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D.4.5.4 curveColengthDerivations
Procedure from library curveInv.lib (see curveInv_lib).
- Usage:
- curveColengthDerivations(I); I ideal
- Assume:
- I is a radical ideal
- Return:
- the colength of derivations of R/I
- Remarks:
- The procedure goes through all branches and computes the colength of
derivations there. Then the d-dimension of the minimal primes is computed.
After that, everything is summed up.
- 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 curveColengthDerivations(I,L)
Example:
| LIB "curveInv.lib";
///////////////////////////////////////
// colength of derivations of curves //
///////////////////////////////////////
// Example 1:
ring R = 0,(x,y,z),ds;
ideal I = x2-y4z,z3y2+xy2;
I = std(radical(I));
curveColengthDerivations(I);
==> 9
// Example 2:
ring S = 0,(x,y),ds;
ideal I = (x+y)*(x2-y3);
curveColengthDerivations(I);
==> 4
// Example 3:
ideal J = (x2-y3)*(x2+y2)*(x-y);
curveColengthDerivations(J);
==> 15
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