How various formats can deal with LaTeX math¶
| Authors: | Hans Petter Langtangen |
|---|---|
| Date: | May 29, 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 sphinx.
Test of equation environments¶
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}
!et
looks like
Maybe this multi-line version is what we actually prefer to write:
!bt
\begin{equation}
u(t)=e^{-at}
label{eq1b}
\end{equation}
!et
The 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*}
!et
Result:
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}
!et
Result:
We can refer to the last equations as the system (3)-(4).
Note: align/alignat environments with labels are anti-aligned in sphinx
Actually, sphinx does not support the align environment with labels, such as we write above, but DocOnce splits in this case the equations into separate, single equations with labels. Hence the user can write one code with align and labels and have it automatically to work in latex, html, sphinx, notebooks, and other formats. The generated sphinx code in the present case is
.. math::
:label: eq2b
u(t)=e^{-at}
.. math::
:label: eq3b
v(t) - 1 = \frac{du}{dt}
If DocOnce had not rewritten the equation it would be rendered in
sphinx as nicely aligned equations without numbers (i.e., as if
we had used the align* environment):
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}
!et
is edited to something like
!bt
\begin{align}
u(t)&=e^{-at}
label{_auto5}\\
v(t) - 1 &= \frac{du}{dt}
label{_auto6}
\end{align}
!et
and the output gets the two equation numbered.
Note that in sphinx the alignment is removed and separate equation
environments are used to get numbered equations in equation systems, cf. the
box above.
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}
!et
The result in sphinx becomes
In sphinx, all alignments are removed, so this double use of &
results in ugly typesetting!
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}
!et
with 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.
With alignat* in sphinx, the equations above are typeset nicely as
Note that if DocOnce had not rewritten of the above equations, they would be rendered similarly in sphinx as
That is, the equation numbers are gone.
Test 7: Multiple, aligned eqnarray equations without label¶
Let us try the old eqnarray* environment.
!bt
\begin{eqnarray*}
u(t)&=& e^{-at}\\
v(t) - 1 &=& \frac{du}{dt}
\end{eqnarray*}
!et
which results in
Test 8: Multiple, eqnarrayed equations with label¶
Here we use eqnarray with labels:
!bt
\begin{eqnarray}
u(t)&=& e^{-at}
label{eq2c}\\
v(t) - 1 &=& \frac{du}{dt}
label{eq3c}
\end{eqnarray}
!et
which results in
Can we refer to the last equations as the system (?)-(?)
in the sphinx format?
No, unfortunately not. Sphinx cannot deal with equation numbers in
eqnarray environments and typeset them as if they were eqnarray*.
But MathJax supports eqnarray with labels.
The rule of thumb is to use align and not eqnarray!
Test 9: The multiline environment with label and number¶
The LaTeX code
!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}
!et
gets rendered as
and we can hopefully refer to the Trapezoidal rule as the formula (11).
This equation will not render in sphinx unless we remove the multiline
environment, which means that it was typeset here without any multiline
information.
The best cross-format solution is to use align instead of multiline
with \nonumber in the first equation!
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{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}
!et
The result becomes
Test 11: Newcommands and boldface bm vs pmb¶
First we use the plain old pmb package for bold math. The formula
!bt
\[ \frac{\partial\u}{\partial t} +
\u\cdot\nabla\u = \nu\nabla^2\u -
\frac{1}{\varrho}\nabla p,\]
!et
and the inline expression $\nabla\pmb{u} (\pmb{x})\cdot\pmb{n}$
(with suitable newcommands using pmb)
get rendered as
and \(\nabla\pmb{u} (\pmb{x})\cdot\pmb{n}\). DocOnce replaces newcommands by the actual latex code when requesting the sphinx output format.
Somewhat nicer fonts may appear with the more modern \bm command:
!bt
\[ \frac{\partial\ubm}{\partial t} +
\ubm\cdot\nabla\ubm = \nu\nabla^2\ubm -
\frac{1}{\varrho}\nabla p,\]
!et
(backslash ubm is a newcommand for bold math \(u\)), for which we get
Moreover,
$\nabla\boldsymbol{u}(\boldsymbol{x})\cdot\boldsymbol{n}$
becomes \(\nabla\boldsymbol{u}(\boldsymbol{x})\cdot\boldsymbol{n}\).
Warning
Note: for the sphinx format, \bm was substituted by DocOnce
to \boldsymbol.
Problematic equations¶
Finally, we collect some problematic formulas in MathJax. They all work fine in LaTeX. Most of them look fine in html too, but some fail in sphinx, ipynb, or markdown.
Colored terms in equations¶
The LaTeX code
!bt
\[ {\color{blue}\frac{\partial\u}{\partial t}} +
\nabla\cdot\nabla\u = \nu\nabla^2\u -
\frac{1}{\varrho}\nabla p,\]
!et
results in
but correct rendering in sphinx requires omitting the \color command:
Bar over symbols¶
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
\[ \bar\f = f_c^{-1}\f,\]
!et
which for sphinx output results in
With sphinx, this formula is not rendered. However, using curly braces for the bar,
!bt
\[ \bar{\f} = f_c^{-1}\f,\]
!et
makes the output correct also for sphinx:
Matrix formulas¶
Here is an align environment with a label and the pmatrix
environment for matrices and vectors in LaTeX.
!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
label{mymatrixeq}\\
\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}
!et
which becomes
The same matrices without labels in an align* environment:
!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*}
!et
The rendered result becomes
