1 | | #11869 computes roots of a polynomial without using them. See #12186 for an example and for indicator code. To do: |

2 | | |

3 | | * move the "compatible embedding" code of #11869 to the beginning of the method, to avoid unnecessary root-finding |

| 1 | In {{{/sage/rings/number_field/number_field.py}}} (as per #11869), when converting number field elements, the parts |

| 2 | |

| 3 | * List of candidates for K(x) |

| 4 | * Find a common field F into which KF and LF both embed |

| 5 | |

| 6 | are independent. The first can be very slow, while the second is likely to fail. So I propose to swap these two parts. |

| 7 | |

| 8 | See #12186 for an example and for indicator code. |