id	sid	tid	token	lemma	pos
cbi-47	1	1	v1i2	v1i2	X
cbi-47	1	2	volume	volume	NOUN
cbi-47	1	3	1	1	NUM
cbi-47	1	4	,	,	PUNCT
cbi-47	1	5	issue	issue	NOUN
cbi-47	1	6	2	2	NUM
cbi-47	1	7	letters	letter	NOUN
cbi-47	1	8	and	and	CCONJ
cbi-47	1	9	notes	note	NOUN
cbi-47	1	10	exploring	explore	VERB
cbi-47	1	11	alternate	alternate	ADJ
cbi-47	1	12	notations	notation	NOUN
cbi-47	1	13	for	for	ADP
cbi-47	1	14	partial	partial	ADJ
cbi-47	1	15	differentials	differential	NOUN
cbi-47	1	16	jonathan	jonathan	PROPN
cbi-47	1	17	bartlett	bartlett	PROPN
cbi-47	1	18	doi	doi	PROPN
cbi-47	1	19	:	:	PUNCT
cbi-47	1	20	10.33014	10.33014	NUM
cbi-47	1	21	/	/	SYM
cbi-47	1	22	issn.2640	issn.2640	ADJ
cbi-47	1	23	-	-	PUNCT
cbi-47	1	24	5652.1.2.bartlett.2	5652.1.2.bartlett.2	ADJ
cbi-47	1	25	recent	recent	ADJ
cbi-47	1	26	work	work	NOUN
cbi-47	1	27	has	have	AUX
cbi-47	1	28	shown	show	VERB
cbi-47	1	29	that	that	SCONJ
cbi-47	1	30	differentials	differential	NOUN
cbi-47	1	31	can	can	AUX
cbi-47	1	32	be	be	AUX
cbi-47	1	33	made	make	VERB
cbi-47	1	34	more	more	ADV
cbi-47	1	35	algebraically	algebraically	ADV
cbi-47	1	36	manipulable	manipulable	ADJ
cbi-47	1	37	if	if	SCONJ
cbi-47	1	38	the	the	DET
cbi-47	1	39	notation	notation	NOUN
cbi-47	1	40	is	be	AUX
cbi-47	1	41	improved	improve	VERB
cbi-47	1	42	(	(	PUNCT
cbi-47	1	43	bartlett	bartlett	PROPN
cbi-47	1	44	and	and	CCONJ
cbi-47	1	45	khurshudyan	khurshudyan	PROPN
cbi-47	1	46	,	,	PUNCT
cbi-47	1	47	2019	2019	NUM
cbi-47	1	48	)	)	PUNCT
cbi-47	1	49	.	.	PUNCT
cbi-47	2	1	can	can	AUX
cbi-47	2	2	this	this	PRON
cbi-47	2	3	also	also	ADV
cbi-47	2	4	be	be	AUX
cbi-47	2	5	the	the	DET
cbi-47	2	6	case	case	NOUN
cbi-47	2	7	with	with	ADP
cbi-47	2	8	the	the	DET
cbi-47	2	9	jacobian	jacobian	ADJ
cbi-47	2	10	notation	notation	NOUN
cbi-47	2	11	for	for	ADP
cbi-47	2	12	partial	partial	ADJ
cbi-47	2	13	differentials	differential	NOUN
cbi-47	2	14	(	(	PUNCT
cbi-47	2	15	i.e.	i.e.	X
cbi-47	2	16	,	,	PUNCT
cbi-47	2	17	∂y	∂y	NOUN
cbi-47	2	18	∂x	∂x	PROPN
cbi-47	2	19	)	)	PUNCT
cbi-47	2	20	?	?	PUNCT
cbi-47	3	1	the	the	DET
cbi-47	3	2	typical	typical	ADJ
cbi-47	3	3	counterexample	counterexample	NOUN
cbi-47	3	4	to	to	ADP
cbi-47	3	5	why	why	SCONJ
cbi-47	3	6	partial	partial	ADJ
cbi-47	3	7	differentials	differential	NOUN
cbi-47	3	8	could	could	AUX
cbi-47	3	9	not	not	PART
cbi-47	3	10	be	be	AUX
cbi-47	3	11	algebraically	algebraically	ADV
cbi-47	3	12	manipulable	manipulable	ADJ
cbi-47	3	13	comes	come	VERB
cbi-47	3	14	from	from	ADP
cbi-47	3	15	an	an	DET
cbi-47	3	16	example	example	NOUN
cbi-47	3	17	similar	similar	ADJ
cbi-47	3	18	to	to	ADP
cbi-47	3	19	the	the	DET
cbi-47	3	20	following	following	NOUN
cbi-47	3	21	.	.	PUNCT
cbi-47	4	1	take	take	VERB
cbi-47	4	2	a	a	DET
cbi-47	4	3	three	three	NUM
cbi-47	4	4	-	-	PUNCT
cbi-47	4	5	variable	variable	NOUN
cbi-47	4	6	equation	equation	NOUN
cbi-47	4	7	,	,	PUNCT
cbi-47	4	8	such	such	ADJ
cbi-47	4	9	as	as	ADP
cbi-47	4	10	y	y	PROPN
cbi-47	4	11	=	=	PUNCT
cbi-47	4	12	x2z	x2z	PROPN
cbi-47	4	13	.	.	PUNCT
cbi-47	5	1	this	this	DET
cbi-47	5	2	equation	equation	NOUN
cbi-47	5	3	has	have	VERB
cbi-47	5	4	six	six	NUM
cbi-47	5	5	partial	partial	ADJ
cbi-47	5	6	derivatives	derivative	NOUN
cbi-47	5	7	.	.	PUNCT
cbi-47	6	1	for	for	ADP
cbi-47	6	2	this	this	DET
cbi-47	6	3	example	example	NOUN
cbi-47	6	4	,	,	PUNCT
cbi-47	6	5	we	we	PRON
cbi-47	6	6	will	will	AUX
cbi-47	6	7	note	note	VERB
cbi-47	6	8	that	that	SCONJ
cbi-47	6	9	∂y	∂y	PROPN
cbi-47	6	10	∂x	∂x	PROPN
cbi-47	6	11	=	=	SYM
cbi-47	6	12	2xz	2xz	PROPN
cbi-47	6	13	and	and	CCONJ
cbi-47	6	14	∂y	∂y	PROPN
cbi-47	6	15	∂z	∂z	PROPN
cbi-47	6	16	=	=	SYM
cbi-47	6	17	x2	x2	PROPN
cbi-47	6	18	.	.	PUNCT
cbi-47	7	1	if	if	SCONJ
cbi-47	7	2	partial	partial	ADJ
cbi-47	7	3	differentials	differential	NOUN
cbi-47	7	4	were	be	AUX
cbi-47	7	5	algebraically	algebraically	ADV
cbi-47	7	6	manipulable	manipulable	ADJ
cbi-47	7	7	,	,	PUNCT
cbi-47	7	8	we	we	PRON
cbi-47	7	9	should	should	AUX
cbi-47	7	10	be	be	AUX
cbi-47	7	11	able	able	ADJ
cbi-47	7	12	to	to	PART
cbi-47	7	13	find	find	VERB
cbi-47	7	14	∂z	∂z	PRON
cbi-47	7	15	∂x	∂x	PROPN
cbi-47	7	16	by	by	ADP
cbi-47	7	17	simple	simple	ADJ
cbi-47	7	18	algebraic	algebraic	ADJ
cbi-47	7	19	manipulation	manipulation	NOUN
cbi-47	7	20	:	:	PUNCT
cbi-47	8	1	∂z	∂z	PROPN
cbi-47	9	1	∂x	∂x	PROPN
cbi-47	9	2	=	=	PUNCT
cbi-47	9	3	∂y	∂y	PROPN
cbi-47	9	4	∂x	∂x	PROPN
cbi-47	9	5	∂y	∂y	SYM
cbi-47	9	6	∂z	∂z	PROPN
cbi-47	9	7	=	=	PUNCT
cbi-47	9	8	2xz	2xz	PROPN
cbi-47	9	9	x2	x2	X
cbi-47	10	1	=	=	PUNCT
cbi-47	10	2	2z	2z	NOUN
cbi-47	10	3	x	x	PUNCT
cbi-47	10	4	however	however	ADV
cbi-47	10	5	,	,	PUNCT
cbi-47	10	6	actually	actually	ADV
cbi-47	10	7	calculating	calculate	VERB
cbi-47	10	8	the	the	DET
cbi-47	10	9	partial	partial	ADJ
cbi-47	10	10	derivative	derivative	NOUN
cbi-47	10	11	of	of	ADP
cbi-47	10	12	z	z	NOUN
cbi-47	10	13	with	with	ADP
cbi-47	10	14	respect	respect	NOUN
cbi-47	10	15	to	to	ADP
cbi-47	10	16	x	x	PUNCT
cbi-47	10	17	directly	directly	ADV
cbi-47	10	18	yields	yield	VERB
cbi-47	10	19	−	−	PROPN
cbi-47	10	20	2z	2z	NUM
cbi-47	10	21	x	x	X
cbi-47	10	22	.	.	PUNCT
cbi-47	11	1	as	as	SCONJ
cbi-47	11	2	was	be	AUX
cbi-47	11	3	the	the	DET
cbi-47	11	4	case	case	NOUN
cbi-47	11	5	in	in	ADP
cbi-47	11	6	bartlett	bartlett	PROPN
cbi-47	11	7	and	and	CCONJ
cbi-47	11	8	khurshudyan	khurshudyan	PROPN
cbi-47	11	9	(	(	PUNCT
