id	sid	tid	token	lemma	pos
ejpam-4941	1	1	european	european	PROPN
ejpam-4941	1	2	journal	journal	PROPN
ejpam-4941	1	3	of	of	ADP
ejpam-4941	1	4	pure	pure	ADJ
ejpam-4941	1	5	and	and	CCONJ
ejpam-4941	1	6	applied	apply	VERB
ejpam-4941	1	7	mathematics	mathematic	NOUN
ejpam-4941	1	8	vol	vol	NOUN
ejpam-4941	1	9	.	.	PUNCT
ejpam-4941	2	1	16	16	NUM
ejpam-4941	2	2	,	,	PUNCT
ejpam-4941	2	3	no	no	INTJ
ejpam-4941	2	4	.	.	NOUN
ejpam-4941	2	5	4	4	NUM
ejpam-4941	2	6	,	,	PUNCT
ejpam-4941	2	7	2023	2023	NUM
ejpam-4941	2	8	,	,	PUNCT
ejpam-4941	2	9	2662	2662	NUM
ejpam-4941	2	10	-	-	SYM
ejpam-4941	2	11	2692	2692	NUM
ejpam-4941	2	12	issn	issn	PROPN
ejpam-4941	2	13	1307	1307	NUM
ejpam-4941	2	14	-	-	SYM
ejpam-4941	2	15	5543	5543	NUM
ejpam-4941	2	16	–	–	PUNCT
ejpam-4941	2	17	ejpam.com	ejpam.com	X
ejpam-4941	2	18	published	publish	VERB
ejpam-4941	2	19	by	by	ADP
ejpam-4941	2	20	new	new	PROPN
ejpam-4941	2	21	york	york	PROPN
ejpam-4941	2	22	business	business	PROPN
ejpam-4941	2	23	global	global	PROPN
ejpam-4941	2	24	crystal	crystal	PROPN
ejpam-4941	2	25	reduced	reduce	VERB
ejpam-4941	2	26	motif	motif	NOUN
ejpam-4941	2	27	via	via	ADP
ejpam-4941	2	28	the	the	DET
ejpam-4941	2	29	vectors	vector	NOUN
ejpam-4941	2	30	exchange	exchange	PROPN
ejpam-4941	2	31	theorem	theorem	VERB
ejpam-4941	2	32	i	i	PRON
ejpam-4941	2	33	:	:	PUNCT
ejpam-4941	2	34	impact	impact	NOUN
ejpam-4941	2	35	of	of	ADP
ejpam-4941	2	36	swapping	swap	VERB
ejpam-4941	2	37	on	on	ADP
ejpam-4941	2	38	two	two	NUM
ejpam-4941	2	39	orthogonalization	orthogonalization	NOUN
ejpam-4941	2	40	processes	process	NOUN
ejpam-4941	2	41	and	and	CCONJ
ejpam-4941	2	42	the	the	DET
ejpam-4941	2	43	ae	ae	PROPN
ejpam-4941	2	44	algorithm	algorithm	PROPN
ejpam-4941	2	45	seddik	seddik	PROPN
ejpam-4941	2	46	abdelalim1	abdelalim1	PROPN
ejpam-4941	2	47	,	,	PUNCT
ejpam-4941	2	48	ilias	ilias	PROPN
ejpam-4941	2	49	elmouki1,∗	elmouki1,∗	NOUN
ejpam-4941	2	50	1	1	NUM
ejpam-4941	2	51	team	team	NOUN
ejpam-4941	2	52	of	of	ADP
ejpam-4941	2	53	algebra	algebra	NOUN
ejpam-4941	2	54	and	and	CCONJ
ejpam-4941	2	55	discrete	discrete	ADJ
ejpam-4941	2	56	mathematics	mathematic	NOUN
ejpam-4941	2	57	,	,	PUNCT
ejpam-4941	2	58	laboratory	laboratory	NOUN
ejpam-4941	2	59	of	of	ADP
ejpam-4941	2	60	fundamental	fundamental	ADJ
ejpam-4941	2	61	and	and	CCONJ
ejpam-4941	2	62	applied	applied	ADJ
ejpam-4941	2	63	mathematics	mathematic	NOUN
ejpam-4941	2	64	(	(	PUNCT
ejpam-4941	2	65	lmfa	lmfa	NOUN
ejpam-4941	2	66	)	)	PUNCT
ejpam-4941	2	67	,	,	PUNCT
ejpam-4941	2	68	faculty	faculty	NOUN
ejpam-4941	2	69	of	of	ADP
ejpam-4941	2	70	sciences	science	NOUN
ejpam-4941	2	71	ain	ain	PROPN
ejpam-4941	2	72	chock	chock	PROPN
ejpam-4941	2	73	(	(	PUNCT
ejpam-4941	2	74	fsac	fsac	NOUN
ejpam-4941	2	75	)	)	PUNCT
ejpam-4941	2	76	,	,	PUNCT
ejpam-4941	2	77	university	university	PROPN
ejpam-4941	2	78	hassan	hassan	PROPN
ejpam-4941	2	79	ii	ii	PROPN
ejpam-4941	2	80	of	of	ADP
ejpam-4941	2	81	casablanca	casablanca	PROPN
ejpam-4941	2	82	(	(	PUNCT
ejpam-4941	2	83	univh2c	univh2c	PROPN
ejpam-4941	2	84	)	)	PUNCT
ejpam-4941	2	85	,	,	PUNCT
ejpam-4941	2	86	morocco	morocco	PROPN
ejpam-4941	2	87	.	.	PUNCT
ejpam-4941	3	1	abstract	abstract	ADJ
ejpam-4941	3	2	.	.	PUNCT
ejpam-4941	4	1	crystallographic	crystallographic	ADJ
ejpam-4941	4	2	literature	literature	PROPN
ejpam-4941	4	3	is	be	AUX
ejpam-4941	4	4	relying	rely	VERB
ejpam-4941	4	5	more	more	ADV
ejpam-4941	4	6	on	on	ADP
ejpam-4941	4	7	observational	observational	ADJ
ejpam-4941	4	8	rules	rule	NOUN
ejpam-4941	4	9	for	for	ADP
ejpam-4941	4	10	the	the	DET
ejpam-4941	4	11	determination	determination	NOUN
ejpam-4941	4	12	of	of	ADP
ejpam-4941	4	13	the	the	DET
ejpam-4941	4	14	motif	motif	NOUN
ejpam-4941	4	15	that	that	PRON
ejpam-4941	4	16	could	could	AUX
ejpam-4941	4	17	generate	generate	VERB
ejpam-4941	4	18	the	the	DET
ejpam-4941	4	19	whole	whole	ADJ
ejpam-4941	4	20	representing	represent	VERB
ejpam-4941	4	21	bravais	bravais	PROPN
ejpam-4941	4	22	lattice	lattice	NOUN
ejpam-4941	4	23	of	of	ADP
ejpam-4941	4	24	a	a	DET
ejpam-4941	4	25	crystal	crystal	NOUN
ejpam-4941	4	26	.	.	PUNCT
ejpam-4941	5	1	here	here	ADV
ejpam-4941	5	2	,	,	PUNCT
ejpam-4941	5	3	we	we	PRON
ejpam-4941	5	4	devise	devise	VERB
ejpam-4941	5	5	an	an	DET
ejpam-4941	5	6	algebraic	algebraic	ADJ
ejpam-4941	5	7	method	method	NOUN
ejpam-4941	5	8	that	that	PRON
ejpam-4941	5	9	can	can	AUX
ejpam-4941	5	10	serve	serve	VERB
ejpam-4941	5	11	in	in	ADP
ejpam-4941	5	12	this	this	DET
ejpam-4941	5	13	regard	regard	NOUN
ejpam-4941	5	14	at	at	ADP
ejpam-4941	5	15	least	least	ADJ
ejpam-4941	5	16	in	in	ADP
ejpam-4941	5	17	cases	case	NOUN
ejpam-4941	5	18	when	when	SCONJ
ejpam-4941	5	19	the	the	DET
ejpam-4941	5	20	associated	associated	ADJ
ejpam-4941	5	21	unit	unit	NOUN
ejpam-4941	5	22	cell	cell	NOUN
ejpam-4941	5	23	is	be	AUX
ejpam-4941	5	24	made	make	VERB
ejpam-4941	5	25	of	of	ADP
ejpam-4941	5	26	quasi	quasi	ADJ
ejpam-4941	5	27	-	-	ADJ
ejpam-4941	5	28	orthogonal	orthogonal	ADJ
ejpam-4941	5	29	vectors	vector	NOUN
ejpam-4941	5	30	.	.	PUNCT
ejpam-4941	6	1	to	to	PART
ejpam-4941	6	2	let	let	VERB
ejpam-4941	6	3	our	our	PRON
ejpam-4941	6	4	approach	approach	NOUN
ejpam-4941	6	5	be	be	AUX
ejpam-4941	6	6	applicable	applicable	ADJ
ejpam-4941	6	7	to	to	ADP
ejpam-4941	6	8	other	other	ADJ
ejpam-4941	6	9	reduction	reduction	NOUN
ejpam-4941	6	10	problems	problem	NOUN
ejpam-4941	6	11	,	,	PUNCT
ejpam-4941	6	12	we	we	PRON
ejpam-4941	6	13	introduce	introduce	VERB
ejpam-4941	6	14	a	a	DET
ejpam-4941	6	15	concept	concept	NOUN
ejpam-4941	6	16	which	which	PRON
ejpam-4941	6	17	is	be	AUX
ejpam-4941	6	18	about	about	ADP
ejpam-4941	6	19	starting	start	VERB
ejpam-4941	6	20	first	first	ADV
ejpam-4941	6	21	from	from	ADP
ejpam-4941	6	22	any	any	DET
ejpam-4941	6	23	’	'	PUNCT
ejpam-4941	6	24	bad	bad	ADJ
ejpam-4941	6	25	’	'	PUNCT
ejpam-4941	6	26	crystal	crystal	NOUN
ejpam-4941	6	27	cell	cell	NOUN
ejpam-4941	6	28	,	,	PUNCT
ejpam-4941	6	29	not	not	PART
ejpam-4941	6	30	necessarily	necessarily	ADV
ejpam-4941	6	31	the	the	DET
ejpam-4941	6	32	primitive	primitive	ADJ
ejpam-4941	6	33	elementary	elementary	ADJ
ejpam-4941	6	34	cell	cell	NOUN
ejpam-4941	6	35	,	,	PUNCT
ejpam-4941	6	36	in	in	ADP
ejpam-4941	6	37	order	order	NOUN
ejpam-4941	6	38	to	to	PART
ejpam-4941	6	39	find	find	VERB
ejpam-4941	6	40	a	a	DET
ejpam-4941	6	41	’	'	PUNCT
ejpam-4941	6	42	good	good	ADJ
ejpam-4941	6	43	’	'	PUNCT
ejpam-4941	6	44	crystal	crystal	NOUN
ejpam-4941	6	45	cell	cell	NOUN
ejpam-4941	6	46	and	and	CCONJ
ejpam-4941	6	47	that	that	PRON
ejpam-4941	6	48	means	mean	VERB
ejpam-4941	6	49	seeking	seek	VERB
ejpam-4941	6	50	a	a	DET
ejpam-4941	6	51	motif	motif	NOUN
ejpam-4941	6	52	made	make	VERB
ejpam-4941	6	53	of	of	ADP
ejpam-4941	6	54	a	a	DET
ejpam-4941	6	55	basis	basis	NOUN
ejpam-4941	6	56	whose	whose	DET
ejpam-4941	6	57	vectors	vector	NOUN
ejpam-4941	6	58	are	be	AUX
ejpam-4941	6	59	close	close	ADJ
ejpam-4941	6	60	-	-	PUNCT
ejpam-4941	6	61	to	to	ADP
ejpam-4941	6	62	-	-	PUNCT
ejpam-4941	6	63	orthogonal	orthogonal	ADJ
ejpam-4941	6	64	.	.	PUNCT
ejpam-4941	7	1	the	the	DET
ejpam-4941	7	2	orthogonalization	orthogonalization	NOUN
ejpam-4941	7	3	loss	loss	NOUN
ejpam-4941	7	4	could	could	AUX
ejpam-4941	7	5	happen	happen	VERB
ejpam-4941	7	6	any	any	DET
ejpam-4941	7	7	time	time	NOUN
ejpam-4941	7	8	of	of	ADP
ejpam-4941	7	9	vectors	vector	NOUN
ejpam-4941	7	10	swapping	swap	VERB
ejpam-4941	7	11	which	which	PRON
ejpam-4941	7	12	represents	represent	VERB
ejpam-4941	7	13	a	a	DET
ejpam-4941	7	14	very	very	ADV
ejpam-4941	7	15	important	important	ADJ
ejpam-4941	7	16	process	process	NOUN
ejpam-4941	7	17	in	in	ADP
ejpam-4941	7	18	dealing	deal	VERB
ejpam-4941	7	19	with	with	ADP
ejpam-4941	7	20	lattice	lattice	NOUN
ejpam-4941	7	21	reduction	reduction	NOUN
ejpam-4941	7	22	,	,	PUNCT
ejpam-4941	7	23	but	but	CCONJ
ejpam-4941	7	24	it	it	PRON
ejpam-4941	7	25	has	have	AUX
ejpam-4941	7	26	insufficiently	insufficiently	ADV
ejpam-4941	7	27	been	be	AUX
ejpam-4941	7	28	discussed	discuss	VERB
ejpam-4941	7	29	in	in	ADP
ejpam-4941	7	30	this	this	DET
ejpam-4941	7	31	subject	subject	NOUN
ejpam-4941	7	32	.	.	PUNCT
ejpam-4941	8	1	thus	thus	ADV
ejpam-4941	8	2	,	,	PUNCT
ejpam-4941	8	3	through	through	ADP
ejpam-4941	8	4	our	our	PRON
ejpam-4941	8	5	present	present	ADJ
ejpam-4941	8	6	version	version	NOUN
ejpam-4941	8	7	of	of	ADP
ejpam-4941	8	8	vectors	vector	NOUN
ejpam-4941	8	9	exchange	exchange	NOUN
ejpam-4941	8	10	theorem	theorem	VERB
ejpam-4941	8	11	,	,	PUNCT
ejpam-4941	8	12	and	and	CCONJ
ejpam-4941	8	13	by	by	ADP
ejpam-4941	8	14	using	use	VERB
ejpam-4941	8	15	examples	example	NOUN
ejpam-4941	8	16	of	of	ADP
ejpam-4941	8	17	two	two	NUM
ejpam-4941	8	18	processes	process	NOUN
ejpam-4941	8	19	,	,	PUNCT
ejpam-4941	8	20	namely	namely	ADV
ejpam-4941	8	21	the	the	DET
ejpam-4941	8	22	gram	gram	NOUN
ejpam-4941	8	23	-	-	PUNCT
ejpam-4941	8	24	schmidt	schmidt	PROPN
ejpam-4941	8	25	(	(	PUNCT
ejpam-4941	8	26	gs	gs	NOUN
ejpam-4941	8	27	)	)	PUNCT
ejpam-4941	8	28	procedure	procedure	NOUN
ejpam-4941	8	29	and	and	CCONJ
ejpam-4941	8	30	its	its	PRON
ejpam-4941	8	31	modified	modified	ADJ
ejpam-4941	8	32	version	version	NOUN
ejpam-4941	8	33	(	(	PUNCT
ejpam-4941	8	34	mgs	mgs	NOUN
ejpam-4941	8	35	)	)	PUNCT
ejpam-4941	8	36	,	,	PUNCT
ejpam-4941	8	37	we	we	PRON
ejpam-4941	8	38	provide	provide	VERB
ejpam-4941	8	39	formulations	formulation	NOUN
ejpam-4941	8	40	for	for	ADP
ejpam-4941	8	41	the	the	DET
ejpam-4941	8	42	new	new	ADJ
ejpam-4941	8	43	reduced	reduce	VERB
ejpam-4941	8	44	unit	unit	NOUN
ejpam-4941	8	45	cell	cell	NOUN
ejpam-4941	8	46	vectors	vector	NOUN
ejpam-4941	8	47	and	and	CCONJ
ejpam-4941	8	48	analyze	analyze	VERB
ejpam-4941	8	49	the	the	DET
ejpam-4941	8	50	impact	impact	NOUN
ejpam-4941	8	51	of	of	ADP
ejpam-4941	8	52	the	the	DET
ejpam-4941	8	53	repeated	repeat	VERB
ejpam-4941	8	54	exchange	exchange	NOUN
ejpam-4941	8	55	of	of	ADP
ejpam-4941	8	56	vectors	vector	NOUN
ejpam-4941	8	57	on	on	ADP
ejpam-4941	8	58	the	the	DET
ejpam-4941	8	59	orthogonalization	orthogonalization	NOUN
ejpam-4941	8	60	precision	precision	NOUN
ejpam-4941	8	61	.	.	PUNCT
ejpam-4941	9	1	finally	finally	ADV
ejpam-4941	9	2	,	,	PUNCT
ejpam-4941	9	3	we	we	PRON
ejpam-4941	9	4	give	give	VERB
ejpam-4941	9	5	a	a	DET
ejpam-4941	9	6	detailed	detailed	ADJ
ejpam-4941	9	7	explanation	explanation	NOUN
ejpam-4941	9	8	to	to	ADP
ejpam-4941	9	9	our	our	PRON
ejpam-4941	9	10	procedure	procedure	NOUN
ejpam-4941	9	11	named	name	VERB
ejpam-4941	9	12	as	as	ADP
ejpam-4941	9	13	abdelalim	abdelalim	NOUN
ejpam-4941	9	14	-	-	PUNCT
ejpam-4941	9	15	elmouki	elmouki	NOUN
ejpam-4941	9	16	(	(	PUNCT
ejpam-4941	9	17	ae	ae	PROPN
ejpam-4941	9	18	)	)	PUNCT
ejpam-4941	9	19	algorithm	algorithm	NOUN
ejpam-4941	9	20	.	.	PUNCT
ejpam-4941	10	1	more	more	ADV
ejpam-4941	10	2	interestingly	interestingly	ADV
ejpam-4941	10	3	,	,	PUNCT
ejpam-4941	10	4	we	we	PRON
ejpam-4941	10	5	show	show	VERB
ejpam-4941	10	6	that	that	SCONJ
ejpam-4941	10	7	mgs	mgs	NOUN
ejpam-4941	10	8	is	be	AUX
ejpam-4941	10	9	not	not	PART
ejpam-4941	10	10	only	only	ADV
ejpam-4941	10	11	better	well	ADJ
ejpam-4941	10	12	than	than	ADP
ejpam-4941	10	13	gs	gs	INTJ
ejpam-4941	10	14	because	because	SCONJ
ejpam-4941	10	15	of	of	ADP
ejpam-4941	10	16	the	the	DET
ejpam-4941	10	17	classical	classical	ADJ
ejpam-4941	10	18	reason	reason	NOUN
ejpam-4941	10	19	related	relate	VERB
ejpam-4941	10	20	to	to	ADP
ejpam-4941	10	21	numerics	numeric	NOUN
ejpam-4941	10	22	,	,	PUNCT
ejpam-4941	10	23	but	but	CCONJ
ejpam-4941	10	24	also	also	ADV
ejpam-4941	10	25	because	because	SCONJ
ejpam-4941	10	26	its	its	PRON
ejpam-4941	10	27	formulation	formulation	NOUN
ejpam-4941	10	28	for	for	ADP
ejpam-4941	10	29	the	the	DET
ejpam-4941	10	30	new	new	ADJ
ejpam-4941	10	31	motif	motif	NOUN
ejpam-4941	10	32	vectors	vector	NOUN
ejpam-4941	10	33	in	in	ADP
ejpam-4941	10	34	four	four	NUM
ejpam-4941	10	35	conditions	condition	NOUN
ejpam-4941	10	36	,	,	PUNCT
ejpam-4941	10	37	has	have	AUX
ejpam-4941	10	38	been	be	AUX
ejpam-4941	10	39	preserved	preserve	VERB
ejpam-4941	10	40	in	in	ADP
ejpam-4941	10	41	three	three	NUM
ejpam-4941	10	42	times	time	NOUN
ejpam-4941	10	43	rather	rather	ADV
ejpam-4941	10	44	than	than	ADP
ejpam-4941	10	45	two	two	NUM
ejpam-4941	10	46	for	for	ADP
ejpam-4941	10	47	gs	gs	NOUN
ejpam-4941	10	48	,	,	PUNCT
ejpam-4941	10	49	and	and	CCONJ
ejpam-4941	10	50	this	this	PRON
ejpam-4941	10	51	may	may	AUX
ejpam-4941	10	52	recommend	recommend	VERB
ejpam-4941	10	53	more	more	ADJ
ejpam-4941	10	54	the	the	DET
ejpam-4941	10	55	introduction	introduction	NOUN
ejpam-4941	10	56	of	of	ADP
ejpam-4941	10	57	mgs	mgs	NOUN
ejpam-4941	10	58	in	in	ADP
ejpam-4941	10	59	a	a	DET
ejpam-4941	10	60	harder	hard	ADJ
ejpam-4941	10	61	problem	problem	NOUN
ejpam-4941	10	62	,	,	PUNCT
ejpam-4941	10	63	namely	namely	ADV
ejpam-4941	10	64	when	when	SCONJ
ejpam-4941	10	65	the	the	DET
ejpam-4941	10	66	crystal	crystal	NOUN
ejpam-4941	10	67	dimension	dimension	NOUN
ejpam-4941	10	68	is	be	AUX
ejpam-4941	10	69	very	very	ADV
ejpam-4941	10	70	big	big	ADJ
ejpam-4941	10	71	.	.	PUNCT
ejpam-4941	11	1	2020	2020	NUM
ejpam-4941	11	2	mathematics	mathematic	NOUN
ejpam-4941	11	3	subject	subject	NOUN
ejpam-4941	11	4	classifications	classification	NOUN
ejpam-4941	11	5	:	:	PUNCT
ejpam-4941	11	6	74e15	74e15	NUM
ejpam-4941	11	7	,	,	PUNCT
ejpam-4941	11	8	06b05	06b05	X
ejpam-4941	11	9	,	,	PUNCT
ejpam-4941	11	10	65y20	65y20	NUM
ejpam-4941	11	11	,	,	PUNCT
ejpam-4941	11	12	68r01	68r01	NOUN
ejpam-4941	11	13	key	key	ADJ
ejpam-4941	11	14	words	word	NOUN
ejpam-4941	11	15	and	and	CCONJ
ejpam-4941	11	16	phrases	phrase	NOUN
ejpam-4941	11	17	:	:	PUNCT
ejpam-4941	11	18	crystallography	crystallography	NOUN
ejpam-4941	11	19	,	,	PUNCT
ejpam-4941	11	20	bravais	bravais	PROPN
ejpam-4941	11	21	lattice	lattice	PROPN
ejpam-4941	11	22	,	,	PUNCT
ejpam-4941	11	23	orthogonalization	orthogonalization	NOUN
ejpam-4941	11	24	,	,	PUNCT
ejpam-4941	11	25	lattice	lattice	NOUN
ejpam-4941	11	26	reduction	reduction	NOUN
ejpam-4941	11	27	1	1	NUM
ejpam-4941	11	28	.	.	PUNCT
ejpam-4941	11	29	introduction	introduction	NOUN
ejpam-4941	11	30	1.1	1.1	NUM
ejpam-4941	11	31	.	.	PUNCT
ejpam-4941	12	1	concrete	concrete	ADJ
ejpam-4941	12	2	context	context	NOUN
ejpam-4941	12	3	of	of	ADP
ejpam-4941	12	4	the	the	DET
ejpam-4941	12	5	problem	problem	NOUN
ejpam-4941	12	6	a	a	DET
ejpam-4941	12	7	point	point	NOUN
ejpam-4941	12	8	in	in	ADP
ejpam-4941	12	9	a	a	DET
ejpam-4941	12	10	crystal	crystal	NOUN
ejpam-4941	12	11	lattice	lattice	NOUN
ejpam-4941	12	12	could	could	AUX
ejpam-4941	12	13	represent	represent	VERB
ejpam-4941	12	14	an	an	DET
ejpam-4941	12	15	atom	atom	NOUN
ejpam-4941	12	16	,	,	PUNCT
ejpam-4941	12	17	ion	ion	NOUN
ejpam-4941	12	18	,	,	PUNCT
ejpam-4941	12	19	or	or	CCONJ
ejpam-4941	12	20	molecule	molecule	NOUN
ejpam-4941	12	21	.	.	PUNCT
ejpam-4941	13	1	if	if	SCONJ
ejpam-4941	13	2	we	we	PRON
ejpam-4941	13	3	take	take	VERB
ejpam-4941	13	4	the	the	DET
ejpam-4941	13	5	example	example	NOUN
ejpam-4941	13	6	of	of	ADP
ejpam-4941	13	7	halite	halite	ADJ
ejpam-4941	13	8	crystal	crystal	PROPN
ejpam-4941	13	9	(	(	PUNCT
ejpam-4941	13	10	nacl	nacl	NOUN
ejpam-4941	13	11	)	)	PUNCT
ejpam-4941	14	1	[	[	X
ejpam-4941	14	2	9	9	NUM
ejpam-4941	14	3	]	]	PUNCT
ejpam-4941	14	4	made	make	VERB
ejpam-4941	14	5	of	of	ADP
ejpam-4941	14	6	sodium	sodium	NOUN
ejpam-4941	14	7	na	na	ADP
ejpam-4941	14	8	and	and	CCONJ
ejpam-4941	14	9	chlorine	chlorine	NOUN
ejpam-4941	14	10	cl	cl	NOUN
ejpam-4941	14	11	,	,	PUNCT
ejpam-4941	14	12	we	we	PRON
ejpam-4941	14	13	find	find	VERB
ejpam-4941	14	14	that	that	SCONJ
ejpam-4941	14	15	∗corresponding	∗corresponde	VERB
ejpam-4941	14	16	author	author	NOUN
ejpam-4941	14	17	.	.	PUNCT
ejpam-4941	15	1	doi	doi	NOUN
ejpam-4941	15	2	:	:	PUNCT
ejpam-4941	15	3	https://doi.org/10.29020/nybg.ejpam.v16i4.4941	https://doi.org/10.29020/nybg.ejpam.v16i4.4941	ADJ
ejpam-4941	15	4	email	email	NOUN
ejpam-4941	15	5	addresses	address	NOUN
ejpam-4941	15	6	:	:	PUNCT
ejpam-4941	15	7	seddikabd@hotmail.com	seddikabd@hotmail.com	X
ejpam-4941	15	8	(	(	PUNCT
ejpam-4941	15	9	s.	s.	PROPN
ejpam-4941	15	10	abdelalim	abdelalim	PROPN
ejpam-4941	15	11	)	)	PUNCT
ejpam-4941	15	12	,	,	PUNCT
ejpam-4941	15	13	i.elmouki@gmail.com	i.elmouki@gmail.com	X
ejpam-4941	15	14	(	(	PUNCT
ejpam-4941	15	15	i.	i.	PROPN
ejpam-4941	15	16	elmouki	elmouki	PROPN
ejpam-4941	15	17	)	)	PUNCT
ejpam-4941	15	18	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4941	15	19	2662	2662	NUM
ejpam-4941	16	1	©	©	PROPN
ejpam-4941	16	2	2023	2023	NUM
ejpam-4941	16	3	ejpam	ejpam	NOUN
ejpam-4941	16	4	all	all	DET
ejpam-4941	16	5	rights	right	NOUN
ejpam-4941	16	6	reserved	reserve	VERB
ejpam-4941	16	7	.	.	PUNCT
ejpam-4941	17	1	s.	s.	PROPN
ejpam-4941	17	2	abdelalim	abdelalim	PROPN
ejpam-4941	17	3	,	,	PUNCT
ejpam-4941	17	4	i.	i.	PROPN
ejpam-4941	17	5	elmouki	elmouki	PROPN
ejpam-4941	17	6	/	/	SYM
ejpam-4941	17	7	eur	eur	PROPN
ejpam-4941	17	8	.	.	PUNCT
ejpam-4941	18	1	j.	j.	PROPN
ejpam-4941	18	2	pure	pure	PROPN
ejpam-4941	18	3	appl	appl	PROPN
ejpam-4941	18	4	.	.	PROPN
ejpam-4941	18	5	math	math	PROPN
ejpam-4941	18	6	,	,	PUNCT
ejpam-4941	18	7	16	16	NUM
ejpam-4941	18	8	(	(	PUNCT
ejpam-4941	18	9	4	4	NUM
ejpam-4941	18	10	)	)	PUNCT
ejpam-4941	18	11	(	(	PUNCT
ejpam-4941	18	12	2023	2023	NUM
ejpam-4941	18	13	)	)	PUNCT
ejpam-4941	18	14	,	,	PUNCT
ejpam-4941	18	15	2662	2662	NUM
ejpam-4941	18	16	-	-	SYM
ejpam-4941	18	17	2692	2692	NUM
ejpam-4941	18	18	2663	2663	NUM
ejpam-4941	18	19	na+	na+	NOUN
ejpam-4941	18	20	and	and	CCONJ
ejpam-4941	18	21	cl−	cl−	NOUN
ejpam-4941	18	22	are	be	AUX
ejpam-4941	18	23	repeated	repeat	VERB
ejpam-4941	18	24	together	together	ADV
ejpam-4941	18	25	(	(	PUNCT
ejpam-4941	18	26	see	see	VERB
ejpam-4941	18	27	this	this	DET
ejpam-4941	18	28	kind	kind	NOUN
ejpam-4941	18	29	of	of	ADP
ejpam-4941	18	30	crystal	crystal	NOUN
ejpam-4941	18	31	structure	structure	NOUN
ejpam-4941	18	32	with	with	ADP
ejpam-4941	18	33	more	more	ADJ
ejpam-4941	18	34	details	detail	NOUN
ejpam-4941	18	35	in	in	ADP
ejpam-4941	18	36	[	[	X
ejpam-4941	18	37	42	42	NUM
ejpam-4941	18	38	]	]	PUNCT
ejpam-4941	18	39	or	or	CCONJ
ejpam-4941	18	40	its	its	PRON
ejpam-4941	18	41	representation	representation	NOUN
ejpam-4941	18	42	in	in	ADP
ejpam-4941	18	43	short	short	ADJ
ejpam-4941	18	44	via	via	ADP
ejpam-4941	18	45	figure	figure	NOUN
ejpam-4941	18	46	1	1	NUM
ejpam-4941	18	47	(	(	PUNCT
ejpam-4941	18	48	a	a	NOUN
ejpam-4941	18	49	)	)	PUNCT
ejpam-4941	18	50	)	)	PUNCT
ejpam-4941	18	51	.	.	PUNCT
ejpam-4941	19	1	in	in	ADP
ejpam-4941	19	2	fact	fact	NOUN
ejpam-4941	19	3	,	,	PUNCT
ejpam-4941	19	4	we	we	PRON
ejpam-4941	19	5	are	be	AUX
ejpam-4941	19	6	working	work	VERB
ejpam-4941	19	7	on	on	ADP
ejpam-4941	19	8	long	long	ADJ
ejpam-4941	19	9	range	range	NOUN
ejpam-4941	19	10	order	order	NOUN
ejpam-4941	19	11	crystal	crystal	NOUN
ejpam-4941	19	12	as	as	SCONJ
ejpam-4941	19	13	we	we	PRON
ejpam-4941	19	14	suppose	suppose	VERB
ejpam-4941	19	15	that	that	SCONJ
ejpam-4941	19	16	from	from	ADP
ejpam-4941	19	17	anywhere	anywhere	ADV
ejpam-4941	19	18	we	we	PRON
ejpam-4941	19	19	look	look	VERB
ejpam-4941	19	20	at	at	ADP
ejpam-4941	19	21	the	the	DET
ejpam-4941	19	22	crystal	crystal	NOUN
ejpam-4941	19	23	,	,	PUNCT
ejpam-4941	19	24	the	the	DET
ejpam-4941	19	25	pattern	pattern	NOUN
ejpam-4941	19	26	of	of	ADP
ejpam-4941	19	27	the	the	DET
ejpam-4941	19	28	points	point	NOUN
ejpam-4941	19	29	is	be	AUX
ejpam-4941	19	30	the	the	DET
ejpam-4941	19	31	same	same	ADJ
ejpam-4941	19	32	everywhere	everywhere	ADV
ejpam-4941	19	33	,	,	PUNCT
ejpam-4941	19	34	forming	form	VERB
ejpam-4941	19	35	of	of	ADP
ejpam-4941	19	36	what	what	PRON
ejpam-4941	19	37	we	we	PRON
ejpam-4941	19	38	will	will	AUX
ejpam-4941	19	39	call	call	VERB
ejpam-4941	19	40	a	a	DET
ejpam-4941	19	41	motif	motif	NOUN
ejpam-4941	19	42	and	and	CCONJ
ejpam-4941	19	43	which	which	PRON
ejpam-4941	19	44	is	be	AUX
ejpam-4941	19	45	contained	contain	VERB
ejpam-4941	19	46	in	in	ADP
ejpam-4941	19	47	a	a	DET
ejpam-4941	19	48	periodically	periodically	ADV
ejpam-4941	19	49	repeating	repeat	VERB
ejpam-4941	19	50	cell	cell	NOUN
ejpam-4941	19	51	called	call	VERB
ejpam-4941	19	52	unit	unit	NOUN
ejpam-4941	19	53	cell	cell	NOUN
ejpam-4941	19	54	.	.	PUNCT
ejpam-4941	20	1	in	in	ADP
ejpam-4941	20	2	the	the	DET
ejpam-4941	20	3	technical	technical	ADJ
ejpam-4941	20	4	part	part	NOUN
ejpam-4941	20	5	of	of	ADP
ejpam-4941	20	6	this	this	DET
ejpam-4941	20	7	work	work	NOUN
ejpam-4941	20	8	thereafter	thereafter	ADV
ejpam-4941	20	9	,	,	PUNCT
ejpam-4941	20	10	a	a	DET
ejpam-4941	20	11	basis	basis	NOUN
ejpam-4941	20	12	will	will	AUX
ejpam-4941	20	13	refer	refer	VERB
ejpam-4941	20	14	to	to	ADP
ejpam-4941	20	15	this	this	DET
ejpam-4941	20	16	unit	unit	NOUN
ejpam-4941	20	17	cell	cell	NOUN
ejpam-4941	20	18	and	and	CCONJ
ejpam-4941	20	19	whose	whose	DET
ejpam-4941	20	20	vectors	vector	NOUN
ejpam-4941	20	21	easily	easily	ADV
ejpam-4941	20	22	help	help	VERB
ejpam-4941	20	23	in	in	ADP
ejpam-4941	20	24	generating	generate	VERB
ejpam-4941	20	25	it	it	PRON
ejpam-4941	20	26	.	.	PUNCT
ejpam-4941	21	1	another	another	DET
ejpam-4941	21	2	example	example	NOUN
ejpam-4941	21	3	would	would	AUX
ejpam-4941	21	4	be	be	AUX
ejpam-4941	21	5	about	about	ADP
ejpam-4941	21	6	fluorite	fluorite	NOUN
ejpam-4941	21	7	crystal	crystal	NOUN
ejpam-4941	21	8	caf2	caf2	NOUN
ejpam-4941	22	1	[	[	X
ejpam-4941	22	2	39	39	NUM
ejpam-4941	22	3	]	]	PUNCT
ejpam-4941	22	4	made	make	VERB
ejpam-4941	22	5	of	of	ADP
ejpam-4941	22	6	calcium	calcium	NOUN
ejpam-4941	22	7	ca	ca	NOUN
ejpam-4941	22	8	and	and	CCONJ
ejpam-4941	22	9	fluorine	fluorine	NOUN
ejpam-4941	22	10	f	f	PROPN
ejpam-4941	22	11	,	,	PUNCT
ejpam-4941	22	12	we	we	PRON
ejpam-4941	22	13	find	find	VERB
ejpam-4941	22	14	that	that	SCONJ
ejpam-4941	22	15	ca+2	ca+2	PROPN
ejpam-4941	22	16	is	be	AUX
ejpam-4941	22	17	repeated	repeat	VERB
ejpam-4941	22	18	every	every	DET
ejpam-4941	22	19	time	time	NOUN
ejpam-4941	22	20	with	with	ADP
ejpam-4941	22	21	two	two	NUM
ejpam-4941	22	22	of	of	ADP
ejpam-4941	22	23	f−	f−	PROPN
ejpam-4941	22	24	(	(	PUNCT
ejpam-4941	22	25	see	see	VERB
ejpam-4941	22	26	this	this	DET
ejpam-4941	22	27	kind	kind	NOUN
ejpam-4941	22	28	of	of	ADP
ejpam-4941	22	29	crystal	crystal	NOUN
ejpam-4941	22	30	structure	structure	NOUN
ejpam-4941	22	31	in	in	ADP
ejpam-4941	22	32	[	[	X
ejpam-4941	22	33	51	51	NUM
ejpam-4941	22	34	]	]	PUNCT
ejpam-4941	22	35	or	or	CCONJ
ejpam-4941	22	36	its	its	PRON
ejpam-4941	22	37	representation	representation	NOUN
ejpam-4941	22	38	in	in	ADP
ejpam-4941	22	39	short	short	ADJ
ejpam-4941	22	40	via	via	ADP
ejpam-4941	22	41	figure	figure	NOUN
ejpam-4941	22	42	1	1	NUM
ejpam-4941	22	43	(	(	PUNCT
ejpam-4941	22	44	b	b	NOUN
ejpam-4941	22	45	)	)	PUNCT
ejpam-4941	22	46	)	)	PUNCT
ejpam-4941	22	47	.	.	PUNCT
ejpam-4941	23	1	we	we	PRON
ejpam-4941	23	2	deduce	deduce	VERB
ejpam-4941	23	3	from	from	ADP
ejpam-4941	23	4	both	both	DET
ejpam-4941	23	5	examples	example	NOUN
ejpam-4941	23	6	,	,	PUNCT
ejpam-4941	23	7	the	the	DET
ejpam-4941	23	8	existence	existence	NOUN
ejpam-4941	23	9	of	of	ADP
ejpam-4941	23	10	a	a	DET
ejpam-4941	23	11	periodic	periodic	ADJ
ejpam-4941	23	12	repetition	repetition	NOUN
ejpam-4941	23	13	of	of	ADP
ejpam-4941	23	14	a	a	DET
ejpam-4941	23	15	group	group	NOUN
ejpam-4941	23	16	of	of	ADP
ejpam-4941	23	17	atoms	atom	NOUN
ejpam-4941	23	18	with	with	ADP
ejpam-4941	23	19	long	long	ADJ
ejpam-4941	23	20	range	range	NOUN
ejpam-4941	23	21	order	order	NOUN
ejpam-4941	23	22	.	.	PUNCT
ejpam-4941	24	1	another	another	DET
ejpam-4941	24	2	property	property	NOUN
ejpam-4941	24	3	of	of	ADP
ejpam-4941	24	4	these	these	DET
ejpam-4941	24	5	crystals	crystal	NOUN
ejpam-4941	24	6	is	be	AUX
ejpam-4941	24	7	about	about	ADP
ejpam-4941	24	8	the	the	DET
ejpam-4941	24	9	translational	translational	ADJ
ejpam-4941	24	10	symmetry	symmetry	NOUN
ejpam-4941	24	11	[	[	X
ejpam-4941	24	12	30	30	NUM
ejpam-4941	24	13	]	]	PUNCT
ejpam-4941	24	14	,	,	PUNCT
ejpam-4941	24	15	and	and	CCONJ
ejpam-4941	24	16	which	which	PRON
ejpam-4941	24	17	means	mean	VERB
ejpam-4941	24	18	wherever	wherever	SCONJ
ejpam-4941	24	19	we	we	PRON
ejpam-4941	24	20	move	move	VERB
ejpam-4941	24	21	the	the	DET
ejpam-4941	24	22	crystal	crystal	NOUN
ejpam-4941	24	23	from	from	ADP
ejpam-4941	24	24	one	one	NUM
ejpam-4941	24	25	repeating	repeat	VERB
ejpam-4941	24	26	unit	unit	NOUN
ejpam-4941	24	27	to	to	ADP
ejpam-4941	24	28	another	another	PRON
ejpam-4941	24	29	,	,	PUNCT
ejpam-4941	24	30	the	the	DET
ejpam-4941	24	31	crystal	crystal	NOUN
ejpam-4941	24	32	remains	remain	VERB
ejpam-4941	24	33	exactly	exactly	ADV
ejpam-4941	24	34	the	the	DET
ejpam-4941	24	35	same	same	ADJ
ejpam-4941	24	36	.	.	PUNCT
ejpam-4941	25	1	let	let	VERB
ejpam-4941	25	2	us	we	PRON
ejpam-4941	25	3	suppose	suppose	VERB
ejpam-4941	25	4	now	now	ADV
ejpam-4941	25	5	,	,	PUNCT
ejpam-4941	25	6	three	three	NUM
ejpam-4941	25	7	hypothetical	hypothetical	ADJ
ejpam-4941	25	8	crystals	crystal	NOUN
ejpam-4941	25	9	whose	whose	DET
ejpam-4941	25	10	repeating	repeat	VERB
ejpam-4941	25	11	cells	cell	NOUN
ejpam-4941	25	12	are	be	AUX
ejpam-4941	25	13	formed	form	VERB
ejpam-4941	25	14	with	with	ADP
ejpam-4941	25	15	just	just	ADV
ejpam-4941	25	16	two	two	NUM
ejpam-4941	25	17	atoms	atom	NOUN
ejpam-4941	25	18	as	as	ADP
ejpam-4941	25	19	in	in	ADP
ejpam-4941	25	20	the	the	DET
ejpam-4941	25	21	case	case	NOUN
ejpam-4941	25	22	of	of	ADP
ejpam-4941	25	23	figure	figure	NOUN
ejpam-4941	25	24	1	1	NUM
ejpam-4941	25	25	(	(	PUNCT
ejpam-4941	25	26	a	a	NOUN
ejpam-4941	25	27	)	)	PUNCT
ejpam-4941	25	28	but	but	CCONJ
ejpam-4941	25	29	whose	whose	DET
ejpam-4941	25	30	representations	representation	NOUN
ejpam-4941	25	31	are	be	AUX
ejpam-4941	25	32	different	different	ADJ
ejpam-4941	25	33	because	because	SCONJ
ejpam-4941	25	34	of	of	ADP
ejpam-4941	25	35	the	the	DET
ejpam-4941	25	36	positioning	positioning	NOUN
ejpam-4941	25	37	of	of	ADP
ejpam-4941	25	38	their	their	PRON
ejpam-4941	25	39	atoms	atom	NOUN
ejpam-4941	25	40	.	.	PUNCT
ejpam-4941	26	1	figure	figure	VERB
ejpam-4941	26	2	1	1	NUM
ejpam-4941	26	3	:	:	PUNCT
ejpam-4941	26	4	(	(	PUNCT
ejpam-4941	26	5	a	a	X
ejpam-4941	26	6	)	)	PUNCT
ejpam-4941	26	7	representation	representation	NOUN
ejpam-4941	26	8	of	of	ADP
ejpam-4941	26	9	nacl	nacl	NOUN
ejpam-4941	26	10	:	:	PUNCT
ejpam-4941	26	11	na+	na+	NOUN
ejpam-4941	26	12	shown	show	VERB
ejpam-4941	26	13	as	as	ADP
ejpam-4941	26	14	bigger	big	ADJ
ejpam-4941	26	15	discs	disc	NOUN
ejpam-4941	26	16	and	and	CCONJ
ejpam-4941	26	17	cl−	cl−	NUM
ejpam-4941	26	18	as	as	ADP
ejpam-4941	26	19	smaller	small	ADJ
ejpam-4941	26	20	discs	disc	NOUN
ejpam-4941	26	21	.	.	PUNCT
ejpam-4941	27	1	(	(	PUNCT
ejpam-4941	27	2	b	b	X
ejpam-4941	27	3	)	)	PUNCT
ejpam-4941	27	4	representation	representation	NOUN
ejpam-4941	27	5	of	of	ADP
ejpam-4941	27	6	caf2	caf2	NOUN
ejpam-4941	27	7	:	:	PUNCT
ejpam-4941	27	8	ca+2	ca+2	NOUN
ejpam-4941	27	9	shown	show	VERB
ejpam-4941	27	10	as	as	ADP
ejpam-4941	27	11	bigger	big	ADJ
ejpam-4941	27	12	discs	disc	NOUN
ejpam-4941	27	13	and	and	CCONJ
ejpam-4941	27	14	f−	f−	NOUN
ejpam-4941	27	15	as	as	ADP
ejpam-4941	27	16	smaller	small	ADJ
ejpam-4941	27	17	discs	disc	NOUN
ejpam-4941	27	18	.	.	PUNCT
ejpam-4941	28	1	for	for	ADP
ejpam-4941	28	2	instance	instance	NOUN
ejpam-4941	28	3	,	,	PUNCT
ejpam-4941	28	4	if	if	SCONJ
ejpam-4941	28	5	we	we	PRON
ejpam-4941	28	6	take	take	VERB
ejpam-4941	28	7	the	the	DET
ejpam-4941	28	8	three	three	NUM
ejpam-4941	28	9	arrangements	arrangement	NOUN
ejpam-4941	28	10	(	(	PUNCT
ejpam-4941	28	11	a	a	X
ejpam-4941	28	12	)	)	PUNCT
ejpam-4941	28	13	,	,	PUNCT
ejpam-4941	28	14	(	(	PUNCT
ejpam-4941	28	15	b	b	X
ejpam-4941	28	16	)	)	PUNCT
ejpam-4941	28	17	and	and	CCONJ
ejpam-4941	28	18	(	(	PUNCT
ejpam-4941	28	19	c	c	NOUN
ejpam-4941	28	20	)	)	PUNCT
ejpam-4941	28	21	shown	show	VERB
ejpam-4941	28	22	in	in	ADP
ejpam-4941	28	23	figure	figure	NOUN
ejpam-4941	28	24	2	2	NUM
ejpam-4941	28	25	,	,	PUNCT
ejpam-4941	28	26	and	and	CCONJ
ejpam-4941	28	27	where	where	SCONJ
ejpam-4941	28	28	we	we	PRON
ejpam-4941	28	29	consider	consider	VERB
ejpam-4941	28	30	the	the	DET
ejpam-4941	28	31	bigger	big	ADJ
ejpam-4941	28	32	discs	disc	NOUN
ejpam-4941	28	33	as	as	ADP
ejpam-4941	28	34	points	point	NOUN
ejpam-4941	28	35	of	of	ADP
ejpam-4941	28	36	what	what	PRON
ejpam-4941	28	37	we	we	PRON
ejpam-4941	28	38	will	will	AUX
ejpam-4941	28	39	call	call	VERB
ejpam-4941	28	40	a	a	DET
ejpam-4941	28	41	lattice	lattice	NOUN
ejpam-4941	28	42	,	,	PUNCT
ejpam-4941	28	43	we	we	PRON
ejpam-4941	28	44	obtain	obtain	VERB
ejpam-4941	28	45	three	three	NUM
ejpam-4941	28	46	different	different	ADJ
ejpam-4941	28	47	forms	form	NOUN
ejpam-4941	28	48	of	of	ADP
ejpam-4941	28	49	lattices	lattice	NOUN
ejpam-4941	28	50	.	.	PUNCT
ejpam-4941	29	1	in	in	ADP
ejpam-4941	29	2	fact	fact	NOUN
ejpam-4941	29	3	,	,	PUNCT
ejpam-4941	29	4	the	the	DET
ejpam-4941	29	5	lattice	lattice	NOUN
ejpam-4941	29	6	is	be	AUX
ejpam-4941	29	7	like	like	ADP
ejpam-4941	29	8	a	a	DET
ejpam-4941	29	9	crystal	crystal	NOUN
ejpam-4941	29	10	,	,	PUNCT
ejpam-4941	29	11	just	just	ADV
ejpam-4941	29	12	for	for	ADP
ejpam-4941	29	13	instance	instance	NOUN
ejpam-4941	29	14	instead	instead	ADV
ejpam-4941	29	15	of	of	ADP
ejpam-4941	29	16	talking	talk	VERB
ejpam-4941	29	17	with	with	ADP
ejpam-4941	29	18	atoms	atom	NOUN
ejpam-4941	29	19	,	,	PUNCT
ejpam-4941	29	20	we	we	PRON
ejpam-4941	29	21	talk	talk	VERB
ejpam-4941	29	22	about	about	ADP
ejpam-4941	29	23	a	a	DET
ejpam-4941	29	24	periodic	periodic	ADJ
ejpam-4941	29	25	arrangement	arrangement	NOUN
ejpam-4941	29	26	of	of	ADP
ejpam-4941	29	27	points	point	NOUN
ejpam-4941	29	28	,	,	PUNCT
ejpam-4941	29	29	then	then	ADV
ejpam-4941	29	30	we	we	PRON
ejpam-4941	29	31	have	have	VERB
ejpam-4941	29	32	crystal	crystal	NOUN
ejpam-4941	29	33	=	=	SYM
ejpam-4941	30	1	lattice+	lattice+	ADP
ejpam-4941	30	2	basis	basis	NOUN
ejpam-4941	30	3	but	but	CCONJ
ejpam-4941	30	4	with	with	ADP
ejpam-4941	30	5	respect	respect	NOUN
ejpam-4941	30	6	to	to	ADP
ejpam-4941	30	7	the	the	DET
ejpam-4941	30	8	definition	definition	NOUN
ejpam-4941	30	9	that	that	PRON
ejpam-4941	30	10	we	we	PRON
ejpam-4941	30	11	have	have	AUX
ejpam-4941	30	12	provided	provide	VERB
ejpam-4941	30	13	before	before	ADV
ejpam-4941	30	14	in	in	ADP
ejpam-4941	30	15	referring	refer	VERB
ejpam-4941	30	16	to	to	ADP
ejpam-4941	30	17	the	the	DET
ejpam-4941	30	18	motif	motif	NOUN
ejpam-4941	30	19	’s	’s	PART
ejpam-4941	30	20	associated	associated	ADJ
ejpam-4941	30	21	unit	unit	NOUN
ejpam-4941	30	22	cell	cell	NOUN
ejpam-4941	30	23	and	and	CCONJ
ejpam-4941	30	24	not	not	PART
ejpam-4941	30	25	exactly	exactly	ADV
ejpam-4941	30	26	any	any	DET
ejpam-4941	30	27	repeating	repeat	VERB
ejpam-4941	30	28	unit	unit	NOUN
ejpam-4941	30	29	cell	cell	NOUN
ejpam-4941	30	30	as	as	ADP
ejpam-4941	30	31	in	in	ADP
ejpam-4941	30	32	[	[	X
ejpam-4941	30	33	20	20	NUM
ejpam-4941	30	34	,	,	PUNCT
ejpam-4941	30	35	29	29	NUM
ejpam-4941	30	36	]	]	PUNCT
ejpam-4941	30	37	as	as	SCONJ
ejpam-4941	30	38	some	some	DET
ejpam-4941	30	39	researchers	researcher	NOUN
ejpam-4941	30	40	do	do	AUX
ejpam-4941	30	41	not	not	PART
ejpam-4941	30	42	totally	totally	ADV
ejpam-4941	30	43	agree	agree	VERB
ejpam-4941	30	44	with	with	ADP
ejpam-4941	30	45	that	that	DET
ejpam-4941	30	46	popular	popular	ADJ
ejpam-4941	30	47	definition	definition	NOUN
ejpam-4941	30	48	.	.	PUNCT
ejpam-4941	31	1	in	in	ADP
ejpam-4941	31	2	fact	fact	NOUN
ejpam-4941	31	3	,	,	PUNCT
ejpam-4941	31	4	in	in	ADP
ejpam-4941	31	5	order	order	NOUN
ejpam-4941	31	6	to	to	PART
ejpam-4941	31	7	avoid	avoid	VERB
ejpam-4941	31	8	any	any	DET
ejpam-4941	31	9	conflict	conflict	NOUN
ejpam-4941	31	10	,	,	PUNCT
ejpam-4941	31	11	we	we	PRON
ejpam-4941	31	12	have	have	AUX
ejpam-4941	31	13	seen	see	VERB
ejpam-4941	31	14	too	too	ADV
ejpam-4941	31	15	that	that	SCONJ
ejpam-4941	31	16	it	it	PRON
ejpam-4941	31	17	is	be	AUX
ejpam-4941	31	18	better	well	ADJ
ejpam-4941	31	19	to	to	PART
ejpam-4941	31	20	introduce	introduce	VERB
ejpam-4941	31	21	the	the	DET
ejpam-4941	31	22	basis	basis	NOUN
ejpam-4941	31	23	as	as	SCONJ
ejpam-4941	31	24	defined	define	VERB
ejpam-4941	31	25	mathematically	mathematically	ADV
ejpam-4941	31	26	rather	rather	ADV
ejpam-4941	31	27	than	than	ADP
ejpam-4941	31	28	considering	consider	VERB
ejpam-4941	31	29	it	it	PRON
ejpam-4941	31	30	as	as	SCONJ
ejpam-4941	31	31	the	the	DET
ejpam-4941	31	32	unit	unit	NOUN
ejpam-4941	31	33	cell	cell	VERB
ejpam-4941	31	34	itself	itself	PRON
ejpam-4941	31	35	because	because	SCONJ
ejpam-4941	31	36	one	one	PRON
ejpam-4941	31	37	would	would	AUX
ejpam-4941	31	38	wonder	wonder	VERB
ejpam-4941	31	39	if	if	SCONJ
ejpam-4941	31	40	the	the	DET
ejpam-4941	31	41	unit	unit	NOUN
ejpam-4941	31	42	cell	cell	NOUN
ejpam-4941	31	43	is	be	AUX
ejpam-4941	31	44	a	a	DET
ejpam-4941	31	45	part	part	NOUN
ejpam-4941	31	46	of	of	ADP
ejpam-4941	31	47	the	the	DET
ejpam-4941	31	48	lattice	lattice	NOUN
ejpam-4941	31	49	,	,	PUNCT
ejpam-4941	31	50	then	then	ADV
ejpam-4941	31	51	crystal	crystal	NOUN
ejpam-4941	31	52	=	=	SYM
ejpam-4941	31	53	lattice	lattice	NOUN
ejpam-4941	31	54	+	+	CCONJ
ejpam-4941	31	55	basis	basis	NOUN
ejpam-4941	31	56	can	can	AUX
ejpam-4941	31	57	simply	simply	ADV
ejpam-4941	31	58	be	be	AUX
ejpam-4941	31	59	reduced	reduce	VERB
ejpam-4941	31	60	to	to	ADP
ejpam-4941	31	61	crystal	crystal	NOUN
ejpam-4941	31	62	=	=	SYM
ejpam-4941	31	63	lattice	lattice	PROPN
ejpam-4941	31	64	.	.	PUNCT
ejpam-4941	32	1	using	use	VERB
ejpam-4941	32	2	examples	example	NOUN
ejpam-4941	32	3	of	of	ADP
ejpam-4941	32	4	atoms	atom	NOUN
ejpam-4941	32	5	and	and	CCONJ
ejpam-4941	32	6	ions	ion	NOUN
ejpam-4941	32	7	,	,	PUNCT
ejpam-4941	32	8	maurice	maurice	PROPN
ejpam-4941	32	9	loyal	loyal	ADJ
ejpam-4941	32	10	huggins	huggins	PROPN
ejpam-4941	32	11	provided	provide	VERB
ejpam-4941	32	12	in	in	ADP
ejpam-4941	32	13	[	[	X
ejpam-4941	32	14	25	25	NUM
ejpam-4941	32	15	]	]	PUNCT
ejpam-4941	32	16	,	,	PUNCT
ejpam-4941	32	17	principles	principle	NOUN
ejpam-4941	32	18	in	in	ADP
ejpam-4941	32	19	order	order	NOUN
ejpam-4941	32	20	to	to	PART
ejpam-4941	32	21	find	find	VERB
ejpam-4941	32	22	the	the	DET
ejpam-4941	32	23	arrangement	arrangement	NOUN
ejpam-4941	32	24	of	of	ADP
ejpam-4941	32	25	points	point	NOUN
ejpam-4941	32	26	in	in	ADP
ejpam-4941	32	27	crystals	crystal	NOUN
ejpam-4941	32	28	and	and	CCONJ
ejpam-4941	32	29	he	he	PRON
ejpam-4941	32	30	concluded	conclude	VERB
ejpam-4941	32	31	that	that	SCONJ
ejpam-4941	32	32	this	this	DET
ejpam-4941	32	33	arrangement	arrangement	NOUN
ejpam-4941	32	34	is	be	AUX
ejpam-4941	32	35	repeating	repeat	VERB
ejpam-4941	32	36	itself	itself	PRON
ejpam-4941	32	37	in	in	ADP
ejpam-4941	32	38	short	short	ADJ
ejpam-4941	32	39	intervals	interval	NOUN
ejpam-4941	32	40	while	while	SCONJ
ejpam-4941	32	41	the	the	DET
ejpam-4941	32	42	motif	motif	NOUN
ejpam-4941	32	43	should	should	AUX
ejpam-4941	32	44	contain	contain	VERB
ejpam-4941	32	45	relatively	relatively	ADV
ejpam-4941	32	46	few	few	ADJ
ejpam-4941	32	47	points	point	NOUN
ejpam-4941	32	48	.	.	PUNCT
ejpam-4941	33	1	here	here	ADV
ejpam-4941	33	2	,	,	PUNCT
ejpam-4941	33	3	we	we	PRON
ejpam-4941	33	4	deduce	deduce	VERB
ejpam-4941	33	5	that	that	SCONJ
ejpam-4941	33	6	even	even	ADV
ejpam-4941	33	7	if	if	SCONJ
ejpam-4941	33	8	we	we	PRON
ejpam-4941	33	9	consider	consider	VERB
ejpam-4941	33	10	the	the	DET
ejpam-4941	33	11	smaller	small	ADJ
ejpam-4941	33	12	discs	disc	NOUN
ejpam-4941	33	13	,	,	PUNCT
ejpam-4941	33	14	or	or	CCONJ
ejpam-4941	33	15	their	their	PRON
ejpam-4941	33	16	points	point	NOUN
ejpam-4941	33	17	of	of	ADP
ejpam-4941	33	18	s.	s.	PROPN
ejpam-4941	33	19	abdelalim	abdelalim	PROPN
ejpam-4941	33	20	,	,	PUNCT
ejpam-4941	33	21	i.	i.	PROPN
ejpam-4941	33	22	elmouki	elmouki	PROPN
ejpam-4941	33	23	/	/	SYM
ejpam-4941	33	24	eur	eur	PROPN
ejpam-4941	33	25	.	.	PUNCT
ejpam-4941	34	1	j.	j.	PROPN
ejpam-4941	34	2	pure	pure	PROPN
ejpam-4941	34	3	appl	appl	PROPN
ejpam-4941	34	4	.	.	PROPN
ejpam-4941	34	5	math	math	PROPN
ejpam-4941	34	6	,	,	PUNCT
ejpam-4941	34	7	16	16	NUM
ejpam-4941	34	8	(	(	PUNCT
ejpam-4941	34	9	4	4	NUM
ejpam-4941	34	10	)	)	PUNCT
ejpam-4941	34	11	(	(	PUNCT
ejpam-4941	34	12	2023	2023	NUM
ejpam-4941	34	13	)	)	PUNCT
ejpam-4941	34	14	,	,	PUNCT
ejpam-4941	34	15	2662	2662	NUM
ejpam-4941	34	16	-	-	SYM
ejpam-4941	34	17	2692	2692	NUM
ejpam-4941	34	18	2664	2664	NUM
ejpam-4941	34	19	h	h	NOUN
ejpam-4941	34	20	!	!	PUNCT
ejpam-4941	34	21	]	]	PUNCT
ejpam-4941	34	22	figure	figure	NOUN
ejpam-4941	34	23	2	2	NUM
ejpam-4941	34	24	:	:	PUNCT
ejpam-4941	34	25	representation	representation	NOUN
ejpam-4941	34	26	of	of	ADP
ejpam-4941	34	27	different	different	ADJ
ejpam-4941	34	28	crystals	crystal	NOUN
ejpam-4941	34	29	where	where	SCONJ
ejpam-4941	34	30	the	the	DET
ejpam-4941	34	31	centers	center	NOUN
ejpam-4941	34	32	of	of	ADP
ejpam-4941	34	33	the	the	DET
ejpam-4941	34	34	bigger	big	ADJ
ejpam-4941	34	35	discs	disc	NOUN
ejpam-4941	34	36	are	be	AUX
ejpam-4941	34	37	considered	consider	VERB
ejpam-4941	34	38	as	as	ADP
ejpam-4941	34	39	the	the	DET
ejpam-4941	34	40	main	main	ADJ
ejpam-4941	34	41	and	and	CCONJ
ejpam-4941	34	42	only	only	ADJ
ejpam-4941	34	43	points	point	NOUN
ejpam-4941	34	44	of	of	ADP
ejpam-4941	34	45	the	the	DET
ejpam-4941	34	46	different	different	ADJ
ejpam-4941	34	47	lattices	lattice	NOUN
ejpam-4941	34	48	obtained	obtain	VERB
ejpam-4941	34	49	in	in	ADP
ejpam-4941	34	50	the	the	DET
ejpam-4941	34	51	three	three	NUM
ejpam-4941	34	52	cases	case	NOUN
ejpam-4941	34	53	.	.	PUNCT
ejpam-4941	35	1	(	(	PUNCT
ejpam-4941	35	2	a	a	X
ejpam-4941	35	3	)	)	PUNCT
ejpam-4941	35	4	result	result	NOUN
ejpam-4941	35	5	of	of	ADP
ejpam-4941	35	6	a	a	DET
ejpam-4941	35	7	lattice	lattice	NOUN
ejpam-4941	35	8	with	with	ADP
ejpam-4941	35	9	points	point	NOUN
ejpam-4941	35	10	forming	form	VERB
ejpam-4941	35	11	shapes	shape	NOUN
ejpam-4941	35	12	as	as	ADP
ejpam-4941	35	13	squares	square	NOUN
ejpam-4941	35	14	.	.	PUNCT
ejpam-4941	36	1	(	(	PUNCT
ejpam-4941	36	2	b	b	X
ejpam-4941	36	3	)	)	PUNCT
ejpam-4941	36	4	result	result	NOUN
ejpam-4941	36	5	of	of	ADP
ejpam-4941	36	6	a	a	DET
ejpam-4941	36	7	lattice	lattice	NOUN
ejpam-4941	36	8	with	with	ADP
ejpam-4941	36	9	points	point	NOUN
ejpam-4941	36	10	forming	form	VERB
ejpam-4941	36	11	shapes	shape	NOUN
ejpam-4941	36	12	as	as	ADP
ejpam-4941	36	13	parallelograms	parallelogram	NOUN
ejpam-4941	36	14	.	.	PUNCT
ejpam-4941	37	1	(	(	PUNCT
ejpam-4941	37	2	c	c	X
ejpam-4941	37	3	)	)	PUNCT
ejpam-4941	37	4	result	result	NOUN
ejpam-4941	37	5	of	of	ADP
ejpam-4941	37	6	a	a	DET
ejpam-4941	37	7	lattice	lattice	NOUN
ejpam-4941	37	8	with	with	ADP
ejpam-4941	37	9	points	point	NOUN
ejpam-4941	37	10	forming	form	VERB
ejpam-4941	37	11	shapes	shape	NOUN
ejpam-4941	37	12	as	as	ADP
ejpam-4941	37	13	centered	center	VERB
ejpam-4941	37	14	squares	square	NOUN
ejpam-4941	37	15	.	.	PUNCT
ejpam-4941	38	1	intersection	intersection	NOUN
ejpam-4941	38	2	with	with	ADP
ejpam-4941	38	3	the	the	DET
ejpam-4941	38	4	bigger	big	ADJ
ejpam-4941	38	5	ones	one	NOUN
ejpam-4941	38	6	,	,	PUNCT
ejpam-4941	38	7	we	we	PRON
ejpam-4941	38	8	will	will	AUX
ejpam-4941	38	9	obtain	obtain	VERB
ejpam-4941	38	10	the	the	DET
ejpam-4941	38	11	same	same	ADJ
ejpam-4941	38	12	patterns	pattern	NOUN
ejpam-4941	38	13	of	of	ADP
ejpam-4941	38	14	the	the	DET
ejpam-4941	38	15	lattices	lattice	NOUN
ejpam-4941	38	16	(	(	PUNCT
ejpam-4941	38	17	a	a	X
ejpam-4941	38	18	)	)	PUNCT
ejpam-4941	38	19	,	,	PUNCT
ejpam-4941	38	20	(	(	PUNCT
ejpam-4941	38	21	b	b	X
ejpam-4941	38	22	)	)	PUNCT
ejpam-4941	38	23	and	and	CCONJ
ejpam-4941	38	24	(	(	PUNCT
ejpam-4941	38	25	c	c	NOUN
ejpam-4941	38	26	)	)	PUNCT
ejpam-4941	38	27	of	of	ADP
ejpam-4941	38	28	figure	figure	NOUN
ejpam-4941	38	29	2	2	NUM
ejpam-4941	38	30	.	.	PUNCT
ejpam-4941	39	1	after	after	ADP
ejpam-4941	39	2	this	this	DET
ejpam-4941	39	3	introductory	introductory	ADJ
ejpam-4941	39	4	description	description	NOUN
ejpam-4941	39	5	of	of	ADP
ejpam-4941	39	6	the	the	DET
ejpam-4941	39	7	transformation	transformation	NOUN
ejpam-4941	39	8	being	be	AUX
ejpam-4941	39	9	followed	follow	VERB
ejpam-4941	39	10	to	to	PART
ejpam-4941	39	11	move	move	VERB
ejpam-4941	39	12	from	from	ADP
ejpam-4941	39	13	the	the	DET
ejpam-4941	39	14	crystal	crystal	NOUN
ejpam-4941	39	15	general	general	ADJ
ejpam-4941	39	16	structure	structure	NOUN
ejpam-4941	39	17	to	to	ADP
ejpam-4941	39	18	the	the	DET
ejpam-4941	39	19	lattice	lattice	NOUN
ejpam-4941	39	20	framework	framework	NOUN
ejpam-4941	39	21	as	as	ADP
ejpam-4941	39	22	an	an	DET
ejpam-4941	39	23	easiest	easy	ADJ
ejpam-4941	39	24	way	way	NOUN
ejpam-4941	39	25	to	to	PART
ejpam-4941	39	26	study	study	VERB
ejpam-4941	39	27	the	the	DET
ejpam-4941	39	28	properties	property	NOUN
ejpam-4941	39	29	of	of	ADP
ejpam-4941	39	30	the	the	DET
ejpam-4941	39	31	complex	complex	ADJ
ejpam-4941	39	32	crystals	crystal	NOUN
ejpam-4941	39	33	,	,	PUNCT
ejpam-4941	39	34	we	we	PRON
ejpam-4941	39	35	introduce	introduce	VERB
ejpam-4941	39	36	in	in	ADP
ejpam-4941	39	37	the	the	DET
ejpam-4941	39	38	next	next	ADJ
ejpam-4941	39	39	subsection	subsection	NOUN
ejpam-4941	39	40	,	,	PUNCT
ejpam-4941	39	41	some	some	DET
ejpam-4941	39	42	technical	technical	ADJ
ejpam-4941	39	43	issues	issue	NOUN
ejpam-4941	39	44	that	that	PRON
ejpam-4941	39	45	are	be	AUX
ejpam-4941	39	46	still	still	ADV
ejpam-4941	39	47	open	open	ADJ
ejpam-4941	39	48	in	in	ADP
ejpam-4941	39	49	this	this	DET
ejpam-4941	39	50	regard	regard	NOUN
ejpam-4941	39	51	and	and	CCONJ
ejpam-4941	39	52	that	that	PRON
ejpam-4941	39	53	has	have	AUX
ejpam-4941	39	54	motivated	motivate	VERB
ejpam-4941	39	55	us	we	PRON
ejpam-4941	39	56	to	to	PART
ejpam-4941	39	57	suggest	suggest	VERB
ejpam-4941	39	58	a	a	DET
ejpam-4941	39	59	mathematicalbased	mathematicalbase	VERB
ejpam-4941	39	60	method	method	NOUN
ejpam-4941	39	61	for	for	ADP
ejpam-4941	39	62	bravais	bravais	NOUN
ejpam-4941	39	63	cell	cell	NOUN
ejpam-4941	39	64	reduction	reduction	NOUN
ejpam-4941	39	65	instead	instead	ADV
ejpam-4941	39	66	of	of	ADP
ejpam-4941	39	67	the	the	DET
ejpam-4941	39	68	observational	observational	ADJ
ejpam-4941	39	69	rules	rule	NOUN
ejpam-4941	39	70	as	as	SCONJ
ejpam-4941	39	71	we	we	PRON
ejpam-4941	39	72	will	will	AUX
ejpam-4941	39	73	discuss	discuss	VERB
ejpam-4941	39	74	hereafter	hereafter	ADV
ejpam-4941	39	75	.	.	PUNCT
ejpam-4941	40	1	1.2	1.2	NUM
ejpam-4941	40	2	.	.	PUNCT
ejpam-4941	40	3	theoretical	theoretical	ADJ
ejpam-4941	40	4	context	context	NOUN
ejpam-4941	40	5	and	and	CCONJ
ejpam-4941	40	6	motivation	motivation	NOUN
ejpam-4941	40	7	1.2.1	1.2.1	NUM
ejpam-4941	40	8	.	.	PUNCT
ejpam-4941	41	1	observational	observational	ADJ
ejpam-4941	41	2	rules	rule	NOUN
ejpam-4941	41	3	to	to	ADP
ejpam-4941	41	4	the	the	DET
ejpam-4941	41	5	best	good	ADJ
ejpam-4941	41	6	of	of	ADP
ejpam-4941	41	7	our	our	PRON
ejpam-4941	41	8	knowledge	knowledge	NOUN
ejpam-4941	41	9	,	,	PUNCT
ejpam-4941	41	10	there	there	PRON
ejpam-4941	41	11	is	be	VERB
ejpam-4941	41	12	no	no	DET
ejpam-4941	41	13	algebraic	algebraic	ADJ
ejpam-4941	41	14	procedure	procedure	NOUN
ejpam-4941	41	15	that	that	PRON
ejpam-4941	41	16	organizes	organize	VERB
ejpam-4941	41	17	the	the	DET
ejpam-4941	41	18	operations	operation	NOUN
ejpam-4941	41	19	followed	follow	VERB
ejpam-4941	41	20	for	for	ADP
ejpam-4941	41	21	the	the	DET
ejpam-4941	41	22	determination	determination	NOUN
ejpam-4941	41	23	of	of	ADP
ejpam-4941	41	24	the	the	DET
ejpam-4941	41	25	unit	unit	NOUN
ejpam-4941	41	26	cell	cell	NOUN
ejpam-4941	41	27	that	that	PRON
ejpam-4941	41	28	could	could	AUX
ejpam-4941	41	29	generate	generate	VERB
ejpam-4941	41	30	the	the	DET
ejpam-4941	41	31	whole	whole	ADJ
ejpam-4941	41	32	representing	represent	VERB
ejpam-4941	41	33	bravais	bravais	PROPN
ejpam-4941	41	34	lattice	lattice	NOUN
ejpam-4941	41	35	of	of	ADP
ejpam-4941	41	36	a	a	DET
ejpam-4941	41	37	crystal	crystal	NOUN
ejpam-4941	41	38	.	.	PUNCT
ejpam-4941	42	1	in	in	ADP
ejpam-4941	42	2	fact	fact	NOUN
ejpam-4941	42	3	,	,	PUNCT
ejpam-4941	42	4	this	this	PRON
ejpam-4941	42	5	is	be	AUX
ejpam-4941	42	6	not	not	PART
ejpam-4941	42	7	feasible	feasible	ADJ
ejpam-4941	42	8	simply	simply	ADV
ejpam-4941	42	9	because	because	SCONJ
ejpam-4941	42	10	of	of	ADP
ejpam-4941	42	11	the	the	DET
ejpam-4941	42	12	complex	complex	ADJ
ejpam-4941	42	13	structures	structure	NOUN
ejpam-4941	42	14	of	of	ADP
ejpam-4941	42	15	crystals	crystal	NOUN
ejpam-4941	42	16	.	.	PUNCT
ejpam-4941	43	1	victor	victor	PROPN
ejpam-4941	43	2	goldschmidt	goldschmidt	PROPN
ejpam-4941	43	3	considered	consider	VERB
ejpam-4941	43	4	to	to	PART
ejpam-4941	43	5	be	be	AUX
ejpam-4941	43	6	the	the	DET
ejpam-4941	43	7	founder	founder	NOUN
ejpam-4941	43	8	of	of	ADP
ejpam-4941	43	9	modern	modern	ADJ
ejpam-4941	43	10	geochemistry	geochemistry	NOUN
ejpam-4941	43	11	and	and	CCONJ
ejpam-4941	43	12	crystal	crystal	NOUN
ejpam-4941	43	13	chemistry	chemistry	NOUN
ejpam-4941	43	14	,	,	PUNCT
ejpam-4941	43	15	reported	report	VERB
ejpam-4941	43	16	in	in	ADP
ejpam-4941	43	17	his	his	PRON
ejpam-4941	43	18	lecture	lecture	NOUN
ejpam-4941	44	1	[	[	X
ejpam-4941	44	2	16	16	NUM
ejpam-4941	44	3	]	]	PUNCT
ejpam-4941	44	4	delivered	deliver	VERB
ejpam-4941	44	5	to	to	ADP
ejpam-4941	44	6	the	the	DET
ejpam-4941	44	7	faraday	faraday	PROPN
ejpam-4941	44	8	society	society	NOUN
ejpam-4941	44	9	in	in	ADP
ejpam-4941	44	10	1929	1929	NUM
ejpam-4941	44	11	,	,	PUNCT
ejpam-4941	44	12	that	that	SCONJ
ejpam-4941	44	13	there	there	PRON
ejpam-4941	44	14	must	must	AUX
ejpam-4941	44	15	be	be	AUX
ejpam-4941	44	16	a	a	DET
ejpam-4941	44	17	relation	relation	NOUN
ejpam-4941	44	18	between	between	ADP
ejpam-4941	44	19	the	the	DET
ejpam-4941	44	20	chemical	chemical	NOUN
ejpam-4941	44	21	composition	composition	NOUN
ejpam-4941	44	22	of	of	ADP
ejpam-4941	44	23	crystalline	crystalline	ADJ
ejpam-4941	44	24	substance	substance	NOUN
ejpam-4941	44	25	and	and	CCONJ
ejpam-4941	44	26	the	the	DET
ejpam-4941	44	27	crystal	crystal	NOUN
ejpam-4941	44	28	geometrical	geometrical	ADJ
ejpam-4941	44	29	structure	structure	NOUN
ejpam-4941	44	30	.	.	PUNCT
ejpam-4941	45	1	w.a	w.a	PROPN
ejpam-4941	45	2	.	.	PROPN
ejpam-4941	45	3	wooster	wooster	PROPN
ejpam-4941	45	4	also	also	ADV
ejpam-4941	45	5	reported	report	VERB
ejpam-4941	45	6	in	in	ADP
ejpam-4941	45	7	1953	1953	NUM
ejpam-4941	45	8	in	in	ADP
ejpam-4941	45	9	[	[	X
ejpam-4941	45	10	53	53	NUM
ejpam-4941	45	11	]	]	PUNCT
ejpam-4941	45	12	that	that	SCONJ
ejpam-4941	45	13	there	there	PRON
ejpam-4941	45	14	is	be	VERB
ejpam-4941	45	15	closer	close	ADJ
ejpam-4941	45	16	relation	relation	NOUN
ejpam-4941	45	17	between	between	ADP
ejpam-4941	45	18	magnetic	magnetic	ADJ
ejpam-4941	45	19	measurements	measurement	NOUN
ejpam-4941	45	20	and	and	CCONJ
ejpam-4941	45	21	the	the	DET
ejpam-4941	45	22	arrangement	arrangement	NOUN
ejpam-4941	45	23	of	of	ADP
ejpam-4941	45	24	atoms	atom	NOUN
ejpam-4941	45	25	in	in	ADP
ejpam-4941	45	26	a	a	DET
ejpam-4941	45	27	crystal	crystal	NOUN
ejpam-4941	45	28	.	.	PUNCT
ejpam-4941	46	1	in	in	ADP
ejpam-4941	46	2	1986	1986	NUM
ejpam-4941	46	3	,	,	PUNCT
ejpam-4941	46	4	per	per	ADP
ejpam-4941	46	5	bak	bak	NOUN
ejpam-4941	46	6	asked	ask	VERB
ejpam-4941	46	7	about	about	ADP
ejpam-4941	46	8	the	the	DET
ejpam-4941	46	9	arrangements	arrangement	NOUN
ejpam-4941	46	10	of	of	ADP
ejpam-4941	46	11	atoms	atom	NOUN
ejpam-4941	46	12	in	in	ADP
ejpam-4941	46	13	crystals	crystal	NOUN
ejpam-4941	46	14	that	that	PRON
ejpam-4941	46	15	are	be	AUX
ejpam-4941	46	16	characterized	characterize	VERB
ejpam-4941	46	17	by	by	ADP
ejpam-4941	46	18	an	an	DET
ejpam-4941	46	19	icosahedral	icosahedral	ADJ
ejpam-4941	46	20	symmetry	symmetry	NOUN
ejpam-4941	46	21	,	,	PUNCT
ejpam-4941	46	22	but	but	CCONJ
ejpam-4941	46	23	he	he	PRON
ejpam-4941	46	24	concluded	conclude	VERB
ejpam-4941	46	25	in	in	ADP
ejpam-4941	46	26	[	[	X
ejpam-4941	46	27	6	6	NUM
ejpam-4941	46	28	]	]	PUNCT
ejpam-4941	46	29	that	that	SCONJ
ejpam-4941	46	30	no	no	DET
ejpam-4941	46	31	mathematical	mathematical	ADJ
ejpam-4941	46	32	model	model	NOUN
ejpam-4941	46	33	could	could	AUX
ejpam-4941	46	34	possibly	possibly	ADV
ejpam-4941	46	35	help	help	VERB
ejpam-4941	46	36	in	in	ADP
ejpam-4941	46	37	describing	describe	VERB
ejpam-4941	46	38	the	the	DET
ejpam-4941	46	39	structures	structure	NOUN
ejpam-4941	46	40	of	of	ADP
ejpam-4941	46	41	such	such	ADJ
ejpam-4941	46	42	crystals	crystal	NOUN
ejpam-4941	46	43	.	.	PUNCT
ejpam-4941	47	1	in	in	ADP
ejpam-4941	47	2	the	the	DET
ejpam-4941	47	3	absence	absence	NOUN
ejpam-4941	47	4	of	of	ADP
ejpam-4941	47	5	convincing	convincing	ADJ
ejpam-4941	47	6	mathematical	mathematical	ADJ
ejpam-4941	47	7	methods	method	NOUN
ejpam-4941	47	8	to	to	PART
ejpam-4941	47	9	deal	deal	VERB
ejpam-4941	47	10	with	with	ADP
ejpam-4941	47	11	this	this	DET
ejpam-4941	47	12	problem	problem	NOUN
ejpam-4941	47	13	,	,	PUNCT
ejpam-4941	47	14	and	and	CCONJ
ejpam-4941	47	15	since	since	SCONJ
ejpam-4941	47	16	s.	s.	PROPN
ejpam-4941	47	17	abdelalim	abdelalim	PROPN
ejpam-4941	47	18	,	,	PUNCT
ejpam-4941	47	19	i.	i.	PROPN
ejpam-4941	47	20	elmouki	elmouki	PROPN
ejpam-4941	47	21	/	/	SYM
ejpam-4941	47	22	eur	eur	PROPN
ejpam-4941	47	23	.	.	PUNCT
ejpam-4941	48	1	j.	j.	PROPN
ejpam-4941	48	2	pure	pure	PROPN
ejpam-4941	48	3	appl	appl	PROPN
ejpam-4941	48	4	.	.	PROPN
ejpam-4941	48	5	math	math	PROPN
ejpam-4941	48	6	,	,	PUNCT
ejpam-4941	48	7	16	16	NUM
ejpam-4941	48	8	(	(	PUNCT
ejpam-4941	48	9	4	4	NUM
ejpam-4941	48	10	)	)	PUNCT
ejpam-4941	48	11	(	(	PUNCT
ejpam-4941	48	12	2023	2023	NUM
ejpam-4941	48	13	)	)	PUNCT
ejpam-4941	48	14	,	,	PUNCT
ejpam-4941	48	15	2662	2662	NUM
ejpam-4941	48	16	-	-	SYM
ejpam-4941	48	17	2692	2692	NUM
ejpam-4941	48	18	2665	2665	NUM
ejpam-4941	48	19	the	the	DET
ejpam-4941	48	20	determination	determination	NOUN
ejpam-4941	48	21	of	of	ADP
ejpam-4941	48	22	a	a	DET
ejpam-4941	48	23	motif	motif	NOUN
ejpam-4941	48	24	is	be	AUX
ejpam-4941	48	25	very	very	ADV
ejpam-4941	48	26	helpful	helpful	ADJ
ejpam-4941	48	27	to	to	ADP
ejpam-4941	48	28	researchers	researcher	NOUN
ejpam-4941	48	29	who	who	PRON
ejpam-4941	48	30	are	be	AUX
ejpam-4941	48	31	interested	interested	ADJ
ejpam-4941	48	32	to	to	PART
ejpam-4941	48	33	know	know	VERB
ejpam-4941	48	34	more	more	ADJ
ejpam-4941	48	35	about	about	ADP
ejpam-4941	48	36	crystals	crystal	NOUN
ejpam-4941	48	37	through	through	ADP
ejpam-4941	48	38	their	their	PRON
ejpam-4941	48	39	geometrical	geometrical	ADJ
ejpam-4941	48	40	shapes	shape	NOUN
ejpam-4941	48	41	,	,	PUNCT
ejpam-4941	48	42	crystallographers	crystallographer	NOUN
ejpam-4941	48	43	suggest	suggest	VERB
ejpam-4941	48	44	some	some	DET
ejpam-4941	48	45	observational	observational	ADJ
ejpam-4941	48	46	rules	rule	NOUN
ejpam-4941	48	47	.	.	PUNCT
ejpam-4941	49	1	for	for	ADP
ejpam-4941	49	2	instance	instance	NOUN
ejpam-4941	49	3	,	,	PUNCT
ejpam-4941	49	4	frank	frank	PROPN
ejpam-4941	49	5	hoffman	hoffman	PROPN
ejpam-4941	49	6	in	in	ADP
ejpam-4941	49	7	[	[	X
ejpam-4941	49	8	22	22	NUM
ejpam-4941	49	9	]	]	PUNCT
ejpam-4941	49	10	,	,	PUNCT
ejpam-4941	49	11	saw	see	VERB
ejpam-4941	49	12	that	that	SCONJ
ejpam-4941	49	13	in	in	ADP
ejpam-4941	49	14	order	order	NOUN
ejpam-4941	49	15	to	to	PART
ejpam-4941	49	16	find	find	VERB
ejpam-4941	49	17	the	the	DET
ejpam-4941	49	18	motif	motif	NOUN
ejpam-4941	49	19	from	from	ADP
ejpam-4941	49	20	which	which	PRON
ejpam-4941	49	21	we	we	PRON
ejpam-4941	49	22	could	could	AUX
ejpam-4941	49	23	generate	generate	VERB
ejpam-4941	49	24	the	the	DET
ejpam-4941	49	25	whole	whole	ADJ
ejpam-4941	49	26	crystal	crystal	NOUN
ejpam-4941	49	27	lattice	lattice	NOUN
ejpam-4941	49	28	,	,	PUNCT
ejpam-4941	49	29	one	one	PRON
ejpam-4941	49	30	could	could	AUX
ejpam-4941	49	31	observe	observe	VERB
ejpam-4941	49	32	,	,	PUNCT
ejpam-4941	49	33	relatively	relatively	ADV
ejpam-4941	49	34	to	to	ADP
ejpam-4941	49	35	the	the	DET
ejpam-4941	49	36	special	special	ADJ
ejpam-4941	49	37	case	case	NOUN
ejpam-4941	49	38	that	that	SCONJ
ejpam-4941	49	39	we	we	PRON
ejpam-4941	49	40	will	will	AUX
ejpam-4941	49	41	treat	treat	VERB
ejpam-4941	49	42	in	in	ADP
ejpam-4941	49	43	this	this	DET
ejpam-4941	49	44	paper	paper	NOUN
ejpam-4941	49	45	,	,	PUNCT
ejpam-4941	49	46	that	that	SCONJ
ejpam-4941	49	47	the	the	DET
ejpam-4941	49	48	sought	seek	VERB
ejpam-4941	49	49	unit	unit	NOUN
ejpam-4941	49	50	cell	cell	NOUN
ejpam-4941	49	51	basis	basis	NOUN
ejpam-4941	49	52	vectors	vector	NOUN
ejpam-4941	49	53	,	,	PUNCT
ejpam-4941	49	54	should	should	AUX
ejpam-4941	49	55	satisfy	satisfy	VERB
ejpam-4941	49	56	the	the	DET
ejpam-4941	49	57	following	follow	VERB
ejpam-4941	49	58	conditions	condition	NOUN
ejpam-4941	49	59	,	,	PUNCT
ejpam-4941	49	60	•	•	NUM
ejpam-4941	49	61	be	be	AUX
ejpam-4941	49	62	short	short	ADJ
ejpam-4941	49	63	as	as	ADV
ejpam-4941	49	64	much	much	ADV
ejpam-4941	49	65	as	as	ADP
ejpam-4941	49	66	possible	possible	ADJ
ejpam-4941	49	67	,	,	PUNCT
ejpam-4941	49	68	•	•	ADV
ejpam-4941	49	69	be	be	AUX
ejpam-4941	49	70	perpendicular	perpendicular	ADJ
ejpam-4941	49	71	to	to	ADP
ejpam-4941	49	72	the	the	DET
ejpam-4941	49	73	symmetry	symmetry	NOUN
ejpam-4941	49	74	plane	plane	NOUN
ejpam-4941	49	75	,	,	PUNCT
ejpam-4941	49	76	•	•	ADV
ejpam-4941	49	77	be	be	AUX
ejpam-4941	49	78	orthogonal	orthogonal	ADJ
ejpam-4941	49	79	.	.	PUNCT
ejpam-4941	50	1	we	we	PRON
ejpam-4941	50	2	retake	retake	VERB
ejpam-4941	50	3	two	two	NUM
ejpam-4941	50	4	examples	example	NOUN
ejpam-4941	50	5	from	from	ADP
ejpam-4941	50	6	the	the	DET
ejpam-4941	50	7	above	above	ADV
ejpam-4941	50	8	-	-	PUNCT
ejpam-4941	50	9	mentioned	mention	VERB
ejpam-4941	50	10	reference	reference	NOUN
ejpam-4941	50	11	but	but	CCONJ
ejpam-4941	50	12	with	with	ADP
ejpam-4941	50	13	application	application	NOUN
ejpam-4941	50	14	now	now	ADV
ejpam-4941	50	15	to	to	ADP
ejpam-4941	50	16	the	the	DET
ejpam-4941	50	17	crystals	crystal	NOUN
ejpam-4941	50	18	considered	consider	VERB
ejpam-4941	50	19	in	in	ADP
ejpam-4941	50	20	figure	figure	NOUN
ejpam-4941	50	21	1	1	NUM
ejpam-4941	50	22	.	.	PUNCT
ejpam-4941	51	1	in	in	ADP
ejpam-4941	51	2	the	the	DET
ejpam-4941	51	3	simplest	simple	ADJ
ejpam-4941	51	4	case	case	NOUN
ejpam-4941	51	5	(	(	PUNCT
ejpam-4941	51	6	a	a	X
ejpam-4941	51	7	)	)	PUNCT
ejpam-4941	51	8	of	of	ADP
ejpam-4941	51	9	figure	figure	NOUN
ejpam-4941	51	10	3	3	NUM
ejpam-4941	51	11	,	,	PUNCT
ejpam-4941	51	12	namely	namely	ADV
ejpam-4941	51	13	the	the	DET
ejpam-4941	51	14	one	one	NOUN
ejpam-4941	51	15	representing	represent	VERB
ejpam-4941	51	16	the	the	DET
ejpam-4941	51	17	halite	halite	ADJ
ejpam-4941	51	18	crystal	crystal	NOUN
ejpam-4941	51	19	nacl	nacl	NOUN
ejpam-4941	51	20	,	,	PUNCT
ejpam-4941	51	21	we	we	PRON
ejpam-4941	51	22	can	can	AUX
ejpam-4941	51	23	deduce	deduce	VERB
ejpam-4941	51	24	that	that	SCONJ
ejpam-4941	51	25	the	the	DET
ejpam-4941	51	26	red	red	ADJ
ejpam-4941	51	27	and	and	CCONJ
ejpam-4941	51	28	black	black	ADJ
ejpam-4941	51	29	unit	unit	NOUN
ejpam-4941	51	30	cells	cell	NOUN
ejpam-4941	51	31	are	be	AUX
ejpam-4941	51	32	equivalent	equivalent	ADJ
ejpam-4941	51	33	and	and	CCONJ
ejpam-4941	51	34	preferred	prefer	VERB
ejpam-4941	51	35	since	since	SCONJ
ejpam-4941	51	36	they	they	PRON
ejpam-4941	51	37	both	both	PRON
ejpam-4941	51	38	satisfy	satisfy	VERB
ejpam-4941	51	39	the	the	DET
ejpam-4941	51	40	above	above	ADJ
ejpam-4941	51	41	conditions	condition	NOUN
ejpam-4941	51	42	.	.	PUNCT
ejpam-4941	52	1	as	as	ADP
ejpam-4941	52	2	an	an	DET
ejpam-4941	52	3	additional	additional	ADJ
ejpam-4941	52	4	remark	remark	NOUN
ejpam-4941	52	5	,	,	PUNCT
ejpam-4941	52	6	one	one	PRON
ejpam-4941	52	7	could	could	AUX
ejpam-4941	52	8	consider	consider	VERB
ejpam-4941	52	9	a	a	DET
ejpam-4941	52	10	cell	cell	NOUN
ejpam-4941	52	11	that	that	PRON
ejpam-4941	52	12	is	be	AUX
ejpam-4941	52	13	not	not	PART
ejpam-4941	52	14	necessarily	necessarily	ADV
ejpam-4941	52	15	made	make	VERB
ejpam-4941	52	16	by	by	ADP
ejpam-4941	52	17	the	the	DET
ejpam-4941	52	18	bravais	bravais	PROPN
ejpam-4941	52	19	crystal	crystal	NOUN
ejpam-4941	52	20	points	point	NOUN
ejpam-4941	52	21	as	as	SCONJ
ejpam-4941	52	22	described	describe	VERB
ejpam-4941	52	23	in	in	ADP
ejpam-4941	52	24	case	case	NOUN
ejpam-4941	52	25	(	(	PUNCT
ejpam-4941	52	26	a	a	NOUN
ejpam-4941	52	27	)	)	PUNCT
ejpam-4941	52	28	of	of	ADP
ejpam-4941	52	29	figure	figure	NOUN
ejpam-4941	52	30	2	2	NUM
ejpam-4941	52	31	,	,	PUNCT
ejpam-4941	52	32	and	and	CCONJ
ejpam-4941	52	33	which	which	PRON
ejpam-4941	52	34	concerns	concern	VERB
ejpam-4941	52	35	the	the	DET
ejpam-4941	52	36	example	example	NOUN
ejpam-4941	52	37	of	of	ADP
ejpam-4941	52	38	the	the	DET
ejpam-4941	52	39	red	red	ADJ
ejpam-4941	52	40	cell	cell	NOUN
ejpam-4941	52	41	that	that	PRON
ejpam-4941	52	42	has	have	VERB
ejpam-4941	52	43	only	only	ADV
ejpam-4941	52	44	one	one	NUM
ejpam-4941	52	45	lattice	lattice	NOUN
ejpam-4941	52	46	point	point	NOUN
ejpam-4941	52	47	in	in	ADP
ejpam-4941	52	48	its	its	PRON
ejpam-4941	52	49	center	center	NOUN
ejpam-4941	52	50	.	.	PUNCT
ejpam-4941	53	1	figure	figure	VERB
ejpam-4941	53	2	3	3	NUM
ejpam-4941	53	3	:	:	PUNCT
ejpam-4941	53	4	(	(	PUNCT
ejpam-4941	53	5	a	a	X
ejpam-4941	53	6	)	)	PUNCT
ejpam-4941	53	7	choice	choice	NOUN
ejpam-4941	53	8	of	of	ADP
ejpam-4941	53	9	red	red	ADJ
ejpam-4941	53	10	and	and	CCONJ
ejpam-4941	53	11	black	black	ADJ
ejpam-4941	53	12	cells	cell	NOUN
ejpam-4941	53	13	as	as	ADP
ejpam-4941	53	14	the	the	DET
ejpam-4941	53	15	generating	generating	PROPN
ejpam-4941	53	16	halite	halite	PROPN
ejpam-4941	53	17	crystal	crystal	PROPN
ejpam-4941	53	18	unit	unit	NOUN
ejpam-4941	53	19	cells	cell	NOUN
ejpam-4941	53	20	.	.	PUNCT
ejpam-4941	54	1	(	(	PUNCT
ejpam-4941	54	2	b	b	X
ejpam-4941	54	3	)	)	PUNCT
ejpam-4941	54	4	choice	choice	NOUN
ejpam-4941	54	5	of	of	ADP
ejpam-4941	54	6	green	green	ADJ
ejpam-4941	54	7	cell	cell	NOUN
ejpam-4941	54	8	as	as	ADP
ejpam-4941	54	9	the	the	DET
ejpam-4941	54	10	generating	generating	ADJ
ejpam-4941	54	11	fluorite	fluorite	NOUN
ejpam-4941	54	12	crystal	crystal	PROPN
ejpam-4941	54	13	unit	unit	NOUN
ejpam-4941	54	14	cells	cell	NOUN
ejpam-4941	54	15	.	.	PUNCT
ejpam-4941	55	1	in	in	ADP
ejpam-4941	55	2	a	a	DET
ejpam-4941	55	3	more	more	ADV
ejpam-4941	55	4	interesting	interesting	ADJ
ejpam-4941	55	5	example	example	NOUN
ejpam-4941	55	6	,	,	PUNCT
ejpam-4941	55	7	if	if	SCONJ
ejpam-4941	55	8	we	we	PRON
ejpam-4941	55	9	consider	consider	VERB
ejpam-4941	55	10	now	now	ADV
ejpam-4941	55	11	the	the	DET
ejpam-4941	55	12	other	other	ADJ
ejpam-4941	55	13	case	case	NOUN
ejpam-4941	55	14	(	(	PUNCT
ejpam-4941	55	15	b	b	NOUN
ejpam-4941	55	16	)	)	PUNCT
ejpam-4941	55	17	of	of	ADP
