compile = truefalse

True means compile the iterator. The default is true.

rank = nonnegint

Specify the starting rank of the iterator. The default is one. 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. For efficiency, each list/set must have at least two elements, otherwise an error is raised.

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.