#15031: Counter-intuitive mismatch between permutations and permutation group
elements
-------------------------------------------------+-------------------------
Reporter: darij | Owner:
Type: defect | Status: new
Priority: major | Milestone:
Component: combinatorics | sage-5.12
Keywords: permutation, permutation | Resolution:
group, symmetric group, sage-combinat, groups | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Dependencies:
Stopgaps: |
-------------------------------------------------+-------------------------
Description changed by darij:
Old description:
> {{{
> sage: T = Tableau([[1,2],[3,4]])
> sage: for p in T.column_stabilizer():
> ....: print p
> ....:
> ()
> (2,4)
> (1,3)
> (1,3)(2,4)
> sage: for p in T.column_stabilizer():
> ....: print T.symmetric_group_action_on_values(p)
> ....:
> ---------------------------------------------------------------------------
> TypeError Traceback (most recent call
> last)
> <ipython-input-2-657a6c3879e0> in <module>()
> 1 for p in T.column_stabilizer():
> ----> 2 print T.symmetric_group_action_on_entries(p)
> 3
>
> /home/darij/sage-5.11.beta3/local/lib/python2.7/site-
> packages/sage/combinat/tableau.pyc in
> symmetric_group_action_on_entries(self, w)
> 2631 Category of elements of Tableaux
> 2632 """
> -> 2633 w = w + [i+1 for i in range(len(w), self.size())] #need
> to ensure that it belongs to Sym_size
> 2634 try:
> 2635 return self.parent()([[w[entry-1] for entry in row]
> for row in self])
>
> TypeError: object of type
> 'sage.groups.perm_gps.permgroup_element.PermutationGroupElement' has no
> len()
> }}}
>
> (This is when #14884 is applied; otherwise it would throw a different
> error.) What is going on is that the {{{column_stabilizer}}} method of a
> tableau returns permutation group elements rather than honest standard
> permutations, whereas the {{{symmetric_group_action_on_entries}}} method
> only eats standard permutations.
>
> Of course, type casting does solve the problem, but this is ugly and not
> completely trivial:
>
> {{{
> sage: p
> (1,3)(2,4)
> sage: parent(p)
> Permutation Group with generators [(), (2,4), (1,3)]
> sage: parent(SymmetricGroup(4)(p))
> Symmetric group of order 4! as a permutation group
> sage: parent(Permutation(p))
> Standard permutations
> }}}
>
> So {{{T.symmetric_group_action_on_entries(SymmetricGroup(4)(p))}}}
> wouldn't work either, but
> {{{T.symmetric_group_action_on_entries(Permutation(p))}}} works.
>
> This is not an error in the classical meaning of the word, but I think
> this is something that should be fixed. How?
New description:
{{{
sage: T = Tableau([[1,2],[3,4]])
sage: for p in T.column_stabilizer():
....: print p
....:
()
(2,4)
(1,3)
(1,3)(2,4)
sage: for p in T.column_stabilizer():
....: print T.symmetric_group_action_on_values(p)
....:
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
<ipython-input-2-657a6c3879e0> in <module>()
1 for p in T.column_stabilizer():
----> 2 print T.symmetric_group_action_on_entries(p)
3
/home/darij/sage-5.11.beta3/local/lib/python2.7/site-
packages/sage/combinat/tableau.pyc in
symmetric_group_action_on_entries(self, w)
2631 Category of elements of Tableaux
2632 """
-> 2633 w = w + [i+1 for i in range(len(w), self.size())] #need
to ensure that it belongs to Sym_size
2634 try:
2635 return self.parent()([[w[entry-1] for entry in row]
for row in self])
TypeError: object of type
'sage.groups.perm_gps.permgroup_element.PermutationGroupElement' has no
len()
}}}
(This is when #14884 is applied; otherwise it would throw a different
error.) What is going on is that the {{{column_stabilizer}}} method of a
tableau returns permutation group elements rather than honest standard
permutations, whereas the {{{symmetric_group_action_on_entries}}} method
only eats standard permutations.
Of course, type casting does solve the problem, but this is ugly and not
completely trivial:
{{{
sage: p
(1,3)(2,4)
sage: parent(p)
Permutation Group with generators [(), (2,4), (1,3)]
sage: parent(SymmetricGroup(4)(p))
Symmetric group of order 4! as a permutation group
sage: parent(Permutation(p))
Standard permutations
}}}
So {{{T.symmetric_group_action_on_entries(SymmetricGroup(4)(p))}}}
wouldn't work either, but
{{{T.symmetric_group_action_on_entries(Permutation(p))}}} works.
This is not an error in the classical meaning of the word, but I think
this is something that should be fixed. How?
Incidentally, it seems that transforming the {{{Permutation(p)}}} typecast
takes an ungodly amount of time...
--
--
Ticket URL: <http://trac.sagemath.org/ticket/15031#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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