cbi-47	11	10	2019	2019	NUM
cbi-47	11	11	)	)	PUNCT
cbi-47	11	12	,	,	PUNCT
cbi-47	11	13	the	the	DET
cbi-47	11	14	reason	reason	NOUN
cbi-47	11	15	for	for	ADP
cbi-47	11	16	the	the	DET
cbi-47	11	17	contradiction	contradiction	NOUN
cbi-47	11	18	is	be	AUX
cbi-47	11	19	not	not	PART
cbi-47	11	20	a	a	DET
cbi-47	11	21	failure	failure	NOUN
cbi-47	11	22	of	of	ADP
cbi-47	11	23	the	the	DET
cbi-47	11	24	power	power	NOUN
cbi-47	11	25	of	of	ADP
cbi-47	11	26	differentials	differential	NOUN
cbi-47	11	27	,	,	PUNCT
cbi-47	11	28	but	but	CCONJ
cbi-47	11	29	merely	merely	ADV
cbi-47	11	30	in	in	ADP
cbi-47	11	31	the	the	DET
cbi-47	11	32	notation	notation	NOUN
cbi-47	11	33	.	.	PUNCT
cbi-47	12	1	to	to	PART
cbi-47	12	2	understand	understand	VERB
cbi-47	12	3	this	this	PRON
cbi-47	12	4	,	,	PUNCT
cbi-47	12	5	let	let	VERB
cbi-47	12	6	us	we	PRON
cbi-47	12	7	look	look	VERB
cbi-47	12	8	at	at	ADP
cbi-47	12	9	where	where	SCONJ
cbi-47	12	10	partial	partial	ADJ
cbi-47	12	11	differentials	differential	NOUN
cbi-47	12	12	come	come	VERB
cbi-47	12	13	from	from	ADP
cbi-47	12	14	.	.	PUNCT
cbi-47	13	1	taking	take	VERB
cbi-47	13	2	our	our	PRON
cbi-47	13	3	original	original	ADJ
cbi-47	13	4	example	example	NOUN
cbi-47	13	5	,	,	PUNCT
cbi-47	13	6	let	let	VERB
cbi-47	13	7	us	we	PRON
cbi-47	13	8	simply	simply	ADV
cbi-47	13	9	take	take	VERB
cbi-47	13	10	the	the	DET
cbi-47	13	11	total	total	ADJ
cbi-47	13	12	differential	differential	NOUN
cbi-47	13	13	.	.	PUNCT
cbi-47	14	1	y	y	NOUN
cbi-47	14	2	=	=	PUNCT
cbi-47	14	3	x2z	x2z	PUNCT
cbi-47	15	1	d(y	d(y	PROPN
cbi-47	15	2	)	)	PUNCT
cbi-47	15	3	=	=	PUNCT
cbi-47	15	4	d(x2z	d(x2z	X
cbi-47	15	5	)	)	PUNCT
cbi-47	15	6	dy	dy	NOUN
cbi-47	15	7	=	=	SYM
cbi-47	15	8	x2	x2	PROPN
cbi-47	15	9	dz	dz	PROPN
cbi-47	15	10	+	+	CCONJ
cbi-47	15	11	2xz	2xz	ADJ
cbi-47	15	12	dx	dx	PROPN
cbi-47	15	13	.	.	PUNCT
cbi-47	16	1	let	let	VERB
cbi-47	16	2	’s	’s	NOUN
cbi-47	16	3	say	say	VERB
cbi-47	16	4	we	we	PRON
cbi-47	16	5	wanted	want	VERB
cbi-47	16	6	the	the	DET
cbi-47	16	7	partial	partial	ADJ
cbi-47	16	8	derivative	derivative	ADJ
cbi-47	16	9	∂y	∂y	PROPN
cbi-47	16	10	∂x	∂x	PROPN
cbi-47	16	11	.	.	PUNCT
cbi-47	17	1	a	a	DET
cbi-47	17	2	partial	partial	ADJ
cbi-47	17	3	derivative	derivative	NOUN
cbi-47	17	4	between	between	ADP
cbi-47	17	5	two	two	NUM
cbi-47	17	6	variables	variable	NOUN
cbi-47	17	7	means	mean	VERB
cbi-47	17	8	that	that	SCONJ
cbi-47	17	9	no	no	DET
cbi-47	17	10	variation	variation	NOUN
cbi-47	17	11	is	be	AUX
cbi-47	17	12	allowed	allow	VERB
cbi-47	17	13	to	to	PART
cbi-47	17	14	happen	happen	VERB
cbi-47	17	15	in	in	ADP
cbi-47	17	16	the	the	DET
cbi-47	17	17	other	other	ADJ
cbi-47	17	18	variables	variable	NOUN
cbi-47	17	19	.	.	PUNCT
cbi-47	18	1	in	in	ADP
cbi-47	18	2	this	this	DET
cbi-47	18	3	case	case	NOUN
cbi-47	18	4	,	,	PUNCT
cbi-47	18	5	the	the	DET
cbi-47	18	6	other	other	ADJ
cbi-47	18	7	variable	variable	NOUN
cbi-47	18	8	is	be	AUX
cbi-47	18	9	z.	z.	PROPN
cbi-47	18	10	if	if	SCONJ
cbi-47	18	11	no	no	DET
cbi-47	18	12	variation	variation	NOUN
cbi-47	18	13	happens	happen	VERB
cbi-47	18	14	in	in	ADP
cbi-47	18	15	z	z	PROPN
cbi-47	18	16	,	,	PUNCT
cbi-47	18	17	that	that	PRON
cbi-47	18	18	means	mean	VERB
cbi-47	18	19	that	that	SCONJ
cbi-47	18	20	dz	dz	PROPN
cbi-47	18	21	must	must	AUX
cbi-47	18	22	be	be	AUX
cbi-47	18	23	zero	zero	NUM
cbi-47	18	24	.	.	PUNCT
cbi-47	19	1	therefore	therefore	ADV
cbi-47	19	2	,	,	PUNCT
cbi-47	19	3	we	we	PRON
cbi-47	19	4	set	set	VERB
cbi-47	19	5	dz	dz	ADJ
cbi-47	19	6	=	=	NOUN
cbi-47	19	7	0	0	PUNCT
cbi-47	19	8	and	and	CCONJ
cbi-47	19	9	solve	solve	VERB
cbi-47	19	10	for	for	ADP
cbi-47	19	11	the	the	DET
cbi-47	19	12	ratio	ratio	NOUN
cbi-47	19	13	of	of	ADP
cbi-47	19	14	the	the	DET
cbi-47	19	15	other	other	ADJ
cbi-47	19	16	differentials	differential	NOUN
cbi-47	19	17	,	,	PUNCT
cbi-47	19	18	like	like	ADP
cbi-47	19	19	this	this	PRON
cbi-47	19	20	:	:	PUNCT
cbi-47	19	21	∂y	∂y	SYM
cbi-47	19	22	=	=	SYM
cbi-47	19	23	x2	x2	PROPN
cbi-47	19	24	(	(	PUNCT
cbi-47	19	25	0	0	NUM
cbi-47	19	26	)	)	PUNCT
cbi-47	19	27	+	+	NUM
cbi-47	19	28	2xz	2xz	ADJ
cbi-47	19	29	∂x	∂x	PROPN
cbi-47	19	30	∂y	∂y	SYM
cbi-47	19	31	=	=	PUNCT
cbi-47	19	32	2xz	2xz	ADJ
cbi-47	19	33	∂x	∂x	PROPN
cbi-47	19	34	∂y	∂y	SYM
cbi-47	19	35	∂x	∂x	PROPN
cbi-47	19	36	=	=	SYM
cbi-47	19	37	2xz	2xz	PROPN
cbi-47	20	1	now	now	ADV
cbi-47	20	2	,	,	PUNCT
cbi-47	20	3	when	when	SCONJ
cbi-47	20	4	we	we	PRON
cbi-47	20	5	solve	solve	VERB
cbi-47	20	6	for	for	ADP
cbi-47	20	7	∂y	∂y	PROPN
cbi-47	20	8	∂z	∂z	PROPN
cbi-47	20	9	,	,	PUNCT
cbi-47	20	10	we	we	PRON
cbi-47	20	11	do	do	VERB
cbi-47	20	12	the	the	DET
cbi-47	20	13	same	same	ADJ
cbi-47	20	14	process	process	NOUN
cbi-47	20	15	,	,	PUNCT
cbi-47	20	16	but	but	CCONJ
cbi-47	20	17	set	set	VERB
cbi-47	20	18	a	a	DET
cbi-47	20	19	different	different	ADJ
cbi-47	20	20	differential	differential	NOUN
cbi-47	20	21	to	to	ADP
cbi-47	20	22	zero	zero	NUM
cbi-47	20	23	(	(	PUNCT
cbi-47	20	24	i.e.	i.e.	X
cbi-47	20	25	,	,	PUNCT
cbi-47	20	26	dx	dx	PROPN
cbi-47	20	27	)	)	PUNCT
cbi-47	20	28	.	.	PUNCT
cbi-47	21	1	note	note	VERB
cbi-47	21	2	that	that	SCONJ
cbi-47	21	3	both	both	PRON
cbi-47	21	4	of	of	ADP
cbi-47	21	5	these	these	DET
cbi-47	21	6	derivatives	derivative	NOUN
cbi-47	21	7	involve	involve	VERB
cbi-47	21	8	∂y	∂y	NOUN
cbi-47	21	9	,	,	PUNCT
cbi-47	21	10	but	but	CCONJ
cbi-47	21	11	they	they	PRON
