一句话：介绍 Ariadne 框架及其严格函数演算，支持欧氏函数模型、方程求解与混合系统分析。
应用数学与动力系统分析通常涉及欧氏域上实值函数的表述与求解，但浮点计算难以保证严格性。本文介绍工具 Ariadne，它提供一套面向欧氏函数的严格函数演算。框架将对象信息清晰分离为 exact、effective、validated 和 approximate 四类，并以此为基础实现函数演算，其中多项式函数模型是具体计算的核心类。作者进一步讨论函数分析中的核心问题，包括代数方程与微分方程的求解，并简述其在混合系统分析中的应用。文中给出执行各类计算的 C++ 与 Python 代码示例，最后讨论函数演算改进及更复杂系统类扩展方面的进展。
Almost all problems in applied mathematics, including the analysis of dynamical systems, deal with spaces of real-valued functions on Euclidean domains in their formulation and solution. In this paper, we describe the the tool Ariadne, which provides a rigorous calculus for working with Euclidean functions. We first introduce the Ariadne framework, which is based on a clean separation of objects as providing exact, effective, validated and approximate information. We then discuss the function calculus as implemented in Ariadne, including polynomial function models which are the fundamental class for concrete computations. We then consider solution of some core problems of functional analysis, namely solution of algebraic equations and differential equations, and briefly discuss their use for the analysis of hybrid systems. We will give examples of C++ and Python code for performing the various calculations. Finally, we will discuss progress on extensions, including improvements to the function calculus and extensions to more complicated classes of system.
DOI 原文 · arXiv · PDF（开放获取） · DBLP
@article{abs-2306-17541,
title = {Rigorous Function Calculi in Ariadne},
author = {Pieter Collins and Luca Geretti and Sanja Zivanovic Gonzalez and Davide Bresolin and Tiziano Villa},
journal = {Logical Methods in Computer Science},
volume = {Volume 21, Issue 3},
year = {2025},
doi = {10.46298/lmcs-21(3:28)2025}
}