Results 21 to 30 of about 268,307 (331)
Formal proofs in real algebraic geometry: from ordered fields to quantifier elimination [PDF]
Logical Methods in Computer Science, 2012 This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic properties.
Assia Mahboubi, Cyril Cohen
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Comparing the number of ideals in quadratic number fields
Mathematical Modelling and Control, 2022 Denote by $ a_{K}(n) $ the number of integral ideals in $ K $ with norm $ n $, where $ K $ is a algebraic number field of degree $ m $ over the rational field $ \mathcal{Q} $. Let $ p $ be a prime number.
Qian Wang, Xue Han
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Isomorphisms of algebraic number fields [PDF]
Journal de théorie des nombres de Bordeaux, 2012 Let ℚ(α) and ℚ(β) be algebraic number fields. We describe a new method to find (if they exist) all isomorphisms, ℚ(β)→ℚ(α). The algorithm is particularly efficient if there is only one isomorphism.
van Hoeij, Mark, Pal, Vivek
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Computation of relative integral bases for algebraic number fields
International Journal of Mathematics and Mathematical Sciences, 1988 At first we are given conditions for existence of relative integral bases for extension (K;k)=n. Then we will construct relative integral bases for extensions OK6(−36)/Ok2(−3), OK6(−36)/Ok3(−33), OK6(−36)/Z.
Mahmood Haghighi
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On some varieties associated with trees [PDF]
, 2014 This article considers some affine algebraic varieties attached to finite trees and closely related to cluster algebras. Their definition involves a canonical coloring of vertices of trees into three colors. These varieties are proved to be smooth and to
Chapoton, Frédéric
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Short Principal Ideal Problem in multicubic fields
Journal of Mathematical Cryptology, 2020 One family of candidates to build a post-quantum cryptosystem upon relies on euclidean lattices. In order to make such cryptosystems more efficient, one can consider special lattices with an additional algebraic structure such as ideal lattices.
Lesavourey Andrea +2 more
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General Quantum Field Theory of Flavor Mixing and Oscillations
Universe, 2021 We review the canonical transformation in quantum physics known as the Bogoliubov transformation and present its application to the general theory of quantum field mixing and oscillations with an arbitrary number of mixed particles with either boson or ...
Chueng-Ryong Ji, Yuriy Mishchenko
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Analytic curves in algebraic varieties over number fields
, 2007 We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'
A Franchetta +41 more
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Observation of Topological Chirality Switching Induced Freezing of a Skyrmion Crystal
Advanced Materials, EarlyView.Using Lorentz Transmission electron microscopy, it is shown that in the insulating van der Waals ferromagnet, CrBr3, a magnetic field can cause Bloch skyrmionic bubbles to spontaneously switch their chirality. As achiral type‐II bubbles are an intermediate state, the bubbles rapidly elongate and shrink when switching, thereby inducing a freezing of the
John Fullerton +10 more
wiley +1 more source
Elementary Fractal Geometry. 2. Carpets Involving Irrational Rotations
Fractal and Fractional, 2022 Self-similar sets with the open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in the plane, based on rotation by irrational angles.
Christoph Bandt, Dmitry Mekhontsev
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