id	sid	tid	token	lemma	pos
ap-762	1	1	ap05_5.vp	ap05_5.vp	NOUN
ap-762	1	2	1	1	NUM
ap-762	1	3	introduction	introduction	NOUN
ap-762	1	4	numeration	numeration	NOUN
ap-762	1	5	systems	system	NOUN
ap-762	1	6	with	with	ADP
ap-762	1	7	an	an	DET
ap-762	1	8	irrational	irrational	ADJ
ap-762	1	9	base	base	NOUN
ap-762	1	10	�	�	NOUN
ap-762	1	11	give	give	VERB
ap-762	1	12	us	we	PRON
ap-762	1	13	an	an	DET
ap-762	1	14	opportunity	opportunity	NOUN
ap-762	1	15	to	to	PART
ap-762	1	16	perform	perform	VERB
ap-762	1	17	exact	exact	ADJ
ap-762	1	18	arithmetic	arithmetic	ADJ
ap-762	1	19	operations	operation	NOUN
ap-762	1	20	with	with	ADP
ap-762	1	21	irrational	irrational	ADJ
ap-762	1	22	numbers	number	NOUN
ap-762	1	23	–	–	PUNCT
ap-762	1	24	a	a	DET
ap-762	1	25	tool	tool	NOUN
ap-762	1	26	necessary	necessary	ADJ
ap-762	1	27	for	for	ADP
ap-762	1	28	the	the	DET
ap-762	1	29	new	new	ADJ
ap-762	1	30	methods	method	NOUN
ap-762	1	31	of	of	ADP
ap-762	1	32	building	build	VERB
ap-762	1	33	aperiodic	aperiodic	ADJ
ap-762	1	34	random	random	ADJ
ap-762	1	35	number	number	NOUN
ap-762	1	36	generators	generator	NOUN
ap-762	1	37	,	,	PUNCT
ap-762	1	38	for	for	ADP
ap-762	1	39	new	new	ADJ
ap-762	1	40	cryptographic	cryptographic	ADJ
ap-762	1	41	methods	method	NOUN
ap-762	1	42	and	and	CCONJ
ap-762	1	43	also	also	ADV
ap-762	1	44	for	for	ADP
ap-762	1	45	the	the	DET
ap-762	1	46	mathematical	mathematical	ADJ
ap-762	1	47	modelling	modelling	NOUN
ap-762	1	48	of	of	ADP
ap-762	1	49	recently	recently	ADV
ap-762	1	50	discovered	discover	VERB
ap-762	1	51	materials	material	NOUN
ap-762	1	52	with	with	ADP
ap-762	1	53	a	a	DET
ap-762	1	54	long	long	ADJ
ap-762	1	55	range	range	NOUN
ap-762	1	56	order	order	NOUN
ap-762	1	57	–	–	PUNCT
ap-762	1	58	so	so	ADV
ap-762	1	59	called	call	VERB
ap-762	1	60	quasicrystals	quasicrystal	NOUN
ap-762	1	61	.	.	PUNCT
ap-762	2	1	the	the	DET
ap-762	2	2	whole	whole	ADJ
ap-762	2	3	field	field	NOUN
ap-762	2	4	of	of	ADP
ap-762	2	5	irrational	irrational	ADJ
ap-762	2	6	numeration	numeration	NOUN
ap-762	2	7	originates	originate	NOUN
ap-762	2	8	from	from	ADP
ap-762	2	9	the	the	DET
ap-762	2	10	article	article	NOUN
ap-762	2	11	of	of	ADP
ap-762	2	12	a.	a.	PROPN
ap-762	2	13	rényi	rényi	PROPN
ap-762	3	1	[	[	X
ap-762	3	2	1	1	NUM
ap-762	3	3	]	]	PUNCT
ap-762	3	4	,	,	PUNCT
ap-762	3	5	in	in	ADP
ap-762	3	6	which	which	PRON
ap-762	3	7	he	he	PRON
ap-762	3	8	proved	prove	VERB
ap-762	3	9	that	that	SCONJ
ap-762	3	10	for	for	ADP
ap-762	3	11	each	each	DET
ap-762	3	12	real	real	ADJ
ap-762	3	13	base	base	NOUN
ap-762	3	14	�	�	PROPN
ap-762	3	15	>	>	PROPN
ap-762	3	16	1	1	NUM
ap-762	3	17	and	and	CCONJ
ap-762	3	18	for	for	ADP
ap-762	3	19	every	every	DET
ap-762	3	20	positive	positive	ADJ
ap-762	3	21	real	real	ADJ
ap-762	3	22	number	number	NOUN
ap-762	3	23	x	x	NOUN
ap-762	3	24	,	,	PUNCT
ap-762	3	25	there	there	PRON
ap-762	3	26	exists	exist	VERB
ap-762	3	27	a	a	DET
ap-762	3	28	unique	unique	ADJ
ap-762	3	29	representation	representation	NOUN
ap-762	3	30	of	of	ADP
ap-762	3	31	the	the	DET
ap-762	3	32	number	number	NOUN
ap-762	3	33	x	x	PUNCT
ap-762	3	34	in	in	ADP
ap-762	3	35	the	the	DET
ap-762	3	36	numeration	numeration	NOUN
ap-762	3	37	system	system	NOUN
ap-762	3	38	with	with	ADP
ap-762	3	39	the	the	DET
ap-762	3	40	base	base	PROPN
ap-762	3	41	�	�	PROPN
ap-762	3	42	.	.	PUNCT
ap-762	4	1	however	however	ADV
ap-762	4	2	,	,	PUNCT
ap-762	4	3	contrary	contrary	ADV
ap-762	4	4	to	to	ADP
ap-762	4	5	the	the	DET
ap-762	4	6	usual	usual	ADJ
ap-762	4	7	numeration	numeration	NOUN
ap-762	4	8	system	system	NOUN
ap-762	4	9	with	with	ADP
ap-762	4	10	an	an	DET
ap-762	4	11	integer	integer	NOUN
ap-762	4	12	base	base	NOUN
ap-762	4	13	(	(	PUNCT
ap-762	4	14	such	such	ADJ
ap-762	4	15	as	as	ADP
ap-762	4	16	binary	binary	ADJ
ap-762	4	17	or	or	CCONJ
ap-762	4	18	decimal	decimal	ADJ
ap-762	4	19	numeration	numeration	NOUN
ap-762	4	20	systems	system	NOUN
ap-762	4	21	)	)	PUNCT
ap-762	4	22	,	,	PUNCT
ap-762	4	23	there	there	PRON
ap-762	4	24	are	be	VERB
ap-762	4	25	several	several	ADJ
ap-762	4	26	strange	strange	ADJ
ap-762	4	27	and	and	CCONJ
ap-762	4	28	unsteady	unsteady	ADJ
ap-762	4	29	(	(	PUNCT
ap-762	4	30	i.e.	i.e.	X
ap-762	4	31	depending	depend	VERB
ap-762	4	32	on	on	ADP
ap-762	4	33	the	the	DET
ap-762	4	34	nature	nature	NOUN
ap-762	4	35	of	of	ADP
ap-762	4	36	the	the	DET
ap-762	4	37	base	base	PROPN
ap-762	4	38	�	�	PROPN
ap-762	4	39	)	)	PUNCT
ap-762	4	40	phenomena	phenomenon	NOUN
ap-762	4	41	,	,	PUNCT
ap-762	4	42	which	which	PRON
ap-762	4	43	have	have	VERB
ap-762	4	44	to	to	PART
ap-762	4	45	be	be	AUX
ap-762	4	46	examined	examine	VERB
ap-762	4	47	and	and	CCONJ
ap-762	4	48	described	describe	VERB
ap-762	4	49	before	before	SCONJ
ap-762	4	50	we	we	PRON
ap-762	4	51	are	be	AUX
ap-762	4	52	able	able	ADJ
ap-762	4	53	to	to	PART
ap-762	4	54	employ	employ	VERB
ap-762	4	55	these	these	DET
ap-762	4	56	systems	system	NOUN
ap-762	4	57	.	.	PUNCT
ap-762	5	1	the	the	DET
ap-762	5	2	work	work	NOUN
ap-762	5	3	is	be	AUX
ap-762	5	4	organized	organize	VERB
ap-762	5	5	as	as	SCONJ
ap-762	5	6	follows	follow	VERB
ap-762	5	7	.	.	PUNCT
ap-762	6	1	in	in	ADP
ap-762	6	2	the	the	DET
ap-762	6	3	first	first	ADJ
ap-762	6	4	part	part	NOUN
ap-762	6	5	,	,	PUNCT
ap-762	6	6	there	there	PRON
ap-762	6	7	is	be	VERB
ap-762	6	8	a	a	DET
ap-762	6	9	survey	survey	NOUN
ap-762	6	10	of	of	ADP
ap-762	6	11	the	the	DET
ap-762	6	12	already	already	ADV
ap-762	6	13	classical	classical	ADJ
ap-762	6	14	�	�	NOUN
ap-762	6	15	-expansions	-expansion	NOUN
ap-762	6	16	of	of	ADP
ap-762	6	17	real	real	ADJ
ap-762	6	18	numbers	number	NOUN
ap-762	6	19	.	.	PUNCT
ap-762	7	1	we	we	PRON
ap-762	7	2	recall	recall	VERB
ap-762	7	3	basic	basic	ADJ
ap-762	7	4	definitions	definition	NOUN
ap-762	7	5	and	and	CCONJ
ap-762	7	6	fundamentals	fundamental	NOUN
ap-762	7	7	;	;	PUNCT
ap-762	7	8	then	then	ADV
ap-762	7	9	we	we	PRON
ap-762	7	10	discuss	discuss	VERB
ap-762	7	11	two	two	NUM
ap-762	7	12	key	key	ADJ
ap-762	7	13	problems	problem	NOUN
ap-762	7	14	of	of	ADP
ap-762	7	15	these	these	DET
ap-762	7	16	numeration	numeration	NOUN
ap-762	7	17	systems	system	NOUN
ap-762	7	18	–	–	PUNCT
ap-762	7	19	the	the	DET
ap-762	7	20	so	so	ADV
ap-762	7	21	-	-	PUNCT
ap-762	7	22	called	call	VERB
ap-762	7	23	finiteness	finiteness	NOUN
ap-762	7	24	property	property	NOUN
ap-762	7	25	and	and	CCONJ
ap-762	7	26	the	the	DET
ap-762	7	27	problem	problem	NOUN
ap-762	7	28	of	of	ADP
ap-762	7	29	fractional	fractional	ADJ
ap-762	7	30	parts	part	NOUN
ap-762	7	31	arising	arise	VERB
ap-762	7	32	under	under	ADP
ap-762	7	33	addition	addition	NOUN
ap-762	7	34	and	and	CCONJ
ap-762	7	35	multiplication	multiplication	NOUN
ap-762	7	36	of	of	ADP
ap-762	7	37	integers	integer	NOUN
ap-762	7	38	.	.	PUNCT
ap-762	8	1	in	in	ADP
ap-762	8	2	the	the	DET
ap-762	8	3	second	second	ADJ
ap-762	8	4	part	part	NOUN
ap-762	8	5	,	,	PUNCT
ap-762	8	6	we	we	PRON
ap-762	8	7	study	study	VERB
ap-762	8	8	a	a	DET
ap-762	8	9	slightly	slightly	ADV
ap-762	8	10	different	different	ADJ
ap-762	8	11	approach	approach	NOUN
ap-762	8	12	to	to	ADP
ap-762	8	13	irrational	irrational	ADJ
ap-762	8	14	representations	representation	NOUN
ap-762	8	15	of	of	ADP
ap-762	8	16	real	real	ADJ
ap-762	8	17	numbers	number	NOUN
ap-762	8	18	,	,	PUNCT
ap-762	8	19	which	which	PRON
ap-762	8	20	is	be	AUX
ap-762	8	21	called	call	VERB
ap-762	8	22	�	�	NOUN
ap-762	8	23	-adic	-adic	ADJ
ap-762	8	24	expansions	expansion	NOUN
ap-762	8	25	.	.	PUNCT
ap-762	9	1	since	since	SCONJ
ap-762	9	2	this	this	DET
ap-762	9	3	concept	concept	NOUN
ap-762	9	4	has	have	AUX
ap-762	9	5	been	be	AUX
ap-762	9	6	much	much	ADV
ap-762	9	7	less	less	ADV
ap-762	9	8	studied	study	VERB
ap-762	9	9	in	in	ADP
ap-762	9	10	the	the	DET
ap-762	9	11	past	past	NOUN
ap-762	9	12	,	,	PUNCT
ap-762	9	13	we	we	PRON
ap-762	9	14	focus	focus	VERB
ap-762	9	15	on	on	ADP
ap-762	9	16	one	one	NUM
ap-762	9	17	particular	particular	ADJ
ap-762	9	18	irrationality	irrationality	NOUN
ap-762	9	19	(	(	PUNCT
ap-762	9	20	namely	namely	ADV
ap-762	9	21	the	the	DET
ap-762	9	22	golden	golden	ADJ
ap-762	9	23	mean	mean	NOUN
ap-762	9	24	�	�	PROPN
ap-762	9	25	)	)	PUNCT
ap-762	9	26	,	,	PUNCT
ap-762	9	27	rather	rather	ADV
ap-762	9	28	than	than	ADP
ap-762	9	29	trying	try	VERB
ap-762	9	30	to	to	PART
ap-762	9	31	explain	explain	VERB
ap-762	9	32	everything	everything	PRON
ap-762	9	33	in	in	ADP
ap-762	9	34	general	general	ADJ
ap-762	9	35	.	.	PUNCT
ap-762	10	1	after	after	ADP
ap-762	10	2	giving	give	VERB
ap-762	10	3	necessary	necessary	ADJ
ap-762	10	4	definitions	definition	NOUN
ap-762	10	5	we	we	PRON
ap-762	10	6	discuss	discuss	VERB
ap-762	10	7	the	the	DET
ap-762	10	8	relations	relation	NOUN
ap-762	10	9	of	of	ADP
ap-762	10	10	these	these	DET
ap-762	10	11	�	�	NOUN
ap-762	10	12	-adic	-adic	ADJ
ap-762	10	13	expansions	expansion	NOUN
ap-762	10	14	with	with	ADP
ap-762	10	15	integers	integer	NOUN
ap-762	10	16	and	and	CCONJ
ap-762	10	17	rationals	rational	NOUN
ap-762	10	18	,	,	PUNCT
ap-762	10	19	and	and	CCONJ
ap-762	10	20	we	we	PRON
ap-762	10	21	also	also	ADV
ap-762	10	22	study	study	VERB
ap-762	10	23	an	an	DET
ap-762	10	24	analogue	analogue	NOUN
ap-762	10	25	to	to	ADP
ap-762	10	26	the	the	DET
ap-762	10	27	finiteness	finiteness	ADJ
ap-762	10	28	problem	problem	NOUN
ap-762	10	29	for	for	ADP
ap-762	10	30	�	�	NOUN
ap-762	10	31	-expansions	-expansion	NOUN
ap-762	10	32	.	.	NOUN
ap-762	10	33	2	2	NUM
ap-762	10	34	beta	beta	NOUN
ap-762	10	35	-	-	PUNCT
ap-762	10	36	numeration	numeration	NOUN
ap-762	10	37	systems	system	NOUN
ap-762	10	38	let	let	VERB
ap-762	10	39	�	�	SYM
ap-762	10	40	>	>	X
ap-762	10	41	1	1	NUM
ap-762	10	42	be	be	VERB
ap-762	10	43	a	a	DET
ap-762	10	44	fixed	fixed	ADJ
ap-762	10	45	real	real	ADJ
ap-762	10	46	number	number	NOUN
ap-762	10	47	.	.	PUNCT
ap-762	11	1	a	a	DET
ap-762	11	2	representation	representation	NOUN
ap-762	11	3	in	in	ADP
ap-762	11	4	base	base	PROPN
ap-762	11	5	�	�	PROPN
ap-762	11	6	(	(	PUNCT
ap-762	11	7	or	or	CCONJ
ap-762	11	8	simply	simply	ADV
ap-762	11	9	�	�	PROPN
ap-762	11	10	-representation	-representation	PROPN
ap-762	11	11	)	)	PUNCT
ap-762	11	12	of	of	ADP
ap-762	11	13	a	a	DET
ap-762	11	14	real	real	ADJ
ap-762	11	15	number	number	NOUN
ap-762	11	16	x	x	SYM
ap-762	11	17	�	�	PROPN
ap-762	11	18	�	�	PROPN
ap-762	11	19	r	r	NOUN
ap-762	11	20	is	be	AUX
ap-762	11	21	an	an	DET
ap-762	11	22	infinite	infinite	ADJ
ap-762	11	23	sequence	sequence	NOUN
ap-762	11	24	(	(	PUNCT
ap-762	11	25	)	)	PUNCT
ap-762	11	26	xi	xi	ADP
ap-762	11	27	n	n	PROPN
ap-762	11	28	i	i	PROPN
ap-762	11	29	�	�	PROPN
ap-762	11	30	�	�	PROPN
ap-762	11	31	�	�	PROPN
ap-762	11	32	�	�	PROPN
ap-762	11	33	,	,	PUNCT
ap-762	11	34	xi	xi	X
ap-762	11	35	�	�	PROPN
ap-762	11	36	z	z	PROPN
ap-762	11	37	such	such	ADJ
ap-762	11	38	that	that	SCONJ
ap-762	11	39	x	x	X
ap-762	11	40	x	x	PUNCT
ap-762	11	41	x	x	PUNCT
ap-762	11	42	x	x	SYM
ap-762	11	43	xn	xn	PROPN
ap-762	11	44	n	n	CCONJ
ap-762	11	45	n	n	CCONJ
ap-762	11	46	n	n	CCONJ
ap-762	11	47	�	�	PROPN
ap-762	11	48	�	�	PROPN
ap-762	11	49	�	�	PROPN
ap-762	11	50	�	�	PROPN
ap-762	11	51	�	�	PROPN
ap-762	11	52	�	�	PROPN
ap-762	11	53	�	�	PROPN
ap-762	11	54	�	�	PROPN
ap-762	11	55	�	�	PROPN
ap-762	11	56	�	�	PROPN
ap-762	11	57	�	�	PROPN
ap-762	11	58	�	�	PROPN
ap-762	11	59	�	�	PROPN
ap-762	11	60	�	�	PROPN
ap-762	11	61	1	1	NUM
ap-762	11	62	1	1	NUM
ap-762	11	63	0	0	NUM
ap-762	11	64	0	0	NUM
ap-762	11	65	1	1	NUM
ap-762	11	66	1	1	NUM
ap-762	11	67	�	�	PROPN
ap-762	11	68	�	�	PROPN
ap-762	11	69	for	for	ADP
ap-762	11	70	some	some	DET
ap-762	11	71	n	n	PRON
ap-762	11	72	�	�	PROPN
ap-762	11	73	z.	z.	PROPN
ap-762	11	74	a	a	DET
ap-762	11	75	particular	particular	ADJ
ap-762	11	76	�	�	NOUN
ap-762	11	77	-representation	-representation	NOUN
ap-762	11	78	with	with	ADP
ap-762	11	79	xi	xi	PROPN
ap-762	11	80	i	i	PRON
ap-762	11	81	i	i	PROPN
ap-762	11	82	n	n	CCONJ
ap-762	11	83	n	n	CCONJ
ap-762	11	84	�	�	PROPN
ap-762	11	85	�	�	PROPN
ap-762	11	86	�	�	PROPN
ap-762	11	87	�	�	PROPN
ap-762	11	88	�	�	PROPN
ap-762	11	89	�	�	PROPN
ap-762	11	90	1	1	NUM
ap-762	11	91	for	for	ADP
ap-762	11	92	all	all	DET
ap-762	11	93	�	�	PROPN
ap-762	11	94	�	�	PROPN
ap-762	11	95	n	n	CCONJ
ap-762	11	96	n	n	NOUN
ap-762	11	97	is	be	AUX
ap-762	11	98	called	call	VERB
ap-762	11	99	�	�	PROPN
ap-762	11	100	-expansion	-expansion	PROPN
ap-762	11	101	,	,	PUNCT
ap-762	11	102	see	see	VERB
ap-762	11	103	[	[	X
ap-762	11	104	1	1	NUM
ap-762	11	105	]	]	PUNCT
ap-762	11	106	.	.	PUNCT
ap-762	12	1	the	the	DET
ap-762	12	2	greedy	greedy	ADJ
ap-762	12	3	algorithm	algorithm	NOUN
ap-762	12	4	computes	compute	VERB
ap-762	12	5	the	the	DET
ap-762	12	6	digits	digit	NOUN
ap-762	12	7	of	of	ADP
ap-762	12	8	the	the	DET
ap-762	12	9	�	�	NOUN
ap-762	12	10	-expansions	-expansion	NOUN
ap-762	12	11	of	of	ADP
ap-762	12	12	a	a	DET
ap-762	12	13	real	real	ADJ
ap-762	12	14	number	number	NOUN
ap-762	12	15	x	x	NOUN
ap-762	12	16	:	:	PUNCT
ap-762	12	17	let	let	VERB
ap-762	12	18	[	[	PUNCT
ap-762	12	19	]	]	X
ap-762	12	20	x	x	X
ap-762	12	21	and	and	CCONJ
ap-762	12	22	{	{	PUNCT
ap-762	12	23	}	}	PUNCT
ap-762	12	24	x	x	PUNCT
ap-762	12	25	denote	denote	VERB
ap-762	12	26	the	the	DET
ap-762	12	27	integer	integer	NOUN
ap-762	12	28	and	and	CCONJ
ap-762	12	29	the	the	DET
ap-762	12	30	fractional	fractional	ADJ
ap-762	12	31	part	part	NOUN
ap-762	12	32	of	of	ADP
ap-762	12	33	x	x	PRON
ap-762	12	34	,	,	PUNCT
ap-762	12	35	respectively	respectively	ADV
ap-762	12	36	.	.	PUNCT
ap-762	13	1	find	find	VERB
ap-762	13	2	n	n	PRON
ap-762	13	3	�	�	PROPN
ap-762	13	4	z	z	PROPN
ap-762	13	5	such	such	ADJ
ap-762	13	6	that	that	SCONJ
ap-762	13	7	�	�	PROPN
ap-762	13	8	�	�	PROPN
ap-762	13	9	n	n	CCONJ
ap-762	13	10	nx	nx	PROPN
ap-762	13	11	�	�	PROPN
ap-762	13	12	�	�	PROPN
ap-762	13	13	1	1	NUM
ap-762	13	14	.	.	PUNCT
ap-762	14	1	put	put	VERB
ap-762	14	2	x	x	X
ap-762	14	3	xn	xn	PROPN
ap-762	14	4	n	n	CCONJ
ap-762	14	5	�	�	PROPN
ap-762	14	6	[	[	PUNCT
ap-762	14	7	]	]	X
ap-762	14	8	�	�	PROPN
ap-762	14	9	and	and	CCONJ
ap-762	14	10	r	r	NOUN
ap-762	14	11	xn	xn	PROPN
ap-762	14	12	n	n	CCONJ
ap-762	14	13	�	�	PROPN
ap-762	14	14	[	[	PUNCT
ap-762	14	15	]	]	X
ap-762	14	16	�	�	PROPN
ap-762	14	17	.	.	PUNCT
ap-762	15	1	for	for	ADP
ap-762	15	2	i	i	PROPN
ap-762	15	3	n	n	CCONJ
ap-762	15	4	n	n	CCONJ
ap-762	15	5	�	�	PROPN
ap-762	15	6	�	�	PROPN
ap-762	15	7	�	�	PROPN
ap-762	15	8	1	1	NUM
ap-762	15	9	2	2	NUM
ap-762	15	10	,	,	PUNCT
ap-762	15	11	,	,	PUNCT
ap-762	15	12	�	�	PROPN
ap-762	15	13	put	put	VERB
ap-762	15	14	x	x	PUNCT
ap-762	15	15	ri	ri	PROPN
ap-762	15	16	i	i	PROPN
ap-762	15	17	�	�	PROPN
ap-762	15	18	�	�	PROPN
ap-762	15	19	[	[	PUNCT
ap-762	15	20	]	]	X
ap-762	15	21	�	�	PROPN
ap-762	15	22	1	1	NUM
ap-762	15	23	and	and	CCONJ
ap-762	15	24	r	r	PROPN
ap-762	15	25	ri	ri	PROPN
ap-762	15	26	i	i	PROPN
ap-762	15	27	�	�	PROPN
ap-762	15	28	�	�	PROPN
ap-762	15	29	[	[	PUNCT
ap-762	15	30	]	]	X
ap-762	15	31	�	�	PROPN
ap-762	15	32	1	1	NUM
ap-762	15	33	.	.	PUNCT
ap-762	16	1	the	the	DET
ap-762	16	2	�	�	PROPN
ap-762	16	3	-expansion	-expansion	PROPN
