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2019-01-31 21:30:24 +0200	commented answer	Factorize characteristic polynomial in SR base ring Awesome thanks. @nbruin if you don't mind, I was missing the possibility for this command: `SR('x')`. This tells Sage basically to use the unknown `x` within the SR field? Or how should I interpret it? 'Cause it is not completely immediate for me that I am using a base ring class as a method, unless I think of it as a short way to instantiate a variable of that class (something like `:` in `C++` class definers).
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2019-01-31 18:52:23 +0200	asked a question	Factorize characteristic polynomial in SR base ring I am total newbie to SAGE so this question might be trivial. How can I factorize the characteristic polynomial obtained by a symbolic matrix in SAGE 8.6? Is there a workaround the fact that `factor()` is not defined on the base ring `SR` which is the one inherited from the symbolic matrix? For example I have in a SAGE/Jupyter notebook something like: `a,b,c = var('a','b','c') M = Matrix(SR,3,3) M[0] = [a, -b, 0] M[1] = [c, a+b, 0] M[2] = [0, 0, 1] e = M.eigenvalues() f = M.charpoly() factor(f)` The last instruction raises a `NotImplementedError` as expected from the fact that `factor` is not defined on `SR`... In my real problem I am computing characteristic polynomials of large (8x8) symbolic matrices and I would like to get at glance all the factors, so as to quickly isolate negative real roots and instead easily discuss conditions for existence and sign of symbolic ones.