#16649: Make `quo_rem` give answers more often
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       Reporter:  bruno             |        Owner:
           Type:  defect            |       Status:  new
       Priority:  major             |    Milestone:  sage-6.3
      Component:  basic arithmetic  |   Resolution:
       Keywords:  quo_rem           |    Merged in:
        Authors:                    |    Reviewers:
Report Upstream:  N/A               |  Work issues:
         Branch:                    |       Commit:
   Dependencies:                    |     Stopgaps:
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Comment (by bruno):

 My proposition is as follows (say for the method `quo_rem` of the `class
 Polynomial_generic_dense`):

 - Remove the test
   {{{#!python
           if not other.leading_coefficient().is_unit():
               raise ArithmeticError("Nonunit leading coefficient")
   }}}
   on lines 7484-7485 of `sage/rings/polynomial/polynomial_element.pyx`.

 - Change the line 7999 (`q = x[n+k-1]/y[n-1]`) by the following:
   {{{#!python
               try:
                   q = R(x[n+k-1]/y[n-1])
               except TypeError:
                   raise ArithmeticError("Division not exact (consider
 coercing to polynomial over the fraction field first")
   }}}

 Does the change make sense?

--
Ticket URL: <http://trac.sagemath.org/ticket/16649#comment:1>
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