texlive[65523] Master/texmf-dist: diffcoeff (11jan23)
commits+karl at tug.org
commits+karl at tug.org
Wed Jan 11 21:44:28 CET 2023
Revision: 65523
http://tug.org/svn/texlive?view=revision&revision=65523
Author: karl
Date: 2023-01-11 21:44:28 +0100 (Wed, 11 Jan 2023)
Log Message:
-----------
diffcoeff (11jan23)
Modified Paths:
--------------
trunk/Master/texmf-dist/doc/latex/diffcoeff/README.txt
trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff.pdf
trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff.tex
trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff-doc.def
trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff.sty
Added Paths:
-----------
trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff4.pdf
trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff4.tex
trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff4.sty
trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff5.def
Modified: trunk/Master/texmf-dist/doc/latex/diffcoeff/README.txt
===================================================================
--- trunk/Master/texmf-dist/doc/latex/diffcoeff/README.txt 2023-01-11 20:43:41 UTC (rev 65522)
+++ trunk/Master/texmf-dist/doc/latex/diffcoeff/README.txt 2023-01-11 20:44:28 UTC (rev 65523)
@@ -11,19 +11,26 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-This is version 4.1 of diffcoeff.sty, and associated files,
-and requires the LaTeX3 bundles l3kernel and l3packages. The
-package eases the consistent writing of ordinary, partial
-and other derivatives of arbitrary order. Version 4.1 resolves
-an error arising from changes to xtemplate and some spacing
-issues in derivative denominators.
+Version 5.0 of diffcoeff introduces many interface incompat-
+ibilities with version 4. For that reason v5.0 and v4.2 are
+are packaged together. Version 4 can always be used to comp-
+ile an older document by using the trailing optional argument
+in the \usepackage statement, e.g., \usepackage{diffcoeff}[=v4]
+The aim in both versions is to ease the writing of differential
+coefficients (derivatives) and related quantities (jacobians,
+differentials). Both versions require xtemplate from the
+l3packages bundle. Version 5 also requires the mleftright
+package.
Manifest
%%%%%%%%
README.txt this document
-diffcoeff.sty LaTeX .sty file
-diffcoeff-doc.def definition file of variant forms
- to be placed with the .sty file
-diffcoeff.pdf documentation
-diffcoeff.tex LaTeX source of documentation
+diffcoeff.sty LaTeX .sty file (current version, v5.0)
+diffcoeff4.sty LaTeX .sty file (older version, v4.2)
+diffcoeff5.def definition file of variant forms in v5
+diffcoeff-doc.def definition file of variant forms in v4
+diffcoeff.pdf documentation for current version, v5
+diffcoeff.tex LaTeX source of documentation for v5.
+diffcoeff4.pdf documentation for older version, v4
+diffcoeff4.tex LaTeX source of documentation for v4
Modified: trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff.pdf
===================================================================
(Binary files differ)
Modified: trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff.tex
===================================================================
--- trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff.tex 2023-01-11 20:43:41 UTC (rev 65522)
+++ trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff.tex 2023-01-11 20:44:28 UTC (rev 65523)
@@ -1,6 +1,6 @@
%% LyX 2.4.0-alpha3 created this file. For more info, see https://www.lyx.org/.
%% Do not edit unless you really know what you are doing.
-\documentclass[english]{article}
+\documentclass[english]{report}
\usepackage{lmodern}
\renewcommand{\sfdefault}{lmss}
\renewcommand{\ttdefault}{lmtt}
@@ -7,15 +7,20 @@
\usepackage[T1]{fontenc}
\usepackage{textcomp}
\usepackage[latin9]{inputenc}
+\setcounter{secnumdepth}{3}
+\setcounter{tocdepth}{3}
\synctex=-1
\usepackage{color}
+\definecolor{shadecolor}{rgb}{1, 0.667969, 0.5}
\usepackage{babel}
+\usepackage{cprotect}
\usepackage{wrapfig}
\usepackage{booktabs}
-\usepackage{calc}
+\usepackage{framed}
\usepackage{url}
\usepackage{amsmath}
\usepackage{amssymb}
+\usepackage{stmaryrd}
\usepackage{esint}
\usepackage[unicode=true,pdfusetitle,
bookmarks=true,bookmarksnumbered=true,bookmarksopen=true,bookmarksopenlevel=2,
@@ -33,24 +38,75 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
\newenvironment{centred}%
- {\begin{center}\baselineskip=13pt\parskip=1pt}{\end{center}}
+ {\begin{center}\baselineskip=13pt\parskip=1pt }{\end{center}}
\newenvironment{example}%
{\begin{center}\ttfamily}{\end{center}}
-\newenvironment{lyxcode}
- {\par\begin{list}{}{
- \setlength{\rightmargin}{\leftmargin}
- \setlength{\listparindent}{0pt}% needed for AMS classes
- \raggedright
- \setlength{\itemsep}{0pt}
- \setlength{\parsep}{0pt}
- \normalfont\ttfamily}%
- \item[]}
- {\end{list}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
-\usepackage{babel}
-\usepackage[def-file=diffcoeff-doc]{diffcoeff}
+\usepackage[def-file=diffcoeff5,spaced=-1]{diffcoeff}
+% nabla in numer, d in denom
+\difdef { f, s } { n }
+ {
+ op-symbol = \nabla,
+ op-symbol-alt = \mathrm{d}
+ }
+% no sub nudge (a sea of white space)
+\difdef { fp } { wsp }
+ { sub-nudge = 0 mu }
+% align op left; no italic nudge
+\difdef { f } { left0 }
+ {
+ *op-set-left = true,
+ *italic-nudge = 0 mu
+ }
+% align op left; italic nudge
+\difdef { fp } { left }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu,
+ *op-set-left = true,
+ *italic-nudge = 3 mu
+ }
+% partial variant of \diff
+\difdef { f } { p }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu
+ }
+% partial, 3mu sep of terms
+\difdef { fp, sp } { 3mu }
+ { multi-term-sep = 3 mu }
+% D jacobian
+\difdef { j } { D }
+ { op-symbol = D }
+% square bracket jabobian
+\difdef { j } { [ }
+ {
+ lvwrap-Ldelim = \onemu\mleft [,
+ lvwrap-Rdelim = \mright ]
+ }
+% mimicking the \Braket command
+% of the braket package
+\difdef{ s }{ bk }
+ {
+ slash-tok = ,
+ op-symbol = ,
+ multi-term-sep = 3mu\middle|\mskip3mu ,
+ outer-Ldelim=\left\langle ,
+ outer-Rdelim=\right\rangle
+ }
+\NewDocumentCommand \Braket { m }
+ {
+ \difoverride {\negmu}
+ \difs.bk.{}{#1}[]
+ }
+
+\ifdefined\showcaptionsetup
+ % Caption package is used. Advise subfig not to load it again.
+ \PassOptionsToPackage{caption=false}{subfig}
+\fi
+\usepackage{subfig}
\makeatother
\begin{document}
@@ -57,128 +113,206 @@
\title{\texttt{diffcoeff}~\\
a \LaTeX{} package to ease\texttt{ }the~\\
writing of differential coefficients \\
- Version 4.1}
+ Version 5.0}
\author{Andrew Parsloe\\
{\small (ajparsloe at gmail.com)}}
\maketitle
\begin{abstract}
-\noindent This package eases the consistent writing of ordinary, partial
-and other derivatives of arbitrary (algebraic or numeric) order. For
-mixed partial derivatives, the total order of differentiation is calculated
-by the package. Optional arguments allow for points of evaluation
-(ordinary derivatives), or variables held constant (partial derivatives),
-and the placement of the differentiand in numerator or appended. The
-package uses \texttt{xtemplate}, allowing systematic fine-tuning of
-the display and generation and use of variant forms, including derivatives
-built from $D$, $\Delta$ or $\delta$. A command for differentials
-ensures the $\dl x$ (or $\dl.up.x$) used in integrals is consistent
-with the form used in derivatives.
+\noindent \verb`diffcoeff` is a \LaTeX{} package to ease the writing
+of ordinary, partial and other derivatives of arbitrary algebraic
+or numeric order. For mixed partial derivatives, the total order of
+differentiation is calculated by the package. Optional arguments allow
+for points of evaluation (ordinary derivatives), or variables held
+constant (partial derivatives), and the placement of the differentiand
+in numerator or appended. Besides $\diff yx$, forms like $\difs yx$
+and $\difcp yx$ are also available, as well as derivatives built
+from $D$, $\Delta$, $\delta$, and configurable jacobians and differentials.
+Other notations like line elements ($\dl.+.{x,y,z}^{2}$) and bra-kets
+are easily produced.
+
+Version 5 of \verb`diffcoeff` more fully embraces the configurability
+offered by \verb`xtemplate` than earlier versions. Some incompatibilities
+have arisen, but all is not lost: version 4 is still available with
+the command
+
+\verb`\usepackage[<options>]{diffcoeff}[=v4]`
\end{abstract}
-\tableofcontents{}
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
-\section{Introduction}
+\subsubsection*{For users of version 4}
-The \LaTeX{} package \texttt{diffcoeff.sty} is written in the expl3
-language of \LaTeX 3\texttt{ }and requires the bundles \texttt{l3kernel}
-which is now part of standard \LaTeX{} (since early 2020) and \texttt{l3packages}
-(the latter for the \texttt{xparse}, \texttt{l3keys2e} and especially
-\texttt{xtemplate} packages\texttt{)}. The package is invoked in the
-usual way by entering
-\begin{lyxcode}
-\textbackslash usepackage\{diffcoeff\}
-\end{lyxcode}
-in the preamble of your document.
+The \verb`\diff` and \verb`\diffp` commands of version 4 of \verb`diffcoeff`
+remain, but lack the `spacing switch' \verb`!` (which on reflection
+was a mistake) and, more noticeably, the `slash switch' \verb`/`.
+Slash-fraction derivatives are now created with the \verb`\difs`
+and \verb`\difsp` commands. New commands \verb`\difc` and \verb`\difcp`
+produce derivatives in `compact notation' like $\difc yx$ and $\difcp yx$.
+To avoid cluttering formulas with a second square-bracket delimited
+optional argument before the differentiand, the order-override option
+has been replaced by a new command \verb`\difoverride`. The order
+of differentiand and variable(s) of differentiation can now be reversed,
+when the differentiand is appended, by using a second star, e.g.,
+\verb`\diffp**`. The two-argument \verb`\diffdef` command of earlier
+versions has been replaced by the three-argument command \verb`\difdef`,
+the additional argument determining which one or more of the \verb`f`,
+\verb`s`, \verb`c`, \verb`fp`, \verb`sp` or \verb`cp` forms the
+defined variant applies to. The differential command \verb`\dl` has
+been rewritten and is now fully template-configurable (allowing easy
+writing of line elements like $\dl.+.{x,y,z}^{2}$), and the jacobian
+command \verb`\jacob` is also configurable. Indeed version 5 of \verb`diffcoeff`
+more fully embraces the configurability offered by the \verb`xtemplate`
+package than previous versions, bringing other notations -- like
+those of the \verb`braket` package -- within its compass.
-\subsubsection*{Note on terminology}
+\subsubsection*{ISO defaults}
-I refer throughout to the quantity or function being differentiated
-as the \emph{differentiand} or \emph{derivand }(in line with \emph{integrand},
-\emph{operand}, etc.).
+Unlike the default set-up in version 4, the defaults in version 5
+of \verb`diffcoeff` are chosen to reflect ISO recommendations; see
+the standard ISO 80000-2. In particular this means upright `d's
+and subscripted parentheses enclosing a derivative to indicate a point
+of evaluation. This document is written with those defaults. For those
+(like the author) who prefer math-italic `d's and a subscripted
+vertical rule to indicate a point of evaluation, the means of creating
+`variant forms' or changing the defaults is readily available; see
+\xA7\xA7\ref{sec:Variant-forms}, \ref{sec:ChangingDefaults}.\end{shaded}%
+\end{minipage}
-\subsubsection*{New in version 4.0}
+\tableofcontents{}
-(See \xA7\ref{sec:Version-comparison} for a comparison of versions.)
-Version 4.0
-\begin{enumerate}
-\item enables the insertion of a small space before the differentiand, either
-as the default behaviour (package option \verb`spaced`) or at explicit
-request (argument \verb`!` of the \verb`\diff` command); see \xA7\ref{subsec:Spacing-before-derivand};
-\item prevents the ligature $df$ that marred previous versions; this is
-now rendered $\dl f$;
-\item offers the document command \verb`\dlp` for the \emph{partial} differential;
-see \xA7\ref{subsec:Partial-differential};
-\item no longer accepts \emph{the braced form} of the\emph{ }trailing optional
-argument specifying a point of evaluation or (for partial derivatives)
-variables held constant. This was a relic from version 1 of \texttt{diffcoeff},
-and has been deprecated since version 2.
-\end{enumerate}
+\chapter{Introduction}
-\subsubsection*{New in version 4.1}
-\begin{enumerate}
-\item changes the code handling the \verb`long-var-wrap` setting to avoid
-a problem with a change in \verb`xtemplate` (see \url{https://tex.stackexchange.com/questions/646976/error-with-package-diffcoeff})\footnote{Based on a suggestion from \noun{Joseph Wright}.};
-\item prevents (hitherto overlooked) ligatures in the \emph{denominators}
-of differential coefficients.
-\end{enumerate}
+\verb`diffcoeff.sty` is written in the \verb`expl3` language of
+\LaTeX 3, now part of standard \LaTeX{} since February 2020. A \LaTeX{}
+distribution from or later than that date is assumed. The package
+also requires the packages \verb`xtemplate` (part of the \verb`l3packages`
+bundle) and \verb`mleftright`. The package is loaded in the usual
+way by entering
+\begin{verbatim}
+ \usepackage{diffcoeff}
+\end{verbatim}
+in the preamble of your document or, if package options are being
+used,\footnote{Angle brackets indicate possible user input (\emph{without} the angle
+brackets).}
+\begin{verbatim}
+ \usepackage[<options>]{diffcoeff}
+\end{verbatim}
+The interface of \verb`diffcoeff` with version 5 has changed from
+earlier versions. If you want the familiar behaviour of version 4,
+add to these commands a trailing optional argument like this,
+\begin{verbatim}
+ \usepackage[<options>]{diffcoeff}[=v4]
+\end{verbatim}
+(with no space after the `=' sign!). Of course you will not get
+the new features of version 5. Working with version 4 is described
+in the document \verb`diffcoeff4.pdf`.
-\subsection{Package options}
+\section{Package options}
-\label{subsec:Package-options}There are three package options, which
+\label{sec:Package-options}There are four package options, which
are entered in a comma-separated list in the optional argument of
-the \texttt{\textbackslash usepackage} command.
+the \verb`\usepackage` command. The \emph{second} and \emph{fourth}
+are new with version 5 of \verb`diffcoeff`.
\begin{enumerate}
-\item The first is a switch, \texttt{ISO}, which turns on formatting conforming
-to ISO recommendations, principally upright `d's:
-\begin{lyxcode}
-\textbackslash usepackage{[}ISO{]}\{diffcoeff\}
-\end{lyxcode}
-The full effect of this option is disscussed in \xA7\ref{sec:Changing-defaults}.
-\item The second is another switch, \texttt{spaced}, and \emph{is new with
-version 4 }of \texttt{diffcoeff}. This switch ensures a small space
-is inserted before the differentiand:
-\begin{lyxcode}
-\textbackslash usepackage{[}spaced{]}\{diffcoeff\}
-\end{lyxcode}
-This is discussed in \xA7\ref{subsec:Spacing-before-derivand}.
-\item The third requires a filename \texttt{<filename>} for a file \texttt{<filename>.def}
-containing definitions of variant forms of derivative:
-\begin{lyxcode}
-\textbackslash usepackage{[}def-file=<filename>{]}\{diffcoeff\}
-\end{lyxcode}
-This is discussed in \xA7\ref{subsec:The-.def-file}. For the present
-document, the call is
-\begin{lyxcode}
-\textbackslash usepackage{[}def-file=diffcoeff-doc{]}\{diffcoeff\}
-\end{lyxcode}
+\item The first package option is the \verb`spaced` option which takes
+three values:
+\begin{enumerate}
+\item \verb`spaced=1` inserts a small space before the differentiand; this
+is the default so that entering \verb`spaced` is equivalent to \verb`spaced=1`;
+\item \verb`spaced=0` inserts no space before the differentiand; \verb`diffcoeff`
+is initialized to \verb`spaced=0` so that if the spaced option is
+not used \verb`spaced=0` is assumed;
+\item \verb`spaced=-1` inserts a small space before the differentiand \emph{if
+it contains more than one token}, and no space otherwise. The present
+document uses \verb`spaced=-1`.
\end{enumerate}
+This option is discussed in \xA7\ref{subsec:Spacing-before-derivand}.
+\item For the second package option, by entering \verb`mleftright` in the
+options list the command \verb`\mleftright` is automatically inserted
+in the preamble. The effect is to change all occurrences of \verb`\left`,
+\verb`\right` in the document to \verb`\mleft`, \verb`\mright`
+so that the spacing around scalable delimiters modified by \verb`\left`,
+\verb`\right` is reduced; see the box below and \xA7\ref{subsec:mleftright}.
+The present document does not use this package option.
+\item The third package option requires the \verb`<filename>` of a file
+with extension \verb`.def`, \verb`<filename>.def`, containing definitions
+of variant forms (see \xA7\ref{sec:Variant-forms}) of derivative:
+\begin{verbatim}
+ \usepackage[def-file=<filename>]{diffcoeff}
+\end{verbatim}
+This is discussed in \xA7\ref{subsec:The-.def-file}. The present document
+uses the package option \verb`def-file=diffcoeff5`.
+\item The fourth package option \verb`DIF` is a comma list of \emph{key=value}
+statements amending the built-in defaults for the `grandparent'
+template \verb`DIF`; see \xA7\ref{subsec:Changing-DIF-defaults}. The
+present document does not use this package option.
+\end{enumerate}
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
+To see the effect of the \verb`mleftright` package, consider the
+expression
+\begin{centred}
+\verb`\[ \ln \left(\frac xy\right),\quad\sin\left(x^2\right). \]`
+$\Longrightarrow$ \[ \ln \left(\frac xy\right),\quad\sin\left(x^2\right). \]
+\end{centred}
+in which there is significant whitespace before and after the parentheses.
+The package \verb`mleftright` enables this whitespace to be reduced
+by using \verb`\mleft`, \verb`\mright` in place of \verb`\left`,
+\verb`\right`:
+\begin{centred}
+\verb`\[ \ln \mleft(\frac xy\mright),\quad\sin\mleft(x^2\mright). \]`
+$\Longrightarrow$ \[ \ln \mleft(\frac xy\mright),\quad\sin\mleft(x^2\mright). \]
+\end{centred}
+\end{shaded}%
+\end{minipage}
+\noindent %
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
+If you put \verb`\mleftright` in the preamble, which is what the
+\verb`mleftright` package option does, then all occurrences of \verb`\left`,
+\verb`\right` in the document will be affected. \verb`\left`, \verb`\right`
+can be restored to their normal behaviour by the command \verb`\mleftrightrestore`.
+Rather than use \verb`\mleft`, \verb`\mright` explicitly, as in
+the example, the same effect can be obtained by using \verb`\left`,
+\verb`\right` and preceding the expression with the command \verb`\mleftright`:
+\begin{verbatim}
+ \mleftright
+ \[ \ln \left(\frac xy\right),\quad\sin \left(x^2\right). \]
+ \mleftrightrestore
+\end{verbatim}
+$\Longrightarrow$ \mleftright
+ \[ \ln \left(\frac xy\right),\quad\sin \left(x^2\right). \]
+ \mleftrightrestore \end{shaded}%
+\end{minipage}\medskip{}
+For the present document, the call is
+\begin{verbatim}
+ \usepackage[def-file=diffcoeff5,spaced=-1]{diffcoeff}
+\end{verbatim}
+
\section{A Rogues' Gallery of derivatives}
-\label{sec:Rogues'-gallery}Browsing through texts on statistical
-mechanics, relativity and classical mechanics I find the following
-choice examples of derivatives `disporting every which way'.
-
-Multi-character variables of differentiation un-parenthesized:
-
+\label{sec:Rogues'-gallery}Browsing through some (rather old) calculus
+textbooks and texts on statistical mechanics, relativity and classical
+mechanics I find the following choice examples of derivatives `disporting
+every which way'.
+\begin{itemize}
+\item Multi-character variables of differentiation un-parenthesized:
\begin{equation}
-\diffp{\frac{\psi}{\Theta}}{\frac{1}{\Theta}},\quad\diffp{E/T}{1/T},\quad\diffp{\ln f}{\ln x_{0}},\quad\diffp\psi{a_{i},\frac{1}{\Theta}},\quad\diffp{\mathcal{L}}{\eta_{,i}^{(r)}}.\label{eq:eg1}
+\diffp{\frac{\psi}{\Theta}}{\frac{1}{\Theta}},\quad\diffp{E/T}{1/T},\quad\diff{\ln f}{\ln x_{0}},\quad\diffp\psi{a_{i},\frac{1}{\Theta}},\quad\diffp{\mathcal{L}}{\eta_{,i}^{(r)}}.\label{eq:eg1}
\end{equation}
-Multi-character variables of differentiation parenthesized:
+\item Multi-character variables of differentiation parenthesized in \emph{higher-order}
+derivatives, where the parentheses do not or (sometimes) do include
+the operator:
\begin{equation}
-\diffp H{\displaystyle \diffp S{q_{k}}[]},\quad\diffp\varepsilon{(1/\Theta)}.\label{eq:eg2}
+\diffp[2]q{\frac{1}{\Theta}},\quad\diffp[2]q{1/\Theta},\quad\diffp[2]\varepsilon{a_{i}},\quad\diff.(dv).[2]{\phi^{i}(x^{i})}{x^{i}}.\label{eq:eg3}
\end{equation}
-Higher-order derivatives where the parentheses do not or sometimes
-do include the operator:
-\begin{equation}
-\diffp[2]q{\frac{1}{\Theta}},\quad\diffp[2]q{1/\Theta},\quad\diffp[2]\varepsilon{a_{i}},\quad\diff.wrapall.[2]{\phi^{i}(x^{i})}{x^{i}}.\label{eq:eg3}
-\end{equation}
-Should the $d$ or $\partial$ be included within the parentheses,
+Should the $\mathrm{d}$ or $\partial$ be included within the parentheses,
as in the last of (\ref{eq:eg3}), or not, as in the others? Logic
says `yes'; practice suggests (generally) `no'.
-
-Indicating a point of evaluation is similarly varied:
+\item Indicating a point of evaluation is similarly varied:
\begin{equation}
-\diff.pvrule.\phi\varepsilon[\varepsilon=\varepsilon_{0}],\quad\diff.pvrule.[2]\phi\varepsilon[\varepsilon=\varepsilon_{0}],\quad\diff.psqbra.{b^{\beta}}{a^{\alpha}}[b=0],\quad\diff.paren.uv[v=0].\label{eq:eg4}
+\diffp.|.\phi\varepsilon[\varepsilon=\varepsilon_{0}],\quad\diff.|.[2]\phi\varepsilon[\varepsilon=\varepsilon_{0}],\quad\diffp.].{b^{\beta}}{a^{\alpha}}[b=0],\quad\diff uv[v=0].\label{eq:eg4}
\end{equation}
ISO 80000-2 (item 2.11.13) favours the last of these -- parentheses
-- for ordinary derivatives. Presumably, partial derivatives should
@@ -185,1920 +319,2889 @@
follow suit, although parentheses are also used to indicate variables
held constant:
\begin{equation}
-\diffp*{\frac{P}{T}}U[V],\quad\diffp S{N_{2}}[U,V,N_{1}],\quad\diffp S/T[V].\label{eq:eg5}
+\diffp*{\frac{P}{T}}U[V],\quad\diffp S{N_{2}}[U,V,N_{1}],\quad\difsp ST[V]\,.\label{eq:eg5}
\end{equation}
-
-Other symbols besides $d$ and $\partial$ are used to denote derivative-like
-quantities. From introductory calculus and from classical mechanics
-and thermodynamics come $\delta$ and $\Delta$, from fluid mechanics
-comes $D$:
+\item Other symbols besides $\mathrm{d}$ and $\partial$ are used to denote
+derivative-like quantities. From introductory calculus and from classical
+mechanics and thermodynamics come $\delta$ and $\Delta$, from fluid
+mechanics comes $\mathrm{D}$:
\begin{equation}
-\diff.delta.yx,\quad\diff.D.\rho t,\quad\diff.pDelta.UT[V],\quad\diff.Delta.U/T,\quad\diff.delta.{\mathcal{L}}{\eta^{(r)}}.\label{eq:eg6}
+\diff.gd.yx,\quad\diff.D'.\rho t,\quad\diff.gD.UT[V],\quad\difs.gD.UT,\quad\diff.gd.{\mathcal{L}}{\eta^{(r)}}.\label{eq:eg6}
\end{equation}
-
-There are those, like the International Organization for Standardization
-(ISO), who stipulate (or prefer) an upright `d' for their derivatives:
+\item There are those, like the International Organization for Standardization
+(ISO), who stipulate (or prefer) an upright $\mathrm{d}$ for their
+derivatives, and there are those (like the author, through sixty years
+of habit) who prefer a math-italic $d$:
\begin{equation}
-\diff.up.yx.\label{eq:eg11}
+\diff yx,\qquad\diff.d'.yx,\label{eq:eg11}
\end{equation}
-When the differentiand is too big or awkward to sit in the numerator
-and is appended to the operator, the $d$ or $\partial$ in the numerator
-is generally centred -- but not always. In texts prior to the age
-of computerised typesetting one will sometimes find the symbol pushed
-to the \emph{left}:
+and of course also in slash-fraction form $\difs yx$, $\difs.d'.yx$.
+Subscripted forms of derivative are also used -- for example, $\difcp Fx$,
+or in the discussion of differential equations one sometimes comes
+across expressions like
+\[
+\difc.bD.[2]y{x}+2\difc.bD.y{x}-4=0.
+\]
+\item When the differentiand is too big or awkward to sit in the numerator
+and is appended to the operator, the $\mathrm{d}$ or $\partial$
+in the numerator is generally centred -- but not always. In texts
+prior to the age of computerised typesetting one will sometimes find
+the symbol pushed to the \emph{left}:
\begin{equation}
-\diff.pleft.*{\diffp{x^{i^{*}}}{x^{k^{*}}}{}}{x^{l^{*}}},\quad\diff.left.*{\left(\frac{m\mathbf{q}_{x}}{\sqrt{1-q^{2}}}\right)}{t}.\label{eq:eg12}
+\diffp.left.*{\diffp.left.{x^{i^{*}}}{x^{k^{*}}}}{x^{l^{*}}},\quad\diff.left0.*{\left(\frac{m\mathbf{q}_{x}}{\sqrt{1-q^{2}}}\right)}{t}.\label{eq:eg12}
\end{equation}
-The observant will note an italic adjustment with the first expression,
-so that the $\partial$ in the numerator and the $\partial$ in the
-denominator line up in a slanting column, but no such adjustment for
-the $d$-s in the second derivative.
-
-Then there is the case when the operator in the numerator differs
+The keen-eyed will note an italic adjustment with the first expression,
+so that the $\partial$s in the numerators are indented a little (to
+line up -- more or less -- in a slanting column with the $\partial$s
+in the denominators).
+\item Then there is the case when the operator in the numerator differs
from that in the denominator. For instance, in tensor calculus acceleration
is sometimes written
\[
-\diff.nabla.{v^{i}}t=\diff{v^{i}}t+\Gamma_{k\hphantom{i}h}^{\hphantom{k}i}v^{h}\diff{y^{k}}t
+\diff.n.{v^{i}}t=\diff{v^{i}}t+\Gamma_{k\hphantom{i}h}^{\hphantom{k}i}v^{h}\diff{y^{k}}t
\]
where $\nabla v^{i}$ is the `absolute differential' of the velocity
$v^{i}$.
+\end{itemize}
+The \verb`diffcoeff` package has the generative power to cope with
+all these variations -- see \xA7\ref{sec:Variant-forms} -- although
+it is unlikely an author should need to call on this capacity to anything
+like the extent required for this Rogues' Gallery.
-Version 2 or later of the \texttt{diffcoeff} package has the generative
-power to cope with all these variations -- see \xA7\ref{sec:Changing-defaults}
--- although it is unlikely an author should need to call on this
-capacity to anything like the extent required for this Rogues' Gallery.
+\chapter{Syntax and use}
-Finally and new with version 4 of \texttt{diffcoeff}, is the ability
-to insert space before the differentiand, something that had to be
-done explicitly by the user before. One way of thinking of a derivative
-is as an operator $\diff{}x$ applied to a function $F(x)$ producing
-another function $F'(x)$, a \emph{derived }function, the derivative.
-Although the original function is included in the numerator of the
-differential coefficient, a small space between the $d$ and $F$
-feels natural to separate the thing operated on from the thing operating:
-\[
-F'(x)=\diff!{F(x)}x.
-\]
-\texttt{diffcoeff} can now produce such spaced derivatives, either
-as the default behaviour or at explicit request; see \xA7\ref{subsec:Spacing-before-derivand}.
+\verb`diffcoeff` aims to ease the writing of derivatives (sometimes
+also called differential coefficients). There are long-established
+shorthands available in a few cases: $\dot{x}$ and $\ddot{x}$ for
+the time derivatives of a function $x$ of time $t$; $y'$ and $y''$
+for the derivatives of a function $y$ (usually) of $x$. But mostly
+derivatives are expressed in fraction form and require more keystrokes
+to compose. It is here that \verb`diffcoeff` is aimed. It uses three
+pairs of commands: \verb`\diff` and \verb`\diffp` to write (upright)
+fraction forms of ordinary and partial derivatives like $\diff yx$,
+$\diffp yx$, generally intended for display-style environments; \verb`\difs`
+and \verb`\difsp` for slash-fraction forms of ordinary and partial
+derivatives like $\difs yx$, $\difsp yx$, generally intended for
+text-style environments; and \verb`\difc` and \verb`\difcp` to write
+compact forms of ordinary and partial derivatives like $\difc yx$
+and $\difcp yx$. (Of these, the `s' forms replace the slash argument
+for the \verb`\diff`, \verb`\diffp` commands in version 4 of \verb`diffcoeff`,
+and the `c' form is new to version 5.\cprotect\footnote{Suggested by a question on \TeX{} StackExchange: \url{https://tex.stackexchange.com/questions/652223/write-a-derivative-operator-without-denominator-using-diffcoef/652298#652298}})
-\newpage{}
+\subsubsection*{Note}
-\section{Ordinary derivatives \protect\label{sec:Ordinary-derivatives}}
+I refer throughout to the quantity or function being differentiated
+as the \emph{differentiand} or \emph{derivand }(in line with \emph{integrand},
+\emph{operand}, etc.) and shall sometimes use \verb`\difx` (resp.
+\verb`\difxp`) to make general statements about any or all of \verb`\diff`,
+\verb`\difs` or \verb`\difc` (resp.\verb`\diffp`, \verb`\difsp`,
+\verb`\difcp`).
-Writing\textbf{ }\texttt{\textbackslash diff\{y\}\{x\}} will produce
-$\diff{y}{x}$ in text style (i.e., placed between \texttt{\textbackslash (
-\textbackslash )} or \texttt{\$ \$}) or
+\section{Syntax}
+
+All commands, \verb`\difx`, \verb`\difxp`, share the same syntax.
+With options present the syntax is
+\begin{verbatim}
+ \difx.name.*[order-spec]{differentiand}
+ {variable(s)}[pt of eval]
+
+ \difx.name.**[order-spec]{variable(s)}
+ {differentiand}[pt of eval]
+\end{verbatim}
+The syntax is identical for \verb`\difxp`. The seven arguments have
+the following meanings:
+\begin{itemize}
+\item \verb`name` (optional) A dot-delimited name to distinguish a variant
+form (non-default form) of derivative; not discussed further until
+\xA7\ref{chap:Templates-defaults-variants} below, and specifically,
+\xA7\ref{sec:Variant-forms}.
+\item \verb`*` (optional) The presence of a star (asterisk) signals: \emph{append}
+the differentiand; its absence means the differentiand appears in
+the numerator of an upright- or slash-fraction form derivative; no
+effect for compact-form derivatives unless (see next) a second \verb`*`
+is present; see \xA7\ref{subsec:Appending-the-differentiand}.
+\item \verb`*` (optional) The presence of a \emph{second} star signals
+that the argument specifying the variable(s) of differentiation comes
+\emph{before} the argument specifying the differentiand; this is sometimes
+convenient when a complicated or lengthy differentiand is appended;
+see \xA7\ref{subsec:Transposing-the-argument}.
+\item \verb`order-spec` (optional) The order of differentiation when differentiating
+in a single variable, or a comma list of orders of differentiation
+for a mixed partial derivative; see \xA7\ref{subsec:Higher-order-derivatives}
+and \xA7\ref{subsec:Mixed-partial-derivatives}.
+\item \verb`differentiand` (mandatory) The function being differentiated.
+\item \verb`variable(s)` (mandatory) The variable of differentiation or
+a comma list of variables of differentiation (for a mixed partial
+derivative).
+\item \verb`pt of eval` (optional) Point of evaluation or, for partial
+derivatives, variable or variables held constant; \emph{no space}
+before the left square bracket; see \xA7\ref{subsec:Point-of-evaluation}.
+\end{itemize}
+
+\section{General use}
+
+\label{sec:General-use}Writing \verb`\diff{y}{x}` will produce $\diff{y}{x}$
+in an inline math environment (i.e., placed between \verb`\( \)`
+or \verb`$ $`) or
\[
\diff{y}{x}
\]
-in display style (i.e., placed between \texttt{\textbackslash{[}
-\textbackslash{]}} ). In fact \texttt{\textbackslash diff yx} (omitting
-the braces) will produce these results, with a saving on keystrokes.
-The braces are needed only when an argument -- the differentiand
-or the variable of differentiation -- is multi-token.
+in display style (placed, for instance, between {\ttfamily\verb`\[ \]`}
+). In fact \verb`\diff yx` (omitting the braces) will produce these
+results, with a saving on keystrokes. The braces are needed only when
+an argument -- the variable of differentiation, or the differentiand
+-- is multi-token:
+\begin{centred}
+\verb`\[ \diff{\ln x}x \]` $\Longrightarrow$ \[ \diff{\ln x}x\]
+\end{centred}
\begin{itemize}
-\item If you want upright `$\mathrm{d}$'s as default, as ISO 80000-2 recommends,
-rather than the math-italic `$d$'s used here, this can easily be
-done with the package option \texttt{ISO}; see \xA7\ref{sec:Changing-defaults}
-on changing default settings.
+\item If you want math-italic `$\mathrm{d}$'s as default, see \xA7\ref{sec:ChangingDefaults}
+on changing default settings. As noted earlier, upright `d's conform
+to the standard ISO 80000-2 and are used in this document.
\end{itemize}
For inclusion in a line of text you might prefer to use a slash-fraction
-form of derivative. That is achieved by inserting a slash, `/', between
-numerator and denominator arguments: \texttt{\textbackslash diff\{\textbackslash ln
-x\}/x} produces $\diff{\ln x}/x$. Braces are required for the numerator
-in this case since it contains more than one token.
+form of derivative. That is achieved with the \verb`\difs` command:
+\verb`$ \difs yx $` produces $ \difs yx $. If you want still more
+compactness, you can use the \verb`\difc` (`c' for \emph{compact})
+command: \verb`$ \difc yx $` produces the form $ \difc yx $.
+Partial derivatives follow the same pattern as ordinary derivatives.
+The commands this time are \texttt{\textbackslash}\verb`diffp`,
+\verb`\difsp` and \verb`\difcp` for (upright) fraction, slash fraction
+and compact forms of partial derivative. Thus \verb`\diffp{F}{x}`,
+or \verb`\diffp Fx` with a saving on keystrokes, produce $\diffp Fx$
+in text style and
+\[
+\diffp{F}{x}
+\]
+in display style. (As for \verb`\diff`, the omission of braces is
+possible when dealing with a single-token differentiand or differentiation
+variable.) For inline use, \verb`\difsp Fx`, displays as $\difsp Fx$
+and \verb`\difcp` displays as $\difcp Fx$. Given that \verb`\partial`
+takes 8 keystrokes to type, all forms\emph{ }economise on keystrokes.
+
\subsection{Spacing before the differentiand}
\label{subsec:Spacing-before-derivand}There are (at least) two different
-ways in which we think of derivatives.\footnote{I thank \noun{Hans Sch\xFClein} for first raising this issue with me
-and for subsequent thoughtful comments. } We are all familiar with the argument presented in elementary calculus
-books where a curve is shown, and a point on the curve through which
-a chord has been drawn. The chord is a side -- the hypotenuse --
-of a small right-angled triangle, the other sides having lengths $\delta x$
-and $\delta y$ and being parallel to the coordinate axes. The slope
-of the chord is $\diffd yx$. By drawing smaller and smaller chords
-through the point, the ratio $\diffd yx$ approaches the slope of
-the tangent to the curve at the point. We write
+ways in which we think of derivatives. We are all familiar with the
+argument presented in elementary calculus books where a curve is shown,
+and also a point on the curve through which a chord has been drawn.
+The chord is the hypotenuse of a small right-angled triangle, the
+other sides having lengths $\delta x$ and $\delta y$ and being parallel
+to the coordinate axes. The slope of the chord is $\diff.gd.yx$.
+By drawing smaller and smaller chords through the point, the ratio
+$\diff.gd.yx$ approaches the slope of the tangent to the curve at
+the point. We write
\[
\diff yx
\]
-for the limit of $\diffd yx$. It is natural to think of $\dl y$
-and $\dl x$ as tiny lengths, like $\delta y$ and $\delta x$, in
-which case it would be quite wrong to insert space between the $d$
-and the $y$ (let alone the $d$ and the $x$). $dy$ is a single
-object, called a differential, and we write expressions like
-\begin{centred}
-\verb`\[ dy=\diff yx dx \]` $\Longrightarrow$
+for the limit of $\diff.gd.yx$. It is natural following this line
+of argument to think of $\dl y$ and $\dl x$ as tiny lengths, like
+$\delta y$ and $\delta x$, in which case it would be quite wrong
+to insert space between the $\mathrm{d}$ and the $y$ (let alone
+the $\mathrm{d}$ and the $x$). $\dl y$ is a single object, called
+a differential, and we write expressions like
\[
\dl y=\diff yx\dl x
\]
-\end{centred}
-and justly call the `fraction' in this expression a differential
-coefficient.
+and justly call the fraction in this expression a \emph{differential
+coefficient}.
But there is another way of viewing differentiation: as a process
-producing (or \emph{deriving}) one function, $f'(x)$, from another,
-$f(x)$. Here the sense is of applying $\diff{}x$ to $f(x)$. Although
-we include $f(x)$ in the numerator it is not attached to the $d$
-and should be separated from it by a small space:
-\begin{centred}
-\verb`\[ f'(x)=\diff!{f(x)}x \]` $\Longrightarrow$
+producing (or \emph{deriving}) one function, $y'(x)$, from another,
+$y(x)$. Here the sense is of applying $\diff{}x$ to a quite separate
+object, the function $y(x)$. Although we include $y(x)$ in the numerator
+it is distinct from the $d$ and should be separated from it by a
+small space:\footnote{I thank \noun{Hans Sch\xFClein} for first raising this issue with me
+and for subsequent thoughtful comments.}
\[
-f'(x)=\diff!{f(x)}x.
+y'(x)=\diff{y(x)}x.
\]
-\end{centred}
-Here the `fraction' on the right is another name for the derived
-function $f'$ and is justly called the derivative of $f$. As you
-can see a small space has been inserted between the $d$ and the $f$
-in the numerator. By default the space is \texttt{3 mu} but with the
-ability to stretch by \texttt{1 mu} or shrink by\texttt{ 2 mu}{\ttfamily\footnote{In \TeX -speak, \texttt{3mu plus 1mu minus 2mu}. }}
-as \TeX{} adjusts lines to fit on the page. (A `mu' is a `math unit'
-and is one eighteenth of a quad.) To achieve this result I have inserted
-an exclamation mark \verb`!` before the braces delimiting the differentiand.
+Here the fraction on the right is another name for the derived function
+$y'$ and is justly called the \emph{derivative} of $y$. As you can
+see a small space has been inserted between the $\mathrm{d}$ and
+the $y$ in the numerator. By default the space is \verb`3 mu` but
+with the ability to stretch by \verb`1 mu` or shrink by\texttt{ }\verb`2 mu`
+--\texttt{ }\verb`3 mu plus 1 mu minus 2 mu`\texttt{ }in \TeX -speak\footnote{Or even \texttt{3muplus1muminus2mu}.}
+-- as \TeX{} adjusts lines to fit on the page. (A `mu' is a `math
+unit' and is one eighteenth of a quad.) The size of the space inserted
+by default can be easily changed; see \xA7\ref{sec:Variant-forms} and
+\xA7\ref{sec:ChangingDefaults}.
\begin{itemize}
-\item You may want all or most of your derivatives to have this space and
-therefore will not want to be inserting exclamation marks in every
-\texttt{\textbackslash diff} command. The \texttt{spaced} package
-option switches the default behaviour to spaced derivatives (in which
-case the \texttt{!} switch now creates an \emph{un-spaced} derivative).
-The size of the space inserted by default can be easily changed; see
-\xA7\ref{sec:Changing-defaults}.
+\item You may want all or most of your derivatives to have this space before
+the derivand. The \verb`spaced=1` package option switches this behaviour
+on. However, I have used the \verb`spaced=-1` option for the present
+document which inserts space only if the derivand contains \emph{more
+than one token}. Thus \verb`y(x)` will have space inserted before
+it, but \verb`y` alone will not. This (I think) maintains the distinction
+between a differential coefficient, thought of as a ratio of tiny
+lengths, and a derivative, thought of as an operator applied to a
+function. \verb`spaced=0` inserts no space before the derivand.
+\item In version 4 of \verb`diffcoeff` an argument was added to the \verb`\diff`
+command to manually introduce a space (the \verb`!` switch) before
+the differentiand. This was a mistake and has been removed. If you
+wish to adjust the spacing, there are plenty of (short) commands in
+\LaTeX{} and \verb`diffcoeff` to do the job; see immediately below,
+\xA7\ref{subsec:Spacing-commands}.
\end{itemize}
-The present document uses the un-spaced default. For backwards compatibility
-(and perhaps because the author has done this for the last 60 years),
-this is the \textquoteleft out-of-the-box\textquoteright{} default
-that \texttt{diffcoeff} uses. Authors should make a habit of using
-one form predominantly. (There is also the possibility which I haven't
-emphasized of spacing multi-token differentiands and leaving single-token
-differentiands unspaced; see \xA7\ref{subsec:A-final-flourish}.)
+Slash-form derivatives also allow space before the derivand. By default
+this is \verb`2 mu plus 1 mu minus 2 mu`, slightly reduced from the
+fraction-form value to avoid visually detaching the initial `d'
+operator from the derivative as a whole. The value can be changed;
+see \xA7\ref{sec:Variant-forms} and \xA7\ref{sec:ChangingDefaults}. For
+the present document, with \verb`spaced=-1`, multi-token derivands
+have the space inserted, single-token derivands do not:
+\begin{centred}
+\verb`$ \difs{\ln\sin x}x, \quad \difs st $` $\Longrightarrow$ $ \difs{\ln\sin x}x, \quad \difs st $.
+\end{centred}
+For \emph{compact-form} derivatives the space before the derivand
+is \emph{always} inserted, irrespective of the setting of the \verb`spaced`
+package option, since the subscript precludes the entire symbol ever
+being viewed as a differential -- it is always an operator operating
+on a function. The inserted space, \verb`1 mu plus 1 mu minus 1 mu`
+by default, can be changed should you wish; see \xA7\ref{sec:Variant-forms}
+and \xA7\ref{sec:ChangingDefaults}:
+\begin{centred}
+\verb`$ \difc{\ln\sin x}x, \quad \difc st $` $\Longrightarrow$ $ \difc{\ln\sin x}x, \quad \difc st $.
+\end{centred}
+(The space is less for compact forms since the subscript already provides
+some visual separation.) The \verb`spaced` package option has the
+same effects on partial derivatives. Thus with \verb`spaced=1` or
+\verb`spaced=-1`, \verb`3 mu plus 1 mu minus 2 mu` of space is inserted
+before the differentiand \verb`F(x,y)` in the first member of the
+following example, space of \verb`2 mu plus 1 mu minus 2 mu` in the
+second, and space of \verb`1 mu plus 1 mu minus 1 mu` in the third:
+\begin{centred}
+\verb`\[ \diffp{F(x,y)}x,\;\difsp{F(x,y)}x,\;\difcp{F(x,y)x, \]`
+\end{centred}
+$\Longrightarrow$ \[ \diffp{F(x,y)}x,\;\difsp{F(x,y)}x,\;\difcp{F(x,y)}x. \]
-Slash-form derivatives also allow space before the differentiand.
-By default this has the same value as applied to the fraction form
-of derivative (but can be changed; see \xA7\ref{sec:Changing-defaults}):
+\noindent But for single-token differentiands in this document the
+space is not inserted for upright and slash-form derivatives:
\begin{centred}
-\verb`$ \diff!{\ln\sin x}/x $` $\Longrightarrow$ $ \diff!{\ln\sin x}/x$.
+\verb`\[ \diffp Fx,\quad \difsp Fx. \]` $\Longrightarrow$ \[ \diffp Fx,\quad \difsp Fx. \]
\end{centred}
-The \verb`\diff` command has other optional arguments (e.g. to specify
-the order of differentiation) but always the exclamation mark, if
-used, immediately precedes the differentiand. It is the positioning
-of the differentiand that it affects after all and its placement immediately
-before that argument seems natural.
+If you always want the space present, use \verb`spaced=1`; if you
+never want the space for upright- or slash-form derivatives, or wish
+to insert such space always `by hand', use \verb`spaced=0`.
-\subsubsection{Ligatures: }
-
-Prior to v.4 of \texttt{diffcoeff}, \texttt{\textbackslash diff fx}
-produced the tight pairing evident in
-\[
-\frac{df}{dx}.
-\]
-This was a bug. From version 4.0 of \texttt{diffcoeff}, such ligatures
-are prevented: \verb`\[ \diff fx \]` $\Longrightarrow$ \[ \diff fx.\]
-
\subsubsection{Spacing commands}
-\label{subsec:Spacing-commands}The \texttt{diffcoeff} package also
-offers four simple spacing commands to fine-tune the display of derivatives
-and of other quantities. These are
+\label{subsec:Spacing-commands}\LaTeX{} has its own explicit spacing
+commands. In particular \verb`\,` which is \verb`3 mu` (a thin space)
+and \verb`\!` which is \verb`-3 mu` (a negative thin space) are
+convenient in math mode. The \verb`diffcoeff` package adds four simple
+spacing commands to `fill in (most of) the gap' between these two.
+These are
\begin{description}
-\item [{\texttt{\textbackslash negmu}}] insert spacing of $-1$ mu
-\item [{\texttt{\textbackslash nilmu}}] insert spacing of $0$ mu (cf.
-use of an empty brace pair \texttt{\textbf{\{\}}} )
-\item [{\texttt{\textbackslash onemu}}] insert spacing of $1$ mu
-\item [{\texttt{\textbackslash twomu}}] insert spacing of $2$ mu
+\item [{\texttt{\textbackslash negmu}}] insert spacing of \verb`-1 mu`;
+\item [{\texttt{\textbackslash nilmu}}] insert spacing of \verb`0 mu`
+(cf. use of an empty brace pair \texttt{\textbf{\{\}}} );
+\item [{\texttt{\textbackslash onemu}}] insert spacing of \verb`1 mu`;
+\item [{\texttt{\textbackslash twomu}}] insert spacing of \verb`2 mu`.
\end{description}
+It is also worth recalling here the reduced spacing around scalable
+delimiters that results from using \verb`\mleft`, \verb`\mright`
+in place of \verb`\left`, \verb`\right`; see \xA7\ref{sec:Package-options}
+for the \verb`mleftright` package option, and the example at \xA7\ref{subsec:mleftright}.
-\subsection{Appending the differentiand: \texttt{\textbackslash diff{*}}}
+\subsection{Higher order derivatives}
-Some differentiands are too big or awkward to be placed neatly in
-the numerator of a derivative and it is natural to append them to
-a preceding differential operator. One way to do this is to leave
-the numerator argument empty in the \texttt{\textbackslash diff}
-command and follow the command with the differentiand. A better way
-is to star the \texttt{\textbackslash diff} command. This tells \texttt{diffcoeff}
-to append the differentiand. Thus suppose the differentiand is a polynomial,
-say $ax^{2}+bx+c$. Add a star (an asterisk) to the \texttt{\textbackslash diff}
-command:
+\label{subsec:Higher-order-derivatives}An optional argument allows
+the order of differentiation to be specified. The order need not be
+a number; an algebraic order of differentiation is perfectly acceptable
+as is a mix of the two:
\begin{centred}
-\verb`\[ \diff*{(ax^2+bx+c)}x \]` $\Longrightarrow$ \[\diff*{(ax^{2}+bx+c)}x\]
+\verb`\[ \diff[2]yx, \quad \diff[n+1]yx. \]` $\Longrightarrow$ \[ \diff[2]yx, \quad \diff[n+1]yx. \]
\end{centred}
-With the \texttt{!} switch or \texttt{spaced} package option, additional
-space (by default \texttt{3mu plus 1mu minus 2mu}) is inserted between
-the operator and the differentiand:
+As mentioned, the braces can be and have been omitted around the $x$
+and $y$ since they are single tokens. The square brackets around
+the optional order-of-differentiation argument are essential. In slash
+form,
\begin{centred}
-\verb`\[ \diff*!{(ax^2+bx+c)}x \]` $\Longrightarrow$ \[\diff*!{(ax^{2}+bx+c)}x.\]
+\verb`$ \difs[2]yx, \quad \difs[n+1]yx $` $\Longrightarrow$ $ \difs[2]yx, \quad \difs[n+1]yx, $
\end{centred}
-A virtue of using an asterisk to append the differentiand is that
-if one isn't sure whether a differentiand should be appended or not,
-it is an easy matter to simply insert or delete the asterisk to compare
-the results. For example, a second derivative is an iterated derivative
--- one in which a derivative forms the differentiand of another derivative:
+the latter of which is a bit of an eyesore. In compact form,
\begin{centred}
-\verb`\[ \diff[2]yx = \diff*{\diff yx}x \]` $\Longrightarrow$ \[ \diff[2]yx=\diff*{\diff yx}x \]
+\verb`$ \difc[2]yx,\quad\difc[n+1]yx $` $\Longrightarrow$ $\difc[2]yx,\quad\difc[n+1]yx$.
\end{centred}
-\noindent which is more elegant to my eye than
+Note that entering \verb`1` as the optional argument has no effect:
\begin{centred}
-\noindent \verb`\[ \diff[2]yx = \diff!{\diff yx}x \]` $\Longrightarrow$
-\[ \diff[2]yx=\diff!{\diff yx}x \]
+\verb`$ \diff[1]yx,\;\difs[1]yx,\;\difc[1]yx $` $\Longrightarrow$
+$\diff[1]yx,\;\difs[1]yx,\;\difc[1]yx $.
\end{centred}
-\noindent although whether the \emph{meaning} is clearer is moot.\emph{
-}It is easy to switch between the two forms on the right, simply by
-inserting or removing the asterisk.
-
-In slash style with the star option, the polynomial example becomes
+For partial derivatives when differentiating in only one variable
+the pattern is the same:
\begin{centred}
-\verb`\[ \diff*{(ax^2+bx+c)}/x \]` $\Longrightarrow$ \[ \diff*{(ax^2+bx+c)}/x \]
+\verb`\[ \diffp[2]yx, \quad \diffp[n+1]yx. \]` $\Longrightarrow$
+\[ \diffp[2]yx, \quad \diffp[n+1]yx. \]
\end{centred}
-\noindent where the parentheses around the differential operator are
-automatically inserted by \texttt{diffcoeff}. Like other elements
-of automatic formatting, this is user-adjustable; see \xA7\ref{sec:Changing-defaults}.
-
-With the \texttt{!} switch or \texttt{spaced} package option, this
-becomes
+For the slash forms,
\begin{centred}
-\verb`\[ \diff*!{(ax^2+bx+c)}/x \]` $\Longrightarrow$ \[ \diff*!{(ax^2+bx+c)}/x \]
+\verb`$ \difsp[2]yx,\quad \difsp[n+1]yx $` $\Longrightarrow$ $ \difsp[2]yx,\quad \difsp[n+1]yx. $
\end{centred}
+and in compact form,
+\begin{centred}
+\verb`$ \difcp[2]yx,\quad \difcp[n+1]yx $` $\Longrightarrow$ $ \difcp[2]yx,\quad \difcp[n+1]yx. $
+\end{centred}
+For partial differentiation in more than one variable -- so-called
+\emph{mixed} partial derivatives -- see \xA7\ref{subsec:Mixed-partial-derivatives}.
-\subsection{Point of evaluation\protect\label{subsec:Point-of-evaluation}}
+\subsection{Appending the differentiand}
-If you want to specify a point at which the derivative is evaluated,
-append a final optional argument. Note that there \emph{must be no
-space} before the left square bracket of the argument:\footnote{In v.1 of \texttt{diffcoeff}, this was brace-delimited. From v.2,
-square-brackets have been used and braces deprecated. From v.4, braces
-are no longer accepted.}
+\label{subsec:Appending-the-differentiand}Some differentiands are
+too big or awkward to be placed neatly in the numerator of a derivative
+and it is natural to \emph{append} them to a preceding differential
+operator. One could leave the numerator argument empty in the \verb`\diff`
+or \verb`\diffp` command and follow the command with the differentiand,
+but \verb`diffcoeff` offers a better way: star the \verb`\diff`
+or \verb`\diffp` command. This tells \verb`diffcoeff` to append
+the differentiand. Thus suppose the differentiand is a polynomial,
+say $ax^{2}+bx+c$. Add a star (an asterisk) to the \verb`\diff`
+command:
\begin{centred}
-\verb`\[ \diff[2]yx[0] \]` $\Longrightarrow\quad{\displaystyle \diff[2]yx[0]}$
+\verb`\[ \diff*{(ax^2+bx+c)}x \]` $\Longrightarrow$ \[\diff*{(ax^{2}+bx+c)}x.\]
\end{centred}
-\noindent If a space does slip in before the final optional argument,
-it will not cause a \LaTeX{} error. Instead, the argument will be treated
-as a square-bracketed mathematical expression following the derivative,
-and typeset as such.
-\begin{itemize}
-\item If you prefer to use subscripted \emph{parentheses} around the derivative
-to indicate a point of evaluation -- as ISO 80000-2 recommends --
-then this can easily be done; see \xA7\ref{sec:Changing-defaults} on
-changing default settings. Or, more simply, use the \texttt{ISO} package
-option.
-\end{itemize}
-Because the slash form spreads the derivative out horizontally, parentheses
-are preferred here to indicate a point of evaluation:
+Or, for a partial derivative, one might want to indicate in the differentiand
+all the variables on which it depends:
\begin{centred}
-\verb`$ \diff{\ln sin x}/{sin x}[x=\pi/6] $` $\Longrightarrow$ $ \diff{\ln\sin x}/{\sin x}[x=\pi/6] $.
+\verb`\[ \diffp*[2]{\Phi(x,y,z)}x \]` $\Longrightarrow$ \[ \diffp*[2]{\Phi(x,y,z)}x. \]
\end{centred}
-\noindent A vertical rule (or `pipe') can easily become too remote
-from the opening $d$ of the differential coefficient: $\diff.svrule.{\ln\sin x}/{\sin x}[x=\pi/6]$;
-parentheses tie the whole cluster of symbols together.
+A virtue of using an asterisk to append the differentiand is that
+if one isn't sure whether a differentiand should be appended or not,
+it is an easy matter to simply insert or delete the asterisk to compare
+the results.
-\subsubsection{Superscripts}
-
-It is easy to add a superscript to a derivative to indicate evaluation
-at two points and the difference between the values:
+For instance, a second derivative is an iterated derivative -- one
+in which a derivative forms the differentiand of another . Thus
\begin{centred}
-\verb`\[ \diff {\sin x}x[0]^{\pi/2} \]` ${\displaystyle \Longrightarrow}$
-\[ \diff{\sin x}x[0]^{\pi/2} \]
+\verb`\[ \diff[2]yx = \diff*{\diff yx}x \]` $\Longrightarrow$ \[ \diff[2]yx=\diff*{\diff yx}x .\]
\end{centred}
-\noindent If you want only the superscript, no subscript, include
-the final optional argument but leave it empty. Thus, for a particle
-of mass $m$ moving along a line, distance $x$ at time $t$, the
-kinetic energy is:
+\noindent This result is more elegant to my eye than what results
+when removing the asterisk,
\begin{centred}
-\noindent \verb`$ \tfrac 12 m \diff x/t[]^2 $` $\Longrightarrow$
-$\tfrac{1}{2}m\diff x/t[]^{2}$.
+\noindent \verb`\[ \diff[2]yx = \diff{\diff yx}x \]` $\Longrightarrow$
+\[ \diff[2]yx=\diff{\diff yx}x ,\]
\end{centred}
+\noindent although whether the \emph{meaning} is clearer is moot.
-\subsection{Order of differentiation}
+Since the differentiand is appended \emph{by default} in compact-form
+derivatives, starring such a derivative has no effect other than when
+a second asterisk is used to transpose the order of arguments.
-An optional first argument allows the order of differentiation to
-be specified. The order need not be a number; an algebraic order of
-differentiation is perfectly acceptable as is a mix of the two:
+\subsubsection{Transposing the argument order}
+
+\label{subsec:Transposing-the-argument}If a \emph{second} asterisk
+follows the first, the order of the arguments specifying the differentiand
+on the one hand and variable or variables of differentiation on the
+other are reversed. Thus it is clearer to the eye to write
\begin{centred}
-\verb`\[ \diff[2]yx \]` $\Longrightarrow$ \[ \diff[2]yx,\]\verb`\[ \diff[n+1]yx \]`
-$\Longrightarrow$ \[ \diff[n+1]yx.\]
+\verb`\[ \diff**x{(ax^2+bxy+cy^2)} \]` $\Longrightarrow$ \[\diff**x{(ax^2+bxy+cy^2)}\]
\end{centred}
-As mentioned, the braces can be and have been omitted around the $x$
-and $y$; the square brackets around the optional argument, the order
-of differentiation, are essential. For a first-order derivative, no
-optional argument is needed and entering \texttt{1} as the optional
-argument has no effect:
+than \verb`\[ \diff*{(ax^2+bxy+cy^2)}x \]`, where the eye has to
+search for the variable of differentiation. This is especially the
+case if the differentiand contains more than one variable and commands
+like \verb`\frac` or \verb`\sqrt` requiring braced arguments:
\begin{centred}
-\verb`$ \diff[1]yx $` $\Longrightarrow$$\diff[1]yx$.
+\verb`\[ \diffp**x{\frac1{\sqrt{x^2-y^2}}} \]` $\Longrightarrow$
+\[ \diffp**x{\frac1{\sqrt{x^2-y^2}}} \]
\end{centred}
-In slash style, \texttt{\$\textbackslash diff{[}2{]}y/x\$} produces
-$\diff[2]y/x$, and \texttt{\$\textbackslash diff{[}n+1{]}y/x\$}
-produces $\diff[n+1]y/x$.
