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

Synopsis

• Usage:

  forceGB(...,ChangeMatrix=>m)

• Inputs:
  • m, a matrix
• Consequences:

  • Set the change of basis matrix from the Gröbner basis to the original generators

Description

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

Further information

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

Functions with optional argument named ChangeMatrix :

• forceGB(...,ChangeMatrix=>...) -- inform Macaulay2 about the change of basis matrix from GB to generators
• gb(...,ChangeMatrix=>...) -- see gb -- compute a Gröbner basis
• hermite(...,ChangeMatrix=>...) (missing documentation)
• LLL(...,ChangeMatrix=>...) -- also find change of basis matrix
• markedGB(...,ChangeMatrix=>...) -- see markedGB(Matrix,Matrix) -- make a marked Gröbner basis
• smithNormalForm(...,ChangeMatrix=>...) -- see smithNormalForm(Matrix) -- smith normal form for a matrix over ZZ or a PID