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November 12, 2009
Thursday, November 12
Colloquium
Time: 15:30
Speaker: Stephen M. Watt (Western)
Title: "Algorithms for symbolic polynomials"
Room: MC 108

Abstract: We wish to compute with polynomials where the exponents are not known in advance. Expressions of this sort arise frequently in practice, for example in the analysis of algorithms, and it is difficult to work with them effectively in current computer algebra systems. There are various simple operations we must be able to perform, such as squaring x2n1 to get x4n2x2n+1, or differentiating to get 2nx2n1. Other operations are less obvious.

We consider the case where multivariate polynomials can have exponents that are themselves integer-valued multivariate polynomials. We call these objects "symbolic polynomials" and show they form a unique factorization domain, naturally related to the polynomial ring. We present algorithms to compute their GCD, factorization and functional decomposition.