J. Kung and G.-C. Rota, in their 1984 paper, write: Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics...
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ISBN:
(数字)9783211774175
ISBN:
(纸本)9783211774168
J. Kung and G.-C. Rota, in their 1984 paper, write: Like the Arabian phoenix rising out of its ashes, the theory of invariants, pronounced dead at the turn of the century, is once again at the forefront of mathematics. The book of Sturmfels is both an easy-to-read textbook for invariant theory and a challenging research monograph that introduces a new approach to the algorithmic side of invariant theory. The Groebner bases method is the main tool by which the central problems in invariant theory become amenable to algorithmic solutions. Students will find the book an easy introduction to this classical and new area of mathematics. Researchers in mathematics, symboliccomputation, and computer science will get access to a wealth of research ideas, hints for applications, outlines and details of algorithms, worked out examples, and research problems.
This book describes some basic principles that allow developers of computer programs (computer scientists, software engineers, programmers) to clearly;about the artifacts they deal with in their daily work: data types...
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ISBN:
(数字)9783030805074
ISBN:
(纸本)9783030805067;9783030805098
This book describes some basic principles that allow developers of computer programs (computer scientists, software engineers, programmers) to clearly;about the artifacts they deal with in their daily work: data types, programming languages, programs written in these languages that compute from given inputs wanted outputs, and programs that describe continuously executing systems. The core message is that clear thinking about programs can be expressed in a single universal language, the formal language of;. Apart from its universal elegance and expressiveness, this “logical” approach to the formal modeling of and reasoning about computer programs has another advantage: due to advances in computational logic (automated theorem proving, satisfiability solving, model checking), nowadays much of this process can be supported by;. This book therefore accompanies its theoretical elaborations by practical demonstrations of various systems and tools thatare based on respectively make use of the presented logical underpinnings.
George Collins’ discovery of Cylindrical Algebraic Decomposition (CAD) as a method for Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major breakthrough in automating mathematic...
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ISBN:
(数字)9783709194591
ISBN:
(纸本)9783211827949
George Collins’ discovery of Cylindrical Algebraic Decomposition (CAD) as a method for Quantifier Elimination (QE) for the elementary theory of real closed fields brought a major breakthrough in automating mathematics with recent important applications in high-tech areas (e.g. robot motion), also stimulating fundamental research in computer algebra over the past three decades.
This volume is a state-of-the-art collection of important papers on CAD and QE and on the related area of algorithmic aspects of real geometry. It contains papers from a symposium held in Linz in 1993, reprints of seminal papers from the area including Tarski’s landmark paper as well as a survey outlining the developments in CAD based QE that have taken place in the last twenty years.
The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are f...
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ISBN:
(数字)9783709107942
ISBN:
(纸本)9783709107935
The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.
The development of polynomial-elimination techniques from classical theory to modern algorithms has undergone a tortuous and rugged path. This can be observed L. van der Waerden's elimination of the "eliminat...
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ISBN:
(数字)9783709162026
ISBN:
(纸本)9783211832417
The development of polynomial-elimination techniques from classical theory to modern algorithms has undergone a tortuous and rugged path. This can be observed L. van der Waerden's elimination of the "elimination theory" chapter from from B. his classic Modern Algebra in later editions, A. Weil's hope to eliminate "from algebraic geometry the last traces of elimination theory," and S. Abhyankar's sug gestion to "eliminate the eliminators of elimination theory. " The renaissance and recognition of polynomial elimination owe much to the advent and advance of mod ern computing technology, based on which effective algorithms are implemented and applied to diverse problems in science and engineering. In the last decade, both theorists and practitioners have more and more realized the significance and power of elimination methods and their underlying theories. Active and extensive research has contributed a great deal of new developments on algorithms and soft ware tools to the subject, that have been widely acknowledged. Their applications have taken place from pure and applied mathematics to geometric modeling and robotics, and to artificial neural networks. This book provides a systematic and uniform treatment of elimination algo rithms that compute various zero decompositions for systems of multivariate poly nomials. The central concepts are triangular sets and systems of different kinds, in terms of which the decompositions are represented. The prerequisites for the concepts and algorithms are results from basic algebra and some knowledge of algorithmic mathematics.
New methodological aspects related to design and implementation of symboliccomputation systems are considered in this volume aiming at integrating such aspects into a homogeneous software environment for scientific c...
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ISBN:
(数字)9783709165317
ISBN:
(纸本)9783211828441
New methodological aspects related to design and implementation of symboliccomputation systems are considered in this volume aiming at integrating such aspects into a homogeneous software environment for scientific computation. The proposed methodology is based on a combination of different techniques: algebraic specification through modular approach and completion algorithms, approximated and exact algebraic computing methods, object-oriented programming paradigm, automated theorem proving through methods à la Hilbert and methods of natural deduction. In particular the proposed treatment of mathematical objects, via techniques for method abstraction, structures classification, and exact representation, the programming methodology which supports the design and implementation issues, and reasoning capabilities supported by the whole framework are described.
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