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

## Synopsis

• 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 representing where the generators of A should be mapped to (akin to ringMap)
• Outputs:

## 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 :

• "dgAlgebraMap(DGAlgebra,DGAlgebra,Matrix)"

## For the programmer

The object dgAlgebraMap is .