ejpam-4941	55	18	figure	figure	NOUN
ejpam-4941	55	19	3	3	NUM
ejpam-4941	55	20	,	,	PUNCT
ejpam-4941	55	21	namely	namely	ADV
ejpam-4941	55	22	representing	represent	VERB
ejpam-4941	55	23	the	the	DET
ejpam-4941	55	24	fluorite	fluorite	NOUN
ejpam-4941	55	25	crystal	crystal	NOUN
ejpam-4941	55	26	caf2	caf2	NOUN
ejpam-4941	55	27	and	and	CCONJ
ejpam-4941	55	28	where	where	SCONJ
ejpam-4941	55	29	we	we	PRON
ejpam-4941	55	30	start	start	VERB
ejpam-4941	55	31	from	from	ADP
ejpam-4941	55	32	the	the	DET
ejpam-4941	55	33	red	red	PROPN
ejpam-4941	55	34	primitive	primitive	ADJ
ejpam-4941	55	35	elementary	elementary	ADJ
ejpam-4941	55	36	cell	cell	NOUN
ejpam-4941	55	37	[	[	X
ejpam-4941	55	38	28	28	NUM
ejpam-4941	55	39	]	]	PUNCT
ejpam-4941	55	40	and	and	CCONJ
ejpam-4941	55	41	which	which	PRON
ejpam-4941	55	42	is	be	AUX
ejpam-4941	55	43	a	a	DET
ejpam-4941	55	44	name	name	NOUN
ejpam-4941	55	45	given	give	VERB
ejpam-4941	55	46	to	to	ADP
ejpam-4941	55	47	the	the	DET
ejpam-4941	55	48	smallest	small	ADJ
ejpam-4941	55	49	given	give	VERB
ejpam-4941	55	50	cell	cell	NOUN
ejpam-4941	55	51	while	while	SCONJ
ejpam-4941	55	52	its	its	PRON
ejpam-4941	55	53	vectors	vector	NOUN
ejpam-4941	55	54	are	be	AUX
ejpam-4941	55	55	called	call	VERB
ejpam-4941	55	56	primitive	primitive	ADJ
ejpam-4941	55	57	translation	translation	NOUN
ejpam-4941	55	58	vectors	vector	NOUN
ejpam-4941	55	59	,	,	PUNCT
ejpam-4941	55	60	then	then	ADV
ejpam-4941	55	61	,	,	PUNCT
ejpam-4941	55	62	we	we	PRON
ejpam-4941	55	63	will	will	AUX
ejpam-4941	55	64	choose	choose	VERB
ejpam-4941	55	65	the	the	DET
ejpam-4941	55	66	centered	center	VERB
ejpam-4941	55	67	green	green	ADJ
ejpam-4941	55	68	unit	unit	NOUN
ejpam-4941	55	69	cell	cell	NOUN
ejpam-4941	55	70	.	.	PUNCT
ejpam-4941	56	1	as	as	ADP
ejpam-4941	56	2	an	an	DET
ejpam-4941	56	3	additional	additional	ADJ
ejpam-4941	56	4	remark	remark	NOUN
ejpam-4941	56	5	,	,	PUNCT
ejpam-4941	56	6	the	the	DET
ejpam-4941	56	7	blue	blue	ADJ
ejpam-4941	56	8	cell	cell	NOUN
ejpam-4941	56	9	are	be	AUX
ejpam-4941	56	10	the	the	DET
ejpam-4941	56	11	intermediary	intermediary	ADJ
ejpam-4941	56	12	cell	cell	NOUN
ejpam-4941	56	13	obtained	obtain	VERB
ejpam-4941	56	14	by	by	ADP
ejpam-4941	56	15	the	the	DET
ejpam-4941	56	16	transformation	transformation	NOUN
ejpam-4941	56	17	of	of	ADP
ejpam-4941	56	18	the	the	DET
ejpam-4941	56	19	red	red	ADJ
ejpam-4941	56	20	cell	cell	NOUN
ejpam-4941	56	21	and	and	CCONJ
ejpam-4941	56	22	then	then	ADV
ejpam-4941	56	23	by	by	ADP
ejpam-4941	56	24	another	another	DET
ejpam-4941	56	25	transformation	transformation	NOUN
ejpam-4941	56	26	,	,	PUNCT
ejpam-4941	56	27	we	we	PRON
ejpam-4941	56	28	obtain	obtain	VERB
ejpam-4941	56	29	the	the	DET
ejpam-4941	56	30	green	green	ADJ
ejpam-4941	56	31	cell	cell	NOUN
ejpam-4941	56	32	.	.	PUNCT
ejpam-4941	57	1	we	we	PRON
ejpam-4941	57	2	will	will	AUX
ejpam-4941	57	3	go	go	VERB
ejpam-4941	57	4	back	back	ADV
ejpam-4941	57	5	to	to	ADP
ejpam-4941	57	6	this	this	DET
ejpam-4941	57	7	point	point	NOUN
ejpam-4941	57	8	in	in	ADP
ejpam-4941	57	9	the	the	DET
ejpam-4941	57	10	next	next	ADJ
ejpam-4941	57	11	section	section	NOUN
ejpam-4941	57	12	with	with	ADP
ejpam-4941	57	13	technical	technical	ADJ
ejpam-4941	57	14	explanation	explanation	NOUN
ejpam-4941	57	15	that	that	PRON
ejpam-4941	57	16	is	be	AUX
ejpam-4941	57	17	more	more	ADV
ejpam-4941	57	18	relevant	relevant	ADJ
ejpam-4941	57	19	to	to	ADP
ejpam-4941	57	20	our	our	PRON
ejpam-4941	57	21	work	work	NOUN
ejpam-4941	57	22	.	.	PUNCT
ejpam-4941	58	1	s.	s.	PROPN
ejpam-4941	58	2	abdelalim	abdelalim	PROPN
ejpam-4941	58	3	,	,	PUNCT
ejpam-4941	58	4	i.	i.	PROPN
ejpam-4941	58	5	elmouki	elmouki	PROPN
ejpam-4941	58	6	/	/	SYM
ejpam-4941	58	7	eur	eur	PROPN
ejpam-4941	58	8	.	.	PUNCT
ejpam-4941	59	1	j.	j.	PROPN
ejpam-4941	59	2	pure	pure	PROPN
ejpam-4941	59	3	appl	appl	PROPN
ejpam-4941	59	4	.	.	PROPN
ejpam-4941	59	5	math	math	PROPN
ejpam-4941	59	6	,	,	PUNCT
ejpam-4941	59	7	16	16	NUM
ejpam-4941	59	8	(	(	PUNCT
ejpam-4941	59	9	4	4	NUM
ejpam-4941	59	10	)	)	PUNCT
ejpam-4941	59	11	(	(	PUNCT
ejpam-4941	59	12	2023	2023	NUM
ejpam-4941	59	13	)	)	PUNCT
ejpam-4941	59	14	,	,	PUNCT
ejpam-4941	59	15	2662	2662	NUM
ejpam-4941	59	16	-	-	SYM
ejpam-4941	59	17	2692	2692	NUM
ejpam-4941	59	18	2666	2666	NUM
ejpam-4941	59	19	in	in	ADP
ejpam-4941	59	20	front	front	NOUN
ejpam-4941	59	21	of	of	ADP
ejpam-4941	59	22	such	such	ADJ
ejpam-4941	59	23	recommendations	recommendation	NOUN
ejpam-4941	59	24	,	,	PUNCT
ejpam-4941	59	25	one	one	PRON
ejpam-4941	59	26	would	would	AUX
ejpam-4941	59	27	also	also	ADV
ejpam-4941	59	28	wonder	wonder	VERB
ejpam-4941	59	29	whether	whether	SCONJ
ejpam-4941	59	30	there	there	PRON
ejpam-4941	59	31	is	be	VERB
ejpam-4941	59	32	a	a	DET
ejpam-4941	59	33	mathematical	mathematical	ADJ
ejpam-4941	59	34	method	method	NOUN
ejpam-4941	59	35	or	or	CCONJ
ejpam-4941	59	36	not	not	PART
ejpam-4941	59	37	and	and	CCONJ
ejpam-4941	59	38	that	that	PRON
ejpam-4941	59	39	could	could	AUX
ejpam-4941	59	40	serve	serve	VERB
ejpam-4941	59	41	in	in	ADP
ejpam-4941	59	42	determining	determine	VERB
ejpam-4941	59	43	that	that	SCONJ
ejpam-4941	59	44	crystal	crystal	NOUN
ejpam-4941	59	45	reduced	reduce	VERB
ejpam-4941	59	46	basis	basis	NOUN
ejpam-4941	59	47	.	.	PUNCT
ejpam-4941	60	1	before	before	ADP
ejpam-4941	60	2	going	go	VERB
ejpam-4941	60	3	further	far	ADV
ejpam-4941	60	4	in	in	ADP
ejpam-4941	60	5	our	our	PRON
ejpam-4941	60	6	study	study	NOUN
ejpam-4941	60	7	,	,	PUNCT
ejpam-4941	60	8	let	let	VERB
ejpam-4941	60	9	us	we	PRON
ejpam-4941	60	10	give	give	VERB
ejpam-4941	60	11	more	more	ADJ
ejpam-4941	60	12	technical	technical	ADJ
ejpam-4941	60	13	information	information	NOUN
ejpam-4941	60	14	about	about	ADP
ejpam-4941	60	15	the	the	DET
ejpam-4941	60	16	story	story	NOUN
ejpam-4941	60	17	of	of	ADP
ejpam-4941	60	18	such	such	ADJ
ejpam-4941	60	19	open	open	ADJ
ejpam-4941	60	20	question	question	NOUN
ejpam-4941	60	21	.	.	PUNCT
ejpam-4941	61	1	1.2.2	1.2.2	X
ejpam-4941	61	2	.	.	PUNCT
ejpam-4941	62	1	literature	literature	NOUN
ejpam-4941	62	2	on	on	ADP
ejpam-4941	62	3	the	the	DET
ejpam-4941	62	4	problem	problem	NOUN
ejpam-4941	62	5	and	and	CCONJ
ejpam-4941	62	6	goal	goal	NOUN
ejpam-4941	62	7	in	in	ADP
ejpam-4941	62	8	1970	1970	NUM
ejpam-4941	62	9	,	,	PUNCT
ejpam-4941	62	10	mighell	mighell	NOUN
ejpam-4941	62	11	and	and	CCONJ
ejpam-4941	62	12	karen	karen	PROPN
ejpam-4941	62	13	,	,	PUNCT
ejpam-4941	62	14	were	be	AUX
ejpam-4941	62	15	among	among	ADP
ejpam-4941	62	16	the	the	DET
ejpam-4941	62	17	first	first	ADJ
ejpam-4941	62	18	authors	author	NOUN
ejpam-4941	62	19	who	who	PRON
ejpam-4941	62	20	wondered	wonder	VERB
ejpam-4941	62	21	about	about	ADP
ejpam-4941	62	22	a	a	DET
ejpam-4941	62	23	method	method	NOUN
ejpam-4941	62	24	in	in	ADP
ejpam-4941	62	25	order	order	NOUN
ejpam-4941	62	26	to	to	PART
ejpam-4941	62	27	find	find	VERB
ejpam-4941	62	28	the	the	DET
ejpam-4941	62	29	crystal	crystal	NOUN
ejpam-4941	62	30	reduced	reduce	VERB
ejpam-4941	62	31	cell	cell	NOUN
ejpam-4941	62	32	[	[	X
ejpam-4941	62	33	45	45	NUM
ejpam-4941	62	34	]	]	PUNCT
ejpam-4941	62	35	,	,	PUNCT
ejpam-4941	62	36	and	and	CCONJ
ejpam-4941	62	37	they	they	PRON
ejpam-4941	62	38	explained	explain	VERB
ejpam-4941	62	39	in	in	ADP
ejpam-4941	62	40	their	their	PRON
ejpam-4941	62	41	report	report	NOUN
ejpam-4941	62	42	in	in	ADP
ejpam-4941	62	43	[	[	X
ejpam-4941	62	44	27	27	NUM
ejpam-4941	62	45	]	]	PUNCT
ejpam-4941	62	46	,	,	PUNCT
ejpam-4941	62	47	that	that	SCONJ
ejpam-4941	62	48	the	the	DET
ejpam-4941	62	49	first	first	ADJ
ejpam-4941	62	50	step	step	NOUN
ejpam-4941	62	51	is	be	AUX
ejpam-4941	62	52	to	to	PART
ejpam-4941	62	53	start	start	VERB
ejpam-4941	62	54	with	with	ADP
ejpam-4941	62	55	the	the	DET
ejpam-4941	62	56	smallest	small	ADJ
ejpam-4941	62	57	possible	possible	ADJ
ejpam-4941	62	58	cell	cell	NOUN
ejpam-4941	62	59	and	and	CCONJ
ejpam-4941	62	60	that	that	PRON
ejpam-4941	62	61	is	be	AUX
ejpam-4941	62	62	called	call	VERB
ejpam-4941	62	63	a	a	DET
ejpam-4941	62	64	primitive	primitive	ADJ
ejpam-4941	62	65	cell	cell	NOUN
ejpam-4941	62	66	,	,	PUNCT
ejpam-4941	62	67	while	while	SCONJ
ejpam-4941	62	68	the	the	DET
ejpam-4941	62	69	problem	problem	NOUN
ejpam-4941	62	70	was	be	AUX
ejpam-4941	62	71	remaining	remain	VERB
ejpam-4941	62	72	to	to	PART
ejpam-4941	62	73	show	show	VERB
ejpam-4941	62	74	which	which	DET
ejpam-4941	62	75	one	one	NUM
ejpam-4941	62	76	of	of	ADP
ejpam-4941	62	77	these	these	DET
ejpam-4941	62	78	many	many	ADJ
ejpam-4941	62	79	possible	possible	ADJ
ejpam-4941	62	80	cells	cell	NOUN
ejpam-4941	62	81	should	should	AUX
ejpam-4941	62	82	be	be	AUX
ejpam-4941	62	83	selected	select	VERB
ejpam-4941	62	84	.	.	PUNCT
ejpam-4941	63	1	in	in	ADP
ejpam-4941	63	2	their	their	PRON
ejpam-4941	63	3	opinion	opinion	NOUN
ejpam-4941	63	4	,	,	PUNCT
ejpam-4941	63	5	they	they	PRON
ejpam-4941	63	6	saw	see	VERB
ejpam-4941	63	7	that	that	DET
ejpam-4941	63	8	niggli	niggli	NOUN
ejpam-4941	63	9	[	[	X
ejpam-4941	63	10	41	41	NUM
ejpam-4941	63	11	]	]	PUNCT
ejpam-4941	63	12	described	describe	VERB
ejpam-4941	63	13	earlier	early	ADV
ejpam-4941	63	14	in	in	ADP
ejpam-4941	63	15	1929	1929	NUM
ejpam-4941	63	16	,	,	PUNCT
ejpam-4941	63	17	what	what	PRON
ejpam-4941	63	18	was	be	AUX
ejpam-4941	63	19	defined	define	VERB
ejpam-4941	63	20	as	as	ADP
ejpam-4941	63	21	a	a	DET
ejpam-4941	63	22	unique	unique	ADJ
ejpam-4941	63	23	reduced	reduce	VERB
ejpam-4941	63	24	cell	cell	NOUN
ejpam-4941	63	25	,	,	PUNCT
ejpam-4941	63	26	but	but	CCONJ
ejpam-4941	63	27	unfortunately	unfortunately	ADV
ejpam-4941	63	28	,	,	PUNCT
ejpam-4941	63	29	no	no	DET
ejpam-4941	63	30	algebraic	algebraic	ADJ
ejpam-4941	63	31	procedure	procedure	NOUN
ejpam-4941	63	32	was	be	AUX
ejpam-4941	63	33	devised	devise	VERB
ejpam-4941	63	34	for	for	ADP
ejpam-4941	63	35	calculating	calculate	VERB
ejpam-4941	63	36	it	it	PRON
ejpam-4941	63	37	if	if	SCONJ
ejpam-4941	63	38	one	one	PRON
ejpam-4941	63	39	starts	start	VERB
ejpam-4941	63	40	from	from	ADP
ejpam-4941	63	41	any	any	DET
ejpam-4941	63	42	cell	cell	NOUN
ejpam-4941	63	43	of	of	ADP
ejpam-4941	63	44	the	the	DET
ejpam-4941	63	45	crystal	crystal	NOUN
ejpam-4941	63	46	.	.	PUNCT
ejpam-4941	64	1	let	let	VERB
ejpam-4941	64	2	us	we	PRON
ejpam-4941	64	3	retake	retake	VERB
ejpam-4941	64	4	the	the	DET
ejpam-4941	64	5	example	example	NOUN
ejpam-4941	64	6	(	(	PUNCT
ejpam-4941	64	7	b	b	NOUN
ejpam-4941	64	8	)	)	PUNCT
ejpam-4941	64	9	of	of	ADP
ejpam-4941	64	10	figure	figure	NOUN
ejpam-4941	64	11	3	3	NUM
ejpam-4941	64	12	,	,	PUNCT
ejpam-4941	64	13	and	and	CCONJ
ejpam-4941	64	14	let	let	VERB
ejpam-4941	64	15	us	we	PRON
ejpam-4941	64	16	consider	consider	VERB
ejpam-4941	64	17	in	in	ADP
ejpam-4941	64	18	figure	figure	NOUN
ejpam-4941	64	19	4	4	NUM
ejpam-4941	64	20	the	the	DET
ejpam-4941	64	21	primitive	primitive	ADJ
ejpam-4941	64	22	translation	translation	NOUN
ejpam-4941	64	23	vectors	vector	NOUN
ejpam-4941	64	24	e1	e1	VERB
ejpam-4941	64	25	and	and	CCONJ
ejpam-4941	64	26	e2	e2	PROPN
ejpam-4941	64	27	referring	refer	VERB
ejpam-4941	64	28	to	to	ADP
ejpam-4941	64	29	the	the	DET
ejpam-4941	64	30	primitive	primitive	ADJ
ejpam-4941	64	31	elementary	elementary	ADJ
ejpam-4941	64	32	red	red	ADJ
ejpam-4941	64	33	cell	cell	NOUN
ejpam-4941	64	34	,	,	PUNCT
ejpam-4941	64	35	e3	e3	NOUN
ejpam-4941	64	36	and	and	CCONJ
ejpam-4941	64	37	e4	e4	PROPN
ejpam-4941	64	38	referring	refer	VERB
ejpam-4941	64	39	to	to	ADP
ejpam-4941	64	40	the	the	DET
ejpam-4941	64	41	blue	blue	ADJ
ejpam-4941	64	42	cell	cell	NOUN
ejpam-4941	64	43	,	,	PUNCT
ejpam-4941	64	44	and	and	CCONJ
ejpam-4941	64	45	finally	finally	ADV
ejpam-4941	64	46	the	the	DET
ejpam-4941	64	47	obtained	obtain	VERB
ejpam-4941	64	48	e5	e5	PROPN
ejpam-4941	64	49	and	and	CCONJ
ejpam-4941	64	50	e6	e6	PROPN
ejpam-4941	64	51	referring	refer	VERB
ejpam-4941	64	52	to	to	ADP
ejpam-4941	64	53	the	the	DET
ejpam-4941	64	54	green	green	ADJ
ejpam-4941	64	55	unit	unit	NOUN
ejpam-4941	64	56	cell	cell	NOUN
ejpam-4941	64	57	.	.	PUNCT
ejpam-4941	65	1	figure	figure	VERB
ejpam-4941	65	2	4	4	NUM
ejpam-4941	65	3	:	:	PUNCT
ejpam-4941	65	4	the	the	DET
ejpam-4941	65	5	sums	sum	NOUN
ejpam-4941	65	6	e1	e1	PROPN
ejpam-4941	65	7	+	+	CCONJ
ejpam-4941	65	8	e2	e2	PROPN
ejpam-4941	65	9	,	,	PUNCT
ejpam-4941	65	10	e3	e3	NOUN
ejpam-4941	65	11	+	+	CCONJ
ejpam-4941	65	12	e4	e4	PROPN
ejpam-4941	65	13	and	and	CCONJ
ejpam-4941	65	14	e5	e5	PROPN
ejpam-4941	65	15	+	+	CCONJ
ejpam-4941	65	16	e6	e6	NOUN
ejpam-4941	65	17	serving	serve	VERB
ejpam-4941	65	18	to	to	PART
ejpam-4941	65	19	make	make	VERB
ejpam-4941	65	20	the	the	DET
ejpam-4941	65	21	red	red	ADJ
ejpam-4941	65	22	,	,	PUNCT
ejpam-4941	65	23	blue	blue	ADJ
ejpam-4941	65	24	and	and	CCONJ
ejpam-4941	65	25	green	green	ADJ
ejpam-4941	65	26	cells	cell	NOUN
ejpam-4941	65	27	in	in	ADP
ejpam-4941	65	28	example	example	NOUN
ejpam-4941	65	29	(	(	PUNCT
ejpam-4941	65	30	b	b	NOUN
ejpam-4941	65	31	)	)	PUNCT
ejpam-4941	65	32	of	of	ADP
ejpam-4941	65	33	figure	figure	NOUN
ejpam-4941	65	34	3	3	NUM
ejpam-4941	65	35	.	.	PUNCT
ejpam-4941	66	1	the	the	DET
ejpam-4941	66	2	transformation	transformation	NOUN
ejpam-4941	66	3	steps	step	NOUN
ejpam-4941	66	4	are	be	AUX
ejpam-4941	66	5	:	:	PUNCT
ejpam-4941	66	6	e3	e3	NOUN
ejpam-4941	66	7	=	=	SYM
ejpam-4941	66	8	e1	e1	PROPN
ejpam-4941	66	9	,	,	PUNCT
ejpam-4941	66	10	e4	e4	NOUN
ejpam-4941	66	11	=	=	PUNCT
ejpam-4941	66	12	e1	e1	PROPN
ejpam-4941	66	13	+	+	CCONJ
ejpam-4941	66	14	e2	e2	PROPN
ejpam-4941	66	15	,	,	PUNCT
ejpam-4941	66	16	e5	e5	NOUN
ejpam-4941	66	17	=	=	PUNCT
ejpam-4941	66	18	e3	e3	PROPN
ejpam-4941	66	19	+	+	X
ejpam-4941	66	20	e4	e4	PROPN
ejpam-4941	66	21	,	,	PUNCT
ejpam-4941	66	22	e6	e6	PROPN
ejpam-4941	66	23	=	=	PROPN
ejpam-4941	66	24	e4	e4	PROPN
ejpam-4941	66	25	−	−	PROPN
ejpam-4941	66	26	e3	e3	NOUN
ejpam-4941	66	27	.	.	PUNCT
ejpam-4941	67	1	if	if	SCONJ
ejpam-4941	67	2	we	we	PRON
ejpam-4941	67	3	look	look	VERB
ejpam-4941	67	4	at	at	ADP
ejpam-4941	67	5	the	the	DET
ejpam-4941	67	6	primitive	primitive	ADJ
ejpam-4941	67	7	translation	translation	NOUN
ejpam-4941	67	8	vectors	vector	NOUN
ejpam-4941	67	9	e1	e1	VERB
ejpam-4941	67	10	and	and	CCONJ
ejpam-4941	67	11	e2	e2	PROPN
ejpam-4941	67	12	in	in	ADP
ejpam-4941	67	13	figure	figure	NOUN
ejpam-4941	67	14	4	4	NUM
ejpam-4941	67	15	,	,	PUNCT
ejpam-4941	67	16	we	we	PRON
ejpam-4941	67	17	can	can	AUX
ejpam-4941	67	18	see	see	VERB
ejpam-4941	67	19	that	that	SCONJ
ejpam-4941	67	20	it	it	PRON
ejpam-4941	67	21	helps	help	VERB
ejpam-4941	67	22	to	to	PART
ejpam-4941	67	23	make	make	VERB
ejpam-4941	67	24	the	the	DET
ejpam-4941	67	25	primitive	primitive	ADJ
ejpam-4941	67	26	elementary	elementary	ADJ
ejpam-4941	67	27	red	red	ADJ
ejpam-4941	67	28	cell	cell	NOUN
ejpam-4941	67	29	in	in	ADP
ejpam-4941	67	30	example	example	NOUN
ejpam-4941	67	31	(	(	PUNCT
ejpam-4941	67	32	b	b	NOUN
ejpam-4941	67	33	)	)	PUNCT
ejpam-4941	67	34	of	of	ADP
ejpam-4941	67	35	figure	figure	NOUN
ejpam-4941	67	36	3	3	NUM
ejpam-4941	67	37	and	and	CCONJ
ejpam-4941	67	38	which	which	PRON
ejpam-4941	67	39	can	can	AUX
ejpam-4941	67	40	generate	generate	VERB
ejpam-4941	67	41	many	many	ADJ
ejpam-4941	67	42	points	point	NOUN
ejpam-4941	67	43	of	of	ADP
ejpam-4941	67	44	the	the	DET
ejpam-4941	67	45	bravais	bravais	PROPN
ejpam-4941	67	46	lattice	lattice	PROPN
ejpam-4941	67	47	,	,	PUNCT
ejpam-4941	67	48	but	but	CCONJ
ejpam-4941	67	49	unfortunately	unfortunately	ADV
ejpam-4941	67	50	,	,	PUNCT
ejpam-4941	67	51	not	not	PART
ejpam-4941	67	52	all	all	PRON
ejpam-4941	67	53	of	of	ADP
ejpam-4941	67	54	them	they	PRON
ejpam-4941	67	55	.	.	PUNCT
ejpam-4941	68	1	in	in	ADP
ejpam-4941	68	2	s.	s.	PROPN
ejpam-4941	68	3	abdelalim	abdelalim	PROPN
ejpam-4941	68	4	,	,	PUNCT
ejpam-4941	68	5	i.	i.	PROPN
ejpam-4941	68	6	elmouki	elmouki	PROPN
ejpam-4941	68	7	/	/	SYM
ejpam-4941	68	8	eur	eur	PROPN
ejpam-4941	68	9	.	.	PUNCT
ejpam-4941	69	1	j.	j.	PROPN
ejpam-4941	69	2	pure	pure	PROPN
ejpam-4941	69	3	appl	appl	PROPN
ejpam-4941	69	4	.	.	PROPN
ejpam-4941	69	5	math	math	PROPN
ejpam-4941	69	6	,	,	PUNCT
ejpam-4941	69	7	16	16	NUM
ejpam-4941	69	8	(	(	PUNCT
ejpam-4941	69	9	4	4	NUM
ejpam-4941	69	10	)	)	PUNCT
ejpam-4941	69	11	(	(	PUNCT
ejpam-4941	69	12	2023	2023	NUM
ejpam-4941	69	13	)	)	PUNCT
ejpam-4941	69	14	,	,	PUNCT
ejpam-4941	69	15	2662	2662	NUM
ejpam-4941	69	16	-	-	SYM
ejpam-4941	69	17	2692	2692	NUM
ejpam-4941	69	18	2667	2667	NUM
ejpam-4941	69	19	spite	spite	NOUN
ejpam-4941	69	20	of	of	ADP
ejpam-4941	69	21	this	this	DET
ejpam-4941	69	22	little	little	ADJ
ejpam-4941	69	23	detail	detail	NOUN
ejpam-4941	69	24	,	,	PUNCT
ejpam-4941	69	25	it	it	PRON
ejpam-4941	69	26	has	have	AUX
ejpam-4941	69	27	also	also	ADV
ejpam-4941	69	28	helped	help	VERB
ejpam-4941	69	29	us	we	PRON
ejpam-4941	69	30	to	to	PART
ejpam-4941	69	31	reach	reach	VERB
ejpam-4941	69	32	the	the	DET
ejpam-4941	69	33	vectors	vector	NOUN
ejpam-4941	69	34	e5	e5	PROPN
ejpam-4941	69	35	and	and	CCONJ
ejpam-4941	69	36	e6	e6	NOUN
ejpam-4941	69	37	by	by	ADP
ejpam-4941	69	38	simple	simple	ADJ
ejpam-4941	69	39	transformation	transformation	NOUN
ejpam-4941	69	40	as	as	SCONJ
ejpam-4941	69	41	we	we	PRON
ejpam-4941	69	42	described	describe	VERB
ejpam-4941	69	43	above	above	ADV
ejpam-4941	69	44	.	.	PUNCT
ejpam-4941	70	1	let	let	VERB
ejpam-4941	70	2	us	we	PRON
ejpam-4941	70	3	now	now	ADV
ejpam-4941	70	4	call	call	VERB
ejpam-4941	70	5	the	the	DET
ejpam-4941	70	6	basis	basis	NOUN
ejpam-4941	70	7	(	(	PUNCT
ejpam-4941	70	8	e1	e1	NOUN
ejpam-4941	70	9	,	,	PUNCT
ejpam-4941	70	10	e2	e2	PROPN
ejpam-4941	70	11	)	)	PUNCT
ejpam-4941	70	12	whose	whose	DET
ejpam-4941	70	13	vectors	vector	NOUN
ejpam-4941	70	14	are	be	AUX
ejpam-4941	70	15	not	not	PART
ejpam-4941	70	16	far	far	ADV
ejpam-4941	70	17	-	-	PUNCT
ejpam-4941	70	18	to	to	ADP
ejpam-4941	70	19	-	-	PUNCT
ejpam-4941	70	20	orthogonal	orthogonal	ADJ
ejpam-4941	70	21	,	,	PUNCT
ejpam-4941	70	22	a	a	DET
ejpam-4941	70	23	’	'	PUNCT
ejpam-4941	70	24	good	good	ADJ
ejpam-4941	70	25	’	'	PUNCT
ejpam-4941	70	26	basis	basis	NOUN
ejpam-4941	70	27	,	,	PUNCT
ejpam-4941	70	28	however	however	ADV
ejpam-4941	70	29	,	,	PUNCT
ejpam-4941	70	30	we	we	PRON
ejpam-4941	70	31	not	not	PART
ejpam-4941	70	32	not	not	PART
ejpam-4941	70	33	assume	assume	VERB
ejpam-4941	70	34	that	that	SCONJ
ejpam-4941	70	35	it	it	PRON
ejpam-4941	70	36	is	be	AUX
ejpam-4941	70	37	’	'	PUNCT
ejpam-4941	70	38	good	good	ADJ
ejpam-4941	70	39	’	'	PUNCT
ejpam-4941	70	40	enough	enough	ADV
ejpam-4941	70	41	compared	compare	VERB
ejpam-4941	70	42	to	to	ADP
ejpam-4941	70	43	basis	basis	NOUN
ejpam-4941	70	44	(	(	PUNCT
ejpam-4941	70	45	e5	e5	PROPN
ejpam-4941	70	46	,	,	PUNCT
ejpam-4941	70	47	e6	e6	PROPN
ejpam-4941	70	48	)	)	PUNCT
ejpam-4941	70	49	which	which	PRON
ejpam-4941	70	50	is	be	AUX
ejpam-4941	70	51	the	the	DET
ejpam-4941	70	52	real	real	ADJ
ejpam-4941	70	53	’	'	PUNCT
ejpam-4941	70	54	good	good	ADJ
ejpam-4941	70	55	’	'	PUNCT
ejpam-4941	70	56	one	one	NUM
ejpam-4941	70	57	and	and	CCONJ
ejpam-4941	70	58	even	even	ADV
ejpam-4941	70	59	the	the	DET
ejpam-4941	70	60	’	'	PUNCT
ejpam-4941	70	61	best	good	ADJ
ejpam-4941	70	62	’	'	PUNCT
ejpam-4941	70	63	to	to	PART
ejpam-4941	70	64	make	make	VERB
ejpam-4941	70	65	the	the	DET
ejpam-4941	70	66	sought	seek	VERB
ejpam-4941	70	67	unit	unit	NOUN
ejpam-4941	70	68	cell	cell	NOUN
ejpam-4941	70	69	or	or	CCONJ
ejpam-4941	70	70	motif	motif	NOUN
ejpam-4941	70	71	.	.	PUNCT
ejpam-4941	71	1	figure	figure	NOUN
ejpam-4941	71	2	5	5	NUM
ejpam-4941	71	3	:	:	PUNCT
ejpam-4941	71	4	vectors	vector	NOUN
ejpam-4941	71	5	e1	e1	VERB
ejpam-4941	71	6	and	and	CCONJ
ejpam-4941	71	7	e2	e2	NOUN
ejpam-4941	71	8	making	make	VERB
ejpam-4941	71	9	a	a	DET
ejpam-4941	71	10	’	'	PUNCT
ejpam-4941	71	11	bad	bad	ADJ
ejpam-4941	71	12	’	'	PUNCT
ejpam-4941	71	13	basis	basis	NOUN
ejpam-4941	71	14	from	from	ADP
ejpam-4941	71	15	which	which	PRON
ejpam-4941	71	16	we	we	PRON
ejpam-4941	71	17	start	start	VERB
ejpam-4941	71	18	to	to	PART
ejpam-4941	71	19	find	find	VERB
ejpam-4941	71	20	a	a	DET
ejpam-4941	71	21	’	'	PUNCT
ejpam-4941	71	22	good	good	ADJ
ejpam-4941	71	23	’	'	PUNCT
ejpam-4941	71	24	one	one	NUM
ejpam-4941	71	25	and	and	CCONJ
ejpam-4941	71	26	that	that	PRON
ejpam-4941	71	27	can	can	AUX
ejpam-4941	71	28	help	help	VERB
ejpam-4941	71	29	us	we	PRON
ejpam-4941	71	30	to	to	PART
ejpam-4941	71	31	generate	generate	VERB
ejpam-4941	71	32	the	the	DET
ejpam-4941	71	33	sought	seek	VERB
ejpam-4941	71	34	motif	motif	NOUN
ejpam-4941	71	35	.	.	PUNCT
ejpam-4941	72	1	here	here	ADV
ejpam-4941	72	2	,	,	PUNCT
ejpam-4941	72	3	in	in	ADP
ejpam-4941	72	4	this	this	DET
ejpam-4941	72	5	work	work	NOUN
ejpam-4941	72	6	,	,	PUNCT
ejpam-4941	72	7	we	we	PRON
ejpam-4941	72	8	consider	consider	VERB
ejpam-4941	72	9	a	a	DET
ejpam-4941	72	10	more	more	ADV
ejpam-4941	72	11	difficult	difficult	ADJ
ejpam-4941	72	12	problem	problem	NOUN
ejpam-4941	72	13	,	,	PUNCT
ejpam-4941	72	14	subject	subject	ADJ
ejpam-4941	72	15	to	to	ADP
ejpam-4941	72	16	a	a	DET
ejpam-4941	72	17	bravais	bravais	NOUN
ejpam-4941	72	18	lattice	lattice	NOUN
ejpam-4941	72	19	reduction	reduction	NOUN
ejpam-4941	72	20	and	and	CCONJ
ejpam-4941	72	21	that	that	PRON
ejpam-4941	72	22	is	be	AUX
ejpam-4941	72	23	about	about	ADP
ejpam-4941	72	24	starting	start	VERB
ejpam-4941	72	25	from	from	ADP
ejpam-4941	72	26	any	any	DET
ejpam-4941	72	27	couple	couple	NOUN
ejpam-4941	72	28	of	of	ADP
ejpam-4941	72	29	vectors	vector	NOUN
ejpam-4941	72	30	like	like	ADP
ejpam-4941	72	31	e1	e1	PROPN
ejpam-4941	72	32	and	and	CCONJ
ejpam-4941	72	33	e2	e2	PROPN
ejpam-4941	72	34	of	of	ADP
ejpam-4941	72	35	figure	figure	NOUN
ejpam-4941	72	36	5	5	NUM
ejpam-4941	72	37	as	as	SCONJ
ejpam-4941	72	38	they	they	PRON
ejpam-4941	72	39	are	be	AUX
ejpam-4941	72	40	supposed	suppose	VERB
ejpam-4941	72	41	not	not	PART
ejpam-4941	72	42	necessarily	necessarily	ADV
ejpam-4941	72	43	making	make	VERB
ejpam-4941	72	44	a	a	DET
ejpam-4941	72	45	primitive	primitive	ADJ
ejpam-4941	72	46	elementary	elementary	ADJ
ejpam-4941	72	47	cell	cell	NOUN
ejpam-4941	72	48	,	,	PUNCT
ejpam-4941	72	49	and	and	CCONJ
ejpam-4941	72	50	let	let	VERB
ejpam-4941	72	51	us	we	PRON
ejpam-4941	72	52	call	call	VERB
ejpam-4941	72	53	(	(	PUNCT
ejpam-4941	72	54	e1	e1	PROPN
ejpam-4941	72	55	,	,	PUNCT
ejpam-4941	72	56	e2	e2	PROPN
ejpam-4941	72	57	)	)	PUNCT
ejpam-4941	72	58	in	in	ADP
ejpam-4941	72	59	this	this	DET
ejpam-4941	72	60	case	case	NOUN
ejpam-4941	72	61	,	,	PUNCT
ejpam-4941	72	62	as	as	ADP
ejpam-4941	72	63	a	a	DET
ejpam-4941	72	64	’	'	PUNCT
ejpam-4941	72	65	bad	bad	ADJ
ejpam-4941	72	66	’	'	PUNCT
ejpam-4941	72	67	basis	basis	NOUN
ejpam-4941	72	68	,	,	PUNCT
ejpam-4941	72	69	then	then	ADV
ejpam-4941	72	70	we	we	PRON
ejpam-4941	72	71	wonder	wonder	VERB
ejpam-4941	72	72	how	how	SCONJ
ejpam-4941	72	73	could	could	AUX
ejpam-4941	72	74	we	we	PRON
ejpam-4941	72	75	start	start	VERB
ejpam-4941	72	76	from	from	ADP
ejpam-4941	72	77	this	this	DET
ejpam-4941	72	78	basis	basis	NOUN
ejpam-4941	72	79	in	in	ADP
ejpam-4941	72	80	order	order	NOUN
ejpam-4941	72	81	to	to	ADP
ejpam-4941	72	82	each	each	PRON
ejpam-4941	72	83	a	a	DET
ejpam-4941	72	84	basis	basis	NOUN
ejpam-4941	72	85	like	like	ADP
ejpam-4941	72	86	(	(	PUNCT
ejpam-4941	72	87	e5	e5	PROPN
ejpam-4941	72	88	,	,	PUNCT
ejpam-4941	72	89	e6	e6	PROPN
ejpam-4941	72	90	)	)	PUNCT
ejpam-4941	72	91	of	of	ADP
ejpam-4941	72	92	figure	figure	NOUN
ejpam-4941	72	93	4	4	NUM
ejpam-4941	72	94	.	.	PUNCT
ejpam-4941	73	1	the	the	DET
ejpam-4941	73	2	most	most	ADV
ejpam-4941	73	3	considered	consider	VERB
ejpam-4941	73	4	practical	practical	ADJ
ejpam-4941	73	5	algorithm	algorithm	NOUN
ejpam-4941	73	6	in	in	ADP
ejpam-4941	73	7	lattice	lattice	NOUN
ejpam-4941	73	8	reduction	reduction	NOUN
ejpam-4941	73	9	is	be	AUX
ejpam-4941	73	10	the	the	DET
ejpam-4941	73	11	lenstra	lenstra	NOUN
ejpam-4941	73	12	-	-	PUNCT
ejpam-4941	73	13	lenstra	lenstra	NOUN
ejpam-4941	73	14	-	-	PUNCT
ejpam-4941	73	15	lovász	lovász	NOUN
ejpam-4941	73	16	(	(	PUNCT
ejpam-4941	73	17	lll	lll	NOUN
ejpam-4941	73	18	)	)	PUNCT
ejpam-4941	73	19	algorithm	algorithm	NOUN
ejpam-4941	73	20	and	and	CCONJ
ejpam-4941	73	21	that	that	PRON
ejpam-4941	73	22	has	have	AUX
ejpam-4941	73	23	been	be	AUX
ejpam-4941	73	24	introduced	introduce	VERB
ejpam-4941	73	25	in	in	ADP
ejpam-4941	73	26	1982	1982	NUM
ejpam-4941	73	27	by	by	ADP
ejpam-4941	73	28	a.	a.	PROPN
ejpam-4941	73	29	k.	k.	PROPN
ejpam-4941	73	30	lenstra	lenstra	PROPN
ejpam-4941	73	31	,	,	PUNCT
ejpam-4941	73	32	h.	h.	PROPN
ejpam-4941	73	33	lenstra	lenstra	PROPN
ejpam-4941	73	34	,	,	PUNCT
ejpam-4941	73	35	jr	jr	PROPN
ejpam-4941	73	36	.	.	PROPN
ejpam-4941	73	37	,	,	PUNCT
ejpam-4941	73	38	j.	j.	PROPN
ejpam-4941	73	39	,	,	PUNCT
ejpam-4941	73	40	and	and	CCONJ
ejpam-4941	73	41	l.	l.	PROPN
ejpam-4941	73	42	lovász	lovász	PROPN
ejpam-4941	74	1	[	[	X
ejpam-4941	74	2	31	31	NUM
ejpam-4941	74	3	]	]	PUNCT
ejpam-4941	74	4	.	.	PUNCT
ejpam-4941	75	1	there	there	PRON
ejpam-4941	75	2	have	have	AUX
ejpam-4941	75	3	always	always	ADV
ejpam-4941	75	4	been	be	AUX
ejpam-4941	75	5	problems	problem	NOUN
ejpam-4941	75	6	that	that	PRON
ejpam-4941	75	7	interested	interested	ADJ
ejpam-4941	75	8	researchers	researcher	NOUN
ejpam-4941	75	9	in	in	ADP
ejpam-4941	75	10	the	the	DET
ejpam-4941	75	11	subjects	subject	NOUN
ejpam-4941	75	12	of	of	ADP
ejpam-4941	75	13	diophantine	diophantine	NOUN
ejpam-4941	75	14	equations	equation	NOUN
ejpam-4941	75	15	as	as	ADP
ejpam-4941	75	16	in	in	ADP
ejpam-4941	75	17	[	[	X
ejpam-4941	75	18	2	2	NUM
ejpam-4941	75	19	,	,	PUNCT
ejpam-4941	75	20	13	13	NUM
ejpam-4941	75	21	]	]	PUNCT
ejpam-4941	75	22	.	.	PUNCT
ejpam-4941	76	1	the	the	DET
ejpam-4941	76	2	lattice	lattice	PROPN
ejpam-4941	76	3	reduction	reduction	NOUN
ejpam-4941	76	4	through	through	ADP
ejpam-4941	76	5	lll	lll	PROPN
ejpam-4941	76	6	has	have	AUX
ejpam-4941	76	7	shown	show	VERB
ejpam-4941	76	8	to	to	PART
ejpam-4941	76	9	be	be	AUX
ejpam-4941	76	10	also	also	ADV
ejpam-4941	76	11	beneficial	beneficial	ADJ
ejpam-4941	76	12	in	in	ADP
ejpam-4941	76	13	solving	solve	VERB
ejpam-4941	76	14	such	such	ADJ
ejpam-4941	76	15	problems	problem	NOUN
ejpam-4941	76	16	as	as	SCONJ
ejpam-4941	76	17	explained	explain	VERB
ejpam-4941	76	18	in	in	ADP
ejpam-4941	76	19	[	[	X
ejpam-4941	76	20	47	47	NUM
ejpam-4941	76	21	]	]	PUNCT
ejpam-4941	76	22	with	with	ADP
ejpam-4941	76	23	examples	example	NOUN
ejpam-4941	76	24	of	of	ADP
ejpam-4941	76	25	linear	linear	PROPN
ejpam-4941	76	26	problems	problem	NOUN
ejpam-4941	76	27	,	,	PUNCT
ejpam-4941	76	28	quadratic	quadratic	ADJ
ejpam-4941	76	29	equations	equation	NOUN
ejpam-4941	76	30	,	,	PUNCT
ejpam-4941	76	31	number	number	NOUN
ejpam-4941	76	32	fields	field	NOUN
ejpam-4941	76	33	and	and	CCONJ
ejpam-4941	76	34	testing	testing	NOUN
ejpam-4941	76	35	conjectures	conjecture	VERB
ejpam-4941	76	36	,	,	PUNCT
ejpam-4941	76	37	while	while	SCONJ
ejpam-4941	76	38	most	most	ADJ
ejpam-4941	76	39	authors	author	NOUN
ejpam-4941	76	40	in	in	ADP
ejpam-4941	76	41	this	this	DET
ejpam-4941	76	42	topic	topic	NOUN
ejpam-4941	76	43	have	have	AUX
ejpam-4941	76	44	been	be	AUX
ejpam-4941	76	45	interested	interested	ADJ
ejpam-4941	76	46	in	in	ADP
ejpam-4941	76	47	the	the	DET
ejpam-4941	76	48	complexity	complexity	NOUN
ejpam-4941	76	49	analysis	analysis	NOUN
ejpam-4941	76	50	of	of	ADP
ejpam-4941	76	51	this	this	DET
ejpam-4941	76	52	method	method	NOUN
ejpam-4941	76	53	in	in	ADP
ejpam-4941	76	54	the	the	DET
ejpam-4941	76	55	hope	hope	NOUN
ejpam-4941	76	56	to	to	PART
ejpam-4941	76	57	find	find	VERB
ejpam-4941	76	58	a	a	DET
ejpam-4941	76	59	high	high	ADJ
ejpam-4941	76	60	performance	performance	NOUN
ejpam-4941	76	61	computer	computer	NOUN
ejpam-4941	76	62	program	program	NOUN
ejpam-4941	77	1	[	[	X
ejpam-4941	77	2	1	1	NUM
ejpam-4941	77	3	,	,	PUNCT
ejpam-4941	77	4	3	3	NUM
ejpam-4941	77	5	,	,	PUNCT
ejpam-4941	77	6	5	5	NUM
ejpam-4941	77	7	,	,	PUNCT
ejpam-4941	77	8	8	8	NUM
ejpam-4941	77	9	,	,	PUNCT
ejpam-4941	77	10	14	14	NUM
ejpam-4941	77	11	,	,	PUNCT
ejpam-4941	77	12	17	17	NUM
ejpam-4941	77	13	–	–	SYM
ejpam-4941	77	14	19	19	NUM
ejpam-4941	77	15	,	,	PUNCT
ejpam-4941	77	16	32	32	NUM
ejpam-4941	77	17	,	,	PUNCT
ejpam-4941	77	18	33	33	NUM
ejpam-4941	77	19	,	,	PUNCT
ejpam-4941	77	20	35	35	NUM
ejpam-4941	77	21	,	,	PUNCT
ejpam-4941	77	22	38	38	NUM
ejpam-4941	77	23	,	,	PUNCT
ejpam-4941	77	24	40	40	NUM
ejpam-4941	77	25	,	,	PUNCT
ejpam-4941	77	26	43	43	NUM
ejpam-4941	77	27	,	,	PUNCT
ejpam-4941	77	28	46	46	NUM
ejpam-4941	77	29	,	,	PUNCT
ejpam-4941	77	30	49	49	NUM
ejpam-4941	77	31	,	,	PUNCT
ejpam-4941	77	32	50	50	NUM
ejpam-4941	77	33	]	]	PUNCT
ejpam-4941	77	34	.	.	PUNCT
ejpam-4941	78	1	this	this	DET
ejpam-4941	78	2	algorithm	algorithm	NOUN
ejpam-4941	78	3	has	have	AUX
ejpam-4941	78	4	been	be	AUX
ejpam-4941	78	5	applied	apply	VERB
ejpam-4941	78	6	to	to	ADP
ejpam-4941	78	7	many	many	ADJ
ejpam-4941	78	8	fields	field	NOUN
ejpam-4941	78	9	such	such	ADJ
ejpam-4941	78	10	as	as	ADP
ejpam-4941	78	11	communication	communication	NOUN
ejpam-4941	78	12	systems	system	NOUN
ejpam-4941	78	13	[	[	X
ejpam-4941	78	14	4	4	NUM
ejpam-4941	78	15	,	,	PUNCT
ejpam-4941	78	16	36	36	NUM
ejpam-4941	78	17	]	]	PUNCT
ejpam-4941	78	18	as	as	ADP
ejpam-4941	78	19	in	in	ADP
ejpam-4941	78	20	the	the	DET
ejpam-4941	78	21	study	study	NOUN
ejpam-4941	78	22	of	of	ADP
ejpam-4941	78	23	the	the	DET
ejpam-4941	78	24	multiple	multiple	ADJ
ejpam-4941	78	25	-	-	PUNCT
ejpam-4941	78	26	input	input	NOUN
ejpam-4941	78	27	and	and	CCONJ
ejpam-4941	78	28	multipleoutput	multipleoutput	NOUN
ejpam-4941	78	29	(	(	PUNCT
ejpam-4941	78	30	mimo	mimo	PROPN
ejpam-4941	78	31	)	)	PUNCT
ejpam-4941	78	32	method	method	NOUN
ejpam-4941	78	33	[	[	X
ejpam-4941	78	34	11	11	NUM
ejpam-4941	78	35	,	,	PUNCT
ejpam-4941	78	36	12	12	NUM
ejpam-4941	78	37	,	,	PUNCT
ejpam-4941	78	38	15	15	NUM
ejpam-4941	78	39	,	,	PUNCT
ejpam-4941	78	40	24	24	NUM
ejpam-4941	78	41	]	]	PUNCT
ejpam-4941	78	42	,	,	PUNCT
ejpam-4941	78	43	while	while	SCONJ
ejpam-4941	78	44	also	also	ADV
ejpam-4941	78	45	being	be	AUX
ejpam-4941	78	46	used	use	VERB
ejpam-4941	78	47	to	to	PART
ejpam-4941	78	48	resolve	resolve	VERB
ejpam-4941	78	49	cryptographic	cryptographic	ADJ
ejpam-4941	78	50	problems	problem	NOUN
ejpam-4941	78	51	as	as	ADP
ejpam-4941	78	52	in	in	ADP
ejpam-4941	78	53	[	[	X
ejpam-4941	78	54	21	21	NUM
ejpam-4941	78	55	,	,	PUNCT
ejpam-4941	78	56	23	23	NUM
ejpam-4941	78	57	,	,	PUNCT
ejpam-4941	78	58	26	26	NUM
ejpam-4941	78	59	,	,	PUNCT
ejpam-4941	78	60	34	34	NUM
ejpam-4941	78	61	]	]	PUNCT
ejpam-4941	78	62	.	.	PUNCT
ejpam-4941	79	1	many	many	ADJ
ejpam-4941	79	2	problems	problem	NOUN
ejpam-4941	79	3	remain	remain	VERB
ejpam-4941	79	4	open	open	ADJ
ejpam-4941	79	5	in	in	ADP
ejpam-4941	79	6	this	this	DET
ejpam-4941	79	7	subject	subject	NOUN
ejpam-4941	79	8	as	as	ADP
ejpam-4941	79	9	for	for	ADP
ejpam-4941	79	10	example	example	NOUN
ejpam-4941	79	11	in	in	ADP
ejpam-4941	79	12	the	the	DET
ejpam-4941	79	13	study	study	NOUN
ejpam-4941	79	14	of	of	ADP
ejpam-4941	79	15	the	the	DET
ejpam-4941	79	16	floating	float	VERB
ejpam-4941	79	17	-	-	PUNCT
ejpam-4941	79	18	point	point	NOUN
ejpam-4941	79	19	[	[	X
ejpam-4941	79	20	48	48	NUM
ejpam-4941	79	21	]	]	PUNCT
ejpam-4941	79	22	.	.	PUNCT
ejpam-4941	80	1	here	here	ADV
ejpam-4941	80	2	,	,	PUNCT
ejpam-4941	80	3	we	we	PRON
ejpam-4941	80	4	choose	choose	VERB
ejpam-4941	80	5	to	to	PART
ejpam-4941	80	6	focus	focus	VERB
ejpam-4941	80	7	on	on	ADP
ejpam-4941	80	8	the	the	DET
ejpam-4941	80	9	proof	proof	NOUN
ejpam-4941	80	10	of	of	ADP
ejpam-4941	80	11	the	the	DET
ejpam-4941	80	12	vectors	vector	NOUN
ejpam-4941	80	13	swapping	swap	VERB
ejpam-4941	80	14	and	and	CCONJ
ejpam-4941	80	15	which	which	PRON
ejpam-4941	80	16	is	be	AUX
ejpam-4941	80	17	a	a	DET
ejpam-4941	80	18	problem	problem	NOUN
ejpam-4941	80	19	that	that	PRON
ejpam-4941	80	20	has	have	AUX
ejpam-4941	80	21	insufficiently	insufficiently	ADV
ejpam-4941	80	22	been	be	AUX
ejpam-4941	80	23	analyzed	analyze	VERB
ejpam-4941	80	24	in	in	ADP
ejpam-4941	80	25	the	the	DET
ejpam-4941	80	26	literature	literature	NOUN
ejpam-4941	80	27	.	.	PUNCT
ejpam-4941	81	1	in	in	ADP
ejpam-4941	81	2	fact	fact	NOUN
ejpam-4941	81	3	,	,	PUNCT
ejpam-4941	81	4	as	as	ADP
ejpam-4941	81	5	the	the	DET
ejpam-4941	81	6	combination	combination	NOUN
ejpam-4941	81	7	of	of	ADP
ejpam-4941	81	8	orthogonalization	orthogonalization	NOUN
ejpam-4941	81	9	with	with	ADP
ejpam-4941	81	10	the	the	DET
ejpam-4941	81	11	vectors	vector	NOUN
ejpam-4941	81	12	swapping	swap	VERB
ejpam-4941	81	13	processes	process	NOUN
ejpam-4941	81	14	,	,	PUNCT
ejpam-4941	81	15	is	be	AUX
ejpam-4941	81	16	s.	s.	PROPN
ejpam-4941	81	17	abdelalim	abdelalim	PROPN
ejpam-4941	81	18	,	,	PUNCT
ejpam-4941	81	19	i.	i.	PROPN
ejpam-4941	81	20	elmouki	elmouki	PROPN
ejpam-4941	81	21	/	/	SYM
ejpam-4941	81	22	eur	eur	PROPN
ejpam-4941	81	23	.	.	PUNCT
ejpam-4941	82	1	j.	j.	PROPN
ejpam-4941	82	2	pure	pure	PROPN
ejpam-4941	82	3	appl	appl	PROPN
ejpam-4941	82	4	.	.	PROPN
ejpam-4941	82	5	math	math	PROPN
ejpam-4941	82	6	,	,	PUNCT
ejpam-4941	82	7	16	16	NUM
ejpam-4941	82	8	(	(	PUNCT
ejpam-4941	82	9	4	4	NUM
ejpam-4941	82	10	)	)	PUNCT
ejpam-4941	82	11	(	(	PUNCT
ejpam-4941	82	12	2023	2023	NUM
ejpam-4941	82	13	)	)	PUNCT
ejpam-4941	82	14	,	,	PUNCT
ejpam-4941	82	15	2662	2662	NUM
ejpam-4941	82	16	-	-	SYM
ejpam-4941	82	17	2692	2692	NUM
ejpam-4941	82	18	2668	2668	NUM
ejpam-4941	82	19	an	an	DET
ejpam-4941	82	20	indispensable	indispensable	ADJ
ejpam-4941	82	21	part	part	NOUN
ejpam-4941	82	22	of	of	ADP
ejpam-4941	82	23	this	this	DET
ejpam-4941	82	24	algorithm	algorithm	NOUN
ejpam-4941	82	25	,	,	PUNCT
ejpam-4941	82	26	we	we	PRON
ejpam-4941	82	27	will	will	AUX
ejpam-4941	82	28	exhibit	exhibit	VERB
ejpam-4941	82	29	through	through	ADP
ejpam-4941	82	30	our	our	PRON
ejpam-4941	82	31	proof	proof	NOUN
ejpam-4941	82	32	of	of	ADP
ejpam-4941	82	33	this	this	DET
ejpam-4941	82	34	first	first	ADJ
ejpam-4941	82	35	suggested	suggest	VERB
ejpam-4941	82	36	version	version	NOUN
ejpam-4941	82	37	of	of	ADP
ejpam-4941	82	38	vectors	vector	NOUN
ejpam-4941	82	39	exchange	exchange	NOUN
ejpam-4941	82	40	theorem	theorem	VERB
ejpam-4941	82	41	that	that	SCONJ
ejpam-4941	82	42	by	by	ADP
ejpam-4941	82	43	the	the	DET
ejpam-4941	82	44	use	use	NOUN
ejpam-4941	82	45	of	of	ADP
ejpam-4941	82	46	any	any	DET
ejpam-4941	82	47	procedure	procedure	NOUN
ejpam-4941	82	48	,	,	PUNCT
ejpam-4941	82	49	there	there	PRON
ejpam-4941	82	50	would	would	AUX
ejpam-4941	82	51	be	be	AUX
ejpam-4941	82	52	a	a	DET
ejpam-4941	82	53	loss	loss	NOUN
ejpam-4941	82	54	of	of	ADP
ejpam-4941	82	55	orthogonalization	orthogonalization	NOUN
ejpam-4941	82	56	especially	especially	ADV
ejpam-4941	82	57	due	due	ADP
ejpam-4941	82	58	to	to	ADP
ejpam-4941	82	59	the	the	DET
ejpam-4941	82	60	repetitive	repetitive	ADJ
ejpam-4941	82	61	exchange	exchange	NOUN
ejpam-4941	82	62	of	of	ADP
ejpam-4941	82	63	vectors	vector	NOUN
ejpam-4941	82	64	in	in	ADP
ejpam-4941	82	65	the	the	DET
ejpam-4941	82	66	lattice	lattice	NOUN
ejpam-4941	82	67	reduction	reduction	NOUN
ejpam-4941	82	68	process	process	NOUN
ejpam-4941	82	69	.	.	PUNCT
ejpam-4941	83	1	as	as	ADP
ejpam-4941	83	2	a	a	DET
ejpam-4941	83	3	final	final	ADJ
ejpam-4941	83	4	result	result	NOUN
ejpam-4941	83	5	,	,	PUNCT
ejpam-4941	83	6	the	the	DET
ejpam-4941	83	7	second	second	ADJ
ejpam-4941	83	8	orthogonalization	orthogonalization	NOUN
ejpam-4941	83	9	method	method	NOUN
ejpam-4941	83	10	will	will	AUX
ejpam-4941	83	11	show	show	VERB
ejpam-4941	83	12	to	to	PART
ejpam-4941	83	13	preserve	preserve	VERB
ejpam-4941	83	14	the	the	DET
ejpam-4941	83	15	orthogonality	orthogonality	NOUN
ejpam-4941	83	16	more	more	ADV
ejpam-4941	83	17	than	than	ADP
ejpam-4941	83	18	the	the	DET
ejpam-4941	83	19	most	most	ADV
ejpam-4941	83	20	used	used	ADJ
ejpam-4941	83	21	one	one	NUM
ejpam-4941	83	22	.	.	PUNCT
ejpam-4941	84	1	going	go	VERB
ejpam-4941	84	2	back	back	ADV
ejpam-4941	84	3	to	to	ADP
ejpam-4941	84	4	the	the	DET
ejpam-4941	84	5	concrete	concrete	ADJ
ejpam-4941	84	6	context	context	NOUN
ejpam-4941	84	7	of	of	ADP
ejpam-4941	84	8	this	this	DET
ejpam-4941	84	9	research	research	NOUN
ejpam-4941	84	10	and	and	CCONJ
ejpam-4941	84	11	which	which	PRON
ejpam-4941	84	12	is	be	AUX
ejpam-4941	84	13	about	about	ADP
ejpam-4941	84	14	seeking	seek	VERB
ejpam-4941	84	15	a	a	DET
ejpam-4941	84	16	crystal	crystal	NOUN
ejpam-4941	84	17	reduced	reduce	VERB
ejpam-4941	84	18	motif	motif	NOUN
ejpam-4941	84	19	while	while	SCONJ
ejpam-4941	84	20	studying	study	VERB
ejpam-4941	84	21	the	the	DET
ejpam-4941	84	22	impact	impact	NOUN
ejpam-4941	84	23	of	of	ADP
ejpam-4941	84	24	the	the	DET
ejpam-4941	84	25	vectors	vector	NOUN
ejpam-4941	84	26	exchange	exchange	NOUN
ejpam-4941	84	27	,	,	PUNCT
ejpam-4941	84	28	we	we	PRON
ejpam-4941	84	29	should	should	AUX
ejpam-4941	84	30	note	note	VERB
ejpam-4941	84	31	that	that	SCONJ
ejpam-4941	84	32	the	the	DET
ejpam-4941	84	33	literature	literature	NOUN
ejpam-4941	84	34	has	have	AUX
ejpam-4941	84	35	not	not	PART
ejpam-4941	84	36	answered	answer	VERB
ejpam-4941	84	37	about	about	ADP
ejpam-4941	84	38	the	the	DET
ejpam-4941	84	39	problem	problem	NOUN
ejpam-4941	84	40	that	that	PRON
ejpam-4941	84	41	we	we	PRON
ejpam-4941	84	42	have	have	AUX
ejpam-4941	84	43	presented	present	VERB
ejpam-4941	84	44	in	in	ADP
ejpam-4941	84	45	figure	figure	NOUN
ejpam-4941	84	46	5	5	NUM
ejpam-4941	84	47	.	.	PUNCT
ejpam-4941	85	1	in	in	ADP
ejpam-4941	85	2	fact	fact	NOUN
ejpam-4941	85	3	,	,	PUNCT
ejpam-4941	85	4	until	until	ADP
ejpam-4941	85	5	nowadays	nowadays	ADV
ejpam-4941	85	6	,	,	PUNCT
ejpam-4941	85	7	the	the	DET
ejpam-4941	85	8	interest	interest	NOUN
ejpam-4941	85	9	has	have	AUX
ejpam-4941	85	10	been	be	AUX
ejpam-4941	85	11	limited	limit	VERB
ejpam-4941	85	12	to	to	ADP
ejpam-4941	85	13	niggli	niggli	NOUN
ejpam-4941	85	14	-	-	PUNCT
ejpam-4941	85	15	like	like	ADJ
ejpam-4941	85	16	reduction	reduction	NOUN
ejpam-4941	85	17	as	as	ADP
ejpam-4941	85	18	in	in	ADP
ejpam-4941	85	19	[	[	X
ejpam-4941	85	20	7	7	NUM
ejpam-4941	85	21	,	,	PUNCT
ejpam-4941	85	22	37	37	NUM
ejpam-4941	85	23	]	]	PUNCT
ejpam-4941	85	24	,	,	PUNCT
ejpam-4941	85	25	in	in	ADP
ejpam-4941	85	26	a	a	DET
ejpam-4941	85	27	tentative	tentative	NOUN
ejpam-4941	85	28	to	to	PART
ejpam-4941	85	29	find	find	VERB
ejpam-4941	85	30	better	well	ADJ
ejpam-4941	85	31	results	result	NOUN
ejpam-4941	85	32	than	than	ADP
ejpam-4941	85	33	the	the	DET
ejpam-4941	85	34	old	old	ADJ
ejpam-4941	85	35	work	work	NOUN
ejpam-4941	85	36	[	[	X
ejpam-4941	85	37	41	41	NUM
ejpam-4941	85	38	]	]	PUNCT
ejpam-4941	85	39	.	.	PUNCT
ejpam-4941	86	1	with	with	ADP
ejpam-4941	86	2	respect	respect	NOUN
ejpam-4941	86	3	to	to	ADP
ejpam-4941	86	4	the	the	DET
ejpam-4941	86	5	practical	practical	ADJ
ejpam-4941	86	6	side	side	NOUN
ejpam-4941	86	7	of	of	ADP
ejpam-4941	86	8	this	this	DET
ejpam-4941	86	9	work	work	NOUN
ejpam-4941	86	10	,	,	PUNCT
ejpam-4941	86	11	we	we	PRON
ejpam-4941	86	12	aim	aim	VERB
ejpam-4941	86	13	to	to	PART
ejpam-4941	86	14	recommend	recommend	VERB
ejpam-4941	86	15	a	a	DET
ejpam-4941	86	16	lattice	lattice	NOUN
ejpam-4941	86	17	reduction	reduction	NOUN
ejpam-4941	86	18	computing	computing	NOUN
ejpam-4941	86	19	procedure	procedure	NOUN
ejpam-4941	86	20	which	which	PRON
ejpam-4941	86	21	respects	respect	VERB
ejpam-4941	86	22	the	the	DET
ejpam-4941	86	23	result	result	NOUN
ejpam-4941	86	24	of	of	ADP
ejpam-4941	86	25	the	the	DET
ejpam-4941	86	26	theorem	theorem	NOUN
ejpam-4941	86	27	that	that	PRON
ejpam-4941	86	28	we	we	PRON
ejpam-4941	86	29	will	will	AUX
ejpam-4941	86	30	state	state	VERB
ejpam-4941	86	31	thereafter	thereafter	ADV
ejpam-4941	86	32	and	and	CCONJ
ejpam-4941	86	33	which	which	PRON
ejpam-4941	86	34	gives	give	VERB
ejpam-4941	86	35	the	the	DET
ejpam-4941	86	36	proof	proof	NOUN
ejpam-4941	86	37	of	of	SCONJ
ejpam-4941	86	38	which	which	DET
ejpam-4941	86	39	orthogonalization	orthogonalization	NOUN
ejpam-4941	86	40	process	process	NOUN
ejpam-4941	86	41	should	should	AUX
ejpam-4941	86	42	be	be	AUX
ejpam-4941	86	43	really	really	ADV
ejpam-4941	86	44	followed	follow	VERB
ejpam-4941	86	45	,	,	PUNCT
ejpam-4941	86	46	differently	differently	ADV
ejpam-4941	86	47	to	to	ADP
ejpam-4941	86	48	what	what	PRON
ejpam-4941	86	49	is	be	AUX
ejpam-4941	86	50	usually	usually	ADV
ejpam-4941	86	51	considered	consider	VERB
ejpam-4941	86	52	.	.	PUNCT
ejpam-4941	87	1	after	after	ADP
ejpam-4941	87	2	the	the	DET
ejpam-4941	87	3	description	description	NOUN
ejpam-4941	87	4	of	of	ADP
ejpam-4941	87	5	the	the	DET
ejpam-4941	87	6	lattice	lattice	PROPN
ejpam-4941	87	7	reduction	reduction	NOUN
ejpam-4941	87	8	problem	problem	NOUN
ejpam-4941	87	9	,	,	PUNCT
ejpam-4941	87	10	we	we	PRON
ejpam-4941	87	11	need	need	VERB
ejpam-4941	87	12	to	to	PART
ejpam-4941	87	13	define	define	VERB
ejpam-4941	87	14	the	the	DET
ejpam-4941	87	15	orthogonalization	orthogonalization	NOUN
ejpam-4941	87	16	processes	process	NOUN
ejpam-4941	87	17	that	that	PRON
ejpam-4941	87	18	will	will	AUX
ejpam-4941	87	19	be	be	AUX
ejpam-4941	87	20	used	use	VERB
ejpam-4941	87	21	in	in	ADP
ejpam-4941	87	22	our	our	PRON
ejpam-4941	87	23	algorithm	algorithm	NOUN
ejpam-4941	87	24	.	.	PUNCT
ejpam-4941	88	1	thus	thus	ADV
ejpam-4941	88	2	,	,	PUNCT
ejpam-4941	88	3	we	we	PRON
ejpam-4941	88	4	start	start	VERB
ejpam-4941	88	5	in	in	ADP
ejpam-4941	88	6	the	the	DET
ejpam-4941	88	7	next	next	ADJ
ejpam-4941	88	8	section	section	NOUN
ejpam-4941	88	9	,	,	PUNCT
ejpam-4941	88	10	by	by	ADP
ejpam-4941	88	11	stating	state	VERB
ejpam-4941	88	12	some	some	DET
ejpam-4941	88	13	important	important	ADJ
ejpam-4941	88	14	properties	property	NOUN
ejpam-4941	88	15	of	of	ADP
ejpam-4941	88	16	the	the	DET
ejpam-4941	88	17	gram	gram	NOUN
ejpam-4941	88	18	-	-	PUNCT
ejpam-4941	88	19	schmidt	schmidt	NOUN
ejpam-4941	88	20	method	method	NOUN
ejpam-4941	88	21	and	and	CCONJ
ejpam-4941	88	22	its	its	PRON
ejpam-4941	88	23	modified	modify	VERB
ejpam-4941	88	24	version	version	NOUN
ejpam-4941	88	25	through	through	ADP
ejpam-4941	88	26	theorem	theorem	NOUN
ejpam-4941	88	27	1	1	NUM
ejpam-4941	88	28	with	with	ADP
ejpam-4941	88	29	original	original	ADJ
ejpam-4941	88	30	statements	statement	NOUN
ejpam-4941	88	31	and	and	CCONJ
ejpam-4941	88	32	proof	proof	NOUN
ejpam-4941	88	33	.	.	PUNCT
ejpam-4941	89	1	2	2	X
ejpam-4941	89	2	.	.	X
ejpam-4941	89	3	orthogonalization	orthogonalization	NOUN
ejpam-4941	89	4	procedures	procedure	NOUN
ejpam-4941	89	5	2.1	2.1	NUM
ejpam-4941	89	6	.	.	PUNCT
ejpam-4941	90	1	gs	gs	NOUN
ejpam-4941	90	2	and	and	CCONJ
ejpam-4941	90	3	mgs	mgs	VERB
ejpam-4941	90	4	from	from	ADP
ejpam-4941	90	5	mathematics	mathematic	NOUN
ejpam-4941	90	6	in	in	ADP
ejpam-4941	90	7	this	this	DET
ejpam-4941	90	8	part	part	NOUN
ejpam-4941	90	9	of	of	ADP
ejpam-4941	90	10	the	the	DET
ejpam-4941	90	11	paper	paper	NOUN
ejpam-4941	90	12	,	,	PUNCT
ejpam-4941	90	13	we	we	PRON
ejpam-4941	90	14	consider	consider	VERB
ejpam-4941	90	15	two	two	NUM
ejpam-4941	90	16	ways	way	NOUN
ejpam-4941	90	17	of	of	ADP
ejpam-4941	90	18	orthogonalization	orthogonalization	NOUN
ejpam-4941	90	19	[	[	X
ejpam-4941	90	20	44	44	NUM
ejpam-4941	90	21	]	]	PUNCT
ejpam-4941	90	22	,	,	PUNCT
ejpam-4941	90	23	namely	namely	ADV
ejpam-4941	90	24	the	the	DET
ejpam-4941	90	25	gram	gram	NOUN
ejpam-4941	90	26	-	-	PUNCT
ejpam-4941	90	27	schmidt	schmidt	NOUN
ejpam-4941	90	28	process	process	NOUN
ejpam-4941	90	29	(	(	PUNCT
ejpam-4941	90	30	gs	gs	NOUN
ejpam-4941	90	31	)	)	PUNCT
ejpam-4941	90	32	and	and	CCONJ
ejpam-4941	90	33	its	its	PRON
ejpam-4941	90	34	modified	modified	ADJ
ejpam-4941	90	35	version	version	NOUN
ejpam-4941	90	36	(	(	PUNCT
ejpam-4941	90	37	mgs	mgs	NOUN
ejpam-4941	90	38	)	)	PUNCT
ejpam-4941	90	39	,	,	PUNCT
ejpam-4941	90	40	then	then	ADV
ejpam-4941	90	41	,	,	PUNCT
ejpam-4941	90	42	we	we	PRON
ejpam-4941	90	43	prove	prove	VERB
ejpam-4941	90	44	through	through	ADP
ejpam-4941	90	45	a	a	DET
ejpam-4941	90	46	numerical	numerical	ADJ
ejpam-4941	90	47	example	example	NOUN
ejpam-4941	90	48	why	why	SCONJ
ejpam-4941	90	49	one	one	NUM
ejpam-4941	90	50	option	option	NOUN
ejpam-4941	90	51	would	would	AUX
ejpam-4941	90	52	be	be	AUX
ejpam-4941	90	53	better	well	ADJ
ejpam-4941	90	54	to	to	PART
ejpam-4941	90	55	consider	consider	VERB
ejpam-4941	90	56	instead	instead	ADV
ejpam-4941	90	57	of	of	ADP
ejpam-4941	90	58	the	the	DET
ejpam-4941	90	59	other	other	ADJ
ejpam-4941	90	60	.	.	PUNCT
ejpam-4941	91	1	in	in	ADP
ejpam-4941	91	2	fact	fact	NOUN
ejpam-4941	91	3	,	,	PUNCT
ejpam-4941	91	4	the	the	DET
ejpam-4941	91	5	reason	reason	NOUN
ejpam-4941	91	6	behind	behind	ADP
ejpam-4941	91	7	choosing	choose	VERB
ejpam-4941	91	8	the	the	DET
ejpam-4941	91	9	mgs	mgs	NOUN
ejpam-4941	91	10	is	be	AUX
ejpam-4941	91	11	due	due	ADJ
ejpam-4941	91	12	to	to	ADP
ejpam-4941	91	13	the	the	DET
ejpam-4941	91	14	fact	fact	NOUN
ejpam-4941	91	15	that	that	SCONJ
ejpam-4941	91	16	this	this	PRON
ejpam-4941	91	17	tries	try	VERB
ejpam-4941	91	18	to	to	PART
ejpam-4941	91	19	correct	correct	VERB
ejpam-4941	91	20	the	the	DET
ejpam-4941	91	21	orthogonalization	orthogonalization	NOUN
ejpam-4941	91	22	at	at	ADP
ejpam-4941	91	23	every	every	DET
ejpam-4941	91	24	step	step	NOUN
ejpam-4941	91	25	of	of	ADP
ejpam-4941	91	26	its	its	PRON
ejpam-4941	91	27	scheme	scheme	NOUN
ejpam-4941	91	28	,	,	PUNCT
ejpam-4941	91	29	which	which	PRON
ejpam-4941	91	30	means	mean	VERB
ejpam-4941	91	31	that	that	SCONJ
ejpam-4941	91	32	sometimes	sometimes	ADV
ejpam-4941	91	33	,	,	PUNCT
ejpam-4941	91	34	we	we	PRON
ejpam-4941	91	35	would	would	AUX
ejpam-4941	91	36	lose	lose	VERB
ejpam-4941	91	37	orthogonality	orthogonality	NOUN
ejpam-4941	91	38	more	more	ADV
ejpam-4941	91	39	if	if	SCONJ
ejpam-4941	91	40	we	we	PRON
ejpam-4941	91	41	follow	follow	VERB
ejpam-4941	91	42	just	just	ADV
ejpam-4941	91	43	the	the	DET
ejpam-4941	91	44	classical	classical	ADJ
ejpam-4941	91	45	approach	approach	NOUN
ejpam-4941	91	46	during	during	ADP
ejpam-4941	91	47	the	the	DET
ejpam-4941	91	48	lattice	lattice	PROPN
ejpam-4941	91	49	basis	basis	NOUN
ejpam-4941	91	50	reduction	reduction	NOUN
ejpam-4941	91	51	.	.	PUNCT
ejpam-4941	92	1	this	this	DET
ejpam-4941	92	2	study	study	NOUN
ejpam-4941	92	3	would	would	AUX
ejpam-4941	92	4	motivate	motivate	VERB
ejpam-4941	92	5	other	other	ADJ
ejpam-4941	92	6	researchers	researcher	NOUN
ejpam-4941	92	7	working	work	VERB
ejpam-4941	92	8	on	on	ADP
ejpam-4941	92	9	this	this	DET
ejpam-4941	92	10	particular	particular	ADJ
ejpam-4941	92	11	topic	topic	NOUN
ejpam-4941	92	12	,	,	PUNCT
ejpam-4941	92	13	to	to	PART
ejpam-4941	92	14	look	look	VERB
ejpam-4941	92	15	for	for	ADP
ejpam-4941	92	16	other	other	ADJ
ejpam-4941	92	17	forms	form	NOUN
ejpam-4941	92	18	of	of	ADP
ejpam-4941	92	19	orthogonalizing	orthogonalize	VERB
ejpam-4941	92	20	their	their	PRON
ejpam-4941	92	21	vectors	vector	NOUN
ejpam-4941	92	22	while	while	SCONJ
ejpam-4941	92	23	searching	search	VERB
ejpam-4941	92	24	good	good	ADJ
ejpam-4941	92	25	bases	basis	NOUN
ejpam-4941	92	26	for	for	ADP
ejpam-4941	92	27	their	their	PRON
ejpam-4941	92	28	lattices	lattice	NOUN
ejpam-4941	92	29	.	.	PUNCT
ejpam-4941	93	1	let	let	VERB
ejpam-4941	93	2	e	e	PRON
ejpam-4941	93	3	be	be	AUX
ejpam-4941	93	4	a	a	DET
ejpam-4941	93	5	vector	vector	NOUN
ejpam-4941	93	6	space	space	NOUN
ejpam-4941	93	7	of	of	ADP
ejpam-4941	93	8	finite	finite	ADJ
ejpam-4941	93	9	dimension	dimension	NOUN
ejpam-4941	93	10	n	n	CCONJ
ejpam-4941	93	11	over	over	ADP
ejpam-4941	93	12	the	the	DET
ejpam-4941	93	13	real	real	ADJ
ejpam-4941	93	14	field	field	NOUN
ejpam-4941	93	15	,	,	PUNCT
ejpam-4941	93	16	with	with	ADP
ejpam-4941	93	17	an	an	DET
ejpam-4941	93	18	inner	inner	ADJ
ejpam-4941	93	19	product	product	NOUN
ejpam-4941	93	20	⟨.	⟨.	NOUN
ejpam-4941	93	21	,	,	PUNCT
ejpam-4941	93	22	.⟩	.⟩	PROPN
ejpam-4941	93	23	:	:	PUNCT
ejpam-4941	94	1	e	e	X
ejpam-4941	94	2	×	×	NOUN
ejpam-4941	94	3	e	e	X
ejpam-4941	94	4	→	→	SYM
ejpam-4941	94	5	r	r	NOUN
ejpam-4941	94	6	,	,	PUNCT
ejpam-4941	94	7	and	and	CCONJ
ejpam-4941	94	8	we	we	PRON
ejpam-4941	94	9	consider	consider	VERB
ejpam-4941	94	10	in	in	ADP
ejpam-4941	94	11	the	the	DET
ejpam-4941	94	12	rest	rest	NOUN
ejpam-4941	94	13	of	of	ADP
ejpam-4941	94	14	the	the	DET
ejpam-4941	94	15	paper	paper	NOUN
ejpam-4941	94	16	,	,	PUNCT
ejpam-4941	94	17	that	that	SCONJ
ejpam-4941	94	18	this	this	DET
ejpam-4941	94	19	function	function	NOUN
ejpam-4941	94	20	induces	induce	VERB
ejpam-4941	94	21	a	a	DET
ejpam-4941	94	22	norm	norm	NOUN
ejpam-4941	94	23	defined	define	VERB
ejpam-4941	94	24	by	by	ADP
ejpam-4941	94	25	√	√	PROPN
ejpam-4941	94	26	⟨.	⟨.	PROPN
ejpam-4941	94	27	,	,	PUNCT
ejpam-4941	94	28	.⟩	.⟩	PROPN
ejpam-4941	94	29	and	and	CCONJ
ejpam-4941	94	30	denoted	denote	VERB
ejpam-4941	94	31	by	by	ADP
ejpam-4941	94	32	|.|	|.|	NOUN
ejpam-4941	94	33	.	.	PUNCT
ejpam-4941	95	1	first	first	ADV
ejpam-4941	95	2	,	,	PUNCT
ejpam-4941	95	3	we	we	PRON
ejpam-4941	95	4	recall	recall	VERB
ejpam-4941	95	5	how	how	SCONJ
ejpam-4941	95	6	we	we	PRON
ejpam-4941	95	7	generally	generally	ADV
ejpam-4941	95	8	construct	construct	VERB
ejpam-4941	95	9	an	an	DET
ejpam-4941	95	10	orthogonal	orthogonal	ADJ
ejpam-4941	95	11	gs	gs	NOUN
ejpam-4941	95	12	basis	basis	NOUN
ejpam-4941	95	13	without	without	ADP
ejpam-4941	95	14	necessarily	necessarily	ADV
ejpam-4941	95	15	orthonormalizing	orthonormalize	VERB
ejpam-4941	95	16	its	its	PRON
ejpam-4941	95	17	new	new	ADJ
ejpam-4941	95	18	vectors	vector	NOUN
ejpam-4941	95	19	.	.	PUNCT
ejpam-4941	96	1	this	this	PRON
ejpam-4941	96	2	is	be	AUX
ejpam-4941	96	3	to	to	PART
ejpam-4941	96	4	say	say	VERB
ejpam-4941	96	5	that	that	SCONJ
ejpam-4941	96	6	in	in	ADP
ejpam-4941	96	7	case	case	NOUN
ejpam-4941	96	8	of	of	ADP
ejpam-4941	96	9	an	an	DET
ejpam-4941	96	10	orthonormalization	orthonormalization	NOUN
ejpam-4941	96	11	process	process	NOUN
ejpam-4941	96	12	,	,	PUNCT
ejpam-4941	96	13	one	one	PRON
ejpam-4941	96	14	would	would	AUX
ejpam-4941	96	15	simply	simply	ADV
ejpam-4941	96	16	consider	consider	VERB
ejpam-4941	96	17	later	later	ADV
ejpam-4941	96	18	,	,	PUNCT
ejpam-4941	96	19	the	the	DET
ejpam-4941	96	20	division	division	NOUN
ejpam-4941	96	21	of	of	ADP
ejpam-4941	96	22	those	those	DET
ejpam-4941	96	23	vectors	vector	NOUN
ejpam-4941	96	24	on	on	ADP
ejpam-4941	96	25	their	their	PRON
ejpam-4941	96	26	norms	norm	NOUN
ejpam-4941	96	27	at	at	ADP
ejpam-4941	96	28	each	each	DET
ejpam-4941	96	29	iteration	iteration	NOUN
ejpam-4941	96	30	.	.	PUNCT
ejpam-4941	97	1	let	let	VERB
ejpam-4941	97	2	us	we	PRON
ejpam-4941	97	3	then	then	ADV
ejpam-4941	97	4	start	start	VERB
ejpam-4941	97	5	with	with	ADP
ejpam-4941	97	6	the	the	DET
ejpam-4941	97	7	definition	definition	NOUN
ejpam-4941	97	8	of	of	ADP
ejpam-4941	97	9	b	b	NOUN
ejpam-4941	97	10	=	=	SYM
ejpam-4941	97	11	(	(	PUNCT
ejpam-4941	97	12	e1	e1	PROPN
ejpam-4941	97	13	,	,	PUNCT
ejpam-4941	97	14	...	...	PUNCT
ejpam-4941	97	15	,	,	PUNCT
ejpam-4941	97	16	en	en	X
ejpam-4941	97	17	)	)	PUNCT
ejpam-4941	97	18	as	as	ADP
ejpam-4941	97	19	a	a	DET
ejpam-4941	97	20	basis	basis	NOUN
ejpam-4941	97	21	of	of	ADP
ejpam-4941	97	22	rn	rn	PROPN
ejpam-4941	97	23	,	,	PUNCT
ejpam-4941	97	24	therefore	therefore	ADV
ejpam-4941	97	25	,	,	PUNCT
ejpam-4941	97	26	the	the	DET
ejpam-4941	97	27	associated	associated	ADJ
ejpam-4941	97	28	gs	gs	PROPN
ejpam-4941	97	29	orthogonal	orthogonal	ADJ
ejpam-4941	97	30	basis	basis	NOUN
ejpam-4941	97	31	b∗	b∗	ADV
ejpam-4941	98	1	=	=	SYM
ejpam-4941	98	2	(	(	PUNCT
ejpam-4941	98	3	e∗1	e∗1	ADJ
ejpam-4941	98	4	,	,	PUNCT
ejpam-4941	98	5	...	...	PUNCT
ejpam-4941	98	6	,	,	PUNCT
ejpam-4941	98	7	e	e	NOUN
ejpam-4941	98	8	∗	∗	NOUN
ejpam-4941	98	9	n	n	CCONJ
ejpam-4941	98	10	)	)	PUNCT
ejpam-4941	98	11	,	,	PUNCT
ejpam-4941	98	12	is	be	AUX
ejpam-4941	98	13	defined	define	VERB
ejpam-4941	98	14	as	as	SCONJ
ejpam-4941	98	15	follows	follow	VERB
ejpam-4941	99	1	e∗1	e∗1	ADJ
ejpam-4941	99	2	=	=	PUNCT
ejpam-4941	99	3	e1	e1	NOUN
ejpam-4941	99	4	e∗2	e∗2	NOUN
ejpam-4941	99	5	=	=	SYM
ejpam-4941	99	6	e2	e2	PROPN
ejpam-4941	99	7	−	−	PROPN
ejpam-4941	99	8	⟨e2	⟨e2	PROPN
ejpam-4941	99	9	,	,	PUNCT
ejpam-4941	99	10	e∗1⟩	e∗1⟩	PROPN
ejpam-4941	99	11	⟨e∗1	⟨e∗1	PROPN
ejpam-4941	99	12	,	,	PUNCT
ejpam-4941	99	13	e∗1⟩	e∗1⟩	ADJ
ejpam-4941	99	14	e∗1	e∗1	PROPN
ejpam-4941	99	15	,	,	PUNCT
ejpam-4941	99	16	s.	s.	PROPN
ejpam-4941	99	17	abdelalim	abdelalim	PROPN
ejpam-4941	99	18	,	,	PUNCT
ejpam-4941	99	19	i.	i.	PROPN
ejpam-4941	99	20	elmouki	elmouki	PROPN
ejpam-4941	99	21	/	/	SYM
ejpam-4941	99	22	eur	eur	PROPN
ejpam-4941	99	23	.	.	PUNCT
ejpam-4941	100	1	j.	j.	PROPN
ejpam-4941	100	2	pure	pure	PROPN
ejpam-4941	100	3	appl	appl	PROPN
ejpam-4941	100	4	.	.	PROPN
ejpam-4941	100	5	math	math	PROPN
ejpam-4941	100	6	,	,	PUNCT
ejpam-4941	100	7	16	16	NUM
ejpam-4941	100	8	(	(	PUNCT
ejpam-4941	100	9	4	4	NUM
ejpam-4941	100	10	)	)	PUNCT
ejpam-4941	100	11	(	(	PUNCT
ejpam-4941	100	12	2023	2023	NUM
ejpam-4941	100	13	)	)	PUNCT
ejpam-4941	100	14	,	,	PUNCT
ejpam-4941	100	15	2662	2662	NUM
ejpam-4941	100	16	-	-	SYM
ejpam-4941	100	17	2692	2692	NUM
ejpam-4941	100	18	2669	2669	NUM
ejpam-4941	100	19	e∗3	e∗3	NOUN
ejpam-4941	100	20	=	=	PUNCT
ejpam-4941	100	21	e3	e3	VERB
ejpam-4941	100	22	−	−	PROPN
ejpam-4941	100	23	⟨e3	⟨e3	NOUN
ejpam-4941	100	24	,	,	PUNCT
ejpam-4941	100	25	e∗1⟩	e∗1⟩	PROPN
ejpam-4941	100	26	⟨e∗1	⟨e∗1	PROPN
ejpam-4941	100	27	,	,	PUNCT
ejpam-4941	100	28	e∗1⟩	e∗1⟩	ADJ
ejpam-4941	100	29	e∗1	e∗1	NOUN
ejpam-4941	100	30	−	−	PROPN
ejpam-4941	101	1	⟨e3	⟨e3	NOUN
ejpam-4941	101	2	,	,	PUNCT
ejpam-4941	101	3	e∗2⟩	e∗2⟩	ADJ
ejpam-4941	101	4	⟨e∗2	⟨e∗2	NOUN
ejpam-4941	101	5	,	,	PUNCT
ejpam-4941	101	6	e∗2⟩	e∗2⟩	ADJ
ejpam-4941	101	7	e∗2	e∗2	NOUN
ejpam-4941	101	8	...	...	PUNCT
ejpam-4941	101	9	...	...	PUNCT
ejpam-4941	102	1	e∗n	e∗n	PROPN
ejpam-4941	102	2	=	=	SYM
ejpam-4941	102	3	en	en	ADP
ejpam-4941	102	4	−	−	PROPN
ejpam-4941	102	5	n−1∑	n−1∑	PROPN
ejpam-4941	102	6	k=1	k=1	PROPN
ejpam-4941	103	1	⟨en	⟨en	PROPN
ejpam-4941	103	2	,	,	PUNCT
ejpam-4941	103	3	e∗k⟩	e∗k⟩	NOUN
ejpam-4941	103	4	⟨e∗k	⟨e∗k	PROPN
ejpam-4941	103	5	,	,	PUNCT
ejpam-4941	103	6	e∗k⟩	e∗k⟩	AUX
ejpam-4941	103	7	e∗k	e∗k	PUNCT
ejpam-4941	103	8	if	if	SCONJ
ejpam-4941	103	9	we	we	PRON
ejpam-4941	103	10	are	be	AUX
ejpam-4941	103	11	considering	consider	VERB
ejpam-4941	103	12	orthonormalization	orthonormalization	NOUN
ejpam-4941	103	13	of	of	ADP
ejpam-4941	103	14	these	these	DET
ejpam-4941	103	15	vectors	vector	NOUN
ejpam-4941	103	16	and	and	CCONJ
ejpam-4941	103	17	which	which	PRON
ejpam-4941	103	18	is	be	AUX
ejpam-4941	103	19	the	the	DET
ejpam-4941	103	20	most	most	ADV
ejpam-4941	103	21	popular	popular	ADJ
ejpam-4941	103	22	step	step	NOUN
ejpam-4941	103	23	to	to	PART
ejpam-4941	103	24	achieve	achieve	VERB
ejpam-4941	103	25	the	the	DET
ejpam-4941	103	26	straightforwardness	straightforwardness	NOUN
ejpam-4941	103	27	of	of	ADP
ejpam-4941	103	28	coordinate	coordinate	NOUN
ejpam-4941	103	29	representation	representation	NOUN
ejpam-4941	103	30	,	,	PUNCT
ejpam-4941	103	31	we	we	PRON
ejpam-4941	103	32	simply	simply	ADV
ejpam-4941	103	33	proceed	proceed	VERB
ejpam-4941	103	34	at	at	ADP
ejpam-4941	103	35	each	each	DET
ejpam-4941	103	36	iteration	iteration	NOUN
ejpam-4941	103	37	of	of	ADP
ejpam-4941	103	38	the	the	DET
ejpam-4941	103	39	orthogonalization	orthogonalization	NOUN
ejpam-4941	103	40	process	process	NOUN
ejpam-4941	103	41	as	as	SCONJ
ejpam-4941	103	42	follows	follow	VERB
ejpam-4941	103	43	e∗i	e∗i	NUM
ejpam-4941	103	44	→	→	SYM
ejpam-4941	103	45	e∗i	e∗i	NUM
ejpam-4941	103	46	|e∗i	|e∗i	NOUN
ejpam-4941	104	1	|	|	ADV
ejpam-4941	104	2	,	,	PUNCT
ejpam-4941	104	3	1	1	NUM
ejpam-4941	104	4	≤	≤	NUM
ejpam-4941	104	5	i	i	PRON
ejpam-4941	104	6	≤	≤	NOUN
ejpam-4941	104	7	n	n	CCONJ
ejpam-4941	104	8	alternatively	alternatively	ADV
ejpam-4941	104	9	,	,	PUNCT
ejpam-4941	104	10	following	follow	VERB
ejpam-4941	104	11	the	the	DET
ejpam-4941	104	12	mgs	mgs	NOUN
ejpam-4941	104	13	process	process	NOUN
ejpam-4941	104	14	,	,	PUNCT
ejpam-4941	104	15	we	we	PRON
ejpam-4941	104	16	consider	consider	VERB
ejpam-4941	104	17	the	the	DET
ejpam-4941	104	18	associated	associated	ADJ
ejpam-4941	104	19	gs	gs	PROPN
ejpam-4941	104	20	orthogonal	orthogonal	ADJ
ejpam-4941	104	21	modified	modify	VERB
ejpam-4941	104	22	basis	basis	NOUN
ejpam-4941	104	23	b∗∗	b∗∗	NOUN
ejpam-4941	104	24	=	=	SYM
ejpam-4941	104	25	(	(	PUNCT
ejpam-4941	104	26	e∗∗1	e∗∗1	PROPN
ejpam-4941	104	27	,	,	PUNCT
ejpam-4941	104	28	...	...	PUNCT
ejpam-4941	104	29	,	,	PUNCT
ejpam-4941	104	30	e∗∗n	e∗∗n	PROPN
ejpam-4941	104	31	)	)	PUNCT
ejpam-4941	104	32	,	,	PUNCT
ejpam-4941	104	33	defined	define	VERB
ejpam-4941	104	34	as	as	SCONJ
ejpam-4941	104	35	follows	follow	VERB
ejpam-4941	104	36	e∗∗1	e∗∗1	NOUN
ejpam-4941	104	37	=	=	NOUN
ejpam-4941	104	38	e1	e1	VERB
ejpam-4941	104	39	e∗∗2	e∗∗2	NOUN
ejpam-4941	104	40	→	→	SYM
ejpam-4941	104	41	e	e	X
ejpam-4941	104	42	∗∗(1	∗∗(1	PROPN
ejpam-4941	104	43	)	)	PUNCT
ejpam-4941	104	44	2	2	NUM
ejpam-4941	104	45	=	=	SYM
ejpam-4941	104	46	e2	e2	PROPN
ejpam-4941	104	47	−	−	PROPN
ejpam-4941	104	48	⟨e2	⟨e2	PROPN
ejpam-4941	104	49	,	,	PUNCT
ejpam-4941	104	50	e∗∗1	e∗∗1	PROPN
ejpam-4941	104	51	⟩	⟩	NOUN
ejpam-4941	104	52	⟨e∗∗1	⟨e∗∗1	NUM
ejpam-4941	104	53	,	,	PUNCT
ejpam-4941	104	54	e∗∗1	e∗∗1	PROPN
ejpam-4941	104	55	⟩	⟩	NOUN
ejpam-4941	104	56	e∗∗1	e∗∗1	NOUN
ejpam-4941	104	57	,	,	PUNCT
ejpam-4941	104	58	e	e	X
ejpam-4941	104	59	∗∗(1	∗∗(1	X
ejpam-4941	104	60	)	)	PUNCT
ejpam-4941	104	61	3	3	NUM
ejpam-4941	104	62	=	=	NOUN
ejpam-4941	104	63	e3	e3	VERB
ejpam-4941	104	64	−	−	PROPN
ejpam-4941	104	65	⟨e3	⟨e3	NOUN
ejpam-4941	104	66	,	,	PUNCT
ejpam-4941	104	67	e∗∗1	e∗∗1	NOUN
ejpam-4941	104	68	⟩	⟩	NOUN
ejpam-4941	104	69	⟨e∗∗1	⟨e∗∗1	NUM
ejpam-4941	104	70	,	,	PUNCT
ejpam-4941	104	71	e∗∗1	e∗∗1	PROPN
ejpam-4941	104	72	⟩	⟩	NOUN
ejpam-4941	104	73	e∗∗1	e∗∗1	PROPN
ejpam-4941	104	74	e∗∗3	e∗∗3	PROPN
ejpam-4941	104	75	→	→	PUNCT
ejpam-4941	104	76	e	e	X
ejpam-4941	104	77	∗∗(2	∗∗(2	PROPN
ejpam-4941	104	78	)	)	PUNCT
ejpam-4941	104	79	3	3	NUM
ejpam-4941	104	80	=	=	SYM
ejpam-4941	104	81	e	e	X
ejpam-4941	104	82	∗∗(1	∗∗(1	PROPN
ejpam-4941	104	83	)	)	PUNCT
ejpam-4941	104	84	3	3	NUM
ejpam-4941	104	85	−	−	NOUN
ejpam-4941	104	86	⟨e∗∗(1)3	⟨e∗∗(1)3	NOUN
ejpam-4941	104	87	,	,	PUNCT
ejpam-4941	104	88	e∗∗2	e∗∗2	PROPN
ejpam-4941	104	89	⟩	⟩	PROPN
ejpam-4941	104	90	⟨e∗∗2	⟨e∗∗2	PROPN
ejpam-4941	104	91	,	,	PUNCT
ejpam-4941	104	92	e∗∗2	e∗∗2	PROPN
ejpam-4941	104	93	⟩	⟩	PROPN
ejpam-4941	104	94	e∗∗2	e∗∗2	PROPN
ejpam-4941	104	95	...	...	PUNCT
ejpam-4941	104	96	...	...	PUNCT
ejpam-4941	105	1	e∗∗(k−1	e∗∗(k−1	X
ejpam-4941	105	2	)	)	PUNCT
ejpam-4941	105	3	n	n	NOUN
ejpam-4941	105	4	=	=	SYM
ejpam-4941	105	5	en	en	ADP
