Each class has a parent class that can be used as a container for bits of code that apply to a more general class of objects. In this section we show how this mechanism works in detail.

The parent of `X` is BasicList, as desired, thus methods applicable to basic lists will also apply also to instances of `X`. One such method is the method for creating a net from a basic list; here is its code:

This code is run automatically to display an instance of `X`, so if we make one, we'll be able to see what it is:

Now let's imagine we wish to treat instances of `X` as vectors, and to negate one by negating its entries. As it happens, no method for this has been installed for basic lists, so trying to negate `x` results in an error.

We install and test a new method as described in installing methods.

This method will apply automatically to subclasses of `X`, as we see now.

For `binary methods`, there is an apparent ambiguity in deciding exactly how inheritance will work. Let's illustrate by making a new subclass `Z` of `X`.

Now let's install two methods, either of which might conceivably be applied to evaluate the expression `y+z`, and see what happens.

The result is the string `Y + X`. The reason is that after finding that no method applies directly for adding an instance of `Y` to an instance of `Z`, the search continues: `Z` is replaced by its parent `X`, and so on. (After enough unsuccessful iterations of this, the second type is reset to `Z`, the first type is replaced by its parent, and the search continues.)

We begin by creating a new type of basic list.

i1 : X = new Type of BasicList o1 = X o1 : Type |

i2 : parent X o2 = BasicList o2 : Type |

i3 : code(net,BasicList) o3 = -- code for method: net(BasicList) /usr/share/Macaulay2/Core/nets.m2:175:20-178:47: --source code: net BasicList := x -> horizontalJoin deepSplice ( net class x, "{", toSequence between(comma,apply(toList x,netn)), |

i4 : x = new X from {2,3,4} o4 = X{2, 3, 4} o4 : X |

i5 : stopIfError = false; |

i6 : - x stdio:6:1:(3): error: no method for prefix operator - applied to object: -- X{2, 3, 4} (of class X) |

i7 : - X := t -> apply(t,i -> -i); |

i8 : - x o8 = X{-2, -3, -4} o8 : X |

i9 : Y = new Type of X; |

i10 : y = new Y from {4,5,6} o10 = Y{4, 5, 6} o10 : Y |

i11 : - y o11 = Y{-4, -5, -6} o11 : Y |

i12 : Z = new Type of X; |

i13 : z = new Z from {7,8,9} o13 = Z{7, 8, 9} o13 : Z |

i14 : Y + X := (a,b) -> "Y + X"; |

i15 : X + Z := (a,b) -> "X + Z"; |

i16 : y + z o16 = Y + X |

The same search order applies to method functions defined with method.