texlive[67525] Master/texmf-dist: numerica (1jul23)
commits+karl at tug.org
commits+karl at tug.org
Sat Jul 1 21:38:22 CEST 2023
Revision: 67525
http://tug.org/svn/texlive?view=revision&revision=67525
Author: karl
Date: 2023-07-01 21:38:21 +0200 (Sat, 01 Jul 2023)
Log Message:
-----------
numerica (1jul23)
Modified Paths:
--------------
trunk/Master/texmf-dist/doc/latex/numerica/README.txt
trunk/Master/texmf-dist/doc/latex/numerica/numerica.pdf
trunk/Master/texmf-dist/doc/latex/numerica/numerica.tex
trunk/Master/texmf-dist/tex/latex/numerica/numerica.sty
Modified: trunk/Master/texmf-dist/doc/latex/numerica/README.txt
===================================================================
--- trunk/Master/texmf-dist/doc/latex/numerica/README.txt 2023-07-01 19:38:12 UTC (rev 67524)
+++ trunk/Master/texmf-dist/doc/latex/numerica/README.txt 2023-07-01 19:38:21 UTC (rev 67525)
@@ -10,12 +10,10 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-This is version 2.0.0 of the numerica package. The packages
-l3kernel, l3packages, amsmath and mathtools are required. The
-commands \nmcIterate, \nmcSolve, \nmcRecur and \nmcTabulate
-available in version 1 of numerica by means of package options
-are now available as separate packages. See numerica.pdf for
-details on how to use the package.
+This is version 2.1.0 of the numerica package. It fixes a
+bug in version 2.0.0 arising from the introduction of the
+\int_if_zero:nTF conditionals into the LaTeX kernel.See
+numerica.pdf for details on how to use the package.
Manifest
%%%%%%%%
Modified: trunk/Master/texmf-dist/doc/latex/numerica/numerica.pdf
===================================================================
(Binary files differ)
Modified: trunk/Master/texmf-dist/doc/latex/numerica/numerica.tex
===================================================================
--- trunk/Master/texmf-dist/doc/latex/numerica/numerica.tex 2023-07-01 19:38:12 UTC (rev 67524)
+++ trunk/Master/texmf-dist/doc/latex/numerica/numerica.tex 2023-07-01 19:38:21 UTC (rev 67525)
@@ -1,4 +1,4 @@
-%% LyX 2.4.0-alpha3 created this file. For more info, see https://www.lyx.org/.
+%% LyX 2.4.0-beta3-devel created this file. For more info, see https://www.lyx.org/.
%% Do not edit unless you really know what you are doing.
\documentclass[english,tableposition=top]{report}
\usepackage{lmodern}
@@ -20,7 +20,7 @@
\usepackage{url}
\usepackage{amsmath}
\usepackage{amssymb}
-\usepackage[unicode=true,pdfusetitle,
+\usepackage[pdfusetitle,
bookmarks=true,bookmarksnumbered=true,bookmarksopen=true,bookmarksopenlevel=2,
breaklinks=true,pdfborder={0 0 1},backref=section,colorlinks=true]
{hyperref}
@@ -39,7 +39,7 @@
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Textclass specific LaTeX commands.
\newenvironment{centred}%
- {\begin{center}\baselineskip=13pt\parskip=1pt}{\end{center}}
+ {\begin{center}}{\end{center}}
\newenvironment{lyxcode}
{\par\begin{list}{}{
\setlength{\rightmargin}{\leftmargin}
@@ -52,10 +52,13 @@
{\end{list}}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% User specified LaTeX commands.
+\usepackage{babel}
\usepackage{numerica}
+
+
\usepackage{upquote}
-\newcommand\rel{\,\varrho\;}
+\newcommand{\rel}{\,\varrho\;}
\DeclareMathOperator{\erf}{erf}
\DeclareMathOperator{\gd}{gd}
@@ -64,66 +67,66 @@
\makeatother
\begin{document}
-\title{\texttt{numerica}}
+\title{\texttt{numerica}~\\
+ {\large version 2.1.0}}
\author{Andrew Parsloe\\
-(\url{ajparsloe at gmail.com})\\
-}
+ (\url{ajparsloe at gmail.com})\\
+ }
\maketitle
\begin{abstract}
-The \verb`numerica` package defines a command to numerically evaluate
+The \texttt{numerica} package defines a command to numerically evaluate
mathematical expressions in the LaTeX form in which they are typeset.
For programs like LyX with a preview facility, or compile-as-you-go
systems, interactive back-of-envelope calculations and numerical exploration
are possible within the document being worked on. The package requires
-the bundles \verb`l3kernel` and \verb`l3packages`, and the \verb`amsmath`
-and \verb`mathtools` packages. \\
-\\
+the bundles \texttt{l3kernel} and \texttt{l3packages}, and the \texttt{amsmath}
+and \texttt{mathtools} packages.
+\end{abstract}
+\noindent{}%
\noindent\begin{minipage}[t]{1\columnwidth}%
\begin{shaded}%
\paragraph*{Note:}
\begin{itemize}
-\item {\normalsize This document applies to version 2.0.0 of }{\normalsize\texttt{numerica.sty}}{\normalsize .}{\small\par}
-\item {\normalsize Reasonably recent versions of the \LaTeX 3 bundles }{\normalsize\texttt{l3kernel}}{\normalsize{}
-and }{\normalsize\texttt{l3packages}}{\normalsize{} are required (although
-much of }{\normalsize\verb`l3kernel`}{\normalsize{} has
-been incorporated into \LaTeXe{} since February 2020).}{\small\par}
-\item {\normalsize The package requires }{\normalsize\texttt{amsmath}}{\normalsize{}
-and }{\normalsize\texttt{mathtools}}{\normalsize .}{\small\par}
-\item {\normalsize I refer many times in this document (especially §\ref{sec:Argument-parsing})
-to }{\normalsize\emph{Handbook of Mathematical Functions}}{\normalsize ,
-edited by Milton Abramowitz and Irene A. Segun, Dover, 1965. This
-is abbreviated to }{\normalsize\emph{HMF}}{\normalsize , often followed
-by a number like 1.2.3 to locate the actual expression referenced.}{\small\par}
-\item {\normalsize Version 2.0.0 of }{\normalsize\texttt{numerica}}{\small\par}
+\item This document applies to version 2.1.0 of \texttt{numerica.sty}.
+\item Reasonably recent versions of the \LaTeX 3 bundles \texttt{l3kernel}
+and \texttt{l3packages} are required (although much of \texttt{l3kernel}
+has been incorporated into \LaTeXe{} since February 2020).
+\item The package requires \texttt{amsmath} and \texttt{mathtools}.
+\item I refer many times in this document (especially §\ref{sec:Argument-parsing})
+to \emph{Handbook of Mathematical Functions}, edited by Milton Abramowitz
+and Irene A. Segun, Dover, 1965. This is abbreviated to \emph{HMF},
+often followed by a number like 1.2.3 to locate the actual expression
+referenced.
+\item Version 2.1.0 of \texttt{numerica} fixes a conflict arising from the
+recent (May 2023) introduction of the \texttt{\textbackslash int\_if\_zero:nTF}
+conditionals into the \LaTeX{} kernel.
+\item Version 2.0.0 of \texttt{numerica}
\begin{itemize}
-\item {\normalsize splits into distinct packages the additional functionality
-previously available with the }{\normalsize\texttt{plus}}{\normalsize{}
-and }{\normalsize\texttt{tables}}{\normalsize{} package options of version
-1;}{\small\par}
-\item {\normalsize allows for user-defined macros and constants (with the
-}{\normalsize\texttt{\textbackslash nmcMacros }}{\normalsize and }{\normalsize\texttt{\textbackslash nmcConstants}}{\normalsize{}
-commands) to be used in expressions to be evaluated;}{\small\par}
-\item {\normalsize rewrites the code and changes the behaviour of }{\normalsize\texttt{\textbackslash nmcReuse}}{\normalsize{}
-to maintain uniformity across all commands (}{\normalsize\texttt{\textbackslash nmcEvaluate}}{\normalsize ,
-}{\normalsize\texttt{\textbackslash nmcInfo}}{\normalsize , }{\normalsize\texttt{\textbackslash nmcMacros}}{\normalsize ,
-}{\normalsize\texttt{\textbackslash nmcConstants}}{\normalsize , }{\normalsize\texttt{\textbackslash nmcReuse}}{\normalsize );
-this command is no longer compatible with its use in v.1;}{\small\par}
-\item {\normalsize changes the behaviour of }{\normalsize\texttt{\textbackslash text}}{\normalsize{}
-and }{\normalsize\texttt{\textbackslash mbox}}{\normalsize{} in the
-}{\normalsize\texttt{\textbackslash eval}}{\normalsize{} command; adds
-}{\normalsize\texttt{\textbackslash textrm}}{\normalsize , }{\normalsize\texttt{\textbackslash textsf}}{\normalsize ,
-and }{\normalsize\texttt{\textbackslash texttt}}{\normalsize{} to compensate;}{\small\par}
-\item {\normalsize includes many adjustments to the code, including around
-nesting of commands;}{\small\par}
-\item {\normalsize adds to and amends documentation.}{\small\par}
+\item splits into distinct packages the additional functionality previously
+available with the \texttt{plus} and \texttt{tables} package options
+of version 1;
+\item allows for user-defined macros and constants (with the \texttt{\textbackslash nmcMacros
+}and \texttt{\textbackslash nmcConstants} commands) to be used in
+expressions to be evaluated;
+\item rewrites the code and changes the behaviour of \texttt{\textbackslash nmcReuse}
+to maintain uniformity across all commands (\texttt{\textbackslash nmcEvaluate},
+\texttt{\textbackslash nmcInfo}, \texttt{\textbackslash nmcMacros},
+\texttt{\textbackslash nmcConstants}, \texttt{\textbackslash nmcReuse});
+this command is no longer compatible with its use in v.1;
+\item changes the behaviour of \texttt{\textbackslash text} and \texttt{\textbackslash mbox}
+in the \texttt{\textbackslash eval} command; adds \texttt{\textbackslash textrm},
+\texttt{\textbackslash textsf}, and \texttt{\textbackslash texttt}
+to compensate;
+\item includes many adjustments to the code, including around nesting of
+commands;
+\item adds to and amends documentation.
\end{itemize}
\end{itemize}
\end{shaded}%
\end{minipage}
-\end{abstract}
\begin{center}
-\tableofcontents{}
+\tableofcontents{}
\par\end{center}
\chapter{Introduction}
@@ -147,7 +150,7 @@
limited only to long division.) } but those I am aware of all require the mathematical expressions
they operate on to be changed to an appropriate syntax. Of these packages
\texttt{xfp} comes closest to my objective with \texttt{numerica}.
-For instance, given a formula
+For instance, given a formula
\begin{centred}
\verb`\frac{\sin (3.5)}{2} + 2\cdot 10^{-3}`
\end{centred}
@@ -154,11 +157,11 @@
(in a math environment), this can be evaluated using \texttt{xfp}
by transforming the expression to \verb`sin(3.5)/2 + 2e-3` and wrapping
this in the command \verb`\fpeval`. In \texttt{numerica} you don't
-need to transform the formula, just wrap it in an \verb`\eval` command:
+need to transform the formula, just wrap it in an \verb`\eval` command:
\begin{centred}
\verb`\eval{ \frac{\sin (3.5)}{2} + 2\cdot 10^{-3} }`.
\end{centred}
-(for the acutal calculation see §\ref{subsec:introSimple-examples}).\texttt{ }
+\noindent (for the acutal calculation see §\ref{subsec:introSimple-examples}).\texttt{ }
\texttt{numerica}, like \texttt{xfp} and a number of other packages,
uses \texttt{l3fp} (the \LaTeX 3 floating point module in \texttt{l3kernel})
@@ -165,10 +168,10 @@
as its calculational engine. To some extent the main command, \verb`\nmcEvaluate`,
short-name form \verb`\eval`, is a pre-processor to \texttt{l3fp},
converting mathematical expressions written in the \LaTeX\texttt{
-}form in which they will be typeset into an `fp-ified' form that
-is digestible by \texttt{l3fp}. The aim is to make the command act
-as a wrapper around such formulas. Ideally, one should not have to
-make \emph{any} adjustment to them, although any text on Fourier series
+}form in which they will be typeset into an `fp-ified' form that is
+digestible by \texttt{l3fp}. The aim is to make the command act as
+a wrapper around such formulas. Ideally, one should not have to make
+\emph{any} adjustment to them, although any text on Fourier series
suggests that hope in full generality is delusional. Surprisingly
often however it \emph{is} possible. We shall see shortly that even
complicated formulas like
@@ -176,7 +179,7 @@
\[
\cos\tfrac{m}{n}\pi-(1-4\sin^{2}\tfrac{m}{3n}\pi)\frac{\sin\tfrac{1}{n}\pi\sin\tfrac{m-1}{n}\pi}{2\sin^{2}\tfrac{m}{3n}\pi},
\]
-and
+and
\[
\left(\frac{1-4\sin^{2}\tfrac{m}{3n}\pi}{2\sin^{2}\tfrac{m}{3n}\pi}\right)\sin\tfrac{2m-3}{3n}\pi\sin\tfrac{m-3}{3n}\pi,
\]
@@ -185,14 +188,15 @@
There is no need to shift the position of the superscript $2$ on
the sines, no need to parenthesize the arguments of $\sin$ and $\cos$,
no need to insert asterisks to indicate multiplication, no need to
-change the \verb`\frac` and \verb`\tfrac`-s to slashes, \texttt{/},
-no need to delete the \verb`\left` and \verb`\right` that qualify
-the big parentheses (in the underlying \LaTeX ) in the second expression.
-Of course, if there are variables in an expression, as in these examples,
-they will need to be assigned values. And how the result of the evaluation
-is presented also requires specifying, but the aim is always: to evaluate
-mathematical expressions in \LaTeX{} with as little adjustment as possible
-to the form in which they are typeset.
+change the \noindent\verb`\frac` and \noindent\verb`\tfrac`-s to
+slashes, \texttt{/}, no need to delete the \noindent\verb`\left`
+and \noindent\verb`\right` that qualify the big parentheses (in the
+underlying \LaTeX ) in the second expression. Of course, if there
+are variables in an expression, as in these examples, they will need
+to be assigned values. And how the result of the evaluation is presented
+also requires specifying, but the aim is always: to evaluate mathematical
+expressions in \LaTeX{} with as little adjustment as possible to the
+form in which they are typeset.
\texttt{numerica} is written in \texttt{expl3}, the programming language
of the \LaTeX 3 project. It uses the \LaTeX 3 module \texttt{l3fp}
@@ -199,11 +203,11 @@
(part of \texttt{l3kernel}) as its calculational engine. This enables
floating point operations to 16 significant figures, with exponents
ranging between $-10000$ and $+10000$. Many functions and operations
-are built into \texttt{l3fp} – arithmetic operations, trigonometric,
+are built into \texttt{l3fp} -- arithmetic operations, trigonometric,
exponential and logarithm functions, factorials, absolute value, max
and min. Others have been constructed for \texttt{numerica }from \texttt{l3fp}
-ingredients – binomial coefficients, hyperbolic functions, sums and
-products – but to the user there should be no discernible difference.
+ingredients -- binomial coefficients, hyperbolic functions, sums
+and products -- but to the user there should be no discernible difference.
Associated packages provide for additional operations: iteration of
functions, finding zeros of functions, recurrence relations, mathematical
@@ -211,7 +215,7 @@
\section{How to use \texttt{numerica}}
-The package is invoked in the usual way: put
+The package is invoked in the usual way: put
\begin{lyxcode}
\textbackslash usepackage\{numerica\}
\end{lyxcode}
@@ -219,7 +223,7 @@
\texttt{amsmath} and \texttt{mathtools} packages and loads these automatically.
\texttt{numerica} will also accept use of some relational symbols
from the \texttt{amssymb} package provided that package is loaded
-by the user; see §\ref{subsec:evalBoolean-output}.
+by the user; see §\ref{subsec:evalBoolean-output}.
\subsection{Package options}
@@ -233,7 +237,7 @@
\label{subsec:Related-packages}In version 1 of \verb`numerica` some
additional functionality for the package could be gained by specifying
-package options – for instance the ability to create tables of function
+package options -- for instance the ability to create tables of function
values or to iterate or find fixed points of functions. However this
manner of invoking the addtional functionality makes the maintaining
of semantic version numbering across the whole \verb`numerica` package
@@ -243,7 +247,7 @@
They are loaded with the familiar \verb`\usepackage` command in the
document preamble and require the availability of the \verb`numerica`
package in your \TeX{} distribution. Neither package requires a \verb`\usepackage{numerica}`
-statement; they take care of that themselves. So, if you enter
+statement; they take care of that themselves. So, if you enter
\begin{lyxcode}
\textbackslash usepackage\{numerica-plus\}
\end{lyxcode}
@@ -258,7 +262,7 @@
terms of the Fibonacci series, or othogonal polynomials defined recurrently.
See the associated document \verb`numerica-plus.pdf` for details.
-If you enter
+If you enter
\begin{lyxcode}
\textbackslash usepackage\{numerica-tables\}
\end{lyxcode}
@@ -266,33 +270,29 @@
in the \verb`numerica` package but also to the command \verb`\nmcTabulate`
which enables the creation of (possibly multi-column) tables of function
values and makes available most of the table formats evident in \emph{HMF}.
-See the associated document \verb`numerica-tables.pdf` for details.
+See the associated document \verb`numerica-tables.pdf` for details.
-A package \verb`numerica-calculus` is currently being developed.
-
\subsection{Simple examples of use}
\label{subsec:introSimple-examples}A simple example of use is provided
-by the document
+by the document
\begin{verbatim}
\documentclass{article}
\usepackage{numerica}
\begin{document}
-
\eval{$ mc^2 $}[m=70,c=299 792 458][8x]
-
\end{document}
-
\end{verbatim}
-\noindent We have a formula between math delimiters: \verb`$ mc^2 $`.
-We have wrapped a command \verb`\eval` around the lot, added an optional
-argument in parentheses specifying numericaal values for the quantities
-\texttt{m} and \texttt{c}, and concluded it all with a trailing optional
-argument specifying that the result should be presented to $8$ places
-of decimals and in scientific notation (the \verb`x`). Running \texttt{pdflatex}
-on this document generates a pdf displaying
+\noindent We have a formula between math delimiters: \noindent\verb`$ mc^2 $`.
+We have wrapped a command \noindent\verb`\eval` around the lot, added
+an optional argument in parentheses specifying numericaal values for
+the quantities \texttt{m} and \texttt{c}, and concluded it all with
+a trailing optional argument specifying that the result should be
+presented to $8$ places of decimals and in scientific notation (the
+\noindent\verb`x`). Running \texttt{pdflatex} on this document generates
+a pdf displaying
\begin{centred}
-\eval{$ mc^2 $}[m=70,c=299 792 458][8x]
+\noindent\noindent\eval{$ mc^2 $}[m=70,c=299 792 458][8x]
\end{centred}
\noindent where the formula ($mc^{2})$ is equated to the numerical
value resulting from substituting the given values of $m$ and $c$.
@@ -300,24 +300,21 @@
is presented to $8$ decimal places in scientific notation. (According
to Einstein's famous equation $E=mc^{2}$ this is the enormous energy
content, in joules, of what was once considered an average adult Caucasian
-male. Only a minute fraction is ever available.)
+male. Only a minute fraction is ever available.)
-A second example is provided by the formula in earlier remarks:
+A second example is provided by the formula in earlier remarks:
\begin{verbatim}
\documentclass{article}
\usepackage{numerica}
\begin{document}
-
- \eval{\[ \frac{\sin(3.5)}{2} + 2\cdot 10^{-3} \]}
-
+ \eval{\[ \frac{\sin(3.5)}{2} + 2\cdot 10^{-3} \]}
\end{document}
-
\end{verbatim}
Running \texttt{pdflatex} on this document produces the result
-\eval{\[ \frac{\sin(3.5)}{2} + 2\cdot 10^{-3} \]}
+\eval{\[ \frac{\sin(3.5)}{2}+2\cdot10^{-3}\] }
-The \verb`\eval` command used in these examples is the main command
+The\verb`\eval` command used in these examples is the main command
of the \texttt{numerica} package. It is discussed in full in the next
chapter, but first some preliminaries.
@@ -326,7 +323,7 @@
\label{subsec:introResultDisplay}In what follows I shall write things
like (but generally more complicated than)
\begin{centred}
-\verb`$ \eval{ 1+1 } $` $\Longrightarrow \eval{ 1 + 1 } $
+\verb`$ \eval{ 1+1 } $` $\Longrightarrow\eval{1+1}$
\end{centred}
to mean: run \texttt{pdflatex} on a document containing \verb`\eval{1+1}`
in the document body to generate a pdf containing the calculated result
@@ -337,7 +334,7 @@
is used \emph{within} a math environment (delimited by the dollar
signs). It is not limited to this behaviour. The command can also
wrap \emph{around} the math delimiters (as we saw in the previous
-examples):
+examples):
\begin{centred}
\verb`\eval{$ 1+1 $}` $\Longrightarrow$ \eval{$ 1+1 $}.
\end{centred}
@@ -345,7 +342,7 @@
\begin{itemize}
\item When the \verb`\eval` command is used\emph{ within} a math environment,
only the \emph{result,} followed possibly by the \emph{variable~=~value
-list} (see §\ref{subsec:evalVv-list}) is displayed.
+list} (see §\ref{subsec:evalVv-list}) is displayed.
\end{itemize}
Environments may include the various AMS environments as well as the
standard \LaTeX{} inline ( \verb`$ $` or \verb`\( \)` ), \texttt{equation}
@@ -355,16 +352,16 @@
\begin{itemize}
\item When the \verb`\eval` command is wrapped\emph{ around} a math environment,
the result is displayed in the form, \emph{formula = result} (followed
-possibly by the \emph{variable~=~value list}) within that environment,
+possibly by the \emph{variable~=~value list}) within that environment,
\begin{itemize}
\item If the formula is long or contains many variables then it may be desirable
to split the display over two lines; see §\ref{subsec:evalChanging-display-format}
-and §\ref{subsec:settings New-line-display},
+and §\ref{subsec:settings New-line-display},
\end{itemize}
\end{itemize}
the whole presented as an inline expression if \verb`$` delimiters
are used, or as a display-style expression otherwise. (See the $mc^{2}$
-example for an illustration.)
+example for an illustration.)
It is not clear to me that wrapping \verb`\eval` \emph{around} the
AMS environments, except for \texttt{multline}, makes much sense,
@@ -374,7 +371,7 @@
\begin{minipage}[t]{0.8\columnwidth}%
\begin{verbatim}
-\eval{ \begin{multline*}
+ \eval{ \begin{multline*}
1+2+3+4+5+6+7+8+9+10+\phantom{0}\\
11+12+13+14+15+16+17+18+19
\end{multline*} }
@@ -382,17 +379,20 @@
%
\end{minipage}
-\medskip{}$\Longrightarrow$ %
+\medskip{}
+ $\Longrightarrow$ %
\begin{minipage}[t]{0.8\columnwidth}%
-\vspace{-2ex}\eval{ \begin{multline*}
- 1+2+3+4+5+6+7+8+9+10+\phantom{0}\\ 11+12+13+14+15+16+17+18+19
-\end{multline*} }%
+\vspace{-2ex}
+\eval{ \begin{multline*}
+ 1+2+3+4+5+6+7+8+9+10+\phantom{0}\\
+ 11+12+13+14+15+16+17+18+19
+ \end{multline*} }%
\end{minipage}
\begin{itemize}
\item It is also possible to dispense with math delimiters entirely, neither
wrapped within nor wrapped around the \verb`\eval` command, but in
that case \texttt{numerica} acts as if \verb`\eval` had been used
-within \verb`\[` and \verb`\]` and displays the result accordingly.
+within \verb`\[` and \verb`\]` and displays the result accordingly.
\end{itemize}
\subsection{Checking}
@@ -415,21 +415,22 @@
\verb`\eval{$ 5\sqrt{7}-3\sqrt{5} $}` $\Longrightarrow$ \eval{$ 5\sqrt{7}-3\sqrt{5} $}.
\end{centred}
-Yes, the simplification was correct. And indeed $y=5\sqrt{7}+3\sqrt{5}$:
+Yes, the simplification was correct. And indeed $y=5\sqrt{7}+3\sqrt{5}$:
\begin{centred}
-\verb`\eval{$ \sqrt{220+30\sqrt{35}} $}` $\Longrightarrow$ \eval{$ \sqrt{220+30\sqrt{35}} $},
+\verb`\eval{$ \sqrt{220+30\sqrt{35}} $}` $\Longrightarrow$ \eval{$ \sqrt{220+30\sqrt{35}} $}
+,
\verb`\eval{$ 5\sqrt{7}+3\sqrt{5} $}` $\Longrightarrow$ \eval{$ 5\sqrt{7}+3\sqrt{5} $}.
\end{centred}
-As a final flourish,
+As a final flourish,
\begin{verbatim}
\eval{$ xy $}
[ x=5\sqrt{7}-3\sqrt{5},
y=5\sqrt{7}+3\sqrt{5} ]
\end{verbatim}
-$\Longrightarrow$ \eval{$ xy $}
- [x=5\sqrt{7}-3\sqrt{5},
- y=5\sqrt{7}+3\sqrt{5}].
+$\Longrightarrow$ \eval{$ xy $}
+ [ x=5\sqrt{7}-3\sqrt{5},
+ y=5\sqrt{7}+3\sqrt{5} ].
\subsection{Exploring}
@@ -441,16 +442,14 @@
\]
did indeed converge to the number $e$ as $n$ increased.\texttt{ }Let's
do that here. Try first $n=10$:
-\begin{center}
+\begin{centred}
\verb`\eval{$ e-(1+1/n)^n $}[n=10][x]` $\Longrightarrow$ \eval{$ e-(1+1/n)^n $}[n=10][x].
-\par\end{center}
-
+\end{centred}
\noindent (The default number of decimal places displayed is $6$.)
The difference between $e$ and $(1+1/n)^{n}$ is about an eighth
($0.125$) when $n=10$, which is encouraging but hardly decisive.
The obvious thing to do is increase the value of $n$. I'll use an
-\verb`align*` environment to `prettify' the presentation of the
-results:
+\verb`align*` environment to `prettify' the presentation of the results:
\begin{verbatim}
\begin{align*}
e-(1+1/n)^{n} & =\eval{e-(1+1/n)^n}[n=1\times10^5][*x],\\
@@ -459,7 +458,7 @@
e-(1+1/n)^{n} & =\eval{e-(1+1/n)^n}[n=1\times10^8][*x].
\end{align*}
\end{verbatim}
-(most of which was written using copy and paste) which produces
+(most of which was written using copy and paste) which produces
\begin{align*}
e-(1+1/n)^{n} & =\eval{e-(1+1/n)^{n}}[n=1\times10^{5}][x],\\
e-(1+1/n)^{n} & =\eval{e-(1+1/n)^{n}}[n=1\times10^{6}][*x],\\
@@ -470,7 +469,7 @@
being of order $1/n$, but that is not what catches the eye. There
is an unanticipated regularity here. 1.35914? Double the number: \verb`$\eval{2\times 1.35914}[5]$`\texttt{
}$\Longrightarrow\eval{2\times1.35914}[5]$ which is close enough
-to $e$ to suggest a relationship, namely,
+to $e$ to suggest a relationship, namely,
\[
\lim_{n\to\infty}n\left(e-\left(1+\frac{1}{n}\right)^{n}\right)=\tfrac{1}{2}e.
\]
@@ -492,13 +491,13 @@
\subsection{Reassuring}
\label{subsec:introReassurance}In the course of some hobbyist investigations
-in plane hyperbolic geometry I derived the formula
+in plane hyperbolic geometry I derived the formula
\[
\Phi_{1}(m,n)=\cos\tfrac{m}{n}\pi-(1-4\sin^{2}\tfrac{m}{3n}\pi)\frac{\sin\tfrac{1}{n}\pi\sin\tfrac{m-1}{n}\pi}{2\sin^{2}\tfrac{m}{3n}\pi},
\]
for $m=2,3,\ldots$ and integral $n\ge2m+1$. A key concern was: when
is $\Phi_{1}$ positive? After an embarrassingly laborious struggle,
-I managed to work this expression into the form
+I managed to work this expression into the form
\[
\Phi_{2}(m,n)=\left(\frac{1-4\sin^{2}\tfrac{m}{3n}\pi}{2\sin^{2}\tfrac{m}{3n}\pi}\right)\sin\tfrac{2m-3}{3n}\pi\sin\tfrac{m-3}{3n}\pi,
\]
@@ -507,7 +506,7 @@
second is positive for $m\ge2$, and the third is positive for $m\ge4$.
All well and good, but given the struggle to derive $\Phi_{2}$, was
I confident that $\Phi_{1}$ and $\Phi_{2}$ really\emph{ }are equal?
-It felt all too likely that I had made a mistake.
+It felt all too likely that I had made a mistake.
The simplest way to check was to see if the two expressions gave the
same numerical answers for a number of $m,\thinspace n$ values. I
@@ -528,49 +527,47 @@
\sin\tfrac{2m-3}{3n}\pi\sin\tfrac{m-3}{3n}\pi
\]}[m=2,n=5]
\end{verbatim}
-I have added some formatting – indenting, line breaks – to make the
-formulas more readable for the present document but otherwise left
-them unaltered. The \verb`\eval` command can be used for even quite
-complicated expressions without needing to tinker with their \LaTeX{}
-form, but you may wish – as here – to adjust white space to clarify
-the component parts of the formula. Running \texttt{pdflatex} on these
-expressions, the results were
+I have added some formatting -- indenting, line breaks -- to make
+the formulas more readable for the present document but otherwise
+left them unaltered. The \verb`\eval` command can be used for even
+quite complicated expressions without needing to tinker with their
+\LaTeX{} form, but you may wish -- as here -- to adjust white space
+to clarify the component parts of the formula. Running \texttt{pdflatex}
+on these expressions, the results were
-\eval{\[
- \cos\tfrac{m}{n}\pi-(1-4\sin^{2}\tfrac{m}{3n}\pi)
- \frac{\sin\tfrac{1}{n}\pi\sin\tfrac{m-1}{n}\pi}
- {2\sin^{2}\tfrac{m}{3n}\pi}
- \]}[m=2,n=5]
+ \eval{\[
+ \cos\tfrac{m}{n}\pi-(1-4\sin^{2}\tfrac{m}{3n}\pi)
+ \frac{\sin\tfrac{1}{n}\pi\sin\tfrac{m-1}{n}\pi}
+ {2\sin^{2}\tfrac{m}{3n}\pi}
+ \]}[m=2,n=5]
+ \eval{\[
+ \left(
+ \frac{1-4\sin^{2}\tfrac{m}{3n}\pi}
+ {2\sin^{2}\tfrac{m}{3n}\pi}
+ \right)
+ \sin\tfrac{2m-3}{3n}\pi\sin\tfrac{m-3}{3n}\pi
+ \]}[m=2,n=5]
-\eval{\[
- \left(
- \frac{1-4\sin^{2}\tfrac{m}{3n}\pi}
- {2\sin^{2}\tfrac{m}{3n}\pi}
- \right)
- \sin\tfrac{2m-3}{3n}\pi\sin\tfrac{m-3}{3n}\pi
- \]}[m=2,n=5]
-
\noindent which was reassuring. Doing it again but with different
values of $m$ and $n$, again the results coincided:
-\eval{\[
- \cos\tfrac{m}{n}\pi-(1-4\sin^{2}\tfrac{m}{3n}\pi)
- \frac{\sin\tfrac{1}{n}\pi\sin\tfrac{m-1}{n}\pi}
- {2\sin^{2}\tfrac{m}{3n}\pi}
- \]}[m=5,n=13]
+ \eval{\[
+ \cos\tfrac{m}{n}\pi-(1-4\sin^{2}\tfrac{m}{3n}\pi)
+ \frac{\sin\tfrac{1}{n}\pi\sin\tfrac{m-1}{n}\pi}
+ {2\sin^{2}\tfrac{m}{3n}\pi}
+ \]}[m=5,n=13]
+ \eval{\[
+ \left(
+ \frac{1-4\sin^{2}\tfrac{m}{3n}\pi}
+ {2\sin^{2}\tfrac{m}{3n}\pi}
+ \right)
+ \sin\tfrac{2m-3}{3n}\pi\sin\tfrac{m-3}{3n}\pi
+ \]}[m=5,n=13]
-\eval{\[
- \left(
- \frac{1-4\sin^{2}\tfrac{m}{3n}\pi}
- {2\sin^{2}\tfrac{m}{3n}\pi}
- \right)
- \sin\tfrac{2m-3}{3n}\pi\sin\tfrac{m-3}{3n}\pi
- \]}[m=5,n=13]
-
\noindent Thus reassured that there was \emph{not }an error in my
laborious derivation of $\Phi_{2}$ from $\Phi_{1}$, it was not difficult
to work back from $\Phi_{2}$ to $\Phi_{1}$ then reverse the argument
-to find a straightforward derivation.
+to find a straightforward derivation.
\chapter{\texttt{\textbackslash nmcEvaluate} (\texttt{\textbackslash eval)}}
@@ -598,30 +595,30 @@
There are five arguments to the \verb`\nmcEvaluate` (or \verb`\eval`)
command, of which only one, the third, is mandatory. All others are
-optional. If all are deployed the command looks like
+optional. If all are deployed the command looks like
\begin{centred}
-\noindent \verb`\nmcEvaluate*[settings]{expr.}[vv-list][num. format]`
+\verb`\nmcEvaluate*[settings]{expr.}[vv-list][num. format]`
\end{centred}
-I discuss the various arguments in the referenced sections.
+I discuss the various arguments in the referenced sections.
\begin{enumerate}
\item \verb`*` optional switch; if present ensures display of only the
numerical result (suppresses display of the formula and vv-list);
-see §\ref{subsec:evalVvSuppresList}
+see §\ref{subsec:evalVvSuppresList}
\item \verb`[settings]` optional comma-separated list of \emph{key=value
-}settings for this particular calculation; see §\ref{sec:settingsOption}
+}settings for this particular calculation; see §\ref{sec:settingsOption}
\item \verb`{expr.}` the only mandatory argument; the mathematical expression/formula
in \LaTeX{} form that is to be evaluated
\item \verb`[vv-list]` optional comma-separated list of \emph{variable=value
-}items; see §\ref{subsec:evalVv-list}
+}items; see §\ref{subsec:evalVv-list}
\item \verb`[num. format]` optional format specification for presentation
of the numerical result (rounding, padding with zeros, scientific
-notation, boolean output); see~§\ref{subsec:evalRoundingEtc}
+notation, boolean output); see~§\ref{subsec:evalRoundingEtc}
\end{enumerate}
Note that arguments 4 and 5 are both square-bracket delimited optional
arguments. Should only one such argument be used, \texttt{numerica}
determines which is intended by looking for an equals sign within
the argument. Its presence indicates the argument is the vv-list;
-its absence indicates the argument is the number format specification.
+its absence indicates the argument is the number format specification.
The vv-list and number-format specification are \emph{trailing} optional
arguments. They do not need to be hard against their preceding arguments;
@@ -633,7 +630,7 @@
by inserting an empty brace pair (\verb`{}`) before the offending
square-bracketed expression. Allowing spaces between the arguments
enables complicated expressions and large vv-lists to be formatted
-with new lines and white space to aid clarity – without requiring
+with new lines and white space to aid clarity -- without requiring
the insertion of comment characters (\verb`%`).
Recommended practice is to minimise the number of optional arguments
@@ -644,13 +641,13 @@
(rounding value, padding with zeros, scientific notation, boolean
output) and placing them in a trailing argument is both convenient
and intuitive for the kind of back-of-envelope calculations envisaged
-for \texttt{numerica}.
+for \texttt{numerica}.
\section{The variable=value list}
\label{subsec:evalVv-list}To evaluate algebraic, trigonometric and
other formulas that involve \emph{variables} we need to give those
-variables values. This is done in the \emph{variable=value list} –
+variables values. This is done in the \emph{variable=value list} --
or \emph{vv-list} for short. This is the fourth argument of the \texttt{\textbackslash nmcEvaluate}
command and is a square-bracket delimited optional argument (optional
because an expression may depend only on constants and numbers).
@@ -665,17 +662,17 @@
in an item} of the vv-list. Thus variables can be multi-token affairs:
$x',x'',x^{iv},x_{n},x'_{n},x''_{mn}$, $^{k}C_{n},var,\mathrm{var},Fred,\mathbf{Fred},\mathcal{FRED}\ldots$
(This criterion for what makes a variable name means a name may contain
-spaces – for instance \verb`x x` should not cause a \verb`numerica`
-error – but such names are not part of mathematical practice.) Usually,
+spaces -- for instance \verb`x x` should not cause a \verb`numerica`
+error -- but such names are not part of mathematical practice.) Usually,
for the kind of back-of-envelope calculations envisaged for \verb`numerica`,
and for ease of typing, most variables will be single letters from
-the Roman or Greek alphabets.
+the Roman or Greek alphabets.
Because equals signs and commas give structure to the vv-list, it
should also be clear that a variable name should not contain a \emph{naked}
equals sign or a \emph{naked} comma. They can be incorporated in a
variable name but only when decently wrapped in braces, like \verb`R_{=}`
-displaying as $R_{=}$ or \verb`X_{,i}` displaying as $X_{,i}$.
+displaying as $R_{=}$ or \verb`X_{,i}` displaying as $X_{,i}$.
Note that $x$ and $\mathrm{x}$ will be treated by \verb`numerica`
as \emph{different} variables since, in the underlying \LaTeX , one
@@ -683,7 +680,7 @@
identical in the pdf may well be distinct in \LaTeX . This is true
particularly of superscripts and subscripts: \verb`x_0` and \verb`x_{0}`
appear identical in the pdf but in the underlying \LaTeX{} they are
-distinct, and will be treated as distinct variables by \verb`numerica`.
+distinct, and will be treated as distinct variables by \verb`numerica`.
Although multi-token variables are perfectly acceptable, \emph{internally}
\verb`numerica` works with single tokens. Variable names can be so
@@ -699,11 +696,11 @@
order of decreasing size of name, working from the names that contain
most tokens down to names containing only two tokens. (Doing the replacing
in this order prevents \emph{parts} of longer names possibly being
-mistaken for shorter variable names.)
+mistaken for shorter variable names.)
The conversion process uses computer resources. Even if there are
no multi-token variables present, \verb`numerica` still needs to
-check that this is so – unless the user alerts the program to the
+check that this is so -- unless the user alerts the program to the
fact. This can be done by making a brief entry \texttt{xx=0 }in the
settings option (the second optional argument of \verb`\nmcEvaluate`);
see §\ref{subsec:settingsMultitokSwitch}. If the user never (or hardly
@@ -714,11 +711,11 @@
\subsection{The vv-list and its use}
A vv-list is a comma-separated list where each item is of the form
-\emph{variable=value}. It might be something simple like
+\emph{variable=value}. It might be something simple like
\begin{lyxcode}
{[}g=9.81,t=2{]}
\end{lyxcode}
-or something more complicated like
+or something more complicated like
\begin{lyxcode}
{[}V\_S=\textbackslash tfrac43\textbackslash pi~r\textasciicircum 3,V\_C=2\textbackslash pi~r\textasciicircum 2h,h=3/2,r=2{]}.
\end{lyxcode}
@@ -737,7 +734,7 @@
To evaluate $y$, first $x$ is assigned a value then $h(x)$ is calculated,
then $g(h(x))$ then $f(g(h(x)))=y$. We work from right to left,
from the innermost to the outermost element. Or consider an example
-like calculating the area of a triangle by means of the formula
+like calculating the area of a triangle by means of the formula
\[
A=\sqrt{s(s-a)(s-b)(s-c)}.
\]
@@ -744,7 +741,7 @@
First we write the formula; then we state how $s$ depends on $a,b,c$,
namely $s=\frac{1}{2}(a+b+c)$, then we give values to $a,b,c$. In
\texttt{numerica} this is mirrored in the layout of the \verb`\eval`
-command:
+command:
\begin{verbatim}
\eval{$ \sqrt{s(s-a)(s-b)(s-c)} $}
[s=\tfrac12(a+b+c),a=3,b=4,c=5]
@@ -753,7 +750,7 @@
entire evaluation occurs from right to left.
This means that the rightmost variable in the vv-list can depend only
-on constants and numbers – although it may be a complicated expression
+on constants and numbers -- although it may be a complicated expression
of those elements. Other variables in the vv-list can depend on variables
\emph{to their right} but not to their left.
@@ -762,29 +759,29 @@
Suppose our expression is $\tfrac{4}{3}\pi r^{3}$, the volume $V_{S}$
of a sphere in terms of its radius $r$, and we want to calculate
the volume for different values of $r$ to get a sense of how rapidly
-volume increases with radius.
+volume increases with radius.
\begin{centred}
-\verb`$ V_S=\eval{ \tfrac43\pi r^3 }[r=1] $` $\Longrightarrow$ $ V_S=\eval{ \tfrac43\pi r^3 }[r=1] $.
+\verb`$ V_S=\eval{ \tfrac43\pi r^3 }[r=1] $` $\Longrightarrow$ $V_{S}=\eval{\tfrac{4}{3}\pi r^{3}}[r=1]$.
\end{centred}
Having set up this calculation it is now an easy matter to change
-the value of $r$ in the vv-list:
+the value of $r$ in the vv-list:
\begin{centred}
\verb`$ V_S=\eval{ \tfrac43\pi r^3 }[r=1.5] $` $\Longrightarrow$
-$ V_S= \eval{ \tfrac43\pi r^3 }[r=1.5] $.
+$V_{S}=\eval{\tfrac{4}{3}\pi r^{3}}[r=1.5]$.
-\verb`$ V_S=\eval{ \tfrac43\pi r^3 }[r=2] $` $ \Longrightarrow $ $V_S= \eval{ \tfrac43\pi r^3 }[r=2] $.
+\verb`$ V_S=\eval{ \tfrac43\pi r^3 }[r=2] $` $\Longrightarrow$ $V_{S}=\eval{\tfrac{4}{3}\pi r^{3}}[r=2]$.
\end{centred}
To compute the volume $V_{C}=\pi r^{2}h$ of a cylinder, we have two
-variables to assign values to:
+variables to assign values to:
\begin{centred}
-\verb`$ V_C=\eval{ \pi r^2h }[h=4/3,r=1] $` $\Longrightarrow$ $ V_C=\eval{ \pi r^2h }[h=4/3,r=1] $.
+\verb`$ V_C=\eval{ \pi r^2h }[h=4/3,r=1] $` $\Longrightarrow$ $V_{C}=\eval{\pi r^{2}h}[h=4/3,r=1]$.
\end{centred}
Although values in the vv-list are generally either numbers or simple
expressions (like \texttt{4/3}), that is not essential. A little more
-complicated is
+complicated is
\begin{centred}
\verb`$ V_C=\eval{ hA_C }[A_C=\pi r^2,h=4/3,r=1] $` $\Longrightarrow$
-$ V_C=\eval{ hA_C }[A_C=\pi r^2,h=4/3,r=1] $.
+$V_{C}=\eval{hA_{C}}[A_{C}=\pi r^{2},h=4/3,r=1]$.
\end{centred}
where calculation of the volume of the cylinder has been split into
two: first calculate the area $A_{C}$ of its circular base and then,
@@ -795,12 +792,13 @@
sides are $a=3$, $b=4$ and $c=5$. (Of course we know this is a
right-angled triangle with area $\tfrac{1}{2}ab=6$.) The semi-perimeter
$s=\tfrac{1}{2}(a+b+c)$ and the area of ABC is \medskip{}
+
\begin{verbatim}
- \eval{$ \sqrt{s(s-a)(s-b)(s-c) $}
+ \eval{$ \sqrt{s(s-a)(s-b)(s-c)} $}
[s=\tfrac12(a+b+c),a=3,b=4,c=5]
\end{verbatim}
$\Longrightarrow$ \eval{$ \sqrt{s(s-a)(s-b)(s-c)} $}
- [s=\tfrac12(a+b+c),a=3,b=4,c=5].
+ [s=\tfrac12(a+b+c),a=3,b=4,c=5] .
\subsubsection{Constants}
@@ -820,14 +818,14 @@
\verb`\eval{$ \gamma $}` $\Longrightarrow$ \eval{$ \gamma $},
-\verb`\eval{$ \phi $}` $\Longrightarrow$ \eval{$ \phi $},
+\verb`\eval{$ \phi $}` $\Longrightarrow$ \eval{$ \phi $} ,
-\verb`\eval{$ \deg $}` $\Longrightarrow$ \eval{$ \deg $},
+~\verb`\eval{$ \deg $}` $\Longrightarrow$ \eval{$ \deg $},
\end{centred}
so that \verb`\eval{$ 180\deg $}` $\Longrightarrow$ \eval{$ 180\deg $}
(as it should).
-Let's combine two of these in a formula:
+Let's combine two of these in a formula:
\begin{centred}
\verb`\eval{$ e^\pi-\pi^e $}` $\Longrightarrow$ \eval{$ e^\pi-\pi^e $},
\end{centred}
@@ -834,6 +832,7 @@
which is close-ish to $\tfrac{1}{4}e$: \verb`\eval{$ \tfrac14e $}`
$\Longrightarrow$ \eval{$ \tfrac14e $}.
+\noindent{}%
\noindent\begin{minipage}[t]{1\columnwidth}%
\begin{shaded}%
In some contexts it may feel natural to use any or all of \verb`\pi`,
@@ -843,38 +842,39 @@
For example, if the triangle we labelled ABC previously was instead
labelled CDE then it has sides $c=3,d=4$ and (note!) $e=5$. It's
area therefore is\medskip{}
+
\begin{verbatim}
\eval{$ \sqrt{s(s-c)(s-d)(s-e)} $}
[s=\tfrac12(c+d+e),c=3,d=4,e=5]
\end{verbatim}
-$\Longrightarrow$
+$\Longrightarrow$ \eval{$ \sqrt{s(s-c)(s-d)(s-e)} $}
+ [s=\tfrac12(c+d+e),c=3,d=4,e=5] .\medskip{}
-\eval{$ \sqrt{s(s-c)(s-d)(s-e)} $}
- [s=\tfrac12(c+d+e),c=3,d=4,e=5].\medskip{}
-
\noindent Since this is the correct area we see that \cprotect\texttt{e}
has been treated as a variable with the assigned value $5$, not as
-the constant. But if \cprotect\texttt{e} (or \verb`\pi` or \verb`\gamma`
-or \verb`\phi`) is not assigned a value in the vv-list then it has,
-by default, the value of the constant. In the case of \cprotect\texttt{e},
-if you wish to use it as a variable, the constant is always available
-as \verb`\exp(1)`. There is no similar alternative available for
-\verb`\pi`, \verb`\gamma` or \verb`\phi`. \end{shaded}%
+the constant. But if \cprotect\texttt{e} (or \noindent\verb`\pi`
+or \noindent\verb`\gamma` or \noindent\verb`\phi`) is not assigned
+a value in the vv-list then it has, by default, the value of the constant.
+In the case of \cprotect\texttt{e}, if you wish to use it as a variable,
+the constant is always available as \noindent\verb`\exp(1)`. There
+is no similar alternative available for \noindent\verb`\pi`, \noindent\verb`\gamma`
+or \noindent\verb`\phi`. \end{shaded}%
\end{minipage}
\subsection{Display of the vv-list}
-By default, the vv-list is displayed with (in fact following) the
-numerical result. That and the format of the display can both be changed.
+\noindent By default, the vv-list is displayed with (in fact following)
+the numerical result. That and the format of the display can both
+be changed.
\subsubsection{Star option: suppressing display of the vv-list}
\label{subsec:evalVvSuppresList}If display of the vv-list is not
wanted at all, only the numerical result, it suffices to attach an
-asterisk (star) to the \texttt{\textbackslash eval} command:
+asterisk (star) to the \texttt{\textbackslash eval} command:
\begin{centred}
\verb`$ V_C=\eval*{ hA_C }[A_C=\pi r^2,h=4/3,r=1] $` $\Longrightarrow$
-$ V_C=\eval*{ hA_C }[A_C=\pi r^2,h=4/3,r=1] $,
+$V_{C}=\eval*{hA_{C}}[A_{C}=\pi r^{2},h=4/3,r=1]$,
\end{centred}
or simply the naked result:
\begin{centred}
@@ -888,7 +888,7 @@
\begin{centred}
\verb`\eval*{$ y $}[y=ax+b,x=2,a=-2,b=2]` $\Longrightarrow$ \eval*{$ y $}[y=ax+b,x=2,a=-2,b=2],
-\verb`$ \eval*{ y }[y=ax+b,x=2,a=-2,b=2] $` $\Longrightarrow$ $ \eval*{ y }[y=ax+b,x=2,a=-2,b=2] $.
+\verb`$ \eval*{ y }[y=ax+b,x=2,a=-2,b=2] $` $\Longrightarrow$ $\eval*{y}[y=ax+b,x=2,a=-2,b=2]$.
\end{centred}
The star option delivers a number as result, pure and simple.
@@ -901,10 +901,10 @@
the previous examples, the base area $A_{C}$ has a different status
from the `fundamental' variables $r$ and $h$. It is an intermediate
value, one that we pass through on the way to the final result. To
-suppress it from display enclose the variable in braces:
+suppress it from display enclose the variable in braces:
\begin{centred}
\verb`$ V_C=\eval{ hA_C }[{A_C}=\pi r^2,h=4/3,r=1] $` $\Longrightarrow$
-$ V_C=\eval{ hA_C }[{A_C}=\pi r^2,h=4/3,r=1] $.
+$V_{C}=\eval{hA_{C}}[{A_{C}}=\pi r^{2},h=4/3,r=1]$.
\end{centred}
As you can see, $A_{C}$ no longer appears in the displayed vv-list.
Of course the name and its value are still recorded `behind the scenes'
@@ -914,10 +914,10 @@
Should the vv-list be empty, or display of \emph{all} variables is
suppressed by wrapping each in braces, then \emph{nothing} is displayed
-where the vv-list would normally be, not even any punctuation:
+where the vv-list would normally be, not even any punctuation:
\begin{centred}
\verb`$ V_C=\eval{ hA_C }[{A_C}=\pi r^2,{h}=4/3,{r}=1] $` $\Longrightarrow$
-$ V_C=\eval{ hA_C }[{A_C}=\pi r^2,{h}=4/3,{r}=1] $
+$V_{C}=\eval{hA_{C}}[{A_{C}}=\pi r^{2},{h}=4/3,{r}=1]$
\end{centred}
If you want a full stop after the result then you will need to add
it by hand or use the \verb`p=.` setting of §\ref{subsec:settingsPunctuation}.
