Singular Manual: BettiNumsS

| #### 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

User manual for Singular version 4.4.1, 2025, generated by texi2html.