From b4fc5f639874db951177ec539299d20908adb654 Mon Sep 17 00:00:00 2001 From: Karl Berry Date: Mon, 9 Jan 2006 00:44:40 +0000 Subject: doc 4 git-svn-id: svn://tug.org/texlive/trunk@80 c570f23f-e606-0410-a88d-b1316a301751 --- Master/texmf-dist/doc/latex/nath/README | 48 + Master/texmf-dist/doc/latex/nath/nathguide.pdf | Bin 0 -> 143532 bytes Master/texmf-dist/doc/latex/nath/nathguide.tex | 1329 ++++++++++++++++++++++++ 3 files changed, 1377 insertions(+) create mode 100644 Master/texmf-dist/doc/latex/nath/README create mode 100644 Master/texmf-dist/doc/latex/nath/nathguide.pdf create mode 100644 Master/texmf-dist/doc/latex/nath/nathguide.tex (limited to 'Master/texmf-dist/doc/latex/nath') diff --git a/Master/texmf-dist/doc/latex/nath/README b/Master/texmf-dist/doc/latex/nath/README new file mode 100644 index 00000000000..3e25b74ca88 --- /dev/null +++ b/Master/texmf-dist/doc/latex/nath/README @@ -0,0 +1,48 @@ +Nath is a LaTeX (both 2e and 2.09) style to separate presentation and content +in mathematical typography. The style delivers a particular context-dependent +presentation on the basis of a rather coarse context-independent notation. +Although essentially backward compatible with LaTeX, Nath aims at producing +traditional math typography. Its name comes from ``NAtural maTH notation'' -- +see M.M., Natural TeX notation in mathematics, in: Proc. Conf. EuroTeX 2001, +Kerkrade, 23--27 September 2001 . + +Nath is a free software distributed under the terms of the GNU General Public +License . + +To install Nath, put the nath.sty file into the TeX input directory. +A LaTeX 2.09 document may start like + + \documentstyle[nath]{article} + +a LaTeX 2e document, like + + \documentclass{article} + \usepackage{nath} + +Nath does not introduce any new fonts. + +Nath helps to prevent wasting human work on something that can be done by +computer. +In particular, delimiters adapt their size to the material enclosed, +(rendering \left and \right almost obsolete), no matter how many \\'s +intervene. +Depending on the context, the command \frac produces either built-up or +case or solidus fractions, with parentheses added whenever required for +preservation of the mathematical meaning. + +Nath is provided as it is; only bug reports and serious discussion should go +to . +On average, LaTeX runs about three times slower with Nath than +without it, depending on the complexity of math formulas. + +The new release dated 11 February 2003 brings mainly several bug fixes +and introduces a new bug (sorry). +The new bug corrected 21 March 2003. + + + + + + + + diff --git a/Master/texmf-dist/doc/latex/nath/nathguide.pdf b/Master/texmf-dist/doc/latex/nath/nathguide.pdf new file mode 100644 index 00000000000..8a4e27bee98 Binary files /dev/null and b/Master/texmf-dist/doc/latex/nath/nathguide.pdf differ diff --git a/Master/texmf-dist/doc/latex/nath/nathguide.tex b/Master/texmf-dist/doc/latex/nath/nathguide.tex new file mode 100644 index 00000000000..0d603f6a497 --- /dev/null +++ b/Master/texmf-dist/doc/latex/nath/nathguide.tex @@ -0,0 +1,1329 @@ +%&LaTeX +\def\AmS{{$\mathcal A$\kern-.1667em + \lower.5ex\hbox{$\mathcal M$}\kern-.125em$\mathcal S$}} + +\documentclass{article} +\usepackage{nath} +\nathstyle{geometry} +\mathindent=4pc + +\makeatletter +\def \@listI{\leftmargin 3ex \topsep 4pt \partopsep 0pt + \itemsep 0pt \parsep 0pt \listparindent 0pt} +\makeatother + +\def\To#1\endTo{\hbox to 4cm{$\displayed{#1}$\hss} \hbox{$#1$}} +\newcounter{p} +\def\sect#1{\refstepcounter{p} \paragraph{\S\arabic{p}. #1.}} +\def\capt#1#2{{\small Table #1: #2}} +\def\stuff#1{\hbox{\vrule height 1.5ex depth .3ex width 0ex}% + \raise .6mm\vbox{\hrule width #1 height .5mm}} +\setbox0\hbox{\tt ????} +\catcode`\?=0 +\def????{\leavevmode\hbox to\wd0{\hss\it stuff\/\hss}} +\def\sref"#1"{\S\ref{#1}} +\def\refname{{\normalsize\bf References}} + +\begin{document} + +\title{A Short Guide to Nath} + +\author{M. Marvan} +\date{14 February 2003} + +\maketitle +%\end{document} + + +\sect{Annotation} +Nath is a \LaTeX\ style to separate presentation and content in mathematical +typography. +The style delivers a particular context-dependent presentation on the +basis of a rather coarse context-independent notation. +Although essentially backward compatible with \LaTeX, +Nath aims at producing traditional math typography even from sources +devoid of aesthetic ambitions. +Its name is derived from ``{\it na\/}tural ma{\it th\/} notation'' +(see~\cite{EuroTeX}). + + +\sect{License} +Nath is a free software distributed under the terms of the GNU General +Public License, see \verb"http://www.gnu.org/copyleft/gpl.html". + + +\sect{Usage} +To install Nath, put the \verb"nath.sty" file into the \TeX\ input +directory. +A \LaTeX~2.09 document may start like +\begin{verbatim} +\documentstyle[nath]{article} +\end{verbatim} +Under \LaTeX~2$_{\varepsilon}$, the effect is achieved with +\begin{verbatim} +\documentclass{article} +\usepackage{nath} +\end{verbatim} +Nath does not introduce any new fonts. +See \sref "OtherPackages" for combining Nath and other \LaTeX\ +styles. + + +\sect{Local options} \label{LocalOptions} +A few Nath options may be set in the body of a document. +The command \verb"\nathstyle" accepts a list of arguments of the form +`{\it name\/}\verb"="{\it value}' or `{\it name}'; the latter having the +same meaning as `{\it name\/}\verb"=on"'. +Currently supported options are +\verb"geometry" (see \sref"Delimiters"), +\verb"tensors" (see \sref"Tensors"), +\verb"leqno" (see \sref"EquationNumbering"), +and \verb"silent" (see \sref"ErrorsWarnings"). + + +\sect{Errors and warnings}\label{ErrorsWarnings} +Nath errors are visualized