Mathematical Sciences: A Software System for Algebraic Geometry Research

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This award supports the development of a computer software system enabling large scale research computing projects dealing with systems of polynomial equations in many variables. The result of the project will be a usable and efficient computer program, which executes the Groebner basis algorithm for computing standard bases and syzygies of ideals and modules over polynomial rings. Improvements over the existing program, Macaulay, will include the addition of a good programming language for the user, the ability to work over more general coefficients rings, and increased speed of execution. This project is in the general area of commutative algebra and the computer-aided computational aspects of this field. There is a growing interest in using computers to answer theoretical questions in algebra and conversely, algebra is quite useful for the development of algorithms. This project makes serious use of both the theory and practice of symbolic calculations to solve real problems in commutative algebra.