- 追加された行はこの色です。
- 削除された行はこの色です。
#rst2hooktail_source
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LaTeX表現集
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数式掲示板では，高校生から社会人までの広い範囲の方々が，物理や数学の問題について論議しています．この場合，通常のテキスト型やHTML型のの数式表現では，分数や上下の添え字が見にくいので，意思の疎通が悪くなうことが多々あります．その状況を打破する為に「数式」掲示板では，簡易LaTeXが用意されており, $\text{\LaTeX}$ を使うと教科書レベルの高い表現力により自分の思考を存分に展開出来ると思います．
この記事では $\text{\LaTeX}$ 数式の表現方法を紹介します。
皆さんが $\text{\LaTeX}$ を使用する際の参考になれば幸いです。
しかし，一番式を使うと効果的であると思われる高校生の皆さんは，知り合いにLaTeX使いがいない限り，どうしても $\text{\LaTeX}$ を敬遠勝ちと思われます．でも頭脳が一番成長している高校生さんこそが $\text{\LaTeX}$ を使い倒すことで，自分の問題を存分に論議し，「指と目」とを通して数式と仲良しになることで，過酷な受験勉強を元気に制覇できたら，嬉しいと思います．
なお微分演算子 $\mathrm{d}$ や虚数単位 $\mathrm{i}$ は立体で書いた方が良い、という意見があります。
本記事中では斜体、立体が入り交じっていますがご容赦ください。
もし，内容に問題があったり，追加項目を感じたりされた場合は，数式掲示板の【手に馴染むLaTeXe #01】 [*]_ にご連絡ください．
.. [*] http://hooktail.maxwell.jp/cgi-bin/yybbs/yybbs.cgi?room=room1&mode=res&no=11396&mode2=preview_pc
.. contents::
簡単な利用法：数式掲示版のローカル・ルール
==============================================
1. 文中の数式は，数式を半角の"\<tex\>"と"\</tex\>"とで挟む．
2. 数式だけの行では，数式を"\<tex\>"と"\</tex\>"とで挟む．
3. 数式の中に全角文字（ひらがな、漢字、、、）を入れてはならない
4. 以下の具体例から類似の表現を"See"から探し，その"Type"からコピーし，自分の書く数式部分にペーストし，修正する．
基本表現
=============
分数
----
.. csv-table::
:header: "表示項目", "See", "Type"
:header: "表示項目", "表示", "入力"
"分数 式番号","$y=a/x=\frac{a}{x} \tag{88}.$","y=a/x=\\frac{a}{x} \\tag{88}."
"分数 式番号","$y=a/x=\frac{a}{x} \tag{88}.$","y=a/x=\\frac{a}{x} \\tag{88}."
添字
-----
.. csv-table::
:header: "表示項目", "See", "Type"
:header: "表示項目", "表示", "入力"
"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!},"
微分・積分
-------------
.. csv-table::
:header: "表示項目", "See", "Type"
:header: "表示項目", "表示", "入力"
"1次微分", "$\dot x = x^{\prime} = d x/d t=\frac{d x(t)}{d t}=\frac{d}{d t}\left(x(t)\right),$", "\\dot x^{\\prime} = dx/dt=\\frac{d x(t)}{d t}=\\frac{d}{d t}\\left(x(t)\\right),"
"2次微分","$ \ddot x = x^{\prime \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),$","\\ddot x^{\\prime \\prime} = d^{2}x/dt^{2}=\\frac{d^{2} x(t)}{d t^{2}}=\\frac{d}{d t^{2}}\\left(x(t)\\right),"
"1次微分", "$\dot x = x^{\prime} = d x/d t=\frac{d x(t)}{d t}=\frac{d}{d t}\left(x(t)\right),$", "\\dot x = x^{\\prime} = dx/dt=\\frac{d x(t)}{d t}=\\frac{d}{d t}\\left(x(t)\\right),"
"2次微分","$ \ddot x = x^{\prime \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),$","\\ddot x = x^{\\prime \\prime} = d^{2}x/dt^{2}=\\frac{d^{2} x(t)}{d t^{2}}=\\frac{d}{d t^{2}}\\left(x(t)\\right),"
"積分 ","$\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. $","\\int\\mspace{-11mu}\\int_{S} f(x,y)\\mspace{2mu}{\\rm d}x \\mspace{2mu}\\rm d}y, \\quad \\oint_{C} f(z){\\rm d}z."
