put number fields in Fields().Infinite()

[chapoton]

and the same for QQ of course

follow up at #24432

[chapoton]

New commits:

​2f98551

trac 23418 fixing some doctests in rings and category folders

[git]

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

​a06ebbc

trac 23418 correct more doctests

[chapoton]

This triggers some problem here:

sage -t --long src/sage/structure/parent.pyx  # 6 doctests failed

[chapoton]

It seems that the morphisms from Sets take over the morphisms from Rings..

[tscrim]

Failures are related to this:

sage: x = QQ['x'].0
sage: t = abs(ZZ.random_element(10^6))
sage: K = NumberField(x^2 + 2*3*7*11, "a"+str(t))
sage: a = K.gen()

sage: Hom(K, a.matrix().parent())
Set of Morphisms from Number Field in a791947 with defining polynomial x^2 + 462 to Full MatrixSpace of 2 by 2 dense matrices over Rational Field in Category of infinite rings
<class 'sage.categories.homset.Homset_with_category'>

compared to vanilla Sage:

sage: Hom(K, a.matrix().parent())
Set of Homomorphisms from Number Field in a395598 with defining polynomial x^2 + 462 to Full MatrixSpace of 2 by 2 dense matrices over Rational Field
sage: type(Hom(K, a.matrix().parent()))
<class 'sage.rings.homset.RingHomset_generic_with_category'>

This differences comes from the fact that the category becomes a join category (in the branch) because that is the meet category computed by Hom:

sage: K.category()._meet_(a.matrix().parent().category())
Category of infinite rings
sage: type(_)
<class 'sage.categories.category.JoinCategory_with_category'>

versus vanilla:

sage: K.category()._meet_(a.matrix().parent().category())
Category of rings
sage: type(_)
<class 'sage.categories.rings.Rings_with_category'>

Now, K is not a subclass of the meet category's parent_class, which causes the Cat.parent_class._Hom_ method to now raise an error:

sage: Cat = K.category()._meet_(a.matrix().parent().category())
sage: Cat.parent_class
<class 'sage.categories.category.JoinCategory.parent_class'>
sage: Cat.parent_class._Hom_(K, a.matrix().parent(), Cat)
---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-6-aa7f8d9cdf73> in <module>()
----> 1 Cat.parent_class._Hom_(K, a.matrix().parent(), Cat)
TypeError: unbound method _Hom_() must be called with JoinCategory.parent_class instance as first argument (got NumberField_quadratic_with_category instance instead)

versus vanilla

sage: Cat = K.category()._meet_(a.matrix().parent().category())
sage: Cat.parent_class
<class 'sage.categories.rings.Rings.parent_class'>
sage: Cat.parent_class._Hom_(K, a.matrix().parent(), Cat)
Set of Homomorphisms from Number Field in a395598 with defining polynomial x^2 + 462 to Full MatrixSpace of 2 by 2 dense matrices over Rational Field

[chapoton]

New commits:

​ba2ec5b

Merge commit '2f98551bf0aa8fc99f98cf2cdecf2fdaf584e5df' in 8.1.b5

[git]

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

​4e88b49

fix

[git]

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

​6d3e532

trac 23418 fix

[vdelecroix]

New commits:

​d2bf048

23418: number fields are infinite