by $\natherrormark$ (or whatever is +\verb"\natherrormark") placed where the error manifests itself +(which may look misplaced). +Unlike errors, Nath warnings appear only in the \verb"log" file and +do so only if the local option (see \sref"LocalOptions") \verb"silent" +is set to \verb"on". + +Be aware that once admissible constructions may produce \TeX\ errors now. +E.g., superfluous braces may be harmful in math formulas except +around macro arguments. +Therefore, \verb"{" and \verb"}" should be used just where something +(a~sub- or superscript, a numerator, a denominator, and similar) +begins or ends. + + +\sect{Math modes}\label{MathModes} +\Nath\ uses two distinct math modes. +The single dollar sign \verb"$" invokes the {\it in-line\/} mode. +The double dollar sign \verb"$$" as well as other math environments +invoke the {\it display\/} mode. + +Observe the difference: +\verb"$(1 + \frac xy)^2$" typesets as $(1 + \frac xy)^2$, while +\begin{verbatim} +$$ +(1 + \frac xy)^2 +$$ +\end{verbatim} +typesets as +$$ +(1 + \frac xy)^2, +$$ +even though the notation is one and the same. + +Commands \verb"\inline" and \verb"\displayed" force either mode +on a subexpression. +Sub- and superscripts are normally typeset in in-line mode; but +\begin{verbatim} +$$ +(\sum_{i=1}^n x_i^p)^{\displayed{\frac 1p}} +$$ +\end{verbatim} +produces the {\it display} mode in the {\it script\/} size: +\nathstyle{debug} +$$ +(\sum_{i=1}^n x_i^p)^{\displayed{\frac 1p}}. +$$ +Never leave delimiters un\verb"\displayed" in these cases. + +The four math style switches of \TeX\ newly refer only to the +{\it size} of math expressions: +\verb"\scriptstyle" and \verb"\scriptscriptstyle" to the script +and second-level-script size of the {\it current\/} size; +\verb"\textstyle" is void; whereas \verb"\displaystyle" has a special +meaning in the context of the principle of smallest fences +(see~\sref "DisplayedFractions"). + + +\sect{Fractions} \label{Fractions} +Fractions indicate division in a very broad sense +(cf.~$\frac{\partial f}{\partial x}$) and may occur in three shapes: +$$ +\text{built-up \ } \frac AB, +\qquad +\text{piece } \hbox{ $\frac 12$}, +\qquad +\text{solidus } \hbox{ $\frac AB$}. +$$ +\Nath\ provides a single universal command \verb"\frac" +(besides of the obvious slash, `\verb"/"'). +The resulting shape is determined by special algorithms +(see~\cite{EuroTeX}). + + +\sect{Displayed fractions} \label{DisplayedFractions} +Non-numeric fractions come out as built up. +According to what we call the {\it principle of smallest fences}, +numeric fractions are typeset built up if and only if this does not +extend any paired delimiters. +E.g., +\begin{verbatim} +$$ +(\frac 12 + x)(\frac 12 + \frac 1x) +$$ +\end{verbatim} +results in +$$ +(\frac 12 + x)(\frac 12 + \frac 1x). +$$ +One can circumvent the rule in two possible ways. +\paritem{(i)} +In order to force a built-up fraction, place \verb"\displaystyle" anywhere +within the nearest pair of delimiters. +E.g., +$$ +(\frac 12 + x\displaystyle)(\frac 12 + \frac 1x) +$$ +results from +\begin{verbatim} +$$ +(\frac 12 + x\displaystyle)(\frac 12 + \frac 1x) +$$ +\end{verbatim} +\paritem{(ii)} +In order to force a case fraction, insert an extra pair of invisible +delimiters. E.g., +$$ +\int x\,dx = \left. \frac12 x^2 \right. +$$ +results from +\begin{verbatim} +$$ +\int x\,dx = \left. \frac12 x^2 \right. +$$ +\end{verbatim} +{\it Compound fractions} have their numerator and denominator in display +mode: +$$ +\frac{1 + \frac xy}{1 - \frac xy}. +$$ +One can, of course, force the in-line mode. Namely, +\begin{verbatim} +$$ +\frac{\inline{1 + \frac xy}}{\inline{1 - \frac xy}} +$$ +\end{verbatim} +or, even better, +\begin{verbatim} +\newcommand\ifrac[2]{\frac{\inline{#1}}{\inline{#2}}} +$$ +\ifrac{1 + \frac xy}{1 - \frac xy} +$$ +\end{verbatim} +(cf. \sref"UserDefinitions") typesets as +\newcommand\ifrac[2]{\frac{\inline{#1}}{\inline{#2}}} +$$ +\ifrac{1 + \frac xy}{1 - \frac xy}. +$$ + + +\sect{In-line fractions} +A \verb"\frac" with numeric arguments results in a case fraction, such +as the Bernoulli number $B_{12} = -\frac {691}{2730}$. +Otherwise we get a solidus fraction and parentheses are added whenever +needed for preservation of the mathematical meaning. +E.g., +\begin{verbatim} +$\frac{\frac ab}{\frac cd}$ +\end{verbatim} +produces $\frac{\frac ab}{\frac cd}$. + +Examples below present one and the same expression in display and in-line +mode. +Roughly speaking, Nath assumes that binary operations other than slash +have less binding power than the slash, +$$ +\To \frac{a + b}{c + d} \endTo, \\ +\To \frac {\frac {a \cdot b}{c} \cdot d}{c \cdot d} \endTo, \\ +\To x + \frac ab \endTo. +$$ +In particular, this rule applies to the binary operations of commutative +algebra: +$$ +\To \frac AB \otimes \frac CD \endTo, \\ +\To \frac{A \otimes B}{C \otimes D} \endTo, +$$ +even though existing tradition may be different in this particular case. +On the other side, {\it juxtaposition} has more binding power than the +slash: +$$ +\To \frac ab \frac cd \endTo, \\ +\To \frac {\partial}{\partial x} \frac fg \endTo, \\ +\To d\frac uv \endTo, \\ +\To \frac {\partial^3 f}{\partial x \,\partial y^2} \endTo, \\ +\To \frac a{bc} \endTo. +$$ +Nath only avoids inserting parentheses between a +fraction and a numeric coefficient, e.g., +$$ +\To -\frac uv + 2\frac uv - \frac 12 \frac ab \endTo, +$$ +unless there is a danger of confusion, e.g., +$$ +\To 2\frac {\pm u}{v} \endTo. +$$ +In case of loose juxtaposition between operator and its argument, +there is no obvious winner, thus +$$ +\To \frac{\sin x}{2} + \sin\frac x2\endTo. +$$ +Of course, no parentheses will be inserted when they are already present +in one or another form: +$$ +\To A [\frac uv]^2 \endTo, \\ +\To \frac{(x,y)}{\lVert x \rVert\,\lVert y \rVert} \endTo +$$ +(the last example uses \verb"\lVert x \rVert \, \lVert y \rVert" in the +denominator). + +Grouping prevents Nath from adding parentheses around the whole fraction: +\verb"$a{\frac bc}$" typesets as $a{\frac bc}$, otherwise as $a\frac bc$. +To be on the safe side, avoid superfluous braces in math formulas +(cf.