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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. It does this by checking the injectivity of the maps defined by multiplication by the elements of X and checks if XA = A.
i1 : A = ZZ/2[x, y, z];
i2 : X1 = {x, y*(x-1), z*(x-1)};
i3 : isRegularSequence(X1, A)

o3 = true
i4 : X2 = {z*(x-1), y*(x-1), x};
i5 : isRegularSequence(X2, A)

o5 = false
i6 : X3 = {1, x, y};
i7 : isRegularSequence(X3, A)

o7 = false

This symbol is provided by the package Depth.

Ways to use isRegularSequence :