\input paperhead    %  Read private macro package
\DoContents         %  Maintain a table of contents
\centerline{\titlefont A Guide to \TeX}
\vskip 4pt
\centerline{\titlefont for the Troff User}
\vskip 8pt
\centerline{\it Mike Urban}
\centerline{\sl TRW Software Productivity Project}
\vskip .5in
\Section{Introduction}
Donald Knuth's \TeX\ system has several advantages over the
\def\Troff/{{\it troff\/}}% Includes the italic correction
standard \Troff/ program distributed with Berkeley or Bell \Unix
\note{UNIX is a Registered Trademark of AT\&T Bell Laboratories.  Some
say that's the problem.}.
\TeX\ is portable, as it
is written in |Pascal|, and is available
on a variety of systems such as \Unix, VMS, TOPS-20%
\note{VMS and TOPS-20 are Trademarks of Digital
Equipment Corporation}, and IBM's
VM/CMS%
\note {VM/CMS is a Trademark of IBM} system. It is inexpensive (\$50 for
the \Unix\ port from the University of Washington),
and it generates device-independent output.  It
also can produce beautiful copy, especially when setting mathematics.
Finally, it has arbitrary-length command
and variable names, which can
provide much greater readability than the 1- and 2-character
symbols of \Troff/
(this property is shared with the
|Scribe|$^{\rm TM}$ system from Unilogic, Inc.).
For example, the first few lines of the file which produced
this paper are:
\begintt
\input paperhead    % Read private macro package
\DoContents         %  Maintain a table of contents
\centerline{\titlefont A Guide to \TeX}
\vskip 4pt
\centerline{\titlefont for the Troff User}
\vskip 8pt
\centerline{\it Mike Urban}
\centerline{\sl TRW Software Productivity Project}
\vskip .5in
\Section{Introduction}
Donald Knuth's \TeX\ system has several advantages over the
\endtt
The only cryptic item in this excerpt is the |\vskip|
primitive, which stands for {\bf Vertical Skip}; the remaining
commands are fairly transparent.

\TeX\ is, however, substantially different in
its general architecture from \Troff/.  Its input is
``stream-oriented'' rather than consisting of discrete lines,
with embedded formatting commands preceded by an {\sl escape\/},
or distinguished
character (the backslash, |\|).  Its treatment of different typefaces is
different from the approach used
by \Troff/, which was designed to drive a particular
(and now somewhat obsolete) variety of typesetter.
Finally, \TeX\ sets up a page of
type using an algorithm based on ``gluing'' together ``boxes'' of
characters, in a manner quite analogous to the way that
traditional printers locked up ``composing sticks'' containing
rows of letters by adjusting external wedges called ``quoins.''
To the casual user setting up a simple document, the difference
may appear to be minor.  However, the consequences can be felt
when one is attempting an operation that is even slightly extraordinary.

For these reasons, using \TeX\ for the first time
may prove to be a strange,
perhaps even frustrating experience for an experienced \Troff/
user, even if a wealth of ``user-friendly'' macros (analogous
to the {\bf --mm} or {\bf --me} macro packages) has been
provided.  This document will attempt to assist the prospective
\TeX\ user in the transition from \Troff/.  It does not pretend
to be a complete description of \TeX, nor is it a ``cookbook''
of conversion techniques for \Troff/ documents.  It is simply
an introduction to the most basic elements of \TeX\ that
assumes some \Troff/ experience.  When in doubt,
the reader is urged to try
out the various features of \TeX\ to see how they behave in
practice, rather than relying on ``thought experiments''
based on the material in this paper or ``{\sl The \TeX book}''.
\Section{Input Format}
\SubSection{Control Sequences}
The \Troff/ input format with which the reader is familiar
consists of lines of text.  Some of these lines begin
with a command character (i.e., a period)
and are considered command lines;
these contain formatting directives.  The remaining lines
contain text to be formatted, with occasional escape
sequences (using a distinguished,
or
{\sl escape\/} character) for
particular formatting operations that cannot be easily
specified at a line-break (such as in the middle of a word),
or for special characters such as the Greek letter `$\alpha$'
(|\(*a|).

In contrast, \TeX\ input is ``stream-oriented'', i.e.,
the boundaries between input lines are
unimportant.  During normal
operations, there is no substantial difference between
a newline and a space (there are two exceptions to be noted
later).  \TeX\ commands (called
{\sl control sequences}) may occur anywhere in the input,
and are distinguished by beginning with an {\sl escape\/} character
(|\|, the backslash)\note
{This character has {\bf nothing} to do with the ASCII `ESC'
character (character code $036_8$) which is labeled {\tt ESC}
or {\tt ESCAPE}
on many terminals.}.
There are two varieties of control sequences.  The
first is called a {\sl control word} and consists of the
escape character followed by one or more alphabetic characters.
The end of a control word is the {\sl first non-alphabetic 
character encountered\/}.  Thus the control
sequence |\TeX|, which sets the word `\TeX,' could be
used in a phrase like |\TeX82| (which produces `\TeX82'),
because the non-alphabetic character `8' signifies the end
of the |\TeX| control word.
However, the phrase
|\TeXnical| would be considered an undefined control word.

The second kind of control sequence, like |\'|, is called a
{\sl control symbol}; it consists of the escape character
followed by a {\sl single nonletter}.  For example, the
escape sequence |\'| is used to accent letters: the input
|P\'olya| yields `P\'olya'.

When a space follows a control word, it is ignored.  For
example, to set the word `\TeX nical' into type, one would type
the input |\TeX  nical|; the space following the |\TeX| control
word ends
the control word, but is otherwise ignored. 
Multiple spaces are treated as a
single space.  So to set the phrase `\TeX\ ignores spaces
after control words' one must say:
\begintt
\TeX\ ignores spaces after control words
\endtt
using the control symbol |\|\] (i.e. an escape followed by a space)
to set an actual space.

There are about 300 {\sl primitive} control sequences built
into \TeX, and 600 more {\sl defined} control sequences (many
of them are {\sl macros}) are supplied as part of the default
version of \TeX.  These 900 definitions
constitute ``{\sl plain \TeX\/}.''  Plain \TeX{}
provides substantially more built-in support than \Troff/ does
without macros, but does not provide all the facilities
(section numbering, tables of contents) of a typical \Troff/ macro
package.  Thus, additional macros (probably supplied in
a macro package) are usually required to format
a complex document, but many simple documents with unnumbered
paragraphs, and even with footnotes, labeled sections,
and page headers,
can be formatted using only the facilities of plain \TeX.
\SubSection{Input lines}
As mentioned above, there are two exceptions to the rule
whereby a newline is treated the same as a space.  The
first case is {\sl comments\/}.  When \TeX\ encounters
a percent sign (|%|), the percent sign and all following
characters up to and including the next newline are ignored
(to set a percent in a document, use the control
symbol |\%|).

The second case is {\sl paragraphs\/}.  When two consecutive
newlines are encountered (i.e. an empty line), the effect is
the same as if a |\par| control word, which represents an
end-of-paragraph command, has occurred.  Thus, a user can set
up a simple document quite easily by simply leaving empty lines
between paragraphs.

One can also use a plain \TeX\ macro, |\obeylines|, to cause
each
newline character to begin a new paragraph,
just as two consecutive newlines normally do.  The
effect is similar to the |.na| request of \Troff/.
However, as there is no
macro to undo this effect, this should be done inside
a {\sl group\/,} to be described later.
\SubSection{Other Strange Characters}
Besides |\| and |%|, there are eight other characters that have
special significance for \TeX\ and should be avoided.  If
one must type them, there are control sequences that can be used to
prevent their special meanings:
$$\vbox{\halign {\hfil{\tt#}\hfil&\quad#\hfil&\quad#\hfil&\quad{\tt#}\hfil\cr
{\sl\quad Character\quad}&\hfil\sl Name\quad&
{\sl Significance\hfil}&{\sl\hfil Control Sequence}\cr
\noalign{\smallskip\hrule\smallskip}
\\&Backslash&Escape&\$\\backslash\$\cr
$\{$&Left Brace&Begin Group&\$\\$\{$\$\cr
$\}$&Right Brace&End Group&\$\\$\}$\$\cr
\$&Dollar Sign&Math Escape&\\\$\cr
\&&Ampersand&Alignment Tab&\\\&\cr
\#&Pound Sign&Parameter&\\\#\cr
|^|&Circumflex&Superscript&|\^|  {\it (accent)}\cr
|_|&Underscore&Subscript&|\_|\cr
|~|&Tilde&Tie&|\~|  {\it (accent)}\cr
\%&Percent&Comment&\\\%\cr
}
}$$
\SubSection{Groups}
The characters |{| and |}| deserve special attention.  These
braces delimit {\sl groups\/}.  Groups correspond, very roughly,
to \Troff/ environments (which most users don't see except
in the effects of such macros as the |.(b|~macro of the {\bf --me}
package).  Basically, any formatting change that occurs
within a group is undone when that group is closed.  For example,
the plain \TeX\ macro |\bf| changes the current font to {\bf bold
face}; to change one word to {\bf bold} in the middle of the
sentence, one says something like
\begintt
to change one word to {\bf bold} in the middle
\endtt
The change to boldface within the group is undone when that group
is closed.

Groups also serve a second function: they delimit parameters for
certain control sequences.  For example, the plain \TeX\ macro
|\centerline| requires a parameter comprising the text to be
centered.  Thus, the first title line of this document was
produced by the input
\begintt
\centerline{\titlefont A Guide to \TeX}
\endtt
as seen in the introduction.  Groups are not precisely analogous
to anything in \Troff/, but are an extremely important element
of \TeX\ syntax.

\Section{Fonts and Sizes}
\SubSection{Fonts}
{\it Troff\/} is oriented towards a
Wang Laboratories, Inc.,
C/A/T~Phototypesetter\note{A device-independent
\Troff/ is available as a separate program product from Western
Electric or maybe some other AT\&T subsidiary.},
and this causes several peculiarities and limitations, such as the
four-font restriction and the limitation of text width to 
$7{1\over2}$ inches.  Furthermore, the phototypesetter produces different
sizes of type by magnifying the letters with lenses.  This causes
the smaller point sizes to be cramped and hard to read, while
the much larger sizes may be more widely spaced than aesthetics
might dictate.

\TeX\ produces device-independent output files with a theoretical
resolution smaller than the wavelength of visible light (65536
basic units to a printer's point).  Characters on the page
are symbols (often called {\sl glyphs\/}) from particular fonts.
The size of the symbol is defined by the font in which it occurs,
just as its shape is.  Thus, ten-point roman (which you are reading
now) is a font completely separate from eight-point roman ({\eightpoint
which you are reading now}).
Plain \TeX\ assumes that the document
will be set in ten-point type, and sets the distance between
lines to account for that.  Plain \TeX\ also defines five control
sequences for changing fonts:
$$\vbox{\halign{\indent#\hfil\qquad&#\hfil\cr
|\rm| switches to the normal ``roman'' typeface:&Roman\cr
|\sl| switches to a slanted roman typeface:&\sl Slanted\cr
|\it| switches to italic style:&\it Italic\cr
|\tt| switches to a typewriter-like face:&\tt Typewriter\cr
|\bf| switches to an extended boldface style:&\bf Bold\cr}}$$
At the beginning of a run you get roman type.  As we saw
earlier, the best way to switch fonts is within a {\sl group\/};
this obviates the need for explicitly switching back to the
previous font.  Notice that these control sequences all change
to the ten-point version of these type styles, regardless of
the point size currently being used.

Users of \Troff/, who are accustomed to using {\it italics\/} for
emphasis and special material, should note carefully the difference
between {\it italics\/} and {\sl slanted letters.  Slanted letters
are just skewed roman letters, \it  but italic letters are drawn
in a completely different style\/}.  Consider, for example,
{\tenu unslanted italic letters}.  Usually, slanted letters can
be used for emphasis or for cited book titles; italics can be
used for special material such as section headings, or names
of \Unix\ programs such as \Troff/.  However, there are no established
conventions for the use of italics versus slanted letters, and the
writer is free to use them as he or she sees fit.

