I read alot of good things about sage a while ago - had a quick play with it following a few tutorials online and it seemed like a pretty handy piece of software but I had no real need to use anything apart from MATLAB or Python so I cant give a comprehensive review.

Sage (mathematics software) - Wikipedia, the free encyclopedia

As for a definition of the GNU Multi-Precision Library, I would describe it loosly as an "addin" that you can use in whatever computing language you are working with to support number types where regular interger and double precision numbers are not big/accurate enough etc. It is not a standalone program.

Elbarto