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D.15.1.10 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
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See also:
arrCenter;
arrCentered;
arrCentral;
arrCentralize.
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