TITLE: Computer Programs for Pure Mathematicians
QUESTION [15 upvotes]: Question: Which computer programs are useful for a pure mathematician to familiarize themselves with?
Less Briefly: I was once told that, now-a-days, any new mathematician worth his beans knows how to TeX up work; when I began my graduate work one of the fourth year students told me he couldn't TeX, I was horrified!  Similarly, a number of my peers were horrified when I told them I'd never used Matlab or Mathematica before.  Currently, I can "get by" in all three of these programs, but it made me think: what programs are popular with pure mathematicians?  I don't mean to limit this to computing things: programs which help to draw pictures and things can also be included.
Lest I Start A Flame War: This is not meant to be a "what is your favorite computer language" question or a poll on who thinks Mathematica is worse than Sage.  This is meant to be a survey on what programs and resources are currently being used by pure mathematicians and may be good to look at and read up on.  
I'm also unsure of how to tag this.

REPLY [2 votes]: GAP (http://www.gap-system.org), which is, as it is written on the GAP website, an open source "system for computational discrete algebra, with particular emphasis on Computational Group Theory. GAP provides a programming language, a library of thousands of functions implementing algebraic algorithms written in the GAP language as well as large data libraries of algebraic objects. GAP is used in research and teaching for studying groups and their representations, rings, vector spaces, algebras, combinatorial structures, and more."
The core GAP system is redistributed with its GAP Packages, which extend further the functionality of the system and improve its performance. Some packages include binaries and require separate compilation.
To obtain GAP, go to Downloads . Windows users may use .exe installer with precompiled binaries. Unix and OS X users would have to compile GAP and packages.