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更加灵活的衍生宏？

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更加灵活的衍生宏？

我正在尝试扩展给出的宏 我可以有一个灵活的偏导数宏吗？ 具体来说，我想添加一个带星号的版本，它不会尝试对各种导数的指数求和，如果指数不是数字，这将很有用。我的尝试如下所示，但我没有取得太大进展。我希望命令的工作方式显示在第二个显示的数学环境中。理想情况下，我只有一个命令，它的行为将如第三个显示的数学环境中所示，但这似乎过于雄心勃勃。

\documentclass[12pt]{article}

\makeatletter
\newcommand\derivative[2]
{
    \begingroup
        \@temptokena{\@gobble}
        \@tempcnta\z@
        \@for\var:=#2\do
        {
            \expandafter\@derivative\var\relax
        }
        \frac
        {
            d
                \ifnum \@tempcnta > \@ne
                    ^{\the\@tempcnta}
                \fi
            #1
        }
        {\the\@temptokena}
    \endgroup
}
\def\@derivative#1#2\relax
{
    \ifx\relax#2\relax
        \advance\@tempcnta by \@ne
        \@temptokena\expandafter{\the\@temptokena \, d #1}
    \else
        \advance\@tempcnta by #2\relax
        \@temptokena\expandafter{\the\@temptokena \, d #1^{#2}}
    \fi
}
\makeatother

\makeatletter
\newcommand\derivativestar[2]
{
    \begingroup
        \@temptokena{\@gobble}
        \@temptokenb{}
        \@for\var:=#2\do
        {
            \expandafter\@derivativestar\var\relax
        }
        \frac
        {
            d^{\@temptokenb} #1
        }
        {\the\@temptokena}
    \endgroup
}
\def\@derivativestar#1#2\relax
{
    % need to test for first token
    \ifx\relax#2\relax
        \@temptokena\expandafter{\the\@temptokena \, d #1}
        \@temptokenb\expandafter{\the\@temptokenb + 1}
    \else
        \@temptokena\expandafter{\the\@temptokena \, d #1^{#2}}
        \@temptokenb\expandafter{\the\@temptokenb + #2}
    \fi
}
\makeatother

\begin{document}

\[
    \derivative{x}{{y}{2},{z}{3}}
\]

\[
    % \derivative*{x}{{y}{m},{z}{n}}
    \frac{d x^{m+n}}{d y^{m} \, d z^{n}}
\]

\[
    % \derivative{x}{{v}{3},{w}{k,2},y,{z}{m}}
    \frac{d x^{k+m+6}}{d v^{3} \, d w^{k+2} \, d y \, d z^{m}}
\]

\end{document}

答案1

从描述来看，您想要的是自动检测非数字输入。这意味着您不需要\derivative*但可以将决定权留给代码。稳健性可能是一个问题：在下面，我假设每个索引都有一个标记（可以解决）。正如您在“传统”LaTeX 中编码的那样，我尽可能坚持相同的方法：

\documentclass[12pt]{article}
\makeatletter
\newcommand{\ifintegerTF}[1]{%
  \ifnum`#1<`0 %
    \expandafter\@secondoftwo
  \else
    \ifnum`#1>`9 %
      \expandafter\expandafter\expandafter\@secondoftwo
    \else
      \expandafter\expandafter\expandafter\@firstoftwo
    \fi  
  \fi
}
\newcommand{\derivative}[2]{%
  \begingroup
    \toks@{}%
    \@temptokena{}%
    \@tempcnta\z@
    \@tempswatrue
    \@for\@tempa:=#2\do{%
      \expandafter\derivative@aux@i\@tempa\stop
    }%
    \frac
      {%
        d%
        \if@tempswa
          \ifnum\@tempcnta>\@ne
            ^{\number\@tempcnta}%
          \fi
          #1%  
        \else
          #1%
          \ifnum\@tempcnta>\z@
            \toks@\expandafter\expandafter\expandafter
              {\expandafter\the\expandafter\toks@ \expandafter + \the\@tempcnta}%
          \fi
          ^{\expandafter\@gobble\the\toks@}%
        \fi
      }
      {\the\@temptokena}
  \endgroup
}
\newcommand{\derivative@aux}{}
\long\def\derivative@aux@i#1#2\stop{%
  \@temptokena\expandafter{\the\@temptokena \, d#1}%
  \ifx\\#2\\
    \advance\@tempcnta\@ne
  \else
    \def\@tempb{\@gobble}%
    \@for\@tempa:=#2\do{%
      \expandafter\derivative@aux@ii\@tempa{#1}%
    }%
   \@temptokena\expandafter\expandafter\expandafter
    {\expandafter\the\expandafter\@temptokena\expandafter^\expandafter{\@tempb}}% 
  \fi
}
\newcommand{\derivative@aux@ii}[2]{%
  \ifintegerTF{#1}
    {\advance\@tempcnta#1 }%
    {%
      \toks@\expandafter{\the\toks@ + #1}%
      \@tempswafalse
    }% 
  \protected@edef\@tempb{\@tempb + #1}%
}


\begin{document}

\[
    \derivative{x}{{y}{2},{z}{3}}
\]

\[
    \derivative{x}{{y}{m},{z}{n}}
\]

\[
    \derivative{x}{{v}{3},{w}{k,2},y,{z}{m}}
\]

\end{document}

关键思想是设置一个标志来指示存在非数字索引值，然后使用该标志确定如何构造输出。

（如果有兴趣，我认为 LaTeX3 版本会更具可读性：我们在那里没有整数测试，但各种扩展问题会更容易解决。）

答案2

我认为 LuaTeX 非常适合这类任务。这是 ConTeXt 中的概念验证解决方案（要转换为 LuaLaTeX，您还需要移植utilities.parsers.settings_to_array函数；请参阅util-prs.luaConTeXt 树中的文件以了解此功能的实现细节）

\startluacode
  thirddata = thirddata or {}
  -- The pairs() iterator in lua does not guarantee the order in which 
  -- keys are accessed. So, instead of directly using settings_to_list
  -- I use a roundabout iterator.
  local settings_to_array = utilities.parsers.settings_to_array

  local format = string.format
  local split  = string.split

  function thirddata.partialD(settings)
      local list = settings_to_array(settings)

      local sum = 0
      local num = {}
      local den = {}

      for i = 1, #list do
         local s = split(list[i], "=")
         local key, value = s[1], s[2]

         local n = tonumber(value)

         if n ~= nil then
            sum = sum + n
         else
            num[#num + 1] = value
         end

         den[i] = format("\\partial %s^{%s}", key, value)
      end


      num[#num + 1] = sum
      num = table.concat(num, "+")
      den = table.concat(den)

      num  = format("\\partial^{%s}", num)


      context.dfrac( num, den)
  end
\stopluacode

\def\partialD%
  {\dosingleargument\dopartialD}

\unprotected\def\dopartialD[#1]{\ctxlua{thirddata.partialD(\!!bs#1\!!es)}}

\enablemode[lmmath]

\starttext
\startTEXpage[offset=3mm]
$\partialD[u=m, x=1, y=2, z=n]$
\stopTEXpage
\stoptext

这使

在此处输入图片描述

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