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)/
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.