Categories for IntegerMod rings

[nthiery]

After this patch, IntegerModRing's inherit properly from categories:

    sage: Z3 = IntegerModRing(3)
    sage: Z3.category()
    Category of commutative rings
    sage: TestSuite(Z3).run(verbose = True)
    running ._test_additive_associativity() . . . pass
    running ._test_an_element() . . . pass
    running ._test_associativity() . . . pass
    running ._test_category() . . . pass
    running ._test_elements() . . . 
      Running the test suite of self.an_element()
      running ._test_category() . . . pass
      running ._test_not_implemented_methods() . . . pass
      running ._test_pickling() . . . pass
      pass
    running ._test_not_implemented_methods() . . . pass
    running ._test_one() . . . pass
    running ._test_pickling() . . . pass
    running ._test_prod() . . . pass
    running ._test_some_elements() . . . pass
    running ._test_zero() . . . pass

And this makes the cool features from #7555 work for Z/nZ.

Potential conflict with #8218 (which has higher priority)

For a later ticket, see: running design discussion on:

http://groups.google.com/group/sage-devel/t/21e21e1ec9cd21fe

CC: @sagetrac-sage-combinat

Component: algebra

Keywords: integer mod rings

Author: Nicolas M. Thiéry

Reviewer: John Palmieri, Rob Beezer

Merged: sage-4.5.2.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/8562

[nthiery]

Work Issues: (didn't run full tests yet)

[nthiery]

comment:2

Ok, the tests passed fine up to some trivialities (*_with_category class name changes). I'll fix this and upload an updated patch soon. The review can start in parallel

[rbeezer]

comment:3

This applies, builds and limited testing (prime and composite orders) indicates that it plays nicely with "addition tables" at #7555 which rely heavily on the category framework. Didn't run tests, but witnessed no problems otherwise.

Good to see how easy it is to insert a new object into the category framework.

I'll come back when the patch is completed.

[loefflerd]

comment:4

Just a heads-up: this looks rather like it might clash with #8218, which is the first of several patches by David Roe which do a substantial amount of work improving finite fields. #8218 has been held up for ages because it moves loads of files around (without substantially changing their content) so even small changes to finite fields will cause conflicts, and there is a lot of really good code waiting on it, so it would be a shame to have to put it off even longer.

David

[nthiery]

comment:5

Replying to @loefflerd:

Just a heads-up: this looks rather like it might clash with #8218, which is the first of several patches by David Roe which do a substantial amount of work improving finite fields. #8218 has been held up for ages because it moves loads of files around (without substantially changing their content) so even small changes to finite fields will cause conflicts, and there is a lot of really good code waiting on it, so it would be a shame to have to put it off even longer.

Thanks for the notice. There is no urgency for that one, so sure, if there is any conflict, #8218 should go first.

David: I won't be touching this patch further. Feel free to update / refactor / merge /... it within the other series of patch whenever it feels right.

[nthiery]

Description changed:

--- 
+++ 
@@ -23,4 +23,9 @@
     running ._test_zero() . . . pass
 ```
 
-This is required to use the cool features from #7555.
+And this makes the cool features from #7555 work for Z/nZ.
+
+Needs work: see: running design discussion on:
+
+http://groups.google.com/group/sage-devel/t/21e21e1ec9cd21fe
+