On mixed polynomials of bidegree (n,1)

• Published in: Theoretical computer science Vol. 681; pp. 41 - 53
• Main Authors: Elkadi, Mohamed, Galligo, André
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 12.06.2017
• Subjects: Complex dynamics; Computer algebra; Harmonic polynomials and rational functions; Interpolation; Mixed polynomial; Root isolation; The fundamental theorem of algebra; Interpolation; Root isolation; The fundamental theorem of algebra; Complex dynamics; Mixed polynomial; Computer algebra; Harmonic polynomials and rational functions
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2017.03.027

Specifying the bidegrees (n,m) of mixed polynomials P(z,z¯) of the single complex variable z, with complex coefficients, allows to investigate interesting roots structures and counting; intermediate between complex and real algebra. Multivariate mixed polynomials appeared in recent papers dealing with Milnor fibrations, but in this paper we focus on the univariate case and m=1, which is closely related to the important subject of harmonic maps. Here we adapt, to this setting, two algorithms of computer algebra: Vandermonde interpolation and a bissection-exclusion method for root isolation. Implemented in Maple, they are used to explore some interesting classes of examples.