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 HGBM

intersection of ideals for zero-dimensional schemes

 Syntax
 `HGBM(L: LIST): IDEAL`

 Description
***** NOT YET IMPLEMENTED *****

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 IntersectList 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. The prefix H comes from Homogeneous since ideals of projective schemes are necessarily homogeneous.

 Example
 ``` Use QQ[x[0..2]]; I1 := IdealOfProjectivePoints([[1,2,1], [0,1,0]]); -- simple projective scheme I2 := IdealOfProjectivePoints([[1,1,1], [2,0,1]])^2; -- another projective scheme HGBM([I1, I2]); -- intersect the ideals ideal(x^3 - xx^2 - 5x^2x + x^2x + 8xx^2 - 4x^3, x^2x + xx^2 - 3xxx - x^2x + 2xx^2, xx^3 - 2x^2x^2 - 5xxx^2 - 4x^2x^2 + 8xx^3 + 10xx^3 - 8x^4, xx^2x + x^3x - 2x^2x^2 - 5xxx^2 - 5x^2x^2 + 8xx^3 + 10xx^3 - 8x^4, x^4x - 2x^3x^2 - 4x^2x^3 - 8xxx^3 - 3x^2x^3 + 16xx^4 + 16xx^4 - 16x^5) ------------------------------- ```