On Feb 24, 2012, at 08:04 , Jacob Hicks wrote:
> When I run:
>
> sage: q = QuadraticForm(ZZ,2,[3,2,5])
> sage: q.polynomial()
> 6*x0^2 + 4*x0*x1 + 10*x1^2
>
> I would expect to get half of this result, which is the quadratic form
> as a polynomial. The doc tests say this is what the behavior should
> be, but I don't understand why. Is this actually the desired behavior
> and if so what am I misunderstanding?
You're in the middle of a centuries-old debate, stemming from the
Lagrange-Gauss smackdown (or maybe it was Legendre; it's been a while). The
issue stems from the desire to equate quadratic forms and symmetric matrices
("b*x0*x1" vs "b/2*x0*x1+b/2*x1*x0"). If you don't use the above, you end up
having to deal with the ring ZZ[1/2]. This is discussed in the Wikipedia
article on quadratic forms (and in other places, like Cassels' "Rational
Quadratic Forms").
HTH
Justin
--
Justin C. Walker, Curmudgeon at Large
Director
Institute for the Enhancement of the Director's Income
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