Algorithms for computing maximal lattices in bilinear (and quadratic) spaces over number fields

@article{Hanke2012AlgorithmsFC,
  title={Algorithms for computing maximal lattices in bilinear (and quadratic) spaces over number fields},
  author={Jonathan Hanke},
  journal={arXiv: Number Theory},
  year={2012}
}
  • J. Hanke
  • Published 13 August 2012
  • Mathematics, Computer Science
  • arXiv: Number Theory
In this paper we describe an algorithm that quickly computes a maximal a-valued lattice in an F-vector space equipped with a non-degenerate bilinear form, where a is a fractional ideal in a number field F. We then apply this construction to give an algorithm to compute an a-maximal lattice in a quadratic space over any number field F where the prime 2 is unramified. We also develop the theory of p-neighbors for a-valued quadratic lattices at an arbitrary prime p of O_F (including when p | 2… 

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