Talk:Defactoring algorithms: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 114: / Line 114: @@
 :::::: [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 21:43, 10 February 2023 (UTC)
+::::::: I am actively trying to understand what you're saying. I'm sorry I missed the point you were trying to make with the GitHub thread. Given how long and obscure it was, I should have asked you to be more specific, rather than try to guess at your intentions. It looked to me, based on a quick look over their code and Cohen's work it was based on, that their algorithm worked in a way fairly similar to my existing understanding of how HNF is computed, whereby tracking unimodular transformations is cheap. It's quite possible that their algorithm looks superficially similar but is completely different. I am not interested enough in this problem to figure it out, though, at least not now. Sorry. So again, it's fine by me for now if you want to keep both algorithms.
+::::::: But I'm still at a loss about how you've gotten the impression that column Hermite defactoring involves a pseudoinverse step. As you can see in the diagram I shared in my previous reply, it does not. The word "pseudoinverse" only appears once in the article, in a tangential footnote. On my end, "column Hermite defactoring" is a method which Dave Keenan and I developed about a year ago, and the only information about it exists on this wiki article. Are you confusing it with something else? These are the steps:
+::::::::# find the transpose A = V<sup>T</sup>;
+::::::::# find the unimodular matrix U = First[HermiteDecomposition[A]];
+::::::::# find the inverse U<sup>-1</sup>;
+::::::::# find the transpose (U<sup>-1</sup>)<sup>T</sup>;
+::::::::# take the first ''r'' rows and return.
+::::::: You can find an example of us computing the entire thing by hand in the article. No pseudoinverse is required. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 22:12, 10 February 2023 (UTC)