#17740: Division of modules by basering elements should not pass to the fraction
field.
-------------------------+-------------------------------------------------
       Reporter:         |        Owner:
  robertwb               |       Status:  needs_work
           Type:         |    Milestone:  sage-6.5
  defect                 |   Resolution:
       Priority:  major  |    Merged in:
      Component:         |    Reviewers:
  coercion               |  Work issues:
       Keywords:         |       Commit:
        Authors:         |  2cb51c095e0e3375dead95c194febd5873ba5e06
Report Upstream:  N/A    |     Stopgaps:
         Branch:         |
  u/robertwb/17440       |
   Dependencies:         |
-------------------------+-------------------------------------------------

Comment (by vdelecroix):

 Still some failing doctests... (the last one only concerns the more recent
 6-5.rc0)

 File `rings/quotient_ring_element.py`
 {{{
 line 360, in sage.rings.quotient_ring_element.QuotientRingElement._div_
 Failed example:
     1/cuberoot
 Exception raised:
     Traceback (most recent call last):
     ...
     TypeError: self must be an integral domain.
 **********************************************************************
 line 362, in sage.rings.quotient_ring_element.QuotientRingElement._div_
 Failed example:
     1/a
 Exception raised:
     Traceback (most recent call last):
     ...
     TypeError: self must be an integral domain.
 **********************************************************************
 File "src/sage/rings/quotient_ring_element.py", line 370, in
 sage.rings.quotient_ring_element.QuotientRingElement._div_
 Failed example:
     1 / S(x1 + x2)
 Expected:
     Traceback (most recent call last):
     ...
     ArithmeticError: Division failed. The numerator is not a multiple of
 the denominator.
 Got:
     Traceback (most recent call last):
     ...
     TypeError: self must be an integral domain.
 }}}


 File `rings/padics/local_generic_element.pyx`
 {{{
 line 63, in
 sage.rings.padics.local_generic_element.LocalGenericElement._div_
 Failed example:
     R = Zp(7, 4, 'fixed-mod'); 1/R(7)
 Expected:
     Traceback (most recent call last):
     ...
     ValueError: cannot invert non-unit
 Got:
     Traceback (most recent call last):
     ...
     TypeError: This implementation of the p-adic ring does not support
 fields of fractions.
 }}}

 File `rings/padics/padic_ZZ_pX_FM_element.pyx`
 {{{
 line 88, in sage.rings.padics.padic_ZZ_pX_FM_element
 Failed example:
     1/a
 Exception raised:
     Traceback (most recent call last):
     ...
     TypeError: This implementation of the p-adic ring does not support
 fields of fractions.
 **********************************************************************
 line 875, in
 sage.rings.padics.padic_ZZ_pX_FM_element.pAdicZZpXFMElement._div_
 Failed example:
     1 / W(14) == ~W(14)
 Exception raised:
     Traceback (most recent call last):
     ...
     TypeError: This implementation of the p-adic ring does not support
 fields of fractions.
 **********************************************************************
 line 877, in
 sage.rings.padics.padic_ZZ_pX_FM_element.pAdicZZpXFMElement._div_
 Failed example:
     1 / w
 Expected:
     Traceback (most recent call last):
     ...
     ValueError: cannot invert non-unit
 Got:
     Traceback (most recent call last):
     ...
     TypeError: This implementation of the p-adic ring does not support
 fields of fractions.
 **********************************************************************
 line 885, in
 sage.rings.padics.padic_ZZ_pX_FM_element.pAdicZZpXFMElement._div_
 Failed example:
     1/(t+t^2)
 Exception raised:
     Traceback (most recent call last):
     ...
     TypeError: This implementation of the p-adic ring does not support
 fields of fraction.
 }}}

 In `modular/modform_hecketriangle/graded_ring_element.py`:
 {{{
 sage -t --long
 src/sage/modular/modform_hecketriangle/graded_ring_element.py
 **********************************************************************
 line 887, in
 sage.modular.modform_hecketriangle.graded_ring_element.FormsRingElement._div_
 Failed example:
     ((E4.as_ring_element())^(-2)).parent() == (E4^(-2)).parent()
 Exception raised:
     Traceback (most recent call last):
     ...
     NotImplementedError: No way to prove that ModularFormsRing(n=8) over
 Integer Ring is an integral domain!
 **********************************************************************
 line 889, in
 sage.modular.modform_hecketriangle.graded_ring_element.FormsRingElement._div_
 Failed example:
     (MR(x)^(-3)).parent()
 Exception raised:
     Traceback (most recent call last):
     ...
     NotImplementedError: No way to prove that
 QuasiMeromorphicModularFormsRing(n=8) over Integer Ring is an integral
 domain!
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/17740#comment:15>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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