# Math derivations with collapsibles

How to export mathematical derivations to html using org-mode , with collapsibles to help organizing the content.

Working as a physisict, I often write technical documentation outlining a mathematical derivation. For this purpose, LaTeX is the standard language. With LaTeX, one can create high-quality documents with beautiful typography and it includes support for practically any mathematical notation you could want.

The challenge with writing down a mathematical derivation is the various levels of abstraction that are involved. If I write out all the little details of how to do each step in the derivation, the resulting document becomes very long and basically impossible to navigate. If on the other hand I just show the most important equations of the derivation, it becomes easier to read and follow the overall structure of the derivation, but very difficult to redo the derivation, since all the little details are missing. Ideally I want both, to include all the little details, but also be able to hide them, in order to get an overview of the derivation as a whole.

The problem is that the standard way of using LaTeX is to first write source code in a .tex file, then compile it to .pdf format. For writing scientic papers or a thesis, the static pdf format is quite well suited. But for my own derivations where I wanted to be able to hide details away, but still have them close at hand, I needed something more dynamic.

I thought for a while about what would be a suitable alternative to pdf, until finally I realized the humble internet browser had just the features I was looking for. I remembered seeing wikipedia articles, where one could click a button to show and hide parts of a mathematical derivation. So I started looking into how I could make similar collapsible derivations in html.

## org-mode

As an avid user of the emacs editor, I found that org-mode seemed to fit what I was looking for. Instead of writing files directly in the .tex format, I would write in the .org format (a kind of markup), and then export that to either .tex or to .html. When editing a file in org-mode, any section or block can be collapsed to more easily navgiate the file. Org-mode even came with builtin support for LaTeX rendering in the .html output using the web based LaTeX renderer MathJax .

Next I wanted to add collapsible structures to my .html output. The theme I was using for the html export was based on Bootstrap, so combining the example in the bootstrap documentation and this org-mode guide I added the following to my ~/.emacs file

(require 'org)

(defun collapsible-template-start (id type post)
"""Template for inserting beginning of collapsible html element."""
(concat "<p>
<a data-toggle=\"collapse\" href=\"#collapsible-" id "\" role=\"button\" aria-expanded=\"false\" aria-controls=\"collapseExample\">
Show " type "
</a>
</p>
<div class=\"collapse\" id=\"collapsible-" id "\">
<div class=\"card card-body\"> " post ))

(defvar collapsible-template-end "      </div>
</div>
")

(defun my/filter-collapsible (text backend info)
"Make Collapsible element."
(pcase backend
(html
(when (string-match-p (regexp-quote "collapsible") text)
(concat (collapsible-template-start (org-id-new) "derivation" "") text collapsible-template-end)
)
)
)
)

#'my/filter-collapsible)


This elisp code wraps any block that contains the word “collapsible” in html div’s that makes the block collapsible, and adds a clickable link with the text Show derivation before the block. Note that since a unique id is required for the link to know which collapsible element to work on, I used the org-id-new function to generate a random id.

To use this, I can add a block like the following to my .org file

#+begin_collapsible
Schrödinger's equation
\begin{align*}
i \frac{d}{dt}\Psi = H\Psi
\end{align*}
#+end_collapsible


Upon export it should look like this (click the link to expand the collapsible, click again to collapse it)

Schrödinger’s equation

\begin{align*} i \frac{d}{dt}\Psi = H\Psi \end{align*}

It is also possible to nest collapsibles. A little care must be taken, since org is not happy about nesting the same type of block. At each nesting level some different superscript should be added to each block, like below.

#+begin_collapsible
Schrödinger's time dependent equation
\begin{align*}
i \frac{d}{dt}\Psi = H\Psi
\end{align*}
#+begin_collapsible1
Schrödinger's time independent equation
\begin{align*}
H\Psi & = E\Psi
\end{align*}
#+end_collapsible1
#+end_collapsible


Which when exported will look like

Schrödinger’s equation

\begin{align*} i \frac{d}{dt}\Psi = H\Psi \end{align*}

Schrödinger’s time independent equation

\begin{align*} H\Psi & = E\Psi \end{align*}

## Hugo

Recently I started building my website using the static site generator Hugo . Using the ox-hugo exporter, I can export org files to Hugo-compatible markdown. For me this provided a really nice workflow, where I would use ox-hugo’s auto export mode to automatically export my org file on every file save, then have Hugo’s livereload automatically update a preview of the finished webpage. So now, everytime I save my org file, I can almost instantly see the effect on the rendered homepage, whereas before I had to run the export command in emacs, and then shift to and refresh the browser.

Instead of exporting the html directly as in the above solution1, I decided to write a shortcode for this purpose. First I added the following to my ~/.emacs file

(require 'org)

(defun my/filter-collapsible-replacer-shortcode (id type post)
(concat "{{< collapsible-split/start id=c" id " type=" type " divclass=\"card card-body\" >}}"  post ))

(defun my/filter-collapsible-hugo (text backend info)
"Make Collapsibles."
(pcase backend
(hugo
(when (string-match-p (regexp-quote "collapsible") text)
(concat (my/filter-collapsible-replacer-shortcode (org-id-new) "derivation" "") text "{{< collapsible-split/end >}}")
)
)
)
)

#'my/filter-collapsible-hugo)


Next, I added the following to a file in [hugo-site-root]/layouts/shortcodes/collapsible-split/start.html

<p>
<a class="collapsed" data-toggle="collapse" href="#collapsible-{{ .Get "id" }}" role="button" aria-expanded="false" aria-controls="collapseExample">
Show {{ .Get "type" }}
</a>
</p>
<div class="collapse mathjax_ignore" id="collapsible-{{ .Get "id" }}">
<div{{ if .Get "divclass" }} class="{{ .Get "divclass" }} collapsible"{{ else }}{{ end }}>


And in [hugo-site-root]/layouts/shortcodes/collapsible-split/end.html I added

  </div>
</div>


I split the collapsible shortcode in two parts to make it work for nested collapsibles. If I use something like {{< .Inner | markdownify >}} or {{< .Inner >}} in a paired shortcode, then either any shortcode inside would not be rendered or any markdown inside would not be rendered.

1. The original solution would also have been complicated by html in markdown files does not get exported unless you set the goldmark unsafe option to true. ↩︎

##### Jens Svensmark
###### Data Scientist

I’m a Data Scientist with a background in physics.