"面積分，線積分 \\rm≡\\mathrm","$ \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),$","\\frac{\\partial f(x,y)}{\\partial x} =\\partial_{x}f(x,y)=f_{x}(x,y),"
ヴェクタ・行列・行列式
ベクトル・行列・行列式
------------------------
.. csv-table::
:header: "表示項目", "See", "Type"
:header: "表示項目", "表示", "入力"
"列ヴェクタと行列の表示","$\left( \begin{array}{cc} A^{1}\\ A^{2}\\ \end{array} \right) =\left(\begin{array}{cc} g^{11} & g^{12} \\ g^{21} & g^{22} \\ \end{array} \right) \left( \begin{array}{cc} A_{1}\\ A_{2}\\ \end{array} \right).$", "\left( \begin{array}{cc} A^{1}\\ A^{2}\\ \end{array} \right) \left(\begin{array}{cc} g^{11} & g^{12} \\ g^{21} & g^{22} \\ \end{array} \right) \left( \begin{array}{cc} A_{1}\\ A_{2}\\ \end{array} \right)."
"2点間のヴェクタ(上の長い矢) ","$ \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. \\ &\text{(inner product or dot product)} $","\\vec A\\cdot\\vec B \\equiv A_xB_x +A_yB_y +A_zB_z."
"ヴェクタ外積 cross-product","$\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}. \\ &\text{(outer product or cross product)} $","\\vec A \\times \\vec B &\\equiv \\begin{vmatrix}\\vec e_{x} & \\vec e_{y} & \\vec e_{z} \\\\ A_x & A_y & A_z \\\ B_x & B_y & B_z \\end{vmatrix}."
"列ベクトルと行列の表示","$\left( \begin{array}{cc} A^{1}\\ A^{2}\\ \end{array} \right) =\left(\begin{array}{cc} g^{11} & g^{12} \\ g^{21} & g^{22} \\ \end{array} \right) \left( \begin{array}{cc} A_{1}\\ A_{2}\\ \end{array} \right).$", "\\left( \\begin{array}{cc} A^{1}\\\\ A^{2}\\\\ \\end{array} \\right) \\left(\\begin{array}{cc} g^{11} & g^{12} \\\\ g^{21} & g^{22} \\\\ \\end{array} \\right) \\left( \\begin{array}{cc} A_{1}\\\\ A_{2}\\\\ \\end{array} \\right)."
"2点間のベクトル(上の長い矢) ","$ \cos\left(\angle \mathrm{AOB}\right) =\frac{\overrightarrow{\mathrm{OA}}\cdot\overrightarrow{\mathrm{OB}}} {|\overrightarrow{\mathrm{OA}}|\cdot|\overrightarrow{\mathrm{OB}}|}.$","\\cos\\left(\\angle \\mathrm{AOB}\\right)= \\frac{\\overrightarrow{\\mathrm{OA}}\\cdot \\overrightarrow{\\mathrm{OB}}} {| \\overrightarrow{\\mathrm{OA}}| \\cdot|\\overrightarrow{\\mathrm{OB}}|}. "
"ベクトル内積 dot-product","${\bm A}\cdot{\bm B} &\equiv A_xB_x +A_yB_y +A_zB_z. \\ &\text{(inner product or dot product)} $","{\\bm A}\\cdot{\\bm B} \\equiv A_xB_x +A_yB_y +A_zB_z."
"ベクトル外積 cross-product","${\bm A} \times {\bm B} &\equiv \begin{vmatrix} {\bm e}_{x} & {\bm e}_{y} & {\bm e}_{z} \\ A_x & A_y & A_z \\ B_x & B_y & B_z \end{vmatrix}. \\ &\text{(outer product or cross product)} $","{\\bm A} \\times {\\bm B} &\\equiv \\begin{vmatrix}{\\bm e}_{x} & {\\bm e}_{y} & {\\bm e}_{z} \\\\ A_x & A_y & A_z \\\ B_x & B_y & B_z \\end{vmatrix}."
ヴェクタ演算子とラプラスの演算子
ベクトル演算子とラプラスの演算子
----------------------------------
.. csv-table::
:header: "表示項目", "See", "Type"
:header: "表示項目", "表示", "入力"
"nabla演算子 ","$ \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","$\bigtriangleup \Psi(\vec r) &=0 \qquad \text{solution:}\Psi(\vec r) \ \text{ harmonic function} \\ &\hookrightarrow \text{Laplace equation} \\ \bigtriangleup \Phi(\vec r) &=q(\vec r) \\ &\hookrightarrow \text{Poisson's equation}$","\\bigtriangleup \\Psi(\vec r) &=0 & \\Psi(\vec r): \quad \\text{harmonic function} \\\\ &\\hookrightarrow \text{Laplace eq.}\\ \\bigtriangleup \\Phi(\vec r) & = q(\vec r) && \hookrightarrow \\text{Poisson's equation}"
"nabla演算子 ","$\nabla &\equiv \frac{\partial}{\partial x}\bm{e}_{x} +\frac{\partial}{\partial y}\bm{e}_{y} +\frac{\partial }{\partial z}\bm{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({\bm r}) &= \nabla f({\bm r})\\ &=\frac{\partial f({\bm r})}{\partial x}{\bm e}_{x} +\frac{\partial f({\bm r})}{\partial y}{\bm e}_{y} +\frac{\partial f({\bm r})}{\partial z}{\bm e}_{z}, $","\\mathrm{grad}\\ f({\bm r}) &=\\overrightarrow{\\bigtriangledown} f({\\bm r})\\\\ &=\\frac{\\partial f({\\bm r})}{\\partial x}{\\bm e}_{x} +\\frac{\\partial f({\\bm r})}{\\partial y}{\\bm e}_{y} +\\frac{\partial f({\\bm r})}{\\partial z}{\\bm e}_{z},"
"divergence:発散","$\mathrm{div}{\bm E}({\bm r},t) &= \nabla \cdot {\bm E}({\bm r},t),\\ &=\frac{\partial E_{x}({\bm r},t)}{\partial x} +\frac{\partial E_{y}({\bm r},t)}{\partial y} +\frac{\partial E_{z}({\bm r},t)}{\partial z}.$ ","\\mathrm{div}{\\bm E}({\\bm r},t)&= \nabla \\cdot {\\bm E}({\\bm r},t),\\\\ &=\\frac{\\partial E_{x}({\\bm r},t)}{\\partial x} +\\frac{\\partial E_{y}({\\bm r},t)}{\\partial y} +\\frac{\\partial E_{z}({\\bm r},t)}{\\partial z}."
"rotation:回転","$\mathrm{rot}{\bm H}({\bm r},t) &= \nabla \times {\bm H}({\bm r},t),\\ &=\begin{vmatrix}{\bm e}_{x} & {\bm e}_{y} & {\bm e}_{z}\\ \dfrac{\partial}{\partial x} & \dfrac{\partial}{\partial y} & \dfrac{\partial}{\partial z} \\ H_{x}({\bm r},t) & H_{y}({\bm r},t) & H_{z}({\bm r},t) \end{vmatrix}.$","\\mathrm{rot}\{\\\bm H}({\\bm r},t) &= \\nabla \\times {\\bm H}({\\bm r},t),\\\\ &=\\begin{vmatrix}{\\bm e}_{x} & {\\bm e}_{y} & {\\bm e}_{z}\\\ \\dfrac{\\partial}{\\partial x} & \\dfrac{\\partial}{\\partial y} & \\dfrac{\partial}{\\partial z} \\\ H_{x}({\\bm r},t) & H_{y}({\\bm r},t) & H_{z}({\\bm r},t) \\end{vmatrix}."