cbi-47	21	12	come	come	VERB
cbi-47	21	13	from	from	ADP
cbi-47	21	14	two	two	NUM
cbi-47	21	15	different	different	ADJ
cbi-47	21	16	modifications	modification	NOUN
cbi-47	21	17	to	to	ADP
cbi-47	21	18	the	the	DET
cbi-47	21	19	original	original	ADJ
cbi-47	21	20	equation	equation	NOUN
cbi-47	21	21	.	.	PUNCT
cbi-47	22	1	therefore	therefore	ADV
cbi-47	22	2	,	,	PUNCT
cbi-47	22	3	the	the	DET
cbi-47	22	4	∂y	∂y	PROPN
cbi-47	22	5	in	in	ADP
cbi-47	22	6	∂y	∂y	PROPN
cbi-47	22	7	∂z	∂z	PROPN
cbi-47	22	8	is	be	AUX
cbi-47	22	9	not	not	PART
cbi-47	22	10	the	the	DET
cbi-47	22	11	same	same	ADJ
cbi-47	22	12	∂y	∂y	NOUN
cbi-47	22	13	that	that	PRON
cbi-47	22	14	is	be	AUX
cbi-47	22	15	in	in	ADP
cbi-47	22	16	∂y	∂y	PROPN
cbi-47	22	17	∂x	∂x	PROPN
cbi-47	22	18	.	.	PUNCT
cbi-47	23	1	indeed	indeed	ADV
cbi-47	23	2	,	,	PUNCT
cbi-47	23	3	the	the	DET
cbi-47	23	4	bottom	bottom	ADJ
cbi-47	23	5	differential	differential	NOUN
cbi-47	23	6	gives	give	VERB
cbi-47	23	7	us	we	PRON
cbi-47	23	8	additional	additional	ADJ
cbi-47	23	9	information	information	NOUN
cbi-47	23	10	about	about	ADP
cbi-47	23	11	which	which	PRON
cbi-47	23	12	∂y	∂y	PRON
cbi-47	23	13	is	be	AUX
cbi-47	23	14	being	be	AUX
cbi-47	23	15	discussed	discuss	VERB
cbi-47	23	16	.	.	PUNCT
cbi-47	24	1	that	that	PRON
cbi-47	24	2	is	be	AUX
cbi-47	24	3	why	why	SCONJ
cbi-47	24	4	the	the	DET
cbi-47	24	5	notation	notation	NOUN
cbi-47	24	6	∂y	∂y	PROPN
cbi-47	24	7	∂x	∂x	PROPN
cbi-47	24	8	can	can	AUX
cbi-47	24	9	not	not	PART
cbi-47	24	10	be	be	AUX
cbi-47	24	11	separated	separate	VERB
cbi-47	24	12	—	—	PUNCT
cbi-47	24	13	information	information	NOUN
cbi-47	24	14	about	about	ADP
cbi-47	24	15	the	the	DET
cbi-47	24	16	numerator	numerator	NOUN
cbi-47	24	17	is	be	AUX
cbi-47	24	18	contained	contain	VERB
cbi-47	24	19	in	in	ADP
cbi-47	24	20	the	the	DET
cbi-47	24	21	denominator	denominator	NOUN
cbi-47	24	22	,	,	PUNCT
cbi-47	24	23	and	and	CCONJ
cbi-47	24	24	is	be	AUX
cbi-47	24	25	therefore	therefore	ADV
cbi-47	24	26	lost	lose	VERB
cbi-47	24	27	when	when	SCONJ
cbi-47	24	28	the	the	DET
cbi-47	24	29	fraction	fraction	NOUN
cbi-47	24	30	is	be	AUX
cbi-47	24	31	split	split	VERB
cbi-47	24	32	.	.	PUNCT
cbi-47	25	1	to	to	PART
cbi-47	25	2	resolve	resolve	VERB
cbi-47	25	3	this	this	DET
cbi-47	25	4	situation	situation	NOUN
cbi-47	25	5	,	,	PUNCT
cbi-47	25	6	we	we	PRON
cbi-47	25	7	merely	merely	ADV
cbi-47	25	8	need	need	VERB
cbi-47	25	9	a	a	DET
cbi-47	25	10	notation	notation	NOUN
cbi-47	25	11	that	that	PRON
cbi-47	25	12	allows	allow	VERB
cbi-47	25	13	us	we	PRON
cbi-47	25	14	to	to	PART
cbi-47	25	15	be	be	AUX
cbi-47	25	16	more	more	ADV
cbi-47	25	17	specific	specific	ADJ
cbi-47	25	18	about	about	ADP
cbi-47	25	19	which	which	DET
cbi-47	25	20	partial	partial	ADJ
cbi-47	25	21	differentials	differential	NOUN
cbi-47	25	22	we	we	PRON
cbi-47	25	23	are	be	AUX
cbi-47	25	24	dealing	deal	VERB
cbi-47	25	25	with	with	ADP
cbi-47	25	26	.	.	PUNCT
cbi-47	26	1	here	here	ADV
cbi-47	26	2	we	we	PRON
cbi-47	26	3	will	will	AUX
cbi-47	26	4	describe	describe	VERB
cbi-47	26	5	two	two	NUM
cbi-47	26	6	possible	possible	ADJ
cbi-47	26	7	approaches	approach	NOUN
cbi-47	26	8	,	,	PUNCT
cbi-47	26	9	each	each	PRON
cbi-47	26	10	with	with	ADP
cbi-47	26	11	different	different	ADJ
cbi-47	26	12	implications	implication	NOUN
cbi-47	26	13	.	.	PUNCT
cbi-47	27	1	i	i	PRON
cbi-47	27	2	do	do	AUX
cbi-47	27	3	n’t	not	PART
cbi-47	27	4	think	think	VERB
cbi-47	27	5	either	either	PRON
cbi-47	27	6	of	of	ADP
cbi-47	27	7	these	these	PRON
cbi-47	27	8	are	be	AUX
cbi-47	27	9	the	the	DET
cbi-47	27	10	“	"	PUNCT
cbi-47	27	11	best	good	ADJ
cbi-47	27	12	”	"	PUNCT
cbi-47	27	13	system	system	NOUN
cbi-47	27	14	,	,	PUNCT
cbi-47	27	15	and	and	CCONJ
cbi-47	27	16	i	i	PRON
cbi-47	27	17	hope	hope	VERB
cbi-47	27	18	that	that	SCONJ
cbi-47	27	19	this	this	DET
cbi-47	27	20	discussion	discussion	NOUN
cbi-47	27	21	sparks	spark	VERB
cbi-47	27	22	additional	additional	ADJ
cbi-47	27	23	ideas	idea	NOUN
cbi-47	27	24	which	which	PRON
cbi-47	27	25	combines	combine	VERB
cbi-47	27	26	the	the	DET
cbi-47	27	27	advantages	advantage	NOUN
cbi-47	27	28	of	of	ADP
cbi-47	27	29	each	each	DET
cbi-47	27	30	system	system	NOUN
cbi-47	27	31	.	.	PUNCT
cbi-47	28	1	it	it	PRON
cbi-47	28	2	is	be	AUX
cbi-47	28	3	also	also	ADV
cbi-47	28	4	possible	possible	ADJ
cbi-47	28	5	that	that	SCONJ
cbi-47	28	6	the	the	DET
cbi-47	28	7	notation	notation	NOUN
cbi-47	28	8	chosen	choose	VERB
cbi-47	28	9	to	to	PART
cbi-47	28	10	represent	represent	VERB
cbi-47	28	11	partial	partial	ADJ
cbi-47	28	12	differentials	differential	NOUN
cbi-47	28	13	is	be	AUX
cbi-47	28	14	based	base	VERB
cbi-47	28	15	on	on	ADP
cbi-47	28	16	your	your	PRON
cbi-47	28	17	own	own	ADJ
cbi-47	28	18	goals	goal	NOUN
cbi-47	28	19	of	of	ADP
cbi-47	28	20	how	how	SCONJ
cbi-47	28	21	to	to	PART
cbi-47	28	22	manipulate	manipulate	VERB
cbi-47	28	23	them	they	PRON
cbi-47	28	24	.	.	PUNCT
cbi-47	29	1	the	the	DET
cbi-47	29	2	two	two	NUM
cbi-47	29	3	systems	system	NOUN
cbi-47	29	4	will	will	AUX
cbi-47	29	5	be	be	AUX
cbi-47	29	6	based	base	VERB
cbi-47	29	7	on	on	ADP
cbi-47	29	8	subscripting	subscripte	VERB
cbi-47	29	9	our	our	PRON
cbi-47	29	10	partial	partial	ADJ
cbi-47	29	11	differentials	differential	NOUN
cbi-47	29	12	.	.	PUNCT
cbi-47	30	1	in	in	ADP
cbi-47	30	2	system	system	NOUN
cbi-47	30	3	1	1	NUM
