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.Sun, 28 Nov 2021 14:10:36 +0100Finding an irreducible polynomial in Z [x] but reducible in F2 [x]https://ask.sagemath.org/question/59796/finding-an-irreducible-polynomial-in-z-x-but-reducible-in-f2-x/Hi everyone, I've been trying to find an irreducible polynomial in Z [x] but reducible in F2 [x].
I tried using this code:
i = 1
a = 0
while a == 0:
R = GF(2) ['x']
for p in R(x)polynomial(i)
i = i + 1
if not p.is_irreducible():
R.change_ring(ZZ)
if p.is_irreducible():
print p
a = 1
As I couldn't think of a way of finding an irreducible in Z and after that changing it to F2 I decided to do it backwards.
I'm in your graceful hands and sorry for my broken English.Wed, 17 Nov 2021 16:59:01 +0100https://ask.sagemath.org/question/59796/finding-an-irreducible-polynomial-in-z-x-but-reducible-in-f2-x/Comment by Escolopendra for <p>Hi everyone, I've been trying to find an irreducible polynomial in Z [x] but reducible in F2 [x]. </p>
<p>I tried using this code:</p>
<pre><code>i = 1
a = 0
while a == 0:
R = GF(2) ['x']
for p in R(x)polynomial(i)
i = i + 1
if not p.is_irreducible():
R.change_ring(ZZ)
if p.is_irreducible():
print p
a = 1
</code></pre>
<p>As I couldn't think of a way of finding an irreducible in Z and after that changing it to F2 I decided to do it backwards.</p>
<p>I'm in your graceful hands and sorry for my broken English.</p>
https://ask.sagemath.org/question/59796/finding-an-irreducible-polynomial-in-z-x-but-reducible-in-f2-x/?comment=59994#post-id-59994Thank you, it helped a lot.Sun, 28 Nov 2021 14:10:36 +0100https://ask.sagemath.org/question/59796/finding-an-irreducible-polynomial-in-z-x-but-reducible-in-f2-x/?comment=59994#post-id-59994Comment by Emmanuel Charpentier for <p>Hi everyone, I've been trying to find an irreducible polynomial in Z [x] but reducible in F2 [x]. </p>
<p>I tried using this code:</p>
<pre><code>i = 1
a = 0
while a == 0:
R = GF(2) ['x']
for p in R(x)polynomial(i)
i = i + 1
if not p.is_irreducible():
R.change_ring(ZZ)
if p.is_irreducible():
print p
a = 1
</code></pre>
<p>As I couldn't think of a way of finding an irreducible in Z and after that changing it to F2 I decided to do it backwards.</p>
<p>I'm in your graceful hands and sorry for my broken English.</p>
https://ask.sagemath.org/question/59796/finding-an-irreducible-polynomial-in-z-x-but-reducible-in-f2-x/?comment=59818#post-id-59818Hint : you are looking for a polynomial that you can factor in $\mathbb{F}_2$ but not in $\mathbb{Z}$. This might give you ideas :
sage: Pz.<z>=ZZ[]
sage: P2.<t>=GF(2)[]
sage: (z+1)^2
z^2 + 2*z + 1
sage: (t+1)^2
t^2 + 1Thu, 18 Nov 2021 17:43:32 +0100https://ask.sagemath.org/question/59796/finding-an-irreducible-polynomial-in-z-x-but-reducible-in-f2-x/?comment=59818#post-id-59818Comment by Escolopendra for <p>Hi everyone, I've been trying to find an irreducible polynomial in Z [x] but reducible in F2 [x]. </p>
<p>I tried using this code:</p>
<pre><code>i = 1
a = 0
while a == 0:
R = GF(2) ['x']
for p in R(x)polynomial(i)
i = i + 1
if not p.is_irreducible():
R.change_ring(ZZ)
if p.is_irreducible():
print p
a = 1
</code></pre>
<p>As I couldn't think of a way of finding an irreducible in Z and after that changing it to F2 I decided to do it backwards.</p>
<p>I'm in your graceful hands and sorry for my broken English.</p>
https://ask.sagemath.org/question/59796/finding-an-irreducible-polynomial-in-z-x-but-reducible-in-f2-x/?comment=59807#post-id-59807I am not going to lie to you. Yeah it is.Wed, 17 Nov 2021 23:02:15 +0100https://ask.sagemath.org/question/59796/finding-an-irreducible-polynomial-in-z-x-but-reducible-in-f2-x/?comment=59807#post-id-59807Comment by Emmanuel Charpentier for <p>Hi everyone, I've been trying to find an irreducible polynomial in Z [x] but reducible in F2 [x]. </p>
<p>I tried using this code:</p>
<pre><code>i = 1
a = 0
while a == 0:
R = GF(2) ['x']
for p in R(x)polynomial(i)
i = i + 1
if not p.is_irreducible():
R.change_ring(ZZ)
if p.is_irreducible():
print p
a = 1
</code></pre>
<p>As I couldn't think of a way of finding an irreducible in Z and after that changing it to F2 I decided to do it backwards.</p>
<p>I'm in your graceful hands and sorry for my broken English.</p>
https://ask.sagemath.org/question/59796/finding-an-irreducible-polynomial-in-z-x-but-reducible-in-f2-x/?comment=59800#post-id-59800Homework ?Wed, 17 Nov 2021 18:23:19 +0100https://ask.sagemath.org/question/59796/finding-an-irreducible-polynomial-in-z-x-but-reducible-in-f2-x/?comment=59800#post-id-59800