texlive[61432] Master/texmf-dist: diffcoeff (28dec21)
commits+karl at tug.org
commits+karl at tug.org
Tue Dec 28 23:49:47 CET 2021
Revision: 61432
http://tug.org/svn/texlive?view=revision&revision=61432
Author: karl
Date: 2021-12-28 23:49:47 +0100 (Tue, 28 Dec 2021)
Log Message:
-----------
diffcoeff (28dec21)
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
Modified: trunk/Master/texmf-dist/doc/latex/diffcoeff/README.txt
===================================================================
--- trunk/Master/texmf-dist/doc/latex/diffcoeff/README.txt 2021-12-28 22:49:31 UTC (rev 61431)
+++ trunk/Master/texmf-dist/doc/latex/diffcoeff/README.txt 2021-12-28 22:49:47 UTC (rev 61432)
@@ -1,29 +1,32 @@
diffcoeff: a package to ease the writing of a variety
-of differential coefficients (derivatives)
+of differential coefficients
-Andrew Parsloe (ajparsloe at gmail.com) 28 December 2020
+Andrew Parsloe (ajparsloe at gmail.com)
This work may be distributed and/or modified under the
conditions of the LaTeX Project Public License, either
-version 1.3 of this license or (at your option) any later
+version 1.3c of this license or (at your option) any later
version. The latest version of this license is in
http://www.latex-project.org/lppl.txt
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-This is version 3.2 of diffcoeff.sty, and associated files,
-and requires the LaTeX3 bundles l3kernel and l3packages.
+This is version 4.0 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 4.0 adds a
+package option enabling a space to be inserted by default
+before the differentiand, prevents the inappropriate forming
+of the ligature df when f is the differentiand, adds a diff-
+erential command for \partial, and no longer accepts a brace-
+delimited final optional argument (a relic from v.1).
-Version 3.2 corrects a bug when an ordinary derivative is in
-the differentiand of a partial derivative. Possible negative
-spacing before a differential is also now available.
-
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-doc.def definition file to be placed
- in same directory as the .pdf
- and .tex files
\ No newline at end of file
+
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 2021-12-28 22:49:31 UTC (rev 61431)
+++ trunk/Master/texmf-dist/doc/latex/diffcoeff/diffcoeff.tex 2021-12-28 22:49:47 UTC (rev 61432)
@@ -1,4 +1,4 @@
-%% LyX 2.3.3 created this file. For more info, see http://www.lyx.org/.
+%% 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}
@@ -5,6 +5,7 @@
\renewcommand{\sfdefault}{lmss}
\renewcommand{\ttdefault}{lmtt}
\usepackage[T1]{fontenc}
+\usepackage{textcomp}
\usepackage[latin9]{inputenc}
\synctex=-1
\usepackage{color}
@@ -29,6 +30,8 @@
\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}
@@ -52,117 +55,97 @@
\title{\texttt{diffcoeff}~\\
a \LaTeX{} package to ease\texttt{ }the~\\
writing of differential coefficients \\
- in all their variety\\
- Version 3.2}
+ Version 4.0}
\author{Andrew Parsloe\\
-{\small{}(ajparsloe at gmail.com)}}
+{\small (ajparsloe at gmail.com)}}
\maketitle
\begin{abstract}
-\noindent This package allows the easy and 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 (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. The package requires the \LaTeX 3 bundles \texttt{l3kernel}
-and \texttt{l3packages}.
+\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}
\tableofcontents{}
\section{Introduction}
-The \LaTeX{} package \texttt{diffcoeff.sty} is written in the expl3 language
-of \LaTeX 3\texttt{ }and requires the bundles \texttt{l3kernel} and \texttt{l3packages}
+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 is part of standard \LaTeX{} (since early 2020) and \texttt{l3packages}
(the latter for the \texttt{xparse}, \texttt{l3keys2e} and \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. There are two package options. The first
-is a switch, \texttt{ISO}, which turns on formatting conforming to ISO
-recommendations:
+in the preamble of your document.
+
+\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}
+
+\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\}
\end{lyxcode}
-The effect of this is discussed in Section~\ref{sec:Changing-defaults}.
-The second is a filename for a file of extension \texttt{.def} containing
-definitions of variant forms of derivative:
+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{[}def-file=<filename>{]}\{diffcoeff\}
+\textbackslash usepackage{[}spaced{]}\{diffcoeff\}
\end{lyxcode}
-This is discussed in Subsection~\ref{subsec:The-.def-file}. Of course
-both options can be used in the same call if desired:
+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{[}ISO,def-file=<filename>{]}\{diffcoeff\}
+\textbackslash usepackage{[}def-file=<filename>{]}\{diffcoeff\}
\end{lyxcode}
-For the present document, the call is
+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}
-with the file \texttt{diffcoeff-doc.def} in the same directory as \texttt{diffcoeff.tex}.
-
-\subsection{Version comparison}
-
-Unlike version 1, version 2 and later are built on the the \texttt{xtemplate}
-package (included in the \texttt{l3packages} bundle) 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 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. See the diffcoeff documentation for further information.} The
-\texttt{\textbackslash diffdef} command is discussed in Subsection~\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, braces can still be used but their use to delimit an \emph{optional}
-argument is now deprecated in \texttt{xparse} on which \texttt{diffcoeff}
-depends. Presumably at some stage this provision will be removed from \texttt{xparse}.
-For future-proofing documents use square brackets.
-\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 in versions 2
-and 3, 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 Subsection~\ref{subsec:D-delta-Delta}.
-\item Version 3 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 Version 3.1 enables the differential command to be used before forms like
-\texttt{\textbackslash vec\{x\}} (an overlooked possibility causing an
-error in version 3).
-\item Version 3 also provides some simple spacing commands that can be useful
-for tweaking standard spacing.
-\item Version 3.2 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 In version 3.2, the differential command \texttt{\textbackslash dl} now
-also allows negative spacing before it.
\end{enumerate}
-\subsubsection*{Note on terminology}
-
-I refer throughout to the quantity or function being differentiated as
-the \emph{differentiand} (in line with \emph{integrand}, \emph{operand},
-etc.).
-
\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'.
+\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:
@@ -173,29 +156,31 @@
\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 do include the
-operator:
+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'.
+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:
+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, classical mechanics and thermodynamics
-come $\delta$ and $\Delta$, from fluid mechanics comes $D$:
+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}
@@ -205,215 +190,253 @@
\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}:
+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.
+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.
-And finally, the operator in the numerator may differ from that in the
-denominator. For instance, in tensor calculus acceleration is sometimes
-written
+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 $v^{i}$.
+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 Section~\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.
+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.
-\section{Ordinary derivatives \label{sec:Ordinary-derivatives}}
+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.
-Writing\textbf{ }\texttt{\textbackslash diff\{y\}\{x\}} will produce $\diff{y}{x}$
-in text style (i.e., placed between \texttt{\$ \$}) or
+\newpage{}
+
+\section{Ordinary derivatives \protect\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 -- differentiand, variable of differentiation --
-is more than a single token.
+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;
-see Section~\ref{sec:Changing-defaults} on changing default settings.
