Typesetting Mathematics - User's Guide USD:24-1
Typesetting Mathematics - User's Guide
(Second Edition)
Brian W. Kernighan and Lorinda L. Cherry
AT&T Bell Laboratories
Murray Hill, New Jersey 07974
ABSTRACT
This is the user's guide for a system for typesetting
mathematics, using the phototypesetters on the UNIX- operating
system.
Mathematical expressions are described in a
language designed to be easy to use by people who know
neither mathematics nor typesetting. Enough of the
language to set in-line expressions like
lim (tan x)sin 2x = 1 or display equations like
x->i̅i̅/2
| |
G(z) = eln G(z) = exp| _k__k_| Sk|k/k
| ≥̅ k |__2_z_4_+...| |
||≥1 | S2k≥1 |... |
| | __z__+...|| _2__2_+ | km |
=| | S1 ||1+ 2 22.2! k2 ___m___|zm
|1+|1z+ 2! || k1 ___2___ ... km |
=|≥̅ | ___1___ k2 m km!|
can be learned0in an hou̅r or so. k1 2 k2! |
| k1,k2,...,km≥0 1 k1!
The language1interfaceskdirectly with the photo-
typesetting language TROFF, so mathematical expressions
can be embedded in the running text of a manuscript,
and the entire document produced in one process. This
user's guide is an example of its output.
The same language may be used with the UNIX for-
matter NROFF to set mathematical expressions on DASI
and GSI terminals and Model 37 teletypes.
-------------------------
- UNIX is a registered trademark of AT&T Bell Labora-
tories in the USA and other countries.
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1. Introduction
EQN is a program for typesetting mathematics on the Graphics
Systems phototypesetters on the UNIX operating system. The EQN
language was designed to be easy to use by people who know nei-
ther mathematics nor typesetting. Thus EQN knows relatively lit-
tle about mathematics. In particular, mathematical symbols like
+, -, x, parentheses, and so on have no special meanings. EQN is
quite happy to set garbage (but it will look good).
EQN works as a preprocessor for the typesetter formatter,
TROFF[1], so the normal mode of operation is to prepare a docu-
ment with both mathematics and ordinary text interspersed, and
let EQN set the mathematics while TROFF does the body of the
text.
On UNIX, EQN will also produce mathematics on DASI and GSI
terminals and on Model 37 teletypes. The input is identical, but
you have to use the programs NEQN and NROFF instead of EQN and
TROFF. Of course, some things won't look as good because termi-
nals don't provide the variety of characters, sizes and fonts
that a typesetter does, but the output is usually adequate for
proofreading.
To use EQN on UNIX,
eqn files | troff
2. Displayed Equations
To tell EQN where a mathematical expression begins and ends,
we mark it with lines beginning .EQ and .EN. Thus if you type the
lines
.EQ
x=y+z
.EN
your output will look like
x=y+z
The .EQ and .EN are copied through untouched; they are not other-
wise processed by EQN. This means that you have to take care of
things like centering, numbering, and so on yourself. The most
common way is to use the TROFF and NROFF macro package package
`-ms' developed by M. E. Lesk[3], which allows you to center,
indent, left-justify and number equations.
With the `-ms' package, equations are centered by default.
To left-justify an equation, use .EQ L instead of .EQ. To indent
it, use .EQ I. Any of these can be followed by an arbitrary
`equation number' which will be placed at the right margin. For
example, the input
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.EQ I (3.1a)
x = f(y/2) + y/2
.EN
produces the output
x=f(y/2)+y/2 (3.1a)
The2e canabeoenteredtwithoutt.EQoands.EN.nWeiwilletalksabout
itkin s̅e̅ction 19.
3. Input spaces
Spaces and newlines within an expression are thrown away by
EQN. (Normal text is left absolutely alone.) Thus between .EQ and
.EN,
x=y+z
and
x = y + z
and
x = y
+ z
and so on all produce the same output
x=y+z
You should use spaces and newlines freely to make your input
equations readable and easy to edit. In particular, very long
lines are a bad idea, since they are often hard to fix if you
make a mistake.
4. Output spaces
To force extra spaces into the output, use a tilde ``~'' for
each space you want:
x~=~y~+~z
gives
x = y + z
You can also use a circumflex ``^'', which gives a space half the
width of a tilde. It is mainly useful for fine-tuning. Tabs may
also be used to position pieces of an expression, but the tab
stops must be set by TROFF commands.
