Singular Manual: zetaDL

| #### D.5.16.4 zetaDL 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 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 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))
    //======================================

User manual for Singular version 4-2-1p3, 2021, generated by texi2html.