On solving composite power polynomial equations
Ημερομηνία
2005Source
Mathematics of ComputationVolume
74Issue
250Pages
853-868Google Scholar check
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Εμφάνιση πλήρους εγγραφήςΕπιτομή
It is well known that a system of power polynomial equations can be reduced to a single-variable polynomial equation by exploiting the so-called Newton's identities. In this work, by further exploring Newton's identities, we discover a binomial decomposition rule for composite elementary symmetric polynomials. Utilizing this decomposition rule, we solve three types of systems of composite power polynomial equations by converting each type to single-variable polynomial equations that can be solved easily. For each type of system, we discuss potential applications and characterize the number of nontrivial solutions (up to permutations) and the complexity of our proposed algorithmic solution. © 2004 American Mathematical Society.