Introduction to nonlinear nanlysis of algebraic equations

Here we demonstrate two simplest methods of solution of polynomial equations, based on constructing a convex polygon. The first method allows to find approximate roots of a polynomial by means of the Hadamard polygon. The second one allows to compute branches of an algebraic curve near its singular point and near infinity by means of the Newton polygon and to draw sketches of real algebraic curves in the plane. Computer algebra algorithms are specified, which essentially simplify these calculations.