Symbolic Computation Applied to Function Factorization Concept: The Rational Scalar Case

Operator theory has many applications in several main scientific research areas such as structural mechanics, aeronautics, quantum mechanics, probability theory, electrical engineering, among others. Factorization theory is closely related to the computation of singular integrals. Some progress has been achieved for some classes of functions whose properties allow the use of a particular strategy in the study of the factorization problem, but there is no general method for obtaining a factorization for a given function. In our work, we design and develop operator theory algorithms. By implementing these algorithms on a computer, using the numeric and symbolic computation capabilities of the Wolfram Mathematica computer algebra system, new tools are created, making the results of lengthy and complex calculations available in a simple way to researchers of different areas. The main goal of this talk is to present new rational factorization algorithms, which have applications in the study of the invertibility of singular integral operators and in the computation of the kernel of certain classes of operators. Several nontrivial examples computed with the algorithms are presented.