265	402	2	.	.	PUNCT
ap-3265	402	3	,	,	PUNCT
ap-3265	402	4	46	46	NUM
ap-3265	402	5	,	,	PUNCT
ap-3265	402	6	053510	053510	NUM
ap-3265	402	7	,	,	PUNCT
ap-3265	402	8	(	(	PUNCT
ap-3265	402	9	2005	2005	NUM
ap-3265	402	10	)	)	PUNCT
ap-3265	402	11	;	;	PUNCT
ap-3265	402	12	iii	iii	X
ap-3265	402	13	.	.	PUNCT
ap-3265	402	14	3d	3d	ADJ
ap-3265	402	15	classical	classical	ADJ
ap-3265	402	16	structure	structure	NOUN
ap-3265	402	17	theory	theory	NOUN
ap-3265	402	18	,	,	PUNCT
ap-3265	402	19	j.	j.	PROPN
ap-3265	402	20	math	math	PROPN
ap-3265	402	21	.	.	PUNCT
ap-3265	403	1	phys	phy	NOUN
ap-3265	403	2	.	.	PUNCT
ap-3265	403	3	,	,	PUNCT
ap-3265	403	4	46	46	NUM
ap-3265	403	5	,	,	PUNCT
ap-3265	403	6	103507	103507	NUM
ap-3265	403	7	,	,	PUNCT
ap-3265	403	8	(	(	PUNCT
ap-3265	403	9	2005	2005	NUM
ap-3265	403	10	)	)	PUNCT
ap-3265	403	11	,	,	PUNCT
ap-3265	403	12	iv	iv	X
ap-3265	403	13	.	.	PUNCT
ap-3265	404	1	the	the	DET
ap-3265	404	2	classical	classical	ADJ
ap-3265	404	3	3d	3d	NUM
ap-3265	404	4	stäckel	stäckel	NOUN
ap-3265	404	5	transform	transform	NOUN
ap-3265	404	6	and	and	CCONJ
ap-3265	404	7	3d	3d	NUM
ap-3265	404	8	classification	classification	NOUN
ap-3265	404	9	theory	theory	NOUN
ap-3265	404	10	„	„	PUNCT
ap-3265	404	11	j.	j.	PROPN
ap-3265	404	12	math	math	PROPN
ap-3265	404	13	.	.	PUNCT
ap-3265	405	1	phys	phy	NOUN
ap-3265	405	2	.	.	PUNCT
ap-3265	405	3	,	,	PUNCT
ap-3265	405	4	47	47	NUM
ap-3265	405	5	,	,	PUNCT
ap-3265	405	6	043514	043514	NUM
ap-3265	405	7	,	,	PUNCT
ap-3265	405	8	(	(	PUNCT
ap-3265	405	9	2006	2006	NUM
ap-3265	405	10	)	)	PUNCT
ap-3265	405	11	;	;	PUNCT
ap-3265	405	12	v	v	X
ap-3265	405	13	:	:	PUNCT
ap-3265	405	14	2d	2d	NUM
ap-3265	405	15	and	and	CCONJ
ap-3265	405	16	3d	3d	NUM
ap-3265	405	17	quantum	quantum	NOUN
ap-3265	405	18	systems	system	NOUN
ap-3265	405	19	.	.	PUNCT
ap-3265	406	1	j.	j.	PROPN
ap-3265	406	2	math	math	PROPN
ap-3265	406	3	.	.	PUNCT
ap-3265	407	1	phys	phy	NOUN
ap-3265	407	2	.	.	PUNCT
ap-3265	407	3	,	,	PUNCT
ap-3265	407	4	47	47	NUM
ap-3265	407	5	,	,	PUNCT
ap-3265	407	6	09350	09350	NUM
ap-3265	407	7	,	,	PUNCT
ap-3265	407	8	(	(	PUNCT
ap-3265	407	9	2006	2006	NUM
ap-3265	407	10	)	)	PUNCT
ap-3265	407	11	;	;	PUNCT
ap-3265	407	12	nondegenerate	nondegenerate	PROPN
ap-3265	407	13	2d	2d	NUM
ap-3265	407	14	complex	complex	ADJ
ap-3265	407	15	euclidean	euclidean	ADJ
ap-3265	407	16	superintegrable	superintegrable	ADJ
ap-3265	407	17	systems	system	NOUN
ap-3265	407	18	and	and	CCONJ
ap-3265	407	19	algebraic	algebraic	ADJ
ap-3265	407	20	varieties	variety	NOUN
ap-3265	407	21	,	,	PUNCT
ap-3265	407	22	j.	j.	PROPN
ap-3265	407	23	phys	phys	PROPN
ap-3265	407	24	.	.	PUNCT
ap-3265	408	1	a	a	DET
ap-3265	408	2	:	:	PUNCT
ap-3265	408	3	math	math	NOUN
ap-3265	408	4	.	.	PUNCT
ap-3265	409	1	theor	theor	PROPN
ap-3265	409	2	.	.	PROPN
ap-3265	409	3	,	,	PUNCT
ap-3265	409	4	40	40	NUM
ap-3265	409	5	,	,	PUNCT
ap-3265	409	6	3399	3399	NUM
ap-3265	409	7	-	-	SYM
ap-3265	409	8	3411	3411	NUM
ap-3265	409	9	,	,	PUNCT
ap-3265	409	10	(	(	PUNCT
ap-3265	409	11	2007	2007	NUM
ap-3265	409	12	)	)	PUNCT
ap-3265	409	13	,	,	PUNCT
ap-3265	409	14	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-3265	409	15	-	-	PUNCT
ap-3265	409	16	8113/40/13/008	8113/40/13/008	NOUN
ap-3265	409	17	[	[	X
ap-3265	409	18	7	7	NUM
ap-3265	409	19	]	]	PUNCT
ap-3265	409	20	daskaloyannis	daskaloyannis	NOUN
ap-3265	409	21	c.	c.	NOUN
ap-3265	409	22	and	and	CCONJ
ap-3265	409	23	tanoudis	tanoudis	PROPN
ap-3265	409	24	y.	y.	NOUN
ap-3265	409	25	,	,	PUNCT
ap-3265	409	26	quantum	quantum	ADJ
ap-3265	409	27	superintegrable	superintegrable	ADJ
ap-3265	409	28	systems	system	NOUN
ap-3265	409	29	with	with	ADP
ap-3265	409	30	quadratic	quadratic	ADJ
ap-3265	409	31	integrals	integral	NOUN
ap-3265	409	32	on	on	ADP
ap-3265	409	33	a	a	DET
ap-3265	409	34	two	two	NUM
ap-3265	409	35	dimensional	dimensional	ADJ
ap-3265	409	36	manifold	manifold	NOUN
ap-3265	409	37	.	.	PUNCT
ap-3265	410	1	j.	j.	PROPN
ap-3265	410	2	math	math	PROPN
ap-3265	410	3	phys	phys	PROPN
ap-3265	410	4	.	.	PUNCT
ap-3265	410	5	,	,	PUNCT
ap-3265	410	6	48	48	NUM
ap-3265	410	7	,	,	PUNCT
ap-3265	410	8	072108	072108	NUM
ap-3265	410	9	(	(	PUNCT
ap-3265	410	10	2007	2007	NUM
ap-3265	410	11	)	)	PUNCT
ap-3265	410	12	.	.	PUNCT
ap-3265	411	1	[	[	X
ap-3265	411	2	8	8	NUM
ap-3265	411	3	]	]	X
ap-3265	411	4	koenigs	koenig	NOUN
ap-3265	411	5	,	,	PUNCT
ap-3265	411	6	g.	g.	PROPN
ap-3265	411	7	,	,	PUNCT
ap-3265	411	8	sur	sur	PROPN
ap-3265	411	9	les	les	PROPN
ap-3265	411	10	géodésiques	géodésique	VERB
ap-3265	411	11	a	a	DET
ap-3265	411	12	intégrales	intégrale	NOUN
ap-3265	411	13	quadratiques	quadratique	NOUN
ap-3265	411	14	.	.	PUNCT
ap-3265	412	1	a	a	DET
ap-3265	412	2	note	note	NOUN
ap-3265	412	3	appearing	appear	VERB
ap-3265	412	4	in	in	ADP
ap-3265	412	5	“	"	PUNCT
ap-3265	412	6	lecons	lecon	NOUN
ap-3265	412	7	sur	sur	PROPN
ap-3265	412	8	la	la	PROPN
ap-3265	412	9	théorie	théorie	PROPN
ap-3265	412	10	générale	générale	PROPN
ap-3265	412	11	des	des	PROPN
ap-3265	412	12	surfaces	surface	NOUN
ap-3265	412	13	”	"	PUNCT
ap-3265	412	14	.	.	PUNCT
ap-3265	413	1	g.	g.	PROPN
ap-3265	413	2	darboux	darboux	VERB
ap-3265	413	3	.	.	PUNCT
ap-3265	414	1	vol	vol	NOUN
ap-3265	414	2	4	4	NUM
ap-3265	414	3	,	,	PUNCT
ap-3265	414	4	368	368	NUM
ap-3265	414	5	-	-	SYM
ap-3265	414	6	404	404	NUM
ap-3265	414	7	,	,	PUNCT
ap-3265	414	8	1896	1896	NUM
