# Use with @reaction_network from DiffEqBiological.jl.

Latexify.jl has methods for dealing with AbstractReactionNetworks. For more information regarding this DSL, turn to its docs. The latexify end of things are pretty simple: feed a reaction network to latexify() and let it do its magic.

using DiffEqBiological
using Latexify
copy_to_clipboard(true)

@reaction_func hill2(x, v, k) = v*x^2/(k^2 + x^2)

rn = @reaction_network MyRnType begin
hill2(y, v_x, k_x), 0 --> x
p_y, 0 --> y
(d_x, d_y), (x, y) --> 0
(r_b, r_u), x ↔ y
end v_x k_x p_y d_x d_y r_b r_u

latexify(rn)
\begin{align} \frac{dx}{dt} =& \frac{v_{x} \cdot y^{2}}{k_{x}^{2} + y^{2}} - d_{x} \cdot x - r_{b} \cdot x + r_{u} \cdot y \\ \frac{dy}{dt} =& p_{y} - d_{y} \cdot y + r_{b} \cdot x - r_{u} \cdot y \\ \end{align}

The method has a keyword for choosing between outputting the ODE or the noise term. While it is not obvious from the latexify output, the noise in the reaction network is correlated.

latexify(rn; noise=true)
\begin{align} \frac{dx}{dt} =& \sqrt{\frac{v_{x} \cdot y^{2}}{k_{x}^{2} + y^{2}}} - \sqrt{d_{x} \cdot x} - \sqrt{r_{b} \cdot x} + \sqrt{r_{u} \cdot y} \\ \frac{dy}{dt} =& \sqrt{p_{y}} - \sqrt{d_{y} \cdot y} + \sqrt{r_{b} \cdot x} - \sqrt{r_{u} \cdot y} \\ \end{align}

## Chemical arrow notation

DiffEqBiologicals reaction network is all about chemical arrow notation, so why should we not be able to render arrows?

Use latexify's env keyword argument to specify that you want :chemical (or the equivalent :arrow, :arrows or :chem).

latexify(rn; env=:chemical)

\begin{align} \require{mhchem} \ce{ \varnothing &->[\frac{v{x} \cdot y^{2}}{k{x}^{2} + y^{2}}] x}\\ \ce{ \varnothing &->[p{y}] y}\\ \ce{ x &->[d{x}] \varnothing}\\ \ce{ y &->[d{y}] \varnothing}\\ \ce{ x &<=>[{r{b}}][{r_{u}}] y}\\ \end{align}

The default output is meant to be rendered directly on the screen. This rendering is typically done by MathJax. To get the chemical arrow notation to render automatically, I have included a MathJax command (\require{mhchem}) in the output string. If you want to use the output in a real LaTeX document, you can pass the keyword argument mathjax=false and this extra command will be omitted. In such case you should also add \usepackage{mhchem} to the preamble of your latex document.

Another keyword argument that may be of use is expand=false (defaults to true). This determines whether your functions should be expanded or not. Also, starred=true will change the outputted latex environment from align to align*. This results in the equations not being numbered.

latexify(rn; env=:chemical, expand=false, starred=true)
\begin{align*} \require{mhchem} \ce{ \varnothing &->[\mathrm{hill2}\left( y, v_{x}, k_{x} \right)] x}\\ \ce{ \varnothing &->[p_{y}] y}\\ \ce{ x &->[d_{x}] \varnothing}\\ \ce{ y &->[d_{y}] \varnothing}\\ \ce{ x &<=>[{r_{b}}][{r_{u}}] y}\\ \end{align*}