재귀 TeX 매크로 \formula(로컬 카운터를 발전시키는 내부 제어 시퀀스 포함)가 있다고 가정해 보겠습니다. 이 매크로는 일단 확장되고 입력되면 모든 요구 사항을 충족하는 표현식을 출력합니다. 예를 들어 f(x)(dvi 출력에서)와 같은 표현식이 있습니다.
이 조판된 수식을 다른 매크로의 대체 "축어적" 텍스트로 사용할 수 있는 반환 문자열로 다시 가져오는 방법은 무엇입니까 \def\secondformula{f(x)}?
다음은 MWE로서 재귀를 통해 모든 차수의 첫 번째 종류의 베셀 함수를 정의하는 수식의 정의입니다.
\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
}
답변1
% 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