+For compact-form derivatives the initial, appending asterisk is always
+implicitly present. However, it must be \emph{explicitly} present
+for the second asterisk to take effect:
+\begin{centred}
+\verb`\[ \difcp yx,\quad \difcp*yx,\quad \difcp**yx \]` $\Longrightarrow$
+\[ \difcp yx,\quad \difcp*yx,\quad \difcp**yx \]
+\end{centred}
-\subsection{Multi-character variables of differentiation}
+\subsubsection{Operator parenthesizing}
-Differentiating a function of a function may involve a multi-character
-differentiation variable. For instance, to differentiate $\ln\sin x$
-in $x$ means forming the product
+In slash style with the star option, the polynomial example becomes
\begin{centred}
-\verb`\[ \diff!{\ln\sin x}{\sin x}\diff{\sin x}x \]` $\Longrightarrow$
-\[\diff!{\ln\sin x}{\sin x}\diff{\sin x}x.\]
+\verb`$ \difs*{(ax^2+bx+c)}x $` $\Longrightarrow$ $ \difs*{(ax^2+bx+c)}x $
\end{centred}
-\noindent (Although I am mainly using un-spaced differentiands in
-this document, a space before the differentiand in the first of these
-derivatives -- the \verb`!` switch -- improves the appearance of
-the expression to my eye.)
-
-Forming the \emph{second} derivative of $\ln\sin x$ will now involve
-forming (among other quantities)
+\noindent where parentheses have been automatically inserted around
+the differential operator. Similarly, for slash-style partial derivatives,
\begin{centred}
-\noindent \verb`\[\diff[2]{\ln\sin x}{\sin x}\]` $\Longrightarrow$
-\[\diff[2]{\ln\sin x}{\sin x}\]
+\verb`\( \difsp*[n]{f(x)}x \)` $\Longrightarrow$ \( \difsp*[n]{f(x)}x \)
\end{centred}
-\noindent Parentheses have been inserted automatically by \texttt{diffcoeff}
-around $\sin x$ in the denominator to avoid any visual hint that
-we are differentiating in the sine of $x^{2}$.
+\noindent parentheses are again inserted automatically around the
+differential operator. Like other elements of automatic formatting,
+this behaviour is user-adjustable; see \xA7\xA7\ref{sec:Variant-forms},
+\ref{sec:ChangingDefaults}.
-The question is: are the parentheses in the right place? Logically,
-no. They should include the $d$: $(d\sin x)^{2}$ -- it is the differential
-$d\sin x$ that is of the second order. But as the examples in the
-Rogues' Gallery show -- see particularly (\ref{eq:eg3}) -- the
-inclination seems to be to do otherwise. This may be because one wants,
-in any case, to parenthesise the variable. A second, outer pair of
-parentheses then seems too fussy and detracts from comprehending the
-symbol `at a glance':
-\[
-\diff.wrapall.[2]{f(x)}{(1/x)}.
-\]
+\subsection{Point of evaluation/variables held constant}
-Customary but illogical notations are familiar in mathematics --
-think of the position of the superscripts in an identity like $\sin^{2}\theta+\cos^{2}\theta=1$.
-But, like other features of the derivative, the manner of this wrapping
-in parentheses of long variables for \emph{higher order} derivatives
-is customisable; see \xA7\ref{sec:Changing-defaults}.
-
-For first order derivatives, parenthesising does not occur. If you
-want the variable of differentiation to be parenthesised, you need
-to insert them yourself:
+\label{subsec:Point-of-evaluation}If you want to specify a point
+at which a derivative is evaluated, append a final optional argument:
\begin{centred}
-\verb`\[\diff {f(x)}{1/x}, \quad \diff {f(x)}{(1/x)}.\]` $\Longrightarrow$
-\[ \diff {f(x)}{1/x}, \quad\diff {f(x)}{(1/x)}.\]
+\verb`\[ \diff[2]yx[0] \]` $\Longrightarrow$ \[ \diff[2]yx[0] \]
\end{centred}
-
-\section{Partial derivatives\protect\label{sec:Partial-derivatives}}
-
-\noindent Partial derivatives follow the same pattern as ordinary
-derivatives, with some extensions. The command this time is \texttt{\textbackslash diffp}.
-Thus \texttt{\textbackslash diffp\{F\}\{x\}}, or, with a saving on
-keystrokes,\texttt{ \textbackslash diffp Fx}, produces $\diffp Fx$
-in text style and
+\noindent Note that there must be \emph{no space} before the left
+square bracket of the trailing argument, otherwise it will be treated
+as part of the wider mathematical expression of which the derivative
+is part and typeset as such. (This should not cause a \LaTeX{} error.)
+\begin{itemize}
+\item If you prefer to use subscripted \emph{square} brackets
\[
-\diffp{F}{x}
+\diffp.].{F(x,y)}x[(0,0)]
\]
-in display style. (As for \texttt{\textbackslash diff}, the omission
-of braces is possible when the differentiand or the differentiation
-variable are single tokens.) As for \texttt{\textbackslash diff},
-there is a slash form, generally preferred for inline use, \texttt{\textbackslash diffp
-F/x}, displaying as $\diffp F/x$. Given that \texttt{\textbackslash partial}
-takes 8 keystrokes to type, the slash form \emph{does }economise on
-keystrokes for a partial derivative.
+or a subscripted vertical rule after the derivative
+\[
+\diffp.|.{F(x,y}x[(0,0)]
+\]
+to indicate a point of evaluation, then this can easily be done; see
+specifically \xA7\ref{subsec:variantPoint-of-evaluation} (or \xA7\ref{sec:ChangingDefaults}
+on changing default settings). Parentheses are the ISO recommendation;
+see ISO 80000-2.
+\end{itemize}
+Because the slash form spreads the derivative out horizontally, parentheses
+are the natural way in this case to indicate a point of evaluation:
+\begin{centred}
+\verb`$ \difs{\ln sin x}{sin x}[x=\pi/3] $` $\Longrightarrow$ $ \difs{\ln\sin x}{\sin x}[x=\pi/3]$.
+\end{centred}
+\noindent A vertical rule can easily become too remote from the opening
+$\mathrm{d}$ of the differential coefficient: $\difs.|.{\ln\sin x}{\sin x}[x=\pi/3]$.
+Parentheses tie the whole cluster of symbols together.
-With either the \verb`spaced` package option (see \xA7\ref{subsec:Package-options})
-or the \verb`!` switch a space, defaulting to \verb`3 mu` with some
-stretch and shrink, can be inserted before the differentiand: \verb`\[ \diffp!{F(x,y)}x \]`
-$\Longrightarrow$ \[ \diffp!{F(x,y)}x. \]
-
-\noindent (But note that if the \verb`spaced` package option is used,
-the \verb`!` switch \emph{removes} any extra space.)
-
-Again an optional argument allows the specification of the order of
-differentiation which may be numeric or algebraic or a mix of the
-two:
+One reason to query the ISO preference for subscripted parentheses
+to indicate a point of evaluation is that subscripted parentheses
+are used with partial derivatives to indicate variables held constant.
+This occurs frequently in thermodynamics for example. In the following
+well-known relation in thermodynamics, the differentiands are appended
+and the trailing argument is used to indicate the variables held constant:
\begin{centred}
-\verb`\[ \diffp[3]F/x , \quad \diffp[n]F/x \]` $\Longrightarrow$
-\[\diffp[3]F/x , \quad \diffp[n]F/x\] \verb`\[ \diffp[n+1]Fx. \]`
-$\Longrightarrow$ \[ \diffp[n+1]Fx. \]
+\verb`\[ \diffp*{\frac PT}U[V] = \diffp*{\frac 1T}V[U] \]` $\Longrightarrow$
+\[ \diffp*{\frac PT}U[V] = \diffp*{\frac 1T}V[U]. \]
\end{centred}
+\noindent This is much easier to write than building the expressions
+`by hand', starting with \verb`\left(` and finishing with \verb`_U`.
-\subsection{Variables held constant}
+\subsubsection{Superscripts}
-In a subject like thermodynamics, there is a need to indicate which
-variables are held constant when the differentiation occurs. To show
-this, append a final square-bracketed optional argument and ensure
-that it follows \emph{immediately} on the preceding mandatory argument.
-A space here will detach the argument from the derivative and result
-in it being treated as a mathematical expression following the derivative.
-Thus to differentiate the entropy $S$ in temperature $T$ while holding
-the volume $V$ constant, write
+It is easy to add a superscript to a derivative to indicate evaluation
+at two points and the difference between the values:
\begin{centred}
-\verb`\[ \diffp ST[V] \]` $\Longrightarrow$ \[ \diffp ST[V]. \]
+\verb`\[ \diff {\sin x}x[0]^{\!\!\pi/2} \]` ${\displaystyle \Longrightarrow}$
+\[ \diff{\sin x}x[0]^{\!\!\pi/2} \]
\end{centred}
-\noindent In slash form the same expression looks like
-\begin{centred}
-\noindent \verb`$ \diffp S/T[V] $` $\Longrightarrow$ $ \diffp S/T[V] $.
-\end{centred}
-This use of a parenthesised, subscripted form to indicate a variable
-or variables held constant, leaves open the question: how do we represent
-a point of evaluation? ISO 80000-2 makes no recommendation for \emph{partial}
-derivatives; presumably we follow the same practice as their recommendation
-for ordinary derivatives:
-\begin{example}
-\verb`\[ \diffp {F(x,y)}x[(0,0)] \]` $\Longrightarrow$ \[ \diffp {F(x,y)}x[(0,0)] \]
-\end{example}
+but to my eye either square brackets or a vertical rule are clearer
+for this purpose (and do not involve nudging the subscript or superscript
+closer to the right delimiter); see \xA7\ref{sec:Variant-forms}.
-However, you may prefer (as many do) to use a vertical rule for this
-purpose:
-\[
-\diff.pvrule.{F(x,y)}x[(0,0)]
-\]
-Making this possibility available is discussed in \xA7\ref{sec:Changing-defaults}.
+\subsubsection{Empty trailing argument}
-An empty final argument produces a parenthesised derivative with no
-subscript,
+\noindent If the trailing argument is included but left empty it will,
+with the default set-up, wrap the derivative in parentheses but with
+no subscript. This fact can be exploited. Thus, for a particle of
+mass $m$ moving along a line, distance $x$ at time $t$, the kinetic
+energy is:
\begin{centred}
-\verb`\[ \diffp yx[] \]` ${\displaystyle \Longrightarrow}$ \[ \diffp yx[] \]
+\noindent \verb`$ \tfrac 12 m \difs xt[]^2 $` $\Longrightarrow$
+$\tfrac{1}{2}m\difs xt[]^{2}$.
\end{centred}
-\noindent which can be useful sometimes. An instance is the writing
-of Lagrange's equations of motion in analytic mechanics:
+Or, again exploiting the parentheses resulting from an empty trailing
+argument, Lagrange's equations of motion in analytic mechanics can
+be written,
\begin{centred}
-\noindent \verb`\[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0 \]`
-$\Longrightarrow$ \[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0. \]
+\verb`\[ \diffp L{q_k}-\diff**t{ \diffp L{\dot{q}_k}[] } = 0 \]`
+$\Longrightarrow$\[\diffp L{q_k}-\diff**t{\diffp L{\dot{q}_k}[]} = 0. \]
\end{centred}
+\noindent (See \xA7\ref{subsec:Transposing-the-argument} for the double
+asterisk.) Like the author, you may feel that there is too much whitespace
+between $\diff{}t$ and the left parenthesis in this expression. One
+obvious remedy is to insert a negative thin space \verb`\!` before
+the second \verb`\diffp` command. Another is to use the package \verb`mleftright`.
-\subsubsection{Text-style derivatives}
+\subsubsection{Use of the package \texttt{mleftright}}
-The \texttt{diffcoeff} package assumes that derivatives formed as
-`numerator over denominator' will be used in display-style expressions,
-and that the slash form will be used for inline use (text style).
-This is the familiar practice in the literature. If one \emph{does}
-use the first form in an inline expression where a variable is held
-constant, say \texttt{\textbackslash diffp ST{[}V{]}} as here $\diffp ST[V]$,
-the result is unsatisfactory, the subscript too tight on the closing
-parenthesis and too much space between parentheses and derivative.
-The matter is easily resolved using `variant forms' -- see \xA7\ref{subsec:Text-and-script-style}
-below -- giving, for our example, $\diff.ptxt.ST[V]$.
+\label{subsec:mleftright}The \verb`mleftright` package `tightens'
+the spacing around \verb`\left`, \verb`\right` delimiters. The user
+either by explicitly replaces \verb`\left`, \verb`\right` by \verb`\mleft`
+and \verb`\mright` or uses the command \verb`\mleftright` which
+effectively turns subsequent occurrences of \verb`\left`, \verb`\right`
+into \verb`\mleft`, \verb`\mright`; \verb`\mleftrightrestore` returns
+\verb`\left`, \verb`\right` to their original selves. This process
+can be `short-circuited' by using the \verb`diffcoeff` package
+option \verb`mleftright` that inserts \verb`\mleftright` in the
+preamble; see \xA7\ref{sec:Package-options}.
-\subsection{Appending the differentiand\protect\label{subsec:Partial-appending}}
+However, that package option is not used in this document. Nonetheless
+\verb`mleftright` is a required package of version 5 of \verb`diffcoeff`
+and its commands are available for use. Hence to reduce the whitespace
+I can write
+\begin{verbatim}
+ \mleftright
+ \[ \diffp L{q_k}-\diff**t{\diffp L{\dot{q}_k}[]} = 0. \]
+ \mleftrightrestore
+\end{verbatim}
+$\Longrightarrow$ \mleftright
+\[ \diffp L{q_k}-\diff**t{\diffp L{\dot{q}_k}[]} = 0. \]
+\mleftrightrestore
-For a long or awkward differentiand, it is generally better to \emph{append}
-it to a preceding differential operator, rather than create a fractional
-form with the long expression in the numerator. As with ordinary derivatives,
-this is achieved by adding an asterisk to (i.e. by starring) the \texttt{\textbackslash diffp}
-command.
-\begin{centred}
-\verb`\[ \diffp*[2]{\Phi(x,y,z)}x \]` $\Longrightarrow$ \[ \diffp*[2]{\Phi(x,y,z)}x. \]
-\end{centred}
-With the \verb`spaced` package option, or with the \verb`!` switch
-if the package option is not used (which is the case for this document),
-one gets
-\begin{centred}
-\verb`\[ \diffp*[2]!{\Phi(x,y,z)}x \]` $\Longrightarrow$ \[ \diffp*[2]!{\Phi(x,y,z)}x \]
-\end{centred}
-which is an improvement (to my eye).
+\noindent which is better, but better still to my eye is to also add
+a negative thin space \verb`\!` before the second \verb`\diffp`
+command:
+\begin{verbatim}
+ \mleftright
+ \[ \diffp L{q_k}-\diff**t{ \!\diffp L{\dot{q}_k}[] } = 0 \]
+\end{verbatim}
+\noindent $\Longrightarrow$ \mleftright\[\diffp L{q_k}-\diff**t{\!\diffp L{\dot{q}_k}[]} = 0. \]
-Alternatively you could leave the first mandatory argument empty and
-manually append the differentiand, but by deleting or inserting an
-asterisk, it is easy to compare the two forms, differentiand-in-the-numerator,
-differentiand-appended, and see which is preferable.
+\noindent The problem is that in addition to the space around \verb`\left`,
+\verb`\right` pairs (which is reduced by issuing the command \verb`\mleftright`),
+there is also the space inserted by \verb`diffcoeff` before a multi-token
+differentiand. The user should be aware of this, and may wish to define
+a `variant form' (see \xA7\ref{sec:Variant-forms}) that introduces
+no space before an appended differentiand.
-In slash form, parentheses are automatically inserted around the differential
-operator when the differentiand is appended,
-\begin{centred}
-\verb`\[ \diffp*[n]{f(x)}/x \]` $\Longrightarrow$ \[ \diffp*[n]{f(x)}/x, \]
-\end{centred}
-\noindent although this behaviour can be changed (\xA7\ref{sec:Changing-defaults}
-again).
+\subsection{Mixed partial derivatives}
-If you wish to both append the differentiand \emph{and} indicate variables
-held constant, then the starred form is much the easier way to achieve
-this. Thus, to express a relation in thermodynamics,
+\label{subsec:Mixed-partial-derivatives}The new thing with partial
+derivatives, not present with ordinary derivatives, is so-called \emph{mixed}
+partial derivatives, where differentiation occurs in more than one
+variable. If each variable is differentiated only to the first order,
+then it is easy to specify the derivative. Suppose $F$ is a function
+of three variables, $x$, $y$ and $z$. Then
\begin{centred}
-\verb`\[ \diffp*{\frac PT}U[V] = \diffp*{\frac 1T}V[U] \]` $\Longrightarrow$
-\[ \diffp*{\frac PT}U[V] = \diffp*{\frac 1T}V[U], \]
+\verb`\[ \diffp F{x,y,z},\quad\diffp{F(x,y,z)}{x,y,z}. \]` $\Longrightarrow$
+\[ \diffp F{x,y,z},\quad \diffp{F(x,y,z)}{x,y,z}. \]
\end{centred}
-\noindent where the starring automatically takes care of the parentheses
-and subscripts.
+(The \verb`spaced=-1` package option inserts space before the multi-token
+differentiand in the second of these.)
-\subsection{Iterated derivatives}
+The variables of differentiation are listed in order in a comma list
+-- \verb`{x,y,z}` -- forming the second mandatory argument. The
+total order of differentiation (3 in this example) was inserted automatically.
+It did not need to be specified or calculated `by hand' -- \verb`diffcoeff`
+did the calculation.
-Derivatives can be the differentiands of derivatives, as seen above
-when writing Lagrange's equations,
+The slash form is
\begin{centred}
-\noindent \verb`\[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0 \]`
-$\Longrightarrow$ \[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0. \]
+\verb`$ \difsp F{x,y,z} $` $\Longrightarrow$ $ \difsp F{x,y,z}$,
\end{centred}
-\noindent However, in versions of \texttt{diffcoeff} before version
-3.2, an ordinary derivative within a partial derivative rendered as
-a partial derivative. That is now corrected, the ordinary derivative
-rendering correctly:
+as expected, and the compact form is
\begin{centred}
-\verb`\[ \diffp*{\diff{x^\mu}{\lambda}}{x^\sigma} \]` $\Longrightarrow$
-\[ \diffp*{\diff{x^\mu}{\lambda}}{x^\sigma}. \]
+\verb`$ \difcp F{x,y,z} $` $\Longrightarrow$ $ \difcp F{x,y,z}$.
\end{centred}
+One might wonder about even more compact notations like $\partial_{xyz}^{\onemu3}F$
+for this example but it becomes messy if different orders of differentiation
+are involved for different variables.
-\subsection{Mixed partial derivatives}
-
-The new thing with partial derivatives, not present with ordinary
-derivatives, is \emph{mixed} partial derivatives, where there is more
-than one variable of differentiation. If each variable is differentiated
-only to the first order, then it is easy to specify the derivative.
-Suppose $F$ is a function of three variables, $x$, $y$ and $z$.
-Then
+To differentiate variables to higher order, their orders need to be
+specified explicitly. To do so use a comma list for the optional argument:
\begin{centred}
-\verb`\[ \diffp F{x,y,z} \]` $\Longrightarrow$ \[ \diffp F{x,y,z}, \]
+\verb`$ \difcp[2,3]F{x,y,z} $` $\Longrightarrow$ $ \difcp[2,3] F{x,y,z}$,
-\verb`\[ \diffp !{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$ \[ \diffp !{F(x,y,z)}{x,y,z}. \]
-\end{centred}
-In the second of these I have inserted space before the differentiand
-by using the \verb`!` switch. If the \verb`spaced` package option
-was being used, this would have been done automatically.
-
-The variables of differentiation are listed in order in a comma list
-forming the second mandatory argument. The total order of differentiation
-(3 in this example) is inserted automatically -- \texttt{diffcoeff}
-does the calculation. There is also a slash form:
-\begin{centred}
-\verb`$ \diffp F/{x,y,z} $` $\Longrightarrow$ $ \diffp F/{x,y,z}$.
-\end{centred}
-If we want to differentiate variables to higher order, then their
-orders need to be specified explicitly. To do so use a comma list
-for the optional argument:
-\begin{centred}
\verb`\[ \diffp[2,3]F{x,y,z} \]` $\Longrightarrow$ \[ \diffp[2,3]F{x,y,z}. \]
\end{centred}
\noindent Notice that the overall order of the derivative -- 6 --
-is again automatically calculated and inserted as a superscript on
-the $\partial$ symbol in the numerator. In this example, the comma
-list of orders has only two members, even though there are three variables.
-It is assumed that the orders given in the comma list apply in sequence
-to the variables, the first order to the first variable, the second
-to the second variable, and so on, and that any subsequent orders
-not listed in the optional argument are, by default, 1. Thus we need
-to specify only 2 and 3 in the example; the order of differentiation
-of $z$ is 1 by default. But you \emph{cannot} use an order specification
-like \texttt{{[} , ,2{]}}. Instead write \texttt{{[}1,1,2{]}}.\textbf{
-}It is only the \emph{tail} of an order specification which can be
-omitted.
+in the second of these is again automatically calculated and inserted
+as a superscript on the $\partial$ symbol in the numerator.
-\subsubsection{Minutiae of spacing (again)\protect\label{subsec:Minutiae-of-spacing}}
+In the example, the comma list of orders has only \emph{two} members,
+although there are \emph{three} variables. It is assumed that the
+orders given in the comma list apply in sequence to the variables,
+the first order to the first variable, the second to the second variable,
+and so on, and that any subsequent orders not listed in the optional
+argument are, by default, 1. Thus we need to specify only 2 and 3
+in the example; the order of differentiation of $z$ is 1 by default.
+But you \emph{cannot} use an order specification like \verb`[,,2]`;
+instead write {\ttfamily\verb`[1,1,2]`} (which is the natural
+thing to do in any case).\textbf{ }It is only the \emph{tail} of an
+order specification which can be omitted.
-In Chapter 18 of the \emph{The\TeX book}, Knuth suggests inserting
-a thin space, {\ttfamily\verb`\,`} (or {\ttfamily\verb`3 mu`}),
-between differentials in appropriate contexts, giving as an example
-$dx\,dy=r\,dr\,d\theta$. In the denominator of a derivative, however,
-that degree of extra spacing seems too great (to my eye), interfering
-with seeing the derivative `as a whole',
-\[
-\diff.pwide.F{x,y,z},
-\]
-especially for the slash-form of derivative: $\diff.pwide.F/{x,y,z}$.
-Some spacing is desirable, but less; by default \texttt{diffcoeff}
-inserts \verb`2 mu` between the differentials in the fraction form
-of derivative and \verb`1 mu`\texttt{ }in the slash form.
+In the other direction, if there are more orders of differentiation
+specified than there are variables, the list of orders is truncated
+to match the number of variables.
-Should a differentiation occur to higher order and so a variable acquire
-a superscript, an adjustment is made to the extra spacing. By default
-\verb`1 mu` is subtracted from the default spacing. Thus in
-\[
-\diffp[2]F{x,y,z},
-\]
-\verb`2 mu` of spacing is inserted between the $\partial y$ and
-$\partial z$, but because the superscript already provides some separation
-between them, only \verb`1 mu` is inserted between $\partial x^{2}$
-and $\partial y$.
+\subsubsection{Algebraic orders of differentiation}
-The values used for the spacing and its adjustment in the presence
-of a superscript can be changed by the user; see \xA7\ref{sec:Changing-defaults}.
-Some other minutiae of spacing are discussed below in \xA7\ref{subsec:Comma-list-of-vars}
-when the variables themselves are super- or subscripted (as happens
-in tensor calculus, for instance).
-
-Note that the \verb`!` switch, if used, is inserted \emph{immediately
-before} the differentiand. It is the placement of the differentiand,
-after all, that it is affecting:
+Orders of differentiation do not need to be numerical. They can also
+be algebraic:
\begin{centred}
-\verb`\[ \diffp[2]!F{x,y,z} \]` $\Longrightarrow$ \[ \diffp[2]!F{x,y,z}. \]
+\verb`\[ \diffp[2m-1,m+1,2]F{x,y,z} \]` $\Longrightarrow$ \[ \diffp[2m-1,m+1,2]F{x,y,z}\]
\end{centred}
-
-\subsubsection{Algebraic orders of differentiation}
-
-Calculation of the overall order of differentiation still occurs even
-when some or all of the individual orders are algebraic variables
-rather than numbers. For example, differentiating in three variables
-to orders \texttt{1, m+1, m-1},
+The total order of differentiation is still calculated by \verb`diffcoeff`.
+Or again,
\begin{centred}
-\verb`\[ \diffp[1,m+1,m-1]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
-\[ \diffp[1,m+1,m-1]{F(x,y,z)}{x,y,z}. \]
+\verb`\[ \diffp[1,km+1,m+k-1]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[1,km+1,m+k-1]{F(x,y,z)}{x,y,z}. \]
\end{centred}
-\subsubsection{Error messages}
+\subsubsection{Order-override command: \texttt{\textbackslash difoverride}}
-Should you specify \emph{more} orders in the comma list of the order
-specification than there are variables, compilation will fail and
-an error message will be sent to the terminal and \LaTeX{} log . For
-example, if on (say) line 53 of my document I specify \texttt{{[}1,m-1,m+1,2{]}}
-for the orders of differentiation but list only \texttt{\{x,y,z\}}
-for the variables, the message will be
-\begin{lyxcode}
-!~Package~diffcoeff~Error:~4~orders~of~differentiation~
+\noindent \label{subsec:Order-override-command}$m+k+km+1$ factorizes
+to $(k+1)(m+1)$ and you may prefer to express the total order of
+differentiation in this form. \verb`diffcoeff` is not a computer
+algebra system and does not do such factorizations but the \verb`\difoverride`
+command offers the means to use the factorized form as the total order
+of differentiation in the derivative. (The \verb`\difoverride` command
+replaces the order-override option of the \verb`\diff` command in
+version 4 of \verb`diffcoeff`. That option is no longer available.)
+\begin{verbatim}
+ \[
+ \difoverride{(k+1)(m+1)}
+ \diffp[1,km+1,m+k-1]{F(x,y,z)}{x,y,z}
+ \]
+\end{verbatim}
+$\Longrightarrow$ \[
+ \difoverride{(k+1)(m+1)}
+ \diffp[1,km+1,m+k-1]{F(x,y,z)}{x,y,z}
+ \]
-specified~for~3~variables;~orders~{[}1,m+1,m-1,2{]}
+\verb`\difoverride` takes only one (mandatory) argument, the total
+order of differentiation, which it stores. When \verb`\difoverride`
+is non-empty, then the algorithm that calculates the total order is
+sidestepped. It does not get called at all. In this way one can present
+not only the total order in whatever manner one wishes but essentially
+arbitrary material as a superscript to the $\partial$ symbol in the
+numerator. (For compact-form derivatives, which do not use a total
+order of differentiation, the command is irrelevant.)
-(on~line~53)~for~variables~x,y,z.
-\end{lyxcode}
-Should you try using a \emph{number} raised to a power in an order
-specification, it will cause an error. For example, if on line 53
-(say) of my document I try to form \texttt{\textbackslash diffp{[}2\textasciicircum 2{]}f\{x,y,z\}}
-compilation will fail with the message
-\begin{lyxcode}
-!~Package~diffcoeff~Error:~number~followed~by~\textasciicircum ~in~the~
+Note that in the example \verb`\difoverride` has been used \emph{within
+}the math environment. This is good practice. It prevents the contents
+of \verb`\difoverride` erroneously overriding the orders of later
+derivatives:
+\begin{verbatim}
+ $ \difoverride{N} \difsp[m,n]f{x,y} $,\quad
+ $ \difsp[1,2]f{x,y} $.
+\end{verbatim}
+$\Longrightarrow$ $ \difoverride{N} \difsp[m,n]f{x,y} $,\quad
+ $ \difsp[1,2]f{x,y} $.
-order~specification~{[}2\textasciicircum n,1,1{]}~on~line~53.~Diffcoeff~
+\noindent There is no spillover here whereas by placing the override
+command outside the math environment the command reaches beyond the
+intended target. To cancel the overreach, I have used \verb`\difoverride`
+with an \emph{empty} argument, :
+\begin{verbatim}
+ \difoverride{K}
+ $ \difsp[m,n]f{x,y} $,\quad
+ $ \difsp[1,2]f{x,y} $,\quad
+ \difoverride{}
+ $ \difsp[1,2]f{x,y}$.
+\end{verbatim}
+$\Longrightarrow$ \difoverride{K} $ \difsp[m,n]f{x,y} $,\quad
+ $ \difsp[1,2]f{x,y} $,\quad
+ \difoverride{} $ \difsp[1,2]f{x,y}$.
-cannot~calculate~the~overall~order~of~differentiation~
+\noindent Clearly one should use the override command \emph{within}
+the math environment.
-in~this~case.~Use~the~order-override~option~to~enter~
+\subsubsection{Parentheses}
-the~overall~order.
-\end{lyxcode}
-The order-overide option mentioned here is discussed next. Similarly,
-you cannot use multiplication (\texttt{\textbackslash times} or \texttt{{*}})\texttt{
-}or division (\texttt{/} or \texttt{\textbackslash div}) signs after
-\emph{numbers} in an order specification; only \texttt{+} or \texttt{-}
-or a left parenthesis (see below) are allowed.
-
-\subsubsection{The order-override option}
-
-\noindent Perhaps the differentiations are to orders \texttt{{[}2km,m-1,m+1{]}}:
+Auto-calculation of the total order accommodates the simple use of
+parentheses:
\begin{centred}
-\noindent \verb`\[ \diffp[2km,m-1,m+1]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
-\[ \diffp[2km,m-1,m+1]{F(x,y,z)}{x,y,z}. \]
+\verb`\[ \diffp[2m-(k+1),2(k+1)-m]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[2m-(k+1),2(k+1)-m]{F(x,y,z)}{x,y,z} \]
\end{centred}
-\noindent Here the overall order is presented as \texttt{2km+2m}.
-You might prefer this to be presented as \texttt{2m(k+1)}. Although
-\texttt{diffcoeff} takes some steps to present the overall order appropriately,
-it is not a computer algebra system and does not factorise expressions.
-If you want to present the order in a manner distinct from that presented
-by \texttt{diffcoeff}, use the \emph{order-override option}.
+This is an example of the use of \emph{dynamic} parentheses: the left
+parenthesis in each case is preceded by a number or a sign. In evaluating
+the total order \verb`diffcoeff` multiplies out the expression (or
+that is the effect).
-This is a second optional argument immediately following the order
-specification. For our last example, filling the override option with
-\texttt{2m(k+1)} gives the desired result:
+On the other hand, an order specification like \verb`[f(n+1),f(n-1)]`
+is an example of the use of \emph{static} parentheses where they are
+part of the familiar `function of' notation -- in this case a function
+$f$ of some variable, say $x$, evaluated at $x=n\pm1$. \verb`diffcoeff`
+\emph{always} interprets a left parenthesis preceded by something
+that is neither number nor sign in this way. It does not try to multiply
+out such expressions when calculating the total order.
+
+The following example combines both uses -- and includes a nested
+pair of (dynamic) parentheses:
\begin{centred}
-\verb`\[ \diffp[2km,m-1,m+1][2m(k+1)]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
-\[ \diffp[2km,m-1,m+1][2m(k+1)]{F(x,y,z)}{x,y,z}. \]
+\verb`\[\diffp[2(f(n)-(m-1)),5-(f(n)+m)]F{x,y}\]` $\Longrightarrow$
+\[\diffp[2(f(n)-(m-1)),5-(f(n)+m)]F{x,y}\]
\end{centred}
-\noindent As another example, left to its own devices, \texttt{diffcoeff}
-produces
+Where confusion arises is with specifications like \verb`[m(k-1)+1,m(k+1)-1]`
+where \verb`m` could be interpreted as either a function or a variable.
+As stated, \verb`diffcoeff` \emph{always} interprets a left parenthesis
+preceded by something that is not a number or a sign as signalling
+`function of'. Hence:
\begin{centred}
-\noindent \verb`\[ \diffp[m/2+n/2,m/2,n/2]F{x,y,z} \]` $\Longrightarrow$
-\[ \diffp[m/2+n/2,m/2,n/2]F{x,y,z}, \]
+\verb`\[\diffp[m(k-1)+1,m(k+1)-1]F{x,y}\]` $\Longrightarrow$ \[\diffp[m(k-1)+1,m(k+1)-1]F{x,y}\]
\end{centred}
-\noindent whereas we would like the total order to be presented as
-$m+n$. Using the override option,
-\begin{centred}
-\noindent \verb`\[ \diffp[m/2+n/2,m/2,n/2][m+n]F{x,y,z} \]` $\Longrightarrow$
-\[ \diffp[m/2+n/2,m/2,n/2][m+n]F{x,y,z}. \]
-\end{centred}
-The order-override option does exactly that: overrides the presentation
-of the calculated order with the manually given one. In fact the calculation
-algorithm does not get called at all when the override option is used
-so that one can in this way present the total order in whatever manner
-one wishes or, indeed, add essentially arbitrary material as a superscript
-to the $\partial$ symbol in the numerator.
+\noindent If, in fact, \verb`m` is intended as a \emph{variable}
+then the order-override command is there to rescue the situation:
+\begin{verbatim}
+ \[
+ \difoverride{2mk}
+ \diffp[m(k-1)+1,m(k+1)-1]F{x,y}
+ \]
+\end{verbatim}
+$\Longrightarrow$ \[
+ \difoverride { 2mk }
+ \diffp[m(k-1)+1,m(k+1)-1]F{x,y}
+ \]
-\subsubsection{Comma list of variables of differentiation\protect\label{subsec:Comma-list-of-vars}}
+\subsubsection{Error messages}
-In tensor calculus the differentiations are almost always in terms
-of super- or subscripted coordinates. In many other contexts this
-is the case too -- the reciprocal of the temperature in thermodynamics
-or generalized coordinates in analytical mechanics. This is why a
-comma list is used in \texttt{diffcoeff} for specifying variables
-of differentiation for mixed partial derivatives. Although it would
-be nice to write the minimal \texttt{\{xy\}} rather than \texttt{\{x,y}\}
-when two variables $x$ and $y$ are involved, the extra writing is
-trivial and the comma list allows a simpler handling of multi-character
-variables. For instance in tensor calculus we get expressions like
+The order-override command is also needed when calculation of the
+total order is beyond the abilities of \verb`diffcoeff`. The package
+is \emph{not} a computer algebra system. It can cope with order specifications
+where variables are followed by diverse arithmetic operators: \verb`n^2`,
+\verb`m\times n`, \verb`m/2` and the like cause no problems. But
+a \emph{number} can be followed \emph{only} by a sign or a variable
+or a left parenthesis. Anything beyond this will raise an error. For
+instance
\begin{centred}
-\verb`\[ \diffp{A_i}{ x^j,x^k } \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^j,x^k }. \]
+\verb`\[ \diffp[2^k]F{x,y} \]`
\end{centred}
-\noindent It is easier to write \texttt{\{x\textasciicircum j,x\textasciicircum k\}}
-here than, say, \texttt{\{\{x\textasciicircum j\}\{x\textasciicircum k\}\}}
-to distinguish the variables. It does mean that should the variable
-of differentiation include a comma then that comma needs to be enclosed
-in braces. There are plenty of instances of this out in the world
-(see, e.g., the last equation of (\ref{eq:eg1})) but it is overall
-a rare occurrence.
+produces a message beginning `\texttt{! Package diffcoeff Error:}'
+and continuing,
+\begin{verbatim}
+ number followed by ^ in the order spec. [2^k,1] on
+ line xx. Calculation of the total order of
+ differentiation fails in this case. Use the
+ \difoverride command to enter the total order.
+ See the diffcoeff documentation for further
+ information.
+\end{verbatim}
+(The \verb`xx` will be replaced by a specific line number in each
+case. Line breaking may also differ from case to case.) To avoid such
+errors and enable compilation to proceed, use the override command:
+\begin{verbatim}
+ \[
+ \difoverride { 2^{n+1} }
+ \diffp[2^n+1,2^n-1]F{x,y}
+ \]
+\end{verbatim}
+$\Longrightarrow$ \[
+ \difoverride { 2^{n+1} }
+ \diffp[2^n+1,2^n-1]F{x,y}
+ \]
-\paragraph*{Minutiae of spacing (yet again):}
+There are limitations on what order specifications the \verb`diffcoeff`
+package can `digest', but in real life that is unlikely to be significant.
+Mixed partial derivatives are used far less often than the pure derivatives,
+and when they \emph{are} used it is nearly always to low numerical
+orders like 1 or 2. For those rare other cases, \verb`\difoverride`
+is always available.
-In \xA7\ref{subsec:Minutiae-of-spacing} above, I discussed a slight
-reduction in the space inserted between the terms occurring in the
-denominator of a mixed partial derivative when a higher order differentiation
-is involved. The superscript appearing on a differentiation variable
-in that case \emph{of itself} introduced a spacing adjustment between
-the terms. But the present discussion involves only first order differentiations
-and no such reduction is automatically made by \texttt{diffcoeff}.
-However it is still possible to explicitly make such an adjustment
-with the \texttt{\textbackslash negmu} command introduced earlier
-(\xA7\ref{subsec:Spacing-commands}), which inserts \texttt{-1 mu} of
-spacing. For our example, in
+\subsubsection{Comma list of variables of differentiation}
+
+\label{subsec:Comma-list-of-vars}In tensor calculus differentiations
+are almost always in terms of super- or subscripted coordinates. In
+many other contexts this is the case too -- the reciprocal of the
+temperature in thermodynamics or generalized coordinates in analytical
+mechanics. This is why a comma list is used in \verb`diffcoeff` for
+specifying variables of differentiation for mixed partial derivatives.
+Although it would be nice to write the minimal \verb`{xy}` rather
+than \verb`{x,y}` when two variables $x$ and $y$ are involved,
+the extra writing is trivial and the comma list allows a simpler handling
+of multi-character variables. For instance in tensor calculus we get
+expressions like
\begin{centred}
-\verb`\[ \diffp{A_i}{ x^j\negmu,x^k } \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^j\negmu,x^k } \]
+\verb`\[ \diffp{A_i}{x^j,x^k} \]` $\Longrightarrow$ \[ \diffp{A_i}{x^j,x^k}. \]
\end{centred}
-\noindent the \texttt{\textbackslash negmu} decreases the spacing
-between the terms from the default \verb`2 mu` to \verb`1 mu`.
-
-\subsubsection{Overkill territory}
-
-Two previous examples illustrate limitations of the algorithm that
-calculates the overall order of differentiation: \texttt{2m/2+2n/2}
-is not simplified to \texttt{m+n} and \texttt{2km+2m} is not factorised
-to \texttt{2m(k+1)}. But there is much that the algorithm \emph{can}
-handle -- for instance, the simple use of parentheses:
+\noindent It is easier to write \verb`{x^j,x^k}` here than, say,
+\verb`{{x^j}{x^k}}` to distinguish the variables. It's also easier
+to read, particularly if the indices themselves get ornamented and
+need surrounding braces:
\begin{centred}
-\verb`\[ \diffp[2m-(k+1),2(k+1)-m]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
-\[ \diffp[2m-(k+1),2(k+1)-m]{F(x,y,z)}{x,y,z}. \]
+\verb`\[ \diffp{A_i}{x^{j'},x^{k'}} \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^{j'},x^{k'} }. \]
\end{centred}
+\noindent Compare that variable specification with \verb`{{x^{j'}}{x^{k'}}}`.
+Admittedly some extra whitespace would help here, but the point stands:
+the comma list requires fewer nested braces -- unless a variable
+of differentiation includes a comma, for then the comma needs to be
+enclosed in braces. There are plenty of instances of this out in the
+world (see, e.g., the last equation of (\ref{eq:eg1})) but it is
+overall a rare occurrence.
-\paragraph*{Dynamic use of parentheses}
+\subsubsection{Spacing in the denominator}
-\noindent For parenthetic expressions to be evaluated as in this example
--- the \emph{dynamic} use of parentheses -- the left parenthesis
-must be preceded at most by a sign or a number; the right parenthesis
-must be followed at most by a sign.
+\label{subsec:Minutiae-of-spacing}In Chapter 18 of the \emph{The
+\TeX book}, Knuth suggests inserting a thin space, {\ttfamily\verb`\,`}
+(or {\ttfamily\verb`3 mu`}), between differentials in appropriate
+contexts, giving as an example $dx\,dy=r\,dr\,d\theta$. In the denominator
+of a derivative, however, that degree of extra spacing -- to my eye
+-- seems too great, interfering with seeing the derivative `as a
+whole',
+\[
+\diffp.3mu.F{x,y,z},
+\]
+especially for the slash-form of derivative: $\difsp.3mu.F{x,y,z}$.
+Some spacing is desirable, but less. By default \verb`diffcoeff`
+inserts \verb`2 mu` (with stretch and shrink) between the differentials:
+$\difsp F{x,y,z}$.
-If a right parenthesis is followed by a \emph{variable}, say by \texttt{m}
-as in the order spec. \texttt{{[}(2n+1)m,(2n-1)m{]}}, it will throw
-an error and halt compilation. A message will be sent to the terminal
-and the \LaTeX{} log like the following (which assumes the order spec.
-was on line 53 of the document):
-\begin{lyxcode}
-!~Package~diffcoeff~Error:~)~followed~by~m~in~the~
+Should a differentiation occur to higher order and so a variable acquire
+a superscript, an adjustment is made to the extra spacing. By default
+\verb`1 mu` is subtracted from the default spacing. Thus in
+\[
+\diffp[2]F{x,y,z},
+\]
+\verb`2 mu` of spacing is inserted between the $\partial y$ and
+$\partial z$, but because the superscript already provides some separation
+between them, only \verb`1 mu` is inserted between $\partial x^{2}$
+and $\partial y$. The values used for the spacing and its adjustment
+in the presence of a superscript can be changed by the user; see Chapter~\ref{chap:Templates-defaults-variants}.
-order~specification~{[}(2n+1)m,(2n-1)m{]}~on~line~53.~
+When the variables themselves are super- or subscripted, as happens
+in tensor calculus, no automatic adjustment is made. Any fine-tuning
+must be done by the user using explicit spacing commands -- like
+\verb`\negmu` (a space of \verb`-1 mu`); see \xA7\ref{subsec:Spacing-commands}:
+\begin{centred}
+\verb`\[ \diffp{A_i}{ x^j\negmu,x^k } \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^j\negmu,x^k }.\]
+\end{centred}
+\noindent The \verb`\negmu` decreases the spacing between the terms
+from the default \verb`2 mu` (with stretch and shrink) to \verb`1 mu`.
-Diffcoeff~cannot~calculate~the~overall~order~of~
+\subsection{Multi-token variables: parenthesizing}
-differentiation~in~this~case.~Use~the~order-override~
-
-option~to~enter~the~overall~order.
-\end{lyxcode}
-This is a limitation on the dynamic use of parentheses -- but they
-\emph{can} be nested.
-
-\paragraph*{Static use of parentheses}
-
-If a left parenthesis is preceded by a \emph{variable} (i.e., not
-a sign or a number) this signals to \texttt{diffcoeff} the \emph{static}
-use of parentheses, something like $f(k)$, `function of $k$'.
-No attempt is made to evaluate what is between them and they are treated
-simply as an extension of the variable. For example,
+Differentiating a function of a function may involve a multi-character
+differentiation variable. For instance, to differentiate $\ln\sin x$
+in $x$ means forming the product
\begin{centred}
-\verb`\[ \diffp[f(k+1)+1,f(k-1)-1]{F(x,y)}{x,y} \]` $\Longrightarrow$
-\[ \diffp[f(k+1)+1,f(k-1)-1]{F(x,y)}{x,y}. \]
+\verb`\[ \diff{\ln\sin x}{\sin x}\diff{\sin x}x \]` $\Longrightarrow$
+\[\diff{\ln\sin x}{\sin x}\diff{\sin x}x.\]
\end{centred}
-\noindent In the static case you \emph{can} follow the right parenthesis
-by a variable without generating an error.\emph{ }You can nest them,
-and you can include static parentheses within a dynamic pair; for
-example,
+Forming the \emph{second} derivative of $\ln\sin x$ will now involve
+forming, among other quantities,
\begin{centred}
-\noindent \verb`\[ \diffp[2(3+f(k))+1,1-3(f(k)-2)]{F(x,y)}{x,y} \]`
-$\Longrightarrow$ \[ \diffp[2(3+f(k))+1,1-3(f(k)-2)]{F(x,y)}{x,y}. \]
+\noindent \verb`\[\diff[2]{\ln\sin x}{\sin x}\]` $\Longrightarrow$
+\[\diff[2]{\ln\sin x}{\sin x}\]
\end{centred}
-\noindent However, the reverse is not possible: you can't have dynamic
-parentheses within a static pair.
+\noindent Parentheses have been inserted automatically by \verb`diffcoeff`
+around $\sin x$ in the denominator to avoid any visual hint that
+we are differentiating in the sine of $x^{2}$.
-\paragraph*{Other refinements}
+\emph{That} is the problem: with a long (multi-character) variable,
+the superscript in a higher order derivative may look as if it applies
+to only part -- the last character -- of a multi-character variable.
+To solve that problem, \verb`diffcoeff` inserts parentheses around
+the variable -- for \emph{higher-order} derivatives, but not for
+first-order derivatives where the problem does not arise. You may
+prefer \verb`diffcoeff` not to parenthesize by default. Changing
+the default setting is easily accomplished; see \xA7\ref{sec:ChangingDefaults}.
-Exponents and subscripts on a \emph{variable} are fine in an order
-specification, so long as the exponent or subscript consists of a
-\emph{single} token:
+And if you do want parentheses, are they in the right place? Logically,
+no. They should include the $d$: $(d\sin x)^{2}$ -- it is the differential
+$d\sin x$ that is of the second order. But as the examples in the
+Rogues' Gallery show -- see particularly (\ref{eq:eg3}) -- the
+inclination seems to be to do otherwise. This may be because one wants
+in any case to parenthesise the variable to show that the `d' symbol
+attaches to the whole variable and not just its \emph{first} character.
+A second, outer pair of parentheses then seems too fussy and detracts
+from comprehending the symbol `at a glance':
+\[
+\diff.(dv).[2]{f(x)}{(x/k)}.
+\]
+Customary but illogical notations are familiar in mathematics --
+think of the position of the superscripts in an identity like $\sin^{2}\theta+\cos^{2}\theta=1$.
+In any case, the manner of this wrapping in parentheses -- if any
+-- of long variables for \emph{higher order} derivatives is customisable
+(\xA7\ref{sec:ChangingDefaults}).
+
+For first order derivatives parenthesising does not occur automatically.
+If you want the variable of differentiation to be parenthesised, you
+need to do it yourself:
\begin{centred}
-\verb`\[ \diffp[m^2+2(k-1),m^2-(k+1)]F{x,y,z,w} \]` $\Longrightarrow$
-\[ \diffp[m^2+2(k-1),m^2-(k+1)]F{x,y,z,w}. \]
+\verb`\[\diff {f(x)}{x/k}, \quad \diff {f(x)}{(x/k)}.\]` $\Longrightarrow$
+\[ \diff {f(x)}{x/k}, \quad\diff {f(x)}{(x/k)}.\]
\end{centred}
-\noindent Braced arguments containing \emph{multiple} tokens as exponents
-or subscripts to variables will generally not halt compilation but
-will usually give nonsensical results, as will \emph{signs} treated
-as superscripts or subscripts. Neither circumstance is checked for
-by \texttt{diffcoeff}.
-
-\paragraph*{Override}
-
-There are limitations on what order specifications the \texttt{diffcoeff}
-package can `digest'; equally, it can digest a wide variety of such
-constructs, but it is \emph{not} a computer algebra system. In all
-those cases where it fails to calculate or present a correct total
-order, the order-override option is available. Yes, this is not as
-convenient as having the overall order calculated automatically but
-(let's remind ourselves) we are deep in overkill territory. Mixed
-partial derivatives are used far less often than the pure derivatives,
-and when they \emph{are} used it is nearly always to orders 1 or 2
-in the variables. Mixed partial derivatives to exotic orders of differentiation
-are rarely used, so that the limitations of the calculational algorithm
-are of little real moment -- and the override option is always available
-for such cases.
-
-\subsection{Parentheses around multi-character variables}
-
-In thermodynamics and statistical mechanics one may want to differentiate
-in the reciprocal of the temperature, $1/T$ (or $1/\Theta$):
+To my eye, in this particular case, the parenthesized version seems
+necessary. The discussion applies equally to ordinary and partial
+derivatives. In thermodynamics and statistical mechanics one may want
+to differentiate in the reciprocal of the temperature, $1/\Theta$
+say:
\begin{centred}
-\verb`\[ \diffp[2]q{\frac 1\Theta} \]` $\Longrightarrow$ \[ \diffp[2]q{\frac 1\Theta}. \]
+\verb`\[ \diffp[2]q{\frac 1\Theta} \]` $\Longrightarrow$ \[ \diffp[2]q{\frac 1\Theta}.\]
\end{centred}
-\noindent In this case and for other \emph{higher order} derivatives
-of multi-character variables of differentiation, the parentheses are
-inserted automatically by \texttt{diffcoeff}. Precisely where parentheses
-should be placed is moot. The placement in this example is not strictly
-logical, although it feels intuitive, but the placement can be customised
-(\xA7\ref{sec:Changing-defaults}).
-
-Parentheses are automatically inserted like this only for higher order
-derivatives. When the differentiation is to first order, parenthesising
+\noindent As noted, when differentiating to first order, parenthesising
is up to the user:
\begin{centred}
\verb`\[ \diffp q{(\frac 1\Theta),V} \]` $\Longrightarrow$ \[ \diffp q{(\frac 1\Theta),V}. \]
\end{centred}
-\subsection{Jacobians}
+\chapter{Templates, defaults \& variants}
-\texttt{diffcoeff} provides a command \texttt{\textbackslash jacob}
-for constructing Jacobians. For example
-\begin{centred}
-\verb`\[ \jacob{u,v,w}{x,y,z} \]` $\Longrightarrow$ \[ \jacob{u,v,w}{x,y,z}. \]
-\end{centred}
-The comma lists can contain any number of variables. \texttt{\textbackslash jacob}
-does \emph{not} check that the two arguments contain the same number
-of variables, so it is perfectly possible to form an object like \texttt{\textbackslash jacob\{u,v,w\}\{x,y\}}
-which as far as I know has no meaning.
+\label{chap:Templates-defaults-variants} \verb`diffcoeff` is built
+on the facilities offered by the \verb`xtemplate` package (included
+in the \LaTeX 3 bundle {\ttfamily\verb`l3packages`}). The
+stuff of \verb`xtemplate` is \emph{templates}, their definition,
+their manipulation. For \verb`diffcoeff` a template is a list of
+parameter values determining how a derivative looks in the pdf. The
+parameters may be broad-brush settings like whether the derivative
+is built from \verb`\frac` or the slash \verb`/` or in compact form,
+or whether the operator symbol is \verb`d` or \verb`\partial` (or
+\verb`\nabla` or \verb`\delta` or \ldots ), or the parameters may
+be finer-grained, determining minutiae of spacing, easily missed at
+a casual glance but giving some cumulative overall effect.\emph{ }Access
+to the parameters is gained through the command \verb`\difdef`\footnote{In version 5; it has \emph{three} arguments and replaces the two-argument
+command \texttt{\textbackslash diffdef} in version 4 of \texttt{diffcoeff}.}, one argument of which is a \emph{key=value} list\emph{ }of parameter
+values. Each such list is given a name (the second argument of \verb`\difdef`)
+and is `turned into a derivative' by placing the name between dots
+as the first argument of the appropriate \verb`\difx`, \verb`\difxp`
+commands\footnote{And -- see Chapter~\ref{chap:Differentials-and-jacobians} -- of
+the differential and jacobian commands, \texttt{\textbackslash dl}
+and \texttt{\textbackslash jacob}.}. All this is discussed in \xA7\ref{sec:Variant-forms} below.
-\section{Changing defaults; variant forms\protect\label{sec:Changing-defaults}}
+\section{Template structure}
-To write the range of different examples displayed in the Rogues'
-Gallery (\xA7\ref{sec:Rogues'-gallery}) I have had to make extensive
-use of forms of derivative other than the default. \texttt{diffcoeff}
-is built on the facilities offered by the \texttt{xtemplate} package
-(included in the \LaTeX 3 bundle \texttt{l3packages)}. These facilities
-are harnessed by means of a command, \texttt{\textbackslash diffdef},
-and a further optional argument of the \texttt{\textbackslash diff}
-command.\texttt{ }
+To write a derivative one doesn't want to have to type a long list
+of \emph{key=value} statements each time. The \emph{default} values
+given to keys is crucial. Only some of the defaults appropriate for,
+say, an upright fraction ordinary derivative are going to be relevant
+for a slash-fraction partial derivative let alone a compact form partial
+derivative. This suggests creating a primary template as a `super-repository'
+of default values and from this creating secondary or child templates
+in which (only) \emph{some }of the defaults are changed -- and, if
+necessary, creating from these child templates children of their own
+(grandchild templates) in which again some further defaults are adjusted.
-\subsection{Default values: ordinary derivatives}
+In \verb`diffcoeff`, the template that is the `primogenitor' of
+the lines of default inheritance is named \verb`DIF`. It is the repository
+of all possible keys used in all possible forms of derivative (at
+least in \verb`diffcoeff`!) and so has keys appropriate to upright-fraction,
+slash-fraction and compact forms of derivative; it has keys appropriate
+to multi-variable partial derivatives and single-variable ordinary
+derivatives, but it is not actually used to form derivatives. That
+is the role of its child templates \verb`DIFF`, \verb`DIFS` and
+\verb`DIFC` corresponding to derivatives of upright-fraction, slash-fraction
+and compact forms. These child templates inherit the defaults of \verb`DIF`
+save for some settings explicitly changed in the child template relevant
+to the specific forms of fraction specified by each.
-Table~\ref{tab:Ordinary-derivatives} lists the keys available for
-forming derivatives and the default values\footnote{Note that a mu is a `math unit', 1/18 of a quad.}
-they have been assigned. These default values have been chosen to
-coincide with those relevant for \emph{ordinary} derivatives -- apart
-from the keys \texttt{denom-term-sep}, \texttt{/-denom-term-sep},
-\texttt{term-sep-adjust} and \texttt{/-term-sep-adjust} which are
-ignored for ordinary derivatives but apply to the case of mixed partial
-derivatives when there is more than one variable of differentiation.
-Keys with an opening slash, /, apply only to the slash form of the
-derivative; keys with an opening asterisk, {*}, apply only when the
-differentiand is appended.
+Apart from the operator symbol, most of the settings in the child
+templates \verb`DIFF`, \verb`DIFS` and \verb`DIFC` are also appropriate
+for partial derivatives. From a code design point of view, there is
+a certain neatness at not multiplying the number of templates in
+play, but actual use -- for instance, forming the `Rogues' gallery'
+of \xA7\ref{sec:Rogues'-gallery} -- suggests the further step of creating
+additional templates specifically for \emph{partial} derivatives\emph{
+}in the three fraction forms. Apart from the operator symbol, the
+templates \verb`DIFFP`, \verb`DIFSP` and \verb`DIFCP` inherit nearly
+all the defaults of their parents \verb`DIFF`, \verb`DIFS` and \verb`DIFC`
+respectively.
-Note that these settings are, in general, font dependent. The values
-given are (in the author's opinion) appropriate for the default \LaTeX{}
-math fonts. There are also likely to be variations required for whether
-a derivative is used in a display-style or text-style or script-style
-expression. That matter is discussed below in \xA7\ref{subsec:Text-and-script-style}.
-All values specifying a space require the unit (\texttt{mu}) to be
-given; a number alone does not suffice.
-\noindent \begin{center}
+Again, actual use suggests two further templates, both direct children
+of \verb`DIF`, for the creation of jacobians, template \verb`DIFJ`,
+and differentials, template \verb`DIFL`, with default values appropriate
+to each. In all \verb`diffcoeff` uses nine templates, the arrows
+in Table~\ref{tab:DIF-defaults} indicating lines of inheritance
+of default values. Only the child and grandchild templates of \verb`DIF`
+are used for actual construction of derivatives (and jacobians and
+differentials). \verb`DIF` itself sits `above the fray'.
+
\begin{table}
-\centering{}\caption{{\small Defaults (ordinary derivatives})\protect\label{tab:Ordinary-derivatives}}
-\begin{tabular}{lr}
+\centering{}\caption{\protect\label{tab:Template-inheritance}Template inheritance}
+\begin{tabular}{ccccc}
+\multicolumn{5}{c}{\texttt{DIF}}\tabularnewline
+$\hphantom{\mathtt{DIF}}$ $\swarrow$ & $\,\,\,\sswarrow$ & $\downarrow$ & $\ssearrow\,\,\,$ & $\searrow$ $\hphantom{\mathtt{IFL}}$\tabularnewline
+\texttt{DIFC} & \texttt{DIFS} & \texttt{DIFF} & \texttt{DIFJ} & \texttt{DIFL}\tabularnewline
+$\downarrow$ & $\downarrow$ & $\downarrow$ & & \tabularnewline
+\texttt{DIFCP} & \texttt{DIFSP} & \texttt{DIFFP} & & \tabularnewline
+\end{tabular}
+\end{table}
+
+
+\section{Default values for template \texttt{DIF}}
+
+\label{sec:Default-values-DIF}Table~\ref{tab:DIF-defaults} lists
+the keys available for forming derivatives and the default values
+assigned in the `grandparent' template, the primogenitor, \verb`DIF`.
+Different forms of derivative demand different defaults for some keys.
+Where a key is relevant for more than one style of derivative the
+default value is chosen according to the following precedence scheme:
+\begin{enumerate}
+\item \emph{ordinary upright}-fraction derivatives in \emph{display}-style
+environments
+\item \emph{ordinary slash}-fraction derivatives in \emph{text}-style environments
+\item \emph{ordinary compact}-form derivatives in \emph{text}-style environments
+\end{enumerate}
+\noindent %
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
+\noindent Users of version 4 of \texttt{diffcoeff} will notice similarities
+with and differences from the earlier version. Some key names remain
+(\verb`op-symbol`), some names have changed (\verb`multi-term-sep`
+for \verb`denom-term-sep`), keys beginning with an asterisk, \verb`*`,
+lack a following hyphen (\verb`*derivand-sep` rather than \verb`*-derivand-sep`),
+some keys have vanished (the \verb`/` keys), and there are some new
+keys (\verb`lvwrap-Ldelim`, \verb`lvwrap-Rdelim`). The redesign
+of the user interface -- \verb`\difs`, \verb`\difsp` for the \verb`/`
+switch, the new compact form commands \verb`\difc`, \verb`\difcp`,
+and bringing the jacobian and differential within the \verb`DIF`
+template structure -- meant revisiting and rethinking the list of
+keys. In the end it seemed simpler (less confusing) to treat this
+as a completely new list rather than an amendment of the earlier one.\end{shaded}%
+\end{minipage}
+
+\medskip{}
+The first column in table~\ref{tab:DIF-defaults} lists key names,
+the second column default values, and the third column to which form
+or forms of derivative the key is \emph{relevant --} meaning that
+assigning a different value to the key can change the appearance of
+the corresponding derivative in some way. The identifiers have these
+meanings:
+\begin{description}
+\item [{f,~fp}] upright fraction ordinary derivative, partial derivative;
+\item [{s,~sp}] slash fraction ordinary derivative, partial derivative;
+\item [{c,~cp}] compact ordinary derivative, partial derivative;
+\item [{j}] jacobian;
+\item [{l}] differential.
