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/packages/math/init.lua

local base = require("packages.base")

local package = pl.class(base)
package._name = "math"

function package:_init ()
   base._init(self)
   local typesetter = require("packages.math.typesetter")
   self.ConvertMathML, self.handleMath = typesetter[1], typesetter[2]
   local texlike = require("packages.math.texlike")
   self.convertTexlike, self.compileToMathML = texlike[1], texlike[2]
   -- Register a new unit that is 1/18th of the current math font size
   SILE.registerUnit("mu", {
      relative = true,
      definition = function (value)
         return value * SILE.settings:get("math.font.size") / 18
      end,
   })
   self:loadPackage("counters")
end

function package.declareSettings (_)
   SILE.settings:declare({
      parameter = "math.font.family",
      type = "string",
      default = "Libertinus Math",
   })
   SILE.settings:declare({
      parameter = "math.font.style",
      type = "string",
      default = "Regular",
   })
   SILE.settings:declare({
      parameter = "math.font.weight",
      type = "integer",
      default = 400,
   })
   SILE.settings:declare({
      parameter = "math.font.filename",
      type = "string",
      default = "",
   })
   SILE.settings:declare({
      parameter = "math.font.size",
      type = "number or integer",
      default = SILE.settings:get("font.size"),
   })
   SILE.settings:registerHook ("font.size", function (size)
      -- Follow document font size changes
      SILE.settings:set("math.font.size", size)
   end)
   -- Whether to show debug boxes around mboxes
   SILE.settings:declare({
      parameter = "math.debug.boxes",
      type = "boolean",
      default = false,
   })
   SILE.settings:declare({
      parameter = "math.displayskip",
      type = "VGlue",
      default = SILE.types.node.vglue("2ex plus 1pt"),
   })
end

function package:registerCommands ()
   self:registerCommand("mathml", function (options, content)
      local mbox
      xpcall(function ()
         mbox = self:ConvertMathML(content)
      end, function (err)
         print(err)
         print(debug.traceback())
      end)
      self:handleMath(mbox, options)
   end)

   self:registerCommand("math", function (options, content)
      local mbox
      xpcall(function ()
         mbox = self:ConvertMathML(self:compileToMathML({}, self:convertTexlike(content)))
      end, function (err)
         print(err)
         print(debug.traceback())
      end)
      self:handleMath(mbox, options)
   end)

   self:registerCommand("math:numberingstyle", function (options, _)
      SILE.typesetter:typeset("(")
      if options.counter then
         SILE.call("show-counter", { id = options.counter })
      elseif options.number then
         SILE.typesetter:typeset(options.number)
      end
      SILE.typesetter:typeset(")")
   end)
end

package.documentation = [[
\begin{document}
\use[module=packages.math]
\set[parameter=math.font.family, value=Libertinus Math]
\set[parameter=math.font.size, value=11]
% Default verbatim font (Hack) is missing a few math symbols
\use[module=packages.font-fallback]
\font:add-fallback[family=Symbola]
\define[command=paragraph]{\smallskip\em{\process.}\novbreak\par}
The \autodoc:package{math} package provides typesetting of formulas directly in a SILE document.

\autodoc:note{Mathematical typesetting in SILE is still in its infancy.
As such, it lacks some features and may contain bugs.
Feedback and contributions are always welcome.}

\noindent To typeset mathematics, you will need an OpenType math font installed on your system.%
%\footnote{A list of freely available math fonts can be found at \href[src=https://www.ctan.org/pkg/unicode-math]{https://www.ctan.org/pkg/unicode-math}}
By default, this package uses Libertinus Math, so it will fail if Libertinus Math can’t be found.
Another font may be specified via the setting \autodoc:setting{math.font.family}.
If required, you can set the font style and weight via \autodoc:setting{math.font.style} and \autodoc:setting{math.font.weight}.
The font size can be set via \autodoc:setting{math.font.size}.

\paragraph{MathML}
The first way to typeset math formulas is to enter them in the MathML format.
MathML is a standard for encoding mathematical notation for the Web and for other types of digital documents.
It is supported by a wide range of tools and represents the most promising format for unifying the encoding of mathematical notation, as well as improving its accessibility (e.g., to blind users).

