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7.5.20.0. 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;
==> // coefficients: QQ(q)
==> // 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
| See also:
weightedRing.
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