Singular

7.5.16.0. qminor

Usage:

qminor(I,J,n); I,J intvec, n int

Return:

poly, the quantum minor of a generic n*n quantum matrix

Assume:

I is the ordered list of the rows to consider in the minor,
J is the ordered list of the columns to consider in the minor,
I and J must have the same number of elements,
n is the order of the quantum matrix algebra you are working with (quantMat(n)).
The base ring should be constructed using quantMat.

LIB "qmatrix.lib";
def r = quantMat(3); // let r be a quantum matrix of order 3
setring r;
intvec u = 1,2;
intvec v = 2,3;
intvec w = 1,2,3;
qminor(w,w,3);
==> y(1)*y(5)*y(9)+(-q)*y(1)*y(6)*y(8)+(-q)*y(2)*y(4)*y(9)+(q^2)*y(2)*y(6)*y(\
   7)+(q^2)*y(3)*y(4)*y(8)+(-q^3)*y(3)*y(5)*y(7)
qminor(u,v,3);
==> y(2)*y(6)+(-q)*y(3)*y(5)
qminor(v,u,3);
==> y(4)*y(8)+(-q)*y(5)*y(7)
qminor(u,u,3);
==> y(1)*y(5)+(-q)*y(2)*y(4)