ejpam-4941	105	6	−	−	PROPN
ejpam-4941	105	7	⟨en	⟨en	NUM
ejpam-4941	105	8	,	,	PUNCT
ejpam-4941	105	9	e∗∗k−1⟩	e∗∗k−1⟩	PROPN
ejpam-4941	105	10	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	105	11	,	,	PUNCT
ejpam-4941	105	12	e	e	X
ejpam-4941	105	13	∗∗	∗∗	X
ejpam-4941	106	1	k−1⟩	k−1⟩	ADV
ejpam-4941	106	2	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	106	3	,	,	PUNCT
ejpam-4941	106	4	k	k	NOUN
ejpam-4941	106	5	=	=	SYM
ejpam-4941	106	6	2	2	NUM
ejpam-4941	106	7	,	,	PUNCT
ejpam-4941	106	8	...	...	PUNCT
ejpam-4941	106	9	,	,	PUNCT
ejpam-4941	106	10	n−	n−	NOUN
ejpam-4941	106	11	1	1	NUM
ejpam-4941	106	12	e∗∗n	e∗∗n	ADV
ejpam-4941	106	13	→	→	SYM
ejpam-4941	106	14	e∗∗(k)n	e∗∗(k)n	PROPN
ejpam-4941	106	15	=	=	PUNCT
ejpam-4941	106	16	e∗∗(k−1	e∗∗(k−1	NOUN
ejpam-4941	106	17	)	)	PUNCT
ejpam-4941	106	18	n	n	CCONJ
ejpam-4941	106	19	−	−	PROPN
ejpam-4941	106	20	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	106	21	)	)	PUNCT
ejpam-4941	106	22	n	n	NOUN
ejpam-4941	106	23	,	,	PUNCT
ejpam-4941	106	24	e∗∗k	e∗∗k	PROPN
ejpam-4941	106	25	⟩	⟩	NOUN
ejpam-4941	106	26	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	106	27	,	,	PUNCT
ejpam-4941	106	28	e∗∗k	e∗∗k	PROPN
ejpam-4941	106	29	⟩	⟩	PROPN
ejpam-4941	106	30	e∗∗k	e∗∗k	PROPN
ejpam-4941	106	31	,	,	PUNCT
ejpam-4941	106	32	k	k	PROPN
ejpam-4941	106	33	=	=	SYM
ejpam-4941	106	34	2	2	NUM
ejpam-4941	106	35	,	,	PUNCT
ejpam-4941	106	36	...	...	PUNCT
ejpam-4941	106	37	,	,	PUNCT
ejpam-4941	106	38	n−	n−	NOUN
ejpam-4941	106	39	1	1	NUM
ejpam-4941	106	40	and	and	CCONJ
ejpam-4941	106	41	if	if	SCONJ
ejpam-4941	106	42	we	we	PRON
ejpam-4941	106	43	are	be	AUX
ejpam-4941	106	44	considering	consider	VERB
ejpam-4941	106	45	orthonormalization	orthonormalization	NOUN
ejpam-4941	106	46	of	of	ADP
ejpam-4941	106	47	these	these	DET
ejpam-4941	106	48	vectors	vector	NOUN
ejpam-4941	106	49	at	at	ADP
ejpam-4941	106	50	every	every	DET
ejpam-4941	106	51	iteration	iteration	NOUN
ejpam-4941	106	52	,	,	PUNCT
ejpam-4941	106	53	we	we	PRON
ejpam-4941	106	54	proceed	proceed	VERB
ejpam-4941	106	55	as	as	SCONJ
ejpam-4941	106	56	follows	follow	VERB
ejpam-4941	106	57	e∗∗1	e∗∗1	NOUN
ejpam-4941	106	58	→	→	SYM
ejpam-4941	106	59	e∗∗1	e∗∗1	NOUN
ejpam-4941	106	60	|e∗∗1	|e∗∗1	NOUN
ejpam-4941	106	61	|	|	ADV
ejpam-4941	106	62	,	,	PUNCT
ejpam-4941	106	63	e∗∗i	e∗∗i	NOUN
ejpam-4941	106	64	→	→	PUNCT
ejpam-4941	106	65	e	e	X
ejpam-4941	106	66	∗∗(i−1	∗∗(i−1	PROPN
ejpam-4941	106	67	)	)	PUNCT
ejpam-4941	106	68	i	i	PROPN
ejpam-4941	106	69	|e∗∗i−1|	|e∗∗i−1|	PROPN
ejpam-4941	106	70	,	,	PUNCT
ejpam-4941	106	71	2	2	NUM
ejpam-4941	106	72	≤	≤	NUM
ejpam-4941	106	73	i	i	PRON
ejpam-4941	106	74	≤	≤	NOUN
ejpam-4941	106	75	n	n	CCONJ
ejpam-4941	106	76	since	since	SCONJ
ejpam-4941	106	77	we	we	PRON
ejpam-4941	106	78	need	need	VERB
ejpam-4941	106	79	to	to	PART
ejpam-4941	106	80	use	use	VERB
ejpam-4941	106	81	some	some	DET
ejpam-4941	106	82	direct	direct	ADJ
ejpam-4941	106	83	but	but	CCONJ
ejpam-4941	106	84	important	important	ADJ
ejpam-4941	106	85	properties	property	NOUN
ejpam-4941	106	86	of	of	ADP
ejpam-4941	106	87	such	such	ADJ
ejpam-4941	106	88	considerations	consideration	NOUN
ejpam-4941	106	89	in	in	ADP
ejpam-4941	106	90	the	the	DET
ejpam-4941	106	91	proof	proof	NOUN
ejpam-4941	106	92	of	of	ADP
ejpam-4941	106	93	theorem	theorem	ADJ
ejpam-4941	106	94	2	2	NUM
ejpam-4941	106	95	hereafter	hereafter	ADV
ejpam-4941	106	96	either	either	CCONJ
ejpam-4941	106	97	in	in	ADP
ejpam-4941	106	98	the	the	DET
ejpam-4941	106	99	case	case	NOUN
ejpam-4941	106	100	of	of	ADP
ejpam-4941	106	101	gs	gs	NOUN
ejpam-4941	106	102	or	or	CCONJ
ejpam-4941	106	103	mgs	mgs	NOUN
ejpam-4941	106	104	,	,	PUNCT
ejpam-4941	106	105	we	we	PRON
ejpam-4941	106	106	prove	prove	VERB
ejpam-4941	106	107	them	they	PRON
ejpam-4941	106	108	now	now	ADV
ejpam-4941	106	109	in	in	ADP
ejpam-4941	106	110	the	the	DET
ejpam-4941	106	111	following	follow	VERB
ejpam-4941	106	112	theorem	theorem	NOUN
ejpam-4941	106	113	and	and	CCONJ
ejpam-4941	106	114	they	they	PRON
ejpam-4941	106	115	concern	concern	VERB
ejpam-4941	106	116	the	the	DET
ejpam-4941	106	117	orthogonality	orthogonality	NOUN
ejpam-4941	106	118	between	between	ADP
ejpam-4941	106	119	vectors	vector	NOUN
ejpam-4941	106	120	when	when	SCONJ
ejpam-4941	106	121	they	they	PRON
ejpam-4941	106	122	are	be	AUX
ejpam-4941	106	123	different	different	ADJ
ejpam-4941	106	124	and	and	CCONJ
ejpam-4941	106	125	the	the	DET
ejpam-4941	106	126	equality	equality	NOUN
ejpam-4941	106	127	between	between	ADP
ejpam-4941	106	128	the	the	DET
ejpam-4941	106	129	linear	linear	ADJ
ejpam-4941	106	130	spans	span	NOUN
ejpam-4941	106	131	between	between	ADP
ejpam-4941	106	132	first	first	ADJ
ejpam-4941	106	133	input	input	NOUN
ejpam-4941	106	134	vectors	vector	NOUN
ejpam-4941	106	135	and	and	CCONJ
ejpam-4941	106	136	the	the	DET
ejpam-4941	106	137	orthogonal	orthogonal	ADJ
ejpam-4941	106	138	vectors	vector	NOUN
ejpam-4941	106	139	obtained	obtain	VERB
ejpam-4941	106	140	.	.	PUNCT
ejpam-4941	107	1	s.	s.	PROPN
ejpam-4941	107	2	abdelalim	abdelalim	PROPN
ejpam-4941	107	3	,	,	PUNCT
ejpam-4941	107	4	i.	i.	PROPN
ejpam-4941	107	5	elmouki	elmouki	PROPN
ejpam-4941	107	6	/	/	SYM
ejpam-4941	107	7	eur	eur	PROPN
ejpam-4941	107	8	.	.	PUNCT
ejpam-4941	108	1	j.	j.	PROPN
ejpam-4941	108	2	pure	pure	PROPN
ejpam-4941	108	3	appl	appl	PROPN
ejpam-4941	108	4	.	.	PROPN
ejpam-4941	108	5	math	math	PROPN
ejpam-4941	108	6	,	,	PUNCT
ejpam-4941	108	7	16	16	NUM
ejpam-4941	108	8	(	(	PUNCT
ejpam-4941	108	9	4	4	NUM
ejpam-4941	108	10	)	)	PUNCT
ejpam-4941	108	11	(	(	PUNCT
ejpam-4941	108	12	2023	2023	NUM
ejpam-4941	108	13	)	)	PUNCT
ejpam-4941	108	14	,	,	PUNCT
ejpam-4941	108	15	2662	2662	NUM
ejpam-4941	108	16	-	-	SYM
ejpam-4941	108	17	2692	2692	NUM
ejpam-4941	108	18	2670	2670	NUM
ejpam-4941	108	19	theorem	theorem	NOUN
ejpam-4941	108	20	1	1	NUM
ejpam-4941	108	21	.	.	PUNCT
ejpam-4941	109	1	let	let	VERB
ejpam-4941	109	2	b	b	NOUN
ejpam-4941	109	3	=	=	SYM
ejpam-4941	109	4	(	(	PUNCT
ejpam-4941	109	5	e1	e1	PROPN
ejpam-4941	109	6	,	,	PUNCT
ejpam-4941	109	7	...	...	PUNCT
ejpam-4941	109	8	,	,	PUNCT
ejpam-4941	109	9	en	en	X
ejpam-4941	109	10	)	)	PUNCT
ejpam-4941	109	11	be	be	AUX
ejpam-4941	109	12	a	a	DET
ejpam-4941	109	13	basis	basis	NOUN
ejpam-4941	109	14	of	of	ADP
ejpam-4941	109	15	rn	rn	PROPN
ejpam-4941	109	16	,	,	PUNCT
ejpam-4941	109	17	b∗∗	b∗∗	X
ejpam-4941	109	18	=	=	SYM
ejpam-4941	109	19	(	(	PUNCT
ejpam-4941	109	20	e∗∗1	e∗∗1	PROPN
ejpam-4941	109	21	,	,	PUNCT
ejpam-4941	109	22	...	...	PUNCT
ejpam-4941	109	23	,	,	PUNCT
ejpam-4941	109	24	e∗∗n	e∗∗n	PROPN
ejpam-4941	109	25	)	)	PUNCT
ejpam-4941	109	26	and	and	CCONJ
ejpam-4941	109	27	b∗	b∗	ADJ
ejpam-4941	109	28	=	=	SYM
ejpam-4941	109	29	(	(	PUNCT
ejpam-4941	109	30	e∗1	e∗1	ADJ
ejpam-4941	109	31	,	,	PUNCT
ejpam-4941	109	32	...	...	PUNCT
ejpam-4941	109	33	,	,	PUNCT
ejpam-4941	109	34	e	e	NOUN
ejpam-4941	109	35	∗	∗	NOUN
ejpam-4941	109	36	n	n	CCONJ
ejpam-4941	109	37	)	)	PUNCT
ejpam-4941	109	38	its	its	PRON
ejpam-4941	109	39	associated	associated	ADJ
ejpam-4941	109	40	mgs	mgs	NOUN
ejpam-4941	109	41	and	and	CCONJ
ejpam-4941	109	42	gs	gs	PROPN
ejpam-4941	109	43	basis	basis	NOUN
ejpam-4941	109	44	respectively	respectively	ADV
ejpam-4941	109	45	,	,	PUNCT
ejpam-4941	109	46	then	then	ADV
ejpam-4941	109	47	,	,	PUNCT
ejpam-4941	109	48	the	the	DET
ejpam-4941	109	49	following	follow	VERB
ejpam-4941	109	50	properties	property	NOUN
ejpam-4941	109	51	are	be	AUX
ejpam-4941	109	52	verified	verify	VERB
ejpam-4941	109	53	•	•	NUM
ejpam-4941	110	1	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	110	2	)	)	PUNCT
ejpam-4941	111	1	i	i	PRON
ejpam-4941	111	2	,	,	PUNCT
ejpam-4941	111	3	e	e	NOUN
ejpam-4941	111	4	∗∗(k	∗∗(k	NOUN
ejpam-4941	111	5	)	)	PUNCT
ejpam-4941	111	6	j	j	PROPN
ejpam-4941	111	7	⟩	⟩	PROPN
ejpam-4941	111	8	=	=	NOUN
ejpam-4941	111	9	0	0	NUM
ejpam-4941	111	10	for	for	ADP
ejpam-4941	111	11	1	1	NUM
ejpam-4941	111	12	≤	≤	NUM
ejpam-4941	111	13	i	i	PRON
ejpam-4941	111	14	≤	≤	PUNCT
ejpam-4941	112	1	k	k	X
ejpam-4941	112	2	<	<	X
ejpam-4941	112	3	j	j	PROPN
ejpam-4941	112	4	≤	≤	PROPN
ejpam-4941	112	5	n	n	CCONJ
ejpam-4941	112	6	,	,	PUNCT
ejpam-4941	112	7	2	2	NUM
ejpam-4941	112	8	≤	≤	NUM
ejpam-4941	112	9	k	k	X
ejpam-4941	112	10	≤	≤	PROPN
ejpam-4941	112	11	n−	n−	PROPN
ejpam-4941	112	12	1	1	NUM
ejpam-4941	112	13	,	,	PUNCT
ejpam-4941	112	14	and	and	CCONJ
ejpam-4941	112	15	⟨e∗i	⟨e∗i	INTJ
ejpam-4941	112	16	,	,	PUNCT
ejpam-4941	112	17	e∗j	e∗j	NUM
ejpam-4941	112	18	⟩	⟩	NOUN
ejpam-4941	112	19	=	=	NOUN
ejpam-4941	112	20	0	0	NUM
ejpam-4941	113	1	for	for	ADP
ejpam-4941	113	2	1	1	NUM
ejpam-4941	113	3	≤	≤	NUM
ejpam-4941	113	4	i	i	PRON
ejpam-4941	113	5	<	<	X
ejpam-4941	113	6	j	j	PROPN
ejpam-4941	113	7	≤	≤	X
ejpam-4941	113	8	n.	n.	NOUN
ejpam-4941	113	9	•	•	NOUN
ejpam-4941	113	10	span(e1	span(e1	NOUN
ejpam-4941	113	11	,	,	PUNCT
ejpam-4941	113	12	...	...	PUNCT
ejpam-4941	113	13	,	,	PUNCT
ejpam-4941	113	14	en	en	X
ejpam-4941	113	15	)	)	PUNCT
ejpam-4941	113	16	=	=	VERB
ejpam-4941	113	17	span(e∗∗1	span(e∗∗1	ADJ
ejpam-4941	113	18	,	,	PUNCT
ejpam-4941	113	19	e	e	X
ejpam-4941	113	20	∗∗(1	∗∗(1	X
ejpam-4941	113	21	)	)	PUNCT
ejpam-4941	113	22	2	2	NUM
ejpam-4941	113	23	,	,	PUNCT
ejpam-4941	113	24	e	e	X
ejpam-4941	113	25	∗∗(2	∗∗(2	PROPN
ejpam-4941	113	26	)	)	PUNCT
ejpam-4941	113	27	3	3	NUM
ejpam-4941	113	28	,	,	PUNCT
ejpam-4941	113	29	...	...	PUNCT
ejpam-4941	113	30	,	,	PUNCT
ejpam-4941	113	31	e	e	NOUN
ejpam-4941	113	32	∗∗(k	∗∗(k	NOUN
ejpam-4941	113	33	)	)	PUNCT
ejpam-4941	113	34	n	n	CCONJ
ejpam-4941	113	35	)	)	PUNCT
ejpam-4941	113	36	,	,	PUNCT
ejpam-4941	113	37	2	2	NUM
ejpam-4941	113	38	≤	≤	NUM
ejpam-4941	113	39	k	k	X
ejpam-4941	113	40	≤	≤	PROPN
ejpam-4941	113	41	n−	n−	PROPN
ejpam-4941	113	42	1	1	NUM
ejpam-4941	113	43	and	and	CCONJ
ejpam-4941	113	44	span(e1	span(e1	NOUN
ejpam-4941	113	45	,	,	PUNCT
ejpam-4941	113	46	...	...	PUNCT
ejpam-4941	113	47	,	,	PUNCT
ejpam-4941	113	48	en	en	X
ejpam-4941	113	49	)	)	PUNCT
ejpam-4941	113	50	=	=	SYM
ejpam-4941	113	51	span(e∗1	span(e∗1	PROPN
ejpam-4941	113	52	,	,	PUNCT
ejpam-4941	113	53	...	...	PUNCT
ejpam-4941	113	54	,	,	PUNCT
ejpam-4941	113	55	e	e	NOUN
ejpam-4941	113	56	∗	∗	NOUN
ejpam-4941	113	57	n	n	CCONJ
ejpam-4941	113	58	)	)	PUNCT
ejpam-4941	113	59	proof	proof	NOUN
ejpam-4941	113	60	.	.	PUNCT
ejpam-4941	114	1	•	•	NUM
ejpam-4941	114	2	–	–	PUNCT
ejpam-4941	114	3	to	to	ADP
ejpam-4941	114	4	the	the	DET
ejpam-4941	114	5	best	good	ADJ
ejpam-4941	114	6	of	of	ADP
ejpam-4941	114	7	our	our	PRON
ejpam-4941	114	8	knowledge	knowledge	NOUN
ejpam-4941	114	9	,	,	PUNCT
ejpam-4941	114	10	there	there	PRON
ejpam-4941	114	11	is	be	VERB
ejpam-4941	114	12	a	a	DET
ejpam-4941	114	13	lack	lack	NOUN
ejpam-4941	114	14	of	of	ADP
ejpam-4941	114	15	rigorous	rigorous	ADJ
ejpam-4941	114	16	proof	proof	NOUN
ejpam-4941	114	17	of	of	ADP
ejpam-4941	114	18	the	the	DET
ejpam-4941	114	19	vectors	vector	NOUN
ejpam-4941	114	20	orthogonality	orthogonality	VERB
ejpam-4941	114	21	in	in	ADP
ejpam-4941	114	22	mgs	mgs	NOUN
ejpam-4941	114	23	case	case	NOUN
ejpam-4941	114	24	.	.	PUNCT
ejpam-4941	115	1	in	in	ADP
ejpam-4941	115	2	fact	fact	NOUN
ejpam-4941	115	3	,	,	PUNCT
ejpam-4941	115	4	as	as	SCONJ
ejpam-4941	115	5	we	we	PRON
ejpam-4941	115	6	will	will	AUX
ejpam-4941	115	7	see	see	VERB
ejpam-4941	115	8	hereafter	hereafter	ADV
ejpam-4941	115	9	,	,	PUNCT
ejpam-4941	115	10	a	a	DET
ejpam-4941	115	11	reasoning	reasoning	NOUN
ejpam-4941	115	12	by	by	ADP
ejpam-4941	115	13	induction	induction	NOUN
ejpam-4941	115	14	will	will	AUX
ejpam-4941	115	15	help	help	VERB
ejpam-4941	115	16	us	we	PRON
ejpam-4941	115	17	in	in	ADP
ejpam-4941	115	18	the	the	DET
ejpam-4941	115	19	proof	proof	NOUN
ejpam-4941	115	20	of	of	ADP
ejpam-4941	115	21	gs	gs	PART
ejpam-4941	115	22	case	case	NOUN
ejpam-4941	115	23	,	,	PUNCT
ejpam-4941	115	24	however	however	ADV
ejpam-4941	115	25	,	,	PUNCT
ejpam-4941	115	26	such	such	ADJ
ejpam-4941	115	27	reasoning	reasoning	NOUN
ejpam-4941	115	28	can	can	AUX
ejpam-4941	115	29	not	not	PART
ejpam-4941	115	30	work	work	VERB
ejpam-4941	115	31	for	for	ADP
ejpam-4941	115	32	mgs	mgs	NOUN
ejpam-4941	115	33	as	as	SCONJ
ejpam-4941	115	34	there	there	PRON
ejpam-4941	115	35	is	be	VERB
ejpam-4941	115	36	no	no	DET
ejpam-4941	115	37	kind	kind	NOUN
ejpam-4941	115	38	of	of	ADP
ejpam-4941	115	39	relation	relation	NOUN
ejpam-4941	115	40	between	between	ADP
ejpam-4941	115	41	the	the	DET
ejpam-4941	115	42	products	product	NOUN
ejpam-4941	115	43	⟨e∗∗(k)j	⟨e∗∗(k)j	NOUN
ejpam-4941	115	44	,	,	PUNCT
ejpam-4941	115	45	e	e	NOUN
ejpam-4941	115	46	∗∗(k−1	∗∗(k−1	X
ejpam-4941	115	47	)	)	PUNCT
ejpam-4941	115	48	i	i	PRON
ejpam-4941	115	49	⟩	⟩	NOUN
ejpam-4941	115	50	and	and	CCONJ
ejpam-4941	115	51	⟨e∗∗(k−1	⟨e∗∗(k−1	PROPN
ejpam-4941	115	52	)	)	PUNCT
ejpam-4941	115	53	j	j	PROPN
ejpam-4941	115	54	,	,	PUNCT
ejpam-4941	115	55	e	e	PROPN
ejpam-4941	115	56	∗∗(k−2	∗∗(k−2	PROPN
ejpam-4941	115	57	)	)	PUNCT
ejpam-4941	116	1	i	i	PRON
ejpam-4941	116	2	⟩	⟩	NOUN
ejpam-4941	116	3	,	,	PUNCT
ejpam-4941	116	4	2	2	NUM
ejpam-4941	116	5	≤	≤	NUM
ejpam-4941	116	6	k	k	X
ejpam-4941	116	7	≤	≤	PROPN
ejpam-4941	116	8	n−	n−	PROPN
ejpam-4941	116	9	1	1	NUM
ejpam-4941	116	10	.	.	PUNCT
ejpam-4941	117	1	then	then	ADV
ejpam-4941	117	2	,	,	PUNCT
ejpam-4941	117	3	we	we	PRON
ejpam-4941	117	4	will	will	AUX
ejpam-4941	117	5	proceed	proceed	VERB
ejpam-4941	117	6	as	as	ADP
ejpam-4941	117	7	in	in	ADP
ejpam-4941	117	8	the	the	DET
ejpam-4941	117	9	following	follow	VERB
ejpam-4941	117	10	three	three	NUM
ejpam-4941	117	11	sub	sub	NOUN
ejpam-4941	117	12	-	-	NOUN
ejpam-4941	117	13	cases	case	NOUN
ejpam-4941	117	14	and	and	CCONJ
ejpam-4941	117	15	general	general	ADJ
ejpam-4941	117	16	case	case	NOUN
ejpam-4941	117	17	.	.	PUNCT
ejpam-4941	118	1	let	let	VERB
ejpam-4941	118	2	us	we	PRON
ejpam-4941	118	3	show	show	VERB
ejpam-4941	118	4	first	first	ADV
ejpam-4941	118	5	why	why	SCONJ
ejpam-4941	118	6	the	the	DET
ejpam-4941	118	7	orthogonality	orthogonality	NOUN
ejpam-4941	118	8	property	property	NOUN
ejpam-4941	118	9	is	be	AUX
ejpam-4941	118	10	verified	verify	VERB
ejpam-4941	118	11	for	for	ADP
ejpam-4941	118	12	j	j	PROPN
ejpam-4941	118	13	=	=	SYM
ejpam-4941	118	14	2	2	NUM
ejpam-4941	118	15	,	,	PUNCT
ejpam-4941	118	16	3	3	NUM
ejpam-4941	118	17	,	,	PUNCT
ejpam-4941	118	18	4	4	NUM
ejpam-4941	118	19	.	.	X
ejpam-4941	119	1	we	we	PRON
ejpam-4941	119	2	start	start	VERB
ejpam-4941	119	3	with	with	ADP
ejpam-4941	119	4	j	j	PROPN
ejpam-4941	119	5	=	=	SYM
ejpam-4941	119	6	2	2	NUM
ejpam-4941	119	7	,	,	PUNCT
ejpam-4941	119	8	i	i	PRON
ejpam-4941	119	9	=	=	NOUN
ejpam-4941	119	10	1	1	NUM
ejpam-4941	119	11	and	and	CCONJ
ejpam-4941	119	12	k	k	NOUN
ejpam-4941	119	13	=	=	SYM
ejpam-4941	119	14	1	1	NUM
ejpam-4941	119	15	,	,	PUNCT
ejpam-4941	119	16	then	then	ADV
ejpam-4941	119	17	we	we	PRON
ejpam-4941	119	18	have	have	VERB
ejpam-4941	119	19	e	e	VERB
ejpam-4941	119	20	∗∗(1	∗∗(1	X
ejpam-4941	119	21	)	)	PUNCT
ejpam-4941	120	1	2	2	NUM
ejpam-4941	120	2	=	=	SYM
ejpam-4941	120	3	e2	e2	PROPN
ejpam-4941	120	4	−	−	PROPN
ejpam-4941	120	5	⟨e2	⟨e2	PROPN
ejpam-4941	120	6	,	,	PUNCT
ejpam-4941	120	7	e∗∗1	e∗∗1	PROPN
ejpam-4941	120	8	⟩	⟩	NOUN
ejpam-4941	120	9	⟨e∗∗1	⟨e∗∗1	NUM
ejpam-4941	120	10	,	,	PUNCT
ejpam-4941	120	11	e∗∗1	e∗∗1	PROPN
ejpam-4941	120	12	⟩	⟩	NOUN
ejpam-4941	120	13	e∗∗1	e∗∗1	PROPN
ejpam-4941	120	14	,	,	PUNCT
ejpam-4941	120	15	⟨e∗∗(1)2	⟨e∗∗(1)2	VERB
ejpam-4941	120	16	,	,	PUNCT
ejpam-4941	120	17	e∗∗1	e∗∗1	PROPN
ejpam-4941	120	18	⟩	⟩	NOUN
ejpam-4941	120	19	=	=	SYM
ejpam-4941	120	20	⟨e2	⟨e2	PROPN
ejpam-4941	120	21	,	,	PUNCT
ejpam-4941	120	22	e∗∗1	e∗∗1	ADJ
ejpam-4941	120	23	⟩	⟩	NOUN
ejpam-4941	120	24	−	−	PROPN
ejpam-4941	121	1	⟨e2	⟨e2	PROPN
ejpam-4941	121	2	,	,	PUNCT
ejpam-4941	121	3	e∗∗1	e∗∗1	PROPN
ejpam-4941	121	4	⟩	⟩	NOUN
ejpam-4941	121	5	⟨e∗∗1	⟨e∗∗1	NUM
ejpam-4941	121	6	,	,	PUNCT
ejpam-4941	121	7	e∗∗1	e∗∗1	PROPN
ejpam-4941	121	8	⟩	⟩	NOUN
ejpam-4941	121	9	⟨e∗∗1	⟨e∗∗1	NUM
ejpam-4941	121	10	,	,	PUNCT
ejpam-4941	121	11	e∗∗1	e∗∗1	PROPN
ejpam-4941	121	12	⟩	⟩	NOUN
ejpam-4941	121	13	=	=	NOUN
ejpam-4941	121	14	0	0	X
ejpam-4941	121	15	.	.	PUNCT
ejpam-4941	122	1	now	now	ADV
ejpam-4941	122	2	,	,	PUNCT
ejpam-4941	122	3	we	we	PRON
ejpam-4941	122	4	take	take	VERB
ejpam-4941	122	5	j	j	PROPN
ejpam-4941	122	6	=	=	SYM
ejpam-4941	122	7	3	3	NUM
ejpam-4941	122	8	,	,	PUNCT
ejpam-4941	122	9	i	i	PRON
ejpam-4941	122	10	=	=	NOUN
ejpam-4941	122	11	1	1	NUM
ejpam-4941	122	12	,	,	PUNCT
ejpam-4941	122	13	2	2	NUM
ejpam-4941	122	14	and	and	CCONJ
ejpam-4941	122	15	k	k	NOUN
ejpam-4941	122	16	=	=	SYM
ejpam-4941	122	17	2	2	NUM
ejpam-4941	122	18	,	,	PUNCT
ejpam-4941	122	19	we	we	PRON
ejpam-4941	122	20	have	have	VERB
ejpam-4941	122	21	e	e	NOUN
ejpam-4941	122	22	∗∗(2	∗∗(2	PROPN
ejpam-4941	122	23	)	)	PUNCT
ejpam-4941	122	24	3	3	NUM
ejpam-4941	122	25	=	=	SYM
ejpam-4941	122	26	e	e	X
ejpam-4941	122	27	∗∗(1	∗∗(1	PROPN
ejpam-4941	122	28	)	)	PUNCT
ejpam-4941	122	29	3	3	NUM
ejpam-4941	122	30	−	−	NOUN
ejpam-4941	122	31	⟨e∗∗(1)3	⟨e∗∗(1)3	NOUN
ejpam-4941	122	32	,	,	PUNCT
ejpam-4941	122	33	e∗∗2	e∗∗2	PROPN
ejpam-4941	122	34	⟩	⟩	PROPN
ejpam-4941	122	35	⟨e∗∗2	⟨e∗∗2	PROPN
ejpam-4941	122	36	,	,	PUNCT
ejpam-4941	122	37	e∗∗2	e∗∗2	PROPN
ejpam-4941	122	38	⟩	⟩	PROPN
ejpam-4941	122	39	e∗∗2	e∗∗2	NOUN
ejpam-4941	122	40	,	,	PUNCT
ejpam-4941	122	41	then	then	ADV
ejpam-4941	122	42	,	,	PUNCT
ejpam-4941	122	43	⟨e∗∗(2)3	⟨e∗∗(2)3	PRON
ejpam-4941	122	44	,	,	PUNCT
ejpam-4941	122	45	e	e	X
ejpam-4941	122	46	∗∗(1	∗∗(1	X
ejpam-4941	122	47	)	)	PUNCT
ejpam-4941	122	48	2	2	NUM
ejpam-4941	122	49	⟩	⟩	NOUN
ejpam-4941	122	50	=	=	SYM
ejpam-4941	122	51	⟨e∗∗(1)3	⟨e∗∗(1)3	NOUN
ejpam-4941	122	52	,	,	PUNCT
ejpam-4941	122	53	e	e	X
ejpam-4941	122	54	∗∗(1	∗∗(1	X
ejpam-4941	122	55	)	)	PUNCT
ejpam-4941	122	56	2	2	NUM
ejpam-4941	122	57	⟩	⟩	NOUN
ejpam-4941	122	58	−	−	NOUN
ejpam-4941	122	59	⟨e∗∗(1)3	⟨e∗∗(1)3	NOUN
ejpam-4941	122	60	,	,	PUNCT
ejpam-4941	122	61	e	e	X
ejpam-4941	122	62	∗∗(1	∗∗(1	X
ejpam-4941	122	63	)	)	PUNCT
ejpam-4941	122	64	2	2	NUM
ejpam-4941	122	65	⟩	⟩	NOUN
ejpam-4941	122	66	⟨e∗∗(1)2	⟨e∗∗(1)2	X
ejpam-4941	122	67	,	,	PUNCT
ejpam-4941	122	68	e	e	X
ejpam-4941	122	69	∗∗(1	∗∗(1	X
ejpam-4941	122	70	)	)	PUNCT
ejpam-4941	122	71	2	2	NUM
ejpam-4941	122	72	⟩	⟩	NOUN
ejpam-4941	122	73	⟨e∗∗(1)2	⟨e∗∗(1)2	X
ejpam-4941	122	74	,	,	PUNCT
ejpam-4941	122	75	e	e	X
ejpam-4941	122	76	∗∗(1	∗∗(1	X
ejpam-4941	122	77	)	)	PUNCT
ejpam-4941	122	78	2	2	NUM
ejpam-4941	122	79	⟩	⟩	NOUN
ejpam-4941	122	80	=	=	NOUN
ejpam-4941	122	81	0	0	X
ejpam-4941	122	82	.	.	PUNCT
ejpam-4941	123	1	we	we	PRON
ejpam-4941	123	2	also	also	ADV
ejpam-4941	123	3	have	have	VERB
ejpam-4941	123	4	,	,	PUNCT
ejpam-4941	123	5	⟨e∗∗(2)3	⟨e∗∗(2)3	PRON
ejpam-4941	123	6	,	,	PUNCT
ejpam-4941	123	7	e∗∗1	e∗∗1	PROPN
ejpam-4941	123	8	⟩	⟩	NOUN
ejpam-4941	123	9	=	=	SYM
ejpam-4941	123	10	⟨e∗∗(1)3	⟨e∗∗(1)3	NOUN
ejpam-4941	123	11	,	,	PUNCT
ejpam-4941	123	12	e∗∗1	e∗∗1	PROPN
ejpam-4941	123	13	⟩	⟩	NOUN
ejpam-4941	123	14	−	−	PROPN
ejpam-4941	123	15	⟨e∗∗(1)3	⟨e∗∗(1)3	NOUN
ejpam-4941	123	16	,	,	PUNCT
ejpam-4941	123	17	e	e	X
ejpam-4941	123	18	∗∗(1	∗∗(1	X
ejpam-4941	123	19	2	2	NUM
ejpam-4941	123	20	⟩	⟩	NOUN
ejpam-4941	123	21	⟨e∗∗(1)2	⟨e∗∗(1)2	X
ejpam-4941	123	22	,	,	PUNCT
ejpam-4941	123	23	e	e	X
ejpam-4941	123	24	∗∗(1	∗∗(1	X
ejpam-4941	123	25	)	)	PUNCT
ejpam-4941	123	26	2	2	NUM
ejpam-4941	123	27	⟩	⟩	NOUN
ejpam-4941	123	28	⟨e∗∗(1)2	⟨e∗∗(1)2	X
ejpam-4941	123	29	,	,	PUNCT
ejpam-4941	123	30	e∗∗1	e∗∗1	PROPN
ejpam-4941	123	31	⟩.	⟩.	PROPN
ejpam-4941	123	32	since	since	ADV
ejpam-4941	123	33	,	,	PUNCT
ejpam-4941	123	34	we	we	PRON
ejpam-4941	123	35	have	have	AUX
ejpam-4941	123	36	already	already	ADV
ejpam-4941	123	37	showed	show	VERB
ejpam-4941	123	38	that	that	SCONJ
ejpam-4941	123	39	⟨e∗∗(1)2	⟨e∗∗(1)2	VERB
ejpam-4941	123	40	,	,	PUNCT
ejpam-4941	123	41	e∗∗1	e∗∗1	PROPN
ejpam-4941	123	42	⟩	⟩	NOUN
ejpam-4941	123	43	=	=	SYM
ejpam-4941	123	44	0	0	NUM
ejpam-4941	123	45	,	,	PUNCT
ejpam-4941	123	46	it	it	PRON
ejpam-4941	123	47	remains	remain	VERB
ejpam-4941	123	48	to	to	PART
ejpam-4941	123	49	show	show	VERB
ejpam-4941	123	50	that	that	DET
ejpam-4941	123	51	⟨e∗∗(1)3	⟨e∗∗(1)3	NOUN
ejpam-4941	123	52	,	,	PUNCT
ejpam-4941	123	53	e∗∗1	e∗∗1	PROPN
ejpam-4941	123	54	⟩	⟩	NOUN
ejpam-4941	123	55	=	=	NOUN
ejpam-4941	123	56	0	0	X
ejpam-4941	123	57	.	.	PUNCT
ejpam-4941	124	1	in	in	ADP
ejpam-4941	124	2	fact	fact	NOUN
ejpam-4941	124	3	,	,	PUNCT
ejpam-4941	124	4	we	we	PRON
ejpam-4941	124	5	have	have	VERB
ejpam-4941	124	6	,	,	PUNCT
ejpam-4941	124	7	⟨e∗∗(1)3	⟨e∗∗(1)3	PRON
ejpam-4941	124	8	,	,	PUNCT
ejpam-4941	124	9	e∗∗1	e∗∗1	PROPN
ejpam-4941	124	10	⟩	⟩	NOUN
ejpam-4941	124	11	=	=	SYM
ejpam-4941	124	12	⟨e∗∗(1)3	⟨e∗∗(1)3	NOUN
ejpam-4941	124	13	,	,	PUNCT
ejpam-4941	124	14	e∗∗1	e∗∗1	NOUN
ejpam-4941	124	15	⟩	⟩	NOUN
ejpam-4941	124	16	−	−	PROPN
ejpam-4941	125	1	⟨e3	⟨e3	NOUN
ejpam-4941	125	2	,	,	PUNCT
ejpam-4941	125	3	e∗∗1	e∗∗1	NOUN
ejpam-4941	125	4	⟩	⟩	NOUN
ejpam-4941	125	5	⟨e∗∗1	⟨e∗∗1	NUM
ejpam-4941	125	6	,	,	PUNCT
ejpam-4941	125	7	e∗∗1	e∗∗1	PROPN
ejpam-4941	125	8	⟩	⟩	NOUN
ejpam-4941	125	9	⟨e∗∗1	⟨e∗∗1	NUM
ejpam-4941	125	10	,	,	PUNCT
ejpam-4941	125	11	e∗∗1	e∗∗1	PROPN
ejpam-4941	125	12	⟩	⟩	NOUN
ejpam-4941	125	13	=	=	SYM
ejpam-4941	125	14	0	0	PROPN
ejpam-4941	125	15	.	.	PUNCT
ejpam-4941	126	1	s.	s.	PROPN
ejpam-4941	126	2	abdelalim	abdelalim	PROPN
ejpam-4941	126	3	,	,	PUNCT
ejpam-4941	126	4	i.	i.	PROPN
ejpam-4941	126	5	elmouki	elmouki	PROPN
ejpam-4941	126	6	/	/	SYM
ejpam-4941	126	7	eur	eur	PROPN
ejpam-4941	126	8	.	.	PUNCT
ejpam-4941	127	1	j.	j.	PROPN
ejpam-4941	127	2	pure	pure	PROPN
ejpam-4941	127	3	appl	appl	PROPN
ejpam-4941	127	4	.	.	PROPN
ejpam-4941	127	5	math	math	PROPN
ejpam-4941	127	6	,	,	PUNCT
ejpam-4941	127	7	16	16	NUM
ejpam-4941	127	8	(	(	PUNCT
ejpam-4941	127	9	4	4	NUM
ejpam-4941	127	10	)	)	PUNCT
ejpam-4941	127	11	(	(	PUNCT
ejpam-4941	127	12	2023	2023	NUM
ejpam-4941	127	13	)	)	PUNCT
ejpam-4941	127	14	,	,	PUNCT
ejpam-4941	127	15	2662	2662	NUM
ejpam-4941	127	16	-	-	SYM
ejpam-4941	127	17	2692	2692	NUM
ejpam-4941	127	18	2671	2671	NUM
ejpam-4941	127	19	an	an	DET
ejpam-4941	127	20	additional	additional	ADJ
ejpam-4941	127	21	last	last	ADJ
ejpam-4941	127	22	example	example	NOUN
ejpam-4941	127	23	will	will	AUX
ejpam-4941	127	24	be	be	AUX
ejpam-4941	127	25	the	the	DET
ejpam-4941	127	26	most	most	ADV
ejpam-4941	127	27	interesting	interesting	ADJ
ejpam-4941	127	28	as	as	SCONJ
ejpam-4941	127	29	it	it	PRON
ejpam-4941	127	30	shows	show	VERB
ejpam-4941	127	31	that	that	SCONJ
ejpam-4941	127	32	the	the	DET
ejpam-4941	127	33	few	few	ADJ
ejpam-4941	127	34	examples	example	NOUN
ejpam-4941	127	35	above	above	ADV
ejpam-4941	127	36	are	be	AUX
ejpam-4941	127	37	not	not	PART
ejpam-4941	127	38	enough	enough	ADJ
ejpam-4941	127	39	to	to	PART
ejpam-4941	127	40	deduce	deduce	VERB
ejpam-4941	127	41	a	a	DET
ejpam-4941	127	42	general	general	ADJ
ejpam-4941	127	43	logic	logic	NOUN
ejpam-4941	127	44	that	that	PRON
ejpam-4941	127	45	imply	imply	VERB
ejpam-4941	127	46	orthogonality	orthogonality	NOUN
ejpam-4941	127	47	for	for	ADP
ejpam-4941	127	48	these	these	DET
ejpam-4941	127	49	three	three	NUM
ejpam-4941	127	50	sub	sub	NOUN
ejpam-4941	127	51	-	-	NOUN
ejpam-4941	127	52	cases	case	NOUN
ejpam-4941	127	53	.	.	PUNCT
ejpam-4941	128	1	thus	thus	ADV
ejpam-4941	128	2	,	,	PUNCT
ejpam-4941	128	3	we	we	PRON
ejpam-4941	128	4	take	take	VERB
ejpam-4941	128	5	now	now	ADV
ejpam-4941	128	6	j	j	NOUN
ejpam-4941	128	7	=	=	SYM
ejpam-4941	128	8	4	4	NUM
ejpam-4941	128	9	,	,	PUNCT
ejpam-4941	128	10	i	i	PRON
ejpam-4941	128	11	=	=	NOUN
ejpam-4941	128	12	1	1	NUM
ejpam-4941	128	13	,	,	PUNCT
ejpam-4941	128	14	2	2	NUM
ejpam-4941	128	15	,	,	PUNCT
ejpam-4941	128	16	3	3	NUM
ejpam-4941	128	17	and	and	CCONJ
ejpam-4941	128	18	k	k	NOUN
ejpam-4941	128	19	=	=	SYM
ejpam-4941	128	20	2	2	NUM
ejpam-4941	128	21	,	,	PUNCT
ejpam-4941	128	22	3	3	NUM
ejpam-4941	128	23	,	,	PUNCT
ejpam-4941	128	24	we	we	PRON
ejpam-4941	128	25	have	have	VERB
ejpam-4941	128	26	e	e	NOUN
ejpam-4941	128	27	∗∗(3	∗∗(3	PROPN
ejpam-4941	128	28	)	)	PUNCT
ejpam-4941	128	29	4	4	NUM
ejpam-4941	128	30	=	=	SYM
ejpam-4941	128	31	e	e	X
ejpam-4941	128	32	∗∗(2	∗∗(2	PROPN
ejpam-4941	128	33	)	)	PUNCT
ejpam-4941	128	34	4	4	NUM
ejpam-4941	128	35	−	−	NOUN
ejpam-4941	128	36	⟨e∗∗(2)4	⟨e∗∗(2)4	X
ejpam-4941	128	37	,	,	PUNCT
ejpam-4941	128	38	e∗∗3	e∗∗3	PROPN
ejpam-4941	128	39	⟩	⟩	PROPN
ejpam-4941	128	40	⟨e∗∗3	⟨e∗∗3	PROPN
ejpam-4941	128	41	,	,	PUNCT
ejpam-4941	129	1	e∗∗3	e∗∗3	PROPN
ejpam-4941	129	2	⟩	⟩	PROPN
ejpam-4941	129	3	e∗∗3	e∗∗3	PROPN
ejpam-4941	129	4	,	,	PUNCT
ejpam-4941	129	5	then	then	ADV
ejpam-4941	129	6	,	,	PUNCT
ejpam-4941	129	7	⟨e∗∗(3)4	⟨e∗∗(3)4	X
ejpam-4941	129	8	,	,	PUNCT
ejpam-4941	129	9	e	e	X
ejpam-4941	129	10	∗∗(2	∗∗(2	PROPN
ejpam-4941	129	11	)	)	PUNCT
ejpam-4941	129	12	3	3	NUM
ejpam-4941	129	13	⟩	⟩	NOUN
ejpam-4941	129	14	=	=	NOUN
ejpam-4941	129	15	⟨e∗∗(2)4	⟨e∗∗(2)4	X
ejpam-4941	129	16	,	,	PUNCT
ejpam-4941	129	17	e	e	X
ejpam-4941	129	18	∗∗(2	∗∗(2	PROPN
ejpam-4941	129	19	)	)	PUNCT
ejpam-4941	129	20	3	3	NUM
ejpam-4941	129	21	⟩	⟩	NOUN
ejpam-4941	129	22	−	−	NOUN
ejpam-4941	129	23	⟨e∗∗(2)4	⟨e∗∗(2)4	X
ejpam-4941	129	24	,	,	PUNCT
ejpam-4941	129	25	e	e	X
ejpam-4941	129	26	∗∗(2	∗∗(2	PROPN
ejpam-4941	129	27	)	)	PUNCT
ejpam-4941	129	28	3	3	NUM
ejpam-4941	129	29	⟩	⟩	NOUN
ejpam-4941	129	30	⟨e∗∗(2)3	⟨e∗∗(2)3	NUM
ejpam-4941	129	31	,	,	PUNCT
ejpam-4941	129	32	e	e	X
ejpam-4941	129	33	∗∗(2	∗∗(2	PROPN
ejpam-4941	129	34	)	)	PUNCT
ejpam-4941	129	35	3	3	NUM
ejpam-4941	129	36	⟩	⟩	NOUN
ejpam-4941	129	37	⟨e∗∗(2)3	⟨e∗∗(2)3	NUM
ejpam-4941	129	38	,	,	PUNCT
ejpam-4941	129	39	e	e	X
ejpam-4941	129	40	∗∗(2	∗∗(2	PROPN
ejpam-4941	129	41	)	)	PUNCT
ejpam-4941	129	42	3	3	NUM
ejpam-4941	129	43	⟩	⟩	NOUN
ejpam-4941	129	44	=	=	NOUN
ejpam-4941	129	45	0	0	X
ejpam-4941	129	46	.	.	PUNCT
ejpam-4941	130	1	we	we	PRON
ejpam-4941	130	2	also	also	ADV
ejpam-4941	130	3	have	have	VERB
ejpam-4941	130	4	,	,	PUNCT
ejpam-4941	130	5	⟨e∗∗(3)4	⟨e∗∗(3)4	X
ejpam-4941	130	6	,	,	PUNCT
ejpam-4941	130	7	e	e	X
ejpam-4941	130	8	∗∗(1	∗∗(1	X
ejpam-4941	130	9	)	)	PUNCT
ejpam-4941	130	10	2	2	NUM
ejpam-4941	130	11	⟩	⟩	NOUN
ejpam-4941	130	12	=	=	NOUN
ejpam-4941	130	13	⟨e∗∗(2)4	⟨e∗∗(2)4	X
ejpam-4941	130	14	,	,	PUNCT
ejpam-4941	130	15	e	e	X
ejpam-4941	130	16	∗∗(1	∗∗(1	X
ejpam-4941	130	17	)	)	PUNCT
ejpam-4941	130	18	2	2	NUM
ejpam-4941	130	19	⟩	⟩	NOUN
ejpam-4941	130	20	−	−	NOUN
ejpam-4941	130	21	⟨e∗∗(2)4	⟨e∗∗(2)4	X
ejpam-4941	130	22	,	,	PUNCT
ejpam-4941	130	23	e	e	X
ejpam-4941	130	24	∗∗(1	∗∗(1	X
ejpam-4941	130	25	)	)	PUNCT
ejpam-4941	130	26	2	2	NUM
ejpam-4941	130	27	⟩	⟩	NOUN
ejpam-4941	130	28	⟨e∗∗(1)2	⟨e∗∗(1)2	X
ejpam-4941	130	29	,	,	PUNCT
ejpam-4941	130	30	e	e	X
ejpam-4941	130	31	∗∗(1	∗∗(1	X
ejpam-4941	130	32	)	)	PUNCT
ejpam-4941	130	33	2	2	NUM
ejpam-4941	130	34	⟩	⟩	NOUN
ejpam-4941	130	35	⟨e∗∗(1)2	⟨e∗∗(1)2	X
ejpam-4941	130	36	,	,	PUNCT
ejpam-4941	130	37	e	e	X
ejpam-4941	130	38	∗∗(1	∗∗(1	X
ejpam-4941	130	39	)	)	PUNCT
ejpam-4941	130	40	2	2	NUM
ejpam-4941	130	41	⟩	⟩	NOUN
ejpam-4941	130	42	=	=	NOUN
ejpam-4941	130	43	0	0	X
ejpam-4941	130	44	.	.	PUNCT
ejpam-4941	131	1	in	in	ADP
ejpam-4941	131	2	addition	addition	NOUN
ejpam-4941	131	3	,	,	PUNCT
ejpam-4941	131	4	we	we	PRON
ejpam-4941	131	5	have	have	VERB
ejpam-4941	131	6	,	,	PUNCT
ejpam-4941	131	7	⟨e∗∗(3)4	⟨e∗∗(3)4	X
ejpam-4941	131	8	,	,	PUNCT
ejpam-4941	131	9	e∗∗1	e∗∗1	PROPN
ejpam-4941	131	10	⟩	⟩	NOUN
ejpam-4941	131	11	=	=	SYM
ejpam-4941	131	12	⟨e∗∗(2)4	⟨e∗∗(2)4	NOUN
ejpam-4941	131	13	,	,	PUNCT
ejpam-4941	131	14	e∗∗1	e∗∗1	PROPN
ejpam-4941	131	15	⟩	⟩	NOUN
ejpam-4941	131	16	−	−	PROPN
ejpam-4941	131	17	⟨e∗∗(2)4	⟨e∗∗(2)4	X
ejpam-4941	131	18	,	,	PUNCT
ejpam-4941	131	19	e	e	X
ejpam-4941	131	20	∗∗(2	∗∗(2	PROPN
ejpam-4941	131	21	3	3	NUM
ejpam-4941	131	22	⟩	⟩	NOUN
ejpam-4941	131	23	⟨e∗∗(2)3	⟨e∗∗(2)3	X
ejpam-4941	131	24	,	,	PUNCT
ejpam-4941	131	25	e	e	X
ejpam-4941	131	26	∗∗(2	∗∗(2	PROPN
ejpam-4941	131	27	)	)	PUNCT
ejpam-4941	131	28	3	3	NUM
ejpam-4941	131	29	⟩	⟩	NOUN
ejpam-4941	131	30	⟨e∗∗(2)3	⟨e∗∗(2)3	X
ejpam-4941	131	31	,	,	PUNCT
ejpam-4941	131	32	e∗∗1	e∗∗1	PROPN
ejpam-4941	131	33	⟩.	⟩.	PROPN
ejpam-4941	131	34	since	since	ADV
ejpam-4941	131	35	,	,	PUNCT
ejpam-4941	131	36	we	we	PRON
ejpam-4941	131	37	have	have	AUX
ejpam-4941	131	38	already	already	ADV
ejpam-4941	131	39	shown	show	VERB
ejpam-4941	131	40	that	that	DET
ejpam-4941	131	41	⟨e∗∗(1)3	⟨e∗∗(1)3	NOUN
ejpam-4941	131	42	,	,	PUNCT
ejpam-4941	131	43	e∗∗1	e∗∗1	PROPN
ejpam-4941	131	44	⟩	⟩	NOUN
ejpam-4941	131	45	=	=	SYM
ejpam-4941	131	46	0	0	NUM
ejpam-4941	131	47	,	,	PUNCT
ejpam-4941	131	48	it	it	PRON
ejpam-4941	131	49	remains	remain	VERB
ejpam-4941	131	50	to	to	PART
ejpam-4941	131	51	show	show	VERB
ejpam-4941	131	52	that	that	SCONJ
ejpam-4941	131	53	⟨e∗∗(2)4	⟨e∗∗(2)4	X
ejpam-4941	131	54	,	,	PUNCT
ejpam-4941	131	55	e∗∗1	e∗∗1	PROPN
ejpam-4941	131	56	⟩	⟩	NOUN
ejpam-4941	131	57	=	=	NOUN
ejpam-4941	131	58	0	0	X
ejpam-4941	131	59	.	.	PUNCT
ejpam-4941	132	1	in	in	ADP
ejpam-4941	132	2	fact	fact	NOUN
ejpam-4941	132	3	,	,	PUNCT
ejpam-4941	132	4	we	we	PRON
ejpam-4941	132	5	have	have	VERB
ejpam-4941	132	6	,	,	PUNCT
ejpam-4941	132	7	⟨e∗∗(2)4	⟨e∗∗(2)4	X
ejpam-4941	132	8	,	,	PUNCT
ejpam-4941	132	9	e∗∗1	e∗∗1	PROPN
ejpam-4941	132	10	⟩	⟩	NOUN
ejpam-4941	132	11	=	=	SYM
ejpam-4941	132	12	⟨e∗∗(1)4	⟨e∗∗(1)4	NOUN
ejpam-4941	132	13	,	,	PUNCT
ejpam-4941	132	14	e∗∗1	e∗∗1	PROPN
ejpam-4941	132	15	⟩	⟩	NOUN
ejpam-4941	132	16	−	−	PROPN
ejpam-4941	132	17	⟨e∗∗(1)4	⟨e∗∗(1)4	NOUN
ejpam-4941	132	18	,	,	PUNCT
ejpam-4941	132	19	e∗∗1	e∗∗1	PROPN
ejpam-4941	132	20	⟩	⟩	NOUN
ejpam-4941	132	21	⟨e∗∗1	⟨e∗∗1	NUM
ejpam-4941	132	22	,	,	PUNCT
ejpam-4941	132	23	e∗∗1	e∗∗1	PROPN
ejpam-4941	132	24	⟩	⟩	NOUN
ejpam-4941	132	25	⟨e∗∗1	⟨e∗∗1	NUM
ejpam-4941	132	26	,	,	PUNCT
ejpam-4941	132	27	e∗∗1	e∗∗1	PROPN
ejpam-4941	132	28	⟩	⟩	NOUN
ejpam-4941	132	29	=	=	NOUN
ejpam-4941	132	30	0	0	NUM
ejpam-4941	132	31	.	.	PUNCT
ejpam-4941	132	32	to	to	PART
ejpam-4941	132	33	generalize	generalize	VERB
ejpam-4941	132	34	all	all	DET
ejpam-4941	132	35	this	this	PRON
ejpam-4941	132	36	,	,	PUNCT
ejpam-4941	132	37	let	let	VERB
ejpam-4941	132	38	us	we	PRON
ejpam-4941	132	39	consider	consider	VERB
ejpam-4941	132	40	1	1	NUM
ejpam-4941	132	41	<	<	X
ejpam-4941	133	1	i	i	PRON
ejpam-4941	133	2	≤	≤	PUNCT
ejpam-4941	134	1	k	k	X
ejpam-4941	134	2	<	<	X
ejpam-4941	134	3	j	j	PROPN
ejpam-4941	134	4	≤	≤	PROPN
ejpam-4941	134	5	n	n	CCONJ
ejpam-4941	134	6	and	and	CCONJ
ejpam-4941	134	7	1	1	NUM
ejpam-4941	134	8	<	<	X
ejpam-4941	134	9	k	k	PROPN
ejpam-4941	134	10	≤	≤	PUNCT
ejpam-4941	134	11	n	n	CCONJ
ejpam-4941	134	12	−	−	PROPN
ejpam-4941	134	13	1	1	NUM
ejpam-4941	134	14	,	,	PUNCT
ejpam-4941	134	15	then	then	ADV
ejpam-4941	134	16	we	we	PRON
ejpam-4941	134	17	have	have	VERB
ejpam-4941	134	18	,	,	PUNCT
ejpam-4941	134	19	⟨e∗∗(k)j	⟨e∗∗(k)j	NOUN
ejpam-4941	134	20	,	,	PUNCT
ejpam-4941	134	21	e	e	NOUN
ejpam-4941	134	22	∗∗(k−1	∗∗(k−1	X
ejpam-4941	134	23	)	)	PUNCT
ejpam-4941	135	1	i	i	PRON
ejpam-4941	135	2	⟩	⟩	NOUN
ejpam-4941	136	1	=	=	PUNCT
ejpam-4941	136	2	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	136	3	)	)	PUNCT
ejpam-4941	136	4	j	j	PROPN
ejpam-4941	136	5	,	,	PUNCT
ejpam-4941	136	6	e	e	NOUN
ejpam-4941	136	7	∗∗(k−1	∗∗(k−1	X
ejpam-4941	136	8	)	)	PUNCT
ejpam-4941	136	9	i	i	PRON
ejpam-4941	136	10	⟩	⟩	NOUN
ejpam-4941	137	1	−	−	NOUN
ejpam-4941	137	2	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	137	3	)	)	PUNCT
ejpam-4941	137	4	j	j	PROPN
ejpam-4941	137	5	,	,	PUNCT
ejpam-4941	137	6	e∗∗k	e∗∗k	PROPN
ejpam-4941	137	7	⟩	⟩	NOUN
ejpam-4941	137	8	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	137	9	,	,	PUNCT
ejpam-4941	137	10	e∗∗k	e∗∗k	PROPN
ejpam-4941	137	11	⟩	⟩	NOUN
ejpam-4941	137	12	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	137	13	,	,	PUNCT
ejpam-4941	137	14	e	e	NOUN
ejpam-4941	137	15	∗∗(k−1	∗∗(k−1	X
ejpam-4941	137	16	)	)	PUNCT
ejpam-4941	137	17	i	i	PRON
ejpam-4941	137	18	⟩	⟩	PROPN
ejpam-4941	137	19	−−	−−	NOUN
ejpam-4941	138	1	if	if	SCONJ
ejpam-4941	138	2	i	i	PRON
ejpam-4941	138	3	=	=	PUNCT
ejpam-4941	138	4	k	k	PROPN
ejpam-4941	138	5	=	=	PUNCT
ejpam-4941	138	6	j	j	PROPN
ejpam-4941	139	1	−	−	PROPN
ejpam-4941	139	2	1	1	NUM
ejpam-4941	139	3	,	,	PUNCT
ejpam-4941	139	4	then	then	ADV
ejpam-4941	139	5	,	,	PUNCT
ejpam-4941	139	6	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	139	7	,	,	PUNCT
ejpam-4941	139	8	e	e	NOUN
ejpam-4941	139	9	∗∗(k−1	∗∗(k−1	X
ejpam-4941	139	10	)	)	PUNCT
ejpam-4941	140	1	i	i	PRON
ejpam-4941	140	2	⟩	⟩	NOUN
ejpam-4941	140	3	=	=	SYM
ejpam-4941	140	4	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	140	5	,	,	PUNCT
ejpam-4941	140	6	e	e	NOUN
ejpam-4941	140	7	∗∗(k−1	∗∗(k−1	X
ejpam-4941	140	8	)	)	PUNCT
ejpam-4941	140	9	k	k	PROPN
ejpam-4941	140	10	⟩	⟩	NOUN
ejpam-4941	140	11	=	=	SYM
ejpam-4941	140	12	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	140	13	,	,	PUNCT
ejpam-4941	140	14	e∗∗k	e∗∗k	PROPN
ejpam-4941	140	15	⟩	⟩	PROPN
ejpam-4941	140	16	and	and	CCONJ
ejpam-4941	140	17	also	also	ADV
ejpam-4941	140	18	,	,	PUNCT
ejpam-4941	140	19	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	140	20	)	)	PUNCT
ejpam-4941	140	21	j	j	PROPN
ejpam-4941	140	22	,	,	PUNCT
ejpam-4941	140	23	e∗∗k	e∗∗k	PROPN
ejpam-4941	140	24	⟩	⟩	NOUN
ejpam-4941	140	25	=	=	SYM
ejpam-4941	140	26	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	140	27	)	)	PUNCT
ejpam-4941	140	28	j	j	PROPN
ejpam-4941	140	29	,	,	PUNCT
ejpam-4941	140	30	e∗∗i	e∗∗i	NOUN
ejpam-4941	140	31	⟩	⟩	NOUN
ejpam-4941	140	32	=	=	PUNCT
ejpam-4941	140	33	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	140	34	)	)	PUNCT
ejpam-4941	140	35	j	j	PROPN
ejpam-4941	140	36	,	,	PUNCT
ejpam-4941	140	37	e	e	NOUN
ejpam-4941	140	38	∗∗(k−1	∗∗(k−1	X
ejpam-4941	140	39	)	)	PUNCT
ejpam-4941	140	40	i	i	PRON
ejpam-4941	140	41	⟩.	⟩.	VERB
ejpam-4941	140	42	thus	thus	ADV
ejpam-4941	140	43	,	,	PUNCT
ejpam-4941	140	44	⟨e∗∗(k)j	⟨e∗∗(k)j	NOUN
ejpam-4941	140	45	,	,	PUNCT
ejpam-4941	140	46	e	e	NOUN
ejpam-4941	140	47	∗∗(k−1	∗∗(k−1	X
ejpam-4941	140	48	)	)	PUNCT
ejpam-4941	140	49	i	i	PRON
ejpam-4941	140	50	⟩	⟩	NOUN
ejpam-4941	140	51	=	=	SYM
ejpam-4941	140	52	0	0	X
ejpam-4941	140	53	.	.	PUNCT
ejpam-4941	141	1	−−	−−	NOUN
ejpam-4941	142	1	if	if	SCONJ
ejpam-4941	142	2	i	i	PRON
ejpam-4941	142	3	<	<	X
ejpam-4941	142	4	k	k	X
ejpam-4941	142	5	,	,	PUNCT
ejpam-4941	142	6	then	then	ADV
ejpam-4941	142	7	,	,	PUNCT
ejpam-4941	142	8	on	on	ADP
ejpam-4941	142	9	one	one	NUM
ejpam-4941	142	10	hand	hand	NOUN
ejpam-4941	142	11	,	,	PUNCT
ejpam-4941	142	12	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	142	13	,	,	PUNCT
ejpam-4941	142	14	e	e	NOUN
ejpam-4941	142	15	∗∗(k−1	∗∗(k−1	X
ejpam-4941	142	16	)	)	PUNCT
ejpam-4941	142	17	i	i	PRON
ejpam-4941	142	18	⟩	⟩	NOUN
ejpam-4941	142	19	=	=	NOUN
ejpam-4941	142	20	0	0	PUNCT
ejpam-4941	142	21	because	because	SCONJ
ejpam-4941	142	22	we	we	PRON
ejpam-4941	142	23	have	have	VERB
ejpam-4941	142	24	,	,	PUNCT
ejpam-4941	142	25	⟨e∗∗(k	⟨e∗∗(k	PRON
ejpam-4941	142	26	)	)	PUNCT
ejpam-4941	142	27	,	,	PUNCT
ejpam-4941	142	28	e∗∗(k−1	e∗∗(k−1	NOUN
ejpam-4941	142	29	)	)	PUNCT
ejpam-4941	143	1	i	i	PRON
ejpam-4941	143	2	⟩	⟩	NOUN
ejpam-4941	143	3	=	=	SYM
ejpam-4941	143	4	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	143	5	,	,	PUNCT
ejpam-4941	143	6	ei⟩	ei⟩	NOUN
ejpam-4941	143	7	−	−	NOUN
ejpam-4941	143	8	⟨ei	⟨ei	NOUN
ejpam-4941	143	9	,	,	PUNCT
ejpam-4941	143	10	e∗∗k−1⟩	e∗∗k−1⟩	PROPN
ejpam-4941	143	11	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	143	12	,	,	PUNCT
ejpam-4941	143	13	e	e	X
ejpam-4941	143	14	∗∗	∗∗	X
ejpam-4941	144	1	k−1⟩	k−1⟩	PROPN
ejpam-4941	144	2	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	144	3	,	,	PUNCT
ejpam-4941	144	4	e	e	X
ejpam-4941	144	5	∗∗	∗∗	PROPN
ejpam-4941	144	6	k	k	PROPN
ejpam-4941	144	7	⟩	⟩	PROPN
ejpam-4941	144	8	s.	s.	PROPN
ejpam-4941	144	9	abdelalim	abdelalim	PROPN
ejpam-4941	144	10	,	,	PUNCT
ejpam-4941	144	11	i.	i.	PROPN
ejpam-4941	144	12	elmouki	elmouki	PROPN
ejpam-4941	144	13	/	/	SYM
ejpam-4941	144	14	eur	eur	PROPN
ejpam-4941	144	15	.	.	PUNCT
ejpam-4941	145	1	j.	j.	PROPN
ejpam-4941	145	2	pure	pure	PROPN
ejpam-4941	145	3	appl	appl	PROPN
ejpam-4941	145	4	.	.	PROPN
ejpam-4941	145	5	math	math	PROPN
ejpam-4941	145	6	,	,	PUNCT
ejpam-4941	145	7	16	16	NUM
ejpam-4941	145	8	(	(	PUNCT
ejpam-4941	145	9	4	4	NUM
ejpam-4941	145	10	)	)	PUNCT
ejpam-4941	145	11	(	(	PUNCT
ejpam-4941	145	12	2023	2023	NUM
ejpam-4941	145	13	)	)	PUNCT
ejpam-4941	145	14	,	,	PUNCT
ejpam-4941	145	15	2662	2662	NUM
ejpam-4941	145	16	-	-	SYM
ejpam-4941	145	17	2692	2692	NUM
ejpam-4941	145	18	2672	2672	NUM
ejpam-4941	145	19	and	and	CCONJ
ejpam-4941	145	20	we	we	PRON
ejpam-4941	145	21	can	can	AUX
ejpam-4941	145	22	just	just	ADV
ejpam-4941	145	23	take	take	VERB
ejpam-4941	145	24	i	i	PRON
ejpam-4941	145	25	=	=	PUNCT
ejpam-4941	146	1	k	k	PROPN
ejpam-4941	146	2	−	−	PROPN
ejpam-4941	146	3	1	1	NUM
ejpam-4941	146	4	which	which	PRON
ejpam-4941	146	5	gives	give	VERB
ejpam-4941	146	6	⟨e∗∗(k	⟨e∗∗(k	PRON
ejpam-4941	146	7	)	)	PUNCT
ejpam-4941	146	8	,	,	PUNCT
ejpam-4941	146	9	e∗∗(k−1	e∗∗(k−1	NOUN
ejpam-4941	146	10	)	)	PUNCT
ejpam-4941	147	1	i	i	PRON
ejpam-4941	147	2	⟩	⟩	NOUN
ejpam-4941	147	3	=	=	NOUN
ejpam-4941	147	4	0	0	X
ejpam-4941	147	5	.	.	PUNCT
ejpam-4941	148	1	on	on	ADP
ejpam-4941	148	2	the	the	DET
ejpam-4941	148	3	other	other	ADJ
ejpam-4941	148	4	hand	hand	NOUN
ejpam-4941	148	5	,	,	PUNCT
ejpam-4941	148	6	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	148	7	)	)	PUNCT
ejpam-4941	148	8	j	j	PROPN
ejpam-4941	148	9	,	,	PUNCT
ejpam-4941	148	10	e	e	NOUN
ejpam-4941	148	11	∗∗(k−1	∗∗(k−1	X
ejpam-4941	148	12	)	)	PUNCT
ejpam-4941	148	13	i	i	PRON
ejpam-4941	148	14	⟩	⟩	NOUN
ejpam-4941	148	15	=	=	PUNCT
ejpam-4941	148	16	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	148	17	)	)	PUNCT
ejpam-4941	148	18	j	j	PROPN
ejpam-4941	148	19	,	,	PUNCT
ejpam-4941	148	20	ei⟩	ei⟩	NOUN
ejpam-4941	148	21	−	−	PROPN
ejpam-4941	148	22	⟨ei	⟨ei	NOUN
ejpam-4941	148	23	,	,	PUNCT
ejpam-4941	148	24	e∗∗k−1⟩	e∗∗k−1⟩	PROPN
ejpam-4941	148	25	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	148	26	,	,	PUNCT
ejpam-4941	148	27	e	e	X
ejpam-4941	148	28	∗∗	∗∗	X
ejpam-4941	149	1	k−1⟩	k−1⟩	PROPN
ejpam-4941	149	2	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	149	3	,	,	PUNCT
ejpam-4941	149	4	e	e	NOUN
ejpam-4941	149	5	∗∗(k−1	∗∗(k−1	X
ejpam-4941	149	6	)	)	PUNCT
ejpam-4941	149	7	j	j	PROPN
ejpam-4941	149	8	⟩	⟩	NOUN
ejpam-4941	150	1	and	and	CCONJ
ejpam-4941	150	2	we	we	PRON
ejpam-4941	150	3	can	can	AUX
ejpam-4941	150	4	just	just	ADV
ejpam-4941	150	5	take	take	VERB
ejpam-4941	150	6	i	i	PRON
ejpam-4941	150	7	=	=	PUNCT
ejpam-4941	151	1	k	k	PROPN
ejpam-4941	151	2	−	−	PROPN
ejpam-4941	151	3	1	1	NUM
ejpam-4941	151	4	which	which	PRON
ejpam-4941	151	5	gives	give	VERB
ejpam-4941	151	6	⟨e∗∗(k−1	⟨e∗∗(k−1	PROPN
ejpam-4941	151	7	)	)	PUNCT
ejpam-4941	151	8	j	j	PROPN
ejpam-4941	151	9	,	,	PUNCT
ejpam-4941	151	10	e	e	NOUN
ejpam-4941	151	11	∗∗(k−1	∗∗(k−1	X
ejpam-4941	151	12	)	)	PUNCT
ejpam-4941	152	1	i	i	PRON
ejpam-4941	152	2	⟩	⟩	NOUN
ejpam-4941	152	3	=	=	NOUN
ejpam-4941	152	4	0	0	NUM
ejpam-4941	152	5	.	.	PUNCT
ejpam-4941	153	1	–	–	PUNCT
ejpam-4941	153	2	if	if	SCONJ
ejpam-4941	153	3	we	we	PRON
ejpam-4941	153	4	consider	consider	VERB
ejpam-4941	153	5	a	a	DET
ejpam-4941	153	6	gs	gs	NOUN
ejpam-4941	153	7	process	process	NOUN
ejpam-4941	153	8	,	,	PUNCT
ejpam-4941	153	9	this	this	PRON
ejpam-4941	153	10	can	can	AUX
ejpam-4941	153	11	not	not	PART
ejpam-4941	153	12	be	be	AUX
ejpam-4941	153	13	deduced	deduce	VERB
ejpam-4941	153	14	directly	directly	ADV
ejpam-4941	153	15	from	from	ADP
ejpam-4941	153	16	the	the	DET
ejpam-4941	153	17	gs	gs	PROPN
ejpam-4941	153	18	formulations	formulation	NOUN
ejpam-4941	153	19	as	as	SCONJ
ejpam-4941	153	20	done	do	VERB
ejpam-4941	153	21	for	for	ADP
ejpam-4941	153	22	mgs	mgs	NOUN
ejpam-4941	153	23	.	.	PUNCT
ejpam-4941	154	1	thus	thus	ADV
ejpam-4941	154	2	,	,	PUNCT
ejpam-4941	154	3	we	we	PRON
ejpam-4941	154	4	proceed	proceed	VERB
ejpam-4941	154	5	by	by	ADP
ejpam-4941	154	6	induction	induction	NOUN
ejpam-4941	154	7	.	.	PUNCT
ejpam-4941	155	1	first	first	ADV
ejpam-4941	155	2	for	for	ADP
ejpam-4941	155	3	j	j	PROPN
ejpam-4941	155	4	=	=	SYM
ejpam-4941	155	5	2	2	NUM
ejpam-4941	155	6	,	,	PUNCT
ejpam-4941	155	7	i	i	PRON
ejpam-4941	155	8	=	=	NOUN
ejpam-4941	155	9	1	1	NUM
ejpam-4941	155	10	,	,	PUNCT
ejpam-4941	155	11	we	we	PRON
ejpam-4941	155	12	have	have	VERB
ejpam-4941	155	13	e∗2	e∗2	NOUN
ejpam-4941	156	1	=	=	SYM
ejpam-4941	156	2	e2	e2	PROPN
ejpam-4941	156	3	−	−	PROPN
ejpam-4941	156	4	⟨e2	⟨e2	PROPN
ejpam-4941	156	5	,	,	PUNCT
ejpam-4941	156	6	e∗1⟩	e∗1⟩	PROPN
ejpam-4941	156	7	⟨e∗1	⟨e∗1	PROPN
ejpam-4941	156	8	,	,	PUNCT
ejpam-4941	156	9	e∗1⟩	e∗1⟩	ADJ
ejpam-4941	156	10	e∗1	e∗1	NOUN
ejpam-4941	156	11	,	,	PUNCT
ejpam-4941	156	12	⟨e∗2	⟨e∗2	NOUN
ejpam-4941	156	13	,	,	PUNCT
ejpam-4941	156	14	e∗1⟩	e∗1⟩	PROPN
ejpam-4941	156	15	=	=	SYM
ejpam-4941	157	1	⟨e2	⟨e2	NOUN
ejpam-4941	157	2	,	,	PUNCT
ejpam-4941	157	3	e∗1⟩	e∗1⟩	ADJ
ejpam-4941	157	4	−	−	PROPN
ejpam-4941	158	1	⟨e2	⟨e2	NOUN
ejpam-4941	158	2	,	,	PUNCT
ejpam-4941	158	3	e∗1⟩	e∗1⟩	PROPN
ejpam-4941	158	4	⟨e∗1	⟨e∗1	PROPN
ejpam-4941	158	5	,	,	PUNCT
ejpam-4941	158	6	e∗1⟩	e∗1⟩	PROPN
ejpam-4941	158	7	⟨e∗1	⟨e∗1	PROPN
ejpam-4941	158	8	,	,	PUNCT
ejpam-4941	158	9	e∗1⟩	e∗1⟩	ADJ
ejpam-4941	158	10	=	=	SYM
ejpam-4941	158	11	0	0	X
ejpam-4941	158	12	.	.	PUNCT
ejpam-4941	158	13	suppose	suppose	VERB
ejpam-4941	158	14	now	now	ADV
ejpam-4941	158	15	that	that	SCONJ
ejpam-4941	158	16	⟨e∗i	⟨e∗i	INTJ
ejpam-4941	158	17	,	,	PUNCT
ejpam-4941	158	18	e∗j	e∗j	NUM
ejpam-4941	158	19	⟩	⟩	NOUN
ejpam-4941	158	20	=	=	NOUN
ejpam-4941	158	21	0	0	NUM
ejpam-4941	158	22	for	for	ADP
ejpam-4941	158	23	1	1	NUM
ejpam-4941	158	24	<	<	X
ejpam-4941	159	1	i	i	PRON
ejpam-4941	159	2	<	<	X
ejpam-4941	159	3	j	j	PROPN
ejpam-4941	159	4	≤	≤	PROPN
ejpam-4941	159	5	n	n	CCONJ
ejpam-4941	160	1	and	and	CCONJ
ejpam-4941	160	2	we	we	PRON
ejpam-4941	160	3	try	try	VERB
ejpam-4941	160	4	to	to	PART
ejpam-4941	160	5	prove	prove	VERB
ejpam-4941	160	6	that	that	SCONJ
ejpam-4941	160	7	⟨e∗i	⟨e∗i	INTJ
ejpam-4941	160	8	,	,	PUNCT
ejpam-4941	160	9	e∗j+1⟩	e∗j+1⟩	PROPN
ejpam-4941	160	10	=	=	PUNCT
ejpam-4941	160	11	0	0	PUNCT
ejpam-4941	161	1	for	for	ADP
ejpam-4941	161	2	1	1	NUM
ejpam-4941	161	3	<	<	X
ejpam-4941	161	4	i	i	PRON
ejpam-4941	161	5	<	<	X
ejpam-4941	161	6	j	j	PROPN
ejpam-4941	161	7	+	+	CCONJ
ejpam-4941	161	8	1	1	NUM
ejpam-4941	161	9	≤	≤	NOUN
ejpam-4941	161	10	n.	n.	NOUN
ejpam-4941	161	11	in	in	ADP
ejpam-4941	161	12	fact	fact	NOUN
ejpam-4941	161	13	,	,	PUNCT
ejpam-4941	161	14	we	we	PRON
ejpam-4941	161	15	have	have	AUX
ejpam-4941	161	16	,	,	PUNCT
ejpam-4941	161	17	⟨e∗i	⟨e∗i	INTJ
ejpam-4941	161	18	,	,	PUNCT
ejpam-4941	161	19	e∗j+1⟩	e∗j+1⟩	PROPN
ejpam-4941	161	20	=	=	PUNCT
ejpam-4941	162	1	⟨e∗i	⟨e∗i	INTJ
ejpam-4941	162	2	,	,	PUNCT
ejpam-4941	162	3	ej+1⟩	ej+1⟩	PROPN
ejpam-4941	163	1	−	−	PROPN
ejpam-4941	164	1	j∑	j∑	INTJ
ejpam-4941	164	2	k=1	k=1	PUNCT
ejpam-4941	164	3	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	164	4	,	,	PUNCT
ejpam-4941	164	5	e	e	PROPN
ejpam-4941	164	6	∗	∗	NOUN
ejpam-4941	164	7	k⟩	k⟩	NOUN
ejpam-4941	164	8	⟨e∗k	⟨e∗k	PROPN
ejpam-4941	164	9	,	,	PUNCT
ejpam-4941	164	10	e∗k⟩	e∗k⟩	PROPN
ejpam-4941	164	11	⟨e∗k	⟨e∗k	PROPN
ejpam-4941	164	12	,	,	PUNCT
ejpam-4941	164	13	e∗i	e∗i	PUNCT
ejpam-4941	164	14	⟩	⟩	NOUN
ejpam-4941	164	15	based	base	VERB
ejpam-4941	164	16	on	on	ADP
ejpam-4941	164	17	the	the	DET
ejpam-4941	164	18	induction	induction	NOUN
ejpam-4941	164	19	assumption	assumption	NOUN
ejpam-4941	164	20	,	,	PUNCT
ejpam-4941	164	21	we	we	PRON
ejpam-4941	164	22	have	have	AUX
ejpam-4941	164	23	⟨e∗i	⟨e∗i	X
ejpam-4941	164	24	,	,	PUNCT
ejpam-4941	164	25	e∗j	e∗j	NUM
ejpam-4941	164	26	⟩	⟩	NOUN
ejpam-4941	164	27	=	=	NOUN
ejpam-4941	164	28	̸	̸	NOUN
ejpam-4941	164	29	0	0	PUNCT
ejpam-4941	165	1	if	if	SCONJ
ejpam-4941	165	2	i	i	PRON
ejpam-4941	165	3	=	=	SYM
ejpam-4941	165	4	j	j	PROPN
ejpam-4941	165	5	and	and	CCONJ
ejpam-4941	165	6	⟨e∗k	⟨e∗k	PROPN
ejpam-4941	165	7	,	,	PUNCT
ejpam-4941	165	8	e∗i	e∗i	PUNCT
ejpam-4941	165	9	⟩	⟩	NOUN
ejpam-4941	165	10	=	=	NOUN
ejpam-4941	165	11	0	0	NUM
ejpam-4941	165	12	for	for	ADP
ejpam-4941	165	13	1	1	NUM
ejpam-4941	165	14	<	<	X
ejpam-4941	165	15	k	k	X
ejpam-4941	165	16	<	<	X
ejpam-4941	165	17	i	i	PRON
ejpam-4941	165	18	(	(	PUNCT
ejpam-4941	165	19	the	the	DET
ejpam-4941	165	20	case	case	NOUN
ejpam-4941	165	21	when	when	SCONJ
ejpam-4941	165	22	k	k	PROPN
ejpam-4941	165	23	=	=	SYM
ejpam-4941	165	24	1	1	NUM
ejpam-4941	165	25	,	,	PUNCT
ejpam-4941	165	26	i	i	PRON
ejpam-4941	165	27	=	=	NOUN
ejpam-4941	165	28	2	2	NUM
ejpam-4941	165	29	,	,	PUNCT
ejpam-4941	165	30	already	already	ADV
ejpam-4941	165	31	verified	verify	VERB
ejpam-4941	165	32	above	above	ADP
ejpam-4941	165	33	)	)	PUNCT
ejpam-4941	165	34	.	.	PUNCT
ejpam-4941	166	1	thus	thus	ADV
ejpam-4941	166	2	,	,	PUNCT
ejpam-4941	166	3	⟨e∗i	⟨e∗i	INTJ
ejpam-4941	166	4	,	,	PUNCT
ejpam-4941	166	5	e∗j+1⟩	e∗j+1⟩	PROPN
ejpam-4941	166	6	=	=	PUNCT
ejpam-4941	167	1	⟨e∗i	⟨e∗i	INTJ
ejpam-4941	167	2	,	,	PUNCT
ejpam-4941	167	3	ej+1⟩	ej+1⟩	PROPN
ejpam-4941	167	4	−	−	PROPN
ejpam-4941	168	1	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	168	2	,	,	PUNCT
ejpam-4941	168	3	e	e	NOUN
ejpam-4941	168	4	∗	∗	NOUN
ejpam-4941	168	5	i	i	PRON
ejpam-4941	168	6	⟩	⟩	NOUN
ejpam-4941	168	7	⟨e∗i	⟨e∗i	INTJ
ejpam-4941	168	8	,	,	PUNCT
ejpam-4941	168	9	e∗i	e∗i	NUM
ejpam-4941	168	10	⟩	⟩	NOUN
ejpam-4941	168	11	⟨e∗i	⟨e∗i	PROPN
ejpam-4941	168	12	,	,	PUNCT
ejpam-4941	168	13	e∗i	e∗i	NUM
ejpam-4941	168	14	⟩	⟩	NOUN
ejpam-4941	168	15	=	=	SYM
ejpam-4941	168	16	0	0	NUM
ejpam-4941	168	17	•	•	NUM
ejpam-4941	168	18	–	–	PUNCT
ejpam-4941	168	19	on	on	ADP
ejpam-4941	168	20	one	one	NUM
ejpam-4941	168	21	hand	hand	NOUN
ejpam-4941	168	22	,	,	PUNCT
ejpam-4941	168	23	we	we	PRON
ejpam-4941	168	24	have	have	VERB
ejpam-4941	168	25	,	,	PUNCT
ejpam-4941	168	26	e∗∗(k)r	e∗∗(k)r	PROPN
ejpam-4941	168	27	=	=	SYM
ejpam-4941	168	28	e∗∗(k−1	e∗∗(k−1	X
ejpam-4941	168	29	)	)	PUNCT
ejpam-4941	168	30	r	r	NOUN
ejpam-4941	168	31	−	−	NOUN
ejpam-4941	168	32	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	168	33	)	)	PUNCT
ejpam-4941	168	34	r	r	NOUN
ejpam-4941	168	35	,	,	PUNCT
ejpam-4941	168	36	e∗∗r	e∗∗r	ADP
ejpam-4941	168	37	⟩	⟩	NOUN
ejpam-4941	168	38	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	168	39	,	,	PUNCT
ejpam-4941	168	40	e∗∗k	e∗∗k	PROPN
ejpam-4941	168	41	⟩	⟩	PROPN
ejpam-4941	168	42	e∗∗k	e∗∗k	PROPN
ejpam-4941	168	43	,	,	PUNCT
ejpam-4941	168	44	k	k	PROPN
ejpam-4941	168	45	=	=	SYM
ejpam-4941	168	46	2	2	NUM
ejpam-4941	168	47	,	,	PUNCT
ejpam-4941	168	48	...	...	PUNCT
ejpam-4941	168	49	,	,	PUNCT
ejpam-4941	168	50	r	r	NOUN
ejpam-4941	168	51	−	−	PROPN
ejpam-4941	168	52	1	1	NUM
ejpam-4941	168	53	=	=	NUM
ejpam-4941	168	54	er	er	INTJ
ejpam-4941	168	55	−	−	PROPN
ejpam-4941	168	56	⟨er	⟨er	NOUN
ejpam-4941	168	57	,	,	PUNCT
ejpam-4941	168	58	e∗∗k−1⟩	e∗∗k−1⟩	PROPN
ejpam-4941	168	59	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	168	60	,	,	PUNCT
ejpam-4941	168	61	e	e	X
ejpam-4941	168	62	∗∗	∗∗	X
ejpam-4941	168	63	k−1⟩	k−1⟩	PRON
ejpam-4941	168	64	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	168	65	−	−	NOUN
ejpam-4941	168	66	⟨e∗∗(k−1	⟨e∗∗(k−1	NUM
ejpam-4941	168	67	)	)	PUNCT
ejpam-4941	168	68	r	r	NOUN
ejpam-4941	168	69	,	,	PUNCT
ejpam-4941	168	70	e∗∗r	e∗∗r	ADP
ejpam-4941	168	71	⟩	⟩	NOUN
ejpam-4941	168	72	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	168	73	,	,	PUNCT
ejpam-4941	168	74	e∗∗k	e∗∗k	PROPN
ejpam-4941	168	75	⟩	⟩	PROPN
ejpam-4941	168	76	e∗∗k	e∗∗k	PROPN
ejpam-4941	168	77	,	,	PUNCT
ejpam-4941	168	78	k	k	PROPN
ejpam-4941	168	79	=	=	SYM
ejpam-4941	168	80	2	2	NUM
ejpam-4941	168	81	,	,	PUNCT
ejpam-4941	168	82	...	...	PUNCT
ejpam-4941	168	83	,	,	PUNCT
ejpam-4941	168	84	r	r	NOUN
ejpam-4941	168	85	−	−	PROPN
ejpam-4941	168	86	1	1	NUM
ejpam-4941	168	87	thus	thus	ADV
ejpam-4941	168	88	,	,	PUNCT
ejpam-4941	168	89	er	er	INTJ
ejpam-4941	168	90	=	=	SYM
ejpam-4941	168	91	e∗∗(k)r	e∗∗(k)r	PROPN
ejpam-4941	168	92	+	+	CCONJ
ejpam-4941	168	93	⟨er	⟨er	PROPN
ejpam-4941	168	94	,	,	PUNCT
ejpam-4941	168	95	e∗∗k−1⟩	e∗∗k−1⟩	PROPN
ejpam-4941	168	96	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	168	97	,	,	PUNCT
ejpam-4941	168	98	e	e	X
ejpam-4941	169	1	∗∗	∗∗	X
ejpam-4941	170	1	k−1⟩	k−1⟩	PROPN
ejpam-4941	170	2	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	170	3	+	+	CCONJ
ejpam-4941	170	4	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	170	5	)	)	PUNCT
ejpam-4941	170	6	r	r	NOUN
ejpam-4941	170	7	,	,	PUNCT
ejpam-4941	170	8	e∗∗r	e∗∗r	ADP
ejpam-4941	170	9	⟩	⟩	NOUN
ejpam-4941	170	10	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	170	11	,	,	PUNCT
ejpam-4941	170	12	e∗∗k	e∗∗k	PROPN
ejpam-4941	170	13	⟩	⟩	PROPN
ejpam-4941	170	14	e∗∗k	e∗∗k	PROPN
ejpam-4941	170	15	,	,	PUNCT
ejpam-4941	170	16	k	k	PROPN
ejpam-4941	170	17	=	=	SYM
ejpam-4941	170	18	2	2	NUM
ejpam-4941	170	19	,	,	PUNCT
ejpam-4941	170	20	...	...	PUNCT
ejpam-4941	170	21	,	,	PUNCT
ejpam-4941	171	1	r	r	NOUN
ejpam-4941	171	2	−	−	PROPN
ejpam-4941	171	3	1	1	NUM
ejpam-4941	171	4	hence	hence	ADV
ejpam-4941	171	5	,	,	PUNCT
ejpam-4941	171	6	ei	ei	PROPN
ejpam-4941	171	7	∈	∈	PROPN
ejpam-4941	171	8	span(e∗∗1	span(e∗∗1	NOUN
ejpam-4941	171	9	,	,	PUNCT
ejpam-4941	171	10	e	e	X
ejpam-4941	171	11	∗∗(1	∗∗(1	X
ejpam-4941	171	12	)	)	PUNCT
ejpam-4941	171	13	2	2	NUM
ejpam-4941	171	14	,	,	PUNCT
ejpam-4941	171	15	e	e	X
ejpam-4941	171	16	∗∗(2	∗∗(2	PROPN
ejpam-4941	171	17	)	)	PUNCT
ejpam-4941	171	18	3	3	NUM
ejpam-4941	171	19	,	,	PUNCT
ejpam-4941	171	20	...	...	PUNCT
ejpam-4941	171	21	,	,	PUNCT
ejpam-4941	171	22	e	e	NOUN
ejpam-4941	171	23	∗∗(k	∗∗(k	NOUN
ejpam-4941	171	24	)	)	PUNCT
ejpam-4941	171	25	r	r	NOUN
ejpam-4941	171	26	)	)	PUNCT
ejpam-4941	171	27	for	for	ADP
ejpam-4941	171	28	all	all	DET
ejpam-4941	171	29	1	1	NUM
ejpam-4941	171	30	≤	≤	NUM
ejpam-4941	171	31	i	i	PRON
ejpam-4941	171	32	≤	≤	ADJ
ejpam-4941	171	33	r	r	NOUN
ejpam-4941	171	34	and	and	CCONJ
ejpam-4941	171	35	with	with	ADP
ejpam-4941	171	36	k	k	PROPN
ejpam-4941	171	37	=	=	SYM
ejpam-4941	171	38	2	2	NUM
ejpam-4941	171	39	,	,	PUNCT
ejpam-4941	171	40	...	...	PUNCT
ejpam-4941	171	41	,	,	PUNCT
ejpam-4941	171	42	r	r	NOUN
ejpam-4941	171	43	−	−	PROPN
ejpam-4941	171	44	1	1	NUM
ejpam-4941	171	45	(	(	PUNCT
ejpam-4941	171	46	because	because	SCONJ
ejpam-4941	171	47	as	as	ADP
ejpam-4941	171	48	a	a	DET
ejpam-4941	171	49	remark	remark	NOUN
ejpam-4941	171	50	,	,	PUNCT
ejpam-4941	171	51	we	we	PRON
ejpam-4941	171	52	have	have	AUX
ejpam-4941	171	53	(	(	PUNCT
ejpam-4941	171	54	e∗∗1	e∗∗1	ADJ
ejpam-4941	171	55	,	,	PUNCT
ejpam-4941	171	56	...	...	PUNCT
ejpam-4941	171	57	,	,	PUNCT
ejpam-4941	171	58	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	171	59	)	)	PUNCT
ejpam-4941	171	60	⊆	⊆	NUM
ejpam-4941	171	61	(	(	PUNCT
ejpam-4941	171	62	e∗∗1	e∗∗1	NOUN
ejpam-4941	171	63	,	,	PUNCT
ejpam-4941	171	64	...	...	PUNCT
ejpam-4941	171	65	,	,	PUNCT
ejpam-4941	171	66	e∗∗k	e∗∗k	PROPN
ejpam-4941	171	67	)	)	PUNCT
ejpam-4941	171	68	implies	imply	VERB
ejpam-4941	171	69	s.	s.	PROPN
ejpam-4941	171	70	abdelalim	abdelalim	PROPN
ejpam-4941	171	71	,	,	PUNCT
ejpam-4941	171	72	i.	i.	PROPN
ejpam-4941	171	73	elmouki	elmouki	PROPN
ejpam-4941	171	74	/	/	SYM
ejpam-4941	171	75	eur	eur	PROPN
ejpam-4941	171	76	.	.	PUNCT
ejpam-4941	172	1	j.	j.	PROPN
ejpam-4941	172	2	pure	pure	PROPN
ejpam-4941	172	3	appl	appl	PROPN
ejpam-4941	172	4	.	.	PROPN
ejpam-4941	172	5	math	math	PROPN
ejpam-4941	172	6	,	,	PUNCT
ejpam-4941	172	7	16	16	NUM
ejpam-4941	172	8	(	(	PUNCT
ejpam-4941	172	9	4	4	NUM
ejpam-4941	172	10	)	)	PUNCT
ejpam-4941	172	11	(	(	PUNCT
ejpam-4941	172	12	2023	2023	NUM
ejpam-4941	172	13	)	)	PUNCT
ejpam-4941	172	14	,	,	PUNCT
ejpam-4941	172	15	2662	2662	NUM
ejpam-4941	172	16	-	-	SYM
ejpam-4941	172	17	2692	2692	NUM
ejpam-4941	172	18	2673	2673	NUM
ejpam-4941	172	19	that	that	PRON
ejpam-4941	172	20	span(e∗∗1	span(e∗∗1	ADJ
ejpam-4941	172	21	,	,	PUNCT
ejpam-4941	172	22	...	...	PUNCT
ejpam-4941	172	23	,	,	PUNCT
ejpam-4941	172	24	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	172	25	)	)	PUNCT
ejpam-4941	172	26	⊆	⊆	NUM
ejpam-4941	172	27	span(e∗∗1	span(e∗∗1	ADJ
ejpam-4941	172	28	,	,	PUNCT
ejpam-4941	172	29	...	...	PUNCT
ejpam-4941	172	30	,	,	PUNCT
ejpam-4941	172	31	e∗∗k	e∗∗k	PROPN
ejpam-4941	172	32	)	)	PUNCT
ejpam-4941	172	33	)	)	PUNCT
ejpam-4941	172	34	.	.	PUNCT
ejpam-4941	173	1	then	then	ADV
ejpam-4941	173	2	,	,	PUNCT
ejpam-4941	173	3	span(e1	span(e1	NOUN
ejpam-4941	173	4	,	,	PUNCT
ejpam-4941	173	5	,	,	PUNCT
ejpam-4941	173	6	...	...	PUNCT
ejpam-4941	173	7	,	,	PUNCT
ejpam-4941	173	8	er	er	INTJ
ejpam-4941	173	9	)	)	PUNCT
ejpam-4941	173	10	≤	≤	NOUN
ejpam-4941	173	11	span(e∗∗1	span(e∗∗1	NOUN
ejpam-4941	173	12	,	,	PUNCT
ejpam-4941	173	13	e	e	X
ejpam-4941	173	14	∗∗(1	∗∗(1	X
ejpam-4941	173	15	)	)	PUNCT
ejpam-4941	173	16	2	2	NUM
ejpam-4941	173	17	,	,	PUNCT
ejpam-4941	173	18	e	e	X
ejpam-4941	173	19	∗∗(2	∗∗(2	PROPN
ejpam-4941	173	20	)	)	PUNCT
ejpam-4941	173	21	3	3	NUM
ejpam-4941	173	22	,	,	PUNCT
ejpam-4941	173	23	...	...	PUNCT
ejpam-4941	173	24	,	,	PUNCT
ejpam-4941	173	25	e	e	NOUN
ejpam-4941	173	26	∗∗(k	∗∗(k	NOUN
ejpam-4941	173	27	)	)	PUNCT
ejpam-4941	173	28	r	r	NOUN
ejpam-4941	173	29	)	)	PUNCT
ejpam-4941	173	30	,	,	PUNCT
ejpam-4941	173	31	1	1	NUM
ejpam-4941	173	32	≤	≤	NUM
ejpam-4941	173	33	i	i	X
ejpam-4941	174	1	≤	≤	ADJ
ejpam-4941	174	2	r	r	NOUN
ejpam-4941	174	3	,	,	PUNCT
ejpam-4941	174	4	k	k	NOUN
ejpam-4941	174	5	=	=	SYM
ejpam-4941	174	6	2	2	NUM
ejpam-4941	174	7	,	,	PUNCT
ejpam-4941	174	8	...	...	PUNCT
ejpam-4941	174	9	,	,	PUNCT
ejpam-4941	174	10	r	r	NOUN
ejpam-4941	174	11	−	−	PROPN
ejpam-4941	174	12	1	1	NUM
ejpam-4941	174	13	.	.	PUNCT
ejpam-4941	175	1	on	on	ADP
ejpam-4941	175	2	the	the	DET
ejpam-4941	175	3	other	other	ADJ
ejpam-4941	175	4	hand	hand	NOUN
ejpam-4941	175	5	,	,	PUNCT
ejpam-4941	175	6	the	the	DET
ejpam-4941	175	7	result	result	NOUN
ejpam-4941	175	8	is	be	AUX
ejpam-4941	175	9	obviously	obviously	ADV
ejpam-4941	175	10	satisfied	satisfied	ADJ
ejpam-4941	175	11	when	when	SCONJ
ejpam-4941	175	12	r	r	NOUN
ejpam-4941	175	13	=	=	NOUN
ejpam-4941	175	14	1	1	NUM
ejpam-4941	175	15	since	since	SCONJ
ejpam-4941	175	16	we	we	PRON
ejpam-4941	175	17	have	have	VERB
ejpam-4941	175	18	e∗∗1	e∗∗1	NOUN
ejpam-4941	175	19	=	=	SYM
ejpam-4941	175	20	e1	e1	NOUN
ejpam-4941	175	21	.	.	PUNCT
ejpam-4941	176	1	suppose	suppose	VERB
ejpam-4941	176	2	now	now	ADV
ejpam-4941	176	3	that	that	SCONJ
ejpam-4941	176	4	r	r	NOUN
ejpam-4941	176	5	≥	≥	NUM
ejpam-4941	176	6	1	1	NUM
ejpam-4941	176	7	,	,	PUNCT
ejpam-4941	176	8	and	and	CCONJ
ejpam-4941	176	9	span(e∗∗1	span(e∗∗1	ADJ
ejpam-4941	176	10	,	,	PUNCT
ejpam-4941	176	11	e	e	X
ejpam-4941	176	12	∗∗(1	∗∗(1	X
ejpam-4941	176	13	)	)	PUNCT
ejpam-4941	176	14	2	2	NUM
ejpam-4941	176	15	,	,	PUNCT
ejpam-4941	176	16	e	e	X
ejpam-4941	176	17	∗∗(2	∗∗(2	PROPN
ejpam-4941	176	18	)	)	PUNCT
ejpam-4941	176	19	3	3	NUM
ejpam-4941	176	20	,	,	PUNCT
ejpam-4941	176	21	...	...	PUNCT
ejpam-4941	176	22	,	,	PUNCT
ejpam-4941	176	23	e	e	NOUN
ejpam-4941	176	24	∗∗(k−1	∗∗(k−1	X
ejpam-4941	176	25	)	)	PUNCT
ejpam-4941	176	26	r	r	NOUN
ejpam-4941	176	27	)	)	PUNCT
ejpam-4941	176	28	⊆	⊆	NUM
ejpam-4941	176	29	span(e1	span(e1	NOUN
ejpam-4941	176	30	,	,	PUNCT
ejpam-4941	176	31	,	,	PUNCT
ejpam-4941	176	32	...	...	PUNCT
ejpam-4941	176	33	,	,	PUNCT
ejpam-4941	176	34	er	er	INTJ
ejpam-4941	176	35	)	)	PUNCT
ejpam-4941	176	36	and	and	CCONJ
ejpam-4941	176	37	let	let	VERB
ejpam-4941	176	38	us	we	PRON
ejpam-4941	176	39	prove	prove	VERB
ejpam-4941	176	40	that	that	DET
ejpam-4941	176	41	span(e∗∗1	span(e∗∗1	NOUN
ejpam-4941	176	42	,	,	PUNCT
ejpam-4941	176	43	e	e	X
ejpam-4941	176	44	∗∗(1	∗∗(1	X
ejpam-4941	176	45	)	)	PUNCT
ejpam-4941	176	46	2	2	NUM
ejpam-4941	176	47	,	,	PUNCT
ejpam-4941	176	48	e	e	X
ejpam-4941	176	49	∗∗(2	∗∗(2	PROPN
ejpam-4941	176	50	)	)	PUNCT
ejpam-4941	176	51	3	3	NUM
ejpam-4941	176	52	,	,	PUNCT
ejpam-4941	176	53	...	...	PUNCT
ejpam-4941	176	54	,	,	PUNCT
ejpam-4941	176	55	e	e	NOUN
ejpam-4941	176	56	∗∗(k	∗∗(k	NOUN
ejpam-4941	176	57	)	)	PUNCT
ejpam-4941	176	58	r	r	NOUN
ejpam-4941	176	59	)	)	PUNCT
ejpam-4941	176	60	⊆	⊆	NUM
ejpam-4941	176	61	span(e1	span(e1	NOUN
ejpam-4941	176	62	,	,	PUNCT
ejpam-4941	176	63	,	,	PUNCT
ejpam-4941	176	64	...	...	PUNCT
ejpam-4941	176	65	,	,	PUNCT
ejpam-4941	176	66	er	er	INTJ
ejpam-4941	176	67	)	)	PUNCT
ejpam-4941	176	68	.	.	PUNCT
ejpam-4941	177	1	(	(	PUNCT
ejpam-4941	177	2	the	the	DET
ejpam-4941	177	3	assumption	assumption	NOUN
ejpam-4941	177	4	span(e∗∗1	span(e∗∗1	NOUN
ejpam-4941	177	5	,	,	PUNCT
ejpam-4941	177	6	e	e	X
ejpam-4941	177	7	∗∗(1	∗∗(1	X
ejpam-4941	177	8	)	)	PUNCT
ejpam-4941	177	9	2	2	NUM
ejpam-4941	177	10	,	,	PUNCT
ejpam-4941	177	11	e	e	X
ejpam-4941	177	12	∗∗(2	∗∗(2	PROPN
ejpam-4941	177	13	)	)	PUNCT
ejpam-4941	177	14	3	3	NUM
ejpam-4941	177	15	,	,	PUNCT
ejpam-4941	177	16	...	...	PUNCT
ejpam-4941	177	17	,	,	PUNCT
ejpam-4941	177	18	e	e	NOUN
ejpam-4941	177	19	∗∗(k−1	∗∗(k−1	X
ejpam-4941	177	20	)	)	PUNCT
ejpam-4941	177	21	r	r	NOUN
ejpam-4941	177	22	)	)	PUNCT
ejpam-4941	177	23	⊆	⊆	NUM
ejpam-4941	177	24	span(e1	span(e1	NOUN
ejpam-4941	177	25	,	,	PUNCT
ejpam-4941	177	26	,	,	PUNCT
ejpam-4941	177	27	...	...	PUNCT
ejpam-4941	177	28	,	,	PUNCT
ejpam-4941	177	29	er	er	INTJ
ejpam-4941	177	30	)	)	PUNCT
ejpam-4941	177	31	should	should	AUX
ejpam-4941	177	32	be	be	AUX
ejpam-4941	177	33	even	even	ADV
ejpam-4941	177	34	true	true	ADJ
ejpam-4941	177	35	as	as	ADP
ejpam-4941	177	36	from	from	ADP
ejpam-4941	177	37	the	the	DET
ejpam-4941	177	38	formulation	formulation	NOUN
ejpam-4941	177	39	,	,	PUNCT
ejpam-4941	177	40	er	er	INTJ
ejpam-4941	177	41	=	=	PUNCT
ejpam-4941	177	42	e∗∗(k−1	e∗∗(k−1	NOUN
ejpam-4941	177	43	)	)	PUNCT
ejpam-4941	178	1	r	r	NOUN
ejpam-4941	178	2	+	+	NUM
ejpam-4941	178	3	⟨er	⟨er	NOUN
ejpam-4941	178	4	,	,	PUNCT
ejpam-4941	178	5	e∗∗k−1⟩	e∗∗k−1⟩	PROPN
ejpam-4941	178	6	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	178	7	,	,	PUNCT
ejpam-4941	178	8	e	e	X
ejpam-4941	178	9	∗∗	∗∗	X
ejpam-4941	178	10	k−1⟩	k−1⟩	ADV
ejpam-4941	178	11	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	178	12	,	,	PUNCT
ejpam-4941	178	13	k	k	NOUN
ejpam-4941	178	14	=	=	SYM
ejpam-4941	178	15	2	2	NUM
ejpam-4941	178	16	,	,	PUNCT
ejpam-4941	178	17	...	...	PUNCT
ejpam-4941	178	18	,	,	PUNCT
ejpam-4941	179	1	r	r	NOUN
ejpam-4941	179	2	−	−	PROPN
ejpam-4941	179	3	1	1	NUM
ejpam-4941	179	4	that	that	DET
ejpam-4941	179	5	sum	sum	NOUN
ejpam-4941	179	6	is	be	AUX
ejpam-4941	179	7	known	know	VERB
ejpam-4941	179	8	to	to	PART
ejpam-4941	179	9	be	be	AUX
