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