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4

ANTS
2004
Springer

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109views Algorithms» more ANTS 2004»

On the Complexity of Computing Units in a Number Field

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On the Complexity of Computing Units in a Number Field

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Given an algebraic number ﬁeld K, such that [K : Q] is constant, we show that the problem of computing the units group O∗ K is in the complexity class SPP. As a consequence, we show that principal ideal testing for an ideal in OK is in SPP. Furthermore, assuming the GRH, the class number of K, and a presentation for the class group of K can also be computed in SPP. A corollary of our result is that solving PELL S EQUATION, recently shown by Hallgren [12] to have a quantum polynomial-time algorithm, is also in SPP.

Vikraman Arvind, Piyush P. Kurur

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Algorithms | ANTS 2004 | Complexity Class Spp | Number ﬁeld K | Principal Ideal Testing |

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Added	30 Jun 2010
Updated	30 Jun 2010
Type	Conference
Year	2004
Where	ANTS
Authors	Vikraman Arvind, Piyush P. Kurur

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