Regression in .divides() for generic polynomials

[defeo]

This used to work prior to #19171:

sage: R.<t> = GF(5)[]
sage: K = R.fraction_field()
sage: A.<x> = K[]
sage: x.divides(x)
True

Now it gives

---------------------------------------------------------------------------                                                            
AttributeError                            Traceback (most recent call last)                                                            
<ipython-input-14-cd2656325e62> in <module>()                                                                                          
----> 1 x.divides(x)                                                                                                                   
                                                                                                                                       
/data/dfl/sage/local/lib/python2.7/site-packages/sage/structure/element.pyx in sage.structure.element.coerce_binop.new_method (build/cy
thonized/sage/structure/element.c:28683)()                                                                                             
   4269     def new_method(self, other, *args, **kwargs):                                                                              
   4270         if have_same_parent(self, other):                                                                                      
-> 4271             return method(self, other, *args, **kwargs)                                                                        
   4272         else:                                                                                                                  
   4273             a, b = coercion_model.canonical_coercion(self, other)                                                              
                                                                                                                                       
/data/dfl/sage/local/lib/python2.7/site-packages/sage/rings/polynomial/polynomial_element.pyx in sage.rings.polynomial.polynomial_elem$
nt.Polynomial.divides (build/cythonized/sage/rings/polynomial/polynomial_element.c:93668)()
  10088             return False  
  10089                                                                                                                                
> 10090         if not self.leading_coefficient().divides(p.leading_coefficient()):              
  10091             return False
  10092

/data/dfl/sage/local/lib/python2.7/site-packages/sage/structure/element.pyx in sage.structure.element.Element.__getattr__ (build/cytho$
ized/sage/structure/element.c:4550)()
    491             AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
    492         """
--> 493         return self.getattr_from_category(name)
    494
    495     cdef getattr_from_category(self, name):

/data/dfl/sage/local/lib/python2.7/site-packages/sage/structure/element.pyx in sage.structure.element.Element.getattr_from_category (bu
ild/cythonized/sage/structure/element.c:4659)()
    504         else:
    505             cls = P._abstract_element_class
--> 506         return getattr_from_other_class(self, cls, name)
    507
    508     def __dir__(self):

/data/dfl/sage/local/lib/python2.7/site-packages/sage/cpython/getattr.pyx in sage.cpython.getattr.getattr_from_other_class (build/cytho
nized/sage/cpython/getattr.c:2536)()
    392         dummy_error_message.cls = type(self)
    393         dummy_error_message.name = name
--> 394         raise AttributeError(dummy_error_message)
    395     attribute = <object>attr
    396     # Check for a descriptor (__get__ in Python)

AttributeError: 'sage.rings.fraction_field_FpT.FpTElement' object has no attribute 'divides'

This is failing because the fraction field elements have no .divides() method.

CC: @bgrenet

Component: basic arithmetic

Keywords: polynomials division

Author: Luca De Feo

Branch/Commit: 4c14569

Reviewer: Jeroen Demeyer

Issue created by migration from https://trac.sagemath.org/ticket/27064

[defeo]

comment:1

I guess the solution is to add a trivial .divides() method to fields? I am not sure why there is no such method already.

[embray]

comment:3

Retarging tickets optimistically to the next milestone. If you are responsible for this ticket (either its reporter or owner) and don't believe you are likely to complete this ticket before the next release (8.7) please retarget this ticket's milestone to sage-pending or sage-wishlist.

[bgrenet]

comment:4

Two solutions (seem to) work:

• Either add a trivial divides method to the ElementMethods of the category Fields;
• Make FpTElement inherits from FieldElement rather than RingElement.

Actually, I do not know why this class FpTElement inherits from RingElement rather than FieldElement. It would even make more sense for it to inherit from FractionFieldElement I would say.

[defeo]

comment:5

FractionFieldElement is a Python class, I don't think it can inherit from it.

But I tested your second solution and it works. I'm preparing the commit.

[defeo]

Branch: u/defeo/regression_in__divides___for_generic_polynomials

[defeo]

Commit: 4c14569

[defeo]

New commits:

4c14569

Made elements of GF(p)(T) inherit from field (instead of ring)

[jdemeyer]

Author: Luca De Feo

[jdemeyer]

Reviewer: Jeroen Demeyer

[jdemeyer]

comment:8

Fine for me if it passes doctests.

[defeo]

comment:9

All doctests (--all --long) pass for me.

[vbraun]

Changed branch from u/defeo/regression_in__divides___for_generic_polynomials to 4c14569