compile = truefalse

True means compile the iterator. The default is true.

rank = nonnegint

Specify the starting rank of the iterator. The default is one. Passing a value greater than one causes the iterator to skip the lower ranks; this can be useful when parallelizing iterators. The starting rank reverts to one when the iterator is reset, reused, or copied.

The CartesianProduct command returns an iterator that generates the Cartesian product of a sequence of lists and sets. The k-th element of the output Array contains an element from the k-th set/list in the input.

The L parameter is a sequence of lists and sets.

If L contains an empty list or set, the iterator returns nothing.

If L is the empty sequence the iterator returns an empty Array.

Internally this iterator uses a loopless, reflected, mixed-radix Gray code for the iterator; see MixedRadixGrayCode.

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

$M≔\mathrm{CartesianProduct}\left(\left[1\,2\,2\right]\,\left\{a\,b\right\}\,\left\{c\,d\,e\right\}\right)\:$

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

 1: 1 a c
 2: 2 a c
 3: 2 a c
 4: 2 b c
 5: 2 b c
 6: 1 b c
 7: 1 b d
 8: 2 b d
 9: 2 b d
10: 2 a d
11: 2 a d
12: 1 a d
13: 1 a e
14: 2 a e
15: 2 a e
16: 2 b e
17: 2 b e
18: 1 b e

$\mathrm{seq}\left(v\left[\right]\,v=M\right)$

$\left[\begin{array}{ccc}1& a& c\end{array}\right],\left[\begin{array}{ccc}2& a& c\end{array}\right],\left[\begin{array}{ccc}2& a& c\end{array}\right],\left[\begin{array}{ccc}2& b& c\end{array}\right],\left[\begin{array}{ccc}2& b& c\end{array}\right],\left[\begin{array}{ccc}1& b& c\end{array}\right],\left[\begin{array}{ccc}1& b& d\end{array}\right],\left[\begin{array}{ccc}2& b& d\end{array}\right],\left[\begin{array}{ccc}2& b& d\end{array}\right],\left[\begin{array}{ccc}2& a& d\end{array}\right],\left[\begin{array}{ccc}2& a& d\end{array}\right],\left[\begin{array}{ccc}1& a& d\end{array}\right],\left[\begin{array}{ccc}1& a& e\end{array}\right],\left[\begin{array}{ccc}2& a& e\end{array}\right],\left[\begin{array}{ccc}2& a& e\end{array}\right],\left[\begin{array}{ccc}2& b& e\end{array}\right],\left[\begin{array}{ccc}2& b& e\end{array}\right],\left[\begin{array}{ccc}1& b& e\end{array}\right]$

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

$18$

$\mathrm{Unrank}\left(M\,4\right)$

$\left[\begin{array}{ccc}2& b& c\end{array}\right]$

$N≔\mathrm{Object}\left(M\,\mathrm{rank}=4\right)\:$

$\mathrm{seq}\left(v\left[\right]\,v=N\right)$

$\left[\begin{array}{ccc}2& b& c\end{array}\right],\left[\begin{array}{ccc}2& b& c\end{array}\right],\left[\begin{array}{ccc}1& b& c\end{array}\right],\left[\begin{array}{ccc}1& b& d\end{array}\right],\left[\begin{array}{ccc}2& b& d\end{array}\right],\left[\begin{array}{ccc}2& b& d\end{array}\right],\left[\begin{array}{ccc}2& a& d\end{array}\right],\left[\begin{array}{ccc}2& a& d\end{array}\right],\left[\begin{array}{ccc}1& a& d\end{array}\right],\left[\begin{array}{ccc}1& a& e\end{array}\right],\left[\begin{array}{ccc}2& a& e\end{array}\right],\left[\begin{array}{ccc}2& a& e\end{array}\right],\left[\begin{array}{ccc}2& b& e\end{array}\right],\left[\begin{array}{ccc}2& b& e\end{array}\right],\left[\begin{array}{ccc}1& b& e\end{array}\right]$

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  H, loopless reflected mixed-radix Gray generation, p. 20.

The Iterator[CartesianProduct] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.

The Iterator[CartesianProduct] command was updated in Maple 2022.

The L parameter was updated in Maple 2022.