Gregory V. Bard
Visiting Assistant Professor of Mathematics

My Software

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I am affiliated with the following four software projects:

• SAGE, the open-source competitor to Maple, Matlab, Mathematica and MAGMA. It once stood for System for Algebra and Geometry Experimentation, but the system has become so large that it has outgrown its old name. Basically, it is a computer algebra system that ties together the vast majority of the known open-source tools in mathematics. For example, Singular, GAP, and NTL, are all famous open-source mathematics tools, and come free with SAGE, bundled together. More importantly, SAGE is a common language and interface for tying all these distinct pieces together. There are about 100 SAGE developers, and they form a dynamic, friendly and enjoyable community.
• M4RI. This is a linear algebra suite for dense matrices over GF(2). It has a website of its own, and while I am the founder and creator of the library, my co-author Martin Albrecht has taken over management of it.
• ANFtoCNF. This is an automatic converter, that takes as input a polynomial system of equations over GF(2), and outputs a Conjunctive Normal Form expression (CNF) for use with a SAT-solver. I hope to release a version soon, but this is a solo-project, and therefore slow.
• Plunge and Descender. For the solution of polynomial systems over the real numbers, this system uses Gradient Descent followed by Broyden's Method, while using Newton's Method for "step search." This is joint work with Alex Golec, who did much of the work in the summer between his freshman and sophomore years as an undergraduate research project under my supervision. The version called Plunge works with quadruple-precision arithmetic in the microprocessor, and Descender with MPFR (Multiple Precision Floating Point Reals), which allows for between 53 and 10,000 bits of precision. We hope to release this in early 2009.