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

## Synopsis

• Function: depth
• Usage:
d = depth(I,M)
d = depth(M)
d = depth(I,I)
• Inputs:
• Outputs:
• d, an integer, the I-depth of a ring, module, or ideal

## Description

The function depth(I,M) computes the I-depth of a ring, module, or ideal. In the most general setting, it does this by computing Ext^i(A^1/I,M) for an A-Module M, and noting where it does not vanish. If the ring in question is a polynomial ring over a field, then it merely computes the codimension of I.

 i1 : A = QQ[x_1..x_3]/ideal(x_1^2, x_1*x_2) o1 = A o1 : QuotientRing i2 : depth A o2 = 1

If I contains a unit, then depth(I,A) outputs infinity.

 i3 : depth(ideal(1_A),A) o3 = infinity o3 : InfiniteNumber

This symbol is provided by the package Depth.m2