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ReducedGBasis
Syntax
ReducedGBasis(M:IDEAL, MODULE, or TAGGED("Quotient")):LIST
Summary
compute a reduced Groebner basis
Description
If M is an ideal or module, this function returns a list whose
components form a reduced Groebner basis for M with respect to the
term-ordering of the current ring. If M is a quotient of the current
ring by an ideal I or of a free module by a submodule N, then the
Groebner basis for M is defined to be that of I or N, respectively.
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 Groebner Framework
GB.Step(I); -- take one step towards computing the Groebner basis
I.GBasis; -- the Groebner basis so far
[t^3 - x]
-------------------------------
GB.Complete(I); -- finish 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]
-------------------------------
See Also