clean(RR,SOSPoly) -- remove squares with very small coefficients from a sum of squares

Synopsis

Function: clean
Usage:

clean (tol, s)
Inputs:
- tol, a real number, the tolerance for the coefficients.
- s, an instance of the type SOSPoly,
Outputs:
- an instance of the type SOSPoly, a cleaned up SOSPoly

Description

Given a sum-of-squares polynomial with real coefficients in the reals, this method removes the squares with coefficients smaller than the given tolerance. It does nothing on inputs with rational coefficients.

i1 : R = RR[x,y];

i2 : s = sosPoly(R, {x^2+.0001*x+1, y}, {2, .0001})

         2              2            2
o2 = 2*(x  + .0001x + 1)  + .0001*(y)

o2 : SOSPoly

i3 : clean( .001, s )

         2     2
o3 = 2*(x  + 1)

o3 : SOSPoly

Ways to use this method: