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Binomial Coefficients
Author

Ilan Vardi
Organization: Wolfram Research, Inc.
Old MathSource #

0203-331
Revision date

1992-06-01
Description

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.
Subjects

*Mathematics > Calculus and Analysis > Special Functions
*Mathematics > Discrete Mathematics > Combinatorics
Keywords

Number Theory, FastBinomial, FastFactorial, BinomialMod, Fast Factorial, Binomial expansion, Binomial coefficients, prime factorization, Binomial.m, Documentation.txt, SampleInput.txt
Downloads Download Wolfram CDF Player

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Documentation.txt (2.6 KB) - Plain-text documentation
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SampleInput.txt (268 B) - Sample input lines from NumberTheory`Binomial`
Download
Binomial.m (5.9 KB) - Mathematica package