Michael Monagan
Roman Pearce
Abstract
We employ two techniques to dramatically improve Maple's performance on the Fermat benchmarks for simplifying rational expressions. First, we factor expanded polynomials to ensure that gcds are identified and cancelled automatically. Second, we replace all expanded polynomials by new variables and normalize the result. To undo the substitutions, we use a C routine for sparse multivariate division by a set of polynomials. The resulting times for the first Fermat benchmark are a factor of 17x faster than Fermat and 39x faster than Magma.
- M. Monagan, R. Pearce. Polynomial Division Using Dynamic Arrays, Heaps, and Packed Exponent Vectors. Proc. of CASC 2007, Springer LNCS 4770, 295--315. Google Scholar
Digital Library
- M. Monagan, R. Pearce. Sparse Polynomial Division Using a Heap. Journal of Symbolic Computation, 46 (7), 807--922, 2011. Google ScholarDigital Library
- R. Lewis, P. Stiller. Solving the recognition problem for six lines using the Dixon resultant. Mathematics and Computers in Simulation, 49 205--219, 1999. Google ScholarDigital Library
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