Re: Plus sets in mathematica..?

• To: mathgroup at smc.vnet.net
• Subject: [mg75952] Re: Plus sets in mathematica..?
• From: Szabolcs <szhorvat at gmail.com>
• Date: Mon, 14 May 2007 03:31:11 -0400 (EDT)
• Organization: University of Bergen
• References: <f26ocl\$4tn\$1@smc.vnet.net>

```changbo wrote:
> I want to make a function "f", its domain is every thinkable two sets, and the result is  {a+b | aâ??A,bâ??B} for A,B.
>
>  ex) A={1,2,3}, B={40,50,60,70},
>  then I have f[A,B] as
>  {41,42,43,51,52,53,61,62,63,71,72,73}.
>
>  How can I construct function "f"? Let me know the source.. Thank you very much
>

Look up Outer in the documentation. Mathematica doesn't have sets, but
Lists, where the order of elements does matter. If you need to treat
lists as sets (i.e. no repeating elements), look up Union.

In[3]:=
A={1,2,3}
B={40,50,60,70}

Out[3]=
{1,2,3}

Out[4]=
{40,50,60,70}

In[5]:=
Outer[Plus,A,B]

Out[5]=
{{41,51,61,71},{42,52,62,72},{43,53,63,73}}

In[6]:=
Flatten@%

Out[6]=
{41,51,61,71,42,52,62,72,43,53,63,73}

In[7]:=
Union@%

Out[7]=
{41,42,43,51,52,53,61,62,63,71,72,73}

Define the function f as
f[a_, b_] := Flatten@Outer[Plus, a, b]

Szabolcs

```

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