Pre Env Eq Mat Frac Margin Indent Size § A4 List Brk Tab Space Box
Count Pic Fig Verb Footnote Ref Idx Graph Color Face C ℂ ℭ Ex MyHelp Help

# $ % \{ \} § ¶ † ‡ \begin{matrix}c \\ ◯ \end{matrix} £ œ Œ æ Æ ø Ø ł Ł ß ¿ ¡ ı ȷ ◯^{R} ^{TM} ˜ ˆ TEX \ ò ó ô ö õ ō ȯ ŏ ǒ ő oo o̧ o. ō å Aa Aa Aa Aa Aa Aa

L^{A}TEX Symbols

α β γ δ ϵ ζ η θ ι κ λ μ ν ξ π ρ σ τ υ ϕ χ ψ ω ε ϑ ϖ ϱ ς φ Γ Δ Θ Λ Ξ Π Σ Υ Φ Ψ Ω { } ⌊ ⌋ ⌈ ⌉ ⟨ ⟩ \ ∥ ↑ ⇑ ↓ ⇓ ↕ ⇕ ± ∓ × ÷ ∗ ⋆ ∘ • · ∩ ∪ ⊎ ⊓ ⊔ ∨ ∧ \ ≀ ⋄ △ ▽ ◁ ▷ ⊕ ⊖ ⊗ ⊘ ⊙ ◯ † ‡ ⨿ ≤ ≥ ≺ ≻ ⪯ ⪰ ≪ ≫ ⊂ ⊃ ⊆ ⊇ ⊏ ⊐ ⊑ ⊒ ⊢ ⊣ ∈ ∋ ∉ ≡ ∼ ≃ ≍ ≈ ≅ ≠ ≐ ∝ ⊧ ⊥ | ∥ ▷◁ ⋊ ⋉ ⌣ ⌢ ≢ ← → ⟵ ⟶ ⇐ ⇒ ⟸ ⟹ ↼ ⇀ ↽ ⇁ ↩ ↪ ↦ ⟼ ↔ ⟷ ⇔ ⟺ ⇝ ↗ ↘ ↙ ↖

∑ ∏ ∐ ∫ ∮ ⋂ ⋃ ⨆ ⋁ ⋀ ⨀ ⨂ ⨁ ⨄

ℵ ℏ ı ȷ ℓ ℘ ℜ ℑ ∂ ∞ ′ ∅ ∇ √ ⊤ ⊥ ∠ △ ∀ ∃ ¬ ¬ ♭ ♮ ♯ ♣ ♢ ♡ ♠

arccos arcsin arctan arg cos cosh cot coth csc deg det dim exp
gcd hom inf ker lg lim lim inf lim sup ln log max min Pr sec
sin sinh sup tan tanh

A A A A A 𝔸 𝔄 x â ǎ ă á à ã ā a⃗ ȧ ä ı ȷ

\overline{x + y} \underline{x + y} { \atop x + y} { \atop x + y} \overbrace{x + y} \underbrace{x + y} \overrightarrow{x + y} \overleftarrow{x + y}

AMS Symbols (Text: ✓ ® ¥ ✠)

⊡ ⊞ ⊠ ▪ ⊟ ⊻ ⊼ ⩞ ⋓ ⋒ ⋏ ⋎ ⋋ ⋌ ∔ ⊺ ⊚ ⊛ ⊝ ⋇ ⋖ ⋗ ⋉ ⋊ ∖ ℧ □ ■ ♢ ♦ ‵ ⋆ ▼ ▲ ▽ ∡ ∢ Ⓢ ∁ ⧸ ⧹ ∅ ∄ Ⅎ ⅁ ð ℶ ℷ ℸ 𝟋 κ 𝕜 ℏ ⟳ ⟲ ⇌ ⇋ ⊩ ⊪ ⊨ ↠ ↞ ⇇ ⇉ ⇈ ⇊ ↾ ⇂ ↿ ⇃ ↣ ↢ ⇆ ⇄ ↰ ↱ ⇝ ↭ ↫ ↬ ≗ ≿ ≳ ⪆ ⊸ ∴ ∵ ≑ ≜ ≾ ≲ ⪅ ⪕ ⪖ ⋞ ⋟ ≼ ≦ ⩽ ≶ ≓ ≒ ≽ ≧ ⩾ ≷ ▷ ◁ ⊵ ⊴ ≬ ▶ ◀ △ ≖ ⋚ ⋛ ⪋ ⪌ ⇛ ⇚ ∝ ⌣ ⌢ ⋐ ⋑ ⫅ ⫆ ≏ ≎ ≪ ≫ ⋔ ∽ ⋍ ≂ ∣ ∥ ∼ ≈ ≊ ≿ ≾ ↶ ↷ ϶ ⌜ ⌝ ⌞ ⌟ ≨ ≩ ≰ ≱ ≮ ≯ ⊀ ⊁ ≨ ≩ ⩽̸ ⩾̸ ⪇ ⪈ ⪯̸ ⪰̸ ⋨ ⋩ ⋦ ⋧ ≦̸ ≧̸ ⪵ ⪶ ⪹ ⪺ ⪉ ⪊ ≁ ≇ ⊊ ⊋ ⫅̸ ⫆̸ ⫋ ⫌ ⫋ ⫌ ⊊ ⊋ ⊈ ⊉ ∦ ∤ ∤ ∦ ⊬ ⊮ ⊭ ⊯ ⋭ ⋬ ⋪ ⋫ ↚ ↛ ⇍ ⇏ ⇎ ↮ ←−− −−→ \underleftarrow{x + y} \underrightarrow{x + y} \overleftrightarrow{x + y} \underleftrightarrow{x + y}

