Declares that the columns of the matrix
f constitute a Groebner basis, autoreduces it, minimizes it, sorts it, and returns a Groebner basis object declaring itself complete, without computing any S-pairs.
Sometimes one knows that a set of polynomials (or columns of such) form a Groebner basis, but
Macaulay 2 doesn't. This is the way to inform the system of this fact.
i1 : gbTrace = 3;
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i2 : R = ZZ[x,y,z];
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i3 : f = matrix{{x^2-3, y^3-1, z^4-2}};
1 3
o3 : Matrix R <--- R
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i4 : g = forceGB f
o4 = GroebnerBasis[status: done; S-pairs encountered up to degree 0]
o4 : GroebnerBasis
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This Groebner basis object is stored with the matrix and can be obtained as usual:
i5 : g === gb(f, StopBeforeComputation=>true)
o5 = true
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Requesting a Groebner basis for
f requires no computation.
i6 : gens gb f
-- ...
o6 = | x2-3 y3-1 z4-2 |
1 3
o6 : Matrix R <--- R
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If an autoreduced Groebner basis is desired, replace f by gens forceGB f first.