1 | initial version |

When you have an element of `x`

of `GF(q^m)`

, `x.polynomial()`

gives you the polynomial (over `GF(q)`

) that represents `x`

, and then you can have its coefficients using `.coefficients()`

:

```
sage: R.<a> = GF(17^22)
sage: x = R.random_element()
sage: x.polynomial().coefficients()
[10, 15, 5, 16, 2, 1, 5, 9, 12, 10, 12, 3, 16, 9, 1, 16, 7, 7, 2, 10, 3, 4]
```

Though, I am not sure about your question since for $x\in\text{GF}(q^m)$, $x^{q^k} = x$.

2 | No.2 Revision |

When you have an element of `x`

of `GF(q^m)`

, `x.polynomial()`

gives you the polynomial (over `GF(q)`

) that represents `x`

, and then you can have its coefficients using `.coefficients()`

:

```
sage: R.<a> = GF(17^22)
sage: x = R.random_element()
sage: x.polynomial().coefficients()
[10, 15, 5, 16, 2, 1, 5, 9, 12, 10, 12, 3, 16, 9, 1, 16, 7, 7, 2, 10, 3, 4]
```

Though, I am not sure about your question since for $x\in\text{GF}(q^m)$, $x^{q^k} = x$.

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.