Abstract

New algorithms for determining discrete and continuous symmetries of polynomials --- also known as binary forms in classical invariant theory --- are presented. Implementations in Mathematica and Maple are discussed and compared. The results are based on a new, comprehensive theory of moving frames that completely characterizes the equivalence and symmetry properties of submanifolds under general Lie group actions. This work was partially supported by NSF Grant DMS 98--03154. 1 Introduction. The purpose of this paper is to explain the detailed implementation of a new algorithm for determining the symmetries of polynomials (binary forms). The method was first described in the second author's new book [24], and the present paper adds details and refinements. We shall demonstrate that the symmetry group of both real and complex binary forms can be completely determined by solving two simultaneous bivariate polynomial equations, which are based on two fundamental covariants of the for...

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