Operator Product Expansions in Lie conformal algebras

[Sam DeHority]

Hi,

Sage has a LieConformalAlgebras module which is able to compute OPEs, or equivalently \lambda-brackets when those brackets close under OPEs. There isn't, however, a "free" Lie Conformal Algebra which allows for OPEs of fields build from normally ordered products using the noncommutative Wick formula.

Is there any interest in expanding the LieConformalAlgebras package to support more general OPEs?

[Reimundo Heluani]

There was a very large PR with a full implementation of vertex operator
algebras including some non-linearly generated. It got caught in review, then
the pandemic and then the birth of a baby in the middle of it. That PR got
broken into several pieces, some for LCAs, another for vertex algebras, then
another for examples and another with the main application I had at the time
for computing classical limits and Poisson vertex algebras.

The rebasing mechanism and maintaining such a large PR for review was
impossible https://github.com/sagemath/sage/issues/29610

I don't think that compiles not even close. The biggest problem is that for
any serious computation Python and the overhead of all the category formalism
of Sage makes these packages useless. Mathematica Thielemann's package was
orders of magnitude faster. I coded a C++ version of this that I was hoping to
use as backend for sage. But adhering to the category formalism is
not-trivial.

R.

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[Travis Scrimshaw]

We should look at that closely sometime Reimundo. I have very strong doubts that it is the category formalism as that really should not be playing any role in creating and manipulating elements. It only comes into play when dealing with multiple (distinct) parents. It might also be that you need to directly implement some shortcuts rather than relying on some general machinery or you are using the wrong data structures.

Best,

Travis