ap-762	16	4	can	can	AUX
ap-762	16	5	be	be	AUX
ap-762	16	6	seen	see	VERB
ap-762	16	7	as	as	ADP
ap-762	16	8	an	an	DET
ap-762	16	9	analogue	analogue	NOUN
ap-762	16	10	to	to	ADP
ap-762	16	11	the	the	DET
ap-762	16	12	ordinary	ordinary	ADJ
ap-762	16	13	expansion	expansion	NOUN
ap-762	16	14	in	in	ADP
ap-762	16	15	a	a	DET
ap-762	16	16	system	system	NOUN
ap-762	16	17	with	with	ADP
ap-762	16	18	an	an	DET
ap-762	16	19	integer	integer	NOUN
ap-762	16	20	base	base	NOUN
ap-762	16	21	(	(	PUNCT
ap-762	16	22	such	such	ADJ
ap-762	16	23	as	as	ADP
ap-762	16	24	a	a	DET
ap-762	16	25	decimal	decimal	ADJ
ap-762	16	26	or	or	CCONJ
ap-762	16	27	binary	binary	ADJ
ap-762	16	28	system	system	NOUN
ap-762	16	29	)	)	PUNCT
ap-762	16	30	,	,	PUNCT
ap-762	16	31	we	we	PRON
ap-762	16	32	usually	usually	ADV
ap-762	16	33	use	use	VERB
ap-762	16	34	the	the	DET
ap-762	16	35	natural	natural	ADJ
ap-762	16	36	notation	notation	NOUN
ap-762	16	37	x	x	PUNCT
ap-762	16	38	x	x	PUNCT
ap-762	16	39	x	x	PUNCT
ap-762	16	40	x	x	SYM
ap-762	16	41	xn	xn	PROPN
ap-762	16	42	n	n	CCONJ
ap-762	16	43	�	�	PROPN
ap-762	16	44	�	�	PROPN
ap-762	16	45	�	�	PROPN
ap-762	16	46	�	�	PROPN
ap-762	16	47	�	�	PROPN
ap-762	16	48	1	1	NUM
ap-762	16	49	0	0	NUM
ap-762	16	50	1	1	NUM
ap-762	16	51	�	�	PROPN
ap-762	16	52	�	�	PROPN
ap-762	16	53	and	and	CCONJ
ap-762	16	54	we	we	PRON
ap-762	16	55	say	say	VERB
ap-762	16	56	that	that	SCONJ
ap-762	16	57	the	the	DET
ap-762	16	58	coefficients	coefficient	NOUN
ap-762	16	59	x	x	SYM
ap-762	16	60	xn	xn	SYM
ap-762	16	61	�	�	PROPN
ap-762	16	62	0	0	NUM
ap-762	16	63	form	form	VERB
ap-762	16	64	the	the	DET
ap-762	16	65	integer	integer	NOUN
ap-762	16	66	part	part	NOUN
ap-762	16	67	,	,	PUNCT
ap-762	16	68	whereas	whereas	SCONJ
ap-762	16	69	the	the	DET
ap-762	16	70	coefficients	coefficient	NOUN
ap-762	16	71	x	x	SYM
ap-762	16	72	x	x	SYM
ap-762	16	73	�	�	PROPN
ap-762	16	74	�	�	PROPN
ap-762	16	75	1	1	NUM
ap-762	16	76	2	2	NUM
ap-762	16	77	�	�	PROPN
ap-762	16	78	form	form	VERB
ap-762	16	79	the	the	DET
ap-762	16	80	fractional	fractional	ADJ
ap-762	16	81	part	part	NOUN
ap-762	16	82	of	of	ADP
ap-762	16	83	the	the	DET
ap-762	16	84	�	�	PROPN
ap-762	16	85	-expansion	-expansion	NOUN
ap-762	16	86	of	of	ADP
ap-762	16	87	a	a	DET
ap-762	16	88	number	number	NOUN
ap-762	16	89	x.	x.	NOUN
ap-762	16	90	a	a	DET
ap-762	16	91	sequence	sequence	NOUN
ap-762	16	92	of	of	ADP
ap-762	16	93	integer	integer	ADJ
ap-762	16	94	coefficients	coefficient	NOUN
ap-762	16	95	that	that	PRON
ap-762	16	96	corresponds	correspond	VERB
ap-762	16	97	to	to	ADP
ap-762	16	98	some	some	DET
ap-762	16	99	�	�	NOUN
ap-762	16	100	-expansion	-expansion	NOUN
ap-762	16	101	is	be	AUX
ap-762	16	102	sometimes	sometimes	ADV
ap-762	16	103	called	call	VERB
ap-762	16	104	admissible	admissible	ADJ
ap-762	16	105	in	in	ADP
ap-762	16	106	the	the	DET
ap-762	16	107	�	�	PROPN
ap-762	16	108	-numeration	-numeration	NOUN
ap-762	16	109	system	system	NOUN
ap-762	16	110	.	.	PUNCT
ap-762	17	1	a	a	DET
ap-762	17	2	sequence	sequence	NOUN
ap-762	17	3	(	(	PUNCT
ap-762	17	4	or	or	CCONJ
ap-762	17	5	string	string	NOUN
ap-762	17	6	)	)	PUNCT
ap-762	17	7	of	of	ADP
ap-762	17	8	integer	integer	NOUN
ap-762	17	9	coefficients	coefficient	NOUN
ap-762	17	10	that	that	PRON
ap-762	17	11	is	be	AUX
ap-762	17	12	not	not	PART
ap-762	17	13	admissible	admissible	ADJ
ap-762	17	14	is	be	AUX
ap-762	17	15	called	call	VERB
ap-762	17	16	forbidden	forbidden	ADJ
ap-762	17	17	.	.	PUNCT
ap-762	18	1	for	for	ADP
ap-762	18	2	the	the	DET
ap-762	18	3	characterization	characterization	NOUN
ap-762	18	4	of	of	ADP
ap-762	18	5	an	an	DET
ap-762	18	6	admissible	admissible	ADJ
ap-762	18	7	sequence	sequence	NOUN
ap-762	18	8	one	one	NUM
ap-762	18	9	needs	need	VERB
ap-762	18	10	to	to	PART
ap-762	18	11	introduce	introduce	VERB
ap-762	18	12	the	the	DET
ap-762	18	13	so	so	ADV
ap-762	18	14	-	-	PUNCT
ap-762	18	15	called	call	VERB
ap-762	18	16	rényi	rényi	NOUN
ap-762	18	17	expansion	expansion	NOUN
ap-762	18	18	of	of	ADP
ap-762	18	19	1	1	NUM
ap-762	18	20	,	,	PUNCT
ap-762	18	21	d	d	PROPN
ap-762	18	22	t	t	PROPN
ap-762	18	23	t	t	PROPN
ap-762	18	24	t	t	PROPN
ap-762	18	25	�	�	PROPN
ap-762	18	26	(	(	PUNCT
ap-762	18	27	)	)	PUNCT
ap-762	18	28	:1	:1	SYM
ap-762	18	29	1	1	NUM
ap-762	18	30	2	2	NUM
ap-762	18	31	3	3	NUM
ap-762	18	32	�	�	PROPN
ap-762	18	33	�	�	PROPN
ap-762	18	34	,	,	PUNCT
ap-762	18	35	where	where	SCONJ
ap-762	18	36	t1	t1	PROPN
ap-762	18	37	�	�	PROPN
ap-762	18	38	[	[	PUNCT
ap-762	18	39	]	]	X
ap-762	18	40	�	�	PROPN
ap-762	18	41	and	and	CCONJ
ap-762	18	42	tn	tn	PROPN
ap-762	18	43	n	n	CCONJ
ap-762	18	44	n	n	CCONJ
ap-762	18	45	�	�	PROPN
ap-762	18	46	�	�	PROPN
ap-762	18	47	�	�	PROPN
ap-762	18	48	2	2	NUM
ap-762	18	49	is	be	AUX
ap-762	18	50	the	the	DET
ap-762	18	51	�	�	NOUN
ap-762	18	52	-expansion	-expansion	PROPN
ap-762	18	53	of1	of1	ADJ
ap-762	18	54	1	1	NUM
ap-762	18	55	�	�	PROPN
ap-762	18	56	t	t	PROPN
ap-762	18	57	�	�	PROPN
ap-762	18	58	.	.	PUNCT
ap-762	19	1	the	the	DET
ap-762	19	2	�	�	PROPN
ap-762	19	3	-expansions	-expansion	NOUN
ap-762	19	4	(	(	PUNCT
ap-762	19	5	or	or	CCONJ
ap-762	19	6	�	�	NOUN
ap-762	19	7	-admissible	-admissible	ADJ
ap-762	19	8	sequences	sequence	NOUN
ap-762	19	9	)	)	PUNCT
ap-762	19	10	are	be	AUX
ap-762	19	11	then	then	ADV
ap-762	19	12	characterized	characterize	VERB
ap-762	19	13	by	by	ADP
ap-762	19	14	the	the	DET
ap-762	19	15	parry	parry	PROPN
ap-762	19	16	condition	condition	NOUN
ap-762	19	17	.	.	PUNCT
ap-762	20	1	theorem	theorem	VERB
ap-762	20	2	1.1	1.1	NUM
ap-762	20	3	:	:	PUNCT
ap-762	20	4	(	(	PUNCT
ap-762	20	5	parry	parry	VERB
ap-762	20	6	[	[	X
ap-762	20	7	2	2	NUM
ap-762	20	8	]	]	PUNCT
ap-762	20	9	)	)	PUNCT
ap-762	20	10	.	.	PUNCT
ap-762	21	1	let	let	VERB
ap-762	21	2	�	�	PROPN
ap-762	21	3	>	>	X
ap-762	21	4	1	1	NUM
ap-762	21	5	be	be	AUX
ap-762	21	6	a	a	DET
ap-762	21	7	real	real	ADJ
ap-762	21	8	number	number	NOUN
ap-762	21	9	.	.	PUNCT
ap-762	22	1	let	let	VERB
ap-762	22	2	d	d	PROPN
ap-762	22	3	t	t	PROPN
ap-762	22	4	t	t	PROPN
ap-762	22	5	t	t	PROPN
ap-762	22	6	�	�	PROPN
ap-762	22	7	(	(	PUNCT
ap-762	22	8	)	)	PUNCT
ap-762	22	9	:1	:1	SYM
ap-762	22	10	1	1	NUM
ap-762	22	11	2	2	NUM
ap-762	22	12	3	3	NUM
ap-762	22	13	�	�	PROPN
ap-762	22	14	�	�	PROPN
ap-762	22	15	be	be	AUX
ap-762	22	16	the	the	DET
ap-762	22	17	rényi	rényi	NOUN
ap-762	22	18	expansion	expansion	NOUN
ap-762	22	19	of	of	ADP
ap-762	22	20	one	one	NUM
ap-762	22	21	.	.	PUNCT
ap-762	23	1	the	the	DET
ap-762	23	2	sequence	sequence	NOUN
ap-762	23	3	(	(	PUNCT
ap-762	23	4	)	)	PUNCT
ap-762	23	5	xi	xi	ADP
ap-762	23	6	n	n	PROPN
ap-762	24	1	i	i	PROPN
ap-762	24	2	m	m	PROPN
ap-762	24	3	�	�	PROPN
ap-762	24	4	�	�	PROPN
ap-762	24	5	with	with	ADP
ap-762	24	6	xi	xi	PROPN
ap-762	24	7	�	�	PROPN
ap-762	24	8	{	{	PUNCT
ap-762	24	9	,	,	PUNCT
ap-762	24	10	,	,	PUNCT
ap-762	24	11	,	,	PUNCT
ap-762	24	12	[	[	PUNCT
ap-762	24	13	]	]	X
ap-762	24	14	}	}	SYM
ap-762	24	15	0	0	SYM
ap-762	24	16	1	1	NUM
ap-762	24	17	�	�	PROPN
ap-762	24	18	�	�	PROPN
ap-762	24	19	is	be	AUX
ap-762	24	20	a	a	DET
ap-762	24	21	�	�	NOUN
ap-762	24	22	-expansion	-expansion	NOUN
ap-762	24	23	of	of	ADP
ap-762	24	24	some	some	DET
ap-762	24	25	x	x	SYM
ap-762	24	26	�	�	PROPN
ap-762	24	27	0	0	NUM
ap-762	24	28	if	if	SCONJ
ap-762	24	29	and	and	CCONJ
ap-762	24	30	only	only	ADV
ap-762	24	31	if	if	SCONJ
ap-762	24	32	x	x	X
ap-762	24	33	x	x	PUNCT
ap-762	24	34	xn	xn	PROPN
ap-762	25	1	p	p	NOUN
ap-762	25	2	n	n	PROPN
ap-762	25	3	p	p	PROPN
ap-762	25	4	m	m	PROPN
ap-762	25	5	�	�	PROPN
ap-762	25	6	�	�	PROPN
ap-762	25	7	�	�	PROPN
ap-762	25	8	1	1	NUM
ap-762	25	9	�	�	PROPN
ap-762	25	10	is	be	AUX
ap-762	25	11	lexicographically	lexicographically	ADV
ap-762	25	12	strictly	strictly	ADV
ap-762	25	13	smaller	small	ADJ
ap-762	25	14	(	(	PUNCT
ap-762	25	15	denoted	denote	VERB
ap-762	25	16	by	by	ADP
ap-762	25	17	the	the	DET
ap-762	25	18	symbol	symbol	NOUN
ap-762	25	19	�	�	PROPN
ap-762	25	20	)	)	PUNCT
ap-762	25	21	than	than	ADP
ap-762	25	22	d	d	PROPN
ap-762	25	23	�	�	PROPN
ap-762	25	24	(	(	PUNCT
ap-762	25	25	)	)	PUNCT
ap-762	25	26	1	1	NUM
ap-762	25	27	for	for	ADP
ap-762	25	28	all	all	DET
ap-762	25	29	0	0	NUM
ap-762	25	30	�	�	PROPN
ap-762	25	31	�	�	PROPN
ap-762	25	32	�	�	PROPN
ap-762	25	33	p	p	NOUN
ap-762	25	34	n	n	NOUN
ap-762	25	35	m.	m.	NOUN
ap-762	25	36	the	the	DET
ap-762	25	37	set	set	NOUN
ap-762	25	38	of	of	ADP
ap-762	25	39	those	those	DET
ap-762	25	40	x	x	SYM
ap-762	25	41	�	�	NOUN
ap-762	25	42	r	r	NOUN
ap-762	25	43	for	for	ADP
ap-762	25	44	which	which	PRON
ap-762	25	45	the	the	DET
ap-762	25	46	�	�	NOUN
ap-762	25	47	-expansion	-expansion	NOUN
ap-762	25	48	of	of	ADP
ap-762	25	49	x	x	PRON
ap-762	25	50	has	have	VERB
ap-762	25	51	only	only	ADV
ap-762	25	52	a	a	DET
ap-762	25	53	finite	finite	ADJ
ap-762	25	54	number	number	NOUN
ap-762	25	55	of	of	ADP
ap-762	25	56	non	non	ADJ
ap-762	25	57	-	-	ADJ
ap-762	25	58	zero	zero	ADJ
ap-762	25	59	fractional	fractional	ADJ
ap-762	25	60	coefficients	coefficient	NOUN
ap-762	25	61	is	be	AUX
ap-762	25	62	denoted	denote	VERB
ap-762	25	63	by	by	ADP
ap-762	25	64	fin	fin	PROPN
ap-762	25	65	(	(	PUNCT
ap-762	25	66	)	)	PUNCT
ap-762	25	67	�	�	PROPN
ap-762	25	68	.	.	PUNCT
ap-762	26	1	if	if	SCONJ
ap-762	26	2	the	the	DET
ap-762	26	3	�	�	PROPN
ap-762	26	4	-expansion	-expansion	NOUN
ap-762	26	5	of	of	ADP
ap-762	26	6	a	a	DET
ap-762	26	7	real	real	ADJ
ap-762	26	8	number	number	NOUN
ap-762	26	9	x	x	NUM
ap-762	26	10	is	be	AUX
ap-762	26	11	of	of	ADP
ap-762	26	12	the	the	DET
ap-762	26	13	form	form	NOUN
ap-762	26	14	x	x	PUNCT
ap-762	26	15	xi	xi	INTJ
ap-762	26	16	i	i	PRON
ap-762	27	1	i	i	PROPN
ap-762	27	2	n	n	NUM
ap-762	27	3	�	�	PROPN
ap-762	27	4	�	�	PROPN
ap-762	27	5	�	�	PROPN
ap-762	27	6	0	0	NUM
ap-762	27	7	,	,	PUNCT
ap-762	27	8	i.e.	i.e.	X
ap-762	27	9	there	there	PRON
ap-762	27	10	is	be	VERB
ap-762	27	11	no	no	DET
ap-762	27	12	fractional	fractional	ADJ
ap-762	27	13	part	part	NOUN
ap-762	27	14	,	,	PUNCT
ap-762	27	15	the	the	DET
ap-762	27	16	number	number	NOUN
ap-762	27	17	x	x	PUNCT
ap-762	27	18	is	be	AUX
ap-762	27	19	said	say	VERB
ap-762	27	20	to	to	PART
ap-762	27	21	be	be	AUX
ap-762	27	22	a	a	DET
ap-762	27	23	�	�	NOUN
ap-762	27	24	-integer	-integer	NOUN
ap-762	27	25	.	.	PUNCT
ap-762	28	1	the	the	DET
ap-762	28	2	set	set	NOUN
ap-762	28	3	of	of	ADP
ap-762	28	4	all	all	DET
ap-762	28	5	�	�	NOUN
ap-762	28	6	-integers	-integer	NOUN
ap-762	28	7	is	be	AUX
ap-762	28	8	denoted	denote	VERB
ap-762	28	9	by	by	ADP
ap-762	28	10	z	z	PROPN
ap-762	28	11	�	�	PROPN
ap-762	28	12	.	.	PROPN
ap-762	28	13	2.1	2.1	NUM
ap-762	28	14	finiteness	finiteness	NOUN
ap-762	28	15	condition	condition	NOUN
ap-762	28	16	in	in	ADP
ap-762	28	17	general	general	ADJ
ap-762	28	18	,	,	PUNCT
ap-762	28	19	the	the	DET
ap-762	28	20	setfin	setfin	NOUN
ap-762	28	21	(	(	PUNCT
ap-762	28	22	)	)	PUNCT
ap-762	28	23	�	�	PROPN
ap-762	28	24	does	do	AUX
ap-762	28	25	not	not	PART
ap-762	28	26	have	have	VERB
ap-762	28	27	to	to	PART
ap-762	28	28	be	be	AUX
ap-762	28	29	closed	close	VERB
ap-762	28	30	under	under	ADP
ap-762	28	31	arithmetic	arithmetic	ADJ
ap-762	28	32	operations	operation	NOUN
ap-762	28	33	,	,	PUNCT
ap-762	28	34	and	and	CCONJ
ap-762	28	35	there	there	PRON
ap-762	28	36	is	be	VERB
ap-762	28	37	no	no	DET
ap-762	28	38	criterion	criterion	NOUN
ap-762	28	39	known	know	VERB
ap-762	28	40	which	which	PRON
ap-762	28	41	would	would	AUX
ap-762	28	42	decide	decide	VERB
ap-762	28	43	whether	whether	SCONJ
ap-762	28	44	fin	fin	NOUN
ap-762	28	45	(	(	PUNCT
ap-762	28	46	)	)	PUNCT
ap-762	28	47	�	�	PROPN
ap-762	28	48	is	be	AUX
ap-762	28	49	a	a	DET
ap-762	28	50	ring	ring	NOUN
ap-762	28	51	.	.	PUNCT
ap-762	29	1	the	the	DET
ap-762	29	2	�	�	PROPN
ap-762	29	3	-numeration	-numeration	PROPN
ap-762	29	4	systems	system	NOUN
ap-762	29	5	for	for	ADP
ap-762	29	6	which	which	PRON
ap-762	29	7	fin	fin	NOUN
ap-762	29	8	(	(	PUNCT
ap-762	29	9	)	)	PUNCT
ap-762	29	10	�	�	PROPN
ap-762	29	11	is	be	AUX
ap-762	29	12	a	a	DET
ap-762	29	13	ring	ring	NOUN
ap-762	29	14	are	be	AUX
ap-762	29	15	equally	equally	ADV
ap-762	29	16	characterized	characterize	VERB
ap-762	29	17	by	by	ADP
ap-762	29	18	the	the	DET
ap-762	29	19	so	so	ADV
ap-762	29	20	-	-	PUNCT
ap-762	29	21	called	call	VERB
ap-762	29	22	property	property	NOUN
ap-762	29	23	(	(	PUNCT
ap-762	29	24	f	f	X
ap-762	29	25	)	)	PUNCT
ap-762	29	26	(	(	PUNCT
ap-762	29	27	f	f	X
ap-762	29	28	)	)	PUNCT
ap-762	29	29	z	z	NOUN
ap-762	29	30	[	[	PUNCT
ap-762	29	31	]	]	X
ap-762	29	32	(	(	PUNCT
ap-762	29	33	)	)	PUNCT
ap-762	29	34	�	�	PROPN
ap-762	29	35	�	�	PROPN
ap-762	29	36	�	�	PROPN
ap-762	29	37	�	�	PROPN
ap-762	29	38	1	1	NUM
ap-762	29	39	fin	fin	NOUN
ap-762	29	40	,	,	PUNCT
ap-762	29	41	24	24	NUM
ap-762	29	42	©	©	PROPN
ap-762	29	43	czech	czech	PROPN
ap-762	29	44	technical	technical	PROPN
ap-762	29	45	university	university	PROPN
ap-762	29	46	publishing	publishing	NOUN
ap-762	29	47	house	house	NOUN
ap-762	29	48	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-762	29	49	acta	acta	PROPN
ap-762	29	50	polytechnica	polytechnica	PROPN
ap-762	29	51	vol	vol	NOUN
ap-762	29	52	.	.	PROPN
ap-762	30	1	45	45	NUM
ap-762	30	2	no	no	NOUN
ap-762	30	3	.	.	PUNCT
ap-762	31	1	5/2005	5/2005	NUM
ap-762	31	2	czech	czech	PROPN
ap-762	31	3	technical	technical	PROPN
ap-762	31	4	university	university	PROPN
ap-762	31	5	in	in	ADP
ap-762	31	6	prague	prague	PROPN
ap-762	31	7	non	non	ADJ
ap-762	31	8	-	-	ADJ
ap-762	31	9	standard	standard	ADJ
ap-762	31	10	numeration	numeration	NOUN
ap-762	31	11	systems	system	NOUN
ap-762	31	12	p.	p.	NOUN
ap-762	31	13	ambrož	ambrož	NOUN
ap-762	32	1	we	we	PRON
ap-762	32	2	study	study	VERB
ap-762	32	3	some	some	DET
ap-762	32	4	properties	property	NOUN
ap-762	32	5	of	of	ADP
ap-762	32	6	non	non	ADJ
ap-762	32	7	-	-	ADJ
ap-762	32	8	standard	standard	ADJ
ap-762	32	9	numeration	numeration	NOUN
ap-762	32	10	systems	system	NOUN
ap-762	32	11	with	with	ADP
ap-762	32	12	an	an	DET
ap-762	32	13	irrational	irrational	ADJ
ap-762	32	14	base	base	NOUN
ap-762	32	15	�	�	PROPN
ap-762	32	16	>	>	SYM
ap-762	32	17	1	1	NUM
ap-762	32	18	,	,	PUNCT
ap-762	32	19	based	base	VERB
ap-762	32	20	on	on	ADP
ap-762	32	21	the	the	DET
ap-762	32	22	so	so	ADV
ap-762	32	23	-	-	PUNCT
ap-762	32	24	called	call	VERB
ap-762	32	25	beta	beta	NOUN
ap-762	32	26	-	-	PUNCT
ap-762	32	27	expansions	expansion	NOUN
ap-762	32	28	of	of	ADP
ap-762	32	29	real	real	ADJ
ap-762	32	30	numbers	number	NOUN
ap-762	32	31	[	[	X
ap-762	32	32	1	1	NUM
ap-762	32	33	]	]	PUNCT
ap-762	32	34	.	.	PUNCT
ap-762	33	1	we	we	PRON
ap-762	33	2	discuss	discuss	VERB
ap-762	33	3	two	two	NUM
ap-762	33	4	important	important	ADJ
ap-762	33	5	properties	property	NOUN
ap-762	33	6	of	of	ADP
ap-762	33	7	these	these	DET
ap-762	33	8	systems	system	NOUN
ap-762	33	9	,	,	PUNCT
ap-762	33	10	namely	namely	ADV
ap-762	33	11	the	the	DET
ap-762	33	12	finiteness	finiteness	ADJ
ap-762	33	13	property	property	NOUN
ap-762	33	14	,	,	PUNCT
ap-762	33	15	stating	state	VERB
ap-762	33	16	whether	whether	SCONJ
ap-762	33	17	the	the	DET
ap-762	33	18	set	set	NOUN
ap-762	33	19	of	of	ADP
ap-762	33	20	finite	finite	ADJ
ap-762	33	21	expansions	expansion	NOUN
ap-762	33	22	in	in	ADP
ap-762	33	23	a	a	DET
ap-762	33	24	given	give	VERB
ap-762	33	25	system	system	NOUN
ap-762	33	26	forms	form	VERB
ap-762	33	27	a	a	DET
ap-762	33	28	ring	ring	NOUN
ap-762	33	29	,	,	PUNCT
ap-762	33	30	and	and	CCONJ
ap-762	33	31	then	then	ADV
ap-762	33	32	the	the	DET
ap-762	33	33	problem	problem	NOUN
ap-762	33	34	of	of	ADP
ap-762	33	35	fractional	fractional	ADJ
ap-762	33	36	digits	digit	NOUN
ap-762	33	37	arising	arise	VERB
ap-762	33	38	under	under	ADP
ap-762	33	39	arithmetic	arithmetic	ADJ
ap-762	33	40	operations	operation	NOUN
ap-762	33	41	with	with	ADP
ap-762	33	42	integers	integer	NOUN
ap-762	33	43	in	in	ADP
ap-762	33	44	a	a	DET
ap-762	33	45	given	give	VERB
ap-762	33	46	system	system	NOUN
ap-762	33	47	.	.	PUNCT
ap-762	34	1	then	then	ADV
ap-762	34	2	we	we	PRON
ap-762	34	3	introduce	introduce	VERB
ap-762	34	4	another	another	DET
ap-762	34	5	way	way	NOUN
ap-762	34	6	of	of	ADP
ap-762	34	7	irrational	irrational	ADJ
ap-762	34	8	representation	representation	NOUN
ap-762	34	9	of	of	ADP
ap-762	34	10	numbers	number	NOUN
ap-762	34	11	,	,	PUNCT
ap-762	34	12	slightly	slightly	ADV
ap-762	34	13	different	different	ADJ
ap-762	34	14	from	from	ADP
ap-762	34	15	classical	classical	ADJ
ap-762	34	16	beta	beta	NOUN
ap-762	34	17	-	-	PUNCT
ap-762	34	18	expansions	expansion	NOUN
ap-762	34	19	.	.	PUNCT
ap-762	35	1	here	here	ADV
ap-762	35	2	we	we	PRON
ap-762	35	3	restrict	restrict	VERB
ap-762	35	4	ourselves	ourselves	PRON
ap-762	35	5	to	to	ADP
ap-762	35	6	one	one	NUM
ap-762	35	7	irrational	irrational	ADJ
ap-762	35	8	base	base	NOUN
ap-762	35	9	–	–	PUNCT
ap-762	35	10	the	the	DET
ap-762	35	11	golden	golden	ADJ
ap-762	35	12	mean	mean	NOUN
ap-762	35	13	�	�	PROPN
ap-762	35	14	–	–	PUNCT
ap-762	35	15	and	and	CCONJ
ap-762	35	16	we	we	PRON
ap-762	35	17	study	study	VERB
ap-762	35	18	the	the	DET
ap-762	35	19	finiteness	finiteness	ADJ
ap-762	35	20	property	property	NOUN
ap-762	35	21	again	again	ADV
ap-762	35	22	.	.	PUNCT
ap-762	36	1	keywords	keyword	NOUN
ap-762	36	2	:	:	PUNCT
ap-762	36	3	numeration	numeration	NOUN
ap-762	36	4	system	system	NOUN
ap-762	36	5	,	,	PUNCT
ap-762	36	6	beta	beta	ADJ
ap-762	36	7	expansion	expansion	NOUN
ap-762	36	8	,	,	PUNCT
ap-762	36	9	tau	tau	NOUN
ap-762	36	10	-	-	PUNCT
ap-762	36	11	adic	adic	ADJ
ap-762	36	12	expansion	expansion	NOUN
ap-762	36	13	.	.	PUNCT
ap-762	37	1	where	where	SCONJ
ap-762	37	2	z	z	NOUN
ap-762	37	3	[	[	PUNCT
ap-762	37	4	]	]	X
ap-762	37	5	�	�	PROPN
ap-762	37	6	denotes	denote	VERB
ap-762	37	7	the	the	DET
ap-762	37	8	ring	ring	NOUN
ap-762	37	9	of	of	ADP
ap-762	37	10	polynomials	polynomial	NOUN
ap-762	37	11	with	with	ADP
ap-762	37	12	integer	integer	ADJ
ap-762	37	13	coefficients	coefficient	NOUN
ap-762	37	14	in	in	ADP
ap-762	37	15	�	�	PROPN
ap-762	37	16	.	.	PUNCT
ap-762	38	1	it	it	PRON
ap-762	38	2	is	be	AUX
ap-762	38	3	known	know	VERB
ap-762	38	4	[	[	X
ap-762	38	5	3	3	NUM
ap-762	38	6	]	]	PUNCT
ap-762	38	7	that	that	SCONJ
ap-762	38	8	the	the	DET
ap-762	38	9	condition	condition	NOUN
ap-762	38	10	(	(	PUNCT
ap-762	38	11	f	f	X
ap-762	38	12	)	)	PUNCT
ap-762	38	13	implies	imply	VERB
ap-762	38	14	that	that	SCONJ
ap-762	38	15	�	�	PROPN
ap-762	38	16	is	be	AUX
ap-762	38	17	a	a	DET
ap-762	38	18	pisot	pisot	ADJ
ap-762	38	19	number	number	NOUN
ap-762	38	20	(	(	PUNCT
ap-762	38	21	an	an	DET
ap-762	38	22	algebraic	algebraic	ADJ
ap-762	38	23	integer	integer	NOUN
ap-762	38	24	with	with	ADP
ap-762	38	25	all	all	DET
ap-762	38	26	its	its	PRON
ap-762	38	27	algebraic	algebraic	ADJ
ap-762	38	28	conjugates	conjugate	NOUN
ap-762	38	29	in	in	ADP
ap-762	38	30	modulus	modulus	NOUN
ap-762	38	31	smaller	small	ADJ
ap-762	38	32	than	than	ADP
ap-762	38	33	one	one	NUM
ap-762	38	34	)	)	PUNCT
ap-762	38	35	.	.	PUNCT
ap-762	39	1	several	several	ADJ
ap-762	39	2	authors	author	NOUN
ap-762	39	3	have	have	AUX
ap-762	39	4	found	find	VERB
ap-762	39	5	partial	partial	ADJ
ap-762	39	6	answers	answer	NOUN
ap-762	39	7	to	to	ADP
ap-762	39	8	the	the	DET
ap-762	39	9	finiteness	finiteness	ADJ
ap-762	39	10	question	question	NOUN
ap-762	39	11	by	by	ADP
ap-762	39	12	giving	give	VERB
ap-762	39	13	some	some	DET
ap-762	39	14	sufficient	sufficient	ADJ
ap-762	39	15	conditions	condition	NOUN
ap-762	39	16	on	on	ADP
ap-762	39	17	the	the	DET
ap-762	39	18	minimal	minimal	ADJ
ap-762	39	19	polynomial	polynomial	NOUN
ap-762	39	20	of	of	ADP
ap-762	39	21	�	�	PROPN
ap-762	39	22	.	.	PUNCT
ap-762	40	1	theorem	theorem	VERB
ap-762	40	2	2.1	2.1	NUM
ap-762	40	3	:	:	PUNCT
ap-762	40	4	(	(	PUNCT
ap-762	40	5	frougny	frougny	NOUN
ap-762	40	6	,	,	PUNCT
ap-762	40	7	solomyak	solomyak	NOUN
ap-762	41	1	[	[	X
ap-762	41	2	3	3	NUM
ap-762	41	3	]	]	PUNCT
ap-762	41	4	)	)	PUNCT
ap-762	41	5	.	.	PUNCT
ap-762	42	1	let	let	VERB
ap-762	42	2	�	�	PROPN
ap-762	42	3	be	be	AUX
ap-762	42	4	a	a	DET
ap-762	42	5	positive	positive	ADJ
ap-762	42	6	root	root	NOUN
ap-762	42	7	of	of	ADP
ap-762	42	8	the	the	DET
ap-762	42	9	polynomial	polynomial	ADJ
ap-762	42	10	m	m	NOUN
ap-762	42	11	x	x	X
ap-762	42	12	x	x	X
ap-762	42	13	a	a	DET
ap-762	42	14	x	x	X
ap-762	42	15	am	be	AUX
ap-762	42	16	m	m	VERB
ap-762	42	17	m	m	ADJ
ap-762	42	18	(	(	PUNCT
ap-762	42	19	)	)	PUNCT
ap-762	42	20	�	�	PROPN
ap-762	42	21	�	�	PROPN
ap-762	42	22	�	�	PROPN
ap-762	42	23	�	�	PROPN
ap-762	42	24	�	�	PROPN
ap-762	42	25	1	1	NUM
ap-762	42	26	1	1	NUM
ap-762	42	27	�	�	PROPN
ap-762	42	28	,	,	PUNCT
ap-762	42	29	ai	ai	VERB
ap-762	42	30	�	�	PROPN
ap-762	42	31	z	z	PROPN
ap-762	42	32	and	and	CCONJ
ap-762	42	33	a	a	DET
ap-762	42	34	a	a	DET
ap-762	42	35	am1	am1	PROPN
ap-762	42	36	2	2	NUM
ap-762	42	37	0	0	NUM
ap-762	42	38	�	�	PROPN
ap-762	42	39	�	�	PROPN
ap-762	42	40	�	�	PROPN
ap-762	42	41	�	�	PROPN
ap-762	42	42	�	�	PROPN
ap-762	42	43	.	.	PUNCT
ap-762	43	1	then	then	ADV
ap-762	43	2	�	�	PROPN
ap-762	43	3	is	be	AUX
ap-762	43	4	a	a	DET
ap-762	43	5	pisot	pisot	ADJ
ap-762	43	6	number	number	NOUN
ap-762	43	7	and	and	CCONJ
ap-762	43	8	property	property	NOUN
ap-762	43	9	(	(	PUNCT
ap-762	43	10	f	f	X
ap-762	43	11	)	)	PUNCT
ap-762	43	12	holds	hold	VERB
ap-762	43	13	for	for	ADP
ap-762	43	14	�	�	PROPN
ap-762	43	15	.	.	PUNCT
ap-762	44	1	theorem	theorem	VERB
ap-762	44	2	2.2	2.2	NUM
ap-762	44	3	:	:	PUNCT
ap-762	44	4	(	(	PUNCT
ap-762	44	5	hollander	hollander	X
ap-762	44	6	[	[	X
ap-762	44	7	4	4	NUM
ap-762	44	8	]	]	NUM
ap-762	44	9	)	)	PUNCT
ap-762	44	10	.	.	PUNCT
ap-762	45	1	let	let	VERB
ap-762	45	2	�	�	PROPN
ap-762	45	3	be	be	AUX
ap-762	45	4	an	an	DET
ap-762	45	5	algebraic	algebraic	ADJ
ap-762	45	6	integer	integer	NOUN
ap-762	45	7	with	with	ADP
ap-762	45	8	the	the	DET
ap-762	45	9	minimal	minimal	ADJ
ap-762	45	10	polynomial	polynomial	ADJ
ap-762	45	11	m	m	NOUN
ap-762	45	12	x	x	X
ap-762	45	13	x	x	X
ap-762	45	14	a	a	DET
ap-762	45	15	x	x	X
ap-762	45	16	am	be	AUX
ap-762	45	17	m	m	VERB
ap-762	45	18	m	m	ADJ
ap-762	45	19	(	(	PUNCT
ap-762	45	20	)	)	PUNCT
ap-762	45	21	�	�	PROPN
ap-762	45	22	�	�	PROPN
ap-762	45	23	�	�	PROPN
ap-762	45	24	�	�	PROPN
ap-762	45	25	�	�	PROPN
ap-762	45	26	1	1	NUM
ap-762	45	27	1	1	NUM
ap-762	45	28	�	�	PROPN
ap-762	45	29	,	,	PUNCT
ap-762	45	30	ai	ai	VERB
ap-762	45	31	�	�	PROPN
ap-762	45	32	z	z	PROPN
ap-762	45	33	,	,	PUNCT
ap-762	45	34	ai	ai	VERB
ap-762	45	35	�	�	PROPN
ap-762	45	36	0	0	NUM
ap-762	45	37	and	and	CCONJ
ap-762	45	38	a	a	DET
ap-762	45	39	a	a	DET
ap-762	45	40	a	a	DET
ap-762	45	41	am1	am1	PROPN
ap-762	45	42	2	2	NUM
ap-762	45	43	3	3	NUM
ap-762	45	44	�	�	PROPN
ap-762	45	45	�	�	PROPN
ap-762	45	46	�	�	PROPN
ap-762	45	47	�	�	PROPN
ap-762	45	48	�	�	PROPN
ap-762	45	49	.	.	PUNCT
ap-762	46	1	then	then	ADV
ap-762	46	2	property	property	NOUN
ap-762	46	3	(	(	PUNCT
ap-762	46	4	f	f	X
ap-762	46	5	)	)	PUNCT
ap-762	46	6	holds	hold	VERB
ap-762	46	7	for	for	ADP
ap-762	46	8	�	�	PROPN
ap-762	46	9	.	.	PUNCT
ap-762	46	10	akiyama	akiyama	PROPN
ap-762	47	1	[	[	X
ap-762	47	2	5	5	NUM
ap-762	47	3	]	]	PUNCT
ap-762	47	4	proved	prove	VERB
ap-762	47	5	a	a	DET
ap-762	47	6	necessary	necessary	ADJ
ap-762	47	7	and	and	CCONJ
ap-762	47	8	sufficient	sufficient	ADJ
ap-762	47	9	condition	condition	NOUN
ap-762	47	10	,	,	PUNCT
ap-762	47	11	however	however	ADV
ap-762	47	12	it	it	PRON
ap-762	47	13	is	be	AUX
ap-762	47	14	unfortunately	unfortunately	ADV
ap-762	47	15	quite	quite	ADV
ap-762	47	16	vague	vague	ADJ
ap-762	47	17	.	.	PUNCT
ap-762	48	1	theorem	theorem	VERB
ap-762	48	2	2.3	2.3	NUM
ap-762	48	3	:	:	PUNCT
ap-762	48	4	(	(	PUNCT
ap-762	48	5	akiyama	akiyama	PROPN
ap-762	49	1	[	[	X
ap-762	49	2	5	5	NUM
ap-762	49	3	]	]	PUNCT
ap-762	49	4	)	)	PUNCT
ap-762	49	5	.	.	PUNCT
ap-762	50	1	let	let	VERB
ap-762	50	2	�	�	PROPN
ap-762	50	3	be	be	AUX
ap-762	50	4	a	a	DET
ap-762	50	5	pisot	pisot	ADJ
ap-762	50	6	number	number	NOUN
ap-762	50	7	of	of	ADP
ap-762	50	8	the	the	DET
ap-762	50	9	degree	degree	NOUN
ap-762	50	10	m.	m.	NOUN
ap-762	50	11	then	then	ADV
ap-762	50	12	�	�	PROPN
ap-762	50	13	has	have	VERB
ap-762	50	14	property	property	NOUN
ap-762	50	15	(	(	PUNCT
ap-762	50	16	f	f	X
ap-762	50	17	)	)	PUNCT
ap-762	51	1	if	if	SCONJ
ap-762	51	2	and	and	CCONJ
ap-762	51	3	only	only	ADV
ap-762	51	4	if	if	SCONJ
ap-762	51	5	every	every	DET
ap-762	51	6	element	element	NOUN
ap-762	51	7	of	of	ADP
ap-762	51	8	x	x	PUNCT
ap-762	51	9	x	x	SYM
ap-762	51	10	x	x	PUNCT
ap-762	51	11	x	x	SYM
ap-762	51	12	j	j	PROPN
ap-762	51	13	mj	mj	PROPN
ap-762	51	14	j	j	PROPN
ap-762	51	15	�	�	PROPN
ap-762	51	16	�	�	PROPN
ap-762	51	17	�	�	PROPN
ap-762	51	18	�	�	PROPN
ap-762	51	19	�	�	PROPN
ap-762	51	20	�	�	PROPN
ap-762	51	21	�	�	PROPN
ap-762	51	22	�	�	PROPN
ap-762	51	23	�	�	PROPN
ap-762	51	24	z	z	PROPN
ap-762	51	25	[	[	PUNCT
ap-762	51	26	]	]	X
ap-762	51	27	|	|	ADV
ap-762	51	28	,	,	PUNCT
ap-762	51	29	|	|	ADV
ap-762	51	30	[	[	PUNCT
ap-762	51	31	]	]	X
ap-762	51	32	,	,	PUNCT
ap-762	51	33	,	,	PUNCT
ap-762	51	34	,	,	PUNCT
ap-762	51	35	(	(	PUNCT
ap-762	51	36	)	)	PUNCT
ap-762	51	37	(	(	PUNCT
ap-762	51	38	)	)	PUNCT
ap-762	51	39	(	(	PUNCT
ap-762	51	40	)	)	PUNCT
ap-762	51	41	�	�	PROPN
ap-762	51	42	�	�	PROPN
ap-762	51	43	�	�	PROPN
ap-762	51	44	0	0	NUM
ap-762	51	45	1	1	NUM
ap-762	51	46	1	1	NUM
ap-762	51	47	2	2	NUM
ap-762	51	48	31	31	NUM
ap-762	51	49	for	for	ADP
ap-762	51	50	�	�	PROPN
ap-762	51	51	�	�	PROPN
ap-762	51	52	�	�	PROPN
ap-762	51	53	�	�	PROPN
ap-762	51	54	�	�	PROPN
ap-762	51	55	�	�	PROPN
ap-762	51	56	has	have	VERB
ap-762	51	57	a	a	DET
ap-762	51	58	finite	finite	ADJ
ap-762	51	59	�	�	NOUN
ap-762	51	60	-expansion	-expansion	NOUN
ap-762	51	61	in	in	ADP
ap-762	51	62	base	base	PROPN
ap-762	51	63	�	�	PROPN
ap-762	51	64	.	.	PUNCT
ap-762	52	1	here	here	ADV
ap-762	52	2	x	x	VERB
ap-762	52	3	i	i	NOUN
ap-762	52	4	(	(	PUNCT
ap-762	52	5	)	)	PUNCT
ap-762	52	6	with	with	ADP
ap-762	52	7	i	i	PROPN
ap-762	52	8	m	m	VERB
ap-762	52	9	�	�	PROPN
ap-762	52	10	1	1	NUM
ap-762	52	11	2	2	NUM
ap-762	52	12	,	,	PUNCT
ap-762	52	13	,	,	PUNCT
ap-762	52	14	,	,	PUNCT
ap-762	52	15	�	�	PROPN
ap-762	52	16	are	be	AUX
ap-762	52	17	the	the	DET
ap-762	52	18	conjugates	conjugate	NOUN
ap-762	52	19	of	of	ADP
ap-762	52	20	x	x	PART
ap-762	52	21	�	�	PROPN
ap-762	52	22	q	q	PROPN
ap-762	52	23	(	(	PUNCT
ap-762	52	24	)	)	PUNCT
ap-762	52	25	�	�	PROPN
ap-762	52	26	in	in	ADP
ap-762	52	27	the	the	DET
ap-762	52	28	algebraic	algebraic	ADJ
ap-762	52	29	field	field	NOUN
ap-762	52	30	.	.	PUNCT
ap-762	53	1	ambrož	ambrož	PROPN
ap-762	53	2	et	et	PROPN
ap-762	53	3	al	al	PROPN
ap-762	53	4	.	.	PUNCT
ap-762	54	1	[	[	X
ap-762	54	2	6	6	NUM
ap-762	54	3	]	]	PUNCT
ap-762	54	4	gave	give	VERB
ap-762	54	5	a	a	DET
ap-762	54	6	partial	partial	ADJ
ap-762	54	7	characterization	characterization	NOUN
ap-762	54	8	of	of	ADP
ap-762	54	9	numbers	number	NOUN
ap-762	54	10	�	�	PROPN
ap-762	54	11	fulfilling	fulfil	VERB
ap-762	54	12	property	property	NOUN
ap-762	54	13	(	(	PUNCT
ap-762	54	14	f	f	X
ap-762	54	15	)	)	PUNCT
ap-762	54	16	in	in	ADP
ap-762	54	17	terms	term	NOUN
ap-762	54	18	of	of	ADP
ap-762	54	19	minimal	minimal	ADJ
ap-762	54	20	forbidden	forbid	VERB
ap-762	54	21	strings	string	NOUN
ap-762	54	22	.	.	PUNCT
ap-762	55	1	definition	definition	NOUN
ap-762	55	2	2.4	2.4	NUM
ap-762	55	3	:	:	PUNCT
ap-762	55	4	let	let	VERB
ap-762	55	5	�	�	PROPN
ap-762	55	6	>	>	X
ap-762	56	1	1	1	X
ap-762	56	2	.	.	PUNCT
ap-762	57	1	a	a	DET
ap-762	57	2	forbidden	forbid	VERB
ap-762	57	3	string	string	NOUN
ap-762	57	4	ukuk	ukuk	NOUN
ap-762	57	5	�	�	PROPN
ap-762	57	6	1	1	NUM
ap-762	57	7	…	…	PUNCT
ap-762	57	8	u0	u0	NOUN
ap-762	57	9	of	of	ADP
ap-762	57	10	non	non	ADJ
ap-762	57	11	-	-	ADJ
ap-762	57	12	negative	negative	ADJ
ap-762	57	13	integers	integer	NOUN
ap-762	57	14	is	be	AUX
ap-762	57	15	called	call	VERB
ap-762	57	16	minimal	minimal	ADJ
ap-762	57	17	,	,	PUNCT
ap-762	57	18	if	if	SCONJ
ap-762	57	19	�	�	PROPN
ap-762	57	20	uk	uk	PROPN
ap-762	57	21	�	�	PROPN
ap-762	57	22	1	1	NUM
ap-762	57	23	…	…	PUNCT
ap-762	57	24	u0	u0	ADJ
ap-762	57	25	and	and	CCONJ
ap-762	57	26	uk	uk	PROPN
ap-762	57	27	…	…	SYM
ap-762	57	28	u1	u1	NOUN
ap-762	57	29	are	be	AUX
ap-762	57	30	admissible	admissible	ADJ
ap-762	57	31	,	,	PUNCT
ap-762	57	32	�	�	PROPN
ap-762	57	33	ui	ui	PROPN
ap-762	57	34	�	�	PROPN
ap-762	57	35	1	1	NUM
ap-762	57	36	implies	imply	VERB
ap-762	57	37	uk	uk	PROPN
ap-762	57	38	…	…	SYM
ap-762	57	39	ui	ui	PROPN
ap-762	57	40	�	�	PROPN
ap-762	57	41	1(ui	1(ui	PROPN
ap-762	57	42	�	�	PROPN
ap-762	57	43	1)ui	1)ui	NUM
ap-762	57	44	�	�	NOUN
ap-762	57	45	1	1	NUM
ap-762	57	46	…	…	PUNCT
ap-762	57	47	u0	u0	ADJ
ap-762	57	48	is	be	AUX
ap-762	57	49	admissible	admissible	ADJ
ap-762	57	50	,	,	PUNCT
ap-762	57	51	for	for	ADP
ap-762	57	52	all	all	DET
ap-762	57	53	i	i	PRON
ap-762	57	54	k	k	PROPN
ap-762	57	55	�	�	PROPN
ap-762	57	56	0	0	NUM
ap-762	57	57	1	1	NUM
ap-762	57	58	,	,	PUNCT
ap-762	57	59	,	,	PUNCT
ap-762	57	60	,	,	PUNCT
ap-762	57	61	�	�	PROPN
ap-762	57	62	.	.	PUNCT
ap-762	58	1	the	the	DET
ap-762	58	2	conditions	condition	NOUN
ap-762	58	3	based	base	VERB
ap-762	58	4	on	on	ADP
ap-762	58	5	the	the	DET
ap-762	58	6	above	above	ADV
ap-762	58	7	-	-	PUNCT
ap-762	58	8	defined	define	VERB
ap-762	58	9	notion	notion	NOUN
ap-762	58	10	of	of	ADP
ap-762	58	11	minimal	minimal	ADJ
ap-762	58	12	forbidden	forbid	VERB
ap-762	58	13	strings	string	NOUN
ap-762	58	14	were	be	AUX
ap-762	58	15	given	give	VERB
ap-762	58	16	by	by	ADP
ap-762	58	17	the	the	DET
ap-762	58	18	following	follow	VERB
ap-762	58	19	two	two	NUM
ap-762	58	20	propositions	proposition	NOUN
ap-762	58	21	.	.	PUNCT
ap-762	59	1	proposition	proposition	NOUN
ap-762	59	2	2.5	2.5	NUM
ap-762	59	3	:	:	PUNCT
ap-762	59	4	(	(	PUNCT
ap-762	59	5	property	property	NOUN
ap-762	59	6	(	(	PUNCT
ap-762	59	7	t	t	PROPN
ap-762	59	8	)	)	PUNCT
ap-762	59	9	)	)	PUNCT
ap-762	59	10	.	.	PUNCT
ap-762	60	1	if	if	SCONJ
ap-762	60	2	fin	fin	PROPN
ap-762	60	3	(	(	PUNCT
ap-762	60	4	)	)	PUNCT
ap-762	60	5	�	�	PROPN
ap-762	60	6	is	be	AUX
ap-762	60	7	closed	close	VERB
ap-762	60	8	under	under	ADP
ap-762	60	9	addition	addition	NOUN
ap-762	60	10	of	of	ADP
ap-762	60	11	two	two	NUM
