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DGAlgebras :: dgAlgebraMap

dgAlgebraMap -- Define a DG algebra map between DG algebras.

Synopsis

Description

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

o1 = R

o1 : QuotientRing
i2 : K1 = koszulComplexDGA(ideal vars R,Variable=>"Y")

o2 = {Ring => R                      }
      Underlying algebra => R[Y ..Y ]
                               1   3
      Differential => {a, b, c}

o2 : DGAlgebra
i3 : K2 = koszulComplexDGA(ideal {b,c},Variable=>"T")

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

o3 : DGAlgebra
i4 : g = dgAlgebraMap(K1,K2,matrix{{Y_2,Y_3}})

o4 = map (R[Y ..Y ], R[T ..T ], {Y , Y , a, b, c})
             1   3      1   2     2   3

o4 : DGAlgebraMap
i5 : isWellDefined g

o5 = true

The function does not check that the DG algebra map is well defined, however.

i6 : f = dgAlgebraMap(K2,K1,matrix{{0,T_1,T_2}})

o6 = map (R[T ..T ], R[Y ..Y ], {0, T , T , a, b, c})
             1   2      1   3        1   2

o6 : DGAlgebraMap
i7 : isWellDefined f

o7 = false

Ways to use dgAlgebraMap :

For the programmer

The object dgAlgebraMap is a method function.