Mathematical Expressions
Mathematical expressions
General
Metanorma AsciiDoc accepts mathematical input in these formats:
-
AsciiMath
-
LaTeX math
-
MathML
Math can be entered using one of the following mechanisms:
-
the
stem:[…],asciimath:[…]and thelatexmath:[…]commands; and -
the
[stem],[asciimath],[latexmath]blocks delimited with++
The math syntax used by stem:[…] and [stem] blocks depends on
the value of the document attribute :stem:. It can be set to:
:stem: latexmath-
any markup within
stemis interpreted as LaTeX math :stem: asciimath-
any markup within
stemis interpreted as AsciiMath :stem:-
(default) when left empty, AsciiMath is selected
stem:[…] and [stem] markup that contains MathML markup
(as detected by an initial <math … >) is interpreted as MathML.
MathML is used as the internal representation of STEM expressions in Metanorma.
Using AsciiMath
AsciiMath can be entered using the asciimath:[…] command and the
[asciimath] block delimited with ++.
The stem:[] and [stem] blocks can also be used if the document attribute
:stem: asciimath has been specified in the document.
AsciiMath is converted into MathML using the plurimath gem.
The syntax of AsciiMath recognized by plurimath can be more strict
than the common MathJax processor of AsciiMath.
The derivative of a distribution stem:[D] is another distribution
stem:[D'] defined for any function stem:[f](stem:[x]) by
stem:[D^( ' ) ( f ) = - D ( d f // d x )].[stem]
++++
f -= lambda x (a * x + b)
++++|
Warning
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Some math expressions are NOT supported by AsciiMath. In that case it is necessary to use LaTeX math or MathML input. |
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Warning
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Encoding brackets inside stem:[]
When we encode inline math expressions that contain brackets we have have to make sure of two things:
As an example, suppose we want to encode this inline expression: \$[x_n,y_n]\$. |
Using LaTeX math
LaTeX math can be entered using the latexmath:[…] command and the
[latexmath] block delimited with ++.
The stem:[] and [stem] blocks can also be used if the document attribute
:stem: latexmath has been specified in the document.
LaTeX math is converted into MathML using Plurimath.
|
Note
|
LaTeX math generated is compliant with the deterministic output of the NIST LaTeXML suite. |
|
Note
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Previously Metanorma used the latexmath gem, which is now superseded by Plurimath. |
|
Note
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Previously, Unicode characters in the LaTeX source were translated into LaTeX escapes through the unicode2latex gem. This is superseded by Plurimath. |
The only change from the above example would be the
nondimensionalization of viscosity, which would become,
latexmath:[\tilde{\tilde{\mu}} = mu / (rho_infty c_infty L)].[latexmath]
++++
\begin{array}{c@{\qquad}c@{\qquad}c}
\tilde{x} = x/L, \tilde{u} = u/c_\infty, \tilde{\rho} = \rho/\rho_\infty,
\tilde{y} = y/L, \tilde{v} = v/c_\infty, \tilde{p} = p/(\rho_\infty c_\infty^2),
\tilde{z} = z/L, \tilde{w} = w/c_\infty, \tilde{\mu} = \mu/\mu_\infty,
\end{array}
++++The LaTeX math eqnarray environment is not supported in Metanorma as
it is not supported by LaTeXML and the latexmath gem.
It is also not recommended by the general
LaTeX community due to inconsistencies in vertical alignment and other aspects
(see Madsen).
The proper LaTeX math syntax used to replace existing eqnarray
equations is to place the equations in separate blocks concatenated
with +.
eqnarray in Metanorma with separate equationsThese equations using the eqnarray environment:
[latexmath]
++++
\begin{eqnarray*}
\bf{z^\prime} & = & \bf{\zeta} \\
\bf{x^\prime} & = & \langle \bf{\eta} \times \bf{\zeta} \rangle
\end{eqnarray*}
++++should be re-arranged as:
[latexmath]
++++
\bf{z^\prime} = \bf{\zeta}
++++
+
[latexmath]
++++
\bf{x^\prime} = \langle \bf{\eta} \times \bf{\zeta} \rangle
++++Formulae
General
Formulae are marked up as [stem] blocks.
Equations
In most flavours, equations and inequalities are both referenced in the same way, as “Formula”.
In some flavours (e.g. ITU), they are referenced differently as “Equations” and “Inequalities”.
Inequalities
Inequalities are indicated through the option attribute %inequality:
[stem%inequality]
++++
{formula-content}
++++Where:
-
{formula-content}is content within a formula.
[stem%inequality]
++++
A < B
++++renders as:
Key
Explanation of symbols used in the formula is specified in a "key" list, which is
specified as a definition list with the [%key]
option [added in https://github.com/metanorma/metanorma-standoc/releases/tag/v1.6.3].
The syntax is as follows:
[stem]
s++++
{some-formula}
++++
[%key]
stem:[{some-symbol}]:: {symbol-description}Where:
-
{some-formula}represents content within a formula -
{some-symbol}represents a symbol within the formula -
{symbol-description}is text that describes information about the symbol
stem) block[stem]
++++
w = (m_D) / (m_s)
++++
[%key]
stem:[w]:: is the mass fraction of grains with a particular defect in the test sample;
stem:[m_D]:: is the mass, in grams, of grains with that defect;
stem:[m_S]:: is the mass, in grams, of the test sample.renders as:
Instead of [%key], the definition list can also be preceded with a paragraph
containing the English word where, though this is not recommended practice.
stem) block using the where keyword[stem]
++++
w = (m_D) / (m_s)
++++
where
stem:[w]:: is the mass fraction of grains with a particular defect in the test sample;
stem:[m_D]:: is the mass, in grams, of grains with that defect;
stem:[m_S]:: is the mass, in grams, of the test sample.