REU, Summer 2008
University of Utah
Computational Algebraic Geometry
Group Photo
Note - This is a website devoted to the computational aspect of the class. As such, it covers just what we've done in the comptuer lab.
Announcements
- June 29th - All the lecture notes for the course are posted and updated, including all the code required to implement a Groebner basis program. Also, posted at the bottom of the webpage is a Maple file that implements all the code covered in the lecture notes up to a procedure that computes a Groebner basis.
- June 23rd - Today we had our first real discussion about Maple programming and we created a procedure for finding the GCD of two polynomials in one variable using Maple and some other procedures we wrote in class.
- June 17th - Today we had our first real meeting about the programming aspects of this class. We covered the very basics of programming. The notes for the talk are available below, and will be revised shortly as there were some typos and some errors in formatting. Tomorrow we will start writing programs that address the material from this class.
Contact Information
Lab Instructor - Patrick Dylan Zwick
Telephone - 801-651-8768 (Cell) 801-585-1963 (Office)
Email - zwick@math.utah.edu
Office - JWB Math Building Room 214
Office Hours - 10:00 AM - 12:00 Noon.
Computer Lab Hours - 4:00 PM - 6:00 PM MTW, 12:00 Noon - 2:00 PM Th, 12:00 Noon - 4:00 PM F.
Handouts
Introductory Lecture
Orderings Handout
Groebner Bases in Maple
Polynomial Division in Maple
Preliminaries for a Multinomial Division Procedure
Source Code
Introductory Examples
Hello World
Count
Count To
Larger
Orderings
Lexicographic Order
C++ Polynomial Class
Polynomial Class
POLYGCD and POLYPID in Maple
POLYGCD and POLYPID Source Code for Maple
A Working Multinomial Division Procedure
Working Multinomial Division
Final Preliminary Stuff for Buchberger's Algorithm
Preliminary Code for Groebner Basis
A Working Groebner Basis Procedure
Working Groebner Basis
Maple Code for Implementing a Groebner Basis Procedure
Working Maple Code
Note - All these Maple procedures need to be instantiated. So, you need to hit return on the source code for each of them in turn in order to run the final Groebner basis procedure.
Prof. Bertram's Maple Code Investigating Automated Theorem Proving
Acceleration Surface
Medians
Parallelogram
Theorem of Apollonius
Theorem of Pappus
Note - To use these you will need to use Maple version 9 or higher. Version 8 is the default version used by the math department, although versions 9 and 10 are available. To open these versions type in any terminal prompt:
Version 9 - /usr/local/bin/xmapleV9
Version 10 - /usr/local/bin/xmapleV10
Jason Underdown's C++ Code for Polynomial Algebra
Page with Link to Code
Old Classes
Knot Theory Spring, 2008
Math 2280 Spring, 2008
Math 1030 Fall, 2007
Math 2210 Summer, 2007
Talks
Notes for Math Department Talks