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depth(Ideal,Ring) -- computes the depth of a ring

Synopsis

Description

The function depth(I,A), computes the I-depth of a ring. It does this by computing Ext^i(A^1/I,A) and noting where it does not vanish.
i1 : A = QQ[x_1..x_3]/ideal(x_1^2, x_1*x_2);
i2 : m = ideal vars A

o2 = ideal (x , x , x )
             1   2   3

o2 : Ideal of A
i3 : depth(m,A)

o3 = 1
If I contains a unit, then depth(I,A) outputs infinity.
i4 : depth(ideal(1),ZZ)

o4 = infinity

o4 : InfiniteNumber

This symbol is provided by the package Depth.