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How to define q-polynomial in a finite field GF(q^m)?

asked 2023-02-09 03:55:29 +0200

Ycs gravatar image

updated 2023-02-09 12:19:59 +0200

Dear all,

A $q$-polynomial of $q$-degree $r$ in $GF(q^m)$ is a polynomial of the form $P(x) = \sum_{i=0}^{r}p_ix^{q^i}$ for $p_i \in GF(q^m)$, $p_r\neq 0$.

How to define this $q$-polynomial in $GF(q^m)$? I do not find this and its operations in Reference Manual.

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answered 2023-02-09 04:21:08 +0200

kwankyu gravatar image

The ring of $q$-polynomials is isomorphic to an Ore polynomial ring. Look at

https://doc.sagemath.org/html/en/refe...

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Thanks very much!!!

Ycs gravatar imageYcs ( 2023-02-09 12:23:08 +0200 )edit

I have other questions. Look at https://ask.sagemath.org/question/663...

Ycs gravatar imageYcs ( 2023-02-10 01:52:04 +0200 )edit

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Asked: 2023-02-09 03:55:29 +0200

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Last updated: Feb 09 '23