ap-3265	414	9	,	,	PUNCT
ap-3265	414	10	chelsea	chelsea	PROPN
ap-3265	414	11	publishing	publish	VERB
ap-3265	414	12	1972	1972	NUM
ap-3265	414	13	.	.	PUNCT
ap-3265	415	1	[	[	X
ap-3265	415	2	9	9	NUM
ap-3265	415	3	]	]	PUNCT
ap-3265	415	4	kalnins	kalnin	NOUN
ap-3265	415	5	e.	e.	PROPN
ap-3265	415	6	g.	g.	PROPN
ap-3265	415	7	,	,	PUNCT
ap-3265	415	8	kress	kress	PROPN
ap-3265	415	9	j.	j.	PROPN
ap-3265	415	10	m.	m.	PROPN
ap-3265	415	11	,	,	PUNCT
ap-3265	415	12	miller	miller	PROPN
ap-3265	415	13	w.	w.	PROPN
ap-3265	415	14	jr	jr	PROPN
ap-3265	415	15	.	.	PROPN
ap-3265	415	16	and	and	CCONJ
ap-3265	415	17	winternitz	winternitz	PROPN
ap-3265	415	18	p.	p.	PROPN
ap-3265	415	19	,	,	PUNCT
ap-3265	415	20	superintegrable	superintegrable	ADJ
ap-3265	415	21	systems	system	NOUN
ap-3265	415	22	in	in	ADP
ap-3265	415	23	darboux	darboux	ADJ
ap-3265	415	24	spaces	space	NOUN
ap-3265	415	25	.	.	PUNCT
ap-3265	416	1	j.	j.	PROPN
ap-3265	416	2	math	math	PROPN
ap-3265	416	3	.	.	PUNCT
ap-3265	417	1	phys	phy	NOUN
ap-3265	417	2	.	.	PUNCT
ap-3265	417	3	,	,	PUNCT
ap-3265	417	4	v.44	v.44	PROPN
ap-3265	417	5	,	,	PUNCT
ap-3265	417	6	5811–5848	5811–5848	NUM
ap-3265	417	7	,	,	PUNCT
ap-3265	417	8	(	(	PUNCT
ap-3265	417	9	2003	2003	NUM
ap-3265	417	10	)	)	PUNCT
ap-3265	417	11	,	,	PUNCT
ap-3265	417	12	doi:10.1063/1.1619580	doi:10.1063/1.1619580	NOUN
ap-3265	417	13	[	[	X
ap-3265	417	14	10	10	NUM
ap-3265	417	15	]	]	PUNCT
ap-3265	417	16	granovskii	granovskii	PROPN
ap-3265	417	17	ya	ya	PROPN
ap-3265	417	18	.	.	PROPN
ap-3265	417	19	i.	i.	PROPN
ap-3265	417	20	,	,	PUNCT
ap-3265	417	21	zhedanov	zhedanov	PROPN
ap-3265	417	22	a.	a.	PROPN
ap-3265	417	23	s.	s.	PROPN
ap-3265	417	24	,	,	PUNCT
ap-3265	417	25	and	and	CCONJ
ap-3265	417	26	lutsenko	lutsenko	PROPN
ap-3265	417	27	i.	i.	PROPN
ap-3265	417	28	m.	m.	PROPN
ap-3265	417	29	,	,	PUNCT
ap-3265	417	30	quadratic	quadratic	ADJ
ap-3265	417	31	algebras	algebra	NOUN
ap-3265	417	32	and	and	CCONJ
ap-3265	417	33	dynamics	dynamic	NOUN
ap-3265	417	34	in	in	ADP
ap-3265	417	35	curved	curved	ADJ
ap-3265	417	36	spaces	space	NOUN
ap-3265	417	37	.	.	PUNCT
ap-3265	418	1	i.	i.	PROPN
ap-3265	418	2	oscillator	oscillator	PROPN
ap-3265	418	3	,	,	PUNCT
ap-3265	418	4	theoret	theoret	ADJ
ap-3265	418	5	.	.	PUNCT
ap-3265	418	6	and	and	CCONJ
ap-3265	418	7	math	math	NOUN
ap-3265	418	8	.	.	PUNCT
ap-3265	419	1	phys	phy	NOUN
ap-3265	419	2	.	.	PUNCT
ap-3265	419	3	,	,	PUNCT
ap-3265	419	4	1992	1992	NUM
ap-3265	419	5	,	,	PUNCT
ap-3265	419	6	91	91	NUM
ap-3265	419	7	,	,	PUNCT
ap-3265	419	8	474	474	NUM
ap-3265	419	9	-	-	SYM
ap-3265	419	10	480	480	NUM
ap-3265	419	11	,	,	PUNCT
ap-3265	419	12	doi:10.1007	doi:10.1007	NOUN
ap-3265	419	13	/	/	SYM
ap-3265	419	14	bf01018846	bf01018846	ADJ
ap-3265	419	15	;	;	PUNCT
ap-3265	419	16	quadratic	quadratic	ADJ
ap-3265	419	17	algebras	algebra	NOUN
ap-3265	419	18	and	and	CCONJ
ap-3265	419	19	dynamics	dynamic	NOUN
ap-3265	419	20	in	in	ADP
ap-3265	419	21	curved	curved	ADJ
ap-3265	419	22	spaces	space	NOUN
ap-3265	419	23	.	.	PUNCT
ap-3265	420	1	ii	ii	PROPN
ap-3265	420	2	.	.	PUNCT
ap-3265	421	1	the	the	DET
ap-3265	421	2	kepler	kepler	PROPN
ap-3265	421	3	problem	problem	NOUN
ap-3265	421	4	,	,	PUNCT
ap-3265	421	5	theoret	theoret	ADJ
ap-3265	421	6	.	.	PUNCT
ap-3265	421	7	and	and	CCONJ
ap-3265	421	8	math	math	NOUN
ap-3265	421	9	.	.	PUNCT
ap-3265	422	1	phys	phy	NOUN
ap-3265	422	2	.	.	PUNCT
ap-3265	422	3	,	,	PUNCT
ap-3265	422	4	91	91	NUM
ap-3265	422	5	,	,	PUNCT
ap-3265	422	6	604	604	NUM
ap-3265	422	7	-	-	SYM
ap-3265	422	8	612	612	NUM
ap-3265	422	9	,	,	PUNCT
ap-3265	422	10	(	(	PUNCT
ap-3265	422	11	1992	1992	NUM
ap-3265	422	12	)	)	PUNCT
ap-3265	422	13	,	,	PUNCT
ap-3265	422	14	doi:10.1007	doi:10.1007	NOUN
ap-3265	422	15	/	/	SYM
ap-3265	422	16	bf01017335	bf01017335	NOUN
ap-3265	423	1	[	[	X
ap-3265	423	2	11	11	NUM
ap-3265	423	3	]	]	PUNCT
ap-3265	423	4	bonatos	bonatos	PROPN
ap-3265	423	5	d.	d.	PROPN
ap-3265	423	6	,	,	PUNCT
ap-3265	423	7	daskaloyannis	daskaloyannis	PROPN
ap-3265	423	8	c.	c.	PROPN
ap-3265	423	9	and	and	CCONJ
ap-3265	423	10	kokkotas	kokkotas	PROPN
ap-3265	423	11	k.	k.	PROPN
ap-3265	423	12	,	,	PUNCT
ap-3265	423	13	deformed	deform	VERB
ap-3265	423	14	oscillator	oscillator	NOUN
ap-3265	423	15	algebras	algebra	NOUN
ap-3265	423	16	for	for	ADP
ap-3265	423	17	two	two	NUM
ap-3265	423	18	-	-	PUNCT
ap-3265	423	19	dimensional	dimensional	ADJ
ap-3265	423	20	quantum	quantum	ADJ
ap-3265	423	21	superintegrable	superintegrable	ADJ
ap-3265	423	22	systems	system	NOUN
ap-3265	423	23	;	;	PUNCT
ap-3265	423	24	phys	phy	NOUN
ap-3265	423	25	.	.	PUNCT
ap-3265	424	1	rev	rev	PROPN
ap-3265	424	2	.	.	PROPN
ap-3265	424	3	,	,	PUNCT
ap-3265	424	4	v.a	v.a	PROPN
ap-3265	424	5	50	50	NUM
ap-3265	424	6	,	,	PUNCT
ap-3265	424	7	3700–3709	3700–3709	NUM
ap-3265	424	8	,	,	PUNCT
ap-3265	424	9	(	(	PUNCT
ap-3265	424	10	1994	1994	NUM
ap-3265	424	11	)	)	PUNCT
ap-3265	424	12	,	,	PUNCT
ap-3265	424	13	doi:10.1103	doi:10.1103	X
ap-3265	424	14	/	/	SYM
ap-3265	424	15	physreva.50.3700	physreva.50.3700	NOUN
ap-3265	425	1	[	[	X
ap-3265	425	2	12	12	NUM
ap-3265	425	3	]	]	PUNCT
ap-3265	425	4	letourneau	letourneau	PROPN
ap-3265	425	5	p.	p.	PROPN
ap-3265	425	6	and	and	CCONJ
ap-3265	425	7	vinet	vinet	PROPN
ap-3265	425	8	l.	l.	PROPN
ap-3265	425	9	,	,	PUNCT
ap-3265	425	10	superintegrable	superintegrable	ADJ
ap-3265	425	11	systems	system	NOUN
ap-3265	425	12	:	:	PUNCT
