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D.15.1.30 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)
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See also:
arrDer;
arrExponents;
arrIsFree.
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