"Laplacian(ラプラシアン：ラプラスの演算子)","$\bigtriangleup &\equiv \left( \frac{\partial^2}{\partial x^2} +\frac{\partial^2}{\partial y^2} +\frac{\partial^2}{\partial z^2}\right)\\ &= \nabla^{2} \\ &= \mathrm{div}\cdot\mathrm{grad}.$","\\bigtriangleup &\\equiv \\left( \\frac{\\partial^2}{\\partial x^2} +\\frac{\\partial^2}{\\partial y^2} +\\frac{\\partial^2}{\\partial z^2}\\right) \\\\ &= \\nabla^2 \\\\ &= \\mathrm{div}\\cdot\\mathrm{grad}."
"ラプラスの方程式 $\text{ }$ ポアッソンの方程式","$\bigtriangleup \Psi({\bm r}) &=0 \qquad \text{solution:}\Psi({\bm r}) \ \text{ harmonic function} \\ &\hookrightarrow \text{Laplace equation} \\ \bigtriangleup \Phi({\bm r}) &=q({\bm r}) \\ &\hookrightarrow \text{Poisson's equation}$","\\bigtriangleup \\Psi({\bm r}) &=0 & \\Psi({\bm r}): \quad \\text{harmonic function} \\\\ &\\hookrightarrow \text{Laplace eq.}\\\\ \\bigtriangleup \\Phi({\bm r}) & = q({\bm r}) && \hookrightarrow \\text{Poisson's equation}"
複素数とオイラの公式
複素数とオイラーの公式
-----------------------
.. csv-table::
:header: "表示項目", "See", "Type"
:header: "表示項目", "表示", "入力"
"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."
"オイラーの公式","$\mathrm{e}^{\mathrm{i}\theta} = \cos(\theta) + \mathrm{i}\sin(\theta)$","\\mathrm{e}^{\\mathrm{i}\\theta} = \\cos(\\theta) + \\mathrm{i}\\sin(\\theta)"
"オイラーの逆公式","$\cos(\theta) = \frac{\mathrm{e}^{\mathrm{i}\theta} + \mathrm{e}^{-\mathrm{i}\theta}}{2},\\ \sin(\theta) = \frac{\mathrm{e}^{\mathrm{i}\theta} - \mathrm{e}^{-\mathrm{i}\theta}}{2\mathrm{i}}$","\\cos(\\theta) = \\frac{\\mathrm{e}^{\\mathrm{i}\\theta} + \\mathrm{e}^{-\\mathrm{i}\\theta}}{2},\\\\ \\sin(\\theta) = \\frac{\\mathrm{e}^{\\mathrm{i}\\theta} - \\mathrm{e}^{-\\mathrm{i}\\theta}}{2\\mathrm{i}}"
指数関数と双曲線関数
-------------------------
.. csv-table::
:header: "表示項目", "See", "Type"
:header: "表示項目", "表示", "入力"
"指数関数 ← 双曲線関数","$\left\{ \begin{array}{lcc} \mathrm{e}^{x} &=\cosh(x)+\sinh(x), & \\ \mathrm{e}^{-x} &=\cosh(x)-\sinh(x), & \end{array} \right.$","\\left\\{ \\begin{array}{l c c} \\mathrm{e}^{x} &=\\cosh(x)+\\sinh(x), & \\\\ \\mathrm{e}^{-x} &=\\cosh(x)-\\sinh(x), & \\end{array} \\right."
