compile = truefalse

True means compile the iterator. The default is true.

The WeightedComposition command returns an iterator that generates all weighted compositions of T with weights W. The order in which the weighted compositions are generated is co-lexicographic. (That is, lexicographic in the reverse of the weighted compositions.)

A weighted composition is a sequence of nonnegative integers, $\left(r_1\,\dots \,r_n\right)$, such that $T\=\sum _{k\=1}^n{W}_k{r}_k$ with $n=\mathrm{numelems}\left(W\right)$. Unlike regular compositions, but like bounded compositions, a weighted composition is understood to be ordered: $r_k$ corresponds to $W_k$.

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

$B≔\mathrm{WeightedComposition}\left(\left[1\,2\,4\right]\,8\right)\:$

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

             1: 8 0 0
             2: 6 1 0
             3: 4 2 0
             4: 2 3 0
             5: 0 4 0
             6: 4 0 1
             7: 2 1 1
             8: 0 2 1
             9: 0 0 2

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

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