Singular Manual: arrEdelmanReiner

D.14.1.28 arrEdelmanReiner

Procedure from library arr.lib (see arr_lib).

Usage:: arrEdelmanReiner();
Return:: the Edelman-Reiner arrangement, which is a free arrangement but the restriction to the 6-th hyperplane is nonfree.
(i.e. counterexample for Orlik-Conjecture)
Note:: the active ring must have at least five variables

Example:

LIB "arr.lib";
ring r=0,x(1..5),dp;
arrEdelmanReiner();
==> _[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)
==>

See also: arrBoolean; arrBraid; arrEdelmanReiner; arrRandom; arrTypeB; arrTypeD.

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