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\centerline{\bf POISSON SERIES PROCESSOR }
\centerline{\bf AND ITS APPLICATION IN CELESTIAL MECHANICS }
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\centerline{T.~V.~IVANOVA}
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\centerline{\it Institute of Theoretical Astronomy of the Russian
Academy of Sciences, St.Petersburg}
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\centerline{\it E-mail 1197@iipah.spb.su}
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A specialized Poisson Series Processor (PSP) is proposed.
It is a typical software for the implementation of analytical
algorithms of Celestial Mechanics. The PSP is a new
realization and development of well known Universal Poisson
Processor (Tarasevich,~1979; Ivanova,~1979; Babaev et al.,~1980)
which has been existed on the BESM-6 computer. The PSP is
designed for manipulating long Poisson (polynomial-trigonometric)
series with the rational or floating-point coefficients.
The Poisson series are the main mathematical objects of
analytical celestial mechanics but the PSP is by no means
restricted to this field of application.
All the programs of the PSP are general and may be used in
theoretical mechanics and physics.

    The most important characteristics of the PSP are as
following:

\noindent 1)~The PSP is written in standard FORTRAN-77 and
practically all the subroutines are machine-independent.

\noindent 2)~The PSP runs under MS-DOS on IBM~PC and under UNIX
on a Sun workstation.

\noindent 3)~The PSP uses the linked list representation of the
series for the dynamical memory allocation.

\noindent 4)~The coefficients of Poisson series are rational or
floating-point numbers. In order to increase the range of the
representation of the rational coefficients the double precision
floating-point numbers for exact operations on these
coefficients have been used. At present the computer operations
on arbitrary length integer and rational numbers are working out.

\noindent 5)~The PSP has no restriction on the number of
polynomial and angular variables and on the ranges of the
associated indices which may be prescribed by the user for
any specific problem.

\noindent 6)~Each term of the series is characterized by the
analytical order of smallness which is defined as the sum of the
polynomial indices multiplied by the weight functions of the
corresponding variables.

\noindent 7)~All the computer operations on the series are formal.
The smallness of a term is determined by its analytical order of
smallness and the numerical estimation of its coefficient.

\noindent 8)~The list of basic operations of the PSP includes
the standard arithmetic operations on series, the partial
differentiation and integration with respect to polynomial
and trigonometric variables, the total differentiation and
integration with respect to time under the assumption that all
the trigonometric variables are linear functions of the time
with numerical values for the frequencies, raising to any integer,
rational and real powers, binomial and Taylor expanding up to
prescribed order, substituting other series in place of power
and trigonometric variables, fast evaluating of the series in
fixing values of some
variables, converting of the series, different sortings and
selectings, etc. The PSP allows to realize input and output of
series in any format or unformatted mode and to type them in the
natural mathematical form.

\noindent 9)~The PSP allows to user to write own procedures
without any difficulty.

\noindent 10)~Due to the hierarchical architecture of the PSP
it is possible easily to modify the system for the objects
slightly different from standard Poisson series (for instance,
for manipulating the exponents instead of the trigonometric
functions or for changing the type of coefficients, etc.) or
for other representation of Poisson series in the computer's
memory. Also it is easily to adapt the PSP for other computers.
\noindent 11)~A special input language is working out by
E.~Yu.~Pariiskaya.
It will allow to user to write his task in the form similar
to the mathematical one by introducing new data types such as
power and trigonometric variables, series and rational numbers
and by creating algebraic library functions.

    The Keplerian Processor and analytical generator of special
celestial mechanics functions based on the PSP are proposed too.
They may be regarded as an illustration of practical application
of the PSP. These systems are designed for implementing
the expansions of the most important mathematical functions for
celestial mechanics such as Legendre and Gegenbauer polynomials,
Bessel and spherical functions, etc.,
for constructing the expansions of the elliptic motion functions
of the unperturbed two-body problem and the expansions of the
typical celestial mechanics functions such as Hansen
coefficients, Newcomb operators, Kaula inclination functions and
their generalizations, etc. The software of this sort is the
necessary tool for the construction of general perturbation
solutions in all analytical celestial mechanics problems.

    The most powerful test of the PSP was to solve the problem on
the transformation of terrestrial dynamical time to barycentric
dynamical time. The analytical complete planetary theory VSOP~87
(Bretagnon,~1987) and Lunar theory ELP~2000 (Chapront-Touse and
Chapront,~1983) were used to realize this analytical
transformation.

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\centerline{\bf References}
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\noindent{\bf Babaev I.~O., Brumberg V.~A., Ivanova T.~V.,
Skripnichenko V.~I., Tarasevich}

      {\bf S.~V. and Vasiliev N.~N.}~:~1980, ``Universal
Poissonian Processor (UPP)'', {\it Internat.

      Conf. on Systems and Techniques of
     Analytical Computing and their Applications in

      Theoretical Physics}, 80, Dubna

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\noindent{\bf Bretagnon P., Francou G.}~:~1988, ``Planetary
theories in rectangular and spherical

variables. VSOP~87 solutions'' {\it Astron.
Astrophys.}, {\bf 202}, 309
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\noindent{\bf Chapront-Touze M., Chapront J.}~:~1983, ``The
Lunar ephemeris ELP~2000'' {\it Astron.
Astrophys.}, {\bf 124}, 50
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\noindent{\bf Ivanova T.~V.}~:~1979, ``Keplerian processor and
analytical generator of celestial

mechanics functions''
{\it Algorithms of Celestial Mechanics}, {\bf 28}, ITA, Leningrad
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\noindent{\bf Tarasevich S.~V.}~:~1979,``UPP -- Universal
Poissonian Processor'', {\it Algorithms of
Celestial

Mechanics}, {\bf 27}, ITA, Leningrad
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