Algorithms for residues and Łojasiewicz exponents
In this paper, the authors use some matrix techniques based on Bezoutian formulations to compute relations of algebraic dependence between \(n+1\) polynomials in \(n\) variables. They also compute bounds for the size of the involved matrices and for the height of their coefficients. Then, they apply these results to develop different algorithms: One for the computation of residues associated to polynomials, another one which decides whether a polynomial map \(f:\mathbb{C}\to\mathbb{C}\) is proper or not, another one to compute the Łojasiewicz exponent of a family of polynomials, and the last one to decide whether a polynomial map \(f:\mathbb{C}\to\mathbb{C}\) is invertible or not and, in case it is, to compute its inverse.
computational aspects of commutative algebra
algebraic dependence between polynomials
scientific article; zbMATH DE number 1526261
scientific article