数学函数数字图书馆与计算机代数系统的比较验证
Comparative Verification of the Digital Library of Mathematical Functions and Computer Algebra Systems
摘要：
数字数学图书馆汇集了多年数学研究的知识。许多学科（例如，物理学、工程学、纯数学和应用数学）在很大程度上依赖于汇编收集的发现。同样，现代研究应用越来越依赖于计算解决方案，这些解决方案通常由计算机代数系统计算和验证。因此，数字数学库和计算机代数系统的正确性、准确性和可靠性是现代研究的重要属性。在本文中，我们提出了一种新的方法来验证一个数字数学库和两个计算机代数系统与另一个通过转换数学表达式从一个系统。我们使用我们以前开发的转换工具（简称LaCASt），从NIST的数学函数的数字图书馆的计算机代数系统Maple和Mathematica的公式。我们所提出的工作的贡献如下：（1）我们提出了最全面的验证计算机代数系统和数字数学库彼此;（2）我们显着提高性能的底层翻译的覆盖率和准确性方面;（3）我们提供了开放获取的Maple和Mathematica的公式在NIST的数学函数数字图书馆的翻译。
英文摘要：
Digital mathematical libraries assemble the knowledge of years of mathematical research. Numerous disciplines (e.g., physics, engineering, pure and applied mathematics) rely heavily on compendia gathered findings. Likewise, modern research applications rely more and more on computational solutions, which are often calculated and verified by computer algebra systems. Hence, the correctness, accuracy, and reliability of both digital mathematical libraries and computer algebra systems is a crucial attribute for modern research. In this paper, we present a novel approach to verify a digital mathematical library and two computer algebra systems with one another by converting mathematical expressions from one system to the other. We use our previously eveloped conversion tool (referred to as LaCASt) to translate formulae from the NIST Digital Library of Mathematical Functions to the computer algebra systems Maple and Mathematica. The contributions of our presented work are as follows: (1) we present the most comprehensive verification of computer algebra systems and digital mathematical libraries with one another; (2) we significantly enhance the performance of the underlying translator in terms of coverage and accuracy; and (3) we provide open access to translations for Maple and Mathematica of the formulae in the NIST Digital Library of Mathematical Functions.
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