Re: Converting a mapping into a well-defined function

*To*: mathgroup at smc.vnet.net*Subject*: [mg56514] Re: [mg56499] Converting a mapping into a well-defined function*From*: "David Park" <djmp at earthlink.net>*Date*: Thu, 28 Apr 2005 02:40:00 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

The only thing I don't understand about the statement of your problem is that you didn't want to sort the resulting B list, but then you reversed the order of e and d, which rather implies that you did sort it. In any case, here is a modification of Carl Woll's remarkable UnsortedUnion routine, which is explained in the Examples under Union in Mathematica Help. Carl's routine takes the Union of a set of exact elements without changing their order (and is very efficient). I modify his routine so the match is made on only the first element of the 2-tuples. UnsortedUnion2[x_] := Module[{f}, f[{a_, b_}] := (f[{a, _}] = Sequence[]; {a, b}); f /@ x] alist = {{a, 5}, {b, 27}, {a, 14}, {c, 4}, {e, 94}, {b, 6}, {d, 9}, {e, 4}}; UnsortedUnion2[alist] {{a, 5}, {b, 27}, {c, 4}, {e, 94}, {d, 9}} David Park djmp at earthlink.net http://home.earthlink.net/~djmp/ From: Gilmar [mailto:gilmar.rodriguez at nwfwmd.state.fl.us] To: mathgroup 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}}. 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!