To render an equation encoded in MathML, simply put it in a \code{mathml} command.
For example, the formula \mathml{\mrow{\msup{\mi{a}\mn{2}} \mo{+} \msup{\mi{b}\mn{2}} \mo{=} \msup{\mi{c}\mn{2}}}} was typeset by the following command:

\begin[type=autodoc:codeblock]{raw}
\mathml{
    \mrow{
        \msup{\mi{a}\mn{2}}
        \mo{+}
        \msup{\mi{b}\mn{2}}
        \mo{=}
        \msup{\mi{c}\mn{2}}
    }
}
\end{raw}

\noindent In an XML document, we could use the more classical XML syntax:

\begin[type=autodoc:codeblock]{raw}
<mathml>
    <mrow>
        <msup> <mi>a</mi> <mn>2</mn> </msup>
        <mo>+</mo>
        <msup> <mi>b</mi> <mn>2</mn> </msup>
        <mo>=</mo>
        <msup> <mi>c</mi> <mn>2</mn> </msup>
    </mrow>
</mathml>
\end{raw}

\noindent By default, formulas are integrated into the flow of text.
To typeset them on their own line, use the \autodoc:parameter{mode=display} option:

\mathml[mode=display]{
    \mrow{
        \msup{\mi{a}\mn{2}}
        \mo{+}
        \msup{\mi{b}\mn{2}}
        \mo{=}
        \msup{\mi{c}\mn{2}}
    }
}

\paragraph{TeX-like syntax}
As the previous examples illustrate, MathML is not really intended to be written by humans and quickly becomes very verbose.
That is why this package also provides a \code{math} command, which understands a syntax similar to the math syntax of TeX.
To typeset the above equation, one only has to type \code{\\math\{a^2 + b^2 = c^2\}}.

Here is a slightly more involved equation:

\begin[type=autodoc:codeblock]{raw}
\begin[mode=display]{math}
    \sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}
\end{math}
\end{raw}

\noindent This renders as:

\begin[mode=display]{math}
    \sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}
\end{math}

The general philosophy of the TeX-like syntax is to be a simple layer on top of MathML, and not to mimic perfectly the syntax of the LaTeX tool.
Its main difference from the SILE syntax is that \code{\\mycommand\{arg1\}\{arg2\}\{arg3\}} is translated into MathML as \code{<mycommand> arg1 arg2 arg3 </mycommand>} whereas in normal SILE syntax, the XML equivalent would be \code{<mycommand>arg1</mycommand> arg2 arg3}.

\code{\\sum}, \code{\\infty}, and \code{\\pi} are only shorthands for the Unicode characters \math{\sum}, \math{\infty} and \math{\pi}.
If it’s more convenient, you can use these Unicode characters directly.
The symbol shorthands are the same as in the TeX package \href[src=https://www.ctan.org/pkg/unicode-math]{\code{unicode-math}}.

\code{\{formula\}} is a shorthand for \code{\\mrow\{formula\}}.
Since parentheses—among other glyphs—stretch vertically to the size of their englobing \code{mrow}, this is useful to typeset parentheses of different sizes on the same line:

\begin[type=autodoc:codeblock]{raw}
\Gamma (\frac{\zeta}{2}) + x^2(x+1)
\end{raw}

\noindent renders as

\begin[mode=display]{math}
    \Gamma (\frac{\zeta}{2}) + x^2(x+1)
\end{math}

\noindent which is ugly.
To keep parentheses around \math{x+1} small, you should put braces around the expression:

\begin[type=autodoc:codeblock]{raw}
\Gamma (\frac{\zeta}{2}) + x^2{(x+1)}
\end{raw}

\begin[mode=display]{math}
    \Gamma (\frac{\zeta}{2}) + x^2{(x+1)}
\end{math}

\noindent To print a brace in a formula, you need to escape it with a backslash.

