This command returns a basis (or minimal generating set, if the ground ring is not a field), of a homogeneous right ideal in a noncommutative ring.
i1 : A = QQ{x,y,z} o1 = A o1 : NCPolynomialRing |
i2 : p = y*z + z*y - x^2 2 o2 = zy+yz-x o2 : A |
i3 : q = x*z + z*x - y^2 2 o3 = zx-y +xz o3 : A |
i4 : r = z^2 - x*y - y*x 2 o4 = z -yx-xy o4 : A |
i5 : I = ncRightIdeal{p,q,r} 2 2 2 o5 = Right ideal {zy+yz-x , zx-y +xz, z -yx-xy} o5 : NCRightIdeal |
i6 : bas = basis(3,I) o6 = | z*x^2-y^2*x+x*z*x z*y*x+y*z*x-x^3 z^2*x-y*x^2-x*y*x z*x*y-y^3+x*z*y z*y^2+y*z*y-x^2*y z^2*y-y*x*y-x*y^2 z*x*z-y^2*z+x*z^2 z*y*z+y*z^2-x^2*z z^3-y*x*z-x*y*z | o6 : NCMatrix |