+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.)
+x\}/x} produces $\diff{\ln x}/x$. Braces are required for the numerator
+in this case since it contains more than one token.
-\subsection{Order of differentiation}
+\subsection{Spacing before the differentiand}
-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{example}
-\textbackslash diff{[}2{]}yx $\Longrightarrow\quad{\displaystyle \diff[2]yx,}$\medskip{}
+\label{subsec:Spacing-before-derivand}There are (at least) two different
+ways in which we think of derivatives.\footnote{I thank 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.
-\textbackslash diff{[}n+1{]}yx $\Longrightarrow\quad{\displaystyle \diff[n+1]yx}.$
-\end{example}
+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 \texttt{1 mu} or shrink\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}.)
-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{example}
-\textbackslash diff{[}1{]}yx $\Longrightarrow\quad{\displaystyle \diff[1]yx.}$
-\end{example}
+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$.
+\end{centred}
+The \verb`\diff` command has other optional arguments (e.g. to specify
+the order of differentiation) but always the exclamation mark, if
+used, immediately precedes the differentiand. It is the positioning
+of the differentiand that it affects after all and its placement immediately
+before that argument seems natural.
-\noindent In slash style, \texttt{\textbackslash diff{[}2{]}y/x} produces
-$\diff[2]y/x$, and \texttt{\textbackslash diff{[}n+1{]}y/x} produces
-$\diff[n+1]y/x$.
+\subsubsection{Ligatures: }
-\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{example}
-\textbackslash diff\{\textbackslash ln\textbackslash sin x\}\{\textbackslash sin
-x\}\textbackslash diff\{\textbackslash sin x\}x $\Longrightarrow\quad{\displaystyle \diff{\ln\sin x}{\sin x}\diff{\sin x}x.}$
-\end{example}
-
-\noindent Forming the \emph{second} derivative of $\ln\sin x$ will now
-involve forming (among other quantities)
-\begin{example}
-\noindent \textbackslash diff{[}2{]}\{\textbackslash ln\textbackslash sin
-x\}\{\textbackslash sin x\} $\Longrightarrow\quad{\displaystyle \diff[2]{\ln\sin x}{\sin x}.}$
-\end{example}
-
-\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 the square of $x$.
-
-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':
+Prior to v.4 of \texttt{diffcoeff}, \texttt{\textbackslash diff fx}
+produced the tight pairing evident in
\[
-\diff.wrapall.[2]{f(x)}{(1/x)}.
+\frac{df}{dx}.
\]
+This was a bug. From version 4.0 of \texttt{diffcoeff}, such ligatures
+are prevented: \verb`\[ \diff fx \]` $\Longrightarrow$ \[ \diff fx.\]
-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 Section~\ref{sec:Changing-defaults}.
+\subsubsection{Spacing commands}
-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{example}
-\textbackslash diff \{f(x)\}\{1/x\}, \textbackslash quad\textbackslash diff
-\{f(x)\}\{(1/x)\} $\Longrightarrow\quad{\displaystyle \diff{f(x)}{1/x},\quad\diff{f(x)}{(1/x)}.}$
-\end{example}
-
-
-\subsubsection{Minutiae of spacing}
-
-You may find the spacing between the `d' and the `f' in the last example
-uncomfortably close. The \texttt{diffcoeff} package offers four simple
-spacing commands to fine-tune the display. These are
+\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
+\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}
-Thus for the last example, inserting \texttt{\textbackslash nilmu} and
-\texttt{\textbackslash onemu} in the appropriate places produces
-\begin{example}
-\textbackslash diff \{\textbackslash nilmu f(x)\}\{\textbackslash onemu
-1/x\}, \textbackslash quad \textbackslash diff \{\textbackslash nilmu
-f(x)\}\{(1/x)\} $\Longrightarrow\quad{\displaystyle \diff{\nilmu f(x)}{\onemu1/x},\quad\diff{\nilmu f(x)}{(1/x)}.}$
-\end{example}
-
\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{example}
-\textbackslash diff{*}\{(ax\textasciicircum 2+bx+c)\}x $\Longrightarrow\quad{\displaystyle \diff*{(ax^{2}+bx+c)}x.}$
-\end{example}
-
-A virtue of using an asterisk 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{example}
-\textbackslash diff{[}2{]}yx = \textbackslash diff{*}\{\textbackslash diff
-yx\}x $\Longrightarrow\quad{\displaystyle \diff[2]yx=\diff*{\diff yx}x},$
-\end{example}
-
+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{example}
-\noindent \textbackslash diff{[}2{]}yx = \textbackslash diff\{\textbackslash diff
-yx\}x $\Longrightarrow\quad{\displaystyle \diff[2]yx=\diff{\diff yx}x},$
-\end{example}
-
+\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.
+}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{example}
-\textbackslash diff{*}\{(ax\textasciicircum 2+bx+c)\}/x $\Longrightarrow\quad\text{\ensuremath{{\displaystyle (\diff{}/{x})(ax^{2}+bx+c)}}, }$
-\end{example}
+\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}.
-\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 Section~\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}}
+\subsection{Point of evaluation\protect\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:
-\begin{example}
-\textbackslash diff{[}2{]}yx{[}0{]} $\Longrightarrow\quad{\displaystyle \diff[2]yx[0]}$
-\end{example}
-
-\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.
+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 Section~\ref{sec:Changing-defaults} on changing
-default settings. Or use the \texttt{ISO} package option; see the introduction.
+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{example}
-\textbackslash diff\{\textbackslash ln sin x\}/\{sin x\}{[}x=\textbackslash pi/6{]}
-$\Longrightarrow\quad{\displaystyle \diff{\ln\sin x}/{\sin x}[x=\pi/6]}$
-\end{example}
-
-\noindent A vertical rule (or `pipe') can become too remote from the opening
-$d$ of the differential coefficient: $\diff.svrule.{\ln\sin x}/{\sin x}[x=\pi/6]$;
+\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}
@@ -420,250 +443,344 @@
It is easy to add a superscript to a derivative to indicate evaluation
at two points and the difference between the values:
-\begin{example}
-\textbackslash diff \{\textbackslash sin x\}x{[}0{]}\textasciicircum\{\textbackslash pi/2\}
-${\displaystyle \Longrightarrow\quad\diff{\sin x}x[0]^{\pi/2}}$
-\end{example}
+\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}
-\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{example}
-\noindent \textbackslash tfrac 12 m \textbackslash diff x/t{[}{]}\textasciicircum 2
-$\Longrightarrow\quad{\displaystyle \tfrac{1}{2}m\diff x/t[]^{2}}.$
-\end{example}
+\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 $\diff[n+1]y/x$.
-\section{Partial derivatives\label{sec:Partial-derivatives}}
-\noindent \begin{flushleft}
-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
+\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\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
+\[
\diffp{F}{x}
\]
-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
+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.
-\par\end{flushleft}
+takes 8 keystrokes to type, the slash form \emph{does }economise on
+keystrokes for a partial derivative.
