M. Bardet, J. Faugère, and B. Salvy, On the complexity of the F5 Gröbner basis algorithm, 2013.

D. Bernstein, The number of roots of a system of equations, Functional Analysis and Its Applications, vol.30, issue.2, pp.183-185, 1975.
DOI : 10.1007/BF01075595

M. Brickenstein, Slimgb: Gr??bner bases with slim polynomials, Revista Matem??tica Complutense, vol.25, issue.3, pp.453-466, 2010.
DOI : 10.1007/s13163-009-0020-0

M. P. Brodmann and R. Y. Sharp, Local cohomology: an algebraic introduction with geometric applications, 1998.

W. Bruns, J. Gubeladze, and N. V. Trung, Normal polytopes, triangulations, and Koszul algebras, J. fur die reine und angewandte Mathematik, vol.485, pp.123-160, 1997.
DOI : 10.1007/b105283_7

D. A. Cox, J. B. Little, and H. K. Schenck, Toric varieties, 2011.
DOI : 10.1090/gsm/124

C. Eder and J. Faugère, A survey on signature-based Gröbner basis computations. arXiv, 1404.

E. Ehrhart, Sur les polyèdres rationnels homothétiqueshomothétiquesà n dimensions, CR Acad. Sci. Paris, vol.254, pp.616-618, 1962.

D. Eisenbud, Commutative Algebra: with a view toward algebraic geometry, 1995.
DOI : 10.1007/978-1-4612-5350-1

I. Z. Emiris, Toric resultants and applications to geometric modelling, Solving polynomial equations, pp.269-300, 2005.
DOI : 10.1007/3-540-27357-3_7

I. Z. Emiris and V. Y. Pan, Symbolic and Numeric Methods for Exploiting Structure in Constructing Resultant Matrices, Journal of Symbolic Computation, vol.33, issue.4, pp.393-413, 2002.
DOI : 10.1006/jsco.2002.0520

J. Faugère, A new efficient algorithm for computing Gröbner bases without reduction to zero (F5), pp.75-83, 2002.

J. Faugère, P. Gianni, D. Lazard, and T. Mora, Efficient Computation of Zero-dimensional Gr??bner Bases by Change of Ordering, Journal of Symbolic Computation, vol.16, issue.4, pp.329-344, 1993.
DOI : 10.1006/jsco.1993.1051

J. Faugère and S. Rahmany, Solving systems of polynomial equations with symmetries using SAGBI-Gröbner bases, ISSAC '09, pp.151-158, 2009.

J. Faugère, M. Safey-el-din, and P. Spaenlehauer, Gr??bner bases of bihomogeneous ideals generated by polynomials of bidegree <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>: Algorithms and complexity, Journal of Symbolic Computation, vol.46, issue.4, pp.406-437, 2011.
DOI : 10.1016/j.jsc.2010.10.014

R. Fröberg, An inequality for Hilbert series of graded algebras., MATHEMATICA SCANDINAVICA, vol.56, pp.117-144, 1985.
DOI : 10.7146/math.scand.a-12092

W. Fulton, Introduction to Toric Varieties, 1993.
DOI : 10.1515/9781400882526

A. Giovini, T. Mora, G. Niesi, L. Robbiano, and C. Traverso, ???One sugar cube, please??? or selection strategies in the Buchberger algorithm, Proceedings of the 1991 international symposium on Symbolic and algebraic computation , ISSAC '91, pp.49-54, 1991.
DOI : 10.1145/120694.120701

M. Hochster, Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes, The Annals of Mathematics, vol.96, issue.2, pp.318-337, 1972.
DOI : 10.2307/1970791

D. Lazard, Gröbner bases, Gaussian elimination and resolution of systems of algebraic equations, Computer algebra, pp.146-156, 1983.

I. Macdonald, Polynomials associated with finite cell-complexes, J. London Math. Soc, vol.4, pp.181-192, 1971.

E. Miller and B. Sturmfels, Combinatorial commutative algebra, 2005.

T. Oda, Convex bodies and algebraic geometry, 1988.
DOI : 10.1007/978-3-642-72547-0

URL : http://gdz.sub.uni-goettingen.de/download/PPN37915000X/PPN37915000X___LOG_0001.pdf

P. Pedersen and B. Sturmfels, Mixed monomial bases, Algorithms in algebraic geometry and applications, pp.307-316, 1995.
DOI : 10.1007/978-3-0348-9104-2_15

J. Rosales and P. A. Garcia-sanchez, On Cohen-Macaulay and Gorenstein simplicial affine semigroups, Proceedings of the Edinburgh Mathematical Society, pp.517-538, 1998.
DOI : 10.1006/jabr.1996.0178

R. P. Stanley, Decompositions of Rational Convex Polytopes, pp.333-342, 1980.
DOI : 10.1016/S0167-5060(08)70717-9

A. Storjohann, Algorithms for matrix canonical forms, 2000.

B. Sturmfels, Sparse elimination theory, Proc. Comp. Algebraic Geom. and Commut. Algebra, pp.377-396, 1991.

B. Sturmfels, Gröbner bases and convex polytopes, AMS, vol.8, 1996.
DOI : 10.1090/ulect/008

V. V. Williams, Multiplying matrices faster than coppersmith-winograd, Proceedings of the 44th symposium on Theory of Computing, STOC '12, pp.887-898, 2012.
DOI : 10.1145/2213977.2214056

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.297.2680