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calculate a Groebner basis
GBasis(M:IDEAL, MODULE, or TAGGED("Quotient")):LIST
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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.
For a reduced Groebner basis, use the command
ReducedGBasis.
The coefficient ring must be a field.
/**/ Use R ::= QQ[t,x,y];
/**/ I := Ideal(t^3-x, t^4-y);
/**/ GBasis(I);
[t^3 - x, -tx + y, t^2y - x^2, x^3 - ty^2]
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For fine control and monitoring of Groebner basis calculations, see
The Interactive Groebner Framework and
Introduction to Panels.