M. Aguiar, C. André, C. Benedetti, N. Bergeron, Z. Chen et al., Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras, Advances in Mathematics, vol.229, issue.4, pp.2310-2337, 2012.
DOI : 10.1016/j.aim.2011.12.024
URL : https://hal.archives-ouvertes.fr/hal-00787493

F. Apery and J. Jouanolou, Elimination: le cas d'une variable. Collection Methodes, 2006.

S. Arora, L. Babai, J. Stern, and Z. Sweedyk, The Hardness of Approximate Optima in Lattices, Codes, and Systems of Linear Equations, Journal of Computer and System Sciences, vol.54, issue.2, pp.317-331, 1997.
DOI : 10.1006/jcss.1997.1472

R. Barakat, Characteristic polynomials of chemical graphs via symmetric function theory, Theoretica Chimica Acta, vol.6, issue.1, pp.35-39, 1986.
DOI : 10.1007/BF00526290

M. Bellare, S. Goldwasser, C. Lund, and A. Russell, Efficient probabilistically checkable proofs and applications to approximations, Proceedings of the twenty-fifth annual ACM symposium on Theory of computing , STOC '93, pp.294-304, 1993.
DOI : 10.1145/167088.167174

O. Benoist, Degré d'homogénéité de l'ensemble des interactions complexes singulieres . Annales de l'Institut Fourier, pp.1189-1214, 2012.

M. Berger, Geometry I, 1987.
DOI : 10.1007/978-3-540-93815-6

D. N. 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

F. Bihan, J. M. Rojas, and C. E. Stella, Faster real feasibility via circuit discriminants, Proceedings of the 2009 international symposium on Symbolic and algebraic computation, ISSAC '09, pp.39-46, 2009.
DOI : 10.1145/1576702.1576711

J. Bosman, A polynomial with galois group sl 2 (F 16 ), 2007.

K. Bringmann, A Near-Linear Pseudopolynomial Time Algorithm for Subset Sum, Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pp.1073-1084, 2017.
DOI : 10.1137/1.9781611974782.69
URL : http://arxiv.org/abs/1610.04712

L. Busé and J. Jouanolou, A computational approach to the discriminant of homogeneous polynomials, 2012.

L. Busé and J. Jouanolou, On the Discriminant Scheme of Homogeneous Polynomials, Mathematics in Computer Science, vol.41, issue.2, pp.175-234, 2014.
DOI : 10.1080/00927870802104410

L. Busé and A. Karasoulou, Resultant of an equivariant polynomial system with respect to the symmetric group, Journal of Symbolic Computation, vol.76, pp.142-157, 2016.
DOI : 10.1016/j.jsc.2015.12.004

J. F. Canny, The complexity of robot motion planning. M.I, 1988.

J. F. Canny and I. Z. Emiris, Efficient incremental algorithms for the sparse resultant and the mixed volume, J. Symb. Comput, vol.20, issue.2, pp.117-149, 1995.

N. L. Carothers, Real Analysis, 2000.
DOI : 10.1017/CBO9780511814228

E. Cattani, A. Dickenstein, and B. Sturmfels, Residues and resultants, Journal of Math. Sciences, vol.5, pp.119-148, 1998.
DOI : 10.1007/3-540-27357-3_1
URL : http://mate.dm.uba.ar/~alidick/papers/chapter1cd.pdf

H. Cheng and Z. Han, Minimal kinematic constraints and mt2, JHEP, vol.0812, p.63, 2008.
DOI : 10.1088/1126-6708/2008/12/063
URL : http://arxiv.org/pdf/0810.5178v2.pdf

T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 2009.

D. A. Cox, J. B. Little, and D. Shea, Using Algebraic Geometry, Graduate Texts in Mathematics, vol.185, 1998.
DOI : 10.1007/978-1-4757-6911-1

C. D. Andrea and M. Sombra, A poisson formula for the sparse resultant, Proceedings of the, p.932, 2015.

A. Dickenstein, A World of Binomials, pp.42-66, 2009.
DOI : 10.1017/CBO9781139107068.003

A. Dickenstein, Plane Mixed Discriminants and Toric Jacobians, 2013.
DOI : 10.1007/978-3-319-08635-4_6
URL : http://arxiv.org/pdf/1304.5809.pdf

A. Dickenstein, I. Z. Emiris, and A. Karasoulou, Plane Mixed Discriminants and Toric Jacobians, of Series in Geometry and Computing, 2014.
DOI : 10.1007/978-3-319-08635-4_6
URL : http://arxiv.org/pdf/1304.5809.pdf

A. Dickenstein, E. M. Feichtner, and B. Sturmfels, Tropical discriminants, Journal of the American Mathematical Society, vol.20, issue.04, pp.1111-1133, 2007.
DOI : 10.1090/S0894-0347-07-00562-0
URL : http://www.ams.org/jams/2007-20-04/S0894-0347-07-00562-0/S0894-0347-07-00562-0.pdf

A. Dickenstein, J. M. Rojas, K. Rusek, and J. Shih, Extremal real algebraic geometry and a-discriminants, Moscow Mathematical J, vol.7, issue.3, pp.425-452, 2007.