"双曲線関数 ← 指数関数","$\left\{ \begin{array}{lcc} \cosh(x) &=\dfrac{\mathrm{e}^{x}+\mathrm{e}^{-x}}{2}, & \\ \sinh(x) &= \dfrac{\mathrm{e}^{x}-\mathrm{e}^{-x}}{2}, & \\ \tanh(x) &= \dfrac{\sinh(x)}{\cosh(x)} &= \dfrac{\mathrm{e}^{x}-\mathrm{e}^{-x}} {\mathrm{e}^{x}+\mathrm{e}^{-x}}. \end{array} \right.$","\\left\\{ \\begin{array}{lcc} \\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."
"指数関数 ← 双曲線関数","$\mathrm{e}^{x} & = \cosh(x)+\sinh(x), \\ \mathrm{e}^{-x} & =\cosh(x)-\sinh(x)$","\\mathrm{e}^{x} & = \\cosh(x)+\\sinh(x), \\\\ \\mathrm{e}^{-x} & =\\cosh(x)-\\sinh(x)"
"双曲線関数 ← 指数関数","$\cosh(x) & =\dfrac{\mathrm{e}^{x}+\mathrm{e}^{-x}}{2},\\ \sinh(x) & = \dfrac{\mathrm{e}^{x}-\mathrm{e}^{-x}}{2},\\ \tanh(x) & = \dfrac{\sinh(x)}{\cosh(x)} = \dfrac{\mathrm{e}^{x}-\mathrm{e}^{-x}} {\mathrm{e}^{x}+\mathrm{e}^{-x}}.$","\\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}}."
"式の横並び：簡易法 &&仕切り", "$u(x,0) =0, && u(0,t) =U, && u(\infty ,t) =0.$", "u(x,0) =0, && u(0,t) =U, && u(\\infty ,t) =0."
記号(Symbols)
==================
.. csv-table:: 記号
:header: "See/Type", "See/Type", "See/Type", "See/Type"
:header: "表示/入力", "表示/入力", "表示/入力", "表示/入力"
"$\pm$ \\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"
矢印と括弧
===============
.. csv-table:: 矢印と括弧
:header: "See \\Type", "See \\Type"
:header: "表示 \\入力", "表示 \\入力"
"$\gets$ \\gets", "$\longleftarrow$ \\longleftarrow"
"$\Leftarrow$ \\Leftarrow", "$\Longleftarrow$ \\Longleftarrow"
"$\to$ \\to", "$\longrightarrow$ \\longrightarrow"
"$\Rightarrow$ \\Rightarrow", "$\Longrightarrow$ \\Longrightarrow"
"$\leftrightarrow$ \\leftrightarrow", "$\longleftrightarrow$ \\longleftrightarrow"
"$\Leftrightarrow$ \\Leftrightarrow", "$\Longleftrightarrow$ \\Longleftrightarrow"
"$\mapsto$ \\mapsto", "$\longmapsto$ \\longmapsto"
"$\hookleftarrow$ \\hookleftarrow", "$\hookrightarrow$ \\hookrightarrow"
"$\rightleftharpoons$ \\rightleftharpoons", "$\upharpoonleft\hspace{-.24em}\downharpoonright$ \\upharpoonleft\\hspace{-.24em}\\downharpoonright"
"$\uparrow$ \\uparrow", "$\downarrow$ \\downarrow"
"$\Uparrow$ \\Uparrow", "$\Downarrow$ \\Downarrow"
"$\updownarrow$ \\updownarrow", "$\Updownarrow$ \\Updownarrow"
"$\upharpoonleft$ \upharpoonleft\", "$\downharpoonright$ \downharpoonright\"
"$|$ |", "$\|$ \\|"
"$\{ x\}$ \\{ x\\}", "$\lceil x \rceil$ \\lceil x \\rceil"
"$\langle x \rangle$ \\langle x \\rangle", "$\lfloor x \rfloor$ \\lfloor x \\rfloor"
賢いドットと省略型ドット
============================
.. csv-table:: 賢いdots と 省略型dotsX
:header: "用法", "See", "Type"
:header: "用法", "表示", "入力"
"賢いdots(カンマ区切り)", "$a_1,a_2,\dots,a_n.$", "a_1,a_2,\\dots,a_n."
