Singular Manual: normalConductor

| #### D.4.19.15 normalConductor Procedure from library `normal.lib` (see normal_lib). Usage: normalConductor(I); I ideal Assume: I is a radical ideal Return: the conductor of R/I as ideal in R Remarks: The procedures makes use of the minimal primes and the generators of the normalization given by the normalization algorithm. Note: the optional parameter can be used if the normalization has already been computed. If a list L contains the output of the procedure normal (with options prim, wd and usering if the ring has a mixed ordering), apply normalConductor(I,L) Example:
    LIB "normal.lib";
    ///////////////////////////////////////////
    // Computation of small conductor ideals //
    ///////////////////////////////////////////
    ring R = 0,(x,y,z),ds;
    ideal I = x2y2 - z;
    normalConductor(I);
    ==> _[1]=1
    // The conductor is the whole ring - so the ring is normal
    // We can also see this using the delta invariant:
    curveDeltaInv(I);
    ==> 0
    ring S = 0,(a,b,c),dp;
    ideal J = abc;
    normalConductor(J);
    ==> _[1]=bc
    ==> _[2]=ac
    ==> _[3]=ab
    // The conductor is not the whole ring - so it is not normal
    // We can also see this using the delta invariant, which is even infinite
    curveDeltaInv(J);
    ==> -1
    kill R,S;
    /////////////////////////////////////
    // Computation of a bigger example //
    /////////////////////////////////////
    ring R = 0,(x,y,z,t),ds;
    ideal I = xyz - yzt, x2y3 - z2t4;
    I = std(radical(I));
    // Ideal I
    I;
    ==> I[1]=x2y-xyt
    ==> I[2]=xyz-yzt
    ==> I[3]=xzt-zt2
    ==> I[4]=xy3-z2t3
    ==> I[5]=y3zt-z3t3
    // Conductor
    normalConductor(I);
    ==> _[1]=xy
    ==> _[2]=xz-zt
    ==> _[3]=yt
    ==> _[4]=x2t-xt2
    ==> _[5]=zt2
    ==> _[6]=y3z
See also: curveConductorMult.

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