On Jan 27, 2009, at 4:02 PM, William Stein wrote: > On Tue, Jan 27, 2009 at 1:51 PM, Robert Bradshaw > <rober...@math.washington.edu> wrote: >> >> >> On Jan 27, 2009, at 12:54 AM, William Stein wrote: >> >>> >>> On Tue, Jan 27, 2009 at 12:45 AM, alia hamieh >>> <aliasham...@gmail.com> wrote: >>>> I'm trying to deal with following problem: >>>> >>>> G=DirichletGroup(75) >>>> chi = list(G)[8] >>>> I need to compute with expressions such as: chi(2)*sqrt(11) >>>> the problem is that we cannot do this multiplication because we >>>> have >>>> "incompatible" operands, the first belongs to the cyclotomic field >>>> of order >>>> 20 and the other one belongs to a symbolic ring. >>>> Is there a way to fix this problem? >>>> >>>> alia >>> >>> You can do the following. It's awkward but it works: >>> >>> sage: G = DirichletGroup(75) >>> sage: chi = list(G)[8] >>> sage: K = G.base_ring() >>> sage: R.<x> = PolynomialRing(K) >>> sage: L.<alpha> = K.extension(x^2 - 11) >>> sage: chi(2) * alpha >>> zeta20^4*alpha >>> >>> Here alpha = sqrt(11). >>> >>> Someday Robert Bradshaw is likely to make your original >>> chi(2)*sqrt(11) work. We'll see. >> >> This would require sqrt(11) to be a number field element rather than >> a symbolic expression. For many things I think that would be a good >> idea, but it has some drawbacks, like when trying to compute sum(sqrt >> (p) for p in primes(1000)) > > But couldn't doing chi(2) * sqrt(11) coerce chi(2) to the symbolic > ring and give > the answer there? I think that should make sense, because cyclotomic > fields are > now equipped with a fixed embedding into C.
Hmm... actually this does happen now: sage: K.<a> = CyclotomicField(35) sage: a + sqrt(11) e^(2*I*pi/35) + sqrt(11) And sage: G = DirichletGroup(75) sage: chi = list(G)[8] sage: chi(2) * sqrt(11) sqrt(11)*e^(2*I*pi/5) This was part of the better symbolic minpoly work (which facilitated coercion in the other direction to, I forgot it finally got in) and now that we have embeddings too it's working. Of all people I should have remembered this--I guess my mind is elsewhere :) So the answer is to upgrade Sage. - Robert --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