A. Dickenstein and L. F. Tabera, Singular Tropical Hypersurfaces, Discrete & Computational Geometry, vol.27, issue.1, pp.430-453, 2012.
DOI : 10.4171/RMI/633
URL : http://repositorio.unican.es/xmlui/bitstream/handle/10902/5253/Singular%20Tropical%20Hipersurfaces.pdf%3Bjsessionid%3D11D187FE499EDDD9B7DB45F9F08BA583?sequence%3D1

J. A. Dieudonne and J. B. , Invariant theory, old and new, Advances in Mathematics, vol.4, issue.1, 1971.
DOI : 10.1016/0001-8708(70)90015-0

I. Dinur, G. Kindler, R. Raz, and S. Safra, Approximating CVP to Within Almost-Polynomial Factors is NP-Hard, Combinatorica, vol.23, issue.2, pp.205-243, 2003.
DOI : 10.1007/s00493-003-0019-y
URL : http://www.matha.mathematik.uni-dortmund.de/~fv/diplom_i/dks98.ps

E. Eisenschmidt, R. Hemmecke, and M. Köppe, Computation of atomic fibers of z-linear maps, Contributions to Discrete Mathematics, vol.6, issue.2, 2011.

I. Emiris, A. Karasoulou, E. Tzanaki, and Z. Zafeirakopoulos, On the space of minkowski summands of a convex polytope, European Workshop on Computational Geometry, 2016.

I. Z. Emiris, V. Fisikopoulos, C. Konaxis, and L. Penaranda, An output-sensitive algorithm for computing projections of resultant polytopes, Proceedings of the 2012 symposuim on Computational Geometry, SoCG '12, pp.179-188, 2012.
DOI : 10.1145/2261250.2261276

I. Z. Emiris, T. Kalinka, C. Konaxis, T. Luu, and . Ba, Sparse implicitization by interpolation: Characterizing non-exactness and an application to computing discriminants, Computer-Aided Design, vol.45, issue.2, pp.252-261, 2013.
DOI : 10.1016/j.cad.2012.10.008
URL : http://preprints.acmac.uoc.gr/192/4/acmac-0192.pdf

I. Z. Emiris and A. Karasoulou, Sparse Discriminants and Applications, Proc. Math. and Stat, vol.84, 2014.
DOI : 10.1007/978-1-4471-6461-6_4

I. Z. Emiris, A. Karasoulou, and C. Tzovas, Approximate subset sum and minkowski decomposition of polytopes, European Workshop on Computational Geometry, 2016.

I. Z. Emiris, A. Karasoulou, and C. Tzovas, Approximate subset sum and minkowski decomposition of polytopes, Mathematics in Computer Science, vol.11, issue.1, p.2017

I. Z. Emiris, C. Konaxis, and Z. Zafeirakopoulos, Minkowski Decomposition and Geometric Predicates in Sparse Implicitization, Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation, ISSAC '15, pp.157-164, 2015.
DOI : 10.1007/BF00159746

I. Z. Emiris and E. Tsigaridas, Minkowski decomposition of convex lattice polygons, Algebraic Geometry and Geometric Modeling, Mathematics and Visualization, pp.217-236, 2006.
DOI : 10.1007/978-3-540-33275-6_14
URL : http://cgi.di.uoa.gr/~et/papers/et-minkowski-decomposition-aggm-2005.pdf

I. Z. Emiris, E. Tsigaridas, and G. Tzoumas, THE PREDICATES FOR THE EXACT VORONOI DIAGRAM OF ELLIPSES UNDER THE EUCLIDIEAN METRIC, International Journal of Computational Geometry & Applications, vol.185, issue.06, pp.567-597, 2008.
DOI : 10.1007/978-3-7091-3406-1_16

I. Z. Emiris, E. Tsigaridas, and G. Tzoumas, Exact Delaunay graph of smooth convex pseudo-circles, 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling on, SPM '09, pp.211-222, 2009.
DOI : 10.1145/1629255.1629282

A. Esterov, Newton Polyhedra of Discriminants of Projections, Discrete & Computational Geometry, vol.37, issue.4, pp.96-148, 2010.
DOI : 10.4310/MRL.2008.v15.n3.a14

W. Stein, Sage Mathematics Software. The Sage Development Team

J. C. Faugére, G. Moroz, F. Rouillier, and M. , Safey El Din. Classification of the perspective-three-point problem: Discriminant variety and real solving polynomial systems of inequalities, Proc. ACM ISSAC, pp.79-86, 2008.

