Computer Algebra Systems & Artificial Intelligence

K. Zotos
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Abstract

From four-function calculators to calculators (or computers) with Computer Algebra System (CAS) software, Mathematics computing technology has advanced. With just a few button pushes, CASs can solve a wide range of mathematical problems, which is a true quantum leap in technology. The implications of having software in the classroom that can, for example, expand and factorize algebraic expressions, solve equations, differentiate functions, and find anti-derivatives are causing the mathematical community to engage in a heated debate about whether this is one of the most exciting or frightening developments in the history of education. It was only a matter of time before Artificial Intelligence entered the field of Science. This is now also the case with Mathematics, one of the dominant, perhaps the most basic, but also the most "difficult" of the sciences. The human mind, for better or for worse, has its limits. As we see in every manifestation of our lives, in this case, technology is being enlisted to help humanity take the next step, whether it has to do with automation and practical matters, or with knowledge and exploration. Creating a model that is understandable to humans is the primary objective of Artificial Intelligence. Additionally, concepts and methods from numerous mathematical fields can be used to prepare these models. In this paper, we will examine the use of AI in CASs and explore some ways to optimize them. The documentation sheets are the data source that we used to examine their characteristics. The research results reveal that there are many tips that we can follow to accelerate performance.
计算机代数系统与人工智能
从四功能计算器到装有计算机代数系统(CAS)软件的计算器(或计算机),数学计算技术不断进步。只需按下几个按钮,CAS 就能解决各种数学问题,这是技术上真正的飞跃。例如,在课堂上使用可以展开和因式分解代数表达式、解方程、微分函数和求反衍数的软件所产生的影响,正引起数学界的激烈争论,讨论这究竟是教育史上最令人兴奋还是最令人恐惧的发展之一。人工智能进入科学领域只是时间问题。数学现在也是如此,它是最主要的科学之一,也许是最基础的科学,但也是最 "困难 "的科学。人类的思维,无论好坏,都有其局限性。正如我们在生活中的每一种表现形式中看到的那样,在这种情况下,技术正在被用来帮助人类迈出下一步,无论是在自动化和实际事务方面,还是在知识和探索方面。创建人类可以理解的模型是人工智能的首要目标。此外,众多数学领域的概念和方法也可用于制作这些模型。本文将研究人工智能在 CAS 中的应用,并探讨优化 CAS 的一些方法。文件表是我们用来研究其特征的数据源。研究结果表明,我们可以遵循许多技巧来加快性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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