M. A. Bucero, C. Bajaj, and B. Mourrain, On the construction of general cubature formula by flat extensions, Linear Algebra Appl, vol.502, pp.104-125, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01158099

N. Akhiezer, The classical moment problem and some related questions in analysis, 1965.

E. Bareiss, Sylvester's identity and multistep integer-preserving Gaussian elimination, Math. Comp, vol.22, pp.565-578, 1968.

E. Bareiss, Computational solutions of matrix problems over an integral domain, J. Inst. Math. Appl, vol.10, pp.68-104, 1972.

S. Basu, R. Pollack, and M. Roy, Algorithms in real algebraic geometry, Algorithms and Computation in Mathematics, vol.10, 2006.
URL : https://hal.archives-ouvertes.fr/hal-01083587

C. Bayer and J. Teichmann, The proof of Tchakaloff's theorem, Proc. Amer. Math. Soc, vol.134, issue.10, pp.3035-3040, 2006.

B. Beckermann and E. Bourreau, How to choose modified moments?, J. Comput. Appl. Math, vol.98, issue.1, pp.81-98, 1998.

M. Ben-or and P. Tiwari, A deterministic algorithm for sparse multivariate polynomial interpolation, Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, STOC '88, pp.301-309, 1988.

J. Bochnak, M. Coste, and M. Roy, Real algebraic geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, vol.36, issue.3

. Springer-verlag, Translated from the 1987 French original, Revised by the authors, 1998.

J. Brachat, P. Comon, B. Mourrain, and E. Tsigaridas, Symmetric tensor decomposition, Linear Algebra Appl, vol.433, pp.1851-1872, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00355713

H. Bungartz and M. Griebel, Sparse grids, vol.13, pp.147-269, 2004.

M. Collowald, A. Cuyt, E. Hubert, W. Lee, and O. Salazar-celis, Numerical reconstruction of convex polytopes from directional moments, Advances in Computational Mathematics, pp.1-21, 2015.
URL : https://hal.archives-ouvertes.fr/hal-00926357

M. Collowald and E. Hubert, Cubatures with symmetry. In preparation, 2018.

R. Cools, Constructing cubature formulae: the science behind the art, Acta numerica, vol.6, pp.1-54, 1997.

R. Cools, I. Mysovskikh, and H. Schmid, Cubature formulae and orthogonal polynomials, J. Comput. Appl. Math, vol.127, issue.1-2, pp.121-152, 2000.

R. Cools and P. Rabinowitz, Monomial cubature rules since "Stroud": a compilation, J. Comput. Appl. Math, vol.48, issue.3, pp.309-326, 1993.

D. Cox, J. Little, and D. O'shea, Using algebraic geometry, volume 185 of Graduate Texts in Mathematics, 2005.

R. Curto and L. Fialkow, Solution of the truncated complex moment problem for flat data, Mem. Amer. Math. Soc, vol.119, issue.568, p.52, 1996.

R. Curto and L. Fialkow, The truncated complex K-moment problem, Trans. Amer. Math. Soc, vol.352, issue.6, pp.2825-2855, 2000.

P. Davis, A construction of nonnegative approximate quadratures, Math. Comp, vol.21, pp.578-582, 1967.

C. Dunkl and Y. Xu, Orthogonal polynomials of several variables, of Encyclopedia of Mathematics and its Applications, vol.81, 2001.

M. Elad, P. Milanfar, and G. Golub, Shape from moments-an estimation theory perspective, IEEE Trans. Signal Process, vol.52, issue.7, pp.1814-1829, 2004.

L. Fialkow and S. Petrovic, A moment matrix approach to multivariable cubature. Integral Equations Operator Theory, vol.52, pp.85-124, 2005.

A. F. Suárez and E. Hubert, Convolution surfaces with varying radius: Formulae for skeletons made of arcs of circles and line segments, 2018.

