$\begingroup$

Like many other mathematicians I use mathematical software like SAGE, GAP, Polymake, and of course $\LaTeX$ extensively. When I chat with colleagues about such software tools, very often someone has an idea of how to extend an existing tool, what (non-existent) tool would be useful, or which piece of documentation should be (re)written. Due to lack of time & energy and often also programming expertise, these ideas rarely materialize.

On the other hand, every now and then I meet programmers with a strong interest in mathematics (who are often actually trained mathematicians), and who are looking for a software project to work on. However, normally they don't really know what's needed and end up doing a non-mathematical project.

This gave me the idea to ask the mathematical community to compile a wish list for mathematical software. Wishes can be very small or or something bigger. Just try to make sure that it's realistic and maybe also give an explanation why you consider your project as interesting.

And if you happen to be a programmer fulfilling one of the wishes, please leave a comment.

It would be great if you could also include an estimate on how complex your project and what the math/coding ratio is -- but this is optional.

tl;dr What software tool would you like to see created?

What existent software tool would you like to see extended by what feature?

What piece of documentation is missing or should be updated/extended?

One suggestion per answer, please.