Sparse polynomial powering using heaps

Authors:
Michael Monagan;Roman Pearce
Affiliations:
Department of Mathematics, Simon Fraser University, Burnaby, B.C., Canada;Department of Mathematics, Simon Fraser University, Burnaby, B.C., Canada
Venue:
CASC'12 Proceedings of the 14th international conference on Computer Algebra in Scientific Computing
Year:
2012

Citing 9
Cited 0

Parallel multiplication and powering of polynomials

Journal of Symbolic Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms

The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Sparse polynomial arithmetic

ACM SIGSAM Bulletin
Efficient polynomial substitutions of a sparse argument

ACM SIGSAM Bulletin
Parallel sparse polynomial multiplication using heaps

Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Computation of powers of multivariate polynomialsover the integers

Journal of Computer and System Sciences
Parallel sparse polynomial division using heaps

Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Sparse polynomial division using a heap

Journal of Symbolic Computation
Polynomial division using dynamic arrays, heaps, and packed exponent vectors

CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

We modify an old algorithm for expanding powers of dense polynomials to make it work for sparse polynomials, by using a heap to sort monomials. It has better complexity and lower space requirements than other sparse powering algorithms for dense polynomials. We show how to parallelize the method, and compare its performance on a series of benchmark problems to other methods and the Magma, Maple and Singular computer algebra systems.