Home Online Manual
Top
Back: appendWeight2Ord
Forward: extendedTensor
FastBack: ncfactor_lib
FastForward: nctools_lib
Up: ncpreim_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document
7.7.14.0. elimWeight
Procedure from library ncpreim.lib (see ncpreim_lib).

Usage:
elimWeight(v); v an intvec

Assume:
The basering is a G-algebra.
The entries of v are in the range 1..nvars(basering) and the corresponding variables generate an admissible subalgebra.

Return:
intvec, say w, such that the ordering (a(w),<), where < is any admissible global ordering, is an elimination ordering for the subalgebra generated by the variables indexed by the entries of the given intvec.

Note:
If no such ordering exists, the zero intvec is returned.

Remark:
Reference: (BGL), (GML)

Example:
 
LIB "ncpreim.lib";
// (Lev): Example 2
ring r = 0,(a,b,x,d),Dp;
matrix D[4][4];
D[1,2] = 3*a;  D[1,4] = 3*x^2;  D[2,3] = -x;
D[2,4] = d;    D[3,4] = 1;
def A = nc_algebra(1,D);
setring A; A;
==> //   characteristic : 0
==> //   number of vars : 4
==> //        block   1 : ordering Dp
==> //                  : names    a b x d
==> //        block   2 : ordering C
==> //   noncommutative relations:
==> //    ba=ab+3a
==> //    da=ad+3x2
==> //    xb=bx-x
==> //    db=bd+d
==> //    dx=xd+1
// Since d*a-a*d = 3*x^2, any admissible ordering has to satisfy
// x^2 < a*d, while any elimination ordering for {x,d} additionally
// has to fulfil a << x and a << d.
// Hence neither a block ordering with weights
// (1,1,1,1) nor a weighted ordering with weight (0,0,1,1) will do.
intvec v = 3,4;
elimWeight(v);
==> 0,0,1,2