1 | initial version |

What you are looking for is the list of all degree-8 irreducible polynomials over $\mathbb F_2$. There is no built-in function for this, but they can be found very easily if you combine `polynomials`

which iterates over all polynomials of a given degree and `is_irreducible`

that tests irreducibilty.

For instance:

```
sage: R = GF(2)['x']
sage: for p in R.polynomials(8):
....: if p.is_irreducible():
....: print(p)
....:
x^8 + x^4 + x^3 + x + 1
x^8 + x^4 + x^3 + x^2 + 1
x^8 + x^5 + x^3 + x + 1
[...]
x^8 + x^7 + x^6 + x^5 + x^4 + x^2 + 1
x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 1
```

You can also built the list of all of them:

```
sage: Irr = [p for p in R.polynomials(8) if p is_irreducible()]
sage: len(Irr)
30
```

Finally, you can have access to some specific irreducible polynomials using `R.irreducible_element(algorithm='...')`

. Have a look at the documentation of `irreducible_element`

for details here.

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