id	sid	tid	token	lemma	pos
ejpam-370	1	1	4_370_aydin.dvi	4_370_aydin.dvi	NUM
ejpam-370	1	2	european	european	ADJ
ejpam-370	1	3	journal	journal	NOUN
ejpam-370	1	4	of	of	ADP
ejpam-370	1	5	pure	pure	ADJ
ejpam-370	1	6	and	and	CCONJ
ejpam-370	1	7	applied	apply	VERB
ejpam-370	1	8	mathematics	mathematic	NOUN
ejpam-370	1	9	vol	vol	NOUN
ejpam-370	1	10	.	.	PUNCT
ejpam-370	2	1	3	3	NUM
ejpam-370	2	2	,	,	PUNCT
ejpam-370	2	3	no	no	INTJ
ejpam-370	2	4	.	.	NOUN
ejpam-370	2	5	5	5	NUM
ejpam-370	2	6	,	,	PUNCT
ejpam-370	2	7	2010	2010	NUM
ejpam-370	2	8	,	,	PUNCT
ejpam-370	2	9	819	819	NUM
ejpam-370	2	10	-	-	SYM
ejpam-370	2	11	830	830	NUM
ejpam-370	2	12	issn	issn	PROPN
ejpam-370	2	13	1307	1307	NUM
ejpam-370	2	14	-	-	SYM
ejpam-370	2	15	5543	5543	NUM
ejpam-370	2	16	–	–	PUNCT
ejpam-370	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-370	2	18	generalized	generalize	VERB
ejpam-370	2	19	iterative	iterative	NOUN
ejpam-370	2	20	decreasing	decrease	VERB
ejpam-370	2	21	dimension	dimension	NOUN
ejpam-370	2	22	method	method	NOUN
ejpam-370	2	23	kemal	kemal	PROPN
ejpam-370	2	24	aydın1,∗	aydın1,∗	NOUN
ejpam-370	2	25	,	,	PUNCT
ejpam-370	2	26	gülnur	gülnur	ADJ
ejpam-370	2	27	çelik	çelik	NOUN
ejpam-370	2	28	kızılkan	kızılkan	PROPN
ejpam-370	2	29	2	2	NUM
ejpam-370	2	30	,	,	PUNCT
ejpam-370	2	31	ali	ali	PROPN
ejpam-370	2	32	osman	osman	PROPN
ejpam-370	2	33	çıbıkdiken	çıbıkdiken	VERB
ejpam-370	2	34	3	3	NUM
ejpam-370	2	35	1	1	NUM
ejpam-370	2	36	selçuk	selçuk	NOUN
ejpam-370	2	37	university	university	NOUN
ejpam-370	2	38	,	,	PUNCT
ejpam-370	2	39	faculty	faculty	NOUN
ejpam-370	2	40	of	of	ADP
ejpam-370	2	41	science	science	NOUN
ejpam-370	2	42	,	,	PUNCT
ejpam-370	2	43	department	department	NOUN
ejpam-370	2	44	of	of	ADP
ejpam-370	2	45	mathematics	mathematics	PROPN
ejpam-370	2	46	,	,	PUNCT
ejpam-370	2	47	konya	konya	PROPN
ejpam-370	2	48	,	,	PUNCT
ejpam-370	2	49	türkiye	türkiye	PROPN
ejpam-370	2	50	2	2	NUM
ejpam-370	2	51	kahramanmaraş	kahramanmaraş	PROPN
ejpam-370	2	52	sütçü	sütçü	NOUN
ejpam-370	2	53	i̇mam	i̇mam	PROPN
ejpam-370	2	54	university	university	NOUN
ejpam-370	2	55	,	,	PUNCT
ejpam-370	2	56	faculty	faculty	NOUN
ejpam-370	2	57	of	of	ADP
ejpam-370	2	58	education	education	NOUN
ejpam-370	2	59	,	,	PUNCT
ejpam-370	2	60	dept	dept	NOUN
ejpam-370	2	61	.	.	PROPN
ejpam-370	2	62	of	of	ADP
ejpam-370	2	63	primary	primary	ADJ
ejpam-370	2	64	math	math	NOUN
ejpam-370	2	65	.	.	PUNCT
ejpam-370	3	1	education	education	NOUN
ejpam-370	3	2	,	,	PUNCT
ejpam-370	3	3	kahramanmaraş	kahramanmaraş	PROPN
ejpam-370	3	4	,	,	PUNCT
ejpam-370	3	5	türkiye	türkiye	PROPN
ejpam-370	3	6	3	3	NUM
ejpam-370	3	7	selçuk	selçuk	PROPN
ejpam-370	3	8	university	university	NOUN
ejpam-370	3	9	,	,	PUNCT
ejpam-370	3	10	k.f.i.v.s	k.f.i.v.s	NOUN
ejpam-370	3	11	.	.	PROPN
ejpam-370	3	12	,	,	PUNCT
ejpam-370	3	13	dept	dept	PROPN
ejpam-370	3	14	.	.	PROPN
ejpam-370	4	1	of	of	ADP
ejpam-370	4	2	computer	computer	NOUN
ejpam-370	4	3	technology	technology	NOUN
ejpam-370	4	4	and	and	CCONJ
ejpam-370	4	5	programming	programming	NOUN
ejpam-370	4	6	,	,	PUNCT
ejpam-370	4	7	konya	konya	PROPN
ejpam-370	4	8	,	,	PUNCT
ejpam-370	4	9	türkiye	türkiye	PROPN
ejpam-370	4	10	abstract	abstract	NOUN
ejpam-370	4	11	.	.	PUNCT
ejpam-370	5	1	in	in	ADP
ejpam-370	5	2	this	this	DET
ejpam-370	5	3	study	study	NOUN
ejpam-370	5	4	,	,	PUNCT
ejpam-370	5	5	we	we	PRON
ejpam-370	5	6	have	have	AUX
ejpam-370	5	7	given	give	VERB
ejpam-370	5	8	a	a	DET
ejpam-370	5	9	generalization	generalization	NOUN
ejpam-370	5	10	of	of	ADP
ejpam-370	5	11	the	the	DET
ejpam-370	5	12	iterative	iterative	NOUN
ejpam-370	5	13	decreasing	decrease	VERB
ejpam-370	5	14	dimension	dimension	NOUN
ejpam-370	5	15	method	method	NOUN
ejpam-370	5	16	given	give	VERB
ejpam-370	5	17	in	in	ADP
ejpam-370	5	18	[	[	X
ejpam-370	5	19	3	3	NUM
ejpam-370	5	20	]	]	PUNCT
ejpam-370	5	21	and	and	CCONJ
ejpam-370	5	22	a	a	DET
ejpam-370	5	23	generalization	generalization	NOUN
ejpam-370	5	24	of	of	ADP
ejpam-370	5	25	the	the	DET
ejpam-370	5	26	iterative	iterative	NOUN
ejpam-370	5	27	decreasing	decrease	VERB
ejpam-370	5	28	dimension	dimension	NOUN
ejpam-370	5	29	algorithm	algorithm	NOUN
ejpam-370	5	30	based	base	VERB
ejpam-370	5	31	on	on	ADP
ejpam-370	5	32	this	this	DET
ejpam-370	5	33	method	method	NOUN
ejpam-370	5	34	.	.	PUNCT
ejpam-370	6	1	the	the	DET
ejpam-370	6	2	algorithm	algorithm	NOUN
ejpam-370	6	3	is	be	AUX
ejpam-370	6	4	suited	suit	VERB
ejpam-370	6	5	for	for	ADP
ejpam-370	6	6	implementation	implementation	NOUN
ejpam-370	6	7	using	use	VERB
ejpam-370	6	8	computer	computer	NOUN
ejpam-370	6	9	algebra	algebra	NOUN
ejpam-370	6	10	systems	system	NOUN
ejpam-370	6	11	such	such	ADJ
ejpam-370	6	12	as	as	ADP
ejpam-370	6	13	maple	maple	NOUN
ejpam-370	6	14	and	and	CCONJ
ejpam-370	6	15	matlab	matlab	PROPN
ejpam-370	6	16	.	.	PUNCT
ejpam-370	7	1	so	so	ADV
ejpam-370	7	2	we	we	PRON
ejpam-370	7	3	also	also	ADV
ejpam-370	7	4	have	have	AUX
ejpam-370	7	5	given	give	VERB
ejpam-370	7	6	symbolic	symbolic	ADJ
ejpam-370	7	7	and	and	CCONJ
ejpam-370	7	8	numerical	numerical	ADJ
ejpam-370	7	9	examples	example	NOUN
ejpam-370	7	10	using	use	VERB
ejpam-370	7	11	this	this	DET
ejpam-370	7	12	algorithm	algorithm	NOUN
ejpam-370	7	13	and	and	CCONJ
ejpam-370	7	14	a	a	DET
ejpam-370	7	15	maple	maple	NOUN
ejpam-370	7	16	procedure	procedure	NOUN
ejpam-370	7	17	for	for	ADP
ejpam-370	7	18	the	the	DET
ejpam-370	7	19	algorithm	algorithm	NOUN
ejpam-370	7	20	.	.	PUNCT
ejpam-370	8	1	2000	2000	NUM
ejpam-370	8	2	mathematics	mathematic	NOUN
ejpam-370	8	3	subject	subject	NOUN
ejpam-370	8	4	classifications	classification	NOUN
ejpam-370	8	5	:	:	PUNCT
ejpam-370	8	6	65f10	65f10	NUM
ejpam-370	8	7	key	key	ADJ
ejpam-370	8	8	words	word	NOUN
ejpam-370	8	9	and	and	CCONJ
ejpam-370	8	10	phrases	phrase	NOUN
ejpam-370	8	11	:	:	PUNCT
ejpam-370	8	12	iterative	iterative	NOUN
ejpam-370	8	13	decreasing	decrease	VERB
ejpam-370	8	14	dimension	dimension	NOUN
ejpam-370	8	15	method	method	NOUN
ejpam-370	8	16	,	,	PUNCT
ejpam-370	8	17	iterative	iterative	NOUN
ejpam-370	8	18	decreasing	decrease	VERB
ejpam-370	8	19	dimension	dimension	NOUN
ejpam-370	8	20	algorithm	algorithm	NOUN
ejpam-370	8	21	,	,	PUNCT
ejpam-370	8	22	linear	linear	ADJ
ejpam-370	8	23	algebraic	algebraic	ADJ
ejpam-370	8	24	equations	equation	NOUN
ejpam-370	8	25	1	1	NUM
ejpam-370	8	26	.	.	PUNCT
ejpam-370	9	1	introduction	introduction	NOUN
ejpam-370	9	2	studying	study	VERB
ejpam-370	9	3	on	on	ADP
ejpam-370	9	4	solution	solution	NOUN
ejpam-370	9	5	of	of	ADP
ejpam-370	9	6	the	the	DET
ejpam-370	9	7	systems	system	NOUN
ejpam-370	9	8	of	of	ADP
ejpam-370	9	9	linear	linear	PROPN
ejpam-370	9	10	algebraic	algebraic	ADJ
ejpam-370	9	11	equation	equation	NOUN
ejpam-370	9	12	ax	ax	NOUN
ejpam-370	9	13	=	=	SYM
ejpam-370	9	14	f	f	X
ejpam-370	9	15	(	(	PUNCT
ejpam-370	9	16	1	1	NUM
ejpam-370	9	17	)	)	PUNCT
ejpam-370	9	18	is	be	AUX
ejpam-370	9	19	a	a	DET
ejpam-370	9	20	classical	classical	ADJ
ejpam-370	9	21	problem	problem	NOUN
ejpam-370	9	22	which	which	PRON
ejpam-370	9	23	is	be	AUX
ejpam-370	9	24	important	important	ADJ
ejpam-370	9	25	not	not	PART
ejpam-370	9	26	only	only	ADV
ejpam-370	9	27	in	in	ADP
ejpam-370	9	28	linear	linear	ADJ
ejpam-370	9	29	algebra	algebra	NOUN
ejpam-370	9	30	but	but	CCONJ
ejpam-370	9	31	also	also	ADV
ejpam-370	9	32	in	in	ADP
ejpam-370	9	33	other	other	ADJ
ejpam-370	9	34	branches	branch	NOUN
ejpam-370	9	35	of	of	ADP
ejpam-370	9	36	science	science	NOUN
ejpam-370	9	37	,	,	PUNCT
ejpam-370	9	38	engineering	engineering	NOUN
ejpam-370	9	39	,	,	PUNCT
ejpam-370	9	40	economics	economic	NOUN
ejpam-370	9	41	.	.	PUNCT
ejpam-370	10	1	a	a	DET
ejpam-370	10	2	decreasing	decrease	VERB
ejpam-370	10	3	dimension	dimension	NOUN
ejpam-370	10	4	method	method	NOUN
ejpam-370	10	5	(	(	PUNCT
ejpam-370	10	6	ddm	ddm	PROPN
ejpam-370	10	7	)	)	PUNCT
ejpam-370	10	8	has	have	AUX
ejpam-370	10	9	been	be	AUX
ejpam-370	10	10	proposed	propose	VERB
ejpam-370	10	11	in	in	ADP
ejpam-370	10	12	[	[	X
ejpam-370	10	13	4	4	NUM
ejpam-370	10	14	]	]	PUNCT
ejpam-370	10	15	to	to	PART
ejpam-370	10	16	solve	solve	VERB
ejpam-370	10	17	the	the	DET
ejpam-370	10	18	system	system	NOUN
ejpam-370	10	19	(	(	PUNCT
ejpam-370	10	20	1	1	NUM
ejpam-370	10	21	)	)	PUNCT
ejpam-370	10	22	where	where	SCONJ
ejpam-370	10	23	a	a	PRON
ejpam-370	10	24	is	be	AUX
ejpam-370	10	25	n	n	PRON
ejpam-370	10	26	×	×	NOUN
ejpam-370	10	27	n	n	CCONJ
ejpam-370	10	28	-regular	-regular	ADJ
ejpam-370	10	29	matrix	matrix	NOUN
ejpam-370	10	30	,	,	PUNCT
ejpam-370	10	31	x	x	PUNCT
ejpam-370	10	32	and	and	CCONJ
ejpam-370	10	33	f	f	PROPN
ejpam-370	10	34	are	be	AUX
ejpam-370	10	35	n	n	PRON
ejpam-370	10	36	vectors	vector	NOUN
ejpam-370	10	37	.	.	PUNCT
ejpam-370	11	1	in	in	ADP
ejpam-370	11	2	[	[	X
ejpam-370	11	3	5	5	NUM
ejpam-370	11	4	]	]	PUNCT
ejpam-370	11	5	(	(	PUNCT
ejpam-370	11	6	therein	therein	ADV
ejpam-370	11	7	[	[	X
ejpam-370	11	8	1	1	NUM
ejpam-370	11	9	,	,	PUNCT
ejpam-370	11	10	2	2	NUM
ejpam-370	11	11	]	]	NUM
ejpam-370	11	12	)	)	PUNCT
ejpam-370	11	13	,	,	PUNCT
ejpam-370	11	14	it	it	PRON
ejpam-370	11	15	has	have	AUX
ejpam-370	11	16	been	be	AUX
ejpam-370	11	17	said	say	VERB
ejpam-370	11	18	that	that	SCONJ
ejpam-370	11	19	the	the	DET
ejpam-370	11	20	proposed	propose	VERB
ejpam-370	11	21	ddm	ddm	NOUN
ejpam-370	11	22	in	in	ADP
ejpam-370	11	23	[	[	X
ejpam-370	11	24	4	4	NUM
ejpam-370	11	25	]	]	PUNCT
ejpam-370	11	26	is	be	AUX
ejpam-370	11	27	same	same	ADJ
ejpam-370	11	28	as	as	ADP
ejpam-370	11	29	the	the	DET
ejpam-370	11	30	well	well	ADV
ejpam-370	11	31	known	know	VERB
ejpam-370	11	32	domain	domain	NOUN
ejpam-370	11	33	decomposition	decomposition	NOUN
ejpam-370	11	34	technique	technique	NOUN
ejpam-370	11	35	based	base	VERB
ejpam-370	11	36	on	on	ADP
ejpam-370	11	37	a	a	DET
ejpam-370	11	38	schur	schur	NOUN
ejpam-370	11	39	complement	complement	NOUN
ejpam-370	11	40	type	type	NOUN
ejpam-370	11	41	method	method	NOUN
ejpam-370	11	42	.	.	PUNCT
ejpam-370	12	1	also	also	ADV
ejpam-370	12	2	it	it	PRON
ejpam-370	12	3	has	have	AUX
ejpam-370	12	4	been	be	AUX
ejpam-370	12	5	said	say	VERB
ejpam-370	12	6	that	that	SCONJ
ejpam-370	12	7	this	this	DET
ejpam-370	12	8	method	method	NOUN
ejpam-370	12	9	costs	cost	VERB
ejpam-370	12	10	more	more	ADJ
ejpam-370	12	11	than	than	ADP
ejpam-370	12	12	the	the	DET
ejpam-370	12	13	standard	standard	ADJ
ejpam-370	12	14	schur	schur	PROPN
ejpam-370	12	15	complement	complement	PROPN
ejpam-370	12	16	method	method	NOUN
ejpam-370	12	17	and	and	CCONJ
ejpam-370	12	18	does	do	AUX
ejpam-370	12	19	not	not	PART
ejpam-370	12	20	decrease	decrease	VERB
ejpam-370	12	21	the	the	DET
ejpam-370	12	22	dimension	dimension	NOUN
ejpam-370	12	23	of	of	ADP
ejpam-370	12	24	the	the	DET
ejpam-370	12	25	linear	linear	PROPN
ejpam-370	12	26	systems	system	NOUN
ejpam-370	12	27	.	.	PUNCT
ejpam-370	13	1	so	so	ADV
ejpam-370	13	2	in	in	ADP
ejpam-370	13	3	[	[	X
ejpam-370	13	4	3	3	NUM
ejpam-370	13	5	]	]	PUNCT
ejpam-370	13	6	,	,	PUNCT
ejpam-370	13	7	the	the	DET
ejpam-370	13	8	authors	author	NOUN
ejpam-370	13	9	improved	improve	VERB
ejpam-370	13	10	ddm	ddm	NOUN
ejpam-370	13	11	and	and	CCONJ
ejpam-370	13	12	gave	give	VERB
ejpam-370	13	13	iterative	iterative	NOUN
ejpam-370	13	14	decreasing	decrease	VERB
ejpam-370	13	15	dimension	dimension	NOUN
ejpam-370	13	16	method	method	NOUN
ejpam-370	13	17	(	(	PUNCT
ejpam-370	13	18	iddm	iddm	PROPN
ejpam-370	13	19	)	)	PUNCT
ejpam-370	13	20	which	which	PRON
ejpam-370	13	21	decreases	decrease	VERB
ejpam-370	13	22	the	the	DET
ejpam-370	13	23	dimension	dimension	NOUN
ejpam-370	13	24	of	of	ADP
ejpam-370	13	25	the	the	DET
ejpam-370	13	26	linear	linear	PROPN
ejpam-370	13	27	systems	system	NOUN
ejpam-370	13	28	,	,	PUNCT
ejpam-370	13	29	one	one	NUM
ejpam-370	13	30	order	order	NOUN
ejpam-370	13	31	in	in	ADP
ejpam-370	13	32	every	every	DET
ejpam-370	13	33	step	step	NOUN
ejpam-370	13	34	without	without	ADP
ejpam-370	13	35	any	any	DET
ejpam-370	13	36	pre	pre	NOUN
ejpam-370	13	37	-	-	NOUN
ejpam-370	13	38	process	process	NOUN
ejpam-370	13	39	.	.	PUNCT
ejpam-370	14	1	∗corresponding	∗corresponde	VERB
ejpam-370	14	2	author	author	NOUN
ejpam-370	14	3	.	.	PUNCT
ejpam-370	15	1	email	email	NOUN
ejpam-370	15	2	addresses	address	NOUN
ejpam-370	15	3	:	:	PUNCT
ejpam-370	15	4	kaydin	kaydin	PROPN
ejpam-370	15	5	�	�	PROPN
ejpam-370	15	6	sel	sel	PROPN
ejpam-370	15	7	uk.edu.tr	uk.edu.tr	PROPN
ejpam-370	15	8	(	(	PUNCT
ejpam-370	15	9	k.	k.	PROPN
ejpam-370	15	10	aydın	aydın	PROPN
ejpam-370	15	11	)	)	PUNCT
ejpam-370	15	12	,	,	PUNCT
ejpam-370	15	13	g	g	PROPN
ejpam-370	15	14	kizilkan�ksu.edu.tr	kizilkan�ksu.edu.tr	PROPN
ejpam-370	15	15	(	(	PUNCT
ejpam-370	15	16	g.	g.	PROPN
ejpam-370	15	17	kızılkan),ao	kızılkan),ao	PROPN
ejpam-370	15	18	diken	diken	PROPN
ejpam-370	15	19	�	�	PROPN
ejpam-370	15	20	sel	sel	PROPN
ejpam-370	15	21	uk.edu.tr	uk.edu.tr	PROPN
ejpam-370	15	22	(	(	PUNCT
ejpam-370	15	23	a.	a.	NOUN
ejpam-370	15	24	çıbıkdiken	çıbıkdiken	VERB
ejpam-370	15	25	)	)	PUNCT
ejpam-370	15	26	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-370	16	1	819	819	NUM
ejpam-370	17	1	c	c	X
ejpam-370	17	2	©	©	PROPN
ejpam-370	17	3	2010	2010	NUM
ejpam-370	17	4	ejpam	ejpam	NOUN
ejpam-370	17	5	all	all	DET
ejpam-370	17	6	rights	right	NOUN
ejpam-370	17	7	reserved	reserve	VERB
ejpam-370	17	8	.	.	PUNCT
ejpam-370	18	1	k.	k.	PROPN
ejpam-370	18	2	aydın	aydın	PROPN
ejpam-370	18	3	,	,	PUNCT
ejpam-370	18	4	g.	g.	PROPN
ejpam-370	18	5	kızılkan	kızılkan	PROPN
ejpam-370	18	6	,	,	PUNCT
ejpam-370	18	7	a.	a.	PROPN
ejpam-370	18	8	çıbıkdiken	çıbıkdiken	VERB
ejpam-370	18	9	/	/	SYM
ejpam-370	18	10	eur	eur	PROPN
ejpam-370	18	11	.	.	PUNCT
ejpam-370	19	1	j.	j.	PROPN
ejpam-370	19	2	pure	pure	PROPN
ejpam-370	19	3	appl	appl	PROPN
ejpam-370	19	4	.	.	PROPN
ejpam-370	19	5	math	math	PROPN
ejpam-370	19	6	,	,	PUNCT
ejpam-370	19	7	3	3	NUM
ejpam-370	19	8	(	(	PUNCT
ejpam-370	19	9	2010	2010	NUM
ejpam-370	19	10	)	)	PUNCT
ejpam-370	19	11	,	,	PUNCT
ejpam-370	19	12	819	819	NUM
ejpam-370	19	13	-	-	SYM
ejpam-370	19	14	830	830	NUM
ejpam-370	19	15	820	820	NUM
ejpam-370	19	16	in	in	ADP
ejpam-370	19	17	this	this	DET
ejpam-370	19	18	study	study	NOUN
ejpam-370	19	19	;	;	PUNCT
ejpam-370	19	20	we	we	PRON
ejpam-370	19	21	have	have	AUX
ejpam-370	19	22	given	give	VERB
ejpam-370	19	23	a	a	DET
ejpam-370	19	24	generalization	generalization	NOUN
ejpam-370	19	25	of	of	ADP
ejpam-370	19	26	iddm	iddm	NOUN
ejpam-370	19	27	in	in	ADP
ejpam-370	19	28	[	[	X
ejpam-370	19	29	3	3	NUM
ejpam-370	19	30	]	]	PUNCT
ejpam-370	19	31	for	for	ADP
ejpam-370	19	32	the	the	DET
ejpam-370	19	33	solution	solution	NOUN
ejpam-370	19	34	of	of	ADP
ejpam-370	19	35	the	the	DET
ejpam-370	19	36	linear	linear	ADJ
ejpam-370	19	37	algebraic	algebraic	ADJ
ejpam-370	19	38	system	system	NOUN
ejpam-370	19	39	(	(	PUNCT
ejpam-370	19	40	1	1	X
ejpam-370	19	41	)	)	PUNCT
ejpam-370	19	42	taking	take	VERB
ejpam-370	19	43	a	a	PRON
ejpam-370	19	44	is	be	AUX
ejpam-370	19	45	any	any	DET
ejpam-370	19	46	m	m	ADJ
ejpam-370	19	47	×n	×n	ADJ
ejpam-370	19	48	matrix	matrix	NOUN
ejpam-370	19	49	instead	instead	ADV
ejpam-370	19	50	of	of	ADP
ejpam-370	19	51	a	a	DET
ejpam-370	19	52	n	n	NUM
ejpam-370	19	53	×	×	NOUN
ejpam-370	19	54	n	n	CCONJ
ejpam-370	19	55	regular	regular	ADJ
ejpam-370	19	56	matrix	matrix	NOUN
ejpam-370	19	57	.	.	PUNCT
ejpam-370	20	1	in	in	ADP
ejpam-370	20	2	section	section	NOUN
ejpam-370	20	3	2	2	NUM
ejpam-370	20	4	;	;	PUNCT
ejpam-370	20	5	we	we	PRON
ejpam-370	20	6	have	have	AUX
ejpam-370	20	7	given	give	VERB
ejpam-370	20	8	symbols	symbol	NOUN
ejpam-370	20	9	and	and	CCONJ
ejpam-370	20	10	we	we	PRON
ejpam-370	20	11	have	have	AUX
ejpam-370	20	12	summarized	summarize	VERB
ejpam-370	20	13	iddm	iddm	NOUN
ejpam-370	20	14	,	,	PUNCT
ejpam-370	20	15	then	then	ADV
ejpam-370	20	16	we	we	PRON
ejpam-370	20	17	have	have	AUX
ejpam-370	20	18	given	give	VERB
ejpam-370	20	19	generalized	generalized	ADJ
ejpam-370	20	20	iterative	iterative	NOUN
ejpam-370	20	21	decreasing	decrease	VERB
ejpam-370	20	22	dimension	dimension	NOUN
ejpam-370	20	23	method	method	NOUN
ejpam-370	20	24	(	(	PUNCT
ejpam-370	20	25	giddm	giddm	NOUN
ejpam-370	20	26	)	)	PUNCT
ejpam-370	20	27	improving	improve	VERB
ejpam-370	20	28	the	the	DET
ejpam-370	20	29	method	method	NOUN
ejpam-370	20	30	in	in	ADP
ejpam-370	20	31	[	[	X
ejpam-370	20	32	3	3	NUM
ejpam-370	20	33	]	]	PUNCT
ejpam-370	20	34	.	.	PUNCT
ejpam-370	21	1	in	in	ADP
ejpam-370	21	2	section	section	NOUN
ejpam-370	21	3	3	3	NUM
ejpam-370	21	4	,	,	PUNCT
ejpam-370	21	5	we	we	PRON
ejpam-370	21	6	have	have	AUX
ejpam-370	21	7	given	give	VERB
ejpam-370	21	8	generalized	generalized	ADJ
ejpam-370	21	9	iterative	iterative	NOUN
ejpam-370	21	10	decreasing	decrease	VERB
ejpam-370	21	11	dimension	dimension	NOUN
ejpam-370	21	12	algorithm	algorithm	NOUN
ejpam-370	21	13	(	(	PUNCT
ejpam-370	21	14	gidda	gidda	NOUN
ejpam-370	21	15	)	)	PUNCT
ejpam-370	21	16	based	base	VERB
ejpam-370	21	17	on	on	ADP
ejpam-370	21	18	giddm	giddm	NOUN
ejpam-370	21	19	and	and	CCONJ
ejpam-370	21	20	some	some	DET
ejpam-370	21	21	symbolic	symbolic	ADJ
ejpam-370	21	22	and	and	CCONJ
ejpam-370	21	23	numerical	numerical	ADJ
ejpam-370	21	24	examples	example	NOUN
ejpam-370	21	25	.	.	PUNCT
ejpam-370	22	1	we	we	PRON
ejpam-370	22	2	have	have	AUX
ejpam-370	22	3	also	also	ADV
ejpam-370	22	4	given	give	VERB
ejpam-370	22	5	a	a	DET
ejpam-370	22	6	maple	maple	NOUN
ejpam-370	22	7	procedure	procedure	NOUN
ejpam-370	22	8	for	for	ADP
ejpam-370	22	9	gidda	gidda	NOUN
ejpam-370	22	10	in	in	ADP
ejpam-370	22	11	section	section	NOUN
ejpam-370	22	12	4	4	NUM
ejpam-370	22	13	.	.	NOUN
ejpam-370	22	14	2	2	NUM
ejpam-370	22	15	.	.	NUM
ejpam-370	22	16	generalized	generalize	VERB
ejpam-370	22	17	iterative	iterative	NOUN
ejpam-370	22	18	decreasing	decrease	VERB
ejpam-370	22	19	dimension	dimension	NOUN
ejpam-370	22	20	method	method	NOUN
ejpam-370	22	21	(	(	PUNCT
ejpam-370	22	22	giddm	giddm	NOUN
ejpam-370	22	23	)	)	PUNCT
ejpam-370	22	24	in	in	ADP
ejpam-370	22	25	this	this	DET
ejpam-370	22	26	section	section	NOUN
ejpam-370	22	27	,	,	PUNCT
ejpam-370	22	28	after	after	SCONJ
ejpam-370	22	29	introduce	introduce	ADJ
ejpam-370	22	30	symbols	symbol	NOUN
ejpam-370	22	31	used	use	VERB
ejpam-370	22	32	in	in	ADP
ejpam-370	22	33	this	this	DET
ejpam-370	22	34	study	study	NOUN
ejpam-370	22	35	and	and	CCONJ
ejpam-370	22	36	iddm	iddm	PROPN
ejpam-370	22	37	given	give	VERB
ejpam-370	22	38	in	in	ADP
ejpam-370	22	39	[	[	X
ejpam-370	22	40	3	3	X
ejpam-370	22	41	]	]	X
ejpam-370	22	42	we	we	PRON
ejpam-370	22	43	are	be	AUX
ejpam-370	22	44	going	go	VERB
ejpam-370	22	45	to	to	PART
ejpam-370	22	46	give	give	VERB
ejpam-370	22	47	giddm	giddm	NOUN
ejpam-370	22	48	which	which	PRON
ejpam-370	22	49	is	be	AUX
ejpam-370	22	50	the	the	DET
ejpam-370	22	51	generalization	generalization	NOUN
ejpam-370	22	52	of	of	ADP
ejpam-370	22	53	iddm	iddm	PROPN
ejpam-370	22	54	.	.	PUNCT
ejpam-370	23	1	the	the	DET
ejpam-370	23	2	symbols	symbol	NOUN
ejpam-370	23	3	will	will	AUX
ejpam-370	23	4	be	be	AUX
ejpam-370	23	5	used	use	VERB
ejpam-370	23	6	similar	similar	ADJ
ejpam-370	23	7	as	as	ADP
ejpam-370	23	8	in	in	ADP
ejpam-370	23	9	[	[	X
ejpam-370	23	10	3	3	NUM
