This talk is divided into two parts. The first part is about finding the classification of small-dimensional solvable Lie algebras. This is done by extending a solvable Lie algebra of smaller dimansion by a derivation. Subsequently, the Groebner basis facilities of Magma are used to find isomorphisms, and obtain a non-redundant list. This procedure has been used to find the classification of the solvable Lie algebras of dimensions 3, 4.

The second part is about the electronic version of the classification of the solvable Lie algebras. I have written Magma functions for constructing the Lie algebras that appear in the classification. This is complemented by a function that, given a solvable Lie algebra of dimension ≤ 4, finds an isomorphism with a Lie algebra from the classification. Here Groebner bases are no longer used; the algorithm is based on the proof of the correctness of the classification.