2008/9/18 John H Palmieri <[EMAIL PROTECTED]>:
>
> On Sep 17, 9:09 pm, "William Stein" <[EMAIL PROTECTED]> wrote:
>> On Wed, Sep 17, 2008 at 8:59 PM, John H Palmieri <[EMAIL PROTECTED]> wrote:
>>
>> > sage: is_FractionField(FractionField(ZZ))
>> > False
>>
>> > Oy. This seems to be intentional: there is a doctest very similar to
>> > this. It doesn't seem right, though. How hard would it be to change?
>> > Is it worth it?
>>
>> In most cases in Sage (maybe all cases),  is_Foo is a data type
>> check.  It's not making a mathematical assertion.  The implementation
>> is almost always a call to isinstance.
>
> Right, I saw that in the source code. How about we change it, in this
> case, from
>
>    return isinstance(x, FractionField_generic)
>
> to
>
>    return isinstance(x, (FractionField_generic, Field))
>
> (Every field is its own fraction field.)  I can submit a trac ticket
> with this change, unless someone convinces me that it's a really bad
> idea.

I think that is a good idea.  If it does cause minor problems they can
surely be fixed.

>
>>
>> > Along the same lines, partial fraction decomposition should work for
>> > rational numbers; this would work if elements of QQ were instances of
>> > FractionFieldElement, right?
>>
>> Or you could just implement it, which would likely be a good idea.
>
> It might be a good idea, but I don't know how to do it.  How do I
> produce, given 1/20, the output 1/4 - 1/5?  That is, how do I tell
> sage to output 1/4 - 1/5, as an element in QQ, I suppose, without
> evaluating it and just printing 1/20?
>

I used to set this as an exercise in my undergaduate number theory
class.  Shall I look for my model solution ? ;)

 Let the rational be a/b.  For each prime power q dividing  b find c
such that a/b-c/q has denom coprime to q, by solving a congruence mod
q.  Repeat until done.

John

>>
>> William
>>
>
> John
> >
>

--~--~---------~--~----~------------~-------~--~----~
To post to this group, send email to sage-support@googlegroups.com
To unsubscribe from this group, send email to [EMAIL PROTECTED]
For more options, visit this group at 
http://groups.google.com/group/sage-support
URLs: http://www.sagemath.org
-~----------~----~----~----~------~----~------~--~---

Reply via email to