In addition to the
five plain \TeX\ fonts, one can easily define a control sequence
which will switch to 
any single font in the font library stored in the \Unix\ file system
(which normally includes the Computer Modern font family you are
now reading).  In effect, one is creating an association between
a font name, used as a control sequence within \TeX, and the name
of the file on disk where the information about the font can be found.
For example, the word `\Unix' which appears
throughout this document is set in
a ten-point small-caps
font.  The \Unix\ file name for this font is |cmcsc10|.
The \Unix\ file names have no intrinsic significance to \TeX,
so to use
|cmcsc10| in this paper, a |\csc| control sequence was defined
and associated with the |cmcsc10| disk file
by saying
\begintt
\font\csc=cmcsc10
\endtt
After the |\font| control sequence, a switch to title font
is accomplished by simply issuing the |\csc| control sequence.
Samples of some of the available fonts have been appended to
this paper.

Plain \TeX\ predefines some control sequences for certain
smaller character
sizes.  For example, |\sevenbf| selects {\sevenbf seven-point boldface}
type.  When switching to a different size of type, one should be
aware that the interline spacing is {\sl not\/} changed, nor are
the definitions for |\sl|, |\bf|, etc. changed; they still refer
to ten-point slanted, boldface, etc.\note{The macro package used
to set this paper includes an {\tt\\eightpoint} macro that changes
all the appropriate definitions
to eight-point type, as in this footnote.
See your \TeX\ guru to see if such a macro is publicly available.}
To use the other available character sizes, such as nine-point
roman,
one must use |\font| to
associate a new control word (e.g. |\ninerm|) with the appropriate
font information file (in this case, |cmr9|).

When switching from a slanty font like {\it italics\/} to a vertical
one like this roman font, a little extra space should be inserted
to prevent the top of the slanty text from getting too close to
the unslanted material.  Otherwise,
it ends up `{\it printed} like this' instead of
`{\it printed\/} like this.'  This so-called {\sl italic
correction\/} should be set with the
control symbol |\/| in the slanty font whenever such a 
switch is made.  For example, the previous sentence began:
\begintt
This so-called {\sl italic correction\/} should be set
\endtt
This isn't too hard to get used to, and can prevent some
uglinesses that \Troff/ doesn't understand or attempt to
deal with.
\tracingpages=1
\SubSection{Special Characters Revisited}
Not every font has every character.  For example, the
roman font doesn't have the inequality signs `$<$' and
`$>$' (they must be typed in Mathematics Mode, to be
described later).  However, if you know the symbols that
{\sl are\/} on the fonts you're using\note{The \TeX book
displays font layout tables in Appendix~E.}, you can produce
these characters using the special |\char| control sequence.
For example, the visible characters in the |\tt| font correspond
to ASCII terminal characters.  Thus, to produce a typewriter-style
backslash (`{\tt\\}', ASCII code 92 decimal), one can type
\begintt
{\tt\char92}
\endtt
By using an ``accent gr\`ave'' or left-quote character, one
can specify the character directly.  For example, the backslash
could also be produced by
\begintt
{\tt\char`\\}
\endtt
Remember, this example only applies to Typewriter font.  Position
92 of the roman font doesn't contain a backslash; thus
|\char`\\| would only produce the double-quote (\char92).

As described in the  later section on ``Macros And Definitions,''
these |\char| sequences can be assigned to {\sl macros\/} or abbreviations,
if they are to be used many times in a single document.
\SubSection{Magnification}
Many of the large type sizes can be obtained satisfactorily
by magnifying ten-point type to larger sizes just as
\Troff/ does.  Indeed, such magnified fonts may be the only
available fonts in the desired size.  One may specify a
magnified font by using the word |scaled| in the font
definition as shown:
\begintt
\font\twelverm=cmr10 scaled 1200
\endtt
The scaling factor (``1200'' in this example) is based on
1000 as a 1:1 ratio; in this example, it specifies that
the normal ten-point letters will be magnified by a factor
of 1.2000 to a size of twelve points.

Plain \TeX\ provides a series of standard magnification steps
that give a series of magnifications of 1.2 times.  They
are specified by a macro called |\magstep| as follows:
$$\vbox{\halign{\tt#\hfil&\hfil\quad#\quad\hfil&\quad#\hfil\cr
\hfil\sl specification&\hfil\sl value&\hfil\sl Changes 10pt to\cr
\noalign{\smallskip\hrule\smallskip}
\\magstep 0&1000&10pt (no change)\cr
\\magstephalf&1095&11pt\cr
\\magstep 1&1200&12pt\cr
\\magstep 2&1440&14pt (a little more)\cr
\\magstep 3&1728&18pt (a little less)\cr
\\magstep 4&2074&21pt (a little less)\cr
\\magstep 5&2488&24pt (a little more)\cr
}}$$
Thus, a specification like
\begintt
\font\elevenrm=cmr10 scaled \magstephalf
\endtt
produces a reasonable eleven-point roman font.

Finally, one can use magnifications to
enlarge the entire contents of
a paper (if all the fonts are available in the 
appropriate magnifications on your installation) by
saying |\magnification=|$n$ where $n$
is an integer such as 1000 (for no change) or can be
a |\magstep| macro.  Thus, if you say
|\magnification=\magstephalf| at the beginning of your paper,
its entire contents will be scaled up to eleven-point (well~$\ldots$
10.95-point) type.
Consult your local \TeX\ guru for a
list of the fonts and sizes available on your facility.
\SubSection{Ligatures}
As with \Troff/, many \TeX\ fonts provide ligatures that
automatically occur when certain consecutive characters are read.
For example, the letters~|ff| in the input will produce the
single glyph~`ff' on the page.
This is intended to improve the appearance of sentences such
as ``If you flex your fingers in a coffin, you can baffle a
giraffe.''
In \TeX, as with \Troff/, this happens automatically, and
the writer rarely needs to think about it.  However,
in \TeX, there are additional
special ligatures that deserve particular attention.
Two consecutive hyphens (|--|) produce an en-dash
(`--'; used for ranges such as `pages 13--34'); Three consecutive
hyphens (|---|) produce a regular punctuation dash (---).
Two consecutive closing single quote characters
(\'{}\'{}) will produce a
closing double-quote ('') while two consecutive opening single-quotes
(\`{}\`{} ---often
referred to on terminal keyboards
as `grave accent' characters) will produce
an opening double-quote (``).  The double-quote character |"| should
not be used.
Finally, two ``Spanish'' ligatures are available: the inverted
question mark `?`' can be typed as a question mark
followed by an open quotation mark(|?|\`{}), and the inverted
exclamation point `!`' can be typed as |!|\`{}.
These are {\sl not\/} control sequences, but are
a property built into the definition of each font.  Thus, they may
not occur in every available font (e.g. typewriter font), although
all the italic, bold, slanted and roman fonts can be expected
to behave this way.

\Section{Composing Text}
\SubSection{Paragraphs and All of That}
99\% of the time, \Troff/ is reading text (with the occasional
font change), filling up output lines as best it can, and outputting
them (with occasional interrupts at page breaks).

\TeX\ is doing
something similar 99\% of the time.  It reads text (with occasional
font changes) into a buffer.  Whenever an end of paragraph is found
(the |\par| macro or an empty line), \TeX\ breaks the text in its
buffer up into lines, breaking those lines at the points which
will produce the most attractive output.  For example,
it may space out an
early line a little more to keep a line with a big word
in it from looking too spaced out later.
Because \TeX\ composes paragraphs, not lines, its output can look
better, and strange tricks are possible.  For example,
the last sentence of this paragraph
ends {\bf flush} with the right margin because I told 
\TeX\ to allow no space at the end of the paragraph.  Another result
of setting paragraphs is that \TeX\ can usually avoid
``widow'' lines at the top and bottom of pages, setting paragraphs
a little more spaced out, if necessary.
{\parfillskip=0pt\par}
One useful feature of the line-breaking algorithm for \TeX\
\tolerance 500
is found in the use of {\sl ties\/}.  Ties
are typed using the character |~| (the tilde character), and
behave just like spaces, except that \TeX\ will never split a line
at a tie.
In \Troff/,
the special sequence `\\\]' (backslash-space) is used
similarly,
but in \Troff/ this is also an ``unpaddable'' space that
cannot be stretched; in \TeX, the {\bf only} effect of the analogous
tie character, the tilde, is to prevent
line breaking.
There are no strict rules for the placement of ties; they
should be used according to stylistic considerations, in places
where a line break is unacceptable.
For example, a phrase like `Chapter~2' should be typed as `|Chapter~2|'
to avoid something that looks like `Chapter
{\parfillskip=0pt\par\parskip=0pt\noindent}2'.  Other
good places for ties
\tolerance 200
include (1)~after the number
in enumerated cases like these; (2)~The space between the
surnames in phrases like `Vincent~Van~Gogh'; (3)~Between math symbols
in apposition as in `dimension~$d$'.

Frequently, one wishes to change the normal paragraph indentation,
or indent a paragraph at both margins, or adjust the amount of space
between paragraphs.  \Troff/ allows one to set registers
and specify local motions for these operations.
\TeX\ allows
something superficially similar, but the actual mechanism is
quite different.  A discussion of {\sl glue\/} is thus appropriate.
\SubSection{Boxes and Glue}
Because \Troff/ targets its output for a phototypesetter
that produces its output on a continuous form, the
composition of elements on the page involves commands to move
up and down the page, or left and right.  Even a `begin page'
command just causes movement downward to the length of the
current page\note{This causes problems when the phototypesetter
is simulated on a page-oriented device and a page length other
than 11 inches is specified.}.

\TeX, however, composes pages
as units rather than as a stream of commands, and builds
them from blocks of text called {\sl boxes\/} (typically paragraphs),
much as hand-set print was built from composing sticks filled
with letters.  The blank space around the boxes (such as the
paragraph indentation or the space between lines) is called
{\sl glue\/}---it is much like the wedges, or {\sl quoins\/}, that
printers used to set a page of print.  Thus, while a \Troff/ command
like |.sp .4i| means ``move down .4 inches,'' the corresponding
\TeX\ control sequence, |\vskip .4in| means ``at this point, there
should be .4 inches of glue.''  Although the difference may seem
to be minor, \TeX's behavior at paragraphs, page breaks, and so on
can only be properly understood if the picture of ``boxes of text
separated by glue'' is kept in mind.  Of course, these boxes
{\sl should not\/} be confused with the boxes that can be drawn around
``boxed tables'' in {\it tbl\/}, or the |.bx| macro in the |-me|
package.  \TeX\ boxes
are simply the units into which text material
is organized on the page.

Of course, the boxes themselves are often composed of other boxes,
surrounded by glue.  The page that gets output is a box made up
of paragraph boxes separated by vertical glue; these paragraph
boxes are composed of line boxes with vertical glue (baseline
spacing) between them; and these line boxes are in their turn
made up of word boxes with horizontal glue (interword spacing)
between them.  If one wants to get really fancy, one can even
put together a box explicitly with |\hbox| (for horizontal boxes)
and |\vbox| (for vertical boxes), as in
\begintt
for \vbox{\hbox{`A box}\hbox{of Text.'}}
\endtt
for \vbox{\hbox{`A box}\hbox{of Text.'}}
This is a vertical box (|\vbox|) composed of two horizontal boxes
(|\hbox|)---the first contains ``|`A box|'', the second ``|of Text.'|''.
Such constructions are usually undertaken by
\TeX perts, and are rarely needed in ordinary applications.
However, one special type of box, called a {\sl rule\/}, is
frequently useful.  A rule is a box that is filled entirely
with ink.  Normally, rules are very thin and are used for
horizontal and vertical lines.  The control sequences |\hrule|
and |\vrule| are used to construct horizontal and vertical rules
respectively.  For example, to construct
the little blot `\vrule height 8pt width 4pt',
I typed
\begintt
the little blot `\vrule height 8pt width 4pt',
\endtt
Vertical rules should be used within paragraphs, horizontal
rules between paragraphs, even if this
means having to specify a wide, flat ``vertical'' rule
in order to get a horizontal line into a paragraph.
Rules have default thicknesses
of 0.4pt, appropriate to thin lines.

