Next:
Introduction
P
OLY
B
O
R
I
Tutorial
Michael Brickenstein
Date:
April 3, 2009
Introduction
Interfaces
Ring Declarations
Example
Ordering
Example
Arithmetic
Set operations
Gröbner bases
Elimination of variables
Example
How to program efficiently
Low level friendly programming
Replace algebra by set operations
Construct power sets
All monomials of degree d
Case study: Graded part of a polynomial
Simple, algebraic solution
Low level friendly, algebraic solution
Highlevel with set operations
Recursive
Decision-diagram style recursive implementation in P
OLY
B
O
R
I
Case study: Evaluation of a polynomial
Substitute a single variable
in a polynomial by a constant
Naive approach
Solution 1: Set operations
Solution 2: Linear Lexicographical Lead rewriting systems
Evaluate a polynomial by plugging in a constant for each variable
Naive approach
Solution 1:
set operations
Solution 2: Linear Lexicographical Lead rewriting systems
General Linear Lexicographical Lead Rewriting Systems
Storing polynomial data in a file
Reinterpretation of Boolean sets as subsets of the vector space
Examples
Lexicographical normal form of a polynomial against a variety
Partial Boolean functions
Building your own Gröbner basis algorithm
Adding a Generator
Interreduction
A minimal Buchberger algorithm
Estimating the number of solutions
About this document ...
2009-04-03