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SagbiGbDetection -- A package for finding term orders for which the given generators of an ideal/algebra form a Gröbner/SAGBI basis (resp.)


The main functions of this package implement the detection algorithms for Gröbner bases of ideals and SAGBI bases of finitely generated subalgebras of a polynomial ring. More precisely, for given generators of an ideal or a polynomial algebra, we find weight vectors representing all possible term orders for which these generators form a Gröbner basis or a SAGBI basis, respectively. If no weight vectors are returned, the given generators do not form a Gröbner/SAGBI basis for any order.

Documentation nodes for the main functions weightVectorsRealizingGB and weightVectorsRealizingSAGBI illustrate typical usage of this package.


  • Gritzmann, Peter, and Bernd Sturmfels. Minkowski addition of polytopes: computational complexity and applications to Gröbner bases. SIAM Journal on Discrete Mathematics 6.2 (1993): 246-269.
  • Sturmfels, Bernd. Grobner bases and convex polytopes. Vol. 8. American Mathematical Soc., 1996.



This documentation describes version 0.1 of SagbiGbDetection.

Source code

The source code from which this documentation is derived is in the file SagbiGbDetection.m2.


For the programmer

The object SagbiGbDetection is a package.