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The theory of Gröbner bases, invented by Bruno Buchberger, is a general method by which many fundamental problems in various branches of mathematics and engineering can be solved by structurally simple algorithms. The method is now available in all major mathematical software systems. This book provides a short and easy-to-read account of the theory of Gröbner bases and its applications. It is in two parts, the first consisting of tutorial lectures, beginning with a general introduction. The subject is then developed in a further twelve tutorials, written by leading experts, on the application of Gröbner bases in various fields of mathematics. In the second part are seventeen original research papers on Gröbner bases. An appendix contains the English translations of the original German papers of Bruno Buchberger in which Gröbner bases were introduced.
Gröbner bases. --- Coding theory --- Gröbner basis theory --- Commutative algebra --- Geometry, Algebraic --- Géométrie algébrique. --- Algorithms --- Algorithmes. --- Anneaux de polynômes. --- Polynomial rings. --- Algèbres commutatives. --- Polynômes --- Polynomials --- 512.56 --- 512.56 Lattices, including Boolean rings and algebras --- Lattices, including Boolean rings and algebras --- Grobner bases. --- Géométrie algébrique --- Algorithmes --- Anneaux de polynômes. --- Algèbres commutatives. --- Polynômes
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This book takes a unique approach to information retrieval by laying down the foundations for a modern algebra of information retrieval based on lattice theory. All major retrieval methods developed so far are described in detail a"" Boolean, Vector Space and probabilistic methods, but also Web retrieval algorithms like PageRank, HITS, and SALSA a"" and the author shows that they all can be treated elegantly in a unified formal way, using lattice theory as the one basic concept. Further, he also demonstrates that the lattice-based approach to information retrieval allows us to formulate new re
Ordered algebraic structures --- algebra --- informatica --- Information systems --- IR (information retrieval) --- wiskunde --- Computer science --- Information retrieval --- Lattice theory --- 512.56 --- 512.56 Lattices, including Boolean rings and algebras --- Lattices, including Boolean rings and algebras --- Lattices (Mathematics) --- Space lattice (Mathematics) --- Structural analysis (Mathematics) --- Algebra, Abstract --- Algebra, Boolean --- Group theory --- Set theory --- Topology --- Transformations (Mathematics) --- Crystallography, Mathematical --- Data retrieval --- Data storage --- Discovery, Information --- Information discovery --- Information storage and retrieval --- Retrieval of information --- Documentation --- Information science --- Information storage and retrieval systems --- Information retrieval. --- Lattice theory. --- Data structures (Computer scienc. --- Information storage and retrieva. --- Algebra. --- Computer science. --- Data Structures and Information Theory. --- Information Storage and Retrieval. --- Order, Lattices, Ordered Algebraic Structures. --- Mathematics of Computing. --- Informatics --- Science --- Mathematics --- Mathematical analysis --- Information storage and retrieval systems. --- Data structures (Computer science) --- Automatic data storage --- Automatic information retrieval --- Automation in documentation --- Computer-based information systems --- Data processing systems --- Data storage and retrieval systems --- Discovery systems, Information --- Information discovery systems --- Information processing systems --- Information retrieval systems --- Machine data storage and retrieval --- Mechanized information storage and retrieval systems --- Computer systems --- Electronic information resources --- Data libraries --- Digital libraries --- Information organization --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Data structures (Computer science). --- Information storage and retrieval. --- Ordered algebraic structures. --- Computer science—Mathematics. --- Algebraic structures, Ordered --- Structures, Ordered algebraic --- Algebra
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