For background: I'm working on a book to help mathematicians learn how to program. However, I need to see some examples from people in the field that have done different kinds of things than I have.

Where have you used programming in your career as a mathematician? (If you haven't feel free to say so, though it isn't very helpful)

I've currently used programming in several math-y settings. Computational Biology, Image Processing (Fourier Transforms and other things like that), writing scripts that comply to a certain data restriction or to a library. I've looked at some computational algebraic geometry, but not much as of yet, and I'd use SAGE or sympy if I needed that.