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D.14.1.10 arrCenter

Procedure from library arr.lib (see arr_lib).

Usage:
arrCenter(A); arr A

Return:
[list] L entry 0 if A not centered or entries 1, x, H, where x is any particular point of the center and H is a matrix consisting of vectors which spanning linear intersection space.
If there is exactly one solution, then H = 0.

Note:
The intersection of all hyperplanes can be expressed in forms of a linear system Ax=b, where (A|b) is the coeff. matrix of the arrange- ment, which is then solved using L-U decomposition

Example:
 
LIB "arr.lib";
ring R = 0,(x,y,z),dp;
arr A= ideal(x,y,x-y+1);    // centerless
arrCenter(A);
==> [1]:
==>    0
arr B= ideal(x,y,z);        // center is a single point
arrCenter(B);
==> [1]:
==>    1
==> [2]:
==>    _[1,1]=0
==>    _[2,1]=0
==>    _[3,1]=0
==> [3]:
==>    _[1,1]=0
arr C= ideal(x,z,x+z);      // center is a line
// here we get a wrong result because the matrix is simplified since A doesn't
// contain any "y" the matrix (A|b) will be 3x3 only.
arrCenter(C);
==> [1]:
==>    1
==> [2]:
==>    _[1,1]=0
==>    _[2,1]=0
==>    _[3,1]=0
==> [3]:
==>    _[1,1]=0
==>    _[2,1]=-1
==>    _[3,1]=0
See also: arrCenter; arrCentered; arrCentral; arrCentralize.