Sparse polynomial arithmetic


Sparse polynomial representations are used in a number of algebraic manipulation systems, including Altran. This paper discusses the arithmetic operations with sparsely represented polynomials; we give particular attention to multiplication and division. We give new algorithms for multiplying two polynomials, with <i>n</i> and <i>m</i> terms, in time <i>mn</i>log<i>m</i>;, these algorithms have the property that, in the usual univariate dense case, the algorithm is bounded by <i>mn.</i> Division algorithms are discussed which run in comparable time.

DOI: 10.1145/1086837.1086847


Citations per Year

53 Citations

Semantic Scholar estimates that this publication has 53 citations based on the available data.

See our FAQ for additional information.

Cite this paper

@article{Johnson1974SparsePA, title={Sparse polynomial arithmetic}, author={Stephen C. Johnson}, journal={ACM SIGSAM Bulletin}, year={1974}, volume={8}, pages={63-71} }