% some small miscellaneous macros
 
%capital roman numerals
\def\Romannumeral#1{\uppercase\expandafter{\romannumeral#1}}
 
%half in textstyle (smaller --- sometimes looks better)
\def\half{\textstyle{1\over2}}
 
%a couple of useful abbreviations
\def\ie{i.\thinspace e.}
\def\eg{e.\thinspace g.}
 
%slant fractions (slightly offset and smaller a/b)
%usage \slfrac{numerator}/{denominator}
\def\slfrac#1/#2{\leavevmode\kern.1em\raise.5ex\hbox{\the\scriptfont0 #1}
\kern-.1em/\kern-.15em\lower.25ex\hbox{\the\scriptfont0 #2}}
 
% makes real and complex number-set symbols with vertical bars
\def\Reals{{\hbox{$\mathpalette{}{I\kern-.2em R}$}}}
\def\Complexes{{\hbox{$\mathpalette{}{C\kern-.46em
          \vrule depth 0ex height 1.4ex width .05em\kern.41em}$}}}
 
%poor man's bold (The TeXbook, p. 386)
\def\pmb#1{\leavevmode\setbox0=\hbox{#1}%
    \kern-.025em\copy0\kern-\wd0
    \kern.05em\copy0\kern-\wd0
    \kern-.025em\raise.0433em\box0}