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, 12 Dec 2021 22:02:52 +0100Cannot understand sage polynomial factor notationhttps://ask.sagemath.org/question/60144/cannot-understand-sage-polynomial-factor-notation/ Hello, I am generating a random polynomial over the field GF(2^6), and when I print it, I cannot undertstand the values of certain factors:
The polynomial looks like this: x^9 + (z6^5 + z6^3)*x + z6^4 + z6^2 + z6
What do z6, z6^5 mean?
I searched but I was unable to find an answer in the docs.
Tue, 07 Dec 2021 18:54:59 +0100https://ask.sagemath.org/question/60144/cannot-understand-sage-polynomial-factor-notation/Answer by John Palmieri for <p>Hello, I am generating a random polynomial over the field GF(2^6), and when I print it, I cannot undertstand the values of certain factors:</p>
<p>The polynomial looks like this: x^9 + (z6^5 + z6^3)*x + z6^4 + z6^2 + z6
What do z6, z6^5 mean?
I searched but I was unable to find an answer in the docs.</p>
https://ask.sagemath.org/question/60144/cannot-understand-sage-polynomial-factor-notation/?answer=60154#post-id-60154This arises when constructing the field.
sage: F = GF(64)
sage: F
Finite Field in z6 of size 2^6
The element "z6" is the generator of F over the prime field GF(2): the command `F.gen()` will return `z6`, and the documentation returned by `F.gen?`says 'Return a generator of "self" over its prime field, which is a root of "self.modulus()".' The documentation returned by `F.modulus?` says 'Return the minimal polynomial of the generator of "self" over the prime finite field.' In this case `F.modulus()` returns `x^6 + x^4 + x^3 + x + 1`.
Tue, 07 Dec 2021 23:35:32 +0100https://ask.sagemath.org/question/60144/cannot-understand-sage-polynomial-factor-notation/?answer=60154#post-id-60154Comment by robbyyt for <p>This arises when constructing the field.</p>
<pre><code>sage: F = GF(64)
sage: F
Finite Field in z6 of size 2^6
</code></pre>
<p>The element "z6" is the generator of F over the prime field GF(2): the command <code>F.gen()</code> will return <code>z6</code>, and the documentation returned by <code>F.gen?</code>says 'Return a generator of "self" over its prime field, which is a root of "self.modulus()".' The documentation returned by <code>F.modulus?</code> says 'Return the minimal polynomial of the generator of "self" over the prime finite field.' In this case <code>F.modulus()</code> returns <code>x^6 + x^4 + x^3 + x + 1</code>.</p>
https://ask.sagemath.org/question/60144/cannot-understand-sage-polynomial-factor-notation/?comment=60229#post-id-60229Thank you very much, I did not see thatSun, 12 Dec 2021 22:02:52 +0100https://ask.sagemath.org/question/60144/cannot-understand-sage-polynomial-factor-notation/?comment=60229#post-id-60229