Output-sensitive algorithms for sumset and sparse polynomial multiplication, Proc. ACM ISSAC, pp.29-36, 2015. ,
Bilinear systems with two supports: Koszul resultant matrices, eigenvalues, and eigenvectors, Proc. of Int'l Symposium on Symbolic and Algebraic Computation (ISSAC'18), pp.63-70, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01787549
Tellegen's principle into practice, Proc. ISSAC, pp.37-44, 2003. ,
Fast algorithms for zero-dimensional polynomial systems using duality, Communication and Computing, vol.14, issue.4, pp.239-272, 2003. ,
URL : https://hal.archives-ouvertes.fr/inria-00072296
Improved algorithms for solving bivariate systems via Rational Univariate Representations, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01114767
Some algebraic and geometric computations in PSPACE, Proc. 20th STOC, pp.460-467, 1988. ,
, J. Canny. Generalised characteristic polynomials. JSC, vol.9, issue.3, pp.241-250, 1990.
Solving systems of nonlinear polynomial equations faster, Proc. ACM ISSAC, pp.121-128, 1989. ,
, Tate resolutions for Segre embeddings. Algebra & Number Theory, vol.2, pp.523-550, 2008.
Sharp estimates for triangular sets, Proc. ACM ISSAC, pp.103-110, 2004. ,
Explicit formulas for the multivariate resultant, J. Pure and Applied Algebra, vol.164, issue.1-2, pp.59-86, 2001. ,
Computing sparse projection operators, Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering, vol.286, pp.121-140, 2001. ,
Multihomogeneous resultant formulae by means of complexes, JSC, vol.36, issue.3, pp.317-342, 2003. ,
Resultants and chow forms via exterior syzygies, Journal of the American Mathematical Society, vol.16, issue.3, pp.537-579, 2003. ,
Multihomogeneous resultant formulae for systems with scaled support, JSC, vol.47, issue.7, pp.820-842, 2012. ,
On the bit complexity of solving bilinear polynomial systems, Proc. of Int'l Symposium on Symbolic and Algebraic Computation (ISSAC'16), pp.215-222, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01401134
Separation bounds for polynomial systems, INRIA, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01105276
The DMM bound: Multivariate (aggregate) separation bounds, Proc. ACM ISSAC, pp.243-250, 2010. ,
URL : https://hal.archives-ouvertes.fr/inria-00393833
Symbolic and Numeric Methods for Exploiting Structure in Constructing Resultant Matrices, JSC, vol.33, issue.4, pp.393-413, 2002. ,
Improved algorithms for computing determinants and resultants, J. of Complexity, vol.21, issue.1, pp.43-71, 2005. ,
Root counts of semi-mixed systems, and an application to counting Nash equilibria, Proc. ACM ISSAC, pp.154-161, 2014. ,
Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree (1, 1): Algorithms and complexity, JSC, vol.46, issue.4, pp.406-437, 2011. ,
Cryptanalysis of minrank, Advances in Cryptology, pp.280-296, 2008. ,
Gröbner bases of bihomogeneous ideals generated by polynomials of bidegree (1,1): Algorithms and complexity, JSC, vol.46, pp.406-437, 2011. ,
Discriminants, Resultants and Multidimensional Determinants, Birkhäuser, 1994. ,
La détermination des points isolés et de la dimension d'une variété algébrique peut se faire en temps polynomial, Proc. Int. Meeting on Commutative Algebra, 1993. ,
A Gröbner free alternative for polynomial system solving, J. of Complexity, vol.17, issue.1, pp.154-211, 2001. ,
Algebraic Geometry, 1977. ,
Accuracy and stability of numerical algorithms, Society for Industrial and Applied Mathematics, 2002. ,
On the bit-complexity of sparse polynomial multiplication, JSC, vol.50, pp.227-254, 2013. ,
URL : https://hal.archives-ouvertes.fr/hal-00476223
Computing multihomogeneous resultants using straight-line programs, JSC, vol.42, issue.1-2, pp.218-235, 2007. ,
A new index calculus algorithm with complexity L(1/4 + o(1)) in small characteristic, Selected Areas in Cryptography-SAC 2013, pp.355-379, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-02177225
On the complexity of computing determinants, Computational Complexity, vol.13, issue.3-4, pp.91-130, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-02102099
Supersparse black box rational function interpolation, Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation, ISSAC '11, pp.177-186, 2011. ,
Deflation and certified isolation of singular zeros of polynomial systems, Proc. ACM ISSAC, pp.249-256, 2011. ,
URL : https://hal.archives-ouvertes.fr/inria-00556021
Singular zeros of polynomial systems, Advances in Shapes, Geometry, and Algebra, vol.10, pp.77-103, 2014. ,
URL : https://hal.archives-ouvertes.fr/inria-00556021
Sparse rational univariate representation, Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '17, pp.301-308, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01528377
On the resultant of a system of forms homogeneous in each of several sets of variables, Trans. AMS, vol.35, issue.1, pp.215-233, 1933. ,
A softly optimal monte carlo algorithm for solving bivariate polynomial systems over the integers, J. of Complexity, vol.34, pp.78-128, 2016. ,
The resultant of a set of lineo-linear equations, Proc. Royal Soc. of South Africa, vol.2, issue.1, pp.373-380, 1910. ,
New technique for decoding codes in the rank metric and its cryptography applications. Problems of Information Transmission, vol.38, pp.237-246, 2002. ,
Univariate polynomials: Nearly optimal algorithms for numerical factorization and root-finding, JSC, vol.33, issue.5, pp.701-733, 2002. ,
Accelerated approximation of the complex roots and factors of a univariate polynomial, Theoretical Computer Science, vol.681, pp.138-145, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01105267
Nearly optimal computations with structured matrices, Theoretical Computer Science, vol.681, pp.117-137, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01105263
Solving zero-dimensional systems through the rational univariate representation, Applicable Algebra in Engineering, vol.9, issue.5, pp.433-461, 1999. ,
URL : https://hal.archives-ouvertes.fr/inria-00098872
Polar varieties and computation of one point in each connected component of a smooth real algebraic set, Proc. ACM ISSAC, pp.224-231, 2003. ,
Bit complexity for multi-homogeneous polynomial system solving -application to polynomial minimization, Journal of Symbolic Computation, vol.87, pp.176-206, 2018. ,
Solving multi-homogeneous and determinantal systems: algorithms, complexity, applications. Thesis, 2012. ,
URL : https://hal.archives-ouvertes.fr/tel-01110756
Multigraded resultants of Sylvester type, J. Algebra, vol.163, issue.1, pp.115-127, 1994. ,
On the degree and weight of the resultant of a multipartite system of equations, Proc. Royal Soc. of London, vol.12, pp.674-676, 1862. ,
Modern computer algebra, 2013. ,
Calculating discriminants by higher direct images, Trans. of AMS, vol.343, issue.1, pp.367-389, 1994. ,
Cohomology of Vector Bundles and Syzygies, 2003. ,
Determinantal formulas for multigraded resultants, J. Alg. Geom, vol.3, issue.4, pp.569-597, 1994. ,
Fundamental problems of algorithmic algebra, 2000. ,