Using Sage to Support Research Mathematics

When using Sage to support research mathematics, the most important point to make is to strongly encourage people to do the extra work to turn their "scruffy research code" into a patch that can be peer reviewed and included in Sage. They will have to 100% doctest it, and the quality of their code may improve dramatically as a result. Including code in Sage means that the code will continue to work as Sage is updated. Also, the code is peer reviewed and has to have examples and documentation for every function. That's a much higher bar than just "reproducible research".

Moreover, getting code up to snuff to include in Sage will often also reveal mistakes that will avoid embarrassment later. I'm fixing some issues related to a soon-to-be-done paper right now that I found when doing just this for trac 11975.

This final step of turning snippets of research code into a peer-reviewed contribution to Sage is: (1) a surprisingly huge amount of very important useful work, (2) something that is emphasized as an option for Sage more than with Magma or Mathematica or Pari (say), (3) something whose value people have to be sold on, since they get no real extra academic credit for it, at present, usually, and journal referees often don't care either way (I do, but I'm probably in the minority there), and (4) something that a *lot* of research mathematicians do not do. As an example of (4), in the last two months I've seen a ton of (separate!) bodies of code which is all sort of secret research code in various Dropbox repos, and which isn't currently squarely aimed at going into Sage. I've also seen a bunch of code related to Edixhoven et al.'s algorithm for computing Galois representation with a similar property (there is now trac 12132, due to my
urging).

I did *not* do this step yet with this recently accepted paper. Instead I used "scrappy research code" in psage to do the fast L-series computations. The referee for Math Comp didn't care either way, actually... I hope this doesn't come back to haunt me, though there are many double checks here (e.g., BSD) so I'm not too worried. I will do this get-it-in-Sage step at some point though.

This will be better for the community in the long run, and better for individual researcher's credibility too. And there is a lot of value in having a stable refereed snapshot of code on which a published (=very stable) paper is based.