It is checked that the derivation (d,f): M → 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 → M, then the derivation (d*p,f*p): F → L maps I to 0 in degrees ≤ 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 |
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 |