# Singular

#### D.15.16.9 BettiNumsS

Procedure from library `goettsche.lib` (see goettsche_lib).

Usage:
BettiNumsS(n, b); n integer, b list of non-negative integers

Return:
list of non-negative integers

Purpose:
computes the Betti numbers of the n-th symmetric power of a variety with Betti numbers b

Note:
an empty list is returned if n<0 or b is not a list of non-negative integers

Example:
 ```LIB "goettsche.lib"; ring r=0, (z), ls; // consider a complex torus T (elliptic curve) with Betti numbers 1,2,1 list b=1,2,1; // get the Betti numbers of the second symmetric power of T print( BettiNumsS(2, b) ); ==> [1]: ==> 1 ==> [2]: ==> 2 ==> [3]: ==> 2 ==> [4]: ==> 2 ==> [5]: ==> 1 // consider a projective plane P_2 with Betti numbers 1,0,1,0,1 b=1,0,1,0,1; // get the Betti numbers of the third symmetric power of P_2 print( BettiNumsS(3, b) ); ==> [1]: ==> 1 ==> [2]: ==> 0 ==> [3]: ==> 1 ==> [4]: ==> 0 ==> [5]: ==> 2 ==> [6]: ==> 0 ==> [7]: ==> 2 ==> [8]: ==> 0 ==> [9]: ==> 2 ==> [10]: ==> 0 ==> [11]: ==> 1 ==> [12]: ==> 0 ==> [13]: ==> 1 ```