Provided by: groff-base_1.23.0-2_amd64 bug


       eqn - format mathematics (equations) for groff or MathML


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

       eqn --help

       eqn -v
       eqn --version


       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

              F =
              m a

       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

       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.

       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 \
                     \D'l \\n(0wu -\\n(0hu-\\n(0du'\
                     special Ca "x \[mi] 3 \[pl] x" ~ 3

              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 \
                     \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'\
                     .nr 0w +2n
                     .nr 0d +1n
                     .nr 0h +1n
                     define box ' special Bx $1 '
                     box(foo) ~ "bar"

       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

       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

       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.

       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

       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
                                      <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

              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

              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).

                               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

                               This much horizontal space is inserted on each side of a  fraction

              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”

              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.

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

              num1             The over primitive shifts up the numerator by at least this amount

              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.

       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.

       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.


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

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

       -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.


              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

       • 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.


       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.


       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


       We first illustrate eqn usage with a trigonometric identity.

              sin ( alpha + beta ) = sin alpha cos beta + cos alpha sin beta

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

              delim $$
              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 ~.

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

       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

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

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)