Talk:Binary quadratic form

Assessment comment

The comment(s) below were originally left at Talk:Binary quadratic form/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

The class number in binary quadratic forms should be same as the class number in the ideal classes of algebraic number fields, so the connection should be pointed out.Bergv (talk) 01:54, 19 October 2009 (UTC)

Last edited at 01:54, 19 October 2009 (UTC). Substituted at 01:48, 5 May 2016 (UTC)

Requested move 27 February 2017

Binary quadratic form → Integral binary quadratic form – most people searching for "binary quadratic form" are actually looking for information about a specific type of binary quadratic form, namely, one whose coefficients are integers. I just went through all the links at the "what links here" page and found that most other pages explicitly state that the quadratic forms in question have integer coefficients, and most of the remaining ones do this implicitly. An exception is the page Paul Bernays -- he did in his work consider binary quadratic forms with more general real number coefficients. Standard textbooks, such as "Binary Quadratic Forms" by Duncan Buell, consider forms with only integer coefficients. Recent redirect traffic to this page only came through "reduction theory of forms", "class number (binary quadratic forms)" and "composition of forms". Before I edited the page this week, the brief mentions of these topics here only concerned integral forms. In my research on binary quadratic forms, I have seen one paper out of dozens discuss reduction of non-integral forms, and I have never seen any mention of composition of forms that weren't integral. Planetmath.org titles their main page for quadratic forms "integral binary quadratic forms" (although that page has some broken functionality). If the move I am suggesting seems sensible and is made, then "binary quadratic form" should redirect to this page and the hatnote should indicate that people searching for binary quadratic forms with other types of coefficients should see quadratic form. Barryriedsmith (talk) 23:35, 27 February 2017 (UTC)

• Weak oppose I agree that this article should be only about integral binary forms. In fact, there are very few results on binary quadratic forms with non-integer coefficients that are specific to the binary case. However the proposed title is very long, and would not be easily found by a direct search (without passing through a redirect). Therefore, I propose to keep the present title, and simply add the hatnote

This article is about binary forms over the integers. For for other binary forms, see Quadratic form.

Clearly a change of the lead would be needed, but it would also needed if the move is done. D.Lazard (talk) 15:00, 28 February 2017 (UTC)