# forceGB(...,ChangeMatrix=>...) -- inform Macaulay2 about the change of basis matrix from GB to generators

## Synopsis

• Usage:
forceGB(...,ChangeMatrix=>m)
• Inputs:
• m,
• 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]; -- registering polynomial ring 3 at 0x7f7085b65600 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

## Further information

• Default value: null
• Function: forceGB -- declare that the columns of a matrix are a Gröbner basis
• Option key: ChangeMatrix -- an optional argument