# Singular

#### D.14.1.30 arrDer

Procedure from library `arr.lib` (see arr_lib).

Usage:
arrDer(A); arr A , multarr A

Return:
[module] The module Der(A) of derivations of the (multi-)arrangement A, i.e. the derivations tangent to each hyperplane of A (resp. with multiplicities)

Note:
This is only defined for central (multi-)arrangements

Example:
 ```LIB "arr.lib"; ring R = 0,(x,y,z),dp; arr A3 = arrBoolean(3); arr B3 = arrTypeB(3); arr G = ideal(x,y,z,x+y+z); //The derivation module of the Boolean 3-arrangement: arrDer(A3); ==> _[1]=z*gen(3) ==> _[2]=y*gen(2) ==> _[3]=x*gen(1) //The derivation module of the Braid 3-arrangement: arrDer(B3); ==> _[1]=x*gen(1)+y*gen(2)+z*gen(3) ==> _[2]=x2y*gen(2)-y3*gen(2)+x2z*gen(3)-z3*gen(3) ==> _[3]=x2y2z*gen(3)-x2z3*gen(3)-y2z3*gen(3)+z5*gen(3) //The derivation module of the generic arrangement: arrDer(G); ==> _[1]=x*gen(1)+y*gen(2)+z*gen(3) ==> _[2]=yz*gen(3)-yz*gen(2) ==> _[3]=xz*gen(3)+yz*gen(2)+z2*gen(3) ==> _[4]=xy*gen(2)+y2*gen(2)+yz*gen(2) ```