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+% \iffalse
+%
+%% File `euler.dtx'.
+%% Copyright (C) 1992 Frank Jensen. All rights reserved.
+%% Copyright (C) 1993--1995 Frank Jensen and Frank Mittelbach.
+%% All rights reserved.
+%
+% Please send error reports and suggestions for improvements to:
+%
+% Frank Jensen
+% Aalborg University
+% DK-9220 Aalborg \O
+% Denmark
+% Internet: <fj@iesd.auc.dk>
+%
+% \fi
+
+\def\fileversion{v2.5}
+\def\filedate{1995/03/05}
+
+% \CheckSum{606}
+%% \CharacterTable
+%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
+%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
+%% Digits \0\1\2\3\4\5\6\7\8\9
+%% Exclamation \! Double quote \" Hash (number) \#
+%% Dollar \$ Percent \% Ampersand \&
+%% Acute accent \' Left paren \( Right paren \)
+%% Asterisk \* Plus \+ Comma \,
+%% Minus \- Point \. Solidus \/
+%% Colon \: Semicolon \; Less than \<
+%% Equals \= Greater than \> Question mark \?
+%% Commercial at \@ Left bracket \[ Backslash \\
+%% Right bracket \] Circumflex \^ Underscore \_
+%% Grave accent \` Left brace \{ Vertical bar \|
+%% Right brace \} Tilde \~}
+%
+% \iffalse
+%<*driver>
+\documentclass{ltxdoc}
+\begin{document}
+ \DocInput{euler.dtx}
+\end{document}
+%</driver>
+% \fi
+%
+% \newcommand\beton{\texttt{beton}}
+% \newcommand\euler{\texttt{euler}}
+% \newcommand\MF{Metafont}
+%
+% \title{The \euler\ package}
+% \author{Frank Jensen\thanks{Updates by Frank Mittelbach.}}
+% \date{\filedate}
+%
+% \maketitle
+%
+% \section{Introduction}
+%
+% The \euler\ package provides a setup for using the AMS Euler family
+% of fonts for math in \LaTeX\ documents. The AMS Euler family was
+% designed by Hermann Zapf, commissioned by the American Mathematical
+% Society. ``The underlying philosophy of Zapf's Euler design was to
+% capture the flavor of mathematics as it might be written by a
+% mathematician with excellent handwriting.''~\cite{concrete-tug}
+%
+% The \euler\ package is based on Knuth's macros for the book
+% ``Concrete Mathematics''~\cite{concrete}. Knuth's macros can be
+% found through anonymous ftp to \texttt{labrea.\allowbreak
+% stanford.edu}: look for the file \texttt{gkpmac.tex} in directory
+% \texttt{pub/tex/local/lib}. The Euler fonts can be found through
+% anonymous ftp to \texttt{e-math.ams.org}: look in directory
+% \texttt{pub/tex/amsfonts}.
+%
+% The purpose of the \euler\ package is to provide the math part of
+% the look of~\cite{concrete}. The other part (text fonts) is
+% provided by the \beton\ package. The reason for creating two
+% packages is to make it easy to use the Euler math fonts together
+% with other text fonts (in particular, it appears that the Euler
+% fonts match many of the popular PostScript fonts pretty well).
+%
+% Basically, the \euler\ package provides the same setup (the same
+% definitions, math codes, etc.)\ as \texttt{gkpmac.tex} with respect
+% to the Euler fonts. However, Knuth~\cite{concrete-tug} admits that
+% the macros were written for one specific project, namely to typeset
+% the ``Concrete Mathematics'' book~\cite{concrete}. So, the \euler\
+% package actually does a little more than \texttt{gkpmac.tex}: for
+% example, some `exotic' symbols, present in CM math italic, are
+% missing from the Euler fonts; the \euler\ package takes care of this
+% (whereas \texttt{gkpmac.tex} does not).
+%
+% The use of the \euler\ package requires a lot of care when entering
+% the manuscript, since the package will cause, e.g., math numerals to
+% come from the Euler Roman fonts; these numerals are easily
+% distinguished from the normal text numerals. This implies that
+% sloppy typing is clearly exposed: imagine how
+% ``|$x$ is either 1 or $-1$|'' will appear when typeset! In general,
+% the typist will in each case have to decide whether an input
+% fragment is a math or a non-math entity. This holds true even for
+% the tiniest details, such as punctuation characters (parentheses,
+% colons, semicolons, commas, and periods).
+%
+% Finally, a few words about the technical quality of the fonts (there
+% are no doubts about their artistic quality): The fonts are not tuned
+% for low resolution rendering: I recommend at least 600dpi. The
+% fonts employ none of the tuning machinery of CM: e.g., they do not
+% use the `blacker' parameter specified in each \MF\ mode definition,
+% indicating that they might look somewhat light on printers that
+% normally require a large `blacker' value.
+%
+% \section{What the \euler\ package provides}
+%
+% The \euler\ package defines two new math alphabet identifiers,
+% |\mathscr| (Euler Script, uppercase letters only) and |\mathfrak|
+% (Euler Fraktur, both lowercase and uppercase letters).
+%
+% By default, the original meaning of |\mathcal| is preserved, but if
+% the \euler\ package is loaded with the \texttt{mathcal} option,
+% |\mathcal| will produce Euler Script letters instead of the usual
+% Computer Modern calligraphic letters.
+%
+% Also, by default, the \euler\ package does not redefine the
+% |\mathbf| math alphabet identifier; it will still produce bold CM
+% letters and digits. However, loading the \euler\ package with the
+% \texttt{mathbf} option will cause |\mathbf| to produce bold Euler
+% Roman letters and digits. Another way to get bold symbols is to use
+% the |\boldsymbol| command provided by the \texttt{amsbsy} package
+% (part of AMS-\LaTeX).
+%
+% Some users do not like the |\hat| accent glyph present in the Euler
+% fonts (the \euler\ package uses this accent glyph be default). To
+% use the |\hat| accent glyph from the text font instead, load the
+% \euler\ package with the \texttt{text-hat-accent} option.
+%
+% In \cite{concrete}, the space around relations in displays was
+% increased (from `5mu plus 5mu' to `10mu minus 3mu'). The \euler\
+% package does not change this space, since this is (for most cases)
+% controlled by the \LaTeX\ \texttt{eqnarray} environment. Also,
+% in~\cite{concrete}, displays are left justified with a suitable
+% indentation; we leave such matters to the general layout.
+%
+% \StopEventually {
+% \begin{thebibliography}{1}
+% \bibitem{concrete}
+% \textsc{R. L. Graham}, \textsc{D. E. Knuth}, and
+% \textsc{O. Patashnik}.
+% \newblock \textit{Concrete Mathematics}.
+% \newblock Addison-Wesley, 1989.
+% \bibitem{concrete-tug}
+% \textsc{D. E. Knuth}.
+% \newblock Typesetting Concrete Mathematics.
+% \newblock \textsl{TUGboat} 10(1):31--36, 1989.
+% \end{thebibliography}
+% }
+%
+% \section{Hello world}
+%
+% First, we announce the package.
+% \begin{macrocode}
+%<*package>
+\NeedsTeXFormat{LaTeX2e}[1994/12/01]
+\ProvidesPackage{euler}[\filedate\space\fileversion]
+\typeout{Package: `euler' \fileversion\space <\filedate> (FJ and FMi)}
+% \end{macrocode}
+%
+% \section{Font and other definitions}
+%
+% The AMS Euler family consists of: Euler Roman (medium and bold),
+% Euler Fraktur (medium and bold), Euler Script (medium and bold), and
+% Euler Extension (medium only). The \texttt{.fd} files for these
+% fonts are defined in the \texttt{amsfonts.fdd} file (part of the
+% AMSFonts distribution).
+%
+% \subsection{Euler Roman}
+%
+% The Euler Roman fonts replace the Computer Modern Math Italic fonts,
+% located in the `letters' math symbol font:
+% \begin{macrocode}
+\DeclareSymbolFont{letters}{U}{eur}{m}{n}
+\SetSymbolFont{letters}{bold}{U}{eur}{b}{n}
+% \end{macrocode}
+%
+% In math mode, digits should come from the Euler Roman fonts. As in
+% standard \LaTeX, we assign the type |\mathalpha| to the digits which
+% means that they will vary with math alphabets. One of the reasons
+% for this is that footnote numbers are set in math mode, and we want
+% these numbers to come from the text font; this is accomplished by
+% setting the \TeX\ primitive |\fam| to zero. (See
+% Section~\ref{footnotes} below.)
+% \begin{macrocode}
+\DeclareMathSymbol{0}\mathalpha{letters}{"30}
+\DeclareMathSymbol{1}\mathalpha{letters}{"31}
+\DeclareMathSymbol{2}\mathalpha{letters}{"32}
+\DeclareMathSymbol{3}\mathalpha{letters}{"33}
+\DeclareMathSymbol{4}\mathalpha{letters}{"34}
+\DeclareMathSymbol{5}\mathalpha{letters}{"35}
+\DeclareMathSymbol{6}\mathalpha{letters}{"36}
+\DeclareMathSymbol{7}\mathalpha{letters}{"37}
+\DeclareMathSymbol{8}\mathalpha{letters}{"38}
+\DeclareMathSymbol{9}\mathalpha{letters}{"39}
+% \end{macrocode}
+% The uppercase greek letters are also taken from the Euler Roman
+% fonts. We make them ordinary symbols (i.e., of type |\mathord|) as
+% opposed to \texttt{plain.tex}, \texttt{gkpmac.tex}, and standard
+% \LaTeX, which make them vary according to |\fam|.
