<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">% cancel.sty  version  2.1  12-Mar-2000.
% Donald Arseneau         asnd@triumf.ca
% I contribute this software to the public domain.  No rights reserved.
%
% Commands:
% ~~~~~~~~~
% \cancel    draws a diagonal line (slash) through its argument. 
% \bcancel   uses the negative slope (a backslash). 
% \xcancel   draws an X (actually \cancel plus \bcancel).
% \cancelto{&lt;value&gt;}{&lt;expression&gt;} draws a diagonal arrow through the 
%            expression, pointing to the value.
%
% The first three work in math and text mode, but \cancelto is only
% for math mode.
% The slope of the line or arrow depends on what is being cancelled.  
%
% Options:
% ~~~~~~~~
% Bt default, none of these commands affects the horizontal spacing, 
% so they might over-print neighboring parts of the formula (or text).
% They do add their height to the expression, so there should never be 
% unintended vertical overlap.  There is a package option [makeroom] to 
% increase the horizontal spacing to make room for the cancellation value.  
% 
% If you use the color package, then you can declare 
%   \renewcommand{\CancelColor}{&lt;color_command&gt;}
% and the cancellation marks will be printed in that color (e.g., \blue).
% However, if you are using color, I recommend lightly shaded blocks rather
% than diagonal arrows for cancelling.
%
% The option [thicklines] asks for heavier lines and arrows. This may be
% useful when the lines are colored a light shade.
%
% The size (math style) of the \cancelto value depends on package options 
% according to this table:
%
% Current style       [samesize]         [smaller]          [Smaller]
% -------------       ----------------   ----------------   ----------------
% \displaystyle       \displaystyle      \textstyle         \scriptstyle
% \textstyle          \textstyle         \scriptstyle       \scriptstyle
% \scriptstyle        \scriptstyle       \scriptscriptstyle \scriptscriptstyle 
% \scriptscriptstyle  \scriptscriptstyle \scriptscriptstyle \scriptscriptstyle
%
% ("smaller" is the default behavior.  It gives textstyle limits in 
% displaystyle, whereas "Smaller" gives scriptstyle limits.)
%
% This package is provided without guarantees or support.  Drawing slashes
% through math to indicate "cancellation" is poor design.  I don't recommend
% that you use this package at all.

\ProvidesPackage{cancel}[2000/03/12 v2.1 Cancel math terms]

\newcommand{\CancelColor}{}
\newcommand{\cancelto}{1}% default option = smaller
\let\canto@fil\hidewidth
\let\canc@thinlines\thinlines

\DeclareOption{samesize}{\def\cancelto{999}}
\DeclareOption{smaller}{\def\cancelto{1}}
\DeclareOption{Smaller}{\def\cancelto{0}}
\DeclareOption{makeroom}{\def\canto@fil{\hfil}}
\DeclareOption{overlap}{\let\canto@fil\hidewidth}
\DeclareOption{thicklines}{\let\canc@thinlines\thicklines}

\ProcessOptions

\DeclareRobustCommand\cancel[1]{\ifmmode
  \mathpalette{\@cancel{\@can@slash{}}}{#1}\else 
  \@cancel{\@can@slash{}}\hbox{#1}\fi}
\DeclareRobustCommand\bcancel[1]{\ifmmode
  \mathpalette{\@cancel{\@can@slash{-}}}{#1}\else 
  \@cancel{\@can@slash{-}}\hbox{#1}\fi}
\DeclareRobustCommand\xcancel[1]{\ifmmode
  \mathpalette{\@cancel{\@can@slash{+}\@can@slash{-}}}{#1}\else 
  \@cancel{\@can@slash{+}\@can@slash{-}}\hbox{#1}\fi}

\newcommand\@cancel[3]{%
\@begin@tempboxa\hbox{\m@th$#2{#3}$}%
\dimen@\height
\setbox\@tempboxa\hbox{$\m@th\vcenter{\box\@tempboxa}$}%
\advance\dimen@-\height % the difference in height
\unitlength\p@ \canc@thinlines
{\/\raise\dimen@\hbox{\ooalign{#1\hfil\box\@tempboxa\hfil \cr}}}%
\@end@tempboxa
}

\def\@can@slash#1{\canto@fil$\m@th \CancelColor\vcenter{\hbox{%
\dimen@\width \@min@pt\dimen@ 2\@min@pt\totalheight6%
\ifdim\totalheight&lt;\dimen@ % wide
 \@min@pt\dimen@ 8%
 \@tempcnta\totalheight \multiply\@tempcnta 5 \divide\@tempcnta\dimen@
 \advance\dimen@ 2\p@ %  "+2"
 \edef\@tempa{(\ifcase\@tempcnta 6,#11\or 4,#11\or 2,#11\or 4,#13\else 1,#11\fi
   ){\strip@pt\dimen@}}%
\else % tall
 \@min@pt\totalheight8% 
 \advance\totalheight2\p@ % "+2"
 \@tempcnta\dimen@ \multiply\@tempcnta 5 \divide\@tempcnta\totalheight
 \dimen@ \ifcase\@tempcnta .16\or .25\or .5\or .75\else 1\fi \totalheight
 \edef\@tempa{(\ifcase\@tempcnta 1,#16\or 1,#14\or 1,#12\or 3,#14\else 1,#11\fi
   ){\strip@pt\dimen@}}%
\fi
\expandafter\line\@tempa}}$\canto@fil \cr}

