num_distinct_partitions SciMax Toolbox numbered_boundaries

SciMax Toolbox >> num_partitions

num_partitions

Maxima Function

Calling Sequence

num_partitions (n)
num_partitions(n,list)

Description

Returns the number of integer partitions of n when n is a nonnegative integer. Otherwise, num_partitions returns a noun expression.

num_partitions(n, list) returns a list of the number of integer partitions of 1, 2, 3, ..., n.

For a nonnegative integer n, num_partitions(n) is equal to cardinality(integer_partitions(n)); however, num_partitions does not actually construct the set of partitions, so it is much faster.

Examples:

(%i1) num_partitions (5) = cardinality (integer_partitions (5));
(%o1)                         7 = 7
(%i2) num_partitions (8, list);
(%o2)            [1, 1, 2, 3, 5, 7, 11, 15, 22]
(%i3) num_partitions (n);
(%o3)                   num_partitions(n)
num_distinct_partitions SciMax Toolbox numbered_boundaries