ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 20 Mar 2020 08:22:43 +0100Polynomials over Quaternions via Determinantshttps://ask.sagemath.org/question/50310/polynomials-over-quaternions-via-determinants/I currently trying to get polynomials over quaternions out of determinants of matrices. Example giving below:
> Q.<i,j,k> = QuaternionAlgebra(SR, -1, -1)
> A=matrix(4,4,[0,j,0,j,j,0,0,j,0,0,0,0,j,j,0,0])
> I=matrix.identity(4)
> P=(j\*A-x\*I)
> P.det()
But it doesn't work. Any idea?draksFri, 20 Mar 2020 08:22:43 +0100https://ask.sagemath.org/question/50310/Factorize characteristic polynomial in SR base ringhttps://ask.sagemath.org/question/45249/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.maurizioThu, 31 Jan 2019 18:26:46 +0100https://ask.sagemath.org/question/45249/convert charpoly()-generated characteristic polynom to symbolic expressionhttps://ask.sagemath.org/question/42486/convert-charpoly-generated-characteristic-polynom-to-symbolic-expression/A characteristic polynom that is generated by the procedure charpoly() has the type:
> sage.rings.polynomial.polynomial_ring.PolynomialRing_field_with_category.element_class.
How can I convert it to one of type 'symbolic expression' without doing 'copy and paste'?
bekalphSun, 03 Jun 2018 19:33:33 +0200https://ask.sagemath.org/question/42486/