~\sref"ErrorsWarnings"). + +To disable parentheses around the numerator or denominator, +a pair of invisible parentheses is needed: +\verb"$\frac{\left.\sin x\right.}{\cos x}$" typesets as +$\frac{\left.\sin x\right.}{\cos x}$, otherwise as +$\frac{\sin x}{\cos x}$. + + + +An important remark is due. +Professional typographers generally follow the rule that `$a/bc$ means +$a$ divided by $bc$.' +Still some mathematicians (especially those with a programming background) +argue that if juxtaposition denotes multiplication, then $a/bc$ means +$a/b \cdot c$, which is $(a/b) \cdot c$ by the commonly accepted rules of +precedence. +However, $ab$ and $a \cdot b$ are different notations and it is the +notation what matters in typography. +Yet the AIP style manual~\cite{AIP} is cautious enough to say just: +``do not write $\frac 1{3x}$ unless you mean $\frac 1{(3x)}$.'' +Altogether, notation $a/bc$ is considered ambiguous by a nonignorable part +of the mathematical community. +Then, at least, the choices made by Nath are known, traditional, and easy +to remember. + +And, of course, it is never unwise to display difficult fractions. + + +\sect{Delimiters} \label{Delimiters} +\TeX's \verb"\left" and \verb"\right" produce rather poor results, +especially when overused or underused. +Under natural notation, every fence is a left or right delimiter by its +very nature, and delimiters do their best to match the material enclosed: +$$ +\frac M + {(1 - \frac {x_1 + \cdots + x_n + pZ} r) + (1 - p \frac{\frac{\partial Z}{\partial x_2} + \cdots + + \frac{\partial Z}{\partial x_n}} \rho)}. +$$ +For matching purposes, every Nath mathematical object is assigned an +auxiliary height and depth; sub- and superscripts as well as accents +do not contribute to these dimensions, hence ``small parts'' may exceed +the fences: +$$ +(\tilde P - \tilde Q) +(1 + \prod_{i = 1}^{\lfloor \sqrt n \rfloor} p_i)^2. +$$ +Needless to say, line breaks are allowed between delimiters. E.g., +$$ +\sin 2nx = 2n \cos x [\sin x \\ +\qquad + \sum_{k = 1}^n (-4)^k + \frac{(n^2 - 1^2)(n^2 - 2^2) \dots (n^2 - k^2)}{(2k - 1)!} + \sin^{2k - 1} x] +$$ +results from the simple +\begin{verbatim} +$$ +\sin 2nx = 2n \cos x [\sin x \\ +\qquad + \sum_{k = 1}^n (-4)^k + \frac{(n^2 - 1^2)(n^2 - 2^2) \dots (n^2 - k^2)}{(2k - 1)!} + \sin^{2k - 1} x] +$$. +\end{verbatim} +The modifiers \verb"\left" and \verb"\right" still +must be used with symmetric delimiters (e.g., vertical lines $\vert$ and +$\Vert$) or when intended to override the +natural disposition (e.g., \verb"\left]"). +% +The newly introduced modifiers \verb"\double" and \verb"\triple" create +double and triple delimiters. E.g., +\verb"$\double[u_1,\dots,u_n\double]$" produces +$\double[u_1,\dots,u_n\double]$. + +The {\it middle delimiters\/}, such as +\verb"\mid" and \verb"\middle|" for $\mid$, +\verb"\Mid" and \verb"\double|" for $\Mid$, and +\verb"\triple|" for $\triple|$, +have the size of the nearest outer pair of delimiters. +For example: +$$ +\{ (x_i) \in R^\infty \mid \sum_{i = 1}^\infty x_i^2 = 1\}. +$$ + +With nested delimiters, there are two ways to ensure that outer delimiters +come out bigger than inner ones. +In display mode this is controlled by a count \verb"\delimgrowth". +Setting the \verb"\delimgrowth" to $n$ makes (approx.) +every $n$th delimiter bigger. +One should set \verb"\delimgrowth=1" when a display contains many +vertical bars (and insert extra \verb"\," between adjacent right and +left bars). + +In in-line mode, the {\it command} \verb"\big" has the effect that the +next entered level of delimiters is set in big size (in the sense of +plain \TeX). +It is not necessary that the \verb"\big" is immediately followed by a +delimiter; and \verb"\bigg" is an abbreviation for \verb"\big\big". +For instance, \verb"$\Delta\big \frac 1{f(x)}$" produces +$\Delta\big \frac 1{f(x)}$; in this way one can enlarge implicit +delimiters such as those induced by the command \verb"\frac". +It is an error to place a \verb"\big" within delimiters that are not big +themselves. +Unbalanced delimiters may be present in an in-line formula +(as is usual in tensor calculus --- cf. \sref"Tensors"), but then cannot +be resized. + +Table 1 lists paired delimiters. +\begin{table} +\normalsize +\label{tab_delim} +\begin{center} +\vskip 2ex +\begin{tabular}{ll|ll} +\multicolumn{2}{c}{Left delimiters} + & \multicolumn{2}{c}{Right delimiters} +\\ +\hline +\verb"(" & $($ + & \verb")" & $)$ +\\ +\verb"[",\verb"\lbrack" & $[$ + & \verb"]",\verb"\rbrack" & $]$ +\\ +\verb"\{", \verb"\lbrace" & $\{$ + & \verb"\}", \verb"\rbrace" & $\}$ +\\ +\verb"<", \verb"\langle" & $<$ + & \verb">", \verb"\rangle" & $>$ +\\ +\verb"\lfloor" & $\lfloor$ + & \verb"\rfloor" & $\rfloor$ +\\ +\verb"\lceil" & $\lceil$ + & \verb"\rceil" & $\rceil$ +\\ +\verb"\lvert", \verb"\left|" & $\left|\right.$ + & \verb"\rvert", \verb"\right|" & $\left.\right|$ +\\ +\verb"\lBrack", \verb"\double[" & $\double[\right.$ + & \verb"\rBrack", \verb"\double]" & $\left.\double]$ +\\ +\verb"\lAngle", \verb"\double<" & $\double<\right.$ + & \verb"\rAngle", \verb"\double>" & $\left.