21.2 Brute Force: Many shrinks

21.2.1 ShrinkBasis[aListOfPolynomials,iterations]

Aliases: None
Description: ShrinkBasis can take a long time to run and returns a {L1,L2,,Lr} of lists of polynomials. Each list Lj of polynomials is contained in aListOfPolynomials. Each list Lj is a generating set for the ideal generated by aListOfPolynomials and the computer makes a limited attempt to show that any proper subset of Lj does not generate the ideal. Moreover, the union of the Lj’s is aListOfPolynomials.
 
ShrinkBasis depends upon the monomial order which is set, because it calls NCMakeGB where it iterates at most iterations times. If all of the runs of NCMakeGB generate Gröbner Bases in iterations iterations, then no proper subset of an Lj is a generating set for the ideal generated by aListOfPolynomials.
 
The command works by brute force. It selects a polynomial from aListOfPolynomials and computes a partial GB for the remaining polynomials (with iterations iterations). It uses these to eliminate the original polynomial.
Arguments: aListOfPolynomials is a list of polynomials. fileName is a string.
Comments / Limitations: Not available before NCAlgebra 1.2