@@ -933,7 +933,7 @@
However, if \verb`\eval` is wrapped around an \emph{appropriate}
environment (like \verb`multline`, but not \verb`equation`) it can
also be done simply by including \texttt{\textbackslash\textbackslash}
-at the end of the formula.
+at the end of the formula.
In the following example I use Brahmagupta's formula for calculating
the area of a cyclic quadrilateral (of which his formula for a triangle
@@ -942,8 +942,8 @@
to a 30-60-90 triangle. The sides are therefore $\surd2,\surd2,\surd3,1$.
Adding the areas of the two triangles, the area of the quadrilateral
is $A=1+\tfrac{1}{2}\surd3$, or in decimal form, \verb`$\eval{1+\tfrac12\surd3}$`
-$\Longrightarrow$ $\eval{1+\tfrac12\surd3}$. Let's check with Brahmagupta's
-formula:
+$\Longrightarrow$ $\eval{1+\tfrac{1}{2}\surd3}$. Let's check with
+Brahmagupta's formula:
\begin{verbatim}
\eval{
\begin{multline*}
@@ -957,8 +957,7 @@
\sqrt{(s-a)(s-b)(s-c)(s-d)}\\
\end{multline*}
}[s=\tfrac12(a+b+c+d),
- a=\surd2,b=\surd2,c=\surd3,d=1]
-
+ a=\surd2,b=\surd2,c=\surd3,d=1] %
\noindent\begin{minipage}[t]{1\columnwidth}%
\begin{shaded}%
@@ -967,11 +966,11 @@
\label{subsec:evalDon't-do-this!}A variable name is what lies to
the left of the equals sign of an item in the vv-list. Since multi-token
variables are converted to single tokens (like \verb`\nmc_a`) before
-any calculating is done, it is possible to sin. Thus :
+any calculating is done, it is possible to sin. Thus :
\begin{centred}
\verb`\eval{$ \sin\pi $}[{\sin\pi}=1]` $\Longrightarrow$ \eval{$ \sin\pi $}[{\sin\pi}=1];
\end{centred}
-and (more?) egregiously,
+and (more?) egregiously,
\begin{centred}
\verb`\eval{$ 10 $}[{10}=20]` $\Longrightarrow$ \eval{$ 10 $}[{10}=20].
\end{centred}
@@ -981,11 +980,12 @@
containing their respective multiple tokens. For display purposes
they expand to those multiple tokens, but for calculating within \verb`numerica`
the single token is used. By this means one can easily create further
-grotesqueries:
+grotesqueries:
\begin{centred}
-\verb`\eval{$ ++ + ++ $}[{++}=1]` $\Longrightarrow$ \eval{$ ++ + ++ $}[{++}=1],
+\verb`\eval{$ {++} + {++} $}[{++}=1]` $\Longrightarrow$ \eval{$ {++} + {++} $}[{++}=1],
-\verb`\eval{$ 2(1+1) $}[{2(1}=3,{+1)}=5]` $\Longrightarrow$ \eval{$ 2(1+1) $}[{2(1}=3,{+1)}=5],
+\verb`\eval{$ {2(1}+{+1)} $}[{2(1}=3,{+1)}=5]` $\Longrightarrow$
+\eval{$ {2(1}+{+1)} $}[{2(1}=3,{+1)}=5],
\verb`\eval{$ 1!! $}[{!!}=42]` $\Longrightarrow$ \eval{$ 1!! $}[{!!}=42].
\end{centred}
@@ -992,45 +992,45 @@
Should \verb`numerica` try to check variable names to avoid consequences
like this? I don't see any reasonable way of doing that. Symbols like
\verb`(` and \verb`+` can easily be part of valid variable names
-– $k^{+},\,k^{-}$, $C_{n}^{(0)}$ and so on. It is left to the user,
-in any \emph{public} document, to avoid such sins. (And they could
-easily construct the displayed expressions in \LaTeX{} if they so wished
-without recourse to \verb`\eval` at all.) See also §\ref{subsec:supplMacrosDisplay}
+-- $k^{+},\,k^{-}$, $C_{n}^{(0)}$ and so on. It is left to the
+user, in any \emph{public} document, to avoid such sins. (And they
+could easily construct the displayed expressions in \LaTeX{} if they
+so wished without recourse to \verb`\eval` at all.) See also §\ref{subsec:supplMacrosDisplay}
where a similar issue arises with user-defined macros.\end{shaded}%
\end{minipage}
\section{Formatting the numerical result}
-\label{subsec:evalRoundingEtc}Internally, values are stored to $16$
-significant figures (if available), calculations are carried out to
-$16$ significant figures, but only rarely do we want to view the
-result to $16$ figures. Generally, we round to some smaller number
+\noindent\label{subsec:evalRoundingEtc}Internally, values are stored
+to $16$ significant figures (if available), calculations are carried
+out to $16$ significant figures, but only rarely do we want to view
+the result to $16$ figures. Generally, we round to some smaller number
of figures. The default rounding value is $6$, meaning by default
at most $6$ decimal places are shown. So far, all results have been
rounded to this figure, although not all digits are always displayed
-– for instance if the sixth one is $0$, or the result is an integer.
+-- for instance if the sixth one is $0$, or the result is an integer.
Like other elements of the display, both rounding value and the (dis)appearance
of trailing zeros can be customized, in this case by means of an optional
argument following the vv-list (or the formula if there is no vv-list).
This optional argument may contain up to four juxtaposed items from
-six possibilities:
+six possibilities:
\begin{itemize}
\item a question mark ?, which gives boolean output, or
\item an integer, the \emph{rounding value}, positive, negative or zero,
-specifying how many decimal places to display the result to, or
+specifying how many decimal places to display the result to, or
\item an asterisk {*}, which pads the result with zeros should it not have
-as many decimal places as the rounding value specifies, or
+as many decimal places as the rounding value specifies, or
\item the character \texttt{x} (lower case!) which presents the result in
-`proper' scientific notation (a form like $1.2345\times10^{5}$
-for 123450), or
+`proper' scientific notation (a form like $1.2345\times10^{5}$ for
+123450), or
\item the character \texttt{t} (lower case!) which presents the result in
a bastardized scientific notation useful in tables (a form like $(5)1.2345$
-for 123450), or
+for 123450), or
\item a character other than \texttt{?}, \texttt{{*}}, \texttt{x}, \texttt{t}
-or an integer, usually one of the letters\texttt{ e d} \texttt{E
-D}, which presents the result in scientific notation with that character
-as the exponent mark (a form like $1.2345\text{e}5$ for $123450$).
+or an integer, usually one of the letters\texttt{ e d} \texttt{E D},
+which presents the result in scientific notation with that character
+as the exponent mark (a form like $1.2345\text{e}5$ for $123450$).
\end{itemize}
If you use \texttt{?} in the same specification as some other character,
the \texttt{?} prevails; if you use \texttt{x} in the same specification
@@ -1039,7 +1039,7 @@
except for \texttt{?} or \texttt{x}, the \texttt{t} prevails.
If you repeat the character serving as the exponent mark in scientific
-notation – say \verb`xx` or \verb`dd` – then scientific notation
+notation -- say \verb`xx` or \verb`dd` -- then scientific notation
extends to numbers in the interval \verb`[1,10)`.
If you repeat a question mark specifying boolean output, then the
@@ -1053,28 +1053,28 @@
displayed. If a number is displayed in scientific notation (see below
§\ref{subsec:evalScientificNotation}) that is still true, but it
can mean differences in the overall number of digits displayed. For
-the moment, I show the effect of rounding in a purely decimal display:
+the moment, I show the effect of rounding in a purely decimal display:
\begin{centred}
-\verb`$ \eval{ 1/3 }[4] $` $\Longrightarrow$ $ \eval{ 1/3 }[4] $
+\verb`$ \eval{ 1/3 }[4] $` $\Longrightarrow$ $\eval{1/3}[4]$.
\end{centred}
In this case \verb`4` was entered in the number-format option and
the result is displayed to four decimal places. The default rounding
-value is $6$:
+value is $6$:
\begin{centred}
-\verb`$ \eval{ 35/3 } $` $\Longrightarrow$ $ \eval{ 35/3 } $
+\verb`$ \eval{ 35/3 } $` $\Longrightarrow$ $\eval{35/3}$.
\end{centred}
-Following the default behaviour in \verb`l3fp`, the calculational
-engine which \verb`numerica` uses, `ties' are rounded to the nearest
-\emph{even} digit. Thus a number ending $55$ with a `choice' of
-rounding to $5$ or $6$ rounds up to the even digit $6$, and a number
-ending $65$ with a `choice' of rounding to $6$ or $7$ rounds
-down to the even digit $6$:
+Following the default behaviour in \texttt{l3fp}, the calculational
+engine which \texttt{numerica} uses, `ties' are rounded to the nearest
+\emph{even} digit. Thus a number ending $55$ with a `choice' of rounding
+to $5$ or $6$ rounds up to the even digit $6$, and a number ending
+$65$ with a `choice' of rounding to $6$ or $7$ rounds down to the
+even digit $6$:
\begin{centred}
-\verb`$ \eval{ 0.1234555 } $` $\Longrightarrow\eval{0.1234555}$
+\verb`$ \eval{ 0.1234555 } $` $\Longrightarrow\eval{0.1234555}$
-\verb`$ \eval{ 0.1234565 } $` $\Longrightarrow\eval{0.1234565}$
+\verb`$ \eval{ 0.1234565 } $` $\Longrightarrow\eval{0.1234565}$
\end{centred}
-\verb`l3fp` works to 16 significant figures and never displays more
+\texttt{l3fp} works to 16 significant figures and never displays more
than that number (and often fewer).
\begin{itemize}
\item In the first of the following although I have specified a rounding
@@ -1087,20 +1087,20 @@
\item in the third I have changed the figure \emph{before} the decimal point
to $1$ so that the $10$ added zeros are now included among the significant
figures;
-\item and in the fourth, I have added $9$ digits before the decimal point:
+\item and in the fourth, I have added $9$ digits before the decimal point:
\end{itemize}
\begin{centred}
\verb`$ \eval{ 0.1234567890123456789 }[19] $` $\Longrightarrow$
-$\eval{ 0.1234567890123456789 }[19]$
+$\eval{0.1234567890123456789}[19]$
\verb`$ \eval{ 0.00000000001234567890123456789 }[19] $` $\Longrightarrow$
-$\eval{ 0.00000000001234567890123456789 }[19]$
+$\eval{0.00000000001234567890123456789}[19]$
\verb`$ \eval{ 1.00000000001234567890123456789 }[19] $` $\Longrightarrow$
-$\eval{ 1.00000000001234567890123456789 }[19]$
+$\eval{1.00000000001234567890123456789}[19]$
\verb`$ \eval{ 987654321.1234567890123456789 }[19] $` $\Longrightarrow$
-$\eval{ 987654321.1234567890123456789 }[19]$
+$\eval{987654321.1234567890123456789}[19]$
\end{centred}
In all cases, no more than $16$ \emph{significant} figures are displayed,
although the number of decimal places displayed may exceed $16$ as
@@ -1107,13 +1107,13 @@
in the second example.
It is possible to use \emph{negative} rounding values. Such a value
-zeroes the specified number of digits \emph{before} the decimal point.
+zeroes the specified number of digits \emph{before} the decimal point.
\begin{centred}
-\verb`$ \eval{ 987654321.123456789 }[-4] $` $\Longrightarrow$ $\eval{ 987654321.123456789 }[-4]$
+\verb`$ \eval{ 987654321.123456789 }[-4] $` $\Longrightarrow$ $ \eval{ 987654321.123456789 }[-4] $
\end{centred}
A rounding value of $0$ rounds to the nearest integer:
\begin{centred}
-\verb`$ \eval{ 987654321.123456789 }[0] $` $\Longrightarrow$ $\eval{ 987654321.123456789 }[0]$
+\verb`$ \eval{ 987654321.123456789 }[0] $` $\Longrightarrow$ $\eval{987654321.123456789}[0]$
\end{centred}
If you wish to change the \emph{default} rounding value from $6$
to some other value, this can be done by creating or editing a file
@@ -1127,16 +1127,16 @@
perhaps for reasons of presentation like aligning columns of figures,
it may be desirable to pad results with zeros. This is achieved by
inserting an asterisk, {*}, into the final optional argument of the
-\verb`\eval` command:
+\verb`\eval` command:
\begin{centred}
-\verb`$ \eval{ 1/4 }[4] $` $\Longrightarrow$ $ \eval{ 1/4 }[4] $,
+\verb`$ \eval{ 1/4 }[4] $` $\Longrightarrow$ $\eval{1/4}[4]$,
-\verb`$ \eval{ 1/4 }[4*] $` $\Longrightarrow$ $ \eval{ 1/4 }[4*] $.
+\verb`$ \eval{ 1/4 }[4*] $` $\Longrightarrow$ $\eval{1/4}[4*]$.
\end{centred}
\subsection{Scientific notation }
-\label{subsec:evalScientificNotation} \verb`l3fp` can output numbers
+\label{subsec:evalScientificNotation} \texttt{l3fp} can output numbers
in scientific notation. For example, $1234$ is rendered as $\eval{1234}[e]$,
denoting $1.234\times10^{3}$ , and $0.008$ as $\eval{0.008}[e]$,
denoting $8\times10^{-3}$. The `e' here, the \emph{exponent mark},
@@ -1150,49 +1150,49 @@
in scientific notation in \verb`numerica` enter \verb`e` in the
trailing optional argument:
\begin{centred}
-\verb`$ \eval{ 123.456789 }[e] $` $\Longrightarrow$ $ \eval{ 123.456789 }[e] $.
+\verb`$ \eval{ 123.456789 }[e] $` $\Longrightarrow$ $\eval{123.456789}[e]$.
\end{centred}
The default rounding value $6$ is in play here, with seven digits
of the significand displayed overall, one preceding the decimal point,
six following it. Compare this with the same number rounded in decimal
-form:
+form:
\begin{centred}
-\verb`$ \eval{ 123.456789012345 } $` $\Longrightarrow$ $ \eval{ 123.456789012345 } $.
+\verb`$ \eval{ 123.456789012345 } $` $\Longrightarrow$ $\eval{123.456789012345}$.
\end{centred}
In this instance, nine digits are displayed, three before the decimal
-point and six after. Similarly compare
+point and six after. Similarly compare
\begin{centred}
-\verb`$ \eval{ 0.0123456789 }[e] $` $\Longrightarrow$ $ \eval{ 0.0123456789 }[e] $
+\verb`$ \eval{ 0.0123456789 }[e] $` $\Longrightarrow$ $\eval{0.0123456789}[e]$
\end{centred}
-with
+with
\begin{centred}
-\verb`$ \eval{ 0.0123456789 } $` $\Longrightarrow$ $ \eval{ 0.0123456789 } $.
+\verb`$ \eval{ 0.0123456789 } $` $\Longrightarrow$ $\eval{0.0123456789}$.
\end{centred}
This time scientific notation has gained two extra decimal digits
to display.
Negative rounding values are pointless for scientific notation. A
-zero might on occasion be relevant:
+zero might on occasion be relevant:
\begin{centred}
-\verb`$ \eval{ 987654321 }[0e] $` $\Longrightarrow$ $ \eval{ 987654321 }[0e] $.
+\verb`$ \eval{ 987654321 }[0e] $` $\Longrightarrow$ $\eval{987654321}[0e]$.
\end{centred}
-Sometimes letters other than `e' are used to indicate scientific
-notation, like `E' or `d' or `D'. With a few exceptions, \texttt{numerica}
-allows any letter or text character to be used as the exponent marker:
+Sometimes letters other than `e' are used to indicate scientific notation,
+like `E' or `d' or `D'. With a few exceptions, \texttt{numerica} allows
+any letter or text character to be used as the exponent marker:
\begin{centred}
\verb`\eval{$ 1/23456789 $}[4d]`\texttt{ $\Longrightarrow$} \eval{$ 1/23456789 $}[4d].
\end{centred}
But when \texttt{x} is inserted in the trailing optional argument,
the output is in the form $d_{0}.d_{1}\ldots d_{m}\times10^{n}$ (except
-when $n=0$), where each $d_{i}$ denotes a digit.
+when $n=0$), where each $d_{i}$ denotes a digit.
\begin{centred}
-\verb`\eval{$ 1/23456789 $}[4x]`\texttt{ $\Longrightarrow$ }\eval{$ 1/23456789 $}[4x] .
+\verb`\eval{$ 1/23456789 $}[4x]`\texttt{ $\Longrightarrow$ }\eval{$ 1/23456789 $}[4x].
\end{centred}
The requirements of tables leads to another form of scientific notation.
Placing \texttt{t} in the trailing argument turns on this table-ready
-form of notation:
+form of notation:
\begin{centred}
-\verb`\eval{$ 1/23456789 $}[4t]`\texttt{ $\Longrightarrow$ }\eval{$ 1/23456789 $}[4t].
+\verb`\eval{$ 1/23456789 $}[4t]`\texttt{ $\Longrightarrow$}\eval{$ 1/23456789 $}[4t].
\end{centred}
This is discussed more fully in the documentation for the \texttt{numerica-tables}
package.
@@ -1200,7 +1200,7 @@
In the next example three options are used in the trailing argument.
The order in which the items are entered does not matter:
\begin{centred}
-\verb`\eval{$ 1/125 $}[*e4]` $\Longrightarrow$ \eval{$ 1/125 $}[*e4].
+\verb`\eval{$ 1/125 $}[*e4]` $\Longrightarrow$ \eval{$ 1/125 $}[*e4].
\end{centred}
Finally, to illustrate that `any' text character\footnote{Be sensible! An equals sign for instance might confuse \texttt{numerica}
into thinking the number-format option is the vv-list, and will certainly
@@ -1219,17 +1219,17 @@
in tables where the alignment of a column of figures might be affected).
\texttt{numerica} offers a means of extending scientific notation
to numbers in this range by repeating the letter chosen as the exponent
-mark in the trailing optional argument.
+mark in the trailing optional argument.
\begin{centred}
-\verb`\eval{$ \pi $}[4tt]` $\Longrightarrow$ \eval{$ \pi $}[4tt]
+\verb`\eval{$ \pi $}[4tt]` $\Longrightarrow$ \eval{$ \pi $}[4tt]
\end{centred}
\subsubsection{\textbackslash eval{*} and scientific notation}
Scientific notation can be used for the numerical result output by
-\verb`\eval*`:
+\verb`\eval*`:
\begin{centred}
-\verb`\eval*{ \pi }[ee]` $\Longrightarrow$ \eval*{ \pi }[ee]
+\verb`\eval*{ \pi }[ee]` $\Longrightarrow$ \eval*{ \pi }[ee]
\end{centred}
There is one catch: if you substitute \texttt{x} for \texttt{e} here,
\LaTeX{} will complain about a missing \verb`$`. An \texttt{x} in
@@ -1240,13 +1240,13 @@
\subsection{Boolean output}
-\label{subsec:evalBoolean-output}\verb`l3fp` can evaluate comparisons,
+\label{subsec:evalBoolean-output}\texttt{l3fp} can evaluate comparisons,
outputting $0$ if the comparison is false, $1$ if it is true. By
entering a question mark, \texttt{?}, in the trailing optional argument,
you can force \verb`numerica` to do the same depending as the result
of a calculation is zero or not. The expression being evaluated does
-not need to be a comparison, \verb`$ \eval{\pi}[?] $` $\Longrightarrow$ $ \eval{\pi}[?]$,
-but comparisons are what this is designed for.
+not need to be a comparison, \verb`$ \eval{\pi}[?] $` $\Longrightarrow$
+$\eval{\pi}[?]$, but comparisons are what this is designed for.
Possible comparison relations are \verb`=`, \verb`<`, \verb`>`,
\verb`\ne`, \verb`\neq`, \verb`\ge`, \verb`\geq`, \verb`\le`,
@@ -1255,22 +1255,21 @@
these (they are not part of standard \emph{mathematical} usage) and
will generate an error. An example where the relation is equality
exhibits a numerological curiosity:\footnote{The \texttt{{[}p=.{]}} of this and the next example ensures a full
-stop appears in the correct place; see §\ref{subsec:settingsPunctuation}.}
+stop appears in the correct place; see §\ref{subsec:settingsPunctuation}.}
\begin{centred}
\verb`\eval[p=.]{\[ \frac1{0.0123456789}=81 \]}[5?]` $\Longrightarrow$
-\eval[p=.]{\[ \frac1{0.0123456789}=81 \]}[5?]\smallskip{}
+\eval[p=.]{\[ \frac1{0.0123456789}=81 \]}[5?]
\end{centred}
Notice the $5$ alongside the question mark in the trailing argument.
That is critical. Change the $5$ to a $6$ (or omit it since the
-default rounding value is $6$) and the outcome is different:
+default rounding value is $6$) and the outcome is different:
\begin{centred}
-\verb`\eval[p=.]{\[ \frac1{0.0123456789}=81 \]}[6?]` $\Longrightarrow$
-\eval[p=.]{\[ \frac1{0.0123456789}=81 \]}[6?]
+\verb`\eval[p=.]{\[ \frac1{0.0123456789}=81 \]}[6?]` $\Longrightarrow$\eval[p=.]{\[ \frac1{0.0123456789}=81 \]}[6?]
\end{centred}
Now the relation is false. Evaluating the fraction to more than $6$
places, say to $9$, we can see what is going on:
\begin{centred}
-\verb`\eval{$ 1/0.0123456789 $}[9]` $\Longrightarrow$ \eval{$ 1/0.0123456789 $}[9].
+\verb`\eval{$ 1/0.0123456789 $}[9]` $\Longrightarrow$\eval{$ 1/0.0123456789 $}[9]
\end{centred}
\subsubsection{Outputting \texttt{T} or \texttt{F}}
@@ -1279,7 +1278,7 @@
$1/0.0123456789=81$ is confusing. It is easy to change the boolean
output from $0,1$ to a more appropriate $F,T$, or \texttt{$\texttt{F,\texttt{T}}$}
by adding one or two more question marks respectively in the number-format
-option.
+option.
\begin{centred}
\verb`\eval[p=.]{\[ \frac1{0.0123456789}=81 \]}[6???]` $\Longrightarrow$
\eval[p=.]{\[ \frac1{0.0123456789}=81 \]}[6???]
@@ -1286,7 +1285,7 @@
\end{centred}
The default boolean output format is chosen to be $0,1$ in case an
\verb`\eval` command is used within another \verb`\eval` command
-(`nesting'– see Chapter~\ref{chap:Nesting}~). The inner command
+(`nesting'-- see Chapter~\ref{chap:Nesting}~). The inner command
needs to output a \emph{numerical} answer.
\subsubsection{Rounding error tolerance}
@@ -1313,16 +1312,17 @@
hence the equality $1/0.0123456789=81$ is true. But when rounded
to $6$ places it is $0.000001$ which \emph{is} distinguishable from
zero and so the equality is false. Truth or falsity depends on the
-rounding value.
+rounding value.
When dealing with numbers generated purely mathematically, rounding
values of $5$ or $6$ are likely to be too small. More useful would
-be rounding values closer to \texttt{l3fp}'s $16$ – perhaps $14$?
-– depending on how severe the calculations are that generate the numbers.
-However if the numbers we are dealing with come from outside mathematics,
-from practical experiments perhaps, then even a rounding value of
-$5$ or $6$ may be too large.
+be rounding values closer to \texttt{l3fp}'s $16$ -- perhaps $14$?
+-- depending on how severe the calculations are that generate the
+numbers. However if the numbers we are dealing with come from outside
+mathematics, from practical experiments perhaps, then even a rounding
+value of $5$ or $6$ may be too large.
+\noindent{}%
\noindent\begin{minipage}[t]{1\columnwidth}%
\begin{shaded}%
Mathematically, the claim that $X=Y$ at a rounding value $n$ is
@@ -1332,26 +1332,28 @@
\]
since this rounds \emph{down} to zero at $n$ places of decimals.
This gives a more accurate test of equality than doing things in the
-opposite order – rounding each number first and then taking the difference.
-One might, for instance, have numbers like $X=0.12345$, $Y=0.12335$.
-Rounding to $n=4$ places, both round to $0.1234$ and yet the difference
-between them is $0.0001$ – they are distinguishable numbers to $4$
-places of decimals. This is why \texttt{numerica} forms the difference
-\emph{before }doing the rounding.\end{shaded}%
+opposite order -- rounding each number first and then taking the
+difference. One might, for instance, have numbers like $X=0.12345$,
+$Y=0.12335$. Rounding to $n=4$ places, both round to $0.1234$ and
+yet the difference between them is $0.0001$ -- they are distinguishable
+numbers to $4$ places of decimals. This is why \texttt{numerica}
+forms the difference \emph{before }doing the rounding.\end{shaded}%
\end{minipage}
\subsubsection{And, Or, Not}
-For logical And \LaTeX{} provides the symbols \verb`\wedge` and \verb`\land`,
-both displaying as $\land$, but \texttt{numerica} adds thin spaces
-( \verb`\,` ) around the symbol for \verb`\land` (copying the package
-\texttt{gn-logic14.sty}). For logical Or \LaTeX{} provides the symbols
-\verb`\vee` and \verb`\lor`, both displaying as $\lor$, but again
-\texttt{numerica} adds thin spaces around the symbol for \verb`\lor`.
+\noindent For logical And \LaTeX{} provides the symbols \noindent\verb`\wedge`
+and \noindent\verb`\land`, both displaying as $\land$, but \texttt{numerica}
+adds thin spaces ( \noindent\verb`\,` ) around the symbol for \noindent\verb`\land`
+(copying the package \texttt{gn-logic14.sty}). For logical Or \LaTeX{}
+provides the symbols \noindent\verb`\vee` and \noindent\verb`\lor`,
+both displaying as $\lor$, but again \texttt{numerica} adds thin
+spaces around the symbol for \noindent\verb`\lor`.
\begin{centred}
-\verb`\eval{$ 1<2 \wedge 2<3 $}[??]` $\Longrightarrow$ \eval{$ 1<2 \wedge 2<3 $}[??],
+\noindent\noindent\verb`\eval{$ 1<2 \wedge 2<3 $}[??]` $\Longrightarrow$\eval{$ 1<2 \wedge 2<3 $}[??],
-\verb`\eval{$ 1<2 \land 2<3 $}[???]` $\Longrightarrow$ \eval{$ 1<2 \land 2<3 $}[???].
+\verb`\eval{$ 1<2 \land 2<3 $}[???]` $\Longrightarrow$\eval{$ 1<2 \land 2<3 $}[???]
+.
\end{centred}
To my eye the second of these with its increased space around the
wedge symbol displays the meaning of the overall expression better
@@ -1360,14 +1362,14 @@
is intended.
\LaTeX{} provides two commands for logical Not, \verb`\neg` and \verb`\lnot`,
-both displaying as $\lnot$ . Not binds tightly to its argument:
+both displaying as $\lnot$ . Not binds tightly to its argument:
\begin{centred}
-\verb`\eval{$ \lnot A \land B $}[A=0,B=0]` $\Longrightarrow$ \eval{$ \lnot A \land B $}[A=0,B=0].
+\verb`\eval{$ \lnot A \land B $}[A=0,B=0]` $\Longrightarrow$ \eval{$ \lnot A \land B $}[A=0,B=0]
\end{centred}
Here \verb`\lnot` acts only on the $A$; if it had acted on $A\land B$
-as a whole the result would have been different:
+as a whole the result would have been different:
\begin{centred}
-\verb`\eval{$ \lnot(A \land B) $}[A=0,B=0]` $\Longrightarrow$ \eval{$ \lnot(A \land B) $}[A=0,B=0].
+\verb`\eval{$ \lnot(A \land B) $}[A=0,B=0]` $\Longrightarrow$ \eval{$ \lnot(A \land B) $}[A=0,B=0]
\end{centred}
For a little flourish, I evaluate a more complicated logical statement:\footnote{Quoting from an article in \emph{Quanta Magazine} (August 2020) by
Kevin Hartnett: `Let’s say you and two friends are planning a party.
@@ -1378,29 +1380,28 @@
wants to leave off Avery or Brad or both of them. Given these constraints,
you could ask: Is there a guest list that satisfies all three party
planners?' I have written $C$ for Kemba, $A$ and $B$ for Avery
-and Brad.}
+and Brad.}
\begin{verbatim}
\eval{$(A\lor\lnot C)\land(C\lor B)\land
(\lnot A\lor\lnot B)$}[A=1,B=0,C=1][???]
\end{verbatim}
$\Longrightarrow$ \eval{$(A\lor\lnot C)\land(C\lor B)\land
- (\lnot A\lor\lnot B)$}[A=1,B=0,C=1][???].
+ (\lnot A\lor\lnot B)$}[A=1,B=0,C=1][???].
\subsubsection{Chains of comparisons}
\texttt{numerica} can handle chains of comparisons like $1<2<1+2<5-1$.
`Behind the scenes' it inserts logical And-s into the chain, $1<2\land2<1+2\land1+2<5-1$,
-and evaluates the modified expression:
-\begin{centred}
-\verb`\eval{$ 1<2<1+2<5-1 $}[?'']` $\Longrightarrow$ \eval{$ 1<2<1+2<5-1 $}[?''].
-\end{centred}
+and evaluates the modified expression:
+\verb`\eval{$ 1<2<1+2<5-1 $}[?'']` $\Longrightarrow$ \eval{$ 1<2<1+2<5-1 $}[?''].
+
\subsubsection{\texttt{amssymb} comparison symbols}
\label{subsec:evalAmssymb-comparisons}\texttt{numerica} accepts some
alternative symbols for the basic comparison relations from the \texttt{amssymb}
package provided that package is loaded, i.e. the preamble of your
-document includes the statement
+document includes the statement
\begin{lyxcode}
\textbackslash usepackage\{amssymb\}
\end{lyxcode}
@@ -1418,13 +1419,13 @@
\label{subsec:evalArithmetic}Addition, subtraction, multiplication,
division, square roots, \emph{$n$}th roots, and exponentiating (raising
-to a power) are all available.
+to a power) are all available.
Multiplication can be rendered explicitly with an asterisk,
\begin{centred}
\verb`\eval{$ 9*9 $}` $\Longrightarrow$ \eval{$ 9*9 $},
\end{centred}
-but that's ugly. More elegant is to use \verb`\times`:
+but that's ugly. More elegant is to use \verb`\times`:
\begin{centred}
\verb`\eval{$ 9\times9 $}` $\Longrightarrow$ \eval{$ 9\times9 $}.
\end{centred}
@@ -1435,13 +1436,13 @@
\verb`\eval{$ ab $}[a=123,b=1/123]` $\Longrightarrow$ \eval{$ ab $}[a=123,b=1/123].
\end{centred}
-Division can be rendered in multiple ways too:
+Division can be rendered in multiple ways too:
\begin{centred}
\verb`\eval{$ 42/6 $}` $\Longrightarrow$ \eval{$ 42/6 $},
\verb`\eval{$ 42\div6 $}` $\Longrightarrow$ \eval{$ 42\div6 $},
\end{centred}
-or by using \verb`\frac` or \verb`\tfrac` or \verb`\dfrac` as in
+or by using \verb`\frac` or \verb`\tfrac` or \verb`\dfrac` as in
\begin{centred}
\verb`\eval{$ \frac{42}6 $}` $\Longrightarrow$ \eval{$ \frac{42}6 $}.
\end{centred}
@@ -1453,9 +1454,10 @@
or in decimal form, $2.5$ (as one does automatically in mathematical
expressions anyway because of the ambiguity in a form like $2\tfrac{1}{2}$).
-Powers are indicated with the superscript symbol \verb`^`:
+Powers are indicated with the superscript symbol \verb`^`:
\begin{centred}
-\verb` \eval{$ 3^{2^2} $}` $\Longrightarrow$ \eval{$ 3^{2^2} $} .
+\verb`\eval{$ 3^{2^2} $}` $\Longrightarrow$ \eval{$ 3^{2^2} $}
+.
\end{centred}
\subsubsection{Square roots and $n$th roots}
@@ -1462,9 +1464,9 @@
\label{subsec:evalSquareRootsEtc}Let us check that 3, 4, 5 and 5,
12, 13 really are Pythagorean triples (I use \verb`\sqrt` in the
-first, \verb`\surd` in the second):
+first, \verb`\surd` in the second):
\begin{centred}
-\verb`\eval{$ \sqrt{3^2+4^2} $}` $\Longrightarrow$ \eval{$\sqrt{3^{2}+4^{2}}$},
+\verb`\eval{$ \sqrt{3^2+4^2} $}` $\Longrightarrow$ \eval{$ \sqrt{3^2+4^2} $},
\verb`\eval{$ \surd(5^2+12^2) $}` $\Longrightarrow$ \eval{$ \surd(5^2+12^2) $}.
\end{centred}
@@ -1472,9 +1474,9 @@
for extracting $n$th roots of a number. This notation is generally
used when $n$ is a small positive integer like $3$ or $4$. This
practice is followed in \texttt{numerica}: $n$ must be a (not necessarily
-small) \emph{positive integer}:
+small) \emph{positive integer}:
\begin{centred}
-\verb`\eval{$ \sqrt[4]{81} $}` $\Longrightarrow$ \eval{$ \sqrt[4]{81} $},
+\verb`\eval{$ \sqrt[4]{81} $}` $\Longrightarrow$ \eval{$ \sqrt[4]{81} $},
\verb`\eval{$ \sqrt[n]{125} $}[n=\floor{\pi}]` $\Longrightarrow$
\eval{$ \sqrt[n]{125} $}[n=\floor{\pi}].
@@ -1490,47 +1492,45 @@
nested within \verb`\bigg` commands), all digested without complaint
(see §\ref{subsec:evalFormatting-commands}; and see §\ref{subsec:settingsPunctuation}
for the \verb`[p=.]`): \medskip{}
+
\begin{verbatim}
\eval[p=.]{\[ \sqrt[3]{\!
\biggl(\!\left.\frac AD\right/\!\frac BC\biggr)
}\]}[A=729,B=81,C=9,D=3]
\end{verbatim}
-$\Longrightarrow$\eval[p=.]
- {\[
- \sqrt[3]
- {\!\biggl(\!\left.\frac AD\right/\!\frac BC\biggr)}
- \]}[A=729,B=81,C=9,D=3]
+$\Longrightarrow$ \eval[p=.]{\[ \sqrt[3]{\!
+ \biggl(\!\left.\frac AD\right/\!\frac BC\biggr)
+ }\]}[A=729,B=81,C=9,D=3]
As implemented in \texttt{numerica}, $n$th roots found using \verb`\sqrt[n]`
-are \verb`n=<integer>`\emph{ }roots. This raises an interesting question:
-if the `$n$' of an $n$th root is the result of a calculation,
-what happens with rounding errors? The calculation may not produce
-an \emph{exact} integer. (This problem also arises with factorials;
-see §\ref{subsec:evalFactorialsBinom}.) The solution employed in
-\texttt{numerica} is to make what is considered an integer depend
-on a rounding value. Most calculations will produce rounding errors
-in distant decimal places. For `int-ifying' calculations, \texttt{numerica}
-uses a rounding value of $14$: a calculation produces an integer
-if, when rounded to $14$ figures, the result is an integer. Since
-\texttt{l3fp} works to $16$ significant figures, a rounding value
-of $14$ allows ample `elbowroom' for rounding errors to be accommodated
-when judging what is an integer and what is not. As a practical matter
-problems should not arise.
+require \verb`n` to be an integer. This raises an interesting question:
+if the `$n$' of an $n$th root is the result of a calculation, what
+happens with rounding errors? The calculation may not produce an \emph{exact}
+integer. (This problem also arises with factorials; see §\ref{subsec:evalFactorialsBinom}.)
+The solution employed in \texttt{numerica} is to make what is considered
+an integer depend on a rounding value. Most calculations will produce
+rounding errors in distant decimal places. For `int-ifying' calculations,
+\texttt{numerica} uses a rounding value of $14$: a calculation produces
+an integer if, when rounded to $14$ figures, the result is an integer.
+Since \texttt{l3fp} works to $16$ significant figures, a rounding
+value of $14$ allows ample `elbowroom' for rounding errors to be
+accommodated when judging what is an integer and what is not. As a
+practical matter problems should not arise.
\subsubsection{\emph{n}th roots of negative numbers}
Odd (in the sense of `not even') integral roots of \emph{negative}
-numbers are available with \verb`\sqrt`,
+numbers are available with \verb`\sqrt`,
\begin{centred}
\verb`\eval{$ \sqrt[3]{-125} $}` $\Longrightarrow$ \eval{$ \sqrt[3]{-125} $},
-\verb`\eval{$ \sqrt[3]{-1.25} $}` $\Longrightarrow$ \eval{$ \sqrt[3]{-0.125} $}.
+\verb`\eval{$ \sqrt[3]{-1.25} $}` $\Longrightarrow$ \eval{$ \sqrt[3]{-1.25} $}.
\end{centred}
\subsubsection{Inverse integer powers }
Of course to find an $n$th root we can also raise to the inverse
-power,
+power,
\begin{centred}
\verb`\eval{$ 81^{1/4} $}` $\Longrightarrow$ \eval{$ 81^{1/4} $}.
\end{centred}
@@ -1544,7 +1544,7 @@
The usual precedence rules apply: multiplication and division bind
equally strongly and more strongly than addition and subtraction which
bind equally stongly. Exponentiating binds most strongly. Evaluation
-occurs from the left.
+occurs from the left.
\begin{centred}
\verb`\eval{$ 4+5\times6+3 $}` $\Longrightarrow$ \eval{$ 4+5\times6+3 $},
@@ -1577,24 +1577,25 @@
\subsection{Modifiers\texttt{ (\textbackslash left \textbackslash right}, etc.)}
-The \verb`\left` and \texttt{\textbackslash right} modifiers and
-also the series of \verb`\big...` modifiers\texttt{ }(\texttt{\textbackslash}\verb`bigl \bigr`,
-\verb`\Bigl \Bigr`, \verb`\biggl \biggr`, \verb`\Biggl \Biggr`)
-are available for use with all brackets (parentheses, square brackets,
-braces):
+The \verb`\left` and \verb`\right` modifiers and also the series
+of \verb`\big...` modifiers\texttt{ }(\verb`\bigl \bigr`, \verb`\Bigl \Bigr`,
+\verb`\biggl \biggr`, \verb`\Biggl \Biggr`) are available for use
+with all brackets (parentheses, square brackets, braces):
\begin{verbatim}
\eval[p=.]{\[ \exp\left(
\dfrac{\ln2}{4}+\dfrac{\ln8}{4}
\right) \]}
\end{verbatim}
-$\Longrightarrow$ \eval[p=.]{\[ \exp\left( \dfrac{\ln2}{4}+\dfrac{\ln8}{4} \right) \]}
+$\Longrightarrow$ \eval[p=.]{\[ \exp\left(
+ \dfrac{\ln2}{4}+\dfrac{\ln8}{4}
+ \right) \]}
\texttt{numerica} also accepts their use with \texttt{.} (dot) and
with \texttt{/} (as noted earlier, the \verb`[p]` and \verb`[p=.]`
-are explained at §\ref{subsec:settingsPunctuation}):
+are explained at §\ref{subsec:settingsPunctuation}):
\begin{centred}
\verb`\eval[p]{\[ \left.\dfrac{3+4}{2+1}\right/\!\dfrac{1+2}{4+5} \]}`
-$\Longrightarrow$ \eval[p=.]{\[ \left. \dfrac{3+4}{2+1} \right/\!\dfrac{1+2}{4+5} \]}
+$\Longrightarrow$ \eval[p]{\[ \left.\dfrac{3+4}{2+1}\right/\!\dfrac{1+2}{4+5} \]}
\end{centred}
They can be nested.
@@ -1612,18 +1613,20 @@
\verb`\asech`, \verb`\acoth`. (\emph{HMF} writes $\text{arcsinh}$,
$\text{arccosh}$, etc. and ISO recommends $\text{arsinh}$, $\text{arcosh}$,
etc. The first seems ill-advised, the second not widely adopted. At
-present neither is catered for in \texttt{numerica}.)\emph{ }
+present neither is catered for in \texttt{numerica}.)
\begin{centred}
-\verb`\eval{$ \arctan1/1\deg $}` $\Longrightarrow$ \eval{$ \arctan 1/1\deg $} ,
+\verb`\eval{$ \arctan1/1\deg $}` $\Longrightarrow$\eval{$ \arctan1/1\deg $}
+,
-\verb`\eval{$ \atanh\tanh3 $}` $\Longrightarrow$ \eval{$ \atanh\tanh3 $} .
+\verb`\eval{$ \atanh\tanh3 $}` $\Longrightarrow$ \eval{$ \atanh\tanh3 $}.
\end{centred}
Inverses can also be constructed using the `$-1$' superscript notation.
Thus
\begin{centred}
-\verb`\eval{$ \sin^{-1}(1/\surd2)/1\deg $}` $\Longrightarrow$ \eval{$ \sin^{-1}(1/\surd2)/1\deg $} ,
+\verb`\eval{$ \sin^{-1}(1/\surd2)/1\deg $}` $\Longrightarrow$ \eval{$ \sin^{-1}(1/\surd2)/1\deg $}
+,
-\verb`\eval{$ \tanh\tanh^{-1}0.5 $}` $\Longrightarrow$ \eval{$ \tanh\tanh^{-1}0.5 $} .
+\verb`\eval{$ \tanh\tanh^{-1}0.5 $}` $\Longrightarrow$ \eval{$ \tanh\tanh^{-1}0.5 $}.
\end{centred}
\noindent\begin{minipage}[t]{1\columnwidth}%
\begin{shaded}%
@@ -1637,13 +1640,13 @@
and square roots for the inverses. Rounding errors mean the values
calculated may not have $16$-figure accuracy. The worst `offenders'
are likely to be the least used, \verb`\acsch` and \verb`\asech`.
-For instance,
+For instance,
\[
\acsch x=\ln\left[\frac{1}{x}+\left(\frac{1}{x^{2}}+1\right)^{1/2}\right],
\]
\begin{centred}
-\verb`\eval{$ \csch \acsch 7 $}[16]` $\Longrightarrow$ \eval{$ \csch \acsch 7 $}[16].
+\verb`\eval{$ \csch \acsch 7 $}[16]` $\Longrightarrow$ \eval{$ \csch \acsch 7 $}[16]
\end{centred}
\end{shaded}%
\end{minipage}
@@ -1650,24 +1653,28 @@
\subsection{Logarithms}
-The natural logarithm \verb`\ln`, base $10$ logarithm \verb`\lg`,
-and binary or base $2$ logarithm \verb`\lb` are all recognized,
-as is \verb`\log`, preferably with a subscripted base:
+\noindent The natural logarithm \noindent\verb`\ln`, base $10$ logarithm
+\noindent\verb`\lg`, and binary or base $2$ logarithm \noindent\verb`\lb`
+are all recognized, as is \noindent\verb`\log`, preferably with a
+subscripted base:
\begin{centred}
-\verb`\eval{$ \log_{12}1728 $}` $\Longrightarrow$ \eval{$ \log_{12}1728 $}
+\noindent\noindent\verb`\eval{$ \log_{12}1728 $}` $\Longrightarrow$
+\eval{$ \log_{12}1728 $}
\end{centred}
-If there is no base indicated, base $10$ is assumed. (The notations
-\verb`\ln`, \verb`\lg`, and \verb`\lb` follow ISO 80000-2 recommendation,
-which frowns upon the use of the unsubscripted \verb`\log` although
-only \verb`\ln` appears widely used.) The base need not be explicitly
-entered as a number. It could be entered as an expression or be specified
-in the vv-list:
+\noindent If there is no base indicated, base $10$ is assumed. (The
+notations \noindent\verb`\ln`, \noindent\verb`\lg`, and \noindent\verb`\lb`
+follow ISO 80000-2 recommendation, which frowns upon the use of the
+unsubscripted \noindent\verb`\log` although only \noindent\verb`\ln`
+appears widely used.) The base need not be explicitly entered as a
+number. It could be entered as an expression or be specified in the
+vv-list:
\begin{centred}
-\verb`\eval*{$ \log_b c $}[b=2,c=1024]` $\Longrightarrow$ \eval*{$ \log_b c $}[b=2,c=1024],
+\noindent\noindent\verb`\eval*{$ \log_b c $}[b=2,c=1024]` $\Longrightarrow$
+\eval*{$ \log_b c $}[b=2,c=1024],
\end{centred}
-the log to base $2$ in this case. It is possible to use the unadorned
-\verb`\log` with a base different from $10$; if you wish to do this
-only for a particular calculation see §\ref{subsec:settingsLogBase},
+\noindent the log to base $2$ in this case. It is possible to use
+the unadorned \noindent\verb`\log` with a base different from $10$;
+if you wish to do this only for a particular calculation see §\ref{subsec:settingsLogBase},
or see §\ref{sec:settingsDefaults} if you want to make this default
behaviour.
@@ -1675,7 +1682,7 @@
Other unary functions supported are the exponential function \verb`\exp`
and signature function \verb`\sgn` (equal to $-1$, $0$, or $1$
-depending as its argument is $<0$, $=0$, or $>0$).
+depending as its argument is $<0$, $=0$, or $>0$).
\subsection{Squaring, cubing, \ldots unary functions}
@@ -1686,16 +1693,17 @@
\]
You do not have to render it $(\sin1.234)^{2}+(\cos1.234)^{2}$ or
(heaven forbid) $(\sin(1.234))^{2}+(\cos(1.234))^{2}$. The everyday
-usage is fine:
+usage is fine:
\begin{centred}
\verb`\eval{$ \sin^2\theta+\cos^2\theta $}[\theta=1.234]` $\Longrightarrow$
-\eval{$ \sin^2\theta+\cos^2\theta $}[\theta=1.234] .
+\eval{$ \sin^2\theta+\cos^2\theta $}[\theta=1.234].
\end{centred}
Equally \texttt{numerica} has no difficulty reading the `correct'
-but pedantic form
+but pedantic form
\begin{centred}
\verb`\eval{$ (\sin(\theta))^2+(\cos(\theta))^2 $}[\theta=1.234]`
-$\Longrightarrow$ \eval{$ (\sin(\theta))^2+(\cos(\theta))^2 $}[\theta=1.234] .
+$\Longrightarrow$ \eval{$ (\sin(\theta))^2+(\cos(\theta))^2 $}[\theta=1.234]
+.
\end{centred}
A hyperbolic identity is corroborated in this example:
\begin{centred}
@@ -1704,16 +1712,16 @@
\verb`\eval{$ 3\sinh x+4\sinh^3x $}[x=1]` $\Longrightarrow$ \eval{$ 3\sinh x+4\sinh^3x $}[x=1].
\end{centred}
In fact all named unary functions in \texttt{numerica} can be squared,
-cubed, etc., in this `incorrect' but familiar way, although the
-practice outside the trigonometric and hyperbolic context seems (vanishingly?)
+cubed, etc., in this `incorrect' but familiar way, although the practice
+outside the trigonometric and hyperbolic context seems (vanishingly?)
rare.
When the argument of the function is parenthesized and raised to a
-power – like $\sin(\pi)^{2}$ – it is read by \texttt{numerica} as
-the `sine of the square of pi', $\sin(\pi^{2})$, and \emph{not
-}as the `square of the sine of pi', $(\sin\pi)^{2}$:
+power -- like $\sin(\pi)^{2}$ -- it is read by \texttt{numerica}
+as the `sine of the square of pi', $\sin(\pi^{2})$, and \emph{not
+}as the `square of the sine of pi', $(\sin\pi)^{2}$:
\begin{centred}
-\verb`\eval{$ \sin(\pi)^2 $}` $\Longrightarrow$ \eval{$ \sin(\pi)^2 $} .
+\verb`\eval{$ \sin(\pi)^2 $}` $\Longrightarrow$ \eval{$ \sin(\pi)^2 $}.
\end{centred}
Things are done like this in \texttt{numerica} above all to handle
the logarithm in a natural way. Surely $\ln x^{n}=n\ln x$, i.e. $\ln x^{n}=\ln(x^{n})$
@@ -1729,14 +1737,14 @@
\verb`\min` or \verb`\gcd` can be of arbitrary length. The arguments
themselves can be expressions or numbers. For \verb`\gcd`, \emph{non-integer
arguments are truncated to integers}. Hence both $y$ and $3y$ are
-independently truncated in the following example – to $81$ and $243$
-respectively:
+independently truncated in the following example -- to $81$ and
+$243$ respectively:
\begin{centred}
\verb`\eval{$ \gcd(12,10x^2,3y,y,63) $}[y=1/0.0123456789,x=3]` $\Longrightarrow$
-\eval{$ \gcd(12,10x^2,3y,y,63) $}[y=1/0.0123456789,x=3] .
+\eval{$ \gcd(12,10x^2,3y,y,63) $}[y=1/0.0123456789,x=3].
\end{centred}
(The truncation occurs in the argument of \verb`\gcd`, not in the
-vv-list.)
+vv-list.)
For $n$-ary functions, squaring, cubing, etc. follows a different
pattern from that for unary functions. For \verb`\max`, \verb`\min`,
@@ -1743,10 +1751,10 @@
\verb`\gcd` the argument of the function is a comma list. Squaring
the argument makes no sense. We understand the superscript as applying
to the function as a whole. (Consistency is not the point here; it
-is what mathematicians do that \texttt{numerica} tries to accommodate.)
+is what mathematicians do that \texttt{numerica} tries to accommodate.)
\begin{centred}
\verb`\eval{$ \gcd(3x,x,\arcsin 1/\deg)^2 $}[x=24]` $\Longrightarrow$
-\eval{$ \gcd(3x,x,\arcsin 1/\deg)^2 $}[x=24] .
+\eval{$ \gcd(3x,x,\arcsin 1/\deg)^2 $}[x=24].
\end{centred}
\subsection{Delimiting arguments with brackets \& modifiers }
@@ -1759,7 +1767,7 @@
(which ensures the concluding full stop appears in the correct place.}
\begin{centred}
\verb`\eval[p=.]{\[ \sin\left\lbrack \dfrac\pi{1+2+3}\right\rbrack \]}`
-$\Longrightarrow$\eval[p=.]{\[ \sin\left\lbrack\dfrac\pi{1+2+3}\right\rbrack \]}
+$\Longrightarrow$ \eval[p=.]{\[ \sin\left\lbrack \dfrac\pi{1+2+3}\right\rbrack \]}
\end{centred}
\subsection{Absolute value, floor \& ceiling functions}
@@ -1766,7 +1774,7 @@
It is tempting to use the \texttt{|} key on the keyboard for inserting
an absolute value sign. \texttt{numerica} accepts this usage, but
-it is deprecated. The spacing is incorrect – compare $|-l|$ using
+it is deprecated. The spacing is incorrect -- compare $|-l|$ using
\texttt{|} against $\lvert-l\rvert$ using \verb`\lvert \rvert`.
