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Is it possible for Mathematica to solve for f(x,y) = 0 such that {x,y} contains {{0,0.5}, {1,0.5}, {0.6,0.8}, {0.4,0.2}} ?

Do we need to specify f(x,y) first ?

Thank you

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    $\begingroup$ The constant function f[x,y]=0 contains those solution, and is found by mathematica using InterpolatingPolynomial: InterpolatingPolynomial[{{{0, 0.5}, 0}, {{1, 0.5}, 0}, {{0.6, 0.8}, 0}, {{0.4, 0.2}, 0}}, {x, y}] $\endgroup$ – Coolwater Jun 11 '14 at 8:48
  • $\begingroup$ There are infinitely many such functions, even among polynomials. This is in fact a duplicate of Get polynomial interpolation formula. I recommend taking a closer look at this answer. $\endgroup$ – Artes Jun 11 '14 at 9:19

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