eqn(1) — Linux manual page

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eqn(1)                   General Commands Manual                  eqn(1)

Name         top

       eqn - format mathematics (equations) for groff or MathML

Synopsis         top

       eqn [-CNrR] [-d xy] [-f global-italic-font] [-m minimum-type-
           size] [-M eqnrc-directory] [-p super/subscript-size-
           reduction] [-s global-type-size] [-T device] [file ...]

       eqn --help

       eqn -v

       eqn --version

Description         top

       The GNU implementation of eqn is part of the groff(7) document
       formatting system.  eqn is a troff(1) preprocessor that
       translates expressions in its own language, embedded in roff(7)
       input files, into mathematical notation typeset by troff(1).  It
       copies each file's contents to the standard output stream,
       translating each equation between lines starting with .EQ and
       .EN, or within a pair of user-specified delimiters.  Normally,
       eqn is not executed directly by the user, but invoked by
       specifying the -e option to groff(1).  While GNU eqn's input
       syntax is highly compatible with AT&T eqn, the output eqn
       produces cannot be processed by AT&T troff; GNU troff (or a troff
       implementing relevant GNU extensions) must be used.  If no file
       operands are present, or if file is “-”, eqn reads the standard
       input stream.

       Unless the -R option is used, eqn searches for the file eqnrc in
       the directories given with the -M option first, then in /usr/
       local/share/groff/site-tmac, and finally in the standard macro
       directory /usr/local/share/groff/1.23.0/tmac.  If it exists and
       is readable, eqn processes it before any input files.

       This man page primarily discusses the differences between GNU eqn
       and AT&T eqn.  Most of the new features of the GNU eqn input
       language are based on TeX.  There are some references to the
       differences between TeX and GNU eqn below; these may safely be
       ignored if you do not know TeX.  Four points are worth note.

       •  GNU eqn emits Presentation MathML output when invoked with the
          “-T MathML” option.

       •  GNU eqn does not support terminal devices well, though it may
          suffice for simple inputs.

       •  GNU eqn sets the input token “...” as an ellipsis on the text
          baseline, not the three centered dots of AT&T eqn.  Set an
          ellipsis on the math axis with the GNU extension macro cdots.

       •  GNU eqn's delim command does not treat an “on” argument as a
          pair of equation delimiters.

   Anatomy of an equation
       eqn input consists of tokens.  Consider a form of Newton's second
       law of motion.  The input

              .EQ
              F =
              m a
              .EN

       becomes F=ma.  Each of F, =, m, and a is a token.  Spaces and
       newlines are interchangeable; they separate tokens but do not
       break lines or produce space in the output.

       Beyond their primary functions, the following input characters
       separate tokens as well.

       { }    Braces perform grouping.  Whereas “e sup a b” expresses
              “(e to the a) times b”, “e sup { a b }” means “e to
              the (a times b)”.  When immediately preceded by a “left”
              or “right” primitive, a brace loses its special meaning.

       ^ ~    are the half space and full space, respectively.  Use them
              to tune the appearance of the output.

       Tab and leader characters separate tokens as well as advancing
       the drawing position to the next tab stop, but are seldom used in
       eqn input.  When they occur, they must appear at the outermost
       lexical scope.  This roughly means that they can't appear within
       braces that are necessary to disambiguate the input; eqn will
       diagnose an error in this event.  (See subsection “Macros” below
       for additional token separation rules.)

       Other tokens are primitives, macros, an argument to either of the
       foregoing, or components of an equation.

       Primitives are fundamental keywords of the eqn language.  They
       can configure an aspect of the preprocessor's state, as when
       setting a “global” font selection or type size (gifont and
       gsize), or declaring or deleting macros (“define” and undef);
       these are termed commands.  Other primitives perform formatting
       operations on the tokens around them (as with fat, over, sqrt, or
       up).

       Equation components include mathematical variables, constants,
       numeric literals, and operators.  eqn remaps some input character
       sequences to groff special character escape sequences for economy
       in equation entry and to ensure that glyphs from an unstyled font
       are used; see groff_char(7).

              +   \[pl]                '    \[fm]
              -   \[mi]                <=   \[<=]
              =   \[eq]                >=   \[>=]

       Macros permit primitives, components, and other macros to be
       collected and used together as a single token.  Predefined macros
       make convenient the preparation of eqn input in a form resembling
       its spoken expression; for example, consider cos, hat, inf, and
       lim.

