### How to transform a univariate polynomial over $\mathbb{F}_{2^n}$ into a multivariate Boolean polynomial over $\mathbb{F}_2^n$

```
python
```

```
F=GF(2^8,'a')
R=PolynomialRing(F,"x,y")
R.inject_variables()
```~~f=x*y-1
~~

f=x*y-1

How can we transform `f`

into a multivariable Boolean polynomial over $\mathbb{F}_{2^8}$, which includes variables $x_0, \ldots, x_7$ and $y_0, \ldots, y_7$ (16 variables in total), and has an algebraic degree of 2?