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

Description

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.

References

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

Version

This documentation describes version 0.1 of SagbiGbDetection.

Citation

If you have used this package in your research, please cite it as follows:

@misc{SagbiGbDetectionSource,
  title = {{SagbiGbDetection: A \emph{Macaulay2} package. Version~0.1}},
  author = {Viktoriia Borovik and Timothy Duff and Elima Shehu},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages}}
}

Exports

Functions and commands
- weightVectorsRealizingGB -- The main function for detecting Gröbner bases
- weightVectorsRealizingSAGBI -- The main function for detecting SAGBI bases
Methods
- weightVectorsRealizingGB(List) -- see weightVectorsRealizingGB -- The main function for detecting Gröbner bases
- weightVectorsRealizingGB(Matrix) -- see weightVectorsRealizingGB -- The main function for detecting Gröbner bases
- weightVectorsRealizingSAGBI(List) -- see weightVectorsRealizingSAGBI -- The main function for detecting SAGBI bases
- weightVectorsRealizingSAGBI(Matrix) -- see weightVectorsRealizingSAGBI -- The main function for detecting SAGBI bases

For the programmer

The object SagbiGbDetection is a package, defined in SagbiGbDetection.m2.

The source of this document is in SagbiGbDetection.m2:139:0.