   Spacing and typeface
       GNU eqn imputes types to the components of an equation, adjusting
       the spacing between them accordingly.  Recognized types are as
       follows; most affect spacing only, whereas the “letter” subtype
       of “ordinary” also assigns a style.

         ordinary      character such as “1”, “a”, or “!”
           letter      character to be italicized by default
           digit       n/a
         operator      large operator such as “Σ”
         binary        binary operator such as “+”
         relation      relational operator such as “=”
         opening       opening bracket such as “(”
         closing       closing bracket such as “)”
         punctuation   punctuation character such as “,”
         inner         sub-formula contained within brackets
         suppress      component to which automatic spacing is not applied

       Two primitives apply types to equation components.

       type t e
              Apply type t to expression e.

       chartype t text
              Assign each character in (unquoted) text type t,
              persistently.

       eqn sets up spacings and styles as if by the following commands.

              chartype "letter"      abcdefghiklmnopqrstuvwxyz
              chartype "letter"      ABCDEFGHIKLMNOPQRSTUVWXYZ
              chartype "letter"      \[*a]\[*b]\[*g]\[*d]\[*e]\[*z]
              chartype "letter"      \[*y]\[*h]\[*i]\[*k]\[*l]\[*m]
              chartype "letter"      \[*n]\[*c]\[*o]\[*p]\[*r]\[*s]
              chartype "letter"      \[*t]\[*u]\[*f]\[*x]\[*q]\[*w]
              chartype "binary"      *\[pl]\[mi]
              chartype "relation"    <>\[eq]\[<=]\[>=]
              chartype "opening"     {([
              chartype "closing"     })]
              chartype "punctuation" ,;:.
              chartype "suppress"    ^~

       eqn assigns all other ordinary and special roff characters,
       including numerals 0–9, the “ordinary” type.  (The “digit” type
       is not used, but is available for customization.)  In keeping
       with common practice in mathematical typesetting, lowercase, but
       not uppercase, Greek letters are assigned the “letter” type to
       style them in italics.  The macros for producing ellipses, “...”,
       cdots, and ldots, use the “inner” type.

   Primitives
       eqn supports without alteration the AT&T eqn primitives above,
       back, bar, bold, define, down, fat, font, from, fwd, gfont,
       gsize, italic, left, lineup, mark, matrix, ndefine, over, right,
       roman, size, sqrt, sub, sup, tdefine, to, under, and up.

   New primitives
       We describe the GNU extension primitives “type” and chartype in
       subsection “Spacing and typeface” above; “set” and “reset” in
       subsection “Customization” below; and gbfont, gifont, and grfont
       in subsection “Fonts” below.  In the following synopses, X can be
       any character not appearing in the parameter thus bracketed.

       e1 accent e2
              Set e2 as an accent over e1.  eqn assumes that e2 is at
              the appropriate height for a lowercase letter without an
              ascender, and shifts it vertically based on e1's height.
              For example, eqn defines hat as follows.

                     accent { roman "^" }

              dotdot, dot, tilde, vec, and dyad are also defined using
              the accent primitive.

       big e  Enlarge the expression e; semantics like those of CSS
              “large” are intended.  In troff output, the type size is
              increased by 5 scaled points.  MathML output emits the
              following.

                     <mstyle mathsize='big'>

       copy file
       include file
              Interpolate the contents of file, omitting lines beginning
              with .EQ or .EN.  If a relative path name, file is sought
              relative to the current working directory.

       ifdef name X anything X
              If name is defined as a primitive or macro, interpret
              anything.

       nosplit text
              As "text", but since text is not quoted it is subject to
              macro expansion; it is not split up and the spacing
              between characters not adjusted per subsection “Spacing
              and typeface” above.

       e opprime
              As prime, but set the prime symbol as an operator on e.
              In the input “A opprime sub 1”, the “1” is tucked under
              the prime as a subscript to the “A” (as is conventional in
              mathematical typesetting), whereas when prime is used,
              the “1” is a subscript to the prime character.  The
              precedence of opprime is the same as that of bar and
              “under”, and higher than that of other primitives except
              accent and uaccent.  In unquoted text, a neutral
              apostrophe (') that is not the first character on the
              input line is treated like opprime.

       sdefine name X anything X
              As “define”, but name is not recognized as a macro if
              called with arguments.

       e1 smallover e2
              As over, but reduce the type size of e1 and e2, and put
              less vertical space between e1 and e2 and the fraction
              bar.  The over primitive corresponds to the TeX \over
              primitive in displayed equation styles; smallover
              corresponds to \over in non-display (“inline”) styles.

