Polynomial Algorithms in Computer Algebra
Course Information
Prerequisite:
Basic knowledge about abstract algebra, linear algebra, discrete mathematics and C language
Objectives
Introduction of algebraic structures, algorithms and computer algebra systems.
Required Text
Polynomial Algorithms in Computer Algebra, Franz Winkler,1996.
First Leaves: A Tutorial Introduction to Maple V, Char, Geddes,etc. 1992.
Grading Policies
Your grade will be based on attendance(30%) and homework (70%). Homework assignments must be submitted on time to receive credit.
Grading scale (+/- grades may be assigned at my discretion):
A 90-100 B 80- 89 C 70- 79 D 60- 69 F 0- 59
Final Exam
: Tuesday, February 9, 3:00-4:30.
Last day to drop this class
: November 20
Course Topics (subject to change)
An general introduction to computer algebra and computer algebra systems
Integer, polynomials, quotient fields, finite fields
Chinese Remainder Theorem and Hensel Lemma
Polynomial remainder squences and squarefree factorization
Polynomial factorization over finite field and integers
Solving linear systems by Bareiss algorithm
Introduction of Hankel matrices
Grobner basis and Wu-Ritt Characteristic Set method
Indefinite summation
Course Index
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