The function
depth(I,A), computes the
I-depth of a ring. In the most general setting, it does this by computing
Ext^i(A^1/I,A) and noting where it does not vanish. If the ring in question is a polynomial ring over a field, then it merely computes the codimension of
I. If the ring in question is a quotient of a polynomial ring over a field and we are computing the depth over the ideal generated by
generators(Ring), then it computes the difference between the dimension of this polynomial ring and the projective dimension of the quotient ring. If the ideal is omitted, then the depth is taken over the ideal generated by
generators(Ring).
i1 : A = QQ[x_1..x_3]/ideal(x_1^2, x_1*x_2);
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i2 : depth A
o2 = 1
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If
I contains a unit, then
depth(I,A) outputs
infinity.
i3 : depth(ideal(1),ZZ)
o3 = infinity
o3 : InfiniteNumber
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This symbol is provided by the package Depth.