QEPCAD

QEPCAD B: A program for computing with semi-algebraic sets using CADs QEPCAD is an implementation of quantifier elimination by partial cylindrical algebraic decomposition due orginally to Hoon Hong, and subsequently added on to by many others. It is an interactive command-line program written in C/C++, and based on the SACLIB library. Presented here is QEPCAD B version 1.x, the ”B” designating a substantial departure from the original QEPCAD and distinguishing it from any development of the original that may proceed in a different direction. QEPCAD and the SACLIB library are the result of a program of research by George Collins and his PhD students that has spanned several decades ... and continues still! I extended and improved QEPCAD for several years. Improvements that didn’t involve changes to the way the program interacted with the user I’d just go ahead and make. However, changes that affected the interaction of QEPCAD and the user, or changes that added new features were ”tacked on” to the program, requiring the user to know about extra commands. Moreover, there was no cannonical source for QEPCAD distribution or documentation, and no internet accessible source at all. This branch of QEPCAD, QEPCAD ”B”, was introduced to address those problems - to make QEPCAD easily accessable through the internet, to provide good documentation, and to incorporate many improvements and extensions in a way that makes them most accessible to the user.

This software is also peer reviewed by journal TOMS.


References in zbMATH (referenced in 214 articles , 1 standard article )

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  1. Bradford, Russell; Davenport, James H.; England, Matthew; McCallum, Scott; Wilson, David: Truth table invariant cylindrical algebraic decomposition (2016)
  2. Dixit, Atul; Moll, Victor H.; Pillwein, Veronika: A hypergeometric inequality (2016)
  3. Eraşcu, Mădălina; Hong, Hoon: Real quantifier elimination for the synthesis of optimal numerical algorithms (case study: square root computation) (2016)
  4. Fukasaku, Ryoya; Iwane, Hidenao; Sato, Yosuke: On the implementation of CGS real QE (2016)
  5. Han, Jingjun; Jin, Zhi; Xia, Bican: Proving inequalities and solving global optimization problems via simplified CAD projection (2016)
  6. Kahle, Thomas: On the feasibility of semi-algebraic sets in Poisson regression (2016)
  7. McCallum, Scott; Hong, Hoon: On using Lazard’s projection in CAD construction (2016)
  8. Strzeboński, Adam: Cylindrical algebraic decomposition using local projections (2016)
  9. Vandaele, Arnaud; Gillis, Nicolas; Glineur, François; Tuyttens, Daniel: Heuristics for exact nonnegative matrix factorization (2016)
  10. Brown, Christopher W.; Košta, Marek: Constructing a single cell in cylindrical algebraic decomposition (2015)
  11. Cimatti, Alessandro; Micheli, Andrea; Roveri, Marco: An SMT-based approach to weak controllability for disjunctive temporal problems with uncertainty (2015)
  12. Hong, Hoon; Tang, Xiaoxian; Xia, Bican: Special algorithm for stability analysis of multistable biological regulatory systems (2015)
  13. Xu, Ming; Li, Zhi-Bin; Yang, Lu: Quantifier elimination for a class of exponential polynomial formulas (2015)
  14. Anai, Hirokazu: Applied algebraic geometry in model based design for manufacturing (2014)
  15. Bradford, Russell; Chen, Changbo; Davenport, James H.; England, Matthew; Moreno Maza, Marc; Wilson, David: Truth table invariant cylindrical algebraic decomposition by regular chains (2014)
  16. Chen, Changbo; Maza, Marc Moreno: An incremental algorithm for computing cylindrical algebraic decompositions (2014)
  17. Duracz, Jan; Konečný, Michal: Polynomial function intervals for floating-point software verification (2014)
  18. Eirinakis, Pavlos; Ruggieri, Salvatore; Subramani, K.; Wojciechowski, Piotr: On quantified linear implications (2014)
  19. Han, Jingjun: A simple quantifier-free formula of positive semidefinite cyclic ternary quartic forms (2014)
  20. Hladík, Milan; Ratschan, Stefan: Efficient solution of a class of quantified constraints with quantifier prefix exists-forall (2014)

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