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5. Symbols, Special Names, Greek
EQN knows some mathematical symbols, some mathematical
names, and the Greek alphabet. For example,
x=2 pi int sin ( omega t)dt
produces
x=2i̅i̅sin(wt)dt
Here the spaces in the input are necessary to tell EQN that int,
pi, sin and omega are separate entities that should get special
treatment. The sin, digit 2, and parentheses are set in roman
type instead of italic; pi and omega are made Greek; and int
becomes the integral sign.
When in doubt, leave spaces around separate parts of the
input. A very common error is to type f(pi) without leaving
spaces on both sides of the pi. As a result, EQN does not recog-
nize pi as a special word, and it appears as f(pi) instead of
f(i̅i̅).
A complete list of EQN names appears in section 23.
Knowledgeable users can also use TROFF four-character names for
anything EQN doesn't know about, like \(bs for the Bell System
sign .
6. Spaces, Again
The only way EQN can deduce that some sequence of letters
might be special is if that sequence is separated from the
letters on either side of it. This can be done by surrounding a
special word by ordinary spaces (or tabs or newlines), as we did
in the previous section.
You can also make special words stand out by surrounding
them with tildes or circumflexes:
x~=~2~pi~int~sin~(~omega~t~)~dt
is much the same as the last example, except that the tildes not
only separate the magic words like sin, omega, and so on, but
also add extra spaces, one space per tilde:
x = 2 i̅i̅ sin ( w t ) dt
Special words can also be separated by braces { } and double
quotes "...", which have special meanings that we will see soon.
7. Subscripts and Superscripts
Subscripts and superscripts are obtained with the words sub
and sup.
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x sup 2 + y sub k
gives
x2+yk
EQN takes care of all the size changes and vertical motions
needed to make the output look right. The words sub and sup must
be surrounded by spaces; x sub2 will give you xsub2 instead of
x2. Furthermore, don't forget to leave a space (or a tilde, etc.)
to mark the end of a subscript or superscript. A common error is
to say something like
y = (x sup 2)+1
which causes
y=(x2)+1
instead of the intended
y=(x2)+1
Subscripted subscripts and superscripted superscripts also
work:
x sub i sub 1
is
xi1
A subscript and superscript on the same thing are printed one
above the other if the subscript comes first:
x sub i sup 2
is
2
xi
Other than this special cayz, sub and sup group to the
right, so x sup y sub z means x , not xyz.
8. Braces for Grouping
Normally, the end of a subscript or superscript is marked
simply by a blank (or tab or tilde, etc.) What if the subscript
or superscript is something that has to be typed with blanks in
it? In that case, you can use the braces { and } to mark the
beginning and end of the subscript or superscript:
e sup {i omega t}
is
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eiwt
Rule: Braces can always be used to force EQN to treat something
as a unit, or just to make your intent perfectly clear. Thus:
x sub {i sub 1} sup 2
is
2
with braces, but xi1
x sub i sub 1 sup 2
is
x 2
which is rather different. i1
Braces can occur within braces if necessary:
e sup {i pi sup {rho +1}}
is
eii̅i̅p+1
The general rule is that anywhere you could use some single thing
like x, you can use an arbitrarily complicated thing if you
enclose it in braces. EQN will look after all the details of
positioning it and making it the right size.
In all cases, make sure you have the right number of braces.
Leaving one out or adding an extra will cause EQN to complain
bitterly.
Occasionally you will have to print braces. To do this,
enclose them in double quotes, like "{". Quoting is discussed in
more detail in section 14.
9. Fractions
To make a fraction, use the word over:
a+b over 2c =1
gives
_±_=1
The line is made the right length and positioned automatically.
Braces can be used to make clear what goes over what:
{alpha + beta} over {sin (x)}
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is
__(_±|__
What happens when there is bothnan)over and a sup in the same
expression? In such an apparently ambiguous case, EQN does the
sup before the over, so
-b sup 2 ove_2_pi
i̅i̅ The rules which decide which operation is
don_e_2_firstein cases like this are summarized in section 23. When
in d̅o̅ubt, however, use braces to make clear what goes with what.
