"수식 표현 안내"의 두 판 사이의 차이

2013년 11월 10일 (일) 04:44 판

웹과 수식표현

http://hyperpolyglot.org/math-notation

HTML 수식표현

웹상에서의 LaTeX을 통한 수식표현

구글 문서에서도 수식표현이 가능
- Google Docs Has an Equation Editor
  - Google Operating System, 2009-9-17
SITMO
- http://www.sitmo.com/latex/
- 구글이나 스프링노트와는 달리 계정없이 수식이미지를 얻을 수 있음
위키피디아
- Wiki의 관련항목에 가서 edit 를 누른뒤,  태그 사이에 LaTeX 명령을 써서, preview로 이미지를 얻기
MimeTeX
- http://www.forkosh.com/mimetex.html
MathJax
- http://www.mathjax.org/
- http://geometry.tistory.com/58

LaTeX 명령어 입문

특정한 수식표현을 배우는 하나의 방법은 Wikipedia를 이용하는 것
- Wiki의 관련항목에 가서 edit 를 눌러보면, TeX 명령들을 카피해서 사용가능. 예)오일러상수 편집모드
LaTeX 관련 페이지
- Latex cheat sheet 페이지도 한번 읽어볼 것
http://en.wikibooks.org/wiki/LaTeX

모르는 명령어 그림으로 알아내기

Detexify2 - LaTeX symbol classifier

LaTeX으로 노트하기

Advice on realtime TeXing
한글 TeX http://ajt.ktug.kr/2007/0102khlee.pdf

LaTeX 명령예

cases

$$ f(n) = \begin{cases} n/2, & \text{if $n$ is even}\\ 3n+1, & \text{if $n$ is odd} \\ \end{cases} $$

atop

$$\tilde y=\left\{ {\ddot x\text{ if $\vec x$ odd}\atop\hat{\,\bar x+1}\text{ if even}}\right.$$

array

$$ \left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array} \right. $$ $$ \begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \\ \end{array} $$

\[A=\left( \begin{array}{c.cccc}&1&2&\cdots&n\\ 1&a_{11}&a_{12}&\cdots&a_{1n}\\ 2&a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\vdots&\ddots&\vdots\\ n&a_{n1}&a_{n2}&\cdots&a_{nn}\end{array}\right)\]

eqnarray

$$\left.\begin{eqnarray} x+y+z&=&3\\2y&=&x+z\\2x+y&=&z\end{eqnarray}\right\}$$

align

\[ \begin{align} & {} \quad \int Y_{l_1}^{m_1}(\theta,\varphi)Y_{l_2}^{m_2}(\theta,\varphi)Y_{l_3}^{m_3}(\theta,\varphi)\,\sin\theta\,\mathrm{d}\theta\,\mathrm{d}\varphi \\ & = \sqrt{\frac{(2l_1+1)(2l_2+1)(2l_3+1)}{4\pi}} \begin{pmatrix} l_1 & l_2 & l_3 \\[8pt] 0 & 0 & 0 \end{pmatrix} \begin{pmatrix} l_1 & l_2 & l_3\\ m_1 & m_2 & m_3 \end{pmatrix} \end{align} \]

\[ \begin{align} \omega_{n} & =\int\cdots\int_{x_1^2+\cdots+x_n^2\leq\ 1} dx_{1}\cdots dx_{n} \\ & = \int_{-1}^{1}\left(\int\cdots \int_{x_1^2+\cdots +x_{n-1}^2\leq\ 1-x_{n}^2} dx_{1}\cdots dx_{n-1}\right)dx_{n} \end{align} \]

http://tex.stackexchange.com/questions/196/eqnarray-vs-align

underbrace

\[\underbrace{i \hbar \frac{\partial}{\partial t} |\varphi_\pm\rangle = \left( \frac{( \mathbf{p} -e \mathbf A)^2}{2 m} + e \phi \right) \hat 1 \mathbf |\varphi_\pm\rangle }_\mathrm{Schr\ddot{o}dinger~equation} - \underbrace{\frac{e \hbar}{2m}\mathbf{\sigma} \cdot \mathbf B \mathbf |\varphi_\pm\rangle }_\text{Stern Gerlach term}\] 파울리 방정식

substack

$$ \sum_{ \substack{ r,s,t\geq 0 \\ r+s=m,s+t=n}} \frac{q^{rt}}{(q)_r(q)_s(q)_t}=\frac{1}{(q)_{m}(q)_{n}} $$

