jamblejoe
commented
2 years ago Turns out that the eigenvalues are not expressable as radicals of polynomials with rational coefficients (or at least SymPy thinks that). See the following:
Traceback (most recent call last):
File "C:\Users\16185722\AppData\Local\Programs\Python\Python310\lib\site-packages\sympy\matrices\eigen.py", line 261, in _eigenvals_dict
eigs = {CRootOf(f, x, idx): 1 for idx in range(degree)}
File "C:\Users\16185722\AppData\Local\Programs\Python\Python310\lib\site-packages\sympy\matrices\eigen.py", line 261, in <dictcomp>
eigs = {CRootOf(f, x, idx): 1 for idx in range(degree)}
File "C:\Users\16185722\AppData\Local\Programs\Python\Python310\lib\site-packages\sympy\polys\rootoftools.py", line 352, in __new__
raise NotImplementedError("CRootOf is not supported over %s" % dom)
NotImplementedError: CRootOf is not supported over ZZ[x]
During handling of the above exception, another exception occurred:
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "C:\Users\16185722\AppData\Local\Programs\Python\Python310\lib\site-packages\sympy\matrices\matrices.py", line 376, in eigenvals
return _eigenvals(self, error_when_incomplete=error_when_incomplete, **flags)
File "C:\Users\16185722\AppData\Local\Programs\Python\Python310\lib\site-packages\sympy\matrices\eigen.py", line 173, in _eigenvals
return _eigenvals_dict(
File "C:\Users\16185722\AppData\Local\Programs\Python\Python310\lib\site-packages\sympy\matrices\eigen.py", line 264, in _eigenvals_dict
raise MatrixError(eigenvals_error_message)
sympy.matrices.common.MatrixError: It is not always possible to express the eigenvalues of a matrix of size 5x5 or higher in radicals. We have CRootOf, but domains other than the rationals are not currently supported. If there are no symbols in the matrix, it should still be possible to compute numeric approximations of the eigenvalues using M.evalf().eigenvals() or M.charpoly().nroots().Could we at least forward that error message to Julia?
EDIT: Code I ran:
from sympy import *
x = Symbol('x')
A = Matrix([[-x, 1, 0, 0, 0, 0, 0, 0, 0, 0],[ 0, -2*x, 1, 1, 0,0, 0, 0, 0, 0],[ 0, 0, -x, 0, 1, 0, 0, 0, 0, 0],[0, 0, 0, -2*x, 1, 0, 1, 0, 0, 0],[0, 0, 0, 0, -2*x, 1, 0, 1, 0, 0],[ 0, 0, 0, 0, 0, -x, 0, 0, 1, 0],[ 0, 0, 0, 0, 0, 0, -x, 1, 0, 0],[ 1, 0, 0, 0, 0, 0, 0, -2*x, 1, 0],[ 0, 1, 0, 0, 0, 0, 0, 0, -2*x, 1],[ 0, 0, 0, 1, 0, 0, 0, 0, 0, -x]])
A.eigenvals()
jverzani
Consider
This results in the error
The error message is cryptic to me so I cannot provide further insigths yet.
and
SymPy v1.1.2.