+\end{description}
+In Table~\ref{tab:DIF-defaults} and following tables, all values
+specifying a space require the unit (\verb`mu`) to be included; a
+number alone does not suffice. (A `mu' is a `math unit', 1/18
+of a quad. A thin space \texttt{\textbackslash ,} is 3 mu.) `Elastic'
+spaces with stretch and shrink can be compacted, like \verb`3muplus1muminus2mu`
+for \verb`3 mu plus 1 mu minus 2 mu`.
+
+Available keys and their defaults are the following (if you are dissatisfied
+with some choices, they can be changed; see the discussion at \xA7\ref{sec:ChangingDefaults}):
+
+\begin{table}
+\centering{}\caption{{\small\texttt{DIF}} {\small defaults}\protect\label{tab:DIF-defaults}}
+\begin{center}
+\begin{tabular}{lrl}
\toprule
-{\small key} & {\small default}\tabularnewline
-\midrule
-{\small op-symbol} & {\small\texttt{d}}\tabularnewline
-{\small op-symbol-alt} & {\small\texttt{op-symbol}}\tabularnewline
-{\small op-order-sep} & {\small\texttt{1 mu}}\tabularnewline
-{\small derivand-sep} & {\small\texttt{3 mu plus 1 mu minus 2 mu}}\tabularnewline
-{\small /-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
-{\small{*}-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
-{\small{*}/-derivand-sep} & {\small\texttt{/-derivand-sep}}\tabularnewline
-{\small denom-term-sep} & {\small\texttt{2 mu}}\tabularnewline
-{\small /-denom-term-sep} & {\small\texttt{1 mu}}\tabularnewline
-{\small term-sep-adjust} & {\small\texttt{-1 mu}}\tabularnewline
-{\small left-delim} & {\small\texttt{\textbackslash left .}}\tabularnewline
-{\small right-delim} & {\small\texttt{\textbackslash right |}}\tabularnewline
-{\small /-left-delim} & {\small\texttt{(}}\tabularnewline
-{\small /-right-delim} & {\small\texttt{)}}\tabularnewline
-{\small elbowroom} & {\small\texttt{0 mu}}\tabularnewline
-{\small /-elbowroom} & {\small\texttt{0 mu}}\tabularnewline
-{\small subscr-nudge} & {\small\texttt{0 mu}}\tabularnewline
-{\small /-subscr-nudge} & {\small\texttt{0 mu}}\tabularnewline
-{\small long-var-wrap} & {\small\texttt{d(v)}}\tabularnewline
-{\small{*}/-op-wrap} & {\small\texttt{true}}\tabularnewline
-{\small{*}-op-left} & {\small\texttt{false}}\tabularnewline
-{\small{*}-italic-nudge} & {\small\texttt{3 mu}}\tabularnewline
+{\small key} & {\small default} & {\small relevance}\tabularnewline
+\midrule
+{\small style} & {\small\texttt{frac}} & {\small f, fp, s, sp, c, cp, j}\tabularnewline
+slash-tok & {\small\texttt{/}} & {\small\phantom{{\small f, fp,}} s, sp, \phantom{{\small c, cp,}}
+j}\tabularnewline
+slash-sep & {\small\texttt{0 mu}} & {\small\phantom{{\small f, fp,}} s, sp, \phantom{{\small c, cp,}}
+j}\tabularnewline
+{\small derivand-sep} & {\small\texttt{3 mu plus 1 mu minus 2 mu}} & {\small f, fp, s, sp, c, cp}\tabularnewline
+{\small op-symbol} & {\small\texttt{\textbackslash mathrm\{d\}}} & {\small f, fp, s, sp, c, cp, j, l}\tabularnewline
+{\small op-symbol-alt} & {\small\texttt{op-symbol}} & {\small f, fp, s, sp, \phantom{{\small c, cp,}} j}\tabularnewline
+{\small op-order-nudge} & {\small\texttt{0 mu}} & {\small f, fp, s, sp, c, cp}\tabularnewline
+{\small var-sup-nudge} & {\small\texttt{1 mu}} & {\small f, fp, s, sp, \phantom{{\small c, cp,} j,} l}\tabularnewline
+{\small multi-term-sep} & {\small\texttt{2 mu plus 1 mu minus 1 mu}} & {\small f, fp, s, sp, c, cp, \phantom{j,} l}\tabularnewline
+{\small term-sep-adjust} & {\small\texttt{-1 mu}} & {\small f, fp, s, sp, c, cp, \phantom{j,} l}\tabularnewline
+{\small long-var-wrap} & {\small\texttt{d(v)}} & {\small f, fp, s, sp, \phantom{{\small c, cp,} j,} l}\tabularnewline
+{\small lvwrap-Ldelim} & {\small\texttt{\textbackslash mleft (}} & {\small f, fp, s, sp, \phantom{{\small c, cp,}} j, l}\tabularnewline
+{\small lvwrap-Rdelim} & {\small\texttt{\textbackslash mright )}} & {\small f, fp, s, sp, \phantom{{\small c, cp,}} j, l}\tabularnewline
+{\small lvwrap-sup-nudge} & {\small\texttt{-2 mu}} & {\small f, fp, s, sp, \phantom{{\small c, cp, j,}} l}\tabularnewline
+{\small outer-Ldelim} & {\small\texttt{\textbackslash left (}} & {\small f, fp, s, sp, c, cp, j, l}\tabularnewline
+{\small outer-Rdelim} & {\small\texttt{\textbackslash right )}} & {\small f, fp, s, sp, c, cp, j, l}\tabularnewline
+{\small elbowroom} & {\small\texttt{0 mu}} & {\small f, fp, s, sp, c, cp, j, l}\tabularnewline
+{\small sub-nudge} & {\small\texttt{-5 mu}} & {\small f, fp, s, sp, c, cp}\tabularnewline
+{\small op-sub-nudge} & {\small\texttt{0 mu}} & {\small\phantom{{\small f, fp, s, sp,}} c, cp}\tabularnewline
+{\small{*}derivand-sep} & {\small\texttt{derivand-sep}} & {\small f, fp, s, sp, c, cp}\tabularnewline
+{\small{*}op-set-left} & {\small\texttt{false}} & {\small f, fp, \phantom{{\small s, sp, c, cp,}} j}\tabularnewline
+{\small{*}italic-nudge} & {\small\texttt{0 mu}} & {\small f, fp, \phantom{{\small s, sp, c, cp,}} j}\tabularnewline
+{\small{*}inner-wrap} & {\small\texttt{false}} & {\small\phantom{{\small f, fp,}} s, sp}\tabularnewline
+{\small{*}inner-Ldelim} & {\small\texttt{(}} & {\small\phantom{{\small f, fp,}} s, sp}\tabularnewline
+{\small{*}inner-Rdelim} & {\small\texttt{)}} & {\small\phantom{{\small f, fp,}} s, sp}\tabularnewline
+{\small{*}outer-Ldelim} & {\small\texttt{\textbackslash big {[}}} & {\small\phantom{{\small f, fp,}} s, sp}\tabularnewline
+{\small{*}outer-Rdelim} & {\small\texttt{\textbackslash big {]}}} & {\small\phantom{{\small f, fp,}} s, sp}\tabularnewline
+{\small{*}sub-nudge} & {\small\texttt{0 mu}} & {\small\phantom{{\small f, fp,}} s, sp}\tabularnewline
\bottomrule
\end{tabular}
+\par\end{center}
\end{table}
-\par\end{center}
+
\begin{description}
-\item [{op-symbol}] the operator symbol; for ordinary derivatives, generally
-one of \texttt{d} or \texttt{\textbackslash mathrm\{d\}}, \texttt{D}
-or \texttt{\textbackslash mathrm\{D\}}, \texttt{\textbackslash delta}
-or \texttt{\textbackslash Delta}; for partial derivatives \texttt{\textbackslash partial};
-default = \texttt{d}
+\item [{style}] the fraction form of derivative;
+\begin{itemize}
+\item for upright-fraction derivatives, \verb`\diff`, \verb`\diffp`, a
+choice of \verb`frac`, \verb`tfrac` or \verb`dfrac`:
+\begin{itemize}
+\item \verb`frac` results in a fraction formed from \verb`\frac`, scalable
+\item \verb`tfrac` results in a fraction formed from \verb`\tfrac`, not
+scalable
+\item \verb`dfrac` results in a fraction formed from \verb`\dfrac`, not
+scalable
+\item default in templates \verb`DIFF`, \verb`DIFFP` = \verb`frac`
+\end{itemize}
+\item for slash-fraction derivatives,\verb`\difs`, \verb`\difsp`, a choice
+of \verb`/`, \verb`auto`, \verb`big`, \verb`Big`, \verb`bigg`
+or \verb`Bigg`
+\begin{itemize}
+\item \verb`/` forms the slash fraction with \verb`/`, not scalable
+\item \verb`auto` forms the slash fraction with \verb`\left. \middle/ \right.`,
+scalable
+\item \verb`big`, \verb`Big`, \verb`bigg` and \verb`Bigg` form the slash
+fraction with \verb`\big/`, \verb`\Big/`, \verb`\bigg/` and \verb`\Bigg/`
+respectively, not scalable
+\item default in templates \verb`DIFS`, \verb`DIFSP` = \verb`/`
+\end{itemize}
+\item for compact-form derivatives, \verb`\difc`, \verb`\difcp`, a choice
+of \texttt{\_} or \verb`dl`
+\begin{itemize}
+\item \_ forms derivatives of compact form like $\difc yx$, $\difcp[1,2]{z}{x,y}$
+\item \verb`dl` forms differentials like $\difc.dl.{}x$ and $\difcp.dl.[2]{}{x,y,z}$
+\item default in templates \verb`DIFC`, \verb`DIFCP` = \texttt{\_}
+\end{itemize}
+\item overall default in template \verb`DIF` = \verb`frac`
+\end{itemize}
+\item [{slash-tok}] token or tokens used for the slash fraction; (see \xA7\ref{subsec:Other-notations}
+for a different assignment) default \verb`/`
+\item [{slash-sep}] space inserted on either side of the \textbf{slash-tok};
+ default \verb`0 mu`
+\item [{derivand-sep}] horizontal space added before the differentiand
+if the \verb`spaced` package option is set to \verb`1`, or before
+a multi-tokened differentiand if the \verb`spaced` package option
+is set to \verb`-1`; note that compact-form derivatives \emph{always
+}have this space inserted; default (appropriate for an upright-fraction
+derivative) = \verb`3mu plus 1mu minus 2mu`
+\item [{op-symbol}] the operator symbol; for ordinary derivatives generally
+one of \verb`d` or \verb`\mathrm{d}`, for partial derivatives \verb`\partial`;
+default = \verb`\mathrm{d}`
\item [{op-symbol-alt}] if different from \textbf{op-symbol} then used
-in the denominator while \textbf{op-symbol} is used in the numerator;
-e.g. for $\diff.nabla.{v^{i}}t$, \texttt{op-symbol = \textbackslash nabla}
-and \texttt{op-symbol-alt = d}; otherwise (and usually) defaults to
-\textbf{op-symbol}
-\item [{op-order-sep}] extra horizontal space added between the op-symbol
+in the denominator of a fraction-form derivative while \verb`op-symbol`
+is used in the numerator; e.g. for the acceleration $\diff.n.{v^{i}}t$,
+\verb`op-symbol = \nabla` and \verb`op-symbol-alt = d`; defaults
+to \textbf{op-symbol} default
+\item [{op-order-nudge}] extra horizontal space added between the op-symbol
and the superscripted order of differentiation in higher order derivatives;
-for the math-italic forms compare $d^{2}$ with $d^{\mkern1mu 2}$,
-$\partial^{2}$ with $\partial^{\mkern1mu 2}$ where the first symbol
-in each case has no extra space and the second has an extra 1 mu;
-default = \texttt{1 mu}
-\item [{derivand-sep}] horizontal space added before the differentiand
-(derivand) if the \verb`spaced` package option is used, or by the
-\verb`!` switch if it is not; the default has some stretch and shrink;
-default = \verb`3mu plus 1mu minus 2mu`
-\item [{/-derivand-sep}] for the slash form of derivative, horizontal space
-added before the differentiand (derivand) if the \verb`spaced` package
-option is used, or by the \verb`!` switch if it is not; default =
-\verb`derivand-sep`
-\item [{{*}-derivand-sep}] when the derivand is appended, horizontal space
-added before the differentiand (derivand) if the \verb`spaced` package
-option is used, or by the \verb`!` switch if it is not; default =
-\verb`derivand-sep`
-\item [{{*}/-derivand-sep}] for the slash form of derivative when the derivand
-is appended, horizontal space added before the differentiand (derivand)
-if the \verb`spaced` package option is used, or by the \verb`!`
-switch if it is not; default = \verb`/-derivand-sep`
-\item [{denom-term-sep}] (mixed partial derivatives only) horizontal spacing
-inserted between the differentials in the denominator of a mixed partial
-derivative to avoid a solid cluster like $\partial x\partial y\partial z$;
-with the default 2 mu this is $\dl.p.x\dl.p.2y\dl.p.2z$; default
-= \texttt{2 mu}
-\item [{/-denom-term-sep}] (mixed partial derivatives only) horizontal
-spacing inserted between the differentials in the denominator of a
-slash-form mixed partial derivative; because a slash-form derivative
-is already spread out horizontally, the default spacing is less than
-for the \texttt{\textbackslash frac} form derivative; default = \texttt{1
-mu}
-\item [{term-sep-adjust}] (mixed partial derivatives only) adjustment (i.e.
-reduction) to \textbf{denom-term-sep} or \textbf{/-denom-term-sep}
+for math-italic forms compare $d^{2}$ with $d^{\mkern1mu 2}$, $\partial^{2}$
+with $\partial^{\mkern1mu 2}$ where the first symbol in each case
+has no extra space and the second has an extra \verb`1 mu`; since
+\textbf{op-symbol }defaults to an upright `d', default = \verb`0 mu`
+\item [{var-sup-nudge}] extra horizontal space added between a variable
+in the denominator of a derivative and the superscripted order of
+differentiation in higher order derivatives (cf \textbf{op-order-nudge});
+default = \verb`1 mu`
+\item [{multi-term-sep}] horizontal spacing inserted between the differentials
+in, for example, the denominator of a mixed partial derivative to
+avoid a solid cluster like $\partial x\partial y\partial z$; with
+the default \verb`2 mu` this is spread a little, $\difcp.dl.{}{x,y,z}$;
+default = \verb`2 mu plus 1 mu minus 1 mu`
+\item [{term-sep-adjust}] adjustment (usually a reduction) to \textbf{multi-term-sep}
when differentiation in a variable occurs to an order other than 1;
-if, e.g., $\dl.p.x^{2}\dl.p.1y\dl.p.2z$ is the denominator of a mixed
+if, e.g., $\difcp.dl.[2]{}{x,y,z}$ is the denominator of a mixed
partial derivative in three variables, because of the superscript
the spacing between $\partial x^{2}$ and $\partial y$ is reduced
by\textbf{ term-sep-adjust} from the spacing between $\partial y$
-and $\partial z$; default = \texttt{-1 mu}
-\item [{left-delim}] the left member of a delimiter pair wrapping the derivative,
-the right member of which is subscripted to indicate a point of evaluation
-or variables held constant; default = \texttt{\textbackslash left
-.}
-\item [{right-delim}] the right member of a delimiter pair wrapping the
-derivative and subscripted to indicate a point of evaluation or variables
-held constant; default = \texttt{\textbackslash right |}
-\item [{/-left-delim}] for the slash form of derivative, the left member
-of a delimiter pair wrapping the derivative and subscripted to indicate
-a point of evaluation or variables held constant; default = \texttt{(}
-\item [{/-right-delim}] for the slash form of derivative, the right member
-of a delimiter pair wrapping the derivative, the right member of which
-is subscripted to indicate a point of evaluation or variables held
-constant; default = \texttt{)}
-\item [{elbowroom}] adjustment to the whitespace between the left and right
-delimiters and the enclosed derivative; negative values reduce the
-space; default = \texttt{0 mu}
-\item [{/-elbowroom}] adjustment to the whitespace between the left and
-right delimiters and the enclosed slash-form derivative; default =
-\texttt{0 mu}
-\item [{subscr-nudge}] horizontal adjustment of the subscript's placing
-relative to the \textbf{right-delim}iter, e.g., a negative value compensates
-for the curving inwards of a large right parenthesis; may be font
-dependent; default = \texttt{0 mu}
-\item [{/-subscr-nudge}] for the slash form of derivative, horizontal adjustment
-of the subscript's placing relative to the /-\textbf{right-delim}iter;
-may be font dependent; default = \texttt{0 mu}
+and $\partial z$; default = {\ttfamily\verb`-1 mu`}
\item [{long-var-wrap}] to avoid ambiguity in higher order derivatives
-it may be advisable to wrap multi-token variables of differentiation
-in parentheses; default = \texttt{d(v)}; the choices are
+it may aid clarity to wrap multi-token variables of differentiation
+in parentheses; the choices are
\begin{description}
-\item [{\texttt{dv}}] no wrapping, e.g. $dx_{i}^{2}$ or $d\frac{1}{\Theta}^{2}$,
-$\partial x_{i}^{2}$ or $\partial\frac{1}{\Theta}^{2}$,
-\item [{\texttt{d(v)}}] wrap the variable only, e.g. $d(x_{i})^{2}$ or
-$d(\frac{1}{\Theta})^{2}$, $\partial(x_{i})^{2}$ or $\partial(\frac{1}{\Theta})^{2}$
-\item [{\texttt{(dv)}}] wrap the op-symbol and variable, e.g. $(dx_{i})^{2}$
-or $(d\frac{1}{\Theta})^{2}$, $(\partial x_{i})^{2}$ or $(\partial\frac{1}{\Theta})^{2}$
+\item [{\texttt{dv\phantom{()}}}] no wrapping, e.g. $\mathrm{d}x_{i}^{2}$
+or $\partial\frac{1}{\Theta}^{2}$,
+\item [{\texttt{d(v)}}] wrap the variable only, e.g. $\mathrm{d}(x_{i})^{2}$
+or $\partial(\frac{1}{\Theta})^{2}$,
+\item [{\texttt{(dv)}}] wrap both op-symbol and variable, e.g. $(\mathrm{d}x_{i})^{2}$
+or $(\partial\frac{1}{\Theta})^{2}$;
+\item [{\texttt{\phantom{(dv)}}}] default = \verb`d(v)`
\end{description}
-\item [{{*}/-op-wrap}] a choice of \texttt{true} or \texttt{false} for
-slash forms of the derivative when the differentiand is appended,
-dictating whether the derivative is wrapped in parentheses, as here
-$\diffp*{F(x,y)}/x$, or not; default = \texttt{true}
-\item [{{*}-op-left}] a choice of \texttt{true} or \texttt{false} indicating
-whether the op-symbol is left-aligned or not when the differentiand
-is appended; generally it is centred; does not apply to slash forms
-of the derivative; default = \texttt{false}
-\item [{{*}-italic-nudge}] if \textbf{{*}-op-left} is \texttt{true}, makes
+\item [{lvwrap-Ldelim}] left delimiter when wrapping a long variable in
+a higher order derivative; also applies to the left delimiter used
+in a jacobian; default = \verb`\mleft (`
+\item [{lvwrap-Rdelim}] right delimiter when wrapping a long variable in
+a higher order derivative; also applies to the right delimiter used
+in a jacobian; default = \verb`\mright )`
+\item [{lvwrap-sup-nudge}] horizontal adjustment to the superscript position
+when a multi-token variable is wrapped in (e.g.) parentheses and its
+order of differentiation is not \verb`1`; default = \verb`-2 mu`
+\item [{outer-Ldelim}] the left member of a delimiter pair wrapping the
+derivative, the right member of which is subscripted to indicate a
+point of evaluation or variables held constant; ISO recommends parentheses
+for this purpose, hence default = {\ttfamily\verb`\left (`}
+\item [{outer-Rdelim}] the right member of a delimiter pair wrapping the
+derivative and subscripted to indicate a point of evaluation or variables
+held constant; ISO recommends parentheses for this purpose, hence
+default = {\ttfamily\verb`\right )`}
+\item [{elbowroom}] adjustment to the whitespace between \textbf{outer-Ldelim},
+\textbf{outer-Rdelim }and the enclosed derivative; negative values
+reduce the space; default = {\ttfamily\verb`0 mu`}
+\item [{sub-nudge}] horizontal adjustment of the subscript's placing relative
+to the \textbf{outer-Rdelim}iter for a point of evaluation or variable
+held constant; a negative value compensates for the curving inwards
+of a large right parenthesis; default = {\ttfamily\verb`-5 mu`}
+\item [{op-sub-nudge}] horizontal adjustment of the position of the subscript
+in derivatives of compact form relative to the operator; since \verb`\mathrm{d}`
+is the default operator, default = \verb`0 mu`
+\item [{{*}derivand-sep}] when the derivand is appended, horizontal space
+added before the differentiand (derivand) depending on the setting
+of the \verb`spaced` package option; default = \textbf{derivand-sep}
+default
+\item [{{*}op-set-left}] a choice of {\ttfamily\verb`true`}
+or {\ttfamily\verb`false`} indicating whether the op-symbol
+is left-aligned or not when the differentiand is appended; generally
+it is centred; applies only to upright-fraction forms of the derivative;
+default = {\ttfamily\verb`false`}
+\item [{{*}italic-nudge}] if \textbf{{*}op-set-left} is \verb`true`, makes
an italic adjustment in the numerator, so that the op-symbols in numerator
-and denominator align in the same slanting column; for an upright
-\texttt{d} this would be set to \texttt{0 mu}; default = \texttt{3
-mu}
+and denominator align in the same slanting column; for \verb`d` or
+\verb`\partial` an appropriate value might be \verb`3 mu`; because
+of the default \verb`\mathrm{d}`, default = \verb`0 mu`
+\item [{{*}inner-wrap}] when the differentiand is appended, a choice of
+\verb`true` or \verb`false` dictating whether the differential operator
+is wrapped in parentheses, as here $\difsp*{F(x,y)}x$, or not; for
+a slash-fraction derivative \verb`true` is an appropriate default,
+but the overall default, appropriate for an upright-fraction derivative,
+= \verb`false`
+\item [{{*}inner-Ldelim}] if \textbf{{*}inner-wrap} is \verb`true`, the\textbf{
+}left member of a delimiter pair around the differential operator;
+default = \verb`(`
+\item [{{*}inner-Rdelim}] if \textbf{{*}inner-wrap} is \verb`true`, the\textbf{
+}right member of a delimiter pair around the differential operator
+; default = \verb`)`
+\item [{{*}outer-Ldelim}] if \textbf{{*}inner-wrap} is \verb`true`, the
+left member of a delimiter pair around both the differential operator
+and appended differentiand, the right member of which may be subscripted
+to indicate a point of evaluation or variables held constant; to avoid
+too many parentheses, given the default values of {*}\textbf{inner-Ldelim},
+{*}\textbf{inner-Rdelim}, default = \verb`\bigl [`
+\item [{{*}outer-Rdelim}] if \textbf{{*}inner-wrap} is \verb`true`, the
+right member of a delimiter pair around the differential operator
+and appended differentiand; may be subscripted to indicate a point
+of evaluation or variables held constant; to avoid too many parentheses,
+given the default values of \textbf{{*}inner-Ldelim}, \textbf{{*}inner-Rdelim},
+default = \verb`\bigr ]`
+\item [{{*}sub-nudge}] if \textbf{{*}inner-wrap} is \verb`true`, horizontal
+adjustment of the subscript's placing relative to the \textbf{{*}outer-Rdelim}iter
+for a point of evaluation or variable held constant; a negative value
+compensates for the curving inwards of a large right parenthesis;
+since the default \textbf{{*}outer-Rdelim} is a square bracket,\textbf{
+}default = \verb`0 mu`
\end{description}
-\subsection{ISO defaults}
+\subsection{Ordinary upright-fraction derivatives; template \texttt{DIFF}}
-\label{subsec:ISO-defaults}You may not like the default settings
-that come with \texttt{diffcoeff}. The package does not follow ISO
-80000-2 -- it does not use upright `d's nor does it wrap an ordinary
-differential coefficient in subscripted parentheses to indicate a
-point of evaluation. Both `defects' can be remedied by calling the
-package with the option \texttt{ISO}:\footnote{One can also use \texttt{ISO=true} to turn the option on and \texttt{ISO=false
-}to turn the option off. }
-\begin{lyxcode}
-\textbackslash usepackage{[}ISO{]}\{diffcoeff\}
-\end{lyxcode}
-\begin{wraptable}[10]{o}{0.4\columnwidth}%
-\centering{}\vspace{-4ex}
- \caption{{\small ISO default changes}\protect\label{tab:ISO-setting-changes}}
-\abovetopsep=.5ex %
+The defaults assigned in template \verb`DIF` are inherited by template
+\verb`DIFF` without change. Template \verb`DIFF` is therefore strictly
+unnecessary but, with templates \verb`DIFS` and \verb`DIFC` in mind,
+was created for the sake of a consistent naming scheme.
+
+The \verb`\diff` command uses the values in the \verb`DIFF` template
+to form an upright-fraction derivative. Only keys with an `f' in
+the third column of Table~\ref{tab:DIF-defaults} are used in this
+process. Keys without an `f' play no part in the process and their
+default values are ignored. See \xA7\ref{subsec:DIFF-(upright-fraction-derivative)}
+for the complete list of \emph{relevant} \verb`DIFF` defaults.
+
+\begin{table}
+\caption{Defaults differing from the parent template}
+
+\begin{centering}
+\subfloat[\texttt{DIFS}\label{tab:DIFS-defaults}]{\centering{}%
\begin{tabular}{lr}
\toprule
-{\small key} & {\small default}\tabularnewline
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small style} & {\small\texttt{/}}\tabularnewline
+{\small derivand-sep} & {\small\texttt{2muplus1muminus2mu}}\tabularnewline
+{\small outer-Ldelim} & {\small\texttt{(}}\tabularnewline
+{\small outer-Rdelim} & {\small\texttt{)}}\tabularnewline
+{\small sub-nudge} & {\small\texttt{0 mu}}\tabularnewline
+{\small{*}inner-wrap} & {\small\texttt{true}}\tabularnewline
+\bottomrule
+\end{tabular}}\hfil\subfloat[\texttt{DIFC}\label{tab:DIFC-defaults}]{\centering{}%
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small style} & {\small\texttt{\_}}\tabularnewline
+{\small derivand-sep} & {\small\texttt{1muplus1muminus1mu}}\tabularnewline
+{\small multi-term-sep} & {\small\texttt{1 mu}}\tabularnewline
+{\small term-sep-adjust} & {\small\texttt{0 mu}}\tabularnewline
+{\small outer-Ldelim} & {\small\texttt{\textbackslash bigl (}}\tabularnewline
+{\small outer-Rdelim} & {\small\texttt{\textbackslash bigr )}}\tabularnewline
+sub-nudge & {\small\texttt{-2 mu}}\tabularnewline
+\bottomrule
+\end{tabular}}
+\par\end{centering}
+\centering{}\subfloat[\texttt{DIFFP}\label{tab:DIFFP-defaults}]{\centering{}%
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
\midrule
-{\small op-symbol} & {\small\texttt{\textbackslash mathrm\{d\}}}\tabularnewline
-{\small op-order-sep} & {\small\texttt{0 mu}}\tabularnewline
-{\small left-delim} & {\small\texttt{\textbackslash left (}}\tabularnewline
-{\small right-delim} & {\small\texttt{\textbackslash right )}}\tabularnewline
-{\small subscr-nudge} & {\small\texttt{-6 mu}}\tabularnewline
+{\small op-symbol} & {\small\texttt{\textbackslash partial}}\tabularnewline
+{\small op-order-nudge} & {\small\texttt{1 mu}}\tabularnewline
+{\small{*}italic-nudge} & {\small\texttt{3 mu}}\tabularnewline
\bottomrule
-\end{tabular}\end{wraptable}%
-
-The uppercase is essential -- an option \texttt{iso} is not recognised.
-The \texttt{ISO} option results in changes to the default settings
-of Table~\ref{tab:Ordinary-derivatives} as listed in Table~\ref{tab:ISO-setting-changes}.
-Any settings not mentioned in Table~\ref{tab:ISO-setting-changes}
-retain the values presented in Table~\ref{tab:Ordinary-derivatives}.
-Note that the subscript nudge figure specified here is \emph{not}
-part of the standard, which makes no recommendation about the subscript's
-positioning. But: the \texttt{-6 mu} figure with a default or latin
-modern font gives a better representation of what is displayed in
-the standard than a zero figure.
-
-Because the `d' is upright with the \texttt{ISO} option, no extra
-space is required between the symbol and the superscript in a higher
-order derivative. Hence the zero value for the \texttt{op-order-sep}.
-ISO recommends subscripted parentheses to indicate a point of evaluation.
-Hence the other entries in the table. Because a large right parenthesis
-(penultimate setting) bends inwards, to the left, a negative value
-for the last entry ensures the subscript does not become detached
-from the derivative, looking lost in a sea of whitespace.
-
-Note that the \texttt{ISO} option will also produce upright `D's in
-derivatives formed from `D'; see \xA7\ref{subsec:D-delta-Delta} below.
-
-\subsection{Partial derivatives}
-
-\begin{wraptable}{o}{0.4\columnwidth}%
-\centering{}\vspace{-4ex}
- \caption{{\small Default changes for partial derivatives}\protect\label{tab:Partial-deriv-defaults}}
-\abovetopsep=.5ex %
+\end{tabular}}\hfil\subfloat[\texttt{DIFSP, DIFCP}\label{tab:DIFSP-DIFCP-defaults}]{\centering{}%
\begin{tabular}{lr}
\toprule
-{\small key} & {\small default}\tabularnewline
+{\small key} & {\small default}\tabularnewline
\midrule
-{\small op-symbol } & {\small\texttt{\textbackslash partial}}\tabularnewline
-{\small left-delim} & {\small\texttt{\textbackslash left (}}\tabularnewline
-{\small right-delim} & {\small\texttt{\textbackslash right )}}\tabularnewline
-{\small subscr-nudge } & {\small\texttt{-6 mu}}\tabularnewline
+{\small op-symbol} & {\small\texttt{\textbackslash partial}}\tabularnewline
+{\small op-order-nudge} & {\small\texttt{1 mu}}\tabularnewline
\bottomrule
-\end{tabular}\end{wraptable}%
+\end{tabular}}
+\end{table}
-The default values given in Table~\ref{tab:Ordinary-derivatives},
-when they are relevant, apply to \emph{ordinary} derivatives. For
-partial derivatives, the defaults are those of Table~\ref{tab:Partial-deriv-defaults}.
-All other keys take the default values listed in Table~\ref{tab:Ordinary-derivatives}.
-The last three entries here are not an attempt at ISO compatibility
-but reflect the use of subscripted parentheses with partial derivatives
-to indicate variables held constant, for instance in the Maxwell relations
-of thermodynamics, one of which is
-\[
-\diffp SV[T]=\diffp PT[V].
-\]
+\subsection{Ordinary slash-fraction derivatives; template \texttt{DIFS}}
-\subsection{Setting your own defaults: \texttt{\textbackslash diffdef\protect\label{subsec:diffdef}}}
+When you use the command \verb`\difs` to form a slash-fraction derivative
+it is the keys in template \verb`DIF` with an `s' in the third
+column of Table~\ref{tab:DIF-defaults} which are used. Table~\ref{tab:DIFS-defaults}
+records those keys used for this purpose which are assigned default
+values \emph{different} from those in \verb`DIF`. See \xA7\ref{subsec:DIFS-(slash-fraction-derivative)}
+for the complete list of \emph{relevant} \verb`DIFS` defaults.
-Versions 2 and later of the \texttt{diffcoeff} package provide a command,
-\texttt{\textbackslash diffdef}, that enables users to set their
-own defaults.\texttt{ }For example, if you wish to use upright `d's
-but not follow the ISO's use of subscripted parentheses to indicate
-a point of evaluation, enter in the preamble of your document the
-command
-\begin{lyxcode}
-\textbackslash diffdef~\{\}~~~~
+\subsection{Ordinary compact-form derivatives; template \texttt{DIFC}}
-~~\{~~~~~~
+When you use the command \verb`\difc` to form a compact derivative
+it is the keys in template \verb`DIF` with a `c' in the third column
+of Table~\ref{tab:DIF-defaults} which are used. Table~\ref{tab:DIFC-defaults}
+records those keys used for this purpose which are assigned default
+values \emph{different} from those in \verb`DIF`. See \xA7\ref{subsec:DIFC-(compact-derivative)}
+for the complete list of \emph{relevant} \verb`DIFC` defaults.
-~~~~op-symbol~~~~=~\textbackslash mathrm\{d\},~~~~
+\subsection{Partial derivatives; templates \texttt{DIFFP}, \texttt{DIFSP}, \texttt{DIFCP}}
-~~~~op-order-sep~=~0~mu
+The default values given in the tables so far apply to ordinary derivatives.
+For \emph{partial} derivatives, only a few defaults change. These
+are listed in Tables~\ref{tab:DIFFP-defaults}, \ref{tab:DIFSP-DIFCP-defaults}.
+All other keys take the default values of the respective parent templates,
+\verb`DIFF`, \verb`DIFS` and \verb`DIFC`.
-~~\}
-\end{lyxcode}
-\noindent Since a list of settings, like this one, is a comma-\emph{separated}
-list, no comma is required for the last entry. That entry is a consequence
-of the first: upright symbols do not require any extra separation
-between the `d' and the superscript in a higher order derivative.
+\section{Variant forms: the \texttt{\textbackslash difdef} command}
-The other point to note is the empty pair of braces after the \texttt{\textbackslash diffdef}
-command. \emph{They matter}. Their emptiness is what determines that
-it is the \emph{default} values that are changed. If they contain
-some content, then that content provides a \emph{name} for the particular
-set of values in the following list. The \texttt{diffcoeff} package
-exploits this facility to cope with the wide variety of forms displayed
-in the Rogues' Gallery of \xA7\ref{sec:Rogues'-gallery}.
+\label{sec:Variant-forms}You may be dissatisfied with the scheme
+of default values listed in the preceding tables and wish to `Re-mould
+it nearer to the Heart's Desire'. How to do so is discussed in \xA7\ref{sec:ChangingDefaults}
+below. In \emph{this} section it is assumed that the user is largely
+satisfied with the assigned defaults but has need to write an occasional
+derivative that deviates from the default form. For instance, to write
+the range of different examples displayed in the Rogues' Gallery (\xA7\ref{sec:Rogues'-gallery})
+I had to make extensive use of such \emph{variant forms} of derivative.
+I needed forms that displayed different ways of indicating a point
+of evaluation, a form that showed a math-italic `d' rather than
+the default upright `d', forms that displayed different parenthesizing
+styles for higher-order derivatives with multi-token variable names,
+and so on.
-\subsubsection{Space before the differentiand}
+The process of defining and using such variants is a two-step process.
+The `using' part is easy: you simply put the name of the variant
+form between dots and append to the relevant \verb`\difx` or \verb`\difxp`
+command.
-\label{subsec:A-final-flourish}\begin{wraptable}{o}{0.6\columnwidth}%
-\begin{centering}
-\caption{Keys for spacing the derivand}
-\medskip{}
-\begin{tabular}{lr}
-\toprule
-{\small key} & {\small default}\tabularnewline
-\midrule
-{\small derivand-sep} & {\small\texttt{3mu plus 1mu minus 2mu}}\tabularnewline
-{\small{*}-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
-{\small /-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
-{\small{*}/-derivand-sep} & {\small\texttt{ /-derivand-sep}}\tabularnewline
-\bottomrule
-\end{tabular}
-\par\end{centering}
-\end{wraptable}%
-The insertion of a small space before the differentiand is effected
-by the \verb`!` key inserted immediately before the differentiand
-argument in the \verb`\diff` command. You may wish to make the insertion
-of this space the \emph{default} behaviour. This is done by using
-the \verb`spaced` package option (which makes the \verb`!` switch
-now reverse this new default and put \emph{no} extra space before
-the derivand). The amount of space inserted is, by default, \verb`3mu plus 1mu minus 2mu`,
-meaning the space is generally $3$mu but can stretch to $4$mu or
-shrink to $1$mu as \TeX{} strives to fit content in a line or on the
-page.
+The `defining' part makes use of a command \verb`\difdef`,
+\begin{verbatim}
+ \difdef{id-list}{variant-name}{key-value list}
+\end{verbatim}
+which has three \emph{mandatory} arguments:
+\begin{enumerate}
+\item \verb`id-list` A comma-list of identifiers, one or more of \verb`f`,
+\verb`s`, \verb`c`, \verb`fp`, \verb`sp`, \verb`cp`, \verb`j`,
+\verb`l` distinguishing the respective templates \verb`DIFF`, \verb`DIFS`,
+\verb`DIFC`, \verb`DIFFP`, \verb`DIFSP`, \verb`DIFCP`, \verb`DIFJ`
+and \verb`DIFL` (for the last two see Chapter~\ref{chap:Differentials-and-jacobians}).
+\item \verb`variant-name` A (preferably brief) name for the variant form;
+it may include characters other than letters, like numbers, punctuation
+marks (excluding full stops), mathematical symbols like \verb`+`
+and \verb`=`, but not control sequences or active characters, nor
+\verb`%` , \verb`#` or braces.
+\item \verb`key-value list` A \emph{key=value} list where the settings
+differ from the default settings for the relevant template or templates
+(as determined by the \verb`id-list`).
+\end{enumerate}
+In the preamble to the present document I have included the following
+definition:
+\begin{verbatim}
+ \difdef { f } { p }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu
+ }
+\end{verbatim}
+This defines a variant, with name \verb`p`, of an ordinary upright-fraction
+derivative (the \verb`f` in the first argument) that displays as
+a partial derivative. To use the variant simply append the name, as
+a dot-delimited argument, to the \verb`\diff` command. For instance,
+repeating an earlier example from thermodynamics,
+\begin{centred}
+\verb`\[ \diff.p.*{\frac PT}U[V] = \diff.p.*{\frac 1T}V[U] \]` $\Longrightarrow$
+\[ \diff.p.*{\frac PT}U[V] = \diff.p.*{\frac 1T}V[U]\]
+\end{centred}
+\noindent The effect is exactly the same as previously and it would
+have been possible to define \verb`\diffp` as this variant by following
+the definition of the variant with the statement,
+\begin{verbatim}
+ \NewDocumentCommand \diffp { } { \diff.p. }
+\end{verbatim}
+\verb`diffcoeff` has not followed this path, instead choosing to
+put the status and configurability of partial derivatives on the same
+footing as ordinary derivatives.
-Perhaps this doesn't suit. You may want a fixed space here, with no
-stretch or shrink. The key to change is \verb`derivand-sep`. By default,
-this setting applies not only to the fraction form of derivative,
-but also to the slash form and to when the derivand is appended.
+\noindent %
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
+The command \verb`\difdef` in version 5 of \verb`diffcoeff` takes
+\emph{three} mandatory arguments for defining variant forms of derivative.
+Do not confuse with the command \verb`\diffdef` of earlier versions
+of \verb`diffcoeff` which took \emph{two }mandatory arguments for
+this purpose. The third argument is required to identify which one
+or more of the fraction forms \verb`f`, \verb`s`, \verb`c`, \verb`fp`,
+\verb`sp`, \verb`cp` of the commands \verb`\difx`, \verb`\difxp`,
+the variant applies to. In earlier versions this was not necessary
+since there was only the one primary derivative command \verb`\diff`.\end{shaded}%
+\end{minipage}
-If you feel a little less space should be used for slash derivatives,
-then the key to change is \verb`/-deriv-sep`. This changed value
-will also be used for an appended derivand in a slash derivative.
+\medskip{}
-Thus to meet both wishes you might put in the preamble of your document
-something like
-\begin{lyxcode}
-\textbackslash diffdef~\{\}~~~~
+The present document comes with a number of variant definitions. These
+are divided into two groups. One, in the preamble, contains definitions,
+like the example just given, designed to illustrate various effects
+in this document -- as in the Rogues' Gallery. These preamble definitions
+are listed in \xA7\ref{sec:Preamble-definitions}. The other, in the
+associated file \verb`diffcoeff5.def`, contains definitions that
+may be of more general usefulness; these are listed in \xA7\ref{sec:The-file-diffcoeff5.def}.
-~~\{~~~~~~
+\subsection{The \texttt{.def} file}
-~~~~derivand-sep~~~=~3~mu,~~~~
+\label{subsec:The-.def-file}A \verb`.def` file (in \verb`diffcoeff`)
+is a text file containing a list of definitions of variant derivatives
+after the fashion of the example above. The reason for placing such
+variant definitions in a file is that they can be easily transferred
+from document to document by means of the \verb`def-file` package
+option. If the name of your \verb`.def` file is \verb`myfile`, then
+invoking \verb`diffcoeff` with the call
+\begin{verbatim}
+ \usepackage[def-file=myfile]{diffcoeff}
+\end{verbatim}
+makes the definitions in \verb`myfile.def` available to your current
+document -- provided \verb`diffcoeff` can find the file.
-~~~~/-derivand-sep~=~2~mu
+The question is: where to put the \verb`.def` file? The directory
+of the current document is an obvious candidate and for the current
+document serves well, but it does mean copying the \verb`.def` file
+from directory to directory to work on \emph{different} documents.
+To make a definition file available for \emph{all} documents, place
+it in the \verb`texmf` tree, preferably not the one created by your
+\TeX{} distribution, but your own \emph{personal} \verb`texmf` tree.
+Provided your \TeX{} distribution knows about your personal \verb`texmf`
+tree and the files it contains, then a \verb`.def` file placed within
+it will be accessible to all documents.
+\noindent \begin{center}
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
-~~\}
-\end{lyxcode}
-This will insert a fixed space of $3$mu before the differentiand
-in both the numerator and when appended in the fraction form of derivative,
-and a fixed space of $2$mu in the slash form of derivative, both
-in the numerator and when appended.
+\subsubsection*{Personal \texttt{texmf} tree?}
-If you want a different spacing when the derivand is appended, the
-keys to change are \verb`*-derivand-sep` and \verb`*/-derivand-sep`.
+This is a directory created by you for `waifs and strays' of the \TeX{}
+system that are not included in standard distributions like MiK\TeX{}
+or \TeX Live. For instance, it is the place for personal packages
+designed for your own particular circumstances or preferences, and
+is structured like the standard \texttt{texmf} hierarchy but placed
+in another location so that there is no chance of its being overwritten
+when your \TeX{} distribution is updated. But that distribution needs
+to be alerted to the existence of your personal \texttt{texmf} tree
+and any new files added to it. For MiK\TeX , open the MiK\TeX{} console,
+click on \textsf{Settings} (in the column on the left) and then the
+\textsf{Directories} tab. Click the \textsf{+} button and navigate
+to your personal texmf tree to add it to the MiK\TeX{} search path,
+using the arrow keys to place it as high in the search path as possible.
+Having added it, you will then need to refresh the filename database
+by clicking on the \textsf{Tasks} menu and selecting the obvious entry.
+I am not familiar with \TeX Live but presume an analogous process
+will apply there.\end{shaded}%
+\end{minipage}
+\par\end{center}
-\paragraph{Selective spacing}
+\begin{center}
+\medskip{}
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
-I have treated the \verb`spaced` package option thus far as if it
-were an \verb`ON/OFF` switch and, indeed, the presence of the package
-option \verb`spaced` behaves as \verb`ON` and its absence as \verb`OFF`.
-Internally, however, \verb`spaced` is equivalent to \verb`spaced=1`
-and its absence to \verb`spaced=0`. Entering \verb`spaced=n` in
-the package option where \verb`n` is a positive integer is equivalent
-to entering \verb`spaced=1` (and hence to simply entering \verb`spaced`),
-but if \verb`n` is a negative integer, a new effect is produced.
+\subsubsection*{\texttt{diffcoeff.def}}
-Entering \verb`spaced=-1` (or any negative integer) will insert a
-space (by default \verb`3mu plus 1mu minus 2mu`) before the differentiand
-provided the differentiand\emph{ is longer than a single token} but
-will insert no space before single-token differentiands. The switch
-\verb`!` reverses this behaviour.
+In earlier versions of \verb`diffcoeff`, if there was no explicit
+\verb`def-file=<filename>` package option statement, then a file
+\verb`diffcoeff.def` was searched for and if found loaded. This is
+no longer the case. Version 5 of file of \verb`diffcoeff` searches
+for a \verb`.def` \emph{only if it is explicitly named} in a package
+option statement. (This decision was made at least in part to avoid
+conflict with a \verb`diffcoeff.def` file from an earlier version
+of \verb`diffcoeff` tucked away in some non-obvious place and producing
+obscure errors in the current version 5.) \end{shaded}%
+\end{minipage}
+\par\end{center}
-\subsection{Variant forms}
+\subsubsection{Log file message}
-For this package I needed to have a number of variant forms available
-to illustrate the wide variety of ways in which derivatives are displayed.
-The \texttt{\textbackslash diffdef} command in which the first argument
-is \emph{filled} provides one half of the means of doing this. I've
-given the single-letter name \texttt{p} to the following settings:
-\begin{lyxcode}
-\textbackslash diffdef~\{~p~\}
+If the\verb`.def` file named in the package option statement cannot
+be located by \TeX , a message to that effect is sent to the terminal
+and log file, but \verb`diffcoeff` continues loading.
-~~\{
+\subsection{Examples of variants}
-~~~~op-symbol~~~~=~\textbackslash partial~,
+The dot-delimited name argument must always be the \emph{first} argument
+of the \verb`\difx` or \verb`\difxp` command, even preceding an
+asterisk (star) signalling `append the differentiand'. Now for some
+examples.
-~~~~left-delim~~~=~\textbackslash left~(~~,
+\paragraph{Acceleration}
-~~~~right-delim~~=~\textbackslash right~)~,
-
-~~~~subscr-nudge~=~-6~mu
-
-~~\}
-\end{lyxcode}
-The second half of providing variant forms is to insert this name,
-\texttt{p}, between dots (periods, full stops) as the \emph{first}
-argument of the \texttt{\textbackslash diff} command. Thus, repeating
-an example at the end of \xA7\ref{subsec:Partial-appending},
+In tensor calculus acceleration is sometimes written $\difs.n.{v^{i}}t$,
+where different operator symbols occur in numerator and denominator.
+In the preamble to this document I have included the definition
+\begin{verbatim}
+ \difdef { f, s } { n }
+ {
+ op-symbol = \nabla,
+ op-symbol-alt = \mathrm{d}
+ }
+\end{verbatim}
+to give both upright- (the \verb`f`) and slash-fraction (the \verb`s`)
+forms of the acceleration. Appending tne dot-delimited name \verb`n`
+to \verb`\difs`, \verb`$ \difs.n.{v^i}t $` $\Longrightarrow$ $ \difs.n.{v^i}t $,
+and appending the dot-delimited name \verb`n` to \verb`\diff`,
\begin{centred}
-\verb`\[ \diff.p.*{\frac PT}U[V] = \diff.p.*{\frac 1T}V[U] \]` $\Longrightarrow$
-\[ \diff.p.*{\frac PT}U[V] = \diff.p.*{\frac 1T}V[U] \]
+\verb`\[ \diff.n.{v^i}t. \]` $\Longrightarrow$ \[ \diff.n.{v^i}t. \]
\end{centred}
-\noindent The effect is exactly the same as previously, when the \texttt{\textbackslash diffp}
-command was used. Indeed, \texttt{diffcoeff} identifies \texttt{\textbackslash diffp}
-with \texttt{\textbackslash diff.p.}:
-\begin{lyxcode}
-\textbackslash NewDocumentCommand~\textbackslash diffp~\{~\}~\{~\textbackslash diff.p.~\}
-\end{lyxcode}
-Note that this identification of \texttt{\textbackslash diffp} with
-\texttt{\textbackslash diff.p.} means there is no equivalent dot-delimited
-argument available for \texttt{\textbackslash diffp}. The \emph{dot-delimited
-argument applies only to} \texttt{\textbackslash diff}.
-For example, to illustrate the upright-d form of derivative, without
-changing the default math-italic form (which I prefer), one might
-enter in the preamble
-\begin{lyxcode}
-\textbackslash diffdef~\{~up~\}~
+\paragraph{Detached subscripts}
-~~\{
+To show the effect of the key \verb`sub-nudge`, the preamble contains
+the definition
+\begin{verbatim}
+ \difdef { fp } { wsp }
+ { sub-nudge = 0 mu }
+\end{verbatim}
+The name \verb`wsp` is a contraction of `whitespace'. The defintion
+applies only to an upright-fraction form of partial derivative (the
+\verb`fp` in the optional argument). By giving \verb`sub-nudge`
+a zero value in the \verb`wsp` variant, the subscript is cast adrift
+(perhaps to float away?) on a sea of whitespace. The default setting,
+\verb`sub-nudge=-5 mu`, maintains visual connection between subscript
+and right parenthesis:
-~~~~op-symbol~~~~=~\textbackslash mathrm\{d\},
+\verb`\[ \diffp.wsp.Fx[0],\quad \diffp Fx[0] \]` $\Longrightarrow$
+\[ \diffp.wsp.Fx[0],\quad \diffp Fx[0] \]
-~~~~op-order-sep~=~0~mu
+\paragraph{Lagrange's equations}
-~~\}
-\end{lyxcode}
-Apart from the \emph{key = value} settings, the critical feature here
-is the name, \texttt{up} (which is at your discretion and could equally
-be \texttt{upright} or \texttt{roman} or even \texttt{Fred} if you
-so fancied). This ensures that the changed settings apply only to
-this particular variant and do not `infect' the overall defaults.
-To use this variant, all that is needed is to add the name, between
-dots, to the \texttt{\textbackslash diff} command:
+An earlier example used Lagrange's equations of motion, which showed
+a problem with the amount of whitespace introduced before a differentiand
+bounded by a \verb`\left`, \verb`\right` pair. The file \verb`diffcoeff5.def`
+contains the definition
+\begin{verbatim}
+ \difdef { f, fp } { *0 }
+ {
+ *derivand-sep = 0 mu ,
+ outer-Ldelim = \mleft ( ,
+ outer-Rdelim = \mright )
+ }
+\end{verbatim}
+The first thing to notice is that the name of the variant, \verb`*0`,
+is not formed from letters (there are other examples below). Now Lagrange's
+equations are rendered (just right to my eye!)
\begin{centred}
-\verb`\[ \diff.up.yx \]` $\Longrightarrow$ \[ \diff.up.yx. \]
+\verb`\[ \diffp L{q_{k}}-\diff.*0.**t{\diffp L{\dot{q}_{k}}[]}=0 \]`
+\[
+\diffp L{q_{k}}-\diff.*0.**t{\diffp L{\dot{q}_{k}}[]}=0.
+\]
\end{centred}
-\noindent Each variant derivative inherits all the default values
-that it does not explicitly countermand. Thus a point of evaluation
-is indicated by a vertical rule which is the \texttt{diffcoeff} default\footnote{\noindent But not the ISO recommendation.}:
-\begin{centred}
-\noindent \verb`\[ \diff.up.*{\frac{F(x)}{G(x)}}x[x=1] \]` $\Longrightarrow$
-\[ \diff.up.*{\frac{F(x)}{G(x)}}x[x=1] \]
-\end{centred}
-\noindent Dot-delimited arguments must always be the \emph{first}
-argument of the \texttt{\textbackslash diff} command, even preceding
-an asterisk (star) as in this example.
-As another example, suppose for the subscripted indication of variables
-held constant in a partial derivative that you want to see what things
-look like if the subscript is \emph{not }nudged in towards the right
-parenthesis. In that case define a variant form
-\begin{lyxcode}
-\textbackslash diffdef~\{~padrift~\}~\{~subscr-nudge~=~0~mu~\}
-\end{lyxcode}
-I have attached a name, \texttt{padrift},\texttt{ }to this setting,
-\begin{centred}
-\verb`\[ \diff.padrift.Fx[y] \]` $\Longrightarrow$ \[ \diff.padrift.Fx[y] \]
-\end{centred}
-\noindent since, to my eye, the subscript seems detached from the
-expression it qualifies -- is it perhaps a typo? -- and `adrift
-in a sea of whitespace'. This is to be compared with the default \verb`\[ \diffp Fx[y] \]`
-$\Longrightarrow$ \[ \diffp Fx[y] \]
+\subsubsection{Editing variant forms}
-\noindent where the subscript is tucked in close to the right parenthesis
-and is clearly connected to it and the expression it delimits.
-
-Some might want to distinguish notationally a point of evaluation
-for a partial derivative from variables held constant, perhaps using
-a vertical rule for the former and (the default) parentheses for the
-latter. It would suffice then to add to the preamble
-\begin{lyxcode}
-\textbackslash diffdef~\{~pvrule~\}~\{~op-symbol~=~\textbackslash partial~\}~
-\end{lyxcode}
-(or some other name of your choosing). This gives
-\begin{centred}
-\verb`\[ \diff.pvrule.{F(x,y)}x[x=1] \]`$\Longrightarrow$ \[ \diff.pvrule.{F(x,y)}x[x=1] \]
-\end{centred}
-
-\subsubsection{Text-style and script-style derivatives\protect\label{subsec:Text-and-script-style}}
-
-As noted earlier, the \texttt{diffcoeff} package assumes that derivatives
-of fraction-like form will be used in display-style expressions and
-that the slash form will be used for inline use (text style). This
-is the usual practice. But if one does want to use the fraction form
-in an inline expression, say \texttt{\textbackslash diffp ST{[}V{]}}
-displaying as $\diffp ST[V]$, then some tweaking of settings is necessary:
-the subscript is obviously too close to the right parenthesis and,
-to my eye, there is too much `elbowroom' between the derivative and
-the enclosing parentheses. Hence define
-
\noindent %
\noindent\begin{minipage}[t]{1\columnwidth}%
-\begin{lyxcode}
-\textbackslash diffdef~\{~ptxt~\}~
+\begin{shaded}%
-~~\{
+\paragraph*{Bug in \texttt{xtemplate}}
-~~~~op-symbol~~~~~~=~\textbackslash partial,
+If you wish to successfully \emph{edit} a variant form that has (already)
+been defined -- by you or in \verb`diffcoeff` or in the \verb`.def`
+file\emph{ }-- then you will need a version of \verb`xtemplate`
+from 2022-12-17 or later. Earlier versions contained a bug that didn't
+otherwise affect the workings of \verb`diffcoeff` but did prevent
+changes being made to already defined variants.\end{shaded}%
+\end{minipage}\medskip{}
-~~~~denom-term-sep~=~1~mu~~~~,
+You may wish to edit an already defined variant form -- perhaps to
+give a \emph{negative} value to \verb`*derivand-sep` in the last
+example. You don't need to repeat the full definition. It suffices
+to change the setting only of the relevant key or keys:
+\begin{verbatim}
+ \difdef { f, fp } { *0 }
+ { *derivand-sep = -3 mu }
+\end{verbatim}
+which gives for Lagrange's equations (too tight to my eye!)
+\[
+\difdef{f,fp}{*0}{*derivand-sep=-3mu}\diffp L{q_{k}}-\diff.*0.**t{\diffp L{\dot{q}_{k}}[]}=0.
+\]
-~~~~left-delim~~~~~=~\textbackslash left~(~,
-~~~~right-delim~~~~=~\textbackslash right~),
+\subsubsection{Parenthesizing multi-token variables}
-~~~~elbowroom~~~~~~=~-2~mu~~~,
+To illustrate the different modes of parenthesizing `long' variables
+in higher order derivatives, I have put these two definitions in \verb`diffcoeff5.def`:
+\begin{verbatim}
+ \difdef { f, fp } { (dv) }
+ { long-var-wrap = (dv) }
-~~~~subscr-nudge~~~=~-3~mu~~~
+ \difdef { f, fp }{ dv }
+ { long-var-wrap = dv }
+\end{verbatim}
+The three possibilities for wrapping multitoken variables can now
+be illustrated:
+\begin{verbatim}
+ \[ \diffp[2]f{x^{i}},\quad
+ \diffp.dv.[2]f{x^{i}},\quad
+ \diffp.(dv).[2]f{x^{i}} \]
+\end{verbatim}
+$\Longrightarrow$ \[ \diffp[2]f{x^i},\quad\diffp.dv.[2]f{x^i},\quad\diffp.(dv).[2]f{x^i} \]
-~~\}
-\end{lyxcode}
-%
-\end{minipage}
+To my eye parenthesizing seems unnecessary in this case, but in the
+following desirable (as in the first, default, setting):
+\begin{verbatim}
+ \[ \diffp[2]F{1/T},\quad
+ \diffp.dv.[2]F{1/T},\quad
+ \diffp.(dv).[2]F{1/T} \]
+\end{verbatim}
+$\Longrightarrow$ \[ \diffp[2]F{1/T},\quad\diffp.dv.[2]F{1/T},\quad\diffp.(dv).[2]F{1/T} \]
-We can now write, for the same example, \texttt{\textbackslash diff.ptxt.ST{[}V{]}}
-which displays as $\diff.ptxt.ST[V]$, where the subscript is better
-positioned and there is a better fit between parentheses and derivative.
+\subsubsection{Point of evaluation}
-\subsubsection{Derivatives from D, \textbackslash delta, \textbackslash Delta\protect\label{subsec:D-delta-Delta}}
+\label{subsec:variantPoint-of-evaluation}Although ISO recommends
+subscripting parentheses to indicate a point of evaluation, some (like
+the author) prefer to subscript a vertical rule and save subscripted
+parentheses for the case of variables held constant in partial derivatives.
+The file \verb`diffcoeff5.def` contains the definition
+\begin{verbatim}
+ \difdef { f, fp, s, sp } { | }
+ {
+ outer-Ldelim = \left . ,
+ outer-Rdelim = \right |,
+ sub-nudge = 0 mu
+ }
+\end{verbatim}
+where the `pipe' character is used for the name of the variant.
+\begin{centred}
+\verb`\[ \diffp.|.{F(x,y)}x[x=1] \]` $\Longrightarrow$ \[ \diffp.|.{F(x,y)}x[x=1] \]
+\end{centred}
+For slash fractions, I think parentheses give a better result than
+a vertical rule:
+\begin{centred}
+\verb`$ \difs yx[0],\quad \difs.|.yx[0] $` $\Longrightarrow$ $\difs yx[0],\quad \difs.|.yx[0]$
+\end{centred}
+They tie the whole expression together. However, it is easy to create
+expressions that suffer from `parenthesis overload':
+\begin{centred}
+\verb`$ \difs{F(x)}{(2x)}[x=0],\quad\difs.|.{F(x)}{(2x)}[x=0] $`
+$\Longrightarrow$ $\difs{F(x)}{(2x)}[x=0],\quad\difs.|.{F(x)}{(2x)}[x=0]$
+\end{centred}
+The vertical rule is better in this case, but best of all in this
+case (to my eye) is the use of \emph{square} brackets. The file \verb`diffcoeff5.def`
+contains the definition
+\begin{verbatim}
+ \difdef { f, fp, s, sp } { ] }
+ {
+ outer-Ldelim = \left [ ,
+ outer-Rdelim = \right ],
+ elbowroom = 1 mu,
+ sub-nudge = 0 mu
+ }
+\end{verbatim}
+giving the result
+\begin{centred}
+\verb`$ \difs.].{F(x)}{(2x)}[x=0] $` $\Longrightarrow$ $ \difs.].{F(x)}{(2x)}[x=0] $,
+\end{centred}
+which both avoids `parenthesis overload' and is `tied together'
+by the square brackets (and at least gives a nod in the direction
+of the ISO standard).