10. Square Roots
To draw a square root, use sqrt:
sqrt a+b + 1 over sqrt {ax sup 2 +bx+c}
is
___ __________
\|a+b+ ________
Warning - square roots of tall\quantities look lousy, because a
root-sign big enough to cover the quantity is too dark and heavy:
sqrt {a sup 2 over b sub 2}
is
__
|_2_
Big square roots are generally better written as something to the
power 1/2: \|
(a2/b2)1/2
which is
(a sup 2 /b sub 2 ) sup half
11. Summation, Integral, Etc.
Summations, integrals, and similar constructions are easy:
sum from i=0 to {i= inf} x sup i
produces
i=oo
≥̅ xi
Notice that we used braces toiindicate where the upper part i=oo
begins and ends. No braces were necessary for the lower part i=0,
because it contained no blanks. The braces will never hurt, and
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if the from and to parts contain any blanks, you must use braces
around them.
The from and to parts are both optional, but if both are
used, they have to occur in that order.
Other useful characters can replace the sum in our example:
int prod union inter
become, respectively,
TT (̅)̅ _)_
Since the thing before the from can be anything, even something
in braces, from-to can often be used in unexpected ways:
lim from {n -> inf} x sub n =0
is
lim xn=0
n->oo
12. Size and Font Changes
By default, equations are set in 10-point type (the same
size as this guide), with standard mathematical conventions to
determine what characters are in roman and what in italic.
Although EQN makes a valiant attempt to use esthetically pleasing
sizes and fonts, it is not perfect. To change sizes and fonts,
use size n and roman, italic, bold and fat. Like sub and sup,
size and font changes affect only the thing that follows them,
and revert to the normal situation at the end of it. Thus
bold x y
is
xy
and
size 14 bold x = y +
size 14 {alpha + beta}
gives
x=y+(+|
As always, you can use braces if you want to affect something
more complicated than a single letter. For example, you can
change the size of an entire equation by
size 12 { ... }
Legal sizes which may follow size are 6, 7, 8, 9, 10, 11,
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12, 14, 16, 18, 20, 22, 24, 28, 36. You can also change the size
by a given amount; for example, you can say size +2 to make the
size two points bigger, or size -3 to make it three points
smaller. This has the advantage that you don't have to know what
the current size is.
If you are using fonts other than roman, italic and bold,
you can say font X where X is a one character TROFF name or
number for the font. Since EQN is tuned for roman, italic and
bold, other fonts may not give quite as good an appearance.
The fat operation takes the current font and widens it by
overstriking: fat grad is \̅̅/̅̅ and fat {x sub i} is xi.
If an entire document is to be in a non-standard size or
font, it is a severe nuisance to have to write out a size and
font change for each equation. Accordingly, you can set a ``glo-
bal'' size or font which thereafter affects all equations. At the
beginning of any equation, you might say, for instance,
.EQ
gsize 16
gfont R
...
.EN
to set the size to 16 and the font to roman thereafter. In place
of R, you can use any of the TROFF font names. The size after
gsize can be a relative change with + or -.
Generally, gsize and gfont will appear at the beginning of a
document but they can also appear thoughout a document: the glo-
bal font and size can be changed as often as needed. For example,
in a footnote= you will typically want the size of equations to
match the size of the footnote text, which is two
points smaller than the main text. Don't forget to
reset the global size at the end of the footnote.
13. Diacritical Marks
To get funny marks on top of letters, there are several
words:
-------------------------
=Like this one, in which we have a few random expres-
sions like xi and i̅i̅2. The sizes for these were set by
the command gsize -2.
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.
x dot ..
x dotdot x
x hat ^
x tilde -̅
x vec -
x dyad _x
x bar x
x under _x
The diacritical mark is placed at the right height. The bar and
u_n_d_e_r_ are made the right length for the entire construct, as in
x+y+z; other marks are centered.
14. Quoted Text
Any input entirely within quotes ("...") is not subject to
any of the font changes and spacing adjustments normally done by
the equation setter. This provides a way to do your own spacing
and adjusting if needed:
italic "sin(x)" + sin (x)
is
sin(x)+sin(x)
Quotes are also used to get braces and other EQN keywords
printed:
"{ size alpha }"
is
{ size alpha }
and
roman "{ size alpha }"
is
{ size alpha }
The construction "" is often used as a place-holder when
grammatically EQN needs something, but you don't actually want
anything in your output. For example, to make 2He, you can't just
type sup 2 roman He because a sup has to be a superscript on
something. Thus you must say
"" sup 2 roman He
To get a literal quote use ``\"''. TROFF characters like
\(bs can appear unquoted, but more complicated things like
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horizontal and vertical motions with \h and \v should always be
quoted. (If you've never heard of \h and \v, ignore this sec-
tion.)
15. Lining Up Equations
Sometimes it's necessary to line up a series of equations at
some horizontal position, often at an equals sign. This is done
with two operations called mark and lineup.
