It is checked that the map $f: M \ \to\ L$ maps the relations in $M$ to 0 up to degree $n$ and that $f$ commutes with the differentials in $M$ and $L$. If $n$ is big enough and ideal(M) is of type List, then it is possible to get that $f$ maps all relations to 0, which is noted as the message "the map is well defined for all degrees". This may happen even if the map does not commute with the differential (see g in the example below).
i1 : L=lieAlgebra({a,b},Signs=>1,LastWeightHomological=>true,
Weights=>{{1,0},{2,1}})
o1 = L
o1 : LieAlgebra
|
i2 : F=lieAlgebra({a,b,c},
Weights=>{{1,0},{2,1},{5,2}},Signs=>1,LastWeightHomological=>true)
o2 = F
o2 : LieAlgebra
|
i3 : D=differentialLieAlgebra{0_F,a a,a a a b}
o3 = D
o3 : LieAlgebra
|
i4 : Q1=D/{a a a a b,a b a b + a c}
o4 = Q1
o4 : LieAlgebra
|
i5 : use F |
i6 : Q2=F/{a a a a b,a b a b + a c}
o6 = Q2
o6 : LieAlgebra
|
i7 : f=map(D,Q1)
warning: the map might not be well defined,
use isWellDefined
o7 = f
o7 : LieAlgebraMap
|
i8 : isWellDefined(6,f) the map is not well defined the map commutes with the differential for all degrees o8 = false |
i9 : g=map(Q1,Q2)
warning: the map might not be well defined,
use isWellDefined
o9 = g
o9 : LieAlgebraMap
|
i10 : isWellDefined(6,g) the map is well defined for all degrees the map does not commute with the differential o10 = false |
i11 : h=map(Q1,D) o11 = h o11 : LieAlgebraMap |
i12 : isWellDefined(6,h) the map is well defined for all degrees the map commutes with the differential for all degrees o12 = true |