ejpam-4941	179	10	unique	unique	ADJ
ejpam-4941	179	11	with	with	ADP
ejpam-4941	179	12	e	e	NOUN
ejpam-4941	179	13	∗∗(k−1	∗∗(k−1	X
ejpam-4941	179	14	)	)	PUNCT
ejpam-4941	179	15	r	r	NOUN
ejpam-4941	179	16	∈	∈	NOUN
ejpam-4941	179	17	span(e1	span(e1	NOUN
ejpam-4941	179	18	,	,	PUNCT
ejpam-4941	179	19	,	,	PUNCT
ejpam-4941	179	20	...	...	PUNCT
ejpam-4941	179	21	,	,	PUNCT
ejpam-4941	179	22	er	er	INTJ
ejpam-4941	179	23	)	)	PUNCT
ejpam-4941	179	24	⊥	⊥	PROPN
ejpam-4941	179	25	and	and	CCONJ
ejpam-4941	179	26	e∗∗k−1	e∗∗k−1	ADJ
ejpam-4941	179	27	⊆	⊆	NUM
ejpam-4941	179	28	span(e1	span(e1	NOUN
ejpam-4941	179	29	,	,	PUNCT
ejpam-4941	179	30	,	,	PUNCT
ejpam-4941	179	31	...	...	PUNCT
ejpam-4941	179	32	,	,	PUNCT
ejpam-4941	179	33	er	er	INTJ
ejpam-4941	179	34	)	)	PUNCT
ejpam-4941	179	35	,	,	PUNCT
ejpam-4941	179	36	2	2	NUM
ejpam-4941	179	37	≤	≤	NUM
ejpam-4941	179	38	k	k	NOUN
ejpam-4941	179	39	≤	≤	NUM
ejpam-4941	179	40	r	r	NOUN
ejpam-4941	179	41	−	−	NOUN
ejpam-4941	179	42	1	1	NUM
ejpam-4941	179	43	)	)	PUNCT
ejpam-4941	179	44	.	.	PUNCT
ejpam-4941	180	1	for	for	ADP
ejpam-4941	180	2	2	2	NUM
ejpam-4941	180	3	≤	≤	NOUN
ejpam-4941	180	4	k	k	NOUN
ejpam-4941	180	5	≤	≤	NUM
ejpam-4941	180	6	r	r	NOUN
ejpam-4941	180	7	−	−	NOUN
ejpam-4941	180	8	1	1	NUM
ejpam-4941	180	9	,	,	PUNCT
ejpam-4941	180	10	we	we	PRON
ejpam-4941	180	11	have	have	VERB
ejpam-4941	180	12	now	now	ADV
ejpam-4941	180	13	,	,	PUNCT
ejpam-4941	180	14	e∗∗(k)r	e∗∗(k)r	PROPN
ejpam-4941	180	15	=	=	SYM
ejpam-4941	180	16	e∗∗(k−1	e∗∗(k−1	X
ejpam-4941	180	17	)	)	PUNCT
ejpam-4941	180	18	r	r	NOUN
ejpam-4941	180	19	−	−	NOUN
ejpam-4941	180	20	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	180	21	)	)	PUNCT
ejpam-4941	180	22	r	r	NOUN
ejpam-4941	180	23	,	,	PUNCT
ejpam-4941	180	24	e∗∗r	e∗∗r	ADP
ejpam-4941	180	25	⟩	⟩	NOUN
ejpam-4941	180	26	⟨e∗∗r	⟨e∗∗r	NOUN
ejpam-4941	180	27	,	,	PUNCT
ejpam-4941	180	28	e∗∗r	e∗∗r	ADP
ejpam-4941	180	29	⟩	⟩	NOUN
ejpam-4941	180	30	e∗∗r	e∗∗r	ADP
ejpam-4941	180	31	,	,	PUNCT
ejpam-4941	180	32	k	k	PROPN
ejpam-4941	180	33	=	=	SYM
ejpam-4941	180	34	2	2	NUM
ejpam-4941	180	35	,	,	PUNCT
ejpam-4941	180	36	...	...	PUNCT
ejpam-4941	180	37	,	,	PUNCT
ejpam-4941	180	38	r	r	NOUN
ejpam-4941	180	39	−	−	PROPN
ejpam-4941	180	40	1	1	NUM
ejpam-4941	180	41	=	=	NUM
ejpam-4941	180	42	er	er	INTJ
ejpam-4941	180	43	−	−	PROPN
ejpam-4941	180	44	⟨er	⟨er	NOUN
ejpam-4941	180	45	,	,	PUNCT
ejpam-4941	180	46	e∗∗k−1⟩	e∗∗k−1⟩	PROPN
ejpam-4941	180	47	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	180	48	,	,	PUNCT
ejpam-4941	180	49	e	e	X
ejpam-4941	180	50	∗∗	∗∗	X
ejpam-4941	180	51	k−1⟩	k−1⟩	PRON
ejpam-4941	180	52	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	180	53	−	−	NOUN
ejpam-4941	180	54	⟨e∗∗(k−1	⟨e∗∗(k−1	NUM
ejpam-4941	180	55	)	)	PUNCT
ejpam-4941	180	56	r	r	NOUN
ejpam-4941	180	57	,	,	PUNCT
ejpam-4941	180	58	e∗∗r	e∗∗r	ADP
ejpam-4941	180	59	⟩	⟩	NOUN
ejpam-4941	180	60	⟨e∗∗r	⟨e∗∗r	NOUN
ejpam-4941	180	61	,	,	PUNCT
ejpam-4941	180	62	e∗∗r	e∗∗r	ADP
ejpam-4941	180	63	⟩	⟩	NOUN
ejpam-4941	180	64	e∗∗r	e∗∗r	ADP
ejpam-4941	180	65	,	,	PUNCT
ejpam-4941	180	66	k	k	PROPN
ejpam-4941	180	67	=	=	SYM
ejpam-4941	180	68	2	2	NUM
ejpam-4941	180	69	,	,	PUNCT
ejpam-4941	180	70	...	...	PUNCT
ejpam-4941	180	71	,	,	PUNCT
ejpam-4941	181	1	r	r	NOUN
ejpam-4941	181	2	−	−	PROPN
ejpam-4941	181	3	1	1	NUM
ejpam-4941	181	4	thus	thus	ADV
ejpam-4941	181	5	,	,	PUNCT
ejpam-4941	181	6	e	e	NOUN
ejpam-4941	181	7	∗∗(k	∗∗(k	NOUN
ejpam-4941	181	8	)	)	PUNCT
ejpam-4941	181	9	r	r	NOUN
ejpam-4941	181	10	=	=	PUNCT
ejpam-4941	181	11	er	er	INTJ
ejpam-4941	181	12	+	+	NUM
ejpam-4941	181	13	f	f	NOUN
ejpam-4941	181	14	with	with	ADP
ejpam-4941	181	15	f	f	PROPN
ejpam-4941	181	16	∈	∈	PROPN
ejpam-4941	181	17	span(e∗∗1	span(e∗∗1	NOUN
ejpam-4941	181	18	,	,	PUNCT
ejpam-4941	181	19	e	e	X
ejpam-4941	181	20	∗∗(1	∗∗(1	X
ejpam-4941	181	21	)	)	PUNCT
ejpam-4941	181	22	2	2	NUM
ejpam-4941	181	23	,	,	PUNCT
ejpam-4941	181	24	e	e	X
ejpam-4941	181	25	∗∗(2	∗∗(2	PROPN
ejpam-4941	181	26	)	)	PUNCT
ejpam-4941	181	27	3	3	NUM
ejpam-4941	181	28	,	,	PUNCT
ejpam-4941	181	29	...	...	PUNCT
ejpam-4941	181	30	,	,	PUNCT
ejpam-4941	181	31	e	e	NOUN
ejpam-4941	181	32	∗∗(k−1	∗∗(k−1	X
ejpam-4941	181	33	)	)	PUNCT
ejpam-4941	181	34	r	r	NOUN
ejpam-4941	181	35	)	)	PUNCT
ejpam-4941	181	36	.	.	PUNCT
ejpam-4941	182	1	then	then	ADV
ejpam-4941	182	2	,	,	PUNCT
ejpam-4941	182	3	since	since	SCONJ
ejpam-4941	182	4	we	we	PRON
ejpam-4941	182	5	have	have	AUX
ejpam-4941	182	6	supposed	suppose	VERB
ejpam-4941	182	7	that	that	DET
ejpam-4941	182	8	span(e∗∗1	span(e∗∗1	ADJ
ejpam-4941	182	9	,	,	PUNCT
ejpam-4941	182	10	e	e	X
ejpam-4941	182	11	∗∗(1	∗∗(1	X
ejpam-4941	182	12	)	)	PUNCT
ejpam-4941	182	13	2	2	NUM
ejpam-4941	182	14	,	,	PUNCT
ejpam-4941	182	15	e	e	X
ejpam-4941	182	16	∗∗(2	∗∗(2	PROPN
ejpam-4941	182	17	)	)	PUNCT
ejpam-4941	182	18	3	3	NUM
ejpam-4941	182	19	,	,	PUNCT
ejpam-4941	182	20	...	...	PUNCT
ejpam-4941	182	21	,	,	PUNCT
ejpam-4941	182	22	e	e	NOUN
ejpam-4941	182	23	∗∗(k−1	∗∗(k−1	X
ejpam-4941	182	24	)	)	PUNCT
ejpam-4941	182	25	r	r	NOUN
ejpam-4941	182	26	)	)	PUNCT
ejpam-4941	182	27	⊆	⊆	NUM
ejpam-4941	182	28	span(e1	span(e1	NOUN
ejpam-4941	182	29	,	,	PUNCT
ejpam-4941	182	30	,	,	PUNCT
ejpam-4941	182	31	...	...	PUNCT
ejpam-4941	182	32	,	,	PUNCT
ejpam-4941	182	33	er	er	INTJ
ejpam-4941	182	34	)	)	PUNCT
ejpam-4941	182	35	,	,	PUNCT
ejpam-4941	182	36	therefore	therefore	ADV
ejpam-4941	182	37	,	,	PUNCT
ejpam-4941	182	38	e	e	NOUN
ejpam-4941	182	39	∗∗(k	∗∗(k	NOUN
ejpam-4941	182	40	)	)	PUNCT
ejpam-4941	182	41	r	r	NOUN
ejpam-4941	182	42	∈	∈	NOUN
ejpam-4941	182	43	span(e1	span(e1	NOUN
ejpam-4941	182	44	,	,	PUNCT
ejpam-4941	182	45	,	,	PUNCT
ejpam-4941	182	46	...	...	PUNCT
ejpam-4941	182	47	,	,	PUNCT
ejpam-4941	182	48	er	er	INTJ
ejpam-4941	182	49	)	)	PUNCT
ejpam-4941	182	50	,	,	PUNCT
ejpam-4941	182	51	hence	hence	ADV
ejpam-4941	182	52	,	,	PUNCT
ejpam-4941	182	53	span(e∗∗1	span(e∗∗1	ADJ
ejpam-4941	182	54	,	,	PUNCT
ejpam-4941	182	55	e	e	X
ejpam-4941	182	56	∗∗(1	∗∗(1	X
ejpam-4941	182	57	)	)	PUNCT
ejpam-4941	182	58	2	2	NUM
ejpam-4941	182	59	,	,	PUNCT
ejpam-4941	182	60	e	e	X
ejpam-4941	182	61	∗∗(2	∗∗(2	PROPN
ejpam-4941	182	62	)	)	PUNCT
ejpam-4941	182	63	3	3	NUM
ejpam-4941	182	64	,	,	PUNCT
ejpam-4941	182	65	...	...	PUNCT
ejpam-4941	182	66	,	,	PUNCT
ejpam-4941	182	67	e	e	NOUN
ejpam-4941	182	68	∗∗(k	∗∗(k	NOUN
ejpam-4941	182	69	)	)	PUNCT
ejpam-4941	182	70	r	r	NOUN
ejpam-4941	182	71	)	)	PUNCT
ejpam-4941	182	72	∈	∈	NOUN
ejpam-4941	182	73	span(e1	span(e1	NOUN
ejpam-4941	182	74	,	,	PUNCT
ejpam-4941	182	75	,	,	PUNCT
ejpam-4941	182	76	...	...	PUNCT
ejpam-4941	182	77	,	,	PUNCT
ejpam-4941	182	78	er	er	INTJ
ejpam-4941	182	79	)	)	PUNCT
ejpam-4941	182	80	.	.	PUNCT
ejpam-4941	183	1	–	–	PUNCT
ejpam-4941	183	2	on	on	ADP
ejpam-4941	183	3	one	one	NUM
ejpam-4941	183	4	hand	hand	NOUN
ejpam-4941	183	5	,	,	PUNCT
ejpam-4941	183	6	if	if	SCONJ
ejpam-4941	183	7	we	we	PRON
ejpam-4941	183	8	suppose	suppose	VERB
ejpam-4941	183	9	that	that	SCONJ
ejpam-4941	183	10	⟨er	⟨er	NOUN
ejpam-4941	183	11	,	,	PUNCT
ejpam-4941	183	12	e∗r⟩	e∗r⟩	NOUN
ejpam-4941	183	13	⟨e∗r	⟨e∗r	NOUN
ejpam-4941	183	14	,	,	PUNCT
ejpam-4941	183	15	e∗r⟩	e∗r⟩	NOUN
ejpam-4941	183	16	=	=	SYM
ejpam-4941	183	17	1	1	X
ejpam-4941	183	18	.	.	PUNCT
ejpam-4941	184	1	then	then	ADV
ejpam-4941	184	2	,	,	PUNCT
ejpam-4941	184	3	e∗r	e∗r	X
ejpam-4941	184	4	=	=	SYM
ejpam-4941	184	5	er	er	INTJ
ejpam-4941	184	6	−	−	PROPN
ejpam-4941	184	7	r−1∑	r−1∑	PROPN
ejpam-4941	184	8	k=1	k=1	PROPN
ejpam-4941	184	9	⟨er	⟨er	PROPN
ejpam-4941	184	10	,	,	PUNCT
ejpam-4941	184	11	e∗k⟩	e∗k⟩	NOUN
ejpam-4941	184	12	⟨e∗k	⟨e∗k	PROPN
ejpam-4941	184	13	,	,	PUNCT
ejpam-4941	184	14	e∗k⟩	e∗k⟩	AUX
ejpam-4941	184	15	e∗k	e∗k	ADV
ejpam-4941	184	16	is	be	AUX
ejpam-4941	184	17	giving	give	VERB
ejpam-4941	184	18	,	,	PUNCT
ejpam-4941	184	19	er	er	INTJ
ejpam-4941	184	20	=	=	NOUN
ejpam-4941	184	21	r∑	r∑	NOUN
ejpam-4941	184	22	k=1	k=1	PROPN
ejpam-4941	184	23	⟨er	⟨er	NOUN
ejpam-4941	184	24	,	,	PUNCT
ejpam-4941	184	25	e∗k⟩	e∗k⟩	NOUN
ejpam-4941	184	26	⟨e∗k	⟨e∗k	PROPN
ejpam-4941	184	27	,	,	PUNCT
ejpam-4941	184	28	e∗k⟩	e∗k⟩	AUX
ejpam-4941	184	29	e∗k	e∗k	PUNCT
ejpam-4941	184	30	∈	∈	PROPN
ejpam-4941	184	31	span(e∗1	span(e∗1	PROPN
ejpam-4941	184	32	,	,	PUNCT
ejpam-4941	184	33	...	...	PUNCT
ejpam-4941	184	34	,	,	PUNCT
ejpam-4941	184	35	e	e	X
ejpam-4941	184	36	∗	∗	NOUN
ejpam-4941	184	37	r	r	NOUN
ejpam-4941	184	38	)	)	PUNCT
ejpam-4941	184	39	.	.	PUNCT
ejpam-4941	185	1	thus	thus	ADV
ejpam-4941	185	2	,	,	PUNCT
ejpam-4941	185	3	span(e1	span(e1	NOUN
ejpam-4941	185	4	,	,	PUNCT
ejpam-4941	185	5	...	...	PUNCT
ejpam-4941	185	6	,	,	PUNCT
ejpam-4941	185	7	er	er	INTJ
ejpam-4941	185	8	)	)	PUNCT
ejpam-4941	185	9	⊆	⊆	NUM
ejpam-4941	185	10	span(e∗1	span(e∗1	PROPN
ejpam-4941	185	11	,	,	PUNCT
ejpam-4941	185	12	...	...	PUNCT
ejpam-4941	185	13	,	,	PUNCT
ejpam-4941	185	14	e	e	X
ejpam-4941	185	15	∗	∗	NOUN
ejpam-4941	185	16	r	r	NOUN
ejpam-4941	185	17	)	)	PUNCT
ejpam-4941	185	18	.	.	PUNCT
ejpam-4941	186	1	on	on	ADP
ejpam-4941	186	2	the	the	DET
ejpam-4941	186	3	other	other	ADJ
ejpam-4941	186	4	hand	hand	NOUN
ejpam-4941	186	5	,	,	PUNCT
ejpam-4941	186	6	by	by	ADP
ejpam-4941	186	7	induction	induction	NOUN
ejpam-4941	186	8	,	,	PUNCT
ejpam-4941	186	9	we	we	PRON
ejpam-4941	186	10	have	have	VERB
ejpam-4941	186	11	for	for	ADP
ejpam-4941	186	12	k	k	PROPN
ejpam-4941	186	13	=	=	SYM
ejpam-4941	186	14	1	1	NUM
ejpam-4941	186	15	,	,	PUNCT
ejpam-4941	186	16	e1	e1	NOUN
ejpam-4941	186	17	=	=	SYM
ejpam-4941	186	18	e∗1	e∗1	NOUN
ejpam-4941	186	19	,	,	PUNCT
ejpam-4941	186	20	then	then	ADV
ejpam-4941	186	21	span(e1	span(e1	NOUN
ejpam-4941	186	22	)	)	PUNCT
ejpam-4941	186	23	=	=	SYM
ejpam-4941	186	24	span(e∗1	span(e∗1	PROPN
ejpam-4941	186	25	)	)	PUNCT
ejpam-4941	186	26	.	.	PUNCT
ejpam-4941	187	1	now	now	ADV
ejpam-4941	187	2	,	,	PUNCT
ejpam-4941	187	3	if	if	SCONJ
ejpam-4941	187	4	we	we	PRON
ejpam-4941	187	5	suppose	suppose	VERB
ejpam-4941	187	6	that	that	SCONJ
ejpam-4941	187	7	span(e∗1	span(e∗1	PROPN
ejpam-4941	187	8	,	,	PUNCT
ejpam-4941	187	9	...	...	PUNCT
ejpam-4941	187	10	,	,	PUNCT
ejpam-4941	187	11	e	e	X
ejpam-4941	187	12	∗	∗	NOUN
ejpam-4941	187	13	r	r	NOUN
ejpam-4941	187	14	)	)	PUNCT
ejpam-4941	187	15	⊆	⊆	NUM
ejpam-4941	187	16	span(e1	span(e1	NOUN
ejpam-4941	187	17	,	,	PUNCT
ejpam-4941	187	18	...	...	PUNCT
ejpam-4941	187	19	,	,	PUNCT
ejpam-4941	187	20	er	er	INTJ
ejpam-4941	187	21	)	)	PUNCT
ejpam-4941	187	22	,	,	PUNCT
ejpam-4941	187	23	then	then	ADV
ejpam-4941	187	24	,	,	PUNCT
ejpam-4941	187	25	we	we	PRON
ejpam-4941	187	26	have	have	VERB
ejpam-4941	187	27	,	,	PUNCT
ejpam-4941	187	28	e∗r+1	e∗r+1	INTJ
ejpam-4941	188	1	=	=	SYM
ejpam-4941	188	2	er+1	er+1	NUM
ejpam-4941	188	3	−	−	NOUN
ejpam-4941	188	4	r∑	r∑	NOUN
ejpam-4941	188	5	k=1	k=1	PUNCT
ejpam-4941	188	6	⟨er+1	⟨er+1	PROPN
ejpam-4941	188	7	,	,	PUNCT
ejpam-4941	188	8	e	e	PROPN
ejpam-4941	188	9	∗	∗	NOUN
ejpam-4941	188	10	k⟩	k⟩	NOUN
ejpam-4941	189	1	⟨e∗k	⟨e∗k	PROPN
ejpam-4941	189	2	,	,	PUNCT
ejpam-4941	189	3	e∗k⟩	e∗k⟩	AUX
ejpam-4941	189	4	e∗k	e∗k	PUNCT
ejpam-4941	189	5	∈	∈	PROPN
ejpam-4941	189	6	span(e1	span(e1	NOUN
ejpam-4941	189	7	,	,	PUNCT
ejpam-4941	189	8	...	...	PUNCT
ejpam-4941	189	9	,	,	PUNCT
ejpam-4941	189	10	er+1	er+1	X
ejpam-4941	189	11	)	)	PUNCT
ejpam-4941	189	12	s.	s.	PROPN
ejpam-4941	189	13	abdelalim	abdelalim	PROPN
ejpam-4941	189	14	,	,	PUNCT
ejpam-4941	189	15	i.	i.	PROPN
ejpam-4941	189	16	elmouki	elmouki	PROPN
ejpam-4941	189	17	/	/	SYM
ejpam-4941	189	18	eur	eur	PROPN
ejpam-4941	189	19	.	.	PUNCT
ejpam-4941	190	1	j.	j.	PROPN
ejpam-4941	190	2	pure	pure	PROPN
ejpam-4941	190	3	appl	appl	PROPN
ejpam-4941	190	4	.	.	PROPN
ejpam-4941	190	5	math	math	PROPN
ejpam-4941	190	6	,	,	PUNCT
ejpam-4941	190	7	16	16	NUM
ejpam-4941	190	8	(	(	PUNCT
ejpam-4941	190	9	4	4	NUM
ejpam-4941	190	10	)	)	PUNCT
ejpam-4941	190	11	(	(	PUNCT
ejpam-4941	190	12	2023	2023	NUM
ejpam-4941	190	13	)	)	PUNCT
ejpam-4941	190	14	,	,	PUNCT
ejpam-4941	190	15	2662	2662	NUM
ejpam-4941	190	16	-	-	SYM
ejpam-4941	190	17	2692	2692	NUM
ejpam-4941	190	18	2674	2674	NUM
ejpam-4941	190	19	this	this	PRON
ejpam-4941	190	20	is	be	AUX
ejpam-4941	190	21	because	because	SCONJ
ejpam-4941	190	22	we	we	PRON
ejpam-4941	190	23	have	have	VERB
ejpam-4941	190	24	first	first	ADJ
ejpam-4941	190	25	r∑	r∑	NOUN
ejpam-4941	190	26	k=1	k=1	PUNCT
ejpam-4941	191	1	⟨er+1	⟨er+1	PROPN
ejpam-4941	191	2	,	,	PUNCT
ejpam-4941	191	3	e	e	PROPN
ejpam-4941	191	4	∗	∗	NOUN
ejpam-4941	191	5	k⟩	k⟩	NOUN
ejpam-4941	191	6	⟨e∗k	⟨e∗k	PROPN
ejpam-4941	191	7	,	,	PUNCT
ejpam-4941	191	8	e∗k⟩	e∗k⟩	AUX
ejpam-4941	191	9	e∗k	e∗k	PUNCT
ejpam-4941	191	10	∈	∈	PROPN
ejpam-4941	191	11	span(e∗1	span(e∗1	PROPN
ejpam-4941	191	12	,	,	PUNCT
ejpam-4941	191	13	...	...	PUNCT
ejpam-4941	191	14	,	,	PUNCT
ejpam-4941	191	15	e	e	X
ejpam-4941	191	16	∗	∗	NOUN
ejpam-4941	191	17	r	r	NOUN
ejpam-4941	191	18	)	)	PUNCT
ejpam-4941	191	19	,	,	PUNCT
ejpam-4941	191	20	and	and	CCONJ
ejpam-4941	191	21	which	which	PRON
ejpam-4941	191	22	is	be	AUX
ejpam-4941	191	23	in	in	ADP
ejpam-4941	191	24	turn	turn	NOUN
ejpam-4941	191	25	by	by	ADP
ejpam-4941	191	26	the	the	DET
ejpam-4941	191	27	induction	induction	NOUN
ejpam-4941	191	28	hypothesis	hypothesis	NOUN
ejpam-4941	191	29	,	,	PUNCT
ejpam-4941	191	30	an	an	DET
ejpam-4941	191	31	element	element	NOUN
ejpam-4941	191	32	of	of	ADP
ejpam-4941	191	33	span(e1	span(e1	NOUN
ejpam-4941	191	34	,	,	PUNCT
ejpam-4941	191	35	...	...	PUNCT
ejpam-4941	191	36	,	,	PUNCT
ejpam-4941	191	37	er	er	INTJ
ejpam-4941	191	38	)	)	PUNCT
ejpam-4941	191	39	.	.	PUNCT
ejpam-4941	192	1	thus	thus	ADV
ejpam-4941	192	2	,	,	PUNCT
ejpam-4941	192	3	by	by	ADP
ejpam-4941	192	4	the	the	DET
ejpam-4941	192	5	formula	formula	NOUN
ejpam-4941	192	6	of	of	ADP
ejpam-4941	192	7	e∗r+1	e∗r+1	NOUN
ejpam-4941	192	8	,	,	PUNCT
ejpam-4941	192	9	we	we	PRON
ejpam-4941	192	10	deduce	deduce	VERB
ejpam-4941	192	11	that	that	SCONJ
ejpam-4941	192	12	span(e	span(e	NOUN
ejpam-4941	192	13	∗	∗	NOUN
ejpam-4941	192	14	1	1	NUM
ejpam-4941	192	15	,	,	PUNCT
ejpam-4941	192	16	...	...	PUNCT
ejpam-4941	192	17	,	,	PUNCT
ejpam-4941	192	18	e	e	X
ejpam-4941	192	19	∗	∗	NOUN
ejpam-4941	192	20	r+1	r+1	PROPN
ejpam-4941	192	21	)	)	PUNCT
ejpam-4941	192	22	⊆	⊆	NUM
ejpam-4941	192	23	span(e1	span(e1	NOUN
ejpam-4941	192	24	,	,	PUNCT
ejpam-4941	192	25	...	...	PUNCT
ejpam-4941	192	26	,	,	PUNCT
ejpam-4941	192	27	er+1	er+1	X
ejpam-4941	192	28	)	)	PUNCT
ejpam-4941	192	29	.	.	PUNCT
ejpam-4941	193	1	we	we	PRON
ejpam-4941	193	2	note	note	VERB
ejpam-4941	193	3	that	that	SCONJ
ejpam-4941	193	4	the	the	DET
ejpam-4941	193	5	properties	property	NOUN
ejpam-4941	193	6	just	just	ADV
ejpam-4941	193	7	stated	state	VERB
ejpam-4941	193	8	above	above	ADV
ejpam-4941	193	9	,	,	PUNCT
ejpam-4941	193	10	are	be	AUX
ejpam-4941	193	11	very	very	ADV
ejpam-4941	193	12	important	important	ADJ
ejpam-4941	193	13	in	in	ADP
ejpam-4941	193	14	the	the	DET
ejpam-4941	193	15	proof	proof	NOUN
ejpam-4941	193	16	of	of	ADP
ejpam-4941	193	17	the	the	DET
ejpam-4941	193	18	following	following	NOUN
ejpam-4941	193	19	theorem	theorem	NOUN
ejpam-4941	193	20	.	.	PROPN
ejpam-4941	193	21	2.2	2.2	NUM
ejpam-4941	193	22	.	.	PUNCT
ejpam-4941	194	1	the	the	DET
ejpam-4941	194	2	vectors	vector	NOUN
ejpam-4941	194	3	exchange	exchange	PROPN
ejpam-4941	194	4	theorem	theorem	VERB
ejpam-4941	194	5	the	the	DET
ejpam-4941	194	6	main	main	ADJ
ejpam-4941	194	7	goal	goal	NOUN
ejpam-4941	194	8	from	from	ADP
ejpam-4941	194	9	this	this	DET
ejpam-4941	194	10	part	part	NOUN
ejpam-4941	194	11	,	,	PUNCT
ejpam-4941	194	12	is	be	AUX
ejpam-4941	194	13	to	to	PART
ejpam-4941	194	14	provide	provide	VERB
ejpam-4941	194	15	a	a	DET
ejpam-4941	194	16	theoretical	theoretical	ADJ
ejpam-4941	194	17	framework	framework	NOUN
ejpam-4941	194	18	that	that	PRON
ejpam-4941	194	19	helps	help	VERB
ejpam-4941	194	20	to	to	PART
ejpam-4941	194	21	define	define	VERB
ejpam-4941	194	22	the	the	DET
ejpam-4941	194	23	new	new	ADJ
ejpam-4941	194	24	motif	motif	NOUN
ejpam-4941	194	25	and	and	CCONJ
ejpam-4941	194	26	whose	whose	DET
ejpam-4941	194	27	basis	basis	NOUN
ejpam-4941	194	28	vectors	vector	NOUN
ejpam-4941	194	29	could	could	AUX
ejpam-4941	194	30	generate	generate	VERB
ejpam-4941	194	31	the	the	DET
ejpam-4941	194	32	whole	whole	ADJ
ejpam-4941	194	33	representing	represent	VERB
ejpam-4941	194	34	bravais	bravais	PROPN
ejpam-4941	194	35	lattice	lattice	NOUN
ejpam-4941	194	36	of	of	ADP
ejpam-4941	194	37	a	a	DET
ejpam-4941	194	38	crystal	crystal	NOUN
ejpam-4941	194	39	,	,	PUNCT
ejpam-4941	194	40	all	all	ADV
ejpam-4941	194	41	around	around	ADP
ejpam-4941	194	42	the	the	DET
ejpam-4941	194	43	case	case	NOUN
ejpam-4941	194	44	when	when	SCONJ
ejpam-4941	194	45	its	its	PRON
ejpam-4941	194	46	associated	associated	ADJ
ejpam-4941	194	47	unit	unit	NOUN
ejpam-4941	194	48	cell	cell	NOUN
ejpam-4941	194	49	is	be	AUX
ejpam-4941	194	50	made	make	VERB
ejpam-4941	194	51	of	of	ADP
ejpam-4941	194	52	quasi	quasi	ADJ
ejpam-4941	194	53	-	-	ADJ
ejpam-4941	194	54	orthogonal	orthogonal	ADJ
ejpam-4941	194	55	vectors	vector	NOUN
ejpam-4941	194	56	.	.	PUNCT
ejpam-4941	195	1	the	the	DET
ejpam-4941	195	2	study	study	NOUN
ejpam-4941	195	3	also	also	ADV
ejpam-4941	195	4	aims	aim	VERB
ejpam-4941	195	5	to	to	PART
ejpam-4941	195	6	exhibit	exhibit	VERB
ejpam-4941	195	7	the	the	DET
ejpam-4941	195	8	change	change	NOUN
ejpam-4941	195	9	that	that	PRON
ejpam-4941	195	10	occurs	occur	VERB
ejpam-4941	195	11	to	to	ADP
ejpam-4941	195	12	the	the	DET
ejpam-4941	195	13	sought	seek	VERB
ejpam-4941	195	14	bravais	bravais	PROPN
ejpam-4941	195	15	lattice	lattice	PROPN
ejpam-4941	195	16	since	since	SCONJ
ejpam-4941	195	17	during	during	ADP
ejpam-4941	195	18	the	the	DET
ejpam-4941	195	19	resolution	resolution	NOUN
ejpam-4941	195	20	of	of	ADP
ejpam-4941	195	21	this	this	DET
ejpam-4941	195	22	problem	problem	NOUN
ejpam-4941	195	23	,	,	PUNCT
ejpam-4941	195	24	we	we	PRON
ejpam-4941	195	25	have	have	VERB
ejpam-4941	195	26	to	to	PART
ejpam-4941	195	27	exchange	exchange	VERB
ejpam-4941	195	28	our	our	PRON
ejpam-4941	195	29	consecutive	consecutive	ADJ
ejpam-4941	195	30	first	first	ADJ
ejpam-4941	195	31	and	and	CCONJ
ejpam-4941	195	32	newly	newly	ADV
ejpam-4941	195	33	input	input	ADJ
ejpam-4941	195	34	vectors	vector	NOUN
ejpam-4941	195	35	many	many	ADJ
ejpam-4941	195	36	times	time	NOUN
ejpam-4941	195	37	.	.	PUNCT
ejpam-4941	196	1	in	in	ADP
ejpam-4941	196	2	fact	fact	NOUN
ejpam-4941	196	3	,	,	PUNCT
ejpam-4941	196	4	we	we	PRON
ejpam-4941	196	5	will	will	AUX
ejpam-4941	196	6	consider	consider	VERB
ejpam-4941	196	7	hereafter	hereafter	ADV
ejpam-4941	196	8	,	,	PUNCT
ejpam-4941	196	9	a	a	DET
ejpam-4941	196	10	new	new	ADJ
ejpam-4941	196	11	basis	basis	NOUN
ejpam-4941	196	12	denoted	denote	VERB
ejpam-4941	196	13	as	as	ADP
ejpam-4941	196	14	(	(	PUNCT
ejpam-4941	196	15	f1	f1	NOUN
ejpam-4941	196	16	,	,	PUNCT
ejpam-4941	196	17	...	...	PUNCT
ejpam-4941	196	18	,	,	PUNCT
ejpam-4941	196	19	fn	fn	NOUN
ejpam-4941	196	20	)	)	PUNCT
ejpam-4941	196	21	of	of	ADP
ejpam-4941	196	22	the	the	DET
ejpam-4941	196	23	bravais	bravais	PROPN
ejpam-4941	196	24	lattice	lattice	PROPN
ejpam-4941	196	25	,	,	PUNCT
ejpam-4941	196	26	and	and	CCONJ
ejpam-4941	196	27	we	we	PRON
ejpam-4941	196	28	define	define	VERB
ejpam-4941	196	29	it	it	PRON
ejpam-4941	196	30	in	in	ADP
ejpam-4941	196	31	a	a	DET
ejpam-4941	196	32	way	way	NOUN
ejpam-4941	196	33	which	which	PRON
ejpam-4941	196	34	respects	respect	VERB
ejpam-4941	196	35	the	the	DET
ejpam-4941	196	36	fact	fact	NOUN
ejpam-4941	196	37	that	that	SCONJ
ejpam-4941	196	38	during	during	ADP
ejpam-4941	196	39	the	the	DET
ejpam-4941	196	40	most	most	ADV
ejpam-4941	196	41	important	important	ADJ
ejpam-4941	196	42	part	part	NOUN
ejpam-4941	196	43	of	of	ADP
ejpam-4941	196	44	lattice	lattice	NOUN
ejpam-4941	196	45	reduction	reduction	NOUN
ejpam-4941	196	46	algorithmic	algorithmic	ADJ
ejpam-4941	196	47	process	process	NOUN
ejpam-4941	196	48	,	,	PUNCT
ejpam-4941	196	49	we	we	PRON
ejpam-4941	196	50	need	need	VERB
ejpam-4941	196	51	to	to	PART
ejpam-4941	196	52	exchange	exchange	VERB
ejpam-4941	196	53	some	some	DET
ejpam-4941	196	54	vectors	vector	NOUN
ejpam-4941	196	55	ej	ej	NOUN
ejpam-4941	196	56	and	and	CCONJ
ejpam-4941	196	57	ej+1	ej+1	PROPN
ejpam-4941	196	58	and	and	CCONJ
ejpam-4941	196	59	which	which	PRON
ejpam-4941	196	60	belong	belong	VERB
ejpam-4941	196	61	to	to	ADP
ejpam-4941	196	62	any	any	DET
ejpam-4941	196	63	given	give	VERB
ejpam-4941	196	64	bad	bad	ADJ
ejpam-4941	196	65	basis	basis	NOUN
ejpam-4941	196	66	(	(	PUNCT
ejpam-4941	196	67	e1	e1	NOUN
ejpam-4941	196	68	,	,	PUNCT
ejpam-4941	196	69	...	...	PUNCT
ejpam-4941	196	70	,	,	PUNCT
ejpam-4941	196	71	en	en	X
ejpam-4941	196	72	)	)	PUNCT
ejpam-4941	196	73	of	of	ADP
ejpam-4941	196	74	the	the	DET
ejpam-4941	196	75	same	same	ADJ
ejpam-4941	196	76	lattice	lattice	NOUN
ejpam-4941	196	77	.	.	PUNCT
ejpam-4941	197	1	the	the	DET
ejpam-4941	197	2	bravais	bravais	PROPN
ejpam-4941	197	3	lattice	lattice	PROPN
ejpam-4941	197	4	l	l	PROPN
ejpam-4941	197	5	is	be	AUX
ejpam-4941	197	6	defined	define	VERB
ejpam-4941	197	7	as	as	ADP
ejpam-4941	197	8	a	a	DET
ejpam-4941	197	9	discrete	discrete	ADJ
ejpam-4941	197	10	subgroup	subgroup	NOUN
ejpam-4941	197	11	of	of	ADP
ejpam-4941	197	12	rn	rn	PROPN
ejpam-4941	197	13	,	,	PUNCT
ejpam-4941	197	14	and	and	CCONJ
ejpam-4941	197	15	we	we	PRON
ejpam-4941	197	16	call	call	VERB
ejpam-4941	197	17	it	it	PRON
ejpam-4941	197	18	as	as	ADP
ejpam-4941	197	19	a	a	DET
ejpam-4941	197	20	bravais	bravais	NOUN
ejpam-4941	197	21	lattice	lattice	NOUN
ejpam-4941	197	22	of	of	ADP
ejpam-4941	197	23	order	order	NOUN
ejpam-4941	198	1	k	k	NOUN
ejpam-4941	198	2	if	if	SCONJ
ejpam-4941	198	3	there	there	PRON
ejpam-4941	198	4	exists	exist	VERB
ejpam-4941	198	5	a	a	DET
ejpam-4941	198	6	family	family	NOUN
ejpam-4941	198	7	of	of	ADP
ejpam-4941	198	8	linearly	linearly	ADV
ejpam-4941	198	9	independent	independent	ADJ
ejpam-4941	198	10	vectors	vector	NOUN
ejpam-4941	198	11	e1	e1	NOUN
ejpam-4941	198	12	,	,	PUNCT
ejpam-4941	198	13	...	...	PUNCT
ejpam-4941	198	14	,	,	PUNCT
ejpam-4941	198	15	en	en	X
ejpam-4941	198	16	in	in	ADP
ejpam-4941	198	17	rn	rn	PROPN
ejpam-4941	199	1	and	and	CCONJ
ejpam-4941	199	2	we	we	PRON
ejpam-4941	199	3	have	have	AUX
ejpam-4941	199	4	l	l	NOUN
ejpam-4941	199	5	defined	define	VERB
ejpam-4941	199	6	by	by	ADP
ejpam-4941	199	7	the	the	DET
ejpam-4941	199	8	set	set	NOUN
ejpam-4941	199	9	{	{	PUNCT
ejpam-4941	199	10	k∑	k∑	PROPN
ejpam-4941	199	11	i=1	i=1	PROPN
ejpam-4941	199	12	aiei	aiei	PROPN
ejpam-4941	199	13	|	|	ADV
ejpam-4941	199	14	ai	ai	VERB
ejpam-4941	199	15	∈	∈	PROPN
ejpam-4941	199	16	z	z	PROPN
ejpam-4941	199	17	}	}	PUNCT
ejpam-4941	199	18	.	.	PUNCT
ejpam-4941	200	1	the	the	DET
ejpam-4941	200	2	importance	importance	NOUN
ejpam-4941	200	3	of	of	ADP
ejpam-4941	200	4	this	this	DET
ejpam-4941	200	5	theoretical	theoretical	ADJ
ejpam-4941	200	6	part	part	NOUN
ejpam-4941	200	7	,	,	PUNCT
ejpam-4941	200	8	can	can	AUX
ejpam-4941	200	9	not	not	PART
ejpam-4941	200	10	be	be	AUX
ejpam-4941	200	11	denied	deny	VERB
ejpam-4941	200	12	as	as	SCONJ
ejpam-4941	200	13	the	the	DET
ejpam-4941	200	14	vectors	vector	NOUN
ejpam-4941	200	15	swapping	swap	VERB
ejpam-4941	200	16	play	play	VERB
ejpam-4941	200	17	a	a	DET
ejpam-4941	200	18	major	major	ADJ
ejpam-4941	200	19	role	role	NOUN
ejpam-4941	200	20	in	in	ADP
ejpam-4941	200	21	the	the	DET
ejpam-4941	200	22	algorithmic	algorithmic	ADJ
ejpam-4941	200	23	process	process	NOUN
ejpam-4941	200	24	of	of	ADP
ejpam-4941	200	25	many	many	ADJ
ejpam-4941	200	26	problems	problem	NOUN
ejpam-4941	200	27	,	,	PUNCT
ejpam-4941	200	28	including	include	VERB
ejpam-4941	200	29	the	the	DET
ejpam-4941	200	30	problem	problem	NOUN
ejpam-4941	200	31	of	of	ADP
ejpam-4941	200	32	reduction	reduction	NOUN
ejpam-4941	200	33	of	of	ADP
ejpam-4941	200	34	lattice	lattice	NOUN
ejpam-4941	200	35	bases	basis	NOUN
ejpam-4941	200	36	,	,	PUNCT
ejpam-4941	200	37	however	however	ADV
ejpam-4941	200	38	,	,	PUNCT
ejpam-4941	200	39	this	this	PRON
ejpam-4941	200	40	has	have	AUX
ejpam-4941	200	41	been	be	AUX
ejpam-4941	200	42	underestimated	underestimate	VERB
ejpam-4941	200	43	in	in	ADP
ejpam-4941	200	44	the	the	DET
ejpam-4941	200	45	understanding	understanding	NOUN
ejpam-4941	200	46	of	of	ADP
ejpam-4941	200	47	the	the	DET
ejpam-4941	200	48	process	process	NOUN
ejpam-4941	200	49	of	of	ADP
ejpam-4941	200	50	lattice	lattice	ADJ
ejpam-4941	200	51	basis	basis	NOUN
ejpam-4941	200	52	reduction	reduction	NOUN
ejpam-4941	200	53	as	as	SCONJ
ejpam-4941	200	54	it	it	PRON
ejpam-4941	200	55	has	have	AUX
ejpam-4941	200	56	rarely	rarely	ADV
ejpam-4941	200	57	been	be	AUX
ejpam-4941	200	58	analyzed	analyze	VERB
ejpam-4941	200	59	in	in	ADP
ejpam-4941	200	60	literature	literature	NOUN
ejpam-4941	200	61	.	.	PUNCT
ejpam-4941	201	1	in	in	ADP
ejpam-4941	201	2	fact	fact	NOUN
ejpam-4941	201	3	,	,	PUNCT
ejpam-4941	201	4	as	as	ADV
ejpam-4941	201	5	far	far	ADV
ejpam-4941	201	6	as	as	SCONJ
ejpam-4941	201	7	we	we	PRON
ejpam-4941	201	8	know	know	VERB
ejpam-4941	201	9	,	,	PUNCT
ejpam-4941	201	10	there	there	PRON
ejpam-4941	201	11	were	be	VERB
ejpam-4941	201	12	only	only	ADV
ejpam-4941	201	13	two	two	NUM
ejpam-4941	201	14	researchers	researcher	NOUN
ejpam-4941	201	15	who	who	PRON
ejpam-4941	201	16	detected	detect	VERB
ejpam-4941	201	17	this	this	DET
ejpam-4941	201	18	issue	issue	NOUN
ejpam-4941	201	19	and	and	CCONJ
ejpam-4941	201	20	tried	try	VERB
ejpam-4941	201	21	to	to	PART
ejpam-4941	201	22	solve	solve	VERB
ejpam-4941	201	23	it	it	PRON
ejpam-4941	201	24	.	.	PUNCT
ejpam-4941	202	1	for	for	ADP
ejpam-4941	202	2	the	the	DET
ejpam-4941	202	3	theoretical	theoretical	ADJ
ejpam-4941	202	4	side	side	NOUN
ejpam-4941	202	5	of	of	ADP
ejpam-4941	202	6	this	this	DET
ejpam-4941	202	7	problem	problem	NOUN
ejpam-4941	202	8	,	,	PUNCT
ejpam-4941	202	9	murray	murray	PROPN
ejpam-4941	202	10	bremner	bremner	PROPN
ejpam-4941	202	11	in	in	ADP
ejpam-4941	202	12	[	[	X
ejpam-4941	202	13	10	10	NUM
ejpam-4941	202	14	]	]	PUNCT
ejpam-4941	202	15	,	,	PUNCT
ejpam-4941	202	16	one	one	NUM
ejpam-4941	202	17	of	of	ADP
ejpam-4941	202	18	the	the	DET
ejpam-4941	202	19	mathematical	mathematical	ADJ
ejpam-4941	202	20	descendants	descendant	NOUN
ejpam-4941	202	21	of	of	ADP
ejpam-4941	202	22	isaac	isaac	PROPN
ejpam-4941	202	23	newton	newton	PROPN
ejpam-4941	202	24	,	,	PUNCT
ejpam-4941	202	25	was	be	AUX
ejpam-4941	202	26	the	the	DET
ejpam-4941	202	27	first	first	ADJ
ejpam-4941	202	28	author	author	NOUN
ejpam-4941	202	29	who	who	PRON
ejpam-4941	202	30	wondered	wonder	VERB
ejpam-4941	202	31	about	about	ADP
ejpam-4941	202	32	the	the	DET
ejpam-4941	202	33	impact	impact	NOUN
ejpam-4941	202	34	of	of	ADP
ejpam-4941	202	35	vectors	vector	NOUN
ejpam-4941	202	36	swapping	swap	VERB
ejpam-4941	202	37	on	on	ADP
ejpam-4941	202	38	the	the	DET
ejpam-4941	202	39	precision	precision	NOUN
ejpam-4941	202	40	of	of	ADP
ejpam-4941	202	41	orthogonalization	orthogonalization	NOUN
ejpam-4941	202	42	as	as	ADP
ejpam-4941	202	43	a	a	DET
ejpam-4941	202	44	repeated	repeat	VERB
ejpam-4941	202	45	exchange	exchange	NOUN
ejpam-4941	202	46	could	could	AUX
ejpam-4941	202	47	lead	lead	VERB
ejpam-4941	202	48	to	to	ADP
ejpam-4941	202	49	a	a	DET
ejpam-4941	202	50	loss	loss	NOUN
ejpam-4941	202	51	of	of	ADP
ejpam-4941	202	52	orthogonality	orthogonality	NOUN
ejpam-4941	202	53	and	and	CCONJ
ejpam-4941	202	54	which	which	PRON
ejpam-4941	202	55	is	be	AUX
ejpam-4941	202	56	developed	develop	VERB
ejpam-4941	202	57	in	in	ADP
ejpam-4941	202	58	time	time	NOUN
ejpam-4941	202	59	of	of	ADP
ejpam-4941	202	60	the	the	DET
ejpam-4941	202	61	iteration	iteration	NOUN
ejpam-4941	202	62	that	that	PRON
ejpam-4941	202	63	comes	come	VERB
ejpam-4941	202	64	just	just	ADV
ejpam-4941	202	65	before	before	SCONJ
ejpam-4941	202	66	the	the	DET
ejpam-4941	202	67	vectors	vector	NOUN
ejpam-4941	202	68	being	be	AUX
ejpam-4941	202	69	swapped	swap	VERB
ejpam-4941	202	70	,	,	PUNCT
ejpam-4941	202	71	and	and	CCONJ
ejpam-4941	202	72	he	he	PRON
ejpam-4941	202	73	even	even	ADV
ejpam-4941	202	74	developed	develop	VERB
ejpam-4941	202	75	a	a	DET
ejpam-4941	202	76	result	result	NOUN
ejpam-4941	202	77	which	which	PRON
ejpam-4941	202	78	meets	meet	VERB
ejpam-4941	202	79	the	the	DET
ejpam-4941	202	80	case	case	NOUN
ejpam-4941	202	81	of	of	ADP
ejpam-4941	202	82	gs	g	NOUN
ejpam-4941	202	83	here	here	ADV
ejpam-4941	202	84	.	.	PUNCT
ejpam-4941	203	1	as	as	ADP
ejpam-4941	203	2	for	for	ADP
ejpam-4941	203	3	the	the	DET
ejpam-4941	203	4	numerical	numerical	ADJ
ejpam-4941	203	5	side	side	NOUN
ejpam-4941	203	6	of	of	ADP
ejpam-4941	203	7	this	this	DET
ejpam-4941	203	8	problem	problem	NOUN
ejpam-4941	203	9	,	,	PUNCT
ejpam-4941	203	10	liguo	liguo	PROPN
ejpam-4941	203	11	et	et	PROPN
ejpam-4941	203	12	al	al	PROPN
ejpam-4941	203	13	.	.	PUNCT
ejpam-4941	204	1	in	in	ADP
ejpam-4941	204	2	[	[	X
ejpam-4941	204	3	52	52	NUM
ejpam-4941	204	4	]	]	PUNCT
ejpam-4941	204	5	tried	try	VERB
ejpam-4941	204	6	to	to	PART
ejpam-4941	204	7	use	use	VERB
ejpam-4941	204	8	the	the	DET
ejpam-4941	204	9	greedy	greedy	ADJ
ejpam-4941	204	10	algorithm	algorithm	NOUN
ejpam-4941	204	11	along	along	ADP
ejpam-4941	204	12	with	with	ADP
ejpam-4941	204	13	the	the	DET
ejpam-4941	204	14	partial	partial	ADJ
ejpam-4941	204	15	column	column	NOUN
ejpam-4941	204	16	reduction	reduction	NOUN
ejpam-4941	204	17	in	in	ADP
ejpam-4941	204	18	order	order	NOUN
ejpam-4941	204	19	to	to	PART
ejpam-4941	204	20	minimize	minimize	VERB
ejpam-4941	204	21	the	the	DET
ejpam-4941	204	22	number	number	NOUN
ejpam-4941	204	23	of	of	ADP
ejpam-4941	204	24	times	time	NOUN
ejpam-4941	204	25	of	of	ADP
ejpam-4941	204	26	swapping	swap	VERB
ejpam-4941	204	27	.	.	PUNCT
ejpam-4941	205	1	in	in	ADP
ejpam-4941	205	2	this	this	DET
ejpam-4941	205	3	part	part	NOUN
ejpam-4941	205	4	of	of	ADP
ejpam-4941	205	5	work	work	NOUN
ejpam-4941	205	6	,	,	PUNCT
ejpam-4941	205	7	we	we	PRON
ejpam-4941	205	8	provide	provide	VERB
ejpam-4941	205	9	a	a	DET
ejpam-4941	205	10	clear	clear	ADJ
ejpam-4941	205	11	definition	definition	NOUN
ejpam-4941	205	12	of	of	ADP
ejpam-4941	205	13	another	another	DET
ejpam-4941	205	14	basis	basis	NOUN
ejpam-4941	205	15	of	of	ADP
ejpam-4941	205	16	l	l	NOUN
ejpam-4941	205	17	for	for	ADP
ejpam-4941	205	18	every	every	DET
ejpam-4941	205	19	condition	condition	NOUN
ejpam-4941	205	20	on	on	ADP
ejpam-4941	205	21	its	its	PRON
ejpam-4941	205	22	range	range	NOUN
ejpam-4941	205	23	j	j	PROPN
ejpam-4941	205	24	and	and	CCONJ
ejpam-4941	205	25	that	that	PRON
ejpam-4941	205	26	is	be	AUX
ejpam-4941	205	27	associated	associate	VERB
ejpam-4941	205	28	to	to	ADP
ejpam-4941	205	29	the	the	DET
ejpam-4941	205	30	index	index	NOUN
ejpam-4941	205	31	of	of	ADP
ejpam-4941	205	32	swapping	swap	VERB
ejpam-4941	205	33	,	,	PUNCT
ejpam-4941	205	34	namely	namely	ADV
ejpam-4941	205	35	between	between	ADP
ejpam-4941	205	36	a	a	DET
ejpam-4941	205	37	vector	vector	NOUN
ejpam-4941	205	38	ej+1	ej+1	NOUN
ejpam-4941	205	39	and	and	CCONJ
ejpam-4941	205	40	ej	ej	INTJ
ejpam-4941	205	41	.	.	PUNCT
ejpam-4941	206	1	as	as	ADP
ejpam-4941	206	2	for	for	ADP
ejpam-4941	206	3	the	the	DET
ejpam-4941	206	4	result	result	NOUN
ejpam-4941	206	5	that	that	PRON
ejpam-4941	206	6	really	really	ADV
ejpam-4941	206	7	exhibits	exhibit	VERB
ejpam-4941	206	8	the	the	DET
ejpam-4941	206	9	originality	originality	NOUN
ejpam-4941	206	10	here	here	ADV
ejpam-4941	206	11	,	,	PUNCT
ejpam-4941	206	12	it	it	PRON
ejpam-4941	206	13	concerns	concern	VERB
ejpam-4941	206	14	s.	s.	PROPN
ejpam-4941	206	15	abdelalim	abdelalim	PROPN
ejpam-4941	206	16	,	,	PUNCT
ejpam-4941	206	17	i.	i.	PROPN
ejpam-4941	206	18	elmouki	elmouki	PROPN
ejpam-4941	206	19	/	/	SYM
ejpam-4941	206	20	eur	eur	PROPN
ejpam-4941	206	21	.	.	PUNCT
ejpam-4941	207	1	j.	j.	PROPN
ejpam-4941	207	2	pure	pure	PROPN
ejpam-4941	207	3	appl	appl	PROPN
ejpam-4941	207	4	.	.	PROPN
ejpam-4941	207	5	math	math	PROPN
ejpam-4941	207	6	,	,	PUNCT
ejpam-4941	207	7	16	16	NUM
ejpam-4941	207	8	(	(	PUNCT
ejpam-4941	207	9	4	4	NUM
ejpam-4941	207	10	)	)	PUNCT
ejpam-4941	207	11	(	(	PUNCT
ejpam-4941	207	12	2023	2023	NUM
ejpam-4941	207	13	)	)	PUNCT
ejpam-4941	207	14	,	,	PUNCT
ejpam-4941	207	15	2662	2662	NUM
ejpam-4941	207	16	-	-	SYM
ejpam-4941	207	17	2692	2692	NUM
ejpam-4941	207	18	2675	2675	NUM
ejpam-4941	207	19	first	first	ADV
ejpam-4941	207	20	proving	prove	VERB
ejpam-4941	207	21	that	that	SCONJ
ejpam-4941	207	22	the	the	DET
ejpam-4941	207	23	orthogonality	orthogonality	NOUN
ejpam-4941	207	24	loss	loss	NOUN
ejpam-4941	207	25	would	would	AUX
ejpam-4941	207	26	be	be	AUX
ejpam-4941	207	27	less	less	ADV
ejpam-4941	207	28	considerable	considerable	ADJ
ejpam-4941	207	29	in	in	ADP
ejpam-4941	207	30	case	case	NOUN
ejpam-4941	207	31	of	of	ADP
ejpam-4941	207	32	mgs	mgs	NOUN
ejpam-4941	207	33	,	,	PUNCT
ejpam-4941	207	34	and	and	CCONJ
ejpam-4941	207	35	even	even	ADV
ejpam-4941	207	36	showing	show	VERB
ejpam-4941	207	37	that	that	SCONJ
ejpam-4941	207	38	this	this	DET
ejpam-4941	207	39	procedure	procedure	NOUN
ejpam-4941	207	40	will	will	AUX
ejpam-4941	207	41	preserve	preserve	VERB
ejpam-4941	207	42	the	the	DET
ejpam-4941	207	43	formulations	formulation	NOUN
ejpam-4941	207	44	of	of	ADP
ejpam-4941	207	45	its	its	PRON
ejpam-4941	207	46	sought	seek	VERB
ejpam-4941	207	47	vectors	vector	NOUN
ejpam-4941	207	48	in	in	ADP
ejpam-4941	207	49	three	three	NUM
ejpam-4941	207	50	times	time	NOUN
ejpam-4941	207	51	rather	rather	ADV
ejpam-4941	207	52	than	than	ADP
ejpam-4941	207	53	two	two	NUM
ejpam-4941	207	54	compared	compare	VERB
ejpam-4941	207	55	to	to	ADP
ejpam-4941	207	56	gs	gs	PROPN
ejpam-4941	207	57	method	method	NOUN
ejpam-4941	207	58	.	.	PUNCT
ejpam-4941	208	1	in	in	ADP
ejpam-4941	208	2	front	front	NOUN
ejpam-4941	208	3	of	of	ADP
ejpam-4941	208	4	the	the	DET
ejpam-4941	208	5	results	result	NOUN
ejpam-4941	208	6	that	that	PRON
ejpam-4941	208	7	we	we	PRON
ejpam-4941	208	8	will	will	AUX
ejpam-4941	208	9	show	show	VERB
ejpam-4941	208	10	hereafter	hereafter	ADV
ejpam-4941	208	11	,	,	PUNCT
ejpam-4941	208	12	one	one	PRON
ejpam-4941	208	13	would	would	AUX
ejpam-4941	208	14	recommend	recommend	VERB
ejpam-4941	208	15	the	the	DET
ejpam-4941	208	16	application	application	NOUN
ejpam-4941	208	17	of	of	ADP
ejpam-4941	208	18	mgs	mgs	NOUN
ejpam-4941	208	19	in	in	ADP
ejpam-4941	208	20	a	a	DET
ejpam-4941	208	21	harder	hard	ADJ
ejpam-4941	208	22	problem	problem	NOUN
ejpam-4941	208	23	,	,	PUNCT
ejpam-4941	208	24	namely	namely	ADV
ejpam-4941	208	25	when	when	SCONJ
ejpam-4941	208	26	the	the	DET
ejpam-4941	208	27	dimension	dimension	NOUN
ejpam-4941	208	28	of	of	ADP
ejpam-4941	208	29	the	the	DET
ejpam-4941	208	30	bravais	bravais	PROPN
ejpam-4941	208	31	crystal	crystal	PROPN
ejpam-4941	208	32	,	,	PUNCT
ejpam-4941	208	33	is	be	AUX
ejpam-4941	208	34	very	very	ADV
ejpam-4941	208	35	big	big	ADJ
ejpam-4941	208	36	.	.	PUNCT
ejpam-4941	209	1	now	now	ADV
ejpam-4941	209	2	,	,	PUNCT
ejpam-4941	209	3	let	let	VERB
ejpam-4941	209	4	us	we	PRON
ejpam-4941	209	5	go	go	VERB
ejpam-4941	209	6	deeper	deeply	ADV
ejpam-4941	209	7	into	into	ADP
ejpam-4941	209	8	the	the	DET
ejpam-4941	209	9	technical	technical	ADJ
ejpam-4941	209	10	part	part	NOUN
ejpam-4941	209	11	.	.	PUNCT
ejpam-4941	210	1	in	in	ADP
ejpam-4941	210	2	fact	fact	NOUN
ejpam-4941	210	3	,	,	PUNCT
ejpam-4941	210	4	since	since	SCONJ
ejpam-4941	210	5	we	we	PRON
ejpam-4941	210	6	are	be	AUX
ejpam-4941	210	7	aiming	aim	VERB
ejpam-4941	210	8	to	to	PART
ejpam-4941	210	9	start	start	VERB
ejpam-4941	210	10	from	from	ADP
ejpam-4941	210	11	any	any	DET
ejpam-4941	210	12	bad	bad	ADJ
ejpam-4941	210	13	basis	basis	NOUN
ejpam-4941	210	14	of	of	ADP
ejpam-4941	210	15	the	the	DET
ejpam-4941	210	16	crystal	crystal	NOUN
ejpam-4941	210	17	as	as	SCONJ
ejpam-4941	210	18	shown	show	VERB
ejpam-4941	210	19	in	in	ADP
ejpam-4941	210	20	the	the	DET
ejpam-4941	210	21	more	more	ADV
ejpam-4941	210	22	simple	simple	ADJ
ejpam-4941	210	23	particular	particular	ADJ
ejpam-4941	210	24	case	case	NOUN
ejpam-4941	210	25	of	of	ADP
ejpam-4941	210	26	figure	figure	NOUN
ejpam-4941	210	27	5	5	NUM
ejpam-4941	210	28	,	,	PUNCT
ejpam-4941	210	29	we	we	PRON
ejpam-4941	210	30	generalize	generalize	VERB
ejpam-4941	210	31	our	our	PRON
ejpam-4941	210	32	problem	problem	NOUN
ejpam-4941	210	33	here	here	ADV
ejpam-4941	210	34	for	for	ADP
ejpam-4941	210	35	any	any	DET
ejpam-4941	210	36	dimension	dimension	NOUN
ejpam-4941	210	37	n	n	CCONJ
ejpam-4941	211	1	and	and	CCONJ
ejpam-4941	211	2	we	we	PRON
ejpam-4941	211	3	consider	consider	VERB
ejpam-4941	211	4	first	first	ADV
ejpam-4941	211	5	the	the	DET
ejpam-4941	211	6	given	give	VERB
ejpam-4941	211	7	vectors	vector	NOUN
ejpam-4941	211	8	e1	e1	NOUN
ejpam-4941	211	9	,	,	PUNCT
ejpam-4941	211	10	...	...	PUNCT
ejpam-4941	211	11	,	,	PUNCT
ejpam-4941	211	12	en	en	ADV
ejpam-4941	211	13	from	from	ADP
ejpam-4941	211	14	l	l	NOUN
ejpam-4941	211	15	,	,	PUNCT
ejpam-4941	211	16	then	then	ADV
ejpam-4941	211	17	,	,	PUNCT
ejpam-4941	211	18	we	we	PRON
ejpam-4941	211	19	define	define	VERB
ejpam-4941	211	20	the	the	DET
ejpam-4941	211	21	exchange	exchange	NOUN
ejpam-4941	211	22	process	process	NOUN
ejpam-4941	211	23	of	of	ADP
ejpam-4941	211	24	the	the	DET
ejpam-4941	211	25	basis	basis	NOUN
ejpam-4941	211	26	generated	generate	VERB
ejpam-4941	211	27	by	by	ADP
ejpam-4941	211	28	these	these	DET
ejpam-4941	211	29	vectors	vector	NOUN
ejpam-4941	211	30	with	with	ADP
ejpam-4941	211	31	the	the	DET
ejpam-4941	211	32	help	help	NOUN
ejpam-4941	211	33	of	of	ADP
ejpam-4941	211	34	other	other	ADJ
ejpam-4941	211	35	vectors	vector	NOUN
ejpam-4941	211	36	f1	f1	NOUN
ejpam-4941	211	37	,	,	PUNCT
ejpam-4941	211	38	...	...	PUNCT
ejpam-4941	211	39	,	,	PUNCT
ejpam-4941	211	40	fn	fn	ADV
ejpam-4941	211	41	from	from	ADP
ejpam-4941	211	42	l	l	NOUN
ejpam-4941	211	43	in	in	ADP
ejpam-4941	211	44	order	order	NOUN
ejpam-4941	211	45	to	to	PART
ejpam-4941	211	46	provide	provide	VERB
ejpam-4941	211	47	in	in	ADP
ejpam-4941	211	48	the	the	DET
ejpam-4941	211	49	end	end	NOUN
ejpam-4941	211	50	,	,	PUNCT
ejpam-4941	211	51	all	all	DET
ejpam-4941	211	52	formulations	formulation	NOUN
ejpam-4941	211	53	of	of	ADP
ejpam-4941	211	54	the	the	DET
ejpam-4941	211	55	orthogonal	orthogonal	ADJ
ejpam-4941	211	56	vectors	vector	NOUN
ejpam-4941	211	57	of	of	ADP
ejpam-4941	211	58	the	the	DET
ejpam-4941	211	59	last	last	ADJ
ejpam-4941	211	60	generated	generate	VERB
ejpam-4941	211	61	orthogonal	orthogonal	ADJ
ejpam-4941	211	62	basis	basis	NOUN
ejpam-4941	211	63	in	in	ADP
ejpam-4941	211	64	function	function	NOUN
ejpam-4941	211	65	of	of	ADP
ejpam-4941	211	66	the	the	DET
ejpam-4941	211	67	first	first	ADJ
ejpam-4941	211	68	considered	consider	VERB
ejpam-4941	211	69	one	one	NUM
ejpam-4941	211	70	.	.	PUNCT
ejpam-4941	212	1	in	in	ADP
ejpam-4941	212	2	the	the	DET
ejpam-4941	212	3	following	following	NOUN
ejpam-4941	212	4	,	,	PUNCT
ejpam-4941	212	5	we	we	PRON
ejpam-4941	212	6	state	state	VERB
ejpam-4941	212	7	the	the	DET
ejpam-4941	212	8	theorem	theorem	NOUN
ejpam-4941	212	9	where	where	SCONJ
ejpam-4941	212	10	we	we	PRON
ejpam-4941	212	11	define	define	VERB
ejpam-4941	212	12	the	the	DET
ejpam-4941	212	13	properties	property	NOUN
ejpam-4941	212	14	of	of	ADP
ejpam-4941	212	15	the	the	DET
ejpam-4941	212	16	new	new	ADJ
ejpam-4941	212	17	orthogonal	orthogonal	ADJ
ejpam-4941	212	18	basis	basis	NOUN
ejpam-4941	212	19	after	after	SCONJ
ejpam-4941	212	20	exchanges	exchange	NOUN
ejpam-4941	212	21	steps	step	NOUN
ejpam-4941	212	22	,	,	PUNCT
ejpam-4941	212	23	and	and	CCONJ
ejpam-4941	212	24	as	as	ADP
ejpam-4941	212	25	above	above	ADV
ejpam-4941	212	26	,	,	PUNCT
ejpam-4941	212	27	we	we	PRON
ejpam-4941	212	28	use	use	VERB
ejpam-4941	212	29	one	one	NUM
ejpam-4941	212	30	star	star	NOUN
ejpam-4941	212	31	to	to	ADP
ejpam-4941	212	32	denoting	denote	VERB
ejpam-4941	212	33	vectors	vector	NOUN
ejpam-4941	212	34	of	of	ADP
ejpam-4941	212	35	the	the	DET
ejpam-4941	212	36	gs	gs	PROPN
ejpam-4941	212	37	orthogonal	orthogonal	ADJ
ejpam-4941	212	38	basis	basis	NOUN
ejpam-4941	212	39	and	and	CCONJ
ejpam-4941	212	40	two	two	NUM
ejpam-4941	212	41	stars	star	NOUN
ejpam-4941	212	42	to	to	ADP
ejpam-4941	212	43	denoting	denote	VERB
ejpam-4941	212	44	vectors	vector	NOUN
ejpam-4941	212	45	of	of	ADP
ejpam-4941	212	46	the	the	DET
ejpam-4941	212	47	mgs	mgs	NOUN
ejpam-4941	212	48	orthogonal	orthogonal	ADJ
ejpam-4941	212	49	basis	basis	NOUN
ejpam-4941	212	50	.	.	PUNCT
ejpam-4941	213	1	theorem	theorem	NOUN
ejpam-4941	213	2	2	2	NUM
ejpam-4941	213	3	.	.	PUNCT
ejpam-4941	214	1	let	let	VERB
ejpam-4941	214	2	(	(	PUNCT
ejpam-4941	214	3	e1	e1	NOUN
ejpam-4941	214	4	,	,	PUNCT
ejpam-4941	214	5	...	...	PUNCT
ejpam-4941	214	6	,	,	PUNCT
ejpam-4941	214	7	en	en	X
ejpam-4941	214	8	)	)	PUNCT
ejpam-4941	214	9	be	be	AUX
ejpam-4941	214	10	a	a	DET
ejpam-4941	214	11	basis	basis	NOUN
ejpam-4941	214	12	of	of	ADP
ejpam-4941	214	13	a	a	DET
ejpam-4941	214	14	lattice	lattice	ADJ
ejpam-4941	214	15	l	l	NOUN
ejpam-4941	214	16	of	of	ADP
ejpam-4941	214	17	order	order	NOUN
ejpam-4941	214	18	n	n	CCONJ
ejpam-4941	214	19	,	,	PUNCT
ejpam-4941	214	20	and	and	CCONJ
ejpam-4941	214	21	(	(	PUNCT
ejpam-4941	214	22	f1	f1	NOUN
ejpam-4941	214	23	,	,	PUNCT
ejpam-4941	214	24	...	...	PUNCT
ejpam-4941	214	25	,	,	PUNCT
ejpam-4941	214	26	fn	fn	X
ejpam-4941	214	27	)	)	PUNCT
ejpam-4941	214	28	another	another	DET
ejpam-4941	214	29	basis	basis	NOUN
ejpam-4941	214	30	of	of	ADP
ejpam-4941	214	31	l	l	NOUN
ejpam-4941	214	32	,	,	PUNCT
ejpam-4941	214	33	with	with	ADP
ejpam-4941	214	34	fi	fi	NOUN
ejpam-4941	214	35	=	=	PUNCT
ejpam-4941	214	36			PUNCT
ejpam-4941	214	37	ei	ei	INTJ
ejpam-4941	214	38	if	if	SCONJ
ejpam-4941	214	39	i	i	PRON
ejpam-4941	214	40	̸=	̸=	PROPN
ejpam-4941	214	41	j	j	PROPN
ejpam-4941	214	42	,	,	PUNCT
ejpam-4941	214	43	j	j	PROPN
ejpam-4941	215	1	+	+	CCONJ
ejpam-4941	215	2	1	1	NUM
ejpam-4941	215	3	ej+1	ej+1	NOUN
ejpam-4941	215	4	if	if	SCONJ
ejpam-4941	215	5	i	i	PRON
ejpam-4941	215	6	=	=	SYM
ejpam-4941	215	7	j	j	PROPN
ejpam-4941	215	8	ej	ej	INTJ
ejpam-4941	215	9	if	if	SCONJ
ejpam-4941	215	10	i	i	PRON
ejpam-4941	215	11	=	=	SYM
ejpam-4941	215	12	j	j	PROPN
ejpam-4941	216	1	+	+	CCONJ
ejpam-4941	216	2	1	1	NUM
ejpam-4941	216	3	then	then	ADV
ejpam-4941	216	4	,	,	PUNCT
ejpam-4941	216	5	the	the	DET
ejpam-4941	216	6	following	follow	VERB
ejpam-4941	216	7	properties	property	NOUN
ejpam-4941	216	8	are	be	AUX
ejpam-4941	216	9	verified	verify	VERB
ejpam-4941	216	10	through	through	ADP
ejpam-4941	216	11	gs	gs	NOUN
ejpam-4941	216	12	and	and	CCONJ
ejpam-4941	216	13	mgs	mgs	VERB
ejpam-4941	216	14	orthogonalization	orthogonalization	NOUN
ejpam-4941	216	15	processes	process	NOUN
ejpam-4941	216	16	in	in	ADP
ejpam-4941	216	17	the	the	DET
ejpam-4941	216	18	context	context	NOUN
ejpam-4941	216	19	of	of	ADP
ejpam-4941	216	20	repeated	repeat	VERB
ejpam-4941	216	21	exchange	exchange	NOUN
ejpam-4941	216	22	of	of	ADP
ejpam-4941	216	23	two	two	NUM
ejpam-4941	216	24	consecutive	consecutive	ADJ
ejpam-4941	216	25	input	input	NOUN
ejpam-4941	216	26	vectors	vector	NOUN
ejpam-4941	216	27	•	•	NOUN
ejpam-4941	216	28	if	if	SCONJ
ejpam-4941	216	29	1	1	NUM
ejpam-4941	216	30	≤	≤	PUNCT
ejpam-4941	216	31	i	i	PRON
ejpam-4941	216	32	<	<	X
ejpam-4941	216	33	j	j	PROPN
ejpam-4941	216	34	,	,	PUNCT
ejpam-4941	216	35	then	then	ADV
ejpam-4941	216	36	f	f	PROPN
ejpam-4941	216	37	∗∗(k	∗∗(k	NOUN
ejpam-4941	216	38	)	)	PUNCT
ejpam-4941	217	1	i	i	PRON
ejpam-4941	217	2	=	=	PUNCT
ejpam-4941	217	3	e	e	X
ejpam-4941	217	4	∗∗(k	∗∗(k	NOUN
ejpam-4941	217	5	)	)	PUNCT
ejpam-4941	218	1	i	i	PRON
ejpam-4941	218	2	,	,	PUNCT
ejpam-4941	218	3	k	k	PROPN
ejpam-4941	218	4	=	=	SYM
ejpam-4941	218	5	2	2	NUM
ejpam-4941	218	6	,	,	PUNCT
ejpam-4941	218	7	...	...	PUNCT
ejpam-4941	218	8	,	,	PUNCT
ejpam-4941	218	9	n−	n−	NOUN
ejpam-4941	218	10	1	1	NUM
ejpam-4941	218	11	,	,	PUNCT
ejpam-4941	218	12	and	and	CCONJ
ejpam-4941	218	13	,	,	PUNCT
ejpam-4941	218	14	f∗	f∗	NOUN
ejpam-4941	218	15	i	i	NOUN
ejpam-4941	218	16	=	=	PUNCT
ejpam-4941	218	17	e∗i	e∗i	NUM
ejpam-4941	218	18	.	.	PUNCT
ejpam-4941	219	1	•	•	INTJ
ejpam-4941	219	2	if	if	SCONJ
ejpam-4941	219	3	i	i	PRON
ejpam-4941	219	4	=	=	SYM
ejpam-4941	219	5	j	j	PROPN
ejpam-4941	219	6	,	,	PUNCT
ejpam-4941	219	7	then	then	ADV
ejpam-4941	219	8	,	,	PUNCT
ejpam-4941	219	9	f	f	PROPN
ejpam-4941	219	10	∗∗(k	∗∗(k	NOUN
ejpam-4941	219	11	)	)	PUNCT
ejpam-4941	219	12	j	j	NOUN
ejpam-4941	219	13	=	=	PUNCT
ejpam-4941	219	14	ej+1	ej+1	PROPN
ejpam-4941	219	15	−	−	PROPN
ejpam-4941	219	16	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	219	17	,	,	PUNCT
ejpam-4941	219	18	e	e	X
ejpam-4941	219	19	∗∗	∗∗	X
ejpam-4941	220	1	k−1⟩	k−1⟩	PROPN
ejpam-4941	220	2	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	220	3	,	,	PUNCT
ejpam-4941	220	4	e	e	X
ejpam-4941	220	5	∗∗	∗∗	X
ejpam-4941	221	1	k−1⟩	k−1⟩	PRON
ejpam-4941	221	2	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	221	3	−	−	NOUN
ejpam-4941	221	4	⟨e∗∗(k−1	⟨e∗∗(k−1	NUM
ejpam-4941	221	5	)	)	PUNCT
ejpam-4941	221	6	j+1	j+1	NOUN
ejpam-4941	221	7	,	,	PUNCT
ejpam-4941	221	8	e∗∗k	e∗∗k	PROPN
ejpam-4941	221	9	⟩	⟩	NOUN
ejpam-4941	221	10	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	221	11	,	,	PUNCT
ejpam-4941	221	12	e∗∗k	e∗∗k	PROPN
ejpam-4941	221	13	⟩	⟩	PROPN
ejpam-4941	221	14	e∗∗k	e∗∗k	PROPN
ejpam-4941	221	15	,	,	PUNCT
ejpam-4941	221	16	k	k	PROPN
ejpam-4941	221	17	=	=	SYM
ejpam-4941	221	18	2	2	NUM
ejpam-4941	221	19	,	,	PUNCT
ejpam-4941	221	20	...	...	PUNCT
ejpam-4941	221	21	,	,	PUNCT
ejpam-4941	221	22	j	j	PROPN
ejpam-4941	221	23	−	−	PROPN
ejpam-4941	221	24	1	1	NUM
ejpam-4941	221	25	,	,	PUNCT
ejpam-4941	221	26	and	and	CCONJ
ejpam-4941	221	27	,	,	PUNCT
ejpam-4941	221	28	f∗	f∗	X
ejpam-4941	221	29	j	j	NOUN
ejpam-4941	221	30	=	=	PUNCT
ejpam-4941	221	31	e∗j+1	e∗j+1	NOUN
ejpam-4941	222	1	+	+	CCONJ
ejpam-4941	222	2	⟨ej+1	⟨ej+1	NUM
ejpam-4941	222	3	,	,	PUNCT
ejpam-4941	222	4	e	e	PROPN
ejpam-4941	222	5	∗	∗	PROPN
ejpam-4941	222	6	j	j	PROPN
ejpam-4941	222	7	⟩	⟩	PROPN
ejpam-4941	222	8	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	222	9	,	,	PUNCT
ejpam-4941	222	10	e∗j	e∗j	PROPN
ejpam-4941	222	11	⟩	⟩	NOUN
ejpam-4941	222	12	e∗j	e∗j	NUM
ejpam-4941	222	13	.	.	PUNCT
ejpam-4941	223	1	•	•	INTJ
ejpam-4941	223	2	if	if	SCONJ
ejpam-4941	223	3	i	i	PRON
ejpam-4941	223	4	=	=	SYM
ejpam-4941	223	5	j	j	PROPN
ejpam-4941	224	1	+	+	NOUN
ejpam-4941	224	2	1	1	NUM
ejpam-4941	224	3	,	,	PUNCT
ejpam-4941	224	4	then	then	ADV
ejpam-4941	224	5	f	f	PROPN
ejpam-4941	224	6	∗∗(k	∗∗(k	NOUN
ejpam-4941	224	7	)	)	PUNCT
ejpam-4941	225	1	j+1	j+1	NOUN
ejpam-4941	225	2	=	=	PUNCT
ejpam-4941	225	3	e	e	X
ejpam-4941	225	4	∗∗(k	∗∗(k	NOUN
ejpam-4941	225	5	)	)	PUNCT
ejpam-4941	225	6	j	j	NOUN
ejpam-4941	225	7	,	,	PUNCT
ejpam-4941	225	8	k	k	PROPN
ejpam-4941	225	9	=	=	SYM
ejpam-4941	225	10	2	2	NUM
ejpam-4941	225	11	,	,	PUNCT
ejpam-4941	225	12	...	...	PUNCT
ejpam-4941	225	13	,	,	PUNCT
ejpam-4941	225	14	n−	n−	NOUN
ejpam-4941	225	15	1	1	NUM
ejpam-4941	225	16	.	.	PUNCT
ejpam-4941	226	1	and	and	CCONJ
ejpam-4941	226	2	,	,	PUNCT
ejpam-4941	226	3	f∗	f∗	NOUN
ejpam-4941	226	4	j+1	j+1	NOUN
ejpam-4941	226	5	=	=	PUNCT
ejpam-4941	226	6	|e∗j+1|2	|e∗j+1|2	VERB
ejpam-4941	226	7	|f∗∗	|f∗∗	NOUN
ejpam-4941	226	8	j	j	PROPN
ejpam-4941	226	9	|2	|2	NUM
ejpam-4941	226	10	e∗j	e∗j	NUM
ejpam-4941	226	11	−	−	NUM
ejpam-4941	226	12	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	226	13	,	,	PUNCT
ejpam-4941	226	14	e	e	PROPN
ejpam-4941	226	15	∗	∗	PROPN
ejpam-4941	226	16	j	j	PROPN
ejpam-4941	226	17	⟩	⟩	PROPN
ejpam-4941	226	18	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	226	19	,	,	PUNCT
ejpam-4941	226	20	e∗j	e∗j	PROPN
ejpam-4941	226	21	⟩	⟩	NOUN
ejpam-4941	226	22	|e∗j	|e∗j	ADJ
ejpam-4941	226	23	|2	|2	NUM
ejpam-4941	226	24	|f∗∗	|f∗∗	NOUN
ejpam-4941	226	25	j	j	PROPN
ejpam-4941	226	26	|2	|2	NUM
ejpam-4941	226	27	e∗j+1	e∗j+1	NOUN
ejpam-4941	226	28	.	.	PUNCT
ejpam-4941	227	1	•	•	INTJ
ejpam-4941	227	2	if	if	SCONJ
ejpam-4941	227	3	i	i	PRON
ejpam-4941	227	4	>	>	X
ejpam-4941	227	5	j	j	PROPN
ejpam-4941	228	1	+	+	CCONJ
ejpam-4941	228	2	1	1	NUM
ejpam-4941	228	3	,	,	PUNCT
ejpam-4941	228	4	then	then	ADV
ejpam-4941	228	5	f	f	PROPN
ejpam-4941	228	6	∗∗(k	∗∗(k	NOUN
ejpam-4941	228	7	)	)	PUNCT
ejpam-4941	229	1	i	i	PRON
ejpam-4941	229	2	=	=	PUNCT
ejpam-4941	229	3	e	e	X
ejpam-4941	229	4	∗∗(k	∗∗(k	NOUN
ejpam-4941	229	5	)	)	PUNCT
ejpam-4941	230	1	i	i	PRON
ejpam-4941	230	2	,	,	PUNCT
ejpam-4941	230	3	k	k	PROPN
ejpam-4941	230	4	=	=	SYM
ejpam-4941	230	5	2	2	NUM
ejpam-4941	230	6	,	,	PUNCT
ejpam-4941	230	7	...	...	PUNCT
ejpam-4941	230	8	,	,	PUNCT
ejpam-4941	230	9	i−	i−	PROPN
ejpam-4941	230	10	1	1	NUM
ejpam-4941	230	11	and	and	CCONJ
ejpam-4941	230	12	,	,	PUNCT
ejpam-4941	230	13	f∗	f∗	NOUN
ejpam-4941	230	14	i	i	NOUN
ejpam-4941	230	15	=	=	PUNCT
ejpam-4941	230	16	e∗i	e∗i	NUM
ejpam-4941	230	17	.	.	PUNCT
ejpam-4941	231	1	at	at	ADP
ejpam-4941	231	2	first	first	ADJ
ejpam-4941	231	3	sight	sight	NOUN
ejpam-4941	231	4	at	at	ADP
ejpam-4941	231	5	the	the	DET
ejpam-4941	231	6	formulations	formulation	NOUN
ejpam-4941	231	7	obtained	obtain	VERB
ejpam-4941	231	8	,	,	PUNCT
ejpam-4941	231	9	we	we	PRON
ejpam-4941	231	10	can	can	AUX
ejpam-4941	231	11	see	see	VERB
ejpam-4941	231	12	that	that	SCONJ
ejpam-4941	231	13	the	the	DET
ejpam-4941	231	14	theorem	theorem	NOUN
ejpam-4941	231	15	proves	prove	VERB
ejpam-4941	231	16	that	that	SCONJ
ejpam-4941	231	17	mgs	mgs	NOUN
ejpam-4941	231	18	can	can	AUX
ejpam-4941	231	19	not	not	PART
ejpam-4941	231	20	only	only	ADV
ejpam-4941	231	21	considered	consider	VERB
ejpam-4941	231	22	better	well	ADJ
ejpam-4941	231	23	than	than	ADP
ejpam-4941	231	24	gs	gs	INTJ
ejpam-4941	231	25	as	as	SCONJ
ejpam-4941	231	26	we	we	PRON
ejpam-4941	231	27	are	be	AUX
ejpam-4941	231	28	used	use	VERB
ejpam-4941	231	29	to	to	PART
ejpam-4941	231	30	understand	understand	VERB
ejpam-4941	231	31	by	by	ADP
ejpam-4941	231	32	checking	check	VERB
ejpam-4941	231	33	s.	s.	PROPN
ejpam-4941	231	34	abdelalim	abdelalim	PROPN
ejpam-4941	231	35	,	,	PUNCT
ejpam-4941	231	36	i.	i.	PROPN
ejpam-4941	231	37	elmouki	elmouki	PROPN
ejpam-4941	231	38	/	/	SYM
ejpam-4941	231	39	eur	eur	PROPN
ejpam-4941	231	40	.	.	PUNCT
ejpam-4941	232	1	j.	j.	PROPN
ejpam-4941	232	2	pure	pure	PROPN
ejpam-4941	232	3	appl	appl	PROPN
ejpam-4941	232	4	.	.	PROPN
ejpam-4941	232	5	math	math	PROPN
ejpam-4941	232	6	,	,	PUNCT
ejpam-4941	232	7	16	16	NUM
ejpam-4941	232	8	(	(	PUNCT
ejpam-4941	232	9	4	4	NUM
ejpam-4941	232	10	)	)	PUNCT
ejpam-4941	232	11	(	(	PUNCT
ejpam-4941	232	12	2023	2023	NUM
ejpam-4941	232	13	)	)	PUNCT
ejpam-4941	232	14	,	,	PUNCT
ejpam-4941	232	15	2662	2662	NUM
ejpam-4941	232	16	-	-	SYM
ejpam-4941	232	17	2692	2692	NUM
ejpam-4941	232	18	2676	2676	NUM
ejpam-4941	232	19	numerics	numeric	NOUN
ejpam-4941	232	20	,	,	PUNCT
ejpam-4941	232	21	but	but	CCONJ
ejpam-4941	232	22	also	also	ADV
ejpam-4941	232	23	because	because	SCONJ
ejpam-4941	232	24	the	the	DET
ejpam-4941	232	25	formulation	formulation	NOUN
ejpam-4941	232	26	of	of	ADP
ejpam-4941	232	27	f	f	PROPN
ejpam-4941	232	28	∗∗(k	∗∗(k	NOUN
ejpam-4941	232	29	)	)	PUNCT
ejpam-4941	233	1	i	i	PRON
ejpam-4941	233	2	,	,	PUNCT
ejpam-4941	233	3	k	k	PROPN
ejpam-4941	233	4	=	=	SYM
ejpam-4941	233	5	2	2	NUM
ejpam-4941	233	6	,	,	PUNCT
ejpam-4941	233	7	...	...	PUNCT
ejpam-4941	233	8	,	,	PUNCT
ejpam-4941	233	9	n−	n−	NOUN
ejpam-4941	233	10	1	1	NUM
ejpam-4941	233	11	.	.	PUNCT
ejpam-4941	233	12	has	have	AUX
ejpam-4941	233	13	been	be	AUX
ejpam-4941	233	14	preserved	preserve	VERB
ejpam-4941	233	15	in	in	ADP
ejpam-4941	233	16	three	three	NUM
ejpam-4941	233	17	times	time	NOUN
ejpam-4941	233	18	rather	rather	ADV
ejpam-4941	233	19	than	than	ADP
ejpam-4941	233	20	two	two	NUM
ejpam-4941	233	21	in	in	ADP
ejpam-4941	233	22	case	case	NOUN
ejpam-4941	233	23	of	of	ADP
ejpam-4941	233	24	gs	gs	NOUN
ejpam-4941	233	25	,	,	PUNCT
ejpam-4941	233	26	and	and	CCONJ
ejpam-4941	233	27	this	this	PRON
ejpam-4941	233	28	may	may	AUX
ejpam-4941	233	29	recommend	recommend	VERB
ejpam-4941	233	30	the	the	DET
ejpam-4941	233	31	introduction	introduction	NOUN
ejpam-4941	233	32	of	of	ADP
ejpam-4941	233	33	mgs	mgs	NOUN
ejpam-4941	233	34	in	in	ADP
ejpam-4941	233	35	a	a	DET
ejpam-4941	233	36	harder	hard	ADJ
ejpam-4941	233	37	problem	problem	NOUN
ejpam-4941	233	38	,	,	PUNCT
ejpam-4941	233	39	namely	namely	ADV
ejpam-4941	233	40	when	when	SCONJ
ejpam-4941	233	41	the	the	DET
ejpam-4941	233	42	dimension	dimension	NOUN
ejpam-4941	233	43	of	of	ADP
ejpam-4941	233	44	the	the	DET
ejpam-4941	233	45	crystal	crystal	NOUN
ejpam-4941	233	46	is	be	AUX
ejpam-4941	233	47	very	very	ADV
ejpam-4941	233	48	big	big	ADJ
ejpam-4941	233	49	.	.	PUNCT
ejpam-4941	234	1	proof	proof	NOUN
ejpam-4941	234	2	.	.	PUNCT
ejpam-4941	235	1	•	•	NUM
ejpam-4941	235	2	by	by	ADP
ejpam-4941	235	3	induction	induction	NOUN
ejpam-4941	235	4	,	,	PUNCT
ejpam-4941	235	5	if	if	SCONJ
ejpam-4941	235	6	i	i	PRON
ejpam-4941	235	7	<	<	X
ejpam-4941	235	8	j	j	PROPN
ejpam-4941	235	9	,	,	PUNCT
ejpam-4941	235	10	already	already	ADV
ejpam-4941	235	11	for	for	ADP
ejpam-4941	235	12	the	the	DET
ejpam-4941	235	13	first	first	ADJ
ejpam-4941	235	14	initial	initial	ADJ
ejpam-4941	235	15	case	case	NOUN
ejpam-4941	235	16	i	i	PRON
ejpam-4941	235	17	=	=	NOUN
ejpam-4941	235	18	1	1	NUM
ejpam-4941	235	19	,	,	PUNCT
ejpam-4941	235	20	we	we	PRON
ejpam-4941	235	21	obviously	obviously	ADV
ejpam-4941	235	22	have	have	VERB
ejpam-4941	235	23	f1	f1	NOUN
ejpam-4941	235	24	=	=	SYM
ejpam-4941	235	25	e1	e1	PROPN
ejpam-4941	235	26	=	=	SYM
ejpam-4941	235	27	e∗∗1	e∗∗1	NOUN
ejpam-4941	235	28	=	=	SYM
ejpam-4941	235	29	f∗∗	f∗∗	NOUN
ejpam-4941	235	30	1	1	NUM
ejpam-4941	235	31	.	.	PUNCT
ejpam-4941	236	1	the	the	DET
ejpam-4941	236	2	same	same	ADJ
ejpam-4941	236	3	if	if	SCONJ
ejpam-4941	236	4	we	we	PRON
ejpam-4941	236	5	consider	consider	VERB
ejpam-4941	236	6	a	a	DET
ejpam-4941	236	7	gs	gs	NOUN
ejpam-4941	236	8	process	process	NOUN
ejpam-4941	236	9	,	,	PUNCT
ejpam-4941	236	10	we	we	PRON
ejpam-4941	236	11	have	have	VERB
ejpam-4941	236	12	f1	f1	NOUN
ejpam-4941	236	13	=	=	SYM
ejpam-4941	236	14	e1	e1	NOUN
ejpam-4941	236	15	=	=	SYM
ejpam-4941	236	16	e∗1	e∗1	ADJ
ejpam-4941	236	17	=	=	SYM
ejpam-4941	236	18	f∗	f∗	NOUN
ejpam-4941	236	19	1	1	NUM
ejpam-4941	236	20	.	.	PUNCT
ejpam-4941	237	1	if	if	SCONJ
ejpam-4941	237	2	now	now	ADV
ejpam-4941	237	3	,	,	PUNCT
ejpam-4941	237	4	we	we	PRON
ejpam-4941	237	5	suppose	suppose	VERB
ejpam-4941	237	6	f∗∗	f∗∗	ADJ
ejpam-4941	237	7	k	k	X
ejpam-4941	237	8	=	=	PUNCT
ejpam-4941	237	9	e∗∗r	e∗∗r	ADP
ejpam-4941	237	10	with	with	ADP
ejpam-4941	237	11	k	k	X
ejpam-4941	237	12	<	<	X
ejpam-4941	237	13	r	r	X
ejpam-4941	237	14	<	<	X
ejpam-4941	237	15	j	j	NOUN
ejpam-4941	237	16	,	,	PUNCT
ejpam-4941	237	17	then	then	ADV
ejpam-4941	237	18	,	,	PUNCT
ejpam-4941	237	19	we	we	PRON
ejpam-4941	237	20	obviously	obviously	ADV
ejpam-4941	237	21	have	have	VERB
ejpam-4941	237	22	f∗∗(k−1	f∗∗(k−1	NUM
ejpam-4941	237	23	)	)	PUNCT
ejpam-4941	238	1	r	r	NOUN
ejpam-4941	238	2	=	=	NOUN
ejpam-4941	238	3	fr	fr	NOUN
ejpam-4941	238	4	−	−	PROPN
ejpam-4941	239	1	⟨fr	⟨fr	PROPN
ejpam-4941	239	2	,	,	PUNCT
ejpam-4941	239	3	f∗∗	f∗∗	PROPN
ejpam-4941	239	4	k−1⟩	k−1⟩	PROPN
ejpam-4941	239	5	⟨f∗∗	⟨f∗∗	ADP
ejpam-4941	239	6	k−1	k−1	PROPN
ejpam-4941	239	7	,	,	PUNCT
ejpam-4941	240	1	f	f	PROPN
ejpam-4941	240	2	∗∗	∗∗	X
ejpam-4941	241	1	k−1⟩	k−1⟩	PRON
ejpam-4941	241	2	f∗∗	f∗∗	PROPN
ejpam-4941	241	3	k−1	k−1	PROPN
ejpam-4941	241	4	,	,	PUNCT
ejpam-4941	241	5	k	k	PROPN
ejpam-4941	241	6	=	=	SYM
ejpam-4941	241	7	2	2	NUM
ejpam-4941	241	8	,	,	PUNCT
ejpam-4941	241	9	...	...	PUNCT
ejpam-4941	241	10	,	,	PUNCT
ejpam-4941	241	11	r	r	NOUN
ejpam-4941	241	12	−	−	PROPN
ejpam-4941	241	13	1	1	NUM
ejpam-4941	241	14	=	=	NUM
ejpam-4941	241	15	er	er	INTJ
ejpam-4941	241	16	−	−	PROPN
ejpam-4941	241	17	⟨er	⟨er	NOUN
ejpam-4941	241	18	,	,	PUNCT
ejpam-4941	241	19	e∗∗k−1⟩	e∗∗k−1⟩	PROPN
ejpam-4941	241	20	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	241	21	,	,	PUNCT
ejpam-4941	241	22	e	e	X
ejpam-4941	241	23	∗∗	∗∗	X
ejpam-4941	241	24	k−1⟩	k−1⟩	ADV
ejpam-4941	241	25	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	241	26	,	,	PUNCT
ejpam-4941	241	27	k	k	NOUN
ejpam-4941	241	28	=	=	SYM
ejpam-4941	241	29	2	2	NUM
ejpam-4941	241	30	,	,	PUNCT
ejpam-4941	241	31	...	...	PUNCT
ejpam-4941	241	32	,	,	PUNCT
ejpam-4941	241	33	r	r	NOUN
ejpam-4941	241	34	−	−	PROPN
ejpam-4941	241	35	1	1	NUM
ejpam-4941	241	36	=	=	SYM
ejpam-4941	241	37	e∗∗(k−1	e∗∗(k−1	NOUN
ejpam-4941	241	38	)	)	PUNCT
ejpam-4941	241	39	r	r	NOUN
ejpam-4941	241	40	,	,	PUNCT
ejpam-4941	241	41	k	k	NOUN
ejpam-4941	241	42	=	=	SYM
ejpam-4941	241	43	2	2	NUM
ejpam-4941	241	44	,	,	PUNCT
ejpam-4941	241	45	...	...	PUNCT
ejpam-4941	241	46	,	,	PUNCT
ejpam-4941	241	47	r	r	NOUN
ejpam-4941	241	48	−	−	PROPN
ejpam-4941	241	49	1	1	NUM
ejpam-4941	241	50	which	which	PRON
ejpam-4941	241	51	implies	imply	VERB
ejpam-4941	241	52	that	that	SCONJ
ejpam-4941	241	53	f∗∗(k	f∗∗(k	NOUN
ejpam-4941	241	54	)	)	PUNCT
ejpam-4941	241	55	r	r	NOUN
ejpam-4941	241	56	=	=	PUNCT
ejpam-4941	241	57	f∗∗(k−1	f∗∗(k−1	X
ejpam-4941	241	58	)	)	PUNCT
ejpam-4941	241	59	r	r	NOUN
ejpam-4941	241	60	−	−	PROPN
ejpam-4941	241	61	⟨f	⟨f	PUNCT
ejpam-4941	241	62	(	(	PUNCT
ejpam-4941	241	63	k−1	k−1	PROPN
ejpam-4941	241	64	)	)	PUNCT
ejpam-4941	241	65	r	r	NOUN
ejpam-4941	241	66	,	,	PUNCT
ejpam-4941	241	67	f∗∗	f∗∗	PROPN
ejpam-4941	241	68	k	k	PROPN
ejpam-4941	241	69	⟩	⟩	PROPN
ejpam-4941	241	70	⟨f∗∗	⟨f∗∗	X
ejpam-4941	242	1	k	k	X
ejpam-4941	242	2	,	,	PUNCT
ejpam-4941	242	3	f∗∗	f∗∗	PROPN
ejpam-4941	242	4	k	k	PROPN
ejpam-4941	242	5	⟩	⟩	PROPN
ejpam-4941	242	6	f∗∗	f∗∗	PROPN
ejpam-4941	242	7	k	k	PROPN
ejpam-4941	242	8	,	,	PUNCT
ejpam-4941	242	9	k	k	PROPN
ejpam-4941	242	10	=	=	SYM
ejpam-4941	242	11	2	2	NUM
ejpam-4941	242	12	,	,	PUNCT
ejpam-4941	242	13	...	...	PUNCT
ejpam-4941	242	14	,	,	PUNCT
ejpam-4941	242	15	r	r	NOUN
ejpam-4941	242	16	−	−	PROPN
ejpam-4941	242	17	1	1	NUM
ejpam-4941	242	18	=	=	SYM
ejpam-4941	242	19	e∗∗(k−1	e∗∗(k−1	NOUN
ejpam-4941	242	20	)	)	PUNCT
ejpam-4941	242	21	r	r	NOUN
ejpam-4941	242	22	−	−	NOUN
ejpam-4941	242	23	⟨e(k−1	⟨e(k−1	NUM
ejpam-4941	242	24	)	)	PUNCT
ejpam-4941	242	25	r	r	NOUN
ejpam-4941	242	26	,	,	PUNCT
ejpam-4941	242	27	e∗∗k	e∗∗k	PROPN
ejpam-4941	242	28	⟩	⟩	NOUN
ejpam-4941	242	29	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	242	30	,	,	PUNCT
ejpam-4941	242	31	e∗∗k	e∗∗k	PROPN
ejpam-4941	242	32	⟩	⟩	PROPN
ejpam-4941	242	33	e∗∗k	e∗∗k	PROPN
ejpam-4941	242	34	,	,	PUNCT
ejpam-4941	242	35	k	k	PROPN
ejpam-4941	242	36	=	=	SYM
ejpam-4941	242	37	2	2	NUM
