From e0c6872cf40896c7be36b11dcc744620f10adf1d Mon Sep 17 00:00:00 2001
From: Norbert Preining <norbert@preining.info>
Date: Mon, 2 Sep 2019 13:46:59 +0900
Subject: Initial commit

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+\sectiontitle{Summary of Commonly-Used Features of Plain \TeX}
+\label{pl-summ}
+
+\sectiontitle{Rules for Ordinary Text (without mathematics)}
+\subsectiontitle{Special Characters}
+All characters on the keyboard have their standard meaning
+in ordinary text with the exception of the
+special characters
+\begin{quote}
+\begin{verbatim}
+# $ % & ~ _ ^ \ { } '
+\end{verbatim}
+\end{quote}
+which have special functions within \TeX.  On the rare
+occasions when these special characters are required in
+the final document they must be  produced by an appropriate
+control sequence.  Thus you should type \verb?\#?, \verb?\$?,
+\verb?\%?, \verb?\&?, \verb?\_?, \verb?\{? and \verb?\}? to
+obtain $\#$, $\$$, $\%$, $\&$, $\_$, $\{$ and $\}$
+respectively.
+
+\subsectiontitle{Special Characters}
+Successive paragraphs in the input file should be separated
+by a completely blank line.  All paragraphs will be
+automatically indented by \TeX\ with the exception of the
+first paragraph of a new section.  (One can override the
+conventions of \TeX\ by placing the control sequence
+\verb?\noindent? of the control sequence \verb?\indent?
+at the beginning of the paragraph.)
+
+\subsectiontitle{Quotation marks}
+To produce single quotation marks use the characters
+\verb?`? (left quote) and \verb?'? (right quote).  For
+double quotation marks use \verb?``? (two left quotes)
+and \verb?''? (two right quotes).  {\it Do not use\/}
+\verb?"? (undirected double quote).  Thus to obtain
+\begin{quotation}
+\small
+``This is easy'' he said.
+\end{quotation}
+you should type
+\begin{quote}
+\begin{verbatim}
+``This is easy'' he said.
+\end{verbatim}
+\end{quote}
+
+The control sequence \verb?\thinspace? can be used to
+separate single quotes from double quotes where
+necessary.
+
+\subsectiontitle{Quotation marks}
+Dashes of various lengths are obtained using \verb?-?,
+\verb?--? and \verb?---?.  You should use \verb?-? for
+hyphenation, \verb?--? when specifying ranges of numbers,
+and \verb?---? to obtain a punctuation dash.  Thus we obtain
+\begin{quotation}
+\small
+The Cayley-Hamilton Theorem.
+\end{quotation}
+\begin{quotation}
+\small
+See pages 95--104.
+\end{quotation}
+\begin{quotation}
+\small
+Use three dashes to obtain a punctuation dash---like this.
+\end{quotation}
+by typing
+\begin{quote}
+\begin{verbatim}
+The Cayley-Hamilton Theorem.
+\end{verbatim}
+\end{quote}
+\begin{quote}
+\begin{verbatim}
+See pages 95--104.
+\end{verbatim}
+\end{quote}
+\begin{quote}
+\begin{verbatim}
+Use three dashes to obtain a punctuation dash---like this.
+\end{verbatim}
+\end{quote}
+
+\subsectiontitle{Changing Fonts}
+The control sequences \verb?\rm?, \verb?\sl?, \verb?\it?, \
+\verb?\tt? and \verb?\bf? change to {\rm roman}, {\sl slanted},
+{\it italic}, {\tt teletype} and {\bf boldface} fonts respectively.
