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D.5.5.9 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
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