A polynomial time algorithm for computing the HNF of a module over the integers of a number field

Details A polynomial time algorithm for computing the HNF of a module over the integers of a number field A polynomial time algorithm for computing the HNF of a module over the integers of a number field

2012-04-05

arxiv.org/abs/1204.1298v1

Computer Science

Symbolic Computation

11 pages

Scientific paper

We present a variation of the modular algorithm for computing the Hermite Normal Form of an $\OK$-module presented by Cohen, where $\OK$ is the ring of integers of a number field K. The modular strategy was conjectured to run in polynomial time by Cohen, but so far, no such proof was available in the literature. In this paper, we provide a new method to prevent the coefficient explosion and we rigorously assess its complexity with respect to the size of the input and the invariants of the field K.

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