Hi Nils, On Wednesday 07 May 2014 16:43:03 Nils Bruin wrote: > On Wednesday, May 7, 2014 9:58:48 AM UTC-7, François Colas wrote: > > What I want to do is a way to evaluate polynomials of K in a power of a > > primitive square root of unity: > > > > omega = CC(e^(2*I*pi/m)) > > F = Hom(K, CC) > > f = F([omega]) > > TypeError: images do not define a valid homomorphism > > > > Does anyone see another way to do this? > > Have you tried using CyclotomicField(m) ? I think that uses specialized > code, which should handle high degrees much better than generic number > field code:
unfortunately that's not the case for the OP, see: https://groups.google.com/forum/#!searchin/sage-devel/QuotientRing| sort:date/sage-devel/qxGMiYDF4eQ/zDcTmXWJH9UJ > sage: K=CyclotomicField(3*5*7*11) > sage: K.coerce_embedding() > Generic morphism: > From: Cyclotomic Field of order 1155 and degree 480 > To: Complex Lazy Field > Defn: zeta1155 -> 0.9999852033056930? + 0.00543996044764063?*I > > Alternatively, if you really want to use an explicit quotient ring > construction: > > f = F([omega],check=False) > > The error you run into otherwise is: > > sage: sage.rings.morphism.RingHomomorphism_im_gens(H,[omega]) > ValueError: relations do not all (canonically) map to 0 under map > determined by images of generators. > > i.e., the cyclotomic polynomial evaluated at omega doesn't return an exact > zero, because CC uses float arithmetic. Cheers, Martin
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