bropd (9nov12)

git-svn-id: svn://tug.org/texlive/trunk@28222 c570f23f-e606-0410-a88d-b1316a301751

4 files changed, 199 insertions, 60 deletions

diff --git a/Master/texmf-dist/doc/latex/bropd/README b/Master/texmf-dist/doc/latex/bropd/README
index 79c3a19eb1a..03953634db4 100644
--- a/Master/texmf-dist/doc/latex/bropd/README
+++ b/Master/texmf-dist/doc/latex/bropd/README
@@ -1,13 +1,13 @@
 bropd package
 
-Version: 1.0 2012/11/04
+Version: 1.1 2012/11/08
 
 by Benjamin Tatlock
 
 The bropd package simplifies the process of writing differential operators and
 brackets in LaTeX. The commands facilitate the easy manipulation of equations
-involving brackets and allow partial differentials to be expressed in an
-alternate form.
+involving brackets and allow partial differentials to be expressed in
+alternate forms.
 
 
 The "bropd" package is copyright 2012 by Benjamin Tatlock
diff --git a/Master/texmf-dist/doc/latex/bropd/bropd.pdf b/Master/texmf-dist/doc/latex/bropd/bropd.pdf
index d90afc955ed..9a87ddfd66a 100644
--- a/Master/texmf-dist/doc/latex/bropd/bropd.pdf
+++ b/Master/texmf-dist/doc/latex/bropd/bropd.pdf
diff --git a/Master/texmf-dist/source/latex/bropd/bropd.dtx b/Master/texmf-dist/source/latex/bropd/bropd.dtx
index 0d809486e86..7cdca792709 100644
--- a/Master/texmf-dist/source/latex/bropd/bropd.dtx
+++ b/Master/texmf-dist/source/latex/bropd/bropd.dtx
@@ -22,31 +22,40 @@ bropd.pdf.
 \input docstrip
 \keepsilent
 \expandafter\preamble\thepreamble\endpreamble
+\askforoverwritefalse
 \generate{\file{bropd.sty}{\from{bropd.dtx}{}}}
 \endgroup
 \documentclass{ltxdoc}
-\usepackage{bropd,ifpdf}
+\usepackage{bropd,color,ifpdf}
+\DoNotIndex{\def}
+\EnableCrossrefs
+\CodelineIndex
+\RecordChanges
 \GetFileInfo{bropd.sty}
 \title{The \textsf{bropd} package\thanks{This documentation corresponds to
 \textsf{bropd}~v\fileversion, dated \filedate.}}
-\author{Benjamin Tatlock}
-\newenvironment{verba}{\begin{verbatim}}{\end{verbatim}}
+\def\auth{Benjamin Tatlock}
+\author{\auth\thanks{\texttt{\kern2.5em\textcolor{white}
+{\char101\char109\char97\char105\char108}\kern-5em\auth\kern-4em\char46\kern
+3.5em\char64\textcolor{white}{bropd}\kern-1em\char108\kern-1em\char105\ 
+\kern-2em\char109\char97\kern1em\char46\textcolor{white}
+{\char111\char114\char103}\kern-2em\ com}}}
 \begin{document}
 \maketitle
 \begin{abstract}
 The \textsf{bropd} package simplifies the process of writing differential
 operators and brackets in \LaTeX. The commands facilitate the easy manipulation
 of equations involving brackets and allow partial differentials to be expressed
-in an alternate form.
+in alternate forms.
 \end{abstract}
 \section{Introduction}
 The \textsf{bropd} package introduces a bracket command that automatically
 selects parentheses, square brackets or braces as appropriate based on the
 number of brackets. As such, brackets can be freely added and removed without
-alterations to the rest an equation. A command for writing ordinary and partial
-differentials is also created with an optional concise form for typesetting
-partial derivatives. This allows equations to be typed in a standard form and
-their style altered globally at a later date.
+alterations to the rest of an equation. Commands for typing ordinary and partial
+differentials are also created, with two optional concise forms for partial
+derivatives. Equations can therefore be written in a standard form and their
+style altered globally at a later date.
 \section{Usage}
 This section outlines the use of the three commands provided by the
 \textsf{bropd} package.