J. C. Faugére and P. J. Spaenlehauer, Algebraic Cryptanalysis of the PKC???2009 Algebraic Surface Cryptosystem, Public Key Cryptography, pp.35-52, 2010.
DOI : 10.1007/978-3-642-13013-7_3

J. C. Faugére and J. Svartz, Solving polynomial systems globally invariant under an action of symmetric group and application to the equillibria of n vortices in the plane, Proc ACM ISSAC, pp.170-178, 2012.

S. Gao, Absolute Irreducibility of Polynomials via Newton Polytopes, Journal of Algebra, vol.237, issue.2, pp.501-520, 2001.
DOI : 10.1006/jabr.2000.8586

S. Gao and A. G. Lauder, Decomposition of polytopes and polynomials. Discrete and Computanional Geometry, pp.89-104, 2001.
DOI : 10.1007/s00454-001-0024-0

I. M. Gel-'fand, M. M. Kapranov, and A. V. Zelevinsky, Hyper-geo-metric functions and toric varieties, Funktsional. Anal. i Prilozhen, vol.23, issue.2, 1989.

I. M. Gelfand, M. M. Kapranov, and A. V. Zelevinsky, Discriminants, resultants & multidimensional determinants, 1994.
DOI : 10.1007/978-0-8176-4771-1

A. N. Godwin, The precise determination of Maxwell sets for cuspoid catastrophes, International Journal of Mathematical Education in Science and Technology, vol.15, issue.2, pp.167-182, 2006.
DOI : 10.1080/0020739840150205

L. González-vega and I. Nacula, Efficient topology determination of implicitly defined algebraic plane curves, Computer Aided Geometric Design, vol.19, issue.9, 2002.
DOI : 10.1016/S0167-8396(02)00167-X

J. A. Green, The characters of the finite general linear groups. Transactions of the, pp.402-447, 1955.

M. B. Green, J. H. Schwarz, and E. Witten, Superstring theory, 2012.
URL : https://hal.archives-ouvertes.fr/jpa-00221917

J. Guárdia, J. Montes, and E. Nart, Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields, Journal de Th??orie des Nombres de Bordeaux, vol.23, issue.3, pp.667-696, 2011.
DOI : 10.5802/jtnb.782

S. Helgason, Differential geometry and symmetric spaces, American Mathematical Soc, vol.341, 2001.
DOI : 10.1090/chel/341

M. Henk, M. Köppe, and R. Weismantel, Integral decomposition of polyhedra and some applications in mixed integer programming, Mathematical Programming, pp.193-206, 2003.
DOI : 10.1007/s10107-002-0315-0

M. Henk, M. Köppe, and R. Weismantel, Integral decomposition of polyhedra and some applications in mixed integer programming, Mathematical Programming, vol.94, issue.2-3, pp.93-206, 2003.
DOI : 10.1007/s10107-002-0315-0

O. H. Ibarra and C. E. Kim, Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems, Journal of the ACM, vol.22, issue.4, pp.463-468, 1975.
DOI : 10.1145/321906.321909

J. Jouanolou, Le formalisme du r??sultant, Advances in Mathematics, vol.90, issue.2, pp.117-263, 1991.
DOI : 10.1016/0001-8708(91)90031-2
URL : https://doi.org/10.1016/0001-8708(91)90031-2

E. Kaltofen, J. P. May, Z. Yang, and L. Zhi, Approximate factorization of multivariate polynomials using singular value decomposition, Journal of Symbolic Computation, vol.43, issue.5, pp.359-376, 2008.
DOI : 10.1016/j.jsc.2007.11.005
URL : https://doi.org/10.1016/j.jsc.2007.11.005

D. Kesh and S. Mehta, Polynomial irreducibility testing through Minkowski summand computation, Proc. Canad. Conf. Comp. Geom, pp.43-46, 2008.

K. Koiliaris and C. Xu, A Faster Pseudopolynomial Time Algorithm for Subset Sum, Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms, pp.1062-1072
DOI : 10.1137/1.9781611974782.68

I. G. Kon, Symmetric Functions and Hall Polynomials, 1995.

V. S. Korolyuk and Y. V. Borovskich, Theory of U-Statistics. Mathematics and Its Applications

A. Kulik and H. Shachnai, There is no EPTAS for two-dimensional knapsack, Information Processing Letters, vol.110, issue.16, pp.707-710, 2010.
DOI : 10.1016/j.ipl.2010.05.031

