To create a fp group you have to define relations on the generators
of a free group. To define the generators, you have to have a
notation for the group. Why not have the _init_ method of the
class define a "(free) base group", "generators (of the free gp)",
"relations"? Something roughly (this is off the top of my head
and almost certainly wrong) like this:
class FinitelyPresentedGroup_class(group.???):
"""
???
"""
def __init__(self, n, rels, names="f"):
???
self.__relations = rels
self.__base_group = gap.new("Fgp := FreeGroup(%s)"%n)
self.__gens = gap.new("GeneratorsOfGroup(Fgp)")
def relations(self):
return self.__relations
def gens(self):
...
etc
I'm glad someone is working on this. You might want to cc Jack Schmidt
([EMAIL PROTECTED]) on your work. He is not on the sage-devel list and he may
or may not have time/interest in helping. But if he has the time, I think he
could be very helpful (and he knows GAP, group theory and programming).
On 5/28/07, Nathan Dunfield <[EMAIL PROTECTED]> wrote:
>
> Dear All,
>
> How does one create new GAP objects that require a multi-step
> command? For instance, to create a finitely presented group in GAP
> one does:
>
> gap: F := FreeGroup(2)
> <free group on the generators [ f1, f2 ]>
> gap: G := F/[F.1*F.2*F.1^-1*F.2^-1]
> <fp group of size infinity on the generators [ f1, f2 ]>
>
> I'm trying to hack up a quick finitely presented group class, and am
> trying to write the _gap_init_ method. In simple cases, _gap_init_
> returns a string, but I can't come up with one that works; e.g. the
> following fails
>
> sage: gap.new("F := FreeGroup(2); F/[F.1*F.2*F.1^-1*F.2^-1]")
> $sage21:=F := FreeGroup(2); F/[F.1*F.2*F.1^-1*F.2^-1];;
> ^
>
> executing $sage21:=F := FreeGroup(2); F/[F.1*F.2*F.1^-1*F.2^-1];;
>
> Now, I could have _gap_init_ return a GAP object created in several
> steps, e.g.
>
> sage: gap.eval("F := FreeGroup(2)")
> '<free group on the generators [ f1, f2 ]>'
> sage: G = gap.new("F/[F.1*F.2*F.1^-1*F.2^-1]");
> sage: G
> <fp group of size infinity on the generators [ f1, f2 ]>
>
> but this has the disadvantage of littering the GAP interpreter with a
> bunch of useless variables (or worse, over-writing something from my
> interactive session).
>
> What's the right solution here? I could assign some awful temporary
> variable name in place of F, but there must be a better way...
>
> Thanks,
>
> Nathan
>
>
> >
>
--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-devel@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at http://groups.google.com/group/sage-devel
URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/
-~----------~----~----~----~------~----~------~--~---
