1 | | {{{ |

2 | | sage: K.<i> = QuadraticField(-1) |

3 | | sage: L = K.extension(x^2 - 6*x - 4, 'a1') |

4 | | sage: eigval = L.gen() |

5 | | sage: eigval_conj = eigval.galois_conjugates(QQbar) |

6 | | sage: f0 = hom(eigval.parent(), QQbar, eigval_conj[0]) |

7 | | sage: f1 = hom(eigval.parent(), QQbar, eigval_conj[1]) |

8 | | sage: f0(i) # wrong embedding!! |

9 | | 0.?e-54 - 1.000000000000000?*I |

10 | | sage: f1(i) # wrong embedding!! |

11 | | 0.?e-54 - 1.000000000000000?*I |

12 | | }}} |

13 | | |

14 | | As the consequence eigenvectors over QQbar could get incorrectly conjugated. In the following example from [https://groups.google.com/g/sage-devel/c/9Ss98-XKR9c devel], the eigenvectors of a matrix over `QuadraticField(-1)` are computed in two ways, one of which incorrectly returns the conjugate of some eigenvectors. |

| 1 | Eigenvectors over QQbar could get incorrectly conjugated. In the following example from [https://groups.google.com/g/sage-devel/c/9Ss98-XKR9c devel], the eigenvectors of a matrix over `QuadraticField(-1)` are computed in two ways, one of which incorrectly returns the conjugate of some eigenvectors. |