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D.4.18.15 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-yt
==> _[2]=xz-zt
==> _[3]=yt
==> _[4]=x2t-xt2
==> _[5]=zt2
==> _[6]=y3z+xz3t-z3t2
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See also:
curveConductorMult.
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