\paragraph{Token kinds}
In the \code{math} syntax, every individual letter is an identifier (MathML tag \code{mi}), every number is a… number (tag \code{mn}) and all other characters are operators (tag \code{mo}).
If this does not suit you, you can explicitly use the \code{\\mi}, \code{\\mn}, or \code{\\mo} tags.
For instance, \code{sin(x)} will be rendered as \math{sin(x)}, because SILE considers the letters s, i and n to be individual identifiers, and identifiers made of one character are italicized by default.
To avoid that, you can specify that \math{\mi{sin}} is an identifier by writing \code{\\mi\{sin\}(x)} and get: \math{\mi{sin}(x)}.
If you prefer it in “double struck” style, this is permitted by the \code{mathvariant} attribute: \code{\\mi[mathvariant=double-struck]\{sin\}(x)} renders as \math{\mi[mathvariant=double-struck]{sin}(x)}.

\paragraph{Atom types and spacing}
Each token automatically gets assigned an atom type from the list below:
\begin{itemize}
  \item{\code{ord}: \code{mi} and \code{mn} tokens, as well as unclassified operators}
  \item{\code{big}: big operators like ‘\math{\sum}’ or ‘\math{\prod}’}
  \item{\code{bin}: binary operators like ‘\math{+}’ or ‘\math{\%}’}
  \item{\code{rel}: relation operators like ‘\math{=}’ or ‘\math{<}’}
  \item{\code{open}: opening operators like ‘\math{(}’ or ‘\math{[}’}
  \item{\code{close}: closing operators like ‘\math{)}’ or ‘\math{]}’}
  \item{\code{punct}: punctuation operators like ‘\math{,}’}
  % TODO: Those are defined in the 'math' package but appear to be unused
  %\item{\code{inner}}
  %\item{\code{over}}
  %\item{\code{under}}
  %\item{\code{accent}}
  %\item{\code{radical}}
  %\item{\code{vcenter}}
\end{itemize}
\noindent The spacing between any two successive tokens is set automatically based on their atom types, and hence may not reflect the actual spacing used in the input.
To make an operator behave like it has a certain atom type, you can use the \code{atom} attribute. For example, \code{a \\mo[atom=bin]\{div\} b} renders as \math[mode=display]{a \mo[atom=bin]{div} b.}

Spaces in math mode are defined in “math units” (mu), which are 1/18 of an em of the current \em{math} font (and are independent of the current text font size).
Standard spaces inserted automatically between tokens come in three varieties: thin (3 mu), medium (4 mu) and thick (5 mu).
If needed, you can insert them manually with the \code{\\thinspace} (or \code{\\,}), \code{\\medspace} (or \code{\\>}), and \code{\\thickspace} (or \code{\\;}) commands.
Negative space counterparts are available as \code{\\negthinspace} (or \code{\\!}), \code{\\negmedspace}, and \code{\\negthickspace}.
The \code{\\enspace}, \code{\\quad}, and \code{\\qquad} commands from normal text mode are also available, but the spaces they insert scale relative to the text font size.
Finally, you can add a space of any size using the \code{\\mspace[width=<dimension>]} command.

\paragraph{Macros}
To save you some typing, the math syntax lets you define macros with the following syntax:

\begin[type=autodoc:codeblock]{raw}
\def{macro-name}{macro-body}
\end{raw}

\noindent where in the macro’s body \code{#1}, \code{#2}, etc. will be replaced by the macro’s arguments.
For instance:

\begin[type=autodoc:codeblock]{raw}
\begin[mode=display]{math}
    \def{diff}{\mfrac{\mo{d}#1}{\mo{d}#2}}
    \def{bi}{\mi[mathvariant=bold-italic]{#1}}

    \diff{\bi{p}}{t} = ∑_i \bi{F}_i
\end{math}
\end{raw}

\noindent results in:

\begin[mode=display]{math}
  \def{diff}{\mfrac{\mo{d}#1}{\mo{d}#2}}
  \def{bi}{\mi[mathvariant=bold-italic]{#1}}
  \diff{\bi{p}}{t} = ∑_i \bi{F}_i
\end{math}

When macros are not enough, creating new mathematical elements is quite simple: one only needs to create a new class deriving from \code{mbox} (defined in \code{packages/math/base-elements.lua}) and define the \code{shape} and \code{output} methods.
\code{shape} must define the \code{width}, \code{height} and \code{depth} attributes of the element, while \code{output} must draw the actual output.
An \code{mbox} may have one or more children (for instance, a fraction has two children—its numerator and denominator).
The \code{shape} and \code{output} methods of the children are called automatically.

