If both $A$ and $B$ are instances of FGLieIdeal, then $S$ is of type FGLieIdeal. Otherwise, if both $A$ and $B$ are instances of LieIdeal, then $S$ is of type LieIdeal. If exactly one of $A$ and $B$ is an instance of LieIdeal, and the other is an instance of LieSubAlgebra, then $S$ is of type LieSubAlgebra. Otherwise, $S$ is of type LieSubSpace.
i1 : F=lieAlgebra({a,b,c,r3,r4,r42},
Weights => {{1,0},{1,0},{2,0},{3,1},{4,1},{4,2}},
Signs=>{0,0,0,1,1,0},LastWeightHomological=>true)
o1 = F
o1 : LieAlgebra
|
i2 : D=differentialLieAlgebra{0_F,0_F,0_F,a c,a a c,r4 - a r3}
o2 = D
o2 : LieAlgebra
|
i3 : I=lieIdeal{b c - a c,a b,b r4 - a r4}
o3 = I
o3 : FGLieIdeal
|
i4 : Q=D/I o4 = Q o4 : LieAlgebra |
i5 : f=map(Q,D) o5 = f o5 : LieAlgebraMap |
i6 : J=lieIdeal{a c}
o6 = J
o6 : FGLieIdeal
|
i7 : K=inverse(f,J) o7 = K o7 : LieIdeal |
i8 : use D |
i9 : I+lieIdeal{a c}
o9 = finitely generated ideal of D
o9 : FGLieIdeal
|
i10 : dims(6,oo)
o10 = | 0 1 4 7 16 30 |
| 0 0 0 0 2 9 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
6 6
o10 : Matrix ZZ <--- ZZ
|
i11 : dims(6,K)
o11 = | 0 1 4 7 16 30 |
| 0 0 0 0 2 9 |
| 0 0 0 0 0 1 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 0 0 0 0 0 |
6 6
o11 : Matrix ZZ <--- ZZ
|