I am interested in the

**number of isomorphism types of nilpotent associative algebras
of class two over arbitrary finite fields**.

It can be shown that this number, considered as a function in q (the number

of elements of the field), is a PORC (Polynomial On Residue Classes) function,

hence there exists a natural number n and polynomials such that the function

behaves like a polynomial for all elements in the same residue class modulo n.

You can find functions giving the number of

isomorphism types of class-2 nilpotent associative algebras

over finite fields with q elements of small ranks r and all dimensions:

number of class-2 algebras.

I also wrote a small library for the computer algebra system **GAP**

that includes all porc functions I have computed so far.

All porc functions are considered as multivariate polynomials in **GAP**.

GAP library.

After the download unzip the package and copy it into the directory of your GAP packages.

Load the package by **LoadPackage("ClassTwoAlgLib");**

On this page you can find a short overview of this library.

To enumerate the isomorphism classes of class two nilpotent algebras over arbitrary fields

I developed together with Prof. Bettina Eick a package for the computer algebra system **GAP**,

which is called **ClassTwoAlg**.

ClassTwoAlg

After the download unzip the package and copy it into the directory of your GAP packages.

Load the package by **LoadPackage("ClassTwoAlg");**

The results which are available within the library *classtwoalglib* (see above)

were computed using this package.