A bug on the command "pdim" ?

@kschwede is already working on this.

Since Jul 1, 2019.

The following statement is taken from the book "A course in ring theory" by D.S.Passman, (page 76).


I've fixed the bivariate polynomial ring **R** and considered the ideal **I = < (x^3 + y)^2 , (x^2 + y^2)^2 , (x + y^3)^2 , (x*y)^2 >** . Hence I get the following short exact sequence

**0 >> I >> R >> R/I >> 0**

Here I expect that **pdim (I) = pdim (R/I) - 1** by the third item of the statement above. But when I do the computations on Macaulay2, it gives me **pdim (I) = pdim (R/I) = 2**. Is there a bug on the command pdim? or am I missing something? I've used the following code on M2.

Macaulay2, version 1.13
with packages: ConwayPolynomials, Elimination, IntegralClosure, InverseSystems, LLLBases, PrimaryDecomposition,
ReesAlgebra, TangentCone, Truncations

i1 : R = QQ[x,y];

i2 : I = ideal((x^3 + y)^2 , (x^2 + y^2)^2 , (x + y^3)^2 , (x*y)^2);

i3 : pdim (module I)

o3 = 2

i4 : pdim (R^1 / I)

o4 = 2