cbi-47	30	4	(	(	PUNCT
cbi-47	30	5	for	for	ADP
cbi-47	30	6	lack	lack	NOUN
cbi-47	30	7	of	of	ADP
cbi-47	30	8	a	a	DET
cbi-47	30	9	better	well	ADJ
cbi-47	30	10	name	name	NOUN
cbi-47	30	11	)	)	PUNCT
cbi-47	30	12	,	,	PUNCT
cbi-47	30	13	we	we	PRON
cbi-47	30	14	will	will	AUX
cbi-47	30	15	subscript	subscript	VERB
cbi-47	30	16	the	the	DET
cbi-47	30	17	partial	partial	ADJ
cbi-47	30	18	differentials	differential	NOUN
cbi-47	30	19	with	with	ADP
cbi-47	30	20	the	the	DET
cbi-47	30	21	variable	variable	NOUN
cbi-47	30	22	that	that	PRON
cbi-47	30	23	was	be	AUX
cbi-47	30	24	allowed	allow	VERB
cbi-47	30	25	to	to	PART
cbi-47	30	26	freely	freely	ADV
cbi-47	30	27	move	move	VERB
cbi-47	30	28	.	.	PUNCT
cbi-47	31	1	in	in	ADP
cbi-47	31	2	the	the	DET
cbi-47	31	3	system	system	NOUN
cbi-47	31	4	2	2	NUM
cbi-47	31	5	,	,	PUNCT
cbi-47	31	6	we	we	PRON
cbi-47	31	7	will	will	AUX
cbi-47	31	8	subscript	subscript	VERB
cbi-47	31	9	the	the	DET
cbi-47	31	10	partial	partial	ADJ
cbi-47	31	11	differentials	differential	NOUN
cbi-47	31	12	with	with	ADP
cbi-47	31	13	the	the	DET
cbi-47	31	14	variables	variable	NOUN
cbi-47	31	15	that	that	PRON
cbi-47	31	16	were	be	AUX
cbi-47	31	17	forced	force	VERB
cbi-47	31	18	to	to	PART
cbi-47	31	19	not	not	PART
cbi-47	31	20	move	move	VERB
cbi-47	31	21	.	.	PUNCT
cbi-47	32	1	so	so	ADV
cbi-47	32	2	,	,	PUNCT
cbi-47	32	3	in	in	ADP
cbi-47	32	4	system	system	NOUN
cbi-47	32	5	1	1	NUM
cbi-47	32	6	,	,	PUNCT
cbi-47	32	7	instead	instead	ADV
cbi-47	32	8	of	of	ADP
cbi-47	32	9	∂y	∂y	PROPN
cbi-47	32	10	∂x	∂x	PROPN
cbi-47	32	11	,	,	PUNCT
cbi-47	32	12	we	we	PRON
cbi-47	32	13	will	will	AUX
cbi-47	32	14	now	now	ADV
cbi-47	32	15	modify	modify	VERB
cbi-47	32	16	the	the	DET
cbi-47	32	17	notation	notation	NOUN
cbi-47	32	18	to	to	PART
cbi-47	32	19	include	include	VERB
cbi-47	32	20	the	the	DET
cbi-47	32	21	variables	variable	NOUN
cbi-47	32	22	which	which	PRON
cbi-47	32	23	were	be	AUX
cbi-47	32	24	allowed	allow	VERB
cbi-47	32	25	to	to	PART
cbi-47	32	26	freely	freely	ADV
cbi-47	32	27	move	move	VERB
cbi-47	32	28	.	.	PUNCT
cbi-47	33	1	therefore	therefore	ADV
cbi-47	33	2	,	,	PUNCT
cbi-47	33	3	the	the	DET
cbi-47	33	4	partial	partial	ADJ
cbi-47	33	5	derivative	derivative	NOUN
cbi-47	33	6	of	of	ADP
cbi-47	33	7	y	y	PROPN
cbi-47	33	8	with	with	ADP
cbi-47	33	9	respect	respect	NOUN
cbi-47	33	10	to	to	ADP
cbi-47	33	11	x	x	X
cbi-47	33	12	will	will	AUX
cbi-47	33	13	be	be	AUX
cbi-47	33	14	∂x	∂x	PROPN
cbi-47	33	15	y	y	PROPN
cbi-47	33	16	∂x	∂x	PROPN
cbi-47	33	17	x	x	X
cbi-47	33	18	.	.	PUNCT
cbi-47	34	1	likewise	likewise	ADV
cbi-47	34	2	,	,	PUNCT
cbi-47	34	3	the	the	DET
cbi-47	34	4	partial	partial	ADJ
cbi-47	34	5	derivative	derivative	NOUN
cbi-47	34	6	of	of	ADP
cbi-47	34	7	y	y	PROPN
cbi-47	34	8	with	with	ADP
cbi-47	34	9	respect	respect	NOUN
cbi-47	34	10	to	to	ADP
cbi-47	34	11	z	z	NOUN
cbi-47	34	12	will	will	AUX
cbi-47	34	13	be	be	AUX
cbi-47	34	14	∂z	∂z	PROPN
cbi-47	34	15	y	y	PROPN
cbi-47	34	16	∂z	∂z	PROPN
cbi-47	34	17	z	z	PROPN
cbi-47	34	18	.	.	PUNCT
cbi-47	35	1	this	this	DET
cbi-47	35	2	notation	notation	NOUN
cbi-47	35	3	can	can	AUX
cbi-47	35	4	be	be	AUX
cbi-47	35	5	further	far	ADV
cbi-47	35	6	simplified	simplify	VERB
cbi-47	35	7	by	by	ADP
cbi-47	35	8	noting	note	VERB
cbi-47	35	9	that	that	SCONJ
cbi-47	35	10	,	,	PUNCT
cbi-47	35	11	if	if	SCONJ
cbi-47	35	12	a	a	DET
cbi-47	35	13	variable	variable	NOUN
cbi-47	35	14	is	be	AUX
cbi-47	35	15	allowed	allow	VERB
cbi-47	35	16	to	to	PART
cbi-47	35	17	freely	freely	ADV
cbi-47	35	18	vary	vary	VERB
cbi-47	35	19	,	,	PUNCT
cbi-47	35	20	that	that	PRON
cbi-47	35	21	is	be	AUX
cbi-47	35	22	the	the	DET
cbi-47	35	23	same	same	ADJ
cbi-47	35	24	as	as	ADP
cbi-47	35	25	being	be	AUX
cbi-47	35	26	a	a	DET
cbi-47	35	27	total	total	ADJ
cbi-47	35	28	differential	differential	NOUN
cbi-47	35	29	.	.	PUNCT
cbi-47	36	1	therefore	therefore	ADV
cbi-47	36	2	,	,	PUNCT
cbi-47	36	3	∂x	∂x	PROPN
cbi-47	36	4	x	x	PUNCT
cbi-47	36	5	=	=	SYM
cbi-47	36	6	dx	dx	PROPN
cbi-47	36	7	.	.	PUNCT
cbi-47	37	1	this	this	PRON
cbi-47	37	2	simplifies	simplify	VERB
cbi-47	37	3	our	our	PRON
cbi-47	37	4	derivatives	derivative	NOUN
cbi-47	37	5	to	to	PART
cbi-47	37	6	∂x	∂x	VERB
cbi-47	37	7	y	y	PROPN
cbi-47	37	8	dx	dx	PROPN
cbi-47	37	9	and	and	CCONJ
cbi-47	37	10	∂z	∂z	PROPN
cbi-47	37	11	y	y	PROPN
cbi-47	37	12	dz	dz	PROPN
cbi-47	37	13	.	.	PUNCT
cbi-47	38	1	this	this	PRON
cbi-47	38	2	also	also	ADV
cbi-47	38	3	means	mean	VERB
cbi-47	38	4	that	that	SCONJ
cbi-47	38	5	a	a	DET
cbi-47	38	6	total	total	ADJ
cbi-47	38	7	derivative	derivative	NOUN
cbi-47	38	8	of	of	ADP
cbi-47	38	9	a	a	DET
cbi-47	38	10	dependent	dependent	ADJ
cbi-47	38	11	variable	variable	NOUN
cbi-47	38	12	is	be	AUX
cbi-47	38	13	simply	simply	ADV
cbi-47	38	14	the	the	DET
cbi-47	38	15	sum	sum	NOUN
cbi-47	38	16	of	of	ADP
cbi-47	38	17	its	its	PRON
cbi-47	38	18	partial	partial	ADJ
cbi-47	38	19	differentials	differential	NOUN
cbi-47	38	20	.	.	PUNCT
cbi-47	39	1	dy	dy	NOUN
cbi-47	39	2	=	=	NOUN
cbi-47	39	3	∂x	∂x	PROPN
cbi-47	39	4	y	y	NOUN
cbi-47	39	5	+	+	CCONJ
cbi-47	39	6	∂z	∂z	PROPN
cbi-47	39	7	y	y	PROPN
cbi-47	39	8	in	in	ADP
cbi-47	39	9	fact	fact	NOUN
cbi-47	39	10	,	,	PUNCT
cbi-47	39	11	we	we	PRON
cbi-47	39	12	can	can	AUX
cbi-47	39	13	actually	actually	ADV
cbi-47	39	14	carry	carry	VERB
cbi-47	39	15	pieces	piece	NOUN
cbi-47	39	16	of	of	ADP
