Re: direct product of two sets

• To: mathgroup at smc.vnet.net
• Subject: [mg53315] Re: [mg53264] direct product of two sets
• From: Richard Phillips <richardp at wolfram.com>
• Date: Wed, 5 Jan 2005 01:21:50 -0500 (EST)
• Organization: Wolfram Research
• Sender: owner-wri-mathgroup at wolfram.com

```Hello Cong,

There are two methods that come to mind:

In[1]:=  A={1, 2, 3};
In[2]:=  B={x, y, z};

In[3]:= Tuples[{A, B}]
Out[3]= {{1, x}, {1, y}, {1, z}, {2, x}, {2, y}, {2, z}, {3, x}, {3, y},
{3, z}}

Note that Tuples is a new function introduced in Version 5.1.

In[4]:= Flatten[Outer[List, A, B, 1], 1]
Out[4]= {{1, x}, {1, y}, {1, z}, {2, x}, {2, y}, {2, z}, {3, x}, {3, y},
{3, z}}

Other short programs will do this too, but I think these are the shortest.

Best wishes,

Richard Phillips
Wolfram Research

ps.
http://mathworld.wolfram.com/CartesianProduct.html
http://mathworld.wolfram.com/DirectProduct.html

```

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