[GAP Forum] Help with the Polycyclic package

[Max Horn]

Dear Ha T. Lam,




Am 29.09.2011 um 16:40 schrieb nullgraph:

> Hello GAP forum,
> 
> I want to work with the Polycyclic package so I've installed and
> successfully tested GAP, KASH and the Alnuth package in Ubuntu (if you
> recall, I asked for help with installation a few days before in a Windows
> environment but have since decided it might be faster to go with Linux). Now
> I'm trying to check if my Polycyclic package is working well. I can
> LoadPackage, I can also try a few simple command like:
> 
> DihedralPcpGroup(4);
> Pcp-group with orders [ 2, 2 ]
> DihedralPcpGroup(8);
> Pcp-group with orders [ 2, 4 ]
> 
> But I don't know enough about Polycyclic groups to do more comprehensive
> test.

The polycyclic manual contains a very brief introduction to the fundamentals. However, if you really want to use the polycyclic package, you may want to first acquire more mathematical knowledge about them. Of course it all depends on what exactly you plan to use polycyclic for.

> Is there a test somewhere that I can run to make sure that my
> installation is correct?

The output from polycyclic you were displaying looked perfectly fine. The last released version of polycyclic does not include a test suite, though future versions will. But it is highly unlikely that your polycyclic installation is defective, so I'd say your installation *is* correct.


> 
> Another question I have is the two built-in
> functions ExampleOfMetabelianPcpGroup(a, k) and ExamplesOfSomePcpGroups(n).
> The manual is not very clear on what they do so I'm not sure if what I get
> is right.

The manual also quite explicitly state that it is intentionally vague on these. To quote: "The functions in this section provide some more example groups to play with. They come with no further description and their investigation is left to the interested user.".

If you would like to "experiment" with groups with more a-priori knowledge about them, I recommend looking at some of the other explicitly described families of groups available from within the polycyclic package, and described in chapter 6 of the manual.

[...]

> ExampleOfMetabelianPcpGroup(5,3);
> Pcp-group with orders [ 0, 0, 0, 0, 0 ]
> 
> As you can see, all I get is zeroes, is this correct?
Yes, this is correct. The zeroes mean that the corresponding pc generator has relative order infinity. For more information, I recommend reading up in the polycyclic manual, especially chapters 2 and 3.


Best regards,
Max