I just tried to run: sage: m = random_prime(10^5) sage: K.<r> = CyclotomicField(m)
and I ran out of RAM! Doing a smaller example: sage: m = random_prime(10^4) sage: %prun K.<r> = CyclotomicField(m) puts sage.rings.number_field.number_field_morphisms.create_embedding_from_approx as the most expensive function call. Continuing to: sage: m = random_prime(2*10^3) sage: K.<r> = CyclotomicField(m) sage: %prun K.ring_of_integers() puts sage.matrix.matrix_integer_dense.Matrix_integer_dense._solve_right_nonsingular_square as the most expensive function call, which would imply John's assumption is right. Cheers, Martin On Tuesday 15 Apr 2014 13:04:27 François Colas wrote: > Hi Vincent, > > In fact that's exactly what I want to do! > > But I am using morphisms: > > m = ZZ(int(random()*10^5+1)) > > R.<r> = NumberField(cyclotomic_polynomial(m)) > > Idl = [] > > for (p, e) in factor(m): > Idl.append(cyclotomic_polynomial(p)) > > K = NumberField(Idl, 'k') > > F = Hom(R, K) > > f = F([...]) > > Unfortunately I also need K with big m for cryptographic purpose... :'( > > Note that even if you have 3 cyclotomic polynomials in Idl (e.g. 11, 13, > 17) it's always slow. > > Le mardi 15 avril 2014 18:48:11 UTC+2, vdelecroix a écrit : > > Hi François, > > > > Might be related to the ticket #16116 on trac > > (http://trac.sagemath.org/ticket/16116). Note that for performance, it > > is possible to use multivariate polynomials as described in the > > ticket. > > > > Best > > Vincent > > > > 2014-04-15 18:30 UTC+02:00, François Colas <fco...@gmail.com <javascript:>>: > > > Hello group, > > > > > > I am playing with quotient ring of Z over cyclotomic polynomial but it > > > > is > > > > > strangely slow: > > > > > > sage: m = random_prime(10^4); m > > > 2437 > > > sage: %time R.<r> = ZZ['z'].quotient(cyclotomic_polynomial(m)) > > > CPU times: user 2.50 s, sys: 0.00 s, total: 2.50 s > > > Wall time: 2.50 s > > > > > > cyclotomic_polynomial(m) is created instantly whatever the size of m but > > > the quotient becomes very long: > > > > > > sage: m = random_prime(10^5); m > > > 16231 > > > sage: %time R.<r> = ZZ['z'].quotient(cyclotomic_polynomial(m)) > > > CPU times: user 217.82 s, sys: 0.00 s, total: 217.82 s > > > Wall time: 217.65 s > > > > > > > > > I am using Sage Version 6.1.1, does anyone could confirm this problem? > > > > Groups > > > > > "sage-devel" group. > > > To unsubscribe from this group and stop receiving emails from it, send > > > > an > > > > > email to sage-devel+...@googlegroups.com <javascript:>. > > > To post to this group, send email to > > > sage-...@googlegroups.com<javascript:>. > > > > > > Visit this group at http://groups.google.com/group/sage-devel. > > > For more options, visit https://groups.google.com/d/optout.
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