+Any change of font made within a group enclosed within curly
+brackets \verb?{? and \verb?}? will only apply to text within
+that group.  On leaving the group, the current font is restored
+to what it was before entering the group.  Thus we can obtain
+\begin{quotation}
+\small
+This sentence contains a word set in {\bf boldface} type
+\end{quotation}
+by typing
+\begin{quote}
+\begin{verbatim}
+This sentence contains a word set in {\bf boldface} type
+\end{verbatim}
+\end{quote}
+
+   The control sequence \verb?\/? produces the so-called
+`italic correction'.  It is sometimes desirable when changing
+from a slanted font (such as {\it italic\/} or {\it slanted\/})
+back to a non-slanted font such as {\rm roman} or
+{\bf boldface}, in order to produce a small amount of extra
+space to compensate for the slantedness of the font, and thus
+improve the appearance of the final document.  However the
+italic correction should not be applied before a period
+(full stop) or a comma.  To obtain
+\begin{quotation}
+\small
+Here is some {\it italicized\/} text.
+\end{quotation}
+one should type
+\begin{quote}
+\begin{verbatim}
+Here is some {\it italicized\/} text.
+\end{verbatim}
+\end{quote}
+However it usually does not matter all that much if you forget
+about this italic correction.
+
+\subsectiontitle{Changing Fonts}
+These are produced by control sequences such as \verb?\'?,
+\verb?\`? and \verb?\"?.  Thus one types \verb?Se\'{a}n?
+and \verb?H\"{o}lder? to obtain `Se\'{a}n' and `H\"{o}lder'
+respectively.  For a full list of such accents, see
+Appendix~\ref{pl-txtcs}.  Note however that accents within
+mathematics are produced in a different fashion.
+
+\subsectiontitle{Producing Blank Space in Plain \TeX}
+To produce (horizontal) blank space within a paragraph, use
+\verb?\hskip?, followed by the length of the blank space.
+The length of the skip should be expressed in a unit recognized
+by \TeX.  These recognized units are given in the following table:
+\begin{quote}
+\begin{tabular}{lll}
+\verb?pt?  & point         & (1 in = 72.27 pt) \\
+\verb?pc?  & pica          & (1 pc = 12 pt) \\
+\verb?in?  & inch          & (1 in = 25.4 mm) \\
+\verb?bp?  & big point     & (1 in = 72 bp) \\
+\verb?cm?  & centimetre    & (1 cm = 10 mm) \\
+\verb?mm?  & millimetre    & \\
+\verb?dd?  & didot point   & (1157 dd = 1238 pt) \\
+\verb?cc?  & cicero        & (1 cc = 12 dd) \\
+\verb?sp?  & scaled point  & (65536 sp = 1 pt)
+\end{tabular}
+\end{quote}
+Thus to produce a horizontal blank space of 20 mm in the middle
+of a paragraph one would type \verb?\hskip 20 mm? (or, better
+still, type `\verb?\hskip 20 mm \relax?' to avoid the
+error that might occur if the following word were to begin
+with the letters `plus').
+
+To produce (vertical) blank space between paragraphs, use
+\verb?\vskip?, followed by the length of the vertical skip.
+
+\subsectiontitle{Producing Blank Space in Plain \TeX}
+To force \TeX\ to produce a blank space where it might not
+otherwise put one, one should precede the blank space with a
+\verb?\? (backslash).  It is often advisable to precede
+with a backslash blank spaces after certain abbreviations
+such as `Dr.', `etc.', and `Math.\ Soc.' (so that one
+should type \verb?Dr.\ Smith? etc.).
+
+If you wish to ensure that \TeX\ does not start a new line
+at a particular blank space, then you can use \verb?~? in
+place of the blank space.  Thus if you type
+\verb?I.~Newton? or \verb?Example~4? then you prevent
+a line break at these places.
+
+\sectiontitle{Rules for obtaining Mathematical Formulae}
+\subsectiontitle{Mathematics embedded in Text}
+Any mathematical expressions embedded in text should be
+preceded and followed by the character \verb?$?.  Thus
+to obtain
+\begin{quotation}
+\small
+Let $f$ be the function defined by $f(x) = x + 7$.
+\end{quotation}
+one should type
+\begin{quote}
+\begin{verbatim}
+Let $f$ be the function defined by $f(x) = x + 7$.
