# isRegularSequence -- whether a list is regular over a ring or module

## Synopsis

• Usage:
isRegularSequence(X,A) or isRegularSequence(X)
• Inputs:
• Outputs:

## Description

Given a list X, the function isRegularSequence tells if X forms a regular sequence. If X consists of homogeneous elements, it does this by comparing the hilbert series of A and the hilbert series of A/XA. Otherwise it checks the injectivity of the maps defined by multiplication by the elements of X and also checks if XA = A.
 i1 : A = ZZ/2[x, y, z]; i2 : X1 = {x, y*(x-1), z*(x-1)}; i3 : isRegularSequence X1 o3 = true i4 : X2 = {z*(x-1), y*(x-1), x}; i5 : isRegularSequence X2 o5 = false i6 : X3 = {1_A, x, y}; i7 : isRegularSequence X3 o7 = false

This symbol is provided by the package Depth.

## Ways to use isRegularSequence :

• "isRegularSequence(List)"
• "isRegularSequence(List,Module)"
• "isRegularSequence(List,Ring)"
• "isRegularSequence(Matrix)"
• "isRegularSequence(Matrix,Module)"
• "isRegularSequence(Matrix,Ring)"

## For the programmer

The object isRegularSequence is .