This command returns a basis (or minimal generating set, if the ground ring is not a field), of a graded 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 : B = A/I --Calling Bergman for NCGB calculation. --running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12160-0/0.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12160-0/3.ter ... Complete! o6 = B o6 : NCQuotientRing |
i7 : bas = basis(4,B) | 4 2 3 2 2 2 3 4 3 2 2 3 | o7 = | x x yx yxyx x y xyxy x y yxy xy y x z xyxz x yz yxyz xy z y z | o7 : NCMatrix |