This page describes the most common use of the Groebner package, namely calculations of Groebner bases and related operations for ideals in (commutative) polynomial rings. The Groebner package is actually much more general and can handle polynomials in skew polynomial rings (see Groebner/details) and modules over (commutative or skew) polynomial rings (see Groebner Bases for Modules). Each command in the Groebner package can be accessed by using either the long form or the short form of the command name in the command calling sequence. As the underlying implementation of the Groebner package is a module, it is also possible to use the form Groebner:-command to access a command from the package. For more information, see Module Members.

References in zbMATH (referenced in 15 articles )

Showing results 1 to 15 of 15.
Sorted by year (citations)

  1. Cox, David A.; Little, John; O’Shea, Donal: Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra (2015)
  2. Jin, Meng; Li, Xiaoliang; Wang, Dongming: A new algorithmic scheme for computing characteristic sets (2013)
  3. Rodríguez-Carbonell, Enric; Kapur, Deepak: Automatic generation of polynomial loop invariants: algebraic foundations (2004)
  4. Koepf, Wolfram; Schmersau, Dieter: Recurrence equations and their classical orthogonal polynomial solutions (2002)
  5. Gatermann, Karin; Lauterbach, Reiner: Automatic classification of normal forms (1998)
  6. Scheen, Christian: Implementation of the Painlevé test for ordinary differential systems (1997)
  7. Gatermann, Karin: Semi-invariants, equivariants and algorithms (1996)
  8. Hietarinta, J.: The complete solution to the constant quantum Yang-Baxter equation in two dimensions (1993)
  9. Hietarinta, Jarmo: Solving the two-dimensional constant quantum Yang-Baxter equation (1993)
  10. Hietarinta, Jarmo: The upper triangular solutions to the three-state constant quantum Yang- Baxter equation (1993)
  11. Ioakimidis, N.I.; Anastasselou, E.G.: Computer-based manipulation of systems of equations in elasticity problems with Gröbner bases (1993)
  12. Möller, H.Michael: On decomposing systems of polynomial equations with finitely many solutions (1993)
  13. Hietarinta, Jarmo: Solving the constant quantum Yang-Baxter equation in 2 dimensions with massive use of factorizing Gröbner basis computations (1992)
  14. Verschelde, Jan; Cools, Ronald: Nonlinear reduction for solving deficient polynomial systems by continuation methods (1992)
  15. Cooper, A.Brinton III: Finding BCH error locator polynomials in one step (1991)