\paragraph{Matrices, aligned equations, and other tables}
Tabular math can be typeset using the \code{table} command (or equivalently the \code{mtable} MathML tag).
For instance, to typeset a matrix:

\begin[type=autodoc:codeblock]{raw}
\begin[mode=display]{math}
    (
    \table{
        1 & 2 & 7 \\
        0 & 5 & 3 \\
        8 & 2 & 1 \\
    }
    )
\end{math}
\end{raw}

\noindent will yield:

\begin[mode=display]{math}
  (\table{
       1 & 2 & 7 \\
       0 & 5 & 3 \\
       8 & 2 & 1 \\
  })
\end{math}

\noindent Tables may also be used to control the alignment of formulas:

\begin[type=autodoc:codeblock]{raw}
\begin[mode=display]{math}
    \{
    \table[columnalign=right center left]{
        u_0 &=& 1 \\
        u_1 &=& 1 \\
        u_n &=& u_{n−1} + u_{n−2}, \forall n ⩾ 2 \\
    }
\end{math}
\end{raw}

\begin[mode=display]{math}
    \{
    \table[columnalign=right center left]{
        u_0 &=& 1 \\
        u_1 &=& 1 \\
        u_n &=& u_{n−1} + u_{n−2}, \forall n ⩾ 2 \\
    }
\end{math}

\noindent Tables currently do not support all attributes required by the MathML standard, but they do allow to control spacing using the \code{rowspacing} and \code{columnspacing} options.

Finally, here is a little secret. This notation:

\begin[type=autodoc:codeblock]{raw}
\table{
    1 & 2 & 7 \\
    0 & 5 & 3 \\
    8 & 2 & 1 \\
}
\end{raw}

\noindent is strictly equivalent to this one:

\begin[type=autodoc:codeblock]{raw}
\table{
        {1} {2} {7}
    }{
        {0} {5} {3}
    }{
        {8} {2} {1}
    }
}
\end{raw}

\noindent In other words, the notation using \code{&} and \code{\\\\} is only a syntactic sugar for a two-dimensional array constructed with braces.

\paragraph{Numbered equations}
Equations can be numbered in display mode.

When \autodoc:parameter{numbered=true}, equations are numbered using a default “equation” counter:
\math[mode=display, numbered=true]{e^{i\pi} = -1}

A different counter can be set by using the option \autodoc:parameter{counter=<id>}, and this setting will also enable numbering.

It is also possible to impose direct numbering using the \autodoc:parameter{number=<value>} option.

The default numbering format is \autodoc:example{(n)}, but this style may be overridden by defining a custom \autodoc:command{\math:numberingstyle} command.
The \code{counter} or the direct value \code{number} is passed as a parameter to this hook, as well as any other options.

\paragraph{Missing features}
This package still lacks support for some mathematical constructs, but hopefully we’ll get there.
Among unsupported constructs are: decorating symbols with so-called accents, such as arrows or hats, “over” or “under” braces, and line breaking inside a formula.

\font:remove-fallback
\end{document}
]]