-In addition to \texttt{\textbackslash diff.p.},\texttt{ diffcoeff}
-has three other \emph{built-in} variant forms that are commonly used:
-\texttt{\textbackslash diff.D.}, \texttt{\textbackslash diff.delta.},
-and \texttt{\textbackslash diff.Delta.}, corresponding to derivatives
-formed from $D$, $\delta$ and $\Delta$ respectively.
+\subsubsection{Upright text-style derivatives}
-In fluid dynamics the \emph{material }or \emph{substantive} derivative
-uses an uppercase $D$ in place of $d$. For example, the continuity
-equation is,
+\verb`diffcoeff` assumes that derivatives of upright-fraction form
+will be used mainly in display-style expressions and that the slash
+form will be used mainly for inline use. But if one does want to use
+the fraction form in an inline expression, then \verb`$ \diffp ST $`
+displaying as $ \diffp ST $ is fine, but adding a trailing optional
+argument, \verb`$ \diffp ST[V] $`, to indicate (in the present example)
+a variable held constant is not: $\diffp ST[V]$. Clearly the subscript
+is too close to the right parenthesis and (to my eye) there is too
+much `elbowroom' between the derivative and the enclosing parentheses.
+Hence the file \verb`diffcoeff5.def` contains the following definition
+for text-style upright fraction derivatives:
+\begin{verbatim}
+ \difdef { f, fp } { t }
+ {
+ style = tfrac ,
+ derivand-sep = 1 mu plus 1 mu minus 1 mu,
+ multi-term-sep = 0 mu ,
+ term-sep-adjust = 0 mu ,
+ wrap-sup-nudge = 0 mu ,
+ outer-Ldelim = \bigl (,
+ outer-Rdelim = \bigr ),
+ elbowroom = -2 mu ,
+ sub-nudge = -3 mu
+ }
+\end{verbatim}
+With this definition, the variant form \verb`$ \diffp.t.ST[V] $`
+displays as $\diffp.t.ST[V]$. The subscript now is better positioned
+and there is a better fit between parentheses and derivative. Note
+that the \verb`style=tfrac` entry in the definition means \verb`\diffp.t.`
+will not scale in a display-style environment and may give a ridiculous
+result if used inappropriately:
\begin{centred}
-\verb`\[ \diff.D.{\rho}t=\diffp\rho t + \mathbf{u\cdot}\nabla\rho \]`$\Longrightarrow$
-\[ \diff.D.{\rho}t=\diffp\rho t + \mathbf{u\cdot}\nabla\rho \]
+\verb`\[ \frac AB\diffp.t.yx \]` $\Longrightarrow$ \[ \frac AB\diffp.t.yx \]
\end{centred}
-\noindent where \texttt{\textbackslash diff.D.} produces the D-derivative.
-If you want upright `D's, then the \texttt{ISO} package option will
-produce that effect. Alternatively,
-\begin{lyxcode}
-\textbackslash diffdef~\{~Up~\}~
+For a non-scaling display-style derivative using \verb`\dfrac`, given
+the defaults in templates \verb`DIFF` and \verb`DIFFP`, the definition
+would be much simpler,
+\begin{verbatim}
+ \difdef { f, fp } { d } { style = dfrac }
+\end{verbatim}
+but there seems little point in so doing.
-~~\{
+\subsubsection{Slash-fraction styles}
-~~~~op-symbol~~~~=~\textbackslash mathrm\{D\},
+The default slash-fraction form \verb`$ \difs yx $` displaying as
+$ \difs yx $ does not scale. It is intended for inline use, but sometimes
+you may want a slash fraction of a different size -- perhaps a fraction
+is present in the differentiand or in the variable of differentiation.
+The file \verb`diffcoeff5.def` contains a definition of a scaling
+slash fraction (name \verb`0`) and a slightly larger-than-default
+slash fraction (name \verb`1`):
+\begin{verbatim}
+ \difdef { s, sp } { 0 }
+ {
+ style = auto ,
+ outer-Ldelim = \left [ ,
+ outer-Rdelim = \right ] ,
+ sub-nudge = 0 mu ,
+ *inner-Ldelim = \mleft ( ,
+ *inner-Rdelim = \mright ),
+ *outer-Ldelim = \left [ ,
+ *outer-Rdelim = \right ]
+ }
+ \difdef { s, sp } { 1 }
+ {
+ style = big ,
+ outer-Ldelim = \bigl (,
+ outer-Rdelim = \bigr ),
+ sub-nudge = -2.5 mu,
+ *inner-Ldelim = \bigl (,
+ *inner-Rdelim = \bigr ),
+ *outer-Ldelim = \bigl [,
+ *outer-Rdelim = \bigr ]
+ }
+\end{verbatim}
+The names arise from the sequence \verb`\big/`, \verb`\Big/`, \verb`\bigg/`,
+\verb`\Bigg/`, hence \verb`1`, \verb`2`, \verb`3`, \verb`4`,
+which leaves \verb`0` for the scaling form (which is built around
+\verb`\left.`, \verb`\middle/`, \verb`\right.`). \verb`diffcoeff5.def`
+does not contain definitions for the \verb`2`, \verb`3`, \verb`4`
+variants, only the two shown, because the larger sizes give ridiculous
+results. For the scaling variant, it is also easy to produce eyesores:
+\begin{centred}
+\verb`\[ \difsp.0.{\frac1Y}{\frac1X} \]` $\Longrightarrow$ \[ \difsp.0.{\frac1Y}{\frac1X} \]
+\end{centred}
+But for small size increases, the results can be pleasing. To the
+author's eye, both \verb`0` and \verb`1` variants give better results
+than the default:
+\begin{centred}
+\verb`$ \difsp.1.{F(x,y)}{\tfrac1x}[0] $` $\Longrightarrow$ $ \difsp.1.{F(x,y)}{\tfrac1x}[0] $
-~~~~op-order-sep~=~0~mu
+\verb`$ \difsp.0.{F(x,y)}{\tfrac1x}[0] $` $\Longrightarrow$ $\difsp.0.{F(x,y)}{\tfrac1x}[0]\vphantom{\bigg|} $
-~~\}
-\end{lyxcode}
-\noindent provides a variant with upright `D's.
+\verb`$ \difsp{F(x,y)}{\tfrac1x}[0] $` $\Longrightarrow$ $ \difsp{F(x,y)}{\tfrac1x}[0] $
+\end{centred}
+Subscripted \emph{square} brackets are chosen for the scaling variant
+so that the setting \verb`sub-nudge=0 mu` is appropriate at all scales.
+They provide good visual contrast with the parentheses of $F(x,y)$.
-In introductory calculus texts the simple $\delta$-derivative is
-used. This is achieved with the \texttt{\textbackslash diff.delta.}
-command: \verb`\[ \diff.delta.yx \]` $\Longrightarrow$ \[ \diff.delta.yx. \]
+\subsubsection{Compact--form derivatives}
-\noindent This form also features in analytical mechanics (in the
-Rogues' Gallery, the final example at (\ref{eq:eg6})).
-
-Similarly, \texttt{\textbackslash diff.Delta.} forms a derivative
-from $\Delta$:
+Two styles are available for compact-form derivatives, derivative
+style \verb`style=_`, and differential style \verb`style=dl`. The
+first is the default style; the orders of differentiation are applied
+to the operator symbol, in this example \verb`\partial`:
\begin{centred}
-\verb`$ \diff.Delta.y/x $` $\Longrightarrow$ $ \diff.Delta.y/x $
+\verb`$ \difcp[3,2]{f}{x,y,z} $` $\Longrightarrow$ $ \difcp[3,2]{f}{x,y,z} $
\end{centred}
-\noindent where the slash form of the derivative is shown in this
-instance.
+But suppose we define a variant form (as is done in \verb`diffcoeff5.def`):
+\begin{verbatim}
+ \difdef { cp } { dl } { style = dl }
+\end{verbatim}
+and use it to form a similar expression but without the differentiand,
+an empty argument in its place:
+\begin{centred}
+\verb`$ \difcp.dl.[3,2]{}{x,y,z} $` $\Longrightarrow$ $ \difcp.dl.[3,2]{}{x,y,z} $
+\end{centred}
+In this \verb`dl` style, the orders of differentiation are applied
+to the \emph{variables}. This allows discussion of, for example, the
+denominator of a mixed partial derivative -- perhaps a remark about
+minutiae of spacing.
-Higher order forms of these derivatives, points of evaluation, appending
-the differentiand with a star argument, all follow exactly as for
-the `pure' \texttt{\textbackslash diff} command.
+\subsubsection{D, \textbackslash delta, \textbackslash Delta derivatives}
-\paragraph{The commands \textbackslash Diff, \textbackslash diffd, \textbackslash Diffd}
+\label{subsec:D-delta-Delta}In introductory calculus texts a derivative-like
+symbol is created with the lowercase Greek delta, $\delta$ . An uppercase
+Greek delta, $\Delta$, is often used in a derivative-like symbol
+for an average. In fluid dynamics the \emph{material} (also \emph{substantive}
+or \emph{total}\,) derivative uses an uppercase $\mathrm{D}$ in
+place of $\mathrm{d}$. Texts on differential equations often use
+a $\mathrm{D}$ operator. The file \verb`diffcoeff5.def` contains
+the definitions
+\begin{verbatim}
+ \difdef { f, s } { gd }
+ { op-symbol = \delta }
+ \difdef { f, s } { gD }
+ { op-symbol = \Delta }
+ \difdef { f, s } { D }
+ { op-symbol = \mathrm{D} }
+ \difdef { c } { bD }
+ {
+ op-symbol = \mathbf{D},
+ op-sub-nudge = -2mu
+ }
+\end{verbatim}
+(where the `g' in the first two suggests `greek'), meaning one
+can write expressions like \verb`$ \difs.gd.yx $` $\Longrightarrow$
+$ \difs.gd.yx $, or \verb`$ \difs.gD.yx $` $\Longrightarrow$ $ \difs.gD.st$
+(for the average speed), or
+\begin{centred}
+\verb`\[ \diff.D.{\rho}t=\diffp\rho t + \mathbf{u\cdot}\nabla\rho \]`$\Longrightarrow$
+\[ \diff.D.{\rho}t=\diffp\rho t + \mathbf{u\cdot}\nabla\rho \]
+\end{centred}
+\noindent for the total derivative of $\rho$ (perhaps in fluid dynamics),
+or
+\begin{centred}
+\noindent \verb`$ \difc.bD.[2]y{x\,}+2\difc.bD.y{x\,}-4=0 $` $\Longrightarrow$
+$ \difc.bD.[2]y{x\,}+2\difc.bD.y{x\,}-4=0 $
+\end{centred}
+for an example in the study of differential equations.
-For compatibility with version 1 of \texttt{diffcoeff}, the commands
-\texttt{\textbackslash Diff}, \texttt{\textbackslash diffd} and
-\texttt{\textbackslash Diffd} are available and also produce the
-$D$, $\delta$ and $\Delta$ derivatives. Just as \texttt{\textbackslash diffp}
-is identified with \texttt{\textbackslash diff.p.} for partial derivatives,
-these commands are identified with \texttt{\textbackslash diff.D.},
-\texttt{\textbackslash diff.delta.}, and \texttt{\textbackslash diff.Delta}
-through the commands
-\begin{lyxcode}
-\textbackslash NewDocumentCommand~\textbackslash Diff~\{\}~~\{\textbackslash diff.D.\}
+\subsection{Other notations}
-\textbackslash NewDocumentCommand~\textbackslash diffd~\{\}~\{\textbackslash diff.delta.\}
+\label{subsec:Other-notations}\verb`diffcoeff` and this document
+are about defining \emph{derivatives} but it is worth pointing out
+that other notations can be built from the \verb`diffcoeff` constituents,
+in particular from the slash fraction forms. For example, some other
+token than \verb`/`, or indeed series of tokens, can be used to link
+numerator and denominator. It could be \verb`\vert` or \verb`\Vert`,
+displaying as $\vert$ and $\Vert$ respectively, or \verb`\otimes`
+(requiring for example \verb`\usepackage{stmaryrd}` in the preamble),
+displaying as $\otimes$, or the sequence of tokens \verb`\otimes\ldots\otimes`
+displaying as $\otimes\ldots\otimes$. The critical key is \verb`slash-tok`,
+with possible extra spacing on either side through the key \verb`slash-sep`.
+Or, one may want to void the \verb`op-symbol` key by giving it an
+empty value or do something like \verb`op-symbol=\mathbf`, or give
+\verb`outer-Ldelim`, \verb`outer-Rdelim` special values, e.g.,\verb`\langle`,
+\verb`\rvert`.
-\textbackslash NewDocumentCommand~\textbackslash Diffd~\{\}~\{\textbackslash diff.Delta.\}
-\end{lyxcode}
-Unless one is using such variant forms frequently, it seems simpler
-to remember that they are available as dot-delimited arguments to
-the \texttt{\textbackslash diff} command, using the obvious name
-in each case, rather than having to remember the precise camel-case
-form of name of the \texttt{\textbackslash Diff}, \texttt{\textbackslash diffd}
-and \texttt{\textbackslash Diffd} commands.
+In the preamble I have included the following definition, in order
+to mimic the \verb`\Braket` command of the \verb`braket` package,
+\begin{verbatim}
+ \difdef{ s }{ bk }
+ {
+ slash-tok = ,
+ op-symbol = ,
+ multi-term-sep = 3mu\middle|\mskip3mu ,
+ outer-Ldelim = \left\langle ,
+ outer-Rdelim = \right\rangle
+ }
+\end{verbatim}
+and supplemented it with the definition:
+\begin{verbatim}
+ \NewDocumentCommand \Braket { m }
+ {
+ \difoverride {\negmu}
+ \difs.bk.{}{#1}[]
+ }
+\end{verbatim}
+Testing the new command, \verb`\Braket`, gives this display:
+\begin{centred}
+\verb`\[ \Braket{\phi,\diffp[2]{}t,\psi} \]` $\Longrightarrow$ \[\Braket{\phi,\diffp[2]{}t,\psi} \]
+\end{centred}
+Comparison with the \verb`\Braket` command of the \verb`braket`
+package, which uses \verb`|` as the separator in the argument rather
+than commas, shows the displayed results to be the same (as far as
+I can judge).
-\subsection{The \texttt{.def} file\protect\label{subsec:The-.def-file}}
+\section{Defaults: setting your own}
-This mechanism of variant formation is how I have been able to illustrate
-in the Rogues' Gallery, \xA7\ref{sec:Rogues'-gallery}, the wide variety
-of different usages culled from the literature. But the thought arises:
-if a variant is to be used only once or twice, isn't this a lot of
-bother? Why not just construct the variant derivative `by hand' out
-of \texttt{\textbackslash frac} and \texttt{\textbackslash mskip}
-for example? The reason for making such definitions is that they can
-be transferred from document to document. For instance, definitions
-placed in the preamble can be copied to the preamble of another document.
+\label{sec:ChangingDefaults}The use of variant forms of derivative
+assumes the user is reasonably satisfied with the default values of
+the various templates. The user may not be. You may want different
+defaults. That is again accomplished by means of the \verb`\difdef`
+command. The procedure is identical with that for defining a variant
+except that \emph{no} \verb`variant-name` is supplied; an empty argument
+is used instead.
-But that is hardly optimal. Instead, \texttt{diffcoeff} allows such
-definitions to be placed in a text file with the the extension \texttt{.def}
-and a name of your choosing. For the present document the file is
-called \texttt{diffcoeff-doc.def} and has been placed in the same
-directory as \texttt{diffcoeff.tex}. To use these definitions, the
-\texttt{diffcoeff} package is called with the command
-\begin{lyxcode}
-\textbackslash usepackage{[}def-file=diffcoeff-doc{]}\{diffcoeff\}
-\end{lyxcode}
-But even this process still means copying a definition file from directory
-to directory as one works on different documents. The solution is
-to make a definition file available for \emph{all} documents and the
-way to do that is by placing it in the texmf tree, preferably not
-the one created by your \TeX{} distribution (perhaps MiKTeX or TexLive),
-but your own \emph{personal} texmf tree.
+For example, suppose you wish to indicate a point of evaluation for
+ordinary upright-fraction derivatives by means of a subscripted vertical
+rule rather than parentheses. In \xA7\ref{subsec:variantPoint-of-evaluation}
+we have seen how to create a variant form with this property but now
+we want to make it the default in the template \verb`DIFF`. That
+is easy -- simply omit any content from the second argument:
+\begin{verbatim}
+ \difdef { f } {}
+ {
+ outer-Ldelim = \left . ,
+ outer-Rdelim = \right |,
+ sub-nudge = 0 mu
+ }
+\end{verbatim}
+\noindent If this is placed in the preamble of your document or in
+your \verb`.def` file (see \xA7\ref{subsec:The-.def-file}) then the
+command \verb`\diff yx[0]` will produce
+\[
+\diff.|.yx[0]
+\]
+by default. By leaving the second argument empty the \verb`\difdef`
+command has changed the default value of those templates indicated
+by the list of identifiers in the first argument -- in the present
+case only the template \verb`DIFF`. In particular, note that the
+new default is \emph{not} inherited by \verb`DIFFP`. Inheritance
+occurs \emph{only} at load time. How to change defaults that will
+be inherited is discussed below in \xA7\ref{subsec:Changing-DIF-defaults}.
-\texttt{\vspace{2ex}
- }
+If you wish to change other defaults of other templates follow the
+same procedure. In the first argument of the \verb`\difdef` command
+insert a comma-list of the derivative identifiers (\verb`f`, \verb`s`,
+\verb`c`, \verb`fp`, \verb`sp`, \verb`cp`, \verb`j` or \verb`l`)
+that you want the new defaults to apply to, \emph{leave the second
+argument empty}, and in the third argument provide the \emph{key=value}
+list of new defaults.
-\noindent %
-\noindent\fbox{\begin{minipage}[t]{1\linewidth - 2\fboxsep - 2\fboxrule}%
-\textbf{Personal texmf tree? }
+For instance, you might prefer math-italic `d's rather than the
+upright ISO recommendation, and you want this to apply across \emph{all}
+ordinary-derivative templates. The most straightforward way of achieving
+that would be through the definition
+\begin{verbatim}
+ \difdef { f, s, c, l } {}
+ {
+ op-symbol = d ,
+ op-order-nudge = 1 mu
+ }
+\end{verbatim}
+which includes the list of identifiers \verb`f, s, c, l` in the first
+argument (the \verb`l` referring to the template \verb`DIFL` of
+the differential -- see \xA7\ref{sec:Differentials}) and leaves the
+second argument empty. Thereafter, all ordinary derivatives will be
+graced with math-italic rather than upright `d's.
-This is a directory for `waifs and strays' of the \TeX{} system that
-are not included in standard distributions like MiK\TeX{} or \TeX Live.
-For instance, it is the place for personal packages designed for your
-own particular circumstances or preferences, and is structured like
-the standard MiK\TeX{} or \TeX Live hierarchy but placed in another
-location so that there is no chance of its being overwritten when
-MiK\TeX{} or \TeX Live are updated. However, those distributions need
-to be alerted to its existence. For MiK\TeX , open the MiK\TeX{} console,
-click on \textsf{Settings} and then the \textsf{Directories} tab.
-Click the \textsf{+} button and navigate to your personal texmf tree
-to add it to the MiK\TeX{} search path. Having added it, you will then
-need to refresh the filename database by clicking on the \textsf{Tasks}
-menu and selecting the obvious entry. I am not familiar with \TeX Live
-but presume an analogous process will apply there.%
-\end{minipage}}
+\subsection{Changing defaults in \texttt{DIF}}
-\medskip{}
+\label{subsec:Changing-DIF-defaults}You might wonder if this last
+effect could not have been obtained more simply by changing the default
+in the `primogenitor' template \verb`DIF` -- perhaps leave both\emph{
+first }and second\emph{ }arguments empty in the \verb`\difdef` command.
+That, however, has no effect. The \verb`\difdef` command does nothing
+if the first argument is empty. Inheritance occurs only once, at time
+of birth -- \emph{load time} -- and not thereafter. If you want
+to make a change affecting a number of templates by changing a default
+in \verb`DIF`, then it has to be done at the time when \verb`diffcoeff`
+is loaded.
-\noindent Provided your \LaTeX{} distribution knows about your personal
-texmf tree, then a \texttt{.def} file placed within it, will be accessible
-to all documents.
+There are two ways to do this. The first is to create a text file
+with the specific name \verb`diffcoeff.DIF` with the desired settings.
+For example, if we want math-italic `d's and a subscripted vertical
+rule for points of evaluation, then the file might look like
+\begin{verbatim}
+ op-symbol = d,
+ op-order-nudge = 1 mu,
+ outer-Ldelim = \left . ,
+ outer-Rdelim = \right |,
+ sub-nudge = 0 mu
+\end{verbatim}
+By locating the file in a place where your \TeX{} distribution can
+find it -- either in the directory of the current document or in
+your personal \verb`texmf` tree (see the earlier discussion at \xA7\ref{subsec:The-.def-file},
+and in particular the need to alert your \TeX{} distro to the presence
+of the file) -- \verb`diffcoeff.DIF` will be read at load time and
+the new defaults not only incorporated into template \verb`DIF` but
+inherited by all child and grandchild templates unless explicitly
+countermanded (for example by \verb`op-symbol = \partial` and similar
+statements in the definitions of those templates).
-\subsubsection{Structure of the \texttt{.def} file}
+The second method is to use the package option \verb`DIF`. For instance
+loading \verb`diffcoeff` with the call
+\begin{verbatim}
+ \usepackage
+ [
+ DIF = { op-symbol = d,
+ op-order-nudge = 1 mu,
+ outer-Ldelim = \left . ,
+ outer-Rdelim = \right |,
+ sub-nudge = 0 mu }
+ ]{diffcoeff}
+\end{verbatim}
+will overwrite the built-in defaults with these new values, which
+will be inherited by child (and grandchild) templates unless explicitly
+countermanded. Notice that since \verb`DIF` is a comma list it requires
+braces around the list of \emph{key=value} statements\emph{.}
-The best way to see what a \texttt{.def} file looks like is to view
-\texttt{diffcoeff-doc.def }in a text editor.\footnote{This file should be in the same directory as \texttt{diffcoeff.pdf}
-and \texttt{diffcoeff.tex} in your \LaTeX{} distribution.}
+If both methods of changing the template \verb`DIF` are employed,
+the order of use is, first, read and act on the file \verb`diffcoeff.DIF`,
+then read and act on the package option \verb`DIF`. (In other words,
+to avoid complicating the preamble, preferably use the file \verb`diffcoeff.DIF`;
+use the package option \verb`DIF` only for fine-tuning -- perhaps
+a setting specific to that particular document.)
-If you want your variant definitions to use defaults different from
-those supplied with the \texttt{diffcoeff} package, then the first
-definition in the \texttt{.def} file should be the one setting the
-new defaults, with an \emph{empty} first argument to the \texttt{\textbackslash diffdef}
-command:
-\begin{lyxcode}
-\textbackslash diffdef~\{\}~~~~
+\chapter{Differentials and jacobians}
-~~\{~~~~~~
+\label{chap:Differentials-and-jacobians}In addition to the six derivative
+commands, \verb`\difx` and \verb`\difxp`, the \verb`diffcoeff`
+package has two further commands, \verb`\dl` and \verb`\jacob`,
+for writing differentials and jabobian determinants respectively.
+These commands use the settings of the templates \verb`DIFL` and
+\verb`DIFJ`, and both are correspondingly configurable by means of
+the \verb`\difdef` command.
-~~~~key-1~=~value-1,~~~~
+\section{Differentials}
-~~~~key-2~=~value-2,
-
-~~~~...
-
-~~~~key-n~=~value-n
-
-~~\}
-\end{lyxcode}
-The key-value list is a comma-separated list; hence the last entry
-doesn't need to end with a comma. Nudge and separation values need
-to include the unit, \texttt{mu}; a numerical value alone will result
-in error.\texttt{ }Because a \texttt{.def} file\texttt{ }is a \LaTeX{}
-file, comments need to start with a \texttt{\%} character.
-
-\subsubsection{\texttt{diffcoeff.def}}
-
-Note that if the \texttt{diffcoeff} package is invoked without an
-explicit \texttt{def-file= <filename>} option statement, as here,
-\begin{lyxcode}
-\textbackslash usepackage\{diffcoeff\}
-\end{lyxcode}
-then it will search in the texmf tree (the \LaTeX{} distribution's
-and your personal one) and the document directory for a file \texttt{diffcoeff.def}
-and if found will load that. This file should contain definitions
-of those variants you are likely to use in multiple documents. In
-my personal texmf tree (which I've put at \texttt{E:\textbackslash texmf\textbackslash}
-on a Windows machine) the file \texttt{diffcoeff.def} is located in
-the directory \texttt{E:\textbackslash texmf\textbackslash tex\textbackslash latex\textbackslash diffcoeff\textbackslash}.
-(The backslashes are replaced by forward slashes on linux machines.)
-
-Variants likely to be of value only to a specific document should
-be added to the preamble of that document. Alternatively, they could
-be added to \texttt{diffcoeff.def} but that added-to file saved to
-the document directory under a \emph{different} name -- e.g. I've
-saved the variants required for the present document under the name
-\texttt{diffcoeff-doc.def}. Many of these variants were created solely
-to illustrate points in the present document and I have no intention
-of using them in my own work. Consequently my \texttt{diffcoeff.def}
-file is smaller, containing only a selection from \texttt{diffcoeff-doc.def}.
-
-\section{Differentials in integrals, etc.}
-
-Forms like $dx$ occur not only in derivatives but also in other contexts,\footnote{I thank \noun{Sergio Callegari} for drawing my attention to this rather
-obvious point, and its omission from previous versions of \texttt{diffcoeff}.} for example, the expression for a total differential like
+\label{sec:Differentials}Forms like $\dl x$ occur not only as components
+of derivatives but also in other contexts like the expression for
+a total differential,
\[
\dl P=\diffp Px\dl x+\diffp Py\dl y+\diffp Pz\dl z,
\]
-or an integral like $\int\sin x\dl2x$, or a multi-variable integral
+or in integrals, like $\int\sin x\dl x$, or multi-variable integrals
like
\[
-\iiintop_{-\infty}^{\infty}V(x,y,z)\dl3x\dl2y\dl2z.
+\iiintop_{-\infty}^{\infty}V(x,y,z)\dl{x,y,z}.
\]
+They also occur in differential geometry and elsewhere in the form
+of line elements like
+\begin{centred}
+$\dl.+.{x,y,z}^2$ \quad{}and\quad{} $c^2\dl.-.{t,x,y,z}^2$.
+\end{centred}
Surely we want the `d's in these expressions to correspond to their
-form (upright or math italic) in derivatives? If, for instance, the
-\texttt{ISO} package option has been set, one doesn't want to be writing
-\texttt{\textbackslash mathrm\{d\}} in every (or indeed any) integral.
-To this end, \texttt{diffcoeff} provides a command \texttt{\textbackslash dl}
-to write the `d' in a differential in a manner consistent with the
-default form used in derivatives. In the present document, the default
-form is math-italic and so
+form (upright or math italic) in derivatives? To this end, \verb`diffcoeff`
+provides a command \verb`\dl` to write the `d' in a differential
+in a manner consistent with the default form used in derivatives.
+In the present document, the default form is upright and so
\begin{centred}
\verb`$ \dl x $` $\Longrightarrow$ $ \dl x. $
\end{centred}
-\noindent It is also possible\footnote{\noindent From version 3.1 of \texttt{diffcoeff}; version 3.0 of the
-package produced a \LaTeX{} error.} to use the command before, for instance, \texttt{\textbackslash mathbf\{x\}}
-or \texttt{\textbackslash vec\{x\}}:
+\noindent To use the command before a multi-token variable of differentiation,
+put the variable in braces:
\begin{centred}
-\verb`$ \dl \vec{x} $` $\Longrightarrow$ $ \dl \vec{x} $,~~~~\verb`$ \dl \mathbf{x} $`
-$\Longrightarrow$$ \dl \mathbf{x}. $
+\verb`$ \dl{\vec{x}},\quad \dl{\mathbf{x}} $` $\Longrightarrow$
+$ \dl{\vec{x}},\quad \dl{\mathbf{x}} $.
\end{centred}
+For the triple integral above, writing the differentials required
+not three but just the \emph{one} command:
+\begin{centred}
+\verb`$ \dl{x,y,z} $` $\Longrightarrow$ $ \dl{x,y,z} $.
+\end{centred}
+To write the line elements I made use of a dot-delimited argument
+producing a variant form of the differential (see below \xA7\ref{subsec:Line-elements}):
+\begin{centred}
+\verb`$ \dl.+.{x,y,z}^2 $` $\Longrightarrow$ $ \dl.+.{x,y,z}^2 $,
-\subsection{Options}
+\verb`$ c^2\dl.-.{t,x,y,z}^2 $` $\Longrightarrow$ $ c^2\dl.-.{t,x,y,z}^2 $.
+\end{centred}
-There are two options available with the differential command.
+\subsection{Template \texttt{DIFL}}
-The first is the dotted name option discussed in \xA7\ref{sec:Changing-defaults}.
-Thus, to illustrate a differential with an upright `d', write
-\begin{centred}
-\verb`$ \dl.up.x $` $\Longrightarrow$ $ \dl.up.x. $
-\end{centred}
-\noindent This presumes that a variant derivative with upright `d's
-has been defined and the definition is available, either in the preamble
-or in an accessible \texttt{.def} file, as discussed in the previous
-section. Alternatively, if you have defined your default derivative
-to use upright `d's (perhaps with the \texttt{ISO} option) then
-\texttt{\textbackslash dl} alone will suffice to produce an upright
-`d'.
+\begin{wraptable}{o}{0.5\columnwidth}%
-\subsubsection{Partial differential}
+\begin{centering}
+\caption{\texttt{DIFL} defaults\protect\label{tab:DIFL-defaults}}
+\begin{center}
+\begin{tabular}{lrr}
+\toprule
+{\small key} & {\small default} & {\small comment}\tabularnewline
+\midrule
+{\small style} & {\small\texttt{dl}} & {\small locked}\tabularnewline
+{\small outer-Ldelim} & {\small\texttt{\textbackslash ,}} & \tabularnewline
+{\small outer-Rdelim} & & \tabularnewline
+\bottomrule
+\end{tabular}
+\par\end{center}
+\par\end{centering}
+\end{wraptable}%
+The differential command \verb`\dl` gives access to a template \verb`DIFL`
+which inherits the default values of the fundamental template \verb`DIF`
+with the (few) changes shown in Table~\ref{tab:DIFL-defaults}. Note
+that the \verb`style` key is fixed at the value \verb`dl`; it cannot
+be changed. The \verb`outer-Ldelim` key inserts a small space before
+the differential; the \verb`outer-Rdelim` key does nothing. For the
+differential, both \verb`outer-Ldelim` and \verb`outer-Rdelim` are
+\emph{always inserted}. This differs from the derivative for which
+\verb`outer-Ldelim` and \verb`outer-Rdelim` are inserted only if
+there is a trailing optional argument. It is as if the differential
+command \verb`\dl` had a built-in empty trailing optional argument.
-\label{subsec:Partial-differential}Since the variant \texttt{\textbackslash diff.p.}
-is defined in \texttt{diffcoeff.sty} itself, \texttt{\textbackslash dl.p.}
-is always available and at 6 keystrokes offers a slightly shorter
-way of writing \texttt{\textbackslash partial} (8 keystrokes). However,
-there are sufficient contexts where expressions like \verb`\partial_x`
-are used, perhaps as a shortcut for a partial derivative, for it to
-be worthwhile to define an appropriate command for this variant. From
-version 4.0, \texttt{diffcoeff} therefore provides \verb`\dlp`, defined
-by
-\begin{lyxcode}
-\textbackslash NewDocumentCommand~\textbackslash dlp~\{\}~\{~\textbackslash dl.p.~\}
-\end{lyxcode}
-Thus, for instance, \verb`$ \dlp_x $` $\Longrightarrow$ $ \dlp_x $.
+That so few of the \verb`DIF` defaults are changed in \verb`DIFL`
+indicates that much of the machinery of derivative formation is irrelevant
+for forming a differential. A list of \emph{relevant} keys for the
+creation of differentials -- those that have some effect on the appearance
+of the thing -- can be found at \xA7\ref{subsec:DIFL-(differential)}.
-\subsubsection{Spacing}
+\subsection{Syntax and options}
-This second option inserts spacing before the `d'. If \texttt{\textbackslash dl}
-is followed by a digit (0, 1, 2, ..., 9) it will insert a horizontal
-space of that number of mu before the `d'; (\texttt{\textbackslash dl0x}
-has the same effect as \texttt{\textbackslash dl x}.)\texttt{ }Thus,
-an alternative way of writing an example in Chapter~18 of \emph{The
-\TeX book} is
+\label{subsec:DifferentialsSyntaxOptions}If all options are present
+the differential command has the syntax
+\begin{verbatim}
+ \dl.name.[order-spec]{variable(s)}^{exponent}
+\end{verbatim}
+where the arguments have the following significance:
+\begin{enumerate}
+\item \verb`name` (optional) A dot-delimited name to distinguish a variant
+form (non-default form) of differential; see \xA7\ref{subsec:Variant-differentials}
+below.
+\item \verb`order-spec` (optional) The power or comma-list of powers to
+which the differential or differentials will be raised. If all powers
+are \verb`1` then no specification is needed; indeed, if fewer powers
+are specified than there are variables, all `missing' powers are
+assumed to be \verb`1`; see the discussion for mixed partial derivatives,
+\xA7\ref{subsec:Mixed-partial-derivatives}.
+\item \verb`variable(s)` (mandatory) The variable or comma-list of variables
+the differential operator applies to. \verb`\dl x`, \verb`\dl{\vec{x}}`,
+\verb`\dl{x,y,z}` are all valid variable specifications, displaying
+as $\dl x$, $\dl{\vec{x}}$ and $\dl{x,y,z}$ respectively.
+\item \verb`exponent` (optional) An exponent to which all differentials
+will be raised; overrides the \verb`order-spec` ; see \xA7\ref{subsec:Line-elements}
+for examples of use.
+\end{enumerate}
+Only the third argument is mandatory, although it may be empty.
+
+\subsection{Variant forms of differential}
+
+\label{subsec:Variant-differentials}The first argument of the differential
+command \verb`\dl` is the optional \verb`name` which is used --
+like the corresponding argument in the derivative commands -- to
+define \emph{variant forms}.
+
+To create such variant forms, the \verb`\defdif` command is again
+used, but with \verb`l` (lowercase \verb`L`) used as the identifier
+in the first argument. For example, you may want a `partial' differential,
+using \verb`\partial` in place of \verb`d`. It seems natural to
+give this the name \verb`p`:
+\begin{verbatim}
+ \difdef { l } { p }
+ { op-symbol = \partial }
+\end{verbatim}
+In fact just this definition can be found in the file \verb`diffcoeff5.def`,
+so that
\begin{centred}
-\verb`$ \dl x\dl3y=r\dl3r\dl3\theta $` $\Longrightarrow$ $ \dl x\dl3y=r\dl3r\dl3\theta. $
+\verb`$ \dl.p.x $` $\Longrightarrow$ $\dl.p.x$
\end{centred}
-\noindent To my eye this is too much space; I prefer
+which is seven keystrokes in all versus ten (space included) for \verb`\partial x`.
+Defining \verb`\dlp` by writing
\begin{centred}
-\noindent \verb`$ \dl x\dl2y=r\dl2r\dl2\theta $` $\Longrightarrow$
-$ \dl x\dl2y=r\dl2r\dl2\theta. $
+\verb`\NewDocumentCommand \dlp {} { \dl.p. }`.
\end{centred}
-\noindent I used \texttt{\textbackslash dl3x\textbackslash dl2y\textbackslash dl2z}
-when writing the triple integral above, \emph{no} extra spacing when
-writing the total differential expression, since the differentials
-are already distinct from the preceding fraction forms $\diff.ptxt.Px$
-etc., and \texttt{\textbackslash dl2x} when writing $\int\sin x\dl2x$.
+saves another keystroke. However, I doubt the few keystrokes saved
+justify the trouble of defining such a variant. The real reason one
+might do so is to ease the writing of expressions like $\dl.p.[3,2]{x,y,z}$
+-- perhaps in a document like the present one to discuss the minutiae
+of spacing in the denominators of mixed partial derivatives.
+\begin{centred}
+\verb`$\dl.p.[3,2]{x,y,z}$` $\Longrightarrow$ $\dl.p.[3,2]{x,y,z}$
+\end{centred}
+As you can see from the example, just as for mixed partial derivatives,
+if more than one variable is specified but the \verb`order-spec`
+contains fewer than that number of entries, \verb`diffcoeff` assumes
+the missing entries are \verb`1`.
-Note that only \emph{one} digit can be used. If two are used, as here,
-\verb`$ \dl20x $` $\Longrightarrow$ $ \dl20x $, the effect is unlikely
-to be what is wanted.
+A second example of a variant form of differential is provided by
+the definition
+\begin{verbatim}
+ \difdef { l } { b }
+ { op-symbol = \mathrm{d}\mathbf }
+\end{verbatim}
+which can be found in the file \verb`diffcoeff5.def`. If you distinguish
+vectors, say, by boldface type, then you can avoid writing \verb`\mathbf`
+for differentials of vectors by using the variant form \verb`\dl.b.`:
+\begin{centred}
+\verb`$ \dl.b.x,\quad \dl.b.{x,y,z} $` $\Longrightarrow$ $ \dl.b.x ,\quad \dl.b.{x,y,z} $.
+\end{centred}
-From version 3.2 of \texttt{diffcoeff} it is possible to also add
-\emph{negative} space before the differential, which might be useful
-in special contexts, perhaps to construct a symbol:
+\subsubsection{Line elements}
+
+\label{subsec:Line-elements}Variant forms can be used to write line
+elements of Pythagorean or Minkowskian form. The definition
+\begin{verbatim}
+ \difdef { l } { + }
+ {
+ multi-term-sep = 0 mu +,
+ term-sep-adjust = 0 mu ,
+ outer-Ldelim =
+ }
+\end{verbatim}
+which can be found in the file \verb`diffcoeff5.def`, inserts a \verb`+`
+sign between terms in the variable specification. Notice that the
+value assigned to the key \verb`multi-term-sep` begins with \verb`0 mu`.
+A dimension here \emph{initially} is essential. Also note that the
+thin space inserted by default before a differential by means of the
+\verb`outer-Ldelim` setting is now removed. But the intriguing feature
+of the definition is what follows the \verb`0 mu` in the \verb`multi-term-sep`
+value: a \verb`+` sign. Applying this variant to \verb`{x,y,z}`
+the result is $ \dl.+.{x,y,z} $, which may be mildly interesting
+but definitely becomes so when we add an exponent to the variable
+spec.:
\begin{centred}
-\verb`$ /\dl-9x $` $\Longrightarrow$ $ /\dl-9x. $
+\verb`$ \dl.+.{x,y,z}^2 $` $\Longrightarrow$ $ \dl.+.{x,y,z}^2 $.
\end{centred}
-\noindent For negative space before the differential, add a minus
-sign before the (single) digit.
+The exponent acts as if an order specification \verb`[2,2,2]` had
+been included. If an order specification \emph{is }included, whatever
+the values listed, the trailing exponent overrides it.
-The spacing digit option \emph{follows} the dot-delimited name option.
-For example, earlier, in the denominator of a mixed partial derivative,
-I have used what is effectively \texttt{\textbackslash dlp x\textbackslash dlp2y\textbackslash dlp2z},
-and the variation to that spacing when a higher-order differentiation
-occurs:
+Similarly, the file \verb`diffcoeff5.def` contains an identical definition
+save that the plus sign is replaced by a minus. This enables the writing
+of a Minkowski metric:
\begin{centred}
-\verb`$ \dlp x^2\dlp1y\dlp2z $` $\Longrightarrow$ $ \dlp x^2\dlp1y\dlp2z. $
+\verb`$ c^2\dl.-.{t,x,y,z}^2 $` $\Longrightarrow$ $ c^2\dl.-.{t,x,y,z}^2 $.
\end{centred}
-\section{Rationale}
+\subsection{Changing defaults}
-Version 1 of the \texttt{diffcoeff} package arose from a need to simplify
-the parsing of differential coefficients for another program I was
-working on which was struggling to `read' all the possible permutations
-of \texttt{\textbackslash frac} or \texttt{\textbackslash tfrac}
-or \texttt{\textbackslash dfrac} or slash forms of the derivative,
-of \texttt{d} or \texttt{\textbackslash mathrm\{d\}} or \texttt{\textbackslash partial}
-or \texttt{D} or \texttt{\textbackslash mathrm\{D\}} or \texttt{\textbackslash nabla},\texttt{
-}and of points of evaluation delimited by vertical rules or parentheses.\texttt{ }Although
-regular expressions coped with most of these cases, it was \emph{messy}.
+To change the \emph{default} values of the \verb`DIFL` template use
+the \verb`\difdef` command but leave its second argument, the \verb`name`
+argument, empty. For instance if you want slightly less space by default
+before a differential than the thin space (\verb`\,` or \verb`3 mu`)
+specified in the \verb`DIFL` template -- say you want \verb`2 mu`
+-- then write
+\begin{verbatim}
+ \difdef { l } {} { outer-Ldelim = \twomu }
+\end{verbatim}
+and ensure that this is in your \verb`.def` file or in the preamble
+of your document. If you want a rubber length, say \verb`3 mu plus 1 mu minus 2 mu`
+(which can also be written more compactly as \verb`3muplus1muminus2mu`),
+then write (notice the \verb`\mskip`)
+\begin{verbatim}
+ \difdef { l } {}
+ { outer-Ldelim = \mskip 3muplus1muminus2mu }
+\end{verbatim}
+The crucial point is to leave the second argument of \verb`\difdef`,
+the \verb`variant name`, empty. That changes the \emph{default} values
+in \verb`DIFL` of the keys listed in the third argument of \verb`\difdef`.
-There are other packages which have commands for the derivative (e.g.,
-\texttt{bropd}, \texttt{commath},\texttt{ esdiff}, \texttt{physymb})
-but none quite gave what I wanted -- although they probably cope
-with most users' needs. \texttt{esdiff} came closest to what I was
-seeking but failed when it came to combining algebraic and numeric
-orders of differentation in a mixed partial derivative (and made heavier
-use of braces than I liked in that case too).
+\subsection{Rationale}
-\subsection{\texttt{diffcoeff.sty}}
+But why bother with the differential command at all? It only seems
+to complicate the simple typing of \verb`d` followed by \verb`x`.
+Admittely typing \verb`\dl x` requires fewer keystrokes than typing
+\verb`\mathrm{d}x` (or even \verb`\mathrm dx`), but there are other,
+more substantive, reasons why one might prefer an explicit command.
+\begin{enumerate}
+\item \emph{Consistency} with the derivative.
+\item \emph{Spacing} is inserted automatically before the differential,
+and between differentials in (e.g.) multiple integrals.
+\item \emph{Parsing integrals} for some other package or program is much
+easier to do when looking for a concluding differential command \verb`\dl`
+than when looking for \verb`d` or \verb`\mathrm{d}` or \verb`\mathnormal{d}`
+(or whatever) followed by an arbitrary variable name.
+\item \emph{Configurability}. There are values other than the defaults that
+can be given to keys to give novel effects for variant forms of differential
+-- see the examples \verb`\dl.b.`, \verb`\dl.+.` and \verb`\dl.-.`
+above.
+\end{enumerate}
-I have tried to make using \texttt{diffcoeff} intuitive. Looking at
-the other packages mentioned, writing something like \texttt{\textbackslash diff{[}n{]}\{f\}\{x\}}
-(which can be trimmed to \texttt{\textbackslash diff{[}n{]}fx} for
-single-token arguments) seems `natural' -- only \texttt{physymb}
-deviates from the pattern.
-\begin{itemize}
-\item It seems consistent with this pattern to use a comma list for specifying
-the orders of differentiation of the variables in a higher order mixed
-partial derivative (and its suppression when all are of order 1)
-\item Having specified the orders, surely the program itself should calculate
-the overall order? \texttt{esdiff} does this for numerical orders;
-\texttt{diffcoeff} does this for both numeric and algebraic orders,
-\end{itemize}
+\section{Jacobians}
+
+\label{subsec:Jacobians}\verb`diffcoeff` provides a command {\ttfamily\verb`\jacob`}
+for writing jacobians -- not the determinant as such but the symbol
+conventionally used to denote the determinant. For example
\begin{centred}
-\verb`\[ \diffp[m-(k+1),m+(k-1)]{F(x,y,z)}{x,y,z} \]`
+\verb`\[ \jacob{u,v,w}{x,y,z} \]` $\Longrightarrow$ \[ \jacob{u,v,w}{x,y,z} \]
\end{centred}
-\begin{example}
-$\Longrightarrow$ \[ \diffp[m-(k+1),m+(k-1)]{F(x,y,z)}{x,y,z} \]
-\end{example}
-
-\begin{itemize}
-\item and where it fails either to calculate at all or to present the result
-in a preferred form, offers the order-override option:
-\end{itemize}
+The comma lists can contain any number of variables, even one or none,
+\[
+\jacob uv,\quad\jacob{}{},
+\]
+nor need the numbers in numerator and denominator be equal. \verb`\jacob`
+does \emph{not} check such things. It is perfectly possible to form
+unbalanced objects like
\begin{centred}
-\verb`\[ \diffp[m+(k+1),m+(k-1)][2(m+k+1)]{F(x,y,z,w)}{x,y,z,w} \]`
+\verb`\[ \jacob{u,v,w}{x,y},\quad\jacob{u,v}{x,y,z}. \]` $\Longrightarrow$
+\[ \jacob{u,v,w}{x,y},\quad\jacob{u,v}{x,y,z}. \]
\end{centred}
-\begin{example}
-$\Longrightarrow$ \[ \diffp[m+(k+1),m+(k-1)][2(m+k+1)]{F(x,y,z,w)}{x,y,z,w} \]
-\end{example}
+Perhaps there are contexts where these are meaningful?
-\begin{itemize}
-\item I wished to avoid the unnecessary writing of superscripts, subscripts
-and brace pairs. In the examples just given, no superscript tokens
-\texttt{\textasciicircum} are written by the user despite the higher-order
-differentiation in $x$ and $y$, and only the two inescapable brace
-pairs are required.
-\item The use of a comma list for the second mandatory argument in a partial
-derivative -- the list of variables -- makes differentiations in
-super- or subscripted symbols (as occurs prolifically in tensor calculus)
-easier to both write and read by avoiding unnecessary brace pairs.
-\end{itemize}
+\subsection{Template \texttt{DIFJ}}
+
+\begin{wraptable}{o}{0.45\columnwidth}%
+\centering{}\caption{\texttt{DIFJ} defaults\protect\label{tab:DIFJ-defaults}}
+\begin{center}
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small op-symbol} & {\small\texttt{\textbackslash partial}}\tabularnewline
+{\small outer-Ldelim} & \tabularnewline
+{\small outer-Rdelim} & \tabularnewline
+\bottomrule
+\end{tabular}
+\par\end{center}\end{wraptable}%
+Jacobians are configurable. Like other commands of \verb`diffcoeff`,
+\verb`\jacob` gives access to a template, in this case \verb`DIFJ`,
+which is a child of the fundamental template \verb`DIF` and inherits
+most of its default values with only a few changes as shown in Table~\ref{tab:DIFJ-defaults}.
+Note that the keys \verb`outer-Ldelim` and \verb`outer-Rdelim` are
+both empty and, as with the differential, are \emph{always inserted}
+-- which is why they are empty by default.
+
+The lack of entries in Table~\ref{tab:DIFJ-defaults} is because
+many keys are irrelevant for forming jacobians -- it doesn't matter
+what their default values are. For a list of \emph{relevant} keys
+-- ones that have some effect on the appearance of a jacobian --
+see \xA7\ref{subsec:DIFJ-(jacobian)}.
+
+\subsection{Syntax and variant forms}
+
+The \verb`\jacob` command has only three arguments. The syntax is
+simple:
+\begin{verbatim}
+ \jacob.name. {numer} {denom}
+\end{verbatim}
+The arguments have the following significance:
+\begin{enumerate}
+\item \verb`name` (optional) The dot-delimited name of a variant form of
+jacobian.
+\item \verb`numer` (mandatory) A comma list of variables forming the numerator
+of the jacobian.
+\item \verb`denom` (mandatory) A comma list of variables forming the denominator
+of the jacobian.
+\end{enumerate}
+The default form of jacobian is an upright fraction with \verb`\partial`
+operators and parentheses around the variable lists in both numerator
+and denominator.
+
+If you want a jacobian in, say, slash-fraction form then once again
+the \verb`\difdef` command is used. The file \verb`diffcoeff5.def`
+contains the definition
+\begin{verbatim}
+ \difdef { j } { s } { style = / }
+\end{verbatim}
+To access this style, use the name -- which is at your discretion
+but here I have chosen \verb`s` (\verb`/` also suggests itself)
+-- between dots after the \verb`\jacob` command:
\begin{centred}
-\verb`\[ \diffp{A_i}{ x^j,x^k } \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^j,x^k } \]
+\verb`$ \jacob.s.{u,v,w}{x,y,z} $` $\Longrightarrow$ $ \jacob.s.{u,v,w}{x,y,z}. $
\end{centred}
-\begin{itemize}
-\item Should a point of evaluation or variables held constant be considered
-part of the derivative? Thermodynamic usage was decisive here. The
-partial derivative alone is ambiguous -- the parentheses and subscript
-are essential to understand what is being stated:
-\[
-\diffp ST[V]
-\]
-Hence provision for these extra elements was included in the derivative
-commands.
-\item Given the position of the subscripted symbol in the displayed derivative,
-it's positioning as the \emph{final} argument in the derivative command
-feels inevitable.
-\item Version 1 of \texttt{diffcoeff} used braces for this argument to avoid
-any possible confusion with a following mathematical expression. That
-use of braces is now deprecated in \texttt{xparse}, has been deprecated
-in \texttt{diffcoeff} since version 2, and is no longer compatible
-with version 4. Later versions of \texttt{diffcoeff} use square brackets,
-conforming with familiar \LaTeX{} practice. The only special remembering
-needed is avoidance of a space before the argument -- and if it does
-slip in, it won't cause a \LaTeX{} error. It will be treated as part
-of a following mathematical expression and displayed as such.
-\item The star option also prompted the question: is it needed? After all,
-one can always leave the first mandatory argument empty and append
-the differentiand `by hand'. But once the provision for points of
-evaluation or variables held constant was incorporated into the derivative
-commands, the star option became the simplest way of handling appended
-differentiands since the parentheses for a variable held constant
-must wrap around the differential operator \emph{and} differentiand.
-Once available, it provides a simple way of switching between (and
-comparing) the appearance of differentiand-in-the-numerator and differentiand-appended.
-\item The slash option was added to the derivative commands after seeing
-how widely such forms are used in texts at all levels. The placement
-of the slash, between the two mandatory arguments, seems more-or-less
-self-evident.
-\item A later option added to \texttt{\textbackslash diff} (and not present
-in version 1) was the dot-delimited name option. Once \texttt{xtemplate}
-was used as the basis of the package this seemed the most straightforward
-way of making available, ready to hand, the wealth of variants that
-\texttt{xtemplate} makes possible. (It's just a pity that the second
-dot is needed, and a single-dot naming scheme can't be used, but \texttt{xparse}
-forces my hand here.)
-\item Having added the dot-delimited name option, the use of a \texttt{def}
-file to store variants or preferred defaults is more-or-less forced,
-otherwise one is faced with making these definitions anew for each
-new document (or locating a previous document and copying from that
-to the new one).
-\item To handle possible differences between display-style and text-style
-(and script-style) derivatives (see \xA7\ref{subsec:Text-and-script-style})
-I considered using \TeX 's \texttt{\textbackslash mathchoice} command.
-This command takes four arguments, corresponding to display-, text-,
-script- and scriptscript-styles and would require forming four derivatives
-each time a derivative is used, `just in case'. In fact fraction-form
-derivatives are used overwhelmingly in display-style expressions,
-the slash form being used for inline use. Given the ease of defining
-a fraction-form variant for text-style use, and the rareness of such
-use, employing variants seemed the way to go. It is the one adopted
-and avoids the computational burden associated with the use of \texttt{\textbackslash mathchoice}.
-\item After version 2 of the package appeared on CTAN, it was pointed out
-to me that there was an issue of consistency between the form of `d'
-used in a derivative (upright or math-italic) and the form used in
-an integral. I had overlooked this matter completely and in version
-3 of the package remedied the omission with the differential command
-\texttt{\textbackslash dl}. A spacing option for \texttt{\textbackslash dl}
-was almost inevitable. From version 4 the partial analogue \texttt{\textbackslash dlp}
-has been added.
-\item Space before the differentiand was requested by a user. Once considered
-it became clear that there are (at least) two ways of thinking of
-a derivative: as $\diff y/x$, a ratio of differentials where $\dl y$
-is a unit and it makes no sense to insert space between the `d'
-and the `y', and as
-\[
-\diff!{F(x)}x
-\]
-where the function $F(x)$ is being operated on by $\diff{}/x$ and
-it is natural to insert space between the `d' and the `F'. With
-that realisation came the need for a simple switch-like package option
-(\verb`spaced`) to turn spacing on or off, and a switch-like argument
-(\verb`!`) to countermand the package option in exceptional cases
-(version 4).
-\end{itemize}
+If you want to change the operator symbol from \verb`\partial` to
+\verb`D`, as I have seen used, then the definition is:
+\begin{verbatim}
+ \difdef { j } { D } { op-symbol = D }
+\end{verbatim}
+(Again the name is at your discretion but \verb`D` seems obvious.)
+I have added this to the preamble of the present document, so that
+\begin{centred}
+\verb`\[ \jacob.D.{u,v,w}{x,y,z} \]` $\Longrightarrow$ \[ \jacob.D.{u,v,w}{x,y,z}.\]
+\end{centred}
+If you want square brackets rather than parentheses around the variable
+lists, then \verb`lvwrap-Ldelim` and \verb`lvwrap-Rdelim` (perhaps
+not intuitively) are the keys to change:
+\begin{verbatim}
+ \difdef { j } { [ }
+ {
+ lvwrap-Ldelim = \onemu\mleft [,
+ lvwrap-Rdelim = \mright ]
+ }
+\end{verbatim}
+the \verb`\onemu` giving, to my eye, better spacing between the \verb`\partial`
+symbols and the left brackets. This definition, too, has been added
+to the preamble so that
+\begin{centred}
+\verb`\[ \jacob.[.{u,v,w}{x,y,z} \]` $\Longrightarrow$ \[ \jacob.[.{u,v,w}{x,y,z}. \]
+\end{centred}
-\section{Version comparison}
+\subsection{Changing defaults}
-\label{sec:Version-comparison}Unlike version 1, version 2 and later
-are built on the the \texttt{xtemplate} package which makes certain
-facilities available which it would be silly not to exploit. Hence
-the coding in the later versions is completely different and there
-are consequences.
+To change the \emph{default} values of the \verb`DIFJ` template leave
+the second argument of the \verb`\difdef` command -- the \verb`variant-name`
+-- empty. For instance, if you want square brackets to be your default
+setting, the \verb`\difdef` command would be
+\begin{verbatim}
+ \difdef { j } {}
+ {
+ lvwrap-Ldelim = \onemu\mleft [,
+ lvwrap-Rdelim = \mright ]
+ }
+\end{verbatim}
+The only difference from the previous definition is the absence of
+the name from the second argument, which is now empty. If this definition
+were added to the preamble or to the \verb`.def` file of your current
+document then writing \verb`\jacob{u,v,w}{x,y,z}` would give the
+same result as obtained above with the variant \verb`\jacob.[.{u,v,w}{x,y,z}`.
+
+\chapter{Reference}
+
+\label{chap:Reference}For convenience I list here the commands of
+\verb`diffcoeff`, the template defaults, and the files and preamble
+definitions associated with this document.
+
+\section{Commands}
+
+\verb`\diff`, \verb`\diffp`, \verb`\difs`, \verb`\difsp`, \verb`\difc`,
+\verb`\difcp` (sometimes summarised as \verb`\difx` and \verb`\difxp`),
+ordinary and partial derivatives of upright-fraction, slash-fraction
+and compact forms respectively, with arguments (all optional unless
+otherwise indicated) and their delimiters:
\begin{enumerate}
-\item From version 2.0
-\begin{enumerate}
-\item The \texttt{\textbackslash diffset} command, formerly used to tweak
-the display of derivatives, has been superseded by the \texttt{\textbackslash diffdef}
-command. \texttt{\textbackslash diffset} now sends a message warning
-of its obsolescence to the terminal and \LaTeX{} log but is otherwise
-functionless. It should not interfere with the compilation of a document
-but any intended fine-tuning of the display by means of the \texttt{\textbackslash diffset}
-command\texttt{ }will not eventuate. The warning message is: \texttt{Obsolete
-command: \textbackslash diffset has been superseded by the \textbackslash diffdef
-command.} \texttt{See the diffcoeff} \texttt{doc\-umentation for
-further information.} The \texttt{\textbackslash diffdef} command
-is discussed in \xA7\ref{subsec:diffdef};
-\item The optional trailing argument used to indicate a point of evaluation
-or variables held constant is now delimited by square brackets, \texttt{{[}}
-and \texttt{{]}}, as other optional arguments are. For compatibility
-with version 1, versions 2 and 3 still accepted braces to delimit
-this argument but from version 4 of \texttt{diffcoeff} only the square-bracket
-delimited argument is accepted. (The use of braces around \emph{optional}
-arguments while once accepted is now deprecated in \texttt{xparse}
-on which \texttt{diffcoeff} depends);
-\item The commands \texttt{\textbackslash Diff}, \texttt{\textbackslash diffd}
-and \texttt{\textbackslash Diffd} used to construct derivatives from
-$D$, $\delta$ and $\Delta$ in version 1, are still available but
-deprecated. A new optional argument in the \texttt{\textbackslash diff}
-command offers these and a host of other possibilities and is now
-the preferred method of forming such variants; see \xA7\ref{subsec:D-delta-Delta}.
+\item \verb`.name.` name of variant form of derivative;
+\item \verb`*` append-differentiand switch;
+\item \verb`*` reverse order of mandatory arguments 6 and 7 when differentiand
+is appended, available only if first star is also present;
+\item \verb`[order(s)]` order of differentiation, or comma list of orders
+of differentiation (for mixed partial derivatives);
+\item \verb`{differentiand}` (mandatory) function being differentiated;
+\item \verb`{variable(s)}` (mandatory) differentiation variable or, for
+mixed partial derivatives, comma list of differentiation variables;
+\item \verb`[pt of eval/const vars]` point of evaluation or, for partial
+derivatives, variables held constant.
