On 5/31/07, Nathan Dunfield <[EMAIL PROTECTED]> wrote:
> William, David, and Jack,
>
> Many thanks for all the excellent suggestions. Initially, I'll use
> Jack's local variable trick, though as David says a more complete
> implementation would probably want to keep track of the parent free
> group. There's also a clean multistep way that doesn't introduce any
> variables in GAP:
>
> sage: F = gap.new("FreeGroup(2)")
> sage: G = F.FactorGroupFpGroupByRels([F.1*F.2*F.1**-1*F.2**-1])
>
> Properly wrapping finitely presented groups would be a slightly tricky
> task, and, unfortunately, this is not my current goal. There's a lot
> more to a fp-group besides just the generators and relations, e.g.
> information about when a group is a subgroup of another group which is
> need for comparing subgroups, computing homorphisms between groups,
> etc. One could, of course, just delegate most of these issue to GAP,
> and that's certainly a reasonable approach to add finitely presented
> groups to Sage. Unfortunately, for what I typically do (e.g. find
> low-index subgroups), Magma is *much* faster than GAP, so I'm only
Do you understand why Magma is *much* faster than GAP at finding
low-index subgroups? Is it just compiled versus interpreted code, or
does MAGMA implement a much better algorithm?
William
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