Processing math: 100%

First time here? Check out the FAQ!

Ask Your Question

Revision history [back]

click to hide/show revision 1
initial version

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 Tk(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 ?

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 Tk(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 ? ?