ap-762	60	12	positive	positive	ADJ
ap-762	60	13	numbers	number	NOUN
ap-762	60	14	,	,	PUNCT
ap-762	60	15	then	then	ADV
ap-762	60	16	�	�	PROPN
ap-762	60	17	must	must	AUX
ap-762	60	18	satisfy	satisfy	VERB
ap-762	60	19	the	the	DET
ap-762	60	20	following	follow	VERB
ap-762	60	21	property	property	NOUN
ap-762	60	22	:	:	PUNCT
ap-762	60	23	for	for	ADP
ap-762	60	24	every	every	DET
ap-762	60	25	minimal	minimal	ADJ
ap-762	60	26	forbidden	forbid	VERB
ap-762	60	27	string	string	NOUN
ap-762	60	28	ukuk	ukuk	NOUN
ap-762	60	29	�	�	PROPN
ap-762	60	30	1	1	NUM
ap-762	60	31	…	…	PUNCT
ap-762	60	32	u0	u0	ADJ
ap-762	60	33	there	there	PRON
ap-762	60	34	exists	exist	VERB
ap-762	60	35	a	a	DET
ap-762	60	36	finite	finite	ADJ
ap-762	60	37	sequence	sequence	NOUN
ap-762	60	38	vnvn	vnvn	PROPN
ap-762	60	39	�	�	PROPN
ap-762	60	40	1	1	NUM
ap-762	60	41	…	…	SYM
ap-762	60	42	v	v	NOUN
ap-762	60	43	of	of	ADP
ap-762	60	44	non	non	ADJ
ap-762	60	45	-	-	ADJ
ap-762	60	46	negative	negative	ADJ
ap-762	60	47	integers	integer	NOUN
ap-762	60	48	,	,	PUNCT
ap-762	60	49	such	such	ADJ
ap-762	60	50	that	that	DET
ap-762	60	51	�	�	PROPN
ap-762	60	52	k	k	PROPN
ap-762	60	53	n	n	CCONJ
ap-762	60	54	,	,	PUNCT
ap-762	60	55	�	�	PROPN
ap-762	60	56	�	�	PROPN
ap-762	60	57	,	,	PUNCT
ap-762	60	58	�	�	PROPN
ap-762	60	59	v	v	AUX
ap-762	60	60	v	v	NUM
ap-762	60	61	u	u	PROPN
ap-762	60	62	u	u	NOUN
ap-762	60	63	un	un	PROPN
ap-762	60	64	n	n	PROPN
ap-762	60	65	k	k	PROPN
ap-762	60	66	k	k	PROPN
ap-762	60	67	�	�	PROPN
ap-762	60	68	�	�	PROPN
ap-762	60	69	�	�	PROPN
ap-762	60	70	�	�	PROPN
ap-762	60	71	�	�	PROPN
ap-762	60	72	�	�	PROPN
ap-762	60	73	�	�	PROPN
ap-762	60	74	�	�	PROPN
ap-762	60	75	�	�	PROPN
ap-762	60	76	�	�	PROPN
ap-762	60	77	�	�	PROPN
ap-762	60	78	�	�	PROPN
ap-762	60	79	1	1	NUM
ap-762	60	80	0	0	NUM
ap-762	60	81	,	,	PUNCT
ap-762	60	82	�	�	PROPN
ap-762	60	83	v	v	ADP
ap-762	60	84	v	v	NUM
ap-762	60	85	v	v	PROPN
ap-762	60	86	u	u	PROPN
ap-762	60	87	un	un	PROPN
ap-762	60	88	n	n	PROPN
ap-762	60	89	k	k	PROPN
ap-762	60	90	n	n	CCONJ
ap-762	60	91	k	k	PROPN
ap-762	60	92	�	�	PROPN
ap-762	60	93	�	�	PROPN
ap-762	60	94	1	1	NUM
ap-762	60	95	000	000	NUM
ap-762	60	96	0	0	NUM
ap-762	60	97	�	�	PROPN
ap-762	60	98	�	�	PROPN
ap-762	60	99	�	�	PROPN
ap-762	60	100	�	�	PROPN
ap-762	60	101	�	�	PROPN
ap-762	60	102	�	�	PROPN
ap-762	60	103	�	�	PROPN
ap-762	60	104	(	(	PUNCT
ap-762	60	105	)	)	PUNCT
ap-762	60	106	times	time	NOUN
ap-762	60	107	.	.	PUNCT
ap-762	61	1	theorem	theorem	VERB
ap-762	61	2	2.6	2.6	NUM
ap-762	61	3	:	:	PUNCT
ap-762	61	4	(	(	PUNCT
ap-762	61	5	ambrož	ambrož	X
ap-762	61	6	et	et	PROPN
ap-762	61	7	al	al	PROPN
ap-762	61	8	.	.	PUNCT
ap-762	62	1	[	[	X
ap-762	62	2	6	6	NUM
ap-762	62	3	]	]	PUNCT
ap-762	62	4	)	)	PUNCT
ap-762	62	5	.	.	PUNCT
ap-762	63	1	let	let	VERB
ap-762	63	2	�	�	PROPN
ap-762	63	3	>	>	X
ap-762	63	4	1	1	NUM
ap-762	63	5	satisfy	satisfy	NOUN
ap-762	63	6	property	property	NOUN
ap-762	63	7	(	(	PUNCT
ap-762	63	8	t	t	NOUN
ap-762	63	9	)	)	PUNCT
ap-762	63	10	,	,	PUNCT
ap-762	63	11	and	and	CCONJ
ap-762	63	12	suppose	suppose	VERB
ap-762	63	13	that	that	SCONJ
ap-762	63	14	for	for	ADP
ap-762	63	15	every	every	DET
ap-762	63	16	minimal	minimal	ADJ
ap-762	63	17	forbidden	forbid	VERB
ap-762	63	18	string	string	NOUN
ap-762	63	19	ukuk	ukuk	NOUN
ap-762	63	20	�	�	PROPN
ap-762	63	21	1	1	NUM
ap-762	63	22	…	…	PUNCT
ap-762	63	23	u0	u0	ADJ
ap-762	63	24	we	we	PRON
ap-762	63	25	have	have	VERB
ap-762	63	26	the	the	DET
ap-762	63	27	following	follow	VERB
ap-762	63	28	condition	condition	NOUN
ap-762	63	29	:	:	PUNCT
ap-762	63	30	if	if	SCONJ
ap-762	63	31	vnvn	vnvn	PROPN
ap-762	63	32	�	�	PROPN
ap-762	63	33	1	1	NUM
ap-762	63	34	…	…	SYM
ap-762	63	35	v	v	NOUN
ap-762	63	36	is	be	AUX
ap-762	63	37	the	the	DET
ap-762	63	38	lexicographically	lexicographically	ADV
ap-762	63	39	greater	great	ADJ
ap-762	63	40	string	string	NOUN
ap-762	63	41	of	of	ADP
ap-762	63	42	(	(	PUNCT
ap-762	63	43	t	t	PROPN
ap-762	63	44	)	)	PUNCT
ap-762	63	45	corresponding	correspond	VERB
ap-762	63	46	to	to	ADP
ap-762	63	47	ukuk	ukuk	NOUN
ap-762	63	48	�	�	PROPN
ap-762	63	49	1	1	NUM
ap-762	63	50	…	…	PUNCT
ap-762	63	51	u0	u0	ADJ
ap-762	63	52	then	then	ADV
ap-762	63	53	v	v	ADP
ap-762	63	54	v	v	NUM
ap-762	63	55	v	v	ADP
ap-762	63	56	u	u	X
ap-762	63	57	u	u	NOUN
ap-762	63	58	un	un	PROPN
ap-762	63	59	n	n	PROPN
ap-762	63	60	k	k	PROPN
ap-762	63	61	k	k	PROPN
ap-762	63	62	�	�	PROPN
ap-762	63	63	�	�	PROPN
ap-762	63	64	�	�	PROPN
ap-762	63	65	�	�	PROPN
ap-762	63	66	�	�	PROPN
ap-762	63	67	�	�	PROPN
ap-762	63	68	�	�	PROPN
ap-762	63	69	�	�	PROPN
ap-762	63	70	�	�	PROPN
ap-762	63	71	1	1	NUM
ap-762	63	72	1	1	NUM
ap-762	63	73	0	0	NUM
ap-762	63	74	�	�	PROPN
ap-762	63	75	�	�	PROPN
ap-762	63	76	�	�	PROPN
ap-762	63	77	.	.	PUNCT
ap-762	64	1	thenfin	thenfin	PROPN
ap-762	64	2	(	(	PUNCT
ap-762	64	3	)	)	PUNCT
ap-762	64	4	�	�	PROPN
ap-762	64	5	is	be	AUX
ap-762	64	6	closed	close	VERB
ap-762	64	7	under	under	ADP
ap-762	64	8	addition	addition	NOUN
ap-762	64	9	of	of	ADP
ap-762	64	10	positive	positive	ADJ
ap-762	64	11	elements	element	NOUN
ap-762	64	12	.	.	PUNCT
ap-762	65	1	moreover	moreover	ADV
ap-762	65	2	,	,	PUNCT
ap-762	65	3	for	for	ADP
ap-762	65	4	every	every	DET
ap-762	65	5	positive	positive	ADJ
ap-762	65	6	x	x	SYM
ap-762	65	7	y	y	PROPN
ap-762	65	8	,	,	PUNCT
ap-762	65	9	(	(	PUNCT
ap-762	65	10	)	)	PUNCT
ap-762	65	11	�	�	PROPN
ap-762	65	12	fin	fin	NOUN
ap-762	65	13	�	�	PROPN
ap-762	65	14	,	,	PUNCT
ap-762	65	15	the	the	DET
ap-762	65	16	�	�	PROPN
ap-762	65	17	-expansion	-expansion	NOUN
ap-762	65	18	of	of	ADP
ap-762	65	19	x	x	SYM
ap-762	65	20	y	y	PROPN
ap-762	65	21	�	�	PROPN
ap-762	65	22	can	can	AUX
ap-762	65	23	be	be	AUX
ap-762	65	24	obtained	obtain	VERB
ap-762	65	25	from	from	ADP
ap-762	65	26	any	any	DET
ap-762	65	27	�	�	NOUN
ap-762	65	28	-representation	-representation	NOUN
ap-762	65	29	of	of	ADP
ap-762	65	30	x	x	SYM
ap-762	65	31	y	y	PRON
ap-762	65	32	�	�	PROPN
ap-762	65	33	using	use	VERB
ap-762	65	34	finitely	finitely	ADV
ap-762	65	35	many	many	ADJ
ap-762	65	36	transcriptions	transcription	NOUN
ap-762	65	37	.	.	PUNCT
ap-762	66	1	finally	finally	ADV
ap-762	66	2	,	,	PUNCT
ap-762	66	3	akiyama	akiyama	PROPN
ap-762	66	4	gave	give	VERB
ap-762	66	5	an	an	DET
ap-762	66	6	algebraic	algebraic	ADJ
ap-762	66	7	characterization	characterization	NOUN
ap-762	66	8	of	of	ADP
ap-762	66	9	cubic	cubic	ADJ
ap-762	66	10	pisot	pisot	ADJ
ap-762	66	11	numbers	number	NOUN
ap-762	66	12	satisfying	satisfy	VERB
ap-762	66	13	property	property	NOUN
ap-762	66	14	(	(	PUNCT
ap-762	66	15	f	f	NOUN
ap-762	66	16	)	)	PUNCT
ap-762	66	17	.	.	PUNCT
ap-762	67	1	theorem	theorem	ADJ
ap-762	67	2	2.7	2.7	NUM
ap-762	67	3	:	:	PUNCT
ap-762	67	4	(	(	PUNCT
ap-762	67	5	akiyama	akiyama	PROPN
ap-762	68	1	[	[	X
ap-762	68	2	7	7	NUM
ap-762	68	3	]	]	PUNCT
ap-762	68	4	)	)	PUNCT
ap-762	68	5	let	let	VERB
ap-762	68	6	�	�	PROPN
ap-762	68	7	be	be	AUX
ap-762	68	8	a	a	DET
ap-762	68	9	cubic	cubic	ADJ
ap-762	68	10	pisot	pisot	ADJ
ap-762	68	11	number	number	NOUN
ap-762	68	12	.	.	PUNCT
ap-762	69	1	�	�	PROPN
ap-762	69	2	has	have	VERB
ap-762	69	3	property	property	NOUN
ap-762	69	4	(	(	PUNCT
ap-762	69	5	f	f	X
ap-762	69	6	)	)	PUNCT
ap-762	70	1	if	if	SCONJ
ap-762	71	1	and	and	CCONJ
ap-762	71	2	only	only	ADV
ap-762	71	3	if	if	SCONJ
ap-762	71	4	�	�	PROPN
ap-762	71	5	is	be	AUX
ap-762	71	6	a	a	DET
ap-762	71	7	root	root	NOUN
ap-762	71	8	of	of	ADP
ap-762	71	9	the	the	DET
ap-762	71	10	following	follow	VERB
ap-762	71	11	polynomial	polynomial	NOUN
ap-762	71	12	with	with	ADP
ap-762	71	13	integer	integer	NOUN
ap-762	71	14	coefficients	coefficient	NOUN
ap-762	72	1	x	x	SYM
ap-762	72	2	ax	ax	NOUN
ap-762	72	3	bx3	bx3	VERB
ap-762	72	4	2	2	NUM
ap-762	72	5	1	1	NUM
ap-762	72	6	�	�	PROPN
ap-762	72	7	�	�	PROPN
ap-762	72	8	�	�	PROPN
ap-762	72	9	where	where	SCONJ
ap-762	72	10	a	a	DET
ap-762	72	11	�	�	NOUN
ap-762	72	12	0	0	NUM
ap-762	72	13	and	and	CCONJ
ap-762	72	14	�	�	PROPN
ap-762	72	15	�	�	PROPN
ap-762	72	16	�	�	PROPN
ap-762	72	17	�	�	PROPN
ap-762	72	18	1	1	NUM
ap-762	72	19	1b	1b	NUM
ap-762	72	20	a	a	PRON
ap-762	72	21	.	.	PUNCT
ap-762	73	1	2.2	2.2	NUM
ap-762	73	2	number	number	NOUN
ap-762	73	3	of	of	ADP
ap-762	73	4	fractional	fractional	ADJ
ap-762	73	5	digits	digit	NOUN
ap-762	73	6	the	the	DET
ap-762	73	7	second	second	ADJ
ap-762	73	8	question	question	NOUN
ap-762	73	9	concerning	concern	VERB
ap-762	73	10	arithmetics	arithmetic	NOUN
ap-762	73	11	in	in	ADP
ap-762	73	12	�	�	NOUN
ap-762	73	13	-numeration	-numeration	NOUN
ap-762	73	14	systems	system	NOUN
ap-762	73	15	is	be	AUX
ap-762	73	16	connected	connect	VERB
ap-762	73	17	to	to	ADP
ap-762	73	18	the	the	DET
ap-762	73	19	fact	fact	NOUN
ap-762	73	20	that	that	SCONJ
ap-762	73	21	for	for	ADP
ap-762	73	22	non	non	ADJ
ap-762	73	23	-	-	ADJ
ap-762	73	24	integer	integer	ADJ
ap-762	73	25	�	�	PROPN
ap-762	73	26	the	the	DET
ap-762	73	27	set	set	PROPN
ap-762	73	28	z	z	PROPN
ap-762	73	29	�	�	PROPN
ap-762	73	30	is	be	AUX
ap-762	73	31	not	not	PART
ap-762	73	32	closed	close	VERB
ap-762	73	33	under	under	ADP
ap-762	73	34	arithmetic	arithmetic	ADJ
ap-762	73	35	operations	operation	NOUN
ap-762	73	36	.	.	PUNCT
ap-762	74	1	however	however	ADV
ap-762	74	2	,	,	PUNCT
ap-762	74	3	sometimes	sometimes	ADV
ap-762	74	4	it	it	PRON
ap-762	74	5	is	be	AUX
ap-762	74	6	true	true	ADJ
ap-762	74	7	that	that	SCONJ
ap-762	74	8	the	the	DET
ap-762	74	9	result	result	NOUN
ap-762	74	10	of	of	ADP
ap-762	74	11	addition	addition	NOUN
ap-762	74	12	or	or	CCONJ
ap-762	74	13	multiplication	multiplication	NOUN
ap-762	74	14	of	of	ADP
ap-762	74	15	two	two	NUM
ap-762	74	16	�	�	NOUN
ap-762	74	17	-integers	-integer	NOUN
ap-762	74	18	has	have	VERB
ap-762	74	19	only	only	ADV
ap-762	74	20	a	a	DET
ap-762	74	21	finite	finite	ADJ
ap-762	74	22	fractional	fractional	ADJ
ap-762	74	23	part	part	NOUN
ap-762	74	24	.	.	PUNCT
ap-762	75	1	then	then	ADV
ap-762	75	2	it	it	PRON
ap-762	75	3	is	be	AUX
ap-762	75	4	interesting	interesting	ADJ
ap-762	75	5	to	to	PART
ap-762	75	6	try	try	VERB
ap-762	75	7	to	to	PART
ap-762	75	8	estimate	estimate	VERB
ap-762	75	9	the	the	DET
ap-762	75	10	maximal	maximal	ADJ
ap-762	75	11	length	length	NOUN
ap-762	75	12	of	of	ADP
ap-762	75	13	such	such	ADJ
ap-762	75	14	fractional	fractional	ADJ
ap-762	75	15	part	part	NOUN
ap-762	75	16	.	.	PUNCT
ap-762	76	1	more	more	ADV
ap-762	76	2	precisely	precisely	ADV
ap-762	76	3	,	,	PUNCT
ap-762	76	4	the	the	DET
ap-762	76	5	task	task	NOUN
ap-762	76	6	is	be	AUX
ap-762	76	7	as	as	SCONJ
ap-762	76	8	follows	follow	VERB
ap-762	76	9	.	.	PUNCT
ap-762	77	1	for	for	ADP
ap-762	77	2	given	give	VERB
ap-762	77	3	�	�	PROPN
ap-762	77	4	find	find	VERB
ap-762	77	5	the	the	DET
ap-762	77	6	value	value	NOUN
ap-762	77	7	,	,	PUNCT
ap-762	77	8	or	or	CCONJ
ap-762	77	9	at	at	ADP
ap-762	77	10	least	least	ADJ
ap-762	77	11	some	some	DET
ap-762	77	12	good	good	ADJ
ap-762	77	13	estimate	estimate	NOUN
ap-762	77	14	,	,	PUNCT
ap-762	77	15	of	of	ADP
ap-762	77	16	the	the	DET
ap-762	77	17	quantities	quantity	NOUN
ap-762	77	18	l	l	NOUN
ap-762	77	19	n	n	NOUN
ap-762	77	20	x	x	SYM
ap-762	77	21	y	y	NOUN
ap-762	77	22	x	x	SYM
ap-762	77	23	y	y	NOUN
ap-762	77	24	x	x	SYM
ap-762	77	25	y	y	PROPN
ap-762	77	26	n	n	PROPN
ap-762	77	27	�	�	PROPN
ap-762	77	28	�	�	PROPN
ap-762	77	29	�	�	PROPN
ap-762	77	30	�	�	PROPN
ap-762	77	31	�	�	PROPN
ap-762	77	32	�	�	PROPN
ap-762	77	33	�	�	PROPN
ap-762	77	34	�	�	PROPN
ap-762	77	35	�	�	PROPN
ap-762	77	36	�	�	PROPN
ap-762	77	37	�	�	PROPN
ap-762	77	38	(	(	PUNCT
ap-762	77	39	):	):	PUNCT
ap-762	77	40	min	min	NOUN
ap-762	77	41	{	{	PUNCT
ap-762	77	42	|	|	ADV
ap-762	77	43	,	,	PUNCT
ap-762	77	44	,	,	PUNCT
ap-762	77	45	(	(	PUNCT
ap-762	77	46	)	)	PUNCT
ap-762	77	47	}	}	PUNCT
ap-762	77	48	,	,	PUNCT
ap-762	77	49	�	�	PROPN
ap-762	77	50	�	�	PROPN
ap-762	77	51	�	�	PROPN
ap-762	77	52	�	�	PROPN
ap-762	77	53	�	�	PROPN
ap-762	77	54	n	n	PROPN
ap-762	77	55	z	z	NOUN
ap-762	77	56	zfin	zfin	NOUN
ap-762	77	57	l	l	PROPN
ap-762	78	1	n	n	NOUN
ap-762	78	2	x	x	SYM
ap-762	78	3	y	y	NOUN
ap-762	78	4	xy	xy	INTJ
ap-762	78	5	xy	xy	PROPN
ap-762	78	6	n	n	PROPN
ap-762	78	7	�	�	PROPN
ap-762	78	8	�	�	PROPN
ap-762	78	9	�	�	PROPN
ap-762	78	10	�	�	PROPN
ap-762	78	11	�	�	PROPN
ap-762	78	12	�	�	PROPN
ap-762	78	13	�	�	PROPN
ap-762	78	14	�	�	PROPN
ap-762	78	15	�	�	PROPN
ap-762	78	16	(	(	PUNCT
ap-762	78	17	):	):	PUNCT
ap-762	78	18	min	min	NOUN
ap-762	78	19	{	{	PUNCT
ap-762	78	20	|	|	ADV
ap-762	78	21	,	,	PUNCT
ap-762	78	22	,	,	PUNCT
ap-762	78	23	(	(	PUNCT
ap-762	78	24	)	)	PUNCT
ap-762	78	25	}	}	PUNCT
ap-762	78	26	�	�	PROPN
ap-762	78	27	�	�	PROPN
ap-762	78	28	�	�	PROPN
ap-762	78	29	�	�	PROPN
ap-762	78	30	�	�	PROPN
ap-762	78	31	n	n	PROPN
ap-762	78	32	z	z	PROPN
ap-762	78	33	zfin	zfin	NOUN
ap-762	78	34	.	.	PUNCT
ap-762	79	1	two	two	NUM
ap-762	79	2	methods	method	NOUN
ap-762	79	3	for	for	ADP
ap-762	79	4	estimation	estimation	NOUN
ap-762	79	5	of	of	ADP
ap-762	79	6	l	l	PROPN
ap-762	79	7	�	�	PROPN
ap-762	79	8	(	(	PUNCT
ap-762	79	9	)	)	PUNCT
ap-762	79	10	�	�	PROPN
ap-762	79	11	,	,	PUNCT
ap-762	79	12	l	l	X
ap-762	79	13	�	�	PROPN
ap-762	79	14	(	(	PUNCT
ap-762	79	15	)	)	PUNCT
ap-762	79	16	�	�	PROPN
ap-762	79	17	are	be	AUX
ap-762	79	18	known	know	VERB
ap-762	79	19	.	.	PUNCT
ap-762	80	1	the	the	DET
ap-762	80	2	first	first	ADJ
ap-762	80	3	of	of	ADP
ap-762	80	4	them	they	PRON
ap-762	80	5	uses	use	VERB
ap-762	80	6	the	the	DET
ap-762	80	7	so	so	ADV
ap-762	80	8	-	-	PUNCT
ap-762	80	9	called	call	VERB
ap-762	80	10	meyer	meyer	PROPN
ap-762	80	11	property	property	NOUN
ap-762	80	12	of	of	ADP
ap-762	80	13	the	the	DET
ap-762	80	14	set	set	NOUN
ap-762	80	15	of	of	ADP
ap-762	80	16	�	�	NOUN
ap-762	80	17	-integers	-integer	NOUN
ap-762	80	18	for	for	ADP
ap-762	80	19	�	�	PROPN
ap-762	80	20	pisot	pisot	ADJ
ap-762	80	21	number	number	NOUN
ap-762	80	22	,	,	PUNCT
ap-762	80	23	namely	namely	ADV
ap-762	80	24	that	that	SCONJ
ap-762	80	25	z	z	NOUN
ap-762	80	26	z	z	NOUN
ap-762	80	27	z	z	PROPN
ap-762	80	28	�	�	PROPN
ap-762	80	29	�	�	PROPN
ap-762	80	30	�	�	PROPN
ap-762	80	31	�	�	PROPN
ap-762	80	32	�	�	PROPN
ap-762	80	33	�	�	PROPN
ap-762	80	34	f	f	PROPN
ap-762	80	35	where	where	SCONJ
ap-762	80	36	f	f	PROPN
ap-762	80	37	is	be	AUX
ap-762	80	38	a	a	DET
ap-762	80	39	finite	finite	ADJ
ap-762	80	40	set	set	NOUN
ap-762	80	41	,	,	PUNCT
ap-762	80	42	and	and	CCONJ
ap-762	80	43	z	z	NOUN
ap-762	80	44	z	z	PROPN
ap-762	80	45	z	z	PROPN
ap-762	80	46	�	�	PROPN
ap-762	80	47	�	�	PROPN
ap-762	80	48	�	�	PROPN
ap-762	80	49	�	�	PROPN
ap-762	80	50	�	�	PROPN
ap-762	80	51	g	g	PROPN
ap-762	80	52	where	where	SCONJ
ap-762	80	53	g	g	PROPN
ap-762	80	54	is	be	AUX
ap-762	80	55	a	a	DET
ap-762	80	56	finite	finite	ADJ
ap-762	80	57	set	set	NOUN
ap-762	80	58	.	.	PUNCT
ap-762	81	1	this	this	DET
ap-762	81	2	method	method	NOUN
ap-762	81	3	is	be	AUX
ap-762	81	4	used	use	VERB
ap-762	81	5	in	in	ADP
ap-762	81	6	[	[	X
ap-762	81	7	6	6	NUM
ap-762	81	8	]	]	PUNCT
ap-762	81	9	to	to	PART
ap-762	81	10	find	find	VERB
ap-762	81	11	values	value	NOUN
ap-762	81	12	of	of	ADP
ap-762	81	13	l	l	PROPN
