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

Synopsis

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.