Also, the identity of the left and right delimiters makes nested absolute
values difficult to parse. \texttt{numerica} does not attempt to do
@@ -1778,7 +1786,7 @@
command of the \texttt{mathtools} package). This takes a mutually
exclusive star (asterisk) or square bracketed optional argument, and
a mandatory braced argument. The starred form expands to \verb`\left\lvert #1 \right\rvert`
-where \verb`#1` is the mandatory argument:
+where \verb`#1` is the mandatory argument:
\begin{centred}
\verb`\eval[p=.]{\[ 3\abs*{\frac{\abs{n}}{21}-1} \]}[n=-7]` $\Longrightarrow$
\eval[p=.]{\[ 3\abs*{\frac{\abs{n}}{21}-1} \]}[n=-7]
@@ -1789,12 +1797,12 @@
\abs[\Big]{\abs{a-c}-\abs[\big]{A-C}}
\]}[A=12,a=-10,C=7,c=-5]
\end{verbatim}
-$\Longrightarrow$ \eval[p=.]{\[
+$\Longrightarrow$ \eval[p=.]{\[
\abs[\Big]{\abs{a-c}-\abs[\big]{A-C}}
- \]}[A=12,a=-10,C=7,c=-5]
+ \]}[A=12,a=-10,C=7,c=-5]
The form without either star or square bracket option dispenses with
-the modifiers altogether:
+the modifiers altogether:
\begin{centred}
\verb`\eval{$ \tfrac12(x+y)+\tfrac12\abs{x-y} $}[x=-3,y=7].` $\Longrightarrow$
\eval{$ \tfrac12(x+y)+\tfrac12\abs{x-y} $}[x=-3,y=7].
@@ -1809,7 +1817,7 @@
where \verb`#1` is the mandatory argument, and for the square bracket
option forms replacing the \verb`\left` and \verb`\right` with the
corresponding \verb`\big` commands. The form without star or square-bracket
-option dispenses with any modifier at all.
+option dispenses with any modifier at all.
\begin{centred}
\verb`\eval{$ \floor{-\pi} $}` $\Longrightarrow$ \eval{$ \floor{-\pi} $},
@@ -1819,13 +1827,13 @@
the ceiling function, $\lceil x\rceil$ is the smallest integer $\ge x$.
Like the absolute value, the floor and ceiling functions, can be nested:
\begin{centred}
-\verb`\eval{$ \floor{-\pi+\ceil{e}} $}` $\Longrightarrow$ \eval{$ \floor{-\pi+\ceil{e}} $}.
+\verb`\eval{$ \floor{-\pi+\ceil{e}} $}` $\Longrightarrow$\eval{$ \floor{-\pi+\ceil{e}} $}.
\end{centred}
\subsubsection{Squaring, cubing, \ldots{} absolute values, etc.}
These three functions can be raised to a power \emph{without} extra
-parentheses:
+parentheses:
\begin{centred}
\verb`\eval{$ \ceil{e}^2 $},` $\Longrightarrow$ \eval{$ \ceil{e}^2 $},
@@ -1843,18 +1851,18 @@
$\Longrightarrow$ \eval{$ (\alpha+\beta)!-\alpha!-\beta! $}[\alpha=2,\beta=3].
\end{centred}
The examples illustrate how \texttt{numerica} interprets the argument
-of the factorial symbol:\texttt{ }it `digests'
+of the factorial symbol: it `digests'
\begin{itemize}
-\item a preceding (possibly multi-digit) integer, or
-\item a preceding variable token, or
-\item a bracketed expression, or
-\item a bracket-like expression.
+\item a preceding (possibly multi-digit) integer, or
+\item a preceding variable token, or
+\item a bracketed expression, or
+\item a bracket-like expression.
\end{itemize}
A bracket-like expression is an absolute value, floor or ceiling function,
-since they delimit arguments in a bracket-like way:
+since they delimit arguments in a bracket-like way:
\begin{centred}
\verb`\eval{$ \abs{-4}!+\floor{\pi}!+\ceil{e}! $}` $\Longrightarrow$
-\eval{$ \abs{-4}!+\floor{\pi}!+\ceil{e}! $}.
+\eval{$ \abs{-4}!+\floor{\pi}!+\ceil{e}! $}
\end{centred}
The result of feeding the factorial an expression different in kind
from one of these four cases may give an error message or an unexpected
@@ -1861,7 +1869,7 @@
result. Use parentheses around such an expression; for example write
$(3^{2})!$, rather than $3^{2}!$.
-Nesting of brackets for factorials is accepted:
+Nesting of brackets for factorials is accepted:
\begin{centred}
\verb`\eval{$ ((5-2)!+1)! $}` $\Longrightarrow$ \eval{$ ((5-2)!+1)! $}.
\end{centred}
@@ -1873,8 +1881,8 @@
since \texttt{numerica} rounds the result of such a calculation by
default to $14$ significant figures before offering it to the factorial.
Since \texttt{l3fp} works to $16$ significant figures, there is ample
-`elbowroom' to accommodate rounding errors before the result of
-a calculation ceases to round to an integer.
+`elbowroom' to accommodate rounding errors before the result of a
+calculation ceases to round to an integer.
\subsubsection{Double factorials}
@@ -1884,9 +1892,9 @@
\begin{centred}
\verb`\eval{$ 6!! $}` $\Longrightarrow$ \eval{$ 6!! $},
-\verb`\eval{$ n!! $}[n=\sqrt{49}]` $\Longrightarrow$ \eval{$ n!! $}[n=\sqrt{49}],
+\verb`\eval{$ n!! $}[n=\sqrt{49}]` $\Longrightarrow$ \eval{$ n!! $}[n=\sqrt{49}].
\end{centred}
-Since $n!=n!!(n-1)!!$ it follows that
+Since $n!=n!!(n-1)!!$ it follows that
\[
n!!=\frac{n!}{(n-1)!!}=\frac{(n+1)!}{(n+1)!!}.
\]
@@ -1898,8 +1906,8 @@
Binomial coefficients are entered in \LaTeX{} with the \verb`\binom`\textbf{
}command. It takes two arguments and has a text-style version \verb`\tbinom`
-and a display-style version \verb`\dbinom`. As implemented in {\ttfamily\verb`numerica`},
-these are \emph{generalised} binomial coefficients:
+and a display-style version \verb`\dbinom`. As implemented in \texttt{numerica},
+these are \emph{generalised} binomial coefficients:
\[
\binom{x}{k}=\frac{x(x-1)\dots(x-k+1)}{k(k-1)\dots1},\quad(x\in\mathbb{R},~k\in\mathbb{N}),
\]
@@ -1906,16 +1914,16 @@
where $x$ need not be a non-negative integer, and where $\binom{x}{0}=1$
by definition. Although the first (or upper) argument can be any real
number, the lower argument \emph{must} be a non-negative integer.
-Thus, \verb`\eval{$ \tbinom53 $}` $\Longrightarrow$ \eval{$\tbinom53$},
-\verb`\eval{$ \tbinom70 $}` $\Longrightarrow$ \eval{$\tbinom70$},
-\verb`\eval{$ \tbinom{4.2}3 $}` $\Longrightarrow$ \eval{$\tbinom{4.2}3$},
+Thus, \verb`\eval{$ \tbinom53 $}` $\Longrightarrow$ \eval{$ \tbinom53 $},
+\verb`\eval{$ \tbinom70 $}` $\Longrightarrow$ \eval{$ \tbinom70 $},
+\verb`\eval{$ \tbinom{4.2}3 $}` $\Longrightarrow$ \eval{$ \tbinom{4.2}3 $},
but if the second (or lower) argument of \verb`\binom` is \emph{not}
-a non-negative integer, {\ttfamily\verb`numerica`} displays
-a message; see §\ref{subsec:errorsIntegerArgs}.
+a non-negative integer, \texttt{numerica} displays a message; see
+§\ref{subsec:errorsIntegerArgs}.
\subsection{Sums and products}
-\verb`numerica` recognizes sums (\verb`\sum` displaying as $\sum$)
+\texttt{numerica} recognizes sums (\verb`\sum` displaying as $\sum$)
and products (\verb`\prod` displaying as $\prod$), and expects both
symbols to have lower and upper summation/product limits specified.
The lower limit must be given in the form \emph{sum/prod variable
@@ -1923,7 +1931,7 @@
be specified (although it can also be given in the form \emph{sum/prod
variable = final value}). The values may be expressions depending
on other variables and values but must evaluate to integers (or infinity
-– see §\ref{sec:settingsInfiniteSumsProds}). Evaluating to an integer
+-- see §\ref{sec:settingsInfiniteSumsProds}). Evaluating to an integer
means that they \emph{round} to an integer, using a rounding value
that is set by default to $14$; (recall that \texttt{l3fp} works
to $16$ significant figures). If a limit evaluates to a non-integer
@@ -1932,39 +1940,42 @@
As an example of expressions in the limits, this example uses the
floor and ceiling functions to convert combinations of constants to
-integers (the \verb`[p]` is explained in §\ref{subsec:settingsPunctuation}),
+integers (the \verb`[p]` is explained in §\ref{subsec:settingsPunctuation}),
\begin{centred}
-\verb`\eval[p]{\[ \sum_{n=\floor{\pi/e}}^{\ceil{\pi e}}n \]}` $\Longrightarrow$\eval[p]{\[ \sum_{n=\floor{\pi/e}}^{\ceil{\pi e}}n \]}
+\verb`\eval[p]{\[ \sum_{n=\floor{\pi/e}}^{\ceil{\pi e}}n \]}` $\Longrightarrow$
+\eval[p]{\[ \sum_{n=\floor{\pi/e}}^{\ceil{\pi e}}n \]}
\end{centred}
-\noindent (which is $\sum_{n=1}^{9}n$).\emph{ }If the upper limit
-is less than the lower limit the result is zero. Notice that there
-is no vv-list. The summation variable does not need to be included
-there unless there are other variables that depend on it. However,
-in the case
+(which is $\sum_{n=1}^{9}n$).\emph{ }If the upper limit is less than
+the lower limit the result is zero. Notice that there is no vv-list.
+The summation variable does not need to be included there unless there
+are other variables that depend on it. However, in the case
\begin{centred}
\verb`\eval[p]{\[ \sum_{k=1}^N\frac1{k^3} \]}[N=100][4]` $\Longrightarrow$
\eval[p]{\[ \sum_{k=1}^N\frac1{k^3} \]}[N=100][4]
\end{centred}
-the upper limit $N$ is necessarily assigned a value in the vv-list.
+the upper limit $N$ is necessarily assigned a value in the vv-list.
-To the author it seems natural to enter the lower limit first, immediately
-after the \verb`\sum` command (the sum is \emph{from }something \emph{to}
-something), but no problem will accrue if the upper limit is placed
-first (after all, the appearance of the formula in the pdf is the
-same):
+\noindent To the author it seems natural to enter the lower limit
+first, immediately after the \noindent\verb`\sum` command (the sum
+is \emph{from }something \emph{to} something), but no problem will
+accrue if the upper limit is placed first (after all, the appearance
+of the formula in the pdf is the same):
\begin{centred}
-\verb`\eval[p=.]{\[ \sum^N_{k=1}\frac1{k^3} \]}[N=100][4]` $\Longrightarrow$
-\eval[p=.]{\[ \sum^N_{k=1}\frac1{k^3} \]}[N=100][4]
+\noindent\noindent\verb`\eval[p=.]{\[ \sum^N_{k=1}\frac1{k^3} \]}[N=100][4]`
+$\Longrightarrow$ \eval[p=.]{\[ \sum^N_{k=1}\frac1{k^3} \]}[N=100][4]
\end{centred}
-Another example of a sum, using binomial coefficients this time, is
+\noindent Another example of a sum, using binomial coefficients this
+time, is
\begin{centred}
-\verb`\eval[p]{\[ \sum_{m=0}^5\binom{5}{m}x^m y^{5-m} \]}[x=0.75,y=2.25]`
+\noindent\noindent\verb`\eval[p]{\[ \sum_{m=0}^5\binom{5}{m}x^m y^{5-m} \]}[x=0.75,y=2.25]`
$\Longrightarrow$ \eval[p]{\[ \sum_{m=0}^5\binom{5}{m}x^m y^{5-m} \]}[x=0.75,y=2.25]
\end{centred}
-which is just \verb`\eval{$(x+y)^5$}[x=0.75,y=2.25]` $\Longrightarrow$
-\eval{$ (x+y)^5 $}[x=0.75,y=2.25], or $3^{5}$.
-
-Now let's calculate a product:
+\noindent which is just
+\begin{centred}
+\noindent\noindent\verb`\eval{$(x+y)^5$}[x=0.75,y=2.25]` $\Longrightarrow$
+\eval{$(x+y)^5$}[x=0.75,y=2.25],
+\end{centred}
+\noindent or $3^{5}$. Now let's calculate a product:
\begin{verbatim}
\eval[p]{\[
\prod_{k=1}^{100}
@@ -1971,16 +1982,19 @@
\biggl(\frac{x^2}{k^2\pi^2} +1\biggr)
\]}[x=1][3]
\end{verbatim}
-$\Longrightarrow$ \eval[p]{\[\prod_{k=1}^{100} \biggl(\frac{x^2}{k^2\pi^2} +1\biggr)\]}[x=1][3]
+$\Longrightarrow$ \eval[p]{\[
+ \prod_{k=1}^{100}
+ \biggl(\frac{x^2}{k^2\pi^2} +1\biggr)
+ \]}[x=1][3]
-\noindent to be compared with \verb`\eval{$ \sinh 1 $}[3]` $\Longrightarrow$
-\eval{$ \sinh1 $}[3]. Obviously more terms than $100$ are required
-in the product to achieve 3-figure accuracy.
+\noindent to be compared with \noindent\verb`\eval{$ \sinh 1 $}[3]`
+$\Longrightarrow$ \eval{$ \sinh 1 $}[3]. Obviously more terms than
+$100$ are required in the product to achieve 3-figure accuracy.
\subsubsection{Infinite sums and products}
-How many more? Let's `go the whole hog' and put $\infty$ in the
-upper limit of this product:
+How many more? Let's `go the whole hog' and put $\infty$ in the upper
+limit of this product:
\begin{verbatim}
\eval[p=.]{\[
\prod_{k=1}^{\infty}
@@ -1987,11 +2001,10 @@
\biggl(\frac{x^2}{k^2\pi^2} +1\biggr)
\]}[x=1][3]
\end{verbatim}
-$\Longrightarrow$ \eval[p=.]
- {\[
- \prod_{k=1}^{\infty}
- \biggl(\frac{x^2}{k^2\pi^2} +1\biggr)
- \]}[x=1][3]
+$\Longrightarrow$ \eval[p=.]{\[
+ \prod_{k=1}^{\infty}
+ \biggl(\frac{x^2}{k^2\pi^2} +1\biggr)
+ \]}[x=1][3]
\noindent Disappointingly, we still get the same result, deficient
by $1$ in the third decimal place. Obviously \texttt{numerica} has
@@ -2018,21 +2031,21 @@
work admirably. For example \verb`\eval{$ (1+0.1234)^{4.321} $}`
$\Longrightarrow$ \eval{$ (1+0.1234)^{4.321} $}. Using binomial
coefficients we can express this as an infinite sum:\medskip{}
+
\begin{verbatim}
\eval[p=.]{\[
\sum_{n=0}^{\infty}\binom{\alpha}{n}x^{n}
\]}[\alpha=4.321,x=0.1234]
\end{verbatim}
-$\Longrightarrow$ \eval[p=.]
- {\[
- \sum_{n=0}^{\infty}\binom{\alpha}{n}x^{n}
- \]}[\alpha=4.321,x=0.1234]
+$\Longrightarrow$ \eval[p=.]{\[
+ \sum_{n=0}^{\infty}\binom{\alpha}{n}x^{n}
+ \]}[\alpha=4.321,x=0.1234]
\subsection{Formatting commands}
\label{subsec:evalFormatting-commands}There are many formatting commands
which change the layout of a formula on the page but do not alter
-its calculational content. \verb`numerica` copes with a great many
+its calculational content. \texttt{numerica} copes with a great many
of these formatting commands, although there will surely be some that
it has overlooked and which will trigger an `Unknown token' message;
see §\ref{sec:evalErrors}. \footnote{Please contact the author in that case: ajparsloe at gmail.com}
@@ -2042,35 +2055,36 @@
These include cryptic forms like \verb`\,` \verb`\:` and \verb`\>`,
\verb`\;` and the corresponding `verbose' forms, \verb`\thinspace`,
\verb`\medspace` and \verb`\thickspace` and their negative equivalents
-\verb`\!` or \verb`\negthinspace`, \verb`\negmedspace` and \verb`\negthickspace`:
+\verb`\!` or \verb`\negthinspace`, \verb`\negmedspace` and \verb`\negthickspace`:
\begin{centred}
\verb`\eval{$ 1\negthickspace+\negthickspace 1 $}` $\Longrightarrow$
\eval{$ 1\negthickspace+\negthickspace 1 $}
\end{centred}
which gives the text spacing of 1+1 as against the usual math spacing
-$1+1$ but doesn't affect the result of the calculation.
+$1+1$ but doesn't affect the result of the calculation.
Other spacing commands are \verb`\quad` and \verb`\qquad`, and \verb`\hspace{arg}`
and \verb`\mspace{arg}`. For \verb`\hspace` there is also a starred
form, \verb`\hspace*{arg}`. Phantoms similarly take an argument:
-\verb`\phantom{arg}`, \verb`\hphantom{arg}` and \verb`\vphantom{arg}`.
+\verb`\phantom{arg}`, \verb`\hphantom{arg}` and \verb`\vphantom{arg}`.
\begin{centred}
\verb`\eval{$ 1\hphantom{mmm}+\hphantom{mmm}1 $}` $\Longrightarrow$
-\eval{$ 1\hphantom{mmm}+ \hphantom{mmm}1 $}.
+\eval{$ 1\hphantom{mmm}+\hphantom{mmm}1 $}.
\end{centred}
Like \verb`\vphantom`, struts allow vertical spacing adjustments.
-\verb`numerica` should digest both \verb`\xmathstrut[optarg]{arg}`
-from \verb`mathtools` and its `baby cousin' \verb`\mathstrut`
-from \TeX . An example from \emph{The \TeX{} book} demonstrating the
-use of \verb`\mathstrut` is
+\texttt{numerica} should digest both \verb`\xmathstrut[optarg]{arg}`
+from \texttt{mathtools} and its `baby cousin' \verb`\mathstrut` from
+\TeX . An example from \emph{The \TeX{} book} demonstrating the use
+of \verb`\mathstrut` is
\begin{verbatim}
\eval{$\sqrt{\mathstrut a}+\sqrt{\mathstrut d}+
\sqrt{\mathstrut y}$}[a=4,d=9,y=16]
\end{verbatim}
-$\Longrightarrow$ \eval{$\sqrt{\mathstrut a}+\sqrt{\mathstrut d}+\sqrt{\mathstrut y}$}[a=4,d=9,y=16],
+$\Longrightarrow$ \eval{$\sqrt{\mathstrut a}+\sqrt{\mathstrut d}+
+ \sqrt{\mathstrut y}$}[a=4,d=9,y=16],
-And here is an evaluation of an expression from the \verb`mathtools`
-documentation using \verb`\xmathstrut`:
+And here is an evaluation of an expression from the \texttt{mathtools}
+documentation using \verb`\xmathstrut`:
\begin{verbatim}
\eval{\[ \frac{ \frac{ \xmathstrut{0.1} x-1 }
{ \xmathstrut{0.25} x-\sin{ x} } }
@@ -2077,14 +2091,14 @@
{\xmathstrut{0.4} \sqrt{ 10-x } } \]}
[x=\pi/6]
\end{verbatim}
-$\Longrightarrow$ \eval{\[ \frac{ \frac{ \xmathstrut{0.1} x-1 }
+$\Longrightarrow$ \eval{\[ \frac{ \frac{ \xmathstrut{0.1} x-1 }
{ \xmathstrut{0.25} x-\sin{ x} } }
- {\xmathstrut{0.4} \sqrt{ 1-x } } \]}
+ {\xmathstrut{0.4} \sqrt{ 10-x } } \]}
[x=\pi/6]
\subsubsection{\texttt{\textbackslash splitfrac}}
-The \verb`mathtools` package provides \verb`\splitfrac` and \verb`\splitdfrac`
+The \texttt{mathtools} package provides \verb`\splitfrac` and \verb`\splitdfrac`
to aid handling of clumsy fractions. The documentation gives an (artificial)
example of use. I've mangled it to produce an even more ridiculous
illustration, adding to the mess an enormous square root, the modifiers
@@ -2096,6 +2110,7 @@
and §\ref{subsec:settingsVvDisplayChangeLocal}. The first puts the
concluding full stop in the right place; the second suppresses the
vv-list.} \medskip{}
+
\begin{verbatim}
\eval[p=.,vvd=]{\[
\sqrt{\left\lparen
@@ -2110,7 +2125,7 @@
{\dfrac z7}\right\rparen}
\]}[x=2,y=5,z=10]
\end{verbatim}
-$\Longrightarrow$ \eval[p=.,vvd=]{\[
+$\Longrightarrow$ \eval[p=.,vvd=]{\[
\sqrt{\left\lparen
\frac{ \splitfrac{xy + xy + xy + xy + xy}
{+ xy + xy + xy + xy}
@@ -2126,48 +2141,48 @@
\subsubsection{Colour}
\label{subsec:Colour}(Anglicised spelling at least for the heading!)
-If you add to the preamble of your document the line
+If you add to the preamble of your document the line
\begin{lyxcode}
\textbackslash usepackage\{color\}
\end{lyxcode}
two commands become available, \verb`\textcolor[optarg]{arg1}{arg2}`
and the declaration form of command, \verb`\color[optarg]{arg}`.
-\verb`numerica` readily accepts the former in a formula to be evaluated:
+\texttt{numerica} readily accepts the former in a formula to be evaluated:
\begin{centred}
\verb`\eval{$ \sin \tfrac\pi6n\textcolor{red}{T}+1 $}[T=9,n=3]` $\Longrightarrow$
-\eval{$ \sin \tfrac\pi6n\textcolor{red}{T}+1 $}[T=9,n=3]
+\eval{$ \sin \tfrac\pi6n\textcolor{red}{T}+1 $}[T=9,n=3]
\end{centred}
-(assuming you had some wish to highlight the time $T$).
+(assuming you had some wish to highlight the time $T$).
However there are restrictions on the use of \verb`\color` in \verb`\eval`
commands. \verb`\color` is a \emph{declaration} form of command.
It has effect until the end of the current group or environment. If
you want to restrict it to only part of that group you need to em-brace
-the command and what it is to apply to,
+the command and what it is to apply to,
\begin{lyxcode}
<pre-stuff>\{\textbackslash color\{red\}<red-stuff>\}<post-stuff\}
\end{lyxcode}
-but that is where the problem arises. \verb`numerica` does not check
+but that is where the problem arises. \texttt{numerica} does not check
for `unannounced' brace groups. It expects a brace group to be introduced
by a preceding instruction like \verb`\sqrt` or \verb`\frac` or
-\verb`^`. When announced in this way, \verb`numerica` can handle
+\verb`^`. When announced in this way, \texttt{numerica} can handle
the brace group appropriately. But the brace group \verb`{\color{red}<red-stuff>}`
-is not so announced. \verb`numerica`'s parsing routine will not recognize
-what it has just swallowed and a \LaTeX{} error will result. So, \verb`\color`
-cannot be used in a formula in a `naked' or unannounced brace group.
-Writing \verb`\eval{$ \color{red} \sin \tfrac\pi6nT+1 $}[T=9,n=3]`
+is not so announced. \texttt{numerica}'s parsing routine will not
+recognize what it has just swallowed and a \LaTeX{} error will result.
+So, \verb`\color` cannot be used in a formula in a `naked' or unannounced
+brace group. Writing \verb`\eval{$ \color{red} \sin \tfrac\pi6nT+1 $}[T=9,n=3]`
is fine, as is
\begin{centred}
\verb`\eval{$ \sin \tfrac\pi6nT+1 \color{red} $}[T=9,n=3]` $\Longrightarrow$
-\eval{$ \sin \tfrac\pi6nT+1 \color{red} $}[T=9,n=3].
+\eval{$ \sin \tfrac\pi6nT+1 \color{red} $}[T=9,n=3].
\end{centred}
So too, because the \verb`\frac` introduces the confining brace group,
-is
+is
\begin{centred}
-\verb`\eval{$ \frac{\color[gray]{0.5}A}B $}[A=12,b=4]` $\Longrightarrow$\eval{$ \frac{\color[gray]{0.5}A}B $}[A=12,B=4],
+\verb`\eval{$ \frac{\color[gray]{0.5}A}b $}[A=12,b=4]` $\Longrightarrow$\eval{$ \frac{\color[gray]{0.5}A}b $}[A=12,b=4]
\end{centred}
where both arguments of the \verb`\color` command are used for grayscale
-output.
+output.
But trying something like \verb`\eval{$ 3{\color[gray]{0.5}x}+1 $}[x=2]`
will cause a \LaTeX{} error and halt compilation since there is no
@@ -2177,13 +2192,13 @@
commands}
\label{subsec:Text-mbox-fonts}Following a rethink of the behaviour
-of a number of font and formatting commands, in version 2 of \verb`numerica`
+of a number of font and formatting commands, in version 2 of \texttt{numerica}
the content of a \verb`\text` or \verb`\mbox` command is \emph{invisible}
to the \verb`\eval` command. \emph{This behaviour is different from
-that of version 1.} Now the content is ignored in a calculation,
+that of version 1.} Now the content is ignored in a calculation,
\begin{centred}
\verb`\eval*{ 1/0.0123456789 \mbox{approx.} }[5]` $\Longrightarrow$
-\eval*{ 1/0.0123456789 \mbox{approx.}}[5],
+\eval*{ 1/0.0123456789 \mbox{approx.} }[5],
\end{centred}
even when the \verb`\text` or \verb`\mbox` contains mathematical
content.
@@ -2196,7 +2211,7 @@
like \verb`2e-1` appearing in the formula or the vv-list can display
correctly by wrapping it in a \verb`\textrm` or \verb`\texttt` command,
rather than displaying inappropriately as the algebraic expression
-$2e-1$.
+$2e-1$.
\subsubsection{\texttt{\textbackslash ensuremath},\texttt{ \$},\texttt{ \textbackslash (},\texttt{
\textbackslash )},\texttt{ \textbackslash{[}},\texttt{ \textbackslash{]}}}
@@ -2206,9 +2221,9 @@
math delimiters are present or not. More generally, should math delimiters
(through some momentary oversight) be used both within and outside
an \verb`\eval` command, the command is processed as if only the
-outside environment is involved; the inner delimiters are ignored:
+outside environment is involved; the inner delimiters are ignored:
\begin{centred}
-\verb`$ \eval{\[ -4^2 \]} $` $\Longrightarrow$ $ \eval{\[ -4^2 \]} $.
+\verb`$ \eval{\[ -4^2 \]} $` $\Longrightarrow$$ \eval{\[ -4^2 \]} $
\end{centred}
\section{Error messages }
@@ -2227,7 +2242,7 @@
in the pdf at the offending places.
Before discussing specific error messages, note that there is a debug
-facility (of a sort) discussed below in §\ref{subsec:settingsDebug}.
+facility (of a sort) discussed below in §\ref{subsec:settingsDebug}.
Error messages are in two parts: a \emph{what} part and a \emph{where}
part.
@@ -2236,7 +2251,7 @@
\label{subsec:errorsMismatched-brackets}An unmatched left parenthesis
or other left bracket (in this case a missing right parenthesis) usually
-results in a \texttt{numerica} error:
+results in a \texttt{numerica} error:
\begin{centred}
\verb`$\eval{\sin(\pi/(1+x)}[x=1]$` $\Longrightarrow$ $\eval{\sin(\pi/(1+x)}[x=1]$
\end{centred}
@@ -2243,30 +2258,29 @@
For the same error in the vv-list, the what-part remains unchanged
but the where-part is altered:
\begin{centred}
-\verb`$\eval{ 1+y }[x=1,y=\sin(\pi/(1+x)]$` $\Longrightarrow$ $\eval{ 1+y }[y=\sin(\pi/(1+x),x=1]$
+\verb`$\eval{ 1+y }[x=1,y=\sin(\pi/(1+x)]$` $\Longrightarrow$ $\eval{ 1+y }[x=1,y=\sin(\pi/(1+x)]$
\end{centred}
The \emph{what} message is the same; the \emph{where} is different.
An unmatched right parenthesis or other right bracket (in this case
a missing \emph{left} parenthesis) usually results in a similar \texttt{numerica}
-error:
+error:
\begin{centred}
\verb`$\eval{2((x+y)/(y+z)))^2}[x=1,y=2,z=3]$` $\Longrightarrow$
-\eval{2((x+y)/(y+z)))^{2}}[x=1,y=2,z=3]
+$\eval{2((x+y)/(y+z)))^2}[x=1,y=2,z=3]$
\end{centred}
But note that an unmatched modifier like \verb`\left` or \verb`\right`
is a \LaTeX{} error and is caught by \LaTeX{} before \texttt{numerica}
-can respond and so results in a terminal and logfile message.
+can respond and so results in a terminal and logfile message.
\subsection{Unknown tokens}
-An `Unknown token' message can arise in a number of ways. If an
-expression involves a number of variables, some of which depend on
-others, their order in the vv-list matters:
-\noindent \begin{center}
-\verb`$\eval{\tfrac12 vt}[t=2,v=gt,g=9.8]$` $\Longrightarrow$ \eval{\tfrac{1}{2}vt}[t=2,v=gt,g=9.8]
-\par\end{center}
-
+An `Unknown token' message can arise in a number of ways. If an expression
+involves a number of variables, some of which depend on others, their
+order in the vv-list matters:
+\begin{centred}
+\verb`$\eval{\tfrac12 vt}[t=2,v=gt,g=9.8]$` $\Longrightarrow$ $\eval{\tfrac12 vt}[t=2,v=gt,g=9.8]$
+\end{centred}
The vv-list is evaluated from the \emph{right} so that in this example
the variable \texttt{v} depends on a quantity \texttt{t} that is not
yet defined. Hence the message. The remedy is to move \texttt{t} to
@@ -2274,30 +2288,30 @@
Similarly, if we use a variable in the formula that has not been assigned
a value in the vv-list, we again get the `Unknown token' message,
-but this time the location is the formula:
+but this time the location is the formula:
\begin{centred}
-\verb`$\eval{\pi r^2h}[r=3]$` $\Longrightarrow$ \eval{\pi r^{2}h}[r=3]
+\verb`$\eval{\pi r^2h}[r=3]$` $\Longrightarrow$ $\eval{\pi r^2h}[r=3]$
\end{centred}
The remedy obviously is to assign a value to \texttt{h} in the vv-list\texttt{.}
The same message will result if a mathematical operation or function
-is used that has not been implemented in \texttt{numerica}:
+is used that has not been implemented in \texttt{numerica}:
\begin{centred}
-\verb`$\eval{u \bmod v }[v=7,u=3]$` $\Longrightarrow$ \eval{u\bmod v}[v=7,u=3]
+\verb`$\eval{u \bmod v }[v=7,u=3]$` $\Longrightarrow$ $\eval{u \bmod v }[v=7,u=3]$
\end{centred}
A missing comma in the vv-list will generally result in an unknown
-token message:
+token message:
\begin{centred}
-\verb`$\eval{axy}[a=3 y=2,x=1]$` $\Longrightarrow$ \eval{axy}[a=3y=2,x=1]
+\verb`$\eval{axy}[a=3 y=2,x=1]$` $\Longrightarrow$ $\eval{axy}[a=3 y=2,x=1]$
\end{centred}
-Because of the missing comma, \verb`numerica` assumes \verb`a` has
-the `value' \verb`3y=2`, an expression which it then tries to evaluate,
-but the variable \verb`y` in this expression has not been assigned
-a value, which generates the message.
+Because of the missing comma, \texttt{numerica} assumes \verb`a`
+has the `value' \verb`3y=2`, an expression which it then tries to
+evaluate, but the variable \verb`y` in this expression has not been
+assigned a value, which generates the message.
-\emph{Extra} commas in the vv-list should cause no problems:
+\emph{Extra} commas in the vv-list should cause no problems:
\begin{centred}
-\verb`$\eval{axy}[,a=3,,y=2,x=1,]$` $\Longrightarrow$ $\eval{axy}[,a=3,,y=2,x=1,]$
+\verb`$\eval{axy}[,a=3,,y=2,x=1,]$` $\Longrightarrow$ $\eval{axy}[,a=3,,y=2,x=1,]$
\end{centred}
The presence of multi-token variables can also cause an unknown token
message if the check for such variables is turned off; see §\ref{subsec:settingsMultitokSwitch}.
@@ -2306,35 +2320,35 @@
Perhaps if one is evaluating a formula with a number of variables
and assigning different experimental values to them to see the effect,
-a variable might be overlooked:
+a variable might be overlooked:
\begin{centred}
-\verb`$\eval{axy}[a=3,y=,x=1]$` $\Longrightarrow$ \eval{axy}[a=3,y=,x=1]
+\verb`$\eval{axy}[a=3,y=,x=1]$` $\Longrightarrow$ $\eval{axy}[a=3,y=,x=1]$
\end{centred}
In the example the variable \verb`y` has been overlooked. The remedy
-is obvious – assign a value to it.
+is obvious -- assign a value to it.
\subsection{Integer argument errors}
\label{subsec:errorsIntegerArgs}Some functions require integer arguments
-– factorials, the second argument of a binomial coefficient, and (in
-\texttt{numerica}) $n$th roots using the optional argument of \texttt{\textbackslash sqrt};
-also summation and product variables. If integers are explicitly entered
-for these arguments there is no problem, but if the value of the argument
-is the result of a calculation, rounding errors require thinking about.
-What accumulation of rounding errors is \emph{too} much so that the
-result of the calculation \emph{cannot} be considered an integer?
-\texttt{numerica} is generous: in the default setup, if a calculation
-rounds to an integer at rounding value $14$ the result of the calculation
-is considered an integer (obviously, the value resulting from the
-rounding). Since \texttt{l3fp} works to $16$ significant figures
-that gives ample room for rounding errors to `get lost in' and be
-ignored, while still ruling out such things as (recall the example
-in §\ref{subsec:evalBoolean-output}),
+-- factorials, the second argument of a binomial coefficient, and
+(in \texttt{numerica}) $n$th roots using the optional argument of
+\texttt{\textbackslash sqrt}; also summation and product variables.
+If integers are explicitly entered for these arguments there is no
+problem, but if the value of the argument is the result of a calculation,
+rounding errors require thinking about. What accumulation of rounding
+errors is \emph{too} much so that the result of the calculation \emph{cannot}
+be considered an integer? \texttt{numerica} is generous: in the default
+setup, if a calculation rounds to an integer at rounding value $14$
+the result of the calculation is considered an integer (obviously,
+the value resulting from the rounding). Since \texttt{l3fp} works
+to $16$ significant figures that gives ample room for rounding errors
+to `get lost in' and be ignored, while still ruling out such things
+as (recall the example in §\ref{subsec:evalBoolean-output}),
\begin{centred}
\verb`\eval{\[ \sum_{n=1}^N n \]}[N=1/0.0123456789]` $\Longrightarrow$
\eval{\[ \sum_{n=1}^N n \]}[N=1/0.0123456789]
\end{centred}
-where $N$ differs from $81$ not until the seventh decimal place.
+where $N$ differs from $81$ not until the seventh decimal place.
The default rounding value of $14$ for `int-ifying' calculations
can be changed: see §\ref{subsec:defaultsIntifyingRounding}.
@@ -2356,9 +2370,9 @@
Otherwise how is one to know whether the base is \verb`e` or $10$
or $2$ or whatever? Nonetheless \texttt{numerica} assumes that when
\verb`\log` is used unsubscripted, the base is 10. Suppose you want
-to make $12$ the base, but forget to put braces around the $12$:
+to make $12$ the base, but forget to put braces around the $12$:
\begin{centred}
-\verb`$\eval{ \log_12 1728 }$` $\Longrightarrow$ $\eval{ \log_12 1728 } $
+\verb`$\eval{ \log_12 1728 }$` $\Longrightarrow$ $\eval{ \log_12 1728 }$
\end{centred}
Here, \texttt{numerica} has taken \texttt{1} as the base (and $21728$
as the argument) of the logarithm and responds accordingly.
@@ -2366,11 +2380,11 @@
\subsection{\texttt{l3fp} errors}
Some errors arising at the \texttt{l3fp} level are trapped and a message
-displayed.
+displayed.
\subsubsection{Dividing by zero}
\begin{centred}
-\verb`$\eval{1/\sin x}[x=0]$` $\Longrightarrow$ \eval{1/\sin x}[x=0]
+\verb`$\eval{1/\sin x}[x=0]$` $\Longrightarrow$ $\eval{1/\sin x}[x=0]$
\end{centred}
Note however that \verb`$\eval{1/\sin x}[x=\pi]$` $\Longrightarrow\,\eval{1/\sin x}[x=\pi]$,
because of rounding errors in distant decimal places. No doubt this
@@ -2381,7 +2395,7 @@
\label{subsec:errorsInverse-powers}Finding inverse integer powers
of \emph{positive} numbers should always be possible, but raising
a \emph{negative} number to an inverse power generates an error even
-when – mathematically – it should not:
+when -- mathematically -- it should not:
\begin{centred}
\verb`\eval{$ (-125)^{1/3} $}` $\Longrightarrow$ \eval{$ (-125)^{1/3} $}
\end{centred}
@@ -2391,31 +2405,31 @@
Can a $q$th root be taken? If our floating point system used (for
ease of illustration) only $4$ significant digits, $p/q=1/3$ would
be the fraction $3333/10^{4}$, an odd numerator over an even denominator.
-But a negative number does not possess an even ($10^{4}$th) root.
+But a negative number does not possess an even ($10^{4}$th) root.
Trying to evaluate a function like a factorial or square root or inverse
trig. function outside its domain of definition also produces this
-error:
+error:
\begin{centred}
-\verb`$\eval{\arccos x}[x=2]$` $\Longrightarrow$ \eval{\arccos x}[x=2]
+\verb`$\eval{\arccos x}[x=2]$` $\Longrightarrow$ $\eval{\arccos x}[x=2]$
\end{centred}
In this case the inverse cosine, which is defined only on the interval
-$[-1,1]$, has been fed the value $2$.
+$[-1,1]$, has been fed the value $2$.
Trying to evaluate an expression that resolves to $0/0$ also produces
-this message:
+this message:
\begin{centred}
-\verb`$\eval{\frac{1-y}{x-2}}[x=2,y=1]$` $\Longrightarrow$ \eval{\frac{1-y}{x-2}}[x=2,y=1]
+\verb`$\eval{\frac{1-y}{x-2}}[x=2,y=1]$` $\Longrightarrow$ $\eval{\frac{1-y}{x-2}}[x=2,y=1]$
\end{centred}
\subsubsection{Overflow/underflow}
The factorial (discussed in §\ref{subsec:evalFactorialsBinom}) provides
-an example of overflow:
+an example of overflow:
\begin{centred}
-\verb`$\eval{3249!}$`\texttt{ }$\Longrightarrow$ \eval{3249!}
+\verb`$\eval{3249!}$`\texttt{ }$\Longrightarrow$ $\eval{3249!}$
\end{centred}
-This is hardly surprising since
+This is hardly surprising since
\begin{centred}
\verb`$\eval{3248!}[x]$` $\Longrightarrow$ $\eval{3248!}[x]$.
\end{centred}
@@ -2423,7 +2437,7 @@
A number in the form $a\times10^{b}$ must have $-10001\le b<10000$.
If this is not the case an overflow or underflow condition occurs.
As the examples show, an overflow condition generates a \texttt{numerica}
-error.
+error.
For underflow, where the number is closer to $0$ than $10^{-10001}$,
\texttt{l3fp} assigns a zero value to the quantity. \texttt{numerica}
@@ -2449,7 +2463,7 @@
nature of the keys. Most settings are generic, applicable not only
to \verb`\nmcEvaluate` but also to other commands that are available
if the packages \texttt{numerica-plus} or \texttt{numerica-tables}
-are loaded; see §\ref{subsec:Related-packages}.
+are loaded; see §\ref{subsec:Related-packages}.
\subsection{\textquoteleft Debug\textquoteright{} facility}
@@ -2464,17 +2478,17 @@
into the settings option. (White space around the equals sign is optional.)
\begin{itemize}
\item \texttt{dbg=0 }turns off the debug function, displays the result or
-error message (this is the default);
-\item \texttt{dbg=1 }equivalent to \texttt{dbg=2{*}3{*}5{*}7};
+error message (this is the default);
+\item \texttt{dbg=1 }equivalent to \texttt{dbg=2{*}3{*}5{*}7};
\end{itemize}
\begin{table}[t]
-\centering
-\noindent \centering{}\caption{Settings options}
-\noindent \begin{center}
+\centering \centering{}\caption{Settings options}
+
+\centering{}%
\begin{tabular}{ll>{\raggedright}p{4cm}>{\raggedright}p{4cm}}
\toprule
{\small key} & {\small type} & {\small meaning} & {\small default}\tabularnewline
-\midrule
+\midrule
{\small\texttt{dbg}} & {\small int} & {\small debug `magic' integer} & {\small\texttt{0}}\tabularnewline
{\small\texttt{view}} & & {\small equivalent to }{\small\texttt{dbg=1}} & \tabularnewline
{\small\texttt{\textasciicircum}} & {\small char} & {\small exponent mark for sci. notation input} & {\small\texttt{e}}\tabularnewline
@@ -2481,39 +2495,38 @@
{\small\texttt{xx}} & {\small int (0/1)} & {\small multi-token variable switch} & {\small\texttt{1}}\tabularnewline
{\small\texttt{()}} & {\small int (0/1/2)} & {\small trig. arg. parsing} & {\small\texttt{0}}\tabularnewline
{\small\texttt{o}} & {\small int (0/1)} & {\small degree switch for trig. functions} & {\small\texttt{1}}\tabularnewline
-{\small\texttt{log}} & {\small num} & {\small base of logarithms for }{\small{\small\verb`\log`}} & {\small\texttt{10}}\tabularnewline
+{\small\texttt{log}} & {\small num} & {\small base of logarithms for }{\small\verb`\log`} & {\small\texttt{10}}\tabularnewline
{\small\texttt{vv@}} & {\small int (0/1)} & {\small vv-list calculation mode} & {\small\texttt{0}}\tabularnewline
-{\small\texttt{vvd}} & {\small token(s)} & {\small vv-list display-style spec.} & {\small\texttt{\{,\}\textbackslash mskip 12mu 6mu minus 9mu(vv)}}\tabularnewline
+{\small\texttt{vvd}} & {\small token(s)} & {\small vv-list display-style spec.} & {\small\texttt{\{,\}\textbackslash mskip 12mu 6mu minus 9mu(vv)}}\tabularnewline
{\small\texttt{vvi}} & {\small token(s)} & {\small vv-list text-style spec.} & {\small\texttt{\{,\}\textbackslash mskip 36mu minus 24mu(vv)}}\tabularnewline
{*} & & {\small suppress equation numbering if }{\small\texttt{\textbackslash\textbackslash}}{\small{}
in }{\small\texttt{vvd}} & \tabularnewline
{\small\texttt{p}} & token(s) & {\small punctuation (esp. in display-style)} & {\small\texttt{,}}\tabularnewline
-{\small\texttt{reuse}} & {\small int} & {\small form of result saved with }{\small{\small\verb`\nmcReuse`}} & {\small\texttt{0}}\tabularnewline
+{\small\texttt{reuse}} & {\small int} & {\small form of result saved with }{\small\verb`\nmcReuse`} & {\small\texttt{0}}\tabularnewline
\bottomrule
\end{tabular}
-\par\end{center}
\end{table}
-The `magic' integers are the following primes and their products
+The `magic' integers are the following primes and their products
\begin{itemize}
\item \texttt{dbg=2} displays the vv-list after multi-token variables have
been converted to their single token form, \texttt{\textbackslash nmc\_a},
-\texttt{\textbackslash nmc\_b}, etc.;
+\texttt{\textbackslash nmc\_b}, etc.;
\item \texttt{dbg=3} displays the formula after multi-token variables have
-been converted to their single token form;
+been converted to their single token form;
\item \texttt{dbg=5} displays the stored variables and their \emph{evaluated}
-values (\texttt{dbg=2} lists the values as expressions);
+values (\texttt{dbg=2} lists the values as expressions);
\item \texttt{dbg=7} displays the formula after it has been fp-ified but
before it has been fed to \texttt{l3fp} to evaluate;
\begin{itemize}
\item should the formula successfully evaluate, the result of the evaluation
-is also displayed (but without any formatting).
+is also displayed (but without any formatting).
\end{itemize}
\end{itemize}
To display two or more of the debug elements simultaneously, use the
product of their debug numbers for the magic integer. This can be
-entered either as the multiplied-out product, or as the `waiting
-to be evaluated' product with asterisks (stars) between the factors.
+entered either as the multiplied-out product, or as the `waiting to
+be evaluated' product with asterisks (stars) between the factors.
Thus \texttt{dbg=6} or \verb`dbg=2*3` display both the vv-list and
formula after multi-token variables have been converted to single
token form; \texttt{dbg=10} or \verb`dbg=2*5` display both the vv-list
@@ -2531,7 +2544,7 @@
uses \verb`align*` and shows how multi-token variables are handled,
how a chain of comparisons is evaluated (§\ref{subsec:evalBoolean-output})
and how formatting instructions in the number-format option are ignored
-in the debug display:
+in the debug display:
\begin{verbatim}
\eval[dbg=1]{ a < 2a' < 3a'' }
[a=\pi,a'=\phi,a''=e\gamma][4???]
@@ -2549,10 +2562,10 @@
if unary functions or fractions are involved. The final element of
both the display and chronologically is the result from evaluating
the formula. This is shown only if $7$ is a factor of the \texttt{dbg}
-integer, and there is no error. Despite the appearance of \verb`???`
+integer, and there is no error. Despite the appearance of \noindent\verb`???`
in the number-format option, the result displays as 1. Results are
never rounded or formatted in the debug display, although as is apparent
-here, the rounding number \verb`4` is used in the comparisons.
+here, the rounding number \noindent\verb`4` is used in the comparisons.
When interpreting the fp-form, differences in the ways \texttt{numerica}
and \texttt{l3fp} read formulas can lead to more or less parentheses
@@ -2559,33 +2572,35 @@
than seem strictly necessary. In particular be aware that in \texttt{l3fp}
function calls bind most tightly so that, for example, \verb`sin 2pi`
evaluates not to zero but to $(\sin2)\times\pi$, and \verb`sin x^2`
-evaluates to $(\sin x)^{2}$. \verb`numerica` takes care of the former
-by inserting extra parentheses and exploits the latter by not inserting
-parentheses:
+evaluates to $(\sin x)^{2}$. \texttt{numerica} takes care of the
+former by inserting extra parentheses and exploits the latter by not
+inserting parentheses:
\begin{verbatim}
\eval[dbg=1]{ \sin 2x \cos^2 y }
[x=\pi/12,y=\pi/4]
\end{verbatim}
-$\Longrightarrow$ \eval[dbg=1]{ \sin 2x \cos^2 y }[x=\pi/12,y=\pi/4]Finally,
-note that those mathematical operations that have no direct representation
-in \verb`l3fp` contribute only their value to the fp-form. This applies
-to sums and products, double factorials, partly to binomial coefficients,
-and also to \verb`\eval` and other commands when nested one within
-another (see Chapter~\ref{chap:Nesting}). The following (ridiculous)
-example illustrates the matter:
+$\Longrightarrow$ \eval[dbg=1]{ \sin 2x \cos^2 y }
+ [x=\pi/12,y=\pi/4]
+
+Finally, note that those mathematical operations that have no direct
+representation in \texttt{l3fp} contribute only their value to the
+fp-form. This applies to sums and products, double factorials, partly
+to binomial coefficients, and also to \verb`\eval` and other commands
+when nested one within another (see Chapter~\ref{chap:Nesting}).
+The following (ridiculous) example illustrates the matter:
\begin{verbatim}
\eval[dbg=1]{\[
\sum_{n=1}^k n + \binom{2k}{m} - \frac1{4k} +
\prod_{n=2}^k (1-1/n) + m!! \]}[m=6,k=5]
\end{verbatim}
-$\Longrightarrow$ \eval[dbg=1]{\[
+$\Longrightarrow$ \eval[dbg=1]{\[
\sum_{n=1}^k n + \binom{2k}{m} - \frac1{4k} +
\prod_{n=2}^k (1-1/n) + m!! \]}[m=6,k=5]
-\noindent ($0$\textdegree{}~C in kelvin!) In the \verb`fp-form`
-line, the various contributions to the overall result are displayed
-simply as numbers because \verb`l3fp` does not (at least as yet)
-handle these elements natively.
+\noindent ($0$°~C in kelvin!) In the \noindent\verb`fp-form` line,
+the various contributions to the overall result are displayed simply
+as numbers because \texttt{l3fp} does not (at least as yet) handle
+these elements natively.
\subsection{Negative \texttt{dbg} values}
@@ -2604,7 +2619,7 @@
\subsection{\texttt{view} setting}
Putting \texttt{dbg=1} may seem a little obscure in order to view
-internal values of \verb`numerica`. In that case, simply writing
+internal values of \texttt{numerica}. In that case, simply writing
\verb`view` in the settings option will produce the same effect as
entering \verb`dbg=1`.
@@ -2615,7 +2630,7 @@
of the \texttt{\textbackslash eval} command. Such output is turned
off by default and needs to be explicitly ordered. Similarly, \emph{inputting}
numbers in scientific notation is turned off by default and needs
-to be explicitly ordered. To turn it on, write
+to be explicitly ordered. To turn it on, write
\begin{lyxcode}
\textasciicircum ~=~<char>
\end{lyxcode}
@@ -2626,47 +2641,52 @@
that it doesn't conflict with the use of the character as a variable
or constant.
\begin{centred}
-\verb`$ \eval[^=@]{ 1.23 at -1 } $` $\Longrightarrow$ $ \eval[^=@]{ 1.23 at -1 } $.