ejpam-4941	242	38	,	,	PUNCT
ejpam-4941	242	39	...	...	PUNCT
ejpam-4941	242	40	,	,	PUNCT
ejpam-4941	242	41	r	r	NOUN
ejpam-4941	242	42	−	−	PROPN
ejpam-4941	242	43	1	1	NUM
ejpam-4941	242	44	=	=	SYM
ejpam-4941	242	45	e∗∗(k)r	e∗∗(k)r	PROPN
ejpam-4941	242	46	,	,	PUNCT
ejpam-4941	242	47	k	k	PROPN
ejpam-4941	242	48	=	=	SYM
ejpam-4941	242	49	2	2	NUM
ejpam-4941	242	50	,	,	PUNCT
ejpam-4941	242	51	...	...	PUNCT
ejpam-4941	242	52	,	,	PUNCT
ejpam-4941	242	53	r	r	NOUN
ejpam-4941	242	54	−	−	PROPN
ejpam-4941	242	55	1	1	NUM
ejpam-4941	242	56	in	in	ADP
ejpam-4941	242	57	fact	fact	NOUN
ejpam-4941	242	58	,	,	PUNCT
ejpam-4941	242	59	if	if	SCONJ
ejpam-4941	242	60	we	we	PRON
ejpam-4941	242	61	consider	consider	VERB
ejpam-4941	242	62	a	a	DET
ejpam-4941	242	63	gs	gs	NOUN
ejpam-4941	242	64	process	process	NOUN
ejpam-4941	242	65	and	and	CCONJ
ejpam-4941	242	66	suppose	suppose	VERB
ejpam-4941	242	67	f∗	f∗	NOUN
ejpam-4941	242	68	k	k	X
ejpam-4941	242	69	=	=	PUNCT
ejpam-4941	242	70	e∗r	e∗r	NOUN
ejpam-4941	242	71	with	with	ADP
ejpam-4941	242	72	k	k	X
ejpam-4941	242	73	<	<	X
ejpam-4941	242	74	r	r	X
ejpam-4941	242	75	<	<	X
ejpam-4941	242	76	j	j	PROPN
ejpam-4941	242	77	,	,	PUNCT
ejpam-4941	242	78	,	,	PUNCT
ejpam-4941	242	79	we	we	PRON
ejpam-4941	242	80	also	also	ADV
ejpam-4941	242	81	have	have	VERB
ejpam-4941	242	82	f∗	f∗	NOUN
ejpam-4941	242	83	r	r	NOUN
ejpam-4941	242	84	=	=	NOUN
ejpam-4941	242	85	fr	fr	ADJ
ejpam-4941	242	86	−	−	PROPN
ejpam-4941	243	1	r−1∑	r−1∑	PROPN
ejpam-4941	243	2	k=1	k=1	PROPN
ejpam-4941	243	3	⟨fr	⟨fr	PROPN
ejpam-4941	243	4	,	,	PUNCT
ejpam-4941	243	5	f∗	f∗	PROPN
ejpam-4941	243	6	k	k	PROPN
ejpam-4941	243	7	⟩	⟩	PROPN
ejpam-4941	244	1	⟨f∗	⟨f∗	PROPN
ejpam-4941	245	1	k	k	PROPN
ejpam-4941	245	2	,	,	PUNCT
ejpam-4941	245	3	f	f	PROPN
ejpam-4941	245	4	∗	∗	X
ejpam-4941	245	5	k	k	PROPN
ejpam-4941	245	6	⟩	⟩	PROPN
ejpam-4941	245	7	e∗k	e∗k	PROPN
ejpam-4941	246	1	=	=	X
ejpam-4941	246	2	er	er	INTJ
ejpam-4941	246	3	−	−	PROPN
ejpam-4941	246	4	r−1∑	r−1∑	PROPN
ejpam-4941	246	5	k=1	k=1	PROPN
ejpam-4941	246	6	⟨fr	⟨fr	PROPN
ejpam-4941	246	7	,	,	PUNCT
ejpam-4941	246	8	f∗	f∗	PROPN
ejpam-4941	246	9	k	k	PROPN
ejpam-4941	246	10	⟩	⟩	PROPN
ejpam-4941	246	11	⟨f∗	⟨f∗	PROPN
ejpam-4941	247	1	k	k	PROPN
ejpam-4941	247	2	,	,	PUNCT
ejpam-4941	247	3	f	f	PROPN
ejpam-4941	247	4	∗	∗	X
ejpam-4941	247	5	k	k	PROPN
ejpam-4941	247	6	⟩	⟩	PROPN
ejpam-4941	247	7	e∗k	e∗k	PROPN
ejpam-4941	248	1	=	=	X
ejpam-4941	248	2	er	er	INTJ
ejpam-4941	248	3	−	−	PROPN
ejpam-4941	248	4	r−1∑	r−1∑	PROPN
ejpam-4941	248	5	k=1	k=1	PROPN
ejpam-4941	248	6	⟨er	⟨er	PROPN
ejpam-4941	248	7	,	,	PUNCT
ejpam-4941	248	8	e∗k⟩	e∗k⟩	NOUN
ejpam-4941	248	9	⟨e∗k	⟨e∗k	PROPN
ejpam-4941	248	10	,	,	PUNCT
ejpam-4941	248	11	e∗k⟩	e∗k⟩	AUX
ejpam-4941	248	12	e∗k	e∗k	ADV
ejpam-4941	248	13	=	=	SYM
ejpam-4941	248	14	e∗r	e∗r	NOUN
ejpam-4941	248	15	•	•	PUNCT
ejpam-4941	248	16	now	now	ADV
ejpam-4941	248	17	,	,	PUNCT
ejpam-4941	248	18	if	if	SCONJ
ejpam-4941	248	19	i	i	PRON
ejpam-4941	248	20	=	=	SYM
ejpam-4941	248	21	j	j	PROPN
ejpam-4941	248	22	,	,	PUNCT
ejpam-4941	248	23	we	we	PRON
ejpam-4941	248	24	have	have	VERB
ejpam-4941	248	25	f	f	NOUN
ejpam-4941	248	26	∗∗(k−1	∗∗(k−1	NUM
ejpam-4941	248	27	)	)	PUNCT
ejpam-4941	248	28	j	j	NOUN
ejpam-4941	249	1	=	=	SYM
ejpam-4941	249	2	fj	fj	PROPN
ejpam-4941	249	3	−	−	PROPN
ejpam-4941	249	4	⟨fj	⟨fj	NUM
ejpam-4941	249	5	,	,	PUNCT
ejpam-4941	249	6	f∗∗	f∗∗	PROPN
ejpam-4941	249	7	k−1⟩	k−1⟩	PROPN
ejpam-4941	249	8	⟨f∗∗	⟨f∗∗	ADP
ejpam-4941	249	9	k−1	k−1	PROPN
ejpam-4941	249	10	,	,	PUNCT
ejpam-4941	249	11	f	f	PROPN
ejpam-4941	250	1	∗∗	∗∗	X
ejpam-4941	251	1	k−1⟩	k−1⟩	PRON
ejpam-4941	251	2	f∗∗	f∗∗	PROPN
ejpam-4941	251	3	k−1	k−1	PROPN
ejpam-4941	251	4	,	,	PUNCT
ejpam-4941	251	5	k	k	PROPN
ejpam-4941	251	6	=	=	SYM
ejpam-4941	251	7	2	2	NUM
ejpam-4941	251	8	,	,	PUNCT
ejpam-4941	251	9	...	...	PUNCT
ejpam-4941	251	10	,	,	PUNCT
ejpam-4941	251	11	j	j	PROPN
ejpam-4941	251	12	−	−	PROPN
ejpam-4941	251	13	1	1	NUM
ejpam-4941	251	14	s.	s.	PROPN
ejpam-4941	251	15	abdelalim	abdelalim	PROPN
ejpam-4941	251	16	,	,	PUNCT
ejpam-4941	251	17	i.	i.	PROPN
ejpam-4941	251	18	elmouki	elmouki	PROPN
ejpam-4941	251	19	/	/	SYM
ejpam-4941	251	20	eur	eur	PROPN
ejpam-4941	251	21	.	.	PUNCT
ejpam-4941	252	1	j.	j.	PROPN
ejpam-4941	252	2	pure	pure	PROPN
ejpam-4941	252	3	appl	appl	PROPN
ejpam-4941	252	4	.	.	PROPN
ejpam-4941	252	5	math	math	PROPN
ejpam-4941	252	6	,	,	PUNCT
ejpam-4941	252	7	16	16	NUM
ejpam-4941	252	8	(	(	PUNCT
ejpam-4941	252	9	4	4	NUM
ejpam-4941	252	10	)	)	PUNCT
ejpam-4941	252	11	(	(	PUNCT
ejpam-4941	252	12	2023	2023	NUM
ejpam-4941	252	13	)	)	PUNCT
ejpam-4941	252	14	,	,	PUNCT
ejpam-4941	252	15	2662	2662	NUM
ejpam-4941	252	16	-	-	SYM
ejpam-4941	252	17	2692	2692	NUM
ejpam-4941	252	18	2677	2677	NUM
ejpam-4941	253	1	=	=	NOUN
ejpam-4941	253	2	ej+1	ej+1	ADP
ejpam-4941	253	3	−	−	PROPN
ejpam-4941	253	4	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	253	5	,	,	PUNCT
ejpam-4941	253	6	e	e	X
ejpam-4941	253	7	∗∗	∗∗	X
ejpam-4941	254	1	k−1⟩	k−1⟩	PROPN
ejpam-4941	254	2	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	254	3	,	,	PUNCT
ejpam-4941	254	4	e	e	X
ejpam-4941	254	5	∗∗	∗∗	X
ejpam-4941	254	6	k−1⟩	k−1⟩	ADV
ejpam-4941	254	7	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	254	8	,	,	PUNCT
ejpam-4941	254	9	k	k	NOUN
ejpam-4941	254	10	=	=	SYM
ejpam-4941	254	11	2	2	NUM
ejpam-4941	254	12	,	,	PUNCT
ejpam-4941	254	13	...	...	PUNCT
ejpam-4941	254	14	,	,	PUNCT
ejpam-4941	254	15	j	j	PROPN
ejpam-4941	254	16	−	−	PROPN
ejpam-4941	254	17	1	1	NUM
ejpam-4941	254	18	which	which	PRON
ejpam-4941	254	19	implies	imply	VERB
ejpam-4941	254	20	that	that	SCONJ
ejpam-4941	254	21	f	f	PROPN
ejpam-4941	254	22	∗∗(k	∗∗(k	NOUN
ejpam-4941	254	23	)	)	PUNCT
ejpam-4941	254	24	j	j	NOUN
ejpam-4941	254	25	=	=	SYM
ejpam-4941	254	26	f	f	PROPN
ejpam-4941	254	27	∗∗(k−1	∗∗(k−1	NUM
ejpam-4941	254	28	)	)	PUNCT
ejpam-4941	254	29	j	j	NOUN
ejpam-4941	254	30	−	−	PROPN
ejpam-4941	254	31	⟨f	⟨f	PUNCT
ejpam-4941	254	32	(	(	PUNCT
ejpam-4941	254	33	k−1	k−1	PROPN
ejpam-4941	254	34	)	)	PUNCT
ejpam-4941	254	35	j	j	PROPN
ejpam-4941	254	36	,	,	PUNCT
ejpam-4941	254	37	f∗∗	f∗∗	PROPN
ejpam-4941	254	38	k	k	PROPN
ejpam-4941	254	39	⟩	⟩	PROPN
ejpam-4941	254	40	⟨f∗∗	⟨f∗∗	X
ejpam-4941	255	1	k	k	X
ejpam-4941	255	2	,	,	PUNCT
ejpam-4941	255	3	f∗∗	f∗∗	PROPN
ejpam-4941	255	4	k	k	PROPN
ejpam-4941	255	5	⟩	⟩	PROPN
ejpam-4941	255	6	f∗∗	f∗∗	PROPN
ejpam-4941	255	7	k	k	PROPN
ejpam-4941	255	8	,	,	PUNCT
ejpam-4941	255	9	k	k	PROPN
ejpam-4941	255	10	=	=	SYM
ejpam-4941	255	11	2	2	NUM
ejpam-4941	255	12	,	,	PUNCT
ejpam-4941	255	13	...	...	PUNCT
ejpam-4941	255	14	,	,	PUNCT
ejpam-4941	255	15	j	j	PROPN
ejpam-4941	255	16	−	−	NOUN
ejpam-4941	255	17	1	1	NUM
ejpam-4941	255	18	=	=	SYM
ejpam-4941	255	19	ej+1	ej+1	ADP
ejpam-4941	255	20	−	−	PROPN
ejpam-4941	255	21	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	255	22	,	,	PUNCT
ejpam-4941	255	23	e	e	X
ejpam-4941	255	24	∗∗	∗∗	X
ejpam-4941	256	1	k−1⟩	k−1⟩	PROPN
ejpam-4941	256	2	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	256	3	,	,	PUNCT
ejpam-4941	256	4	e	e	X
ejpam-4941	256	5	∗∗	∗∗	X
ejpam-4941	257	1	k−1⟩	k−1⟩	PRON
ejpam-4941	257	2	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	257	3	−	−	NOUN
ejpam-4941	257	4	⟨e∗∗(k−1	⟨e∗∗(k−1	NUM
ejpam-4941	257	5	)	)	PUNCT
ejpam-4941	257	6	j+1	j+1	NOUN
ejpam-4941	257	7	,	,	PUNCT
ejpam-4941	257	8	e∗∗k	e∗∗k	PROPN
ejpam-4941	257	9	⟩	⟩	NOUN
ejpam-4941	257	10	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	257	11	,	,	PUNCT
ejpam-4941	257	12	e∗∗k	e∗∗k	PROPN
ejpam-4941	257	13	⟩	⟩	PROPN
ejpam-4941	257	14	e∗∗k	e∗∗k	PROPN
ejpam-4941	257	15	,	,	PUNCT
ejpam-4941	257	16	k	k	PROPN
ejpam-4941	257	17	=	=	SYM
ejpam-4941	257	18	2	2	NUM
ejpam-4941	257	19	,	,	PUNCT
ejpam-4941	257	20	...	...	PUNCT
ejpam-4941	257	21	,	,	PUNCT
ejpam-4941	257	22	j	j	PROPN
ejpam-4941	257	23	−	−	NOUN
ejpam-4941	257	24	1	1	NUM
ejpam-4941	257	25	as	as	ADP
ejpam-4941	257	26	for	for	ADP
ejpam-4941	257	27	the	the	DET
ejpam-4941	257	28	gs	gs	PROPN
ejpam-4941	257	29	process	process	NOUN
ejpam-4941	257	30	,	,	PUNCT
ejpam-4941	257	31	we	we	PRON
ejpam-4941	257	32	have	have	VERB
ejpam-4941	257	33	f∗	f∗	NOUN
ejpam-4941	257	34	j	j	PROPN
ejpam-4941	257	35	=	=	SYM
ejpam-4941	257	36	fj	fj	PROPN
ejpam-4941	258	1	−	−	PROPN
ejpam-4941	258	2	j−1∑	j−1∑	INTJ
ejpam-4941	258	3	k=1	k=1	X
ejpam-4941	258	4	⟨fj	⟨fj	X
ejpam-4941	258	5	,	,	PUNCT
ejpam-4941	258	6	f∗	f∗	PROPN
ejpam-4941	258	7	k	k	PROPN
ejpam-4941	258	8	⟩	⟩	PROPN
ejpam-4941	259	1	⟨f∗	⟨f∗	PROPN
ejpam-4941	260	1	k	k	PROPN
ejpam-4941	260	2	,	,	PUNCT
ejpam-4941	260	3	f	f	PROPN
ejpam-4941	260	4	∗	∗	X
ejpam-4941	260	5	k	k	PROPN
ejpam-4941	260	6	⟩	⟩	PROPN
ejpam-4941	260	7	f∗	f∗	NOUN
ejpam-4941	260	8	k	k	NOUN
ejpam-4941	260	9	=	=	SYM
ejpam-4941	260	10	ej+1	ej+1	NUM
ejpam-4941	260	11	−	−	PROPN
ejpam-4941	261	1	j−1∑	j−1∑	INTJ
ejpam-4941	262	1	k=1	k=1	PROPN
ejpam-4941	263	1	⟨fj	⟨fj	X
ejpam-4941	263	2	,	,	PUNCT
ejpam-4941	263	3	f∗	f∗	PROPN
ejpam-4941	263	4	k	k	PROPN
ejpam-4941	263	5	⟩	⟩	PROPN
ejpam-4941	264	1	⟨f∗	⟨f∗	PROPN
ejpam-4941	265	1	k	k	PROPN
ejpam-4941	265	2	,	,	PUNCT
ejpam-4941	265	3	f	f	PROPN
ejpam-4941	265	4	∗	∗	X
ejpam-4941	265	5	k	k	PROPN
ejpam-4941	265	6	⟩	⟩	PROPN
ejpam-4941	265	7	f∗	f∗	NOUN
ejpam-4941	265	8	k	k	NOUN
ejpam-4941	265	9	=	=	SYM
ejpam-4941	265	10	ej+1	ej+1	NUM
ejpam-4941	265	11	−	−	PROPN
ejpam-4941	265	12	j−1∑	j−1∑	NOUN
ejpam-4941	265	13	k=1	k=1	PUNCT
ejpam-4941	265	14	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	265	15	,	,	PUNCT
ejpam-4941	265	16	e	e	PROPN
ejpam-4941	265	17	∗	∗	NOUN
ejpam-4941	265	18	k⟩	k⟩	NOUN
ejpam-4941	266	1	⟨e∗k	⟨e∗k	PROPN
ejpam-4941	266	2	,	,	PUNCT
ejpam-4941	266	3	e∗k⟩	e∗k⟩	AUX
ejpam-4941	266	4	e∗k	e∗k	ADV
ejpam-4941	266	5	=	=	SYM
ejpam-4941	266	6	ej+1	ej+1	PROPN
ejpam-4941	266	7	−	−	NOUN
ejpam-4941	267	1	j∑	j∑	INTJ
ejpam-4941	267	2	k=1	k=1	PUNCT
ejpam-4941	268	1	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	268	2	,	,	PUNCT
ejpam-4941	268	3	e	e	PROPN
ejpam-4941	268	4	∗	∗	NOUN
ejpam-4941	268	5	k⟩	k⟩	NOUN
ejpam-4941	269	1	⟨e∗k	⟨e∗k	PROPN
ejpam-4941	269	2	,	,	PUNCT
ejpam-4941	269	3	e∗k⟩	e∗k⟩	AUX
ejpam-4941	269	4	e∗k	e∗k	VERB
ejpam-4941	269	5	+	+	PUNCT
ejpam-4941	269	6	⟨ej+1	⟨ej+1	NOUN
ejpam-4941	269	7	,	,	PUNCT
ejpam-4941	269	8	e	e	PROPN
ejpam-4941	269	9	∗	∗	PROPN
ejpam-4941	269	10	j	j	PROPN
ejpam-4941	269	11	⟩	⟩	PROPN
ejpam-4941	269	12	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	269	13	,	,	PUNCT
ejpam-4941	269	14	e∗j	e∗j	PROPN
ejpam-4941	269	15	⟩	⟩	NOUN
ejpam-4941	269	16	e∗j	e∗j	NUM
ejpam-4941	269	17	=	=	SYM
ejpam-4941	269	18	e∗j+1	e∗j+1	NOUN
ejpam-4941	270	1	+	+	CCONJ
ejpam-4941	270	2	⟨ej+1	⟨ej+1	NOUN
ejpam-4941	270	3	,	,	PUNCT
ejpam-4941	270	4	e	e	PROPN
ejpam-4941	270	5	∗	∗	PROPN
ejpam-4941	270	6	j	j	PROPN
ejpam-4941	270	7	⟩	⟩	PROPN
ejpam-4941	270	8	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	270	9	,	,	PUNCT
ejpam-4941	270	10	e∗j	e∗j	PROPN
ejpam-4941	270	11	⟩	⟩	NOUN
ejpam-4941	270	12	e∗j	e∗j	NUM
ejpam-4941	270	13	•	•	NUM
ejpam-4941	270	14	now	now	ADV
ejpam-4941	270	15	,	,	PUNCT
ejpam-4941	270	16	if	if	SCONJ
ejpam-4941	270	17	i	i	PRON
ejpam-4941	270	18	=	=	SYM
ejpam-4941	270	19	j	j	PROPN
ejpam-4941	271	1	+	+	CCONJ
ejpam-4941	271	2	1	1	NUM
ejpam-4941	271	3	,	,	PUNCT
ejpam-4941	271	4	we	we	PRON
ejpam-4941	271	5	have	have	VERB
ejpam-4941	271	6	f	f	NOUN
ejpam-4941	271	7	∗∗(k−1	∗∗(k−1	NOUN
ejpam-4941	271	8	)	)	PUNCT
ejpam-4941	271	9	j+1	j+1	X
ejpam-4941	271	10	=	=	PUNCT
ejpam-4941	272	1	fj+1	fj+1	NUM
ejpam-4941	272	2	−	−	PROPN
ejpam-4941	272	3	⟨fj+1	⟨fj+1	PROPN
ejpam-4941	272	4	,	,	PUNCT
ejpam-4941	272	5	f	f	PROPN
ejpam-4941	273	1	∗∗	∗∗	X
ejpam-4941	274	1	k−1⟩	k−1⟩	PROPN
ejpam-4941	274	2	⟨f∗∗	⟨f∗∗	VERB
ejpam-4941	274	3	k−1	k−1	PROPN
ejpam-4941	274	4	,	,	PUNCT
ejpam-4941	275	1	f	f	PROPN
ejpam-4941	275	2	∗∗	∗∗	X
ejpam-4941	276	1	k−1⟩	k−1⟩	PRON
ejpam-4941	276	2	f∗∗	f∗∗	PROPN
ejpam-4941	276	3	k−1	k−1	PROPN
ejpam-4941	276	4	,	,	PUNCT
ejpam-4941	276	5	k	k	PROPN
ejpam-4941	276	6	=	=	SYM
ejpam-4941	276	7	2	2	NUM
ejpam-4941	276	8	,	,	PUNCT
ejpam-4941	276	9	...	...	PUNCT
ejpam-4941	276	10	,	,	PUNCT
ejpam-4941	276	11	j	j	PROPN
ejpam-4941	276	12	−	−	PROPN
ejpam-4941	276	13	1	1	NUM
ejpam-4941	276	14	=	=	SYM
ejpam-4941	276	15	ej	ej	NOUN
ejpam-4941	276	16	−	−	PROPN
ejpam-4941	276	17	⟨ej	⟨ej	PROPN
ejpam-4941	276	18	,	,	PUNCT
ejpam-4941	276	19	e∗∗k−1⟩	e∗∗k−1⟩	PROPN
ejpam-4941	276	20	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	276	21	,	,	PUNCT
ejpam-4941	276	22	e	e	X
ejpam-4941	276	23	∗∗	∗∗	X
ejpam-4941	276	24	k−1⟩	k−1⟩	ADV
ejpam-4941	276	25	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	276	26	,	,	PUNCT
ejpam-4941	276	27	k	k	NOUN
ejpam-4941	276	28	=	=	SYM
ejpam-4941	276	29	2	2	NUM
ejpam-4941	276	30	,	,	PUNCT
ejpam-4941	276	31	...	...	PUNCT
ejpam-4941	276	32	,	,	PUNCT
ejpam-4941	276	33	j	j	PROPN
ejpam-4941	276	34	−	−	PROPN
ejpam-4941	276	35	1	1	NUM
ejpam-4941	276	36	=	=	SYM
ejpam-4941	276	37	e	e	NOUN
ejpam-4941	276	38	∗∗(k−1	∗∗(k−1	X
ejpam-4941	276	39	)	)	PUNCT
ejpam-4941	276	40	j	j	NOUN
ejpam-4941	276	41	,	,	PUNCT
ejpam-4941	276	42	k	k	PROPN
ejpam-4941	276	43	=	=	SYM
ejpam-4941	276	44	2	2	NUM
ejpam-4941	276	45	,	,	PUNCT
ejpam-4941	276	46	...	...	PUNCT
ejpam-4941	276	47	,	,	PUNCT
ejpam-4941	276	48	j	j	PROPN
ejpam-4941	276	49	−	−	PROPN
ejpam-4941	276	50	1	1	NUM
ejpam-4941	276	51	which	which	PRON
ejpam-4941	276	52	implies	imply	VERB
ejpam-4941	276	53	that	that	SCONJ
ejpam-4941	276	54	f	f	PROPN
ejpam-4941	276	55	∗∗(k	∗∗(k	NOUN
ejpam-4941	276	56	)	)	PUNCT
ejpam-4941	277	1	j+1	j+1	X
ejpam-4941	277	2	=	=	PUNCT
ejpam-4941	277	3	f	f	NOUN
ejpam-4941	277	4	∗∗(k−1	∗∗(k−1	NUM
ejpam-4941	277	5	)	)	PUNCT
ejpam-4941	278	1	j+1	j+1	PUNCT
ejpam-4941	278	2	−	−	PROPN
ejpam-4941	278	3	⟨f	⟨f	PUNCT
ejpam-4941	278	4	(	(	PUNCT
ejpam-4941	278	5	k−1	k−1	PROPN
ejpam-4941	278	6	)	)	PUNCT
ejpam-4941	278	7	j+1	j+1	NOUN
ejpam-4941	278	8	,	,	PUNCT
ejpam-4941	278	9	f∗∗	f∗∗	PROPN
ejpam-4941	278	10	k	k	PROPN
ejpam-4941	278	11	⟩	⟩	PROPN
ejpam-4941	278	12	⟨f∗∗	⟨f∗∗	X
ejpam-4941	279	1	k	k	X
ejpam-4941	279	2	,	,	PUNCT
ejpam-4941	279	3	f∗∗	f∗∗	PROPN
ejpam-4941	279	4	k	k	PROPN
ejpam-4941	279	5	⟩	⟩	PROPN
ejpam-4941	279	6	f∗∗	f∗∗	PROPN
ejpam-4941	279	7	k	k	PROPN
ejpam-4941	279	8	,	,	PUNCT
ejpam-4941	279	9	k	k	PROPN
ejpam-4941	279	10	=	=	SYM
ejpam-4941	279	11	2	2	NUM
ejpam-4941	279	12	,	,	PUNCT
ejpam-4941	279	13	...	...	PUNCT
ejpam-4941	279	14	,	,	PUNCT
ejpam-4941	279	15	j	j	PROPN
ejpam-4941	279	16	−	−	PROPN
ejpam-4941	279	17	1	1	NUM
ejpam-4941	279	18	s.	s.	PROPN
ejpam-4941	279	19	abdelalim	abdelalim	PROPN
ejpam-4941	279	20	,	,	PUNCT
ejpam-4941	279	21	i.	i.	PROPN
ejpam-4941	279	22	elmouki	elmouki	PROPN
ejpam-4941	279	23	/	/	SYM
ejpam-4941	279	24	eur	eur	PROPN
ejpam-4941	279	25	.	.	PUNCT
ejpam-4941	280	1	j.	j.	PROPN
ejpam-4941	280	2	pure	pure	PROPN
ejpam-4941	280	3	appl	appl	PROPN
ejpam-4941	280	4	.	.	PROPN
ejpam-4941	280	5	math	math	PROPN
ejpam-4941	280	6	,	,	PUNCT
ejpam-4941	280	7	16	16	NUM
ejpam-4941	280	8	(	(	PUNCT
ejpam-4941	280	9	4	4	NUM
ejpam-4941	280	10	)	)	PUNCT
ejpam-4941	280	11	(	(	PUNCT
ejpam-4941	280	12	2023	2023	NUM
ejpam-4941	280	13	)	)	PUNCT
ejpam-4941	280	14	,	,	PUNCT
ejpam-4941	280	15	2662	2662	NUM
ejpam-4941	280	16	-	-	SYM
ejpam-4941	280	17	2692	2692	NUM
ejpam-4941	280	18	2678	2678	NUM
ejpam-4941	280	19	=	=	SYM
ejpam-4941	280	20	e	e	NOUN
ejpam-4941	280	21	∗∗(k−1	∗∗(k−1	X
ejpam-4941	280	22	)	)	PUNCT
ejpam-4941	280	23	j	j	PROPN
ejpam-4941	280	24	−	−	PROPN
ejpam-4941	280	25	⟨e(k−1	⟨e(k−1	NUM
ejpam-4941	280	26	)	)	PUNCT
ejpam-4941	280	27	j	j	PROPN
ejpam-4941	280	28	,	,	PUNCT
ejpam-4941	280	29	e∗∗k	e∗∗k	PROPN
ejpam-4941	280	30	⟩	⟩	NOUN
ejpam-4941	280	31	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	280	32	,	,	PUNCT
ejpam-4941	280	33	e∗∗k	e∗∗k	PROPN
ejpam-4941	280	34	⟩	⟩	PROPN
ejpam-4941	280	35	e∗∗k	e∗∗k	PROPN
ejpam-4941	280	36	,	,	PUNCT
ejpam-4941	280	37	k	k	PROPN
ejpam-4941	280	38	=	=	SYM
ejpam-4941	280	39	2	2	NUM
ejpam-4941	280	40	,	,	PUNCT
ejpam-4941	280	41	...	...	PUNCT
ejpam-4941	280	42	,	,	PUNCT
ejpam-4941	280	43	j	j	PROPN
ejpam-4941	280	44	−	−	PROPN
ejpam-4941	280	45	1	1	NUM
ejpam-4941	280	46	=	=	SYM
ejpam-4941	280	47	e	e	NOUN
ejpam-4941	280	48	∗∗(k	∗∗(k	NOUN
ejpam-4941	280	49	)	)	PUNCT
ejpam-4941	280	50	j	j	NOUN
ejpam-4941	280	51	,	,	PUNCT
ejpam-4941	280	52	k	k	PROPN
ejpam-4941	280	53	=	=	SYM
ejpam-4941	280	54	2	2	NUM
ejpam-4941	280	55	,	,	PUNCT
ejpam-4941	280	56	...	...	PUNCT
ejpam-4941	280	57	,	,	PUNCT
ejpam-4941	280	58	j	j	PROPN
ejpam-4941	280	59	−	−	NOUN
ejpam-4941	280	60	1	1	NUM
ejpam-4941	280	61	as	as	ADP
ejpam-4941	280	62	for	for	ADP
ejpam-4941	280	63	the	the	DET
ejpam-4941	280	64	gs	gs	PROPN
ejpam-4941	280	65	process	process	NOUN
ejpam-4941	280	66	,	,	PUNCT
ejpam-4941	280	67	we	we	PRON
ejpam-4941	280	68	have	have	AUX
ejpam-4941	280	69	f∗	f∗	NOUN
ejpam-4941	280	70	j+1	j+1	PRON
ejpam-4941	281	1	=	=	PUNCT
ejpam-4941	282	1	fj+1	fj+1	NOUN
ejpam-4941	283	1	−	−	NOUN
ejpam-4941	284	1	j∑	j∑	INTJ
ejpam-4941	284	2	k=1	k=1	PUNCT
ejpam-4941	285	1	⟨fj+1	⟨fj+1	PROPN
ejpam-4941	285	2	,	,	PUNCT
ejpam-4941	285	3	f	f	PROPN
ejpam-4941	285	4	∗	∗	NOUN
ejpam-4941	285	5	k	k	PROPN
ejpam-4941	285	6	⟩	⟩	PROPN
ejpam-4941	285	7	⟨f∗	⟨f∗	PROPN
ejpam-4941	286	1	k	k	PROPN
ejpam-4941	286	2	,	,	PUNCT
ejpam-4941	286	3	f	f	PROPN
ejpam-4941	286	4	∗	∗	X
ejpam-4941	286	5	k	k	PROPN
ejpam-4941	286	6	⟩	⟩	PROPN
ejpam-4941	286	7	f∗	f∗	NOUN
ejpam-4941	286	8	k	k	PROPN
ejpam-4941	286	9	=	=	SYM
ejpam-4941	286	10	ej	ej	PROPN
ejpam-4941	287	1	−	−	PROPN
ejpam-4941	288	1	j−1∑	j−1∑	INTJ
ejpam-4941	289	1	k=1	k=1	X
ejpam-4941	290	1	⟨ej	⟨ej	PROPN
ejpam-4941	290	2	,	,	PUNCT
ejpam-4941	290	3	f∗	f∗	PROPN
ejpam-4941	290	4	k	k	PROPN
ejpam-4941	290	5	⟩	⟩	PROPN
ejpam-4941	290	6	⟨f∗	⟨f∗	PROPN
ejpam-4941	291	1	k	k	PROPN
ejpam-4941	291	2	,	,	PUNCT
ejpam-4941	291	3	f	f	PROPN
ejpam-4941	291	4	∗	∗	X
ejpam-4941	291	5	k	k	PROPN
ejpam-4941	291	6	⟩	⟩	PROPN
ejpam-4941	291	7	f∗	f∗	NOUN
ejpam-4941	291	8	k	k	PROPN
ejpam-4941	292	1	+	+	CCONJ
ejpam-4941	292	2	⟨ej	⟨ej	NOUN
ejpam-4941	292	3	,	,	PUNCT
ejpam-4941	292	4	f∗	f∗	X
ejpam-4941	292	5	j	j	PROPN
ejpam-4941	292	6	⟩	⟩	PROPN
ejpam-4941	292	7	⟨f∗	⟨f∗	PROPN
ejpam-4941	293	1	j	j	PROPN
ejpam-4941	293	2	,	,	PUNCT
ejpam-4941	293	3	f	f	PROPN
ejpam-4941	293	4	∗	∗	PROPN
ejpam-4941	293	5	j	j	PROPN
ejpam-4941	293	6	⟩	⟩	PROPN
ejpam-4941	293	7	f∗	f∗	NOUN
ejpam-4941	293	8	j	j	PROPN
ejpam-4941	294	1	=	=	PRON
ejpam-4941	294	2	ej	ej	PROPN
ejpam-4941	294	3	−	−	PROPN
ejpam-4941	294	4	j−1∑	j−1∑	INTJ
ejpam-4941	294	5	k=1	k=1	X
ejpam-4941	294	6	⟨ej	⟨ej	PROPN
ejpam-4941	294	7	,	,	PUNCT
ejpam-4941	294	8	e∗k⟩	e∗k⟩	PROPN
ejpam-4941	294	9	⟨e∗k	⟨e∗k	PROPN
ejpam-4941	294	10	,	,	PUNCT
ejpam-4941	294	11	e∗k⟩	e∗k⟩	AUX
ejpam-4941	294	12	e∗k	e∗k	VERB
ejpam-4941	294	13	+	+	CCONJ
ejpam-4941	294	14	〈	〈	PROPN
ejpam-4941	294	15	ej	ej	X
ejpam-4941	294	16	,	,	PUNCT
ejpam-4941	294	17	e	e	NOUN
ejpam-4941	294	18	∗	∗	NOUN
ejpam-4941	294	19	j+1	j+1	PROPN
ejpam-4941	295	1	+	+	X
ejpam-4941	296	1	⟨ej+1	⟨ej+1	NOUN
ejpam-4941	296	2	,	,	PUNCT
ejpam-4941	296	3	e	e	PROPN
ejpam-4941	296	4	∗	∗	PROPN
ejpam-4941	296	5	j	j	PROPN
ejpam-4941	296	6	⟩	⟩	PROPN
ejpam-4941	296	7	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	296	8	,	,	PUNCT
ejpam-4941	296	9	e∗j	e∗j	PROPN
ejpam-4941	296	10	⟩	⟩	NOUN
ejpam-4941	296	11	e∗j	e∗j	NUM
ejpam-4941	296	12	〉	〉	NOUN
ejpam-4941	297	1	|f∗	|f∗	PROPN
ejpam-4941	297	2	j	j	PROPN
ejpam-4941	297	3	|2	|2	NUM
ejpam-4941	297	4	〈	〈	PROPN
ejpam-4941	297	5	ej	ej	X
ejpam-4941	297	6	,	,	PUNCT
ejpam-4941	297	7	e	e	NOUN
ejpam-4941	297	8	∗	∗	NOUN
ejpam-4941	297	9	j+1	j+1	PROPN
ejpam-4941	297	10	+	+	X
ejpam-4941	297	11	⟨ej+1	⟨ej+1	NOUN
ejpam-4941	297	12	,	,	PUNCT
ejpam-4941	297	13	e	e	PROPN
ejpam-4941	297	14	∗	∗	PROPN
ejpam-4941	297	15	j	j	PROPN
ejpam-4941	297	16	⟩	⟩	PROPN
ejpam-4941	297	17	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	297	18	,	,	PUNCT
ejpam-4941	297	19	e∗j	e∗j	PROPN
ejpam-4941	297	20	⟩	⟩	NOUN
ejpam-4941	297	21	e∗j	e∗j	NUM
ejpam-4941	297	22	〉	〉	NOUN
ejpam-4941	297	23	n.b	n.b	NOUN
ejpam-4941	297	24	.	.	PUNCT
ejpam-4941	298	1	|f∗	|f∗	PROPN
ejpam-4941	298	2	j	j	PROPN
ejpam-4941	298	3	|2	|2	NUM
ejpam-4941	298	4	=	=	PUNCT
ejpam-4941	298	5	|e∗j+1|2	|e∗j+1|2	X
ejpam-4941	298	6	+	+	SYM
ejpam-4941	298	7	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	298	8	,	,	PUNCT
ejpam-4941	298	9	e	e	PROPN
ejpam-4941	298	10	∗	∗	PROPN
ejpam-4941	298	11	j	j	PROPN
ejpam-4941	298	12	⟩	⟩	PROPN
ejpam-4941	298	13	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	298	14	,	,	PUNCT
ejpam-4941	298	15	e∗j	e∗j	PROPN
ejpam-4941	298	16	⟩	⟩	NOUN
ejpam-4941	298	17	2	2	NUM
ejpam-4941	298	18	|e∗j	|e∗j	ADJ
ejpam-4941	298	19	|2	|2	NUM
ejpam-4941	299	1	and	and	CCONJ
ejpam-4941	299	2	then	then	ADV
ejpam-4941	299	3	,	,	PUNCT
ejpam-4941	299	4	we	we	PRON
ejpam-4941	299	5	have	have	VERB
ejpam-4941	299	6	,	,	PUNCT
ejpam-4941	299	7	f∗	f∗	NOUN
ejpam-4941	299	8	j+1	j+1	NOUN
ejpam-4941	299	9	=	=	PUNCT
ejpam-4941	299	10	e∗j	e∗j	NUM
ejpam-4941	299	11	−	−	NUM
ejpam-4941	299	12	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	299	13	,	,	PUNCT
ejpam-4941	299	14	e	e	PROPN
ejpam-4941	299	15	∗	∗	PROPN
ejpam-4941	299	16	j	j	PROPN
ejpam-4941	299	17	⟩	⟩	PROPN
ejpam-4941	299	18	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	299	19	,	,	PUNCT
ejpam-4941	299	20	e∗j	e∗j	PROPN
ejpam-4941	299	21	⟩	⟩	PROPN
ejpam-4941	299	22	⟨ej	⟨ej	NOUN
ejpam-4941	299	23	,	,	PUNCT
ejpam-4941	300	1	e∗j	e∗j	PROPN
ejpam-4941	300	2	⟩	⟩	NOUN
ejpam-4941	300	3	|f∗	|f∗	PROPN
ejpam-4941	300	4	j	j	PROPN
ejpam-4941	300	5	|2	|2	NUM
ejpam-4941	300	6	(	(	PUNCT
ejpam-4941	300	7	ej	ej	PROPN
ejpam-4941	300	8	+	+	SYM
ejpam-4941	300	9	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	300	10	,	,	PUNCT
ejpam-4941	300	11	e	e	PROPN
ejpam-4941	300	12	∗	∗	PROPN
ejpam-4941	300	13	j	j	PROPN
ejpam-4941	300	14	⟩	⟩	PROPN
ejpam-4941	300	15	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	300	16	,	,	PUNCT
ejpam-4941	300	17	e∗j	e∗j	PROPN
ejpam-4941	300	18	⟩	⟩	NOUN
ejpam-4941	300	19	e∗j+1	e∗j+1	NOUN
ejpam-4941	300	20	)	)	PUNCT
ejpam-4941	301	1	since	since	SCONJ
ejpam-4941	301	2	ej	ej	PROPN
ejpam-4941	301	3	=	=	SYM
ejpam-4941	301	4	e∗j	e∗j	PROPN
ejpam-4941	301	5	−	−	PROPN
ejpam-4941	301	6	j−1∑	j−1∑	PROPN
ejpam-4941	301	7	k=1	k=1	PROPN
ejpam-4941	301	8	⟨ek	⟨ek	PROPN
ejpam-4941	301	9	,	,	PUNCT
ejpam-4941	301	10	e∗j	e∗j	PROPN
ejpam-4941	301	11	⟩	⟩	NOUN
ejpam-4941	301	12	⟨e∗j	⟨e∗j	NOUN
ejpam-4941	301	13	,	,	PUNCT
ejpam-4941	301	14	e∗j	e∗j	PROPN
ejpam-4941	301	15	⟩	⟩	NOUN
ejpam-4941	301	16	e∗k	e∗k	PROPN
ejpam-4941	301	17	.	.	PUNCT
ejpam-4941	302	1	then	then	ADV
ejpam-4941	302	2	,	,	PUNCT
ejpam-4941	302	3	⟨ej	⟨ej	NOUN
ejpam-4941	302	4	,	,	PUNCT
ejpam-4941	302	5	e∗j	e∗j	PROPN
ejpam-4941	302	6	⟩	⟩	NOUN
ejpam-4941	302	7	=	=	NOUN
ejpam-4941	302	8	⟨e∗j	⟨e∗j	NOUN
ejpam-4941	302	9	,	,	PUNCT
ejpam-4941	302	10	e∗j	e∗j	PROPN
ejpam-4941	302	11	⟩.	⟩.	PROPN
ejpam-4941	302	12	hence	hence	ADV
ejpam-4941	302	13	,	,	PUNCT
ejpam-4941	302	14	f∗	f∗	NOUN
ejpam-4941	302	15	j+1	j+1	NOUN
ejpam-4941	302	16	=	=	PUNCT
ejpam-4941	302	17	e∗j	e∗j	NUM
ejpam-4941	302	18	−	−	NUM
ejpam-4941	302	19	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	302	20	,	,	PUNCT
ejpam-4941	302	21	e	e	PROPN
ejpam-4941	302	22	∗	∗	PROPN
ejpam-4941	302	23	j	j	PROPN
ejpam-4941	302	24	⟩	⟩	PROPN
ejpam-4941	302	25	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	302	26	,	,	PUNCT
ejpam-4941	302	27	e∗j	e∗j	PROPN
ejpam-4941	302	28	⟩	⟩	NOUN
ejpam-4941	302	29	2	2	NUM
ejpam-4941	302	30	|e∗j	|e∗j	ADJ
ejpam-4941	302	31	|2	|2	NUM
ejpam-4941	302	32	|f∗	|f∗	PROPN
ejpam-4941	302	33	j	j	PROPN
ejpam-4941	302	34	|2	|2	NUM
ejpam-4941	302	35	−	−	PROPN
ejpam-4941	302	36	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	302	37	,	,	PUNCT
ejpam-4941	302	38	e	e	PROPN
ejpam-4941	302	39	∗	∗	PROPN
ejpam-4941	302	40	j	j	PROPN
ejpam-4941	302	41	⟩	⟩	PROPN
ejpam-4941	302	42	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	302	43	,	,	PUNCT
ejpam-4941	302	44	e∗j	e∗j	PROPN
ejpam-4941	302	45	⟩	⟩	NOUN
ejpam-4941	302	46	|e∗j	|e∗j	ADJ
ejpam-4941	302	47	|2	|2	NUM
ejpam-4941	302	48	|f∗	|f∗	PROPN
ejpam-4941	302	49	j	j	PROPN
ejpam-4941	302	50	|2	|2	NUM
ejpam-4941	302	51	e∗j+1	e∗j+1	NOUN
ejpam-4941	302	52	=	=	PUNCT
ejpam-4941	303	1	|f∗	|f∗	PROPN
ejpam-4941	303	2	j	j	PROPN
ejpam-4941	303	3	|2	|2	NUM
ejpam-4941	303	4	−	−	PROPN
ejpam-4941	303	5	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	303	6	,	,	PUNCT
ejpam-4941	303	7	e	e	PROPN
ejpam-4941	303	8	∗	∗	PROPN
ejpam-4941	303	9	j	j	PROPN
ejpam-4941	303	10	⟩	⟩	PROPN
ejpam-4941	303	11	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	303	12	,	,	PUNCT
ejpam-4941	303	13	e∗j	e∗j	PROPN
ejpam-4941	303	14	⟩	⟩	NOUN
ejpam-4941	303	15	2	2	NUM
ejpam-4941	303	16	|e∗j	|e∗j	ADJ
ejpam-4941	303	17	|2	|2	NUM
ejpam-4941	303	18	|f∗	|f∗	PROPN
ejpam-4941	303	19	j	j	PROPN
ejpam-4941	303	20	|2	|2	NUM
ejpam-4941	303	21	e∗j	e∗j	NUM
ejpam-4941	303	22	−	−	NUM
ejpam-4941	303	23	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	303	24	,	,	PUNCT
ejpam-4941	303	25	e	e	PROPN
ejpam-4941	303	26	∗	∗	PROPN
ejpam-4941	303	27	j	j	PROPN
ejpam-4941	303	28	⟩	⟩	PROPN
ejpam-4941	303	29	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	303	30	,	,	PUNCT
ejpam-4941	303	31	e∗j	e∗j	PROPN
ejpam-4941	303	32	⟩	⟩	NOUN
ejpam-4941	303	33	2	2	NUM
ejpam-4941	303	34	|e∗j	|e∗j	ADJ
ejpam-4941	303	35	|2	|2	NUM
ejpam-4941	303	36	|f∗	|f∗	PROPN
ejpam-4941	303	37	j	j	PROPN
ejpam-4941	303	38	|2	|2	NUM
ejpam-4941	303	39	=	=	PUNCT
ejpam-4941	303	40	|e∗j+1|2	|e∗j+1|2	PROPN
ejpam-4941	303	41	|f∗	|f∗	PROPN
ejpam-4941	303	42	j	j	PROPN
ejpam-4941	303	43	|2	|2	NUM
ejpam-4941	304	1	e∗j	e∗j	NUM
ejpam-4941	304	2	−	−	NUM
ejpam-4941	304	3	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	304	4	,	,	PUNCT
ejpam-4941	304	5	e	e	PROPN
ejpam-4941	304	6	∗	∗	PROPN
ejpam-4941	304	7	j	j	PROPN
ejpam-4941	304	8	⟩	⟩	PROPN
ejpam-4941	304	9	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	304	10	,	,	PUNCT
ejpam-4941	304	11	e∗j	e∗j	PROPN
ejpam-4941	304	12	⟩	⟩	NOUN
ejpam-4941	304	13	2	2	NUM
ejpam-4941	304	14	|e∗j	|e∗j	ADJ
ejpam-4941	304	15	|2	|2	NUM
ejpam-4941	304	16	|f∗	|f∗	PROPN
ejpam-4941	304	17	j	j	PROPN
ejpam-4941	304	18	|2	|2	NUM
ejpam-4941	304	19	•	•	NOUN
ejpam-4941	304	20	–	–	PUNCT
ejpam-4941	304	21	for	for	ADP
ejpam-4941	304	22	i	i	PRON
ejpam-4941	304	23	>	>	X
ejpam-4941	304	24	j	j	PROPN
ejpam-4941	305	1	+	+	CCONJ
ejpam-4941	305	2	1	1	NUM
ejpam-4941	305	3	,	,	PUNCT
ejpam-4941	305	4	we	we	PRON
ejpam-4941	305	5	already	already	ADV
ejpam-4941	305	6	know	know	VERB
ejpam-4941	305	7	by	by	ADP
ejpam-4941	305	8	definition	definition	NOUN
ejpam-4941	305	9	of	of	ADP
ejpam-4941	305	10	the	the	DET
ejpam-4941	305	11	basis	basis	NOUN
ejpam-4941	305	12	in	in	ADP
ejpam-4941	305	13	this	this	DET
ejpam-4941	305	14	case	case	NOUN
ejpam-4941	305	15	,	,	PUNCT
ejpam-4941	305	16	that	that	DET
ejpam-4941	305	17	fi	fi	NOUN
ejpam-4941	305	18	=	=	X
ejpam-4941	305	19	ei	ei	PROPN
ejpam-4941	305	20	.	.	PUNCT
ejpam-4941	306	1	but	but	CCONJ
ejpam-4941	306	2	let	let	VERB
ejpam-4941	306	3	us	we	PRON
ejpam-4941	306	4	start	start	VERB
ejpam-4941	306	5	with	with	ADP
ejpam-4941	306	6	this	this	DET
ejpam-4941	306	7	result	result	NOUN
ejpam-4941	306	8	.	.	PUNCT
ejpam-4941	307	1	since	since	SCONJ
ejpam-4941	307	2	ei	ei	NOUN
ejpam-4941	307	3	can	can	AUX
ejpam-4941	307	4	be	be	AUX
ejpam-4941	307	5	decomposed	decompose	VERB
ejpam-4941	307	6	into	into	ADP
ejpam-4941	307	7	a	a	DET
ejpam-4941	307	8	unique	unique	ADJ
ejpam-4941	307	9	sum	sum	NOUN
ejpam-4941	307	10	of	of	ADP
ejpam-4941	307	11	an	an	DET
ejpam-4941	307	12	element	element	NOUN
ejpam-4941	307	13	of	of	ADP
ejpam-4941	307	14	span(e1	span(e1	NOUN
ejpam-4941	307	15	,	,	PUNCT
ejpam-4941	307	16	...	...	PUNCT
ejpam-4941	307	17	,	,	PUNCT
ejpam-4941	307	18	ei−1	ei−1	PROPN
ejpam-4941	307	19	)	)	PUNCT
ejpam-4941	307	20	⊥	⊥	PROPN
ejpam-4941	307	21	and	and	CCONJ
ejpam-4941	307	22	an	an	DET
ejpam-4941	307	23	element	element	NOUN
ejpam-4941	307	24	of	of	ADP
ejpam-4941	307	25	span(e1	span(e1	NOUN
ejpam-4941	307	26	,	,	PUNCT
ejpam-4941	307	27	...	...	PUNCT
ejpam-4941	307	28	,	,	PUNCT
ejpam-4941	307	29	ei−1	ei−1	PROPN
ejpam-4941	307	30	)	)	PUNCT
ejpam-4941	307	31	,	,	PUNCT
ejpam-4941	307	32	i.e.	i.e.	X
ejpam-4941	307	33	ei	ei	ADP
ejpam-4941	307	34	∈	∈	PROPN
ejpam-4941	307	35	span(e1	span(e1	NOUN
ejpam-4941	307	36	,	,	PUNCT
ejpam-4941	307	37	...	...	PUNCT
ejpam-4941	307	38	,	,	PUNCT
ejpam-4941	307	39	ei−1	ei−1	PROPN
ejpam-4941	307	40	)	)	PUNCT
ejpam-4941	307	41	⊥⊕span(e1	⊥⊕span(e1	NOUN
ejpam-4941	307	42	,	,	PUNCT
ejpam-4941	307	43	...	...	PUNCT
ejpam-4941	307	44	,	,	PUNCT
ejpam-4941	307	45	ei−1	ei−1	PROPN
ejpam-4941	307	46	)	)	PUNCT
ejpam-4941	307	47	while	while	SCONJ
ejpam-4941	307	48	knowing	know	VERB
ejpam-4941	307	49	that	that	SCONJ
ejpam-4941	307	50	,	,	PUNCT
ejpam-4941	307	51	ei	ei	X
ejpam-4941	307	52	=	=	SYM
ejpam-4941	307	53	e	e	NOUN
ejpam-4941	307	54	∗∗(k	∗∗(k	NOUN
ejpam-4941	307	55	)	)	PUNCT
ejpam-4941	307	56	i	i	PRON
ejpam-4941	307	57	+	+	NUM
ejpam-4941	307	58	⟨ei	⟨ei	PROPN
ejpam-4941	307	59	,	,	PUNCT
ejpam-4941	307	60	e∗∗k−1⟩	e∗∗k−1⟩	PROPN
ejpam-4941	307	61	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	307	62	,	,	PUNCT
ejpam-4941	307	63	e	e	X
ejpam-4941	307	64	∗∗	∗∗	X
ejpam-4941	308	1	k−1⟩	k−1⟩	PROPN
ejpam-4941	308	2	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	308	3	+	+	CCONJ
ejpam-4941	308	4	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	308	5	)	)	PUNCT
ejpam-4941	308	6	i	i	PRON
ejpam-4941	308	7	,	,	PUNCT
ejpam-4941	308	8	e∗∗i	e∗∗i	PROPN
ejpam-4941	308	9	⟩	⟩	PROPN
ejpam-4941	308	10	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	308	11	,	,	PUNCT
ejpam-4941	308	12	e∗∗k	e∗∗k	PROPN
ejpam-4941	308	13	⟩	⟩	PROPN
ejpam-4941	308	14	e∗∗k	e∗∗k	PROPN
ejpam-4941	308	15	,	,	PUNCT
ejpam-4941	308	16	k	k	PROPN
ejpam-4941	308	17	=	=	SYM
ejpam-4941	308	18	2	2	NUM
ejpam-4941	308	19	,	,	PUNCT
ejpam-4941	308	20	...	...	PUNCT
ejpam-4941	308	21	,	,	PUNCT
ejpam-4941	308	22	r	r	NOUN
ejpam-4941	308	23	−	−	PROPN
ejpam-4941	308	24	1	1	NUM
ejpam-4941	308	25	s.	s.	PROPN
ejpam-4941	308	26	abdelalim	abdelalim	PROPN
ejpam-4941	308	27	,	,	PUNCT
ejpam-4941	308	28	i.	i.	PROPN
ejpam-4941	308	29	elmouki	elmouki	PROPN
ejpam-4941	308	30	/	/	SYM
ejpam-4941	308	31	eur	eur	PROPN
ejpam-4941	308	32	.	.	PUNCT
ejpam-4941	309	1	j.	j.	PROPN
ejpam-4941	309	2	pure	pure	PROPN
ejpam-4941	309	3	appl	appl	PROPN
ejpam-4941	309	4	.	.	PROPN
ejpam-4941	309	5	math	math	PROPN
ejpam-4941	309	6	,	,	PUNCT
ejpam-4941	309	7	16	16	NUM
ejpam-4941	309	8	(	(	PUNCT
ejpam-4941	309	9	4	4	NUM
ejpam-4941	309	10	)	)	PUNCT
ejpam-4941	309	11	(	(	PUNCT
ejpam-4941	309	12	2023	2023	NUM
ejpam-4941	309	13	)	)	PUNCT
ejpam-4941	309	14	,	,	PUNCT
ejpam-4941	309	15	2662	2662	NUM
ejpam-4941	309	16	-	-	SYM
ejpam-4941	309	17	2692	2692	NUM
ejpam-4941	309	18	2679	2679	NUM
ejpam-4941	309	19	and	and	CCONJ
ejpam-4941	309	20	at	at	ADP
ejpam-4941	309	21	the	the	DET
ejpam-4941	309	22	same	same	ADJ
ejpam-4941	309	23	time	time	NOUN
ejpam-4941	309	24	,	,	PUNCT
ejpam-4941	309	25	we	we	PRON
ejpam-4941	309	26	also	also	ADV
ejpam-4941	309	27	know	know	VERB
ejpam-4941	309	28	from	from	ADP
ejpam-4941	309	29	theorem	theorem	ADJ
ejpam-4941	309	30	1	1	NUM
ejpam-4941	309	31	that	that	DET
ejpam-4941	309	32	span(e1	span(e1	NOUN
ejpam-4941	309	33	,	,	PUNCT
ejpam-4941	309	34	...	...	PUNCT
ejpam-4941	309	35	,	,	PUNCT
ejpam-4941	309	36	ei−1	ei−1	PROPN
ejpam-4941	309	37	)	)	PUNCT
ejpam-4941	309	38	=	=	PUNCT
ejpam-4941	309	39	span(e∗∗1	span(e∗∗1	ADJ
ejpam-4941	309	40	,	,	PUNCT
ejpam-4941	309	41	e	e	X
ejpam-4941	309	42	∗∗(1	∗∗(1	X
ejpam-4941	309	43	)	)	PUNCT
ejpam-4941	309	44	2	2	NUM
ejpam-4941	309	45	,	,	PUNCT
ejpam-4941	309	46	e	e	X
ejpam-4941	309	47	∗∗(2	∗∗(2	PROPN
ejpam-4941	309	48	)	)	PUNCT
ejpam-4941	309	49	3	3	NUM
ejpam-4941	309	50	,	,	PUNCT
ejpam-4941	309	51	...	...	PUNCT
ejpam-4941	309	52	,	,	PUNCT
ejpam-4941	309	53	e	e	NOUN
ejpam-4941	309	54	∗∗(k	∗∗(k	NOUN
ejpam-4941	309	55	)	)	PUNCT
ejpam-4941	309	56	i−1	i−1	PROPN
ejpam-4941	309	57	)	)	PUNCT
ejpam-4941	309	58	,	,	PUNCT
ejpam-4941	310	1	2	2	NUM
ejpam-4941	310	2	≤	≤	NUM
ejpam-4941	310	3	k	k	PROPN
ejpam-4941	310	4	≤	≤	PROPN
ejpam-4941	310	5	n−1	n−1	PROPN
ejpam-4941	310	6	,	,	PUNCT
ejpam-4941	310	7	then	then	ADV
ejpam-4941	310	8	,	,	PUNCT
ejpam-4941	310	9	the	the	DET
ejpam-4941	310	10	element	element	NOUN
ejpam-4941	310	11	of	of	ADP
ejpam-4941	310	12	span(e∗∗1	span(e∗∗1	ADJ
ejpam-4941	310	13	,	,	PUNCT
ejpam-4941	310	14	...	...	PUNCT
ejpam-4941	310	15	,	,	PUNCT
ejpam-4941	310	16	e∗∗i−1	e∗∗i−1	PROPN
ejpam-4941	310	17	)	)	PUNCT
ejpam-4941	310	18	⊥	⊥	NOUN
ejpam-4941	310	19	is	be	AUX
ejpam-4941	310	20	exactly	exactly	ADV
ejpam-4941	310	21	e	e	NOUN
ejpam-4941	310	22	∗∗(k	∗∗(k	NOUN
ejpam-4941	310	23	)	)	PUNCT
ejpam-4941	311	1	i	i	PRON
ejpam-4941	311	2	,	,	PUNCT
ejpam-4941	311	3	therefore	therefore	ADV
ejpam-4941	311	4	,	,	PUNCT
ejpam-4941	311	5	we	we	PRON
ejpam-4941	311	6	can	can	AUX
ejpam-4941	311	7	say	say	VERB
ejpam-4941	311	8	that	that	SCONJ
ejpam-4941	311	9	,	,	PUNCT
ejpam-4941	311	10	ei	ei	PROPN
ejpam-4941	311	11	∈	∈	PROPN
ejpam-4941	311	12	span(e∗∗1	span(e∗∗1	NOUN
ejpam-4941	311	13	,	,	PUNCT
ejpam-4941	311	14	...	...	PUNCT
ejpam-4941	311	15	,	,	PUNCT
ejpam-4941	311	16	e	e	NOUN
ejpam-4941	311	17	∗∗(k−1	∗∗(k−1	X
ejpam-4941	311	18	)	)	PUNCT
ejpam-4941	311	19	i−1	i−1	PROPN
ejpam-4941	311	20	)	)	PUNCT
ejpam-4941	311	21	⊥	⊥	PROPN
ejpam-4941	311	22	⊕	⊕	PROPN
ejpam-4941	311	23	span(e∗∗1	span(e∗∗1	NOUN
ejpam-4941	311	24	,	,	PUNCT
ejpam-4941	311	25	...	...	PUNCT
ejpam-4941	311	26	,	,	PUNCT
ejpam-4941	311	27	e	e	NOUN
ejpam-4941	311	28	∗∗(k−1	∗∗(k−1	X
ejpam-4941	311	29	)	)	PUNCT
ejpam-4941	311	30	i−1	i−1	PROPN
ejpam-4941	311	31	)	)	PUNCT
ejpam-4941	311	32	.	.	PUNCT
ejpam-4941	312	1	similarly	similarly	ADV
ejpam-4941	312	2	,	,	PUNCT
ejpam-4941	312	3	by	by	ADP
ejpam-4941	312	4	having	have	VERB
ejpam-4941	312	5	,	,	PUNCT
ejpam-4941	312	6	fi	fi	NOUN
ejpam-4941	312	7	=	=	SYM
ejpam-4941	312	8	f	f	PROPN
ejpam-4941	312	9	∗∗(k	∗∗(k	NOUN
ejpam-4941	312	10	)	)	PUNCT
ejpam-4941	312	11	i	i	PRON
ejpam-4941	312	12	+	+	CCONJ
ejpam-4941	312	13	⟨fi	⟨fi	NOUN
ejpam-4941	312	14	,	,	PUNCT
ejpam-4941	312	15	f∗∗	f∗∗	PROPN
ejpam-4941	312	16	k−1⟩	k−1⟩	PROPN
ejpam-4941	312	17	⟨f∗∗	⟨f∗∗	ADP
ejpam-4941	312	18	k−1	k−1	PROPN
ejpam-4941	312	19	,	,	PUNCT
ejpam-4941	312	20	f	f	PROPN
ejpam-4941	312	21	∗∗	∗∗	X
ejpam-4941	313	1	k−1⟩	k−1⟩	PRON
ejpam-4941	313	2	f∗∗	f∗∗	PROPN
ejpam-4941	313	3	k−1	k−1	PROPN
ejpam-4941	313	4	+	+	CCONJ
ejpam-4941	313	5	⟨f∗∗(k−1	⟨f∗∗(k−1	X
ejpam-4941	313	6	)	)	PUNCT
ejpam-4941	314	1	i	i	PRON
ejpam-4941	314	2	,	,	PUNCT
ejpam-4941	314	3	f∗∗	f∗∗	VERB
ejpam-4941	314	4	i	i	PROPN
ejpam-4941	314	5	⟩	⟩	PROPN
ejpam-4941	314	6	⟨f∗∗	⟨f∗∗	X
ejpam-4941	315	1	k	k	X
ejpam-4941	315	2	,	,	PUNCT
ejpam-4941	315	3	f∗∗	f∗∗	PROPN
ejpam-4941	315	4	k	k	PROPN
ejpam-4941	315	5	⟩	⟩	PROPN
ejpam-4941	315	6	e∗∗k	e∗∗k	PROPN
ejpam-4941	315	7	,	,	PUNCT
ejpam-4941	315	8	k	k	PROPN
ejpam-4941	315	9	=	=	SYM
ejpam-4941	315	10	2	2	NUM
ejpam-4941	315	11	,	,	PUNCT
ejpam-4941	315	12	...	...	PUNCT
ejpam-4941	315	13	,	,	PUNCT
ejpam-4941	315	14	r	r	NOUN
ejpam-4941	315	15	−	−	PROPN
ejpam-4941	315	16	1	1	NUM
ejpam-4941	315	17	and	and	CCONJ
ejpam-4941	315	18	which	which	PRON
ejpam-4941	315	19	also	also	ADV
ejpam-4941	315	20	gives	give	VERB
ejpam-4941	315	21	in	in	ADP
ejpam-4941	315	22	the	the	DET
ejpam-4941	315	23	end	end	NOUN
ejpam-4941	316	1	that	that	SCONJ
ejpam-4941	316	2	,	,	PUNCT
ejpam-4941	316	3	fi	fi	NOUN
ejpam-4941	316	4	∈	∈	PROPN
ejpam-4941	316	5	span(f∗∗	span(f∗∗	ADJ
ejpam-4941	316	6	1	1	NUM
ejpam-4941	316	7	,	,	PUNCT
ejpam-4941	316	8	...	...	PUNCT
ejpam-4941	316	9	,	,	PUNCT
ejpam-4941	316	10	f	f	PROPN
ejpam-4941	316	11	∗∗(k−1	∗∗(k−1	X
ejpam-4941	316	12	)	)	PUNCT
ejpam-4941	316	13	i−1	i−1	PROPN
ejpam-4941	316	14	)	)	PUNCT
ejpam-4941	316	15	⊥	⊥	PROPN
ejpam-4941	316	16	⊕	⊕	PROPN
ejpam-4941	316	17	span(f∗∗	span(f∗∗	ADJ
ejpam-4941	316	18	1	1	NUM
ejpam-4941	316	19	,	,	PUNCT
ejpam-4941	316	20	...	...	PUNCT
ejpam-4941	316	21	,	,	PUNCT
ejpam-4941	316	22	f∗∗	f∗∗	PROPN
ejpam-4941	316	23	i−1(k	i−1(k	VERB
ejpam-4941	316	24	−	−	PROPN
ejpam-4941	316	25	1	1	NUM
ejpam-4941	316	26	)	)	PUNCT
ejpam-4941	316	27	)	)	PUNCT
ejpam-4941	316	28	.	.	PUNCT
ejpam-4941	317	1	from	from	ADP
ejpam-4941	317	2	another	another	DET
ejpam-4941	317	3	side	side	NOUN
ejpam-4941	317	4	,	,	PUNCT
ejpam-4941	317	5	we	we	PRON
ejpam-4941	317	6	can	can	AUX
ejpam-4941	317	7	say	say	VERB
ejpam-4941	317	8	that	that	PRON
ejpam-4941	317	9	⟨fi	⟨fi	PROPN
ejpam-4941	317	10	,	,	PUNCT
ejpam-4941	317	11	f∗∗	f∗∗	PROPN
ejpam-4941	317	12	k−1⟩	k−1⟩	PROPN
ejpam-4941	317	13	⟨f∗∗	⟨f∗∗	ADP
ejpam-4941	317	14	k−1	k−1	PROPN
ejpam-4941	317	15	,	,	PUNCT
ejpam-4941	317	16	f	f	PROPN
ejpam-4941	318	1	∗∗	∗∗	X
ejpam-4941	319	1	k−1⟩	k−1⟩	PRON
ejpam-4941	319	2	f∗∗	f∗∗	PROPN
ejpam-4941	319	3	k−1	k−1	PROPN
ejpam-4941	319	4	+	+	CCONJ
ejpam-4941	319	5	⟨f∗∗(k−1	⟨f∗∗(k−1	X
ejpam-4941	319	6	)	)	PUNCT
ejpam-4941	320	1	i	i	PRON
ejpam-4941	320	2	,	,	PUNCT
ejpam-4941	320	3	f∗∗	f∗∗	VERB
ejpam-4941	320	4	i	i	PROPN
ejpam-4941	320	5	⟩	⟩	PROPN
ejpam-4941	320	6	⟨f∗∗	⟨f∗∗	X
ejpam-4941	321	1	k	k	X
ejpam-4941	321	2	,	,	PUNCT
ejpam-4941	321	3	f∗∗	f∗∗	PROPN
ejpam-4941	321	4	k	k	PROPN
ejpam-4941	321	5	⟩	⟩	PROPN
ejpam-4941	321	6	e∗∗k	e∗∗k	PROPN
ejpam-4941	321	7	and	and	CCONJ
ejpam-4941	321	8	⟨ei	⟨ei	PROPN
ejpam-4941	321	9	,	,	PUNCT
ejpam-4941	321	10	e∗∗k−1⟩	e∗∗k−1⟩	PROPN
ejpam-4941	321	11	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	321	12	,	,	PUNCT
ejpam-4941	321	13	e	e	X
ejpam-4941	321	14	∗∗	∗∗	X
ejpam-4941	321	15	k−1⟩	k−1⟩	PROPN
ejpam-4941	321	16	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	321	17	+	+	CCONJ
ejpam-4941	321	18	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	321	19	)	)	PUNCT
ejpam-4941	321	20	i	i	PRON
ejpam-4941	321	21	,	,	PUNCT
ejpam-4941	321	22	e∗∗i	e∗∗i	PROPN
ejpam-4941	321	23	⟩	⟩	PROPN
ejpam-4941	321	24	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	321	25	,	,	PUNCT
ejpam-4941	321	26	e∗∗k	e∗∗k	PROPN
ejpam-4941	321	27	⟩	⟩	PROPN
ejpam-4941	321	28	e∗∗k	e∗∗k	PROPN
ejpam-4941	321	29	are	be	AUX
ejpam-4941	321	30	in	in	ADP
ejpam-4941	321	31	span(f∗∗	span(f∗∗	ADJ
ejpam-4941	321	32	1	1	NUM
ejpam-4941	321	33	,	,	PUNCT
ejpam-4941	321	34	...	...	PUNCT
ejpam-4941	321	35	,	,	PUNCT
ejpam-4941	321	36	f	f	PROPN
ejpam-4941	321	37	∗∗(k−1	∗∗(k−1	PRON
ejpam-4941	321	38	)	)	PUNCT
ejpam-4941	321	39	i−1	i−1	PROPN
ejpam-4941	321	40	)	)	PUNCT
ejpam-4941	321	41	and	and	CCONJ
ejpam-4941	321	42	span(e∗∗1	span(e∗∗1	ADJ
ejpam-4941	321	43	,	,	PUNCT
ejpam-4941	321	44	...	...	PUNCT
ejpam-4941	321	45	,	,	PUNCT
ejpam-4941	321	46	e	e	NOUN
ejpam-4941	321	47	∗∗(k−1	∗∗(k−1	X
ejpam-4941	321	48	)	)	PUNCT
ejpam-4941	321	49	i−1	i−1	PROPN
ejpam-4941	321	50	)	)	PUNCT
ejpam-4941	321	51	respectively	respectively	ADV
ejpam-4941	321	52	,	,	PUNCT
ejpam-4941	321	53	then	then	ADV
ejpam-4941	321	54	again	again	ADV
ejpam-4941	321	55	,	,	PUNCT
ejpam-4941	321	56	by	by	ADP
ejpam-4941	321	57	theorem	theorem	NOUN
ejpam-4941	321	58	1	1	NUM
ejpam-4941	321	59	,	,	PUNCT
ejpam-4941	321	60	it	it	PRON
ejpam-4941	321	61	becomes	become	VERB
ejpam-4941	321	62	the	the	DET
ejpam-4941	321	63	same	same	ADJ
ejpam-4941	321	64	as	as	ADP
ejpam-4941	321	65	saying	say	VERB
ejpam-4941	321	66	they	they	PRON
ejpam-4941	321	67	are	be	AUX
ejpam-4941	321	68	in	in	ADP
ejpam-4941	321	69	span(f1	span(f1	NOUN
ejpam-4941	321	70	,	,	PUNCT
ejpam-4941	321	71	...	...	PUNCT
ejpam-4941	321	72	,	,	PUNCT
ejpam-4941	321	73	fi−1	fi−1	PROPN
ejpam-4941	321	74	)	)	PUNCT
ejpam-4941	321	75	and	and	CCONJ
ejpam-4941	321	76	span(e1	span(e1	NOUN
ejpam-4941	321	77	,	,	PUNCT
ejpam-4941	321	78	...	...	PUNCT
ejpam-4941	321	79	,	,	PUNCT
ejpam-4941	321	80	ei−1	ei−1	PROPN
ejpam-4941	321	81	)	)	PUNCT
ejpam-4941	321	82	respectively	respectively	ADV
ejpam-4941	321	83	and	and	CCONJ
ejpam-4941	321	84	which	which	PRON
ejpam-4941	321	85	born	bear	VERB
ejpam-4941	321	86	in	in	ADP
ejpam-4941	321	87	turn	turn	NOUN
ejpam-4941	321	88	can	can	AUX
ejpam-4941	321	89	be	be	AUX
ejpam-4941	321	90	reduced	reduce	VERB
ejpam-4941	321	91	to	to	PART
ejpam-4941	321	92	span(e1	span(e1	VERB
ejpam-4941	321	93	,	,	PUNCT
ejpam-4941	321	94	...	...	PUNCT
ejpam-4941	321	95	,	,	PUNCT
ejpam-4941	321	96	ei−1	ei−1	PROPN
ejpam-4941	321	97	)	)	PUNCT
ejpam-4941	321	98	because	because	SCONJ
ejpam-4941	321	99	we	we	PRON
ejpam-4941	321	100	have	have	VERB
ejpam-4941	321	101	fi	fi	NOUN
ejpam-4941	321	102	=	=	SYM
ejpam-4941	321	103	ei	ei	PROPN
ejpam-4941	321	104	.	.	PROPN
ejpam-4941	321	105	from	from	ADP
ejpam-4941	321	106	the	the	DET
ejpam-4941	321	107	formulation	formulation	NOUN
ejpam-4941	321	108	of	of	ADP
ejpam-4941	321	109	fi	fi	NOUN
ejpam-4941	321	110	and	and	CCONJ
ejpam-4941	321	111	ei	ei	NOUN
ejpam-4941	321	112	,	,	PUNCT
ejpam-4941	321	113	we	we	PRON
ejpam-4941	321	114	can	can	AUX
ejpam-4941	321	115	now	now	ADV
ejpam-4941	321	116	deduce	deduce	VERB
ejpam-4941	321	117	directly	directly	ADV
ejpam-4941	321	118	that	that	SCONJ
ejpam-4941	321	119	f∗	f∗	VERB
ejpam-4941	321	120	i	i	PRON
ejpam-4941	321	121	and	and	CCONJ
ejpam-4941	321	122	e∗i	e∗i	NUM
ejpam-4941	321	123	are	be	AUX
ejpam-4941	321	124	both	both	PRON
ejpam-4941	321	125	in	in	ADP
ejpam-4941	321	126	span(e1	span(e1	NOUN
ejpam-4941	321	127	,	,	PUNCT
ejpam-4941	321	128	...	...	PUNCT
ejpam-4941	321	129	,	,	PUNCT
ejpam-4941	321	130	ei−1	ei−1	PROPN
ejpam-4941	321	131	)	)	PUNCT
ejpam-4941	321	132	⊥	⊥	PROPN
ejpam-4941	321	133	and	and	CCONJ
ejpam-4941	321	134	that	that	SCONJ
ejpam-4941	321	135	they	they	PRON
ejpam-4941	321	136	are	be	AUX
ejpam-4941	321	137	even	even	ADV
ejpam-4941	321	138	equal	equal	ADJ
ejpam-4941	321	139	.	.	PUNCT
ejpam-4941	322	1	–	–	PUNCT
ejpam-4941	322	2	as	as	ADP
ejpam-4941	322	3	for	for	ADP
ejpam-4941	322	4	the	the	DET
ejpam-4941	322	5	gs	gs	PROPN
ejpam-4941	322	6	process	process	NOUN
ejpam-4941	322	7	,	,	PUNCT
ejpam-4941	322	8	and	and	CCONJ
ejpam-4941	322	9	considering	consider	VERB
ejpam-4941	322	10	the	the	DET
ejpam-4941	322	11	same	same	ADJ
ejpam-4941	322	12	introductory	introductory	ADJ
ejpam-4941	322	13	result	result	NOUN
ejpam-4941	322	14	in	in	ADP
ejpam-4941	322	15	the	the	DET
ejpam-4941	322	16	previous	previous	ADJ
ejpam-4941	322	17	case	case	NOUN
ejpam-4941	322	18	,	,	PUNCT
ejpam-4941	322	19	we	we	PRON
ejpam-4941	322	20	choose	choose	VERB
ejpam-4941	322	21	now	now	ADV
ejpam-4941	322	22	to	to	PART
ejpam-4941	322	23	proceed	proceed	VERB
ejpam-4941	322	24	otherwise	otherwise	ADV
ejpam-4941	322	25	by	by	ADP
ejpam-4941	322	26	saying	say	VERB
ejpam-4941	322	27	that	that	SCONJ
ejpam-4941	322	28	since	since	SCONJ
ejpam-4941	322	29	we	we	PRON
ejpam-4941	322	30	have	have	VERB
ejpam-4941	322	31	,	,	PUNCT
ejpam-4941	322	32	fi	fi	NOUN
ejpam-4941	322	33	=	=	SYM
ejpam-4941	322	34	f∗	f∗	NOUN
ejpam-4941	323	1	i	i	NOUN
ejpam-4941	323	2	+	+	PROPN
ejpam-4941	323	3	i−1∑	i−1∑	PROPN
ejpam-4941	323	4	k=1	k=1	PART
ejpam-4941	323	5	⟨fi	⟨fi	PROPN
ejpam-4941	323	6	,	,	PUNCT
ejpam-4941	323	7	f∗	f∗	NOUN
ejpam-4941	323	8	k	k	PROPN
ejpam-4941	323	9	⟩	⟩	PROPN
ejpam-4941	323	10	⟨f∗	⟨f∗	PROPN
ejpam-4941	324	1	k	k	PROPN
ejpam-4941	324	2	,	,	PUNCT
ejpam-4941	324	3	f	f	PROPN
ejpam-4941	324	4	∗	∗	X
ejpam-4941	324	5	k	k	PROPN
ejpam-4941	324	6	⟩	⟩	PROPN
ejpam-4941	324	7	f∗	f∗	NOUN
ejpam-4941	324	8	i	i	PRON
ejpam-4941	324	9	and	and	CCONJ
ejpam-4941	324	10	ei	ei	X
ejpam-4941	324	11	=	=	PUNCT
ejpam-4941	324	12	e∗i	e∗i	PUNCT
ejpam-4941	324	13	+	+	CCONJ
ejpam-4941	324	14	i−1∑	i−1∑	NOUN
ejpam-4941	324	15	k=1	k=1	PROPN
ejpam-4941	324	16	⟨ei	⟨ei	X
ejpam-4941	324	17	,	,	PUNCT
ejpam-4941	324	18	e∗k⟩	e∗k⟩	PROPN
ejpam-4941	324	19	⟨e∗k	⟨e∗k	PROPN
ejpam-4941	324	20	,	,	PUNCT
ejpam-4941	324	21	e∗k⟩	e∗k⟩	PROPN
ejpam-4941	324	22	e∗k	e∗k	PUNCT
ejpam-4941	324	23	.	.	PUNCT
ejpam-4941	325	1	then	then	ADV
ejpam-4941	325	2	,	,	PUNCT
ejpam-4941	325	3	the	the	DET
ejpam-4941	325	4	fact	fact	NOUN
ejpam-4941	325	5	that	that	SCONJ
ejpam-4941	325	6	we	we	PRON
ejpam-4941	325	7	have	have	AUX
ejpam-4941	325	8	fi	fi	NOUN
ejpam-4941	325	9	−	−	NOUN
ejpam-4941	325	10	ei	ei	NOUN
ejpam-4941	325	11	=	=	SYM
ejpam-4941	325	12	0	0	NUM
ejpam-4941	325	13	,	,	PUNCT
ejpam-4941	325	14	it	it	PRON
ejpam-4941	325	15	gives	give	VERB
ejpam-4941	325	16	us	we	PRON
ejpam-4941	325	17	,	,	PUNCT
ejpam-4941	325	18	f∗	f∗	NOUN
ejpam-4941	325	19	i	i	PRON
ejpam-4941	325	20	−	−	VERB
ejpam-4941	326	1	e∗i	e∗i	NUM
ejpam-4941	326	2	=	=	PUNCT
ejpam-4941	326	3	−	−	PROPN
ejpam-4941	326	4	i−1∑	i−1∑	NUM
ejpam-4941	326	5	k=1	k=1	X
ejpam-4941	326	6	⟨fi	⟨fi	PROPN
ejpam-4941	326	7	,	,	PUNCT
ejpam-4941	326	8	f∗	f∗	NOUN
ejpam-4941	326	9	k	k	PROPN
ejpam-4941	326	10	⟩	⟩	PROPN
ejpam-4941	326	11	⟨f∗	⟨f∗	PROPN
ejpam-4941	327	1	k	k	PROPN
ejpam-4941	327	2	,	,	PUNCT
ejpam-4941	327	3	f	f	PROPN
ejpam-4941	327	4	∗	∗	X
ejpam-4941	327	5	k	k	PROPN
ejpam-4941	327	6	⟩	⟩	PROPN
ejpam-4941	327	7	f∗	f∗	NOUN
ejpam-4941	327	8	i	i	PRON
ejpam-4941	328	1	+	+	PROPN
ejpam-4941	328	2	i−1∑	i−1∑	NUM
ejpam-4941	328	3	k=1	k=1	PROPN
ejpam-4941	328	4	⟨ei	⟨ei	X
ejpam-4941	328	5	,	,	PUNCT
ejpam-4941	328	6	e∗k⟩	e∗k⟩	AUX
ejpam-4941	328	7	⟨e∗i	⟨e∗i	INTJ
ejpam-4941	328	8	,	,	PUNCT
ejpam-4941	328	9	e∗k⟩	e∗k⟩	AUX
ejpam-4941	328	10	e∗k	e∗k	PROPN
ejpam-4941	328	11	.	.	PUNCT
ejpam-4941	329	1	with	with	ADP
ejpam-4941	329	2	−	−	PROPN
ejpam-4941	329	3	i−1∑	i−1∑	PROPN
ejpam-4941	329	4	k=1	k=1	PROPN
ejpam-4941	329	5	⟨fi	⟨fi	PROPN
ejpam-4941	329	6	,	,	PUNCT
ejpam-4941	329	7	f∗	f∗	NOUN
ejpam-4941	329	8	k	k	PROPN
ejpam-4941	329	9	⟩	⟩	PROPN
ejpam-4941	329	10	⟨f∗	⟨f∗	PROPN
ejpam-4941	330	1	k	k	PROPN
ejpam-4941	330	2	,	,	PUNCT
ejpam-4941	330	3	f	f	PROPN
ejpam-4941	330	4	∗	∗	X
ejpam-4941	330	5	k	k	PROPN
ejpam-4941	330	6	⟩	⟩	PROPN
ejpam-4941	330	7	f∗	f∗	NOUN
ejpam-4941	330	8	i	i	PRON
ejpam-4941	331	1	+	+	PROPN
ejpam-4941	331	2	i−1∑	i−1∑	NUM
ejpam-4941	331	3	k=1	k=1	PROPN
ejpam-4941	331	4	⟨ei	⟨ei	X
ejpam-4941	331	5	,	,	PUNCT
ejpam-4941	331	6	e∗k⟩	e∗k⟩	PROPN
ejpam-4941	331	7	⟨e∗k	⟨e∗k	PROPN
ejpam-4941	331	8	,	,	PUNCT
ejpam-4941	331	9	e∗k⟩	e∗k⟩	AUX
ejpam-4941	331	10	e∗k	e∗k	PUNCT
ejpam-4941	331	11	∈	∈	PROPN
ejpam-4941	331	12	vect(e1	vect(e1	NOUN
ejpam-4941	331	13	,	,	PUNCT
ejpam-4941	331	14	...	...	PUNCT
ejpam-4941	331	15	,	,	PUNCT
ejpam-4941	331	16	ei−1	ei−1	PROPN
ejpam-4941	331	17	)	)	PUNCT
ejpam-4941	331	18	,	,	PUNCT
ejpam-4941	331	19	then	then	ADV
ejpam-4941	331	20	,	,	PUNCT
ejpam-4941	331	21	we	we	PRON
ejpam-4941	331	22	have	have	VERB
ejpam-4941	331	23	,	,	PUNCT
ejpam-4941	331	24	f∗	f∗	NOUN
ejpam-4941	331	25	i	i	PRON
ejpam-4941	331	26	−	−	VERB
ejpam-4941	332	1	e∗i	e∗i	NUM
ejpam-4941	332	2	∈	∈	PROPN
ejpam-4941	332	3	vect(e1	vect(e1	NOUN
ejpam-4941	332	4	,	,	PUNCT
ejpam-4941	332	5	...	...	PUNCT
ejpam-4941	332	6	,	,	PUNCT
ejpam-4941	332	7	ei−1	ei−1	PROPN
ejpam-4941	332	8	)	)	PUNCT
ejpam-4941	332	9	⊥	⊥	PROPN
ejpam-4941	332	10	,	,	PUNCT
ejpam-4941	332	11	and	and	CCONJ
ejpam-4941	332	12	which	which	PRON
ejpam-4941	332	13	finally	finally	ADV
ejpam-4941	332	14	gives	give	VERB
ejpam-4941	332	15	f∗	f∗	NOUN
ejpam-4941	332	16	i	i	NOUN
ejpam-4941	332	17	=	=	PUNCT
ejpam-4941	332	18	e∗i	e∗i	NUM
ejpam-4941	332	19	.	.	PUNCT
ejpam-4941	333	1	as	as	ADP
ejpam-4941	333	2	an	an	DET
ejpam-4941	333	3	application	application	NOUN
ejpam-4941	333	4	of	of	ADP
ejpam-4941	333	5	the	the	DET
ejpam-4941	333	6	results	result	NOUN
ejpam-4941	333	7	stated	state	VERB
ejpam-4941	333	8	in	in	ADP
ejpam-4941	333	9	theorems	theorem	NOUN
ejpam-4941	333	10	1	1	NUM
ejpam-4941	333	11	and	and	CCONJ
ejpam-4941	333	12	2	2	NUM
ejpam-4941	333	13	,	,	PUNCT
ejpam-4941	333	14	we	we	PRON
ejpam-4941	333	15	show	show	VERB
ejpam-4941	333	16	in	in	ADP
ejpam-4941	333	17	the	the	DET
ejpam-4941	333	18	next	next	ADJ
ejpam-4941	333	19	section	section	NOUN
ejpam-4941	333	20	,	,	PUNCT
ejpam-4941	333	21	how	how	SCONJ
ejpam-4941	333	22	the	the	DET
ejpam-4941	333	23	properties	property	NOUN
ejpam-4941	333	24	just	just	ADV
ejpam-4941	333	25	proven	prove	VERB
ejpam-4941	333	26	above	above	ADV
ejpam-4941	333	27	,	,	PUNCT
ejpam-4941	333	28	are	be	AUX
ejpam-4941	333	29	incorporated	incorporate	VERB
ejpam-4941	333	30	in	in	ADP
ejpam-4941	333	31	the	the	DET
ejpam-4941	333	32	following	follow	VERB
ejpam-4941	333	33	algorithm	algorithm	NOUN
ejpam-4941	333	34	and	and	CCONJ
ejpam-4941	333	35	that	that	SCONJ
ejpam-4941	333	36	we	we	PRON
ejpam-4941	333	37	devise	devise	VERB
ejpam-4941	333	38	to	to	ADP
ejpam-4941	333	39	serving	serve	VERB
ejpam-4941	333	40	the	the	DET
ejpam-4941	333	41	crystal	crystal	NOUN
ejpam-4941	333	42	lattice	lattice	PROPN
ejpam-4941	333	43	reduction	reduction	NOUN
ejpam-4941	333	44	.	.	PUNCT
ejpam-4941	334	1	s.	s.	PROPN
ejpam-4941	334	2	abdelalim	abdelalim	PROPN
ejpam-4941	334	3	,	,	PUNCT
ejpam-4941	334	4	i.	i.	PROPN
ejpam-4941	334	5	elmouki	elmouki	PROPN
ejpam-4941	334	6	/	/	SYM
ejpam-4941	334	7	eur	eur	PROPN
ejpam-4941	334	8	.	.	PUNCT
ejpam-4941	335	1	j.	j.	PROPN
ejpam-4941	335	2	pure	pure	PROPN
ejpam-4941	335	3	appl	appl	PROPN
ejpam-4941	335	4	.	.	PROPN
ejpam-4941	335	5	math	math	PROPN
ejpam-4941	335	6	,	,	PUNCT
ejpam-4941	335	7	16	16	NUM
ejpam-4941	335	8	(	(	PUNCT
ejpam-4941	335	9	4	4	NUM
ejpam-4941	335	10	)	)	PUNCT
ejpam-4941	335	11	(	(	PUNCT
ejpam-4941	335	12	2023	2023	NUM
ejpam-4941	335	13	)	)	PUNCT
ejpam-4941	335	14	,	,	PUNCT
ejpam-4941	335	15	2662	2662	NUM
ejpam-4941	335	16	-	-	SYM
ejpam-4941	335	17	2692	2692	NUM
ejpam-4941	335	18	2680	2680	NUM
ejpam-4941	335	19	3	3	NUM
ejpam-4941	335	20	.	.	PUNCT
ejpam-4941	336	1	application	application	NOUN
ejpam-4941	336	2	for	for	ADP
ejpam-4941	336	3	bravais	bravais	NOUN
ejpam-4941	336	4	cell	cell	NOUN
ejpam-4941	336	5	reduction	reduction	NOUN
ejpam-4941	336	6	3.1	3.1	NUM
ejpam-4941	336	7	.	.	PUNCT
ejpam-4941	337	1	ae	ae	PROPN
ejpam-4941	337	2	algorithm	algorithm	PROPN
ejpam-4941	337	3	from	from	ADP
ejpam-4941	337	4	theory	theory	NOUN
ejpam-4941	337	5	in	in	ADP
ejpam-4941	337	6	this	this	DET
ejpam-4941	337	7	section	section	NOUN
ejpam-4941	337	8	,	,	PUNCT
ejpam-4941	337	9	we	we	PRON
ejpam-4941	337	10	will	will	AUX
ejpam-4941	337	11	explain	explain	VERB
ejpam-4941	337	12	how	how	SCONJ
ejpam-4941	337	13	we	we	PRON
ejpam-4941	337	14	can	can	AUX
ejpam-4941	337	15	implement	implement	VERB
ejpam-4941	337	16	our	our	PRON
ejpam-4941	337	17	algorithm	algorithm	NOUN
ejpam-4941	337	18	using	use	VERB
ejpam-4941	337	19	the	the	DET
ejpam-4941	337	20	results	result	NOUN
ejpam-4941	337	21	of	of	ADP
ejpam-4941	337	22	theorem	theorem	NOUN
ejpam-4941	337	23	2	2	NUM
ejpam-4941	337	24	.	.	PUNCT
ejpam-4941	338	1	the	the	DET
ejpam-4941	338	2	steps	step	NOUN
ejpam-4941	338	3	of	of	ADP
ejpam-4941	338	4	the	the	DET
ejpam-4941	338	5	algorithm	algorithm	NOUN
ejpam-4941	338	6	that	that	PRON
ejpam-4941	338	7	we	we	PRON
ejpam-4941	338	8	will	will	AUX
ejpam-4941	338	9	explain	explain	VERB
ejpam-4941	338	10	in	in	ADP
ejpam-4941	338	11	details	detail	NOUN
ejpam-4941	338	12	hereafter	hereafter	ADV
ejpam-4941	338	13	are	be	AUX
ejpam-4941	338	14	defined	define	VERB
ejpam-4941	338	15	by	by	ADP
ejpam-4941	338	16	the	the	DET
ejpam-4941	338	17	following	follow	VERB
ejpam-4941	338	18	points	point	NOUN
ejpam-4941	338	19	•	•	ADP
ejpam-4941	338	20	initial	initial	ADJ
ejpam-4941	338	21	step	step	NOUN
ejpam-4941	338	22	and	and	CCONJ
ejpam-4941	338	23	objective	objective	NOUN
ejpam-4941	338	24	,	,	PUNCT
ejpam-4941	338	25	with	with	ADP
ejpam-4941	338	26	the	the	DET
ejpam-4941	338	27	three	three	NUM
ejpam-4941	338	28	subpoints	subpoint	NOUN
ejpam-4941	338	29	,	,	PUNCT
ejpam-4941	338	30	–	–	PUNCT
ejpam-4941	338	31	basis	basis	NOUN
ejpam-4941	338	32	vectors	vector	NOUN
ejpam-4941	338	33	input	input	VERB
ejpam-4941	338	34	,	,	PUNCT
ejpam-4941	338	35	–	–	PUNCT
ejpam-4941	338	36	basis	basis	NOUN
ejpam-4941	338	37	reduction	reduction	NOUN
ejpam-4941	338	38	input	input	NOUN
ejpam-4941	338	39	,	,	PUNCT
ejpam-4941	338	40	with	with	ADP
ejpam-4941	338	41	introduction	introduction	NOUN
ejpam-4941	338	42	of	of	ADP
ejpam-4941	338	43	the	the	DET
ejpam-4941	338	44	modified	modify	VERB
ejpam-4941	338	45	size	size	NOUN
ejpam-4941	338	46	reduction	reduction	NOUN
ejpam-4941	338	47	as	as	ADV
ejpam-4941	338	48	long	long	ADV
ejpam-4941	338	49	as	as	SCONJ
ejpam-4941	338	50	the	the	DET
ejpam-4941	338	51	modified	modify	VERB
ejpam-4941	338	52	lovász	lovász	NOUN
ejpam-4941	338	53	for	for	ADP
ejpam-4941	338	54	the	the	DET
ejpam-4941	338	55	mgs	mgs	NOUN
ejpam-4941	338	56	case	case	NOUN
ejpam-4941	338	57	,	,	PUNCT
ejpam-4941	338	58	–	–	PUNCT
ejpam-4941	338	59	basis	basis	NOUN
ejpam-4941	338	60	vectors	vector	NOUN
ejpam-4941	338	61	output	output	VERB
ejpam-4941	338	62	.	.	PUNCT
ejpam-4941	339	1	•	•	NUM
ejpam-4941	339	2	intermediary	intermediary	ADJ
ejpam-4941	339	3	step	step	NOUN
ejpam-4941	339	4	,	,	PUNCT
ejpam-4941	339	5	•	•	NUM
ejpam-4941	339	6	vectors	vector	NOUN
ejpam-4941	339	7	exchange	exchange	NOUN
ejpam-4941	339	8	theorem	theorem	VERB
ejpam-4941	339	9	step	step	NOUN
ejpam-4941	339	10	.	.	PUNCT
ejpam-4941	340	1	in	in	ADP
ejpam-4941	340	2	fact	fact	NOUN
ejpam-4941	340	3	,	,	PUNCT
ejpam-4941	340	4	the	the	DET
ejpam-4941	340	5	new	new	ADJ
ejpam-4941	340	6	conditions	condition	NOUN
ejpam-4941	340	7	on	on	ADP
ejpam-4941	340	8	the	the	DET
ejpam-4941	340	9	lattice	lattice	NOUN
ejpam-4941	340	10	reduction	reduction	NOUN
ejpam-4941	340	11	have	have	AUX
ejpam-4941	340	12	given	give	VERB
ejpam-4941	340	13	us	we	PRON
ejpam-4941	340	14	the	the	DET
ejpam-4941	340	15	idea	idea	NOUN
ejpam-4941	340	16	to	to	PART
ejpam-4941	340	17	call	call	VERB
ejpam-4941	340	18	our	our	PRON
ejpam-4941	340	19	procedure	procedure	NOUN
ejpam-4941	340	20	by	by	ADP
ejpam-4941	340	21	the	the	DET
ejpam-4941	340	22	name	name	NOUN
ejpam-4941	340	23	of	of	ADP
ejpam-4941	340	24	ae	ae	PROPN
ejpam-4941	340	25	algorithm	algorithm	PROPN
ejpam-4941	340	26	where	where	SCONJ
ejpam-4941	340	27	ae	ae	PROPN
ejpam-4941	340	28	referring	refer	VERB
ejpam-4941	340	29	to	to	ADP
ejpam-4941	340	30	our	our	PRON
ejpam-4941	340	31	names	name	NOUN
ejpam-4941	340	32	since	since	SCONJ
ejpam-4941	340	33	to	to	ADP
ejpam-4941	340	34	the	the	DET
ejpam-4941	340	35	best	good	ADJ
ejpam-4941	340	36	of	of	ADP
ejpam-4941	340	37	our	our	PRON
ejpam-4941	340	38	knowledge	knowledge	NOUN
ejpam-4941	340	39	,	,	PUNCT
ejpam-4941	340	40	it	it	PRON
ejpam-4941	340	41	is	be	AUX
ejpam-4941	340	42	the	the	DET
ejpam-4941	340	43	first	first	ADJ
ejpam-4941	340	44	time	time	NOUN
ejpam-4941	340	45	a	a	DET
ejpam-4941	340	46	theorem	theorem	VERB
ejpam-4941	340	47	-	-	PUNCT
ejpam-4941	340	48	based	base	VERB
ejpam-4941	340	49	mathematical	mathematical	ADJ
ejpam-4941	340	50	algorithm	algorithm	NOUN
ejpam-4941	340	51	is	be	AUX
ejpam-4941	340	52	designed	design	VERB
ejpam-4941	340	53	for	for	ADP
ejpam-4941	340	54	the	the	DET
ejpam-4941	340	55	crystal	crystal	NOUN
ejpam-4941	340	56	reduction	reduction	NOUN
ejpam-4941	340	57	with	with	ADP
ejpam-4941	340	58	incorporation	incorporation	NOUN
ejpam-4941	340	59	of	of	ADP
ejpam-4941	340	60	the	the	DET
ejpam-4941	340	61	more	more	ADV
ejpam-4941	340	62	convincing	convincing	ADJ
ejpam-4941	340	63	mgs	mgs	NOUN
ejpam-4941	340	64	process	process	NOUN
ejpam-4941	340	65	,	,	PUNCT
ejpam-4941	340	66	while	while	SCONJ
ejpam-4941	340	67	suggesting	suggest	VERB
ejpam-4941	340	68	the	the	DET
ejpam-4941	340	69	two	two	NUM
ejpam-4941	340	70	new	new	ADJ
ejpam-4941	340	71	conditions	condition	NOUN
ejpam-4941	340	72	on	on	ADP
ejpam-4941	340	73	size	size	NOUN
ejpam-4941	340	74	reduction	reduction	NOUN
ejpam-4941	340	75	and	and	CCONJ
ejpam-4941	340	76	quasi	quasi	NOUN
ejpam-4941	340	77	-	-	NOUN
ejpam-4941	340	78	orthogonality	orthogonality	NOUN
ejpam-4941	340	79	.	.	PUNCT
ejpam-4941	341	1	one	one	NUM
ejpam-4941	341	2	of	of	ADP
ejpam-4941	341	3	the	the	DET
ejpam-4941	341	4	application	application	NOUN
ejpam-4941	341	5	of	of	ADP
ejpam-4941	341	6	vectors	vector	NOUN
ejpam-4941	341	7	swapping	swap	VERB
ejpam-4941	341	8	,	,	PUNCT
ejpam-4941	341	9	is	be	AUX
ejpam-4941	341	10	its	its	PRON
ejpam-4941	341	11	introduction	introduction	NOUN
ejpam-4941	341	12	in	in	ADP
ejpam-4941	341	13	algorithms	algorithm	NOUN
ejpam-4941	341	14	that	that	PRON
ejpam-4941	341	15	are	be	AUX
ejpam-4941	341	16	designed	design	VERB
ejpam-4941	341	17	for	for	ADP
ejpam-4941	341	18	the	the	DET
ejpam-4941	341	19	reduction	reduction	NOUN
ejpam-4941	341	20	of	of	ADP
ejpam-4941	341	21	lattice	lattice	NOUN
ejpam-4941	341	22	bases	basis	NOUN
ejpam-4941	341	23	.	.	PUNCT
ejpam-4941	342	1	we	we	PRON
ejpam-4941	342	2	try	try	VERB
ejpam-4941	342	3	in	in	ADP
ejpam-4941	342	4	this	this	DET
ejpam-4941	342	5	part	part	NOUN
ejpam-4941	342	6	to	to	PART
ejpam-4941	342	7	convert	convert	VERB
ejpam-4941	342	8	the	the	DET
ejpam-4941	342	9	logical	logical	ADJ
ejpam-4941	342	10	implementation	implementation	NOUN
ejpam-4941	342	11	of	of	ADP
ejpam-4941	342	12	vectors	vector	NOUN
ejpam-4941	342	13	swapping	swap	VERB
ejpam-4941	342	14	treated	treat	VERB
ejpam-4941	342	15	in	in	ADP
ejpam-4941	342	16	the	the	DET
ejpam-4941	342	17	vector	vector	NOUN
ejpam-4941	342	18	exchange	exchange	NOUN
ejpam-4941	342	19	theorem	theorem	VERB
ejpam-4941	342	20	as	as	ADP
ejpam-4941	342	21	an	an	DET
ejpam-4941	342	22	algorithmic	algorithmic	ADJ
ejpam-4941	342	23	process	process	NOUN
ejpam-4941	342	24	.	.	PUNCT
ejpam-4941	343	1	in	in	ADP
ejpam-4941	343	2	general	general	ADJ
ejpam-4941	343	3	,	,	PUNCT
ejpam-4941	343	4	we	we	PRON
ejpam-4941	343	5	define	define	VERB
ejpam-4941	343	6	the	the	DET
ejpam-4941	343	7	main	main	ADJ
ejpam-4941	343	8	goal	goal	NOUN
ejpam-4941	343	9	from	from	ADP
ejpam-4941	343	10	reducing	reduce	VERB
ejpam-4941	343	11	a	a	DET
ejpam-4941	343	12	bravais	bravais	NOUN
ejpam-4941	343	13	lattice	lattice	PROPN
ejpam-4941	343	14	basis	basis	NOUN
ejpam-4941	343	15	as	as	ADP
ejpam-4941	343	16	the	the	DET
ejpam-4941	343	17	process	process	NOUN
ejpam-4941	343	18	which	which	PRON
ejpam-4941	343	19	starts	start	VERB
ejpam-4941	343	20	from	from	ADP
ejpam-4941	343	21	this	this	DET
ejpam-4941	343	22	input	input	NOUN
ejpam-4941	343	23	in	in	ADP
ejpam-4941	343	24	order	order	NOUN
ejpam-4941	343	25	to	to	PART
ejpam-4941	343	26	obtain	obtain	VERB
ejpam-4941	343	27	this	this	DET
ejpam-4941	343	28	output	output	NOUN
ejpam-4941	343	29	initial	initial	ADJ
ejpam-4941	343	30	step	step	NOUN
ejpam-4941	343	31	and	and	CCONJ
ejpam-4941	343	32	objective	objective	ADJ
