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B.8.0.1 quant
Procedure from library qmatrix.lib (see qmatrix_lib).
- Usage:
- quant(n [, p]); n integer (n>1), p an optional integer
- Purpose:
- compute the quantum matrix ring of order n;
- Return:
- ring (of quantum matrices). If p is specified, the quantum parameter q
will be specialized at p-th root of unity
- Note:
- You have to 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 reading
the rows of the usual matrix representation.
Example:
| LIB "qmatrix.lib";
def r=quant(2); // generate O_q(M_2) at q generic
setring r; r;
==> // characteristic : 0
==> // 1 parameter : q
==> // minpoly : 0
==> // 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=quant(2,5); // generate O_q(M_2) at q^5=1
setring r; r;
==> // characteristic : 0
==> // 1 parameter : q
==> // minpoly : (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)
| qminor
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