On mixed polynomials of bidegree (n, 1)

Mohamed Elkadi (1) , André Galligo (2, 3)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 GALAAD2 - Géométrie , Algèbre, Algorithmes
3 LJAD - Laboratoire Jean Alexandre Dieudonné

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.

Domaines: Géométrie différentielle [math.DG]; Calcul formel [cs.SC]

Mohamed Elkadi, André Galligo. On mixed polynomials of bidegree (n, 1). 2016. ⟨hal-01292822⟩