The list b should contain LieElement of the same weight. The output is the dimension for the inverse image under f of the space generated by b. This dimension for a MapLie f and a list b of elements of degree n may also be computed as the dimension of the intersection of imageBasisLie(n,f) and b plus the dimension of the kernel of f in degree n (or n - degLie(f) if f is a derivation).
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+y,x-y}) o3 = f o3 : MapLie |
i4 : d = derLie(f,{x x,x y}) o4 = d o4 : DerLie |
i5 : invImageLie(f,{x y x}) o5 = 1 |
i6 : invImageLie(d,{x y x}) o6 = 2 |
i7 : useLie L o7 = L o7 : LieAlgebra |
i8 : length intersectionLie(3,{imageBasisLie(3,f),{x y x}})+length kernelBasisLie(3,f) o8 = 1 |
i9 : length intersectionLie(3,{imageBasisLie(3,d),{x y x}})+length kernelBasisLie(2,d) o9 = 2 |