bgg -- the ith differential of the complex R(M)

• Usage:

  bgg(i,M,E)

• Inputs:
  • i, an integer, the cohomological index
  • M, a module, graded S-module
  • E, a polynomial ring, exterior algebra
• Outputs:
  • a matrix, a matrix representing the ith differential

i1 : S = ZZ/32003[x_0..x_2]; 

i2 : E = ZZ/32003[e_0..e_2, SkewCommutative=>true];

i3 : M = coker matrix {{x_0^2, x_1^2, x_2^2}};

i4 : bgg(1,M,E)

o4 = {-2} | e_1 e_0 0   |
     {-2} | e_2 0   e_0 |
     {-2} | 0   e_2 e_1 |

             3      3
o4 : Matrix E  <-- E

i5 : bgg(2,M,E)

o5 = {-3} | e_2 e_1 e_0 |

             1      3
o5 : Matrix E  <-- E