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