# partition_integer_into_canonic_parts¶

mathtools.partition_integer_into_canonic_parts(n, decrease_parts_monotonically=True)

Partitions integer n into canonic parts.

Returns all parts positive on positive n:

>>> for n in range(1, 11):
...     print(n, mathtools.partition_integer_into_canonic_parts(n))
...
1 (1,)
2 (2,)
3 (3,)
4 (4,)
5 (4, 1)
6 (6,)
7 (7,)
8 (8,)
9 (8, 1)
10 (8, 2)

Returns all parts negative on negative n:

>>> for n in reversed(range(-20, -10)):
...     print(n, mathtools.partition_integer_into_canonic_parts(n))
...
-11 (-8, -3)
-12 (-12,)
-13 (-12, -1)
-14 (-14,)
-15 (-15,)
-16 (-16,)
-17 (-16, -1)
-18 (-16, -2)
-19 (-16, -3)
-20 (-16, -4)

Returns parts that increase monotonically:

>>> for n in range(11, 21):
...     print(n, mathtools.partition_integer_into_canonic_parts(n,
...         decrease_parts_monotonically=False))
...
11 (3, 8)
12 (12,)
13 (1, 12)
14 (14,)
15 (15,)
16 (16,)
17 (1, 16)
18 (2, 16)
19 (3, 16)
20 (4, 16)

Returns tuple with parts that decrease monotonically.

Returns tuple of integers.