cbi-47	39	17	the	the	DET
cbi-47	39	18	par78	par78	NOUN
cbi-47	39	19	letters	letter	NOUN
cbi-47	39	20	and	and	CCONJ
cbi-47	39	21	notes	note	VERB
cbi-47	39	22	tial	tial	ADJ
cbi-47	39	23	derivative	derivative	NOUN
cbi-47	39	24	around	around	ADV
cbi-47	39	25	in	in	ADP
cbi-47	39	26	the	the	DET
cbi-47	39	27	subscripts	subscript	NOUN
cbi-47	39	28	,	,	PUNCT
cbi-47	39	29	by	by	ADP
cbi-47	39	30	saying	say	VERB
cbi-47	39	31	∂x+z	∂x+z	ADJ
cbi-47	39	32	y	y	PROPN
cbi-47	39	33	=	=	SYM
cbi-47	39	34	∂x	∂x	PROPN
cbi-47	39	35	y	y	NOUN
cbi-47	39	36	+	+	NUM
cbi-47	39	37	∂z	∂z	PROPN
cbi-47	39	38	y.	y.	NOUN
cbi-47	39	39	this	this	PRON
cbi-47	39	40	can	can	AUX
cbi-47	39	41	have	have	VERB
cbi-47	39	42	benefit	benefit	NOUN
cbi-47	39	43	in	in	ADP
cbi-47	39	44	large	large	ADJ
cbi-47	39	45	,	,	PUNCT
cbi-47	39	46	multivariable	multivariable	ADJ
cbi-47	39	47	equations	equation	NOUN
cbi-47	39	48	,	,	PUNCT
cbi-47	39	49	as	as	SCONJ
cbi-47	39	50	the	the	DET
cbi-47	39	51	subscript	subscript	NOUN
cbi-47	39	52	can	can	AUX
cbi-47	39	53	simply	simply	ADV
cbi-47	39	54	be	be	AUX
cbi-47	39	55	added	add	VERB
cbi-47	39	56	to	to	ADP
cbi-47	39	57	as	as	SCONJ
cbi-47	39	58	additional	additional	ADJ
cbi-47	39	59	partials	partial	NOUN
cbi-47	39	60	are	be	AUX
cbi-47	39	61	added	add	VERB
cbi-47	39	62	in	in	ADP
cbi-47	39	63	.	.	PUNCT
cbi-47	40	1	when	when	SCONJ
cbi-47	40	2	all	all	PRON
cbi-47	40	3	of	of	ADP
cbi-47	40	4	the	the	DET
cbi-47	40	5	variables	variable	NOUN
cbi-47	40	6	are	be	AUX
cbi-47	40	7	included	include	VERB
cbi-47	40	8	,	,	PUNCT
cbi-47	40	9	then	then	ADV
cbi-47	40	10	the	the	DET
cbi-47	40	11	partial	partial	ADJ
cbi-47	40	12	differential	differential	NOUN
cbi-47	40	13	is	be	AUX
cbi-47	40	14	the	the	DET
cbi-47	40	15	same	same	ADJ
cbi-47	40	16	as	as	ADP
cbi-47	40	17	the	the	DET
cbi-47	40	18	total	total	ADJ
cbi-47	40	19	differential	differential	NOUN
cbi-47	40	20	.	.	PUNCT
cbi-47	41	1	the	the	DET
cbi-47	41	2	drawback	drawback	NOUN
cbi-47	41	3	to	to	PART
cbi-47	41	4	system	system	VERB
cbi-47	41	5	1	1	NUM
cbi-47	41	6	is	be	AUX
cbi-47	41	7	that	that	SCONJ
cbi-47	41	8	it	it	PRON
cbi-47	41	9	only	only	ADV
cbi-47	41	10	fully	fully	ADV
cbi-47	41	11	works	work	VERB
cbi-47	41	12	when	when	SCONJ
cbi-47	41	13	y	y	PROPN
cbi-47	41	14	is	be	AUX
cbi-47	41	15	a	a	DET
cbi-47	41	16	dependent	dependent	ADJ
cbi-47	41	17	variable	variable	NOUN
cbi-47	41	18	,	,	PUNCT
cbi-47	41	19	and	and	CCONJ
cbi-47	41	20	all	all	DET
cbi-47	41	21	other	other	ADJ
cbi-47	41	22	variables	variable	NOUN
cbi-47	41	23	are	be	AUX
cbi-47	41	24	independent	independent	ADJ
cbi-47	41	25	variables	variable	NOUN
cbi-47	41	26	.	.	PUNCT
cbi-47	42	1	if	if	SCONJ
cbi-47	42	2	the	the	DET
cbi-47	42	3	other	other	ADJ
cbi-47	42	4	variables	variable	NOUN
cbi-47	42	5	are	be	AUX
cbi-47	42	6	have	have	VERB
cbi-47	42	7	dependencies	dependency	NOUN
cbi-47	42	8	among	among	ADP
cbi-47	42	9	them	they	PRON
cbi-47	42	10	,	,	PUNCT
cbi-47	42	11	the	the	DET
cbi-47	42	12	system	system	NOUN
cbi-47	42	13	breaks	break	VERB
cbi-47	42	14	down	down	ADP
cbi-47	42	15	.	.	PUNCT
cbi-47	43	1	for	for	ADP
cbi-47	43	2	instance	instance	NOUN
cbi-47	43	3	,	,	PUNCT
cbi-47	43	4	if	if	SCONJ
cbi-47	43	5	x	x	X
cbi-47	43	6	=	=	SYM
cbi-47	43	7	f	f	X
cbi-47	43	8	(	(	PUNCT
cbi-47	43	9	z	z	NOUN
cbi-47	43	10	)	)	PUNCT
cbi-47	43	11	,	,	PUNCT
cbi-47	43	12	then	then	ADV
cbi-47	43	13	∂x	∂x	PROPN
cbi-47	43	14	x	x	PUNCT
cbi-47	43	15	is	be	AUX
cbi-47	43	16	not	not	PART
cbi-47	43	17	equal	equal	ADJ
cbi-47	43	18	to	to	ADP
cbi-47	43	19	dx	dx	PROPN
cbi-47	43	20	,	,	PUNCT
cbi-47	43	21	and	and	CCONJ
cbi-47	43	22	dy	dy	NOUN
cbi-47	43	23	is	be	AUX
cbi-47	43	24	not	not	PART
cbi-47	43	25	equal	equal	ADJ
cbi-47	43	26	to	to	ADP
cbi-47	43	27	the	the	DET
cbi-47	43	28	sum	sum	NOUN
cbi-47	43	29	of	of	ADP
cbi-47	43	30	its	its	PRON
cbi-47	43	31	partials	partial	NOUN
cbi-47	43	32	,	,	PUNCT
cbi-47	43	33	depending	depend	VERB
cbi-47	43	34	on	on	ADP
cbi-47	43	35	the	the	DET
cbi-47	43	36	particular	particular	ADJ
cbi-47	43	37	formula	formula	NOUN
cbi-47	43	38	those	those	DET
cbi-47	43	39	partials	partial	NOUN
cbi-47	43	40	come	come	VERB
cbi-47	43	41	from	from	ADP
cbi-47	43	42	.	.	PUNCT
cbi-47	44	1	the	the	DET
cbi-47	44	2	other	other	ADJ
cbi-47	44	3	system	system	NOUN
cbi-47	44	4	,	,	PUNCT
cbi-47	44	5	system	system	NOUN
cbi-47	44	6	2	2	NUM
cbi-47	44	7	,	,	PUNCT
cbi-47	44	8	takes	take	VERB
cbi-47	44	9	this	this	PRON
cbi-47	44	10	into	into	ADP
cbi-47	44	11	account	account	NOUN
cbi-47	44	12	by	by	ADP
cbi-47	44	13	,	,	PUNCT
cbi-47	44	14	instead	instead	ADV
cbi-47	44	15	of	of	ADP
cbi-47	44	16	subscripting	subscripte	VERB
cbi-47	44	17	which	which	PRON
cbi-47	44	18	variables	variable	NOUN
cbi-47	44	19	are	be	AUX
cbi-47	44	20	allowed	allow	VERB
cbi-47	44	21	to	to	PART
cbi-47	44	22	freely	freely	ADV
cbi-47	44	23	vary	vary	VERB
cbi-47	44	24	,	,	PUNCT
cbi-47	44	25	subscripts	subscript	NOUN
cbi-47	44	26	which	which	PRON
cbi-47	44	27	differentials	differential	NOUN
cbi-47	44	28	were	be	AUX
cbi-47	44	29	forcibly	forcibly	ADV
cbi-47	44	30	set	set	VERB
cbi-47	44	31	to	to	ADP
cbi-47	44	32	zero	zero	NUM
cbi-47	44	33	.	.	PUNCT
cbi-47	45	1	this	this	DET
cbi-47	45	2	system	system	NOUN
cbi-47	45	3	makes	make	VERB
cbi-47	45	4	fewer	few	ADJ
cbi-47	45	5	requirements	requirement	NOUN
cbi-47	45	6	of	of	ADP
cbi-47	45	7	the	the	DET
cbi-47	45	8	equation	equation	NOUN
cbi-47	45	9	itself	itself	PRON
cbi-47	45	10	(	(	PUNCT
cbi-47	45	11	because	because	SCONJ
cbi-47	45	12	it	it	PRON
cbi-47	45	13	specifies	specify	VERB
cbi-47	45	14	what	what	PRON
cbi-47	45	15	we	we	PRON
cbi-47	45	16	are	be	AUX
cbi-47	45	17	doing	do	VERB
cbi-47	45	18	to	to	ADP
cbi-47	45	19	the	the	DET
cbi-47	45	20	equation	equation	NOUN
cbi-47	45	21	)	)	PUNCT
cbi-47	45	22	,	,	PUNCT
cbi-47	45	23	but	but	CCONJ
cbi-47	45	24	also	also	ADV
cbi-47	45	25	lends	lend	VERB
cbi-47	45	26	itself	itself	PRON
cbi-47	45	27	,	,	PUNCT
cbi-47	45	28	as	as	ADV
cbi-47	45	29	far	far	ADV
cbi-47	45	30	as	as	SCONJ
cbi-47	45	31	i	i	PRON
cbi-47	45	32	can	can	AUX
cbi-47	45	33	currently	currently	ADV
cbi-47	45	34	tell	tell	VERB
cbi-47	45	35	,	,	PUNCT
cbi-47	45	36	to	to	ADP
cbi-47	45	37	fewer	few	ADJ
cbi-47	45	38	simplification	simplification	NOUN
cbi-47	45	39	mechanisms	mechanism	NOUN
cbi-47	45	40	.	.	PUNCT
cbi-47	46	1	therefore	therefore	ADV
cbi-47	46	2	,	,	PUNCT
cbi-47	46	3	the	the	DET
cbi-47	46	4	partial	partial	ADJ
cbi-47	46	5	derivative	derivative	NOUN
cbi-47	46	6	of	of	ADP
cbi-47	46	7	y	y	PROPN
cbi-47	46	8	with	with	ADP
cbi-47	46	9	respect	respect	NOUN
cbi-47	46	10	to	to	ADP
cbi-47	46	11	x	x	SYM
cbi-47	46	12	(	(	PUNCT
cbi-47	46	13	where	where	SCONJ
cbi-47	46	14	dz	dz	ADJ
cbi-47	46	15	=	=	NOUN
cbi-47	46	16	0	0	NUM
cbi-47	46	17	)	)	PUNCT
cbi-47	46	18	would	would	AUX
cbi-47	46	19	be	be	AUX
cbi-47	46	20	specified	specify	VERB
cbi-47	46	21	as	as	ADP
cbi-47	46	22	∂z	∂z	PROPN
cbi-47	46	23	y	y	PROPN
cbi-47	46	24	∂z	∂z	PROPN
cbi-47	46	25	x	x	INTJ
cbi-47	46	26	.	.	PUNCT
cbi-47	47	1	this	this	PRON
cbi-47	47	2	can	can	AUX
cbi-47	47	3	get	get	VERB
cbi-47	47	4	unweildy	unweildy	ADJ
cbi-47	47	5	in	in	ADP
cbi-47	47	6	equations	equation	NOUN
cbi-47	47	7	with	with	ADP
cbi-47	47	8	a	a	DET
cbi-47	47	9	large	large	ADJ
cbi-47	47	10	number	number	NOUN
cbi-47	47	11	of	of	ADP
cbi-47	47	12	variables	variable	NOUN
cbi-47	47	13	,	,	PUNCT
cbi-47	47	14	as	as	SCONJ
cbi-47	47	15	you	you	PRON
cbi-47	47	16	would	would	AUX
cbi-47	47	17	need	need	VERB
cbi-47	47	18	to	to	PART
cbi-47	47	19	subscript	subscript	VERB
cbi-47	47	20	every	every	DET
cbi-47	47	21	variable	variable	NOUN
cbi-47	47	22	whose	whose	DET
cbi-47	47	23	differential	differential	NOUN
cbi-47	47	24	which	which	PRON
cbi-47	47	25	was	be	AUX
cbi-47	47	26	set	set	VERB
cbi-47	47	27	to	to	ADP
cbi-47	47	28	zero	zero	NUM
cbi-47	47	29	.	.	PUNCT
cbi-47	48	1	in	in	ADP
cbi-47	48	2	any	any	DET
cbi-47	48	3	case	case	NOUN
cbi-47	48	4	,	,	PUNCT
cbi-47	48	5	both	both	DET
cbi-47	48	6	system	system	NOUN
cbi-47	48	7	1	1	NUM
cbi-47	48	8	and	and	CCONJ
cbi-47	48	9	system	system	NOUN
cbi-47	48	10	2	2	NUM
cbi-47	48	11	allow	allow	VERB
cbi-47	48	12	for	for	ADP
cbi-47	48	13	extending	extend	VERB
cbi-47	48	14	algebraic	algebraic	ADJ
cbi-47	48	15	manipulability	manipulability	NOUN
cbi-47	48	16	to	to	ADP
cbi-47	48	17	partial	partial	ADJ
cbi-47	48	18	differentials	differential	NOUN
cbi-47	48	19	.	.	PUNCT
cbi-47	49	1	the	the	DET
cbi-47	49	2	advantage	advantage	NOUN
cbi-47	49	3	of	of	ADP
cbi-47	49	4	system	system	NOUN
cbi-47	49	5	1	1	NUM
cbi-47	49	6	is	be	AUX
cbi-47	49	7	that	that	SCONJ
cbi-47	49	8	it	it	PRON
cbi-47	49	9	has	have	VERB
cbi-47	49	10	rules	rule	NOUN
cbi-47	49	11	for	for	ADP
cbi-47	49	12	interchanging	interchange	VERB
cbi-47	49	13	partial	partial	ADJ
cbi-47	49	14	and	and	CCONJ
cbi-47	49	15	total	total	ADJ
cbi-47	49	16	differentials	differential	NOUN
cbi-47	49	17	,	,	PUNCT
cbi-47	49	18	but	but	CCONJ
cbi-47	49	19	the	the	DET
cbi-47	49	20	disadvantage	disadvantage	NOUN
cbi-47	49	21	that	that	PRON
cbi-47	49	22	you	you	PRON
cbi-47	49	23	must	must	AUX
cbi-47	49	24	know	know	VERB
cbi-47	49	25	a	a	DET
cbi-47	49	26	priori	priori	ADJ
cbi-47	49	27	which	which	PRON
cbi-47	49	28	variables	variable	NOUN
cbi-47	49	29	are	be	AUX
cbi-47	49	30	dependent	dependent	ADJ
cbi-47	49	31	and	and	CCONJ
cbi-47	49	32	independent	independent	ADJ
cbi-47	49	33	.	.	PUNCT
cbi-47	50	1	the	the	DET
cbi-47	50	2	advantage	advantage	NOUN
cbi-47	50	3	of	of	ADP
cbi-47	50	4	system	system	NOUN
cbi-47	50	5	2	2	NUM
cbi-47	50	6	is	be	AUX
cbi-47	50	7	that	that	SCONJ
cbi-47	50	8	you	you	PRON
cbi-47	50	9	do	do	AUX
cbi-47	50	10	not	not	PART
cbi-47	50	11	need	need	VERB
cbi-47	50	12	the	the	DET
cbi-47	50	13	knowledge	knowledge	NOUN
cbi-47	50	14	of	of	ADP
cbi-47	50	15	which	which	PRON
cbi-47	50	16	variables	variable	NOUN
cbi-47	50	17	are	be	AUX
cbi-47	50	18	dependent	dependent	ADJ
cbi-47	50	19	and	and	CCONJ
cbi-47	50	20	independent	independent	ADJ
cbi-47	50	21	,	,	PUNCT
cbi-47	50	22	but	but	CCONJ
cbi-47	50	23	building	build	VERB
cbi-47	50	24	up	up	ADP
cbi-47	50	25	total	total	ADJ
cbi-47	50	26	differentials	differential	NOUN
cbi-47	50	27	from	from	ADP
cbi-47	50	28	partial	partial	ADJ
cbi-47	50	29	ones	one	NOUN
cbi-47	50	30	is	be	AUX
cbi-47	50	31	more	more	ADV
cbi-47	50	32	complicated	complicated	ADJ
cbi-47	50	33	.	.	PUNCT
cbi-47	51	1	unfortunately	unfortunately	ADV
cbi-47	51	2	,	,	PUNCT
cbi-47	51	3	the	the	DET
cbi-47	51	4	notation	notation	NOUN
cbi-47	51	5	for	for	ADP
cbi-47	51	6	system	system	NOUN
cbi-47	51	7	1	1	NUM
cbi-47	51	8	and	and	CCONJ
cbi-47	51	9	system	system	NOUN
cbi-47	51	10	2	2	NUM
cbi-47	51	11	are	be	AUX
