代数、几何和微分方程中的符号计算

IF 0.8 4区计算机科学 Q3 COMPUTER SCIENCE, THEORY & METHODS

Information and Computation Pub Date : 2024-08-02 DOI:10.1016/j.ic.2024.105200

Franz Winkler

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引用次数: 0

摘要

在这篇调查文章中，我们描述了代数与几何中的符号计算如何导致代数微分方程的符号解，即公式解。代数微分方程的符号解可以从相应代数变量的参数化推导出来。这些参数反过来又可以通过消元法（即求解多项式方程组的方法）计算出来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Symbolic computation in algebra, geometry, and differential equations

In this survey article we describe how symbolic computation in algebra and geometry leads to symbolic, i.e., formula solutions of algebraic differential equations. Symbolic solutions of algebraic differential equations can be derived from parametrizations of corresponding algebraic varieties. Such parametrizations in turn can be computed by elimination methods, i.e., methods for solving systems of polynomial equations.

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来源期刊

Information and Computation 工程技术-计算机：理论方法

CiteScore

2.30

自引率

0.00%

发文量

119

审稿时长

140 days

期刊介绍： Information and Computation welcomes original papers in all areas of theoretical computer science and computational applications of information theory. Survey articles of exceptional quality will also be considered. Particularly welcome are papers contributing new results in active theoretical areas such as -Biological computation and computational biology- Computational complexity- Computer theorem-proving- Concurrency and distributed process theory- Cryptographic theory- Data base theory- Decision problems in logic- Design and analysis of algorithms- Discrete optimization and mathematical programming- Inductive inference and learning theory- Logic & constraint programming- Program verification & model checking- Probabilistic & Quantum computation- Semantics of programming languages- Symbolic computation, lambda calculus, and rewriting systems- Types and typechecking