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Development Release: Kongoni GNU/Linux 2011 Beta 1
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combinatorics(n) Tcl Math Library combinatorics(n) NAME
combinatorics - Combinatorial functions in the Tcl Math Library SYNOPSIS
package require Tcl 8.2 package require math ?1.2? ::math::ln_Gamma z ::math::factorial x ::math::choose n k ::math::Beta z w DESCRIPTION
The math package contains implementations of several functions useful in combinatorial problems. COMMANDS
::math::ln_Gamma z Returns the natural logarithm of the Gamma function for the argument z. The Gamma function is defined as the improper integral from zero to positive infinity of t**(x-1)*exp(-t) dt The approximation used in the Tcl Math Library is from Lanczos, ISIAM J. Numerical Analysis, series B, volume 1, p. 86. For "x > 1", the absolute error of the result is claimed to be smaller than 5.5*10**-10 -- that is, the resulting value of Gamma when exp( ln_Gamma( x) ) is computed is expected to be precise to better than nine significant figures. ::math::factorial x Returns the factorial of the argument x. For integer x, 0 <= x <= 12, an exact integer result is returned. For integer x, 13 <= x <= 21, an exact floating-point result is returned on machines with IEEE floating point. For integer x, 22 <= x <= 170, the result is exact to 1 ULP. For real x, x >= 0, the result is approximated by computing Gamma(x+1) using the ::math::ln_Gamma function, and the result is expected to be precise to better than nine significant figures. It is an error to present x <= -1 or x > 170, or a value of x that is not numeric. ::math::choose n k Returns the binomial coefficient C(n, k) C(n,k) = n! / k! (n-k)! If both parameters are integers and the result fits in 32 bits, the result is rounded to an integer. Integer results are exact up to at least n = 34. Floating point results are precise to better than nine significant figures. ::math::Beta z w Returns the Beta function of the parameters z and w. Beta(z,w) = Beta(w,z) = Gamma(z) * Gamma(w) / Gamma(z+w) Results are returned as a floating point number precise to better than nine significant digits provided that w and z are both at least 1. math 4.2 combinatorics(n)
