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DGAlgebras :: killCycles

killCycles -- Adjoins variables to make non-bounding cycles boundaries in the lowest positive degree with nontrivial homology.

Synopsis

Description

i1 : R = ZZ/101[a,b,c,d]/ideal{a^3,b^3,c^3-d^4}

o1 = R

o1 : QuotientRing
i2 : A = koszulComplexDGA(R)

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

o2 : DGAlgebra
i3 : A.diff

o3 = map (R[T ..T ], R[T ..T ], {a, b, c, d, a, b, c, d})
             1   4      1   4

o3 : RingMap R[T ..T ] <--- R[T ..T ]
                1   4          1   4
i4 : B = killCycles(A)

o4 = {Ring => R                                              }
      Underlying algebra => R[T ..T ]
                               1   7
                                    2     2       2      3
      Differential => {a, b, c, d, a T , b T , - c T  + d T }
                                      1     2       3      4

o4 : DGAlgebra
i5 : B.diff

                                              2     2       2      3
o5 = map (R[T ..T ], R[T ..T ], {a, b, c, d, a T , b T , - c T  + d T , a, b, c, d})
             1   7      1   7                   1     2       3      4

o5 : RingMap R[T ..T ] <--- R[T ..T ]
                1   7          1   7

Ways to use killCycles :

For the programmer

The object killCycles is a method function with options.