Details:
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  07477171 
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 