Γ Δ Θ Δ Ξ Π Σ Υ Φ Ψ Ω ∫∫ ∫∫∫ ∫ ··· ∫ \overline{lim} \underline{lim} \underrightarrow{lim} \underleftarrow{lim}

Â Ǎ Ã Á À Ȧ Ä Ă Ā A⃗ A A^{∼} A˘ A^{∨} A. A.. \begin{matrix}... \\ x \end{matrix} \begin{matrix}.... \\ x \end{matrix} · · · . . . ... ⋮

Preamble Top

class: article report book slides letter

jarticle jreport jbook tarticle treport tbook jsarticle jsbook

[10pt 11pt 12pt a4paper a5paper b4paper b5paper a4j a5j b4j b5j landscape onecolumn twocolumn oneside twoside notitlepage titlepage fleqn leqno final draft tate openbib openright openany]

packages: AMS amscd amsthm graphicx color hyperref dvipdfm PapersizeSpecial pagesize offset pagestyle: plain empty headings myheadings \thispagestyle{pstyle} title newtheorem

Environment document

abstract itemize enumarate description quotation quote center verbatim tabular equation equation* array slide bibliography

\newenvironment{name}[narg][default]{bigdef}{enddef} \renewenvironment{name}[narg]{bigdef}{enddef}

AMS L^{A}TEX

align align* falign falign* alignat alignat* xalignat xalignat* xxalignat gather gather* multline multline* ⇒ subequation split aligned alignedat gathered text intertext

\numberwithin{equation}{section} (in Preamble) ⇒ \notag \tag{ } \tag*{ } \eqref{ } \\[len] \theparentequation

\theequation ⇐ {\arabic{section},\arabic{equation}}  Count

x + y f(x) ⟵_{1st}^{2nd} ⟶_{1st}^{2nd} X^{a} X_{a} ∑_{{1 \atop 234}} ∑_{{1 \atop 234}} \begin{aligned}& 6 \\ {2 \atop 1} & ∏{4 \atop 3} \\ & 5 \end{aligned}

\mathop* \DeclareMathOperator* ^{⇒}

Matrix: ({··· \atop ···}) [{··· \atop ···}] \{{··· \atop ···}\} |{··· \atop ···}| ∥{··· \atop ···}∥ {··· \atop ···} ( {··· \atop ···}) ⋮({··· \atop ···})^{···}

MaxMatrixCols hdotsfor cases ⇒

\frac{a}{b} \binom{n}{k} \sqrt[3]{4} amscd: \begin{matrix}A & ⟶_{down}^{up} & B \\ ^{l}↓^{r} & & ↑ \\ C & & D \end{matrix}

Frac: \frac \tfrac \dfrac \cfrac[pos] (pos: l or r) \genfrac{ldelim}{rdelim}{thick}{style}{num}{denom} style: 0 ∼ 3 (\displaystyle, \textstyle, \scriptstyle, \scriptscriptstyle)

Top 1 inch+\voffset  em ex zw zh 1 mm=2.845pt 1 pt=0.35146mm 1 inch=25.4mm Margin 1 inch+\hoffset \topmargin \headheight \headsep \textwidth \paperwidth \textheight \paperheight \oddsidemargin \evensidemargin \parindent  \marginparwidth \marginparpush \marginparsep \footskip \footheight \topskip

• starting reference point: x-position = 1 inch+\hoffset+\odd(enen)sidemargin y-position = 1 inch +\voffset+\topmargin+\headheight+\headsep

+\topskip \textheight ≒ \baselineskip × (#(lines/page)−1)+\topskip line space = \baselineskip ×\baselinestretch (=1 default value) \parskip = 0pt plus 1pt

Indent

\leftline \centerline \rightline flushleft center flushright \hangafter=#lines \hangindent=len

after #lines or top −#lines Size

\columnseprule \textwidth \textheight \columnwidth \columnsep

\scrptstyle \scritpscriptstyle (disp.) \tiny \scriptsize \footnotesize \small \normalsize \large \Large \LARGE \huge \Huge

