J. Berthomieu, B. Boyer, and J. Faugère, Linear algebra for computing Gröbner bases of linear recursive multidimensional sequences, Journal of Symbolic Computation, vol.83, pp.36-67, 2017.

G. Birkhoff, The algebra of multivariate interpolation. Constructive approaches to mathematical models, pp.345-363, 1979.

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

M. Collowald and E. Hubert, A moment matrix approach to computing symmetric cubatures, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01188290

C. D. Boor, Gauss elimination by segments and multivariate polynomial interpolation, Approximation and Computation: A Festschrift in Honor of Walter Gautschi, pp.1-22, 1994.

C. , D. Boor, and A. Ron, On multivariate polynomial interpolation. Constructive Approximation, vol.6, p.3, 1990.

C. , D. Boor, and A. Ron, The least solution for the polynomial interpolation problem, Mathematische Zeitschrift, vol.210, p.1, 1992.

C. Fassino and H. M. Möller, Multivariate polynomial interpolation with perturbed data, Numerical Algorithms, vol.71, pp.273-292, 2016.

A. Fässler and E. Stiefel, Group theoretical methods and their applications, 1992.

J. Faugere, P. Gianni, D. Lazard, and T. Mora, Efficient computation of zero-dimensional Gröbner bases by change of ordering, Journal of Symbolic Computation, vol.16, pp.329-344, 1993.

J. Faugère and C. Mou, Sparse FGLM algorithms, Journal of Symbolic Computation, vol.80, pp.538-569, 2017.

J. Faugere and J. Svartz, Grobner bases of ideals invariant under a commutative group: the non-modular case, Proc. ISSAC 2013, pp.347-354, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00819337

K. Gatermann, Symbolic solution of polynomial equation systems with symmetry, ISSAC'90, pp.112-119, 1990.

K. Gatermann, Linear representations of finite groups and the ideal theoretical construction of G-invariant cubature formulas, Numerical integration, vol.357, pp.25-35, 1991.

K. Gatermann, Computer algebra methods for equivariant dynamical systems, Lecture Notes in Mathematics, vol.1728, 2000.

K. Gatermann and F. Guyard, Gröbner bases, invariant theory and equivariant dynamics, J. Symbolic Comput, vol.28, pp.275-302, 1999.

K. Gatermann and P. A. Parrilo, Symmetry groups, semidefinite programs, and sums of squares, J. Pure Appl. Algebra, vol.192, pp.95-128, 2004.

G. Golub and C. Van-loan, Matrix Computations, 1996.

E. Hubert and G. Labahn, Rational invariants of scalings from Hermite normal forms, Proc. ISSAC 2012. ACM, pp.219-226, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00657991

E. Hubert and G. Labahn, Scaling invariants and symmetry reduction of dynamical systems, Found. Comput. Math, vol.13, pp.479-516, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00668882

E. Hubert and G. Labahn, Computation of the Invariants of, Finite Abelian Groups. Mathematics of Computations, vol.85, pp.3029-3050, 2016.

M. Javanbakht and T. Sauer, Numerical computation of H-bases, BIT Numerical Mathematics, vol.59, pp.417-442, 2019.

T. Krick, A. Szanto, and M. Valdettaro, Symmetric interpolation, Exchange Lemma and Sylvester sums, Comm. Algebra, vol.45, pp.3231-3250, 2017.

F. S. Macaulay, The algebraic theory of modular systems, Cambridge Tracts in Mathematics and Mathematical Physics, vol.19, 1916.

M. G. Marinari, H. M. Möller, and T. Mora, Gröbner bases of ideals given by dual bases, ISSAC'91. ACM, pp.55-63, 1991.

H. M. Möller and B. Buchberger, The construction of multivariate polynomials with preassigned zeros, European Computer Algebra Conference, 1982.

H. M. Möller and T. Sauer, H-bases for polynomial interpolation and system solving, Advances in Computational Mathematics, vol.12, pp.335-362, 2000.

B. Mourrain, Fast algorithm for border bases of Artinian Gorenstein algebras, ISSAC'17 Kaiserslautern, pp.333-340, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01515366

G. Pistone, E. Riccomagno, and H. P. Wynn, Algebraic statistics: Computational commutative algebra in statistics, 2000.

G. Pistone and H. P. Wynn, Generalised confounding with Gröbner bases, Biometrika, vol.83, pp.653-666, 1996.

C. Riener and M. Safey-el-din, Real root finding for equivariant semialgebraic systems, Proc. ISSAC, pp.335-342, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01819106

C. Riener, T. Theobald, L. J. Andrén, and J. B. Lasserre, Exploiting symmetries in SDP-relaxations for polynomial optimization, Math. Oper. Res, vol.38, p.1, 2013.

E. Rodriguez-bazan and E. Hubert, Symmetry Preserving Interpolation, ISSAC'19, 2019.
URL : https://hal.archives-ouvertes.fr/hal-01994016

T. Sauer, Gröbner bases, H-bases and interpolation, Trans. Amer. Math. Soc, vol.353, pp.2293-2308, 2001.

T. Sauer, Prony's method in several variables, Numer. Math, vol.136, 2017.

T. Sauer, Prony's method in several variables: symbolic solutions by universal interpolation, J. Symbolic Comput, vol.84, pp.95-112, 2018.

J. P. Serre, Linear representations of finite groups, 1977.

J. Verschelde and K. Gatermann, Symmetric Newton polytopes for solving sparse polynomial systems, Adv. in Appl. Math, vol.16, pp.95-127, 1995.