The word mark may appear once at any place in an equation.
It remembers the horizontal position where it appeared. Succes-
sive equations can contain one occurrence of the word lineup. The
place where lineup appears is made to line up with the place
marked by the previous mark if at all possible. Thus, for exam-
ple, you can say
.EQ I
x+y mark = z
.EN
.EQ I
x lineup = 1
.EN
to produce
x+y=z
x=1
For reasons too complicated to talk about, when you use EQN and
`-ms', use either .EQ I or .EQ L. mark and lineup don't work with
centered equations. Also bear in mind that mark doesn't look
ahead;
x mark =1
...
x+y lineup =z
isn't going to work, because there isn't room for the x+y part
after the mark remembers where the x is.
16. Big Brackets, Etc.
To get big brackets [ ], braces { }, parentheses ( ), and
bars |~| around things, use the left and right commands:
left { a over b + 1 right }
~=~ left ( c over d right )
+ left [ e right ]
is |
|_+1| = |_|
|b | |d|+|
| |e|
|
The resulting brackets are made big enough to cover whatever they
enclose. Other characters can be used besides these, but the are
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not likely to look very good. One exception is the floor and
ceiling characters:
left floor x over y right floor
<= left ceiling a over b right ceiling
produces
|_|
|y|≤|_|
|b|
Several warnings about brackets are in order. First, braces
are typically bigger than brackets and parentheses, because they
are made up of three, five, seven, etc., pieces, while brackets
can be made up of two, three, etc. Second, big left and right
parentheses often look poor, because the character set is poorly
designed.
The right part may be omitted: a ``left something'' need not
have a corresponding ``right something''. If the right part is
omitted, put braces around the thing you want the left bracket to
encompass. Otherwise, the resulting brackets may be too large.
If you want to omit the left part, things are more compli-
cated, because technically you can't have a right without a
corresponding left. Instead you have to say
left "" ..... right )
for example. The left "" means a ``left nothing''. This satisfies
the rules without hurting your output.
17. Piles
There is a general facility for making vertical piles of
things; it comes in several flavors. For example:
A ~=~ left [
pile { a above b above c }
~~ pile { x above y above z }
right ]
will make
|a x|
A = |b y|
The elements of the pile (there|canzbe as many as you want) are
centered one above another, at the right height for most pur-
poses. The keyword above is used to separate the pieces; braces
are used around the entire list. The elements of a pile can be as
complicated as needed, even containing more piles.
Three other forms of pile exist: lpile makes a pile with the
elements left-justified; rpile makes a right-justified pile; and
cpile makes a centered pile, just like pile. The vertical spacing
between the pieces is somewhat larger for l-, r- and cpiles than
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it is for ordinary piles.
roman sign (x)~=~
left {
lpile {1 above 0 above -1}
~~ lpile
{if~x>0 above if~x=0 above if~x<0}
makes
|
|1
sign(x) = |0 if x>0
|-1 if x=0
| if x<0
Notice the left brace without a matching right one.
18. Matrices
It is also possible to make matrices. For example, to make a
neat array like
xi x2
yi y2
you have to type
matrix {
ccol { x sub i above y sub i }
ccol { x sup 2 above y sup 2 }
}
This produces a matrix with two centered columns. The elements of
the columns are then listed just as for a pile, each element
separated by the word above. You can also use lcol or rcol to
left or right adjust columns. Each column can be separately
adjusted, and there can be as many columns as you like.
The reason for using a matrix instead of two adjacent piles,
by the way, is that if the elements of the piles don't all have
the same height, they won't line up properly. A matrix forces
them to line up, because it looks at the entire structure before
deciding what spacing to use.
A word of warning about matrices - each column must have the
same number of elements in it. The world will end if you get this
wrong.
19. Shorthand for In-line Equations
In a mathematical document, it is necessary to follow
mathematical conventions not just in display equations, but also
in the body of the text, for example by making variable names
like x italic. Although this could be done by surrounding the
appropriate parts with .EQ and .EN, the continual repetition of
.EQ and .EN is a nuisance. Furthermore, with `-ms', .EQ and .EN
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imply a displayed equation.
EQN provides a shorthand for short in-line expressions. You
can define two characters to mark the left and right ends of an
in-line equation, and then type expressions right in the middle
of text lines. To set both the left and right characters to dol-
lar signs, for example, add to the beginning of your document the
three lines
.EQ
delim $$
.EN
Having done this, you can then say things like
Let $alpha sub i$ be the primary variable, and let $beta$
be zero. Then we can show that $x sub 1$ is $>=0$.
