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];
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i2 : X1 = {x, y*(x-1), z*(x-1)};
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i3 : isRegularSequence X1
o3 = true
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i4 : X2 = {z*(x-1), y*(x-1), x};
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i5 : isRegularSequence X2
o5 = false
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i6 : X3 = {1_A, x, y};
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i7 : isRegularSequence X3
o7 = false
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This symbol is provided by the package Depth.