# Obtain a SymmetricReduction of a bivariate (symmetric) function given in Piecewise form

I would like to re-express the following bivariate (symmetric) function (defined over the unit square)

f[x, y] = Piecewise[{{p1, 0 < y < x < 1}, {p2, y == x}, {p3, 0 < x < y < 1}}]


where

p1 = -(x - 1)^3 (x (x + 3) - 5 y^2 + 1); p3 = -(y - 1)^3 (-5 x^2 + y (y + 3) + 1);
p2 = p3 /. y -> x;


as a (bivariate) polynomial in the two symmetric polynomials, s1 = x + y and s2 = x y.

Can the SymmetricReduction command be applied to such a problem (involving a function defined in Piecewise form)?

• Why not apply SymmetricReduction[] to p1 and p3 before feeding 'em to Piecewise[]? – J. M.'s technical difficulties Feb 29 '16 at 5:38
• Welcome to Mathematica.SE! 1) As you receive help, try to give it too, by answering questions in your area of expertise. 2) Take the tour and check the faqs! 3) When you see good questions and answers, vote them up by clicking the gray triangles, because the credibility of the system is based on the reputation gained by users sharing their knowledge. Also, please remember to accept the answer, if any, that solves your problem, by clicking the checkmark sign! – user9660 Feb 29 '16 at 6:53
• Thanks! I did try what J. M. suggested. No apparent simplification, however. – Paul B. Slater Feb 29 '16 at 14:39
• Thanks! I did try what J.M. suggested. No apparent simplification, however. I simply want to obtain a bivariate polynomial in s1 and s2 in "standard" form. That is, without the use of the Piecewise command. Something like "s1^3 +s1 s2 +s2^2.....", by way of illustration. – Paul B. Slater Feb 29 '16 at 14:42