This command reduces the input modulo a noncommutative Groebner basis. It will either reduce it using top-level Macaulay code, or via a call to Bergman, depending on the size and degree of the input element.
i1 : A = QQ{x,y,z}
o1 = A
o1 : NCPolynomialRing
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i2 : p = y*z + z*y - x^2
2
o2 = zy+yz-x
o2 : A
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i3 : q = x*z + z*x - y^2
2
o3 = zx-y +xz
o3 : A
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i4 : r = z^2 - x*y - y*x
2
o4 = z -yx-xy
o4 : A
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i5 : I = ncIdeal {p,q,r}
2 2 2
o5 = Two-sided ideal {zy+yz-x , zx-y +xz, z -yx-xy}
o5 : NCIdeal
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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
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i7 : z^6 % Igb
2 2 3 3
o7 = yxyxyx+xyxyxy+3x yxy +3x y
o7 : A
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