Collaborative Research: A Software System for Research in Algebraic Geometry, Commutative Algebra, and their Applications

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With the advent of widely available fast computing, computational experiments have become more important in every branch of science and mathematics. Macaulay2 is a software system that leads in facilitating the use of symbolic and symbolic-numeric computation in multidisciplinary investigations. The computations it can perform have uses in many fields of mathematics, computer science, and natural sciences. The research under this project extends the computational methods built into Macaulay2. The project will promote collaborations between Macaulay2 developers from the research community, on the one hand, and applied scientists and pure mathematicians, on the other. This project provides research training opportunities for students.Macaulay2 is an open-source computer algebra system dedicated to solving systems of polynomial equations in many variables as well as computing and processing data that describe the underlying geometry of the solution sets. The three major aspects of this proposal are: research on core mathematical topics and applications outside mathematics; the maintenance and development of Macaulay2 as part of the infrastructure of research; and the development of manpower through training, conferences and collaborations, especially involving young researchers. The impact outside mathematics includes investigating problems from physics, biology, computer vision, and other areas where nonlinear algebra is a key ingredient. The project will maintain and develop Macaulay2 as a major tool for research, especially by improving the core algorithms for Groebner bases and free resolutions and by improving its facilities that combine symbolic and numerical computation.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.