Description:

Macaulay 2 is a software system devoted to supporting research in algebraic
geometry and commutative algebra, whose creation has been funded by the
National Science Foundation since 1992.
Macaulay 2 includes core algorithms for computing Gröbner bases and graded
or multi-graded free resolutions of modules over quotient rings of graded
or multi-graded polynomial rings with a monomial ordering. The core
algorithms are accessible through a versatile high level interpreted user
language with a powerful debugger supporting the creation of new classes of
mathematical objects and the installation of methods for computing
specifically with them. Macaulay 2 can compute Betti numbers, Ext,
cohomology of coherent sheaves on projective varieties, primary
decomposition of ideals, integral closure of rings, and more.