Module _ List -- map from free module to some generators

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : I = ideal vars R

o2 = ideal (x, y, z)

o2 : Ideal of R

i3 : f = I_{0,2}

o3 = {1} | 1 0 |
     {1} | 0 0 |
     {1} | 0 1 |

o3 : Matrix

i4 : image f

o4 = image | x z |

                             1
o4 : R-module, submodule of R

i5 : M = image syz vars R

o5 = image {1} | -y 0  -z |
           {1} | x  -z 0  |
           {1} | 0  y  x  |

                             3
o5 : R-module, submodule of R

i6 : g = M_{1}

o6 = {2} | 0 |
     {2} | 1 |
     {2} | 0 |

                   1
o6 : Matrix M <-- R

i7 : source g

      1
o7 = R

o7 : R-module, free, degrees {2}

i8 : target g

o8 = image {1} | -y 0  -z |
           {1} | x  -z 0  |
           {1} | 0  y  x  |

                             3
o8 : R-module, submodule of R