@@ -63,28 +72,34 @@ which is displayed as\[\od{y}{x}.\]The order of the differential can be
 specified as an optional argument, illustrated here with the command
 \verb|\od[2]{u}{x}=-\omega^2u| which results in\[\od[2]{u}{x}=-\omega^2u.\]When
 using \verb|\od| with a sans-serif font, the package should be loaded with the
-optional argument \verb|sans|.\subsubsection{Partial differential}The command
-\verb|\pd| follows the same form as \verb|\od|, but instead produces partial
-differentials. By default \verb|\pd{u}{t}=6u\pd{u}{x}-\pd[3]{u}{x}|
+optional argument \verb|sans|.
+\subsubsection{Partial differential}The command \verb|\pd| follows the same form as \verb|\od|, but instead produces partial differentials. By default,
+\verb|\pd{u}{t}=6u\pd{u}{x}-\pd[3]{u}{x}|
 produces\[\pd{u}{t}=6u\pd{u}{x}-\pd[3]{u}{x}.\]Loading the package with the
 option \verb|pdshort| results in an alternative format for partial
-differentials:\[u_t=6uu_x-u_{xxx}\]Note that when using this form, the
-\verb|\br| function \emph{must} follow \verb|\pd| when the first argument is
-left empty, as demonstrated by \verb|\pd{}{z}\br{x+y}| which results
-in\[\br{x+y}_z.\]If the optional argument is not a positive integer, the default
-form is reverted to, as with \verb|\pd[n]xy|:\[\pd[n]xy\]The syntax for partial
-differentials is extended to allow the second order term such
-as\[\pd{u}{x,t}\]to be easily typeset with \verb|\pd{u}{x,t}|.
+differentials:\[u_t=6uu_x-u_{xxx}\]If the optional argument is not a positive
+integer, the default form is reverted to, as with \verb|\pd[n]xy|:\[\pd[n]xy\]A
+second alternative form is produced when the option \verb|pdalt| is
+specified:\[\partial_tu=6u\partial_xu-\partial_{xxx}u\]The syntax for partial
+differentials is extended to allow higher order terms such
+as\[\pd{u}{x,x,t}\]to be easily typeset with \verb|\pd{u}{x,x,t}|. When applying
+a partial derivative to a longer term, the first argument can be left blank and
+the longer string written as an additional argument, as demonstrated by
+\verb|\pd{}{z}{x+y}| which results in\[\pd{}{z}{x+y}.\]To prevent brackets from
+being placed after a partial differential with an empty numerator, use
+\verb|!| for the first argument, for example, \verb|\pd{!}{x}|:\[\pd{!}{x}\]
 \subsection{Further examples}
 Combining the commands provided by this package allows more complex terms to be
 written concisely. The \verb|\br| allows equations with multiple brackets to be
 constructed and manipulated quickly and easily. An example of this is
-\verb|\br{x-y}\br{Q-\frac12\br{P+\br{x-1}\br{\br{A+B}\br{u+c}-t}}}|, which
-results in\[\br{x-y}\br{Q-\frac12\br{P+\br{x-1}\br{\br{A+B}\br{u+c}-t}}}.\]
-The form of the partial differentials written with the \verb|\pd| command can be
-changed at any time.\verb|\pd Et+\sum_{i=1}^3\pd{}{x_i}\br{\br{E+p}u_i}|
-produces\[\pd Et+\sum_{i=1}^3\pd{}{x_i}\br{\br{E+p}u_i}\]
