ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 18 Dec 2017 06:13:27 -0600how to define Skew Polynomial Ring over Cyclotomic Fieldhttps://ask.sagemath.org/question/40199/how-to-define-skew-polynomial-ring-over-cyclotomic-field/how to define Skew Polynomial Ring in x over Cyclotomic Field of order 7 and degree 6 twisted by zeta7 |--> zeta7^2
when i execute those commands
K = CyclotomicField(7)
sigma = K.hom([K.gen()^2])
S.< x > = K['x',sigma]
I have this message error
> AssertionError: coercion from
> Cyclotomic Field of order 7 and degree
> 6 to Skew Polynomial Ring in x over
> Cyclotomic Field of order 7 and degree
> 6 twisted by zeta7 |--> zeta7^2
> already registered or discoveredSun, 17 Dec 2017 04:36:39 -0600https://ask.sagemath.org/question/40199/how-to-define-skew-polynomial-ring-over-cyclotomic-field/Answer by dan_fulea for <p>how to define Skew Polynomial Ring in x over Cyclotomic Field of order 7 and degree 6 twisted by zeta7 |--> zeta7^2
when i execute those commands</p>
<p>K = CyclotomicField(7)</p>
<p>sigma = K.hom([K.gen()^2])</p>
<p>S.< x > = K['x',sigma]</p>
<p>I have this message error </p>
<blockquote>
<p>AssertionError: coercion from
Cyclotomic Field of order 7 and degree
6 to Skew Polynomial Ring in x over
Cyclotomic Field of order 7 and degree
6 twisted by zeta7 |--> zeta7^2
already registered or discovered</p>
</blockquote>
https://ask.sagemath.org/question/40199/how-to-define-skew-polynomial-ring-over-cyclotomic-field/?answer=40210#post-id-40210The following is a workaround. (Some internals want to deal with a ring, this was only a feeling i had while trying to trace back the error. So i also insisted to use only rings.)
R.<X> = PolynomialRing( QQ )
K.<a> = R.quotient( X^6 + X^5 + X^4 + X^3 + X^2 + X + 1 )
g = K.hom( a^2, K )
S.<x> = SkewPolynomialRing( K, g )
Test:
print S
print (x+a)^3
This gives:
Skew Polynomial Ring in x
over Univariate Quotient Polynomial Ring in a over Rational Field
with modulus X^6 + X^5 + X^4 + X^3 + X^2 + X + 1
twisted by a |--> a^2
x^3 + (a^4 + a^2 + a)*x^2 + (a^4 + a^3 + a^2)*x + a^3
(Result was rearranged manually to fit here in the width.)
Mon, 18 Dec 2017 06:13:27 -0600https://ask.sagemath.org/question/40199/how-to-define-skew-polynomial-ring-over-cyclotomic-field/?answer=40210#post-id-40210