# Roman Pearce

From 2005-2017 I was a research associate and member of the
Computer Algebra Group at the CECM.

Everything here is joint work with Michael Monagan at Simon Fraser University, supported by NSERC and Maplesoft.

### Groebner Bases and Polynomial Systems

mgb
is a C library for computing Groebner bases modulo a prime.

This library has been integrated into Maple and is used by default.

polynomial systems benchmark

### Sparse Distributed Multivariate Polynomials

sdmp is a C library for sparse multivariate polynomial arithmetic.

Our polynomial data structure is now used in Maple by default.

### Publications

An Algorithm For Splitting Polynomial Systems Based on F4 presented at PASCO 2017.

A Compact Parallel Implementation of F4 presented at PASCO 2015

The design of Maple's sum-of-products and POLY data structures for representing mathematical objects in the CCA.

POLY: a new polynomial data structure for Maple 17 demonstrated at ISSAC 2012

Sparse Polynomial Powering Using Heaps presented at CASC 2012

Parallel Sparse Polynomial Division Using Heaps
presented at PASCO 2010

Parallel Sparse Polynomial Multiplication Using Heaps
presented at ISSAC 2009

Sparse Polynomial Division Using a Heap
in the Journal of Symbolic Computation.

Polynomial Division using Dynamic Arrays, Heaps, and Packed Exponent Vectors
presented at CASC 2007.

Rational Expression Simplification Modulo a Polynomial Ideal
presented at ISSAC 2006.

### Features in Maple

Maple 2018: sparse linear systems mod p, faster F4/FGLM

Maple 2017: ?updates,Maple2017,Performance

Maple 2016: Groebner bases,
modp1 speedup

Maple 18: poly improvements, sparse powering

Maple 17: poly data structure and algorithms

Maple 16: parallel division, heap efficiency gains

Maple 15: powering algorithms, Kronecker substitution, Z_{p} multiprecision

Maple 14: sdmp Z/Q

Maple 13:
sdmp Z_{p},
dense linear solver

Maple 12: sparse linear solver over Q

Maple 11: Groebner package,
simplify fractions with side relations

Maple 10: PolynomialIdeals package

Feel free to drop me a line.
My personal email is roman underscore pearce at hotmail dot com.