#rst2hooktail_source
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LaTeX初級テンプレート
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- by LaTeX友の会・事務局 since 2006-08-06
.. csv-table:: 数式のテンプレート
:header: "表示項目", "原稿表示", "TeX表示"
"分数 式番号","y=a/x=\\frac{a}{x} \\tag{88}"," $y=a/x=\frac{a}{x} \tag{88} $ "
"上付添え字","x^2+y^2=r^2"," $x^2+y^2=r^{2}$ "
"下付添え字 ","_{\\it n}\\mathrm{C}_{\\it r} = \\frac{n!}{(n-r)!r!},"," $_{\it n}\mathrm{C}_{\it r} = \frac{n!}{(n-r)!r!},$ "
"1次微分","\\dot x^{\\prime} = dx/dt
=\\frac{d x(t)}{d t}
=\\frac{d}{d t}\\left(x(t)\\right),"," $ \dot x = x^{\prime} = d x/d t=\frac{d x(t)}{d t}=\frac{d}{d t}\left(x(t)\right), $ "
"2次微分","\\ddot x^{\\prime \\prime} = d^{2}x/dt^{2}
=\\frac{d^{2} x(t)}{d t^{2}}
=\\frac{d}{d t^{2}}\\left(x(t)\\right),"," $ \ddot x = x^{\prime} = d^{2} x/d t^{2}=\frac{d^{2} x(t)}{d t^{2}}=\frac{d^{2}}{d t^{2}}\left(x(t)\right), $ "
"積分 ","\\int f(x)dx, \\ g(x)=\\int^{x} f(x')dx', \\ \\int_{\\alpha}^{\\beta} f(x)dx."," $ \int f(x)dx, \ g(x)=\int^{x} f(x')dx', \ \int_{\alpha}^{\beta} f(x)dx. $ "
"面積分，線積分 \\rm≡\\mathrm","\\int\\mspace{-11mu}\\int_{S} f(x,y)\\mspace{2mu}{\\rm d}x \\mspace{2mu}\\rm d}y, \\quad \\oint_{C} f(z){\\rm d}z."," $ \int\mspace{-11mu}\int_{S} f(x,y) \mspace{2mu}{\rm d} x \mspace{2mu}{\rm d}y, \quad \oint_{C} f(z){\rm d}z. $ "
"偏微分 ","\\frac{\\partial f(x,y)}{\\partial x} =\\partial_{x}f(x,y)=f_{x}(x,y),"," $ \frac{\partial f(x,y)}{\partial x} =\partial_{x}f(x,y)=f_{x}(x,y), $ "
"2点間のヴェクタ(上の長い矢) ","\\cos\\left(\\angle \\mathrm{AOB}\\right)= \\frac{\\overrightarrow{\\mathrm{OA}}\\cdot \\overrightarrow{\\mathrm{OB}}}{| \\overrightarrow{\\mathrm{OA}}| \\cdot|\\overrightarrow{\\mathrm{OB}}|}. "," $ \cos\left(\angle \mathrm{AOB}\right)=\frac{\overrightarrow{\mathrm{OA}}\cdot\overrightarrow{\mathrm{OB}}}{|\overrightarrow{\mathrm{OA}}|\cdot|\overrightarrow{\mathrm{OB}}|}.$ "
"ヴェクタ(上→，太斜体) \\bm≡\boldmath","\\vec A &= A_x\\vec e_x +A_y\\vec e_y +A_z\\vec e_z, \\\\ \\bm{A} &=A_x\\bm{i} +A_{y}\\mspace{3mu}\\bm{j} +A_z\\bm{k},","$ \vec A &= A_x\vec e_x +A_y\vec e_y+A_z\vec e_z, \\ \bm{A} &=A_x\bm{i}+A_{y}\mspace{3mu}\bm{j}+A_z\bm{k}.$"
"ヴェクタ内積 dot-product","\\vec A\\cdot\\vec B \\equiv A_xB_x +A_yB_y +A_zB_z.","$\vec A\cdot\vec B &\equiv A_xB_x +A_yB_y +A_zB_z. \\ &\text{(inner product or dot product)} $"
"ヴェクタ外積 cross-product","\\vec A \\times \\vec B &\\equiv \\begin{vmatrix}\\vec e_{x} & \\vec e_{y} & \\vec e_{z} \\\\ A_x & A_y & A_z \\\ B_x & B_y & B_z \\end{vmatrix}.","$\vec A \times \vec B &\equiv \begin{vmatrix}\vec e_{x} & \vec e_{y} & \vec e_{z} \\ A_x & A_y & A_z \\ B_x & B_y & B_z \end{vmatrix}. \\ &\text{(outer product or cross product)} $"