+\noindent\noindent\verb`$ \eval[^=@]{ 1.23 at -1 } $` $\Longrightarrow$
+$ \eval[^=@]{ 1.23 at -1 } $.
\end{centred}
-With letters for the exponent mark – say \verb`d` or \verb`e` –
-the problem is interpreting forms like \texttt{8d-3} or \texttt{2e-1}.
-Does such a form denote a number in scientific notation or an algebraic
-expression? In \texttt{numerica}, if the settings option shows \texttt{\textasciicircum =d},
-then a form like \texttt{8d-3} is treated as a number in scientific
-notation. Similarly for \texttt{e} or any other letter used as the
-exponent marker for the input of scientific numbers. (But only one
-character can be so used at a time.) Note that the number \emph{must}
-start with a digit: \verb`e-1` for instance does not, and will be
-treated as an algebraic expression involving the exponential constant:
+\noindent With letters for the exponent mark -- say \noindent\verb`d`
+or \noindent\verb`e` -- the problem is interpreting forms like \texttt{8d-3}
+or \texttt{2e-1}. Does such a form denote a number in scientific notation
+or an algebraic expression? In \texttt{numerica}, if the settings
+option shows \texttt{\textasciicircum =d}, then a form like \texttt{8d-3}
+is treated as a number in scientific notation. Similarly for \texttt{e}
+or any other letter used as the exponent marker for the input of scientific
+numbers. (But only one character can be so used at a time.) Note that
+the number \emph{must} start with a digit: \noindent\verb`e-1` for
+instance does not, and will be treated as an algebraic expression
+involving the exponential constant:
\begin{centred}
-\verb`$ \eval[^=e]{ x+e-1 }[x=1] $` $\Longrightarrow$ $ \eval[^=e]{ x+e-1 }[x=1] $
+\noindent\noindent\verb`$ \eval[^=e]{ x+e-1 }[x=1] $` $\Longrightarrow$
+$ \eval[^=e]{ x+e-1 }[x=1] $
\end{centred}
-but
+\noindent but
\begin{centred}
-\verb`$ \eval[^=e]{ x+1e-1 }[x=1] $` $\Longrightarrow$ $ \eval[^=e]{ x+1e-1 }[x=1] $.
+\noindent\noindent\verb`$ \eval[^=e]{ x+1e-1 }[x=1] $` $\Longrightarrow$
+$ \eval[^=e]{ x+1e-1 }[x=1] $.
\end{centred}
-A problem of appearance arises if scientific numbers appear in the
-vv-list or formula and either is displayed in the result. A number
-like \verb`2e-1` will display as $2e-1$, as if it were an algebraic
-expression. In version 1 of \verb`numerica` the cure was to wrap
-\verb`2e-1` in a \verb`\text` or \verb`\mbox` command. In version
-2 of \verb`numerica` the behaviour of \verb`\text` and \verb`\mbox`
+\noindent A problem of appearance arises if scientific numbers appear
+in the vv-list or formula and either is displayed in the result. A
+number like \noindent\verb`2e-1` will display as $2e-1$, as if it
+were an algebraic expression. In version 1 of \texttt{numerica} the
+cure was to wrap \noindent\verb`2e-1` in a \noindent\verb`\text`
+or \noindent\verb`\mbox` command. In version 2 of \texttt{numerica}
+the behaviour of \noindent\verb`\text` and \noindent\verb`\mbox`
has been re-thought; see §\ref{subsec:Text-mbox-fonts}. Their contents
-are now invisible to the \verb`\eval` command. The solution is to
-wrap \verb`2e-1` in a \verb`\textrm` or \verb`\textsf` or \verb`\texttt`
-command. These commands were not recognized by \verb`\eval` in version
+are now invisible to the \noindent\verb`\eval` command. The solution
+is to wrap \noindent\verb`2e-1` in a \noindent\verb`\textrm` or
+\noindent\verb`\textsf` or \noindent\verb`\texttt` command. These
+commands were not recognized by \noindent\verb`\eval` in version
1 but \emph{are} in version 2:
\begin{centred}
-\verb`\eval[^=e]{$ 5x $ }[x=\texttt{2e-1}]` $\Longrightarrow$ \eval[^=e]{$ 5x $ }[x=\texttt{2e-1}]
-,
+\noindent\noindent\verb`\eval[^=e]{$ 5x $ }[x=\texttt{2e-1}]` $\Longrightarrow$
+\eval[^=e]{$ 5x $ }[x=\texttt{2e-1}],
-\verb`\eval[^=e]{$ 5\texttt{2e-1} $ }` $\Longrightarrow$ \eval[^=e]{$ 5(\texttt{2e-1}) $ }
-.
+\verb`\eval[^=e]{$ 5\texttt{2e-1} $ }` $\Longrightarrow$ \eval[^=e]{$ 5\texttt{2e-1} $ }.
\end{centred}
If you use a particular character as the exponent marker for inputting
numbers in scientific notation, it is good practice \emph{not} to
use that character as a variable, not because it will cause an error
-but because it makes expressions harder to read.
+but because it makes expressions harder to read.
\subsection{Multi-token variables}
@@ -2678,7 +2698,7 @@
This conversion takes time. Even if there are no multi-token variables
used at all, \texttt{numerica} still needs to check that that is so.
There is a setting that allows a user to turn off or turn on the check
-for such variables by entering
+for such variables by entering
\begin{lyxcode}
xx~=~<integer>
\end{lyxcode}
@@ -2695,15 +2715,15 @@
an error results. We don't need to enter \texttt{xx=1} in the first
of the following examples because the check for multi-token variables
is on by default. Explicitly turning it off in the second produces
-an error.
+an error.
\begin{centred}
\verb`\eval{$ x_0^{\,2} $}[x_0=5]` $\Longrightarrow$ \eval{$ x_0^{\,2} $}[x_0=5],\medskip{}
-\verb`\eval[xx=0]{$ x_0^{\,2} $}[x_0=5]` $\Longrightarrow$ \eval[xx=0]{$ x_0^{\,2} $}[x_0=5]
+ \verb`\eval[xx=0]{$ x_0^{\,2} $}[x_0=5]` $\Longrightarrow$ \eval[xx=0]{$ x_0^{\,2} $}[x_0=5]
\end{centred}
\subsection{Parsing arguments of trigonometric functions}
-This setting allows a wider range of arguments to trigonometric functions
+This setting allows a wider range of arguments to trigonometric functions
to be parsed (think Fourier series) without needing to insert extra
parentheses in order for them to be read correctly by \verb`\eval`;
see §\ref{subsec:parseTrigFns}.
@@ -2714,20 +2734,20 @@
use degrees rather than radians with trigonometric functions. This
can be switched on simply by entering a lowercase \texttt{o} in the
settings option. (The author hopes the charitable eye sees a degree
-symbol in the \texttt{o}.) Thus
-\begin{centred}
+symbol in the \texttt{o}.) Thus
+
\verb`\eval[o]{$ \sin 30 $}` $\Longrightarrow$ \eval[o]{$ \sin 30 $},
\verb`\eval[o]{$ \arcsin 0.5 $}` $\Longrightarrow$ \eval[o]{$ \arcsin 0.5 $}.
-\end{centred}
+
This is a \verb`0/1` switch, \verb`0` signifying \verb`off` or
-`don't use degrees', \verb`1` signifying \verb`on` or `do use
-degrees'. Although the \verb`o` default is \verb`1`, out-of-the-box
-\verb`numerica` assumes radians are being used. Thus if \verb`o`
-is absent from the settings option of an \verb`\eval` command, the
-out-of-the-box setting prevails and radians are used, but if \verb`o`
-is present, it is equivalent to \verb`o=1`. To explicitly turn off
-the use of degrees requires the full setting, \verb`o=0`.
+`don't use degrees', \verb`1` signifying \verb`on` or `do use degrees'.
+Although the \verb`o` default is \verb`1`, out-of-the-box \texttt{numerica}
+assumes radians are being used. Thus if \verb`o` is absent from the
+settings option of an \verb`\eval` command, the out-of-the-box setting
+prevails and radians are used, but if \verb`o` is present, it is
+equivalent to \verb`o=1`. To explicitly turn off the use of degrees
+requires the full setting, \verb`o=0`.
If you want to change the out-of-the-box setting you need to put the
line \verb`use-degrees = 1` into a configuration file; see §\ref{sec:settingsDefaults}.
@@ -2754,11 +2774,11 @@
of a calculation. This is certainly true of sums and products. If
a parameter in the vv-list depends on the variable then that parameter
will need to be recalculated, perhaps repeatedly, in the course of
-a calculation. By entering either
+a calculation. By entering either
\begin{lyxcode}
vv@~=~<integer>
\end{lyxcode}
-or (as in version 1 of \verb`numerica`),
+or (as in version 1 of \texttt{numerica}),
\begin{lyxcode}
vvmode~=~<integer>
\end{lyxcode}
@@ -2771,7 +2791,7 @@
this setting was available. To the author's eye, the \texttt{@} sign
seems sufficiently close to a symbol like $\circlearrowleft$, suggesting\texttt{
}redo or recalculate, that \texttt{vv@} is now preferred. The \texttt{@}
-symbol is – universally? – available on keyboards and \texttt{vv@}
+symbol is -- universally? -- available on keyboards and \texttt{vv@}
is only half as many keypresses as \texttt{vvmode}.}
For example, in a sum it may be desirable to place the summand, or
@@ -2779,15 +2799,16 @@
changes during the course of the calculation, we need to enter \texttt{vv@=1}
in the settings option. Repeating an earlier sum (the seting \verb`p=.`
is discussed in §\ref{subsec:settingsPunctuation}), \medskip{}
+
\begin{verbatim}
\eval[p=.,vv@=1]{\[ \sum_{k=1}^N f(k) \]}
[N=100,f(k)=1/k^3,{k}=1][4]
\end{verbatim}
-$\Longrightarrow$ \eval[p=.,vv@=1]{\[ \sum_{k=1}^N f(k) \]}
- [N=100,f(k)=1/k^3,{k}=1][4]
+$\Longrightarrow$ \eval[p=.,vv@=1]{\[ \sum_{k=1}^N f(k) \]}
+ [N=100,f(k)=1/k^3,{k}=1][4]
As you can see, the summand \texttt{f(k)} has been given explicit
-form in the vv-list – equated to \texttt{1/k\textasciicircum 3}.
+form in the vv-list -- equated to \texttt{1/k\textasciicircum 3}.
That means we need to give a preceding value to \texttt{k} in the
vv-list to avoid an unknown token message, hence the rightmost entry.
But we don't want \texttt{k=1} appearing in the final display, so
@@ -2802,11 +2823,11 @@
example; with more complicated expressions it noticeably takes longer.
Because it is necessary to activate this switch when using \emph{implicit}
-notations – like $f(k)$ in the example – rather than the explicit
+notations -- like $f(k)$ in the example -- rather than the explicit
form of the function in the main argument, it seems natural to call
\texttt{vv@=1} \emph{implicit }mode and \texttt{vv@=0} (the default)
-\emph{explicit }mode. Most calculations are explicit mode – the vv-list
-is evaluated only once.\emph{ }
+\emph{explicit }mode. Most calculations are explicit mode -- the
+vv-list is evaluated only once.\emph{ }
\subsection{Changing the vv-list display format}
@@ -2813,7 +2834,7 @@
\label{subsec:settingsVvDisplayChangeLocal}In previous formulas with
variables the vv-list has been displayed following the result. It
is wrapped in parentheses following a comma followed by a space. These
-formatting elements – comma, space, parentheses – can all be changed
+formatting elements -- comma, space, parentheses -- can all be changed
with the settings option.
The default format specification is
@@ -2820,7 +2841,7 @@
\begin{lyxcode}
\{,\}\textbackslash mskip~12mu~plus~6mu~minus~9mu(vv)
\end{lyxcode}
-for a text-style display (an inline formula) and
+for a text-style display (an inline formula) and
\begin{lyxcode}
\{,\}\textbackslash mskip~36mu~minus~24mu(vv)
\end{lyxcode}
@@ -2841,15 +2862,15 @@
with variables so that the evaluated result is pushed well to the
left by the vv-list. (But see below, §\ref{subsec:settings New-line-display}.)
-If you want to change these defaults, enter in the settings option
+If you want to change these defaults, enter in the settings option
\begin{lyxcode}
vvi~=~<new~specification>
\end{lyxcode}
-to change the inline display and
+to change the inline display and
\begin{lyxcode}
vvd~=~<new~specification>
\end{lyxcode}
-to change the display-style display For example the settings
+to change the display-style display For example the settings
\begin{lyxcode}
vvi~=~\{,\}\textbackslash quad(vv)
@@ -2857,23 +2878,23 @@
\end{lyxcode}
would give a comma (in braces since the settings option is a comma-separated
list) and a fixed space (of one or two quads) between the result and
-the parenthesized vv-list.
+the parenthesized vv-list.
The vv-list itself in the display specification is represented by
the placeholder \texttt{vv}. If the \texttt{vv} is omitted from the
-specification, then the vv-list will not appear at all:
+specification, then the vv-list will not appear at all:
\begin{centred}
-\verb`\eval[vvi=?!]{$ \pi $}[\pi=3]` $\Longrightarrow$ \eval[vvi=?!]{$ \pi $}[\pi=3]
+\verb`\eval[vvi=?!]{$ \pi $}[\pi=3]` $\Longrightarrow$ \eval[vvi=?!]{$ \pi $}[\pi=3]
\end{centred}
More relevantly, it may well be the case that all variables in the
vv-list are suppressed (wrapped in braces). In that case nothing is
-displayed. Compare the last example with
+displayed. Compare the last example with
\begin{centred}
\verb`\eval[vvi=?!]{$ \pi $}[{\pi}=3]` $\Longrightarrow$ \eval[vvi=?!]{$ \pi $}[{\pi}=3]
\end{centred}
-and
+and
\begin{centred}
-\verb`\eval[vvi=?!]{$ \pi $}` $\Longrightarrow$ \eval[vvi=?!]{$ \pi $}
+\verb`\eval[vvi=?!]{$ \pi $}` $\Longrightarrow$ \eval[vvi=?!]{$ \pi $}.
\end{centred}
See also the punctuation setting below, §\ref{subsec:settingsPunctuation}.
@@ -2883,7 +2904,7 @@
with many variables, hence a full vv-list, may not fit comfortably
on a line. In an earlier example I used Brahmagupta's formula to calculate
the area of a triangle. It squeezed onto a line. I shall now use his
-formula for the area of a cyclic quadrilateral:
+formula for the area of a cyclic quadrilateral:
\[
A=\sqrt{(s-a)(s-b)(s-c)(s-d)}.
\]
@@ -2894,8 +2915,8 @@
hypotenuse to a 30-60-90 triangle. The sides are therefore $\surd2,\surd2,\surd3,1$.
Adding the areas of the two triangles, the area of the quadrilateral
is $A=1+\tfrac{1}{2}\surd3$, or in decimal form, \verb`$\eval{1+\tfrac12\surd3}$`
-$\Longrightarrow$ $\eval{1+\tfrac12\surd3}$. Let's check with Brahmagupta's
-formula:
+$\Longrightarrow$ $\eval{1+\tfrac{1}{2}\surd3}$. Let's check with
+Brahmagupta's formula:
\begin{verbatim}
\eval[p=.,vvd={,}\\(vv),*]
{\[ \sqrt{(s-a)(s-b)(s-c)(s-d)} \]}
@@ -2904,7 +2925,7 @@
\end{verbatim}
$\Longrightarrow$ \eval[p=.,vvd={,}\\(vv),*]
{\[ \sqrt{(s-a)(s-b)(s-c)(s-d)} \]}
- [s=\tfrac12(a+b+c+d),
+ [s=\tfrac12(a+b+c+d),
a=\surd2,b=\surd2,c=\surd3,d=1]
\noindent The values agree. The point to note here is the\texttt{
@@ -2911,24 +2932,24 @@
vvd=\{,\}\textbackslash\textbackslash (vv)} and the \texttt{{*}}
in the settings option. The \texttt{\textbackslash\textbackslash}
in a specification for \texttt{vvd} acts as a trigger for \texttt{numerica}
-to replace whatever math delimiters are enclosed by the \verb`\eval`
-command with a \verb`multline` environment. As you can see, the specification
-inserts a comma after the formula and places the parenthesized vv-list
-on a new line. The star \texttt{{*}} if present suppresses equation
-numbering by turning the \verb`multline` into a \verb`multline*`
-environment.
+to replace whatever math delimiters are enclosed by the \noindent\verb`\eval`
+command with a \noindent\verb`multline` environment. As you can see,
+the specification inserts a comma after the formula and places the
+parenthesized vv-list on a new line. The star \texttt{{*}} if present
+suppresses equation numbering by turning the \noindent\verb`multline`
+into a \noindent\verb`multline*` environment.
Things to note in the use of\texttt{ \textbackslash\textbackslash}
-in a \texttt{vvd} specification are that
+in a \texttt{vvd} specification are that
\begin{itemize}
\item it applies only to the \texttt{vvd} specification, not the \texttt{vvi}
-spec.;
+spec.;
\item it applies only when\emph{ }\verb`\eval`\emph{ wraps around }a math
environment of some kind;
\item it has no effect when the \verb`\eval` command is used \emph{within}
a math environment when the presentation of the result is of the form
\emph{result, vv-list}. The formula is not displayed and so the pressure
-on space is less and the `ordinary' vv-list specification is used.
+on space is less and the `ordinary' vv-list specification is used.
\end{itemize}
\subsection{Punctuation}
@@ -2948,8 +2969,8 @@
We want it to display as if it were the last element \emph{before}
the closing delimiter.
-Explicitly putting it there – \verb`\eval{\[ 1+1. \]}` – means the
-punctuation mark becomes part of the formula. Potentially \texttt{numerica}
+Explicitly putting it there -- \verb`\eval{\[ 1+1. \]}` -- means
+the punctuation mark becomes part of the formula. Potentially \texttt{numerica}
then needs to check not just for a fullstop but also other possible
punctuation marks like comma, semicolon, perhaps even exclamation
and question marks. All these marks have roles in mathematics or \texttt{l3fp}.
@@ -2961,16 +2982,15 @@
\begin{lyxcode}
p~=~<char(s)>~
\end{lyxcode}
-to place the {\ttfamily\verb`<char(s)>`} after the result
-but within the environment delimiters. The default punctuation mark
-is the comma so that simply entering \texttt{p} will produce a comma
-in the appropriate place. This saves having to write \texttt{p=\{,\}}
-as would otherwise be required, since the settings option is a \emph{comma}-separated
-list.
+to place the \verb`<char(s)>` after the result but within the environment
+delimiters. The default punctuation mark is the comma so that simply
+entering \texttt{p} will produce a comma in the appropriate place.
+This saves having to write \texttt{p=\{,\}} as would otherwise be
+required, since the settings option is a \emph{comma}-separated list.
Nor is one limited to a single punctuation mark:
\begin{centred}
-\verb`\eval[p=\ (but no 8!)]{\[ \frac{1}{81} \]}[9]` $\Longrightarrow$
+\verb`\eval[p=\ \text{(but no 8!)}]{\[ \frac{1}{81} \]}[9]` $\Longrightarrow$
\eval[p=\ \text{(but no 8!)}]{\[ \frac{1}{81} \]}[9]
\end{centred}
@@ -2985,7 +3005,7 @@
\label{sec:settingsInfiniteSumsProds}There are ways of tweaking various
default settings to nudge infinite sums and products to a correct
limit. These tweaks are applied via the settings option of the \verb`\eval`
-command.
+command.
The normal convergence criterion used by \texttt{numerica} to determine
when to stop adding/multiplying terms in an infinite sum/product is
@@ -3009,32 +3029,30 @@
limit. In a product the equivalent would be a term taking unit value.
Sometimes the initial terms of series or products are `irregular'
and take these `stopping' values meaning sum or product would stop
-after only one or two additions/multiplications and far from any limit.
+after only one or two additions/multiplications and far from any limit.
\begin{table}[t]
-\centering
-\noindent \centering{}\caption{Settings for infinite sums \& products}\label{tab:settingsSumsProducts}
-\noindent \begin{center}
-{\small{}%
+\centering{}\caption{Settings for infinite sums \& products}\label{tab:settingsSumsProducts}
+ {\small{}%
\begin{tabular}{ll>{\raggedright}p{4cm}l}
\toprule
-key & type & meaning & default\tabularnewline
+{\small key} & {\small type} & {\small meaning} & {\small default}\tabularnewline
\midrule
-\texttt{S+} & int & extra rounding for stopping criterion & \texttt{2}\tabularnewline
-\texttt{S?} & $\text{int}\ge0$ & stopping criterion query terms for sums & \texttt{0}\tabularnewline
-\texttt{P+} & int & extra rounding for stopping criterion & \texttt{2}\tabularnewline
-\texttt{P?} & $\text{int}\ge0$ & stopping criterion query terms for products & \texttt{0}\tabularnewline
+{\small\texttt{S+ }} & {\small int} & {\small extra rounding for stopping criterion} & {\small\texttt{2}}\tabularnewline
+{\small\texttt{S? }} & {\small$\text{int}\ge0$} & {\small stopping criterion query terms for sums} & {\small\texttt{0}}\tabularnewline
+{\small\texttt{P+ }} & {\small int} & {\small extra rounding for stopping criterion} & {\small\texttt{2}}\tabularnewline
+{\small\texttt{P?}}{\small{} } & {\small$\text{int}\ge0$} & {\small stopping criterion query terms for products} & {\small\texttt{0}}\tabularnewline
\bottomrule
\end{tabular}}
-\par\end{center}
\end{table}
+
To cope with these possibilities, \texttt{numerica} offers two settings
for sums, two for products, summarized in Table~\ref{tab:settingsSumsProducts}.
-These are entered in the settings option of the \verb`\eval` command.
+These are entered in the settings option of the \verb`\eval` command.
\begin{itemize}
\item \texttt{S+=<integer> }or \texttt{P+=<integer>} additional rounding
on top of the specified (or default) rounding for the calculation;
-default = $2$
+default = $2$
\begin{itemize}
\item the larger the additional \texttt{<integer>} is, the more likely that
sum or product has attained a stable value at the specified rounding
@@ -3043,7 +3061,7 @@
\item \texttt{S?=<integer${}\,\mathtt{\ge0}$> }or \texttt{P?=<integer${}\,\mathtt{\ge0}$>}
the number of final terms to query after the stopping criterion has
been achieved to confirm that it is not an `accident' of particular
-values; default = $0$
+values; default = $0$
\begin{itemize}
\item a final few terms to be summed/multiplied and the rounded result after
each such operation to be compared with the rounded result at the
@@ -3052,7 +3070,7 @@
$r$ and let the number of final checking terms be $m$. Suppose $T_{k_{0}}$
is the first term at which the stopping criterion is achieved: $\left(T_{k_{0}}\right)_{r+n}=\left(T_{k_{0}+1}\right)_{r+n}$.
What we require of the final query terms is that $\left(T_{k_{0}}\right)_{r+n}=\left(T_{k_{0}+1+j}\right)_{r+n}$
-for $j=0,1,\ldots,m$.
+for $j=0,1,\ldots,m$.
\end{itemize}
\end{itemize}
Previously we found that the infinite product for $\sinh1$ with the
@@ -3065,26 +3083,28 @@
\biggl(\frac{x^2}{k^2\pi^2} +1\biggr)
\]}[x=1][3] \nmcInfo{prod}.
\end{verbatim}
-\noindent $\Longrightarrow$ \noindent \eval[p,P+=3]{\[
- \prod_{k=1}^{\infty}
- \biggl(\frac{x^2}{k^2\pi^2} +1\biggr)
-\]}[x=1][3] \nmcInfo{prod}.
+\noindent$\Longrightarrow$ \eval[p,P+=3]{\[
+ \prod_{k=1}^{\infty}
+ \biggl(\frac{x^2}{k^2\pi^2} +1\biggr)
+ \]}[x=1][3] \nmcInfo{prod}.
\noindent To obtain that last item of information (350 factors), I've
-anticipated a little and used the command \verb`\nmcInfo` with the
-argument \verb`prod`; see §\ref{sec:supplInfo}. The product now
-produces the correct three-figure value, but it takes $350$ factors
-to do so.
+anticipated a little and used the command \noindent\verb`\nmcInfo`
+with the argument \noindent\verb`prod`; see §\ref{sec:supplInfo}.
+The product now produces the correct three-figure value, but it takes
+$350$ factors to do so.
Knowing how many terms or factors have been needed helps assess how
trustworthy the result from an infinite sum or product is. For example,
-for the exponential series,
+for the exponential series,
\begin{verbatim}
\eval[p]{\[
\sum_{k=0}^\infty \frac1{k!}
\]}[9] \nmcInfo{sum}.
\end{verbatim}
-$\Longrightarrow$ \eval[p]{\[\sum_{k=0}^\infty \frac1{k!} \]}[9] \nmcInfo{sum}.
+$\Longrightarrow$ \eval[p]{\[
+ \sum_{k=0}^\infty \frac1{k!}
+ \]}[9] \nmcInfo{sum}.
To $9$ places of decimals, using the default value \texttt{S+=2},
the exponential series arrives at the right sum after only $15$ terms.
@@ -3092,13 +3112,14 @@
the correct nine-figure value). By contrast, if we didn't know the
value of $\sinh1$ beforehand, noting the number of factors required
would make us justly cautious about accepting the result of the infinite
-product calculation.
+product calculation.
+\noindent{}%
\noindent\begin{minipage}[t]{1\columnwidth}%
\begin{shaded}%
One way to gain confidence in a result is to choose a possibly unrealistic
-rounding value – say, the default $6$ for the infinite product –
-then use \emph{negative} values for the extra rounding, \texttt{S+=-5},
+rounding value -- say, the default $6$ for the infinite product
+-- then use \emph{negative} values for the extra rounding, \texttt{S+=-5},
\texttt{S+=-4}, \ldots{} , so that the stopping criterion applies at
rounding values $s$ of $6+(-5)=1$, one decimal place, $6+(-4)=2$,
two decimal places, and so on, but the result is always presented
@@ -3120,12 +3141,17 @@
geometric rather than arithmetic progressions, but for inverse fourth
powers the scale factor ($\approx1.7$) is sufficiently small that
for these low values of $s$ the number of terms required does not
-grow too quickly (e.g. $1.7^6\approx\eval{1.7^6}[0]$). It is a standard
-result (Euler) that the series sums to $\pi^{4}/90$: \verb`$ \eval{ \pi^4/90 } $`
-$\Longrightarrow$ $ \eval{ \pi^4/90 } $ to six places, and indeed,
-with the default \texttt{S+=2},
+grow too quickly (e.g. $1.7^{6}\approx\eval{1.7^{6}}[0]$). \end{shaded}%
+\end{minipage}
+
+\noindent{}%
+\noindent\begin{minipage}[t]{1\columnwidth}%
+\begin{shaded}%
+It is a standard result (Euler) that the series sums to $\pi^{4}/90$:
+\verb`$ \eval{ \pi^4/90 } $` $\Longrightarrow$ $\eval{\pi^{4}/90}$
+to six places, and indeed, with the default \texttt{S+=2},
\begin{centred}
-\verb`\eval[p]{\[ \sum_{k=1}^\infty \frac1{k^4} \]}` $\Longrightarrow$
+\verb`\eval[p=.]{\[ \sum_{k=1}^\infty \frac1{k^4} \]}` $\Longrightarrow$
\eval[p=.]{\[ \sum_{k=1}^\infty \frac1{k^4} \]}
\end{centred}
\end{shaded}%
@@ -3133,8 +3159,8 @@
\subsection{Premature ending of infinite sums}
-All the series considered so far have been monotonic. Trigonometric
-series will generally not be so, nor even single-signed.
+\noindent All the series considered so far have been monotonic. Trigonometric
+series will generally not be so, nor even single-signed.
Trigonometric sums are computationally intensive and so, for the following
example, I have specified a rounding value of 2. The series
@@ -3141,7 +3167,7 @@
\[
\sum_{n=1}^{\infty}\frac{4}{n^{2}\pi^{2}}(1-\cos n\pi)\cos2\pi nt
\]
-is the Fourier series for the triangular wave function \textbackslash\!/\!\textbackslash\!/\!\textbackslash\!/\!\textbackslash{}
+is the Fourier series for the triangular wave function \textbackslash\negthinspace{}/\negthinspace{}\textbackslash\negthinspace{}/\negthinspace{}\textbackslash\negthinspace{}/\negthinspace{}\textbackslash{}
\ldots{} of period 1, symmetric about the origin where it takes its
maximum value 1, crossing the axis at $t=0.25$ and descending to
its minimum $-1$ at $t=0.5$, before ascending to a second maximum
@@ -3150,7 +3176,7 @@
vanishes both when $n$ is even and when $4nt$ is an odd integer.
If $t=0.1$ then $4nt$ is never an odd integer so the summand vanishes
only for $n$ even, every second term. We expect the result to be
-$1-4\times0.1=0.6$.
+$1-4\times0.1=0.6$.
\begin{verbatim}
\eval[p]{\[
\sum_{n=1}^{\infty}
@@ -3158,13 +3184,13 @@
(1-\cos n\pi)\cos2\pi nt
\]}[t=0.1][2] \nmcInfo{sum}.
\end{verbatim}
-$\Longrightarrow$ \eval[p]{\[
- \sum_{n=1}^{\infty}
- \frac{4}{n^{2}\pi^{2}}
- (1-\cos n\pi)\cos2\pi nt
-\]}[t=0.1][2] \info{sum}.
+$\Longrightarrow$ \eval[p]{\[
+ \sum_{n=1}^{\infty}
+ \frac{4}{n^{2}\pi^{2}}
+ (1-\cos n\pi)\cos2\pi nt
+ \]}[t=0.1][2] \nmcInfo{sum}.
-\noindent Only one term? Of course – since for the second term $n$
+\noindent Only one term? Of course -- since for the second term $n$
is even, the term vanishes and the stopping criterion is satisfied.
The way around this problem is to query terms \emph{beyond} the one
where the stopping criterion is achieved, i.e., to set \texttt{S?}
@@ -3176,22 +3202,23 @@
(1-\cos n\pi)\cos2\pi nt
\]}[t=0.1][2] \nmcInfo{sum}.
\end{verbatim}
-$\Longrightarrow$ \eval[p,S?=1]{\[
- \sum_{n=1}^{\infty}
- \frac{4}{n^{2}\pi^{2}}
- (1-\cos n\pi)\cos2\pi nt
-\]}[t=0.1][2] \info{sum}.
+$\Longrightarrow$ \eval[p,S?=1]{\[
+ \sum_{n=1}^{\infty}
+ \frac{4}{n^{2}\pi^{2}}
+ (1-\cos n\pi)\cos2\pi nt
+ \]}[t=0.1][2] \nmcInfo{sum}.
+\noindent{}%
\noindent\begin{minipage}[t]{1\columnwidth}%
\begin{shaded}%
\begin{wraptable}{o}{0.35\columnwidth}%
\centering{}\vspace{-5ex}
-\caption{Finite sums}\label{tab:settingsFinite-sums}
-\abovetopsep=2ex %
+ \caption{Finite sums}\label{tab:settingsFinite-sums}
+ \abovetopsep=2ex %
\begin{tabular}{cc}
\toprule
$N$ & $\Sigma$\tabularnewline
-\midrule
+\midrule
$63$ & $0.6001$\tabularnewline
$64$ & $0.6001$\tabularnewline
$65$ & $0.5999$\tabularnewline
@@ -3199,6 +3226,7 @@
$67$ & $0.5999$\tabularnewline
\bottomrule
\end{tabular}\end{wraptable}%
+
Table~\ref{tab:settingsFinite-sums} lists the results of evaluating
the \emph{finite }sums from $n=1$ to $N$ for values of $N$ around
$65$. Since the specified rounding value is $2$ for the calculation,
@@ -3212,10 +3240,10 @@
at the $65$th term. Should we be confident in the result? Increase
the number of query terms to $3$ (there is no point in increasing
\texttt{S?} to $2$ because of the vanishing of the even terms), the
-sum stops after $113$ terms, with the same $0.6$ result. \end{shaded}%
+sum stops after $113$ terms, with the same $0.6$ result.\end{shaded}%
\end{minipage}
-For a final example, consider the error function
+\noindent For a final example, consider the error function
\[
\erf z=\dfrac{2}{\sqrt{\pi}}\int_{0}^{z}e^{-t^{2}}dt
\]
@@ -3223,12 +3251,12 @@
\[
\erf z=\sum_{n=0}^{\infty}(-1)^{n}\frac{z^{2n+1}}{n!(2n+1)}.
\]
-(\verb`\erf` expanding to \verb`erf` has been defined in the preamble
-to this document using \verb`\DeclareMathOperator`.) We calculate
-this sum for $z=2$ to $10$ places of decimals. Although this is
-an alternating series, it is obvious that the summand never vanishes
-when $z\ne0$ as here. Hence there seems no need to change the default
-value \texttt{S?=0}.
+(\noindent\verb`\erf` expanding to \noindent\verb`erf` has been
+defined in the preamble to this document using \noindent\verb`\DeclareMathOperator`.)
+We calculate this sum for $z=2$ to $10$ places of decimals. Although
+this is an alternating series, it is obvious that the summand never
+vanishes when $z\ne0$ as here. Hence there seems no need to change
+the default value \texttt{S?=0}.
\begin{verbatim}
\eval[p]{\[
\frac2{\sqrt{\pi}}
@@ -3236,11 +3264,11 @@
\frac{z^{2n+1}}{n!(2n+1)}
\]}[z=2][10*] \nmcInfo{sum}.
\end{verbatim}
-$\Longrightarrow$ \eval[p]{\[
- \frac2{\sqrt{\pi}}
- \sum_{n=0}^\infty(-1)^n
- \frac{z^{2n+1}}{n!(2n+1)}
-\]}[z=2][10*] \nmcInfo{sum}.
+$\Longrightarrow$ \eval[p]{\[
+ \frac2{\sqrt{\pi}}
+ \sum_{n=0}^\infty(-1)^n
+ \frac{z^{2n+1}}{n!(2n+1)}
+ \]}[z=2][10*] \nmcInfo{sum}.
According to \emph{HMF }Table 7.1, this calculated value of $\erf2$
is correct to all $10$ places. But beyond $z=2$ errors will begin
@@ -3264,8 +3292,8 @@
\subsection{Double sums or products}
-Sums or products can be iterate d. For instance, the exponential function
-can be calculated this way:
+Sums or products can be iterated. For instance, the exponential function
+can be calculated this way:
\begin{verbatim}
\eval[p]
{\[ \sum_{k=0}^{\infty}
@@ -3272,10 +3300,10 @@
\prod_{m=1}^{k}\frac{x}{m} \]}[x=2]
\end{verbatim}
$\Longrightarrow$ \eval[p]
- {\[ \sum_{k=0}^{\infty}
- \prod_{m=1}^{k}\frac{x}{m} \]}[x=2]
+ {\[ \sum_{k=0}^{\infty}
+ \prod_{m=1}^{k}\frac{x}{m} \]}[x=2]
-\noindent which is \verb`\eval{$ e^2 $}` $\Longrightarrow\eval{\ensuremath{e^{2}}}$.
+\noindent which is \noindent\verb`\eval{$ e^2 $}` $\Longrightarrow\eval{\ensuremath{e^{2}}}$.
A second example is afforded by Euler's transformation of series (\emph{HMF~}3.6.27).
To calculate $e^{-1}$ we use
@@ -3284,9 +3312,11 @@
{\[ \sum_{n=0}^{\infty}
\frac{(-1)^{n}}{n!} \]}[3] \info{sum}.
\end{verbatim}
-$\Longrightarrow$ \eval[p]{\[ \sum_{n=0}^{\infty}\frac{(-1)^{n}}{n!} \]}[3] \info{sum}.
+$\Longrightarrow$ \eval[p]
+ {\[ \sum_{n=0}^{\infty}
+ \frac{(-1)^{n}}{n!} \]}[3] \info{sum}.
-Following Euler, this series can be transformed to the form
+Following Euler, this series can be transformed to the form
\begin{verbatim}
\eval[p,S?=1]{\[
\sum_{k=0}^\infty \frac{(-1)^k}{2^{k+1}}
@@ -3293,17 +3323,21 @@
\sum_{n=0}^k(-1)^n\binom kn \frac1{(k-n)!}
\]}[3] \nmcInfo{sum}.
\end{verbatim}
-$\Longrightarrow$ \eval[p,S?=1]{\[ \sum_{k=0}^\infty \frac{(-1)^k}{2^{k+1}}\sum_{n=0}^k(-1)^n\binom kn \frac1{(k-n)!} \]}[3] \nmcInfo{sum}.
+$\Longrightarrow$ \eval[p,S?=1]{\[
+ \sum_{k=0}^\infty \frac{(-1)^k}{2^{k+1}}
+ \sum_{n=0}^k(-1)^n\binom kn \frac1{(k-n)!}
+ \]}[3] \nmcInfo{sum}.
-\noindent Note the setting \verb`S?=1`. Without it, the summation
-stops after $1$ term, the $k=0$ term, because the $k=1$ term vanishes.
-With \verb`S?=1` it takes $16$ terms of the \emph{outer }sum to
-reach the stopping criterion. Since that sum starts at $0$, that
-means that changing the upper limit from $\infty$ to $15$ should
-give the same result – which it does – but it takes $\tfrac{1}{2}\times16\times17=136$
-terms in total to get there, to be compared with the $9$ terms of
-the earlier simpler sum, and the terms are more complicated. Obviously
-such double sums are computationally intensive.
+\noindent Note the setting \noindent\verb`S?=1`. Without it, the
+summation stops after $1$ term, the $k=0$ term, because the $k=1$
+term vanishes. With \noindent\verb`S?=1` it takes $16$ terms of
+the \emph{outer }sum to reach the stopping criterion. Since that sum
+starts at $0$, that means that changing the upper limit from $\infty$
+to $15$ should give the same result -- which it does -- but it
+takes $\tfrac{1}{2}\times16\times17=136$ terms in total to get there,
+to be compared with the $9$ terms of the earlier simpler sum, and
+the terms are more complicated. Obviously such double sums are computationally
+intensive.
\section{Changing default values}
@@ -3319,16 +3353,15 @@
entry per line (although this is not essential).The key names are
noticeably more verbose than the corresponding keys of the settings
option.\emph{ }The possible keys are listed in Table~\ref{tab:settingsDefaults},
-together with their current default values.
+together with their current default values.
\begin{table}[t]
-\centering
-\noindent \centering{}\caption{Default values, \texttt{\textbackslash eval} command}\label{tab:settingsDefaults}
-\noindent \begin{center}
+\centering{}\caption{Default values, \texttt{\textbackslash eval} command}\label{tab:settingsDefaults}
+ %
\begin{tabular}{ll}
\toprule
{\small key} & {\small value}\tabularnewline
-\midrule
+\midrule
{\small rounding} & {\small\texttt{6}}\tabularnewline
{\small pad} & {\small\texttt{0}}\tabularnewline
{\small output-sci-notation} & {\small\texttt{0}}\tabularnewline
@@ -3351,8 +3384,8 @@
{\small eval-reuse} & {\small\texttt{0}}\tabularnewline
\bottomrule
\end{tabular}
-\par\end{center}
\end{table}
+
Keys taking one of two possible values, \verb`0` (for \verb`false/off`)
or \verb`1` (for \verb`true/on`), are \verb`pad` (the result with
zeros), \verb`output-sci-notation`, \verb`input-sci-notation`, (check
@@ -3371,7 +3404,7 @@
and then choosing a character to act as the exponent marker. Because
\texttt{l3fp} uses \texttt{e} for this character, \texttt{numerica}
has made \texttt{e} its default. But this option is turned off by
-default (hence the \texttt{0} against this key).
+default (hence the \texttt{0} against this key).
\end{itemize}
\item The next block of rows concern general elements that can be changed
for individual calculations with the settings option of \verb`\eval`;
@@ -3389,11 +3422,11 @@
and products. These correspond to the keys \texttt{S+}, \texttt{S?}
and \texttt{P+}, \texttt{P?} of the settings option that can be used
to tweak the behaviour of the stopping criterion for such sums or
-products; see §\ref{sec:settingsInfiniteSumsProds}.
-\item The last block is for `left-overs': specifying at what rounding
-value a floating point should be considered an integer (see §\ref{subsec:defaultsIntifyingRounding}
+products; see §\ref{sec:settingsInfiniteSumsProds}.
+\item The last block is for `left-overs': specifying at what rounding value
+a floating point should be considered an integer (see §\ref{subsec:defaultsIntifyingRounding}
below), and specifying what kind of result is saved to file when the
-\verb`\nmcReuse` command is used (see §\ref{subsec:supplReuseEvalSetting}).
+\verb`\nmcReuse` command is used (see §\ref{subsec:supplReuseEvalSetting}).
\end{itemize}
If you are dissatisfied with any of the default values listed, then
in a text editor create a new file called \texttt{numerica.cfg} and
@@ -3403,17 +3436,17 @@
results always presented in proper scientific notation,\emph{ $d.d_{1}d_{2}d_{3}d_{4}\times10^{n}$},
then add a comma after \texttt{4} and enter on a new line (recommended
but not strictly necessary; the comma is the crucial thing), \texttt{output-sci-notation~=~1,}
-(note the comma) and on another new line, \texttt{output-exponent-char~=~x}.
+(note the comma) and on another new line, \texttt{output-exponent-char~=~x}.
Perhaps you also want a non-zero setting for the final query terms
for infinite sums and products. This makes sense if you are largely
-dealing with non-monotonic series – like Fourier series. Even the
+dealing with non-monotonic series -- like Fourier series. Even the
Euler transformation of the exponential series for $e^{-1}$ discussed
above required a non-zero \texttt{S?}. If you wish to make this change
then add a comma and on a new line add (for instance) \texttt{sum-query-terms~=~1,}
and again on a new line, \texttt{prod-query-terms~=}~1. If this
is all you wish to change, then no comma is necessary after this final
-entry. Your newly created file should look something like
+entry. Your newly created file should look something like
\begin{lyxcode}
rounding~~~~~~~~~~~~~=~4,
@@ -3431,7 +3464,7 @@
lacks a comma. Now save the file with the name \texttt{numerica.cfg}.
This file will be read by \texttt{numerica} near the end of its loading
process. These settings will be \texttt{numerica}'s defaults for the
-relevant keys.
+relevant keys.
\subsection{Location of \texttt{numerica.cfg}}
@@ -3443,13 +3476,13 @@
tree) but also include the current document directory. But what happens
when you start working on another document? Will you remember to copy
\texttt{numerica.cfg} to its new location? That is why your \emph{personal
-texmf tree} is a better place.
+texmf tree} is a better place.
\subsubsection{Personal texmf tree? }
\label{subsec:settingsPersonal-texmf-tree}This is a directory for
-`waifs and strays' of the \TeX{} system that are not included in
-the standard distributions like MiK\TeX{} or \TeX Live. Here you place
+`waifs and strays' of the \TeX{} system that are not included in the
+standard distributions like MiK\TeX{} or \TeX Live. Here you place
personal packages designed for your own particular circumstances.
These may include your own \TeX{} or \LaTeX{} package, say \texttt{mypackage.sty},
achieving some small or singular effect that doesn't warrant wider
@@ -3456,13 +3489,13 @@
distribution on CTAN. Here you might place configuration files for
other packages with your preferences (unless the package requires
some specific location). Here you can put your personal bibliography
-files.
+files.
Your personal texmf tree 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 packages in MiK\TeX{} or
\TeX Live are updated. But these distributions need to be alerted
-to its existence.
+to its existence.
For example, in the MiK\TeX{} console, click on \textsf{Settings},
and then on the \textsf{Directories} tab of the resulting dialog.
@@ -3494,16 +3527,16 @@
seems reasonable to conclude that it has \emph{really }not given an
integer answer, not just that rounding errors have accumulated. If
you want to change this `int-ifying' value for a particular calculation,
-then add a line to \texttt{numerica.cfg} like
+then add a line to \texttt{numerica.cfg} like
\begin{lyxcode}
intify-rounding~=~<integer>
\end{lyxcode}
Since \texttt{l3fp} works to $16$ significant figures, values of
-{\ttfamily\verb`<integer>`} greater than $16$ are pointless.
-Generally int-ifying rounding values will be less than but close to
-$16$ (although when testing the code I used some ridiculous values
-like $3$ or $4$). If other entries follow this one in the file,
-then conclude the line with a comma.
+\verb`<integer>` greater than $16$ are pointless. Generally int-ifying
+rounding values will be less than but close to $16$ (although when
+testing the code I used some ridiculous values like $3$ or $4$).
+If other entries follow this one in the file, then conclude the line
+with a comma.
\section{Parsing mathematical arguments}
@@ -3511,8 +3544,8 @@
package is to require minimal, preferably no, adjustment to the \LaTeX{}
form in which an expression is typeset in order to evaluate it. But
mathematicians do not follow codified rules of the kind programming
-languages insist on when writing formulas – like parenthesizing the
-arguments of functions, or inserting explicit multiplication signs
+languages insist on when writing formulas -- like parenthesizing
+the arguments of functions, or inserting explicit multiplication signs
({*}) between juxtaposed terms. Hence the question of where the arguments
of mathematical functions end is acute. For a few functions \LaTeX{}
delimits the argument: think of \verb`\sqrt`, \verb`\frac`, \verb`\binom`;
@@ -3534,7 +3567,7 @@
command joins the next token to the argument (\emph{cleaves to});
the \verb`\Q` command severs the next token from the argument (\emph{cleaves
apart}). Neither command is added to the argument nor leaves a visible
-trace in the output.
+trace in the output.
Thus, without \verb`\q`,
\begin{centred}
@@ -3542,15 +3575,15 @@
\eval{$ \sin(n+\tfrac12)(x-t) $}[n=3,x=t+\pi,t=1.234],
\end{centred}
which is $(\sin\tfrac{7}{2})\times\pi$. With \verb`\q` between the
-bracketed factors,
+bracketed factors,
\begin{centred}
\verb`\eval{$ \sin(n+\tfrac12)\q(x-t) $}[n=3,x=t+\pi,t=1.234]` $\Longrightarrow$
\eval{$ \sin(n+\tfrac12)\q(x-t) $}[n=3,x=t+\pi,t=1.234],
\end{centred}
-which is $\sin(\tfrac{7}{2}\pi)$. Similarly, without \verb`\q`,
+which is $\sin(\tfrac{7}{2}\pi)$. Similarly, without \verb`\q`,
\begin{centred}
\verb`\eval[p]{\[ \cos\frac{2\pi}{T}n(t+\tfrac12T) \]}[T=2,t=1,n=3]`
-$\Longrightarrow$ \eval[p]{\[ \cos\frac{2\pi}{T}n(t+\tfrac12T) \]}[T=2,t=1,n=3]
+$\Longrightarrow$\eval[p]{\[ \cos\frac{2\pi}{T}n(t+\tfrac12T) \]}[T=2,t=1,n=3]
\end{centred}
which is $(\cos\pi)\times3\times(1+\tfrac{1}{2}\times2)$. With \verb`\q`
used twice, once after the fraction and once before the left parenthesis,
@@ -3559,7 +3592,9 @@
\cos\frac{2\pi}{T}\q n\q(t+\tfrac12T)
\]}[T=2,t=1,n=3]
\end{verbatim}
-$\Longrightarrow$ \eval[p]{\[ \cos\frac{2\pi}{T}\q n\q(t+\tfrac12T) \]}[T=2,t=1,n=3]
+$\Longrightarrow$ \eval[p]{\[
+ \cos\frac{2\pi}{T}\q n\q(t+\tfrac12T)
+ \]}[T=2,t=1,n=3]
\noindent which is $\cos(\pi\times3\times2)$.
@@ -3569,14 +3604,14 @@
is discussed in §\ref{subsec:parseTrigFns} below.
For the \verb`\Q` command which splits an argument we have, without
-it,
+it,
\begin{centred}
-\verb`\eval{$ 1/2e $}` $\Longrightarrow$ \eval{$ 1/2e $},
+\verb`\eval{$ 1/2e $}` $\Longrightarrow$\eval{$ 1/2e $},
\end{centred}
which is the reciprocal of $2e$, whereas with the \verb`\Q` command
-inserted before \verb`e`,
+inserted before \verb`e`,
\begin{centred}
-\verb`\eval{$ 1/2\Q e $}` $\Longrightarrow$ \eval{$ 1/2\Q e $},
+\verb`\eval{$ 1/2\Q e $}` $\Longrightarrow$\eval{$ 1/2\Q e $},
\end{centred}
which is one half of $e$, although it is unlikely to be read that
way. If one half of $e$ is intended then parenthesize the $1/2$
@@ -3607,58 +3642,58 @@
\begin{table}
\centering
-\caption{ Parsing groups}\label{tab:settingsParsing-groups}
-{\ttfamily{}%
+\caption{Parsing groups}
+\label{tab:settingsParsing-groups} \texttt{{}{}}{\ttfamily{}%
\begin{tabular}{ll}
\toprule
-{\small\textrm{group}} & {\small\textrm{function/operation}}\tabularnewline
-\midrule
-{\small\textrm{I}} & {\small\textrm{surd, logical Not}}\tabularnewline
-{\small\textrm{II}} & {\small\textrm{unary functions (direct trig. functions default), /}}\tabularnewline
-{\small\textrm{III}} & {\small\textrm{direct trig. functions with special setting}}\tabularnewline
-{\small\textrm{IV}} & {\small\textrm{sums, products}}\tabularnewline
-{\small\textrm{V}} & {\small\textrm{comparisons}}\tabularnewline
-{\small\textrm{VI}} & {\small\textrm{logical And, logical Or}}\tabularnewline
+{\small\texttt{group}} & {\small\texttt{function/operation}}\tabularnewline
+\midrule
+{\small\texttt{I}} & {\small\texttt{surd, logical Not}}\tabularnewline
+{\small\texttt{II}} & {\small\texttt{unary functions (direct trig. functions default), /}}\tabularnewline
+{\small\texttt{III}} & {\small\texttt{direct trig. functions with special setting}}\tabularnewline
+{\small\texttt{IV}} & {\small\texttt{sums, products}}\tabularnewline
+{\small\texttt{V}} & {\small\texttt{comparisons}}\tabularnewline
+{\small\texttt{VI}} & {\small\texttt{logical And, logical Or}}\tabularnewline
\bottomrule
\end{tabular}}
+\end{table}
-\end{table}
- A formula is a sequence of tokens and brace groups. All parsing occurs
+A formula is a sequence of tokens and brace groups. All parsing occurs
from the left, \LaTeX{} argument by \LaTeX{} argument, where \emph{argument}
-means either a token (an N-type argument in \verb`expl3`-speak) or
-a brace group (an n-type argument). To distinguish \LaTeX{} arguments
+means either a token (an N-type argument in \texttt{expl3}-speak)
+or a brace group (an n-type argument). To distinguish \LaTeX{} arguments
from mathematical arguments I shall when necessary refer to L-args
and M-args. A mathematical argument may end \emph{at} an L-arg, meaning
immediately before the L-arg, or end \emph{with} the L-arg, meaning
immediately after the L-arg. Ending or not will in general depend
-on whether the argument is in \emph{first position} – the position
+on whether the argument is in \emph{first position} -- the position
immediately following a function token like \verb`\sin` or \verb`\log`
-– or in \emph{general position} – any later position (although for
-trigonometric functions we will also need to consider \emph{second}
-and even \emph{third }positions).
