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_normal__Form__Bergman.out
-- -*- M2-comint -*- hash: 5228689541174388256 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 :