maxMinors -- computes the ideal generated by the maximal non-vanishing minors of a given matrix

• Usage:

  maxMinors M

• Inputs:
  • M, a matrix, with entries in a ring R.
• Outputs:
  • an ideal, the ideal generated by maximal non-vanishing minors of the matrix M.

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : M = matrix{{x,0},{-y,x},{0,-y}}

o2 = | x  0  |
     | -y x  |
     | 0  -y |

             3      2
o2 : Matrix R  <-- R

i3 : maxMinors M

             2         2
o3 = ideal (x , -x*y, y )

o3 : Ideal of R

i4 : N = matrix{{0_R}}

o4 = 0

             1      1
o4 : Matrix R  <-- R

i5 : maxMinors N

o5 = ideal 1

o5 : Ideal of R