-- -*- M2-comint -*- hash: 1451222560

i1 : A = QQ{x,y,z}

o1 = A

o1 : NCPolynomialRing

i2 : f = y*z + z*y - x^2

            2
o2 = zy+yz-x

o2 : A

i3 : g = x*z + z*x - y^2

         2
o3 = zx-y +xz

o3 : A

i4 : h = z^2 - x*y - y*x

      2
o4 = z -yx-xy

o4 : A

i5 : I = ncIdeal {f,g,h}

                             2      2      2
o5 = Two-sided ideal {zy+yz-x , zx-y +xz, z -yx-xy}

o5 : NCIdeal

i6 : Igb = ncGroebnerBasis I
--Calling Bergman for NCGB calculation.
Complete!

      2    2                2
o6 = y x-xy ; Lead Term = (y x, 1)
       2  2                  2
     yx -x y; Lead Term = (yx , 1)
         2
     zx-y +xz; Lead Term = (zx, 1)
            2
     zy+yz-x ; Lead Term = (zy, 1)
      2                      2
     z -yx-xy; Lead Term = (z , 1)

o6 : NCGroebnerBasis

i7 : normalFormBergman(z^17,Igb)
--Calling Bergman for NF calculation for 1 elements.
Complete!
Writing bergman input file.
Writing bergman init file.

                                           2             2    3           3     4         4     5       5     6     6     7   7     8 8
o7 = yxyxyxyxyxyxyxyxz+xyxyxyxyxyxyxyxyz+8x yxyxyxyxyxyxy z+8x yxyxyxyxyxy z+28x yxyxyxyxy z+28x yxyxyxy z+56x yxyxy z+56x yxy z+70x y z

o7 : A

i8 : 
