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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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