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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,
   })
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 = "integer",
      default = 10,
   })
   -- 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.nodefactory.vglue("2ex plus 1pt"),
   })
end

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

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

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