Computing in k[x1,...,xn]/I

Roman Pearce, MITACS, SFU

Monday March 1st, 2004, in K9509 at 3:30pm.

  Relatively common tasks in computer algebra can lead to polynomial
  computations over general domains.  One example is Q(s,c)/, which 
  pops up every time we have to compute with trigonometric expressions.  Some 
  of these domains can be very problematic, lacking unique factorization or any 
  form of the Euclidean algorithm.  Specialized algorithms have been developed 
  for a few of them, but we will discuss a general approach based on algebraic 
  geometry and Groebner bases.  Specifically, we will address polynomial 
  division (with a remainder and a quotient), and a new method for rational 
  expression simplification in the quotient ring k[x1,...,xn]/I.