Opened 2 years ago

Closed 19 months ago

#26615 closed task (duplicate)

Prepare arbitrary relative extension of p-adic fields

Reported by: caruso Owned by:
Priority: major Milestone: sage-duplicate/invalid/wontfix
Component: padics Keywords: padicBordeaux
Cc: roed Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description (last modified by caruso)

Eventually Sage should be able to create an arbitrary extension (ramified or not) of any p-adic field (Qp or one of its extension). However, for speed and numerical stability, it's convenient to represent internally all p-adic fields as an Eisenstein extension over an unramified extension.

In order to conceal this, David Roe and I (discussion on zulip) propose to make the following changes:

  • we add the attributes base, ram_name (optional) and unram_name (optional) to the factory
  • we add a method standard_basis (we should find a better wording) that returns a basis of the field over Qp coming from the presentation "Eisenstein over unramified"
  • when we create a new p-adic field with base base, we compute and store the transformation matrix between the standard basis of the current field and the basis coming from the given generator and the standard basis of the base
  • when we create a new p-adic field with base base, we register a coercion map from the base to the field (this coercion map has to implement a method section... which could use the method polynomial discussed below)
  • we modify the method polynomial so that x.polynomial() returns a polynomial P over the base such that P(self.gen()) = x (this should take advantage of the transformation matrix we stored before)
  • we modify the printing mode terse so that it uses the method polynomial described above
  • if either ram_name (except for unramified extensions) or unram_name (except for totally ramified extensions) is not given, the printing mode series should raise an error

Change History (6)

comment:1 Changed 2 years ago by caruso

  • Description modified (diff)

comment:2 Changed 19 months ago by roed

  • Keywords padicBordeaux added

comment:3 Changed 19 months ago by saraedum

probably all of this will be done in #28466.

comment:4 Changed 19 months ago by caruso

  • Milestone changed from sage-8.5 to sage-duplicate/invalid/wontfix
  • Status changed from new to needs_review

Sure.

comment:5 Changed 19 months ago by caruso

  • Status changed from needs_review to positive_review

comment:6 Changed 19 months ago by chapoton

  • Resolution set to duplicate
  • Status changed from positive_review to closed
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