homology(Matrix,Matrix) -- homology of a pair of maps

Synopsis

• Function: homology

• Usage:

  M = homology(f,g)

• Inputs:
  • f, a matrix
  • g, a matrix
• Outputs:
  • M, a module, computes the homology module (kernel f)/(image g).

Description

In the following example, we ensure that the source of f and the target of f are exactly the same, taking even the degrees into account, and we ensure that f is homogeneous.

i1 : R = QQ[x]/x^5;

i2 : f = map(R^1,R^1,{{x^3}}, Degree => 3)

o2 = | x3 |

             1      1
o2 : Matrix R  <-- R

i3 : M = homology(f,f)

o3 = subquotient (| x2 |, | x3 |)

                               1
o3 : R-module, subquotient of R

i4 : prune M

o4 = cokernel {2} | x |

                            1
o4 : R-module, quotient of R