ejpam-4941	343	33	•	•	ADJ
ejpam-4941	343	34	basis	basis	NOUN
ejpam-4941	343	35	vectors	vector	NOUN
ejpam-4941	343	36	input	input	NOUN
ejpam-4941	343	37	:	:	PUNCT
ejpam-4941	343	38	choose	choose	VERB
ejpam-4941	343	39	a	a	DET
ejpam-4941	343	40	random	random	ADJ
ejpam-4941	343	41	first	first	ADJ
ejpam-4941	343	42	input	input	NOUN
ejpam-4941	343	43	basis	basis	NOUN
ejpam-4941	343	44	(	(	PUNCT
ejpam-4941	343	45	e1	e1	NOUN
ejpam-4941	343	46	,	,	PUNCT
ejpam-4941	343	47	...	...	PUNCT
ejpam-4941	343	48	en	en	X
ejpam-4941	343	49	)	)	PUNCT
ejpam-4941	343	50	of	of	ADP
ejpam-4941	343	51	a	a	DET
ejpam-4941	343	52	bravais	bravais	PROPN
ejpam-4941	343	53	lattice	lattice	PROPN
ejpam-4941	343	54	l.	l.	PROPN
ejpam-4941	343	55	•	•	NUM
ejpam-4941	343	56	basis	basis	NOUN
ejpam-4941	343	57	reduction	reduction	NOUN
ejpam-4941	343	58	input	input	NOUN
ejpam-4941	343	59	:	:	PUNCT
ejpam-4941	343	60	choose	choose	VERB
ejpam-4941	343	61	any	any	DET
ejpam-4941	343	62	real	real	ADJ
ejpam-4941	343	63	constant	constant	ADJ
ejpam-4941	343	64	by	by	ADP
ejpam-4941	343	65	which	which	DET
ejpam-4941	343	66	l	l	NOUN
ejpam-4941	343	67	basis	basis	NOUN
ejpam-4941	343	68	is	be	AUX
ejpam-4941	343	69	determined	determine	VERB
ejpam-4941	343	70	whether	whether	SCONJ
ejpam-4941	343	71	it	it	PRON
ejpam-4941	343	72	is	be	AUX
ejpam-4941	343	73	reduced	reduce	VERB
ejpam-4941	343	74	or	or	CCONJ
ejpam-4941	343	75	not	not	PART
ejpam-4941	343	76	in	in	ADP
ejpam-4941	343	77	the	the	DET
ejpam-4941	343	78	sense	sense	NOUN
ejpam-4941	343	79	of	of	ADP
ejpam-4941	343	80	’	'	PUNCT
ejpam-4941	343	81	quasi	quasi	ADJ
ejpam-4941	343	82	-	-	NOUN
ejpam-4941	343	83	orthogonality	orthogonality	NOUN
ejpam-4941	343	84	’	'	PUNCT
ejpam-4941	343	85	as	as	ADP
ejpam-4941	343	86	in	in	ADP
ejpam-4941	343	87	definition	definition	NOUN
ejpam-4941	343	88	2	2	NUM
ejpam-4941	343	89	and	and	CCONJ
ejpam-4941	343	90	which	which	PRON
ejpam-4941	343	91	could	could	AUX
ejpam-4941	343	92	serve	serve	VERB
ejpam-4941	343	93	as	as	ADP
ejpam-4941	343	94	an	an	DET
ejpam-4941	343	95	additional	additional	ADJ
ejpam-4941	343	96	condition	condition	NOUN
ejpam-4941	343	97	to	to	PART
ejpam-4941	343	98	combine	combine	VERB
ejpam-4941	343	99	with	with	ADP
ejpam-4941	343	100	the	the	DET
ejpam-4941	343	101	results	result	NOUN
ejpam-4941	343	102	of	of	ADP
ejpam-4941	343	103	theorem	theorem	NOUN
ejpam-4941	343	104	2	2	NUM
ejpam-4941	343	105	.	.	PUNCT
ejpam-4941	344	1	it	it	PRON
ejpam-4941	344	2	is	be	AUX
ejpam-4941	344	3	also	also	ADV
ejpam-4941	344	4	important	important	ADJ
ejpam-4941	344	5	to	to	PART
ejpam-4941	344	6	note	note	VERB
ejpam-4941	344	7	that	that	DET
ejpam-4941	344	8	reduction	reduction	NOUN
ejpam-4941	344	9	through	through	ADP
ejpam-4941	344	10	orthogonalization	orthogonalization	NOUN
ejpam-4941	344	11	alone	alone	ADV
ejpam-4941	344	12	,	,	PUNCT
ejpam-4941	344	13	is	be	AUX
ejpam-4941	344	14	mostly	mostly	ADV
ejpam-4941	344	15	used	use	VERB
ejpam-4941	344	16	as	as	ADP
ejpam-4941	344	17	an	an	DET
ejpam-4941	344	18	introductory	introductory	ADJ
ejpam-4941	344	19	step	step	NOUN
ejpam-4941	344	20	for	for	ADP
ejpam-4941	344	21	reduction	reduction	NOUN
ejpam-4941	344	22	in	in	ADP
ejpam-4941	344	23	such	such	ADJ
ejpam-4941	344	24	problems	problem	NOUN
ejpam-4941	344	25	in	in	ADP
ejpam-4941	344	26	the	the	DET
ejpam-4941	344	27	sense	sense	NOUN
ejpam-4941	344	28	of	of	ADP
ejpam-4941	344	29	’	'	PUNCT
ejpam-4941	344	30	size	size	NOUN
ejpam-4941	344	31	’	'	PUNCT
ejpam-4941	344	32	as	as	ADP
ejpam-4941	344	33	in	in	ADP
ejpam-4941	344	34	definition	definition	NOUN
ejpam-4941	344	35	1	1	NUM
ejpam-4941	344	36	in	in	ADP
ejpam-4941	344	37	below	below	ADV
ejpam-4941	344	38	,	,	PUNCT
ejpam-4941	344	39	thus	thus	ADV
ejpam-4941	344	40	,	,	PUNCT
ejpam-4941	344	41	it	it	PRON
ejpam-4941	344	42	is	be	AUX
ejpam-4941	344	43	very	very	ADV
ejpam-4941	344	44	recommended	recommended	ADJ
ejpam-4941	344	45	that	that	SCONJ
ejpam-4941	344	46	the	the	DET
ejpam-4941	344	47	computist	computist	NOUN
ejpam-4941	344	48	chooses	choose	VERB
ejpam-4941	344	49	two	two	NUM
ejpam-4941	344	50	constants	constant	NOUN
ejpam-4941	344	51	and	and	CCONJ
ejpam-4941	344	52	condition	condition	NOUN
ejpam-4941	344	53	for	for	ADP
ejpam-4941	344	54	i	i	PRON
ejpam-4941	344	55	=	=	NOUN
ejpam-4941	344	56	2	2	NUM
ejpam-4941	344	57	,	,	PUNCT
ejpam-4941	344	58	...	...	PUNCT
ejpam-4941	344	59	,	,	PUNCT
ejpam-4941	344	60	n	n	CCONJ
ejpam-4941	344	61	,	,	PUNCT
ejpam-4941	344	62	k	k	PROPN
ejpam-4941	344	63	=	=	SYM
ejpam-4941	344	64	2	2	NUM
ejpam-4941	344	65	,	,	PUNCT
ejpam-4941	344	66	...	...	PUNCT
ejpam-4941	344	67	,	,	PUNCT
ejpam-4941	344	68	i−	i−	PROPN
ejpam-4941	344	69	1	1	NUM
ejpam-4941	344	70	on	on	ADP
ejpam-4941	344	71	the	the	DET
ejpam-4941	344	72	two	two	NUM
ejpam-4941	344	73	quantities	quantity	NOUN
ejpam-4941	344	74	∣∣∣∣∣⟨f	∣∣∣∣∣⟨f	PROPN
ejpam-4941	344	75	∗∗(k−1	∗∗(k−1	NUM
ejpam-4941	344	76	)	)	PUNCT
ejpam-4941	345	1	i	i	PRON
ejpam-4941	345	2	,	,	PUNCT
ejpam-4941	345	3	f∗∗	f∗∗	PROPN
ejpam-4941	345	4	k	k	PROPN
ejpam-4941	345	5	⟩	⟩	PROPN
ejpam-4941	345	6	⟨f∗∗	⟨f∗∗	X
ejpam-4941	346	1	k	k	X
ejpam-4941	346	2	,	,	PUNCT
ejpam-4941	346	3	f∗∗	f∗∗	PROPN
ejpam-4941	346	4	k	k	PROPN
ejpam-4941	346	5	⟩	⟩	PROPN
ejpam-4941	346	6	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4941	346	7	for	for	ADP
ejpam-4941	346	8	the	the	DET
ejpam-4941	346	9	mgs	mgs	NOUN
ejpam-4941	346	10	case	case	NOUN
ejpam-4941	346	11	or	or	CCONJ
ejpam-4941	346	12	the	the	DET
ejpam-4941	346	13	quantity	quantity	NOUN
ejpam-4941	346	14	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-4941	346	15	⟨fi	⟨fi	NOUN
ejpam-4941	346	16	,	,	PUNCT
ejpam-4941	346	17	f∗	f∗	PROPN
ejpam-4941	346	18	j	j	PROPN
ejpam-4941	346	19	⟩	⟩	PROPN
ejpam-4941	346	20	⟨f∗	⟨f∗	PROPN
ejpam-4941	347	1	j	j	PROPN
ejpam-4941	347	2	,	,	PUNCT
ejpam-4941	347	3	f	f	PROPN
ejpam-4941	347	4	∗	∗	PROPN
ejpam-4941	347	5	j	j	PROPN
ejpam-4941	347	6	⟩	⟩	PROPN
ejpam-4941	347	7	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4941	347	8	when	when	SCONJ
ejpam-4941	347	9	it	it	PRON
ejpam-4941	347	10	is	be	AUX
ejpam-4941	347	11	about	about	ADP
ejpam-4941	347	12	the	the	DET
ejpam-4941	347	13	gs	gs	PROPN
ejpam-4941	347	14	case	case	NOUN
ejpam-4941	347	15	and	and	CCONJ
ejpam-4941	347	16	by	by	ADP
ejpam-4941	347	17	which	which	PRON
ejpam-4941	347	18	it	it	PRON
ejpam-4941	347	19	is	be	AUX
ejpam-4941	347	20	decided	decide	VERB
ejpam-4941	347	21	whether	whether	SCONJ
ejpam-4941	347	22	to	to	PART
ejpam-4941	347	23	go	go	VERB
ejpam-4941	347	24	to	to	ADP
ejpam-4941	347	25	the	the	DET
ejpam-4941	347	26	first	first	ADJ
ejpam-4941	347	27	intermediary	intermediary	ADJ
ejpam-4941	347	28	step	step	NOUN
ejpam-4941	347	29	in	in	ADP
ejpam-4941	347	30	below	below	ADP
ejpam-4941	347	31	or	or	CCONJ
ejpam-4941	347	32	not	not	PART
ejpam-4941	347	33	.	.	PUNCT
ejpam-4941	348	1	to	to	PART
ejpam-4941	348	2	get	get	VERB
ejpam-4941	348	3	a	a	DET
ejpam-4941	348	4	clearer	clear	ADJ
ejpam-4941	348	5	idea	idea	NOUN
ejpam-4941	348	6	about	about	ADP
ejpam-4941	348	7	this	this	DET
ejpam-4941	348	8	part	part	NOUN
ejpam-4941	348	9	,	,	PUNCT
ejpam-4941	348	10	we	we	PRON
ejpam-4941	348	11	provide	provide	VERB
ejpam-4941	348	12	the	the	DET
ejpam-4941	348	13	following	follow	VERB
ejpam-4941	348	14	definition	definition	NOUN
ejpam-4941	348	15	.	.	PUNCT
ejpam-4941	349	1	s.	s.	PROPN
ejpam-4941	349	2	abdelalim	abdelalim	PROPN
ejpam-4941	349	3	,	,	PUNCT
ejpam-4941	349	4	i.	i.	PROPN
ejpam-4941	349	5	elmouki	elmouki	PROPN
ejpam-4941	349	6	/	/	SYM
ejpam-4941	349	7	eur	eur	PROPN
ejpam-4941	349	8	.	.	PUNCT
ejpam-4941	350	1	j.	j.	PROPN
ejpam-4941	350	2	pure	pure	PROPN
ejpam-4941	350	3	appl	appl	PROPN
ejpam-4941	350	4	.	.	PROPN
ejpam-4941	350	5	math	math	PROPN
ejpam-4941	350	6	,	,	PUNCT
ejpam-4941	350	7	16	16	NUM
ejpam-4941	350	8	(	(	PUNCT
ejpam-4941	350	9	4	4	NUM
ejpam-4941	350	10	)	)	PUNCT
ejpam-4941	350	11	(	(	PUNCT
ejpam-4941	350	12	2023	2023	NUM
ejpam-4941	350	13	)	)	PUNCT
ejpam-4941	350	14	,	,	PUNCT
ejpam-4941	350	15	2662	2662	NUM
ejpam-4941	350	16	-	-	SYM
ejpam-4941	350	17	2692	2692	NUM
ejpam-4941	350	18	2681	2681	NUM
ejpam-4941	350	19	definition	definition	NOUN
ejpam-4941	350	20	1	1	NUM
ejpam-4941	350	21	.	.	PUNCT
ejpam-4941	351	1	(	(	PUNCT
ejpam-4941	351	2	the	the	DET
ejpam-4941	351	3	modified	modify	VERB
ejpam-4941	351	4	condition	condition	NOUN
ejpam-4941	351	5	for	for	ADP
ejpam-4941	351	6	size	size	NOUN
ejpam-4941	351	7	reduction	reduction	NOUN
ejpam-4941	351	8	devised	devise	VERB
ejpam-4941	351	9	for	for	ADP
ejpam-4941	351	10	mgs	mgs	NOUN
ejpam-4941	351	11	)	)	PUNCT
ejpam-4941	351	12	the	the	DET
ejpam-4941	351	13	bravais	bravais	PROPN
ejpam-4941	351	14	crystal	crystal	PROPN
ejpam-4941	351	15	basis	basis	NOUN
ejpam-4941	351	16	(	(	PUNCT
ejpam-4941	351	17	e1	e1	NOUN
ejpam-4941	351	18	,	,	PUNCT
ejpam-4941	351	19	...	...	PUNCT
ejpam-4941	351	20	en	en	X
ejpam-4941	351	21	)	)	PUNCT
ejpam-4941	351	22	is	be	AUX
ejpam-4941	351	23	reduced	reduce	VERB
ejpam-4941	351	24	in	in	ADP
ejpam-4941	351	25	the	the	DET
ejpam-4941	351	26	sense	sense	NOUN
ejpam-4941	351	27	of	of	ADP
ejpam-4941	351	28	size	size	NOUN
ejpam-4941	351	29	if	if	SCONJ
ejpam-4941	351	30	it	it	PRON
ejpam-4941	351	31	verifies	verify	VERB
ejpam-4941	351	32	–	–	PUNCT
ejpam-4941	351	33	mgs	mgs	NOUN
ejpam-4941	351	34	case.∣∣∣∣∣⟨f	case.∣∣∣∣∣⟨f	NOUN
ejpam-4941	351	35	∗∗(k−1	∗∗(k−1	NOUN
ejpam-4941	351	36	)	)	PUNCT
ejpam-4941	351	37	i	i	PRON
ejpam-4941	351	38	,	,	PUNCT
ejpam-4941	351	39	f∗∗	f∗∗	PROPN
ejpam-4941	351	40	k	k	PROPN
ejpam-4941	351	41	⟩	⟩	PROPN
ejpam-4941	351	42	⟨f∗∗	⟨f∗∗	X
ejpam-4941	352	1	k	k	X
ejpam-4941	352	2	,	,	PUNCT
ejpam-4941	352	3	f∗∗	f∗∗	PROPN
ejpam-4941	352	4	k	k	PROPN
ejpam-4941	352	5	⟩	⟩	PROPN
ejpam-4941	352	6	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4941	352	7	≤	≤	NUM
ejpam-4941	352	8	εmgs	εmgs	NOUN
ejpam-4941	352	9	,	,	PUNCT
ejpam-4941	352	10	i	i	PRON
ejpam-4941	352	11	=	=	NOUN
ejpam-4941	352	12	2	2	NUM
ejpam-4941	352	13	,	,	PUNCT
ejpam-4941	352	14	...	...	PUNCT
ejpam-4941	352	15	,	,	PUNCT
ejpam-4941	352	16	n	n	CCONJ
ejpam-4941	352	17	,	,	PUNCT
ejpam-4941	352	18	k	k	PROPN
ejpam-4941	352	19	=	=	SYM
ejpam-4941	352	20	2	2	NUM
ejpam-4941	352	21	,	,	PUNCT
ejpam-4941	352	22	...	...	PUNCT
ejpam-4941	352	23	,	,	PUNCT
ejpam-4941	352	24	i−	i−	PROPN
ejpam-4941	352	25	1	1	NUM
ejpam-4941	352	26	.	.	PUNCT
ejpam-4941	352	27	–	–	PUNCT
ejpam-4941	352	28	gs	gs	X
ejpam-4941	353	1	case.∣∣∣∣∣	case.∣∣∣∣∣	PROPN
ejpam-4941	353	2	⟨fi	⟨fi	PROPN
ejpam-4941	353	3	,	,	PUNCT
ejpam-4941	353	4	f∗	f∗	PROPN
ejpam-4941	353	5	j	j	PROPN
ejpam-4941	353	6	⟩	⟩	PROPN
ejpam-4941	353	7	⟨f∗	⟨f∗	PROPN
ejpam-4941	354	1	j	j	PROPN
ejpam-4941	354	2	,	,	PUNCT
ejpam-4941	354	3	f	f	PROPN
ejpam-4941	354	4	∗	∗	PROPN
ejpam-4941	354	5	j	j	PROPN
ejpam-4941	354	6	⟩	⟩	PROPN
ejpam-4941	354	7	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-4941	354	8	≤	≤	PROPN
ejpam-4941	355	1	εgs	εgs	PROPN
ejpam-4941	355	2	,	,	PUNCT
ejpam-4941	355	3	i	i	PRON
ejpam-4941	355	4	=	=	NOUN
ejpam-4941	355	5	2	2	NUM
ejpam-4941	355	6	,	,	PUNCT
ejpam-4941	355	7	...	...	PUNCT
ejpam-4941	355	8	,	,	PUNCT
ejpam-4941	355	9	n	n	CCONJ
ejpam-4941	355	10	,	,	PUNCT
ejpam-4941	355	11	j	j	PROPN
ejpam-4941	355	12	=	=	SYM
ejpam-4941	355	13	1	1	NUM
ejpam-4941	355	14	,	,	PUNCT
ejpam-4941	355	15	...	...	PUNCT
ejpam-4941	355	16	,	,	PUNCT
ejpam-4941	355	17	i−	i−	PROPN
ejpam-4941	355	18	1	1	NUM
ejpam-4941	355	19	,	,	PUNCT
ejpam-4941	355	20	with	with	ADP
ejpam-4941	355	21	εmgs	εmgs	NOUN
ejpam-4941	355	22	,	,	PUNCT
ejpam-4941	355	23	εgs	εgs	NOUN
ejpam-4941	355	24	∈	∈	PROPN
ejpam-4941	356	1	[	[	X
ejpam-4941	356	2	1/2	1/2	NUM
ejpam-4941	356	3	,	,	PUNCT
ejpam-4941	356	4	1	1	NUM
ejpam-4941	356	5	[	[	NOUN
ejpam-4941	356	6	.	.	PUNCT
ejpam-4941	356	7	definition	definition	NOUN
ejpam-4941	356	8	2	2	NUM
ejpam-4941	356	9	.	.	PUNCT
ejpam-4941	357	1	(	(	PUNCT
ejpam-4941	357	2	the	the	DET
ejpam-4941	357	3	modified	modify	VERB
ejpam-4941	357	4	condition	condition	NOUN
ejpam-4941	357	5	for	for	ADP
ejpam-4941	357	6	quasi	quasi	ADJ
ejpam-4941	357	7	-	-	ADJ
ejpam-4941	357	8	orthogonality	orthogonality	NOUN
ejpam-4941	357	9	devised	devise	VERB
ejpam-4941	357	10	for	for	ADP
ejpam-4941	357	11	mgs	mgs	NOUN
ejpam-4941	357	12	)	)	PUNCT
ejpam-4941	357	13	the	the	DET
ejpam-4941	357	14	bravais	bravais	PROPN
ejpam-4941	357	15	crystal	crystal	PROPN
ejpam-4941	357	16	basis	basis	NOUN
ejpam-4941	357	17	(	(	PUNCT
ejpam-4941	357	18	e1	e1	NOUN
ejpam-4941	357	19	,	,	PUNCT
ejpam-4941	357	20	...	...	PUNCT
ejpam-4941	357	21	en	en	X
ejpam-4941	357	22	)	)	PUNCT
ejpam-4941	357	23	is	be	AUX
ejpam-4941	357	24	reduced	reduce	VERB
ejpam-4941	357	25	in	in	ADP
ejpam-4941	357	26	the	the	DET
ejpam-4941	357	27	sense	sense	NOUN
ejpam-4941	357	28	of	of	ADP
ejpam-4941	357	29	quasi	quasi	NOUN
ejpam-4941	357	30	-	-	NOUN
ejpam-4941	357	31	orthogonality	orthogonality	ADJ
ejpam-4941	357	32	if	if	SCONJ
ejpam-4941	357	33	it	it	PRON
ejpam-4941	357	34	verifies	verify	VERB
ejpam-4941	357	35	–	–	PUNCT
ejpam-4941	357	36	mgs	mgs	NOUN
ejpam-4941	357	37	case	case	NOUN
ejpam-4941	357	38	.	.	PUNCT
ejpam-4941	358	1	(	(	PUNCT
ejpam-4941	358	2	proposition	proposition	NOUN
ejpam-4941	358	3	)	)	PUNCT
ejpam-4941	358	4	ε|e∗∗k	ε|e∗∗k	NOUN
ejpam-4941	358	5	|2	|2	NUM
ejpam-4941	358	6	≤	≤	NUM
ejpam-4941	358	7	∣∣∣e∗∗(k−1	∣∣∣e∗∗(k−1	ADJ
ejpam-4941	358	8	)	)	PUNCT
ejpam-4941	359	1	j+1	j+1	PROPN
ejpam-4941	360	1	+	+	PUNCT
ejpam-4941	360	2	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	360	3	)	)	PUNCT
ejpam-4941	360	4	j+1	j+1	NOUN
ejpam-4941	360	5	,	,	PUNCT
ejpam-4941	360	6	e∗∗k	e∗∗k	PROPN
ejpam-4941	360	7	⟩	⟩	NOUN
ejpam-4941	360	8	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	360	9	,	,	PUNCT
ejpam-4941	360	10	e∗∗k	e∗∗k	PROPN
ejpam-4941	360	11	⟩	⟩	PROPN
ejpam-4941	360	12	e∗∗k	e∗∗k	PROPN
ejpam-4941	360	13	∣∣∣2	∣∣∣2	NOUN
ejpam-4941	360	14	,	,	PUNCT
ejpam-4941	361	1	k	k	PROPN
ejpam-4941	361	2	=	=	SYM
ejpam-4941	361	3	2	2	NUM
ejpam-4941	361	4	,	,	PUNCT
ejpam-4941	361	5	...	...	PUNCT
ejpam-4941	361	6	,	,	PUNCT
ejpam-4941	361	7	j	j	PROPN
ejpam-4941	361	8	,	,	PUNCT
ejpam-4941	361	9	with	with	ADP
ejpam-4941	361	10	ε	ε	PROPN
ejpam-4941	361	11	∈]ε2mgs	∈]ε2mgs	PROPN
ejpam-4941	361	12	,	,	PUNCT
ejpam-4941	361	13	1	1	NUM
ejpam-4941	361	14	[	[	NOUN
ejpam-4941	361	15	.	.	PUNCT
ejpam-4941	361	16	–	–	PUNCT
ejpam-4941	361	17	gs	gs	NOUN
ejpam-4941	361	18	case	case	NOUN
ejpam-4941	361	19	.	.	PUNCT
ejpam-4941	362	1	ε|e∗j	ε|e∗j	PROPN
ejpam-4941	362	2	|2	|2	NUM
ejpam-4941	362	3	≤	≤	NOUN
ejpam-4941	362	4	∣∣∣e∗j+1	∣∣∣e∗j+1	PUNCT
ejpam-4941	363	1	+	+	CCONJ
ejpam-4941	363	2	⟨ej+1	⟨ej+1	NOUN
ejpam-4941	363	3	,	,	PUNCT
ejpam-4941	363	4	e	e	PROPN
ejpam-4941	363	5	∗	∗	PROPN
ejpam-4941	363	6	j	j	PROPN
ejpam-4941	363	7	⟩	⟩	PROPN
ejpam-4941	363	8	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	363	9	,	,	PUNCT
ejpam-4941	363	10	e∗j	e∗j	PROPN
ejpam-4941	363	11	⟩	⟩	NOUN
ejpam-4941	363	12	e∗j	e∗j	NUM
ejpam-4941	363	13	∣∣∣2	∣∣∣2	NOUN
ejpam-4941	363	14	,	,	PUNCT
ejpam-4941	363	15	j	j	PROPN
ejpam-4941	363	16	=	=	SYM
ejpam-4941	363	17	1	1	NUM
ejpam-4941	363	18	,	,	PUNCT
ejpam-4941	363	19	...	...	PUNCT
ejpam-4941	363	20	,	,	PUNCT
ejpam-4941	363	21	n	n	CCONJ
ejpam-4941	363	22	with	with	ADP
ejpam-4941	363	23	ε	ε	PROPN
ejpam-4941	363	24	∈]ε2gs	∈]ε2gs	PROPN
ejpam-4941	363	25	,	,	PUNCT
ejpam-4941	363	26	1	1	X
ejpam-4941	363	27	[	[	PUNCT
ejpam-4941	363	28	(	(	PUNCT
ejpam-4941	363	29	known	know	VERB
ejpam-4941	363	30	as	as	ADP
ejpam-4941	363	31	the	the	DET
ejpam-4941	363	32	lovász	lovász	ADJ
ejpam-4941	363	33	condition	condition	NOUN
ejpam-4941	363	34	[	[	X
ejpam-4941	363	35	31	31	NUM
ejpam-4941	363	36	]	]	PUNCT
ejpam-4941	363	37	)	)	PUNCT
ejpam-4941	363	38	.	.	PUNCT
ejpam-4941	364	1	proof	proof	NOUN
ejpam-4941	364	2	.	.	PUNCT
ejpam-4941	365	1	now	now	ADV
ejpam-4941	365	2	,	,	PUNCT
ejpam-4941	365	3	we	we	PRON
ejpam-4941	365	4	prove	prove	VERB
ejpam-4941	365	5	the	the	DET
ejpam-4941	365	6	proposition	proposition	NOUN
ejpam-4941	365	7	stated	state	VERB
ejpam-4941	365	8	in	in	ADP
ejpam-4941	365	9	definition	definition	NOUN
ejpam-4941	365	10	2	2	NUM
ejpam-4941	365	11	and	and	CCONJ
ejpam-4941	365	12	that	that	PRON
ejpam-4941	365	13	is	be	AUX
ejpam-4941	365	14	about	about	ADP
ejpam-4941	365	15	the	the	DET
ejpam-4941	365	16	modified	modify	VERB
ejpam-4941	365	17	version	version	NOUN
ejpam-4941	365	18	of	of	ADP
ejpam-4941	365	19	the	the	DET
ejpam-4941	365	20	lovász	lovász	ADJ
ejpam-4941	365	21	condition	condition	NOUN
ejpam-4941	365	22	,	,	PUNCT
ejpam-4941	365	23	namely	namely	ADV
ejpam-4941	365	24	the	the	DET
ejpam-4941	365	25	quasi	quasi	ADJ
ejpam-4941	365	26	-	-	ADJ
ejpam-4941	365	27	orthogonality	orthogonality	ADJ
ejpam-4941	365	28	condition	condition	NOUN
ejpam-4941	365	29	that	that	SCONJ
ejpam-4941	365	30	we	we	PRON
ejpam-4941	365	31	are	be	AUX
ejpam-4941	365	32	suggesting	suggest	VERB
ejpam-4941	365	33	in	in	ADP
ejpam-4941	365	34	this	this	DET
ejpam-4941	365	35	paper	paper	NOUN
ejpam-4941	365	36	for	for	ADP
ejpam-4941	365	37	the	the	DET
ejpam-4941	365	38	mgs	mgs	NOUN
ejpam-4941	365	39	case	case	NOUN
ejpam-4941	365	40	.	.	PUNCT
ejpam-4941	366	1	from	from	ADP
ejpam-4941	366	2	the	the	DET
ejpam-4941	366	3	theorem	theorem	NOUN
ejpam-4941	366	4	2	2	NUM
ejpam-4941	366	5	,	,	PUNCT
ejpam-4941	366	6	we	we	PRON
ejpam-4941	366	7	can	can	AUX
ejpam-4941	366	8	see	see	VERB
ejpam-4941	366	9	that	that	PRON
ejpam-4941	366	10	for	for	ADP
ejpam-4941	366	11	i	i	PRON
ejpam-4941	366	12	=	=	SYM
ejpam-4941	366	13	j	j	PROPN
ejpam-4941	366	14	,	,	PUNCT
ejpam-4941	366	15	namely	namely	ADV
ejpam-4941	366	16	at	at	ADP
ejpam-4941	366	17	the	the	DET
ejpam-4941	366	18	time	time	NOUN
ejpam-4941	366	19	of	of	ADP
ejpam-4941	366	20	the	the	DET
ejpam-4941	366	21	vectors	vector	NOUN
ejpam-4941	366	22	swapping	swap	VERB
ejpam-4941	366	23	,	,	PUNCT
ejpam-4941	366	24	we	we	PRON
ejpam-4941	366	25	have	have	VERB
ejpam-4941	366	26	,	,	PUNCT
ejpam-4941	366	27	f	f	PROPN
ejpam-4941	366	28	∗∗(k	∗∗(k	NOUN
ejpam-4941	366	29	)	)	PUNCT
ejpam-4941	366	30	j	j	NOUN
ejpam-4941	367	1	=	=	PUNCT
ejpam-4941	367	2	ej+1	ej+1	PROPN
ejpam-4941	367	3	−	−	PROPN
ejpam-4941	367	4	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	367	5	,	,	PUNCT
ejpam-4941	367	6	e	e	X
ejpam-4941	367	7	∗∗	∗∗	X
ejpam-4941	367	8	k−1⟩	k−1⟩	PROPN
ejpam-4941	367	9	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	367	10	,	,	PUNCT
ejpam-4941	367	11	e	e	X
ejpam-4941	367	12	∗∗	∗∗	X
ejpam-4941	368	1	k−1⟩	k−1⟩	DET
ejpam-4941	368	2	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	368	3	−	−	NOUN
ejpam-4941	368	4	⟨e∗∗(k−1	⟨e∗∗(k−1	NUM
ejpam-4941	368	5	)	)	PUNCT
ejpam-4941	368	6	j+1	j+1	NOUN
ejpam-4941	368	7	,	,	PUNCT
ejpam-4941	368	8	e∗∗k	e∗∗k	PROPN
ejpam-4941	368	9	⟩	⟩	NOUN
ejpam-4941	368	10	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	368	11	,	,	PUNCT
ejpam-4941	368	12	e∗∗k	e∗∗k	PROPN
ejpam-4941	368	13	⟩	⟩	PROPN
ejpam-4941	368	14	e∗∗k	e∗∗k	PROPN
ejpam-4941	368	15	,	,	PUNCT
ejpam-4941	368	16	k	k	PROPN
ejpam-4941	368	17	=	=	SYM
ejpam-4941	368	18	2	2	NUM
ejpam-4941	368	19	,	,	PUNCT
ejpam-4941	368	20	...	...	PUNCT
ejpam-4941	368	21	,	,	PUNCT
ejpam-4941	368	22	j	j	PROPN
ejpam-4941	368	23	,	,	PUNCT
ejpam-4941	368	24	thus	thus	ADV
ejpam-4941	368	25	,	,	PUNCT
ejpam-4941	368	26	by	by	ADP
ejpam-4941	368	27	using	use	VERB
ejpam-4941	368	28	the	the	DET
ejpam-4941	368	29	definition	definition	NOUN
ejpam-4941	368	30	of	of	ADP
ejpam-4941	368	31	mgs	mgs	NOUN
ejpam-4941	368	32	formulation	formulation	NOUN
ejpam-4941	368	33	at	at	ADP
ejpam-4941	368	34	n	n	PROPN
ejpam-4941	368	35	=	=	SYM
ejpam-4941	368	36	j	j	PROPN
ejpam-4941	369	1	+	+	NOUN
ejpam-4941	369	2	1	1	NUM
ejpam-4941	369	3	,	,	PUNCT
ejpam-4941	369	4	we	we	PRON
ejpam-4941	369	5	get	get	VERB
ejpam-4941	369	6	,	,	PUNCT
ejpam-4941	369	7	f	f	PROPN
ejpam-4941	369	8	∗∗(k	∗∗(k	NOUN
ejpam-4941	369	9	)	)	PUNCT
ejpam-4941	369	10	j	j	NOUN
ejpam-4941	370	1	=	=	SYM
ejpam-4941	370	2	e	e	NOUN
ejpam-4941	370	3	∗∗(k−1	∗∗(k−1	X
ejpam-4941	370	4	)	)	PUNCT
ejpam-4941	371	1	j+1	j+1	PUNCT
ejpam-4941	371	2	−	−	NOUN
ejpam-4941	371	3	⟨e(k−1	⟨e(k−1	NUM
ejpam-4941	371	4	)	)	PUNCT
ejpam-4941	372	1	j+1	j+1	NOUN
ejpam-4941	372	2	,	,	PUNCT
ejpam-4941	372	3	e∗∗k	e∗∗k	PROPN
ejpam-4941	372	4	⟩	⟩	NOUN
ejpam-4941	372	5	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	372	6	,	,	PUNCT
ejpam-4941	372	7	e∗∗k	e∗∗k	PROPN
ejpam-4941	372	8	⟩	⟩	PROPN
ejpam-4941	372	9	e∗∗k	e∗∗k	PROPN
ejpam-4941	372	10	,	,	PUNCT
ejpam-4941	372	11	k	k	PROPN
ejpam-4941	372	12	=	=	SYM
ejpam-4941	372	13	2	2	NUM
ejpam-4941	372	14	,	,	PUNCT
ejpam-4941	372	15	...	...	PUNCT
ejpam-4941	372	16	,	,	PUNCT
ejpam-4941	372	17	j.	j.	PROPN
ejpam-4941	372	18	then	then	ADV
ejpam-4941	372	19	,	,	PUNCT
ejpam-4941	372	20	|f∗∗(k	|f∗∗(k	NOUN
ejpam-4941	372	21	)	)	PUNCT
ejpam-4941	372	22	j	j	PROPN
ejpam-4941	372	23	|2	|2	NUM
ejpam-4941	372	24	=	=	SYM
ejpam-4941	372	25	|e∗∗(k−1	|e∗∗(k−1	NOUN
ejpam-4941	372	26	)	)	PUNCT
ejpam-4941	372	27	j+1	j+1	NOUN
ejpam-4941	372	28	|2	|2	NUM
ejpam-4941	372	29	+	+	CCONJ
ejpam-4941	372	30	(	(	PUNCT
ejpam-4941	372	31	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	372	32	)	)	PUNCT
ejpam-4941	372	33	j+1	j+1	NOUN
ejpam-4941	372	34	,	,	PUNCT
ejpam-4941	372	35	e∗∗k	e∗∗k	PROPN
ejpam-4941	372	36	⟩	⟩	NOUN
ejpam-4941	372	37	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	372	38	,	,	PUNCT
ejpam-4941	372	39	e∗∗k	e∗∗k	PROPN
ejpam-4941	372	40	⟩	⟩	PROPN
ejpam-4941	372	41	)	)	PUNCT
ejpam-4941	372	42	2	2	NUM
ejpam-4941	372	43	|e∗∗k	|e∗∗k	NOUN
ejpam-4941	372	44	|2	|2	NUM
ejpam-4941	372	45	,	,	PUNCT
ejpam-4941	372	46	k	k	PROPN
ejpam-4941	372	47	=	=	SYM
ejpam-4941	372	48	2	2	NUM
ejpam-4941	372	49	,	,	PUNCT
ejpam-4941	372	50	...	...	PUNCT
ejpam-4941	372	51	,	,	PUNCT
ejpam-4941	372	52	j	j	PROPN
ejpam-4941	372	53	,	,	PUNCT
ejpam-4941	372	54	and	and	CCONJ
ejpam-4941	372	55	which	which	PRON
ejpam-4941	372	56	gives	give	VERB
ejpam-4941	372	57	,	,	PUNCT
ejpam-4941	372	58	|e∗∗(k−1	|e∗∗(k−1	NOUN
ejpam-4941	372	59	)	)	PUNCT
ejpam-4941	372	60	j+1	j+1	NOUN
ejpam-4941	372	61	|2	|2	NUM
ejpam-4941	372	62	=	=	SYM
ejpam-4941	372	63	|f∗∗(k	|f∗∗(k	NOUN
ejpam-4941	372	64	)	)	PUNCT
ejpam-4941	372	65	j	j	PROPN
ejpam-4941	372	66	|2	|2	NUM
ejpam-4941	372	67	−	−	PROPN
ejpam-4941	372	68	(	(	PUNCT
ejpam-4941	372	69	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	372	70	)	)	PUNCT
ejpam-4941	372	71	j+1	j+1	NOUN
ejpam-4941	372	72	,	,	PUNCT
ejpam-4941	372	73	e∗∗k	e∗∗k	PROPN
ejpam-4941	372	74	⟩	⟩	NOUN
ejpam-4941	372	75	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	372	76	,	,	PUNCT
ejpam-4941	372	77	e∗∗k	e∗∗k	PROPN
ejpam-4941	372	78	⟩	⟩	PROPN
ejpam-4941	372	79	)	)	PUNCT
ejpam-4941	372	80	2	2	NUM
ejpam-4941	372	81	|e∗∗k	|e∗∗k	NOUN
ejpam-4941	372	82	|2	|2	NUM
ejpam-4941	372	83	,	,	PUNCT
ejpam-4941	372	84	k	k	PROPN
ejpam-4941	372	85	=	=	SYM
ejpam-4941	372	86	2	2	NUM
ejpam-4941	372	87	,	,	PUNCT
ejpam-4941	372	88	...	...	PUNCT
ejpam-4941	372	89	,	,	PUNCT
ejpam-4941	372	90	j.	j.	PROPN
ejpam-4941	372	91	but	but	CCONJ
ejpam-4941	372	92	before	before	ADP
ejpam-4941	372	93	this	this	PRON
ejpam-4941	372	94	,	,	PUNCT
ejpam-4941	372	95	in	in	ADP
ejpam-4941	372	96	order	order	NOUN
ejpam-4941	372	97	to	to	PART
ejpam-4941	372	98	obtain	obtain	VERB
ejpam-4941	372	99	shorter	short	ADJ
ejpam-4941	372	100	vector	vector	NOUN
ejpam-4941	372	101	with	with	ADP
ejpam-4941	372	102	respect	respect	NOUN
ejpam-4941	372	103	to	to	ADP
ejpam-4941	372	104	f	f	PROPN
ejpam-4941	372	105	∗∗(k	∗∗(k	NOUN
ejpam-4941	372	106	)	)	PUNCT
ejpam-4941	372	107	j	j	NOUN
ejpam-4941	372	108	,	,	PUNCT
ejpam-4941	372	109	we	we	PRON
ejpam-4941	372	110	need	need	VERB
ejpam-4941	372	111	s.	s.	PROPN
ejpam-4941	372	112	abdelalim	abdelalim	PROPN
ejpam-4941	372	113	,	,	PUNCT
ejpam-4941	372	114	i.	i.	PROPN
ejpam-4941	372	115	elmouki	elmouki	PROPN
ejpam-4941	372	116	/	/	SYM
ejpam-4941	372	117	eur	eur	PROPN
ejpam-4941	372	118	.	.	PUNCT
ejpam-4941	373	1	j.	j.	PROPN
ejpam-4941	373	2	pure	pure	PROPN
ejpam-4941	373	3	appl	appl	PROPN
ejpam-4941	373	4	.	.	PROPN
ejpam-4941	373	5	math	math	PROPN
ejpam-4941	373	6	,	,	PUNCT
ejpam-4941	373	7	16	16	NUM
ejpam-4941	373	8	(	(	PUNCT
ejpam-4941	373	9	4	4	NUM
ejpam-4941	373	10	)	)	PUNCT
ejpam-4941	373	11	(	(	PUNCT
ejpam-4941	373	12	2023	2023	NUM
ejpam-4941	373	13	)	)	PUNCT
ejpam-4941	373	14	,	,	PUNCT
ejpam-4941	373	15	2662	2662	NUM
ejpam-4941	373	16	-	-	SYM
ejpam-4941	373	17	2692	2692	NUM
ejpam-4941	373	18	2682	2682	NUM
ejpam-4941	373	19	through	through	ADP
ejpam-4941	373	20	its	its	PRON
ejpam-4941	373	21	formulation	formulation	NOUN
ejpam-4941	373	22	shorter	short	ADJ
ejpam-4941	373	23	vector	vector	NOUN
ejpam-4941	373	24	e∗∗k	e∗∗k	PROPN
ejpam-4941	373	25	,	,	PUNCT
ejpam-4941	373	26	which	which	PRON
ejpam-4941	373	27	is	be	AUX
ejpam-4941	373	28	the	the	DET
ejpam-4941	373	29	same	same	ADJ
ejpam-4941	373	30	as	as	ADP
ejpam-4941	373	31	saying	say	VERB
ejpam-4941	373	32	that	that	SCONJ
ejpam-4941	373	33	by	by	ADP
ejpam-4941	373	34	the	the	DET
ejpam-4941	373	35	formulation	formulation	NOUN
ejpam-4941	373	36	of	of	ADP
ejpam-4941	373	37	|f∗∗(k	|f∗∗(k	NOUN
ejpam-4941	373	38	)	)	PUNCT
ejpam-4941	373	39	j	j	NOUN
ejpam-4941	373	40	|2	|2	NUM
ejpam-4941	373	41	,	,	PUNCT
ejpam-4941	373	42	we	we	PRON
ejpam-4941	373	43	need	need	VERB
ejpam-4941	373	44	the	the	DET
ejpam-4941	373	45	existence	existence	NOUN
ejpam-4941	373	46	of	of	ADP
ejpam-4941	373	47	some	some	DET
ejpam-4941	373	48	ε	ε	PROPN
ejpam-4941	373	49	that	that	PRON
ejpam-4941	373	50	is	be	AUX
ejpam-4941	373	51	close	close	ADJ
ejpam-4941	373	52	to	to	ADP
ejpam-4941	373	53	1	1	NUM
ejpam-4941	373	54	and	and	CCONJ
ejpam-4941	373	55	such	such	ADJ
ejpam-4941	373	56	that	that	DET
ejpam-4941	373	57	ε|e∗∗k	ε|e∗∗k	NOUN
ejpam-4941	373	58	|2	|2	NUM
ejpam-4941	373	59	≤	≤	NUM
ejpam-4941	373	60	|e∗∗(k−1	|e∗∗(k−1	NOUN
ejpam-4941	373	61	)	)	PUNCT
ejpam-4941	374	1	j+1	j+1	NOUN
ejpam-4941	374	2	|2	|2	NUM
ejpam-4941	375	1	+	+	CCONJ
ejpam-4941	375	2	(	(	PUNCT
ejpam-4941	375	3	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	375	4	)	)	PUNCT
ejpam-4941	375	5	j+1	j+1	NOUN
ejpam-4941	375	6	,	,	PUNCT
ejpam-4941	375	7	e∗∗k	e∗∗k	PROPN
ejpam-4941	375	8	⟩	⟩	NOUN
ejpam-4941	375	9	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	375	10	,	,	PUNCT
ejpam-4941	375	11	e∗∗k	e∗∗k	PROPN
ejpam-4941	375	12	⟩	⟩	PROPN
ejpam-4941	375	13	)	)	PUNCT
ejpam-4941	375	14	2	2	NUM
ejpam-4941	375	15	|e∗∗k	|e∗∗k	NOUN
ejpam-4941	375	16	|2	|2	NUM
ejpam-4941	375	17	,	,	PUNCT
ejpam-4941	375	18	k	k	PROPN
ejpam-4941	375	19	=	=	SYM
ejpam-4941	375	20	2	2	NUM
ejpam-4941	375	21	,	,	PUNCT
ejpam-4941	375	22	...	...	PUNCT
ejpam-4941	375	23	,	,	PUNCT
ejpam-4941	375	24	j.	j.	PROPN
ejpam-4941	375	25	then	then	ADV
ejpam-4941	375	26	,	,	PUNCT
ejpam-4941	375	27	going	go	VERB
ejpam-4941	375	28	back	back	ADV
ejpam-4941	375	29	to	to	ADP
ejpam-4941	375	30	the	the	DET
ejpam-4941	375	31	equality	equality	NOUN
ejpam-4941	375	32	on	on	ADP
ejpam-4941	375	33	|e∗∗(k−1	|e∗∗(k−1	NOUN
ejpam-4941	375	34	)	)	PUNCT
ejpam-4941	376	1	j+1	j+1	NUM
ejpam-4941	376	2	|2	|2	NUM
ejpam-4941	376	3	,	,	PUNCT
ejpam-4941	376	4	it	it	PRON
ejpam-4941	376	5	can	can	AUX
ejpam-4941	376	6	be	be	AUX
ejpam-4941	376	7	changed	change	VERB
ejpam-4941	376	8	now	now	ADV
ejpam-4941	376	9	to	to	ADP
ejpam-4941	376	10	the	the	DET
ejpam-4941	376	11	inequality	inequality	NOUN
ejpam-4941	376	12	,	,	PUNCT
ejpam-4941	376	13	|e∗∗(k−1	|e∗∗(k−1	NOUN
ejpam-4941	376	14	)	)	PUNCT
ejpam-4941	377	1	j+1	j+1	NOUN
ejpam-4941	377	2	|2	|2	NUM
ejpam-4941	377	3	≥	≥	NOUN
ejpam-4941	377	4	ε−	ε−	NOUN
ejpam-4941	377	5	(	(	PUNCT
ejpam-4941	377	6	⟨e∗∗(k−1	⟨e∗∗(k−1	X
ejpam-4941	377	7	)	)	PUNCT
ejpam-4941	377	8	j+1	j+1	NOUN
ejpam-4941	377	9	,	,	PUNCT
ejpam-4941	377	10	e∗∗k	e∗∗k	PROPN
ejpam-4941	377	11	⟩	⟩	NOUN
ejpam-4941	377	12	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	377	13	,	,	PUNCT
ejpam-4941	377	14	e∗∗k	e∗∗k	PROPN
ejpam-4941	377	15	⟩	⟩	PROPN
ejpam-4941	377	16	)	)	PUNCT
ejpam-4941	377	17	2	2	NUM
ejpam-4941	377	18			PROPN
ejpam-4941	377	19	|e∗∗k	|e∗∗k	NOUN
ejpam-4941	377	20	|2	|2	NUM
ejpam-4941	377	21	,	,	PUNCT
ejpam-4941	377	22	k	k	PROPN
ejpam-4941	377	23	=	=	SYM
ejpam-4941	377	24	2	2	NUM
ejpam-4941	377	25	,	,	PUNCT
ejpam-4941	377	26	...	...	PUNCT
ejpam-4941	377	27	,	,	PUNCT
ejpam-4941	377	28	j	j	PROPN
ejpam-4941	377	29	,	,	PUNCT
ejpam-4941	377	30	which	which	PRON
ejpam-4941	377	31	is	be	AUX
ejpam-4941	377	32	equivalent	equivalent	ADJ
ejpam-4941	377	33	to	to	ADP
ejpam-4941	377	34	the	the	DET
ejpam-4941	377	35	condition	condition	NOUN
ejpam-4941	377	36	stated	state	VERB
ejpam-4941	377	37	in	in	ADP
ejpam-4941	377	38	definition	definition	NOUN
ejpam-4941	377	39	2	2	NUM
ejpam-4941	377	40	.	.	PUNCT
ejpam-4941	377	41	just	just	ADV
ejpam-4941	377	42	as	as	ADP
ejpam-4941	377	43	remark	remark	NOUN
ejpam-4941	377	44	,	,	PUNCT
ejpam-4941	377	45	if	if	SCONJ
ejpam-4941	377	46	we	we	PRON
ejpam-4941	377	47	take	take	VERB
ejpam-4941	377	48	ε	ε	PROPN
ejpam-4941	377	49	in	in	ADP
ejpam-4941	377	50	]	]	PUNCT
ejpam-4941	377	51	ε2mgs	ε2mgs	ADV
ejpam-4941	377	52	,	,	PUNCT
ejpam-4941	377	53	1	1	NUM
ejpam-4941	377	54	[	[	X
ejpam-4941	377	55	,	,	PUNCT
ejpam-4941	377	56	it	it	PRON
ejpam-4941	377	57	is	be	AUX
ejpam-4941	377	58	better	well	ADJ
ejpam-4941	377	59	to	to	PART
ejpam-4941	377	60	say	say	VERB
ejpam-4941	377	61	that	that	SCONJ
ejpam-4941	377	62	the	the	DET
ejpam-4941	377	63	this	this	DET
ejpam-4941	377	64	condition	condition	NOUN
ejpam-4941	377	65	is	be	AUX
ejpam-4941	377	66	verified	verify	VERB
ejpam-4941	377	67	if	if	SCONJ
ejpam-4941	377	68	ε	ε	PROPN
ejpam-4941	377	69	is	be	AUX
ejpam-4941	377	70	close	close	ADJ
ejpam-4941	377	71	to	to	ADP
ejpam-4941	377	72	1	1	NUM
ejpam-4941	377	73	as	as	ADP
ejpam-4941	377	74	in	in	ADP
ejpam-4941	377	75	this	this	DET
ejpam-4941	377	76	case	case	NOUN
ejpam-4941	377	77	,	,	PUNCT
ejpam-4941	377	78	the	the	DET
ejpam-4941	377	79	crystal	crystal	NOUN
ejpam-4941	377	80	basis	basis	NOUN
ejpam-4941	377	81	will	will	AUX
ejpam-4941	377	82	be	be	AUX
ejpam-4941	377	83	more	more	ADV
ejpam-4941	377	84	reduced	reduce	VERB
ejpam-4941	377	85	.	.	PUNCT
ejpam-4941	378	1	•	•	NUM
ejpam-4941	378	2	basis	basis	NOUN
ejpam-4941	378	3	vectors	vector	NOUN
ejpam-4941	378	4	output	output	VERB
ejpam-4941	378	5	:	:	PUNCT
ejpam-4941	378	6	obtaining	obtain	VERB
ejpam-4941	378	7	an	an	DET
ejpam-4941	378	8	mgs	mgs	NOUN
ejpam-4941	378	9	reduced	reduce	VERB
ejpam-4941	378	10	basis	basis	NOUN
ejpam-4941	378	11	(	(	PUNCT
ejpam-4941	378	12	f∗∗	f∗∗	NOUN
ejpam-4941	378	13	1	1	NUM
ejpam-4941	378	14	,	,	PUNCT
ejpam-4941	378	15	...	...	PUNCT
ejpam-4941	378	16	f∗∗	f∗∗	NOUN
ejpam-4941	378	17	n	n	CCONJ
ejpam-4941	378	18	)	)	PUNCT
ejpam-4941	378	19	or	or	CCONJ
ejpam-4941	378	20	gs	gs	PROPN
ejpam-4941	378	21	reduced	reduce	VERB
ejpam-4941	378	22	basis	basis	NOUN
ejpam-4941	378	23	(	(	PUNCT
ejpam-4941	378	24	f∗	f∗	NOUN
ejpam-4941	378	25	1	1	NUM
ejpam-4941	378	26	,	,	PUNCT
ejpam-4941	378	27	...	...	PUNCT
ejpam-4941	378	28	f	f	PROPN
ejpam-4941	378	29	∗	∗	NOUN
ejpam-4941	378	30	n	n	CCONJ
ejpam-4941	378	31	)	)	PUNCT
ejpam-4941	378	32	associated	associate	VERB
ejpam-4941	378	33	to	to	ADP
ejpam-4941	378	34	some	some	DET
ejpam-4941	378	35	basis	basis	NOUN
ejpam-4941	378	36	(	(	PUNCT
ejpam-4941	378	37	f1	f1	NOUN
ejpam-4941	378	38	,	,	PUNCT
ejpam-4941	378	39	...	...	PUNCT
ejpam-4941	378	40	fn	fn	X
ejpam-4941	378	41	)	)	PUNCT
ejpam-4941	378	42	and	and	CCONJ
ejpam-4941	378	43	which	which	PRON
ejpam-4941	378	44	was	be	AUX
ejpam-4941	378	45	defined	define	VERB
ejpam-4941	378	46	in	in	ADP
ejpam-4941	378	47	the	the	DET
ejpam-4941	378	48	first	first	ADJ
ejpam-4941	378	49	step	step	NOUN
ejpam-4941	378	50	or	or	CCONJ
ejpam-4941	378	51	before	before	ADP
ejpam-4941	378	52	reduction	reduction	NOUN
ejpam-4941	378	53	as	as	ADP
ejpam-4941	378	54	fi	fi	NOUN
ejpam-4941	378	55	=	=	PUNCT
ejpam-4941	378	56			PUNCT
ejpam-4941	378	57	ei	ei	INTJ
ejpam-4941	378	58	if	if	SCONJ
ejpam-4941	378	59	i	i	PRON
ejpam-4941	378	60	̸=	̸=	PROPN
ejpam-4941	378	61	j	j	PROPN
ejpam-4941	378	62	,	,	PUNCT
ejpam-4941	378	63	j	j	PROPN
ejpam-4941	379	1	+	+	CCONJ
ejpam-4941	379	2	1	1	NUM
ejpam-4941	379	3	ej+1	ej+1	NOUN
ejpam-4941	379	4	if	if	SCONJ
ejpam-4941	379	5	i	i	PRON
ejpam-4941	379	6	=	=	SYM
ejpam-4941	379	7	j	j	PROPN
ejpam-4941	379	8	ej	ej	INTJ
ejpam-4941	379	9	if	if	SCONJ
ejpam-4941	379	10	i	i	PRON
ejpam-4941	379	11	=	=	SYM
ejpam-4941	379	12	j	j	PROPN
ejpam-4941	380	1	+	+	CCONJ
ejpam-4941	380	2	1	1	NUM
ejpam-4941	380	3	once	once	ADV
ejpam-4941	380	4	fi	fi	NOUN
ejpam-4941	380	5	is	be	AUX
ejpam-4941	380	6	defined	define	VERB
ejpam-4941	380	7	,	,	PUNCT
ejpam-4941	380	8	it	it	PRON
ejpam-4941	380	9	comes	come	VERB
ejpam-4941	380	10	the	the	DET
ejpam-4941	380	11	step	step	NOUN
ejpam-4941	380	12	where	where	SCONJ
ejpam-4941	380	13	we	we	PRON
ejpam-4941	380	14	are	be	AUX
ejpam-4941	380	15	in	in	ADP
ejpam-4941	380	16	front	front	NOUN
ejpam-4941	380	17	of	of	ADP
ejpam-4941	380	18	the	the	DET
ejpam-4941	380	19	first	first	ADJ
ejpam-4941	380	20	result	result	NOUN
ejpam-4941	380	21	of	of	ADP
ejpam-4941	380	22	the	the	DET
ejpam-4941	380	23	vectors	vector	NOUN
ejpam-4941	380	24	exchange	exchange	NOUN
ejpam-4941	380	25	theorem	theorem	NOUN
ejpam-4941	380	26	and	and	CCONJ
ejpam-4941	380	27	which	which	PRON
ejpam-4941	380	28	states	state	VERB
ejpam-4941	380	29	that	that	SCONJ
ejpam-4941	380	30	in	in	ADP
ejpam-4941	380	31	conditions	condition	NOUN
ejpam-4941	380	32	1	1	NUM
ejpam-4941	380	33	≤	≤	NUM
ejpam-4941	380	34	i	i	PRON
ejpam-4941	380	35	<	<	X
ejpam-4941	380	36	j	j	PROPN
ejpam-4941	380	37	or	or	CCONJ
ejpam-4941	380	38	i	i	PRON
ejpam-4941	380	39	>	>	X
ejpam-4941	380	40	j	j	PROPN
ejpam-4941	381	1	+	+	CCONJ
ejpam-4941	381	2	1	1	NUM
ejpam-4941	381	3	,	,	PUNCT
ejpam-4941	381	4	we	we	PRON
ejpam-4941	381	5	have	have	VERB
ejpam-4941	381	6	the	the	DET
ejpam-4941	381	7	equality	equality	NOUN
ejpam-4941	381	8	between	between	ADP
ejpam-4941	381	9	the	the	DET
ejpam-4941	381	10	orthogonal	orthogonal	ADJ
ejpam-4941	381	11	basis	basis	NOUN
ejpam-4941	381	12	of	of	ADP
ejpam-4941	381	13	the	the	DET
ejpam-4941	381	14	input	input	NOUN
ejpam-4941	381	15	random	random	ADJ
ejpam-4941	381	16	vector	vector	NOUN
ejpam-4941	381	17	and	and	CCONJ
ejpam-4941	381	18	the	the	DET
ejpam-4941	381	19	orthogonal	orthogonal	ADJ
ejpam-4941	381	20	basis	basis	NOUN
ejpam-4941	381	21	of	of	ADP
ejpam-4941	381	22	the	the	DET
ejpam-4941	381	23	vector	vector	NOUN
ejpam-4941	381	24	that	that	PRON
ejpam-4941	381	25	copied	copy	VERB
ejpam-4941	381	26	it	it	PRON
ejpam-4941	381	27	.	.	PUNCT
ejpam-4941	382	1	thus	thus	ADV
ejpam-4941	382	2	,	,	PUNCT
ejpam-4941	382	3	without	without	ADP
ejpam-4941	382	4	forgetting	forget	VERB
ejpam-4941	382	5	the	the	DET
ejpam-4941	382	6	remark	remark	NOUN
ejpam-4941	382	7	given	give	VERB
ejpam-4941	382	8	above	above	ADV
ejpam-4941	382	9	in	in	ADP
ejpam-4941	382	10	the	the	DET
ejpam-4941	382	11	part	part	NOUN
ejpam-4941	382	12	of	of	ADP
ejpam-4941	382	13	input	input	NOUN
ejpam-4941	382	14	,	,	PUNCT
ejpam-4941	382	15	we	we	PRON
ejpam-4941	382	16	simply	simply	ADV
ejpam-4941	382	17	go	go	VERB
ejpam-4941	382	18	to	to	ADP
ejpam-4941	382	19	the	the	DET
ejpam-4941	382	20	computation	computation	NOUN
ejpam-4941	382	21	of	of	ADP
ejpam-4941	382	22	its	its	PRON
ejpam-4941	382	23	associated	associated	ADJ
ejpam-4941	382	24	orthogonal	orthogonal	ADJ
ejpam-4941	382	25	bases	basis	NOUN
ejpam-4941	382	26	(	(	PUNCT
ejpam-4941	382	27	f∗∗	f∗∗	NOUN
ejpam-4941	382	28	1	1	NUM
ejpam-4941	382	29	,	,	PUNCT
ejpam-4941	382	30	...	...	PUNCT
ejpam-4941	382	31	f∗∗	f∗∗	NOUN
ejpam-4941	382	32	n	n	CCONJ
ejpam-4941	382	33	)	)	PUNCT
ejpam-4941	382	34	or	or	CCONJ
ejpam-4941	382	35	(	(	PUNCT
ejpam-4941	382	36	f∗	f∗	NOUN
ejpam-4941	382	37	1	1	NUM
ejpam-4941	382	38	,	,	PUNCT
ejpam-4941	382	39	...	...	PUNCT
ejpam-4941	382	40	f	f	PROPN
ejpam-4941	382	41	∗	∗	NOUN
ejpam-4941	382	42	n	n	CCONJ
ejpam-4941	382	43	)	)	PUNCT
ejpam-4941	382	44	using	use	VERB
ejpam-4941	382	45	either	either	CCONJ
ejpam-4941	382	46	mgs	mgs	NOUN
ejpam-4941	382	47	or	or	CCONJ
ejpam-4941	382	48	gs	gs	PROPN
ejpam-4941	382	49	defined	define	VERB
ejpam-4941	382	50	respectively	respectively	ADV
ejpam-4941	382	51	as	as	SCONJ
ejpam-4941	382	52	follows	follow	VERB
ejpam-4941	382	53	intermediary	intermediary	ADJ
ejpam-4941	382	54	step	step	NOUN
ejpam-4941	382	55	•	•	NOUN
ejpam-4941	382	56	mgs	mgs	NOUN
ejpam-4941	382	57	case	case	NOUN
ejpam-4941	382	58	:	:	PUNCT
ejpam-4941	382	59	–	–	PUNCT
ejpam-4941	382	60	if	if	SCONJ
ejpam-4941	382	61	1	1	NUM
ejpam-4941	382	62	≤	≤	PUNCT
ejpam-4941	382	63	i	i	PRON
ejpam-4941	382	64	<	<	X
ejpam-4941	382	65	j	j	PROPN
ejpam-4941	382	66	,	,	PUNCT
ejpam-4941	382	67	then	then	ADV
ejpam-4941	382	68	we	we	PRON
ejpam-4941	382	69	proceed	proceed	VERB
ejpam-4941	382	70	by	by	ADP
ejpam-4941	382	71	the	the	DET
ejpam-4941	382	72	following	follow	VERB
ejpam-4941	382	73	formulations	formulation	NOUN
ejpam-4941	382	74	f∗∗	f∗∗	VERB
ejpam-4941	382	75	1	1	NUM
ejpam-4941	382	76	=	=	SYM
ejpam-4941	382	77	f1	f1	NOUN
ejpam-4941	382	78	f∗∗	f∗∗	NOUN
ejpam-4941	382	79	2	2	NUM
ejpam-4941	382	80	→	→	SYM
ejpam-4941	382	81	f	f	X
ejpam-4941	382	82	∗∗(1	∗∗(1	PROPN
ejpam-4941	382	83	)	)	PUNCT
ejpam-4941	382	84	2	2	NUM
ejpam-4941	382	85	=	=	SYM
ejpam-4941	382	86	f2	f2	PROPN
ejpam-4941	382	87	−	−	PROPN
ejpam-4941	382	88	⟨f2	⟨f2	NOUN
ejpam-4941	382	89	,	,	PUNCT
ejpam-4941	382	90	f∗∗	f∗∗	NOUN
ejpam-4941	382	91	1	1	NUM
ejpam-4941	382	92	⟩	⟩	NOUN
ejpam-4941	382	93	⟨f∗∗	⟨f∗∗	ADJ
ejpam-4941	382	94	1	1	NUM
ejpam-4941	382	95	,	,	PUNCT
ejpam-4941	382	96	f∗∗	f∗∗	NOUN
ejpam-4941	382	97	1	1	NUM
ejpam-4941	382	98	⟩	⟩	NOUN
ejpam-4941	382	99	f∗∗	f∗∗	NOUN
ejpam-4941	382	100	1	1	NUM
ejpam-4941	382	101	,	,	PUNCT
ejpam-4941	382	102	f	f	PROPN
ejpam-4941	382	103	∗∗(1	∗∗(1	PROPN
ejpam-4941	382	104	)	)	PUNCT
ejpam-4941	382	105	3	3	NUM
ejpam-4941	382	106	=	=	SYM
ejpam-4941	382	107	f3	f3	NOUN
ejpam-4941	382	108	−	−	PROPN
ejpam-4941	382	109	⟨f3	⟨f3	ADJ
ejpam-4941	382	110	,	,	PUNCT
ejpam-4941	382	111	f∗∗	f∗∗	NOUN
ejpam-4941	382	112	1	1	NUM
ejpam-4941	382	113	⟩	⟩	NOUN
ejpam-4941	382	114	⟨f∗∗	⟨f∗∗	ADJ
ejpam-4941	382	115	1	1	NUM
ejpam-4941	382	116	,	,	PUNCT
ejpam-4941	382	117	f∗∗	f∗∗	NOUN
ejpam-4941	382	118	1	1	NUM
ejpam-4941	382	119	⟩	⟩	NOUN
ejpam-4941	382	120	f∗∗	f∗∗	NOUN
ejpam-4941	382	121	1	1	NUM
ejpam-4941	382	122	f∗∗	f∗∗	NOUN
ejpam-4941	382	123	3	3	NUM
ejpam-4941	382	124	→	→	SYM
ejpam-4941	382	125	f	f	X
ejpam-4941	382	126	∗∗(2	∗∗(2	PROPN
ejpam-4941	382	127	)	)	PUNCT
ejpam-4941	382	128	3	3	NUM
ejpam-4941	382	129	=	=	SYM
ejpam-4941	382	130	f	f	X
ejpam-4941	382	131	∗∗(1	∗∗(1	PROPN
ejpam-4941	382	132	)	)	PUNCT
ejpam-4941	382	133	3	3	NUM
ejpam-4941	382	134	−	−	NOUN
ejpam-4941	382	135	⟨f∗∗(1	⟨f∗∗(1	NOUN
ejpam-4941	382	136	)	)	PUNCT
ejpam-4941	382	137	3	3	NUM
ejpam-4941	382	138	,	,	PUNCT
ejpam-4941	382	139	f∗∗	f∗∗	NOUN
ejpam-4941	382	140	2	2	NUM
ejpam-4941	382	141	⟩	⟩	NOUN
ejpam-4941	382	142	⟨f∗∗	⟨f∗∗	NUM
ejpam-4941	382	143	2	2	NUM
ejpam-4941	382	144	,	,	PUNCT
ejpam-4941	382	145	f∗∗	f∗∗	NOUN
ejpam-4941	382	146	2	2	NUM
ejpam-4941	382	147	⟩	⟩	NOUN
ejpam-4941	382	148	f∗∗	f∗∗	NOUN
ejpam-4941	382	149	2	2	NUM
ejpam-4941	382	150	...	...	PUNCT
ejpam-4941	382	151	...	...	PUNCT
ejpam-4941	382	152	f∗∗(k−1	f∗∗(k−1	X
ejpam-4941	382	153	)	)	PUNCT
ejpam-4941	383	1	n	n	NOUN
ejpam-4941	383	2	=	=	SYM
ejpam-4941	383	3	fn	fn	PROPN
ejpam-4941	383	4	−	−	PROPN
ejpam-4941	383	5	⟨fn	⟨fn	NOUN
ejpam-4941	383	6	,	,	PUNCT
ejpam-4941	383	7	f∗∗	f∗∗	PROPN
ejpam-4941	383	8	k−1⟩	k−1⟩	PROPN
ejpam-4941	383	9	⟨f∗∗	⟨f∗∗	ADP
ejpam-4941	383	10	k−1	k−1	PROPN
ejpam-4941	383	11	,	,	PUNCT
ejpam-4941	383	12	f	f	PROPN
ejpam-4941	383	13	∗∗	∗∗	X
ejpam-4941	384	1	k−1⟩	k−1⟩	PRON
ejpam-4941	384	2	f∗∗	f∗∗	PROPN
ejpam-4941	384	3	k−1	k−1	PROPN
ejpam-4941	384	4	,	,	PUNCT
ejpam-4941	384	5	k	k	PROPN
ejpam-4941	384	6	=	=	SYM
ejpam-4941	384	7	2	2	NUM
ejpam-4941	384	8	,	,	PUNCT
ejpam-4941	384	9	...	...	PUNCT
ejpam-4941	384	10	,	,	PUNCT
ejpam-4941	384	11	n−	n−	NOUN
ejpam-4941	384	12	1	1	NUM
ejpam-4941	384	13	s.	s.	PROPN
ejpam-4941	384	14	abdelalim	abdelalim	PROPN
ejpam-4941	384	15	,	,	PUNCT
ejpam-4941	384	16	i.	i.	PROPN
ejpam-4941	384	17	elmouki	elmouki	PROPN
ejpam-4941	384	18	/	/	SYM
ejpam-4941	384	19	eur	eur	PROPN
ejpam-4941	384	20	.	.	PUNCT
ejpam-4941	385	1	j.	j.	PROPN
ejpam-4941	385	2	pure	pure	PROPN
ejpam-4941	385	3	appl	appl	PROPN
ejpam-4941	385	4	.	.	PROPN
ejpam-4941	385	5	math	math	PROPN
ejpam-4941	385	6	,	,	PUNCT
ejpam-4941	385	7	16	16	NUM
ejpam-4941	385	8	(	(	PUNCT
ejpam-4941	385	9	4	4	NUM
ejpam-4941	385	10	)	)	PUNCT
ejpam-4941	385	11	(	(	PUNCT
ejpam-4941	385	12	2023	2023	NUM
ejpam-4941	385	13	)	)	PUNCT
ejpam-4941	385	14	,	,	PUNCT
ejpam-4941	385	15	2662	2662	NUM
ejpam-4941	385	16	-	-	SYM
ejpam-4941	385	17	2692	2692	NUM
ejpam-4941	385	18	2683	2683	NUM
ejpam-4941	385	19	f∗∗	f∗∗	NOUN
ejpam-4941	385	20	n	n	CCONJ
ejpam-4941	385	21	→	→	SYM
ejpam-4941	385	22	f∗∗(k	f∗∗(k	ADJ
ejpam-4941	385	23	)	)	PUNCT
ejpam-4941	385	24	n	n	NOUN
ejpam-4941	385	25	=	=	PUNCT
ejpam-4941	385	26	e∗∗(k−1	e∗∗(k−1	NOUN
ejpam-4941	385	27	)	)	PUNCT
ejpam-4941	385	28	n	n	CCONJ
ejpam-4941	385	29	−	−	PROPN
ejpam-4941	385	30	⟨f∗∗(k−1	⟨f∗∗(k−1	NUM
ejpam-4941	385	31	)	)	PUNCT
ejpam-4941	386	1	n	n	CCONJ
ejpam-4941	386	2	,	,	PUNCT
ejpam-4941	386	3	f∗∗	f∗∗	PROPN
ejpam-4941	386	4	k	k	PROPN
ejpam-4941	386	5	⟩	⟩	PROPN
ejpam-4941	386	6	⟨f∗∗	⟨f∗∗	X
ejpam-4941	387	1	k	k	X
ejpam-4941	387	2	,	,	PUNCT
ejpam-4941	387	3	f∗∗	f∗∗	PROPN
ejpam-4941	387	4	k	k	PROPN
ejpam-4941	387	5	⟩	⟩	PROPN
ejpam-4941	387	6	f∗∗	f∗∗	PROPN
ejpam-4941	387	7	k	k	PROPN
ejpam-4941	387	8	,	,	PUNCT
ejpam-4941	387	9	k	k	PROPN
ejpam-4941	387	10	=	=	SYM
ejpam-4941	387	11	2	2	NUM
ejpam-4941	387	12	,	,	PUNCT
ejpam-4941	387	13	...	...	PUNCT
ejpam-4941	387	14	,	,	PUNCT
ejpam-4941	387	15	n−	n−	NOUN
ejpam-4941	387	16	1	1	NUM
ejpam-4941	387	17	–	–	PUNCT
ejpam-4941	387	18	if	if	SCONJ
ejpam-4941	387	19	i	i	PRON
ejpam-4941	387	20	>	>	X
ejpam-4941	387	21	j	j	PROPN
ejpam-4941	388	1	+	+	CCONJ
ejpam-4941	388	2	1	1	NUM
ejpam-4941	388	3	,	,	PUNCT
ejpam-4941	388	4	then	then	ADV
ejpam-4941	388	5	we	we	PRON
ejpam-4941	388	6	use	use	VERB
ejpam-4941	388	7	from	from	ADP
ejpam-4941	388	8	theorem	theorem	ADJ
ejpam-4941	388	9	2	2	NUM
ejpam-4941	388	10	,	,	PUNCT
ejpam-4941	388	11	the	the	DET
ejpam-4941	388	12	equality	equality	NOUN
ejpam-4941	388	13	f	f	PROPN
ejpam-4941	388	14	∗∗(k	∗∗(k	NOUN
ejpam-4941	388	15	)	)	PUNCT
ejpam-4941	388	16	i	i	PRON
ejpam-4941	389	1	=	=	PUNCT
ejpam-4941	389	2	e	e	X
ejpam-4941	389	3	∗∗(k	∗∗(k	NOUN
ejpam-4941	389	4	)	)	PUNCT
ejpam-4941	390	1	i	i	PRON
ejpam-4941	390	2	,	,	PUNCT
ejpam-4941	390	3	k	k	PROPN
ejpam-4941	390	4	=	=	SYM
ejpam-4941	390	5	2	2	NUM
ejpam-4941	390	6	,	,	PUNCT
ejpam-4941	390	7	...	...	PUNCT
ejpam-4941	390	8	,	,	PUNCT
ejpam-4941	390	9	i−	i−	PROPN
ejpam-4941	390	10	1	1	NUM
ejpam-4941	390	11	.	.	NOUN
ejpam-4941	390	12	•	•	NUM
ejpam-4941	390	13	gs	gs	NOUN
ejpam-4941	390	14	case	case	NOUN
ejpam-4941	390	15	:	:	PUNCT
ejpam-4941	390	16	–	–	PUNCT
ejpam-4941	390	17	if	if	SCONJ
ejpam-4941	390	18	1	1	NUM
ejpam-4941	390	19	≤	≤	PUNCT
ejpam-4941	390	20	i	i	PRON
ejpam-4941	390	21	<	<	X
ejpam-4941	390	22	j	j	PROPN
ejpam-4941	390	23	,	,	PUNCT
ejpam-4941	390	24	we	we	PRON
ejpam-4941	390	25	proceed	proceed	VERB
ejpam-4941	390	26	by	by	ADP
ejpam-4941	390	27	the	the	DET
ejpam-4941	390	28	following	follow	VERB
ejpam-4941	390	29	formulations	formulation	NOUN
ejpam-4941	390	30	f∗	f∗	NOUN
ejpam-4941	390	31	1	1	NUM
ejpam-4941	390	32	=	=	SYM
ejpam-4941	390	33	f1	f1	NOUN
ejpam-4941	390	34	f∗	f∗	NOUN
ejpam-4941	390	35	2	2	NUM
ejpam-4941	390	36	=	=	SYM
ejpam-4941	390	37	f2	f2	PROPN
ejpam-4941	390	38	−	−	PROPN
ejpam-4941	390	39	⟨f2	⟨f2	PROPN
ejpam-4941	390	40	,	,	PUNCT
ejpam-4941	390	41	f∗	f∗	NOUN
ejpam-4941	390	42	1	1	NUM
ejpam-4941	390	43	⟩	⟩	NOUN
ejpam-4941	390	44	⟨f∗	⟨f∗	NOUN
ejpam-4941	390	45	1	1	NUM
ejpam-4941	390	46	,	,	PUNCT
ejpam-4941	390	47	f	f	PROPN
ejpam-4941	390	48	∗	∗	NOUN
ejpam-4941	390	49	1	1	NUM
ejpam-4941	390	50	⟩	⟩	NOUN
ejpam-4941	390	51	f∗	f∗	NOUN
ejpam-4941	390	52	1	1	NUM
ejpam-4941	390	53	,	,	PUNCT
ejpam-4941	391	1	f∗	f∗	X
ejpam-4941	391	2	3	3	NUM
ejpam-4941	391	3	=	=	SYM
ejpam-4941	391	4	f3	f3	NOUN
ejpam-4941	391	5	−	−	PROPN
ejpam-4941	391	6	⟨f3	⟨f3	ADJ
ejpam-4941	391	7	,	,	PUNCT
ejpam-4941	391	8	f∗	f∗	NOUN
ejpam-4941	391	9	1	1	NUM
ejpam-4941	391	10	⟩	⟩	NOUN
ejpam-4941	391	11	⟨f∗	⟨f∗	NOUN
ejpam-4941	391	12	1	1	NUM
ejpam-4941	391	13	,	,	PUNCT
ejpam-4941	391	14	f	f	PROPN
ejpam-4941	391	15	∗	∗	NOUN
ejpam-4941	391	16	1	1	NUM
ejpam-4941	391	17	⟩	⟩	NOUN
ejpam-4941	391	18	f∗	f∗	NOUN
ejpam-4941	391	19	1	1	NUM
ejpam-4941	391	20	−	−	NOUN
ejpam-4941	391	21	⟨e3	⟨e3	NOUN
ejpam-4941	391	22	,	,	PUNCT
ejpam-4941	391	23	e∗2⟩	e∗2⟩	PRON
ejpam-4941	391	24	⟨f∗	⟨f∗	NOUN
ejpam-4941	391	25	2	2	NUM
ejpam-4941	391	26	,	,	PUNCT
ejpam-4941	391	27	f	f	PROPN
ejpam-4941	391	28	∗	∗	NOUN
ejpam-4941	391	29	2	2	NUM
ejpam-4941	391	30	⟩	⟩	NOUN
ejpam-4941	391	31	f∗	f∗	NOUN
ejpam-4941	391	32	2	2	NUM
ejpam-4941	391	33	...	...	PUNCT
ejpam-4941	391	34	...	...	PUNCT
ejpam-4941	392	1	f∗	f∗	NOUN
ejpam-4941	392	2	n	n	NOUN
ejpam-4941	392	3	=	=	SYM
ejpam-4941	392	4	fn	fn	PROPN
ejpam-4941	392	5	−	−	PROPN
ejpam-4941	392	6	n−1∑	n−1∑	PROPN
ejpam-4941	392	7	k=1	k=1	PROPN
ejpam-4941	392	8	⟨fn	⟨fn	PROPN
ejpam-4941	392	9	,	,	PUNCT
ejpam-4941	392	10	f∗	f∗	PROPN
ejpam-4941	392	11	k	k	PROPN
ejpam-4941	392	12	⟩	⟩	PROPN
ejpam-4941	393	1	⟨f∗	⟨f∗	PROPN
ejpam-4941	394	1	k	k	PROPN
ejpam-4941	394	2	,	,	PUNCT
ejpam-4941	394	3	f	f	PROPN
ejpam-4941	394	4	∗	∗	X
ejpam-4941	394	5	k	k	PROPN
ejpam-4941	394	6	⟩	⟩	PROPN
ejpam-4941	394	7	f∗	f∗	NOUN
ejpam-4941	394	8	k	k	X
ejpam-4941	394	9	–	–	PUNCT
ejpam-4941	394	10	if	if	SCONJ
ejpam-4941	394	11	i	i	PRON
ejpam-4941	394	12	>	>	X
ejpam-4941	394	13	j	j	PROPN
ejpam-4941	395	1	+	+	CCONJ
ejpam-4941	395	2	1	1	NUM
ejpam-4941	395	3	,	,	PUNCT
ejpam-4941	395	4	then	then	ADV
ejpam-4941	395	5	we	we	PRON
ejpam-4941	395	6	use	use	VERB
ejpam-4941	395	7	from	from	ADP
ejpam-4941	395	8	theorem	theorem	ADJ
ejpam-4941	395	9	2	2	NUM
ejpam-4941	395	10	,	,	PUNCT
ejpam-4941	395	11	the	the	DET
ejpam-4941	395	12	equality	equality	NOUN
ejpam-4941	395	13	f∗	f∗	NOUN
ejpam-4941	395	14	i	i	NOUN
ejpam-4941	395	15	=	=	PUNCT
ejpam-4941	395	16	e∗i	e∗i	NUM
ejpam-4941	395	17	.	.	PUNCT
ejpam-4941	396	1	as	as	ADP
ejpam-4941	396	2	for	for	ADP
ejpam-4941	396	3	the	the	DET
ejpam-4941	396	4	next	next	ADJ
ejpam-4941	396	5	step	step	NOUN
ejpam-4941	396	6	and	and	CCONJ
ejpam-4941	396	7	which	which	PRON
ejpam-4941	396	8	concerns	concern	VERB
ejpam-4941	396	9	the	the	DET
ejpam-4941	396	10	vectors	vector	NOUN
ejpam-4941	396	11	swapping	swap	VERB
ejpam-4941	396	12	and	and	CCONJ
ejpam-4941	396	13	that	that	PRON
ejpam-4941	396	14	is	be	AUX
ejpam-4941	396	15	presented	present	VERB
ejpam-4941	396	16	by	by	ADP
ejpam-4941	396	17	using	use	VERB
ejpam-4941	396	18	the	the	DET
ejpam-4941	396	19	second	second	ADJ
ejpam-4941	396	20	,	,	PUNCT
ejpam-4941	396	21	third	third	ADJ
ejpam-4941	396	22	and	and	CCONJ
ejpam-4941	396	23	fourth	fourth	ADJ
ejpam-4941	396	24	results	result	NOUN
ejpam-4941	396	25	of	of	ADP
ejpam-4941	396	26	the	the	DET
ejpam-4941	396	27	vectors	vector	NOUN
ejpam-4941	396	28	exchange	exchange	NOUN
ejpam-4941	396	29	theorem	theorem	VERB
ejpam-4941	396	30	,	,	PUNCT
ejpam-4941	396	31	namely	namely	ADV
ejpam-4941	396	32	when	when	SCONJ
ejpam-4941	396	33	we	we	PRON
ejpam-4941	396	34	are	be	AUX
ejpam-4941	396	35	either	either	CCONJ
ejpam-4941	396	36	in	in	ADP
ejpam-4941	396	37	condition	condition	NOUN
ejpam-4941	397	1	i	i	PRON
ejpam-4941	397	2	=	=	SYM
ejpam-4941	397	3	j	j	PROPN
ejpam-4941	397	4	or	or	CCONJ
ejpam-4941	397	5	i	i	PRON
ejpam-4941	397	6	=	=	SYM
ejpam-4941	397	7	j	j	PROPN
ejpam-4941	398	1	+	+	NOUN
ejpam-4941	398	2	1	1	NUM
ejpam-4941	398	3	,	,	PUNCT
ejpam-4941	398	4	then	then	ADV
ejpam-4941	398	5	we	we	PRON
ejpam-4941	398	6	have	have	VERB
ejpam-4941	398	7	the	the	DET
ejpam-4941	398	8	following	follow	VERB
ejpam-4941	398	9	algorithmic	algorithmic	ADJ
ejpam-4941	398	10	form	form	NOUN
ejpam-4941	398	11	vectors	vector	NOUN
ejpam-4941	398	12	exchange	exchange	NOUN
ejpam-4941	398	13	theorem	theorem	VERB
ejpam-4941	398	14	step	step	NOUN
ejpam-4941	398	15	mgs	mgs	NOUN
ejpam-4941	398	16	case	case	NOUN
ejpam-4941	398	17	:	:	PUNCT
ejpam-4941	398	18	•	•	INTJ
ejpam-4941	398	19	if	if	SCONJ
ejpam-4941	398	20	i	i	PRON
ejpam-4941	398	21	=	=	SYM
ejpam-4941	398	22	j	j	PROPN
ejpam-4941	398	23	,	,	PUNCT
ejpam-4941	398	24	set	set	VERB
ejpam-4941	398	25	f	f	PROPN
ejpam-4941	398	26	∗∗(k	∗∗(k	NOUN
ejpam-4941	398	27	)	)	PUNCT
ejpam-4941	399	1	j	j	NOUN
ejpam-4941	400	1	=	=	PUNCT
ejpam-4941	400	2	ej+1	ej+1	PROPN
ejpam-4941	400	3	−	−	PROPN
ejpam-4941	400	4	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	400	5	,	,	PUNCT
ejpam-4941	400	6	e	e	X
ejpam-4941	400	7	∗∗	∗∗	X
ejpam-4941	400	8	k−1⟩	k−1⟩	PROPN
ejpam-4941	400	9	⟨e∗∗k−1	⟨e∗∗k−1	PROPN
ejpam-4941	400	10	,	,	PUNCT
ejpam-4941	400	11	e	e	X
ejpam-4941	400	12	∗∗	∗∗	X
ejpam-4941	401	1	k−1⟩	k−1⟩	DET
ejpam-4941	401	2	e∗∗k−1	e∗∗k−1	PROPN
ejpam-4941	401	3	−	−	NOUN
ejpam-4941	401	4	⟨e(k−1	⟨e(k−1	NUM
ejpam-4941	401	5	)	)	PUNCT
ejpam-4941	401	6	j+1	j+1	NOUN
ejpam-4941	401	7	,	,	PUNCT
ejpam-4941	401	8	e∗∗k	e∗∗k	PROPN
ejpam-4941	401	9	⟩	⟩	NOUN
ejpam-4941	401	10	⟨e∗∗k	⟨e∗∗k	NOUN
ejpam-4941	401	11	,	,	PUNCT
ejpam-4941	401	12	e∗∗k	e∗∗k	PROPN
ejpam-4941	401	13	⟩	⟩	PROPN
ejpam-4941	401	14	e∗∗k	e∗∗k	PROPN
ejpam-4941	401	15	,	,	PUNCT
ejpam-4941	401	16	k	k	PROPN
ejpam-4941	401	17	=	=	SYM
ejpam-4941	401	18	2	2	NUM
ejpam-4941	401	19	,	,	PUNCT
ejpam-4941	401	20	...	...	PUNCT
ejpam-4941	401	21	,	,	PUNCT
ejpam-4941	401	22	j	j	PROPN
ejpam-4941	401	23	−	−	PROPN
ejpam-4941	401	24	1	1	NUM
ejpam-4941	401	25	.	.	X
ejpam-4941	401	26	•	•	NOUN
ejpam-4941	401	27	if	if	SCONJ
ejpam-4941	401	28	i	i	PRON
ejpam-4941	401	29	=	=	SYM
ejpam-4941	401	30	j	j	PROPN
ejpam-4941	401	31	+	+	CCONJ
ejpam-4941	401	32	1	1	NUM
ejpam-4941	401	33	,	,	PUNCT
ejpam-4941	401	34	set	set	VERB
ejpam-4941	401	35	f	f	PROPN
ejpam-4941	401	36	∗∗(k	∗∗(k	NOUN
ejpam-4941	401	37	)	)	PUNCT
ejpam-4941	401	38	j+1	j+1	NOUN
ejpam-4941	401	39	=	=	PUNCT
ejpam-4941	401	40	e	e	X
ejpam-4941	401	41	∗∗(k	∗∗(k	NOUN
ejpam-4941	401	42	)	)	PUNCT
ejpam-4941	401	43	j	j	NOUN
ejpam-4941	401	44	,	,	PUNCT
ejpam-4941	401	45	k	k	PROPN
ejpam-4941	401	46	=	=	SYM
ejpam-4941	401	47	2	2	NUM
ejpam-4941	401	48	,	,	PUNCT
ejpam-4941	401	49	...	...	PUNCT
ejpam-4941	401	50	,	,	PUNCT
ejpam-4941	401	51	n−	n−	NOUN
ejpam-4941	401	52	1	1	NUM
ejpam-4941	401	53	.	.	PUNCT
ejpam-4941	402	1	gs	gs	PROPN
ejpam-4941	402	2	case	case	NOUN
ejpam-4941	402	3	:	:	PUNCT
ejpam-4941	402	4	•	•	INTJ
ejpam-4941	402	5	if	if	SCONJ
ejpam-4941	402	6	i	i	PRON
ejpam-4941	402	7	=	=	SYM
ejpam-4941	402	8	j	j	PROPN
ejpam-4941	402	9	,	,	PUNCT
ejpam-4941	402	10	set	set	VERB
ejpam-4941	402	11	f∗	f∗	NOUN
ejpam-4941	402	12	j	j	NOUN
ejpam-4941	402	13	=	=	PUNCT
ejpam-4941	402	14	e∗j+1	e∗j+1	NOUN
ejpam-4941	403	1	+	+	CCONJ
ejpam-4941	403	2	⟨ej+1	⟨ej+1	NUM
ejpam-4941	403	3	,	,	PUNCT
ejpam-4941	403	4	e	e	PROPN
ejpam-4941	403	5	∗	∗	PROPN
ejpam-4941	403	6	j	j	PROPN
ejpam-4941	403	7	⟩	⟩	PROPN
ejpam-4941	403	8	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	403	9	,	,	PUNCT
ejpam-4941	403	10	e∗j	e∗j	PROPN
ejpam-4941	403	11	⟩	⟩	NOUN
ejpam-4941	403	12	e∗j	e∗j	NUM
ejpam-4941	403	13	.	.	PUNCT
ejpam-4941	404	1	•	•	INTJ
ejpam-4941	404	2	if	if	SCONJ
ejpam-4941	404	3	i	i	PRON
ejpam-4941	404	4	=	=	SYM
ejpam-4941	404	5	j	j	PROPN
ejpam-4941	405	1	+	+	CCONJ
ejpam-4941	405	2	1	1	NUM
ejpam-4941	405	3	,	,	PUNCT
ejpam-4941	405	4	set	set	VERB
ejpam-4941	405	5	f∗	f∗	NOUN
ejpam-4941	405	6	j+1	j+1	NOUN
ejpam-4941	405	7	=	=	PUNCT
ejpam-4941	405	8	|e∗j+1|2	|e∗j+1|2	VERB
ejpam-4941	405	9	|f∗∗	|f∗∗	NOUN
ejpam-4941	405	10	j	j	PROPN
ejpam-4941	405	11	|2	|2	NUM
ejpam-4941	406	1	e∗j	e∗j	NUM
ejpam-4941	406	2	−	−	NUM
ejpam-4941	406	3	⟨ej+1	⟨ej+1	PROPN
ejpam-4941	406	4	,	,	PUNCT
ejpam-4941	406	5	e	e	PROPN
ejpam-4941	406	6	∗	∗	PROPN
ejpam-4941	406	7	j	j	PROPN
ejpam-4941	406	8	⟩	⟩	PROPN
ejpam-4941	406	9	⟨e∗j	⟨e∗j	PROPN
ejpam-4941	406	10	,	,	PUNCT
ejpam-4941	406	11	e∗j	e∗j	PROPN
ejpam-4941	406	12	⟩	⟩	NOUN
ejpam-4941	406	13	|e∗j	|e∗j	ADJ
ejpam-4941	406	14	|2	|2	NUM
ejpam-4941	406	15	|f∗∗	|f∗∗	NOUN
ejpam-4941	406	16	j	j	PROPN
ejpam-4941	406	17	|2	|2	NUM
ejpam-4941	406	18	e∗j+1	e∗j+1	NOUN
ejpam-4941	406	19	.	.	PUNCT
ejpam-4941	407	1	in	in	ADP
ejpam-4941	407	2	order	order	NOUN
ejpam-4941	407	3	to	to	PART
ejpam-4941	407	4	present	present	VERB
ejpam-4941	407	5	a	a	DET
ejpam-4941	407	6	concrete	concrete	ADJ
ejpam-4941	407	7	application	application	NOUN
ejpam-4941	407	8	of	of	ADP
ejpam-4941	407	9	the	the	DET
ejpam-4941	407	10	algorithm	algorithm	NOUN
ejpam-4941	407	11	above	above	ADV
ejpam-4941	407	12	,	,	PUNCT
ejpam-4941	407	13	we	we	PRON
ejpam-4941	407	14	provide	provide	VERB
ejpam-4941	407	15	a	a	DET
ejpam-4941	407	16	numerical	numerical	ADJ
ejpam-4941	407	17	example	example	NOUN
ejpam-4941	407	18	in	in	ADP
ejpam-4941	407	19	the	the	DET
ejpam-4941	407	20	following	follow	VERB
ejpam-4941	407	21	section	section	NOUN
ejpam-4941	407	22	.	.	PUNCT
ejpam-4941	408	1	s.	s.	PROPN
ejpam-4941	408	2	abdelalim	abdelalim	PROPN
ejpam-4941	408	3	,	,	PUNCT
ejpam-4941	408	4	i.	i.	PROPN
ejpam-4941	408	5	elmouki	elmouki	PROPN
ejpam-4941	408	6	/	/	SYM
ejpam-4941	408	7	eur	eur	PROPN
ejpam-4941	408	8	.	.	PUNCT
ejpam-4941	409	1	j.	j.	PROPN
ejpam-4941	409	2	pure	pure	PROPN
ejpam-4941	409	3	appl	appl	PROPN
ejpam-4941	409	4	.	.	PROPN
ejpam-4941	409	5	math	math	PROPN
ejpam-4941	409	6	,	,	PUNCT
ejpam-4941	409	7	16	16	NUM
ejpam-4941	409	8	(	(	PUNCT
ejpam-4941	409	9	4	4	NUM
ejpam-4941	409	10	)	)	PUNCT
ejpam-4941	409	11	(	(	PUNCT
ejpam-4941	409	12	2023	2023	NUM
ejpam-4941	409	13	)	)	PUNCT
ejpam-4941	409	14	,	,	PUNCT
ejpam-4941	409	15	2662	2662	NUM
ejpam-4941	409	16	-	-	SYM
ejpam-4941	409	17	2692	2692	NUM
ejpam-4941	409	18	2684	2684	NUM
ejpam-4941	409	19	3.2	3.2	NUM
ejpam-4941	409	20	.	.	PUNCT
ejpam-4941	410	1	ae	ae	PROPN
ejpam-4941	410	2	algorithm	algorithm	PROPN
ejpam-4941	410	3	from	from	ADP
ejpam-4941	410	4	numerics	numeric	NOUN
ejpam-4941	410	5	in	in	ADP
ejpam-4941	410	6	this	this	DET
ejpam-4941	410	7	section	section	NOUN
ejpam-4941	410	8	,	,	PUNCT
ejpam-4941	410	9	we	we	PRON
ejpam-4941	410	10	will	will	AUX
ejpam-4941	410	11	we	we	PRON
ejpam-4941	410	12	explain	explain	VERB
ejpam-4941	410	13	how	how	SCONJ
ejpam-4941	410	14	the	the	DET
ejpam-4941	410	15	ae	ae	PROPN
ejpam-4941	410	16	algorithm	algorithm	NOUN
ejpam-4941	410	17	can	can	AUX
ejpam-4941	410	18	be	be	AUX
ejpam-4941	410	19	used	use	VERB
ejpam-4941	410	20	through	through	ADP
ejpam-4941	410	21	a	a	DET
ejpam-4941	410	22	numerical	numerical	ADJ
ejpam-4941	410	23	example	example	NOUN
ejpam-4941	410	24	.	.	PUNCT
ejpam-4941	411	1	mathematically	mathematically	ADV
ejpam-4941	411	2	speaking	speak	VERB
ejpam-4941	411	3	,	,	PUNCT
ejpam-4941	411	4	we	we	PRON
ejpam-4941	411	5	have	have	AUX
ejpam-4941	411	6	showed	show	VERB
ejpam-4941	411	7	in	in	ADP
ejpam-4941	411	8	theorem	theorem	NOUN
ejpam-4941	411	9	1	1	NUM
ejpam-4941	411	10	above	above	ADP
ejpam-4941	411	11	that	that	DET
ejpam-4941	411	12	gs	gs	PROPN
ejpam-4941	411	13	and	and	CCONJ
ejpam-4941	411	14	mgs	mgs	NOUN
ejpam-4941	411	15	processes	process	NOUN
ejpam-4941	411	16	are	be	AUX
ejpam-4941	411	17	proven	prove	VERB
ejpam-4941	411	18	to	to	PART
ejpam-4941	411	19	produce	produce	VERB
ejpam-4941	411	20	orthogonal	orthogonal	ADJ
ejpam-4941	411	21	vectors	vector	NOUN
ejpam-4941	411	22	,	,	PUNCT
ejpam-4941	411	23	however	however	ADV
ejpam-4941	411	24	,	,	PUNCT
ejpam-4941	411	25	the	the	DET
ejpam-4941	411	26	main	main	ADJ
ejpam-4941	411	27	reason	reason	NOUN
ejpam-4941	411	28	behind	behind	ADP
ejpam-4941	411	29	thinking	think	VERB
ejpam-4941	411	30	about	about	ADP
ejpam-4941	411	31	these	these	DET
ejpam-4941	411	32	two	two	NUM
ejpam-4941	411	33	different	different	ADJ
ejpam-4941	411	34	ways	way	NOUN
ejpam-4941	411	35	in	in	ADP
ejpam-4941	411	36	order	order	NOUN
ejpam-4941	411	37	to	to	PART
ejpam-4941	411	38	orthogonalize	orthogonalize	VERB
ejpam-4941	411	39	vectors	vector	NOUN
ejpam-4941	411	40	,	,	PUNCT
ejpam-4941	411	41	is	be	AUX
ejpam-4941	411	42	that	that	SCONJ
ejpam-4941	411	43	when	when	SCONJ
ejpam-4941	411	44	it	it	PRON
ejpam-4941	411	45	comes	come	VERB
ejpam-4941	411	46	to	to	ADP
ejpam-4941	411	47	numerical	numerical	PROPN
ejpam-4941	411	48	computing	computing	NOUN
ejpam-4941	411	49	,	,	PUNCT
ejpam-4941	411	50	we	we	PRON
ejpam-4941	411	51	come	come	VERB
ejpam-4941	411	52	in	in	ADP
ejpam-4941	411	53	front	front	NOUN
ejpam-4941	411	54	of	of	ADP
ejpam-4941	411	55	a	a	DET
ejpam-4941	411	56	slight	slight	ADJ
ejpam-4941	411	57	difference	difference	NOUN
ejpam-4941	411	58	in	in	ADP
ejpam-4941	411	59	the	the	DET
ejpam-4941	411	60	orthogonality	orthogonality	NOUN
ejpam-4941	411	61	results	result	NOUN
ejpam-4941	411	62	but	but	CCONJ
ejpam-4941	411	63	that	that	PRON
ejpam-4941	411	64	may	may	AUX
ejpam-4941	411	65	become	become	VERB
ejpam-4941	411	66	important	important	ADJ
ejpam-4941	411	67	for	for	ADP
ejpam-4941	411	68	some	some	DET
ejpam-4941	411	69	problems	problem	NOUN
ejpam-4941	411	70	.	.	PUNCT
ejpam-4941	412	1	thus	thus	ADV
ejpam-4941	412	2	,	,	PUNCT
ejpam-4941	412	3	to	to	PART
ejpam-4941	412	4	get	get	AUX
ejpam-4941	412	5	convinced	convince	VERB
ejpam-4941	412	6	by	by	ADP
ejpam-4941	412	7	the	the	DET
ejpam-4941	412	8	choice	choice	NOUN
ejpam-4941	412	9	of	of	ADP
ejpam-4941	412	10	mgs	mgs	NOUN
ejpam-4941	412	11	as	as	ADP
ejpam-4941	412	12	example	example	NOUN
ejpam-4941	412	13	,	,	PUNCT
ejpam-4941	412	14	we	we	PRON
ejpam-4941	412	15	decide	decide	VERB
ejpam-4941	412	16	to	to	PART
ejpam-4941	412	17	produce	produce	VERB
ejpam-4941	412	18	numerical	numerical	ADJ
ejpam-4941	412	19	results	result	NOUN
ejpam-4941	412	20	using	use	VERB
ejpam-4941	412	21	our	our	PRON
ejpam-4941	412	22	own	own	ADJ
ejpam-4941	412	23	python	python	NOUN
ejpam-4941	412	24	code	code	NOUN
ejpam-4941	412	25	as	as	SCONJ
ejpam-4941	412	26	we	we	PRON
ejpam-4941	412	27	could	could	AUX
ejpam-4941	412	28	only	only	ADV
ejpam-4941	412	29	find	find	VERB
ejpam-4941	412	30	very	very	ADV
ejpam-4941	412	31	few	few	ADJ
ejpam-4941	412	32	examples	example	NOUN
ejpam-4941	412	33	in	in	ADP
ejpam-4941	412	34	literature	literature	NOUN
