Homogenity, pseudo-homogenity, and Gröbner basis computations

  • Thomas Becker
Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 539)


Let K[X] be a multivariate polynomial ring over a field K, and let U ⊑ X. We call fK[X] pseudo-homogeneous in U if either it contains no variable of U, or each of its terms does. U ⊑ X is called an H-set for FK[X] if each fF is pseudo-homogeneous in U. We show that when computing an elimination ideal of some ideal (F) of K[X] w.r.t. V ⊑ X, one may disregard all those elements of F that contain variables from some H-set U ⊑ X/V for F. For given F and V, we compute a maximal H-set for F contained in V. Furthermore, we discuss how one can compute gradings by weighted total degree that make a given finite FK[X] homogeneous. For certain limited purposes, one can then compute truncated Gröbner bases instead of full ones.


Integer Linear Programming Finite Subset Critical Pair Finite Basis Integer Linear Programming Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Thomas Becker
    • 1
  1. 1.Fakultät für Mathematik und InformatikUniversität PassauPassauFR Germany

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