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: |
Description (last modified by )
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) andunram_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 methodsection
... which could use the methodpolynomial
discussed below) - we modify the method
polynomial
so thatx.polynomial()
returns a polynomialP
over the base such thatP(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 methodpolynomial
described above - if either
ram_name
(except for unramified extensions) orunram_name
(except for totally ramified extensions) is not given, the printing modeseries
should raise an error
Change History (6)
comment:1 Changed 2 years ago by
- Description modified (diff)
comment:2 Changed 19 months ago by
- Keywords padicBordeaux added
comment:3 Changed 19 months ago by
comment:4 Changed 19 months ago by
- 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
- Status changed from needs_review to positive_review
comment:6 Changed 19 months ago by
- Resolution set to duplicate
- Status changed from positive_review to closed
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probably all of this will be done in #28466.