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 -~----------~----~----~----~------~----~------~--~---
