Hans Petter Langtangen, Simula Research Laboratory and University of Oslo
Date: May 25, 2016
Summary. The purpose of this document is to test LaTeX math in DocOnce with various output formats. Most LaTeX math constructions are renedered correctly by MathJax in plain HTML, but some combinations of constructions may fail. Unfortunately, only a subset of what works in html MathJax also works in sphinx MathJax. The same is true for markdown MathJax expresions (e.g., Jupyter notebooks). Tests and examples are provided to illustrate what may go wrong.
The recommendation for writing math that translates to MathJax in
html, sphinx, and markdown is to stick to the environments
\[ ... \], equation, equation*, align, align*, alignat,
and alignat* only. Test the math with sphinx output; if it works in that
format, it should work elsewhere too.
The current version of the document is translated from DocOnce source to the format ipynb.
Test 1: Inline math. We can get an inline equation
$u(t)=e^{-at}$ rendered as $u(t)=e^{-at}$.
Test 2: A single equation with label. An equation with number,
!bt
\begin{equation} u(t)=e^{-at} \label{eq1a}\end{equation}
!etlooks like
Maybe this multi-line version is what we actually prefer to write:
!bt
\begin{equation}
u(t)=e^{-at}
\label{eq1b}
\end{equation}
!etThe result is the same:
We can refer to this equation through its label eq1b: (2).
Test 3: Multiple, aligned equations without label and number. MathJax has
historically had some problems with rendering many LaTeX math environments,
but the align* and align environments have always worked.
!bt
\begin{align*}
u(t)&=e^{-at}\\
v(t) - 1 &= \frac{du}{dt}
\end{align*}
!etResult:
Test 4: Multiple, aligned equations with label. Here, we
use align with user-prescribed labels:
!bt
\begin{align}
u(t)&=e^{-at}
\label{eq2b}\\
v(t) - 1 &= \frac{du}{dt}
\label{eq3b}
\end{align}
!etResult:
We can refer to the last equations as the system (3)-(4).
Test 5: Multiple, aligned equations without label. In LaTeX,
equations within an align environment is automatically given numbers.
To ensure that an html document with MathJax gets the same equation numbers
as its latex/pdflatex companion, DocOnce generates labels in equations where
there is no label prescribed. For example,
!bt
\begin{align}
u(t)&=e^{-at}
\\
v(t) - 1 &= \frac{du}{dt}
\end{align}
!etis edited to something like
!bt
\begin{align}
u(t)&=e^{-at}
\label{_auto5}\\
v(t) - 1 &= \frac{du}{dt}
\label{_auto6}
\end{align}
!etand the html output gets the two equation numbered.
Test 6: Multiple, aligned equations with multiple alignments.
The align environment can be used with two & alignment characters, e.g.,
!bt
\begin{align}
\frac{\partial u}{\partial t} &= \nabla^2 u, & x\in (0,L),
\ t\in (0,T]\\
u(0,t) &= u_0(x), & x\in [0,L]
\end{align}
!etThe result in ipynb becomes
A better solution is usually to use an alignat environment:
!bt
\begin{alignat}{2}
\frac{\partial u}{\partial t} &= \nabla^2 u, & x\in (0,L),
\ t\in (0,T]\\
u(0,t) &= u_0(x), & x\in [0,L]
\end{alignat}
!etwith the rendered result
align/alignat environments with equation numbers are anti-aligned!
In the sphinx, ipynb, and pandoc output formats, DocOnce rewrites
the equations in an alignat environment as individual equations in
equation environments (or more precisely, sphinx can work with
alignat* so only numbered alignat equations get rewritten as individual
equations). If the alignment is somewhat important, try the best with a
manual rewrite in terms of separate equation environments, and stick to
align* and alignat* in sphinx.
If DocOnce had not do rewritten of the above equations, they would be rendered in ipynb as
$$ \begin{equation} \frac{\partial u}{\partial t} = \nabla^2 u, x\in (0,L), \ t\in (0,T] \end{equation} !et
Test 7: Multiple, aligned eqnarray equations without label. Let us
try the old eqnarray* environment.
!bc latexcod
!bt
\begin{eqnarray*}
u(t)&=& e^{-at}\\
v(t) - 1 &=& \frac{du}{dt}
\end{eqnarray*}
!et
!ec
which results in
!bt
\begin{eqnarray*}
u(t)&=& e^{-at}\\
v(t) - 1 &=& \frac{du}{dt}
\end{eqnarray*}
$$
Test 8: Multiple, eqnarrayed equations with label.
