A complete algorithm to find exact minimal polynomial by approximations
Xiaolin Qin, Yong Feng, Jingwei Chen, Jingzhong Zhang · International Journal of Computer Mathematics · 2012
Based on an improved parameterized integer relation construction method, a complete algorithm is proposed for finding an exact minimal polynomial from its approximate root. It relies on a study of the error controlling for its approximation. We provide a sufficient condition on the precision of the approximation, depending only on the degree and the height of its minimal polynomial. Our result is superior to the existent error controlling on obtaining an exact rational or algebraic number from its approximation. Moreover, some applications are presented and compared with the subsistent methods.