Rational Expression Simplification with Polynomial Side Relations

Mr. Roman Pearce, Simon Fraser Univeristy, Masters defense

Thursday August 4th, 2005 at 10:30am in K9509.

Abstract: 

The goal of this thesis is to develop generic algorithms for computing
in polynomial quotient rings and their fields of fractions.  We present
two methods for simplifying ratioanl expressions over k[x1,...,xn]/I.
the first method uses Groebner bases for modules to compute an equivalent
expression whose largest term is minimal wrt respect to a given monomial
order.  The second method solves systems of linear equations to find 
equivalent expressions and conducts a brute force search to find an
expression of minimal total degree.