
Rational Expression Simplification with Polynomial Side RelationsMr. Roman Pearce, Simon Fraser Univeristy, Masters defense
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. 