ap-3265	425	13	polynomial	polynomial	ADJ
ap-3265	425	14	algebras	algebra	NOUN
ap-3265	425	15	and	and	CCONJ
ap-3265	425	16	quasi	quasi	ADJ
ap-3265	425	17	-	-	ADJ
ap-3265	425	18	exactly	exactly	ADV
ap-3265	425	19	solvable	solvable	ADJ
ap-3265	425	20	hamiltonians	hamiltonian	NOUN
ap-3265	425	21	.	.	PUNCT
ap-3265	426	1	ann	ann	PROPN
ap-3265	426	2	.	.	PUNCT
ap-3265	427	1	phys	phy	NOUN
ap-3265	427	2	.	.	PUNCT
ap-3265	427	3	,	,	PUNCT
ap-3265	427	4	v.243	v.243	NOUN
ap-3265	427	5	,	,	PUNCT
ap-3265	427	6	144–168	144–168	NUM
ap-3265	427	7	,	,	PUNCT
ap-3265	427	8	(	(	PUNCT
ap-3265	427	9	1995	1995	NUM
ap-3265	427	10	)	)	PUNCT
ap-3265	427	11	,	,	PUNCT
ap-3265	427	12	doi:10.1006	doi:10.1006	PROPN
ap-3265	427	13	/	/	SYM
ap-3265	428	1	aphy.1995.1094	aphy.1995.1094	NOUN
ap-3265	428	2	[	[	X
ap-3265	428	3	13	13	NUM
ap-3265	428	4	]	]	PUNCT
ap-3265	428	5	kalnins	kalnin	NOUN
ap-3265	428	6	e.	e.	PROPN
ap-3265	428	7	g.	g.	PROPN
ap-3265	428	8	,	,	PUNCT
ap-3265	428	9	kress	kress	PROPN
ap-3265	428	10	j.	j.	PROPN
ap-3265	428	11	m.	m.	PROPN
ap-3265	428	12	,miller	,miller	PUNCT
ap-3265	428	13	w.	w.	PROPN
ap-3265	428	14	jr	jr	PROPN
ap-3265	428	15	.	.	PROPN
ap-3265	428	16	and	and	CCONJ
ap-3265	428	17	pogosyan	pogosyan	PROPN
ap-3265	428	18	g.	g.	PROPN
ap-3265	428	19	s.	s.	PROPN
ap-3265	428	20	,	,	PUNCT
ap-3265	428	21	completeness	completeness	NOUN
ap-3265	428	22	of	of	ADP
ap-3265	428	23	superintegrability	superintegrability	NOUN
ap-3265	428	24	in	in	ADP
ap-3265	428	25	two	two	NUM
ap-3265	428	26	-	-	PUNCT
ap-3265	428	27	dimensional	dimensional	ADJ
ap-3265	428	28	constant	constant	ADJ
ap-3265	428	29	curvature	curvature	NOUN
ap-3265	428	30	spaces	space	NOUN
ap-3265	428	31	.	.	PUNCT
ap-3265	429	1	j.	j.	PROPN
ap-3265	429	2	phys	phys	PROPN
ap-3265	429	3	.	.	PUNCT
ap-3265	430	1	a	a	DET
ap-3265	430	2	:	:	PUNCT
ap-3265	430	3	math	math	PROPN
ap-3265	430	4	gen	gen	PROPN
ap-3265	430	5	.	.	PROPN
ap-3265	430	6	34	34	NUM
ap-3265	430	7	,	,	PUNCT
ap-3265	430	8	4705–4720	4705–4720	NUM
ap-3265	430	9	(	(	PUNCT
ap-3265	430	10	2001	2001	NUM
ap-3265	430	11	)	)	PUNCT
ap-3265	430	12	,	,	PUNCT
ap-3265	430	13	doi:10.1088/0305	doi:10.1088/0305	NOUN
ap-3265	430	14	-	-	NOUN
ap-3265	430	15	4470/34/22/311	4470/34/22/311	NUM
ap-3265	431	1	[	[	X
ap-3265	431	2	14	14	NUM
ap-3265	431	3	]	]	X
ap-3265	431	4	kress	kress	PROPN
ap-3265	431	5	j.	j.	PROPN
ap-3265	431	6	m.	m.	PROPN
ap-3265	431	7	,	,	PUNCT
ap-3265	431	8	equivalence	equivalence	NOUN
ap-3265	431	9	of	of	ADP
ap-3265	431	10	superintegrable	superintegrable	ADJ
ap-3265	431	11	systems	system	NOUN
ap-3265	431	12	in	in	ADP
ap-3265	431	13	two	two	NUM
ap-3265	431	14	dimensions	dimension	NOUN
ap-3265	431	15	.	.	PUNCT
ap-3265	432	1	phys	phy	NOUN
ap-3265	432	2	.	.	PUNCT
ap-3265	433	1	atomic	atomic	ADJ
ap-3265	433	2	nuclei	nucleus	NOUN
ap-3265	433	3	,	,	PUNCT
ap-3265	433	4	70	70	NUM
ap-3265	433	5	,	,	PUNCT
ap-3265	433	6	560	560	NUM
ap-3265	433	7	-	-	SYM
ap-3265	433	8	566	566	NUM
ap-3265	433	9	,	,	PUNCT
ap-3265	433	10	(	(	PUNCT
ap-3265	433	11	2007	2007	NUM
ap-3265	433	12	)	)	PUNCT
ap-3265	433	13	,	,	PUNCT
ap-3265	433	14	doi:10.1088/0305	doi:10.1088/0305	NOUN
ap-3265	433	15	-	-	NOUN
ap-3265	433	16	4470/34/22/311	4470/34/22/311	NOUN
ap-3265	434	1	[	[	X
ap-3265	434	2	15	15	NUM
ap-3265	434	3	]	]	X
ap-3265	434	4	kalnins	kalnin	NOUN
ap-3265	434	5	e.	e.	PROPN
ap-3265	434	6	g.	g.	PROPN
ap-3265	434	7	and	and	CCONJ
ap-3265	434	8	miller	miller	PROPN
ap-3265	434	9	w.	w.	PROPN
ap-3265	434	10	jr	jr	PROPN
ap-3265	434	11	.	.	PROPN
ap-3265	434	12	,	,	PUNCT
ap-3265	434	13	quadratic	quadratic	ADJ
ap-3265	434	14	algebra	algebra	NOUN
ap-3265	434	15	contractions	contraction	NOUN
ap-3265	434	16	and	and	CCONJ
ap-3265	434	17	2nd	2nd	ADJ
ap-3265	434	18	order	order	NOUN
ap-3265	434	19	superintegrable	superintegrable	ADJ
ap-3265	434	20	systems	system	NOUN
ap-3265	434	21	,	,	PUNCT
ap-3265	434	22	anal	anal	NOUN
ap-3265	434	23	.	.	PUNCT
ap-3265	434	24	appl	appl	PROPN
ap-3265	434	25	.	.	PROPN
ap-3265	434	26	12	12	NUM
ap-3265	434	27	,	,	PUNCT
ap-3265	434	28	583	583	NUM
ap-3265	434	29	-	-	SYM
ap-3265	434	30	612	612	NUM
ap-3265	434	31	,	,	PUNCT
ap-3265	434	32	(	(	PUNCT
ap-3265	434	33	2014	2014	NUM
ap-3265	434	34	)	)	PUNCT
ap-3265	434	35	,	,	PUNCT
ap-3265	434	36	doi:10.1142	doi:10.1142	NOUN
ap-3265	434	37	/	/	SYM
ap-3265	434	38	s0219530514500377	s0219530514500377	PROPN
ap-3265	435	1	[	[	X
ap-3265	435	2	16	16	NUM
ap-3265	435	3	]	]	PUNCT
ap-3265	435	4	kalnins	kalnin	NOUN
ap-3265	435	5	e.	e.	PROPN
ap-3265	435	6	g.	g.	PROPN
ap-3265	435	7	,	,	PUNCT
ap-3265	435	8	miller	miller	PROPN
ap-3265	435	9	w.	w.	PROPN
ap-3265	435	10	jr	jr	PROPN
ap-3265	435	11	.	.	PROPN
ap-3265	435	12	and	and	CCONJ
ap-3265	435	13	post	post	PROPN
ap-3265	435	14	s.	s.	PROPN
ap-3265	435	15	,	,	PUNCT
ap-3265	435	16	wilson	wilson	PROPN
ap-3265	435	17	polynomials	polynomial	NOUN
ap-3265	435	18	and	and	CCONJ
ap-3265	435	19	the	the	DET
ap-3265	435	20	generic	generic	ADJ
ap-3265	435	21	superintegrable	superintegrable	ADJ
ap-3265	435	22	system	system	NOUN
ap-3265	435	23	on	on	ADP
ap-3265	435	24	the	the	DET
ap-3265	435	25	2	2	NUM
ap-3265	435	26	-	-	PUNCT
ap-3265	435	27	sphere	sphere	NOUN
ap-3265	435	28	,	,	PUNCT
ap-3265	435	29	j.	j.	PROPN
ap-3265	435	30	phys	phys	PROPN
ap-3265	435	31	.	.	PUNCT
ap-3265	436	1	a	a	DET
ap-3265	436	2	:	:	PUNCT
ap-3265	436	3	math	math	NOUN