       space n
              Set extra vertical spacing around the equation, replacing
              the default values, where n is an integer in hundredths of
              an em.  If positive, n increases vertical spacing before
              the equation; if negative, it does so after the equation.
              This primitive provides an interface to groff's \x escape
              sequence, but with the opposite sign convention.  It has
              no effect if the equation is part of a pic(1) picture.

       special troff-macro e
              Construct an object by calling troff-macro on e.  The
              troff string 0s contains the eqn output for e, and the
              registers 0w, 0h, 0d, 0skern, and 0skew the width, height,
              depth, subscript kern, and skew of e, respectively.  (The
              subscript kern of an object indicates how much a subscript
              on that object should be “tucked in”, or placed to the
              left relative to a non-subscripted glyph of the same size.
              The skew of an object is how far to the right of the
              center of the object an accent over it should be placed.)
              The macro must modify 0s so that it outputs the desired
              result, returns the drawing position to the text baseline
              at the beginning of e, and updates the foregoing registers
              to correspond to the new dimensions of the result.

              Suppose you want a construct that “cancels” an expression
              by drawing a diagonal line through it.

                     .de Ca
                     .  ds 0s \
                     \Z'\\*(0s'\
                     \v'\\n(0du'\
                     \D'l \\n(0wu -\\n(0hu-\\n(0du'\
                     \v'\\n(0hu'
                     ..
                     .EQ
                     special Ca "x \[mi] 3 \[pl] x" ~ 3
                     .EN

              We use the \[mi] and \[pl] special characters instead of +
              and - because they are part of the argument to a troff
              macro, so eqn does not transform them to mathematical
              glyphs for us.  Here's a more complicated construct that
              draws a box around an expression; the bottom of the box
              rests on the text baseline.  We define the eqn macro box
              to wrap the call of the troff macro Bx.

                     .de Bx
                     .ds 0s \
                     \Z'\\h'1n'\\*[0s]'\
                     \v'\\n(0du+1n'\
                     \D'l \\n(0wu+2n 0'\
                     \D'l 0 -\\n(0hu-\\n(0du-2n'\
                     \D'l -\\n(0wu-2n 0'\
                     \D'l 0 \\n(0hu+\\n(0du+2n'\
                     \h'\\n(0wu+2n'
                     .nr 0w +2n
                     .nr 0d +1n
                     .nr 0h +1n
                     ..
                     .EQ
                     define box ' special Bx $1 '
                     box(foo) ~ "bar"
                     .EN

       split "text"
              As text, but since text is quoted, it is not subject to
              macro expansion; it is split up and the spacing between
              characters adjusted per subsection “Spacing and typeface”
              above.

       e1 uaccent e2
              Set e2 as an accent under e1.  e2 is assumed to be at the
              appropriate height for a letter without a descender;  eqn
              vertically shifts it depending on whether e1 has a
              descender.  utilde is predefined using uaccent as a tilde
              accent below the baseline.

       undef name
              Remove definition of macro or primitive name, making it
              undefined.

       vcenter e
              Vertically center e about the math axis, a horizontal line
              upon which fraction bars and characters such as “+” and
              “−” are aligned.  MathML already behaves this way, so eqn
              ignores this primitive when producing that output format.
              The built-in sum macro is defined as if by the following.

                     define sum ! { type "operator" vcenter size +5 \(*S } !

   Extended primitives
       GNU eqn extends the syntax of some AT&T eqn primitives,
       introducing one deliberate incompatibility.

       delim on
              eqn recognizes an “on” argument to the delim primitive
              specially, restoring any delimiters previously disabled
              with “delim off”.  If delimiters haven't been specified,
              neither command has effect.  Few eqn documents are
              expected to use “o” and “n” as left and right delimiters,
              respectively.  If yours does, swap them, or select others.

       col n { ... }
       ccol n { ... }
       lcol n { ... }
       rcol n { ... }
       pile n { ... }
       cpile n { ... }
       lpile n { ... }
       rpile n { ... }
              The integer value n, in hundredths of an em, uses the
              formatter's \x escape sequence to increase the vertical
              spacing between rows; eqn ignores it when producing
              MathML.  Negative values are accepted but have no effect.
              If more than one n occurs in a matrix or pile, the largest
              is used.

   Customization
       When eqn generates troff input, the appearance of equations is
       controlled by a large number of parameters.  They have no effect
       when generating MathML, which delegates typesetting to a MathML
       rendering engine.  Configure these parameters with the “set” and
       “reset” primitives.

       set p n
              assigns parameter p the integer value n; n is interpreted
              in units of hundredths of an em unless otherwise stated.
              For example,
                     set x_height 45
              says that eqn should assume that the font's x-height is
              0.45 ems.

       reset p
              restores the default value of parameter p.

