将类似 C 的数学表达式转换为 LaTeX

Question

（我重写了代码，使其由三个独立的文件组成：生成屏幕截图的驱动程序 tex 文件；设置主用户宏的样式文件（由驱动程序文件加载），称为\prettymath；以及执行实际工作的 lua 文件（通过dofile指令从样式文件加载）。）

以下基于 LuaLaTeX 的解决方案不应被视为成熟的工具。目前，它主要是为了展示 Lua 的一些字符串函数在解决手头问题方面的实用性和多功能性。

它处理**指数符号，删除单个实例，将选定的小写希腊字母（例如和）*的罗马字母表示转换为其“原生”希腊字符字形，并以漂亮的方式打印积分表达式、选定的三字母 mathop 函数（、、和——扩展此列表应该很简单）以及平方根和分数。它可以处理嵌套分数和平方根。当然，这个列表远非完整。希望下面显示的代码是相当不言自明的，这样（我希望）处理其他情况不会太难。alphapisincostandet

驱动文件：

% !TeX program = lualatex
% Test file to check out operation of 'cmath2latex' package
\documentclass{article}
\usepackage{cmath2latex} 

% set up three test strings
\newcommand\mystringa{sqrt(3**(x)*(a*sin(exp(theta)) 
  *cos(2*pi)) / (det (A)*tan(gamma)) ) }
\newcommand\mystringb{3*c/(a+2), 1/pi, pi/2, 2*pi/3, a/b, 
  x/(y+z), (x+y)/z, (a/b)/(c/d)}
\newcommand\mystringc{sqrt( sqrt(sqrt(256))), Integral 
  (sqrt((2**(y))/(y)) , y )}

\begin{document}
\everymath{\displaystyle} % just for this example

\verb&sqrt(3**(x)*(a*sin(exp(theta))*cos(2*pi)) / (det (A)*tan(gamma)) )&

\prettymath{\mystringa}

\bigskip
\verb&3*c/(a+2), 1/pi, pi/2, 2*pi/3, a/b, x/(y+z), (x+y)/z, (a/b)/(c/d)&

\prettymath{\mystringb}

\bigskip
\verb&sqrt( sqrt(sqrt(256))), Integral (sqrt((2**(y))/y) , y )&

\prettymath{\mystringc}
\end{document}

样式文件；我建议你将其命名为cmath2latex.sty：

% !TeX program = lualatex
\ProvidesPackage{cmath2latex}[2017/01/09, version 0.01]

\usepackage{luacode} % for "\luastring" macro
\usepackage{amsmath} % for "\ensuremath" macro

%% Load the Lua code
\directlua{dofile("cmath2latex.lua")} 

%% The LaTeX macro "\prettymath" calls the Lua function
%% "prettymath" and outputs the result in math mode
\newcommand\prettymath[1]{\ensuremath{\directlua{%
    tex.sprint(prettymath(\luastring{#1}))}}}

包含 Lua 代码的文件；我建议您将其命名为“cmath2latex.lua”：

-- cmath2latex.lua
-- This file is loaded by cmath2latex.sty via a dofile call

-- "prettymath" is called by the "\prettymath" LaTeX macro
-- (which is defined in "prettymath.sty")

function prettymath ( s )

-- exponential notation
  s = s:gsub ( "%*%*%s-(%b())" , do_exp )

-- multiplication: delete all single instances of "*"
  s = s:gsub ( "%*" , "" )

-- integrals
  s = s:gsub ( "Integral%s-(%b())", do_integral )

-- some Greek letters
  s = s:gsub ( "alpha" , do_gr_letter )
  s = s:gsub ( "beta"  , do_gr_letter )
  s = s:gsub ( "gamma" , do_gr_letter )
  s = s:gsub ( "Gamma" , do_gr_letter )
  s = s:gsub ( "delta" , do_gr_letter )
  s = s:gsub ( "Delta" , do_gr_letter )
  s = s:gsub ( "theta" , do_gr_letter )
  s = s:gsub ( "pi"    , do_gr_letter )
  s = s:gsub ( "Pi"    , do_gr_letter )

-- some pre-defined 3-letter operators w/ args in parens
  s = s:gsub ( "(cos)%s-(%b())" , do_mathop )
  s = s:gsub ( "(det)%s-(%b())" , do_mathop )
  s = s:gsub ( "(exp)%s-(%b())" , do_mathop )
  s = s:gsub ( "(lim)%s-(%b())" , do_mathop )
  s = s:gsub ( "(sin)%s-(%b())" , do_mathop )
  s = s:gsub ( "(tan)%s-(%b())" , do_mathop )

-- sqrt function
  for i=1,3 do  -- allow for nested sqrt expressions
    s = s:gsub ( "sqrt%s-(%b())", do_sqrt )
  end

-- fraction expressions
  s = s:gsub ( "(%b())%s-/%s-(%b())" ,    do_frac_2parens )
  s = s:gsub ( "([\\%w]+)%s-/%s-(%b())" , do_frac_1parens_numer )
  s = s:gsub ( "(%b())%s-/%s-([\\%w]+)" , do_frac_1parens_denom )
  s = s:gsub ( "([\\%w]+)%s-/%s-([\\%w]+)", "\\frac{%1}{%2}" )

-- Feel free to add more string.gsub ops as needed...

-- Return the modified string
return s

end -- end of 'prettymath' function


-- Finally, set up the helper Lua functions

function strip ( x ) -- remove first and last char of string "x"
  return x:sub(2,-2)
end
function do_exp ( u )
  return ( "^{" .. strip(u) .. "}"  )
end
function do_gr_letter ( u )
  return ( "\\"..u )
end
function do_mathop ( u , v )
  return ( "\\" .. u .. v )
end
function do_integral ( u )
  u = strip(u)
  return ( "\\int\\! " ..  u:gsub ( "^(.*),(.*)$" ,
      "%1 \\,\\mathrm{d} %2" ) )
end
function do_sqrt ( u )
  return ( "\\sqrt{" .. strip(u) .. "}" )
end

-- process expressions involving fractions

function do_frac_1parens_numer ( u , v )
  return ( "\\frac{" .. u .. "}{" .. strip(v) .. "}" )
end
function do_frac_1parens_denom ( u , v )
  return ( "\\frac{" .. strip(u) .. "}{" .. v .. "}" )
end
function do_frac_2parens ( u , v )
  return ( "\\frac{" .. strip(u) .. "}{" .. strip(v) .."}" )
end

Answer 1