Zeros, multiplicities, and idempotents for zero-dimensional systems, In Algorithms in Algebraic Geometry and Applications, pp.1-15, 1996. ,
Degeneracy loci and polynomial equation solving, Foundations of Computational Mathematics, vol.15, issue.1, pp.159-184, 2015. ,
Generalized polar varieties and an efficient real elimination, Kybernetika, vol.40, issue.5, pp.519-550, 2004. ,
Generalized polar varieties: Geometry and algorithms, Journal of Complexity, vol.21, issue.4, pp.377-412, 2005. ,
Lower and upper bounds for the number of lattice points in a simplex, SIAM Journal on Applied Mathematics, vol.22, issue.1, pp.106-108, 1972. ,
The number of roots of a system of equations, Funkcional. Anal. i Prilo?en, vol.9, issue.3, pp.1-4, 1975. ,
Polynomial equation solving by lifting procedures for ramified fibers, Theoretical Computer Science, vol.315, issue.2-3, pp.335-369, 2004. ,
Using Algebraic Geometry, vol.185, 2006. ,
Commutative Algebra: with a View Toward Algebraic Geometry, Graduate Texts in Mathematics, 1995. ,
Computing critical points for invariant algebraic systems, 2020. ,
Computing loci of rank defects of linear matrices using Gröbner bases and applications to cryptology, Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, pp.257-264, 2010. ,
Critical points and Gröbner bases: the unmixed case, Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, pp.162-169, 2012. ,
Algebraic solution of systems of polynomial equations using Groebner bases, AAECC, vol.356, pp.247-257, 1989. ,
Straight-line programs in geometric elimination theory, J. of Pure and Applied Algebra, vol.124, pp.101-146, 1998. ,
When polynomial equation systems can be solved fast, AAECC-11, vol.948, pp.205-231, 1995. ,
A Gröbner-free alternative for polynomial system solving, Journal of Complexity, vol.17, issue.1, pp.154-211, 2001. ,
Solving determinantal systems using homotopy techniques, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-01719170
Intersection theory and deformation algorithms: the multi-homogeneous case, 2002. ,
Deformation techniques for efficient polynomial equation solving, Journal of Complexity, vol.16, issue.1, pp.70-109, 2000. ,
Computing isolated roots of sparse polynomial systems in affine space, Theoretical Computer Science, vol.411, issue.44, pp.3894-3904, 2010. ,
Affine solution sets of sparse polynomial systems, Journal of Symbolic Computation, vol.51, pp.34-54, 2013. ,
Elimination for generic sparse polynomial systems, Discrete and Computational Geometry, vol.51, issue.3, pp.578-599, 2014. ,
A polyhedral method for solving sparse polynomial systems, Mathematics of Computation, vol.64, issue.212, pp.1541-1555, 1995. ,
A global weighted version of Bézout's theorem. The Arnoldfest, vol.24, pp.115-129, 1997. ,
Deformation techniques for sparse systems, Foundations of Computational Mathematics, vol.9, issue.1, pp.1-50, 2009. ,
Grundzüge einer arithmetischen Theorie der algebraischen Grössen, vol.92, pp.1-122, 1882. ,
The Algebraic Theory of Modular Systems, 1916. ,
Solving zero-dimensional systems through the Rational Univariate Representation. Applicable Algebra in Engineering, vol.9, pp.433-461, 1999. ,
URL : https://hal.archives-ouvertes.fr/inria-00073264
El Din andÉ. Schost. A nearly optimal algorithm for deciding connectivity queries in smooth and bounded real algebraic sets, Journal of ACM, vol.63, issue.6, pp.1-48, 2017. ,
Bit complexity for multi-homogeneous polynomial system solving -application to polynomial minimization, Journal of Symbolic Computation, vol.87, pp.176-206, 2018. ,
Critical point computations on smooth varieties: degree and complexity bounds, Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, pp.183-190, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01312750
On the complexity of computing critical points with Gröbner bases, SIAM Journal on Optimization, vol.24, issue.3, pp.1382-1401, 2014. ,
An upper estimate on integral points in real simplices with an application in singularity theory, Mathematical Research Letters, vol.6, pp.911-921, 2006. ,