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.

翻译：几乎应用数学中的所有问题，包括动力系统分析，在其表述与求解过程中都涉及欧几里得域上的实值函数空间。本文描述了工具Ariadne，它提供了处理欧几里得函数的严格演算方法。我们首先介绍Ariadne框架，该框架基于将对象清晰区分为精确、有效、验证与近似信息。接着讨论Ariadne中实现的函数演算，包括作为具体计算基础类别的多项式函数模型。随后考虑泛函分析中的一些核心问题，即代数方程与微分方程的求解，并简要探讨其在混合系统分析中的应用。我们将给出使用C++和Python代码执行各类计算的示例。最后，讨论扩展方面的进展，包括函数演算的改进以及对更复杂系统类别的拓展。