TraceObj -- whether to use trace as the objective function

Description

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

Functions with optional argument named TraceObj :

solveSOS(...,TraceObj=>...)

For the programmer

The object TraceObj is a symbol.