================================================================= LaTeX表現集 ================================================================= 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。 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。 .. contents:: 基本表現 ============= 分数 ---- .. csv-table:: :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}." 添字 ----- .. csv-table:: :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", "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 = 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. $","\\int\\mspace{-11mu}\\int_{S} f(x,y)\\mspace{2mu}{\\rm d}x \\mspace{2mu}{\\rm d}y, \\quad \\oint_{C} f(z){\\rm d}z." "偏微分 ","$ \frac{\partial f(x,y)}{\partial x} =\partial_{x}f(x,y)=f_{x}(x,y),$","\\frac{\\partial f(x,y)}{\\partial x} =\\partial_{x}f(x,y)=f_{x}(x,y)," ベクトル・行列・行列式 ------------------------ .. csv-table:: :header: "表示項目", "表示", "入力" "列ベクトルと行列の表示","$\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)} $","{\\bm A} \\times {\\bm B} &\\equiv \\begin{vmatrix}{\\bm e}_{x} & {\\bm e}_{y} & {\\bm e}_{z} \\\\ A_x & A_y & A_z \\\ B_x & B_y & B_z \\end{vmatrix}." ベクトル演算子とラプラスの演算子 ---------------------------------- .. csv-table:: :header: "表示項目", "表示", "入力" "nabla演算子 ","$\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}" 複素数とオイラーの公式 ----------------------- .. csv-table:: :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", "表示", "入力" "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: "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: "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", "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$", "a_1 + \\dotsb" "dotsm (multiplications)", "$a_1 \dotsm$", "a_1 \\dotsm" "dotsi (integrals)", "$\int \dotsi$", "\\int \\dotsi" ギリシャ文字(小文字，大文字・立体，大文字・斜体) =================================================== .. csv-table:: Greek letters :header: "表示/入力", "表示/入力", "表示/入力", "表示/入力" "$\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: "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", "$\sqrt{-1}=\mathrm{e}^{\mathrm{i}\pi / 2}$" @@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@@