"賢いdots(二項演算子)", "$a_1 + a_2 + \dots + a_n$", "a_1 + a_2 + \\dots + a_n"
"賢いdots(多項並べ)", "$a_1 a_2 \dots a_n$", "a_1 a_2 \\dots a_n"
"賢いdots(多重積分)", "$\int \dots \int $", "\\int \\dots \\int"
"dotsc (commas)", "$a_1,\dotsc$", "a_1,\\dotsc"
"dotsb (binary op. or relations)", "$a_1 + \dotsb$", "a_1 + \dotsb"
"dotsb (binary op. or relations)", "$a_1 + \dotsb$", "a_1 + \\dotsb"
"dotsm (multiplications)", "$a_1 \dotsm$", "a_1 \\dotsm"
"dotsi (integrals)", "$\int \dotsi$", "\int \dotsi"
"dotsi (integrals)", "$\int \dotsi$", "\\int \\dotsi"
ギリシャ文字(小文字，大文字・立体，大文字・斜体)
===================================================
.. csv-table:: Greek letters
:header: "See/Type", "See/Type", "See/Type", "See/Type"
:header: "表示/入力", "表示/入力", "表示/入力", "表示/入力"
"$\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"
数学での「数の種類分け」記号
=================================
.. csv-table::
:header: "See", "Type", "See", "Type", "意味", "例"
:header: "表示", "入力", "表示", "入力", "意味", "例"
"$\mathbb{N}$", "\\mathbb{N}", "$\mathbf{N}$", "\\mathbf{N}", "自然数の全体", "$1,2,\dots$"
"$\mathbb{Z}$","\\mathbb{Z}", "$\mathbf{Z}$", "\\mathbf{Z}", "整数全体", "$0,\pm1,\pm2,\dots$"
"$\mathbb{Q}$","\\mathbb{Q}", "$\mathbf{Q}$", "\\mathbf{Q}", "有理数全体", "$\pm 2/3$"
"$\mathbb{R}$","\\mathbb{R}", "$\mathbf{R}$", "\\mathbf{R}", "実数全体", "$\sqrt{2}, \pi, e=\mathrm{e}^{1}$"
"$\mathbb{C}$","\\mathbb{C}", "$\mathbf{C}$", "\\mathbf{C}", "複素数全体", "$\sqrt{-1}=\mathrm{e}^{\mathrm{i}\pi / 2}$"
ローカル・ルール
===================
@@reference: hooktail.maxwell.jp/bbslog/11108.html,数式掲示板 スレッド No.11108@@
@@reference: hooktail.maxwell.jp/bbslog/11307.html,数式掲示板 スレッド No.11307@@
@@reference: hooktail.maxwell.jp/bbslog/11396.html,数式掲示板 スレッド No.11396@@
@@author: CO@@
@@accept: 2006-11-27@@
@@category: その他@@
@@id: latexImpress@@
.. csv-table:: ローカル・ルール
:header: "See", "Type", "意味", "使用例"
"$\unit{Nm}\unit{s^{-1}}$", "\\unit{Nm}\\unit{s^{-1}}", "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", "→付きの細いナブラ", "未実装"
"$\bigtriangleup$", "\\Lap", "細いラプラシアン", "未実装"
準備中
===========
<tex>
\kern1pt{\scriptstyle \cup\kern-5pt\raisebox{1.4pt} {\hbox{\small $\shortmid$}}}
</tex>
<tex>\bigodot, && \bigotimes, && \bigoplus_{\sum k_{j}n_{j}=m}\mathbf{K}x_{n_{1}}^{k_1}, && \biguplus</tex>
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
制作
-------
- by LaTeX友の会・事務局 since 2006-08-06
@@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/LaTeX表現集 のバックアップの現在との差分(No.2)