-or, with \verb|pdshort|,\[E_t+\sum_{i=1}^3\br{\br{E+p}u_i}_{x_i}.\]
+\verb|\br{x-y}\br{Q-\frac12\br{P+\br{x-1}\br{\br{a+b}\br{u+c}-\od st}}}|, which
+results in\[\br{x-y}\br{Q-\frac12\br{P+\br{x-1}\br{\br{A+B}\br{u+c}-\od st}}}.\]
+The form of the partial differentials written with the \verb|\pd| command can
+be changed at any time. \verb|\pd Et+\sum_{i=1}^3\pd{}{x_i}{\br{E+p}u_i}|
+produces\[\pd Et+\sum_{i=1}^3\pd{}{x_i}{\br{E+p}u_i}\]by default. With
+\verb|pdshort|, the same input instead
+creates\[E_t+\sum_{i=1}^3\br{\br{E+p}u_i}_{x_i},\]while with \verb|pdalt| the
+output is\[\partial_tE+\sum_{i=1}^3\partial_{x_i}\br{\br{E+p}u_i}.\]
 \StopEventually{\typeout{**************************************************}
 \typeout{*}
 \typeout{* To finish the installation, you have to move the}
@@ -98,31 +113,46 @@ or, with \verb|pdshort|,\[E_t+\sum_{i=1}^3\br{\br{E+p}u_i}_{x_i}.\]
 \clearpage
 \DocInput{bropd.dtx}
 \clearpage
+\PrintChanges
 \Finale
 %</batchfile>
 % \fi
 % \section{Implementation}
 % Announce the name, package version and \LaTeXe\ requirement
+% \changes{v1.0}{2012/11/04}{Initial version}
 %    \begin{macrocode}
 \NeedsTeXFormat{LaTeX2e}
 \ProvidesPackage{bropd}
-[2012/11/04 1.0 automated typing of brackets and differential operators]
+[2012/11/08 1.1 automated typing of brackets and differential operators]
 %    \end{macrocode}
 % Initiate conditionals and counters
 %    \begin{macrocode}
-\newif\if@bropd@a\newif\if@bropd@b\newif\if@bropd@s
+\newif\if@bropd@a\newif\if@bropd@b\newif\if@bropd@s\newif\if@bropd@u
 \newcounter{@bropd@c}\newcounter{@bropd@d}
 \newcounter{@bropd@e}\newcounter{@bropd@f}
 %    \end{macrocode}
 % Provide optional arguments for alternative form partial differential and
 % sans-serif fonts
 %    \begin{macrocode}
-\DeclareOption{pdshort}{\@bropd@atrue}
+\DeclareOption{pdshort}{\@bropd@atrue\@bropd@ufalse}
+\DeclareOption{pdalt}{\@bropd@atrue\@bropd@utrue}
 \DeclareOption{sans}{\@bropd@strue}\ProcessOptions
 %    \end{macrocode}
+% Define character for \verb|\pd| with empty numerator and no brackets following
+%    \begin{macrocode}
+\def\@bropd@t{!}
+%    \end{macrocode}
+% \begin{macro}{\@bropd@g}
 % Internal command for default partial differential form
 %    \begin{macrocode}
-\newcommand\@bropd@g[4]{\def\@bropd@h{#1}
+\def\@bropd@g#1#2#3#4{\def\@bropd@h{#1}
+%    \end{macrocode}
+% Create numerator
+%    \begin{macrocode}
+\ifx\@bropd@o\@bropd@t\let\@bropd@o\empty\fi
+%    \end{macrocode}
+% Reset counters
+%    \begin{macrocode}
 \ifx\@bropd@h\empty
 \setcounter{@bropd@c}0\setcounter{@bropd@d}1
 \let\@bropd@h\empty
@@ -132,9 +162,9 @@ or, with \verb|pdshort|,\[E_t+\sum_{i=1}^3\br{\br{E+p}u_i}_{x_i}.\]
 %    \begin{macrocode}
 \@for\@bropd@i:=#3\do{\stepcounter{@bropd@c}}
 \frac{#4\ifnum\value{@bropd@c}>1
-^{\arabic{@bropd@c}}\fi#2}
+^{\arabic{@bropd@c}}\fi\@bropd@o}
 %    \end{macrocode}
-% Cycle through each term for the denominator.  If a term is the same as the
