ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 10 Feb 2023 01:52:04 +0100How to define q-polynomial in a finite field GF(q^m)?https://ask.sagemath.org/question/66305/how-to-define-q-polynomial-in-a-finite-field-gfqm/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.Thu, 09 Feb 2023 03:55:29 +0100https://ask.sagemath.org/question/66305/how-to-define-q-polynomial-in-a-finite-field-gfqm/Answer by kwankyu for <p>Dear all,</p>
<p>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 $p_i \in GF(q^m)$, $p_r\neq 0$.</p>
<p>How to define this $q$-polynomial in $GF(q^m)$? I do not find this and its operations in Reference Manual.</p>
https://ask.sagemath.org/question/66305/how-to-define-q-polynomial-in-a-finite-field-gfqm/?answer=66306#post-id-66306The ring of $q$-polynomials is isomorphic to an Ore polynomial ring. Look at
https://doc.sagemath.org/html/en/reference/noncommutative_polynomial_rings/index.htmlThu, 09 Feb 2023 04:21:08 +0100https://ask.sagemath.org/question/66305/how-to-define-q-polynomial-in-a-finite-field-gfqm/?answer=66306#post-id-66306Comment by Ycs for <p>The ring of $q$-polynomials is isomorphic to an Ore polynomial ring. Look at</p>
<p><a href="https://doc.sagemath.org/html/en/reference/noncommutative_polynomial_rings/index.html">https://doc.sagemath.org/html/en/refe...</a></p>
https://ask.sagemath.org/question/66305/how-to-define-q-polynomial-in-a-finite-field-gfqm/?comment=66322#post-id-66322I have other questions. Look at https://ask.sagemath.org/question/66323/q-polynomial-and-rank-decoding-problem/Fri, 10 Feb 2023 01:52:04 +0100https://ask.sagemath.org/question/66305/how-to-define-q-polynomial-in-a-finite-field-gfqm/?comment=66322#post-id-66322Comment by Ycs for <p>The ring of $q$-polynomials is isomorphic to an Ore polynomial ring. Look at</p>
<p><a href="https://doc.sagemath.org/html/en/reference/noncommutative_polynomial_rings/index.html">https://doc.sagemath.org/html/en/refe...</a></p>
https://ask.sagemath.org/question/66305/how-to-define-q-polynomial-in-a-finite-field-gfqm/?comment=66313#post-id-66313Thanks very much!!!Thu, 09 Feb 2023 12:23:08 +0100https://ask.sagemath.org/question/66305/how-to-define-q-polynomial-in-a-finite-field-gfqm/?comment=66313#post-id-66313