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Macaulay2Doc :: dim(Module)

dim(Module) -- compute the Krull dimension

Synopsis

Description

Computes the Krull dimension of the module M
i1 : R = ZZ/31991[a,b,c,d]

o1 = R

o1 : PolynomialRing
i2 : I = monomialCurveIdeal(R,{1,2,3})

             2                    2
o2 = ideal (c  - b*d, b*c - a*d, b  - a*c)

o2 : Ideal of R
i3 : M = Ext^1(I,R)

o3 = cokernel {-3} | c b a |
              {-3} | d c b |

                            2
o3 : R-module, quotient of R
i4 : dim M

o4 = 2
i5 : N = Ext^0(I,R)

o5 = image {-2} | c2-bd |
           {-2} | bc-ad |
           {-2} | b2-ac |

                             3
o5 : R-module, submodule of R
i6 : dim N

o6 = 4
Note that the dimension of the zero module is -1.

See also