Opened 5 years ago

Last modified 3 years ago

## #21161 closed enhancement

# repr of NumberFields (the parents) should indicate its embedding if there is one — at Version 1

Reported by: | mkoeppe | Owned by: | |
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Priority: | major | Milestone: | sage-8.8 |

Component: | number fields | Keywords: | number field |

Cc: | vdelecroix, jipilab, cremona, tscrim, mmezzarobba, jdemeyer | Merged in: | |

Authors: | Reviewers: | ||

Report Upstream: | N/A | Work issues: | |

Branch: | Commit: | ||

Dependencies: | Stopgaps: |

### Description (last modified by )

As discussed in #21105, number fields with coercion embeddings, in particular with real embeddings, behave quite differently from those without - but there's no indication of embeddings in the print representation:

sage: K.<a> = NumberField(x^2 - 2) sage: a.parent() Number Field in a with defining polynomial x^2 - 2 sage: K.<sqrt2> = NumberField(x^2 - 2, embedding=1.4) sage: sqrt2.parent() Number Field in sqrt2 with defining polynomial x^2 - 2

I propose to change the print representation when there is an embedding, for example like this:

sage: K.<sqrt2> = NumberField(x^2 - 2, embedding=1.4) sage: sqrt2.parent() Real Number Field in sqrt2 as the root of the defining polynomial x^2 - 2 near 1.41421356237309?

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