CoCoA:Bin

Bin

binomial coefficient

Description

This function computes the binomial coefficient, N choose K

according to the formula

     (N)(N-1)(N-2)...(N-K+1)/ K!

The same formula is used if N is a polynomial. The integer K cannot be negative.

Example

  Bin(4,2);
6
-------------------------------
  Bin(-4,3);
-20
-------------------------------
  Bin(x^2+2y,3);
1/6x^6 + x^4y - 1/2x^4 + 2x^2y^2 - 2x^2y + 4/3y^3 + 1/3x^2 - 2y^2 + 2/3y
-------------------------------
  It = (x^2+2y)(x^2+2y-1)(x^2+2y-2)/6;
TRUE
-------------------------------

Syntax

Bin(N:INT or POLY, K:INT):INT

BinExp

EvalBinExp

   <type>integer</type>
   <type>polynomial</type>