       Available parameters p are as follows; defaults are shown in
       parentheses.  We intend these descriptions to be expository
       rather than rigorous.

       minimum_size
              sets a floor for the type size (in scaled points) at which
              equations are set (5).

       fat_offset
              The fat primitive emboldens an equation by overprinting
              two copies of the equation horizontally offset by this
              amount (4).  In MathML mode, components to which
              fat_offset applies instead use the following.
                     <mstyle mathvariant='double-struck'>

       over_hang
              A fraction bar is longer by twice this amount than the
              maximum of the widths of the numerator and denominator; in
              other words, it overhangs the numerator and denominator by
              at least this amount (0).

       accent_width
              When bar or under is applied to a single character, the
              line is this long (31).  Normally, bar or under produces a
              line whose length is the width of the object to which it
              applies; in the case of a single character, this tends to
              produce a line that looks too long.

       delimiter_factor
              Extensible delimiters produced with the left and right
              primitives have a combined height and depth of at least
              this many thousandths of twice the maximum amount by which
              the sub-equation that the delimiters enclose extends away
              from the axis (900).

       delimiter_shortfall
              Extensible delimiters produced with the left and right
              primitives have a combined height and depth not less than
              the difference of twice the maximum amount by which the
              sub-equation that the delimiters enclose extends away from
              the axis and this amount (50).

       null_delimiter_space
              This much horizontal space is inserted on each side of a
              fraction (12).

       script_space
              The width of subscripts and superscripts is increased by
              this amount (5).

       thin_space
              This amount of space is automatically inserted after
              punctuation characters (17).

       medium_space
              This amount of space is automatically inserted on either
              side of binary operators (22).

       thick_space
              This amount of space is automatically inserted on either
              side of relations (28).

       half_space
              configures the width of the space produced by the ^ token
              (17).

       full_space
              configures the width of the space produced by the ~ token
              (28).

       x_height
              The height of lowercase letters without ascenders such as
              “x” (45).

       axis_height
              The height above the baseline of the center of characters
              such as “+” and “−” (26).  It is important that this value
              is correct for the font you are using.

       default_rule_thickness
              This should be set to the thickness of the \[ru]
              character, or the thickness of horizontal lines produced
              with the \D escape sequence (4).

       num1   The over primitive shifts up the numerator by at least
              this amount (70).

       num2   The smallover primitive shifts up the numerator by at
              least this amount (36).

       denom1 The over primitive shifts down the denominator by at least
              this amount (70).

       denom2 The smallover primitive shifts down the denominator by at
              least this amount (36).

       sup1   Normally superscripts are shifted up by at least this
              amount (42).

       sup2   Superscripts within superscripts or upper limits or
              numerators of smallover fractions are shifted up by at
              least this amount (37).  Conventionally, this is less than
              sup1.

       sup3   Superscripts within denominators or square roots or
              subscripts or lower limits are shifted up by at least this
              amount (28).  Conventionally, this is less than sup2.

       sub1   Subscripts are normally shifted down by at least this
              amount (20).

       sub2   When there is both a subscript and a superscript, the
              subscript is shifted down by at least this amount (23).

       sup_drop
              The baseline of a superscript is no more than this much
              below the top of the object on which the superscript is
              set (38).

       sub_drop
              The baseline of a subscript is at least this much below
              the bottom of the object on which the subscript is set
              (5).

       big_op_spacing1
              The baseline of an upper limit is at least this much above
              the top of the object on which the limit is set (11).

       big_op_spacing2
              The baseline of a lower limit is at least this much below
              the bottom of the object on which the limit is set (17).

       big_op_spacing3
              The bottom of an upper limit is at least this much above
              the top of the object on which the limit is set (20).

       big_op_spacing4
              The top of a lower limit is at least this much below the
              bottom of the object on which the limit is set (60).

       big_op_spacing5
              This much vertical space is added above and below limits
              (10).

       baseline_sep
              The baselines of the rows in a pile or matrix are normally
              this far apart (140).  Usually equal to the sum of num1
              and denom1.

       shift_down
              The midpoint between the top baseline and the bottom
              baseline in a matrix or pile is shifted down by this much
              from the axis (26).  Usually equal to axis_height.

       column_sep
              This much space is added between columns in a matrix
              (100).

