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

Synopsis

Usage:

isRegularSequence(X,A) or isRegularSequence(X)
Inputs:
- X, a List or Matrix
- A, a Ring or Module
Outputs:
- a Boolean value

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 a method function.