forceGB(...,ChangeMatrix=>...) -- specify the change of basis matrix from a Gröbner basis to the generators of a module

Usage:

forceGB(...,ChangeMatrix=>m)
Inputs:
- m, a matrix
Consequences:
- Set the change of basis matrix from the Gröbner basis to the original generators

Description

The matrix m should have size a by b, where a is the number of columns of the original matrix, and b is the number of columns of f.

i1 : gbTrace = 3

o1 = 3

i2 : R = ZZ[x,y,z];

i3 : f = matrix{{x^2-3, y^3-1, z^4-2}};

             1      3
o3 : Matrix R  <-- R

i4 : g = forceGB(f, ChangeMatrix=>id_(source f));

i5 : x^2*y^3 // g

o5 = {2} | y3 |
     {3} | 3  |
     {4} | 0  |

             3      1
o5 : Matrix R  <-- R

forceGB(...,ChangeMatrix=>...) -- specify the change of basis matrix from a Gröbner basis to the generators of a module
gb(...,ChangeMatrix=>...) -- see gb -- compute a Gröbner basis
markedGB(...,ChangeMatrix=>...) -- see markedGB(Matrix,Matrix) -- make a marked Gröbner basis
smithNormalForm(...,ChangeMatrix=>...) -- see smithNormalForm(Matrix) -- smith normal form for a matrix over a PID

The source of this document is in Macaulay2Doc/functions/forceGB-doc.m2:68:0.