#269: Add __mod__ to coercion model
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Reporter: dmharvey | Owner: somebody
Type: enhancement | Status: new
Priority: major | Milestone: sage-7.1
Component: coercion | Resolution:
Keywords: | Merged in:
Authors: Jeroen Demeyer | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: #2034 | Stopgaps:
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Description changed by jdemeyer:
Old description:
> Add `__mod__` to the coercion model for `Element` and change `__mod__` to
> `_mod_` where applicable.
>
> This does not change any semantics of remaindering, but it does fix
> remaindering in a few cases where coercion is involved.
>
> As proof-of-concept for refactoring more generally the arithmetic methods
> on `Element`, the implementation of `__mod__` is different from the usual
> implementation:
> 1. `_mod_` will be added to `Element` and not `RingElement` or similar.
> 2. The prototype is `cpdef _mod_(self, Element other)` with no typing for
> the return value.
> 3. We do not implement the in-place `__imod__` which is useless anyway
> with coercion.
>
> My intention is that eventually all arithmetic methods should be
> implemented like `__mod__`.
New description:
Add `__mod__` to the coercion model for `Element` and change `__mod__` to
`_mod_` where applicable.
We change the behaviour of `__mod__` for integer mod rings: the following
(which is mathematically meaningless) is now an error:
{{{
sage: a = next_prime(2**31)
sage: b = Integers(a)(100)
sage: a % b
Traceback (most recent call last):
...
ZeroDivisionError: reduction modulo 100 not defined
}}}
Apart from this, this branch does not change any semantics of
remaindering.
As proof-of-concept for refactoring more generally the arithmetic methods
on `Element`, the implementation of `__mod__` is different from the usual
implementation:
1. `_mod_` will be added to `Element` and not `RingElement` or similar.
2. The prototype is `cpdef _mod_(self, Element other)` with no typing for
the return value.
3. We do not implement the in-place `__imod__` which is useless anyway
with coercion.
My intention is that eventually all arithmetic methods should be
implemented like `__mod__`.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/269#comment:21>
Sage <http://www.sagemath.org>
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