On Thursday, November 7, 2013 9:00:36 AM UTC-8, ccandide wrote: > > I dont' understand why Sage is unable to give an exact expression for the > eigenvalues of the following matrix : > > sage: A= matrix([[0,1],[1,-2]]) > sage: [a for a,_,_ in A.eigenvectors_right()] > [-2.414213562373095?, 0.4142135623730951?] >
I think it is an exact expression, but it's not printed very well. sage: b = A.eigenvectors_right()[0][0] sage: b -2.414213562373095? sage: parent(b) Algebraic Field sage: (b+1)^2 # note no imprecision in this answer 2 sage: b == -sqrt(2) - 1 True sage: b.degree() 2 sage: b.as_number_field_element() (Number Field in a with defining polynomial y^2 - 2, a - 1, Ring morphism: From: Number Field in a with defining polynomial y^2 - 2 To: Algebraic Real Field Defn: a |--> -1.414213562373095?) sage: b._exact_value() a - 1 where a^2 - 2 = 0 and a in -1.414213562373095? -- You received this message because you are subscribed to the Google Groups "sage-support" 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 http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
