欧拉分形变例

Question

AMS 的字体系列eufm具有某些小写变体，即 d、f、g、k、t、u，如下表第二行所示。我的问题是：使用 (La)TeX，如何将它们（部分）设为默认？我查看了一些选项或一些编码信息，但目前还没有找到任何东西。

Answer 1

如果你的目的只是访问这些字形，可以按如下方式进行

\documentclass{article}
\usepackage{amsmath}

% from amsfonts.sty
%\DeclareMathAlphabet{\mathfrak}{U}{euf}{m}{n}
%\SetMathAlphabet{\mathfrak}{bold}{U}{euf}{b}{n}
\DeclareSymbolFont{eulerfraktur}{U}{euf}{m}{n}
\SetSymbolFont{eulerfraktur}{bold}{U}{euf}{b}{n}
\DeclareSymbolFontAlphabet{\mathfrak}{eulerfraktur}
\DeclareMathSymbol{\varfrakd}{\mathord}{eulerfraktur}{"00}
\DeclareMathSymbol{\varvarfrakd}{\mathord}{eulerfraktur}{"01}
\DeclareMathSymbol{\varfrakf}{\mathord}{eulerfraktur}{"02}
\DeclareMathSymbol{\varvarfrakf}{\mathord}{eulerfraktur}{"03}
\DeclareMathSymbol{\varfrakg}{\mathord}{eulerfraktur}{"04}
\DeclareMathSymbol{\varfrakk}{\mathord}{eulerfraktur}{"05}
\DeclareMathSymbol{\varfrakt}{\mathord}{eulerfraktur}{"06}
\DeclareMathSymbol{\varfraku}{\mathord}{eulerfraktur}{"07}

\begin{document}

$\mathfrak{d}\ne\varfrakd\ne\varvarfrakd$

$\mathfrak{f}\ne\varfrakf\ne\varvarfrakf$

$\mathfrak{g}+\mathfrak{k}+\mathfrak{t}+\mathfrak{u}$

$\varfrakg+\varfrakk+\varfrakt+\varfraku$

\end{document}

如果你想替换，比如说\mathfrak{f}用\varfrakf，那就有点复杂了。我将为所有\var（不是\varvar）添加替换：

\documentclass{article}
\usepackage{amsmath}

% from amsfonts.sty
%\DeclareMathAlphabet{\mathfrak}{U}{euf}{m}{n}
%\SetMathAlphabet{\mathfrak}{bold}{U}{euf}{b}{n}
\DeclareSymbolFont{eulerfraktur}{U}{euf}{m}{n}
\SetSymbolFont{eulerfraktur}{bold}{U}{euf}{b}{n}
\DeclareSymbolFontAlphabet{\usemathfrak}{eulerfraktur}
\DeclareMathSymbol{\varfrakd}{\mathord}{eulerfraktur}{"00}
\DeclareMathSymbol{\varvarfrakd}{\mathord}{eulerfraktur}{"01}
\DeclareMathSymbol{\varfrakf}{\mathord}{eulerfraktur}{"02}
\DeclareMathSymbol{\varvarfrakf}{\mathord}{eulerfraktur}{"03}
\DeclareMathSymbol{\varfrakg}{\mathord}{eulerfraktur}{"04}
\DeclareMathSymbol{\varfrakk}{\mathord}{eulerfraktur}{"05}
\DeclareMathSymbol{\varfrakt}{\mathord}{eulerfraktur}{"06}
\DeclareMathSymbol{\varfraku}{\mathord}{eulerfraktur}{"07}

\ExplSyntaxOn
\NewDocumentCommand{\mathfrak}{m}
 {
  \tl_set:Nn \l_tmpa_tl { #1 }
  \regex_replace_all:nnN { ([dfgktu]) } { \c{varfrak\1} } \l_tmpa_tl
  \usemathfrak{\l_tmpa_tl}
 }
\ExplSyntaxOff


\begin{document}

$\mathfrak{dfgktu}$

$\usemathfrak{dfgktu}$ % for comparison

\end{document}

您仍可以使用原版\usemathfrak。

如果您想使用，只需删除下面\varvarfrakf的定义\varfrakf和一个。var