-- -*- M2-comint -*- hash: 6703199554172406678

i1 : X = hirzebruchSurface 1;

i2 : Y = toricProjectiveSpace 1;

i3 : f = map(Y, X, matrix {{1, 0}})

o3 = | 1 0 |

o3 : ToricMap Y <--- X

i4 : f' = picardGroup f

o4 = | 1 |
     | 0 |

              2       1
o4 : Matrix ZZ  <-- ZZ

i5 : assert (isWellDefined f and source f' == picardGroup Y and
         target f' == picardGroup X)

i6 : f'' = cartierDivisorGroup f

o6 = | 0 1 |
     | 0 0 |
     | 1 0 |
     | 0 0 |

              4       2
o6 : Matrix ZZ  <-- ZZ

i7 : assert(f' * fromCDivToPic Y  == fromCDivToPic X  * f'')

i8 : W = weightedProjectiveSpace {1, 1, 2};

i9 : Z = toricBlowup({0, 1, 4}, (W ** toricProjectiveSpace 1), {0, -2, 1});

i10 : assert (not isSmooth W and not isSmooth Z)

i11 : g = map(W, Z, matrix{{1,0,0},{0,1,0}})

o11 = | 1 0 0 |
      | 0 1 0 |

o11 : ToricMap W <--- Z

i12 : g' = picardGroup g

o12 = | 0  |
      | -1 |
      | 0  |

               3       1
o12 : Matrix ZZ  <-- ZZ

i13 : assert (isWellDefined g and source g' == picardGroup W and
          target g' == picardGroup Z)

i14 : g'' = cartierDivisorGroup g

o14 = | 0 0  0 |
      | 0 0  0 |
      | 1 0  0 |
      | 0 -1 0 |
      | 0 1  1 |
      | 0 0  0 |

               6       3
o14 : Matrix ZZ  <-- ZZ

i15 : assert(g' * fromCDivToPic W  == fromCDivToPic Z  * g'')

i16 : 
