Timeline for Signature of a quadratic form

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Apr 28, 2017 at 0:45	comment	added	Will Jagy		Denis, I think you are right. I am looking at my quadratic forms books, it seems Hermite reduction is far more specific thing. I saw your sum as part of that and incorrectly put his name on this general method.
Apr 27, 2017 at 20:42	comment	added	Denis Serre		@Will. There is one difficulty, in that you can at some point have to reduce a quadratic form with no square at all. But then the form represents zero and you just look for a hyperbolic plane. I don't know the terminology Hermite (though he was a French mathematician). Perhaps the method has different names in different countries.
Apr 27, 2017 at 16:52	comment	added	Will Jagy		Denis, could you please comment on my answer? Your method is what I know from books on integral quadratic forms, and I associate it with the name Hermite. Really just repeated completing the square(s) until all terms are exhausted, and not difficult. Then in 2015, on MSE, I came across the method in my answer, and started asking about it math.stackexchange.com/questions/1388421/… My feeling is that they are really the same method, minor difference in finding either $P$ or $P^{-1}$ first in $P^T AP=D$
Apr 27, 2017 at 6:07	history	answered	Denis Serre	CC BY-SA 3.0