Provided by: groff-base_1.23.0-5_amd64 bug

Name

       eqn - format mathematics (equations) for groff or MathML

Synopsis

       eqn [-CNrR] [-d xy] [-f F] [-m n] [-M dir] [-p n] [-s n] [-T dev] [file ...]

       eqn --help

       eqn -v
       eqn --version

Description

       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 given on the command line, 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/share/groff/site-tmac, and finally in the standard macro directory  /usr/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.

       Three points are worth special 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.

   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.

       The following input characters not only separate tokens, but manage their grouping and spacing 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 (gfont and gsize), or
       declaring or deleting macros (“define” and undef); these are termed commands.  Other  primitives  perform
       formatting operations on the tokens after 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 referred to by 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
       The GNU extension primitives “type” and chartype are  discussed  in  subsection  “Spacing  and  typeface”
       above;  “set” in subsection “Customization” below; and grfont and gbfont 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.  e2 is assumed to be at the appropriate height for a lowercase letter
              without  an  ascender;    eqn  vertically shifts it depending on e1's height.  For example, hat is
              defined as follows.

                     accent { "^" }

              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 reduces the type size of e1 and e2, and puts 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, consider swapping 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) increases the vertical spacing  between  rows,  using
              groff's \x escape sequence (the value has no effect in MathML mode).  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 primitive.

       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.

              Available  parameters  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.  It
                               also configures the width of the space produced by the ^ token (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.  It
                               also 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 primitives gfont, grfont, and gbfont.  The defaults are the styles I, R,
       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.  This is a GNU extension.

       gfont f
              Select f as the italic font.

       grfont f
              Select f as the roman font.  This is a GNU extension.

Options

       --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 “gfont 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.   This  option  allows  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 subscripts at most once relative to the base type size for the equation.

       -R     Don't load eqnrc.

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

       -T dev Prepare  output  for  the  device dev.  In most cases, the effect of this is to define a macro dev
              with a value of 1; eqnrc uses this to provide definitions appropriate for the device.  However, if
              the  specified  driver is “MathML”, the output is MathML markup rather than troff input, and eqnrc
              is not loaded at all.  The default output device is ps.

Files

       /usr/share/groff/1.23.0/tmac/eqnrc
              Initialization file.

MathML mode limitations

       MathML is designed on the assumption 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.

       • eqn customization parameters 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

       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 “gfont PI”  does  not  select  groff's
       Palatino italic font for the global italic face; you must use “gfont "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

       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

       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 illustrates use of fractions and radicals, and affords an opportunity  to  use  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

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

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