return package

1	local base = require("packages.base")	10✔
2
3	local package = pl.class(base)	10✔
4	package._name = "math"	10✔
5
6	function package:_init ()	10✔
7	base._init(self)	10✔
8	local typesetter = require("packages.math.typesetter")	10✔
9	self.ConvertMathML, self.handleMath = typesetter[1], typesetter[2]	10✔
10	local texlike = require("packages.math.texlike")	10✔
11	self.convertTexlike, self.compileToMathML = texlike[1], texlike[2]	10✔
12	-- Register a new unit that is 1/18th of the current math font size
13	SILE.registerUnit("mu", {	20✔
14	relative = true,
15	definition = function (value)
16	return value * SILE.settings:get("math.font.size") / 18	1,150✔
17	end,
18	})
19	self:loadPackage("counters")	10✔
20	end
21
22	function package.declareSettings (_)	10✔
23	SILE.settings:declare({	10✔
24	parameter = "math.font.family",
25	type = "string",
26	default = "Libertinus Math",
27	})
28	SILE.settings:declare({	10✔
29	parameter = "math.font.style",
30	type = "string",
31	default = "Regular",
32	})
33	SILE.settings:declare({	10✔
34	parameter = "math.font.weight",
35	type = "integer",
36	default = 400,
37	})
38	SILE.settings:declare({	10✔
39	parameter = "math.font.filename",
40	type = "string",
41	default = "",
42	})
43	SILE.settings:declare({	20✔
44	parameter = "math.font.size",
45	type = "number or integer",
46	default = SILE.settings:get("font.size"),	20✔
47	})
48	SILE.settings:registerHook ("font.size", function (size)	20✔
49	-- Follow document font size changes
NEW 50	SILE.settings:set("math.font.size", size)	×
51	end)
52	-- Whether to show debug boxes around mboxes
53	SILE.settings:declare({	10✔
54	parameter = "math.debug.boxes",
55	type = "boolean",
56	default = false,
57	})
58	SILE.settings:declare({	20✔
59	parameter = "math.displayskip",
60	type = "VGlue",
61	default = SILE.types.node.vglue("2ex plus 1pt"),	20✔
62	})
63	end
64
65	function package:registerCommands ()	10✔
66	self:registerCommand("mathml", function (options, content)	20✔
67	local mbox
68	xpcall(function ()	44✔
69	mbox = self:ConvertMathML(content)	44✔
70	end, function (err)	44✔
UNCOV 71	print(err)	×
UNCOV 72	print(debug.traceback())	×
73	end)
74	self:handleMath(mbox, options)	22✔
75	end)
76
77	self:registerCommand("math", function (options, content)	20✔
78	local mbox
79	xpcall(function ()	80✔
80	mbox = self:ConvertMathML(self:compileToMathML({}, self:convertTexlike(content)))	160✔
81	end, function (err)	80✔
UNCOV 82	print(err)	×
UNCOV 83	print(debug.traceback())	×
84	end)
85	self:handleMath(mbox, options)	40✔
86	end)
87
88	self:registerCommand("math:numberingstyle", function (options, _)	20✔
UNCOV 89	SILE.typesetter:typeset("(")	×
UNCOV 90	if options.counter then	×
UNCOV 91	SILE.call("show-counter", { id = options.counter })	×
UNCOV 92	elseif options.number then	×
93	SILE.typesetter:typeset(options.number)	×
94	end
95	SILE.typesetter:typeset(")")	×
96	end)
97	end
98
99	package.documentation = [[
100	\begin{document}
101	\use[module=packages.math]
102	\set[parameter=math.font.family, value=Libertinus Math]
103	\set[parameter=math.font.size, value=11]
104	% Default verbatim font (Hack) is missing a few math symbols
105	\use[module=packages.font-fallback]
106	\font:add-fallback[family=Symbola]
107	\define[command=paragraph]{\smallskip\em{\process.}\novbreak\par}
108	The \autodoc:package{math} package provides typesetting of formulas directly in a SILE document.
109
110	\autodoc:note{Mathematical typesetting in SILE is still in its infancy.
111	As such, it lacks some features and may contain bugs.
112	Feedback and contributions are always welcome.}
113
114	\noindent To typeset mathematics, you will need an OpenType math font installed on your system.%
115	%\footnote{A list of freely available math fonts can be found at \href[src=https://www.ctan.org/pkg/unicode-math]{https://www.ctan.org/pkg/unicode-math}}
116	By default, this package uses Libertinus Math, so it will fail if Libertinus Math can’t be found.
