# 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 ==> : ==> 2 ==> : ==> 2 ==> : ==> 2 ==> : ==> 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 ==> : ==> 0 ==> : ==> 1 ==> : ==> 0 ==> : ==> 2 ==> : ==> 0 ==> : ==> 2 ==> : ==> 0 ==> : ==> 2 ==> : ==> 0 ==> : ==> 1 ==> : ==> 0 ==> : ==> 1 ```

### Misc 