Corecursive Coding of High Computational Derivatives and Power Series

Jerzy Karczmarczuk

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arXiv · 2501.13194

Corecursive Coding of High Computational Derivatives and Power Series

Jerzy Karczmarczuk

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Abstract

We discuss the functional lazy techniques in generation and handling of arbitrarily long sequences of derivatives of numerical expressions in one ``variable''; the domain to which the paper belongs is usually nicknamed ``Automatic differentiation''. Two models thereof are considered, the chains of ``pure'' derivatives, and the infinite power series, similar, but algorithmically a bit different. We deal with their arithmetic/algebra, and with more convoluted procedures, such as composition and reversion. Some more specific applications of these structures are also presented.

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Jerzy Karczmarczuk. 2025-01-22. Corecursive Coding of High Computational Derivatives and Power Series. https://arxiv.org/abs/2501.13194

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