ejpam-4941	412	35	,	,	PUNCT
ejpam-4941	412	36	explained	explain	VERB
ejpam-4941	412	37	just	just	ADV
ejpam-4941	412	38	through	through	ADP
ejpam-4941	412	39	pen	pen	NOUN
ejpam-4941	412	40	or	or	CCONJ
ejpam-4941	412	41	text	text	NOUN
ejpam-4941	412	42	rather	rather	ADV
ejpam-4941	412	43	than	than	ADP
ejpam-4941	412	44	programs	program	NOUN
ejpam-4941	412	45	.	.	PUNCT
ejpam-4941	413	1	as	as	ADP
ejpam-4941	413	2	an	an	DET
ejpam-4941	413	3	important	important	ADJ
ejpam-4941	413	4	remark	remark	NOUN
ejpam-4941	413	5	,	,	PUNCT
ejpam-4941	413	6	most	most	ADJ
ejpam-4941	413	7	numerical	numerical	ADJ
ejpam-4941	413	8	experiments	experiment	NOUN
ejpam-4941	413	9	and	and	CCONJ
ejpam-4941	413	10	problems	problem	NOUN
ejpam-4941	413	11	in	in	ADP
ejpam-4941	413	12	lattice	lattice	NOUN
ejpam-4941	413	13	reduction	reduction	NOUN
ejpam-4941	413	14	problems	problem	NOUN
ejpam-4941	413	15	,	,	PUNCT
ejpam-4941	413	16	have	have	AUX
ejpam-4941	413	17	focused	focus	VERB
ejpam-4941	413	18	only	only	ADV
ejpam-4941	413	19	in	in	ADP
ejpam-4941	413	20	providing	provide	VERB
ejpam-4941	413	21	examples	example	NOUN
ejpam-4941	413	22	with	with	ADP
ejpam-4941	413	23	the	the	DET
ejpam-4941	413	24	assumption	assumption	NOUN
ejpam-4941	413	25	that	that	SCONJ
ejpam-4941	413	26	the	the	DET
ejpam-4941	413	27	dimension	dimension	NOUN
ejpam-4941	413	28	of	of	ADP
ejpam-4941	413	29	the	the	DET
ejpam-4941	413	30	lattice	lattice	NOUN
ejpam-4941	413	31	is	be	AUX
ejpam-4941	413	32	equal	equal	ADJ
ejpam-4941	413	33	to	to	ADP
ejpam-4941	413	34	the	the	DET
ejpam-4941	413	35	dimension	dimension	NOUN
ejpam-4941	413	36	of	of	ADP
ejpam-4941	413	37	the	the	DET
ejpam-4941	413	38	space	space	NOUN
ejpam-4941	413	39	,	,	PUNCT
ejpam-4941	413	40	and	and	CCONJ
ejpam-4941	413	41	this	this	PRON
ejpam-4941	413	42	does	do	AUX
ejpam-4941	413	43	not	not	PART
ejpam-4941	413	44	meet	meet	VERB
ejpam-4941	413	45	the	the	DET
ejpam-4941	413	46	general	general	ADJ
ejpam-4941	413	47	definition	definition	NOUN
ejpam-4941	413	48	since	since	SCONJ
ejpam-4941	413	49	it	it	PRON
ejpam-4941	413	50	is	be	AUX
ejpam-4941	413	51	also	also	ADV
ejpam-4941	413	52	allowed	allow	VERB
ejpam-4941	413	53	to	to	PART
ejpam-4941	413	54	consider	consider	VERB
ejpam-4941	413	55	its	its	PRON
ejpam-4941	413	56	order	order	NOUN
ejpam-4941	413	57	smaller	small	ADJ
ejpam-4941	413	58	than	than	ADP
ejpam-4941	413	59	the	the	DET
ejpam-4941	413	60	one	one	NUM
ejpam-4941	413	61	of	of	ADP
ejpam-4941	413	62	the	the	DET
ejpam-4941	413	63	space	space	NOUN
ejpam-4941	413	64	.	.	PUNCT
ejpam-4941	414	1	the	the	DET
ejpam-4941	414	2	illustrations	illustration	NOUN
ejpam-4941	414	3	in	in	ADP
ejpam-4941	414	4	figure	figure	NOUN
ejpam-4941	414	5	2	2	NUM
ejpam-4941	414	6	where	where	SCONJ
ejpam-4941	414	7	we	we	PRON
ejpam-4941	414	8	are	be	AUX
ejpam-4941	414	9	moving	move	VERB
ejpam-4941	414	10	from	from	ADP
ejpam-4941	414	11	third	third	ADJ
ejpam-4941	414	12	dimensional	dimensional	ADJ
ejpam-4941	414	13	crystals	crystal	NOUN
ejpam-4941	414	14	to	to	ADP
ejpam-4941	414	15	second	second	ADJ
ejpam-4941	414	16	dimensional	dimensional	ADJ
ejpam-4941	414	17	lattice	lattice	NOUN
ejpam-4941	414	18	,	,	PUNCT
ejpam-4941	414	19	is	be	AUX
ejpam-4941	414	20	a	a	DET
ejpam-4941	414	21	good	good	ADJ
ejpam-4941	414	22	example	example	NOUN
ejpam-4941	414	23	to	to	PART
ejpam-4941	414	24	get	get	VERB
ejpam-4941	414	25	this	this	DET
ejpam-4941	414	26	point	point	NOUN
ejpam-4941	414	27	.	.	PUNCT
ejpam-4941	415	1	example	example	NOUN
ejpam-4941	415	2	.	.	PUNCT
ejpam-4941	416	1	let	let	VERB
ejpam-4941	416	2	us	we	PRON
ejpam-4941	416	3	suppose	suppose	VERB
ejpam-4941	416	4	that	that	SCONJ
ejpam-4941	416	5	we	we	PRON
ejpam-4941	416	6	have	have	VERB
ejpam-4941	416	7	a	a	DET
ejpam-4941	416	8	hypothetical	hypothetical	ADJ
ejpam-4941	416	9	fourth	fourth	ADJ
ejpam-4941	416	10	dimensional	dimensional	ADJ
ejpam-4941	416	11	bravais	bravais	NOUN
ejpam-4941	416	12	crystal	crystal	NOUN
ejpam-4941	416	13	while	while	SCONJ
ejpam-4941	416	14	the	the	DET
ejpam-4941	416	15	representing	represent	VERB
ejpam-4941	416	16	lattice	lattice	NOUN
ejpam-4941	416	17	is	be	AUX
ejpam-4941	416	18	considered	consider	VERB
ejpam-4941	416	19	to	to	PART
ejpam-4941	416	20	be	be	AUX
ejpam-4941	416	21	defined	define	VERB
ejpam-4941	416	22	in	in	ADP
ejpam-4941	416	23	the	the	DET
ejpam-4941	416	24	third	third	ADJ
ejpam-4941	416	25	dimension	dimension	NOUN
ejpam-4941	416	26	.	.	PUNCT
ejpam-4941	417	1	thus	thus	ADV
ejpam-4941	417	2	,	,	PUNCT
ejpam-4941	417	3	we	we	PRON
ejpam-4941	417	4	take	take	VERB
ejpam-4941	417	5	for	for	ADP
ejpam-4941	417	6	example	example	NOUN
ejpam-4941	417	7	our	our	PRON
ejpam-4941	417	8	input	input	NOUN
ejpam-4941	417	9	vectors	vector	NOUN
ejpam-4941	417	10	defined	define	VERB
ejpam-4941	417	11	as	as	ADP
ejpam-4941	417	12	follows	follow	VERB
ejpam-4941	417	13	,	,	PUNCT
ejpam-4941	417	14	e1	e1	NOUN
ejpam-4941	417	15	=	=	SYM
ejpam-4941	417	16	(	(	PUNCT
ejpam-4941	417	17	1	1	NUM
ejpam-4941	417	18	,	,	PUNCT
ejpam-4941	417	19	δ	δ	PROPN
ejpam-4941	417	20	,	,	PUNCT
ejpam-4941	417	21	0	0	NUM
ejpam-4941	417	22	,	,	PUNCT
ejpam-4941	417	23	0	0	NUM
ejpam-4941	417	24	)	)	PUNCT
ejpam-4941	417	25	,	,	PUNCT
ejpam-4941	417	26	e2	e2	PROPN
ejpam-4941	417	27	=	=	SYM
ejpam-4941	417	28	(	(	PUNCT
ejpam-4941	417	29	1	1	NUM
ejpam-4941	417	30	,	,	PUNCT
ejpam-4941	417	31	0	0	NUM
ejpam-4941	417	32	,	,	PUNCT
ejpam-4941	417	33	δ	δ	PROPN
ejpam-4941	417	34	,	,	PUNCT
ejpam-4941	417	35	0	0	NUM
ejpam-4941	417	36	)	)	PUNCT
ejpam-4941	417	37	,	,	PUNCT
ejpam-4941	417	38	e3	e3	NOUN
ejpam-4941	417	39	=	=	SYM
ejpam-4941	417	40	(	(	PUNCT
ejpam-4941	417	41	1	1	NUM
ejpam-4941	417	42	,	,	PUNCT
ejpam-4941	417	43	0	0	NUM
ejpam-4941	417	44	,	,	PUNCT
ejpam-4941	417	45	0	0	NUM
ejpam-4941	417	46	,	,	PUNCT
ejpam-4941	417	47	δ	δ	PROPN
ejpam-4941	417	48	)	)	PUNCT
ejpam-4941	417	49	with	with	ADP
ejpam-4941	417	50	δ	δ	PROPN
ejpam-4941	417	51	=	=	SYM
ejpam-4941	417	52	0.001	0.001	NUM
ejpam-4941	417	53	.	.	PUNCT
ejpam-4941	418	1	let	let	VERB
ejpam-4941	418	2	us	we	PRON
ejpam-4941	418	3	take	take	VERB
ejpam-4941	418	4	now	now	ADV
ejpam-4941	418	5	the	the	DET
ejpam-4941	418	6	new	new	ADJ
ejpam-4941	418	7	basis	basis	NOUN
ejpam-4941	418	8	fi	fi	NOUN
ejpam-4941	418	9	=	=	NOUN
ejpam-4941	418	10	ei	ei	NOUN
ejpam-4941	418	11	with	with	ADP
ejpam-4941	418	12	1	1	NUM
ejpam-4941	418	13	≤	≤	NUM
ejpam-4941	419	1	i	i	PRON
ejpam-4941	419	2	<	<	X
ejpam-4941	419	3	j	j	PROPN
ejpam-4941	419	4	or	or	CCONJ
ejpam-4941	419	5	i	i	PRON
ejpam-4941	419	6	>	>	X
ejpam-4941	419	7	j	j	PROPN
ejpam-4941	420	1	+	+	CCONJ
ejpam-4941	420	2	1	1	NUM
ejpam-4941	420	3	and	and	CCONJ
ejpam-4941	420	4	which	which	PRON
ejpam-4941	420	5	correspond	correspond	VERB
ejpam-4941	420	6	to	to	ADP
ejpam-4941	420	7	conditions	condition	NOUN
ejpam-4941	420	8	when	when	SCONJ
ejpam-4941	420	9	there	there	PRON
ejpam-4941	420	10	is	be	VERB
ejpam-4941	420	11	not	not	PART
ejpam-4941	420	12	yet	yet	ADV
ejpam-4941	420	13	any	any	DET
ejpam-4941	420	14	vectors	vector	NOUN
ejpam-4941	420	15	swapping	swap	VERB
ejpam-4941	420	16	.	.	PUNCT
ejpam-4941	421	1	thus	thus	ADV
ejpam-4941	421	2	,	,	PUNCT
ejpam-4941	421	3	we	we	PRON
ejpam-4941	421	4	are	be	AUX
ejpam-4941	421	5	allowed	allow	VERB
ejpam-4941	421	6	to	to	PART
ejpam-4941	421	7	rewrite	rewrite	VERB
ejpam-4941	421	8	our	our	PRON
ejpam-4941	421	9	input	input	NOUN
ejpam-4941	421	10	vectors	vector	NOUN
ejpam-4941	421	11	in	in	ADP
ejpam-4941	421	12	this	this	DET
ejpam-4941	421	13	case	case	NOUN
ejpam-4941	421	14	as	as	ADP
ejpam-4941	421	15	f1	f1	NOUN
ejpam-4941	421	16	=	=	SYM
ejpam-4941	421	17	e1	e1	PROPN
ejpam-4941	421	18	,	,	PUNCT
ejpam-4941	421	19	f2	f2	PROPN
ejpam-4941	421	20	=	=	PROPN
ejpam-4941	421	21	e2	e2	PROPN
ejpam-4941	421	22	,	,	PUNCT
ejpam-4941	421	23	f3	f3	NOUN
ejpam-4941	421	24	=	=	NOUN
ejpam-4941	421	25	e3	e3	NOUN
ejpam-4941	421	26	then	then	ADV
ejpam-4941	421	27	,	,	PUNCT
ejpam-4941	421	28	if	if	SCONJ
ejpam-4941	421	29	we	we	PRON
ejpam-4941	421	30	just	just	ADV
ejpam-4941	421	31	consider	consider	VERB
ejpam-4941	421	32	the	the	DET
ejpam-4941	421	33	non	non	ADJ
ejpam-4941	421	34	-	-	ADJ
ejpam-4941	421	35	normalized	normalized	ADJ
ejpam-4941	421	36	case	case	NOUN
ejpam-4941	421	37	for	for	ADP
ejpam-4941	421	38	both	both	DET
ejpam-4941	421	39	processes	process	NOUN
ejpam-4941	421	40	and	and	CCONJ
ejpam-4941	421	41	fix	fix	VERB
ejpam-4941	421	42	the	the	DET
ejpam-4941	421	43	same	same	ADJ
ejpam-4941	421	44	number	number	NOUN
ejpam-4941	421	45	of	of	ADP
ejpam-4941	421	46	digits	digit	NOUN
ejpam-4941	421	47	of	of	ADP
ejpam-4941	421	48	precision	precision	NOUN
ejpam-4941	421	49	for	for	ADP
ejpam-4941	421	50	all	all	DET
ejpam-4941	421	51	calculations	calculation	NOUN
ejpam-4941	421	52	of	of	ADP
ejpam-4941	421	53	the	the	DET
ejpam-4941	421	54	products	product	NOUN
ejpam-4941	421	55	to	to	ADP
ejpam-4941	421	56	32	32	NUM
ejpam-4941	421	57	,	,	PUNCT
ejpam-4941	421	58	we	we	PRON
ejpam-4941	421	59	find	find	VERB
ejpam-4941	421	60	the	the	DET
ejpam-4941	421	61	following	follow	VERB
ejpam-4941	421	62	numerical	numerical	ADJ
ejpam-4941	421	63	values	value	NOUN
ejpam-4941	421	64	of	of	ADP
ejpam-4941	421	65	the	the	DET
ejpam-4941	421	66	inner	inner	ADJ
ejpam-4941	421	67	products	product	NOUN
ejpam-4941	421	68	as	as	ADP
ejpam-4941	421	69	follow	follow	VERB
ejpam-4941	421	70	•	•	NUM
ejpam-4941	421	71	mgs	mgs	NOUN
ejpam-4941	421	72	process	process	NOUN
ejpam-4941	421	73	s.	s.	PROPN
ejpam-4941	421	74	abdelalim	abdelalim	PROPN
ejpam-4941	421	75	,	,	PUNCT
ejpam-4941	421	76	i.	i.	PROPN
ejpam-4941	421	77	elmouki	elmouki	PROPN
ejpam-4941	421	78	/	/	SYM
ejpam-4941	421	79	eur	eur	PROPN
ejpam-4941	421	80	.	.	PUNCT
ejpam-4941	422	1	j.	j.	PROPN
ejpam-4941	422	2	pure	pure	PROPN
ejpam-4941	422	3	appl	appl	PROPN
ejpam-4941	422	4	.	.	PROPN
ejpam-4941	422	5	math	math	PROPN
ejpam-4941	422	6	,	,	PUNCT
ejpam-4941	422	7	16	16	NUM
ejpam-4941	422	8	(	(	PUNCT
ejpam-4941	422	9	4	4	NUM
ejpam-4941	422	10	)	)	PUNCT
ejpam-4941	422	11	(	(	PUNCT
ejpam-4941	422	12	2023	2023	NUM
ejpam-4941	422	13	)	)	PUNCT
ejpam-4941	422	14	,	,	PUNCT
ejpam-4941	422	15	2662	2662	NUM
ejpam-4941	422	16	-	-	SYM
ejpam-4941	422	17	2692	2692	NUM
ejpam-4941	422	18	2685	2685	NUM
ejpam-4941	422	19	f∗∗	f∗∗	NOUN
ejpam-4941	422	20	1	1	NUM
ejpam-4941	422	21	=	=	SYM
ejpam-4941	422	22	(	(	PUNCT
ejpam-4941	422	23	1	1	NUM
ejpam-4941	422	24	,	,	PUNCT
ejpam-4941	422	25	δ	δ	PROPN
ejpam-4941	422	26	,	,	PUNCT
ejpam-4941	422	27	0	0	NUM
ejpam-4941	422	28	,	,	PUNCT
ejpam-4941	422	29	0	0	NUM
ejpam-4941	422	30	)	)	PUNCT
ejpam-4941	422	31	f∗∗	f∗∗	NOUN
ejpam-4941	422	32	2	2	NUM
ejpam-4941	422	33	=	=	SYM
ejpam-4941	422	34	(	(	PUNCT
ejpam-4941	422	35	9.99999×	9.99999×	NOUN
ejpam-4941	422	36	10−07,−9.99999×	10−07,−9.99999×	NUM
ejpam-4941	422	37	10−04	10−04	NOUN
ejpam-4941	422	38	,	,	PUNCT
ejpam-4941	422	39	δ	δ	PROPN
ejpam-4941	422	40	,	,	PUNCT
ejpam-4941	422	41	0	0	NUM
ejpam-4941	422	42	)	)	PUNCT
ejpam-4941	422	43	=	=	NOUN
ejpam-4941	422	44	f∗	f∗	NOUN
ejpam-4941	422	45	2	2	NUM
ejpam-4941	422	46	f∗∗	f∗∗	NOUN
ejpam-4941	422	47	3	3	NUM
ejpam-4941	422	48	=	=	SYM
ejpam-4941	422	49	(	(	PUNCT
ejpam-4941	422	50	4.9999975×	4.9999975×	NOUN
ejpam-4941	422	51	10−07,−4.9999975×	10−07,−4.9999975×	NUM
ejpam-4941	422	52	10−04,−4.9999975×	10−04,−4.9999975×	NUM
ejpam-4941	422	53	10−04	10−04	NOUN
ejpam-4941	422	54	,	,	PUNCT
ejpam-4941	422	55	δ	δ	PROPN
ejpam-4941	422	56	)	)	PUNCT
ejpam-4941	422	57	̸=	̸=	PROPN
ejpam-4941	422	58	f∗	f∗	NOUN
ejpam-4941	422	59	3	3	NUM
ejpam-4941	422	60	(	(	PUNCT
ejpam-4941	422	61	even	even	ADV
ejpam-4941	422	62	it	it	PRON
ejpam-4941	422	63	does	do	AUX
ejpam-4941	422	64	not	not	PART
ejpam-4941	422	65	look	look	VERB
ejpam-4941	422	66	so	so	ADV
ejpam-4941	422	67	at	at	ADP
ejpam-4941	422	68	first	first	ADJ
ejpam-4941	422	69	sight	sight	NOUN
ejpam-4941	422	70	,	,	PUNCT
ejpam-4941	422	71	see	see	VERB
ejpam-4941	422	72	proof	proof	NOUN
ejpam-4941	422	73	below	below	ADV
ejpam-4941	422	74	)	)	PUNCT
ejpam-4941	422	75	and	and	CCONJ
ejpam-4941	422	76	which	which	PRON
ejpam-4941	422	77	gives	give	VERB
ejpam-4941	422	78	,	,	PUNCT
ejpam-4941	422	79	⟨f∗∗	⟨f∗∗	X
ejpam-4941	422	80	1	1	NUM
ejpam-4941	422	81	,	,	PUNCT
ejpam-4941	422	82	f∗∗	f∗∗	NOUN
ejpam-4941	422	83	2	2	NUM
ejpam-4941	422	84	⟩	⟩	NOUN
ejpam-4941	422	85	=	=	SYM
ejpam-4941	422	86	0.00000000000000016089962580334832	0.00000000000000016089962580334832	NUM
ejpam-4941	422	87	=	=	SYM
ejpam-4941	422	88	⟨f∗	⟨f∗	PROPN
ejpam-4941	422	89	1	1	NUM
ejpam-4941	422	90	.f	.f	PROPN
ejpam-4941	422	91	∗	∗	VERB
ejpam-4941	422	92	2	2	NUM
ejpam-4941	422	93	⟩	⟩	NOUN
ejpam-4941	422	94	⟨f∗∗	⟨f∗∗	NUM
ejpam-4941	422	95	1	1	NUM
ejpam-4941	422	96	.f∗∗	.f∗∗	PROPN
ejpam-4941	422	97	3	3	NUM
ejpam-4941	422	98	⟩	⟩	NOUN
ejpam-4941	422	99	=	=	NOUN
ejpam-4941	423	1	0.00000000000000008044991878079256	0.00000000000000008044991878079256	NUM
ejpam-4941	423	2	=	=	SYM
ejpam-4941	423	3	⟨f∗	⟨f∗	PROPN
ejpam-4941	423	4	1	1	NUM
ejpam-4941	423	5	.f	.f	PROPN
ejpam-4941	423	6	∗	∗	VERB
ejpam-4941	423	7	3	3	NUM
ejpam-4941	423	8	⟩	⟩	NOUN
ejpam-4941	423	9	⟨f∗∗	⟨f∗∗	NUM
ejpam-4941	423	10	2	2	NUM
ejpam-4941	423	11	.f∗∗	.f∗∗	PROPN
ejpam-4941	423	12	3	3	NUM
ejpam-4941	423	13	⟩	⟩	NOUN
ejpam-4941	423	14	=	=	NOUN
ejpam-4941	423	15	0.00000000000000000000000000000000	0.00000000000000000000000000000000	NUM
ejpam-4941	423	16	or	or	CCONJ
ejpam-4941	423	17	just	just	ADV
ejpam-4941	423	18	0	0	NUM
ejpam-4941	423	19	with	with	ADP
ejpam-4941	423	20	⟨f∗	⟨f∗	PROPN
ejpam-4941	423	21	1	1	NUM
ejpam-4941	423	22	.f	.f	PROPN
ejpam-4941	423	23	∗	∗	VERB
ejpam-4941	423	24	2	2	NUM
ejpam-4941	423	25	⟩	⟩	NOUN
ejpam-4941	423	26	and	and	CCONJ
ejpam-4941	423	27	⟨f∗∗	⟨f∗∗	NOUN
ejpam-4941	423	28	1	1	NUM
ejpam-4941	423	29	.f∗∗	.f∗∗	PROPN
ejpam-4941	423	30	3	3	NUM
ejpam-4941	423	31	⟩	⟩	NOUN
ejpam-4941	423	32	computed	compute	VERB
ejpam-4941	423	33	as	as	ADP
ejpam-4941	423	34	in	in	ADP
ejpam-4941	423	35	the	the	DET
ejpam-4941	423	36	following	following	NOUN
ejpam-4941	423	37	,	,	PUNCT
ejpam-4941	423	38	•	•	NUM
ejpam-4941	423	39	gs	gs	NOUN
ejpam-4941	423	40	process	process	NOUN
ejpam-4941	423	41	f∗	f∗	NOUN
ejpam-4941	423	42	1	1	NUM
ejpam-4941	423	43	=	=	SYM
ejpam-4941	423	44	(	(	PUNCT
ejpam-4941	423	45	1	1	NUM
ejpam-4941	423	46	,	,	PUNCT
ejpam-4941	423	47	δ	δ	PROPN
ejpam-4941	423	48	,	,	PUNCT
ejpam-4941	423	49	0	0	NUM
ejpam-4941	423	50	,	,	PUNCT
ejpam-4941	423	51	0	0	NUM
ejpam-4941	423	52	)	)	PUNCT
ejpam-4941	423	53	f∗	f∗	NOUN
ejpam-4941	423	54	2	2	NUM
ejpam-4941	423	55	=	=	SYM
ejpam-4941	423	56	(	(	PUNCT
ejpam-4941	423	57	9.99999×	9.99999×	NOUN
ejpam-4941	423	58	10−07,−9.99999×	10−07,−9.99999×	NUM
ejpam-4941	423	59	10−04	10−04	NOUN
ejpam-4941	423	60	,	,	PUNCT
ejpam-4941	423	61	δ	δ	PROPN
ejpam-4941	423	62	,	,	PUNCT
ejpam-4941	423	63	0	0	NUM
ejpam-4941	423	64	)	)	PUNCT
ejpam-4941	423	65	f∗	f∗	NOUN
ejpam-4941	423	66	3	3	NUM
ejpam-4941	423	67	=	=	SYM
ejpam-4941	423	68	(	(	PUNCT
ejpam-4941	423	69	4.9999975×	4.9999975×	NOUN
ejpam-4941	423	70	10−07,−4.9999975×	10−07,−4.9999975×	NUM
ejpam-4941	423	71	10−04,−4.9999975×	10−04,−4.9999975×	NUM
ejpam-4941	423	72	10−04	10−04	NOUN
ejpam-4941	423	73	,	,	PUNCT
ejpam-4941	423	74	δ	δ	PROPN
ejpam-4941	423	75	)	)	PUNCT
ejpam-4941	423	76	and	and	CCONJ
ejpam-4941	423	77	which	which	PRON
ejpam-4941	423	78	gives	give	VERB
ejpam-4941	423	79	,	,	PUNCT
ejpam-4941	423	80	⟨f∗	⟨f∗	PROPN
ejpam-4941	423	81	1	1	NUM
ejpam-4941	423	82	,	,	PUNCT
ejpam-4941	423	83	f	f	PROPN
ejpam-4941	423	84	∗	∗	NOUN
ejpam-4941	423	85	2	2	NUM
ejpam-4941	423	86	⟩	⟩	NOUN
ejpam-4941	423	87	=	=	SYM
ejpam-4941	423	88	0.00000000000000016089962580334832	0.00000000000000016089962580334832	NUM
ejpam-4941	423	89	⟨f∗	⟨f∗	NOUN
ejpam-4941	423	90	1	1	NUM
ejpam-4941	423	91	.f	.f	PROPN
ejpam-4941	423	92	∗	∗	VERB
ejpam-4941	423	93	3	3	NUM
ejpam-4941	423	94	⟩	⟩	NOUN
ejpam-4941	423	95	=	=	NOUN
ejpam-4941	423	96	0.00000000000000008044991878079256	0.00000000000000008044991878079256	NUM
ejpam-4941	423	97	⟨f∗	⟨f∗	NOUN
ejpam-4941	423	98	2	2	NUM
ejpam-4941	423	99	.f	.f	PROPN
ejpam-4941	423	100	∗	∗	VERB
ejpam-4941	423	101	3	3	NUM
ejpam-4941	423	102	⟩	⟩	NOUN
ejpam-4941	423	103	=	=	NOUN
ejpam-4941	423	104	0.00000000000000016089930816599310	0.00000000000000016089930816599310	NUM
ejpam-4941	423	105	proof	proof	NOUN
ejpam-4941	423	106	.	.	PUNCT
ejpam-4941	424	1	as	as	SCONJ
ejpam-4941	424	2	we	we	PRON
ejpam-4941	424	3	noted	note	VERB
ejpam-4941	424	4	above	above	ADV
ejpam-4941	424	5	,	,	PUNCT
ejpam-4941	424	6	if	if	SCONJ
ejpam-4941	424	7	we	we	PRON
ejpam-4941	424	8	look	look	VERB
ejpam-4941	424	9	at	at	ADP
ejpam-4941	424	10	the	the	DET
ejpam-4941	424	11	values	value	NOUN
ejpam-4941	424	12	of	of	ADP
ejpam-4941	424	13	the	the	DET
ejpam-4941	424	14	components	component	NOUN
ejpam-4941	424	15	of	of	ADP
ejpam-4941	424	16	orthogonal	orthogonal	ADJ
ejpam-4941	424	17	vectors	vector	NOUN
ejpam-4941	424	18	for	for	ADP
ejpam-4941	424	19	both	both	DET
ejpam-4941	424	20	processes	process	NOUN
ejpam-4941	424	21	,	,	PUNCT
ejpam-4941	424	22	one	one	PRON
ejpam-4941	424	23	would	would	AUX
ejpam-4941	424	24	observe	observe	VERB
ejpam-4941	424	25	at	at	ADP
ejpam-4941	424	26	first	first	ADJ
ejpam-4941	424	27	sight	sight	NOUN
ejpam-4941	424	28	that	that	PRON
ejpam-4941	424	29	f∗∗	f∗∗	VERB
ejpam-4941	424	30	3	3	NUM
ejpam-4941	424	31	=	=	SYM
ejpam-4941	424	32	f∗	f∗	NOUN
ejpam-4941	424	33	3	3	NUM
ejpam-4941	424	34	which	which	PRON
ejpam-4941	424	35	is	be	AUX
ejpam-4941	424	36	not	not	PART
ejpam-4941	424	37	true	true	ADJ
ejpam-4941	424	38	because	because	SCONJ
ejpam-4941	424	39	if	if	SCONJ
ejpam-4941	424	40	we	we	PRON
ejpam-4941	424	41	are	be	AUX
ejpam-4941	424	42	having	have	VERB
ejpam-4941	424	43	this	this	PRON
ejpam-4941	424	44	,	,	PUNCT
ejpam-4941	424	45	then	then	ADV
ejpam-4941	424	46	there	there	PRON
ejpam-4941	424	47	would	would	AUX
ejpam-4941	424	48	be	be	AUX
ejpam-4941	424	49	no	no	DET
ejpam-4941	424	50	need	need	NOUN
ejpam-4941	424	51	to	to	PART
ejpam-4941	424	52	compute	compute	VERB
ejpam-4941	424	53	those	those	DET
ejpam-4941	424	54	products	product	NOUN
ejpam-4941	424	55	.	.	PUNCT
ejpam-4941	425	1	in	in	ADP
ejpam-4941	425	2	fact	fact	NOUN
ejpam-4941	425	3	,	,	PUNCT
ejpam-4941	425	4	this	this	PRON
ejpam-4941	425	5	is	be	AUX
ejpam-4941	425	6	a	a	DET
ejpam-4941	425	7	very	very	ADV
ejpam-4941	425	8	important	important	ADJ
ejpam-4941	425	9	note	note	NOUN
ejpam-4941	425	10	for	for	ADP
ejpam-4941	425	11	readers	reader	NOUN
ejpam-4941	425	12	who	who	PRON
ejpam-4941	425	13	want	want	VERB
ejpam-4941	425	14	to	to	PART
ejpam-4941	425	15	try	try	VERB
ejpam-4941	425	16	both	both	DET
ejpam-4941	425	17	mgs	mgs	NOUN
ejpam-4941	425	18	and	and	CCONJ
ejpam-4941	425	19	gs	gs	PROPN
ejpam-4941	425	20	methods	method	NOUN
ejpam-4941	425	21	,	,	PUNCT
ejpam-4941	425	22	to	to	PART
ejpam-4941	425	23	do	do	VERB
ejpam-4941	425	24	for	for	ADP
ejpam-4941	425	25	f∗∗	f∗∗	PROPN
ejpam-4941	425	26	3	3	NUM
ejpam-4941	425	27	and	and	CCONJ
ejpam-4941	425	28	f∗	f∗	NOUN
ejpam-4941	425	29	3	3	NUM
ejpam-4941	425	30	the	the	DET
ejpam-4941	425	31	same	same	ADJ
ejpam-4941	425	32	as	as	SCONJ
ejpam-4941	425	33	we	we	PRON
ejpam-4941	425	34	did	do	VERB
ejpam-4941	425	35	for	for	ADP
ejpam-4941	425	36	getting	get	VERB
ejpam-4941	425	37	a	a	DET
ejpam-4941	425	38	precision	precision	NOUN
ejpam-4941	425	39	on	on	ADP
ejpam-4941	425	40	the	the	DET
ejpam-4941	425	41	above	above	ADJ
ejpam-4941	425	42	products	product	NOUN
ejpam-4941	425	43	,	,	PUNCT
ejpam-4941	425	44	and	and	CCONJ
ejpam-4941	425	45	as	as	SCONJ
ejpam-4941	425	46	we	we	PRON
ejpam-4941	425	47	can	can	AUX
ejpam-4941	425	48	observe	observe	VERB
ejpam-4941	425	49	now	now	ADV
ejpam-4941	425	50	,	,	PUNCT
ejpam-4941	425	51	that	that	SCONJ
ejpam-4941	425	52	if	if	SCONJ
ejpam-4941	425	53	we	we	PRON
ejpam-4941	425	54	fix	fix	VERB
ejpam-4941	425	55	the	the	DET
ejpam-4941	425	56	number	number	NOUN
ejpam-4941	425	57	of	of	ADP
ejpam-4941	425	58	digits	digit	NOUN
ejpam-4941	425	59	of	of	ADP
ejpam-4941	425	60	precision	precision	NOUN
ejpam-4941	425	61	again	again	ADV
ejpam-4941	425	62	to	to	ADP
ejpam-4941	425	63	32	32	NUM
ejpam-4941	425	64	,	,	PUNCT
ejpam-4941	425	65	we	we	PRON
ejpam-4941	425	66	obtain	obtain	VERB
ejpam-4941	425	67	the	the	DET
ejpam-4941	425	68	following	follow	VERB
ejpam-4941	425	69	real	real	ADJ
ejpam-4941	425	70	values	value	NOUN
ejpam-4941	425	71	of	of	ADP
ejpam-4941	425	72	f∗∗	f∗∗	NOUN
ejpam-4941	425	73	3	3	NUM
ejpam-4941	425	74	and	and	CCONJ
ejpam-4941	425	75	f∗	f∗	NOUN
ejpam-4941	425	76	3	3	NUM
ejpam-4941	425	77	,	,	PUNCT
ejpam-4941	425	78	f∗∗	f∗∗	PROPN
ejpam-4941	425	79	3	3	NUM
ejpam-4941	425	80	=	=	SYM
ejpam-4941	425	81	(	(	PUNCT
ejpam-4941	425	82	0.00000049999975008057487955320276	0.00000049999975008057487955320276	NUM
ejpam-4941	425	83	,	,	PUNCT
ejpam-4941	425	84	−0.00049999975000012493366735588651	−0.00049999975000012493366735588651	ADV
ejpam-4941	425	85	,	,	PUNCT
ejpam-4941	425	86	−0.00049999975000012504208757313506	−0.00049999975000012504208757313506	PROPN
ejpam-4941	425	87	,	,	PUNCT
ejpam-4941	425	88	δ	δ	PROPN
ejpam-4941	425	89	)	)	PUNCT
ejpam-4941	425	90	f∗	f∗	NOUN
ejpam-4941	426	1	3	3	NUM
ejpam-4941	426	2	=	=	SYM
ejpam-4941	426	3	(	(	PUNCT
ejpam-4941	426	4	0.00000049999975000012517253064701	0.00000049999975000012517253064701	NUM
ejpam-4941	426	5	,	,	PUNCT
ejpam-4941	426	6	s.	s.	PROPN
ejpam-4941	426	7	abdelalim	abdelalim	PROPN
ejpam-4941	426	8	,	,	PUNCT
ejpam-4941	426	9	i.	i.	PROPN
ejpam-4941	426	10	elmouki	elmouki	PROPN
ejpam-4941	426	11	/	/	SYM
ejpam-4941	426	12	eur	eur	PROPN
ejpam-4941	426	13	.	.	PUNCT
ejpam-4941	427	1	j.	j.	PROPN
ejpam-4941	427	2	pure	pure	PROPN
ejpam-4941	427	3	appl	appl	PROPN
ejpam-4941	427	4	.	.	PROPN
ejpam-4941	427	5	math	math	PROPN
ejpam-4941	427	6	,	,	PUNCT
ejpam-4941	427	7	16	16	NUM
ejpam-4941	427	8	(	(	PUNCT
ejpam-4941	427	9	4	4	NUM
ejpam-4941	427	10	)	)	PUNCT
ejpam-4941	427	11	(	(	PUNCT
ejpam-4941	427	12	2023	2023	NUM
ejpam-4941	427	13	)	)	PUNCT
ejpam-4941	427	14	,	,	PUNCT
ejpam-4941	427	15	2662	2662	NUM
ejpam-4941	427	16	-	-	SYM
ejpam-4941	427	17	2692	2692	NUM
ejpam-4941	427	18	2686	2686	NUM
ejpam-4941	427	19	−0.00049999974991967528932523823215	−0.00049999974991967528932523823215	NOUN
ejpam-4941	427	20	,	,	PUNCT
ejpam-4941	427	21	−0.00049999975008057479484990803797	−0.00049999975008057479484990803797	PROPN
ejpam-4941	427	22	,	,	PUNCT
ejpam-4941	427	23	δ	δ	PROPN
ejpam-4941	427	24	)	)	PUNCT
ejpam-4941	427	25	thus	thus	ADV
ejpam-4941	427	26	,	,	PUNCT
ejpam-4941	427	27	f∗∗	f∗∗	PROPN
ejpam-4941	427	28	3	3	NUM
ejpam-4941	427	29	̸=	̸=	PROPN
ejpam-4941	427	30	f∗	f∗	NOUN
ejpam-4941	427	31	3	3	NUM
ejpam-4941	427	32	.	.	PUNCT
ejpam-4941	428	1	even	even	ADV
ejpam-4941	428	2	if	if	SCONJ
ejpam-4941	428	3	we	we	PRON
ejpam-4941	428	4	try	try	VERB
ejpam-4941	428	5	now	now	ADV
ejpam-4941	428	6	the	the	DET
ejpam-4941	428	7	normalized	normalized	ADJ
ejpam-4941	428	8	case	case	NOUN
ejpam-4941	428	9	for	for	ADP
ejpam-4941	428	10	both	both	DET
ejpam-4941	428	11	processes	process	NOUN
ejpam-4941	428	12	,	,	PUNCT
ejpam-4941	428	13	we	we	PRON
ejpam-4941	428	14	find	find	VERB
ejpam-4941	428	15	that	that	SCONJ
ejpam-4941	428	16	mgs	mgs	NOUN
ejpam-4941	428	17	is	be	AUX
ejpam-4941	428	18	again	again	ADV
ejpam-4941	428	19	better	well	ADJ
ejpam-4941	428	20	than	than	ADP
ejpam-4941	428	21	gs	gs	INTJ
ejpam-4941	428	22	as	as	SCONJ
ejpam-4941	428	23	we	we	PRON
ejpam-4941	428	24	have	have	VERB
ejpam-4941	428	25	for	for	ADP
ejpam-4941	428	26	this	this	DET
ejpam-4941	428	27	case	case	NOUN
ejpam-4941	428	28	,	,	PUNCT
ejpam-4941	428	29	⟨f∗∗	⟨f∗∗	X
ejpam-4941	428	30	1	1	NUM
ejpam-4941	428	31	,	,	PUNCT
ejpam-4941	428	32	f∗∗	f∗∗	NOUN
ejpam-4941	429	1	2	2	NUM
ejpam-4941	429	2	⟩	⟩	NOUN
ejpam-4941	429	3	=	=	SYM
ejpam-4941	429	4	⟨f∗	⟨f∗	PROPN
ejpam-4941	429	5	1	1	NUM
ejpam-4941	429	6	.f	.f	PROPN
ejpam-4941	429	7	∗	∗	VERB
ejpam-4941	429	8	2	2	NUM
ejpam-4941	429	9	⟩	⟩	NOUN
ejpam-4941	429	10	⟨f∗∗	⟨f∗∗	NUM
ejpam-4941	429	11	1	1	NUM
ejpam-4941	429	12	.f∗∗	.f∗∗	PROPN
ejpam-4941	429	13	3	3	NUM
ejpam-4941	429	14	⟩	⟩	NOUN
ejpam-4941	429	15	=	=	NOUN
ejpam-4941	429	16	0.00000000000000000000000000000000	0.00000000000000000000000000000000	NUM
ejpam-4941	429	17	or	or	CCONJ
ejpam-4941	429	18	just	just	ADV
ejpam-4941	429	19	0	0	NUM
ejpam-4941	430	1	̸=	̸=	PROPN
ejpam-4941	430	2	⟨f∗	⟨f∗	PROPN
ejpam-4941	430	3	1	1	NUM
ejpam-4941	430	4	.f	.f	PROPN
ejpam-4941	430	5	∗	∗	VERB
ejpam-4941	430	6	3	3	NUM
ejpam-4941	430	7	⟩	⟩	NOUN
ejpam-4941	430	8	=	=	SYM
ejpam-4941	430	9	0.00000099999999999999995474811183	0.00000099999999999999995474811183	NUM
ejpam-4941	430	10	⟨f∗∗	⟨f∗∗	SYM
ejpam-4941	430	11	2	2	NUM
ejpam-4941	430	12	.f∗∗	.f∗∗	PROPN
ejpam-4941	430	13	3	3	NUM
ejpam-4941	430	14	⟩	⟩	NOUN
ejpam-4941	430	15	=	=	SYM
ejpam-4941	430	16	⟨f∗	⟨f∗	PROPN
ejpam-4941	430	17	2	2	NUM
ejpam-4941	430	18	.f	.f	PROPN
ejpam-4941	430	19	∗	∗	VERB
ejpam-4941	430	20	3	3	NUM
ejpam-4941	430	21	⟩	⟩	NOUN
ejpam-4941	430	22	we	we	PRON
ejpam-4941	430	23	can	can	AUX
ejpam-4941	430	24	now	now	ADV
ejpam-4941	430	25	deduce	deduce	VERB
ejpam-4941	430	26	from	from	ADP
ejpam-4941	430	27	our	our	PRON
ejpam-4941	430	28	example	example	NOUN
ejpam-4941	430	29	and	and	CCONJ
ejpam-4941	430	30	via	via	ADP
ejpam-4941	430	31	mgs	mgs	NOUN
ejpam-4941	430	32	,	,	PUNCT
ejpam-4941	430	33	in	in	ADP
ejpam-4941	430	34	both	both	DET
ejpam-4941	430	35	non	non	ADJ
ejpam-4941	430	36	-	-	ADJ
ejpam-4941	430	37	normalized	normalized	ADJ
ejpam-4941	430	38	and	and	CCONJ
ejpam-4941	430	39	normalized	normalize	VERB
ejpam-4941	430	40	cases	case	NOUN
ejpam-4941	430	41	,	,	PUNCT
ejpam-4941	430	42	that	that	SCONJ
ejpam-4941	430	43	we	we	PRON
ejpam-4941	430	44	can	can	AUX
ejpam-4941	430	45	obtain	obtain	VERB
ejpam-4941	430	46	better	well	ADJ
ejpam-4941	430	47	results	result	NOUN
ejpam-4941	430	48	about	about	ADP
ejpam-4941	430	49	the	the	DET
ejpam-4941	430	50	orthogonalization	orthogonalization	NOUN
ejpam-4941	430	51	of	of	ADP
ejpam-4941	430	52	our	our	PRON
ejpam-4941	430	53	input	input	NOUN
ejpam-4941	430	54	vectors	vector	NOUN
ejpam-4941	430	55	either	either	CCONJ
ejpam-4941	430	56	for	for	ADP
ejpam-4941	430	57	f2	f2	PRON
ejpam-4941	430	58	and	and	CCONJ
ejpam-4941	430	59	f3	f3	PROPN
ejpam-4941	430	60	in	in	ADP
ejpam-4941	430	61	the	the	DET
ejpam-4941	430	62	first	first	ADJ
ejpam-4941	430	63	case	case	NOUN
ejpam-4941	430	64	,	,	PUNCT
ejpam-4941	430	65	or	or	CCONJ
ejpam-4941	430	66	for	for	ADP
ejpam-4941	430	67	f1	f1	NOUN
ejpam-4941	430	68	and	and	CCONJ
ejpam-4941	430	69	f3	f3	PROPN
ejpam-4941	430	70	in	in	ADP
ejpam-4941	430	71	the	the	DET
ejpam-4941	430	72	second	second	ADJ
ejpam-4941	430	73	case	case	NOUN
ejpam-4941	430	74	.	.	PUNCT
ejpam-4941	431	1	now	now	ADV
ejpam-4941	431	2	,	,	PUNCT
ejpam-4941	431	3	we	we	PRON
ejpam-4941	431	4	consider	consider	VERB
ejpam-4941	431	5	the	the	DET
ejpam-4941	431	6	conditions	condition	NOUN
ejpam-4941	431	7	on	on	ADP
ejpam-4941	431	8	i	i	PRON
ejpam-4941	431	9	when	when	SCONJ
ejpam-4941	431	10	we	we	PRON
ejpam-4941	431	11	need	need	VERB
ejpam-4941	431	12	to	to	PART
ejpam-4941	431	13	swap	swap	VERB
ejpam-4941	431	14	the	the	DET
ejpam-4941	431	15	vectors	vector	NOUN
ejpam-4941	431	16	,	,	PUNCT
ejpam-4941	431	17	namely	namely	ADV
ejpam-4941	431	18	when	when	SCONJ
ejpam-4941	431	19	we	we	PRON
ejpam-4941	431	20	take	take	VERB
ejpam-4941	431	21	the	the	DET
ejpam-4941	431	22	new	new	ADJ
ejpam-4941	431	23	basis	basis	NOUN
ejpam-4941	431	24	defined	define	VERB
ejpam-4941	431	25	by	by	ADP
ejpam-4941	431	26	fi	fi	NOUN
ejpam-4941	431	27	=	=	NOUN
ejpam-4941	431	28	ej+1	ej+1	X
ejpam-4941	431	29	if	if	SCONJ
ejpam-4941	431	30	i	i	PRON
ejpam-4941	431	31	=	=	SYM
ejpam-4941	431	32	j	j	PROPN
ejpam-4941	431	33	or	or	CCONJ
ejpam-4941	431	34	fi	fi	NOUN
ejpam-4941	432	1	=	=	NOUN
ejpam-4941	432	2	ej	ej	INTJ
ejpam-4941	432	3	if	if	SCONJ
ejpam-4941	432	4	i	i	PRON
ejpam-4941	432	5	=	=	SYM
ejpam-4941	432	6	j	j	PROPN
ejpam-4941	432	7	+	+	NOUN
ejpam-4941	432	8	1	1	X
ejpam-4941	432	9	.	.	PUNCT
ejpam-4941	432	10	this	this	PRON
ejpam-4941	432	11	can	can	AUX
ejpam-4941	432	12	simply	simply	ADV
ejpam-4941	432	13	translated	translate	VERB
ejpam-4941	432	14	to	to	ADP
ejpam-4941	432	15	a	a	DET
ejpam-4941	432	16	different	different	ADJ
ejpam-4941	432	17	way	way	NOUN
ejpam-4941	432	18	,	,	PUNCT
ejpam-4941	432	19	by	by	ADP
ejpam-4941	432	20	stating	state	VERB
ejpam-4941	432	21	that	that	SCONJ
ejpam-4941	432	22	fj	fj	PROPN
ejpam-4941	432	23	=	=	PUNCT
ejpam-4941	432	24	ej+1	ej+1	PROPN
ejpam-4941	432	25	and	and	CCONJ
ejpam-4941	432	26	fj+1	fj+1	PRON
ejpam-4941	432	27	=	=	SYM
ejpam-4941	432	28	ej	ej	PROPN
ejpam-4941	432	29	and	and	CCONJ
ejpam-4941	432	30	which	which	PRON
ejpam-4941	432	31	both	both	PRON
ejpam-4941	432	32	correspond	correspond	VERB
ejpam-4941	432	33	to	to	ADP
ejpam-4941	432	34	the	the	DET
ejpam-4941	432	35	original	original	ADJ
ejpam-4941	432	36	case	case	NOUN
ejpam-4941	432	37	when	when	SCONJ
ejpam-4941	432	38	we	we	PRON
ejpam-4941	432	39	generally	generally	ADV
ejpam-4941	432	40	swap	swap	VERB
ejpam-4941	432	41	vectors	vector	NOUN
ejpam-4941	432	42	ej+1	ej+1	NOUN
ejpam-4941	432	43	and	and	CCONJ
ejpam-4941	432	44	ej	ej	INTJ
ejpam-4941	432	45	.	.	PUNCT
ejpam-4941	433	1	until	until	ADP
ejpam-4941	433	2	now	now	ADV
ejpam-4941	433	3	,	,	PUNCT
ejpam-4941	433	4	we	we	PRON
ejpam-4941	433	5	have	have	AUX
ejpam-4941	433	6	shown	show	VERB
ejpam-4941	433	7	how	how	SCONJ
ejpam-4941	433	8	to	to	PART
ejpam-4941	433	9	use	use	VERB
ejpam-4941	433	10	mgs	mgs	NOUN
ejpam-4941	433	11	and	and	CCONJ
ejpam-4941	433	12	gs	gs	X
ejpam-4941	433	13	in	in	ADP
ejpam-4941	433	14	order	order	NOUN
ejpam-4941	433	15	to	to	PART
ejpam-4941	433	16	implement	implement	VERB
ejpam-4941	433	17	them	they	PRON
ejpam-4941	433	18	in	in	ADP
ejpam-4941	433	19	the	the	DET
ejpam-4941	433	20	first	first	ADJ
ejpam-4941	433	21	intermediary	intermediary	ADJ
ejpam-4941	433	22	step	step	NOUN
ejpam-4941	433	23	,	,	PUNCT
ejpam-4941	433	24	and	and	CCONJ
ejpam-4941	433	25	why	why	SCONJ
ejpam-4941	433	26	it	it	PRON
ejpam-4941	433	27	is	be	AUX
ejpam-4941	433	28	preferable	preferable	ADJ
ejpam-4941	433	29	to	to	PART
ejpam-4941	433	30	use	use	VERB
ejpam-4941	433	31	mgs	mgs	NOUN
ejpam-4941	433	32	instead	instead	ADV
ejpam-4941	433	33	of	of	ADP
ejpam-4941	433	34	gs	gs	INTJ
ejpam-4941	433	35	.	.	PUNCT
ejpam-4941	434	1	in	in	ADP
ejpam-4941	434	2	order	order	NOUN
ejpam-4941	434	3	to	to	PART
ejpam-4941	434	4	understand	understand	VERB
ejpam-4941	434	5	how	how	SCONJ
ejpam-4941	434	6	the	the	DET
ejpam-4941	434	7	vectors	vector	NOUN
ejpam-4941	434	8	exchange	exchange	NOUN
ejpam-4941	434	9	process	process	NOUN
ejpam-4941	434	10	and	and	CCONJ
ejpam-4941	434	11	make	make	VERB
ejpam-4941	434	12	the	the	DET
ejpam-4941	434	13	operations	operation	NOUN
ejpam-4941	434	14	clear	clear	ADJ
ejpam-4941	434	15	,	,	PUNCT
ejpam-4941	434	16	let	let	VERB
ejpam-4941	434	17	us	we	PRON
ejpam-4941	434	18	first	first	ADV
ejpam-4941	434	19	suppose	suppose	VERB
ejpam-4941	434	20	again	again	ADV
ejpam-4941	434	21	that	that	SCONJ
ejpam-4941	434	22	we	we	PRON
ejpam-4941	434	23	just	just	ADV
ejpam-4941	434	24	start	start	VERB
ejpam-4941	434	25	working	work	VERB
ejpam-4941	434	26	and	and	CCONJ
ejpam-4941	434	27	we	we	PRON
ejpam-4941	434	28	did	do	AUX
ejpam-4941	434	29	not	not	PART
ejpam-4941	434	30	decide	decide	VERB
ejpam-4941	434	31	to	to	PART
ejpam-4941	434	32	swap	swap	VERB
ejpam-4941	434	33	any	any	DET
ejpam-4941	434	34	vectors	vector	NOUN
ejpam-4941	434	35	.	.	PUNCT
ejpam-4941	435	1	then	then	ADV
ejpam-4941	435	2	,	,	PUNCT
ejpam-4941	435	3	as	as	SCONJ
ejpam-4941	435	4	explained	explain	VERB
ejpam-4941	435	5	before	before	ADV
ejpam-4941	435	6	,	,	PUNCT
ejpam-4941	435	7	we	we	PRON
ejpam-4941	435	8	retake	retake	VERB
ejpam-4941	435	9	,	,	PUNCT
ejpam-4941	435	10	f1	f1	NOUN
ejpam-4941	435	11	=	=	SYM
ejpam-4941	435	12	(	(	PUNCT
ejpam-4941	435	13	1	1	NUM
ejpam-4941	435	14	,	,	PUNCT
ejpam-4941	435	15	δ	δ	PROPN
ejpam-4941	435	16	,	,	PUNCT
ejpam-4941	435	17	0	0	NUM
ejpam-4941	435	18	,	,	PUNCT
ejpam-4941	435	19	0	0	NUM
ejpam-4941	435	20	)	)	PUNCT
ejpam-4941	435	21	,	,	PUNCT
ejpam-4941	435	22	f2	f2	PROPN
ejpam-4941	435	23	=	=	SYM
ejpam-4941	435	24	(	(	PUNCT
ejpam-4941	435	25	1	1	NUM
ejpam-4941	435	26	,	,	PUNCT
ejpam-4941	435	27	0	0	NUM
ejpam-4941	435	28	,	,	PUNCT
ejpam-4941	435	29	δ	δ	PROPN
ejpam-4941	435	30	,	,	PUNCT
ejpam-4941	435	31	0	0	NUM
ejpam-4941	435	32	)	)	PUNCT
ejpam-4941	435	33	,	,	PUNCT
ejpam-4941	435	34	f3	f3	PROPN
ejpam-4941	435	35	=	=	SYM
ejpam-4941	435	36	(	(	PUNCT
ejpam-4941	435	37	1	1	NUM
ejpam-4941	435	38	,	,	PUNCT
ejpam-4941	435	39	0	0	NUM
ejpam-4941	435	40	,	,	PUNCT
ejpam-4941	435	41	0	0	NUM
ejpam-4941	435	42	,	,	PUNCT
ejpam-4941	435	43	δ	δ	PROPN
ejpam-4941	435	44	)	)	PUNCT
ejpam-4941	435	45	we	we	PRON
ejpam-4941	435	46	have	have	VERB
ejpam-4941	435	47	f∗∗	f∗∗	ADJ
ejpam-4941	435	48	1	1	NUM
ejpam-4941	435	49	=	=	SYM
ejpam-4941	435	50	f1	f1	NOUN
ejpam-4941	435	51	,	,	PUNCT
ejpam-4941	435	52	then	then	ADV
ejpam-4941	435	53	we	we	PRON
ejpam-4941	435	54	use	use	VERB
ejpam-4941	435	55	it	it	PRON
ejpam-4941	435	56	to	to	PART
ejpam-4941	435	57	reduce	reduce	VERB
ejpam-4941	435	58	the	the	DET
ejpam-4941	435	59	vector	vector	NOUN
ejpam-4941	435	60	f2	f2	PROPN
ejpam-4941	435	61	.	.	PUNCT
ejpam-4941	436	1	thus	thus	ADV
ejpam-4941	436	2	,	,	PUNCT
ejpam-4941	436	3	we	we	PRON
ejpam-4941	436	4	get	get	VERB
ejpam-4941	436	5	in	in	ADP
ejpam-4941	436	6	this	this	DET
ejpam-4941	436	7	step	step	NOUN
ejpam-4941	436	8	,	,	PUNCT
ejpam-4941	436	9	f1	f1	NOUN
ejpam-4941	436	10	=	=	SYM
ejpam-4941	436	11	f∗∗	f∗∗	NOUN
ejpam-4941	436	12	1	1	NUM
ejpam-4941	436	13	,	,	PUNCT
ejpam-4941	436	14	f2	f2	PROPN
ejpam-4941	436	15	=	=	NOUN
ejpam-4941	436	16	f	f	PROPN
ejpam-4941	436	17	∗∗new1	∗∗new1	PROPN
ejpam-4941	436	18	2	2	NUM
ejpam-4941	436	19	,	,	PUNCT
ejpam-4941	436	20	f3	f3	NOUN
ejpam-4941	436	21	=	=	SYM
ejpam-4941	436	22	f3	f3	PROPN
ejpam-4941	436	23	for	for	ADP
ejpam-4941	436	24	the	the	DET
ejpam-4941	436	25	size	size	NOUN
ejpam-4941	436	26	reduction	reduction	NOUN
ejpam-4941	436	27	,	,	PUNCT
ejpam-4941	436	28	we	we	PRON
ejpam-4941	436	29	can	can	AUX
ejpam-4941	436	30	see	see	VERB
ejpam-4941	436	31	that	that	SCONJ
ejpam-4941	436	32	we	we	PRON
ejpam-4941	436	33	have	have	AUX
ejpam-4941	436	34	,	,	PUNCT
ejpam-4941	436	35	⟨f∗∗(1)new1	⟨f∗∗(1)new1	PROPN
ejpam-4941	436	36	2	2	NUM
ejpam-4941	436	37	,	,	PUNCT
ejpam-4941	436	38	f∗∗	f∗∗	NOUN
ejpam-4941	436	39	1	1	NUM
ejpam-4941	436	40	⟩	⟩	NOUN
ejpam-4941	436	41	⟨f∗∗	⟨f∗∗	ADJ
ejpam-4941	436	42	1	1	NUM
ejpam-4941	436	43	,	,	PUNCT
ejpam-4941	436	44	f∗∗	f∗∗	NOUN
ejpam-4941	436	45	1	1	NUM
ejpam-4941	436	46	⟩	⟩	NOUN
ejpam-4941	436	47	=	=	NOUN
ejpam-4941	436	48	0.00000000000000016089946490388340	0.00000000000000016089946490388340	NUM
ejpam-4941	436	49	which	which	PRON
ejpam-4941	436	50	satisfies	satisfy	VERB
ejpam-4941	436	51	the	the	DET
ejpam-4941	436	52	condition	condition	NOUN
ejpam-4941	436	53	in	in	ADP
ejpam-4941	436	54	definition	definition	NOUN
ejpam-4941	436	55	1	1	NUM
ejpam-4941	436	56	.	.	PUNCT
ejpam-4941	437	1	as	as	ADP
ejpam-4941	437	2	for	for	ADP
ejpam-4941	437	3	the	the	DET
ejpam-4941	437	4	quasi	quasi	ADJ
ejpam-4941	437	5	-	-	ADJ
ejpam-4941	437	6	orthogonality	orthogonality	ADJ
ejpam-4941	437	7	condition	condition	NOUN
ejpam-4941	437	8	of	of	ADP
ejpam-4941	437	9	definition	definition	NOUN
ejpam-4941	437	10	2	2	NUM
ejpam-4941	437	11	,	,	PUNCT
ejpam-4941	437	12	we	we	PRON
ejpam-4941	437	13	find	find	VERB
ejpam-4941	437	14	that	that	SCONJ
ejpam-4941	437	15	for	for	ADP
ejpam-4941	437	16	s.	s.	PROPN
ejpam-4941	437	17	abdelalim	abdelalim	PROPN
ejpam-4941	437	18	,	,	PUNCT
ejpam-4941	437	19	i.	i.	PROPN
ejpam-4941	437	20	elmouki	elmouki	PROPN
ejpam-4941	437	21	/	/	SYM
ejpam-4941	437	22	eur	eur	PROPN
ejpam-4941	437	23	.	.	PUNCT
ejpam-4941	438	1	j.	j.	PROPN
ejpam-4941	438	2	pure	pure	PROPN
ejpam-4941	438	3	appl	appl	PROPN
ejpam-4941	438	4	.	.	PROPN
ejpam-4941	438	5	math	math	PROPN
ejpam-4941	438	6	,	,	PUNCT
ejpam-4941	438	7	16	16	NUM
ejpam-4941	438	8	(	(	PUNCT
ejpam-4941	438	9	4	4	NUM
ejpam-4941	438	10	)	)	PUNCT
ejpam-4941	438	11	(	(	PUNCT
ejpam-4941	438	12	2023	2023	NUM
ejpam-4941	438	13	)	)	PUNCT
ejpam-4941	438	14	,	,	PUNCT
ejpam-4941	438	15	2662	2662	NUM
ejpam-4941	438	16	-	-	SYM
ejpam-4941	438	17	2692	2692	NUM
ejpam-4941	438	18	2687	2687	NUM
ejpam-4941	438	19	ε	ε	X
ejpam-4941	438	20	=	=	SYM
ejpam-4941	438	21	0.75	0.75	NUM
ejpam-4941	438	22	,	,	PUNCT
ejpam-4941	438	23	the	the	DET
ejpam-4941	438	24	condition	condition	NOUN
ejpam-4941	438	25	is	be	AUX
ejpam-4941	438	26	not	not	PART
ejpam-4941	438	27	satisfied	satisfied	ADJ
ejpam-4941	438	28	,	,	PUNCT
ejpam-4941	438	29	then	then	ADV
ejpam-4941	438	30	,	,	PUNCT
ejpam-4941	438	31	we	we	PRON
ejpam-4941	438	32	have	have	VERB
ejpam-4941	438	33	to	to	PART
ejpam-4941	438	34	swap	swap	VERB
ejpam-4941	438	35	vectors	vector	NOUN
ejpam-4941	438	36	f∗∗	f∗∗	VERB
ejpam-4941	438	37	1	1	NUM
ejpam-4941	438	38	and	and	CCONJ
ejpam-4941	438	39	f	f	PROPN
ejpam-4941	438	40	∗∗new1	∗∗new1	PROPN
ejpam-4941	438	41	2	2	NUM
ejpam-4941	438	42	,	,	PUNCT
ejpam-4941	438	43	which	which	PRON
ejpam-4941	438	44	means	mean	VERB
ejpam-4941	438	45	,	,	PUNCT
ejpam-4941	438	46	we	we	PRON
ejpam-4941	438	47	have	have	VERB
ejpam-4941	438	48	now	now	ADV
ejpam-4941	438	49	,	,	PUNCT
ejpam-4941	439	1	f1	f1	PROPN
ejpam-4941	440	1	=	=	SYM
ejpam-4941	441	1	f	f	PROPN
ejpam-4941	442	1	∗∗new1	∗∗new1	PROPN
ejpam-4941	442	2	2	2	NUM
ejpam-4941	442	3	,	,	PUNCT
ejpam-4941	442	4	f2	f2	ADV
ejpam-4941	442	5	=	=	SYM
ejpam-4941	442	6	f∗∗	f∗∗	NOUN
ejpam-4941	442	7	1	1	NUM
ejpam-4941	442	8	,	,	PUNCT
ejpam-4941	442	9	f3	f3	NOUN
ejpam-4941	442	10	=	=	SYM
ejpam-4941	442	11	f3	f3	PROPN
ejpam-4941	442	12	again	again	ADV
ejpam-4941	442	13	,	,	PUNCT
ejpam-4941	442	14	for	for	ADP
ejpam-4941	442	15	the	the	DET
ejpam-4941	442	16	size	size	NOUN
ejpam-4941	442	17	reduction	reduction	NOUN
ejpam-4941	442	18	,	,	PUNCT
ejpam-4941	442	19	we	we	PRON
ejpam-4941	442	20	can	can	AUX
ejpam-4941	442	21	see	see	VERB
ejpam-4941	442	22	that	that	SCONJ
ejpam-4941	442	23	we	we	PRON
ejpam-4941	442	24	have	have	AUX
ejpam-4941	442	25	,	,	PUNCT
ejpam-4941	442	26	⟨f∗∗(1)new1	⟨f∗∗(1)new1	PROPN
ejpam-4941	442	27	2	2	NUM
ejpam-4941	442	28	,	,	PUNCT
ejpam-4941	442	29	f∗∗	f∗∗	NOUN
ejpam-4941	442	30	1	1	NUM
ejpam-4941	442	31	⟩	⟩	NOUN
ejpam-4941	442	32	⟨f∗∗	⟨f∗∗	ADJ
ejpam-4941	442	33	1	1	NUM
ejpam-4941	442	34	,	,	PUNCT
ejpam-4941	442	35	f∗∗	f∗∗	NOUN
ejpam-4941	442	36	1	1	NUM
ejpam-4941	442	37	⟩	⟩	NOUN
ejpam-4941	442	38	=	=	NOUN
ejpam-4941	442	39	0.00000000000000029761705115610202	0.00000000000000029761705115610202	NUM
ejpam-4941	442	40	which	which	PRON
ejpam-4941	442	41	satisfies	satisfy	VERB
ejpam-4941	442	42	the	the	DET
ejpam-4941	442	43	condition	condition	NOUN
ejpam-4941	442	44	in	in	ADP
ejpam-4941	442	45	definition	definition	NOUN
ejpam-4941	442	46	1	1	NUM
ejpam-4941	442	47	.	.	PUNCT
ejpam-4941	443	1	as	as	ADP
ejpam-4941	443	2	for	for	ADP
ejpam-4941	443	3	the	the	DET
ejpam-4941	443	4	quasi	quasi	ADJ
ejpam-4941	443	5	-	-	ADJ
ejpam-4941	443	6	orthogonality	orthogonality	ADJ
ejpam-4941	443	7	condition	condition	NOUN
ejpam-4941	443	8	of	of	ADP
ejpam-4941	443	9	definition	definition	NOUN
ejpam-4941	443	10	2	2	NUM
ejpam-4941	443	11	,	,	PUNCT
ejpam-4941	443	12	we	we	PRON
ejpam-4941	443	13	find	find	VERB
ejpam-4941	443	14	that	that	SCONJ
ejpam-4941	443	15	the	the	DET
ejpam-4941	443	16	condition	condition	NOUN
ejpam-4941	443	17	is	be	AUX
ejpam-4941	443	18	satisfied	satisfied	ADJ
ejpam-4941	443	19	.	.	PUNCT
ejpam-4941	444	1	then	then	ADV
ejpam-4941	444	2	,	,	PUNCT
ejpam-4941	444	3	no	no	DET
ejpam-4941	444	4	need	need	NOUN
ejpam-4941	444	5	to	to	PART
ejpam-4941	444	6	swap	swap	VERB
ejpam-4941	444	7	any	any	DET
ejpam-4941	444	8	vectors	vector	NOUN
ejpam-4941	444	9	in	in	ADP
ejpam-4941	444	10	this	this	DET
ejpam-4941	444	11	step	step	NOUN
ejpam-4941	444	12	.	.	PUNCT
ejpam-4941	445	1	this	this	PRON
ejpam-4941	445	2	means	mean	VERB
ejpam-4941	445	3	we	we	PRON
ejpam-4941	445	4	repeat	repeat	VERB
ejpam-4941	445	5	the	the	DET
ejpam-4941	445	6	process	process	NOUN
ejpam-4941	445	7	again	again	ADV
ejpam-4941	445	8	,	,	PUNCT
ejpam-4941	445	9	and	and	CCONJ
ejpam-4941	445	10	then	then	ADV
ejpam-4941	445	11	retake	retake	VERB
ejpam-4941	445	12	f∗∗	f∗∗	NOUN
ejpam-4941	445	13	1	1	NUM
ejpam-4941	445	14	=	=	SYM
ejpam-4941	445	15	f	f	NOUN
ejpam-4941	445	16	∗∗new1	∗∗new1	PROPN
ejpam-4941	445	17	2	2	NUM
ejpam-4941	445	18	but	but	CCONJ
ejpam-4941	445	19	use	use	VERB
ejpam-4941	445	20	these	these	DET
ejpam-4941	445	21	last	last	ADJ
ejpam-4941	445	22	two	two	NUM
ejpam-4941	445	23	first	first	ADJ
ejpam-4941	445	24	vectors	vector	NOUN
ejpam-4941	445	25	in	in	ADP
ejpam-4941	445	26	order	order	NOUN
ejpam-4941	445	27	to	to	PART
ejpam-4941	445	28	get	get	VERB
ejpam-4941	445	29	the	the	DET
ejpam-4941	445	30	new	new	ADJ
ejpam-4941	445	31	reduced	reduce	VERB
ejpam-4941	445	32	vector	vector	NOUN
ejpam-4941	445	33	f	f	PROPN
ejpam-4941	445	34	∗∗new2	∗∗new2	PROPN
ejpam-4941	445	35	2	2	NUM
ejpam-4941	445	36	which	which	PRON
ejpam-4941	445	37	we	we	PRON
ejpam-4941	445	38	will	will	AUX
ejpam-4941	445	39	use	use	VERB
ejpam-4941	445	40	now	now	ADV
ejpam-4941	445	41	for	for	ADP
ejpam-4941	445	42	the	the	DET
ejpam-4941	445	43	reduction	reduction	NOUN
ejpam-4941	445	44	of	of	ADP
ejpam-4941	445	45	f3	f3	PROPN
ejpam-4941	445	46	.	.	PUNCT
ejpam-4941	446	1	then	then	ADV
ejpam-4941	446	2	,	,	PUNCT
ejpam-4941	446	3	we	we	PRON
ejpam-4941	446	4	have	have	VERB
ejpam-4941	446	5	,	,	PUNCT
ejpam-4941	446	6	f1	f1	PROPN
ejpam-4941	447	1	=	=	SYM
ejpam-4941	447	2	f	f	PROPN
ejpam-4941	447	3	∗∗new1	∗∗new1	PROPN
ejpam-4941	447	4	2	2	NUM
ejpam-4941	447	5	,	,	PUNCT
ejpam-4941	447	6	f2	f2	PROPN
ejpam-4941	447	7	=	=	SYM
ejpam-4941	447	8	f	f	PROPN
ejpam-4941	447	9	∗∗new2	∗∗new2	PROPN
ejpam-4941	447	10	2	2	NUM
ejpam-4941	447	11	,	,	PUNCT
ejpam-4941	447	12	f3	f3	NOUN
ejpam-4941	447	13	=	=	SYM
ejpam-4941	448	1	f	f	PROPN
ejpam-4941	448	2	∗∗new1	∗∗new1	PROPN
ejpam-4941	448	3	3	3	NUM
ejpam-4941	448	4	now	now	ADV
ejpam-4941	448	5	,	,	PUNCT
ejpam-4941	448	6	for	for	ADP
ejpam-4941	448	7	the	the	DET
ejpam-4941	448	8	size	size	NOUN
ejpam-4941	448	9	reduction	reduction	NOUN
ejpam-4941	448	10	,	,	PUNCT
ejpam-4941	448	11	we	we	PRON
ejpam-4941	448	12	can	can	AUX
ejpam-4941	448	13	see	see	VERB
ejpam-4941	448	14	that	that	SCONJ
ejpam-4941	448	15	we	we	PRON
ejpam-4941	448	16	have	have	VERB
ejpam-4941	448	17	,	,	PUNCT
ejpam-4941	448	18	⟨f∗∗(1)new2	⟨f∗∗(1)new2	NOUN
ejpam-4941	448	19	2	2	NUM
ejpam-4941	448	20	,	,	PUNCT
ejpam-4941	448	21	f	f	PROPN
ejpam-4941	449	1	∗∗(1)new1	∗∗(1)new1	PROPN
ejpam-4941	449	2	2	2	NUM
ejpam-4941	449	3	⟩	⟩	NOUN
ejpam-4941	449	4	⟨f∗∗(1)new1	⟨f∗∗(1)new1	ADJ
ejpam-4941	449	5	2	2	NUM
ejpam-4941	449	6	,	,	PUNCT
ejpam-4941	449	7	f	f	PROPN
ejpam-4941	449	8	∗∗(1)new1	∗∗(1)new1	PROPN
ejpam-4941	449	9	2	2	NUM
ejpam-4941	449	10	⟩	⟩	NOUN
ejpam-4941	449	11	=	=	NOUN
ejpam-4941	449	12	0.00000000000000002049319288085836	0.00000000000000002049319288085836	NUM
ejpam-4941	449	13	and	and	CCONJ
ejpam-4941	449	14	⟨f∗∗(2)new1	⟨f∗∗(2)new1	NOUN
ejpam-4941	449	15	3	3	NUM
ejpam-4941	449	16	,	,	PUNCT
ejpam-4941	449	17	f	f	PROPN
ejpam-4941	449	18	∗∗(1)new2	∗∗(1)new2	PROPN
ejpam-4941	449	19	2	2	NUM
ejpam-4941	449	20	⟩	⟩	NOUN
ejpam-4941	449	21	⟨f∗∗(1)new2	⟨f∗∗(1)new2	NOUN
ejpam-4941	449	22	2	2	NUM
ejpam-4941	449	23	,	,	PUNCT
ejpam-4941	449	24	f	f	PROPN
ejpam-4941	449	25	∗∗(1)new2	∗∗(1)new2	PROPN
ejpam-4941	449	26	2	2	NUM
ejpam-4941	449	27	⟩	⟩	NOUN
ejpam-4941	449	28	=	=	SYM
ejpam-4941	449	29	0.00000000000000000000014925455088	0.00000000000000000000014925455088	NUM
ejpam-4941	449	30	which	which	PRON
ejpam-4941	449	31	both	both	PRON
ejpam-4941	449	32	satisfy	satisfy	VERB
ejpam-4941	449	33	the	the	DET
ejpam-4941	449	34	condition	condition	NOUN
ejpam-4941	449	35	in	in	ADP
ejpam-4941	449	36	definition	definition	NOUN
ejpam-4941	449	37	1	1	NUM
ejpam-4941	449	38	.	.	PUNCT
ejpam-4941	450	1	as	as	ADP
ejpam-4941	450	2	for	for	ADP
ejpam-4941	450	3	the	the	DET
ejpam-4941	450	4	quasi	quasi	ADJ
ejpam-4941	450	5	-	-	ADJ
ejpam-4941	450	6	orthogonality	orthogonality	ADJ
ejpam-4941	450	7	condition	condition	NOUN
ejpam-4941	450	8	of	of	ADP
ejpam-4941	450	9	definition	definition	NOUN
ejpam-4941	450	10	2	2	NUM
ejpam-4941	450	11	,	,	PUNCT
ejpam-4941	450	12	we	we	PRON
ejpam-4941	450	13	find	find	VERB
ejpam-4941	450	14	that	that	SCONJ
ejpam-4941	450	15	the	the	DET
ejpam-4941	450	16	condition	condition	NOUN
ejpam-4941	450	17	is	be	AUX
ejpam-4941	450	18	not	not	PART
ejpam-4941	450	19	satisfied	satisfied	ADJ
ejpam-4941	450	20	between	between	ADP
ejpam-4941	450	21	f	f	PROPN
ejpam-4941	450	22	∗∗(2)new1	∗∗(2)new1	PROPN
ejpam-4941	450	23	3	3	PROPN
ejpam-4941	450	24	and	and	CCONJ
ejpam-4941	450	25	f	f	NOUN
ejpam-4941	450	26	∗∗(1)new2	∗∗(1)new2	PROPN
ejpam-4941	450	27	2	2	PROPN
ejpam-4941	450	28	.	.	PUNCT
ejpam-4941	451	1	then	then	ADV
ejpam-4941	451	2	,	,	PUNCT
ejpam-4941	451	3	we	we	PRON
ejpam-4941	451	4	should	should	AUX
ejpam-4941	451	5	swap	swap	VERB
ejpam-4941	451	6	these	these	DET
ejpam-4941	451	7	vectors	vector	NOUN
ejpam-4941	451	8	.	.	PUNCT
ejpam-4941	452	1	this	this	PRON
ejpam-4941	452	2	means	mean	VERB
ejpam-4941	452	3	,	,	PUNCT
ejpam-4941	452	4	we	we	PRON
ejpam-4941	452	5	will	will	AUX
ejpam-4941	452	6	have	have	VERB
ejpam-4941	452	7	now	now	ADV
ejpam-4941	452	8	,	,	PUNCT
ejpam-4941	452	9	f1	f1	PROPN
ejpam-4941	453	1	=	=	SYM
ejpam-4941	453	2	f	f	PROPN
ejpam-4941	453	3	∗∗new1	∗∗new1	PROPN
ejpam-4941	453	4	2	2	NUM
ejpam-4941	453	5	,	,	PUNCT
ejpam-4941	453	6	f2	f2	PROPN
ejpam-4941	453	7	=	=	NOUN
ejpam-4941	453	8	f	f	PROPN
ejpam-4941	453	9	∗∗new1	∗∗new1	PROPN
ejpam-4941	453	10	3	3	NUM
ejpam-4941	453	11	,	,	PUNCT
ejpam-4941	454	1	f3	f3	PROPN
ejpam-4941	454	2	=	=	SYM
ejpam-4941	454	3	f	f	PROPN
ejpam-4941	454	4	∗∗new2	∗∗new2	PROPN
ejpam-4941	454	5	2	2	NUM
ejpam-4941	454	6	in	in	ADP
ejpam-4941	454	7	this	this	DET
ejpam-4941	454	8	step	step	NOUN
ejpam-4941	454	9	,	,	PUNCT
ejpam-4941	454	10	we	we	PRON
ejpam-4941	454	11	find	find	VERB
ejpam-4941	454	12	that	that	SCONJ
ejpam-4941	454	13	the	the	DET
ejpam-4941	454	14	conditions	condition	NOUN
ejpam-4941	454	15	on	on	ADP
ejpam-4941	454	16	both	both	DET
ejpam-4941	454	17	size	size	NOUN
ejpam-4941	454	18	reduction	reduction	NOUN
ejpam-4941	454	19	and	and	CCONJ
ejpam-4941	454	20	quasi	quasi	ADJ
ejpam-4941	454	21	-	-	ADJ
ejpam-4941	454	22	orthogonality	orthogonality	NOUN
ejpam-4941	454	23	are	be	AUX
ejpam-4941	454	24	satisfied	satisfied	ADJ
ejpam-4941	454	25	,	,	PUNCT
ejpam-4941	454	26	then	then	ADV
ejpam-4941	454	27	we	we	PRON
ejpam-4941	454	28	keep	keep	VERB
ejpam-4941	454	29	those	those	DET
ejpam-4941	454	30	last	last	ADJ
ejpam-4941	454	31	vectors	vector	NOUN
ejpam-4941	454	32	.	.	PUNCT
ejpam-4941	455	1	4	4	X
ejpam-4941	455	2	.	.	X
ejpam-4941	455	3	conclusion	conclusion	NOUN
ejpam-4941	455	4	in	in	ADP
ejpam-4941	455	5	this	this	DET
ejpam-4941	455	6	paper	paper	NOUN
ejpam-4941	455	7	,	,	PUNCT
ejpam-4941	455	8	we	we	PRON
ejpam-4941	455	9	have	have	AUX
ejpam-4941	455	10	introduced	introduce	VERB
ejpam-4941	455	11	a	a	DET
ejpam-4941	455	12	theoretical	theoretical	ADJ
ejpam-4941	455	13	concept	concept	NOUN
ejpam-4941	455	14	which	which	PRON
ejpam-4941	455	15	is	be	AUX
ejpam-4941	455	16	about	about	ADP
ejpam-4941	455	17	seeking	seek	VERB
ejpam-4941	455	18	a	a	DET
ejpam-4941	455	19	’	'	PUNCT
ejpam-4941	455	20	good	good	ADJ
ejpam-4941	455	21	’	'	PUNCT
ejpam-4941	455	22	crystal	crystal	NOUN
ejpam-4941	455	23	cell	cell	NOUN
ejpam-4941	455	24	starting	start	VERB
ejpam-4941	455	25	from	from	ADP
ejpam-4941	455	26	any	any	DET
ejpam-4941	455	27	’	'	PUNCT
ejpam-4941	455	28	bad	bad	ADJ
ejpam-4941	455	29	’	'	PUNCT
ejpam-4941	455	30	crystal	crystal	NOUN
ejpam-4941	455	31	cell	cell	NOUN
ejpam-4941	455	32	,	,	PUNCT
ejpam-4941	455	33	in	in	ADP
ejpam-4941	455	34	order	order	NOUN
ejpam-4941	455	35	to	to	PART
ejpam-4941	455	36	determine	determine	VERB
ejpam-4941	455	37	the	the	DET
ejpam-4941	455	38	reduced	reduce	VERB
ejpam-4941	455	39	unit	unit	NOUN
ejpam-4941	455	40	cell	cell	NOUN
ejpam-4941	455	41	whose	whose	DET
ejpam-4941	455	42	vectors	vector	NOUN
ejpam-4941	455	43	are	be	AUX
ejpam-4941	455	44	close	close	ADJ
ejpam-4941	455	45	-	-	PUNCT
ejpam-4941	455	46	to	to	ADP
ejpam-4941	455	47	-	-	PUNCT
ejpam-4941	455	48	orthogonal	orthogonal	ADJ
ejpam-4941	455	49	,	,	PUNCT
ejpam-4941	455	50	through	through	ADP
ejpam-4941	455	51	a	a	DET
ejpam-4941	455	52	major	major	ADJ
ejpam-4941	455	53	part	part	NOUN
ejpam-4941	455	54	of	of	ADP
ejpam-4941	455	55	bravais	bravais	PROPN
ejpam-4941	455	56	basis	basis	NOUN
ejpam-4941	455	57	reduction	reduction	NOUN
ejpam-4941	455	58	,	,	PUNCT
ejpam-4941	455	59	namely	namely	ADV
ejpam-4941	455	60	the	the	DET
ejpam-4941	455	61	steps	step	NOUN
ejpam-4941	455	62	of	of	ADP
ejpam-4941	455	63	the	the	DET
ejpam-4941	455	64	first	first	ADJ
ejpam-4941	455	65	version	version	NOUN
ejpam-4941	455	66	that	that	PRON
ejpam-4941	455	67	we	we	PRON
ejpam-4941	455	68	have	have	AUX
ejpam-4941	455	69	suggested	suggest	VERB
ejpam-4941	455	70	for	for	SCONJ
ejpam-4941	455	71	the	the	DET
ejpam-4941	455	72	vectors	vector	NOUN
ejpam-4941	455	73	exchange	exchange	NOUN
ejpam-4941	455	74	references	reference	NOUN
ejpam-4941	455	75	2688	2688	NUM
ejpam-4941	455	76	theorem	theorem	VERB
ejpam-4941	455	77	2	2	NUM
ejpam-4941	455	78	.	.	PUNCT
ejpam-4941	456	1	in	in	ADP
ejpam-4941	456	2	fact	fact	NOUN
ejpam-4941	456	3	,	,	PUNCT
ejpam-4941	456	4	we	we	PRON
ejpam-4941	456	5	studied	study	VERB
ejpam-4941	456	6	the	the	DET
ejpam-4941	456	7	special	special	ADJ
ejpam-4941	456	8	case	case	NOUN
ejpam-4941	456	9	when	when	SCONJ
ejpam-4941	456	10	we	we	PRON
ejpam-4941	456	11	have	have	AUX
ejpam-4941	456	12	known	know	VERB
ejpam-4941	456	13	beforehand	beforehand	ADV
ejpam-4941	456	14	that	that	SCONJ
ejpam-4941	456	15	the	the	DET
ejpam-4941	456	16	motif	motif	NOUN
ejpam-4941	456	17	should	should	AUX
ejpam-4941	456	18	be	be	AUX
ejpam-4941	456	19	made	make	VERB
ejpam-4941	456	20	of	of	ADP
ejpam-4941	456	21	quasi	quasi	ADJ
ejpam-4941	456	22	-	-	ADJ
ejpam-4941	456	23	orthogonal	orthogonal	ADJ
ejpam-4941	456	24	vectors	vector	NOUN
ejpam-4941	456	25	.	.	PUNCT
ejpam-4941	457	1	in	in	ADP
ejpam-4941	457	2	addition	addition	NOUN
ejpam-4941	457	3	,	,	PUNCT
ejpam-4941	457	4	this	this	DET
ejpam-4941	457	5	work	work	NOUN
ejpam-4941	457	6	has	have	AUX
ejpam-4941	457	7	more	more	ADV
ejpam-4941	457	8	interestingly	interestingly	ADV
ejpam-4941	457	9	answered	answer	VERB
ejpam-4941	457	10	about	about	ADP
ejpam-4941	457	11	a	a	DET
ejpam-4941	457	12	more	more	ADV
ejpam-4941	457	13	general	general	ADJ
ejpam-4941	457	14	problem	problem	NOUN
ejpam-4941	457	15	often	often	ADV
ejpam-4941	457	16	not	not	PART
ejpam-4941	457	17	taking	take	VERB
ejpam-4941	457	18	enough	enough	ADJ
ejpam-4941	457	19	place	place	NOUN
ejpam-4941	457	20	in	in	ADP
ejpam-4941	457	21	the	the	DET
ejpam-4941	457	22	literature	literature	NOUN
ejpam-4941	457	23	,	,	PUNCT
ejpam-4941	457	24	and	and	CCONJ
ejpam-4941	457	25	which	which	PRON
ejpam-4941	457	26	is	be	AUX
ejpam-4941	457	27	about	about	ADP
ejpam-4941	457	28	investigating	investigate	VERB
ejpam-4941	457	29	theoretically	theoretically	ADV
ejpam-4941	457	30	,	,	PUNCT
ejpam-4941	457	31	the	the	DET
ejpam-4941	457	32	impact	impact	NOUN
ejpam-4941	457	33	of	of	ADP
ejpam-4941	457	34	the	the	DET
ejpam-4941	457	35	repeated	repeat	VERB
ejpam-4941	457	36	exchange	exchange	NOUN
ejpam-4941	457	37	of	of	ADP
ejpam-4941	457	38	vectors	vector	NOUN
ejpam-4941	457	39	,	,	PUNCT
ejpam-4941	457	40	on	on	ADP
ejpam-4941	457	41	the	the	DET
ejpam-4941	457	42	precision	precision	NOUN
ejpam-4941	457	43	of	of	ADP
ejpam-4941	457	44	two	two	NUM
ejpam-4941	457	45	different	different	ADJ
ejpam-4941	457	46	orthogonalization	orthogonalization	NOUN
ejpam-4941	457	47	methods	method	NOUN
ejpam-4941	457	48	,	,	PUNCT
ejpam-4941	457	49	in	in	ADP
ejpam-4941	457	50	times	time	NOUN
ejpam-4941	457	51	of	of	ADP
ejpam-4941	457	52	the	the	DET
ejpam-4941	457	53	reduction	reduction	NOUN
ejpam-4941	457	54	process	process	NOUN
ejpam-4941	457	55	of	of	ADP
ejpam-4941	457	56	bravais	bravais	PROPN
ejpam-4941	457	57	basis	basis	NOUN
ejpam-4941	457	58	.	.	PUNCT
ejpam-4941	458	1	another	another	DET
ejpam-4941	458	2	major	major	ADJ
ejpam-4941	458	3	point	point	NOUN
ejpam-4941	458	4	that	that	PRON
ejpam-4941	458	5	we	we	PRON
ejpam-4941	458	6	have	have	AUX
ejpam-4941	458	7	succeeded	succeed	VERB
ejpam-4941	458	8	to	to	PART
ejpam-4941	458	9	prove	prove	VERB
ejpam-4941	458	10	in	in	ADP
ejpam-4941	458	11	this	this	DET
ejpam-4941	458	12	paper	paper	NOUN
ejpam-4941	458	13	,	,	PUNCT
ejpam-4941	458	14	is	be	AUX
ejpam-4941	458	15	that	that	DET
ejpam-4941	458	16	mgs	mgs	NOUN
ejpam-4941	458	17	was	be	AUX
ejpam-4941	458	18	better	well	ADJ
ejpam-4941	458	19	than	than	ADP
ejpam-4941	458	20	gs	gs	INTJ
ejpam-4941	458	21	,	,	PUNCT
ejpam-4941	458	22	not	not	PART
ejpam-4941	458	23	only	only	ADV
ejpam-4941	458	24	in	in	ADP
ejpam-4941	458	25	numerics	numeric	NOUN
ejpam-4941	458	26	as	as	ADP
ejpam-4941	458	27	traditionally	traditionally	ADV
ejpam-4941	458	28	known	know	VERB
ejpam-4941	458	29	,	,	PUNCT
ejpam-4941	458	30	but	but	CCONJ
ejpam-4941	458	31	because	because	SCONJ
ejpam-4941	458	32	of	of	ADP
ejpam-4941	458	33	its	its	PRON
ejpam-4941	458	34	preservation	preservation	NOUN
ejpam-4941	458	35	of	of	ADP
ejpam-4941	458	36	the	the	DET
ejpam-4941	458	37	orthogonality	orthogonality	NOUN
ejpam-4941	458	38	formulations	formulation	NOUN
ejpam-4941	458	39	in	in	ADP
ejpam-4941	458	40	spite	spite	NOUN
ejpam-4941	458	41	of	of	ADP
ejpam-4941	458	42	the	the	DET
ejpam-4941	458	43	vectors	vector	NOUN
ejpam-4941	458	44	swapping	swap	VERB
ejpam-4941	458	45	in	in	ADP
ejpam-4941	458	46	three	three	NUM
ejpam-4941	458	47	conditions	condition	NOUN
ejpam-4941	458	48	rather	rather	ADV
ejpam-4941	458	49	than	than	ADP
ejpam-4941	458	50	two	two	NUM
ejpam-4941	458	51	for	for	ADP
ejpam-4941	458	52	gs	gs	NOUN
ejpam-4941	458	53	,	,	PUNCT
ejpam-4941	458	54	and	and	CCONJ
ejpam-4941	458	55	which	which	PRON
ejpam-4941	458	56	can	can	AUX
ejpam-4941	458	57	lead	lead	VERB
ejpam-4941	458	58	to	to	PART
ejpam-4941	458	59	mgs	mgs	VERB
ejpam-4941	458	60	to	to	PART
ejpam-4941	458	61	be	be	AUX
ejpam-4941	458	62	more	more	ADV
ejpam-4941	458	63	recommended	recommend	VERB
ejpam-4941	458	64	in	in	ADP
ejpam-4941	458	65	future	future	NOUN
ejpam-4941	458	66	in	in	ADP
ejpam-4941	458	67	more	more	ADV
ejpam-4941	458	68	complicated	complicated	ADJ
ejpam-4941	458	69	cases	case	NOUN
ejpam-4941	458	70	,	,	PUNCT
ejpam-4941	458	71	for	for	ADP
ejpam-4941	458	72	instance	instance	NOUN
ejpam-4941	458	73	when	when	SCONJ
ejpam-4941	458	74	the	the	DET
ejpam-4941	458	75	dimension	dimension	NOUN
ejpam-4941	458	76	is	be	AUX
ejpam-4941	458	77	very	very	ADV
ejpam-4941	458	78	big	big	ADJ
ejpam-4941	458	79	.	.	PUNCT
ejpam-4941	459	1	acknowledgements	acknowledgement	NOUN
ejpam-4941	459	2	a	a	DET
ejpam-4941	459	3	special	special	ADJ
ejpam-4941	459	4	thanks	thank	NOUN
ejpam-4941	459	5	to	to	ADP
ejpam-4941	459	6	the	the	DET
ejpam-4941	459	7	editor	editor	NOUN
ejpam-4941	459	8	professor	professor	PROPN
ejpam-4941	459	9	dr	dr	PROPN
ejpam-4941	459	10	.	.	PROPN
ejpam-4941	459	11	eyup	eyup	PROPN
ejpam-4941	459	12	cetin	cetin	PROPN
ejpam-4941	459	13	.	.	PUNCT
ejpam-4941	460	1	we	we	PRON
ejpam-4941	460	2	would	would	AUX
ejpam-4941	460	3	also	also	ADV
ejpam-4941	460	4	like	like	VERB
ejpam-4941	460	5	to	to	PART
ejpam-4941	460	6	thank	thank	VERB
ejpam-4941	460	7	all	all	DET
ejpam-4941	460	8	the	the	DET
ejpam-4941	460	9	three	three	NUM
ejpam-4941	460	10	anonymous	anonymous	ADJ
ejpam-4941	460	11	referees	referee	NOUN
ejpam-4941	460	12	for	for	ADP
ejpam-4941	460	13	their	their	PRON
ejpam-4941	460	14	time	time	NOUN
ejpam-4941	460	15	,	,	PUNCT
ejpam-4941	460	16	effort	effort	NOUN
ejpam-4941	460	17	and	and	CCONJ
ejpam-4941	460	18	help	help	VERB
ejpam-4941	460	19	for	for	ADP
ejpam-4941	460	20	improving	improve	VERB
ejpam-4941	460	21	the	the	DET
ejpam-4941	460	22	content	content	NOUN
ejpam-4941	460	23	of	of	ADP
ejpam-4941	460	24	our	our	PRON
ejpam-4941	460	25	paper	paper	NOUN
ejpam-4941	460	26	.	.	PUNCT
ejpam-4941	461	1	references	reference	NOUN
ejpam-4941	461	2	[	[	X
ejpam-4941	461	3	1	1	NUM
ejpam-4941	461	4	]	]	PUNCT
ejpam-4941	461	5	k.	k.	PROPN
ejpam-4941	461	6	aardal	aardal	PROPN
ejpam-4941	461	7	and	and	CCONJ
ejpam-4941	461	8	f.	f.	PROPN
ejpam-4941	461	9	eisenbrand	eisenbrand	PROPN
ejpam-4941	461	10	.	.	PUNCT
ejpam-4941	462	1	the	the	DET
ejpam-4941	462	2	lll	lll	PROPN
ejpam-4941	462	3	algorithm	algorithm	NOUN
ejpam-4941	462	4	and	and	CCONJ
ejpam-4941	462	5	integer	integer	NOUN
ejpam-4941	462	6	programming	programming	NOUN
ejpam-4941	462	7	.	.	PUNCT
ejpam-4941	463	1	in	in	ADP
ejpam-4941	463	2	the	the	DET
ejpam-4941	463	3	lll	lll	PROPN
ejpam-4941	463	4	algorithm	algorithm	NOUN
ejpam-4941	463	5	:	:	PUNCT
ejpam-4941	463	6	survey	survey	NOUN
ejpam-4941	463	7	and	and	CCONJ
ejpam-4941	463	8	applications	application	NOUN
ejpam-4941	463	9	.	.	PUNCT
ejpam-4941	464	1	p.293	p.293	NUM
ejpam-4941	464	2	-	-	SYM
ejpam-4941	464	3	314	314	NUM
ejpam-4941	464	4	,	,	PUNCT
ejpam-4941	464	5	berlin	berlin	PROPN
ejpam-4941	464	6	,	,	PUNCT
ejpam-4941	464	7	heidelberg	heidelberg	PROPN
ejpam-4941	464	8	:	:	PUNCT
ejpam-4941	464	9	springer	springer	PROPN
ejpam-4941	464	10	berlin	berlin	PROPN
ejpam-4941	464	11	heidelberg	heidelberg	PROPN
ejpam-4941	464	12	,	,	PUNCT
ejpam-4941	464	13	2009	2009	NUM
ejpam-4941	464	14	.	.	PUNCT
ejpam-4941	465	1	[	[	X
ejpam-4941	465	2	2	2	X
ejpam-4941	465	3	]	]	PUNCT
ejpam-4941	465	4	s.	s.	PROPN
ejpam-4941	465	5	abdelalim	abdelalim	PROPN
ejpam-4941	465	6	h.	h.	PROPN
ejpam-4941	465	7	el	el	PROPN
ejpam-4941	465	8	adlouni	adlouni	PROPN
ejpam-4941	465	9	and	and	CCONJ
ejpam-4941	465	10	h.	h.	PROPN
ejpam-4941	465	11	diany	diany	PROPN
ejpam-4941	465	12	.	.	PUNCT
ejpam-4941	466	1	the	the	DET
ejpam-4941	466	2	diophantine	diophantine	NOUN
ejpam-4941	466	3	equation	equation	NOUN
ejpam-4941	466	4	x3	x3	NOUN
ejpam-4941	466	5	+	+	CCONJ
ejpam-4941	466	6	y3	y3	NOUN
ejpam-4941	466	7	=	=	SYM
ejpam-4941	466	8	2z2	2z2	NUM
ejpam-4941	466	9	.	.	PUNCT
ejpam-4941	467	1	gulf	gulf	PROPN
ejpam-4941	467	2	journal	journal	PROPN