+% Cycle through each term for the denominator. If a term is the same as the
 % previous, add to counter, otherwise print along with counter value
 %    \begin{macrocode}
 {\@for\@bropd@i:=#3\do{
@@ -154,14 +184,18 @@ or, with \verb|pdshort|,\[E_t+\sum_{i=1}^3\br{\br{E+p}u_i}_{x_i}.\]
 \else
 %    \end{macrocode}
 % If optional argument provided, display partial differential to stated order
+% \changes{v\fileversion}\filedate{Fixed higher order differentials with
+% denominators containing commands}
 %    \begin{macrocode}
-\frac{#4^{#1}#2}{#4#3^{#1}}
+\frac{#4^{#1}\@bropd@o}{#4\noexpand#3^{#1}}
 \fi}
 %    \end{macrocode}
-% Internal command for brackets.  Evaluate terms within brackets to determine
+% \end{macro}
+% \begin{macro}{\@bropd@j}
+% Internal command for brackets. Evaluate terms within brackets to determine
 % the highest bracket level
 %    \begin{macrocode}
-\newcommand\@bropd@j[1]{\setcounter{@bropd@f}0
+\def\@bropd@j#1{\setcounter{@bropd@f}0
 {\renewcommand{\br}[1]{\stepcounter{@bropd@e}{##1}
 \ifnum\value{@bropd@e}>\value{@bropd@f}
 \setcounter{@bropd@f}{\value{@bropd@e}}
@@ -186,7 +220,9 @@ or, with \verb|pdshort|,\[E_t+\sum_{i=1}^3\br{\br{E+p}u_i}_{x_i}.\]
 \if@bropd@a
 \let\@bropd@l\empty
 %    \end{macrocode}
-% External bracket command
+% \end{macro}
+% \begin{macro}{\br}
+% External command for brackets
 %    \begin{macrocode}
 \newcommand\br[1]{\let\@bropd@m\@bropd@l
 \@bropd@j{\let\@bropd@l\empty#1\let\@bropd@l\@bropd@m}
@@ -198,15 +234,22 @@ or, with \verb|pdshort|,\[E_t+\sum_{i=1}^3\br{\br{E+p}u_i}_{x_i}.\]
 \fi
 \let\@bropd@l\empty
 \@bropd@n}
+\if@bropd@u
 %    \end{macrocode}
-% External command for alternative partial differential command
+% \end{macro}
+% \begin{macro}{\@bropd@q}
+% Internal command for first alternative partial differential command
+% \changes{v\fileversion}\filedate{Added second alternative form for partial
+% differentials}
 %    \begin{macrocode}
-\newcommand\pd[3][]{\def\@bropd@h{#1}
+\def\@bropd@q#1#2#3{\def\@bropd@h{#1}
 \ifx\@bropd@h\empty
 \@bropd@bfalse
 \else
 %    \end{macrocode}
 % Default partial differential if character provided as optional argument
+% \changes{v\fileversion}\filedate{Allowed partial differential with empty
+% numerator without need for bracket command after}
 %    \begin{macrocode}
 \if!\ifnum9<1#1!\else_\fi
 \@bropd@bfalse
@@ -214,12 +257,48 @@ or, with \verb|pdshort|,\[E_t+\sum_{i=1}^3\br{\br{E+p}u_i}_{x_i}.\]
 \@bropd@btrue
 \fi
 \fi
-\if@bropd@b\@bropd@g{#1}{#2}{\noexpand#3}\partial
+\ifx\@bropd@o\@bropd@t
+\@bropd@btrue\let\@bropd@o\empty
+\fi
+\if@bropd@b\@bropd@g{#1}\@bropd@o{\noexpand#3}\partial
+\else
+%    \end{macrocode}
+% Construct alternate form partial differential
+%    \begin{macrocode}
+\partial_{\ifx\@bropd@h\empty
+\@for\@bropd@i:=#3\do\@bropd@i\else\setcounter{@bropd@c}0
+\loop
+\ifnum\value{@bropd@c}<#1
+#3\stepcounter{@bropd@c}
+\repeat
+\fi}
+\@bropd@o
+\fi}
+\else
