.EQ
delim $$
.EN
.th EQN I 2/22/74
.sh NAME
eqn  \*-  typeset mathematics
.sh SYNOPSIS
.bd eqn
[ file ] ...
.sh DESCRIPTION
.it Eqn
is a
troff (I)
preprocessor
for typesetting mathematics
on the Graphics Systems phototypesetter.
Usage is almost always
.s3
	eqn file ... | troff
.s3
If no files are specified, 
.it eqn
reads from the standard input.
A line beginning with ``.EQ'' marks the start of an equation;
the end of an equation
is marked by a line beginning with ``.EN''.
Neither of these lines is altered or defined by
.it eqn,
so you can define them yourself to get
centering, numbering, etc.
All other lines are treated as comments, and passed through
untouched.
.s3
Spaces, tabs, newlines, braces, double quotes,
tilde and circumflex are the only delimiters.
Braces ``{}'' are used for grouping.
Use tildes ``~'' to get extra spaces in an equation.
.s3
.vs 13p
Subscripts and superscripts are produced with the keywords
.bd sub
and
.bd sup.
Thus
.it "x sub i" 
makes
$x sub i$, 
.it "a sub i sup 2"
produces
$a sub i sup 2$,
and
.it "e sup {x sup 2 + y sup 2}"
gives
$e sup {x sup 2 + y sup 2}$.
Fractions are made with
.bd over.
.it "a over b"
is $a over b$ and
.it "1 over sqrt {ax sup 2 +bx+c}"
is
$1 over sqrt {ax sup 2 +bx+c}$ .
.bd sqrt
makes square roots.
.s3
The keywords
.bd from
and
.bd to
introduce lower and upper
limits on arbitrary things:
$lim from {n-> inf} sum from 0 to n x sub i$
is made with
.it "lim from {n-> inf} sum from 0 to n x sub i."
Left and right brackets, braces, etc., of the right height are made with
.bd left
and
.bd right:
.it "left [ x sup 2 + y sup 2 over alpha right ] ~=~1"
produces
$left [ x sup 2 + y sup 2 over alpha right ] ~=~1$.
The
.bd right
clause is optional.
.s3
Vertical piles of things are made with 
.bd "pile, lpile, cpile,"
and
.bd rpile:
.it "pile {a above b above c}"
produces
$pile {a above b above c}$.
There can be an arbitrary number of elements in a pile.
.bd lpile
left-justifies,
.bd pile
and
.bd cpile
center, with different vertical spacing,
and 
.bd rpile
right justifies.
.s3
.vs 12p
Diacritical marks are made with
.bd dot,
.bd dotdot,
.bd hat,
.bd bar:
.it "x dot = f(t) bar"
is
$x dot = f(t) bar$.
Default sizes and fonts can be changed with
.bd "size n"
and various of
.bd roman,
.bd italic,
and
.bd bold.
.s3
Keywords like 
.it sum
.EQ
( sum )
.EN
.it int
.EQ
( int )
.EN
.it inf
.EQ
( inf )
.EN
and shorthands like
>=
.EQ
(>=)
.EN
\*->
.EQ
(->),
.EN
!=
.EQ
( != ),
.EN
are recognized.
Spell out Greek letters in the desired case, as in
.it "alpha, GAMMA."
Mathematical words like sin, cos, log are made Roman automatically.
Troff (I)
four-character escapes like \\(bs (\(bs)
can be used anywhere.
Strings enclosed in double quotes "..."
are passed through untouched.
.sh "SEE ALSO"
A System for Typesetting Mathematics
(Computer Science Technical Report #17, Bell Laboratories, 1974.)
.br
TROFF Users' Manual (internal memorandum)
.br
TROFF Made Trivial (internal memorandum)
.br
troff (I), neqn (I)
.sh BUGS
Undoubtedly.
Watch out for small or large point sizes \*-
it's tuned too well for size 10.
Be cautious if inserting horizontal or vertical motions,
and of backslashes in general.