Genetic Algorithm for Finding Approximate Roots of a Cyclotomic Polynomial

The newly-proposed genetic algorithm for finding approximate roots of a cyclotomic polynomial in this paper refers to the process in which m individuals are selected to produce randomly m original points in the original groups.Then by using the fitness function 1/(1+|f(x)|),individuals' fitness is calculated,selection,crossover and mutation of initial population are performed to integrate individuals with good fitness into the next generation.The result will come out when the ordered number of the approximate roots and the precision are achieved.The algorithm is optimized by using dynamic adaptive,restartion,polynomial division to restrain the premature convergence efficiently.The algorithm is practicable and efficient in finding approximate roots of a cyclotomic polynomial,and gives a new method to judge a polynomial that can pitch cirle.