ap-762	81	14	�	�	PROPN
ap-762	81	15	(	(	PUNCT
ap-762	81	16	)	)	PUNCT
ap-762	81	17	�	�	PROPN
ap-762	81	18	,	,	PUNCT
ap-762	81	19	l	l	X
ap-762	81	20	�	�	PROPN
ap-762	81	21	(	(	PUNCT
ap-762	81	22	)	)	PUNCT
ap-762	81	23	�	�	PROPN
ap-762	81	24	for	for	ADP
ap-762	81	25	�	�	PROPN
ap-762	81	26	the	the	DET
ap-762	81	27	pisot	pisot	ADJ
ap-762	81	28	number	number	NOUN
ap-762	81	29	,	,	PUNCT
ap-762	81	30	solution	solution	NOUN
ap-762	81	31	of	of	ADP
ap-762	81	32	the	the	DET
ap-762	81	33	equation	equation	NOUN
ap-762	81	34	x	x	PUNCT
ap-762	82	1	x	x	SYM
ap-762	82	2	x3	x3	VERB
ap-762	82	3	225	225	NUM
ap-762	82	4	15	15	NUM
ap-762	82	5	2	2	NUM
ap-762	82	6	�	�	PROPN
ap-762	82	7	�	�	PROPN
ap-762	82	8	�	�	PROPN
ap-762	82	9	.	.	PUNCT
ap-762	83	1	the	the	DET
ap-762	83	2	second	second	ADJ
ap-762	83	3	,	,	PUNCT
ap-762	83	4	much	much	ADV
ap-762	83	5	more	more	ADV
ap-762	83	6	widely	widely	ADV
ap-762	83	7	used	use	VERB
ap-762	83	8	method	method	NOUN
ap-762	83	9	for	for	ADP
ap-762	83	10	estimation	estimation	NOUN
ap-762	83	11	of	of	ADP
ap-762	83	12	l	l	PROPN
ap-762	83	13	�	�	PROPN
ap-762	83	14	(	(	PUNCT
ap-762	83	15	)	)	PUNCT
ap-762	83	16	�	�	PROPN
ap-762	83	17	,	,	PUNCT
ap-762	83	18	l	l	X
ap-762	83	19	�	�	PROPN
ap-762	83	20	(	(	PUNCT
ap-762	83	21	)	)	PUNCT
ap-762	83	22	�	�	PROPN
ap-762	83	23	is	be	AUX
ap-762	83	24	based	base	VERB
ap-762	83	25	on	on	ADP
ap-762	83	26	the	the	DET
ap-762	83	27	following	follow	VERB
ap-762	83	28	theorem	theorem	VERB
ap-762	83	29	.	.	PUNCT
ap-762	84	1	several	several	ADJ
ap-762	84	2	version	version	NOUN
ap-762	84	3	of	of	ADP
ap-762	84	4	this	this	DET
ap-762	84	5	method	method	NOUN
ap-762	84	6	are	be	AUX
ap-762	84	7	employed	employ	VERB
ap-762	84	8	in	in	ADP
ap-762	84	9	[	[	X
ap-762	84	10	6	6	NUM
ap-762	84	11	,	,	PUNCT
ap-762	84	12	8	8	NUM
ap-762	84	13	,	,	PUNCT
ap-762	84	14	9	9	NUM
ap-762	84	15	,	,	PUNCT
ap-762	84	16	10	10	NUM
ap-762	84	17	,	,	PUNCT
ap-762	84	18	11	11	NUM
ap-762	84	19	,	,	PUNCT
ap-762	84	20	12	12	NUM
ap-762	84	21	]	]	PUNCT
ap-762	84	22	.	.	PUNCT
ap-762	85	1	theorem	theorem	VERB
ap-762	85	2	2.8	2.8	NUM
ap-762	85	3	:	:	PUNCT
ap-762	85	4	(	(	PUNCT
ap-762	85	5	guimond	guimond	NOUN
ap-762	85	6	et	et	PROPN
ap-762	85	7	al	al	PROPN
ap-762	85	8	.	.	PUNCT
ap-762	86	1	[	[	X
ap-762	86	2	10	10	NUM
ap-762	86	3	]	]	NUM
ap-762	86	4	)	)	PUNCT
ap-762	86	5	.	.	PUNCT
ap-762	87	1	let	let	VERB
ap-762	87	2	�	�	PROPN
ap-762	87	3	>	>	X
ap-762	87	4	1	1	NUM
ap-762	87	5	be	be	AUX
ap-762	87	6	an	an	DET
ap-762	87	7	algebraic	algebraic	ADJ
ap-762	87	8	number	number	NOUN
ap-762	87	9	,	,	PUNCT
ap-762	87	10	and	and	CCONJ
ap-762	87	11	let	let	VERB
ap-762	87	12	�	�	PROPN
ap-762	87	13	�	�	PROPN
ap-762	87	14	be	be	AUX
ap-762	87	15	its	its	PRON
ap-762	87	16	algebraic	algebraic	ADJ
ap-762	87	17	conjugate	conjugate	NOUN
ap-762	87	18	.	.	PUNCT
ap-762	88	1	for	for	ADP
ap-762	88	2	z	z	PROPN
ap-762	88	3	�	�	PROPN
ap-762	88	4	q	q	PROPN
ap-762	88	5	(	(	PUNCT
ap-762	88	6	)	)	PUNCT
ap-762	88	7	�	�	PROPN
ap-762	88	8	we	we	PRON
ap-762	88	9	denote	denote	VERB
ap-762	88	10	by	by	ADP
ap-762	88	11	�	�	PROPN
ap-762	88	12	z	z	PROPN
ap-762	88	13	the	the	DET
ap-762	88	14	image	image	NOUN
ap-762	88	15	of	of	ADP
ap-762	88	16	z	z	NOUN
ap-762	88	17	under	under	ADP
ap-762	88	18	the	the	DET
ap-762	88	19	field	field	NOUN
ap-762	88	20	isomorphism	isomorphism	PROPN
ap-762	88	21	�	�	PROPN
ap-762	88	22	�	�	PROPN
ap-762	88	23	:	:	PUNCT
ap-762	88	24	(	(	PUNCT
ap-762	88	25	)	)	PUNCT
ap-762	88	26	(	(	PUNCT
ap-762	88	27	)	)	PUNCT
ap-762	88	28	q	q	PRON
ap-762	88	29	q	q	PROPN
ap-762	88	30	�	�	PROPN
ap-762	88	31	�	�	PROPN
ap-762	88	32	.	.	PUNCT
ap-762	89	1	if	if	SCONJ
ap-762	89	2	h	h	NOUN
ap-762	90	1	z	z	NOUN
ap-762	90	2	z	z	PROPN
ap-762	91	1	z	z	NOUN
ap-762	91	2	:	:	PUNCT
ap-762	91	3	sup	sup	ADJ
ap-762	91	4	{	{	PUNCT
ap-762	91	5	|	|	ADV
ap-762	91	6	}	}	PUNCT
ap-762	91	7	�	�	PROPN
ap-762	91	8	�	�	PROPN
ap-762	91	9	�	�	PROPN
ap-762	91	10	�	�	PROPN
ap-762	91	11	�	�	PROPN
ap-762	91	12	�	�	PROPN
ap-762	91	13	,	,	PUNCT
ap-762	91	14	k	k	PROPN
ap-762	91	15	z	z	PROPN
ap-762	92	1	z	z	PROPN
ap-762	92	2	z	z	PROPN
ap-762	93	1	z	z	ADJ
ap-762	93	2	:	:	PUNCT
ap-762	93	3	inf	inf	ADJ
ap-762	93	4	{	{	PUNCT
ap-762	93	5	|	|	ADV
ap-762	93	6	\	\	NOUN
ap-762	93	7	}	}	PUNCT
ap-762	93	8	�	�	PROPN
ap-762	93	9	�	�	PROPN
ap-762	93	10	�	�	PROPN
ap-762	93	11	�	�	PROPN
ap-762	93	12	�	�	PROPN
ap-762	93	13	�	�	PROPN
ap-762	93	14	�	�	PROPN
ap-762	93	15	0	0	NUM
ap-762	93	16	,	,	PUNCT
ap-762	93	17	then	then	ADV
ap-762	93	18	1	1	NUM
ap-762	93	19	2	2	NUM
ap-762	93	20	�	�	PROPN
ap-762	93	21	�	�	PROPN
ap-762	93	22	�	�	PROPN
ap-762	93	23	�	�	PROPN
ap-762	93	24	�	�	PROPN
ap-762	93	25	�	�	PROPN
ap-762	93	26	�	�	PROPN
ap-762	93	27	�	�	PROPN
ap-762	93	28	�	�	PROPN
ap-762	93	29	�	�	PROPN
ap-762	93	30	�	�	PROPN
ap-762	93	31	l	l	NOUN
ap-762	93	32	h	h	NOUN
ap-762	94	1	k	k	PROPN
ap-762	94	2	and	and	CCONJ
ap-762	94	3	1	1	NUM
ap-762	94	4	2	2	NUM
ap-762	94	5	�	�	PROPN
ap-762	94	6	�	�	PROPN
ap-762	94	7	�	�	PROPN
ap-762	94	8	�	�	PROPN
ap-762	94	9	�	�	PROPN
ap-762	94	10	�	�	PROPN
ap-762	94	11	�	�	PROPN
ap-762	94	12	�	�	PROPN
ap-762	94	13	�	�	PROPN
ap-762	94	14	�	�	PROPN
ap-762	94	15	�	�	PROPN
ap-762	94	16	l	l	NOUN
ap-762	94	17	h	h	PROPN
ap-762	95	1	k	k	PROPN
ap-762	95	2	.	.	PUNCT
ap-762	96	1	some	some	DET
ap-762	96	2	known	know	VERB
ap-762	96	3	results	result	NOUN
ap-762	96	4	on	on	ADP
ap-762	96	5	the	the	DET
ap-762	96	6	values	value	NOUN
ap-762	96	7	of	of	ADP
ap-762	96	8	l	l	PROPN
ap-762	96	9	�	�	PROPN
ap-762	96	10	(	(	PUNCT
ap-762	96	11	)	)	PUNCT
ap-762	96	12	�	�	PROPN
ap-762	96	13	,	,	PUNCT
ap-762	96	14	l	l	X
ap-762	96	15	�	�	PROPN
ap-762	96	16	(	(	PUNCT
ap-762	96	17	)	)	PUNCT
ap-762	96	18	�	�	PROPN
ap-762	96	19	�	�	PROPN
ap-762	96	20	knuth	knuth	PROPN
ap-762	97	1	[	[	X
ap-762	97	2	13	13	NUM
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ap-762	97	5	l	l	X
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ap-762	97	21	.	.	PUNCT
ap-762	98	1	�	�	PROPN
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ap-762	98	5	.	.	PUNCT
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ap-762	99	5	l	l	X
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ap-762	99	10	(	(	PUNCT
ap-762	99	11	)	)	PUNCT
ap-762	99	12	(	(	PUNCT
ap-762	99	13	)	)	PUNCT
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ap-762	99	16	1	1	NUM
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ap-762	99	22	x	x	PUNCT
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ap-762	99	34	(	(	PUNCT
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ap-762	99	46	x	x	PUNCT
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ap-762	99	49	�	�	PROPN
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ap-762	99	51	.	.	PUNCT
ap-762	100	1	�	�	PROPN
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ap-762	100	4	al	al	PROPN
ap-762	100	5	.	.	PUNCT
ap-762	101	1	[	[	X
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ap-762	101	3	]	]	PUNCT
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ap-762	101	8	equation	equation	NOUN
ap-762	101	9	x	x	PUNCT
ap-762	101	10	mx	mx	PROPN
ap-762	101	11	n2	n2	PROPN
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ap-762	101	14	,	,	PUNCT
ap-762	101	15	m	m	PROPN
ap-762	101	16	n	n	PRON
ap-762	101	17	�	�	PROPN
ap-762	101	18	©	©	PROPN
ap-762	101	19	czech	czech	PROPN
ap-762	101	20	technical	technical	PROPN
ap-762	101	21	university	university	PROPN
ap-762	101	22	publishing	publishing	NOUN
ap-762	101	23	house	house	NOUN
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ap-762	101	25	25	25	NUM
ap-762	101	26	czech	czech	PROPN
ap-762	101	27	technical	technical	PROPN
ap-762	101	28	university	university	PROPN
ap-762	101	29	in	in	ADP
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ap-762	101	34	.	.	PROPN
ap-762	102	1	45	45	NUM
ap-762	102	2	no	no	NOUN
ap-762	102	3	.	.	PUNCT
ap-762	103	1	5/2005	5/2005	NUM
ap-762	103	2	2	2	NUM
ap-762	103	3	1	1	NUM
ap-762	103	4	1	1	NUM
ap-762	103	5	2	2	NUM
ap-762	103	6	1	1	NUM
ap-762	103	7	m	m	NOUN
ap-762	103	8	m	m	VERB
ap-762	103	9	n	n	ADV
ap-762	103	10	l	l	NOUN
ap-762	103	11	m	m	VERB
ap-762	103	12	m	m	VERB
ap-762	103	13	n	n	PRON
ap-762	103	14	�	�	PROPN
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ap-762	103	17	!	!	PUNCT
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ap-762	104	1	#	#	PUNCT
ap-762	104	2	"	"	PUNCT
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ap-762	104	8	%	%	NOUN
ap-762	104	9	"	"	PUNCT
ap-762	104	10	"	"	PUNCT
ap-762	104	11	�	�	PROPN
ap-762	104	12	(	(	PUNCT
ap-762	104	13	)	)	PUNCT
ap-762	104	14	�	�	PROPN
ap-762	104	15	,	,	PUNCT
ap-762	104	16	l	l	PROPN
ap-762	104	17	l	l	X
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ap-762	104	23	(	(	PUNCT
ap-762	104	24	)	)	PUNCT
ap-762	104	25	(	(	PUNCT
ap-762	104	26	)	)	PUNCT
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ap-762	104	28	(	(	PUNCT
ap-762	104	29	)	)	PUNCT
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ap-762	104	33	22	22	NUM
ap-762	104	34	.	.	PUNCT
ap-762	105	1	�	�	PROPN
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ap-762	106	1	[	[	X
ap-762	106	2	15	15	NUM
ap-762	106	3	]	]	SYM
ap-762	106	4	:	:	PUNCT
ap-762	106	5	l	l	X
ap-762	106	6	�	�	PROPN
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ap-762	106	9	)	)	PUNCT
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ap-762	106	11	6	6	NUM
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ap-762	106	13	�	�	PROPN
ap-762	106	14	root	root	NOUN
ap-762	106	15	of	of	ADP
ap-762	106	16	the	the	DET
ap-762	106	17	equation	equation	NOUN
ap-762	106	18	x	x	PUNCT
ap-762	106	19	x	x	SYM
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ap-762	106	21	2	2	NUM
ap-762	106	22	1	1	NUM
ap-762	106	23	�	�	PROPN
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ap-762	106	25	�	�	PROPN
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ap-762	106	28	is	be	AUX
ap-762	106	29	the	the	DET
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ap-762	106	31	-	-	PUNCT
ap-762	106	32	called	call	VERB
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ap-762	106	35	.	.	PUNCT
ap-762	107	1	�	�	PROPN
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ap-762	108	3	]	]	PUNCT
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ap-762	108	6	tribonacci	tribonacci	PROPN
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ap-762	108	8	5	5	NUM
ap-762	108	9	6	6	NUM
ap-762	108	10	�	�	PROPN
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ap-762	108	14	(	(	PUNCT
ap-762	108	15	)	)	PUNCT
ap-762	108	16	�	�	PROPN
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ap-762	108	19	6	6	NUM
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ap-762	108	24	(	(	PUNCT
ap-762	108	25	)	)	PUNCT
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ap-762	108	31	(	(	PUNCT
ap-762	108	32	)	)	PUNCT
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ap-762	108	34	5	5	NUM
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ap-762	108	39	(	(	PUNCT
ap-762	108	40	)	)	PUNCT
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ap-762	108	44	�	�	PROPN
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ap-762	108	46	of	of	ADP
ap-762	108	47	the	the	DET
ap-762	108	48	equation	equation	NOUN
ap-762	108	49	x	x	PUNCT
ap-762	109	1	x	x	SYM
ap-762	109	2	x3	x3	VERB
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ap-762	109	4	15	15	NUM
ap-762	109	5	2	2	NUM
ap-762	109	6	�	�	PROPN
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ap-762	109	9	.	.	PUNCT
ap-762	109	10	�	�	PROPN
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ap-762	110	8	for	for	ADP
ap-762	110	9	the	the	DET
ap-762	110	10	tribonacci	tribonacci	PROPN
ap-762	110	11	addition	addition	NOUN
ap-762	110	12	,	,	PUNCT
ap-762	110	13	l	l	X
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ap-762	110	16	(	(	PUNCT
ap-762	110	17	)	)	PUNCT
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ap-762	110	19	5	5	NUM
ap-762	110	20	.	.	PUNCT
ap-762	110	21	�	�	PROPN
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ap-762	110	25	.	.	PUNCT
ap-762	111	1	[	[	X
ap-762	111	2	8	8	NUM
ap-762	111	3	]	]	PUNCT
ap-762	111	4	for	for	ADP
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ap-762	111	6	�	�	PROPN
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ap-762	111	9	the	the	DET
ap-762	111	10	equation	equation	NOUN
ap-762	112	1	x	x	PUNCT
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ap-762	112	4	2	2	NUM
ap-762	112	5	1	1	NUM
ap-762	112	6	�	�	PROPN
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ap-762	112	9	5	5	NUM
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ap-762	112	11	�	�	PROPN
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ap-762	112	73	x	x	PUNCT
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ap-762	113	2	1	1	NUM
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ap-762	113	4	�	�	PROPN
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ap-762	114	1	a	a	DET
ap-762	114	2	�	�	NOUN
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ap-762	114	4	representation	representation	NOUN
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ap-762	114	6	a	a	DET
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ap-762	114	8	number	number	NOUN
ap-762	114	9	x	x	SYM
ap-762	114	10	�	�	NOUN
ap-762	114	11	r	r	NOUN
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ap-762	114	13	a	a	DET
ap-762	114	14	left	left	ADJ
ap-762	114	15	-	-	PUNCT
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ap-762	114	17	sequence	sequence	NOUN
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ap-762	114	19	)	)	PUNCT
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ap-762	114	25	�	�	PROPN
ap-762	114	26	,	,	PUNCT
ap-762	114	27	di	di	X
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ap-762	114	37	that	that	SCONJ
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ap-762	114	40	i	i	PRON
ap-762	114	41	i	i	PROPN
ap-762	114	42	n	n	PROPN
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ap-762	114	45	�	�	PROPN
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ap-762	114	48	(	(	PUNCT
ap-762	114	49	)	)	PUNCT
ap-762	114	50	�	�	PROPN
ap-762	114	51	.	.	PUNCT
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ap-762	115	2	is	be	AUX
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ap-762	116	9	0	0	NUM
ap-762	116	10	1	1	NUM
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ap-762	117	4	a	a	DET
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ap-762	117	7	representation	representation	NOUN
ap-762	117	8	is	be	AUX
ap-762	117	9	obtained	obtain	VERB
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ap-762	117	11	the	the	DET
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ap-762	117	13	�	�	PROPN
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ap-762	118	5	by	by	ADP
ap-762	118	6	&	&	CCONJ
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ap-762	118	10	(	(	PUNCT
