Python正则表达式可简化LaTex分数 [英] Python Regex to Simplify LaTex Fractions
问题描述
这是我的python程序:
This is my python program:
def fractionSimplifier(content):
content.replace('\\dfrac','\\frac')
pat = re.compile('\\frac\{(.*?)\}\{\\frac\{(.*?)\}\{(.*?)\}\}')
match = pat.match(content)
expr = ""
if match:
expr = '\\frac{{{0}*{2}}}{{{1}}}'.format(*match.group())
#print expr
return expr
这是应该编辑的LaTex代码.
This is the LaTex code that should be edited.
%Jacobi
\begin{equation}
\sum_{\ell\hiderel{=}0}^n\frac{(\JacobiP{\alpha}{\beta}{\ell}@{x})^2}{\mathcal{A}_\ell}=\frac{\frac{\pochhammer{n+\alpha+\beta+1}{n}}{2^nn!}}{\mathcal{A}_n\frac{\pochhammer{n+1+\alpha+\beta+1}{n+1}}{2^n+1n+1!}}\frac{\JacobiP{\alpha}{\beta}{n+1}@{x}\JacobiP{\alpha}{\beta}{n}@{y}-\JacobiP{\alpha}{\beta}{n}@{x}\JacobiP{\alpha}{\beta}{n+1}@{y}}{x-y}
\end{equation}
%Ultraspherical(Gegenbauer)
\begin{equation}
\sum_{\ell\hiderel{=}0}^n\frac{(\Ultraspherical{\lambda}{\ell}@{x})^2}{\frac{2^{1-2\lambda}\pi\EulerGamma@{\ell+2\lambda}}{(\ell+\lambda)\left(\EulerGamma@{\lambda}\right)^2\ell!}}=\frac{\frac{2^n\pochhammer{\lambda}{n}}{n!}}{\frac{2^{1-2\lambda}\pi\EulerGamma@{n+2\lambda}}{(n+\lambda)\left(\EulerGamma@{\lambda}\right)^2n!}\frac{2^n+1\pochhammer{\lambda}{n+1}}{n+1!}}\frac{\Ultraspherical{\lambda}{n+1}@{x}\Ultraspherical{\lambda}{n}@{y}-\Ultraspherical{\lambda}{n}@{x}\Ultraspherical{\lambda}{n+1}@{y}}{x-y}
\end{equation}
%Chebyshevoffirstkind
\begin{equation}
\sum_{\ell\hiderel{=}0}^n\frac{(\ChebyT{\ell}@{x})^2}{\frac{\cpi}{\epsilon_\ell}}=\frac{\frac{2^n}{\epsilon_n}}{\frac{\cpi}{\epsilon_n}\frac{2^n+1}{\epsilon+1_n+1}}\frac{\ChebyT{n+1}@{x}\ChebyT{n}@{y}-\ChebyT{n}@{x}\ChebyT{n+1}@{y}}{x-y}
\end{equation}
%Chebyshevofsecondkind
\begin{equation}
\sum_{\ell\hiderel{=}0}^n\frac{(\ChebyU{\ell}@{x})^2}{\frac{\pi}{2}}=\frac{2^n}{\frac{\pi}{2}2^n+1}\frac{\ChebyU{n+1}@{x}\ChebyU{n}@{y}-\ChebyU{n}@{x}\ChebyU{n+1}@{y}}{x-y}
\end{equation}
%Chebyshevofthirdkind
\begin{equation}
\sum_{\ell\hiderel{=}0}^n\frac{(\ChebyV{\ell}@{x})^2}{\pi}=\frac{2^n}{\pi2^n+1}\frac{\ChebyV{n+1}@{x}\ChebyV{n}@{y}-\ChebyV{n}@{x}\ChebyV{n+1}@{y}}{x-y}
\end{equation}
%Chebyshevoffourthkind
\begin{equation}
\sum_{\ell\hiderel{=}0}^n\frac{(\ChebyW{\ell}@{x})^2}{\pi}=\frac{2^n}{\pi2^n+1}\frac{\ChebyW{n+1}@{x}\ChebyW{n}@{y}-\ChebyW{n}@{x}\ChebyW{n+1}@{y}}{x-y}
\end{equation}
%ShiftedChebyshevoffirstkind
\begin{equation}
\sum_{\ell\hiderel{=}0}^n\frac{(\ChebyTs{\ell}@{x})^2}{\frac{\cpi}{\epsilon_\ell}}=\frac{\frac{2^n}{\epsilon_n}}{\frac{\cpi}{\epsilon_n}\frac{2^n+1}{\epsilon+1_n+1}}\frac{\ChebyTs{n+1}@{x}\ChebyTs{n}@{y}-\ChebyTs{n}@{x}\ChebyTs{n+1}@{y}}{x-y}
\end{equation}
%ShiftedChebyshevofsecondkind
\begin{equation}
\sum_{\ell\hiderel{=}0}^n\frac{(\ChebyUs{\ell}@{x})^2}{\frac{\pi}{8}}=\frac{2^{2n}}{\frac{\pi}{8}2^{2n+1}}\frac{\ChebyUs{n+1}@{x}\ChebyUs{n}@{y}-\ChebyUs{n}@{x}\ChebyUs{n+1}@{y}}{x-y}
\end{equation}
%Legendre
\begin{equation}
\sum_{\ell\hiderel{=}0}^n\frac{(\LegendrePoly{\ell}@{x})^2}{\frac{2}{(2\ell+1)}}=\frac{\frac{2^n\pochhammer{\frac{1}{2}}{n}}{n!}}{\frac{2}{(2n+1)}\frac{2^n+1\pochhammer{\frac{1}{2}}{n+1}}{n+1!}}\frac{\LegendrePoly{n+1}@{x}\LegendrePoly{n}@{y}-\LegendrePoly{n}@{x}\LegendrePoly{n+1}@{y}}{x-y}
