Hi folks, In trying to improve the documentation and doctests of the database of common graphs [1], I come across what I think is rather inconsistent or perhaps wrong. First, I created the bull graph using the built-in graph generator. Then I computed the characteristic polynomial of the bull graph using the built-in characteristic polynomial method:
[mv...@sage ~]$ sage ---------------------------------------------------------------------- | Sage Version 4.4.3, Release Date: 2010-06-04 | | Type notebook() for the GUI, and license() for information. | ---------------------------------------------------------------------- sage: B = graphs.BullGraph() sage: B.characteristic_polynomial() x^5 - 5*x^3 - 2*x^2 + 3*x sage: M = B.adjacency_matrix(); M [0 1 1 0 0] [1 0 1 1 0] [1 1 0 0 1] [0 1 0 0 0] [0 0 1 0 0] sage: M.characteristic_polynomial() x^5 - 5*x^3 - 2*x^2 + 3*x I then computed the characteristic polynomial from the definition det(M - xI), where M is a square matrix, x a variable, and I the identity matrix of dimensions the same as M: sage: Id = identity_matrix(ZZ, 5); Id [1 0 0 0 0] [0 1 0 0 0] [0 0 1 0 0] [0 0 0 1 0] [0 0 0 0 1] sage: D = M - x*Id sage: D.determinant() -x^5 + 5*x^3 + 2*x^2 - 3*x As you can see, these two characteristic polynomials differ in only their signs. One can be obtained from the other by multiplying through by -1. What I would like to know is: Is there some reason for this inconsistency? Or are the two characteristic polynomials above "essentially" the same? [1] http://www.sagemath.org/doc/reference/sage/graphs/graph_generators.html -- Regards Minh Van Nguyen -- 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
