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TitleOn Solving Composite Power Polynomial Equations
Author(s) Christoforos N. Hadjicostis, Yingquan Wu
TypeTechnical Report, Misc
AbstractIt 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 non-trivial solutions (up to permutations) and the complexity of our proposed algorithmic procedure.

KeywordsPower polynomial, composite power polynomial, Newton's identities, system of polynomial equations
Translation No
Refereed No