+\end{verbatim}
+\end{quote}
+
+\subsectiontitle{Displayed Mathematical Formulae}
+Any displayed mathematical formulae should be preceded
+and followed by \verb?$$?.  Thus to obtain
+\begin{quotation}
+\small
+Let $g$ be the function defined by
+$$g(x,y) = xy + x + y + 2.$$
+The function $g$ is positive when both $x$ and $y$ are positive.
+\end{quotation}
+one should type
+\begin{quote}
+\begin{verbatim}
+Let $g$ be the function defined by
+$$g(x,y) = xy + x + y + 2.$$
+The function $g$ is positive when both $x$ and $y$ are positive.
+\end{verbatim}
+\end{quote}
+
+\subsectiontitle{Special Characters in Mathematics Mode}
+All characters on the keyboard have their standard meaning
+in mathematical expressions with the exception of the
+special characters
+\begin{quote}
+\begin{verbatim}
+# $ % & ~ _ ^ \ { } '
+\end{verbatim}
+\end{quote}
+which have special functions within \TeX.  On the rare
+occasions when these special characters are required in
+the final document they must be  produced by an appropriate
+control sequence.  Thus you should type \verb?\#?, \verb?\$?,
+\verb?\%?, \verb?\&?, \verb?\_?, \verb?\{? and \verb?\}? to
+obtain $\#$, $\$$, $\%$, $\&$, $\_$, $\{$ and $\}$
+respectively.  To obtain $\backslash$ in mathematics mode,
+type \verb?\backslash?.
+
+   The character \verb?'? is used to put a superscript
+prime after a character.  Thus if we type \verb?$f'$? and
+\verb?$g''$? we obtain $f'$ and $g''$ respectively.
+
+\subsectiontitle{Superscripts and Subscripts}
+Superscripts and subscripts are produced using the characters
+\verb?^? and \verb?_? respectively.  Thus we obtain
+$t^2 + x_1 - x^3_1$ by typeint \verb?$t^2 + x_1 - x^3_1$?.
+If a superscript or subscript consists of more than one
+character then the superscripts and subscripts should be
+enclosed in curly brackets.  Thus one obtains $a_{i,j}$ by
+typing \verb?$a_{i,j}$?.  One can obtain double subscripts:
+we obtain $s_{n_j}$ by typing \verb?$s_{n_j}$?.
+
+\subsectiontitle{Greek Letters}
+Greek letters are obtained by preceding the name of the
+letter by a backslash.  Thus we obtain
+$\alpha, \beta, \gamma$ by typing
+\verb?$\alpha, \beta, \gamma$?.  See Appendix~\ref{pl-mthcs}
+for a list of Greek letters.  Some Greek letters have variant
+forms---see Appendix~\ref{pl-mthcs}.
+
+\subsectiontitle{Mathematical Symbols}
+Mathematical symbols such as $\div$, $\equiv$, $\otimes$,
+$\sum$, $\in$, $\cup$, $\cap$ and $\to$ are obtained using
+the appropriate control sequences---see Appendix~\ref{pl-mthcs}.
+
+\subsectiontitle{Accents in Mathematics}
+These are produced using the appropriate control
+sequence---see Appendix~\ref{pl-mthcs}.
+
+\subsectiontitle{Standard Functions}
+Certain standard functions such as $\sin$ and $\log$ are
+obtained by preceding the name with a backslash---see
+Appendix~\ref{pl-mthcs} for a full list of these.  To obtain
+a function or similar expression not on this list you should
+convert to the roman font (e.g., to obtain ${\rm Aut}(G)$ one
+should type \verb?${\rm Aut}(G)$?).
+
+\subsectiontitle{Fractions}
+Fractions are obtained in Plain \TeX\ using the control sequence
+\verb?\over?.  We type
+\begin{quote}
+\verb?{? {\it numerator\/} \verb?\over? {\it denominator\/} \verb?}?