Finally, a rule will have a default length equal to the box which
contains it.  This can sometimes be confusing, but one important
result is that a horizontal rule, when between paragraphs,
is as wide as the page.  This can be useful in setting off diagrams
and the like.  For example, |\hrule| was typed after this paragraph.
\hrule\smallskip
\SubSubSection{Dimensions}
Just as \Troff/ lets you describe distances in inches, points, ems,
etc., \TeX\ permits a variety of units in which the dimensions of
glue and boxes can be specified:
$$\halign{\indent\tt#&\quad#\hfil\cr
pt&point (baselines in this paper are 12 pt apart)\cr
pc&pica ($\rm1\,pc=12\,pt$)\cr
in&inch ($\rm1\,in=72.27\,pt$)\cr
bp&big point ($\rm72\,bp=1\,in$)\cr
cm&centimeter ($\rm2.54\,cm=1\,in$)\cr
mm&millimeter ($\rm10\,mm=1\,cm$)\cr
dd&did\^ot point ($\rm1157\,dd=1238\,pt$)\cr
cc&cicero ($\rm1\,cc=12\,dd$)\cr
sp&scaled point ($\rm65536\,sp=1\,pt$)\cr}$$
\filbreak
In addition, there are two other context-dependent units of measure
whose actual size depends on the current font:
{\par\narrower\parskip 0pt\obeylines\nobreak
{\bf em} is the width of a ``printer's em'' in the current font.
\nobreak{\bf ex} is the ``x-height'' of the current font.
}
The ``em'' will be familiar to \Troff/ users---it is the same
as the |m| unit used in such \Troff/ parameters as |10m|, and, in the
days of mechanical type, was based on the width of the letter
`M'.  This is typically the same as the point size of the
current font.
Similarly, the ``x-height'' is nominally the height of the
letter `x', although this may not be exactly true in
every font.  

In fact, each font defines its own em and ex values.  In 10-point
roman, the font
you are now reading, $1\,{\rm em}=10\,{\rm pt}$
and $1\,{\rm ex}\approx4.3\,{\rm pt}.$
The figures for {\bf Bold face} type of the same size are
11.5 and 4.44 respectively.
\SubSubSection{Using Glue}
When glue is placed into the document, it appears as white
space.
\TeX\ provides several control sequences that place glue
into the document.  |\hskip 1in| will insert one inch of
horizontal glue
(i.e. a one-inch space)
between words at the current position in the document..
|\vskip 8pt| will terminate the current paragraph and
follow it with 8 points of (vertical) glue.  One very useful type
of horizontal glue is |\quad|, which simulates a ``printer's
quad'', i.e. a 1-em space.

There are also three types of useful vertical glue defined
as plain \TeX\ macros, which are
sometimes helpful in formatting.  The control sequence |\smallskip| generates
a 3-point skip, |\medskip| a 6-point skip, and |\bigskip| a 12-point
skip.
$$\vbox{
\hbox to 4in{This line is followed by a |\smallskip|,\hfil} \smallskip
\hbox to 4in{this by a |\medskip|,\hfil}\medskip
\hbox to 4in{and this by a |\bigskip|.\hfil} \bigskip
\hbox to 4in{The sizes of these skips are independent of the current font size.\hfil}}$$

Several parameters can be set to govern the glue
to be placed at critical points in the document.  For example,
the glue between lines in this document is set so that the distance between
baselines is 12 points.  This can be adjusted by saying
|\baselineskip=14pt|, for example,
if wider spacing is desired (e.g. for 12-point type).  Here are
some other useful
parameters:
$$\vbox{\halign{#\quad\hfil&\it#\hfil&\quad#\hfil\cr
\hfil\sl Name&\hfil\rm\sl Default\hfil&\hfil\sl Description\hfil\cr
\noalign{\smallskip}
|\parskip|&0pt&Space between paragraphs\cr
|\leftskip|&0pt&Placed at left of each line of a paragraph\cr
|\rightskip|&0pt&Placed at right of each line of a paragraph\cr
|\topskip|&10pt&Glue at top of page\cr
|\parindent|&20pt&Paragraph indentation\cr
|\hsize|&6.5in&Width of text on the page\cr
|\vsize|&8.9in&Vertical size of text area on the page\cr
}}$$
\SubSubSection{Stretching and Shrinking}
Actually, glue is more than just rigid wedges between boxes.
It also has a certain amount of elasticity.  For example, when
\TeX\ sets a line of text, the glue between the words in the
line is able to shrink or stretch a certain amount in order
to adjust that line's spacing.  Similarly, the |\parskip| glue
between paragraphs is actually able to stretch an additional point
if necessary to improve the appearance of a page, and
the |\smallskip| series of skips can shrink {\bf or} stretch by as
much as 33\% of their natural lengths to assist in page formatting.

Some glue is infinitely elastic.  If you think of the printer's
page filled with rigid steel boxes of type and wedges between, this
infinitely stretchable glue is like a powerful spring.  
The name of horizontally stretchable glue is |\hfil|\note
{You can also specify such glue as {\tt\\hskip} or {\tt\\vskip} glue,
with a dimension of {\tt0pt plus 1fil}.  The {\tt plus 1fil} tells
\TeX\ that this glue can stretch to ``one degree of infinity''
as needed.  You can even make it ``infinitely shrinkable'' by
saying {\tt0pt minus 1fil}, or both at the same time.}.  If you type
|\line{\hfil Text}| then \TeX\ will set a line of type
the width of the page, with
the word ``Text'' at the far right end.  The |\centerline| macro
seen at the beginning of this paper is a |\line| with springs
at {\sl both} sides of the text.
\SubSection{Up, Down, Left, Right}
We've already seen how to add vertical and horizontal glue (effectively
skipping down and right) to create ``white space'' on the page.
One can also use vertical and horizontal glue with a {\sl negative\/}
dimension to move upwards or to the left, although this is rarely
useful.
There are a few other useful primitives for ``moving around'' the
page.  The primitive control word |\kern| specifies unstretchable
glue.
The name derives from a printer's term referring to type that projects
beyond the body of a letter.  |\kern| is normally used between letters
to move them further apart or closer together (|\hskip|, nearly identical
in semantics, can be used as well).
For example, the letters `T' and `E' in ``\TeX'' have been
moved closer together by the command |\kern-.1667em|.  Notice the
size of this glue is negative and pulls the letter boxes on either
side closer together than normal.  The `E' in `\TeX' has also been
lowered; this was done with the control sequence |\lower .5ex\hbox{E}|.
This is rather complex.  The |\hbox{E}| places the letter `E' in its
own horizontal box; the |\lower .5ex| sequence moves the baseline
of that box lower by .5ex.  Similarly, one can raise a box above
its normal baseline by using |\raise| instead of |\lower| (or
by using |\lower| with a negative dimension).
Normally, someone setting a simple document
will not need to set up his or her own |\hbox|es, just as one
rarely requires the horizontal and vertical movements of \Troff/.

Sometimes, one wishes to set type that
behaves
as if it takes up no space at all (e.g., for overstriking).
Plain \TeX\ provides two macros, |\rlap| and |\llap| for this.
|\rlap{something}| sets `something' and then backspaces as if
nothing had been set at all.  Similarly, |\llap{something}|
sets `something' at the left of the current point, overlapping
whatever was on the left.
Using typewriter font, for example,
one can typeset `{\tt\rlap{/}=}' by saying `|\rlap{/}=|' or `|/\llap{=}|'.

\Section{Page Composition}
Although plain \TeX\ is not as complete a document composition
system as a typical \Troff/ macro package, it does provide
several convenient features for composing technical documents.
\SubSection{Section Headings}
Plain \TeX\ does not provide the sophisticated numbered
headings (with several levels of section number) that
are found in the |-mm| and |-me| macro packages for
\Troff/, or the |Article| document type for |Scribe|.
However, there is a |\beginsection| macro that
can be used to set
a bold heading for a paragraph.  For example:
\begintt
\beginsection 1. An Example
|medskip
This paragraph isn't indented, even
though subsequent paragraphs would be.  A more
extensive example of this appears in Appendix~B
of ``{\sl The \TeX book}.''
\endtt
produces the following result:
\bigskip
\leftline{\bf 1. An Example}\nobreak\smallskip\vskip-\parskip\noindent
This paragraph isn't indented, even
though subsequent paragraphs would be.  A more
extensive example of this appears in Appendix~B
of ``{\sl The \TeX book}.''

Plain \TeX\ also includes
a |\proclaim| macro that can be used to
present theorems or similarly assertive statements.
\begintt
\proclaim Rule 225(a).  All proclamations must end their
labels with periods, and will appear in slanted type.
\endtt
\proclaim Rule 225(a).  All proclamations must end their
labels with periods, and will appear in slanted type.

The text of the proclamation comprises an entire paragraph, and
thus ends at the next empty line (or |\par|).
\SubSection{Page Headers and Footers}
Plain \TeX\ normally produces pages with no header lines and
a page number centered at the bottom.  If something else is wanted,
macros are provided to change them.  |\footline| defines
the footer line.  For example, a paper might set
up a footer line
with the command:
\nobreak
\begintt
\footline={\tenrm Rogue for Pacifists\hfil\folio}
\endtt
to produce a footer line like:
\nobreak\vskip 12pt
\line{\tenrm Rogue for Pacifists\hfil\folio}
\par\noindent
As with \Troff/, it is a good idea to explicitly set the
font to ten-point roman type.  Otherwise, the footer
will be set in whatever font happens to be in effect
when the page break occurs.
The alert reader will have noted the use of |\folio| for
the page number.  This useful (if somewhat
cryptically named) macro produces the Arabic
representation of the page number if it is positive, and
the Roman numeral representation of the number if it is
negative.  The page number begins at 1 and is incremented
after every page (or decremented if it is negative).  If
you want to adjust it yourself, you can issue the command
|\pageno=|$n$, where $n$ is the (possibly negative) new page number.

The header line can be set up the same way, using
|\headline=|.  In fact, the
document {\sl Using Nroff and --ME\/}, by Eric Allman, uses
a header line exactly analogous to the footer line
of the previous example.

Three-part headers and footers are trickier,
because just putting |\hfil| glue between the parts will center
the middle section between the left and right sections, rather
than centering it on the page.  The control sequences
|\rlap| and |\llap|
can be used to good effect here, since their results behave as if they
are of zero width.  Think of this as ``allowing the |\hfil|
springs to push against the sides of the page,'' and
you get the idea.  For example, the footer line of this page was
set with the input
\begintt
\footline= {
   \tenrm                % Ten-point roman
   \rlap{\TeX\ For {\it Troff\/} Users} % Takes no space, types to right
   \hfil\folio\hfil      % Centered Page number
   \llap{Sample}         % Also no space, types to left
}
\endtt
\footline= {
   \tenrm                % Ten-point roman
   \rlap{\TeX\ For {\it Troff\/} Users} % Takes no space
   \hfil\folio\hfil % Centered Page number
   \llap{Sample}         % Also no space
   \global\footline={\hss\tenrm\folio\hss}% Sneaky
}
\SubSection{Footnotes and Figures}
Most documents require some kind of ``movable'' text,
i.e. text that is to be set somewhere other than where it appears
in the input.  In general, \TeX\ calls such items {\sl inserts} and
provides powerful, if complex, primitives for the effective manipulation
of such material.  Fortunately, plain \TeX\ provides fairly handy
macros for doing some of the more familiar types of inserts.

