منابع مشابه
Short Bases of Lattices over Number Fields
Lattices over number elds arise from a variety of sources in algorithmic algebra and more recently cryptography. Similar to the classical case of Z-lattices, the choice of a nice, short (pseudo)-basis is important in many applications. In this article, we provide the rst algorithm that computes such a short (pseudo)-basis. We utilize the LLL algorithm for Z-lattices together with the Bosma-Pohs...
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We study semi-stable ideal lattices coming from quadratic number fields. We prove that all ideal lattices of trace type from rings of integers of imaginary quadratic number fields are semi-stable. For real quadratic fields, we demonstrate infinite families of semi-stable and unstable ideal lattices, establishing explicit conditions on the canonical basis of an ideal that ensure stability; in pa...
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We enumerate all totally real number fields F with root discriminant δF ≤ 14. There are 1229 such fields, each with degree [F : Q] ≤ 9. In this article, we consider the following problem. Problem 1. Given B ∈ R>0, enumerate the set NF (B) of totally real number fields F with root discriminant δF ≤ B, up to isomorphism. To solve Problem 1, for each n ∈ Z>0 we enumerate the set NF (n,B) = {F ∈ NF...
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It is shown how root lattices and their reciprocals might serve as the right pool for the construction of quasicrystalline structure models. All non-periodic symmetries observed so far are covered in minimal embedding with maximal symmetry. For the construction of quasiperiodic tiling models by means of projection from higherdimensional periodic structures, the primitive hypercubic lattices are...
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ژورنال
عنوان ژورنال: Bulletin of Mathematical Sciences
سال: 2020
ISSN: 1664-3607,1664-3615
DOI: 10.1142/s1664360720500216