|  |  7.5.23.0. quantMat Procedure from libraryqmatrix.lib(see  qmatrix_lib).
 
Example:Usage:
quantMat(n [, p]); n integer (n>1), p an optional integer
Return:
ring (of quantum matrices). If p is specified, the quantum parameter q
will be specialized at the p-th root of unity
 
Purpose:
compute the quantum matrix ring of order n
Note:
activate this ring with the "setring" command.
The usual representation of the variables in this quantum
 algebra is not used because double indexes are not allowed
 in the variables. Instead the variables are listed by reading
 the rows of the usual matrix representation, that is, there
 will be n*n variables (one for each entry an n*N generic matrix),
 listed row-wise
 
 See also:
 qminor.|  | LIB "qmatrix.lib";
def r = quantMat(2); // generate O_q(M_2) at q generic
setring r;   r;
==> // coefficients: QQ(q)
==> // number of vars : 4
==> //        block   1 : ordering Dp
==> //                  : names    y(1) y(2) y(3) y(4)
==> //        block   2 : ordering C
==> // noncommutative relations:
==> //    y(2)y(1)=1/(q)*y(1)*y(2)
==> //    y(3)y(1)=1/(q)*y(1)*y(3)
==> //    y(4)y(1)=y(1)*y(4)+(-q^2+1)/(q)*y(2)*y(3)
==> //    y(4)y(2)=1/(q)*y(2)*y(4)
==> //    y(4)y(3)=1/(q)*y(3)*y(4)
kill r;
def r = quantMat(2,5); // generate O_q(M_2) at q^5=1
setring r;   r;
==> // coefficients: QQ[q]/(q^4+q^3+q^2+q+1)
==> // number of vars : 4
==> //        block   1 : ordering Dp
==> //                  : names    y(1) y(2) y(3) y(4)
==> //        block   2 : ordering C
==> // noncommutative relations:
==> //    y(2)y(1)=(-q^3-q^2-q-1)*y(1)*y(2)
==> //    y(3)y(1)=(-q^3-q^2-q-1)*y(1)*y(3)
==> //    y(4)y(1)=y(1)*y(4)+(-q^3-q^2-2*q-1)*y(2)*y(3)
==> //    y(4)y(2)=(-q^3-q^2-q-1)*y(2)*y(4)
==> //    y(4)y(3)=(-q^3-q^2-q-1)*y(3)*y(4)
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