Originally the NORT package was created for building Poincare -- Dulac normal forms (Edneral,Khrustalev,1985,1992) till fixed order. It is written in Standard LISP and contains procedures for treating truncated multivariate power series of an arbitrary dimension. Besides of procedures for arithmetic operations with such series there are special procedures for the creation of normal forms and procedures for substitutions, calculations of roots, for differentiating, for printing and for inverting multivariate power series. The package can be used as a separate unit under a Standard Lisp environment or as a REDUCE package.
Complex numerical coefficients of the truncated power series may be evaluated in three different arithmetics: precision rational, floating point and approximate rational (Rodionov A.Ya,in progress), in according to the user's choice. Separately user may choose a representation of numbers (in a floating point or in a rational form) for output. This output has a REDUCE acceptable form, but REDUCE's internal procedures are not used by the NORT.
The program uses a recurrent polynomial representation separated in each order of the stored series. There is a compact enough use of memory. So for 8 - dimensional problem we managed to treat pieces of series with 150000 elements on computer with 64 Mbyte of RAM.
References
Edneral, V.F., Khrustalev, O.A. (1985) The Normalizing Transformation for Nonlinear Systems of ODE. The Realization of the Algorithm; Proceedings of the International Conference on Computer Algebra and its Application in Theoretical Physics (USSR, Dubna, September 1985). Dubna: JINR publ., 219--224. In Russian.
Edneral, V.F., Khrustalev, O.A. (1992) Program for Recasting ODE Systems in the Normal Form; "Programmirovanie" (Sov. J. of Programming), # 5, 73--80. In Russian.
Edneral, V.F. (1993) Computer Generation of Normalizing Transformation for Systems of Nonlinear ODE; Proceedings of the 1993 International Symposium on Symbolic and Algebraic Computation (Kiev, Ukraine, July 6-8, 1993). N.Y., ACM Press, edited by M.Bronstein, pp. 14-- 19.
Vasiliev N.N., Edneral V.F., (1995) About Constructing Canonical Basis for the Ring of Formal Power Series; The Abstracts of the conference "Computer Methods of Celestial Mechanics (S.-Petersburg, Russia, October 17--20, 1995)", pp. 72--73. In Russian.
Edneral V.F., (1995) To the Question of Multidimensional Power Series Solving; The Abstracts of the PoSSo-95 "PoSSo Open Workshop on Applications of PoSSo and Real Solving, (Iraklio, Greece, June 7--10, 1995)", p. 34.
