### Multiplication of elements of extension fields

Let

```
p=13
R = GF(p)
_.<v> = PolynomialRing(R)
R4.<v> = R.extension(v^4 - 2, 'v')
_.<w> = PolynomialRing(R4)
R16.<w> = R4.extension(w^4-v, 'w')
```

I need to compute

```
f1 = R16(1)
for i in range(34):
A=R4.random_element() #in my case, this is not random, its derived by an function
f1 = f1^2*A #this is not the whole code, but it displayes the problem
```

This element stays allways in R4. But the result i expect, is an element of R16.

So: How can I tell sage to use the R16 multiplication instead? I need a full degree 15 polynomial. If it is possible, in one variable (w, since w^4=v).