How to let a long equation be broken between pages?
I have a huge equation consisting of several matrices. It is stuck together and has to be moved completely between pages causing white spaces in the preceding page. I had to resize it but seems that breaking it is a much better solution. I want to let it break, i.e., e.g. half of at the bottom of one page and the rest in the beginning of the next page. I'm using a double column paper style.
This is what I got,
documentclass[10pt, twocolumn, twoside, journal]{IEEEtran}
%makeatletter
%letIEEEproofproof
%letIEEEendproofendproof
%letproof@undefined
%letendproof@undefined
%makeatother
%letproofrelax
%letendproofrelax
%IEEEoverridecommandlockouts
%overrideIEEEmargins
usepackage{amsmath, amsfonts, amssymb, color, enumerate, amsthm, graphicx}
usepackage{tikz, subcaption, cite}
usepackage{color, xcolor, soul, bm}
PassOptionsToPackage{hyphens}{url}usepackage{hyperref}
hypersetup{
colorlinks = true, %Colours links instead of ugly boxes
urlcolor = blue, %Colour for external hyperlinks
linkcolor = blue, %Colour of internal links
citecolor = green %Colour of citations
}
usepackage[normalem]{ulem}
newtheorem{problem}{Problem}
newtheorem{theorem}{Theorem}
newtheorem{corollary}{Corollary}
newtheorem{assumption}{Assumption}
newtheorem{proposition}{Proposition}
newtheorem{lemma}{Lemma}
newtheorem{remark}{Remark}
newtheorem{definition}{Definition}
newtheorem{example}{Example}
usepackage{epsfig}
usepackage{psfrag}
DeclareMathOperator{diag}{diag}
usepackage{tcolorbox}
newcommand{JW}[1]{{color{red}#1}}
include{user_newcommands}
usepackage{algorithm}
usepackage{algpseudocode}
allowdisplaybreaks
%newcommand{ShS}[1]{$clubsuit$footnote{SHREYAS: #1}}
%newcommand{mathcolorbox}[2]{colorbox{#1}{$displaystyle #2$}}
defendtheorem{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendlemma{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendproposition{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendexample{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendremark{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defenddefinition{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
begin{document}
begin{equation}
resizebox{.45textwidth}{!}{$
begin{split}
&L_g^{-1}mathbf{e}_i mathbf{e}_{ij}^{sf T}L_g^{-1} = begin{bmatrix}
frac{1}{w_1} & 0 & cdots & overbrace{0}^{j^text{th}} & cdots & overbrace{0}^{i^text{th}} & cdots & 0\
frac{1}{w_1} & frac{1}{w_2} & cdots & 0 & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots \
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & frac{1}{w_n}
end{bmatrix}\
× begin{bmatrix}
0\
0\
vdots\
vdots\
vdots\
underbrace{1}_{i^text{th}}\
vdots\
0
end{bmatrix} begin{bmatrix}
0\
0\
vdots\
underbrace{-1}_{j^text{th}}\
vdots\
underbrace{1}_{i^text{th}}\
vdots\
0
end{bmatrix}^{sf T} begin{bmatrix}
frac{1}{w_1} & 0 & cdots & 0 & cdots & 0 & cdots & 0\
frac{1}{w_1} & frac{1}{w_2} & cdots & 0 & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots \
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & frac{1}{w_n}
end{bmatrix}\
&=begin{bmatrix}
0\
0\
vdots\
0\
vdots\
underbrace{frac{1}{w_i}}_{i^text{th}}\
vdots\
frac{1}{w_i}
end{bmatrix} begin{bmatrix}
0 & cdots & underbrace{0}_{j^text{th}} & frac{1}{w_{j+1}} & frac{1}{w_{j+2}} & cdots & underbrace{frac{1}{w_i}}_{i^text{th}} & 0 & cdots & 0
end{bmatrix}\
&=begin{bmatrix}
0 & 0 & cdots & overbrace{0}^{j^text{th}} & overbrace{0}^{{j+1}^text{th}} & overbrace{0}^{{j+2}^text{th}} & cdots & overbrace{0}^{i^text{th}} & cdots & 0\
0 & 0 & cdots & 0 & 0 & 0 & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & vdots & vdots & & vdots & & vdots\
0 & 0 & cdots & 0 & frac{1}{w_i w_{j+1}} & frac{1}{w_i w_{j+2}} & cdots & frac{1}{w_i^2} & cdots & 0\
vdots & vdots & & vdots & vdots & vdots & & vdots & & vdots\
0 & 0 & cdots & 0 & cdots & cdots & cdots & cdots & cdots & 0
end{bmatrix} geq 0
%}
end{split}
$}
end{equation}
end{document}
pdftex split
add a comment |
I have a huge equation consisting of several matrices. It is stuck together and has to be moved completely between pages causing white spaces in the preceding page. I had to resize it but seems that breaking it is a much better solution. I want to let it break, i.e., e.g. half of at the bottom of one page and the rest in the beginning of the next page. I'm using a double column paper style.
