Reduce a polynomial into symmetric part and remainder over elementary symmetric polynomials
Differs from the .wl reference: `SymmetricReduction` two-argument form
SymmetricReduction[f, {x1, …, xn}]
SymmetricReduction[f, {x1, …, xn}, {s1, …, sn}]
SymmetricReduction[x ^ 2 + y ^ 2, {x, y}]
→ {-2*x*y + (x + y)^2, 0}SymmetricReduction[x ^ 2 - y ^ 2, {x, y}]
→ {-2*x*y + (x + y)^2, -2*y^2}SymmetricReduction[x ^ 2 - y ^ 2, {x, y}, {s1, s2}]
→ {s1^2 - 2*s2, -2*y^2}