# 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^2*z-z-1
```

Is there way in Sage to decompose p as

```
p= (− (1/2)*z+1)*f1+((1/2)*z)*f2
```