MATHEMATICS OF COMPUTATION Volume 00, Number 0, Pages 000–000 SXXAN L(1/3) ALGORITHM FOR IDEAL CLASS GROUP AND REGULATOR COMPUTATION IN CERTAIN NUMBER FIELDS

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Attached Table 2䚷䚷List of Categories, Areas, Disciplines and Research Fields (1) Grants-in-Aid for Scientific Research FY2014 List of Categories, Areas, Disciplines and Research Fields Category: Integrated Discipline

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• Education
• Academia
• Science and technology
• Medicine
• Science
• technology
• engineering
• and mathematics
• Book:Part of a series on Science
• Outline of academic disciplines

J. Symbolic Computation, 351–369 Lattices of Compatibly Embedded Finite Fields† WIEB BOSMA‡, JOHN CANNON§ AND ALLAN STEEL¶ Computational Algebra Group, School of Mathematics and Statistics, The Univers

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• Field theory
• Polynomials
• Computer algebra
• Finite fields
• Abstract algebra
• Conway polynomial
• Field
• Minimal polynomial
• Embedding
• Model theory
• Factorization of polynomials
• Duality

Attached Table 2䇭䇭List of Categories, Areas, Disciplines and Research Fields (1) Grants-in-Aid for Scientific Research FY2013 List of Categories, Areas, Disciplines and Research Fields Category: Integrated Discipline

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• Education
• Philosophy of education
• Science
• Medicine
• Science
• technology
• engineering
• and mathematics
• Book:Part of a series on Science
• Outline of academic disciplines

On Curves over Finite Fields with Jacobians of Small Exponent Kevin Ford Department of Mathematics, 1409 West Green Street University of Illinois at Urbana-Champaign Urbana, IL 61801, USA

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Edwards Curves and the ECM Factorisation Method Peter Birkner Eindhoven University of Technology The 12th Workshop on Elliptic Curve Cryptography

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• Abstract algebra
• Algebra
• Mathematics
• Finite fields
• Integer factorization algorithms
• Group theory
• Elliptic curve cryptography
• Lenstra elliptic curve factorization
• Elliptic curves
• Elliptic curve
• Torsion
• Order

Explicit Primality Criteria for h #2k ± 1 Wieb Bosma Mathematics of Computation, Vol. 61, No. 203, Special Issue Dedicated to Derrick Henry Lehmer. (Jul., 1993), ppStable URL: http://links.jstor.org/sici?sici=

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• Mathematics
• Discrete mathematics
• Number theory
• Modular arithmetic
• Integer sequences
• Finite fields
• Quadratic residue
• Prime number
• Quadratic reciprocity
• XTR
• Coprime integers
• Factorial

. . Mono-anabelian Reconstruction of Number Fields

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• Algebra
• Abstract algebra
• Mathematics
• Algebraic geometry
• Field theory
• Galois theory
• Anabelian geometry
• Algebraic number theory
• Galois group
• Algebraic number field
• Field
• Inter-universal Teichmller theory

GAUSSIAN FIELDS Notes for Lectures Ofer Zeitouni Department of Mathematics Weizmann Institute, Rehovot 76100, Israel and

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• Stochastic processes
• Algebra of random variables
• Hilbert space
• Estimation theory
• KarhunenLove theorem
• Signal processing
• Gaussian free field
• Multivariate random variable
• Reproducing kernel Hilbert space
• Covariance
• Normal distribution
• Gaussian function

AAECC 1,AAECC Applicable Algebra in Engineering, Communication and Computing

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• Algebra
• Abstract algebra
• Mathematics
• Algebraic number theory
• Cyclotomic fields
• Polynomials
• Ring theory
• Field theory
• Root of unity
• Cyclotomic polynomial
• Algebraic number field
• Integral element