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The Maxima on-line user's manual

Algebra Calculator

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Num_partitions Calculator

Num_partitions

Function: num_partitions (<n>)

num_partitions (5) = cardinality (integer_partitions (5));
 num_partitions (8, list);
 num_partitions (n);

Function: num_partitions (<n>, list) 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)

(%o1)                                true
(%i2) 

Num_partitions Example

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