\end{enumerate}
-\item Version 3.0
+\begin{description}
+\item [{\texttt{\textbackslash difoverride}}] order-override command with
+one mandatory argument:
+\end{description}
\begin{enumerate}
-\item adds a command, \texttt{\textbackslash dl} (from \emph{d}ifferentia\emph{l})
-to write differentials like $dx$ that occur in integrals and in other
-contexts in a manner consistent with the form used in derivatives.
-After all, if one is using upright `d's in derivatives, similarly
-upright `d's should occur in these other contexts;\footnote{This rather obvious lack in version 2 was pointed out to me by Sergio
-Callegari.}
-\item provides some simple spacing commands that can be useful for tweaking
-standard spacing.
+\item \verb`{total order}` total order of differentiation; may be (and
+generally is) empty.\newpage{}
\end{enumerate}
-\item Version 3.1 enables the differential command to be used before forms
-like \texttt{\textbackslash vec\{x\}} (an overlooked possibility
-causing an error in earlier versions).
-\item Version 3.2
+\begin{description}
+\item [{\texttt{\textbackslash jacob}}] jacobian with arguments and delimiters:
+\end{description}
\begin{enumerate}
-\item allows negative spacing before the differential command \texttt{\textbackslash dl};
-\item fixes a bug in which an ordinary derivative as the differentiand of
-a partial derivative displayed as a partial derivative. It now displays,
-as it should, as an ordinary derivative.
+\item \verb`.name.` (optional) name of variant form of jacobian;
+\item \verb`{numer}` (mandatory) comma list of variables forming the numerator;
+\item \verb`{denom}` (mandatory) comma list of variables forming the denominator.
\end{enumerate}
-\item Version 4.0
-\begin{enumerate}
-\item enables the insertion of a small space before the differentiand, either
-as the default behaviour (package option \verb`spaced`) or at explicit
-request (argument \verb`!` of the \verb`\diff` command); see \xA7\ref{subsec:Spacing-before-derivand}.
-\item prevents the ligature $df$ that marred previous versions; this is
-now rendered $\dl f$.
-\item offers the document command \verb`\dlp` for the \emph{partial} differential;
-see \xA7\ref{subsec:Partial-differential};
-\item no longer accepts \emph{the braced form} of the\emph{ }trailing optional
-argument specifying a point of evaluation or (for partial derivatives)
-variables held constant. This was a relic from version 1 of \texttt{diffcoeff},
-and has been deprecated since version 2.
-\end{enumerate}
-\item Version 4.1
-\begin{enumerate}
-\item changes the code for the \verb`long-var-wrap` setting to avoid a
-problem arising from a change in \verb`xtemplate`;
-\item improves spacing between operator and variable in \emph{denominators}
-of differential coefficients (e.g. prevents ligatures).
-\end{enumerate}
-\end{enumerate}
-
-\section{Commands}
\begin{description}
-\item [{\texttt{\textbackslash diff}}] arguments (all optional unless
-otherwise indicated):
+\item [{\texttt{\textbackslash dl}}] differential with arguments and delimiters:
\begin{enumerate}
-\item .\emph{name}. for the given settings
-\item {*} append-differentiand switch
-\item {[}\emph{order}{]} or {[}\emph{comma-list of orders}{]} of differentiation
-\item {[}\emph{order-override}{]}
-\item ! countermand before-differentiand spacing of the \verb`spaced` package
-option
-\item \{\emph{differentiand}\} (mandatory)
-\item / slash-form switch
-\item \{\emph{comma list of differentiation variables}\} (mandatory)
-\item {[}\emph{point of evaluation/variables held constant}{]}
+\item \verb`.name.` (optional) name of variant form of differential;
+\item \verb`[order(s)]` (optional) order of differential or comma list
+of orders of differentials;
+\item \verb`{variable(s)}` (mandatory) variable or comma list of variables;
+\item \verb`^{exponent}` (optional) exponent that overrides the \verb`order(s)`
+specification, raising each differential to this power.
\end{enumerate}
-\item [{\texttt{\textbackslash diffdef}}] arguments (all mandatory):
+\item [{\texttt{\textbackslash difdef}}] with arguments (all mandatory)
+and delimiters:
\begin{enumerate}
-\item \{\emph{name}\}
-\item \{\emph{key=value comma list}\}
+\item \verb`{id(s)}` comma list of one, some or all of the identifiers
+\verb`f`, \verb`s`, \verb`c`, \verb`fp`, \verb`sp`, \verb`cp`,
+\verb`j`, \verb`l` identifying upright fraction, slash fraction
+and compact ordinary derivatives; upright fraction, slash fraction
+and compact partial derivatives, and jacobians and differentials;
+\item \verb`{name}` name for a variant form of derivative; as well as letters
+may include numbers and other keyboard characters, but not braces,
+\verb`%` or \verb`#`;
+\item \verb`{settings}` comma list of changed \emph{key=value} settings.
\end{enumerate}
-\item [{\texttt{\textbackslash diffp}}] \texttt{= \textbackslash diff.p.}
-\item [{\texttt{\textbackslash dl}}] arguments (all optional):
-\begin{enumerate}
-\item .\emph{name}. (as for \texttt{\textbackslash diff})
-\item \emph{minus sign} (optional, use only if negative spacing before the
-`d' is wanted)
-\item \emph{digit} (insert spacing of this number of mu before the `d')
-\end{enumerate}
-\item [{\texttt{\textbackslash dpl}}] \texttt{= \textbackslash dl.p.}
\item [{\texttt{\textbackslash negmu}}] insert a $-1$ mu space
\item [{\texttt{\textbackslash nilmu}}] insert a $0$ mu space
\item [{\texttt{\textbackslash onemu}}] insert a $1$ mu space
\item [{\texttt{\textbackslash twomu}}] insert a $2$ mu space
\end{description}
-Deprecated (why try remembering the special names when the forms on
-the right are self-explanatory):
-\begin{description}
-\item [{\texttt{\textbackslash Diff}}] preferred form: \texttt{\textbackslash diff.D.}
-\item [{\texttt{\textbackslash diffd}}] preferred form \texttt{\textbackslash diff.delta.}
-\item [{\texttt{\textbackslash Diffd}}] preferred form\texttt{ \textbackslash diff.Delta.}
-\end{description}
+\section{Templates}
+
+The following lists record the default values of the templates used
+by \verb`diffcoeff`. A marginal \verb`>` indicates where a setting
+differs from that in \verb`DIF`, \verb`>>` where a setting differs
+from that in \verb`DIFF`, \verb`DIFS` or \verb`DIFC` as the case
+may be. For the latter templates, only \emph{relevant }keys have been
+listed -- those which affect the appearance of the derivative (or
+jacobian or differential).
+
+\subsection{\texttt{DIF} (primogenitor)}
+\begin{verbatim}
+ style = frac,
+ slash-tok = /,
+ slash-sep = 0 mu,
+ derivand-sep = 3 mu plus 1 mu minus 2 mu,
+ op-symbol = \mathrm{d},
+ op-symbol-alt = \KeyValue{ op-symbol },
+ op-order-nudge = 0 mu,
+ var-sup-nudge = 1 mu,
+ multi-term-sep = 2 mu plus 1 mu minus 1 mu,
+ term-sep-adjust = -1 mu,
+ long-var-wrap = d(v),
+ lvwrap-Ldelim = \mleft (,
+ lvwrap-Rdelim = \mright ),
+ lvwrap-sup-nudge = -2 mu,
+ outer-Ldelim = \left (,
+ outer-Rdelim = \right ),
+ elbowroom = 0 mu,
+ sub-nudge = -5 mu,
+ op-sub-nudge = 0 mu,
+ *derivand-sep = \KeyValue{ derivand-sep },
+ *op-set-left = false,
+ *italic-nudge = 0 mu,
+ *inner-wrap = false,
+ *inner-Ldelim = (,
+ *inner-Rdelim = ),
+ *outer-Ldelim = \big [,
+ *outer-Rdelim = \big ],
+ *sub-nudge = 0 mu
+\end{verbatim}
+
+\subsection{\texttt{DIFF} (upright-fraction derivative)}
+
+\label{subsec:DIFF-(upright-fraction-derivative)}Relevant keys and
+default values for template \verb`DIFF`.
+\begin{verbatim}
+ style = frac,
+ derivand-sep = 3 mu plus 1 mu minus 2 mu,
+ op-symbol = \mathrm{d},
+ op-symbol-alt = \KeyValue { op-symbol },
+ op-order-nudge = 0 mu,
+ var-sup-nudge = 1 mu,
+ multi-term-sep = 2 mu plus 1 mu minus 1 mu,
+ term-sep-adjust = -1 mu,
+ long-var-wrap = d(v),
+ lvwrap-Ldelim = \mleft (,
+ lvwrap-Rdelim = \mright ),
+ lvwrap-sup-nudge = -2 mu,
+ outer-Ldelim = \left (,
+ outer-Rdelim = \right ),
+ elbowroom = 0 mu,
+ sub-nudge = -5 mu,
+ *derivand-sep = \KeyValue { derivand-sep },
+ *op-set-left = false,
+ *italic-nudge = 0 mu
+\end{verbatim}
+
+\subsubsection{\texttt{DIFFP}}
+
+\verb`DIFF` defaults as above with these changes:
+\begin{verbatim}
+>> op-symbol = \partial,
+>> op-order-nudge = 1 mu,
+>> *italic-nudge = 3 mu
+\end{verbatim}
+
+\subsection{\texttt{DIFS} (slash-fraction derivative)}
+
+\label{subsec:DIFS-(slash-fraction-derivative)}Relevant keys and
+default values for template \verb`DIFS`.
+\begin{verbatim}
+> style = /,
+ slash-tok = /,
+ slash-sep = 0 mu,
+> derivand-sep = 2 mu plus 1 mu minus 2 mu,
+ op-symbol = \mathrm{d},
+ op-symbol-alt = \KeyValue { op-symbol },
+ op-order-nudge = 0 mu,
+ var-sup-nudge = 1 mu,
+ multi-term-sep = 2 mu plus 1 mu minus 1 mu,
+ term-sep-adjust = -1 mu,
+ long-var-wrap = d(v),
+ lvwrap-Ldelim = \mleft (,
+ lvwrap-Rdelim = \mright ),
+ lvwrap-sup-nudge = -2 mu,
+> outer-Ldelim = (,
+> outer-Rdelim = ),
+ elbowroom = 0 mu,
+> sub-nudge = 0 mu,
+ *derivand-sep = \KeyValue { derivand-sep },
+> *inner-wrap = true,
+ *inner-Ldelim = (,
+ *inner-Rdelim = ),
+ *outer-Ldelim = \big [,
+ *outer-Rdelim = \big ],
+ *sub-nudge = 0 mu
+\end{verbatim}
+
+\subsubsection{\texttt{DIFSP}}
+
+\verb`DIFS` defaults as above with these changes:
+\begin{verbatim}
+>> op-symbol = \partial,
+>> op-order-nudge = 1 mu
+\end{verbatim}
+
+\subsection{\texttt{DIFC} (compact derivative)}
+
+\label{subsec:DIFC-(compact-derivative)}Relevant keys and default
+values for template \verb`DIFC`.
+\begin{verbatim}
+> style = _ ,
+> derivand-sep = 1 mu plus 1 mu minus 2 mu,
+ op-symbol = \mathrm{d},
+ op-order-nudge = 0 mu,
+> multi-term-sep = 1 mu,
+> term-sep-adjust = 0 mu,
+> outer-Ldelim = \bigl (,
+> outer-Rdelim = \bigr ),
+ elbowroom = 0 mu,
+> sub-nudge = -2 mu,
+ op-sub-nudge = 0 mu,
+ *derivand-sep = \KeyValue { derivand-sep }
+\end{verbatim}
+
+\subsubsection{\texttt{DIFCP}}
+
+\verb`DIFC` defaults as above with these changes:
+\begin{verbatim}
+>> op-symbol = \partial,
+>> op-order-nudge = 1 mu
+\end{verbatim}
+
+\subsection{\texttt{DIFJ} (jacobian)}
+
+\label{subsec:DIFJ-(jacobian)}Relevant keys and default values for
+template \verb`DIFJ`.
+\begin{verbatim}
+ style = frac,
+ slash-tok = /,
+ slash-sep = 0 mu,
+> op-symbol = \partial,
+ op-symbol-alt = \KeyValue{ op-symbol },
+ lvwrap-Ldelim = \mleft (,
+ lvwrap-Rdelim = \mright ),
+> outer-Ldelim = ,
+> outer-Rdelim = ,
+ elbowroom = 0 mu ,
+ *op-set-left = false,
+ *italic-nudge = 0 mu
+\end{verbatim}
+
+\subsection{\texttt{DIFL} (differential)}
+
+\label{subsec:DIFL-(differential)}Relevant keys and default values
+for template \verb`DIFL`.
+\begin{verbatim}
+ op-symbol = \mathrm{d},
+ var-sup-nudge = 1 mu,
+ multi-term-sep = 2 mu plus 1 mu minus 1 mu,
+ term-sep-adjust = -1 mu,
+> long-var-wrap = dv,
+ lvwrap-Ldelim = \mleft (,
+ lvwrap-Rdelim = \mright ),
+ lvwrap-sup-nudge = -2 mu,
+> outer-Ldelim = \, ,
+> outer-Rdelim = ,
+ elbowroom = 0 mu
+\end{verbatim}
+
+\section{The file \texttt{diffcoeff5.def}}
+
+\label{sec:The-file-diffcoeff5.def}
+\begin{verbatim}
+% file `diffcoeff5.def'
+% definitions for variant forms
+% 2023/01/03
+% Andrew Parsloe ajparsloe at gmail.com
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% material derivative
+\difdef { f, s } { D }
+ { op-symbol = \mathrm{D} }
+% math italic
+\difdef { f, s, c } { d' }
+ {
+ op-symbol = d,
+ op-order-nudge = 1 mu
+ }
+\difdef { f, s, c } { D' }
+ {
+ op-symbol = D,
+ op-order-nudge = 1 mu
+ }
+% Greek
+\difdef { f, s } { gd }
+ { op-symbol = \delta }
+\difdef { f, s } { gD }
+ { op-symbol = \Delta }
+% spaceless appending
+\difdef { f, fp } { *0 }
+ {
+ *derivand-sep = 0 mu ,
+ outer-Ldelim = \mleft ( ,
+ outer-Rdelim = \mright )
+ }
+% tfrac, nonscalable
+\difdef { f, fp } { t }
+ {
+ style = tfrac ,
+ derivand-sep = 1 mu plus 1 mu minus 1 mu,
+ multi-term-sep = 0 mu ,
+ term-sep-adjust = 0 mu ,
+ lvwrap-sup-nudge = 0 mu ,
+ outer-Ldelim = \bigl (,
+ outer-Rdelim = \bigr ),
+ elbowroom = -2 mu ,
+ sub-nudge = -3 mu
+ }
+% slash fractions: 0=scalable,
+% 1=big, 2=Big, 3=bigg, 4=Bigg
+% but > 1 gives eyesores
+\difdef { s, sp } { 0 }
+ {
+ style = auto ,
+ outer-Ldelim = \left [ ,
+ outer-Rdelim = \right ] ,
+ sub-nudge = 0 mu ,
+ *inner-Ldelim = \mleft ( ,
+ *inner-Rdelim = \mright ),
+ *outer-Ldelim = \left [ ,
+ *outer-Rdelim = \right ]
+ }
+\difdef { s, sp } { 1 }
+ {
+ style = big ,
+ outer-Ldelim = \bigl (,
+ outer-Rdelim = \bigr ),
+ sub-nudge = -2.5 mu,
+ *inner-Ldelim = \bigl (,
+ *inner-Rdelim = \bigr ),
+ *outer-Ldelim = \bigl [,
+ *outer-Rdelim = \bigr ]
+ }
+% vrule point of evaluation
+\difdef { f, fp, s, sp } { | }
+ {
+ outer-Ldelim = \left . ,
+ outer-Rdelim = \right |,
+ sub-nudge = 0 mu
+ }
+% sq. bracket pt of eval.
+\difdef { f, fp, s, sp } { ] }
+ {
+ outer-Ldelim = \left [ ,
+ outer-Rdelim = \right ],
+ elbowroom = 1 mu,
+ sub-nudge = 0 mu
+ }
+% long var wrap
+\difdef { f, fp } { (dv) }
+ { long-var-wrap = (dv) }
+\difdef { f, fp } { dv }
+ { long-var-wrap = dv }
+% compact, D operator
+\difdef { c } { D }
+ {
+ op-symbol = \mathrm{D},
+ op-sub-nudge = -2mu
+ }
+\difdef { c } { D' }
+ {
+ op-symbol = D,
+ op-sub-nudge = -2mu
+ }
+% bold
+\difdef { c } { bD }
+ {
+ op-symbol = \mathbf{D},
+ op-sub-nudge = -2mu
+ }
+% differential style
+\difdef { c, cp } { dl }
+ { style = dl }
+%%%%%%%%%%% differential %%%%%%%%%%
+% partial
+\difdef { l } { p }
+ { op-symbol = \partial }
+% bold
+\difdef { l } { b }
+ { op-symbol = \mathrm{d}\mathbf }
+
+% line elements: Pythagoras (+)
+\difdef { l } { + }
+ {
+ multi-term-sep = 0 mu +,
+ term-sep-adjust = 0 mu ,
+ outer-Ldelim =
+ }
+% Minkowski (-)
+\difdef { l } { - }
+ {
+ multi-term-sep = 0 mu -,
+ term-sep-adjust = 0 mu ,
+ outer-Ldelim =
+ }
+%%%%%%%%%% jacobian %%%%%%%%%%
+% slash fraction
+\difdef { j } { s }
+ { style = / }
+\end{verbatim}
+
+\section{Preamble definitions}
+
+\label{sec:Preamble-definitions}The preamble to the present document
+contains the command
+\begin{verbatim}
+\usepackage[def-file=diffcoeff5,spaced=-1]{diffcoeff}
+\end{verbatim}
+and definitions:
+\begin{verbatim}
+% nabla in numer, d in denom
+\difdef { f, s } { n }
+ {
+ op-symbol = \nabla,
+ op-symbol-alt = \mathrm{d}
+ }
+% no sub nudge (a sea of white space)
+\difdef { fp } { wsp }
+ { sub-nudge = 0 mu }
+% align op left; no italic nudge
+\difdef { f } { left0 }
+ {
+ *op-set-left = true,
+ *italic-nudge = 0 mu
+ }
+% align op left; italic nudge
+\difdef { fp } { left }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu,
+ *op-set-left = true,
+ *italic-nudge = 3 mu
+ }
+% partial variant of \diff
+\difdef { f } { p }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu
+ }
+% partial, 3mu sep of terms
+\difdef { fp, sp } { 3mu }
+ { multi-term-sep = 3 mu }
+% D jacobian
+\difdef { j } { D }
+ { op-symbol = D }
+% square bracket jabobian
+\difdef { j } { [ }
+ {
+ lvwrap-Ldelim = \onemu\mleft [,
+ lvwrap-Rdelim = \mright ]
+ }
+% mimicking the \Braket command
+% of the braket package
+\difdef{ s }{ bk }
+ {
+ slash-tok = ,
+ op-symbol = ,
+ multi-term-sep = 3mu\middle|\mskip3mu ,
+ outer-Ldelim=\left\langle ,
+ outer-Rdelim=\right\rangle
+ }
+\NewDocumentCommand \Braket { m }
+ {
+ \difoverride {\negmu}
+ \difs.bk.{}{#1}[]
+ }
+\end{verbatim}
+
+\section{\texttt{\textbackslash DeclareChildTemplate}}
+
+\verb`xtemplate` provides only a single function, \verb`\DeclareRestrictedTemplate`,
+for creating a child template from a parent. \emph{All} the keys of
+the child template are present in the parent. The child inherits not
+only the keys of the parent but the default settings of those keys.
+Some of those settings are `marked' so that they cannot be changed
+by any \emph{instance} of the child (the \emph{restricted} keys) .
+
+Unfortunately there is no similar function available in \verb`xtemplate`
+at present by which one can create a child with \emph{new} as well
+as restricted default values. I found I could achieve this functionality
+with the following code cobbled together from publicly declared functions
+in \verb`xtemplate`.
+\begin{verbatim}
+% Child template with both new and restricted defaults
+% #1 object; #2 parent template; #3 child template;
+% #4 restricted, #5 new defaults (both key=value)
+\NewDocumentCommand \DeclareChildTemplate { m m m m m }
+ {
+ \DeclareRestrictedTemplate {#1} {#2} {#3} {}
+ \EditTemplateDefaults {#1} {#3} {#5}
+ \DeclareRestrictedTemplate {#1} {#3} {#3} {#4}
+ }
+\end{verbatim}
+The first \verb`\DeclareRestrictedTemplate` call creates the child
+template \verb`#3` from the parent template \verb`#2`, inheriting
+all its keys and default values. \emph{No} restrictions are imposed
+at this stage because the following \verb`\EditTemplateDefaults`
+would immediately cancel them. That statement specifies the \emph{new}
+defaults \verb`#5` of the child -- those that differ from the parent.
+The default settings \verb`#4` of the parent that are restricted
+to particular values in the child are imposed by the second \verb`\DeclareRestrictedTemplate`
+call through the aritifice of treating the child template \verb`#3`
+as a child of itself. In that way its new defaults are not lost.
\end{document}
Added: trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff4.pdf
===================================================================
(Binary files differ)
Index: trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff4.pdf
===================================================================
--- trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff4.pdf 2023-01-11 20:43:41 UTC (rev 65522)
+++ trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff4.pdf 2023-01-11 20:44:28 UTC (rev 65523)
Property changes on: trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff4.pdf
___________________________________________________________________
Added: svn:mime-type
## -0,0 +1 ##
+application/pdf
\ No newline at end of property
Added: trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff4.tex
===================================================================
--- trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff4.tex (rev 0)
+++ trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff4.tex 2023-01-11 20:44:28 UTC (rev 65523)
@@ -0,0 +1,2272 @@
+%% LyX 2.4.0-alpha3 created this file. For more info, see https://www.lyx.org/.
+%% Do not edit unless you really know what you are doing.
+\documentclass[english]{article}
+\usepackage{lmodern}
+\renewcommand{\sfdefault}{lmss}
+\renewcommand{\ttdefault}{lmtt}
+\usepackage[T1]{fontenc}
+\usepackage{textcomp}
+\usepackage[latin9]{inputenc}
+\synctex=-1
+\usepackage{color}
+\definecolor{shadecolor}{rgb}{1, 0.667969, 0.5}
+\usepackage{babel}
+\usepackage{cprotect}
+\usepackage{wrapfig}
+\usepackage{booktabs}
+\usepackage{calc}
+\usepackage{framed}
+\usepackage{url}
+\usepackage{amsmath}
+\usepackage{amssymb}
+\usepackage{esint}
+\usepackage[unicode=true,pdfusetitle,
+ bookmarks=true,bookmarksnumbered=true,bookmarksopen=true,bookmarksopenlevel=2,
+ breaklinks=true,pdfborder={0 0 1},backref=section,colorlinks=true,pdfpagemode=FullScreen]
+ {hyperref}
+\hypersetup{
+ pdfborderstyle=}
+
+\makeatletter
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% LyX specific LaTeX commands.
+\newcommand{\noun}[1]{\textsc{#1}}
+%% Because html converters don't know tabularnewline
+\providecommand{\tabularnewline}{\\}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
+\newenvironment{centred}%
+ {\begin{center}\baselineskip=13pt\parskip=1pt }{\end{center}}
+\newenvironment{example}%
+{\begin{center}\ttfamily}{\end{center}}
+\newenvironment{lyxcode}
+ {\par\begin{list}{}{
+ \setlength{\rightmargin}{\leftmargin}
+ \setlength{\listparindent}{0pt}% needed for AMS classes
+ \raggedright
+ \setlength{\itemsep}{0pt}
+ \setlength{\parsep}{0pt}
+ \normalfont\ttfamily}%
+ \item[]}
+ {\end{list}}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
+\usepackage[def-file=diffcoeff-doc]{diffcoeff}[=v4]
+
+\makeatother
+
+\begin{document}
+\title{\texttt{diffcoeff}~\\
+ a \LaTeX{} package to ease\texttt{ }the~\\
+ writing of differential coefficients \\
+ Version 4.2}
+\author{Andrew Parsloe\\
+{\small (ajparsloe at gmail.com)}}
+\maketitle
+\begin{abstract}
+\noindent This package eases the consistent writing of ordinary, partial
+and other derivatives of arbitrary (algebraic or numeric) order. For
+mixed partial derivatives, the total order of differentiation is calculated
+by the package. Optional arguments allow for points of evaluation
+(ordinary derivatives), or variables held constant (partial derivatives),
+and the placement of the differentiand in numerator or appended. The
+package uses \texttt{xtemplate}, allowing systematic fine-tuning of
+the display and generation and use of variant forms, including derivatives
+built from $D$, $\Delta$ or $\delta$. A command for differentials
+ensures the $\dl x$ (or $\dl.up.x$) used in integrals is consistent
+with the form used in derivatives.
+\end{abstract}
+\noindent %
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
+
+\subsubsection*{Version 4.2/version 5.0 incompatibility}
+
+Version 4.2 of \verb`diffcoeff` is issued at the same time as version
+5.0. The latter is a complete rewrite of the package with many changes
+to the user interface, arising above all from separating the fraction
+types into separate commands (\verb`\diff`, \verb`\diffp` for upright
+fractions; \verb`\difs`, \verb`\difsp` for slash fractions; and
+\verb`\difc`, \verb`\difcp` for a new, compact style of derivative).
+Although some elements of the earlier version are carried over, most
+documents that use version 4 will fail to compile properly with version
+5. To enable older documents to continue to compile, the \verb`\usepackage`
+statement in the preamble needs a trailing optional argument added
+to it:
+\begin{verbatim}
+ \usepackage[<options>]{diffcoeff}[=v4]
+\end{verbatim}
+The trailing argument \verb`[=v4]` (no spaces!) ensures \verb`diffcoeff4.sty`
+rather than \verb`diffcoeff.sty` is used to compile the document.
+Otherwise, version 4.2 makes no visible change to \verb`diffcoeff`
+version 4.1 other than to documentation. (It also tidies a line of
+code for the differential command \verb`\dl`.)\end{shaded}%
+\end{minipage}
+
+\tableofcontents{}
+
+\section{Introduction}
+
+The \LaTeX{} package \texttt{diffcoeff} is written in the expl3 language
+of \LaTeX 3\texttt{ }and requires the bundles \texttt{l3kernel} which
+is now part of standard \LaTeX{} (since early 2020) and \texttt{l3packages}
+(the latter for the \texttt{xparse}, \texttt{l3keys2e} and especially
+\texttt{xtemplate} packages\texttt{)}. The package is loaded by entering
+\begin{lyxcode}
+\textbackslash usepackage{[}<options>{]}\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+in the preamble of your document, where \verb`<options>` are package
+options input by the user; see below. The trailing optional argument,
+\verb`[=v4]`, is necessary to ensure your document compiles with
+version 4 of \verb`diffcoeff` rather than the new version 5 in which
+there are many changes to the user interface.
+
+\subsubsection*{Note on terminology}
+
+I refer throughout to the quantity or function being differentiated
+as the \emph{differentiand} or \emph{derivand }(in line with \emph{integrand},
+\emph{operand}, etc.).
+
+\subsubsection*{New in version 4.0}
+
+(See \xA7\ref{sec:Version-comparison} for a comparison of versions.)
+Version 4.0
+\begin{enumerate}
+\item enables the insertion of a small space before the differentiand, either
+as the default behaviour (package option \verb`spaced`) or at explicit
+request (argument \verb`!` of the \verb`\diff` command); see \xA7\ref{subsec:Spacing-before-derivand};
+\item prevents the ligature $df$ that marred previous versions; this is
+now rendered $\dl f$;
+\item offers the document command \verb`\dlp` for the \emph{partial} differential;
+see \xA7\ref{subsec:Partial-differential};
+\item no longer accepts \emph{the braced form} of the\emph{ }trailing optional
+argument specifying a point of evaluation or (for partial derivatives)
+variables held constant. This was a relic from version 1 of \texttt{diffcoeff},
+and has been deprecated since version 2.
+\end{enumerate}
+
+\subsubsection*{New in version 4.1}
+\begin{enumerate}
+\item changes the code handling the \verb`long-var-wrap` setting to avoid
+a problem with a change in \verb`xtemplate` (see \url{https://tex.stackexchange.com/questions/646976/error-with-package-diffcoeff})\footnote{Based on a suggestion from \noun{Joseph Wright}.};
+\item prevents (hitherto overlooked) ligatures in the \emph{denominators}
+of differential coefficients.
+\end{enumerate}
+
+\subsubsection*{New in version 4.2}
+\begin{enumerate}
+\item tidies a line of code in the definition of the differential (has no
+visible effect);
+\item amends documentation in light of the issue of version 5 and the resulting
+interface changes.
+\end{enumerate}
+
+\subsection{Package options}
+
+\label{subsec:Package-options}There are three package options, which
+are entered in a comma-separated list in the optional argument of
+the \texttt{\textbackslash usepackage} command.
+\begin{enumerate}
+\item The first is a switch, \texttt{ISO}, which turns on formatting conforming
+to ISO recommendations, principally upright `d's:
+\begin{lyxcode}
+\textbackslash usepackage{[}ISO{]}\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+The full effect of this option is disscussed in \xA7\ref{sec:Changing-defaults}.
+\item The second is another switch, \texttt{spaced}, and \emph{is new with
+version 4 }of \texttt{diffcoeff}. This switch ensures a small space
+is inserted before the differentiand:
+\begin{lyxcode}
+\textbackslash usepackage{[}spaced{]}\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+This is discussed in \xA7\ref{subsec:Spacing-before-derivand}.
+\item The third requires a filename \texttt{<filename>} for a file \texttt{<filename>.def}
+containing definitions of variant forms of derivative:
+\begin{lyxcode}
+\textbackslash usepackage{[}def-file=<filename>{]}\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+This is discussed in \xA7\ref{subsec:The-.def-file}. For the present
+document, the call is
+\begin{lyxcode}
+\textbackslash usepackage{[}def-file=diffcoeff-doc{]}\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+\end{enumerate}
+
+\section{A Rogues' Gallery of derivatives}
+
+\label{sec:Rogues'-gallery}Browsing through texts on statistical
+mechanics, relativity and classical mechanics I find the following
+choice examples of derivatives `disporting every which way'.
+
+Multi-character variables of differentiation un-parenthesized:
+
+\begin{equation}
+\diffp{\frac{\psi}{\Theta}}{\frac{1}{\Theta}},\quad\diffp{E/T}{1/T},\quad\diffp{\ln f}{\ln x_{0}},\quad\diffp\psi{a_{i},\frac{1}{\Theta}},\quad\diffp{\mathcal{L}}{\eta_{,i}^{(r)}}.\label{eq:eg1}
+\end{equation}
+Multi-character variables of differentiation parenthesized:
+\begin{equation}
+\diffp H{\displaystyle \diffp S{q_{k}}[]},\quad\diffp\varepsilon{(1/\Theta)}.\label{eq:eg2}
+\end{equation}
+Higher-order derivatives where the parentheses do not or sometimes
+do include the operator:
+\begin{equation}
+\diffp[2]q{\frac{1}{\Theta}},\quad\diffp[2]q{1/\Theta},\quad\diffp[2]\varepsilon{a_{i}},\quad\diff.wrapall.[2]{\phi^{i}(x^{i})}{x^{i}}.\label{eq:eg3}
+\end{equation}
+Should the $d$ or $\partial$ be included within the parentheses,
+as in the last of (\ref{eq:eg3}), or not, as in the others? Logic
+says `yes'; practice suggests (generally) `no'.
+
+Indicating a point of evaluation is similarly varied:
+\begin{equation}
+\diff.pvrule.\phi\varepsilon[\varepsilon=\varepsilon_{0}],\quad\diff.pvrule.[2]\phi\varepsilon[\varepsilon=\varepsilon_{0}],\quad\diff.psqbra.{b^{\beta}}{a^{\alpha}}[b=0],\quad\diff.paren.uv[v=0].\label{eq:eg4}
+\end{equation}
+ISO 80000-2 (item 2.11.13) favours the last of these -- parentheses
+-- for ordinary derivatives. Presumably, partial derivatives should
+follow suit, although parentheses are also used to indicate variables
+held constant:
+\begin{equation}
+\diffp*{\frac{P}{T}}U[V],\quad\diffp S{N_{2}}[U,V,N_{1}],\quad\diffp S/T[V].\label{eq:eg5}
+\end{equation}
+
+Other symbols besides $d$ and $\partial$ are used to denote derivative-like
+quantities. From introductory calculus and from classical mechanics
+and thermodynamics come $\delta$ and $\Delta$, from fluid mechanics
+comes $D$:
+\begin{equation}
+\diff.delta.yx,\quad\diff.D.\rho t,\quad\diff.pDelta.UT[V],\quad\diff.Delta.U/T,\quad\diff.delta.{\mathcal{L}}{\eta^{(r)}}.\label{eq:eg6}
+\end{equation}
+
+There are those, like the International Organization for Standardization
+(ISO), who stipulate (or prefer) an upright `d' for their derivatives:
+\begin{equation}
+\diff.up.yx.\label{eq:eg11}
+\end{equation}
+When the differentiand is too big or awkward to sit in the numerator
+and is appended to the operator, the $d$ or $\partial$ in the numerator
+is generally centred -- but not always. In texts prior to the age
+of computerised typesetting one will sometimes find the symbol pushed
+to the \emph{left}:
+\begin{equation}
+\diff.pleft.*{\diffp{x^{i^{*}}}{x^{k^{*}}}{}}{x^{l^{*}}},\quad\diff.left.*{\left(\frac{m\mathbf{q}_{x}}{\sqrt{1-q^{2}}}\right)}{t}.\label{eq:eg12}
+\end{equation}
+The observant will note an italic adjustment with the first expression,
+so that the $\partial$ in the numerator and the $\partial$ in the
+denominator line up in a slanting column, but no such adjustment for
+the $d$-s in the second derivative.
+
+Then there is the case when the operator in the numerator differs
+from that in the denominator. For instance, in tensor calculus acceleration
+is sometimes written
+\[
+\diff.nabla.{v^{i}}t=\diff{v^{i}}t+\Gamma_{k\hphantom{i}h}^{\hphantom{k}i}v^{h}\diff{y^{k}}t
+\]
+where $\nabla v^{i}$ is the `absolute differential' of the velocity
+$v^{i}$.
+
+Version 2 or later of the \texttt{diffcoeff} package has the generative
+power to cope with all these variations -- see \xA7\ref{sec:Changing-defaults}
+-- although it is unlikely an author should need to call on this
+capacity to anything like the extent required for this Rogues' Gallery.
+
+Finally and new with version 4 of \texttt{diffcoeff}, is the ability
+to insert space before the differentiand, something that had to be
+done explicitly by the user before. One way of thinking of a derivative
+is as an operator $\diff{}x$ applied to a function $F(x)$ producing
+another function $F'(x)$, a \emph{derived }function, the derivative.
+Although the original function is included in the numerator of the
+differential coefficient, a small space between the $d$ and $F$
+feels natural to separate the thing operated on from the thing operating:
+\[
+F'(x)=\diff!{F(x)}x.
+\]
+\texttt{diffcoeff} can now produce such spaced derivatives, either
+as the default behaviour or at explicit request; see \xA7\ref{subsec:Spacing-before-derivand}.
+
+\section{Ordinary derivatives }
+
+\label{sec:Ordinary-derivatives}Writing\textbf{ }\texttt{\textbackslash diff\{y\}\{x\}}
+will produce $\diff{y}{x}$ in text style (i.e., placed between \texttt{\textbackslash (
+\textbackslash )} or \texttt{\$ \$}) or
+\[
+\diff{y}{x}
+\]
+in display style (i.e., placed between \texttt{\textbackslash{[}
+\textbackslash{]}} ). In fact \texttt{\textbackslash diff yx} (omitting
+the braces) will produce these results, with a saving on keystrokes.
+The braces are needed only when an argument -- the differentiand
+or the variable of differentiation -- is multi-token.
+\begin{itemize}
+\item If you want upright `$\mathrm{d}$'s as default, as ISO 80000-2 recommends,
+rather than the math-italic `$d$'s used here, this can easily be
+done with the package option \texttt{ISO}; see \xA7\ref{sec:Changing-defaults}
+on changing default settings.
+\end{itemize}
+For inclusion in a line of text you might prefer to use a slash-fraction
+form of derivative. That is achieved by inserting a slash, `/', between
+numerator and denominator arguments: \texttt{\textbackslash diff\{\textbackslash ln
+x\}/x} produces $\diff{\ln x}/x$. Braces are required for the numerator
+in this case since it contains more than one token.
+
+\subsection{Spacing before the differentiand}
+
+\label{subsec:Spacing-before-derivand}There are (at least) two different
+ways in which we think of derivatives.\footnote{I thank \noun{Hans Sch\xFClein} for first raising this issue with me
+and for subsequent thoughtful comments. } We are all familiar with the argument presented in elementary calculus
+books where a curve is shown, and a point on the curve through which
+a chord has been drawn. The chord is a side -- the hypotenuse --
+of a small right-angled triangle, the other sides having lengths $\delta x$
+and $\delta y$ and being parallel to the coordinate axes. The slope
+of the chord is $\diffd yx$. By drawing smaller and smaller chords
+through the point, the ratio $\diffd yx$ approaches the slope of
+the tangent to the curve at the point. We write
+\[
+\diff yx
+\]
+for the limit of $\diffd yx$. It is natural to think of $\dl y$
+and $\dl x$ as tiny lengths, like $\delta y$ and $\delta x$, in
+which case it would be quite wrong to insert space between the $d$
+and the $y$ (let alone the $d$ and the $x$). $dy$ is a single
+object, called a differential, and we write expressions like
+\begin{centred}
+\verb`\[ dy=\diff yx dx \]` $\Longrightarrow$
+\[
+\dl y=\diff yx\dl x
+\]
+\end{centred}
+and justly call the `fraction' in this expression a differential
+coefficient.
+
+But there is another way of viewing differentiation: as a process
+producing (or \emph{deriving}) one function, $f'(x)$, from another,
+$f(x)$. Here the sense is of applying $\diff{}x$ to $f(x)$. Although
+we include $f(x)$ in the numerator it is not attached to the $d$
+and should be separated from it by a small space:
+\begin{centred}
+\verb`\[ f'(x)=\diff!{f(x)}x \]` $\Longrightarrow$
+\[
+f'(x)=\diff!{f(x)}x.
+\]
+\end{centred}
+Here the fraction on the right is another name for the derived function
+$f'$ and is justly called the derivative of $f$. As you can see
+a small space has been inserted between the $d$ and the $f$ in the
+numerator. By default the space is \texttt{3 mu} but with the ability
+to stretch by \texttt{1 mu} or shrink by\texttt{ 2 mu}{\ttfamily\footnote{In \TeX -speak, \texttt{3mu plus 1mu minus 2mu}. }}
+as \TeX{} adjusts lines to fit on the page. (A `mu' is a `math unit'
+and is one eighteenth of a quad.) To achieve this result I have inserted
+an exclamation mark \verb`!` before the braces delimiting the differentiand.
+\begin{itemize}
+\item You may want all or most of your derivatives to have this space and
+therefore will not want to be inserting exclamation marks in every
+\texttt{\textbackslash diff} command. The \texttt{spaced} package
+option switches the default behaviour to spaced derivatives (in which
+case the \texttt{!} switch now creates an \emph{un-spaced} derivative).
+The size of the space inserted by default can be easily changed; see
+\xA7\ref{sec:Changing-defaults}.
+\end{itemize}
+The present document uses the un-spaced default. For backwards compatibility
+(and perhaps because the author has done this for the last 60 years),
+this is the \textquoteleft out-of-the-box\textquoteright{} default
+that \texttt{diffcoeff} uses. Authors should make a habit of using
+one form predominantly. (There is also the possibility which I haven't
+emphasized of spacing multi-token differentiands and leaving single-token
+differentiands unspaced; see \xA7\ref{subsec:A-final-flourish}.)
+
+Slash-form derivatives also allow space before the differentiand.
+By default this has the same value as applied to the fraction form
+of derivative (but can be changed; see \xA7\ref{sec:Changing-defaults}):
+\begin{centred}
+\verb`$ \diff!{\ln\sin x}/x $` $\Longrightarrow$ $ \diff!{\ln\sin x}/x$.
+\end{centred}
+The \verb`\diff` command has other optional arguments (e.g. to specify
+the order of differentiation) but always the exclamation mark, if
+used, immediately precedes the differentiand. It is the positioning
+of the differentiand that it affects after all and its placement immediately
+before that argument seems natural.
+
+\subsubsection{Ligatures: }
+
+Prior to v.4 of \texttt{diffcoeff}, \texttt{\textbackslash diff fx}
+produced the tight pairing evident in
+\[
+\frac{df}{dx}.
+\]
+This was a bug. From version 4.0 of \texttt{diffcoeff}, such ligatures
+are prevented: \verb`\[ \diff fx \]` $\Longrightarrow$ \[ \diff fx.\]
+
+\subsubsection{Spacing commands}
+
+\label{subsec:Spacing-commands}The \texttt{diffcoeff} package also
+offers four simple spacing commands to fine-tune the display of derivatives
+and of other quantities. These are
+\begin{description}
+\item [{\texttt{\textbackslash negmu}}] insert spacing of $-1$ mu
+\item [{\texttt{\textbackslash nilmu}}] insert spacing of $0$ mu (cf.
+use of an empty brace pair \texttt{\textbf{\{\}}} )
+\item [{\texttt{\textbackslash onemu}}] insert spacing of $1$ mu
+\item [{\texttt{\textbackslash twomu}}] insert spacing of $2$ mu
+\end{description}
+
+\subsection{Appending the differentiand: \texttt{\textbackslash diff{*}}}
+
+Some differentiands are too big or awkward to be placed neatly in
+the numerator of a derivative and it is natural to append them to
+a preceding differential operator. One way to do this is to leave
+the numerator argument empty in the \texttt{\textbackslash diff}
+command and follow the command with the differentiand. A better way
+is to star the \texttt{\textbackslash diff} command. This tells \texttt{diffcoeff}
+to append the differentiand. Thus suppose the differentiand is a polynomial,
+say $ax^{2}+bx+c$. Add a star (an asterisk) to the \texttt{\textbackslash diff}
+command:
+\begin{centred}
+\verb`\[ \diff*{(ax^2+bx+c)}x \]` $\Longrightarrow$ \[\diff*{(ax^{2}+bx+c)}x\]
+\end{centred}
+With the \texttt{!} switch or \texttt{spaced} package option, additional
+space (by default \texttt{3mu plus 1mu minus 2mu}) is inserted between
+the operator and the differentiand:
+\begin{centred}
+\verb`\[ \diff*!{(ax^2+bx+c)}x \]` $\Longrightarrow$ \[\diff*!{(ax^{2}+bx+c)}x.\]
+\end{centred}
+A virtue of using an asterisk to append the differentiand is that
+if one isn't sure whether a differentiand should be appended or not,
+it is an easy matter to simply insert or delete the asterisk to compare
+the results. For example, a second derivative is an iterated derivative
+-- one in which a derivative forms the differentiand of another derivative:
+\begin{centred}
+\verb`\[ \diff[2]yx = \diff*{\diff yx}x \]` $\Longrightarrow$ \[ \diff[2]yx=\diff*{\diff yx}x \]
+\end{centred}
+\noindent which is more elegant to my eye than
+\begin{centred}
+\noindent \verb`\[ \diff[2]yx = \diff!{\diff yx}x \]` $\Longrightarrow$
+\[ \diff[2]yx=\diff!{\diff yx}x \]
+\end{centred}
+\noindent although whether the \emph{meaning} is clearer is moot.\emph{
+}It is easy to switch between the two forms on the right, simply by
+inserting or removing the asterisk.
+
+In slash style with the star option, the polynomial example becomes
+\begin{centred}
+\verb`\[ \diff*{(ax^2+bx+c)}/x \]` $\Longrightarrow$ \[ \diff*{(ax^2+bx+c)}/x \]
+\end{centred}
+\noindent where the parentheses around the differential operator are
+automatically inserted by \texttt{diffcoeff}. Like other elements
+of automatic formatting, this is user-adjustable; see \xA7\ref{sec:Changing-defaults}.
+
+With the \texttt{!} switch or \texttt{spaced} package option, this
+becomes
+\begin{centred}
+\verb`\[ \diff*!{(ax^2+bx+c)}/x \]` $\Longrightarrow$ \[ \diff*!{(ax^2+bx+c)}/x \]
+\end{centred}
+
+\subsection{Point of evaluation}
+
+\label{subsec:Point-of-evaluation}If you want to specify a point
+at which the derivative is evaluated, append a final optional argument.
+Note that there \emph{must be no space} before the left square bracket
+of the argument:\footnote{In v.1 of \texttt{diffcoeff}, this was brace-delimited. From v.2,
+square-brackets have been used and braces deprecated. From v.4, braces
+are no longer accepted.}
+\begin{centred}
+\verb`\[ \diff[2]yx[0] \]` $\Longrightarrow\quad{\displaystyle \diff[2]yx[0]}$
+\end{centred}
+\noindent If a space does slip in before the final optional argument,
+it will not cause a \LaTeX{} error. Instead, the argument will be treated
+as a square-bracketed mathematical expression following the derivative,
+and typeset as such.
+\begin{itemize}
+\item If you prefer to use subscripted \emph{parentheses} around the derivative
+to indicate a point of evaluation -- as ISO 80000-2 recommends --
+then this can easily be done; see \xA7\ref{sec:Changing-defaults} on
+changing default settings. Or, more simply, use the \texttt{ISO} package
+option.
+\end{itemize}
+Because the slash form spreads the derivative out horizontally, parentheses
+are preferred here to indicate a point of evaluation:
+\begin{centred}
+\verb`$ \diff{\ln sin x}/{sin x}[x=\pi/6] $` $\Longrightarrow$ $ \diff{\ln\sin x}/{\sin x}[x=\pi/6] $.
+\end{centred}
+\noindent A vertical rule (or `pipe') can easily become too remote
+from the opening $d$ of the differential coefficient: $\diff.svrule.{\ln\sin x}/{\sin x}[x=\pi/6]$;
+parentheses tie the whole cluster of symbols together.
+
+\subsubsection{Superscripts}
+
+It is easy to add a superscript to a derivative to indicate evaluation
+at two points and the difference between the values:
+\begin{centred}
+\verb`\[ \diff {\sin x}x[0]^{\pi/2} \]` ${\displaystyle \Longrightarrow}$
+\[ \diff{\sin x}x[0]^{\pi/2} \]
+\end{centred}
+\noindent If you want only the superscript, no subscript, include
+the final optional argument but leave it empty. Thus, for a particle
+of mass $m$ moving along a line, distance $x$ at time $t$, the
+kinetic energy is:
+\begin{centred}
+\noindent \verb`$ \tfrac 12 m \diff x/t[]^2 $` $\Longrightarrow$
+$\tfrac{1}{2}m\diff x/t[]^{2}$.
+\end{centred}
+
+\subsection{Order of differentiation}
+
+An optional first argument allows the order of differentiation to
+be specified. The order need not be a number; an algebraic order of
+differentiation is perfectly acceptable as is a mix of the two:
+\begin{centred}
+\verb`\[ \diff[2]yx \]` $\Longrightarrow$ \[ \diff[2]yx,\]\verb`\[ \diff[n+1]yx \]`
+$\Longrightarrow$ \[ \diff[n+1]yx.\]
+\end{centred}
+As mentioned, the braces can be and have been omitted around the $x$
+and $y$; the square brackets around the optional argument, the order
+of differentiation, are essential. For a first-order derivative, no
+optional argument is needed and entering \texttt{1} as the optional
+argument has no effect:
+\begin{centred}
+\verb`$ \diff[1]yx $` $\Longrightarrow$$\diff[1]yx$.
+\end{centred}
+In slash style, \texttt{\$\textbackslash diff{[}2{]}y/x\$} produces
+$\diff[2]y/x$, and \texttt{\$\textbackslash diff{[}n+1{]}y/x\$}
+produces $\diff[n+1]y/x$.
+
+\subsection{Multi-character variables of differentiation}
+
+Differentiating a function of a function may involve a multi-character
+differentiation variable. For instance, to differentiate $\ln\sin x$
+in $x$ means forming the product
+\begin{centred}
+\verb`\[ \diff!{\ln\sin x}{\sin x}\diff{\sin x}x \]` $\Longrightarrow$
+\[\diff!{\ln\sin x}{\sin x}\diff{\sin x}x.\]
+\end{centred}
+\noindent (Although I am mainly using un-spaced differentiands in
+this document, a space before the differentiand in the first of these
+derivatives -- the \verb`!` switch -- improves the appearance of
+the expression to my eye.)
+
+Forming the \emph{second} derivative of $\ln\sin x$ will now involve
+forming (among other quantities)
+\begin{centred}
+\noindent \verb`\[\diff[2]{\ln\sin x}{\sin x}\]` $\Longrightarrow$
+\[\diff[2]{\ln\sin x}{\sin x}\]
+\end{centred}
+\noindent Parentheses have been inserted automatically by \texttt{diffcoeff}
+around $\sin x$ in the denominator to avoid any visual hint that
+we are differentiating in the sine of $x^{2}$.
+
+The question is: are the parentheses in the right place? Logically,
+no. They should include the $d$: $(d\sin x)^{2}$ -- it is the differential
+$d\sin x$ that is of the second order. But as the examples in the
+Rogues' Gallery show -- see particularly (\ref{eq:eg3}) -- the
+inclination seems to be to do otherwise. This may be because one wants,
+in any case, to parenthesise the variable. A second, outer pair of
+parentheses then seems too fussy and detracts from comprehending the
+symbol `at a glance':
+\[
+\diff.wrapall.[2]{f(x)}{(1/x)}.
+\]
+
+Customary but illogical notations are familiar in mathematics --
+think of the position of the superscripts in an identity like $\sin^{2}\theta+\cos^{2}\theta=1$.
+But, like other features of the derivative, the manner of this wrapping
+in parentheses of long variables for \emph{higher order} derivatives
+is customisable; see \xA7\ref{sec:Changing-defaults}.
+
+For first order derivatives, parenthesising does not occur. If you
+want the variable of differentiation to be parenthesised, you need
+to insert them yourself:
+\begin{centred}
+\verb`\[\diff {f(x)}{1/x}, \quad \diff {f(x)}{(1/x)}.\]` $\Longrightarrow$
+\[ \diff {f(x)}{1/x}, \quad\diff {f(x)}{(1/x)}.\]
+\end{centred}
+
+\section{Partial derivatives}
+
+\noindent \label{sec:Partial-derivatives}Partial derivatives follow
+the same pattern as ordinary derivatives, with some extensions. The
+command this time is \texttt{\textbackslash diffp}. Thus \texttt{\textbackslash diffp\{F\}\{x\}},
+or, with a saving on keystrokes,\texttt{ \textbackslash diffp Fx},
+produces $\diffp Fx$ in text style and
+\[
+\diffp{F}{x}
+\]
+in display style. (As for \texttt{\textbackslash diff}, the omission
+of braces is possible when the differentiand or the differentiation
+variable are single tokens.) As for \texttt{\textbackslash diff},
+there is a slash form, generally preferred for inline use, \texttt{\textbackslash diffp
+F/x}, displaying as $\diffp F/x$. Given that \texttt{\textbackslash partial}
+takes 8 keystrokes to type, the slash form \emph{does }economise on
+keystrokes for a partial derivative.
+
+With either the \verb`spaced` package option (see \xA7\ref{subsec:Package-options})
+or the \verb`!` switch a space, defaulting to \verb`3 mu` with some
+stretch and shrink, can be inserted before the differentiand: \verb`\[ \diffp!{F(x,y)}x \]`
+$\Longrightarrow$ \[ \diffp!{F(x,y)}x. \]
+
+\noindent (But note that if the \verb`spaced` package option is used,
+the \verb`!` switch \emph{removes} any extra space.)
+
+Again an optional argument allows the specification of the order of
+differentiation which may be numeric or algebraic or a mix of the
+two:
+\begin{centred}
+\verb`\[ \diffp[3]F/x , \quad \diffp[n]F/x \]` $\Longrightarrow$
+\[\diffp[3]F/x , \quad \diffp[n]F/x\] \verb`\[ \diffp[n+1]Fx. \]`
+$\Longrightarrow$ \[ \diffp[n+1]Fx. \]
+\end{centred}
+
+\subsection{Variables held constant}
+
+In a subject like thermodynamics, there is a need to indicate which
+variables are held constant when the differentiation occurs. To show
+this, append a final square-bracketed optional argument and ensure
+that it follows \emph{immediately} on the preceding mandatory argument.
+A space here will detach the argument from the derivative and result
+in it being treated as a mathematical expression following the derivative.
+Thus to differentiate the entropy $S$ in temperature $T$ while holding
+the volume $V$ constant, write
+\begin{centred}
+\verb`\[ \diffp ST[V] \]` $\Longrightarrow$ \[ \diffp ST[V]. \]
+\end{centred}
+\noindent In slash form the same expression looks like
+\begin{centred}
+\noindent \verb`$ \diffp S/T[V] $` $\Longrightarrow$ $ \diffp S/T[V] $.
+\end{centred}
+This use of a parenthesised, subscripted form to indicate a variable
+or variables held constant, leaves open the question: how do we represent
+a point of evaluation? ISO 80000-2 makes no recommendation for \emph{partial}
+derivatives; presumably we follow the same practice as their recommendation
+for ordinary derivatives:
+\begin{example}
+\verb`\[ \diffp {F(x,y)}x[(0,0)] \]` $\Longrightarrow$ \[ \diffp {F(x,y)}x[(0,0)] \]
+\end{example}
+
+However, you may prefer (as many do) to use a vertical rule for this
+purpose:
+\[
+\diff.pvrule.{F(x,y)}x[(0,0)]
+\]
+Making this possibility available is discussed in \xA7\ref{sec:Changing-defaults}.
+
+An empty final argument produces a parenthesised derivative with no
+subscript,
+\begin{centred}
+\verb`\[ \diffp yx[] \]` ${\displaystyle \Longrightarrow}$ \[ \diffp yx[] \]
+\end{centred}
+\noindent which can be useful sometimes. An instance is the writing
+of Lagrange's equations of motion in analytic mechanics:
+\begin{centred}
+\noindent \verb`\[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0 \]`
+$\Longrightarrow$ \[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0. \]
+\end{centred}
+
+\subsubsection{Text-style derivatives}
+
+The \texttt{diffcoeff} package assumes that derivatives formed as
+`numerator over denominator' will be used in display-style expressions,
+and that the slash form will be used for inline use (text style).
+This is the familiar practice in the literature. If one \emph{does}
+use the first form in an inline expression where a variable is held
+constant, say \texttt{\textbackslash diffp ST{[}V{]}} as here $\diffp ST[V]$,
+the result is unsatisfactory, the subscript too tight on the closing
+parenthesis and too much space between parentheses and derivative.
+The matter is easily resolved using `variant forms' -- see \xA7\ref{subsec:Text-and-script-style}
+below -- giving, for our example, $\diff.ptxt.ST[V]$.
+
+\subsection{Appending the differentiand}
+
+\label{subsec:Partial-appending}For a long or awkward differentiand,
+it is generally better to \emph{append} it to a preceding differential
+operator, rather than create a fractional form with the long expression
+in the numerator. As with ordinary derivatives, this is achieved by
+adding an asterisk to (i.e. by starring) the \texttt{\textbackslash diffp}
+command.
+\begin{centred}
+\verb`\[ \diffp*[2]{\Phi(x,y,z)}x \]` $\Longrightarrow$ \[ \diffp*[2]{\Phi(x,y,z)}x. \]
+\end{centred}
+With the \verb`spaced` package option, or with the \verb`!` switch
+if the package option is not used (which is the case for this document),
+one gets
+\begin{centred}
+\verb`\[ \diffp*[2]!{\Phi(x,y,z)}x \]` $\Longrightarrow$ \[ \diffp*[2]!{\Phi(x,y,z)}x \]
+\end{centred}
+which is an improvement (to my eye).
+
+Alternatively you could leave the first mandatory argument empty and
+manually append the differentiand, but by deleting or inserting an
+asterisk, it is easy to compare the two forms, differentiand-in-the-numerator,
+differentiand-appended, and see which is preferable.
+
+In slash form, parentheses are automatically inserted around the differential
+operator when the differentiand is appended,
+\begin{centred}
+\verb`\[ \diffp*[n]{f(x)}/x \]` $\Longrightarrow$ \[ \diffp*[n]{f(x)}/x, \]
+\end{centred}
+\noindent although this behaviour can be changed (\xA7\ref{sec:Changing-defaults}
+again).
+
+If you wish to both append the differentiand \emph{and} indicate variables
+held constant, then the starred form is much the easier way to achieve
+this. Thus, to express a relation in thermodynamics,
+\begin{centred}
+\verb`\[ \diffp*{\frac PT}U[V] = \diffp*{\frac 1T}V[U] \]` $\Longrightarrow$
+\[ \diffp*{\frac PT}U[V] = \diffp*{\frac 1T}V[U], \]
+\end{centred}
+\noindent where the starring automatically takes care of the parentheses
+and subscripts.
+
+\subsection{Iterated derivatives}
+
+Derivatives can be the differentiands of derivatives, as seen above
+when writing Lagrange's equations,
+\begin{centred}
+\noindent \verb`\[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0 \]`
+$\Longrightarrow$ \[ \diffp L{q_k}-\diff*{\diffp L{\dot{q}_k}[]}t = 0. \]
+\end{centred}
+\noindent However, in versions of \texttt{diffcoeff} before version
+3.2, an ordinary derivative within a partial derivative rendered as
+a partial derivative. That is now corrected, the ordinary derivative
+rendering correctly:
+\begin{centred}
+\verb`\[ \diffp*{\diff{x^\mu}{\lambda}}{x^\sigma} \]` $\Longrightarrow$
+\[ \diffp*{\diff{x^\mu}{\lambda}}{x^\sigma}. \]
+\end{centred}
+
+\subsection{Mixed partial derivatives}
+
+The new thing with partial derivatives, not present with ordinary
+derivatives, is \emph{mixed} partial derivatives, where there is more
+than one variable of differentiation. If each variable is differentiated
+only to the first order, then it is easy to specify the derivative.
+Suppose $F$ is a function of three variables, $x$, $y$ and $z$.
+Then
+\begin{centred}
+\verb`\[ \diffp F{x,y,z} \]` $\Longrightarrow$ \[ \diffp F{x,y,z}, \]
+
+\verb`\[ \diffp !{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$ \[ \diffp !{F(x,y,z)}{x,y,z}. \]
+\end{centred}
+In the second of these I have inserted space before the differentiand
+by using the \verb`!` switch. If the \verb`spaced` package option
+was being used, this would have been done automatically.
+
+The variables of differentiation are listed in order in a comma list
+forming the second mandatory argument. The total order of differentiation
+(3 in this example) is inserted automatically -- \texttt{diffcoeff}
+does the calculation. There is also a slash form:
+\begin{centred}
+\verb`$ \diffp F/{x,y,z} $` $\Longrightarrow$ $ \diffp F/{x,y,z}$.
