In fact, I'm trying to write my own ring of complex integers. But as I don't know much about the sage internals and desing I wanted to ask first (and to avoid duplicating efforts)
Where can I see Joel Mohler work ? (is in the mercurial repository) On 3/31/07, Robert Bradshaw <[EMAIL PROTECTED]> wrote: > > > This is because I currently lives in the (inexact) field of complex > numbers. This will change. Joel Mohler is currently doing a lot of > work on implementing number fields right now, so hopefully this will > work in the near future. If you were interested in working on it you > might want to see what he's done so far. > > - Robert > > On Mar 31, 2007, at 7:10 AM, Pablo De Napoli wrote: > > > Hi, > > > > I want to ask you some questions concerning the arithmetic of number > > fields in Sage. > > > > Does Sage currently support factoring in Gaussian integers (i.e. in > > the ring > > Z[I] of complex numbers with integral real/imaginary parts)? > > I thing this would be a nice feature to have. > > > > In pari/gp for example this works: > > > > ? factor(5*I) > > %1 = > > [2 + I 1] > > > > [1 + 2*I 1] > > > > in sage > > > > factor(5*I) > > gives an error. > > > > Obviously factoring depends on the ring in which we are working on, > > so that for example the factorization of 5 would be different in > > the ring > > Z or in the ring Z[I] > > > > Currently Z[I] seems not to be a supported ring in sage, even though > > you can create a quadratic field > > > > F=QuadraticFiled(-1,'a') > > (number field in a with defining polynomial x^2+1) > > > > and after doing > > a= F.gen() > > > > 'a' behaves algebraically as the complex number I (i.e. a^2=-1) > > [ Mathematically 'a' is not the complex number 'I', as it could be > > also the complex > > number '-I' wich is also a root of the same minimal polynomial x^2 > > +1 ; > > however there exists the function complex_imbedding() that > > gives the corresponding complex number: > > > > sage: a.complex_embedding () > > 1.00000000000000*I > > > > assuming that a=I) > > > > but there seems to be no implementation of factorization in > > quadratic fields (of course in those fields in wich there is a unique > > decomposition into primes), nor a notion of the subring of > > algebraic integers. > > > > My question is: what would be the best way to implement this? > > > > Perphaps the best way would be creating a new > > ring sage.ring.complex_integer representing gaussian_integers > > for representing Gaussian integers > > > > I see that currently a complex number like > > > > 2+3*I > > > > is represented in sage, by using float point representation. > > > > z=2+3*I > > sage: type(z) > > <type 'sage.rings.complex_number.ComplexNumber' > > > sage: z.real() > > 2.00000000000000 > > sage: type(z.real()) > > <type 'sage.rings.real_mpfr.RealNumber'> > > sage: > > > > and this could lead to rounding errors. It would be better to do > > exact integer arithmetic, when dealing with Gaussian integers. > > > > best > > regards > > > > Pablo > > > > > > > > > > --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@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-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
