The list b should contain generalExpressionLie of the same degree n (and also homological degree d in the second case). The output is the dimension for the inverse image under f of the space generated by b. This dimension for a MapLie f may also be computed as the dimension of the intersection of image(f) and b plus the dimension of kernel(f) in degree n.
i1 : L=lieAlgebra({x,y},{},genSigns=>1) o1 = L o1 : LieAlgebra |
i2 : M=lieAlgebra({a,b},{},genSigns=>1) o2 = M o2 : LieAlgebra |
i3 : f = mapLie(L,M,{[x],[]}) o3 = f o3 : MapLie |
i4 : d = derLie(f,{[x,x],[x,y]}) o4 = d o4 : DerLie |
i5 : invImageLie(3,f,{[x,y,x]}) o5 = 2 |
i6 : invImageLie(3,d,{[x,y,x]}) o6 = 3 |
i7 : length intersectionLie(3,{imageBasisLie(3,f),{[x,y,x]}})+length kernelBasisLie(3,f) o7 = 2 |