SAGE: Software for Algebra and Geometry Experimentation

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The investigator and his colleagues are creating wide-ranging open source mathematical software to support research in cryptography, number theory, algebra, geometry, and numerical computation. They are sutdying distributed computation with complicated algebraic objects in heterogenous networks, exact linear algebra, computation with elliptic curves, highly optimized polynomial arithmetic, and protocols for communication between mathematical software systems.This project involves creating open source mathematical software that plays a key roll in research in cryptography, number theory, geometry, and other area. It promotes the progress of science by making many highly optimized research-oriented algorithms widely available, and making it easy to simultaneously create and work with objects defined in almost any mathematical software package. This project also stimulates new forms of collaboration between researchers in diverse areas of mathematics, and between undegraduates, graduate students, and professors.