Gruppentheoretische Konstruktion von symmetrischen Kubaturformeln

Abstract: "G-invariant cubature formulas for numerical integration over n-dimensional, G-invariant integration regions are computed symbolically. The nodes are the common zeros of some d-orthogonal polynomials which build an H-basis of an ideal. Approaches for these polynomials depending on parameters are made with the help of the theory of linear representations of a group G. This theory is also used for the effective computation of necessary conditions which determines the parameters. Another approach uses invariant theory and gröbner bases."