Closed 3ef7b55e-0755-45b8-beb1-59dea5994ae8 closed 14 years ago
Changed author from cjh to Chris Hall
Reviewer: John Cremona
My student David Roberts implemented this in Magma, following the Mulders & Storjohann paper, and used it in the implementation of a lattice-based method for point-finding on curves over function fields F_q(T). So I am familiar with the algorithm. But when I gave a talk about the method in Leiden in 2006, I found that Hendrik Lenstra had never heard of Weak Popov Form, though his brother Arjen Lenstra's thesis (which dates back to the original LLL paper, so they could factor multivariate polynomials) had something entirely equivalent under another name. From what I remember, the upshot is that for most constant fields one might be better off using theory to bound degrees and then using linear algebra over the ground field.
The patch applies fine to 4.4.3 and long tests in the two files touched pass.
Otherwise it looks ok to me, given that the tests work, but I have not had time to go through the important part of the code in great detail and have no more time right now.
Work Issues: minor
Attachment: trac_9069.patch.gz
Latest version of the patch incorporates minor changes made in response to Cremona's comments. Specifically, responses to his respective comments are:
Fine! Patch applies fine to 4.4.4.alpha1.
Changed work issues from minor to none
Merged: sage-4.5.2.alpha0
Changed author from Chris Hall to Christopher Hall
unique name please
Implement weak Popov form for a matrix over a rational function field k(t)
CC: @burcin @koffie @mminzlaff
Component: linear algebra
Author: Christopher Hall
Reviewer: John Cremona
Merged: sage-4.5.2.alpha0
Issue created by migration from https://trac.sagemath.org/ticket/9069