B. Buchberger, Bruno Buchberger???s PhD thesis 1965: An algorithm for finding the basis elements of the residue class ring of a zero dimensional polynomial ideal, Logic, Mathematics and Computer Science: Interactions in honor of Bruno Buchberger, pp.3-4475, 2006.
DOI : 10.1016/j.jsc.2005.09.007

A. Colin, Solving a system of algebraic equations with symmetries, Journal of Pure and Applied Algebra, vol.117, issue.118, pp.195-215, 1996.
DOI : 10.1016/S0022-4049(97)00011-X

URL : https://hal.archives-ouvertes.fr/hal-01148896

D. Cox, J. Little, and D. Shea, Ideals, varieties, and algorithms. Undergraduate Texts in Mathematics An introduction to computational algebraic geometry and commutative algebra, 2007.

J. Faugère, A new efficient algorithm for computing Gröbner bases (F4), Journal of Pure and Applied Algebra, vol.139, pp.1-361, 1999.

J. Faugère, A new efficient algorithm for computing Gröbner bases without reduction to zero (F5), Proceedings of the 2002 international symposium on Symbolic and algebraic computation, ISSAC '02, pp.75-83, 2002.

J. Faugère, M. Hering, and J. Phan, The membrane inclusions curvature equations, Advances in Applied Mathematics, vol.31, issue.4, pp.643-658, 2003.
DOI : 10.1016/S0196-8858(03)00039-3

J. Faugère and S. Rahmany, Solving systems of polynomial equations with symmetries using SAGBI-Gröbner bases, ISSAC '09: Proceedings of the 2009 international symposium on Symbolic and algebraic computation, ISSAC '09, pp.151-158, 2009.

J. Faugère and J. Svartz, Software and benchmarks

J. Faugère and J. Svartz, Solving polynomial systems globally invariant under an action of the symmetric group and application to the equilibria of N vortices in the plane, Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC '12, pp.170-178
DOI : 10.1145/2442829.2442856

J. C. 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

P. Flajolet and R. Sedgewick, Analytic combinatorics, 2009.
DOI : 10.1017/CBO9780511801655

URL : https://hal.archives-ouvertes.fr/inria-00072739

G. Björck, Functions of modulus 1 on Zn , whose Fourier transforms have constant modulus, and "cyclic n-roots, Recent Advances in Fourier Analysis and its applica tions, pp.131-140, 1990.

K. Gatemann, Symbolic solution polynomial equation systems with symmetry, Proceedings of the international symposium on Symbolic and algebraic computation , ISSAC '90, pp.112-119, 1990.
DOI : 10.1145/96877.96907

J. Hoffstein, J. Pipher, and J. H. Silverman, NTRU: A ring-based public key cryptosystem, Algorithmic number theory, pp.267-288, 1998.
DOI : 10.1007/BFb0054868

D. Lazard, Gröbner bases, Gaussian elimination and resolution of systems of algebraic equations, Computer Algebra, EUROCAL'83, pp.146-156, 1983.

P. Spaenlehauer, Solving multi-homogeneous and determinantal systems. Algorithms -Complexity -Applications
URL : https://hal.archives-ouvertes.fr/tel-01110756

R. P. Stanley, Invariants of finite groups and their applications to combinatorics, Bulletin of the American Mathematical Society, vol.1, issue.3, pp.475-511, 1979.
DOI : 10.1090/S0273-0979-1979-14597-X

S. Steidel, Gr??bner bases of symmetric ideals, Journal of Symbolic Computation, vol.54, issue.0, pp.72-86, 2013.
DOI : 10.1016/j.jsc.2013.01.005

B. Sturmfels, Algorithms in Invariant Theory. Texts and Monographs in Symbolic Computation, 2008.