+\end{centred}
+If we want to differentiate variables to higher order, then their
+orders need to be specified explicitly. To do so use a comma list
+for the optional argument:
+\begin{centred}
+\verb`\[ \diffp[2,3]F{x,y,z} \]` $\Longrightarrow$ \[ \diffp[2,3]F{x,y,z}. \]
+\end{centred}
+\noindent Notice that the overall order of the derivative -- 6 --
+is again automatically calculated and inserted as a superscript on
+the $\partial$ symbol in the numerator. In this example, the comma
+list of orders has only two members, even though there are three variables.
+It is assumed that the orders given in the comma list apply in sequence
+to the variables, the first order to the first variable, the second
+to the second variable, and so on, and that any subsequent orders
+not listed in the optional argument are, by default, 1. Thus we need
+to specify only 2 and 3 in the example; the order of differentiation
+of $z$ is 1 by default. But you \emph{cannot} use an order specification
+like \texttt{{[} , ,2{]}}. Instead write \texttt{{[}1,1,2{]}}.\textbf{
+}It is only the \emph{tail} of an order specification which can be
+omitted.
+
+\subsubsection{Minutiae of spacing (again)}
+
+\label{subsec:Minutiae-of-spacing}In Chapter 18 of the \emph{The\TeX book},
+Knuth suggests inserting a thin space, {\ttfamily\verb`\,`}
+(or {\ttfamily\verb`3 mu`}), between differentials in appropriate
+contexts, giving as an example $dx\,dy=r\,dr\,d\theta$. In the denominator
+of a derivative, however, that degree of extra spacing seems too great
+(to my eye), interfering with seeing the derivative `as a whole',
+\[
+\diff.pwide.F{x,y,z},
+\]
+especially for the slash-form of derivative: $\diff.pwide.F/{x,y,z}$.
+Some spacing is desirable, but less; by default \texttt{diffcoeff}
+inserts \verb`2 mu` between the differentials in the fraction form
+of derivative and \verb`1 mu`\texttt{ }in the slash form.
+
+Should a differentiation occur to higher order and so a variable acquire
+a superscript, an adjustment is made to the extra spacing. By default
+\verb`1 mu` is subtracted from the default spacing. Thus in
+\[
+\diffp[2]F{x,y,z},
+\]
+\verb`2 mu` of spacing is inserted between the $\partial y$ and
+$\partial z$, but because the superscript already provides some separation
+between them, only \verb`1 mu` is inserted between $\partial x^{2}$
+and $\partial y$.
+
+The values used for the spacing and its adjustment in the presence
+of a superscript can be changed by the user; see \xA7\ref{sec:Changing-defaults}.
+Some other minutiae of spacing are discussed below in \xA7\ref{subsec:Comma-list-of-vars}
+when the variables themselves are super- or subscripted (as happens
+in tensor calculus, for instance).
+
+Note that the \verb`!` switch, if used, is inserted \emph{immediately
+before} the differentiand. It is the placement of the differentiand,
+after all, that it is affecting:
+\begin{centred}
+\verb`\[ \diffp[2]!F{x,y,z} \]` $\Longrightarrow$ \[ \diffp[2]!F{x,y,z}. \]
+\end{centred}
+
+\subsubsection{Algebraic orders of differentiation}
+
+Calculation of the overall order of differentiation still occurs even
+when some or all of the individual orders are algebraic variables
+rather than numbers. For example, differentiating in three variables
+to orders \texttt{1, m+1, m-1},
+\begin{centred}
+\verb`\[ \diffp[1,m+1,m-1]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[1,m+1,m-1]{F(x,y,z)}{x,y,z}. \]
+\end{centred}
+
+\subsubsection{Error messages}
+
+Should you specify \emph{more} orders in the comma list of the order
+specification than there are variables, compilation will fail and
+an error message will be sent to the terminal and \LaTeX{} log . For
+example, if on (say) line 53 of my document I specify \texttt{{[}1,m-1,m+1,2{]}}
+for the orders of differentiation but list only \texttt{\{x,y,z\}}
+for the variables, the message will be
+\begin{lyxcode}
+!~Package~diffcoeff~Error:~4~orders~of~differentiation~
+
+specified~for~3~variables;~orders~{[}1,m+1,m-1,2{]}
+
+(on~line~53)~for~variables~x,y,z.
+\end{lyxcode}
+Should you try using a \emph{number} raised to a power in an order
+specification, it will cause an error. For example, if on line 53
+(say) of my document I try to form \texttt{\textbackslash diffp{[}2\textasciicircum 2{]}f\{x,y,z\}}
+compilation will fail with the message
+\begin{lyxcode}
+!~Package~diffcoeff~Error:~number~followed~by~\textasciicircum ~in~the~
+
+order~specification~{[}2\textasciicircum n,1,1{]}~on~line~53.~Diffcoeff~
+
+cannot~calculate~the~overall~order~of~differentiation~
+
+in~this~case.~Use~the~order-override~option~to~enter~
+
+the~overall~order.
+\end{lyxcode}
+The order-overide option mentioned here is discussed next. Similarly,
+you cannot use multiplication (\texttt{\textbackslash times} or \texttt{{*}})\texttt{
+}or division (\texttt{/} or \texttt{\textbackslash div}) signs after
+\emph{numbers} in an order specification; only \texttt{+} or \texttt{-}
+or a left parenthesis (see below) are allowed.
+
+\subsubsection{The order-override option}
+
+\noindent Perhaps the differentiations are to orders \texttt{{[}2km,m-1,m+1{]}}:
+\begin{centred}
+\noindent \verb`\[ \diffp[2km,m-1,m+1]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[2km,m-1,m+1]{F(x,y,z)}{x,y,z}. \]
+\end{centred}
+\noindent Here the overall order is presented as \texttt{2km+2m}.
+You might prefer this to be presented as \texttt{2m(k+1)}. Although
+\texttt{diffcoeff} takes some steps to present the overall order appropriately,
+it is not a computer algebra system and does not factorise expressions.
+If you want to present the order in a manner distinct from that presented
+by \texttt{diffcoeff}, use the \emph{order-override option}.
+
+This is a second optional argument immediately following the order
+specification. For our last example, filling the override option with
+\texttt{2m(k+1)} gives the desired result:
+\begin{centred}
+\verb`\[ \diffp[2km,m-1,m+1][2m(k+1)]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[2km,m-1,m+1][2m(k+1)]{F(x,y,z)}{x,y,z}. \]
+\end{centred}
+\noindent As another example, left to its own devices, \texttt{diffcoeff}
+produces
+\begin{centred}
+\noindent \verb`\[ \diffp[m/2+n/2,m/2,n/2]F{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[m/2+n/2,m/2,n/2]F{x,y,z}, \]
+\end{centred}
+\noindent whereas we would like the total order to be presented as
+$m+n$. Using the override option,
+\begin{centred}
+\noindent \verb`\[ \diffp[m/2+n/2,m/2,n/2][m+n]F{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[m/2+n/2,m/2,n/2][m+n]F{x,y,z}. \]
+\end{centred}
+The order-override option does exactly that: overrides the presentation
+of the calculated order with the manually given one. In fact the calculation
+algorithm does not get called at all when the override option is used
+so that one can in this way present the total order in whatever manner
+one wishes or, indeed, add essentially arbitrary material as a superscript
+to the $\partial$ symbol in the numerator.
+
+\subsubsection{Comma list of variables of differentiation}
+
+\label{subsec:Comma-list-of-vars}In tensor calculus the differentiations
+are almost always in terms of super- or subscripted coordinates. In
+many other contexts this is the case too -- the reciprocal of the
+temperature in thermodynamics or generalized coordinates in analytical
+mechanics. This is why a comma list is used in \texttt{diffcoeff}
+for specifying variables of differentiation for mixed partial derivatives.
+Although it would be nice to write the minimal \texttt{\{xy\}} rather
+than \texttt{\{x,y}\} when two variables $x$ and $y$ are involved,
+the extra writing is trivial and the comma list allows a simpler handling
+of multi-character variables. For instance in tensor calculus we get
+expressions like
+\begin{centred}
+\verb`\[ \diffp{A_i}{ x^j,x^k } \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^j,x^k }. \]
+\end{centred}
+\noindent It is easier to write \texttt{\{x\textasciicircum j,x\textasciicircum k\}}
+here than, say, \texttt{\{\{x\textasciicircum j\}\{x\textasciicircum k\}\}}
+to distinguish the variables. It does mean that should the variable
+of differentiation include a comma then that comma needs to be enclosed
+in braces. There are plenty of instances of this out in the world
+(see, e.g., the last equation of (\ref{eq:eg1})) but it is overall
+a rare occurrence.
+
+\paragraph*{Minutiae of spacing (yet again):}
+
+In \xA7\ref{subsec:Minutiae-of-spacing} above, I discussed a slight
+reduction in the space inserted between the terms occurring in the
+denominator of a mixed partial derivative when a higher order differentiation
+is involved. The superscript appearing on a differentiation variable
+in that case \emph{of itself} introduced a spacing adjustment between
+the terms. But the present discussion involves only first order differentiations
+and no such reduction is automatically made by \texttt{diffcoeff}.
+However it is still possible to explicitly make such an adjustment
+with the \texttt{\textbackslash negmu} command introduced earlier
+(\xA7\ref{subsec:Spacing-commands}), which inserts \texttt{-1 mu} of
+spacing. For our example, in
+\begin{centred}
+\verb`\[ \diffp{A_i}{ x^j\negmu,x^k } \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^j\negmu,x^k } \]
+\end{centred}
+\noindent the \texttt{\textbackslash negmu} decreases the spacing
+between the terms from the default \verb`2 mu` to \verb`1 mu`.
+
+\subsubsection{Overkill territory}
+
+Two previous examples illustrate limitations of the algorithm that
+calculates the overall order of differentiation: \texttt{2m/2+2n/2}
+is not simplified to \texttt{m+n} and \texttt{2km+2m} is not factorised
+to \texttt{2m(k+1)}. But there is much that the algorithm \emph{can}
+handle -- for instance, the simple use of parentheses:
+\begin{centred}
+\verb`\[ \diffp[2m-(k+1),2(k+1)-m]{F(x,y,z)}{x,y,z} \]` $\Longrightarrow$
+\[ \diffp[2m-(k+1),2(k+1)-m]{F(x,y,z)}{x,y,z}. \]
+\end{centred}
+
+\paragraph*{Dynamic use of parentheses}
+
+\noindent For parenthetic expressions to be evaluated as in this example
+-- the \emph{dynamic} use of parentheses -- the left parenthesis
+must be preceded at most by a sign or a number; the right parenthesis
+must be followed at most by a sign.
+
+If a right parenthesis is followed by a \emph{variable}, say by \texttt{m}
+as in the order spec. \texttt{{[}(2n+1)m,(2n-1)m{]}}, it will throw
+an error and halt compilation. A message will be sent to the terminal
+and the \LaTeX{} log like the following (which assumes the order spec.
+was on line 53 of the document):
+\begin{lyxcode}
+!~Package~diffcoeff~Error:~)~followed~by~m~in~the~
+
+order~specification~{[}(2n+1)m,(2n-1)m{]}~on~line~53.~
+
+Diffcoeff~cannot~calculate~the~overall~order~of~
+
+differentiation~in~this~case.~Use~the~order-override~
+
+option~to~enter~the~overall~order.
+\end{lyxcode}
+This is a limitation on the dynamic use of parentheses -- but they
+\emph{can} be nested.
+
+\paragraph*{Static use of parentheses}
+
+If a left parenthesis is preceded by a \emph{variable} (i.e., not
+a sign or a number) this signals to \texttt{diffcoeff} the \emph{static}
+use of parentheses, something like $f(k)$, `function of $k$'.
+No attempt is made to evaluate what is between them and they are treated
+simply as an extension of the variable. For example,
+\begin{centred}
+\verb`\[ \diffp[f(k+1)+1,f(k-1)-1]{F(x,y)}{x,y} \]` $\Longrightarrow$
+\[ \diffp[f(k+1)+1,f(k-1)-1]{F(x,y)}{x,y}. \]
+\end{centred}
+\noindent In the static case you \emph{can} follow the right parenthesis
+by a variable without generating an error.\emph{ }You can nest them,
+and you can include static parentheses within a dynamic pair; for
+example,
+\begin{centred}
+\noindent \verb`\[ \diffp[2(3+f(k))+1,1-3(f(k)-2)]{F(x,y)}{x,y} \]`
+$\Longrightarrow$ \[ \diffp[2(3+f(k))+1,1-3(f(k)-2)]{F(x,y)}{x,y}. \]
+\end{centred}
+\noindent However, the reverse is not possible: you can't have dynamic
+parentheses within a static pair.
+
+\paragraph*{Other refinements}
+
+Exponents and subscripts on a \emph{variable} are fine in an order
+specification, so long as the exponent or subscript consists of a
+\emph{single} token:
+\begin{centred}
+\verb`\[ \diffp[m^2+2(k-1),m^2-(k+1)]F{x,y,z,w} \]` $\Longrightarrow$
+\[ \diffp[m^2+2(k-1),m^2-(k+1)]F{x,y,z,w}. \]
+\end{centred}
+\noindent Braced arguments containing \emph{multiple} tokens as exponents
+or subscripts to variables will generally not halt compilation but
+will usually give nonsensical results, as will \emph{signs} treated
+as superscripts or subscripts. Neither circumstance is checked for
+by \texttt{diffcoeff}.
+
+\paragraph*{Override}
+
+There are limitations on what order specifications the \texttt{diffcoeff}
+package can `digest'; equally, it can digest a wide variety of such
+constructs, but it is \emph{not} a computer algebra system. In all
+those cases where it fails to calculate or present a correct total
+order, the order-override option is available. Yes, this is not as
+convenient as having the overall order calculated automatically but
+(let's remind ourselves) we are deep in overkill territory. Mixed
+partial derivatives are used far less often than the pure derivatives,
+and when they \emph{are} used it is nearly always to orders 1 or 2
+in the variables. Mixed partial derivatives to exotic orders of differentiation
+are rarely used, so that the limitations of the calculational algorithm
+are of little real moment -- and the override option is always available
+for such cases.
+
+\subsection{Parentheses around multi-character variables}
+
+In thermodynamics and statistical mechanics one may want to differentiate
+in the reciprocal of the temperature, $1/T$ (or $1/\Theta$):
+\begin{centred}
+\verb`\[ \diffp[2]q{\frac 1\Theta} \]` $\Longrightarrow$ \[ \diffp[2]q{\frac 1\Theta}. \]
+\end{centred}
+\noindent In this case and for other \emph{higher order} derivatives
+of multi-character variables of differentiation, the parentheses are
+inserted automatically by \texttt{diffcoeff}. Precisely where parentheses
+should be placed is moot. The placement in this example is not strictly
+logical, although it feels intuitive, but the placement can be customised
+(\xA7\ref{sec:Changing-defaults}).
+
+Parentheses are automatically inserted like this only for higher order
+derivatives. When the differentiation is to first order, parenthesising
+is up to the user:
+\begin{centred}
+\verb`\[ \diffp q{(\frac 1\Theta),V} \]` $\Longrightarrow$ \[ \diffp q{(\frac 1\Theta),V}. \]
+\end{centred}
+
+\subsection{Jacobians}
+
+\texttt{diffcoeff} provides a command \texttt{\textbackslash jacob}
+for constructing Jacobians. For example
+\begin{centred}
+\verb`\[ \jacob{u,v,w}{x,y,z} \]` $\Longrightarrow$ \[ \jacob{u,v,w}{x,y,z}. \]
+\end{centred}
+The comma lists can contain any number of variables. \texttt{\textbackslash jacob}
+does \emph{not} check that the two arguments contain the same number
+of variables, so it is perfectly possible to form an object like \texttt{\textbackslash jacob\{u,v,w\}\{x,y\}}
+which as far as I know has no meaning.
+
+\section{Changing defaults; variant forms}
+
+\label{sec:Changing-defaults}To write the range of different examples
+displayed in the Rogues' Gallery (\xA7\ref{sec:Rogues'-gallery}) I have
+had to make extensive use of forms of derivative other than the default.
+\texttt{diffcoeff} is built on the facilities offered by the \texttt{xtemplate}
+package (included in the \LaTeX 3 bundle \texttt{l3packages)}. These
+facilities are harnessed by means of a command, \texttt{\textbackslash diffdef},
+and a further optional argument of the \texttt{\textbackslash diff}
+command.\texttt{ }
+
+\subsection{Default values: ordinary derivatives}
+
+Table~\ref{tab:Ordinary-derivatives} lists the keys available for
+forming derivatives and the default values\footnote{Note that a mu is a `math unit', 1/18 of a quad.}
+they have been assigned. These default values have been chosen to
+coincide with those relevant for \emph{ordinary} derivatives -- apart
+from the keys \texttt{denom-term-sep}, \texttt{/-denom-term-sep},
+\texttt{term-sep-adjust} and \texttt{/-term-sep-adjust} which are
+ignored for ordinary derivatives but apply to the case of mixed partial
+derivatives when there is more than one variable of differentiation.
+Keys with an opening slash, /, apply only to the slash form of the
+derivative; keys with an opening asterisk, {*}, apply only when the
+differentiand is appended.
+
+Note that these settings are, in general, font dependent. The values
+given are (in the author's opinion) appropriate for the default \LaTeX{}
+math fonts. There are also likely to be variations required for whether
+a derivative is used in a display-style or text-style or script-style
+expression. That matter is discussed below in \xA7\ref{subsec:Text-and-script-style}.
+All values specifying a space require the unit (\texttt{mu}) to be
+given; a number alone does not suffice.
+\noindent \begin{center}
+\begin{table}
+\centering
+\centering{}\caption{{\small Defaults (ordinary derivatives})\protect\label{tab:Ordinary-derivatives}}
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small op-symbol} & {\small\texttt{d}}\tabularnewline
+{\small op-symbol-alt} & {\small\texttt{op-symbol}}\tabularnewline
+{\small op-order-sep} & {\small\texttt{1 mu}}\tabularnewline
+{\small derivand-sep} & {\small\texttt{3 mu plus 1 mu minus 2 mu}}\tabularnewline
+{\small /-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
+{\small{*}-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
+{\small{*}/-derivand-sep} & {\small\texttt{/-derivand-sep}}\tabularnewline
+{\small denom-term-sep} & {\small\texttt{2 mu}}\tabularnewline
+{\small /-denom-term-sep} & {\small\texttt{1 mu}}\tabularnewline
+{\small term-sep-adjust} & {\small\texttt{-1 mu}}\tabularnewline
+{\small left-delim} & {\small\texttt{\textbackslash left .}}\tabularnewline
+{\small right-delim} & {\small\texttt{\textbackslash right |}}\tabularnewline
+{\small /-left-delim} & {\small\texttt{(}}\tabularnewline
+{\small /-right-delim} & {\small\texttt{)}}\tabularnewline
+{\small elbowroom} & {\small\texttt{0 mu}}\tabularnewline
+{\small /-elbowroom} & {\small\texttt{0 mu}}\tabularnewline
+{\small subscr-nudge} & {\small\texttt{0 mu}}\tabularnewline
+{\small /-subscr-nudge} & {\small\texttt{0 mu}}\tabularnewline
+{\small long-var-wrap} & {\small\texttt{d(v)}}\tabularnewline
+{\small{*}/-op-wrap} & {\small\texttt{true}}\tabularnewline
+{\small{*}-op-left} & {\small\texttt{false}}\tabularnewline
+{\small{*}-italic-nudge} & {\small\texttt{3 mu}}\tabularnewline
+\bottomrule
+\end{tabular}
+\end{table}
+\par\end{center}
+\begin{description}
+\item [{op-symbol}] the operator symbol; for ordinary derivatives, generally
+one of \texttt{d} or \texttt{\textbackslash mathrm\{d\}}, \texttt{D}
+or \texttt{\textbackslash mathrm\{D\}}, \texttt{\textbackslash delta}
+or \texttt{\textbackslash Delta}; for partial derivatives \texttt{\textbackslash partial};
+default = \texttt{d}
+\item [{op-symbol-alt}] if different from \textbf{op-symbol} then used
+in the denominator while \textbf{op-symbol} is used in the numerator;
+e.g. for $\diff.nabla.{v^{i}}t$, \texttt{op-symbol = \textbackslash nabla}
+and \texttt{op-symbol-alt = d}; otherwise (and usually) defaults to
+\textbf{op-symbol}
+\item [{op-order-sep}] extra horizontal space added between the op-symbol
+and the superscripted order of differentiation in higher order derivatives;
+for the math-italic forms compare $d^{2}$ with $d^{\mkern1mu 2}$,
+$\partial^{2}$ with $\partial^{\mkern1mu 2}$ where the first symbol
+in each case has no extra space and the second has an extra 1 mu;
+default = \texttt{1 mu}
+\item [{derivand-sep}] horizontal space added before the differentiand
+(derivand) if the \verb`spaced` package option is used, or by the
+\verb`!` switch if it is not; the default has some stretch and shrink;
+default = \verb`3mu plus 1mu minus 2mu`
+\item [{/-derivand-sep}] for the slash form of derivative, horizontal space
+added before the differentiand (derivand) if the \verb`spaced` package
+option is used, or by the \verb`!` switch if it is not; default =
+\verb`derivand-sep`
+\item [{{*}-derivand-sep}] when the derivand is appended, horizontal space
+added before the differentiand (derivand) if the \verb`spaced` package
+option is used, or by the \verb`!` switch if it is not; default =
+\verb`derivand-sep`
+\item [{{*}/-derivand-sep}] for the slash form of derivative when the derivand
+is appended, horizontal space added before the differentiand (derivand)
+if the \verb`spaced` package option is used, or by the \verb`!`
+switch if it is not; default = \verb`/-derivand-sep`
+\item [{denom-term-sep}] (mixed partial derivatives only) horizontal spacing
+inserted between the differentials in the denominator of a mixed partial
+derivative to avoid a solid cluster like $\partial x\partial y\partial z$;
+with the default 2 mu this is $\dl.p.x\dl.p.2y\dl.p.2z$; default
+= \texttt{2 mu}
+\item [{/-denom-term-sep}] (mixed partial derivatives only) horizontal
+spacing inserted between the differentials in the denominator of a
+slash-form mixed partial derivative; because a slash-form derivative
+is already spread out horizontally, the default spacing is less than
+for the \texttt{\textbackslash frac} form derivative; default = \texttt{1
+mu}
+\item [{term-sep-adjust}] (mixed partial derivatives only) adjustment (i.e.
+reduction) to \textbf{denom-term-sep} or \textbf{/-denom-term-sep}
+when differentiation in a variable occurs to an order other than 1;
+if, e.g., $\dl.p.x^{2}\dl.p.1y\dl.p.2z$ is the denominator of a mixed
+partial derivative in three variables, because of the superscript
+the spacing between $\partial x^{2}$ and $\partial y$ is reduced
+by\textbf{ term-sep-adjust} from the spacing between $\partial y$
+and $\partial z$; default = \texttt{-1 mu}
+\item [{left-delim}] the left member of a delimiter pair wrapping the derivative,
+the right member of which is subscripted to indicate a point of evaluation
+or variables held constant; default = \texttt{\textbackslash left
+.}
+\item [{right-delim}] the right member of a delimiter pair wrapping the
+derivative and subscripted to indicate a point of evaluation or variables
+held constant; default = \texttt{\textbackslash right |}
+\item [{/-left-delim}] for the slash form of derivative, the left member
+of a delimiter pair wrapping the derivative and subscripted to indicate
+a point of evaluation or variables held constant; default = \texttt{(}
+\item [{/-right-delim}] for the slash form of derivative, the right member
+of a delimiter pair wrapping the derivative, the right member of which
+is subscripted to indicate a point of evaluation or variables held
+constant; default = \texttt{)}
+\item [{elbowroom}] adjustment to the whitespace between the left and right
+delimiters and the enclosed derivative; negative values reduce the
+space; default = \texttt{0 mu}
+\item [{/-elbowroom}] adjustment to the whitespace between the left and
+right delimiters and the enclosed slash-form derivative; default =
+\texttt{0 mu}
+\item [{subscr-nudge}] horizontal adjustment of the subscript's placing
+relative to the \textbf{right-delim}iter, e.g., a negative value compensates
+for the curving inwards of a large right parenthesis; may be font
+dependent; default = \texttt{0 mu}
+\item [{/-subscr-nudge}] for the slash form of derivative, horizontal adjustment
+of the subscript's placing relative to the /-\textbf{right-delim}iter;
+may be font dependent; default = \texttt{0 mu}
+\item [{long-var-wrap}] to avoid ambiguity in higher order derivatives
+it may be advisable to wrap multi-token variables of differentiation
+in parentheses; default = \texttt{d(v)}; the choices are
+\begin{description}
+\item [{\texttt{dv}}] no wrapping, e.g. $dx_{i}^{2}$ or $d\frac{1}{\Theta}^{2}$,
+$\partial x_{i}^{2}$ or $\partial\frac{1}{\Theta}^{2}$,
+\item [{\texttt{d(v)}}] wrap the variable only, e.g. $d(x_{i})^{2}$ or
+$d(\frac{1}{\Theta})^{2}$, $\partial(x_{i})^{2}$ or $\partial(\frac{1}{\Theta})^{2}$
+\item [{\texttt{(dv)}}] wrap the op-symbol and variable, e.g. $(dx_{i})^{2}$
+or $(d\frac{1}{\Theta})^{2}$, $(\partial x_{i})^{2}$ or $(\partial\frac{1}{\Theta})^{2}$
+\end{description}
+\item [{{*}/-op-wrap}] a choice of \texttt{true} or \texttt{false} for
+slash forms of the derivative when the differentiand is appended,
+dictating whether the derivative is wrapped in parentheses, as here
+$\diffp*{F(x,y)}/x$, or not; default = \texttt{true}
+\item [{{*}-op-left}] a choice of \texttt{true} or \texttt{false} indicating
+whether the op-symbol is left-aligned or not when the differentiand
+is appended; generally it is centred; does not apply to slash forms
+of the derivative; default = \texttt{false}
+\item [{{*}-italic-nudge}] if \textbf{{*}-op-left} is \texttt{true}, makes
+an italic adjustment in the numerator, so that the op-symbols in numerator
+and denominator align in the same slanting column; for an upright
+\texttt{d} this would be set to \texttt{0 mu}; default = \texttt{3
+mu}
+\end{description}
+
+\subsection{ISO defaults}
+
+\label{subsec:ISO-defaults}\begin{wraptable}[10]{o}{0.4\columnwidth}%
+\centering{}\vspace{-5.35ex}
+ \caption{{\small ISO default changes}\protect\label{tab:ISO-setting-changes}}
+\abovetopsep=.5ex %
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small op-symbol} & {\small\texttt{\textbackslash mathrm\{d\}}}\tabularnewline
+{\small op-order-sep} & {\small\texttt{0 mu}}\tabularnewline
+{\small left-delim} & {\small\texttt{\textbackslash left (}}\tabularnewline
+{\small right-delim} & {\small\texttt{\textbackslash right )}}\tabularnewline
+{\small subscr-nudge} & {\small\texttt{-6 mu}}\tabularnewline
+\bottomrule
+\end{tabular}\end{wraptable}%
+You may not like the default settings that come with \texttt{diffcoeff}.
+The package does not follow ISO 80000-2 -- it does not use upright
+`d's nor does it wrap an ordinary differential coefficient in subscripted
+parentheses to indicate a point of evaluation. Both `defects' can
+be remedied by calling the package with the option \texttt{ISO}:\footnote{One can also use \texttt{ISO=true} to turn the option on and \texttt{ISO=false
+}to turn the option off. }
+\begin{lyxcode}
+\textbackslash usepackage{[}ISO{]}\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+The uppercase is essential -- an option \texttt{iso} is not recognised.
+The \texttt{ISO} option results in changes to the default settings
+of Table~\ref{tab:Ordinary-derivatives} as listed in Table~\ref{tab:ISO-setting-changes}.
+Any settings not mentioned in Table~\ref{tab:ISO-setting-changes}
+retain the values presented in Table~\ref{tab:Ordinary-derivatives}.
+Note that the subscript nudge figure specified here is \emph{not}
+part of the standard, which makes no recommendation about the subscript's
+positioning. But: the \texttt{-6 mu} figure with a default or latin
+modern font gives a better representation of what is displayed in
+the standard than a zero figure.
+
+Because the `d' is upright with the \texttt{ISO} option, no extra
+space is required between the symbol and the superscript in a higher
+order derivative. Hence the zero value for the \texttt{op-order-sep}.
+ISO recommends subscripted parentheses to indicate a point of evaluation.
+Hence the other entries in the table. Because a large right parenthesis
+(penultimate setting) bends inwards, to the left, a negative value
+for the last entry ensures the subscript does not become detached
+from the derivative, looking lost in a sea of whitespace.
+
+Note that the \texttt{ISO} option will also produce upright `D's in
+derivatives formed from `D'; see \xA7\ref{subsec:D-delta-Delta} below.
+
+\subsection{Partial derivatives}
+
+\begin{wraptable}{o}{0.4\columnwidth}%
+\centering{}\vspace{-5.35ex}
+ \caption{{\small Default changes for partial derivatives}\protect\label{tab:Partial-deriv-defaults}}
+\abovetopsep=.5ex %
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small op-symbol} & {\small\texttt{\textbackslash partial}}\tabularnewline
+{\small left-delim} & {\small\texttt{\textbackslash left (}}\tabularnewline
+{\small right-delim} & {\small\texttt{\textbackslash right )}}\tabularnewline
+{\small subscr-nudge} & {\small\texttt{-6 mu}}\tabularnewline
+\bottomrule
+\end{tabular}\end{wraptable}%
+The default values given in Table~\ref{tab:Ordinary-derivatives},
+when they are relevant, apply to \emph{ordinary} derivatives. For
+partial derivatives, some defaults change. These are listed in Table~\ref{tab:Partial-deriv-defaults}.
+All other keys take the default values of Table~\ref{tab:Ordinary-derivatives}.
+
+The last three entries here reflect the use of subscripted parentheses
+with partial derivatives to indicate variables held constant, for
+instance in the Maxwell relations of thermodynamics, one of which
+is
+\[
+\diffp SV[T]=\diffp PT[V]
+\]
+
+
+\subsection{Setting your own defaults: \texttt{\textbackslash diffdef}}
+
+\label{subsec:diffdef}Versions 2 and later of the \texttt{diffcoeff}
+package provide a command, \texttt{\textbackslash diffdef}, that
+enables users to set their own defaults.\texttt{ }For example, if
+you wish to use upright `d's but not follow ISO's use of subscripted
+parentheses to indicate a point of evaluation, enter in the preamble
+of your document the command
+\begin{lyxcode}
+\textbackslash diffdef~\{\}~~~~
+
+~~\{~~~~~~
+
+~~~~op-symbol~~~~=~\textbackslash mathrm\{d\},~~~~
+
+~~~~op-order-sep~=~0~mu
+
+~~\}
+\end{lyxcode}
+\noindent Since a list of settings, like this one, is a comma-\emph{separated}
+list, no comma is required for the last entry. That entry is a consequence
+of the first: upright symbols do not require any extra separation
+between the `d' and the superscript in a higher order derivative.
+
+The other point to note is the empty pair of braces after the \texttt{\textbackslash diffdef}
+command. \emph{They matter}. Their emptiness is what determines that
+it is the \emph{default} values that are changed. If they contain
+some content, then that content provides a \emph{name} for the particular
+set of values in the following list. The \texttt{diffcoeff} package
+exploits this facility to cope with the wide variety of forms displayed
+in the Rogues' Gallery of \xA7\ref{sec:Rogues'-gallery}.
+
+\subsubsection{Space before the differentiand}
+
+\label{subsec:A-final-flourish}\begin{wraptable}{o}{0.6\columnwidth}%
+\begin{centering}
+\caption{Keys for spacing the derivand}
+\medskip{}
+\begin{tabular}{lr}
+\toprule
+{\small key} & {\small default}\tabularnewline
+\midrule
+{\small derivand-sep} & {\small\texttt{3mu plus 1mu minus 2mu}}\tabularnewline
+{\small{*}-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
+{\small /-derivand-sep} & {\small\texttt{derivand-sep}}\tabularnewline
+{\small{*}/-derivand-sep} & {\small\texttt{ /-derivand-sep}}\tabularnewline
+\bottomrule
+\end{tabular}
+\par\end{centering}
+\end{wraptable}%
+The insertion of a small space before the differentiand is effected
+by the \verb`!` key inserted immediately before the differentiand
+argument in the \verb`\diff` command. You may wish to make the insertion
+of this space the \emph{default} behaviour. This is done by using
+the \verb`spaced` package option (which makes the \verb`!` switch
+now reverse this new default and put \emph{no} extra space before
+the derivand). The amount of space inserted is, by default, \verb`3mu plus 1mu minus 2mu`,
+meaning the space is generally $3$mu but can stretch to $4$mu or
+shrink to $1$mu as \TeX{} strives to fit content in a line or on the
+page.
+
+Perhaps this doesn't suit. You may want a fixed space here, with no
+stretch or shrink. The key to change is \verb`derivand-sep`. By default,
+this setting applies not only to the fraction form of derivative,
+but also to the slash form and to when the derivand is appended.
+
+If you feel a little less space should be used for slash derivatives,
+then the key to change is \verb`/-deriv-sep`. This changed value
+will also be used for an appended derivand in a slash derivative.
+
+Thus to meet both wishes you might put in the preamble of your document
+something like
+\begin{lyxcode}
+\textbackslash diffdef~\{\}~~~~
+
+~~\{~~~~~~
+
+~~~~derivand-sep~~~=~3~mu,~~~~
+
+~~~~/-derivand-sep~=~2~mu
+
+~~\}
+\end{lyxcode}
+This will insert a fixed space of $3$mu before the differentiand
+in both the numerator and when appended in the fraction form of derivative,
+and a fixed space of $2$mu in the slash form of derivative, both
+in the numerator and when appended.
+
+If you want a different spacing when the derivand is appended, the
+keys to change are \verb`*-derivand-sep` and \verb`*/-derivand-sep`.
+
+\paragraph{Selective spacing}
+
+I have treated the \verb`spaced` package option thus far as if it
+were an \verb`ON/OFF` switch and, indeed, the presence of the package
+option \verb`spaced` behaves as \verb`ON` and its absence as \verb`OFF`.
+Internally, however, \verb`spaced` is equivalent to \verb`spaced=1`
+and its absence to \verb`spaced=0`. Entering \verb`spaced=n` in
+the package option where \verb`n` is a positive integer is equivalent
+to entering \verb`spaced=1` (and hence to simply entering \verb`spaced`),
+but if \verb`n` is a negative integer, a new effect is produced.
+
+Entering \verb`spaced=-1` (or any negative integer) as a package
+option will insert a space (by default \verb`3mu plus 1mu minus 2mu`)
+before the differentiand provided the differentiand\emph{ is longer
+than a single token} but will insert no space before single-token
+differentiands. The switch \verb`!` reverses this behaviour.
+
+\subsection{Variant forms}
+
+For this package I needed a number of variant forms to illustrate
+the wide variety of ways in which derivatives are displayed. The \texttt{\textbackslash diffdef}
+command in which the first argument is \emph{filled} provides one
+half of the means of doing this. I've given the single-letter name
+\texttt{p} to the following settings:
+\begin{lyxcode}
+\textbackslash diffdef~\{~p~\}
+
+~~\{
+
+~~~~op-symbol~~~~=~\textbackslash partial~,
+
+~~~~left-delim~~~=~\textbackslash left~(~~,
+
+~~~~right-delim~~=~\textbackslash right~)~,
+
+~~~~subscr-nudge~=~-6~mu
+
+~~\}
+\end{lyxcode}
+The second half of providing variant forms is to insert this name,
+\texttt{p}, between dots (periods, full stops) as the \emph{first}
+argument of the \texttt{\textbackslash diff} command. Thus, repeating
+an example at the end of \xA7\ref{subsec:Partial-appending},
+\begin{centred}
+\verb`\[ \diff.p.*{\frac PT}U[V] = \diff.p.*{\frac 1T}V[U] \]` $\Longrightarrow$
+\[ \diff.p.*{\frac PT}U[V] = \diff.p.*{\frac 1T}V[U] \]
+\end{centred}
+\noindent The effect is exactly the same as previously, when the \texttt{\textbackslash diffp}
+command was used. Indeed, \texttt{diffcoeff} identifies \texttt{\textbackslash diffp}
+with \texttt{\textbackslash diff.p.}:
+\begin{lyxcode}
+\textbackslash NewDocumentCommand~\textbackslash diffp~\{~\}~\{~\textbackslash diff.p.~\}
+\end{lyxcode}
+Note that this identification of \texttt{\textbackslash diffp} with
+\texttt{\textbackslash diff.p.} means there is no equivalent dot-delimited
+argument available for \texttt{\textbackslash diffp}. The \emph{dot-delimited
+argument applies only to} \texttt{\textbackslash diff}.
+
+For example, to illustrate the upright-d form of derivative, without
+changing the default math-italic form (which I prefer), one might
+enter in the preamble
+\begin{lyxcode}
+\textbackslash diffdef~\{~up~\}~
+
+~~\{
+
+~~~~op-symbol~~~~=~\textbackslash mathrm\{d\},
+
+~~~~op-order-sep~=~0~mu
+
+~~\}
+\end{lyxcode}
+Apart from the \emph{key = value} settings, the critical feature here
+is the name, \texttt{up} (which is at your discretion and could equally
+be \texttt{upright} or \texttt{roman} or even \texttt{Fred} if you
+so fancied). This ensures that the changed settings apply only to
+this particular variant and do not `infect' the overall defaults.
+To use this variant, all that is needed is to add the name, between
+dots, to the \texttt{\textbackslash diff} command:
+\begin{centred}
+\verb`\[ \diff.up.yx \]` $\Longrightarrow$ \[ \diff.up.yx. \]
+\end{centred}
+\noindent Each variant derivative inherits all the default values
+that it does not explicitly countermand. Thus a point of evaluation
+is indicated by a vertical rule which is the \texttt{diffcoeff} default\footnote{\noindent But not the ISO recommendation.}:
+\begin{centred}
+\noindent \verb`\[ \diff.up.*{\frac{F(x)}{G(x)}}x[x=1] \]` $\Longrightarrow$
+\[ \diff.up.*{\frac{F(x)}{G(x)}}x[x=1] \]
+\end{centred}
+\noindent Dot-delimited arguments must always be the \emph{first}
+argument of the \texttt{\textbackslash diff} command, even preceding
+an asterisk (star) as in this example.
+
+As another example, suppose for the subscripted indication of variables
+held constant in a partial derivative that you want to see what things
+look like if the subscript is \emph{not }nudged in towards the right
+parenthesis. In that case define a variant form
+\begin{lyxcode}
+\textbackslash diffdef~\{~padrift~\}~\{~subscr-nudge~=~0~mu~\}
+\end{lyxcode}
+I have attached a name, \texttt{padrift},\texttt{ }to this setting,
+\begin{centred}
+\verb`\[ \diff.padrift.Fx[y] \]` $\Longrightarrow$ \[ \diff.padrift.Fx[y] \]
+\end{centred}
+\noindent since, to my eye, the subscript seems detached from the
+expression it qualifies -- is it perhaps a typo? -- and `adrift
+in a sea of whitespace'. This is to be compared with the default \verb`\[ \diffp Fx[y] \]`
+$\Longrightarrow$ \[ \diffp Fx[y] \]
+
+\noindent where the subscript is tucked in close to the right parenthesis
+and is clearly connected to it and the expression it delimits.
+
+Some might want to distinguish notationally a point of evaluation
+for a partial derivative from variables held constant, perhaps using
+a vertical rule for the former and (the default) parentheses for the
+latter. It would suffice then to add to the preamble
+\begin{centred}
+\verb`\diffdef { pvrule } { op-symbol = \partial }`
+\end{centred}
+This gives
+\begin{centred}
+\verb`\[ \diff.pvrule.{F(x,y)}x[x=1] \]`$\Longrightarrow$ \[ \diff.pvrule.{F(x,y)}x[x=1] \]
+\end{centred}
+
+\subsubsection{Text-style and script-style derivatives}
+
+\label{subsec:Text-and-script-style}As noted earlier, the \texttt{diffcoeff}
+package assumes that derivatives of fraction-like form will be used
+in display-style expressions and that the slash form will be used
+for inline use (text style). This is the usual practice. But if one
+does want to use the fraction form in an inline expression, say \texttt{\textbackslash diffp
+ST{[}V{]}} displaying as $\diffp ST[V]$, then some tweaking of settings
+is necessary: the subscript is obviously too close to the right parenthesis
+and, to my eye, there is too much `elbowroom' between the derivative
+and the enclosing parentheses. Hence define
+
+\noindent %
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{lyxcode}
+\textbackslash diffdef~\{~ptxt~\}~
+
+~~\{
+
+~~~~op-symbol~~~~~~=~\textbackslash partial,
+
+~~~~denom-term-sep~=~1~mu~~~~,
+
+~~~~left-delim~~~~~=~\textbackslash left~(~,
+
+~~~~right-delim~~~~=~\textbackslash right~),
+
+~~~~elbowroom~~~~~~=~-2~mu~~~,
+
+~~~~subscr-nudge~~~=~-3~mu~~~
+
+~~\}
+\end{lyxcode}
+%
+\end{minipage}
+
+We can now write, for the same example, \texttt{\textbackslash diff.ptxt.ST{[}V{]}}
+which displays as $\diff.ptxt.ST[V]$, where the subscript is better
+positioned and there is a better fit between parentheses and derivative.
+
+\subsubsection{Derivatives from D, \textbackslash delta, \textbackslash Delta}
+
+\label{subsec:D-delta-Delta}In addition to \texttt{\textbackslash diff.p.},\texttt{
+diffcoeff} has three other \emph{built-in} variant forms that are
+commonly used: \texttt{\textbackslash diff.D.}, \texttt{\textbackslash diff.delta.},
+and \texttt{\textbackslash diff.Delta.}, corresponding to derivatives
+formed from $D$, $\delta$ and $\Delta$ respectively.
+
+In fluid dynamics the \emph{material }or \emph{substantive} derivative
+uses an uppercase $D$ in place of $d$. For example, the continuity
+equation is,
+\begin{centred}
+\verb`\[ \diff.D.{\rho}t=\diffp\rho t + \mathbf{u\cdot}\nabla\rho \]`$\Longrightarrow$
+\[ \diff.D.{\rho}t=\diffp\rho t + \mathbf{u\cdot}\nabla\rho \]
+\end{centred}
+\noindent where \texttt{\textbackslash diff.D.} produces the D-derivative.
+If you want upright `D's, then the \texttt{ISO} package option will
+produce that effect. Alternatively,
+\begin{lyxcode}
+\textbackslash diffdef~\{~Up~\}~
+
+~~\{
+
+~~~~op-symbol~~~~=~\textbackslash mathrm\{D\},
+
+~~~~op-order-sep~=~0~mu
+
+~~\}
+\end{lyxcode}
+\noindent provides a variant with upright `D's.
+
+In introductory calculus texts the simple $\delta$-derivative is
+used. This is achieved with the \texttt{\textbackslash diff.delta.}
+command: \verb`\[ \diff.delta.yx \]` $\Longrightarrow$ \[ \diff.delta.yx. \]
+
+\noindent This form also features in analytical mechanics (in the
+Rogues' Gallery, the final example at (\ref{eq:eg6})).
+
+Similarly, \texttt{\textbackslash diff.Delta.} forms a derivative
+from $\Delta$:
+\begin{centred}
+\verb`$ \diff.Delta.y/x $` $\Longrightarrow$ $ \diff.Delta.y/x $
+\end{centred}
+\noindent where the slash form of the derivative is shown in this
+instance.
+
+Higher order forms of these derivatives, points of evaluation, appending
+the differentiand with a star argument, all follow exactly as for
+the `pure' \texttt{\textbackslash diff} command.
+
+\paragraph{The commands \textbackslash Diff, \textbackslash diffd, \textbackslash Diffd}
+
+For compatibility with version 1 of \texttt{diffcoeff}, the commands
+\texttt{\textbackslash Diff}, \texttt{\textbackslash diffd} and
+\texttt{\textbackslash Diffd} are available and also produce the
+$D$, $\delta$ and $\Delta$ derivatives. Just as \texttt{\textbackslash diffp}
+is identified with \texttt{\textbackslash diff.p.} for partial derivatives,
+these commands are identified with \texttt{\textbackslash diff.D.},
+\texttt{\textbackslash diff.delta.}, and \texttt{\textbackslash diff.Delta}
+through the commands
+\begin{lyxcode}
+\textbackslash NewDocumentCommand~\textbackslash Diff~\{\}~~\{\textbackslash diff.D.\}
+
+\textbackslash NewDocumentCommand~\textbackslash diffd~\{\}~\{\textbackslash diff.delta.\}
+
+\textbackslash NewDocumentCommand~\textbackslash Diffd~\{\}~\{\textbackslash diff.Delta.\}
+\end{lyxcode}
+Unless one is using such variant forms frequently, it seems simpler
+to remember that they are available as dot-delimited arguments to
+the \texttt{\textbackslash diff} command, using the obvious name
+in each case, rather than having to remember the precise camel-case
+form of name of the \texttt{\textbackslash Diff}, \texttt{\textbackslash diffd}
+and \texttt{\textbackslash Diffd} commands.
+
+\subsection{The \texttt{.def} file}
+
+\label{subsec:The-.def-file}This mechanism of variant formation is
+how I have been able to illustrate in the Rogues' Gallery, \xA7\ref{sec:Rogues'-gallery},
+the wide variety of different usages culled from the literature. But
+the thought arises: if a variant is to be used only once or twice,
+isn't this a lot of bother? Why not just construct the variant derivative
+`by hand' out of \texttt{\textbackslash frac} and \texttt{\textbackslash mskip}
+for example? The reason for making such definitions is that they can
+be transferred from document to document. For instance, definitions
+placed in the preamble can be copied to the preamble of another document.
+
+But that is hardly optimal. Instead, \texttt{diffcoeff} allows such
+definitions to be placed in a text file with the the extension \texttt{.def}
+and a name of your choosing. For the present document the file is
+called \texttt{diffcoeff-doc.def} and should have been placed alongside
+the \verb`.sty` file in your \TeX{} distribution. The contents of
+this file can be seen at \xA7To use these definitions, the \texttt{diffcoeff}
+package is called with the command
+\begin{lyxcode}
+\textbackslash usepackage{[}def-file=diffcoeff-doc{]}\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+But even this process still means copying a definition file from directory
+to directory as one works on different documents. The solution is
+to make a definition file available for \emph{all} documents and the
+way to do that is by placing it in the texmf tree, preferably not
+the one created by your \TeX{} distribution (perhaps MiKTeX or TexLive),
+but your own \emph{personal} texmf tree.
+
+\texttt{\vspace{2ex}
+ }
+
+\noindent %
+\noindent\fbox{\begin{minipage}[t]{1\linewidth - 2\fboxsep - 2\fboxrule}%
+\textbf{Personal texmf tree? }
+
+This is a directory for `waifs and strays' of the \TeX{} system that
+are not included in standard distributions like MiK\TeX{} or \TeX Live.
+For instance, it is the place for personal packages designed for your
+own particular circumstances or preferences, and is structured like
+the standard MiK\TeX{} or \TeX Live hierarchy but placed in another
+location so that there is no chance of its being overwritten when
+MiK\TeX{} or \TeX Live are updated. However, those distributions need
+to be alerted to its existence. For MiK\TeX , open the MiK\TeX{} console,
+click on \textsf{Settings} and then the \textsf{Directories} tab.
+Click the \textsf{+} button and navigate to your personal texmf tree
+to add it to the MiK\TeX{} search path. Having added it, you will then
+need to refresh the filename database by clicking on the \textsf{Tasks}
+menu and selecting the obvious entry. I am not familiar with \TeX Live
+but presume an analogous process will apply there.%
+\end{minipage}}
+
+\medskip{}
+
+\noindent Provided your \LaTeX{} distribution knows about your personal
+texmf tree, then a \texttt{.def} file placed within it, will be accessible
+to all documents.
+
+\subsubsection{Structure of the \texttt{.def} file}
+
+The best way to see what a \texttt{.def} file looks like is to view
+\texttt{diffcoeff-doc.def }in a text editor.
+
+If you want your variant definitions to use defaults different from
+those supplied with the \texttt{diffcoeff} package, then the first
+definition in the \texttt{.def} file should be the one setting the
+new defaults, with an \emph{empty} first argument to the \texttt{\textbackslash diffdef}
+command:
+\begin{lyxcode}
+\textbackslash diffdef~\{\}~~~~
+
+~~\{~~~~~~
+
+~~~~key-1~=~value-1,~~~~
+
+~~~~key-2~=~value-2,
+
+~~~~...
+
+~~~~key-n~=~value-n
+
+~~\}
+\end{lyxcode}
+The key-value list is a comma-separated list; hence the last entry
+doesn't need to end with a comma. Nudge and separation values need
+to include the unit, \texttt{mu}; a numerical value alone will result
+in error.\texttt{ }Because a \texttt{.def} file\texttt{ }is a \LaTeX{}
+file, comments need to start with a \texttt{\%} character.
+
+\subsubsection{\texttt{diffcoeff.def}}
+
+Note that if the \texttt{diffcoeff} package is invoked without an
+explicit \texttt{def-file= <filename>} option statement, as here,
+\begin{lyxcode}
+\textbackslash usepackage\{diffcoeff\}{[}=v4{]}
+\end{lyxcode}
+then it will search in the texmf tree (the \LaTeX{} distribution's
+and your personal one) and the document directory for a file \texttt{diffcoeff.def}
+and if found will load that. This file should contain definitions
+of those variants you are likely to use in multiple documents. In
+my personal texmf tree (which I've put at \texttt{E:\textbackslash texmf\textbackslash}
+on a Windows machine) the file \texttt{diffcoeff.def} is located in
+the directory \texttt{E:\textbackslash texmf\textbackslash tex\textbackslash latex\textbackslash diffcoeff\textbackslash}.
+(The backslashes are replaced by forward slashes on linux machines.)
+
+Variants likely to be of value only to a specific document should
+be added to the preamble of that document. Alternatively, they could
+be added to \texttt{diffcoeff.def} but that added-to file saved to
+the document directory under a \emph{different} name -- e.g. I've
+saved the variants required for the present document under the name
+\texttt{diffcoeff-doc.def}. Many of these variants were created solely
+to illustrate points in the present document and I have no intention
+of using them in my own work. Consequently my \texttt{diffcoeff.def}
+file is smaller, containing only a selection from \texttt{diffcoeff-doc.def}.
+
+\section{Differentials in integrals, etc.}
+
+Forms like $dx$ occur not only in derivatives but also in other contexts,\footnote{I thank \noun{Sergio Callegari} for drawing my attention to this rather
+obvious point, and its omission from previous versions of \texttt{diffcoeff}.} for example, the expression for a total differential like
+\[
+\dl P=\diffp Px\dl x+\diffp Py\dl y+\diffp Pz\dl z,
+\]
+or an integral like $\int\sin x\dl2x$, or a multi-variable integral
+like
+\[
+\iiintop_{-\infty}^{\infty}V(x,y,z)\dl3x\dl2y\dl2z.
+\]
+Surely we want the `d's in these expressions to correspond to their
+form (upright or math italic) in derivatives? If, for instance, the
+\texttt{ISO} package option has been set, one doesn't want to be writing
+\texttt{\textbackslash mathrm\{d\}} in every (or indeed any) integral.
+To this end, \texttt{diffcoeff} provides a command \texttt{\textbackslash dl}
+to write the `d' in a differential in a manner consistent with the
+default form used in derivatives. In the present document, the default
+form is math-italic and so
+\begin{centred}
+\verb`$ \dl x $` $\Longrightarrow$ $ \dl x. $
+\end{centred}
+\noindent It is also possible\footnote{\noindent From version 3.1 of \texttt{diffcoeff}; version 3.0 of the
+package produced a \LaTeX{} error.} to use the command before, for instance, \texttt{\textbackslash mathbf\{x\}}
+or \texttt{\textbackslash vec\{x\}}:
+\begin{centred}
+\verb`$ \dl \vec{x} $` $\Longrightarrow$ $ \dl \vec{x} $,~~~~\verb`$ \dl \mathbf{x} $`
+$\Longrightarrow$$ \dl \mathbf{x}. $
+\end{centred}
+
+\subsection{Options}
+
+There are two options available with the differential command.
+
+The first is the dotted name option discussed in \xA7\ref{sec:Changing-defaults}.
+Thus, to illustrate a differential with an upright `d', write
+\begin{centred}
+\verb`$ \dl.up.x $` $\Longrightarrow$ $ \dl.up.x. $
+\end{centred}
+\noindent This presumes that a variant derivative with upright `d's
+has been defined and the definition is available, either in the preamble
+or in an accessible \texttt{.def} file, as discussed in the previous
+section. Alternatively, if you have defined your default derivative
+to use upright `d's (perhaps with the \texttt{ISO} option) then
+\texttt{\textbackslash dl} alone will suffice to produce an upright
+`d'.
+
+\subsubsection{Partial differential}
+
+\label{subsec:Partial-differential}Since the variant \texttt{\textbackslash diff.p.}
+is defined in \texttt{diffcoeff4.sty} itself, \texttt{\textbackslash dl.p.}
+is always available and at 6 keystrokes offers a slightly shorter
+way of writing \texttt{\textbackslash partial} (8 keystrokes). However,
+there are sufficient contexts where expressions like \verb`\partial_x`
+are used, perhaps as a shortcut for a partial derivative, for it to
+be worthwhile to define an appropriate command for this variant. From
+version 4.0, \texttt{diffcoeff} therefore provides \verb`\dlp`, defined
+by
+\begin{lyxcode}
+\textbackslash NewDocumentCommand~\textbackslash dlp~\{\}~\{~\textbackslash dl.p.~\}
+\end{lyxcode}
+Thus, for instance, \verb`$ \dlp_x $` $\Longrightarrow$ $ \dlp_x $.
+
+\subsubsection{Spacing}
+
+This second option inserts spacing before the `d'. If \texttt{\textbackslash dl}
+is followed by a digit (0, 1, 2, ..., 9) it will insert a horizontal
+space of that number of mu before the `d'; (\texttt{\textbackslash dl0x}
+has the same effect as \texttt{\textbackslash dl x}.)\texttt{ }Thus,
+an alternative way of writing an example in Chapter~18 of \emph{The
+\TeX book} is
+\begin{centred}
+\verb`$ \dl x\dl3y=r\dl3r\dl3\theta $` $\Longrightarrow$ $ \dl x\dl3y=r\dl3r\dl3\theta. $
+\end{centred}
+\noindent To my eye this is too much space; I prefer
+\begin{centred}
+\noindent \verb`$ \dl x\dl2y=r\dl2r\dl2\theta $` $\Longrightarrow$
+$ \dl x\dl2y=r\dl2r\dl2\theta. $
+\end{centred}
+\noindent I used \texttt{\textbackslash dl3x\textbackslash dl2y\textbackslash dl2z}
+when writing the triple integral above, \emph{no} extra spacing when
+writing the total differential expression, since the differentials
+are already distinct from the preceding fraction forms $\diff.ptxt.Px$
+etc., and \texttt{\textbackslash dl2x} when writing $\int\sin x\dl2x$.
+
+Note that only \emph{one} digit can be used. If two are used, as here,
+\verb`$ \dl20x $` $\Longrightarrow$ $ \dl20x $, the effect is unlikely
+to be what is wanted.
+
+From version 3.2 of \texttt{diffcoeff} it is possible to also add
+\emph{negative} space before the differential, which might be useful
+in special contexts, perhaps to construct a symbol:
+\begin{centred}
+\verb`$ /\dl-9x $` $\Longrightarrow$ $ /\dl-9x. $
+\end{centred}
+\noindent For negative space before the differential, add a minus
+sign before the (single) digit.
+
+The spacing digit option \emph{follows} the dot-delimited name option.
+For example, earlier, in the denominator of a mixed partial derivative,
+I have used what is effectively \texttt{\textbackslash dlp x\textbackslash dlp2y\textbackslash dlp2z},
+and the variation to that spacing when a higher-order differentiation
+occurs:
+\begin{centred}
+\verb`$ \dlp x^2\dlp1y\dlp2z $` $\Longrightarrow$ $ \dlp x^2\dlp1y\dlp2z. $
+\end{centred}
+
+\subsection{Rationale}
+
+Version 1 of the \texttt{diffcoeff} package arose from a need to simplify
+the parsing of differential coefficients for another program I was
+working on which was struggling to `read' all the possible permutations
+of \texttt{\textbackslash frac} or \texttt{\textbackslash tfrac}
+or \texttt{\textbackslash dfrac} or slash forms of the derivative,
+of \texttt{d} or \texttt{\textbackslash mathrm\{d\}} or \texttt{\textbackslash partial}
+or \texttt{D} or \texttt{\textbackslash mathrm\{D\}} or \texttt{\textbackslash nabla},\texttt{
+}and of points of evaluation delimited by vertical rules or parentheses.\texttt{ }Although
+regular expressions coped with most of these cases, it was \emph{messy}.
+
+There are other packages which have commands for the derivative (e.g.,
+\texttt{bropd}, \texttt{commath},\texttt{ esdiff}, \texttt{physymb})
+but none quite gave what I wanted -- although they probably cope
+with most users' needs. \texttt{esdiff} came closest to what I was
+seeking but failed when it came to combining algebraic and numeric
+orders of differentation in a mixed partial derivative (and made heavier
+use of braces than I liked in that case too).
+
+\subsubsection{\texttt{diffcoeff.sty}}
+
+I have tried to make using \texttt{diffcoeff} intuitive. Looking at
+the other packages mentioned, writing something like \texttt{\textbackslash diff{[}n{]}\{f\}\{x\}}
+(which can be trimmed to \texttt{\textbackslash diff{[}n{]}fx} for
+single-token arguments) seems `natural' -- only \texttt{physymb}
+deviates from the pattern.
+\begin{itemize}
+\item It seems consistent with this pattern to use a comma list for specifying
+the orders of differentiation of the variables in a higher order mixed
+partial derivative (and its suppression when all are of order 1)
+\item Having specified the orders, surely the program itself should calculate
+the overall order? \texttt{esdiff} does this for numerical orders;
+\texttt{diffcoeff} does this for both numeric and algebraic orders,
+\end{itemize}
+\begin{centred}
+\verb`\[ \diffp[m-(k+1),m+(k-1)]{F(x,y,z)}{x,y,z} \]`
+\end{centred}
+\begin{example}
+$\Longrightarrow$ \[ \diffp[m-(k+1),m+(k-1)]{F(x,y,z)}{x,y,z} \]
+\end{example}
+
+\begin{itemize}
+\item and where it fails either to calculate at all or to present the result
+in a preferred form, offers the order-override option:
+\end{itemize}
+\begin{centred}
+\verb`\[ \diffp[m+(k+1),m+(k-1)][2(m+k+1)]{F(x,y,z,w)}{x,y,z,w} \]`
+\end{centred}
+\begin{example}
+$\Longrightarrow$ \[ \diffp[m+(k+1),m+(k-1)][2(m+k+1)]{F(x,y,z,w)}{x,y,z,w} \]
+\end{example}
+
+\begin{itemize}
+\item I wished to avoid the unnecessary writing of superscripts, subscripts
+and brace pairs. In the examples just given, no superscript tokens
+\texttt{\textasciicircum} are written by the user despite the higher-order
+differentiation in $x$ and $y$, and only the two inescapable brace
+pairs are required.
