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CGSQE/SyNRAC: a real quantifier elimination package based on the computation of comprehensive Gröbner systems. (English) Zbl 1365.68488

MSC:

68W30 Symbolic computation and algebraic computation
13-04 Software, source code, etc. for problems pertaining to commutative algebra
13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases)

Software:

CGSQE; Maple; SYNRAC
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Full Text: DOI

References:

[1] Becker, E. and Wörmann, T.: On the trace formula for quadratic forms. Recent advances in real algebraic geometry and quadratic forms (Berkeley, CA, 1990/1991; San Francisco, CA, 1991), pp. 271–291, Contemp. Math., 155, Amer. Math. Soc., Providence, RI, 1994.
[2] Collins, G, E.: Quantifier elimination for real closed fields by cylindrical algebraic decomposition. Automata theory and formal languages (Second GI Conf., Kaiserslautern, 1975), pp. 134–183. Lecture Notes in Comput. Sci., Vol. 33, Springer, Berlin, 1975.
[3] Fukasaku, R., Iwane, H. and Sato, Y.: Real Quantifier Elimination by Computation of Comprehensive Gröbner Systems. Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC 2015), pp. 173–180, ACM, 2015. · Zbl 1345.68282
[4] Fukasaku, R., Iwane, H. and Sato, Y.: Improving a CGS-QE algorithm. Proceedings of Sixth International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS 2015), Lecture Notes in Comput. Sci., Vol. 9582, pp. 231–235, Springer, 2016. · Zbl 1460.13051
[5] Iwane, H., Yanami, H. and Anai, H.: SyNRAC: A Toolbox for Solving Real Algebraic Constraints. Mathematical Software - ICMS 2014, pp. 518–522. Lecture Notes in Comput. Sci., Vol. 8592, Springer, Berlin, 2014. · Zbl 1437.13005
[6] Pedersen, P., Roy, M.-F., and Szpirglas, A.: Counting real zeroes in the multivariate case. Computational Algebraic Geometry, pp. 203–224, Progress in Mathematics, Vol. 109, 1993. · Zbl 0806.14042
[7] Suzuki, A. and Sato, Y.: A Simple Algorithm to Compute Comprehensive Gröbner Bases Using Gröbner Bases. Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC 2006), pp. 326–331, ACM, 2006. · Zbl 1356.13040
[8] Weispfenning, V.: Comprehensive Gröbner bases, J. of Symbolic Computation, Vol. 14/1, pp. 1–29, 1992. · Zbl 0784.13013
[9] Weispfenning, V.: Quantifier Elimination for Real Algebra - The Cubic Case. Proceedings of International Symposium on Symbolic and Algebraic Computation (ISSAC 1994), pp. 258–263, ACM, 1994. · Zbl 0919.03030
[10] Weispfenning, V.: Quantifier Elimination for Real Algebra - The Quadratic Case and Beyon. Appl. Algebra Eng. Commun. Comput. 8, no. 2, pp. 85–101, 1997. · Zbl 0867.03003
[11] Weispfenning, V.: A New Approach to Quantifier Elimination for Real Algebra. Quantifier Elimination and Cylindrical Algebraic Decomposition, pp. 376–392, Springer, 1998. · Zbl 0900.03046
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