Opened 6 years ago

Last modified 6 weeks ago

## #22150 needs_work enhancement

# Set embedding of extension in QQ[2^(1/3)]

Reported by: | vdelecroix | Owned by: | |
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Priority: | major | Milestone: | |

Component: | number fields | Keywords: | |

Cc: | Merged in: | ||

Authors: | Vincent Delecroix | Reviewers: | |

Report Upstream: | N/A | Work issues: | see patchbot report |

Branch: | u/vdelecroix/22150 (Commits, GitHub, GitLab) | Commit: | 3360768681a2d913a9ec7987aa423278aca15cf5 |

Dependencies: | Stopgaps: |

### Description (last modified by )

Before

sage: QQ[2^(1/3)].coerce_embedding() Generic morphism: From: Number Field in a with defining polynomial x^3 - 2 To: Real Lazy Field Defn: a -> 1.259921049894873?

After

sage: QQ[2^(1/3)].coerce_embedding() Generic morphism: From: Number Field in a with defining polynomial x^3 - 2 To: Algebraic Real Field Defn: a -> 1.259921049894873?

### Change History (11)

### comment:1 Changed 6 years ago by

Branch: | → u/vdelecroix/22150 |
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Commit: | → 3360768681a2d913a9ec7987aa423278aca15cf5 |

Status: | new → needs_review |

### comment:2 Changed 6 years ago by

Status: | needs_review → needs_work |
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Work issues: | → see patchbot report |

### comment:3 Changed 6 years ago by

Needs rebase.

Moreover, there is a problem coming from

sage: sqrt(-3).is_real() True

### comment:5 Changed 6 years ago by

Milestone: | sage-7.5 → sage-duplicate/invalid/wontfix |
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Status: | needs_work → needs_review |

so we can close this as duplicate, right ?

### comment:6 Changed 6 years ago by

Hmm. currently we get:

Generic morphism: From: Number Field in a with defining polynomial x^3 - 2 To: Real Lazy Field Defn: a -> 1.259921049894873?

with target the real lazy field instead of AA.

### comment:7 Changed 6 years ago by

Milestone: | sage-duplicate/invalid/wontfix → sage-8.0 |
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Status: | needs_review → needs_work |

It would have been better if you just have read the ticket description.

### comment:9 follow-up: 10 Changed 6 years ago by

Description: | modified (diff) |
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The branch is not either. I think that #23117 was actually a bad idea. Coercion should not go through the real lazy field.

### comment:10 Changed 6 years ago by

Replying to vdelecroix:

The branch is not either. I think that #23117 was actually a bad idea. Coercion should not go through the real lazy field.

I agree that complex embeddings should go to `QQbar`

or something like that by default, but for me this is a separate issue, already tracked elsewhere.

However, having the `K[α]`

syntax create the “standard” embedding makes more sense to me (less confusing, probably breaks fewer existing things) than having it attempt to embed the number field in `α`

's parent or something like that—if that's what you have in mind.

### comment:11 Changed 6 weeks ago by

Milestone: | sage-8.0 |
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New commits:

`22150 set embedding appropriately in QQ[2^(1/3)]`