On 23 October 2016 at 17:32, John Cremona <john.crem...@gmail.com> wrote:
> On 23 October 2016 at 15:28, vdelecroix <20100.delecr...@gmail.com> wrote:
>> Le dimanche 23 octobre 2016 16:20:25 UTC+2, John Cremona a écrit :
>>>
>>> I see that despite the title of that ticket, this is (at present)
>>> about r%n when r =p/q is rational.
>>
>>
>> The ticket also cares about the case where n is rational. Moreover my
>> proposed branch makes % part of the coercion system (when one of the
>> argument is rational). So standard coercion rules apply.
>
> OK
>
>>
>> However, concerning this thread, my question is about r%n with r=p/q being
>> rational.
>>
>>> Questions:
>>>
>>> 1. What is the proposed behaviour when q is not invertible modulo n?
>>> Or more generally, if q*x=p (mod n) has no solutions, or more than
>>> one solution (mod n)?
>>
>>
>> The very same behavior as with the two implementation I proposed. In other
>> words, raise the same errors as inverse_mod does when it complains.
>
> OK and this should be documented somehow, though I'm not sure how to
> document the behaviour of operators.
>
>>
>> Concerning the non-uniqueness, it is just a matter of having an extra
>> argument to inverse_mod on integers and using it here. Do you think it might
>> be useful?
>
> No, anyone wanting all solutions would be able to get them a different way.
>
>>
>>>
>>> 2. Is the output going to be an element of Z/nZ, or of Z (as your
>>> sample code suggests)?
>>
>>
>> I was thinking about Z since for Z/nZ the direct conversion just works
>> Zmod(n)(r).
>
> That's reasonable, and what people would expect with an operator such as %.
>
> thanks for the answers. As for you question, do we need a name to
> shadow the operator %? If we do, then "mod"?
I thought about it. The main problem is that `mod` already contains
specification and implementation at the level of commutative rings and
fields
Return a representative for ``self`` modulo the ideal I (or the
ideal generated by the elements of I if I is not an ideal.)
And we have
sage: (2/3).mod(5)
0
sage: (1/2).mod(2)
0
which is true, meaningless and incompatible with what I want...
Vincent
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