"Mike Hansen" <[EMAIL PROTECTED]> writes:
> I put my code species code that I've written so far based on your work up on
> the sage-combinat patch server. I made a blog posting about it which you can
> find at http://blog.phasing.org . I also put up syntax-highlighted versions
> of the relevant code that you can find here:
> http://blog.phasing.org/static/species/ , and there is a static demo page
> here:
> http://sage.math.washington.edu/home/mhansen/CombinatorialSpeciesDemo.html
Many thanks. Is there a documented version available? I tried to understand
what happens for isomorphismtypes of (usual) composition, but I failed...
I guess, the code in question is
def _isomorphism_types(self, s):
"""
EXAMPLES:
sage: from sage.combinat.species.species import SetSpecies,
CycleSpecies, PermutationSpecies
sage: E = SetSpecies(); C = CycleSpecies()
sage: L = E(C)
sage: len(L.isomorphism_types([1,2,3]).list())
3
"""
return self._composition_aux("isomorphism_types", s)
def _composition_aux(self, attr, s):
structure_class = self._structure_class
from sage.combinat.cartesian_product import CartesianProduct
P = PartitionSpecies()
for pi in getattr(P, attr)(s):
gs = CartesianProduct(*[getattr(self._G,attr)(part) for part in pi])
fs = getattr(self._F,attr)(pi)
for res in CartesianProduct(fs, gs):
yield structure_class(self, *res)
This looks deceptively simple. Are you sure it's correct?
In particular, I couldn't find Knuth's multipartitions anywhere. Were you able
to do without? Help is much appreciated.
> I was wondering if you'd be willing to release Aldor-Combinat to me under GPL
> v2 or later since that is the license I'd like to release my code under to be
> compatible with the rest of Sage.
I cannot answer that one, but I guess it shouldn't be a problem. It's not a
problem for me, at least.
> I'm going to be doing some work with Robert Miller in upcoming weeks on
> generating isomorphism class representatives for functorial composition. He
> wrote a clean-room implementation of the algorithms in nauty for graph
> isomorphism testing and generating non-isomorphic simple graphs. This summer
> he's working on generalizing that code to work with other types of
> combinatorial objects.
Wow.
> I'll probably be working on the multisort case later on. Due to lack of
> funds, I can't make it out to RISC this summer, but I'd be more than happy to
> join in your discussions about multisort species.
I did most of the maths involved (i.e., how to generate isotypes of a
composition of multisort species), it's mainly a problem of representation.
The trouble is, so far I did not find a reasonable way to do composition such
that the output are *representatives* of isomorphismtypes -- the approach taken
in the trunk version of Ralf's code and mine. But if your code above solves
this problem, then there is little left to do!
In iso-experiment, which is the branch implementing proper isotypes of
composition, the labels are replaced by all ones. But obviously, that won't
work for functorial composition...
Martin
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