Exploratory Experimentation and Computation in the Mathematical Sciences: Theory and Practice

看似不同的数学研究项目依赖于微妙的实验数学方法，并揭示了当前计算机代数系统和符号-数字-图形工具的弱点。该项目解决了高精度数学和科学计算中的效率，有效性，可靠性和可验证性问题。这将通过开发增强的工具来实现，这些工具用于追求具有挑战性的研究问题所驱动的特殊功能的高级计算。重点是易处理的组件，出现在以前的研究有效的高精度算法的多重积分，如出现在整个数学物理，数论和其他地方。

Seemingly disparate mathematical research projects rely on subtle experimental mathematics methods, and have unveiled weaknesses in current computer algebra systems and symbolic-numeric-graphic tools. The project attacks issues of efficiency, effectiveness, reliability, and certifiability in high-precision mathematical and scientific computation. This will be done by developing enhanced tools for advanced computation of special functions driven by pursuit of challenging research problems. The focus is on tractable components that arose in prior research on effective high-precision algorithms for multiple integrals, such as arise throughout mathematical physics, number theory and elsewhere.