koszul(ZZ,Matrix) -- a differential in a Koszul complex

• Function: koszul

• Usage:

  g = koszul(i,f)

• Inputs:
  • i, an integer
  • f, a matrix, a 1 by n matrix
• Outputs:
  • g, a matrix, the i-th differential in the Koszul complex of the matrix f

i1 : R = QQ[x_1..x_4];

i2 : f = matrix{{x_1..x_4}}

o2 = | x_1 x_2 x_3 x_4 |

             1      4
o2 : Matrix R  <-- R

i3 : koszul(2,f)

o3 = {1} | -x_2 -x_3 0    -x_4 0    0    |
     {1} | x_1  0    -x_3 0    -x_4 0    |
     {1} | 0    x_1  x_2  0    0    -x_4 |
     {1} | 0    0    0    x_1  x_2  x_3  |

             4      6
o3 : Matrix R  <-- R