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Macaulay2Doc :: pdim(Module)

pdim(Module) -- calculate the projective dimension of a module

Synopsis

Description

i1 : R = QQ[x,y,z];
i2 : I = ideal(x^2, x*y, y*z);

o2 : Ideal of R
i3 : M = R^1/I

o3 = cokernel | x2 xy yz |

                            1
o3 : R-module, quotient of R
i4 : res M

      1      3      2
o4 = R  <-- R  <-- R  <-- 0
                           
     0      1      2      3

o4 : ChainComplex
i5 : pdim M

o5 = 2
Notice this is one more than the projective dimension of I as an R-module.
i6 : res(module I)

      3      2
o6 = R  <-- R  <-- 0
                    
     0      1      2

o6 : ChainComplex
i7 : pdim(module I)

o7 = 1