Algorithmic And Experimental Methods In Algebra Geometry And Number Theory PDF Download
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| Author | : Gebhard Böckle |
| Publisher | : Springer |
| Total Pages | : 753 |
| Release | : 2018-03-22 |
| Genre | : Mathematics |
| ISBN | : 3319705660 |
Download Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory Book in PDF, ePub and Kindle
This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.
| Author | : B.Heinrich Matzat |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 431 |
| Release | : 2012-12-06 |
| Genre | : Computers |
| ISBN | : 364259932X |
Download Algorithmic Algebra and Number Theory Book in PDF, ePub and Kindle
This book contains 22 lectures presented at the final conference of the Ger man research program (Schwerpunktprogramm) Algorithmic Number The ory and Algebra 1991-1997, sponsored by the Deutsche Forschungsgemein schaft. The purpose of this research program and of the meeting was to bring together developers of computer algebra software and researchers using com putational methods to gain insight into experimental problems and theoret ical questions in algebra and number theory. The book gives an overview on algorithmic methods and on results ob tained during this period. This includes survey articles on the main research projects within the program: • algorithmic number theory emphasizing class field theory, constructive Galois theory, computational aspects of modular forms and of Drinfeld modules • computational algebraic geometry including real quantifier elimination and real algebraic geometry, and invariant theory of finite groups • computational aspects of presentations and representations of groups, especially finite groups of Lie type and their Heeke algebras, and of the isomorphism problem in group theory. Some of the articles illustrate the current state of computer algebra sys tems and program packages developed with support by the research pro gram, such as KANT and LiDIA for algebraic number theory, SINGULAR, RED LOG and INVAR for commutative algebra and invariant theory respec tively, and GAP, SYSYPHOS and CHEVIE for group theory and representation theory.
| Author | : Saugata Basu |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 602 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 3662053551 |
Download Algorithms in Real Algebraic Geometry Book in PDF, ePub and Kindle
In this first-ever graduate textbook on the algorithmic aspects of real algebraic geometry, the main ideas and techniques presented form a coherent and rich body of knowledge, linked to many areas of mathematics and computing. Mathematicians already aware of real algebraic geometry will find relevant information about the algorithmic aspects. Researchers in computer science and engineering will find the required mathematical background. This self-contained book is accessible to graduate and undergraduate students.
| Author | : M. Pohst |
| Publisher | : Cambridge University Press |
| Total Pages | : 520 |
| Release | : 1997-09-25 |
| Genre | : Mathematics |
| ISBN | : 9780521596695 |
Download Algorithmic Algebraic Number Theory Book in PDF, ePub and Kindle
Now in paperback, this classic book is addresssed to all lovers of number theory. On the one hand, it gives a comprehensive introduction to constructive algebraic number theory, and is therefore especially suited as a textbook for a course on that subject. On the other hand many parts go beyond an introduction an make the user familliar with recent research in the field. For experimental number theoreticians new methods are developed and new results are obtained which are of great importance for them. Both computer scientists interested in higher arithmetic and those teaching algebraic number theory will find the book of value.
| Author | : Thorsten Theobald |
| Publisher | : American Mathematical Society |
| Total Pages | : 312 |
| Release | : 2024-04-18 |
| Genre | : Mathematics |
| ISBN | : 1470476363 |
Download Real Algebraic Geometry and Optimization Book in PDF, ePub and Kindle
This book provides a comprehensive and user-friendly exploration of the tremendous recent developments that reveal the connections between real algebraic geometry and optimization, two subjects that were usually taught separately until the beginning of the 21st century. Real algebraic geometry studies the solutions of polynomial equations and polynomial inequalities over the real numbers. Real algebraic problems arise in many applications, including science and engineering, computer vision, robotics, and game theory. Optimization is concerned with minimizing or maximizing a given objective function over a feasible set. Presenting key ideas from classical and modern concepts in real algebraic geometry, this book develops related convex optimization techniques for polynomial optimization. The connection to optimization invites a computational view on real algebraic geometry and opens doors to applications. Intended as an introduction for students of mathematics or related fields at an advanced undergraduate or graduate level, this book serves as a valuable resource for researchers and practitioners. Each chapter is complemented by a collection of beneficial exercises, notes on references, and further reading. As a prerequisite, only some undergraduate algebra is required.
