D. Adrovic and J. Verschelde, Computing Puiseux series for algebraic surfaces, Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC '12, pp.20-27, 2012.
DOI : 10.1145/2442829.2442837

A. Bockmayr and F. Eisenbrand, Cutting Planes and the Elementary Closure in Fixed Dimension, Mathematics of Operations Research, vol.26, issue.2, pp.304-312, 2001.
DOI : 10.1287/moor.26.2.304.10555
URL : https://hal.archives-ouvertes.fr/inria-00101099

H. E. Campbell and J. Chuai, INVARIANT FIELDS AND LOCALIZED INVARIANT RINGS OF p-GROUPS, The Quarterly Journal of Mathematics, vol.58, issue.2, pp.151-157, 2007.
DOI : 10.1093/qmath/ham011

A. Charnow, On the Fixed Field of a Linear Abelian Group, Journal of the London Mathematical Society, vol.2, issue.1, pp.348-350, 1969.
DOI : 10.1112/jlms/s2-1.1.348

H. Derksen and G. Kemper, Computational Invariant Theory. Invariant Theory and Algebraic Transformation Groups I, 2002.

J. Faugere, M. Safey-el-din, and T. Verron, On the complexity of computing gröbner bases for quasi-homogeneous systems, Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC '13, pp.189-196, 2013.

J. Faugere and J. Svartz, Gröbner bases of ideals invariant under a commutative group : the nonmodular case, Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC '13, pp.347-354, 2013.

E. Fischer, Die Isomorphie der Invariantenkörper der endlicher Abelschen Gruppen linearer Transformationen, Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl, pp.77-80, 1915.

E. Fischer, Zur Theorie der endlichen Abelschen Gruppen, Mathematische Annalen, vol.77, issue.1, pp.81-88, 1915.
DOI : 10.1007/BF01456820

K. Gatermann, Symbolic solution of polynomial equation systems with symmetry, Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC'90, pp.112-119, 1990.

R. A. Horn and C. R. Johnson, Matrix Analysis, 1985.

J. A. Howell, Spans in the module (Z m ) s . Linear and Multilinear Algebra, pp.67-77, 1986.

E. Hubert, Algebraic and Differential Invariants, Foundations of Computational Mathematics number 403 in London Mathematical Society Lecture Note Series, 2011.
DOI : 10.1017/CBO9781139095402.009
URL : https://hal.archives-ouvertes.fr/hal-00763310

E. Hubert, Rational Invariants of a Group Action, Journees Nationales de Calcul Formel CEDRAM -Center for Diffusion of Academic Mathematical Journals, p.10, 2013.
DOI : 10.5802/ccirm.19
URL : https://hal.archives-ouvertes.fr/hal-00839283

E. Hubert and I. Kogan, Rational invariants of a group action. Construction and rewriting, Journal of Symbolic Computation, vol.42, issue.1-2, pp.203-217, 2007.
DOI : 10.1016/j.jsc.2006.03.005
URL : https://hal.archives-ouvertes.fr/hal-00839283

E. Hubert and I. Kogan, Smooth and Algebraic Invariants of a Group Action: Local and Global Constructions, Foundations of Computational Mathematics, vol.7, issue.4, pp.455-493, 2007.
DOI : 10.1007/s10208-006-0219-0
URL : https://hal.archives-ouvertes.fr/inria-00198857

E. Hubert and G. Labahn, Rational invariants of scalings from Hermite normal forms, Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, ISSAC '12, pp.219-226, 2012.
DOI : 10.1145/2442829.2442862
URL : https://hal.archives-ouvertes.fr/hal-00657991

E. Hubert and G. Labahn, Scaling Invariants and Symmetry Reduction of Dynamical Systems, Foundations of Computational Mathematics, vol.12, issue.2, pp.479-516, 2013.
DOI : 10.1007/s10208-013-9165-9
URL : https://hal.archives-ouvertes.fr/hal-00668882

T. Kamke and G. Kemper, Algorithmic Invariant Theory of Nonreductive Groups, Qualitative Theory of Dynamical Systems, vol.244, issue.6, pp.79-110, 2012.
DOI : 10.1007/s12346-011-0059-4

M. Kang, Fixed fields of triangular matrix groups, Journal of Algebra, vol.302, issue.2, pp.845-847, 2006.
DOI : 10.1016/j.jalgebra.2006.03.037

G. Kemper, The computation of invariant fields and a new proof of a theorem by Rosenlicht. Transformation Groups, pp.657-670, 2007.

H. Lenstra, Rational functions invariant under a finite abelian group, Inventiones Mathematicae, vol.28, issue.2, pp.299-325, 1974.
DOI : 10.1007/BF01389732

T. Miyata, Invariants of certain groups. I. Nagoya Math, J, vol.41, pp.69-73, 1971.

B. Mourrain and P. Trebuchet, Toric border bases, Proceedings of the International Symposium on Symbolic and Algebraic Computation, p.14, 2014.

J. Müller-quade and T. Beth, Calculating generators for invariant fields of linear algebraic groups In Applied algebra, algebraic algorithms and error-correcting codes, LNCS, vol.1719, 1999.

M. D. Neusel and M. Sezer, Characterizing separating invariants, 2010.

V. W. Noonburg, A Neural Network Modeled by an Adaptive Lotka-Volterra System, SIAM Journal on Applied Mathematics, vol.49, issue.6, pp.1779-1792, 1989.
DOI : 10.1137/0149109

F. Pauer and A. Unterkircher, Gr??bner Bases for Ideals in Laurent Polynomial Rings and their Application to Systems of Difference Equations, Applicable Algebra in Engineering, Communication and Computing, vol.9, issue.4, pp.271-291, 1999.
DOI : 10.1007/s002000050108

V. L. Popov and E. B. Vinberg, Invariant Theory, Algebraic geometry. IV, Encyclopedia of Mathematical Sciences, 1994.

A. Schrijver, Theory of Linear and Integer Programming, 1986.

J. Serre, Linear Representations of Finite Groups, Graduate Texts in Mathematics, vol.42, 1996.
DOI : 10.1007/978-1-4684-9458-7

A. Storjohann, Algorithms for Matrix Canonical Forms, 2000.

A. Storjohann and G. Labahn, Asymptotically fast computation of Hermite normal forms of integer matrices, Proceedings of the 1996 international symposium on Symbolic and algebraic computation , ISSAC '96, pp.259-266, 1996.
DOI : 10.1145/236869.237083

A. Storjohann and T. Mulders, Fast Algorithms for Linear Algebra Modulo N, Algorithms ESA'98, pp.139-150, 1998.
DOI : 10.1007/3-540-68530-8_12

B. Sturmfels, Algorithms in Invariant Theory. Texts and Monographs in Symbolic Computation, 1993.

R. Swan, Invariant rational functions and a problem of Steenrod, Inventiones Mathematicae, vol.2, issue.2, pp.148-158, 1969.
DOI : 10.1007/BF01389798