Re: Searching for a function

*To*: mathgroup at smc.vnet.net*Subject*: [mg70837] Re: Searching for a function*From*: Bill Rowe <readnewsciv at sbcglobal.net>*Date*: Sat, 28 Oct 2006 23:38:27 -0400 (EDT)

On 10/28/06 at 5:21 AM, banerjee.28 at osu.edu (Bonny Banerjee) wrote: >Is it possible for Mathematica to solve this problem: >Given sets A and B, does there exist a function from A to B? If yes, >what is the function? >Here is an example: >Let, A = {x such that 0<x<11 and Mod[x,2]==0} >B = {y such that 0<y<11 and Mod[y+1,2]==0} >Then, there exists a function from A to B >y = x - 1 >Thus, is there a way to specify arbitrary sets A, B, and use >Mathematica to figure out whether there exits a function from A to B >or not? Yes and no. Yes, in the sense that for any finite data set there is always a function that exactly maps members of A to B. If nothing else, a polynomial of degree Length[data]-1 will do the trick though not usually the best choice. For this purpose, cubic interpolation is usually a better choice Cubic interpolation can be accomplished using the built in function Interpolation But the general problem you are expressing, that is find an arbitrary function from a finite list of points at which the function has been sampled has no solution or perhaps more correctly no unique solution. -- To reply via email subtract one hundred and four