크기

large

$$ \large f^\prime(x)\ = \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x} $$

Large

$$ \Large f^\prime(x)\ = \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x} $$

LARGE

$$ \LARGE f^\prime(x)\ = \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x} $$

그리스 문자

$$\alpha \beta \gamma \delta \epsilon (\varepsilon) \zeta \eta \theta (\vartheta) \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon \phi (\varphi) \chi \psi \omega$$

$$A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon \Phi X \Psi \Omega$$

글꼴

$$\text{mathcal }\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\text{mathscr }\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\text{mathbb }\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\text{mathbf }\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\text{mathbf }\mathbf{abcdefghijklmnopqrstuvwxyz}$$ $$\text{mathfrak }\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$ $$\text{mathfrak }\mathfrak{abcdefghijklmnopqrstuvwxyz}$$

기타

$\chi(t)=\left(\frac{t}{p}\right)$
$\operatorname{Re} a > 0 $
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$720\div12=60$
$\exists c \in (a,b) \quad \mathbf{s.t.} \quad f'(c)=\frac{f(b)-f(a)}{b-a}$
$\mathcal{H}om$
$G\"odel$ http://www.phil.cam.ac.uk/teaching_staff/Smith/LaTeX/other-macros/godelcorners.html
$\Large\begin{array}{rccclBCB} &f&\longr[75]^{\alpha:{\normalsize f\rightar~g}}&g\\ \large\gamma&\longd[50]&&\longd[50]&\large\gamma\\ &u&\longr[75]_\beta&v\end{array}$

\Large\begin{array}{rccclBCB} &f&\longr[75]^{\alpha:{\normalsize f\rightar~g}}&g\\ \large\gamma&\longd[50]&&\longd[50]&\large\gamma\\ &u&\longr[75]_\beta&v\end{array}

$\Large\overbrace{a,...,a}^{\text{k a^,s}}, \underbrace{b,...,b}_{\text{l b^,s}}\hspace{10} \large\underbrace{\overbrace{a...a}^{\text{k a^,s}}, \overbrace{b...b}^{\text{l b^,s}}}_{\text{k+l elements}}$

\Large\overbrace{a,...,a}^{\text{k a^,s}}, \underbrace{b,...,b}_{\text{l b^,s}}\hspace{10} \large\underbrace{\overbrace{a...a}^{\text{k a^,s}}, \overbrace{b...b}^{\text{l b^,s}}}_{\text{k+l elements}}

