up previous next
ArrDerMod

set of generators of the module of logarithmic derivations of an arrangement of hyperplanes

Syntax
ArrDerMod(Q: RINGELEM): MAT

Description
This function returns the matrix whose columns are a set of generators of the module of logarithmic derivations of an arrangement of hyperplanes described by its defining equation Q.

Example
/**/ use QQ[x,y];	
/**/ A := [x, x-y, y];
/**/ Q_A := product(A);	
/**/ ArrDerMod(Q_A);
matrix( /*RingWithID(70, "QQ[x,y]")*/
 [[x, 0],
  [y, x*y -y^2]])

/**/ use QQ[x,y,z];    
/**/ A := [x, x+z, y, 2*y-3*z];
/**/ ArrDerMod(product(A));
matrix( /*RingWithID(78, "QQ[x,y,z]")*/
 [[x, 0, 0, 0],
  [y, y^2 +(-3/2)*y*z, 0, x*y +y*z],
  [z, 0, x*y +(-3/2)*x*z +y*z +(-3/2)*z^2, x*z +z^2]])	

See Also