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.

Authors

• Viktoriia Borovik <[email protected]>
• Timothy Duff <[email protected]>
• Elima Shehu <[email protected]>

Version

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.

Exports