Hi Stefan,
On 2013-08-29, Stefan <stefanvanz...@gmail.com> wrote:
> Actually, this is not quite true. reduce() is, by default, called
> automatically for elements of exact rings at creation time. It will
> correctly get rid of common factors, but it does not normalize the leading
> coefficients:
Bad. But of course, it is all only defined up to units.
>> I'd rather have a slow hash than a totally broken hash.
>>
>
> Meh. I still want to do this billions of times.
Well, with a broken hash, it would work wrong billions of times.
> Actually, this does not hold in my example (with the polynomial ring
> defined above):
>
> sage: cmp((c+1)^2, c^2 + 2*c+1)
> 0
It is a totally different problem. My example was about symbolic variables,
which is a totally different story, even though on the surface it seems
to be almost the same as your original example ("we have two equal elements
a and b of a ring, but Sage does not recognise that a is in set([b])").
Best regards,
Simon
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