A Combinatorial Problem on Polynomials and Rational Functions

Rational Functions Certify Combinatorial Identities

This paper presents a general method for proving and discovering combinatorial identities: to prove an identity one can present a certi cate that consists of a pair of functions of two integer variables. To prove the identity, take the two functions that are given, check that condition (1) below is satis ed (a simple mechanical task), and check the equally simple fact that the boundary conditio...

Computer Algebra of Polynomials and Rational Functions

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On Decomposition of Tame Polynomials and Rational Functions

In this paper we present algorithmic considerations and theoretical results about the relation between the orders of certain groups associated to the components of a polynomial and the order of the group that corresponds to the polynomial, proving it for arbitrary tame polynomials, and considering the case of rational functions.

Numerical solution of Troesch's problem using Christov rational functions

We present a collocation method to obtain the approximate solution of Troesch's problem which arises in the confinement of a plasma column by radiation pressure and applied physics. By using the Christov rational functions and collocation points, this method transforms Troesch's problem into a system of nonlinear algebraic equations. The rate of convergence is shown to be exponential. The numer...

Faber Polynomials for Rational Mapping Functions