Carleton University
Technical Report TR-228
September 1993
Power Roots of Polynomials over Arbitrary Fields
Vincenzo Acciaro
Abstract
Let F be an arbitrary field, and f(x) a polynomial in one variable over F of degree 2: 1. Given a polynomial g( x) #- 0 over F and an integer m > 1 we give necessary and sufficient conditions for the existence of a polynomial z(x) E F[x] such that z(xr = g(x) (mod f(x)). We show how our results can be specialized to IR, 4J and to finite fields. Since our proofs are constructive it is possible to translate them into an effective algorithm when F is a computable field (e.g. a finite field or an algebraic number field).