`minpoly()` returns incorrect minimal polynomial over RR but correct answer over QQ

[Newtech66]

Steps To Reproduce

In SageCell,

H = matrix(RR,
       [[-3,  0,  0, -1,  0, -1, -1,  0],
       [ 0, -1, -1,  0, -1,  0,  0, -1],
       [ 0, -1, -1,  0, -1,  0,  0, -1],
       [-1,  0,  0,  1,  0, -1, -1,  0],
       [ 0, -1, -1,  0, -1,  0,  0, -1],
       [-1,  0,  0, -1,  0,  1, -1,  0],
       [-1,  0,  0, -1,  0, -1,  1,  0],
       [ 0, -1, -1,  0, -1,  0,  0,  3]]
      )
cp = H.charpoly()
mp = H.minpoly()
print('Characteristic polynomial:', cp)
print('Minimal polynomial:', mp)
print(H^5 + 2*H^4 - 20*H^3 - 24*H^2 + 96*H)

outputs

Characteristic polynomial: x^8 - 24.0000000000000*x^6 + 16.0000000000000*x^5 + 144.000000000000*x^4 - 192.000000000000*x^3
Minimal polynomial: x^8 - 24.0000000000000*x^6 + 16.0000000000000*x^5 + 144.000000000000*x^4 - 192.000000000000*x^3
[0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000]
[0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000]
[0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000]
[0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000]
[0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000]
[0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000]
[0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000]
[0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000]

Defining H with QQ correctly returns the above polynomial as the minimal polynomial.

Expected Behavior

I should get the correct minimal polynomial x^5 + 2*x^4 - 20*x^3 - 24*x^2 + 96*x in RR.

Actual Behavior

I only get the correct answer in QQ.

Additional Information

This is also somewhat strange to me because the matrix given has some eigenvalues which are not in QQ (it has an eigenvalue 2*sqrt(3)).

Environment

• Sage Version: SageCell

Checklist

• I have searched the existing issues for a bug report that matches the one I want to file, without success.
• I have read the documentation and troubleshoot guide

[user202729]

not very surprising, minimal polynomial is not particularly well-defined over inexact rings. Somewhat relevant pull request #39017 , might be adapted to matrices.