Say F is a free algebra over n generators of degree 1, and i want to compute in this algebra but i only need to get my expressions up to degree k. For example, if k=2, (ab+a)∗b should be ab.
For now, i have been doing the computation and truncating everything above degree k, but the time complexity is too high when i launch a big computation.
I am actually asking how to compute in the tensor Algebra T(V) modulo T≥k(V). For free Lie algebras, this can be done using nilpotent Lie algebras, (for example L = LieAlgebra(QQ, 3, step=3) implements a 3-nilpotent Free Lie algebra). How to do this with Free algebras ?