On 8 February 2010 13:29, Burcin Erocal <[email protected]> wrote: > Hi Nils, > > I'll leave the maxima floats question to the experts. > > On Mon, 8 Feb 2010 00:48:47 -0800 (PST) > Nils Bruin <[email protected]> wrote: > >> Incidentally, >> sage: S.operands()[0].operands()[0].operands()[3].pyobject() >> 5*I + 5 >> sage: type(S.operands()[0].operands()[0].operands()[3].pyobject()) >> <type >> 'sage.rings.number_field.number_field_element_quadratic.NumberFieldElement_quadratic'> >> >> Isn't this a bit strange? A constant like sqrt(2) in SR is not >> represented as a quadratic number. Why is I special? > > If we use number fields for algebraic numbers, then the degree of the > extension over QQ grows to unreasonable values rather quickly. E.g., > if we add \sqrt{2}, \sqrt[3]{2}, sqrt[5]{2}, ... the degree will be > proportional to factorial(n). Though, I would also like all the numeric > values to be in the coefficients. > > I admit that I have no idea how QQbar manages this situation. There is > also a recent article called "Computing with algebraically closed > fields" in the JSC by Allan Steel [1] which might be of interest. > > [1] http://dx.doi.org/10.1016/j.jsc.2009.09.005
This is a new version of Allan Steel's method implemented in Magma for some time, lying behind Magma's AlgebraicallyClosedField which is similar in some ways to Sage's QQbar. It seems that he can now handle positive characteristic (but I have not read the article). I used to use Magma's AlgebraicallyClosedField a lot, just as I now use QQbar a lot. (See the bug in QQbar's sqrt() which I just posted!) But I don't know enough about how either works to make a sensible comparison. John > > > Cheers, > Burcin > > -- > To post to this group, send an email to [email protected] > To unsubscribe from this group, send an email to > [email protected] > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
