Opened 10 years ago

Closed 2 years ago

#11827 closed enhancement (worksforme)

Documentation clarifying model used in _reduce_model and global_minimal_model

Reported by: dianey Owned by: cremona
Priority: trivial Milestone: sage-duplicate/invalid/wontfix
Component: elliptic curves Keywords: restricted, global_minimal_model, _reduce_model
Cc: aly.deines, katestange, embray Merged in:
Authors: dianey Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description

_reduce_model and global_minimal_model transform a curve into its unique restricted type, but this is not explicit in the documentation.

Attachments (1)

trac_11827.patch (1.3 KB) - added by dianey 10 years ago.
comments on restricted model

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Change History (14)

Changed 10 years ago by dianey

comments on restricted model

comment:1 Changed 10 years ago by dianey

  • Cc katestange added

comment:2 follow-up: Changed 10 years ago by katestange

I think it would be helpful to describe the meaning of "restricted model" in a sentence in the documentation also.

comment:3 in reply to: ↑ 2 Changed 10 years ago by cremona

Replying to katestange:

I think it would be helpful to describe the meaning of "restricted model" in a sentence in the documentation also.

I agree. "restricted type" is not standard terminology. In my book I called the restricted models (over Q) "reduced" which is clear (I think!), but over number fields one has much more freedom: even if there is a global minimal model, one can still scale by units [u,r,s,t] with r=s=t=0 (which makes a huge difference to the appearance of the equation, even for real quadratic fields; here my choice would be, given a fixed set of fundamental units to scale so that the Discriminant lies in a certain fundamental region under the standard Euclidean embedding, up to translation by the images of the 12'th powers of units (which act discretely). I did once implement that in Magma. And then one still has to reduce modulo translations ([u,r,s,t] with u=1), where the standard thing to do is force a1,a2,a3 to be in a fixed "small" set of residues modulo 2, 3, 2.

This is tedious though not hard to implement, and then should (of course) be properly documented.

comment:4 Changed 8 years ago by jdemeyer

  • Milestone changed from sage-5.11 to sage-5.12

comment:5 Changed 7 years ago by vbraun_spam

  • Milestone changed from sage-6.1 to sage-6.2

comment:6 Changed 7 years ago by vbraun_spam

  • Milestone changed from sage-6.2 to sage-6.3

comment:7 Changed 7 years ago by vbraun_spam

  • Milestone changed from sage-6.3 to sage-6.4

comment:8 Changed 5 years ago by cremona

Most of what has been described above has been implemented: global minimal models where they exist and semi-global minimal models otherwise in #18662 (but see also #19665). Reduction via scaling by units was done earlier for real quadratic fields and has just been extended to the general case (#19689).

The above is reasonably well documented. If you do not think so, say so here, otherwise this ticket will be closed.

comment:9 Changed 3 years ago by cremona

  • Milestone changed from sage-6.4 to sage-duplicate/invalid/wontfix

comment:10 Changed 2 years ago by cremona

  • Status changed from new to needs_review

Please close (see comments)

comment:11 Changed 2 years ago by chapoton

  • Cc embray added
  • Status changed from needs_review to positive_review

please close

comment:12 Changed 2 years ago by embray

I granted you TICKET_ADMIN permissions, so if you want to do triage now you can.

comment:13 Changed 2 years ago by embray

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