Computing some classes of Cauchy type singular integrals with Mathematica software. We construct an algorithm, [SInt], for computing some classes of Cauchy type singular integrals on the unit circle. The design of [SInt] is 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 [A. C. Conceição et al., in: Operator Theory: Advances and Applications 202, 87–109 (2010; Zbl 1208.47017)] allows 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
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References in zbMATH (referenced in 3 articles , 1 standard article )
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- Conceição, Ana C.; Pereira, José C.: Exploring the spectra of some classes of singular integral operators with symbolic computation (2016)
- Conceição, Ana C.; Marreiros, Rui C.: On the kernel of a singular integral operator with non-Carleman shift and conjugation (2015)
- Conceição, Ana C.; Kravchenko, Viktor G.; Pereira, José C.: Computing some classes of Cauchy type singular integrals with Mathematica software (2013)