The generators of M=f.sourceLie are mapped to the elements in the last argument defs and they should be given as generalExpressionLie in L=f.targetLie. If no f of class MapLie is given, then the current Lie algebra L is used and the derivation d maps L to L (and f is the identity map). The set of elements of class DerLie is a Lie algebra with Lie multiplication multDerLie, however it does not belong to LieAlgebra if we do not have a finite presentation. It is checked by the program that d maps the relations in d.sourceLie to zero.
i1 : L=lieAlgebra({x,y},{},genSigns=>1) o1 = L o1 : LieAlgebra |
i2 : M=lieAlgebra({a,b},{[b,a,b]},genSigns=>0,genWeights=>{2,2}) o2 = M o2 : LieAlgebra |
i3 : f = mapLie(L,M,{[x,x],[]}) o3 = f o3 : MapLie |
i4 : d1 = derLie(f,{[x,x],[x,y]}) o4 = d1 o4 : DerLie |
i5 : peek d1 o5 = DerLie{[b, a, b] => [] } a => [x, x] b => [x, y] maplie => f signDer => 0 sourceLie => M targetLie => L weightDer => {0, 0} |
i6 : evalDerLie(d1,[a,a,b]) o6 = {{-2}, {[x, x, x, y, x, x]}} o6 : List |
i7 : useLie L o7 = L o7 : LieAlgebra |
i8 : d2 = derLie({[x,x,y],[x,x,y]}) o8 = d2 o8 : DerLie |
i9 : peek d2 o9 = DerLie{maplie => MapLie{...4...}} signDer => 0 sourceLie => L targetLie => L weightDer => {2, 0} x => [x, x, y] y => [x, x, y] |
i10 : peek d2.maplie o10 = MapLie{sourceLie => L} targetLie => L x => [x] y => [y] |
i11 : evalDerLie(d2,[x,x,y]) 1 1 o11 = {{- -, -}, {[x, x, y, x, x], [y, x, y, x, x]}} 2 2 o11 : List |