ejpam-370	23	11	]	]	PUNCT
ejpam-370	23	12	in	in	ADP
ejpam-370	23	13	this	this	DET
ejpam-370	23	14	study	study	NOUN
ejpam-370	23	15	.	.	PUNCT
ejpam-370	24	1	2.1	2.1	NUM
ejpam-370	24	2	.	.	PUNCT
ejpam-370	25	1	symbols	symbol	NOUN
ejpam-370	25	2	let	let	VERB
ejpam-370	25	3	us	we	PRON
ejpam-370	25	4	give	give	VERB
ejpam-370	25	5	some	some	DET
ejpam-370	25	6	symbols	symbol	NOUN
ejpam-370	25	7	and	and	CCONJ
ejpam-370	25	8	explanations	explanation	NOUN
ejpam-370	25	9	used	use	VERB
ejpam-370	25	10	in	in	ADP
ejpam-370	25	11	procedure	procedure	NOUN
ejpam-370	25	12	.	.	PUNCT
ejpam-370	26	1	n	n	X
ejpam-370	26	2	:	:	PUNCT
ejpam-370	26	3	n	n	CCONJ
ejpam-370	26	4	=	=	PUNCT
ejpam-370	26	5	min{m	min{m	PROPN
ejpam-370	26	6	,	,	PUNCT
ejpam-370	26	7	n	n	CCONJ
ejpam-370	26	8	}	}	PUNCT
ejpam-370	26	9	k	k	NOUN
ejpam-370	26	10	:	:	PUNCT
ejpam-370	27	1	k	k	X
ejpam-370	27	2	=	=	SYM
ejpam-370	27	3	1(1)n	1(1)n	NUM
ejpam-370	27	4	,	,	PUNCT
ejpam-370	27	5	(	(	PUNCT
ejpam-370	27	6	k	k	NOUN
ejpam-370	27	7	=	=	SYM
ejpam-370	27	8	1	1	NUM
ejpam-370	27	9	,	,	PUNCT
ejpam-370	27	10	2	2	NUM
ejpam-370	27	11	,	,	PUNCT
ejpam-370	27	12	...	...	PUNCT
ejpam-370	27	13	,	,	PUNCT
ejpam-370	27	14	n	n	CCONJ
ejpam-370	27	15	)	)	PUNCT
ejpam-370	27	16	iteration	iteration	NOUN
ejpam-370	27	17	step	step	NOUN
ejpam-370	27	18	a(k	a(k	PROPN
ejpam-370	27	19	)	)	PUNCT
ejpam-370	27	20	:	:	PUNCT
ejpam-370	27	21	mk	mk	PROPN
ejpam-370	27	22	×nk	×nk	PROPN
ejpam-370	27	23	reduced	reduce	VERB
ejpam-370	27	24	coefficient	coefficient	NOUN
ejpam-370	27	25	matrix	matrix	NOUN
ejpam-370	27	26	a(k)ps	a(k)ps	PROPN
ejpam-370	27	27	:	:	PUNCT
ejpam-370	27	28	a	a	DET
ejpam-370	27	29	(	(	PUNCT
ejpam-370	27	30	k	k	NOUN
ejpam-370	27	31	)	)	PUNCT
ejpam-370	27	32	i	i	PRON
ejpam-370	27	33	j	j	PROPN
ejpam-370	28	1	6=	6=	ADP
ejpam-370	28	2	0	0	NUM
ejpam-370	28	3	which	which	PRON
ejpam-370	28	4	is	be	AUX
ejpam-370	28	5	the	the	DET
ejpam-370	28	6	first	first	ADJ
ejpam-370	28	7	non	non	ADJ
ejpam-370	28	8	-	-	ADJ
ejpam-370	28	9	zero	zero	NUM
ejpam-370	28	10	element	element	NOUN
ejpam-370	28	11	of	of	ADP
ejpam-370	28	12	matrix	matrix	NOUN
ejpam-370	28	13	a(k	a(k	NUM
ejpam-370	28	14	)	)	PUNCT
ejpam-370	28	15	pk	pk	NOUN
ejpam-370	28	16	:	:	PUNCT
ejpam-370	28	17	p	p	X
ejpam-370	28	18	which	which	PRON
ejpam-370	28	19	is	be	AUX
ejpam-370	28	20	the	the	DET
ejpam-370	28	21	number	number	NOUN
ejpam-370	28	22	in	in	ADP
ejpam-370	28	23	a(k)ps	a(k)ps	PROPN
ejpam-370	28	24	6=	6=	ADP
ejpam-370	28	25	0	0	NUM
ejpam-370	28	26	mk	mk	NOUN
ejpam-370	28	27	:	:	PUNCT
ejpam-370	28	28	mk	mk	X
ejpam-370	29	1	=	=	NOUN
ejpam-370	29	2	m	m	VERB
ejpam-370	29	3	−	−	PROPN
ejpam-370	29	4	k−1	k−1	PROPN
ejpam-370	29	5	∑	∑	PROPN
ejpam-370	29	6	i=1	i=1	PROPN
ejpam-370	29	7	pi	pi	NOUN
ejpam-370	29	8	;	;	PUNCT
ejpam-370	29	9	0	0	NUM
ejpam-370	29	10	∑	∑	PUNCT
ejpam-370	29	11	i=1	i=1	PROPN
ejpam-370	29	12	pi	pi	NOUN
ejpam-370	29	13	=	=	SYM
ejpam-370	29	14	0	0	NUM
ejpam-370	30	1	nk	nk	NOUN
ejpam-370	30	2	:	:	PUNCT
ejpam-370	31	1	nk	nk	PROPN
ejpam-370	31	2	=	=	PROPN
ejpam-370	31	3	n	n	CCONJ
ejpam-370	31	4	−	−	PROPN
ejpam-370	31	5	k+	k+	NOUN
ejpam-370	31	6	1	1	NUM
ejpam-370	31	7	x	x	SYM
ejpam-370	31	8	(	(	PUNCT
ejpam-370	31	9	k	k	NOUN
ejpam-370	31	10	)	)	PUNCT
ejpam-370	31	11	:	:	PUNCT
ejpam-370	32	1	nk	nk	PROPN
ejpam-370	32	2	solution	solution	NOUN
ejpam-370	32	3	vector	vector	NOUN
ejpam-370	32	4	of	of	ADP
ejpam-370	32	5	reduced	reduce	VERB
ejpam-370	32	6	system	system	NOUN
ejpam-370	32	7	f	f	PROPN
ejpam-370	32	8	(	(	PUNCT
ejpam-370	32	9	k	k	NOUN
ejpam-370	32	10	)	)	PUNCT
ejpam-370	32	11	:	:	PUNCT
ejpam-370	33	1	mk	mk	PROPN
ejpam-370	33	2	right	right	ADJ
ejpam-370	33	3	side	side	NOUN
ejpam-370	33	4	vector	vector	NOUN
ejpam-370	33	5	of	of	ADP
ejpam-370	33	6	reduced	reduced	ADJ
ejpam-370	33	7	system	system	NOUN
ejpam-370	33	8	a	a	DET
ejpam-370	33	9	(	(	PUNCT
ejpam-370	33	10	k	k	NOUN
ejpam-370	33	11	)	)	PUNCT
ejpam-370	33	12	i	i	PRON
ejpam-370	33	13	j	j	NOUN
ejpam-370	33	14	:	:	PUNCT
ejpam-370	33	15	(	(	PUNCT
ejpam-370	33	16	i	i	PROPN
ejpam-370	33	17	,	,	PUNCT
ejpam-370	33	18	j	j	PROPN
ejpam-370	33	19	)	)	PUNCT
ejpam-370	33	20	element	element	NOUN
ejpam-370	33	21	of	of	ADP
ejpam-370	33	22	matrix	matrix	NOUN
ejpam-370	33	23	a(k	a(k	NUM
ejpam-370	33	24	)	)	PUNCT
ejpam-370	33	25	x	x	X
ejpam-370	33	26	(	(	PUNCT
ejpam-370	33	27	k	k	NOUN
ejpam-370	33	28	)	)	PUNCT
ejpam-370	33	29	i	i	PRON
ejpam-370	33	30	:	:	PUNCT
ejpam-370	34	1	i	i	PRON
ejpam-370	34	2	th	th	INTJ
ejpam-370	34	3	element	element	NOUN
ejpam-370	34	4	of	of	ADP
ejpam-370	34	5	vector	vector	NOUN
ejpam-370	34	6	x	x	INTJ
ejpam-370	34	7	(	(	PUNCT
ejpam-370	34	8	k	k	NOUN
ejpam-370	34	9	)	)	PUNCT
ejpam-370	34	10	f	f	NOUN
ejpam-370	34	11	(	(	PUNCT
ejpam-370	34	12	k	k	X
ejpam-370	34	13	)	)	PUNCT
ejpam-370	35	1	i	i	PRON
ejpam-370	35	2	:	:	PUNCT
ejpam-370	35	3	i	i	PRON
ejpam-370	35	4	th	th	INTJ
ejpam-370	35	5	element	element	NOUN
ejpam-370	35	6	of	of	ADP
ejpam-370	35	7	vector	vector	NOUN
ejpam-370	35	8	f	f	PROPN
ejpam-370	35	9	(	(	PUNCT
ejpam-370	35	10	k	k	NOUN
ejpam-370	35	11	)	)	PUNCT
ejpam-370	35	12	u(k	u(k	PROPN
ejpam-370	35	13	)	)	PUNCT
ejpam-370	35	14	:	:	PUNCT
ejpam-370	35	15	vector	vector	NOUN
ejpam-370	35	16	composed	compose	VERB
ejpam-370	35	17	of	of	ADP
ejpam-370	35	18	f	f	PROPN
ejpam-370	35	19	(	(	PUNCT
ejpam-370	35	20	k)p	k)p	PROPN
ejpam-370	35	21	element	element	NOUN
ejpam-370	35	22	of	of	ADP
ejpam-370	35	23	vector	vector	NOUN
ejpam-370	35	24	f	f	PROPN
ejpam-370	35	25	(	(	PUNCT
ejpam-370	35	26	k	k	NOUN
ejpam-370	35	27	)	)	PUNCT
ejpam-370	35	28	v(k	v(k	PROPN
ejpam-370	35	29	)	)	PUNCT
ejpam-370	35	30	:	:	PUNCT
ejpam-370	35	31	vector	vector	NOUN
ejpam-370	35	32	composed	compose	VERB
ejpam-370	35	33	of	of	ADP
ejpam-370	35	34	f	f	PROPN
ejpam-370	35	35	(	(	PUNCT
ejpam-370	35	36	k	k	X
ejpam-370	35	37	)	)	PUNCT
ejpam-370	35	38	i	i	PRON
ejpam-370	35	39	,	,	PUNCT
ejpam-370	35	40	i	i	PRON
ejpam-370	35	41	=	=	SYM
ejpam-370	35	42	p+	p+	VERB
ejpam-370	35	43	1(1)mk	1(1)mk	NUM
ejpam-370	35	44	element	element	NOUN
ejpam-370	35	45	of	of	ADP
ejpam-370	35	46	vector	vector	NOUN
ejpam-370	35	47	f	f	PROPN
ejpam-370	35	48	(	(	PUNCT
ejpam-370	35	49	k	k	NOUN
ejpam-370	35	50	)	)	PUNCT
ejpam-370	35	51	a	a	DET
ejpam-370	35	52	(	(	PUNCT
ejpam-370	35	53	k	k	NOUN
ejpam-370	35	54	)	)	PUNCT
ejpam-370	35	55	1	1	NUM
ejpam-370	35	56	:	:	PUNCT
ejpam-370	35	57	matrix	matrix	NOUN
ejpam-370	35	58	composed	compose	VERB
ejpam-370	35	59	of	of	ADP
ejpam-370	35	60	first	first	ADJ
ejpam-370	35	61	non	non	ADJ
ejpam-370	35	62	-	-	ADJ
ejpam-370	35	63	zero	zero	NUM
ejpam-370	35	64	row	row	NOUN
ejpam-370	35	65	vector	vector	NOUN
ejpam-370	35	66	of	of	ADP
ejpam-370	35	67	matrix	matrix	NOUN
ejpam-370	35	68	a(k	a(k	NUM
ejpam-370	35	69	)	)	PUNCT
ejpam-370	35	70	a	a	DET
ejpam-370	35	71	(	(	PUNCT
ejpam-370	35	72	k	k	NOUN
ejpam-370	35	73	)	)	PUNCT
ejpam-370	35	74	2	2	NUM
ejpam-370	35	75	:	:	PUNCT
ejpam-370	35	76	matrix	matrix	NOUN
ejpam-370	35	77	composed	compose	VERB
ejpam-370	35	78	remain	remain	VERB
ejpam-370	35	79	line	line	NOUN
ejpam-370	35	80	vector	vector	NOUN
ejpam-370	35	81	of	of	ADP
ejpam-370	35	82	matrix	matrix	NOUN
ejpam-370	35	83	a(k	a(k	NUM
ejpam-370	35	84	)	)	PUNCT
ejpam-370	35	85	x	x	X
ejpam-370	36	1	(	(	PUNCT
ejpam-370	36	2	k	k	NOUN
ejpam-370	36	3	)	)	PUNCT
ejpam-370	36	4	0	0	NUM
ejpam-370	37	1	:	:	PUNCT
ejpam-370	37	2	special	special	ADJ
ejpam-370	37	3	solution	solution	NOUN
ejpam-370	37	4	vector	vector	NOUN
ejpam-370	37	5	of	of	ADP
ejpam-370	37	6	a	a	DET
ejpam-370	37	7	(	(	PUNCT
ejpam-370	37	8	k	k	NOUN
ejpam-370	37	9	)	)	PUNCT
ejpam-370	37	10	1	1	NUM
ejpam-370	37	11	x	x	SYM
ejpam-370	37	12	(	(	PUNCT
ejpam-370	37	13	k	k	NOUN
ejpam-370	37	14	)	)	PUNCT
ejpam-370	37	15	=	=	SYM
ejpam-370	37	16	u(k	u(k	PROPN
ejpam-370	37	17	)	)	PUNCT
ejpam-370	37	18	r(k	r(k	PROPN
ejpam-370	37	19	)	)	PUNCT
ejpam-370	37	20	:	:	PUNCT
ejpam-370	37	21	base	base	NOUN
ejpam-370	37	22	matrix	matrix	NOUN
ejpam-370	37	23	of	of	ADP
ejpam-370	37	24	solution	solution	NOUN
ejpam-370	37	25	space	space	NOUN
ejpam-370	37	26	of	of	ADP
ejpam-370	37	27	a	a	DET
ejpam-370	37	28	(	(	PUNCT
ejpam-370	37	29	k	k	NOUN
ejpam-370	37	30	)	)	PUNCT
ejpam-370	37	31	1	1	NUM
ejpam-370	37	32	x	x	SYM
ejpam-370	37	33	(	(	PUNCT
ejpam-370	37	34	k	k	NOUN
ejpam-370	37	35	)	)	PUNCT
ejpam-370	37	36	=	=	SYM
ejpam-370	37	37	0	0	NUM
ejpam-370	38	1	note	note	NOUN
ejpam-370	38	2	:	:	PUNCT
ejpam-370	38	3	if	if	SCONJ
ejpam-370	38	4	a	a	PRON
ejpam-370	38	5	is	be	AUX
ejpam-370	38	6	a	a	DET
ejpam-370	38	7	n×n	n×n	PROPN
ejpam-370	38	8	-regular	-regular	ADJ
ejpam-370	38	9	matrix	matrix	NOUN
ejpam-370	38	10	,	,	PUNCT
ejpam-370	38	11	then	then	ADV
ejpam-370	38	12	it	it	PRON
ejpam-370	38	13	is	be	AUX
ejpam-370	38	14	clear	clear	ADJ
ejpam-370	38	15	that	that	SCONJ
ejpam-370	38	16	mk	mk	NOUN
ejpam-370	38	17	=	=	SYM
ejpam-370	38	18	nk	nk	PROPN
ejpam-370	38	19	=	=	PUNCT
ejpam-370	38	20	n−k+1	n−k+1	PROPN
ejpam-370	38	21	for	for	ADP
ejpam-370	38	22	k	k	PROPN
ejpam-370	38	23	=	=	SYM
ejpam-370	38	24	1(1)n	1(1)n	PROPN
ejpam-370	38	25	.	.	PUNCT
ejpam-370	39	1	k.	k.	PROPN
ejpam-370	39	2	aydın	aydın	PROPN
ejpam-370	39	3	,	,	PUNCT
ejpam-370	39	4	g.	g.	PROPN
ejpam-370	39	5	kızılkan	kızılkan	PROPN
ejpam-370	39	6	,	,	PUNCT
ejpam-370	39	7	a.	a.	PROPN
ejpam-370	39	8	çıbıkdiken	çıbıkdiken	VERB
ejpam-370	39	9	/	/	SYM
ejpam-370	39	10	eur	eur	PROPN
ejpam-370	39	11	.	.	PUNCT
ejpam-370	40	1	j.	j.	PROPN
ejpam-370	40	2	pure	pure	PROPN
ejpam-370	40	3	appl	appl	PROPN
ejpam-370	40	4	.	.	PROPN
ejpam-370	40	5	math	math	PROPN
ejpam-370	40	6	,	,	PUNCT
ejpam-370	40	7	3	3	NUM
ejpam-370	40	8	(	(	PUNCT
ejpam-370	40	9	2010	2010	NUM
ejpam-370	40	10	)	)	PUNCT
ejpam-370	40	11	,	,	PUNCT
ejpam-370	40	12	819	819	NUM
ejpam-370	40	13	-	-	SYM
ejpam-370	40	14	830	830	NUM
ejpam-370	40	15	821	821	NUM
ejpam-370	40	16	2.2	2.2	NUM
ejpam-370	40	17	.	.	PUNCT
ejpam-370	41	1	iddm	iddm	PROPN
ejpam-370	41	2	let	let	VERB
ejpam-370	41	3	us	we	PRON
ejpam-370	41	4	summarize	summarize	VERB
ejpam-370	41	5	iddm	iddm	NOUN
ejpam-370	41	6	given	give	VERB
ejpam-370	41	7	in	in	ADP
ejpam-370	41	8	[	[	X
ejpam-370	41	9	3	3	NUM
ejpam-370	41	10	]	]	PUNCT
ejpam-370	41	11	.	.	PUNCT
ejpam-370	42	1	consider	consider	VERB
ejpam-370	42	2	a	a	DET
ejpam-370	42	3	system	system	NOUN
ejpam-370	42	4	of	of	ADP
ejpam-370	42	5	linear	linear	ADJ
ejpam-370	42	6	algebraic	algebraic	ADJ
ejpam-370	42	7	equation	equation	NOUN
ejpam-370	42	8	ax	ax	NOUN
ejpam-370	42	9	=	=	PUNCT
ejpam-370	42	10	f	f	PROPN
ejpam-370	42	11	;	;	PUNCT
ejpam-370	42	12	a	a	PRON
ejpam-370	42	13	-	-	PUNCT
ejpam-370	42	14	regular	regular	ADJ
ejpam-370	42	15	(	(	PUNCT
ejpam-370	42	16	2	2	NUM
ejpam-370	42	17	)	)	PUNCT
ejpam-370	42	18	where	where	SCONJ
ejpam-370	42	19	a	a	PRON
ejpam-370	42	20	is	be	AUX
ejpam-370	42	21	a	a	DET
ejpam-370	42	22	n	n	NUM
ejpam-370	42	23	×	×	NOUN
ejpam-370	42	24	n	n	PRON
ejpam-370	42	25	-matrix	-matrix	NOUN
ejpam-370	42	26	,	,	PUNCT
ejpam-370	42	27	x	x	PUNCT
ejpam-370	42	28	and	and	CCONJ
ejpam-370	42	29	f	f	PROPN
ejpam-370	42	30	are	be	AUX
ejpam-370	42	31	n	n	PRON
ejpam-370	42	32	-vectors	-vector	NOUN
ejpam-370	42	33	.	.	PUNCT
ejpam-370	43	1	suppose	suppose	VERB
ejpam-370	43	2	that	that	SCONJ
ejpam-370	43	3	k	k	PROPN
ejpam-370	43	4	=	=	PUNCT
ejpam-370	43	5	1(1)n	1(1)n	PROPN
ejpam-370	43	6	is	be	AUX
ejpam-370	43	7	the	the	DET
ejpam-370	43	8	iteration	iteration	NOUN
ejpam-370	43	9	step	step	NOUN
ejpam-370	43	10	,	,	PUNCT
ejpam-370	43	11	a(k	a(k	NUM
ejpam-370	43	12	)	)	PUNCT
ejpam-370	43	13	is	be	AUX
ejpam-370	43	14	a	a	DET
ejpam-370	43	15	nk	nk	PROPN
ejpam-370	43	16	×	×	PROPN
ejpam-370	43	17	nk	nk	PROPN
ejpam-370	43	18	coefficient	coefficient	NOUN
ejpam-370	43	19	matrix	matrix	NOUN
ejpam-370	43	20	of	of	ADP
ejpam-370	43	21	reduced	reduce	VERB
ejpam-370	43	22	system	system	NOUN
ejpam-370	43	23	and	and	CCONJ
ejpam-370	43	24	f	f	PROPN
ejpam-370	43	25	(	(	PUNCT
ejpam-370	43	26	k	k	NOUN
ejpam-370	43	27	)	)	PUNCT
ejpam-370	43	28	is	be	AUX
ejpam-370	43	29	a	a	DET
ejpam-370	43	30	right	right	ADJ
ejpam-370	43	31	side	side	NOUN
ejpam-370	43	32	vector	vector	NOUN
ejpam-370	43	33	of	of	ADP
ejpam-370	43	34	reduced	reduce	VERB
ejpam-370	43	35	system	system	NOUN
ejpam-370	43	36	as	as	ADP
ejpam-370	43	37	following	follow	VERB
ejpam-370	43	38	a(k	a(k	NUM
ejpam-370	43	39	)	)	PUNCT
ejpam-370	44	1	=	=	PUNCT
ejpam-370	44	2	(	(	PUNCT
ejpam-370	44	3	a	a	PRON
ejpam-370	44	4	k	k	X
ejpam-370	44	5	=	=	SYM
ejpam-370	44	6	1	1	NUM
ejpam-370	44	7	,	,	PUNCT
ejpam-370	44	8	a	a	DET
ejpam-370	44	9	(	(	PUNCT
ejpam-370	44	10	k−1	k−1	PROPN
ejpam-370	44	11	)	)	PUNCT
ejpam-370	44	12	2	2	NUM
ejpam-370	44	13	r(k−1	r(k−1	NOUN
ejpam-370	44	14	)	)	PUNCT
ejpam-370	44	15	k	k	NOUN
ejpam-370	45	1	=	=	SYM
ejpam-370	45	2	2(1)n	2(1)n	NUM
ejpam-370	45	3	;	;	PUNCT
ejpam-370	45	4	f	f	PROPN
ejpam-370	45	5	(	(	PUNCT
ejpam-370	45	6	k	k	NOUN
ejpam-370	45	7	)	)	PUNCT
ejpam-370	45	8	=	=	PUNCT
ejpam-370	46	1	(	(	PUNCT
ejpam-370	46	2	f	f	X
ejpam-370	46	3	k	k	NOUN
ejpam-370	46	4	=	=	SYM
ejpam-370	46	5	1	1	NUM
ejpam-370	46	6	,	,	PUNCT
ejpam-370	46	7	v(k−1)−	v(k−1)−	NOUN
ejpam-370	46	8	a	a	DET
ejpam-370	46	9	(	(	PUNCT
ejpam-370	46	10	k−1	k−1	PROPN
ejpam-370	46	11	)	)	PUNCT
ejpam-370	46	12	2	2	NUM
ejpam-370	46	13	x	x	X
ejpam-370	46	14	(	(	PUNCT
ejpam-370	46	15	k−1	k−1	PROPN
ejpam-370	46	16	)	)	PUNCT
ejpam-370	46	17	0	0	PUNCT
ejpam-370	47	1	k	k	NOUN
ejpam-370	47	2	=	=	SYM
ejpam-370	47	3	2(1)n	2(1)n	NUM
ejpam-370	47	4	.	.	PUNCT
ejpam-370	48	1	x	x	X
ejpam-370	48	2	(	(	PUNCT
ejpam-370	48	3	k	k	NOUN
ejpam-370	48	4	)	)	PUNCT
ejpam-370	48	5	0	0	NUM
ejpam-370	48	6	is	be	AUX
ejpam-370	48	7	a	a	DET
ejpam-370	48	8	special	special	ADJ
ejpam-370	48	9	solution	solution	NOUN
ejpam-370	48	10	as	as	ADP
ejpam-370	48	11	x	x	X
ejpam-370	48	12	(	(	PUNCT
ejpam-370	48	13	k	k	NOUN
ejpam-370	48	14	)	)	PUNCT
ejpam-370	48	15	0	0	NUM
ejpam-370	49	1	=	=	SYM
ejpam-370	49	2	�	�	PROPN
ejpam-370	49	3	0	0	NUM
ejpam-370	49	4	...	...	PUNCT
ejpam-370	49	5	0	0	NUM
ejpam-370	50	1	f	f	NOUN
ejpam-370	50	2	(	(	PUNCT
ejpam-370	50	3	k	k	NOUN
ejpam-370	50	4	)	)	PUNCT
ejpam-370	50	5	1	1	NUM
ejpam-370	50	6	a	a	DET
ejpam-370	50	7	(	(	PUNCT
ejpam-370	50	8	k	k	NOUN
ejpam-370	50	9	)	)	PUNCT
ejpam-370	50	10	1s	1	NOUN
ejpam-370	50	11	0	0	NUM
ejpam-370	50	12	...	...	SYM
ejpam-370	50	13	0	0	NUM
ejpam-370	51	1	�	�	PROPN
ejpam-370	51	2	t	t	PROPN
ejpam-370	51	3	where	where	SCONJ
ejpam-370	51	4	a	a	DET
ejpam-370	51	5	(	(	PUNCT
ejpam-370	51	6	k	k	NOUN
ejpam-370	51	7	)	)	PUNCT
ejpam-370	51	8	1s	1s	PROPN
ejpam-370	51	9	6=	6=	NUM
ejpam-370	51	10	0	0	NUM
ejpam-370	51	11	,	,	PUNCT
ejpam-370	51	12	(	(	PUNCT
ejpam-370	51	13	1≤	1≤	X
ejpam-370	51	14	s	s	PART
ejpam-370	51	15	≤	≤	PROPN
ejpam-370	51	16	nk	nk	PROPN
ejpam-370	51	17	)	)	PUNCT
ejpam-370	51	18	which	which	PRON
ejpam-370	51	19	is	be	AUX
ejpam-370	51	20	the	the	DET
ejpam-370	51	21	first	first	ADJ
ejpam-370	51	22	non	non	ADJ
ejpam-370	51	23	-	-	ADJ
ejpam-370	51	24	zero	zero	NUM
ejpam-370	51	25	element	element	NOUN
ejpam-370	51	26	of	of	ADP
ejpam-370	51	27	matrix	matrix	NOUN
ejpam-370	51	28	a	a	DET
ejpam-370	51	29	(	(	PUNCT
ejpam-370	51	30	k	k	NOUN
ejpam-370	51	31	)	)	PUNCT
ejpam-370	51	32	1	1	NUM
ejpam-370	51	33	and	and	CCONJ
ejpam-370	51	34	r(k	r(k	PROPN
ejpam-370	51	35	)	)	PUNCT
ejpam-370	51	36	=	=	PRON
ejpam-370	51	37			PROPN
ejpam-370	51	38			X
ejpam-370	51	39			PROPN
ejpam-370	51	40			PROPN
ejpam-370	51	41			PROPN
ejpam-370	51	42			PROPN
ejpam-370	51	43			PROPN
ejpam-370	51	44			PROPN
ejpam-370	51	45			PROPN
ejpam-370	51	46			PROPN
ejpam-370	51	47			NOUN
ejpam-370	51	48			PROPN
ejpam-370	51	49			PROPN
ejpam-370	51	50			PROPN
ejpam-370	51	51			PROPN
ejpam-370	51	52			PROPN
ejpam-370	51	53			PROPN
ejpam-370	51	54			PROPN
ejpam-370	51	55			PROPN
ejpam-370	51	56			PROPN
ejpam-370	51	57			NOUN
ejpam-370	51	58	r	r	NOUN
ejpam-370	51	59	(	(	PUNCT
ejpam-370	51	60	k	k	NOUN
ejpam-370	51	61	)	)	PUNCT
ejpam-370	51	62	1×(nk−1	1×(nk−1	NUM
ejpam-370	51	63	)	)	PUNCT
ejpam-370	51	64	i(nk−1)×(nk−1	i(nk−1)×(nk−1	PROPN
ejpam-370	51	65	)	)	PUNCT
ejpam-370	51	66	!	!	PUNCT
ejpam-370	52	1	s	s	PART
ejpam-370	53	1	=	=	SYM
ejpam-370	53	2	1	1	NUM
ejpam-370	53	3	,	,	PUNCT
ejpam-370	53	4			NOUN
ejpam-370	53	5			NOUN
ejpam-370	53	6			NOUN
ejpam-370	53	7			NOUN
ejpam-370	53	8	i(s−1)×(s−1	i(s−1)×(s−1	PROPN
ejpam-370	53	9	)	)	PUNCT
ejpam-370	53	10	0(s−1)×(nk−s	0(s−1)×(nk−s	NUM
ejpam-370	53	11	)	)	PUNCT
ejpam-370	53	12	01×(s−1	01×(s−1	NUM
ejpam-370	53	13	)	)	PUNCT
ejpam-370	53	14	r	r	NOUN
ejpam-370	53	15	(	(	PUNCT
ejpam-370	53	16	k	k	NOUN
ejpam-370	53	17	)	)	PUNCT
ejpam-370	53	18	1×(nk−s	1×(nk−s	NUM
ejpam-370	53	19	)	)	PUNCT
ejpam-370	53	20	0(nk−s)×(s−1	0(nk−s)×(s−1	NOUN
ejpam-370	53	21	)	)	PUNCT
ejpam-370	53	22	i(nk−s)×(nk−s	i(nk−s)×(nk−s	PROPN
ejpam-370	53	23	)	)	PUNCT
ejpam-370	53	24			PROPN
ejpam-370	53	25			NOUN
ejpam-370	53	26			VERB
ejpam-370	53	27			PUNCT
ejpam-370	54	1	s	s	X
ejpam-370	54	2	=	=	PUNCT
ejpam-370	54	3	2(1)nk−	2(1)nk−	NUM
ejpam-370	54	4	1	1	NUM
ejpam-370	54	5	,	,	PUNCT
ejpam-370	54	6	i(nk−1)×(nk−1	i(nk−1)×(nk−1	PROPN
ejpam-370	54	7	)	)	PUNCT
ejpam-370	54	8	01×(nk−1	01×(nk−1	NUM
ejpam-370	54	9	)	)	PUNCT
ejpam-370	54	10	!	!	PUNCT
ejpam-370	55	1	s	s	PART
ejpam-370	56	1	=	=	NOUN
ejpam-370	56	2	nk	nk	PROPN
ejpam-370	56	3	.	.	PUNCT
ejpam-370	57	1	(	(	PUNCT
ejpam-370	57	2	3	3	X
ejpam-370	57	3	)	)	PUNCT
ejpam-370	57	4	then	then	ADV
ejpam-370	57	5	the	the	DET
ejpam-370	57	6	solution	solution	NOUN
ejpam-370	57	7	of	of	ADP
ejpam-370	57	8	linear	linear	ADJ
ejpam-370	57	9	system	system	NOUN
ejpam-370	57	10	(	(	PUNCT
ejpam-370	57	11	2	2	X
ejpam-370	57	12	)	)	PUNCT
ejpam-370	57	13	is	be	AUX
ejpam-370	57	14	given	give	VERB
ejpam-370	57	15	to	to	PART
ejpam-370	57	16	be	be	AUX
ejpam-370	57	17	x	x	X
ejpam-370	58	1	=	=	SYM
ejpam-370	58	2	x	x	SYM
ejpam-370	58	3	(	(	PUNCT
ejpam-370	58	4	1	1	NUM
ejpam-370	58	5	)	)	PUNCT
ejpam-370	58	6	=	=	SYM
ejpam-370	58	7	n	n	CCONJ
ejpam-370	58	8	∑	∑	ADP
ejpam-370	58	9	i=1	i=1	PROPN
ejpam-370	58	10			PROPN
ejpam-370	58	11			NOUN
ejpam-370	58	12			NOUN
ejpam-370	58	13	i−1	i−1	PROPN
ejpam-370	58	14	∏	∏	PROPN
ejpam-370	58	15	j=1	j=1	PROPN
ejpam-370	58	16	r	r	PROPN
ejpam-370	58	17	(	(	PUNCT
ejpam-370	58	18	j	j	NOUN
ejpam-370	58	19	)	)	PUNCT
ejpam-370	58	20			PROPN
ejpam-370	58	21			VERB
ejpam-370	58	22			PUNCT
ejpam-370	59	1	x	x	X
ejpam-370	59	2	(	(	PUNCT
ejpam-370	59	3	i	i	NOUN
ejpam-370	59	4	)	)	PUNCT
ejpam-370	59	5	0	0	NUM
ejpam-370	59	6	;	;	PUNCT
ejpam-370	59	7	i−1	i−1	PROPN
ejpam-370	59	8	∏	∏	PROPN
ejpam-370	59	9	j=1	j=1	PROPN
ejpam-370	59	10	r	r	PROPN
ejpam-370	59	11	(	(	PUNCT
ejpam-370	59	12	j	j	NOUN
ejpam-370	59	13	)	)	PUNCT
ejpam-370	59	14	=	=	PRON
ejpam-370	59	15	(	(	PUNCT
ejpam-370	59	16	r(1)r(2	r(1)r(2	PROPN
ejpam-370	59	17	)	)	PUNCT
ejpam-370	59	18	.	.	PUNCT
ejpam-370	59	19	.	.	PUNCT
ejpam-370	59	20	.	.	PUNCT
ejpam-370	60	1	r(i−1	r(i−1	PROPN
ejpam-370	60	2	)	)	PUNCT
ejpam-370	61	1	i	i	PRON
ejpam-370	61	2	>	>	X
ejpam-370	62	1	1	1	NUM
ejpam-370	62	2	,	,	PUNCT
ejpam-370	62	3	i	i	PRON
ejpam-370	62	4	i	i	NOUN
ejpam-370	62	5	=	=	NOUN
ejpam-370	62	6	1	1	X
