I am a research associate at Simon Fraser University and a member of the Computer Algebra Group at the CECM. My primary interests are sparse multivariate polynomials, high performance computing, sparse linear algebra, and solving polynomial systems. I use the Maple computer algebra system.
Michael Monagan and I have written the sdmp library for sparse distributed multivariate polynomial arithmetic. It implements multiplication, exact division, and division with remainder. This release contains the new parallel algorithm for multiplication (x86 only). You can use sdmp:-num_cpus() to set the number of threads and set infolevel[sdmp] := 2; to see time measurements. We are continuing to develop more parallel routines, so keep in mind that this is not the final product.
To use the software you need a copy of Maple 12 or higher. Download sdmp.mpl and the version of libsdmp2.so for your platform below. The worksheet sdmp.mw is a demo that is a little out of date.
June 17th, 2009:
libsdmp2.so for x86-32 Linux
libsdmp2.so for x86-64 Linux
libsdmp2.so for x86/PPC 32/64 bit Mac (universal)
sdmp.mpl
sdmp.mw
Papers:
Parallel Sparse Polynomial Multiplication Using Heaps (ISSAC 2009)
Sparse Polynomial Division Using a Heap (submitted to JSC, updated Fall 2009)
Polynomial Division using Dynamic Arrays, Heaps, and Packed Exponent Vectors (CASC 2007)
Posters:
Parallel Sparse Polynomial Multiplication Using Heaps (ISSAC 2009)
Sparse Polynomial Arithmetic Using Heaps of Pointers (ISSAC 2007)
Talks:
High Performance Computing on the Desktop (CECM Day 2009)
Parallel Sparse Polynomial Multiplication Using Heaps (ISSAC 2009)
Sparse polynomial arithmetic part I: High Performance (MOCAA 2008)
Sparse polynomial arithmetic part II: A proposal to dramatically speed up polynomials in Maple. (MOCAA 2008)
Polynomial Division using Dynamic Arrays, Heaps, and Packed Exponent Vectors (CASC 2007)
Maplesoft Talk, June 2009: slides
I rewrote the Groebner package for Maple 11 to integrate the FGb and RS libraries and add new functionality. Some of the improvements are documented on MaplePrimes here. I would like to thank Juergen Gerhard for all his efforts to help me get this done, and Michael Monagan for putting up with it.
At ISSAC 2006 I presented a paper on Rational Expression Simplification Modulo a Polynomial Ideal. Here are slides from my talk. The algorithms are integrated into Maple 11's `simplify/siderels`.
I was in Linz, Austria at the RICAM Special Semester on Groebner bases. Here are the slides from my talk.
I wrote the PolynomialIdeals package for computing with ideals in commutative polynomial rings, included in Maple 10. It implements prime and primary decomposition, computation of the radical, and automatic Groebner basis conversion via FGLM or the Groebner Walk. I would like to thank the following people for their contributions: Jeff Farr (Groebner Walk, VanishingIdeal), Jennifer DeKline (documentation, testing), Juergen Gerhard (code cleanup and review), and Michael Monagan.
Anyways, feel free to drop me a line.
My email address is rpearcea at cecm dot sfu dot ca