#11827: Documentation clarifying model used in _reduce_model and
global_minimal_model
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Reporter: dianey | Owner: cremona
Type: enhancement | Status: new
Priority: trivial | Milestone: sage-4.7.2
Component: elliptic curves | Keywords: restricted,
global_minimal_model, _reduce_model
Work_issues: | Upstream: N/A
Reviewer: | Author: dianey
Merged: | Dependencies:
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Comment(by cremona):
Replying to [comment:2 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.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11827#comment:3>
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