#10850: composition and comparison of number-field homomorphisms
------------------------------+---------------------------------------------
Reporter: fwclarke | Owner: davidloeffler
Type: defect | Status: positive_review
Priority: major | Milestone: sage-4.7.2
Component: number fields | Keywords:
Work_issues: | Upstream: N/A
Reviewer: David Loeffler | Author: Francis Clarke
Merged: | Dependencies:
------------------------------+---------------------------------------------
Description changed by leif:
Old description:
> As of 4.6.2.rc0, when homomorphisms of number fields are composed the
> result has type `RingHomomorphism_im_gens` rather than
> `NumberFieldHomomorphism_im_gens`:
> {{{
> sage: K = QuadraticField(2)
> sage: e, f = End(K)
> sage: type(f)
> <class
> 'sage.rings.number_field.morphism.NumberFieldHomomorphism_im_gens'>
> sage: type(f*f)
> <type 'sage.rings.morphism.RingHomomorphism_im_gens'>
> }}}
> Consequently, comparison fails to work correctly:
> {{{
> sage: f*f == e
> False
> sage: f*f
> Ring endomorphism of Number Field in a with defining polynomial x^2 - 2
> Defn: a |--> a
> sage: e
> Ring endomorphism of Number Field in a with defining polynomial x^2 - 2
> Defn: a |--> a
> }}}
>
> Moreover, for relative number fields composition yields a formal
> composite
> map:
> {{{
> sage: L.<a, b> = NumberField([x^2 - 2, x^2 - 3])
> sage: g = End(L)[1]
> sage: type(g*g)
> <type 'sage.categories.map.FormalCompositeMap'>
> }}}
> and this means that powers beyond cubes produce an error:
> {{{
> sage: g^4
> Traceback (most recent call last)
> ...
> AttributeError: 'sage.categories.map.FormalCompositeMap' object has no
> attribute '_rational_'
> }}}
> Comparison for homomorphisms out of relative number fields needs fixing
> too, because they are not standard im_gens homomorphisms.
>
> The patch deals with these issues.
New description:
As of 4.6.2.rc0, when homomorphisms of number fields are composed the
result has type `RingHomomorphism_im_gens` rather than
`NumberFieldHomomorphism_im_gens`:
{{{
sage: K = QuadraticField(2)
sage: e, f = End(K)
sage: type(f)
<class 'sage.rings.number_field.morphism.NumberFieldHomomorphism_im_gens'>
sage: type(f*f)
<type 'sage.rings.morphism.RingHomomorphism_im_gens'>
}}}
Consequently, comparison fails to work correctly:
{{{
sage: f*f == e
False
sage: f*f
Ring endomorphism of Number Field in a with defining polynomial x^2 - 2
Defn: a |--> a
sage: e
Ring endomorphism of Number Field in a with defining polynomial x^2 - 2
Defn: a |--> a
}}}
Moreover, for relative number fields composition yields a formal composite
map:
{{{
sage: L.<a, b> = NumberField([x^2 - 2, x^2 - 3])
sage: g = End(L)[1]
sage: type(g*g)
<type 'sage.categories.map.FormalCompositeMap'>
}}}
and this means that powers beyond cubes produce an error:
{{{
sage: g^4
Traceback (most recent call last)
...
AttributeError: 'sage.categories.map.FormalCompositeMap' object has no
attribute '_rational_'
}}}
Comparison for homomorphisms out of relative number fields needs fixing
too, because they are not standard im_gens homomorphisms.
The patch deals with these issues.
----
Apply [attachment:trac_10850.patch] to the Sage library.
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10850#comment:3>
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