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+% 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}