ap-762	118	11	)	)	PUNCT
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ap-762	118	13	(	(	PUNCT
ap-762	118	14	)	)	PUNCT
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ap-762	118	17	n	n	NOUN
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ap-762	119	1	i	i	PRON
ap-762	120	1	i	i	VERB
ap-762	120	2	i	i	PRON
ap-762	120	3	n	n	CCONJ
ap-762	120	4	�	�	PROPN
ap-762	120	5	�	�	PROPN
ap-762	120	6	�	�	PROPN
ap-762	120	7	�	�	PROPN
ap-762	120	8	�	�	PROPN
ap-762	120	9	�	�	PROPN
ap-762	120	10	�	�	PROPN
ap-762	120	11	�	�	PROPN
ap-762	120	12	.	.	PUNCT
ap-762	121	1	if	if	SCONJ
ap-762	121	2	all	all	DET
ap-762	121	3	finite	finite	VERB
ap-762	121	4	factors	factor	NOUN
ap-762	121	5	of	of	ADP
ap-762	121	6	the	the	DET
ap-762	121	7	sequence	sequence	NOUN
ap-762	121	8	(	(	PUNCT
ap-762	121	9	)	)	PUNCT
ap-762	121	10	di	di	NOUN
ap-762	121	11	n	n	PROPN
ap-762	121	12	i	i	PROPN
ap-762	121	13	�	�	PROPN
ap-762	121	14	�	�	PROPN
ap-762	121	15	�	�	PROPN
ap-762	121	16	are	be	AUX
ap-762	121	17	admissible	admissible	ADJ
ap-762	121	18	in	in	ADP
ap-762	121	19	the	the	DET
ap-762	121	20	�	�	PROPN
ap-762	121	21	-numeration	-numeration	NOUN
ap-762	121	22	system	system	NOUN
ap-762	121	23	,	,	PUNCT
ap-762	121	24	the	the	DET
ap-762	121	25	sequence	sequence	NOUN
ap-762	121	26	(	(	PUNCT
ap-762	121	27	)	)	PUNCT
ap-762	121	28	di	di	NOUN
ap-762	121	29	n	n	PROPN
ap-762	121	30	i	i	PROPN
ap-762	121	31	�	�	PROPN
ap-762	121	32	�	�	PROPN
ap-762	121	33	�	�	PROPN
ap-762	121	34	is	be	AUX
ap-762	121	35	said	say	VERB
ap-762	121	36	to	to	PART
ap-762	121	37	be	be	AUX
ap-762	121	38	the	the	DET
ap-762	121	39	�	�	NOUN
ap-762	121	40	-adic	-adic	ADJ
ap-762	121	41	expansion	expansion	NOUN
ap-762	121	42	of	of	ADP
ap-762	121	43	the	the	DET
ap-762	121	44	number	number	NOUN
ap-762	121	45	x	x	NOUN
ap-762	121	46	,	,	PUNCT
ap-762	121	47	and	and	CCONJ
ap-762	121	48	it	it	PRON
ap-762	121	49	is	be	AUX
ap-762	121	50	denoted	denote	VERB
ap-762	121	51	�	�	PROPN
ap-762	121	52	�	�	PROPN
ap-762	121	53	x	x	SYM
ap-762	121	54	.	.	PUNCT
ap-762	121	55	3.1	3.1	NUM
ap-762	121	56	basic	basic	ADJ
ap-762	121	57	properties	property	NOUN
ap-762	121	58	of	of	ADP
ap-762	121	59	�	�	NOUN
ap-762	121	60	-adic	-adic	ADJ
ap-762	121	61	expansions	expansion	NOUN
ap-762	121	62	we	we	PRON
ap-762	121	63	know	know	VERB
ap-762	121	64	[	[	X
ap-762	121	65	3	3	X
ap-762	121	66	]	]	PUNCT
ap-762	121	67	that	that	DET
ap-762	121	68	fin	fin	NOUN
ap-762	121	69	(	(	PUNCT
ap-762	121	70	)	)	PUNCT
ap-762	122	1	[	[	PUNCT
ap-762	122	2	]	]	X
ap-762	122	3	{	{	PUNCT
ap-762	122	4	|	|	ADV
ap-762	122	5	,	,	PUNCT
ap-762	122	6	}	}	PUNCT
ap-762	122	7	�	�	PROPN
ap-762	122	8	�	�	PROPN
ap-762	122	9	�	�	PROPN
ap-762	122	10	�	�	PROPN
ap-762	122	11	�	�	PROPN
ap-762	122	12	�	�	PROPN
ap-762	122	13	�	�	PROPN
ap-762	122	14	z	z	PROPN
ap-762	122	15	za	za	PROPN
ap-762	122	16	b	b	PROPN
ap-762	122	17	a	a	DET
ap-762	122	18	b	b	NOUN
ap-762	122	19	.	.	PUNCT
ap-762	123	1	hence	hence	ADV
ap-762	123	2	for	for	ADP
ap-762	123	3	any	any	DET
ap-762	123	4	z	z	PROPN
ap-762	123	5	�	�	PROPN
ap-762	123	6	�	�	PROPN
ap-762	123	7	z	z	VERB
ap-762	123	8	there	there	PRON
ap-762	123	9	exist	exist	VERB
ap-762	123	10	m	m	NOUN
ap-762	123	11	n	n	CCONJ
ap-762	123	12	,	,	PUNCT
ap-762	123	13	�	�	PROPN
ap-762	123	14	z	z	PROPN
ap-762	123	15	,	,	PUNCT
ap-762	123	16	m	m	PROPN
ap-762	123	17	n	n	PRON
ap-762	123	18	�	�	PROPN
ap-762	123	19	such	such	ADJ
ap-762	123	20	that	that	SCONJ
ap-762	123	21	z	z	NOUN
ap-762	123	22	zi	zi	NOUN
ap-762	124	1	i	i	INTJ
ap-762	125	1	i	i	PRON
ap-762	125	2	m	m	VERB
ap-762	125	3	n	n	PRON
ap-762	125	4	�	�	PROPN
ap-762	125	5	�	�	PROPN
ap-762	125	6	�	�	PROPN
ap-762	125	7	thus	thus	ADV
ap-762	125	8	z	z	PROPN
ap-762	125	9	zi	zi	NOUN
ap-762	126	1	i	i	INTJ
ap-762	127	1	i	i	PRON
ap-762	127	2	m	m	VERB
ap-762	127	3	n	n	PRON
ap-762	127	4	�	�	PROPN
ap-762	127	5	�	�	PROPN
ap-762	127	6	�	�	PROPN
ap-762	127	7	(	(	PUNCT
ap-762	127	8	�	�	PROPN
ap-762	127	9	�	�	PROPN
ap-762	127	10	,	,	PUNCT
ap-762	127	11	i.e.	i.e.	X
ap-762	127	12	for	for	ADP
ap-762	127	13	each	each	DET
ap-762	127	14	z	z	PROPN
ap-762	127	15	�	�	PROPN
ap-762	127	16	�	�	PROPN
ap-762	127	17	z	z	PROPN
ap-762	127	18	the	the	DET
ap-762	127	19	�	�	PROPN
ap-762	127	20	-adic	-adic	ADJ
ap-762	127	21	expansion	expansion	NOUN
ap-762	127	22	�	�	PROPN
ap-762	127	23	�	�	PROPN
ap-762	127	24	�	�	PROPN
ap-762	127	25	�	�	PROPN
ap-762	127	26	z	z	PROPN
ap-762	127	27	z	z	PROPN
ap-762	127	28	is	be	AUX
ap-762	127	29	a	a	DET
ap-762	127	30	finite	finite	ADJ
ap-762	127	31	word	word	NOUN
ap-762	127	32	with	with	ADP
ap-762	127	33	some	some	DET
ap-762	127	34	possible	possible	ADJ
ap-762	127	35	fractional	fractional	ADJ
ap-762	127	36	part	part	NOUN
ap-762	127	37	.	.	PUNCT
ap-762	128	1	for	for	ADP
ap-762	128	2	negative	negative	ADJ
ap-762	128	3	integers	integer	NOUN
ap-762	128	4	z	z	PROPN
ap-762	128	5	�	�	PROPN
ap-762	128	6	�	�	PROPN
ap-762	128	7	z	z	PROPN
ap-762	128	8	we	we	PRON
ap-762	128	9	have	have	VERB
ap-762	128	10	the	the	DET
ap-762	128	11	following	follow	VERB
ap-762	128	12	proposition	proposition	NOUN
ap-762	128	13	.	.	PUNCT
ap-762	129	1	proposition	proposition	NOUN
ap-762	129	2	3.1	3.1	NUM
ap-762	129	3	:	:	PUNCT
ap-762	129	4	(	(	PUNCT
ap-762	129	5	ambrož	ambrož	NOUN
ap-762	130	1	[	[	X
ap-762	130	2	16	16	NUM
ap-762	130	3	]	]	PUNCT
ap-762	130	4	)	)	PUNCT
ap-762	130	5	.	.	PUNCT
ap-762	131	1	letz	letz	PROPN
ap-762	131	2	�	�	PROPN
ap-762	131	3	�	�	PROPN
ap-762	131	4	z	z	PROPN
ap-762	131	5	be	be	VERB
ap-762	131	6	a	a	DET
ap-762	131	7	negative	negative	ADJ
ap-762	131	8	integer	integer	NOUN
ap-762	131	9	.	.	PUNCT
ap-762	132	1	its	its	PRON
ap-762	132	2	�	�	NOUN
ap-762	132	3	-adic	-adic	ADJ
ap-762	132	4	expansion	expansion	NOUN
ap-762	132	5	�	�	PROPN
ap-762	132	6	�	�	PROPN
ap-762	132	7	z	z	PROPN
ap-762	132	8	is	be	AUX
ap-762	132	9	a	a	DET
ap-762	132	10	left	left	ADJ
ap-762	132	11	infinite	infinite	NOUN
ap-762	132	12	,	,	PUNCT
ap-762	132	13	eventually	eventually	ADV
ap-762	132	14	periodic	periodic	ADJ
ap-762	132	15	word	word	NOUN
ap-762	132	16	of	of	ADP
ap-762	132	17	the	the	DET
ap-762	132	18	form	form	NOUN
ap-762	132	19	�	�	PROPN
ap-762	132	20	�	�	PROPN
ap-762	132	21	�	�	PROPN
ap-762	132	22	�	�	PROPN
ap-762	132	23	z	z	PROPN
ap-762	132	24	v	v	PROPN
ap-762	132	25	(	(	PUNCT
ap-762	132	26	)	)	PUNCT
ap-762	132	27	10	10	NUM
ap-762	132	28	,	,	PUNCT
ap-762	132	29	where	where	SCONJ
ap-762	132	30	v	v	ADP
ap-762	132	31	x	x	SYM
ap-762	132	32	�	�	PROPN
ap-762	132	33	�	�	PROPN
ap-762	132	34	,	,	PUNCT
ap-762	132	35	x	x	X
ap-762	132	36	�	�	PROPN
ap-762	132	37	fin	fin	NOUN
ap-762	132	38	(	(	PUNCT
ap-762	132	39	)	)	PUNCT
ap-762	132	40	�	�	PROPN
ap-762	132	41	.	.	PUNCT
ap-762	133	1	moreover	moreover	ADV
ap-762	133	2	,	,	PUNCT
ap-762	133	3	in	in	ADP
ap-762	133	4	[	[	X
ap-762	133	5	16	16	NUM
ap-762	133	6	]	]	X
ap-762	133	7	,	,	PUNCT
ap-762	133	8	an	an	DET
ap-762	133	9	algorithm	algorithm	NOUN
ap-762	133	10	is	be	AUX
ap-762	133	11	given	give	VERB
ap-762	133	12	for	for	ADP
ap-762	133	13	computing	compute	VERB
ap-762	133	14	�	�	NOUN
ap-762	133	15	-adic	-adic	ADJ
ap-762	133	16	expansions	expansion	NOUN
ap-762	133	17	of	of	ADP
ap-762	133	18	negative	negative	ADJ
ap-762	133	19	integers	integer	NOUN
ap-762	133	20	.	.	PUNCT
ap-762	134	1	since	since	SCONJ
ap-762	134	2	most	most	ADJ
ap-762	134	3	of	of	ADP
ap-762	134	4	the	the	DET
ap-762	134	5	�	�	NOUN
ap-762	134	6	-adic	-adic	ADJ
ap-762	134	7	expansions	expansion	NOUN
ap-762	134	8	that	that	PRON
ap-762	134	9	we	we	PRON
ap-762	134	10	are	be	AUX
ap-762	134	11	dealing	deal	VERB
ap-762	134	12	with	with	ADP
ap-762	134	13	are	be	AUX
ap-762	134	14	left	leave	VERB
ap-762	134	15	infinite	infinite	ADJ
ap-762	134	16	,	,	PUNCT
ap-762	134	17	eventually	eventually	ADV
ap-762	134	18	periodic	periodic	ADJ
ap-762	134	19	,	,	PUNCT
ap-762	134	20	we	we	PRON
ap-762	134	21	define	define	VERB
ap-762	134	22	the	the	DET
ap-762	134	23	following	follow	VERB
ap-762	134	24	two	two	NUM
ap-762	134	25	sets	set	NOUN
ap-762	134	26	of	of	ADP
ap-762	134	27	numbers	number	NOUN
ap-762	134	28	.	.	PUNCT
ap-762	135	1	iep	iep	PROPN
ap-762	135	2	(	(	PUNCT
ap-762	135	3	):	):	PUNCT
ap-762	135	4	{	{	PUNCT
ap-762	135	5	|	|	INTJ
ap-762	135	6	(	(	PUNCT
ap-762	135	7	)	)	PUNCT
ap-762	135	8	}	}	PUNCT
ap-762	135	9	�	�	PROPN
ap-762	135	10	�	�	PROPN
ap-762	135	11	�	�	PROPN
ap-762	135	12	�	�	PROPN
ap-762	135	13	�	�	PROPN
ap-762	135	14	�	�	PROPN
ap-762	135	15	�	�	PROPN
ap-762	135	16	�	�	PROPN
ap-762	135	17	�	�	PROPN
ap-762	135	18	�	�	PROPN
ap-762	135	19	�	�	PROPN
ap-762	135	20	x	x	SYM
ap-762	135	21	r	r	NOUN
ap-762	135	22	x	x	PUNCT
ap-762	135	23	d	d	NOUN
ap-762	136	1	d	d	NOUN
ap-762	136	2	d	d	X
ap-762	136	3	dk	dk	PROPN
ap-762	136	4	k	k	PROPN
ap-762	136	5	k	k	PROPN
ap-762	136	6	�	�	PROPN
ap-762	136	7	�	�	PROPN
ap-762	136	8	�	�	PROPN
ap-762	136	9	1	1	NUM
ap-762	136	10	0	0	NUM
ap-762	136	11	,	,	PUNCT
ap-762	136	12	fep	fep	PROPN
ap-762	136	13	(	(	PUNCT
ap-762	136	14	):	):	PUNCT
ap-762	136	15	{	{	PUNCT
ap-762	136	16	|	|	INTJ
ap-762	136	17	(	(	PUNCT
ap-762	136	18	)	)	PUNCT
ap-762	136	19	}	}	PUNCT
ap-762	136	20	�	�	PROPN
ap-762	136	21	�	�	PROPN
ap-762	136	22	�	�	PROPN
ap-762	136	23	�	�	PROPN
ap-762	136	24	�	�	PROPN
ap-762	136	25	�	�	PROPN
ap-762	136	26	�	�	PROPN
ap-762	136	27	�	�	PROPN
ap-762	136	28	�	�	PROPN
ap-762	136	29	�	�	PROPN
ap-762	136	30	�	�	PROPN
ap-762	136	31	�	�	PROPN
ap-762	136	32	�	�	PROPN
ap-762	136	33	x	x	SYM
ap-762	136	34	r	r	NOUN
ap-762	136	35	x	x	PUNCT
ap-762	137	1	d	d	NOUN
ap-762	137	2	d	d	X
ap-762	138	1	d	d	X
ap-762	138	2	d	d	PROPN
ap-762	138	3	d	d	X
ap-762	138	4	dk	dk	PROPN
ap-762	138	5	k	k	PROPN
ap-762	138	6	k	k	PROPN
ap-762	138	7	m	m	PROPN
ap-762	138	8	�	�	PROPN
ap-762	138	9	�	�	PROPN
ap-762	138	10	�	�	PROPN
ap-762	138	11	�	�	PROPN
ap-762	138	12	1	1	NUM
ap-762	138	13	0	0	NUM
ap-762	138	14	1	1	NUM
ap-762	138	15	,	,	PUNCT
ap-762	138	16	indeed	indeed	ADV
ap-762	138	17	,	,	PUNCT
ap-762	138	18	z	z	PROPN
ap-762	138	19	f	f	X
ap-762	138	20	�	�	PROPN
ap-762	138	21	�	�	PROPN
ap-762	138	22	ep	ep	PROPN
ap-762	138	23	(	(	PUNCT
ap-762	138	24	)	)	PUNCT
ap-762	138	25	�	�	PROPN
ap-762	138	26	.	.	PUNCT
ap-762	139	1	concerning	concern	VERB
ap-762	139	2	rational	rational	ADJ
ap-762	139	3	numbers	number	NOUN
ap-762	139	4	,	,	PUNCT
ap-762	139	5	there	there	PRON
ap-762	139	6	is	be	VERB
ap-762	139	7	also	also	ADV
ap-762	139	8	an	an	DET
ap-762	139	9	algorithm	algorithm	NOUN
ap-762	139	10	for	for	ADP
ap-762	139	11	computing	compute	VERB
ap-762	139	12	their	their	PRON
ap-762	139	13	�	�	NOUN
ap-762	139	14	-adic	-adic	ADJ
ap-762	139	15	expansions	expansion	NOUN
ap-762	139	16	[	[	X
ap-762	139	17	16	16	NUM
ap-762	139	18	]	]	X
ap-762	139	19	,	,	PUNCT
ap-762	139	20	which	which	PRON
ap-762	139	21	was	be	AUX
ap-762	139	22	used	use	VERB
ap-762	139	23	to	to	PART
ap-762	139	24	prove	prove	VERB
ap-762	139	25	that	that	SCONJ
ap-762	139	26	also	also	ADV
ap-762	139	27	every	every	DET
ap-762	139	28	rational	rational	ADJ
ap-762	139	29	number	number	NOUN
ap-762	139	30	has	have	VERB
ap-762	139	31	its	its	PRON
ap-762	139	32	�	�	NOUN
ap-762	139	33	-adic	-adic	ADJ
ap-762	139	34	expansion	expansion	NOUN
ap-762	139	35	,	,	PUNCT
ap-762	139	36	eventually	eventually	ADV
ap-762	139	37	periodic	periodic	ADJ
ap-762	139	38	to	to	ADP
ap-762	139	39	the	the	DET
ap-762	139	40	left	left	NOUN
ap-762	139	41	,	,	PUNCT
ap-762	139	42	more	more	ADV
ap-762	139	43	precisely	precisely	ADV
ap-762	139	44	we	we	PRON
ap-762	139	45	have	have	VERB
ap-762	139	46	q	q	PROPN
ap-762	140	1	i	i	PRON
ap-762	140	2	(	(	PUNCT
ap-762	140	3	�	�	PROPN
ap-762	140	4	�	�	PROPN
ap-762	140	5	�	�	PROPN
ap-762	140	6	(	(	PUNCT
ap-762	140	7	,	,	PUNCT
ap-762	140	8	]	]	X
ap-762	140	9	(	(	PUNCT
ap-762	140	10	)	)	PUNCT
ap-762	140	11	11	11	NUM
ap-762	140	12	ep	ep	PROPN
ap-762	140	13	�	�	PROPN
ap-762	140	14	and	and	CCONJ
ap-762	140	15	q	q	NOUN
ap-762	140	16	f	f	PROPN
ap-762	140	17	�	�	PROPN
ap-762	140	18	�	�	PROPN
ap-762	140	19	ep	ep	PROPN
ap-762	140	20	(	(	PUNCT
ap-762	140	21	)	)	PUNCT
ap-762	140	22	�	�	PROPN
ap-762	140	23	.	.	PUNCT
ap-762	141	1	3.2	3.2	NUM
ap-762	141	2	finiteness	finiteness	NOUN
ap-762	141	3	condition	condition	NOUN
ap-762	141	4	in	in	ADP
ap-762	141	5	accordance	accordance	NOUN
ap-762	141	6	with	with	ADP
ap-762	141	7	the	the	DET
ap-762	141	8	usual	usual	ADJ
ap-762	141	9	�	�	NOUN
ap-762	141	10	-expansions	-expansion	NOUN
ap-762	141	11	,	,	PUNCT
ap-762	141	12	it	it	PRON
ap-762	141	13	is	be	AUX
ap-762	141	14	interesting	interesting	ADJ
ap-762	141	15	to	to	PART
ap-762	141	16	inspect	inspect	VERB
ap-762	141	17	the	the	DET
ap-762	141	18	properties	property	NOUN
ap-762	141	19	of	of	ADP
ap-762	141	20	the	the	DET
ap-762	141	21	set	set	ADJ
ap-762	141	22	fep	fep	NOUN
ap-762	141	23	(	(	PUNCT
ap-762	141	24	)	)	PUNCT
ap-762	141	25	�	�	PROPN
ap-762	141	26	�	�	PROPN
ap-762	141	27	,	,	PUNCT
ap-762	141	28	which	which	PRON
ap-762	141	29	can	can	AUX
ap-762	141	30	be	be	AUX
ap-762	141	31	seen	see	VERB
ap-762	141	32	as	as	ADP
ap-762	141	33	a	a	DET
ap-762	141	34	�	�	NOUN
ap-762	141	35	-adic	-adic	ADJ
ap-762	141	36	correlate	correlate	NOUN
ap-762	141	37	of	of	ADP
ap-762	141	38	the	the	DET
ap-762	141	39	set	set	VERB
ap-762	141	40	fin	fin	NOUN
ap-762	141	41	(	(	PUNCT
ap-762	141	42	)	)	PUNCT
ap-762	141	43	�	�	PROPN
ap-762	141	44	.	.	PUNCT
ap-762	142	1	in	in	ADP
ap-762	142	2	[	[	X
ap-762	142	3	17	17	NUM
ap-762	142	4	]	]	PUNCT
ap-762	142	5	there	there	PRON
ap-762	142	6	is	be	VERB
ap-762	142	7	a	a	DET
ap-762	142	8	proof	proof	NOUN
ap-762	142	9	that	that	SCONJ
ap-762	142	10	the	the	DET
ap-762	142	11	set	set	ADJ
ap-762	142	12	fep	fep	NOUN
ap-762	142	13	(	(	PUNCT
ap-762	142	14	)	)	PUNCT
ap-762	142	15	�	�	PROPN
ap-762	142	16	�	�	PROPN
ap-762	142	17	is	be	AUX
ap-762	142	18	closed	close	VERB
ap-762	142	19	under	under	ADP
ap-762	142	20	the	the	DET
ap-762	142	21	addition	addition	NOUN
ap-762	142	22	.	.	PUNCT
ap-762	143	1	the	the	DET
ap-762	143	2	proof	proof	NOUN
ap-762	143	3	is	be	AUX
ap-762	143	4	of	of	ADP
ap-762	143	5	a	a	DET
ap-762	143	6	constructive	constructive	ADJ
ap-762	143	7	type	type	NOUN
ap-762	143	8	,	,	PUNCT
ap-762	143	9	consisting	consist	VERB
ap-762	143	10	of	of	ADP
ap-762	143	11	building	build	VERB
ap-762	143	12	a	a	DET
ap-762	143	13	right	right	NOUN
ap-762	143	14	to	to	PART
ap-762	143	15	left	left	VERB
ap-762	143	16	transducer	transducer	NOUN
ap-762	143	17	performing	perform	VERB
ap-762	143	18	the	the	DET
ap-762	143	19	addition	addition	NOUN
ap-762	143	20	,	,	PUNCT
ap-762	143	21	which	which	PRON
ap-762	143	22	preserves	preserve	VERB
ap-762	143	23	the	the	DET
ap-762	143	24	periodicity	periodicity	NOUN
ap-762	143	25	of	of	ADP
ap-762	143	26	its	its	PRON
ap-762	143	27	input	input	NOUN
ap-762	143	28	.	.	PUNCT
ap-762	144	1	when	when	SCONJ
ap-762	144	2	we	we	PRON
ap-762	144	3	know	know	VERB
ap-762	144	4	that	that	DET
ap-762	144	5	fep	fep	PROPN
ap-762	144	6	(	(	PUNCT
ap-762	144	7	)	)	PUNCT
ap-762	144	8	�	�	PROPN
ap-762	144	9	�	�	PROPN
ap-762	144	10	is	be	AUX
