This command returns a basis (or minimal generating set, if the ground ring is not a field), of a homogeneous left 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 = ncLeftIdeal{p,q,r} 2 2 2 o5 = Left ideal {zy+yz-x , zx-y +xz, z -yx-xy} o5 : NCLeftIdeal |
i6 : bas = basis(3,I) | 2 2 3 2 2 3 2 2 2 2 2 2 2 2 3 | o6 = | xzx-xy +x z yzx-y +yxz z x-zy +zxz xzy+xyz-x yzy+y z-yx z y+zyz-zx xz -xyx-x y yz -y x-yxy z -zyx-zxy | o6 : NCMatrix |