       matrix_side_sep
              This much space is added at each side of a matrix (17).

       draw_lines
              If non-zero, eqn draws lines using the troff \D escape
              sequence, rather than the \l escape sequence and the \[ru]
              special character.  The eqnrc file sets the default: 1 on
              ps, html, and the X11 devices, otherwise 0.

       body_height
              is the presumed height of an equation above the text
              baseline; eqn adds any excess as extra pre-vertical line
              spacing with troff's \x escape sequence (85).

       body_depth
              is the presumed depth of an equation below the text
              baseline; eqn adds any excess as extra post-vertical line
              spacing with troff's \x escape sequence (35).

       nroff  If non-zero, then ndefine behaves like define and tdefine
              is ignored, otherwise tdefine behaves like define and
              ndefine is ignored.  The eqnrc file sets the default: 1 on
              ascii, latin1, utf8, and cp1047 devices, otherwise 0.

   Macros
       In GNU eqn, macros can take arguments.  A word defined by any of
       the define, ndefine, or tdefine primitives followed immediately
       by a left parenthesis is treated as a parameterized macro call:
       subsequent tokens up to a matching right parenthesis are treated
       as comma-separated arguments.  In this context only, commas and
       parentheses also serve as token separators.  A macro argument is
       not terminated by a comma inside parentheses nested within it.
       In a macro definition, $n, where n is between 1 and 9 inclusive,
       is replaced by the nth argument; if there are fewer than
       n arguments, it is replaced by nothing.

   Predefined macros
       GNU eqn supports the predefined macros offered by AT&T eqn: and,
       approx, arc, cos, cosh, del, det, dot, dotdot, dyad, exp, for,
       grad, half, hat, if, inter, Im, inf, int, lim, ln, log, max, min,
       nothing, partial, prime, prod, Re, sin, sinh, sum, tan, tanh,
       tilde, times, union, vec, ==, !=, +=, ->, <-, <<, >>, and “...”.
       The lowercase classical Greek letters are available as alpha,
       beta, chi, delta, epsilon, eta, gamma, iota, kappa, lambda, mu,
       nu, omega, omicron, phi, pi, psi, rho, sigma, tau, theta,
       upsilon, xi, and zeta.  Spell them with an initial capital letter
       (Alpha) or in full capitals (ALPHA) to obtain uppercase forms.

       GNU eqn further defines the macros cdot, cdots, and utilde (all
       discussed above), dollar, which sets a dollar sign, and ldots,
       which sets an ellipsis on the text baseline.

   Fonts
       eqn uses up to three typefaces to set an equation: italic
       (oblique), roman (upright), and bold.  Assign each a groff
       typeface with the GNU extension primitives grfont, gifont, and
       gbfont.  The defaults are the styles R, I, and B (applied to the
       current font family).  The chartype primitive (see above) sets a
       character's type, which determines the face used to set it.  The
       “letter” type is set in italics; others are set in roman.  Use
       the bold primitive to select an (upright) bold style.

       gbfont f
              Select f as the bold font.

       gifont f
              Select f as the italic font.  GNU eqn recognizes gfont as
              a synonym for AT&T compatibility.

       grfont f
              Select f as the roman font.

Options         top

       --help displays a usage message, while -v and --version show
       version information; all exit afterward.

       -C     Recognize .EQ and .EN even when followed by a character
              other than space or newline.

       -d xy  Specify delimiters x for left and y for right ends of
              equations not bracketed by .EQ/.EN.  x and y need not be
              distinct.  Any “delim xy” statements in the source file
              override this option.

       -f F   is equivalent to “gifont F”.

       -m n   is equivalent to “set minimum_size n”.

       -M dir Search dir for eqnrc before those listed in section
              “Description” above.

       -N     Prohibit newlines within delimiters, allowing eqn to
              recover better from missing closing delimiters.

       -p n   Set sub- and superscripts n points smaller than the
              surrounding text.  This option is deprecated.  eqn
              normally sets sub- and superscripts at 70% of the type
              size of the surrounding text.

       -r     Reduce the type size of super- and subscripts at most once
              relative to the base type size.

       -R     Don't load eqnrc.

       -s n   is equivalent to “gsize n”.  This option is deprecated.

       -T dev Prepare output for the device dev.  This option defines a
              macro dev with the value 1; eqnrc thereby provides
              definitions appropriate to the device.  However, if dev is
              “MathML”, eqn produces output in that language rather than
              roff, and eqnrc is not loaded.  The default device is ps.

