An Advanced Manipulator For Poisson Series With Numerical Coefficients

Details An Advanced Manipulator For Poisson Series With Numerical Coefficients An Advanced Manipulator For Poisson Series With Numerical Coefficients

Jun 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006dda....37.1502b&link_type=abstract

American Astronomical Society, DDA meeting #37, #15.02; Bulletin of the American Astronomical Society, Vol. 38, p.676

Astronomy and Astrophysics

Astronomy

Scientific paper

The availability of an efficient and featureful manipulator for Poisson deries with numerical coefficients is a standard need for celestial mechanicians and has arisen during our work on the analytical development of the Tide-Generating-Potential (TGP). In the harmonic expansion of the TGP the Poisson series appearing in the theories of motion of the celestial bodies are subjected to a wide set of mathematical operations, ranging from simple additions and multiplications to more sophisticated operations on Legendre polynomials and spherical harmonics with Poisson series as arguments. To perform these operations we have developed an algebraic manipulator, called Piranha, structured as an object-oriented multi-platform C++ library. Piranha handles series with real and complex coefficients, and operates with an arbitrary degree of precision. It supports advanced features such as trigonometric operations and the generation of special functions from Poisson series. Piranha is provided with a proof-of-concept, multi-platform GUI, which serves as a testbed and benchmark for the library. We describe Piranha's architecture and characteristics, what it accomplishes currently and how it will be extended in the future (e.g., to handle series with symbolic coefficients in a consistent fashion with its current design).

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