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Power roots of polynomials over arbitrary fields

Published online by Cambridge University Press:  17 April 2009

Vincenzo Acciaro
Vincenzo Acciaro
Affiliation:
School of Computer Science Carelton University Ottawa, Ontario K1S 5B6, Canada
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Abstract

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Let F be an arbitrary field, and f(x) a polynomial in one variable over F of degree ≥ 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) ∈ F[x] such that z(x)m ≡ g(x) (mod f(x)). We show how our results can be specialised to ℝ, ℂ 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 (for example, a finite field or an algebraic number field).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 50 , Issue 2 , October 1994 , pp. 327 - 335
Copyright
Copyright © Australian Mathematical Society 1994

References

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