List Top

\begin{list}{default label}{decls} item list \end{list}

\topsep+\parskip+\partopsep \parsep \itemsep+\parsep \topsep+\parskip+\partopsep \listparindent \itemindent \leftmargin  \rightmargin \labelwidth \itemindent \labelsep

indent of label: \leftmargin−\labelwidth−\labelsep+\itemindent default: \rightmargin = \listparindent = \itemindent = 0 pt

\labelsep = 0.5 em \begin{trivlist} item list \end{trivlist}

\leftmargin = \labelwidth = 0 pt, \parsep = \parskip \begin{enumarate} item list \end{enumarate}

1 → (a) → i → A \labelenumi \labelenumii \labelenumiii

    \labelenumiv ⇐ Ex. {[\bfseries\arabic{enumiv}]}  Count

\begin{itemize} item list \end{itemize}

• → – → ∗ → · \labelitemi \labelitemii \labelitemiii \begin{description} item list \end{description}

    \descritionlabel ⇐ Ex. {\hspace{\labelsep}\textsf{#1}}

Space

\vspace{len}  \vspace*{len}  \vfill=\vspace{\fill}
\hspace{len}  \hspace*{len}  \hfill=\hspace{\fill}

\fill=\stretch{1} \stretch{value} \dotfill \hrulefill \smallskip 3pt±1pt \medskip 6pt±2pt \bigskip 12pt±4pt \! −\frac{3}{18} \, \frac{3}{18} \> \frac{4}{18} \; \frac{5}{18} \ \frac{9}{18} \quad 1 \qquad 2 em

Break

\par \fussy \sloppy \parskip \parindent \\[len] \newline \linebreak[lev] \nolinebreak[lev] lev:0–4 (default) \newpage \clearpage \cleardoublepage \samepage \pagebreak[lev] \nopagebreak[lev] \enlargethispage{len} \raggedbottom \flushbottom

Box Top

\makebox[width][pos]{text} \framebox[width][pos]{text} \mbox{text} \fbox{text} \frame{text} \raisebox{lift}[height][depth]{text} \width \height \depth \totalheight \fboxrule=0.4pt \fboxsep=3pt \thinlines \thicklines \linethickness{len} \unitlength \makebox(w,h)[ipos]{text} \framebox(w,h)[ipos]{text} \begin{minipage}[pos][height][inner pos]{width}text\end{minipage} \parbox[pos][height][inner pos]{width}{text} pos: c l r s inner pos: c t b s \shortstack[pos]{text\\⋯ text} \rule[lift]{width}{total height}

cb t l lt lb  rrt rb

\newsavebox{cmd} declare box \savebox{cmd}[width][pos]{text} fill box \sbox{cmd}{text} fill box \begin{lrbox}{cmd} text \end{lrbox} fill box \usebox{cmd} use contents

Tab longtable

tabbing \kill \pushtabs \poptabs ⇒ indent: \+ \− this indent: \< left col: \’ right most: \‘

\begin{tabbing} ⋯ \= ⋯ \= ⋯ \= ⋯ \kill ⋯ \> ⋯ \> ⋯ \> ⋯ \\ ⋯ \> ⋯ \> ⋯ \’ \> ⋯ \+ \\ ⋯ \> \‘ ⋯ \\

\end{tabbing}

tabular[pos]{cols}  pos: t b  ⇒

cols = column: l c r p{width} separator: | || @{decl.} \tabcolsep=len \doublerulesep=len \hline

tabular*{width}[pos]{cols} \extracolsep{\fill}

\begin{tabular}{| c | l | l | r |}\hline ⋯ & ⋯ & ⋯ & ⋯ \\ \hline ⋯ & ⋯ & ⋯ & ⋯ \\ \hline

\end{tabular} \[ \begin{array}{| c | l | r @{.} l |}\hline

⋯ & ⋯ & ⋯ & ⋯ \\ \hline ⋯ & ⋯ & ⋯ & ⋯ \\ ⋯ & \multicolumn{2}{c |}{⋯ } \\ \hline \end{array} \]

\[ array[pos]{cols} \] \arrayrulewidth=len \extrarowheight=len \arraystretch⇐val \cline{m–n} \hline from the m-th column to the n-th \vline \multicolumn{ncol}{col}{text} col=column separator more column: p{width} = \parbox[t]{width} ⇒

m{width} ≒ \parbox{width} b{width} = \parbox[b]{width}

separator: >{decl.} (pre-col.) <{decl.} (post-col.) !{decl.} (any) cols: |c||r@{.}l|>{\parindent=5mm}m{2cm}| >{$}c<{$}| ⇒ | col1 || col2.col3 |\parabox{2cm}{\paraindent=5mm col4}|$col5$|

Picture Top

picture(Dx,Dy)(x,y) \unitlength= \put(x,y){object} \multiput(x,y)(Dx,Dy){num}{object}

(0, 0)(x, y) Dy Dx

object:

\line(Dx,Dy){L} −6 ≤Dx, Dy≤ 6, Dx, Dy: integer \vector(Dx,Dy){L} −4 ≤Dx, Dy≤ 4, Dx, Dy: integer \circle{diam} \circle*{diam} (fill circle) \oval(Dx,Dy)[pos] pos: l c r t u b

Xy-pic  Young  bar

Figure

figure[pos] table[pos] figure*[pos] table*[pos]

\figurename \tablename pos: h (here) t (top) b (bottom) p (last page) (h>t>b>p) ratio (0≤ratio≤1): \topflaction \bottomfraction \textflaction

\dbltopflaction \dblfloatpagefraction len: \floatsep \textfloatsep \intextsep \dblfloatsep \dbltextfloatsep \usepackage{floatfig} floatingfigure[width] \usepackage{wrapfig} wrapfigure[nlines]{rl}{width}

Verb

\verb|text| verbatim \verb*|text| verbatim* ( for a space)

Footnote Count

\footnote[count]{text} \footnotemark[count] \footnotetext[count]{text} \footnotesep= \renewcommand{\footnoterule}{rule}

rule: \noindent\rule{130mm}{0.5mm}\vspace{1mm}

Reference

\label{label} \ref{label} \eqref{label} \pageref{label} thebibliography{widest entry} \bibitem[label]{cite key}contents \cite[text]{cite key list}

Index

\makeindex ⇒ \usepackage{makeidx} ⇒ \printindex \index{key@visual ! key_{2}@visual_{2} ! ⋯ |see{text}}

|( (top of pages) |) (end of pages) \seename (see) \indexname (Index)

Counter Top

part section subsection subsubsection paragraph subparagraph

equation  figure  table  page  footnote  mpfootnote
enumi  enumii  enumiii  enumiv  (List)

\newcounter{counter} \value{counter} \setcounter{counter}{value} \addtocounter{counter}{value} \advance\value{counter} by value \multiply\value{counter} by value \divide\value{counter} by value \renewcommand{\thecounter}{format} ⇒

\arabic \alph \Alph \roman \Roman \fnsymbol

Ex: \renewcommand{\thepage}{--\arabic{page}--}
    \setcounter{page}{12}

Chapter

\part \chapter \section \subsection \subsubsection \paragraph \subparagraph \appendix \partname \chaptername ⇒ \prepartname \postpartname \prechaptername \postchaptername \abstractname \appendixname \contentsname \figurename \tablename \listfigurename \listtablename \refname \bibname

1 inch = 72.27 pt = 25.4 mm, 1 pt = 0.35146 mm

A4: \begin{cases}\paperwidth = 210 mm = 597 pt \\ \paperheight = 297mm = 845 pt \end{cases}

\documentclass[a4paper]{article}

\textwidth=345pt=121.25mm \textheight=598pt=210.2mm \oddsidemargin=53pt=18.6mm \topmargin=17pt=6.0mm \headheight=12pt=4.2mm \headsep=25pt=8.8mm \marginparwidth=57pt=20.0mm \marginparsep=11pt=3.9mm

\documentclass[a4j]{jarticle}

\textwidth=418pt=146.9mm \textheight=641pt=225.3mm \oddsidemargin=17pt=6.0mm \topmargin=−3pt=−1.1mm \headheight=12pt=4.2mm \headsep=25pt=8.8mm \marginparwidth=60pt=21.1mm \marginparsep=10pt=3.5mm

\documentclass[a4j]{jsarticle}

\textwidth=453pt=159.2mm \textheight=634pt=222.8mm \oddsidemargin=0pt=0mm \topmargin=4pt=1.4mm \headheight=20pt=7.0mm \headsep=18pt=6.3mm \marginparwidth=18pt=6.3mm \marginparsep=18pt=6.3mm

Graphics Top

\usepackage[opt]{graphicx} \usepackage[opt]{graphicx,color} opt: dvips dviout dvipdfm xdvi pdftex draft final hiresbb \includegraphics[para]{file name} para: width=len, height=len, scale=value, keepaspectratio, clip bb=x_{1} y_{1} x_{2} y_{2} (ex. bb=0 0 640 480), hiresbb, draft trim=l b r t (by 1/72 inch, ex. trim=0 0 5 0) angle=value (by degree)

\rotatebox[opt]{angle}{text} angle: counterclockwise by degree opt: origin=lrctbB (B:Baseline), x=len, y=len units=6.2832 (by radian)

\saclebox{scale}[vscale]{text} scalebox \reflectbox{text} reflectbox \resizebox{width}{height}{text} \width \height \hsize !=keep ratio

ex: \resizebox{0.9\hsize}{!}{⋯ } \resizebox*{width}{height+depth}{text}

{\color[opt]{col}text} \textcolor[opt]{col}{text} col: black white red green blue cyan magenta yellow [opt]{col}: [gray]{val} [rgb]{r,g,b} [cmyk]{c,m,y,k} [named]{color} \colorbox[opt]{col}{text} colorbox \fcolorbox[opt]{frame col}{fill col}{text} fcolorbox

