Multi-derivative one-step methods based upon Euler-Maclaurin integration formulae are considered for the solution of canonical Hamiltonian dynamical systems. Despite the negative result that simplecticity may not be attained by any multi-derivative Runge--Kutta methods, we show that Euler--MacLaurin formulae are all topologically conjugate to a symplectic formula. This feature entitles them to play a role in the context of geometric integration and, to make their implementation competitive with the existing integrators, we explore the possibility of computing the underlying higher order derivatives with the aid of the Infinity Computer.

中文翻译：

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欧拉-麦克劳林方法的共轭辛性性质及其在无穷大计算机上的实现

考虑了基于欧拉-麦克劳林积分公式的多导数一步法求解正则哈密顿动力系统。尽管任何多导数 Runge--Kutta 方法都无法获得简单性的负面结果，但我们证明了 Euler--MacLaurin 公式都是与辛公式拓扑共轭的。此功能使它们能够在几何积分的背景下发挥作用，并且为了使它们的实现与现有积分器具有竞争力，我们探索了在无限计算机的帮助下计算基础高阶导数的可能性。