Comment #16 on issue 3501 by [email protected]: Missing partitions in
sympy.utilities.iterables.multiset_partitions
http://code.google.com/p/sympy/issues/detail?id=3501
Sorry for any confusion. I am not using the terminology consistently and am
probably (still) a bit confused by the relationship betweeen the code in
utilities.iterables and combinatorics.partitions.
For the "expose the core of" remark, I didn't realize that yes, your
multiset_partitions code is a perfectly good implementation of set
partitions. It even has a provision for avoiding creation of the cache in
this case. BTW, I think there is a bug in this bit -- you set canon = None
(if no dups are found) but later test against canon == 0. Shouldn't one be
changed?
What I meant with my point number 2 is that if I feed multiset_partitions
input in which is just the same element repeated n times, the output is
isomorphic (except for the m parameter) to the partitions of the integer n.
(And in my earlier comment, I was confusing combinatorics and utilities
implementations of integer partitions.)
In code:
from sympy.utilities.iterables import partitions
for m in xrange(1, 6):
print [p for p in multiset_partitions('aaaaa', m)]
for p in partitions(5):
print p
Except that for large n, the second expression is using a much faster
algorithm.
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