compile = truefalse

True means compile the iterator. The default is true.

maxparts = posint

Specifies the maximum number of integers in each composition. The default is n.

parts = nonnegint

Specifies the number of integers in each composition. Must be either 0 (the default) or greater than one and less than or equal to n. The default, 0, is ignored. A non-zero value cannot be used with the maxparts option.

The Composition command returns an iterator that generates all compositions of the integer n.

A composition of integer n is a sequence of positive integers that sum to n.

The n parameter is the integer to decompose.  It must be greater than one.

The output of the iterator is an array of fixed length n. The composition is in the indices 1 to $\mathrm{length}\left(P\right)$, where P is the assigned iterator.

$\mathrm{with}\left(\mathrm{Iterator}\right)\:$

$n≔5\:$

$P≔\mathrm{Composition}\left(n\right)\:$

$\mathrm{Print}\left(P\,'\mathrm{showrank}'\right)\:$

 1: 5
 2: 4 1
 3: 3 1 1
 4: 3 2
 5: 2 1 2
 6: 2 1 1 1
 7: 2 2 1
 8: 2 3
 9: 1 1 3
10: 1 1 2 1
11: 1 1 1 1 1
12: 1 1 1 2
13: 1 2 2
14: 1 2 1 1
15: 1 3 1
16: 1 4

$\mathrm{Number}\left(P\right)$

$16$

$\mathrm{seq}\left(\mathrm{add}\left(p\left[k\right]\,k=1..\mathrm{length}\left(P\right)\right)\,p=P\right)$

$5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5$

Knuth, Donald Ervin. The Art of Computer Programming, volume 4, fascicle 2; generating all tuples and permutations, sec. 7.2.1.1, generating all n-tuples, algorithm A, p. 77, answer 12.

The Iterator[Composition] command was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.