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D.15.6.2 curveConductorMult
Procedure from library curveInv.lib (see curveInv_lib).
- Usage:
- curveConductorMult(I); I ideal
- Assume:
- I is a radical ideal, dim(R/I) = 1
- Return:
- the multiplicity of the conductor
- 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 curveConductorMult(I,L)
Example:
| | LIB "curveInv.lib";
//////////////////////////////////////////////
// Mutltiplicity of the conductor of curves //
//////////////////////////////////////////////
ring R = 0,(x,y,z),ds;
// Example 1:
ideal I = x2-y4z,z3y2+xy2;
I = std(radical(I));
curveConductorMult(I);
==> 23
// Example 2:
ideal I = x*(y+z)^3 - y3, x2y2 + z5;
==> // ** redefining I (ideal I = x*(y+z)^3 - y3, x2y2 + z5;)
I = std(radical(I));
curveConductorMult(I);
==> 19
kill R;
////////////////////////////////////////////////////////
// Mutltiplicity of the conductor of Gorenstein curve //
////////////////////////////////////////////////////////
ring R = 0,(x,y),ds;
ideal I = xy;
// In such a case, the conductor multiplicity c satisfies: c = 2*delta
// Delta invariant:
curveDeltaInv(I);
==> 1
// Conductor Multiplicity:
curveConductorMult(I);
==> 2
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See also:
normalConductor.
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