Name  Synopsis  Description  Options  Files  MathML Mode Limitations  Bugs  See Also  COLOPHON 

eqn(1) General Commands Manual eqn(1)
eqn  format equations for groff or MathML
eqn [rCNR] [d xy] [f F] [m n] [M dir] [p n] [s n] [T name] [file ...] eqn help eqn v eqn version
The GNU version of eqn is part of the groff(7) document formatting system. eqn compiles descriptions of equations embedded in roff(7) input files into commands that are understood by troff(1). Normally, it should be invoked using the e option of groff(1). Its syntax is compatible with AT&T eqn, its output cannot be processed with AT&T troff; it must be processed with GNU troff. If no file operands are given on the command line, or if file is “”, the standard input stream is read. Unless the R option is given, eqn searches for the file eqnrc in the directories given with the M option first, then in /usr/local/lib/ groff/sitetmac, /usr/local/share/groff/sitetmac, and finally in the standard macro directory /usr/local/share/groff/1.22.4/tmac. If it exists, eqn processes it before the other input files. Only the differences between GNU eqn and AT&T eqn are described in this document. 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 provide the functionality of neqn: it does not support lowresolution, typewriterlike devices (although it may work adequately for very simple input). • GNU eqn sets the input token “...” as three periods or low dots, rather than the three centered dots of AT&T eqn. To get three centered dots, write cdots or “cdot cdot cdot”. Controlling delimiters If not in compatibility mode, eqn recognizes delim on as a command to restore the delimiters which have been previously disabled with a call to “delim off”. If delimiters haven't been specified, the call has no effect. Automatic spacing eqn gives each component of an equation a type, and adjusts the spac‐ ing between components using that type. Possible types are described in the table below. ordinary an ordinary character such as “1” or “x” operator a large operator such as “Σ” binary a binary operator such as “+” relation a relation such as “=” opening a opening bracket such as “(” closing a closing bracket such as “)” punctuation a punctuation character such as “,” inner a subformula contained within brackets suppress a type without automatic spacing adjustment Components of an equation get a type in one of two ways. type t e This yields an equation component that contains e but that has type t, where t is one of the types mentioned above. For ex‐ ample, times is defined as follows. type "binary" \(mu The name of the type doesn't have to be quoted, but quoting it protects it from macro expansion. chartype t text Unquoted groups of characters are split up into individual characters, and the type of each character is looked up; this changes the type that is stored for each character; it says that the characters in text from now on have type t. For ex‐ ample, chartype "punctuation" .,;: would make the characters “.,;:” have type punctuation when‐ ever they subsequently appeared in an equation. The type t can also be letter or digit; in these cases chartype changes the font type of the characters. See subsection “Fonts” be‐ low. New primitives big e Enlarges the expression it modifies; intended to have seman‐ tics like CSS “large”. In troff output, the point size is in‐ creased by 5; in MathML output, the expression uses <mstyle mathsize='big'> e1 smallover e2 This is similar to over; smallover reduces the size of e1 and e2; it also puts less vertical space between e1 or e2 and the fraction bar. The over primitive corresponds to the TeX \over primitive in display styles; smallover corresponds to \over in nondisplay styles. vcenter e This vertically centers e about the math axis. The math axis is the vertical position about which characters such as “+” and “−” are centered; it is also the vertical position used for fraction bars. For example, sum is defined as follows. { type "operator" vcenter size +5 \(*S } vcenter is silently ignored when generating MathML. e1 accent e2 This sets e2 as an accent over e1. e2 is assumed to be at the correct height for a lowercase letter; e2 is moved down ac‐ cording to whether e1 is taller or shorter than a lowercase letter. For example, hat is defined as follows. accent { "^" } dotdot, dot, tilde, vec, and dyad are also defined using the accent primitive. e1 uaccent e2 This sets e2 as an accent under e1. e2 is assumed to be at the correct height for a character without a descender; e2 is moved down if e1 has a descender. utilde is predefined using uaccent as a tilde accent below the baseline. split "text" This has the same effect as simply text but text is not subject to macro expansion because it is quoted; text is split up and the spacing between individual characters is adjusted. nosplit text This has the same effect as "text" but because text is not quoted it is subject to macro expan‐ sion; text is not split up and the spacing between individual characters is not adjusted. e opprime This is a variant of prime that acts as an operator on e. It produces a different result from prime in a case such as “A opprime sub 1”: with opprime the “1” is tucked under the prime as a subscript to the “A” (as is conventional in mathematical typesetting), whereas with prime the “1” is a subscript to the prime character. The precedence of opprime is the same as that of bar and under, which is higher than that of everything except accent and uaccent. In unquoted text, a neutral apos‐ trophe (') that is not the first character on the input line is treated like opprime. special text e This constructs a new object from e using a troff(1) macro named text. When the macro is called, the