Gregory V. Bard
Visiting Assistant Professor of Mathematics
My Software
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.