ap-3265	436	4	.	.	PUNCT
ap-3265	437	1	theor	theor	PROPN
ap-3265	437	2	.	.	PROPN
ap-3265	438	1	40	40	NUM
ap-3265	438	2	,	,	PUNCT
ap-3265	438	3	11525	11525	NUM
ap-3265	438	4	-	-	SYM
ap-3265	438	5	11538	11538	NUM
ap-3265	438	6	(	(	PUNCT
ap-3265	438	7	2007	2007	NUM
ap-3265	438	8	)	)	PUNCT
ap-3265	438	9	,	,	PUNCT
ap-3265	438	10	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-3265	438	11	-	-	SYM
ap-3265	438	12	8113/40/38/005	8113/40/38/005	NUM
ap-3265	439	1	222	222	NUM
ap-3265	439	2	http://dx.doi.org/10.1016/0375-9601(90)90611-q	http://dx.doi.org/10.1016/0375-9601(90)90611-q	NOUN
ap-3265	439	3	http://dx.doi.org/10.1063/1.1386927	http://dx.doi.org/10.1063/1.1386927	PROPN
ap-3265	439	4	http://dx.doi.org/10.3842/sigma.2007.025	http://dx.doi.org/10.3842/sigma.2007.025	NOUN
ap-3265	439	5	http://dx.doi.org/10.1088/1751-8113/40/13/008	http://dx.doi.org/10.1088/1751-8113/40/13/008	NOUN
ap-3265	439	6	http://dx.doi.org/10.1063/1.1619580	http://dx.doi.org/10.1063/1.1619580	PROPN
ap-3265	439	7	http://dx.doi.org/10.1007/bf01018846	http://dx.doi.org/10.1007/bf01018846	NOUN
ap-3265	439	8	;	;	PUNCT
ap-3265	439	9	http://dx.doi.org/10.1007/bf01017335	http://dx.doi.org/10.1007/bf01017335	PROPN
ap-3265	439	10	http://dx.doi.org/10.1103/physreva.50.3700	http://dx.doi.org/10.1103/physreva.50.3700	PROPN
ap-3265	439	11	http://dx.doi.org/10.1006/aphy.1995.1094	http://dx.doi.org/10.1006/aphy.1995.1094	VERB
ap-3265	439	12	http://dx.doi.org/10.1088/0305-4470/34/22/311	http://dx.doi.org/10.1088/0305-4470/34/22/311	NOUN
ap-3265	439	13	http://dx.doi.org/10.1088/0305-4470/34/22/311	http://dx.doi.org/10.1088/0305-4470/34/22/311	NOUN
ap-3265	440	1	http://dx.doi.org/10.1142/s0219530514500377	http://dx.doi.org/10.1142/s0219530514500377	NOUN
ap-3265	440	2	http://dx.doi.org/10.1088/1751-8113/40/38/005	http://dx.doi.org/10.1088/1751-8113/40/38/005	ADJ
ap-3265	440	3	vol	vol	NOUN
ap-3265	440	4	.	.	PUNCT
ap-3265	441	1	56	56	NUM
ap-3265	441	2	no	no	NOUN
ap-3265	441	3	.	.	PUNCT
ap-3265	442	1	3/2016	3/2016	NUM
ap-3265	442	2	laplace	laplace	NOUN
ap-3265	442	3	equations	equation	NOUN
ap-3265	442	4	,	,	PUNCT
ap-3265	442	5	conformal	conformal	ADJ
ap-3265	442	6	superintegrability	superintegrability	NOUN
ap-3265	442	7	and	and	CCONJ
ap-3265	442	8	bôcher	bôcher	NOUN
ap-3265	442	9	contractions	contraction	NOUN
ap-3265	442	10	[	[	X
ap-3265	442	11	17	17	NUM
ap-3265	442	12	]	]	X
ap-3265	442	13	kalnins	kalnin	NOUN
ap-3265	442	14	e.	e.	PROPN
ap-3265	442	15	g.	g.	PROPN
ap-3265	442	16	,	,	PUNCT
ap-3265	442	17	miller	miller	PROPN
ap-3265	442	18	w.	w.	PROPN
ap-3265	442	19	jr	jr	PROPN
ap-3265	442	20	.	.	PROPN
ap-3265	442	21	and	and	CCONJ
ap-3265	442	22	post	post	VERB
ap-3265	442	23	s.	s.	PROPN
ap-3265	442	24	,	,	PUNCT
ap-3265	442	25	models	model	NOUN
ap-3265	442	26	for	for	ADP
ap-3265	442	27	quadratic	quadratic	ADJ
ap-3265	442	28	algebras	algebra	NOUN
ap-3265	442	29	associated	associate	VERB
ap-3265	442	30	with	with	ADP
ap-3265	442	31	second	second	ADJ
ap-3265	442	32	order	order	NOUN
ap-3265	442	33	superintegrable	superintegrable	ADJ
ap-3265	442	34	systems	system	NOUN
ap-3265	442	35	,	,	PUNCT
ap-3265	442	36	sigma	sigma	X
ap-3265	442	37	4	4	NUM
ap-3265	442	38	,	,	PUNCT
ap-3265	442	39	008	008	NUM
ap-3265	442	40	,	,	PUNCT
ap-3265	442	41	21	21	NUM
ap-3265	442	42	pages	page	NOUN
ap-3265	442	43	;	;	PUNCT
ap-3265	442	44	arxiv:0801.2848	arxiv:0801.2848	NUM
ap-3265	442	45	,	,	PUNCT
ap-3265	442	46	(	(	PUNCT
ap-3265	442	47	2008	2008	NUM
ap-3265	442	48	)	)	PUNCT
ap-3265	442	49	,	,	PUNCT
ap-3265	442	50	doi:10.3842	doi:10.3842	NOUN
ap-3265	442	51	/	/	SYM
ap-3265	442	52	sigma.2008.008	sigma.2008.008	NOUN
ap-3265	443	1	[	[	X
ap-3265	443	2	18	18	NUM
ap-3265	443	3	]	]	PUNCT
ap-3265	443	4	kalnins	kalnin	NOUN
ap-3265	443	5	e.	e.	PROPN
ap-3265	443	6	g.	g.	PROPN
ap-3265	443	7	,	,	PUNCT
ap-3265	443	8	miller	miller	PROPN
ap-3265	443	9	w.	w.	PROPN
ap-3265	443	10	jr	jr	PROPN
ap-3265	443	11	.	.	PROPN
ap-3265	443	12	and	and	CCONJ
ap-3265	443	13	post	post	VERB
ap-3265	443	14	s.	s.	PROPN
ap-3265	443	15	,	,	PUNCT
ap-3265	443	16	two	two	NUM
ap-3265	443	17	-	-	PUNCT
ap-3265	443	18	variable	variable	NOUN
ap-3265	443	19	wilson	wilson	PROPN
ap-3265	443	20	polynomials	polynomial	NOUN
ap-3265	443	21	and	and	CCONJ
ap-3265	443	22	the	the	DET
ap-3265	443	23	generic	generic	ADJ
ap-3265	443	24	superintegrable	superintegrable	ADJ
ap-3265	443	25	system	system	NOUN
ap-3265	443	26	on	on	ADP
ap-3265	443	27	the	the	DET
ap-3265	443	28	3	3	NUM
ap-3265	443	29	-	-	PUNCT
ap-3265	443	30	sphere	sphere	NOUN
ap-3265	443	31	,	,	PUNCT
ap-3265	443	32	http://www.emis.de/journals/sigma/2011/051/	http://www.emis.de/journals/sigma/2011/051/	PROPN
ap-3265	444	1	[	[	PUNCT
ap-3265	444	2	math	math	NOUN
ap-3265	444	3	-	-	PUNCT
ap-3265	444	4	ph	ph	NOUN
ap-3265	444	5	]	]	X
ap-3265	444	6	,	,	PUNCT
ap-3265	444	7	sigma	sigma	PROPN
ap-3265	444	8	,	,	PUNCT
ap-3265	444	9	7	7	NUM
ap-3265	444	10	,	,	PUNCT
ap-3265	444	11	051	051	NUM
ap-3265	444	12	(	(	PUNCT
ap-3265	444	13	2011	2011	NUM
ap-3265	444	14	)	)	PUNCT
ap-3265	444	15	26	26	NUM
ap-3265	444	16	pages	page	NOUN
ap-3265	444	17	,	,	PUNCT
ap-3265	444	18	doi:10.3842	doi:10.3842	NOUN
ap-3265	444	19	/	/	SYM
ap-3265	444	20	sigma.2011.051	sigma.2011.051	PROPN
ap-3265	445	1	[	[	X
ap-3265	445	2	19	19	NUM
ap-3265	445	3	]	]	X
ap-3265	445	4	post	post	NOUN
ap-3265	445	5	,	,	PUNCT
