#8500: Add the set of TransitiveGroups
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Reporter: nborie | Owner: nborie
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.3.4
Component: group_theory | Keywords: transitive group
Author: Nicolas Borie | Upstream: N/A
Reviewer: | Merged:
Work_issues: |
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Description changed by nborie:
Old description:
> TransitiveGroup are already in Sage and work only if you have the right
> database installed. As I offen test systematicly over all transitive
> groups, I will be happy to get this number in Sage.
>
> {{{
> sage: TransitiveGroup(7,7)
> Transitive group number 7 of degree 7
> sage: TransitiveGroup(7,8)
> verbose 0 (846: permgroup_named.py, __init__) Warning: Computing with
> TransitiveGroups requires the optional database_gap package. Please
> install it.
> Transitive group number 8 of degree 7
> }}}
>
> I had also the set of TransitiveGroups() (The whole Gap database as a set
> with categories) and TransitiveGroups(degree) (The set of TransitiveGroup
> of a given degree with categories).
New description:
depend on #8524
The goal of this patch is implement a proper infinite set of category
InfiniteEnumeratedSet of transitive groups. This set is built as a
disjoint union of Finite Enumerated Sets of all set of Transitive groups
of a given degree.
This allows a user to do:
{{{
for G in TransitiveGroups(i):
any_test(G) # any test over all transitive groups of a given degree
for G in TransitiveGroups():
other_test(G) # test over all transitive groups
}}}
This will requires the optional database_gap.
As the database of Gap is finite, the enumeration stop with a
NonImplementedError at degree 30.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8500#comment:10>
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