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

Usage:

phi = dgAlgebraMap(B,A,M)
Inputs:
- A, an instance of the type DGAlgebra, Source
- B, an instance of the type DGAlgebra, Target
- M, a matrix, A matrix representing where the generators of A should be mapped to (akin to ringMap)
Outputs:
- phi, an instance of the type DGAlgebraMap,

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   ]
                               1,1   1,3
      Differential => {a, b, c}

o2 : DGAlgebra

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

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

o3 : DGAlgebra

i4 : g = dgAlgebraMap(K1,K2,matrix{{Y_(1,2),Y_(1,3)}})

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

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_(1,1),T_(1,2)}})

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

o6 : DGAlgebraMap

i7 : isWellDefined f

o7 = false

Ways to use dgAlgebraMap:

dgAlgebraMap(DGAlgebra,DGAlgebra,Matrix)

For the programmer

The object dgAlgebraMap is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:9021:0.