Results 21 to 30 of about 382,616 (334)
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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Construction of Complex Lattice Codes via Cyclotomic Fields
Trends in Computational and Applied Mathematics, 2022 Through algebraic number theory and Construction $A$ we extend an algebraic procedure which generates complex lattice codes from the polynomial ring \mathbb{F}_{2}[x]/(x^{n}-1), where \mathbb{F}_{2}=\{0,1\}, by using ideals from the generalized ...
E. D. Carvalho +3 more
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Constructions of Dense Lattices over Number Fields
Trends in Computational and Applied Mathematics, 2020 In this work, we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2,3,4,5,6,8 and 12, which are rotated versions of the lattices Lambda_n, for n =2,3,4,5,6,8 and K_12.
Antonio A. Andrade +3 more
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Point counting for foliations over number fields
Forum of Mathematics, Pi, 2022 Let${\mathbb M}$ be an affine variety equipped with a foliation, both defined over a number field ${\mathbb K}$. For an algebraic $V\subset {\mathbb M}$ over ${\mathbb K}$, write $\delta _{V}$ for the maximum of the degree and log-height of V.
Gal Binyamini
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Quartic surfaces, their bitangents and rational points [PDF]
Épijournal de Géométrie Algébrique, 2023 Let X be a smooth quartic surface not containing lines, defined over a number field K. We prove that there are only finitely many bitangents to X which are defined over K.
Pietro Corvaja, Francesco Zucconi
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The Impact of Mental Computation on Children’s Mathematical Communication, Problem Solving, Reasoning, and Algebraic Thinking [PDF]
Athens Journal of Education, 2020 Moving from arithmetic to algebraic thinking at early grades is foundational in the study of number patterns and number relationships. This qualitative study investigates mental computational activity in a third grade classroom’s and its relationship to ...
Roland Pourdavood +2 more
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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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Lower bounds on the class number of algebraic function fields defined over any finite field [PDF]
, 2011 We give lower bounds on the number of effective divisors of degree $\leq g-1$ with respect to the number of places of certain degrees of an algebraic function field of genus $g$ defined over a finite field.
Ballet, Stéphane, Rolland, Robert
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A Construction of Rotated Lattices via Totally Real Subfields of the Cyclotomic Field Q(z_p)
Trends in Computational and Applied Mathematics, 2019 The theory of lattices have shown to be useful in information theory and rotated lattices with high modulations diversity have been extensively studied as an alternative approach for transmission over a Rayleigh-fading channel, where the performance of ...
Antonio A. Andrade +2 more
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Algebraic number theory and code design for Rayleigh fading channels [PDF]
, 2004 Algebraic number theory is having an increasing impact in code design for many different coding applications, such as single antenna fading channels and more recently, MIMO systems.
Oggier, F., Viterbo, E.
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