The most common insert is a footnote, which consists of text
to go at the bottom of a page.  The plain \TeX\ |\footnote| macro
can be used within a paragraph\footnote{*}{Like this.}; for example,
the footnote in the present sentence was typed in the following
way:
\nobreak
\begintt
... within a paragraph\footnote{*}{Like this.}; for example, ...
\endtt
There are two parameters to |\footnote|: the reference mark (which
will appear in the footnote and in the paragraph), and the text of
the footnote.  If necessary, long footnotes are automatically
split between pages,
and footnotes normally appear in normal sized type as in this
example\footnote{**}{This paper uses a
private macro (not part of plain \TeX) to automatically
number footnotes and display them in eight-point type; this
footnote was produced with plain \TeX.}.  Note that
footnotes {\sl must} appear in
the context of a paragraph, or anything else ``horizontal''
that contributes to the page, e.g. in a |\centerline|.    If
you insist on using a footnote in a more exotic
context (e.g. the caption of a ``floating keep''), the esoteric
macro |\vfootnote| must be used instead of |\footnote|.

The second kind of insert that many people use is exemplified by
the ``floating keep'' construct of the |-me| macro package.  In this
case, an illustration or figure is to be kept together and set
onto the page at the earliest convenient time.  There are three
kinds of floating inserts in plain \TeX.  The first, |\topinsert|,
places its material, which ends with |\endinsert|,
at the top of the current page, if possible,
otherwise the material will be placed at the top of the next page.
For example:
\nobreak
\begintt
\topinsert
   \centerline{\vbox{
      \hbox{$\spadesuit$ A K 8 4}
      \hbox{$\heartsuit$ K 3 2}
      \hbox{$\diamondsuit$ 5}
      \hbox{$\clubsuit$ A K J 9 6}
   }}
\vskip 12pt
\centerline{{\bf Figure 1.} Example of a figure}
\endinsert
\endtt
|\topinsert| automatically adds some extra space to separate
the caption from the following text.
%\topinsert\vskip 3in
\topinsert
   \centerline{\vbox{
      \hbox{$\spadesuit$ A K 8 4}
      \hbox{$\heartsuit$ K 3 2}
      \hbox{$\diamondsuit$ 5}
      \hbox{$\clubsuit$ A K J 9 6}
   }}
\vskip 12pt
\centerline{{\bf Figure 1.} Example of a figure}
\endinsert

The second floating insert, |\midinsert| is much more like the |.(z|
construct of the |-me| package; it tries to insert the material in place
in the middle of the current page.  If it succeeds, the material
is placed in a vertical box with about 12 points of space above and below.
If this can't be done, the effect is that of a |\topinsert|.

Finally, the macro |\pageinsert| justifies its material to the size
of a full page and places the result on the following page.  For
example, the following produces a familiar result:
\nobreak
\begintt
\pageinsert
   \vfil % vertical centering 
   \centerline{This page intentionally left blank}
   \vfil % vertical centering
\endinsert
\endtt
\pageinsert
   \vfil % vertical centering
   \centerline{This page intentionally left blank}
   \vfil % vertical centering
\endinsert
\SubSection{Other Keeps}
Plain \TeX\ doesn't provide all the macros that one might want
to use for keeps, displays, and the like.  However, it's fairly
easy to tell \TeX\ to try to avoid breaking up a group.  Simply
set the cryptic parameter |\interlinepenalty=150| within that
group, and this will make line breaks within the group into very poor
candidates for page breaking.  Another strategy is to use
the control word |\filbreak|.  |\filbreak| causes the remainder
of the current page to be filled with vertical glue, {\bf unless}
it can be filled with additional text that is itself followed
by |\filbreak|.  If every paragraph had |\filbreak| after it, 
every page of a document would have only complete paragraphs on the
page.

Similarly, while there is no specific ``display'' macro
to correspond to the |.(l| macro of |-me| or
the |.DS| macro of |-mm|, one
can specify |\obeylines| within a group
to cause each newline to begin a new
paragraph.  One might also wish to set |\parindent|
to an appropriate value for the lines within the group.  You
can even have an entire group of centered lines by specifying |\obeylines|,
setting |\parindent| to zero, and |\leftskip| and |\rightskip|
(i.e. the left and right margins) to
be infinitely extensible glue\note{i.e. {\tt \\leftskip=0pt
plus 1fil} and {\tt \\rightskip=0pt plus 1fil}}.  There
may be some prepackaged
macro facilities available on your system for doing these sorts of
things.

\Section{Tables}
Users of \Troff/ often find themselves setting up tables
in their documents by using {\it tbl\/}, a program that
turns (relatively) simple table descriptions into the
complicated commands that unvarnished \Troff/ requires
to set the document.  Plain \TeX\ has its own built-in
facility for the creation of small (less than one page)
tables.  While \TeX\ table descriptions may be
somewhat harder to read than the corresponding
input for {\it tbl},
the table mechanism is well-integrated with the other
\TeX\ facilities, and there is no preprocessor required.
\SubSection{Tabs}
The easiest kind of table is one that uses ``tab stops''
set regularly across the page, analogous to the physical stops
in a typewriter.  In \TeX, one can set these tab stops by
saying |\settabs| $n$ |\columns|.  This divides the line
into $n$ equal parts.  To use the tab stops, one types
text that begins with the control sequence |\+| 
and ends with the sequence |\cr|. 
``|\cr|'' stands for Carriage-Return,
and suggests a time when typewriters had carriages.  If you forget
to end a tabbed line with |\cr|, \TeX\ will become very confused.
Of course, this means that the text for a single tabbed line may
occupy several lines in the input file, as long as it ends
with |\cr|.

The \TeX\ tab character is the ampersand, |&|; while this
can be changed to something else, the syntax-changing commands
of \TeX\ are (deliberately) somewhat opaque, and you probably
don't want to try it.  Here's an example of using tabs (stolen
shamelessly from ``{\sl The \TeX book\/}''):\penalty 200
\begintt
\settabs 4 \columns
\+&&Text that starts in the third column\cr
\+&Text that starts in the second column\cr
\+\it Text that starts in the first column, and&&&
 the fourth, and&beyond!\cr
\endtt
The result of all this is:
\penalty 200
\medskip
\settabs 4 \columns
\+&&Text that starts in the third column\cr
\+&Text that starts in the second column\cr
\+\it Text that starts in the first column, and&&&
 the fourth, and&beyond!\cr
\def\tick{\kern-0.2pt\vbox to 0pt{\kern-36pt\leaders\hbox{\vrule height 1pt
\vbox to4pt{}}\vfil}}
\vskip-\baselineskip
\+\tick&\tick&\tick&\tick&\tick\cr
\medskip
There are several interesting features in this example.  The
ampersand isn't exactly like a mechanical tab because it backs up,
if necessary, to reach the next numerical tab stop; this makes
tab-based tables somewhat easier than their \Troff/ counterparts, in
which one must always know when a field will slop over into
the next tabbed column.  Thus, in the last line, three |&|'s were required
to get to column~4, even though the first entry had extended
into column~2.  Lines~2~and~3 show that the |\cr| can end a line even
if some fields are not specified.  The last pair of lines shows
that spaces are ignored after ampersands; hence you can end an
input line harmlessly at such a point without getting extraneous
spaces.  The last line also shows that each individual entry
in a tabbed line is implicitly grouped as if it were in braces;
for this reason, no braces were required around the |\it| section.

The dashed columns, by the way, are pedagogical, and do not normally
appear.
\SubSection{General Tab Stops}
For somewhat more complicated tables, there's a second form of the
|\settabs| control sequence, in which a sample line (usually
consisting of the widest entries to be found in each field) is
supplied in order to set the tab stops.  The tabs are placed
at the positions of the |&|'s in the sample line, but the
sample line itself will {\bf not}
actually appear in the output.  There should be
some extra space between columns, to prevent the text in adjacent
columns from touching.  For example:\penalty 200
\begintt
\settabs\+\hskip 1in&Section Three\quad&\cr % Sample line
\+&Section One&Commands\cr
\+&Section Two&System Calls\cr
\+&Section Three&Subroutines\cr
\endtt
causes the following three lines to be typeset:\penalty 200
{\interlinepenalty=150
\medskip
\settabs\+\hskip 1in&Section Three\quad&\cr % Sample line
\+&Section One&Commands\cr
\+&Section Two&System Calls\cr
\+&Section Three&Subroutines\cr
}
\medskip
Notice that the sample line will typically end with |&\cr|, because
the text following the last tab isn't used for anything.  In other
words, the {\bf only} thing a sample field does is determine the
amount of space to the {\sl next} tab stop.  Also notice that each
tabbed line in this example
begins with a tab, so as to get the 1-inch indentation
(|\hskip 1in|) that was specified for the first field width in the
sample line.

Tabbed entries can also contain stretchable glue%
\note{{\tt\\hfill} glue (with two `l's) must be used here,
as you need
something ``infinitely more stretchable'' than the normal {\tt\\hfil}
glue that \TeX\ uses to left-justify the tabbed entries.  In
effect, the {\tt\\hfill} glue overrides the normal glue.}, allowing one
to do centering and justifying.  For example:\penalty 200
\begintt
\settabs 2 \columns
\+\hfill This material&\hfill While this\hfill&\cr
\+\hfill is flush right&\hfill material is centered\hfill&\cr
\+\hfill in the left-hand column&\hfill in the right-hand column.\hfill&\cr
\endtt
produces the following:\penalty 200
\penalty 200
\medskip
\settabs 2 \columns
\+\hfill This material&\hfill While this\hfill&\cr
\+\hfill is flush right&\hfill material is centered\hfill&\cr
\+\hfill in the left-hand column&\hfill in the right-hand column.\hfill&\cr
\medskip
\SubSection{Alignments}
Finally, there is a general mechanism, known as {\sl alignment},
which can be used to set generalized tables.  The details of
alignments can get quite complex, and a full chapter is devoted
to them in ``{\sl The \TeX book\/}.''  However, a short explanation
and example may be of
interest.
The command |\halign| is used to set up arbitrary tables.  The
general format is
\penalty 200\begintt
\halign{|begingroup|it Line Template |endgroup\cr
|begingroup|it table lines, each ending with |endgroup\cr
}
\endtt
\noindent Each table line will be ``plugged into'' the line template,
with the individual line elements (separated, as before,
with ampersands) substituted wherever
a pound-sign (|#|, also known as ``sharp-sign'' or ``octothorpe'')
occurs in the template.  As a specific example,
suppose we want to set the following table:
\penalty 200
\medskip
$$\vbox{\halign{\hfil\bf#\hfil & \quad#\hfil\cr
\sl Section&\sl Subject\cr
&\cr
1&Commands\cr
2&System Calls\cr
3&Subroutines\cr
4&Special Files\cr
5&File Formats\cr
6&Games\cr
7&Miscellany\cr
8&System Maintenance\cr}}$$
\medskip
To accomplish this, the
line template must include the |\hfil| glue used to center
and justify the columns, and the boldface shift for the numerals
that appear
in the first column.  In fact, it looks like this:\penalty 200
\begintt
\hfil\bf#\hfil & \quad#\hfil\cr
\endtt
The first column,` |\hfil\bf#\hfil|' will automatically have its
text, represented by the pound-sign,
centered by the two |\hfil| commands, and emboldened
by the |\bf|.  As with tabbing (which is really just a special
case of alignment), the font change is implicitly grouped
within the single table entry.  The second column,
`|\quad#\hfil|' will have a 1-em padding at the beginning,
and will be left-justified by the |\hfil| glue at the end.
Here's the whole command:\penalty 200
\begintt
\halign
   {\hfil\bf#\hfil & \quad#\hfil\cr

\sl Section&\sl Subject\cr
&\cr
1&Commands\cr
2&System Calls\cr
3&Subroutines\cr
4&Special Files\cr
5&File Formats\cr
6&Games\cr
7&Miscellany\cr
8&System Maintenance\cr}
\endtt
Notice how the normal fonts were overridden in the title line, and
how an empty line was set to separate the title line from the remainder
of the table.  As an alternative way to get some space between
lines in an alignment, you can say\penalty 200
\begintt
\noalign{|begingroup|it material|endgroup| }
\endtt\penalty200
after a |\cr| in an alignment and that material will be copied  
in place without being aligned.  For example, `|\noalign{\smallskip}|'
is an easy way to get a small skip between two lines of a table.

