Clean up dead links in sage/rings/number_field documentation

[davidloeffler]

Touching all files in sage/rings/number_field and running sage -docbuild --warn-links reference html reveals a bunch of errors:

<autodoc>:1: WARNING: py:class reference target not found: sage.categories.map.Map
<autodoc>:1: WARNING: py:class reference target not found: sage.categories.map.Map
/storage/masiao/sage-5.0.beta10/local/lib/python2.7/site-packages/sage/rings/number_field/number_field.py:docstring of sage.rings.number_field.number_field.NumberField_generic.reduced_gram_matrix:13: WARNING: py:meth reference target not found: Minkowski_embedding
docstring of sage.rings.number_field.number_field_base.NumberField:5: WARNING: py:class reference target not found: NoetherianRing
/storage/masiao/sage-5.0.beta10/local/lib/python2.7/site-packages/sage/rings/number_field/number_field_ideal.py:docstring of sage.rings.number_field.number_field_ideal.NumberFieldIdeal.S_ideal_class_log:1: WARNING: py:meth reference target not found: _ideal_class_log
<autodoc>:1: WARNING: py:class reference target not found: sage.categories.map.Map

The patch below fixes these. It also sorts out a genuine bug I spotted in the process (the maximal_order method of relative number fields doesn't have an option to return a p-maximal order).

[davidloeffler]

Patch against 5.0.beta10

[davidloeffler]

The previous patch had a silly typo and some trailing whitespace, so here's a new one.

[kcrisman]

Comments:

• I can't give the new code itself positive review, although it seems correct (mostly I have questions about the change to absolute_degree. Maybe that could be moved to a different ticket if one doesn't find a reviewer?
• I can, however, suggest a trivial fix - the second-to-last line below had new_codomain, not new_domain (I'd add a patch, but see the previous comment):

      def extend_domain(self, new_domain):
          r"""
          INPUT:
   
          - ``self`` -- a member of Hom(Y, Z)
          - ``new_domain`` -- an object X such that there is a canonical coercion
            `\phi` in Hom(X, Y)
  

  Also, maybe we want to just turn that double-underscore attribute into a single-underscore attribute? Here at SD 40.5 that is being suggested strongly for any occurrences of such things.
• In the nearly identical two occurrences of

  self.__maximal_order[v] = RelativeOrder(self, abs_order, is_maximal=True, check=False)
  

  is it possible that the first one is not supposed to have the [v]?

[was]

Hi,

The new code looks fine, though the new v option should be documented in the docstring:

        INPUT:
       
        -  ``v`` - (default: None) None, a prime, or a list of
           primes.

           - if v is None, return the maximal order.

           - if v is a prime, return an order that is p-maximal.

           - if v is a list, return an order that is maximal at each
             prime in the list v.

So if somebody adds the above to the docstring, then we should give this a positive review.

[benjaminfjones]

document INPUT for maximal_order

[benjaminfjones]

I documented the input for maximal_order. Apply trac_12767_INPUT.patch​ and it should be good to go.