wedgeProduct(ZZ,ZZ,Module) -- the exterior multiplication map

• Function: wedgeProduct

• Usage:

  wedgeProduct(p,q,F)

• Inputs:
  • p, an integer
  • q, an integer
  • F, a module, a free module
• Outputs:
  • a matrix, representing the multiplication map from exteriorPower(p,M) ** exteriorPower(q,M) to exteriorPower(p+q,M)

i1 : F = QQ^4

       4
o1 = QQ

o1 : QQ-module, free

i2 : wedgeProduct(1,1,F)

o2 = | 0 1 0 0 -1 0 0 0 0  0  0 0 0  0  0  0 |
     | 0 0 1 0 0  0 0 0 -1 0  0 0 0  0  0  0 |
     | 0 0 0 0 0  0 1 0 0  -1 0 0 0  0  0  0 |
     | 0 0 0 1 0  0 0 0 0  0  0 0 -1 0  0  0 |
     | 0 0 0 0 0  0 0 1 0  0  0 0 0  -1 0  0 |
     | 0 0 0 0 0  0 0 0 0  0  0 1 0  0  -1 0 |

              6       16
o2 : Matrix QQ  <-- QQ