That doesn't mean the math you implement in this software will be easy! But I expect that the programming itself won't prove to be much of an obstacle.
I definitely recommend you learn one or more of these languages -- but not necessarily to the scale where you're writing large and complicated programs. I use PARI/GP, a software package similar to Sage which is well suited for number theory in particular -- and my particular use case is a 40-to-150 line program that carries out some particular computation I'm interested in. Usually it will just be simple functions, array manipulations, for loops, computations, library calls -- programming at the level you'd master by the end of an intro CS course.