### The Maxima on-line user's manual

Algebra Calculator

#### Num_partitions

Function: 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) ```

### Related Examples

##### num_partitions

num_partitions (30);

Calculate

##### num_partitions

num_partitions(12);

Calculate

##### num_partitions

? num_partitions;

Calculate

##### num_partitions

num_partitions (30);

Calculate

##### num_partitions

num_partitions(12);

Calculate

##### num_partitions

? num_partitions;

Calculate