# Math 262A, Fall 1999 Homework and handouts

6/27/01: When the class was taught, everyone had accounts on a computer where all the software and worksheets were installed.  You should be able to view the PDF images of the worksheets even if you do not have Maple or the various packages written for it.  No attempt has been made to update the worksheets to current versions of Maple or the various packages.  If you want to modify or execute the worksheets, you will have to get Maple and download and install the relevant packages.  The majority of the worksheets require Koepf's software, and many of the homework worksheets contain solutions originally provided on Koepf's website.

## Class handouts

 Date Worksheet Description 10/17/99 zdemo1.mws PDF Zeilberger's Algorithm 10/17/99 gosperdemo.mws PDF Gosper Sum demo 10/25/99 koepf4.7.mws PDF Showing sums are equal, without being able to evaluate the sums in closed form 10/27/99 sum2int1.mws PDF Creative Telescoping for multisums/integrals (Zeilberger's DOUBLE_SUM_SINGLE_INTEGRAL) 10/27/99 int3.mws PDF Creative Telescoping for a triple integral (Zeilberger's TRIPLE_INTEGRAL) 10/27/99 demo1.nb (Mathematica) Demo of Kurt Wegschaider's MultiSum 10/29/99 WZdemo.mws PDF WZ method demo 11/1/99 extendedalg.mws PDF Koepf's "Extended Gosper" algorithm 11/2/99 oredemo1.mws PDF Ore Algebras, Non-Commutative Division and Euclidean Algorithm (intro to Chyzak's software) 11/8/99 hyperdemo.mws PDF Polynomial/Hypergeometric solutions of recurrences 11/11/99 resultant_lcm.mws PDF LCM, GCD of commutative and noncommutative polynomials using resultants 11/17/99 dfin_closure.mws PDF Sum/product/... of D-finite functions is D-finite 12/2/99 celine_gb.mws PDF Sums via noncommutative Grobner bases 12/2/99 gbsample1.mws PDF Using commutative Grobner bases to solve a system of polynomial equations via elimination ideals

## Homework

 Date Assigned Assignment (PDF) Answer key Description 10/6/99 Homework 1 Part 1 PDF Part 2 MWS  PDF Hypergeometric series notation 10/13/99 Homework 2 Part 1 PDF Part 2 MWS  PDF Proving simple hypergeometric identities by hand. Recurrences. Sister Celine's Method. 10/22/99 Homework 3 Part 1 PDF Part 2 MWS  PDF Gosper's Algorithm 10/29/99 Homework 4 Part 1 MWS  PDF Part 2 MWS  PDF Zeilberger's Algorithm (Zeilberger's EKHAD) 11/5/99 Homework 5 MWS  PDF WZ method. Extensions of the algorithms. 11/12/99 Homework 6 Part 1 PDF Part 2 MWS  PDF Petkovsek's Algorithm. Classical methods of solving recurrence equations: Reduction of Order. 11/19/99 Homework 7 Part 1 PDF Part 2 MWS  PDF GCD, LCM of recurrences. More classical methods of solving recurrence equations: Wronskians, Resultants, Taylor series. 11/24/99 Homework 8 Part 1 PDF Part 2 MWS  PDF Factorization of operators. Ore algebras. D-finite functions. Grobner bases. 12/10/99 Homework 9 MWS  PDF Guessing sequences (Sloane, Gfun, Rate)