There was also some other magic involved in centering the
table on the page, to be described in the next section.  Basically,
the alignment was placed in its own |\vbox|, and that vertical
box was horizontally centered.

The examples of this section have been simple ones, but cover
most of the types of tables that are used in most
documents (such as the tables of dimensions or special characters
used in the earlier sections of this document).  People with more
complex needs will have to consult a \TeX\ guru, or learn more
from the chapter on alignments in ``{\sl The \TeX book\/}.''

\Section{Setting Mathematics}
\def\Eqn/{{\it eqn\/}}
Many people find that the most useful adjunct to \Troff/ is
the program \Eqn/, which provides a ``pronounceable''
way to describe mathematical equations for typesetting.  \TeX\ provides
a built-in {\sl mathematics mode\/} in which the meanings
of the letters and control sequences are changed to allow
easier equation settings.

Actually, there are two forms of mathematics mode in
\TeX: {\sl text\/} math mode, and {\sl display\/} math mode.
Text math mode is used for the in-line expressions specified
by the |delim| feature of \Eqn/.  It is delimited by 
single dollar signs.  For example, one can say something
like
\nobreak\begintt
Let $x$ be the sum of $y$ and $z/2$.
\endtt
in the middle of a paragraph, and produce something like
`Let $x$ be the sum of $y$ and $z/2$.'  Note that
math mode sets letters in italics but numerals in
roman font.

Display math mode is for setting equations between paragraphs
just as the |.EQ| and |.EN| macros of \Eqn/ do.  The display
math delimiters are double dollar signs, |$$|.  For example,
to display the equation $$x+5$$ this document includes
a line that says:
\nobreak
\begintt
to display the equation $$x+5$$ this document includes
\endtt
Note that display math mode automatically centers the
display on the page and provides the extra vertical spacing
around it.

\TeX's math mode contains a great deal of built-in knowledge
about equation spacing, and therefore {\sl ignores\/} spaces
that occur between the dollar signs (just as \Eqn/
does).  For example |$  x  $| has
the same effect as |$x$|.  You can always force extra space
by using |\quad|, |\|\] (escape-space),
or a glue specification; there are also
special control sequences for thinner spaces.
\SubSection{Greek Letters}
Unlike \Eqn/, which converts words like `omega' into the
corresponding Greek letters, \TeX\ requires control words
to produce these.
While this may,  at first, seem a nuisance, one is freed
from having to worry about `reserved words' in \TeX.
For example, to produce
$$x=2\pi\int\sin(\omega t)dt$$
one would type
|$$x=2\pi\int\sin(\omega t)dt$$|.  Upper-case Greek letters
(which are pronounced like |GAMMA| in \Eqn/) have names
like |\Gamma| in \TeX.  Math mode provides a host of other
math characters like |\infty| for `$\infty$'; 
Appendix~A lists several of these.
\SubSection{Subscripts and Superscripts}
\TeX\ math mode provides a simple method of superscripting
and subscripting, using the special characters |^| and |_|,
respectively.  For example, to set `$x^2$' one types |$x^2$|.
Similarly, `$\alpha_0$' is pronounced |$\alpha_0$|.  These
characters normally apply only to the next single character.
If you want more things subscripted or superscripted, you
can group them.  For example, `$x^{y_2}$' is typed as
|$x^{y_2}$|.  However, unlike \Eqn/, \TeX\ considers
a construct like
|$x^y^z$| illegal; you should specify |$x^{y^z}$| or
|$x^{yz}$|, depending on what is meant.

One can, however, specify |$x^2_3$| in order to obtain
`$x^2_3$';  |$x_3^2$| is equivalent.  Notice that 
simultaneous su$\rm_b^{per\kern-1pt}$scripts are stacked
over one another.  A special character `$\prime$', designed specifically
for being shrunk and raised for superscripting, is designated
by the control word |\prime|.  For example, one might 
refer to |$f^\prime(x)$| to set `$f^\prime(x)$'.  Plain \TeX\ provides
a convenient abbreviation: a single quote.  For example,
you could also say |$f'(x)$| (for `$f'(x)$')
or even |$f'''(x)$| for `$f'''(x)$'.
\SubSection{Fractions}
\TeX\ fractions are similar to \Eqn/'s treatment.  One can
type |$a/b$| to obtain `$a/b$,' but if one wants an
equation like $${x+y^2}\over{k+1}$$ one may type
`|$${x+y^2}\over{k+1}$$|'.  This can be taken to excess; Knuth
warns one against expressions like |$$a\over{b\over 2}$$|,
which produces the formula $$a\over{b\over 2}$$  This looks
fairly awful; the recommended alternative is |$$a\over{b/2}$$|,
which produces
$$a\over{b/2}$$
Plain \TeX\ also provides an operator |\choose|
for producing binomial coefficients such as $n\choose2$, which
is typed as |$n\choose 2$|.
\SubSection{Square Roots}
The control squence |\sqrt| produces square roots.
For example |$\sqrt2$| produces `$\sqrt2$' and
\begintt
$$\sqrt{x^3+\sqrt\alpha}$$
\endtt
produces
$$\sqrt{x^3+\sqrt\alpha}$$
You can produce other roots using |\root| and |\of|.  For
example, |$$\root 3 \of {x+y}$$| produces $$\root 3 \of {x+y}$$
\TeX\ is able to handle fairly tall formulas without getting
too ugly.  For example, the input
\nobreak\begintt
$$\sqrt{a^2\over{b_2}}$$
\endtt
produces
$$\sqrt{a^2\over{b_2}}$$ which is
substantially better than the ugly example on page~4
of the \Eqn/ manual.  A similar method produces
lines below or above formulas: |$\overline{x+y}$| produces
`$\overline{x+y}$.'  
\SubSection{Large Operators}
{\raggedright
Plain \TeX\ provides {\sl large operators\/} like 
$\sum$, $\int$ and $\prod$, which
produce larger symbols in display math mode than in text.
For example |$\sum x_n$| produces $\sum x_n$, but
|$$\sum x_n$$| produces $$\sum x_n$$
If one wishes to add ``limits'' to such operators, they
can be typed like subscripts.  For example,\hfil\break
|$$\sum_{n=1} ^m x_n$$| produces $$\sum_{n=1}^m x_n$$
The |\int| operator, $\int$, normally has its limits placed
to the sides of the operator.  For example, |$$\int _0 ^{\infty}$$|
produces
$$\int_0^{\infty}$$  If one wishes to change this convention, one
can type `|\limits|' directly after the |\int| operator.  For
example, |$$\int\limits_0^{\pi\over 2}$$| yields $$\int\limits_0^{\pi\over 2}$$
Certain defined control
sequences in plain \TeX\ also accept limits.  For example,
$$\lim_{n\to\infty}x_n=0$$
is produced by |$$\lim_{n\to\infty}x_n=0$$|.
}
\SubSection{Fonts}
Normally, text in math mode is set in math italic (similar, but not
identical to text italic).  Sometimes, one wants roman
type as part of a formula, especially with such mathematical functions
as `log' and `sin'.  Plain \TeX\ defines several control sequences
such as |\sin|, |\ln|, and |\lim| which always are set in roman
type.  You can also switch explicitly to roman by typing |\rm|.
For example, `$x^3+{\rm lower\ order\ terms}$' can be set by
typing |$x^3+{\rm lower\ order\ terms}$|.  Notice that spaces
had to be explicitly inserted by preceding them with the
backslash, because \TeX\ ignores spaces in math mode.

Bold face can also be used.  For example, |$\bf a+b=\Phi_m$|
produces `$\bf a+b=\Phi_m$'.  Plain \TeX\ arranges matters
so that the |\bf| control sequence only affects alphabetic
characters when in mathematics mode.  There is also a `calligraphic'
font for use with upper-case (and {\sl only\/} upper-case) letters
in math mode.  |$\cal EXAMPLE$| produces `$\cal EXAMPLE$'.  Finally,
|\it|, |\sl|, and |\tt| can be used, but cannot be produced in
subscript size.
\SubSection{Accents}
Plain \TeX\ defines eight control sequences for placing
accents over letters in mathematics mode:
\nobreak\vskip 8pt
\leftline{\vbox{\halign{\hskip .5in\tt\$\\# a\$&\hskip 1in$#$\cr
hat&\hat a\cr
check&\check a\cr
tilde&\tilde a\cr
dot&\dot a\cr
ddot&\ddot a\cr
breve&\breve a\cr
bar&\bar a\cr
vec&\vec a\cr}
}}
Note that the |dyad| accent of \Eqn/ is not present in plain
\TeX.  Also
note that |\underline| and |\overline| can be used to place
a bar over or under any formula.

\SubSection{Alignments}
The |mark| and |lineup| constructs of \Eqn/ are used to
align equations.  In \TeX, this can be done using the powerful
|\halign| mechanism as described in the previous section.  However,
plain \TeX\ also provides some special-purpose alignment macros
for doing some of the more common operations without resorting
to |\halign|.

The most common use of aligned formulas is in multi-line
displays that should be lined up by their `=' signs.
Plain \TeX\ provides the |\eqalign| macro for this purpose.
For
example, the example (that can't be done with |mark|) in the
\Eqn/ manual:
$$\eqalign{x&=1\cr x+y&=z\cr}$$ was typed as
\nobreak\begintt
$$\eqalign {
   x & =1 \cr
   x+y & = z\cr
}$$
\endtt
The right-hand side can start with an equals-sign or any other
symbol.  For example, one might wish to say something like:
$$\eqalign {
   x+y+z & < 5\cr
   z & = y/42\cr
   y\sin z & > x\log z\cr
}$$
with the equality and inequality symbols aligned.
This can be typed as
\begintt
$$\eqalign {
   x+y+z & < 5\cr
   z & = y/42\cr
   y\sin z & > x\log z\cr
}$$
\endtt

Another type of aligned display is something like
$$f(x)=\cases{
   x,& for $x\ge 0$;\cr
   0,& otherwise.\cr}$$
For this sort of display, the special macro |\cases| is defined.
This example was typed as
\nobreak\begintt
$$f(x)=\cases{
   x,& for $x\ge 0$;\cr
   0,& otherwise.\cr}$$
\endtt
Note that the first column is implicitly in mathematics mode, but
the second column is {\sl not\/}.  For example, the `$x\ge 0$'
of the first line had to be set explicitly in math mode.  The
|\cases| macro automatically typesets its own `$\{$' in the
appropriate size.

Finally, matrices can be set up using the |\matrix| alignment
macro.  For example, a neat array like
$$\matrix{
   x_i & x^2 \cr
   y_i & y^2 \cr
}$$
can be set up by typing
\begintt
$$\matrix{
   x_i & x^2 \cr
   y_i & y^2 \cr
}$$
\endtt
To set the array with big parentheses around it, |\pmatrix|
can be used instead of |\matrix|, to produce
$$\pmatrix{
   x_i & x^2 \cr
   y_i & y^2 \cr
}$$
Of course, there are other ways of typing arbitrary brackets,
as described in the next section.
\SubSection{Big Brackets, Etc.}
Plain \TeX\ provides an assortment of brackets and delimiters
that can be used for formulas.  The obvious ones are the
parentheses and brackets; one can also use |\{| and |\}| for
braces in math mode.  In addition, there are
|$\lfloor$| for `$\lfloor$', |$\lceil$| for `$\lceil$',
and |$\langle$| for `$\langle$'.  The right-hand versions
are |$\rfloor$|, |$\rceil$|, and |$\rangle$|.
One can also use the vertical bar, \vrt, as a delimeter
(e.g. to signify absolute value).