\end{equation}
%ShiftedLegendre
\begin{equation}
\sum_{\ell\hiderel{=}0}^n\frac{(\LegendrePolys{\ell}@{x})^2}{\frac{1}{(2\ell+1)}}=\frac{\frac{2^{2n}\pochhammer{\frac{1}{2}}{n}}{n!}}{\frac{1}{(2n+1)}\frac{2^{2n+1}\pochhammer{\frac{1}{2}}{n+1}}{n+1!}}\frac{\LegendrePolys{n+1}@{x}\LegendrePolys{n}@{y}-\LegendrePolys{n}@{x}\LegendrePolys{n+1}@{y}}{x-y}
\end{equation}
%Laguerre
\begin{equation}
\sum_{\ell\hiderel{=}0}^n\frac{(\LaguerreL[\alpha]{\ell}@{x})^2}{\frac{\EulerGamma@{\ell+\alpha+1}}{\ell!}}=\frac{\frac{\opminus^n}{n!}}{\frac{\EulerGamma@{n+\alpha+1}}{n!}\frac{\opmin+1us^n+1}{n+1!}}\frac{\LaguerreL[\alpha]{n+1}@{x}\LaguerreL[\alpha]{n}@{y}-\LaguerreL[\alpha]{n}@{x}\LaguerreL[\alpha]{n+1}@{y}}{x-y}
\end{equation}
%Hermite
\begin{equation}
\sum_{\ell\hiderel{=}0}^n\frac{(\HermiteH{\ell}@{x})^2}{\pi^{\frac{1}{2}}2^\ell\ell!}=\frac{2^n}{\pi^{\frac{1}{2}}2^nn!2^n+1}\frac{\HermiteH{n+1}@{x}\HermiteH{n}@{y}-\HermiteH{n}@{x}\HermiteH{n+1}@{y}}{x-y}
\end{equation}
%Hermite
\begin{equation}
\sum_{\ell\hiderel{=}0}^n\frac{(\HermiteHe{\ell}@{x})^2}{(2\pi)^{\frac{1}{2}}\ell!}=\frac{1}{(2\pi)^{\frac{1}{2}}n!1}\frac{\HermiteHe{n+1}@{x}\HermiteHe{n}@{y}-\HermiteHe{n}@{x}\HermiteHe{n+1}@{y}}{x-y}
\end{equation}
\ frac {(\ ChebyU {\ ell} @ {x})^ 2} * {\ frac {\ pi} {2}} 是我要寻找的特定部分第二类切比雪夫案.由于它是另一个分数的分母，因此我想使用Python正则表达式将其从 a/(b/c)更改为(ac)/b .
\frac{(\ChebyU{\ell}@{x})^2}*{\frac{\pi}{2}} is the fraction I am looking at for the specific case of Chebyshev of Second Kind. Since it is a fraction in the denominator of another fraction I would like to use Python regex to change this from a/(b/c) to (ac)/b.
示例输出:
%Chebyshev of second kind
\begin{equation}
\sum_{\ell \hiderel{=} 0}^n\frac{(2 \ChebyU{\ell}@{x} )^2}{\pi}*=\frac{ 2^n }{ \frac{\pi}{2} 2^n+1 }\frac{ \ChebyU{n+1}@{x} \ChebyU{n}@{y} - \ChebyU{n}@{x} \ChebyU{n+1}@{y} }{x-y}
\end{equation}
我的目标是对所有不同的积分执行此操作.我的python程序目前根本不更改代码，不胜感激！谢谢.
My goal is to do this for all the different integrals. My python program currently does not change the code at all, any help is appreciated! Thank you.
推荐答案
此处有一些问题.
-
pat.match在re.compile命令中，您可以转义{}，这是不必要的，并且转义的反斜杠也不够.如所写，字符串引号内的\\ f被理解为\ f，然后被re库理解为控制字符.要么放四个反斜杠\\\\ f，或者最好使用原始字符串输入(在此处解释):In
re.compilecommand you escape{}which is unnecessary, and do not escape backslashes enough. As written,\\finside string quotes is understood as\f, which then is understood as a control character by re library. Either put four backslashes\\\\for, better, use raw string input (explained here):re.compile(r'\\frac{(.*?)}{\\frac{(.*?)}{(.*?)}}')-
.format(* match.group())应该是.format(* match.groups())
在进行了上述更改之后，它有些起作用:您的第二种切比雪夫"示例的输出为
With the above changes, it works somewhat: the output for your "Chebyshev of second kind" example is
\frac{(\ChebyU{\ell}@{x})^2*2}{\pi}按预期.
其他说明:
- 您的代码目前无法处理多个匹配项
- 您没有代码将expr替换为原始字符串来代替比赛
- 在LaTeX中，不是使用星号，而是使用
\ cdot - 使用正则表达式解析复杂的数学公式通常不是一个好主意.
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