#15276: Translation problem between Sage and Gap for cyclotomic field
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Reporter: vincent.beck | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-7.3
Component: algebra | Resolution:
Keywords: CyclotomicField | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps: incorrectAnswerMarker
-----------------------------------+-------------------------------------
Changes (by vdelecroix):
* milestone: sage-6.4 => sage-7.3
* author: Vincent Beck =>
Old description:
> Something strange is happening with the command CyclotomicField and the
> order of the associated generator. Everything works very well for n which
> is different from 2 mod 4 but does not work for n =2 mod 4 as seen in the
> following lines.
>
> This is right:
> {{{
> sage: K7.<s> = CyclotomicField(7)
> sage: gap(K7)
> CF(7)
> sage: gap(s)
> E(7)
> sage: K7(_)
> s
> }}}
> This is wrong
> {{{
> sage: K6.<s> = CyclotomicField(6)
> sage: gap(K6)
> CF(3)
> sage: gap(s)
> E(3)
> sage: K6(_)
> s - 1
> }}}
New description:
Something strange is happening with the command CyclotomicField and the
order of the associated generator. Everything works very well for n which
is different from 2 mod 4 but does not work for n =2 mod 4 as seen in the
following lines.
This is right:
{{{
sage: K7.<s> = CyclotomicField(7)
sage: gap(K7)
CF(7)
sage: gap(s)
E(7)
sage: K7(_)
s
}}}
This is wrong
{{{
sage: K6.<s> = CyclotomicField(6)
sage: gap(K6)
CF(3)
sage: gap(s) # this is wrong!
E(3)
sage: K6(_) # coherent with above
s - 1
}}}
Note that the following works fine
{{{
sage: UCF = UniversalCyclotomicField()
sage: UCF(s)
-E(3)^2
sage: K6(_)
s
}}}
--
--
Ticket URL: <https://trac.sagemath.org/ticket/15276#comment:7>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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