Hello,
I'm new to sage devel so I'll focus on my problem description.
What I need is to work with a "subsets quotient".
X = (in most cases finite) set
Y = P(X) power set of X
G subgroup of the permutation group over the elements of X
For g in G and x in X we know gx, the action of g over x.
I have to define the action of g over y in this way:
for y={y_1,\dots,y_k} in Y gy={gy_1,\dots,gy_k}.
I have also to take care of two structure over Y:
B=(Y,union,intersection) is a Boolean algebra, but for now I don't need it.
P=(Y,inclusion as <=) is a poset.
Over the set of orbits G//Y I have this partial order: o<=o' iff exists
y,y' s.t. y in o, y' in o' and y <= y'.
P is a poset, G//Y is a poset, I will call G//Y the "quotient of P", and I
will write P/G.
#Now we arrive to Sage#
I'm wonder if I can define, for a general group G, a class from combinat
that take care of my P/G structure. I need to work with representative
elements of P/G, I need the structure of poset (in particular I need all
work with chains in P/G).
Tanks to
http://thales.math.uqam.ca/~saliola/sage/SienaLectures/worksheets/pdf/Worksheet_9__Combinatorics__Iterators_Generators_.pdf
(p.9), I tried to define this simple class (in which G=Z/nZ and I have
troubles in __iter__ because in my second "if" in the "for" is wrong):
class Quotient(CombinatorialClass):
def __init__(self,n):
"""
The quotient class
"""
self._n = n
self._S = Subsets(range(self._n))
def SumSet(self,s,k):
if s == set([]):
return set([])
else:
return set([ Mod(x+k,self._n) for x in s ])
def __iter__(self):
for s in self._S:
if self._S.next(s) == None:
yield s
else:
if any([ set(self._S.next(s)) == self.SumSet(t,k+1) for t
in self._S for k in range(self._n-1) ]):
continue
else:
yield s
def __repr__(self):
return "Quotient for %s" % self._n
I think that with a good definition of my action of G over Y in Sage, I can
solve my problem but I'm not capable to do this kind of stuff alone :)
P.S.
For now I use gap.eval like this:
e=gap.eval('G := Group((1,2,3,4))')
e=gap.eval('s := Combinations([1,2,3,4])')
e=gap.eval("list := Orbits(G,s,OnSets)")
# in list I have all the orbits
M=FiniteSetMaps(list,[ l[1] for l in list])
def EstractRep(l):
return l[1]
f = M(EstractRep)
dictionary = f.fibers()
# in dictionary I have the 1-1 relation between an orbit and one of its
representative elements
# for chains extraction I''ll use some "for" with tests like this
gap.eval("IsSubset([1,2],[1])")
# I have some trouble with the following
gap.eval("IsSubset([[2,3],[1,2]],[1])")
Thank you very much,
Giulio.
--
You received this message because you are subscribed to the Google Groups
"sage-combinat-devel" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-combinat-devel+unsubscr...@googlegroups.com.
To post to this group, send email to sage-combinat-devel@googlegroups.com.
Visit this group at http://groups.google.com/group/sage-combinat-devel.
For more options, visit https://groups.google.com/d/optout.