\ifcase\cancelto
 \def\cancelto#1#2{\mathchoice    %  Smaller option
  {\@cancelto\scriptstyle{#1}\displaystyle{#2}}%
  {\@cancelto\scriptstyle{#1}\textstyle{#2}}%
  {\@cancelto\scriptscriptstyle{#1}\scriptstyle{#2}}%
  {\@cancelto\scriptscriptstyle{#1}\scriptscriptstyle{#2}}%
  }
\or
 \def\cancelto#1#2{\mathchoice    %  smaller option (default)
  {\@cancelto\textstyle{#1}\displaystyle{#2}}%
  {\@cancelto\scriptstyle{#1}\textstyle{#2}}%
  {\@cancelto\scriptscriptstyle{#1}\scriptstyle{#2}}%
  {\@cancelto\scriptscriptstyle{#1}\scriptscriptstyle{#2}}%
  }
\else
 \def\cancelto#1#2{\mathchoice    %  samesize option
  {\@cancelto\textstyle{#1}\displaystyle{#2}}%
  {\@cancelto\textstyle{#1}\textstyle{#2}}%
  {\@cancelto\scriptstyle{#1}\scriptstyle{#2}}%
  {\@cancelto\scriptscriptstyle{#1}\scriptscriptstyle{#2}}%
  }
\fi

\newcommand\@cancelto[4]{%
\@begin@tempboxa\hbox{\m@th$#3{#4}$}%
\dimen@\width % wide
\@min@pt\dimen@ 2\@min@pt\totalheight4
\ifdim\totalheight&lt;\dimen@
 \@tempcnta\totalheight \multiply\@tempcnta 5 \divide\@tempcnta\dimen@
 \@tempdimb 3\p@ % extra width for arrowhead ("+2")
 \advance\dimen@ \ifcase\@tempcnta 5\or 5\or 4\or 3\else 2\fi \p@
 \@min@pt\dimen@9\advance\dimen@\p@ 
 \edef\@tempa{\ifcase\@tempcnta 5441\or 5441\or 5421\or 4443\else 3611\fi
      {\strip@pt\dimen@}{\strip@pt\@tempdimb}}%
 \def\@tempb{Cancel #4 to #2; case wide }%
\else % tall
 \advance\totalheight3\p@ % "+2"
 \@tempcnta\dimen@ \multiply\@tempcnta 5 \divide\@tempcnta\totalheight
 \advance\totalheight3\p@ % "+2"
 \dimen@ \ifcase\@tempcnta .25\or .25\or .5\or .75\else 1\fi \totalheight
 \@tempdimb \ifcase\@tempcnta .8\or .8\or 1.2\or 1.5\else 2\fi \p@
 \edef\@tempa{\ifcase\@tempcnta 0814\or 0814\or 1812\or 2734\else 3611\fi
      {\strip@pt\dimen@}{\strip@pt\@tempdimb}}%
\fi
\dimen@\height
\setbox\@tempboxa\hbox{$\m@th\vcenter{\box\@tempboxa}$}%
\advance\dimen@-\height % the difference in height
\unitlength\p@ \canc@thinlines
{\/\raise\dimen@\hbox{\expandafter\canto@vector\@tempa{#1}{#2}}}%
\@end@tempboxa
}

% #1, #2 offset of label   #6 extra width to clear arrowhead
% #3, #4 vector direction  #7 superscript label style
% #5 vector width          #8 superscript label
\def\canto@vector#1#2#3#4#5#6#7#8{%
  \dimen@.5\p@
  \setbox\z@\vbox{\boxmaxdepth.5\p@
   \hbox{\kern-1.2\p@\kern#1\dimen@$#7{#8}\m@th$}}%
  \ifx\canto@fil\hidewidth  \wd\z@\z@ \else \kern-#6\unitlength \fi
  \ooalign{%
    \canto@fil$\m@th \CancelColor
    \vcenter{\hbox{\dimen@#6\unitlength \kern\dimen@
      \multiply\dimen@#4\divide\dimen@#3 \vrule\@depth\dimen@\@width\z@
      \vector(#3,#4){#5}%
    }}^{\raise#2\dimen@\copy\z@\kern-\scriptspace}$%
    \canto@fil \cr
    \hfil \box\@tempboxa \kern\wd\z@ \hfil \cr}}

\def\@min@pt#1#2{\ifdim#1&lt;#2\p@ #1#2\p@ \relax\fi}
</pre></body></html>