2026-09-20T01:25:10Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/49378 2023-07-11 col_2142_5131 col_2142_10761 com_2142_5130 com_2142_10755 com_2142_234

Campbell, Roy H. Schmidt, Maxie 2014-05-30T16:40:58Z 2014-05-30T16:40:58Z 2014-05 2014-05-30T16:40:58Z 2014-05 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2014-04-29T20:41:45Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 4 Schmidt_Maxie.tex: 91825 bytes, checksum: 852cc9a0af65c99ffc5e267f0897f268 (MD5) Schmidt_Maxie.pdf: 3922434 bytes, checksum: 269c094200aa120337534c9bc79e28ef (MD5) GuessSequenceData.m: 24675 bytes, checksum: 935546c79321c1333fdf6cc45208ab9b (MD5) GuessPolySequenceFormulas.m: 56066 bytes, checksum: be1097b9af4ecd3601990e4e1c1cae64 (MD5) Made available in DSpace on 2014-05-30T16:40:58Z (GMT). No. of bitstreams: 5 Maxie_Schmidt.pdf: 3922434 bytes, checksum: 269c094200aa120337534c9bc79e28ef (MD5) GuessSequenceData.m: 24675 bytes, checksum: 935546c79321c1333fdf6cc45208ab9b (MD5) GuessPolySequenceFormulas.m: 56066 bytes, checksum: be1097b9af4ecd3601990e4e1c1cae64 (MD5) Schmidt_Maxie.tex: 91825 bytes, checksum: 852cc9a0af65c99ffc5e267f0897f268 (MD5) license.txt: 4063 bytes, checksum: 2b44d0697763825819e3810cc9de55bb (MD5) http://hdl.handle.net/2142/49378 en Copyright 2014 Maxie Schmidt sequence recognition polynomial sequence recognition Stirling numbers A computer algebra package for polynomial sequence recognition text Computer Science 1434 Computer Science 0112 University of Illinois at Urbana-Champaign Thesis M.S. MS:Computer Science -UIUC 10KS0112MS