DISCOVERER: a tool for solving semi-algebraic systems

SNAP (Symbolic Numeric Algebra for Polynomials) package for Mathematica provides various functions to compute approximate algebraic properties including approximate GCD and factorization of polynomials for example. For practical situations, the package does not have enough functionalities yet. However, the aim of this package is showing how an unified tolerance mechanism that we introduced for the package works. With that, we can continue approximate calculations under certified tolerances without special skills in symbolic-numeric algebra.

[1]  George E. Collins,et al.  Partial Cylindrical Algebraic Decomposition for Quantifier Elimination , 1991, J. Symb. Comput..

[2]  Richard D. Jenks,et al.  AXIOM: the scientific computation system , 1992 .

[3]  Hirokazu Anai,et al.  Development of SyNRAC , 2005, International Conference on Computational Science.

[4]  Bican Xia,et al.  A complete algorithm for automated discovering of a class of inequality-type theorems , 2001, Science in China Series F Information Sciences.

[5]  Masayuki Noro,et al.  Risa/Asir—a computer algebra system , 1992, ISSAC '92.

[6]  Thomas Sturm,et al.  New Domains for Applied Quantifier Elimination , 2006, CASC.

[7]  Barbara J. Grosz,et al.  for the Study of Language and , 2002 .

[8]  Kosaku Nagasaka.  新人賞受賞論文 Using Coefficient-wise Tolerance in Symbolic-Numeric Algorithms for Polynomials , 2006 .

[9]  Akira Suzuki,et al.  A simple algorithm to compute comprehensive Gröbner bases using Gröbner bases , 2006, ISSAC '06.

[10]  Thomas Sturm,et al.  REDLOG: computer algebra meets computer logic , 1997, SIGS.

[11]  Ting Zhang,et al.  Real solution isolation using interval arithmetic , 2006, Comput. Math. Appl..

[12]  Katsusuke Nabeshima,et al.  A speed-up of the algorithm for computing comprehensive Gröbner systems , 2007, ISSAC '07.

[13]  Bican Xia,et al.  AUTOMATED DEDUCTION IN REAL GEOMETRY , 2004 .

[14]  Bican Xia,et al.  An Algorithm for Isolating the Real Solutions of Semi-algebraic Systems , 2002, J. Symb. Comput..

[15]  Antonio Montes,et al.  Improving the DISPGB algorithm using the discriminant ideal , 2006, J. Symb. Comput..

[16]  Bican Xia,et al.  A complete algorithm for counting real solutions of polynomial systems of equations and inequalities , 2002 .

[17]  Richard J. Fateman,et al.  A Review of Mathematica , 1992, J. Symb. Comput..

[18]  Bican Xia,et al.  Automated Deduction in Geometry , 2000, Lecture Notes in Computer Science.

[19]  Mark Sofroniou,et al.  Precise numerical computation , 2005, J. Log. Algebraic Methods Program..

[20]  Hirokazu Anai,et al.  Development of SyNRAC-Formula Description and New Functions , 2004, International Conference on Computational Science.

[21]  Hirokazu Anai,et al.  SyNRAC: A Maple-Package for Solving Real Algebraic Constraints , 2003, International Conference on Computational Science.

[22]  佐藤 洋祐,et al.  特集 Comprehensive Grobner Bases , 2007 .

[23]  Antonio Montes,et al.  A New Algorithm for Discussing Gröbner Bases with Parameters , 2002, J. Symb. Comput..

[24]  H. Yanami,et al.  Fixed-structure robust controller synthesis based on symbolic-numeric computation: design algorithms with a CACSD toolbox , 2004, Proceedings of the 2004 IEEE International Conference on Control Applications, 2004..