\double>$ +\\ +\verb"\lFloor" & $\lFloor$ + & \verb"\rFloor" & $\rFloor$ +\\ +\verb"\lCeil" & $\lCeil$ + & \verb"\rCeil" & $\rCeil$ +\\ +\verb"\lVert", \verb"\ldouble|" & $\ldouble|\rdouble.$ + & \verb"\rvert", \verb"\rdouble|" & $\ldouble.\rdouble|$ +\\ +\verb"\triple[" & $\triple[\right.$ + & \verb"\triple]" & $\left.\triple]$ +\\ +\verb"\triple<" & $\triple<\right.$ + & \verb"\triple>" & $\left.\triple>$ +\\ +\verb"\ltriple|" & $\ltriple|$ + & \verb"\rtriple|" & $\rtriple|$ +\end{tabular} +\vskip 2ex +\end{center} +\capt{1}{Paired delimiters} +\end{table} +To enable \verb"<" and \verb">" as a notation for angle braces, +one must set \verb"\nathstyle{geometry}" +(this misusage of notation is common in geometry and math physics). +As symbols of ordering, $\lt$ and $\gt$ can be always accessed through +`\verb"\lt"' and `\verb"\gt"'. + +While in math modes, brackets \verb"[", \verb"]" +never denote optional arguments. +This helps to avoid common \LaTeX\ misinterpretations, as with +\verb"\\[". +On the other side, {\it grouping} interspersed with delimiters --- once +harmless --- is a serious defect now (cf.~\sref"ErrorsWarnings"). +E.g., \verb"({x)}" derails \TeX\ if used in display mode. +%(Braces around a macro argument are safe.) + + +\sect{Operators} \label{Operators} +Nath typsets \verb"\lambda\mathop{\rm id} - g" as +$$\lambda\mathop{\rm id} - g,$$ +whereas \TeX\ would put uneven spacing around the +minus sign: \hbox{$\lambda \old{mathop}{\rm id} - g$}, +erroneously considering the minus sign a unary operator +(by \cite[rule~5 on p.~442]{texb}). + +In subscripts of big operators, \verb"\\" is allowed and starts a new +line, e.g., +\begin{verbatim} +$$ +\sum_{i,j \in K \\ i \ne j} a_{ij} +$$ +\end{verbatim} +prints as +$$ +\sum_{i,j \in K \\ i \ne j} a_{ij}. +$$ + +Within math, the exclamation mark \verb"!" alone ensures suitable +spacing around factorials: \verb"C^n_k = \frac{n!}{(n - k)!k!}" +typesets as $C^n_k = \frac{n!}{(n - k)! k!}$ or +$$ +C^n_k = \frac{n!}{(n - k)! k!}. +$$ +May be doubled: $(2n)!! = n! 2^n$. + +Finally, integral signs stick one to another unless something else +intervenes: +\begin{verbatim} +$$ +\int\int\int_M dV. +$$ +\end{verbatim} +produces +$$ +\int\int\int_M dV. +$$ + + +\sect{Abbreviations} \label{Abbreviations} +According to typographic tradition, names of variables that are +abbreviations should be typeset in roman, for which +Nath offers a handy notation: abbreviations are letter strings +starting from the back quote~`\verb"`"'. +E.g., \verb"$`e^{\pi`i}$" and \verb"$`ad_x y$" typeset as +$`e^{\pi`i} = -1$ and $`ad_x y$, respectively. + +Strings containing more than one letter, such as \verb"`span", +become math operators. +Until now they must have been declared in advance with some additional +care to avoid conflicts (\verb"\span" is a \TeX\ primitive). +Some more examples: +$$ +H' = H_{`symm}' + H_{`antisymm}', \\ +\bar f = f|_{`int U}, \\ +a = `const_1, \\ +G = `SO(n). +$$ + + +\sect{Roots} \label{Roots} +Nath's \verb"\sqrt" differs in several aspects. +Firstly, its vertical size never depends on the presence of subscripts: +$$ +\sqrt{a} + \sqrt{a_j}. +$$ +%\end{document} +Secondly, nested \verb"\sqrt"'s are aligned at the top: +$$ +\cos\frac \pi{10} = \frac 14 \sqrt{10 + 2 \sqrt 5}. +$$ +(Compare it with the \TeX's +$$ +\cos\frac \pi{10} = \frac 14 \old{sqrt}{10 + 2 \old{sqrt} 5}.\text{)} +$$ +Thirdly, no optional arguments are allowed. +\LaTeX's \verb"\sqrt[3]{x}" must be replaced with +\verb"\root{3}{x}" to produce $\root{3}{x}$. + + +\sect{Special symbols} \label{SpecialSymbols} +Nath introduces \verb"\vin" and \verb"\niv" as names of the important +symbols `$\vin$' and `$\niv$' not included in any standard math font. + +Arrows \verb"\to", \verb"\ot", \verb"\otto", and \verb"\mapsto" are +expandable and descriptable via sub- and superscripts. +Thus, +\begin{verbatim} +$$ +A \to^f_{\text{isomorphism}} B, \qquad a \mapsto^f a' +$$ +\end{verbatim} +gives +$$A \to^f_{\text{isomorphism}} B, \qquad a \mapsto^f a'.$$ + +The command \verb"\adot" denotes the centered dot to be used a +an argument placeholder, as in $f(\adot)$ or $g(\adot,\adot)$. + + +\sect{Horizontal braces} \label{HorizontalBraces} +The upper and lower horizontal braces are created with +\verb"\underbrace{"{\it expression\/}\verb"}_{"{\it label\/}\verb"}" +and +\verb"\overbrace{"{\it expression\/}\verb"}_{"{\it label\/}\verb"}", +respectively. +For instance, +\begin{verbatim} +$$ +f^n(x) = \underbrace{f(f(\dots f(}_{n \text{ times}}x) \dots)) +$$ +\end{verbatim} +results in +\delimgrowth = 1 +$$ +f^n(x) = \underbrace{f(f(\dots f(}_{n \text{ times}}x) \dots)) +$$ +Observe that the construction does not interfere with the displayed mode +of delimiters. + + +\sect{Accents} \label{Accents} +Hat, tilde, and bar accents are extensible and grow wider with the size of +the accented material: +$$ +\hat a + \hat{ab} + \hat{abc}. +$$ +When these accents outreach their limit of extensibility, they take the +superscript position: +$$ +\hat{a + b + c}. +$$ +A sequence of accents goes from top to down or from right to left. +For instance, +\verb"\hat\bar a +" \verb"\hat\bar{ab} +" \verb"\hat\bar{abc}" gives +$$ +\hat\bar a + \hat\bar{ab} + \hat\bar{abc}, +$$ +whereas \verb"\hat\bar{a + b + c}" typesets as +$$ +\hat\bar{a + b + c}. +$$ +All kinds of things may happen if braces intervene as in +\verb"\bar{\bar{ab}}". + +Let us note that \verb"\bar" is not arbitrarily extensible, unlike +\verb"\overline". +For instance, \verb"\hat{\overline{a + b + c}}" gives +$\hat{\overline{a + b + c}}$ +(over- and underlines and arrows are {\it not\/} accents). +Over a single character, there is no limit on the number and type of +accents in the sequence; e.g., +$$ +\hat\ddot\tilde