Name
SageMath (aka. SAGE)
Description
It is a free and open-source mathematics software meant to be a viable free alternative to Mathematica, Maple and Matlab. It covers a wide range of mathematical fields, from basic algebra to advanced multi-disciplinary areas such as differential geometry.
It can run in the terminal or through a format-rich notebook style interface in your browser. It's reasonably fast and its being used by both professors, students and researchers.
Source
The developers offer a dev stable PPA at ppa:aims/sagemath (see, http://www.sagemath.org/download-linux.html)
Architectures
x86 and amd64 are supported.
Rationale
It's an excellent addition to the always important Education section of Boutique and it covers a topic still missing. It's a full blown mathematical package with an impressive array of high quality features that only loses to the commercial alternatives on the matter of performance.
It's under constant and active development and has replaced many commercial mathematical software on schools and universities and at home by hobbyist and researchers alike. Well documented and based on sound and established technologies, such as python, and renown mathematical libraries in C and C++, conferring the software with an healthy dose of stability and mathematical accuracy.