Markdown-here does not seem to handle long equations

[GLorieul]

Hi,

To add to what has been reported earlier on a similar subject here, I would like to present here some limitations of Google Charts that have caused me trouble while using Markdown-here v2.12.0 (2015-09-07).

User case

I am writing an e-mail to my PhD supervisors to inform them of a mistake I found in a previous PhD dissertation in numerical methods. For that purpose, an e-mail appears to me as the right medium. Of course because of the nature of the subject, it has to contain equations…

As part of the e-mail I have a small demonstration that is quite "technical" (i.e. a fair bit of calculations).

Problem occurs with Markdown-here + google charts

However, calculations can get quite long and for instance one of the equations that I must write is the following :

$\Delta (u \times v ) = \left\{ \begin{matrix} [ b \, \Delta r + r \, \Delta b + 2 \, \nabla b \cdot \Delta r ] - [ c \, \Delta q + q \, \Delta c + 2 \, \nabla c \cdot \nabla q ] \\ [ c \, \Delta p + p \, \Delta c + 2 \, \nabla c \cdot \Delta p ] - [ a \, \Delta r + r \, \Delta a + 2 \, \nabla a \cdot \nabla r ] \\ [ a \, \Delta q + q \, \Delta a + 2 \, \nabla a \cdot \Delta q ] - [ b \, \Delta p + p \, \Delta b + 2 \, \nabla b \cdot \nabla p ] \end{matrix} \right\}$

Unfortunately this line doesn't render, eventhough it is syntaxly correct… Indeed, it can be compiled by storing it in a *.tex file

\documentclass[10pt, a4paper]{article}
\usepackage{amsmath}

\begin{document}
\[
\Delta (u \times v ) = \left\{ \begin{matrix} [ b \, \Delta r + r \, \Delta b + 2 \, \nabla b \cdot \Delta r ] - [ c \, \Delta q + q \, \Delta c + 2 \, \nabla c \cdot \nabla q ] \\ [ c \, \Delta p + p \, \Delta c + 2 \, \nabla c \cdot \Delta p ] - [ a \, \Delta r + r \, \Delta a + 2 \, \nabla a \cdot \nabla r ] \\ [ a \, \Delta q + q \, \Delta a + 2 \, \nabla a \cdot \Delta q ] - [ b \, \Delta p + p \, \Delta b + 2 \, \nabla b \cdot \nabla p ] \end{matrix} \right\}
\]
\end{document}

and invoking pdflatex on it…

pdflatex main.tex

After having played a little bit with the markdown source, I had the impression that if the line gets too long then markdown-here doesn't render it… Perhaps this is a limitation of google Chart ?

Problem doesn't occur with pandoc + mathjax

Previously, I have generated some *.html documents using pandoc. It uses mathjax instead of Google charts, and rendering the previous equation does not cause any issue at all!

To see it in action, create a doc.md file and fill it with

$$\Delta (u \times v ) = \left\{ \begin{matrix} [ b \, \Delta r + r \, \Delta b + 2 \, \nabla b \cdot \Delta r ] - [ c \, \Delta q + q \, \Delta c + 2 \, \nabla c \cdot \nabla q ] \\ [ c \, \Delta p + p \, \Delta c + 2 \, \nabla c \cdot \Delta p ] - [ a \, \Delta r + r \, \Delta a + 2 \, \nabla a \cdot \nabla r ] \\ [ a \, \Delta q + q \, \Delta a + 2 \, \nabla a \cdot \Delta q ] - [ b \, \Delta p + p \, \Delta b + 2 \, \nabla b \cdot \nabla p ] \end{matrix} \right\}$$

(Pandoc requires two dollar signs '$'). Then, transform it into a *.html file by invoking

pandoc --mathjax --standalone -o doc.md.html doc.md

Eventually open doc.md.html using your favorite web browser.