Files         top

       /usr/local/share/groff/1.23.0/tmac/eqnrc
              initializes the preprocessor for troff output.  Any valid
              eqn input is accepted.

MathML mode limitations         top

       MathML's design assumes that it cannot know the exact physical
       characteristics of the media and devices on which it will be
       rendered.  It does not support control of motions and sizes to
       the same degree troff does.

       •  GNU eqn's rendering parameters (see section “Customziation”
          above) have no effect on generated MathML.

       •  The special, up, down, fwd, and back primitives cannot be
          implemented, and yield a MathML “<merror>” message instead.

       •  The vcenter primitive is silently ignored, as centering on the
          math axis is the MathML default.

       •  Characters that eqn sets extra large in troff mode—notably the
          integral sign—may appear too small and need to have their
          “<mstyle>” wrappers adjusted by hand.

       As in its troff mode, eqn in MathML mode leaves the .EQ and .EN
       tokens in place, but emits nothing corresponding to delim
       delimiters.  They can, however, be recognized as character
       sequences that begin with “<math>”, end with “</math>”, and do
       not cross line boundaries.

Caveats         top

       Tokens must be double-quoted in eqn input if they are not to be
       recognized as names of macros or primitives, or if they are to be
       interpreted by troff.  In particular, short ones, like “pi” and
       “PI”, can collide with troff identifiers.  For instance, the eqn
       command “gifont PI” does not select groff's Palatino italic font
       for the global italic face; you must use “gifont "PI"” instead.

       Delimited equations are set at the type size current at the
       beginning of the input line, not necessarily that immediately
       preceding the opening delimiter.

       Unlike TeX, eqn does not inherently distinguish displayed and
       inline equation styles; see the smallover primitive above.
       However, macro packages frequently define EQ and EN macros such
       that the equation within is displayed.  These macros may accept
       arguments permitting the equation to be labeled or captioned; see
       the package's documentation.

Bugs         top

       eqn abuses terminology—its “equations” can be inequalities, bare
       expressions, or unintelligible gibberish.  But there's no
       changing it now.

       In nroff mode, lowercase Greek letters are rendered in roman
       instead of italic style.

       In MathML mode, the mark and lineup features don't work.  These
       could, in theory, be implemented with “<maligngroup>” elements.

       In MathML mode, each digit of a numeric literal gets a separate
       “<mn></mn>” pair, and decimal points are tagged with “<mo></mo>”.
       This is allowed by the specification, but inefficient.

Examples         top

       We first illustrate eqn usage with a trigonometric identity.

              .EQ
              sin ( alpha + beta ) = sin alpha cos beta + cos alpha sin beta
              .EN

       It can be convenient to set up delimiters if mathematical content
       will appear frequently in running text.

              .EQ
              delim $$
              .EN
              Having cached a table of logarithms,
              the property $ln ( x y ) = ln x + ln y$ sped calculations.

       The quadratic formula affords an opportunity to use fractions,
       radicals, and the full space token ~.

              .EQ
              x = { - b ~ \[+-] ~ sqrt { b sup 2 - 4 a c } } over { 2 a }
              .EN

       Alternatively, we could define the plus-minus sign as a binary
       operator.  Automatic spacing puts 0.06 em less space on either
       side of the plus-minus than ~ does, this being the difference
       between the widths of the medium_space parameter used by binary
       operators and that of the full space.  Independently, we can
       define a macro “frac” for setting fractions.

              .EQ
              chartype "binary" \[+-]
              define frac ! { $1 } over { $2 } !
              x = frac(- b \[+-] sqrt { b sup 2 - 4 a c }, 2 a)
              .EN

See also         top

       “Typesetting Mathematics—User's Guide” (2nd edition), by Brian W.
       Kernighan and Lorinda L. Cherry, 1978, AT&T Bell Laboratories
       Computing Science Technical Report No. 17.

       The TeXbook, by Donald E. Knuth, 1984, Addison-Wesley
       Professional.  Appendix G discusses many of the parameters from
       section “Customization” above in greater detail.

       groff_char(7) documents a variety of special character escape
       sequences useful in mathematical typesetting.  See subsections
       “Logical symbols”, “Mathematical symbols”, and “Greek glyphs” in
       particular.

       groff(1), troff(1), pic(1), groff_font(5)

COLOPHON         top

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       for this manual page, see ⟨http://www.gnu.org/software/groff/⟩.
       This page was obtained from the project's upstream Git repository
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groff 1.23.0.1273-9d53-dirty   6 June 2024                        eqn(1)