Converting Groups and G-sets from Gap to UACalc Files

By William DeMeo with additions by David Stanovsky

Converting groups and G-sets:

The GAP program, gap2uacalc.g will convert both transitive G-sets as well as groups into (universal) algebras suitable for loading into UACalc.

The two functions are called gset2uacalc and group2uacalc. For example, to turn the group S3 into a uacalc algebra file, you would execute the following in GAP:

gap> Read("gap2uacalc.g");
gap> G:=SymmetricGroup(3);
gap> group2uacalc([G, "S3"]); # you can leave off the name "S3" if you want

To turn the right regular S3-set -- i.e. the algebra: S3 acting on itself by right multiplication -- into a uacalc file,

gap> act:=Action(G,G,OnRight);
gap> gset2uacalc([act, "S3action"]);

(Note: if you leave off the name "S3action", the program automatically names the algebra S3, in this case, which would overwrite the algebra file you created above for the group S3.)

It is now possible to convert a gap matrix into an algebra with a single binary operation (sometimes called a binary). An example of its use

gap> LoadPackage("loops");
gap> M := MultiplicationTable(MoufangLoop(12,1));
gap> table2uacalc([M, "MoufangLoop_12_1"]);

More details as well as more examples are given in the comments of the file gap2uacalc.g.