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
