#17294: Add gcd to number field elements
-------------------------------------+-------------------------------------
       Reporter:  jdemeyer           |        Owner:
           Type:  enhancement        |       Status:  needs_work
       Priority:  major              |    Milestone:  sage-6.4
      Component:  number fields      |   Resolution:
       Keywords:                     |    Merged in:
        Authors:  Jeroen Demeyer     |    Reviewers:  Vincent Delecroix
Report Upstream:  N/A                |  Work issues:
         Branch:                     |       Commit:
  u/jdemeyer/ticket/17294            |  671d58fadd54519c02145d8905baf635b40c6e02
   Dependencies:                     |     Stopgaps:
-------------------------------------+-------------------------------------
Changes (by vbraun):

 * status:  positive_review => needs_work


Comment:

 {{{
 sage -t --warn-long 47.1 src/sage/categories/quotient_fields.py
 **********************************************************************
 File "src/sage/categories/quotient_fields.py", line 101, in
 sage.categories.quotient_fields.QuotientFields.ElementMethods.gcd
 Failed example:
     gcd(t, i)
 Expected:
     Traceback (most recent call last):
     ...
     TypeError: unable to find gcd
 Got:
     <BLANKLINE>
     Traceback (most recent call last):
       File "/mnt/disk/home/release/Sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 496, in _run
         self.compile_and_execute(example, compiler, test.globs)
       File "/mnt/disk/home/release/Sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 858, in compile_and_execute
         exec(compiled, globs)
       File "<doctest
 sage.categories.quotient_fields.QuotientFields.ElementMethods.gcd[13]>",
 line 1, in <module>
         gcd(t, i)
       File "/mnt/disk/home/release/Sage/local/lib/python2.7/site-
 packages/sage/rings/arith.py", line 1551, in gcd
         return GCD(b, **kwargs)
       File "sage/structure/element.pyx", line 3473, in
 sage.structure.element.NamedBinopMethod.__call__
 (build/cythonized/sage/structure/element.c:28398)
         return self._func(x,y, **kwds)
       File "sage/rings/polynomial/polynomial_element.pyx", line 3713, in
 sage.rings.polynomial.polynomial_element.Polynomial.gcd
 (build/cythonized/sage/rings/polynomial/polynomial_element.c:34450)
         raise NotImplementedError("%s does not provide a gcd
 implementation for univariate polynomials"%self.base_ring())
     NotImplementedError: Maximal Order in Number Field in i with defining
 polynomial x^2 + 1 does not provide a gcd implementation for univariate
 polynomials
 **********************************************************************
 File "src/sage/categories/quotient_fields.py", line 177, in
 sage.categories.quotient_fields.QuotientFields.ElementMethods.lcm
 Failed example:
     lcm(t, i)
 Expected:
     Traceback (most recent call last):
     ...
     AttributeError:
 'sage.rings.polynomial.polynomial_element.Polynomial_generic_dense' object
 has no attribute 'gcd'
 Got:
     <BLANKLINE>
     Traceback (most recent call last):
       File "/mnt/disk/home/release/Sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 496, in _run
         self.compile_and_execute(example, compiler, test.globs)
       File "/mnt/disk/home/release/Sage/local/lib/python2.7/site-
 packages/sage/doctest/forker.py", line 858, in compile_and_execute
         exec(compiled, globs)
       File "<doctest
 sage.categories.quotient_fields.QuotientFields.ElementMethods.lcm[11]>",
 line 1, in <module>
         lcm(t, i)
       File "/mnt/disk/home/release/Sage/local/lib/python2.7/site-
 packages/sage/rings/arith.py", line 1698, in lcm
         return LCM(b)
       File "sage/structure/element.pyx", line 3473, in
 sage.structure.element.NamedBinopMethod.__call__
 (build/cythonized/sage/structure/element.c:28398)
         return self._func(x,y, **kwds)
       File "sage/rings/polynomial/polynomial_element.pyx", line 3722, in
 sage.rings.polynomial.polynomial_element.Polynomial.lcm
 (build/cythonized/sage/rings/polynomial/polynomial_element.c:34544)
         g = self.gcd(other)
       File "sage/structure/element.pyx", line 3473, in
 sage.structure.element.NamedBinopMethod.__call__
 (build/cythonized/sage/structure/element.c:28398)
         return self._func(x,y, **kwds)
       File "sage/rings/polynomial/polynomial_element.pyx", line 3713, in
 sage.rings.polynomial.polynomial_element.Polynomial.gcd
 (build/cythonized/sage/rings/polynomial/polynomial_element.c:34450)
         raise NotImplementedError("%s does not provide a gcd
 implementation for univariate polynomials"%self.base_ring())
     NotImplementedError: Maximal Order in Number Field in i with defining
 polynomial x^2 + 1 does not provide a gcd implementation for univariate
 polynomials
 **********************************************************************
 2 items had failures:
    1 of  19 in
 sage.categories.quotient_fields.QuotientFields.ElementMethods.gcd
    1 of  17 in
 sage.categories.quotient_fields.QuotientFields.ElementMethods.lcm
     [153 tests, 2 failures, 0.99 s]
 ----------------------------------------------------------------------
 sage -t --warn-long 47.1 src/sage/categories/quotient_fields.py  # 2
 doctests failed
 ----------------------------------------------------------------------
 }}}

--
Ticket URL: <http://trac.sagemath.org/ticket/17294#comment:15>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
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