# Singular

##### 7.7.15.0. Gweights
Procedure from library `nctools.lib` (see nctools_lib).

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

Return:
intvec

Purpose:
compute an appropriate weight int vector for a G-algebra, i.e., such that \foral\;i<j\;\;lm_w(d_{ij}) <_w x_i x_j.
the polynomials d_{ij} are taken from r itself, if it is of the type ring
or defined by the given square polynomial matrix

Theory:
`Gweights` returns an integer vector, whose weighting should be used to redefine the G-algebra in order to get the same non-commutative structure w.r.t. a weighted ordering. 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 a G-algebra with the new appropriate (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; def S = nc_algebra(C,D); setring S; S; ==> // 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(S); ==> 2,1,1,1 def D=fetch(r,D); Gweights(D); ==> 2,1,1,1 ```