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

- Function: depth
- Usage:
    `d = depth(I,M)`
    `d = depth(M)`
    `d = depth(I,I)`
- Inputs:
  - I, an ideal,
  - M, a ring, or Module or Ideal
- 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

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Depth.m2:682:0.