The rif algorithm is effective provided it can effectively perform elimination on the algebraic systems it generates and transform such systems to constant rank form. The radical rif algorithm is a realization of the rif algorithm for polynomially nonlinear pde systems which uses Buchberger's algorithm for elimination and algorithms for constructing the radical of a polynomial ideal to realize the constant rank condition. Various applications including the symmetry analysis of differential equations are discussed.
Reference:
G. J. Reid, A. D. Wittkopf and A. Boulton (1994).
Reduction of systems of nonlinear partial differential equations to
simplified involutive forms.
Available at
http://www.iam.ubc.ca/tr/1994/iam94-14.
