I think that sounds a good idea; but can we call the parameter "extend" and not "base_extend"? First, as that is less frightening for users (who will need examples to show that for a real matrix, if you want complex eigenvalues you have to ask for them), and also for consistency with (for example) the sqrt() function.
John On 14 June 2010 14:12, mmarco <mma...@unizar.es> wrote: > During the discusion about ticket 8974 > https://webmail.unizar.es/horde/imp/login.php > i noted that the behaviour of eigenvectors, eigenspaces and > eigenvalues method of matrices is not mathematically correct. Or being > more precise, it does not translate directly into mathematically > correct methods for endomorphisms of vector spaces; since these > methods work in an extension of the base field (if necessary), while > vector spaces are defned with a precise base field. > > Since David Loeffler insists that the methods implemented for > endomorphism objects must be the same as the ones for the underlying > matrices (and i agree that it is a good thing), i suggest to include > an option in these methods that allows to distinguish if you want the > result in a field extension or if you want to stick to the base field. > > Something like this: > > sage: M=matrix(QQ,[[1,2,3],[4,5,6],[7,8,9]]) > sage: M.eigenvalues(base_extend=True) > [0, -1.116843969807043?, 16.11684396980705?] > sage: M.eigenvalues(base_extend=False) > [0] > sage: M.eigenspaces(base_extend=True) > [ > (0, Vector space of degree 3 and dimension 1 over Rational Field > User basis matrix: > [ 1 -2 1]), > (a1, Vector space of degree 3 and dimension 1 over Number Field in a1 > with defining polynomial x^2 - 15*x - 18 > User basis matrix: > [ 1 1/18*a1 + 1/3 1/9*a1 - 1/3]) > ] > sage: M.eigenspaces(base_extend=True) > [ > (0, Vector space of degree 3 and dimension 1 over Rational Field > User basis matrix: > [ 1 -2 1])] > > > So, what do you think? > > Miguel > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