-\begin{flushleft}
-Again an optional argument allows the specification of the order of differentiation
-and it may be numeric or algebraic or a mix of the two:
-\par\end{flushleft}
-\begin{example}
-\textbackslash diffp{[}3{]}F/x , \textbackslash quad \textbackslash diffp{[}n{]}F/x
-$\Longrightarrow\quad{\displaystyle {\displaystyle {\displaystyle \diffp[3]F/x}},\quad{\displaystyle \diffp[n]F/x.}}$\medskip{}
- \textbackslash diffp{[}n+1{]}Fx $\Longrightarrow\quad{\displaystyle {\displaystyle \diffp[n+1]Fx,}}$
-\end{example}
+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 variable
-or 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{example}
-\textbackslash diffp ST{[}V{]} $\Longrightarrow\quad{\displaystyle \diffp ST[V]}$
-\end{example}
-
+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{example}
-\noindent \textbackslash diffp S/T{[}V{]} $\Longrightarrow\quad{\displaystyle \diffp{S}/{T}[V]}.$
-\end{example}
-
-This use of a parenthesised, subscripted form to indicate a variable or
-variables held constant, leaves open the question: how do we represent
+\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}
-\textbackslash diffp \{F(x,y)\}x{[}(0,0){]} $\Longrightarrow\quad{\displaystyle \diffp{F(x,y)}x[(0,0)]}$
+\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:
+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 Section~\ref{sec:Changing-defaults}.
+Making this possibility available is discussed in \xA7\ref{sec:Changing-defaults}.
-An empty final argument produces a parenthesised derivative with no subscript:
-\begin{example}
-\textbackslash diffp yx{[}{]}${\displaystyle \Longrightarrow\quad\diffp yx[]}.$
-\end{example}
+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}
-\noindent This can be useful sometimes, e.g. for writing Lagrange's equations
-of motion in analytic mechanics:
-\begin{example}
-\noindent \textbackslash diffp L\{q\_k\}-\textbackslash diff{*}\{\textbackslash diffp
-L\{\textbackslash dot\{q\}\_k\}{[}{]}\}t = 0 $\Longrightarrow\quad{\displaystyle \diffp L{q_{k}}-\diff*{\diffp L{\dot{q}_{k}}[]}t}=0.$
-\end{example}
-
-
\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 Subsection~\ref{subsec:Text-and-script-style} below -- giving, for
-our example, $\diff.ptxt.ST[V]$.
+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}}
+\subsection{Appending the differentiand\protect\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{example}
-\textbackslash diffp{*}{[}2{]}\{\textbackslash Phi(x,y,z)\}x $\Longrightarrow\quad{\displaystyle \diffp*[2]{\Phi(x,y,z)}x.}$
-\end{example}
+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 Alternatively you could leave the first mandatory argument empty
-and manually append the differentiand, but by deleting or inserting an
+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{example}
-\textbackslash diffp{*}{[}n{]}\{f(x)\}/x $\Longrightarrow\quad{\displaystyle \diffp*[n]{f(x)}/x,}$
-\end{example}
-
-\noindent although this behaviour can be changed (Section~\ref{sec:Changing-defaults}
+\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{example}
-\textbackslash diffp{*}\{\textbackslash frac PT\}U{[}V{]} = \textbackslash diffp{*}\{\textbackslash frac
-1T\}V{[}U{]} $\Longrightarrow\quad{\displaystyle \diffp*{\frac{P}{T}}U[V]=\diffp*{\frac{1}{T}}V[U]}$
-\end{example}
-
+\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{example}
-\textbackslash diffp L\{q\_k\}-\textbackslash diff{*}\{\textbackslash diffp
-L\{\textbackslash dot\{q\}\_k\}{[}{]}\}t = 0 $\Longrightarrow\quad{\displaystyle \diffp L{q_{k}}-\diff*{\diffp L{\dot{q}_{k}}[]}t}=0.$
-\end{example}
+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}
-\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{example}
-\textbackslash diffp{*}\{\textbackslash diff\{x\textasciicircum\textbackslash mu\}\{\textbackslash lambda\}\}\{x\textasciicircum\textbackslash sigma\}
-$\Longrightarrow\quad{\displaystyle \diffp*{\diff{x^{\mu}}{\lambda}}{x^{\sigma}}}$
-\end{example}
-
-
\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{example}
-\textbackslash diffp F\{x,y,z\} $\Longrightarrow\quad{\displaystyle \diffp F{x,y,z}}.$
-\end{example}
+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`\[ \diffp F{x,y,z} \]` $\Longrightarrow$ \[ \diffp F{x,y,z}, \]
-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{example}
-\textbackslash diffp F/\{x,y,z\} $\Longrightarrow\quad{\displaystyle \diffp F/{x,y,z}}.$
-\end{example}
+\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.
-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{example}
-\textbackslash diffp{[}2,3{]}F\{x,y,z\} $\Longrightarrow\quad{\displaystyle \diffp[2,3]F{x,y,z}.}$
-\end{example}
+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.
-\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)\protect\label{subsec:Minutiae-of-spacing}}
-\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, \texttt{\textbackslash ,} (or 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',
+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
-2 mu between the differentials in the fraction form of derivative and 1
-mu in the slash form.
+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 1
-mu is subtracted from the default spacing. Thus in
+a superscript, an adjustment is made to the extra spacing. By default
+\verb`1 mu` is subtracted from the default spacing. Thus in
\[
\diffp[2]F{x,y,z},
\]
-2 mu of spacing is inserted between the $\partial y$ and $\partial z$,
-but because the superscript already provides some separation between them,
-only 1 mu is inserted between $\partial x^{2}$ and $\partial y$.
+\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 adjusted by the user; see Section~\ref{sec:Changing-defaults}.
-Some other minutiae of spacing are discussed below in Subsection~\ref{subsec:Comma-list-of-vars}
-when the variables themselves are super- or subscripted (as happens in
-tensor calculus, for instance).
+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{example}
-\textbackslash diffp{[}1,m+1,m-1{]}\{F(x,y,z)\}\{x,y,z\} $\Longrightarrow\quad{\displaystyle \diffp[1,m+1,m-1]{F(x,y,z)}{x,y,z}.}$
-\end{example}
+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 line 53 (say)
-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
+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~
@@ -671,9 +788,9 @@
(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\}}
+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~
@@ -686,120 +803,118 @@
the~overall~order.
\end{lyxcode}
-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.
+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{example}
-\noindent \textbackslash diffp{[}2km,m-1,m+1{]}\{F(x,y,z)\}\{x,y,z\} $\Longrightarrow\quad{\displaystyle \diffp[2km,m-1,m+1]{F(x,y,z)}{x,y,z}.}$
-\end{example}
+\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}.
-\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{example}
-\textbackslash diffp{[}2km,m-1,m+1{]}{[}2m(k+1){]}\{F(x,y,z)\}\{x,y,z\}
-$\Longrightarrow\quad{\displaystyle \diffp[2km,m-1,m+1][2m(k+1)]{F(x,y,z)}{x,y,z}}.$
-\end{example}
-
+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{example}
-\noindent \textbackslash diffp{[}m/2+n/2,m/2,n/2{]}F\{x,y,z\} $\Longrightarrow\quad{\displaystyle \diffp[m/2+n/2,m/2,n/2]F{x,y,z},}$
-\end{example}
-
-\noindent whereas we would like the total order to be presented as $m+n$.
