#6204: [with patch, needs work] make norms for degree 1 relative number fields
work; add doctests
---------------------------+------------------------------------------------
 Reporter:  ncalexan       |       Owner:  was                                
     Type:  enhancement    |      Status:  new                                
 Priority:  major          |   Milestone:  sage-4.0.2                         
Component:  number theory  |    Keywords:  degree 1 relative number field norm
 Reviewer:                 |      Author:                                     
   Merged:                 |  
---------------------------+------------------------------------------------

Comment(by davidloeffler):

 Hold it, this fails doctests under 4.0.1:

 {{{
 da...@groke:~/sage-4.0.1.rc2/devel/sage-nfstuff/sage/rings/number_field>
 sage -t number_field_ideal_rel.py
 sage -t  "devel/sage-
 nfstuff/sage/rings/number_field/number_field_ideal_rel.py"
 **********************************************************************
 File "/home/david/sage-4.0.1.rc2/devel/sage-
 nfstuff/sage/rings/number_field/number_field_ideal_rel.py", line 361:
     sage: L.ideal(b).relative_norm()
 Exception raised:
     Traceback (most recent call last):
       File "/home/david/sage-4.0/local/bin/ncadoctest.py", line 1231, in
 run_one_test
         self.run_one_example(test, example, filename, compileflags)
       File "/home/david/sage-4.0/local/bin/sagedoctest.py", line 38, in
 run_one_example
         OrigDocTestRunner.run_one_example(self, test, example, filename,
 compileflags)
       File "/home/david/sage-4.0/local/bin/ncadoctest.py", line 1172, in
 run_one_example
         compileflags, 1) in test.globs
       File "<doctest __main__.example_11[19]>", line 1, in <module>
         L.ideal(b).relative_norm()###line 361:
     sage: L.ideal(b).relative_norm()
       File "/home/david/sage-4.0.1.rc2/local/lib/python2.5/site-
 packages/sage/rings/number_field/number_field_ideal_rel.py", line 370, in
 relative_norm
         return K.ideal(map(K, self.gens()))
       File "parent.pyx", line 323, in
 sage.structure.parent.Parent.__call__ (sage/structure/parent.c:4130)
       File "coerce_maps.pyx", line 82, in
 sage.structure.coerce_maps.DefaultConvertMap_unique._call_
 (sage/structure/coerce_maps.c:3058)
       File "coerce_maps.pyx", line 77, in
 sage.structure.coerce_maps._call_ (sage/structure/coerce_maps.c:2949)
       File "/home/david/sage-4.0.1.rc2/local/lib/python2.5/site-
 packages/sage/rings/number_field/number_field.py", line 941, in
 _element_constructor_
         return self._coerce_from_other_number_field(x)
       File "/home/david/sage-4.0.1.rc2/local/lib/python2.5/site-
 packages/sage/rings/number_field/number_field.py", line 4317, in
 _coerce_from_other_number_field
         raise TypeError, "Cannot coerce element into this number field"
     TypeError: Cannot coerce element into this number field
 **********************************************************************
 File "/home/david/sage-4.0.1.rc2/devel/sage-
 nfstuff/sage/rings/number_field/number_field_ideal_rel.py", line 480:
     sage: L.ideal(b).ideal_below()
 Exception raised:
     Traceback (most recent call last):
       File "/home/david/sage-4.0/local/bin/ncadoctest.py", line 1231, in
 run_one_test
         self.run_one_example(test, example, filename, compileflags)
       File "/home/david/sage-4.0/local/bin/sagedoctest.py", line 38, in
 run_one_example
         OrigDocTestRunner.run_one_example(self, test, example, filename,
 compileflags)
       File "/home/david/sage-4.0/local/bin/ncadoctest.py", line 1172, in
 run_one_example
         compileflags, 1) in test.globs
       File "<doctest __main__.example_13[50]>", line 1, in <module>
         L.ideal(b).ideal_below()###line 480:
     sage: L.ideal(b).ideal_below()
       File "/home/david/sage-4.0.1.rc2/local/lib/python2.5/site-