This works as you might expect - spaces, newlines, and so on are
significant in the text, but not in the equation part itself.
Multiple equations can occur in a single input line.
Enough room is left before and after n line that contains
in-line expressions that something like ≥̅ xi does not interfere
with the lines surrounding it. i=1
To turn off the delimiters,
.EQ
delim off
.EN
Warning: don't use braces, tildes, circumflexes, or double quotes
as delimiters - chaos will result.
20. Definitions
EQN provides a facility so you can give a frequently-used
string of characters a name, and thereafter just type the name
instead of the whole string. For example, if the sequence
x sub i sub 1 + y sub i sub 1
appears repeatedly throughout a paper, you can save re-typing it
each time by defining it like this:
define xy 'x sub i sub 1 + y sub i sub 1'
This makes xy a shorthand for whatever characters occur between
the single quotes in the definition. You can use any character
instead of quote to mark the ends of the definition, so long as
it doesn't appear inside the definition.
Now you can use xy like this:
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.EQ
f(x) = xy ...
.EN
and so on. Each occurrence of xy will expand into what it was
defined as. Be careful to leave spaces or their equivalent around
the name when you actually use it, so EQN will be able to iden-
tify it as special.
There are several things to watch out for. First, although
definitions can use previous definitions, as in
.EQ
define xi ' x sub i '
define xi1 ' xi sub 1 '
.EN
don't define something in terms of itself' A favorite error is to
say
define X ' roman X '
This is a guaranteed disaster, since X is now defined in terms of
itself. If you say
define X ' roman "X" '
however, the quotes protect the second X, and everything works
fine.
EQN keywords can be redefined. You can make / mean over by
saying
define / ' over '
or redefine over as / with
define over ' / '
If you need different things to print on a terminal and on
the typesetter, it is sometimes worth defining a symbol dif-
ferently in NEQN and EQN. This can be done with ndefine and tde-
fine. A definition made with ndefine only takes effect if you are
running NEQN; if you use tdefine, the definition only applies for
EQN. Names defined with plain define apply to both EQN and NEQN.
21. Local Motions
Although EQN tries to get most things at the right place on
the paper, it isn't perfect, and occasionally you will need to
tune the output to make it just right. Small extra horizontal
spaces can be obtained with tilde and circumflex. You can also
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say back n and fwd n to move small amounts horizontally. n is how
far to move in 1/100's of an em (an em is about the width of the
letter `m'.) Thus back 50 moves back about half the width of an
m. Similarly you can move things up or down with up n and down n.
As with sub or sup, the local motions affect the next thing in
the input, and this can be something arbitrarily complicated if
it is enclosed in braces.
22. A Large Example
Here is the complete source for the three display equations
in the abstract of this guide.
.EQ I
G(z)~mark =~ e sup { ln ~ G(z) }
~=~ exp left (
sum from k>=1 {S sub k z sup k} over k right )
~=~ prod from k>=1 e sup {S sub k z sup k /k}
.EN
.EQ I
lineup = left ( 1 + S sub 1 z +
{ S sub 1 sup 2 z sup 2 } over 2! + ... right )
left ( 1+ { S sub 2 z sup 2 } over 2
+ { S sub 2 sup 2 z sup 4 } over { 2 sup 2 cdot 2! }
+ ... right ) ...
.EN
.EQ I
lineup = sum from m>=0 left (
sum from
pile { k sub 1 ,k sub 2 ,..., k sub m >=0
above
k sub 1 +2k sub 2 + ... +mk sub m =m}
{ S sub 1 sup {k sub 1} } over {1 sup k sub 1 k sub 1 ! } ~
{ S sub 2 sup {k sub 2} } over {2 sup k sub 2 k sub 2 ! } ~
...
{ S sub m sup {k sub m} } over {m sup k sub m k sub m ! }
right ) z sup m
.EN
23. Keywords, Precedences, Etc.
If you don't use braces, EQN will do operations in the order
shown in this list.
dyad vec under bar tilde hat dot dotdot
fwd back down up
fat roman italic bold size
sub sup sqrt over
from to
These operations group to the left:
over sqrt left right
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All others group to the right.
Digits, parentheses, brackets, punctuation marks, and these
mathematical words are converted to Roman font when encountered:
sin cos tan sinh cosh tanh arc
max min lim log ln exp
Re Im and if for det
These character sequences are recognized and translated as shown.