\fboxrule=len \fboxsep=len \definecolor{name}{opt}{value}

GreenYellow  Yellow  Goldenrod  Dandelion  Apricot
Peach Melon YellowOrange Orange BurntOrange Bittersweet
RedOrange Mahogany Maroon BrickRed Red OrangeRed
RubineRed WildStrawberry Salmon CarnationPink Magenta
VioletRed Rhodamine Mulberry RedViolet Fuchsia Lavender
Thistle Orchid DarkOrchid Purple Plum Violet RoyalPurple
BlueViolet Periwinkle CadetBlue CornflowerBlue MidnightBlue
NavyBlue RoyalBlue Blue Cerulean Cyan ProcessBlue
SkyBlue Turquoise TealBlue Aquamarine BlueGreen Emerald
JungleGreen SeaGreen Green ForestGreen PineGreen LimeGreen
YellowGreen SpringGreen OliveGreen RawSienna Sepia Brown
Tan Gray Black White

Sample Top

\text··{ } : Roman Boldface Italic Slanted Sans Serif

Typewriter Small Caps

\normalfont \rmfamily \sffamily \ttfamily \mcfamily \gtfamily \bfseries \mdseries \upshape \itshape \slshape \scshape 𝔄 𝔅 ℭ 𝔇 𝔈 𝔉 𝔊 ℌ ℑ 𝔍 𝔎 𝔏 𝔐 𝔑 𝔒 𝔓 𝔔 ℜ 𝔖 𝔗 𝔘 𝔙 𝔚 𝔛 𝔜 ℨ 𝔞 𝔟 𝔠 𝔡 𝔢 𝔣 𝔤 𝔥 𝔦 𝔧 𝔨 𝔩 𝔪 𝔫 𝔬 𝔭 𝔮 𝔯 𝔰 𝔱 𝔲 𝔳 𝔴 𝔵 𝔶 𝔷 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z 𝔸 𝔹 ℂ 𝔻 𝔼 𝔽 𝔾 ℍ 𝕀 𝕁 𝕂 𝕃 𝕄 ℕ 𝕆 ℙ ℚ ℝ 𝕊 𝕋 𝕌 𝕍 𝕎 𝕏 𝕐 ℤ \sideset \mathop \overset \stackrel \atop \atopwithdelims

{b \atop a}∑_{c}^{d} Φ_{n=1}^{∞} abc ab^{c}  aaa^{bb^{c}}  {c \atop ab}  {c \atop ab} \left⟨{b \atop a}\right⟩  ba\} abc

(\overbrace{0, …, 0, 1, …, 1}^{p+q}, 2, …, 2 _{q+r})

Macros Top

\ensuremath{math-text} \newif\ifname \nametrue \namefalse

\ifname true-case \else false-case \fi \IfFileExists{filename}{true-case}{false-case}

Sample Macros Top

\ruby{text}{ruby}{font}: pL^{A}TEX \ruby \kenten{text}: pL^{A}TEX \kenten \kintou{len}{text}: pL^{A}TEX \kintou{1cm} \slantbox{angle}{text}: −30 ≤ angle ≤ 30 (by degree, use graphicx)

  \slantbox{-12}{slant} \slantbox{30}  slant

\coord{#1}{#2}{#3}: (#1_{#2}, …, #1_{#3})

\coord x1n: (x_{1}, …, x_{n}) \set{#1}{#2}{#3}: {#1_{#2}, …, #1_{#3}}

\set a1n: {a_{1}, …, a_{n}} \setdef{#1}{#2}: {#1;#2}

  \setdef{(x,y)}{x^2+y^2=1}:  {(x, y) ; x^{2} + y^{2} = 1}
  \setdef[|]{(x,y)}{x^2+y^2=1}:  {(x, y) | x^{2} + y^{2} = 1}

\ang{#1}{#2}: ⟨#1,#2⟩

  \ang\alpha\beta:  ⟨α, β⟩
  \ang[|]\alpha\beta:  ⟨α|β⟩

\begin{equation}
\begin{split}
 a& =b+c-d\\[-3pt]
  & \quad +e-f\\
  & =g+h
\end{split}
\end{equation}

\begin{aligned}a & = b + c − d \\ & + e − f \\ & = g + h \end{aligned} (1)^{⇐}

\begin{multline}
 a+b+c+d+e+f\\
 +i+j+k+l+m+n
\end{multline}

\begin{matrix}a + b + c + d + e + f \\ + i + j + k + l + m + n (2) \end{matrix}

\begin{gather}
 a_1=b_1+c_1\label{eq1}\\
 a_2=b_2+c_2-d_2+e_2
\end{gather}

\begin{matrix}a_{1} = b_{1} + c_{1} & (3) \\ a_{2} = b_{2} + c_{2} − d_{2} + e_{2} & (4) \end{matrix}