string 0s contains the output for e, and the number registers 0w, 0h, 0d, 0skern, and 0skew contain the width, height, depth, subscript kern, and skew of e. (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 nonsubscripted 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 with its origin at the current point, and increase the current horizontal position by the width of the object. The number registers must also be modified so that they correspond to the result. For example, suppose you wanted a construct that “cancels” an expression by drawing a diagonal line through it. .EQ define cancel 'special Ca' .EN .de Ca . ds 0s \ \Z'\\*(0s'\ \v'\\n(0du'\ \D'l \\n(0wu \\n(0hu\\n(0du'\ \v'\\n(0hu' .. You could then cancel an expression e with “cancel { e }”. Here's a more complicated construct that draws a box around an expression. .EQ define box 'special Bx' .EN .de Bx .ds 0s \ \Z'\h'1n'\\*(0s'\ \Z'\ \v'\\n(0du+1n'\ \D'l \\n(0wu+2n 0'\ \D'l 0 \\n(0hu\\n(0du2n'\ \D'l \\n(0wu2n 0'\ \D'l 0 \\n(0hu+\\n(0du+2n'\ '\ \h'\\n(0wu+2n' .nr 0w +2n .nr 0d +1n .nr 0h +1n .. space n A positive value of the integer n (in hundredths of an em) sets the vertical spacing before the equation, a negative value sets the spacing after the equation, replacing the de‐ fault values. This primitive provides an interface to groff's \x escape (but with opposite sign). This keyword has no effect if the equation is part of a pic picture. Extended primitives 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 (the value has no effect in MathML mode). Negative values are pos‐ sible but have no effect. If there is more than a single value given in a matrix, the biggest one is used. Customization When eqn is generating troff markup, the appearance of equations is controlled by a large number of parameters. They have no effect when generating MathML mode, which pushes typesetting and fine motions downstream to a MathML rendering engine. These parameters can be set using the set command. set p n This sets parameter p to value n, where n is an integer. For example, set x_height 45 says that eqn should assume an x height of 0.45 ems. Possible parameters are as follows. Values are in units of hundredths of an em unless otherwise stated. These descrip‐ tions are intended to be expository rather than definitive. minimum_size eqn won't set anything at a smaller point size than this. The value is in points. fat_offset The fat primitive emboldens an equation by overprinting two copies of the equation horizontally offset by this amount. This parameter is not used in MathML mode; in‐ stead, fat text uses <mstyle mathvariant='doublestruck'> 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 denomi‐ nator by at least this amount. accent_width When bar or under is applied to a single character, the line is this long. 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 subequation that the delimiters enclose ex‐ tends away from the axis. 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 subequation that the delimiters enclose ex‐ tends away from the axis and this amount. null_delimiter_space 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. thin_space This amount of space is automatically inserted after punctuation characters. medium_space This amount of space is automatically inserted on ei‐ ther side of binary operators. thick_space This amount of space is automatically inserted on ei‐ ther side of relations. x_height The height of lowercase letters without ascenders such as “x”. axis_height The height above the baseline of the center of charac‐ ters such as “+” and “−”. It is important that this value is correct for the font you are using. default_rule_thickness This should set to the thickness of the \[ru] charac‐ ter, or the thickness of horizontal lines produced with the \D escape sequence. num1 The over command shifts up the numerator by at least this amount. num2 The smallover command shifts up the numerator by at least this amount. denom1 The over command shifts down the denominator by at least this amount. denom2 The smallover command shifts down the denominator by at least this amount. sup1 Normally superscripts are shifted up by at least this amount. sup2 Superscripts within superscripts or upper limits or nu‐ merators of smallover fractions are shifted up by at least this amount. This is usually less than sup1. sup3 Superscripts within denominators or square roots or subscripts or lower limits are shifted up by at least this amount. This is usually less than sup2. sub1 Subscripts are normally shifted down by at least this amount. sub2 When there is both a subscript and a superscript, the subscript is shifted down by at least this amount. sup_drop The baseline of a superscript is no more than this much amount below the top of the object on which the super‐ script is set. sub_drop The baseline of a subscript is at least this much below the bottom of the object on which the subscript is set. 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. big_op_spacing2 The baseline of a lower limit is at least this much be‐ low the bottom of the object on which the limit is set. 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. 