> > > I don't know what you mean here. Sage has Jordan decomposition over > > algebraic numbers. > > > > I checked generalizedEigenvectors matrix [[1, x], [0, 1]] but this gives > a > > wrong result: > > > > (5) -> m := matrix([[1,x],[0,1]]) > > > > +1 x+ > > (5) | | > > +0 1+ > > Type: > > Matrix(Polynomial(Integer)) > > (6) -> generalizedEigenvectors m > > > > +0+ +1+ > > (6) [[eigval= 1,geneigvec= [| |,| |]]] > > +1+ +0+ > > Type: List(Record(eigval: > > > Union(Fraction(Polynomial(Integer)),SuchThat(Symbol,Polynomial(Integer))),geneigvec: > > > > List(Matrix(Fraction(Polynomial(Integer)))))) > > Why do you think it is wrong? The first vector is an eigenvector, > the second is in kernel of (A - 1)^2 and linearly independent of the > first. This gives Jordan form: > > [ 1 lambda ] > [ ] > [ 0 1 ] > > Matrices with different lambda are equivalent, so this is > Jordan form of input matrix. More generally, generalized > eigenvectors corresponding to lambda gives you basis of > subspace where (A - lambda) is nilpotent. Since in > your case m - 1 is nilpotent the result is rather trivial. > > I didn't understand the output, now I do, thanks! It does appear similar to sage:
sage: R.<x> = PolynomialRing(QQ) sage: m = matrix([[1, x],[0,1]]) sage: m.jordan_form(transformation =true) ( [1 1] [x 0] [0 1], [0 1] ) Do you have an example of a limit where maxima and sympy fail? Martin -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/fricas-devel. For more options, visit https://groups.google.com/d/optout.