This is what I got,
documentclass[10pt, twocolumn, twoside, journal]{IEEEtran}
%makeatletter
%letIEEEproofproof
%letIEEEendproofendproof
%letproof@undefined
%letendproof@undefined
%makeatother
%letproofrelax
%letendproofrelax
%IEEEoverridecommandlockouts
%overrideIEEEmargins
usepackage{amsmath, amsfonts, amssymb, color, enumerate, amsthm, graphicx}
usepackage{tikz, subcaption, cite}
usepackage{color, xcolor, soul, bm}
PassOptionsToPackage{hyphens}{url}usepackage{hyperref}
hypersetup{
colorlinks = true, %Colours links instead of ugly boxes
urlcolor = blue, %Colour for external hyperlinks
linkcolor = blue, %Colour of internal links
citecolor = green %Colour of citations
}
usepackage[normalem]{ulem}
newtheorem{problem}{Problem}
newtheorem{theorem}{Theorem}
newtheorem{corollary}{Corollary}
newtheorem{assumption}{Assumption}
newtheorem{proposition}{Proposition}
newtheorem{lemma}{Lemma}
newtheorem{remark}{Remark}
newtheorem{definition}{Definition}
newtheorem{example}{Example}
usepackage{epsfig}
usepackage{psfrag}
DeclareMathOperator{diag}{diag}
usepackage{tcolorbox}
newcommand{JW}[1]{{color{red}#1}}
include{user_newcommands}
usepackage{algorithm}
usepackage{algpseudocode}
allowdisplaybreaks
%newcommand{ShS}[1]{$clubsuit$footnote{SHREYAS: #1}}
%newcommand{mathcolorbox}[2]{colorbox{#1}{$displaystyle #2$}}
defendtheorem{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendlemma{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendproposition{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendexample{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendremark{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defenddefinition{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
begin{document}
begin{equation}
resizebox{.45textwidth}{!}{$
begin{split}
&L_g^{-1}mathbf{e}_i mathbf{e}_{ij}^{sf T}L_g^{-1} = begin{bmatrix}
frac{1}{w_1} & 0 & cdots & overbrace{0}^{j^text{th}} & cdots & overbrace{0}^{i^text{th}} & cdots & 0\
frac{1}{w_1} & frac{1}{w_2} & cdots & 0 & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots \
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & frac{1}{w_n}
end{bmatrix}\
× begin{bmatrix}
0\
0\
vdots\
vdots\
vdots\
underbrace{1}_{i^text{th}}\
vdots\
0
end{bmatrix} begin{bmatrix}
0\
0\
vdots\
underbrace{-1}_{j^text{th}}\
vdots\
underbrace{1}_{i^text{th}}\
vdots\
0
end{bmatrix}^{sf T} begin{bmatrix}
frac{1}{w_1} & 0 & cdots & 0 & cdots & 0 & cdots & 0\
frac{1}{w_1} & frac{1}{w_2} & cdots & 0 & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots \
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & frac{1}{w_n}
end{bmatrix}\
&=begin{bmatrix}
0\
0\
vdots\
0\
vdots\
underbrace{frac{1}{w_i}}_{i^text{th}}\
vdots\
frac{1}{w_i}
end{bmatrix} begin{bmatrix}
0 & cdots & underbrace{0}_{j^text{th}} & frac{1}{w_{j+1}} & frac{1}{w_{j+2}} & cdots & underbrace{frac{1}{w_i}}_{i^text{th}} & 0 & cdots & 0
end{bmatrix}\
&=begin{bmatrix}
0 & 0 & cdots & overbrace{0}^{j^text{th}} & overbrace{0}^{{j+1}^text{th}} & overbrace{0}^{{j+2}^text{th}} & cdots & overbrace{0}^{i^text{th}} & cdots & 0\
0 & 0 & cdots & 0 & 0 & 0 & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & vdots & vdots & & vdots & & vdots\
0 & 0 & cdots & 0 & frac{1}{w_i w_{j+1}} & frac{1}{w_i w_{j+2}} & cdots & frac{1}{w_i^2} & cdots & 0\
vdots & vdots & & vdots & vdots & vdots & & vdots & & vdots\
0 & 0 & cdots & 0 & cdots & cdots & cdots & cdots & cdots & 0
end{bmatrix} geq 0
%}
end{split}
$}
end{equation}
end{document}
pdftex split
add a comment |
I have a huge equation consisting of several matrices. It is stuck together and has to be moved completely between pages causing white spaces in the preceding page. I had to resize it but seems that breaking it is a much better solution. I want to let it break, i.e., e.g. half of at the bottom of one page and the rest in the beginning of the next page. I'm using a double column paper style.
