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+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 <www.ntg.nl/eurotex/marvan-3.pdf>.
+
+Nath is a free software distributed under the terms of the GNU General Public
+License <www.gnu.org/copyleft/gpl.html>.
+
+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 <M.Marvan@math.slu.cz>.
+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.
+
+
+
+
+
+
+
+
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+%&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}
+
+
+
+
+
+
+
+
+
+