Here we use eqnarray with labels:
!bt
\begin{eqnarray*}
u(t)&=& e^{-at}\\
v(t) - 1 &=& \frac{du}{dt}
\end{eqnarray*}
!etwhich results in
!bt
\begin{eqnarray}
u(t)&=& e^{-at}
\label{eq2c}\\
v(t) - 1 &=& \frac{du}{dt}
\label{eq3c}
\end{eqnarray}
!etgets rendered as
and we can hopefully refer to the Trapezoidal rule as the formula (14).
Test 10: Splitting equations using a split environment.
Although align can be used to split too long equations, a more obvious
command is split:
!bt
\begin{multline}
\int_a^b f(x)dx = \sum_{j=0}^{n} \frac{1}{2} h(f(a+jh) +
f(a+(j+1)h)) \\
=\frac{h}{2}f(a) + \frac{h}{2}f(b) + \sum_{j=1}^n f(a+jh)
\label{multiline:eq1}
\end{multline}
!etThe result becomes
Test 11: Newcommands and boldface bm vs pmb. First we use the plain old pmb package for bold math. The formula
!bt
\begin{equation}
\begin{split}
\int_a^b f(x)dx = \sum_{j=0}^{n} \frac{1}{2} h(f(a+jh) +
f(a+(j+1)h)) \\
=\frac{h}{2}f(a) + \frac{h}{2}f(b) + \sum_{j=1}^n f(a+jh)
\end{split}
\end{equation}
!etand the inline expression $\nabla\pmb{u} (\pmb{x})\cdot\pmb{n}$
(with suitable newcommands using pmb)
get rendered as
and $\nabla\pmb{u} (\pmb{x})\cdot\pmb{n}$.
Somewhat nicer fonts may appear with the more modern \bm command:
!bt
\[ \frac{\partial\u}{\partial t} +
\u\cdot\nabla\u = \nu\nabla^2\u -
\frac{1}{\varrho}\nabla p,\]
!et(backslash ubm is a newcommand for bold math $u$), for which we get
Moreover,
!bt
\[ \frac{\partial\ubm}{\partial t} +
\ubm\cdot\nabla\ubm = \nu\nabla^2\ubm -
\frac{1}{\varrho}\nabla p,\]
!etbecomes $\nabla\boldsymbol{u}(\boldsymbol{x})\cdot\boldsymbol{n}$.
Warning.
Note: for the ipynb format, \bm was substituted by DocOnce
to \boldsymbol.
Problematic equations. Finally, we collect some problematic formulas in MathJax. They all work fine in LaTeX.
$\nabla\boldsymbol{u}(\boldsymbol{x})\cdot\boldsymbol{n}$results in
but correct rendering in sphinx requires omitting the \color command.
Sometimes one must be extra careful with the LaTeX syntax to get sphinx MathJax to render a formula correctly. Consider the combination of a bar over a bold math symbol:
!bt
\[ {\color{blue}\frac{\partial\u}{\partial t}} +
\nabla\cdot\nabla\u = \nu\nabla^2\u -
\frac{1}{\varrho}\nabla p,\]
!etwhich for ipynb output results in
With sphinx, this formula is not rendered. However, using curly braces for the bar,
!bt
\[ \bar\f = f_c^{-1}\f,\]
!etmakes the output correct also for sphinx:
Matrix Environment. Nested environments with labled pmatrix environments cause wired representation in ipynb and html.
!bt
\[ \bar{\f} = f_c^{-1}\f,\]
!etwhich becomes
The same matrices without labels seem to translate better:
!bt
\begin{align}
\begin{pmatrix}
G_2 + G_3 & -G_3 & -G_2 & 0 \\
-G_3 & G_3 + G_4 & 0 & -G_4 \\
-G_2 & 0 & G_1 + G_2 & 0 \\
0 & -G_4 & 0 & G_4
\end{pmatrix}
&=
\begin{pmatrix}
v_1 \\
v_2 \\
v_3 \\
v_4
\end{pmatrix}
+ \cdots \\
\begin{pmatrix}
C_5 + C_6 & -C_6 & 0 & 0 \\
-C_6 & C_6 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 0 & 0
\end{pmatrix}
\frac{d}{dt} &=
\begin{pmatrix}
v_1 \\
v_2 \\
v_3 \\
v_4
\end{pmatrix} =
\begin{pmatrix}
0 \\
0 \\
0 \\
-i_0
\end{pmatrix}
\end{align}
!etwhich becomes