#9411: Given points on an elliptic curve, this finds a LLL reduced
ZZ-independent
set
---------------------------------------------+------------------------------
Reporter: aly.deines | Owner: cremona
Type: enhancement | Status: needs_work
Priority: minor | Milestone:
Component: elliptic curves | Keywords: LLL, rank,
sd35.5
Work_issues: improve documentation | Upstream: N/A
Reviewer: John Cremona, Paul Zimmermann | Author: Aly Deines,
John Cremona
Merged: | Dependencies:
---------------------------------------------+------------------------------
Changes (by zimmerma):
* keywords: LLL, rank => LLL, rank, sd35.5
* reviewer: John Cremona => John Cremona, Paul Zimmermann
* status: needs_review => needs_work
* work_issues: => improve documentation
Comment:
all doctests pass on top of sage-4.8.alpha6.
However I suggest adding an example checking the relation between the
input points, {{{newpoints}}}
and the output matrix {{{U}}}:
{{{
sage: E = EllipticCurve([0, 1, 1, -2, 42])
sage: Pi = E.gens()
sage: Qi, U = E.lll_reduce(Pi)
sage: all(sum(U[i,j]*Pi[i] for i in range(4)) == Qi[j] for j in range(4))
True
}}}
And please add an example where an {{{height_matrix}}} is given, for
example
(this also gives an example where the precision matters):
{{{
sage: E = EllipticCurve([0, 1, 1, -2, 42])
sage: Pi = E.gens()
sage: H=E.height_pairing_matrix(Pi,3)
sage: E.lll_reduce(Pi,height_matrix=H)
([(-4 : 1 : 1), (-3 : 5 : 1), (-2 : 6 : 1), (1 : -7 : 1)], [1 0 0 1]
[0 1 0 1]
[0 0 0 1]
[0 0 1 1])
}}}
Also, I guess "number of bits of precision of result" should read "number
of bits of precision of intermediate computations" (in fact the precision
of the height matrix computation, which is
given as input to Pari).
Paul
PS: the doctest coverage could be 100% if we could remove the deprecate
function
{{{local_information}}}. Can this be done?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9411#comment:9>
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