#7946: Fix TestSuite failures for schemes
-------------------------------------+-------------------------------------
       Reporter:  nthiery            |        Owner:  AlexGhitza
           Type:  defect             |       Status:  needs_review
       Priority:  major              |    Milestone:  sage-6.2
      Component:  algebraic          |   Resolution:
  geometry                           |    Merged in:
       Keywords:                     |    Reviewers:
        Authors:  Peter Bruin        |  Work issues:
Report Upstream:  N/A                |       Commit:
         Branch:                     |  5fd92eed3024163fa068bea8e3644d677f151adc
  u/pbruin/7946-scheme_point_improvements|     Stopgaps:
   Dependencies:  #16158             |
-------------------------------------+-------------------------------------
Changes (by {'newvalue': u'Peter Bruin', 'oldvalue': ''}):

 * status:  new => needs_review
 * commit:   => 5fd92eed3024163fa068bea8e3644d677f151adc
 * branch:   => u/pbruin/7946-scheme_point_improvements
 * author:   => Peter Bruin


Old description:

> Here is the complete `TestSuite` report:
> {{{
> sage: S=Spec(ZZ)
> sage: x=S.an_element()
> }}}
> {{{
> sage: TestSuite(S).run()
> Failure in _test_an_element:
> Traceback (most recent call last):
> ...
> NotImplementedError
> ------------------------------------------------------------
>   Failure in _test_category:
>   Traceback (most recent call last):
>   ...
>   AssertionError: False is not true
>   ------------------------------------------------------------
>   Failure in _test_pickling:
>   Traceback (most recent call last):
>   ...
>   AssertionError: Point on Spectrum of Integer Ring defined by the
> Principal ideal (991) of Integer Ring != Point on Spectrum of Integer
> Ring defined by the Principal ideal (991) of Integer Ring
>   ------------------------------------------------------------
>   The following tests failed: _test_category, _test_pickling
> Failure in _test_elements
> Failure in _test_some_elements:
> Traceback (most recent call last):
> ...
> NotImplementedError
> ------------------------------------------------------------
> The following tests failed: _test_an_element, _test_elements,
> _test_some_elements
> }}}
> {{{
> sage: TestSuite(x).run()
> Failure in _test_category:
> Traceback (most recent call last):
> ...
> AssertionError: False is not true
> ------------------------------------------------------------
> Failure in _test_pickling:
> Traceback (most recent call last):
> ...
> AssertionError: Point on Spectrum of Integer Ring defined by the
> Principal ideal (991) of Integer Ring != Point on Spectrum of Integer
> Ring defined by the Principal ideal (991) of Integer Ring
> ------------------------------------------------------------
> The following tests failed: _test_category, _test_pickling
> }}}
>
> (Note: the `NotImplementedError` that one gets after applying #16158 is a
> different one than before.)

New description:

 Consider the following situation:
 {{{
 sage: S = Spec(ZZ)
 sage: x = S.an_element()
 }}}
 Running `TestSuite(S)` and `TestSuite(x)` yields several failures.  A
 related problem is
 {{{
 sage: S
 Spectrum of Integer Ring
 sage: parent(x)
 Set of rational points of Spectrum of Integer Ring
 }}}
 whereas we expect `parent(x) is S`.

 Here is the complete `TestSuite` report:
 {{{
 sage: TestSuite(S).run()
 Failure in _test_an_element:
 Traceback (most recent call last):
 ...
 NotImplementedError
 ------------------------------------------------------------
   Failure in _test_category:
   Traceback (most recent call last):
   ...
   AssertionError: False is not true
   ------------------------------------------------------------
   Failure in _test_pickling:
   Traceback (most recent call last):
   ...
   AssertionError: Point on Spectrum of Integer Ring defined by the
 Principal ideal (991) of Integer Ring != Point on Spectrum of Integer Ring
 defined by the Principal ideal (991) of Integer Ring
   ------------------------------------------------------------
   The following tests failed: _test_category, _test_pickling
 Failure in _test_elements
 Failure in _test_some_elements:
 Traceback (most recent call last):
 ...
 NotImplementedError
 ------------------------------------------------------------
 The following tests failed: _test_an_element, _test_elements,
 _test_some_elements
 }}}
 {{{
 sage: TestSuite(x).run()
 Failure in _test_category:
 Traceback (most recent call last):
 ...
 AssertionError: False is not true
 ------------------------------------------------------------
 Failure in _test_pickling:
 Traceback (most recent call last):
 ...
 AssertionError: Point on Spectrum of Integer Ring defined by the Principal
 ideal (991) of Integer Ring != Point on Spectrum of Integer Ring defined
 by the Principal ideal (991) of Integer Ring
 ------------------------------------------------------------
 The following tests failed: _test_category, _test_pickling
 }}}

 (Note: the `NotImplementedError` that one gets after applying #16158 is a
 different one than before.)

--

Comment:

 The attached branch makes affine schemes, and points on them, cooperate
 better with the category and coercion code.  The `TestSuite` now runs
 without failures.

--
Ticket URL: <http://trac.sagemath.org/ticket/7946#comment:8>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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