+% \begin{macrocode}
+\DeclareMathSymbol\Gamma \mathord{letters}{"00}
+\DeclareMathSymbol\Delta \mathord{letters}{"01}
+\DeclareMathSymbol\Theta \mathord{letters}{"02}
+\DeclareMathSymbol\Lambda \mathord{letters}{"03}
+\DeclareMathSymbol\Xi \mathord{letters}{"04}
+\DeclareMathSymbol\Pi \mathord{letters}{"05}
+\DeclareMathSymbol\Sigma \mathord{letters}{"06}
+\DeclareMathSymbol\Upsilon\mathord{letters}{"07}
+\DeclareMathSymbol\Phi \mathord{letters}{"08}
+\DeclareMathSymbol\Psi \mathord{letters}{"09}
+\DeclareMathSymbol\Omega \mathord{letters}{"0A}
+% \end{macrocode}
+% Euler doesn't have the special variants of |\sigma| and |\rho|:
+% \begin{macrocode}
+\let\varsigma=\sigma
+\let\varrho=\rho
+% \end{macrocode}
+%
+% \begin{macro}{\mathbf}
+% If the \euler\ package is loaded with the \texttt{mathbf}
+% option, |\mathbf| should produce bold Euler Roman letters and
+% digits.
+% \begin{macrocode}
+\DeclareOption{mathbf}
+ {\AtBeginDocument{\DeclareMathAlphabet\mathbf{U}{eur}{b}{n}}}
+% \end{macrocode}
+% \end{macro}
+% Note the use of |\AtBeginDocument|; it ensures that the redefinition
+% overrides the default settings (Section~\ref{text-fonts}).
+%
+% \subsection{Euler Fraktur}
+%
+% \begin{macro}{\mathfrak}
+% The Euler Fraktur fonts get their own math symbol font. We define a
+% math alphabet identifier---|\mathfrak|---to access this symbol font.
+% For compatibility with previous versions of the \euler\
+% package, we define |\frak| as an alias for |\mathfrak| (the
+% \texttt{amsfonts} package also provides this alias).
+% \begin{macrocode}
+\DeclareSymbolFont{EulerFraktur}{U}{euf}{m}{n}
+\SetSymbolFont{EulerFraktur}{bold}{U}{euf}{b}{n}
+\DeclareSymbolFontAlphabet\mathfrak{EulerFraktur}
+\@ifpackageloaded{amsfonts}{}{\newcommand\frak{\mathfrak}}
+% \end{macrocode}
+% \end{macro}
+%
+% The following characters come from the Euler Fraktur symbol font (as
+% defined in \texttt{gkpmac.tex}):
+% \begin{macrocode}
+\DeclareMathSymbol{!}\mathord {EulerFraktur}{"21}
+\DeclareMathSymbol{(}\mathopen {EulerFraktur}{"28}
+\DeclareMathSymbol{)}\mathclose{EulerFraktur}{"29}
+\DeclareMathSymbol{+}\mathbin {EulerFraktur}{"2B}
+\DeclareMathSymbol{-}\mathbin {EulerFraktur}{"2D}
+\DeclareMathSymbol{=}\mathrel {EulerFraktur}{"3D}
+\DeclareMathSymbol{[}\mathopen {EulerFraktur}{"5B}
+\DeclareMathSymbol{]}\mathclose{EulerFraktur}{"5D}
+% \end{macrocode}
+% There is a curious detail here: The type of `!' is |\mathclose| in
+% \texttt{plain.tex} (and standard \LaTeX) but |\mathord| in
+% \texttt{gkpmac.tex}. The reason for this is probably that one
+% should not use Euler punctuation characters as part of the
+% text,\footnote{In particular, one should watch out for punctuation
+% characters in displays: Is, e.g., an exclamation point part of a
+% formula or part of the text? (With Computer Modern, it didn't
+% really matter, but it does matter with Euler!)} and punctuation
+% characters in math are usually operators. E.g., in CSP
+% (Communicating Sequential Processes), `!'~denotes an output
+% operation, a tightly binding binary operator; there is usually no
+% space around this operator (to indicate the high precedence).
+%
+% The Euler Fraktur symbol font contains more punctuation characters
+% than defined above. We want to use these characters as they look
+% better when they appear in math formulas (there are some strange
+% looking formulas in~\cite{concrete}). Even if one may argue that,
+% e.g., semicolon is most often used in the text sense (in displays),
+% it is more consistent and easier to remember if everything in math
+% mode is Euler.
+% \begin{macrocode}
+\DeclareMathSymbol{"}\mathord {EulerFraktur}{"7D}
+\DeclareMathSymbol{&}\mathord {EulerFraktur}{"26}
+\DeclareMathSymbol{:}\mathrel {EulerFraktur}{"3A}
+\DeclareMathSymbol{;}\mathpunct{EulerFraktur}{"3B}
+\DeclareMathSymbol{?}\mathord {EulerFraktur}{"3F}
+\DeclareMathSymbol{^}\mathord {EulerFraktur}{"5E}
+\DeclareMathSymbol{`}\mathord {EulerFraktur}{"12}
+% \end{macrocode}
+% Here, we also changed the type of `?' to |\mathord| to be consistent
+% with the type of~`!'. Regarding the math codes assigned by
+% \texttt{INITEX}: The Euler fonts do not have the glyphs for |\#|,
+% |\$|, |\%|, and \texttt{@}, so these glyphs are still taken from the
+% text fonts. Note also that we do not set the math code for the
+% other quote character: it is active in math mode (code
+% \texttt{"8000}); it produces primes (and should continue to do so).
