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) 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 -y*x^2+x^2*y -y^2*x+x*y^2 z*x*y-y^3+x*z*y z*y^2+y*z*y-y*x^2 z^2*y-y^2*x-y*x*y -z*x^2+x^2*z -z*y*x-y^3+y*x*z+x^3 -z*y^2+z*x*z+y*x^2+x*y*x -z*x*y+y^3+x*y*z-x^3 -z*y^2+y^2*z z*y*z-z*x^2+y^2*x+y*x*y -y*x^2+x*z^2-x*y*x y*z^2-y^2*x-y*x*y z^3-z*y*x-z*x*y | o6 : NCMatrix |