+\end{quote}
+to obtain the required fraction.  Thus to obtain
+$$f(x) = { 2 x \over (1 + x^2)^2 }$$
+we type
+\begin{quote}
+\begin{verbatim}
+$$f(x) = { 2 x \over (1 + x^2)^2 }$$
+\end{verbatim}
+\end{quote}
+
+\subsectiontitle{Roots}
+Square roots are obtained using the control sequence
+\verb?\sqrt?.  Thus to obtain $\sqrt{3x + 7}$ we
+type \verb?$\sqrt{3x + 7}$?.  To obtain an $n$th
+root in Plain \TeX\ we use the construction
+\begin{quote}
+\verb?\root? $n$ \verb?\of {? {\it expression} \verb?}?
+\end{quote}
+Thus $\root 3 \of {3x + 7}$ is obtained by typing
+\verb?$\root 3 \of {3x + 7}$?.
+
+\subsectiontitle{Ellipsis}
+Ellipsis (three dots) is obtained in mathematical formulae
+using the control sequences \verb?\cdots? (centred ellipsis)
+and \verb?\ldots? (lowered ellipsis).  Thus to obtain
+$x_1 + x_2 + \cdots + x_n$ and $x_1, x_2, \ldots, x_n$
+we type \verb?$x_1 + x_2 + \cdots + x_n$? and
+\verb?$x_1, x_2, \ldots, x_n$? respectively.
+
+\subsectiontitle{Delimiters}
+To surround a subformula with delimiters large enough to enclose
+the subformula we use the construction
+\begin{quote}
+\verb?\left(? $\ldots$ {\it subformula} $\ldots$ \verb?\right)?
+\end{quote}
+(where the parentheses \verb?(? $\ldots$ \verb?)? may be replaced
+by any other pair of delimiters such as
+\verb?[? $\ldots$ \verb?]? or \verb?\{? $\ldots$ \verb?\}?).
+Thus to obtain the equation
+$$f(x) = \left( 1 + { 2x \over x^2 + 1 } \right) - \sin(x)$$
+we type
+\begin{quote}
+\begin{verbatim}
+$$f(x) = \left( 1 + { 2x \over x^2 + 1 } \right) - \sin(x)$$
+\end{verbatim}
+\end{quote}
+
+\subsectiontitle{Embedding Text in Mathematics}
+Text can be embedded in mathematics using the control sequence
+\verb?\hbox?.  Thus if we type
+\begin{quote}
+\begin{verbatim}
+$$V' = \{ f \in X' : f(v) = 0 \hbox{ for all } v \in V \}$$
+\end{verbatim}
+\end{quote}
+we obtain
+$$V' = \{ f \in X' : f(v) = 0 \hbox{ for all } v \in V \}$$
+
+\subsectiontitle{Inserting and Removing Blank Space in Formulae}
+The control sequence \verb?\quad? produces a `quad'
+of blank space (a `quad' is approximately the width of the
+letter `m').  The control sequence \verb?\qquad? produces two
+quads of blank space.  The control sequence \verb?\,? inserts a
+thin blank space and the control sequence \verb?\!? removes a
+thin space.  One uses \verb?\,? and \verb?\!? to improve the
+appearance of mathematical formulae. For example, if we
+type
+\begin{quote}
+\begin{verbatim}
+$$\int_0^\pi \sin x dx = 2,$$
+\end{verbatim}
+\end{quote}
+we obtain
+$$\int_0^\pi \sin x dx = 2,$$
+whereas if we type
+\begin{quote}
+\begin{verbatim}
+$$\int_0^\pi \sin x \,dx = 2,$$
+\end{verbatim}
+\end{quote}
+we obtain
+$$\int_0^\pi \sin x \,dx = 2,$$
+and this equation has a more satisfactory appearance.
+
+\subsectiontitle{Further Features of Plain \TeX}
+There are plenty of control sequences in Plain \TeX\ for
+accomplishing various tasks.  Among the most widely used
+of these are \verb?\eqalign? (for producing multiline
+formulae), \verb?\cases? (for equations which divide up
+into a number of cases) \verb?\matrix? (for producing
+arrays) and \verb?\pmatrix? (for producing matrices
+surrounded by large parentheses).
+
-- 
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