A computer algebra package for polynomial sequence recognition

The software package developed in the thesis research implements functions for the intelligent guessing of polynomial sequence formulas based on user-defined expected sequence factors of the input coefficients. We present a specialized hybrid approach to finding exact representations for polynomial sequences that is motivated by the need for an automated procedures to discover the precise forms of these sums based on user guidance, or intuition, as to special sequence factors present in the formulas. In particular, the package combines the user input on the expected special sequence factors in the polynomial coefficient formulas with calls to the existing functions as subroutines that then process formulas for the remaining sequence terms already recognized by these packages. The factorization--based approach to polynomial sequence recognition is unique to this package and allows the search functions to find expressions for polynomial sums involving Stirling numbers and other special triangular sequences that are not readily handled by other software packages. The thesis contains a number of concrete, working examples of the package that are intended to both demonstrate usage and to document its current sequence recognition capabilities.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• Schmidt, Maxie

Contributors dc:contributor

• Campbell, Roy H.

• sequence recognition
• polynomial sequence recognition
• Stirling numbers

Statement dc:rights

• Copyright 2014 Maxie Schmidt

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/49378

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/49378