INVESTIGADORES
DICKENSTEIN Alicia Marcela
congresos y reuniones científicas
Título:
Complex solutions of polynomial equations and residues
Autor/es:
A. DICKENSTEIN
Lugar:
M'Bour
Reunión:
Otro; ? CIMPA School on Méthodes Algorithmiques et Applications en Géométrie Algébrique Réelle et Théorie des Nombres; 2014
Institución organizadora:
CIMPA
Resumen:
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