#6812: Enumerate integer vectors modulo to the action of a Permutation Group
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Reporter: nborie |
Owner: nborie
Type: enhancement |
Status: needs_review
Priority: major |
Milestone: sage-5.1
Component: combinatorics |
Resolution:
Keywords: enumeration, integer, list, permutation, group | Work
issues: long time tests, information about listing infinite sets
Report Upstream: N/A |
Reviewers: Karl-Dieter Crisman, Simon King
Authors: Nicolas Borie | Merged
in:
Dependencies: |
Stopgaps:
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Comment (by nborie):
> There should not only be a fast `ClonableIntArray.list()`, but also a
fast
> `ClonableIntArray.tuple()`: Sometimes, one needs a tuple, not a list,
and it
> would be awkward and slow to first transfrom the clonable int array into
a list
> and transform that into a tuple.
Added on the todo list... But not mine todo list in fact. Florent Hivert
(clone C array structure author) is going to patch his module. I will ask
him if he can do something. The conversion to tuple should be implemented
on the ClonableArray class in sage/structure/list_clone.pyx and thus we
will get the fast conversion by inheritance. If we can optimize the
conversion for integer, we will override it on the ClonableIntArray class.
To avoid any conflict on merging, I will tell some words to Florent.
> You know that my application of your work would be: Compute non-modular
> invariant rings of permutation groups. For that purpose, it would be
good if
> clonable int arrays could be used to define exponent vectors of a
monomial. But
> that should clearly be on a different ticket.
Yep, I had to deal the same problem. For information, for the case I
managed to compute with symmetric polynomials as homogeneous set of
parameter (the powersums polynomials), selecting only the canonical
monomials under staircase whose automorphism group is not the whole
symmetric group (the orbit sum over G of the monomial is not trivially a
symmetric polynomial), the enumeration engine make you find NEW secondary
invariants with an average of 70% of chance. So, I can imagine your
algorithmic will really save a lot of normal form computation. This rate
is ok until 10 variables but falls at 30% for the only case at 14
variables (TransitiveGroup(14,61)) my algorithmic managed to compute. (you
can see my algorithmic verbose here
http://www.math.u-psud.fr/~borie/papers/14_61.txt)
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6812#comment:64>
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