On the enumeration of finite L-algebras

The repository contains database of several finite L-algebras. This is based on the paper

C. Dietzel, P. Menchón, L. Vendramin. On the enumeration of finite L-algebras.

Here is a short description of some of the files.

The files L.g has methods to construct finite L-algebras. The difference between these files is related to the symmetry breaking.

$ gap L.g 
gap> construct_L(4);
Running savilerow. I found 44 solutions
I constructed 44 L-algebras in 3780ms (= 0:00:03.780)

The difference between L.g and L_partial.g is related to the symmetry breaking.

$ gap L_partial.g 
gap> construct_L(4);
Running savilerow. I found 44 solutions
I constructed 44 L-algebras in 442ms (= 0:00:00.442)

The files enumerate_L.g and enumerate_hilbert.g only enumerate structures, the construction is not performed.

$ gap enumerate_L.g 
gap> enumerate_L(4);
Created output file for domain filtering L4.eprime.minion
Created output file L4.eprime.minion
Created information file L4.eprime.info
Running savilerow. There are 44 L-algebras in 435ms (= 0:00:00.435)

There are similar files for constructing and enumerating finite Hilbert algebras.

L-algebras of size 8

The database of L-algebras of size 8 requires a different approach. We split the calculation into three cases:

Diamond poset. To enumerate/construct these L-algebras use the Python script diamond/diamond.py. The database (for GAP, compressed) is data/diamond8.tar.
Trivial poset (i.e. discrete L-algebras). To enumerate/construct discrete L-algebras use the Python script discrete/discrete.py. The database (GAP, compressed) is data/discrete8.tar.
Other posets. To enumerate/construct these L-algebras use the Python script non_discrete/non_discrete.py. The database (for GAP, compressed) is data/non_discrete8.tar.

vendramin/L

On the enumeration of finite L-algebras

L-algebras of size 8