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DGAlgebras :: acyclicClosure

acyclicClosure -- Compute theae acyclic closure of a DGAlgebra.

Synopsis

Description

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

o1 = R

o1 : QuotientRing
i2 : A = koszulComplexDGA(R);
i3 : B = acyclicClosure(A,EndDegree=>3)

o3 = {Ring => R                                  }
      Underlying algebra => R[T ..T ]
                               1   6
                                 2     2     2
      Differential => {a, b, c, a T , b T , c T }
                                   1     2     3

o3 : DGAlgebra
i4 : toComplex(B,8)

      1      3      6      10      15      21      28      36      45
o4 = R  <-- R  <-- R  <-- R   <-- R   <-- R   <-- R   <-- R   <-- R
                                                                   
     0      1      2      3       4       5       6       7       8

o4 : ChainComplex
i5 : B.diff

                                           2     2     2
o5 = map (R[T ..T ], R[T ..T ], {a, b, c, a T , b T , c T , a, b, c})
             1   6      1   6                1     2     3

o5 : RingMap R[T ..T ] <--- R[T ..T ]
                1   6          1   6

See also

Ways to use acyclicClosure :

For the programmer

The object acyclicClosure is a method function with options.