arXiv Open Access 2018

Additive Decompositions in Primitive Extensions

Shaoshi Chen Hao Du Ziming Li

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Abstrak

This paper extends the classical Ostrogradsky-Hermite reduction for rational functions to more general functions in primitive extensions of certain types. For an element $f$ in such an extension $K$, the extended reduction decomposes $f$ as the sum of a derivative in $K$ and another element $r$ such that $f$ has an antiderivative in $K$ if and only if $r=0$; and $f$ has an elementary antiderivative over $K$ if and only if $r$ is a linear combination of logarithmic derivatives over the constants when $K$ is a logarithmic extension. Moreover, $r$ is minimal in some sense. Additive decompositions may lead to reduction-based creative-telescoping methods for nested logarithmic functions, which are not necessarily $D$-finite.

Topik & Kata Kunci

cs.SC

Penulis (3)

Shaoshi Chen

Hao Du

Ziming Li

Format Sitasi

APA MLA BibTeX

Chen, S., Du, H., Li, Z. (2018). Additive Decompositions in Primitive Extensions. https://arxiv.org/abs/1802.02329

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Informasi Jurnal

Tahun Terbit: 2018
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