CS 680-501 Computer Algebra II Syllabus
- Course Description
This course continues the survey of fundamental ideas in symbolic
mathematical computation. Topics typically covered include: p-adic
lifting, polynomial factorization, solution of systems of polynomial
equations, Grobner bases. Additional topics may include: polynomial
real and complex zero isolation, the CAD algorithm and its application
to quantifier elimination, algorithms for symbolic integration.
- Course Objective
To obtain an understanding of the design, implementation, and
analysis of computer algebra algorithms. More specifically students
will become familiar with the underlying mathematics and algorithm
design, implementation and analysis of algorithms for the exact
solution of polynomial equations. Students
should be able to use, implement and analyze the fundamental algorithms
for polynomial factorization, root isolation and refinement, and the
exact solution of systems of polynomial equations using Groebner bases
and resultant techniques.
The course will require several computational assignments utilizing
Maple, and several programming assignments using both Maple and C
- Computer Algebra I.
Office: 271 Korman Center
office hours: MW 1-3 and T 4-6, additional hours by appointment.
- W 6:00-9:00 in Commonwealth 306
Keith Geddes, Stephen Czapor, and George Labahn
Algorithms for Computer Algebra.
Kluwer Academic Publishers, 1992.
- Interpolation and Hensel Lifting
- Polynomial factorization
- Root Isolation and Refinement
- Solving Systems of Equations
- Groebner Bases
- Quantifier Elimination
- Homework assignments (five) 50% (10% each)
- Programming project 50%
Created: 3/27/00 by firstname.lastname@example.org