koszul(Matrix) -- the Koszul complex

• Function: koszul

• Usage:

  g = koszul f

• Inputs:
  • f, a matrix, a 1 by n matrix
• Outputs:
  • g, a complex, 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 : C = koszul f

      1      4      6      4      1
o3 = R  <-- R  <-- R  <-- R  <-- R
                                  
     0      1      2      3      4

o3 : Complex

i4 : C.dd^2

o4 = 0

o4 : ComplexMap