Contained in the files below are the programs that were used in the calculations in the
paper "Regular algebras of dimension 4 with 3 generators." Some
more comments about what the programs do are given in the files themselves.
Also, in the files we pasted in the output from the Maple programs so
that the reader doesn't need to have Maple to see what the output of the program was.
1. The first program is used to write an expression in the free algebra
with parameter coefficients in terms of reduced words with respect to
some relations. It is used to compute the overlaps among some relations, and then
Maple is used to solve for the values of the parameters for which all overlaps resolve.
Diamond lemma with parameters
2. This program is used to find normal elements of degree 2 in an algebra with given relations.
It also uses the reduction routine of the first program. The program is applied to the various examples
of regular algebras produced in the paper.
Finding normal elements of degree 2
3. This program is a series of adjustments to the preceding program used to find normal elements of
higher degree in the one example of regular algebra (family F) we found that had no normal elements of degree 2.
Finding higher degree normal elements for example F
4. The last program calculates the matrix giving the unknown map d3 in a potential free resolution
of the trivial module k for our examples of regular algebras.
Finding the matrix for the map d3 in a free resolution of k