ap-3265	445	6	s.	s.	PROPN
ap-3265	445	7	,	,	PUNCT
ap-3265	445	8	models	model	NOUN
ap-3265	445	9	of	of	ADP
ap-3265	445	10	quadratic	quadratic	ADJ
ap-3265	445	11	algebras	algebra	NOUN
ap-3265	445	12	generated	generate	VERB
ap-3265	445	13	by	by	ADP
ap-3265	445	14	superintegrable	superintegrable	ADJ
ap-3265	445	15	systems	system	NOUN
ap-3265	445	16	in	in	ADP
ap-3265	445	17	2d.sigma	2d.sigma	NUM
ap-3265	445	18	7	7	NUM
ap-3265	445	19	(	(	PUNCT
ap-3265	445	20	2011	2011	NUM
ap-3265	445	21	)	)	PUNCT
ap-3265	445	22	,	,	PUNCT
ap-3265	445	23	036	036	PROPN
ap-3265	445	24	,	,	PUNCT
ap-3265	445	25	20	20	NUM
ap-3265	445	26	pages	page	NOUN
ap-3265	445	27	arxiv:1104.0734	arxiv:1104.0734	NUM
ap-3265	445	28	,	,	PUNCT
ap-3265	445	29	doi:10.3842	doi:10.3842	NOUN
ap-3265	445	30	/	/	SYM
ap-3265	445	31	sigma.2011.036	sigma.2011.036	NOUN
ap-3265	445	32	[	[	X
ap-3265	445	33	20	20	NUM
ap-3265	445	34	]	]	X
ap-3265	445	35	li	li	PROPN
ap-3265	445	36	q	q	X
ap-3265	445	37	,	,	PUNCT
ap-3265	445	38	and	and	CCONJ
ap-3265	445	39	miller	miller	PROPN
ap-3265	445	40	w.	w.	PROPN
ap-3265	445	41	jr	jr	PROPN
ap-3265	445	42	,	,	PUNCT
ap-3265	445	43	wilson	wilson	PROPN
ap-3265	445	44	polynomials	polynomial	NOUN
ap-3265	445	45	/	/	SYM
ap-3265	445	46	functions	function	NOUN
ap-3265	445	47	and	and	CCONJ
ap-3265	445	48	intertwining	intertwine	VERB
ap-3265	445	49	operators	operator	NOUN
ap-3265	445	50	for	for	ADP
ap-3265	445	51	the	the	DET
ap-3265	445	52	generic	generic	ADJ
ap-3265	445	53	quantum	quantum	ADJ
ap-3265	445	54	superintegrable	superintegrable	ADJ
ap-3265	445	55	system	system	NOUN
ap-3265	445	56	on	on	ADP
ap-3265	445	57	the	the	DET
ap-3265	445	58	2	2	NUM
ap-3265	445	59	-	-	PUNCT
ap-3265	445	60	sphere	sphere	NOUN
ap-3265	445	61	,	,	PUNCT
ap-3265	445	62	2015	2015	NUM
ap-3265	445	63	j.	j.	PROPN
ap-3265	445	64	phys	phys	PROPN
ap-3265	445	65	.	.	PUNCT
ap-3265	445	66	:	:	PUNCT
ap-3265	446	1	conf	conf	PROPN
ap-3265	446	2	.	.	PUNCT
ap-3265	446	3	ser	ser	NOUN
ap-3265	446	4	.	.	PUNCT
ap-3265	447	1	597	597	NUM
ap-3265	447	2	012059	012059	NUM
ap-3265	447	3	(	(	PUNCT
ap-3265	447	4	http://iopscience.iop.org/1742-6596/597/1/012059	http://iopscience.iop.org/1742-6596/597/1/012059	X
ap-3265	447	5	)	)	PUNCT
ap-3265	448	1	[	[	X
ap-3265	448	2	21	21	NUM
ap-3265	448	3	]	]	X
ap-3265	448	4	digital	digital	ADJ
ap-3265	448	5	library	library	NOUN
ap-3265	448	6	of	of	ADP
ap-3265	448	7	mathematical	mathematical	ADJ
ap-3265	448	8	functions	function	NOUN
ap-3265	448	9	(	(	PUNCT
ap-3265	448	10	http://dlmf.nist.gov	http://dlmf.nist.gov	NOUN
ap-3265	448	11	)	)	PUNCT
ap-3265	448	12	.	.	PUNCT
ap-3265	449	1	[	[	X
ap-3265	449	2	22	22	NUM
ap-3265	449	3	]	]	PUNCT
ap-3265	449	4	inönü	inönü	NOUN
ap-3265	449	5	e.	e.	PROPN
ap-3265	449	6	and	and	CCONJ
ap-3265	449	7	wigner	wigner	PROPN
ap-3265	449	8	e.	e.	PROPN
ap-3265	449	9	p.	p.	PROPN
ap-3265	449	10	,	,	PUNCT
ap-3265	449	11	on	on	ADP
ap-3265	449	12	the	the	DET
ap-3265	449	13	contraction	contraction	NOUN
ap-3265	449	14	of	of	ADP
ap-3265	449	15	groups	group	NOUN
ap-3265	449	16	and	and	CCONJ
ap-3265	449	17	their	their	PRON
ap-3265	449	18	representations	representation	NOUN
ap-3265	449	19	.	.	PUNCT
ap-3265	450	1	proc	proc	NOUN
ap-3265	450	2	.	.	PUNCT
ap-3265	451	1	nat	nat	PROPN
ap-3265	451	2	.	.	PUNCT
ap-3265	452	1	acad	acad	PROPN
ap-3265	452	2	.	.	PUNCT
ap-3265	453	1	sci	sci	PROPN
ap-3265	453	2	.	.	PUNCT
ap-3265	454	1	(	(	PUNCT
ap-3265	454	2	us	us	PROPN
ap-3265	454	3	)	)	PUNCT
ap-3265	454	4	,	,	PUNCT
ap-3265	454	5	39	39	NUM
ap-3265	454	6	,	,	PUNCT
ap-3265	454	7	510	510	NUM
ap-3265	454	8	-	-	SYM
ap-3265	454	9	524	524	NUM
ap-3265	454	10	,	,	PUNCT
ap-3265	454	11	(	(	PUNCT
ap-3265	454	12	1953	1953	NUM
ap-3265	454	13	)	)	PUNCT
ap-3265	454	14	,	,	PUNCT
ap-3265	454	15	doi:10.1073	doi:10.1073	NOUN
ap-3265	454	16	/	/	SYM
ap-3265	454	17	pnas.39.6.510	pnas.39.6.510	NUM
ap-3265	454	18	[	[	X
ap-3265	454	19	23	23	NUM
ap-3265	454	20	]	]	X
ap-3265	454	21	weimar	weimar	PROPN
ap-3265	454	22	-	-	PUNCT
ap-3265	454	23	woods	woods	PROPN
ap-3265	454	24	e.	e.	PROPN
ap-3265	454	25	,	,	PUNCT
ap-3265	454	26	the	the	DET
ap-3265	454	27	three	three	NUM
ap-3265	454	28	-	-	PUNCT
ap-3265	454	29	dimensional	dimensional	ADJ
ap-3265	454	30	real	real	ADJ
ap-3265	454	31	lie	lie	NOUN
ap-3265	454	32	algebras	algebra	NOUN
ap-3265	454	33	and	and	CCONJ
ap-3265	454	34	their	their	PRON
ap-3265	454	35	contractions	contraction	NOUN
ap-3265	454	36	,	,	PUNCT
ap-3265	454	37	j.	j.	PROPN
ap-3265	454	38	math	math	PROPN
ap-3265	454	39	.	.	PUNCT
ap-3265	455	1	phys	phy	NOUN
ap-3265	455	2	.	.	PUNCT
ap-3265	455	3	,	,	PUNCT
ap-3265	455	4	32	32	NUM
ap-3265	455	5	,	,	PUNCT
ap-3265	455	6	2028	2028	NUM
ap-3265	455	7	-	-	SYM
ap-3265	455	8	2033	2033	NUM
ap-3265	455	9	(	(	PUNCT
ap-3265	455	10	1991	1991	NUM
ap-3265	455	11	)	)	PUNCT
ap-3265	455	12	,	,	PUNCT
ap-3265	455	13	doi:10.1063/1.529222	doi:10.1063/1.529222	PROPN
ap-3265	455	14	[	[	X
ap-3265	455	15	24	24	NUM
ap-3265	455	16	]	]	X
ap-3265	455	17	nesterenko	nesterenko	PROPN
ap-3265	455	18	m.	m.	NOUN
ap-3265	455	19	and	and	CCONJ
ap-3265	455	20	popovych	popovych	PROPN
ap-3265	455	21	r.	r.	PROPN
ap-3265	455	22	,	,	PUNCT
ap-3265	455	23	contractions	contraction	NOUN
ap-3265	455	24	of	of	ADP
ap-3265	455	25	low	low	ADJ
ap-3265	455	26	-	-	PUNCT
ap-3265	455	27	dimensional	dimensional	ADJ
ap-3265	455	28	lie	lie	NOUN
