Zeroth Tanaka prolongation of free nilpotent Lie algebras

[ehaka]

An implementation of the zeroth Tanaka prolongation of a free nilpotent Lie algebra. A free nilpotent Lie algebra of nilpotency step s is a graded Lie algebra V_1+...+V_s generated by its homogeneous component of degree 1.
The zeroth Tanaka prolongation is a larger graded Lie algebra V_0+V_1+...+V_s, where the V_0 component consists of all possible grading-preserving derivations of the original Lie algebra.
See Warhurst: Tanaka prolongation of free Lie algebras.

Depends on #26076

Component: algebra

Keywords: Lie algebras, Tanaka prolongation, derivations

Issue created by migration from https://trac.sagemath.org/ticket/26081

[ehaka]

comment:1

Some implementation already exists in a codebase that I need to clean up and import into Sage.

[ehaka]

Dependencies: #26076