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GBasis

Syntax

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

Summary

calculate a Groebner basis

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 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.

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 ::= Q[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".

See Also