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 Title Algorithms for near solutions to polynomial equations Author(s) Shih Ping Tung Type Article in Journal Abstract Let F ( x , y ) be a polynomial over a field K and m a nonnegative integer. We call a polynomial g over K an m -near solution of F ( x , y ) if there exists a c ∈ K such that F ( x , g ) = c x^m , and the number c is called an m -value of F ( x , y ) corresponding to g . In particular, c can be 0. Hence, by viewing F ( x , y ) = 0 as a polynomial equation over K [ x ] with variable y , every solution of the equation F ( x , y ) = 0 in K [ x ] is also an m -near solution. We provide an algorithm that gives all m -near solutions of a given polynomial F ( x , y ) over K , and this algorithm is polynomial time reducible to solving one variable equations over K . We introduce approximate solutions to analyze the algorithm. We also give some interesting properties of approximate solutions. Keywords Algorithms, Near solution, Polynomial equations ISSN 0747-7171 URL http://www.sciencedirect.com/science/article/pii/S0747717109000765 Language English Journal Journal of Symbolic Computation Volume 44 Number 10 Pages 1410 - 1424 Year 2009 Edition 0 Translation No Refereed No
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