Macaulay2 is a free computer algebra system developed by Daniel Grayson (UIUC) and Michael Stillman (Cornell) for computation in commutative algebra and algebraic geometry. Stillman, along with Dave Bayer had authored the predecessor, Macaulay. Macaulay2 uses its own high level programming language, intended to closely match the syntax used by mathematicians in the field. Both are published under the GNU General Public License version 2.
In a 2006 interview, Andrei Okounkov cited Macaulay2 along with TeX as a successful open source project used in mathematics and suggested that funding agencies look into and learn from these examples.
Macaulay2 can use emacs GNU TeXmacs.