Add equations to the docs

[lockwo]

It would be beneficial to have the basic equations for what the ODE/SDE systems are actually getting converted into in the docs. For example, just put eq 23 of https://homepages.inf.ed.ac.uk/stg/research/stochasticsimulation/papers/JChemPhys_113_297.pdf for the SDE system

[lockwo]

The reaction DSL could perhaps just have the SDE case along with the existing ODE case

[TorkelE]

There is an equation here: https://docs.sciml.ai/Catalyst/dev/introduction_to_catalyst/introduction_to_catalyst/#Chemical-Langevin-equation-(CLE)-stochastic-differential-equation-(SDE)-models, but increasing visibility for stuff like this would probably make sense. We had a plan on also adding a dedicated theory section that goes through stuff like this properly, but wouldn't be certain when that would actually be ready.

Not sure what you mean with

The reaction DSL could perhaps just have the SDE case along with the existing ODE case

[isaacsas]

I think adding a section that complements the rate law section by showing the equations makes sense. We can then link it there and have it as a standalone page. It would be good to both give general formulas and some specific examples there.

[TorkelE]

Agreed. I remember when I read through the literature for my PhD, it was surprisingly hard to find a good resource which simply listed all the various equations derived from CRNs in a straightforward manner. Creating such a resource would probably be beneficial to the community. Also then using it as a link makes loads of sense, yeah, I think that could become very good.

[isaacsas]

It is worth mentioning that we don't exactly in the SDE case generate equation (23), we generate the analogoue of (23) but using the ODE rate laws in place of the propensities. I opened another issue about adding (23) as an option to generate too.

[lockwo]

Thanks for the quick PR!