sosPoly -- make an SOS polynomial

Synopsis

• Usage:

  s = sosPoly (SDPR)

  s = sosPoly (mon,Q)

  s = sosPoly (R,polys,coeffs)

• Inputs:
  • SDPR, an instance of the type SDPResult, the result of an SDP computation
  • Q, a matrix, positive semidefinite (Gram matrix)
  • mon, a matrix, a vector of monomials
  • R, a ring,
  • polys, a list, of polynomials
  • coeffs, a list, of scalars
• Outputs:
  • s, an instance of the type SOSPoly,

Description

i1 : R = QQ[x,y];

i2 : f = 2*x^4+5*y^4-2*x^2*y^2+2*x^3*y;

i3 : sosPoly solveSOS f

            83 2    2 2    43  20 2       2    231773   2 2
o3 = (5)(- ---x  + y )  + (--)(--x  + x*y)  + (------)(x )
           200             20  43              344000

o3 : SOSPoly

i4 : Q = matrix(QQ,{{1,1,1},{1,1,1},{1,1,1}});

              3       3
o4 : Matrix QQ  <-- QQ

i5 : mon = matrix{{1},{x},{y}};

             3      1
o5 : Matrix R  <-- R

i6 : sosPoly(mon,Q)

                   2
o6 = (1)(x + y + 1)

o6 : SOSPoly

i7 : s = sosPoly(R, {x+1,y}, {2,3} )

              2        2
o7 = 2*(x + 1)  + 3*(y)

o7 : SOSPoly

See also

• solveSOS -- solve a sum-of-squares problem
• Solver -- picking a semidefinite programming solver