cbi-47	51	12	identical	identical	ADJ
cbi-47	51	13	,	,	PUNCT
cbi-47	51	14	so	so	SCONJ
cbi-47	51	15	it	it	PRON
cbi-47	51	16	would	would	AUX
cbi-47	51	17	be	be	AUX
cbi-47	51	18	confusing	confusing	ADJ
cbi-47	51	19	to	to	PART
cbi-47	51	20	use	use	VERB
cbi-47	51	21	them	they	PRON
cbi-47	51	22	both	both	PRON
cbi-47	51	23	.	.	PUNCT
cbi-47	52	1	another	another	DET
cbi-47	52	2	alternative	alternative	NOUN
cbi-47	52	3	would	would	AUX
cbi-47	52	4	be	be	AUX
cbi-47	52	5	to	to	PART
cbi-47	52	6	use	use	VERB
cbi-47	52	7	set	set	NOUN
cbi-47	52	8	notation	notation	NOUN
cbi-47	52	9	.	.	PUNCT
cbi-47	53	1	so	so	ADV
cbi-47	53	2	,	,	PUNCT
cbi-47	53	3	using	use	VERB
cbi-47	53	4	system	system	NOUN
cbi-47	53	5	1	1	NUM
cbi-47	53	6	,	,	PUNCT
cbi-47	53	7	you	you	PRON
cbi-47	53	8	could	could	AUX
cbi-47	53	9	say	say	VERB
cbi-47	53	10	∂d∈x	∂d∈x	PROPN
cbi-47	53	11	y	y	PROPN
cbi-47	53	12	∂d∈x	∂d∈x	ADV
cbi-47	53	13	x	x	INTJ
cbi-47	53	14	,	,	PUNCT
cbi-47	53	15	while	while	SCONJ
cbi-47	53	16	system	system	NOUN
cbi-47	53	17	2	2	NUM
cbi-47	53	18	would	would	AUX
cbi-47	53	19	say	say	VERB
cbi-47	53	20	,	,	PUNCT
cbi-47	53	21	∂d!z	∂d!z	NOUN
cbi-47	53	22	y	y	NOUN
cbi-47	53	23	∂d!z	∂d!z	NOUN
cbi-47	53	24	x	x	INTJ
cbi-47	53	25	.	.	PUNCT
cbi-47	54	1	basically	basically	ADV
cbi-47	54	2	,	,	PUNCT
cbi-47	54	3	this	this	PRON
cbi-47	54	4	uses	use	VERB
cbi-47	54	5	set	set	VERB
cbi-47	54	6	notation	notation	NOUN
cbi-47	54	7	to	to	PART
cbi-47	54	8	say	say	VERB
cbi-47	54	9	which	which	DET
cbi-47	54	10	elements	element	NOUN
cbi-47	54	11	were	be	AUX
cbi-47	54	12	allowed	allow	VERB
cbi-47	54	13	to	to	PART
cbi-47	54	14	be	be	AUX
cbi-47	54	15	modified	modify	VERB
cbi-47	54	16	.	.	PUNCT
cbi-47	55	1	there	there	PRON
cbi-47	55	2	are	be	VERB
cbi-47	55	3	drawbacks	drawback	NOUN
cbi-47	55	4	here	here	ADV
cbi-47	55	5	,	,	PUNCT
cbi-47	55	6	too	too	ADV
cbi-47	55	7	,	,	PUNCT
cbi-47	55	8	as	as	SCONJ
cbi-47	55	9	it	it	PRON
cbi-47	55	10	makes	make	VERB
cbi-47	55	11	it	it	PRON
cbi-47	55	12	look	look	VERB
cbi-47	55	13	like	like	ADP
cbi-47	55	14	system	system	NOUN
cbi-47	55	15	1	1	NUM
cbi-47	55	16	and	and	CCONJ
cbi-47	55	17	system	system	NOUN
cbi-47	55	18	2	2	NUM
cbi-47	55	19	are	be	AUX
cbi-47	55	20	combinable	combinable	ADJ
cbi-47	55	21	,	,	PUNCT
cbi-47	55	22	but	but	CCONJ
cbi-47	55	23	i	i	PRON
cbi-47	55	24	am	be	AUX
cbi-47	55	25	not	not	PART
cbi-47	55	26	sure	sure	ADJ
cbi-47	55	27	that	that	SCONJ
cbi-47	55	28	they	they	PRON
cbi-47	55	29	are	be	AUX
cbi-47	55	30	.	.	PUNCT
cbi-47	56	1	additionally	additionally	ADV
cbi-47	56	2	,	,	PUNCT
cbi-47	56	3	the	the	DET
cbi-47	56	4	notation	notation	NOUN
cbi-47	56	5	itself	itself	PRON
cbi-47	56	6	is	be	AUX
cbi-47	56	7	quite	quite	ADV
cbi-47	56	8	unweildy	unweildy	ADJ
cbi-47	56	9	.	.	PUNCT
cbi-47	57	1	the	the	DET
cbi-47	57	2	primary	primary	ADJ
cbi-47	57	3	point	point	NOUN
cbi-47	57	4	of	of	ADP
cbi-47	57	5	this	this	DET
cbi-47	57	6	exercise	exercise	NOUN
cbi-47	57	7	is	be	AUX
cbi-47	57	8	to	to	PART
cbi-47	57	9	show	show	VERB
cbi-47	57	10	that	that	SCONJ
cbi-47	57	11	(	(	PUNCT
cbi-47	57	12	a	a	X
cbi-47	57	13	)	)	PUNCT
cbi-47	57	14	the	the	DET
cbi-47	57	15	problem	problem	NOUN
cbi-47	57	16	of	of	ADP
cbi-47	57	17	the	the	DET
cbi-47	57	18	algebraic	algebraic	ADJ
cbi-47	57	19	manipulability	manipulability	NOUN
cbi-47	57	20	of	of	ADP
cbi-47	57	21	partial	partial	ADJ
cbi-47	57	22	differentials	differential	NOUN
cbi-47	57	23	is	be	AUX
cbi-47	57	24	primarily	primarily	ADV
cbi-47	57	25	a	a	DET
cbi-47	57	26	notational	notational	ADJ
cbi-47	57	27	problem	problem	NOUN
cbi-47	57	28	,	,	PUNCT
cbi-47	57	29	and	and	CCONJ
cbi-47	57	30	(	(	PUNCT
cbi-47	57	31	b	b	X
cbi-47	57	32	)	)	PUNCT
cbi-47	57	33	to	to	PART
cbi-47	57	34	start	start	VERB
cbi-47	57	35	the	the	DET
cbi-47	57	36	conversation	conversation	NOUN
cbi-47	57	37	about	about	ADP
cbi-47	57	38	what	what	PRON
cbi-47	57	39	notation	notation	NOUN
cbi-47	57	40	might	might	AUX
cbi-47	57	41	possibly	possibly	ADV
cbi-47	57	42	replace	replace	VERB
cbi-47	57	43	the	the	DET
cbi-47	57	44	current	current	ADJ
cbi-47	57	45	notation	notation	NOUN
cbi-47	57	46	,	,	PUNCT
cbi-47	57	47	and	and	CCONJ
cbi-47	57	48	the	the	DET
cbi-47	57	49	benefits	benefit	NOUN
cbi-47	57	50	and	and	CCONJ
cbi-47	57	51	drawbacks	drawback	NOUN
cbi-47	57	52	of	of	ADP
cbi-47	57	53	each	each	DET
cbi-47	57	54	option	option	NOUN
cbi-47	57	55	.	.	PUNCT
cbi-47	58	1	bartlett	bartlett	PROPN
cbi-47	58	2	,	,	PUNCT
cbi-47	58	3	j	j	PROPN
cbi-47	58	4	l	l	PROPN
cbi-47	58	5	and	and	CCONJ
cbi-47	58	6	a	a	DET
cbi-47	58	7	zh	zh	X
cbi-47	58	8	khurshudyan	khurshudyan	NOUN
cbi-47	58	9	(	(	PUNCT
cbi-47	58	10	2019	2019	NUM
cbi-47	58	11	)	)	PUNCT
cbi-47	58	12	.	.	PUNCT
cbi-47	59	1	“	"	PUNCT
cbi-47	59	2	extending	extend	VERB
cbi-47	59	3	the	the	DET
cbi-47	59	4	algebraic	algebraic	ADJ
cbi-47	59	5	manipulability	manipulability	NOUN
cbi-47	59	6	of	of	ADP
cbi-47	59	7	differentials	differential	NOUN
cbi-47	59	8	”	"	PUNCT
cbi-47	59	9	.	.	PUNCT
cbi-47	60	1	in	in	ADP
cbi-47	60	2	:	:	PUNCT
cbi-47	60	3	dynamics	dynamic	NOUN
cbi-47	60	4	of	of	ADP
cbi-47	60	5	continuous	continuous	ADJ
cbi-47	60	6	,	,	PUNCT
cbi-47	60	7	discrete	discrete	ADJ
cbi-47	60	8	and	and	CCONJ
cbi-47	60	9	impulsive	impulsive	ADJ
cbi-47	60	10	systems	system	NOUN
cbi-47	60	11	,	,	PUNCT
cbi-47	60	12	series	series	NOUN
