Opened 5 years ago

Closed 4 months ago

# relative number field subfield method -- unclear documentation

Reported by: Owned by: dmharvey davidloeffler major sage-5.11 number fields sd51 sage-5.11.rc0 Alejandro Argaez Michiel Kosters N/A

### Description

Consider

```sage: R.<a> = NumberField(x^4 - 2*x^2 - 1)
sage: S.<i> = R.extension(x^2 + 1)
sage: S.subfield(a + i/a)
```

The S.subfield method documentation says that it constructs QQ(alpha), but this is false, I think it constructs R(alpha). In the above example, S.subfield(a + i/a) returns a number field of degree 8 over Q, whereas a + i/a has degree 4 over QQ (the minimal polynomial is x^4 - 4x^2 + 8).

### comment:1 Changed 5 years ago by mabshoff

• Milestone set to sage-3.4.1

### comment:2 Changed 4 years ago by davidloeffler

• Component changed from number theory to number fields
• Owner changed from was to davidloeffler

### Changed 4 months ago by ArgaezG

patch against sage 5.10

### comment:3 Changed 4 months ago by ArgaezG

• Authors set to Alejandro Argaez
• Report Upstream set to N/A
• Status changed from new to needs_review

### comment:5 Changed 4 months ago by ArgaezG

• Reviewers set to Michiel Kosters
• Status changed from needs_review to positive_review

I happy with changes suggested by Michiel, and he is happy with mine.

### comment:6 Changed 4 months ago by mkosters

Apply trac_5392_subfield_review.patch after trac_5392.patch​

### comment:7 Changed 4 months ago by jdemeyer

• Status changed from positive_review to needs_work

The reviewer patch needs a proper commit message, use hg qrefresh -e for this.

### comment:8 follow-up: ↓ 9 Changed 4 months ago by mkosters

@jdemeyer: is it correct now?

### comment:9 in reply to: ↑ 8 Changed 4 months ago by mstreng

• Status changed from needs_work to positive_review