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D.2.3.4 binomial
Procedure from library general.lib (see general_lib).
- Usage:
- binomial(n,k); n,k integers
- Return:
- binomial(n,k); binomial coefficient n choose k
- of type bigint (computed in characteristic 0)
- Note:
- In any characteristic, binomial(n,k) = coefficient of x^k in (1+x)^n
Example:
| LIB "general.lib";
binomial(200,100);""; //type string, computed in char 0
int n,k = 200,100;
ring r = 0,x,dp;
number b1 = binomial(n,k,0); //type number, computed in ring r
poly b2 = coeffs((x+1)^n,x)[k+1,1]; //coefficient of x^k in (x+1)^n
b1-b2; //b1 and b2 should coincide
| prime
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