Simultaneously good bases of a lattice and its reciprocal lattice.
Johan Hastad, Jeffrey C. Lagarias (1990)
Mathematische Annalen
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Johan Hastad, Jeffrey C. Lagarias (1990)
Mathematische Annalen
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Ulrich Halbritter, Michael E. Pohst (2000)
Journal de théorie des nombres de Bordeaux
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In this paper we introduce multiplicative lattices in and determine finite unions of suitable simplices as fundamental domains for sublattices of finite index. For this we define cyclic non-negative bases in arbitrary lattices. These bases are then used to calculate Shintani cones in totally real algebraic number fields. We mainly concentrate our considerations to lattices in two and three dimensions corresponding to cubic and quartic fields.
L. J. Mordell (1935)
Compositio Mathematica
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A. Zygmund (1972)
Studia Mathematica
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J. L. Ericksen (1982)
Rendiconti del Seminario Matematico della Università di Padova
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Boris Gruber (1970)
Časopis pro pěstování matematiky
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J. Paris (1977)
Fundamenta Mathematicae
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Yuichi Futa, Yasunari Shidama (2017)
Formalized Mathematics
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In this article, we formalize in Mizar [5] the definition of dual lattice and their properties. We formally prove that a set of all dual vectors in a rational lattice has the construction of a lattice. We show that a dual basis can be calculated by elements of an inverse of the Gram Matrix. We also formalize a summation of inner products and their properties. Lattice of ℤ-module is necessary for lattice problems, LLL(Lenstra, Lenstra and Lovász) base reduction algorithm and cryptographic...
S. Bernau, H. Lacey (1976)
Studia Mathematica
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T. Figiel (1980)
Studia Mathematica
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