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 GBasis

calculate a Groebner basis
 Syntax
 ``` GBasis(M:IDEAL, MODULE, or TAGGED("Quotient")):LIST ```

 Description
If M is an ideal or module, this function returns a list whose components form a Groebner basis for M with respect to the term-ordering of the polynomial ring of M. If M is a quotient 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.

If M is a variable, then the result is stored in M for later use. It can be retrieved as M.GBasis and can also be seen using the command Describe.

For a reduced Groebner basis, use the command ReducedGBasis.

The coefficient ring must be a field.

 Example
 ``` Use R ::= QQ[t,x,y]; I := Ideal(t^3-x,t^4-y); Describe I; Record[Type = IDEAL, Value = Record[Gens = [t^3 - x, t^4 - y]]] ------------------------------- GBasis(I); [t^3 - x, -tx + y, t^2y - x^2, x^3 - ty^2] ------------------------------- Describe(I); -- the Groebner basis has been stored in I Record[Type = IDEAL, Value = Record[Gens = [t^3 - x, t^4 - y], GBasis = [t^3 - x, -tx + y, t^2y - x^2, x^3 - ty^2]]] ------------------------------- I.GBasis; [t^3 - x, -tx + y, t^2y - x^2, x^3 - ty^2] ------------------------------- ```
For fine control and monitoring of Groebner basis calculations, see The Interactive Groebner Framework and Introduction to Panels.