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SymbolicPowers :: bigHeight

bigHeight -- computes the big height of an ideal

Synopsis

Description

Big height of an ideal: the largest height of an associated prime. The algorithm is based on the following result by Eisenbud-Huneke-Vasconcelos, in their 1993 Inventiones Mathematicae paper:

codim Extd(M,R) ≥d for all d

If P is an associated prime of M of codimension d := codim P > codim M, then codim Extd(M,R) = d and the annihilator of Extd(M,R) is contained in P

If codim Extd(M,R) = d, then there really is an associated prime of codimension d.

i1 : R = QQ[x,y,z,a,b]

o1 = R

o1 : PolynomialRing
i2 : J = intersect(ideal(x,y,z),ideal(a,b))

o2 = ideal (z*b, y*b, x*b, z*a, y*a, x*a)

o2 : Ideal of R
i3 : bigHeight(J)

o3 = 3

Caveat

bigHeight works faster than assPrimesHeight

See also

Ways to use bigHeight :