Q=L/x
Consider first the case where $L$ has zero differential, and where $L$ is finitely presented as a quotient of a free Lie algebra $F$. In this case, the output $Q$ is also finitely presented as a quotient of $F$.






In case $L$ has a nonzero differential, the program adds relations depending on the fact that the ideal should be invariant under the differential. These extra (nonnormalized) relations may be looked upon using describe(LieAlgebra). Observe that $D$ is not free in this example, see differentialLieAlgebra.








If the input Lie algebra $L$ is given as a finitely presented Lie algebra $M$ modulo an ideal $J$ that is not (known to be) finitely generated (e.g., the kernel of a homomorphism ), then the output Lie algebra $Q$ is presented as a quotient of a finitely presented Lie algebra $N$ by an ideal $I$, where $N$ is given as $M$ modulo a lifting of the input list $x$ to $M$, and $I$ is the image of the natural map from $M$ to $N$ applied to $J$, see image(LieAlgebraMap,LieSubSpace).