\begin{align}
 a_{11}& =b_{11}&
  a_{12}& =b_{12}\\
 a_{21}& =b_{21}&
  a_{22}& =b_{22}+c_{22}
\end{align}

\begin{aligned}a_{11} & = b_{11} & a_{12} & = b_{12} & (5) \\ a_{21} & = b_{21} & a_{22} & = b_{22} + c_{22} & (6) \end{aligned}

\begin{align*}
 x& = y_1-y_2-\cdots
  && \text{by Lemma}\\
  & = y'\circ y^*
  && \text{by \eqref{eq1}}
\end{align*}

x = y_{1} − y_{2} − ⋯ by Lemma
= y′ ∘ y^{∗}  by (3)

\begin{alignat*}{2}
 x& = y_1-y_2-\cdots
  &\qquad& \text{by Lemma}\\
  & = y'\circ y^*
  && \text{by \eqref{eq1}}
\end{alignat*}

x = y_{1} − y_{2} − ⋯  by Lemma
= y′ ∘ y^{∗}  by (3)

\begin{flalign}
 a_{11}& =b_{11}&
  a_{12}& =b_{12}\\
 a_{21}& =b_{21}&
  a_{22}& =b_{22}+c_{22}
\end{flalign}

\begin{aligned}a_{11} & = b_{11} & a_{12} & = b_{12} & (7) \\ a_{21} & = b_{21} & a_{22} & = b_{22} + c_{22} & (8) \end{aligned}

\begin{align}
 x^2+y^2 &= z^2 \label{eqx}\\
 x^3+y^3 &= z^3 \notag\\
 x^4+y^4 &= z^4 \tag*{[4th]}\\
 x^5+y^5 &= z^5 \tag{\ref{eqx}'}
\end{align}

⇐
x^{2} + y^{2} = z^{2}  (9)
x^{3} + y^{3} = z^{3}
x^{4} + y^{4} = z^{4}  [4th]
x^{5} + y^{5} = z^{5}  (9’)

\begin{subequations}
\begin{align}
 x^6+y^6 &= z^6\\
 x^7+y^7 &= z^7
\end{align}
\end{subequations}

\begin{aligned}x^{6} + y^{6} & = z^{6} & (10a) \\ x^{7} + y^{7} & = z^{7} & (10b) \end{aligned}

\[\begin{gathered}[b]
 xy = c\\ x + y = b
\end{gathered}  \qquad
\begin{aligned}[t]
 c &= x(b-x)\\ &= -x^2+bx
\end{aligned}  \]

\begin{matrix}x + y = b \\ xy = c \end{matrix}  \begin{aligned}c & = x(b − x) \\ & = bx − x^{2} \end{aligned}

\begin{equation}
 \overset{*}U=\underset{*}X+\overset{a}{\underset{b}Z}
  \quad \xleftarrow[\xi]{b\to\infty} \quad
 \sum\nolimits' a_n = \sideset{_1^2}{_3^4}\prod_k b_k
  + \sideset{}{'}\sum
     _{\substack{0\le m\le n\\0\le n\le\infty}}c_n^m
\end{equation}

U^{∗} = X_{∗} + Z_{b}^{a} ⟶_{ξ}^{b→∞} ∑′ a_{n} = \begin{aligned}{2 \atop 1} & ∏{4 \atop 3} \\ & k \end{aligned} b_{k} + ^{∑′} ; \begin{matrix}0≤m≤n \\ 0≤n≤∞ \end{matrix} c_{n}^{m}  (11)

\DeclareMathOperator*{\esssup}{ess\,sup} % Preamble
\DeclareMathOperator{\Hom}{Hom} % Preamble
\newcommand{\abs}[1]{\lvert#1\rvert}
\newcommand{\norm}[1]{\lVert#1\rVert}
\begin{equation}
 \norm{f}_\infty = \esssup_{x\in\mathbb R^n}\abs{f(x)}
 \text{ and } \Hom_R(A,B)^* = \Hom_R(B^*,A^*)
\end{equation}

∥f∥_{∞} = ess sup_{x∈ℝ^{n}}|f(x)| and Hom_{R}(A, B)^{∗} = Hom_{R}(B^{∗}, A^{∗}) (12)

⇐ \[\begin{CD}

 A @>{up}>{d}> B @>>> C \\
 @V{l}V{r}V    @.  @AAA \\
 D @=          D @>>> E
\end{CD}\]

