#20561: Return cycle type of a permutation
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Reporter: andrew.mathas | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.2
Component: group theory | Resolution:
Keywords: permutation, | Merged in:
cycle type | Reviewers:
Authors: Andrew Mathas | Work issues:
Report Upstream: N/A | Commit:
Branch: | 35145b98cacc56bdee36bc8836218d6c4dec5e06
u/andrew.mathas/return_cycle_type_of_a_permutation| Stopgaps:
Dependencies: |
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Comment (by andrew.mathas):
I am amused how much bandwidth such a trivial ticket can generate:)
I agree with vdelecroix that allowing singletons to be ignored will
probably be useful, is more consistent with the other `cycle_*` methods
and that it is trivial to implement. For all of these reasons, it should
be implemented so I have added an optional `singletons` argument for this.
I also agree with Travis that the casual user will expect that
`cycle_type` will return a partition so I have made this the default,
using `_Partitions` as Travis recommends. The non-casual user may well not
want a partition so I have added a second optional argument `as_list` that
, when `True`, will cause a list to be returned.
Here are some new timings with these changes:
{{{#!python
sage: S = SymmetricGroup(100)
sage: p = S.random_element()
sage: %timeit c = p.cycle_type()
10000 loops, best of 3: 47.5 µs per loop
sage: %timeit c = p.cycle_type(singletons=True)
10000 loops, best of 3: 50.2 µs per loop
sage: %timeit c = p.cycle_type(as_list=True)
100000 loops, best of 3: 11.9 µs per loop
sage: %timeit c = p.cycle_type(singletons=True, as_list=True)
100000 loops, best of 3: 11.6 µs per loop
sage: %timeit c = p.cycle_tuples()
100000 loops, best of 3: 9.83 µs per loop
}}}
So it seems that returning a partition is relatively costly but I think
that it is more user friendly so should be the default. I have added a
remark in the documentation that `as_list=True` should be used when speed
is an issue.
----
New commits:
||[http://git.sagemath.org/sage.git/commit/?id=18f179963a10ef1b0facb71591f88080f3f0ba1a
18f1799]||{{{Merge branch 'develop' into
t/20561/return_cycle_type_of_a_permutation}}}||
||[http://git.sagemath.org/sage.git/commit/?id=35145b98cacc56bdee36bc8836218d6c4dec5e06
35145b9]||{{{Adding comment about using as_list for speed}}}||
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Ticket URL: <http://trac.sagemath.org/ticket/20561#comment:16>
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