cbi-47	60	13	a	a	PRON
cbi-47	60	14	:	:	PUNCT
cbi-47	60	15	mathematical	mathematical	ADJ
cbi-47	60	16	analysis	analysis	NOUN
cbi-47	60	17	26.3	26.3	NUM
cbi-47	60	18	,	,	PUNCT
cbi-47	60	19	pp	pp	ADJ
cbi-47	60	20	.	.	PUNCT
cbi-47	61	1	217–230	217–230	NUM
cbi-47	61	2	.	.	PUNCT
cbi-47	62	1	the	the	DET
cbi-47	62	2	unlearnable	unlearnable	ADJ
cbi-47	62	3	checkerboard	checkerboard	NOUN
cbi-47	62	4	pattern	pattern	NOUN
cbi-47	62	5	eric	eric	PROPN
cbi-47	62	6	holloway	holloway	PROPN
cbi-47	62	7	doi	doi	PROPN
cbi-47	62	8	:	:	PUNCT
cbi-47	62	9	10.33014	10.33014	NUM
cbi-47	62	10	/	/	SYM
cbi-47	62	11	issn.2640	issn.2640	PROPN
cbi-47	62	12	-	-	PUNCT
cbi-47	62	13	5652.1.2.holloway.1	5652.1.2.holloway.1	NOUN
cbi-47	62	14	in	in	ADP
cbi-47	62	15	the	the	DET
cbi-47	62	16	history	history	NOUN
cbi-47	62	17	of	of	ADP
cbi-47	62	18	machine	machine	NOUN
cbi-47	62	19	learning	learning	NOUN
cbi-47	62	20	,	,	PUNCT
cbi-47	62	21	a	a	DET
cbi-47	62	22	famous	famous	ADJ
cbi-47	62	23	upset	upset	NOUN
cbi-47	62	24	was	be	AUX
cbi-47	62	25	the	the	DET
cbi-47	62	26	disproving	disproving	NOUN
cbi-47	62	27	of	of	ADP
cbi-47	62	28	the	the	DET
cbi-47	62	29	perceptron	perceptron	PROPN
cbi-47	62	30	’s	’s	PART
cbi-47	62	31	generality	generality	NOUN
cbi-47	62	32	by	by	ADP
cbi-47	62	33	use	use	NOUN
cbi-47	62	34	of	of	ADP
cbi-47	62	35	the	the	DET
cbi-47	62	36	xor	xor	PROPN
cbi-47	62	37	problem	problem	NOUN
cbi-47	62	38	.	.	PUNCT
cbi-47	63	1	there	there	PRON
cbi-47	63	2	is	be	VERB
cbi-47	63	3	no	no	DET
cbi-47	63	4	linear	linear	ADJ
cbi-47	63	5	separator	separator	NOUN
cbi-47	63	6	than	than	SCONJ
cbi-47	63	7	can	can	AUX
cbi-47	63	8	classify	classify	VERB
cbi-47	63	9	the	the	DET
cbi-47	63	10	points	point	NOUN
cbi-47	63	11	with	with	ADP
cbi-47	63	12	100	100	NUM
cbi-47	63	13	%	%	NOUN
cbi-47	63	14	accuracy	accuracy	NOUN
cbi-47	63	15	(	(	PUNCT
cbi-47	63	16	russell	russell	NOUN
cbi-47	63	17	and	and	CCONJ
cbi-47	63	18	norvig	norvig	NOUN
cbi-47	63	19	,	,	PUNCT
cbi-47	63	20	2009	2009	NUM
cbi-47	63	21	,	,	PUNCT
cbi-47	63	22	pg	pg	INTJ
cbi-47	63	23	.	.	PROPN
cbi-47	63	24	741	741	NUM
cbi-47	63	25	)	)	PUNCT
cbi-47	63	26	.	.	PUNCT
cbi-47	64	1	figure	figure	VERB
cbi-47	64	2	1	1	NUM
cbi-47	64	3	:	:	PUNCT
cbi-47	64	4	difficulty	difficulty	NOUN
cbi-47	64	5	of	of	ADP
cbi-47	64	6	linear	linear	ADJ
cbi-47	64	7	separation	separation	NOUN
cbi-47	64	8	in	in	ADP
cbi-47	64	9	an	an	DET
cbi-47	64	10	xor	xor	PROPN
cbi-47	64	11	x1	x1	PROPN
cbi-47	64	12	x2	x2	PROPN
cbi-47	64	13	in	in	ADP
cbi-47	64	14	response	response	NOUN
cbi-47	64	15	,	,	PUNCT
cbi-47	64	16	the	the	DET
cbi-47	64	17	multilayer	multilayer	PROPN
cbi-47	64	18	perceptron	perceptron	PROPN
cbi-47	64	19	was	be	AUX
cbi-47	64	20	invented	invent	VERB
cbi-47	64	21	,	,	PUNCT
cbi-47	64	22	which	which	PRON
cbi-47	64	23	eventually	eventually	ADV
cbi-47	64	24	became	become	VERB
cbi-47	64	25	the	the	DET
cbi-47	64	26	modern	modern	ADJ
cbi-47	64	27	day	day	NOUN
cbi-47	64	28	neural	neural	ADJ
cbi-47	64	29	network	network	NOUN
cbi-47	64	30	.	.	PUNCT
cbi-47	65	1	however	however	ADV
cbi-47	65	2	,	,	PUNCT
cbi-47	65	3	the	the	DET
cbi-47	65	4	neural	neural	ADJ
cbi-47	65	5	network	network	NOUN
cbi-47	65	6	,	,	PUNCT
cbi-47	65	7	and	and	CCONJ
cbi-47	65	8	other	other	ADJ
cbi-47	65	9	machine	machine	NOUN
cbi-47	65	10	learning	learning	NOUN
cbi-47	65	11	paradigms	paradigm	NOUN
cbi-47	65	12	,	,	PUNCT
cbi-47	65	13	still	still	ADV
cbi-47	65	14	have	have	VERB
cbi-47	65	15	a	a	DET
cbi-47	65	16	problem	problem	NOUN
cbi-47	65	17	learning	learn	VERB
cbi-47	65	18	a	a	DET
cbi-47	65	19	tiled	tile	VERB
cbi-47	65	20	xor	xor	PROPN
cbi-47	65	21	pattern	pattern	NOUN
cbi-47	65	22	called	call	VERB
cbi-47	65	23	the	the	DET
cbi-47	65	24	checkerboard	checkerboard	NOUN
cbi-47	65	25	,	,	PUNCT
cbi-47	65	26	see	see	VERB
cbi-47	65	27	figure	figure	NOUN
cbi-47	65	28	3	3	NUM
cbi-47	65	29	.	.	PUNCT
cbi-47	66	1	the	the	DET
cbi-47	66	2	checkerboard	checkerboard	NOUN
cbi-47	66	3	classifications	classification	NOUN
cbi-47	66	4	can	can	AUX
cbi-47	66	5	be	be	AUX
cbi-47	66	6	generated	generate	VERB
cbi-47	66	7	using	use	VERB
cbi-47	66	8	a	a	DET
cbi-47	66	9	logic	logic	NOUN
cbi-47	66	10	expression	expression	NOUN
cbi-47	66	11	.	.	PUNCT
cbi-47	67	1	to	to	PART
cbi-47	67	2	generate	generate	VERB
cbi-47	67	3	the	the	DET
cbi-47	67	4	classifications	classification	NOUN
cbi-47	67	5	from	from	ADP
cbi-47	67	6	2n	2n	NUM
cbi-47	67	7	variables	variable	NOUN
cbi-47	67	8	,	,	PUNCT
cbi-47	67	9	we	we	PRON
cbi-47	67	10	use	use	VERB
cbi-47	67	11	the	the	DET
cbi-47	67	12	logic	logic	NOUN
cbi-47	67	13	expression	expression	NOUN
cbi-47	67	14	x1	x1	PROPN
cbi-47	67	15	⊕	⊕	PROPN
cbi-47	67	16	xn+1	xn+1	PROPN
cbi-47	67	17	.	.	PUNCT
cbi-47	68	1	here	here	ADV
cbi-47	68	2	is	be	AUX
cbi-47	68	3	an	an	DET
cbi-47	68	4	example	example	NOUN
cbi-47	68	5	with	with	ADP
cbi-47	68	6	4	4	NUM
cbi-47	68	7	variables	variable	NOUN
cbi-47	68	8	,	,	PUNCT
cbi-47	68	9	x1	x1	PROPN
cbi-47	68	10	,	,	PUNCT
cbi-47	68	11	x2	x2	PROPN
cbi-47	68	12	,	,	PUNCT
cbi-47	68	13	x3	x3	ADJ
cbi-47	68	14	and	and	CCONJ
cbi-47	68	15	x4	x4	PROPN
cbi-47	68	16	.	.	PUNCT
cbi-47	69	1	the	the	DET
cbi-47	69	2	logic	logic	NOUN
cbi-47	69	3	expression	expression	NOUN
cbi-47	69	4	is	be	AUX
cbi-47	69	5	x1	x1	PROPN
cbi-47	69	6	⊕	⊕	PROPN
cbi-47	69	7	x3	x3	PROPN
cbi-47	69	8	.	.	PUNCT