>>> I'll second this. Are there *any* computer algebra systems (or
>>> programming languages for that matter) out there such that 4/2 != 2 !=
>>> 2.0? Code would simply be too hard to write.
>>
>> Ada, I guess. It should give error if you try to compare integer with float.
>
> Ah, no wonder it's s
On Thu, Jun 12, 2014 at 10:19 AM, Vincent Delecroix
<20100.delecr...@gmail.com> wrote:
> 2014-06-12 19:13 UTC+02:00, Robert Bradshaw :
>> On Thu, Jun 12, 2014 at 12:50 AM, Marc Mezzarobba
>> wrote:
>>
>>> But here is a similar example right from the Sage library (adapted from
>>> http://wiki.sagem
On Thursday, June 12, 2014 6:44:44 PM UTC+1, William wrote:
>
> > sage: sum(FiniteEnumeratedSet([0,1,2]))
> > 3
> > sage: FiniteEnumeratedSet(GF(3))
> > sage: sum(FiniteEnumeratedSet([0,1,2]))
> > 0
>
> But I would rather blame the use of caching rather than equality
> testing.
The issue i
On Thu, Jun 12, 2014 at 10:19 AM, Vincent Delecroix
<20100.delecr...@gmail.com> wrote:
> 2014-06-12 19:13 UTC+02:00, Robert Bradshaw :
>> On Thu, Jun 12, 2014 at 12:50 AM, Marc Mezzarobba
>> wrote:
>>
>>> But here is a similar example right from the Sage library (adapted from
>>> http://wiki.sagem
2014-06-12 19:13 UTC+02:00, Robert Bradshaw :
> On Thu, Jun 12, 2014 at 12:50 AM, Marc Mezzarobba
> wrote:
>
>> But here is a similar example right from the Sage library (adapted from
>> http://wiki.sagemath.org/EqualityCoercion):
>>
>> sage: FiniteEnumeratedSet(GF(3))
>> {0, 1, 2}
>> sage: add(Fi
2014-06-12 19:10 UTC+02:00, Robert Bradshaw :
> On Thu, Jun 12, 2014 at 8:41 AM, Nils Bruin wrote:
>> On Thursday, June 12, 2014 12:48:37 AM UTC-7, Marc Mezzarobba wrote:
>>>
>>> Sure. But why not have
>>>
>>> sage: bool(sin(x)^2+cos(x)^2==1)
>>> True
>>>
>>> return False as well, and let the user
On Thu, Jun 12, 2014 at 12:50 AM, Marc Mezzarobba wrote:
> But here is a similar example right from the Sage library (adapted from
> http://wiki.sagemath.org/EqualityCoercion):
>
> sage: FiniteEnumeratedSet(GF(3))
> {0, 1, 2}
> sage: add(FiniteEnumeratedSet([0,1,2]))
> 0
Um, isn't that what you
On Thu, Jun 12, 2014 at 8:41 AM, Nils Bruin wrote:
> On Thursday, June 12, 2014 12:48:37 AM UTC-7, Marc Mezzarobba wrote:
>>
>> Sure. But why not have
>>
>> sage: bool(sin(x)^2+cos(x)^2==1)
>> True
>>
>> return False as well, and let the user test that
>>
>> (rhs-lhs).simplify_full() == 0
>
> That
On Tuesday, June 10, 2014 12:16:46 AM UTC+1, Nils Bruin wrote:
>
> Also, if we'd actually have the category as "Category of subsets of GF(5)"
> we would probably end up with the memory leaks that parametrized categories
> tend to cause. Still, it may be worth investigating how such containers
>
Hi Nils,
> Also, if we'd actually have the category as "Category of subsets of GF(5)"
> we would probably end up with the memory leaks that parametrized categories
> tend to cause. Still, it may be worth investigating how such containers
> should interact with the category framework. Do we want/ne
2014-06-10 1:16 UTC+02:00, Nils Bruin :
> On Monday, June 9, 2014 3:50:06 PM UTC-7, Volker Braun wrote:
>>
>> This seems like it would be a good solution in Sage, namely provide
>> associative containers that participate in coercion and ensure that all
>> elements have the same type. E.g.
>>
>> sag
On Mon, 9 Jun 2014 15:50:06 -0700 (PDT)
Volker Braun wrote:
> On Monday, June 9, 2014 11:08:33 PM UTC+1, Nils Bruin wrote:
>
> > At any particular moment, though, an associative array has an index
> > universe, so as long as equality and hash are consistent within that
> > universe
> >
>
> Th
On Monday, June 9, 2014 3:50:06 PM UTC-7, Volker Braun wrote:
>
> This seems like it would be a good solution in Sage, namely provide
> associative containers that participate in coercion and ensure that all
> elements have the same type. E.g.
>
> sage: s = SageSet([3, 8]); s # universe = ZZ
On Monday, June 9, 2014 11:08:33 PM UTC+1, Nils Bruin wrote:
> At any particular moment, though, an associative array has an index
> universe, so as long as equality and hash are consistent within that
> universe
>
This seems like it would be a good solution in Sage, namely provide
associative
On Monday, June 9, 2014 2:19:32 PM UTC-7, William wrote:
> I wanted to understand what you just claimed, so in Magma [1] I typed
> this:
>
> 5 eq GF(7)!5
>
> but it output "true".So clearly I completely misunderstood your
> claim. Can you be more precise?
>
Sorry, you didn't misunde
Hi,
> and as discussed there, it's a compromise that was considered the least
> bad. The main problem is that if you want, for all integers a,b and
> distinct primes p,q, that
>
> GF(p)(a) == GF(p)(b) implies a == GF(p)(b) and
> GF(q)(a) == GF(q)(b) implies a == GF(q)(b)
I do not want that! Consi
On Mon, Jun 9, 2014 at 2:14 PM, Nils Bruin wrote:
> The consistent solution, and one that is mathematically defendable, would be
> to have a != GF(p)(a) for integers a (i.e., always force explicit coercion
> for equality to hold). So that is making "==" strict enough to allow hash to
> meet its re
On Monday, June 9, 2014 1:44:41 PM UTC-7, Erik Massop wrote:
>
> On Mon, 09 Jun 2014 16:48:09 +0200
> leif > wrote:
>
> > Volker Braun wrote:
> > > On Monday, June 9, 2014 12:54:56 AM UTC+1, vdelecroix wrote:
> > >
> > > sage: {3, AA(3)}
> > > {3, 3}
> > >
> > >
> > > IMHO you shou
On Monday, June 9, 2014 9:44:41 PM UTC+1, Erik Massop wrote:
>
> IMHO this should be disallowed. All objects that implement __hash__
> should live up to contract of __hash__, which is that a==b implies
> hash(a)==hash(b)
I totally agree that the situation is currently unsatisfactory, but the
s
On Mon, 09 Jun 2014 16:48:09 +0200
leif wrote:
> Volker Braun wrote:
> > On Monday, June 9, 2014 12:54:56 AM UTC+1, vdelecroix wrote:
> >
> > sage: {3, AA(3)}
> > {3, 3}
> >
> >
> > IMHO you should never put sage objects with different parents into an
> > associative container.
>
> Altho
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