Procedure from library reszeta.lib (see reszeta_lib).
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 multiplicites as needed in computation of zeta
function
l[4]: intvec N of multiplicities as needed in compuation of zeta
function
l[5]: string specifying characteristic polynomial of monodromy,
if "A" was specified
Example:
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))
//======================================
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