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Algebra --- Data processing --- Gröbner bases --- Differentiable dynamical systems

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Gröbner bases --- 512.622 --- Grobner bases --- Gröbner basis theory --- Polynomials, including binomials and prime factors --- Gröbner bases. --- 512.622 Polynomials, including binomials and prime factors --- Gröbner bases --- Commutative algebra

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This self-contained monograph is the first to feature the intersection of the structure theory of noncommutative associative algebras and the algorithmic aspect of Groebner basis theory. A double filtered-graded transfer of data in using noncommutative Groebner bases leads to effective exploitation of the solutions to several structural-computational problems, e.g., an algorithmic recognition of quadric solvable polynomial algebras, computation of GK-dimension and multiplicity for modules, and elimination of variables in noncommutative setting. All topics included deal with algebras of (q-)differential operators as well as some other operator algebras, enveloping algebras of Lie algebras, typical quantum algebras, and many of their deformations.

Associative rings --- Grobner bases. --- ALGEBRA --- Filtered rings. --- Gröbner bases --- Algebra --- Filtered rings --- Data processing. --- data processing. --- Data processing --- Grèobner bases --- Mathematical Theory --- Mathematics --- Physical Sciences & Mathematics --- Associative rings. --- Rings (Algebra). --- Algorithms. --- Associative Rings and Algebras. --- Algorism --- Arithmetic --- Algebraic rings --- Ring theory --- Algebraic fields --- Rings (Algebra) --- Foundations --- Associative rings - Data processing. --- ALGEBRA - data processing. --- Algebra - Data processing

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Computational Commutative Algebra 2 is the natural continuation of Computational Commutative Algebra 1 with some twists, starting with the differently coloured cover graphics. The first volume had 3 chapters, 20 sections, 44 tutorials, and some amusing quotes. Since bigger is better, this book contains 3 chapters filling almost twice as many pages, 23 sections (some as big as a whole chapter), and 55 tutorials (some as big as a whole section). The number of jokes and quotes has increased exponentially due to the little-known fact that a good mathematical joke is better than a dozen mediocre papers. The main part of this book is a breathtaking passeggiata through the computational domains of graded rings and modules and their Hilbert functions. Besides Gröbner bases, we encounter Hilbert bases, border bases, SAGBI bases, and even SuperG bases. The tutorials traverse areas ranging from algebraic geometry and combinatorics to photogrammetry, magic squares, coding theory, statistics, and automatic theorem proving. Whereas in the first volume gardening and chess playing were not treated, in this volume they are. This is a book for learning, teaching, reading, and most of all, enjoying the topic at hand. The theories it describes can be applied to anything from children's toys to oil production. If you buy it, probably one spot on your desk will be lost forever!

Gröbner bases --- Commutative algebra --- Grobner, Bases de --- Algebre commutative --- Data processing --- Informatique --- Commutative algebra -- Data processing. --- Gröbner bases. --- Gröbner basis theory --- Mathematics. --- Computer science --- Algebra. --- Algebraic geometry. --- Computer mathematics. --- Algorithms. --- Computational Mathematics and Numerical Analysis. --- Symbolic and Algebraic Manipulation. --- Algebraic Geometry. --- Data processing. --- Algebra --- Geometry, algebraic. --- Algebraic geometry --- Geometry --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Algorism --- Arithmetic --- Mathematics --- Mathematical analysis --- Foundations --- Combinatorial analysis. --- QA 150-272 Algebra. --- Computer science—Mathematics. --- Group theory. --- Group Theory and Generalizations. --- Groups, Theory of --- Substitutions (Mathematics) --- Commutative algebra - Data processing --- Algebre commutative - Informatique

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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