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3.13.4. Example: Interactive Groebner Basis Computation

Example

Use R ::= Q[t,x,y,z];
I := Ideal(t^3-x,t^4-y,t^5-z);
GB.Start_GBasis(I);  -- start the interactive framework
I.GBasis;  -- the Groebner basis is initially empty
Null
-------------------------------
GB.Step(I); -- a single step of the computation
I.GBasis;
I.GBasis;
[t^3 - x]
-------------------------------
GB.Steps(I,4); -- 4 more steps
I.GBasis;
[t^3 - x, -tx + y, t^2y - x^2]
-------------------------------
GB.Complete(I); -- complete the computation
I.GBasis;
[t^3 - x, -tx + y, -ty + z, -y^2 + xz, -x^2 + tz, t^2z - xy]
-------------------------------
ReducedGBasis(I);
[t^3 - x, tx - y, ty - z, y^2 - xz, x^2 - tz, t^2z - xy]
-------------------------------

Note that Groebner bases calculated in the interactive framework may
not be reduced, as illustrated in the final step of the example.