# SOSTOOLS - Express a Matrix polynomials as Polynomial

We know that to express an polynomial as SOS, we can write it as a Matrix SOS

Now we take an example, use SOStools in Matlab to get SOS for $$f(a,b,c)=16(a^2+b^2+c^2)^3-9\left[(a^3+3b^2c)^2+(3ac^2+b^3)^2+(3a^2b+c^3)^2\right]$$ Use the following command

$$\text{syms a b c}\\ \text{option.solver = 'sedumi';}\\ \text{p=16*(a^2+b^2+c^2)^3-9*(a^3+3*b^2*c)^2-9*(3*a*c^2+b^3)^2-9*(3*a^2*b+c^3)^2;}\\ \text{[Q,Z]=findsos(p,'rational',option);}$$

Then we can found a Matrix SOS.

Now I want to express this Matrix SOS as SOS polynomials (I mean the sum of SOS), how can I do it in Matlab or Maple?

I have read the user's guide, and I found a piece of related information:

But I still don't know how to use this for my problem. Thanks for help!