Last Updated on September 5, 2023
Macaulay 2 is a computer algebra system devoted to supporting research in algebraic geometry, commutative algebra, and their applications.
Macaulay2 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. Macaulay2 can compute Betti numbers, Ext, cohomology of coherent sheaves on projective varieties, primary decomposition of ideals, integral closure of rings, and more.
Macaulay2 uses its own high level programming language, intended to closely match the syntax used by mathematicians in the field.
- Aims to support efficient computation associated with a wide variety of high level mathematical objects, including Galois fields, number fields, polynomial rings, exterior algebras, Weyl algebras, quotient rings, ideals, modules, homomorphisms of rings and modules, graded modules, maps between graded modules, chain complexes, maps between chain complexes, free resolutions, algebraic varieties, and coherent sheaves.
- Simple yet powerful interpreted language. Every object has a type, such as Type, ZZ (integer), String, HashTable, Ring, Matrix, Function, etc. The core mathematical algorithms are written in C++ and compiled, not interpreted.
- Cross-platform support – runs under Linux, Mac OS X, Windows, and FreeBSD.
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