-Using the override option,
-\begin{example}
-\noindent \textbackslash diffp{[}m/2+n/2,m/2,n/2{]}{[}m+n{]}F\{x,y,z\}
-$\Longrightarrow\quad{\displaystyle \diffp[m/2+n/2,m/2,n/2][m+n]F{x,y,z}}.$
-\end{example}
-
+\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
+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}}
+\subsubsection{Comma list of variables of differentiation\protect\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{example}
-\textbackslash diffp\{A\_i\}\{ x\textasciicircum j,x\textasciicircum k
-\} $\Longrightarrow\quad{\displaystyle \diffp{A_{i}}{x^{j},x^{k}}.}$
-\end{example}
-
+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.
+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 Subsection~\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, which inserts \texttt{-1 mu} of spacing. For our example,
-\begin{example}
-\textbackslash diffp\{A\_i\}\{ x\textasciicircum j\textbackslash negmu,x\textasciicircum k
-\} $\Longrightarrow\quad{\displaystyle \diffp{A_{i}}{x^{j}\negmu,x^{k}},}$
-\end{example}
+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`.
-\noindent the \texttt{\textbackslash negmu} decreasing the spacing between
-the terms from the default 2 mu to 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{example}
-\textbackslash diffp{[}2m-(k+1),2(k+1)-m{]}\{F(x,y,z)\}\{x,y,z\} $\Longrightarrow\quad{\displaystyle \diffp[2m-(k+1),2(k+1)-m]{F(x,y,z)}{x,y,z}}.$
-\end{example}
+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.
+-- 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):
+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~
@@ -811,323 +926,340 @@
option~to~enter~the~overall~order.
\end{lyxcode}
-This is a limitation on the dynamic use of parentheses -- but they \emph{can}
-be nested.
+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. No attempt is made to evaluate what is between them and they
-are treated simply as an extension of the variable. For example,
-\begin{example}
-\textbackslash diffp{[}f(k+1)+1,f(k-1)-1{]}\{F(x,y)\}\{x,y\} $\Longrightarrow\quad{\displaystyle \diffp[f(k+1)+1,f(k-1)-1]{F(x,y)}{x,y}}.$
-\end{example}
-
+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. 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{example}
-\noindent \textbackslash diffp{[}2(3+f(k))+1,1-3(f(k)-2){]}\{F(x,y)\}\{x,y\}
-$\Longrightarrow\quad{\displaystyle \diffp[2(3+f(k))+1,1-3(f(k)-2)]{F(x,y)}{x,y}}.$
-\end{example}
-
+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{example}
-\textbackslash diffp{[}m\textasciicircum 2+2(k-1),m\textasciicircum 2-(k+1){]}F\{x,y,z,w\}
-$\Longrightarrow\quad{\displaystyle \diffp[m^{2}+2(k-1),m^{2}-(k+1)]F{x,y,z,w}}.$
-\end{example}
-
+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}.
+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.
+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{example}
-\textbackslash diffp{[}2{]}q\{\textbackslash frac 1\textbackslash Theta\}
-$\Longrightarrow\quad{\displaystyle \diffp[2]q{\frac{1}{\Theta}}.}$
-\end{example}
+\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}).
-\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 (Section~\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{example}
-\textbackslash diffp q\{(\textbackslash frac 1\textbackslash Theta),V\}
-$\Longrightarrow{\displaystyle \quad\diffp q{(\frac{1}{\Theta}),V}.}$
-\end{example}
+\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{example}
-\textbackslash jacob\{u,v,w\}\{x,y,z\} $\Longrightarrow\quad{\displaystyle \jacob{u,v,w}{x,y,z}.}$
-\end{example}
-
+\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\}}
+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}}
+\section{Changing defaults; variant forms\protect\label{sec:Changing-defaults}}
-To write the range of different examples displayed in the Rogues' Gallery
-(Section~\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 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{ }
-How a derivative is displayed in a document is determined by specifying
-values in a `key = value' list. This is done with the \texttt{\textbackslash diffdef}
-command, which also allows a name to be associated with the list. By using
-that name as an argument in the \texttt{\textbackslash diff} command,
-a derivative is formed shaped by those values. Examples will make the process
-clear.
-
\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 an em in the math font used.}
-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} 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.
+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.
-\begin{wraptable}[22]{o}{0.5\columnwidth}%
-\noindent \begin{centering}
-\vspace{-4.5ex}
- \caption{{\small{}Defaults (ordinary derivatives})\label{tab:Ordinary-derivatives}}
-\par\end{centering}
-\noindent \centering{}\abovetopsep=.5ex{}%
+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{}\caption{{\small Defaults (ordinary derivatives})\protect\label{tab:Ordinary-derivatives}}
\begin{tabular}{lr}
\toprule
-{\small{}key} & {\small{}default}\tabularnewline
+{\small key} & {\small default}\tabularnewline
\midrule
-{\small{}op-symbol} & \texttt{\small{}d}\tabularnewline
-{\small{}op-symbol-alt} & \texttt{\small{}= op-symbol}\tabularnewline
-{\small{}op-order-sep} & \texttt{\small{}1 mu}\tabularnewline
-{\small{}{*}-op-left} & \texttt{\small{}false}\tabularnewline
-{\small{}{*}-italic-nudge} & \texttt{\small{}3 mu}\tabularnewline
-{\small{}{*}/-op-wrap} & \texttt{\small{}true}\tabularnewline
-{\small{}long-var-wrap} & \texttt{\small{}d(v)}\tabularnewline
-{\small{}denom-term-sep} & \texttt{\small{}2 mu}\tabularnewline
-{\small{}/-denom-term-sep} & \texttt{\small{}1 mu}\tabularnewline
-term-sep-adjust & \texttt{-1 mu}\tabularnewline
-{\small{}left-delim} & \texttt{\small{}\textbackslash left .}\tabularnewline
-{\small{}right-delim} & \texttt{\small{}\textbackslash right |}\tabularnewline
-{\small{}elbowroom} & \texttt{\small{}0 mu}\tabularnewline
-{\small{}subscr-nudge} & \texttt{\small{}0 mu}\tabularnewline
-{\small{}/-left-delim} & \texttt{\small{}(}\tabularnewline
-{\small{}/-right-delim} & \texttt{\small{})}\tabularnewline
-{\small{}/-elbowroom} & \texttt{\small{}0 mu}\tabularnewline
-{\small{}/-subscr-nudge} & \texttt{\small{}0 mu}\tabularnewline
+{\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{wraptable}%
-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 Subsection~\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.
