Efficient Gaussian Elimination Method for Symbolic Determinants and Linear Systems

Although the Gauss,an ehmmatlon method is considered to be inefficient for symbolic determinants w,th multivariate polynomial entries or symbohc hnear systems, it can be made efficient by a simple technique. The technique is to replace all the diagonal elements by new independent variables and to introduce a special multiplication operator. Empirical studies show that the new method is much more efficmnt than the fraction-free Gaussmn elimination method and that it is comparable to the minor expansion method with regard to the way in whmh dense multivariate determinants are calculated. The new method is more useful for solving symbohc linear systems than the determinant calculation.