+-- or in \emph{general position} -- any later position (although
+for trigonometric functions we will also need to consider \emph{second}
+and even \emph{third }positions).
For counting position, we need to allow for formatting elements and
-multi-token numbers – in both decimal and scientific formats. Formatting
+multi-token numbers -- in both decimal and scientific formats. Formatting
elements do not change the position count. This applies to things
like thin spaces or phantoms (and their arguments) or modifiers like
\verb`\left` or \verb`\biggl`. Multi-token numbers (in decimal or
scientific formats) are treated as single items; they advance the
-position count by exactly one. \LaTeX{} functions – like \verb`\frac`
-– which take \LaTeX{} arguments again advance the position count only
-by one. Mathematically, the fraction is viewed as a single unit.
+position count by exactly one. \LaTeX{} functions -- like \verb`\frac`
+-- which take \LaTeX{} arguments again advance the position count
+only by one. Mathematically, the fraction is viewed as a single unit.
-I shall refer to a token or a token and its \LaTeX{} arguments – like
-\verb`\frac` and its arguments – as an \emph{item}. Similarly, a
-(possibly multi-token) number is an item. Also it will help to distinguish
+I shall refer to a token or a token and its \LaTeX{} arguments --
+like \verb`\frac` and its arguments -- as an \emph{item}. Similarly,
+a (possibly multi-token) number is an item. Also it will help to distinguish
tokens within brackets where both brackets lie to the right of a function
from those that do not. The former I call \emph{clothed}; the latter
are \emph{naked}. Thus the plus sign in $(\sin x+y)$ is naked relative
to the sine (one bracket to the left of the function), but is clothed
-in $\sin(x+y)$ (both brackets to the right of the function).
+in $\sin(x+y)$ (both brackets to the right of the function).
\subsubsection{Parsing group I}
-The only functions in this category are the surd and logical Not.
+The only functions in this category are the surd and logical Not.
Why distinguish the surd from other unary functions? Surely we all
agree that \verb`\sin2\pi`, displaying as $\sin2\pi$, vanishes?
@@ -3666,22 +3701,22 @@
But \verb`\surd2\pi`, displaying as $\surd2\pi$, is understood to
be the product $\surd2\times\pi$. The argument of the surd ends with
the $2$. The surd binds more tightly to its argument than is true
-of unary functions generally.
+of unary functions generally.
-For parsing group I
+For parsing group I
\begin{enumerate}
\item if a left bracket is in first position, the mathematical argument
-ends with the matching right bracket; otherwise
+ends with the matching right bracket; otherwise
\item the argument ends with the item in first position and any L- or M-args
-required by that item.
+required by that item.
\end{enumerate}
If the factorial sign \verb`!` \emph{preceded} its argument, it too
would belong to this parsing state, for it also binds tightly like
the surd. This means that an expression like $\surd4!$ is intrinsically
ambiguous. Is it the square root of $24$ or the factorial of $2$?
-In \texttt{numerica} it produces the (perhaps rather odd) error
+In \texttt{numerica} it produces the (perhaps rather odd) error
\begin{centred}
-\verb`\eval{$ \surd 4! $}` $\Longrightarrow$ \eval{$ \surd4! $}
+\verb`\eval{$ \surd 4! $}` $\Longrightarrow$ \eval{$ \surd 4! $}
\end{centred}
The surd has seized the argument; there is nothing for the factorial
to operate on. The same error arises if the $4$ is parenthesized,
@@ -3691,7 +3726,7 @@
for them.
Exponents cause no problem because taking square roots and raising
-to a power are commutative operations – the result is the same whichever
+to a power are commutative operations -- the result is the same whichever
is performed first.
\begin{centred}
\verb`\eval{$ \surd 3^4 $}` $\Longrightarrow$ \eval{$ \surd 3^4 $}.
@@ -3703,7 +3738,7 @@
hyperbolic functions, their inverses, the various logarithms and the
exponential functions, the signum function \verb`\sgn`, and the denominators
of slash fractions \verb`/`. Note however that there is a setting
-switch which enables trigonometric functions to handle parentheses
+switch which enables trigonometric functions to handle parentheses
in arguments more generally; see §\ref{subsec:parseTrigFns}.
\begin{itemize}
\item In parsing group II we wish to accommodate usages like $\ln z^{n}=n\ln z$
@@ -3714,46 +3749,46 @@
\item An approximation to Stirling's formula for the factorial is often
written $\ln N!\approx N\ln N-N$ (widely used in texts on statistical
mechanics). Hence the factorial sign should also be considered part
-of the argument.
+of the argument.
\item $\ln xy=\ln x+\ln y$ means the argument must reach over a product
of variables. Identities like $\sin2z=2\sin z\cos z$ mean the argument
also reaches over numbers, and expressions like $\sin\tfrac{1}{2}\pi x$
(\emph{HMF} 4.3.104) mean that it further reaches over \verb`\tfrac`-s
-and constants.
+and constants.
\item Essentially \emph{anything }can be in first position, and without
-parentheses; e.g.
+parentheses; e.g.
\begin{itemize}
\item unary functions: $\ln\ln z$ (\emph{HMF} 4.1.52), $\ln\tan\dfrac{z}{2}$
-(\emph{HMF} 4.3.116),
+(\emph{HMF} 4.3.116),
\item fractions: $\ln\dfrac{z_{1}}{z_{2}}$ (\emph{HMF} 4.1.9), $\arcsin\dfrac{(2ax+b)}{(b^{2}-4ac)^{1/2}}$
-(\emph{HMF} 3.3.36), $\ln\dfrac{\tan z}{z}$ (\emph{HMF} 4.3.73),
-\item absolute values: $\ln\abs*{\dfrac{a+x}{a-x}}$ (\emph{HMF} 3.3.25),
+(\emph{HMF} 3.3.36), $\ln\dfrac{\tan z}{z}$ (\emph{HMF} 4.3.73),
+\item absolute values: $\ln\abs*{\dfrac{a+x}{a-x}}$ (\emph{HMF} 3.3.25),
\item square roots: $\arctan\sqrt{\dfrac{\nu_{1}}{\nu_{2}}F}$ (\emph{HMF
-}26.6.8)
+}26.6.8)
\end{itemize}
\end{itemize}
-With these examples in mind, for parsing group II
+With these examples in mind, for parsing group II
\begin{enumerate}
\item if a left bracket is in first position, the mathematical argument
ends with the matching right bracket and any attached exponent, or
-factorial or double factorial sign; otherwise
+factorial or double factorial sign; otherwise
\item the mathematical argument includes the item in first position and
any L- or M-args required by that item;
\begin{enumerate}
-\item if the item in first position is a number, variable, constant or \verb`\tfrac`
+\item if the item in first position is a number, variable, constant or \ \verb`\tfrac`
\begin{enumerate}
\item the argument appends the next item if it is a number, variable, constant
-or \verb`\tfrac`, and so on recursively; or
+or \verb`\tfrac`, and so on recursively; or
\item the argument appends the next item if it is an exponent, or facorial
-or double factorial sign, and ends there; otherwise
-\item the argument ends.
+or double factorial sign, and ends there; otherwise
+\item the argument ends.
\end{enumerate}
\item if the item in first position is not a number, variable, constant
-or \verb`\tfrac`
+or \verb`\tfrac`
\begin{enumerate}
\item the argument appends the next item if it is an exponent, or factorial
-or double factorial sign, and ends there; otherwise
-\item the argument ends.
+or double factorial sign, and ends there; otherwise
+\item the argument ends.
\end{enumerate}
\end{enumerate}
\end{enumerate}
@@ -3762,7 +3797,7 @@
which exhibits all elements.
Illustrating 1, the exponent is included in the argument but not the
-following variable:
+following variable:
\begin{centred}
\verb`\eval{$ \log_{10}(1+2+3+4)^3n $}[n=5]` $\Longrightarrow$ \eval{$ \log_{10}(1+2+3+4)^3n $}[n=5].
\end{centred}
@@ -3773,12 +3808,12 @@
be considered part of the argument of the logarithm. If that is the
case, inserting a \verb`\q` command before \verb`n` would achieve
this, but that would still be confusing for the reader of the pdf.
-Inserting parentheses is the only sensible thing to do.
+Inserting parentheses is the only sensible thing to do.
Illustrating 2(a)ii, again the exponent is included in the argument
-but not the following variable:
+but not the following variable:
\begin{centred}
-\verb`\eval{$ \log_{10}m^3n $}[m=10,n=5]` $\Longrightarrow$ \eval{$ \log_{10}m^3n $}[m=10,n=5].
+\verb`\eval{$ \log_{10}m^3n $}[m=10,n=5]` $\Longrightarrow$ \eval{$ \log_{10}m^3n $}[m=10,n=5]
\end{centred}
Again, for the sake of the reader and as one naturally does to avoid
ambiguity, the variable $n$ should precede the logarithm. If in fact
@@ -3785,9 +3820,9 @@
the intention was for the $n$ to be included in the argument of the
logarithm, then again the \verb`\q` command could be used or, better
in this case, the $n$ could be shifted to precede the $m$, which
-illustrates 2(a)i:
+illustrates 2(a)i:
\begin{centred}
-\verb`\eval{$ \log_{10}nm^3 $}[m=10,n=5]` $\Longrightarrow$ \eval{$ \log_{10}nm^3 $}[m=10,n=5],
+\verb`\eval{$ \log_{10}nm^3 $}[m=10,n=5]` $\Longrightarrow$ \eval{$ \log_{10}nm^3 $}[m=10,n=5]
\end{centred}
the logarithm of $5000$, or better still, $m^{3}n$ could (and should)
be parenthesized for the sake of the reader.
@@ -3797,21 +3832,20 @@
going to miss some instances where a different outcome might be desirable.
Where an argument ends is affected by visual appearance in the pdf.
It is simple and easy to remember if it is understood that anything
-that breaks the `visual flow' of juxtaposed numbers, variables,
-constants and \verb`\tfrac`-s ends the argument. An exponent does
-just that. If you feel there is ambiguity, parenthesize to clarify.
+that breaks the `visual flow' of juxtaposed numbers, variables, constants
+and \verb`\tfrac`-s ends the argument. An exponent does just that.
+If you feel there is ambiguity, parenthesize to clarify.
Illustrating 2(b)ii, the argument stops with the \verb`\dfrac` and
-its arguments and does not extend to the following constant:
+its arguments and does not extend to the following constant:
\begin{centred}
\verb`\eval{$ \sin\dfrac12\pi $}` $\Longrightarrow$ \eval{$ \sin\dfrac12\pi $}.
\end{centred}
Obviously, someone writing an expression like this intends the $\pi$
to be part of the argument. In that case, a \verb`\tfrac` should
-be used since the \verb`\dfrac` breaks the `visual flow' of the
-argument.
+be used since the \verb`\dfrac` breaks the `visual flow' of the argument.
\begin{description}
-\item [{Fractions}]~
+\item [{Fractions}] ~
But why not a plain \verb`\frac`? After all, for an inline expression
it displays in the same way as a \verb`\tfrac`. I considered making
@@ -3822,7 +3856,7 @@
or \verb`\[ \]` delimiters, which ruled it out. Because \verb`\frac`
sometimes displays as \verb`\dfrac`, it is treated like \verb`\dfrac`
(but see §\ref{subsec:parseTrigFns}, specifically \texttt{()=2}).
-\item [{Slash~fractions}]~
+\item [{Slash~fractions}] ~
It is easy to write ambiguous expressions using the slash $/$ to
indicate fractions or division. How should $\pi/2n$ be interpreted?
@@ -3849,25 +3883,26 @@
$\sec\pi(\tfrac{1}{4}+\tfrac{1}{2}az)$ (\emph{HMF }19.3.3), $\cos(2m+p)z$
(\emph{HMF }20.2.3), $\sin(2n+1)v$ (\emph{HMF }16.38.1). Looking
through various texts discussing Fourier series it is easy to find
-examples like
+examples like
\[
\cos\frac{2\pi}{T}nt,\quad\cos\frac{2\pi}{T}n(t+\tfrac{1}{2}T),
\]
-and
+and
\[
\cos(N+\tfrac{1}{2})\frac{2\pi\tau}{T},\quad\sin2\pi\left(\frac{x}{\lambda}-\frac{t}{T}\right).
\]
In the last of these \verb`\left` and \verb`\right` have been used
-to enlarge the parentheses.
+to enlarge the parentheses.
All these usages can be accommodated by adjusting a setting in the
settings option (§\ref{sec:settingsOption}) of the \verb`\eval`
-command:
+command:
\begin{lyxcode}
()~=~<integer>
\end{lyxcode}
-where \texttt{<integer>} is one of \texttt{0, 1, 2}.
+where \texttt{<integer>} is one of \texttt{0, 1, 2}.
+\noindent{}%
\noindent\begin{minipage}[t]{1\columnwidth}%
\begin{shaded}%
I remain unsure whether to persist with the \texttt{()} setting. A
@@ -3878,63 +3913,63 @@
or \texttt{\textbackslash Q}, to achieve the same effects does mean
modifying formulas, but is straightforward and easier to understand.
(And \texttt{\textbackslash q} and \texttt{\textbackslash Q} have
-no effect on the visual appearance of formulas.)\end{shaded}%
+no visual effect.)\end{shaded}%
\end{minipage}
-For convenience of statement in what follows call parentheses, square
-brackets or braces \emph{brackets}. If preceded by a \verb`\left`
-or \verb`\right` or \verb`\biggl` or \verb`\biggr` etc. modifier,
-call them \emph{Brackets}, with an uppercase `B'. Modifiers do not
-contribute to the position count, so that a left Bracket in first
-position means the modifier and left bracket are both considered to
-be in first position. When it is immaterial whether it is a bracket
+\noindent For convenience of statement in what follows call parentheses,
+square brackets or braces \emph{brackets}. If preceded by a \noindent\verb`\left`
+or \noindent\verb`\right` or \noindent\verb`\biggl` or \noindent\verb`\biggr`
+etc. modifier, call them \emph{Brackets}, with an uppercase `B'. Modifiers
+do not contribute to the position count, so that a left Bracket in
+first position means the modifier and left bracket are both considered
+to be in first position. When it is immaterial whether it is a bracket
or a Bracket I write b/Bracket. The rules that follow do not prescribe
what mathematicians \emph{ought} to do but are intended to be descriptive
of certain patterns of mathematical practice as discerned in \emph{HMF}
-and a number of texts (about half a dozen) on Fourier series.
+and a number of texts (about half a dozen) on Fourier series.
\begin{description}
\item [{\texttt{()=0}}] is the \emph{default} setting, parsing group II
-behaviour; b/Brackets are included in the argument only if
+behaviour; b/Brackets are included in the argument only if
\begin{itemize}
-\item the left b/Bracket is in first position;
+\item the left b/Bracket is in first position;
\begin{itemize}
\item if the first item beyond the matching right b/Bracket is an exponent,
or factorial or double factorial sign, it is appended to the argument,
-which ends there, otherwise
-\item the argument ends with the right b/Bracket.
+which ends there, otherwise
+\item the argument ends with the right b/Bracket.
\end{itemize}
\end{itemize}
\end{description}
The default setting allows things like $\sin\tfrac{1}{2}a$, $\cos2\pi nt$
and $\tan(A+B)$. It does \emph{not} encompass examples like $\tan\tfrac{1}{2}(A+B)$
-or $\cos2(n+\tfrac{1}{2})\pi$. For that we need the setting \verb`()=1`:
+or $\cos2(n+\tfrac{1}{2})\pi$. For that we need the setting \verb`()=1`:
\begin{description}
\item [{\texttt{()=1}}] includes a b/Bracketed expression in the argument,
provided
\begin{itemize}
-\item the left Bracket is in first position;
+\item the left Bracket is in first position;
\begin{itemize}
\item if the first item beyond the matching right Bracket is an exponent,
or factorial or double factorial sign, it is appended to the argument,
-which ends there, otherwise
-\item the argument ends with the right Bracket.
+which ends there, otherwise
+\item the argument ends with the right Bracket.
\end{itemize}
\item or the item in first position is a number, variable, constant or \verb`\tfrac`
-and the left bracket is in second position;
+and the left bracket is in second position;
\begin{itemize}
\item if the first item beyond the matching right bracket is an exponent,
or factorial or double factorial sign, it is appended to the argument,
-which ends there, or
+which ends there, or
\item if the first item beyond the matching right bracket is a number, variable,
constant, or \verb`\tfrac` it is appended to the argument, and so
-on recursively, until
+on recursively, until
\begin{itemize}
\item an exponent, or factorial or double factorial sign is met, which is
-appended to the argument which ends there, or
+appended to the argument which ends there, or
\item an item is met which is \emph{not} an exponent, or factorial or double
factorial sign, or a number, variable, constant or \verb`\tfrac`,
-at which point the argument ends, or
-\item the end of the formula is reached.
+at which point the argument ends, or
+\item the end of the formula is reached.
\end{itemize}
\end{itemize}
\end{itemize}
@@ -3943,23 +3978,22 @@
$\sec\pi(\tfrac{1}{4}+\tfrac{1}{2}az)$, $\cos(2m+p)z$, $\sin(2n+1)v$
are all accommodated, as is $\sin\tfrac{1}{2}(m+n)\pi$ with items
on both sides of the parentheses. But, note, there must be at most
-\emph{one} item before the left parenthesis:
+\emph{one} item before the left parenthesis:
\begin{centred}
-\verb`\eval[()=1]{$ \sin\tfrac16(m+n)\pi $}[m=1,n=2]`. $\Longrightarrow$
-\eval[()=1]{$ \sin\tfrac16(m+n)\pi $}[m=1,n=2],
+\verb`\eval[()=1]{$ \sin\tfrac16(m+n)\pi $}[m=1,n=2]` $\Longrightarrow$
+\eval[()=1]{$ \sin\tfrac16(m+n)\pi $}[m=1,n=2].
\end{centred}
-whereas, with two items before the left parenthesis,
+whereas, with two items before the left parenthesis,
\begin{centred}
\verb`\eval[()=1]{$ \sin2\tfrac1{12}(m+n)\pi $}[m=1,n=2]`. $\Longrightarrow$
-
\eval[()=1]{$ \sin2\tfrac1{12}(m+n)\pi $}[m=1,n=2].
\end{centred}
Whatever the \verb`()` setting, \texttt{numerica} does not check
-what is included between the parentheses (or brackets generally) –
+what is included between the parentheses (or brackets generally) --
it could be anything. However inserting \verb`\left`, \verb`\right`
or other modifiers before the parentheses restricts the argument of
the sine in this example, despite the \verb`()=1` setting, to the
-\verb`\tfrac`:
+\verb`\tfrac`:
\begin{centred}
\verb`\eval[()=1]{$ \sin\tfrac16\left(m+n\right)\pi $}[m=1,n=2]`
$\Longrightarrow$ \eval[()=1]{$ \sin\tfrac16\left(m+n\right)\pi $}[m=1,n=2].
@@ -3967,10 +4001,10 @@
Although \verb`()=1` serves well for the kinds of expressions and
identities involved in trigonometry, perusal of any text on Fourier
series will show it does not cover the kinds of expressions met there.
-For that we need
+For that we need
\begin{description}
\item [{\texttt{()=2}}] includes a b/Bracketed expression in the argument
-provided
+provided
\begin{itemize}
\item the left b/Bracket is in first position, or the item in first position
is a number, variable, constant, \verb`\dfrac`, \verb`\frac` or
@@ -3977,45 +4011,44 @@
\verb`\tfrac` and the left b/Bracket is in second position, or the
items in first and second positions are numbers, variables, constants,
\verb`\dfrac`-s, \verb`\frac`-s or \verb`\tfrac`-s and the left
-b/Bracket is in third position;
+b/Bracket is in third position;
\begin{itemize}
\item if the first item beyond the matching right b/Bracket is an exponent,
or factorial or double factorial sign, it is appended to the argument,
-which ends there, or
+which ends there, or
\item if the first item beyond the matching right b/Bracket is a number,
variable, constant, \verb`\dfrac`, \verb`\frac` or \verb`\tfrac`
-it is appended to the argument, and so on recursively, until
+it is appended to the argument, and so on recursively, until
\begin{itemize}
\item an exponent, or factorial or double factorial sign is met, which is
-appended to the argument which ends there, or
+appended to the argument which ends there, or
\item an item is met which is \emph{not} an exponent, or factorial or double
factorial sign, or a number, variable, constant, \verb`\dfrac`, \verb`\frac`
-or \verb`\tfrac`, at which point the argument ends, or
-\item the end of the formula is reached.
+or \verb`\tfrac`, at which point the argument ends, or
+\item the end of the formula is reached.
\end{itemize}
\end{itemize}
\end{itemize}
\end{description}
-{\ttfamily\verb`()=2`} draws no distinction between brackets
-and Brackets. It allows all \verb`()=1` possibilities but also \emph{two
-}items (of a suitable kind) before a left b/Bracket; it also treats
-\verb`\dfrac`-s and \verb`\frac`-s like \verb`\tfrac`-s for determining
-the scope of arguments.
+\verb`()=2` draws no distinction between brackets and Brackets. It
+allows all \verb`()=1` possibilities but also \emph{two }items (of
+a suitable kind) before a left b/Bracket; it also treats \verb`\dfrac`-s
+and \verb`\frac`-s like \verb`\tfrac`-s for determining the scope
+of arguments.
The following examples are taken from different texts on Fourier series.
The first shows a \verb`\frac` being included in the argument, the
-second shows \emph{two} items – including a \verb`\frac` – preceding
+second shows \emph{two} items -- including a \verb`\frac` -- preceding
the left parenthesis, the third shows a \verb`\frac` to the right
of the parentheses, and the fourth shows parentheses using \verb`\left`-\verb`\right`
-modifiers with two items preceding them:
+modifiers with two items preceding them:
\[
\cos\frac{2\pi}{T}nt,\quad\cos\frac{2\pi}{T}n(t+\tfrac{1}{2}T),\quad\text{\ensuremath{\sin(N+\tfrac{1}{2})\frac{2\pi\tau}{T}}\ensuremath{\quad}and}\quad\sin2\pi\left(\frac{x}{\lambda}-\frac{t}{T}\right).
\]
All these usages are accommodated by the \verb`()=2` setting. For
-instance
+instance
\begin{verbatim}
- \eval[p,()=2]
- {
+ \eval[p,()=2]{
\[ \sin(N+\tfrac12)\frac{2\pi\tau}T \]
}[N=1,\tau=2,T=3]
\end{verbatim}
@@ -4022,13 +4055,14 @@
$\Longrightarrow$ \eval[p,()=2]
{
\[ \sin(N+\tfrac12)\frac{2\pi\tau}T \]
- }[N=1,\tau=2,T=3]which is the sine of $2\pi=(\tfrac{3}{2})\times(\tfrac{4}{3}\pi)$
-where a \verb`\frac` trailing the parentheses has been included in
-the argument, and \emph{not }$(\sin\tfrac{3}{2})(\tfrac{4}{3}\pi)$.
-Or consider
+ }[N=1,\tau=2,T=3]
+
+\noindent which is the sine of $2\pi=(\tfrac{3}{2})\times(\tfrac{4}{3}\pi)$
+where a \noindent\verb`\frac` trailing the parentheses has been included
+in the argument, and \emph{not }$(\sin\tfrac{3}{2})(\tfrac{4}{3}\pi)$.
+Or consider
\begin{verbatim}
- \eval[p,()=2]
- {\[
+ \eval[p,()=2]{\[
\sin2\pi\left(\frac{x}{\lambda}
-\frac{t}{T}\right)
\]}[x=1,\lambda=2,t=3,T=4]
@@ -4044,20 +4078,20 @@
However a usage like $\sin(n+\tfrac{1}{2})(x-t)$, noted in two different
texts, is not available without explicit use of the \verb`\q` command
-between the parenthesized groups.
+between the parenthesized groups.
\subsubsection{Parsing group IV}
The only members of this group are \verb`\sum` and \verb`\prod`.
-For parsing group IV
+For parsing group IV
\begin{enumerate}
\item the argument ends
\begin{enumerate}
\item at the first naked plus or minus sign encountered, or
-\item at the first comparison sign or comparison command encountered, or
-\item at the first logical And or logical Or sign encountered, or
-\item at the end of the formula.
+\item at the first comparison sign or comparison command encountered, or
+\item at the first logical And or logical Or sign encountered, or
+\item at the end of the formula.
\end{enumerate}
\end{enumerate}
In practice this means mainly (a) and (d), and seems to be the instinctive
@@ -4064,11 +4098,11 @@
practice. \emph{HMF} has multiple examples in multiple chapters of
the argument to a sum ending at a naked plus sign: 7.3.12 \& 7.3.14,
9.1.11 \& 9.1.77, 9.6.35 \& 9.6.43, 11.1.9, \ldots{} (at that point
-I stopped looking). They were all of the form
+I stopped looking). They were all of the form
\[
\sum\text{argument}+\ldots
\]
- A minus sign serving the same purpose was harder to find but \emph{HMF}
+A minus sign serving the same purpose was harder to find but \emph{HMF}
10.4.65 \& 10.4.67 are two instances. I considered whether a \verb`\times`
or slash fraction sign \verb`/` might end the argument of a sum,
but surely we need to allow things like $\sum1/n^{2}$ which rules
@@ -4078,7 +4112,7 @@
Because they are evaluated using the same code as sums I (unthinkingly)
placed products with sums but doubts later intruded. In \emph{HMF}
-products occur only occasionally and are almost all of the form
+products occur only occasionally and are almost all of the form
\[
\prod\left(\text{argument}\right)
\]
@@ -4095,7 +4129,7 @@
\]
although \emph{HMF}, for the same expression, encloses the two factors
within (large) square brackets, as if some ambiguity existed as to
-how far the reach of the \verb`\prod` extended.
+how far the reach of the \verb`\prod` extended.
\emph{Tentatively} I retain products here in the same group as sums.
@@ -4108,13 +4142,13 @@
\texttt{numerica} handles comparisons, it is the argument on the right-hand
side of the relation that needs determining.
-For parsing group V
+For parsing group V
\begin{enumerate}
-\item the argument ends at
+\item the argument ends at
\begin{enumerate}
-\item the first logical And or logical Or encountered, or
-\item the first comparison sign or command encountered, or
-\item the end of the formula.
+\item the first logical And or logical Or encountered, or
+\item the first comparison sign or command encountered, or
+\item the end of the formula.
\end{enumerate}
\end{enumerate}
@@ -4123,12 +4157,12 @@
Logical And and logical Or are the sole members of this group. It
is the right-hand side of the And or Or command that needs determining.
-For parsing group VI
+For parsing group VI
\begin{enumerate}
-\item the argument ends at
+\item the argument ends at
\begin{enumerate}
-\item the first logical And or logical Or encountered, or
-\item the end of the formula.
+\item the first logical And or logical Or encountered, or
+\item the end of the formula.
\end{enumerate}
\end{enumerate}
@@ -4140,21 +4174,21 @@
often do write formulas. It is \emph{how things look in the pdf},
not \LaTeX , that is the guide. You are always free to parenthesize
as you see fit and to insert cleave commands (\verb`\q` or \verb`\Q`)
-to force outcomes.
+to force outcomes.
(But note that parenthesizing has its limits. For sums, writing
\[
\sum\left(\mathtt{<stuff>}\right)\mathtt{<more\ stuff>}
\]
- does not necessarily end the summand at the right parenthesis: it
+does not necessarily end the summand at the right parenthesis: it
ends at the first naked $+$ or $-$ sign, or \verb`\Q` command,
-encountered.)
+encountered.)
The rule should always be to write expressions that are clear to the
reader of the pdf. An expression that is ambiguous to the reader,
even if it fits within the parsing rules, is to be deprecated. The
\emph{intent} is that \verb`\eval` can parse unambiguous expressions
-correctly.
+correctly.
\chapter{Supplementary commands}
@@ -4163,9 +4197,9 @@
\verb`\nmcConstants` and \verb`\nmcReuse`, supplementary to the
principal command \verb`\nmcEvaluate`. They use the same machinery
as \verb`\nmcEvaluate` and so have the same syntax. If all arguments
-are present it is
+are present it is
\begin{centred}
-\noindent \verb`\nmc<cmd>*[settings]{main arg}[vv-list][rounding]`
+\verb`\nmc<cmd>*[settings]{main arg}[vv-list][rounding]`
\end{centred}
where \verb`<cmd>` is one of \verb`Info`, \verb`Macros`, \verb`Constants`
and \verb`Reuse`. All four commands have short-name forms: \verb`\info`,
@@ -4173,15 +4207,15 @@
Generally the final two optional arguments will not be used. The user
should be aware of this if following a command with a square bracketed
-expression – the expression will be absorbed without trace unless
+expression -- the expression will be absorbed without trace unless
it is preceded by, for example, an empty brace pair.
Because the commands share the machinery of \verb`\nmcEvaluate`,
the settings discussed earlier (Chapter~\ref{chap:Settings}) for
the \verb`\eval` command are also available for these commands, although
-they will, in the main, be irrelevant. The `debug' code has been
-used by the \verb`view` setting of some of these supplementary commands
-to produce its effects.
+they will, in the main, be irrelevant. The `debug' code has been used
+by the \verb`view` setting of some of these supplementary commands
+to produce its effects.
The starred form of command is available in all four cases and in
all cases produces a pure number. If both star and \verb`view` are
@@ -4189,8 +4223,8 @@
\section{Feedback on \textquoteleft infinite\textquoteright{} processes:\texttt{ \textbackslash nmcInfo}}
-\label{sec:supplInfo}Used after the evaluation of an `infinite'
-process, the \verb`\nmcInfo` command, or its short-name form \verb`\info`
+\label{sec:supplInfo}Used after the evaluation of an `infinite' process,
+the \verb`\nmcInfo` command, or its short-name form \verb`\info`
will tell you how many terms or factors or other operations\footnote{It also applies to the commands \texttt{\textbackslash nmcIterate
}and \texttt{\textbackslash nmcSolve} from the \texttt{numerica-plus
}package and to derivatives and integrals from the \texttt{numerica-calculus}
@@ -4203,15 +4237,15 @@
\verb`sum` or \verb`prod`. The display, as we have seen in earlier
examples, is a number followed by a space then a descriptor. For \verb`sum`
and \verb`prod` the descriptors are \verb`terms` and \verb`factors`.
-Starring \verb`\nmcInfo` – \verb`\nmcInfo*{arg}` or \verb`\info*{arg}`
-– suppresses the descriptor and leaves only the number. This allows
+Starring \verb`\nmcInfo` -- \verb`\nmcInfo*{arg}` or \verb`\info*{arg}`
+-- suppresses the descriptor and leaves only the number. This allows
the starred form to be nested in an \verb`\eval` command, which might
-sometimes be convenient.
+sometimes be convenient.
As an example, let's test `the hard way' a standard identity, $\cosh^{2}x-\sinh^{2}x=1$.
We know that $\cosh x=\sum_{n=0}^{\infty}\frac{x^{2n}}{(2n)!}$ and
$\sinh x=x\prod_{k=1}^{\infty}\left(1+\frac{x^{2}}{k^{2}\pi^{2}}\right)$.
-The difference of their squares should be $1$:
+The difference of their squares should be $1$:
\begin{verbatim}
\eval{\[
\left[\sum_{n=0}^{\infty}
@@ -4224,11 +4258,12 @@
\end{verbatim}
$\Longrightarrow$ \eval{\[
\left[\sum_{n=0}^{\infty}
- \frac{x^{2n}}{(2n)!}\right]^2-
- \left[x\prod_{k=1}^{\infty}
- \left(1+\frac{x^{2}}{k^{2}\pi^{2}}\right)
- \right]^2
- \]}[x=1][3] \info{sum},\quad\info{prod}.
+ \frac{x^{2n}}{(2n)!}
+ \right]^2-
+ \left[x\prod_{k=1}^{\infty}
+ \left(1+\frac{x^{2}}{k^{2}\pi^{2}}\right)
+ \right]^2
+ \]}[x=1][3] \info{sum},\quad \info{prod}.
Nearly right. Obviously the product converges only slowly which is
where the error comes from (see the discussion in §\ref{sec:settingsInfiniteSumsProds},
@@ -4235,7 +4270,7 @@
where we needed the extra rounding setting \texttt{P+=3} and $350$
factors to get a correct 3-figure value). The point of the example
is to show the information command being used for both sum and product
-in the one evaluation. One does not exclude the other.
+in the one evaluation. One does not exclude the other.
\subsection{Suppressing the descriptor: \texttt{\textbackslash nmcInfo{*}}}
@@ -4249,19 +4284,21 @@
\end{verbatim}
$\Longrightarrow$ \eval{$
\sum_{k=0}^{\infty}\binom \alpha k x^k
- $}[x=1/2,\alpha=3],
-requiring $ \info*{sum}-1 $ additions. (Four terms added, therefore $3$ additions.)
+ $}[x=1/2,\alpha=3],
+ requiring $ \info*{sum}-1 $ additions. (Four terms summed, therefore $3$ additions.)
\subsection{Errors}
Should the \emph{wrong} argument be used in the \verb`\nmcInfo` command,
-no harm is done:
+no harm is done:
\begin{verbatim}
\eval{$
\sum_{k=0}^{\infty}\binom \alpha k x^k
- $}[x=1/2,\alpha=3], \ \info{prod}
+ $}[x=1/2,\alpha=3], \ \info{prod}
\end{verbatim}
-$\Longrightarrow$ \eval{$ \sum_{k=0}^{\infty}\binom \alpha k x^k $}[x=1/2,\alpha=3],\ \info{prod}.\medskip{}
+$\Longrightarrow$ \eval{$
+ \sum_{k=0}^{\infty}\binom \alpha k x^k
+ $}[x=1/2,\alpha=3], \ \info{prod}.\medskip{}
$119$ \emph{factors}? The information command is remembering a previous
result, the last time \verb`prod` was used as its argument. Changing
@@ -4268,13 +4305,15 @@
the argument from \verb`prod` to \verb`sum` reveals the correct
number of \emph{terms}.
-Should a non-existent argument be used, an error message is generated:
+Should a non-existent argument be used, an error message is generated:
\begin{verbatim}
\eval{$
\sum_{k=0}^{\infty}\binom \alpha k x^k
$}[x=1/2,\alpha=3], \\ \info{Fred}
\end{verbatim}
-$\Longrightarrow$ \eval{$ \sum_{k=0}^{\infty}\binom \alpha k x^k $}[x=1/2,\alpha=3],\\ \info{Fred}
+$\Longrightarrow$ \eval{$
+ \sum_{k=0}^{\infty}\binom \alpha k x^k
+ $}[x=1/2,\alpha=3], \\ \info{Fred}
\subsection{\texttt{view} setting}
@@ -4282,16 +4321,14 @@
of \verb`\nmcEvaluate`. Most of the settings available for \verb`\eval`
are also available for \verb`\info` but of these only one seems relevant:
the \verb`dbg` setting. However, rather than use the obscure \verb`dbg=<integer>`
-(which is possible), it suffices to enter \verb`view` in this argument:
+(which is possible), it suffices to enter \verb`view` in this argument:
\begin{centred}
-\verb`\info[view]{}` $\Longrightarrow$ \info[view] {}
+\verb`\info[view]{}` $\Longrightarrow$ \info[view]{}
\end{centred}
The result is a display of all the current values of all the `infinite'
processes available. All such values are initialized to $0$. (Further
-processes \verb`iter` and \verb`solve` become relevant if the \verb`numerica-plus`
-package is used; \verb`deriv` and \verb`integ` become relevant if
-the \verb`numerica-calculus` package, currently under development,
-is used.)
+processes \verb`iter` and \verb`solve` become relevant if the \texttt{numerica-plus}
+package is used.)
\section{User-defined macros: \texttt{\textbackslash nmcMacros}}
@@ -4304,21 +4341,22 @@
long list of macros, each containing the value of a physical constant.} approached me with a similar problem. Suppose one has defined a macro
to contain a value, say
\begin{itemize}
-\item \verb`\def\myvalue{0.35}`, or
-\item \verb`\newcommand\myvalue{0.35}`, or
-\item \verb`\NewDocumentCommand\myvalue{}{0.35}`, if you're using \verb`xparse`.
+\item \verb`\def\myvalue{0.35}`, or
+\item \verb`\newcommand\myvalue{0.35}`, or
+\item \verb`\NewDocumentCommand\myvalue{}{0.35}`, if you're using \verb`xparse`.
\end{itemize}
(If you're using the document processor \LyX{} then there is good reason
to prefer \verb`\gdef` to define your macro, \verb`\gdef\myvalue{0.35}`;
see Chapter~\ref{chap:LyX}). After one of these commands, \verb`\myvalue`
-is now known to \LaTeX , but it is not known to \verb`numerica`.
-The quantities \verb`numerica` \emph{does }know about are variables
+is now known to \LaTeX , but it is not known to \texttt{numerica}.
+The quantities \texttt{numerica} \emph{does }know about are variables
in the vv-list of an \verb`\eval` command, and those \LaTeX{} (and
-\verb`amsmath` and \verb`mathtools`) commands used for writing mathematical
-expressions. These quantities are stored in \verb`numerica` in structures
-called property lists. Since \verb`\myvalue` is not recorded in these
-lists yet, putting \verb`x=\myvalue` in the formula or vv-list of
-an \verb`\eval` command will produce an `Unknown token' error message:
+\texttt{amsmath} and \texttt{mathtools}) commands used for writing
+mathematical expressions. These quantities are stored in \texttt{numerica}
+in structures called property lists. Since \verb`\myvalue` is not
+recorded in these lists yet, putting \verb`x=\myvalue` in the formula
+or vv-list of an \verb`\eval` command will produce an `Unknown token'
+error message:
\begin{verbatim}
\NewDocumentCommand \myvalue {} {0.35}
\eval{ \myvalue }
@@ -4326,19 +4364,19 @@
$\Longrightarrow$ \NewDocumentCommand \myvalue {} {0.35}
\eval{ \myvalue }
-With version 2 of \verb`numerica` a command is now available, \verb`\nmcMacros`,
+With version 2 of \texttt{numerica} a command is now available, \verb`\nmcMacros`,
to register macros and their values with the property lists used internally
-by \verb`numerica`. (This command was not available in version 1.)
+by \texttt{numerica}. (This command was not available in version 1.)
The macro must have been defined earlier in the document or in a supporting
-package.
+package.
The basic usage is simple. If you have a list of macros you wish to
make available to \verb`\nmcEvaluate`, enter them in a comma list
-in the mandatory argument of \verb`\nmcMacros`:
+in the mandatory argument of \verb`\nmcMacros`:
\begin{lyxcode}
\textbackslash nmcMacros\{~\textbackslash macro1,~\textbackslash macro2,~\ldots ~\}
\end{lyxcode}
-There is an equivalent short-name form of the command, \verb`\macros`.
+There is an equivalent short-name form of the command, \verb`\macros`.
Multiple \verb`\nmcMacros` commands can be used in a document. If
the command is placed in the preamble (\emph{after} the definition
@@ -4346,38 +4384,38 @@
are available throughout the document, otherwise they are available
from the position of the \verb`\macros` statement. However, macros
do not need to be defined in your current document provided they are
-defined and accessible from elsewhere – for example from a loaded
+defined and accessible from elsewhere -- for example from a loaded
\LaTeX{} package. But always an \verb`\nmcMacros` command is required
-to `register' them with \verb`numerica` for use in an \verb`\eval`
-command.
+to `register' them with \texttt{numerica} for use in an \verb`\eval`
+command.
\subsection{What can be stored in a macro?}
Generally a user-defined macro will store a number. This macro might
-well be defined in an external package – for example the \verb`mandi`
+well be defined in an external package -- for example the \texttt{mandi}
package defines a large number of macros containing the values of
physical constants, some fundamental like the speed of light, others
-contingent like the earth–moon distance. If the \verb`mandi` package
+contingent like the earth--moon distance. If the \texttt{mandi} package
is loaded then writing, for instance,
\begin{verbatim}
\macros{ \electronmassprecisevalue,
\protonmassprecisevalue }
\end{verbatim}
-will make these two macros available for use in \verb`numerica`.
-One could then write in the vv-list of an \verb`\eval` command
+will make these two macros available for use in \texttt{numerica}.
+One could then write in the vv-list of an \verb`\eval` command
\begin{verbatim}
-m_e=\electronmassprecisevalue,m_p=\protonmassprecisevalue
+ m_e=\electronmassprecisevalue,m_p=\protonmassprecisevalue
\end{verbatim}
which would allow (among other things) calculation of the mass ratio
$m_{p}/m_{e}$ of proton to electron. (The length of name of some
-of the macros in the \verb`mandi` package has a pedagogical purpose,
+of the macros in the \texttt{mandi} package has a pedagogical purpose,
but makes them unwieldy for direct use in mathematical expressions.)
\subsubsection{Macros containing formulas }
Numbers are not the only quantities that can be stored in a macro
-for use in \verb`numerica`. In fact any mathematical expression that
-can be \verb`\eval`-uated can be stored in a macro:
+for use in \texttt{numerica}. In fact any mathematical expression
+that can be \verb`\eval`-uated can be stored in a macro:
\begin{verbatim}
\NewDocumentCommand \mysumC {}
{ \sum_{n=1}^{100}1/n - \ln 100 }
@@ -4389,11 +4427,11 @@
\macros{ \mysumC }
\eval{$ \mysumC $}[4], \medskip{}
-\noindent (to be compared with Euler's constant \eval{$ \gamma $}[4]
-– obviously many more terms are needed). The \verb`\eval` command
-wraps around math delimiters in the example. Hence the result is presented
-in the form \emph{formula=result}. In that presentation, note how
-\verb`\mysumC` displays as the formula it contains.
+\noindent (to be compared with Euler's constant $\eval{\gamma}[4]$
+-- obviously many more terms are needed). The \noindent\verb`\eval`
+command wraps around math delimiters in the example. Hence the result
+is presented in the form \emph{formula=result}. In that presentation,
+note how \noindent\verb`\mysumC` displays as the formula it contains.
\paragraph{The essential space: }
@@ -4400,14 +4438,14 @@
But the critical thing to notice in the example is \emph{the space
preceding }\verb`\sum`\emph{ in the definition of }\verb`\mysumC`.
When a formula starts with an expandable token, \emph{this space is
-essential}. For macros to register successfully with \verb`numerica`,
+essential}. For macros to register successfully with \texttt{numerica},
the first character in their definition must be \emph{un}expandable.
Thus a digit is fine: storing a number in a macro is straightforward
and you don't need to fuss about such niceties. But a control sequence
like \verb`\sum` does expand (to $\sum$ ). If it is the initial
token of the formula, then it will cause a possibly obscure error
-– see §\ref{subsec:supplMacrosErrors} – unless preceded by an unexpandable
-token. Hence the space before \verb`\sum` in the \verb`\NewDocumentCommand`
+-- see §\ref{subsec:supplMacrosErrors} -- unless preceded by an
+unexpandable token. Hence the space before \verb`\sum` in the \verb`\NewDocumentCommand`
statement. (On the other hand the spacing in the \verb`\macros` statement
is purely aesthetic.)
@@ -4414,13 +4452,13 @@
When using macros from another package, this is a matter to be aware
of. If the macros contain only numbers, there should be no problem,
but if they contain more complicated expressions, the absence of an
-initial space could make them unusable in \verb`numerica`.
+initial space could make them unusable in \texttt{numerica}.
\subsubsection{Vv-list}
In the example it would be nice to be able to vary the number of terms
summed. This is easily done by using a vv-list in the \verb`\macros`
-statement:
+statement:
\begin{verbatim}
\NewDocumentCommand \mysumN {}
{ \sum_{n=1}^{N}1/n - \ln N }
@@ -4432,15 +4470,16 @@
\macros{ \mysumN }[N=150]
\eval{$ \mysumN $}.\medskip{}
-\noindent \verb`numerica` needs a definite value to store; it does
-not store the formula as such. To give \verb`\mysumN` a definite
-value, give the variable \verb`N` a value. This is done in the vv-list
-added to the \verb`\macros` statement: \verb`N=150`. In this way
-a definite value is stored in \verb`numerica` against the macro \verb`\mysumN`.
-The definition of the macro is unaffected. If a new value is given
-to \verb`N` in the \verb`\macros` statement (which is the point
-of using a variable), the old value is overwritten and the new value
-is used in subsequent calculations.
+\noindent\texttt{numerica} needs a definite value to store; it does
+not store the formula as such. To give \noindent\verb`\mysumN` a
+definite value, give the variable \noindent\verb`N` a value. This
+is done in the vv-list added to the \noindent\verb`\macros` statement:
+\noindent\verb`N=150`. In this way a definite value is stored in
+\texttt{numerica} against the macro \noindent\verb`\mysumN`. The
+definition of the macro is unaffected. If a new value is given to
+\noindent\verb`N` in the \noindent\verb`\macros` statement (which
+is the point of using a variable), the old value is overwritten and
+the new value is used in subsequent calculations.
\subsection{Seeing what macros are available}
@@ -4447,14 +4486,14 @@
Perhaps your document has a number of \verb`\nmcMacros` statements
scattered through it and you want to remind yourself of what exactly
has been stored. \verb`\nmcMacros` has the \verb`view` setting for
-this purpose. Writing
+this purpose. Writing
\begin{centred}
-\verb`\macros[view]{}` $\Longrightarrow$ \macros[view]{}
+\verb`\macros[view]{}` $\Longrightarrow$\macros[view]{}
\end{centred}
-produces a list of all macros registered with \verb`numerica` and
-their values, as you can see.
+produces a list of all macros registered with \texttt{numerica} and
+their values, as you can see.
-If the braced argument is not empty, the display is slightly modified:
+If the braced argument is not empty, the display is slightly modified:
\begin{verbatim}
\def\mydef{ \sin(m\pi/n) }
\newcommand\mynewcmd{ \cos(m\pi/n) }
@@ -4464,40 +4503,40 @@
\newcommand\mynewcmd{ \cos(m\pi/n) }
\macros[view]{ \mydef,\mynewcmd }[m=3,n=18]
-\noindent \verb`\mydef` and \verb`\mynewcmd` have been added to
-those available for use in \verb`numerica`.
+\noindent\noindent\verb`\mydef` and \noindent\verb`\mynewcmd` have
+been added to those available for use in \texttt{numerica}.
\subsubsection{Freeing macros from storage}
-Rather than cluttering \verb`numerica`'s property lists with no-longer-needed
+Rather than cluttering \texttt{numerica}'s property lists with no-longer-needed
macros, it is possible to remove them from there with the \verb`free`
setting. This has no effect on the \LaTeX{} definition of the macro.
-It merely `de-registers' the macro with \verb`numerica`.
+It merely `de-registers' the macro with \texttt{numerica}.
\begin{centred}
\verb`\macros[free,view]{ \mysumC }` $\Longrightarrow$ \macros[free,view]{ \mysumC }
\end{centred}
-If you want to free \emph{all} macros registered with \verb`numerica`
+If you want to free \emph{all} macros registered with \texttt{numerica}
use an empty main argument with the \verb`free` setting. For an example,
see just below.
\subsubsection{Counting how many macros are available}
-You can count how many macros are currently registered with \verb`numerica`
-by starring the \verb`\nmcMacros`~command:
+You can count how many macros are currently registered with \texttt{numerica}
+by starring the \verb`\nmcMacros`~command:
\begin{centred}
-\verb`\macros*{}` $\Longrightarrow$ \macros*{}.
+\verb`\macros*{}` $\Longrightarrow$ \macros*{}
\end{centred}
If the braced argument is not empty, the list of macros it contains
-will be added to those registered with \verb`numerica` and included
+will be added to those registered with \texttt{numerica} and included
in the overall count.
Note that the \verb`view` setting prevails over starring if both
-are used.
+are used.
The star can also be used with the \verb`free` setting. As mentioned
-above, if the main argument is empty, then \emph{all} macros are freed:
+above, if the main argument is empty, then \emph{all} macros are freed:
\begin{centred}
-\verb`\macros*[free]{}` $\Longrightarrow$ \macros*[free]{ }
+\verb`\macros*[free]{}` $\Longrightarrow$\macros*[free]{}
\end{centred}
\subsection{Errors}
@@ -4504,34 +4543,32 @@
\label{subsec:supplMacrosErrors}If a macro is used in a \verb`\macros`
statement and the macro has not been defined in the document or a
-supporting package it will cause an error:
-\begin{verbatim}
- \macros{ \mymacro }
-\end{verbatim}
-$\Longrightarrow$ \macros{\mymacro }
-
+supporting package it will cause an error:
+\begin{centred}
+\verb`\macros{ \mymacro }` $\Longrightarrow$ \macros{ \mymacro }
+\end{centred}
\noindent As noted in the introduction to this section, an undefined
-macro used in an \verb`\eval`-uation will cause an `Unknown token'
-message in \verb`numerica`. The solution in this and the preceding
-case is (obviously) to define the macro.
+macro used in an \noindent\verb`\eval`-uation will cause an `Unknown
+token' message in \texttt{numerica}. The solution in this and the
+preceding case is (obviously) to define the macro.
If a macro contains a formula which begins with an expandable token
and a preceding space is omitted (see above), then entering that macro
-in a \verb`\macros` statement to register it with \verb`numerica`
-will generally cause a puzzling error:
+in a \verb`\macros` statement to register it with \texttt{numerica}
+will generally cause a puzzling error:
\begin{verbatim}
\newcommand\mysin{\sin(\pi/7)}
\macros{ \mysin }
\end{verbatim}
-$\Longrightarrow$ \newcommand\mysin{\sin(\pi/7)}
+$\Longrightarrow$ \newcommand\mysin{\sin(\pi/7)}
\macros{ \mysin }
-\noindent The \verb`\protect` seems to be plucked from nowhere. In
-fact it comes from the expansion of \verb`\sin`. If \verb`\sum`
+\noindent The \noindent\verb`\protect` seems to be plucked from nowhere.
