# Solving systems of algebraic equations

1 CALFOR - Calcul formel
LIP6 - Laboratoire d'Informatique de Paris 6
2 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Let $f1,\dots,fk$ be $k$ multivariate polynomials which have a finite number of common zeros in the algebraic closure of the ground field, counting the common zeros at infinity. An algorithm is given and proved which reduces the computations of these zeros to the resolution of a single univariate equation whose degree is the number of common zeros. This algorithm gives the whole algebraic and geometric structure of the set of zeros (multiplicities, conjugate zeros, hellip;). When all the polynomials have the same degree, the complexity of this algorithm is polynomial relative to the generic number of solutions. Translation by Michael Abramson of the paper Résolution des systèmes d'équations algébriques. Theoretical Computer Sciences, 15 (1981), 77-110.
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Type de document :
Article dans une revue
ACM SIGSAM Bulletin, 2001, 35 (3), pp.11-37. 〈10.1145/569746.569750〉
Domaine :

https://hal.inria.fr/inria-00100674
Contributeur : Publications Loria <>
Soumis le : mardi 26 septembre 2006 - 14:48:52
Dernière modification le : jeudi 11 janvier 2018 - 06:27:20

### Citation

Daniel Lazard. Solving systems of algebraic equations. ACM SIGSAM Bulletin, 2001, 35 (3), pp.11-37. 〈10.1145/569746.569750〉. 〈inria-00100674〉

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