Applications of Bezout Matrices
The notion of Bezout matrix is an essential tool in studying broad variety of subjects: zeroes of polynomials, stability of differential equations, rational transformations of algebraic curves, systems of commuting non-selfadjoint operators, boundaries of quadrature domains etc. We present the package of programms which:
- compute the Bezout matrix of two given polynomials;
- determine whether two given polynomials have a common zero or not;
- determine the number of common zeroes of two given polynomials;
- determine the number of zeroes of a given polynomial in the upper half-plane, in the lower half-plane and the number of its real zeros;
- compute the polynomial that defines the image of the complex line under the rational transformation defined by three given polynomials;
- compute the polynomial that defines the image of a given Riemann sphere under the rational transformation defined by three given polynomials;
- compute the polynomial that defines the boundary of the quadrature domain as the image of the unit disk under the transformation defined by a given polynomial;
- efficiently compute the inverse of the Bezout matrix of two given polynomials if zeroes of one of the polynomials are known;
- compute the vessel which is the image of a given operator node under a given rational transformation;
- compute the signature of a given matrix.