ap-3265	455	29	algebras	algebra	NOUN
ap-3265	455	30	,	,	PUNCT
ap-3265	455	31	j.	j.	PROPN
ap-3265	455	32	math	math	PROPN
ap-3265	455	33	.	.	PUNCT
ap-3265	456	1	phys	phy	NOUN
ap-3265	456	2	.	.	PUNCT
ap-3265	456	3	,	,	PUNCT
ap-3265	456	4	47	47	NUM
ap-3265	456	5	123515	123515	NUM
ap-3265	456	6	,	,	PUNCT
ap-3265	456	7	(	(	PUNCT
ap-3265	456	8	2006	2006	NUM
ap-3265	456	9	)	)	PUNCT
ap-3265	456	10	.	.	PUNCT
ap-3265	457	1	[	[	X
ap-3265	457	2	25	25	NUM
ap-3265	457	3	]	]	PUNCT
ap-3265	457	4	kalnins	kalnin	NOUN
ap-3265	457	5	e.	e.	PROPN
ap-3265	457	6	g.	g.	PROPN
ap-3265	457	7	,	,	PUNCT
ap-3265	457	8	miller	miller	PROPN
ap-3265	457	9	w.	w.	PROPN
ap-3265	457	10	jr	jr	PROPN
ap-3265	457	11	and	and	CCONJ
ap-3265	457	12	post	post	PROPN
ap-3265	457	13	s.	s.	PROPN
ap-3265	457	14	,	,	PUNCT
ap-3265	457	15	contractions	contraction	NOUN
ap-3265	457	16	of	of	ADP
ap-3265	457	17	2d	2d	NUM
ap-3265	457	18	2nd	2nd	ADJ
ap-3265	457	19	order	order	NOUN
ap-3265	457	20	quantum	quantum	ADJ
ap-3265	457	21	superintegrable	superintegrable	ADJ
ap-3265	457	22	systems	system	NOUN
ap-3265	457	23	and	and	CCONJ
ap-3265	457	24	the	the	DET
ap-3265	457	25	askey	askey	ADJ
ap-3265	457	26	scheme	scheme	NOUN
ap-3265	457	27	for	for	ADP
ap-3265	457	28	hypergeometric	hypergeometric	ADJ
ap-3265	457	29	orthogonal	orthogonal	ADJ
ap-3265	457	30	polynomials	polynomial	NOUN
ap-3265	457	31	sigma	sigma	NOUN
ap-3265	457	32	,	,	PUNCT
ap-3265	457	33	9	9	NUM
ap-3265	457	34	057	057	NUM
ap-3265	457	35	,	,	PUNCT
ap-3265	457	36	28	28	NUM
ap-3265	457	37	pages	page	NOUN
ap-3265	457	38	,	,	PUNCT
ap-3265	457	39	(	(	PUNCT
ap-3265	457	40	2013	2013	NUM
ap-3265	457	41	)	)	PUNCT
ap-3265	457	42	,	,	PUNCT
ap-3265	457	43	doi:10.3842	doi:10.3842	NOUN
ap-3265	457	44	/	/	SYM
ap-3265	457	45	sigma.2013.057	sigma.2013.057	NOUN
ap-3265	457	46	[	[	X
ap-3265	457	47	26	26	NUM
ap-3265	457	48	]	]	X
ap-3265	457	49	kalnins	kalnin	NOUN
ap-3265	457	50	e.	e.	PROPN
ap-3265	457	51	g.	g.	PROPN
ap-3265	457	52	,	,	PUNCT
ap-3265	457	53	kress	kress	PROPN
ap-3265	457	54	j.m	j.m	PROPN
ap-3265	457	55	,	,	PUNCT
ap-3265	457	56	miller	miller	PROPN
ap-3265	457	57	w.	w.	PROPN
ap-3265	457	58	jr	jr	PROPN
ap-3265	457	59	and	and	CCONJ
ap-3265	457	60	post	post	PROPN
ap-3265	457	61	,	,	PUNCT
ap-3265	457	62	s.	s.	PROPN
ap-3265	457	63	,	,	PUNCT
ap-3265	457	64	laplace	laplace	NOUN
ap-3265	457	65	-	-	PUNCT
ap-3265	457	66	type	type	NOUN
ap-3265	457	67	equations	equation	NOUN
ap-3265	457	68	as	as	ADP
ap-3265	457	69	conformal	conformal	ADJ
ap-3265	457	70	superintegrable	superintegrable	ADJ
ap-3265	457	71	systems	system	NOUN
ap-3265	457	72	,	,	PUNCT
ap-3265	457	73	advances	advance	NOUN
ap-3265	457	74	in	in	ADP
ap-3265	457	75	applied	apply	VERB
ap-3265	457	76	mathematics	mathematic	NOUN
ap-3265	457	77	46	46	NUM
ap-3265	457	78	(	(	PUNCT
ap-3265	457	79	2011	2011	NUM
ap-3265	457	80	)	)	PUNCT
ap-3265	457	81	396416	396416	NUM
ap-3265	457	82	.	.	PUNCT
ap-3265	458	1	[	[	X
ap-3265	458	2	27	27	NUM
ap-3265	458	3	]	]	X
ap-3265	458	4	capel	capel	PROPN
ap-3265	458	5	j.j	j.j	PROPN
ap-3265	458	6	.	.	PROPN
ap-3265	458	7	and	and	CCONJ
ap-3265	458	8	kress	kress	PROPN
ap-3265	458	9	j.m	j.m	PROPN
ap-3265	458	10	.	.	PROPN
ap-3265	458	11	,	,	PUNCT
ap-3265	458	12	invariant	invariant	ADJ
ap-3265	458	13	classification	classification	NOUN
ap-3265	458	14	of	of	ADP
ap-3265	458	15	second	second	ADJ
ap-3265	458	16	-	-	PUNCT
ap-3265	458	17	order	order	NOUN
ap-3265	458	18	conformally	conformally	ADV
ap-3265	458	19	flat	flat	ADJ
ap-3265	458	20	superintegrable	superintegrable	ADJ
ap-3265	458	21	systems	system	NOUN
ap-3265	458	22	,	,	PUNCT
ap-3265	458	23	j.	j.	PROPN
ap-3265	458	24	phys	phys	PROPN
ap-3265	458	25	.	.	PUNCT
ap-3265	459	1	a	a	DET
ap-3265	459	2	:	:	PUNCT
ap-3265	459	3	math	math	NOUN
ap-3265	459	4	.	.	PUNCT
ap-3265	460	1	theor	theor	PROPN
ap-3265	460	2	.	.	PUNCT
ap-3265	461	1	47	47	NUM
ap-3265	461	2	(	(	PUNCT
ap-3265	461	3	2014	2014	NUM
ap-3265	461	4	)	)	PUNCT
ap-3265	461	5	,	,	PUNCT
ap-3265	461	6	495202	495202	NUM
ap-3265	461	7	.	.	PUNCT
ap-3265	462	1	[	[	X
ap-3265	462	2	28	28	NUM
ap-3265	462	3	]	]	X
ap-3265	462	4	bôcher	bôcher	NOUN
ap-3265	462	5	m.	m.	NOUN
ap-3265	462	6	,	,	PUNCT
ap-3265	462	7	ueber	ueber	PROPN
ap-3265	462	8	die	die	VERB
ap-3265	462	9	reihenentwickelungen	reihenentwickelungen	PROPN
ap-3265	462	10	der	der	NOUN
ap-3265	462	11	potentialtheorie	potentialtheorie	NOUN
ap-3265	462	12	,	,	PUNCT
ap-3265	462	13	b.	b.	PROPN
ap-3265	462	14	g.	g.	PROPN
ap-3265	462	15	teubner	teubner	PROPN
ap-3265	462	16	,	,	PUNCT
ap-3265	462	17	leipzig	leipzig	NOUN
ap-3265	462	18	1894	1894	NUM
ap-3265	462	19	.	.	PUNCT
ap-3265	463	1	[	[	X
ap-3265	463	2	29	29	NUM
ap-3265	463	3	]	]	X
ap-3265	463	4	kalnins	kalnin	NOUN
ap-3265	463	5	e	e	NOUN
ap-3265	463	6	,	,	PUNCT
ap-3265	463	7	g.	g.	PROPN
ap-3265	463	8	,	,	PUNCT
ap-3265	463	9	miller	miller	PROPN
ap-3265	463	10	w.	w.	PROPN
ap-3265	463	11	jr	jr	PROPN
ap-3265	463	12	.	.	PROPN
ap-3265	463	13	and	and	CCONJ
ap-3265	463	14	post	post	VERB
ap-3265	463	15	s.	s.	PROPN
ap-3265	463	16	,	,	PUNCT
ap-3265	463	17	coupling	couple	VERB
ap-3265	463	18	constant	constant	ADJ
ap-3265	463	19	metamorphosis	metamorphosis	NOUN
ap-3265	463	20	and	and	CCONJ
ap-3265	463	21	nth	nth	NOUN
ap-3265	463	22	order	order	NOUN
ap-3265	463	23	symmetries	symmetry	NOUN
ap-3265	463	24	in	in	ADP
ap-3265	463	25	classical	classical	ADJ
