dim(Module) -- compute the Krull dimension

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} | a -b c |
              {-3} | b -c d |

                            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