+In fact it comes from the expansion of \noindent\verb`\sin`. If \noindent\verb`\sum`
had been the first token in the macro definition, again with no preceding
-space, then \verb`\protect` would have been replaced by the even
-more puzzling \verb`\DOTSB`. The solution is to insert a space as
-the first token in the macro definition.
+space, then \noindent\verb`\protect` would have been replaced by
+the even more puzzling \noindent\verb`\DOTSB`. The solution is to
+insert a space as the first token in the macro definition.
If a macro is defined but the \verb`\macros` statement is overlooked,
and the macro is used in an \verb`\eval`-uation, it will generate
@@ -4539,20 +4576,21 @@
If your macro stores a formula with variables, and you forget to give
those variables values in the \verb`\macros` statement that will
-produce a message:
+produce a message:
\begin{verbatim}
\def\mysumk{ \sum_{n=1}^k n }
\macros{ \mysumk }
\end{verbatim}
-$\Longrightarrow$ \def\mysumk{ \sum_{n=1}^k n }
+$\Longrightarrow$ \def\mysumk{ \sum_{n=1}^k n }
\macros{ \mysumk }
\noindent The `where' part of the message is specific in this case,
-but is generally `\verb`\nmcMacros` command'.
+but is generally `\noindent\verb`\nmcMacros` command'.
-And of course there can be `all the usual suspects' discussed at
-§\ref{sec:evalErrors} in the evaluation of the vv-list or the formula.
+And of course there can be `all the usual suspects' discussed at §\ref{sec:evalErrors}
+in the evaluation of the vv-list or the formula.
+\noindent{}%
\noindent\begin{minipage}[t]{1\columnwidth}%
\begin{shaded}%
@@ -4560,11 +4598,11 @@
\label{subsec:supplMacrosDisplay}As shown in earlier examples, macros
display as their content. Thus \verb`\mysumC` displayed as $\sum_{n=1}^{100}1/n-\ln100$.
-But once a macro is known to \LaTeX{} (not necessarily to \verb`numerica`)
+But once a macro is known to \LaTeX{} (not necessarily to \cprotect\texttt{numerica})
it can be used as a variable name. This has the same potential for
abuse as noted earler for multi-token variables (§\ref{subsec:evalDon't-do-this!}).
In the following example note that there is no \verb`\macros` statement.
-It suffices for the macro to be known to \LaTeX .
+It suffices for the macro to be known to \LaTeX .
\begin{verbatim}
\def\mymac{1}
\eval[vvi=\,???]{$ \mymac+\mymac $}[\mymac=2]
@@ -4572,20 +4610,20 @@
$\Longrightarrow$ \def\mymac{1}
\eval[vvi=\,???]{$ \mymac+\mymac $}[\mymac=2]
-The value assigned to a variable name – in this case \verb`\mymac`
-– by \verb`numerica` for \cprotect\emph{calculational} purposes and
-how that variable name \cprotect\emph{displays} in \LaTeX{} are two
-separate things. One relies on the user not to do something deliberately
-deceptive.\end{shaded}%
+The value assigned to a variable name -- in this case \verb`\mymac`
+-- by \cprotect\texttt{numerica} for \cprotect\emph{calculational}
+purposes and how that variable name \cprotect\emph{displays} in \LaTeX{}
+are two separate things. One relies on the user not to do something
+deliberately deceptive.\end{shaded}%
\end{minipage}
\subsection{Rounding value}
-\label{subsec:supplMacrosRounding}Values are stored to $16$ significant
-figures (if available). In most cases appending a rounding value to
-a \verb`\macros` statement has no effect on the value stored. In
-the following example note the \verb`o` setting, meaning the sine
-reads angles in degrees:
+\noindent\label{subsec:supplMacrosRounding}Values are stored to
+$16$ significant figures (if available). In most cases appending
+a rounding value to a \noindent\verb`\macros` statement has no effect
+on the value stored. In the following example note the \noindent\verb`o`
+setting, meaning the sine reads angles in degrees:
\begin{verbatim}
\NewDocumentCommand\testi{}{ \sin 60 }
\NewDocumentCommand\testii{}{ \sin 60 }
@@ -4600,7 +4638,7 @@
\macros[view]{}
\noindent Despite the different rounding values the same $16$ figures
-are stored in both \verb`\testi` and \verb`\testii`.
+are stored in both \noindent\verb`\testi` and \noindent\verb`\testii`.
For the \verb`\eval` command, rounding values specify how results
are \emph{displayed}. The rounding value matters only \emph{after},
@@ -4612,7 +4650,7 @@
but most of them will be `wrong' since the infinite sum or product
has stopped early, after only a finite number of terms or factors.
Exactly how many of the first few figures are correct depends on the
-rounding value. An example may clarify the matter.
+rounding value. An example may clarify the matter.
\begin{verbatim}
\macros[free]{}
\def\zetaiii{ \sum_{n=1}^\infty 1/n^3 }
@@ -4621,7 +4659,7 @@
\macros[view]{ \zetaiii }[6]
\info{sum}
\end{verbatim}
-$\Longrightarrow$ \macros[free]{}
+$\Longrightarrow$ \macros[free]{}
\def\zetaiii{ \sum_{n=1}^\infty 1/n^3 }
\macros[view]{ \zetaiii }[3]
\info{sum}
@@ -4647,8 +4685,8 @@
or the viscosity of water, rather than having to enter them in the
vv-list for each calculation. Or a parameter might be held constant
for a particular problem or class of problems where other variables
-change – for example triangles of constant perimeter but varying sides.
-This is the purpose of the \verb`\nmcConstants` command.
+change -- for example triangles of constant perimeter but varying
+sides. This is the purpose of the \verb`\nmcConstants` command.
The symbols used to denote constants are subject to exactly the same
constraints and freedoms as the symbols used to denote variables.
@@ -4657,31 +4695,31 @@
combinations like the Rydberg constants \verb`R_\infty` or \verb`R_{\mathrm{H}}`
from atomic physics, or \verb`\mu_0` and \verb`\epsilon_0` used
to denote the permeability and permittivity of free space, or personal
-constants like \verb`total` of no wider significance. \verb`numerica`
-handles all these different forms of constant with the command \verb`\nmcConstants`:
+constants like \verb`total` of no wider significance. \texttt{numerica}
+handles all these different forms of constant with the command \verb`\nmcConstants`:
\begin{verbatim}
\nmcConstants{ const-n=value-n, ... ,
const2=value2, const1=value1 }
\end{verbatim}
-This is the simplest use – each constant is assigned a (numerical)
+This is the simplest use -- each constant is assigned a (numerical)
value. But it is easy to envisage situations where it would be convenient
to have a constant with value $1/\sqrt{2\pi}$ say, or another with
value $e^{\tfrac{\pi}{2}}$, and so on. That is easy: simply put the
-expession for the value on the right:
+expession for the value on the right:
\begin{verbatim}
\constants{ a=1/\sqrt{2\pi},b=e^{\tfrac\pi2} }
\end{verbatim}
-Or the values could be expressions depending on parameters:
+Or the values could be expressions depending on parameters:
\begin{verbatim}
\constants{ s=\tfrac12(a+b+c) }[a=3,b=5,c=7]
\end{verbatim}
-Some constants might depend on earlier constants in the list:
+Some constants might depend on earlier constants in the list:
\begin{verbatim}
\constants{ A=\sqrt{s(s-a)(s-b)(s-c),
s=\tfrac12(a+b+c) }[a=3,b=5,c=7]
\end{verbatim}
Or the values could involve an `infinite' process, requiring a rounding
-number:
+number:
\begin{verbatim}
\constants{ \zeta=\sum_{n=1}^\infty(1/n^k) }[k=4][5]
\end{verbatim}
@@ -4710,13 +4748,13 @@
is going to involve not only this mapping from multi- to single tokens
but the evaluation of a long vv-list. In that case it seems better
to make the default behaviour replacement of one constant list by
-another, rather than appending them.
+another, rather than appending them.
\subsection{Adding constants to a list}
Despite the default behaviour, there will be occasions when you want
to add a new constant or constants to the current list. This is easily
-done with the \verb`add` setting. For instance,
+done with the \verb`add` setting. For instance,
\begin{verbatim}
\nmcConstants[add]{ \sigma=5.67\times10^{-8},
k_B = 1.381\times10^{-23} }
@@ -4739,7 +4777,7 @@
in the vv-list of the \verb`\eval` command, and its well-known reciprocal
(close to $137)$ in the main argument. Note that the constants do
not need to be entered in the vv-list of the \verb`\eval` command.
-Their values are available from the \verb`\constants` statements.
+Their values are available from the \verb`\constants` statements.
\begin{verbatim}
\constants{ c=2.99792458\times10^{8},
h=6.62607015\times10^{-34},
@@ -4748,18 +4786,18 @@
{ \epsilon_0=8.854187817\times10^{-12} }
\eval{$ 1/\alpha $}[\alpha=e^2/2\epsilon_0hc]
\end{verbatim}
-$\Longrightarrow$ \constants{ c=2.99792458\times10^{8},
+$\Longrightarrow$ \constants{ c=2.99792458\times10^{8},
h=6.62607015\times10^{-34},
e=1.602176634\times10^{-19} }
- \constants[view,add]{
- \epsilon_0=8.854187817\times10^{-12} }
+ \constants[view,add]
+ { \epsilon_0=8.854187817\times10^{-12} }
\eval{$ 1/\alpha $}[\alpha=e^2/2\epsilon_0hc].
The \verb`view` setting produces a now familiar kind of display.
It shows that the three-token \verb`\epsilon_0` (the control sequence
\verb`\epsilon`, the underscore \verb`_` and the digit \verb`0`)
-has been replaced by \verb`\nmc_q` – which may look as if it is also
-three tokens but is in fact a single control sequence.
+has been replaced by \verb`\nmc_q` -- which may look as if it is
+also three tokens but is in fact a single control sequence.
\subsubsection{Example 2: local constants}
@@ -4779,7 +4817,7 @@
The question was really about understanding these laws and how to
think with them. Here, $s$ is the distance travelled in time $t,$
with initial speed $u$ at $t=0$, speed $v$ at time $t$, and constant
-acceleration $a$ – a deceleration in this case.
+acceleration $a$ -- a deceleration in this case.
The given data provide our constants: distance $x=1$ metre, initial
speed $u=1000*50/(60*60)=(10/36)*50$ metres per second, final speed
@@ -4790,7 +4828,7 @@
kilograms, and a test mass, $M$ say, which we will leave as a variable.
But dealing with weight, we will need the acceleration due to gravity.
For the kind of rough estimating we are doing, $g=10$ metres per
-second per second will be an adequate approximation.
+second per second will be an adequate approximation.
\begin{verbatim}
\constants{ x=1,v=0,u=(10/36)50,m=5,g=10 }
\end{verbatim}
@@ -4806,7 +4844,7 @@
western adult male (but is doubtless a considerable underestimate
now). Hence the test force is $Mg$. Let's do the calculations. (I
have altered the \verb`\constants` statement to allow for a later
-comparison with the effect of a small increase in speed.)
+comparison with the effect of a small increase in speed.)
\begin{verbatim}
\constants{ x=1,u=(10/36)U,m=5,g=10 }[U=50]
\eval{$ mu^2/2x $}[0], \par
@@ -4817,14 +4855,14 @@
\eval{$ Mg $}[M=70].
The force required to hold on to the baby is noticeably less than
-that required to lift a $70$~kg person – in fact about the same
+that required to lift a $70$~kg person -- in fact about the same
as that needed to lift a $50$~kg person. But we have ignored the
-force experienced by the mothers forearms – perhaps doubling $m$
+force experienced by the mothers forearms -- perhaps doubling $m$
(baby plus forearms) would give a better estimate of the force she
experiences. In that case $mu^{2}/2x$ obviously doubles and the total
-force required by the woman to retain her baby – now $964$ newtons
-– is significantly more than that required to lift a $70$~kg person.
-I think it almost certain that the baby is torn from her arms.
+force required by the woman to retain her baby -- now $964$ newtons
+-- is significantly more than that required to lift a $70$~kg person.
+I think it almost certain that the baby is torn from her arms.
What difference does increasing the speed to 60 km/hr make?
\begin{verbatim}
@@ -4833,19 +4871,19 @@
\eval{$ Mg $}[M=70].
\end{verbatim}
$\Longrightarrow$ \constants{ x=1,u=(10/36)U,m=5,g=10 }[U=60]
- \eval{$ mu^2/2x $}[0], \par
+ \eval{$ mu^2/2x $}[1], \par
\eval{$ Mg $}[M=70].
Now the force of baby alone is comparable to that required to lift
a $70$ kg person. Including the woman's forearms in $m$, doubling
-$m$ say, will result in a force twice as great – like that required
+$m$ say, will result in a force twice as great -- like that required
to lift two $70$~kg people or one $140$~kg person. There is no
-chance of the woman holding on to her baby. The force is too great.
+chance of the woman holding on to her baby. The force is too great.
\subsubsection{Example 3: macros and constants}
Constants can depend on previously defined and registered user macros.
-Suppose I have defined two macros
+Suppose I have defined two macros
\begin{verbatim}
\NewDocumentCommand\electronmassprecisevalue {}
{9.1093837015\times10^{-31}}
@@ -4852,17 +4890,17 @@
\NewDocumentCommand\protonmassprecisevalue {}
{1.672621898\times10^{-27}}
\end{verbatim}
-(I have taken both the names and the values from the \verb`mandi`
+(I have taken both the names and the values from the \texttt{mandi}
package.) The long explicit names of the macros has a pedagogic purpose,
but they are too cumbersome to use in calculations. For that purpose
we need, first, a \verb`\macros` statement registering the two macros
-with \verb`numerica`, and then a \verb`\constants` statement like
+with \texttt{numerica}, and then a \verb`\constants` statement like
\begin{verbatim}
\nmcConstants{ m_e=\electronmassprecisevalue,
m_p=\protonmassprecisevalue }
\end{verbatim}
With that \verb`m_e` and \verb`m_p` could be entered in formulas,
-taking the values contained in the macros. Let's do it:
+taking the values contained in the macros. Let's do it:
\begin{verbatim}
\NewDocumentCommand\electronmassprecisevalue {}
{9.1093837015\times10^{-31}}
@@ -4874,15 +4912,15 @@
m_p=\protonmassprecisevalue }
\eval{$ m_p/m_e $}
\end{verbatim}
-$\Longrightarrow$ \NewDocumentCommand\electronmassprecisevalue {}
+$\Longrightarrow$ \NewDocumentCommand\electronmassprecisevalue {}
{9.1093837015\times10^{-31}}
-\NewDocumentCommand\protonmassprecisevalue {}
+ \NewDocumentCommand\protonmassprecisevalue {}
{1.672621898\times10^{-27}}
-\nmcMacros{ \electronmassprecisevalue,
+ \nmcMacros{ \electronmassprecisevalue,
\protonmassprecisevalue }
-\nmcConstants{ m_e=\electronmassprecisevalue,
+ \nmcConstants{ m_e=\electronmassprecisevalue,
m_p=\protonmassprecisevalue }
-\eval{$ m_p/m_e $},
+ \eval{$ m_p/m_e $},
\noindent the familiar mass ratio of proton and electron.
@@ -4889,7 +4927,7 @@
\subsection{Viewing, counting constants}
To see all constants currently `in play', use the \verb`view` setting
-in the \verb`\constants` command. The main argument can be empty,
+in the \verb`\constants` command. The main argument can be empty,
\begin{centred}
\verb`\constants[view]{}` $\Longrightarrow$ \constants[view]{}
\end{centred}
@@ -4896,13 +4934,13 @@
or contain a list of constants. In the latter case, the display is
of the above form but featuring the constants of the new list or,
if the \verb`add` setting is used, featuring the joined lists, old
-and new:
+and new:
\begin{centred}
\verb`\constants[view,add]{X=42}` $\Longrightarrow$ \constants[view,add]{X=42}
\end{centred}
To count how many constants are currently in play, star the \verb`\constants`
command. The number will depend on whether the main argument is empty
-or not, and whether the \verb`add` setting is active:
+or not, and whether the \verb`add` setting is active:
\begin{centred}
\verb`\constants*{}` $\Longrightarrow$ \constants*{}.
\end{centred}
@@ -4911,11 +4949,11 @@
\subsection{Errors}
-When contemplating error messages from \verb`numerica` it needs to
-be remembered that \emph{multi-token} constants are added to the vv-list
-for every calculation. Hence an error may not be in the vv-list as
-indicated in the message but in the \verb`\constants` statement,
-specifically, the multi-token constants.
+When contemplating error messages from \texttt{numerica} it needs
+to be remembered that \emph{multi-token} constants are added to the
+vv-list for every calculation. Hence an error may not be in the vv-list
+as indicated in the message but in the \verb`\constants` statement,
+specifically, the multi-token constants.
\section{Saving and reusing results: \texttt{\textbackslash nmcReuse}}
@@ -4926,8 +4964,9 @@
which saves a result to a control sequence that can then be used elsewhere
in the document, expanding to the saved result. The control sequence
and its content are also saved to file, allowing the possibility of
-using the result in other documents.
+using the result in other documents.
+\noindent{}%
\noindent\begin{minipage}[t]{1\columnwidth}%
\begin{shaded}%
The \texttt{\textbackslash nmcReuse} command in version 2 of \texttt{numerica
@@ -4935,24 +4974,24 @@
the command was used in version 1. I found that I could bring \texttt{\textbackslash nmcReuse}
along with \texttt{\textbackslash nmcMacros} and \texttt{\textbackslash nmcConstants}
into the coding scheme used for \texttt{\textbackslash nmcEvaluate}
-and the reasons for doing so were too compelling. \end{shaded}%
+and the reasons for doing so were too compelling.\end{shaded}%
\end{minipage}
\subsection{Use of \texttt{\textbackslash nmcReuse}}
-As noted, all the supplementary commands share the syntax of the \verb`\eval`
-command, so that \verb`\nmcReuse` has an optional settings argument
-preceding a mandatory main argument, followed by two trailing optional
-arguments. \verb`\nmcReuse` does not use the last two. The command
-is used mainly in two ways:
+\noindent As noted, all the supplementary commands share the syntax
+of the \noindent\verb`\eval` command, so that \noindent\verb`\nmcReuse`
+has an optional settings argument preceding a mandatory main argument,
+followed by two trailing optional arguments. \noindent\verb`\nmcReuse`
+does not use the last two. The command is used mainly in two ways:
\begin{enumerate}
-\item {\small\verb`\nmcReuse{}`}{\small , which loads the saved control
-sequences from file, if not already loaded; and}{\small\par}
-\item {\small\verb`\nmcReuse{csname}`}{\small , which loads the saved
-control sequences from file, if not already loaded, assigns the latest
-result from }{\small\verb`\eval`}{\small{} to the control sequence
-}{\small\verb`\csname`}{\small , and saves }{\small\verb`\csname`}{\small{}
-to file.}{\small\par}
+\item {\small{\small\verb`\nmcReuse{}`}}{\small , which loads the
+saved control sequences from file, if not already loaded; and}{\small\par}
+\item {\small{\small\verb`\nmcReuse{csname}`}}{\small , which loads
+the saved control sequences from file, if not already loaded, assigns
+the latest result from }{\small{\small\verb`\eval`}}{\small{}
+to the control sequence }{\small{\small\verb`\csname`}}{\small ,
+and saves }{\small{\small\verb`\csname`}}{\small{} to file.}{\small\par}
\end{enumerate}
You may wish to put \verb`\nmcReuse{}` in the preamble of your document
(\emph{after} \verb`\usepackage{numerica}` of course). In that way,
@@ -4963,12 +5002,12 @@
Note that only the \emph{name}, \verb`csname`, of the control sequence
is supplied to \verb`\reuse`, not the control sequence (\verb`\csname`).
The name should be composed of letters only. If the name has already
-been defined in \LaTeX{} a \verb`numerica` error is produced, see
+been defined in \LaTeX{} a \texttt{numerica} error is produced, see
below §\ref{subsec:reuseDeletingOverwriting:}, although if you want
to save a \emph{new} value in a previously saved control sequence,
that can be done without invoking a message; see §\ref{subsec:reuseDeletingOverwriting:}.
-Once defined {\small with a }{\small\verb`\nmcReuse{csname}`}
+Once defined {\small with a }{\small{\small\verb`\nmcReuse{csname}`}}
command, \verb`\csname` becomes available for use elsewhere in the
document.
@@ -4978,7 +5017,7 @@
This is the \emph{full} result. It may include the vv-list; it may
include formatting elements; it may include math delimiters. Thus,
using \verb`\csname` in your document (after the command \verb`\nmcReuse{csname}`)
-may not be straightforward – simply writing \verb`\csname` where
+may not be straightforward -- simply writing \verb`\csname` where
you want the value it expands to, may produce a \LaTeX{} error and
halt compilation. You may have to write \verb`$ \csname $` or provide
some other math environment in order for the control sequence to display
@@ -5001,109 +5040,127 @@
\label{subsec:suppleReuse.nmc-file}The file that control sequences
are saved to has a filename composed of the document name with the
extension \verb`.nmc`. If your document is \verb`mydoc.tex` (so
-that the \LaTeX{} command {\small\verb`\jobname`} expands to
-\verb`mydoc`) then the file to which results are saved is \verb`mydoc.nmc`,
-located in the document directory.
+that the \LaTeX{} command {\small{\small\verb`\jobname expands to \verb`}}{\small{}
+mydoc`) then the file to which results are saved is }{\small{\small\verb`mydoc.nmc`}}{\small ,
+located in the document directory.}{\small\par}
-\verb`mydoc.nmc` is a comma list of pairs of the form \verb`\csname {value}`.
-Thus, the contents of \verb`mydoc.nmc` might be \texttt{\textbackslash csname1
-\{value1\},\textbackslash csname2 \{value2\},..., \textbackslash csname$n$
-\{value$n$\}}. If \verb`mydoc.nmc` does not already exist then it
-is created in the document directory, and \verb`\csname {value}`
-becomes its first element.
+{\small{\small\verb`mydoc.nmc`}}{\small{} is a comma list of
+pairs of the form }{\small{\small\verb`\csname {value}`}}{\small .
+Thus, the contents of }{\small{\small\verb`mydoc.nmc`}}{\small{}
+might be }{\small\texttt{\textbackslash csname1 \{value1\},\textbackslash csname2
+\{value2\},..., \textbackslash csname$n$ \{value$n$\}}}{\small .
+If }{\small{\small\verb`mydoc.nmc`}}{\small{} does not already
+exist then it is created in the document directory, and }{\small{\small\verb`\csname {value}`}}{\small{}
+becomes its first element.}{\small\par}
\paragraph{Editing the \texttt{.nmc} file externally}
-The \verb`.nmc` file is a text file and can be edited in a text editor.
-Thus it is possible to externally add control sequences and values
-to it provided the structure of the file is strictly adhered to. It
-is also possible to delete items from it or rename control sequences
-or edit values by the same mechanism. Editing the file externally
-like this, or renaming it, or transferring items from one \verb`.nmc`
-file to another, provides a way of using saved values in multiple
-documents.
+{\small The }{\small{\small\verb`.nmc`}}{\small{} file is a text
+file and can be edited in a text editor. Thus it is possible to externally
+add control sequences and values to it provided the structure of the
+file is strictly adhered to. It is also possible to delete items from
+it or rename control sequences or edit values by the same mechanism.
+Editing the file externally like this, or renaming it, or transferring
+items from one }{\small{\small\verb`.nmc`}}{\small{} file to
+another, provides a way of using saved values in multiple documents.}{\small\par}
\subsubsection{Messages}
-If a control sequence \verb`\csname` is already known to \LaTeX ,
-then writing \verb`\reuse` \verb`{csname}` will produce a \verb`numerica`
-message and the result of the latest \verb`\eval`-uation will \emph{not}
-be saved:
+{\small If a control sequence }{\small{\small\verb`\csname`}}{\small{}
+is already known to \LaTeX , then writing }{\small{\small\verb`\reuse`}}{\small{}
+}{\small{\small\verb`{csname}`}}{\small{} will produce a }\texttt{numerica}{\small{}
+message and the result of the latest }{\small{\small\verb`\eval`}}{\small -uation
+will }{\small\emph{not}}{\small{} be saved: }{\small\par}
\begin{verbatim}
\eval*{\sum_{n=1}^{10}n}\par
\reuse{sigma}
\end{verbatim}
-$\Longrightarrow$ \eval*{\sum_{n=1}^{10}n} \par \reuse{sigma}
+{\small$\Longrightarrow$ }{\small{} \eval*{\sum_{n=1}^{10}n}\par
+ \reuse{sigma}}{\small\par}
-If there is no result to save – perhaps an \verb`\eval`-uation produces
-an error message instead – then another message is generated:
+{\small If there is no result to save -- perhaps an }{\small{\small\verb`\eval`}}{\small -uation
+produces an error message instead -- then another message is generated: }{\small\par}
\begin{verbatim}
\eval*{1/0}\par
\reuse{oops}
\end{verbatim}
-$\Longrightarrow$ \eval*{1/0}\par
- \reuse{oops}
+{\small$\Longrightarrow$ }{\small{} \eval*{1/0}\par
+ \reuse{oops}}{\small\par}
\subsubsection{Deleting and renewing}
-\label{subsec:reuseDeletingOverwriting:}There may be occasions when
-you wish to change a previously saved value and yet, irritatingly,
+{\small\label{subsec:reuseDeletingOverwriting:}There may be occasions
+when you wish to change a previously saved value and yet, irritatingly,
the control sequence name will now be known to \LaTeX{} and so will
generate an `already known' message. If you choose a different name
for the control sequence to save the new value to, do you want the
-old name cluttering the \verb`.nmc` file? Deleting and renewing the
-values of saved control sequences are controlled by the settings \verb`delete`
-and \verb`renew`.
+old name cluttering the }{\small{\small\verb`.nmc`}}{\small{}
+file? Deleting and renewing the values of saved control sequences
+are controlled by the settings }{\small{\small\verb`delete`}}{\small{}
+and }{\small{\small\verb`renew`}}{\small .}{\small\par}
-Entering \verb`delete` in the settings option \emph{deletes} a control
-sequence and its value from the \verb`.nmc` file and undefines it
-in \LaTeX{} terms. Thus \verb`\reuse[delete]` \verb`{csname}` would
-delete \verb`\csname` and its value from the \verb`.nmc` file and
-undefine \verb`\csname`. If \verb`\csname` is not present in the
-file, nothing happens. Entering \verb`renew` replaces the value of
-a saved control sequence with a new value. If there is no such \emph{saved}
-control sequence but the control sequence is otherwise known to \LaTeX{}
-the `already defined' message will still be generated. This prevents
-giving control sequences like \verb`\sin`~or \verb`\frac` new meanings
-with the \verb`renew` setting.
+{\small Entering }{\small{\small\verb`delete`}}{\small{} in the
+settings option }{\small\emph{deletes}}{\small{} a control sequence
+and its value from the }{\small{\small\verb`.nmc`}}{\small{}
+file and undefines it in \LaTeX{} terms. Thus }{\small{\small\verb`\reuse[delete]`}}{\small{}
+}{\small{\small\verb`{csname}`}}{\small{} would delete }{\small{\small\verb`\csname`}}{\small{}
+and its value from the }{\small{\small\verb`.nmc`}}{\small{}
+file and undefine }{\small{\small\verb`\csname`}}{\small .
+If }{\small{\small\verb`\csname`}}{\small{} is not present in
+the file, nothing happens. Entering }{\small{\small\verb`renew`}}{\small{}
+replaces the value of a saved control sequence with a new value. If
+there is no such }{\small\emph{saved}}{\small{} control sequence but
+the control sequence is otherwise known to \LaTeX{} the `already defined'
+message will still be generated. This prevents giving control sequences
+like }{\small{\small\verb`\sin`}}{\small{} or }{\small{\small\verb`\frac`}}{\small{}
+new meanings with the }{\small{\small\verb`renew`}}{\small{}
+setting. }{\small\par}
\begin{itemize}
-\item \verb`\reuse[delete]{csname}` deletes \verb`\csname` and its value
-from the \verb`.nmc` file and from memory if present; otherwise has
-no effect;
-\item \verb`\reuse{csname}` (the default) saves the result of the latest
-\verb`\eval` command to \verb`\csname`, provided \verb`\csname`
-is not already defined; in that case a warning message is presented
-and the result is not saved;
-\item \verb`\reuse[renew]{csname}` behaves like the default mode unless
-\verb`\csname` is already a saved control sequence in the \verb`.nmc`
+\item {\small{\small\verb`\reuse[delete]{csname}`}}{\small{} deletes
+}{\small{\small\verb`\csname`}}{\small{} and its value from
+the }{\small{\small\verb`.nmc`}}{\small{} file and from memory
+if present; otherwise has no effect; }{\small\par}
+\item {\small{\small\verb`\reuse{csname}`}}{\small{} (the default)
+saves the result of the latest }{\small{\small\verb`\eval`}}{\small{}
+command to }{\small{\small\verb`\csname`}}{\small , provided
+}{\small{\small\verb`\csname`}}{\small{} is not already defined;
+in that case a warning message is presented and the result is not
+saved; }{\small\par}
+\item {\small{\small\verb`\reuse[renew]{csname}`}}{\small{} behaves
+like the default mode unless }{\small{\small\verb`\csname`}}{\small{}
+is already a saved control sequence in the }{\small{\small\verb`.nmc`}}{\small{}
file, in which case its previous value is replaced by the result of
-the latest \verb`\eval` command;
-\item if \verb`delete` and \verb`renew` are used together, whichever occurs
-second prevails.
+the latest }{\small{\small\verb`\eval`}}{\small{} command; }{\small\par}
+\item {\small if }{\small{\small\verb`delete`}}{\small{} and }{\small{\small\verb`renew`}}{\small{}
+are used together, whichever occurs second prevails. }{\small\par}
\end{itemize}
-In the following example, the first \verb`\reuse` deletes \verb`\suma`
-should it be present in the \verb`.nmc` file, the second saves the
-result, $55$, of the latest \verb`\eval`-uation (in fact an \verb`\eval*`-uation)
-and the third overwrites that saved value with the new value, $210$.
+{\small In the following example, the first }{\small{\small\verb`\reuse`}}{\small{}
+deletes }{\small{\small\verb`\suma`}}{\small{} should it be
+present in the }{\small{\small\verb`.nmc`}}{\small{} file, the
+second saves the result, $55$, of the latest }{\small{\small\verb`\eval`}}{\small -uation
+(in fact an }{\small{\small\verb`\eval*`}}{\small -uation)
+and the third overwrites that saved value with the new value, $210$. }{\small\par}
\begin{verbatim}
\reuse[delete]{suma}
- \eval*{\sum_{n=1}^{10}n} \par
+ \eval*{\sum_{n=1}^{10}n} \qquad
\reuse{suma}
- \eval*{\sum_{n=1}^{20}n} \par
+ \eval*{\sum_{n=1}^{20}n}
\reuse[renew]{suma}
\end{verbatim}
-$\Longrightarrow$ \reuse[delete]{suma}
-\eval*{\sum_{n=1}^{10}n} \par
-\reuse{suma}
-\eval*{\sum_{n=1}^{20}n} \par
-\reuse[renew]{suma}
+{\small$\Longrightarrow$ }{\small{} \reuse[delete]{suma}
+ \eval*{\sum_{n=1}^{10}n} \qquad
+ \reuse{suma}
+ \eval*{\sum_{n=1}^{20}n}
+ \reuse[renew]{suma}}{\small\par}
\subsubsection{Viewing what has been saved}
-\label{subsec:reuseSeeingSaved}It would be good in this example to
-see that the new value $210$ has in fact been saved. That is easy.
-Simply enter \verb`view` in the settings option of \verb`\nmcReuse`
-(I've removed the now unnecessary \verb`\par` tokens from the example.)
+{\small\label{subsec:reuseSeeingSaved}It would be good in this example
+to see that the new value $210$ has in fact been saved. That is easy.
+Simply enter }{\small{\small\verb`view`}}{\small{} in the settings
+option of }{\small{\small\verb`\nmcReuse`}}{\small{} (I've removed
+the now unnecessary }{\small{\small\verb`\par`}}{\small{} tokens
+from the example.) }{\small\par}
\begin{verbatim}
\reuse[delete]{suma}
\eval*{\sum_{n=1}^{10}n}
@@ -5111,321 +5168,361 @@
\eval*{\sum_{n=1}^{20}n}
\reuse[renew,view]{suma}
\end{verbatim}
-$\Longrightarrow$ \reuse[delete]{suma}
+{\small$\Longrightarrow$ }{\small{} \reuse[delete]{suma}
\eval*{\sum_{n=1}^{10}n}
\reuse[view]{suma}
- \eval*{\sum_{n=1}^{20}n}
- \reuse[renew,view]{suma}
+ \eval*{\sum_{n=1}^{20}n}
+ \reuse[renew,view]{suma}}{\small\par}
-\noindent First the original value $55$ was saved to \verb`\suma`
-but then the value was overwritten by the new value $210$.
+\noindent{\small First the original value $55$ was saved to }{\small\noindent{\small\verb`\suma`}}{\small{}
+but then the value was overwritten by the new value $210$.}{\small\par}
-The \verb`view` setting allows us to see how formatting is stored
-if the \emph{un}starred form of the \verb`\eval` command is used.
-In the following example, \verb`\eval` wraps around math delimiters:
+{\small The }{\small{\small\verb`view`}}{\small{} setting allows
+us to see how formatting is stored if the }{\small\emph{un}}{\small starred
+form of the }{\small{\small\verb`\eval`}}{\small{} command is
+used. In the following example, \verb`\eval` wraps around math delimiters: }{\small\par}
\begin{centred}
-\verb`\eval{$ 1+1 $} \reuse[view,renew]{two}` $\Longrightarrow$
-\eval{$ 1+1 $} \reuse[view,renew]{two}
+{\small{\small\verb`\eval{$ 1+1 $} \reuse[view,renew]{two}`}}{\small{}
+$\Longrightarrow$ }{\small\eval{$ 1+1 $} \reuse[view,renew]{two}}{\small\par}
\end{centred}
-The full \emph{formula=result} display has been captured in \verb`\two`
-along with the math delimiters. If a vv-list is also involved, things
-become messy (but informative):
+{\small The full }{\small\emph{formula=result}}{\small{} display has
+been captured in }{\small{\small\verb`\two`}}{\small{} along
+with the math delimiters. If a vv-list is also involved, things become
+messy (but informative): }{\small\par}
\begin{verbatim}
\eval{$ x+y $}[x=1,y=2]
\reuse[view,renew]{three}
\end{verbatim}
-$\Longrightarrow$ \eval{$ x+y $}[x=1,y=2]
- \reuse[view,renew]{three}
+{\small$\Longrightarrow$ }{\small{} \eval{$ x+y $}[x=1,y=2]
+ \reuse[view,renew]{three}}{\small\par}
-You may want to see \emph{all} saved control sequences. In that case
-use an \emph{empty} main argument: \verb`\nmcReuse[view]{}`. We now
-have enough saved control sequences to make this worthwhile:
+{\small You may want to see }{\small\emph{all}}{\small{} saved control
+sequences. In that case use an }{\small\emph{empty}}{\small{} main argument:
+}{\small{\small\verb`\nmcReuse[view]{}`}}{\small . We now have
+enough saved control sequences to make this worthwhile: }{\small\par}
\begin{verbatim}
\reuse[view]{}
\end{verbatim}
-$\Longrightarrow$ \reuse [view]{}
+{\small$\Longrightarrow$ }{\small{} \reuse[view]{}}{\small\par}
-\noindent (The \verb`\seven` that appears here is defined shortly.
-Its appearance \emph{before} definition is presumably due to \LaTeX{}
-making a number of passes when compiling this document.)
+\noindent{\small (The }{\small\noindent{\small\verb`\seven`}}{\small{}
+that appears here is defined shortly. Its appearance }{\small\emph{before}}{\small{}
+definition is presumably due to \LaTeX{} making a number of passes
+when compiling this document.)}{\small\par}
\subsubsection{Counting saved control sequences: \texttt{\textbackslash nmcReuse{*}}}
-Because \verb`\nmcReuse` uses the same machinery as \verb`\nmcEvaluate`,
-it has a starred form, \verb`\nmcReuse*`, which produces a purely
-numerical result (just like \verb`\eval*`, \verb`info*`, \verb`\macros*`
-and \verb`\constants*`). In this case, the number is the count of
-how many control sequences have been saved:
-\begin{centred}
-\verb`\reuse*{}` $\Longrightarrow$ \reuse*{ }.
-\end{centred}
+{\small Because }{\small{\small\verb`\nmcReuse`}}{\small{} uses
+the same machinery as }{\small{\small\verb`\nmcEvaluate`}}{\small ,
+it has a starred form, }{\small{\small\verb`\nmcReuse*`}}{\small ,
+which produces a purely numerical result (just like }{\small{\small\verb`\eval*`}}{\small ,
+}{\small{\small\verb`info*`}}{\small , }{\small{\small\verb`\macros*`}}{\small{}
+and }{\small{\small\verb`\constants*`}}{\small ). In this case,
+the number is the count of how many control sequences have been saved: }{\small\par}
+{\small{\small\verb`\reuse*{}`}}{\small{} $\Longrightarrow$
+}{\small\reuse*{}}{\small\par}
+
\subsection{\texttt{reuse} setting of \texttt{\textbackslash eval} command}
-\label{subsec:supplReuseEvalSetting}Using \verb`\eval*` for a calculation
-ensures a purely numerical result, with no vv-list or formatting in
-the display of the result. But sometimes we might want the full display
-yet wish to save only the numerical result. This is the point of the
-\verb`reuse` setting of the \verb`\eval` command.
+{\small\label{subsec:supplReuseEvalSetting}Using }{\small{\small\verb`\eval*`}}{\small{}
+for a calculation ensures a purely numerical result, with no vv-list
+or formatting in the display of the result. But sometimes we might
+want the full display yet wish to save only the numerical result.
+This is the point of the }{\small{\small\verb`reuse`}}{\small{}
+setting of the }{\small{\small\verb`\eval`}}{\small{} command.}{\small\par}
-For the \emph{starred} form of the \verb`\eval` command it is always
-\emph{only the numerical result} that is saved, whatever the value
-of the \texttt{reuse} key in the settings option of the \verb`\eval`
-command.
+{\small For the }{\small\emph{starred}}{\small{} form of the }{\small{\small\verb`\eval`}}{\small{}
+command it is always }{\small\emph{only the numerical result}}{\small{}
+that is saved, whatever the value of the }{\small\texttt{reuse}}{\small{}
+key in the settings option of the }{\small{\small\verb`\eval`}}{\small{}
+command.}{\small\par}
-For the \emph{unstarred} form of the \verb`\eval` command exactly
-what is saved with \verb`\nmcReuse` depends on the \texttt{reuse}
-setting:
+{\small For the }{\small\emph{unstarred}}{\small{} form of the }{\small{\small\verb`\eval`}}{\small{}
+command exactly what is saved with }{\small{\small\verb`\nmcReuse`}}{\small{}
+depends on the }{\small\texttt{reuse}}{\small{} setting: }{\small\par}
\begin{lyxcode}
-reuse~=~<integer>
+{\small reuse~=~<integer>}{\small\par}
\end{lyxcode}
-where \verb`<integer>` can take one of two values,
+{\small where }{\small{\small\verb`<integer>`}}{\small{} can
+take one of two values, }{\small\par}
\begin{itemize}
-\item \texttt{reuse=0} (the default) saves\emph{ the form that is displayed}
-including the vv-list if there is one and possibly a formatting component
-(like math delimiters). Note that if the vv-list is empty, a formatting
-component (math delimiters) may still be present in the saved result;
-\item \texttt{reuse=1} (or, indeed, any non-zero integer) saves only the
-numerical result with no other elements of the display (no vv-list,
-no formatting component, no math delimiters).
+\item {\small\texttt{reuse=0}}{\small{} (the default) saves}{\small\emph{
+the form that is displayed}}{\small{} including the vv-list if there
+is one and possibly a formatting component (like math delimiters).
+Note that if the vv-list is empty, a formatting component (math delimiters)
+may still be present in the saved result; }{\small\par}
+\item {\small\texttt{reuse=1}}{\small{} (or, indeed, any non-zero integer)
+saves only the numerical result with no other elements of the display
+(no vv-list, no formatting component, no math delimiters). }{\small\par}
\end{itemize}
-As we saw earlier, saving the result from \verb`\eval{$ x+y $}[x=1,y=2]`,
-corresponding to \verb`reuse=0`, means the full display is saved.
-Check by writing \verb`\three` $\Longrightarrow$ \three. The full
-display was saved (including math delimiters).
+{\small As we saw earlier, saving the result from }{\small{\small\verb`\eval{$ x+y $}[x=1,y=2]`}}{\small ,
+corresponding to }{\small{\small\verb`reuse=0`}}{\small , means
+the full display is saved. Check by writing }{\small{\small\verb`\three`}}{\small{}
+$\Longrightarrow$ }{\small{\small\three}}{\small . The full
+display was saved (including math delimiters).}{\small\par}
-On the other hand, with {\ttfamily\verb`reuse=1`} only
-the numerical value is saved:
+{\small On the other hand, with }{\small{\small\verb`reuse=1`}}{\small{}
+only the numerical value is saved: }{\small\par}
\begin{centred}
-\verb`\eval[reuse=1]{$ x + y $}[x=3,y=4] \reuse[renew]{seven}` $\Longrightarrow$
-\eval[reuse=1]{$ x + y $}[x=3,y=4] \reuse[renew]{seven}.
+{\small{\small\verb`\eval[reuse=1]{$ x + y $}[x=3,y=4] \reuse[renew]{seven}`}}{\small{}
+$\Longrightarrow$ }{\small\eval[reuse=1]{$ x + y $}[x=3,y=4] \reuse[renew]{seven}}{\small .}{\small\par}
\end{centred}
-The numerical result only of the calculation should be saved, although
-the formula and vv-list are displayed as the result of the \verb`\eval`-uation.
-We can easily check: \verb`\seven` $\Longrightarrow$ \seven. Indeed,
-only the numerical result was saved.
+{\small The numerical result only of the calculation should be saved,
+although the formula and vv-list are displayed as the result of the
+}{\small{\small\verb`\eval`}}{\small -uation. We can easily
+check: }{\small{\small\verb`\seven`}}{\small{} $\Longrightarrow$
+}{\small{\small\seven}}{\small . Indeed, only the numerical
+result was saved.}{\small\par}
-\chapter{Nesting commands}
+\chapter{Nesting commands}
-\label{chap:Nesting} The \verb`\eval` command and the supplementary
-commands of the previous chapter can be \emph{nested} –\emph{ }used
-within other \verb`\eval` or supplementary commands. Nesting may
-occur in the main argument, or the vv-list, or the settings option,
-or some combination of all three. With the commands currently introduced,
-nesting is unlikely to be a major concern, but it becomes significant
-for the commands defined in the associated package \texttt{numerica-plus}
-(see §\ref{subsec:Related-packages}). Since those additional commands
-are not available for this document, the examples below use the commands
-introduced earlier: \verb`\eval`, \verb`\info`, \verb`\macros`,
-\verb`\constants` and \verb`\reuse`.
+{\small\label{chap:Nesting} The }{\small{\small\verb`\eval`}}{\small{}
+command and the supplementary commands of the previous chapter can
+be }{\small\emph{nested}}{\small{} --}{\small\emph{ }}{\small used within
+other }{\small{\small\verb`\eval`}}{\small{} or supplementary
+commands. Nesting may occur in the main argument, or the vv-list,
+or the settings option, or some combination of all three. With the
+commands currently introduced, nesting is unlikely to be a major concern,
+but it becomes significant for the commands defined in the associated
+package }{\small\texttt{numerica-plus}}{\small{} (see §\ref{subsec:Related-packages}).
+Since those additional commands are not available for this document,
+the examples below use the commands introduced earlier: }{\small{\small\verb`\eval`}}{\small ,
+}{\small{\small\verb`\info`}}{\small , }{\small{\small\verb`\macros`}}{\small ,
+}{\small{\small\verb`\constants`}}{\small{} and }{\small{\small\verb`\reuse`}}{\small .}{\small\par}
\section{Nesting in the formula}
-Consider a statement like \verb`\eval{...\eval...}`. There is an
-inner \verb`\eval` and an outer \verb`\eval`. The inner \verb`\eval`
-`digests' \emph{its} \LaTeX{} formula to produce an \verb`l3fp`-readable
-expression which is fed to \verb`l3fp` to evaluate. The result is
-then returned to (the inner) \verb`\eval` to display. In version
-1 of \verb`numerica` that meant the inner command \emph{had} to be
-starred, \verb`\eval*`, so that no display formatting was fed to
-the outer command to try to digest (and cause an error).\emph{ }In
-version 2 of \verb`numerica` this is no longer the case. \verb`numerica`
+{\small Consider a statement like }{\small{\small\verb`\eval{...\eval...}`}}{\small .
+There is an inner }{\small{\small\verb`\eval`}}{\small{} and
+an outer }{\small{\small\verb`\eval`}}{\small . The inner }{\small{\small\verb`\eval`}}{\small{}
+`digests' }{\small\emph{its}}{\small{} \LaTeX{} formula to produce an
+}\texttt{l3fp}{\small -readable expression which is fed to }{\small{\small\verb`l3fp`}}{\small{}
+to evaluate. The result is then returned to (the inner) }{\small{\small\verb`\eval`}}{\small{}
+to display. In version 1 of }\texttt{numerica}{\small{} that meant the
+inner command }{\small\emph{had}}{\small{} to be starred, }{\small{\small\verb`\eval*`}}{\small ,
+so that no display formatting was fed to the outer command to try
+to digest (and cause an error).}{\small\emph{ }}{\small In version
+2 of }\texttt{numerica}{\small{} this is no longer the case. }\texttt{numerica}{\small{}
detects whether a command is inner or outer, and if inner, suppresses
all display formatting, producing only a number, as if the command
-had been starred:
+had been starred: }{\small\par}
\begin{centred}
-\verb`\eval{$ \sin(\eval{\sin x}[x=\pi/6]\pi) + 1 $}` $\Longrightarrow$
-\eval{$ \sin(\eval{\sin x}[x=\pi/6]\pi) + 1$}.
+{\small{\small\verb`\eval{$ \sin(\eval{\sin x}[x=\pi/6]\pi) + 1 $}`}}{\small{}
+$\Longrightarrow$ }{\small\eval{$ \sin(\eval{\sin x}[x=\pi/6]\pi) + 1 $}}{\small .}{\small\par}
\end{centred}
-In the presentation of the overall result, the inner \verb`\eval`
-command is evaluated, displaying as a number.
+{\small In the presentation of the overall result, the inner }{\small{\small\verb`\eval`}}{\small{}
+command is evaluated, displaying as a number.}{\small\par}
-In this example, the \verb`x=\pi/6` could be removed from the inner
-\verb`\eval` and placed in the vv-list of the outer command since
-outer variables are available to the inner command:
+{\small In this example, the }{\small{\small\verb`x=\pi/6`}}{\small{}
+could be removed from the inner }{\small{\small\verb`\eval`}}{\small{}
+and placed in the vv-list of the outer command since outer variables
+are available to the inner command: }{\small\par}
\begin{centred}
-\verb`\eval{$ \sin(\eval{\sin x}\pi) + 1 $}[x=\pi/6]` $\Longrightarrow$
-\eval{$ \sin(\eval{\sin x}\pi) + 1$}[x=\pi/6].
+{\small{\small\verb`\eval{$ \sin(\eval{\sin x}\pi) + 1 $}[x=\pi/6]`}}{\small{}
+$\Longrightarrow$ }{\small\eval{$ \sin(\eval{\sin x}\pi) + 1 $}[x=\pi/6]}{\small .}{\small\par}
\end{centred}
-Just to show that it is possible, the next example shows \verb`\eval`
-being used in a \verb`\constants` command. The \verb`o` setting
-in the \verb`\constants` command pervades its argument; hence it
-needs to be explicitly turned off for the \verb`\eval` if \verb`\sin(\pi/6)`
-is to evaluate as expected.
+{\small Just to show that it is possible, the next example shows }{\small{\small\verb`\eval`}}{\small{}
+being used in a }{\small{\small\verb`\constants`}}{\small{}
+command. The }{\small{\small\verb`o`}}{\small{} setting in the
+}{\small{\small\verb`\constants`}}{\small{} command pervades
+its argument; hence it needs to be explicitly turned off for the }{\small{\small\verb`\eval`}}{\small{}
+if }{\small{\small\verb`\sin(\pi/6)`}}{\small{} is to evaluate
+as expected. }{\small\par}
\begin{verbatim}
\constants[o]{ y=\sin 30,x=\eval[o=0]{\sin(\pi/6)} }
\eval{$ x+y $}
\end{verbatim}
-$\Longrightarrow$ \constants[o]{ y=\sin 30,x=\eval[o=0]{\sin(\pi/6)} }
- \eval{$ x+y $}.
+{\small$\Longrightarrow$ }{\small{} \constants[o]{ y=\sin 30,x=\eval[o=0]{\sin(\pi/6)} }
+ \eval{$ x+y $}}{\small .}{\small\par}
\subsection{Math delimiters and double evaluations}
-Any math delimiters in the inner \verb`\eval` are ignored. (This
-also differs from version 1 of \verb`numerica` where they caused
-an error.) Obviously it is simpler to omit them as I have done in
-the examples.
+{\small Any math delimiters in the inner }{\small{\small\verb`\eval`}}{\small{}
+are ignored. (This also differs from version 1 of }\texttt{numerica}{\small{}
+where they caused an error.) Obviously it is simpler to omit them
+as I have done in the examples.}{\small\par}
-However, math delimiters in the \emph{outer} \verb`\eval` command
-still have their normal effect and produce a \emph{formula = result,
-(vv-list)} display. One consequence of such a display is that the
-formula in the \emph{inner} \verb`\eval` command is evaluated \emph{twice}
-– once when the overall result is being calculated (i.e. the formula
-of the \emph{outer} \verb`\eval`) and later when the overall display
-of the result is created. In the \emph{formula} part of the \emph{formula
-= result, {[}vv-list{]}} display, the tokens in the \emph{formula}
-are expanded to their display form. For example, \verb`\sin` is expanded
-to $\sin$, \verb`\pi` is expanded to $\pi$ – and the inner \verb`\eval`
-is expanded to the numerical result of its evaluation – a second evaluation.
-If the inner formula is simple, this will be of little moment, but
-should the inner formula contain, say, a slowly converging infinite
-series, then evaluating it twice is a bad idea and it would be better
-to remove the delimiters from the outer \verb`\eval`. That prevents
-the second evaluation.