ejpam-370	62	7	.	.	PUNCT
ejpam-370	63	1	(	(	PUNCT
ejpam-370	63	2	4	4	NUM
ejpam-370	63	3	)	)	PUNCT
ejpam-370	63	4	2.3	2.3	NUM
ejpam-370	63	5	.	.	PUNCT
ejpam-370	64	1	generalized	generalize	VERB
ejpam-370	64	2	iterative	iterative	NOUN
ejpam-370	64	3	decreasing	decrease	VERB
ejpam-370	64	4	dimension	dimension	NOUN
ejpam-370	64	5	method	method	NOUN
ejpam-370	64	6	(	(	PUNCT
ejpam-370	64	7	giddm	giddm	PROPN
ejpam-370	64	8	)	)	PUNCT
ejpam-370	64	9	let	let	VERB
ejpam-370	64	10	us	we	PRON
ejpam-370	64	11	consider	consider	VERB
ejpam-370	64	12	a	a	DET
ejpam-370	64	13	system	system	NOUN
ejpam-370	64	14	of	of	ADP
ejpam-370	64	15	linear	linear	ADJ
ejpam-370	64	16	algebraic	algebraic	ADJ
ejpam-370	64	17	equation	equation	NOUN
ejpam-370	64	18	ax	ax	NOUN
ejpam-370	64	19	=	=	X
ejpam-370	64	20	a(1)x	a(1)x	X
ejpam-370	64	21	(	(	PUNCT
ejpam-370	64	22	1	1	NUM
ejpam-370	64	23	)	)	PUNCT
ejpam-370	64	24	=	=	SYM
ejpam-370	64	25	f	f	PROPN
ejpam-370	64	26	(	(	PUNCT
ejpam-370	64	27	1	1	NUM
ejpam-370	64	28	)	)	PUNCT
ejpam-370	64	29	=	=	SYM
ejpam-370	64	30	f	f	PROPN
ejpam-370	64	31	(	(	PUNCT
ejpam-370	64	32	5	5	NUM
ejpam-370	64	33	)	)	PUNCT
ejpam-370	64	34	where	where	SCONJ
ejpam-370	64	35	a	a	PRON
ejpam-370	64	36	is	be	AUX
ejpam-370	64	37	a	a	DET
ejpam-370	64	38	m	m	NOUN
ejpam-370	64	39	×	×	NOUN
ejpam-370	64	40	n	n	DET
ejpam-370	64	41	-matrix	-matrix	NOUN
ejpam-370	64	42	,	,	PUNCT
ejpam-370	64	43	x	x	X
ejpam-370	64	44	is	be	AUX
ejpam-370	64	45	a	a	DET
ejpam-370	64	46	n	n	PRON
ejpam-370	64	47	-vector	-vector	NOUN
ejpam-370	64	48	and	and	CCONJ
ejpam-370	64	49	f	f	PROPN
ejpam-370	64	50	is	be	AUX
ejpam-370	64	51	a	a	DET
ejpam-370	64	52	m	m	NOUN
ejpam-370	64	53	-vector	-vector	NOUN
ejpam-370	64	54	and	and	CCONJ
ejpam-370	64	55	examine	examine	VERB
ejpam-370	64	56	the	the	DET
ejpam-370	64	57	solution	solution	NOUN
ejpam-370	64	58	of	of	ADP
ejpam-370	64	59	the	the	DET
ejpam-370	64	60	linear	linear	ADJ
ejpam-370	64	61	system	system	NOUN
ejpam-370	64	62	(	(	PUNCT
ejpam-370	64	63	5	5	NUM
ejpam-370	64	64	)	)	PUNCT
ejpam-370	64	65	according	accord	VERB
ejpam-370	64	66	to	to	ADP
ejpam-370	64	67	situations	situation	NOUN
ejpam-370	64	68	of	of	ADP
ejpam-370	64	69	m	m	NOUN
ejpam-370	64	70	and	and	CCONJ
ejpam-370	64	71	n	n	PROPN
ejpam-370	64	72	.	.	PUNCT
ejpam-370	65	1	now	now	ADV
ejpam-370	65	2	,	,	PUNCT
ejpam-370	65	3	we	we	PRON
ejpam-370	65	4	divide	divide	VERB
ejpam-370	65	5	the	the	DET
ejpam-370	65	6	given	give	VERB
ejpam-370	65	7	system	system	NOUN
ejpam-370	65	8	into	into	ADP
ejpam-370	65	9	two	two	NUM
ejpam-370	65	10	systems	system	NOUN
ejpam-370	65	11	such	such	ADJ
ejpam-370	65	12	that	that	SCONJ
ejpam-370	65	13	a	a	DET
ejpam-370	65	14	(	(	PUNCT
ejpam-370	65	15	1	1	NUM
ejpam-370	65	16	)	)	SYM
ejpam-370	65	17	1	1	NUM
ejpam-370	65	18	x	x	SYM
ejpam-370	65	19	(	(	PUNCT
ejpam-370	65	20	1	1	NUM
ejpam-370	65	21	)	)	PUNCT
ejpam-370	65	22	=	=	SYM
ejpam-370	65	23	u(1	u(1	PROPN
ejpam-370	65	24	)	)	PUNCT
ejpam-370	65	25	;	;	PUNCT
ejpam-370	65	26	a	a	DET
ejpam-370	65	27	(	(	PUNCT
ejpam-370	65	28	1	1	NUM
ejpam-370	65	29	)	)	SYM
ejpam-370	65	30	1	1	NUM
ejpam-370	65	31	=	=	SYM
ejpam-370	65	32	�	�	PROPN
ejpam-370	65	33	ap	ap	PROPN
ejpam-370	65	34	j	j	PROPN
ejpam-370	65	35	�	�	PROPN
ejpam-370	65	36	j=1(1)n	j=1(1)n	PROPN
ejpam-370	65	37	,	,	PUNCT
ejpam-370	65	38	u(1	u(1	PROPN
ejpam-370	65	39	)	)	PUNCT
ejpam-370	65	40	=	=	SYM
ejpam-370	65	41	�	�	PROPN
ejpam-370	65	42	fp	fp	PROPN
ejpam-370	65	43	�	�	PROPN
ejpam-370	65	44	(	(	PUNCT
ejpam-370	65	45	6	6	NUM
ejpam-370	65	46	)	)	PUNCT
ejpam-370	65	47	a	a	DET
ejpam-370	65	48	(	(	PUNCT
ejpam-370	65	49	1	1	NUM
ejpam-370	65	50	)	)	SYM
ejpam-370	65	51	2	2	NUM
ejpam-370	65	52	x	x	SYM
ejpam-370	65	53	(	(	PUNCT
ejpam-370	65	54	1	1	NUM
ejpam-370	65	55	)	)	PUNCT
ejpam-370	65	56	=	=	SYM
ejpam-370	65	57	v(1	v(1	PROPN
ejpam-370	65	58	)	)	PUNCT
ejpam-370	65	59	;	;	PUNCT
ejpam-370	65	60	a	a	DET
ejpam-370	65	61	(	(	PUNCT
ejpam-370	65	62	1	1	NUM
ejpam-370	65	63	)	)	SYM
ejpam-370	65	64	2	2	NUM
ejpam-370	65	65	=	=	SYM
ejpam-370	65	66	�	�	PROPN
ejpam-370	65	67	ai	ai	VERB
ejpam-370	65	68	j	j	PROPN
ejpam-370	65	69	�	�	PROPN
ejpam-370	65	70	j=1(1)n	j=1(1)n	PROPN
ejpam-370	65	71	i	i	PROPN
ejpam-370	65	72	=	=	PROPN
ejpam-370	65	73	p+1(1)m	p+1(1)m	ADJ
ejpam-370	65	74	,	,	PUNCT
ejpam-370	65	75	v(1	v(1	PROPN
ejpam-370	65	76	)	)	PUNCT
ejpam-370	65	77	=	=	SYM
ejpam-370	65	78	�	�	PROPN
ejpam-370	65	79	fi	fi	NOUN
ejpam-370	65	80	�	�	PROPN
ejpam-370	65	81	i	i	NOUN
ejpam-370	65	82	=	=	NOUN
ejpam-370	65	83	p+1(1)m	p+1(1)m	ADJ
ejpam-370	65	84	(	(	PUNCT
ejpam-370	65	85	7	7	NUM
ejpam-370	65	86	)	)	PUNCT
ejpam-370	65	87	k.	k.	PROPN
ejpam-370	65	88	aydın	aydın	PROPN
ejpam-370	65	89	,	,	PUNCT
ejpam-370	65	90	g.	g.	PROPN
ejpam-370	65	91	kızılkan	kızılkan	PROPN
ejpam-370	65	92	,	,	PUNCT
ejpam-370	65	93	a.	a.	PROPN
ejpam-370	65	94	çıbıkdiken	çıbıkdiken	VERB
ejpam-370	65	95	/	/	SYM
ejpam-370	65	96	eur	eur	PROPN
ejpam-370	65	97	.	.	PUNCT
ejpam-370	66	1	j.	j.	PROPN
ejpam-370	66	2	pure	pure	PROPN
ejpam-370	66	3	appl	appl	PROPN
ejpam-370	66	4	.	.	PROPN
ejpam-370	66	5	math	math	PROPN
ejpam-370	66	6	,	,	PUNCT
ejpam-370	66	7	3	3	NUM
ejpam-370	66	8	(	(	PUNCT
ejpam-370	66	9	2010	2010	NUM
ejpam-370	66	10	)	)	PUNCT
ejpam-370	66	11	,	,	PUNCT
ejpam-370	66	12	819	819	NUM
ejpam-370	66	13	-	-	SYM
ejpam-370	66	14	830	830	NUM
ejpam-370	66	15	822	822	NUM
ejpam-370	66	16	where	where	SCONJ
ejpam-370	66	17	p	p	NOUN
ejpam-370	66	18	is	be	AUX
ejpam-370	66	19	the	the	DET
ejpam-370	66	20	number	number	NOUN
ejpam-370	66	21	of	of	ADP
ejpam-370	66	22	first	first	ADJ
ejpam-370	66	23	non	non	ADJ
ejpam-370	66	24	-	-	ADJ
ejpam-370	66	25	zero	zero	NUM
ejpam-370	66	26	row	row	NOUN
ejpam-370	66	27	of	of	ADP
ejpam-370	66	28	matrix	matrix	NOUN
ejpam-370	66	29	a(1	a(1	NOUN
ejpam-370	66	30	)	)	PUNCT
ejpam-370	66	31	.	.	PUNCT
ejpam-370	67	1	if	if	SCONJ
ejpam-370	67	2	p	p	X
ejpam-370	67	3	>	>	X
ejpam-370	67	4	1	1	NUM
ejpam-370	67	5	,	,	PUNCT
ejpam-370	67	6	for	for	SCONJ
ejpam-370	67	7	the	the	DET
ejpam-370	67	8	equation	equation	NOUN
ejpam-370	67	9	(	(	PUNCT
ejpam-370	67	10	5	5	NUM
ejpam-370	67	11	)	)	PUNCT
ejpam-370	67	12	to	to	PART
ejpam-370	67	13	have	have	VERB
ejpam-370	67	14	a	a	DET
ejpam-370	67	15	solution	solution	NOUN
ejpam-370	67	16	,	,	PUNCT
ejpam-370	67	17	f	f	PROPN
ejpam-370	67	18	(	(	PUNCT
ejpam-370	67	19	1	1	X
ejpam-370	67	20	)	)	PUNCT
ejpam-370	67	21	i	i	NOUN
ejpam-370	67	22	=	=	NOUN
ejpam-370	67	23	0	0	NUM
ejpam-370	67	24	,	,	PUNCT
ejpam-370	67	25	i	i	PRON
ejpam-370	67	26	=	=	NOUN
ejpam-370	67	27	1(1)p−	1(1)p−	NUM
ejpam-370	67	28	1	1	NUM
ejpam-370	67	29	must	must	AUX
ejpam-370	67	30	be	be	AUX
ejpam-370	67	31	satisfied	satisfied	ADJ
ejpam-370	67	32	.	.	PUNCT
ejpam-370	68	1	x	x	PUNCT
ejpam-370	68	2	(	(	PUNCT
ejpam-370	68	3	1	1	NUM
ejpam-370	68	4	)	)	PUNCT
ejpam-370	68	5	0	0	NUM
ejpam-370	68	6	is	be	AUX
ejpam-370	68	7	chosen	choose	VERB
ejpam-370	68	8	to	to	PART
ejpam-370	68	9	be	be	AUX
ejpam-370	68	10	x	x	X
ejpam-370	68	11	(	(	PUNCT
ejpam-370	68	12	1	1	NUM
ejpam-370	68	13	)	)	PUNCT
ejpam-370	68	14	0	0	NUM
ejpam-370	69	1	=	=	SYM
ejpam-370	69	2	�	�	PROPN
ejpam-370	69	3	0	0	NUM
ejpam-370	69	4	...	...	PUNCT
ejpam-370	69	5	0	0	NUM
ejpam-370	70	1	f	f	X
ejpam-370	70	2	(	(	PUNCT
ejpam-370	70	3	1)p	1)p	NUM
ejpam-370	70	4	a	a	PRON
ejpam-370	70	5	(	(	PUNCT
ejpam-370	70	6	1	1	NUM
ejpam-370	70	7	)	)	PUNCT
ejpam-370	70	8	ps	ps	NOUN
ejpam-370	70	9	0	0	NUM
ejpam-370	70	10	...	...	SYM
ejpam-370	70	11	0	0	NUM
ejpam-370	70	12	�	�	PROPN
ejpam-370	70	13	t	t	PROPN
ejpam-370	70	14	(	(	PUNCT
ejpam-370	70	15	8)	8)	NUM
ejpam-370	70	16	which	which	PRON
ejpam-370	70	17	is	be	AUX
ejpam-370	70	18	a	a	DET
ejpam-370	70	19	special	special	ADJ
ejpam-370	70	20	solution	solution	NOUN
ejpam-370	70	21	of	of	ADP
ejpam-370	70	22	(	(	PUNCT
ejpam-370	70	23	6	6	NUM
ejpam-370	70	24	)	)	PUNCT
ejpam-370	70	25	.	.	PUNCT
ejpam-370	71	1	in	in	ADP
ejpam-370	71	2	(	(	PUNCT
ejpam-370	71	3	8)	8)	NUM
ejpam-370	71	4	,	,	PUNCT
ejpam-370	71	5	a(1)ps	a(1)ps	NOUN
ejpam-370	71	6	6=	6=	PRON
ejpam-370	71	7	0	0	NUM
ejpam-370	71	8	(	(	PUNCT
ejpam-370	71	9	1≤	1≤	NUM
ejpam-370	71	10	s	s	PART
ejpam-370	71	11	≤	≤	NUM
ejpam-370	71	12	n	n	PRON
ejpam-370	71	13	,	,	PUNCT
ejpam-370	71	14	1≤	1≤	NUM
ejpam-370	71	15	p	p	X
ejpam-370	71	16	≤	≤	NUM
ejpam-370	71	17	m	m	PROPN
ejpam-370	71	18	)	)	PUNCT
ejpam-370	71	19	is	be	AUX
ejpam-370	71	20	the	the	DET
ejpam-370	71	21	first	first	ADJ
ejpam-370	71	22	non	non	ADJ
ejpam-370	71	23	-	-	ADJ
ejpam-370	71	24	zero	zero	NUM
ejpam-370	71	25	element	element	NOUN
ejpam-370	71	26	of	of	ADP
ejpam-370	71	27	matrix	matrix	NOUN
ejpam-370	71	28	a(1	a(1	NOUN
ejpam-370	71	29	)	)	PUNCT
ejpam-370	71	30	.	.	PUNCT
ejpam-370	72	1	then	then	ADV
ejpam-370	72	2	,	,	PUNCT
ejpam-370	72	3	x	x	X
ejpam-370	72	4	(	(	PUNCT
ejpam-370	72	5	1	1	X
ejpam-370	72	6	)	)	PUNCT
ejpam-370	72	7	h	h	NOUN
ejpam-370	72	8	-homogeneous	-homogeneous	ADJ
ejpam-370	72	9	solution	solution	NOUN
ejpam-370	72	10	of	of	ADP
ejpam-370	72	11	(	(	PUNCT
ejpam-370	72	12	6	6	NUM
ejpam-370	72	13	)	)	PUNCT
ejpam-370	72	14	is	be	AUX
ejpam-370	72	15	obtained	obtain	VERB
ejpam-370	72	16	to	to	PART
ejpam-370	72	17	be	be	AUX
ejpam-370	72	18	x	x	X
ejpam-370	72	19	(	(	PUNCT
ejpam-370	72	20	1	1	NUM
ejpam-370	72	21	)	)	PUNCT
ejpam-370	72	22	h	h	NOUN
ejpam-370	72	23	=	=	SYM
ejpam-370	72	24	r(1)x	r(1)x	X
ejpam-370	72	25	(	(	PUNCT
ejpam-370	72	26	2	2	NUM
ejpam-370	72	27	)	)	PUNCT
ejpam-370	72	28	where	where	SCONJ
ejpam-370	72	29	x	x	X
ejpam-370	72	30	(	(	PUNCT
ejpam-370	72	31	2	2	NUM
ejpam-370	72	32	)	)	PUNCT
ejpam-370	72	33	is	be	AUX
ejpam-370	72	34	a	a	DET
ejpam-370	72	35	n2	n2	ADJ
ejpam-370	72	36	-	-	PUNCT
ejpam-370	72	37	vector	vector	NOUN
ejpam-370	72	38	composed	compose	VERB
ejpam-370	72	39	of	of	ADP
ejpam-370	72	40	x	x	PROPN
ejpam-370	72	41	i	i	NOUN
ejpam-370	72	42	-	-	PUNCT
ejpam-370	72	43	parametric	parametric	ADJ
ejpam-370	72	44	variables	variable	NOUN
ejpam-370	72	45	for	for	ADP
ejpam-370	72	46	i	i	PRON
ejpam-370	72	47	=	=	SYM
ejpam-370	72	48	1(1)m2	1(1)m2	NUM
ejpam-370	72	49	,	,	PUNCT
ejpam-370	72	50	i	i	PROPN
ejpam-370	72	51	6=	6=	SYM
ejpam-370	72	52	s	s	PROPN
ejpam-370	72	53	and	and	CCONJ
ejpam-370	72	54	r(1	r(1	PROPN
ejpam-370	72	55	)	)	PUNCT
ejpam-370	72	56	is	be	AUX
ejpam-370	72	57	a	a	DET
ejpam-370	72	58	matrix	matrix	NOUN
ejpam-370	72	59	composed	compose	VERB
ejpam-370	72	60	of	of	ADP
ejpam-370	72	61	the	the	DET
ejpam-370	72	62	base	base	NOUN
ejpam-370	72	63	vector	vector	NOUN
ejpam-370	72	64	of	of	ADP
ejpam-370	72	65	this	this	DET
ejpam-370	72	66	solution	solution	NOUN
ejpam-370	72	67	space	space	NOUN
ejpam-370	72	68	as	as	ADP
ejpam-370	72	69	r(1	r(1	PROPN
ejpam-370	72	70	)	)	PUNCT
ejpam-370	72	71	=	=	PUNCT
ejpam-370	73	1			PROPN
ejpam-370	73	2			X
ejpam-370	73	3			PROPN
ejpam-370	73	4			PROPN
ejpam-370	73	5			PROPN
ejpam-370	73	6			PROPN
ejpam-370	73	7			PROPN
ejpam-370	73	8			PROPN
ejpam-370	73	9			PROPN
ejpam-370	73	10			PROPN
ejpam-370	73	11			NOUN
ejpam-370	73	12			PROPN
ejpam-370	73	13			PROPN
ejpam-370	73	14			PROPN
ejpam-370	73	15			PROPN
ejpam-370	73	16			PROPN
ejpam-370	73	17			PROPN
ejpam-370	73	18			PROPN
ejpam-370	73	19			PROPN
ejpam-370	73	20			PROPN
ejpam-370	73	21			NOUN
ejpam-370	73	22	r	r	NOUN
ejpam-370	73	23	(	(	PUNCT
ejpam-370	73	24	1	1	NUM
ejpam-370	73	25	)	)	PUNCT
ejpam-370	73	26	1×(n−1	1×(n−1	NUM
ejpam-370	73	27	)	)	PUNCT
ejpam-370	73	28	i(n−1)×(n−1	i(n−1)×(n−1	PROPN
ejpam-370	73	29	)	)	PUNCT
ejpam-370	73	30	!	!	PUNCT
ejpam-370	73	31	s	s	PART
ejpam-370	74	1	=	=	SYM
ejpam-370	74	2	1	1	NUM
ejpam-370	74	3	,	,	PUNCT
ejpam-370	74	4			NOUN
ejpam-370	74	5			NOUN
ejpam-370	74	6			NOUN
ejpam-370	74	7			NOUN
ejpam-370	74	8	i(s−1)×(s−1	i(s−1)×(s−1	PROPN
ejpam-370	74	9	)	)	PUNCT
ejpam-370	74	10	0(s−1)×(n−s	0(s−1)×(n−s	NUM
ejpam-370	74	11	)	)	PUNCT
ejpam-370	74	12	01×(s−1	01×(s−1	NUM
ejpam-370	74	13	)	)	PUNCT
ejpam-370	74	14	r	r	NOUN
ejpam-370	74	15	(	(	PUNCT
ejpam-370	74	16	1	1	NUM
ejpam-370	74	17	)	)	PUNCT
ejpam-370	74	18	1×(n−s	1×(n−s	NUM
ejpam-370	74	19	)	)	PUNCT
ejpam-370	74	20	0(n−s)×(s−1	0(n−s)×(s−1	NUM
ejpam-370	74	21	)	)	PUNCT
ejpam-370	74	22	i(n−s)×(n−s	i(n−s)×(n−s	NUM
ejpam-370	74	23	)	)	PUNCT
ejpam-370	74	24			PROPN
ejpam-370	74	25			NOUN
ejpam-370	74	26			VERB
ejpam-370	74	27			PUNCT
ejpam-370	74	28	s	s	X
ejpam-370	74	29	=	=	SYM
ejpam-370	74	30	2(1)n	2(1)n	NUM
ejpam-370	74	31	−	−	NOUN
ejpam-370	74	32	1	1	NUM
ejpam-370	74	33	,	,	PUNCT
ejpam-370	74	34	i(n−1)×(n−1	i(n−1)×(n−1	ADJ
ejpam-370	74	35	)	)	PUNCT
ejpam-370	74	36	01×(n−1	01×(n−1	NUM
ejpam-370	74	37	)	)	PUNCT
ejpam-370	74	38	!	!	PUNCT
ejpam-370	75	1	s	s	PART
ejpam-370	76	1	=	=	PUNCT
ejpam-370	76	2	n	n	PROPN
ejpam-370	76	3	where	where	SCONJ
ejpam-370	76	4	r	r	NOUN
ejpam-370	76	5	(	(	PUNCT
ejpam-370	76	6	1	1	NUM
ejpam-370	76	7	)	)	PUNCT
ejpam-370	76	8	1×(n−s	1×(n−s	NUM
ejpam-370	76	9	)	)	PUNCT
ejpam-370	76	10	=	=	SYM
ejpam-370	76	11	�	�	PROPN
ejpam-370	76	12	r	r	NOUN
ejpam-370	76	13	(	(	PUNCT
ejpam-370	76	14	1	1	NUM
ejpam-370	76	15	)	)	PUNCT
ejpam-370	76	16	1(s+1	1(s+1	NUM
ejpam-370	76	17	)	)	PUNCT
ejpam-370	76	18	r	r	NOUN
ejpam-370	76	19	(	(	PUNCT
ejpam-370	76	20	1	1	NUM
ejpam-370	76	21	)	)	PUNCT
ejpam-370	76	22	1(s+2	1(s+2	NUM
ejpam-370	76	23	)	)	PUNCT
ejpam-370	76	24	.	.	PUNCT
ejpam-370	76	25	.	.	PUNCT
ejpam-370	76	26	.	.	PUNCT
ejpam-370	77	1	r	r	NOUN
ejpam-370	77	2	(	(	PUNCT
ejpam-370	77	3	1	1	NUM
ejpam-370	77	4	)	)	PUNCT
ejpam-370	77	5	1n	1n	PROPN
ejpam-370	77	6	�	�	PROPN
ejpam-370	77	7	;	;	PUNCT
ejpam-370	77	8	r	r	NOUN
ejpam-370	77	9	(	(	PUNCT
ejpam-370	77	10	1	1	NUM
ejpam-370	77	11	)	)	PUNCT
ejpam-370	77	12	1	1	NUM
ejpam-370	77	13	j	j	NOUN
ejpam-370	77	14	=	=	PUNCT
ejpam-370	78	1	−	−	PROPN
ejpam-370	78	2	a	a	DET
ejpam-370	78	3	(	(	PUNCT
ejpam-370	78	4	1	1	NUM
ejpam-370	78	5	)	)	PUNCT
ejpam-370	78	6	p	p	NOUN
ejpam-370	78	7	j	j	PROPN
ejpam-370	78	8	a	a	DET
ejpam-370	78	9	(	(	PUNCT
ejpam-370	78	10	1	1	NUM
ejpam-370	78	11	)	)	PUNCT
ejpam-370	78	12	ps	ps	PROPN
ejpam-370	78	13	,	,	PUNCT
ejpam-370	78	14	j	j	PROPN
ejpam-370	78	15	=	=	PUNCT
ejpam-370	78	16	s+	s+	NUM
ejpam-370	78	17	1(1)n	1(1)n	NUM
ejpam-370	78	18	.	.	PUNCT
ejpam-370	79	1	the	the	DET
ejpam-370	79	2	general	general	ADJ
ejpam-370	79	3	solution	solution	NOUN
ejpam-370	79	4	of	of	ADP
ejpam-370	79	5	(	(	PUNCT
ejpam-370	79	6	6	6	NUM
ejpam-370	79	7	)	)	PUNCT
ejpam-370	79	8	is	be	AUX
ejpam-370	79	9	achieved	achieve	VERB
ejpam-370	79	10	as	as	ADP
ejpam-370	79	11	x	x	X
ejpam-370	79	12	(	(	PUNCT
ejpam-370	79	13	1	1	NUM
ejpam-370	79	14	)	)	PUNCT
ejpam-370	79	15	=	=	SYM
ejpam-370	80	1	x	x	SYM
ejpam-370	80	2	(	(	PUNCT
ejpam-370	80	3	1	1	NUM
ejpam-370	80	4	)	)	PUNCT
ejpam-370	80	5	0	0	PUNCT
ejpam-370	81	1	+	+	ADV
ejpam-370	81	2	r(1)x	r(1)x	X
ejpam-370	81	3	(	(	PUNCT
ejpam-370	81	4	2	2	NUM
ejpam-370	81	5	)	)	PUNCT
ejpam-370	81	6	,	,	PUNCT
ejpam-370	81	7	where	where	SCONJ
ejpam-370	81	8	x	x	X
ejpam-370	81	9	(	(	PUNCT
ejpam-370	81	10	1	1	NUM
ejpam-370	81	11	)	)	PUNCT
ejpam-370	81	12	0	0	NUM
ejpam-370	81	13	is	be	AUX
ejpam-370	81	14	a	a	DET
ejpam-370	81	15	n	n	NUM
ejpam-370	81	16	-vector	-vector	NOUN
ejpam-370	81	17	and	and	CCONJ
ejpam-370	81	18	r(1	r(1	PROPN
ejpam-370	81	19	)	)	PUNCT
ejpam-370	81	20	is	be	AUX
ejpam-370	81	21	a	a	DET
ejpam-370	81	22	n	n	NUM
ejpam-370	81	23	×	×	NOUN
ejpam-370	81	24	(	(	PUNCT
ejpam-370	81	25	n	n	CCONJ
ejpam-370	81	26	−	−	PROPN
ejpam-370	81	27	1)-matrix	1)-matrix	NUM
ejpam-370	81	28	.	.	PUNCT
ejpam-370	82	1	by	by	ADP
ejpam-370	82	2	substituting	substitute	VERB
ejpam-370	82	3	solution	solution	NOUN
ejpam-370	82	4	x	x	PUNCT
ejpam-370	82	5	(	(	PUNCT
ejpam-370	82	6	1	1	NUM
ejpam-370	82	7	)	)	PUNCT
ejpam-370	82	8	into	into	ADP
ejpam-370	82	9	system	system	NOUN
ejpam-370	82	10	(	(	PUNCT
ejpam-370	82	11	7	7	NUM
ejpam-370	82	12	)	)	PUNCT
ejpam-370	82	13	,	,	PUNCT
ejpam-370	82	14	we	we	PRON
ejpam-370	82	15	have	have	VERB
ejpam-370	82	16	a	a	DET
ejpam-370	82	17	new	new	ADJ
ejpam-370	82	18	linear	linear	ADJ
ejpam-370	82	19	algebraic	algebraic	ADJ
ejpam-370	82	20	system	system	NOUN
ejpam-370	82	21	as	as	ADP
ejpam-370	82	22	following	follow	VERB
ejpam-370	82	23	a(2)x	a(2)x	PROPN
ejpam-370	82	24	(	(	PUNCT
ejpam-370	82	25	2	2	NUM
ejpam-370	82	26	)	)	PUNCT
ejpam-370	82	27	=	=	SYM
ejpam-370	82	28	f	f	PROPN
ejpam-370	82	29	(	(	PUNCT
ejpam-370	82	30	2	2	NUM
ejpam-370	82	31	)	)	PUNCT
ejpam-370	82	32	,	,	PUNCT
ejpam-370	82	33	(	(	PUNCT
ejpam-370	82	34	9	9	X
ejpam-370	82	35	)	)	PUNCT
ejpam-370	82	36	where	where	SCONJ
ejpam-370	82	37	a(2	a(2	NOUN
ejpam-370	82	38	)	)	PUNCT
ejpam-370	82	39	=	=	SYM
ejpam-370	82	40	a	a	PRON
ejpam-370	82	41	(	(	PUNCT
ejpam-370	82	42	1	1	NUM
ejpam-370	82	43	)	)	PUNCT
ejpam-370	82	44	2	2	NUM
ejpam-370	82	45	r(1	r(1	PROPN
ejpam-370	82	46	)	)	PUNCT
ejpam-370	82	47	and	and	CCONJ
ejpam-370	82	48	f	f	PROPN
ejpam-370	82	49	(	(	PUNCT
ejpam-370	82	50	2	2	NUM
ejpam-370	82	51	)	)	PUNCT
ejpam-370	82	52	=	=	SYM
ejpam-370	83	1	v(1	v(1	ADJ
ejpam-370	83	2	)	)	PUNCT
ejpam-370	83	3	−	−	PROPN
ejpam-370	83	4	a	a	DET
ejpam-370	83	5	(	(	PUNCT
ejpam-370	83	6	1	1	NUM
ejpam-370	83	7	)	)	SYM
ejpam-370	83	8	2	2	NUM
ejpam-370	83	9	x	x	SYM
ejpam-370	83	10	(	(	PUNCT
ejpam-370	83	11	1	1	NUM
ejpam-370	83	12	)	)	PUNCT
ejpam-370	83	13	0	0	NUM
ejpam-370	83	14	.	.	PUNCT
ejpam-370	84	1	applying	apply	VERB
ejpam-370	84	2	the	the	DET
ejpam-370	84	3	steps	step	NOUN
ejpam-370	84	4	given	give	VERB
ejpam-370	84	5	above	above	ADV
ejpam-370	84	6	to	to	ADP
ejpam-370	84	7	the	the	DET
ejpam-370	84	8	system	system	NOUN
ejpam-370	84	9	(	(	PUNCT
ejpam-370	84	10	9	9	NUM
ejpam-370	84	11	)	)	PUNCT
ejpam-370	84	12	,	,	PUNCT
ejpam-370	84	13	we	we	PRON
ejpam-370	84	14	can	can	AUX
ejpam-370	84	15	write	write	VERB
ejpam-370	84	16	the	the	DET
ejpam-370	84	17	systems	system	NOUN
ejpam-370	84	18	followed	follow	VERB
ejpam-370	84	19	by	by	ADP
ejpam-370	84	20	each	each	DET
ejpam-370	84	21	other	other	ADJ
ejpam-370	84	22	as	as	ADP
ejpam-370	84	23	a(k)x	a(k)x	PROPN
ejpam-370	84	24	(	(	PUNCT
ejpam-370	84	25	k	k	NOUN
ejpam-370	84	26	)	)	PUNCT
ejpam-370	84	27	=	=	SYM
ejpam-370	84	28	f	f	X
ejpam-370	84	29	(	(	PUNCT
ejpam-370	84	30	k	k	NOUN
ejpam-370	84	31	)	)	PUNCT
ejpam-370	84	32	;	;	PUNCT
ejpam-370	84	33	k	k	PROPN
ejpam-370	84	34	=	=	SYM
ejpam-370	84	35	2(1)n	2(1)n	NUM
ejpam-370	84	36	(	(	PUNCT
ejpam-370	84	37	10	10	NUM
ejpam-370	84	38	)	)	PUNCT
ejpam-370	84	39	where	where	SCONJ
ejpam-370	84	40	a(k	a(k	NUM
ejpam-370	84	41	)	)	PUNCT
ejpam-370	84	42	=	=	PUNCT
ejpam-370	85	1	a	a	DET
ejpam-370	85	2	(	(	PUNCT
ejpam-370	85	3	k−1	k−1	PROPN
ejpam-370	85	4	)	)	PUNCT
ejpam-370	85	5	2	2	NUM
ejpam-370	85	6	r(k−1	r(k−1	NOUN
ejpam-370	85	7	)	)	PUNCT
ejpam-370	85	8	,	,	PUNCT
ejpam-370	85	9	f	f	PROPN
ejpam-370	85	10	(	(	PUNCT
ejpam-370	85	11	k	k	NOUN
ejpam-370	85	12	)	)	PUNCT
ejpam-370	85	13	=	=	VERB
ejpam-370	85	14	v(k−1)−	v(k−1)−	NOUN
ejpam-370	85	15	a	a	PRON
ejpam-370	85	16	(	(	PUNCT
ejpam-370	85	17	k−1	k−1	PROPN
ejpam-370	85	18	)	)	PUNCT
ejpam-370	85	19	2	2	NUM
ejpam-370	85	20	x	x	X
ejpam-370	85	21	(	(	PUNCT
ejpam-370	85	22	k−1	k−1	PROPN
ejpam-370	85	23	)	)	PUNCT