+\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};
+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}
-\end{description}
-~\vspace{-5ex}
-
-\begin{description}
-\item [{op-order-sep}] extra horizontal space added between the op-symbol and
-the superscripted order of differentiation in higher order derivatives;
-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 [{{*}-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}
-\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 [{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-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
+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 [{/-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} 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 $\partial y$
+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 |}
+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 [{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 [{/-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 slash-form derivative; default = \texttt{0
-mu}
+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}
-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
+\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}[9]{o}{0.4\columnwidth}%
+\begin{wraptable}[10]{o}{0.4\columnwidth}%
\centering{}\vspace{-4ex}
- \caption{{\small{}ISO default changes}\label{tab:ISO-setting-changes}}
+ \caption{{\small ISO default changes}\protect\label{tab:ISO-setting-changes}}
\abovetopsep=.5ex %
\begin{tabular}{lr}
\toprule
-{\small{}key} & {\small{}default}\tabularnewline
+{\small key} & {\small default}\tabularnewline
\midrule
-{\small{}op-symbol} & \texttt{\small{}\textbackslash mathrm\{d\}}\tabularnewline
-{\small{}op-order-sep} & \texttt{\small{}0 mu}\tabularnewline
-{\small{}left-delim} & \texttt{\small{}\textbackslash left (}\tabularnewline
-{\small{}right-delim} & \texttt{\small{}\textbackslash right )}\tabularnewline
-{\small{}subscr-nudge} & \texttt{\small{}-6 mu}\tabularnewline
+{\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}%
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.
+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.
+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 Subsection~\ref{subsec:D-delta-Delta} below.
+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{-4.5ex}
- \caption{{\small{}Default changes: partial derivatives}\label{tab:Partial-deriv-defaults}}
+\centering{}\vspace{-4ex}
+ \caption{{\small Default changes for partial derivatives}\protect\label{tab:Partial-deriv-defaults}}
\abovetopsep=.5ex %
\begin{tabular}{lr}
\toprule
-{\small{}key} & {\small{}default}\tabularnewline
+{\small key} & {\small default}\tabularnewline
\midrule
-{\small{}op-symbol } & \texttt{\small{}\textbackslash partial}\tabularnewline
-{\small{}left-delim} & \texttt{\small{}\textbackslash left (}\tabularnewline
-{\small{}right-delim} & \texttt{\small{}\textbackslash right )}\tabularnewline
-{\small{}subscr-nudge } & \texttt{\small{}-6 mu}\tabularnewline
+{\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,
-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
+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
\[
\diffp SV[T]=\diffp PT[V].
@@ -1134,55 +1266,121 @@
\]
-\subsection{Setting your own defaults: \texttt{\textbackslash diffdef\label{subsec:diffdef}}}
+\subsection{Setting your own defaults: \texttt{\textbackslash diffdef\protect\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 the ISO's use of
-subscripted parentheses to indicate a point of evaluation, enter in the
-preamble of your document the command\vspace{-2ex}
-
+\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}
-\noindent %
-\noindent\begin{minipage}[t]{1\columnwidth}%
-\begin{lyxcode}
\textbackslash diffdef~\{\}~~~~
-\begin{lyxcode}
-\{~~~~~~
-\begin{lyxcode}
-op-symbol~~~~=~\textbackslash mathrm\{d\},~~~~
-op-order-sep~=~0~mu
+~~\{~~~~~~
+
+~~~~op-symbol~~~~=~\textbackslash mathrm\{d\},~~~~
+
+~~~~op-order-sep~=~0~mu
+
+~~\}
\end{lyxcode}
-\}
-\end{lyxcode}
-\end{lyxcode}
-%
-\end{minipage}
-\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.
+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 Section~\ref{sec:Rogues'-gallery}.
+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) 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 to have a number of variant forms available to
-illustrate the wide variety of ways in which derivatives are displayed.
+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:
-
-\noindent %
-\noindent\begin{minipage}[t]{1\columnwidth}%
+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~\}
@@ -1198,35 +1396,29 @@
~~\}
\end{lyxcode}
-%
-\end{minipage}
-
-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 Subsection~\ref{subsec:Partial-appending},
-\begin{example}
-\textbackslash diff.p.{*}\{\textbackslash frac PT\}U{[}V{]} = \textbackslash diff.p.{*}\{\textbackslash frac
-1T\}V{[}U{]} $\Longrightarrow\quad{\displaystyle \diff.p.*{\frac{P}{T}}U[V]=\diff.p.*{\frac{1}{T}}V[U]}$
-\end{example}
-
+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.}, saving a few keystrokes and maintaining
-compatibility with version 1 of the package. In \LaTeXe{} synatx,
+with \texttt{\textbackslash diff.p.}:
\begin{lyxcode}
-\textbackslash newcommand~\{~\textbackslash diffp~\}~\{~\textbackslash diff.p.~\}
+\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 dot-delimited argument applies only to \texttt{\textbackslash diff}.
+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
+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}
-\noindent %
-\noindent\begin{minipage}[t]{1\columnwidth}%
-\begin{lyxcode}
\textbackslash diffdef~\{~up~\}~
~~\{
@@ -1237,83 +1429,69 @@
~~\}
\end{lyxcode}
-%
-\end{minipage}
-\end{lyxcode}
-Apart from the 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{example}
-\textbackslash diff.up.yx $\Longrightarrow\quad{\displaystyle \diff.up.yx}.$
-\end{example}
+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.
-\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{example}
-\noindent \textbackslash diff.up.{*}\{\textbackslash frac\{F(x)\}\{G(x)\}\}x{[}x=1{]}
-$\Longrightarrow\quad{\displaystyle \diff.up.*{\frac{F(x)}{G(x)}}x[x=1]}$
-\end{example}
-
-\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
+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{example}
-\textbackslash diff.padrift.Fx{[}y{]} $\Longrightarrow{\displaystyle \diff.padrift.Fx[y]}$
-\end{example}
+\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 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
-\begin{example}
-\noindent \textbackslash diffp Fx{[}y{]} $\Longrightarrow{\displaystyle \diffp Fx[y]}$
-\end{example}
-
\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
+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}
-\noindent %
-\noindent\begin{minipage}[t]{1\columnwidth}%
-\begin{lyxcode}
\textbackslash diffdef~\{~pvrule~\}~\{~op-symbol~=~\textbackslash partial~\}~
\end{lyxcode}
-%
-\end{minipage}
-\end{lyxcode}
(or some other name of your choosing). This gives
-\begin{example}
-\textbackslash diff.pvrule.\{F(x,y)\}x{[}x=1{]}$\Longrightarrow{\displaystyle \diff.pvrule.{F(x,y)}x[x=1]}$
-\end{example}
+\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}}
-\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
+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}%
@@ -1339,35 +1517,29 @@
%
\end{minipage}
-This gives, for the same example, \texttt{\textbackslash diff.ptxt.ST{[}V{]}}
-displaying as $\diff.ptxt.ST[V]$, where the subscript is better positioned
-and there is a better fit between parentheses and derivative.