+{\small However, math delimiters in the }{\small\emph{outer}}{\small{}
+}{\small{\small\verb`\eval`}}{\small{} command still have their
+normal effect and produce a }{\small\emph{formula = result, (vv-list)}}{\small{}
+display. One consequence of such a display is that the formula in
+the }{\small\emph{inner}}{\small{} }{\small{\small\verb`\eval`}}{\small{}
+command is evaluated }{\small\emph{twice}}{\small{} -- once when the
+overall result is being calculated (i.e. the formula of the }{\small\emph{outer}}{\small{}
+}{\small{\small\verb`\eval`}}{\small ) and later when the overall
+display of the result is created. In the }{\small\emph{formula}}{\small{}
+part of the }{\small\emph{formula = result, {[}vv-list{]}}}{\small{}
+display, the tokens in the }{\small\emph{formula}}{\small{} are expanded
+to their display form. For example, }{\small{\small\verb`\sin`}}{\small{}
+is expanded to $\sin$, }{\small{\small\verb`\pi`}}{\small{}
+is expanded to $\pi$ -- and the inner }{\small{\small\verb`\eval`}}{\small{}
+is expanded to the numerical result of its evaluation -- a second
+evaluation. If the inner formula is simple, this will be of little
+moment, but should the inner formula contain, say, a slowly converging
+infinite series, then evaluating it twice is a bad idea and it would
+be better to remove the delimiters from the outer }{\small{\small\verb`\eval`}}{\small .
+That prevents the second evaluation.}{\small\par}
-The problem does not arise if the outer \verb`\eval` lies within
-a math environment (e.g. \verb`$ \eval{...} $`) since that produces
-a display of the form \emph{result, {[}vv-list{]}.} The formula is
-not displayed and so the second evaluation does not occur. The inner
-\verb`\eval` is evaluated once only to calculate the result.
+{\small The problem does not arise if the outer }{\small{\small\verb`\eval`}}{\small{}
+lies within a math environment (e.g. }{\small{\small\verb`$ \eval{...} $`}}{\small )
+since that produces a display of the form }{\small\emph{result, {[}vv-list{]}.}}{\small{}
+The formula is not displayed and so the second evaluation does not
+occur. The inner }{\small{\small\verb`\eval`}}{\small{} is evaluated
+once only to calculate the result.}{\small\par}
\section{Nesting in the vv-list}
-The inner \verb`\eval` can be placed in the vv-list of the outer
-command. If the vv-list of the inner \verb`\eval` contains a comma
+{\small The inner }{\small{\small\verb`\eval`}}{\small{} can
+be placed in the vv-list of the outer command. If the vv-list of the
+inner }{\small{\small\verb`\eval`}}{\small{} contains a comma
(meaning there are at least two variables), then the entire inner
-\verb`\eval` and its \LaTeX{} arguments needs to be wrapped in braces
-to hide the comma or commas of its vv-list from the outer \verb`\eval`.
-To show the effect of not doing so, I have slightly complicated the
-previous example by adding a second (unnecessary) variable. The first
-example is with braces, the second without:
+}{\small{\small\verb`\eval`}}{\small{} and its \LaTeX{} arguments
+needs to be wrapped in braces to hide the comma or commas of its vv-list
+from the outer }{\small{\small\verb`\eval`}}{\small . To show
+the effect of not doing so, I have slightly complicated the previous
+example by adding a second (unnecessary) variable. The first example
+is with braces, the second without: }{\small\par}
\begin{centred}
-\verb`\eval{$ \sin k\pi + 1 $}[k={\eval{y\sin x}[x=\pi/6,y=1]}]`
-$\Longrightarrow$ \eval{$ \sin k\pi + 1 $} [k={\eval{y\sin x}[x=\pi/6,y=1]}].
+{\small{\small\verb`\eval{$ \sin k\pi + 1 $}[k={\eval{y\sin x}[x=\pi/6,y=1]}]`}}{\small{}
+$\Longrightarrow$ }{\small\eval{$ \sin k\pi + 1 $}[k={\eval{y\sin x}[x=\pi/6,y=1]}]}{\small .}{\small\par}
-\verb`\eval{$ \sin k\pi + 1 $}[k=\eval{y\sin x}[x=\pi/6,y=1]]` $\Longrightarrow$
-\eval{$ \sin k\pi + 1 $}[k=\eval{y\sin x}[x=\pi/6,y=1]].
+{\small{\small\verb`\eval{$ \sin k\pi + 1 $}[k=\eval{y\sin x}[x=\pi/6,y=1]]`}}{\small{}
+$\Longrightarrow$ }{\small\eval{$ \sin k\pi + 1 $}[k=\eval{y\sin x}[x=\pi/6,y=1]]}{\small\par}
\end{centred}
-The vv-list of the outer \verb`\eval` is parsed as containing two
-entries, \verb`k=\eval` \verb`{y\sin x}[x=\pi/6` and \verb`y=1]`.
+{\small The vv-list of the outer }{\small{\small\verb`\eval`}}{\small{}
+is parsed as containing two entries, }{\small{\small\verb`k=\eval`}}{\small{}
+}{\small{\small\verb`{y\sin x}[x=\pi/6`}}{\small{} and }{\small{\small\verb`y=1]`}}{\small .
Both will cause errors but since the vv-list is evaluated from the
-right, it is \verb`y=1]` which actually does so.
+right, it is }{\small{\small\verb`y=1]`}}{\small{} which actually
+does so.}{\small\par}
\section{Nesting in the settings option}
-This will be rare, but commands can occur in the settings option of
-the outer command. The \verb`\info` command provides a good example.
-I have included it in the punctuation setting of an \verb`\eval`-uation.
+{\small This will be rare, but commands can occur in the settings option
+of the outer command. The \verb`\info` command provides a good example.
+I have included it in the punctuation setting of an \verb`\eval`-uation. }{\small\par}
\begin{verbatim}
\eval[p=\mbox{,\qquad\info{sum} terms.}]
- {\[ \sum_{n=0}^{\infty}\frac{(-1)^{n}}{n!} \]}[3]
+ {\[ \sum_{n=0}^{\infty}\frac{(-1)^{n}}{n!} \]}[3]
\end{verbatim}
-$\Longrightarrow$ \eval[p=\mbox{,\qquad\info{sum} terms.}]{\[ \sum_{n=0}^{\infty}\frac{(-1)^{n}}{n!} \]}[3]
+{\small$\Longrightarrow$ }{\small{} \eval[p=\mbox{,\qquad\info{sum} terms.}]
+ {\[ \sum_{n=0}^{\infty}\frac{(-1)^{n}}{n!} \]}[3]}{\small\par}
-Because of the \verb`\[ \]` math delimiters, if the \verb`\info`
-command had been placed \emph{after} the \texttt{\textbackslash eval}
+{\small Because of the }{\small{\small\verb`\[ \]`}}{\small{}
+math delimiters, if the }{\small{\small\verb`\info`}}{\small{}
+command had been placed }{\small\emph{after}}{\small{} the }{\small\texttt{\textbackslash eval}}{\small{}
command, it would have slid down to the next line. Used in the settings,
-as here, the display is \emph{inside} the \verb`\[ \]` delimiters,
-on the same line as the expression. This may be significant for adjusting
-vertical spacing of later parts of the document – widow and orphan
-control for instance.
+as here, the display is }{\small\emph{inside}}{\small{} the }{\small{\small\verb`\[ \]`}}{\small{}
+delimiters, on the same line as the expression. This may be significant
+for adjusting vertical spacing of later parts of the document --
+widow and orphan control for instance.}{\small\par}
-A point to note is the explicit writing of the `terms' descriptor.
-Normally \verb`\info{sum}` would automatically supply the descriptor,
-but as noted earlier, nesting of one command in another suppresses
-all elements of display of the inner command beyond the numerical
-result. It is as if the inner command is starred. Because the \verb`\info`
-command is nested in the \verb`\eval` command, the `terms' descriptor
-is suppressed and has had to be explicitly supplied by hand.
+{\small A point to note is the explicit writing of the `terms' descriptor.
+Normally }{\small{\small\verb`\info{sum}`}}{\small{} would automatically
+supply the descriptor, but as noted earlier, nesting of one command
+in another suppresses all elements of display of the inner command
+beyond the numerical result. It is as if the inner command is starred.
+Because the }{\small{\small\verb`\info`}}{\small{} command is
+nested in the }{\small{\small\verb`\eval`}}{\small{} command,
+the `terms' descriptor is suppressed and has had to be explicitly
+supplied by hand.}{\small\par}
\section{Rounding and display}
-In the display of the overall result, it is the result of the inner
-command which is shown, not the formula that the inner command acts
-on. How that number is displayed is determined by the number-format
-specification of the \emph{inner} command. Note however that this
-specification affects only how the result of the inner command is
-shown. Always 16 figures are passed from the inner command to the
-outer, as you can see in this example:
+{\small In the display of the overall result, it is the result of the
+inner command which is shown, not the formula that the inner command
+acts on. How that number is displayed is determined by the number-format
+specification of the }{\small\emph{inner}}{\small{} command. Note however
+that this specification affects only how the result of the inner command
+is shown. Always 16 figures are passed from the inner command to the
+outer, as you can see in this example: }{\small\par}
\begin{verbatim}
\eval{$ \pi - \eval{ \pi }[4] $}[15]
\end{verbatim}
-$\Longrightarrow$ \eval{$ \pi - \eval{ \pi }[4] $}[15].
+{\small$\Longrightarrow$ }{\small{} \eval{$ \pi - \eval{ \pi }[4] $}[15]}{\small .}{\small\par}
-\noindent The outer result would not be zero to $15$ places of decimals
-if the inner result were restricted to $4$ decimal places. It is
-only the \emph{display} of the inner result which is so restricted.
+\noindent{\small The outer result would not be zero to $15$ places
+of decimals if the inner result were restricted to $4$ decimal places.
+It is only the }{\small\emph{display}}{\small{} of the inner result
+which is so restricted.}{\small\par}
-For infinite sums and products (and for \verb`\nmcIterate` and \verb`\nmcSolve`
-of the \verb`numerica-plus` package), the rounding value is not just
-for display purposes but is also used to determine the result. This
-may require judicious use of the extra rounding setting to get a sensible
-display. In the first instance below, the second sum stops at an effective
-rounding value of $5+2=7$, since the default extra rounding is $+2$,
-and the first sum (the inner one) also stops at $7=4+3$. No surprise
-then that the overall result is $0$. In the second instance, the
-inner sum stops at a rounding value of $4+2=6$. Although the left-hand
-side of the display is unaltered, the result is no longer $0$.
+{\small For infinite sums and products (and for }{\small{\small\verb`\nmcIterate`}}{\small{}
+and }{\small{\small\verb`\nmcSolve`}}{\small{} of the }\texttt{numerica}{\small{}
+package), the rounding value is not just for display purposes but
+is also used to determine the result. This may require judicious use
+of the extra rounding setting to get a sensible display. In the first
+instance below, the second sum stops at an effective rounding value
+of $5+2=7$, since the default extra rounding is $+2$, and the first
+sum (the inner one) also stops at $7=4+3$. No surprise then that
+the overall result is $0$. In the second instance, the inner sum
+stops at a rounding value of $4+2=6$. Although the left-hand side
+of the display is unaltered, the result is no longer $0$. }{\small\par}
\begin{verbatim}
\eval{$ \eval[S+=3]{\sum_{n=1}^\infty 1/n^3}[4*]
- \sum_{n=1}^\infty 1/n^3$}[5]
\end{verbatim}
-$\Longrightarrow$ \eval{$ \eval[S+=3]{\sum_{n=1}^\infty 1/n^3}[4*]
- - \sum_{n=1}^\infty 1/n^3$}[5]
+{\small$\Longrightarrow$ }{\small{} \eval{$ \eval[S+=3]{\sum_{n=1}^\infty 1/n^3}[4*]
+ - \sum_{n=1}^\infty 1/n^3$}[5]}{\small\par}
-\noindent whereas
+\noindent{\small whereas }{\small\par}
\begin{verbatim}
\eval{$ \eval[S+=2]{\sum_{n=1}^\infty 1/n^3}[4*]
- \sum_{n=1}^\infty 1/n^3$}[5]
\end{verbatim}
-$\Longrightarrow$ \eval{$ \eval[S+=2]{\sum_{n=1}^\infty 1/n^3}[4*]
- - \sum_{n=1}^\infty 1/n^3$}[5].
+{\small$\Longrightarrow$ }{\small{} \eval{$ \eval[S+=2]{\sum_{n=1}^\infty 1/n^3}[4*]
+ - \sum_{n=1}^\infty 1/n^3$}[5]}{\small .}{\small\par}
\section{Error messages}
-Errors in an inner command create a small change in error message
-display.
+{\small Errors in an inner command create a small change in error message
+display. }{\small\par}
\begin{centred}
-\verb`\eval{ 1 + \eval{ 1 + \eval{ k } } }` $\Longrightarrow$ \eval{ 1 + \eval{ 1 + \eval{ k } } }
+{\small{\small\verb`\eval{ 1 + \eval{ 1 + \eval{ k } } }`}}{\small{}
+$\Longrightarrow$ }{\small\eval{ 1 + \eval{ 1 + \eval{ k } } }}{\small\par}
-\verb`\eval{ x + \eval{ k }[k=\arcsin 2] }[x=1]` $\Longrightarrow$
-\eval{ x + \eval{ k }[k=\arcsin 2] }[x=1]
+{\small{\small\verb`\eval{ x + \eval{ k }[k=\arcsin 2] }[x=1]`}}{\small{}
+$\Longrightarrow$ }{\small\eval{ x + \eval{ k }[k=\arcsin 2] }[x=1]}{\small\par}
\end{centred}
-An integer is added to the `where' part of the error message. The
-integer indicates the \emph{level of nesting} where the error occurs.
+{\small An integer is added to the `where' part of the error message.
+The integer indicates the }{\small\emph{level of nesting}}{\small{}
+where the error occurs.}{\small\par}
-If there is no nesting where the error occurs, the integer is suppressed,
-even though there may be nesting elsewhere in the overall expression.
-This is in the interests of straightforwardness when nesting is absent,
-which will be overwhelmingly the most common situation.
+{\small If there is no nesting where the error occurs, the integer
+is suppressed, even though there may be nesting elsewhere in the overall
+expression. This is in the interests of straightforwardness when nesting
+is absent, which will be overwhelmingly the most common situation. }{\small\par}
\begin{centred}
-\verb`\eval{ k + \eval{ x }[x=1] }[k=\arcsin 2]` $\Longrightarrow$
-\eval{ k + \eval{ x }[x=1] }[k=\arcsin 2]
+{\small{\small\verb`\eval{ k + \eval{ x }[x=1] }[k=\arcsin 2]`}}{\small{}
+$\Longrightarrow$ }{\small\eval{ k + \eval{ x }[x=1] }[k=\arcsin 2]}{\small\par}
\end{centred}
\section{Debugging}
-\label{subsec:nestDebugging}It is worth looking at the debug display
-when \verb`\eval` commands are nested. For the outer \verb`\eval`
-command:
+{\small\label{subsec:nestDebugging}It is worth looking at the debug
+display when }{\small{\small\verb`\eval`}}{\small{} commands
+are nested. For the outer }{\small{\small\verb`\eval`}}{\small{}
+command: }{\small\par}
\begin{centred}
-\verb`\eval[dbg=1]{$ \sin \eval*{\sin x}[x=\pi/6]\pi + 1 $}` $\Longrightarrow$
-\eval[dbg=210]{$ \sin \eval*{\sin x}[x=\pi/6]\pi + 1$}
+{\small{\small\verb`\eval[dbg=1]{$ \sin \eval*{\sin x}[x=\pi/6]\pi + 1 $}`}}{\small{}
+$\Longrightarrow$ }{\small\eval[dbg=1]{$ \sin \eval*{\sin x}[x=\pi/6]\pi + 1 $}}{\small\par}
\end{centred}
-There is no vv-list for the outer command whence the two empty slots
-in the display but when the inner \verb`\eval` is in the vv-list,
-they are filled:
+{\small There is no vv-list for the outer command whence the two empty
+slots in the display but when the inner }{\small{\small\verb`\eval`}}{\small{}
+is in the vv-list, they are filled: }{\small\par}
\begin{centred}
-\verb`\eval[dbg=1]{$ \sin k\pi + 1 $}[k=\eval*{\sin x}[x=\pi/6]]`
-$\Longrightarrow$ \eval[dbg=1]{$ \sin k\pi + 1$} [k=\eval*{\sin x}[x=\pi/6]]
+{\small{\small\verb`\eval[dbg=1]{$ \sin k\pi + 1 $}[k=\eval*{\sin x}[x=\pi/6]]`}}{\small{}
+$\Longrightarrow$ }{\small\eval[dbg=1]{$ \sin k\pi + 1 $}[k=\eval*{\sin x}[x=\pi/6]]}{\small\par}
\end{centred}
-For the inner \verb`\eval` command debugging may still work but in
-an idiosyncratic way. To clarify exactly what is going on I have added
-a \verb`\left( \right)` pair around the entire inner \verb`\eval`
-command. Note that I have also used a \emph{negative} \texttt{dbg}
-value. With a positive value, the right parenthesis is pressed toward
-the right margin of the page. The negative value limits the display
-to the text width and gives the much neater result shown.
+{\small For the inner }{\small{\small\verb`\eval`}}{\small{}
+command debugging may still work but in an idiosyncratic way. To clarify
+exactly what is going on I have added a }{\small{\small\verb`\left( \right)`}}{\small{}
+pair around the entire inner }{\small{\small\verb`\eval`}}{\small{}
+command. Note that I have also used a }{\small\emph{negative}}{\small{}
+}{\small\texttt{dbg}}{\small{} value. With a positive value, the right
+parenthesis is pressed toward the right margin of the page. The negative
+value limits the display to the text width and gives the much neater
+result shown. }{\small\par}
\begin{verbatim}
\eval[()=2]{$
\sin\left(
@@ -5432,672 +5529,729 @@
\eval*[dbg=-1]{ \sin x }[x=\pi/6]
\right)\pi + 1 $}
\end{verbatim}
-$\Longrightarrow$ \eval[()=2]{$
+{\small$\Longrightarrow$ }{\small{} \eval[()=2]{$
\sin\left(
\eval*[dbg=-1]{ \sin x }[x=\pi/6]
- \right)\pi + 1 $}
+ \right)\pi + 1 $}}{\small\par}
-\medskip{}
-The debug display from the inner \verb`\eval` command has been inserted
-into the formula of the outer \verb`\eval` in the position occupied
-by the inner \verb`\eval`. I did not deliberately code for this,
-but have decided to leave it as is despite the potential for some
-rather odd displays, since there can be no confusion about which \verb`\eval`
+{\small\medskip{}
+ The debug display from the inner }{\small{\small\verb`\eval`}}{\small{}
+command has been inserted into the formula of the outer }{\small{\small\verb`\eval`}}{\small{}
+in the position occupied by the inner }{\small{\small\verb`\eval`}}{\small .
+I did not deliberately code for this, but have decided to leave it
+as is despite the potential for some rather odd displays, since there
+can be no confusion about which }{\small{\small\verb`\eval`}}{\small{}
command is being `debugged'. In this last example, in order to both
-use \verb`\left(...\right)` and have the calculation give the previous
-result I have employed the setting \verb`()=2` in the outer \verb`\eval`;
-see §\ref{subsec:parseTrigFns}.
+use }{\small{\small\verb`\left(...\right)`}}{\small{} and have
+the calculation give the previous result I have employed the setting
+}{\small{\small\verb`()=2`}}{\small{} in the outer }{\small{\small\verb`\eval`}}{\small ;
+see §\ref{subsec:parseTrigFns}.}{\small\par}
\chapter{Using \texttt{numerica} with \protect\LyX}
-\label{chap:LyX}The document processor \LyX{} has a facility that
-enables snippets from a document to be compiled separately and the
-results presented to the user without having to compile the entire
+{\small\label{chap:LyX}The document processor \LyX{} has a facility
+that enables snippets from a document to be compiled separately and
+the results presented to the user without having to compile the entire
document. The present document was written in \LyX . The demonstration
-calculations were evaluated using this \emph{instant preview} facility.
+calculations were evaluated using this }{\small\emph{instant preview}}{\small{}
+facility.}{\small\par}
-To use \texttt{numerica} in \LyX{} go to \textsf{Document \lyxarrow{}
-Settings \lyxarrow{} LaTeX Preamble} and enter
+{\small To use }{\small\texttt{numerica}}{\small{} in \LyX{} go to }{\small\textsf{Document
+\lyxarrow{} Settings \lyxarrow{} LaTeX Preamble}}{\small{} and enter }{\small\par}
\begin{lyxcode}
-\textbackslash usepackage\{numerica\}
+{\small\textbackslash usepackage\{numerica\}}{\small\par}
\end{lyxcode}
-then click \textsf{OK}. You may wish to follow the above line in the
-preamble with \verb`\nmcReuse{}`:
+{\small then click }{\small\textsf{OK}}{\small . You may wish to follow
+the above line in the preamble with }{\small{\small\verb`\nmcReuse{}`}}{\small : }{\small\par}
\begin{lyxcode}
-\textbackslash usepackage{[}lyx{]}\{numerica\}
+{\small\textbackslash usepackage{[}lyx{]}\{numerica\}}{\small\par}
-\textbackslash nmcReuse\{\}
+{\small\textbackslash nmcReuse\{\}}{\small\par}
\end{lyxcode}
-In that case, type the extra line and \emph{then} click \textsf{OK}.
-The additional line ensures all saved values are available in your
-document from the outset.
+{\small In that case, type the extra line and }{\small\emph{then}}{\small{}
+click }{\small\textsf{OK}}{\small . The additional line ensures all
+saved values are available in your document from the outset.}{\small\par}
\section{Instant~preview}
-The instant preview facility of \LyX{} performs mini-\LaTeX{} runs on
-selected parts of a document (for instance, the mathematical parts)
-and displays the results in \LyX{} while the user continues to work
-on the surrounding document.\texttt{ numerica} uses these mini-\LaTeX{}
-runs to do its evaluations and display their results. That means you
-get feedback on your calculations almost immediately.
+{\small The instant preview facility of \LyX{} performs mini-\LaTeX{}
+runs on selected parts of a document (for instance, the mathematical
+parts) and displays the results in \LyX{} while the user continues
+to work on the surrounding document.}{\small\texttt{ numerica}}{\small{}
+uses these mini-\LaTeX{} runs to do its evaluations and display their
+results. That means you get feedback on your calculations almost immediately.}{\small\par}
-To use this facility first ensure that instant preview is turned on.
-This means selecting \textsf{Tools \lyxarrow Preferences \lyxarrow Look
-\& Feel \lyxarrow{} Display}, ensuring that the \textsf{Display graphics}
-checkbox is checked, and against \textsf{Instant preview} selecting
-\textsf{On}, then clicking \textsf{OK}.
+{\small To use this facility first ensure that instant preview is turned
+on. This means selecting }{\small\textsf{Tools \lyxarrow Preferences
+\lyxarrow Look \& Feel \lyxarrow{} Display}}{\small , ensuring that
+the }{\small\textsf{Display graphics}}{\small{} checkbox is checked,
+and against }{\small\textsf{Instant preview}}{\small{} selecting }{\small\textsf{On}}{\small ,
+then clicking }{\small\textsf{OK}}{\small .}{\small\par}
\subsection{Document location}
-It also matters where your document is located. You may have your
-own local or personal texmf tree (see §\ref{subsec:settingsPersonal-texmf-tree}).
-If your document is located there, perhaps in the \verb`doc` folder,
-then not all features of preview will work as expected. Presumably
+{\small It also matters where your document is located. You may have
+your own local or personal texmf tree (see §\ref{subsec:settingsPersonal-texmf-tree}).
+If your document is located there, perhaps in the }{\small{\small\verb`doc`}}{\small{}
+folder, then not all features of preview will work as expected. Presumably
this is because both \LyX{} and your \LaTeX{} distribution (e.g. \TeX Live
or MiK\TeX ) are interacting with the location and interfere. Move
your document to another location which your \LaTeX{} distribution
-has no interest in, and open it in \LyX{} there.
+has no interest in, and open it in \LyX{} there.}{\small\par}
\subsection{Global vs local previewing}
-\label{subsec:LyXGlobal-vs-local}Compilation of previews occurs in
-two distinct modes.
+{\small\label{subsec:LyXGlobal-vs-local}Compilation of previews occurs
+in two distinct modes.}{\small\par}
\paragraph{Global preview generation:}
-When a document is opened (and preview is \emph{on}), all previews
-in the document are formed in sequence in the one \LaTeX{} run. This
-is the global mode. The mini-\LaTeX{} run may well be substantial.
-It compiles a \verb`.tex` file that begins with the document's preamble
-with some additions then comes \verb`\begin{document}`. That is followed
-by a sequence of preview environments,
+{\small When a document is opened (and preview is }{\small\emph{on}}{\small ),
+all previews in the document are formed in sequence in the one \LaTeX{}
+run. This is the global mode. The mini-\LaTeX{} run may well be substantial.
+It compiles a }{\small{\small\verb`.tex`}}{\small{} file that
+begins with the document's preamble with some additions then comes
+}{\small{\small\verb`\begin{document}`}}{\small . That is followed
+by a sequence of preview environments, }{\small\par}
\begin{lyxcode}
-\textbackslash begin\{preview\}
+{\small\textbackslash begin\{preview\}}{\small\par}
-<stuff>
+{\small <stuff>}{\small\par}
-\textbackslash end\{preview\}
+{\small\textbackslash end\{preview\}}{\small\par}
\end{lyxcode}
-one for each preview in the document. Finally there is an \verb`\end{document}`
+{\small one for each preview in the document. Finally there is an }{\small{\small\verb`\end{document}`}}{\small{}
statement. The critical point is that all previews are between the
-same \verb`\begin{document}`, \verb`\end{document}` statements,
-and so earlier previews in the sequence can communicate with later
-ones.
+same }{\small{\small\verb`\begin{document}`}}{\small , }{\small{\small\verb`\end{document}`}}{\small{}
+statements, and so earlier previews in the sequence can communicate
+with later ones.}{\small\par}
\paragraph{Local preview generation:}
-The other mode in which preview operates is local. Suppose you have
-your document open and want to add to it, for instance with a simple
-evaluation, \verb`\eval{x+y}[x=1,y=2]` in an ERT inset in a preview
-inset. The resulting mini-\LaTeX{} run is of the form
+{\small The other mode in which preview operates is local. Suppose
+you have your document open and want to add to it, for instance with
+a simple evaluation, }{\small{\small\verb`\eval{x+y}[x=1,y=2]`}}{\small{}
+in an ERT inset in a preview inset. The resulting mini-\LaTeX{} run
+is of the form }{\small\par}
\begin{lyxcode}
-<preamble>
+{\small <preamble>}{\small\par}
-\textbackslash begin\{document\}
+{\small\textbackslash begin\{document\}}{\small\par}
-\textbackslash begin\{preview\}
+{\small\textbackslash begin\{preview\}}{\small\par}
-\textbackslash eval\{x+y\}{[}x=1,y=2{]}
+{\small\textbackslash eval\{x+y\}{[}x=1,y=2{]}}{\small\par}
-\textbackslash end\{preview\}
+{\small\textbackslash end\{preview\}}{\small\par}
-\textbackslash end\{document\}
+{\small\textbackslash end\{document\}}{\small\par}
\end{lyxcode}
-The preamble is as before but there is only \emph{one} preview between
-the \verb`\begin{document}`, \verb`\end{document}` statements. That
-preview is isolated from all other, previous previews and will be
-isolated from all other, later previews.
+{\small The preamble is as before but there is only }{\small\emph{one}}{\small{}
+preview between the }{\small{\small\verb`\begin{document}`}}{\small ,
+}{\small{\small\verb`\end{document}`}}{\small{} statements.
+That preview is isolated from all other, previous previews and will
+be isolated from all other, later previews.}{\small\par}
-This has implications for the supplementary commands of the previous
-chapter and means that if you want to transfer information (a macro,
-a constant, a result) from one preview to another, you need to do
-it through the preamble or by means of an external file or, in some
-cases, by forcing a global preview run in which all previews are recompiled
-between the same \verb`\begin{document}`, \verb`\end{document}`
-statements.
+{\small This has implications for the supplementary commands of the
+previous chapter and means that if you want to transfer information
+(a macro, a constant, a result) from one preview to another, you need
+to do it through the preamble or by means of an external file or,
+in some cases, by forcing a global preview run in which all previews
+are recompiled between the same }{\small{\small\verb`\begin{document}`}}{\small ,
+}{\small{\small\verb`\end{document}`}}{\small{} statements.}{\small\par}
\subsubsection{Forcing a global preview run}
-Closing then opening a document is one way to force a global preview
-compilation. Another is to change the zoom level. This causes \LyX{}
-to recompile all previews at the new zoom level. But you may not want
-to work at the new zoom level. Going back to the old zoom level will
-force a second recompilation of all previews. For a large document
-\emph{two} recompilations is too heavy a burden. The secret is to
-combine a zoom in and a zoom out into one command and attach it to
-a shortcut.
+{\small Closing then opening a document is one way to force a global
+preview compilation. Another is to change the zoom level. This causes
+\LyX{} to recompile all previews at the new zoom level. But you may
+not want to work at the new zoom level. Going back to the old zoom
+level will force a second recompilation of all previews. For a large
+document }{\small\emph{two}}{\small{} recompilations is too heavy a
+burden. The secret is to combine a zoom in and a zoom out into one
+command and attach it to a shortcut.}{\small\par}
-If you go to \textsf{Tools \lyxarrow{} Preferences \lyxarrow{} Editing
-\lyxarrow{} Shortcuts}, click on the \textsf{New} button and enter
+{\small If you go to }{\small\textsf{Tools \lyxarrow{} Preferences \lyxarrow{}
+Editing \lyxarrow{} Shortcuts}}{\small , click on the }{\small\textsf{New}}{\small{}
+button and enter }{\small\par}
\begin{lyxcode}
-command-sequence~buffer-zoom-in;~buffer-zoom-out
+{\small command-sequence~buffer-zoom-in;~buffer-zoom-out}{\small\par}
\end{lyxcode}
-then assign a shortcut to it (\verb`Alt+Z` for zoom?) you will gain
-a simple means of forcing a global recompilation of previews.
+{\small then assign a shortcut to it (}{\small{\small\verb`Alt+Z`}}{\small{}
+for zoom?) you will gain a simple means of forcing a global recompilation
+of previews.}{\small\par}
\section{Mathed}
-(Mathed = the \LyX{} mathematics editor.) If you have instant preview
-\emph{on} then one way to use \texttt{numerica} in \LyX{} is to enter
-an \verb`\eval` command in mathed. Clicking the cursor outside the
-editor with the mouse or moving it outside with the arrow keys will
-then trigger formation of a preview of the editor's contents – a snippet
-of what will be shown in the pdf. This will be displayed in mathed's
-place after a generally short `pause for thought' as the mini-\LaTeX{}
-run progresses behind the scenes.
+{\small (Mathed = the \LyX{} mathematics editor.) If you have instant
+preview }{\small\emph{on}}{\small{} then one way to use }{\small\texttt{numerica}}{\small{}
+in \LyX{} is to enter an }{\small{\small\verb`\eval`}}{\small{}
+command in mathed. Clicking the cursor outside the editor with the
+mouse or moving it outside with the arrow keys will then trigger formation
+of a preview of the editor's contents -- a snippet of what will be
+shown in the pdf. This will be displayed in mathed's place after a
+generally short `pause for thought' as the mini-\LaTeX{} run progresses
+behind the scenes.}{\small\par}
-The original expression can be recovered by clicking on the preview.
-The content of mathed is immediately displayed and can be edited.
+{\small The original expression can be recovered by clicking on the
+preview. The content of mathed is immediately displayed and can be
+edited.}{\small\par}
\subsection{\protect\LaTeX{} braces~\{~~\}}
-\LyX{} does not support \texttt{numerica}'s \verb`\eval` command `out
-of the box' as it does, say, \verb`\frac` or \verb`\sqrt`. To use
-the \verb`\eval` command in mathed you will need to supply the braces
-used to delimit its mandatory argument. (For \verb`\frac` and \verb`\sqrt`
+{\small\LyX{} does not support }{\small\texttt{numerica}}{\small 's
+}{\small{\small\verb`\eval`}}{\small{} command `out of the box'
+as it does, say, }{\small{\small\verb`\frac`}}{\small{} or }{\small{\small\verb`\sqrt`}}{\small .
+To use the }{\small{\small\verb`\eval`}}{\small{} command in
+mathed you will need to supply the braces used to delimit its mandatory
+argument. (For }{\small{\small\verb`\frac`}}{\small{} and }{\small{\small\verb`\sqrt`}}{\small{}
by contrast, \LyX{} supplies these automatically in the form of blue-outlined
-boxes.) Unfortunately the \verb`{` key\footnote{\textsf{Shift+{[}} on my keyboard.}
+boxes.) Unfortunately the }{\small{\small\verb`{`}}{\small{}
+key}{\small\footnote{{\small\textsf{Shift+{[}}}{\small{} on my keyboard.}}}{\small{}
does not insert a left brace into the document but rather an escaped
-left brace \verb`\{` as you can see by looking at \textsf{View \lyxarrow{}
-Code Preview Pane}. Escaped braces like this are used for grouping
-terms in \emph{mathematics}; they are not the delimiters of a \LaTeX{}
-argument.
+left brace }{\small{\small\verb`\{`}}{\small{} as you can see
+by looking at }{\small\textsf{View \lyxarrow{} Code Preview Pane}}{\small .
+Escaped braces like this are used for grouping terms in }{\small\emph{mathematics}}{\small ;
+they are not the delimiters of a \LaTeX{} argument.}{\small\par}
-The brace delimiters for \LaTeX{} arguments are entered in mathed by
-typing a backslash \textsf{\textbackslash{} }then a left brace\textsf{
-\{} – two separate key presses rather than a single combined press.
-This enters a balanced pair of (unescaped) braces with the cursor
-sitting between them waiting for input. Alternatively, if you have
-already written an expression that you want to place between braces,
-select it, then type \textsf{\textbackslash{} }then\textsf{ \{}.
+{\small The brace delimiters for \LaTeX{} arguments are entered in mathed
+by typing a backslash }{\small\textsf{\textbackslash{} }}{\small then
+a left brace}{\small\textsf{ \{}}{\small{} -- two separate key presses
+rather than a single combined press. This enters a balanced pair of
+(unescaped) braces with the cursor sitting between them waiting for
+input. Alternatively, if you have already written an expression that
+you want to place between braces, select it, then type }{\small\textsf{\textbackslash{}
+}}{\small then}{\small\textsf{ \{}}{\small .}{\small\par}
\section{Preview insets}
-There are problems with using mathed for calculations.
+{\small There are problems with using mathed for calculations. }{\small\par}
\begin{itemize}
-\item Expressions entered in mathed are necessarily of the form \verb`$ \eval... $`
-or more generally \verb`delimiter` \verb`\eval...` \verb`delimiter`.
-But you may wish to wrap the \verb`\eval` command \emph{around} the
-math delimiters to produce a \emph{formula=result} form of display.
-In mathed the only way to effect such a display is to write the \emph{formula=
-}part yourself – which may involve no more than copy and paste but
-is still additional mouse work/key pressing.
-\item Mathed does not accept carriage returns. If you want to format a complicated
-expression for readability by breaking it into separate lines, you
-can't. The expression is jammed into the one line, along with the
-settings option content and the vv-list, often extending well beyond
-the edge of the screen.
+\item {\small Expressions entered in mathed are necessarily of the form }{\small{\small\verb`$ \eval... $`}}{\small{}
+or more generally }{\small{\small\verb`delimiter`}}{\small{}
+}{\small{\small\verb`\eval...`}}{\small{} }{\small{\small\verb`delimiter`}}{\small .
+But you may wish to wrap the }{\small{\small\verb`\eval`}}{\small{}
+command }{\small\emph{around}}{\small{} the math delimiters to produce
+a }{\small\emph{formula=result}}{\small{} form of display. In mathed
+the only way to effect such a display is to write the }{\small\emph{formula=
+}}{\small part yourself -- which may involve no more than copy and
+paste but is still additional mouse work/key pressing. }{\small\par}
+\item {\small Mathed does not accept carriage returns. If you want to format
+a complicated expression for readability by breaking it into separate
+lines, you can't. The expression is jammed into the one line, along
+with the settings option content and the vv-list, often extending
+well beyond the edge of the screen. }{\small\par}
\end{itemize}
-For these reasons I have come to prefer \emph{not} using mathed for
-calculations but instead to use preview insets wrapped around \TeX -code
-(ERT) insets. \LyX{} uses the shortcut \textsf{Ctrl+L} to insert an
-ERT inset. Since \LyX{} now does no printing itself, the shortcut \textsf{Ctrl+P}
-that was formerly used for printing is available for other purposes.
-On my keyboard, the \textsf{P} key lies diagonally up and to the right
-but adjacent to the \textsf{L} key. I suggest assigning \textsf{Ctrl+P}
-to inserting a preview inset. Then typing \textsf{Ctrl+P Ctrl+L} –
-which means holding the \textsf{Ctrl} key down and tapping two diagonally
-adjacent keys, \textsf{P} followed immediately by \textsf{L} – will
-insert an ERT inset inside a preview inset with the cursor sitting
-inside the ERT inset waiting for input. In the ERT inset you can enter
-carriage returns, and so format complicated expressions. You can place
-the vv-list on a separate line or onto consecutive lines. And when
-you have finished, clicking outside the preview inset will trigger
-preview into doing its thing and present the result `before your
-eyes'.
+{\small For these reasons I have come to prefer }{\small\emph{not}}{\small{}
+using mathed for calculations but instead to use preview insets wrapped
+around \TeX -code (ERT) insets. \LyX{} uses the shortcut }{\small\textsf{Ctrl+L}}{\small{}
+to insert an ERT inset. Since \LyX{} now does no printing itself, the
+shortcut }{\small\textsf{Ctrl+P}}{\small{} that was formerly used for
+printing is available for other purposes. On my keyboard, the }{\small\textsf{P}}{\small{}
+key lies diagonally up and to the right but adjacent to the }{\small\textsf{L}}{\small{}
+key. I suggest assigning }{\small\textsf{Ctrl+P}}{\small{} to inserting
+a preview inset. Then typing }{\small\textsf{Ctrl+P Ctrl+L}}{\small{}
+-- which means holding the }{\small\textsf{Ctrl}}{\small{} key down
+and tapping two diagonally adjacent keys, }{\small\textsf{P}}{\small{}
+followed immediately by }{\small\textsf{L}}{\small{} -- will insert
+an ERT inset inside a preview inset with the cursor sitting inside
+the ERT inset waiting for input. In the ERT inset you can enter carriage
+returns, and so format complicated expressions. You can place the
+vv-list on a separate line or onto consecutive lines. And when you
+have finished, clicking outside the preview inset will trigger preview
+into doing its thing and present the result `before your eyes'.}{\small\par}
-To assign the suggested shortcut, go to \textsf{Tools \lyxarrow{} Preferences
-\lyxarrow{} Editing \lyxarrow{} Shortcuts}. Under \textsf{Cursor, Mouse
-and Editing Functions} in the main window on the right, scroll down
-until you come to \textsf{preview-insert}, select it, then click \textsf{Modify}.
-Now press \textsf{Ctrl+P}. The shortcut will magically appear in the
-greyed, depressed key.\textsf{ }Click \textsf{OK} and then \textsf{OK}
-in the \textsf{Preferences} window to close it. (Most of the examples
-in this document have been evaluated in this way, using \textsf{Ctrl+P
-Ctrl+L.)}
+{\small To assign the suggested shortcut, go to }{\small\textsf{Tools
+\lyxarrow{} Preferences \lyxarrow{} Editing \lyxarrow{} Shortcuts}}{\small .
+Under }{\small\textsf{Cursor, Mouse and Editing Functions}}{\small{}
+in the main window on the right, scroll down until you come to }{\small\textsf{preview-insert}}{\small ,
+select it, then click }{\small\textsf{Modify}}{\small . Now press }{\small\textsf{Ctrl+P}}{\small .
+The shortcut will magically appear in the greyed, depressed key.}{\small\textsf{
+}}{\small Click }{\small\textsf{OK}}{\small{} and then }{\small\textsf{OK}}{\small{}
+in the }{\small\textsf{Preferences}}{\small{} window to close it. (Most
+of the examples in this document have been evaluated in this way,
+using }{\small\textsf{Ctrl+P Ctrl+L.)}}{\small\par}
\section{Errors }
-Instant preview will display error messages generated by \verb`numerica`
+{\small Instant preview will display error messages generated by }\texttt{numerica}{\small{}
in \LyX{} just as it does the results of calculations. Clicking on
the message will show the underlying expression which can then be
-edited. However \LaTeX{} errors will \emph{not} produce a preview;
-formation of the preview will stall. To find precisely what has gone
-wrong, you will need to look at the \LaTeX{} log, but not the log of
-the overall document; rather the \emph{preview} log.
+edited. However \LaTeX{} errors will }{\small\emph{not}}{\small{} produce
+a preview; formation of the preview will stall. To find precisely
+what has gone wrong, you will need to look at the \LaTeX{} log, but
+not the log of the overall document; rather the }{\small\emph{preview}}{\small{}
+log.}{\small\par}
\subsection{Temporary directory of \protect\LyX}
-Unfortunately this is tucked away in a temporary directory and is
-not immediately accessible in \LyX{} (unlike the main \LaTeX{} log from
-\textsf{Document \lyxarrow{} \LaTeX{} Log}). When \LyX{} is started,
-it sets up a temporary directory in which to perform various tasks.
-On Windows systems this will be located in \texttt{C:\textbackslash Users\textbackslash <your
-name>\textbackslash AppData\textbackslash Local\textbackslash Temp}
-and will have a name like \texttt{lyx\_tmpdir.XOsSGhBc1344}.
+{\small Unfortunately this is tucked away in a temporary directory
+and is not immediately accessible in \LyX{} (unlike the main \LaTeX{}
+log from }{\small\textsf{Document \lyxarrow{} \LaTeX{} Log}}{\small ).
+When \LyX{} is started, it sets up a temporary directory in which to
+perform various tasks. On Windows systems this will be located in
+}{\small\texttt{C:\textbackslash Users\textbackslash <your name>\textbackslash AppData\textbackslash Local\textbackslash Temp}}{\small{}
+and will have a name like }{\small\texttt{lyx\_tmpdir.XOsSGhBc1344}}{\small .}{\small\par}
-One of the tasks \LyX{} uses this temporary directory for is to create
-preview images when a document is opened. If you look inside \LyX 's
-temporary directory when a document is first loaded, you will see
-a subdirectory created, with a name like \texttt{lyx\_tmpbuf0}. There
-may already be such directories there, in which case the number on
-the end will be greater than \texttt{0} – it depends on whether other
-documents are or have been open in the current instance of \LyX .
-Inside the appropriate \texttt{lyx\_tmpbuf}\texttt{\emph{n}} folder
-will be the preview log with a name like \texttt{lyxpreviewZL1344.log}.
+{\small One of the tasks \LyX{} uses this temporary directory for is
+to create preview images when a document is opened. If you look inside
+\LyX 's temporary directory when a document is first loaded, you will
+see a subdirectory created, with a name like }{\small\texttt{lyx\_tmpbuf0}}{\small .
+There may already be such directories there, in which case the number
+on the end will be greater than }{\small\texttt{0}}{\small{} -- it
+depends on whether other documents are or have been open in the current
+instance of \LyX . Inside the appropriate }{\small\texttt{lyx\_tmpbuf}}{\small\texttt{\emph{n}}}{\small{}
+folder will be the preview log with a name like }{\small\texttt{lyxpreviewZL1344.log}}{\small .
It will usually be accompanied by other files with extensions like
-\texttt{.dvi}, \texttt{.tex}, and – depending on the number of previews
-in your document – a number, perhaps a lot, of image files with the
-extension \texttt{.png}, each one of which is a preview. For a document
-just loaded there will be only the one preview log, but if you have
-added preview insets or math insets to your document\textsf{ }in the
-current editing session there will be a number of such logs and you
-will need to determine the relevant one by the time stamp.
+}{\small\texttt{.dvi}}{\small , }{\small\texttt{.tex}}{\small , and
+-- depending on the number of previews in your document -- a number,
+perhaps a lot, of image files with the extension }{\small\texttt{.png}}{\small ,
+each one of which is a preview. For a document just loaded there will
+be only the one preview log, but if you have added preview insets
+or math insets to your document}{\small\textsf{ }}{\small in the current
+editing session there will be a number of such logs and you will need
+to determine the relevant one by the time stamp.}{\small\par}
-The log files are text files and can be opened in a text editor. The
-relevant part of the log is towards the end (just before the final
-statistical summary) where you will find a list of entries like \texttt{Preview: Snippet
-1 641947 163840 7864588}. If there is an error, it will be noted here
-among these snippets and will generally make clear what needs remedying.
+{\small The log files are text files and can be opened in a text editor.
+The relevant part of the log is towards the end (just before the final
+statistical summary) where you will find a list of entries like }{\small\texttt{Preview: Snippet
+1 641947 163840 7864588}}{\small . If there is an error, it will be
+noted here among these snippets and will generally make clear what
+needs remedying.}{\small\par}
\subsection{CPU usage, \protect\LaTeX{} processes}
-It is possible when a preview stalls that the \LaTeX{} process associated
-with the preview will continue to run, using CPU cycles, slowing overall
-computer performance, and perhaps resulting in extra fan use giving
-a different sound to the computer. In Windows 10, the \textsf{Task
-Manager} (\textsf{Ctrl+Shift+esc}) under the \textsf{Details} tab
-shows the current executables running. The \textsf{CPU} column will
-show which processes are preoccupying the CPU. Check whether one or
-more of these processes looks \LaTeX -related (e.g. \texttt{latex.exe}
-or \texttt{pdflatex.exe}, or \texttt{miktex-pdftex.exe} if using MiK\TeX ).
-Click the \textsf{Name} column to sort the processes by name and look
-for the relevant name in the list, select it, and end the process
-(click the \textsf{End Task} button).
+{\small It is possible when a preview stalls that the \LaTeX{} process
+associated with the preview will continue to run, using CPU cycles,
+slowing overall computer performance, and perhaps resulting in extra
+fan use giving a different sound to the computer. In Windows 10, the
+}{\small\textsf{Task Manager}}{\small{} (}{\small\textsf{Ctrl+Shift+esc}}{\small )
+under the }{\small\textsf{Details}}{\small{} tab shows the current executables
+running. The }{\small\textsf{CPU}}{\small{} column will show which processes
+are preoccupying the CPU. Check whether one or more of these processes
+looks \LaTeX -related (e.g. }{\small\texttt{latex.exe}}{\small{} or
+}{\small\texttt{pdflatex.exe}}{\small , or }{\small\texttt{miktex-pdftex.exe}}{\small{}
+if using MiK\TeX ). Click the }{\small\textsf{Name}}{\small{} column
+to sort the processes by name and look for the relevant name in the
+list, select it, and end the process (click the }{\small\textsf{End
+Task}}{\small{} button).}{\small\par}
-I am not familiar with the corresponding situation on Linux or Mac.
+{\small I am not familiar with the corresponding situation on Linux
+or Mac.}{\small\par}
\section{Hyperref support vs speed}
-If you want the pdf produced from your document to support hyperref
-links and show an outline window in your pdf viewer (generally placed
-on the left in the viewer) then you need to ensure the checkbox at
-\textsf{Document Settings \lyxarrow{} PDF Properties \lyxarrow{} Use
-Hyperref Support} is indeed checked. But you don't need to do this
-until the final compilation of the document. The advantage of leaving
-this until the last is that in a large document with many previews
-the time for preview generation is essentially halved. If hyperref
-support is enabled, preview generation not only creates all the individual
-image files that are the previews (files of extension \verb`.png`)
-but also requires the compilation of a single pdf document showing
-all the previews in sequence. (Like the previews, the pdf document
-`hides' in the termporary directory where \LyX{} does its work.)
-In other words, \emph{two} images are created for each preview, the
-\verb`.png` image which is the one \LyX{} displays, and another image
-buried inside the pdf of all images. That second step does not occur
-if hyperref support is disabled. In a small document, this is not
-going to matter; in a large document it becomes significant. It is
-well worth temporarily turning off hyperref support and then, when
-the time for final compilation comes, turning it back on.
+{\small If you want the pdf produced from your document to support
+hyperref links and show an outline window in your pdf viewer (generally
+placed on the left in the viewer) then you need to ensure the checkbox
+at }{\small\textsf{Document Settings \lyxarrow{} PDF Properties \lyxarrow{}
+Use Hyperref Support}}{\small{} is indeed checked. But you don't need
+to do this until the final compilation of the document. The advantage
+of leaving this until the last is that in a large document with many
+previews the time for preview generation is essentially halved. If
+hyperref support is enabled, preview generation not only creates all
+the individual image files that are the previews (files of extension
+}{\small{\small\verb`.png`}}{\small ) but also requires the
+compilation of a single pdf document showing all the previews in sequence.
+(Like the previews, the pdf document `hides' in the termporary directory
+where \LyX{} does its work.) In other words, }{\small\emph{two}}{\small{}
+images are created for each preview, the }{\small{\small\verb`.png`}}{\small{}
+image which is the one \LyX{} displays, and another image buried inside
+the pdf of all images. That second step does not occur if hyperref
+support is disabled. In a small document, this is not going to matter;
+in a large document it becomes significant. It is well worth temporarily
+turning off hyperref support and then, when the time for final compilation
+comes, turning it back on.}{\small\par}
\section{Supplementary commands in \protect\LyX}
-There are some difficulties using the supplementary commands successfully
-with instant preview.
+{\small There are some difficulties using the supplementary commands
+successfully with instant preview.}{\small\par}
\subsection{Reuse of earlier previews}
-One is that whenever \LyX{} has generated a preview image for a particular
-\LaTeX{} expression, it will use that same image whenever it meets
-that same \LaTeX{} expression later. That means that a statement like
-\verb`\macros[view]{}` and the same statement later will display
-the same image, even though there may have been macros defined or
-freed in between. The same goes for all the other supplementary functions,
-including, for example, \verb`\info{sum}`. A second instance of \verb`\info{sum}`
+{\small One is that whenever \LyX{} has generated a preview image for
+a particular \LaTeX{} expression, it will use that same image whenever
+it meets that same \LaTeX{} expression later. That means that a statement
+like }{\small{\small\verb`\macros[view]{}`}}{\small{} and the
+same statement later will display the same image, even though there
+may have been macros defined or freed in between. The same goes for
+all the other supplementary functions, including, for example, }{\small{\small\verb`\info{sum}`}}{\small .