A ⟶_{d}^{up} B ⟶ C
l↓^{r}  ↑
D  D ⟶ E

\begin{align}
 u & \equiv v+1 \pmod{n^2} \\
 u & \equiv v+1 \mod{n^2} \\
 u & \equiv v+1 \pod{n^2}
\end{align}

\begin{aligned}u & ≡ v + 1 (mod n^{2}) & (13) \\ u & ≡ v + 1 mod n^{2} & (14) \\ u & ≡ v + 1 (n^{2}) & (15) \end{aligned}

\begin{equation}
 \cfrac 1{2+
   \cfrac 3{4+
    \cfrac[r]5{6+\cdots

}}}

\end{equation}

\frac{1}{2 + \frac{3}{4 + \frac{5}{6 + ⋯}}}  (16)

\begin{equation}
\genfrac{[}{]}{1pt}{}{n-3}{m}
\end{equation}

[\frac{n − 3}{m}]  (17)

\[\begin{vmatrix}
 a & \cdots & b & \cdots & d \\
 \vdots&\ddots&\vdots&%
        \ddots&\vdots\\
 e & \cdots & f & \cdots & g \\
 m & \hdotsfor{3} & n
\end{vmatrix}\]

|\begin{matrix}a & ⋯ & b & ⋯ & d \\ ⋮ & ... & ⋮ & ... & ⋮ \\ e & ⋯ & f & ⋯ & g \\ m & . . . . . . . . . . . & n \end{matrix}|

\[E_{ij}=\bordermatrix{
  &      &i&                 \cr
  &&\vdots&                  \cr
j &\cdots&1&\phantom{\cdots} \cr
  &      &\phantom{\vdots}} \]

E_{ij} = ( i ; ⋮ ; j ⋯ 1  )

\[ Y(x)= \begin{cases}
   1 &\text{if $x>0$,}\\
  -1 &\text{if $x<0$}
         \end{cases} \]

Y (x) = \begin{cases}1 & if x > 0, \\ −1 & if x < 0 \end{cases}

$\sqrt\{\mathstrut\{a\}\}+\sqrt\{\mathstrut\{f\}\}$    \sqrt{a} + \sqrt{f}
$\sqrt\{a\}+\sqrt\{f\}$                             \sqrt{a} + \sqrt{f}

\begin{tabular}{|c||l|r|}  \hline               _{⇐}
\multicolumn{3}{|c|}{Rooms}\\    \hline
\multicolumn{1}{|c||}{Floor} & Name &
  \multicolumn{1}{c|}{Area}\\    \hline\hline
 1 & kitchen &  $42 m^2$\\       \hline
   & study   &  $57 m^2$\\       \cline{2-3}
 2 & living  & $120 m^2$\\       \hline
\end{tabular}

Rooms

Floor Name  Area
1  kitchen 42m^{2}
study  57m^{2}
2  living 120m^{2}

\newcommand{\topsp}[1]{\vbox{\vbox to#1{}\ vbox to1em{}}}
\newcommand{\tbsp}[2]{\rule{0pt}{#1}\rule[−#2]{0pt}{0pt}}
\begin{tabular}{|l@{\ \vrule width 2pt\ }c|r|}
\hline\topsp{2mm}%
 1 & 2 & 3\\[2mm]           \hline
 A & B & C\tbsp{8mm}{4mm}\\ \hline
 a-1 & b-2 & c-3\\          \hline
\end{tabular}

1  2  3
A B  C
a-1 b-2 c-3

\tabcolsep=10mm
\begin{tabular}{|l|p{40mm}|}  \hline
 tabular & This is used for text.            \\ \hline
 array   & This is mainly used for equations.\\ \hline
\end{tabular}

tabular This is used for text. array This is mainly used for

equations.

\begin{tabular}{r@{.}l}
     3 & 14259\\
$-$\ 2 & 71828\\ \hline
     0 & 42431
\end{tabular}

\begin{matrix}3. & 14259 \\ − 2. & 71828 \\ 0. & 42431 \end{matrix}

\begin{tabular*}{0.5\textwidth}%
{@{\extracolsep{\fill}}|l|c|r|}\hline
 1234 & A & B\\ \hline
\end{tabular*}

1234  A  B

\begin{tabbing}  _{⇐}
 aaa \= \hspace{10mm} \= cccc\kill
 aa  \> bb  \> cc\\
 aaa \> bbb \> c
\end{tabbing}

aa bb cc aaa bbb c

\begin{tabbing}
AA\=BB\=CC\=DD\=EE       \kill
 a\> b\> c\> d\> e\+\+\+ \\
             a\> b       \\
\<\< a\> b               \\
             a\> b \`g\- \\
         a\> b   \`ggg   \\
         a\> b\> y\' c   \\
\pushtabs
 A\=A\=A\=\kill \\ \\
 1\>2\>3\\
 4\>5\>6\\         \\
\poptabs
 \a={O}\> \a'{a}\> \a`{e}\\
\end{tabbing}

a b c d e

a b a b

a b  g
a b  ggg

a by c

1 2 3 4 5 6

Ō á è

\usepackage{array}
\begin{tabular}{!{\vrule width 2pt}>{\bfseries}c!|%
   >{$}c<{$}|>{\setlength{\parindent}{5mm}}m{2cm}%
   !{\vrule width 2pt}}
\noalign{\hrule height 2pt}
 Differential & (x^3)' = 3x^2
   & Study in this week.\par Review!\\    \hline
 Integral & \int x^2\,dx = \frac23x^3 + C
   & Study in this month.           \\
\noalign{\hrule height 2pt}
\end{tabular}

Differential (x^{3})′ = 3x^{2}

Study in this week. Review!