+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}}
+\subsubsection{Derivatives from D, \textbackslash delta, \textbackslash Delta\protect\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 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{example}
-\textbackslash diff.D.\{\textbackslash rho\}t=\textbackslash diffp\textbackslash rho
-t + \textbackslash mathbf\{u\textbackslash cdot\}\textbackslash nabla\textbackslash rho
-$\Longrightarrow{\displaystyle \diff.D.\rho t=\diffp\rho t+\mathbf{u\cdot}\nabla\rho}$
-\end{example}
-
+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, \vspace{-2ex}
-
+If you want upright `D's, then the \texttt{ISO} package option will
+produce that effect. Alternatively,
\begin{lyxcode}
-\noindent %
-\noindent\begin{minipage}[t]{1\columnwidth}%
-\begin{lyxcode}
\textbackslash diffdef~\{~Up~\}~
~~\{
@@ -1378,84 +1550,78 @@
~~\}
\end{lyxcode}
-%
-\end{minipage}
-\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
-\begin{example}
-\textbackslash diff.delta.yx $\Longrightarrow{\displaystyle \diff.delta.yx}.$
-\end{example}
+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})).
+\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{example}
-\textbackslash diff.Delta.y/x $\Longrightarrow{\displaystyle \diff.Delta.y/x,}$
-\end{example}
+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.
-\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.
+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.},
+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 commands equivalent to\footnote{In fact the actual commands in \texttt{diffcoeff.sty} use the syntax of
-the \texttt{xparse} package, e.g. \texttt{\textbackslash NewDocumentCommand
-\{ \textbackslash Diff \} \{ \} \{ }\textbackslash diff.D. \}, and similarly
-for the others.}
+through the commands
\begin{lyxcode}
-\textbackslash newcommand\{\textbackslash Diff\}\{\textbackslash diff.D.\}
+\textbackslash NewDocumentCommand~\textbackslash Diff~\{\}~~\{\textbackslash diff.D.\}
-\textbackslash newcommand\{\textbackslash diffd\}\{\textbackslash diff.delta.\}
+\textbackslash NewDocumentCommand~\textbackslash diffd~\{\}~\{\textbackslash diff.delta.\}
-\textbackslash newcommand\{\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.
+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}}
+\subsection{The \texttt{.def} file\protect\label{subsec:The-.def-file}}
This mechanism of variant formation is how I have been able to illustrate
-in the Rogues' Gallery, Section~\ref{sec:Rogues'-gallery}, the wide variety
+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 mkern} 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.
+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 has been placed in the same directory as \texttt{diffcoeff.tex}. To
-use these definitions, the \texttt{diffcoeff} package is called with the
-command
+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.
+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}
}
@@ -1464,19 +1630,20 @@
\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
-a similar process will apply there.%
+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{}
@@ -1487,68 +1654,61 @@
\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.\footnote{This file should be in the same directory as \texttt{diffcoeff.pdf} and
-\texttt{diffcoeff.tex} in your \LaTeX{} distribution.}
+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 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}
+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}
-\noindent %
-\noindent\begin{minipage}[t]{1\columnwidth}%
-\begin{lyxcode}
\textbackslash diffdef~\{\}~~~~
-\begin{lyxcode}
-\{~~~~~~
-\begin{lyxcode}
-key-1~=~value-1,~~~~
-key-2~=~value-2,
+~~\{~~~~~~
-...
+~~~~key-1~=~value-1,~~~~
-key-n~=~value-n
+~~~~key-2~=~value-2,
+
+~~~~...
+
+~~~~key-n~=~value-n
+
+~~\}
\end{lyxcode}
-\}
-\end{lyxcode}
-\end{lyxcode}
-%
-\end{minipage}
-\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.
+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,
+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{D:\textbackslash texmf\textbackslash}
-on a Windows machine) the file \texttt{diffcoeff.def} is located in the
-directory \texttt{D:\textbackslash texmf\textbackslash tex\textbackslash latex\textbackslash diffcoeff\textbackslash}.
+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}.
+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.}
@@ -1557,176 +1717,179 @@
\[
\dl P=\diffp Px\dl x+\diffp Py\dl y+\diffp Pz\dl z,
\]
-or an integral like $\int\sin x\dl2x$, or a multi-variable integral like
+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{example}
-\textbackslash dl x $\Longrightarrow\dl x.$
-\end{example}
+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}
-\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 vec\{x\}}
-or \texttt{\textbackslash mathbf\{x\}}:
-\begin{example}
-\textbackslash dl \textbackslash vec\{x\} $\Longrightarrow\dl\vec{x}$~~~~\textbackslash dl
-\textbackslash mathbf\{x\} $\Longrightarrow\dl0\mathbf{x}.$
-\end{example}
-
-
\subsection{Options}
There are two options available with the differential command.
-The first is the dotted name option discussed in Section~\ref{sec:Changing-defaults}.
+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{example}
-\textbackslash dl.up.x $\Longrightarrow\dl.up.x.$
-\end{example}
+\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'.
-\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}
-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). But the only reason one might use this variant `in earnest'
-is because of the convenience offered by the second option to the \texttt{\textbackslash dl}
-command.
+\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 $.
\subsubsection{Spacing}
This second option inserts spacing before the `d'. If \texttt{\textbackslash dl}
-is followed by a digit (0, 1, 2, ..., 9) it will insert a horizontal space
-of that number of mu before the `d'; (\texttt{\textbackslash dl0x} has
-the same effect as \texttt{\textbackslash dl x}.)\texttt{ }Thus, an alternative
-way of writing an example in Chapter~18 of \emph{The \TeX book} is
-\begin{example}
-\textbackslash dl x\textbackslash dl3y=r\textbackslash dl3r\textbackslash dl3\textbackslash theta
-$\Longrightarrow\dl x\dl3y=r\dl3r\dl3\theta.$
-\end{example}
-
+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{example}
-\noindent \textbackslash dl x\textbackslash dl2y=r\textbackslash dl2r\textbackslash dl2\textbackslash theta
-$\Longrightarrow\dl x\dl2y=r\dl2r\dl2\theta$
-\end{example}
-
+\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 $\int\sin x\dl2x$.
+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,
-\begin{example}
-\textbackslash dl20x $\Longrightarrow\dl20x$
-\end{example}
+\verb`$ \dl20x $` $\Longrightarrow$ $ \dl20x $, the effect is unlikely
+to be what is wanted.
-\noindent the effect is unlikely to be what is wanted.
+From version 3.2 of \texttt{diffcoeff} it is possible to also add
+\emph{negative} space before the differential, which might be useful
+in special contexts, perhaps to construct a symbol:
+\begin{centred}
+\verb`$ /\dl-9x $` $\Longrightarrow$ $ /\dl-9x. $
+\end{centred}
+\noindent For negative space before the differential, add a minus
+sign before the (single) digit.
-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{example}
-/\textbackslash dl-9x $\Longrightarrow/\dl-9x.$
-\end{example}
-
-\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, to illustrate spacing in the denominator of a mixed partial
-derivative, I have earlier used \texttt{\textbackslash dl.p.x\textbackslash dl.p.2y\textbackslash dl.p.2z},
-and the variation to that spacing when a higher-order differentiation occurs:
-\begin{example}
-\textbackslash dl.p.x\textasciicircum 2\textbackslash dl.p.1y\textbackslash dl.p.2z
-$\Longrightarrow\dl.p.x^{2}\dl.p.1y\dl.p.2z.$
-\end{example}
+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}
-
\section{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}.
