Albert is an interactive program to assist the specialist in the study of nonassociative algebra. The program was first designed and implemented at Clemson University about 1990 by D. Jacobs and S.V. Muddana, with assistance from A.J. Offutt, under an NSF grant. Enhancements were made by K. Prabhu, D. Lee, and T. Whiteley. In 2008 the code was modified to compile under the latest gcc compiler found on most Unix and Linux computers.

The main problem addressed by Albert is the recognition of polynomial identities in varieties of nonassociative algebras.

In 2014, Kent A. Vander Velden and Irvin R. Hentzel made major modifications to Albert. Version 4.0 includes reworking how Albert stores problems, optimization of some of the calculations, and parallelization of longer running routines.

The parallelization uses OpenMP, so is restricted to a single machine. Parallelization is used in the conversion of substitutions to equations, the conversion of equations to the sparse matrix, and the reduction of the sparse matrix. The Makefile assumes support for OpenMP, but OpenMP can be disabled. The new program has been tested under Linux.

The code is now hosted on github. Researchers wishing to just use the program can download the zip file. If a developer wishes to make improvements, the individual source files are located in the git repository. Questions about the code can be directed to Kent or Irvin.

Click HERE to obtain the Albert User's Guide.

Click HERE to download the Albert 4.0 zip file.

Click HERE to reach the git repository for the source code.

Some papers about or using Albert:

Rings with (a,b,c) = (a,c,b) and (a,[b,c],d) = 0: A Case Study Using Albert, I. Hentzel, D. Jacobs, and E. Kleinfeld, 1993.

The Albert Nonassociative Algebra System: A Progress Report, D.P. Jacobs, 1994.

A Condition Guaranteeing Commutativity, I.R. Hentzel and D. Pokrass Jacobs, 1992.

Experimenting with the Identity (xy)z = y(zx), I.R. Hentzel, D.P. Jacobs, S.V. Muddana, 1993.

A Computer Algebra System for Nonassociative Identities, D.P. Jacobs, S.V. Muddana, A.J. Offutt, 1990