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D.15.5.1 GoettscheF
Procedure from library goettsche.lib (see goettsche_lib).
- Usage:
- GoettscheF(z, t, n, b); z, t polynomials, n integer, b list of non-negative integers
- Return:
- polynomial in z and t
- Purpose:
- computes the Goettsche's formula up to degree n in t
- Note:
- zero is returned if n<0 or b is not a list of non-negative integers
or if there are not enough Betti numbers
Example:
| | LIB "goettsche.lib";
ring r=0, (t, z), ls;
// consider the projective plane with Betti numbers 1,0,1,0,1
list b=1,0,1,0,1;
// get the Goettsche's formula up to degree 3
print( GoettscheF(z, t, 3, b) );
==> 1+t+tz2+tz4+t2+2t2z2+3t2z4+2t2z6+t2z8+t3+2t3z2+5t3z4+6t3z6+5t3z8+2t3z10+t\
3z12
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