#18308: No coercion for Galois group elements in different subgroups
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Reporter: jdemeyer | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-6.7
Component: number fields | Resolution:
Keywords: | Merged in:
Authors: | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by jdemeyer:
Old description:
> This is essentially #4105 but for Galois group elements.
>
> {{{
> sage: K.<a> = NumberField(x^6 + 40*x^3 + 1372)
> sage: G = K.galois_group()
> sage: L = [G.artin_symbol(Q) for Q in K.primes_above(5)]
> sage: L[0] * L[1]
> TypeError: unsupported operand parent(s) for '*': 'Subgroup [(),
> (1,5)(2,4)(3,6)] of Galois group of Number Field in a with defining
> polynomial x^6 + 40*x^3 + 1372' and 'Subgroup [(), (1,2)(3,4)(5,6)] of
> Galois group of Number Field in a with defining polynomial x^6 + 40*x^3 +
> 1372'
> }}}
>
> This also causes the following doctest (removed in #17890) to fail:
> {{{
> sage: K.<a> = NumberField(x^6 + 40*x^3 + 1372)
> sage: G = K.galois_group()
> sage: sorted([G.artin_symbol(Q) for Q in K.primes_above(5)])
> [(1,2)(3,4)(5,6), (1,3)(2,6)(4,5), (1,5)(2,4)(3,6)]
> }}}
New description:
This is essentially #4105 but for Galois group elements.
{{{
sage: K.<a> = NumberField(x^6 + 40*x^3 + 1372)
sage: G = K.galois_group()
sage: L = [G.artin_symbol(Q) for Q in K.primes_above(5)]
sage: L[0] * L[1]
TypeError: unsupported operand parent(s) for '*': 'Subgroup [(),
(1,5)(2,4)(3,6)] of Galois group of Number Field in a with defining
polynomial x^6 + 40*x^3 + 1372' and 'Subgroup [(), (1,2)(3,4)(5,6)] of
Galois group of Number Field in a with defining polynomial x^6 + 40*x^3 +
1372'
}}}
This also causes a doctest failure in
`src/doc/en/thematic_tutorials/explicit_methods_in_number_theory/nf_galois_groups.rst`
(marked as `random` for now):
{{{
sage: P = K.primes_above(2)[0]
sage: G.inertia_group(P)
Subgroup [(), (1,4,6)(2,5,3), (1,6,4)(2,3,5)] of Galois group of
Number Field in alpha with defining polynomial x^6 + 40*x^3 + 1372
sage: [G.artin_symbol(Q) for Q in K.primes_above(5)] # random order,
see Trac #18308
[(1,3)(2,6)(4,5), (1,2)(3,4)(5,6), (1,5)(2,4)(3,6)]
}}}
--
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Ticket URL: <http://trac.sagemath.org/ticket/18308#comment:2>
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