Sometimes one wishes
to get a larger version of these symbols.  To do this, precede them
by `|\bigl|' for the left side and `|\bigr|' for the right.  This
can make formulas easier to read.  For example,
\begintt
|$$\bigl(x-s(x)\bigr)\bigl(y-s(y)\bigr)$$|
\endtt
produces
$$\bigl(x-s(x)\bigr)\bigl(y-s(y)\bigr)$$

In \Eqn/, there is a generalized mechanism that produces brackets
big enough for whatever they enclose, using the keywords |left| and
|right|.  The mechanism in \TeX\ is quite similar.  For example,
the example on page~6 of the \Eqn/ manual,
$$\left\{a\over b + 1\right\}
=\left(c\over d \right)
+\left[e\right]
$$
is produced by the input
\begintt
$$\left\{a\over b + 1\right\}
=\left(c\over d \right)
+\left[e\right]
$$
\endtt

The |\left| and |\right| delimiters {\sl must\/} pair up with one
another, just as braces do in \TeX\ groups.  However, one can
use a period (`|.|') as a null delimiter in unbalanced groups.
For example, 
\begintt
$$x=\left\{y\over 3\right.$$
\endtt
produces
$$x=\left\{y\over 3\right.$$
The `|\right.|' sequence outputs nothing, but closes the
group begun by the |\left\{| sequence.
\SubSection {Displayed Text}
Display math mode can also be used to center and set off
textual material or alignments.  To do this, simply place
the material in a box using |\hbox| or |\vbox|.  For example,
\nobreak
\begintt
$$\hbox{Display Text}$$
\endtt
produces
$$\hbox{Display Text}$$
Notice that the text occurs in the regular text font (ten-point
Roman) rather than math italics.
An even more practical use of this technique is for alignments.
A table can be centered easily.
\begintt
$$\vbox
 {\halign
  {\tt#\hfil & \quad #\hfil \cr
   \bf\hfil Name & \bf\hfil Supplier\cr
\noalign {\smallskip\hrule\smallskip}
   \TeX   & University of Washington\cr
   TROFF  & Bell Laboratories\cr
   SCRIBE & Unilogic, Ltd.\cr
   DSR    & DEC (VMS Only)\cr
}}$$
\endtt
produces
$$\vbox
 {\halign
  {\tt#\hfil & \quad #\hfil \cr
   \bf\hfil Name & \bf\hfil Supplier\cr
\noalign {\smallskip\hrule\smallskip}
   \TeX   & University of Washington\cr
   TROFF  & Bell Laboratories\cr
   SCRIBE & Unilogic, Ltd.\cr
   DSR    & DEC (VMS Only)\cr
}}$$
complete with the spacing that separates it from the surrounding
textual material.
\SubSection {More Reading}
This section has outlined some of the more straightforward uses of
math mode.  There are many other facilities, as described in
``{\sl The \TeX book\/}''.  Consult that volume for
additional ideas.

\Section{Macros and Definitions}
We have already shown one instance in which a \TeX\ control
sequence was defined or modified by the user.  This was
the use of |\font| to define a font-switching control
sequence.
However, one can also define a new \TeX\ control sequence
by using the primitive |\def|.  Such new control sequences
are called {\sl macros\/} as they are, in effect, short
abbreviations for longer streams of commands.
It is, of course, possible to define whole
families of macros similar in function to the macro packages
such as {\bf --me} or {\bf --mm} in \Troff/, or the `document
formats' such as {\bf @Make(Report)} of |Scribe|.  Knuth's
{\sl\TeX book\/} was produced using such a package\note
{This package is described in Appendix~E of that book.
Some of Knuth's macros were stolen for
this document.}, and the
numbered
section headings and footnotes for this document were produced
by the author's own macros such as the |\Section| macro seen in
the example at the beginning of the document.

However, 
even when using a very complete  macro package, one sometimes
wishes to define often-used sequences for a particular paper.
For example, this paper
uses a macro, |\Unix|, which is similar to |\TeX| but  produces
`\Unix' in 10-point small-caps font.  It was defined as follows:
\begintt
\font\csc=cmcsc10 % Small-caps font
\def\Unix{{\csc Unix}} % Extra grouping for font-change
\endtt
As a result, whenever |\Unix| is seen in the input
for this paper, \TeX\
substitutes the
sequence |{\csc Unix}|. 

As another example, one might wish to refer to the backslash
character many times in typewriter-font examples (for instance,
if one were writing a document about \TeX).  In this case, it
might be useful to define a control sequence such as |\\| as
follows:
\begintt
\def\\{\char`\\}
\endtt
After which an example like |\this\example\here| could be
typed as
\begintt
{\tt \\this\\example\\here}
\endtt

If you have a file containing a group of useful macros and definitions,
or even just a useful section of text that you wish to
repeat, you can use the \TeX\ primitive |\input|, which operates
much like the |.so| primitive of \Troff/.  For example, the
definitions of |\Section| and so on for this paper are
contained in a file called |paperhead.tex|; the first line
of this document is |\input paperhead|.
If the file to be input isn't in the current working directory,
a ``macro library'' directory is searched.  This allows commonly-used
macro packages, such as the American Mathematical Society's
{$\cal A$\kern-.1667em\lower.5ex\hbox{$\cal M$}\kern-.125em $\cal S$-\TeX}
package, to be publicly available with a minimum of fuss.

It is also possible to generate a separate runnable version of
\TeX\ that has a built-in set of macros other than those used
by plain \TeX.  One such system is the excellent 
L\kern-.2em\raise.3ex\hbox{\csc a}\kern-.09em\TeX\
document preparation system created by Leslie Lamport of
SRI International, which presents a far more complete system
for producing complex text documents than plain \TeX.

More complex macros with parameters, etc., are possible, but
are `big-league' material outside the scope of this paper.
The grouping features of \TeX, combined with a powerful
set of conditionals,
give \TeX\ a structured-language-like
appearance, compared to that of \Troff/.
The Truly Ambitious should read ``{\sl The \TeX book\/}'' by Donald
Knuth, which is the ultimate font of \TeX nical knowledge.

\Section{Running \TeX\ under \Unix}
\TeX82 is written in |PASCAL| and the user interface is
nearly identical on the various operating systems to which
it has been ported.  The \TeX\ source code is placed
in a file with a name like `{\it filename\/\tt.tex}'.
The input should end with a |\bye| macro, which automatically
fills out the last page with |\vfil| glue, outputs it,
and terminates \TeX.
Assuming
a Bourne shell, the command to invoke \TeX\ will be
$${\hbox{\tt\$ tex \it filename}}$$
Assuming that  |tex| is found, \TeX\ will print
something like
\begintt
This is TeX, Version 1.0 for Berkeley UNIX (preloaded format=plain 83.12.9)
(filename.tex [1])
Output written to filename.dvi (1 page, 2092 bytes)
Transcript written on filename.log.
$
\endtt
\TeX\ lists the files as it reads them, and displays the numbers
of the pages as they are produced (in brackets).  It writes
error messages and warnings,
and some occasionally cryptic information,
in {\it filename\/\tt.log} and
produces a device-independent (`dvi') representation
of the result in {\it filename\/\tt.dvi}.  This file can be
sent to  your typesetting device by giving it as input to
the appropriate device driver program.  Consult your local \TeX\
guru for information on the device drivers available at your
site.

If \TeX\ detects errors in the input, and it has a terminal input
device, it will attempt to interact with the user and allow
him or her to correct the error.  The help facilities built
into \TeX\ allow the user to receive an explanation of the
error, and provide some guidance as to possible remedies.
Type a question-mark and hit the |return| key if you're in doubt.
One
can, as an alternative, add the command |\batchmode| to the input file to
suppress this interaction. In this case, \TeX\ can be run
in background mode (redirecting output to |/dev/null|); the
output for errors and warnings will still be placed in the
appropriate |.log| file for later examination.

\Section{A Short Example}
\def\boxit#1{\vbox{\hrule\hbox{\vrule\kern3pt\vbox{\kern3pt#1
\kern3pt}\kern3pt\vrule}\hrule}}
\vfil
\centerline{\parfillskip=0pt\boxit{\boxit
{\vbox{\hsize 4in\tolerance 800\noindent
\advance\count0 by 1
Pages \number\count0
\advance\count0 by 1
\ and \number\count0
\ contain a short sample of \TeX\ input,
demonstrating some of the features discussed in this
document.  The result is on page
\advance\count0 by 1
\number\count0.  Note
that the page number in the sample output follows the
page numbering in this document, rather than being
`1' as it would be if the sample were run separately.
The reader should inspect closely the left and right
single quotes in the input, which can be rather hard to
distinguish in the `tt' font.}}}}
\vfil\eject
\begintt
\font\titletype=cmbx10 scaled \magstep 1 % 12-point boldface
\footline={\TeX\ Sample \hfil Page \folio}
\headline={\hfil{\bf S A M P L E}\hfil}
\vskip .25in
\line{\hfil Sample Output}  % Right-justified
\line{\hfil Feb 30, 1986}   % text due to \hfil
\vskip 12pt
\centerline{\titletype \TeX\ Sample}
\vskip 1cm
This material, which appears in 10-point type (possibly
magnified) , demonstrates
several features: (1)~Ties.  (2)~Floating Keeps for figures.
(3)~General syntax. (4)~Equations and tables.  (5)~Verbatim
mode using {\tt obeylines}.
\beginsection Footnotes and Accents.
|bigskip
This is a new paragraph.  It contains a footnote\footnote{*}
{Which doesn't tell you much}, and contains some fascinating
accent marks like the accent gr\`ave, and the accents in
phrases like ``\c c'est la vie'' and ``\^gis revido.''  This
paragraph also demonstrated the double-quote ligatures---which
are somewhat hard to read in the `tt' font---and the long
dashes.
|bigskip
Here's yet another new paragraph, this one
indented, since it is not at the beginning
of a section.  Notice that the interparagraph
spacing is zero, unlike the main body of the paper.
In Figure~1,
we see an equation from ``{\sl A System for Typesetting Mathematics\/}''
by Kernighan and Cherry.
\midinsert % A displayed Equation from Kernighan and Cherry
\def\emx{e^{mx}} % This is done with EQN defines in Kernighan and Cherry
\def\mab{m\sqrt{ab}}
\def\sa{\sqrt a}
\def\sb{\sqrt b}
$${\int\limits{dx\over{a\emx-be^{-mx}}}}=\cases{
{1\over{2\mab}}\log
{{\sa\emx-\sb}\over{\sa\emx+\sb}}&\cr
&\cr
{1\over{\mab}}\tanh^{-i}({\sa\over\sb}\emx)&\cr
&\cr
{-1\over{\mab}}\coth^{-i}({\sa\over\sb}\emx)&\cr
}$$
\centerline{Figure 1.  An Equation}
\endinsert
Furthermore, here is a table from M. Lesk's
``{\sl Tbl---A Program to Format Tables\/}'':
\endtt\vfil\eject\begintt
\vskip 10pt
\settabs\+Language\quad&Carnegie-Mellon\quad&\cr
\+\hfil Language\hfil & \hfil Authors\hfil & \quad Runs on\cr %centered
\+ \cr % Skip a line
\+ Fortran & Many & Almost anything\cr
\+ PL/1 & IBM & 360/370\cr
\+ C & BTL & 11/45,H6000,370\cr
\+ BLISS & Carnegie-Mellon & PDP-10,11\cr
\+ IDS & Honeywell & H6000\cr
\+ Pascal & Stanford & 370\cr
\endtt\begintt
\bigskip
Finally, here's an example of {\tt obeylines}:
{\obeylines\parindent=1in\parskip=0pt % Single-space, 1-inch indent
\endtt\begintt
This material
has no interparagraph gap
between the lines, but each
line is, in effect, a new paragraph} % End of Obeylines
\endtt\begintt
Now to finish up.
\bye
\endtt
\vfil\eject % Throw a new page.
{
\parskip=0pt plus 1pt
%\font\titletype=cmbx10 at 12 truept% 12-point boldface if magnified
\font\titletype=cmbx10 scaled \magstep 1 % 12-point boldface
\footline={\TeX\ Sample \hfil Page \folio}
\headline={\hfil{\bf S A M P L E}\hfil}
\vskip .25in
\line{\hfil Sample Output}  % Right-justified
\line{\hfil Feb 30, 1986}   % text due to \hfil
\vskip 12pt
\centerline{\titletype \TeX\ Sample}
\vskip 1cm
This material, which appears in 10-point type (possibly
magnified), demonstrates
several features: (1)~Ties.  (2)~Floating Keeps for figures.
(3)~General syntax. (4)~Equations and tables.  (5)~Verbatim
mode using {\tt obeylines}.
\beginsection Footnotes and Accents.

