Opened 6 years ago

Last modified 7 days ago

#22008 new defect

complex_embedding on relative number fields is inconsistent with the base field

Reported by: Edgar Costa Owned by:
Priority: major Milestone: sage-9.8
Component: number fields Keywords: complex_embedding relative
Cc: Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description (last modified by Vincent Delecroix)

Here is a minimal example, with a trivial extension.

QQx.<x> = QQ[]
L.<b> = NumberField(x^2 - x - 1)
Ly.<y> = L[];
M.<c> = NumberField(y)
print(L(b).complex_embedding())
print(M(b).complex_embedding())

-0.618033988749895
1.61803398874989

Change History (7)

comment:1 Changed 5 years ago by Jonathan Bober

sage: L.absolute_field('z')
Number Field in z with defining polynomial x^2 - x - 1
sage: M.absolute_field('z')
Number Field in z with defining polynomial x^2 + x - 1

comment:2 Changed 17 months ago by Vincent Delecroix

Description: modified (diff)
Milestone: sage-7.5sage-9.4

comment:3 Changed 17 months ago by Vincent Delecroix

As written in the documentation, the function complex_embedding returns the image of the i-th embedding into the complex numbers (default is i=0). Here is the list

sage: L.complex_embeddings()
[
Ring morphism:
  From: Number Field in b with defining polynomial x^2 - x - 1 with b = 1.618033988749895?
  To:   Complex Field with 53 bits of precision
  Defn: b |--> -0.618033988749895,
Ring morphism:
  From: Number Field in b with defining polynomial x^2 - x - 1 with b = 1.618033988749895?
  To:   Complex Field with 53 bits of precision
  Defn: b |--> 1.61803398874989
]

In particular

  • i=0 is not the complex embedding coming from the coercion embedding
  • for extension fields this list is not sorted according to the embedding of the base

I definitely agree that this is confusing. To my mind, the function b.complex_embedding() is to blame and it is a mistake to have made i=0 the default.

comment:4 Changed 13 months ago by Matthias Köppe

Milestone: sage-9.4sage-9.5

comment:5 Changed 9 months ago by Matthias Köppe

Milestone: sage-9.5sage-9.6

comment:6 Changed 5 months ago by Matthias Köppe

Milestone: sage-9.6sage-9.7

comment:7 Changed 7 days ago by Matthias Köppe

Milestone: sage-9.7sage-9.8
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