-- -*- M2-comint -*- {* hash: -1724870117 *}

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

o1 = A

o1 : PolynomialRing

i2 : N = image matrix{{x*y,0},{0,x*z},{y*z,z^2}}

o2 = image | xy 0  |
           | 0  xz |
           | yz z2 |

                             3
o2 : A-module, submodule of A

i3 : N + x*N

o3 = image | xy 0  x2y 0   |
           | 0  xz 0   x2z |
           | yz z2 xyz xz2 |

                             3
o3 : A-module, submodule of A

i4 : f = matrix{{x*y,x*z},{y*z,z^2}}

o4 = | xy xz |
     | yz z2 |

             2       2
o4 : Matrix A  <--- A

i5 : M = image f

o5 = image | xy xz |
           | yz z2 |

                             2
o5 : A-module, submodule of A

i6 : g = gens M

o6 = | xy xz |
     | yz z2 |

             2       2
o6 : Matrix A  <--- A

i7 : f == g

o7 = true

i8 : N = cokernel f

o8 = cokernel | xy xz |
              | yz z2 |

                            2
o8 : A-module, quotient of A

i9 : presentation N

o9 = | xy xz |
     | yz z2 |

             2       2
o9 : Matrix A  <--- A

i10 : presentation M

o10 = {2} | -z |
      {2} | y  |

              2       1
o10 : Matrix A  <--- A

i11 : syz f

o11 = {2} | -z |
      {2} | y  |

              2       1
o11 : Matrix A  <--- A

i12 : kernel f

o12 = image {2} | -z |
            {2} | y  |

                              2
o12 : A-module, submodule of A

i13 :