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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | )abbrev category CFCAT CombinatorialFunctionCategory
++ Author: Manuel Bronstein
++ Date Last Updated: 14 May 1991
++ Description:
++ Category for the usual combinatorial functions;
CombinatorialFunctionCategory() : Category == SIG where
SIG ==> with
binomial : ($, $) -> $
++ binomial(n,r) returns the \spad{(n,r)} binomial coefficient
++ (often denoted in the literature by \spad{C(n,r)}).
++ Note that \spad{C(n,r) = n!/(r!(n-r)!)} where \spad{n >= r >= 0}.
++
++X [binomial(5,i) for i in 0..5]
factorial : $ -> $
++ factorial(n) computes the factorial of n
++ (denoted in the literature by \spad{n!})
++ Note that \spad{n! = n (n-1)! when n > 0}; also, \spad{0! = 1}.
permutation : ($, $) -> $
++ permutation(n, m) returns the number of
++ permutations of n objects taken m at a time.
++ Note that \spad{permutation(n,m) = n!/(n-m)!}.
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