Chapter 5 - Programming the Partition Method for a Power Series Expansion

Abstract

A programming methodology is concerned with: (1) the analysis of a problem by developing algorithms based on modern programming techniques, (2) designing programs in appropriate languages and (3) implementation on a suitable platform. Chapter 5 completes the programming methodology for the partition method for a power series expansion that began with the presentation of the BRCP algorithm in Chapter 3 and continued with the general theory of partition method for a power series expansion in the previous chapter. The results of these chapters are employed to produce two C/C++ codes, which generate the coefficients in a general symbolic form that can be introduced into Mathematica. Both programs are fully listed in Appendix B, where they appear as Programs 1 and 2. The first program calculates the coefficients Dk and Ek in Theorem 4.1 for k ranging from unity to a specified number, while the second calculates only one coefficient, which is useful when the number of partitions becomes too large. By assigning values to the coefficients of the inner and outer power series, the coefficients of the resulting power series expansion can be calculated using either the integer arithmetic routines in Mathematica, thereby avoiding rounded-off decimal values, or they can be evaluated via the symbolic routines to yield polynomial coefficients.