Compute the Bezoutian of two polynomials defined over a common base ring. This is defined by
and has size defined by the maximum of the degrees of \(f\) and \(g\).
a quadratic form over \(R\)
sage: R = PolynomialRing(ZZ, 'x') sage: f = R([1,2,3]) sage: g = R([2,5]) sage: Q = BezoutianQuadraticForm(f, g) ; Q Quadratic form in 2 variables over Integer Ring with coefficients: [ 1 -12 ] [ * -15 ]
Constructs the direct sum of \(r\) copies of the quadratic form \(xy\) representing a hyperbolic plane defined over the base ring \(R\).
sage: HyperbolicPlane_quadratic_form(ZZ) Quadratic form in 2 variables over Integer Ring with coefficients: [ 0 1 ] [ * 0 ]