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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="___The_sp__Macaulay2_splanguage.html" title="">The Macaulay2 language</a> > <a href="_inheritance.html" title="">inheritance</a></div>
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<div><h1>inheritance</h1>
<div>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.<p/>
We begin by creating a new type of basic list.<table class="examples"><tr><td><pre>i1 : X = new Type of BasicList
o1 = X
o1 : Type</pre>
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<tr><td><pre>i2 : parent X
o2 = BasicList
o2 : Type</pre>
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The parent of <tt>X</tt> is <a href="___Basic__List.html" title="the class of all basic lists">BasicList</a>, as desired, thus methods applicable to basic lists will also apply also to instances of <tt>X</tt>. One such method is the method for creating a net from a basic list; here is its code:<table class="examples"><tr><td><pre>i3 : code(net,BasicList)
o3 = -- code for method: net(BasicList)
/builddir/build/BUILD/Macaulay2-1.3.1-r10737/Macaulay2/m2/nets.m2:177:20-180:47: --source code:
net BasicList := x -> horizontalJoin deepSplice (
net class x,
"{",
toSequence between(comma,apply(toList x,netn)),</pre>
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This code is run automatically to display an instance of <tt>X</tt>, so if we make one, we'll be able to see what it is:<table class="examples"><tr><td><pre>i4 : x = new X from {2,3,4}
o4 = X{2, 3, 4}
o4 : X</pre>
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Now let's imagine we wish to treat instances of <tt>X</tt> as vectors, and to negate one by negating its entries. As it happens, no method for this has been installed for basic lists, as we can check with <a href="_lookup.html" title="look up methods">lookup</a>.<table class="examples"><tr><td><pre>i5 : lookup(symbol -, X) === null
o5 = false</pre>
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We install and test a new method as described in <a href="_installing_spmethods.html" title="">installing methods</a>.<table class="examples"><tr><td><pre>i6 : - X := t -> apply(t,i -> -i);</pre>
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<tr><td><pre>i7 : - x
o7 = X{-2, -3, -4}
o7 : X</pre>
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This method will apply automatically to subclasses of <tt>X</tt>, as we see now.<table class="examples"><tr><td><pre>i8 : Y = new Type of X;</pre>
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<tr><td><pre>i9 : y = new Y from {4,5,6}
o9 = Y{4, 5, 6}
o9 : Y</pre>
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<tr><td><pre>i10 : - y
o10 = Y{-4, -5, -6}
o10 : Y</pre>
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For <tt>binary methods</tt>, there is an apparent ambiguity in deciding exactly how inheritance will work. Let's illustrate by making a new subclass <tt>Z</tt> of <tt>X</tt>.<table class="examples"><tr><td><pre>i11 : Z = new Type of X;</pre>
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<tr><td><pre>i12 : z = new Z from {7,8,9}
o12 = Z{7, 8, 9}
o12 : Z</pre>
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Now let's install two methods, either of which might conceivably be applied to evaluate the expression <tt>y+z</tt>, and see what happens.<table class="examples"><tr><td><pre>i13 : Y + X := (a,b) -> YX;</pre>
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<tr><td><pre>i14 : X + Z := (a,b) -> XZ;</pre>
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<tr><td><pre>i15 : y + z
o15 = YX
o15 : Symbol</pre>
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The result is the symbol <tt>YX</tt>. The reason is that after finding that no method applies directly for adding an instance of <tt>Y</tt> to an instance of <tt>Z</tt>, the search continues: <tt>Z</tt> is replaced by its parent <tt>X</tt>, and so on. (After enough unsuccessful iterations of this, the second type is reset to <tt>Z</tt>, the first type is replaced by its parent, and the search continues.)<p/>
The same search order applies to method functions defined with <a href="_method.html" title="make a new method function">method</a>.</div>
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