M. J. Magazine and M. Chern, A Note on Approximation Schemes for Multidimensional Knapsack Problems, Mathematics of Operations Research, vol.9, issue.2, pp.244-247, 1984.
DOI : 10.1287/moor.9.2.244

D. Manocha and J. Demmel, Algorithms for Intersecting Parametric and Algebraic Curves II: Multiple Intersections, Graphical Models and Image Processing, vol.57, issue.2, pp.81-100, 1995.
DOI : 10.1006/gmip.1995.1010

P. Mcmullen, Representations of polytopes and polyhedral sets, Geometriae Dedicata, vol.2, issue.1, pp.83-99, 1973.
DOI : 10.1007/BF00149284

W. Meyer, Indecomposable polytopes, Transactions of the American Mathematical Society, vol.190, pp.77-86, 1974.
DOI : 10.1090/S0002-9947-1974-0338929-4

T. Miwa, M. Jimbo, and E. Date, Solitons: Differential equations, symmetries and infinite dimensional algebras, 2000.

G. Moroz, F. Rouiller, D. Chablat, and P. Wenger, On the determination of cusp points of 3-rpr parallel manipulators. Mechanism and Machine Theory, pp.451555-1567, 2010.

J. Nie, Discriminants and nonnegative polynomials, Journal of Symbolic Computation, vol.47, issue.2, pp.167-191, 2012.
DOI : 10.1016/j.jsc.2011.08.023
URL : https://doi.org/10.1016/j.jsc.2011.08.023

A. M. Ostrowski, On multiplication and factorization of polynomials, II. Irreducibility discussion, Aequationes Mathematicae, vol.14, issue.1-2, pp.1-31, 1976.
DOI : 10.1007/BF01836201

P. Pedersen and B. Sturmfels, Product formulas for resultants and Chow forms, Mathematische Zeitschrift, vol.46, issue.no. 2, pp.377-396, 1993.
DOI : 10.1515/9781400882526

N. Perminov and S. Shakirov, Discriminants of symmetric polynomials, 2009.

E. F. Rincón, Computing tropical linear spaces, Journal of Symbolic Computation, vol.51, pp.86-93, 2013.
DOI : 10.1016/j.jsc.2012.03.008

S. Sahi and H. Salmasian, The Capelli problem for <mml:math altimg="si1.gif" 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" xmlns:sa="http://www.elsevier.com/xml/common/struct-aff/dtd"><mml:mrow><mml:mi mathvariant="fraktur">gl</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>m</mml:mi><mml:mo stretchy="false">|</mml:mo><mml:mi>n</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> and the spectrum of invariant differential operators, Advances in Mathematics, vol.303, pp.1-38, 2016.
DOI : 10.1016/j.aim.2016.08.015

T. Saito, The discriminant and the determinant of a hypersurface of even dimension, Mathematical Research Letters, vol.19, issue.4, pp.855-871, 2012.
DOI : 10.4310/MRL.2012.v19.n4.a10

F. A. Salem, S. Gao, and A. G. Lauder, Factoring polynomials via polytopes, Proc ACM ISSAC, pp.4-11, 2004.

A. Sergeev and A. Veselov, <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:msub><mml:mi mathvariant="italic">BC</mml:mi><mml:mo>???</mml:mo></mml:msub></mml:math> Calogero???Moser operator and super Jacobi polynomials, Advances in Mathematics, vol.222, issue.5, pp.1687-1726, 2009.
DOI : 10.1016/j.aim.2009.06.014

M. Shub and S. Smale, Complexity of bézout's theorem i. geometric aspects, J. Amer. Math. Soc, vol.6, issue.2, pp.459-501, 1993.

R. Stanley, Some combinatorial properties of Jack symmetric functions, Advances in Mathematics, vol.77, issue.1, pp.76-115, 1989.
DOI : 10.1016/0001-8708(89)90015-7

B. Sturmfels, The newton polytope of the resultant, Journal of Algebraic Combinatorics, vol.3, issue.2, pp.207-236, 1994.
DOI : 10.1023/A:1022497624378

J. J. Sylvester, Sur l'extension de la théorie des résultants algébriques, Comptes Rendus de l'Académie des Sciences, pp.1074-1079, 1864.

H. Tuy, Convex Analysis and Global Optimization, 2016.

G. J. Woeginger and G. J. Woeginger, When does a dynamic programming formulation guarantee the existence of an FPTAS? When does a dynamic programming formulation guarantee the existence of a fully polynomial time approximation scheme (FPTAS)?, Proc. ACM-SIAM Symposium on Discrete Algorithms, SODA '99, pp.820-82957, 1999.

P. A. Worfolk, Zeros of equivariant vector fields: Algorithms for an invariant approach, Journal of Symbolic Computation, vol.17, issue.6, pp.487-511, 1994.
DOI : 10.1006/jsco.1994.1031