sumBetti -- Computes the sum of Betti numbers.

• Usage:

  sumBetti M

• Inputs:
  • M, a module,
• Outputs:
  • an integer, sum of the Betti numbers of the resolution of M

i1 : S = QQ[a..f];

i2 : m = matrix{{a,b,d,e},{b,c,e,f}}

o2 = | a b d e |
     | b c e f |

             2      4
o2 : Matrix S  <-- S

i3 : M = coker m

o3 = cokernel | a b d e |
              | b c e f |

                            2
o3 : S-module, quotient of S

i4 : sumBetti M

o4 = 12