+%    \end{macrocode}
+% Internal command for second alternative partial differential command
+%    \begin{macrocode}
+\def\@bropd@q#1#2#3{\def\@bropd@h{#1}
+\ifx\@bropd@h\empty
+\@bropd@bfalse
+\else
+%    \end{macrocode}
+% Default partial differential if character provided as optional argument
+%    \begin{macrocode}
+\if!\ifnum9<1#1!\else_\fi
+\@bropd@bfalse
+\else
+\@bropd@btrue
+\fi
+\fi
+\ifx\@bropd@o\@bropd@t
+\@bropd@btrue\let\@bropd@o\empty
+\fi
+\if@bropd@b\@bropd@g{#1}\@bropd@o{\noexpand#3}\partial
 \else
 %    \end{macrocode}
 % Construct alternate form partial differential
 %    \begin{macrocode}
-\def\@bropd@o{#2}
 \def\@bropd@p{\ifx\@bropd@h\empty
 \@for\@bropd@i:=#3\do\@bropd@i\else\setcounter{@bropd@c}0
 \loop
@@ -228,26 +307,46 @@ or, with \verb|pdshort|,\[E_t+\sum_{i=1}^3\br{\br{E+p}u_i}_{x_i}.\]
 \repeat
 \fi}
 \ifx\@bropd@o\empty
-\let\@bropd@l\@bropd@p\else{#2}{_{\@bropd@p}}\fi\fi}
+\let\@bropd@l\@bropd@p\else{\@bropd@o}{_{\@bropd@p}}\fi\fi}
+\fi
 \else
 %    \end{macrocode}
-% External command for default partial differentials
+% Internal command for default partial differentials
 %    \begin{macrocode}
-\newcommand\pd[3][]{\@bropd@g{#1}{#2}{\noexpand#3}\partial}
+\def\@bropd@q#1#2#3{\@bropd@g{#1}{#2}{\noexpand#3}\partial}
 %    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\br}
 % External command for brackets
 %    \begin{macrocode}
 \newcommand\br[1]{\@bropd@j{#1}\@bropd@k}
 \fi
 %    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\pd}
+% \changes{v\fileversion}\filedate{Brackets automatically added after empty
+% numerator}
+%    \begin{macrocode}
+\newcommand\pd[3][]{\def\@bropd@o{#2}
+\ifx\@bropd@o\empty
+\let\@bropd@v\br
+\else
+\let\@bropd@v\empty
+\fi
+\@bropd@q{#1}{#2}{#3}\@bropd@v}
+%    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\@bropd@r}
 % Format ordinary differential based on font type
 %    \begin{macrocode}
 \if@bropd@s
-\newcommand\@bropd@r{\mathsf{d}}
+\def\@bropd@r{\mathsf d}
 \else
-\newcommand\@bropd@r{\mathrm{d}}
+\def\@bropd@r{\mathrm d}
 \fi
 %    \end{macrocode}
+% \end{macro}
+% \begin{macro}{\od}
 % External command for ordinary differentials
 %    \begin{macrocode}
 \newcommand\od[3][]{\def\@bropd@h{#1}
@@ -255,4 +354,5 @@ or, with \verb|pdshort|,\[E_t+\sum_{i=1}^3\br{\br{E+p}u_i}_{x_i}.\]
 {\@bropd@r#3\ifx\@bropd@h\empty\else^{#1}\fi}}
 \endinput
 %    \end{macrocode}
+% \end{macro}
 % \endinput
diff --git a/Master/texmf-dist/tex/latex/bropd/bropd.sty b/Master/texmf-dist/tex/latex/bropd/bropd.sty
index 5f16b74b052..30495203af6 100644
--- a/Master/texmf-dist/tex/latex/bropd/bropd.sty
+++ b/Master/texmf-dist/tex/latex/bropd/bropd.sty
@@ -23,19 +23,22 @@
 %% bropd.pdf.
 \NeedsTeXFormat{LaTeX2e}
 \ProvidesPackage{bropd}
-[2012/11/04 1.0 automated typing of brackets and differential operators]
-\newif\if@bropd@a\newif\if@bropd@b\newif\if@bropd@s
+[2012/11/08 1.1 automated typing of brackets and differential operators]