Also (smaller detail) pandoc + mathjax seems to handles the line breaks better. For instance the following text is a rewrite of the above equation with line breaks so as to make it much more human-readable.

$$
    \Delta (u \times v )
=
    \left\{
    \begin{matrix}
        [ b \, \Delta r + r \, \Delta b + 2 \, \nabla b \cdot \Delta r ]
    -
        [ c \, \Delta q + q \, \Delta c + 2 \, \nabla c \cdot \nabla q ]
    \\
        [ c \, \Delta p + p \, \Delta c + 2 \, \nabla c \cdot \Delta p ]
    -
        [ a \, \Delta r + r \, \Delta a + 2 \, \nabla a \cdot \nabla r ]
    \\
        [ a \, \Delta q + q \, \Delta a + 2 \, \nabla a \cdot \Delta q ]
    -
        [ b \, \Delta p + p \, \Delta b + 2 \, \nabla b \cdot \nabla p ]
    \end{matrix}
    \right\}
$$

It can be parsed properly by mathjax, whereas Google Charts requires '$' to be followed directly by a non-space character which makes the syntax a bit awkward :

$\Delta (u \times v )
=
    \left\{
    \begin{matrix}
        [ b \, \Delta r + r \, \Delta b + 2 \, \nabla b \cdot \Delta r ]
    \\
        c
    \end{matrix}
    \right\}$

When I look at the html source code that has been generated,

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
  <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
  <meta http-equiv="Content-Style-Type" content="text/css" />
  <meta name="generator" content="pandoc" />
  <title></title>
  <style type="text/css">code{white-space: pre;}</style>
  <script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>
</head>
<body>
<p><span class="math display">\[\Delta (u \times v ) = \left\{ \begin{matrix} [ b \, \Delta r + r \, \Delta b + 2 \, \nabla b \cdot \Delta r ] - [ c \, \Delta q + q \, \Delta c + 2 \, \nabla c \cdot \nabla q ] \\ [ c \, \Delta p + p \, \Delta c + 2 \, \nabla c \cdot \Delta p ] - [ a \, \Delta r + r \, \Delta a + 2 \, \nabla a \cdot \nabla r ] \\ [ a \, \Delta q + q \, \Delta a + 2 \, \nabla a \cdot \Delta q ] - [ b \, \Delta p + p \, \Delta b + 2 \, \nabla b \cdot \nabla p ] \end{matrix} \right\}\]</span></p>
</body>
</html>

what pandoc has done is stupidly simple :

1. It added a link to mathjax in the <head> section of the *.html file

   <script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>
   

2. It copied and pasted the Latex source code into a <span> block (and replaced the $$ [...] $$ tag by a \[ [...] \] tag)

   \[ [...] \]

What I did eventually : text + Unicode

Since I could not get Markdown-here to do what I wanted, and since I did not want to write my own html code (or to generate it through pandoc), I sent my e-mail in text form and used unicode to write my equations… For instance the previous line can be writen using unicode as:

         ⎧ [b.Δr + r.Δb + 2.∇b·∇r] - [c.Δq + qΔc + 2.Δc·∇q] ⎫
Δ(u×v) = ⎨ [c.Δp + p.Δc + 2.∇c·∇p] - [a.Δr + rΔa + 2.Δa·∇r] ⎬
         ⎩ [a.Δq + q.Δa + 2.∇a·∇q] - [b.Δp + pΔb + 2.Δb·∇p] ⎭

Summary

It seems Markdown-here cannot handle long formulas (to double-check), probably because Google Charts does not allow it (to double-check).

As you can see, the difficulty I encountered lead me to not use markdown-here at all, and to switch back to the good old text e-mail… Which is a shame because apart from that, I am very happy with your extension so far… (Actually, I love to use it to write minutes of meetings!)

I am not sure what the best solution could be:

1. Keep using Markdown + google charts (i.e. do nothing)
2. Use Markdown + mathjax (i.e. dump google charts) (or Katex?)
3. Or allow the user to select the rendering service he/she would like to use?
4. Some other solution?

Anyway many thanks for your work, that is a very useful extension you have made! ;) (even-though this corner case is causing me trouble…)

Cheers,

Gaël

[GLorieul]

A less extreme case is

$\Delta(a \times b)
~=~
    \Delta a \, \times \, b
~+~
    a \, \times \, \Delta b
+
    2.\sum_i
\left[
    \frac{\partial a_i}{\partial x_i}
\times
    \frac{\partial b_i}{\partial x_i}
\right]$

which can be rendered. This time, it is a fairly short equation. However, add 100 to it and it no longer renders:

$\Delta(a \times b)
~=~
    \Delta a \, \times \, b
~+~
    a \, \times \, \Delta b
+
    2.\sum_i
\left[
    \frac{\partial a_i}{\partial x_i}
\times
    \frac{\partial b_i}{\partial x_i}
\right] + 100$

although it renders if you only add 10 instead of 100…