Maybe there is no bug, but the problem is that it take a very very long time to compute the minimal polynomial of the absolute value of an algebraic number.
Le dimanche 30 mars 2014 16:21:06 UTC+2, Paul Mercat a écrit : > > I can confirm that the error comes from the comparaison of two elements of > QQbar, because the comparaison of absolutes values of two complexe > conjugate doesn't work > > sage: a = Automaton([(0, 0, 0), (0, 1, 1), (1, 1, 1), (1, 2, 0), (2, 0, > 0), (2, 3, 1), (3, 4, 1), (3, 7, 0), (4, 1, 1), (4, 5, 0), (5, 0, 0), (5, > 6, 1), (6, 7, 0), (6, 37, 1), (7, 3, 1), (7, 8, 0), (8, 0, 0), (8, 9, 1), > (9, 2, 0), (9, 10, 1), (10, 2, 0), (10, 11, 1), (11, 2, 0), (11, 12, 1), > (12, 13, 0), (12, 34, 1), (13, 14, 0), (13, 24, 1), (14, 1, 1), (14, 15, > 0), (15, 16, 0), (15, 33, 1), (16, 0, 0), (16, 17, 1), (17, 1, 1), (17, 18, > 0), (18, 3, 1), (18, 19, 0), (19, 1, 1), (19, 20, 0), (20, 1, 1), (20, 21, > 0), (21, 22, 0), (21, 31, 1), (22, 23, 0), (23, 0, 0), (23, 24, 1), (24, 4, > 1), (24, 25, 0), (25, 26, 1), (25, 29, 0), (26, 7, 0), (26, 27, 1), (27, 1, > 1), (27, 28, 0), (28, 6, 1), (28, 19, 0), (29, 0, 0), (29, 30, 1), (30, 10, > 1), (30, 18, 0), (31, 2, 0), (31, 32, 1), (32, 2, 0), (32, 3, 1), (33, 2, > 0), (33, 17, 1), (34, 35, 1), (35, 1, 1), (35, 36, 0), (36, 16, 0), (36, > 26, 1), (37, 5, 0), (37, 11, 1)]) > sage: m = a.graph().adjacency_matrix() > sage: e = m.eigenvalues() > sage: l = [abs(el) for el in e] > sage: l[19]==l[20] #doesn't terminate !!!! > > Le dimanche 30 mars 2014 16:09:28 UTC+2, Paul Mercat a écrit : >> >> I think I know where is the problem. >> I have tried to reimplemente the function max, and I've see that it >> doesn't terminate when there is a comparaison between two complex >> conjugates. >> >> The bug with max comes from a bug in the comparaison of two elements of >> QQbar : it should detect when two algebraic numbers are equals, but it >> doesn't and so it try to compute with more and more precision to see which >> one is greater, but it doesn't terminates because there are equals. >> >> Maybe I will try to fix this. >> >> Paul >> >> Le dimanche 30 mars 2014 16:00:14 UTC+2, Paul Mercat a écrit : >>> >>> If I do what you propose, it works. >>> But I want the maximum of the list in QQbar, not in RR, and I don't >>> understand why the max function take all this time. >>> And it also doesn't work with key=abs. >>> >>> Paul >>> >>> Le dimanche 30 mars 2014 15:49:45 UTC+2, John Cremona a écrit : >>>> >>>> m is an integer matrix and its eigenvalues (which are not all rel >>>> anyway) are returned as algebraic numbers (try e[0].parent()). >>>> >>>> Perhaps you want this: >>>> sage: max([RR(ei) for ei in e if ei in RR]) >>>> 1.99801167774722 >>>> >>>> but note that only 22 of the 38 eigenvalues are real. >>>> >>>> John >>>> >>>> >>>> On 30 March 2014 14:32, Paul Mercat <mer...@yahoo.fr> wrote: >>>> > The function max sometimes doesn't work in sage. >>>> > Here is an example : >>>> > >>>> > sage: a = Automaton([(0, 0, 0), (0, 1, 1), (1, 1, 1), (1, 2, 0), (2, >>>> 0, 0), >>>> > (2, 3, 1), (3, 4, 1), (3, 7, 0), (4, 1, 1), (4, 5, 0), (5, 0, 0), (5, >>>> 6, 1), >>>> > (6, 7, 0), (6, 37, 1), (7, 3, 1), (7, 8, 0), (8, 0, 0), (8, 9, 1), >>>> (9, 2, >>>> > 0), (9, 10, 1), (10, 2, 0), (10, 11, 1), (11, 2, 0), (11, 12, 1), >>>> (12, 13, >>>> > 0), (12, 34, 1), (13, 14, 0), (13, 24, 1), (14, 1, 1), (14, 15, 0), >>>> (15, 16, >>>> > 0), (15, 33, 1), (16, 0, 0), (16, 17, 1), (17, 1, 1), (17, 18, 0), >>>> (18, 3, >>>> > 1), (18, 19, 0), (19, 1, 1), (19, 20, 0), (20, 1, 1), (20, 21, 0), >>>> (21, 22, >>>> > 0), (21, 31, 1), (22, 23, 0), (23, 0, 0), (23, 24, 1), (24, 4, 1), >>>> (24, 25, >>>> > 0), (25, 26, 1), (25, 29, 0), (26, 7, 0), (26, 27, 1), (27, 1, 1), >>>> (27, 28, >>>> > 0), (28, 6, 1), (28, 19, 0), (29, 0, 0), (29, 30, 1), (30, 10, 1), >>>> (30, 18, >>>> > 0), (31, 2, 0), (31, 32, 1), (32, 2, 0), (32, 3, 1), (33, 2, 0), (33, >>>> 17, >>>> > 1), (34, 35, 1), (35, 1, 1), (35, 36, 0), (36, 16, 0), (36, 26, 1), >>>> (37, 5, >>>> > 0), (37, 11, 1)]) >>>> > sage: m = a.graph().adjacency_matrix() >>>> > sage: e = m.eigenvalues() >>>> > sage: print e >>>> > sage: max(e) #doesn't terminate !!! >>>> > >>>> > Do you know why it doesn't work ? >>>> > >>>> > Paul >>>> > >>>> > -- >>>> > You received this message because you are subscribed to the Google >>>> Groups >>>> > "sage-devel" group. >>>> > To unsubscribe from this group and stop receiving emails from it, >>>> send an >>>> > email to sage-devel+...@googlegroups.com. >>>> > To post to this group, send email to sage-...@googlegroups.com. >>>> > Visit this group at http://groups.google.com/group/sage-devel. >>>> > For more options, visit https://groups.google.com/d/optout. >>>> >>> -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
