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Depth :: isRegularSequence

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

Synopsis

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 :

For the programmer

The object isRegularSequence is a method function.