@@ 32번째 줄: / 32번째 줄: @@
 * http://en.wikibooks.org/wiki/LaTeX
+===모르는 명령어 그림으로 알아내기===
-==모르는 명령어 그림으로 알아내기==
 * [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
 ==LaTeX으로 노트하기==
 * [http://math.berkeley.edu/%7Eanton/index.php?m1=me&m2=TeXadvice Advice on realtime TeXing]
 * 한글 TeX http://ajt.ktug.kr/2007/0102khlee.pdf
-==LaTeX 명령예1==
+==LaTeX 명령예==
-* <math>\chi(t)=\left(\frac{t}{p}\right)</math>
+===cases===
-* <math>\operatorname{Re} a > 0 </math>
-* <math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>
-* <math>e^{i \pi} +1 = 0</math>
-* <math>2\pi-3\times\frac{3\pi}{5}=\frac{\pi}{5}</math>
-* <math>\frac{\sqrt{3}}{5}</math>
-* <math>720\div12=60</math>
-* <math>\large f^\prime(x)\ =         \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}</math>
-* <math>\Large A\ =\ \large\left(         \begin{array}{c.cccc}&1&2&\cdots&n\\      1&a_{11}&a_{12}&\cdots&a_{1n}\\         2&a_{21}&a_{22}&\cdots&a_{2n}\\         \vdots&\vdots&\vdots&\ddots&\vdots\\         n&a_{n1}&a_{n2}&\cdots&a_{nn}\end{array}\right)</math>
-$$ \LARGE\tilde y=\left\{  {\ddot x\text{ if $\vec x$ odd}\atop\hat{\,\bar x+1}\text{ if even}}\right.$$
-$$\Large\left.\begin{eqnarray}    x+y+z&=&3\\2y&=&x+z\\2x+y&=&z\end{eqnarray}\right\}$$
-* <math>\int e^{-\frac{x^2}{2}} dx</math>
-$$ \int e^{-\frac{x^2}{2}} dx$$
-$$e^x=\lim_{n\to\infty} \left(1+\frac{x}{n}\right)^n$$
-$\sum_{k=1}^{\infty}\frac{1}{k^2}=\frac{\pi^2}{6}$
-$\int_{a}^{b}f(x)dx=F(b)-F(a)$
-$\exists c \in (a,b) \quad \mathbf{s.t.} \quad f'(c)=\frac{f(b)-f(a)}{b-a}$
-==LaTeX 명령예2==
-'''cases'''
 $$
 f(n) =
@@ 91번째 줄: / 51번째 줄: @@
 \end{cases}
 $$
+====atop====
+$$\tilde y=\left\{  {\ddot x\text{ if $\vec x$ odd}\atop\hat{\,\bar x+1}\text{ if even}}\right.$$
-'''연립방정식'''
+===array===
 $$ \left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array} \right. $$
+$$ \begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \\ \end{array} $$
+:<math>A=\left(         \begin{array}{c.cccc}&1&2&\cdots&n\\      1&a_{11}&a_{12}&\cdots&a_{1n}\\         2&a_{21}&a_{22}&\cdots&a_{2n}\\         \vdots&\vdots&\vdots&\ddots&\vdots\\         n&a_{n1}&a_{n2}&\cdots&a_{nn}\end{array}\right)</math>
-'''array'''
-$$ \begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \\ \end{array} $$
+===eqnarray===
+$$\left.\begin{eqnarray}    x+y+z&=&3\\2y&=&x+z\\2x+y&=&z\end{eqnarray}\right\}$$
-'''align'''
+===align===
 :<math>
 \begin{align}
@@ 129번째 줄: / 95번째 줄: @@
-'''underbrace'''
+===underbrace===
 :<math>\underbrace{i \hbar \frac{\partial}{\partial t} |\varphi_\pm\rangle = \left( \frac{( \mathbf{p} -e \mathbf A)^2}{2 m} + e \phi \right) \hat 1 \mathbf |\varphi_\pm\rangle }_\mathrm{Schr\ddot{o}dinger~equation} - \underbrace{\frac{e \hbar}{2m}\mathbf{\sigma} \cdot \mathbf B \mathbf |\varphi_\pm\rangle }_\text{Stern Gerlach term}</math>
 [[파울리 방정식]]
-'''substack'''
+===substack===
 $$
 \sum_{
@@ 143번째 줄: / 109번째 줄: @@
 $$
-==서체==
-$\alpha \beta \gamma \delta \epsilon (\varepsilon) \zeta \eta \theta
+===크기===
+;large
+$$
+\large f^\prime(x)\ =         \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}
+$$
+;Large
+$$
+\Large f^\prime(x)\ =         \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}
