using basis computation to determine pseudo-multiplicative independence
This paper describes a procedure for determining when a set of rational functions are pseudo-multiplicatively independent, i.e. when no non-trivial power product of the rational functions can be a constant. The method used is to derive a multiplicative basis of factors of the numerators and denominators of the rational functions; the basis is then used to derive a system of homogeneous linear equations which will have a non-trivial solution if and only if the rational functions are pseudo-multiplicatively dependent. Algorithms which find a basis for a set of Gaussian rational functions and the corresponding linear equations are presented in detail and bounds on their theoretical computing times are derived.
computation dependencies paper power product method factor systems algorithm