Message from discussion Maple: extracting data from sets of sets

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From: Axel Vogt <&nore...@axelvogt.de>
Newsgroups: comp.soft-sys.math.maple
Subject: Re: Maple: extracting data from sets of sets
Date: Sat, 27 Feb 2010 17:12:48 +0100
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Roger Kopler wrote:
> Hi,  I have a question about extracting data from a set to be used in a 
> function.  Suppose I have an object of the sort:
> 
> X:={{a=3,b=-3},{a=2,b=2},{a=0,b=3},{a=2,b=-4},{a=0,b=2},{a=2,b=0}};
> 
> and a function of the sort:
> 
> f:=(a,b)->a+b*sqrt(2);
> 
> How can I extract the values in the pairs (a,b) in X and use them in the 
> function f to create a set of 6 elements, i.e. {f(a,b) where {a,b} in X} 
> (and, no, I don't want to do this manually because I want to apply this 
> procedure, if it exists, to a set X containing a much larger number of 
> elements than 6)
> 
> Any help would be much appreciated.  Thanks in advance. 

   eval(f(a,b),op(1,X)); # uses the 1st equation in X

                                    1/2
                                 2 2

and by running to all of them gives you all, for example

   {seq( eval(f(a,b),op(j,X)), j=1 .. nops(X))};

or

   {seq( eval(f(a,b),xi), xi in X)};