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. big_op_spacing5 This much vertical space is added above and below lim‐ its. baseline_sep The baselines of the rows in a pile or matrix are nor‐ mally this far apart. In most cases this should be 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. In most cases this should be equal to axis_height. column_sep This much space is added between columns in a matrix. matrix_side_sep This much space is added at each side of a matrix. draw_lines If this is nonzero, lines are drawn using the \D es‐ cape sequence, rather than with the \l escape sequence and the \[ru] character. body_height The amount by which the height of the equation exceeds this is added as extra space before the line containing the equation (using \x). The default value is 85. body_depth The amount by which the depth of the equation exceeds this is added as extra space after the line containing the equation (using \x). The default value is 35. nroff If this is nonzero, then ndefine behaves like define and tdefine is ignored, otherwise tdefine behaves like define and ndefine is ignored. The default value is 0. (This is typically changed to 1 by the eqnrc file for the ascii, latin1, utf8, and cp1047 devices.) A more precise description of the role of many of these param‐ eters can be found in Appendix H of The TeXbook. Macros Macros can take arguments. In a macro body, $n where n is between 1 and 9, is replaced by the nth argument if the macro is called with arguments; if there are fewer than n arguments, it is replaced by nothing. A word containing a left parenthesis where the part of the word before the left parenthesis has been defined using the define command is recognized as a macro call with arguments; characters fol‐ lowing the left parenthesis up to a matching right parenthesis are treated as commaseparated arguments. Commas inside nested parenthe‐ ses do not terminate an argument. sdefine name X anything X This is like the define command, but name is not recognized if called with arguments. include "file" copy "file" Include the contents of file (include and copy are synonyms). Lines of file beginning with .EQ or .EN are ignored. ifdef name X anything X If name has been defined by define (or has been automatically defined because name is the output device) process anything; otherwise ignore anything. X can be any character not appear‐ ing in anything. undef name Remove definition of name, making it undefined. Besides the macros mentioned above, the following definitions are available: Alpha, Beta, ..., Omega (this is the same as ALPHA, BETA, ..., OMEGA), ldots (three dots on the baseline), and dollar. Fonts eqn normally uses at least two fonts to set an equation: an italic font for letters, and a roman font for everything else. The AT&T eqn gfont command changes the font that is used as the italic font. By default this is I. The font that is used as the roman font can be changed using the new grfont command. grfont f Set the roman font to f. The italic primitive uses the current italic font set by gfont; the roman primitive uses the current roman font set by grfont. There is also a new gbfont command, which changes the font used by the bold primitive. If you only use the roman, italic and bold primitives to changes fonts within an equation, you can change all the fonts used by your equations just by using gfont, grfont and gbfont commands. You can control which characters are treated as letters (and there‐ fore set in italics) by using the chartype command described above. A type of letter causes a character to be set in italic type. A type of digit causes a character to be set in roman type.
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, and do not handle the “delim on” statement specially. d xy Specify delimiters x and y for the left and right ends, respectively, of inline equations. Any delim statements in the source file override this. f F This is equivalent to a “gfont F” command. m n Set the minimum point size to n. eqn will not reduce the size of subscripts or superscripts to a smaller size than n. M dir Search dir for eqnrc before the default directories. N Don't allow newlines within delimiters. This option allows eqn to recover better from missing closing delimiters. p n This says that subscripts and superscripts should be n points smaller than the surrounding text. This option is deprecated. Normally, eqn sets subscripts and superscripts at 70% of the size of the surrounding text. r Only one size reduction. R Don't load eqnrc. s n This is equivalent to a “gsize n” command. This option is deprecated. eqn normally sets equations at whatever the current point size is when the equation is encountered. T name The output is for device name. Normally, the only effect of this is to define a macro name with a value of 1; eqnrc uses this to provide definitions appropriate for the output device. However, if the specified device is “MathML”, the output is MathML markup rather than troff commands, and eqnrc is not loaded at all. The default output device is ps.
/usr/local/share/groff/1.22.4/tmac/eqnrc Initialization file.
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 fine control of motions and sizes to the same degree troff does. Thus: • eqn parameters have no effect on the generated MathML. • The special, up, down, fwd, and back operations cannot be implemented, and yield a MathML “<merror>” message instead. • The vcenter keyword 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 delimiters in place for displayed equations, but emits no explicit delimiters around inline equations. They can, however, be recognized as strings that begin with “<math>” and end with “</math>” and do not cross line boundaries. See section “Bugs” below for translation limits specific to eqn.
Inline equations are set at the point size that is current at the beginning of the input line. 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.
“Typesetting Mathematics—User's Guide” (2nd edition); Computing Science Technical Report #17; Brian W. Kernighan, Lorinda L. Cherry; AT&T Bell Laboratories; 1978. The TeXbook; Donald E. Knuth; AddisonWesley Professional; 1984. groff(1), troff(1), pic(1), groff_font(5)
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