I wrote a couple methods that relied on Partition(x).next() where 'x'
is a list of Integers. Essentially I wanted to print out all the
possible partitions of an Integer so I wrote the following functions:
def get_partitions(x,y=[]):
"""
Gets the list of the input argument and all the
partitions of it that follow it lexicographically.
See Partition.next().
"""
if type(x) is Integer:
return get_partitions([x])
y.append(x)
x = Partition(x).next()
if x != False:
return get_partitions(x)
return y
def print_partitions(x):
"""
Prints the argument and the list of partitions that
follow it lexicographically.
"""
part = get_partitions(x)
for i in part:
print i
Now I would expect that when I call print_partitions(x), where 'x' is
an Integer that SAGE would print all possible partitions of 'x'. The
first time I call the function it works as expected. However, for
each call after that, it seems to concatenate the results to the
results of all the previous calls. Here's an example:
sage: print_partitions(10)
[10]
[9, 1]
[8, 2]
[8, 1, 1]
[7, 3]
[7, 2, 1]
[7, 1, 1, 1]
[6, 4]
[6, 3, 1]
[6, 2, 2]
[6, 2, 1, 1]
[6, 1, 1, 1, 1]
[5, 5]
[5, 4, 1]
[5, 3, 2]
[5, 3, 1, 1]
[5, 2, 2, 1]
[5, 2, 1, 1, 1]
[5, 1, 1, 1, 1, 1]
[4, 4, 2]
[4, 4, 1, 1]
[4, 3, 3]
[4, 3, 2, 1]
[4, 3, 1, 1, 1]
[4, 2, 2, 2]
[4, 2, 2, 1, 1]
[4, 2, 1, 1, 1, 1]
[4, 1, 1, 1, 1, 1, 1]
[3, 3, 3, 1]
[3, 3, 2, 2]
[3, 3, 2, 1, 1]
[3, 3, 1, 1, 1, 1]
[3, 2, 2, 2, 1]
[3, 2, 2, 1, 1, 1]
[3, 2, 1, 1, 1, 1, 1]
[3, 1, 1, 1, 1, 1, 1, 1]
[2, 2, 2, 2, 2]
[2, 2, 2, 2, 1, 1]
[2, 2, 2, 1, 1, 1, 1]
[2, 2, 1, 1, 1, 1, 1, 1]
[2, 1, 1, 1, 1, 1, 1, 1, 1]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
sage: print_partitions(5)
[10]
[9, 1]
[8, 2]
[8, 1, 1]
[7, 3]
[7, 2, 1]
[7, 1, 1, 1]
[6, 4]
[6, 3, 1]
[6, 2, 2]
[6, 2, 1, 1]
[6, 1, 1, 1, 1]
[5, 5]
[5, 4, 1]
[5, 3, 2]
[5, 3, 1, 1]
[5, 2, 2, 1]
[5, 2, 1, 1, 1]
[5, 1, 1, 1, 1, 1]
[4, 4, 2]
[4, 4, 1, 1]
[4, 3, 3]
[4, 3, 2, 1]
[4, 3, 1, 1, 1]
[4, 2, 2, 2]
[4, 2, 2, 1, 1]
[4, 2, 1, 1, 1, 1]
[4, 1, 1, 1, 1, 1, 1]
[3, 3, 3, 1]
[3, 3, 2, 2]
[3, 3, 2, 1, 1]
[3, 3, 1, 1, 1, 1]
[3, 2, 2, 2, 1]
[3, 2, 2, 1, 1, 1]
[3, 2, 1, 1, 1, 1, 1]
[3, 1, 1, 1, 1, 1, 1, 1]
[2, 2, 2, 2, 2]
[2, 2, 2, 2, 1, 1]
[2, 2, 2, 1, 1, 1, 1]
[2, 2, 1, 1, 1, 1, 1, 1]
[2, 1, 1, 1, 1, 1, 1, 1, 1]
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
[5]
[4, 1]
[3, 2]
[3, 1, 1]
[2, 2, 1]
[2, 1, 1, 1]
[1, 1, 1, 1, 1]
Notice that the second function call displays the partitions of 10
before displaying the expected partitions of 5. This behavior occurs
when I use just the get_partitions() function. The print_partitions()
relies on that function so I think the problem is in get_partitions()
or in the Partition(x).next() function. Does anyone see the problem?
Thanks.
-Jake (mekaj)
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