On the combinatorial and algebraic complexity of quantifier elimination, Thus, from Proposition 2.1, Step, pp.1002-1045, 1996. ,
DOI : 10.1145/235809.235813
Algorithms in real algebraic geometry, of Algorithms and Computation in Mathematics, 2006. ,
DOI : 10.1007/978-3-662-05355-3
URL : https://hal.archives-ouvertes.fr/hal-01083587
Real Algebraic Geometry, 1998. ,
DOI : 10.1007/978-3-662-03718-8
Sums of squares of real polynomials, Symp. in Pure Math, vol.58, issue.2, pp.103-126, 1995. ,
DOI : 10.1090/pspum/058.2/1327293
Complexity of integer quasiconvex polynomial optimization, Journal of Complexity, vol.21, issue.4, pp.543-556, 2005. ,
DOI : 10.1016/j.jco.2005.04.004
Sums of polynomial squares over totally real fields are rational sums of squares, Proc. American Math, pp.921-930, 2009. ,
Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars, Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, ISSAC '08, pp.155-163, 2008. ,
DOI : 10.1145/1390768.1390792
Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients, Journal of Symbolic Computation, vol.47, issue.1, 2009. ,
DOI : 10.1016/j.jsc.2011.08.002
Private communication, 2009. ,
Computing integral points in convex semialgebraic sets, Annual IEEE Symposium on 0, pp.162-171, 1997. ,
Integer Optimization on Convex Semialgebraic Sets, Discrete & Computational Geometry, vol.23, issue.2, pp.207-224, 2000. ,
DOI : 10.1007/PL00009496
Polynomial Instances of the Positive Semidefinite and Euclidean Distance Matrix Completion Problems, SIAM Journal on Matrix Analysis and Applications, vol.22, issue.3, pp.874-894, 2001. ,
DOI : 10.1137/S0895479899352689
Factoring polynomials with rational coefficients, Mathematische Annalen, vol.32, issue.4, pp.515-534, 1982. ,
DOI : 10.1007/BF01457454
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.310.318
Integer Programming with a Fixed Number of Variables, Mathematics of Operations Research, vol.8, issue.4, pp.538-5483689168, 1983. ,
DOI : 10.1287/moor.8.4.538
Some useful bounds, Computer Algebra, Symbolic and Algebraic Computation. Supplementum to Computing, pp.259-263, 1982. ,
DOI : 10.1007/978-3-7091-7551-4_16
A Macaulay 2 package for computing sum of squares decompositions of polynomials with rational coefficients, Proc. SNC'07, pp.207-208, 2007. ,
Computing sum of squares decompositions with rational coefficients, Theoretical Computer Science, vol.409, issue.2, pp.269-281, 2008. ,
DOI : 10.1016/j.tcs.2008.09.025
On the complexity of semidefinite programs, Journal of Global Optimization, vol.10, issue.4, pp.351-365, 1997. ,
DOI : 10.1023/A:1008203903341
An algorithm for sums of squares of real polynomials, Journal of Pure and Applied Algebra, vol.127, issue.1, pp.99-104, 1998. ,
DOI : 10.1016/S0022-4049(97)83827-3
Factorization of univariate integer polynomials by diophantine aproximation and an improved basis reduction algorithm, pp.436-447, 1984. ,
Complexity results for factoring univariate polynomials over the rationals, 2007. ,