Re: Converting a mapping into a well-defined function

*To*: mathgroup at smc.vnet.net*Subject*: [mg56541] Re: Converting a mapping into a well-defined function*From*: "Carl K. Woll" <carlw at u.washington.edu>*Date*: Thu, 28 Apr 2005 02:40:42 -0400 (EDT)*Organization*: University of Washington*References*: <d4msni$257$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

"Gilmar" <gilmar.rodriguez at nwfwmd.state.fl.us> wrote in message news:d4msni$257$1 at smc.vnet.net... > 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}}. > One possibility is the following: f[x_]:=Module[{tmp}, tmp = Transpose[{x[[All,1]],Range[Length[x]],x[[All,2]]}]; Split[Sort[tmp],#1[[1]]===#2[[1]]&][[All,1,{1,3}]] ] For your example, A={{a,5},{b,27},{a,14},{c,4},{e,94},{b,6},{d,9},{e,4}}; f[A] {{a, 5}, {b, 27}, {c, 4}, {d, 9}, {e, 94}} as desired. > 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! > If you are interested in creating such a function, then one idea follows: g[x_] := Module[{}, Clear[h]; Set @@@ Reverse[{h[#1], #2}& @@@ x]; ] g[A] ?h Global`h h[a] = 5 h[b] = 27 h[c] = 4 h[d] = 9 h[e] = 94 Carl Woll