117	Another font may be specified via the setting \autodoc:setting{math.font.family}.
118	If required, you can set the font style and weight via \autodoc:setting{math.font.style} and \autodoc:setting{math.font.weight}.
119	The font size can be set via \autodoc:setting{math.font.size}.
120
121	\paragraph{MathML}
122	The first way to typeset math formulas is to enter them in the MathML format.
123	MathML is a standard for encoding mathematical notation for the Web and for other types of digital documents.
124	It is supported by a wide range of tools and represents the most promising format for unifying the encoding of mathematical notation, as well as improving its accessibility (e.g., to blind users).
125
126	To render an equation encoded in MathML, simply put it in a \code{mathml} command.
127	For example, the formula \mathml{\mrow{\msup{\mi{a}\mn{2}} \mo{+} \msup{\mi{b}\mn{2}} \mo{=} \msup{\mi{c}\mn{2}}}} was typeset by the following command:
128
129	\begin[type=autodoc:codeblock]{raw}
130	\mathml{
131	\mrow{
132	\msup{\mi{a}\mn{2}}
133	\mo{+}
134	\msup{\mi{b}\mn{2}}
135	\mo{=}
136	\msup{\mi{c}\mn{2}}
137	}
138	}
139	\end{raw}
140
141	\noindent In an XML document, we could use the more classical XML syntax:
142
143	\begin[type=autodoc:codeblock]{raw}
144	<mathml>
145	<mrow>
146	<msup> <mi>a</mi> <mn>2</mn> </msup>
147	<mo>+</mo>
148	<msup> <mi>b</mi> <mn>2</mn> </msup>
149	<mo>=</mo>
150	<msup> <mi>c</mi> <mn>2</mn> </msup>
151	</mrow>
152	</mathml>
153	\end{raw}
154
155	\noindent By default, formulas are integrated into the flow of text.
156	To typeset them on their own line, use the \autodoc:parameter{mode=display} option:
157
158	\mathml[mode=display]{
159	\mrow{
160	\msup{\mi{a}\mn{2}}
161	\mo{+}
162	\msup{\mi{b}\mn{2}}
163	\mo{=}
164	\msup{\mi{c}\mn{2}}
165	}
166	}
167
168	\paragraph{TeX-like syntax}
169	As the previous examples illustrate, MathML is not really intended to be written by humans and quickly becomes very verbose.
170	That is why this package also provides a \code{math} command, which understands a syntax similar to the math syntax of TeX.
171	To typeset the above equation, one only has to type \code{\\math\{a^2 + b^2 = c^2\}}.
172
173	Here is a slightly more involved equation:
174
175	\begin[type=autodoc:codeblock]{raw}
176	\begin[mode=display]{math}
177	\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}
178	\end{math}
179	\end{raw}
180
181	\noindent This renders as:
182
183	\begin[mode=display]{math}
184	\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}
185	\end{math}
186
187	The general philosophy of the TeX-like syntax is to be a simple layer on top of MathML, and not to mimic perfectly the syntax of the LaTeX tool.
188	Its main difference from the SILE syntax is that \code{\\mycommand\{arg1\}\{arg2\}\{arg3\}} is translated into MathML as \code{<mycommand> arg1 arg2 arg3 </mycommand>} whereas in normal SILE syntax, the XML equivalent would be \code{<mycommand>arg1</mycommand> arg2 arg3}.
189
190	\code{\\sum}, \code{\\infty}, and \code{\\pi} are only shorthands for the Unicode characters \math{\sum}, \math{\infty} and \math{\pi}.
191	If it’s more convenient, you can use these Unicode characters directly.
192	The symbol shorthands are the same as in the TeX package \href[src=https://www.ctan.org/pkg/unicode-math]{\code{unicode-math}}.
193
194	\code{\{formula\}} is a shorthand for \code{\\mrow\{formula\}}.
195	Since parentheses—among other glyphs—stretch vertically to the size of their englobing \code{mrow}, this is useful to typeset parentheses of different sizes on the same line:
196
197	\begin[type=autodoc:codeblock]{raw}
198	\Gamma (\frac{\zeta}{2}) + x^2(x+1)
199	\end{raw}
200
201	\noindent renders as
202
203	\begin[mode=display]{math}
204	\Gamma (\frac{\zeta}{2}) + x^2(x+1)
205	\end{math}
206
207	\noindent which is ugly.
208	To keep parentheses around \math{x+1} small, you should put braces around the expression:
