Singular

D.15.2.35 multarrRestrict

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

Return:
[multarr] the restricted hyperplane Multi-Arrangement (A^X) with multiplicities i.e. counting how often one element of the restricted arrangement occurs as intersetion of hyperplane of the first arrangement. This definition is due to Guenter M. Ziegler.

Note:
A has to be non-empty.

Remarks:
We restrict A to the flat X, defined by the equations in A[v]. The restriction will only be performed, if the ideal defining the flat X is monomial (i.e. X is an intersection of coordinate planes). If the optional argument CC is given, the arrangement is transformed in such a way that X has the above form.

Example:
 ```LIB "arr.lib"; ring R = 0,x(1..5),dp; arr A = arrEdelmanReiner(); A; ==> _[1]=x(1) ==> _[2]=x(2) ==> _[3]=x(3) ==> _[4]=x(4) ==> _[5]=x(5) ==> _[6]=x(1)-x(2)-x(3)-x(4)-x(5) ==> _[7]=x(1)-x(2)-x(3)-x(4)+x(5) ==> _[8]=x(1)-x(2)-x(3)+x(4)-x(5) ==> _[9]=x(1)-x(2)-x(3)+x(4)+x(5) ==> _[10]=x(1)-x(2)+x(3)-x(4)-x(5) ==> _[11]=x(1)-x(2)+x(3)-x(4)+x(5) ==> _[12]=x(1)-x(2)+x(3)+x(4)-x(5) ==> _[13]=x(1)-x(2)+x(3)+x(4)+x(5) ==> _[14]=x(1)+x(2)-x(3)-x(4)-x(5) ==> _[15]=x(1)+x(2)-x(3)-x(4)+x(5) ==> _[16]=x(1)+x(2)-x(3)+x(4)-x(5) ==> _[17]=x(1)+x(2)-x(3)+x(4)+x(5) ==> _[18]=x(1)+x(2)+x(3)-x(4)-x(5) ==> _[19]=x(1)+x(2)+x(3)-x(4)+x(5) ==> _[20]=x(1)+x(2)+x(3)+x(4)-x(5) ==> _[21]=x(1)+x(2)+x(3)+x(4)+x(5) ==> multarr AR = multarrRestrict(A,6,"CC"); AR; ==> _[1]=(x(2)+1/4*x(3)+1/4*x(4)+1/4*x(5))^2 ==> _[2]=(x(2)+4*x(3)-x(4)-x(5))^2 ==> _[3]=(x(2)-x(3)+4*x(4)-x(5))^2 ==> _[4]=(x(2)-x(3)-x(4)+4*x(5))^2 ==> _[5]=(x(2)-x(3)-x(4)-x(5))^2 ==> _[6]=(x(2)-x(3)-x(4)+3/2*x(5))^1 ==> _[7]=(x(2)-x(3)+3/2*x(4)-x(5))^1 ==> _[8]=(x(2)-x(3)+3/2*x(4)+3/2*x(5))^1 ==> _[9]=(x(2)-x(3)+2/3*x(4)+2/3*x(5))^1 ==> _[10]=(x(2)+3/2*x(3)-x(4)-x(5))^1 ==> _[11]=(x(2)+3/2*x(3)-x(4)+3/2*x(5))^1 ==> _[12]=(x(2)+2/3*x(3)-x(4)+2/3*x(5))^1 ==> _[13]=(x(2)+3/2*x(3)+3/2*x(4)-x(5))^1 ==> _[14]=(x(2)+2/3*x(3)+2/3*x(4)-x(5))^1 ==> _[15]=(x(2)+2/3*x(3)+2/3*x(4)+2/3*x(5))^1 ==> ```