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MathGroup Archive 1995

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Re: I'm looking for an algorithm: Cartesian Product

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1663] Re: I'm looking for an algorithm: Cartesian Product
  • From: wagner at bullwinkle.cs.Colorado.EDU (Dave Wagner)
  • Date: Tue, 11 Jul 1995 03:57:13 -0400
  • Organization: University of Colorado, Boulder

In article <3ti27l$klt at news0.cybernetics.net>,
Hala Skaf <Hala.Skaf at loria.fr> wrote:
>
>Hello,
>
>     I'm looking for an algorithm that can compute 
> Cartesian Product for several sets. For example:
>
> How can I compute the Cartesian Product of:
>
>	E1={a1 a2} E2={b1 b2 b3} E3={z1 z2}
>
In[3]:=
    Outer[List, {a1, a2}, {b1, b2, b3}, {z1, z2}]
Out[3]=
    {{{{a1, b1, z1}, {a1, b1, z2}}, 
       {{a1, b2, z1}, {a1, b2, z2}}, 
       {{a1, b3, z1}, {a1, b3, z2}}}, 
      {{{a2, b1, z1}, {a2, b1, z2}}, 
       {{a2, b2, z1}, {a2, b2, z2}}, 
       {{a2, b3, z1}, {a2, b3, z2}}}}

In[4]:=
    Flatten[%, 2]
Out[4]=
    {{a1, b1, z1}, {a1, b1, z2}, {a1, b2, z1}, 
      {a1, b2, z2}, {a1, b3, z1}, {a1, b3, z2}, 
      {a2, b1, z1}, {a2, b1, z2}, {a2, b2, z1}, 
      {a2, b2, z2}, {a2, b3, z1}, {a2, b3, z2}}

		Dave Wagner
		Principia Consulting
		(303) 786-8371
		dbwagner at princon.com
		http://www.princon.com/princon


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