Computational Aspects in Spaces of Bivariate Polynomial of w-Degree n

Multivariate ideal interpolation schemes are deeply connected with H-bases. Both the definition of a H-basis and of an ideal interpolation space depend of the notion of degree used in the grading decomposition of the polynomial spaces. We studied, in the case of bivariate polynomials, a generalized degree, introduced by T. Sauer and named w-degree. This article give some theoretical results that allow us to construct algorithms for calculus of the dimension of the homogeneous spaces of bivariate polynomials of w – degree n. We implemented these algorithms in C++ language. The analysis of the results obtained, leads us to another theoretical conjecture which we proved in the end.