Yes! I don’t know why this isn’t more commonly done.https://twitter.com/MathPrinceps/status/1102050069228937216 …
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Gauss knew this. (Disquisitiones Arithmeticae 152)pic.twitter.com/niJEA9w9Qz
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Replying to @robinhouston
In fact, this is a celebrated point of disagreement between Lagrange and Gauss, who held opposing views on the question of whether a quadratic form's "middle coefficient" ought, or ought not, to have a preliminary factor of 2. (These days, expert opinion agrees with Lagrange.)
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Replying to @MathPrinceps @robinhouston
My own impression, for whatever it's worth, is that this dispute is ultimately insubstantial; I think Gauss was right to maintain that his way of doing things excludes nothing that Lagrange's approach includes. But the story does get rather intricate -- perhaps surprisingly so.
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Replying to @MathPrinceps
It sounds fascinating. Is there somewhere I can read more about this?
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Yes, there is. I recall being most enlightened on this subject by a footnote -- can't quite remember which -- in Olaf Neumann's fascinating contribution to a collection of papers assessing the long-term influence of Gauss's Disquisitiones Arithmeticae:http://bit.ly/2DvOsyY
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