Computing some classes of Cauchy type singular integrals with Mathematica software

We constructed an algorithm, SInt], for computing some classes of Cauchy type singular integrals on the unit circle. The design of SInt] was focused on the possibility of implementing on a computer all the extensive symbolic and numeric calculations present in the algorithm. Furthermore, we show how the factorization algorithm described in Conceição et al. (2010) allowed us to construct and implement the SIntAFact] algorithm for calculating several interesting singular integrals that cannot be computed by SInt]. All the above techniques were implemented using the symbolic computation capabilities of the computer algebra system Mathematica. The corresponding source code of SInt] is made available in this paper. Several examples of nontrivial singular integrals computed with both algorithms are presented.