### D.4.32 rstandard_lib

Library:
  rstandard.lib
Purpose:
  Computes Janet bases and border bases for ideals

Authors:
  Shamsa Kanwal lotus_zone16@yahoo.com
  Gerhard Pfister pfister@mathematik.uni-kl.de

Overview:
  Computing Janet bases and border bases for any ordering using the idea of r-standard bases (defined by V. Gerdt)

References:
  [1] A. Kehrein, M. Kreuzer, L. Robbiano: An algebrists view on border bases, in: A. Dickenstein and I. Emiris (eds.), Solving Polynomial Equations: Foundations, Algorithms and Applications, Springer, Heidelberg 2005, 169-202.

  [2] V.P. Gerdt: Involute Algorithms for Computing Groebner Bases, In Computational Commutative and Non-Computational Algebra Geometry, S.Conjocaru, G. Pfister and V. Ufnarovski (Eds.), NATO Science Series,105 Press 2005, 199-255.

Procedures:

> D.4.32.1 borderBasis |  | computes a border basis of the ideal I
> D.4.32.2 modBorder |  | computes a border basis of the ideal I using modular methods
> D.4.32.3 rJanet |  | computes a Janet basis of the ideal I
> D.4.32.4 modJanet |  | computes a Janet basis of the ideal I using modular methods

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