Complex solutions of polynomial equations and residues

A. DICKENSTEIN

M'Bour

Otro; ? CIMPA School on Méthodes Algorithmiques et Applications en Géométrie Algébrique Réelle et Théorie des Nombres; 2014

CIMPA

1 - Equations, ideals, varieties. Quotient algebras. 2 -Solving systems of polynomial equations with finite solutions via elimination and via eigenvalues. 3 -Solving systems of polynomial equations with finite solutions via resultants. Sparse systems. 4 -Residues in one variable. Duality and Bezoutian, interpolation, ideal membership, partial fraction decomposition, computation of traces and Newton sums. 5 -Multidimensional residues: Integral definition, geometric definition and algebraic definition via Bezoutians. Local and global duality. 6 -Computation of residues, multivariate Euler-Jacobi vanishing theorem, applications. Bibliography: 1.      David Cox, John Little and Don O'Shea: Using Algebraic Geometry. GTM 185, Springer, 2nd edition, 2005. 2.      A.Dickenstein and I.Emiris (eds.): Solving Polynomial Equations: Foundations, Algorithms, and Applications, Springer, 2005. 3.      M. Elkadi and B. Mourrain: Introduction a La Resolution Des Systemes Polynomiaux, Mathématiques & Applications 59, Springer, 2007. 4.      E. Kunz, with the assistance of and contributions by D. A. Cox, and A. Dickenstein: Residues and Duality for Projective Algebraic Varieties,  University Lecture Series, vol. 47, AMS, 2008