CISC 822 Algebraic Algorithms
Course meeting time in Smith 102A:
2:00-3:15 Tuesdays, Thursdays.
General Description includes text, prereqs. etc.
Instructor: David Saunders,
home page includes
office location, office hours, phone #s, etc.
Viète, a source of our algebraic notational convention [JC, thanks for the link].
2005Oct20. FFT, application to poly and ints.
Homework set
Sep 27-Oct20 presentations on applications of EGcd and CRA
2005Sep22.
Sketch of exact arithmetic with real numbers.
Ideals and CRA in ZZ/mZZ.
CRA in general.
2005Sep20.
Coset arithmetic and modular systems. coset.tex handout.
The Hermite Interpolation Problem.
2005Sep15.
2005Sep13.
EEA and Fibonacci numbers, Chinese Remainder Algorithm.
2005Sep08.
The extended Euclidean algorithm with application to inversion in a finite field
2005Sep06.
Rings, Fields, Euclidean Domains.
domains.tex handout.
2005Sep01.
Polynomial multiplication and division, in principle and in implementation.
2005Aug30.
By way of introduction, sampled from linbox.pdf.
Reading assigments
-
Next up: chapter 8.
-
Read chapter 5 sections 6 thru 11 and present your section.
-
Read chapter 5 up through section 5.5
-
Read chapter 4 up through section 4.4
-
First Reading assignment:
This is rather extensive. Future readings,
will be fewer pages (but with the intent of more careful study).
Here "scan" means read through, not necessarily absorbing all details. The point is to have the general idea of what is there so that it can be consulted later if the need arises.
On the other hand, "Read" means to read more carefully, absorb what you see and synthesize it with what you already know.
- Scan Introduction. Purpose: overview of topics, see authors' general view of computer algebra, aka symbolic mathematical computation.
- Scan chapter 1. Purpose: see some sample applications for which
numerical floating point approximation won't do.
Exact or symbolic computation is needed.
- Scan chapter 2.1, 2.2. Purpose: familiarity with notation used.
- Read chapter 2.3. Purpose:
- Review classical methods of arithmetic as
a base case against which to compare faster methods studied later.
- Compare multiplication of polynomials and of integers (algorithms 2.3 and 2.4).
Tentative conclusion: integers are harder to deal with.
- Compare multiplication and division (algorithms 2.3 and 2.5). Tentative conclusion: division is more complicated than multiplication.
- Read chapter 3. Purpose: understand EEA, Extended Euclidean Algorithm.