 packages/sage/rings/number_field/number_field_ideal_rel.py", line 489, in
 ideal_below
         return K.ideal(map(K, self.gens()))
       File "parent.pyx", line 323, in
 sage.structure.parent.Parent.__call__ (sage/structure/parent.c:4130)
       File "coerce_maps.pyx", line 82, in
 sage.structure.coerce_maps.DefaultConvertMap_unique._call_
 (sage/structure/coerce_maps.c:3058)
       File "coerce_maps.pyx", line 77, in
 sage.structure.coerce_maps._call_ (sage/structure/coerce_maps.c:2949)
       File "/home/david/sage-4.0.1.rc2/local/lib/python2.5/site-
 packages/sage/rings/number_field/number_field.py", line 941, in
 _element_constructor_
         return self._coerce_from_other_number_field(x)
       File "/home/david/sage-4.0.1.rc2/local/lib/python2.5/site-
 packages/sage/rings/number_field/number_field.py", line 4317, in
 _coerce_from_other_number_field
         raise TypeError, "Cannot coerce element into this number field"
     TypeError: Cannot coerce element into this number field
 **********************************************************************
 File "/home/david/sage-4.0.1.rc2/devel/sage-
 nfstuff/sage/rings/number_field/number_field_ideal_rel.py", line 482:
     sage: L.ideal(b^2 + 2).ideal_below()
 Exception raised:
     Traceback (most recent call last):
       File "/home/david/sage-4.0/local/bin/ncadoctest.py", line 1231, in
 run_one_test
         self.run_one_example(test, example, filename, compileflags)
       File "/home/david/sage-4.0/local/bin/sagedoctest.py", line 38, in
 run_one_example
         OrigDocTestRunner.run_one_example(self, test, example, filename,
 compileflags)
       File "/home/david/sage-4.0/local/bin/ncadoctest.py", line 1172, in
 run_one_example
         compileflags, 1) in test.globs
       File "<doctest __main__.example_13[51]>", line 1, in <module>
         L.ideal(b**Integer(2) + Integer(2)).ideal_below()###line 482:
     sage: L.ideal(b^2 + 2).ideal_below()
       File "/home/david/sage-4.0.1.rc2/local/lib/python2.5/site-
 packages/sage/rings/number_field/number_field_ideal_rel.py", line 489, in
 ideal_below
         return K.ideal(map(K, self.gens()))
       File "parent.pyx", line 323, in
 sage.structure.parent.Parent.__call__ (sage/structure/parent.c:4130)
       File "coerce_maps.pyx", line 82, in
 sage.structure.coerce_maps.DefaultConvertMap_unique._call_
 (sage/structure/coerce_maps.c:3058)
       File "coerce_maps.pyx", line 77, in
 sage.structure.coerce_maps._call_ (sage/structure/coerce_maps.c:2949)
       File "/home/david/sage-4.0.1.rc2/local/lib/python2.5/site-
 packages/sage/rings/number_field/number_field.py", line 941, in
 _element_constructor_
         return self._coerce_from_other_number_field(x)
       File "/home/david/sage-4.0.1.rc2/local/lib/python2.5/site-
 packages/sage/rings/number_field/number_field.py", line 4317, in
 _coerce_from_other_number_field
         raise TypeError, "Cannot coerce element into this number field"
     TypeError: Cannot coerce element into this number field
 **********************************************************************
 2 items had failures:
    1 of  21 in __main__.example_11
    2 of  52 in __main__.example_13
 ***Test Failed*** 3 failures.
 For whitespace errors, see the file
 /home/david/sage-4.0.1.rc2/tmp/.doctest_number_field_ideal_rel.py
          [6.2 s]
 exit code: 1024

 ----------------------------------------------------------------------
 The following tests failed:


         sage -t  "devel/sage-
 nfstuff/sage/rings/number_field/number_field_ideal_rel.py"
 Total time for all tests: 6.2 seconds
 }}}

 I'm changing this back to "needs work". The problem seems to be that we
 need to work around a pari bug in "gens_reduced" as well as in
 "relative_norm".

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6204#comment:3>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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