"nabla演算子 ","\\overrightarrow{\\bigtriangledown} \\equiv \\frac{\\partial}{\\partial x}\\vec e_{x} +\\frac{\\partial}{\\partial y}\\vec e_{y} +\\frac{\\partial }{\\partial z}\\vec e_{z}, \\\\ \\nabla \\equiv \\frac{\\partial}{\\partial x}\\bm{e}_{x} +\\frac{\partial}{\\partial y}\\bm{e}_{y} +\\frac{\\partial }{\\partial z}\\bm{e}_{z}. ","$ \overrightarrow{\bigtriangledown} &\equiv \frac{\partial}{\partial x}\vec e_{x} +\frac{\partial}{\partial y}\vec e_{y} +\frac{\partial }{\partial z}\vec e_{z}, \\ \nabla &\equiv \frac{\partial}{\partial x}\bm{e}_{x} +\frac{\partial}{\partial y}\bm{e}_{y} +\frac{\partial }{\partial z}\bm{e}_{z}. $"
"gradient:勾配","\\mathrm{grad}\\ f(\vec r) &=\\overrightarrow{\\bigtriangledown} f(\\vec r)\\\\ &=\\frac{\\partial f(\\vec r)}{\\partial x}\\vec e_{x} +\\frac{\\partial f(\\vec r)}{\\partial y}\\vec e_{y} +\\frac{\partial f(\\vec r)}{\\partial z}\\vec e_{z},","$ \mathrm{grad}\ f(\vec r) &=\overrightarrow{\bigtriangledown} f(\vec r)\\ &=\frac{\partial f(\vec r)}{\partial x}\vec e_{x} +\frac{\partial f(\vec r)}{\partial y}\vec e_{y} +\frac{\partial f(\vec r)}{\partial z}\vec e_{z}, $"
"divergence:発散","\\mathrm{div}\\ \\vec E(\\vec r,t)&= \\overrightarrow{\\bigtriangledown} \\cdot \\vec E(\\vec r,t),\\\\ &=\\frac{\\partial E_{x}(\\vec r,t)}{\\partial x} +\\frac{\\partial E_{y}(\\vec r,t)}{\\partial y} +\\frac{\\partial E_{z}(\\vec r,t)}{\\partial z}.","$\mathrm{div}\ \vec E(\vec r,t) &= \overrightarrow{\bigtriangledown} \cdot \vec E(\vec r,t),\\ &=\frac{\partial E_{x}(\vec r,t)}{\partial x} +\frac{\partial E_{y}(\vec r,t)}{\partial y} +\frac{\partial E_{z}(\vec r,t)}{\partial z}.$ "
"rotation:回転","\\mathrm{rot}\\ \\vec H(\\vec r,t) &=\\overrightarrow{\bigtriangledown} \\times \\vec H(\\vec r,t),\\\\ &=\\begin{vmatrix}\\vec e_{x} & \\vec e_{y} & \\vec e_{z}\\\ \\dfrac{\\partial}{\\partial x} & \\dfrac{\\partial}{\\partial y} & \\dfrac{\partial}{\\partial z} \\\ H_{x}(\\vec r,t) & H_{y}(\\vec r,t) & H_{z}(\\vec r,t) \\end{vmatrix}.","$\mathrm{rot}\ \vec H(\vec r,t) &=\overrightarrow{\bigtriangledown} \times \vec H(\vec r,t),\\ &=\begin{vmatrix}\vec e_{x} & \vec e_{y} & \vec e_{z}\\ \dfrac{\partial}{\partial x} & \dfrac{\partial}{\partial y} & \dfrac{\partial}{\partial z} \\ H_{x}(\vec r,t) & H_{y}(\vec r,t) & H_{z}(\vec r,t) \end{vmatrix}.$"
