ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 14 Jan 2021 16:03:58 +0100How to do low degree computation in a Free Algebra ?https://ask.sagemath.org/question/55269/how-to-do-low-degree-computation-in-a-free-algebra/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 $T_{\geq k}(V)$. 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 ?qfaesThu, 14 Jan 2021 16:03:58 +0100https://ask.sagemath.org/question/55269/