+\item The use of a comma list for the second mandatory argument in a partial
+derivative -- the list of variables -- makes differentiations in
+super- or subscripted symbols (as occurs prolifically in tensor calculus)
+easier to both write and read by avoiding unnecessary brace pairs.
+\end{itemize}
+\begin{centred}
+\verb`\[ \diffp{A_i}{ x^j,x^k } \]` $\Longrightarrow$ \[ \diffp{A_i}{ x^j,x^k } \]
+\end{centred}
+\begin{itemize}
+\item Should a point of evaluation or variables held constant be considered
+part of the derivative? Thermodynamic usage was decisive here. The
+partial derivative alone is ambiguous -- the parentheses and subscript
+are essential to understand what is being stated:
+\[
+\diffp ST[V]
+\]
+Hence provision for these extra elements was included in the derivative
+commands.
+\item Given the position of the subscripted symbol in the displayed derivative,
+it's positioning as the \emph{final} argument in the derivative command
+feels inevitable.
+\item Version 1 of \texttt{diffcoeff} used braces for this argument to avoid
+any possible confusion with a following mathematical expression. That
+use of braces is now deprecated in \texttt{xparse}, has been deprecated
+in \texttt{diffcoeff} since version 2, and is no longer compatible
+with version 4. Later versions of \texttt{diffcoeff} use square brackets,
+conforming with familiar \LaTeX{} practice. The only special remembering
+needed is avoidance of a space before the argument -- and if it does
+slip in, it won't cause a \LaTeX{} error. It will be treated as part
+of a following mathematical expression and displayed as such.
+\item The star option also prompted the question: is it needed? After all,
+one can always leave the first mandatory argument empty and append
+the differentiand `by hand'. But once the provision for points of
+evaluation or variables held constant was incorporated into the derivative
+commands, the star option became the simplest way of handling appended
+differentiands since the parentheses for a variable held constant
+must wrap around the differential operator \emph{and} differentiand.
+Once available, it provides a simple way of switching between (and
+comparing) the appearance of differentiand-in-the-numerator and differentiand-appended.
+\item The slash option was added to the derivative commands after seeing
+how widely such forms are used in texts at all levels. The placement
+of the slash, between the two mandatory arguments, seems more-or-less
+self-evident.
+\item A later option added to \texttt{\textbackslash diff} (and not present
+in version 1) was the dot-delimited name option. Once \texttt{xtemplate}
+was used as the basis of the package this seemed the most straightforward
+way of making available, ready to hand, the wealth of variants that
+\texttt{xtemplate} makes possible. (It's just a pity that the second
+dot is needed, and a single-dot naming scheme can't be used, but \texttt{xparse}
+forces my hand here.)
+\item Having added the dot-delimited name option, the use of a \texttt{def}
+file to store variants or preferred defaults is more-or-less forced,
+otherwise one is faced with making these definitions anew for each
+new document (or locating a previous document and copying from that
+to the new one).
+\item To handle possible differences between display-style and text-style
+(and script-style) derivatives (see \xA7\ref{subsec:Text-and-script-style})
+I considered using \TeX 's \texttt{\textbackslash mathchoice} command.
+This command takes four arguments, corresponding to display-, text-,
+script- and scriptscript-styles and would require forming four derivatives
+each time a derivative is used, `just in case'. In fact fraction-form
+derivatives are used overwhelmingly in display-style expressions,
+the slash form being used for inline use. Given the ease of defining
+a fraction-form variant for text-style use, and the rareness of such
+use, employing variants seemed the way to go. It is the one adopted
+and avoids the computational burden associated with the use of \texttt{\textbackslash mathchoice}.
+\item After version 2 of the package appeared on CTAN, it was pointed out
+to me that there was an issue of consistency between the form of `d'
+used in a derivative (upright or math-italic) and the form used in
+an integral. I had overlooked this matter completely and in version
+3 of the package remedied the omission with the differential command
+\texttt{\textbackslash dl}. A spacing option for \texttt{\textbackslash dl}
+was almost inevitable. From version 4 the partial analogue \texttt{\textbackslash dlp}
+has been added.
+\item Space before the differentiand was requested by a user. Once considered
+it became clear that there are (at least) two ways of thinking of
+a derivative: as $\diff y/x$, a ratio of differentials where $\dl y$
+is a unit and it makes no sense to insert space between the `d'
+and the `y', and as
+\[
+\diff!{F(x)}x
+\]
+where the function $F(x)$ is being operated on by $\diff{}/x$ and
+it is natural to insert space between the `d' and the `F'. With
+that realisation came the need for a simple switch-like package option
+(\verb`spaced`) to turn spacing on or off, and a switch-like argument
+(\verb`!`) to countermand the package option in exceptional cases
+(version 4).
+\end{itemize}
+
+\section{Reference}
+
+\subsection{Commands}
+\begin{description}
+\item [{\texttt{\textbackslash diff}}] arguments (all optional unless
+otherwise indicated):
+\begin{enumerate}
+\item .\emph{name}. for the given settings
+\item {*} append-differentiand switch
+\item {[}\emph{order}{]} or {[}\emph{comma-list of orders}{]} of differentiation
+\item {[}\emph{order-override}{]}
+\item ! countermand before-differentiand spacing of the \verb`spaced` package
+option
+\item \{\emph{differentiand}\} (mandatory)
+\item / slash-form switch
+\item \{\emph{comma list of differentiation variables}\} (mandatory)
+\item {[}\emph{point of evaluation/variables held constant}{]}
+\end{enumerate}
+\item [{\texttt{\textbackslash diffdef}}] arguments (all mandatory):
+\begin{enumerate}
+\item \{\emph{name}\}
+\item \{\emph{key=value comma list}\}
+\end{enumerate}
+\item [{\texttt{\textbackslash diffp}}] \texttt{= \textbackslash diff.p.}
+\item [{\texttt{\textbackslash dl}}] arguments (all optional):
+\begin{enumerate}
+\item .\emph{name}. (as for \texttt{\textbackslash diff})
+\item \emph{minus sign} (optional, use only if negative spacing before the
+`d' is wanted)
+\item \emph{digit} (insert spacing of this number of mu before the `d')
+\end{enumerate}
+\item [{\texttt{\textbackslash dpl}}] \texttt{= \textbackslash dl.p.}
+\item [{\texttt{\textbackslash negmu}}] insert a $-1$ mu space
+\item [{\texttt{\textbackslash nilmu}}] insert a $0$ mu space
+\item [{\texttt{\textbackslash onemu}}] insert a $1$ mu space
+\item [{\texttt{\textbackslash twomu}}] insert a $2$ mu space
+\end{description}
+Deprecated (why try remembering the special names when the forms on
+the right are self-explanatory):
+\begin{description}
+\item [{\texttt{\textbackslash Diff}}] preferred form: \texttt{\textbackslash diff.D.}
+\item [{\texttt{\textbackslash diffd}}] preferred form \texttt{\textbackslash diff.delta.}
+\item [{\texttt{\textbackslash Diffd}}] preferred form\texttt{ \textbackslash diff.Delta.}
+\end{description}
+
+\subsection{The file \texttt{diffcoeff-doc.def}}
+
+\label{sec:diffcoeff-doc.def}The file \verb`diffcoeff-doc.def` contains
+the following definitions:
+\begin{verbatim}
+%%%%%%%%%% ordinary %%%%%%%%%%
+% ( ) for pt of eval.
+\diffdef { paren }
+ {
+ left-delim = \left ( ,
+ right-delim = \right ),
+ subscr-nudge = -6 mu
+ }
+
+% upright
+\diffdef { up }
+ {
+ op-symbol = \mathrm{d},
+ op-order-sep = 0 mu
+ }
+
+\diffdef { Up }
+ {
+ op-symbol = \mathrm{D},
+ op-order-sep = 0 mu
+ }
+
+% wrap long vars: (d longvar)
+\diffdef { wrapall } {long-var-wrap = (dv)}
+
+% nabla in numerator, d in denominator
+\diffdef { nabla }
+ {
+ op-symbol = \nabla,diffcoeff-doc.def
+ op-symbol-alt = d
+ }
+
+% align op left; no italic nudge
+\diffdef { left }
+ {
+ *-op-left = true,
+ *-italic-nudge = 0 mu
+ }
+
+% slash-form: vrule for pt of eval
+\diffdef { svrule }
+ {
+ /-left-delim = ,
+ /-right-delim = |
+ }
+
+%%%%%%%%%% partial %%%%%%%%%%
+% partial, vrule for pt of eval.
+\diffdef { pvrule } { op-symbol = \partial }
+
+% partial, no subscr nudge (adrift in a sea of white space)
+\diffdef { padrift }
+ {
+ op-symbol = \partial,
+ left-delim = \left ( ,
+ right-delim = \right ),
+ subscr-nudge = 0 mu
+ }
+
+% partial, [ ] for pt of eval.
+\diffdef { psqbra }
+ {
+ op-symbol = \partial,
+ left-delim = \left [ ,
+ right-delim = \right ],
+ subscr-nudge = 0 mu
+ }
+
+% Delta as partial deriv.
+\diffdef { pDelta }
+ {
+ op-symbol = \Delta ,
+ op-order-sep = 0 mu ,
+ left-delim = \left ( ,
+ right-delim = \right ),
+ subscr-nudge = -6 mu
+ }
+
+% align op left; italic nudge
+\diffdef { pleft }
+ {
+ op-symbol = \partial,
+ *-op-left = true ,
+ *-italic-nudge = 3 mu ,
+ left-delim = \left ( ,
+ right-delim = \right ),
+ subscr-nudge = -3 mu
+ }
+
+% partial, textstyle
+\diffdef { ptxt }
+ {
+ op-symbol = \partial,
+ denom-term-sep = 1 mu ,
+ left-delim = \left ( ,
+ right-delim = \right ),
+ elbowroom = -2 mu ,
+ subscr-nudge = -3 mu
+ }
+
+% partial, wide sep of terms
+\diffdef { pwide }
+ {
+ op-symbol = \partial,
+ denom-term-sep = 3 mu ,
+ /-denom-term-sep = 3 mu ,
+ left-delim = \left ( ,
+ right-delim = \right ),
+ subscr-nudge = -6 mu
+ }
+
+ %%%%%%%%%% differential %%%%%%%%%%
+ \diffdef { up }
+ { op-symbol = \mathrm{d} }
+\end{verbatim}
+
+
+\subsection{Version comparison}
+
+\label{sec:Version-comparison}Unlike version 1, version 2 and later
+are built on the the \texttt{xtemplate} package which makes certain
+facilities available which it would be silly not to exploit. Hence
+the coding in the later versions is completely different and there
+are consequences.
+\begin{enumerate}
+\item From version 2.0
+\begin{enumerate}
+\item The \texttt{\textbackslash diffset} command, formerly used to tweak
+the display of derivatives, has been superseded by the \texttt{\textbackslash diffdef}
+command. \texttt{\textbackslash diffset} now sends a message warning
+of its obsolescence to the terminal and \LaTeX{} log but is otherwise
+functionless. It should not interfere with the compilation of a document
+but any intended fine-tuning of the display by means of the \texttt{\textbackslash diffset}
+command\texttt{ }will not eventuate. The warning message is: \texttt{Obsolete
+command: \textbackslash diffset has been superseded by the \textbackslash diffdef
+command.} \texttt{See the diffcoeff} \texttt{doc\-umentation for
+further information.} The \texttt{\textbackslash diffdef} command
+is discussed in \xA7\ref{subsec:diffdef};
+\item The optional trailing argument used to indicate a point of evaluation
+or variables held constant is now delimited by square brackets, \texttt{{[}}
+and \texttt{{]}}, as other optional arguments are. For compatibility
+with version 1, versions 2 and 3 still accepted braces to delimit
+this argument but from version 4 of \texttt{diffcoeff} only the square-bracket
+delimited argument is accepted. (The use of braces around \emph{optional}
+arguments while once accepted is now deprecated in \texttt{xparse}
+on which \texttt{diffcoeff} depends);
+\item The commands \texttt{\textbackslash Diff}, \texttt{\textbackslash diffd}
+and \texttt{\textbackslash Diffd} used to construct derivatives from
+$D$, $\delta$ and $\Delta$ in version 1, are still available but
+deprecated. A new optional argument in the \texttt{\textbackslash diff}
+command offers these and a host of other possibilities and is now
+the preferred method of forming such variants; see \xA7\ref{subsec:D-delta-Delta}.
+\end{enumerate}
+\item Version 3.0
+\begin{enumerate}
+\item adds a command, \texttt{\textbackslash dl} (from \emph{d}ifferentia\emph{l})
+to write differentials like $dx$ that occur in integrals and in other
+contexts in a manner consistent with the form used in derivatives.
+After all, if one is using upright `d's in derivatives, similarly
+upright `d's should occur in these other contexts;\footnote{This rather obvious lack in version 2 was pointed out to me by Sergio
+Callegari.}
+\item provides some simple spacing commands that can be useful for tweaking
+standard spacing.
+\end{enumerate}
+\item Version 3.1 enables the differential command to be used before forms
+like \texttt{\textbackslash vec\{x\}} (an overlooked possibility
+causing an error in earlier versions).
+\item Version 3.2
+\begin{enumerate}
+\item allows negative spacing before the differential command \texttt{\textbackslash dl};
+\item fixes a bug in which an ordinary derivative as the differentiand of
+a partial derivative displayed as a partial derivativ\texttt{diffcoeff-doc.def}e.
+It now displays, as it should, as an ordinary derivative.
+\end{enumerate}
+\item Version 4.0
+\begin{enumerate}
+\item enables the insertion of a small space before the differentiand, either
+as the default behaviour (package option \verb`spaced`) or at explicit
+request (argument \verb`!` of the \verb`\diff` command); see \xA7\ref{subsec:Spacing-before-derivand}.
+\item prevents the ligature $df$ that marred previous versions; this is
+now rendered $\dl f$.
+\item offers the document command \verb`\dlp` for the \emph{partial} differential;
+see \xA7\ref{subsec:Partial-differential};
+\item no longer accepts \emph{the braced form} of the\emph{ }trailing optional
+argument specifying a point of evaluation or (for partial derivatives)
+variables held constant. This was a relic from version 1 of \texttt{diffcoeff},
+and has been deprecated since version 2.
+\end{enumerate}
+\item Version 4.1
+\begin{enumerate}
+\item changes the code for the \verb`long-var-wrap` setting to avoid a
+problem arising from a change in \verb`xtemplate`;
+\item improves spacing between operator and variable in \emph{denominators}
+of differential coefficients (e.g. prevents ligatures).
+\end{enumerate}
+\item Version 4.2
+\begin{enumerate}
+\item see the announcement at the start of this document.
+\end{enumerate}
+\end{enumerate}
+
+\end{document}
Property changes on: trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff4.tex
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Modified: trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff-doc.def
===================================================================
--- trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff-doc.def 2023-01-11 20:43:41 UTC (rev 65522)
+++ trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff-doc.def 2023-01-11 20:44:28 UTC (rev 65523)
@@ -114,4 +114,8 @@
left-delim = \left ( ,
right-delim = \right ),
subscr-nudge = -6 mu
- }
\ No newline at end of file
+ }
+
+ %%%%%%%%%% differential %%%%%%%%%%
+ \diffdef { up }
+ { op-symbol = \mathrm{d} }
\ No newline at end of file
Modified: trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff.sty
===================================================================
--- trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff.sty 2023-01-11 20:43:41 UTC (rev 65522)
+++ trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff.sty 2023-01-11 20:44:28 UTC (rev 65523)
@@ -7,96 +7,163 @@
%
% Andrew Parsloe ajparsloe at gmail.com
%
-\RequirePackage{expl3}
-\RequirePackage{xparse,l3keys2e,xtemplate}
-\ProvidesExplPackage {diffcoeff} {2022/06/14} {4.1}
- {Write differential coefficients consistently and easily.}
-%
+\DeclareRelease{v4}{}{diffcoeff4.sty}
+\DeclareCurrentRelease{}{2023/01/02}
+
+\RequirePackage{xtemplate,mleftright}
+\ProvidesExplPackage {diffcoeff} {2023/01/02} {5.0}
+ {Write differential coefficients easily and consistently.}
\keys_define:nn { diffcoeff }
{
- ISO .bool_set:N = \l__diffcoeff_ISO_bool,
- spaced .int_set:N = \l__diffcoeff_spaced_int,
- spaced .default:n = 1,
- spaced .initial:n = 0,
- def-file .tl_gset:N = \g__diffcoeff_def_tl,
- def-file .initial:n = diffcoeff,
- def-file .default:n = diffcoeff
+ spaced .int_set:N = \l__diffcoeff_spaced_int,
+ spaced .default:n = 1,
+ spaced .initial:n = 0,
+ mleftright .bool_set:N = \l__diffcoeff_mLR_bool,
+ mleftright .default:n = true,
+ mleftright .initial:n = false,
+ def-file .tl_gset:N = \g__diffcoeff_def_tl,
+ DIF .clist_set:N = \l__diffcoeff_dif_clist
}
-\ProcessKeysPackageOptions { diffcoeff }
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\cs_generate_variant:Nn \tl_if_eq:nnTF { nV }
-
-\tl_new:N \l__diffcoeff_oporder_tl
+\IfFormatAtLeastTF {2020-10-01} {}
+ { \RequirePackage { xparse } }
+\IfFormatAtLeastTF {2022-06-01}
+ { \ProcessKeyOptions [ diffcoeff ] }
+ {
+ \RequirePackage { l3keys2e }
+ \ProcessKeysOptions { diffcoeff }
+ }
+\bool_if:NT \l__diffcoeff_mLR_bool
+ { \mleftright }
+%%%%%%%%%% messages %%%%%%%%%
+\cs_new:Npn \__diffcoeff_msg_autocalc:n #1
+ {
+ in~the~order~spec.~[#1]~\msg_line_context:.~Calculation~of~the~
+ total~order~of~differentiation~fails~in~this~case.~
+ Use~the~\tl_to_str:n { \difoverride }command~to~enter~the~total~order.~
+ \msg_see_documentation_text:n {diffcoeff}
+ }
+\cs_new:Npn \__diffcoeff_msg_style:nnn #1#2#3
+ {
+ The~style~specified~in~the~current~instance,~#1,~
+ \msg_line_context:,~#3~Reverting~to~default~style~#2.
+ }
+\tl_const:Nn \c__diffcoeff_msg_vcon_tl
+ { Version~5~of~diffcoeff~does~not~support~the~use~of~ }
+\tl_const:Nn \c__diffcoeff_msg_revert_tl
+ { Or~revert~to~version~4~by~appending~[=v4]~to~the~preamble~call;~
+ for~example,~\tl_to_str:n{\usepackage}{diffcoeff}[=v4] }
+\msg_new:nnn { diffcoeff } { file-not-found } { File~#1.def~not~found. }
+\msg_new:nnn { diffcoeff } { order-spec-general }
+ { #3~followed~by~#2~\__diffcoeff_msg_autocalc:n { #1 } }
+\msg_new:nnn { diffcoeff } { unknown-style }
+ { \__diffcoeff_msg_style:nnn {#1} {#2} { is~unknown. } }
+\msg_new:nnn { diffcoeff } { wrong-style }
+ { \__diffcoeff_msg_style:nnn {#1} {#2} { conflicts~with~its~template. } }
+\msg_new:nnn { diffcoeff } { version-conflict }
+ {
+ \c__diffcoeff_msg_vcon_tl #1~\msg_line_context:.~\tl_to_str:n { #2 }
+ \msg_see_documentation_text:n {diffcoeff}~\c__diffcoeff_msg_revert_tl
+ }
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\bool_new:N \l__diffcoeff_multitok_bool
+\bool_new:N \l__diffcoeff_append_bool
+\bool_new:N \l__diffcoeff_op_left_bool
+\bool_new:N \l__diffcoeff_dl_bool
+\bool_new:N \l__diffcoeff_exponent_bool
+\tl_new:N \l__diffcoeff_override_tl
+\tl_new:N \l__diffcoeff_frac_tl
\tl_new:N \l__diffcoeff_derivand_tl
-\tl_new:N \l__diffcoeff_type_tl
-\tl_new:N \l__diffcoeff_tot_order_tl
+\tl_new:N \l__diffcoeff_instance_tl
+\tl_new:N \l__diffcoeff_ord_tl
+\tl_new:N \l__diffcoeff_var_tl
+\tl_new:N \l__diffcoeff_tot_ord_tl
+\tl_new:N \l__diffcoeff_vph_tl
+\tl_new:N \l__diffcoeff_exponent_tl
\tl_new:N \l__diffcoeff_curr_num_tl
\tl_new:N \l__diffcoeff_curr_var_tl
\tl_new:N \l__diffcoeff_paren_tl
-
-\tl_const:Nn \c__diffcoeff_digits_tl { 1234567890 }
-
-\seq_new:N \l__diffcoeff_orders_seq
+\seq_new:N \l__diffcoeff_ords_seq
\seq_new:N \l__diffcoeff_vars_seq
-\seq_new:N \l__diffcoeff_denom_seq
\seq_new:N \l__diffcoeff_paren_seq
-
-\prop_new:N \l__diffcoeff_vars_prop
-
-\bool_new:N \l__diffcoeff_op_left_bool
-\bool_new:N \l__diffcoeff_single_var_bool
-\bool_new:N \l__diffcoeff_opwrap_bool
-\bool_new:N \l__diffcoeff_integ_bool
-\bool_new:N \l__diffcoeff_spaced_bool
-\bool_new:N \l__diffcoeff_altsep_bool
-
-\int_new:N \l__diffcoeff_vars_int
-\int_new:N \l__diffcoeff_format_int
+\int_new:N \l__diffcoeff_group_int
+\int_new:N \l__diffcoeff_style_int
\int_new:N \l__diffcoeff_curr_tok_int
\int_new:N \l__diffcoeff_curr_state_int
\int_new:N \l__diffcoeff_nos_int
\int_new:N \l__diffcoeff_parenvar_int
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\DeclareObjectType { derivative } { 3 }
-
-% defaults: ordinary deriv. values
-\DeclareTemplateInterface { derivative } { DERIV } { 3 }
+\prop_new:N \l__diffcoeff_vars_prop
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\DeclareObjectType { diffcoeff } { 5 }
+% #1 append boolean; #2 order spec(clist); #3 derivand(tl);
+% #4 diff variables(clist); #5 pt of eval(tl)
+\DeclareTemplateInterface { diffcoeff } { DIF } { 5 }
{
- op-symbol : tokenlist = d ,
+ style-group : choice { f, s, c, j, l } = f,
+ style : choice { frac, tfrac, dfrac,
+ /, auto, big, Big, bigg, Bigg,
+ _, dl
+ } = frac ,
+ slash-tok : tokenlist = / ,
+ slash-sep : tokenlist = 0 mu,
+ derivand-sep : tokenlist = 3 mu plus 1 mu minus 2 mu,
+ op-symbol : tokenlist = \mathrm{d},
op-symbol-alt : tokenlist = \KeyValue { op-symbol },
- op-order-sep : muskip = 1 mu ,
- derivand-sep : muskip = 3 mu plus 1 mu minus 2 mu,
+ op-order-nudge : tokenlist = 0 mu ,
+ var-sup-nudge : tokenlist = 1 mu ,
+ multi-term-sep : tokenlist = 2 mu plus 1 mu minus 1 mu,
+ term-sep-adjust : tokenlist = -1 mu,
long-var-wrap : choice { dv, d(v), (dv) }
- = d(v) ,
- denom-term-sep : muskip = 2 mu ,
- term-sep-adjust : muskip = -1 mu ,
- left-delim : tokenlist = \left . ,
- right-delim : tokenlist = \right |,
- elbowroom : muskip = 0 mu ,
- subscr-nudge : muskip = 0 mu ,
- *-derivand-sep : muskip = \KeyValue { derivand-sep },
- *-op-left : boolean = false ,
- *-italic-nudge : muskip = 3 mu ,
- /-derivand-sep : muskip = \KeyValue { derivand-sep },
- /-denom-term-sep : muskip = 1 mu ,
- /-left-delim : tokenlist = ( ,
- /-right-delim : tokenlist = ) ,
- /-elbowroom : muskip = 0 mu ,
- /-subscr-nudge : muskip = 0 mu ,
- */-derivand-sep : muskip = \KeyValue { /-derivand-sep },
- */-op-wrap : boolean = true
+ = d(v) ,
+ lvwrap-Ldelim : tokenlist = \mleft (,
+ lvwrap-Rdelim : tokenlist = \mright ),
+ lvwrap-sup-nudge : tokenlist = -2 mu,
+ outer-Ldelim : tokenlist = \left ( ,
+ outer-Rdelim : tokenlist = \right ),
+ elbowroom : tokenlist = 0 mu ,
+ sub-nudge : tokenlist = -5 mu,
+ op-sub-nudge : tokenlist = 0 mu ,
+ *derivand-sep : tokenlist = \KeyValue { derivand-sep },
+ *op-set-left : boolean = false,
+ *italic-nudge : tokenlist = 0 mu ,
+ *inner-wrap : boolean = false,
+ *inner-Ldelim : tokenlist = (,
+ *inner-Rdelim : tokenlist = ),
+ *outer-Ldelim : tokenlist = \bigl [,
+ *outer-Rdelim : tokenlist = \bigr ],
+ *sub-nudge : tokenlist = 0 mu
}
-% #1 order spec(seqvar); #2 order override(tlvar)
-% #3 derivand(tlvar); #4 denominator(seqvar)
-% #5 subscript(tlvar)
-\DeclareTemplateCode { derivative } { DERIV } { 3 }
+\DeclareTemplateCode { diffcoeff } { DIF } { 5 }
{
- op-symbol = \l__diffcoeff_op_tl,
- op-symbol-alt = \l__diffcoeff_op_alt_tl,
- op-order-sep = \l__diffcoeff_oporder_muskip,
- derivand-sep = \l__diffcoeff_derivsep_muskip,
+ style-group = {
+ f = \int_set:Nn \l__diffcoeff_group_int { 0 },
+ s = \int_set:Nn \l__diffcoeff_group_int { 1 },
+ c = \int_set:Nn \l__diffcoeff_group_int { 2 },
+ j = \int_set:Nn \l__diffcoeff_group_int { 3 },
+ l = \int_set:Nn \l__diffcoeff_group_int { 4 }
+ },
+ style = {
+ frac = \__diffcoeff_style:nn { 0 } {},
+ tfrac = \__diffcoeff_style:nn { 1 } {},
+ dfrac = \__diffcoeff_style:nn { 2 } {},
+ / = \__diffcoeff_style:nn { 3 } {},
+ auto = \__diffcoeff_style:nn { 4 } {},
+ big = \__diffcoeff_style:nn { 5 } { big },
+ Big = \__diffcoeff_style:nn { 5 } { Big },
+ bigg = \__diffcoeff_style:nn { 5 } { bigg },
+ Bigg = \__diffcoeff_style:nn { 5 } { Bigg },
+ _ = \__diffcoeff_style:nn { 6 } {},
+ dl = \__diffcoeff_style:nn { 7 } {},
+ unknown = \__diffcoeff_style:nn { 9 } {}
+ },
+ slash-tok = \l__diffcoeff_slashtok_tl,
+ slash-sep = \l__diffcoeff_slashsep_tl,
+ derivand-sep = \l__diffcoeff_derivsep_tl,
+ op-symbol = \l__diffcoeff_opi_tl,
+ op-symbol-alt = \l__diffcoeff_opii_tl,
+ op-order-nudge = \l__diffcoeff_opordsep_tl,
+ var-sup-nudge = \l__diffcoeff_varsupnudge_tl,
+ multi-term-sep = \l__diffcoeff_termsep_tl,
+ term-sep-adjust = \l__diffcoeff_sep_adj_tl,
long-var-wrap = {
dv = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
\__diffcoeff_wrap_longvars_dv:nn,
@@ -105,307 +172,164 @@
(dv) = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
\__diffcoeff_wrap_longvars_dvii:nn,
unknown = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
- \__diffcoeff_wrap_longvars_dvi:nn
+ \__diffcoeff_wrap_longvars_dvi:nn
},
- denom-term-sep = \l__diffcoeff_varsep_muskip,
- term-sep-adjust = \l__diffcoeff_sep_adj_muskip,
- left-delim = \l__diffcoeff_ldelim_tl,
- right-delim = \l__diffcoeff_rdelim_tl,
- elbowroom = \l__diffcoeff_elbowrm_muskip ,
- subscr-nudge = \l__diffcoeff_subnudge_muskip,
- *-derivand-sep = \l__diffcoeff_derivsepi_muskip,
- *-op-left = \l__diffcoeff_op_left_bool,
- *-italic-nudge = \l__diffcoeff_opnudge_muskip,
- /-derivand-sep = \l__diffcoeff_derivsepii_muskip,
- /-denom-term-sep = \l_tmpb_muskip,
- /-left-delim = \l__diffcoeff_ldelimi_tl,
- /-right-delim = \l__diffcoeff_rdelimi_tl,
- /-elbowroom = \l_tmpc_muskip,
- /-subscr-nudge = \l_tmpd_muskip,
- */-derivand-sep = \l__diffcoeff_derivsepiii_muskip,
- */-op-wrap = \l__diffcoeff_opwrap_bool
+ lvwrap-Ldelim = \l__diffcoeff_lvw_ldelim_tl,
+ lvwrap-Rdelim = \l__diffcoeff_lvw_rdelim_tl,
+ lvwrap-sup-nudge = \l__diffcoeff_lvsupnudge_tl,
+ outer-Ldelim = \l__diffcoeff_ldelim_tl,
+ outer-Rdelim = \l__diffcoeff_rdelim_tl,
+ elbowroom = \l__diffcoeff_elbowrm_tl ,
+ sub-nudge = \l__diffcoeff_subnudge_tl,
+ op-sub-nudge = \l__diffcoeff_opsubnudge_tl,
+ *derivand-sep = \l__diffcoeff_derivsepi_tl,
+ *op-set-left = \l__diffcoeff_op_left_bool,
+ *italic-nudge = \l__diffcoeff_opleftnudge_tl,
+ *inner-wrap = \l__diffcoeff_innerwrap_bool,
+ *inner-Ldelim = \l__diffcoeff_lopwrap_tl,
+ *inner-Rdelim = \l__diffcoeff_ropwrap_tl,
+ *outer-Ldelim = \l__diffcoeff_ldelimapp_tl,
+ *outer-Rdelim = \l__diffcoeff_rdelimapp_tl,
+ *sub-nudge = \l__diffcoeff_subnudgeapp_tl
}
{
\AssignTemplateKeys
-
- \bool_if:NF\l__diffcoeff_integ_bool
- {
- \int_compare:nNnT { \l__diffcoeff_format_int } > { 1 }
- { \__diffcoeff_slash_vals: }
- \__diffcoeff_build:nnn { #1 } { #2 } { #3 }
- }
+ \__diffcoeff_check_style:nn
+ { \l__diffcoeff_group_int } { \l__diffcoeff_style_int }
+ \__diffcoeff_append:n { #1 }
+ \exp_args:Nx \__diffcoeff_orders:nn { \clist_count:n {#4} } { #2 }
+ \__diffcoeff_override:N \l__diffcoeff_override_tl
+ \__diffcoeff_derivand:n { #3 }
+ \__diffcoeff_build:nn { #4 } { #5 }
}
%%%%%%%%%%
-\cs_new:Npn \__diffcoeff_slash_vals:
- {
- \muskip_set:Nn \l__diffcoeff_varsep_muskip \l_tmpb_muskip
- \muskip_set:Nn \l__diffcoeff_elbowrm_muskip \l_tmpc_muskip
- \muskip_set:Nn \l__diffcoeff_subnudge_muskip \l_tmpd_muskip
- \tl_set:NV \l__diffcoeff_ldelim_tl \l__diffcoeff_ldelimi_tl
- \tl_set:NV \l__diffcoeff_rdelim_tl \l__diffcoeff_rdelimi_tl
- }
-% #1 diff'and; #2 vars clist; #3 trailing arg
-\cs_new:Npn \__diffcoeff_build:nnn #1#2#3
+\cs_new_protected:Npn \__diffcoeff_style:nn #1#2
{
- \tl_set:Nn \l__diffcoeff_derivand_tl { #1 }
- \seq_set_from_clist:Nn \l__diffcoeff_vars_seq { #2 }
- \bool_if:nT
- {
- !\l__diffcoeff_opwrap_bool &&
- \int_compare_p:nNn { \l__diffcoeff_format_int } > { 1 }
- }
- { \int_set:Nn \l__diffcoeff_format_int { 4 } }
- \__diffcoeff_spaced:n { \l__diffcoeff_spaced_int }
- \bool_if:nTF
- {
- ( \l__diffcoeff_altsep_bool && !\l__diffcoeff_spaced_bool )
- || ( !\l__diffcoeff_altsep_bool && \l__diffcoeff_spaced_bool )
- }
- { \__diffcoeff_derivsep: }
- { \tl_put_left:Nn \l__diffcoeff_derivand_tl { \mskip 0 mu } }
- \tl_if_novalue:nF { #3 }
- { \l__diffcoeff_ldelim_tl \mskip \l__diffcoeff_elbowrm_muskip }
- \bool_if:NTF \l__diffcoeff_single_var_bool
+ \int_set:Nn \l__diffcoeff_style_int { #1 }
+ \tl_set:Nn \l__diffcoeff_frac_tl { \prg_do_nothing: }
+ \int_case:nn { #1 }
{
- \tl_set:Nx \l_tmpa_tl { \seq_use:Nn \l__diffcoeff_vars_seq { , } }
- \__diffcoeff_single:NNN \l__diffcoeff_tot_order_tl \l__diffcoeff_derivand_tl \l_tmpa_tl
- }
- {
- \int_zero:N \l_tmpa_int
- \seq_mapthread_function:NNN \l__diffcoeff_orders_seq
- \l__diffcoeff_vars_seq \__diffcoeff_map_orders:nn
- \__diffcoeff_mixed:NNN \l__diffcoeff_tot_order_tl
- \l__diffcoeff_derivand_tl \l__diffcoeff_denom_seq
- }
- \tl_if_novalue:nF { #3 }
- {
- \mskip \l__diffcoeff_elbowrm_muskip \l__diffcoeff_rdelim_tl
- \tl_if_empty:nF { #3 }
- {
- \c_math_subscript_token
- { \mskip \l__diffcoeff_subnudge_muskip { #3 } }
+ { 0 } { \tl_set:Nn \l__diffcoeff_frac_tl { \frac } }
+ { 1 } { \tl_set:Nn \l__diffcoeff_frac_tl { \tfrac } }
+ { 2 } { \tl_set:Nn \l__diffcoeff_frac_tl { \dfrac } }
+ { 3 } { \tl_set:Nn \l__diffcoeff_frac_tl { \difstfrac } }
+ { 4 } { \tl_set:Nn \l__diffcoeff_frac_tl { \difsafrac } }
+ { 5 } { \tl_set:Nn \l__diffcoeff_frac_tl { \difsbfrac[#2] } }
+ { 6 } { \tl_set:Nn \l__diffcoeff_frac_tl {} }
+ { 7 } { \bool_set_true:N \l__diffcoeff_dl_bool }
+ { 9 }
+ {
+ \msg_error:nnxx { diffcoeff } { unknown-style }
+ { \l__diffcoeff_instance_tl }
+ { \__diffcoeff_style_group:n { \l__diffcoeff_group_int } }
}
}
}
-%%%%%%%%%%%%%%%%%%%%
-\cs_new_protected:Npn \__diffcoeff_spaced:n #1
- {
- \int_case:nn { \int_sign:n { #1 } }
- {
- { 1 } { \bool_set_true:N \l__diffcoeff_spaced_bool }
- { 0 } { \bool_set_false:N \l__diffcoeff_spaced_bool }
- { -1 }
- {
- \int_compare:nNnTF { 1 } <
- { \tl_count:N \l__diffcoeff_derivand_tl }
- { \bool_set_true:N \l__diffcoeff_spaced_bool }
- { \bool_set_false:N \l__diffcoeff_spaced_bool }
- }
- }
- }
-\cs_new_protected:Npn \__diffcoeff_derivsep:
- {
- \tl_put_left:Nx \l__diffcoeff_derivand_tl
- {
- \int_case:nn { \l__diffcoeff_format_int }
- {
- { 0 } { \mskip \l__diffcoeff_derivsep_muskip }
- { 1 } { \mskip \l__diffcoeff_derivsepi_muskip }
- { 2 } { \mskip \l__diffcoeff_derivsepii_muskip }
- { 3 } { \mskip \l__diffcoeff_derivsepiii_muskip }
- { 4 } { \mskip \l__diffcoeff_derivsepiii_muskip }
- }
+% #1 group int; #2 style int
+\cs_new_protected:Npn \__diffcoeff_check_style:nn #1#2
+ {
+ \bool_if:nF
+ {
+ ( \int_compare_p:nNn { \int_div_truncate:nn {#2} {3} } = { #1 }
+ && \int_compare_p:nNn { #1 } < { 3 } ) % f,s,c
+ || ( \int_compare_p:nNn { \int_div_truncate:nn {#2} {2} } < { #1 }
+ && \int_compare_p:nNn { #1 } = { 3 } ) % j
+ || \int_compare_p:nNn { #1 + #2 } = { 11 } % l
}
- }
-\cs_new:Npn \__diffcoeff_wrap_longvars_dv:nn #1#2
- { \l__diffcoeff_op_alt_tl { {}#2 }^{ #1 } }
-\cs_new:Npn \__diffcoeff_wrap_longvars_dvi:nn #1#2
- { \l__diffcoeff_op_alt_tl { {}(#2) }^{ #1 } }
-\cs_new:Npn \__diffcoeff_wrap_longvars_dvii:nn #1#2
- { (\l__diffcoeff_op_alt_tl { {}#2) }^{ #1 } }
-% (ptl) form denom #1 from orders seq & #2 from vars seq
-\cs_new_protected:Npn \__diffcoeff_map_orders:nn #1#2
- {
- \tl_if_eq:nnTF { #1 } { 1 }
- { \seq_put_right:Nn \l__diffcoeff_denom_seq { \l__diffcoeff_op_alt_tl { #2 } } }
{
- \int_compare:nNnTF { \tl_count:n { #2 } } = { 1 }
+ \msg_warning:nnxx { diffcoeff } { wrong-style }
+ { \l__diffcoeff_instance_tl }
+ { \__diffcoeff_style_group:n { #1 } }
+ \int_compare:nNnTF { #1 } = { 3 }
+ { \__diffcoeff_style:nn { 0 } {} }
{
- \seq_put_right:Nn \l__diffcoeff_denom_seq
- { \l__diffcoeff_op_alt_tl { #2 }^{ #1 } }
+ \int_compare:nNnTF { #1 } = { 4 }
+ { \__diffcoeff_style:nn { 7 } {} }
+ { \__diffcoeff_style:nn { 3*#1 } {} }
}
- {
- \seq_put_right:Nn \l__diffcoeff_denom_seq
- { \__diffcoeff_wrap_longvars:nn { #1\vphantom{)} } { #2 } }
- }
}
+ \bool_if:nT
+ { \int_compare_p:nNn { #1 } > { 0 } && \int_if_even_p:n { #1 } }
+ { \tl_set_eq:NN \l__diffcoeff_opii_tl \l__diffcoeff_opi_tl }
+ \int_compare:nNnF { #1 } = { 1 }
+ { \bool_set_false:N \l__diffcoeff_innerwrap_bool }
}
-% #1 order(tlvar) ; #2 diff'iand(tlvar); #3 denom(tlvar)
-\cs_new:Npn \__diffcoeff_single:NNN #1#2#3
- {
- \__diffcoeff_numer:N { #1 }
- \__diffcoeff_form_deriv:NNn
- \l__diffcoeff_oporder_tl
- \l__diffcoeff_derivand_tl
- { \__diffcoeff_denom_single:NN #1 #3 }
- }
-% #1 total order; #2 derivand; #3 denom seq
-\cs_new_protected:Npn \__diffcoeff_mixed:NNN #1#2#3
+\cs_new:Npn \__diffcoeff_style_group:n #1
+ { \clist_item:nn { frac, /, _, frac, dl } { #1 + 1 } }
+\cs_new:Npn \__diffcoeff_style_aux:n #1
{
- \__diffcoeff_numer:N #1
- \__diffcoeff_form_deriv:NNn
- \l__diffcoeff_oporder_tl
- \l__diffcoeff_derivand_tl
- { \__diffcoeff_denom_sep:N #3 }
+ \int_compare:nNnTF { #1 } = { 3 } { { 0 } {} }
+ {
+ \int_compare:nNnTF { #1 } = { 4 } { { 7 } {} }
+ { { 3*#1 } {} }
+ }
}
-\cs_new:Npn \__diffcoeff_denom_sep:N #1
+%%%%%%%%% append? (& wrap slash diff operator?)
+\cs_new_protected:Npn \__diffcoeff_append:n #1
{
- \int_zero:N \l_tmpa_int
- \seq_map_inline:Nn #1
- {
- \int_incr:N \l_tmpa_int ##1
- \int_compare:nNnT { \l_tmpa_int } < { \l__diffcoeff_vars_int }
- {
- \seq_pop:NN \l__diffcoeff_orders_seq \l_tmpa_tl
- \str_if_eq:VnTF \l_tmpa_tl { 1 }
- { \mskip \l__diffcoeff_varsep_muskip }
- {
- \mskip \muskip_eval:n { \l__diffcoeff_varsep_muskip +
- \l__diffcoeff_sep_adj_muskip }
- }
- }
+ \bool_if:nTF
+ { #1 || \int_compare_p:nNn { \l__diffcoeff_group_int } = {2} }
+ {
+ \bool_set_true:N \l__diffcoeff_append_bool
+ \bool_if:NT \l__diffcoeff_innerwrap_bool
+ { \tl_put_right:Nn \l__diffcoeff_frac_tl { * } }
}
+ { \bool_set_false:N \l__diffcoeff_append_bool }
}
-% #1(tl) total order
-\cs_new_protected:Npn \__diffcoeff_numer:N #1
- {
- \bool_if:NTF \l__diffcoeff_op_left_bool
+%%%%%%%%%
+% #1(int) no. of vars; #2(clist) orders spec
+\cs_new_protected:Npn \__diffcoeff_orders:nn #1#2
+ {
+ \bool_if:NTF \l__diffcoeff_exponent_bool
{
- \tl_set:Nn \l__diffcoeff_oporder_tl
- { \mskip \l__diffcoeff_opnudge_muskip }
+ \exp_args:NNx \seq_set_from_clist:Nn \l__diffcoeff_ords_seq
+ { \prg_replicate:nn { #1 } { \l__diffcoeff_exponent_tl, } }
}
- { \tl_clear:N \l__diffcoeff_oporder_tl }
- \tl_put_right:No \l__diffcoeff_oporder_tl \l__diffcoeff_op_tl
- \exp_args:NnV \tl_if_eq:nnF { 1 } #1
- {
- \tl_put_right:Nn \l__diffcoeff_oporder_tl
- { \mskip \l__diffcoeff_oporder_muskip ^ { #1 } }
- }
- \bool_if:NT \l__diffcoeff_op_left_bool
- { \tl_put_right:Nn \l__diffcoeff_oporder_tl { \hfill } }
- }
-% #1 order; #2 var
-\cs_new_protected:Npn \__diffcoeff_denom_single:NN #1#2
- {
- \tl_if_eq:nVTF { 1 } #1
- { \l__diffcoeff_op_alt_tl {}#2 }
{
- \int_compare:nNnTF { \tl_count:N #2 } = { 1 }
- { \l__diffcoeff_op_alt_tl {}#2^{ #1 } }
- { \__diffcoeff_wrap_longvars:nn { #1\vphantom) } { #2 } }
+ \seq_set_from_clist:Nn \l__diffcoeff_ords_seq { #2 }
+ \exp_args:Nnx\__diffcoeff_adj_ords_seq:nn { #1 }
+ { \seq_count:N \l__diffcoeff_ords_seq }
}
+ \tl_set:Nx \l__diffcoeff_vph_tl {\seq_use:Nn\l__diffcoeff_ords_seq {} }
}
-% #1 op+order; #2 diff'iand; #3 denom
-% 0 frac; 1 frac append; 2 slash ; 3 ( slash ) append; 4 slash append
-\cs_new:Npn \__diffcoeff_form_deriv:NNn #1#2#3
+\cs_new_protected:Npn \__diffcoeff_adj_ords_seq:nn #1#2
{
- \int_case:nn { \l__diffcoeff_format_int }
- {
- { 0 } { \frac { #1 #2 } { #3 } }
- { 1 } { \frac { #1 } { #3 } #2 }
- { 2 } { #1 #2 / #3 }
- { 3 } { ( #1 / #3 ) #2 }
- { 4 } { #1 / #3 #2 }
+ \int_compare:nNnTF { #1 } < { #2 }
+ { % truncate
+ \int_step_inline:nn { #2 - #1 }
+ { \seq_pop_right:NN \l__diffcoeff_ords_seq \l_tmpa_tl }
}
+ { % pad
+ \int_step_inline:nnnn { 1 + #2 } { 1 } { #1 }
+ { \seq_put_right:Nn \l__diffcoeff_ords_seq { 1 } }
+ }
}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% differential
-% #1 variant; #2 = space in mu before d (0--9)
-% note \group_end placement for \vec{x} etc
-\NewDocumentCommand \dl { d.. t- m }
+\cs_new_protected:Npn \__diffcoeff_override:N #1
{
- \group_begin:
- \bool_set_true:N \l__diffcoeff_integ_bool
- \bool_set_true:N \l__diffcoeff_single_var_bool
- \seq_set_from_clist:Nn \l__diffcoeff_orders_seq { 1 }
- \tl_set:Nn \l__diffcoeff_tot_order_tl { 1 }
- \IfValueTF { #1 }
- { \tl_set:Nn \l__diffcoeff_type_tl { .#1 } }
- { \tl_set:Nn \l__diffcoeff_type_tl { } }
- \UseInstance { derivative } { ord\l__diffcoeff_type_tl }
- \l__diffcoeff_orders_seq \l__diffcoeff_tot_order_tl
- \c_empty_tl \c_empty_seq \c_empty_tl
- \tl_if_in:NnTF \c__diffcoeff_digits_tl { #3 }
- { \mskip \IfBooleanT #2 { - }#3 mu \l__diffcoeff_op_tl \group_end: }
- { \l__diffcoeff_op_tl \group_end: {} #3 }
- }
-\NewDocumentCommand \negmu {} { \mskip -1 mu }
-\NewDocumentCommand \nilmu {} { \mskip 0 mu }
-\NewDocumentCommand \onemu {} { \mskip 1 mu }
-\NewDocumentCommand \twomu {} { \mskip 2 mu }
-% derivative
-% #1(tl) = name of variant; #2(*)= append diff'iand boolean
-% #3(clist) = orders of diff. in each var.; #4(tl) = order override
-% #5(bool) spacing switch; #6(tl) = diff'iand; #7( / ) = slash boolean
-% #8(clist) = vars of diff.; #9(tl) = pt of eval./vars held const
-\NewDocumentCommand \diff { d.. s O{1} o t! >{\TrimSpaces} m t/ m !o }
- {
- \group_begin:
- \IfBooleanTF #5
- { \bool_set_true:N \l__diffcoeff_altsep_bool }
- { \bool_set_false:N \l__diffcoeff_altsep_bool }
- \seq_set_from_clist:Nn \l__diffcoeff_orders_seq { #3 }
- \int_set:Nn \l_tmpb_int { \seq_count:N \l__diffcoeff_orders_seq }
- \int_set:Nn \l__diffcoeff_vars_int { \clist_count:n { #8 } }
- \int_compare:nNnTF { \l__diffcoeff_vars_int } = { 1 }
- { \bool_set_true:N \l__diffcoeff_single_var_bool }
- {
- \int_compare:nNnTF { \l__diffcoeff_vars_int } < { \l_tmpb_int }
- {
- \msg_error:nnxxxx { diffcoeff } { numbers-conflict }
- { \int_use:N \l__diffcoeff_vars_int } { \int_use:N \l_tmpb_int }
- { \seq_use:Nn \l__diffcoeff_orders_seq { , } }
- { \clist_use:nn { #8 } { , } }
- }
- { % pad orders seq if nec.
- \int_step_inline:nnnn
- { 1 + \l_tmpb_int } { 1 } { \l__diffcoeff_vars_int }
- { \seq_put_right:Nn \l__diffcoeff_orders_seq { 1 } }
- }
- }
- % override/calc total order
- \IfValueTF { #4 }
- { \tl_set:Nn \l__diffcoeff_tot_order_tl { #4 } }
+ \tl_if_empty:NTF { #1 }
{
- \bool_if:NTF \l__diffcoeff_single_var_bool
- { \tl_set:Nn \l__diffcoeff_tot_order_tl { #3 } }
- {
- \__diffcoeff_calc_tot_order:NN \l__diffcoeff_orders_seq
- \l__diffcoeff_tot_order_tl
- }
+ \__diffcoeff_calc_tot_order:NN \l__diffcoeff_ords_seq
+ \l__diffcoeff_tot_ord_tl
}
- \IfValueTF { #1 }
- { \tl_set:Nn \l__diffcoeff_type_tl { .#1 } }
- { \tl_set:Nn \l__diffcoeff_type_tl { } }
- % append? slash?
- \int_zero:N \l__diffcoeff_format_int
- \IfBooleanT #2 { \int_incr:N \l__diffcoeff_format_int }
- \IfBooleanT #7 { \int_add:Nn \l__diffcoeff_format_int { 2 } }
- \UseInstance { derivative } { ord\l__diffcoeff_type_tl } {#6}{#8}{#9}
- \group_end:
- } % end of \diff
-%%%%%%%%%%%%%%%%%%%
-% #2(seq) expr in; #1(tlv) expr out
-\cs_new:Npn \__diffcoeff_calc_tot_order:NN #1 #2
+ { \tl_set:Nn \l__diffcoeff_tot_ord_tl { #1 } }
+ \seq_pop_right:NN \l__diffcoeff_ords_seq \l__diffcoeff_ord_tl
+ }
+%%%%%%%%%% calc. total order %%%%%%%%%%
+% #1(seq) expr in; #2(tl) expr out
+\cs_new_protected:Npn \__diffcoeff_calc_tot_order:NN #1 #2
{
\tl_clear:N \l__diffcoeff_nos_tl
- \exp_args:Nx\__diffcoeff_digest_expr:n { \seq_use:Nn #1 { + } }
+ \exp_args:Nx \__diffcoeff_digest_expr:n { \seq_use:Nn #1 { + } }
\prop_if_empty:NTF \l__diffcoeff_vars_prop
{ \tl_set:NV #2 \l__diffcoeff_nos_tl }
- { \__diffcoeff_evaluate:NN \l__diffcoeff_vars_prop #2 }
+ {
+ \int_compare:nNnT { \l__diffcoeff_nos_int } = { 0 }
+ { \tl_clear:N \l__diffcoeff_nos_tl }
+ \__diffcoeff_evaluate:NN \l__diffcoeff_vars_prop #2
+ }
}
-\cs_new:Npn \__diffcoeff_digest_expr:n #1
- {
+\cs_new_protected:Npn \__diffcoeff_digest_expr:n #1
+ {
\tl_set:Nn \l__diffcoeff_curr_num_tl { + }
\tl_set:Nn \l__diffcoeff_paren_tl { +1 }
\tl_set:Nn \l__diffcoeff_nos_tl { 0 }
@@ -419,13 +343,11 @@
}
\int_set:Nn \l__diffcoeff_nos_int { \l__diffcoeff_nos_tl }
\tl_set:Nx \l__diffcoeff_nos_tl { \int_use:N \l__diffcoeff_nos_int }
- \int_compare:nNnT { \l__diffcoeff_nos_int } = { 0 }
- { \tl_clear:N \l__diffcoeff_nos_tl }
}
% #1 curr tok (tl); #2 <== curr tok ndx (int)
\cs_new_protected:Npn \__diffcoeff_get_curr_ndx:nN #1#2
{
- \tl_if_in:NnTF \c__diffcoeff_digits_tl { #1 }
+ \tl_if_in:nnTF { 1234567890 } { #1 }
{ \int_set:Nn #2 { 1 } } % digit
{
\str_case:nnF { #1 }
@@ -461,7 +383,7 @@
{
{ 0 } % tok = s
{
- \tl_if_eq:nVTF { #1 } \l__diffcoeff_curr_num_tl
+ \str_if_eq:nVTF { #1 } \l__diffcoeff_curr_num_tl
{ \tl_set:Nn \l__diffcoeff_curr_num_tl { + } }
{ \tl_set:Nn \l__diffcoeff_curr_num_tl { - } }
}
@@ -497,11 +419,11 @@
{ 1 } % tok = d
{ \tl_put_right:Nn \l__diffcoeff_curr_num_tl { #1 } }
{ 2 } % tok = v
- {
- \tl_if_in:nnTF { ^ \times * / \div } { #1 }
- {
- \msg_error:nnxxx { diffcoeff } { order-specification }
- { \seq_use:Nn \l__diffcoeff_orders_seq { , } }
+ {
+ \tl_if_in:nnTF { ^ \times * / } { #1 }
+ {
+ \msg_error:nnxxx { diffcoeff } { order-spec-general }
+ { \seq_use:Nn \l__diffcoeff_ords_seq { , } }
{ #1 } { number }
}
{ \tl_set:Nn \l__diffcoeff_curr_var_tl { #1 } }
@@ -511,7 +433,7 @@
\seq_push:NV \l__diffcoeff_paren_seq \l__diffcoeff_paren_tl
\tl_put_left:Nn \l__diffcoeff_paren_tl { * }
\tl_put_left:NV \l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
- \tl_set:Nn \l__diffcoeff_curr_num_tl { + }
+ \tl_set:Nn \l__diffcoeff_curr_num_tl { + }
\int_set:Nn #3 { 0 }
}
{ 4 } % tok = )
@@ -584,8 +506,8 @@
\int_set_eq:NN #2 #3
}
{
- \msg_error:nnxxx { diffcoeff } { order-specification }
- { \seq_use:Nn \l__diffcoeff_orders_seq { , } } { #1 } { ) }
+ \msg_error:nnxxx { diffcoeff } { order-spec-general }
+ { \seq_use:Nn \l__diffcoeff_ords_seq { , } } { #1 } { ) }
}
}
% #1 is var. (tlvar); #2 is num. (tlvar); #3 num. coeff. (tlvar)
@@ -598,7 +520,7 @@
}
% #1 (propv) key=var, val=coeff; #2 <= total order
\cs_new_protected:Npn \__diffcoeff_evaluate:NN #1#2
- {
+ {
\prop_map_inline:Nn #1 { \seq_put_left:Nn \l_tmpa_seq { ##1 } }
\seq_sort:Nn \l_tmpa_seq
{
@@ -610,15 +532,17 @@
\prop_pop:NnN #1 { ##1 } \l_tmpb_tl
\seq_put_right:Nx \l_tmpb_seq { \int_eval:n \l_tmpb_tl }
}
- \tl_clear:N \l_tmpa_tl
- \seq_mapthread_function:NNN \l_tmpa_seq \l_tmpb_seq
- \__diffcoeff_tot_order:nn
+ \tl_set:Nx \l_tmpa_tl
+ {
+ \seq_mapthread_function:NNN \l_tmpa_seq \l_tmpb_seq
+ \__diffcoeff_tot_order:nn
+ }
\exp_args:NV \tl_if_head_eq_charcode:nNTF \l_tmpa_tl +
{
\tl_set:Nx \l_tmpb_tl { \tl_tail:N \l_tmpa_tl }
\int_compare:nNnT { \l__diffcoeff_nos_int } > { 0 }
{ \tl_put_left:Nn \l__diffcoeff_nos_tl { + } }
- \tl_concat:NNN #2 \l_tmpb_tl \l__diffcoeff_nos_tl
+ \tl_concat:NNN #2 \l_tmpb_tl \l__diffcoeff_nos_tl
}
{
\int_compare:nNnTF { \l__diffcoeff_nos_int } > { 0 }
@@ -630,116 +554,367 @@
\cs_new:Npn \__diffcoeff_tot_order:nn #1#2
{
\int_compare:nNnTF { #2 } > { 0 }
+ { \int_compare:nNnTF { #2 } = { 1 } { +#1 } { +#2#1 } }
+ {
+ \int_compare:nNnT { #2 } < { 0 }
+ { \int_compare:nNnTF { #2 } = { -1 } { -#1 } { #2#1 } }
+ }
+ }
+%%%%%%%%% derivand
+\cs_new_protected:Npn \__diffcoeff_derivand:n #1
+ {
+ \tl_set:Nn \l__diffcoeff_derivand_tl { #1 }
+ \int_compare:nNnTF { \tl_count:N \l__diffcoeff_derivand_tl } > { 1 }
+ { \bool_set_true:N \l__diffcoeff_multitok_bool }
{
- \int_compare:nNnTF { #2 } = { 1 }
- { \tl_put_left:Nn \l_tmpa_tl { +#1 } }
- { \tl_put_left:Nn \l_tmpa_tl { +#2#1 } }
+ \str_if_eq:VnTF \l__diffcoeff_derivand_tl { ! }
+ { \msg_error:nnnn { diffcoeff } { version-conflict } { #1 } {} }
+ {
+ \str_if_eq:VnT \l__diffcoeff_derivand_tl { [ }
+ { \msg_error:nnnn { diffcoeff } { version-conflict } { the~
+ order-override~argument } { Use~\difoverride instead.~ } }
+ }
}
+ }
+%%%%%%%%% build #1 vars clist; #2 trailing arg
+\cs_new_protected:Npn \__diffcoeff_build:nn #1#2
+ {
+ \str_if_eq:nnT { #1 } { / }
+ {
+ \msg_error:nnnn { diffcoeff } { version-conflict } { / }
+ { Use~\difs or~\difsp instead.~ }
+ }
+ \seq_set_from_clist:Nn \l__diffcoeff_vars_seq { #1 }
+ \seq_pop_right:NN \l__diffcoeff_vars_seq \l__diffcoeff_var_tl
+ \tl_put_left:Nx \l__diffcoeff_derivand_tl
+ { \__diffcoeff_spaced:n { \l__diffcoeff_spaced_int } }
+ \tl_if_novalue:nF { #2 }
+ { \__diffcoeff_delim:N l \mskip \l__diffcoeff_elbowrm_tl }
+ \__diffcoeff_form_deriv:xNN
+ { \__diffcoeff_build_numer:Vn \l__diffcoeff_tot_ord_tl
+ { \l__diffcoeff_style_int } }
+ \__diffcoeff_build_denom:
+ \l__diffcoeff_derivand_tl
+ \tl_if_novalue:nF { #2 }
+ { \__diffcoeff_trailing_arg:n { #2 } }
+ }
+\cs_new:Npn \__diffcoeff_delim:N #1
+ {
+ \bool_if:nTF { \l__diffcoeff_innerwrap_bool && \l__diffcoeff_append_bool }
+ { \use:c { l__diffcoeff_#1 delimapp_tl } }
+ { \use:c { l__diffcoeff_#1 delim_tl } }
+ }
+\cs_new:Npn \__diffcoeff_subnudge:
+ {
+ \bool_if:nTF { \l__diffcoeff_innerwrap_bool && \l__diffcoeff_append_bool }
+ { \l__diffcoeff_subnudgeapp_tl } { \l__diffcoeff_subnudge_tl }
+ }
+\cs_new:Npn \__diffcoeff_trailing_arg:n #1
+ {
+ \mskip \l__diffcoeff_elbowrm_tl \__diffcoeff_delim:N r
+ \tl_if_empty:nF { #1 }
+ { \c_math_subscript_token { \mskip \__diffcoeff_subnudge: #1 } }
+ }
+\cs_new:Npn \__diffcoeff_spaced:n #1
+ {
+ \int_case:nn { \int_sign:n { #1 } }
{
- \int_compare:nNnT { #2 } < { 0 }
- {
- \int_compare:nNnTF { #2 } = { -1 }
- { \tl_put_right:Nn \l_tmpa_tl { -#1 } }
- { \tl_put_right:Nn \l_tmpa_tl { #2#1 } }
+ { 1 } { \__diffcoeff_derivsep: }
+ { 0 } { \mskip 0 mu }
+ {-1 }
+ {
+ \bool_lazy_or:nnT { \l__diffcoeff_multitok_bool }
+ { \int_compare_p:nNn { \l__diffcoeff_group_int } = { 2 } }
+ { \__diffcoeff_derivsep: }
}
+ }
+ }
+\cs_new:Npn \__diffcoeff_derivsep:
+ {
+ \bool_if:NTF \l__diffcoeff_append_bool
+ { \mskip \l__diffcoeff_derivsepi_tl }
+ { \mskip \l__diffcoeff_derivsep_tl }
+ }
+%%%%%%%%% numerator #1 total order tl #2 style int
+\cs_new:Npn \__diffcoeff_build_numer:nn #1#2
+ {
+ \int_compare:nNnF { #2 } > { 5 }
+ {
+ \bool_if:NT \l__diffcoeff_op_left_bool
+ { \mskip \l__diffcoeff_opleftnudge_tl }
+ \exp_not:o \l__diffcoeff_opi_tl
+ \str_if_eq:nnF {#1} {1}
+ { ^ { \mskip \l__diffcoeff_opordsep_tl \exp_not:o {#1} } }
+ \bool_if:NT \l__diffcoeff_op_left_bool
+ { \exp_not:o { \hfill } }
}
+ }
+\cs_generate_variant:Nn \__diffcoeff_build_numer:nn { V }
+%%%%%%%%%% denominator %%%%%%%%%
+\cs_new:Npn \__diffcoeff_build_denom:
+ {
+ \seq_mapthread_function:NNN \l__diffcoeff_ords_seq
+ \l__diffcoeff_vars_seq \__diffcoeff_build_denom_items:nn
+ \__diffcoeff_build_denom_item:VV \l__diffcoeff_ord_tl \l__diffcoeff_var_tl
+ \str_if_eq:VnF \l__diffcoeff_ord_tl { 1 }
+ {
+ \int_compare:nNnT { \l__diffcoeff_group_int } < { 2 }
+ { \mskip -\l__diffcoeff_sep_adj_tl}
+ }
}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% create new instances or edit existing ones
-% #1 = name; #2 = key-value list
-\NewDocumentCommand \diffdef { > { \TrimSpaces } m m }
+\cs_new:Npn \__diffcoeff_build_denom_items:nn#1#2
{
- \tl_if_empty:nTF { #1 }
+ \__diffcoeff_build_denom_item:nn {#1} {#2}
+ \mskip \l__diffcoeff_termsep_tl
+ }
+% #1 order #2 var
+\cs_new:Npn \__diffcoeff_build_denom_item:nn #1#2
+ {
+ \int_compare:nNnTF { \l__diffcoeff_style_int } = { 6 }
+ { \__diffcoeff_build_denom_difc:onn \l__diffcoeff_vph_tl {#1}{#2} }
+ { \__diffcoeff_build_denom_dif:nn {#1} {#2} }
+ }
+\cs_generate_variant:Nn \__diffcoeff_build_denom_item:nn { VV }
+% #1 vphantom orders #2 order #3 var
+\cs_new:Npn \__diffcoeff_build_denom_difc:nnn #1#2#3
+ {
+ \exp_not:o \l__diffcoeff_opii_tl \c_math_subscript_token
+ { \mskip \l__diffcoeff_opsubnudge_tl {}#3 } ^
+ {
+ \mskip \l__diffcoeff_opordsep_tl \exp_not:o { \vphantom{#1} }
+ \str_if_eq:nnF { #2 } { 1 }
+ { \exp_not:o {#2} \mskip \l__diffcoeff_sep_adj_tl }
+ }
+ }
+\cs_generate_variant:Nn \__diffcoeff_build_denom_difc:nnn { o }
+% #1 order #2 var
+\cs_new:Npn \__diffcoeff_build_denom_dif:nn #1#2
+ {
+ \str_if_eq:nnTF { #1 } { 1 }
+ { \exp_not:o { \l__diffcoeff_opii_tl #2 } }
{
- \EditTemplateDefaults { derivative }
- { DERIV } { #2 }
- \EditInstance { derivative } { ord } { #2 }
+ \int_compare:nNnTF { \tl_count:n { #2 } } = { 1 }
+ { \exp_not:o { \l__diffcoeff_opii_tl {}#2^
+ { \mskip \l__diffcoeff_varsupnudge_tl #1 } } }
+ { \__diffcoeff_wrap_longvars:nn { #1 } { #2 } }
+ \mskip \l__diffcoeff_sep_adj_tl
}
+ }
+\cs_new:Npn \__diffcoeff_wrap_longvars_dv:nn #1#2
+ { \exp_not:o { \l__diffcoeff_opii_tl {{}#2 }^
+ { \mskip \l__diffcoeff_varsupnudge_tl #1 } } }
+\cs_new:Npn \__diffcoeff_wrap_longvars_dvi:nn #1#2
+ {
+ \exp_not:o { \l__diffcoeff_opii_tl \l__diffcoeff_lvw_ldelim_tl #2
+ \l__diffcoeff_lvw_rdelim_tl^{ \mskip \l__diffcoeff_lvsupnudge_tl #1 } }
+ }
+\cs_new:Npn \__diffcoeff_wrap_longvars_dvii:nn #1#2
+ {
+ \exp_not:o { \l__diffcoeff_lvw_ldelim_tl \l__diffcoeff_opii_tl {}#2
+ \l__diffcoeff_lvw_rdelim_tl^{ \mskip \l__diffcoeff_lvsupnudge_tl #1 } }
+ }
+%%%%%%%%%%
+% #1 op+order; #2 denom; #3 diff'iand
+\cs_new:Npn \__diffcoeff_form_deriv:nNN #1#2#3
+ {
+ \bool_if:NTF \l__diffcoeff_append_bool
+ { \l__diffcoeff_frac_tl { #1 } { #2 } #3 }
+ { \l__diffcoeff_frac_tl { #1 #3 } { #2 } }
+ }
+\cs_generate_variant:Nn \__diffcoeff_form_deriv:nNN { x }
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\file_get:nnNT { diffcoeff.DIF } {} \l_tmpa_tl
+ { \exp_args:Nnno \EditTemplateDefaults { diffcoeff } { DIF } \l_tmpa_tl }
+\exp_args:Nnno \EditTemplateDefaults { diffcoeff } { DIF }
+ \l__diffcoeff_dif_clist
+% Child template with some restricted, some new defaults.