This is a new paragraph.  It contains a footnote\footnote{*}
{Which doesn't tell you much}, and contains some fascinating
accent marks like the accent gr\`ave, and the accents in
phrases like ``\c c'est la vie'' and ``\^gis revido.''  This
paragraph also demonstrated the double-quote ligatures---which
are somewhat hard to read in the `tt' font---and the long
dashes.

Here's yet another new paragraph, this one
indented, since it is not at the beginning
of a section.  Notice that the interparagraph
spacing is zero, unlike the main body of the paper.
In Figure~1,
we see an equation from ``{\sl A System for Typesetting Mathematics\/}''
by Kernighan and Cherry.
\midinsert % A displayed Equation from Kernighan and Cherry
\def\emx{e^{mx}} % This is done with EQN defines in Kernighan and Cherry
\def\mab{m\sqrt{ab}}
\def\sa{\sqrt a}
\def\sb{\sqrt b}
$${\int{dx\over{a\emx-be^{-mx}}}}=\cases{
{1\over{2\mab}}\log
{{\sa\emx-\sb}\over{\sa\emx+\sb}}&\cr
&\cr
{1\over{\mab}}\tanh^{-i}({\sa\over\sb}\emx)&\cr
&\cr
{-1\over{\mab}}\coth^{-i}({\sa\over\sb}\emx)&\cr
}$$
%
%$${\int\limits{dx\over{ae^{mx}-be^{-mx}}}}=\cases{
%{1\over{2m\sqrt{ab}}}\log
%{{\sqrt{a}e^{mx}-\sqrt{b}}\over{\sqrt{a}e^{mx}+\sqrt{b}}}&\cr
%&\cr
%{1\over{m\sqrt{ab}}}\tanh^{-i}({\sqrt{a}\over\sqrt{b}}e^{mx})&\cr
%&\cr
%{-1\over{m\sqrt{ab}}}\coth^{-i}({\sqrt{a}\over\sqrt{b}}e^{mx})&\cr
%}$$
\centerline{Figure 1.  An Equation}
\endinsert

Furthermore, here is a table from M. Lesk's
``{\sl Tbl---A Program to Format Tables\/}'':
\vskip 10pt
\settabs\+Language\quad&Carnegie-Mellon\quad&\cr
\+\hfil Language\hfil & \hfil Authors\hfil & \quad Runs on\cr %centered
\+ \cr % Skip a line
\+ Fortran & Many & Almost anything\cr
\+ PL/1 & IBM & 360/370\cr
\+ C & BTL & 11/45,H6000,370\cr
\+ BLISS & Carnegie-Mellon & PDP-10,11\cr
\+ IDS & Honeywell & H6000\cr
\+ Pascal & Stanford & 370\cr

\bigskip
Finally, here's an example of {\tt obeylines}:
{\obeylines\parindent=1in\parskip=0pt % Single-space, 1-inch indent

This material
has no interparagraph gap
between the lines, but each
line is, in effect, a new paragraph} % End of Obeylines

Now to finish up.
\vfil\eject
\headline={\line{\hss}}
\footline={\hss\folio\hss}
}

{
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   SpecChars.tex  -- Print the special characters available in math
%                     mode.
%
%   This version swiped from TeX82, version 0.97, with PLAIN.TEX loaded.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  Major munging applied 1/84 to jive with Appendix F of the TeXbook
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\def\ctr#1{\hss#1\hss}
\def\\{\char `\\}
\def\v{\vrule height 20pt depth 10pt width 0pt}
\tabskip 1em
\parskip 6pt plus 2pt
\abovedisplayskip 0pt
\belowdisplayskip 0pt
\def\dcolumn#1{$\vcenter
               {
                \halign{\v$\ctr{##}$&$\displaystyle\ctr{##}$&{\tt ##}\cr#1}
               }$
             }
\def\column#1{$\vcenter
               {
                \halign{$\ctr{##}$&{\tt ##}\cr#1}
               }$
             }
\def\sect#1{\penalty-1000
            \vskip 12pt plus 6pt
            {\sl #1}
            \vskip 4pt
            \penalty9999\ignorespaces}
\Appendix{A}{Special characters available in \TeX's ``math mode''}

There are many special-purpose characters available from \TeX, but most of
them don't appear on most keyboards.  Therefore, the following control
sequences have been pre-defined in plain.tex for your convenience.
Note, however, that most of these special sequences are {\sl only\/}
available in math mode.  Consult Appendix~F of {\sl The \TeX book\/}
for complete details.

\sect{(a) Lower-case Greek letters:}
\hbox to \hsize{
    \hfill
    \column{
        \alpha&\\alpha\cr
        \beta&\\beta\cr
        \gamma&\\gamma\cr
        \delta&\\delta\cr
        \epsilon&\\epsilon\cr
        \zeta&\\zeta\cr
        \eta&\\eta\cr
        \theta&\\theta\cr
        \iota&\\iota\cr
    }
    \column{
        \kappa&\\kappa\cr
        \lambda&\\lambda\cr
        \mu&\\mu\cr
        \nu&\\nu\cr
        \xi&\\xi\cr
        \pi&\\pi\cr
        \rho&\\rho\cr
        \sigma&\\sigma\cr
        \tau&\\tau\cr
    }
    \column{
        \upsilon&\\upsilon\cr
        \phi&\\phi\cr
        \chi&\\chi\cr
        \psi&\\psi\cr
        \omega&\\omega\cr
        \varepsilon&\\varepsilon\cr
        \varpi&\\varpi\cr
        \vartheta&\\vartheta\cr
        \varphi&\\varphi\cr
    }
    \hfill
}

\filbreak
\sect{(b) Upper-case Greek letters:}
\hbox to \hsize{
    \hfill
    \column{
        \Gamma&\\Gamma\cr
        \Delta&\\Delta\cr
        \Theta&\\Theta\cr
        \Lambda&\\Lambda\cr
        \Xi&\\Xi\cr
        \Pi&\\Pi\cr
    }
    \column{
        \Sigma&\\Sigma\cr
        \Upsilon&\\Upsilon\cr
        \Phi&\\Phi\cr
        \Psi&\\Psi\cr
        \Omega&\\Omega\cr
    }
%    \column{
%        \Gammait&\\Gammait\cr
%        \Deltait&\\Deltait\cr
%        \Thetait&\\Thetait\cr
%        \Lambdait&\\Lambdait\cr
%        \Xiit&\\Xiit\cr
%        \Piit&\\Piit\cr
%    }
%    \column{
%        \Sigmait&\\Sigmait\cr
%        \Upsilonit&\\Upsilonit\cr
%        \Phiit&\\Phiit\cr
%        \Psiit&\\Psiit\cr
%        \Omegait&\\Omegait\cr
%    }
    \hfill
}

\filbreak
\sect{(c) Script letters (Characters from the {\tt \\cal} font):}
{\def\{{\char`\{}\def\}{\char`\}}
\hbox to \hsize{
    \hfill
    \column{
        {\cal A}&\{\\cal A\}\cr
        {\cal B}&\{\\cal B\}\cr
        {\cal C}&\{\\cal C\}\cr
        {\cal D}&\{\\cal D\}\cr
        {\cal E}&\{\\cal E\}\cr
        {\cal F}&\{\\cal F\}\cr
        {\cal G}&\{\\cal G\}\cr
        {\cal H}&\{\\cal H\}\cr
        {\cal I}&\{\\cal I\}\cr
    }
    \column{
        {\cal J}&\{\\cal J\}\cr
        {\cal K}&\{\\cal K\}\cr
        {\cal L}&\{\\cal L\}\cr
        {\cal M}&\{\\cal M\}\cr
        {\cal N}&\{\\cal N\}\cr
        {\cal O}&\{\\cal O\}\cr
        {\cal P}&\{\\cal P\}\cr
        {\cal Q}&\{\\cal Q\}\cr
        {\cal R}&\{\\cal R\}\cr
    }
    \column{
        {\cal S}&\{\\cal S\}\cr
        {\cal T}&\{\\cal T\}\cr
        {\cal U}&\{\\cal U\}\cr
        {\cal V}&\{\\cal V\}\cr
        {\cal W}&\{\\cal W\}\cr
        {\cal X}&\{\\cal X\}\cr
        {\cal Y}&\{\\cal Y\}\cr
        {\cal Z}&\{\\cal Z\}\cr
    }
    \hfill
}}
There are also ``oldstyle numerals'' available via
{\tt \$\\oldstyle 0123456789\$}: $\oldstyle 0123456789$.
\filbreak
\sect{(d) Binary operators:}
\hbox to \hsize{
    \hfill
    \column{
        \mp&\\mp\cr
        \pm&\\pm\cr
        \setminus&\\setminus\cr
        \cdot&\\cdot\cr
        \times&\\times\cr
        \ast&\\ast\cr
	\star&\\star\cr
        \diamond&\\diamond\cr
        \circ&\\circ\cr
        \bullet&\\bullet\cr
        \div&\\div\cr
    }
    \column{
        \cap&\\cap\cr
        \cup&\\cup\cr
        \uplus&\\uplus\cr
        \sqcap&\\sqcap\cr
        \sqcup&\\sqcup\cr
        \triangleleft&\\triangleleft\cr
        \triangleright&\\triangleright\cr
        \wr&\\wr\cr
        \bigcirc&\\bigcirc\cr
        \bigtriangleup&\\bigtriangleup\cr
        \bigtriangledown&\\bigtriangdown\cr
    }
    \column{
        \lor&\\lor (or \\vee)\cr
        \land&\\land (or \\wedge)\cr
        \oplus&\\oplus\cr
        \ominus&\\ominus\cr
        \otimes&\\otimes\cr
        \oslash&\\oslash\cr
        \odot&\\odot\cr
        \dagger&\\dagger\cr
        \ddagger&\\ddagger\cr
        \amalg&\\amalg\cr
    }
    \hfill
}

