Rational Expression Simplification with Polynomial Side Relations

Mr. Roman Pearce, Simon Fraser Univeristy, Masters defense

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


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.