ejpam-370	85	24	0	0	PUNCT
ejpam-370	85	25	.	.	PUNCT
ejpam-370	86	1	it	it	PRON
ejpam-370	86	2	is	be	AUX
ejpam-370	86	3	known	know	VERB
ejpam-370	86	4	that	that	SCONJ
ejpam-370	86	5	the	the	DET
ejpam-370	86	6	general	general	ADJ
ejpam-370	86	7	solutions	solution	NOUN
ejpam-370	86	8	of	of	ADP
ejpam-370	86	9	the	the	DET
ejpam-370	86	10	system	system	NOUN
ejpam-370	86	11	(	(	PUNCT
ejpam-370	86	12	10	10	NUM
ejpam-370	86	13	)	)	PUNCT
ejpam-370	86	14	are	be	AUX
ejpam-370	86	15	x	x	X
ejpam-370	86	16	(	(	PUNCT
ejpam-370	86	17	k	k	NOUN
ejpam-370	86	18	)	)	PUNCT
ejpam-370	86	19	=	=	SYM
ejpam-370	86	20	x	x	SYM
ejpam-370	86	21	(	(	PUNCT
ejpam-370	86	22	k	k	NOUN
ejpam-370	86	23	)	)	PUNCT
ejpam-370	86	24	0	0	PUNCT
ejpam-370	87	1	+	+	CCONJ
ejpam-370	87	2	r(k)x	r(k)x	PROPN
ejpam-370	87	3	(	(	PUNCT
ejpam-370	87	4	k+1	k+1	NOUN
ejpam-370	87	5	)	)	PUNCT
ejpam-370	87	6	if	if	SCONJ
ejpam-370	87	7	the	the	DET
ejpam-370	87	8	solutions	solution	NOUN
ejpam-370	87	9	exist	exist	VERB
ejpam-370	87	10	.	.	PUNCT
ejpam-370	88	1	here	here	ADV
ejpam-370	88	2	r(k	r(k	PROPN
ejpam-370	88	3	)	)	PUNCT
ejpam-370	88	4	is	be	AUX
ejpam-370	88	5	a	a	DET
ejpam-370	88	6	matrix	matrix	NOUN
ejpam-370	88	7	as	as	SCONJ
ejpam-370	88	8	given	give	VERB
ejpam-370	88	9	in	in	ADP
ejpam-370	88	10	(	(	PUNCT
ejpam-370	88	11	3	3	NUM
ejpam-370	88	12	)	)	PUNCT
ejpam-370	88	13	.	.	PUNCT
ejpam-370	89	1	now	now	ADV
ejpam-370	89	2	,	,	PUNCT
ejpam-370	89	3	we	we	PRON
ejpam-370	89	4	are	be	AUX
ejpam-370	89	5	going	go	VERB
ejpam-370	89	6	to	to	PART
ejpam-370	89	7	examine	examine	VERB
ejpam-370	89	8	the	the	DET
ejpam-370	89	9	situations	situation	NOUN
ejpam-370	89	10	for	for	ADP
ejpam-370	89	11	solution	solution	NOUN
ejpam-370	89	12	of	of	ADP
ejpam-370	89	13	linear	linear	ADJ
ejpam-370	89	14	system	system	NOUN
ejpam-370	89	15	(	(	PUNCT
ejpam-370	89	16	5	5	NUM
ejpam-370	89	17	)	)	PUNCT
ejpam-370	89	18	.	.	PUNCT
ejpam-370	90	1	k.	k.	PROPN
ejpam-370	90	2	aydın	aydın	PROPN
ejpam-370	90	3	,	,	PUNCT
ejpam-370	90	4	g.	g.	PROPN
ejpam-370	90	5	kızılkan	kızılkan	PROPN
ejpam-370	90	6	,	,	PUNCT
ejpam-370	90	7	a.	a.	PROPN
ejpam-370	90	8	çıbıkdiken	çıbıkdiken	VERB
ejpam-370	90	9	/	/	SYM
ejpam-370	90	10	eur	eur	PROPN
ejpam-370	90	11	.	.	PUNCT
ejpam-370	91	1	j.	j.	PROPN
ejpam-370	91	2	pure	pure	PROPN
ejpam-370	91	3	appl	appl	PROPN
ejpam-370	91	4	.	.	PROPN
ejpam-370	91	5	math	math	PROPN
ejpam-370	91	6	,	,	PUNCT
ejpam-370	91	7	3	3	NUM
ejpam-370	91	8	(	(	PUNCT
ejpam-370	91	9	2010	2010	NUM
ejpam-370	91	10	)	)	PUNCT
ejpam-370	91	11	,	,	PUNCT
ejpam-370	91	12	819	819	NUM
ejpam-370	91	13	-	-	SYM
ejpam-370	91	14	830	830	NUM
ejpam-370	91	15	823	823	NUM
ejpam-370	91	16	case	case	NOUN
ejpam-370	91	17	1	1	NUM
ejpam-370	91	18	.	.	PUNCT
ejpam-370	91	19	suppose	suppose	VERB
ejpam-370	91	20	that	that	SCONJ
ejpam-370	91	21	a(n	a(n	NOUN
ejpam-370	91	22	)	)	PUNCT
ejpam-370	91	23	6=	6=	ADP
ejpam-370	91	24	0	0	X
ejpam-370	91	25	.	.	PUNCT
ejpam-370	92	1	we	we	PRON
ejpam-370	92	2	have	have	VERB
ejpam-370	92	3	three	three	NUM
ejpam-370	92	4	situations	situation	NOUN
ejpam-370	92	5	according	accord	VERB
ejpam-370	92	6	to	to	ADP
ejpam-370	92	7	m	m	PROPN
ejpam-370	92	8	and	and	CCONJ
ejpam-370	92	9	n	n	PROPN
ejpam-370	92	10	.	.	PUNCT
ejpam-370	93	1	a	a	X
ejpam-370	93	2	)	)	PUNCT
ejpam-370	93	3	if	if	SCONJ
ejpam-370	93	4	m	m	NOUN
ejpam-370	93	5	=	=	SYM
ejpam-370	93	6	n	n	PROPN
ejpam-370	93	7	,	,	PUNCT
ejpam-370	93	8	the	the	DET
ejpam-370	93	9	system	system	NOUN
ejpam-370	93	10	(	(	PUNCT
ejpam-370	93	11	5	5	NUM
ejpam-370	93	12	)	)	PUNCT
ejpam-370	93	13	is	be	AUX
ejpam-370	93	14	same	same	ADJ
ejpam-370	93	15	as	as	ADP
ejpam-370	93	16	in	in	ADP
ejpam-370	93	17	iddm	iddm	NOUN
ejpam-370	93	18	,	,	PUNCT
ejpam-370	93	19	i.e.	i.e.	X
ejpam-370	93	20	a	a	PRON
ejpam-370	93	21	is	be	AUX
ejpam-370	93	22	a	a	DET
ejpam-370	93	23	regular	regular	ADJ
ejpam-370	93	24	matrix	matrix	NOUN
ejpam-370	93	25	and	and	CCONJ
ejpam-370	93	26	its	its	PRON
ejpam-370	93	27	solution	solution	NOUN
ejpam-370	93	28	has	have	AUX
ejpam-370	93	29	been	be	AUX
ejpam-370	93	30	given	give	VERB
ejpam-370	93	31	by	by	ADP
ejpam-370	93	32	equation	equation	NOUN
ejpam-370	93	33	(	(	PUNCT
ejpam-370	93	34	4	4	NUM
ejpam-370	93	35	)	)	PUNCT
ejpam-370	93	36	.	.	PUNCT
ejpam-370	94	1	b	b	X
ejpam-370	94	2	)	)	PUNCT
ejpam-370	94	3	if	if	SCONJ
ejpam-370	94	4	m	m	VERB
ejpam-370	94	5	<	<	X
ejpam-370	94	6	n	n	PROPN
ejpam-370	94	7	,	,	PUNCT
ejpam-370	94	8	then	then	ADV
ejpam-370	94	9	the	the	DET
ejpam-370	94	10	solution	solution	NOUN
ejpam-370	94	11	of	of	ADP
ejpam-370	94	12	(	(	PUNCT
ejpam-370	94	13	5	5	NUM
ejpam-370	94	14	)	)	PUNCT
ejpam-370	94	15	is	be	AUX
ejpam-370	94	16	expressed	express	VERB
ejpam-370	94	17	by	by	ADP
ejpam-370	94	18	substituting	substitute	VERB
ejpam-370	94	19	x	x	X
ejpam-370	94	20	(	(	PUNCT
ejpam-370	94	21	k+1	k+1	NOUN
ejpam-370	94	22	)	)	PUNCT
ejpam-370	94	23	solution	solution	NOUN
ejpam-370	94	24	into	into	ADP
ejpam-370	94	25	x	x	SYM
ejpam-370	94	26	(	(	PUNCT
ejpam-370	94	27	k	k	NOUN
ejpam-370	94	28	)	)	PUNCT
ejpam-370	94	29	solution	solution	NOUN
ejpam-370	94	30	for	for	ADP
ejpam-370	94	31	k	k	NOUN
ejpam-370	94	32	=	=	SYM
ejpam-370	94	33	n(−1)1	n(−1)1	NUM
ejpam-370	94	34	as	as	SCONJ
ejpam-370	94	35	follows	follow	VERB
ejpam-370	94	36	x	x	PUNCT
ejpam-370	94	37	=	=	SYM
ejpam-370	94	38	n	n	CCONJ
ejpam-370	94	39	∑	∑	ADP
ejpam-370	94	40	i=1	i=1	PROPN
ejpam-370	94	41			PROPN
ejpam-370	94	42			NOUN
ejpam-370	94	43			NOUN
ejpam-370	94	44	i−1	i−1	PROPN
ejpam-370	94	45	∏	∏	PROPN
ejpam-370	94	46	j=1	j=1	PROPN
ejpam-370	94	47	r	r	PROPN
ejpam-370	94	48	(	(	PUNCT
ejpam-370	94	49	j	j	NOUN
ejpam-370	94	50	)	)	PUNCT
ejpam-370	94	51			PROPN
ejpam-370	94	52			VERB
ejpam-370	94	53			PUNCT
ejpam-370	95	1	x	x	X
ejpam-370	95	2	(	(	PUNCT
ejpam-370	95	3	i	i	NOUN
ejpam-370	95	4	)	)	PUNCT
ejpam-370	95	5	0	0	PUNCT
ejpam-370	96	1	+	+	NUM
ejpam-370	96	2			NOUN
ejpam-370	96	3			NOUN
ejpam-370	96	4			NOUN
ejpam-370	96	5	n	n	CCONJ
ejpam-370	96	6	∏	∏	NOUN
ejpam-370	96	7	j=1	j=1	NOUN
ejpam-370	96	8	r	r	PROPN
ejpam-370	96	9	(	(	PUNCT
ejpam-370	96	10	j	j	NOUN
ejpam-370	96	11	)	)	PUNCT
ejpam-370	96	12			PROPN
ejpam-370	96	13			VERB
ejpam-370	96	14			PUNCT
ejpam-370	97	1	x	x	X
ejpam-370	97	2	(	(	PUNCT
ejpam-370	97	3	n+1	n+1	NOUN
ejpam-370	97	4	)	)	PUNCT
ejpam-370	97	5	,	,	PUNCT
ejpam-370	97	6	where	where	SCONJ
ejpam-370	97	7	x	x	X
ejpam-370	97	8	(	(	PUNCT
ejpam-370	97	9	n+1	n+1	NOUN
ejpam-370	97	10	)	)	PUNCT
ejpam-370	97	11	=	=	SYM
ejpam-370	97	12	�	�	PROPN
ejpam-370	97	13	x	x	SYM
ejpam-370	97	14	(	(	PUNCT
ejpam-370	97	15	n+1	n+1	NOUN
ejpam-370	97	16	)	)	PUNCT
ejpam-370	97	17	1	1	NUM
ejpam-370	97	18	x	x	SYM
ejpam-370	97	19	(	(	PUNCT
ejpam-370	97	20	n+1	n+1	NOUN
ejpam-370	97	21	)	)	PUNCT
ejpam-370	97	22	2	2	NUM
ejpam-370	97	23	.	.	PUNCT
ejpam-370	97	24	.	.	PUNCT
ejpam-370	97	25	.	.	PUNCT
ejpam-370	98	1	x	x	PUNCT
ejpam-370	98	2	(	(	PUNCT
ejpam-370	98	3	n+1	n+1	NOUN
ejpam-370	98	4	)	)	PUNCT
ejpam-370	98	5	nn+1	nn+1	PROPN
ejpam-370	98	6	�	�	PROPN
ejpam-370	98	7	t	t	PROPN
ejpam-370	98	8	and	and	CCONJ
ejpam-370	98	9	x	x	X
ejpam-370	98	10	(	(	PUNCT
ejpam-370	98	11	n+1	n+1	PROPN
ejpam-370	98	12	)	)	PUNCT
ejpam-370	98	13	j	j	PROPN
ejpam-370	98	14	(	(	PUNCT
ejpam-370	98	15	j	j	PROPN
ejpam-370	98	16	=	=	SYM
ejpam-370	98	17	1(1)nn+1	1(1)nn+1	NUM
ejpam-370	98	18	)	)	PUNCT
ejpam-370	98	19	are	be	AUX
ejpam-370	98	20	the	the	DET
ejpam-370	98	21	arbitrary	arbitrary	ADJ
ejpam-370	98	22	parameters	parameter	NOUN
ejpam-370	98	23	.	.	PUNCT
ejpam-370	99	1	c	c	X
ejpam-370	99	2	)	)	PUNCT
ejpam-370	99	3	if	if	SCONJ
ejpam-370	99	4	m	m	VERB
ejpam-370	99	5	>	>	X
ejpam-370	99	6	n	n	PROPN
ejpam-370	99	7	,	,	PUNCT
ejpam-370	99	8	then	then	ADV
ejpam-370	99	9	the	the	DET
ejpam-370	99	10	system	system	NOUN
ejpam-370	99	11	a(n)x	a(n)x	PROPN
ejpam-370	99	12	(	(	PUNCT
ejpam-370	99	13	n	n	CCONJ
ejpam-370	99	14	)	)	PUNCT
ejpam-370	100	1	=	=	SYM
ejpam-370	100	2	f	f	PROPN
ejpam-370	100	3	(	(	PUNCT
ejpam-370	100	4	n	n	CCONJ
ejpam-370	100	5	)	)	PUNCT
ejpam-370	100	6	is	be	AUX
ejpam-370	100	7	obtained	obtain	VERB
ejpam-370	100	8	,	,	PUNCT
ejpam-370	100	9	where	where	SCONJ
ejpam-370	100	10	a(n	a(n	NOUN
ejpam-370	100	11	)	)	PUNCT
ejpam-370	100	12	is	be	AUX
ejpam-370	100	13	a	a	DET
ejpam-370	100	14	mn	mn	PROPN
ejpam-370	100	15	×	×	NOUN
ejpam-370	100	16	1	1	NUM
ejpam-370	100	17	matrix	matrix	NOUN
ejpam-370	100	18	,	,	PUNCT
ejpam-370	100	19	f	f	PROPN
ejpam-370	100	20	(	(	PUNCT
ejpam-370	100	21	n	n	CCONJ
ejpam-370	100	22	)	)	PUNCT
ejpam-370	100	23	is	be	AUX
ejpam-370	100	24	a	a	DET
ejpam-370	100	25	mn	mn	PROPN
ejpam-370	100	26	-vector	-vector	NOUN
ejpam-370	100	27	and	and	CCONJ
ejpam-370	100	28	x	x	ADJ
ejpam-370	100	29	(	(	PUNCT
ejpam-370	100	30	n	n	CCONJ
ejpam-370	100	31	)	)	PUNCT
ejpam-370	100	32	is	be	AUX
ejpam-370	100	33	a	a	DET
ejpam-370	100	34	1	1	NUM
ejpam-370	100	35	-vector	-vector	NOUN
ejpam-370	100	36	given	give	VERB
ejpam-370	100	37	as	as	ADP
ejpam-370	100	38	a(n	a(n	NOUN
ejpam-370	100	39	)	)	PUNCT
ejpam-370	100	40	=	=	SYM
ejpam-370	100	41			PROPN
ejpam-370	100	42			NOUN
ejpam-370	100	43			NOUN
ejpam-370	100	44			NOUN
ejpam-370	100	45			NOUN
ejpam-370	100	46			NOUN
ejpam-370	100	47			PROPN
ejpam-370	100	48	a	a	DET
ejpam-370	100	49	(	(	PUNCT
ejpam-370	100	50	n	n	CCONJ
ejpam-370	100	51	)	)	PUNCT
ejpam-370	100	52	11	11	NUM
ejpam-370	100	53	a	a	PRON
ejpam-370	100	54	(	(	PUNCT
ejpam-370	100	55	n	n	CCONJ
ejpam-370	100	56	)	)	PUNCT
ejpam-370	100	57	21	21	NUM
ejpam-370	100	58	...	...	PUNCT
ejpam-370	100	59	a	a	PRON
ejpam-370	100	60	(	(	PUNCT
ejpam-370	100	61	n	n	CCONJ
ejpam-370	100	62	)	)	PUNCT
ejpam-370	100	63	mn1	mn1	PROPN
ejpam-370	100	64			PROPN
ejpam-370	100	65			NOUN
ejpam-370	100	66			VERB
ejpam-370	100	67			NOUN
ejpam-370	100	68			NOUN
ejpam-370	100	69			NOUN
ejpam-370	100	70			PUNCT
ejpam-370	101	1	,	,	PUNCT
ejpam-370	101	2	f	f	X
ejpam-370	101	3	(	(	PUNCT
ejpam-370	101	4	n	n	CCONJ
ejpam-370	101	5	)	)	PUNCT
ejpam-370	101	6	=	=	SYM
ejpam-370	101	7			PROPN
ejpam-370	101	8			NOUN
ejpam-370	101	9			NOUN
ejpam-370	101	10			NOUN
ejpam-370	101	11			NOUN
ejpam-370	101	12			NOUN
ejpam-370	101	13			PROPN
ejpam-370	101	14	f	f	X
ejpam-370	101	15	(	(	PUNCT
ejpam-370	101	16	n	n	CCONJ
ejpam-370	101	17	)	)	PUNCT
ejpam-370	101	18	1	1	NUM
ejpam-370	101	19	f	f	NOUN
ejpam-370	101	20	(	(	PUNCT
ejpam-370	101	21	n	n	CCONJ
ejpam-370	101	22	)	)	PUNCT
ejpam-370	101	23	2	2	NUM
ejpam-370	101	24	...	...	PUNCT
ejpam-370	101	25	f	f	X
ejpam-370	101	26	(	(	PUNCT
ejpam-370	101	27	n	n	CCONJ
ejpam-370	101	28	)	)	PUNCT
ejpam-370	101	29	mn	mn	PROPN
ejpam-370	101	30			PROPN
ejpam-370	101	31			NOUN
ejpam-370	101	32			VERB
ejpam-370	101	33			NOUN
ejpam-370	101	34			NOUN
ejpam-370	101	35			NOUN
ejpam-370	101	36			PUNCT
ejpam-370	101	37	,	,	PUNCT
ejpam-370	101	38	x	x	X
ejpam-370	101	39	(	(	PUNCT
ejpam-370	101	40	n	n	CCONJ
ejpam-370	101	41	)	)	PUNCT
ejpam-370	101	42	=	=	SYM
ejpam-370	101	43	�	�	PROPN
ejpam-370	101	44	x	x	SYM
ejpam-370	101	45	(	(	PUNCT
ejpam-370	101	46	n	n	CCONJ
ejpam-370	101	47	)	)	PUNCT
ejpam-370	101	48	1	1	NUM
ejpam-370	101	49	�	�	PROPN
ejpam-370	101	50	.	.	PUNCT
ejpam-370	102	1	here	here	ADV
ejpam-370	102	2	,	,	PUNCT
ejpam-370	102	3	if	if	SCONJ
ejpam-370	102	4	a(n	a(n	ADP
ejpam-370	102	5	)	)	PUNCT
ejpam-370	102	6	=	=	PUNCT
ejpam-370	103	1	a	a	DET
ejpam-370	103	2	(	(	PUNCT
ejpam-370	103	3	n	n	CCONJ
ejpam-370	103	4	)	)	PUNCT
ejpam-370	103	5	11	11	NUM
ejpam-370	103	6	f	f	NOUN
ejpam-370	103	7	(	(	PUNCT
ejpam-370	103	8	n	n	CCONJ
ejpam-370	103	9	)	)	PUNCT
ejpam-370	103	10	1	1	NUM
ejpam-370	103	11	f	f	NOUN
ejpam-370	103	12	(	(	PUNCT
ejpam-370	103	13	n	n	CCONJ
ejpam-370	103	14	)	)	PUNCT
ejpam-370	103	15	(	(	PUNCT
ejpam-370	103	16	f	f	X
ejpam-370	103	17	(	(	PUNCT
ejpam-370	103	18	n	n	CCONJ
ejpam-370	103	19	)	)	PUNCT
ejpam-370	103	20	6=	6=	ADP
ejpam-370	103	21	0	0	NUM
ejpam-370	103	22	)	)	PUNCT
ejpam-370	103	23	,	,	PUNCT
ejpam-370	103	24	x	x	X
ejpam-370	103	25	(	(	PUNCT
ejpam-370	103	26	n	n	CCONJ
ejpam-370	103	27	)	)	PUNCT
ejpam-370	103	28	=	=	SYM
ejpam-370	103	29	x	x	X
ejpam-370	103	30	(	(	PUNCT
ejpam-370	103	31	n	n	CCONJ
ejpam-370	103	32	)	)	PUNCT
ejpam-370	103	33	0	0	NUM
ejpam-370	103	34	=	=	SYM
ejpam-370	103	35	�	�	PROPN
ejpam-370	103	36	f	f	PROPN
ejpam-370	103	37	(	(	PUNCT
ejpam-370	103	38	n	n	CCONJ
ejpam-370	103	39	)	)	PUNCT
ejpam-370	103	40	1	1	NUM
ejpam-370	103	41	a	a	DET
ejpam-370	103	42	(	(	PUNCT
ejpam-370	103	43	n	n	CCONJ
ejpam-370	103	44	)	)	PUNCT
ejpam-370	103	45	11	11	NUM
ejpam-370	103	46	�	�	PROPN
ejpam-370	103	47	and	and	CCONJ
ejpam-370	103	48	if	if	SCONJ
ejpam-370	103	49	f	f	PROPN
ejpam-370	103	50	(	(	PUNCT
ejpam-370	103	51	n	n	CCONJ
ejpam-370	103	52	)	)	PUNCT
ejpam-370	103	53	=	=	SYM
ejpam-370	103	54	0	0	NUM
ejpam-370	103	55	,	,	PUNCT
ejpam-370	103	56	x	x	X
ejpam-370	103	57	(	(	PUNCT
ejpam-370	103	58	n	n	CCONJ
ejpam-370	103	59	)	)	PUNCT
ejpam-370	103	60	=	=	SYM
ejpam-370	103	61	x	x	X
ejpam-370	103	62	(	(	PUNCT
ejpam-370	103	63	n	n	CCONJ
ejpam-370	103	64	)	)	PUNCT
ejpam-370	103	65	0	0	NUM
ejpam-370	104	1	=	=	SYM
ejpam-370	104	2	0	0	X
ejpam-370	104	3	.	.	PUNCT
ejpam-370	105	1	therefore	therefore	ADV
ejpam-370	105	2	,	,	PUNCT
ejpam-370	105	3	the	the	DET
ejpam-370	105	4	solution	solution	NOUN
ejpam-370	105	5	of	of	ADP
ejpam-370	105	6	(	(	PUNCT
ejpam-370	105	7	5	5	NUM
ejpam-370	105	8	)	)	PUNCT
ejpam-370	105	9	is	be	AUX
ejpam-370	105	10	x	x	X
ejpam-370	105	11	=	=	SYM
ejpam-370	105	12	n	n	CCONJ
ejpam-370	105	13	∑	∑	ADP
ejpam-370	105	14	i=1	i=1	PROPN
ejpam-370	105	15			PROPN
ejpam-370	105	16			NOUN
ejpam-370	105	17			NOUN
ejpam-370	105	18	i−1	i−1	PROPN
ejpam-370	105	19	∏	∏	PROPN
ejpam-370	105	20	j=1	j=1	PROPN
ejpam-370	105	21	r	r	PROPN
ejpam-370	105	22	(	(	PUNCT
ejpam-370	105	23	j	j	NOUN
ejpam-370	105	24	)	)	PUNCT
ejpam-370	105	25			PROPN
ejpam-370	105	26			VERB
ejpam-370	105	27			PUNCT
ejpam-370	106	1	x	x	X
ejpam-370	106	2	(	(	PUNCT
ejpam-370	106	3	i	i	NOUN
ejpam-370	106	4	)	)	PUNCT
ejpam-370	106	5	0	0	PUNCT
ejpam-370	106	6	.	.	PUNCT
ejpam-370	107	1	but	but	CCONJ
ejpam-370	107	2	,	,	PUNCT
ejpam-370	107	3	if	if	SCONJ
ejpam-370	107	4	a(n	a(n	NOUN
ejpam-370	107	5	)	)	PUNCT
ejpam-370	107	6	6=	6=	ADP
ejpam-370	107	7	a	a	DET
ejpam-370	107	8	(	(	PUNCT
ejpam-370	107	9	n	n	CCONJ
ejpam-370	107	10	)	)	PUNCT
ejpam-370	107	11	11	11	NUM
ejpam-370	107	12	f	f	NOUN
ejpam-370	107	13	(	(	PUNCT
ejpam-370	107	14	n	n	CCONJ
ejpam-370	107	15	)	)	PUNCT
ejpam-370	107	16	1	1	NUM
ejpam-370	107	17	f	f	NOUN
ejpam-370	107	18	(	(	PUNCT
ejpam-370	107	19	n	n	CCONJ
ejpam-370	107	20	)	)	PUNCT
ejpam-370	107	21	(	(	PUNCT
ejpam-370	107	22	f	f	X
ejpam-370	107	23	(	(	PUNCT
ejpam-370	107	24	n	n	CCONJ
ejpam-370	107	25	)	)	PUNCT
ejpam-370	107	26	6=	6=	ADP
ejpam-370	107	27	0	0	NUM
ejpam-370	107	28	)	)	PUNCT
ejpam-370	107	29	,	,	PUNCT
ejpam-370	107	30	the	the	DET
ejpam-370	107	31	equation	equation	NOUN
ejpam-370	107	32	(	(	PUNCT
ejpam-370	107	33	5	5	NUM
ejpam-370	107	34	)	)	PUNCT
ejpam-370	107	35	has	have	VERB
ejpam-370	107	36	no	no	DET
ejpam-370	107	37	solution	solution	NOUN
ejpam-370	107	38	.	.	PUNCT
ejpam-370	108	1	case	case	NOUN
ejpam-370	108	2	2	2	X
ejpam-370	108	3	.	.	PUNCT
ejpam-370	108	4	suppose	suppose	VERB
ejpam-370	108	5	that	that	SCONJ
ejpam-370	108	6	a(k	a(k	NUM
ejpam-370	108	7	)	)	PUNCT
ejpam-370	108	8	6=	6=	ADP
ejpam-370	108	9	0	0	NUM
ejpam-370	109	1	(	(	PUNCT
ejpam-370	109	2	k	k	X
ejpam-370	109	3	<	<	X
ejpam-370	109	4	n	n	CCONJ
ejpam-370	109	5	)	)	PUNCT
ejpam-370	109	6	and	and	CCONJ
ejpam-370	109	7	mk	mk	X
ejpam-370	109	8	=	=	SYM
ejpam-370	109	9	1	1	NUM
ejpam-370	109	10	or	or	CCONJ
ejpam-370	109	11	pk	pk	NOUN
ejpam-370	109	12	.	.	PROPN
ejpam-370	109	13	in	in	ADP
ejpam-370	109	14	this	this	DET
ejpam-370	109	15	case	case	NOUN
ejpam-370	109	16	;	;	PUNCT
ejpam-370	109	17	for	for	ADP
ejpam-370	109	18	all	all	PRON
ejpam-370	109	19	of	of	ADP
ejpam-370	109	20	the	the	DET
ejpam-370	109	21	situations	situation	NOUN
ejpam-370	109	22	of	of	ADP
ejpam-370	109	23	m	m	PROPN
ejpam-370	109	24	and	and	CCONJ
ejpam-370	109	25	n	n	CCONJ
ejpam-370	109	26	,	,	PUNCT
ejpam-370	109	27	the	the	DET
ejpam-370	109	28	solution	solution	NOUN
ejpam-370	109	29	of	of	ADP
ejpam-370	109	30	the	the	DET
ejpam-370	109	31	system	system	NOUN
ejpam-370	109	32	(	(	PUNCT
ejpam-370	109	33	5	5	NUM
ejpam-370	109	34	)	)	PUNCT
ejpam-370	109	35	is	be	AUX
ejpam-370	109	36	obtained	obtain	VERB
ejpam-370	109	37	as	as	SCONJ
ejpam-370	109	38	follows	follow	VERB
ejpam-370	109	39	x	x	NOUN
ejpam-370	109	40	=	=	SYM
ejpam-370	109	41	k	k	X
ejpam-370	109	42	∑	∑	PUNCT
ejpam-370	109	43	i=1	i=1	PROPN
ejpam-370	109	44			PROPN
ejpam-370	109	45			NOUN
ejpam-370	109	46			NOUN
ejpam-370	109	47	i−1	i−1	PROPN
ejpam-370	109	48	∏	∏	PROPN
ejpam-370	109	49	j=1	j=1	PROPN
ejpam-370	109	50	r	r	PROPN
ejpam-370	109	51	(	(	PUNCT
ejpam-370	109	52	j	j	NOUN
ejpam-370	109	53	)	)	PUNCT
ejpam-370	109	54			PROPN
ejpam-370	109	55			VERB
ejpam-370	109	56			PUNCT
ejpam-370	110	1	x	x	X
ejpam-370	110	2	(	(	PUNCT
ejpam-370	110	3	i	i	NOUN
ejpam-370	110	4	)	)	PUNCT
ejpam-370	110	5	0	0	PUNCT
ejpam-370	111	1	+	+	NUM
ejpam-370	111	2			NOUN
ejpam-370	111	3			NOUN
ejpam-370	111	4			NOUN
ejpam-370	111	5	k	k	PROPN
ejpam-370	111	6	∏	∏	PUNCT
ejpam-370	111	7	j=1	j=1	ADJ
ejpam-370	111	8	r	r	PROPN
ejpam-370	111	9	(	(	PUNCT
ejpam-370	111	10	j	j	NOUN
ejpam-370	111	11	)	)	PUNCT
ejpam-370	111	12			PROPN
ejpam-370	111	13			VERB
ejpam-370	111	14			PUNCT
ejpam-370	112	1	x	x	X
ejpam-370	112	2	(	(	PUNCT
ejpam-370	112	3	k+1	k+1	NOUN
ejpam-370	112	4	)	)	PUNCT
ejpam-370	112	5	,	,	PUNCT
ejpam-370	112	6	k.	k.	PROPN
ejpam-370	112	7	aydın	aydın	PROPN
ejpam-370	112	8	,	,	PUNCT
ejpam-370	112	9	g.	g.	PROPN
ejpam-370	112	10	kızılkan	kızılkan	PROPN
ejpam-370	112	11	,	,	PUNCT
ejpam-370	112	12	a.	a.	PROPN
ejpam-370	112	13	çıbıkdiken	çıbıkdiken	VERB
ejpam-370	112	14	/	/	SYM
ejpam-370	112	15	eur	eur	PROPN
ejpam-370	112	16	.	.	PUNCT
ejpam-370	113	1	j.	j.	PROPN
ejpam-370	113	2	pure	pure	PROPN
ejpam-370	113	3	appl	appl	PROPN
ejpam-370	113	4	.	.	PROPN
ejpam-370	113	5	math	math	PROPN
ejpam-370	113	6	,	,	PUNCT
ejpam-370	113	7	3	3	NUM
ejpam-370	113	8	(	(	PUNCT
ejpam-370	113	9	2010	2010	NUM
ejpam-370	113	10	)	)	PUNCT
ejpam-370	113	11	,	,	PUNCT
ejpam-370	113	12	819	819	NUM
ejpam-370	113	13	-	-	SYM
ejpam-370	113	14	830	830	NUM
ejpam-370	113	15	824	824	NUM
ejpam-370	114	1	where	where	SCONJ
ejpam-370	114	2	x	x	PUNCT
ejpam-370	114	3	(	(	PUNCT
ejpam-370	114	4	k+1	k+1	NOUN
ejpam-370	114	5	)	)	PUNCT
ejpam-370	114	6	=	=	SYM
ejpam-370	114	7	�	�	PROPN
ejpam-370	114	8	x	x	SYM
ejpam-370	114	9	(	(	PUNCT
ejpam-370	114	10	k+1	k+1	NOUN
ejpam-370	114	11	)	)	PUNCT
ejpam-370	114	12	1	1	NUM
ejpam-370	114	13	x	x	SYM
ejpam-370	114	14	(	(	PUNCT
ejpam-370	114	15	k+1	k+1	NOUN
ejpam-370	114	16	)	)	PUNCT
ejpam-370	114	17	2	2	NUM
ejpam-370	114	18	.	.	PUNCT
ejpam-370	114	19	.	.	PUNCT
ejpam-370	114	20	.	.	PUNCT
ejpam-370	115	1	x	x	PUNCT
ejpam-370	115	2	(	(	PUNCT
ejpam-370	115	3	k+1	k+1	NOUN
ejpam-370	115	4	)	)	PUNCT
ejpam-370	115	5	nk+1	nk+1	NUM
ejpam-370	115	6	�	�	PROPN
ejpam-370	115	7	t	t	PROPN
ejpam-370	115	8	;	;	PUNCT
