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7.5.7.0. Gweights
Procedure from library nctools.lib (see nctools_lib).

Usage:
Gweights(r); r a ring or a square matrix

Return:
intvec

Purpose:
compute the weight vector for the following G-algebra:
for r itself, if it is of the type ring,
or for a G-algebra, defined by the square polynomial matrix r

Theory:
Gweights returns a vector, which must be used to redefine the G-algebra. If the input is a matrix and the output is the zero vector then there is not a G-algebra structure associated to these relations with respect to the given variables. Another possibility is to use weightedRing to obtain directly the G-algebra with the new weighted ordering.

Example:
 
LIB "nctools.lib";
ring r = (0,q),(a,b,c,d),lp;
matrix C[4][4];
C[1,2]=q; C[1,3]=q; C[1,4]=1; C[2,3]=1; C[2,4]=q; C[3,4]=q;
matrix D[4][4];
D[1,4]=(q-1/q)*b*c;
ncalgebra(C,D);
r;
==> //   characteristic : 0
==> //   1 parameter    : q 
==> //   minpoly        : 0
==> //   number of vars : 4
==> //        block   1 : ordering lp
==> //                  : names    a b c d 
==> //        block   2 : ordering C
==> //   noncommutative relations:
==> //    ba=(q)*ab
==> //    ca=(q)*ac
==> //    da=ad+(q2-1)/(q)*bc
==> //    db=(q)*bd
==> //    dc=(q)*cd
Gweights(r);
==> 2,1,1,1
Gweights(D);
==> 2,1,1,1
weightedRing


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