+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 would
-like in that case too).
+\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{\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.
+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,
+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}
-\textbackslash diffp{[}m-(k+1),m+(k-1){]}\{F(x,y,z)\}\{x,y,z\}
-
-$\Longrightarrow{\displaystyle \diffp[m-(k+1),m+(k-1)]{F(x,y,z)}{x,y,z}},$
+$\Longrightarrow$ \[ \diffp[m-(k+1),m+(k-1)]{F(x,y,z)}{x,y,z} \]
\end{example}
\begin{itemize}
-\item and where it fails, either to calculate at all or to present the result
+\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}
-\textbackslash diffp{[}m+(k+1),m+(k-1){]}{[}2(m+k+1){]}\{F(x,y,z,w)\}\{x,y,z,w\}
-
-$\Longrightarrow{\displaystyle \diffp[m+(k+1),m+(k-1)][2(m+k+1)]{F(x,y,z,w)}{x,y,z,w}}.$
+$\Longrightarrow$ \[ \diffp[m+(k+1),m+(k-1)][2(m+k+1)]{F(x,y,z,w)}{x,y,z,w} \]
\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 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.
+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{example}
-\textbackslash diffp\{A\_i\}\{ x\textasciicircum j,x\textasciicircum k
-\} $\Longrightarrow\quad{\displaystyle \diffp{A_{i}}{x^{j},x^{k}}.}$
-\end{example}
-
+\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:
+\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:
\[
\diffp ST[V]
\]
@@ -1733,85 +1896,180 @@
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 commands
+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}. Consequently later versions
-of the package 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 The final option added to \texttt{\textbackslash diff} (and not present
+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 Subsection~\ref{subsec:Text-and-script-style})
+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.
-The demands of writing the present document forced another, the dot-delimited
-name option.
+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{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 derivative. 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}
+\end{enumerate}
+
\section{Commands}
\begin{description}
-\item [{\texttt{\textbackslash diff}}] options:
+\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}{]}
-\item \{as for previous, but using braces\} (deprecated)
\end{enumerate}
-\item [{\texttt{\textbackslash diffdef}}] options:
+\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}}] options:
+\item [{\texttt{\textbackslash diffp}}] \texttt{= \textbackslash diff.p.}
+\end{description}
+\newpage{}
+\begin{description}
+\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{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 negmu}}] insert a $-1$ mu space
@@ -1819,7 +2077,8 @@
\item [{\texttt{\textbackslash onemu}}] insert a $1$ mu space
\item [{\texttt{\textbackslash twomu}}] insert a $2$ mu space
\end{description}
-Deprecated:
+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.}
Modified: trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff-doc.def
===================================================================
--- trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff-doc.def 2021-12-28 22:49:31 UTC (rev 61431)
+++ trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff-doc.def 2021-12-28 22:49:47 UTC (rev 61432)
@@ -18,15 +18,13 @@
\diffdef { up }
{
op-symbol = \mathrm{d},
- op-order-sep = 0 mu ,
- /-op-order-sep = 0 mu
+ op-order-sep = 0 mu
}
\diffdef { Up }
{
op-symbol = \mathrm{D},
- op-order-sep = 0 mu ,
- /-op-order-sep = 0 mu
+ op-order-sep = 0 mu
}
% wrap long vars: (d longvar)
@@ -80,7 +78,6 @@
{
op-symbol = \Delta ,
op-order-sep = 0 mu ,
- /-op-order-sep = 0 mu ,
left-delim = \left ( ,
right-delim = \right ),
subscr-nudge = -6 mu
Modified: trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff.sty
===================================================================
--- trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff.sty 2021-12-28 22:49:31 UTC (rev 61431)
+++ trunk/Master/texmf-dist/tex/latex/diffcoeff/diffcoeff.sty 2021-12-28 22:49:47 UTC (rev 61432)
@@ -9,22 +9,26 @@
%
\RequirePackage{expl3}
\RequirePackage{xparse,l3keys2e,xtemplate}
-\ProvidesExplPackage {diffcoeff} {2019/12/28} {3.2}
+\ProvidesExplPackage {diffcoeff} {2021/12/24} {4.0}
{Write differential coefficients consistently and easily.}
-%
+%
\keys_define:nn { diffcoeff }
{
- ISO .bool_gset:N = \g__diffcoeff_ISO_bool,
- def-file .tl_gset:N = \g__diffcoeff_def_tl ,
- def-file .initial:n = 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
}
\ProcessKeysPackageOptions { diffcoeff }
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\cs_generate_variant:Nn \tl_if_eq:nnTF { nV }
\tl_new:N \l__diffcoeff_oporder_tl
-\tl_new:N \l__diffcoeff_differentiand_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
@@ -45,6 +49,8 @@
\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
@@ -62,36 +68,36 @@
op-symbol : tokenlist = d ,
op-symbol-alt : tokenlist = \KeyValue { op-symbol },
op-order-sep : muskip = 1 mu ,
- /-op-order-sep : muskip = 1 mu ,
- *-op-left : boolean = false ,
- *-italic-nudge : muskip = 3 mu ,
- */-op-wrap : boolean = true ,
+ 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 ,
- /-denom-term-sep : muskip = 1 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
+ /-subscr-nudge : muskip = 0 mu ,
+ */-derivand-sep : muskip = \KeyValue { /-derivand-sep },
+ */-op-wrap : boolean = true
}
% #1 order spec(seqvar); #2 order override(tlvar)
-% #3 differentiand(tlvar); #4 denominator(seqvar)
+% #3 derivand(tlvar); #4 denominator(seqvar)
% #5 subscript(tlvar)
\DeclareTemplateCode { derivative } { DERIV } { 5 }
{
- op-symbol = \l__diffcoeff_op_tl ,
- op-symbol-alt = \l__diffcoeff_op_alt_tl ,