W +$$ +results from \verb"\hat\ddot\tilde W". +Over an expression, a non-extensible accent, like \verb"\dot", +makes others non-extensible as well. +Thus, \verb"\hat{ab} +" \verb"\dot{ab} +" \verb"\dot\hat{ab} +" +\verb"\hat\dot{ab}" gives +$$ +\hat{ab} + \dot{ab} + \dot\hat{ab} + \hat\dot{ab}. +$$ + + +\sect{Arrays} \label{Arrays} +Entries are typeset in display mode: +$$ +\left|\, +\begin{array}{cc} x & 1 \\ 1 & \frac 1x \end{array} +\,\right| = 0. +$$ +Moreover, arrays grow smaller when used in sub- and superscripts: +$$ +`e^{\displayed{(\begin{matrix} a & b \\ c & d \end{matrix})}}. +$$ +A \verb"matrix" environment differs from \verb"array" in that it does not +have any preamble. +As a special case, \verb"\binom{"{\it m}\verb"}{"{\it n}\verb"}" +creates the binomial coefficient $\binom mn$. + + +\sect{Tensors} \label{Tensors} +With \verb"\nathstyle{tensors}", first-level sub- and superscripts to +ordinary symbols occupy predetermined positions. +Thus, +\nathstyle{tensors} +$$ +A^{[k} B^{l]}_{(k} C_{l)} +$$ +\nathstyle{tensors=off} +results from +\begin{verbatim} +\nathstyle{tensors=on} +$$ +A^{[k} B^{l]}_{(k} C_{l)} +$$ +\end{verbatim} +(unbalanced delimiters are allowed in in-line style). + + +\sect{Displayed formulas} \label{DisplayedFormulas} +Displayed formulas are indented by \verb"\mathindent" of default +value of 4\,pc. +With \verb"\mathindent" set to a negative length, displayed formulas +are centered. +Formulas enclosed between double dollars \verb"$$" are unnumbered. +Alternatively one may enclose them between \verb"\[" and \verb"\]". +Ends of lines (any formula may be multiline) are marked with +\verb"\\". +Nath does not support automatic line breaks (as does the Downes style +\cite{downes}). + +E.g., \verb"$$ ???? = ????, \\ ???? = ????. $$" typesets as a left-aligned +multiline formula (the punctuation is important, see~\sref "Punctuation"): +$$ +\stuff{2cm} = \stuff{5cm}, \\ \stuff{4cm} = \stuff{2cm}. +$$ +To achieve finer arrangements, one may begin every continuation line with +a number of \verb"\quad"'s; e.g., +two in front of a binary relation, three in front of a binary operation: +\begin{verbatim} +$$ +???? = ???? + (???? \\ +\qqquad + ????) \\ +\qquad = ???? \\ +\qquad = ???? . +$$ +\end{verbatim} +gives +$$ +\stuff{4cm} = \stuff{1cm} + (\stuff{2cm} \\ +\qqquad + \stuff{5cm}) \\ +\qquad = \stuff{7cm} \\ +\qquad = \stuff{6cm}\,. +$$ + + +\sect{Walls} \label{Walls} +Walls represent a simple and convenient tool to achieve better +visual appearance of complex displayed equations. +The syntax is \verb"\wall ???? \\" \verb"???? \\" $\cdots$ +\verb"\\ ???? \return", +and can be arbitrarily nested. +The \verb"\wall" makes every next line to start at the +``wall'' until removed by \verb"\return". +For instance, +\begin{verbatim} +$$ +???? +\wall = ???? + (\wall - ???? \\ + + ????) + \return + = ???? \\ + = ????. +\return +$$ +\end{verbatim} +gives +$$ +\stuff{1cm} +\wall = \stuff{1cm} + (\wall - \stuff{4cm} +\\ ++ \stuff{5cm}) \return += \stuff{7cm} \\ += \stuff{6cm}\,. \return +$$ +The typical placement of \verb"\wall" is in front of a relation symbol +or immediately after an opening delimiter anywhere in the left half +of a formula. + +A simple alternative is \verb"\padded{"{\it A}\verb"}", which prefixes +each continuation line with {\it A} until stopped by \verb"\return". +Typically, {\it A} is a kern: +\begin{verbatim} +$$ +\padded\qquad \padded\quad ???? = ???? + (???? \\ + + ???? \\ + + ????) + \return + = ???? \\ + = ???? +\return +$$ +\end{verbatim} +gives +$$ +\padded\qquad \padded\quad \stuff{4cm} = \stuff{1.5cm} + (\stuff{2cm} \\ + + \stuff{6cm} \\ + + \stuff{5cm}) + \return + = \stuff{7cm} \\ + = \stuff{4cm}\,. +\return +$$ +With short formulas it may be easier to prefix each line with explicit +\verb"\quad"'s as we did in \sref "DisplayedFormulas". + +See \sref"Punctuation" on the interplay between walls and punctuation. + + +\sect{Alignments} \label{Alignments} +Unfortunately, display mode of delimiters interferes badly with alignments +unless every cell is balanced (as is, e.g., with matrices). +The recommended solution is to fill the cells with balanced +wall/return blocks. E.g., +\begin{verbatim} +\begin{eqnarray*} +???? &=& \wall ???? \\ + + ???? \\ + + ????, + \return +\\ +???? &=& ???? +\end{eqnarray*} +\end{verbatim} +produces +\begin{eqnarray*} +\stuff{5mm} &=& \wall \stuff{7cm} \\ + + \stuff{7cm} \\ + + \stuff{3cm}, + \return +\\ +\stuff{3mm} &=& \stuff{5cm}. +\end{eqnarray*} +Walls save \verb"&"'s and ensure vertical +centering of the equation numbers (see \sref"EquationNumbering"). + + +\sect{Equation numbering} \label{EquationNumbering} +A formula enclosed between \verb"\begin{equation}" and \verb"\end{equation}" +obtains a single number (the value of \verb"\theequation") on the right. +Putting the command \verb"\numbered" inside of an unnumbered formula has +the same effect: +\begin{verbatim} +$$ +????. \numbered +$$ +\end{verbatim} +results in +$$ +\stuff{8cm}. \numbered \label{numbered} +$$ +Alternatively, \verb"\eqno{"$A$\verb"}" makes $A$ the equation number. + +In emergency, the equation number goes one line below the formula: +\begin{equation} \label{long} +\stuff{10cm} +\end{equation} +We already know that any formula may be multiline. +If so, the equation number is centered: +\begin{equation} +\stuff{8cm}, \label{short1} \\ +\stuff{7cm}. \label{short2} +\end{equation} +To have centered numbers within the \verb"eqnarray" environment, use +wall/return blocks as described in~\sref "Alignments" (but then +the equation numbers may be overwritten with the formula content without +warning). + +There is also the \verb"eqns" environment, which puts a number on +each line: +\begin{eqns} +\stuff{8cm}, \label{short3} \\ +\stuff{7cm}. \label{short4} +\end{eqns} +It also uses larger and breakable interline space. +Multiline blocks then may be created by using the walls (\sref"Walls"). + +Equation numbering is normally determined by \verb"\theequation". +The environment \verb"subabc" introduces a subordinate numbering by letters, +\begin{subabc} +\begin{equation} +A = B, \label{A} +\end{equation} +no matter how many numbered equations are enclosed, +\begin{equation} +C = D. \label{C} +\end{equation} +\end{subabc} +This output was obtained from +\begin{verbatim} +\begin{subabc} +\begin{equation} +A = B, \label{A} +\end{equation} +no matter how many numbered equations are enclosed, +\begin{equation} +C = D. \label{C} +\end{equation} +\end{subabc} +\end{verbatim} +After \verb"\end{subabc}", the original numbering mode is restored: +\begin{equation} +E = F. \label{E} +\end{equation} +Every numbered equation should be referred to somewhere, hence it should +have a label --- a warning (\sref"ErrorsWarnings") is issued if it does not. + +To put equation numbers on the left, call either the documentstyle +option \verb"leqno" or the local option \verb"\nathstyle{leqno}". + + +\sect{Items} \label{Items} +Lay typographers tend to overuse list environments. +Rather than list items, numbered statements so often encountered in theorems +and definitions may be alternatively formatted as numbered paragraphs. +Nath's command \verb"\paritem{"{\it item label\/}\verb"}" starts a numbered +paragraph and may occur even within a displayed formula. +Our next example demonstrates this: + +\bigskip\noindent +The following statements on a real function $f$ are equivalent: +\paritem{(i)} $f$ is continuous; +$$ +\paritem{(ii)} f(\lim_{i\to\infty} x_i) = \lim_{i\to\infty} f(x_i) +$$ +for every converging sequence $x_i$. + +In a left-numbered formula, \verb"\paritem" supersedes the numbering +and a warning is issued. + + +\sect{Punctuation} \label{Punctuation} +Nath provides a simple tool to encourage line breaks after punctuation in +in-line mode. +Namely, \verb*"\ " denotes a breakable space no matter where it is used. +Therefore, \verb"$a = b,\ c = d$" will break after the comma, +$a = b,\ c = d$, rather than after the `\,$=$\,' sign. +The inclination to break is measured by \verb"\punctpenalty" +(if a positive integer less than 10000). + +Three dots are denoted by \verb"\dots". +In some contexts, their proper place is at the level of math axis, +e.g., $a_1 + \dots + a_n$. +Nath uses a very simple rule --- the dots are not raised if and only +if they follow a comma or a semicolon. +Accordingly, we have $a_1, \dots, a_n$ and $a_1; \dots; a_n$. + +Punctuation after displayed formulas is important for recognizing +continuing lines. +Without punctuation, what seems to be a system of equations +$$ +U_x = AU \\ +-U_y = BU +$$ +may well be a chain of them: +$$ +U_x = AU +-U_y = BU. +$$ +To disambiguate your notation, be sure to insert comma (or semicolon +or full stop or \verb"\text") at the end of each line that is not continued: +$$ +U_x = AU, \\ +-U_y = BU. +$$ +(Observe that the minus sign starting the second line is typeset closer +to $U$ --- becomes a unary operator.) + + +\sect{Spacing} \label{Spacing} +Nath's displayed formulas use frozen spacing (\TeX's ``skips'' and ``glues'' +neither stretch nor shrink). +While it is seldom useful to stretch a displayed formula, one may +wish to shrink formulas too wide to fit between the margins. +Within the \verb"tight" environment, displayed formulas occupy slightly less +horizontal space. +E.g., +$$ +\sin^6 x = + -\frac 1{32} \cos 6x + \frac 3{16} \cos 4x + - \frac{15}{32} \cos 2x + \frac 5{16} +$$ +becomes +\begin{tight} +$$ +\sin^6 x = + -\frac 1{32} \cos 6x + \frac 3{16} \cos 4x + - \frac{15}{32} \cos 2x + \frac 5{16} +$$ +\end{tight} +if written as +\begin{verbatim} +\begin{tight} +$$ +\sin^6 x = + -\frac 1{32} \cos 6x + \frac 3{16} \cos 4x + - \frac{15}{32} \cos 2x + \frac 5{16} +$$ +\end{tight} +\end{verbatim} + +Striving for safe defaults, Nath sets even interword spaces in text. +\TeX perts may wish to call \verb"\nonfrenchspacing" +(see~\cite[p. 74]{texb}) to achieve a century-old look. + + +\sect{User definitions} \label{UserDefinitions} +Feel free to introduce your own commands by using \verb"\newcommand" +or \verb"\def". +We already gave a useful example of \verb"\ifrac" +in~\sref"DisplayedFractions". + +Here is another example: +A first-order partial derivative suitable for all math modes and sizes +can be introduced via +\begin{verbatim} +\newcommand\pd[2]{\frac{\partial#1}{\partial#2}} +\end{verbatim} +We then have +\newcommand\pd[2]{\frac{\partial#1}{\partial#2}}% +$\big(\pd f x \pd g y)^2$ or $`e^{(\pd f x \pd g y)^2}$ or +$$ +(\pd f x \pd g y)^2 +$$ +from one and the same \verb"(\pd f x \pd g y)^2". + +The price is that fragile commands occurring inside in-line math may +have to be protected (any in-line mode material must be considered a +``moving argument''). +Nath commands are robust by design and need no \verb"\protect"ing. +When encountering a mysterious error, such as ``undefined command +\verb"\wrapfrac@",'' fragile commands are to be blamed. +Besides \verb"\protect", Nath offers \verb"\makerobust", a command +that takes an already assigned control sequence as argument and makes +it robust. + + + +\sect{Efficiency} +Nath helps to prevent wasting human work on something that can +be done by computer. +On average, \LaTeX\ runs about three times slower with Nath than +without it, depending on the complexity of math formulas. + + +\sect{Other