CS 780 Avanced Symbolic Computation

Winter 2004

Course Outline

1. Symbolic Integration and Symbolic-Numeric Integration (12 hours)
   • Basic concepts of differential algebra (1.5 hours)
   • Rational function integration (Hermite and Rothstein/Trager methods) (1.5 hours)
   • Elementary functions and Liouville's Principle (1.5 hours)
   • Risch algorithm for transcendental elementary functions (3 hours)
   • Algebraic functions (1.5 hours)
   • Meijer G method for definite integrals (1.5 hours)
   • Symbolic-numeric techniques for definite integrals (1.5 hours)
     
2. Groebner Bases and Solving Non-Linear Systems (12 hours)
   • Simplification of expressions with respect to side relations (1.5 hours)
   • Term orderings and reduction (1.5 hours)
   • Groebner bases and Buchberger's algorithm (3 hours)
   • Elimination Theory (3 hours)
   • Robotics and Automatic Geometric Theorem Proving (3 hours)
     
3. SNAP: Symbolic-Numeric Algorithms for Polynomials (12 hours)
   • Approximate polynomials (1 hour)
     • definitions and models of computation
     • Basic operations and error analysis
   • Approximate GCD (4 hours)
     • Karmarkar-Lakshman Algorithm
     • Corless, Trager, Gianni & Watt and SVD based methods
   • Approximate Multi-variate Polynomial Factorization (3 hours)
   • Approximate Polynomial Systems (4 hours)