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.