Using the trace as the objective function is a heuristic for obtaining sum-of-squares decompositions with small number of squares. Here we repeat Example 5 from [P05] and recover the shorter solution from that paper.
i1 : R = QQ[x,y]/ideal(x^2 + y^2 - 1); |
i2 : f = 10-x^2-y; |
i3 : sosPoly solveSOS (f, 2) 1 2 2 83 2 o3 = (7)(y - --) + (6)(x) + (--)(1) 14 28 o3 : SOSPoly |
i4 : sosPoly solveSOS (f, 2, TraceObj=>true) 1 2 35 2 o4 = (9)(- --y + 1) + (--)(y) 18 36 o4 : SOSPoly |