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Algebraic Curves and Surfaces: A History of Shapes
, 2023 International audienceThis volume collects the lecture notes of the school TiME2019 (Treasures in Mathematical Encounters). The aim of this book is manifold, it intends to overview the wide topic of algebraic curves and surfaces (also with a view to ...
Postinghel, Elisa +2 more
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Multiplication polynomials and relative Manin-Mumford [PDF]
, 2015 After the introduction we prove in chapter 2 that the resultant of the standard multiplication polynomials $A_n,B_n$ of an elliptic curve in the form $y^2 = x^3+ax+b$ is $(16\Delta)^{{n^2(n^2-1) \over 6}}$, where $\Delta=-(4a^3+27b^2)$ is the ...
Schmidt, Harry
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Trace zero varieties in cryptography : optimal representation and index calculus [PDF]
, 2014 The trace zero variety associated to an elliptic or hyperelliptic curve is an abelian variety defined over a finite field F_q. Its F_q-rational points yield a finite group, the trace zero subgroup of the degree zero Picard group of the original curve ...
Massierer, Maike
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Discrete Differential Form Subdivision and Vector Field Generation over Volumetric Domain [PDF]
, 2012 This thesis presents a new method to construct smooth l- and 2-form subdivision schemes over the 3D volumetric domain. Based on the subdivided 1- and 2-form coefficient field, smooth vector fields can be constructed using Whitney forms.
Huang, Jinghao
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International Journal of Mathematical Combinatorics, Vol.3 [PDF]
, 2009 The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 460 pages approx.
Mao, Linfan (Editor-in-Chief)
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Geometric Algebra and Algebraic Geometry of Loop and Potts Models
, 2022 We uncover a connection between two seemingly separate subjects in integrable models: the representation theory of the affine Temperley-Lieb algebra, and the algebraic structure of solutions to the Bethe equations of the XXZ spin chain.
Zhang, Yang +3 more
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Tropical Effective Primary and Dual Nullstellens"atze [PDF]
, 2015 Tropical algebra is an emerging field with a number of applications in various areas of mathematics. In many of these applications appeal to tropical polynomials allows to study properties of mathematical objects such as algebraic varieties and algebraic
Podolskii, Vladimir V. +5 more
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Hyperelliptic curves and their applications to cryptography.
, 2002 Cryptosystems based on hyperelliptic curves were first presented by N. Koblitz, in 1989 (c.f. [11]). In 1996, a first attempt was made to give an elementary introduction to hyperelliptic curves (c.f. [3]).
Nali, Deholo.
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On the Shape of Curves that are Rational in Polar Coordinates [PDF]
, 2012 Note of the authors: The final version of this paper was published as Alcázar\ud J.G., Díaz Toca G.M. (2012), On the Shape of Curves that are Rational in Polar\ud Coordinates, Computer Aided Geometric Design, Vol. 29 Issue 9, pp. 665-675.In this paper we
Díaz Toca, Gema María +2 more
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Nonsolvable number fields ramified only at 3 and 5 [PDF]
, 2011 For p = 3 and p = 5, we exhibit a finite nonsolvable extension of Q which is ramified only at p, proving in the affirmative a conjecture of Gross.
Lassina Dembélé +5 more
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