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D.14.1.35 multarrRestrict

Procedure from library arr.lib (see arr_lib).

[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.

A has to be non-empty.

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.

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
See also: arrRestrict; multarrMultRestrict; multarrRestrict.