"Laplacian(ラプラシアン：ラプラスの演算子)","\\bigtriangleup &\\equiv \\left( \\frac{\\partial^2}{\\partial x^2} +\\frac{\\partial^2}{\\partial y^2} +\\frac{\\partial^2}{\\partial z^2}\\right) \\\\ &= \\overrightarrow{\\bigtriangledown}^2 \\\\ &= \\mathrm{div}\\cdot\\mathrm{grad}.","$\bigtriangleup &\equiv \left( \frac{\partial^2}{\partial x^2} +\frac{\partial^2}{\partial y^2} +\frac{\partial^2}{\partial z^2}\right)\\ &= \overrightarrow{\bigtriangledown}^{2} \\ &= \mathrm{div}\cdot\mathrm{grad}.$"
"ラプラスの方程式 $\text{ }$ ポアッソンの方程式","\\bigtriangleup \\Psi(\vec r) &=0 & \\Psi(\vec r): \quad \\text{harmonic function} \\\\ &\\leftarrow \text{Laplace eq.}\\ \\bigtriangleup \\Phi(\vec r) & = q(\vec r) && \leftarrow \\text{Poisson's equation}","$\bigtriangleup \Psi(\vec r) &=0 \qquad \text{solution:}\Psi(\vec r) \ \text{ harmonic function} \\ &\nwarrow \text{Laplace equation} \\ \bigtriangleup \Phi(\vec r) &=q(\vec r) \\ &\nwarrow \text{Poisson's equation}$"
"複素数 成分により表示","z=x+\\mathrm{i}y =r\\mathrm{e}^{+\\mathrm{i}\\theta} =r\\left(\\cos(\\theta)+\\mathrm{i}\\sin(\\theta)\\right), \\\\ \\bar z =x-\\mathrm{i}y=r\\mathrm{e}^{-\\mathrm{i}\\theta} =r\\left(\\cos(\\theta)-\\mathrm{i}\\sin(\\theta)\\right).","$z=x+\mathrm{i}y=r\mathrm{e}^{+\mathrm{i}\theta} =r\left(\cos(\theta)+\mathrm{i}\sin(\theta)\right), \\ \bar z=x-\mathrm{i}y=r\mathrm{e}^{-\mathrm{i}\theta} = r\left(\cos(\theta)-\mathrm{i}\sin(\theta)\right),$"
"オイラの公式","\\left\\{ \\begin{array}{l c} \\mathrm{e}^{\\mathrm{i}\\theta} & =\\cos(\\theta)+\\mathrm{i}\\sin(\\theta), \\\\ \\mathrm{e}^{-\\mathrm{i}\\theta} & =\cos(\\theta)-\\mathrm{i}\\sin(\\theta).\\end{array} \\right.","$\left\{ \begin{array}{l c} \mathrm{e}^{\mathrm{i}\theta} & =\cos(\theta)+\mathrm{i}\sin(\theta), \\ \mathrm{e}^{-\mathrm{i}\theta} & =\cos(\theta)-\mathrm{i}\sin(\theta).\end{array} \right.$"
"オイラの逆公式","\\left\\{ \\begin{array}{l c} \\cos(\theta) &=\\dfrac{\\mathrm{e}^{\\mathrm{i}\\theta} +\\mathrm{e}^{-\\mathrm{i}\\theta}}{2},\\\\ \\sin(\theta) &=\\dfrac{\\mathrm{e}^{\\mathrm{i}\\theta} -\\mathrm{e}^{-\\mathrm{i}\\theta}}{2\\mathrm{i}}, \\end{array} \\right.","$\left\{ \begin{array}{l c} \cos(\theta) &=\dfrac{\mathrm{e}^{\mathrm{i}\theta} +\mathrm{e}^{-\mathrm{i}\theta}}{2},\\ \sin(\theta) &=\dfrac{\mathrm{e}^{\mathrm{i}\theta} -\mathrm{e}^{-\mathrm{i}\theta}}{2\mathrm{i}}, \end{array} \right.$"
"指数関数と双曲線関数","\\left\\{ \\begin{array}{l c} \\mathrm{e}^{x} &=\\cosh(x)+\\sinh(x), \\\\ \\mathrm{e}^{-x} &=\\cosh(x)-\\sinh(x), \\end{array} \\right. \\\\ \\left\\{ \\begin{array}{lcc} \\cosh(x) &=\\dfrac{\\mathrm{e}^{x}+\\mathrm{e}^{-x}}{2}, & \\\\ \\sinh(x) &= \\dfrac{\\mathrm{e}^{x}-\\mathrm{e}^{-x}}{2}, & \\\\ \\tanh(x) &= \\dfrac{\\sinh(x)}{\\cosh(x)} &= \dfrac{\\mathrm{e}^{x}-\\mathrm{e}^{-x}} {\\mathrm{e}^{x}+\\mathrm{e}^{-x}}. \\end{array} \\right.","$\left\{ \begin{array}{l c} \mathrm{e}^{x} &=\cosh(x)+\sinh(x), \\ \mathrm{e}^{-x} &=\cosh(x)-\sinh(x), \end{array} \right. \\ \left\{ \begin{array}{lcc} \cosh(x) &=\dfrac{\mathrm{e}^{x}+\mathrm{e}^{-x}}{2}, & \\ \sinh(x) &= \dfrac{\mathrm{e}^{x}-\mathrm{e}^{-x}}{2}, & \\ \tanh(x) &= \dfrac{\sinh(x)}{\cosh(x)} &= \dfrac{\mathrm{e}^{x}-\mathrm{e}^{-x}} {\mathrm{e}^{x}+\mathrm{e}^{-x}}. \end{array} \right.$"
.. csv-table:: Symbols
:header: "See/Type", "See/Type", "See/Type", "See/Type"
"$\pm$ \\pm", "$\circ$ \\circ", "$\bullet$ \\bullet", "$\cdot$ \\cdot"
"$\aleph$ \\aleph", "$\hbar$ \\hbar", "$\Re$ \\Re", "$\Im$ \\Im"
"$\infty$ \\infty", "$\emptyset$ \\emptyset", "$\forall$ \\forall", "$\exists$ \\exists"
"$\cap$ \\cap", "$\cup$ \\cup", "$\vee$ \\vee", "$\wedge$ \\wedge"
"$\subset$ \\subset", "$\supset$ \\supset", "$\sqsubset$ \\sqsubset", "$\sqsupset$ \\sqsupset"
"$\subseteq$ \\subseteq", "$\supseteq$ \\supseteq", "$\vdash$ \\vdash", "$\dashv$ \\dashv"
"$\in$ \\in", "$\notin$ \\notin", "$\ni$ \\ni", "$\not\ni$ \\not\\ni"
"$\parallel$ \\parallel", "$\perp$ \\perp", "$\sim$ \\sim", "$\simeq$ \\simeq"
"$\equiv$ \\equiv", "$\approx$ \\approx", "$\propto$ \\propto", "$\neq$ \\neq"
"$\le$ \\le", "$\ll$ \\ll", "$\ge$ \\ge", "$\gg$ \\gg"
■15■ 矢印と点
--------------------------- ◇原稿の表示◇ ---------------------------+
<pre> gets longleftarrow
Leftarrow Longleftarrow
to longrightarrow
Rightarrow Longrightarrow
leftrightarrow longleftrightarrow
Leftrightarrow Longleftrightarrow
mapsto longmapsto
hookleftarrow hookrightarrow
賢いdots(カンマ区切り) dotsc (commas)
賢いdots(二項演算子) dotsc (binary op. or relations)
賢いdots(多項並べ) dotsc (multiplications)
賢いdots(多重積分) dotsc (integrals)
</pre>--------------------------- ◇TeXの表示◇ ----------------------------+
<tex>
\begin{array}{cc|cc|}
gets &\gets &longleftarrow &\longleftarrow \\
Leftarrow &\Leftarrow &Longleftarrow &\Longleftarrow \\
to &\to &longrightarrow &\longrightarrow \\
Rightarrow &\Rightarrow &Longrightarrow &\Longrightarrow \\
\cline{1-4}
leftrightarrow &\leftrightarrow
&longleftrightarrow &\longleftrightarrow \\
Leftrightarrow &\Leftrightarrow
&Longleftrightarrow &\Longleftrightarrow \\
mapsto &\mapsto &longmapsto &\longmapsto \\
hookleftarrow &\hookleftarrow &hookrightarrow &\hookrightarrow \\
\cline{3-4}
rightleftharpoons &\rightleftharpoons \\
\cline{1-4}
dots &a_1,a_2,\dots,a_n. &dotsc &a_1,\dotsc \\
dots &a_1 + a_2 + \dots + a_n &dotsb &a_1 + \dotsb \\
dots &a_1 a_2 \dots a_n &dotsm &a_1 \dotsm \\
dots &\int \dots \int &dotsi &\int \dots
\end{array}
</tex>
.. csv-table:: Greek letters
