# Singular          #### D.15.10.4 curveColengthDerivations

Procedure from library `curveInv.lib` (see curveInv_lib).

Usage:
curveColengthDerivations(I); I ideal

Assume:

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 ```

### Misc 