>= ≥
<= ≤
== _=
!= /
+- ±
-> ->
<- <-
<< <<
>> >>
inf oo
partial `
half 1/2
prime '
approx ~
nothing
cdot .
times x
del \̅/̅
grad \̅/̅
... ...
,..., ,...,
sum ≥̅
int
prod TT
union (̅)̅
inter _)_
To obtain Greek letters, simply spell them out in whatever
case you want:
DELTA _\_ iota i
GAMMA I̅ kappa k
LAMBDA /\ lambda \
OMEGA _ mu u
PHI | nu v
PI TT omega w
PSI | omicrono
SIGMA ≥̅ phi |
THETA - pi i̅i̅
UPSILON Y psi|
XI _ rho p
alpha ( sigma o̅
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beta | tau i̅ chi x theta -
delta ` upsilonu epsilon - xi
eta n zeta gamma /
These are all the words known to EQN (except for characters
with names), together with the section where they are discussed.
above 17, 18 lpile 17
back 21 mark 15
bar 13 matrix 18
bold 12 ndefine20
ccol 18 over 9
col 18 pile 17
cpile 17 rcol 18
define 20 right 16
delim 19 roman 12
dot 13 rpile 17
dotdot 13 size 12
down 21 sqrt 10
dyad 13 sub 7
fat 12 sup 7
font 12 tdefine20
from 11 tilde 13
fwd 21 to 11
gfont 12 under 13
gsize 12 up 21
hat 13 vec 13
italic 12 ~, ^ 4, 6
lcol 18 { } 8
left 16 "..." 8, 14
lineup 15
24. Troubleshooting
If you make a mistake in an equation, like leaving out a
brace (very common) or having one too many (very common) or hav-
ing a sup with nothing before it (common), EQN will tell you with
the message
syntax error between lines x and y, file z
where x and y are approximately the lines between which the trou-
ble occurred, and z is the name of the file in question. The line
numbers are approximate - look nearby as well. There are also
self-explanatory messages that arise if you leave out a quote or
try to run EQN on a non-existent file.
If you want to check a document before actually printing it
(on UNIX only),
eqn files >/dev/null
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will throw away the output but print the messages.
If you use something like dollar signs as delimiters, it is
easy to leave one out. This causes very strange troubles. The
program checkeq checks for misplaced or missing dollar signs and
similar troubles.
In-line equations can only be so big because of an internal
buffer in TROFF. If you get a message ``word overflow'', you have
exceeded this limit. If you print the equation as a displayed
equation this message will usually go away. The message ``line
overflow'' indicates you have exceeded an even bigger buffer. The
only cure for this is to break the equation into two separate
ones.
On a related topic, EQN does not break equations by itself -
you must split long equations up across multiple lines by your-
self, marking each by a separate .EQ ... .EN sequence. EQN does
warn about equations that are too long to fit on one line.
25. Use on UNIX
To print a document that contains mathematics on the UNIX
typesetter,
eqn files | troff
If there are any TROFF options, they go after the TROFF part of
the command. For example,
eqn files | troff -ms
A compatible version of EQN can be used on devices like
teletypes and DASI and GSI terminals which have half-line forward
and reverse capabilities. To print equations on a Model 37 tele-
type, for example, use
neqn files | nroff
The language for equations recognized by NEQN is identical to
that of EQN, although of course the output is more restricted.
To use a GSI or DASI terminal as the output device,
neqn files | nroff -Tx
where x is the terminal type you are using, such as 300 or 300S.
EQN and NEQN can be used with the TBL program[2] for setting
tables that contain mathematics. Use TBL before [N]EQN, like
this:
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tbl files | eqn | troff
tbl files | neqn | nroff
26. Acknowledgments
We are deeply indebted to J. F. Ossanna, the author of
TROFF, for his willingness to extend TROFF to make our task
easier, and for his continuous assistance during the development
and evolution of EQN. We are also grateful to A. V. Aho for
advice on language design, to S. C. Johnson for assistance with
the YACC compiler-compiler, and to all the EQN users who have
made helpful suggestions and criticisms.
References
[1] J. F. Ossanna, ``NROFF/TROFF User's Manual'', Bell Labora-
tories Computing Science Technical Report #54, 1976.
[2] M. E. Lesk, ``Typing Documents on UNIX'', Bell Laboratories,
1976.
[3] M. E. Lesk, ``TBL - A Program for Setting Tables'', Bell
Laboratories Computing Science Technical Report #49, 1976.
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