\filbreak
\sect{(e) Binary relations:}
\hbox to \hsize{
    \hfill
    \column{
	\leq&\\leq\cr
	\prec&\\prec\cr
	\preceq&\\preceq\cr
	\ll&\\ll\cr
	\subset&\\subset\cr
	\subseteq&\\subseteq\cr
	\sqsubseteq&\\sqsubseteq\cr
	\in&\\in\cr
	\vdash&\\vdash\cr
	\smile&\\smile\cr
	\frown&\\frown\cr
    }
    \hfill
    \column{
	\geq&\\geq\cr
	\succ&\\succ\cr
	\succeq&\\succeq\cr
	\gg&\\gg\cr
	\supset&\\supset\cr
	\supseteq&\\subseteq\cr
	\sqsupseteq&\\sqsubseteq\cr
	\ni&\\ni\cr
	\dashv&\\dashv\cr
	\mid&\\mid\cr
	\parallel&\\parallel\cr
    }
    \hfill
    \column{
        \equiv&\\equiv\cr
        \sim&\\sim\cr
        \simeq&\\simeq\cr
        \asymp&\\asymp\cr
        \approx&\\approx\cr
        \cong&\\cong\cr
        \bowtie&\\bowtie\cr
        \propto&\\propto\cr
        \models&\\models\cr
        \doteq&\\doteq\cr
        \perp&\\perp\cr
    }
    \hfill
}
\noindent
You can also use the control sequence {\tt \\not} to negate or ``cross out''
most of the relations above.  For example, the symbol
``$\mathrel{\not\subseteq}$''
is really two symbols, obtained by typing ``{\tt \\not\\subseteq}''.
(The slashing character in the symbol font has a width of zero, so it will overlap
the following character.)  But watch out: you should actually type
``{\tt \\mathrel\char`\{\\not\\subseteq\char`\}}'', in order to prevent
\TeX\ from breaking a line after {\tt \\not}.
\filbreak
\sect{(f) Arrows : }
\vskip 6pt plus 2pt
\hbox to \hsize{
    \hfill
    \column{
        \uparrow&\\uparrow\cr
        \Uparrow&\\Uparrow\cr
        \downarrow&\\downarrow\cr
        \Downarrow&\\Downarrow\cr
        \updownarrow&\\updownarrow\cr
        \Updownarrow&\\Updownarrow\cr
        \nearrow&\\nearrow\cr
        \searrow&\\searrow\cr
        \swarrow&\\swarrow\cr
        \nwarrow&\\nwarrow\cr
    }
    \column{
        \longleftarrow&\\longleftarrow\cr
        \Longleftarrow&\\Longleftarrow\cr
        \longrightarrow&\\longrightarrow\cr
        \Longrightarrow&\\Longrightarrow\cr
        \longleftrightarrow&\\longleftrightarrow\cr
        \Longleftrightarrow&\\Longleftrightarrow\cr
        \longmapsto&\\longmapsto\cr
        \hookrightarrow&\\hookrightarrow\cr
        \rightharpoonup&\\rightharpoonup\cr
        \rightharpoondown&\\rightharpoondown\cr
    }
    \column{
        \leftarrow&\\leftarrow\cr
        \Leftarrow&\\Leftarrow\cr
        \rightarrow&\\rightarrow\cr
        \Rightarrow&\\Rightarrow\cr
        \leftrightarrow&\\leftrightarrow\cr
        \Leftrightarrow&\\Leftrightarrow\cr
        \mapsto&\\mapsto\cr
        \hookleftarrow&\\hookleftarrow\cr
        \leftharpoonup&\\leftharpoonup\cr
        \leftharpoondown&\\leftharpoondown\cr
        \rightleftharpoons&\\rightleftharpoons\cr
    }
    \hfill
}

\filbreak
\sect{(g) ``Large'' operators (text and display styles):}
\hbox to \hsize{
    \hfill
    \dcolumn{
        \bigwedge&\bigwedge&\\bigwedge\cr
        \bigvee&\bigvee&\\bigvee\cr
        \int&\int&\\int\cr
        \oint&\oint&\\oint\cr
    }
    \dcolumn{
        \sum&\sum&\\sum\cr
        \prod&\prod&\\prod\cr
        \coprod&\coprod&\\coprod\cr
        \bigoplus&\bigoplus&\\bigoplus\cr
        \bigotimes&\bigotimes&\\bigotimes\cr
        \bigodot&\bigodot&\\bigodot\cr
    }
    \dcolumn{
        \bigcap&\bigcap&\\bigcap\cr
        \bigcup&\bigcup&\\bigcup\cr
        \biguplus&\biguplus&\\biguplus\cr
        \bigsqcup&\bigsqcup&\\bigsqcup\cr
    }
    \hfill
}

\filbreak
\sect{(h) Brackets:}
$$\vbox{
    \halign{$\ctr{#}$&{\tt #}\quad&$\ctr{#}$&{\tt #}\cr
        \lfloor&\\lfloor&\rfloor&\\rfloor\cr
        \lceil&\\lceil&\rceil&\\rceil\cr
        \lbrack&\\lbrack&\rbrack&\\rbrack\cr
        \{&\\\char`\{\ (or \\lbrace)&\}&\\\char`\}\ (or \\rbrace)\cr
        \langle&\\langle&\rangle&\\rangle\cr
    }
}$$

\filbreak
\sect{(i) Miscellaneous math symbols:}
\hbox to \hsize{
    \hfill
    \column{
        \imath&\\imath\cr
        \jmath&\\jmath\cr
	\ell&\\ell\cr
        \Re&\\Re\cr
        \Im&\\Im\cr
        \aleph&\\aleph\cr
        \wp&\\wp\cr
        \infty&\\infty\cr
    }
    \column{
        \emptyset&\\emptyset\cr
        \exists&\\exists\cr
        \forall&\\forall\cr
	\triangle&\\triangle\cr
        \angle&\\angle\cr
        \lnot&\\lnot (or \\neg)\cr
        \nabla&\\nabla\cr
    }
    \column{
        \partial&\\partial\cr
        \prime&\\prime\cr
        \smallint&\\smallint\cr
        \top&\\top\cr
        \bot&\\bot\cr
        \surd&\\surd\cr
	\hbar&\\hbar\cr
    }
    \hfill
}

\filbreak
\sect{(j) Miscellaneous nonmath symbols (math mode required):}
\hbox to \hsize{
    \hfill
    \column{
        \spadesuit&\\spadesuit\cr
        \heartsuit&\\heartsuit\cr
        \diamondsuit&\\diamondsuit\cr
        \clubsuit&\\clubsuit\cr
    }
    \column{
	\sharp&\\sharp\cr
	\flat&\\flat\cr
	\natural&\\natural\cr
    }
    \hfill
}
\filbreak
\sect{(k) Miscellaneous nonmath symbols (math mode {\bf not} required):}
\hbox to \hsize{
    \hfill
    \column{
        \$&\\\char `\$\cr
        \%&\\\char `\%\cr
        \copyright&\\copyright\cr
    }
    \column{
        \#&\\\char `\#\cr
        \S&\\S\cr
        \P&\\P\cr
    }
    \column{
        \&&\\\char `\&\cr
        \ddag&\\ddag\cr
        \dag&\\dag\cr
    }
    \hfill
}
}

%\vfil\eject
%\centerline{\twelveb Appendix B}
%\vskip 4pt
%\centerline{\twelveb Font Samples}
%\vskip 8pt
\Appendix{B}{Font Samples}
Plain \TeX\ predefines control sequences for the\ math\ italic, bold
and roman styles of the Computer Modern family in five-point,
seven-point and ten-point (the default).  The predefined fonts
are as follows:
$$\halign{#\quad&#\hfil\cr
|\tenrm|&Normal ten-point roman\cr
|\teni|&\teni ten-point\ math\ italic\cr
|\tenit|&\tenit ten-point text italic\cr
|\tenbf|&\tenbf ten-point bold extended\cr
|\tensl|&\tensl ten-point slanted roman\cr
|\tentt|&\tentt ten-point typewriter\cr
\noalign{\smallskip}
|\sevenrm|&\sevenrm seven-point roman\cr
|\seveni|&\seveni seven-point\ math\ italic\cr
|\sevenbf|&\sevenbf seven-point bold extended\cr
\noalign{\smallskip}
|\fiverm|&\fiverm five-point roman\cr
|\fivei|&\fivei five-point\ math\ italic\cr
|\fivebf|&\fivebf five-point bold extended\cr}$$

Note that the Math Italic fonts are intended to
be used in Mathematics Mode only, and hence
behave somewhat strangely if used for normal text

For fonts other than the predefined ones, the |\font| operation must be used
to associate a keyword with the font information file.
Here are some of the fonts distributed with the \Unix\
version of \TeX:
\vskip 10pt
\def\Fsample#1:#2.{\font\nonce=#1\line{\rlap{\tt#1}\hskip 1in\nonce#2\hfil}\vskip 3pt}
\Fsample cmssq8:8-point sans-serif.
\Fsample cmss10:10-point sans-serif.
%\Fsample cmssmc10:Emboldened 10-point sans-serif.
%\Fsample cminch:BIG.
\vskip 5pt
\Fsample cmssqi8:8-point slanted sans-serif.
%\Fsample cmssi10:10-point slanted sans-serif.
\vskip 5pt
\Fsample cmssbx10:10-point bold sans-serif.
\vskip 5pt
\Fsample cmr6:6-point roman.
\Fsample cmr8:8-point roman.
\Fsample cmr9:9-point roman.
\vskip 5pt
\Fsample cmsl8:8-point slanted.
\Fsample cmsl9:9-point slanted.
%\Fsample cmbxsl10:10-point bold slanted.
\vskip 5pt
\Fsample cmbx6:6-point bold.
\Fsample cmbx8:8-point bold.
\Fsample cmbx9:9-point bold.
\vskip 5pt
\Fsample cmmi6:6-point\ math\ italic.
\Fsample cmmi8:8-point\ math\ italic.
\Fsample cmmi9:9-point\ math\ italic.
\Fsample cmti7:7-point text italic.
\Fsample cmti8:8-point text italic.
\Fsample cmti9:9-point text italic.
%\Fsample cmbi10:10-point\ bold\ math\ italic.
\vskip 5pt
%\Fsample cmtt8:8-point typewriter.
\Fsample cmtt9:9-point typewriter.
\Fsample cmsltt10:10-point slanted typewriter.
%\Fsample cmitt10:10-point italic typewriter.
\vskip 5pt
\Fsample cmcsc10:10-point Small Capitals.
\vskip 5pt
\Fsample cmu10:10-point unslanted italics.
\Fsample cmdunh10:Tall thin letters for no known purpose.

\vfil\eject
{\parindent=0pt\parskip=10pt\pretolerance=400
\frenchspacing
\centerline{\twelveb Bibliography}
\vskip 8pt

\def\Hpar{\par\hangindent .75in\hangafter=1}
\Hpar
{\csc American Mathematical Society} 
``Differences between \TeX82 and \TeX80.'' In {\sl \TeX\ and Metafont:
Errata and Changes}. Published for the \TeX\ Users Group by the American
Mathematical Society, Providence, RI. September 1983

\Hpar
{\csc Furuta, R., Scofield, J. {\rm and} Shaw, A.} ``Document Formatting
Systems: Survey, Concepts, and Issues.'' In {\sl Computing Surveys\/},
{\bf 14}, 3 (Sept.~1982), 417-472.

\Hpar
{\csc Kernighan, B.~W.~{\rm and} Cherry, L.~L.} ``Typesetting
Mathematics --- User's Guide (Second Edition).'' In {\sl Unix Programmer's
Manual\/}, Volume 2A.  Western Electric Co., Greensboro NC 1976

\Hpar
{\csc Knuth, D.~E.} ``\TeX, a system for technical text.'' In {\sl \TeX\ and
Metafont: New Directions in Typesetting\/}, part 2.  Digital Press
and the American Mathematical Society, Bedford, MA, and
Providence, RI.  1979

\Hpar
{\csc Knuth, D.~E.}
{\sl The \TeX book\/}.  Addison-Wesley Publishing and the
American Mathematical Society, Reading, MA, and Providence, RI.
1984

\Hpar
{\csc Lamport, L.}
{\sl The
L\kern-.2em\raise.3ex\hbox{\csc a}\kern-.09em\TeX\
Document Preparation System}.  Forthcoming in 1985.

\Hpar
{\csc Lesk, M.~E. {\rm and} Kernighan, B.~W.} ``Tbl --- A Program
to Format Tables.'' In {\sl UNIX Programmer's
Manual\/}, Volume 2A.  Western Electric Co., Greensboro NC 1976

\Hpar
{\csc Ossana, J.~F.} ``NROFF/TROFF User's Manual.'' In {\sl UNIX Programmer's
Manual\/}, Volume 2A.  Western Electric Co., Greensboro NC 1974

\Hpar
{\csc Reid, B.~K.} {\sl Scribe Introductory User's Manual\/}.  Unilogic
Inc., Pittsburgh PA, 1980

\Hpar
{\csc Urban, M.}{\sl An Introduction to
L\kern-.2em\raise.3ex\hbox{\csc a}\kern-.09em\TeX}.  TRW Inc., 1985

}
\PrintTOC
\bye