K. Geddes, S. Czapor, and G. Labahn, Algorithms for computer algebra, 1992.

M. Giesbrecht, G. Labahn, and W. Lee, Symbolic-numeric sparse interpolation of multivariate polynomials, J. Symbolic Comput, vol.44, issue.8, pp.943-959, 2009.
DOI : 10.1145/1145768.1145792
URL : http://www.cecm.sfu.ca/~pborwein/MITACS/papers/wenshin.pdf

G. Golub and G. Meurant, Matrices, moments and quadrature with applications, Princeton Series in Applied Mathematics, 2010.
DOI : 10.1515/9781400833887

G. Golub, P. Milanfar, and J. Varah, A stable numerical method for inverting shape from moments, SIAM J. Sci. Comput, vol.21, issue.4, p.0, 1999.
DOI : 10.1137/s1064827597328315

N. Gravin, J. Lasserre, D. Pasechnik, and S. Robins, The Inverse Moment Problem for Convex Polytopes, Discrete Comput. Geom, vol.48, issue.3, pp.596-621, 2012.
DOI : 10.1007/s00454-012-9426-4
URL : https://link.springer.com/content/pdf/10.1007%2Fs00454-012-9426-4.pdf

W. Greub, Die Grundlehren der Mathematischen Wissenschaften, vol.97, 1967.

P. Henrici, Power series-integration-conformal mapping-location of zeros, vol.1, 1988.

D. Henrion, S. Naldi, and M. Safey-el-din, Exact algorithms for linear matrix inequalities, SIAM J. Optim, vol.26, issue.4, pp.2512-2539, 2016.
DOI : 10.1137/15m1036543
URL : https://hal.archives-ouvertes.fr/hal-01184320

H. Hong and W. Stocher, Exact division applied to diagonalizing symmetric matrices, 1994.

E. Hubert, Convolution surfaces based on polygons for infinite and compact support kernels, Graphical Models, vol.74, issue.1, pp.1-13, 2012.
DOI : 10.1016/j.gmod.2011.07.001
URL : https://hal.archives-ouvertes.fr/inria-00536840

E. Hubert and M. Cani, Convolution Surfaces based on Polygonal Curve Skeletons. (An Application of Symbolic Integration to Graphics), Journal of Symbolic Computation, vol.47, issue.6, pp.680-699, 2012.
DOI : 10.1016/j.jsc.2011.12.026
URL : https://hal.archives-ouvertes.fr/inria-00429358

T. Hughes, A. Reali, and G. Sangalli, Efficient quadrature for nurbs-based isogeometric analysis, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.5-8, pp.301-313, 2010.
DOI : 10.1016/j.cma.2008.12.004

E. Kaltofen and Y. Lakshman, Improved sparse multivariate polynomial interpolation algorithms, Symbolic and algebraic computation, vol.358, pp.467-474, 1988.
DOI : 10.1007/3-540-51084-2_44

M. Collowald and &. E. Hubert,

E. Kaltofen and W. Lee, Early termination in sparse interpolation algorithms, International Symposium on Symbolic and Algebraic Computation (ISSAC'2002, vol.36, pp.365-400, 2003.
DOI : 10.1016/s0747-7171(03)00088-9
URL : https://doi.org/10.1016/s0747-7171(03)00088-9

S. Kunis, T. Peter, T. Roemer, and U. Von-der-ohe, A multivariate generalization of prony's method, 2015.
DOI : 10.1016/j.laa.2015.10.023
URL : http://arxiv.org/pdf/1506.00450

J. Lasserre, Global optimization with polynomials and the problem of moments, SIAM J. Optim, vol.11, issue.3, p.1, 2000.

J. Lasserre, Moments, positive polynomials and their applications, vol.1, 2010.
DOI : 10.1142/p665

J. Lasserre, The existence of Gaussian cubature formulas, J. Approx. Theory, vol.164, issue.5, pp.572-585, 2012.

M. Laurent, Revisiting two theorems of Curto and Fialkow on moment matrices, Proc. Amer. Math. Soc, vol.133, issue.10, pp.2965-2976, 2005.

M. Laurent, Sums of squares, moment matrices and optimization over polynomials, Emerging applications of algebraic geometry, vol.149, pp.157-270, 2009.
DOI : 10.1007/978-0-387-09686-5_7
URL : http://homepages.cwi.nl/~monique/files/moment-ima.pdf

M. Laurent and B. Mourrain, A generalized flat extension theorem for moment matrices, Arch. Math. (Basel), vol.93, issue.1, pp.87-98, 2009.
DOI : 10.1007/s00013-009-0007-6
URL : http://www.cwi.nl/~monique/files/archivlm.pdf

O. P. Le-ma??trema??tre and O. M. Knio, Spectral methods for uncertainty quantification. Scientific Computation, 2010.

H. Li, J. Sun, and Y. Xu, Discrete Fourier analysis, cubature, and interpolation on a hexagon and a triangle, SIAM J. Numer. Anal, vol.46, issue.4, pp.1653-1681, 2008.
DOI : 10.1137/060671851
URL : http://arxiv.org/pdf/0712.3093