+% \begin{macrocode}
+\DeclareMathDelimiter{(}{EulerFraktur}{"28}{largesymbols}{"00}
+\DeclareMathDelimiter{)}{EulerFraktur}{"29}{largesymbols}{"01}
+\DeclareMathDelimiter{[}{EulerFraktur}{"5B}{largesymbols}{"02}
+\DeclareMathDelimiter{]}{EulerFraktur}{"5D}{largesymbols}{"03}
+% \end{macrocode}
+%
+% \begin{macro}{\oldstylenums}
+% \begin{macro}{\TextOldstyle}\begin{macro}{\MathOldstyle}
+% We provide a new definition of the |\oldstylenums| macro: this
+% definition allows us to modify the generation of non-aligning (aka
+% ``oldstyle'') numerals in text and in math separately, using two
+% hooks, |\TextOldstyle| and |\MathOldstyle|.
+% \begin{macrocode}
+\DeclareRobustCommand\oldstylenums[1]%
+ {\begingroup
+ \spaceskip\fontdimen\tw@\font
+ \TextOldstyle \MathOldstyle #1%
+ \endgroup}
+% \end{macrocode}
+% In math, the |\oldstylenums| macro should produce Euler oldstyle
+% digits (located in the Euler Fraktur fonts):
+% \begin{macrocode}
+\def\MathOldstyle{\mathgroup\symEulerFraktur}
+% \end{macrocode}
+% By default, oldstyle digits in text come from the Computer Modern
+% fonts:
+% \begin{macrocode}
+\providecommand\TextOldstyle{\usefont{OML}{cmm}\f@series{it}}
+% \end{macrocode}
+% \end{macro}\end{macro}\end{macro}
+%
+% \subsection{Euler Script}
+%
+% \begin{macro}{\mathscr}
+% Like the Euler Fraktur fonts, the Euler Script fonts also get their
+% own symbol font. We define a math alphabet
+% identifier---|\mathscr|---to access this symbol font. For
+% compatibility with previous versions of the \euler\ package,
+% we define |\scr| as an alias for |\mathscr|.
+% \begin{macrocode}
+\DeclareSymbolFont{EulerScript}{U}{eus}{m}{n}
+\SetSymbolFont{EulerScript}{bold}{U}{eus}{b}{n}
+\DeclareSymbolFontAlphabet\mathscr{EulerScript}
+\newcommand\scr{\mathscr}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\mathcal}
+% If the \euler\ package is loaded with the \texttt{mathcal}
+% option, |\mathcal| should produce Euler Script letters.
+% \begin{macrocode}
+\DeclareOption{mathcal}{\renewcommand\mathcal{\mathscr}}
+% \end{macrocode}
+% \end{macro}
+%
+% The following is equivalent to the definitions in \texttt{gkpmac.tex}
+% concerning the Euler Script fonts:
+% \begin{macrocode}
+\DeclareMathSymbol\aleph\mathord{EulerScript}{"40}
+%\DeclareMathSymbol\equiv\mathrel{EulerScript}{"11}
+%\let\cong=\equiv % lowres bars weren't spaced right
+%\DeclareMathSymbol\leq \mathrel{EulerScript}{"14}
+%\let\le=\leq % seems to have been eliminated
+%\DeclareMathSymbol\geq \mathrel{EulerScript}{"15}
+%\let\ge=\geq % ditto
+\DeclareMathSymbol\Re \mathord{EulerScript}{"3C}
+\DeclareMathSymbol\Im \mathord{EulerScript}{"3D}
+% \end{macrocode}
+% Knuth used a slightly different version of the Euler Script fonts
+% that had special `$\le$' and `$\ge$' glyphs. Actually, the source
+% for the AMS Euler Script medium (but not the bold) font also
+% contains these glyphs; however, they are commented out (no
+% explanation is given). The definitions of |\equiv| and |\cong| are
+% also commented out in \texttt{gkpmac.tex} (with the reason as given
+% above, i.e., problems with low resolution rendering).
+% \begin{macrocode}
+\DeclareMathDelimiter\vert
+ \mathord{EulerScript}{"6A}{largesymbols}{"0C}
+\DeclareMathDelimiter\backslash
+ \mathord{EulerScript}{"6E}{largesymbols}{"0F}
+% \end{macrocode}
+%
+% The Euler Script fonts constitute a partial replacement for the
+% Computer Modern `symbols' math symbol fonts. (None of the remaining
+% definitions in this section were included in \texttt{gkpmac.tex}.)
+% \begin{macrocode}
+%\DeclareMathSymbol{-}\mathbin{EulerScript}{"00} % already done
+\DeclareMathSymbol{|}\mathord{EulerScript}{"6A}
+\DeclareMathDelimiter{|}{EulerScript}{"6A}{largesymbols}{"0C}
+% \end{macrocode}
+% (The minus signs in the Euler Fraktur and Script fonts are
+% identical, i.e., the sources are identical.)
