On Feb 2, 2017, at 12:51 , Watson Ladd wrote:
> Dear all,
>
> I believe the q.polynomial() routine where q is a quadratic form is off by
> a factor of 2. Or at least it should be. If we take the form q of dimension
> 2 such that
> q(1, 0)=q(0,1)=1, and q(1,1)=2, then q.polynomial() is 2*x_0^2+2*x_1^2,
> which seems weird to me. Also the documentation should state we take twice
> the Gram
> matrix as the input matrix: this isn't inherently clear.
This "weirdness" has been with us since the 18th or 19th centuries :-}
I think it was cemented into the landscape by Gauss's Disquisitiones: his idea
of a binary quadratic form is one of the form
a*x^2 + 2*b*x*y + c*y^2
If you want a "less weird" (Langrange) approach, and are interested only in
binary forms, look at the class BinaryQF.
HTH
Justin
PS: Weil's "Number theory: an approach..." discusses this (from an historical
perspective).
--
Justin C. Walker, Curmudgeon at Large
Institute for the Absorption of Federal Funds
-----------
I want to die, peacefully in my sleep, like my grandfather;
not screaming in terror, like his passengers.
--
You received this message because you are subscribed to the Google Groups
"sage-support" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/sage-support.
For more options, visit https://groups.google.com/d/optout.
