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)
79 4 2 71 2 63 2
o3 = (--)(y - --) + (--)(x) + (---)(1)
8 79 8 632
o3 : SOSPoly
|
i4 : sosPoly solveSOS (f, 2, TraceObj=>true)
1 2 35 2
o4 = (9)(- --y + 1) + (--)(y)
18 36
o4 : SOSPoly
|