example.txt

#example 17

A = [x y z] # variables
#f=x^6+y^6-2*x^2*y^2+x^4+y^4
f=2*(x^8+y^8+z^8)-(x^6*y^2+x^6*z^2+y^6*x^2+y^6*z^2+z^6*x^2+z^6*y^2)-2*(x^4*y^4+x^4*z^4+y^4*z^4)+2*(x^4*y^2*z^2+y^4*x^2*z^2+z^4*y^2*x^2)  # constant polynomail declare
findsos(f) # find sos decomposition of polynomial f


#example 18
M= { 1 x y x^2 x*y y^2 x^3 } # monomial used in  unkown polynomial


f1=4*x^2-y^2
g=x-y
s=sos(M) # an unknown sos polynomial whose support is M (evey  momomial of s must occur in set M ),in orther words s =f_1^2+...+f_s^2 

cg=poly(M)# an unknown polynomial whose suppport is M

g*cg +s == f1 #solve a constraintd polynomails problem 

#example 19
f2=1-x^2-y^2 # first coffiecient must be non-negative
f3=x^2+4*y^2-10 
s2=sos(M)
s3=sos(M)
s4=sos(M)
# constraints polys only occour in left and constant poly only occur in right part
s4+s2+s3 == 10 # solve a constraintd polynomails problem 

ff= x^2+2*x*y+y^2+1
s6=sos(M)
M1={ 1 }
s7= sos(M1)

s6+s7 == ff