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 |
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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: |
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)
Change History (14)
Changed 10 years ago by
comment:1 Changed 10 years ago by
- Cc katestange added
comment:2 follow-up: ↓ 3 Changed 10 years ago by
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
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
- Milestone changed from sage-5.11 to sage-5.12
comment:5 Changed 7 years ago by
- Milestone changed from sage-6.1 to sage-6.2
comment:6 Changed 7 years ago by
- Milestone changed from sage-6.2 to sage-6.3
comment:7 Changed 7 years ago by
- Milestone changed from sage-6.3 to sage-6.4
comment:8 Changed 5 years ago by
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
- Milestone changed from sage-6.4 to sage-duplicate/invalid/wontfix
comment:10 Changed 2 years ago by
- Status changed from new to needs_review
Please close (see comments)
comment:11 Changed 2 years ago by
- Cc embray added
- Status changed from needs_review to positive_review
please close
comment:12 Changed 2 years ago by
I granted you TICKET_ADMIN
permissions, so if you want to do triage now you can.
comment:13 Changed 2 years ago by
- Resolution set to worksforme
- Status changed from positive_review to closed
comments on restricted model