Improving the DISPGB algorithm using the discriminant ideal. In this paper we use Weispfenning’s CCGB ideas to make substantial improvements on Montes’ DISPGB algorithm. It now includes rewriting of the discussion tree using the discriminant ideal and provides a compact and effective discussion. We also describe the new algorithms in the DPGB library containing the improved DISPGB as well as new routines for checking whether a given basis is a CGB or not, and for obtaining a CGB. Examples and tests are also provided.

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  1. Lu, Dong; Sun, Yao; Wang, Dingkang: A survey on algorithms for computing comprehensive Gröbner systems and comprehensive Gröbner bases (2019)
  2. DeCastro-García, Noemí: Feedback equivalence of convolutional codes over finite rings (2017)
  3. Dehghani Darmian, Mahdi; Hashemi, Amir: Parametric FGLM algorithm (2017)
  4. Hashemi, Amir; Dehghani Darmian, Mahdi; Barkhordar, Marzieh: Gröbner systems conversion (2017)
  5. Hashemi, Amir; M.-Alizadeh, Benyamin; Dehghani Darmian, Mahdi: Computing comprehensive Gröbner systems: a comparison of two methods (2017)
  6. Kapur, Deepak: Comprehensive Gröbner basis theory for a parametric polynomial ideal and the associated completion algorithm (2017)
  7. Kredel, Heinz: Comprehensive Gröbner bases in a Java computer algebra system (2014)
  8. Darmian, Mahdi Dehghani; Hashemi, Amir; Montes, Antonio: Erratum to “A new algorithm for discussing Gröbner bases with parameters” [J. Symbolic Comput. 33 (1-2) (2002) 183-208] (2011)
  9. Sato, Yosuke; Inoue, Shutaro; Suzuki, Akira; Nabeshima, Katsusuke; Sakai, Ko: Boolean Gröbner bases (2011)
  10. Montes, Antonio; Wibmer, Michael: Gröbner bases for polynomial systems with parameters (2010)
  11. Nabeshima, Katsusuke: On the computation of parametric Gröbner bases for modules and syzygies (2010)
  12. Inoue, Shutaro: On the computation of comprehensive Boolean Gröbner bases (2009)
  13. Jin, Meng: Properties of regular systems and algorithmic improvements for regular decomposition (2009)
  14. Manubens, Montserrat; Montes, Antonio: Minimal canonical comprehensive Gröbner systems (2009)
  15. Lazard, Daniel; Rouillier, Fabrice: Solving parametric polynomial systems (2007)
  16. Manubens, Montserrat; Montes, Antonio: Improving the DISPGB algorithm using the discriminant ideal (2006)