BUILT-IN MATHEMATICA SYMBOL

Tuples

generates a list of all possible n-tuples of elements from list.

Tuples

generates a list of all possible tuples whose i

element is from

.

MORE INFORMATION

The elements of list are treated as distinct, so that Tuples for a list of length k gives output of length .

The order of elements in Tuples is based on the order of elements in list, so that Tuples gives .

Tuples generates a list of all possible ... arrays of elements in list.

The object list need not have head List. The head at each level in the arrays generated by Tuples will be the same as the head of list.

EXAMPLES

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Basic Examples (3)

All possible 3-tuples of

and

:

The first element given is always picked first:

All ways of picking one element from each list:

All possible 3-tuples of

and

:

In[1]:=

Out[1]=

The first element given is always picked first:

In[1]:=

Out[1]=

All ways of picking one element from each list:

In[1]:=

Out[1]=

Generalizations & Extensions (3)

Each occurrence of an element is picked separately:

All possible 2×2 arrays formed from

and

:

Tuples with any head:

Applications (8)

Digits of successive base-2 numbers:

All possible trigrams of

and

:

Neighborhood rules for an elementary cellular automaton:

Digit sequences, or evolution of a substitution system:

2D lattice of points:

Connect pairs of points in all possible ways:

Properties & Relations (3)

All possible digit sequences:

Results from Outer involve extra sublists:

Subsets picks each element at most once, and treats reorderings as equivalent:

Possible Issues (1)

With one argument, Tuples picks an element from each sublist:

With two arguments, Tuples treats each sublist as a complete element:

Neat Examples (6)

3D lattice of points: