Singular

D.5.14.4 zetaDL

Assume:

L is the output of resolution of singularities

Compute:

local Denef-Loeser zeta function, if string s1 is present and has the value 'local'; global Denef-Loeser zeta function otherwise
if string s1 or s2 has the value "A", additionally the characteristic polynomial of the monodromy is computed

Return:

list l
if a is not present:
l[1]: string specifying the top. zeta function
l[2]: string specifying characteristic polynomial of monodromy, if "A" was specified
if a is present:
l[1]: string specifying the top. zeta function
l[2]: list ast,
ast[1]=chi(Ei^*)
ast[2]=chi(Eij^*)
ast[3]=chi(Eijk^*)
l[3]: intvec nu of multiplicities as needed in computation of zeta function
l[4]: intvec N of multiplicities as needed in computation of zeta function
l[5]: string specifying characteristic polynomial of monodromy, if "A" was specified

LIB "reszeta.lib";
ring R=0,(x,y,z),dp;
ideal I=x2+y2+z3;
list re=resolve(I,"K");
zetaDL(re,1);
==> [1]:
==>    (s+4)/(3s2+7s+4)
I=(xz+y2)*(xz+y2+x2)+z5;
list L=resolve(I,"K");
zetaDL(L,1);
==> [1]:
==>    (20s2+130s+87)/(160s3+396s2+323s+87)
//===== expected zeta function =========
// (20s^2+130s+87)/((1+s)*(3+4s)*(29+40s))
//======================================