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HH DifferentialModule -- computes the homology of a differential module

Description

This computes the homology of a differential module. More specifically: since we interpret differential modules as 3-term complexes, this returns the zeroth homology module.

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing
 
i2 : M = R^1/ideal(x^2,y^2)

o2 = cokernel | x2 y2 |

                            1
o2 : R-module, quotient of R
 
i3 : phi = map(M,M,x*y)

o3 = | xy |

o3 : Matrix M <-- M
 
i4 : D = differentialModule phi

o4 = M  <-- M <-- M
                   
     -1     0     1

o4 : DifferentialModule
 
i5 : HH D

o5 = subquotient (| y -x |, | xy x2 y2 |)

                               1
o5 : R-module, subquotient of R

See also

Ways to use this method:

The source of this document is in MultigradedBGG.m2:498:0.