packages} \label{OtherPackages} +Nath is not guaranteed to be compatible with other \LaTeX\ packages. +However, some combinations turn out to be safe and useful. +For example, when starting a \LaTeX~2.09 document with +\begin{verbatim} +\documentstyle[amssymb,nath]{article} +\end{verbatim} +or a \LaTeX~2$_{\varepsilon}$ document with +\begin{verbatim} +\documentclass{article} +\usepackage{amssymb,nath} +\end{verbatim} +one invokes \verb"amssymb", a component of the famous \AmS-\LaTeX\ +package from the American Mathematical Society, thereby introducing a +wider range of mathematical symbols. +Users can also enable text mode \verb"amsmath" commands by starting a +\LaTeX~2$_{\varepsilon}$ document with +\begin{verbatim} +\usepackage{amsmath,nath} +\end{verbatim} +(math mode commands must be those of Nath). + + +\sect{Commands of enhanced functionality} +\def??#1??{\if#1**\else{\rm#1}\fi} +\def\sref.#1.{\S\ref{#1}} +\def\ct.#1.{\cite{#1}} +\def\mpst{$\mapsto$} +\def\vn{$\vin$} +\def\nv{$\niv$} +\catcode`\Z=14 +\setbox0\hbox{\verb*"\ "} +\def\u{\leavevmode\box0} +A number of math commands have been redefined; +\verb"\old{"{\it command\/}\verb"}" often provides access +to what \verb"\"{\it command\/} was before Nath redefined it +(see the source code of this guide for examples). + +Here is the list of all enhanced and newly introduced commands: +\begin{verbatim} +?u ??a breakable space in math (?sref.Spacing.)?? +\\ ??see ?sref.Operators. and ?sref.DisplayedFormulas.?? +\abbreviation ??a long form of?? ` ??in math (?sref.Abbreviations.)?? +\adot ??argument placeholder (?sref.SpecialSymbols.)?? +\arraycolsep ??macro, formerly a dimension register (?sref.Arrays.)?? +\big ??making inline delimiters bigger Z +(?sref.Delimiters.)?? +\bigg ??same as?? \big\big ??(?sref.Delimiters.)?? +\biggg ??same as?? \big\big\big ??(?sref.Delimiters.)?? +\biggl ??same as?? \big\big\left +\bigl ??same as?? \big\left +\binom ??binomial coefficient (?sref.Arrays.)?? +\delimgrowth ??see ?sref.Delimiters.?? +\displayed ??forcing displayed math mode (?sref.MathModes.)?? +\double ??doubling a delimiter (?sref.Delimiters.)?? +\eqno ??equation number (?sref.EquationNumbering.)?? +\natherrormark ??a mark to visualize nath errors Z +(?sref.ErrorsWarnings.)?? +\factorial ??long form of?? ! ??in math (?sref.Operators.)?? +\fbox ??making frame around a subformula?? +\frac ??fraction (?sref.Fractions.)?? +\gt ??greater than sign (?sref.Delimiters.)?? +\hat ??attaching hat accent (?sref.Accents.)?? +\inline ??forcing in-line math mode (?sref.MathModes.)?? +\int ??integral sign (?sref.Operators.)?? +\langle ??left angle bracket (?sref.Delimiters.)?? +\lAngle ??left double angle bracket (?sref.Delimiters.)?? +\lbrace ??left brace (?sref.Delimiters.)?? +\lbrack ??left bracket (?sref.Delimiters.)?? +\lBrack ??left double bracket (?sref.Delimiters.)?? +\lceil ??left ceiling bracket (?sref.Delimiters.)?? +\lCeil ??left double ceiling bracket (?sref.Delimiters.)?? +\ldouble ??left doubling (?sref.Delimiters.)?? +\left ??left modifier (?sref.Delimiters.)?? +\lfloor ??left floor bracket (?sref.Delimiters.)?? +\lFloor ??left double floor bracket (?sref.Delimiters.)?? +\lnull ??left invisible fence (?sref.Delimiters.)?? +\lt ??less than sign (?sref.Delimiters.)?? +\ltriple ??left tripling (?sref.Delimiters.)?? +\lvert ??left vertical line (?sref.Delimiters.)?? +\lVert ??left double vertical line (?sref.Delimiters.)?? +\mapsto ??sizeable `?mpst' (?sref.SpecialSymbols.)?? +\mathop ??see ?sref.Operators.?? +\mathstrut ??see ?ct.texb.?? +\mid ??middle vertical line (?sref.Delimiters.)?? +\Mid ??middle double vertical line (?sref.Delimiters.)?? +\middle ??middle modifier (?sref.Delimiters.)?? +\Nath ??logo?? +\nathstyle ??local options (?sref.LocalOptions.)?? +\niv ??the symbol `?nv' (?sref.SpecialSymbols.)?? +\nonumber ??suppresses equation number (?sref.EquationNumbering.)?? +\numbered ??forces equation number (?sref.EquationNumbering.)?? +\old ??see the beginning of this section?? +\ot ??sizeable left arrow (?sref.SpecialSymbols.)?? +\otto ??sizeable left-right arrow (?sref.SpecialSymbols.)?? +\overbrace ??horizontal braces over unbalanced math material?? Z ??(?sref.HorizontalBraces.)?? + +\overleftarrow ??left arrow over an expression?? +\overleftrightarrow ??left-right arrow over an expression?? +\overline ??overline an expression (?sref.Accents.)?? +\overrightarrow ??right arrow over an expression?? +\padded ??like a wall, with every next line padded (?sref.Walls.)?? +\paritem ??numbered statement (?sref.Items.)?? +\punctpenalty ??penalty inserted after punctuation in math Z +(?sref.Punctuation.)?? +\quad ??1em space (?sref.DisplayedFormulas.)?? +\qquad ??2em space (?sref.DisplayedFormulas.)?? +\qqquad ??3em space (?sref.DisplayedFormulas.)?? +\rangle ??right angle bracket (?sref.Delimiters.)?? +\rAngle ??right double angle bracket (?sref.Delimiters.)?? +\rbrace ??right brace (?sref.Delimiters.)?? +\rbrack ??right bracket (?sref.Delimiters.)?? +\rBrack ??right double bracket (?sref.Delimiters.)?? +\rceil ??right ceiling bracket (?sref.Delimiters.)?? +\rCeil ??right double ceiling bracket (?sref.Delimiters.)?? +\rdouble ??right doubling (?sref.Delimiters.)?? +\return ??ends?? \wall ??and?? \padded ??(?sref.Walls.)?? +\right ??right modifier (?sref.Delimiters.)?? +\rfloor ??right floor bracket (?sref.Delimiters.)?? +\rFloor ??right double floor bracket (?sref.Delimiters.)?? +\rnull ??right invisible fence (?sref.Delimiters.)?? +\root ??arbitrary root (?sref.Roots.)?? +\rtriple ??right tripling (?sref.Delimiters.)?? +\rvert ??right vertical line (?sref.Delimiters.)?? +\rVert ??right double vertical line (?sref.Delimiters.)