up previous next
GroebnerFanIdeals

all reduced Groebner bases of an ideal

Syntax
GroebnerFanIdeals(I: IDEAL): LIST of IDEAL

Description
Returns all reduced Groebner bases of the IDEAL I as a LIST of ideals. See CallOnGroebnerFanIdeals for a more efficient usage (without storing the whole list).

This function used to be called AllReducedGroebnerBases up to version 5.1.4.

Example
/**/ Use R ::= QQ[a,b,c];
/**/ I := ideal(b^3+c^2-1, b^2+a^2+c-1, a^2+b^3-1);
/**/ l := GroebnerFanIdeals(I);
/**/ [ len(GBasis(I)) | I in l];
[4, 4, 6, 6, 5, 6, 4, 4, 4, 3, 4, 3, 3, 3, 4, 3, 3]

-- The ideal in [Sturmfels, Example 3.9] has 360 marked reduced Groebner bases
/**/ Use R ::= QQ[a,b,c];
/**/ I := ideal(a^5+b^3+c^2-1, b^2+a^2+c-1, c^3+a^6+b^5-1);
/**/ l := GroebnerFanIdeals(I);
/**/ len(l);
360

See Also