Details:
Title  Some Applications of Bezoutians in Effective Algebraic Geometry  Author(s)  Mohamed Elkadi, Bernard Mourrain  Type  Technical Report, Misc  Abstract  In this report, we investigate some problems of effectivity, related to algebraic residue theory. We show how matrix techniques based on Bezoutian formulations, enable us to derive new algorithms for these problems, as well as new bounds for the polynomials involved in these computations. More precisely, we focus on the computation of relations of algebraic dependencies between n 1 polynomials in n variables and showhow to deduce the residue of n polynomials in n variables. Applications for testing the properness of a polynomial map, for computing its Lojasiewicz exponent, and for inverting polynomial maps are also considered. We also show how Bezoutian matrices, enable us to compute a nontrivial multiple of the resultant on any irreducible algebraic variety and decompose an algebraic variety into irreducible components.  Keywords  bezoutian matrix, algebraic residue, Lojasiewicz exponent, polynomial equations, resultant  Length  41 
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 Language  English  Number  RR3572  Pages  38 p.  Year  1998  Edition  0  Translation 
No  Refereed 
No 