+% \begin{macrocode}
+\DeclareMathSymbol\neg \mathord{EulerScript}{"3A}
+\let\lnot=\neg
+\DeclareMathSymbol\wedge \mathbin{EulerScript}{"5E}
+\let\land=\wedge
+\DeclareMathSymbol\vee \mathbin{EulerScript}{"5F}
+\let\lor=\vee
+\DeclareMathSymbol\setminus\mathbin{EulerScript}{"6E}
+\DeclareMathSymbol\sim \mathrel{EulerScript}{"18}
+\DeclareMathSymbol\mid \mathrel{EulerScript}{"6A}
+\DeclareMathDelimiter\arrowvert
+ \mathord{EulerScript}{"6A}{largesymbols}{"3C} % ???
+% \end{macrocode}
+% (There are no |\approx| or |\simeq| to go with |\sim|.) In Plain
+% \TeX\null, the characters |{|, |\|, and~|}| are assigned math codes
+% (and |\| is also given a delimiter code); these are the only visible
+% ASCII (7-bit) characters that we don't give a math code (we don't
+% assign math codes to any of the invisible ASCII characters).
+%
+% The Euler Script fonts also contain a section sign~(\S):
+% \begin{macrocode}
+\DeclareMathSymbol\mathsection\mathord{EulerScript}{"78}
+% \end{macrocode}
+%
+% \subsection{Euler Extension}
+%
+% We allocate a new symbol font group for this font:
+% \begin{macrocode}
+\DeclareSymbolFont{EulerExtension}{U}{euex}{m}{n}
+% \end{macrocode}
+% This font contains some alternative versions of some Computer Modern
+% symbols. The \texttt{amsmath} package (part of AMS-\LaTeX)
+% redefines the |\coprod|, |\prod|, and |\sum| symbols; to make the
+% \euler\ package work correctly with the \texttt{amsmath}
+% package, we need to take different actions depending on whether the
+% \texttt{amsmath} package has been loaded before the \euler\
+% package or not. Note: This will \emph{not} work with the
+% \texttt{amstex} package.
+% \begin{macrocode}
+\@ifpackageloaded{amsmath}
+ {\DeclareMathSymbol\coprod@\mathop{EulerExtension}{"60}%
+ \DeclareMathSymbol\prod@ \mathop{EulerExtension}{"51}%
+ \DeclareMathSymbol\sum@ \mathop{EulerExtension}{"50}}
+ {\DeclareMathSymbol\coprod \mathop{EulerExtension}{"60}%
+ \DeclareMathSymbol\prod \mathop{EulerExtension}{"51}%
+ \DeclareMathSymbol\sum \mathop{EulerExtension}{"50}}
+% \end{macrocode}
+% We shall respectfully ask the user not to use the \texttt{amstex}
+% package.
+% \begin{macrocode}
+\AtBeginDocument
+ {\@ifpackageloaded{amstex}%
+ {\PackageWarningNoLine{euler}{Please do not use `amstex'.
+ Use `amsmath' instead}{}}}
+% \end{macrocode}
+% \begin{macrocode}
+\DeclareMathSymbol\intop \mathop {EulerExtension}{"52}
+\DeclareMathSymbol\ointop \mathop {EulerExtension}{"48}
+\DeclareMathSymbol\braceld\mathord{EulerExtension}{"7A}
+\DeclareMathSymbol\bracerd\mathord{EulerExtension}{"7B}
+\DeclareMathSymbol\bracelu\mathord{EulerExtension}{"7C}
+\DeclareMathSymbol\braceru\mathord{EulerExtension}{"7D}
+\DeclareMathSymbol\infty \mathord{EulerExtension}{"31}
+% \end{macrocode}
+% It is not enough to substitute the Euler integral sign for the
+% Computer Modern integral sign, if we are using the \texttt{amsmath}
+% package. The multiple integral signs will look bad. The following
+% will make them look better.
