A computer algebra package for polynomial sequence recognition
Schmidt, Maxie
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https://hdl.handle.net/2142/49378
Description
Title
A computer algebra package for polynomial sequence recognition
Author(s)
Schmidt, Maxie
Issue Date
2014-05-30T16:40:58Z
Director of Research (if dissertation) or Advisor (if thesis)
Campbell, Roy H.
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
sequence recognition
polynomial sequence recognition
Stirling numbers
Abstract
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.
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