209
210	\begin[type=autodoc:codeblock]{raw}
211	\Gamma (\frac{\zeta}{2}) + x^2{(x+1)}
212	\end{raw}
213
214	\begin[mode=display]{math}
215	\Gamma (\frac{\zeta}{2}) + x^2{(x+1)}
216	\end{math}
217
218	\noindent To print a brace in a formula, you need to escape it with a backslash.
219
220	\paragraph{Token kinds}
221	In the \code{math} syntax, every individual letter is an identifier (MathML tag \code{mi}), every number is a… number (tag \code{mn}) and all other characters are operators (tag \code{mo}).
222	If this does not suit you, you can explicitly use the \code{\\mi}, \code{\\mn}, or \code{\\mo} tags.
223	For instance, \code{sin(x)} will be rendered as \math{sin(x)}, because SILE considers the letters s, i and n to be individual identifiers, and identifiers made of one character are italicized by default.
224	To avoid that, you can specify that \math{\mi{sin}} is an identifier by writing \code{\\mi\{sin\}(x)} and get: \math{\mi{sin}(x)}.
225	If you prefer it in “double struck” style, this is permitted by the \code{mathvariant} attribute: \code{\\mi[mathvariant=double-struck]\{sin\}(x)} renders as \math{\mi[mathvariant=double-struck]{sin}(x)}.
226
227	\paragraph{Atom types and spacing}
228	Each token automatically gets assigned an atom type from the list below:
229	\begin{itemize}
230	\item{\code{ord}: \code{mi} and \code{mn} tokens, as well as unclassified operators}
231	\item{\code{big}: big operators like ‘\math{\sum}’ or ‘\math{\prod}’}
232	\item{\code{bin}: binary operators like ‘\math{+}’ or ‘\math{\%}’}
233	\item{\code{rel}: relation operators like ‘\math{=}’ or ‘\math{<}’}
234	\item{\code{open}: opening operators like ‘\math{(}’ or ‘\math{[}’}
235	\item{\code{close}: closing operators like ‘\math{)}’ or ‘\math{]}’}
236	\item{\code{punct}: punctuation operators like ‘\math{,}’}
237	% TODO: Those are defined in the 'math' package but appear to be unused
238	%\item{\code{inner}}
239	%\item{\code{over}}
240	%\item{\code{under}}
241	%\item{\code{accent}}
242	%\item{\code{radical}}
243	%\item{\code{vcenter}}
244	\end{itemize}
245	\noindent The spacing between any two successive tokens is set automatically based on their atom types, and hence may not reflect the actual spacing used in the input.
246	To make an operator behave like it has a certain atom type, you can use the \code{atom} attribute. For example, \code{a \\mo[atom=bin]\{div\} b} renders as \math[mode=display]{a \mo[atom=bin]{div} b.}
247
248	Spaces in math mode are defined in “math units” (mu), which are 1/18 of an em of the current \em{math} font (and are independent of the current text font size).
249	Standard spaces inserted automatically between tokens come in three varieties: thin (3 mu), medium (4 mu) and thick (5 mu).
250	If needed, you can insert them manually with the \code{\\thinspace} (or \code{\\,}), \code{\\medspace} (or \code{\\>}), and \code{\\thickspace} (or \code{\\;}) commands.
251	Negative space counterparts are available as \code{\\negthinspace} (or \code{\\!}), \code{\\negmedspace}, and \code{\\negthickspace}.
252	The \code{\\enspace}, \code{\\quad}, and \code{\\qquad} commands from normal text mode are also available, but the spaces they insert scale relative to the text font size.
253	Finally, you can add a space of any size using the \code{\\mspace[width=<dimension>]} command.
254
255	\paragraph{Macros}
256	To save you some typing, the math syntax lets you define macros with the following syntax:
257
258	\begin[type=autodoc:codeblock]{raw}
259	\def{macro-name}{macro-body}
260	\end{raw}
261
262	\noindent where in the macro’s body \code{#1}, \code{#2}, etc. will be replaced by the macro’s arguments.
263	For instance:
264
265	\begin[type=autodoc:codeblock]{raw}
266	\begin[mode=display]{math}
267	\def{diff}{\mfrac{\mo{d}#1}{\mo{d}#2}}
268	\def{bi}{\mi[mathvariant=bold-italic]{#1}}
269
270	\diff{\bi{p}}{t} = ∑_i \bi{F}_i
271	\end{math}
