COMPUTING MINIMAL POLYNOMIALS OF RADICAL EXPRESSIONS

Described is a technology, such as implemented in a computational software program, by which a minimal polynomial is efficiently determined for a radical expression based upon its structure of the radical expression. An annihilation polynomial is found based upon levels of the radical to obtain roots of the radical. A numerical method performs a zero test or multiple zero tests to find the minimal polynomial. In one implementation, the set of roots corresponding to a radical expression is found. The annihilation polynomial is computed by grouping roots of the set according to their conjugation relationship and multiplying factor polynomials level by level. A selection mechanism selects the minimal polynomial based upon the annihilation polynomial's factors.