This is what I got,
documentclass[10pt, twocolumn, twoside, journal]{IEEEtran}
%makeatletter
%letIEEEproofproof
%letIEEEendproofendproof
%letproof@undefined
%letendproof@undefined
%makeatother
%letproofrelax
%letendproofrelax
%IEEEoverridecommandlockouts
%overrideIEEEmargins
usepackage{amsmath, amsfonts, amssymb, color, enumerate, amsthm, graphicx}
usepackage{tikz, subcaption, cite}
usepackage{color, xcolor, soul, bm}
PassOptionsToPackage{hyphens}{url}usepackage{hyperref}
hypersetup{
colorlinks = true, %Colours links instead of ugly boxes
urlcolor = blue, %Colour for external hyperlinks
linkcolor = blue, %Colour of internal links
citecolor = green %Colour of citations
}
usepackage[normalem]{ulem}
newtheorem{problem}{Problem}
newtheorem{theorem}{Theorem}
newtheorem{corollary}{Corollary}
newtheorem{assumption}{Assumption}
newtheorem{proposition}{Proposition}
newtheorem{lemma}{Lemma}
newtheorem{remark}{Remark}
newtheorem{definition}{Definition}
newtheorem{example}{Example}
usepackage{epsfig}
usepackage{psfrag}
DeclareMathOperator{diag}{diag}
usepackage{tcolorbox}
newcommand{JW}[1]{{color{red}#1}}
include{user_newcommands}
usepackage{algorithm}
usepackage{algpseudocode}
allowdisplaybreaks
%newcommand{ShS}[1]{$clubsuit$footnote{SHREYAS: #1}}
%newcommand{mathcolorbox}[2]{colorbox{#1}{$displaystyle #2$}}
defendtheorem{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendlemma{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendproposition{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendexample{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendremark{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defenddefinition{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
begin{document}
begin{equation}
resizebox{.45textwidth}{!}{$
begin{split}
&L_g^{-1}mathbf{e}_i mathbf{e}_{ij}^{sf T}L_g^{-1} = begin{bmatrix}
frac{1}{w_1} & 0 & cdots & overbrace{0}^{j^text{th}} & cdots & overbrace{0}^{i^text{th}} & cdots & 0\
frac{1}{w_1} & frac{1}{w_2} & cdots & 0 & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots \
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & frac{1}{w_n}
end{bmatrix}\
× begin{bmatrix}
0\
0\
vdots\
vdots\
vdots\
underbrace{1}_{i^text{th}}\
vdots\
0
end{bmatrix} begin{bmatrix}
0\
0\
vdots\
underbrace{-1}_{j^text{th}}\
vdots\
underbrace{1}_{i^text{th}}\
vdots\
0
end{bmatrix}^{sf T} begin{bmatrix}
frac{1}{w_1} & 0 & cdots & 0 & cdots & 0 & cdots & 0\
frac{1}{w_1} & frac{1}{w_2} & cdots & 0 & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots \
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & frac{1}{w_n}
end{bmatrix}\
&=begin{bmatrix}
0\
0\
vdots\
0\
vdots\
underbrace{frac{1}{w_i}}_{i^text{th}}\
vdots\
frac{1}{w_i}
end{bmatrix} begin{bmatrix}
0 & cdots & underbrace{0}_{j^text{th}} & frac{1}{w_{j+1}} & frac{1}{w_{j+2}} & cdots & underbrace{frac{1}{w_i}}_{i^text{th}} & 0 & cdots & 0
end{bmatrix}\
&=begin{bmatrix}
0 & 0 & cdots & overbrace{0}^{j^text{th}} & overbrace{0}^{{j+1}^text{th}} & overbrace{0}^{{j+2}^text{th}} & cdots & overbrace{0}^{i^text{th}} & cdots & 0\
0 & 0 & cdots & 0 & 0 & 0 & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & vdots & vdots & & vdots & & vdots\
0 & 0 & cdots & 0 & frac{1}{w_i w_{j+1}} & frac{1}{w_i w_{j+2}} & cdots & frac{1}{w_i^2} & cdots & 0\
vdots & vdots & & vdots & vdots & vdots & & vdots & & vdots\
0 & 0 & cdots & 0 & cdots & cdots & cdots & cdots & cdots & 0
end{bmatrix} geq 0
%}
end{split}
$}
end{equation}
end{document}
pdftex split
I have a huge equation consisting of several matrices. It is stuck together and has to be moved completely between pages causing white spaces in the preceding page. I had to resize it but seems that breaking it is a much better solution. I want to let it break, i.e., e.g. half of at the bottom of one page and the rest in the beginning of the next page. I'm using a double column paper style.
