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Macaulay2Doc :: homology(Matrix,Matrix)

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

Synopsis

Description

Here g and f should be composable maps with f*g equal to zero.

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