Macaulay computer algebra system
Encyclopedia
Macaulay is a computer algebra system
for doing polynomial
computations, particularly Gröbner basis
calculations. Macaulay is designed for solving problems in commutative algebra
and algebraic geometry
.
It is named after F.S. Macaulay
, who worked in elimination theory
.
Macaulay was developed by Dave Bayer
and Mike Stillman and was later completely rewritten by Dan Grayson and Mike Stillman as Macaulay2
.
Computer algebra system
A computer algebra system is a software program that facilitates symbolic mathematics. The core functionality of a CAS is manipulation of mathematical expressions in symbolic form.-Symbolic manipulations:...
for doing polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
computations, particularly Gröbner basis
Gröbner basis
In computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating subset of an ideal I in a polynomial ring R...
calculations. Macaulay is designed for solving problems in commutative algebra
Commutative algebra
Commutative algebra is the branch of abstract algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra...
and algebraic geometry
Algebraic geometry
Algebraic geometry is a branch of mathematics which combines techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry. It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex...
.
It is named after F.S. Macaulay
Francis Sowerby Macaulay
Francis Sowerby Macaulay FRS was an English mathematician who made significant contributions to algebraic geometry. He is most famous for his 1916 book, The Algebraic Theory of Modular Systems, which greatly influenced the later course of algebraic geometry...
, who worked in elimination theory
Elimination theory
In commutative algebra and algebraic geometry, elimination theory is the classical name for algorithmic approaches to eliminating between polynomials of several variables....
.
Macaulay was developed by Dave Bayer
Dave Bayer
Dave Bayer is an American mathematician. He is currently a professor of mathematics at Barnard College, Columbia University. He was math consultant for the film A Beautiful Mind, and also acted in it as one of the "Pen Ceremony" professors. He is also one of few people to have both an Erdős number...
and Mike Stillman and was later completely rewritten by Dan Grayson and Mike Stillman as Macaulay2
Macaulay2
Macaulay2 is a free computer algebra system developed by Daniel Grayson and Michael Stillman 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...
.