+% \begin{macrocode}
+\AtBeginDocument
+ {\@ifpackageloaded{amsmath}%
+ {\def\intkern@{\mkern -6mu }%
+ \def\ints@#1{\mkern -3mu
+ \mathop{\mkern 3mu
+ \intop
+ \ifnum #1=\z@ \intdots@ \else
+ \intkern@
+ \ifnum #1>\tw@ \intop\intkern@
+ \ifnum #1>\thr@@ \intop\intkern@ \fi
+ \fi
+ \fi
+ \intop
+ }\ilimits@
+ }%
+ }{}}
+% \end{macrocode}
+% All Euler arrows come from the Euler Extension font:
+% \begin{macrocode}
+\DeclareMathSymbol\nearrow\mathrel{EulerExtension}{"25}
+\DeclareMathSymbol\searrow\mathrel{EulerExtension}{"26}
+\DeclareMathSymbol\nwarrow\mathrel{EulerExtension}{"2D}
+\DeclareMathSymbol\swarrow\mathrel{EulerExtension}{"2E}
+% \end{macrocode}
+% \begin{macrocode}
+\DeclareMathSymbol\Leftrightarrow\mathrel{EulerExtension}{"2C}
+\DeclareMathSymbol\Leftarrow \mathrel{EulerExtension}{"28}
+\DeclareMathSymbol\Rightarrow \mathrel{EulerExtension}{"29}
+\DeclareMathSymbol\leftrightarrow\mathrel{EulerExtension}{"24}
+\DeclareMathSymbol\leftarrow \mathrel{EulerExtension}{"20}
+\let\gets=\leftarrow
+\DeclareMathSymbol\rightarrow \mathrel{EulerExtension}{"21}
+\let\to=\rightarrow
+% \end{macrocode}
+% \begin{macrocode}
+\DeclareMathDelimiter\uparrow
+ \mathrel{EulerExtension}{"22}{largesymbols}{"78}
+\DeclareMathDelimiter\downarrow
+ \mathrel{EulerExtension}{"23}{largesymbols}{"79}
+\DeclareMathDelimiter\updownarrow
+ \mathrel{EulerExtension}{"6C}{largesymbols}{"3F}
+\DeclareMathDelimiter\Uparrow
+ \mathrel{EulerExtension}{"2A}{largesymbols}{"7E}
+\DeclareMathDelimiter\Downarrow
+ \mathrel{EulerExtension}{"2B}{largesymbols}{"7F}
+\DeclareMathDelimiter\Updownarrow
+ \mathrel{EulerExtension}{"6D}{largesymbols}{"77}
+% \end{macrocode}
+% \begin{macrocode}
+\DeclareMathSymbol\leftharpoonup \mathrel{EulerExtension}{"18}
+\DeclareMathSymbol\leftharpoondown \mathrel{EulerExtension}{"19}
+\DeclareMathSymbol\rightharpoonup \mathrel{EulerExtension}{"1A}
+\DeclareMathSymbol\rightharpoondown\mathrel{EulerExtension}{"1B}
+% \end{macrocode}
+%
+% Note the funny mixture of the Euler Script and Extension fonts:
+% \begin{macrocode}
+\DeclareMathDelimiter\lbrace
+ \mathopen{EulerScript}{"66}{EulerExtension}{"08}
+\DeclareMathDelimiter\rbrace
+ \mathclose{EulerScript}{"67}{EulerExtension}{"09}
+% \end{macrocode}
+%
+% \section{More math}
+%
+% Actually, we still need some Computer Modern fonts: We need the
+% equals sign for long/extensible (horizontal) double arrows, and we
+% need the minus sign for the single arrows! The Euler Extension font
+% is based on the \MF\ code for Computer Modern, and we need the
+% Computer Modern equals and minus signs to make long/extensible arrows.
+%
+% We allocate math alphabets to produce the equals and minus signs for
+% arrows. Note that since Euler arrows are only available in medium
+% weight (they come from the Euler Extension font which is only
+% available in medium weight), we let all math versions of these math
+% alphabets refer to medium weight fonts.
+% \begin{macrocode}
+\DeclareMathAlphabet\cm@equals@alphabet{OT1}{cmr}{m}{n}
+\DeclareMathAlphabet\cm@minus@alphabet{OMS}{cmsy}{m}{n}
+% \end{macrocode}
+% Note that we use OT1 encoding for the |\cm@equals@alphabet|, even
+% though T1 encoding may be the default for the users system.
+%
+% Also, note that we already have the Computer Modern \texttt{cmsy}
+% family assigned to a symbol font (namely the `symbols' symbol font).
+% However, taking the minus sign directly from this symbol font would
+% make long/extensible arrows come out wrong in the `bold' math
+% version. (It is perhaps ``overkill'' to allocate a math alphabet
+% just for this purpose?)
+%
+% \begin{macro}{\Relbar}\begin{macro}{\relbar}
+% The long arrows are made using the macros |\Relbar| (for double
+% arrows) and |\relbar| (for single arrows). The standard \LaTeX\
+% definitions of these macros use the `\texttt{=}' and `\texttt{-}'
+% characters to produce the extension part of the long arrows. Since
+% we have changed the math codes of these characters (they are now
+% taken from the Euler Fraktur fonts in math mode), we have to
+% redefine the |\Relbar| and |\relbar| macros.
+% \begin{macrocode}
+\def\Relbar{\mathrel{\cm@equals@alphabet{\mathchar"703D}}}
+\def\cm@minus{{\cm@minus@alphabet{\mathchar"7000}}}
+\def\relbar{\mathrel{\smash\cm@minus}}
+ % \smash, because - has the same height as +
+% \end{macrocode}
+% \end{macro}\end{macro}
+%
+% \begin{macro}{\leftarrowfill}\begin{macro}{\rightarrowfill}
+% Unfortunately, since the definitions of the ``arrow-filling'' macros
+% (|\leftarrowfill| and |\rightarrowfill|) in standard \LaTeX\ still
+% use explicit minus signs (instead of |\relbar|), we also have to
+% redefine those macros:
+% \begin{macrocode}
+\def\leftarrowfill
+ {$\m@th\mathord\leftarrow\mkern-6mu%
+ \cleaders\hbox{$\mkern-2mu\cm@minus\mkern-2mu$}\hfill
+ \mkern-6mu\cm@minus$}
+\def\rightarrowfill
+ {$\m@th\cm@minus\mkern-6mu%
+ \cleaders\hbox{$\mkern-2mu\cm@minus\mkern-2mu$}\hfill
+ \mkern-6mu\mathord\rightarrow$}
+% \end{macrocode}
+% We have defined |\cm@minus| to produce a Computer Modern minus sign
+% of type |\mathord|. We thereby save a few |\mathord| tokens
+% (compared to the definitions of |\leftarrowfill| and
+% |\rightarrowfill| in standard \LaTeX).
