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Integral closure : Rees algebras, multiplicities, algorithms
Integral Closure gives an account of theoretical and algorithmic developments on the integral closure of algebraic structures. These are shared concerns in commutative algebra, algebraic geometry, number theory and the computational aspects of these fields. The overall goal is to determine and analyze the equations of the assemblages of the set of solutions that arise under various processes and algorithms. It gives a comprehensive treatment of Rees algebras and multiplicity theory - while pointing to applications in many other problem areas. Its main goal is to provide complexity estimates by tracking numerically invariants of the structures that may occur.
Ideals, Varieties, and Algorithms : An Introduction to Computational Algebraic Geometry and Commutative Algebra
Algebraic Geometry is the study of systems of polynomial equations in one or more variables.The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory.
Discovering Mathematics with Magma : Reducing the Abstract to the Concrete
This volume celebrates the first decade of the Computer Algebra system Magma. With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. The book range over much of Magma's coverage of algorithmic algebra: from number theory and algebraic geometry, via representation theory and group theory to some branches of discrete mathematics and graph theory. A basic introduction to the Magma language is given in an appendix. The book is simultaneously an invitation to learn a new programming language in the context of contemporary research problems, and an exposition of the types of problem that can be investigated using computational algebra.
Computing in Algebraic Geometry : A Quick Start using SINGULAR
Algebraic geometry generally studies the properties of solution sets of systems of polynomial equations without direct reference to the actual polynomials used in these systems. … This is especially desirable for classwork where the development of the abstract machinery generally outlasts the patience of the students, except possibly the most motivated ones.
Computing and Combinatorics ; 13th Annual International Conference, COCOON 2007, Banff, Canada, July 16-19, 2007, Proceedings
The Book covers most aspects of theoretical computer scienceand combinatorics related to computing.It exploring research, development, and novel applications of computing and combinatorics.
Arithmetic of finite fields ; 2nd International Workshop, WAIFI 2008 Siena, Italy, July 6-9, 2008 Proceedings
This book constitutes the refereed proceedings of the Second International Workshop on the Arithmetic of Finite Fields, WAIFI 2008, held in Siena, Italy, in July 2008.
Arithmetic of finite fields ; 1st International Workshop, WAIFI 2007, Madrid, Spain, June 21-22, 2007, Proceedings
This book presented structures in finite fields, efficient implementation and architectures, efficient finite field arithmetic, classification and construction of mappings over finite fields, curve algebra, cryptography, codes, and discrete structures.
Applied algebra, algebraic algorithms and error-correcting codes ; 17th International Symposium, AAECC-17, Bangalore, India, December 16-20, 2007, Proceedings
Among the subjects addressed are block codes, including list-decoding algorithms; algebra and codes: rings, fields, algebraic geometry codes; algebra: rings and fields, polynomials, permutations, lattices; cryptography: cryptanalysis and complexity; computational algebra: algebraic algorithms and transforms; sequences and boolean functions.
Applied algebra, algebraic algorithms and error-correcting codes ; 16th International Symposium, AAECC-16, Las Vegas, NV, USA, February 20-24, 2006, Proceedings
This book constitutes the refereed proceedings of the 16th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-16, held in Las Vegas, NV, USA in February 2006. The 25 revised full papers presented together with 7 invited papers were carefully reviewed and selected from 32 submissions. Among the subjects addressed are block codes; algebra and codes: rings, fields, and AG codes; cryptography; sequences; decoding algorithms; and algebra: constructions in algebra, Galois groups, differential algebra, and polynomials.
Advances in cryptology – ASIACRYPT 2007 ; 13th International conference on the theory and application of cryptology and information security, Kuching, Malaysia, December 2-6, 2007, Proceedings
The book are organized in topical sections on number theory and elliptic curve, protocol, hash function design, group/broadcast cryptography, mac and implementation, multiparty computation, block ciphers, foundation, public key encryption, and cryptanalysi.