ap-762	144	11	closed	close	VERB
ap-762	144	12	under	under	ADP
ap-762	144	13	addition	addition	NOUN
ap-762	144	14	of	of	ADP
ap-762	144	15	positive	positive	ADJ
ap-762	144	16	elements	element	NOUN
ap-762	144	17	,	,	PUNCT
ap-762	144	18	it	it	PRON
ap-762	144	19	is	be	AUX
ap-762	144	20	quite	quite	ADV
ap-762	144	21	easy	easy	ADJ
ap-762	144	22	to	to	PART
ap-762	144	23	prove	prove	VERB
ap-762	144	24	that	that	SCONJ
ap-762	144	25	it	it	PRON
ap-762	144	26	is	be	AUX
ap-762	144	27	a	a	DET
ap-762	144	28	ring	ring	NOUN
ap-762	144	29	.	.	PUNCT
ap-762	145	1	finally	finally	ADV
ap-762	145	2	,	,	PUNCT
ap-762	145	3	there	there	PRON
ap-762	145	4	has	have	AUX
ap-762	145	5	been	be	AUX
ap-762	145	6	shown	show	VERB
ap-762	145	7	a	a	DET
ap-762	145	8	relation	relation	NOUN
ap-762	145	9	between	between	ADP
ap-762	145	10	eventually	eventually	ADV
ap-762	145	11	periodic	periodic	ADJ
ap-762	145	12	�	�	NOUN
ap-762	145	13	-adic	-adic	ADJ
ap-762	145	14	expansions	expansion	NOUN
ap-762	145	15	and	and	CCONJ
ap-762	145	16	the	the	DET
ap-762	145	17	elements	element	NOUN
ap-762	145	18	of	of	ADP
ap-762	145	19	the	the	DET
ap-762	145	20	ring	ring	NOUN
ap-762	145	21	q	q	PROPN
ap-762	145	22	(	(	PUNCT
ap-762	145	23	)	)	PUNCT
ap-762	145	24	�	�	PROPN
ap-762	145	25	.	.	PUNCT
ap-762	146	1	theorem	theorem	VERB
ap-762	146	2	3.2	3.2	NUM
ap-762	146	3	:	:	PUNCT
ap-762	146	4	(	(	PUNCT
ap-762	146	5	ambrož	ambrož	NOUN
ap-762	147	1	[	[	X
ap-762	147	2	17	17	NUM
ap-762	147	3	]	]	PUNCT
ap-762	147	4	)	)	PUNCT
ap-762	147	5	.	.	PUNCT
ap-762	148	1	the	the	DET
ap-762	148	2	field	field	NOUN
ap-762	148	3	q	q	X
ap-762	148	4	(	(	PUNCT
ap-762	148	5	)	)	PUNCT
ap-762	148	6	�	�	PROPN
ap-762	148	7	�	�	PROPN
ap-762	148	8	(	(	PUNCT
ap-762	148	9	and	and	CCONJ
ap-762	148	10	therefore	therefore	ADV
ap-762	148	11	also	also	ADV
ap-762	148	12	the	the	DET
ap-762	148	13	fieldq	fieldq	ADJ
ap-762	148	14	(	(	PUNCT
ap-762	148	15	)	)	PUNCT
ap-762	148	16	�	�	PROPN
ap-762	148	17	)	)	PUNCT
ap-762	148	18	is	be	AUX
ap-762	148	19	equal	equal	ADJ
ap-762	148	20	to	to	ADP
ap-762	148	21	the	the	DET
ap-762	148	22	setfep	setfep	PROPN
ap-762	148	23	(	(	PUNCT
ap-762	148	24	)	)	PUNCT
ap-762	148	25	�	�	PROPN
ap-762	148	26	�	�	PROPN
ap-762	148	27	of	of	ADP
ap-762	148	28	all	all	DET
ap-762	148	29	real	real	ADJ
ap-762	148	30	numbers	number	NOUN
ap-762	148	31	having	have	VERB
ap-762	148	32	eventually	eventually	ADV
ap-762	148	33	periodic	periodic	ADJ
ap-762	148	34	�	�	NOUN
ap-762	148	35	-adic	-adic	ADJ
ap-762	148	36	expansion	expansion	NOUN
ap-762	148	37	with	with	ADP
ap-762	148	38	a	a	DET
ap-762	148	39	finite	finite	ADJ
ap-762	148	40	fractional	fractional	ADJ
ap-762	148	41	part	part	NOUN
ap-762	148	42	.	.	PUNCT
ap-762	149	1	4	4	NUM
ap-762	149	2	future	future	ADJ
ap-762	149	3	perspectives	perspective	NOUN
ap-762	149	4	there	there	PRON
ap-762	149	5	are	be	VERB
ap-762	149	6	several	several	ADJ
ap-762	149	7	objectives	objective	NOUN
ap-762	149	8	that	that	PRON
ap-762	149	9	can	can	AUX
ap-762	149	10	be	be	AUX
ap-762	149	11	pursued	pursue	VERB
ap-762	149	12	in	in	ADP
ap-762	149	13	the	the	DET
ap-762	149	14	future	future	NOUN
ap-762	149	15	.	.	PUNCT
ap-762	150	1	concerning	concern	VERB
ap-762	150	2	the	the	DET
ap-762	150	3	already	already	ADV
ap-762	150	4	classical	classical	ADJ
ap-762	150	5	�	�	NOUN
ap-762	150	6	-expansions	-expansion	NOUN
ap-762	150	7	,	,	PUNCT
ap-762	150	8	there	there	PRON
ap-762	150	9	is	be	VERB
ap-762	150	10	always	always	ADV
ap-762	150	11	the	the	DET
ap-762	150	12	challenging	challenging	ADJ
ap-762	150	13	problem	problem	NOUN
ap-762	150	14	of	of	ADP
ap-762	150	15	the	the	DET
ap-762	150	16	algebraic	algebraic	ADJ
ap-762	150	17	characterization	characterization	NOUN
ap-762	150	18	of	of	ADP
ap-762	150	19	numbers	number	NOUN
ap-762	150	20	�	�	PROPN
ap-762	150	21	satisfying	satisfy	VERB
ap-762	150	22	property	property	NOUN
ap-762	150	23	(	(	PUNCT
ap-762	150	24	f	f	NOUN
ap-762	150	25	)	)	PUNCT
ap-762	150	26	.	.	PUNCT
ap-762	151	1	moreover	moreover	ADV
ap-762	151	2	,	,	PUNCT
ap-762	151	3	there	there	PRON
ap-762	151	4	is	be	VERB
ap-762	151	5	a	a	DET
ap-762	151	6	lot	lot	NOUN
ap-762	151	7	of	of	ADP
ap-762	151	8	work	work	NOUN
ap-762	151	9	to	to	PART
ap-762	151	10	be	be	AUX
ap-762	151	11	done	do	VERB
ap-762	151	12	while	while	SCONJ
ap-762	151	13	looking	look	VERB
ap-762	151	14	for	for	ADP
ap-762	151	15	the	the	DET
ap-762	151	16	number	number	NOUN
ap-762	151	17	of	of	ADP
ap-762	151	18	fractional	fractional	ADJ
ap-762	151	19	digits	digit	NOUN
ap-762	151	20	arising	arise	VERB
ap-762	151	21	under	under	ADP
ap-762	151	22	arithmetic	arithmetic	ADJ
ap-762	151	23	operations	operation	NOUN
ap-762	151	24	.	.	PUNCT
ap-762	152	1	finally	finally	ADV
ap-762	152	2	,	,	PUNCT
ap-762	152	3	there	there	PRON
ap-762	152	4	is	be	VERB
ap-762	152	5	an	an	DET
ap-762	152	6	open	open	ADJ
ap-762	152	7	question	question	NOUN
ap-762	152	8	[	[	X
ap-762	152	9	6	6	NUM
ap-762	152	10	]	]	PUNCT
ap-762	152	11	of	of	ADP
ap-762	152	12	finding	find	VERB
ap-762	152	13	arithmetic	arithmetic	ADJ
ap-762	152	14	algorithms	algorithm	NOUN
ap-762	152	15	working	work	VERB
ap-762	152	16	with	with	ADP
ap-762	152	17	infinite	infinite	NOUN
ap-762	152	18	,	,	PUNCT
ap-762	152	19	but	but	CCONJ
ap-762	152	20	periodic	periodic	ADJ
ap-762	152	21	�	�	NOUN
ap-762	152	22	-expansions	-expansion	NOUN
ap-762	152	23	.	.	PUNCT
ap-762	153	1	a	a	DET
ap-762	153	2	partial	partial	ADJ
ap-762	153	3	answer	answer	NOUN
ap-762	153	4	to	to	ADP
ap-762	153	5	the	the	DET
ap-762	153	6	last	last	ADJ
ap-762	153	7	question	question	NOUN
ap-762	153	8	was	be	AUX
ap-762	153	9	recently	recently	ADV
ap-762	153	10	given	give	VERB
ap-762	153	11	by	by	ADP
ap-762	153	12	the	the	DET
ap-762	153	13	author	author	NOUN
ap-762	153	14	in	in	ADP
ap-762	153	15	[	[	X
ap-762	153	16	18	18	NUM
ap-762	153	17	]	]	PUNCT
ap-762	153	18	.	.	PUNCT
ap-762	154	1	concerning	concern	VERB
ap-762	154	2	the	the	DET
ap-762	154	3	second	second	ADJ
ap-762	154	4	notion	notion	NOUN
ap-762	154	5	of	of	ADP
ap-762	154	6	irrational	irrational	ADJ
ap-762	154	7	representation	representation	NOUN
ap-762	154	8	–	–	PUNCT
ap-762	154	9	�	�	NOUN
ap-762	154	10	-adic	-adic	ADJ
ap-762	154	11	expansions	expansion	NOUN
ap-762	154	12	–	–	PUNCT
ap-762	154	13	there	there	PRON
ap-762	154	14	are	be	VERB
ap-762	154	15	also	also	ADV
ap-762	154	16	several	several	ADJ
ap-762	154	17	possible	possible	ADJ
ap-762	154	18	ways	way	NOUN
ap-762	154	19	of	of	ADP
ap-762	154	20	future	future	ADJ
ap-762	154	21	research	research	NOUN
ap-762	154	22	.	.	PUNCT
ap-762	155	1	it	it	PRON
ap-762	155	2	seems	seem	VERB
ap-762	155	3	quite	quite	ADV
ap-762	155	4	obvious	obvious	ADJ
ap-762	155	5	that	that	SCONJ
ap-762	155	6	it	it	PRON
ap-762	155	7	will	will	AUX
ap-762	155	8	be	be	AUX
ap-762	155	9	only	only	ADV
ap-762	155	10	a	a	DET
ap-762	155	11	question	question	NOUN
ap-762	155	12	of	of	ADP
ap-762	155	13	solving	solve	VERB
ap-762	155	14	some	some	DET
ap-762	155	15	technical	technical	ADJ
ap-762	155	16	obstacles	obstacle	NOUN
ap-762	155	17	to	to	PART
ap-762	155	18	broaden	broaden	VERB
ap-762	155	19	the	the	DET
ap-762	155	20	�	�	NOUN
ap-762	155	21	-adic	-adic	ADJ
ap-762	155	22	expansions	expansion	NOUN
ap-762	155	23	onto	onto	ADP
ap-762	155	24	the	the	DET
ap-762	155	25	�	�	NOUN
ap-762	155	26	-adic	-adic	ADJ
ap-762	155	27	expansions	expansion	NOUN
ap-762	155	28	,	,	PUNCT
ap-762	155	29	for	for	ADP
ap-762	155	30	some	some	DET
ap-762	155	31	class	class	NOUN
ap-762	155	32	of	of	ADP
ap-762	155	33	�	�	PROPN
ap-762	155	34	.	.	PUNCT
ap-762	156	1	indeed	indeed	ADV
ap-762	156	2	,	,	PUNCT
ap-762	156	3	those	those	DET
ap-762	156	4	classes	class	NOUN
ap-762	156	5	of	of	ADP
ap-762	156	6	�	�	PROPN
ap-762	156	7	fulfilling	fulfil	VERB
ap-762	156	8	the	the	DET
ap-762	156	9	property	property	NOUN
ap-762	156	10	(	(	PUNCT
ap-762	156	11	f	f	X
ap-762	156	12	)	)	PUNCT
ap-762	156	13	are	be	AUX
ap-762	156	14	suitable	suitable	ADJ
ap-762	156	15	candidates	candidate	NOUN
ap-762	156	16	.	.	PUNCT
ap-762	157	1	on	on	ADP
ap-762	157	2	the	the	DET
ap-762	157	3	other	other	ADJ
ap-762	157	4	hand	hand	NOUN
ap-762	157	5	,	,	PUNCT
ap-762	157	6	the	the	DET
ap-762	157	7	proof	proof	NOUN
ap-762	157	8	of	of	ADP
ap-762	157	9	the	the	DET
ap-762	157	10	finiteness	finiteness	ADJ
ap-762	157	11	property	property	NOUN
ap-762	157	12	for	for	ADP
ap-762	157	13	the	the	DET
ap-762	157	14	�	�	PROPN
ap-762	157	15	-adic	-adic	ADJ
ap-762	157	16	expansions	expansion	NOUN
ap-762	157	17	is	be	AUX
ap-762	157	18	deeply	deeply	ADV
ap-762	157	19	connected	connect	VERB
ap-762	157	20	with	with	ADP
ap-762	157	21	the	the	DET
ap-762	157	22	nature	nature	NOUN
ap-762	157	23	of	of	ADP
ap-762	157	24	the	the	DET
ap-762	157	25	system	system	NOUN
ap-762	157	26	itself	itself	PRON
ap-762	157	27	and	and	CCONJ
ap-762	157	28	its	its	PRON
ap-762	157	29	generalization	generalization	NOUN
ap-762	157	30	for	for	ADP
ap-762	157	31	some	some	DET
ap-762	157	32	other	other	ADJ
ap-762	157	33	irrationalities	irrationality	NOUN
ap-762	157	34	will	will	AUX
ap-762	157	35	be	be	AUX
ap-762	157	36	difficult	difficult	ADJ
ap-762	157	37	or	or	CCONJ
ap-762	157	38	even	even	ADV
ap-762	157	39	impossible	impossible	ADJ
ap-762	157	40	to	to	PART
ap-762	157	41	perform	perform	VERB
ap-762	157	42	without	without	ADP
ap-762	157	43	changing	change	VERB
ap-762	157	44	the	the	DET
ap-762	157	45	approach	approach	NOUN
ap-762	157	46	.	.	PUNCT
ap-762	158	1	acknowledgment	acknowledgment	NOUN
ap-762	158	2	the	the	DET
ap-762	158	3	author	author	NOUN
ap-762	158	4	acknowledges	acknowledge	VERB
ap-762	158	5	financial	financial	ADJ
ap-762	158	6	support	support	NOUN
ap-762	158	7	from	from	ADP
ap-762	158	8	the	the	DET
ap-762	158	9	grant	grant	NOUN
ap-762	158	10	agency	agency	NOUN
ap-762	158	11	of	of	ADP
ap-762	158	12	the	the	DET
ap-762	158	13	czech	czech	PROPN
ap-762	158	14	republic	republic	PROPN
ap-762	158	15	gačr	gačr	PROPN
ap-762	158	16	201/05/0169	201/05/0169	PROPN
ap-762	158	17	.	.	PUNCT
ap-762	159	1	references	reference	NOUN
ap-762	159	2	[	[	X
ap-762	159	3	1	1	NUM
ap-762	159	4	]	]	SYM
ap-762	159	5	rényi	rényi	NOUN
ap-762	159	6	,	,	PUNCT
ap-762	159	7	a.	a.	NOUN
ap-762	159	8	:	:	PUNCT
ap-762	159	9	“	"	PUNCT
ap-762	159	10	representation	representation	NOUN
ap-762	159	11	for	for	ADP
ap-762	159	12	real	real	ADJ
ap-762	159	13	numbers	number	NOUN
ap-762	159	14	and	and	CCONJ
ap-762	159	15	their	their	PRON
ap-762	159	16	ergodic	ergodic	ADJ
ap-762	159	17	properties	property	NOUN
ap-762	159	18	.	.	PUNCT
ap-762	159	19	”	"	PUNCT
ap-762	160	1	acta	acta	PROPN
ap-762	160	2	math	math	PROPN
ap-762	160	3	.	.	PUNCT
ap-762	161	1	acad	acad	PROPN
ap-762	161	2	.	.	PUNCT
ap-762	162	1	sci	sci	PROPN
ap-762	162	2	.	.	PROPN
ap-762	162	3	hungar	hungar	PROPN
ap-762	162	4	,	,	PUNCT
ap-762	162	5	vol	vol	NOUN
ap-762	162	6	.	.	NOUN
ap-762	162	7	8	8	NUM
ap-762	162	8	(	(	PUNCT
ap-762	162	9	1957	1957	NUM
ap-762	162	10	)	)	PUNCT
ap-762	162	11	,	,	PUNCT
ap-762	163	1	p.	p.	NOUN
ap-762	163	2	477–493	477–493	NUM
ap-762	163	3	.	.	PUNCT
ap-762	164	1	[	[	X
ap-762	164	2	2	2	NUM
ap-762	164	3	]	]	X
ap-762	164	4	parry	parry	PROPN
ap-762	164	5	,	,	PUNCT
ap-762	164	6	w.	w.	PROPN
ap-762	164	7	:	:	PUNCT
ap-762	164	8	“	"	PUNCT
ap-762	164	9	on	on	ADP
ap-762	164	10	the	the	DET
ap-762	164	11	�	�	NOUN
ap-762	164	12	-expansions	-expansion	NOUN
ap-762	164	13	of	of	ADP
ap-762	164	14	real	real	ADJ
ap-762	164	15	numbers	number	NOUN
ap-762	164	16	.	.	PUNCT
ap-762	164	17	”	"	PUNCT
ap-762	164	18	acta	acta	PROPN
ap-762	164	19	math	math	PROPN
ap-762	164	20	.	.	PUNCT
ap-762	165	1	acad	acad	PROPN
ap-762	165	2	.	.	PUNCT
ap-762	166	1	sci	sci	PROPN
ap-762	166	2	.	.	PROPN
ap-762	166	3	hungar	hungar	PROPN
ap-762	166	4	,	,	PUNCT
ap-762	166	5	vol	vol	NOUN
ap-762	166	6	.	.	PROPN
ap-762	166	7	11	11	NUM
ap-762	166	8	(	(	PUNCT
ap-762	166	9	1960	1960	NUM
ap-762	166	10	)	)	PUNCT
ap-762	166	11	,	,	PUNCT
ap-762	167	1	p.	p.	NOUN
ap-762	167	2	401–416	401–416	NUM
ap-762	167	3	.	.	PUNCT
ap-762	168	1	[	[	X
ap-762	168	2	3	3	NUM
ap-762	168	3	]	]	X
ap-762	168	4	frougny	frougny	NOUN
ap-762	168	5	,	,	PUNCT
ap-762	168	6	c.	c.	NOUN
ap-762	168	7	,	,	PUNCT
ap-762	168	8	solomyak	solomyak	PROPN
ap-762	168	9	,	,	PUNCT
ap-762	168	10	b.	b.	PROPN
ap-762	168	11	:	:	PUNCT
ap-762	168	12	“	"	PUNCT
ap-762	168	13	finite	finite	VERB
ap-762	168	14	beta	beta	ADJ
ap-762	168	15	expansions	expansion	NOUN
ap-762	168	16	.	.	PUNCT
ap-762	168	17	”	"	PUNCT
ap-762	168	18	ergod	ergod	NOUN
ap-762	168	19	.	.	PUNCT
ap-762	169	1	th	th	X
ap-762	169	2	.	.	PUNCT
ap-762	169	3	and	and	CCONJ
ap-762	169	4	dynam	dynam	PROPN
ap-762	169	5	.	.	PUNCT
ap-762	170	1	sys	sys	PROPN
ap-762	170	2	.	.	PROPN
ap-762	170	3	,	,	PUNCT
ap-762	170	4	vol	vol	NOUN
ap-762	170	5	.	.	PROPN
ap-762	170	6	12	12	NUM
ap-762	170	7	(	(	PUNCT
ap-762	170	8	1992	1992	NUM
ap-762	170	9	)	)	PUNCT
ap-762	170	10	,	,	PUNCT
ap-762	171	1	p.	p.	NOUN
ap-762	171	2	713–723	713–723	NUM
ap-762	171	3	.	.	PUNCT
ap-762	172	1	[	[	X
ap-762	172	2	4	4	NUM
ap-762	172	3	]	]	X
ap-762	172	4	hollander	hollander	NOUN
ap-762	172	5	,	,	PUNCT
ap-762	172	6	m.	m.	NOUN
ap-762	172	7	:	:	PUNCT
ap-762	172	8	“	"	PUNCT
ap-762	172	9	linear	linear	ADJ
ap-762	172	10	numeration	numeration	NOUN
ap-762	172	11	systems	system	NOUN
ap-762	172	12	,	,	PUNCT
ap-762	172	13	finite	finite	VERB
ap-762	172	14	beta	beta	NOUN
ap-762	172	15	-	-	PUNCT
ap-762	172	16	expansions	expansion	NOUN
ap-762	172	17	,	,	PUNCT
ap-762	172	18	and	and	CCONJ
ap-762	172	19	discrete	discrete	ADJ
ap-762	172	20	spectrum	spectrum	NOUN
ap-762	172	21	of	of	ADP
ap-762	172	22	substitution	substitution	NOUN
ap-762	172	23	dynamical	dynamical	ADJ
ap-762	172	24	systems	system	NOUN
ap-762	172	25	.	.	PUNCT
ap-762	172	26	”	"	PUNCT
ap-762	173	1	phd	phd	NOUN
ap-762	173	2	thesis	thesis	PROPN
ap-762	173	3	,	,	PUNCT
ap-762	173	4	washington	washington	PROPN
ap-762	173	5	university	university	PROPN
ap-762	173	6	,	,	PUNCT
ap-762	173	7	1996	1996	NUM
ap-762	173	8	.	.	PUNCT
ap-762	174	1	26	26	NUM
ap-762	175	1	©	©	PROPN
ap-762	175	2	czech	czech	PROPN
ap-762	175	3	technical	technical	PROPN
ap-762	175	4	university	university	PROPN
ap-762	175	5	publishing	publishing	NOUN
ap-762	175	6	house	house	NOUN
ap-762	175	7	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-762	175	8	acta	acta	PROPN
ap-762	175	9	polytechnica	polytechnica	PROPN
ap-762	175	10	vol	vol	NOUN
ap-762	175	11	.	.	PROPN
ap-762	176	1	45	45	NUM
ap-762	176	2	no	no	NOUN
ap-762	176	3	.	.	PUNCT
ap-762	177	1	5/2005	5/2005	NUM
ap-762	177	2	czech	czech	PROPN
ap-762	177	3	technical	technical	PROPN
ap-762	177	4	university	university	PROPN
ap-762	177	5	in	in	ADP
ap-762	177	6	prague	prague	PROPN
ap-762	177	7	[	[	X
ap-762	177	8	5	5	NUM
ap-762	177	9	]	]	PUNCT
ap-762	177	10	akiyama	akiyama	NOUN
ap-762	177	11	,	,	PUNCT
ap-762	177	12	s.	s.	PROPN
ap-762	177	13	:	:	PUNCT
ap-762	177	14	“	"	PUNCT
ap-762	177	15	pisot	pisot	ADJ
ap-762	177	16	numbers	number	NOUN
ap-762	177	17	and	and	CCONJ