+% \end{macro}\end{macro}
+%
+% There are a few symbols in the original Computer Modern Math Italic
+% fonts that are not present in the Euler fonts. We simply take them
+% from the CM fonts.
+% \begin{macrocode}
+\DeclareSymbolFont{cmmigroup}{OML}{cmm}{m}{it}
+\SetSymbolFont{cmmigroup}{bold}{OML}{cmm}{b}{it}
+\DeclareMathAccent\vec \mathord{cmmigroup}{"7E}
+\DeclareMathSymbol\triangleleft \mathbin{cmmigroup}{"2F}
+\DeclareMathSymbol\triangleright\mathbin{cmmigroup}{"2E}
+\DeclareMathSymbol\star \mathbin{cmmigroup}{"3F}
+\DeclareMathSymbol\lhook \mathrel{cmmigroup}{"2C}
+\DeclareMathSymbol\rhook \mathrel{cmmigroup}{"2D}
+\DeclareMathSymbol\flat \mathord{cmmigroup}{"5B}
+\DeclareMathSymbol\natural \mathord{cmmigroup}{"5C}
+\DeclareMathSymbol\sharp \mathord{cmmigroup}{"5D}
+\DeclareMathSymbol\smile \mathrel{cmmigroup}{"5E}
+\DeclareMathSymbol\frown \mathrel{cmmigroup}{"5F}
+% \end{macrocode}
+% Note that the arrow head of |\vec| is slanted; this looks a bit
+% strange in combination with an upright font such as Euler Roman.
+%
+% Also, note that in the `bold' math version, arrows with hooks will
+% come out wrong (the hooks will be bold, but the arrow heads will be
+% of medium weight). This can be repaired in a similar way as the
+% long/extensible arrows, but is it worth it to allocate a math
+% alphabet just for this purpose?
+%
+% Finally, Knuth wanted a little extra space before the prime
+% superscript:
+% \begin{macrocode}
+\begingroup
+ \catcode`\'=\active
+ \gdef'{^\bgroup\mskip2mu\prim@s} % more space before '
+\endgroup
+% \end{macrocode}
+%
+% Open question: The |\dots| and |\ldots| macros produce dots
+% (periods) from the Euler fonts; the |\ddots| and |\vdots| macros
+% produce dots from the text font; and the |\cdots| macro produces
+% dots from the Computer Modern `symbols' math symbol font. Should we
+% do something about this?
+%
+% \section{Text fonts in math}\label{text-fonts}
+%
+% The text fonts used in math through math alphabets and the
+% `operators' symbol font should be the same as the fonts used for the
+% main text. (It is now easy to replace the fonts for the `operators'
+% symbol font, since the uppercase greek letters are now taken from
+% the Euler Roman fonts.)
+%
+% In order to reduce the total number of fonts needed, we shall---if
+% possible---use text fonts in the same encoding for both text and
+% math. We therefore determine whether T1 encoding has been selected
+% as the default encoding. We define a switch---|\ifCorkEncoding|---for
+% that purpose.
+% \begin{macrocode}
+\newif\ifCorkEncoding
+\edef\@tempa{\encodingdefault}\def\@tempb{T1}
+\ifx\@tempa\@tempb
+ \CorkEncodingtrue
+\else
+ \CorkEncodingfalse
+\fi
+% \end{macrocode}
+% Note that we determine the encoding to use at the time the \euler\
+% package is loaded (\emph{not} at the end of the preamble). This
+% allows the user to retain OT1 encoding for text fonts used in math
+% (other packages may depend on that) by selecting T1 encoding
+% \emph{after} the \euler\ package has been loaded.
+%
+% We redefine the `operators' symbol font and all math alphabets
+% defined by the \LaTeX\ kernel. Due to the current implementation of
+% math accents that take their glyphs from text fonts, all text fonts
+% must be used in a common encoding. The only \LaTeX\ `base' package
+% that defines extra math alphabets is the \texttt{oldlfont} package.
+% However, this package cannot be used together with the \euler\
+% package (it allocates too many symbol fonts). In other words, the
+% following setup should suffice for most users.