Integral ∫ x^{2} dx = \frac{2}{3}x^{3} + C

Study in this month.

              longtable  dcolumn multirow  ⇐
\usepackage{longtable}
%\setlongtable
\begin{longtable}[pos]{cols} % pos:c l r
%%\setlength{\LTleft}{}  % \fill
%%\setlength{\LTright}{}  % \fill
%%\setlength{\LTpre}{}  % \bigskipamount
%%\setlength{\LTpost}{}  % \bigskipamount
%%\setlength{\LTcapwidth}{} % 4in
%\caption{}  % \caption*{title}
%\\ \hline           % \caption[short title]{long title}
%%%
%%\multicolumn{}{}{} \\ \hline
%% & &               \\ \hline
%%\endfirsthead      % first page
%%%
%\hline
%\multicolumn{}{}{} \\ \hline
% & &                \\ \hline
%\endhead            % each page
%%%
%%\hline
%%\multicolumn{}{}{} \\ \hline
%%\endfoot           % each page
%%%
%%\hline
%%\multicolumn{}{}{} \\ \hline
%%\endlastfoot       % last page
% & &                \kill
  & &                \\
  & &                \\
%\newpage
  & &                \\
\end{longtable}
\usepackage{dcolumn} decimal places=-1: no limit

D{inputsep}{outputsep}{decimal places}

\usepackage{multirow}

\multirow{nrow}[njot]{width}[vmove↑]{text}

⇐

   Counter           Value          Type
part           \thepart           \Roman
chapter        \thechapter        \arabic
section        \thesection        \arabic
subsection     \thesubsection     \arabic
subsubsection  \thesubsubsection  \arabic
paragraph      \theparagraph      \arabic
subparagraph   \thesubparagraph   \arabic
equation       \theequation       \arabic
figure         \thefigure         \arabic
table          \thetable          \arabic
page           \thepage           \arabic
footnote       \thefootnote       \arabic
mpfootnote     \thempfootnote     \arabic
enumi          \theenumi          \arabic
enumii         \theenumii         \alph
enumiii        \theenumiii        \roman
enumiv         \theenumiv         \Alph

⇐

          Name           Definition
    \partname         Part

    \prepartname
    \postpartname

    \chaptername      Chapter

    \prechaptername
    \postchaptername

    \abstractname     Abstract
    \appendixname     Appendix
    \contentsname     Contents
    \figurename       Figure
    \tablename        Table
    \listfigurename   List of Figures
    \listtablename    List of Tables
    \refname          References
    \bibname          Bibliography
    \indexname        Index
    \seename          see

Top

                         bar
\usepackage{bar}
\begin{barenv}
\setwidth{32}               % width of a bar by point
\setstyle{\small\bfseries}  % font
\setxaxis{1998}{2005}{1}
\setxname{year}
\setstyle{\small\rmfamily}
\setyaxis[10]{0}{63}{10}    % [offset]{origin}{end}{step}
\setyname{total \%}
%\setprecision{digits}
\setstretch{1.5}            % vertical stretch
\setlinestyle{dotted}       % solid or dotted
\hlineon                    % horizontal line
\setdepth{10}               % 3 dimensional ≥10
%\sethspace{val}  % val:0∼1
\setnumberpos{down}
  % empty, axis, down, inside, outside, up
\bar{22}{1}   \bar{32.5}{2} % \bar{height}{idx}[text]
\bar{42}{3}   \bar{51.2}{4} % idx:0∼8
\bar{46.4}{5} \bar{55.6}{8}
\bar{40.4}{7} \bar{34.5}{6}
\end{barenv}
\centerline{\legend8{2003(max)} % \legendidx{text}

  [figure: \overline{0}; 10; 20; 30; 40; 50; 60; 22; 32.5; ......; ......; ......; ......; 42; ......; ......; ......; 51.2; ......; ......; 46.4; ......; 55.6; .....; ......; 40.4; ......; 34.5; ......; ......; ......; ......; ......; 1998; 1999; 2000; 2001; 2002; 2003; 2004; 2005; year; total %; ^{.....}; ^{.....}; ^{.....}; ^{.....}]

2003(max)

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Character Codes

    0 1 2 3 4 5 6 7 8 9 a b c d e f
20    ! " # $ % $ ' ( ) * + , - . /   09 TAB
30  0 1 2 3 4 5 6 7 8 9 : ; < = > ?   0d CR
40  @ A B C D E F G H I J K L M N O   0a LF
50  P Q R S T U V W X Y Z [ \ ] ˆ
60  ` a b c d e f g h i j k l m n o
70  p q r s t u v w x y z { | } ∼