ejpam-370	115	9	x	x	X
ejpam-370	115	10	(	(	PUNCT
ejpam-370	115	11	k+1	k+1	NOUN
ejpam-370	115	12	)	)	PUNCT
ejpam-370	115	13	j	j	PROPN
ejpam-370	115	14	(	(	PUNCT
ejpam-370	115	15	j	j	PROPN
ejpam-370	115	16	=	=	SYM
ejpam-370	115	17	1(1)nk+1	1(1)nk+1	NUM
ejpam-370	115	18	)	)	PUNCT
ejpam-370	115	19	are	be	AUX
ejpam-370	115	20	the	the	DET
ejpam-370	115	21	arbitrary	arbitrary	ADJ
ejpam-370	115	22	parameters	parameter	NOUN
ejpam-370	115	23	and	and	CCONJ
ejpam-370	115	24	f	f	PROPN
ejpam-370	115	25	(	(	PUNCT
ejpam-370	115	26	k	k	X
ejpam-370	115	27	)	)	PUNCT
ejpam-370	115	28	i	i	NOUN
ejpam-370	115	29	=	=	NOUN
ejpam-370	115	30	0	0	NUM
ejpam-370	115	31	,	,	PUNCT
ejpam-370	115	32	i	i	PRON
ejpam-370	115	33	=	=	NOUN
ejpam-370	115	34	1(1)p−	1(1)p−	PROPN
ejpam-370	115	35	1	1	NUM
ejpam-370	115	36	for	for	ADP
ejpam-370	115	37	p	p	NOUN
ejpam-370	115	38	>	>	X
ejpam-370	115	39	1	1	NUM
ejpam-370	115	40	.	.	PUNCT
ejpam-370	115	41	case	case	NOUN
ejpam-370	115	42	3	3	X
ejpam-370	115	43	.	.	PUNCT
ejpam-370	115	44	suppose	suppose	VERB
ejpam-370	115	45	that	that	SCONJ
ejpam-370	115	46	a(k	a(k	NUM
ejpam-370	115	47	)	)	PUNCT
ejpam-370	116	1	=	=	SYM
ejpam-370	116	2	0	0	PUNCT
ejpam-370	117	1	(	(	PUNCT
ejpam-370	117	2	k	k	PROPN
ejpam-370	117	3	≤	≤	PROPN
ejpam-370	117	4	n	n	CCONJ
ejpam-370	117	5	)	)	PUNCT
ejpam-370	117	6	.	.	PUNCT
ejpam-370	118	1	a	a	X
ejpam-370	118	2	)	)	PUNCT
ejpam-370	118	3	if	if	SCONJ
ejpam-370	118	4	f	f	PROPN
ejpam-370	118	5	(	(	PUNCT
ejpam-370	118	6	k	k	NOUN
ejpam-370	118	7	)	)	PUNCT
ejpam-370	118	8	=	=	SYM
ejpam-370	118	9	0	0	NUM
ejpam-370	118	10	,	,	PUNCT
ejpam-370	118	11	then	then	ADV
ejpam-370	118	12	the	the	DET
ejpam-370	118	13	solution	solution	NOUN
ejpam-370	118	14	of	of	ADP
ejpam-370	118	15	the	the	DET
ejpam-370	118	16	system	system	NOUN
ejpam-370	118	17	(	(	PUNCT
ejpam-370	118	18	5	5	NUM
ejpam-370	118	19	)	)	PUNCT
ejpam-370	118	20	is	be	AUX
ejpam-370	118	21	obtained	obtain	VERB
ejpam-370	118	22	as	as	SCONJ
ejpam-370	118	23	follows	follow	VERB
ejpam-370	118	24	x	x	NOUN
ejpam-370	118	25	=	=	SYM
ejpam-370	118	26	k−1	k−1	PROPN
ejpam-370	118	27	∑	∑	PUNCT
ejpam-370	118	28	i=1	i=1	PROPN
ejpam-370	118	29			PROPN
ejpam-370	118	30			NOUN
ejpam-370	118	31			NOUN
ejpam-370	118	32	i−1	i−1	PROPN
ejpam-370	118	33	∏	∏	PROPN
ejpam-370	118	34	j=1	j=1	PROPN
ejpam-370	118	35	r	r	PROPN
ejpam-370	118	36	(	(	PUNCT
ejpam-370	118	37	j	j	NOUN
ejpam-370	118	38	)	)	PUNCT
ejpam-370	118	39			PROPN
ejpam-370	118	40			VERB
ejpam-370	118	41			PUNCT
ejpam-370	119	1	x	x	X
ejpam-370	119	2	(	(	PUNCT
ejpam-370	119	3	i	i	NOUN
ejpam-370	119	4	)	)	PUNCT
ejpam-370	119	5	0	0	PUNCT
ejpam-370	120	1	+	+	NUM
ejpam-370	120	2			NOUN
ejpam-370	120	3			NOUN
ejpam-370	120	4			NOUN
ejpam-370	120	5	k−1	k−1	PROPN
ejpam-370	120	6	∏	∏	NUM
ejpam-370	120	7	j=1	j=1	NOUN
ejpam-370	120	8	r	r	PROPN
ejpam-370	120	9	(	(	PUNCT
ejpam-370	120	10	j	j	NOUN
ejpam-370	120	11	)	)	PUNCT
ejpam-370	120	12			PROPN
ejpam-370	120	13			VERB
ejpam-370	120	14			PUNCT
ejpam-370	121	1	x	x	X
ejpam-370	121	2	(	(	PUNCT
ejpam-370	121	3	k	k	NOUN
ejpam-370	121	4	)	)	PUNCT
ejpam-370	121	5	,	,	PUNCT
ejpam-370	121	6	where	where	SCONJ
ejpam-370	121	7	x	x	X
ejpam-370	121	8	(	(	PUNCT
ejpam-370	121	9	k	k	NOUN
ejpam-370	121	10	)	)	PUNCT
ejpam-370	121	11	=	=	SYM
ejpam-370	121	12	�	�	PROPN
ejpam-370	121	13	x	x	SYM
ejpam-370	121	14	(	(	PUNCT
ejpam-370	121	15	k	k	NOUN
ejpam-370	121	16	)	)	PUNCT
ejpam-370	121	17	1	1	NUM
ejpam-370	121	18	x	x	SYM
ejpam-370	121	19	(	(	PUNCT
ejpam-370	121	20	k	k	NOUN
ejpam-370	121	21	)	)	PUNCT
ejpam-370	121	22	2	2	NUM
ejpam-370	121	23	.	.	PUNCT
ejpam-370	121	24	.	.	PUNCT
ejpam-370	121	25	.	.	PUNCT
ejpam-370	122	1	x	x	X
ejpam-370	122	2	(	(	PUNCT
ejpam-370	122	3	k	k	NOUN
ejpam-370	122	4	)	)	PUNCT
ejpam-370	122	5	nk	nk	PROPN
ejpam-370	122	6	�	�	PROPN
ejpam-370	122	7	t	t	PROPN
ejpam-370	122	8	;	;	PUNCT
ejpam-370	122	9	x	x	SYM
ejpam-370	122	10	(	(	PUNCT
ejpam-370	122	11	k	k	NOUN
ejpam-370	122	12	)	)	PUNCT
ejpam-370	122	13	j	j	PROPN
ejpam-370	122	14	(	(	PUNCT
ejpam-370	122	15	j	j	PROPN
ejpam-370	122	16	=	=	SYM
ejpam-370	122	17	1(1)nk	1(1)nk	NUM
ejpam-370	122	18	)	)	PUNCT
ejpam-370	122	19	are	be	AUX
ejpam-370	122	20	the	the	DET
ejpam-370	122	21	arbitrary	arbitrary	ADJ
ejpam-370	122	22	parameters	parameter	NOUN
ejpam-370	122	23	and	and	CCONJ
ejpam-370	122	24	f	f	PROPN
ejpam-370	122	25	(	(	PUNCT
ejpam-370	122	26	k	k	X
ejpam-370	122	27	)	)	PUNCT
ejpam-370	122	28	i	i	NOUN
ejpam-370	122	29	=	=	NOUN
ejpam-370	122	30	0	0	NUM
ejpam-370	122	31	,	,	PUNCT
ejpam-370	122	32	i	i	PRON
ejpam-370	122	33	=	=	NOUN
ejpam-370	122	34	1(1)p−	1(1)p−	NUM
ejpam-370	122	35	1for	1for	PROPN
ejpam-370	122	36	p	p	X
ejpam-370	122	37	>	>	X
ejpam-370	122	38	1	1	NUM
ejpam-370	122	39	.	.	X
ejpam-370	122	40	b	b	X
ejpam-370	122	41	)	)	PUNCT
ejpam-370	122	42	if	if	SCONJ
ejpam-370	122	43	f	f	PROPN
ejpam-370	122	44	(	(	PUNCT
ejpam-370	122	45	k	k	NOUN
ejpam-370	122	46	)	)	PUNCT
ejpam-370	122	47	6=	6=	ADP
ejpam-370	122	48	0	0	NUM
ejpam-370	122	49	,	,	PUNCT
ejpam-370	122	50	then	then	ADV
ejpam-370	122	51	(	(	PUNCT
ejpam-370	122	52	5	5	X
ejpam-370	122	53	)	)	PUNCT
ejpam-370	122	54	is	be	AUX
ejpam-370	122	55	an	an	DET
ejpam-370	122	56	inconsistent	inconsistent	ADJ
ejpam-370	122	57	system	system	NOUN
ejpam-370	122	58	and	and	CCONJ
ejpam-370	122	59	has	have	VERB
ejpam-370	122	60	no	no	DET
ejpam-370	122	61	solution	solution	NOUN
ejpam-370	122	62	.	.	PUNCT
ejpam-370	123	1	3	3	X
ejpam-370	123	2	.	.	NUM
ejpam-370	123	3	generalized	generalize	VERB
ejpam-370	123	4	iterative	iterative	NOUN
ejpam-370	123	5	decreasing	decrease	VERB
ejpam-370	123	6	dimension	dimension	NOUN
ejpam-370	123	7	algorithm	algorithm	NOUN
ejpam-370	123	8	(	(	PUNCT
ejpam-370	123	9	gidda	gidda	NOUN
ejpam-370	123	10	)	)	PUNCT
ejpam-370	123	11	here	here	ADV
ejpam-370	123	12	,	,	PUNCT
ejpam-370	123	13	we	we	PRON
ejpam-370	123	14	are	be	AUX
ejpam-370	123	15	going	go	VERB
ejpam-370	123	16	to	to	PART
ejpam-370	123	17	give	give	VERB
ejpam-370	123	18	an	an	DET
ejpam-370	123	19	algorithm	algorithm	NOUN
ejpam-370	123	20	based	base	VERB
ejpam-370	123	21	on	on	ADP
ejpam-370	123	22	giddm	giddm	NOUN
ejpam-370	123	23	.	.	PUNCT
ejpam-370	124	1	gidda	gidda	NOUN
ejpam-370	124	2	is	be	AUX
ejpam-370	124	3	the	the	DET
ejpam-370	124	4	modification	modification	NOUN
ejpam-370	124	5	of	of	ADP
ejpam-370	124	6	the	the	DET
ejpam-370	124	7	algorithm	algorithm	NOUN
ejpam-370	124	8	idda	idda	NOUN
ejpam-370	124	9	given	give	VERB
ejpam-370	124	10	in	in	ADP
ejpam-370	124	11	[	[	X
ejpam-370	124	12	3	3	NUM
ejpam-370	124	13	]	]	PUNCT
ejpam-370	124	14	.	.	PUNCT
ejpam-370	125	1	input	input	NOUN
ejpam-370	125	2	.	.	PUNCT
ejpam-370	126	1	a	a	DET
ejpam-370	126	2	m	m	NOUN
ejpam-370	126	3	×	×	NOUN
ejpam-370	126	4	n	n	PRON
ejpam-370	126	5	matrix	matrix	NOUN
ejpam-370	126	6	,	,	PUNCT
ejpam-370	126	7	f	f	PROPN
ejpam-370	126	8	m	m	PROPN
ejpam-370	126	9	-vector	-vector	NOUN
ejpam-370	126	10	.	.	PUNCT
ejpam-370	127	1	step	step	NOUN
ejpam-370	127	2	1	1	NUM
ejpam-370	127	3	.	.	PUNCT
ejpam-370	128	1	get	get	VERB
ejpam-370	128	2	n	n	PRON
ejpam-370	128	3	=	=	NOUN
ejpam-370	128	4	min{m	min{m	PROPN
ejpam-370	128	5	,	,	PUNCT
ejpam-370	128	6	n	n	CCONJ
ejpam-370	128	7	}	}	PUNCT
ejpam-370	128	8	,	,	PUNCT
ejpam-370	128	9	a(1	a(1	PROPN
ejpam-370	128	10	)	)	PUNCT
ejpam-370	128	11	=	=	SYM
ejpam-370	129	1	a	a	PROPN
ejpam-370	129	2	,	,	PUNCT
ejpam-370	129	3	f	f	PROPN
ejpam-370	129	4	(	(	PUNCT
ejpam-370	129	5	1	1	NUM
ejpam-370	129	6	)	)	PUNCT
ejpam-370	129	7	=	=	SYM
ejpam-370	129	8	f	f	PROPN
ejpam-370	129	9	.	.	PUNCT
ejpam-370	130	1	step	step	NOUN
ejpam-370	130	2	2	2	NUM
ejpam-370	130	3	.	.	PUNCT
ejpam-370	131	1	k	k	X
ejpam-370	131	2	=	=	PUNCT
ejpam-370	131	3	1(1)n−	1(1)n−	NUM
ejpam-370	131	4	1	1	NUM
ejpam-370	131	5	,	,	PUNCT
ejpam-370	131	6	2.1	2.1	NUM
ejpam-370	131	7	.	.	PUNCT
ejpam-370	131	8	calculate	calculate	NOUN
ejpam-370	131	9	a(k	a(k	PROPN
ejpam-370	131	10	)	)	PUNCT
ejpam-370	131	11	,	,	PUNCT
ejpam-370	131	12	f	f	PROPN
ejpam-370	131	13	(	(	PUNCT
ejpam-370	131	14	k	k	NOUN
ejpam-370	131	15	)	)	PUNCT
ejpam-370	131	16	,	,	PUNCT
ejpam-370	131	17	mk	mk	PROPN
ejpam-370	131	18	and	and	CCONJ
ejpam-370	131	19	nk	nk	PROPN
ejpam-370	131	20	.	.	PROPN
ejpam-370	131	21	2.2	2.2	NUM
ejpam-370	131	22	.	.	PUNCT
ejpam-370	132	1	control	control	NOUN
ejpam-370	132	2	if	if	SCONJ
ejpam-370	132	3	a	a	DET
ejpam-370	132	4	(	(	PUNCT
ejpam-370	132	5	k	k	NOUN
ejpam-370	132	6	)	)	PUNCT
ejpam-370	132	7	i	i	PRON
ejpam-370	132	8	j	j	PROPN
ejpam-370	133	1	6=	6=	ADP
ejpam-370	133	2	0	0	NUM
ejpam-370	133	3	for	for	ADP
ejpam-370	133	4	i	i	PRON
ejpam-370	133	5	=	=	SYM
ejpam-370	133	6	1(1)mk	1(1)mk	PROPN
ejpam-370	133	7	,	,	PUNCT
ejpam-370	133	8	j	j	PROPN
ejpam-370	133	9	=	=	SYM
ejpam-370	133	10	1(1)nk	1(1)nk	NUM
ejpam-370	133	11	;	;	PUNCT
ejpam-370	133	12	let	let	VERB
ejpam-370	133	13	a(k)ps	a(k)ps	PRON
ejpam-370	133	14	6=	6=	ADP
ejpam-370	133	15	0	0	NUM
ejpam-370	133	16	is	be	AUX
ejpam-370	133	17	first	first	ADJ
ejpam-370	133	18	element	element	NOUN
ejpam-370	133	19	and	and	CCONJ
ejpam-370	133	20	take	take	VERB
ejpam-370	133	21	p	p	NOUN
ejpam-370	133	22	=	=	SYM
ejpam-370	133	23	pk	pk	PROPN
ejpam-370	133	24	.	.	PROPN
ejpam-370	133	25	otherwise	otherwise	ADV
ejpam-370	133	26	go	go	VERB
ejpam-370	133	27	step	step	NOUN
ejpam-370	133	28	4	4	NUM
ejpam-370	133	29	.	.	NOUN
ejpam-370	134	1	2.3	2.3	NUM
ejpam-370	134	2	.	.	PUNCT
ejpam-370	135	1	if	if	SCONJ
ejpam-370	135	2	p	p	X
ejpam-370	135	3	>	>	X
ejpam-370	135	4	1	1	NUM
ejpam-370	135	5	,	,	PUNCT
ejpam-370	135	6	control	control	VERB
ejpam-370	135	7	if	if	SCONJ
ejpam-370	135	8	f	f	PROPN
ejpam-370	135	9	(	(	PUNCT
ejpam-370	135	10	k	k	X
ejpam-370	135	11	)	)	PUNCT
ejpam-370	135	12	i	i	NOUN
ejpam-370	136	1	=	=	PUNCT
ejpam-370	136	2	0	0	PUNCT
ejpam-370	137	1	for	for	ADP
ejpam-370	137	2	i	i	PRON
ejpam-370	137	3	=	=	SYM
ejpam-370	137	4	1(1)p−	1(1)p−	NUM
ejpam-370	137	5	1	1	NUM
ejpam-370	137	6	.	.	PUNCT
ejpam-370	138	1	if	if	SCONJ
ejpam-370	138	2	∃i	∃i	PROPN
ejpam-370	138	3	∋	∋	NOUN
ejpam-370	138	4	f	f	PROPN
ejpam-370	138	5	(	(	PUNCT
ejpam-370	138	6	k	k	X
ejpam-370	138	7	)	)	PUNCT
ejpam-370	138	8	i	i	PROPN
ejpam-370	138	9	6=	6=	NUM
ejpam-370	138	10	0	0	NUM
ejpam-370	138	11	then	then	ADV
ejpam-370	138	12	go	go	VERB
ejpam-370	138	13	output	output	NOUN
ejpam-370	138	14	2	2	NUM
ejpam-370	138	15	.	.	NOUN
ejpam-370	138	16	2.4	2.4	NUM
ejpam-370	138	17	.	.	PUNCT
ejpam-370	139	1	if	if	SCONJ
ejpam-370	139	2	mk	mk	PROPN
ejpam-370	139	3	=	=	SYM
ejpam-370	139	4	1	1	NUM
ejpam-370	139	5	or	or	CCONJ
ejpam-370	139	6	pk	pk	NOUN
ejpam-370	139	7	,	,	PUNCT
ejpam-370	139	8	calculate	calculate	NOUN
ejpam-370	139	9	x	x	SYM
ejpam-370	139	10	(	(	PUNCT
ejpam-370	139	11	k	k	NOUN
ejpam-370	139	12	)	)	PUNCT
ejpam-370	139	13	0	0	NUM
ejpam-370	139	14	,	,	PUNCT
ejpam-370	139	15	r(k	r(k	PROPN
ejpam-370	139	16	)	)	PUNCT
ejpam-370	139	17	,	,	PUNCT
ejpam-370	139	18	m=	m=	X
ejpam-370	139	19	k	k	NOUN
ejpam-370	139	20	and	and	CCONJ
ejpam-370	139	21	go	go	VERB
ejpam-370	139	22	output	output	NOUN
ejpam-370	139	23	1	1	NUM
ejpam-370	139	24	.	.	X
ejpam-370	139	25	2.5	2.5	NUM
ejpam-370	139	26	.	.	PUNCT
ejpam-370	140	1	determine	determine	VERB
ejpam-370	140	2	a	a	DET
ejpam-370	140	3	(	(	PUNCT
ejpam-370	140	4	k	k	NOUN
ejpam-370	140	5	)	)	PUNCT
ejpam-370	140	6	1	1	NUM
ejpam-370	140	7	,	,	PUNCT
ejpam-370	140	8	a	a	DET
ejpam-370	140	9	(	(	PUNCT
ejpam-370	140	10	k	k	NOUN
ejpam-370	140	11	)	)	PUNCT
ejpam-370	140	12	2	2	NUM
ejpam-370	140	13	,	,	PUNCT
ejpam-370	140	14	u(k	u(k	PROPN
ejpam-370	140	15	)	)	PUNCT
ejpam-370	140	16	,	,	PUNCT
ejpam-370	140	17	v(k	v(k	PROPN
ejpam-370	140	18	)	)	PUNCT
ejpam-370	140	19	.	.	PUNCT
ejpam-370	141	1	2.6	2.6	NUM
ejpam-370	141	2	.	.	PUNCT
ejpam-370	141	3	calculate	calculate	NOUN
ejpam-370	141	4	x	x	SYM
ejpam-370	141	5	(	(	PUNCT
ejpam-370	141	6	k	k	NOUN
ejpam-370	141	7	)	)	PUNCT
ejpam-370	141	8	0	0	NUM
ejpam-370	141	9	and	and	CCONJ
ejpam-370	141	10	r(k	r(k	PROPN
ejpam-370	141	11	)	)	PUNCT
ejpam-370	141	12	.	.	PUNCT
ejpam-370	142	1	step	step	NOUN
ejpam-370	142	2	3	3	NUM
ejpam-370	142	3	.	.	PUNCT
ejpam-370	143	1	for	for	ADP
ejpam-370	143	2	k	k	PROPN
ejpam-370	143	3	=	=	PUNCT
ejpam-370	143	4	n	n	PRON
ejpam-370	143	5	calculate	calculate	VERB
ejpam-370	143	6	a(k	a(k	PROPN
ejpam-370	143	7	)	)	PUNCT
ejpam-370	143	8	,	,	PUNCT
ejpam-370	143	9	f	f	PROPN
ejpam-370	143	10	(	(	PUNCT
ejpam-370	143	11	k	k	NOUN
ejpam-370	143	12	)	)	PUNCT
ejpam-370	143	13	,	,	PUNCT
ejpam-370	143	14	mk	mk	PROPN
ejpam-370	143	15	and	and	CCONJ
ejpam-370	143	16	nk	nk	PROPN
ejpam-370	143	17	.	.	PROPN
ejpam-370	143	18	3.1	3.1	NUM
ejpam-370	143	19	.	.	PUNCT
ejpam-370	143	20	control	control	NOUN
ejpam-370	143	21	if	if	SCONJ
ejpam-370	143	22	a	a	DET
ejpam-370	143	23	(	(	PUNCT
ejpam-370	143	24	k	k	NOUN
ejpam-370	143	25	)	)	PUNCT
ejpam-370	143	26	i	i	PRON
ejpam-370	143	27	j	j	PROPN
ejpam-370	144	1	6=	6=	ADP
ejpam-370	144	2	0	0	NUM
ejpam-370	144	3	for	for	ADP
ejpam-370	144	4	i	i	PRON
ejpam-370	144	5	=	=	SYM
ejpam-370	144	6	1(1)mk	1(1)mk	PROPN
ejpam-370	144	7	,	,	PUNCT
ejpam-370	144	8	j	j	PROPN
ejpam-370	144	9	=	=	SYM
ejpam-370	144	10	1(1)nk	1(1)nk	NUM
ejpam-370	144	11	;	;	PUNCT
ejpam-370	144	12	let	let	VERB
ejpam-370	144	13	a(k)ps	a(k)ps	PRON
ejpam-370	144	14	6=	6=	ADP
ejpam-370	144	15	0	0	NUM
ejpam-370	144	16	is	be	AUX
ejpam-370	144	17	first	first	ADJ
ejpam-370	144	18	element	element	NOUN
ejpam-370	144	19	and	and	CCONJ
ejpam-370	144	20	take	take	VERB
ejpam-370	144	21	p	p	NOUN
ejpam-370	144	22	=	=	SYM
ejpam-370	144	23	pk	pk	PROPN
ejpam-370	144	24	.	.	PROPN
ejpam-370	144	25	otherwise	otherwise	ADV
ejpam-370	144	26	go	go	VERB
ejpam-370	144	27	step	step	NOUN
ejpam-370	144	28	4	4	NUM
ejpam-370	144	29	.	.	NOUN
ejpam-370	144	30	3.2	3.2	NUM
ejpam-370	144	31	.	.	PUNCT
ejpam-370	145	1	if	if	SCONJ
ejpam-370	145	2	m	m	VERB
ejpam-370	145	3	<	<	X
ejpam-370	145	4	n	n	X
ejpam-370	145	5	,	,	PUNCT
ejpam-370	145	6	calculate	calculate	NOUN
ejpam-370	145	7	x	x	SYM
ejpam-370	145	8	(	(	PUNCT
ejpam-370	145	9	k	k	NOUN
ejpam-370	145	10	)	)	PUNCT
ejpam-370	145	11	0	0	NUM
ejpam-370	145	12	,	,	PUNCT
ejpam-370	145	13	r(k	r(k	PROPN
ejpam-370	145	14	)	)	PUNCT
ejpam-370	145	15	,	,	PUNCT
ejpam-370	145	16	take	take	VERB
ejpam-370	145	17	m	m	NOUN
ejpam-370	145	18	=	=	SYM
ejpam-370	145	19	k	k	PROPN
ejpam-370	145	20	and	and	CCONJ
ejpam-370	145	21	go	go	VERB
ejpam-370	145	22	output	output	NOUN
ejpam-370	145	23	1	1	NUM
ejpam-370	145	24	3.3	3.3	NUM
ejpam-370	145	25	.	.	PUNCT
ejpam-370	146	1	if	if	SCONJ
ejpam-370	146	2	a(k	a(k	NUM
ejpam-370	146	3	)	)	PUNCT
ejpam-370	147	1	=	=	SYM
ejpam-370	147	2	a	a	DET
ejpam-370	147	3	(	(	PUNCT
ejpam-370	147	4	k	k	NOUN
ejpam-370	147	5	)	)	PUNCT
ejpam-370	147	6	11	11	NUM
ejpam-370	147	7	f	f	NOUN
ejpam-370	147	8	(	(	PUNCT
ejpam-370	147	9	k	k	NOUN
ejpam-370	147	10	)	)	PUNCT
ejpam-370	147	11	1	1	NUM
ejpam-370	147	12	f	f	NOUN
ejpam-370	147	13	(	(	PUNCT
ejpam-370	147	14	k	k	NOUN
ejpam-370	147	15	)	)	PUNCT
ejpam-370	147	16	or	or	CCONJ
ejpam-370	147	17	f	f	PROPN
ejpam-370	147	18	(	(	PUNCT
ejpam-370	147	19	k	k	NOUN
ejpam-370	147	20	)	)	PUNCT
ejpam-370	147	21	=	=	SYM
ejpam-370	147	22	0	0	NUM
ejpam-370	147	23	,	,	PUNCT
ejpam-370	147	24	calculate	calculate	NOUN
ejpam-370	147	25	x	x	SYM
ejpam-370	147	26	(	(	PUNCT
ejpam-370	147	27	k	k	NOUN
ejpam-370	147	28	)	)	PUNCT
ejpam-370	147	29	0	0	NUM
ejpam-370	147	30	,	,	PUNCT
ejpam-370	147	31	take	take	VERB
ejpam-370	147	32	m	m	NOUN
ejpam-370	147	33	=	=	SYM
ejpam-370	147	34	k	k	PROPN
ejpam-370	147	35	and	and	CCONJ
ejpam-370	147	36	go	go	VERB
ejpam-370	147	37	output	output	NOUN
ejpam-370	147	38	1	1	NUM
ejpam-370	147	39	.	.	PUNCT
ejpam-370	148	1	k.	k.	PROPN
ejpam-370	148	2	aydın	aydın	PROPN
ejpam-370	148	3	,	,	PUNCT
ejpam-370	148	4	g.	g.	PROPN
ejpam-370	148	5	kızılkan	kızılkan	PROPN
ejpam-370	148	6	,	,	PUNCT
ejpam-370	148	7	a.	a.	PROPN
ejpam-370	148	8	çıbıkdiken	çıbıkdiken	VERB
ejpam-370	148	9	/	/	SYM
ejpam-370	148	10	eur	eur	PROPN
ejpam-370	148	11	.	.	PUNCT
ejpam-370	149	1	j.	j.	PROPN
ejpam-370	149	2	pure	pure	PROPN
ejpam-370	149	3	appl	appl	PROPN
ejpam-370	149	4	.	.	PROPN
ejpam-370	149	5	math	math	PROPN
ejpam-370	149	6	,	,	PUNCT
ejpam-370	149	7	3	3	NUM
ejpam-370	149	8	(	(	PUNCT
ejpam-370	149	9	2010	2010	NUM
ejpam-370	149	10	)	)	PUNCT
ejpam-370	149	11	,	,	PUNCT
ejpam-370	149	12	819	819	NUM
ejpam-370	149	13	-	-	SYM
ejpam-370	149	14	830	830	NUM
ejpam-370	149	15	825	825	NUM
ejpam-370	149	16	3.4	3.4	NUM
ejpam-370	149	17	.	.	PUNCT
ejpam-370	150	1	if	if	SCONJ
ejpam-370	150	2	a(k	a(k	NUM
ejpam-370	150	3	)	)	PUNCT
ejpam-370	151	1	6=	6=	ADP
ejpam-370	151	2	a	a	PRON
ejpam-370	151	3	(	(	PUNCT
ejpam-370	151	4	k	k	NOUN
ejpam-370	151	5	)	)	PUNCT
ejpam-370	151	6	11	11	NUM
ejpam-370	151	7	f	f	NOUN
ejpam-370	151	8	(	(	PUNCT
ejpam-370	151	9	k	k	NOUN
ejpam-370	151	10	)	)	PUNCT
ejpam-370	151	11	1	1	NUM
ejpam-370	151	12	f	f	NOUN
ejpam-370	151	13	(	(	PUNCT
ejpam-370	151	14	k	k	NOUN
ejpam-370	151	15	)	)	PUNCT
ejpam-370	151	16	,	,	PUNCT
ejpam-370	151	17	go	go	VERB
ejpam-370	151	18	output	output	NOUN
ejpam-370	151	19	2	2	NUM
ejpam-370	151	20	.	.	PUNCT
ejpam-370	151	21	step	step	NOUN
ejpam-370	151	22	4	4	NUM
ejpam-370	151	23	.	.	PUNCT
ejpam-370	152	1	control	control	NOUN
ejpam-370	152	2	if	if	SCONJ
ejpam-370	152	3	f	f	PROPN
ejpam-370	152	4	(	(	PUNCT
ejpam-370	152	5	k	k	X
ejpam-370	152	6	)	)	PUNCT
ejpam-370	152	7	i	i	NOUN
ejpam-370	153	1	=	=	PUNCT
ejpam-370	153	2	0	0	PUNCT
ejpam-370	154	1	for	for	ADP
ejpam-370	154	2	i	i	PRON
ejpam-370	154	3	=	=	PROPN
ejpam-370	154	4	1(1)mk	1(1)mk	NUM
ejpam-370	154	5	.	.	PUNCT
ejpam-370	155	1	if	if	SCONJ
ejpam-370	155	2	∃i	∃i	PROPN
ejpam-370	155	3	∋	∋	NOUN
ejpam-370	155	4	f	f	PROPN
ejpam-370	155	5	(	(	PUNCT
ejpam-370	155	6	k	k	X
ejpam-370	155	7	)	)	PUNCT
ejpam-370	155	8	i	i	PROPN
ejpam-370	155	9	6=	6=	NUM
ejpam-370	155	10	0	0	NUM
ejpam-370	155	11	then	then	ADV
ejpam-370	155	12	go	go	VERB
ejpam-370	155	13	output	output	NOUN
ejpam-370	155	14	2	2	NUM
ejpam-370	155	15	.	.	NOUN
ejpam-370	155	16	4.1	4.1	NUM
ejpam-370	155	17	.	.	PUNCT
ejpam-370	156	1	take	take	VERB
ejpam-370	156	2	m	m	NOUN
ejpam-370	156	3	=	=	PUNCT
ejpam-370	156	4	k−	k−	PROPN
ejpam-370	156	5	1	1	NUM
ejpam-370	156	6	and	and	CCONJ
ejpam-370	156	7	go	go	VERB
ejpam-370	156	8	output	output	NOUN
ejpam-370	156	9	1	1	NUM
ejpam-370	156	10	.	.	PUNCT
ejpam-370	157	1	output	output	NOUN
ejpam-370	157	2	1	1	NUM
ejpam-370	157	3	.	.	PUNCT
ejpam-370	157	4	x	x	X
ejpam-370	158	1	=	=	PUNCT
ejpam-370	158	2	m	m	VERB
ejpam-370	158	3	∑	∑	ADJ
ejpam-370	158	4	i=1	i=1	PROPN
ejpam-370	158	5	i−1	i−1	PROPN
ejpam-370	158	6	∏	∏	PROPN
ejpam-370	158	7	j=1	j=1	PROPN
ejpam-370	158	8	r	r	PROPN
ejpam-370	158	9	(	(	PUNCT
ejpam-370	158	10	j	j	NOUN
ejpam-370	158	11	)	)	PUNCT
ejpam-370	158	12	!	!	PUNCT
ejpam-370	159	1	x	x	PUNCT
ejpam-370	159	2	(	(	PUNCT
ejpam-370	159	3	i	i	NOUN
ejpam-370	159	4	)	)	PUNCT
ejpam-370	159	5	0	0	PUNCT
ejpam-370	160	1	+	+	CCONJ
ejpam-370	160	2	m	m	VERB
ejpam-370	160	3	∏	∏	NUM
ejpam-370	160	4	j=1	j=1	ADJ
ejpam-370	160	5	r	r	PROPN
ejpam-370	160	6	(	(	PUNCT
ejpam-370	160	7	j	j	NOUN
ejpam-370	160	8	)	)	PUNCT