- op-order-sep = \l__diffcoeff_oporder_muskip ,
- /-op-order-sep = \l_tmpa_muskip ,
- *-op-left = \l__diffcoeff_op_left_bool ,
- *-italic-nudge = \l__diffcoeff_opnudge_muskip ,
- */-op-wrap = \l__diffcoeff_opwrap_bool ,
+ 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:Npn \__diffcoeff_wrap_longvars:nn #1#2
{ \l__diffcoeff_op_alt_tl {#2}^{#1} },
@@ -101,18 +107,24 @@
{ (\l__diffcoeff_op_alt_tl {#2)}^{#1} },
unknown = \cs_set:Npn \__diffcoeff_wrap_longvars:nn #1#2
{ \l__diffcoeff_op_alt_tl {(#2)}^{#1} }
- } ,
- denom-term-sep = \l__diffcoeff_varsep_muskip ,
- /-denom-term-sep = \l_tmpb_muskip ,
- term-sep-adjust = \l__diffcoeff_sep_adj_muskip ,
- left-delim = \l__diffcoeff_ldelim_tl ,
- right-delim = \l__diffcoeff_rdelim_tl ,
+ },
+ 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,
- /-left-delim = \l_tmpa_tl ,
- /-right-delim = \l_tmpb_tl ,
- /-elbowroom = \l_tmpc_muskip ,
- /-subscr-nudge = \l_tmpd_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
@@ -127,25 +139,36 @@
%%%%%%%%%%
\cs_new:Npn \__diffcoeff_slash_vals:
{
- \muskip_set:Nn \l__diffcoeff_oporder_muskip \l_tmpa_muskip
- \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_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_tmpa_tl
- \tl_set:NV \l__diffcoeff_rdelim_tl \l_tmpb_tl
+ \tl_set:NV \l__diffcoeff_ldelim_tl \l__diffcoeff_ldelimi_tl
+ \tl_set:NV \l__diffcoeff_rdelim_tl \l__diffcoeff_rdelimi_tl
}
\cs_new:Npn \__diffcoeff_build:NNNNN #1#2#3#4#5
{
- \bool_if:NF \l__diffcoeff_opwrap_bool
+ \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 } }
\exp_args:NV\tl_if_novalue:nF #5
- { \l__diffcoeff_ldelim_tl \mkern \l__diffcoeff_elbowrm_muskip }
+ { \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 #4 { , } }
\__diffcoeff_single:NNN #2 #3 \l_tmpa_tl
}
- {
+ {
\int_zero:N \l_tmpa_int
\seq_mapthread_function:NNN #1 #4 \__diffcoeff_map_orders:nn
\__diffcoeff_mixed:NNN #2 #3 \l__diffcoeff_denom_seq
@@ -152,7 +175,7 @@
}
\exp_args:NV\tl_if_novalue:nF #5
{
- \mkern \l__diffcoeff_elbowrm_muskip \l__diffcoeff_rdelim_tl
+ \mskip \l__diffcoeff_elbowrm_muskip \l__diffcoeff_rdelim_tl
\exp_args:NV\tl_if_empty:nF #5
{
\c_math_subscript_token
@@ -161,6 +184,35 @@
}
}
%%%%%%%%%%%%%%%%%%%%
+\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 }
+ }
+ }
+ }
% (ptl) form denom from #1 orders seq & #2 vars seq
\cs_new_protected:Npn \__diffcoeff_map_orders:nn #1#2
{
@@ -184,16 +236,16 @@
\__diffcoeff_numer:N { #1 }
\__diffcoeff_form_deriv:NNn
\l__diffcoeff_oporder_tl
- \l__diffcoeff_differentiand_tl
+ \l__diffcoeff_derivand_tl
{ \__diffcoeff_denom_single:NN #1 #3 }
}
-% #1 total order; #2 differentiand; #3 denom seq
+% #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_differentiand_tl
+ \l__diffcoeff_derivand_tl
{ \__diffcoeff_denom_sep:N #3 }
}
\cs_new:Npn \__diffcoeff_denom_sep:N #1
@@ -206,9 +258,9 @@
{
\seq_pop:NN \l__diffcoeff_orders_seq \l_tmpa_tl
\str_if_eq:VnTF \l_tmpa_tl { 1 }
- { \mkern \l__diffcoeff_varsep_muskip }
+ { \mskip \l__diffcoeff_varsep_muskip }
{
- \mkern \muskip_eval:n { \l__diffcoeff_varsep_muskip +
+ \mskip \muskip_eval:n { \l__diffcoeff_varsep_muskip +
\l__diffcoeff_sep_adj_muskip }
}
}
@@ -244,16 +296,16 @@
}
}
% #1 op+order; #2 diff'iand; #3 denom
-% 0 frac; 1 frac append; 2 slash ; 3 slash append
+% 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 } }
+ { 1 } { \frac { #1 } { #3 } #2 }
{ 2 } { #1 #2 / #3 }
- { 3 } { ( #1 / #3 ) { #2 } }
- { 4 } { #1 / #3 { #2 } }
+ { 3 } { ( #1 / #3 ) #2 }
+ { 4 } { #1 / #3 #2 }
}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -274,25 +326,27 @@
\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 }
- { \mkern \IfBooleanT #2 { - }#3 mu \l__diffcoeff_op_tl \group_end: }
+ { \mskip \IfBooleanT #2 { - }#3 mu \l__diffcoeff_op_tl \group_end: }
{ \l__diffcoeff_op_tl \group_end: {} #3 }
}
-\NewDocumentCommand \negmu {} { \mkern -1 mu }
-\NewDocumentCommand \nilmu {} { \mkern 0 mu }
-\NewDocumentCommand \onemu {} { \mkern 1 mu }
-\NewDocumentCommand \twomu {} { \mkern 2 mu }
+\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(tl) = diff'iand; #6( / ) = slash boolean
-% #7(clist) = vars of diff.; #8(tl) = pt of eval./vars held const
-% #9(tl) = as #8 (for backwards compat)
-\NewDocumentCommand \diff { d.. s O{1} o m t/ m !O{#9} g }
+% #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:
- \tl_set:Nn \l__diffcoeff_differentiand_tl { #5 }
- \tl_set:Nn \l__diffcoeff_trailing_tl { #8 }
- \seq_set_from_clist:Nn \l__diffcoeff_vars_seq { #7 }
+ \IfBooleanTF #5
+ { \bool_set_true:N \l__diffcoeff_altsep_bool }
+ { \bool_set_false:N \l__diffcoeff_altsep_bool }
+ \tl_set:Nn \l__diffcoeff_derivand_tl { #6 }
+ \tl_set:Nn \l__diffcoeff_trailing_tl { #9 }
+ \seq_set_from_clist:Nn \l__diffcoeff_vars_seq { #8 }
\seq_set_from_clist:Nn \l__diffcoeff_orders_seq { #3 }
\int_set:Nn \l__diffcoeff_vars_int
{ \seq_count:N \l__diffcoeff_vars_seq }
@@ -330,12 +384,11 @@
% append? slash?
\int_zero:N \l__diffcoeff_format_int
\IfBooleanT #2 { \int_incr:N \l__diffcoeff_format_int }
- \IfBooleanT #6 { \int_add:Nn \l__diffcoeff_format_int { 2 } }
-
+ \IfBooleanT #7 { \int_add:Nn \l__diffcoeff_format_int { 2 } }
\UseInstance { derivative } { ord\l__diffcoeff_type_tl }
\l__diffcoeff_orders_seq
\l__diffcoeff_tot_order_tl
- \l__diffcoeff_differentiand_tl
+ \l__diffcoeff_derivand_tl
\l__diffcoeff_vars_seq
\l__diffcoeff_trailing_tl
\group_end:
@@ -616,7 +669,7 @@
% ordinary & D
\DeclareInstance { derivative } { ord } { DERIV } { }
-\bool_if:NTF \g__diffcoeff_ISO_bool
+\bool_if:NTF \l__diffcoeff_ISO_bool
{
\diffdef { }
{
@@ -638,7 +691,8 @@
right-delim = \right ) ,
subscr-nudge = -6 mu
}
-\NewDocumentCommand \diffp { } { \diff.p. }
+\NewDocumentCommand \diffp {} { \diff.p. }
+\NewDocumentCommand \dlp {} { \dl.p. }
% delta
\diffdef { delta }
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