272	\end{raw}
273
274	\noindent results in:
275
276	\begin[mode=display]{math}
277	\def{diff}{\mfrac{\mo{d}#1}{\mo{d}#2}}
278	\def{bi}{\mi[mathvariant=bold-italic]{#1}}
279	\diff{\bi{p}}{t} = ∑_i \bi{F}_i
280	\end{math}
281
282	When macros are not enough, creating new mathematical elements is quite simple: one only needs to create a new class deriving from \code{mbox} (defined in \code{packages/math/base-elements.lua}) and define the \code{shape} and \code{output} methods.
283	\code{shape} must define the \code{width}, \code{height} and \code{depth} attributes of the element, while \code{output} must draw the actual output.
284	An \code{mbox} may have one or more children (for instance, a fraction has two children—its numerator and denominator).
285	The \code{shape} and \code{output} methods of the children are called automatically.
286
287	\paragraph{Matrices, aligned equations, and other tables}
288	Tabular math can be typeset using the \code{table} command (or equivalently the \code{mtable} MathML tag).
289	For instance, to typeset a matrix:
290
291	\begin[type=autodoc:codeblock]{raw}
292	\begin[mode=display]{math}
293	(
294	\table{
295	1 & 2 & 7 \\
296	0 & 5 & 3 \\
297	8 & 2 & 1 \\
298	}
299	)
300	\end{math}
301	\end{raw}
302
303	\noindent will yield:
304
305	\begin[mode=display]{math}
306	(\table{
307	1 & 2 & 7 \\
308	0 & 5 & 3 \\
309	8 & 2 & 1 \\
310	})
311	\end{math}
312
313	\noindent Tables may also be used to control the alignment of formulas:
314
315	\begin[type=autodoc:codeblock]{raw}
316	\begin[mode=display]{math}
317	\{
318	\table[columnalign=right center left]{
319	u_0 &=& 1 \\
320	u_1 &=& 1 \\
321	u_n &=& u_{n−1} + u_{n−2}, \forall n ⩾ 2 \\
322	}
323	\end{math}
324	\end{raw}
325
326	\begin[mode=display]{math}
327	\{
328	\table[columnalign=right center left]{
329	u_0 &=& 1 \\
330	u_1 &=& 1 \\
331	u_n &=& u_{n−1} + u_{n−2}, \forall n ⩾ 2 \\
332	}
333	\end{math}
334
335	\noindent Tables currently do not support all attributes required by the MathML standard, but they do allow to control spacing using the \code{rowspacing} and \code{columnspacing} options.
336
337	Finally, here is a little secret. This notation:
338
339	\begin[type=autodoc:codeblock]{raw}
340	\table{
341	1 & 2 & 7 \\
342	0 & 5 & 3 \\
343	8 & 2 & 1 \\
344	}
345	\end{raw}
346
347	\noindent is strictly equivalent to this one:
348
349	\begin[type=autodoc:codeblock]{raw}
350	\table{
351	{1} {2} {7}
352	}{
353	{0} {5} {3}
354	}{
355	{8} {2} {1}
356	}
357	}
358	\end{raw}
359
360	\noindent In other words, the notation using \code{&} and \code{\\\\} is only a syntactic sugar for a two-dimensional array constructed with braces.
361
362	\paragraph{Numbered equations}
363	Equations can be numbered in display mode.
364
365	When \autodoc:parameter{numbered=true}, equations are numbered using a default “equation” counter:
366	\math[mode=display, numbered=true]{e^{i\pi} = -1}
367
368	A different counter can be set by using the option \autodoc:parameter{counter=<id>}, and this setting will also enable numbering.
369
370	It is also possible to impose direct numbering using the \autodoc:parameter{number=<value>} option.
371
372	The default numbering format is \autodoc:example{(n)}, but this style may be overridden by defining a custom \autodoc:command{\math:numberingstyle} command.
373	The \code{counter} or the direct value \code{number} is passed as a parameter to this hook, as well as any other options.
374
375	\paragraph{Missing features}
376	This package still lacks support for some mathematical constructs, but hopefully we’ll get there.
377	Among unsupported constructs are: decorating symbols with so-called accents, such as arrows or hats, “over” or “under” braces, and line breaking inside a formula.
378
379	\font:remove-fallback
380	\end{document}
381	]]	10✔
382
383	return package	10✔

sile-typesetter / sile / 11622284370

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