# eqn - format mathematics (equations) for groff or MathML - man(1) - [phpMan] > **TLDR:** Equation preprocessor for the groff (GNU Troff) document formatting system. > - Process input with equations, saving the output for future typesetting with groff to PostScript: `eqn {{path/to/input.eqn}} > {{path/to/output.roff}}` - Typeset an input file with equations to PDF using the [me] macro package: `eqn -T {{pdf}} {{path/to/input.eqn}} | groff -{{me}} -T {{pdf}} > {{path/to/output.pdf}}` *Source: tldr-pages* --- [_eqn_(1)](https://www.chedong.com/phpMan.php/man/eqn/1/markdown) General Commands Manual [_eqn_(1)](https://www.chedong.com/phpMan.php/man/eqn/1/markdown) ## 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)](https://www.chedong.com/phpMan.php/man/groff/7/markdown) document formatting system. _eqn_ is a [_troff_(1)](https://www.chedong.com/phpMan.php/man/troff/1/markdown) preprocessor that translates expressions in its own language, embedded in [_roff_(7)](https://www.chedong.com/phpMan.php/man/roff/7/markdown) input files, into mathematical notation typeset by [_troff_(1)](https://www.chedong.com/phpMan.php/man/troff/1/markdown). 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)](https://www.chedong.com/phpMan.php/man/groff/1/markdown). While GNU _eqn_'s input syn‐ tax 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 be‐ fore 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 cen‐ tered 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 spac‐ ing 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 subsec‐ tion “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 opera‐ tors. _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)](https://www.chedong.com/phpMan.php/man/groffchar/7/markdown). + \[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 re‐ sembling 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 subsec‐ tion “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 low‐ ercase 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 fol‐ lowing. **copy _**file_ **include _**file_ Interpolate the contents of _file_, omitting lines beginning with **.EQ **or **.EN**. If a rel‐ ative 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 **prim‐ itive 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 be‐ fore the equation; if negative, it does so after the equation. This primitive pro‐ vides an interface to _groff_'s **\x **escape sequence, but with the opposite sign conven‐ tion. It has no effect if the equation is part of a [_pic_(1)](https://www.chedong.com/phpMan.php/man/pic/1/markdown) 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 regis‐ ters 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 expres‐ sion; 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 incompati‐ bility. ### delim on _eqn_ recognizes an “**on**” argument to the **delim **primitive specially, restoring any delim‐ iters 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). Neg‐ ative 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. **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 delim‐ iters 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 delim‐ iters 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 bi‐ nary operators (**22**). **thick_space **This amount of space is automatically inserted on either side of re‐ lations. 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**). Conven‐ tionally, 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**). Usu‐ ally 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 **de‐ vices, 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-sepa‐ rated arguments. In this context only, commas and parentheses also serve as token separa‐ tors. 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 _n_th argu‐ ment; 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 avail‐ able 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 de‐ faults are the styles **I**, **R**, and **B **(applied to the current font family). The **chartype **primi‐ tive (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 ### -d _ **.EQ**/**.EN**. _x_ and _y_ need not be distinct. Any “**delim _**xy_” statements in the source file override this option. ### -f _ ### -m _ ### -M _ ### -N missing closing delimiters. ### -p _ deprecated. _eqn_ normally sets sub- and superscripts at 70% of the type size of the surrounding text. ### -r equation. ### -R ### -s _ ### -T _ 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 mo‐ tions 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 “” message instead. • The **vcenter **primitive is silently ignored, as centering on the math axis is the MathML de‐ fault. • Characters that _eqn_ sets extra large in _troff_ mode—notably the integral sign—may appear too small and need to have their “” 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 se‐ quences that begin with “”, end with “”, 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 unintelligi‐ ble 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 imple‐ mented with “” elements. In MathML mode, each digit of a numeric literal gets a separate “” pair, and decimal points are tagged with “”. 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 differ‐ ence 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)](https://www.chedong.com/phpMan.php/man/groffchar/7/markdown), particularly subsections “Logical symbols”, “Mathematical symbols”, and “Greek glyphs”, documents a variety of special character escape sequences useful in mathematical typesetting. [_groff_(1)](https://www.chedong.com/phpMan.php/man/groff/1/markdown), [_troff_(1)](https://www.chedong.com/phpMan.php/man/troff/1/markdown), [_pic_(1)](https://www.chedong.com/phpMan.php/man/pic/1/markdown), [_groff_font_(5)](https://www.chedong.com/phpMan.php/man/grofffont/5/markdown) groff 1.23.0 31 March 2024 [_eqn_(1)](https://www.chedong.com/phpMan.php/man/eqn/1/markdown)