The optional argument RoundTol specifies the minimal rounding precision in $d$ binary digits.
Sumsofsquares problems are solved numerically using a semidefinite programming solver, and afterwards the package attempts to round the floating point solution to rational numbers. The rounding strategy is guaranteed to work whenever the space of Gram matrices is full dimensional. For optimization problems the rounding may cause a loss in optimality. The argument RoundTol allows to control the tradeoff between optimality and simplicity. Higher values of RoundTol lead to better solutions.






One can also skip the rounding by setting RoundTol => infinity.


References: Computing sum of squares decompositions with rational coefficients, H. Peyrl and P. Parrilo, in Theoretical Computer Science 409 (2008) p. 269–281.