Talk:Quadratic Frobenius test

Quadratic Frobenius Test

This page discusses the specific "Quadratic Frobenius Test" which is a specific algorithm which includes a quadratic Frobenius test. The naming conventions being used make this distinction extremely subtle (e.g. 2018 edits by User:Cherkash�). It is debatable whether this test deserves a separate page at all, versus a section of the Frobenius pseudoprime page. Another alternative is to change this page to describe a generic quadratic Frobenius test (e.g. section 3.6.2 of Crandall and Pomerance 2005) and put this test in as a separate section. This seems like a good solution to me, and solves the naming issue. DAJ NT (talk) 18:31, 13 November 2018 (UTC)

The article's lead says it's a test, not an algorithm that's – so the distinction between "generic" QFT vs. "specific" QFT as you alleged in your first sentence above, DAJ NT, is not clear at all from the article in its current shape. Perhaps it should be further edited to make your point above clear? If indeed we are talking about just a specific algo/implementation of a more generic test, then a strong argument could be made about the subject not deserving a separate page – so I would definitely support your suggestion above. cherkash (talk) 14:31, 14 November 2018 (UTC)

The lead also says "It should not be confused with the more general Frobenius test using a quadratic polynomial" -- i.e. a quadratic Frobenius test. The page was created and continues to describe a specific algorithm described in one of Grantham's papers, that includes steps not related to the Frobenius test but let Grantham meet probabality goals. It looks like this naming distinction has been going on since the article's creation.

I think there is merit in having this be a generic page. Generic descriptions can be found in Grantham (2000), Prime Numbers: A Computational Perspective by Crandall and Pomerance (2005), and Loebenberger (2008). There have been at least three papers extending the idea (EQFT, SQFT, MQFT), but the heart of all of them is a Frobenius test using a simple quadratic. I believe this also encompasses more recent tests such as those described on arXiv from Khashin (2013,2016/2018) and Underwood (2017), each of which are specific algorithms for a quadratic Frobenius test.

I'll put it on my todo list unless someone else gets to it. DAJ NT (talk) 19:05, 14 November 2018 (UTC)

This sounds good. I do believe a generic page is more appropriate then in view of what you mentioned above. cherkash (talk) 21:47, 15 November 2018 (UTC)

Need to define mod with two arguments

This notation $whatever\,{\bmod {\,}}{\big (}n,x^{2}-bx-c)$ is not defined here, or anywhere on Wikipedia that I can see. MathPerson (talk) 17:48, 2 April 2019 (UTC)