?? +\scriptscriptstyle ??setting size to second next level script size?? +\scriptstyle ??setting size to next level script size?? +\sqrt ??square root (?sref.Roots.)?? +\stackrel ??as in ?LaTeX?? +\text ??text within math?? +\tilde ??attaching tilde accent (?sref.Accents.)?? +\to ??sizeable right arrow (?sref.SpecialSymbols.)?? +\triple ??tripling a delimiter (?sref.Delimiters.)?? +\underbrace ??horizontal braces under unbalanced math material?? Z ??(?sref.HorizontalBraces.)?? + +\underleftarrow ??left arrow under an expression?? +\underleftrightarrow ??left-right arrow under an expression?? +\underline ??underline an expression?? +\underrightarrow ??right arrow under an expression?? +\vin ??the symbol `?vn' (?sref.SpecialSymbols.)?? +\wall ??begin a wall/return block (?sref.Walls.)?? +\end{verbatim} +Redefined and new environments: +\begin{verbatim} +array ??see ?sref.Arrays.?? +cases ??as in ?TeX?? +eqnsabc eqns ??within?? subabc +eqnarray ??as in ?LaTeX?? +eqnarray* ??as in ?LaTeX?? +eqnarrayabc eqnarray ??within?? subabc +eqns ??a pile of equations (?sref.EquationNumbering.)?? +equation ??as in ?LaTeX?? +matrix ??see ?sref.Arrays.?? +subabc ??subnumbering by letters (?sref.EquationNumbering.)?? +tight ??tighter spacing (?sref.Spacing.)?? +\end{verbatim} +The following characters are active, retaining their previous meaning: +\verb"$",~\verb"^",~\verb"_". +Other characters become active in math mode: +\begin{verbatim} +( ??see ?sref.Delimiters.?? +) ??see ?sref.Delimiters.?? +[ ??see ?sref.Delimiters.?? +] ??see ?sref.Delimiters.?? +< ??see ?sref.Delimiters.?? +> ??see ?sref.Delimiters.?? +, ??see ?sref.Punctuation.?? +; ??see ?sref.Punctuation.?? +! ??see ?sref.Operators.?? +` ??see ?sref.Abbreviations.?? +\end{verbatim} +Commands that became obsolete are still preserved in reduced form for +backward compatibility: +\begin{verbatim} +\Big ??ignored?? +\Bigg ??ignored?? +\Biggl ??same as?? \left +\biggm ??same as?? \middle +\Biggm ??same as?? \middle +\biggr ??same as?? \right +\Biggr ??same as?? \right +\Bigl ??same as?? \left +\bigm ??same as?? \middle +\Bigm ??same as?? \middle +\bigr ??same as?? \right +\Bigr ??same as?? \right +\mathchoice ??useless?? +\mathpalette ??useless?? +\textstyle ??ignored?? +\end{verbatim} +The following \TeX\ commands are disabled: +\begin{verbatim} +\atop +\over +\choose +\end{verbatim} +The following \LaTeX\ environment is disabled: +\begin{verbatim} +math +\end{verbatim} +New ifs (correspond to local options): +\begin{verbatim} +\ifgeometry ??see ?sref.Delimiters.?? +\ifleqno ??see ?sref.EquationNumbering.?? +\ifsilent ??see ?sref.ErrorsWarnings.?? +\iftensors ??see ?sref.Tensors.?? +\end{verbatim} +New dimension registers: +\begin{verbatim} +\arraycolsepdim ??former?? \arraycolsep +\displaylineskiplimit +\mathindent ??see ?sref.DisplayedFormulas.?? +\mex ??a prorated?? ex +\paritemwd ??see ?sref.Items.?? +\end{verbatim} +New skips (self-explanatory): +\begin{verbatim} +\displaybaselineskip +\displaylineskip +\interdisplayskip +\intereqnsskip +\beloweqnsskip +\end{verbatim} +New boxes: +\begin{verbatim} +\sizebox ??delimiters match it (?sref.Delimiters.)?? +\end{verbatim} +Moreover, Nath takes box and token registers on the fly. + + +\sect{Final remarks} \label{FinalRemarks} +Nath is a scientific software intended to assist and ease the process +of scientific publication. +By disburdening the encoding of mathematics, Nath tries to uphold +\TeX's position as a language suitable for both scientific and +typographic purposes --- especially if alternatives are still elusive. + +Nath is provided as it is; only bug reports and serious discussion +should go to \verb"M.Marvan@"\verb"math.slu.cz". + +\setbox0\hbox{\tt kkkk} +\def????{\leavevmode\hbox to\wd0{\hss\it stuff\/\hss}} + + +\sect{Release 2003} \label{Release2003} +Fixing several bugs, a new release is available since February 2003. + +As a new feature, Nath takes care of the interline spacing in arrays. +There is a new dimension register \verb"\arrayrowsepdim" to hold the +minimal interline space. +Also, the default setting of \verb"\doublerulesep" is \verb"\arrayrulewidth", +so that horizontal lines produced by successive \verb"\hline"'s +stick one to another, and similarly for the vertical lines: +$$ +\begin{array}{||ccc||} +\hline\hline +p & q & r \\ +\hline +1 & 1 & 0 \\ +1 & 0 & 0 \\ +\frac12 & 1 & 0 \\ +\hline\hline +\end{array} +$$ +These changes do not affect the \verb"tabular" environment. + +The \verb"\padded" command now applies to continuation lines only. +For example +$$ +\padded{\qquad} +\stuff{3cm} = \stuff{3.5cm} \\ + - \stuff{6cm}, \\ +\stuff{4cm} = \stuff{1.5cm} \\ + - \stuff{7cm}, \\ +\stuff{2cm} = (\stuff{2cm}, \\ + -\stuff{2cm}). +\return +$$ +is produced by a single \verb"\padded"--\verb"\return" pair: +\begin{verbatim} +\padded{\qquad} +???? = ???? \\ + - ????, \\ +???? = ???? \\ + - ????, \\ +???? = (????, \\ + -????). +\return +\end{verbatim} +(Commas that occur within delimiters do not start a new equation.) + +Some errors still survive. +In particular, double accents do not work with MathTime fonts. + + +\begin{thebibliography}{9} +\small + +\bibitem{AIP} +{\it AIP Style Manual}, 4th edition +(Amer. Inst. Physics, New York, 1990). +\bibitem{downes} +M. Downes, Breaking equations, {\it TUGboat} 18 (1997) 182--194. +\bibitem{texb} +D.E. Knuth, {\it The \TeX book} (Addison Wesley, Reading, 1984). +\bibitem{EuroTeX} +M. Marvan, Natural \TeX\ notation in mathematics, +in: Proc. Conf. {\it Euro\TeX\ 2001}, Kerkrade, 23--27 September 2001; +online {\tt www.ntg.nl/eurotex/marvan-3.pdf}. +\end{thebibliography} + +\end{document} + + + + + + + + + + -- cgit v1.2.3