## CGSQE

 swMATH ID: 20574 Software Authors: Fukasaku, Ryoya; Iwane, Hidenao; Sato, Yosuke Description: CGSQE/SyNRAC: a real quantifier elimination package based on the computation of comprehensive Gr”obner systems. CGSQE is a Maple package for real quantifier elimination (QE) we are developing. It works cooperating with SyNRAC which is also a Maple package for real QE one of the authors is developing. For a given first order formula, CGSQE eliminates all possible quantifiers using the underlying equational constraints by the computation of comprehensive Gr”obner systems (CGSs). In case all quantifiers are not removable, it transforms the given formula into a formula which contains only strict inequalities of quantified variables, then uses a cylindrical algebraic decomposition based real QE program of SyNRAC to remove the remaining quantifiers. The core algorithm of CGSQE is a CGS real QE algorithm which was first introduced by Weispfenning in 1998 and further improved by us in 2015 so that we can make a satisfactorily practical implementation. CGSQE is superior to other real QE implementations for many examples which contain many equational constraints. In the software presentation, we would like to show high-performance computation of CGSQE. Homepage: http://dl.acm.org/citation.cfm?id=3015313 Dependencies: Maple Related Software: REDLOG; QEPCAD; PGB; SYNRAC; Maple Cited in: 2 Publications

### Cited by 3 Authors

 2 Fukasaku, Ryoya 2 Iwane, Hidenao 2 Sato, Yosuke

### Cited in 2 Serials

 1 Mathematics in Computer Science 1 ACM Communications in Computer Algebra

### Cited in 3 Fields

 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Computer science (68-XX)