J. Lyness and G. Monegato, Quadrature rules for regions having regular hexagonal symmetry, SIAM J. Numer. Anal, vol.14, issue.2, pp.283-295, 1977.
DOI : 10.1137/0714018

Y. Ma, C. Wang, and L. Zhi, A certificate for semidefinite relaxations in computing positive-dimensional real radical ideals, J. Symbolic Comput, vol.72, pp.1-20, 2016.
DOI : 10.1016/j.jsc.2014.12.002

B. Malgrange, Cartan involutiveness = Mumford regularity, Commutative algebra, vol.331, pp.193-205, 2001.
DOI : 10.1090/conm/331/05911

B. Malgrange, Systèmes différentiels involutifs, volume 19 of Panoramas et Synthèses

. Société-mathématique-de-france, , 2005.

A. Mantzaflaris, B. Juettler, B. Khoromskij, and U. Langer, Matrix generation in isogeometric analysis by low rank tensor approximation, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01084421

P. Milanfar, G. Verghese, C. Karl, and A. Willsky, Reconstructing polygons from moments with connections to array processing, IEEE Transactions on Signal Processing, vol.43, pp.432-443, 1995.

H. Möller, Lower bounds for the number of nodes in cubature formulae, In Numerische Integration (Tagung, Math. Forschungsinst, vol.45, pp.221-230, 1978.

B. Mourrain, Polynomial exponential decomposition from moments, Found. Comput. Math, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01367730

D. Potts and M. Tasche, Parameter estimation for exponential sums by approximate prony method, Signal Processing, vol.90, issue.5, pp.1631-1642, 2010.

D. Potts and M. Tasche, Parameter estimation for multivariate exponential sums, Electron. Trans. Numer. Anal, vol.40, pp.204-224, 2013.

M. Putinar, A note on Tchakaloff's theorem, Proc. Amer. Math. Soc, vol.125, issue.8, pp.2409-2414, 1997.

J. Radon, Zur mechanischen Kubatur. Monatsh. Math, vol.52, pp.286-300, 1948.

C. , Baron de Prony) Riche. Essai expérimental et analytique sur les lois de la dilatabilité des fluidesélastique fluidesélastique et sur celles de la force expansive de la vapeur de l'eau et de la vapeur de l'alkool, ` a différentes températures, J. de l' ´ Ecole Polytechnique, vol.1, pp.24-76, 1795.

H. Richter, Parameterfreie Abschätzung und Realisierung von Erwartungswerten, Bl. Deutsch. Ges. Versicherungsmath, vol.3, pp.147-162, 1957.

C. Riener and M. Schweighofer, Optimization approaches to quadrature: new characterizations of Gaussian quadrature on the line and quadrature with few nodes on plane algebraic curves, on the plane and in higher dimensions, J. Complexity, vol.45, pp.22-54, 2018.

R. Rockafellar, Convex analysis, Princeton Mathematical Series, issue.28, 1970.

F. Rouillier, Formules de Bareiss et réduction de formes quadratiques, C. R. Acad. Sci. Paris Sér. I Math, vol.320, issue.10, pp.1273-1277, 1995.

R. A. Sack and A. F. Donovan, An algorithm for Gaussian quadrature given modified moments, Numer. Math, vol.18, pp.465-478

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

H. Schmid and Y. Xu, On bivariate Gaussian cubature formulae, Proc. Amer. Math. Soc, vol.122, issue.3, pp.833-841, 1994.

K. Schmüdgen, The moment problem, Graduate Texts in Mathematics, vol.277, 2017.

J. Stoer and R. Bulirsch, Introduction to numerical analysis, Texts in Applied Mathematics, vol.12, 2002.

A. Stroud, Approximate calculation of multiple integrals, 1971.

M. Sylvester, Sur une extension du théorème de clebsch relatif aux courbes duquatrì eme degré. Comptes rendus hebdomadiares des séances de l'Académie des sciences, vol.102, p.1886

G. Szegö-;-providence and R. I. , Orthogonal polynomials, 1975.

V. Tchakaloff, Formules de cubatures mécaniquesmécaniquesà coefficients non négatifs, Bull. Sci. Math, vol.81, issue.2, pp.123-134, 1957.

F. Zhang, Matrix theory