ejpam-370	160	9	!	!	PUNCT
ejpam-370	161	1	x	x	PUNCT
ejpam-370	161	2	(	(	PUNCT
ejpam-370	161	3	m+1	m+1	NUM
ejpam-370	161	4	)	)	PUNCT
ejpam-370	161	5	.	.	PUNCT
ejpam-370	162	1	output	output	NOUN
ejpam-370	162	2	2	2	NUM
ejpam-370	162	3	.	.	PUNCT
ejpam-370	163	1	no	no	DET
ejpam-370	163	2	solution	solution	NOUN
ejpam-370	163	3	.	.	PUNCT
ejpam-370	164	1	note	note	NOUN
ejpam-370	164	2	:	:	PUNCT
ejpam-370	164	3	vector	vector	NOUN
ejpam-370	164	4	x	x	X
ejpam-370	164	5	(	(	PUNCT
ejpam-370	164	6	m+1	m+1	NUM
ejpam-370	164	7	)	)	PUNCT
ejpam-370	164	8	in	in	ADP
ejpam-370	164	9	output	output	NOUN
ejpam-370	164	10	1	1	NUM
ejpam-370	164	11	is	be	AUX
ejpam-370	164	12	a	a	DET
ejpam-370	164	13	parametric	parametric	ADJ
ejpam-370	164	14	vector	vector	NOUN
ejpam-370	164	15	in	in	ADP
ejpam-370	164	16	nm+1	nm+1	NOUN
ejpam-370	164	17	-	-	NOUN
ejpam-370	164	18	dimension	dimension	NOUN
ejpam-370	164	19	,	,	PUNCT
ejpam-370	164	20	i.e.	i.e.	X
ejpam-370	164	21	x	x	X
ejpam-370	164	22	(	(	PUNCT
ejpam-370	164	23	m+1	m+1	NUM
ejpam-370	164	24	)	)	PUNCT
ejpam-370	164	25	j	j	NOUN
ejpam-370	164	26	(	(	PUNCT
ejpam-370	164	27	j	j	PROPN
ejpam-370	164	28	=	=	SYM
ejpam-370	164	29	1(1)nm	1(1)nm	PROPN
ejpam-370	164	30	)	)	PUNCT
ejpam-370	164	31	are	be	AUX
ejpam-370	164	32	the	the	DET
ejpam-370	164	33	arbitrary	arbitrary	ADJ
ejpam-370	164	34	parameters	parameter	NOUN
ejpam-370	164	35	,	,	PUNCT
ejpam-370	164	36	if	if	SCONJ
ejpam-370	164	37	nm+1	nm+1	PROPN
ejpam-370	164	38	6=	6=	SYM
ejpam-370	164	39	0	0	NUM
ejpam-370	164	40	.	.	PUNCT
ejpam-370	165	1	if	if	SCONJ
ejpam-370	165	2	nm+1	nm+1	PROPN
ejpam-370	165	3	=	=	SYM
ejpam-370	165	4	0	0	NUM
ejpam-370	165	5	,	,	PUNCT
ejpam-370	165	6	x	x	X
ejpam-370	165	7	(	(	PUNCT
ejpam-370	165	8	m+1	m+1	NUM
ejpam-370	165	9	)	)	PUNCT
ejpam-370	166	1	=	=	SYM
ejpam-370	166	2	0	0	X
ejpam-370	166	3	.	.	PUNCT
ejpam-370	167	1	now	now	ADV
ejpam-370	167	2	,	,	PUNCT
ejpam-370	167	3	we	we	PRON
ejpam-370	167	4	are	be	AUX
ejpam-370	167	5	going	go	VERB
ejpam-370	167	6	to	to	PART
ejpam-370	167	7	give	give	VERB
ejpam-370	167	8	some	some	DET
ejpam-370	167	9	examples	example	NOUN
ejpam-370	167	10	solved	solve	VERB
ejpam-370	167	11	using	use	VERB
ejpam-370	167	12	algorithm	algorithm	NOUN
ejpam-370	167	13	gidda	gidda	NOUN
ejpam-370	167	14	.	.	PUNCT
ejpam-370	168	1	example	example	NOUN
ejpam-370	169	1	1	1	NUM
ejpam-370	169	2	.	.	X
ejpam-370	169	3	input	input	NOUN
ejpam-370	169	4	:	:	PUNCT
ejpam-370	169	5	a=	a=	NOUN
ejpam-370	169	6			NOUN
ejpam-370	169	7			NOUN
ejpam-370	169	8			NOUN
ejpam-370	169	9			NOUN
ejpam-370	169	10			NOUN
ejpam-370	169	11	1	1	NUM
ejpam-370	169	12	−2	−2	NOUN
ejpam-370	169	13	2	2	NUM
ejpam-370	169	14	3	3	NUM
ejpam-370	169	15	2	2	NUM
ejpam-370	169	16	1	1	NUM
ejpam-370	169	17	1	1	NUM
ejpam-370	169	18	−1	−1	NOUN
ejpam-370	169	19	3	3	NUM
ejpam-370	169	20	−1	−1	NOUN
ejpam-370	169	21	3	3	NUM
ejpam-370	169	22	2	2	NUM
ejpam-370	169	23	5	5	NUM
ejpam-370	169	24	0	0	NUM
ejpam-370	169	25	4	4	NUM
ejpam-370	169	26	1	1	NUM
ejpam-370	169	27			NOUN
ejpam-370	169	28			NOUN
ejpam-370	169	29			VERB
ejpam-370	169	30			NOUN
ejpam-370	169	31			PUNCT
ejpam-370	169	32	,	,	PUNCT
ejpam-370	169	33	f	f	X
ejpam-370	169	34	=	=	SYM
ejpam-370	169	35			PROPN
ejpam-370	169	36			NOUN
ejpam-370	169	37			NOUN
ejpam-370	169	38			NOUN
ejpam-370	169	39			NOUN
ejpam-370	169	40	1	1	NUM
ejpam-370	169	41	−1	−1	NOUN
ejpam-370	169	42	0	0	NUM
ejpam-370	169	43	−1	−1	NOUN
ejpam-370	169	44			PROPN
ejpam-370	169	45			NOUN
ejpam-370	169	46			VERB
ejpam-370	169	47			NOUN
ejpam-370	169	48			PUNCT
ejpam-370	169	49	.	.	PUNCT
ejpam-370	170	1	step	step	NOUN
ejpam-370	170	2	1	1	NUM
ejpam-370	170	3	.	.	PUNCT
ejpam-370	171	1	n	n	CCONJ
ejpam-370	172	1	=	=	NOUN
ejpam-370	172	2	min{4,4}=	min{4,4}=	PROPN
ejpam-370	172	3	4	4	NUM
ejpam-370	172	4	.	.	PUNCT
ejpam-370	172	5	step	step	NOUN
ejpam-370	172	6	2	2	NUM
ejpam-370	172	7	.	.	NUM
ejpam-370	172	8	x	x	PUNCT
ejpam-370	173	1	(	(	PUNCT
ejpam-370	173	2	1	1	NUM
ejpam-370	173	3	)	)	PUNCT
ejpam-370	173	4	0	0	NUM
ejpam-370	174	1	=	=	SYM
ejpam-370	174	2			PROPN
ejpam-370	174	3			NOUN
ejpam-370	174	4			NOUN
ejpam-370	174	5			NOUN
ejpam-370	174	6			NOUN
ejpam-370	174	7	1	1	NUM
ejpam-370	174	8	0	0	NUM
ejpam-370	174	9	0	0	NUM
ejpam-370	174	10	0	0	NUM
ejpam-370	174	11			NOUN
ejpam-370	174	12			NOUN
ejpam-370	174	13			VERB
ejpam-370	174	14			NOUN
ejpam-370	174	15			X
ejpam-370	174	16	,	,	PUNCT
ejpam-370	174	17	r(1	r(1	PROPN
ejpam-370	174	18	)	)	PUNCT
ejpam-370	175	1	=	=	SYM
ejpam-370	175	2			PROPN
ejpam-370	175	3			NOUN
ejpam-370	175	4			NOUN
ejpam-370	175	5			NOUN
ejpam-370	175	6			NOUN
ejpam-370	175	7	2	2	NUM
ejpam-370	175	8	−2	−2	NOUN
ejpam-370	175	9	−3	−3	NOUN
ejpam-370	175	10	1	1	NUM
ejpam-370	175	11	0	0	NUM
ejpam-370	175	12	0	0	NUM
ejpam-370	175	13	0	0	NUM
ejpam-370	175	14	1	1	NUM
ejpam-370	175	15	0	0	NUM
ejpam-370	175	16	0	0	NUM
ejpam-370	175	17	0	0	NUM
ejpam-370	175	18	1	1	NUM
ejpam-370	175	19			NOUN
ejpam-370	175	20			NOUN
ejpam-370	175	21			VERB
ejpam-370	175	22			NOUN
ejpam-370	175	23			PUNCT
ejpam-370	176	1	x	x	X
ejpam-370	176	2	(	(	PUNCT
ejpam-370	176	3	2	2	NUM
ejpam-370	176	4	)	)	PUNCT
ejpam-370	176	5	0	0	NUM
ejpam-370	176	6	=	=	SYM
ejpam-370	176	7			PROPN
ejpam-370	176	8			NOUN
ejpam-370	176	9			PRON
ejpam-370	176	10	−3	−3	ADJ
ejpam-370	176	11	5	5	NUM
ejpam-370	176	12	0	0	NUM
ejpam-370	176	13	0	0	NUM
ejpam-370	176	14			NOUN
ejpam-370	176	15			NOUN
ejpam-370	176	16			PUNCT
ejpam-370	176	17	,	,	PUNCT
ejpam-370	176	18	r(2	r(2	PROPN
ejpam-370	176	19	)	)	PUNCT
ejpam-370	176	20	=	=	SYM
ejpam-370	176	21			NOUN
ejpam-370	176	22			NOUN
ejpam-370	176	23			NOUN
ejpam-370	176	24	3	3	NUM
ejpam-370	176	25	5	5	NUM
ejpam-370	176	26	7	7	NUM
ejpam-370	176	27	5	5	NUM
ejpam-370	176	28	1	1	NUM
ejpam-370	176	29	0	0	NUM
ejpam-370	176	30	0	0	NUM
ejpam-370	176	31	1	1	NUM
ejpam-370	176	32			NOUN
ejpam-370	176	33			NOUN
ejpam-370	176	34			PUNCT
ejpam-370	176	35	.	.	PUNCT
ejpam-370	177	1	a(3	a(3	PROPN
ejpam-370	177	2	)	)	PUNCT
ejpam-370	178	1	=	=	SYM
ejpam-370	178	2	0	0	NUM
ejpam-370	178	3	,	,	PUNCT
ejpam-370	178	4	f	f	PROPN
ejpam-370	178	5	(	(	PUNCT
ejpam-370	178	6	3	3	NUM
ejpam-370	178	7	)	)	PUNCT
ejpam-370	178	8	=	=	SYM
ejpam-370	178	9	0	0	NUM
ejpam-370	178	10	and	and	CCONJ
ejpam-370	178	11	m	m	PROPN
ejpam-370	178	12	=	=	ADJ
ejpam-370	178	13	2⇒	2⇒	NUM
ejpam-370	178	14	x	x	SYM
ejpam-370	178	15	(	(	PUNCT
ejpam-370	178	16	3	3	NUM
ejpam-370	178	17	)	)	PUNCT
ejpam-370	178	18	=	=	SYM
ejpam-370	178	19	�	�	PROPN
ejpam-370	178	20	x	x	SYM
ejpam-370	178	21	(	(	PUNCT
ejpam-370	178	22	3	3	NUM
ejpam-370	178	23	)	)	SYM
ejpam-370	178	24	1	1	NUM
ejpam-370	178	25	x	x	SYM
ejpam-370	178	26	(	(	PUNCT
ejpam-370	178	27	3	3	NUM
ejpam-370	178	28	)	)	SYM
ejpam-370	178	29	2	2	NUM
ejpam-370	178	30	�	�	NOUN
ejpam-370	178	31	=	=	SYM
ejpam-370	178	32	�	�	PROPN
ejpam-370	178	33	a	a	DET
ejpam-370	178	34	b	b	PROPN
ejpam-370	178	35	�	�	PROPN
ejpam-370	178	36	,	,	PUNCT
ejpam-370	178	37	a	a	PRON
ejpam-370	178	38	,	,	PUNCT
ejpam-370	178	39	b	b	X
ejpam-370	178	40	∈	∈	PROPN
ejpam-370	178	41	r	r	NOUN
ejpam-370	178	42	output	output	NOUN
ejpam-370	178	43	.	.	PUNCT
ejpam-370	179	1	solution	solution	NOUN
ejpam-370	179	2	x	x	PUNCT
ejpam-370	179	3	=	=	SYM
ejpam-370	179	4			PROPN
ejpam-370	179	5			NOUN
ejpam-370	179	6			NOUN
ejpam-370	179	7			NOUN
ejpam-370	179	8			NOUN
ejpam-370	179	9	−1	−1	NOUN
ejpam-370	179	10	5	5	NUM
ejpam-370	179	11	−	−	NOUN
ejpam-370	179	12	4	4	NUM
ejpam-370	179	13	5	5	NUM
ejpam-370	179	14	a−	a−	NOUN
ejpam-370	179	15	1	1	NUM
ejpam-370	179	16	5	5	NUM
ejpam-370	179	17	b	b	NOUN
ejpam-370	179	18	−3	−3	NOUN
ejpam-370	179	19	5	5	NUM
ejpam-370	179	20	+	+	CCONJ
ejpam-370	179	21	3	3	NUM
ejpam-370	179	22	5	5	NUM
ejpam-370	179	23	a+	a+	SYM
ejpam-370	179	24	4	4	NUM
ejpam-370	179	25	5	5	NUM
ejpam-370	179	26	b	b	NOUN
ejpam-370	179	27	a	a	PRON
ejpam-370	179	28	b	b	NOUN
ejpam-370	179	29			NOUN
ejpam-370	179	30			NOUN
ejpam-370	179	31			VERB
ejpam-370	179	32			NOUN
ejpam-370	179	33			PUNCT
ejpam-370	179	34	.	.	PUNCT
ejpam-370	180	1	example	example	NOUN
ejpam-370	181	1	2	2	NUM
ejpam-370	181	2	.	.	X
ejpam-370	181	3	input	input	NOUN
ejpam-370	181	4	:	:	PUNCT
ejpam-370	181	5	a=	a=	NOUN
ejpam-370	181	6			NOUN
ejpam-370	181	7			NOUN
ejpam-370	181	8			NOUN
ejpam-370	181	9			NOUN
ejpam-370	181	10			NOUN
ejpam-370	181	11	1	1	NUM
ejpam-370	181	12	2	2	NUM
ejpam-370	181	13	1	1	NUM
ejpam-370	181	14	−2	−2	NOUN
ejpam-370	181	15	2	2	NUM
ejpam-370	181	16	3	3	NUM
ejpam-370	181	17	1	1	NUM
ejpam-370	181	18	1	1	NUM
ejpam-370	181	19			NOUN
ejpam-370	181	20			NOUN
ejpam-370	181	21			VERB
ejpam-370	181	22			NOUN
ejpam-370	181	23			PUNCT
ejpam-370	181	24	,	,	PUNCT
ejpam-370	181	25	f	f	X
ejpam-370	181	26	=	=	SYM
ejpam-370	181	27			PROPN
ejpam-370	181	28			NOUN
ejpam-370	181	29			NOUN
ejpam-370	181	30			NOUN
ejpam-370	181	31			NOUN
ejpam-370	181	32	3	3	NUM
ejpam-370	181	33	4	4	NUM
ejpam-370	181	34	25	25	NUM
ejpam-370	181	35	4	4	NUM
ejpam-370	181	36	13	13	NUM
ejpam-370	181	37	4	4	NUM
ejpam-370	181	38			NOUN
ejpam-370	181	39			NOUN
ejpam-370	181	40			VERB
ejpam-370	181	41			NOUN
ejpam-370	181	42			PUNCT
ejpam-370	181	43	.	.	PUNCT
ejpam-370	182	1	step	step	NOUN
ejpam-370	182	2	1	1	NUM
ejpam-370	182	3	.	.	PUNCT
ejpam-370	183	1	n	n	CCONJ
ejpam-370	183	2	=	=	NOUN
ejpam-370	183	3	min{4,2}=	min{4,2}=	PART
ejpam-370	184	1	2	2	NUM
ejpam-370	184	2	.	.	PUNCT
ejpam-370	184	3	k.	k.	PROPN
ejpam-370	184	4	aydın	aydın	PROPN
ejpam-370	184	5	,	,	PUNCT
ejpam-370	184	6	g.	g.	PROPN
ejpam-370	184	7	kızılkan	kızılkan	PROPN
ejpam-370	184	8	,	,	PUNCT
ejpam-370	184	9	a.	a.	PROPN
ejpam-370	184	10	çıbıkdiken	çıbıkdiken	VERB
ejpam-370	184	11	/	/	SYM
ejpam-370	184	12	eur	eur	PROPN
ejpam-370	184	13	.	.	PUNCT
ejpam-370	185	1	j.	j.	PROPN
ejpam-370	185	2	pure	pure	PROPN
ejpam-370	185	3	appl	appl	PROPN
ejpam-370	185	4	.	.	PROPN
ejpam-370	185	5	math	math	PROPN
ejpam-370	185	6	,	,	PUNCT
ejpam-370	185	7	3	3	NUM
ejpam-370	185	8	(	(	PUNCT
ejpam-370	185	9	2010	2010	NUM
ejpam-370	185	10	)	)	PUNCT
ejpam-370	185	11	,	,	PUNCT
ejpam-370	185	12	819	819	NUM
ejpam-370	185	13	-	-	SYM
ejpam-370	185	14	830	830	NUM
ejpam-370	185	15	826	826	NUM
ejpam-370	185	16	step	step	NOUN
ejpam-370	185	17	2	2	NUM
ejpam-370	185	18	.	.	NUM
ejpam-370	185	19	x	x	PUNCT
ejpam-370	185	20	(	(	PUNCT
ejpam-370	185	21	1	1	NUM
ejpam-370	185	22	)	)	PUNCT
ejpam-370	185	23	0	0	NUM
ejpam-370	186	1	=	=	SYM
ejpam-370	186	2	�	�	PROPN
ejpam-370	186	3	3	3	NUM
ejpam-370	186	4	0	0	NUM
ejpam-370	186	5	�	�	PROPN
ejpam-370	186	6	,	,	PUNCT
ejpam-370	186	7	r(1	r(1	PROPN
ejpam-370	186	8	)	)	PUNCT
ejpam-370	186	9	=	=	SYM
ejpam-370	186	10	�	�	PROPN
ejpam-370	186	11	−2	−2	PROPN
ejpam-370	186	12	1	1	NUM
ejpam-370	186	13	�	�	PROPN
ejpam-370	186	14	a(2	a(2	PROPN
ejpam-370	186	15	)	)	PUNCT
ejpam-370	186	16	=	=	PUNCT
ejpam-370	187	1	a	a	PRON
ejpam-370	187	2	(	(	PUNCT
ejpam-370	187	3	2	2	NUM
ejpam-370	187	4	)	)	PUNCT
ejpam-370	187	5	11	11	NUM
ejpam-370	187	6	f	f	NOUN
ejpam-370	187	7	(	(	PUNCT
ejpam-370	187	8	2	2	NUM
ejpam-370	187	9	)	)	PUNCT
ejpam-370	187	10	1	1	NUM
ejpam-370	187	11	f	f	NOUN
ejpam-370	187	12	(	(	PUNCT
ejpam-370	187	13	2	2	NUM
ejpam-370	187	14	)	)	PUNCT
ejpam-370	187	15	and	and	CCONJ
ejpam-370	187	16	m=	m=	X
ejpam-370	187	17	2⇒	2⇒	NUM
ejpam-370	187	18	x	x	SYM
ejpam-370	187	19	(	(	PUNCT
ejpam-370	187	20	2	2	NUM
ejpam-370	187	21	)	)	PUNCT
ejpam-370	187	22	0	0	NUM
ejpam-370	188	1	=	=	SYM
ejpam-370	188	2	�	�	PROPN
ejpam-370	188	3	−1	−1	NOUN
ejpam-370	188	4	4	4	NUM
ejpam-370	188	5	�	�	PROPN
ejpam-370	188	6	output	output	NOUN
ejpam-370	188	7	.	.	PUNCT
ejpam-370	189	1	solution	solution	NOUN
ejpam-370	189	2	x	x	X
ejpam-370	189	3	=	=	SYM
ejpam-370	189	4	�	�	PROPN
ejpam-370	189	5	7	7	NUM
ejpam-370	189	6	2	2	NUM
ejpam-370	189	7	−1	−1	NOUN
ejpam-370	189	8	4	4	NUM
ejpam-370	189	9	�	�	PROPN
ejpam-370	189	10	.	.	PUNCT
ejpam-370	190	1	example	example	NOUN
ejpam-370	191	1	3	3	NUM
ejpam-370	191	2	.	.	X
ejpam-370	191	3	input	input	NOUN
ejpam-370	191	4	:	:	PUNCT
ejpam-370	191	5	a=	a=	NOUN
ejpam-370	191	6			NOUN
ejpam-370	191	7			NOUN
ejpam-370	191	8			NOUN
ejpam-370	191	9			NOUN
ejpam-370	191	10			NOUN
ejpam-370	191	11	1	1	NUM
ejpam-370	191	12	2	2	NUM
ejpam-370	191	13	1	1	NUM
ejpam-370	191	14	−2	−2	NOUN
ejpam-370	191	15	2	2	NUM
ejpam-370	191	16	3	3	NUM
ejpam-370	191	17	1	1	NUM
ejpam-370	191	18	1	1	NUM
ejpam-370	191	19			NOUN
ejpam-370	191	20			NOUN
ejpam-370	191	21			VERB
ejpam-370	191	22			NOUN
ejpam-370	191	23			PUNCT
ejpam-370	191	24	,	,	PUNCT
ejpam-370	191	25	f	f	X
ejpam-370	191	26	=	=	SYM
ejpam-370	191	27			PROPN
ejpam-370	191	28			NOUN
ejpam-370	191	29			NOUN
ejpam-370	191	30			NOUN
ejpam-370	191	31			NOUN
ejpam-370	191	32	3	3	NUM
ejpam-370	191	33	1	1	NUM
ejpam-370	191	34	5	5	NUM
ejpam-370	191	35	2	2	NUM
ejpam-370	191	36			NOUN
ejpam-370	191	37			NOUN
ejpam-370	191	38			VERB
ejpam-370	191	39			NOUN
ejpam-370	191	40			PUNCT
ejpam-370	191	41	.	.	PUNCT
ejpam-370	192	1	step	step	NOUN
ejpam-370	192	2	1	1	NUM
ejpam-370	192	3	.	.	PUNCT
ejpam-370	193	1	n	n	CCONJ
ejpam-370	193	2	=	=	NOUN
ejpam-370	193	3	min{4,2}=	min{4,2}=	PART
ejpam-370	193	4	2	2	NUM
ejpam-370	193	5	.	.	NOUN
ejpam-370	193	6	step	step	NOUN
ejpam-370	193	7	2	2	NUM
ejpam-370	193	8	.	.	NUM
ejpam-370	193	9	x	x	PUNCT
ejpam-370	193	10	(	(	PUNCT
ejpam-370	193	11	1	1	NUM
ejpam-370	193	12	)	)	PUNCT
ejpam-370	193	13	0	0	NUM
ejpam-370	194	1	=	=	SYM
ejpam-370	194	2	�	�	PROPN
ejpam-370	194	3	3	3	NUM
ejpam-370	194	4	0	0	NUM
ejpam-370	194	5	�	�	PROPN
ejpam-370	194	6	,	,	PUNCT
ejpam-370	194	7	r(1	r(1	PROPN
ejpam-370	194	8	)	)	PUNCT
ejpam-370	194	9	=	=	SYM
ejpam-370	194	10	�	�	PROPN
ejpam-370	194	11	−2	−2	PROPN
ejpam-370	194	12	1	1	NUM
ejpam-370	194	13	�	�	PROPN
ejpam-370	194	14	a(2	a(2	PROPN
ejpam-370	194	15	)	)	PUNCT
ejpam-370	194	16	=	=	SYM
ejpam-370	194	17			NOUN
ejpam-370	194	18			NOUN
ejpam-370	194	19			PRON
ejpam-370	194	20	−4	−4	X
ejpam-370	194	21	−1	−1	NOUN
ejpam-370	194	22	−1	−1	NOUN
ejpam-370	194	23			PROPN
ejpam-370	194	24			VERB
ejpam-370	194	25			PUNCT
ejpam-370	195	1	,	,	PUNCT
ejpam-370	195	2	f	f	X
ejpam-370	195	3	(	(	PUNCT
ejpam-370	195	4	2	2	NUM
ejpam-370	195	5	)	)	PUNCT
ejpam-370	195	6	=	=	SYM
ejpam-370	195	7			PROPN
ejpam-370	195	8			NOUN
ejpam-370	195	9			NOUN
ejpam-370	195	10	−2	−2	NOUN
ejpam-370	195	11	−1	−1	ADV
ejpam-370	195	12	−1	−1	NOUN
ejpam-370	195	13			PROPN
ejpam-370	195	14			NOUN
ejpam-370	195	15			PUNCT
ejpam-370	195	16	,	,	PUNCT
ejpam-370	195	17	a(2	a(2	PROPN
ejpam-370	195	18	)	)	PUNCT
ejpam-370	195	19	6=	6=	ADP
ejpam-370	195	20	a	a	DET
ejpam-370	195	21	(	(	PUNCT
ejpam-370	195	22	2	2	NUM
ejpam-370	195	23	)	)	PUNCT
ejpam-370	195	24	11	11	NUM
ejpam-370	195	25	f	f	NOUN
ejpam-370	195	26	(	(	PUNCT
ejpam-370	195	27	2	2	NUM
ejpam-370	195	28	)	)	PUNCT
ejpam-370	195	29	1	1	NUM
ejpam-370	195	30	f	f	NOUN
ejpam-370	195	31	(	(	PUNCT
ejpam-370	195	32	2	2	NUM
ejpam-370	195	33	)	)	PUNCT
ejpam-370	195	34	output	output	NOUN
ejpam-370	195	35	.	.	PUNCT
ejpam-370	196	1	no	no	DET
ejpam-370	196	2	solution	solution	NOUN
ejpam-370	196	3	.	.	PUNCT
ejpam-370	197	1	4	4	X
ejpam-370	197	2	.	.	NOUN
ejpam-370	197	3	maple	maple	NOUN
ejpam-370	197	4	procedure	procedure	NOUN
ejpam-370	197	5	for	for	ADP
ejpam-370	197	6	gidda>#a	gidda>#a	PROPN
ejpam-370	197	7	maple	maple	NOUN
ejpam-370	197	8	pro	pro	ADJ
ejpam-370	197	9	edure	edure	NOUN
ejpam-370	197	10	:	:	PUNCT
ejpam-370	197	11	to	to	PART
ejpam-370	197	12	ompute	ompute	VERB
ejpam-370	197	13	the	the	DET
ejpam-370	197	14	solution	solution	NOUN
ejpam-370	197	15	of	of	ADP
ejpam-370	197	16	the	the	DET
ejpam-370	197	17	given	give	VERB
ejpam-370	197	18	linear	linear	PROPN
ejpam-370	197	19	system.>restart;>with(linearalgebra	system.>restart;>with(linearalgebra	PROPN
ejpam-370	197	20	,	,	PUNCT
ejpam-370	197	21	multiply);>with(linalg	multiply);>with(linalg	PROPN
ejpam-370	197	22	,	,	PUNCT
ejpam-370	197	23	oldim	oldim	NOUN
ejpam-370	197	24	,	,	PUNCT
ejpam-370	197	25	rowdim	rowdim	NOUN
ejpam-370	197	26	,	,	PUNCT
ejpam-370	197	27	blo	blo	NOUN
ejpam-370	197	28	kmatrix	kmatrix	NOUN
ejpam-370	197	29	,	,	PUNCT
ejpam-370	197	30	ve	ve	VERB
ejpam-370	197	31	tdim);>gidda:=pro	tdim);>gidda:=pro	X
ejpam-370	197	32	(	(	PUNCT
ejpam-370	197	33	a::matrix	a::matrix	NUM
ejpam-370	197	34	,	,	PUNCT
ejpam-370	197	35	f::ve	f::ve	PROPN
ejpam-370	197	36	tor)global	tor)global	PROPN
ejpam-370	197	37	n	n	SYM
ejpam-370	197	38	,	,	PUNCT
ejpam-370	197	39	b	b	PROPN
ejpam-370	197	40	,	,	PUNCT
ejpam-370	197	41	m	m	PROPN
ejpam-370	197	42	,	,	PUNCT
ejpam-370	197	43	n	n	CCONJ
ejpam-370	197	44	,	,	PUNCT
ejpam-370	197	45	u	u	NOUN
ejpam-370	197	46	,	,	PUNCT
ejpam-370	197	47	v	v	NOUN
ejpam-370	197	48	,	,	PUNCT
ejpam-370	197	49	a1,a2,x0,rr	a1,a2,x0,rr	PROPN
ejpam-370	197	50	,	,	PUNCT
ejpam-370	197	51	x	x	X
ejpam-370	197	52	,	,	PUNCT
ejpam-370	197	53	s	s	PART
ejpam-370	197	54	,	,	PUNCT
ejpam-370	197	55	xs;lo	xs;lo	PROPN
ejpam-370	197	56	al	al	PROPN
ejpam-370	197	57	g	g	PROPN
ejpam-370	197	58	,	,	PUNCT
ejpam-370	197	59	m	m	PROPN
ejpam-370	197	60	,	,	PUNCT
ejpam-370	197	61	z	z	PROPN
ejpam-370	197	62	,	,	PUNCT
ejpam-370	197	63	i	i	PRON
ejpam-370	197	64	,	,	PUNCT
ejpam-370	197	65	j	j	PROPN
ejpam-370	197	66	,	,	PUNCT
ejpam-370	197	67	p	p	X
ejpam-370	197	68	,	,	PUNCT
ejpam-370	197	69	s	s	X
ejpam-370	197	70	,	,	PUNCT
ejpam-370	197	71	k	k	PROPN
ejpam-370	197	72	,	,	PUNCT
ejpam-370	197	73	t	t	PROPN
ejpam-370	197	74	,	,	PUNCT
ejpam-370	197	75	r	r	NOUN
ejpam-370	197	76	,	,	PUNCT
ejpam-370	197	77	r	r	NOUN
ejpam-370	197	78	,	,	PUNCT
ejpam-370	197	79	h1,h2,b1,b2,b3,b4,b5,b6	h1,h2,b1,b2,b3,b4,b5,b6	NOUN
ejpam-370	197	80	,	,	PUNCT
ejpam-370	197	81	output1	output1	ADV
ejpam-370	197	82	,	,	PUNCT
ejpam-370	197	83	output2	output2	ADJ
ejpam-370	197	84	,	,	PUNCT
ejpam-370	197	85	step4,cal	step4,cal	ADJ
ejpam-370	197	86	ulatex0	ulatex0	ADJ
ejpam-370	197	87	,	,	PUNCT
ejpam-370	197	88	cal	cal	X
ejpam-370	197	89	ulater	ulater	NOUN
ejpam-370	197	90	,	,	PUNCT
ejpam-370	197	91	find\_ps	find\_ps	PROPN
ejpam-370	197	92	,	,	PUNCT
ejpam-370	197	93	bul;output1:=	bul;output1:=	PROPN
ejpam-370	197	94	pro	pro	X
ejpam-370	197	95	(	(	PUNCT
ejpam-370	197	96	)	)	PUNCT
ejpam-370	197	97	rr[0	rr[0	NOUN
ejpam-370	197	98	℄	℄	PROPN
ejpam-370	197	99	:=	:=	PUNCT
ejpam-370	197	100	matrix(n[1	matrix(n[1	PROPN
ejpam-370	197	101	℄	℄	PROPN
ejpam-370	197	102	,	,	PUNCT
ejpam-370	197	103	n[1	n[1	PROPN
ejpam-370	197	104	℄	℄	ADJ
ejpam-370	197	105	,	,	PUNCT
ejpam-370	197	106	shape	shape	NOUN
ejpam-370	197	107	=	=	SYM
ejpam-370	197	108	identity	identity	NOUN
ejpam-370	197	109	)	)	PUNCT
ejpam-370	197	110	;	;	PUNCT
ejpam-370	197	111	x:=	x:=	PROPN
ejpam-370	197	112	x0[1	x0[1	PROPN
ejpam-370	198	1	℄	℄	PROPN
ejpam-370	198	2	;for	;for	ADP
ejpam-370	198	3	i	i	PRON
ejpam-370	198	4	from	from	ADP
ejpam-370	198	5	1	1	NUM
ejpam-370	198	6	to	to	ADP
ejpam-370	198	7	m-1	m-1	PROPN
ejpam-370	198	8	do	do	VERB
ejpam-370	198	9	rr[i	rr[i	PROPN
ejpam-370	198	10	℄	℄	PROPN
ejpam-370	198	11	:=	:=	PUNCT
ejpam-370	198	12	r[i	r[i	PROPN
ejpam-370	198	13	℄	℄	PROPN
ejpam-370	198	14	;	;	PUNCT
ejpam-370	198	15	rr[i	rr[i	PROPN
ejpam-370	198	16	℄	℄	PROPN