+% \begin{macrocode}
+\ifCorkEncoding
+ \AtBeginDocument
+ {\DeclareSymbolFont{operators}{T1}\rmdefault\mddefault\updefault
+ \SetSymbolFont{operators}{bold}{T1}\rmdefault\bfdefault\updefault
+ \DeclareMathAlphabet\mathbf{T1}\rmdefault\bfdefault\updefault
+ \DeclareMathAlphabet\mathsf{T1}\sfdefault\mddefault\updefault
+ \DeclareMathAlphabet\mathit{T1}\rmdefault\mddefault\itdefault
+ \DeclareMathAlphabet\mathtt{T1}\ttdefault\mddefault\updefault
+ \SetMathAlphabet\mathsf{bold}{T1}\sfdefault\bfdefault\updefault
+ \SetMathAlphabet\mathit{bold}{T1}\rmdefault\bfdefault\itdefault}
+\else
+ \AtBeginDocument
+ {\DeclareSymbolFont{operators}{OT1}\rmdefault\mddefault\updefault
+ \SetSymbolFont{operators}{bold}{OT1}\rmdefault\bfdefault\updefault
+ \DeclareMathAlphabet\mathbf{OT1}\rmdefault\bfdefault\updefault
+ \DeclareMathAlphabet\mathsf{OT1}\sfdefault\mddefault\updefault
+ \DeclareMathAlphabet\mathit{OT1}\rmdefault\mddefault\itdefault
+ \DeclareMathAlphabet\mathtt{OT1}\ttdefault\mddefault\updefault
+ \SetMathAlphabet\mathsf{bold}{OT1}\sfdefault\bfdefault\updefault
+ \SetMathAlphabet\mathit{bold}{OT1}\rmdefault\bfdefault\itdefault}
+\fi
+% \end{macrocode}
+% Note that we perform the setup at the end of the preamble (and not
+% while the \euler\ package is being input). This implies that any
+% changes made to, e.g., |\rmdefault| by a package loaded after the
+% \euler\ package are seen.
+%
+% The standard \LaTeX\ math setup assumes that OT1 encoded text fonts
+% are used in math. When using T1 encoded fonts, we have to redefine
+% the macros that access accents from the text fonts.
+% \begin{macrocode}
+\ifCorkEncoding
+ \DeclareMathAccent\grave\mathalpha{operators}{"00}
+ \DeclareMathAccent\acute\mathalpha{operators}{"01}
+ \DeclareMathAccent\tilde\mathalpha{operators}{"03}
+ \DeclareMathAccent\ddot \mathalpha{operators}{"04}
+ \DeclareMathAccent\check\mathalpha{operators}{"07}
+ \DeclareMathAccent\breve\mathalpha{operators}{"08}
+ \DeclareMathAccent\bar \mathalpha{operators}{"09}
+ \DeclareMathAccent\dot \mathalpha{operators}{"0A}
+\fi
+% \end{macrocode}
+%
+% \begin{macro}{\hat}
+% There is one more accent that is normally taken from the `operators'
+% symbol font, namely the |\hat| accent. This is the only accent
+% provided by the Euler fonts; we shall use this accent by default.
+% (A curious fact is that Knuth devoted a fairly large portion of
+% \texttt{gkpmac.tex} to the construction of a $\phi$ with a hat
+% accent---using the |\widehat| macro).
+% \begin{macrocode}
+\DeclareMathAccent\hat\mathalpha{EulerFraktur}{"5E}
+% \end{macrocode}
+% However, some users do not like this |\hat| accent. They prefer the
+% accent glyph to be taken from the text font (similar to the other
+% accents).
+% \begin{macrocode}
+\DeclareOption{text-hat-accent}
+ {\ifCorkEncoding
+ \DeclareMathAccent\hat\mathalpha{operators}{"02}%
+ \else
+ \DeclareMathAccent\hat\mathalpha{operators}{"5E}%
+ \fi}
+% \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\hbar}
+% The |\hbar| macro in standard \LaTeX\ is composed of the letter~`h'
+% from the `letters' symbol font and the macron (`bar') accent from
+% the `operators' symbol font. With the `letters' symbol font now
+% being Euler Roman, the bar is no longer positioned correctly. We
+% choose the following definition (the \texttt{9mu} in the original
+% definition has been changed to \texttt{8mu}):
+% \begin{macrocode}
+\ifCorkEncoding
+ \DeclareMathSymbol\euler@hbar\mathord{operators}{"09}
+\else
+ \DeclareMathSymbol\euler@hbar\mathord{operators}{"16}
+\fi
+\def\hbar{{\euler@hbar\mkern-8muh}}
+% \end{macrocode}
+% \end{macro}
+%
+% \section{Footnotes}\label{footnotes}
+%
+% \begin{macro}{\@makefnmark}
+% Footnote numbers are not math entities, so they should be produced
+% by digits from the text font. Since footnote markers (whether they
+% are numbers or symbols) are produced in math mode, we can accomplish
+% this by selecting |\operator@font|; this will cause digits to be
+% taken from the `operators' symbol font (which is the same as the
+% font used for text; see previous section).
+% \begin{macrocode}
+\def\@makefnmark{\hbox{$\operator@font^{\@thefnmark}\m@th$}}
+% \end{macrocode}
+% \end{macro}
+%
+% \section{Processing options}
+%
+% Finally, we must remember to process the options:
+% \begin{macrocode}
+\ProcessOptions
+%</package>
+% \end{macrocode}
+%
+% \Finale
+\endinput
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