source(SimplicialModuleMap) -- get the source of a map of simplicial modules

i1 : R = ZZ/101[a..d]

o1 = R

o1 : PolynomialRing

i2 : I = ideal(a^2, b^2, c^2)

             2   2   2
o2 = ideal (a , b , c )

o2 : Ideal of R

i3 : J = I + ideal(a*b*c)

             2   2   2
o3 = ideal (a , b , c , a*b*c)

o3 : Ideal of R

i4 : FI = simplicialModule(freeResolution I, Degeneracy => true)

      1      4      10      20
o4 = R  <-- R  <-- R   <-- R  <-- ...
                            
     0      1      2       3

o4 : SimplicialModule

i5 : FJ = simplicialModule(freeResolution J, Degeneracy => true)

      1      5      15      34
o5 = R  <-- R  <-- R   <-- R  <-- ...
                            
     0      1      2       3

o5 : SimplicialModule

i6 : f = randomSimplicialMap(FJ, FI, Cycle=>true)

          1              1
o6 = 0 : R  <---------- R  : 0
               | 24 |

          5                           4
     1 : R  <----------------------- R  : 1
               {0} | 24 0  0  0  |
               {2} | 0  24 0  0  |
               {2} | 0  0  24 0  |
               {2} | 0  0  0  24 |
               {3} | 0  0  0  0  |

          15                                             10
     2 : R   <----------------------------------------- R   : 2
                {0} | 24 0  0  0  0  0  0  0  0  0  |
                {2} | 0  24 0  0  0  0  0  0  0  0  |
                {2} | 0  0  24 0  0  0  0  0  0  0  |
                {2} | 0  0  0  24 0  0  0  0  0  0  |
                {3} | 0  0  0  0  0  0  0  0  0  0  |
                {2} | 0  0  0  0  24 0  0  0  0  0  |
                {2} | 0  0  0  0  0  24 0  0  0  0  |
                {2} | 0  0  0  0  0  0  24 0  0  0  |
                {3} | 0  0  0  0  0  0  0  0  0  0  |
                {4} | 0  0  0  0  0  0  0  24 0  0  |
                {4} | 0  0  0  0  0  0  0  0  0  0  |
                {4} | 0  0  0  0  0  0  0  0  0  0  |
                {4} | 0  0  0  0  0  0  0  0  24 0  |
                {4} | 0  0  0  0  0  0  0  0  0  0  |
                {4} | 0  0  0  0  0  0  0  0  0  24 |

          34                                                                             20
     3 : R   <------------------------------------------------------------------------- R   : 3
                {0} | 24 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {2} | 0  24 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {2} | 0  0  24 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {2} | 0  0  0  24 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {3} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {2} | 0  0  0  0  24 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {2} | 0  0  0  0  0  24 0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {2} | 0  0  0  0  0  0  24 0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {3} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {2} | 0  0  0  0  0  0  0  24 0  0  0  0  0  0  0  0  0  0  0  0    |
                {2} | 0  0  0  0  0  0  0  0  24 0  0  0  0  0  0  0  0  0  0  0    |
                {2} | 0  0  0  0  0  0  0  0  0  24 0  0  0  0  0  0  0  0  0  0    |
                {3} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  24 0  0  0  0  0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  24 0  0  0  0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  24 0  0  0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  24 0  0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  24 0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  24 0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  24 0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  24 0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0    |
                {4} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  24 0    |
                {5} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  24c  |
                {5} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  -24b |
                {5} | 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  24a  |

o6 : SimplicialModuleMap

i7 : source f

      1      4      10      20
o7 = R  <-- R  <-- R   <-- R  <-- ...
                            
     0      1      2       3

o7 : SimplicialModule

i8 : assert isWellDefined f

i9 : assert isSimplicialMorphism f

i10 : assert(source f == FI)

i11 : assert(target f == FJ)

i12 : kk = coker vars R

o12 = cokernel | a b c d |

                             1
o12 : R-module, quotient of R

i13 : F = simplicialModule(freeResolution kk, Degeneracy => true)

       1      5      15      35      70
o13 = R  <-- R  <-- R   <-- R   <-- R  <-- ...
                                     
      0      1      2       3       4

o13 : SimplicialModule

i14 : source dd^F == F

o14 = true

i15 : target dd^F == F

o15 = true

i16 : degree dd^F == -1

o16 = true