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Manuscript Title: Resolution of many particle electrodynamics by symbolic manipulation. | ||

Authors: T.C. Scott, R.A. Moore, M.B. Monagan | ||

Program title: LIENARD | ||

Catalogue identifier: ABFX_v1_0Distribution format: gz | ||

Journal reference: Comput. Phys. Commun. 52(1989)261 | ||

Programming language: Maple. | ||

Computer: VAX 8650. | ||

Operating system: UNIX. | ||

RAM: 1000K words | ||

Word size: 32 | ||

Keywords: Computer algebra, Relativistic Many-particle theory, Time delays, Lienard-wiechert Potentials, Maple, Symbolic computation. | ||

Classification: 5. | ||

Nature of problem:For the purpose of analysis and eventual use for quantum mechanics, one desires to map relativistic physical quantities of interest, namely the time delays, Lienard-Wiechert potentials and their resulting forces, into equivalent expressions in terms of only one time variable. Since the resulting expressions cannot be written in closed form, one resorts to series expansions of these quantities in powers of 1/c. | ||

Solution method:By formulating vectors and their dot-products in a compact form, by extending Maple's functionality to handle such quantities and by exploiting Maple's efficient differentiation procedure, each of the relativistic physical quantities is expanded in a power series in 1/c to a high-order. Pade techniques are implemented in the Maple system via procedures which can convert any series into a rational polynomial or continued fraction. | ||

Restrictions:Available computer memory. Memory required grows exponentially as the series is computed to higher order. However, the series is nonetheless computed to very high order within the memory limit of the VAX (16M bytes). | ||

Running time:Varies widely, depending on the number of series coefficients calculated and the nature of the series. Increases exponentially as the series is computed to higher order. However, for the first 6 terms of the series, the amount of CPU time required was the order of a few seconds, for all cases. |

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