Martin Rubey wrote: > Jason Grout <[EMAIL PROTECTED]> writes: > >>> Why is your coefficients different from mine? >> >> I specifically asked for the coefficient of "x". You just asked for the >> coefficients, but didn't specify what variable was the variable of your >> polynomial. > > OK, I think I understand now: Sage interprets the x as element of > SymbolicRing, > since it does the coercion afterwards... > > Being used to FriCAS, I thought that characteristic_polynomial('x') would > return a polynomial in x with coefficients from Symbolic Ring. It doesn't > really, since it coerces the x into an element of SymbolicRing. > > Oh dear.
Good point. I hadn't thought about it that way before. Yes, that is what seems to be happening: sage: f = function('f') sage: m = matrix([[f(i,j) for j in range(2)] for i in range(2)]) sage: R.<x> = SR[] sage: type(x) <type 'sage.rings.polynomial.polynomial_element.Polynomial_generic_dense'> sage: g=m.characteristic_polynomial(x) sage: g (f(0, 0) - x)*(f(1, 1) - x) - f(0, 1)*f(1, 0) sage: type(g) <class 'sage.calculus.calculus.SymbolicArithmetic'> I think SR is somewhat viral in this regard. Anything that has to do with SR gets converted to SR, with the current implementation. I think the symbolics rewrite will make this a lot better, though. Jason --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---