# Singular

##### 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 ```