It is checked that the derivation $(d,f): M \ \to\ L$ maps the ideal of relations in $M$ to 0 up to degree $n$. More precisely, if $M=F/I$ where $F$ is free, and $p$ is the projection $F$ \ \to\ $M$, then the derivation $(d*p,f*p): F \ \to\ L$ maps $I$ to 0 in degrees $\le\ n$. If $n$ is big enough and $I$ is a list, then it is possible to get the information "the derivation is well defined for all degrees".
i1 : F=lieAlgebra{a,b}
o1 = F
o1 : LieAlgebra
|
i2 : L=F/{a a a b,b b b a}
o2 = L
o2 : LieAlgebra
|
i3 : e=euler L o3 = e o3 : LieDerivation |
i4 : isWellDefined(4,e) the derivation is well defined for all degrees o4 = true |
i5 : d4=lieDerivation{0_L,a b a b a}
warning: the derivation might not be well defined, use isWellDefined
o5 = d4
o5 : LieDerivation
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i6 : isWellDefined(4,d4) o6 = false |
i7 : d5=lieDerivation{0_L,b a b a b a}
warning: the derivation might not be well defined, use isWellDefined
o7 = d5
o7 : LieDerivation
|
i8 : isWellDefined(4,d5) the derivation is well defined for all degrees o8 = true |
i9 : di=innerDerivation(a b a b a) o9 = d5 o9 : LieDerivation |
i10 : isWellDefined(4,di) the derivation is well defined for all degrees o10 = true |
i11 : di===d5 o11 = true |