再帰的な TeX マクロ\formula(内部制御シーケンスでローカル カウンターを進める) があり、これを展開してタイプセットすると、すべてのニーズを満たす式 (たとえば、dvi 出力の f(x) のような式) が出力されるとします。
このタイプセットされた数式を、別のマクロの「逐語的」テキストの置き換えとして使用できる文字列として返すにはどうすればよいでしょうか\def\secondformula{f(x)}。
ここで、MWEとして、再帰を通して任意の次数の第一種ベッセル関数を定義する式の定義を示します。
\newcount\BesselOrder
\newcount\BesselOrderMinusOne
\def\BesselZERO{besj0(x)}
\def\BesselONE{besj1(x)}
\def\Recursion{%
\advance\BesselOrder by -1
\advance\BesselOrderMinusOne by -1
((2 * \the\BesselOrder / x) * {\BesselJ{\the\BesselOrder}} - \BesselJ{\the\BesselOrderMinusOne})
}
\def\BesselJ#1{%
\BesselOrder=#1%
\BesselOrderMinusOne = \BesselOrder%
\advance\BesselOrderMinusOne by -1%
\ifnum\BesselOrder = 0
\let\next=\BesselZERO
\fi
\ifnum\BesselOrder = 1
\let\next = \BesselONE
\fi
\ifnum\BesselOrder > 1
\let\next = \Recursion
\fi
\next
}
答え1
% This is to be compiled with e-TeX. (Not TeX and also not LaTeX.)
\overfullrule=0pt
\parindent=0ex
\parskip=\baselineskip
\begingroup\catcode`\%=12 \lowercase{\endgroup\def\percentchar{%}}%
% Pete's bessel-routine:
% ======================
\newcount\BesselOrder
\newcount\BesselOrderMinusOne
\def\BesselZERO{besj0(x)}
\def\BesselONE{besj1(x)}
\def\Recursion{%
\advance\BesselOrder by -1
\advance\BesselOrderMinusOne by -1
((2 * \the\BesselOrder/ x) * {\BesselJ{\the\BesselOrder}} - \BesselJ{\the\BesselOrderMinusOne})
}
\def\BesselJ#1{%
\BesselOrder=#1%
\BesselOrderMinusOne = \BesselOrder%
\advance\BesselOrderMinusOne by -1%
\ifnum\BesselOrder = 0
\let\next=\BesselZERO
\fi
\ifnum\BesselOrder = 1
\let\next = \BesselONE
\fi
\ifnum\BesselOrder > 1
\let\next = \Recursion
\fi
\next
}
% Ulrich's bessel-routine:
% ========================
%
% The routine doesn't need temporary assignments and the like and is based
% on expansion only.
%
% !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
% !!!! Due to the \numexpr-thingie e-TeX-extensions are required. !!!!
% !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
%
% The routine as a trick for triggering expansion uses \romannumeral-expansion:
% When due to \romannumeral (La)TeX does gather together a sequence of digits
% trailed by a space as the number which it has to convert, expandable tokens
% get expanded.
% When in the end a number is gathered together which is not positive, as the result
% of the conversion (La)TeX will not deliver any token at all.
% Thus one can nicely (ab)use \romannumeral for triggering a lot of
% expansion-work and flipping-arguments-around-work as long as one ensures
% that in the end \romannumeral will not find a positive number.
%
% Due to \romannumeral-expansion \UDBesselJ will deliver the result in
% two expansion-steps/after "being hit" by two \expandafter .
%
% !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
% !!! \UDBesselJ will take its toll at the semantic nest and at the input-stack. !!!
% !!! !!!
% !!! Don't use it with all too large values in the argument. !!!
% !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
\long\def\exchange#1#2{#2#1}%
\long\def\passfirsttosecond#1#2{#2{#1}}%
\long\def\firstoftwo#1#2{#1}%
\long\def\secondoftwo#1#2{#2}%
\def\romannumeralstop{ }%
\def\UDBesselJ#1{%
\romannumeral0%
\ifnum#1 = 0 \expandafter\firstoftwo\else\expandafter\secondoftwo\fi
{\romannumeralstop besj0(x)}{%
\ifnum#1 = 1 \expandafter\firstoftwo\else\expandafter\secondoftwo\fi
{\romannumeralstop besj1(x)}{%
\ifnum#1 > 1 \expandafter\firstoftwo\else\expandafter\secondoftwo\fi
{%
\expandafter\exchange\expandafter{%
\romannumeral0%
\exchange{ }{\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter}%
\expandafter\UDBesselJ\expandafter{\the\numexpr#1-2\relax}) %
}{%
\expandafter\passfirsttosecond\expandafter{%
\romannumeral0%
\exchange{ }{\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter\expandafter}%
\expandafter\UDBesselJ\expandafter{\the\numexpr#1-1\relax}%
}%
{\expandafter\exchange\expandafter{\the\numexpr#1-1\relax}{\romannumeralstop((2 * }/ x) * } - %
}%
}{\romannumeralstop}%
}%
}%
}%
% Testing the routines:
% =====================
{\tt\string\BesselJ\string{4\string}} yields:\hfil\break
\BesselJ{4}
\hbox to\hsize{\null\hrulefill\null}\nointerlineskip
{\tt\string\UDBesselJ\string{4\string}} yields:\hfil\break
\UDBesselJ{4}
\hbox to\hsize{\null\hrulefill\null}\nointerlineskip
{\tt\string\expandafter\string\expandafter\string\expandafter\string\def\hfil\break
\string\expandafter\string\expandafter\string\expandafter\string\secondformula\hfil\break
\string\expandafter\string\expandafter\string\expandafter\string{\percentchar\hfil\break
\string\UDBesselJ\string{4\string}\string}}
yields the macro
\expandafter\expandafter\expandafter\def
\expandafter\expandafter\expandafter\secondformula
\expandafter\expandafter\expandafter{%
\UDBesselJ{4}}%
{\tt\string\secondformula:}
{\tt\meaning\secondformula}
\hbox to\hsize{\null\hrulefill\null}\nointerlineskip
{\tt\string\secondformula} yields:\hfil\break
\secondformula
\bye