+% #1 object type #2 parent template #3 child template
+% #4 restricted defaults (key=value) #5 new defaults (key=value)
+\NewDocumentCommand \DeclareChildTemplate { m m m m m }
+ {
+ \DeclareRestrictedTemplate {#1} {#2} {#3} {}
+ \EditTemplateDefaults {#1} {#3} {#5}
+ \DeclareRestrictedTemplate {#1} {#3} {#3} {#4}
+ }
+% create new, edit existing templates/instances;
+% #1 edit defaults with (no *) or without (*) inheritance;
+% #2 id: f,s,c,fp, sp, cp, j,l; #3 name; #4 key-value list
+\NewDocumentCommand \difdef { >{ \TrimSpaces } m >{ \TrimSpaces } m m }
+ {
+ \clist_map_inline:nn { #1 }
{
- \IfInstanceExistTF { derivative } { ord.#1 }
- { \EditInstance { derivative } { ord.#1 } { #2 } }
+ \tl_if_empty:nTF { #2 }
{
- \DeclareInstance { derivative } { ord.#1 }
- { DERIV } { #2 }
+ \DeclareChildTemplate { diffcoeff }
+ { DIF\str_uppercase:n {##1} } { DIF\str_uppercase:n {##1} }
+ { style-group = \use_i:nn ##1 \c_empty_tl } { #3 }
+ \DeclareInstance { diffcoeff } { dif##1 }
+ { DIF\str_uppercase:n {##1} } {}
}
+ {
+ \IfInstanceExistTF { diffcoeff } { dif##1.#2 }
+ { \EditInstance { diffcoeff } { dif##1.#2 } { #3 } }
+ { \exp_args:Nnnx
+ \DeclareInstance { diffcoeff } { dif##1.#2 }
+ { DIF\str_uppercase:n {##1} } { #3 }
+ }
+ }
}
}
-% relic from version 1
-\NewDocumentCommand \diffset { o }
- { \msg_warning:nn { diffcoeff } { obsolete } }
-
-% ordinary & D
-\DeclareInstance { derivative } { ord } { DERIV } { }
-\bool_if:NTF \l__diffcoeff_ISO_bool
+\DeclareDocumentCommand \diffdef { m m }
+ {
+ \msg_error:nnnn { diffcoeff } { version-conflict } { \diffdef~(two~
+ arguments) } { Use~\difdef~(three~arguments)~instead.~ }
+ }
+\DeclareChildTemplate { diffcoeff } { DIF } { DIFF }
+ { style-group = f } {}
+\DeclareChildTemplate { diffcoeff } { DIFF } { DIFFP }
+ { style-group = f }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu,
+ *italic-nudge = 3 mu
+ }
+\DeclareChildTemplate { diffcoeff } { DIF } { DIFS }
+ { style-group = s }
{
- \diffdef { }
- {
- op-symbol = \mathrm{d},
- op-order-sep = 0 mu ,
- left-delim = \left ( ,
- right-delim = \right ) ,
- subscr-nudge = -6 mu
- }
- \diffdef { D } { op-symbol = \mathrm{D} }
+ style = /,
+ derivand-sep = 2 mu plus 1 mu minus 2 mu,
+ outer-Ldelim = (,
+ outer-Rdelim = ),
+ sub-nudge = 0 mu,
+ *inner-wrap = true
}
- { \diffdef { D } { op-symbol = D } }
-
-% partial
-\diffdef { p }
+\DeclareChildTemplate { diffcoeff } { DIFS } { DIFSP }
+ { style-group = s }
{
- op-symbol = \partial ,
- left-delim = \left ( ,
- right-delim = \right ) ,
- subscr-nudge = -6 mu
+ op-symbol = \partial,
+ op-order-nudge = 1 mu
}
-\NewDocumentCommand \diffp {} { \diff.p. }
-\NewDocumentCommand \dlp {} { \dl.p. }
-
-% delta
-\diffdef { delta }
- {
- op-symbol = \delta ,
- op-order-sep = 0 mu
+\DeclareChildTemplate { diffcoeff } { DIF } { DIFC }
+ { style-group = c }
+ {
+ style = _ ,
+ derivand-sep = 1 mu plus 1 mu minus 1 mu ,
+ multi-term-sep = 1 mu ,
+ term-sep-adjust = 0 mu ,
+ outer-Ldelim = \bigl (,
+ outer-Rdelim = \bigr ),
+ sub-nudge = -2 mu
}
-\diffdef { Delta }
+\DeclareChildTemplate { diffcoeff } { DIFC } { DIFCP }
+ { style-group = c }
+ {
+ op-symbol = \partial,
+ op-order-nudge = 1 mu
+ }
+\DeclareInstance { diffcoeff } { diff } { DIFF } {}
+\DeclareInstance { diffcoeff } { diffp } { DIFFP } {}
+\DeclareInstance { diffcoeff } { difs } { DIFS } {}
+\DeclareInstance { diffcoeff } { difsp } { DIFSP } {}
+\DeclareInstance { diffcoeff } { difc } { DIFC } {}
+\DeclareInstance { diffcoeff } { difcp } { DIFCP } {}
+% jacobian
+\DeclareChildTemplate { diffcoeff } { DIF } { DIFJ }
+ { style-group = j }
{
- op-symbol = \Delta ,
- op-order-sep = 0 mu
+ op-symbol = \partial,
+ outer-Ldelim = ,
+ outer-Rdelim =
}
-% for compatibility with version 1
-\NewDocumentCommand \Diff { } { \diff.D. }
-\NewDocumentCommand \diffd { } { \diff.delta. }
-\NewDocumentCommand \Diffd { } { \diff.Delta. }
+\DeclareInstance { diffcoeff } { difj } { DIFJ } {}
+% differential
+\DeclareChildTemplate { diffcoeff } { DIF } { DIFL }
+ { style-group = l }
+ {
+ style = dl ,
+ derivand-sep = 0 mu,
+ long-var-wrap = dv ,
+ outer-Ldelim = {\,},
+ outer-Rdelim =
+ }
+\DeclareInstance { diffcoeff } { difl } { DIFL } {}
-% user-defined
-\file_if_exist:nT { \g__diffcoeff_def_tl.def }
+\file_if_exist:nTF { \g__diffcoeff_def_tl.def }
{ \file_input:n { \g__diffcoeff_def_tl.def } }
-%%%%%%%%%%%%%%%%%%%%
-% Jacobian
-\NewDocumentCommand \jacob { m t/ m }
- {
- \group_begin:
- \IfBooleanTF #2
- { \partial(#1) / \partial(#3) }
- { \frac{ \partial(#1) } { \partial(#3) } }
- \group_end:
+ {
+ \tl_if_empty:NF \g__diffcoeff_def_tl
+ { \msg_note:nnx { diffcoeff } { file-not-found }
+ { \g__diffcoeff_def_tl } }
}
-%%%%%%%%%%%%%%%%%%%%
-% messages
-\msg_new:nnn { diffcoeff } { order-specification }
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\NewDocumentCommand \negmu {} { \mskip -1 mu }
+\NewDocumentCommand \nilmu {} { \mskip 0 mu }
+\NewDocumentCommand \onemu {} { \mskip 1 mu }
+\NewDocumentCommand \twomu {} { \mskip 2 mu }
+\NewDocumentCommand \difstfrac { s m m }
+ { \__diffcoeff_slashfracs:Nnnn #1 { #2 } { #3 } {} }
+\NewDocumentCommand \difsbfrac { o s m m }
+ { \__diffcoeff_slashfracs:Nnnn #2 { #3 } { #4 } { \use:c{#1} } }
+\NewDocumentCommand \difsafrac { s m m }
+ { \__diffcoeff_slashfracs:Nnnn #1 { \left. #2\vphantom{#3} }
+ { #3\right.} { \middle } }
+\cs_new:Npn \__diffcoeff_slashfracs:Nnnn #1#2#3#4
{
- #3~followed~by~#2~in~the~order~specification~[#1]~\msg_line_context:.~
- Diffcoeff~cannot~calculate~the~overall~order~of~differentiation~in~
- this~case.~Use~the~order-override~option~to~enter~the~overall~order.
+ \bool_if:NT #1 { \l__diffcoeff_lopwrap_tl }
+ #2 \mskip \l__diffcoeff_slashsep_tl
+ #4 \l__diffcoeff_slashtok_tl
+ \mskip \l__diffcoeff_slashsep_tl #3
+ \bool_if:NT #1 { \l__diffcoeff_ropwrap_tl }
}
-\msg_new:nnn { diffcoeff } { obsolete }
- {
- Obsolete~command:~\diffset is~superseded~by~the~\diffdef\
- command.~\msg_see_documentation_text:n { diffcoeff }
+% derivatives
+% #1(tl) variant name; #2(*) append boolean; #3(*) switch #5#6 order;
+% #4(clist) diff. orders; #5(tl) = derivand; #6(clist) = diff. vars;
+% #7(tl) = pt of eval./vars held const
+\clist_map_inline:nn { f,s,c, fp, sp, cp }
+ {
+ \exp_args:Nc \NewDocumentCommand {dif#1}
+ { >{\TrimSpaces} D..{} s s O{1} >{\TrimSpaces} m m !o }
+ {
+ \IfBooleanTF ##3
+ { \__diffcoeff_inputs:nnnnnnn {#1}
+ {##1} {##2} {##4} {##6} {##5} {##7} }
+ { \__diffcoeff_inputs:nnnnnnn {#1}
+ {##1} {##2} {##4} {##5} {##6} {##7} }
+ }
}
-\msg_new:nnn { diffcoeff } { numbers-conflict }
+\cs_new_protected:Npn \__diffcoeff_inputs:nnnnnnn #1#2#3#4#5#6#7
{
- #2~orders~of~differentiation~specified~for~#1~variables;~
- orders~[#3]\ (\msg_line_context:)~for~variables~#4.
+ \group_begin:
+ \tl_set:Nx \l__diffcoeff_instance_tl
+ { dif#1 \tl_if_empty:nF { #2 } { .#2 } }
+ \UseInstance { diffcoeff } { \l__diffcoeff_instance_tl }
+ {#3} {#4} {#5} {#6} {#7}
+ \group_end:
}
+\NewDocumentCommand \difoverride { >{\TrimSpaces} m }
+ { \tl_set:Nn \l__diffcoeff_override_tl { #1 } }
+% Jacobian
+\NewDocumentCommand \jacob { >{\TrimSpaces} D..{} m m }
+ {
+ \group_begin:
+ \int_zero:N \l__diffcoeff_spaced_int
+ \tl_set:Nx \l__diffcoeff_instance_tl
+ { difj \tl_if_empty:nF { #1 } { .#1 } }
+ \UseInstance { diffcoeff } { \l__diffcoeff_instance_tl }
+ { \c_false_bool } {}
+ { \l__diffcoeff_lvw_ldelim_tl #2 \l__diffcoeff_lvw_rdelim_tl }
+ { {\l__diffcoeff_lvw_ldelim_tl #3\l__diffcoeff_lvw_rdelim_tl } } {}
+ \group_end:
+ }
+% differential; #1 variant ; #2 ord(s); #3 vars; #4 exponent
+\NewDocumentCommand \dl { >{ \TrimSpaces } D..{} O{1} m e{^} }
+ {
+ \group_begin:
+ \tl_set:Nx \l__diffcoeff_instance_tl
+ { difl \tl_if_empty:nF { #1 } { .#1 } }
+ \difoverride {}
+ \tl_set:Nn \l__diffcoeff_exponent_tl { #4 }
+ \tl_if_novalue:nTF {#4}
+ { \bool_set_false:N \l__diffcoeff_exponent_bool }
+ { \bool_set_true:N \l__diffcoeff_exponent_bool }
+ \UseInstance { diffcoeff } { \l__diffcoeff_instance_tl }
+ {\c_false_bool} {#2} {} {#3} {}
+ \group_end:
+ }
% end of file diffcoeff.sty
\ No newline at end of file
Added: trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff4.sty
===================================================================
--- trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff4.sty (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff4.sty 2023-01-11 20:44:28 UTC (rev 65523)
@@ -0,0 +1,744 @@
+% This is file `diffcoeff4.sty'.
+%
+% This work may be distributed and/or modified under the conditions
+% of the LaTeX Project Public License, either version 1.3c
+% (2008-05-04) of this license or any later version; see
+% http://www.latex-project.org/lppl.txt
+%
+% Andrew Parsloe ajparsloe at gmail.com
+%
+\RequirePackage{expl3}
+\RequirePackage{xparse,l3keys2e,xtemplate}
+\ProvidesExplPackage {diffcoeff4} {2022/07/30} {4.2}
+ {Write differential coefficients easily and consistently.}
+%
+\keys_define:nn { diffcoeff4 }
+ {
+ ISO .bool_set:N = \l__diffcoeff_ISO_bool,
+ spaced .int_set:N = \l__diffcoeff_spaced_int,
+ spaced .default:n = 1,
+ spaced .initial:n = 0,
+ def-file .tl_gset:N = \g__diffcoeff_def_tl,
+ def-file .initial:n = diffcoeff,
+ def-file .default:n = diffcoeff
+ }
+\ProcessKeysPackageOptions { diffcoeff4 }
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\cs_generate_variant:Nn \tl_if_eq:nnTF { nV }
+
+\tl_new:N \l__diffcoeff_oporder_tl
+\tl_new:N \l__diffcoeff_derivand_tl
+\tl_new:N \l__diffcoeff_type_tl
+\tl_new:N \l__diffcoeff_tot_order_tl
+\tl_new:N \l__diffcoeff_curr_num_tl
+\tl_new:N \l__diffcoeff_curr_var_tl
+\tl_new:N \l__diffcoeff_paren_tl
+
+\tl_const:Nn \c__diffcoeff_digits_tl { 1234567890 }
+
+\seq_new:N \l__diffcoeff_orders_seq
+\seq_new:N \l__diffcoeff_vars_seq
+\seq_new:N \l__diffcoeff_denom_seq
+\seq_new:N \l__diffcoeff_paren_seq
+
+\prop_new:N \l__diffcoeff_vars_prop
+
+\bool_new:N \l__diffcoeff_op_left_bool
+\bool_new:N \l__diffcoeff_single_var_bool
+\bool_new:N \l__diffcoeff_opwrap_bool
+\bool_new:N \l__diffcoeff_integ_bool
+\bool_new:N \l__diffcoeff_spaced_bool
+\bool_new:N \l__diffcoeff_altsep_bool
+
+\int_new:N \l__diffcoeff_vars_int
+\int_new:N \l__diffcoeff_format_int
+\int_new:N \l__diffcoeff_curr_tok_int
+\int_new:N \l__diffcoeff_curr_state_int
+\int_new:N \l__diffcoeff_nos_int
+\int_new:N \l__diffcoeff_parenvar_int
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\DeclareObjectType { derivative } { 3 }
+
+% defaults: ordinary deriv. values
+\DeclareTemplateInterface { derivative } { DERIV } { 3 }
+ {
+ op-symbol : tokenlist = d ,
+ op-symbol-alt : tokenlist = \KeyValue { op-symbol },
+ op-order-sep : muskip = 1 mu ,
+ derivand-sep : muskip = 3 mu plus 1 mu minus 2 mu,
+ long-var-wrap : choice { dv, d(v), (dv) }
+ = d(v) ,
+ denom-term-sep : muskip = 2 mu ,
+ term-sep-adjust : muskip = -1 mu ,
+ left-delim : tokenlist = \left . ,
+ right-delim : tokenlist = \right |,
+ elbowroom : muskip = 0 mu ,
+ subscr-nudge : muskip = 0 mu ,
+ *-derivand-sep : muskip = \KeyValue { derivand-sep },
+ *-op-left : boolean = false ,
+ *-italic-nudge : muskip = 3 mu ,
+ /-derivand-sep : muskip = \KeyValue { derivand-sep },
+ /-denom-term-sep : muskip = 1 mu ,
+ /-left-delim : tokenlist = ( ,
+ /-right-delim : tokenlist = ) ,
+ /-elbowroom : muskip = 0 mu ,
+ /-subscr-nudge : muskip = 0 mu ,
+ */-derivand-sep : muskip = \KeyValue { /-derivand-sep },
+ */-op-wrap : boolean = true
+ }
+% #1 order spec(seqvar); #2 order override(tlvar)
+% #3 derivand(tlvar); #4 denominator(seqvar)
+% #5 subscript(tlvar)
+\DeclareTemplateCode { derivative } { DERIV } { 3 }
+ {
+ op-symbol = \l__diffcoeff_op_tl,
+ op-symbol-alt = \l__diffcoeff_op_alt_tl,
+ op-order-sep = \l__diffcoeff_oporder_muskip,
+ derivand-sep = \l__diffcoeff_derivsep_muskip,
+ long-var-wrap = {
+ dv = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
+ \__diffcoeff_wrap_longvars_dv:nn,
+ d(v) = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
+ \__diffcoeff_wrap_longvars_dvi:nn,
+ (dv) = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
+ \__diffcoeff_wrap_longvars_dvii:nn,
+ unknown = \cs_set_eq:NN \__diffcoeff_wrap_longvars:nn
+ \__diffcoeff_wrap_longvars_dvi:nn
+ },
+ denom-term-sep = \l__diffcoeff_varsep_muskip,
+ term-sep-adjust = \l__diffcoeff_sep_adj_muskip,
+ left-delim = \l__diffcoeff_ldelim_tl,
+ right-delim = \l__diffcoeff_rdelim_tl,
+ elbowroom = \l__diffcoeff_elbowrm_muskip ,
+ subscr-nudge = \l__diffcoeff_subnudge_muskip,
+ *-derivand-sep = \l__diffcoeff_derivsepi_muskip,
+ *-op-left = \l__diffcoeff_op_left_bool,
+ *-italic-nudge = \l__diffcoeff_opnudge_muskip,
+ /-derivand-sep = \l__diffcoeff_derivsepii_muskip,
+ /-denom-term-sep = \l_tmpb_muskip,
+ /-left-delim = \l__diffcoeff_ldelimi_tl,
+ /-right-delim = \l__diffcoeff_rdelimi_tl,
+ /-elbowroom = \l_tmpc_muskip,
+ /-subscr-nudge = \l_tmpd_muskip,
+ */-derivand-sep = \l__diffcoeff_derivsepiii_muskip,
+ */-op-wrap = \l__diffcoeff_opwrap_bool
+ }
+ {
+ \AssignTemplateKeys
+
+ \bool_if:NF\l__diffcoeff_integ_bool
+ {
+ \int_compare:nNnT { \l__diffcoeff_format_int } > { 1 }
+ { \__diffcoeff_slash_vals: }
+ \__diffcoeff_build:nnn { #1 } { #2 } { #3 }
+ }
+ }
+%%%%%%%%%%
+\cs_new:Npn \__diffcoeff_slash_vals:
+ {
+ \muskip_set:Nn \l__diffcoeff_varsep_muskip \l_tmpb_muskip
+ \muskip_set:Nn \l__diffcoeff_elbowrm_muskip \l_tmpc_muskip
+ \muskip_set:Nn \l__diffcoeff_subnudge_muskip \l_tmpd_muskip
+ \tl_set:NV \l__diffcoeff_ldelim_tl \l__diffcoeff_ldelimi_tl
+ \tl_set:NV \l__diffcoeff_rdelim_tl \l__diffcoeff_rdelimi_tl
+ }
+% #1 diff'and; #2 vars clist; #3 trailing arg
+\cs_new:Npn \__diffcoeff_build:nnn #1#2#3
+ {
+ \tl_set:Nn \l__diffcoeff_derivand_tl { #1 }
+ \seq_set_from_clist:Nn \l__diffcoeff_vars_seq { #2 }
+ \bool_if:nT
+ {
+ !\l__diffcoeff_opwrap_bool &&
+ \int_compare_p:nNn { \l__diffcoeff_format_int } > { 1 }
+ }
+ { \int_set:Nn \l__diffcoeff_format_int { 4 } }
+ \__diffcoeff_spaced:n { \l__diffcoeff_spaced_int }
+ \bool_if:nTF
+ {
+ ( \l__diffcoeff_altsep_bool && !\l__diffcoeff_spaced_bool )
+ || ( !\l__diffcoeff_altsep_bool && \l__diffcoeff_spaced_bool )
+ }
+ { \__diffcoeff_derivsep: }
+ { \tl_put_left:Nn \l__diffcoeff_derivand_tl { \mskip 0 mu } }
+ \tl_if_novalue:nF { #3 }
+ { \l__diffcoeff_ldelim_tl \mskip \l__diffcoeff_elbowrm_muskip }
+ \bool_if:NTF \l__diffcoeff_single_var_bool
+ {
+ \tl_set:Nx \l_tmpa_tl { \seq_use:Nn \l__diffcoeff_vars_seq { , } }
+ \__diffcoeff_single:NNN \l__diffcoeff_tot_order_tl \l__diffcoeff_derivand_tl \l_tmpa_tl
+ }
+ {
+ \int_zero:N \l_tmpa_int
+ \seq_mapthread_function:NNN \l__diffcoeff_orders_seq
+ \l__diffcoeff_vars_seq \__diffcoeff_map_orders:nn
+ \__diffcoeff_mixed:NNN \l__diffcoeff_tot_order_tl
+ \l__diffcoeff_derivand_tl \l__diffcoeff_denom_seq
+ }
+ \tl_if_novalue:nF { #3 }
+ {
+ \mskip \l__diffcoeff_elbowrm_muskip \l__diffcoeff_rdelim_tl
+ \tl_if_empty:nF { #3 }
+ {
+ \c_math_subscript_token
+ { \mskip \l__diffcoeff_subnudge_muskip { #3 } }
+ }
+ }
+ }
+%%%%%%%%%%%%%%%%%%%%
+\cs_new_protected:Npn \__diffcoeff_spaced:n #1
+ {
+ \int_case:nn { \int_sign:n { #1 } }
+ {
+ { 1 } { \bool_set_true:N \l__diffcoeff_spaced_bool }
+ { 0 } { \bool_set_false:N \l__diffcoeff_spaced_bool }
+ { -1 }
+ {
+ \int_compare:nNnTF { 1 } <
+ { \tl_count:N \l__diffcoeff_derivand_tl }
+ { \bool_set_true:N \l__diffcoeff_spaced_bool }
+ { \bool_set_false:N \l__diffcoeff_spaced_bool }
+ }
+ }
+ }
+\cs_new_protected:Npn \__diffcoeff_derivsep:
+ {
+ \tl_put_left:Nx \l__diffcoeff_derivand_tl
+ {
+ \int_case:nn { \l__diffcoeff_format_int }
+ {
+ { 0 } { \mskip \l__diffcoeff_derivsep_muskip }
+ { 1 } { \mskip \l__diffcoeff_derivsepi_muskip }
+ { 2 } { \mskip \l__diffcoeff_derivsepii_muskip }
+ { 3 } { \mskip \l__diffcoeff_derivsepiii_muskip }
+ { 4 } { \mskip \l__diffcoeff_derivsepiii_muskip }
+ }
+ }
+ }
+\cs_new:Npn \__diffcoeff_wrap_longvars_dv:nn #1#2
+ { \l__diffcoeff_op_alt_tl { {}#2 }^{ #1 } }
+\cs_new:Npn \__diffcoeff_wrap_longvars_dvi:nn #1#2
+ { \l__diffcoeff_op_alt_tl { {}(#2) }^{ #1 } }
+\cs_new:Npn \__diffcoeff_wrap_longvars_dvii:nn #1#2
+ { (\l__diffcoeff_op_alt_tl { {}#2) }^{ #1 } }
+% (ptl) form denom #1 from orders seq & #2 from vars seq
+\cs_new_protected:Npn \__diffcoeff_map_orders:nn #1#2
+ {
+ \tl_if_eq:nnTF { #1 } { 1 }
+ { \seq_put_right:Nn \l__diffcoeff_denom_seq { \l__diffcoeff_op_alt_tl { #2 } } }
+ {
+ \int_compare:nNnTF { \tl_count:n { #2 } } = { 1 }
+ {
+ \seq_put_right:Nn \l__diffcoeff_denom_seq
+ { \l__diffcoeff_op_alt_tl { #2 }^{ #1 } }
+ }
+ {
+ \seq_put_right:Nn \l__diffcoeff_denom_seq
+ { \__diffcoeff_wrap_longvars:nn { #1\vphantom{)} } { #2 } }
+ }
+ }
+ }
+% #1 order(tlvar) ; #2 diff'iand(tlvar); #3 denom(tlvar)
+\cs_new:Npn \__diffcoeff_single:NNN #1#2#3
+ {
+ \__diffcoeff_numer:N { #1 }
+ \__diffcoeff_form_deriv:NNn
+ \l__diffcoeff_oporder_tl
+ \l__diffcoeff_derivand_tl
+ { \__diffcoeff_denom_single:NN #1 #3 }
+ }
+% #1 total order; #2 derivand; #3 denom seq
+\cs_new_protected:Npn \__diffcoeff_mixed:NNN #1#2#3
+ {
+ \__diffcoeff_numer:N #1
+ \__diffcoeff_form_deriv:NNn
+ \l__diffcoeff_oporder_tl
+ \l__diffcoeff_derivand_tl
+ { \__diffcoeff_denom_sep:N #3 }
+ }
+\cs_new:Npn \__diffcoeff_denom_sep:N #1
+ {
+ \int_zero:N \l_tmpa_int
+ \seq_map_inline:Nn #1
+ {
+ \int_incr:N \l_tmpa_int ##1
+ \int_compare:nNnT { \l_tmpa_int } < { \l__diffcoeff_vars_int }
+ {
+ \seq_pop:NN \l__diffcoeff_orders_seq \l_tmpa_tl
+ \str_if_eq:VnTF \l_tmpa_tl { 1 }
+ { \mskip \l__diffcoeff_varsep_muskip }
+ {
+ \mskip \muskip_eval:n { \l__diffcoeff_varsep_muskip +
+ \l__diffcoeff_sep_adj_muskip }
+ }
+ }
+ }
+ }
+% #1(tl) total order
+\cs_new_protected:Npn \__diffcoeff_numer:N #1
+ {
+ \bool_if:NTF \l__diffcoeff_op_left_bool
+ {
+ \tl_set:Nn \l__diffcoeff_oporder_tl
+ { \mskip \l__diffcoeff_opnudge_muskip }
+ }
+ { \tl_clear:N \l__diffcoeff_oporder_tl }
+ \tl_put_right:No \l__diffcoeff_oporder_tl \l__diffcoeff_op_tl
+ \exp_args:NnV \tl_if_eq:nnF { 1 } #1
+ {
+ \tl_put_right:Nn \l__diffcoeff_oporder_tl
+ { \mskip \l__diffcoeff_oporder_muskip ^ { #1 } }
+ }
+ \bool_if:NT \l__diffcoeff_op_left_bool
+ { \tl_put_right:Nn \l__diffcoeff_oporder_tl { \hfill } }
+ }
+% #1 order; #2 var
+\cs_new_protected:Npn \__diffcoeff_denom_single:NN #1#2
+ {
+ \tl_if_eq:nVTF { 1 } #1
+ { \l__diffcoeff_op_alt_tl {}#2 }
+ {
+ \int_compare:nNnTF { \tl_count:N #2 } = { 1 }
+ { \l__diffcoeff_op_alt_tl {}#2^{ #1 } }
+ { \__diffcoeff_wrap_longvars:nn { #1\vphantom) } { #2 } }
+ }
+ }
+% #1 op+order; #2 diff'iand; #3 denom
+% 0 frac; 1 frac append; 2 slash ; 3 ( slash ) append; 4 slash append
+\cs_new:Npn \__diffcoeff_form_deriv:NNn #1#2#3
+ {
+ \int_case:nn { \l__diffcoeff_format_int }
+ {
+ { 0 } { \frac { #1 #2 } { #3 } }
+ { 1 } { \frac { #1 } { #3 } #2 }
+ { 2 } { #1 #2 / #3 }
+ { 3 } { ( #1 / #3 ) #2 }
+ { 4 } { #1 / #3 #2 }
+ }
+ }
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% differential
+% #1 variant; #2 = space in mu before d (0--9)
+% note \group_end placement for \vec{x} etc
+\NewDocumentCommand \dl { d.. t- m }
+ {
+ \group_begin:
+ \bool_set_true:N \l__diffcoeff_integ_bool
+ \bool_set_true:N \l__diffcoeff_single_var_bool
+ \seq_set_from_clist:Nn \l__diffcoeff_orders_seq { 1 }
+ \tl_set:Nn \l__diffcoeff_tot_order_tl { 1 }
+ \IfValueTF { #1 }
+ { \tl_set:Nn \l__diffcoeff_type_tl { .#1 } }
+ { \tl_set:Nn \l__diffcoeff_type_tl { } }
+ \UseInstance { derivative } { ord\l__diffcoeff_type_tl }
+ \c_empty_tl \c_empty_seq \c_empty_tl
+ \tl_if_in:NnTF \c__diffcoeff_digits_tl { #3 }
+ { \mskip \IfBooleanT #2 { - }#3 mu \l__diffcoeff_op_tl \group_end: }
+ { \l__diffcoeff_op_tl \group_end: {} #3 }
+ }
+\NewDocumentCommand \negmu {} { \mskip -1 mu }
+\NewDocumentCommand \nilmu {} { \mskip 0 mu }
+\NewDocumentCommand \onemu {} { \mskip 1 mu }
+\NewDocumentCommand \twomu {} { \mskip 2 mu }
+% derivative
+% #1(tl) = name of variant; #2(*)= append diff'iand boolean
+% #3(clist) = orders of diff. in each var.; #4(tl) = order override
+% #5(bool) spacing switch; #6(tl) = diff'iand; #7( / ) = slash boolean
+% #8(clist) = vars of diff.; #9(tl) = pt of eval./vars held const
+\NewDocumentCommand \diff { d.. s O{1} o t! >{\TrimSpaces} m t/ m !o }
+ {
+ \group_begin:
+ \IfBooleanTF #5
+ { \bool_set_true:N \l__diffcoeff_altsep_bool }
+ { \bool_set_false:N \l__diffcoeff_altsep_bool }
+ \seq_set_from_clist:Nn \l__diffcoeff_orders_seq { #3 }
+ \int_set:Nn \l_tmpb_int { \seq_count:N \l__diffcoeff_orders_seq }
+ \int_set:Nn \l__diffcoeff_vars_int { \clist_count:n { #8 } }
+ \int_compare:nNnTF { \l__diffcoeff_vars_int } = { 1 }
+ { \bool_set_true:N \l__diffcoeff_single_var_bool }
+ {
+ \int_compare:nNnTF { \l__diffcoeff_vars_int } < { \l_tmpb_int }
+ {
+ \msg_error:nnxxxx { diffcoeff } { numbers-conflict }
+ { \int_use:N \l__diffcoeff_vars_int } { \int_use:N \l_tmpb_int }
+ { \seq_use:Nn \l__diffcoeff_orders_seq { , } }
+ { \clist_use:nn { #8 } { , } }
+ }
+ { % pad orders seq if nec.
+ \int_step_inline:nnnn
+ { 1 + \l_tmpb_int } { 1 } { \l__diffcoeff_vars_int }
+ { \seq_put_right:Nn \l__diffcoeff_orders_seq { 1 } }
+ }
+ }
+ % override/calc total order
+ \IfValueTF { #4 }
+ { \tl_set:Nn \l__diffcoeff_tot_order_tl { #4 } }
+ {
+ \bool_if:NTF \l__diffcoeff_single_var_bool
+ { \tl_set:Nn \l__diffcoeff_tot_order_tl { #3 } }
+ {
+ \__diffcoeff_calc_tot_order:NN \l__diffcoeff_orders_seq
+ \l__diffcoeff_tot_order_tl
+ }
+ }
+ \IfValueTF { #1 }
+ { \tl_set:Nn \l__diffcoeff_type_tl { .#1 } }
+ { \tl_set:Nn \l__diffcoeff_type_tl { } }
+ % append? slash?
+ \int_zero:N \l__diffcoeff_format_int
+ \IfBooleanT #2 { \int_incr:N \l__diffcoeff_format_int }
+ \IfBooleanT #7 { \int_add:Nn \l__diffcoeff_format_int { 2 } }
+ \UseInstance { derivative } { ord\l__diffcoeff_type_tl } {#6}{#8}{#9}
+ \group_end:
+ } % end of \diff
+%%%%%%%%%%%%%%%%%%%
+% #2(seq) expr in; #1(tlv) expr out
+\cs_new:Npn \__diffcoeff_calc_tot_order:NN #1 #2
+ {
+ \tl_clear:N \l__diffcoeff_nos_tl
+ \exp_args:Nx\__diffcoeff_digest_expr:n { \seq_use:Nn #1 { + } }
+ \prop_if_empty:NTF \l__diffcoeff_vars_prop
+ { \tl_set:NV #2 \l__diffcoeff_nos_tl }
+ { \__diffcoeff_evaluate:NN \l__diffcoeff_vars_prop #2 }
+ }
+\cs_new:Npn \__diffcoeff_digest_expr:n #1
+ {
+ \tl_set:Nn \l__diffcoeff_curr_num_tl { + }
+ \tl_set:Nn \l__diffcoeff_paren_tl { +1 }
+ \tl_set:Nn \l__diffcoeff_nos_tl { 0 }
+ \int_zero:N \l__diffcoeff_curr_state_int
+ \int_zero:N \l__diffcoeff_curr_tok_int
+ \tl_map_inline:nn { #1+ }
+ {
+ \__diffcoeff_get_curr_ndx:nN { ##1 } \l__diffcoeff_curr_tok_int
+ \__diffcoeff_transitions:nNN { ##1 }
+ \l__diffcoeff_curr_state_int \l__diffcoeff_curr_tok_int
+ }
+ \int_set:Nn \l__diffcoeff_nos_int { \l__diffcoeff_nos_tl }
+ \tl_set:Nx \l__diffcoeff_nos_tl { \int_use:N \l__diffcoeff_nos_int }
+ \int_compare:nNnT { \l__diffcoeff_nos_int } = { 0 }
+ { \tl_clear:N \l__diffcoeff_nos_tl }
+ }
+% #1 curr tok (tl); #2 <== curr tok ndx (int)
+\cs_new_protected:Npn \__diffcoeff_get_curr_ndx:nN #1#2
+ {
+ \tl_if_in:NnTF \c__diffcoeff_digits_tl { #1 }
+ { \int_set:Nn #2 { 1 } } % digit
+ {
+ \str_case:nnF { #1 }
+ {
+ { + } { \int_set:Nn #2 { 0 } }
+ { - } { \int_set:Nn #2 { 0 } }
+ { ( } { \int_set:Nn #2 { 3 } }
+ { ) } { \int_set:Nn #2 { 4 } }
+ }
+ { \int_set:Nn #2 { 2 } } % var
+ }
+ }
+% #1(tl) curr tok; #2(int) curr state; #3(int) curr tok ndx
+\cs_new:Npn \__diffcoeff_transitions:nNN #1#2#3
+ {
+ \int_case:nn { #2 }
+ {
+ { 0 } % sgn + -
+ { \__diffcoeff_sgn_transitions:nNN { #1 }#2#3 }
+ { 1 } % num
+ { \__diffcoeff_num_transitions:nNN { #1 }#2#3 }
+ { 2 } % alg
+ { \__diffcoeff_alg_transitions:nNN { #1 }#2#3 }
+ { 4 } % )
+ { \__diffcoeff_rpar_transitions:nNN { #1 }#2#3 }
+ }
+ }
+% transitions from the signed state
+% #1(tl) curr tok; #2(int) 0, curr state; #3 curr tok ndx
+\cs_new_protected:Npn \__diffcoeff_sgn_transitions:nNN #1#2#3
+ {
+ \int_case:nnT { #3 }
+ {
+ { 0 } % tok = s
+ {
+ \tl_if_eq:nVTF { #1 } \l__diffcoeff_curr_num_tl
+ { \tl_set:Nn \l__diffcoeff_curr_num_tl { + } }
+ { \tl_set:Nn \l__diffcoeff_curr_num_tl { - } }
+ }
+ { 1 } % tok = d
+ { \tl_put_right:Nn \l__diffcoeff_curr_num_tl { #1 } }
+ { 2 } % tok = v
+ {
+ \tl_put_right:Nn \l__diffcoeff_curr_num_tl { 1 }
+ \tl_set:Nn \l__diffcoeff_curr_var_tl { #1 }
+ }
+ { 3 } % tok = (
+ {
+ \seq_push:NV \l__diffcoeff_paren_seq \l__diffcoeff_paren_tl
+ \tl_put_left:NV \l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
+ \tl_set:Nn \l__diffcoeff_curr_num_tl { + }
+ \int_set:Nn #3 { 0 }
+ }
+ }
+ { \int_set_eq:NN #2 #3 }
+ }
+% transitions from the numeric state
+% #1 = curr. tok.; #2 = 0, curr. state; #3 curr. tok. index
+\cs_new_protected:Npn \__diffcoeff_num_transitions:nNN #1#2#3
+ {
+ \int_case:nnT { #3 }
+ {
+ { 0 } % tok = s
+ {
+ \tl_put_right:NV\l__diffcoeff_nos_tl
+ { \l__diffcoeff_paren_tl * \l__diffcoeff_curr_num_tl }
+ \tl_set:Nn \l__diffcoeff_curr_num_tl { #1 }
+ }
+ { 1 } % tok = d
+ { \tl_put_right:Nn \l__diffcoeff_curr_num_tl { #1 } }
+ { 2 } % tok = v
+ {
+ \tl_if_in:nnTF { ^ \times * / \div } { #1 }
+ {
+ \msg_error:nnxxx { diffcoeff } { order-specification }
+ { \seq_use:Nn \l__diffcoeff_orders_seq { , } }
+ { #1 } { number }
+ }
+ { \tl_set:Nn \l__diffcoeff_curr_var_tl { #1 } }
+ }
+ { 3 } % tok = (
+ {
+ \seq_push:NV \l__diffcoeff_paren_seq \l__diffcoeff_paren_tl
+ \tl_put_left:Nn \l__diffcoeff_paren_tl { * }
+ \tl_put_left:NV \l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
+ \tl_set:Nn \l__diffcoeff_curr_num_tl { + }
+ \int_set:Nn #3 { 0 }
+ }
+ { 4 } % tok = )
+ {
+ \tl_put_right:NV \l__diffcoeff_nos_tl
+ { \l__diffcoeff_paren_tl * \l__diffcoeff_curr_num_tl }
+ }
+ }
+ {
+ \int_set_eq:NN #2 #3 }
+ }
+% transitions from the algebraic state
+% #1 = curr. tok.; #2 = 2, curr. state; #3 curr. tok. index
+\cs_new:Npn \__diffcoeff_alg_transitions:nNN #1#2#3
+ {
+ \int_case:nnT { #3 }
+ {
+ { 0 } % tok = s
+ {
+ \int_compare:nNnTF { \l__diffcoeff_parenvar_int } = { 0 }
+ {
+ \__diffcoeff_store_var:NNN \l__diffcoeff_curr_var_tl
+ \l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
+ \tl_clear:N \l__diffcoeff_curr_var_tl
+ \tl_set:Nn \l__diffcoeff_curr_num_tl { #1 }
+ }
+ {
+ \tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
+ \int_set:Nn #3 { 2 }
+ }
+ }
+ { 1 } % tok = d
+ {
+ \tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
+ \int_set:Nn #3 { 2 }
+ }
+ { 2 } % tok = v
+ { \tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 } }
+ { 3 } % tok = (
+ {
+ \tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
+ \int_set:Nn #3 { 2 }
+ \int_incr:N \l__diffcoeff_parenvar_int
+ }
+ { 4 } % tok = )
+ {
+ \int_compare:nNnTF { \l__diffcoeff_parenvar_int } = { 0 }
+ {
+ \__diffcoeff_store_var:NNN \l__diffcoeff_curr_var_tl
+ \l__diffcoeff_paren_tl \l__diffcoeff_curr_num_tl
+ \tl_clear:N \l__diffcoeff_curr_var_tl
+ }
+ {
+ \tl_put_right:Nn \l__diffcoeff_curr_var_tl { #1 }
+ \int_set:Nn #3 { 2 }
+ \int_decr:N \l__diffcoeff_parenvar_int
+ }
+ }
+ }
+ { \int_set_eq:NN #2 #3 }
+ }
+% transitions from the ) state
+% #1 = curr. tok.; #2 = 4, curr. state; #3 curr. tok. index
+\cs_new:Npn \__diffcoeff_rpar_transitions:nNN #1#2#3
+ {
+ \int_compare:nNnTF { \int_mod:nn { #3 } { 4} } = { 0 }
+ {
+ \tl_set:Nn \l__diffcoeff_curr_num_tl { #1 }
+ \seq_pop:NN \l__diffcoeff_paren_seq \l__diffcoeff_paren_tl
+ \int_set_eq:NN #2 #3
+ }
+ {
+ \msg_error:nnxxx { diffcoeff } { order-specification }
+ { \seq_use:Nn \l__diffcoeff_orders_seq { , } } { #1 } { ) }
+ }
+ }
+% #1 is var. (tlvar); #2 is num. (tlvar); #3 num. coeff. (tlvar)
+\cs_new:Npn \__diffcoeff_store_var:NNN #1#2#3
+ {
+ \prop_get:NVNF \l__diffcoeff_vars_prop #1 \l_tmpa_tl
+ { \tl_clear:N \l_tmpa_tl }
+ \tl_put_right:NV \l_tmpa_tl { #2 * #3 }
+ \prop_put:NVV \l__diffcoeff_vars_prop #1 \l_tmpa_tl
+ }
+% #1 (propv) key=var, val=coeff; #2 <= total order
+\cs_new_protected:Npn \__diffcoeff_evaluate:NN #1#2
+ {
+ \prop_map_inline:Nn #1 { \seq_put_left:Nn \l_tmpa_seq { ##1 } }
+ \seq_sort:Nn \l_tmpa_seq
+ {
+ \int_compare:nNnTF { \tl_count:n { ##1 } } < { \tl_count:n { ##2 } }
+ { \sort_return_same: } { \sort_return_swapped: }
+ }
+ \seq_map_inline:Nn \l_tmpa_seq
+ {
+ \prop_pop:NnN #1 { ##1 } \l_tmpb_tl
+ \seq_put_right:Nx \l_tmpb_seq { \int_eval:n \l_tmpb_tl }
+ }
+ \tl_clear:N \l_tmpa_tl
+ \seq_mapthread_function:NNN \l_tmpa_seq \l_tmpb_seq
+ \__diffcoeff_tot_order:nn
+ \exp_args:NV \tl_if_head_eq_charcode:nNTF \l_tmpa_tl +
+ {
+ \tl_set:Nx \l_tmpb_tl { \tl_tail:N \l_tmpa_tl }
+ \int_compare:nNnT { \l__diffcoeff_nos_int } > { 0 }
+ { \tl_put_left:Nn \l__diffcoeff_nos_tl { + } }
+ \tl_concat:NNN #2 \l_tmpb_tl \l__diffcoeff_nos_tl
+ }
+ {
+ \int_compare:nNnTF { \l__diffcoeff_nos_int } > { 0 }
+ { \tl_concat:NNN #2 \l__diffcoeff_nos_tl \l_tmpa_tl }
+ { \tl_concat:NNN #2 \l_tmpa_tl \l__diffcoeff_nos_tl }
+ }
+ \tl_set_rescan:Nno #2 { } #2
+ }
+\cs_new:Npn \__diffcoeff_tot_order:nn #1#2
+ {
+ \int_compare:nNnTF { #2 } > { 0 }
+ {
+ \int_compare:nNnTF { #2 } = { 1 }
+ { \tl_put_left:Nn \l_tmpa_tl { +#1 } }
+ { \tl_put_left:Nn \l_tmpa_tl { +#2#1 } }
+ }
+ {
+ \int_compare:nNnT { #2 } < { 0 }
+ {
+ \int_compare:nNnTF { #2 } = { -1 }
+ { \tl_put_right:Nn \l_tmpa_tl { -#1 } }
+ { \tl_put_right:Nn \l_tmpa_tl { #2#1 } }
+ }
+ }
+ }
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% create new instances or edit existing ones
+% #1 = name; #2 = key-value list
+\NewDocumentCommand \diffdef { > { \TrimSpaces } m m }
+ {
+ \tl_if_empty:nTF { #1 }
+ {
+ \EditTemplateDefaults { derivative }
+ { DERIV } { #2 }
+ \EditInstance { derivative } { ord } { #2 }
+ }
+ {
+ \IfInstanceExistTF { derivative } { ord.#1 }
+ { \EditInstance { derivative } { ord.#1 } { #2 } }
+ {
+ \DeclareInstance { derivative } { ord.#1 }
+ { DERIV } { #2 }
+ }
+ }
+ }
+% relic from version 1
+\NewDocumentCommand \diffset { o }
+ { \msg_warning:nn { diffcoeff } { obsolete } }
+
+% ordinary & D
+\DeclareInstance { derivative } { ord } { DERIV } { }
+\bool_if:NTF \l__diffcoeff_ISO_bool
+ {
+ \diffdef { }
+ {
+ op-symbol = \mathrm{d},
+ op-order-sep = 0 mu ,
+ left-delim = \left ( ,
+ right-delim = \right ) ,
+ subscr-nudge = -6 mu
+ }
+ \diffdef { D } { op-symbol = \mathrm{D} }
+ }
+ { \diffdef { D } { op-symbol = D } }
+
+% partial
+\diffdef { p }
+ {
+ op-symbol = \partial ,
+ left-delim = \left ( ,
+ right-delim = \right ) ,
+ subscr-nudge = -6 mu
+ }
+\NewDocumentCommand \diffp {} { \diff.p. }
+\NewDocumentCommand \dlp {} { \dl.p. }
+
+% delta
+\diffdef { delta }
+ {
+ op-symbol = \delta ,
+ op-order-sep = 0 mu
+ }
+\diffdef { Delta }
+ {
+ op-symbol = \Delta ,
+ op-order-sep = 0 mu
+ }
+% for compatibility with version 1
+\NewDocumentCommand \Diff { } { \diff.D. }
+\NewDocumentCommand \diffd { } { \diff.delta. }
+\NewDocumentCommand \Diffd { } { \diff.Delta. }
+
+% user-defined
+\file_if_exist:nT { \g__diffcoeff_def_tl.def }
+ { \file_input:n { \g__diffcoeff_def_tl.def } }
+%%%%%%%%%%%%%%%%%%%%
+% Jacobian
+\NewDocumentCommand \jacob { m t/ m }
+ {
+ \group_begin:
+ \IfBooleanTF #2
+ { \partial(#1) / \partial(#3) }
+ { \frac{ \partial(#1) } { \partial(#3) } }
+ \group_end:
+ }
+%%%%%%%%%%%%%%%%%%%%
+% messages
+\msg_new:nnn { diffcoeff } { order-specification }
+ {
+ #3~followed~by~#2~in~the~order~specification~[#1]~\msg_line_context:.~
+ Diffcoeff~cannot~calculate~the~overall~order~of~differentiation~in~
+ this~case.~Use~the~order-override~option~to~enter~the~overall~order.
+ }
+\msg_new:nnn { diffcoeff } { obsolete }
+ {
+ Obsolete~command:~\diffset is~superseded~by~the~\diffdef\
+ command.~\msg_see_documentation_text:n { diffcoeff }
+ }
+\msg_new:nnn { diffcoeff } { numbers-conflict }
+ {
+ #2~orders~of~differentiation~specified~for~#1~variables;~
+ orders~[#3]\ (\msg_line_context:)~for~variables~#4.
+ }
+% end of file diffcoeff4.sty
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff4.sty
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
Added: trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff5.def
===================================================================
--- trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff5.def (rev 0)
+++ trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff5.def 2023-01-11 20:44:28 UTC (rev 65523)
@@ -0,0 +1,136 @@
+% file `diffcoef5.def'
+% definitions for variant forms
+% 2023/01/03
+% Andrew Parsloe ajparsloe at gmail.com
+%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% material derivative
+\difdef { f, s } { D }
+ { op-symbol = \mathrm{D} }
+% math italic
+\difdef { f, s, c } { d' }
+ {
+ op-symbol = d,
+ op-order-nudge = 1 mu
+ }
+\difdef { f, s, c } { D' }
+ {
+ op-symbol = D,
+ op-order-nudge = 1 mu
+ }
+% Greek
+\difdef { f, s } { gd }
+ { op-symbol = \delta }
+\difdef { f, s } { gD }
+ { op-symbol = \Delta }
+% spaceless appending
+\difdef { f, fp } { *0 }
+ {
+ *derivand-sep = 0 mu ,
+ outer-Ldelim = \mleft ( ,
+ outer-Rdelim = \mright )
+ }
+% tfrac, nonscalable
+\difdef { f, fp } { t }
+ {
+ style = tfrac ,
+ derivand-sep = 1 mu plus 1 mu minus 1 mu,
+ multi-term-sep = 0 mu ,
+ term-sep-adjust = 0 mu ,
+ lvwrap-sup-nudge = 0 mu ,
+ outer-Ldelim = \bigl (,
+ outer-Rdelim = \bigr ),
+ elbowroom = -2 mu ,
+ sub-nudge = -3 mu
+ }
+% slash fractions: 0=scalable,
+% 1=big, 2=Big, 3=bigg, 4=Bigg
+% but > 1 gives eyesores
+\difdef { s, sp } { 0 }
+ {
+ style = auto ,
+ outer-Ldelim = \left [ ,
+ outer-Rdelim = \right ] ,
+ sub-nudge = 0 mu ,
+ *inner-Ldelim = \mleft ( ,
+ *inner-Rdelim = \mright ),
+ *outer-Ldelim = \left [ ,
+ *outer-Rdelim = \right ]
+ }
+\difdef { s, sp } { 1 }
+ {
+ style = big ,
+ outer-Ldelim = \bigl (,
+ outer-Rdelim = \bigr ),
+ sub-nudge = -2.5 mu,
+ *inner-Ldelim = \bigl (,
+ *inner-Rdelim = \bigr ),
+ *outer-Ldelim = \bigl [,
+ *outer-Rdelim = \bigr ]
+ }
+% vrule point of evaluation
+\difdef { f, fp, s, sp } { | }
+ {
+ outer-Ldelim = \left . ,
+ outer-Rdelim = \right |,
+ sub-nudge = 0 mu
+ }
+% sq. bracket pt of eval.
+\difdef { f, fp, s, sp } { ] }
+ {
+ outer-Ldelim = \left [ ,
+ outer-Rdelim = \right ],
+ elbowroom = 1 mu,
+ sub-nudge = 0 mu
+ }
+% long var wrap
+\difdef { f, fp } { (dv) }
+ { long-var-wrap = (dv) }
+\difdef { f, fp } { dv }
+ { long-var-wrap = dv }
+% compact, D operator
+\difdef { c } { D }
+ {
+ op-symbol = \mathrm{D},
+ op-sub-nudge = -2mu
+ }
+\difdef { c } { D' }
+ {
+ op-symbol = D,
+ op-sub-nudge = -2mu
+ }
+% bold
+\difdef { c } { bD }
+ {
+ op-symbol = \mathbf{D},
+ op-sub-nudge = -2mu
+ }
+% differential style
+\difdef { c, cp } { dl }
+ { style = dl }
+%%%%%%%%%%% differential %%%%%%%%%%
+% partial
+\difdef { l } { p }
+ { op-symbol = \partial }
+% bold
+\difdef { l } { b }
+ { op-symbol = \mathrm{d}\mathbf }
+
+% line elements: Pythagoras
+\difdef { l } { + }
+ {
+ multi-term-sep = 0 mu +,
+ term-sep-adjust = 0 mu ,
+ outer-Ldelim =
+ }
+% Minkowski
+\difdef { l } { - }
+ {
+ multi-term-sep = 0 mu -,
+ term-sep-adjust = 0 mu ,
+ outer-Ldelim =
+ }
+%%%%%%%%%% jacobian %%%%%%%%%%
+% slash fraction
+\difdef { j } { s }
+ { style = / }
\ No newline at end of file
Property changes on: trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff5.def
___________________________________________________________________
Added: svn:eol-style
## -0,0 +1 ##
+native
\ No newline at end of property
More information about the tex-live-commits
mailing list.