What exactly is gauss composition? I've heard of Manjul Bhargava's work, which apparently generalized gauss composition, but what is gauss composition? I would like to add that I've been thinking about quadratics polynomials with rational coefficients, and I discovered this composition law that turns the set of quadratic polynomials into an abelian group. Let f(x)=ax^2+bx+c and g(x)=zx^2+dx+r be two quadratic polynomials with rational coefficients. Denote the set of quadratic polynomials with rational coefficients by T{x}. Then the composition law %:T{x} X T{x}--->T{x} defined by f(x)%g(x)=azx^2+bdx+cr turns T{x} into an abelian group. This has probably already been figured out before, but an interesting note!(adsbygoogle = window.adsbygoogle || []).push({});

Sincerely,

mathguy

EDIT:(simple explanations please, thank you.)

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Gauss Composition? and a naive composition law

**Physics Forums | Science Articles, Homework Help, Discussion**