append_change = truefalse

True means append an integer indicating the change to the output Array. The magnitude of the integer is the index that changed, the sign is the direction of the change. The default is false.

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 MixedRadixGrayCode command returns an iterator that generates a mixed-radix Gray code.

The radices parameter is a list of positive integers that specify the radices of the number. The k-th integer is the radix at the k-th index.

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

$M≔\mathrm{MixedRadixGrayCode}\left(\left[2\,4\,3\right]\right)\:$

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

$\left[\begin{array}{ccc}0& 0& 0\end{array}\right],\left[\begin{array}{ccc}1& 0& 0\end{array}\right],\left[\begin{array}{ccc}1& 1& 0\end{array}\right],\left[\begin{array}{ccc}0& 1& 0\end{array}\right],\left[\begin{array}{ccc}0& 2& 0\end{array}\right],\left[\begin{array}{ccc}1& 2& 0\end{array}\right],\left[\begin{array}{ccc}1& 3& 0\end{array}\right],\left[\begin{array}{ccc}0& 3& 0\end{array}\right],\left[\begin{array}{ccc}0& 3& 1\end{array}\right],\left[\begin{array}{ccc}1& 3& 1\end{array}\right],\left[\begin{array}{ccc}1& 2& 1\end{array}\right],\left[\begin{array}{ccc}0& 2& 1\end{array}\right],\left[\begin{array}{ccc}0& 1& 1\end{array}\right],\left[\begin{array}{ccc}1& 1& 1\end{array}\right],\left[\begin{array}{ccc}1& 0& 1\end{array}\right],\left[\begin{array}{ccc}0& 0& 1\end{array}\right],\left[\begin{array}{ccc}0& 0& 2\end{array}\right],\left[\begin{array}{ccc}1& 0& 2\end{array}\right],\left[\begin{array}{ccc}1& 1& 2\end{array}\right],\left[\begin{array}{ccc}0& 1& 2\end{array}\right],\left[\begin{array}{ccc}0& 2& 2\end{array}\right],\left[\begin{array}{ccc}1& 2& 2\end{array}\right],\left[\begin{array}{ccc}1& 3& 2\end{array}\right],\left[\begin{array}{ccc}0& 3& 2\end{array}\right]$

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

$24$

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

$\left[\begin{array}{ccc}0& 1& 0\end{array}\right]$

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

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

$\left[\begin{array}{ccc}0& 1& 0\end{array}\right],\left[\begin{array}{ccc}0& 2& 0\end{array}\right],\left[\begin{array}{ccc}1& 2& 0\end{array}\right],\left[\begin{array}{ccc}1& 3& 0\end{array}\right],\left[\begin{array}{ccc}0& 3& 0\end{array}\right],\left[\begin{array}{ccc}0& 3& 1\end{array}\right],\left[\begin{array}{ccc}1& 3& 1\end{array}\right],\left[\begin{array}{ccc}1& 2& 1\end{array}\right],\left[\begin{array}{ccc}0& 2& 1\end{array}\right],\left[\begin{array}{ccc}0& 1& 1\end{array}\right],\left[\begin{array}{ccc}1& 1& 1\end{array}\right],\left[\begin{array}{ccc}1& 0& 1\end{array}\right],\left[\begin{array}{ccc}0& 0& 1\end{array}\right],\left[\begin{array}{ccc}0& 0& 2\end{array}\right],\left[\begin{array}{ccc}1& 0& 2\end{array}\right],\left[\begin{array}{ccc}1& 1& 2\end{array}\right],\left[\begin{array}{ccc}0& 1& 2\end{array}\right],\left[\begin{array}{ccc}0& 2& 2\end{array}\right],\left[\begin{array}{ccc}1& 2& 2\end{array}\right],\left[\begin{array}{ccc}1& 3& 2\end{array}\right],\left[\begin{array}{ccc}0& 3& 2\end{array}\right]$

$N≔\mathrm{MixedRadixGrayCode}\left(\left[3\,4\right]\,\mathrm{append\_change}\right)\:$

$$\begin{gathered} \mathbf{for}V\mathbf{in}N\mathbf{do} \\ \mathrm{printf}\left(''\%d\; :\; \%d\backslash n''\,V\left[1..2\right]\,V\left[3\right]\right) \\ \mathbf{end}\mathbf{do}\: \end{gathered}$$

0 0 : 0
1 0 : 1
2 0 : 1
2 1 : 2
1 1 : -1
0 1 : -1
0 2 : 2
1 2 : 1
2 2 : 1
2 3 : 2
1 3 : -1
0 3 : -1

facts := proc(n :: posint)
local F,T,m,iter,p;
uses Iterator;
    # Factor n into the form [[p1,e1],...,[pm,em]],
    # where n = p1^e1*...*pm^em.
    F := op(2,ifactors(n));
    m := numelems(F);

    # Assign a procedure that converts a Vector (of exponents)
    # to an integer, using F.
    T := proc(V)
    local i;
        mul(F[i,1]^V[i],i=1..m);
    end proc;

    # Iterate through all factors.
    seq(T(p), p=MixedRadixGrayCode([seq(f[2]+1,f=F)]));
end proc:

$\mathrm{facts}\left(72\right)$

$1,2,4,8,24,12,6,3,9,18,36,72$

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[MixedRadixGrayCode] command was introduced in Maple 2016.

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

The radices parameter was updated in Maple 2022.