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ReducedGBasis

compute reduced Groebner basis

Syntax
ReducedGBasis(M:IDEAL, MODULE, or TAGGED("Quotient")):LIST

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 polynomial ring of M. If M is a quotient of a 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 ::= QQ[t,x,y,z];
/**/  I := ideal(t^3-x, t^4-y, t^5-z);
                             --***OBSOLETE MANUAL: WORK IN PROGRESS***
  $gb.Start_GBasis(I);  -- start the Interactive Groebner Framework
  $gb.Steps(I,1);  -- 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);
[y^2 -x*z, t*y -z, x^2 -t*z, t*x -y, t^2*z -x*y, t^3 -x]

See Also