This is what I got,
documentclass[10pt, twocolumn, twoside, journal]{IEEEtran}
%makeatletter
%letIEEEproofproof
%letIEEEendproofendproof
%letproof@undefined
%letendproof@undefined
%makeatother
%letproofrelax
%letendproofrelax
%IEEEoverridecommandlockouts
%overrideIEEEmargins
usepackage{amsmath, amsfonts, amssymb, color, enumerate, amsthm, graphicx}
usepackage{tikz, subcaption, cite}
usepackage{color, xcolor, soul, bm}
PassOptionsToPackage{hyphens}{url}usepackage{hyperref}
hypersetup{
colorlinks = true, %Colours links instead of ugly boxes
urlcolor = blue, %Colour for external hyperlinks
linkcolor = blue, %Colour of internal links
citecolor = green %Colour of citations
}
usepackage[normalem]{ulem}
newtheorem{problem}{Problem}
newtheorem{theorem}{Theorem}
newtheorem{corollary}{Corollary}
newtheorem{assumption}{Assumption}
newtheorem{proposition}{Proposition}
newtheorem{lemma}{Lemma}
newtheorem{remark}{Remark}
newtheorem{definition}{Definition}
newtheorem{example}{Example}
usepackage{epsfig}
usepackage{psfrag}
DeclareMathOperator{diag}{diag}
usepackage{tcolorbox}
newcommand{JW}[1]{{color{red}#1}}
include{user_newcommands}
usepackage{algorithm}
usepackage{algpseudocode}
allowdisplaybreaks
%newcommand{ShS}[1]{$clubsuit$footnote{SHREYAS: #1}}
%newcommand{mathcolorbox}[2]{colorbox{#1}{$displaystyle #2$}}
defendtheorem{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendlemma{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendproposition{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendexample{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defendremark{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
defenddefinition{hspace*{fill}~IEEEQEDopenparendtrivlistunskip}
begin{document}
begin{equation}
resizebox{.45textwidth}{!}{$
begin{split}
&L_g^{-1}mathbf{e}_i mathbf{e}_{ij}^{sf T}L_g^{-1} = begin{bmatrix}
frac{1}{w_1} & 0 & cdots & overbrace{0}^{j^text{th}} & cdots & overbrace{0}^{i^text{th}} & cdots & 0\
frac{1}{w_1} & frac{1}{w_2} & cdots & 0 & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots \
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & frac{1}{w_n}
end{bmatrix}\
× begin{bmatrix}
0\
0\
vdots\
vdots\
vdots\
underbrace{1}_{i^text{th}}\
vdots\
0
end{bmatrix} begin{bmatrix}
0\
0\
vdots\
underbrace{-1}_{j^text{th}}\
vdots\
underbrace{1}_{i^text{th}}\
vdots\
0
end{bmatrix}^{sf T} begin{bmatrix}
frac{1}{w_1} & 0 & cdots & 0 & cdots & 0 & cdots & 0\
frac{1}{w_1} & frac{1}{w_2} & cdots & 0 & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots \
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & 0\
vdots & vdots & & vdots & & vdots & & vdots\
frac{1}{w_1} & frac{1}{w_2} & cdots & frac{1}{w_j} & cdots & frac{1}{w_i} & cdots & frac{1}{w_n}
end{bmatrix}\
&=begin{bmatrix}
0\
0\
vdots\
0\
vdots\
underbrace{frac{1}{w_i}}_{i^text{th}}\
vdots\
frac{1}{w_i}
end{bmatrix} begin{bmatrix}
0 & cdots & underbrace{0}_{j^text{th}} & frac{1}{w_{j+1}} & frac{1}{w_{j+2}} & cdots & underbrace{frac{1}{w_i}}_{i^text{th}} & 0 & cdots & 0
end{bmatrix}\
&=begin{bmatrix}
0 & 0 & cdots & overbrace{0}^{j^text{th}} & overbrace{0}^{{j+1}^text{th}} & overbrace{0}^{{j+2}^text{th}} & cdots & overbrace{0}^{i^text{th}} & cdots & 0\
0 & 0 & cdots & 0 & 0 & 0 & cdots & 0 & cdots & 0\
vdots & vdots & & vdots & vdots & vdots & & vdots & & vdots\
0 & 0 & cdots & 0 & frac{1}{w_i w_{j+1}} & frac{1}{w_i w_{j+2}} & cdots & frac{1}{w_i^2} & cdots & 0\
vdots & vdots & & vdots & vdots & vdots & & vdots & & vdots\
0 & 0 & cdots & 0 & cdots & cdots & cdots & cdots & cdots & 0
end{bmatrix} geq 0
%}
end{split}
$}
end{equation}
end{document}
pdftex split
pdftex split
asked 16 mins ago
MohammadMohammad
535
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