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Re: Converting a mapping into a well-defined function

• To: mathgroup at smc.vnet.net
• Subject: [mg56540] Re: [mg56499] Converting a mapping into a well-defined function
• From: János <janos.lobb at yale.edu>
• Date: Thu, 28 Apr 2005 02:40:41 -0400 (EDT)
• References: <200504270153.VAA01768@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Using UnsortedUnion from the Help under Union

In[29]:=
UnsortedUnion[x_] :=
   Module[{f},
    f[y_] := (f[y] = Sequence[
         ]; y); f /@ x]

In[1]:=
setA = {{a, 5}, {b, 27},
    {a, 14}, {c, 4}, {e, 94},
    {b, 6}, {d, 9}, {e, 4}}

In[62]:=
Extract[setA,
   ({First[First[Position[
         setA, #1]]]} & ) /@
    UnsortedUnion[
     Transpose[setA][[1]]]]
Out[62]=
{{a, 5}, {b, 27}, {c, 4},
   {e, 94}, {d, 9}}

Then you can Sort it to get your result, or replace UnsortedUnion  
with Union in the Extract

In[79]:=
Extract[setA,
   ({First[First[Position[
         setA, #1]]]} & ) /@
    Union[Transpose[setA][[
      1]]]]
Out[79]=
{{a, 5}, {b, 27}, {c, 4},
   {d, 9}, {e, 94}}

János
On Apr 26, 2005, at 9:53 PM, Gilmar wrote:

> Dear Mathematica User Friends:
>
> I need to build a module that takes a non-empty set A
> (whose elements are 2-tuples), and appends (or not) those 2-tuples
> to a set B  according to the following criteria:
>
> (1.) if the abscissa of a 2-tuple in A is unique (among the abscissas
> of all the other 2-tuples in A), then the module appends that 2-tuple
> to the set B.
>
> (2.) if there are n 2-tuples in A that share the same abscissa, then
> the module appends the first of those 2-tuples to B ("first" here  
> means
> the first of such n 2-tuple encountered, as you read A from left to
> right),but does not append the rest to B.
>
> (3.) the module does not attempt to sort the set B, after the  
> appending
> process is completed.
>
> Example:
>
> If A = {{a,5},{b,27},{a,14},{c,4},{e,94},{b,6},{d,9},{e,4}}
>
> then
>
> B=Module[A]={{a,5},{b,27},{c,4},{d,9},{e,94}}.
>
> Another way to re-phrase the above example;
>
> if A defines a mapping:
>
> A(a)=5, A(b)=27, A(a)=14, A(c)=4, A(e)=94, A(b)=6, A(d)=9, A(e)=4
>
> them the module converts the mapping A into a well-defined function:
>
> A(a)=5, A(b)=27, A(c)=4, A(d)=9, A(e)=94.
>
> Thank you for your help!

• References:
  • Converting a mapping into a well-defined function
    • From: "Gilmar" <gilmar.rodriguez@nwfwmd.state.fl.us>