+A second instance of }{\small{\small\verb`\info{sum}`}}{\small{}
will display the image generated by the first instance even though
-further infinite sums may have been evaluated between the \verb`\info`
-statements.
+further infinite sums may have been evaluated between the }{\small{\small\verb`\info`}}{\small{}
+statements.}{\small\par}
-The remedy is to make some small but insignificant difference to the
-\LaTeX{} expression in the second instance – generally a change in
-white space will do. For example: first time \verb`\macros[view]{}`,
-second time \verb`\macros[view]{ }` where a space has been inserted
-between the braces; or: first time \verb`\info{sum}`, second time
-\verb`\info{ sum}` where a space has been inserted before \verb`sum`.
+{\small The remedy is to make some small but insignificant difference
+to the \LaTeX{} expression in the second instance -- generally a change
+in white space will do. For example: first time }{\small{\small\verb`\macros[view]{}`}}{\small ,
+second time }{\small{\small\verb`\macros[view]{ }`}}{\small{}
+where a space has been inserted between the braces; or: first time
+}{\small{\small\verb`\info{sum}`}}{\small , second time }{\small{\small\verb`\info{ sum}`}}{\small{}
+where a space has been inserted before }{\small{\small\verb`sum`}}{\small .
This will ensure \LyX{} doesn't fall back on the previously generated
-image.
+image.}{\small\par}
\subsection{\textquoteleft Stalled\textquoteright{} previews}
-It is possible to put content into an ERT inset inside a preview inset
-(\textsf{Ctrl+P Ctrl+L}) and for nothing to happen. The preview has
-apparently stalled. Certainly this can be the case if there is an
-error in the input (e.g. a missing brace) but it also occurs if there
-is no output to display. For instance \verb`\constants{ c=300000000 }`
-does not produce any visual output. There is nothing for the preview
-to display and so the preview inset sits there, apparently stalled.
-This is a security measure for previews in \LyX{} to provide at least
-some guard against malicious code being run in the preview. If the
-preview resolved, it would disappear completely from view in the \LyX{}
-window.
+{\small It is possible to put content into an ERT inset inside a preview
+inset (}{\small\textsf{Ctrl+P Ctrl+L}}{\small ) and for nothing to
+happen. The preview has apparently stalled. Certainly this can be
+the case if there is an error in the input (e.g. a missing brace)
+but it also occurs if there is no output to display. For instance
+}{\small{\small\verb`\constants{ c=300000000 }`}}{\small{} does
+not produce any visual output. There is nothing for the preview to
+display and so the preview inset sits there, apparently stalled. This
+is a security measure for previews in \LyX{} to provide at least some
+guard against malicious code being run in the preview. If the preview
+resolved, it would disappear completely from view in the \LyX{} window.}{\small\par}
-If you find the visual appearance of such apparently stalled previews
-distracting, the addition of some displayable content to the preview
-will result in it resolving to that content; the content could be
-as small as a full stop.
+{\small If you find the visual appearance of such apparently stalled
+previews distracting, the addition of some displayable content to
+the preview will result in it resolving to that content; the content
+could be as small as a full stop.}{\small\par}
\subsection{Using \texttt{\textbackslash nmcMacros}}
-As noted earlier, previews are mini-\LaTeX{} runs, either local or
-global. Each local preview is of the form<preamble>
+{\small As noted earlier, previews are mini-\LaTeX{} runs, either local
+or global. Each local preview is of the form<preamble> }{\small\par}
\begin{lyxcode}
-\textbackslash begin\{document\}
+{\small\textbackslash begin\{document\}}{\small\par}
-\textbackslash begin\{preview\}
+{\small\textbackslash begin\{preview\}}{\small\par}
-<stuff>
+{\small <stuff>}{\small\par}
-\textbackslash end\{preview\}
+{\small\textbackslash end\{preview\}}{\small\par}
-\textbackslash end\{document\}
+{\small\textbackslash end\{document\}}{\small\par}
\end{lyxcode}
-Whatever goes into or comes out of the preview is isolated from any
-other local preview, unless it is through the preamble or an external
-file. Sometimes a global preview run can overcome this problem for
-then all the previews lie between the same \verb`\begin{document}`,
-\verb`end{document}` statements. However, this does not help with
-macro definitions. \verb`\def`, \verb`\newcommand`, \verb`\NewDocumentCommand`
-all provide \emph{local} definitions which remain trapped within their
-own \verb`\begin{preview}`, \verb`\end{preview}`) statements. Another
-preview, say containing an \verb`\eval` command, between a different
-pair of \verb`\begin{preview}`, \verb`\end{preview}`) statements,
-will not know about the macro definition.
+{\small Whatever goes into or comes out of the preview is isolated
+from any other local preview, unless it is through the preamble or
+an external file. Sometimes a global preview run can overcome this
+problem for then all the previews lie between the same }{\small{\small\verb`\begin{document}`}}{\small ,
+}{\small{\small\verb`end{document}`}}{\small{} statements. However,
+this does not help with macro definitions. }{\small{\small\verb`\def`}}{\small ,
+}{\small{\small\verb`\newcommand`}}{\small , }{\small{\small\verb`\NewDocumentCommand`}}{\small{}
+all provide }{\small\emph{local}}{\small{} definitions which remain
+trapped within their own }{\small{\small\verb`\begin{preview}`}}{\small ,
+}{\small{\small\verb`\end{preview}`}}{\small ) statements.
+Another preview, say containing an }{\small{\small\verb`\eval`}}{\small{}
+command, between a different pair of }{\small{\small\verb`\begin{preview}`}}{\small ,
+}{\small{\small\verb`\end{preview}`}}{\small ) statements,
+will not know about the macro definition.}{\small\par}
-There are (at least) three ways out:
+{\small There are (at least) three ways out: }{\small\par}
\begin{enumerate}
-\item Confine everything to the same preview inset: the definition of a
-macro, the \verb`\macros` statement, and the use of the macro in
-an \verb`\eval` command.
-\item Confine macro definitions to the preamble (\textsf{Document \lyxarrow{}
-Settings \lyxarrow{} \LaTeX{} Preamble}).
-\item Within previews use \verb`\gdef` (or \verb`\global\def`) exclusively
+\item {\small Confine everything to the same preview inset: the definition
+of a macro, the }{\small{\small\verb`\macros`}}{\small{} statement,
+and the use of the macro in an }{\small{\small\verb`\eval`}}{\small{}
+command. }{\small\par}
+\item {\small Confine macro definitions to the preamble (}{\small\textsf{Document
+\lyxarrow{} Settings \lyxarrow{} \LaTeX{} Preamble}}{\small ). }{\small\par}
+\item {\small Within previews use }{\small{\small\verb`\gdef`}}{\small{}
+(or }{\small{\small\verb`\global\def`}}{\small ) exclusively
for making your macro definitions; this makes the macro available
-to all later previews.
+to all later previews. }{\small\par}
\end{enumerate}
\subsection{Using \texttt{\textbackslash nmcConstants}}
-Because \verb`\nmcConstants` doesn't use \verb`\def` or \verb`\newcommand`
-or \verb`\NewDocumentCommand` it is not subject to the same localisation
-problem as \verb`\nmcMacros`, but the reach of a \verb`\constants`
-command will still be confined to its own preview unless a \emph{global}
-preview run is forced; see above §\ref{subsec:LyXGlobal-vs-local}.
+{\small Because }{\small{\small\verb`\nmcConstants`}}{\small{}
+doesn't use }{\small{\small\verb`\def`}}{\small{} or }{\small{\small\verb`\newcommand`}}{\small{}
+or }{\small{\small\verb`\NewDocumentCommand`}}{\small{} it is
+not subject to the same localisation problem as }{\small{\small\verb`\nmcMacros`}}{\small ,
+but the reach of a }{\small{\small\verb`\constants`}}{\small{}
+command will still be confined to its own preview unless a }{\small\emph{global}}{\small{}
+preview run is forced; see above §\ref{subsec:LyXGlobal-vs-local}.}{\small\par}
\subsection{Using \texttt{\textbackslash nmcReuse}}
-As noted earlier, \LyX{} creates its previews in a temporary directory,
-not the document directory. If you want to save values from your current
-document – say, \texttt{mydoc.lyx} – to \texttt{mydoc.nmc} then you
-do so as described earlier (§\ref{sec:supplReuse}), but the file
-\texttt{mydoc.nmc} containing the saved results will be located in
-the temporary directory. When \LyX{} is closed the file will be deleted
-along with all the other contents of that directory.
+{\small As noted earlier, \LyX{} creates its previews in a temporary
+directory, not the document directory. If you want to save values
+from your current document -- say, }{\small\texttt{mydoc.lyx}}{\small{}
+-- to }{\small\texttt{mydoc.nmc}}{\small{} then you do so as described
+earlier (§\ref{sec:supplReuse}), but the file }{\small\texttt{mydoc.nmc}}{\small{}
+containing the saved results will be located in the temporary directory.
+When \LyX{} is closed the file will be deleted along with all the other
+contents of that directory.}{\small\par}
-Fortunately \LyX{} has a copying mechanism for getting files out of
-the temporary directory and into the document directory. When a document
-is exported – say to pdf – it is possible to specify a \emph{copier}
-to automatically copy back to the document directory or subdirectory
-various files in the temporary directory. We want the \texttt{.nmc}
-file containing the saved values to be copied back. Go to \textsf{Tools
-\lyxarrow{} Preferences \lyxarrow{} File Handling \lyxarrow{} File Formats}
-and find \textsf{PDF (pdflatex)} (assuming export to \texttt{pdf}
-by this route) in the list of formats. In\textsf{ }the \textsf{Copier}
-slot of the dialogue insert the following line of code:
+{\small Fortunately \LyX{} has a copying mechanism for getting files
+out of the temporary directory and into the document directory. When
+a document is exported -- say to pdf -- it is possible to specify
+a }{\small\emph{copier}}{\small{} to automatically copy back to the
+document directory or subdirectory various files in the temporary
+directory. We want the }{\small\texttt{.nmc}}{\small{} file containing
+the saved values to be copied back. Go to }{\small\textsf{Tools \lyxarrow{}
+Preferences \lyxarrow{} File Handling \lyxarrow{} File Formats}}{\small{}
+and find }{\small\textsf{PDF (pdflatex)}}{\small{} (assuming export
+to }{\small\texttt{pdf}}{\small{} by this route) in the list of formats.
+In}{\small\textsf{ }}{\small the }{\small\textsf{Copier}}{\small{} slot
+of the dialogue insert the following line of code: }{\small\par}
\begin{lyxcode}
{\small python~-tt~\$\$s/scripts/ext\_copy.py~-e~nmc,pdf~-d~\$\$i~\$\$o}{\small\par}
\end{lyxcode}
-\verb`ext_copy.py` is a python script that is supplied with \LyX .
-The \texttt{-e nmc,pdf -d} part of the line tells \texttt{ext\_copy.py}
-that on export to \texttt{pdf} by the \texttt{pdflatex} route\texttt{
-}to copy any files with the extensions \texttt{.nmc} or \texttt{.pdf}
-from the temporary directory where \LyX{} does its work back to the
-document directory – the \verb`-d` option (which became available
-with \LyX{} 2.3.0).
+{\small{\small\verb`ext_copy.py`}}{\small{} is a python script
+that is supplied with \LyX . The }{\small\texttt{-e nmc,pdf -d}}{\small{}
+part of the line tells }{\small\texttt{ext\_copy.py}}{\small{} that
+on export to }{\small\texttt{pdf}}{\small{} by the }{\small\texttt{pdflatex}}{\small{}
+route}{\small\texttt{ }}{\small to copy any files with the extensions
+}{\small\texttt{.nmc}}{\small{} or }{\small\texttt{.pdf}}{\small{} from
+the temporary directory where \LyX{} does its work back to the document
+directory -- the }{\small{\small\verb`-d`}}{\small{} option
+(which became available with \LyX{} 2.3.0).}{\small\par}
-But if you have a complex document, it may take too much time to want
-to export to pdf before closing \LyX , particularly if there are a
-lot of evaluations in the document. Much faster is to export to \emph{plain
-text}, not because you want a plain text version of your document
-but because it too can be used to trigger the copier mechanism. Go
-to \textsf{Tools \lyxarrow{} Preferences \lyxarrow{} File Handling \lyxarrow{}
-File Formats} and find \textsf{Plain text} in the list of formats.
-In the \textsf{Copier} slot enter
+{\small But if you have a complex document, it may take too much time
+to want to export to pdf before closing \LyX , particularly if there
+are a lot of evaluations in the document. Much faster is to export
+to }{\small\emph{plain text}}{\small , not because you want a plain
+text version of your document but because it too can be used to trigger
+the copier mechanism. Go to }{\small\textsf{Tools \lyxarrow{} Preferences
+\lyxarrow{} File Handling \lyxarrow{} File Formats}}{\small{} and find
+}{\small\textsf{Plain text}}{\small{} in the list of formats. In the
+}{\small\textsf{Copier}}{\small{} slot enter }{\small\par}
\begin{lyxcode}
{\small python~-tt~\$\$s/scripts/ext\_copy.py~-e~nmc~-d~\$\$i~\$\$o}{\small\par}
\end{lyxcode}
-The only difference from the previous copier command is the absence
-of \texttt{pdf}.\footnote{I'm assuming that you don't actually want the plain text version of
-the file copied back. If you do, then change \texttt{-e nmc} to \texttt{-e
-nmc,txt}.} This will copy \texttt{mydoc.nmc} with its saved values from the
-temporary directory back to the document directory. To effect the
-export, go to \textsf{File \lyxarrow{} Export }and find \textsf{Plain
-text} in the list of formats and click on it.
+{\small The only difference from the previous copier command is the
+absence of }{\small\texttt{pdf}}{\small .}{\small\footnote{{\small I'm assuming that you don't actually want the plain text version
+of the file copied back. If you do, then change }{\small\texttt{-e
+nmc}}{\small{} to }{\small\texttt{-e nmc,txt}}{\small .}}}{\small{} This will copy }{\small\texttt{mydoc.nmc}}{\small{} with its
+saved values from the temporary directory back to the document directory.
+To effect the export, go to }{\small\textsf{File \lyxarrow{} Export
+}}{\small and find }{\small\textsf{Plain text}}{\small{} in the list
+of formats and click on it.}{\small\par}
-A shortcut would be nice. For that go to \textsf{Tools \lyxarrow{}
-Preferences \lyxarrow{} Editing \lyxarrow{} Shortcuts}, click on \textsf{New},
-enter \texttt{buffer-export text} in the \textsf{Function:} slot,
-click on the blank key against \textsf{Shortcut:} and type your shortcut.
-You may have to try a number before you find one that hasn't already
-been assigned. (I'm using \textsf{Ctrl+}; for no particular reason
-beyond the fact that it fits under the fingers easily and saving values
-to the document directory has a punctuation-like feel to it, a pause
-in the process of writing.) It is now an easy matter to press the
-shortcut at the end of a \LyX{} session to copy all the values saved
-in \texttt{mydoc.nmc} back to a file of the same name in the document
-directory. And it is brisk, not least because plain text export ignores
-ERT insets (and hence preview insets wrapped around ERT insets), nor
-does it evaluate \verb`\eval` commands in math insets.
+{\small A shortcut would be nice. For that go to }{\small\textsf{Tools
+\lyxarrow{} Preferences \lyxarrow{} Editing \lyxarrow{} Shortcuts}}{\small ,
+click on }{\small\textsf{New}}{\small , enter }{\small\texttt{buffer-export
+text}}{\small{} in the }{\small\textsf{Function:}}{\small{} slot, click
+on the blank key against }{\small\textsf{Shortcut:}}{\small{} and type
+your shortcut. You may have to try a number before you find one that
+hasn't already been assigned. (I'm using }{\small\textsf{Ctrl+}}{\small ;
+for no particular reason beyond the fact that it fits under the fingers
+easily and saving values to the document directory has a punctuation-like
+feel to it, a pause in the process of writing.) It is now an easy
+matter to press the shortcut at the end of a \LyX{} session to copy
+all the values saved in }{\small\texttt{mydoc.nmc}}{\small{} back to
+a file of the same name in the document directory. And it is brisk,
+not least because plain text export ignores ERT insets (and hence
+preview insets wrapped around ERT insets), nor does it evaluate }{\small{\small\verb`\eval`}}{\small{}
+commands in math insets.}{\small\par}
\subsubsection{A final tweak?}
-But one still needs to \emph{remember} to press the shortcut. The
-thought arises: can \emph{closing} the current document trigger the
-copying process? \LyX{} provides a means of linking two commands and
-assigning a keyboard shortcut to them with its \texttt{command-sequence}
-\LyX{} function. I suggest assigning a shortcut\textsf{ }to
+{\small But one still needs to }{\small\emph{remember}}{\small{} to press
+the shortcut. The thought arises: can }{\small\emph{closing}}{\small{}
+the current document trigger the copying process? \LyX{} provides a
+means of linking two commands and assigning a keyboard shortcut to
+them with its }{\small\texttt{command-sequence}}{\small{} \LyX{} function.
+I suggest assigning a shortcut}{\small\textsf{ }}{\small to }{\small\par}
\begin{lyxcode}
-command-sequence~buffer-export~text;~view-close
+{\small command-sequence~buffer-export~text;~view-close}{\small\par}
\end{lyxcode}
-Indeed, why not reassign the current shortcut for \texttt{view-close},\texttt{
-}which is \textsf{Ctrl+W} on my system, to this command sequence?
-(I use the \texttt{cua} key bindings – check the \textsf{Bind file:}
-slot in \textsf{Tools \lyxarrow{} Preferences \lyxarrow{} Editing \lyxarrow{}
-Shortcuts}.)
+{\small Indeed, why not reassign the current shortcut for }{\small\texttt{view-close}}{\small ,}{\small\texttt{
+}}{\small which is }{\small\textsf{Ctrl+W}}{\small{} on my system, to
+this command sequence? (I use the }{\small\texttt{cua}}{\small{} key
+bindings -- check the }{\small\textsf{Bind file:}}{\small{} slot in
+}{\small\textsf{Tools \lyxarrow{} Preferences \lyxarrow{} Editing \lyxarrow{}
+Shortcuts}}{\small .)}{\small\par}
-Please note, however, that \emph{this will work as intended only from
-\LyX{} 2.4.0}.\footnote{Due for release in 2021.} For \LyX{} 2.3 and
-earlier, the command sequence will generally fail because of `asynchronous'
-processing – \texttt{buffer-export }and \texttt{view-close} use different
-threads and the latter may well start before the former is complete.
-From \LyX{} 2.4.0 this defect has been fixed. You press your shortcut,
-the export to plain text occurs and the \texttt{.nmc} file is copied
-back to the document directory, then the current view is closed.
+{\small Please note, however, that }{\small\emph{this will work as
+intended only from \LyX{} 2.4.0}}{\small .}{\small\footnote{{\small Much delayed; due for release in 2023.}}}{\small{}
+For \LyX{} 2.3 and earlier, the command sequence will generally fail
+because of `asynchronous' processing -- }{\small\texttt{buffer-export
+}}{\small and }{\small\texttt{view-close}}{\small{} use different threads
+and the latter may well start before the former is complete. From
+\LyX{} 2.4.0 this defect has been fixed. You press your shortcut, the
+export to plain text occurs and the }{\small\texttt{.nmc}}{\small{}
+file is copied back to the document directory, then the current view
+is closed.}{\small\par}
-Note that in the other direction, the \verb`.nmc` file in your document
-directory is \emph{automatically} copied to the temporary directory
-when needed. Nothing needs to be done by you, the user.
+{\small Note that in the other direction, the }{\small{\small\verb`.nmc`}}{\small{}
+file in your document directory is }{\small\emph{automatically}}{\small{}
+copied to the temporary directory when needed. Nothing needs to be
+done by you, the user.}{\small\par}
\subsubsection{Use of \protect\LyX{} notes}
-The central fact about a \LyX{} note is that it does not contribute
+{\small The central fact about a \LyX{} note is that it does not contribute
to the pdf. But instant preview still works there. This suggests a
possibility: that a calculation be performed within a \LyX{} note and
-the result saved using \verb`\nmcReuse` within the same note. The
-saved value is now available \emph{from file} for use elsewhere in
-the document. In this way, some selected content from a LyX note \emph{can}
-find its way into the pdf when the document is compiled.
+the result saved using }{\small{\small\verb`\nmcReuse`}}{\small{}
+within the same note. The saved value is now available }{\small\emph{from
+file}}{\small{} for use elsewhere in the document. In this way, some
+selected content from a LyX note }{\small\emph{can}}{\small{} find its
+way into the pdf when the document is compiled.}{\small\par}
\chapter{Reference summary}
\section{Commands defined in \texttt{numerica}}
\begin{enumerate}
-\item \texttt{\textbackslash nmcEvaluate, \textbackslash eval }
-\item \texttt{\textbackslash q, \textbackslash Q }(`cleave' commands)
-\item \texttt{\textbackslash nmcInfo, \textbackslash info}
-\item \texttt{\textbackslash nmcMacros, \textbackslash macros}
-\item \texttt{\textbackslash nmcConstants, \textbackslash constants}
-\item \texttt{\textbackslash nmcReuse, \textbackslash reuse}
+\item {\small\texttt{\textbackslash nmcEvaluate, \textbackslash eval }}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash q, \textbackslash Q }}{\small (`cleave'
+commands) }{\small\par}
+\item {\small\texttt{\textbackslash nmcInfo, \textbackslash info}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash nmcMacros, \textbackslash macros}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash nmcConstants, \textbackslash constants}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash nmcReuse, \textbackslash reuse}}{\small{} }{\small\par}
\end{enumerate}
-Provided they have not already been defined when \texttt{numerica}
-is loaded, the following commands are defined in \texttt{numerica}
-using \verb`\DeclareMathOperator` from \texttt{amsmath} :
+{\small Provided they have not already been defined when }{\small\texttt{numerica}}{\small{}
+is loaded, the following commands are defined in }{\small\texttt{numerica}}{\small{}
+using }{\small{\small\verb`\DeclareMathOperator`}}{\small{}
+from }{\small\texttt{amsmath}}{\small{} : }{\small\par}
\begin{enumerate}
-\item \texttt{\textbackslash arccsc, \textbackslash arcsec, \textbackslash arccot}
-\item \texttt{\textbackslash csch, \textbackslash sech}
-\item \texttt{\textbackslash asinh, \textbackslash acosh, \textbackslash atanh,
-\textbackslash acsch, \textbackslash asech, \textbackslash acoth}
-\item \texttt{\textbackslash sgn, \textbackslash lb}
+\item {\small\texttt{\textbackslash arccsc, \textbackslash arcsec, \textbackslash arccot}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash csch, \textbackslash sech}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash asinh, \textbackslash acosh, \textbackslash atanh,
+\textbackslash acsch, \textbackslash asech, \textbackslash acoth}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash sgn, \textbackslash lb}}{\small{} }{\small\par}
\end{enumerate}
-Provided they have not already been defined, the following commands
-are defined in \texttt{numerica} using \verb`\DeclarePairedDelimiter`
-from \texttt{mathtools}:
+{\small Provided they have not already been defined, the following
+commands are defined in }{\small\texttt{numerica}}{\small{} using }{\small{\small\verb`\DeclarePairedDelimiter`}}{\small{}
+from }{\small\texttt{mathtools}}{\small : }{\small\par}
\begin{lyxcode}
-\textbackslash abs,~\textbackslash ceil,~\textbackslash floor
+{\small\textbackslash abs,~\textbackslash ceil,~\textbackslash floor}{\small\par}
\end{lyxcode}
-The following commands have been redefined in \texttt{numerica} to
-give more spacing around the underlying \verb`\wedge` and \verb`\vee`
-symbols:
+{\small The following commands have been redefined in }{\small\texttt{numerica}}{\small{}
+to give more spacing around the underlying }{\small{\small\verb`\wedge`}}{\small{}
+and }{\small{\small\verb`\vee`}}{\small{} symbols: }{\small\par}
\begin{lyxcode}
-\textbackslash land,~\textbackslash lor
+{\small\textbackslash land,~\textbackslash lor}{\small\par}
\end{lyxcode}
\section{\textquoteleft Digestible\textquoteright{} content}
-\texttt{numerica} knows how to deal with the following content, meaning
-that any of these elements occurring within an \verb`\eval` command
-should not of itself cause a \texttt{numerica} error. Not all formatting
-commands affect display of the output.
+{\small\texttt{numerica}}{\small{} knows how to deal with the following
+content, meaning that any of these elements occurring within an }{\small{\small\verb`\eval`}}{\small{}
+command should not of itself cause a }{\small\texttt{numerica}}{\small{}
+error. Not all formatting commands affect display of the output. }{\small\par}
\begin{enumerate}
-\item variable names (sequences of tokens given values in the variable~=~value
-list)
-\item digits, decimal point
+\item {\small variable names (sequences of tokens given values in the variable~=~value
+list) }{\small\par}
+\item {\small digits, decimal point }{\small\par}
\begin{enumerate}
-\item \texttt{1, 2, 3, 4, 5, 6, 7, 8, 9, 0, .}
+\item {\small\texttt{1, 2, 3, 4, 5, 6, 7, 8, 9, 0, .}}{\small{} }{\small\par}
\end{enumerate}
-\item constants
+\item {\small constants }{\small\par}
\begin{enumerate}
-\item \texttt{e, \textbackslash pi, \textbackslash gamma, \textbackslash phi,
-\textbackslash deg, \textbackslash infty}
+\item {\small\texttt{e, \textbackslash pi, \textbackslash gamma, \textbackslash phi,
+\textbackslash deg, \textbackslash infty}}{\small{} }{\small\par}
\end{enumerate}
-\item arithmetic operators
+\item {\small arithmetic operators }{\small\par}
\begin{enumerate}
-\item \texttt{+, -, {*}, /, \textasciicircum , \textbackslash times, \textbackslash cdot,
-\textbackslash div}
+\item {\small\texttt{+, -, {*}, /, \textasciicircum , \textbackslash times,
+\textbackslash cdot, \textbackslash div}}{\small{} }{\small\par}
\end{enumerate}
-\item logical operators
+\item {\small logical operators }{\small\par}
\begin{enumerate}
-\item \texttt{\textbackslash wedge, \textbackslash land, \textbackslash vee,
-\textbackslash lor, \textbackslash neg, \textbackslash lnot}
+\item {\small\texttt{\textbackslash wedge, \textbackslash land, \textbackslash vee,
+\textbackslash lor, \textbackslash neg, \textbackslash lnot}}{\small{} }{\small\par}
\end{enumerate}
-\item comparisons
+\item {\small comparisons }{\small\par}
\begin{enumerate}
-\item \texttt{=, <, >, \textbackslash ne, \textbackslash neq, \textbackslash le,
-\textbackslash leq, \textbackslash ge, \textbackslash geq}
-\item (if \texttt{amssymb} loaded) \texttt{\textbackslash nless, \textbackslash ngtr,
-\textbackslash geqq, \textbackslash geqslant, \textbackslash leqq,
-\textbackslash leqslant, \textbackslash ngeq, \textbackslash ngeqq,
-\textbackslash ngeqslant, \textbackslash nleq, \textbackslash nleqq,
-\textbackslash nleqslant}
+\item {\small\texttt{=, <, >, \textbackslash ne, \textbackslash neq, \textbackslash le,
+\textbackslash leq, \textbackslash ge, \textbackslash geq}}{\small{} }{\small\par}
+\item {\small (if }{\small\texttt{amssymb}}{\small{} loaded) }{\small\texttt{\textbackslash nless,
+\textbackslash ngtr, \textbackslash geqq, \textbackslash geqslant,
+\textbackslash leqq, \textbackslash leqslant, \textbackslash ngeq,
+\textbackslash ngeqq, \textbackslash ngeqslant, \textbackslash nleq,
+\textbackslash nleqq, \textbackslash nleqslant}}{\small{} }{\small\par}
\end{enumerate}
-\item brackets, bracket-like elements, modifiers
+\item {\small brackets, bracket-like elements, modifiers }{\small\par}
\begin{enumerate}
-\item \texttt{( ), {[} {]}, \textbackslash\{ \textbackslash\}}
-\item \texttt{\textbackslash lparen \textbackslash rparen} (from \texttt{mathtools})\texttt{,
-\textbackslash lbrack \textbackslash rbrack, \textbackslash lbrace
-\textbackslash rbrace}
-\item \texttt{\textbackslash lvert \textbackslash rvert, \textbackslash lfloor
-\textbackslash rfloor, \textbackslash lceil \textbackslash rceil}
-\item \texttt{| |} (no nesting, deprecated)
-\item \texttt{\textbackslash left \textbackslash right, \textbackslash bigl
+\item {\small\texttt{( ), {[} {]}, \textbackslash\{ \textbackslash\}}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash lparen \textbackslash rparen}}{\small{}
+(from }{\small\texttt{mathtools}}{\small )}{\small\texttt{, \textbackslash lbrack
+\textbackslash rbrack, \textbackslash lbrace \textbackslash rbrace}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash lvert \textbackslash rvert, \textbackslash lfloor
+\textbackslash rfloor, \textbackslash lceil \textbackslash rceil}}{\small{} }{\small\par}
+\item {\small\texttt{| |}}{\small{} (no nesting, deprecated) }{\small\par}
+\item {\small\texttt{\textbackslash left \textbackslash right, \textbackslash bigl
\textbackslash bigr, \textbackslash Bigl \textbackslash Bigr, \textbackslash biggl
-\textbackslash biggr, \textbackslash Biggl \textbackslash Biggr}
-\item \texttt{.} \texttt{/ |} (used with a modifier)
-\item \texttt{\textbackslash abs{[}{]}\{\}, \textbackslash abs{*}\{\},
+\textbackslash biggr, \textbackslash Biggl \textbackslash Biggr}}{\small{} }{\small\par}
+\item {\small\texttt{.}}{\small{} }{\small\texttt{/ |}}{\small{} (used with
+a modifier) }{\small\par}
+\item {\small\texttt{\textbackslash abs{[}{]}\{\}, \textbackslash abs{*}\{\},
\textbackslash floor{[}{]}\{\}, \textbackslash floor{*}\{\}, \textbackslash ceil{[}{]}\{\},
-\textbackslash ceil{*}\{\}}
+\textbackslash ceil{*}\{\}}}{\small{} }{\small\par}
\end{enumerate}
-\item unary functions (in the mathematical sense)
+\item {\small unary functions (in the mathematical sense) }{\small\par}
\begin{enumerate}
-\item \texttt{\textbackslash sin, \textbackslash cos, \textbackslash tan,
-\textbackslash csc, \textbackslash sec, \textbackslash cot}
-\item \texttt{\textbackslash arcsin, \textbackslash arccos, \textbackslash arctan,
-arccsc, \textbackslash arcsec, \textbackslash arccot }
-\item \texttt{\textbackslash sin\textasciicircum\{-1\}, \textbackslash cos\textasciicircum\{-1\},
+\item {\small\texttt{\textbackslash sin, \textbackslash cos, \textbackslash tan,
+\textbackslash csc, \textbackslash sec, \textbackslash cot}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash arcsin, \textbackslash arccos, \textbackslash arctan,
+arccsc, \textbackslash arcsec, \textbackslash arccot }}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash sin\textasciicircum\{-1\}, \textbackslash cos\textasciicircum\{-1\},
\textbackslash tan\textasciicircum\{-1\}, \textbackslash csc\textasciicircum\{-1\},
-\textbackslash sec\textasciicircum\{-1\}, \textbackslash cot\textasciicircum\{-1\}}
-\item \texttt{\textbackslash sinh, \textbackslash cosh, \textbackslash tanh,
-\textbackslash csch, \textbackslash sech, \textbackslash coth }
-\item \texttt{\textbackslash asinh, \textbackslash acosh, \textbackslash atanh,
-\textbackslash csch, \textbackslash sech, \textbackslash acoth}
-\item \texttt{\textbackslash sinh\textasciicircum\{-1\}, \textbackslash cosh\textasciicircum\{-1\},
+\textbackslash sec\textasciicircum\{-1\}, \textbackslash cot\textasciicircum\{-1\}}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash sinh, \textbackslash cosh, \textbackslash tanh,
+\textbackslash csch, \textbackslash sech, \textbackslash coth }}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash asinh, \textbackslash acosh, \textbackslash atanh,
+\textbackslash csch, \textbackslash sech, \textbackslash acoth}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash sinh\textasciicircum\{-1\}, \textbackslash cosh\textasciicircum\{-1\},
\textbackslash tanh\textasciicircum\{-1\}, \textbackslash csch\textasciicircum\{-1\},
-\textbackslash sech\textasciicircum\{-1\}, \textbackslash acoth\textasciicircum\{-1\}}
-\item \texttt{\textbackslash exp, \textbackslash lb, \textbackslash lg,
+\textbackslash sech\textasciicircum\{-1\}, \textbackslash acoth\textasciicircum\{-1\}}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash exp, \textbackslash lb, \textbackslash lg,
\textbackslash ln, \textbackslash log, \textbackslash log\_\{\},
-\textbackslash sgn, \textbackslash surd}
-\item \texttt{\textbackslash sqrt\{\}, \textbackslash abs{[}{]}\{\}, \textbackslash abs{*}\{\},
-\textbackslash floor{[}{]}\{\}, \textbackslash floor{*}\{\}, \textbackslash ceil{[}{]}\{\},
-\textbackslash ceil{*}\{\}}
-\item \texttt{!, !! }(prepended argument)
+\textbackslash sgn, \textbackslash surd}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash sqrt\{\}, \textbackslash abs{[}{]}\{\},
+\textbackslash abs{*}\{\}, \textbackslash floor{[}{]}\{\}, \textbackslash floor{*}\{\},
+\textbackslash ceil{[}{]}\{\}, \textbackslash ceil{*}\{\}}}{\small{} }{\small\par}
+\item {\small\texttt{!, !! }}{\small (prepended argument) }{\small\par}
\end{enumerate}
-\item binary functions
+\item {\small binary functions }{\small\par}
\begin{enumerate}
-\item \texttt{\textbackslash tfrac\{\}\{\}, \textbackslash frac\{\}\{\},
-\textbackslash dfrac\{\}\{\}}
-\item \texttt{\textbackslash tbinom\{\}\{\}, \textbackslash binom\{\}\{\},
-\textbackslash dbinom\{\}\{\}}
-\item \texttt{\textbackslash sqrt{[}{]}\{\}}
+\item {\small\texttt{\textbackslash tfrac\{\}\{\}, \textbackslash frac\{\}\{\},
+\textbackslash dfrac\{\}\{\}}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash tbinom\{\}\{\}, \textbackslash binom\{\}\{\},
+\textbackslash dbinom\{\}\{\}}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash sqrt{[}{]}\{\}}}{\small{} }{\small\par}
\end{enumerate}
-\item $n$-ary functions
+\item {\small$n$-ary functions }{\small\par}
\begin{enumerate}
-\item \texttt{\textbackslash min, \textbackslash max, \textbackslash gcd}
+\item {\small\texttt{\textbackslash min, \textbackslash max, \textbackslash gcd}}{\small{} }{\small\par}
\end{enumerate}
-\item sum, prod
+\item {\small sum, prod }{\small\par}
\begin{enumerate}
-\item \texttt{\textbackslash sum\_\{\}\textasciicircum , \textbackslash prod\_\{\}\textasciicircum{} }
+\item {\small\texttt{\textbackslash sum\_\{\}\textasciicircum , \textbackslash prod\_\{\}\textasciicircum{}
+}}{\small{} }{\small\par}
\end{enumerate}
-\item formatting commands
+\item {\small formatting commands }{\small\par}
\begin{enumerate}
-\item \texttt{,} (comma, in $n$-ary functions)
-\item \texttt{\{\}, \textbackslash\textbackslash , \&, \textbackslash to}
-\item \texttt{\textbackslash begin\{\}, \textbackslash end\{\}, \$, \textbackslash{[},
-\textbackslash{]}}
-\item \texttt{\textbackslash dots, \textbackslash ldots, \textbackslash cdots}
-\item \texttt{\textbackslash{} , \textbackslash ,{}, \textbackslash ;,
-\textbackslash :, \textbackslash !, \textbackslash >}
-\item \texttt{\textbackslash thinspace, \textbackslash medspace, \textbackslash thickspace,}
-\item \textbackslash\texttt{negthinspace, \textbackslash negmedspace,
-\textbackslash negthickspace,}
-\item \textbackslash\texttt{hspace{*}\{\}, \textbackslash mspace\{\},}
-\item \texttt{\textbackslash quad, \textbackslash qquad , \textbackslash hfill,
-\textbackslash hfil}
-\item \texttt{\textbackslash phantom\{\}, \textbackslash vphantom\{\},
-\textbackslash hphantom\{\}}
-\item \texttt{\textbackslash xmathstrut{[}{]}\{\}} \texttt{, \textbackslash splitfrac\{\}\{\},
-\textbackslash splitdfrac\{\}\{\} }(from \texttt{mathtools}), \texttt{\textbackslash mathstrut}
-\item \texttt{\textbackslash displaystyle, \textbackslash textstyle, \textbackslash scriptstyle,
-\textbackslash scriptscriptstyle}
-\item \texttt{\textbackslash label\{\}, \textbackslash ensuremath\{\},
-\textbackslash text\{\}, \textbackslash mbox\{\}, \textbackslash smash\{\}}
-\item \texttt{\textbackslash color{[}{]}\{\}, \textbackslash textcolor{[}{]}\{\}\{\}}
+\item {\small\texttt{,}}{\small{} (comma, in $n$-ary functions) }{\small\par}
+\item {\small\texttt{\{\}, \textbackslash\textbackslash , \&, \textbackslash to}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash begin\{\}, \textbackslash end\{\},
+\$, \textbackslash{[}, \textbackslash{]}}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash dots, \textbackslash ldots, \textbackslash cdots}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash{} , \textbackslash ,}} \{\}{\small\texttt{,
+\textbackslash ;, \textbackslash :, \textbackslash !, \textbackslash >}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash thinspace, \textbackslash medspace,
+\textbackslash thickspace,}}{\small{} }{\small\par}
+\item {\small\textbackslash}{\small\texttt{negthinspace, \textbackslash negmedspace,
+\textbackslash negthickspace,}}{\small{} }{\small\par}
+\item {\small\textbackslash}{\small\texttt{hspace{*}\{\}, \textbackslash mspace\{\},}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash quad, \textbackslash qquad , \textbackslash hfill,
+\textbackslash hfil}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash phantom\{\}, \textbackslash vphantom\{\},
+\textbackslash hphantom\{\}}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash xmathstrut{[}{]}\{\}}}{\small{} }{\small\texttt{,
+\textbackslash splitfrac\{\}\{\}, \textbackslash splitdfrac\{\}\{\}
+}}{\small (from }{\small\texttt{mathtools}}{\small ), }{\small\texttt{\textbackslash mathstrut}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash displaystyle, \textbackslash textstyle,
+\textbackslash scriptstyle, \textbackslash scriptscriptstyle}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash label\{\}, \textbackslash ensuremath\{\},
+\textbackslash text\{\}, \textbackslash mbox\{\}, \textbackslash smash\{\}}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash color{[}{]}\{\}, \textbackslash textcolor{[}{]}\{\}\{\}}}{\small{} }{\small\par}
\end{enumerate}
-\item font commands
+\item {\small font commands }{\small\par}
\begin{enumerate}
-\item \texttt{\textbackslash mathrm\{\}, \textbackslash mathit\{\}, \textbackslash mathcal\{\},
-\textbackslash mathtt\{\}, \textbackslash mathbf\{\}, \textbackslash mathbb\{\},
-\textbackslash mathsf\{\}, \textbackslash mathfrak\{\}, \textbackslash mathscr\{\}}
-\item \texttt{\textbackslash mathnormal\{\}, \textbackslash boldsymbol\{\}}
-\item \texttt{\textbackslash textrm, \textbackslash textsf, \textbackslash texttt}
+\item {\small\texttt{\textbackslash mathrm\{\}, \textbackslash mathit\{\},
+\textbackslash mathcal\{\}, \textbackslash mathtt\{\}, \textbackslash mathbf\{\},
+\textbackslash mathbb\{\}, \textbackslash mathsf\{\}, \textbackslash mathfrak\{\},
+\textbackslash mathscr\{\}}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash mathnormal\{\}, \textbackslash boldsymbol\{\}}}{\small{} }{\small\par}
+\item {\small\texttt{\textbackslash textrm, \textbackslash textsf, \textbackslash texttt}}{\small{} }{\small\par}
\end{enumerate}
\end{enumerate}
@@ -6105,62 +6259,68 @@
\subsection{Available \texttt{\textbackslash nmcEvaluate} settings}
\begin{center}
+{\small{}%
\begin{tabular}[t]{>{\raggedright}p{1.5cm}l>{\raggedright}m{4cm}>{\raggedright}m{4cm}}
\toprule
{\small key} & {\small type} & {\small meaning} & {\small default}\tabularnewline
-\midrule
+\midrule
{\small\texttt{dbg}} & {\small int} & {\small debug `magic' integer} & {\small\texttt{0}}\tabularnewline
-{\small\texttt{view}} & & {\small equivalent to }{\small\texttt{dbg=1}} & \tabularnewline
+{\small\texttt{view}} & & {\small equivalent to }{\small\texttt{dbg=1}} & \tabularnewline
{\small\texttt{\textasciicircum}} & {\small char} & {\small exponent mark for sci. notation input} & {\small\texttt{e}}\tabularnewline
{\small\texttt{xx}} & {\small int (0/1)} & {\small multi-token variable switch} & {\small\texttt{1}}\tabularnewline
{\small\texttt{()}} & {\small int (0/1/2)} & {\small trig. function arg. parsing} & {\small\texttt{0}}\tabularnewline
{\small\texttt{o}} & {\small int (0/1)} & {\small degree switch for trig. funcions} & {\small\texttt{1}}\tabularnewline
-{\small\texttt{log}} & {\small num} & {\small base of logarithms for }{\small{\small\verb`\log`}} & {\small\texttt{10}}\tabularnewline
+{\small\texttt{log}} & {\small num} & {\small base of logarithms for }{\small{\small\verb`\log`}}{\small} & {\small\texttt{10}}\tabularnewline
{\small\texttt{vv@}} & {\small int (0/1)} & {\small vv-list calculation mode} & {\small\texttt{0}}\tabularnewline
{\small\texttt{vvmode}} & {\small int (0/1)} & {\small equivalent to }{\small\texttt{vv@}} & {\small\texttt{0}}\tabularnewline
{\small\texttt{vvd}} & {\small token(s)} & {\small vv-list display-style spec.} & {\small\texttt{\{,\}\textbackslash mskip 12mu plus 6mu minus 9mu(vv)}}\tabularnewline
{\small\texttt{vvi}} & {\small token(s)} & {\small vv-list text-style spec.} & {\small\texttt{\{,\}\textbackslash mskip 36mu minus 24mu(vv)}}\tabularnewline
-{*} & & {\small switch to suppress equation numbering (if }{\small\texttt{\textbackslash\textbackslash}}{\small{}
+{\small{*}} & & {\small switch to suppress equation numbering (if }{\small\texttt{\textbackslash\textbackslash}}{\small{}
in }{\small\texttt{vvd}}{\small )} & \tabularnewline
-{\small\texttt{p}} & char(s) & {\small punctuation (esp. in display-style)} & {\small\texttt{,}}\tabularnewline
+{\small\texttt{p}} & {\small char(s)} & {\small punctuation (esp. in display-style)} & {\small\texttt{,}}\tabularnewline
{\small\texttt{S+}} & {\small int} & {\small extra rounding for stopping criterion, sums} & {\small\texttt{2}}\tabularnewline
{\small\texttt{S?}} & {\small$\text{int}\ge0$} & {\small query stopping with these final terms, sums} & {\small\texttt{0}}\tabularnewline
{\small\texttt{P+}} & {\small int} & {\small extra rounding for stopping criterion, products} & {\small\texttt{2}}\tabularnewline
{\small\texttt{P?}} & {\small$\text{int}\ge0$} & {\small query stopping with these final terms, products} & {\small\texttt{0}}\tabularnewline
-{\small\texttt{reuse}} & {\small int} & {\small form of result saved with }{\small{\small\verb`\nmcReuse`}} & {\small\texttt{0}}\tabularnewline
+{\small\texttt{reuse}} & {\small int} & {\small form of result saved with }{\small{\small\verb`\nmcReuse`}}{\small} & {\small\texttt{0}}\tabularnewline
\bottomrule
-\end{tabular}
+\end{tabular}}{\small\par}
\par\end{center}
\subsection{Available settings for supplementary commands}
-All settings for \verb`\nmcEvaluate`, the \verb`view` setting in
-particular (although most will be irrelevant), plus for
+{\small All settings for }{\small{\small\verb`\nmcEvaluate`}}{\small ,
+the }{\small{\small\verb`view`}}{\small{} setting in particular
+(although most will be irrelevant), plus for }{\small\par}
\begin{itemize}
-\item \verb`\nmcMacros`
+\item {\small{\small\verb`\nmcMacros`}}{\small{} }{\small\par}
\begin{itemize}
-\item \verb`free` `deregister' a macro from \verb`numerica`
+\item {\small{\small\verb`free`}}{\small{} `deregister' a macro from
+}\texttt{numerica}{\small{} }{\small\par}
\end{itemize}
-\item \verb`\nmcConstants`
+\item {\small{\small\verb`\nmcConstants`}}{\small{} }{\small\par}
\begin{itemize}
-\item \verb`add` add the new list of constants to the current one
+\item {\small{\small\verb`add`}}{\small{} add the new list of constants
+to the current one }{\small\par}
\end{itemize}
-\item \verb`\nmcReuse`
+\item {\small{\small\verb`\nmcReuse`}}{\small{} }{\small\par}
\begin{itemize}
-\item \verb`delete` remove the listed control sequences from the \verb`.nmc`
-file
-\item \verb`renew` change the value of a control sequence in the \verb`.nmc`
-file
+\item {\small{\small\verb`delete`}}{\small{} remove the listed control
+sequences from the }{\small{\small\verb`.nmc`}}{\small{} file }{\small\par}
+\item {\small{\small\verb`renew`}}{\small{} change the value of a
+control sequence in the }{\small{\small\verb`.nmc`}}{\small{}
+file }{\small\par}
\end{itemize}
\end{itemize}
\subsection{Available configuration file settings}
\begin{center}
-\bigskip{}
+{\small\bigskip{}
+ }{\small{}%
\begin{tabular}{ll}
\toprule
-key & default\tabularnewline
-\midrule
+{\small key} & {\small default}\tabularnewline
+\midrule
{\small\texttt{rounding}} & {\small\texttt{6}}\tabularnewline
{\small\texttt{pad}} & {\small\texttt{0}}\tabularnewline
{\small\texttt{output-sci-notation}} & {\small\texttt{0}}\tabularnewline
@@ -6172,7 +6332,7 @@
{\small\texttt{logarithm-base}} & {\small\texttt{10}}\tabularnewline
{\small\texttt{intify-rounding}} & {\small\texttt{14}}\tabularnewline
{\small\texttt{vv-display}} & {\small\texttt{\{,\}\textbackslash mskip 36mu minus 24mu(vv)}}\tabularnewline
-{\small\texttt{vv-inline}} & {\small\texttt{\{,\}\textbackslash mskip 12mu 6mu minus 9mu(vv)}}\tabularnewline
+{\small\texttt{vv-inline}} & {\small\texttt{\{,\}\textbackslash mskip 12mu 6mu minus 9mu(vv)}}\tabularnewline
{\small\texttt{sum-extra-rounding}} & {\small\texttt{2}}\tabularnewline
{\small\texttt{sum-query-terms}} & {\small\texttt{0}}\tabularnewline
{\small\texttt{prod-extra-rounding}} & {\small\texttt{2}}\tabularnewline
@@ -6179,6 +6339,8 @@
{\small\texttt{prod-query-terms}} & {\small\texttt{0}}\tabularnewline
{\small\texttt{eval-reuse}} & {\small\texttt{0}}\tabularnewline
\bottomrule
-\end{tabular}
+\end{tabular}}{\small\par}
\par\end{center}
+
+{\small{} }{\small\par}
\end{document}
Modified: trunk/Master/texmf-dist/tex/latex/numerica/numerica.sty
===================================================================
--- trunk/Master/texmf-dist/tex/latex/numerica/numerica.sty 2023-07-01 19:38:12 UTC (rev 67524)
+++ trunk/Master/texmf-dist/tex/latex/numerica/numerica.sty 2023-07-01 19:38:21 UTC (rev 67525)
@@ -8,11 +8,11 @@
% Andrew Parsloe (ajparsloe at gmail.com)
%
\RequirePackage{l3keys2e}
-\RequirePackage{amsmath,mathtools,etoolbox}
+\RequirePackage{amsmath,mathtools}
\ProvidesExplPackage
{numerica}
- {2021/12/07}
- {2.0.0}
+ {2023/06/28}
+ {2.1.0}
{Numerically evaluate mathematical expressions in their LaTeX form}
% needs amsmath
\cs_if_free:NT \arccsc { \DeclareMathOperator{\arccsc}{arccsc} }
@@ -50,12 +50,15 @@
\tl_new:N \l__nmc_toss_tl
\seq_new:N \l_tmpc_seq
%
-\prg_new_conditional:Npnn \int_if_zero:n #1 { p,T,F,TF }
- {
- \int_compare:nNnTF { #1 } = { 0 }
- { \prg_return_true: }
- { \prg_return_false: }
- }
+\cs_if_exist:NF \int_if_zero_p:n
+ {
+ \prg_new_conditional:Npnn \int_if_zero:n #1 { p,T,F,TF }
+ {
+ \int_compare:nNnTF { #1 } = { 0 }
+ { \prg_return_true: }
+ { \prg_return_false: }
+ }
+ }
\prg_new_conditional:Npnn \__nmc_if_mod_zero:nn #1#2 { p,T,F,TF }
{
\bool_if:nTF
@@ -634,7 +637,9 @@
{
\group_begin:
\__nmc_initialize:Nn ##1 { #2 }
+
\__nmc_inputs_get:nnnnn { #2 } { ##2 } { ##3 } {##4 } {##5 }
+
\bool_if:NF \g__nmc_error_bool
{ \use:c { __nmc_#2_process: } }
\int_if_zero:nTF { \l__nmc_dbg_int }
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