ejpam-370	198	17	:=	:=	X
ejpam-370	198	18	multiply(rr[i-1	multiply(rr[i-1	PROPN
ejpam-370	198	19	℄	℄	PROPN
ejpam-370	198	20	,rr[i	,rr[i	PUNCT
ejpam-370	198	21	℄	℄	PROPN
ejpam-370	198	22	);s[i	);s[i	PROPN
ejpam-370	198	23	℄	℄	PROPN
ejpam-370	198	24	:=	:=	PUNCT
ejpam-370	198	25	multiply(rr[i	multiply(rr[i	PROPN
ejpam-370	198	26	℄	℄	PROPN
ejpam-370	198	27	,	,	PUNCT
ejpam-370	198	28	x0[i+1	x0[i+1	PROPN
ejpam-370	198	29	℄	℄	PROPN
ejpam-370	198	30	)	)	PUNCT
ejpam-370	198	31	;	;	PUNCT
ejpam-370	199	1	x:=	x:=	PROPN
ejpam-370	199	2	x	x	PUNCT
ejpam-370	200	1	+	+	PUNCT
ejpam-370	200	2	s[i	s[i	NOUN
ejpam-370	200	3	℄	℄	NOUN
ejpam-370	200	4	;	;	PUNCT
ejpam-370	200	5	end	end	NOUN
ejpam-370	200	6	do	do	AUX
ejpam-370	200	7	:	:	PUNCT
ejpam-370	200	8	for	for	ADP
ejpam-370	200	9	i	i	PRON
ejpam-370	200	10	from	from	ADP
ejpam-370	200	11	1	1	NUM
ejpam-370	200	12	to	to	PART
ejpam-370	200	13	m	m	PROPN
ejpam-370	200	14	do	do	VERB
ejpam-370	200	15	rr[i	rr[i	PROPN
ejpam-370	200	16	℄	℄	PROPN
ejpam-370	200	17	:=	:=	PUNCT
ejpam-370	200	18	r[i	r[i	PROPN
ejpam-370	200	19	℄	℄	PROPN
ejpam-370	200	20	;	;	PUNCT
ejpam-370	200	21	rr[i	rr[i	PROPN
ejpam-370	200	22	℄	℄	PROPN
ejpam-370	200	23	:=	:=	X
ejpam-370	200	24	multiply(rr[i-1	multiply(rr[i-1	PROPN
ejpam-370	200	25	℄	℄	PROPN
ejpam-370	200	26	,	,	PUNCT
ejpam-370	200	27	rr[i	rr[i	PROPN
ejpam-370	200	28	℄	℄	PROPN
ejpam-370	200	29	)	)	PUNCT
ejpam-370	200	30	;	;	PUNCT
ejpam-370	200	31	end	end	NOUN
ejpam-370	200	32	do;if	do;if	PROPN
ejpam-370	200	33	n[m+1	n[m+1	PROPN
ejpam-370	200	34	℄	℄	NOUN
ejpam-370	200	35	=0	=0	NOUN
ejpam-370	200	36	then	then	ADV
ejpam-370	200	37	xs:=	xs:=	PUNCT
ejpam-370	200	38	ve	ve	AUX
ejpam-370	200	39	tor(1	tor(1	VERB
ejpam-370	200	40	..	..	PUNCT
ejpam-370	201	1	oldim(rr[m	oldim(rr[m	PROPN
ejpam-370	201	2	℄	℄	PROPN
ejpam-370	201	3	)	)	PUNCT
ejpam-370	201	4	,	,	PUNCT
ejpam-370	202	1	0);else	0);else	NUM
ejpam-370	202	2	xs:=	xs:=	X
ejpam-370	202	3	ve	ve	AUX
ejpam-370	202	4	tor(1	tor(1	VERB
ejpam-370	202	5	..	..	PUNCT
ejpam-370	203	1	oldim(rr[m	oldim(rr[m	PROPN
ejpam-370	203	2	℄	℄	PROPN
ejpam-370	203	3	)	)	PUNCT
ejpam-370	203	4	,	,	PUNCT
ejpam-370	204	1	symbol	symbol	NOUN
ejpam-370	204	2	=	=	PUNCT
ejpam-370	204	3	a	a	X
ejpam-370	204	4	)	)	PUNCT
ejpam-370	204	5	;	;	PUNCT
ejpam-370	204	6	end	end	VERB
ejpam-370	204	7	if	if	SCONJ
ejpam-370	204	8	:	:	PUNCT
ejpam-370	204	9	x:=	x:=	ADJ
ejpam-370	204	10	x	x	PUNCT
ejpam-370	204	11	+	+	NUM
ejpam-370	204	12	multiply(rr[m	multiply(rr[m	PROPN
ejpam-370	204	13	℄	℄	PROPN
ejpam-370	204	14	,	,	PUNCT
ejpam-370	204	15	xs	xs	PROPN
ejpam-370	204	16	)	)	PUNCT
ejpam-370	204	17	;	;	PUNCT
ejpam-370	205	1	print(x	print(x	VERB
ejpam-370	205	2	)	)	PUNCT
ejpam-370	205	3	;	;	PUNCT
ejpam-370	205	4	break;end	break;end	VERB
ejpam-370	205	5	pro	pro	ADJ
ejpam-370	205	6	:	:	PUNCT
ejpam-370	205	7	k.	k.	PROPN
ejpam-370	205	8	aydın	aydın	PROPN
ejpam-370	205	9	,	,	PUNCT
ejpam-370	205	10	g.	g.	PROPN
ejpam-370	205	11	kızılkan	kızılkan	PROPN
ejpam-370	205	12	,	,	PUNCT
ejpam-370	205	13	a.	a.	PROPN
ejpam-370	205	14	çıbıkdiken	çıbıkdiken	VERB
ejpam-370	205	15	/	/	SYM
ejpam-370	205	16	eur	eur	PROPN
ejpam-370	205	17	.	.	PUNCT
ejpam-370	206	1	j.	j.	PROPN
ejpam-370	206	2	pure	pure	PROPN
ejpam-370	206	3	appl	appl	PROPN
ejpam-370	206	4	.	.	PROPN
ejpam-370	206	5	math	math	PROPN
ejpam-370	206	6	,	,	PUNCT
ejpam-370	206	7	3	3	NUM
ejpam-370	206	8	(	(	PUNCT
ejpam-370	206	9	2010	2010	NUM
ejpam-370	206	10	)	)	PUNCT
ejpam-370	206	11	,	,	PUNCT
ejpam-370	206	12	819	819	NUM
ejpam-370	206	13	-	-	SYM
ejpam-370	206	14	830	830	NUM
ejpam-370	206	15	827output2:=pro	827output2:=pro	NOUN
ejpam-370	206	16	(	(	PUNCT
ejpam-370	206	17	)	)	PUNCT
ejpam-370	206	18	printf("no	printf("no	PRON
ejpam-370	206	19	solution	solution	NOUN
ejpam-370	206	20	"	"	PUNCT
ejpam-370	206	21	)	)	PUNCT
ejpam-370	206	22	;	;	PUNCT
ejpam-370	206	23	break;end	break;end	VERB
ejpam-370	206	24	pro	pro	ADJ
ejpam-370	206	25	:	:	PUNCT
ejpam-370	206	26	step4:=pro	step4:=pro	ADJ
ejpam-370	206	27	(	(	PUNCT
ejpam-370	206	28	)	)	PUNCT
ejpam-370	206	29	if	if	SCONJ
ejpam-370	206	30	verify(g[k	verify(g[k	PROPN
ejpam-370	206	31	℄	℄	PROPN
ejpam-370	206	32	,ve	,ve	PUNCT
ejpam-370	206	33	tor(1	tor(1	PROPN
ejpam-370	206	34	..	..	PUNCT
ejpam-370	206	35	ve	ve	VERB
ejpam-370	206	36	tdim(g[k	tdim(g[k	NOUN
ejpam-370	206	37	℄	℄	PROPN
ejpam-370	206	38	),0),ve	),0),ve	PROPN
ejpam-370	206	39	tor)=false	tor)=false	PRON
ejpam-370	206	40	then	then	ADV
ejpam-370	206	41	output2();end	output2();end	VERB
ejpam-370	206	42	if	if	SCONJ
ejpam-370	206	43	:	:	PUNCT
ejpam-370	206	44	m:=k-1	m:=k-1	NOUN
ejpam-370	206	45	;	;	PUNCT
ejpam-370	206	46	output1();end	output1();end	NOUN
ejpam-370	206	47	pro	pro	ADJ
ejpam-370	206	48	:	:	PUNCT
ejpam-370	206	49	cal	cal	ADJ
ejpam-370	206	50	ulatex0:=pro	ulatex0:=pro	ADJ
ejpam-370	206	51	(	(	PUNCT
ejpam-370	206	52	)	)	PUNCT
ejpam-370	206	53	x0[k	x0[k	PROPN
ejpam-370	206	54	℄	℄	PROPN
ejpam-370	206	55	:=ve	:=ve	PROPN
ejpam-370	206	56	tor(1	tor(1	PROPN
ejpam-370	206	57	..	..	PUNCT
ejpam-370	206	58	n[k	n[k	PROPN
ejpam-370	206	59	℄	℄	PROPN
ejpam-370	206	60	)	)	PUNCT
ejpam-370	206	61	;	;	PUNCT
ejpam-370	206	62	x0[k	x0[k	PROPN
ejpam-370	206	63	℄	℄	PROPN
ejpam-370	206	64	[s[k	[s[k	X
ejpam-370	206	65	℄	℄	PROPN
ejpam-370	206	66	℄	℄	PROPN
ejpam-370	206	67	:=(g[k	:=(g[k	PROPN
ejpam-370	206	68	℄	℄	PROPN
ejpam-370	206	69	[p[k	[p[k	X
ejpam-370	206	70	℄	℄	PROPN
ejpam-370	206	71	℄	℄	PROPN
ejpam-370	206	72	)/(b[k	)/(b[k	PROPN
ejpam-370	206	73	℄	℄	PROPN
ejpam-370	206	74	[p[k	[p[k	X
ejpam-370	206	75	℄	℄	PROPN
ejpam-370	206	76	,s[k	,s[k	PUNCT
ejpam-370	206	77	℄	℄	PROPN
ejpam-370	206	78	℄	℄	PROPN
ejpam-370	206	79	)	)	PUNCT
ejpam-370	206	80	;	;	PUNCT
ejpam-370	206	81	}	}	PUNCT
ejpam-370	206	82	end	end	VERB
ejpam-370	206	83	pro	pro	ADJ
ejpam-370	206	84	:	:	PUNCT
ejpam-370	206	85	cal	cal	ADJ
ejpam-370	206	86	ulate	ulate	ADJ
ejpam-370	206	87	r:=pro	r:=pro	NOUN
ejpam-370	206	88	(	(	PUNCT
ejpam-370	206	89	)	)	PUNCT
ejpam-370	206	90	r[k	r[k	PROPN
ejpam-370	206	91	℄	℄	PROPN
ejpam-370	206	92	:=matrix(1,1	:=matrix(1,1	SYM
ejpam-370	206	93	..	..	SYM
ejpam-370	206	94	n[k	n[k	PROPN
ejpam-370	206	95	℄	℄	PROPN
ejpam-370	206	96	-s[k	-s[k	PROPN
ejpam-370	206	97	℄	℄	PROPN
ejpam-370	206	98	);for	);for	PUNCT
ejpam-370	206	99	z	z	NOUN
ejpam-370	206	100	from	from	ADP
ejpam-370	206	101	1	1	NUM
ejpam-370	206	102	to	to	ADP
ejpam-370	206	103	n[k	n[k	PROPN
ejpam-370	206	104	℄	℄	PROPN
ejpam-370	206	105	-s[k	-s[k	PROPN
ejpam-370	206	106	℄	℄	PROPN
ejpam-370	206	107	do	do	AUX
ejpam-370	206	108	r[k	r[k	PROPN
ejpam-370	206	109	℄	℄	NOUN
ejpam-370	206	110	[1,z	[1,z	ADP
ejpam-370	206	111	℄	℄	PROPN
ejpam-370	206	112	:=-((b[k	:=-((b[k	PROPN
ejpam-370	206	113	℄	℄	PROPN
ejpam-370	206	114	[p[k	[p[k	X
ejpam-370	206	115	℄	℄	PROPN
ejpam-370	206	116	,s[k	,s[k	PUNCT
ejpam-370	206	117	℄	℄	PROPN
ejpam-370	206	118	+z	+z	ADJ
ejpam-370	206	119	℄	℄	ADJ
ejpam-370	206	120	)/(b[k	)/(b[k	NOUN
ejpam-370	206	121	℄	℄	PROPN
ejpam-370	206	122	[p[k	[p[k	X
ejpam-370	206	123	℄	℄	PROPN
ejpam-370	206	124	,s[k	,s[k	PUNCT
ejpam-370	206	125	℄	℄	PROPN
ejpam-370	206	126	℄	℄	PROPN
ejpam-370	206	127	)	)	PUNCT
ejpam-370	206	128	)	)	PUNCT
ejpam-370	207	1	;	;	PUNCT
ejpam-370	207	2	end	end	NOUN
ejpam-370	207	3	do	do	AUX
ejpam-370	207	4	:	:	PUNCT
ejpam-370	207	5	h1:=matrix(n[k	h1:=matrix(n[k	PROPN
ejpam-370	207	6	℄	℄	PROPN
ejpam-370	207	7	-1,n[k	-1,n[k	PROPN
ejpam-370	207	8	℄	℄	PROPN
ejpam-370	207	9	-1,shape	-1,shape	NOUN
ejpam-370	207	10	=	=	NOUN
ejpam-370	207	11	identity	identity	NOUN
ejpam-370	207	12	)	)	PUNCT
ejpam-370	207	13	;	;	PUNCT
ejpam-370	207	14	h2:=matrix(1,n[k	h2:=matrix(1,n[k	PROPN
ejpam-370	207	15	℄	℄	PROPN
ejpam-370	207	16	-1,0);b1:=matrix(s[k	-1,0);b1:=matrix(s[k	PROPN
ejpam-370	207	17	℄	℄	PROPN
ejpam-370	207	18	-1,s[k	-1,s[k	PROPN
ejpam-370	207	19	℄	℄	PROPN
ejpam-370	207	20	-1,shape	-1,shape	NOUN
ejpam-370	207	21	=	=	NOUN
ejpam-370	207	22	identity	identity	NOUN
ejpam-370	207	23	)	)	PUNCT
ejpam-370	207	24	;	;	PUNCT
ejpam-370	207	25	b2:=matrix(s[k	b2:=matrix(s[k	NOUN
ejpam-370	207	26	℄	℄	PROPN
ejpam-370	207	27	-1,n[k	-1,n[k	PROPN
ejpam-370	207	28	℄	℄	PROPN
ejpam-370	207	29	-s[k	-s[k	PROPN
ejpam-370	207	30	℄	℄	PROPN
ejpam-370	207	31	,0);b3:=matrix(1,s[k	,0);b3:=matrix(1,s[k	PUNCT
ejpam-370	207	32	℄	℄	PROPN
ejpam-370	207	33	-1,0	-1,0	NUM
ejpam-370	207	34	)	)	PUNCT
ejpam-370	207	35	;	;	PUNCT
ejpam-370	207	36	b4:=r[k	b4:=r[k	PROPN
ejpam-370	207	37	℄	℄	PROPN
ejpam-370	207	38	;	;	PUNCT
ejpam-370	207	39	b5:=matrix(n[k	b5:=matrix(n[k	ADP
ejpam-370	207	40	℄	℄	PROPN
ejpam-370	207	41	-s[k	-s[k	PROPN
ejpam-370	207	42	℄	℄	PROPN
ejpam-370	207	43	,s[k	,s[k	PUNCT
ejpam-370	207	44	℄	℄	PROPN
ejpam-370	207	45	-1,0);b6:=matrix(n[k	-1,0);b6:=matrix(n[k	PROPN
ejpam-370	207	46	℄	℄	PROPN
ejpam-370	207	47	-s[k	-s[k	PROPN
ejpam-370	207	48	℄	℄	PROPN
ejpam-370	207	49	,n[k	,n[k	PUNCT
ejpam-370	207	50	℄	℄	PROPN
ejpam-370	207	51	-s[k	-s[k	PROPN
ejpam-370	207	52	℄	℄	PROPN
ejpam-370	207	53	,shape	,shape	PUNCT
ejpam-370	207	54	=	=	SYM
ejpam-370	207	55	identity);if	identity);if	ADJ
ejpam-370	207	56	s[k	s[k	NOUN
ejpam-370	207	57	℄	℄	NOUN
ejpam-370	207	58	=1	=1	NOUN
ejpam-370	207	59	then	then	ADV
ejpam-370	207	60	r[k	r[k	PROPN
ejpam-370	207	61	℄	℄	NOUN
ejpam-370	207	62	:=	:=	X
ejpam-370	207	63	onvert(blo	onvert(blo	PROPN
ejpam-370	207	64	kmatrix(2,1,[r[k	kmatrix(2,1,[r[k	PROPN
ejpam-370	207	65	℄	℄	PROPN
ejpam-370	207	66	,h1	,h1	PUNCT
ejpam-370	207	67	℄	℄	PROPN
ejpam-370	207	68	),matrix);end	),matrix);end	PUNCT
ejpam-370	207	69	if	if	SCONJ
ejpam-370	207	70	:	:	PUNCT
ejpam-370	207	71	if	if	SCONJ
ejpam-370	207	72	s[k	s[k	NOUN
ejpam-370	207	73	℄	℄	NOUN
ejpam-370	207	74	=n[k	=n[k	PROPN
ejpam-370	207	75	℄	℄	PROPN
ejpam-370	207	76	then	then	ADV
ejpam-370	207	77	r[k	r[k	PROPN
ejpam-370	207	78	℄	℄	NOUN
ejpam-370	207	79	:=	:=	X
ejpam-370	207	80	onvert(blo	onvert(blo	PROPN
ejpam-370	207	81	kmatrix(2,1,[h1,h2	kmatrix(2,1,[h1,h2	PROPN
ejpam-370	207	82	℄	℄	PROPN
ejpam-370	207	83	),matrix);end	),matrix);end	PUNCT
ejpam-370	207	84	if	if	SCONJ
ejpam-370	207	85	:	:	PUNCT
ejpam-370	207	86	if	if	SCONJ
ejpam-370	207	87	(	(	PUNCT
ejpam-370	207	88	s[k	s[k	NOUN
ejpam-370	207	89	℄	℄	ADJ
ejpam-370	207	90	\texttt{>}=2	\texttt{>}=2	PROPN
ejpam-370	207	91	and	and	CCONJ
ejpam-370	207	92	s[k	s[k	NOUN
ejpam-370	207	93	℄	℄	NOUN
ejpam-370	207	94	\texttt{<}=n[k	\texttt{<}=n[k	PROPN
ejpam-370	207	95	℄	℄	PROPN
ejpam-370	207	96	-1	-1	PRON
ejpam-370	207	97	)	)	PUNCT
ejpam-370	207	98	thenr[k	thenr[k	PROPN
ejpam-370	207	99	℄	℄	PROPN
ejpam-370	207	100	:=	:=	X
ejpam-370	207	101	onvert(blo	onvert(blo	PROPN
ejpam-370	207	102	kmatrix(3,2,[b1,b2,b3,b4,b5,b6	kmatrix(3,2,[b1,b2,b3,b4,b5,b6	PROPN
ejpam-370	207	103	℄	℄	PROPN
ejpam-370	207	104	),matrix	),matrix	PROPN
ejpam-370	207	105	)	)	PUNCT
ejpam-370	207	106	;	;	PUNCT
ejpam-370	207	107	end	end	VERB
ejpam-370	207	108	if	if	SCONJ
ejpam-370	207	109	:	:	PUNCT
ejpam-370	207	110	end	end	VERB
ejpam-370	207	111	pro	pro	ADJ
ejpam-370	207	112	:	:	PUNCT
ejpam-370	207	113	find\_ps:=pro	find\_ps:=pro	PROPN
ejpam-370	207	114	(	(	PUNCT
ejpam-370	207	115	)	)	PUNCT
ejpam-370	207	116	bul:=0	bul:=0	NOUN
ejpam-370	207	117	;	;	PUNCT
ejpam-370	207	118	for	for	ADP
ejpam-370	207	119	i	i	PRON
ejpam-370	207	120	from	from	ADP
ejpam-370	207	121	1	1	NUM
ejpam-370	207	122	to	to	ADP
ejpam-370	207	123	m[k	m[k	PROPN
ejpam-370	207	124	℄	℄	PROPN
ejpam-370	207	125	do	do	AUX
ejpam-370	207	126	for	for	ADP
ejpam-370	207	127	j	j	PROPN
ejpam-370	207	128	from	from	ADP
ejpam-370	207	129	1	1	NUM
ejpam-370	207	130	to	to	ADP
ejpam-370	207	131	n[k	n[k	PROPN
ejpam-370	207	132	℄	℄	PROPN
ejpam-370	207	133	doif	doif	PROPN
ejpam-370	207	134	bul=0	bul=0	NOUN
ejpam-370	207	135	and	and	CCONJ
ejpam-370	207	136	b[k	b[k	NOUN
ejpam-370	207	137	℄	℄	PROPN
ejpam-370	207	138	[i	[i	X
ejpam-370	207	139	,	,	PUNCT
ejpam-370	207	140	j	j	PROPN
ejpam-370	207	141	℄	℄	PROPN
ejpam-370	207	142	\texttt{<>}0	\texttt{<>}0	NUM
ejpam-370	207	143	then	then	ADV
ejpam-370	207	144	p[k	p[k	PROPN
ejpam-370	207	145	℄	℄	PROPN
ejpam-370	207	146	:=i;s[k	:=i;s[k	X
ejpam-370	207	147	℄	℄	PROPN
ejpam-370	207	148	:=j	:=j	PROPN
ejpam-370	207	149	;	;	PUNCT
ejpam-370	207	150	bul:=1;end	bul:=1;end	VERB
ejpam-370	207	151	if	if	SCONJ
ejpam-370	207	152	:	:	PUNCT
ejpam-370	207	153	end	end	NOUN
ejpam-370	207	154	do	do	AUX
ejpam-370	207	155	:	:	PUNCT
ejpam-370	207	156	end	end	VERB
ejpam-370	207	157	do	do	AUX
ejpam-370	207	158	:	:	PUNCT
ejpam-370	207	159	if	if	SCONJ
ejpam-370	207	160	bul=0	bul=0	NOUN
ejpam-370	207	161	then	then	ADV
ejpam-370	207	162	step4	step4	PROPN
ejpam-370	207	163	(	(	PUNCT
ejpam-370	207	164	)	)	PUNCT
ejpam-370	207	165	;	;	PUNCT
ejpam-370	207	166	end	end	VERB
ejpam-370	207	167	if	if	SCONJ
ejpam-370	207	168	:	:	PUNCT
ejpam-370	207	169	end	end	VERB
ejpam-370	207	170	pro	pro	ADJ
ejpam-370	207	171	:>	:>	ADJ
ejpam-370	207	172	#	#	ADJ
ejpam-370	207	173	main	main	ADJ
ejpam-370	207	174	pro	pro	ADJ
ejpam-370	207	175	edurem[1	edurem[1	NOUN
ejpam-370	207	176	℄	℄	ADJ
ejpam-370	207	177	:=rowdim(a	:=rowdim(a	NOUN
ejpam-370	207	178	)	)	PUNCT
ejpam-370	207	179	;	;	PUNCT
ejpam-370	207	180	n[1	n[1	PROPN
ejpam-370	207	181	℄	℄	ADJ
ejpam-370	207	182	:=	:=	PUNCT
ejpam-370	207	183	oldim(a	oldim(a	PROPN
ejpam-370	207	184	)	)	PUNCT
ejpam-370	207	185	;	;	PUNCT
ejpam-370	207	186	g[1	g[1	PROPN
ejpam-370	207	187	℄	℄	PROPN
ejpam-370	207	188	:=ve	:=ve	PROPN
ejpam-370	207	189	tor(1	tor(1	PROPN
ejpam-370	207	190	..	..	PUNCT
ejpam-370	208	1	m[1	m[1	PROPN
ejpam-370	208	2	℄	℄	PROPN
ejpam-370	208	3	);b[1	);b[1	NOUN
ejpam-370	208	4	℄	℄	PROPN
ejpam-370	208	5	:=matrix(1	:=matrix(1	PUNCT
ejpam-370	208	6	..	..	PUNCT
ejpam-370	208	7	m[1	m[1	PROPN
ejpam-370	208	8	℄	℄	PROPN
ejpam-370	208	9	,1	,1	PROPN
ejpam-370	208	10	..	..	PUNCT
ejpam-370	208	11	n[1	n[1	PROPN
ejpam-370	208	12	℄	℄	PROPN
ejpam-370	208	13	)	)	PUNCT
ejpam-370	208	14	;	;	PUNCT
ejpam-370	208	15	n:=min(m[1	n:=min(m[1	PROPN
ejpam-370	208	16	℄	℄	PROPN
ejpam-370	208	17	,n[1	,n[1	PUNCT
ejpam-370	208	18	℄	℄	PROPN
ejpam-370	208	19	)	)	PUNCT
ejpam-370	208	20	;	;	PUNCT
ejpam-370	208	21	b[1	b[1	PROPN
ejpam-370	208	22	℄	℄	PROPN
ejpam-370	208	23	:=a	:=a	PROPN
ejpam-370	208	24	;	;	PUNCT
ejpam-370	208	25	g[1	g[1	PROPN
ejpam-370	208	26	℄	℄	PROPN
ejpam-370	208	27	:=f;for	:=f;for	X
ejpam-370	208	28	k	k	PROPN
ejpam-370	208	29	from	from	ADP
ejpam-370	208	30	1	1	NUM
ejpam-370	208	31	to	to	PART
ejpam-370	208	32	n-1	n-1	VERB
ejpam-370	208	33	doif	doif	NOUN
ejpam-370	208	34	k<>1	k<>1	NOUN
ejpam-370	208	35	then	then	ADV
ejpam-370	208	36	m[k	m[k	PROPN
ejpam-370	208	37	℄	℄	PROPN
ejpam-370	208	38	:=rowdim(a)-sum(p[t	:=rowdim(a)-sum(p[t	PROPN
ejpam-370	208	39	℄	℄	PROPN
ejpam-370	208	40	,t=1	,t=1	PUNCT
ejpam-370	208	41	..	..	PUNCT
ejpam-370	208	42	k-1	k-1	PROPN
ejpam-370	208	43	)	)	PUNCT
ejpam-370	208	44	;	;	PUNCT
ejpam-370	208	45	n[k	n[k	PROPN
ejpam-370	208	46	℄	℄	PROPN
ejpam-370	208	47	:=	:=	X
ejpam-370	208	48	oldim(a)-k+1;end	oldim(a)-k+1;end	VERB
ejpam-370	208	49	if	if	SCONJ
ejpam-370	208	50	:	:	PUNCT
ejpam-370	208	51	k.	k.	PROPN
ejpam-370	208	52	aydın	aydın	PROPN
ejpam-370	208	53	,	,	PUNCT
ejpam-370	208	54	g.	g.	PROPN
ejpam-370	208	55	kızılkan	kızılkan	PROPN
ejpam-370	208	56	,	,	PUNCT
ejpam-370	208	57	a.	a.	PROPN
ejpam-370	208	58	çıbıkdiken	çıbıkdiken	VERB
ejpam-370	208	59	/	/	SYM
ejpam-370	208	60	eur	eur	PROPN
ejpam-370	208	61	.	.	PUNCT
ejpam-370	209	1	j.	j.	PROPN
ejpam-370	209	2	pure	pure	PROPN
ejpam-370	209	3	appl	appl	PROPN
ejpam-370	209	4	.	.	PROPN
ejpam-370	209	5	math	math	PROPN
ejpam-370	209	6	,	,	PUNCT
ejpam-370	209	7	3	3	NUM
ejpam-370	209	8	(	(	PUNCT
ejpam-370	209	9	2010	2010	NUM
ejpam-370	209	10	)	)	PUNCT
ejpam-370	209	11	,	,	PUNCT
ejpam-370	209	12	819	819	NUM
ejpam-370	209	13	-	-	SYM
ejpam-370	209	14	830	830	NUM
ejpam-370	209	15	828find\_ps();if	828find\_ps();if	NUM
ejpam-370	209	16	p[k	p[k	NOUN
ejpam-370	209	17	℄	℄	NOUN
ejpam-370	209	18	>1	>1	NOUN
ejpam-370	209	19	then	then	ADV
ejpam-370	209	20	for	for	ADP
ejpam-370	209	21	i	i	PRON
ejpam-370	209	22	from	from	ADP
ejpam-370	209	23	1	1	NUM
ejpam-370	209	24	to	to	ADP
ejpam-370	209	25	p[k	p[k	NOUN
ejpam-370	209	26	℄	℄	PROPN
ejpam-370	209	27	-1	-1	NOUN
ejpam-370	209	28	do	do	VERB
ejpam-370	209	29	if	if	SCONJ
ejpam-370	209	30	g[k	g[k	PROPN
ejpam-370	209	31	℄	℄	PROPN
ejpam-370	209	32	[i	[i	X
ejpam-370	209	33	℄	℄	PROPN
ejpam-370	209	34	<>0	<>0	PROPN
ejpam-370	209	35	then	then	ADV
ejpam-370	209	36	output2();end	output2();end	VERB
ejpam-370	209	37	if	if	SCONJ
ejpam-370	209	38	:	:	PUNCT
ejpam-370	209	39	end	end	NOUN
ejpam-370	209	40	do	do	AUX
ejpam-370	209	41	:	:	PUNCT
ejpam-370	209	42	end	end	VERB
ejpam-370	209	43	if	if	SCONJ
ejpam-370	209	44	:	:	PUNCT
ejpam-370	209	45	if	if	SCONJ
ejpam-370	209	46	m[k	m[k	PROPN
ejpam-370	209	47	℄	℄	PROPN
ejpam-370	209	48	=1	=1	NOUN
ejpam-370	209	49	or	or	CCONJ
ejpam-370	209	50	m[k	m[k	PROPN
ejpam-370	209	51	℄	℄	PROPN
ejpam-370	209	52	=p[k	=p[k	NOUN
ejpam-370	209	53	℄	℄	PROPN
ejpam-370	209	54	then	then	ADV
ejpam-370	209	55	cal	cal	PROPN
ejpam-370	209	56	ulatex0	ulatex0	PROPN
ejpam-370	209	57	(	(	PUNCT
ejpam-370	209	58	)	)	PUNCT
ejpam-370	209	59	;	;	PUNCT
ejpam-370	209	60	cal	cal	PROPN
ejpam-370	209	61	ulater	ulater	NOUN
ejpam-370	209	62	(	(	PUNCT
ejpam-370	209	63	)	)	PUNCT
ejpam-370	209	64	;	;	PUNCT
ejpam-370	209	65	m:=k;output1	m:=k;output1	PROPN
ejpam-370	209	66	(	(	PUNCT
ejpam-370	209	67	)	)	PUNCT
ejpam-370	209	68	;	;	PUNCT
ejpam-370	209	69	end	end	VERB
ejpam-370	209	70	if	if	SCONJ
ejpam-370	209	71	:	:	PUNCT
ejpam-370	209	72	u[k	u[k	PROPN
ejpam-370	209	73	℄	℄	PROPN
ejpam-370	209	74	:=ve	:=ve	PUNCT
ejpam-370	209	75	tor(1	tor(1	PROPN
ejpam-370	209	76	..	..	PUNCT
ejpam-370	209	77	1	1	NUM
ejpam-370	209	78	)	)	PUNCT
ejpam-370	209	79	;	;	PUNCT
ejpam-370	209	80	u[k	u[k	PROPN
ejpam-370	209	81	℄	℄	PROPN
ejpam-370	209	82	:=g[k	:=g[k	SYM
ejpam-370	209	83	℄	℄	PROPN
ejpam-370	209	84	[p[1	[p[1	X
ejpam-370	209	85	℄	℄	PROPN
ejpam-370	209	86	℄	℄	PROPN
ejpam-370	209	87	;	;	PUNCT
ejpam-370	209	88	v[k	v[k	PROPN
ejpam-370	209	89	℄	℄	PROPN
ejpam-370	209	90	:=ve	:=ve	PUNCT
ejpam-370	209	91	tor(1	tor(1	PROPN
ejpam-370	209	92	..	..	PUNCT
ejpam-370	209	93	m[k	m[k	PROPN
ejpam-370	209	94	℄	℄	PROPN
ejpam-370	209	95	-p[k	-p[k	PROPN
ejpam-370	209	96	℄	℄	PROPN
ejpam-370	209	97	);for	);for	PUNCT
ejpam-370	209	98	i	i	PRON
ejpam-370	209	99	from	from	ADP
ejpam-370	209	100	1	1	NUM
ejpam-370	209	101	to	to	ADP
ejpam-370	209	102	m[k	m[k	PROPN
ejpam-370	209	103	℄	℄	PROPN
ejpam-370	209	104	-p[k	-p[k	PROPN
ejpam-370	209	105	℄	℄	PROPN
ejpam-370	209	106	do	do	AUX
ejpam-370	209	107	v[k	v[k	PROPN
ejpam-370	209	108	℄	℄	PROPN
ejpam-370	209	109	[i	[i	X
ejpam-370	209	110	℄	℄	ADJ
ejpam-370	209	111	:=g[k	:=g[k	SYM
ejpam-370	209	112	℄	℄	PROPN
ejpam-370	209	113	[p[k	[p[k	X
ejpam-370	209	114	℄	℄	PROPN
ejpam-370	209	115	+i	+i	PROPN
ejpam-370	209	116	℄	℄	NOUN
ejpam-370	209	117	;	;	PUNCT
ejpam-370	209	118	end	end	NOUN
ejpam-370	209	119	do	do	VERB
ejpam-370	209	120	:	:	PUNCT
ejpam-370	209	121	a1[k	a1[k	PROPN
ejpam-370	209	122	℄	℄	PROPN
ejpam-370	209	123	:=matrix(1,1	:=matrix(1,1	PUNCT
