Isomorphisms of absolute fields can not be used in change_ring

[sagetrac-jvlangen]

For a polynomial f defined over a number field K, when replacing K by its absolute field L = K.absolute_field(names='b') there might be an error when changing f with the appropriate isomorphism f.change_ring(L.structure()[1]).

The problem arises from the fact that change_ring wants to check whether the isomorphism is part of K.Hom(L) by calling K.Hom(L)(L.structure()[1]) which gives an error if L.structure()[1] is not an instance of NumberFieldHomomorphism_im_gens which it not necessarily is. Here is a minimal working example

sage: K.<a> = CyclotomicField(8)
sage: L.<b> = K.absolute_field()
sage: phi = L.structure()[1]
sage: phi.parent() == K.Hom(L)
True
sage: K.Hom(L)(phi)
Traceback (most recent call last):
...
TypeError: unable to convert Isomorphism given by variable name change map:
  From: Cyclotomic Field of order 8 and degree 4
  To:   Number Field in b with defining polynomial x^4 + 1 to an element of Number Field in b with defining polynomial x^4 + 1

The error seems a consequence of a call to K.Hom(L) interpreting the argument as an element of the codomain if it is not an instance of NumberFieldHomomorphism_im_gens.

Here is the example failing on change_ring where the error message is even less insightful

sage: K.<a> = CyclotomicField(8)
sage: L.<b> = K.absolute_field()
sage: R.<x> = K[]
sage: f = x^2 + a
sage: f.change_ring(L.structure()[1])
Traceback (most recent call last):
...
TypeError: 

Depends on #29008
Depends on #29010

Component: number fields

Keywords: absolute field

Author: Peter Bruin

Branch/Commit: 5939e98

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/28869

[embray]

comment:1

Ticket retargeted after milestone closed

[pjbruin]

comment:2

One way to solve this is by moving ring homsets to the new coercion model; among other things, when doing R.Hom(S)(f), this will check if f already has R.Hom(S) as its parent without checking the exact type. I am working on this.

[pjbruin]

Dependencies: #29008

[pjbruin]

Changed dependencies from #29008 to #29008, #29010

[pjbruin]

Branch: u/pbruin/28869-NumberFieldHomset_coercion

[pjbruin]

Author: Peter Bruin

[pjbruin]

Commit: 4470ebf

[sagetrac-git]

Changed commit from 4470ebf to 8c010d7

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

8c010d7

Trac 28869: add more doctests

[pjbruin]

comment:7

The last commit modifies/adds doctests to cover all NumberFieldHomset classes (absolute fields, relative fields and cyclotomic fields).

[sagetrac-git]

Changed commit from 8c010d7 to 5939e98

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

5939e98

Trac 28869: make _element_constructor_() always return an instance of element_class

[tscrim]

comment:9

LGTM.

[tscrim]

Reviewer: Travis Scrimshaw

[vbraun]

Changed branch from u/pbruin/28869-NumberFieldHomset_coercion to 5939e98