+\newif\if@bropd@a\newif\if@bropd@b\newif\if@bropd@s\newif\if@bropd@u
 \newcounter{@bropd@c}\newcounter{@bropd@d}
 \newcounter{@bropd@e}\newcounter{@bropd@f}
-\DeclareOption{pdshort}{\@bropd@atrue}
+\DeclareOption{pdshort}{\@bropd@atrue\@bropd@ufalse}
+\DeclareOption{pdalt}{\@bropd@atrue\@bropd@utrue}
 \DeclareOption{sans}{\@bropd@strue}\ProcessOptions
-\newcommand\@bropd@g[4]{\def\@bropd@h{#1}
+\def\@bropd@t{!}
+\def\@bropd@g#1#2#3#4{\def\@bropd@h{#1}
+\ifx\@bropd@o\@bropd@t\let\@bropd@o\empty\fi
 \ifx\@bropd@h\empty
 \setcounter{@bropd@c}0\setcounter{@bropd@d}1
 \let\@bropd@h\empty
 \@for\@bropd@i:=#3\do{\stepcounter{@bropd@c}}
 \frac{#4\ifnum\value{@bropd@c}>1
-^{\arabic{@bropd@c}}\fi#2}
+^{\arabic{@bropd@c}}\fi\@bropd@o}
 {\@for\@bropd@i:=#3\do{
 \ifx\@bropd@i\@bropd@h
 \stepcounter{@bropd@d}
@@ -51,9 +54,9 @@
 \ifnum\value{@bropd@d}>1
 ^{\arabic{@bropd@d}}\fi}
 \else
-\frac{#4^{#1}#2}{#4#3^{#1}}
+\frac{#4^{#1}\@bropd@o}{#4\noexpand#3^{#1}}
 \fi}
-\newcommand\@bropd@j[1]{\setcounter{@bropd@f}0
+\def\@bropd@j#1{\setcounter{@bropd@f}0
 {\renewcommand{\br}[1]{\stepcounter{@bropd@e}{##1}
 \ifnum\value{@bropd@e}>\value{@bropd@f}
 \setcounter{@bropd@f}{\value{@bropd@e}}
@@ -84,7 +87,8 @@
 \fi
 \let\@bropd@l\empty
 \@bropd@n}
-\newcommand\pd[3][]{\def\@bropd@h{#1}
+\if@bropd@u
+\def\@bropd@q#1#2#3{\def\@bropd@h{#1}
 \ifx\@bropd@h\empty
 \@bropd@bfalse
 \else
@@ -94,9 +98,36 @@
 \@bropd@btrue
 \fi
 \fi
-\if@bropd@b\@bropd@g{#1}{#2}{\noexpand#3}\partial
+\ifx\@bropd@o\@bropd@t
+\@bropd@btrue\let\@bropd@o\empty
+\fi
+\if@bropd@b\@bropd@g{#1}\@bropd@o{\noexpand#3}\partial
+\else
+\partial_{\ifx\@bropd@h\empty
+\@for\@bropd@i:=#3\do\@bropd@i\else\setcounter{@bropd@c}0
+\loop
+\ifnum\value{@bropd@c}<#1
+#3\stepcounter{@bropd@c}
+\repeat
+\fi}
+\@bropd@o
+\fi}
+\else
+\def\@bropd@q#1#2#3{\def\@bropd@h{#1}
+\ifx\@bropd@h\empty
+\@bropd@bfalse
+\else
+\if!\ifnum9<1#1!\else_\fi
+\@bropd@bfalse
+\else
+\@bropd@btrue
+\fi
+\fi
+\ifx\@bropd@o\@bropd@t
+\@bropd@btrue\let\@bropd@o\empty
+\fi
+\if@bropd@b\@bropd@g{#1}\@bropd@o{\noexpand#3}\partial
 \else
-\def\@bropd@o{#2}
 \def\@bropd@p{\ifx\@bropd@h\empty
 \@for\@bropd@i:=#3\do\@bropd@i\else\setcounter{@bropd@c}0
 \loop
@@ -105,15 +136,23 @@
 \repeat
 \fi}
 \ifx\@bropd@o\empty
-\let\@bropd@l\@bropd@p\else{#2}{_{\@bropd@p}}\fi\fi}
+\let\@bropd@l\@bropd@p\else{\@bropd@o}{_{\@bropd@p}}\fi\fi}
+\fi
 \else
-\newcommand\pd[3][]{\@bropd@g{#1}{#2}{\noexpand#3}\partial}
+\def\@bropd@q#1#2#3{\@bropd@g{#1}{#2}{\noexpand#3}\partial}
 \newcommand\br[1]{\@bropd@j{#1}\@bropd@k}
 \fi
+\newcommand\pd[3][]{\def\@bropd@o{#2}
+\ifx\@bropd@o\empty
+\let\@bropd@v\br
+\else
+\let\@bropd@v\empty
+\fi
+\@bropd@q{#1}{#2}{#3}\@bropd@v}
 \if@bropd@s
-\newcommand\@bropd@r{\mathsf{d}}
+\def\@bropd@r{\mathsf d}
 \else
-\newcommand\@bropd@r{\mathrm{d}}
+\def\@bropd@r{\mathrm d}
 \fi
 \newcommand\od[3][]{\def\@bropd@h{#1}
 \frac{\@bropd@r\ifx\@bropd@h\empty\else^{#1}\fi#2}