翻訳と辞書 Words near each other ・ Regular Show (season 6) ・ Regular Show (season 7) ・ Regular Show (season 8) ・ Regular singular point ・ Regular skew apeirohedron ・ Regular skew polyhedron ・ Regular solution ・ Regular sound correspondences between Hungarian and other Uralic languages ・ Regular space ・ Regular surface ・ Regular temperament ・ Regular tree grammar ・ Regular tuning ・ Regular Urban Survivors ・ Regular way contracts ・ RegularChains ・ Regulares ・ Regularis Concordia ・ Regularis Concordia (Winchester) ・ Regularity rally ・ Regularity theorem ・ Regularity theorem for Lebesgue measure ・ Regularization ・ Regularization (linguistics) ・ Regularization (mathematics) ・ Regularization (physics) ・ Regularization by spectral filtering ・ Regularization perspectives on support vector machines ・ Regularized canonical correlation analysis ・ Regularized Inglish Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク RegularChains ： ウィキペディア英語版 RegularChains The RegularChains package in the computer algebra software package Maple is a collection of commands for solving systems of polynomial equations, inequations and inequalities symbolically. This package also allows the user to manipulate and study the solutions of such systems. == Main Features == The main two commands are Triangularize and RealTriangularize. Each of them computes from a system of polynomials $S$ a set of simpler systems $S\_1,\backslash ldots,\; S\_n$ such that a point is a solution of $S$ if and only if it is a solution of one of the systems $S\_1,\backslash ldots,\; S\_n$. Each of these simpler systems is called a regular chain in the case of Triangularize and a regular semi-algebraic system in the case of RealTriangularize. In both cases, each of these simpler systems has a triangular shape and remarkable properties. For this reason, the set $S\_1,\backslash ldots,\; S\_n$ is called a triangular decomposition of the system $S$. In addition to its main functions Triangularize and RealTriangularize, the RegularChains package has six subpackages and other commands. The MatrixTools subpackage provides commands for solving linear systems of equations modulo the saturated ideal of a regular chain. Among other operations are computations of matrix inverses and lower echelon forms. These commands are considered here in a non-standard context. Indeed, the coefficients of these matrices are polynomials and the computations are performed modulo (the saturated ideal of) a regular chain. Since this latter is not required to be a prime ideal, the commands of this subpackage allows you to do linear algebra computations over non-integral domains. The ConstructibleSetTools subpackage provides a large set of commands for manipulating constructible sets. Constructible sets are the fundamental objects of Algebraic Geometry, and they play there the role that ideals play in Polynomial Algebra. In broad terms, a constructible set is the solution set of a system of polynomial equations and inequations. Constructible sets appear naturally in many questions, from high-school problems to advanced research topics. The SemiAlgebraicSetTools subpackage contains a collection of commands for isolating and counting real roots of zero-dimensional semi-algebraic systems or regular chains (that is regular chains with a finite number of complex solutions). It also offers various commands for studying the real solutions of polynomial systems of positive dimension or with parameters. In particular, commands for real root classification, cylindrical algebraic decomposition and partial cylindrical algebraic decomposition sampling are available. Several inspection functions on semi-algebraic systems and their solution sets (namely, semi-algebraic sets) are also provided. They are intended to support the command RealRootClassification, RealTriangularize, LazyRealTriangularize and SamplePoints. The ParametricSystemTools subpackage provides commands for solving systems of equations that depend on parameters. Given a parametric polynomial system $F$, this subpackage can be used to answer questions such as: for which values of the parameters does $F$ have solutions? finitely many solutions? $N$ real solutions, for a given $N$? The ChainTools subpackage provides advanced operations on regular chains. Most of these commands allow you to inspect, construct and transform regular chains, or to check the properties of a polynomial with respect to a regular chain. Some commands operate transformations on a set of regular chains. They can be used to analyze the results computed by the command Triangularize. The FastArithmeticTools subpackage contains a collection of commands for computing with regular chains in prime characteristic using asymptotically fast algorithms. Most of the underlying polynomial arithmetic is performed at C level and relies on (multi-dimensional) Fast Fourier Transform (FFT). This imposes some constraints on the characteristic. One of the main purposes of this subpackage is to offer efficient basic routines in order to suppor the implementation of modular algorithms for computing with regular chains and algebraic numbers. == See also == *Characteristic set *Regular chain *Regular semi-algebraic system *Triangular decomposition 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「RegularChains」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.