On Wed, 05 May 2010 at 05:38PM -0700, Eva wrote: > My question: what is the best way to enumerate vectors in Z^d (for an > arbitrary d that my function will be passed as a parameter, so I don't > know its value in advance) starting with 0, then going through all > vectors with just a single 1 and all other entries 0, then going > through all vectors with a single -1 and all other entries 0, then > going through all vectors with two 1's or -1's and all other entries > 0, etc.? Ideally I could find the next vector in my sequence of > vectors to consider one-at-a-time, so that I don't generate more > vectors than I need to, but I suspect it will be easier to generate > vectors in the sequence in batches, such as all vectors with a single > 1 entry, then all vectors with a single -1 entry, and so on.
One starting point is IntegerVectors -- try IntegerVectors? in a Sage
session. You can do IntegerVectors(5,3) to get an iterator for all
vectors of nonnegative integers of length 3 that sum to 5.
Others may have better ideas, but my first guess is that you'll work with
IntegerVectors(n,d) (for n = 1, 2, 3...) and for each vector, look at
all the nonzero entries and flip the signs in all possible ways. For a
integer vector v, you can find the nonzero entries with something like
[i for i, val in enumerate(v) if val != 0]
and then call Subsets on that list and flip signs:
for indices in Subsets([i for i, val in enumerate(v) if val != 0]):
w = v[:]
for index in indices:
w[index] *= -1
# now do your coset test stuff
There are probably much better ways to do this, but the above will work,
I think. You can also ask your question in the sage-combinat-devel
group.
Dan
--
--- Dan Drake
----- http://mathsci.kaist.ac.kr/~drake
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