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

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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.