+$$
+;LARGE
+$$
+\LARGE f^\prime(x)\ =         \lim_{\Delta x\to0}\frac{f(x+\Delta x)-f(x)}{\Delta x}
+$$
+===그리스 문자===
+$$\alpha \beta \gamma \delta \epsilon (\varepsilon) \zeta \eta \theta
 (\vartheta) \iota \kappa \lambda \mu \nu \xi o \pi \rho \sigma \tau \upsilon
-\phi (\varphi) \chi \psi \omega$.
+\phi (\varphi) \chi \psi \omega$$
-$A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon
+$$A B \Gamma \Delta E Z H \Theta I K \Lambda M N \Xi O \Pi P \Sigma T \Upsilon
-\Phi X \Psi \Omega$.
+\Phi X \Psi \Omega$$
+===글꼴===
 $$\text{mathcal }\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$
 $$\text{mathscr }\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$
@@ 159번째 줄: / 142번째 줄: @@
 $$\text{mathfrak }\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}$$
 $$\text{mathfrak }\mathfrak{abcdefghijklmnopqrstuvwxyz}$$
+===기타===
+* <math>\chi(t)=\left(\frac{t}{p}\right)</math>
+* <math>\operatorname{Re} a > 0 </math>
+* <math>x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}</math>
+* <math>720\div12=60</math>
+* $\exists c \in (a,b) \quad \mathbf{s.t.} \quad f'(c)=\frac{f(b)-f(a)}{b-a}$
+* <math>\mathcal{H}om</math>
+* <math>G\"odel</math> http://www.phil.cam.ac.uk/teaching_staff/Smith/LaTeX/other-macros/godelcorners.html
+* <math>\Large\begin{array}{rccclBCB}    &f&\longr[75]^{\alpha:{\normalsize f\rightar~g}}&g\\    \large\gamma&\longd[50]&&\longd[50]&\large\gamma\\    &u&\longr[75]_\beta&v\end{array}</math>
+# \Large\begin{array}{rccclBCB}    &f&\longr[75]^{\alpha:{\normalsize f\rightar~g}}&g\\    \large\gamma&\longd[50]&&\longd[50]&\large\gamma\\    &u&\longr[75]_\beta&v\end{array}
+* <math>\Large\overbrace{a,...,a}^{\text{k a^,s}},    \underbrace{b,...,b}_{\text{l b^,s}}\hspace{10}    \large\underbrace{\overbrace{a...a}^{\text{k a^,s}},    \overbrace{b...b}^{\text{l b^,s}}}_{\text{k+l elements}}</math>
+# \Large\overbrace{a,...,a}^{\text{k a^,s}},    \underbrace{b,...,b}_{\text{l b^,s}}\hspace{10}    \large\underbrace{\overbrace{a...a}^{\text{k a^,s}},    \overbrace{b...b}^{\text{l b^,s}}}_{\text{k+l elements}}
 == 관련된 항목들 ==
@@ 166번째 줄: / 165번째 줄: @@
 * [[행렬과 연립방정식의 수식표현]]
 * [[화살표 모음]]
-==예==
-<math>\mathcal{H}om</math>
-<math>G\"odel</math>
-http://www.phil.cam.ac.uk/teaching_staff/Smith/LaTeX/other-macros/godelcorners.html
-* <math>\Large\begin{array}{rccclBCB}    &f&\longr[75]^{\alpha:{\normalsize f\rightar~g}}&g\\    \large\gamma&\longd[50]&&\longd[50]&\large\gamma\\    &u&\longr[75]_\beta&v\end{array}</math>
-# \Large\begin{array}{rccclBCB}    &f&\longr[75]^{\alpha:{\normalsize f\rightar~g}}&g\\    \large\gamma&\longd[50]&&\longd[50]&\large\gamma\\    &u&\longr[75]_\beta&v\end{array}
-* <math>\Large\overbrace{a,...,a}^{\text{k a^,s}},    \underbrace{b,...,b}_{\text{l b^,s}}\hspace{10}    \large\underbrace{\overbrace{a...a}^{\text{k a^,s}},    \overbrace{b...b}^{\text{l b^,s}}}_{\text{k+l elements}}</math>
-# \Large\overbrace{a,...,a}^{\text{k a^,s}},    \underbrace{b,...,b}_{\text{l b^,s}}\hspace{10}    \large\underbrace{\overbrace{a...a}^{\text{k a^,s}},    \overbrace{b...b}^{\text{l b^,s}}}_{\text{k+l elements}}
 [[분류:수식표현]]