up previous next
 GBM

intersection of ideals for zero-dimensional schemes
 Syntax
 ``` GBM(L:LIST):IDEAL ```

 Description
This function computes the intersection of ideals corresponding to zero-dimensional schemes: GBM is for affine schemes, and HGBM for projective schemes. The list L must be a list of ideals. The function IntersectionList should be used for computing the intersection of a collection of general ideals.

The name GBM comes from the name of the algorithm used: Generalized Buchberger-Moeller.

 Example
 ``` Use QQ[x,y,z]; I1 := IdealOfPoints([[1,2,1], [0,1,0]]); -- a simple affine scheme I2 := IdealOfPoints([[1,1,1], [2,0,1]])^2; -- another affine scheme GBM([I1, I2]); -- intersect the ideals Ideal(xz + yz - z^2 - x - y + 1, z^3 - 2z^2 + z, yz^2 - 2yz - z^2 + y + 2z - 1, y^2z - y^2 - yz + y, xy^2 + y^3 - 2x^2 - 5xy - 5y^2 + 2z^2 + 8x + 10y - 4z - 6, x^2y - y^3 + 2x^2 + 2xy + 4y^2 - 3z^2 - 8x - 8y + 6z + 5, x^3 + y^3 - 7x^2 - 5xy - 4y^2 + 5z^2 + 16x + 10y - 10z - 7, y^4 - 2y^3 - 4x^2 - 8xy - 3y^2 + 4z^2 + 16x + 16y - 8z - 12) ------------------------------- ```