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decompose polynomial by ideal members

R.<x,y,z> = QQ[]; f1=x^2+z^2-1; f2=x^2+z^2+(z^2-1)^2 I=ideal(f1,f2); p=x^2+(1/2)y^2z-z-1 Is there way in Sage to decompose p as p= (− (1/2)z+1)f1+((1/2)z)f2

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decompose polynomial by ideal members

Let

R.<x,y,z> = QQ[]; f1=x^2+z^2-1; f2=x^2+z^2+(z^2-1)^2 
I=ideal(f1,f2); p=x^2+(1/2)y^2z-z-1
p=x^2+(1/2)*y^2*z-z-1

Is there way in Sage to decompose p as as

p= (− (1/2)z+1)f1+((1/2)z)f2

(1/2)*z+1)*f1+((1/2)*z)*f2