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