Exact SOS certificate: q_i = sum_p coefficient(i,p)*w_p.
Order p: 12,13,14,23,24,34. Omitted coefficients are zero.
Weights: 1,1,1,1,1,1,1,1,2,2.

q1, weight 1:
  w12: 2*a*b*e**2 + a*b - 2*a*c**2*d*f + 2*b*c*d*f - 2*b*d*e
  w13: 2*a*f*(b*e - c*d)
  w14: a*b*e - a*c*d - b*d
  w23: (a*c - b)*(2*c*f**2 + c - 2*e*f)
  w24: 2*a*b*d + a*c**2*f - a*c*e - b*c*f + 2*b*e
  w34: 2*a*c**2*e + 2*a*c*f - 2*b*c*e - b*f

q2, weight 1:
  w12: 2*a*f*(b*e - c*d)
  w13: a*(2*b*f**2 + b - 2*d*f)
  w14: a*(b*f - d)
  w23: a*(2*c*f**2 + c - 2*e*f)
  w24: a*(c*f - e)
  w34: 2*a*(b*d + c*e + f)

q3, weight 1:
  w12: a*b*f + 2*a*c**2*d + a*d - 2*b*c*d
  w13: -a*b*e + a*c*d - b*d
  w23: 2*a*b*d + 2*a*c**2*f**3 + a*c**2*f - 4*a*c*e*f**2 - a*c*e + 2*a*e**2*f - 2*b*c*f**3 - b*c*f + 2*b*e*f**2 + 2*c*d*f**2 + 2*c*d - 2*d*e*f
  w24: a*c**2*f**2 - 2*a*c*e*f + a*e**2 - b*c*f**2 + 2*b*e*f - d*e
  w34: 2*a*c**2*e*f - 2*a*c*e**2 + 2*a*c*f**2 - 2*a*e*f - 2*b*c*e*f - b*f**2 + 2*c*d*e + d*f

q4, weight 1:
  w12: c*(2*a*c*e*f - 2*a*e**2 - a - 2*b*e*f + 2*d*e)
  w13: c*(2*a*c*f**2 + a*c - 2*a*e*f - 2*b*f**2 - b + 2*d*f)
  w14: c*(a*c*f - a*e - b*f + 2*d)
  w24: -c*(2*a*d + e)
  w34: c*(2*a*c*d - 2*b*d - f)

q5, weight 1:
  w12: 2*a*c**2*e + a*c*f + a*e - 2*b*c*e
  w13: -2*a*c**2*f**3 - a*c**2*f + 4*a*c*e*f**2 + a*c*e - 2*a*e**2*f + 2*b*c*f**3 + b*c*f - 2*b*e*f**2 - 2*b*e - 2*c*d*f**2 + 2*d*e*f
  w14: -a*c**2*f**2 + 2*a*c*e*f - a*e**2 + b*c*f**2 - 2*c*d*f + d*e
  w23: e*(2*a*b + c)
  w24: -2*a*f*(b*e - c*d)
  w34: 2*a*b*e**2 - 2*a*c**2*d*f + 2*b*c*d*f - 2*b*d*e + c*f**2 - e*f

q6, weight 1:
  w12: 2*f*(a*c**2*f**2 + a*c**2 - 2*a*c*e*f + a*e**2 + a - b*c*f**2 - b*c + b*e*f + c*d*f - d*e)
  w13: -b*f
  w14: f*(b*f - d)
  w23: f*(2*a*b + c)
  w24: -f*(2*a*b*f - 2*a*d + c*f - e)
  w34: 2*a*f*(b*e - c*d)

q7, weight 1:
  w12: 2*a*c**2*f**2 + 2*a*c**2 - 2*a*c*e*f + a - 2*b*c*f**2 - 2*b*c + b*e*f + c*d*f
  w13: -a*c**2*e*f + a*c*e**2 + a*c*f**2 + a*c - a*e*f + b*c*e*f - b - c*d*e
  w14: -a*c**2*e - a*e + b*c*e + b*f
  w23: -a*b*e**2 - a*b*f**2 + a*b + a*c**2*d*f + a*d*f - b*c*d*f + b*d*e + c
  w24: -2*a*b*f + a*c**2*d + a*d - b*c*d - c*f
  w34: 2*a*b*e - b*d + c*e

q8, weight 1:
  w12: 2*a*c*e*f - 2*a*e**2 - a - b*e*f - c*d*f + 2*d*e
  w13: -a*c**2*e*f + a*c*e**2 + a*c*f**2 + a*c - a*e*f + b*c*e*f - c*d*e
  w14: -a*c**2*e - a*e + b*c*e + d
  w23: -a*b*e**2 - a*b*f**2 - a*b + a*c**2*d*f + a*d*f - b*c*d*f + b*d*e
  w24: a*c**2*d - a*d - b*c*d - e
  w34: 2*a*c*d - b*d + c*e

q9, weight 2:
  w12: f*(b*e - c*d)
  w13: (2*b*f**2 + b - 2*d*f)/2
  w14: (b*f - d)/2
  w23: (2*c*f**2 + c - 2*e*f)/2
  w24: (c*f - e)/2
  w34: b*d + c*e + f

q10, weight 2:
  w13: (2*a*c**2*e*f - 2*a*c*e**2 + 2*a*c*f**2 - 2*a*e*f - 2*b*c*e*f - 2*b*f**2 - b + 2*c*d*e + 2*d*f)/2
  w14: (2*a*c**2*e + 2*a*c*f - 2*b*c*e - b*f + d)/2
  w23: (2*a*b*e**2 + 2*a*b*f**2 + 2*a*b - 2*a*c**2*d*f - 2*a*d*f + 2*b*c*d*f - 2*b*d*e + 2*c*f**2 + c - 2*e*f)/2
  w24: -(2*a*c**2*d + 2*a*d - 2*b*c*d - c*f + e)/2
