## Assignments

Assignment 1 (.pdf)

Assignment 2 (.pdf)

Assignment 3 (.pdf)

Assignment 4 (.pdf)

Assignment 5 (.pdf)

Bonus Assignment (.pdf)

MATH 801 Students

Course Project

Assignment 6 (.pdf)

## Solutions

Assignment 1

Question 1

Question 2

Question 3

Question 4

Assignment 2

Question 1

Question 2

Question 3

Question 4

Question 5

Assignment 3

Question 1

Question 2

Question 3

Question 4

Question 4

Question 5

Assignment 4

Question 1

Question 2

Question 3

Question 4

Assignment 5

Question 1

Question 2

Question 3

Question 4

Question 5

Bonus

Question 1a

Question 1b

Question 2

# Intro to Computer Algebra, Spring 2017

## MACM 401, MATH 701 and MATH 801

## Final Exam

The final exam starts Wednesday April 17th. Pick up from my office K 10501 between 9am and 10am. Hand in by 10am Thursday April 18th. You may put it under my office door if I am not in. Good luck. Michael Monagan.

### Office Hours

Mondays 9-10am, Tuesdays and Fridays 10-11am, Room K10501.

### Content

- (2) Algorithms for long integer multiplication and GCD computation.
- (2) Unique factorization and Euclidean.
- (2) Polynomial rings, pseudo division and polynomial GCD computation.
- (2) The Chinese remainder theorem and polynomial interpolation.
- (2) The Fast Fourier Transform and fast multiplication.
- (2) Polynomial GCD computation and the Sylvester resultant.
- (3) The P-adic Newton iteration, Hensel's lemma and Hensel lifting.
- (3) Polynomial factorization over finite fields and the integers.
- (1) Representation and differentiation of formulae on a computer.
- (2) Algorithms for rational function integration.
- (4) The Risch decision procedure for elementary function integrals.

### Textbook

*Algorithms for Computer Algebra* by Geddes, Czapor and Labahn

### Maple

We will use Maple extensively for calculations and programming in this course. SFU has a site license for Maple. Maple is installed on the PCs and MACs in the assignment lab, the CECM lab, university open labs and the library. Maple is available from Maplesoft for a very good price at Maple 18 for Canadian Students for $99. I have obtained a discount code for the class for 25% which I will give out in class.

The following Maple worksheet [ in Maple worksheet format (.mws) and
Adobe PDF format (.pdf) ] contains notes for how to use Maple.
Please read through this even if you have used Maple before.

MapleNotes.mws MapleNotes.pdf

### Handouts

January 3rd: Course Information Sheet (.txt)

January 17th: Table of integer and polynomial commands in Maple (.pdf)

April 4th: Tables of complexities for classical integer algorithms and classical quadratic algorithms.