| Author | : Laureano Gonzalez-Vega |
| Publisher | : Birkhäuser |
| Total Pages | : 407 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034891040 |
Download Algorithms in Algebraic Geometry and Applications Book in PDF, ePub and Kindle
The present volume contains a selection of refereed papers from the MEGA-94 symposium held in Santander, Spain, in April 1994. They cover recent developments in the theory and practice of computation in algebraic geometry and present new applications in science and engineering, particularly computer vision and theory of robotics. The volume will be of interest to researchers working in the areas of computer algebra and symbolic computation as well as to mathematicians and computer scientists interested in gaining access to these topics.
| Author | : Teo Mora |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 524 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : 9780817635466 |
Download Effective Methods in Algebraic Geometry Book in PDF, ePub and Kindle
On Lack of Effectiveness in Semi-algebraic Geometry.- A simple constructive proof of Canonical Resolution of Singularities.- Local Membership Problems for Polynomial Ideals.- Un Algorithme pour le Calcul des Résultants.- On algorithms for real algebraic plane curves.- Duality methods for the membership problem.- Exemples d'ensembles de Points en Position Uniforme.- Efficient Algorithms and Bounds for Wu-Ritt Characteristic Sets.- Noetherian Properties and Growth of some Associative Algebras.- Codes and Elliptic Curves.- Algorithmes - disons rapides - pour la décomposition d'une variété algébrique en composantes irréductibles et équidimensionnelles.- Complexity of Solving Systems of Linear Equations over the Rings of Differential Operators.- Membership problem, Representation problem and the Computation of the Radical for one-dimensional Ideals.- On the Complexity of Zero-dimensional Algebraic Systems.- A Single Exponential Bound on the Complexity of Computing Gröbner Bases of Zero Dimensional Ideals.- Algorithms for a Multiple Algebraic Extension.- Elementary constructive theory of ordered fields.- Effective real Nullstellensatz and variants.- Algorithms for the Solution of Systems of Linear Equations in Commutative Rings.- Une conjecture sur les anneaux de Chow A(G, ?) renforcée par un calcul formel.- Construction de courbes de genre 2 à partir de leurs modules.- Computing Syzygies à la Gau?-Jordan.- The non-scalar Model of Complexity in Computational Geometry.- Géométrie et Interpretations Génériques, un Algorithme.- Canonical Bases: Relations with Standard Bases, Finiteness Conditions and Application to Tame Automorphisms.- The tangent cone algorithm and some applications to local algebraic geometry.- Effective Methods for Systems of Algebraic Partial Differential Equations.- Finding roots of equations involving functions defined by first order algebraic differential equations.- Some Effective Methods in the Openness of Loci for Cohen-Macaulay and Gorenstein Properties.- Sign determination on zero dimensional sets.- A Classification of Finite-dimensional Monomial Algebras.- An algorithm related to compactifications of adjoint groups.- Deciding Consistency of Systems of Polynomial in Exponent Inequalities in Subexponential Time.
| Author | : Guillaume Hanrot |
| Publisher | : Springer |
| Total Pages | : 407 |
| Release | : 2010-07-08 |
| Genre | : Computers |
| ISBN | : 3642145183 |
Download Algorithmic Number Theory Book in PDF, ePub and Kindle
This book constitutes the refereed proceedings of the 9th International Algorithmic Number Theory Symposium, ANTS 2010, held in Nancy, France, in July 2010. The 25 revised full papers presented together with 5 invited papers were carefully reviewed and selected for inclusion in the book. The papers are devoted to algorithmic aspects of number theory, including elementary number theory, algebraic number theory, analytic number theory, geometry of numbers, algebraic geometry, finite fields, and cryptography.
| Author | : Kevin Buzzard |
| Publisher | : Springer Nature |
| Total Pages | : 377 |
| Release | : |
| Genre | : |
| ISBN | : 3031645294 |
Download Mathematical Software – ICMS 2024 Book in PDF, ePub and Kindle
| Author | : Antonio Campillo |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 2012 |
| Genre | : Mathematics |
| ISBN | : 0821869000 |
Download Zeta Functions in Algebra and Geometry Book in PDF, ePub and Kindle
Contains the proceedings of the Second International Workshop on Zeta Functions in Algebra and Geometry held May 3-7, 2010 at the Universitat de les Illes Balears, Palma de Mallorca, Spain. The conference focused on the following topics: arithmetic and geometric aspects of local, topological, and motivic zeta functions, Poincare series of valuations, zeta functions of groups, rings, and representations, prehomogeneous vector spaces and their zeta functions, and height zeta functions.
