M. Bardet, J. Faugère, and B. Salvy, On the complexity of the F5 GrÃ?b-ner basis algorithm, J. Symbolic Comput, vol.70, pp.49-70, 2015.

M. R. Bender, J. Faugère, and E. Tsigaridas, Towards Mixed Gröbner Basis Algorithms: The Multihomogeneous and Sparse Case, Proc. ACM ISSAC, pp.71-78, 2018.

N. Botbol and M. Chardin, Castelnuovo Mumford regularity with respect to multigraded ideals, Journal of Algebra, vol.474, pp.361-392, 2017.

J. Canny and I. Emiris, An e cient algorithm for the sparse mixed resultant, Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, pp.89-104, 1993.

M. Chardin, Bounds for Castelnuovo-Mumford Regularity in Terms of Degrees of De ning Equations, Commutative Algebra, pp.67-73, 2003.

D. Cifuentes and P. Parrilo, Exploiting Chordal Structure in Polynomial Ideals: A Gröbner Bases Approach, SIAM J. Discr. Math, vol.30, pp.1534-1570, 2016.

D. A. Cox, J. Little, and D. O'shea, Using Algebraic Geometry, 2005.

D. A. Cox, J. B. Little, and H. K. Schenck, , 2011.

C. Eder and J. Faugère, A survey on signature-based algorithms for computing Gröbner bases, J. Symbolic Comput, vol.80, pp.719-784, 2017.

D. Eisenbud, Commutative Algebra: with a View Toward Algebraic Geometry, 2004.

I. Z. Emiris, On the Complexity of Sparse Elimination, Journal of Complexity, vol.12, pp.134-166, 1996.

I. Z. Emiris and B. Mourrain, Computer Algebra Methods for Studying and Computing Molecular Conformations, Algorithmica, vol.25, issue.2, pp.372-402, 1999.

J. C. Faugère, A New E cient Algorithm for Computing Gröbner Bases Without Reduction to Zero (F5), Proc. ACM ISSAC (ISSAC '02), pp.75-83, 2002.

J. C. Faugère, P. Gianni, D. Lazard, and T. Mora, E cient Computation of Zero-dimensional GrÃ?bner Bases by Change of Ordering, J. Symbolic Comput, vol.16, issue.4, pp.329-344, 1993.

J. Faugère, P. Spaenlehauer, and J. Svartz, Sparse Gröbner bases: the unmixed case, Proc. ACM ISSAC, pp.178-185, 2014.

J. Faugã?re, P. Gaudry, L. Huot, and G. Renault, Polynomial Systems Solving by Fast Linear Algebra, 2013.

I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, Resultants, and Multidimensional Determinants, 1994.

R. Gilmer, Commutative Semigroup Rings, 1984.

J. Heintz and J. Morgenstern, On the Intrinsic Complexity of Elimination Theory, Journal of Complexity, vol.9, pp.471-498, 1993.
URL : https://hal.archives-ouvertes.fr/inria-00074751

M. I. Herrero, G. Jeronimo, and J. Sabia, A ne solution sets of sparse polynomial systems, J. Symbolic Comput, vol.51, pp.34-54, 2013.

B. Huber and B. Sturmfels, A polyhedral method for solving sparse polynomial systems, Math. Comp, vol.64, pp.1541-1555, 1995.

D. Lazard, GrÃ?bner-Bases, Gaussian Elimination and Resolution of Systems of Algebraic Equations, Proc. of the European Computer Algebra Conference (EUROCAL '83), pp.146-156, 1983.

D. Maclagan and G. G. Smith, Multigraded Castelnuovo-Mumford Regularity, J. Reine Angew. Math. (Crelles Journal, p.571, 2004.

C. Massri, Solving a sparse system using linear algebra, J. Symbolic Comput, vol.73, pp.157-174, 2016.

E. W. Mayr, Some Complexity Results for Polynomial Ideals, Journal of Complexity, vol.13, pp.303-325, 1997.

E. Miller and B. Sturmfels, Combinatorial Commutative Algebra, 2005.

C. Mou and Y. Bai, On the Chordality of Polynomial Sets in Triangular Decomposition in Top-Down Style, Proc. ACM ISSAC, pp.287-294, 2018.

J. M. Rojas, Solving degenerate sparse polynomial systems faster, J. Symbolic Comput, vol.28, pp.155-186, 1999.

M. Sombra, A Sparse E ective Nullstellensatz, Advances in Applied Mathematics, vol.22, pp.271-295, 1999.

B. Sturmfels, Sparse elimination theory, Proc. Comp. Algebraic Geom. and Commut. Algebra. CUP, pp.264-298, 1993.

B. Sturmfels, On the Newton polytope of the resultant, Journal of Algebraic Combinatorics, vol.3, pp.207-236, 1994.

B. Sturmfels, GrÃ?bner Bases and Convex Polytopes, 1996.

B. Sturmfels, Solving systems of polynomial equations. Number 97, 2002.

A. Szanto, Solving over-determined systems by the subresultant method (with an appendix by Marc Chardin), J. Symbolic Comput, vol.43, pp.46-74, 2008.

S. Telen, B. Mourrain, and M. Van-barel, Solving Polynomial Systems via a Stabilized Representation of Quotient Algebras, SIAM J. Matrix Anal. Appl, vol.39, issue.3, pp.1421-1447, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01630425

J. Verschelde, P. Verlinden, and R. Cools, Homotopies Exploiting Newton Polytopes for Solving Sparse Polynomial Systems, SIAM J. Numer. Anal, vol.31, issue.3, pp.915-930, 1994.

J. Weyman and A. Zelevinsky, Multigraded formulae for multigraded resultants, J. Algebr. Geom, vol.3, pp.569-597, 1994.