ap-762	177	18	greedy	greedy	ADJ
ap-762	177	19	algorithm	algorithm	NOUN
ap-762	177	20	.	.	PUNCT
ap-762	177	21	”	"	PUNCT
ap-762	178	1	in	in	ADP
ap-762	178	2	:	:	PUNCT
ap-762	178	3	number	number	NOUN
ap-762	178	4	theory	theory	NOUN
ap-762	178	5	(	(	PUNCT
ap-762	178	6	eger	eger	NOUN
ap-762	178	7	,	,	PUNCT
ap-762	178	8	1996	1996	NUM
ap-762	178	9	)	)	PUNCT
ap-762	178	10	.	.	PUNCT
ap-762	179	1	berlin	berlin	PROPN
ap-762	179	2	:	:	PUNCT
ap-762	179	3	de	de	ADJ
ap-762	179	4	gruyter	gruyter	NOUN
ap-762	179	5	,	,	PUNCT
ap-762	179	6	1998	1998	NUM
ap-762	179	7	,	,	PUNCT
ap-762	179	8	p.	p.	NOUN
ap-762	179	9	9–21	9–21	PROPN
ap-762	179	10	.	.	PUNCT
ap-762	180	1	[	[	X
ap-762	180	2	6	6	NUM
ap-762	180	3	]	]	PUNCT
ap-762	180	4	ambrož	ambrož	NOUN
ap-762	180	5	,	,	PUNCT
ap-762	180	6	p.	p.	NOUN
ap-762	180	7	,	,	PUNCT
ap-762	180	8	frougny	frougny	PROPN
ap-762	180	9	,	,	PUNCT
ap-762	180	10	c.	c.	NOUN
ap-762	180	11	,	,	PUNCT
ap-762	180	12	masáková	masáková	PROPN
ap-762	180	13	,	,	PUNCT
ap-762	180	14	z.	z.	PROPN
ap-762	180	15	,	,	PUNCT
ap-762	180	16	pelantová	pelantová	PROPN
ap-762	180	17	,	,	PUNCT
ap-762	180	18	e.	e.	PROPN
ap-762	180	19	:	:	PUNCT
ap-762	180	20	“	"	PUNCT
ap-762	180	21	arithmetics	arithmetic	NOUN
ap-762	180	22	on	on	ADP
ap-762	180	23	number	number	NOUN
ap-762	180	24	systems	system	NOUN
ap-762	180	25	with	with	ADP
ap-762	180	26	irrational	irrational	ADJ
ap-762	180	27	bases	basis	NOUN
ap-762	180	28	.	.	PUNCT
ap-762	180	29	”	"	PUNCT
ap-762	181	1	bull	bull	NOUN
ap-762	181	2	.	.	PUNCT
ap-762	182	1	belg	belg	PROPN
ap-762	182	2	.	.	PUNCT
ap-762	183	1	math	math	NOUN
ap-762	183	2	.	.	PUNCT
ap-762	184	1	soc	soc	PROPN
ap-762	184	2	.	.	PUNCT
ap-762	185	1	simon	simon	PROPN
ap-762	185	2	stevin	stevin	PROPN
ap-762	185	3	,	,	PUNCT
ap-762	185	4	vol	vol	NOUN
ap-762	185	5	.	.	PROPN
ap-762	185	6	10	10	NUM
ap-762	185	7	(	(	PUNCT
ap-762	185	8	2003	2003	NUM
ap-762	185	9	)	)	PUNCT
ap-762	185	10	,	,	PUNCT
ap-762	185	11	p.	p.	NOUN
ap-762	185	12	641–659	641–659	NUM
ap-762	185	13	.	.	PUNCT
ap-762	186	1	[	[	X
ap-762	186	2	7	7	NUM
ap-762	186	3	]	]	X
ap-762	186	4	akiyama	akiyama	NOUN
ap-762	186	5	,	,	PUNCT
ap-762	186	6	s.	s.	PROPN
ap-762	186	7	:	:	PUNCT
ap-762	186	8	“	"	PUNCT
ap-762	186	9	cubic	cubic	ADJ
ap-762	186	10	pisot	pisot	ADJ
ap-762	186	11	units	unit	NOUN
ap-762	186	12	with	with	ADP
ap-762	186	13	finite	finite	ADJ
ap-762	186	14	beta	beta	ADJ
ap-762	186	15	expansions	expansion	NOUN
ap-762	186	16	.	.	PUNCT
ap-762	186	17	”	"	PUNCT
ap-762	187	1	in	in	ADP
ap-762	187	2	:	:	PUNCT
ap-762	187	3	algebraic	algebraic	ADJ
ap-762	187	4	number	number	NOUN
ap-762	187	5	theory	theory	NOUN
ap-762	187	6	and	and	CCONJ
ap-762	187	7	diphantine	diphantine	ADJ
ap-762	187	8	analysis	analysis	NOUN
ap-762	187	9	(	(	PUNCT
ap-762	187	10	graz	graz	PROPN
ap-762	187	11	,	,	PUNCT
ap-762	187	12	1998	1998	NUM
ap-762	187	13	)	)	PUNCT
ap-762	187	14	.	.	PUNCT
ap-762	188	1	berlin	berlin	PROPN
ap-762	188	2	:	:	PUNCT
ap-762	188	3	de	de	ADJ
ap-762	188	4	gruyter	gruyter	NOUN
ap-762	188	5	,	,	PUNCT
ap-762	188	6	2000	2000	NUM
ap-762	188	7	,	,	PUNCT
ap-762	188	8	p.	p.	NOUN
ap-762	188	9	11–26	11–26	NUM
ap-762	188	10	.	.	PUNCT
ap-762	189	1	[	[	X
ap-762	189	2	8	8	NUM
ap-762	189	3	]	]	PUNCT
ap-762	189	4	ambrož	ambrož	NOUN
ap-762	189	5	,	,	PUNCT
ap-762	189	6	p.	p.	NOUN
ap-762	189	7	,	,	PUNCT
ap-762	189	8	masáková	masáková	PROPN
ap-762	189	9	,	,	PUNCT
ap-762	189	10	z.	z.	PROPN
ap-762	189	11	,	,	PUNCT
ap-762	189	12	pelantová	pelantová	PROPN
ap-762	189	13	,	,	PUNCT
ap-762	189	14	e.	e.	PROPN
ap-762	189	15	:	:	PUNCT
ap-762	189	16	“	"	PUNCT
ap-762	189	17	addition	addition	NOUN
ap-762	189	18	and	and	CCONJ
ap-762	189	19	multiplication	multiplication	NOUN
ap-762	189	20	of	of	ADP
ap-762	189	21	beta	beta	NOUN
ap-762	189	22	-	-	PUNCT
ap-762	189	23	integers	integer	NOUN
ap-762	189	24	in	in	ADP
ap-762	189	25	generalized	generalized	ADJ
ap-762	189	26	tribonacci	tribonacci	NUM
ap-762	189	27	base	base	NOUN
ap-762	189	28	.	.	PUNCT
ap-762	189	29	”	"	PUNCT
ap-762	190	1	to	to	PART
ap-762	190	2	appear	appear	VERB
ap-762	190	3	in	in	ADP
ap-762	190	4	j.	j.	PROPN
ap-762	190	5	autom	autom	PROPN
ap-762	190	6	.	.	PUNCT
ap-762	191	1	lang	lang	PROPN
ap-762	191	2	.	.	PUNCT
ap-762	191	3	comb	comb	PROPN
ap-762	191	4	.	.	PUNCT
ap-762	192	1	[	[	X
ap-762	192	2	9	9	NUM
ap-762	192	3	]	]	SYM
ap-762	192	4	bernat	bernat	NOUN
ap-762	192	5	,	,	PUNCT
ap-762	192	6	j.	j.	PROPN
ap-762	192	7	:	:	PUNCT
ap-762	192	8	computation	computation	NOUN
ap-762	192	9	of	of	ADP
ap-762	192	10	for	for	ADP
ap-762	192	11	pisot	pisot	ADJ
ap-762	192	12	numbers	number	NOUN
ap-762	192	13	.	.	PUNCT
ap-762	193	1	preprint	preprint	NOUN
ap-762	193	2	,	,	PUNCT
ap-762	193	3	2004	2004	NUM
ap-762	193	4	.	.	PUNCT
ap-762	194	1	[	[	X
ap-762	194	2	10	10	NUM
ap-762	194	3	]	]	SYM
ap-762	194	4	guimond	guimond	NOUN
ap-762	194	5	,	,	PUNCT
ap-762	194	6	l.	l.	PROPN
ap-762	194	7	-s	-s	PROPN
ap-762	194	8	.	.	PROPN
ap-762	194	9	,	,	PUNCT
ap-762	194	10	masáková	masáková	PROPN
ap-762	194	11	,	,	PUNCT
ap-762	194	12	z.	z.	PROPN
ap-762	194	13	,	,	PUNCT
ap-762	194	14	pelantová	pelantová	PROPN
ap-762	194	15	,	,	PUNCT
ap-762	194	16	e.	e.	PROPN
ap-762	194	17	:	:	PUNCT
ap-762	194	18	“	"	PUNCT
ap-762	194	19	arithmetics	arithmetic	NOUN
ap-762	194	20	on	on	ADP
ap-762	194	21	beta	beta	NOUN
ap-762	194	22	-	-	PUNCT
ap-762	194	23	expansions	expansion	NOUN
ap-762	194	24	.	.	PUNCT
ap-762	194	25	”	"	PUNCT
ap-762	195	1	acta	acta	PROPN
ap-762	195	2	arith	arith	PROPN
ap-762	195	3	,	,	PUNCT
ap-762	195	4	vol	vol	NOUN
ap-762	195	5	.	.	PROPN
ap-762	195	6	112	112	NUM
ap-762	195	7	(	(	PUNCT
ap-762	195	8	2004	2004	NUM
ap-762	195	9	)	)	PUNCT
ap-762	195	10	,	,	PUNCT
ap-762	195	11	p.	p.	NOUN
ap-762	195	12	23–40	23–40	NUM
ap-762	195	13	.	.	PUNCT
ap-762	196	1	[	[	X
ap-762	196	2	11	11	NUM
ap-762	196	3	]	]	PUNCT
ap-762	196	4	messaoudi	messaoudi	ADJ
ap-762	196	5	,	,	PUNCT
ap-762	196	6	a.	a.	NOUN
ap-762	196	7	:	:	PUNCT
ap-762	196	8	“	"	PUNCT
ap-762	196	9	généralization	généralization	NOUN
ap-762	196	10	de	de	X
ap-762	196	11	la	la	X
ap-762	196	12	multiplication	multiplication	X
ap-762	196	13	de	de	X
ap-762	196	14	fibonacci	fibonacci	PROPN
ap-762	196	15	.	.	PUNCT
ap-762	196	16	”	"	PUNCT
ap-762	197	1	math	math	NOUN
ap-762	197	2	.	.	PUNCT
ap-762	198	1	slovaca	slovaca	PROPN
ap-762	198	2	,	,	PUNCT
ap-762	198	3	vol	vol	NOUN
ap-762	198	4	.	.	PROPN
ap-762	199	1	50	50	NUM
ap-762	199	2	(	(	PUNCT
ap-762	199	3	2000	2000	NUM
ap-762	199	4	)	)	PUNCT
ap-762	199	5	,	,	PUNCT
ap-762	200	1	p.	p.	NOUN
ap-762	200	2	135–148	135–148	NUM
ap-762	200	3	.	.	PUNCT
ap-762	201	1	[	[	X
ap-762	201	2	12	12	NUM
ap-762	201	3	]	]	PUNCT
ap-762	201	4	messaoudi	messaoudi	ADJ
ap-762	201	5	,	,	PUNCT
ap-762	201	6	a.	a.	NOUN
ap-762	201	7	:	:	PUNCT
ap-762	201	8	“	"	PUNCT
ap-762	201	9	fronti	fronti	X
ap-762	201	10	re	re	X
ap-762	201	11	du	du	PROPN
ap-762	201	12	fractal	fractal	PROPN
ap-762	201	13	de	de	PROPN
ap-762	201	14	rauzy	rauzy	NOUN
ap-762	201	15	et	et	PROPN
ap-762	201	16	syst	syst	VERB
ap-762	201	17	me	i	PRON
ap-762	201	18	de	de	PROPN
ap-762	201	19	numeration	numeration	PROPN
ap-762	201	20	complexe	complexe	PROPN
ap-762	201	21	.	.	PUNCT
ap-762	201	22	”	"	PUNCT
ap-762	202	1	acta	acta	PROPN
ap-762	202	2	arith	arith	PROPN
ap-762	202	3	.	.	PUNCT
ap-762	202	4	,	,	PUNCT
ap-762	202	5	vol	vol	NOUN
ap-762	202	6	.	.	PROPN
ap-762	203	1	95	95	NUM
ap-762	203	2	(	(	PUNCT
ap-762	203	3	2000	2000	NUM
ap-762	203	4	)	)	PUNCT
ap-762	203	5	,	,	PUNCT
ap-762	204	1	p.	p.	NOUN
ap-762	204	2	195–224	195–224	NUM
ap-762	204	3	.	.	PUNCT
ap-762	205	1	[	[	X
ap-762	205	2	13	13	NUM
ap-762	205	3	]	]	SYM
ap-762	205	4	knuth	knuth	PROPN
ap-762	205	5	,	,	PUNCT
ap-762	205	6	d.	d.	PROPN
ap-762	205	7	e.	e.	PROPN
ap-762	205	8	:	:	PUNCT
ap-762	205	9	“	"	PUNCT
ap-762	205	10	fibonacci	fibonacci	NOUN
ap-762	205	11	multiplication	multiplication	NOUN
ap-762	205	12	.	.	PUNCT
ap-762	205	13	”	"	PUNCT
ap-762	206	1	appl	appl	PROPN
ap-762	206	2	.	.	PROPN
ap-762	206	3	math	math	PROPN
ap-762	206	4	.	.	PUNCT
ap-762	207	1	lett	lett	PROPN
ap-762	207	2	.	.	PROPN
ap-762	207	3	,	,	PUNCT
ap-762	207	4	vol	vol	NOUN
ap-762	207	5	.	.	PROPN
ap-762	207	6	1	1	NUM
ap-762	207	7	(	(	PUNCT
ap-762	207	8	1988	1988	NUM
ap-762	207	9	)	)	PUNCT
ap-762	207	10	,	,	PUNCT
ap-762	207	11	p.	p.	NOUN
ap-762	207	12	57–60	57–60	NUM
ap-762	207	13	.	.	PUNCT
ap-762	208	1	[	[	X
ap-762	208	2	14	14	NUM
ap-762	208	3	]	]	X
ap-762	208	4	burdík	burdík	PROPN
ap-762	208	5	,	,	PUNCT
ap-762	208	6	č	č	PROPN
ap-762	208	7	.	.	PROPN
ap-762	208	8	,	,	PUNCT
ap-762	208	9	frougny	frougny	PROPN
ap-762	208	10	,	,	PUNCT
ap-762	208	11	c.	c.	PROPN
ap-762	208	12	,	,	PUNCT
ap-762	208	13	gazeau	gazeau	PROPN
ap-762	208	14	,	,	PUNCT
ap-762	208	15	j.	j.	PROPN
ap-762	208	16	-p	-p	PROPN
ap-762	208	17	.	.	PROPN
ap-762	208	18	,	,	PUNCT
ap-762	208	19	krejcar	krejcar	PROPN
ap-762	208	20	,	,	PUNCT
ap-762	208	21	r.	r.	PROPN
ap-762	208	22	:	:	PUNCT
ap-762	208	23	“	"	PUNCT
ap-762	208	24	beta	beta	NOUN
ap-762	208	25	-	-	PUNCT
ap-762	208	26	integers	integer	NOUN
ap-762	208	27	as	as	ADP
ap-762	208	28	natural	natural	ADJ
ap-762	208	29	counting	counting	NOUN
ap-762	208	30	system	system	NOUN
ap-762	208	31	for	for	ADP
ap-762	208	32	quasicrystals	quasicrystal	NOUN
ap-762	208	33	.	.	PUNCT
ap-762	208	34	”	"	PUNCT
ap-762	209	1	j.	j.	PROPN
ap-762	209	2	phys	phys	PROPN
ap-762	209	3	.	.	PUNCT
ap-762	210	1	a	a	DET
ap-762	210	2	,	,	PUNCT
ap-762	210	3	vol	vol	NOUN
ap-762	210	4	.	.	PROPN
ap-762	210	5	31	31	NUM
ap-762	210	6	(	(	PUNCT
ap-762	210	7	1998	1998	NUM
ap-762	210	8	)	)	PUNCT
ap-762	210	9	,	,	PUNCT
ap-762	210	10	p.	p.	NOUN
ap-762	210	11	6449–6472	6449–6472	NUM
ap-762	210	12	.	.	PUNCT
ap-762	211	1	[	[	X
ap-762	211	2	15	15	NUM
ap-762	211	3	]	]	X
ap-762	211	4	messaoudi	messaoudi	ADJ
ap-762	211	5	,	,	PUNCT
ap-762	211	6	a.	a.	NOUN
ap-762	211	7	:	:	PUNCT
ap-762	211	8	“	"	PUNCT
ap-762	211	9	tribonacci	tribonacci	NUM
ap-762	211	10	multiplication	multiplication	NOUN
ap-762	211	11	.	.	PUNCT
ap-762	211	12	”	"	PUNCT
ap-762	212	1	appl	appl	PROPN
ap-762	212	2	.	.	PROPN
ap-762	212	3	math	math	PROPN
ap-762	212	4	.	.	PUNCT
ap-762	213	1	lett	lett	PROPN
ap-762	213	2	.	.	PROPN
ap-762	213	3	,	,	PUNCT
ap-762	213	4	vol	vol	NOUN
ap-762	213	5	.	.	PROPN
ap-762	213	6	15	15	NUM
ap-762	213	7	(	(	PUNCT
ap-762	213	8	2002	2002	NUM
ap-762	213	9	)	)	PUNCT
ap-762	213	10	,	,	PUNCT
ap-762	213	11	p.	p.	NOUN
ap-762	213	12	981–985	981–985	NUM
ap-762	213	13	.	.	PUNCT
ap-762	214	1	[	[	X
ap-762	214	2	16	16	NUM
ap-762	214	3	]	]	PUNCT
ap-762	214	4	ambrož	ambrož	NOUN
ap-762	214	5	,	,	PUNCT
ap-762	214	6	p.	p.	NOUN
ap-762	214	7	:	:	PUNCT
ap-762	214	8	“	"	PUNCT
ap-762	214	9	on	on	ADP
ap-762	214	10	the	the	DET
ap-762	214	11	tau	tau	NOUN
ap-762	214	12	-	-	PUNCT
ap-762	214	13	adic	adic	ADJ
ap-762	214	14	expansions	expansion	NOUN
ap-762	214	15	of	of	ADP
ap-762	214	16	real	real	ADJ
ap-762	214	17	numbers	number	NOUN
ap-762	214	18	.	.	PUNCT
ap-762	214	19	”	"	PUNCT
ap-762	215	1	in	in	ADP
ap-762	215	2	:	:	PUNCT
ap-762	215	3	‘	'	PUNCT
ap-762	215	4	words	word	NOUN
ap-762	215	5	2005	2005	NUM
ap-762	215	6	,	,	PUNCT
ap-762	215	7	5th	5th	ADJ
ap-762	215	8	international	international	ADJ
ap-762	215	9	conference	conference	NOUN
ap-762	215	10	on	on	ADP
ap-762	215	11	words	word	NOUN
ap-762	215	12	,	,	PUNCT
ap-762	215	13	actes	acte	NOUN
ap-762	215	14	’	'	PUNCT
ap-762	215	15	,	,	PUNCT
ap-762	215	16	s.	s.	PROPN
ap-762	215	17	brlek	brlek	PROPN
ap-762	215	18	and	and	CCONJ
ap-762	215	19	c.	c.	PROPN
ap-762	215	20	reutenauer	reutenauer	NOUN
ap-762	215	21	,	,	PUNCT
ap-762	215	22	(	(	PUNCT
ap-762	215	23	eds	ed	NOUN
ap-762	215	24	.	.	PUNCT
ap-762	215	25	)	)	PUNCT
ap-762	215	26	.	.	PUNCT
ap-762	216	1	publications	publication	NOUN
ap-762	216	2	du	du	PROPN
ap-762	216	3	lacim	lacim	PROPN
ap-762	216	4	vol	vol	PROPN
ap-762	216	5	.	.	PROPN
ap-762	217	1	36	36	NUM
ap-762	217	2	(	(	PUNCT
ap-762	217	3	2005	2005	NUM
ap-762	217	4	)	)	PUNCT
ap-762	217	5	,	,	PUNCT
ap-762	218	1	p.	p.	NOUN
ap-762	218	2	79–89	79–89	NUM
ap-762	218	3	.	.	PUNCT
ap-762	219	1	[	[	X
ap-762	219	2	17	17	NUM
ap-762	219	3	]	]	PUNCT
ap-762	219	4	ambrož	ambrož	NOUN
ap-762	219	5	,	,	PUNCT
ap-762	219	6	p.	p.	NOUN
ap-762	219	7	:	:	PUNCT
ap-762	220	1	addition	addition	NOUN
ap-762	220	2	of	of	ADP
ap-762	220	3	eventually	eventually	ADV
ap-762	220	4	periodic	periodic	ADJ
ap-762	220	5	tau	tau	ADJ
ap-762	220	6	-	-	PUNCT
ap-762	220	7	adic	adic	ADJ
ap-762	220	8	expansions	expansion	NOUN
ap-762	220	9	.	.	PUNCT
ap-762	221	1	preprint	preprint	NOUN
ap-762	221	2	,	,	PUNCT
ap-762	221	3	2005	2005	NUM
ap-762	221	4	.	.	PUNCT
ap-762	222	1	[	[	X
ap-762	222	2	18	18	NUM
ap-762	222	3	]	]	PUNCT
ap-762	222	4	ambrož	ambrož	NOUN
ap-762	222	5	,	,	PUNCT
ap-762	222	6	p.	p.	NOUN
ap-762	222	7	:	:	PUNCT
ap-762	223	1	addition	addition	NOUN
ap-762	223	2	in	in	ADP
ap-762	223	3	pisot	pisot	ADJ
ap-762	223	4	numeration	numeration	NOUN
ap-762	223	5	systems	system	NOUN
ap-762	223	6	.	.	PUNCT
ap-762	224	1	preprint	preprint	NOUN
ap-762	224	2	,	,	PUNCT
ap-762	224	3	2004	2004	NUM
ap-762	224	4	.	.	PUNCT
ap-762	225	1	ing	ing	PROPN
ap-762	225	2	.	.	PUNCT
ap-762	226	1	petr	petr	PROPN
ap-762	226	2	ambrož	ambrož	PROPN
ap-762	226	3	phone	phone	PROPN
ap-762	226	4	:	:	PUNCT
ap-762	226	5	+420	+420	PROPN
ap-762	226	6	224	224	NUM
ap-762	226	7	358	358	NUM
ap-762	226	8	564	564	NUM
ap-762	226	9	email	email	NOUN
ap-762	226	10	:	:	PUNCT
ap-762	226	11	ampy@linux.fjfi.cvut.cz	ampy@linux.fjfi.cvut.cz	PROPN
ap-762	226	12	department	department	NOUN
ap-762	226	13	of	of	ADP
ap-762	226	14	mathematics	mathematics	PROPN
ap-762	226	15	czech	czech	PROPN
ap-762	226	16	technical	technical	PROPN
ap-762	226	17	university	university	PROPN
ap-762	226	18	in	in	ADP
ap-762	226	19	prague	prague	PROPN
ap-762	226	20	faculty	faculty	NOUN
ap-762	226	21	of	of	ADP
ap-762	226	22	nuclear	nuclear	ADJ
ap-762	226	23	science	science	NOUN
ap-762	226	24	and	and	CCONJ
ap-762	226	25	physical	physical	ADJ
ap-762	226	26	engineering	engineering	NOUN
ap-762	226	27	trojanova	trojanova	ADP
ap-762	226	28	13	13	NUM
ap-762	226	29	120	120	NUM
ap-762	226	30	00	00	NUM
ap-762	226	31	praha	praha	PROPN
ap-762	226	32	2	2	NUM
ap-762	226	33	,	,	PUNCT
ap-762	226	34	czech	czech	PROPN
ap-762	226	35	republic	republic	NOUN
ap-762	226	36	©	©	PROPN
ap-762	226	37	czech	czech	PROPN
ap-762	226	38	technical	technical	PROPN
ap-762	226	39	university	university	PROPN
ap-762	226	40	publishing	publishing	NOUN
ap-762	226	41	house	house	NOUN
ap-762	226	42	http://ctn.cvut.cz/ap/	http://ctn.cvut.cz/ap/	PROPN
ap-762	226	43	27	27	NUM
ap-762	226	44	czech	czech	PROPN
ap-762	226	45	technical	technical	PROPN
ap-762	226	46	university	university	PROPN
ap-762	226	47	in	in	ADP
ap-762	226	48	prague	prague	PROPN
ap-762	226	49	acta	acta	PROPN
ap-762	226	50	polytechnica	polytechnica	PROPN
ap-762	226	51	vol	vol	NOUN
ap-762	226	52	.	.	PROPN
ap-762	227	1	45	45	NUM
ap-762	227	2	no	no	NOUN
ap-762	227	3	.	.	PUNCT
ap-762	228	1	5/2005	5/2005	NUM