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Finding eisenstein elements in cyclic number fields of odd prime degree

Published online by Cambridge University Press:  17 April 2009

Vincenzo Acciaro
Vincenzo Acciaro
Affiliation:
School of Computer Science, Carleton University, Ottawa, Ont, Kl.S 5B6, Canada
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Abstract

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Let L = Q[α] be a cyclic number field of odd prime degree q over the field Q of rationals. In this paper we give an algorithm to compute the discriminant of L/Q, which relies upon a fast method to find Eisenstein elements in L. The algorithm accepts as input the minimal polynomial of α over Q and a complete factorisation of the discriminant of α, and computes, in time polynomial in the size of the input, a list consisting of all the ramified primes with corresponding Eisenstein elements.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 52 , Issue 2 , October 1995 , pp. 331 - 340
Copyright
Copyright © Australian Mathematical Society 1995

References

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