ejpam-370	209	124	..	..	PROPN
ejpam-370	209	125	n[k	n[k	PROPN
ejpam-370	209	126	℄	℄	PROPN
ejpam-370	209	127	);for	);for	PUNCT
ejpam-370	209	128	j	j	PROPN
ejpam-370	209	129	from	from	ADP
ejpam-370	209	130	1	1	NUM
ejpam-370	209	131	to	to	ADP
ejpam-370	209	132	n[k	n[k	PROPN
ejpam-370	209	133	℄	℄	PROPN
ejpam-370	209	134	do	do	AUX
ejpam-370	209	135	a1[k	a1[k	PROPN
ejpam-370	209	136	℄	℄	PROPN
ejpam-370	209	137	[1,j	[1,j	X
ejpam-370	209	138	℄	℄	PROPN
ejpam-370	209	139	:=b[k	:=b[k	PROPN
ejpam-370	209	140	℄	℄	PROPN
ejpam-370	209	141	[p[k	[p[k	X
ejpam-370	209	142	℄	℄	PROPN
ejpam-370	209	143	,j	,j	PUNCT
ejpam-370	209	144	℄	℄	PROPN
ejpam-370	209	145	;	;	PUNCT
ejpam-370	209	146	end	end	NOUN
ejpam-370	209	147	do	do	VERB
ejpam-370	209	148	:	:	PUNCT
ejpam-370	209	149	a2[k	a2[k	PROPN
ejpam-370	209	150	℄	℄	PROPN
ejpam-370	209	151	:=matrix(1	:=matrix(1	PUNCT
ejpam-370	209	152	..	..	PUNCT
ejpam-370	209	153	(m[k	(m[k	PROPN
ejpam-370	209	154	℄	℄	PROPN
ejpam-370	209	155	-p[k	-p[k	PROPN
ejpam-370	209	156	℄	℄	PROPN
ejpam-370	209	157	),1	),1	PROPN
ejpam-370	209	158	..	..	PUNCT
ejpam-370	209	159	n[k	n[k	PROPN
ejpam-370	209	160	℄	℄	PROPN
ejpam-370	209	161	);for	);for	PUNCT
ejpam-370	209	162	i	i	PRON
ejpam-370	209	163	from	from	ADP
ejpam-370	209	164	1	1	NUM
ejpam-370	209	165	to	to	ADP
ejpam-370	209	166	m[k	m[k	PROPN
ejpam-370	209	167	℄	℄	PROPN
ejpam-370	209	168	-p[k	-p[k	PROPN
ejpam-370	209	169	℄	℄	PROPN
ejpam-370	209	170	do	do	VERB
ejpam-370	209	171	for	for	ADP
ejpam-370	209	172	j	j	PROPN
ejpam-370	209	173	from	from	ADP
ejpam-370	209	174	1	1	NUM
ejpam-370	209	175	to	to	ADP
ejpam-370	209	176	n[k	n[k	PROPN
ejpam-370	209	177	℄	℄	PROPN
ejpam-370	209	178	doa2[k	doa2[k	PROPN
ejpam-370	209	179	℄	℄	PROPN
ejpam-370	209	180	[i	[i	X
ejpam-370	209	181	,	,	PUNCT
ejpam-370	209	182	j	j	PROPN
ejpam-370	209	183	℄	℄	PROPN
ejpam-370	209	184	:=b[k	:=b[k	PROPN
ejpam-370	209	185	℄	℄	PROPN
ejpam-370	209	186	[p[k	[p[k	X
ejpam-370	209	187	℄	℄	PROPN
ejpam-370	209	188	+i	+i	PROPN
ejpam-370	209	189	,	,	PUNCT
ejpam-370	209	190	j	j	PROPN
ejpam-370	209	191	℄	℄	PROPN
ejpam-370	209	192	;	;	PUNCT
ejpam-370	209	193	end	end	NOUN
ejpam-370	209	194	do	do	AUX
ejpam-370	209	195	:	:	PUNCT
ejpam-370	209	196	end	end	VERB
ejpam-370	209	197	do	do	VERB
ejpam-370	209	198	:	:	PUNCT
ejpam-370	209	199	cal	cal	NUM
ejpam-370	209	200	ulatex0	ulatex0	PROPN
ejpam-370	209	201	(	(	PUNCT
ejpam-370	209	202	)	)	PUNCT
ejpam-370	209	203	;	;	PUNCT
ejpam-370	209	204	cal	cal	PROPN
ejpam-370	209	205	ulater	ulater	NOUN
ejpam-370	209	206	(	(	PUNCT
ejpam-370	209	207	)	)	PUNCT
ejpam-370	209	208	;	;	PUNCT
ejpam-370	209	209	b[k+1	b[k+1	PROPN
ejpam-370	209	210	℄	℄	PROPN
ejpam-370	209	211	:=multiply(a2[k	:=multiply(a2[k	X
ejpam-370	209	212	℄	℄	PROPN
ejpam-370	209	213	,r[k	,r[k	PUNCT
ejpam-370	209	214	℄	℄	PROPN
ejpam-370	209	215	);g[k+1	);g[k+1	VERB
ejpam-370	209	216	℄	℄	PROPN
ejpam-370	209	217	:=v[k	:=v[k	PROPN
ejpam-370	209	218	℄	℄	PROPN
ejpam-370	209	219	-multiply(a2[k	-multiply(a2[k	PROPN
ejpam-370	209	220	℄	℄	PROPN
ejpam-370	209	221	,x0[k	,x0[k	PUNCT
ejpam-370	209	222	℄	℄	PROPN
ejpam-370	209	223	);end	);end	X
ejpam-370	210	1	do	do	VERB
ejpam-370	210	2	:	:	PUNCT
ejpam-370	210	3	k:=n	k:=n	PROPN
ejpam-370	210	4	;	;	PUNCT
ejpam-370	211	1	m[k	m[k	PROPN
ejpam-370	211	2	℄	℄	PROPN
ejpam-370	211	3	:=rowdim(a)-sum(p[t	:=rowdim(a)-sum(p[t	PROPN
ejpam-370	211	4	℄	℄	PROPN
ejpam-370	211	5	,t=1	,t=1	PUNCT
ejpam-370	211	6	..	..	PUNCT
ejpam-370	211	7	k-1	k-1	PROPN
ejpam-370	211	8	)	)	PUNCT
ejpam-370	211	9	;	;	PUNCT
ejpam-370	211	10	n[k	n[k	PROPN
ejpam-370	211	11	℄	℄	PROPN
ejpam-370	211	12	:=	:=	X
ejpam-370	211	13	oldim(a)-k+1;find_ps();if	oldim(a)-k+1;find_ps();if	X
ejpam-370	211	14	m[1	m[1	PROPN
ejpam-370	211	15	℄	℄	PROPN
ejpam-370	211	16	<n[1	<n[1	PROPN
ejpam-370	211	17	℄	℄	PROPN
ejpam-370	211	18	then	then	ADV
ejpam-370	211	19	cal	cal	PROPN
ejpam-370	211	20	ulatex0	ulatex0	PROPN
ejpam-370	211	21	(	(	PUNCT
ejpam-370	211	22	)	)	PUNCT
ejpam-370	211	23	;	;	PUNCT
ejpam-370	211	24	cal	cal	PROPN
ejpam-370	211	25	ulater	ulater	NOUN
ejpam-370	211	26	(	(	PUNCT
ejpam-370	211	27	)	)	PUNCT
ejpam-370	211	28	;	;	PUNCT
ejpam-370	211	29	m:=k;output1	m:=k;output1	PROPN
ejpam-370	211	30	(	(	PUNCT
ejpam-370	211	31	)	)	PUNCT
ejpam-370	211	32	;	;	PUNCT
ejpam-370	211	33	end	end	VERB
ejpam-370	211	34	if	if	SCONJ
ejpam-370	211	35	:	:	PUNCT
ejpam-370	211	36	if	if	SCONJ
ejpam-370	211	37	verify	verify	VERB
ejpam-370	211	38	(	(	PUNCT
ejpam-370	211	39	onvert(b[k	onvert(b[k	NUM
ejpam-370	211	40	℄	℄	PROPN
ejpam-370	211	41	,ve	,ve	PUNCT
ejpam-370	211	42	tor),(b[k	tor),(b[k	PROPN
ejpam-370	211	43	℄	℄	PROPN
ejpam-370	211	44	[1,1	[1,1	X
ejpam-370	211	45	℄	℄	PROPN
ejpam-370	211	46	)/(g[k	)/(g[k	PROPN
ejpam-370	211	47	℄	℄	PROPN
ejpam-370	211	48	[1	[1	ADJ
ejpam-370	211	49	℄	℄	PROPN
ejpam-370	211	50	)*g[k	)*g[k	SYM
ejpam-370	211	51	℄	℄	ADJ
ejpam-370	211	52	,ve	,ve	PUNCT
ejpam-370	211	53	tor	tor	NOUN
ejpam-370	211	54	)	)	PUNCT
ejpam-370	211	55	orverify(g[k	orverify(g[k	NOUN
ejpam-370	211	56	℄	℄	PROPN
ejpam-370	211	57	,ve	,ve	PUNCT
ejpam-370	211	58	tor(1	tor(1	PROPN
ejpam-370	211	59	..	..	PUNCT
ejpam-370	211	60	ve	ve	VERB
ejpam-370	211	61	tdim(g[k	tdim(g[k	NOUN
ejpam-370	211	62	℄	℄	ADJ
ejpam-370	211	63	),0	),0	PUNCT
ejpam-370	211	64	)	)	PUNCT
ejpam-370	211	65	)	)	PUNCT
ejpam-370	211	66	then	then	ADV
ejpam-370	211	67	cal	cal	X
ejpam-370	211	68	ulatex0	ulatex0	PROPN
ejpam-370	211	69	(	(	PUNCT
ejpam-370	211	70	)	)	PUNCT
ejpam-370	211	71	;	;	PUNCT
ejpam-370	211	72	m:=k;output1	m:=k;output1	PROPN
ejpam-370	211	73	(	(	PUNCT
ejpam-370	211	74	)	)	PUNCT
ejpam-370	211	75	;	;	PUNCT
ejpam-370	211	76	else	else	ADV
ejpam-370	211	77	output2	output2	PROPN
ejpam-370	211	78	(	(	PUNCT
ejpam-370	211	79	)	)	PUNCT
ejpam-370	211	80	;	;	PUNCT
ejpam-370	211	81	end	end	VERB
ejpam-370	211	82	if	if	SCONJ
ejpam-370	211	83	:	:	PUNCT
ejpam-370	211	84	end	end	VERB
ejpam-370	211	85	pro	pro	ADJ
ejpam-370	211	86	:	:	PUNCT
ejpam-370	211	87	example	example	NOUN
ejpam-370	211	88	4	4	NUM
ejpam-370	211	89	.	.	X
ejpam-370	211	90	>	>	PUNCT
ejpam-370	211	91	a:=matrix([[1,-2,2,3	a:=matrix([[1,-2,2,3	PROPN
ejpam-370	211	92	℄	℄	PROPN
ejpam-370	211	93	,[2,1,1,-1	,[2,1,1,-1	PUNCT
ejpam-370	211	94	℄	℄	PROPN
ejpam-370	211	95	,[3,-1,3,2	,[3,-1,3,2	PUNCT
ejpam-370	211	96	℄	℄	PROPN
ejpam-370	211	97	,[5,0,4,1	,[5,0,4,1	PUNCT
ejpam-370	211	98	℄	℄	PROPN
ejpam-370	211	99	℄	℄	PROPN
ejpam-370	211	100	)	)	PUNCT
ejpam-370	211	101	;	;	PUNCT
ejpam-370	211	102	a=	a=	NOUN
ejpam-370	211	103			NOUN
ejpam-370	211	104			NOUN
ejpam-370	211	105			NOUN
ejpam-370	211	106			NOUN
ejpam-370	211	107			NOUN
ejpam-370	211	108	1	1	NUM
ejpam-370	211	109	−2	−2	NOUN
ejpam-370	211	110	2	2	NUM
ejpam-370	211	111	3	3	NUM
ejpam-370	211	112	2	2	NUM
ejpam-370	211	113	1	1	NUM
ejpam-370	211	114	1	1	NUM
ejpam-370	211	115	−1	−1	NOUN
ejpam-370	211	116	3	3	NUM
ejpam-370	211	117	−1	−1	NOUN
ejpam-370	211	118	3	3	NUM
ejpam-370	211	119	2	2	NUM
ejpam-370	211	120	5	5	NUM
ejpam-370	211	121	0	0	NUM
ejpam-370	211	122	4	4	NUM
ejpam-370	211	123	1	1	NUM
ejpam-370	211	124			NOUN
ejpam-370	211	125			NOUN
ejpam-370	211	126			VERB
ejpam-370	211	127			VERB
ejpam-370	211	128	>f:=ve	>f:=ve	PROPN
ejpam-370	211	129	tor([1,-1,0,-1	tor([1,-1,0,-1	PROPN
ejpam-370	211	130	℄	℄	PROPN
ejpam-370	211	131	)	)	PUNCT
ejpam-370	211	132	;	;	PUNCT
ejpam-370	211	133	f	f	PROPN
ejpam-370	211	134	=	=	SYM
ejpam-370	211	135			PROPN
ejpam-370	211	136			NOUN
ejpam-370	211	137			NOUN
ejpam-370	211	138			NOUN
ejpam-370	211	139			NOUN
ejpam-370	211	140	1	1	NUM
ejpam-370	211	141	−1	−1	NOUN
ejpam-370	211	142	0	0	NUM
ejpam-370	211	143	−1	−1	NOUN
ejpam-370	211	144			PROPN
ejpam-370	211	145			NOUN
ejpam-370	211	146			VERB
ejpam-370	211	147			NOUN
ejpam-370	212	1	>gidda(a	>gidda(a	INTJ
ejpam-370	212	2	,	,	PUNCT
ejpam-370	212	3	f	f	PROPN
ejpam-370	212	4	)	)	PUNCT
ejpam-370	212	5	;	;	PUNCT
ejpam-370	212	6			PROPN
ejpam-370	212	7			NOUN
ejpam-370	212	8			NOUN
ejpam-370	212	9			NOUN
ejpam-370	212	10			NOUN
ejpam-370	212	11	−1	−1	NOUN
ejpam-370	212	12	5	5	NUM
ejpam-370	212	13	−	−	NOUN
ejpam-370	212	14	4	4	NUM
ejpam-370	212	15	5	5	NUM
ejpam-370	212	16	a1	a1	NOUN
ejpam-370	212	17	−	−	NOUN
ejpam-370	212	18	1	1	NUM
ejpam-370	212	19	5	5	NUM
ejpam-370	212	20	a2	a2	NOUN
ejpam-370	212	21	−3	−3	NOUN
ejpam-370	213	1	5	5	NUM
ejpam-370	213	2	+	+	CCONJ
ejpam-370	213	3	3	3	NUM
ejpam-370	213	4	5	5	NUM
ejpam-370	213	5	a1	a1	NOUN
ejpam-370	213	6	+	+	CCONJ
ejpam-370	213	7	4	4	NUM
ejpam-370	213	8	5	5	NUM
ejpam-370	213	9	a2	a2	PROPN
ejpam-370	213	10	a1	a1	PROPN
ejpam-370	213	11	a2	a2	PROPN
ejpam-370	213	12			PROPN
ejpam-370	213	13			NOUN
ejpam-370	213	14			VERB
ejpam-370	213	15			NOUN
ejpam-370	213	16			PUNCT
ejpam-370	214	1	references	reference	NOUN
ejpam-370	214	2	829	829	NUM
ejpam-370	214	3	example	example	NOUN
ejpam-370	214	4	5	5	NUM
ejpam-370	214	5	.	.	X
ejpam-370	215	1	>	>	PUNCT
ejpam-370	215	2	a:=matrix([[1,2,-3,1,-1,-2,4	a:=matrix([[1,2,-3,1,-1,-2,4	PROPN
ejpam-370	215	3	℄	℄	PROPN
ejpam-370	215	4	,[2,4,-6,2,-2,-4,8	,[2,4,-6,2,-2,-4,8	PROPN
ejpam-370	215	5	℄	℄	PROPN
ejpam-370	215	6	,[3,6,-9,3,-3,-6,12	,[3,6,-9,3,-3,-6,12	PUNCT
ejpam-370	215	7	℄	℄	PROPN
ejpam-370	215	8	,[1,-1,3,-2,0,1,2	,[1,-1,3,-2,0,1,2	PUNCT
ejpam-370	215	9	℄	℄	PROPN
ejpam-370	215	10	℄	℄	PROPN
ejpam-370	215	11	)	)	PUNCT
ejpam-370	215	12	;	;	PUNCT
ejpam-370	215	13	a=	a=	NOUN
ejpam-370	215	14			NOUN
ejpam-370	215	15			NOUN
ejpam-370	215	16			NOUN
ejpam-370	215	17			NOUN
ejpam-370	215	18			NOUN
ejpam-370	215	19	1	1	NUM
ejpam-370	215	20	2	2	NUM
ejpam-370	215	21	−3	−3	NOUN
ejpam-370	215	22	1	1	NUM
ejpam-370	215	23	−1	−1	NOUN
ejpam-370	215	24	−2	−2	NOUN
ejpam-370	215	25	4	4	NUM
ejpam-370	215	26	2	2	NUM
ejpam-370	215	27	4	4	NUM
ejpam-370	215	28	−6	−6	SYM
ejpam-370	215	29	2	2	NUM
ejpam-370	215	30	−2	−2	NOUN
ejpam-370	215	31	−4	−4	NOUN
ejpam-370	215	32	8	8	NUM
ejpam-370	215	33	3	3	NUM
ejpam-370	215	34	6	6	NUM
ejpam-370	215	35	−9	−9	NOUN
ejpam-370	215	36	3	3	NUM
ejpam-370	215	37	−3	−3	NOUN
ejpam-370	215	38	−6	−6	NOUN
ejpam-370	215	39	12	12	NUM
ejpam-370	215	40	1	1	NUM
ejpam-370	215	41	−1	−1	NOUN
ejpam-370	215	42	3	3	NUM
ejpam-370	215	43	−2	−2	NOUN
ejpam-370	215	44	0	0	NUM
ejpam-370	215	45	1	1	NUM
ejpam-370	215	46	2	2	NUM
ejpam-370	215	47			NOUN
ejpam-370	215	48			NOUN
ejpam-370	215	49			VERB
ejpam-370	215	50			VERB
ejpam-370	215	51	>f:=ve	>f:=ve	PROPN
ejpam-370	215	52	tor([4,8,12,1	tor([4,8,12,1	NOUN
ejpam-370	215	53	℄	℄	PROPN
ejpam-370	215	54	)	)	PUNCT
ejpam-370	215	55	;	;	PUNCT
ejpam-370	216	1	f	f	PROPN
ejpam-370	216	2	=	=	SYM
ejpam-370	216	3			PROPN
ejpam-370	216	4			NOUN
ejpam-370	216	5			NOUN
ejpam-370	216	6			NOUN
ejpam-370	216	7			NOUN
ejpam-370	216	8	4	4	NUM
ejpam-370	216	9	8	8	NUM
ejpam-370	216	10	12	12	NUM
ejpam-370	216	11	1	1	NUM
ejpam-370	216	12			NOUN
ejpam-370	216	13			NOUN
ejpam-370	216	14			VERB
ejpam-370	216	15			NOUN
ejpam-370	217	1	>gidda(a	>gidda(a	INTJ
ejpam-370	217	2	,	,	PUNCT
ejpam-370	217	3	f	f	PROPN
ejpam-370	217	4	)	)	PUNCT
ejpam-370	217	5	;	;	PUNCT
ejpam-370	218	1			PROPN
ejpam-370	218	2			NOUN
ejpam-370	218	3			NOUN
ejpam-370	218	4			NOUN
ejpam-370	218	5			NOUN
ejpam-370	218	6			NOUN
ejpam-370	218	7			NOUN
ejpam-370	218	8			NOUN
ejpam-370	218	9			NOUN
ejpam-370	218	10			NOUN
ejpam-370	218	11			NOUN
ejpam-370	218	12	−2−	−2−	PROPN
ejpam-370	218	13	a1	a1	NOUN
ejpam-370	218	14	+	+	NUM
ejpam-370	218	15	a2	a2	PROPN
ejpam-370	218	16	+	+	CCONJ
ejpam-370	218	17	1	1	NUM
ejpam-370	218	18	3	3	NUM
ejpam-370	218	19	a3	a3	NOUN
ejpam-370	218	20	−	−	NOUN
ejpam-370	218	21	8	8	NUM
ejpam-370	218	22	3	3	NUM
ejpam-370	218	23	a5	a5	PROPN
ejpam-370	218	24	1	1	NUM
ejpam-370	218	25	+	+	NUM
ejpam-370	218	26	2a1−	2a1−	NUM
ejpam-370	218	27	a2	a2	NOUN
ejpam-370	218	28	+	+	CCONJ
ejpam-370	218	29	1	1	NUM
ejpam-370	218	30	3	3	NUM
ejpam-370	218	31	a3	a3	NOUN
ejpam-370	218	32	+	+	CCONJ
ejpam-370	218	33	a4	a4	NOUN
ejpam-370	218	34	−	−	ADP
ejpam-370	218	35	2	2	NUM
ejpam-370	218	36	3	3	NUM
ejpam-370	218	37	a5	a5	NOUN
ejpam-370	218	38	a1	a1	NOUN
ejpam-370	218	39	a2	a2	PROPN
ejpam-370	218	40	a3	a3	PROPN
ejpam-370	218	41	a4	a4	PROPN
ejpam-370	218	42	a5	a5	PROPN
ejpam-370	218	43			NOUN
ejpam-370	218	44			NOUN
ejpam-370	218	45			VERB
ejpam-370	218	46			NOUN
ejpam-370	218	47			NOUN
ejpam-370	218	48			NOUN
ejpam-370	218	49			NOUN
ejpam-370	218	50			NOUN
ejpam-370	218	51			NOUN
ejpam-370	218	52			NOUN
ejpam-370	218	53			PUNCT
ejpam-370	219	1	5	5	X
ejpam-370	219	2	.	.	X
ejpam-370	219	3	conclusion	conclusion	NOUN
ejpam-370	219	4	giddm	giddm	NOUN
ejpam-370	219	5	produces	produce	VERB
ejpam-370	219	6	a	a	DET
ejpam-370	219	7	special	special	ADJ
ejpam-370	219	8	x	x	X
ejpam-370	219	9	(	(	PUNCT
ejpam-370	219	10	k	k	NOUN
ejpam-370	219	11	)	)	PUNCT
ejpam-370	219	12	0	0	NUM
ejpam-370	219	13	solutions	solution	NOUN
ejpam-370	219	14	and	and	CCONJ
ejpam-370	219	15	r(k	r(k	NOUN
ejpam-370	219	16	)	)	PUNCT
ejpam-370	219	17	matrices	matrix	NOUN
ejpam-370	219	18	by	by	ADP
ejpam-370	219	19	reducing	reduce	VERB
ejpam-370	219	20	the	the	DET
ejpam-370	219	21	dimension	dimension	NOUN
ejpam-370	219	22	of	of	ADP
ejpam-370	219	23	a	a	DET
ejpam-370	219	24	given	give	VERB
ejpam-370	219	25	system	system	NOUN
ejpam-370	219	26	of	of	ADP
ejpam-370	219	27	linear	linear	ADJ
ejpam-370	219	28	algebraic	algebraic	ADJ
ejpam-370	219	29	equation	equation	NOUN
ejpam-370	219	30	.	.	PUNCT
ejpam-370	220	1	it	it	PRON
ejpam-370	220	2	obtains	obtain	VERB
ejpam-370	220	3	the	the	DET
ejpam-370	220	4	solution	solution	NOUN
ejpam-370	220	5	depending	depend	VERB
ejpam-370	220	6	on	on	ADP
ejpam-370	220	7	x	x	X
ejpam-370	220	8	(	(	PUNCT
ejpam-370	220	9	k	k	NOUN
ejpam-370	220	10	)	)	PUNCT
ejpam-370	220	11	0	0	NUM
ejpam-370	220	12	and	and	CCONJ
ejpam-370	220	13	r(k	r(k	PROPN
ejpam-370	220	14	)	)	PUNCT
ejpam-370	220	15	.	.	PUNCT
ejpam-370	221	1	gidda	gidda	NOUN
ejpam-370	221	2	is	be	AUX
ejpam-370	221	3	suited	suit	VERB
ejpam-370	221	4	for	for	ADP
ejpam-370	221	5	implementation	implementation	NOUN
ejpam-370	221	6	using	use	VERB
ejpam-370	221	7	computer	computer	NOUN
ejpam-370	221	8	algebra	algebra	NOUN
ejpam-370	221	9	systems	system	NOUN
ejpam-370	221	10	such	such	ADJ
ejpam-370	221	11	as	as	ADP
ejpam-370	221	12	maple	maple	NOUN
ejpam-370	221	13	and	and	CCONJ
ejpam-370	221	14	matlab	matlab	PROPN
ejpam-370	221	15	.	.	PUNCT
ejpam-370	222	1	references	reference	NOUN
ejpam-370	222	2	[	[	X
ejpam-370	222	3	1	1	NUM
ejpam-370	222	4	]	]	X
ejpam-370	222	5	g.h	g.h	PROPN
ejpam-370	222	6	.	.	PROPN
ejpam-370	222	7	golub	golub	PROPN
ejpam-370	222	8	and	and	CCONJ
ejpam-370	222	9	j.m	j.m	PROPN
ejpam-370	222	10	.	.	PROPN
ejpam-370	222	11	ortega	ortega	PROPN
ejpam-370	222	12	.	.	PUNCT
ejpam-370	223	1	scientific	scientific	ADJ
ejpam-370	223	2	computing	computing	NOUN
ejpam-370	223	3	:	:	PUNCT
ejpam-370	223	4	an	an	DET
ejpam-370	223	5	introduction	introduction	NOUN
ejpam-370	223	6	with	with	ADP
ejpam-370	223	7	parallel	parallel	ADJ
ejpam-370	223	8	computing	computing	NOUN
ejpam-370	223	9	.	.	PUNCT
ejpam-370	224	1	academic	academic	ADJ
ejpam-370	224	2	press	press	PROPN
ejpam-370	224	3	,	,	PUNCT
ejpam-370	224	4	boston	boston	PROPN
ejpam-370	224	5	,	,	PUNCT
ejpam-370	224	6	ma	ma	PROPN
ejpam-370	224	7	,	,	PUNCT
ejpam-370	224	8	1993	1993	NUM
ejpam-370	224	9	.	.	PUNCT
ejpam-370	225	1	[	[	X
ejpam-370	225	2	2	2	NUM
ejpam-370	225	3	]	]	X
ejpam-370	225	4	g.h	g.h	PROPN
ejpam-370	225	5	.	.	PROPN
ejpam-370	225	6	golub	golub	PROPN
ejpam-370	225	7	and	and	CCONJ
ejpam-370	225	8	c.f	c.f	PROPN
ejpam-370	225	9	.	.	PROPN
ejpam-370	225	10	van	van	PROPN
ejpam-370	225	11	loan	loan	PROPN
ejpam-370	225	12	.	.	PUNCT
ejpam-370	226	1	matrix	matrix	NOUN
ejpam-370	226	2	computations	computation	NOUN
ejpam-370	226	3	.	.	PUNCT
ejpam-370	227	1	the	the	DET
ejpam-370	227	2	johns	johns	PROPN
ejpam-370	227	3	hopkins	hopkins	PROPN
ejpam-370	227	4	university	university	PROPN
ejpam-370	227	5	press	press	PROPN
ejpam-370	227	6	,	,	PUNCT
ejpam-370	227	7	baltimore	baltimore	PROPN
ejpam-370	227	8	,	,	PUNCT
ejpam-370	227	9	md	md	PROPN
ejpam-370	227	10	,	,	PUNCT
ejpam-370	227	11	1983	1983	NUM
ejpam-370	227	12	.	.	PUNCT
ejpam-370	228	1	[	[	X
ejpam-370	228	2	3	3	X
ejpam-370	228	3	]	]	PUNCT
ejpam-370	228	4	t.	t.	PROPN
ejpam-370	228	5	keskin	keskin	PROPN
ejpam-370	228	6	and	and	CCONJ
ejpam-370	228	7	k.	k.	PROPN
ejpam-370	228	8	aydın	aydın	PROPN
ejpam-370	228	9	.	.	PUNCT
ejpam-370	229	1	iterative	iterative	NOUN
ejpam-370	229	2	decreasing	decrease	VERB
ejpam-370	229	3	dimension	dimension	NOUN
ejpam-370	229	4	algorithm	algorithm	NOUN
ejpam-370	229	5	.	.	PUNCT
ejpam-370	230	1	comp	comp	PROPN
ejpam-370	230	2	.	.	PUNCT
ejpam-370	231	1	and	and	CCONJ
ejpam-370	231	2	math	math	NOUN
ejpam-370	231	3	.	.	PUNCT
ejpam-370	232	1	with	with	ADP
ejpam-370	232	2	appl	appl	PROPN
ejpam-370	232	3	.	.	PROPN
ejpam-370	232	4	,	,	PUNCT
ejpam-370	232	5	53:1153–1158	53:1153–1158	NUM
ejpam-370	232	6	,	,	PUNCT
ejpam-370	232	7	2007	2007	NUM
ejpam-370	232	8	.	.	PUNCT
ejpam-370	233	1	references	reference	NOUN
ejpam-370	233	2	830	830	NUM
ejpam-370	233	3	[	[	X
ejpam-370	233	4	4	4	NUM
ejpam-370	233	5	]	]	PUNCT
ejpam-370	233	6	h.	h.	PROPN
ejpam-370	233	7	wang	wang	PROPN
ejpam-370	233	8	and	and	CCONJ
ejpam-370	233	9	j.	j.	PROPN
ejpam-370	233	10	jiang	jiang	PROPN
ejpam-370	233	11	.	.	PUNCT
ejpam-370	234	1	solution	solution	NOUN
ejpam-370	234	2	of	of	ADP
ejpam-370	234	3	the	the	DET
ejpam-370	234	4	system	system	NOUN
ejpam-370	234	5	of	of	ADP
ejpam-370	234	6	linear	linear	PROPN
ejpam-370	234	7	algebraic	algebraic	ADJ
ejpam-370	234	8	equations	equation	NOUN
ejpam-370	234	9	by	by	ADP
ejpam-370	234	10	decreasing	decrease	VERB
ejpam-370	234	11	dimension	dimension	NOUN
ejpam-370	234	12	.	.	PUNCT
ejpam-370	235	1	app	app	PROPN
ejpam-370	235	2	.	.	PROPN
ejpam-370	235	3	math	math	PROPN
ejpam-370	235	4	.	.	PUNCT
ejpam-370	236	1	and	and	CCONJ
ejpam-370	236	2	comput	comput	ADJ
ejpam-370	236	3	.	.	PUNCT
ejpam-370	236	4	,	,	PUNCT
ejpam-370	236	5	109:51–57	109:51–57	NUM
ejpam-370	236	6	,	,	PUNCT
ejpam-370	236	7	2000	2000	NUM
ejpam-370	236	8	.	.	PUNCT
ejpam-370	237	1	[	[	X
ejpam-370	237	2	5	5	X
ejpam-370	237	3	]	]	PUNCT
ejpam-370	237	4	j.	j.	PROPN
ejpam-370	237	5	zhang	zhang	PROPN
ejpam-370	237	6	.	.	PUNCT
ejpam-370	238	1	comments	comment	NOUN
ejpam-370	238	2	on	on	ADP
ejpam-370	238	3	solution	solution	NOUN
ejpam-370	238	4	of	of	ADP
ejpam-370	238	5	the	the	DET
ejpam-370	238	6	system	system	NOUN
ejpam-370	238	7	of	of	ADP
ejpam-370	238	8	linear	linear	PROPN
ejpam-370	238	9	algebraic	algebraic	ADJ
ejpam-370	238	10	equations	equation	NOUN
ejpam-370	238	11	by	by	ADP
ejpam-370	238	12	decreasing	decrease	VERB
ejpam-370	238	13	dimension	dimension	NOUN
ejpam-370	238	14	.	.	PUNCT
ejpam-370	239	1	appl	appl	PROPN
ejpam-370	239	2	.	.	PROPN
ejpam-370	239	3	math	math	PROPN
ejpam-370	239	4	.	.	PUNCT
ejpam-370	240	1	and	and	CCONJ
ejpam-370	240	2	comput	comput	ADJ
ejpam-370	240	3	.	.	PUNCT
ejpam-370	240	4	,	,	PUNCT
ejpam-370	240	5	128:95–98	128:95–98	NUM
ejpam-370	240	6	,	,	PUNCT
ejpam-370	240	7	2002	2002	NUM
ejpam-370	240	8	.	.	PUNCT