#3544: PermutationGroup.is_transitive is broken
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Reporter: boothby | Owner: tbd
Type: defect | Status: new
Priority: major | Milestone: sage-3.4.1
Component: algebra | Resolution:
Keywords: |
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Comment (by was):
Some remarks:
* In GAP it is clearly documented that IsTransitive(G) returns whether
or not G is transitive on the set of points moved by G. That's why this
"bug" happens (this ticket).
* In Magma, all permutation groups G are embedded in a specific S_n and
IsTransitive returns whether or not G is transitive on [1..n].
* Sage has a degree method for permutation groups, which gives back an
n.
I think we view permutation groups as contained in S_n, which naturally
acts on [1..n], so that should be the default. I think permutations
groups should also at some point in the future be equipable with an action
on any set. But the resulting object will be "a permutation group
equipped with an action", and is_transitive will be defined relative to
that. So for this ticket, we just need to decide on the default set acted
on by a permutation group generated by a list of permutations. I think
the most natural choice is the set {1,2, ..., n} given the embedding in
S_n.
Anyway, I've attached a patch that fixes the bug, and makes
is_transitive() return whether or not the group is transitive on
{{{[1..G.degree()]}}}. I also fixed a few surrounding docstrings and
added one to load_hap, so that doctest coverage for the file permgroup.py
is now 100%.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3544#comment:7>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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