PGB

We describe a new software package, named PGB, for computing parametric polynomial systems and related objects. PGB is applicable to a wide range of expressions for many of which there has not been any software available up to now. The purpose of this paper is to illustrate how to solve using that package.

Keywords for this software

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References in zbMATH (referenced in 18 articles , 2 standard articles )

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  1. Nabeshima, Katsusuke; Ohara, Katsuyoshi; Tajima, Shinichi: Comprehensive Gröbner systems in PBW algebras, Bernstein-Sato ideals and holonomic (D)-modules (2018)
  2. Dehghani Darmian, Mahdi; Hashemi, Amir: Parametric FGLM algorithm (2017)
  3. Kapur, Deepak: Comprehensive Gröbner basis theory for a parametric polynomial ideal and the associated completion algorithm (2017)
  4. Zhou, Jie; Wang, Dingkang; Sun, Yao: Automated reducible geometric theorem proving and discovery by Gröbner basis method (2017)
  5. Chen, Zhenghong; Tang, Xiaoxian; Xia, Bican: Generic regular decompositions for parametric polynomial systems (2015)
  6. Kredel, Heinz: Parametric solvable polynomial rings and applications (2015)
  7. Kredel, Heinz: Comprehensive Gröbner bases in a Java computer algebra system (2014)
  8. Kapur, Deepak; Sun, Yao; Wang, Dingkang: An efficient algorithm for computing a comprehensive Gröbner system of a parametric polynomial system (2013)
  9. Nabeshima, Katsusuke: On the computation of parametric Gröbner bases for modules and syzygies (2010)
  10. Kredel, Heinz: Comprehensive Gröbner bases in a Java computer algebra system (2009)
  11. Nabeshima, Katsusuke: PGB: a package for computing parametric polynomial systems (2009)
  12. Nagasaka, Kosaku: A study on Gröbner basis with inexact input (2009)
  13. Sato, Yosuke; Suzuki, Akira: Computation of inverses in residue class rings of parametric polynomial ideals (2009)
  14. Nabeshima, Katsusuke: PGB: a package for computing parametric Gröbner and related objects (2007) ioport
  15. Nabeshima, Katsusuke: A speed-up of the algorithm for computing comprehensive Gröbner systems (2007)
  16. Contino, Roberto; Nomura, Yasunori; Pomarol, Alex: Higgs as a holographic pseudo-Goldstone boson (2003)
  17. Kuchment, Peter: The mathematics of photonic crystals (2001)
  18. Saber, Hussein M.; Ravindran, A.: A partitioning gradient based (PGB) algorithm for solving nonlinear goal programming problems (1996)