# depthsOfPowers -- Computes depth of powers of an ideal

## Synopsis

• Usage:
L = depthsOfPowers(s,c,I)
L = depthsOfPowers(s,I)
• Inputs:
• s, an integer, number of powers to compute
• c, an integer, (If omitted, it will use c = codim I)
• I, an ideal,
• Outputs:
• L, a list, The depths of the powers of I from 1 to s-c+1.

## Description

Computes the depth of $S/I^k$ for $k$ from 1 to $s-c+1$.

 i1 : R = QQ[a,b,c,d,e,f]; i2 : I = ideal (b*c, b*d, b*e, d*e, a*d*f, e*f); o2 : Ideal of R i3 : depthsOfPowers(6,3,I) o3 = {3, 1, 1, 1} o3 : List

## Ways to use depthsOfPowers :

• "depthsOfPowers(ZZ,Ideal)"
• "depthsOfPowers(ZZ,ZZ,Ideal)"

## For the programmer

The object depthsOfPowers is .