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DGAlgebras :: toComplex(DGAlgebra,ZZ)

toComplex(DGAlgebra,ZZ) -- Converts a DGAlgebra to a ChainComplex

Synopsis

Description

i1 : R = ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3,d^3}

o1 = R

o1 : QuotientRing
i2 : A = acyclicClosure(R,EndDegree=>3)

o2 = {Ring => R                                           }
      Underlying algebra => R[T ..T ]
                               1   8
                                    2     2     2     2
      Differential => {a, b, c, d, a T , b T , c T , d T }
                                      1     2     3     4

o2 : DGAlgebra

The above will be a resolution of the residue field over R, since R is a complete intersection.

i3 : C = toComplex(A, 10)

      1      4      10      20      35      56      84      120      165      220      286
o3 = R  <-- R  <-- R   <-- R   <-- R   <-- R   <-- R   <-- R    <-- R    <-- R    <-- R
                                                                                       
     0      1      2       3       4       5       6       7        8        9        10

o3 : ChainComplex
i4 : apply(10, i -> prune HH_i(C))

o4 = {cokernel | d c b a |, 0, 0, 0, 0, 0, 0, 0, 0, 0}

o4 : List