:header: "See/Type", "See/Type", "See/Type", "See/Type"
"$\alpha$ \\alpha", "$\eta$ \\eta", "$\nu$ \\nu", "$\tau$ \\tau"
"$\beta$ \\beta", "$\theta$ \\theta", "$\xi$ \\xi", "$\upsilon$ \\upsilon"
"$\gamma$ \\gamma", "$\iota$ \\iota", "omicron", "$\phi$ \\phi"
"$\delta$ \\delta", "$\kappa$ \\kappa", "$\pi$ \\pi", "$\chi$ \\chi"
"$\epsilon$ \\epsilon", "$\lambda$ \\lambda", "$\rho$ \\rho", "$\psi$ \\psi"
"$\zeta$ \\zeta", "$\mu$ \\mu", "$\sigma$ \\sigma", "$\omega$ \\omega"
"$\Gamma$ \\Gamma", "$\Theta$ \\Theta", "$\Xi$ \\Xi", "$\Upsilon$ \\Upsilon"
"$\Delta$ \\Delta", "$\Lambda$ \\Lambda", "$\Pi$ \\Pi", "$\Phi$ \\Phi"
" ", " ", "$\Sigma$ \\Sigma", "$\Psi$ \\Psi"
" ", " ", " ", "$\Omega$ \\Omega"
"$\varGamma$ \\varGamma", "$\varTheta$ \\varTheta", "$\varXi$ \\varXi", "$\varUpsilon$ \\varUpsilon"
"$\varDelta$ \\varDelta", "$\varLambda$ \\varLambda", "$\varPi$ \\varPi", "$\varPhi$ \\varPhi"
" ", " ", "$\varSigma$ \\varSigma", "$\varPsi$ \\varPsi"
" ", " ", " ", "$\varOmega$ \\varOmega"
.. csv-table:: 数学記号
:header: "See", "Type", "意味", "例"
"$\mathbb{N}$", "\\mathbb{N}", "自然数の全体", "$1,2,\dots$"
"$\mathbb{Z}$","\\mathbb{Z}", "整数全体", "$0,\pm1,\pm2,\dots$"
"$\mathbb{Q}$","\\mathbb{Q}", "有理数全体", "$\pm 2/3$"
"$\mathbb{R}$","\\mathbb{R}", "実数全体", "$\sqrt{2}, \pi, e=\mathrm{e}^{1}$"
"$\mathbb{C}$","\\mathbb{C}", "複素数全体", "$\mathrm{e}^{\mathrm{i}\pi}-1=0$"
.. csv-table:: ローカル・ルール
:header: "See", "Type", "意味", "使用例"
"$\unit{Nms^{-1}}$", "\unit{Nm}", "単位間に細いギャップで立体", "単位表示"
"$\bm{A}$", "\\bm{A}", "太いシンボル文字", "ヴェクトル"
"$\mathrm{e}$", "\\rme", "指数関数のe", "未実装"
"$\mathrm{i}$", "\\rmi", "純虚数のi", "未実装"
"$\mathrm{d}$", "\\rmd", "微積分のd", "未実装"
"$\overrightarrow{\bigtriangledown}$", "\\Nab", "→付きナブラ", "未実装"
"$\bigtriangleup$", "\\Lap", "細いラプラシアン", "未実装"
関連資料
==========
1. 【「数学用語の使い方」と「TeXでの表し方」】 ← 数学掲示版
- http://hooktail.maxwell.jp/cgi-bin/yybbs/yybbs.cgi?room=room1&mode=res&no=11108&mode2=preview_pc
- 物理関連のTeX表記について，上記のスレッドの中のNo.11360以降の「MXKさん，toorisugari no Hiroさん，Chappyさん」との論議．MXKさん紹介によれば「IoP(Institute of Physics)のスタイルファイルでも見たほうが早いですね。」
- ftp://ftp.iop.org/pub/journals/latex2e/IOPLaTeXGuidelines.pdf ← No.11386にtoorisugari no Hiroさんの訳(主要部)
2. 【LaTeX初級テンプレート】 LaTeX友の会 ← 数学掲示版
- http://hooktail.maxwell.jp/cgi-bin/yybbs/yybbs.cgi?room=room1&mode=res&no=11307&mode2=preview_pc
3. 【手に馴染むLaTeXe #01】← 数学掲示版
- http://hooktail.maxwell.jp/cgi-bin/yybbs/yybbs.cgi?room=room1&mode=res&no=11396&mode2=preview_pc
@@author:mNeji as LaTeX友の会・収集係@@
@@accept: 執筆中 from 2006-08-28@@
@@category: TeXのTIPS@@
@@id: latexTemplate@@
記事ソース/れいてふ・てんぷれーと のバックアップソース(No.58)
