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Binomial Coefficients
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| Organization: | Wolfram Research, Inc. |
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0203-331
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1992-06-01
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This package implements fast evaluation of binomial coefficients. The evaluation of the standard binomial coefficients is accomplished using their prime factorization. This reduces the number of multiplications by a factor of log. In the case of Binomial[2n,n], there exists a still better algorithm due to the coefficient's explicit factorization. These algorithms require the function PrimePi[x]. The package also implements a method to compute factorials that is faster than the built-in version for large arguments.
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Number Theory, FastBinomial, FastFactorial, BinomialMod, Fast Factorial, Binomial expansion, Binomial coefficients, prime factorization, Binomial.m, Documentation.txt, SampleInput.txt
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| Documentation.txt (2.6 KB) - Plain-text documentation | | SampleInput.txt (268 B) - Sample input lines from NumberTheory`Binomial` | | Binomial.m (5.9 KB) - Mathematica package |
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