ejpam-4941	467	3	of	of	ADP
ejpam-4941	467	4	mathematics	mathematic	NOUN
ejpam-4941	467	5	,	,	PUNCT
ejpam-4941	467	6	4(4	4(4	NUM
ejpam-4941	467	7	)	)	PUNCT
ejpam-4941	467	8	.	.	PUNCT
ejpam-4941	468	1	p.67	p.67	PROPN
ejpam-4941	468	2	-	-	VERB
ejpam-4941	468	3	73	73	NUM
ejpam-4941	468	4	,	,	PUNCT
ejpam-4941	468	5	2016	2016	NUM
ejpam-4941	468	6	.	.	PUNCT
ejpam-4941	469	1	[	[	X
ejpam-4941	469	2	3	3	NUM
ejpam-4941	469	3	]	]	PUNCT
ejpam-4941	469	4	a.	a.	NOUN
ejpam-4941	469	5	akhavi	akhavi	PROPN
ejpam-4941	469	6	.	.	PUNCT
ejpam-4941	470	1	the	the	DET
ejpam-4941	470	2	optimal	optimal	ADJ
ejpam-4941	470	3	lll	lll	NOUN
ejpam-4941	470	4	algorithm	algorithm	NOUN
ejpam-4941	470	5	is	be	AUX
ejpam-4941	470	6	still	still	ADV
ejpam-4941	470	7	polynomial	polynomial	ADJ
ejpam-4941	470	8	in	in	ADP
ejpam-4941	470	9	fixed	fix	VERB
ejpam-4941	470	10	dimension	dimension	NOUN
ejpam-4941	470	11	.	.	PUNCT
ejpam-4941	471	1	theoretical	theoretical	ADJ
ejpam-4941	471	2	computer	computer	NOUN
ejpam-4941	471	3	science	science	NOUN
ejpam-4941	471	4	,	,	PUNCT
ejpam-4941	471	5	297(1	297(1	NUM
ejpam-4941	471	6	-	-	SYM
ejpam-4941	471	7	3	3	NUM
ejpam-4941	471	8	)	)	PUNCT
ejpam-4941	471	9	,	,	PUNCT
ejpam-4941	471	10	p.3	p.3	NOUN
ejpam-4941	471	11	-	-	PUNCT
ejpam-4941	471	12	23	23	NUM
ejpam-4941	471	13	,	,	PUNCT
ejpam-4941	471	14	2003	2003	NUM
ejpam-4941	471	15	.	.	PUNCT
ejpam-4941	472	1	[	[	X
ejpam-4941	472	2	4	4	X
ejpam-4941	472	3	]	]	PUNCT
ejpam-4941	472	4	s.	s.	PROPN
ejpam-4941	472	5	roger	roger	PROPN
ejpam-4941	472	6	a.	a.	PROPN
ejpam-4941	472	7	gonzalez	gonzalez	PROPN
ejpam-4941	472	8	v.	v.	ADP
ejpam-4941	472	9	almenar	almenar	PROPN
ejpam-4941	472	10	and	and	CCONJ
ejpam-4941	472	11	a.	a.	NOUN
ejpam-4941	472	12	m.	m.	NOUN
ejpam-4941	472	13	vidal	vidal	PROPN
ejpam-4941	472	14	.	.	PUNCT
ejpam-4941	472	15	extended	extend	VERB
ejpam-4941	472	16	lll	lll	NOUN
ejpam-4941	472	17	algorithm	algorithm	NOUN
ejpam-4941	472	18	for	for	ADP
ejpam-4941	472	19	efficient	efficient	ADJ
ejpam-4941	472	20	signal	signal	NOUN
ejpam-4941	472	21	precoding	precoding	NOUN
ejpam-4941	472	22	in	in	ADP
ejpam-4941	472	23	multiuser	multiuser	NOUN
ejpam-4941	472	24	communication	communication	NOUN
ejpam-4941	472	25	systems	system	NOUN
ejpam-4941	472	26	.	.	PUNCT
ejpam-4941	473	1	ieee	ieee	NOUN
ejpam-4941	473	2	communications	communication	NOUN
ejpam-4941	473	3	letters	letter	NOUN
ejpam-4941	473	4	,	,	PUNCT
ejpam-4941	473	5	14(3	14(3	NUM
ejpam-4941	473	6	)	)	PUNCT
ejpam-4941	473	7	,	,	PUNCT
ejpam-4941	473	8	p.220	p.220	NOUN
ejpam-4941	473	9	-	-	PUNCT
ejpam-4941	473	10	222	222	NUM
ejpam-4941	473	11	,	,	PUNCT
ejpam-4941	473	12	2010	2010	NUM
ejpam-4941	473	13	.	.	PUNCT
ejpam-4941	474	1	[	[	X
ejpam-4941	474	2	5	5	X
ejpam-4941	474	3	]	]	PUNCT
ejpam-4941	474	4	k.	k.	PROPN
ejpam-4941	474	5	arimoto	arimoto	PROPN
ejpam-4941	474	6	.	.	PUNCT
ejpam-4941	475	1	on	on	ADP
ejpam-4941	475	2	lll	lll	PROPN
ejpam-4941	475	3	lattice	lattice	PROPN
ejpam-4941	475	4	basis	basis	NOUN
ejpam-4941	475	5	reduction	reduction	NOUN
ejpam-4941	475	6	over	over	ADP
ejpam-4941	475	7	imaginary	imaginary	ADJ
ejpam-4941	475	8	quadratic	quadratic	ADJ
ejpam-4941	475	9	fields	field	NOUN
ejpam-4941	475	10	by	by	ADP
ejpam-4941	475	11	introducing	introduce	VERB
ejpam-4941	475	12	reduction	reduction	NOUN
ejpam-4941	475	13	parameters	parameter	NOUN
ejpam-4941	475	14	.	.	PUNCT
ejpam-4941	476	1	int	int	NOUN
ejpam-4941	476	2	.	.	PUNCT
ejpam-4941	477	1	j.	j.	PROPN
ejpam-4941	477	2	math	math	PROPN
ejpam-4941	477	3	.	.	PUNCT
ejpam-4941	478	1	comput	comput	NOUN
ejpam-4941	478	2	.	.	PUNCT
ejpam-4941	479	1	sci	sci	PROPN
ejpam-4941	479	2	.	.	PROPN
ejpam-4941	479	3	,	,	PUNCT
ejpam-4941	479	4	15(2	15(2	NUM
ejpam-4941	479	5	)	)	PUNCT
ejpam-4941	479	6	,	,	PUNCT
ejpam-4941	479	7	p.611	p.611	NOUN
ejpam-4941	479	8	-	-	PUNCT
ejpam-4941	479	9	619	619	NUM
ejpam-4941	479	10	,	,	PUNCT
ejpam-4941	479	11	2020	2020	NUM
ejpam-4941	479	12	.	.	PUNCT
ejpam-4941	480	1	[	[	X
ejpam-4941	480	2	6	6	NUM
ejpam-4941	480	3	]	]	PUNCT
ejpam-4941	480	4	p.	p.	NOUN
ejpam-4941	480	5	bak	bak	PROPN
ejpam-4941	480	6	.	.	PUNCT
ejpam-4941	481	1	icosahedral	icosahedral	ADJ
ejpam-4941	481	2	crystals	crystal	NOUN
ejpam-4941	481	3	:	:	PUNCT
ejpam-4941	481	4	where	where	SCONJ
ejpam-4941	481	5	are	be	AUX
ejpam-4941	481	6	the	the	DET
ejpam-4941	481	7	atoms	atom	NOUN
ejpam-4941	481	8	?	?	PUNCT
ejpam-4941	482	1	physical	physical	ADJ
ejpam-4941	482	2	review	review	NOUN
ejpam-4941	482	3	letters	letter	NOUN
ejpam-4941	482	4	,	,	PUNCT
ejpam-4941	482	5	56(8	56(8	NUM
ejpam-4941	482	6	)	)	PUNCT
ejpam-4941	482	7	,	,	PUNCT
ejpam-4941	482	8	p.861	p.861	NOUN
ejpam-4941	482	9	,	,	PUNCT
ejpam-4941	482	10	1986	1986	NUM
ejpam-4941	482	11	.	.	PUNCT
ejpam-4941	483	1	[	[	X
ejpam-4941	483	2	7	7	X
ejpam-4941	483	3	]	]	X
ejpam-4941	483	4	l.	l.	PROPN
ejpam-4941	483	5	c.	c.	PROPN
ejpam-4941	483	6	andrews	andrews	PROPN
ejpam-4941	483	7	h.	h.	PROPN
ejpam-4941	483	8	j.	j.	PROPN
ejpam-4941	483	9	bernstein	bernstein	PROPN
ejpam-4941	483	10	and	and	CCONJ
ejpam-4941	483	11	n.	n.	PROPN
ejpam-4941	483	12	k.	k.	PROPN
ejpam-4941	483	13	sauter	sauter	PROPN
ejpam-4941	483	14	.	.	PUNCT
ejpam-4941	484	1	selling	sell	VERB
ejpam-4941	484	2	reduction	reduction	NOUN
ejpam-4941	484	3	versus	versus	ADP
ejpam-4941	484	4	niggli	niggli	NOUN
ejpam-4941	484	5	reduction	reduction	NOUN
ejpam-4941	484	6	for	for	ADP
ejpam-4941	484	7	crystallographic	crystallographic	ADJ
ejpam-4941	484	8	lattices	lattice	NOUN
ejpam-4941	484	9	.	.	PUNCT
ejpam-4941	485	1	acta	acta	PROPN
ejpam-4941	485	2	crystallographica	crystallographica	PROPN
ejpam-4941	485	3	section	section	PROPN
ejpam-4941	485	4	a	a	DET
ejpam-4941	485	5	:	:	PUNCT
ejpam-4941	485	6	foundations	foundation	NOUN
ejpam-4941	485	7	and	and	CCONJ
ejpam-4941	485	8	advances	advance	NOUN
ejpam-4941	485	9	,	,	PUNCT
ejpam-4941	485	10	75(1	75(1	NOUN
ejpam-4941	485	11	)	)	PUNCT
ejpam-4941	485	12	,	,	PUNCT
ejpam-4941	485	13	p.115	p.115	PROPN
ejpam-4941	485	14	-	-	SYM
ejpam-4941	485	15	120	120	NUM
ejpam-4941	485	16	,	,	PUNCT
ejpam-4941	485	17	2019	2019	NUM
ejpam-4941	485	18	.	.	PUNCT
ejpam-4941	486	1	[	[	X
ejpam-4941	486	2	8	8	NUM
ejpam-4941	486	3	]	]	X
ejpam-4941	486	4	y.	y.	PROPN
ejpam-4941	486	5	bilu	bilu	PROPN
ejpam-4941	486	6	and	and	CCONJ
ejpam-4941	486	7	g.	g.	PROPN
ejpam-4941	486	8	hanrot	hanrot	PROPN
ejpam-4941	486	9	.	.	PUNCT
ejpam-4941	487	1	solving	solve	VERB
ejpam-4941	487	2	thue	thue	PROPN
ejpam-4941	487	3	equations	equation	NOUN
ejpam-4941	487	4	of	of	ADP
ejpam-4941	487	5	high	high	ADJ
ejpam-4941	487	6	degree	degree	NOUN
ejpam-4941	487	7	.	.	PUNCT
ejpam-4941	488	1	journal	journal	NOUN
ejpam-4941	488	2	of	of	ADP
ejpam-4941	488	3	number	number	NOUN
ejpam-4941	488	4	theory	theory	NOUN
ejpam-4941	488	5	,	,	PUNCT
ejpam-4941	488	6	60(2	60(2	NUM
ejpam-4941	488	7	)	)	PUNCT
ejpam-4941	488	8	,	,	PUNCT
ejpam-4941	488	9	p.373	p.373	NOUN
ejpam-4941	488	10	-	-	PUNCT
ejpam-4941	488	11	392	392	NUM
ejpam-4941	488	12	,	,	PUNCT
ejpam-4941	488	13	1996	1996	NUM
ejpam-4941	488	14	.	.	PUNCT
ejpam-4941	489	1	references	reference	NOUN
ejpam-4941	489	2	2689	2689	NUM
ejpam-4941	489	3	[	[	X
ejpam-4941	489	4	9	9	NUM
ejpam-4941	489	5	]	]	X
ejpam-4941	489	6	r.	r.	PROPN
ejpam-4941	489	7	l.	l.	PROPN
ejpam-4941	489	8	bonewitz	bonewitz	PROPN
ejpam-4941	489	9	.	.	PUNCT
ejpam-4941	490	1	rocks	rock	NOUN
ejpam-4941	490	2	and	and	CCONJ
ejpam-4941	490	3	minerals	mineral	NOUN
ejpam-4941	490	4	.	.	PUNCT
ejpam-4941	491	1	dk	dk	PROPN
ejpam-4941	491	2	publishing	publishing	NOUN
ejpam-4941	491	3	.	.	PUNCT
ejpam-4941	492	1	isbn	isbn	ADJ
ejpam-4941	492	2	:	:	PUNCT
ejpam-4941	492	3	978	978	NUM
ejpam-4941	492	4	-	-	SYM
ejpam-4941	492	5	0	0	NUM
ejpam-4941	492	6	-	-	PUNCT
ejpam-4941	492	7	7566	7566	NUM
ejpam-4941	492	8	-	-	PUNCT
ejpam-4941	492	9	9042	9042	NUM
ejpam-4941	492	10	-	-	SYM
ejpam-4941	492	11	7	7	NUM
ejpam-4941	492	12	.	.	PUNCT
ejpam-4941	492	13	p.110	p.110	NOUN
ejpam-4941	492	14	,	,	PUNCT
ejpam-4941	492	15	2012	2012	NUM
ejpam-4941	492	16	.	.	PUNCT
ejpam-4941	493	1	[	[	X
ejpam-4941	493	2	10	10	NUM
ejpam-4941	493	3	]	]	PUNCT
ejpam-4941	493	4	m.	m.	PROPN
ejpam-4941	493	5	r.	r.	PROPN
ejpam-4941	493	6	bremner	bremner	PROPN
ejpam-4941	493	7	.	.	PUNCT
ejpam-4941	494	1	lattice	lattice	PROPN
ejpam-4941	494	2	basis	basis	NOUN
ejpam-4941	494	3	reduction	reduction	NOUN
ejpam-4941	494	4	:	:	PUNCT
ejpam-4941	494	5	an	an	DET
ejpam-4941	494	6	introduction	introduction	NOUN
ejpam-4941	494	7	to	to	ADP
ejpam-4941	494	8	the	the	DET
ejpam-4941	494	9	lll	lll	NOUN
ejpam-4941	494	10	algorithm	algorithm	NOUN
ejpam-4941	494	11	and	and	CCONJ
ejpam-4941	494	12	its	its	PRON
ejpam-4941	494	13	applications	application	NOUN
ejpam-4941	494	14	.	.	PUNCT
ejpam-4941	495	1	crc	crc	PROPN
ejpam-4941	495	2	press	press	PROPN
ejpam-4941	495	3	.	.	PUNCT
ejpam-4941	496	1	isbn	isbn	ADJ
ejpam-4941	496	2	:	:	PUNCT
ejpam-4941	496	3	1439807027	1439807027	NUM
ejpam-4941	496	4	,	,	PUNCT
ejpam-4941	496	5	9781439807026	9781439807026	NUM
ejpam-4941	496	6	,	,	PUNCT
ejpam-4941	496	7	p.332	p.332	NOUN
ejpam-4941	496	8	,	,	PUNCT
ejpam-4941	496	9	2011	2011	NUM
ejpam-4941	496	10	.	.	PUNCT
ejpam-4941	497	1	[	[	X
ejpam-4941	497	2	11	11	NUM
ejpam-4941	497	3	]	]	PUNCT
ejpam-4941	497	4	c.	c.	PROPN
ejpam-4941	497	5	f.	f.	PROPN
ejpam-4941	497	6	liao	liao	PROPN
ejpam-4941	497	7	l.	l.	PROPN
ejpam-4941	497	8	w.	w.	PROPN
ejpam-4941	497	9	chai	chai	PROPN
ejpam-4941	497	10	and	and	CCONJ
ejpam-4941	497	11	y.	y.	PROPN
ejpam-4941	497	12	h.	h.	PROPN
ejpam-4941	497	13	huang	huang	PROPN
ejpam-4941	497	14	.	.	PROPN
ejpam-4941	497	15	loop	loop	NOUN
ejpam-4941	497	16	-	-	PUNCT
ejpam-4941	497	17	reduction	reduction	NOUN
ejpam-4941	497	18	lll	lll	NOUN
ejpam-4941	497	19	algorithm	algorithm	NOUN
ejpam-4941	497	20	and	and	CCONJ
ejpam-4941	497	21	architecture	architecture	NOUN
ejpam-4941	497	22	for	for	ADP
ejpam-4941	497	23	lattice	lattice	NOUN
ejpam-4941	497	24	-	-	PUNCT
ejpam-4941	497	25	reduction	reduction	NOUN
ejpam-4941	497	26	-	-	PUNCT
ejpam-4941	497	27	aided	aid	VERB
ejpam-4941	497	28	mimo	mimo	PROPN
ejpam-4941	497	29	detection	detection	PROPN
ejpam-4941	497	30	.	.	PUNCT
ejpam-4941	498	1	journal	journal	NOUN
ejpam-4941	498	2	of	of	ADP
ejpam-4941	498	3	electrical	electrical	ADJ
ejpam-4941	498	4	and	and	CCONJ
ejpam-4941	498	5	computer	computer	NOUN
ejpam-4941	498	6	engineering	engineering	NOUN
ejpam-4941	498	7	,	,	PUNCT
ejpam-4941	498	8	2012	2012	NUM
ejpam-4941	498	9	,	,	PUNCT
ejpam-4941	498	10	p.1	p.1	NOUN
ejpam-4941	498	11	-	-	PUNCT
ejpam-4941	498	12	7	7	NUM
ejpam-4941	498	13	,	,	PUNCT
ejpam-4941	498	14	2012	2012	NUM
ejpam-4941	498	15	.	.	PUNCT
ejpam-4941	499	1	[	[	X
ejpam-4941	499	2	12	12	NUM
ejpam-4941	499	3	]	]	X
ejpam-4941	499	4	d.	d.	NOUN
ejpam-4941	499	5	chunxiao	chunxiao	PROPN
ejpam-4941	499	6	and	and	CCONJ
ejpam-4941	499	7	y.	y.	PROPN
ejpam-4941	499	8	fei	fei	PROPN
ejpam-4941	499	9	.	.	PUNCT
ejpam-4941	500	1	performance	performance	NOUN
ejpam-4941	500	2	simulation	simulation	NOUN
ejpam-4941	500	3	on	on	ADP
ejpam-4941	500	4	low	low	ADJ
ejpam-4941	500	5	-	-	PUNCT
ejpam-4941	500	6	complexity	complexity	NOUN
ejpam-4941	500	7	lll	lll	NOUN
ejpam-4941	500	8	-	-	PUNCT
ejpam-4941	500	9	based	base	VERB
ejpam-4941	500	10	algorithm	algorithm	NOUN
ejpam-4941	500	11	for	for	ADP
ejpam-4941	500	12	mimo	mimo	PROPN
ejpam-4941	500	13	system	system	PROPN
ejpam-4941	500	14	.	.	PUNCT
ejpam-4941	501	1	telecommunications	telecommunication	NOUN
ejpam-4941	501	2	and	and	CCONJ
ejpam-4941	501	3	radio	radio	NOUN
ejpam-4941	501	4	engineering	engineering	NOUN
ejpam-4941	501	5	,	,	PUNCT
ejpam-4941	501	6	77(14	77(14	NOUN
ejpam-4941	501	7	)	)	PUNCT
ejpam-4941	501	8	,	,	PUNCT
ejpam-4941	501	9	p.12491264	p.12491264	NOUN
ejpam-4941	501	10	,	,	PUNCT
ejpam-4941	501	11	2018	2018	NUM
ejpam-4941	501	12	.	.	PUNCT
ejpam-4941	502	1	[	[	X
ejpam-4941	502	2	13	13	NUM
ejpam-4941	502	3	]	]	PUNCT
ejpam-4941	502	4	h.	h.	PROPN
ejpam-4941	502	5	diany	diany	PROPN
ejpam-4941	502	6	and	and	CCONJ
ejpam-4941	502	7	s.	s.	PROPN
ejpam-4941	502	8	abdelalim	abdelalim	PROPN
ejpam-4941	502	9	.	.	PUNCT
ejpam-4941	503	1	characterization	characterization	NOUN
ejpam-4941	503	2	of	of	ADP
ejpam-4941	503	3	the	the	DET
ejpam-4941	503	4	solution	solution	NOUN
ejpam-4941	503	5	of	of	ADP
ejpam-4941	503	6	the	the	DET
ejpam-4941	503	7	diophantine	diophantine	NOUN
ejpam-4941	503	8	equation	equation	NOUN
ejpam-4941	503	9	x2	x2	NOUN
ejpam-4941	504	1	+	+	CCONJ
ejpam-4941	504	2	y2	y2	NOUN
ejpam-4941	504	3	=	=	SYM
ejpam-4941	504	4	2z2	2z2	NUM
ejpam-4941	504	5	.	.	PUNCT
ejpam-4941	505	1	gulf	gulf	PROPN
ejpam-4941	505	2	journal	journal	PROPN
ejpam-4941	505	3	of	of	ADP
ejpam-4941	505	4	mathematics	mathematic	NOUN
ejpam-4941	505	5	,	,	PUNCT
ejpam-4941	505	6	3(2	3(2	NUM
ejpam-4941	505	7	)	)	PUNCT
ejpam-4941	505	8	.	.	PUNCT
ejpam-4941	506	1	p.1	p.1	NOUN
ejpam-4941	506	2	-	-	PUNCT
ejpam-4941	506	3	4	4	NUM
ejpam-4941	506	4	,	,	PUNCT
ejpam-4941	506	5	2015	2015	NUM
ejpam-4941	506	6	.	.	PUNCT
ejpam-4941	507	1	[	[	X
ejpam-4941	507	2	14	14	NUM
ejpam-4941	507	3	]	]	PUNCT
ejpam-4941	507	4	m.	m.	NOUN
ejpam-4941	507	5	haslbeck	haslbeck	PROPN
ejpam-4941	507	6	a.	a.	PROPN
ejpam-4941	507	7	yamada	yamada	PROPN
ejpam-4941	507	8	s.	s.	PROPN
ejpam-4941	507	9	joosten	joosten	VERB
ejpam-4941	507	10	r.	r.	PROPN
ejpam-4941	507	11	thiemann	thiemann	PROPN
ejpam-4941	507	12	j.	j.	PROPN
ejpam-4941	507	13	divasón	divasón	PROPN
ejpam-4941	507	14	and	and	CCONJ
ejpam-4941	507	15	r.	r.	PROPN
ejpam-4941	507	16	bottesch	bottesch	PROPN
ejpam-4941	507	17	.	.	PUNCT
ejpam-4941	508	1	a	a	DET
ejpam-4941	508	2	verified	verify	VERB
ejpam-4941	508	3	lll	lll	NOUN
ejpam-4941	508	4	algorithm	algorithm	NOUN
ejpam-4941	508	5	.	.	PUNCT
ejpam-4941	509	1	archive	archive	NOUN
ejpam-4941	509	2	of	of	ADP
ejpam-4941	509	3	formal	formal	ADJ
ejpam-4941	509	4	proofs	proof	NOUN
ejpam-4941	509	5	,	,	PUNCT
ejpam-4941	509	6	p.1	p.1	NOUN
ejpam-4941	509	7	-	-	PUNCT
ejpam-4941	509	8	251	251	NUM
ejpam-4941	509	9	,	,	PUNCT
ejpam-4941	509	10	2018	2018	NUM
ejpam-4941	509	11	.	.	PUNCT
ejpam-4941	510	1	[	[	X
ejpam-4941	510	2	15	15	X
ejpam-4941	510	3	]	]	PUNCT
ejpam-4941	510	4	t.	t.	PROPN
ejpam-4941	510	5	fujino	fujino	PROPN
ejpam-4941	510	6	.	.	PUNCT
ejpam-4941	511	1	gram	gram	NOUN
ejpam-4941	511	2	-	-	PUNCT
ejpam-4941	511	3	schmidt	schmidt	NOUN
ejpam-4941	511	4	combined	combine	VERB
ejpam-4941	511	5	lll	lll	PROPN
ejpam-4941	511	6	lattice	lattice	NOUN
ejpam-4941	511	7	-	-	PUNCT
ejpam-4941	511	8	reduction	reduction	NOUN
ejpam-4941	511	9	aided	aid	VERB
ejpam-4941	511	10	detection	detection	NOUN
ejpam-4941	511	11	in	in	ADP
ejpam-4941	511	12	mimo	mimo	PROPN
ejpam-4941	511	13	systems	systems	PROPN
ejpam-4941	511	14	.	.	PUNCT
ejpam-4941	512	1	rev	rev	PROPN
ejpam-4941	512	2	journal	journal	PROPN
ejpam-4941	512	3	on	on	ADP
ejpam-4941	512	4	electronics	electronic	NOUN
ejpam-4941	512	5	and	and	CCONJ
ejpam-4941	512	6	communications	communication	NOUN
ejpam-4941	512	7	,	,	PUNCT
ejpam-4941	512	8	1(2	1(2	NUM
ejpam-4941	512	9	)	)	PUNCT
ejpam-4941	512	10	,	,	PUNCT
ejpam-4941	512	11	p.106	p.106	NOUN
ejpam-4941	512	12	-	-	PUNCT
ejpam-4941	512	13	114	114	NUM
ejpam-4941	512	14	,	,	PUNCT
ejpam-4941	512	15	2011	2011	NUM
ejpam-4941	512	16	.	.	PUNCT
ejpam-4941	513	1	[	[	X
ejpam-4941	513	2	16	16	X
ejpam-4941	513	3	]	]	PUNCT
ejpam-4941	513	4	v.	v.	ADP
ejpam-4941	513	5	m.	m.	NOUN
ejpam-4941	513	6	goldschmidt	goldschmidt	PROPN
ejpam-4941	513	7	.	.	PUNCT
ejpam-4941	514	1	crystal	crystal	NOUN
ejpam-4941	514	2	structure	structure	NOUN
ejpam-4941	514	3	and	and	CCONJ
ejpam-4941	514	4	chemical	chemical	NOUN
ejpam-4941	514	5	constitution	constitution	NOUN
ejpam-4941	514	6	.	.	PUNCT
ejpam-4941	515	1	transactions	transaction	NOUN
ejpam-4941	515	2	of	of	ADP
ejpam-4941	515	3	the	the	DET
ejpam-4941	515	4	faraday	faraday	PROPN
ejpam-4941	515	5	society	society	PROPN
ejpam-4941	515	6	,	,	PUNCT
ejpam-4941	515	7	25	25	NUM
ejpam-4941	515	8	,	,	PUNCT
ejpam-4941	515	9	p.253	p.253	NUM
ejpam-4941	515	10	-	-	SYM
ejpam-4941	515	11	283	283	NUM
ejpam-4941	515	12	,	,	PUNCT
ejpam-4941	515	13	1929	1929	NUM
ejpam-4941	515	14	.	.	PUNCT
ejpam-4941	516	1	[	[	X
ejpam-4941	516	2	17	17	NUM
ejpam-4941	516	3	]	]	PUNCT
ejpam-4941	516	4	t.	t.	PROPN
ejpam-4941	516	5	bogart	bogart	PROPN
ejpam-4941	516	6	j.	j.	PROPN
ejpam-4941	516	7	goodrick	goodrick	PROPN
ejpam-4941	516	8	and	and	CCONJ
ejpam-4941	516	9	k.	k.	PROPN
ejpam-4941	516	10	woods	woods	PROPN
ejpam-4941	516	11	.	.	PUNCT
ejpam-4941	517	1	a	a	DET
ejpam-4941	517	2	parametric	parametric	ADJ
ejpam-4941	517	3	version	version	NOUN
ejpam-4941	517	4	of	of	ADP
ejpam-4941	517	5	lll	lll	NOUN
ejpam-4941	517	6	and	and	CCONJ
ejpam-4941	517	7	some	some	DET
ejpam-4941	517	8	consequences	consequence	NOUN
ejpam-4941	517	9	:	:	PUNCT
ejpam-4941	517	10	parametric	parametric	ADJ
ejpam-4941	517	11	shortest	short	ADJ
ejpam-4941	517	12	and	and	CCONJ
ejpam-4941	517	13	closest	close	ADJ
ejpam-4941	517	14	vector	vector	NOUN
ejpam-4941	517	15	problems	problem	NOUN
ejpam-4941	517	16	.	.	PUNCT
ejpam-4941	518	1	siam	siam	PROPN
ejpam-4941	518	2	journal	journal	PROPN
ejpam-4941	518	3	on	on	ADP
ejpam-4941	518	4	discrete	discrete	ADJ
ejpam-4941	518	5	mathematics	mathematic	NOUN
ejpam-4941	518	6	,	,	PUNCT
ejpam-4941	518	7	34(4	34(4	NUM
ejpam-4941	518	8	)	)	PUNCT
ejpam-4941	518	9	,	,	PUNCT
ejpam-4941	518	10	p.2363	p.2363	NOUN
ejpam-4941	518	11	-	-	PUNCT
ejpam-4941	518	12	2387	2387	NUM
ejpam-4941	518	13	,	,	PUNCT
ejpam-4941	518	14	2020	2020	NUM
ejpam-4941	518	15	.	.	PUNCT
ejpam-4941	519	1	[	[	X
ejpam-4941	519	2	18	18	NUM
ejpam-4941	519	3	]	]	X
ejpam-4941	519	4	d.	d.	PROPN
ejpam-4941	519	5	g.	g.	PROPN
ejpam-4941	519	6	papachristoudis	papachristoudis	PROPN
ejpam-4941	519	7	s.	s.	PROPN
ejpam-4941	519	8	t.	t.	PROPN
ejpam-4941	519	9	halkidis	halkidis	PROPN
ejpam-4941	519	10	and	and	CCONJ
ejpam-4941	519	11	g.	g.	PROPN
ejpam-4941	519	12	stephanides	stephanides	PROPN
ejpam-4941	519	13	.	.	PUNCT
ejpam-4941	520	1	an	an	DET
ejpam-4941	520	2	experimental	experimental	ADJ
ejpam-4941	520	3	comparison	comparison	NOUN
ejpam-4941	520	4	of	of	ADP
ejpam-4941	520	5	some	some	DET
ejpam-4941	520	6	lll	lll	ADJ
ejpam-4941	520	7	-	-	PUNCT
ejpam-4941	520	8	type	type	NOUN
ejpam-4941	520	9	lattice	lattice	NOUN
ejpam-4941	520	10	basis	basis	NOUN
ejpam-4941	520	11	reduction	reduction	NOUN
ejpam-4941	520	12	algorithms	algorithm	NOUN
ejpam-4941	520	13	.	.	PUNCT
ejpam-4941	521	1	international	international	ADJ
ejpam-4941	521	2	journal	journal	PROPN
ejpam-4941	521	3	of	of	ADP
ejpam-4941	521	4	applied	applied	ADJ
ejpam-4941	521	5	and	and	CCONJ
ejpam-4941	521	6	computational	computational	ADJ
ejpam-4941	521	7	mathematics	mathematic	NOUN
ejpam-4941	521	8	,	,	PUNCT
ejpam-4941	521	9	1(3	1(3	NUM
ejpam-4941	521	10	)	)	PUNCT
ejpam-4941	521	11	,	,	PUNCT
ejpam-4941	521	12	p.327	p.327	NOUN
ejpam-4941	521	13	-	-	PUNCT
ejpam-4941	521	14	342	342	NUM
ejpam-4941	521	15	,	,	PUNCT
ejpam-4941	521	16	2015	2015	NUM
ejpam-4941	521	17	.	.	PUNCT
ejpam-4941	522	1	[	[	X
ejpam-4941	522	2	19	19	NUM
ejpam-4941	522	3	]	]	X
ejpam-4941	522	4	g.	g.	PROPN
ejpam-4941	522	5	hanrot	hanrot	PROPN
ejpam-4941	522	6	.	.	PUNCT
ejpam-4941	523	1	lll	lll	PROPN
ejpam-4941	523	2	:	:	PUNCT
ejpam-4941	523	3	a	a	DET
ejpam-4941	523	4	tool	tool	NOUN
ejpam-4941	523	5	for	for	ADP
ejpam-4941	523	6	effective	effective	ADJ
ejpam-4941	523	7	diophantine	diophantine	NOUN
ejpam-4941	523	8	approximation	approximation	NOUN
ejpam-4941	523	9	.	.	PUNCT
ejpam-4941	524	1	in	in	ADP
ejpam-4941	524	2	the	the	DET
ejpam-4941	524	3	lll	lll	PROPN
ejpam-4941	524	4	algorithm	algorithm	NOUN
ejpam-4941	524	5	:	:	PUNCT
ejpam-4941	524	6	survey	survey	NOUN
ejpam-4941	524	7	and	and	CCONJ
ejpam-4941	524	8	applications	application	NOUN
ejpam-4941	524	9	.	.	PUNCT
ejpam-4941	525	1	p.215	p.215	PROPN
ejpam-4941	525	2	-	-	PUNCT
ejpam-4941	525	3	263	263	NUM
ejpam-4941	525	4	,	,	PUNCT
ejpam-4941	525	5	berlin	berlin	PROPN
ejpam-4941	525	6	,	,	PUNCT
ejpam-4941	525	7	heidelberg	heidelberg	PROPN
ejpam-4941	525	8	:	:	PUNCT
ejpam-4941	525	9	springer	springer	PROPN
ejpam-4941	525	10	berlin	berlin	PROPN
ejpam-4941	525	11	heidelberg	heidelberg	PROPN
ejpam-4941	525	12	,	,	PUNCT
ejpam-4941	525	13	2009	2009	NUM
ejpam-4941	525	14	.	.	PUNCT
ejpam-4941	526	1	[	[	X
ejpam-4941	526	2	20	20	NUM
ejpam-4941	526	3	]	]	PUNCT
ejpam-4941	526	4	w.	w.	PROPN
ejpam-4941	526	5	a.	a.	PROPN
ejpam-4941	526	6	harrison	harrison	PROPN
ejpam-4941	526	7	.	.	PUNCT
ejpam-4941	527	1	solid	solid	ADJ
ejpam-4941	527	2	state	state	NOUN
ejpam-4941	527	3	theory	theory	NOUN
ejpam-4941	527	4	.	.	PUNCT
ejpam-4941	528	1	courier	courier	NOUN
ejpam-4941	528	2	corporation	corporation	NOUN
ejpam-4941	528	3	.	.	PUNCT
ejpam-4941	529	1	isbn	isbn	ADJ
ejpam-4941	529	2	:	:	PUNCT
ejpam-4941	529	3	0486639487	0486639487	NUM
ejpam-4941	529	4	,	,	PUNCT
ejpam-4941	529	5	9780486639482	9780486639482	NUM
ejpam-4941	529	6	.	.	PUNCT
ejpam-4941	530	1	p.554	p.554	PROPN
ejpam-4941	530	2	,	,	PUNCT
ejpam-4941	530	3	1980	1980	NUM
ejpam-4941	530	4	.	.	PUNCT
ejpam-4941	531	1	[	[	X
ejpam-4941	531	2	21	21	NUM
ejpam-4941	531	3	]	]	PUNCT
ejpam-4941	531	4	m.	m.	NOUN
ejpam-4941	531	5	van	van	PROPN
ejpam-4941	531	6	hoeij	hoeij	PROPN
ejpam-4941	531	7	.	.	PUNCT
ejpam-4941	532	1	factoring	factoring	NOUN
ejpam-4941	532	2	polynomials	polynomial	NOUN
ejpam-4941	532	3	and	and	CCONJ
ejpam-4941	532	4	the	the	DET
ejpam-4941	532	5	knapsack	knapsack	NOUN
ejpam-4941	532	6	problem	problem	NOUN
ejpam-4941	532	7	.	.	PUNCT
ejpam-4941	533	1	journal	journal	NOUN
ejpam-4941	533	2	of	of	ADP
ejpam-4941	533	3	number	number	NOUN
ejpam-4941	533	4	theory	theory	NOUN
ejpam-4941	533	5	,	,	PUNCT
ejpam-4941	533	6	95(2	95(2	NOUN
ejpam-4941	533	7	)	)	PUNCT
ejpam-4941	533	8	,	,	PUNCT
ejpam-4941	533	9	p.167	p.167	NOUN
ejpam-4941	533	10	-	-	SYM
ejpam-4941	533	11	189	189	NUM
ejpam-4941	533	12	,	,	PUNCT
ejpam-4941	533	13	2002	2002	NUM
ejpam-4941	533	14	.	.	PUNCT
ejpam-4941	534	1	[	[	X
ejpam-4941	534	2	22	22	NUM
ejpam-4941	534	3	]	]	X
ejpam-4941	534	4	f.	f.	PROPN
ejpam-4941	534	5	hoffmann	hoffmann	PROPN
ejpam-4941	534	6	.	.	PUNCT
ejpam-4941	535	1	introduction	introduction	NOUN
ejpam-4941	535	2	to	to	ADP
ejpam-4941	535	3	crystallography	crystallography	NOUN
ejpam-4941	535	4	.	.	PUNCT
ejpam-4941	536	1	springer	springer	NOUN
ejpam-4941	536	2	nature	nature	PROPN
ejpam-4941	536	3	.	.	PUNCT
ejpam-4941	537	1	isbn	isbn	ADJ
ejpam-4941	537	2	:	:	PUNCT
ejpam-4941	537	3	978	978	NUM
ejpam-4941	537	4	-	-	SYM
ejpam-4941	537	5	3	3	NUM
ejpam-4941	537	6	-	-	PUNCT
ejpam-4941	537	7	03035110	03035110	NUM
ejpam-4941	537	8	-	-	PUNCT
ejpam-4941	537	9	6	6	NUM
ejpam-4941	537	10	.	.	PUNCT
ejpam-4941	538	1	p.309	p.309	PROPN
ejpam-4941	538	2	,	,	PUNCT
ejpam-4941	538	3	2020	2020	NUM
ejpam-4941	538	4	.	.	PUNCT
ejpam-4941	539	1	references	reference	NOUN
ejpam-4941	539	2	2690	2690	NUM
ejpam-4941	540	1	[	[	X
ejpam-4941	540	2	23	23	NUM
ejpam-4941	540	3	]	]	X
ejpam-4941	540	4	n.	n.	PROPN
ejpam-4941	540	5	a.	a.	PROPN
ejpam-4941	540	6	howgrave	howgrave	PROPN
ejpam-4941	540	7	-	-	PUNCT
ejpam-4941	540	8	graham	graham	PROPN
ejpam-4941	540	9	and	and	CCONJ
ejpam-4941	540	10	n.	n.	PROPN
ejpam-4941	540	11	p.	p.	PROPN
ejpam-4941	540	12	smart	smart	ADJ
ejpam-4941	540	13	.	.	PUNCT
ejpam-4941	541	1	lattice	lattice	NOUN
ejpam-4941	541	2	attacks	attack	NOUN
ejpam-4941	541	3	on	on	ADP
ejpam-4941	541	4	digital	digital	ADJ
ejpam-4941	541	5	signature	signature	NOUN
ejpam-4941	541	6	schemes	scheme	NOUN
ejpam-4941	541	7	.	.	PUNCT
ejpam-4941	542	1	designs	design	NOUN
ejpam-4941	542	2	,	,	PUNCT
ejpam-4941	542	3	codes	code	NOUN
ejpam-4941	542	4	and	and	CCONJ
ejpam-4941	542	5	cryptography	cryptography	NOUN
ejpam-4941	542	6	,	,	PUNCT
ejpam-4941	542	7	23	23	NUM
ejpam-4941	542	8	,	,	PUNCT
ejpam-4941	542	9	p.283	p.283	NOUN
ejpam-4941	542	10	-	-	PUNCT
ejpam-4941	542	11	290	290	NUM
ejpam-4941	542	12	,	,	PUNCT
ejpam-4941	542	13	2001	2001	NUM
ejpam-4941	542	14	.	.	PUNCT
ejpam-4941	543	1	[	[	X
ejpam-4941	543	2	24	24	NUM
ejpam-4941	543	3	]	]	PUNCT
ejpam-4941	543	4	l.	l.	PROPN
ejpam-4941	543	5	huazhang	huazhang	PROPN
ejpam-4941	543	6	and	and	CCONJ
ejpam-4941	543	7	l.	l.	PROPN
ejpam-4941	543	8	jianping	jianping	PROPN
ejpam-4941	543	9	.	.	PUNCT
ejpam-4941	544	1	a	a	DET
ejpam-4941	544	2	novel	novel	ADJ
ejpam-4941	544	3	independent	independent	ADJ
ejpam-4941	544	4	processing	processing	NOUN
ejpam-4941	544	5	lll	lll	NOUN
ejpam-4941	544	6	algorithm	algorithm	NOUN
ejpam-4941	544	7	for	for	ADP
ejpam-4941	544	8	mimo	mimo	PROPN
ejpam-4941	544	9	detection	detection	PROPN
ejpam-4941	544	10	.	.	PUNCT
ejpam-4941	545	1	telecommunications	telecommunication	NOUN
ejpam-4941	545	2	and	and	CCONJ
ejpam-4941	545	3	radio	radio	NOUN
ejpam-4941	545	4	engineering	engineering	NOUN
ejpam-4941	545	5	,	,	PUNCT
ejpam-4941	545	6	75(7	75(7	NUM
ejpam-4941	545	7	)	)	PUNCT
ejpam-4941	545	8	,	,	PUNCT
ejpam-4941	545	9	p.607	p.607	NOUN
ejpam-4941	545	10	-	-	PUNCT
ejpam-4941	545	11	620	620	NUM
ejpam-4941	545	12	,	,	PUNCT
ejpam-4941	545	13	2016	2016	NUM
ejpam-4941	545	14	.	.	PUNCT
ejpam-4941	546	1	[	[	X
ejpam-4941	546	2	25	25	NUM
ejpam-4941	546	3	]	]	PUNCT
ejpam-4941	546	4	m.	m.	NOUN
ejpam-4941	546	5	l.	l.	PROPN
ejpam-4941	546	6	huggins	huggins	PROPN
ejpam-4941	546	7	.	.	PUNCT
ejpam-4941	547	1	principles	principle	NOUN
ejpam-4941	547	2	determining	determine	VERB
ejpam-4941	547	3	the	the	DET
ejpam-4941	547	4	arrangement	arrangement	NOUN
ejpam-4941	547	5	of	of	ADP
ejpam-4941	547	6	atoms	atom	NOUN
ejpam-4941	547	7	and	and	CCONJ
ejpam-4941	547	8	ions	ion	NOUN
ejpam-4941	547	9	in	in	ADP
ejpam-4941	547	10	crystals	crystal	NOUN
ejpam-4941	547	11	.	.	PUNCT
ejpam-4941	548	1	the	the	DET
ejpam-4941	548	2	journal	journal	NOUN
ejpam-4941	548	3	of	of	ADP
ejpam-4941	548	4	physical	physical	ADJ
ejpam-4941	548	5	chemistry	chemistry	NOUN
ejpam-4941	548	6	,	,	PUNCT
ejpam-4941	548	7	35(5	35(5	NUM
ejpam-4941	548	8	)	)	PUNCT
ejpam-4941	548	9	,	,	PUNCT
ejpam-4941	548	10	p.1270	p.1270	PROPN
ejpam-4941	548	11	-	-	SYM
ejpam-4941	548	12	1280	1280	NUM
ejpam-4941	548	13	,	,	PUNCT
ejpam-4941	548	14	2002	2002	NUM
ejpam-4941	548	15	.	.	PUNCT
ejpam-4941	549	1	[	[	X
ejpam-4941	549	2	26	26	NUM
ejpam-4941	549	3	]	]	PUNCT
ejpam-4941	549	4	a.	a.	NOUN
ejpam-4941	549	5	joux	joux	PROPN
ejpam-4941	549	6	and	and	CCONJ
ejpam-4941	549	7	j.	j.	PROPN
ejpam-4941	549	8	stern	stern	PROPN
ejpam-4941	549	9	.	.	PUNCT
ejpam-4941	550	1	lattice	lattice	PROPN
ejpam-4941	550	2	reduction	reduction	NOUN
ejpam-4941	550	3	:	:	PUNCT
ejpam-4941	550	4	a	a	DET
ejpam-4941	550	5	toolbox	toolbox	NOUN
ejpam-4941	550	6	for	for	ADP
ejpam-4941	550	7	the	the	DET
ejpam-4941	550	8	cryptanalyst	cryptanalyst	NOUN
ejpam-4941	550	9	.	.	PUNCT
ejpam-4941	551	1	journal	journal	PROPN
ejpam-4941	551	2	of	of	ADP
ejpam-4941	551	3	cryptology	cryptology	NOUN
ejpam-4941	551	4	,	,	PUNCT
ejpam-4941	551	5	11	11	NUM
ejpam-4941	551	6	,	,	PUNCT
ejpam-4941	551	7	p.161	p.161	NOUN
ejpam-4941	551	8	-	-	SYM
ejpam-4941	551	9	185	185	NUM
ejpam-4941	551	10	.	.	PUNCT
ejpam-4941	551	11	,	,	PUNCT
ejpam-4941	551	12	1998	1998	NUM
ejpam-4941	551	13	.	.	PUNCT
ejpam-4941	552	1	[	[	X
ejpam-4941	552	2	27	27	NUM
ejpam-4941	552	3	]	]	PUNCT
ejpam-4941	552	4	a.	a.	PROPN
ejpam-4941	552	5	d.	d.	PROPN
ejpam-4941	552	6	mighell	mighell	PROPN
ejpam-4941	552	7	v.	v.	ADP
ejpam-4941	552	8	l.	l.	PROPN
ejpam-4941	552	9	karen	karen	PROPN
ejpam-4941	552	10	and	and	CCONJ
ejpam-4941	552	11	r.	r.	PROPN
ejpam-4941	552	12	munro	munro	PROPN
ejpam-4941	552	13	.	.	PUNCT
ejpam-4941	553	1	determination	determination	NOUN
ejpam-4941	553	2	of	of	ADP
ejpam-4941	553	3	reduced	reduce	VERB
ejpam-4941	553	4	cells	cell	NOUN
ejpam-4941	553	5	in	in	ADP
ejpam-4941	553	6	crystallography	crystallography	NOUN
ejpam-4941	553	7	.	.	PUNCT
ejpam-4941	554	1	a	a	DET
ejpam-4941	554	2	century	century	NOUN
ejpam-4941	554	3	of	of	ADP
ejpam-4941	554	4	excellence	excellence	NOUN
ejpam-4941	554	5	in	in	ADP
ejpam-4941	554	6	measurements	measurement	NOUN
ejpam-4941	554	7	,	,	PUNCT
ejpam-4941	554	8	standards	standard	NOUN
ejpam-4941	554	9	,	,	PUNCT
ejpam-4941	554	10	and	and	CCONJ
ejpam-4941	554	11	technology	technology	NOUN
ejpam-4941	554	12	.	.	PUNCT
ejpam-4941	555	1	a	a	DET
ejpam-4941	555	2	chronicle	chronicle	NOUN
ejpam-4941	555	3	of	of	ADP
ejpam-4941	555	4	selected	select	VERB
ejpam-4941	555	5	nbs	nbs	PROPN
ejpam-4941	555	6	/	/	SYM
ejpam-4941	555	7	nist	nist	PROPN
ejpam-4941	555	8	publications	publication	NOUN
ejpam-4941	555	9	1901	1901	NUM
ejpam-4941	555	10	-	-	SYM
ejpam-4941	555	11	2000	2000	NUM
ejpam-4941	555	12	nist	nist	NOUN
ejpam-4941	555	13	special	special	ADJ
ejpam-4941	555	14	publication	publication	NOUN
ejpam-4941	555	15	958	958	NUM
ejpam-4941	555	16	.	.	PUNCT
ejpam-4941	556	1	p.	p.	NOUN
ejpam-4941	556	2	188	188	NUM
ejpam-4941	556	3	-	-	SYM
ejpam-4941	556	4	190	190	NUM
ejpam-4941	556	5	,	,	PUNCT
ejpam-4941	556	6	2001	2001	NUM
ejpam-4941	556	7	.	.	PUNCT
ejpam-4941	557	1	[	[	X
ejpam-4941	557	2	28	28	NUM
ejpam-4941	557	3	]	]	X
ejpam-4941	557	4	s.	s.	PROPN
ejpam-4941	557	5	f.	f.	PROPN
ejpam-4941	557	6	kettle	kettle	PROPN
ejpam-4941	557	7	and	and	CCONJ
ejpam-4941	557	8	l.	l.	PROPN
ejpam-4941	557	9	j.	j.	PROPN
ejpam-4941	557	10	norrby	norrby	PROPN
ejpam-4941	557	11	.	.	PUNCT
ejpam-4941	558	1	really	really	ADV
ejpam-4941	558	2	,	,	PUNCT
ejpam-4941	558	3	your	your	PRON
ejpam-4941	558	4	lattices	lattice	NOUN
ejpam-4941	558	5	are	be	AUX
ejpam-4941	558	6	all	all	ADV
ejpam-4941	558	7	primitive	primitive	ADJ
ejpam-4941	558	8	,	,	PUNCT
ejpam-4941	558	9	mr	mr	PROPN
ejpam-4941	558	10	.	.	PROPN
ejpam-4941	558	11	bravais	bravais	PROPN
ejpam-4941	558	12	!	!	PROPN
ejpam-4941	559	1	journal	journal	PROPN
ejpam-4941	559	2	of	of	ADP
ejpam-4941	559	3	chemical	chemical	PROPN
ejpam-4941	559	4	education	education	NOUN
ejpam-4941	559	5	,	,	PUNCT
ejpam-4941	559	6	70(12	70(12	NUM
ejpam-4941	559	7	)	)	PUNCT
ejpam-4941	559	8	,	,	PUNCT
ejpam-4941	559	9	p.959	p.959	NOUN
ejpam-4941	559	10	,	,	PUNCT
ejpam-4941	559	11	1993	1993	NUM
ejpam-4941	559	12	.	.	PUNCT
ejpam-4941	560	1	[	[	X
ejpam-4941	560	2	29	29	NUM
ejpam-4941	560	3	]	]	X
ejpam-4941	560	4	c.	c.	PROPN
ejpam-4941	560	5	kittel	kittel	PROPN
ejpam-4941	560	6	.	.	PUNCT
ejpam-4941	561	1	introduction	introduction	NOUN
ejpam-4941	561	2	to	to	ADP
ejpam-4941	561	3	solid	solid	ADJ
ejpam-4941	561	4	state	state	NOUN
ejpam-4941	561	5	physics	physic	NOUN
ejpam-4941	561	6	.	.	PUNCT
ejpam-4941	562	1	american	american	PROPN
ejpam-4941	562	2	journal	journal	PROPN
ejpam-4941	562	3	of	of	ADP
ejpam-4941	562	4	physics	physics	PROPN
ejpam-4941	562	5	,	,	PUNCT
ejpam-4941	562	6	21(8	21(8	NUM
ejpam-4941	562	7	)	)	PUNCT
ejpam-4941	562	8	.	.	PUNCT
ejpam-4941	563	1	p.650	p.650	NOUN
ejpam-4941	563	2	,	,	PUNCT
ejpam-4941	563	3	1953	1953	NUM
ejpam-4941	563	4	.	.	PUNCT
ejpam-4941	564	1	[	[	X
ejpam-4941	564	2	30	30	NUM
ejpam-4941	564	3	]	]	PUNCT
ejpam-4941	564	4	j.	j.	PROPN
ejpam-4941	564	5	w.	w.	PROPN
ejpam-4941	564	6	lauher	lauher	PROPN
ejpam-4941	564	7	.	.	PUNCT
ejpam-4941	565	1	symmetry	symmetry	NOUN
ejpam-4941	565	2	and	and	CCONJ
ejpam-4941	565	3	crystal	crystal	NOUN
ejpam-4941	565	4	design	design	NOUN
ejpam-4941	565	5	.	.	PUNCT
ejpam-4941	566	1	proceedings	proceeding	NOUN
ejpam-4941	566	2	from	from	ADP
ejpam-4941	566	3	the	the	DET
ejpam-4941	566	4	symposium	symposium	NOUN
ejpam-4941	566	5	;	;	PUNCT
ejpam-4941	566	6	crystals	crystal	NOUN
ejpam-4941	566	7	in	in	ADP
ejpam-4941	566	8	supramolecular	supramolecular	ADJ
ejpam-4941	566	9	chemistry	chemistry	NOUN
ejpam-4941	566	10	.	.	PUNCT
ejpam-4941	567	1	aca	aca	PROPN
ejpam-4941	567	2	transactions	transaction	NOUN
ejpam-4941	567	3	.	.	PUNCT
ejpam-4941	568	1	volume	volume	NOUN
ejpam-4941	568	2	39	39	NUM
ejpam-4941	568	3	.	.	PUNCT
ejpam-4941	569	1	4031	4031	NUM
ejpam-4941	569	2	.	.	PUNCT
ejpam-4941	570	1	p.35	p.35	X
ejpam-4941	570	2	,	,	PUNCT
ejpam-4941	570	3	2004	2004	NUM
ejpam-4941	570	4	.	.	PUNCT
ejpam-4941	571	1	[	[	X
ejpam-4941	571	2	31	31	NUM
ejpam-4941	571	3	]	]	PUNCT
ejpam-4941	571	4	a.	a.	PROPN
ejpam-4941	571	5	k.	k.	PROPN
ejpam-4941	571	6	lenstra	lenstra	PROPN
ejpam-4941	571	7	h.	h.	PROPN
ejpam-4941	571	8	w.	w.	PROPN
ejpam-4941	571	9	lenstra	lenstra	PROPN
ejpam-4941	571	10	and	and	CCONJ
ejpam-4941	571	11	l.	l.	PROPN
ejpam-4941	571	12	lovász	lovász	PROPN
ejpam-4941	571	13	.	.	PUNCT
ejpam-4941	572	1	factoring	factoring	NOUN
ejpam-4941	572	2	polynomials	polynomial	NOUN
ejpam-4941	572	3	with	with	ADP
ejpam-4941	572	4	rational	rational	ADJ
ejpam-4941	572	5	coefficients	coefficient	NOUN
ejpam-4941	572	6	.	.	PUNCT
ejpam-4941	573	1	math	math	PROPN
ejpam-4941	573	2	ann	ann	PROPN
ejpam-4941	573	3	261	261	NUM
ejpam-4941	573	4	,	,	PUNCT
ejpam-4941	573	5	p.515–534	p.515–534	NOUN
ejpam-4941	573	6	,	,	PUNCT
ejpam-4941	573	7	1982	1982	NUM
ejpam-4941	573	8	.	.	PUNCT
ejpam-4941	574	1	[	[	X
ejpam-4941	574	2	32	32	NUM
ejpam-4941	574	3	]	]	PUNCT
ejpam-4941	574	4	g.	g.	PROPN
ejpam-4941	574	5	h.	h.	PROPN
ejpam-4941	574	6	cho	cho	PROPN
ejpam-4941	574	7	h.	h.	PROPN
ejpam-4941	574	8	s.	s.	PROPN
ejpam-4941	574	9	lee	lee	PROPN
ejpam-4941	574	10	s.	s.	PROPN
ejpam-4941	574	11	lim	lim	PROPN
ejpam-4941	574	12	and	and	CCONJ
ejpam-4941	574	13	y.	y.	PROPN
ejpam-4941	574	14	kim	kim	PROPN
ejpam-4941	574	15	.	.	PUNCT
ejpam-4941	575	1	storage	storage	NOUN
ejpam-4941	575	2	efficient	efficient	ADJ
ejpam-4941	575	3	algorithm	algorithm	NOUN
ejpam-4941	575	4	for	for	ADP
ejpam-4941	575	5	hermite	hermite	ADJ
ejpam-4941	575	6	normal	normal	ADJ
ejpam-4941	575	7	form	form	NOUN
ejpam-4941	575	8	using	use	VERB
ejpam-4941	575	9	lll	lll	PROPN
ejpam-4941	575	10	.	.	PUNCT
ejpam-4941	576	1	linear	linear	PROPN
ejpam-4941	576	2	algebra	algebra	NOUN
ejpam-4941	576	3	and	and	CCONJ
ejpam-4941	576	4	its	its	PRON
ejpam-4941	576	5	applications	application	NOUN
ejpam-4941	576	6	,	,	PUNCT
ejpam-4941	576	7	613	613	NUM
ejpam-4941	576	8	,	,	PUNCT
ejpam-4941	576	9	p.183	p.183	NOUN
ejpam-4941	576	10	-	-	PUNCT
ejpam-4941	576	11	200	200	NUM
ejpam-4941	576	12	,	,	PUNCT
ejpam-4941	576	13	2021	2021	NUM
ejpam-4941	576	14	.	.	PUNCT
ejpam-4941	577	1	[	[	X
ejpam-4941	577	2	33	33	NUM
ejpam-4941	577	3	]	]	PUNCT
ejpam-4941	577	4	j.	j.	PROPN
ejpam-4941	577	5	bai	bai	PROPN
ejpam-4941	577	6	n.	n.	PROPN
ejpam-4941	577	7	liu	liu	PROPN
ejpam-4941	577	8	and	and	CCONJ
ejpam-4941	577	9	z.	z.	PROPN
ejpam-4941	577	10	li	li	PROPN
ejpam-4941	577	11	.	.	PUNCT
ejpam-4941	578	1	new	new	ADJ
ejpam-4941	578	2	lattice	lattice	PROPN
ejpam-4941	578	3	reduction	reduction	NOUN
ejpam-4941	578	4	algorithm	algorithm	NOUN
ejpam-4941	578	5	based	base	VERB
ejpam-4941	578	6	on	on	ADP
ejpam-4941	578	7	gauss	gauss	NOUN
ejpam-4941	578	8	and	and	CCONJ
ejpam-4941	578	9	lll	lll	NOUN
ejpam-4941	578	10	reduction	reduction	NOUN
ejpam-4941	578	11	.	.	PUNCT
ejpam-4941	579	1	j.	j.	PROPN
ejpam-4941	579	2	comput	comput	PROPN
ejpam-4941	579	3	.	.	PUNCT
ejpam-4941	580	1	eng	eng	PROPN
ejpam-4941	580	2	,	,	PUNCT
ejpam-4941	580	3	39(11	39(11	NUM
ejpam-4941	580	4	)	)	PUNCT
ejpam-4941	580	5	,	,	PUNCT
ejpam-4941	580	6	p.147	p.147	NOUN
ejpam-4941	580	7	-	-	PUNCT
ejpam-4941	580	8	149	149	NUM
ejpam-4941	580	9	,	,	PUNCT
ejpam-4941	580	10	2013	2013	NUM
ejpam-4941	580	11	.	.	PUNCT
ejpam-4941	581	1	[	[	X
ejpam-4941	581	2	34	34	NUM
ejpam-4941	581	3	]	]	PUNCT
ejpam-4941	581	4	a.	a.	NOUN
ejpam-4941	581	5	may	may	AUX
ejpam-4941	581	6	.	.	PUNCT
ejpam-4941	582	1	using	use	VERB
ejpam-4941	582	2	lll	lll	NOUN
ejpam-4941	582	3	-	-	PUNCT
ejpam-4941	582	4	reduction	reduction	NOUN
ejpam-4941	582	5	for	for	ADP
ejpam-4941	582	6	solving	solve	VERB
ejpam-4941	582	7	rsa	rsa	NOUN
ejpam-4941	582	8	and	and	CCONJ
ejpam-4941	582	9	factorization	factorization	NOUN
ejpam-4941	582	10	problems	problem	NOUN
ejpam-4941	582	11	.	.	PUNCT
ejpam-4941	583	1	in	in	ADP
ejpam-4941	583	2	the	the	DET
ejpam-4941	583	3	lll	lll	PROPN
ejpam-4941	583	4	algorithm	algorithm	NOUN
ejpam-4941	583	5	:	:	PUNCT
ejpam-4941	583	6	survey	survey	NOUN
ejpam-4941	583	7	and	and	CCONJ
ejpam-4941	583	8	applications	application	NOUN
ejpam-4941	583	9	.	.	PUNCT
ejpam-4941	584	1	p.315	p.315	ADJ
ejpam-4941	584	2	-	-	NUM
ejpam-4941	584	3	348	348	NUM
ejpam-4941	584	4	,	,	PUNCT
ejpam-4941	584	5	berlin	berlin	PROPN
ejpam-4941	584	6	,	,	PUNCT
ejpam-4941	584	7	heidelberg	heidelberg	PROPN
ejpam-4941	584	8	:	:	PUNCT
ejpam-4941	584	9	springer	springer	PROPN
ejpam-4941	584	10	berlin	berlin	PROPN
ejpam-4941	584	11	heidelberg	heidelberg	PROPN
ejpam-4941	584	12	,	,	PUNCT
ejpam-4941	584	13	2009	2009	NUM
ejpam-4941	584	14	.	.	PUNCT
ejpam-4941	585	1	[	[	X
ejpam-4941	585	2	35	35	NUM
ejpam-4941	585	3	]	]	X
ejpam-4941	585	4	s.	s.	PROPN
ejpam-4941	585	5	mehrotra	mehrotra	PROPN
ejpam-4941	585	6	and	and	CCONJ
ejpam-4941	585	7	z.	z.	PROPN
ejpam-4941	585	8	li	li	PROPN
ejpam-4941	585	9	.	.	PROPN
ejpam-4941	585	10	segment	segment	PROPN
ejpam-4941	585	11	lll	lll	PROPN
ejpam-4941	585	12	reduction	reduction	NOUN
ejpam-4941	585	13	of	of	ADP
ejpam-4941	585	14	lattice	lattice	NOUN
ejpam-4941	585	15	bases	basis	NOUN
ejpam-4941	585	16	using	use	VERB
ejpam-4941	585	17	modular	modular	ADJ
ejpam-4941	585	18	arithmetic	arithmetic	ADJ
ejpam-4941	585	19	.	.	PUNCT
ejpam-4941	586	1	algorithms	algorithm	NOUN
ejpam-4941	586	2	,	,	PUNCT
ejpam-4941	586	3	3(3	3(3	NUM
ejpam-4941	586	4	)	)	PUNCT
ejpam-4941	586	5	,	,	PUNCT
ejpam-4941	586	6	p.224	p.224	NOUN
ejpam-4941	586	7	-	-	SYM
ejpam-4941	586	8	243	243	NUM
ejpam-4941	586	9	,	,	PUNCT
ejpam-4941	586	10	2010	2010	NUM
ejpam-4941	586	11	.	.	PUNCT
ejpam-4941	587	1	[	[	X
ejpam-4941	587	2	36	36	NUM
ejpam-4941	587	3	]	]	X
ejpam-4941	587	4	c.	c.	PROPN
ejpam-4941	587	5	ling	ling	PROPN
ejpam-4941	587	6	w.	w.	PROPN
ejpam-4941	587	7	h.	h.	PROPN
ejpam-4941	587	8	mow	mow	PROPN
ejpam-4941	587	9	and	and	CCONJ
ejpam-4941	587	10	n.	n.	PROPN
ejpam-4941	587	11	howgrave	howgrave	PROPN
ejpam-4941	587	12	-	-	PUNCT
ejpam-4941	587	13	graham	graham	PROPN
ejpam-4941	587	14	.	.	PUNCT
ejpam-4941	588	1	reduced	reduce	VERB
ejpam-4941	588	2	and	and	CCONJ
ejpam-4941	588	3	fixed	fix	VERB
ejpam-4941	588	4	-	-	PUNCT
ejpam-4941	588	5	complexity	complexity	NOUN
ejpam-4941	588	6	variants	variant	NOUN
ejpam-4941	588	7	of	of	ADP
ejpam-4941	588	8	the	the	DET
ejpam-4941	588	9	lll	lll	NOUN
ejpam-4941	588	10	algorithm	algorithm	NOUN
ejpam-4941	588	11	for	for	ADP
ejpam-4941	588	12	communications	communication	NOUN
ejpam-4941	588	13	.	.	PUNCT
ejpam-4941	589	1	ieee	ieee	NOUN
ejpam-4941	589	2	transactions	transaction	NOUN
ejpam-4941	589	3	on	on	ADP
ejpam-4941	589	4	communications	communication	NOUN
ejpam-4941	589	5	,	,	PUNCT
ejpam-4941	589	6	61(3	61(3	NUM
ejpam-4941	589	7	)	)	PUNCT
ejpam-4941	589	8	,	,	PUNCT
ejpam-4941	589	9	p.1040	p.1040	VERB
ejpam-4941	589	10	-	-	PUNCT
ejpam-4941	589	11	1050	1050	NUM
ejpam-4941	589	12	,	,	PUNCT
ejpam-4941	589	13	2013	2013	NUM
ejpam-4941	589	14	.	.	PUNCT
ejpam-4941	590	1	references	reference	NOUN
ejpam-4941	590	2	2691	2691	NUM
ejpam-4941	591	1	[	[	X
ejpam-4941	591	2	37	37	NUM
ejpam-4941	591	3	]	]	PUNCT
ejpam-4941	591	4	a.	a.	NOUN
ejpam-4941	591	5	mujica	mujica	PROPN
ejpam-4941	591	6	.	.	PUNCT
ejpam-4941	592	1	lattice	lattice	NOUN
ejpam-4941	592	2	reduction	reduction	NOUN
ejpam-4941	592	3	using	use	VERB
ejpam-4941	592	4	a	a	DET
ejpam-4941	592	5	euclidean	euclidean	ADJ
ejpam-4941	592	6	algorithm	algorithm	NOUN
ejpam-4941	592	7	.	.	PUNCT
ejpam-4941	593	1	acta	acta	PROPN
ejpam-4941	593	2	crystallographica	crystallographica	PROPN
ejpam-4941	593	3	section	section	PROPN
ejpam-4941	593	4	a	a	DET
ejpam-4941	593	5	:	:	PUNCT
ejpam-4941	593	6	foundations	foundation	NOUN
ejpam-4941	593	7	and	and	CCONJ
ejpam-4941	593	8	advances	advance	NOUN
ejpam-4941	593	9	,	,	PUNCT
ejpam-4941	593	10	73(1	73(1	NUM
ejpam-4941	593	11	)	)	PUNCT
ejpam-4941	593	12	,	,	PUNCT
ejpam-4941	593	13	p.61	p.61	NOUN
ejpam-4941	593	14	-	-	SYM
ejpam-4941	593	15	68	68	NUM
ejpam-4941	593	16	.	.	NUM
ejpam-4941	593	17	,	,	PUNCT
ejpam-4941	593	18	2017	2017	NUM
ejpam-4941	593	19	.	.	PUNCT
ejpam-4941	594	1	[	[	X
ejpam-4941	594	2	38	38	NUM
ejpam-4941	594	3	]	]	PUNCT
ejpam-4941	594	4	h.	h.	PROPN
ejpam-4941	594	5	napias	napias	PROPN
ejpam-4941	594	6	.	.	PUNCT
ejpam-4941	595	1	a	a	DET
ejpam-4941	595	2	generalization	generalization	NOUN
ejpam-4941	595	3	of	of	ADP
ejpam-4941	595	4	the	the	DET
ejpam-4941	595	5	lll	lll	NOUN
ejpam-4941	595	6	-	-	PUNCT
ejpam-4941	595	7	algorithm	algorithm	NOUN
ejpam-4941	595	8	over	over	ADP
ejpam-4941	595	9	euclidean	euclidean	ADJ
ejpam-4941	595	10	rings	ring	NOUN
ejpam-4941	595	11	or	or	CCONJ
ejpam-4941	595	12	orders	order	NOUN
ejpam-4941	595	13	.	.	PUNCT
ejpam-4941	596	1	journal	journal	PROPN
ejpam-4941	596	2	de	de	PROPN
ejpam-4941	596	3	théorie	théorie	PROPN
ejpam-4941	596	4	des	des	PROPN
ejpam-4941	596	5	nombres	nombres	PROPN
ejpam-4941	596	6	de	de	X
ejpam-4941	596	7	bordeaux	bordeaux	PROPN
ejpam-4941	596	8	,	,	PUNCT
ejpam-4941	596	9	8(2	8(2	NUM
ejpam-4941	596	10	)	)	PUNCT
ejpam-4941	596	11	,	,	PUNCT
ejpam-4941	596	12	p.387	p.387	NOUN
ejpam-4941	596	13	-	-	SYM
ejpam-4941	596	14	396	396	NUM
ejpam-4941	596	15	,	,	PUNCT
ejpam-4941	596	16	1996	1996	NUM
ejpam-4941	596	17	.	.	PUNCT
ejpam-4941	597	1	[	[	X
ejpam-4941	597	2	39	39	NUM
ejpam-4941	597	3	]	]	PUNCT
ejpam-4941	597	4	w.	w.	PROPN
ejpam-4941	597	5	d.	d.	PROPN
ejpam-4941	597	6	nesse	nesse	PROPN
ejpam-4941	597	7	.	.	PUNCT
ejpam-4941	598	1	introduction	introduction	NOUN
ejpam-4941	598	2	to	to	ADP
ejpam-4941	598	3	mineralogy	mineralogy	NOUN
ejpam-4941	598	4	.	.	PUNCT
ejpam-4941	599	1	new	new	PROPN
ejpam-4941	599	2	york	york	PROPN
ejpam-4941	599	3	:	:	PUNCT
ejpam-4941	599	4	oxford	oxford	PROPN
ejpam-4941	599	5	university	university	PROPN
ejpam-4941	599	6	press	press	NOUN
ejpam-4941	599	7	.	.	PUNCT
ejpam-4941	600	1	isbn	isbn	ADJ
ejpam-4941	600	2	:	:	PUNCT
ejpam-4941	600	3	9780195106916	9780195106916	NUM
ejpam-4941	600	4	.	.	PUNCT
ejpam-4941	601	1	p.376	p.376	NOUN
ejpam-4941	601	2	-	-	PUNCT
ejpam-4941	601	3	377	377	NUM
ejpam-4941	601	4	,	,	PUNCT
ejpam-4941	601	5	2000	2000	NUM
ejpam-4941	601	6	.	.	PUNCT
ejpam-4941	602	1	[	[	X
ejpam-4941	602	2	40	40	NUM
ejpam-4941	602	3	]	]	PUNCT
ejpam-4941	602	4	p.	p.	PROPN
ejpam-4941	602	5	q.	q.	PROPN
ejpam-4941	602	6	nguyen	nguyen	PROPN
ejpam-4941	602	7	and	and	CCONJ
ejpam-4941	602	8	d.	d.	PROPN
ejpam-4941	602	9	stehlé.	stehlé.	PROPN
ejpam-4941	602	10	an	an	DET
ejpam-4941	602	11	lll	lll	NOUN
ejpam-4941	602	12	algorithm	algorithm	NOUN
ejpam-4941	602	13	with	with	ADP
ejpam-4941	602	14	quadratic	quadratic	ADJ
ejpam-4941	602	15	complexity	complexity	NOUN
ejpam-4941	602	16	.	.	PUNCT
ejpam-4941	603	1	siam	siam	PROPN
ejpam-4941	603	2	journal	journal	PROPN
ejpam-4941	603	3	on	on	ADP
ejpam-4941	603	4	computing	computing	NOUN
ejpam-4941	603	5	,	,	PUNCT
ejpam-4941	603	6	39(3	39(3	NUM
ejpam-4941	603	7	)	)	PUNCT
ejpam-4941	603	8	,	,	PUNCT
ejpam-4941	603	9	p.874	p.874	X
ejpam-4941	603	10	-	-	SYM
ejpam-4941	603	11	903	903	NUM
ejpam-4941	603	12	,	,	PUNCT
ejpam-4941	603	13	2009	2009	NUM
ejpam-4941	603	14	.	.	PUNCT
ejpam-4941	604	1	[	[	X
ejpam-4941	604	2	41	41	NUM
ejpam-4941	604	3	]	]	PUNCT
ejpam-4941	604	4	p.	p.	NOUN
ejpam-4941	604	5	niggli	niggli	NOUN
ejpam-4941	604	6	.	.	PUNCT
ejpam-4941	605	1	krystallographische	krystallographische	PROPN
ejpam-4941	605	2	und	und	PROPN
ejpam-4941	605	3	strukturtheoretische	strukturtheoretische	PROPN
ejpam-4941	605	4	grundbegriffe	grundbegriffe	NOUN
ejpam-4941	605	5	.	.	PUNCT
ejpam-4941	606	1	handbuch	handbuch	PROPN
ejpam-4941	606	2	der	der	PROPN
ejpam-4941	606	3	experimentalphysik	experimentalphysik	PROPN
ejpam-4941	606	4	,	,	PUNCT
ejpam-4941	606	5	bd	bd	PROPN
ejpam-4941	606	6	vii	vii	PROPN
ejpam-4941	606	7	,	,	PUNCT
ejpam-4941	606	8	1	1	NUM
ejpam-4941	606	9	.	.	X
ejpam-4941	606	10	geologiska	geologiska	PROPN
ejpam-4941	606	11	föreningen	föreningen	PROPN
ejpam-4941	607	1	i	i	PROPN
ejpam-4941	607	2	stockholm	stockholm	PROPN
ejpam-4941	607	3	förhandlingar	förhandlingar	PROPN
ejpam-4941	607	4	,	,	PUNCT
ejpam-4941	607	5	51(1	51(1	NUM
ejpam-4941	607	6	)	)	PUNCT
ejpam-4941	607	7	,	,	PUNCT
ejpam-4941	607	8	p.121	p.121	NUM
ejpam-4941	607	9	-	-	PUNCT
ejpam-4941	607	10	122	122	NUM
ejpam-4941	607	11	,	,	PUNCT
ejpam-4941	607	12	1929	1929	NUM
ejpam-4941	607	13	.	.	PUNCT
ejpam-4941	608	1	[	[	X
ejpam-4941	608	2	42	42	NUM
ejpam-4941	608	3	]	]	PUNCT
ejpam-4941	608	4	k.	k.	PROPN
ejpam-4941	608	5	panchuk	panchuk	PROPN
ejpam-4941	608	6	.	.	PUNCT
ejpam-4941	609	1	physical	physical	ADJ
ejpam-4941	609	2	geology	geology	NOUN
ejpam-4941	609	3	.	.	PUNCT
ejpam-4941	610	1	first	first	PROPN
ejpam-4941	610	2	university	university	PROPN
ejpam-4941	610	3	of	of	ADP
ejpam-4941	610	4	saskatchewan	saskatchewan	PROPN
ejpam-4941	610	5	edition	edition	PROPN
ejpam-4941	610	6	.	.	PUNCT
ejpam-4941	611	1	chapter	chapter	NOUN
ejpam-4941	611	2	5	5	NUM
ejpam-4941	611	3	.	.	PUNCT
ejpam-4941	612	1	p.1	p.1	NOUN
ejpam-4941	612	2	-	-	PUNCT
ejpam-4941	612	3	26	26	NUM
ejpam-4941	612	4	,	,	PUNCT
ejpam-4941	612	5	2019	2019	NUM
ejpam-4941	612	6	.	.	PUNCT
ejpam-4941	613	1	[	[	X
ejpam-4941	613	2	43	43	NUM
ejpam-4941	613	3	]	]	X
ejpam-4941	613	4	y.	y.	PROPN
ejpam-4941	613	5	park	park	PROPN
ejpam-4941	613	6	and	and	CCONJ
ejpam-4941	613	7	j.	j.	PROPN
ejpam-4941	613	8	park	park	PROPN
ejpam-4941	613	9	.	.	PUNCT
ejpam-4941	614	1	analysis	analysis	NOUN
ejpam-4941	614	2	of	of	ADP
ejpam-4941	614	3	the	the	DET
ejpam-4941	614	4	upper	upper	ADJ
ejpam-4941	614	5	bound	bind	VERB
ejpam-4941	614	6	on	on	ADP
ejpam-4941	614	7	the	the	DET
ejpam-4941	614	8	complexity	complexity	NOUN
ejpam-4941	614	9	of	of	ADP
ejpam-4941	614	10	lll	lll	PROPN
ejpam-4941	614	11	algorithm	algorithm	NOUN
ejpam-4941	614	12	.	.	PUNCT
ejpam-4941	615	1	journal	journal	NOUN
ejpam-4941	615	2	of	of	ADP
ejpam-4941	615	3	the	the	DET
ejpam-4941	615	4	korean	korean	ADJ
ejpam-4941	615	5	society	society	NOUN
ejpam-4941	615	6	for	for	ADP
ejpam-4941	615	7	industrial	industrial	ADJ
ejpam-4941	615	8	and	and	CCONJ
ejpam-4941	615	9	applied	apply	VERB
ejpam-4941	615	10	mathematics	mathematic	NOUN
ejpam-4941	615	11	,	,	PUNCT
ejpam-4941	615	12	20(2	20(2	NUM
ejpam-4941	615	13	)	)	PUNCT
ejpam-4941	615	14	,	,	PUNCT
ejpam-4941	615	15	p.107121	p.107121	VERB
ejpam-4941	615	16	,	,	PUNCT
ejpam-4941	615	17	2016	2016	NUM
ejpam-4941	615	18	.	.	PUNCT
ejpam-4941	616	1	[	[	X
ejpam-4941	616	2	44	44	NUM
ejpam-4941	616	3	]	]	PUNCT
ejpam-4941	616	4	j.	j.	PROPN
ejpam-4941	616	5	r.	r.	PROPN
ejpam-4941	616	6	rice	rice	PROPN
ejpam-4941	616	7	.	.	PUNCT
ejpam-4941	617	1	experiments	experiment	NOUN
ejpam-4941	617	2	on	on	ADP
ejpam-4941	617	3	gram	gram	NOUN
ejpam-4941	617	4	-	-	PUNCT
ejpam-4941	617	5	schmidt	schmidt	NOUN
ejpam-4941	617	6	orthogonalization	orthogonalization	NOUN
ejpam-4941	617	7	.	.	PUNCT
ejpam-4941	618	1	mathematics	mathematic	NOUN
ejpam-4941	618	2	of	of	ADP
ejpam-4941	618	3	computation	computation	NOUN
ejpam-4941	618	4	,	,	PUNCT
ejpam-4941	618	5	20(94	20(94	NUM
ejpam-4941	618	6	)	)	PUNCT
ejpam-4941	618	7	,	,	PUNCT
ejpam-4941	618	8	p.325	p.325	PROPN
ejpam-4941	618	9	-	-	X
ejpam-4941	618	10	328	328	NUM
ejpam-4941	618	11	,	,	PUNCT
ejpam-4941	618	12	1966	1966	NUM
ejpam-4941	618	13	.	.	PUNCT
ejpam-4941	619	1	[	[	X
ejpam-4941	619	2	45	45	NUM
ejpam-4941	619	3	]	]	PUNCT
ejpam-4941	619	4	a.	a.	NOUN
ejpam-4941	619	5	t.	t.	PROPN
ejpam-4941	619	6	santoro	santoro	PROPN
ejpam-4941	619	7	and	and	CCONJ
ejpam-4941	619	8	a.	a.	PROPN
ejpam-4941	619	9	d.	d.	PROPN
ejpam-4941	619	10	mighell	mighell	PROPN
ejpam-4941	619	11	.	.	PUNCT
ejpam-4941	620	1	determination	determination	NOUN
ejpam-4941	620	2	of	of	ADP
ejpam-4941	620	3	reduced	reduced	ADJ
ejpam-4941	620	4	cells	cell	NOUN
ejpam-4941	620	5	.	.	PUNCT
ejpam-4941	621	1	acta	acta	PROPN
ejpam-4941	621	2	crystallographica	crystallographica	PROPN
ejpam-4941	621	3	section	section	PROPN
ejpam-4941	621	4	a	a	DET
ejpam-4941	621	5	:	:	PUNCT
ejpam-4941	621	6	crystal	crystal	NOUN
ejpam-4941	621	7	physics	physics	PROPN
ejpam-4941	621	8	,	,	PUNCT
ejpam-4941	621	9	diffraction	diffraction	NOUN
ejpam-4941	621	10	,	,	PUNCT
ejpam-4941	621	11	theoretical	theoretical	ADJ
ejpam-4941	621	12	and	and	CCONJ
ejpam-4941	621	13	general	general	ADJ
ejpam-4941	621	14	crystallography	crystallography	NOUN
ejpam-4941	621	15	,	,	PUNCT
ejpam-4941	621	16	26(1	26(1	NUM
ejpam-4941	621	17	)	)	PUNCT
ejpam-4941	621	18	,	,	PUNCT
ejpam-4941	621	19	p.124	p.124	NUM
ejpam-4941	621	20	-	-	SYM
ejpam-4941	621	21	127	127	NUM
ejpam-4941	621	22	,	,	PUNCT
ejpam-4941	621	23	1970	1970	NUM
ejpam-4941	621	24	.	.	PUNCT
ejpam-4941	622	1	[	[	X
ejpam-4941	622	2	46	46	NUM
ejpam-4941	622	3	]	]	X
ejpam-4941	622	4	c.	c.	PROPN
ejpam-4941	622	5	p.	p.	PROPN
ejpam-4941	622	6	schnorr	schnorr	PROPN
ejpam-4941	622	7	.	.	PUNCT
ejpam-4941	623	1	fast	fast	ADJ
ejpam-4941	623	2	lll	lll	NOUN
ejpam-4941	623	3	-	-	PUNCT
ejpam-4941	623	4	type	type	NOUN
ejpam-4941	623	5	lattice	lattice	NOUN
ejpam-4941	623	6	reduction	reduction	NOUN
ejpam-4941	623	7	.	.	PUNCT
ejpam-4941	624	1	information	information	NOUN
ejpam-4941	624	2	and	and	CCONJ
ejpam-4941	624	3	computation	computation	NOUN
ejpam-4941	624	4	,	,	PUNCT
ejpam-4941	624	5	204(1	204(1	NUM
ejpam-4941	624	6	)	)	PUNCT
ejpam-4941	624	7	,	,	PUNCT
ejpam-4941	624	8	p.1	p.1	NOUN
ejpam-4941	624	9	-	-	SYM
ejpam-4941	624	10	25	25	NUM
ejpam-4941	624	11	,	,	PUNCT
ejpam-4941	624	12	2006	2006	NUM
ejpam-4941	624	13	.	.	PUNCT
ejpam-4941	625	1	[	[	X
ejpam-4941	625	2	47	47	NUM
ejpam-4941	625	3	]	]	X
ejpam-4941	625	4	d.	d.	PROPN
ejpam-4941	625	5	simon	simon	PROPN
ejpam-4941	625	6	.	.	PROPN
ejpam-4941	626	1	selected	select	VERB
ejpam-4941	626	2	applications	application	NOUN
ejpam-4941	626	3	of	of	ADP
ejpam-4941	626	4	lll	lll	NOUN
ejpam-4941	626	5	in	in	ADP
ejpam-4941	626	6	number	number	NOUN
ejpam-4941	626	7	theory	theory	NOUN
ejpam-4941	626	8	.	.	PUNCT
ejpam-4941	627	1	in	in	ADP
ejpam-4941	627	2	the	the	DET
ejpam-4941	627	3	lll	lll	PROPN
ejpam-4941	627	4	algorithm	algorithm	NOUN
ejpam-4941	627	5	:	:	PUNCT
ejpam-4941	627	6	survey	survey	NOUN
ejpam-4941	627	7	and	and	CCONJ
ejpam-4941	627	8	applications	application	NOUN
ejpam-4941	627	9	.	.	PUNCT
ejpam-4941	627	10	p.265	p.265	NOUN
ejpam-4941	627	11	-	-	PUNCT
ejpam-4941	627	12	282	282	NUM
ejpam-4941	627	13	,	,	PUNCT
ejpam-4941	627	14	berlin	berlin	PROPN
ejpam-4941	627	15	,	,	PUNCT
ejpam-4941	627	16	heidelberg	heidelberg	PROPN
ejpam-4941	627	17	:	:	PUNCT
ejpam-4941	627	18	springer	springer	PROPN
ejpam-4941	627	19	berlin	berlin	PROPN
ejpam-4941	627	20	heidelberg	heidelberg	PROPN
ejpam-4941	627	21	,	,	PUNCT
ejpam-4941	627	22	2009	2009	NUM
ejpam-4941	627	23	.	.	PUNCT
ejpam-4941	628	1	[	[	X
ejpam-4941	628	2	48	48	NUM
ejpam-4941	628	3	]	]	X
ejpam-4941	628	4	d.	d.	PROPN
ejpam-4941	628	5	stehlé.	stehlé.	PROPN
ejpam-4941	628	6	floating	float	VERB
ejpam-4941	628	7	-	-	PUNCT
ejpam-4941	628	8	point	point	NOUN
ejpam-4941	628	9	lll	lll	NOUN
ejpam-4941	628	10	:	:	PUNCT
ejpam-4941	628	11	theoretical	theoretical	ADJ
ejpam-4941	628	12	and	and	CCONJ
ejpam-4941	628	13	practical	practical	ADJ
ejpam-4941	628	14	aspects	aspect	NOUN
ejpam-4941	628	15	.	.	PUNCT
ejpam-4941	629	1	in	in	ADP
ejpam-4941	629	2	the	the	DET
ejpam-4941	629	3	lll	lll	PROPN
ejpam-4941	629	4	algorithm	algorithm	NOUN
ejpam-4941	629	5	:	:	PUNCT
ejpam-4941	629	6	survey	survey	NOUN
ejpam-4941	629	7	and	and	CCONJ
ejpam-4941	629	8	applications	application	NOUN
ejpam-4941	629	9	.	.	PUNCT
ejpam-4941	629	10	p.179	p.179	NOUN
ejpam-4941	629	11	-	-	PUNCT
ejpam-4941	629	12	213	213	NUM
ejpam-4941	629	13	,	,	PUNCT
ejpam-4941	629	14	berlin	berlin	PROPN
ejpam-4941	629	15	,	,	PUNCT
ejpam-4941	629	16	heidelberg	heidelberg	PROPN
ejpam-4941	629	17	:	:	PUNCT
ejpam-4941	629	18	springer	springer	PROPN
ejpam-4941	629	19	berlin	berlin	PROPN
ejpam-4941	629	20	heidelberg	heidelberg	PROPN
ejpam-4941	629	21	,	,	PUNCT
ejpam-4941	629	22	2009	2009	NUM
ejpam-4941	629	23	.	.	PUNCT
ejpam-4941	630	1	[	[	X
ejpam-4941	630	2	49	49	NUM
ejpam-4941	630	3	]	]	PUNCT
ejpam-4941	630	4	t.	t.	PROPN
ejpam-4941	630	5	plantard	plantard	PROPN
ejpam-4941	630	6	w.	w.	PROPN
ejpam-4941	630	7	susilo	susilo	PROPN
ejpam-4941	630	8	and	and	CCONJ
ejpam-4941	630	9	z.	z.	PROPN
ejpam-4941	630	10	zhang	zhang	PROPN
ejpam-4941	630	11	.	.	PUNCT
ejpam-4941	631	1	lll	lll	PROPN
ejpam-4941	631	2	for	for	ADP
ejpam-4941	631	3	ideal	ideal	ADJ
ejpam-4941	631	4	lattices	lattice	NOUN
ejpam-4941	631	5	:	:	PUNCT
ejpam-4941	631	6	re	re	NOUN
ejpam-4941	631	7	-	-	NOUN
ejpam-4941	631	8	evaluation	evaluation	NOUN
ejpam-4941	631	9	of	of	ADP
ejpam-4941	631	10	the	the	DET
ejpam-4941	631	11	security	security	NOUN
ejpam-4941	631	12	of	of	ADP
ejpam-4941	631	13	gentry	gentry	NOUN
ejpam-4941	631	14	–	–	PUNCT
ejpam-4941	631	15	halevi	halevi	PROPN
ejpam-4941	631	16	’s	’s	PART
ejpam-4941	631	17	fhe	fhe	PROPN
ejpam-4941	631	18	scheme	scheme	NOUN
ejpam-4941	631	19	.	.	PUNCT
ejpam-4941	632	1	designs	design	NOUN
ejpam-4941	632	2	,	,	PUNCT
ejpam-4941	632	3	codes	code	NOUN
ejpam-4941	632	4	and	and	CCONJ
ejpam-4941	632	5	cryptography	cryptography	NOUN
ejpam-4941	632	6	,	,	PUNCT
ejpam-4941	632	7	76	76	NUM
ejpam-4941	632	8	,	,	PUNCT
ejpam-4941	632	9	p.325	p.325	X
ejpam-4941	632	10	-	-	PUNCT
ejpam-4941	632	11	344	344	NUM
ejpam-4941	632	12	,	,	PUNCT
ejpam-4941	632	13	2015	2015	NUM
ejpam-4941	632	14	.	.	PUNCT
ejpam-4941	633	1	[	[	X
ejpam-4941	633	2	50	50	NUM
ejpam-4941	633	3	]	]	PUNCT
ejpam-4941	633	4	b.	b.	PROPN
ejpam-4941	633	5	vallée	vallée	PROPN
ejpam-4941	633	6	and	and	CCONJ
ejpam-4941	633	7	a.	a.	NOUN
ejpam-4941	633	8	vera	vera	NOUN
ejpam-4941	633	9	.	.	PUNCT
ejpam-4941	634	1	probabilistic	probabilistic	ADJ
ejpam-4941	634	2	analyses	analysis	NOUN
ejpam-4941	634	3	of	of	ADP
ejpam-4941	634	4	lattice	lattice	ADJ
ejpam-4941	634	5	reduction	reduction	NOUN
ejpam-4941	634	6	algorithms	algorithm	NOUN
ejpam-4941	634	7	.	.	PUNCT
ejpam-4941	635	1	in	in	ADP
ejpam-4941	635	2	the	the	DET
ejpam-4941	635	3	lll	lll	PROPN
ejpam-4941	635	4	algorithm	algorithm	NOUN
ejpam-4941	635	5	:	:	PUNCT
ejpam-4941	635	6	survey	survey	NOUN
ejpam-4941	635	7	and	and	CCONJ
ejpam-4941	635	8	applications	application	NOUN
ejpam-4941	635	9	.	.	PUNCT
ejpam-4941	636	1	p.71	p.71	PROPN
ejpam-4941	636	2	-	-	PUNCT
ejpam-4941	636	3	143	143	NUM
ejpam-4941	636	4	,	,	PUNCT
ejpam-4941	636	5	berlin	berlin	PROPN
ejpam-4941	636	6	,	,	PUNCT
ejpam-4941	636	7	heidelberg	heidelberg	PROPN
ejpam-4941	636	8	:	:	PUNCT
ejpam-4941	636	9	springer	springer	PROPN
ejpam-4941	636	10	berlin	berlin	PROPN
ejpam-4941	636	11	heidelberg	heidelberg	PROPN
ejpam-4941	636	12	,	,	PUNCT
ejpam-4941	636	13	2009	2009	NUM
ejpam-4941	636	14	.	.	PUNCT
ejpam-4941	637	1	references	reference	NOUN
ejpam-4941	637	2	2692	2692	NUM
ejpam-4941	637	3	[	[	X
ejpam-4941	637	4	51	51	NUM
ejpam-4941	637	5	]	]	PUNCT
ejpam-4941	637	6	m.	m.	NOUN
ejpam-4941	637	7	vehkamäki	vehkamäki	NOUN
ejpam-4941	637	8	.	.	PUNCT
ejpam-4941	638	1	atomic	atomic	ADJ
ejpam-4941	638	2	layer	layer	NOUN
ejpam-4941	638	3	deposition	deposition	NOUN
ejpam-4941	638	4	of	of	ADP
ejpam-4941	638	5	multicomponent	multicomponent	ADJ
ejpam-4941	638	6	oxide	oxide	NOUN
ejpam-4941	638	7	materials	material	NOUN
ejpam-4941	638	8	.	.	PUNCT
ejpam-4941	639	1	university	university	NOUN
ejpam-4941	639	2	of	of	ADP
ejpam-4941	639	3	helsinki	helsinki	PROPN
ejpam-4941	639	4	and	and	CCONJ
ejpam-4941	639	5	for	for	ADP
ejpam-4941	639	6	the	the	DET
ejpam-4941	639	7	academic	academic	ADJ
ejpam-4941	639	8	dissertation	dissertation	NOUN
ejpam-4941	639	9	at	at	ADP
ejpam-4941	639	10	the	the	DET
ejpam-4941	639	11	faculty	faculty	NOUN
ejpam-4941	639	12	of	of	ADP
ejpam-4941	639	13	science	science	NOUN
ejpam-4941	639	14	.	.	PUNCT
ejpam-4941	640	1	isbn	isbn	ADJ
ejpam-4941	640	2	:	:	PUNCT
ejpam-4941	640	3	978	978	NUM
ejpam-4941	640	4	-	-	SYM
ejpam-4941	640	5	952	952	NUM
ejpam-4941	640	6	-	-	PUNCT
ejpam-4941	640	7	10	10	NUM
ejpam-4941	640	8	-	-	PUNCT
ejpam-4941	640	9	4452	4452	NUM
ejpam-4941	640	10	-	-	SYM
ejpam-4941	640	11	6	6	NUM
ejpam-4941	640	12	.	.	PUNCT
ejpam-4941	640	13	p.1	p.1	NOUN
ejpam-4941	640	14	-	-	PUNCT
ejpam-4941	640	15	69	69	NUM
ejpam-4941	640	16	,	,	PUNCT
ejpam-4941	640	17	2007	2007	NUM
ejpam-4941	640	18	.	.	PUNCT
ejpam-4941	641	1	[	[	X
ejpam-4941	641	2	52	52	NUM
ejpam-4941	641	3	]	]	PUNCT
ejpam-4941	641	4	l.	l.	PROPN
ejpam-4941	641	5	u.	u.	PROPN
ejpam-4941	641	6	liguo	liguo	PROPN
ejpam-4941	641	7	l.	l.	PROPN
ejpam-4941	641	8	i.	i.	PROPN
ejpam-4941	641	9	u.	u.	PROPN
ejpam-4941	641	10	wanke	wanke	PROPN
ejpam-4941	641	11	and	and	CCONJ
ejpam-4941	641	12	l.	l.	PROPN
ejpam-4941	641	13	i.	i.	PROPN
ejpam-4941	641	14	jiangwei	jiangwei	PROPN
ejpam-4941	641	15	.	.	PUNCT
ejpam-4941	642	1	an	an	DET
ejpam-4941	642	2	efficient	efficient	ADJ
ejpam-4941	642	3	lll	lll	NOUN
ejpam-4941	642	4	reduction	reduction	NOUN
ejpam-4941	642	5	algorithm	algorithm	NOUN
ejpam-4941	642	6	.	.	PUNCT
ejpam-4941	643	1	geomatics	geomatic	NOUN
ejpam-4941	643	2	and	and	CCONJ
ejpam-4941	643	3	information	information	NOUN
ejpam-4941	643	4	science	science	NOUN
ejpam-4941	643	5	at	at	ADP
ejpam-4941	643	6	wuhan	wuhan	PROPN
ejpam-4941	643	7	university	university	PROPN
ejpam-4941	643	8	.	.	PUNCT
ejpam-4941	644	1	vol	vol	NOUN
ejpam-4941	644	2	41	41	NUM
ejpam-4941	644	3	.	.	PUNCT
ejpam-4941	645	1	no	no	INTJ
ejpam-4941	645	2	.	.	NOUN
ejpam-4941	646	1	8	8	NUM
ejpam-4941	646	2	.	.	X
ejpam-4941	646	3	doi	doi	NOUN
ejpam-4941	646	4	.	.	PUNCT
ejpam-4941	647	1	10.13203	10.13203	NUM
ejpam-4941	647	2	/	/	SYM
ejpam-4941	647	3	j.whugis20140484	j.whugis20140484	NOUN
ejpam-4941	647	4	,	,	PUNCT
ejpam-4941	647	5	2016	2016	NUM
ejpam-4941	647	6	.	.	PUNCT
ejpam-4941	648	1	[	[	X
ejpam-4941	648	2	53	53	NUM
ejpam-4941	648	3	]	]	PUNCT
ejpam-4941	648	4	w.	w.	PROPN
ejpam-4941	648	5	a.	a.	PROPN
ejpam-4941	648	6	wooster	wooster	PROPN
ejpam-4941	648	7	.	.	PUNCT
ejpam-4941	649	1	physical	physical	ADJ
ejpam-4941	649	2	properties	property	NOUN
ejpam-4941	649	3	and	and	CCONJ
ejpam-4941	649	4	atomic	atomic	ADJ
ejpam-4941	649	5	arrangements	arrangement	NOUN
ejpam-4941	649	6	in	in	ADP
ejpam-4941	649	7	crystals	crystal	NOUN
ejpam-4941	649	8	.	.	PUNCT
ejpam-4941	650	1	reports	report	NOUN
ejpam-4941	650	2	on	on	ADP
ejpam-4941	650	3	progress	progress	NOUN
ejpam-4941	650	4	in	in	ADP
ejpam-4941	650	5	physics	physics	PROPN
ejpam-4941	650	6	,	,	PUNCT
ejpam-4941	650	7	16(1	16(1	NUM
ejpam-4941	650	8	)	)	PUNCT
ejpam-4941	650	9	,	,	PUNCT
ejpam-4941	650	10	p.62	p.62	PROPN
ejpam-4941	650	11	,	,	PUNCT
ejpam-4941	650	12	1953	1953	NUM
ejpam-4941	650	13	.	.	PUNCT