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Computing Knopfmacher's Limit, or My First Foray into Computational Mathematics, Reprise
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| Organization: | Wolfram Research, Inc. |
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ACA 2009
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Montréal, Québec, Canada
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A talk from ACA 2009, Montreal, June 2009
Session:
Applications of Math Software to Mathematical Research
Abstract:
I will discuss a problem I encountered over a decade ago, and worked on via internet with someone I (alas) never met. It involves a mix of number theory, real analysis, hard-core computation, and some slightly perplexing results.
In brief, we begin with a function expressed as a certain infinite product; Arnold Knopfmacher encountered it in an attempt to approximate the number of irreducible factors of univariate polynomials over Galois fields and raised the question of how to obtain a certain limit to this function. We derive and execute an effective algorithm for the task at hand. We'll also indicate why the most "obvious" approach does not work well in practice, or at all in theory.
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computational number theory, real analysis
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http://aca2009.etsmtl.ca
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| ACA2009_Knopfmacher_limit_talk.pdf (74.2 KB) - PDF Document | | Knopfmacher_limit.pdf (111.7 KB) - PDF Document | | ACA2009_Knopfmacher_limit_talk.nb (129.4 KB) - Mathematica Notebook | | Knopfmacher_limit.nb (165.1 KB) - Mathematica Notebook |
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