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• matrices
  • Fixed some corner cases when Matrix.eigenvals gives wrong result when multiplicity=False. (#25283 by @sylee957)

This will be added to https://github.com/sympy/sympy/wiki/Release-Notes-for-1.13.

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Fixes #25282

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- matrices
  - Fixed some corner cases when `Matrix.eigenvals` gives wrong result when `multiplicity=False`.
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Update

The release notes on the wiki have been updated.

Maybe use charpoly.all_roots(multiple=False)

Thanks for the PR! There are CI failures, which however don't seem to be related to this PR.

Have you considered using factorization of the characteristic polynomial to compute the eigenvalues with their algebraic multiplicities? That approach seems much faster according to my test on my example:

from sympy import Matrix, symbols
from time import time

dd = sd = [0] * 11 + [1]
ds = [2, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0]
ss = ds.copy()
ss[8] = 2

def rotate(x, i):
    return x[i:] + x[:i]

mat = []
for i in range(12):
    mat.append(rotate(ss, i) + rotate(sd, i))
for i in range(12):
    mat.append(rotate(ds, i) + rotate(dd, i))
mat = Matrix(mat)

t = time()
factors = mat.charpoly(symbols('lambda')).factor_list()
print('charpoly.factor_list takes:', time()-t)

t = time()
eigenvalues = mat.eigenvals()
print('eigenvals takes:', time()-t)

Output:

charpoly.factor_list takes: 0.08691191673278809
eigenvals takes: 0.9043083190917969

Once we get the irreducible factors, we can populate the eigenvalue dict with roots of the irreducible factors (CRootOf(p, i) for i = 0, ..., d-1 for a factor p of degree d, or x0 for a factor x - x0 of degree 1) and it seems that that would match the current eigenvals output.

The 2.7 failing backlog prevents the merges though

Have you considered using factorization of the characteristic polynomial to compute the eigenvalues with their algebraic multiplicities?

Once we get the irreducible factors, we can populate the eigenvalue dict with roots of the irreducible factors (CRootOf(p, i) for i = 0, ..., d-1 for a factor p of degree d, or x0 for a factor x - x0 of degree 1) and it seems that that would match the current eigenvals output.

The all_roots method already does this. The additional time compared to factor_list is taken up by root isolation for the CRootOfs.