ap-3265	463	26	and	and	CCONJ
ap-3265	463	27	quantum	quantum	NOUN
ap-3265	463	28	mechanics	mechanic	NOUN
ap-3265	463	29	,	,	PUNCT
ap-3265	463	30	j.	j.	PROPN
ap-3265	463	31	phys	phys	PROPN
ap-3265	463	32	.	.	PUNCT
ap-3265	464	1	a	a	DET
ap-3265	464	2	:	:	PUNCT
ap-3265	464	3	math	math	NOUN
ap-3265	464	4	.	.	PUNCT
ap-3265	465	1	theor	theor	PROPN
ap-3265	465	2	.	.	PUNCT
ap-3265	466	1	43	43	NUM
ap-3265	466	2	(	(	PUNCT
ap-3265	466	3	2010	2010	NUM
ap-3265	466	4	)	)	PUNCT
ap-3265	466	5	035202	035202	NUM
ap-3265	466	6	.	.	PUNCT
ap-3265	467	1	(	(	PUNCT
ap-3265	467	2	20	20	NUM
ap-3265	467	3	pages	page	NOUN
ap-3265	467	4	)	)	PUNCT
ap-3265	467	5	,	,	PUNCT
ap-3265	468	1	doi:10.1088/1751	doi:10.1088/1751	NOUN
ap-3265	468	2	-	-	PUNCT
ap-3265	468	3	8113/43/3/035202	8113/43/3/035202	NOUN
ap-3265	468	4	[	[	X
ap-3265	468	5	30	30	NUM
ap-3265	468	6	]	]	X
ap-3265	468	7	kalnins	kalnin	NOUN
ap-3265	468	8	e.g.	e.g.	ADV
ap-3265	468	9	,	,	PUNCT
ap-3265	468	10	miller	miller	PROPN
ap-3265	468	11	w.	w.	PROPN
ap-3265	468	12	jr	jr	PROPN
ap-3265	468	13	.	.	PROPN
ap-3265	468	14	,	,	PUNCT
ap-3265	468	15	and	and	CCONJ
ap-3265	468	16	reid	reid	PROPN
ap-3265	468	17	g.j	g.j	PROPN
ap-3265	468	18	.	.	PROPN
ap-3265	468	19	,	,	PUNCT
ap-3265	468	20	separation	separation	NOUN
ap-3265	468	21	of	of	ADP
ap-3265	468	22	variables	variable	NOUN
ap-3265	468	23	for	for	ADP
ap-3265	468	24	complex	complex	ADJ
ap-3265	468	25	riemannian	riemannian	ADJ
ap-3265	468	26	spaces	space	NOUN
ap-3265	468	27	of	of	ADP
ap-3265	468	28	constant	constant	ADJ
ap-3265	468	29	curvature	curvature	NOUN
ap-3265	468	30	.	.	PUNCT
ap-3265	469	1	i.	i.	PROPN
ap-3265	469	2	orthogonal	orthogonal	PROPN
ap-3265	469	3	separable	separable	PROPN
ap-3265	469	4	coordinates	coordinate	NOUN
ap-3265	469	5	for	for	ADP
ap-3265	469	6	snc	snc	PROPN
ap-3265	469	7	and	and	CCONJ
ap-3265	469	8	enc	enc	PROPN
ap-3265	469	9	,	,	PUNCT
ap-3265	469	10	proc	proc	NOUN
ap-3265	469	11	.	.	PUNCT
ap-3265	470	1	r.	r.	PROPN
ap-3265	470	2	soc	soc	PROPN
ap-3265	470	3	.	.	PUNCT
ap-3265	471	1	lond	lond	PROPN
ap-3265	471	2	.	.	PUNCT
ap-3265	472	1	a	a	DET
ap-3265	472	2	394	394	NUM
ap-3265	472	3	(	(	PUNCT
ap-3265	472	4	1984	1984	NUM
ap-3265	472	5	)	)	PUNCT
ap-3265	472	6	,	,	PUNCT
ap-3265	472	7	pp	pp	ADP
ap-3265	472	8	.	.	PUNCT
ap-3265	473	1	183	183	NUM
ap-3265	473	2	-	-	SYM
ap-3265	473	3	206	206	NUM
ap-3265	473	4	,	,	PUNCT
ap-3265	473	5	doi:10.1098	doi:10.1098	PROPN
ap-3265	473	6	/	/	SYM
ap-3265	473	7	rspa.1984.0075	rspa.1984.0075	PROPN
ap-3265	473	8	[	[	X
ap-3265	473	9	31	31	NUM
ap-3265	473	10	]	]	PUNCT
ap-3265	473	11	bromwich	bromwich	PROPN
ap-3265	473	12	t.	t.	PROPN
ap-3265	473	13	j.	j.	PROPN
ap-3265	473	14	a.	a.	PROPN
ap-3265	473	15	,	,	PUNCT
ap-3265	473	16	quadratic	quadratic	ADJ
ap-3265	473	17	forms	form	NOUN
ap-3265	473	18	and	and	CCONJ
ap-3265	473	19	their	their	PRON
ap-3265	473	20	classification	classification	NOUN
ap-3265	473	21	by	by	ADP
ap-3265	473	22	means	mean	NOUN
ap-3265	473	23	of	of	ADP
ap-3265	473	24	invariant	invariant	ADJ
ap-3265	473	25	factors	factor	NOUN
ap-3265	473	26	.	.	PUNCT
ap-3265	474	1	cambridge	cambridge	PROPN
ap-3265	474	2	tract	tract	NOUN
ap-3265	474	3	no	no	INTJ
ap-3265	474	4	.	.	NOUN
ap-3265	475	1	3	3	X
ap-3265	475	2	.	.	X
ap-3265	475	3	cambridge	cambridge	PROPN
ap-3265	475	4	university	university	PROPN
ap-3265	475	5	press	press	NOUN
ap-3265	475	6	,	,	PUNCT
ap-3265	475	7	1906	1906	NUM
ap-3265	475	8	,	,	PUNCT
ap-3265	475	9	reprint	reprint	NOUN
ap-3265	475	10	hafner	hafner	PROPN
ap-3265	475	11	,	,	PUNCT
ap-3265	475	12	new	new	PROPN
ap-3265	475	13	york	york	PROPN
ap-3265	475	14	,	,	PUNCT
ap-3265	475	15	1971	1971	NUM
ap-3265	475	16	.	.	PUNCT
ap-3265	476	1	[	[	X
ap-3265	476	2	32	32	NUM
ap-3265	476	3	]	]	PUNCT
ap-3265	476	4	e.g.	e.g.	ADV
ap-3265	476	5	kalnins	kalnin	NOUN
ap-3265	476	6	,	,	PUNCT
ap-3265	476	7	w.	w.	PROPN
ap-3265	476	8	miller	miller	PROPN
ap-3265	476	9	,	,	PUNCT
ap-3265	476	10	jr	jr	PROPN
ap-3265	476	11	.	.	PROPN
ap-3265	476	12	,	,	PUNCT
ap-3265	476	13	and	and	CCONJ
ap-3265	476	14	e.	e.	PROPN
ap-3265	476	15	subag	subag	PROPN
ap-3265	476	16	,	,	PUNCT
ap-3265	476	17	bôcher	bôcher	AUX
ap-3265	476	18	contractions	contraction	NOUN
ap-3265	476	19	of	of	ADP
ap-3265	476	20	conformally	conformally	ADV
ap-3265	476	21	superintegrable	superintegrable	ADJ
ap-3265	476	22	laplace	laplace	NOUN
ap-3265	476	23	equations	equation	NOUN
ap-3265	476	24	,	,	PUNCT
ap-3265	476	25	(	(	PUNCT
ap-3265	476	26	submitted	submit	VERB
ap-3265	476	27	)	)	PUNCT
ap-3265	476	28	,	,	PUNCT
ap-3265	476	29	arxiv:1512.09315	arxiv:1512.09315	PROPN
ap-3265	476	30	,	,	PUNCT
ap-3265	476	31	2016	2016	NUM
ap-3265	476	32	;	;	PUNCT
ap-3265	476	33	e.g.	e.g.	ADV
ap-3265	476	34	kalnins	kalnin	NOUN
ap-3265	476	35	,	,	PUNCT
ap-3265	476	36	w.	w.	PROPN
ap-3265	476	37	miller	miller	PROPN
ap-3265	476	38	,	,	PUNCT
ap-3265	476	39	jr	jr	PROPN
ap-3265	476	40	.	.	PROPN
ap-3265	476	41	,	,	PUNCT
ap-3265	476	42	and	and	CCONJ
ap-3265	476	43	e.	e.	PROPN
ap-3265	476	44	subag	subag	PROPN
ap-3265	476	45	,	,	PUNCT
ap-3265	476	46	bôcher	bôcher	AUX
ap-3265	476	47	contractions	contraction	NOUN
ap-3265	476	48	of	of	ADP
ap-3265	476	49	conformally	conformally	ADV
ap-3265	476	50	superintegrable	superintegrable	ADJ
ap-3265	476	51	laplace	laplace	NOUN
ap-3265	476	52	equations	equation	NOUN
ap-3265	476	53	:	:	PUNCT
