AM511b Notes

Robert M. Corless

March 13, 1995

• Contents
• Announcements
• Key ideas from last time
• References for today's lecture
• Gröbner bases and systems of polynomial equations
  • Definitions
• Recipes
  • Recipe 0---Main property
  • Recipe 1---existence of solutions
  • Recipe 2---existence of a finite number of solutions
  • Recipe 3---reduction to triangular form
  • Recipe 4---the Shape Lemma
• Recipe 5---Linear Algebra Methods
  • Some more definitions
  • Multivariate division by an ideal
  • S-polynomials and Buchberger's algorithm
    • Buchberger's Algorithm
  • The vector space of reduced polynomials
  • Roots of the system are eigenvalues of a commuting family
• About this document ...