#18263: reintroduce `__neg__` for magmas cartesian product
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       Reporter:  vdelecroix  |        Owner:
           Type:  defect      |       Status:  new
       Priority:  major       |    Milestone:  sage-6.7
      Component:  categories  |   Resolution:
       Keywords:              |    Merged in:
        Authors:              |    Reviewers:
Report Upstream:  N/A         |  Work issues:
         Branch:              |       Commit:
   Dependencies:  #16836      |     Stopgaps:
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Description changed by vdelecroix:

Old description:

> In #16836 the `__neg__` operation for cartesian product was moved from
> `AdditiveMagmas` to the `AdditiveMagmas.WithInverse()`. The operation was
> ambiguous but the feature is lost. It should be decided in this ticket
> what should be done with it.
>
> One should also restore the `TODO` section about `NN` being lazily import
> (or fix it ;-)

New description:

 In #16836 the `__neg__` operation for cartesian product was moved from
 `AdditiveMagmas` to the `AdditiveMagmas.WithInverse()`. The operation was
 ambiguous but the feature is lost. We just revert the removal.

 Moreover, there was a bug in Cartesian products of
 `CombinatorialFreeModule` as this generic `__neg__` was called instead of
 the customized `_neg_` which worked (see
 [http://trac.sagemath.org/ticket/16836#comment:22 #16836 comment:22] and
 [http://trac.sagemath.org/ticket/16836#comment:23 #16836 comment:23])! One
 solution is to use `__neg__` everywhere instead of `_neg_`.

--

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Ticket URL: <http://trac.sagemath.org/ticket/18263#comment:1>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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