ap-3265	476	54	detailed	detailed	ADJ
ap-3265	476	55	computations	computation	NOUN
ap-3265	476	56	,	,	PUNCT
ap-3265	476	57	arxiv:1601.02876	arxiv:1601.02876	NOUN
ap-3265	476	58	,	,	PUNCT
ap-3265	476	59	2016	2016	NUM
ap-3265	476	60	[	[	X
ap-3265	476	61	33	33	NUM
ap-3265	476	62	]	]	X
ap-3265	476	63	capel	capel	PROPN
ap-3265	476	64	j.j	j.j	PROPN
ap-3265	476	65	.	.	PROPN
ap-3265	476	66	,	,	PUNCT
ap-3265	476	67	kress	kress	PROPN
ap-3265	476	68	j.m	j.m	PROPN
ap-3265	476	69	.	.	PROPN
ap-3265	476	70	and	and	CCONJ
ap-3265	476	71	post	post	VERB
ap-3265	476	72	s.	s.	PROPN
ap-3265	476	73	,	,	PUNCT
ap-3265	476	74	invariant	invariant	ADJ
ap-3265	476	75	classification	classification	NOUN
ap-3265	476	76	and	and	CCONJ
ap-3265	476	77	limits	limit	NOUN
ap-3265	476	78	of	of	ADP
ap-3265	476	79	maximally	maximally	ADV
ap-3265	476	80	superintegrable	superintegrable	ADJ
ap-3265	476	81	systems	system	NOUN
ap-3265	476	82	in	in	ADP
ap-3265	476	83	3d	3d	NUM
ap-3265	476	84	,	,	PUNCT
ap-3265	476	85	sigma	sigma	PROPN
ap-3265	476	86	,	,	PUNCT
ap-3265	476	87	11	11	NUM
ap-3265	476	88	(	(	PUNCT
ap-3265	476	89	2015	2015	NUM
ap-3265	476	90	)	)	PUNCT
ap-3265	476	91	,	,	PUNCT
ap-3265	476	92	038	038	NUM
ap-3265	476	93	,	,	PUNCT
ap-3265	476	94	17	17	NUM
ap-3265	476	95	pages	page	NOUN
ap-3265	476	96	arxiv:1501.06601	arxiv:1501.06601	NUM
ap-3265	476	97	,	,	PUNCT
ap-3265	476	98	doi:10.3842	doi:10.3842	NOUN
ap-3265	476	99	/	/	SYM
ap-3265	476	100	sigma.2015.038	sigma.2015.038	PROPN
ap-3265	476	101	223	223	NUM
ap-3265	476	102	http://arxiv.org/abs/0801.2848	http://arxiv.org/abs/0801.2848	PROPN
ap-3265	476	103	http://dx.doi.org/10.3842/sigma.2008.008	http://dx.doi.org/10.3842/sigma.2008.008	NOUN
ap-3265	476	104	http://dx.doi.org/10.3842/sigma.2011.051	http://dx.doi.org/10.3842/sigma.2011.051	X
ap-3265	476	105	http://arxiv.org/abs/1104.0734	http://arxiv.org/abs/1104.0734	ADV
ap-3265	476	106	http://dx.doi.org/10.3842/sigma.2011.036	http://dx.doi.org/10.3842/sigma.2011.036	X
ap-3265	476	107	http://dx.doi.org/10.1073/pnas.39.6.510	http://dx.doi.org/10.1073/pnas.39.6.510	X
ap-3265	476	108	http://dx.doi.org/10.1063/1.529222	http://dx.doi.org/10.1063/1.529222	PROPN
ap-3265	476	109	http://dx.doi.org/10.3842/sigma.2013.057	http://dx.doi.org/10.3842/sigma.2013.057	NOUN
ap-3265	476	110	http://dx.doi.org/10.1088/1751-8113/43/3/035202	http://dx.doi.org/10.1088/1751-8113/43/3/035202	PROPN
ap-3265	476	111	http://dx.doi.org/10.1098/rspa.1984.0075	http://dx.doi.org/10.1098/rspa.1984.0075	VERB
ap-3265	476	112	http://arxiv.org/abs/1512.09315	http://arxiv.org/abs/1512.09315	PROPN
ap-3265	476	113	http://arxiv.org/abs/1601.02876	http://arxiv.org/abs/1601.02876	NOUN
ap-3265	476	114	http://arxiv.org/abs/1501.06601	http://arxiv.org/abs/1501.06601	PROPN
ap-3265	476	115	http://dx.doi.org/10.3842/sigma.2015.038	http://dx.doi.org/10.3842/sigma.2015.038	PROPN
ap-3265	476	116	acta	acta	PROPN
ap-3265	476	117	polytechnica	polytechnica	PROPN
ap-3265	476	118	56(3):214–223	56(3):214–223	PROPN
ap-3265	476	119	,	,	PUNCT
ap-3265	476	120	2016	2016	NUM
ap-3265	476	121	1	1	NUM
ap-3265	476	122	introduction	introduction	NOUN
ap-3265	476	123	1.1	1.1	NUM
ap-3265	476	124	the	the	DET
ap-3265	476	125	big	big	ADJ
ap-3265	476	126	picture	picture	NOUN
ap-3265	476	127	:	:	PUNCT
ap-3265	476	128	contractions	contraction	NOUN
ap-3265	476	129	and	and	CCONJ
ap-3265	476	130	special	special	ADJ
ap-3265	476	131	functions	function	NOUN
ap-3265	476	132	1.2	1.2	NUM
ap-3265	476	133	the	the	DET
ap-3265	476	134	problems	problem	NOUN
ap-3265	476	135	and	and	CCONJ
ap-3265	476	136	the	the	DET
ap-3265	476	137	proposed	propose	VERB
ap-3265	476	138	solutions	solution	NOUN
ap-3265	476	139	2	2	NUM
ap-3265	476	140	the	the	DET
ap-3265	476	141	laplace	laplace	NOUN
ap-3265	476	142	equation	equation	NOUN
ap-3265	476	143	3	3	NUM
ap-3265	476	144	the	the	DET
ap-3265	476	145	bôcher	bôcher	NOUN
ap-3265	476	146	method	method	VERB
ap-3265	476	147	3.1	3.1	NUM
ap-3265	476	148	relation	relation	NOUN
ap-3265	476	149	to	to	ADP
ap-3265	476	150	separation	separation	NOUN
ap-3265	476	151	of	of	ADP
ap-3265	476	152	variables	variable	NOUN
ap-3265	476	153	3.2	3.2	NUM
ap-3265	476	154	bôcher	bôcher	NOUN
ap-3265	476	155	limits	limit	VERB
ap-3265	476	156	4	4	NUM
ap-3265	476	157	the	the	DET
ap-3265	476	158	8	8	NUM
ap-3265	476	159	classes	class	NOUN
ap-3265	476	160	of	of	ADP
ap-3265	476	161	nondegenerate	nondegenerate	NOUN
ap-3265	476	162	conformally	conformally	ADV
ap-3265	476	163	superintegrable	superintegrable	ADJ
ap-3265	476	164	systems	system	NOUN
ap-3265	476	165	4.1	4.1	NUM
ap-3265	476	166	summary	summary	NOUN
ap-3265	476	167	of	of	ADP
ap-3265	476	168	bôcher	bôcher	NOUN
ap-3265	476	169	contractions	contraction	NOUN
ap-3265	476	170	of	of	ADP
ap-3265	476	171	laplace	laplace	NOUN
ap-3265	476	172	superintegrable	superintegrable	ADJ
ap-3265	476	173	systems	system	NOUN
ap-3265	476	174	5	5	NUM
ap-3265	476	175	helmholtz	helmholtz	NOUN
ap-3265	476	176	contractions	contraction	NOUN
ap-3265	476	177	from	from	ADP
ap-3265	476	178	bôcher	bôcher	NOUN
ap-3265	476	179	contractions	contraction	NOUN
ap-3265	476	180	6	6	NUM
ap-3265	476	181	conclusions	conclusion	NOUN
ap-3265	476	182	and	and	CCONJ
ap-3265	476	183	discussion	discussion	NOUN
ap-3265	476	184	acknowledgements	acknowledgement	NOUN
ap-3265	476	185	references	reference	NOUN