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### 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 ?

 2 None slelievre 15189 ●16 ●140 ●302 http://carva.org/samue...

### 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) step=3) implements a 3-nilpotent Free free Lie algebra). How to do this with Free free algebras ? ?