On mixed polynomials of bidegree \((n,1)\). (English) Zbl 1371.68332
Summary: Specifying the bidegrees \((n, m)\) of mixed polynomials \(P(z, \overline{z})\) 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.
MSC:
| 68W30 | Symbolic computation and algebraic computation |
| 12D10 | Polynomials in real and complex fields: location of zeros (algebraic theorems) |
Keywords:
harmonic polynomials; rational functions; fundamental theorem of algebra; complex dynamics; mixed polynomial; computer algebra; interpolation; root isolationSoftware:
MapleReferences:
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