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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="_binary_spmethods.html" title="">binary methods</a></div>
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<div><h1>binary methods</h1>
<div>The method for computing a sum <tt>x+y</tt> depends on the types of <tt>x</tt> and <tt>y</tt>. For example, the method for adding an integer <tt>x</tt> and a polynomial <tt>y</tt> differs from the method for adding two integers modulo 111. Because both the type of <tt>x</tt> and the type of <tt>y</tt> must enter into the selection of the method, we refer to these methods as binary methods. Each binary method is a function of two variables, and is stored either in the class of <tt>x</tt> or in the class of <tt>y</tt>.<p/>
Let's assume that <tt>X</tt> is the class (or type) of <tt>x</tt>, and that <tt>Y</tt> is the class of <tt>y</tt>. The way to install a method for the addition of an instance <tt>x</tt> of class <tt>X</tt> to an instance <tt>y</tt> of class <tt>Y</tt> is with a statement of the form <pre>X + Y := (x,y) -> ( ... )</pre>
where <tt>( ... )</tt> represents the body of the function, consisting of suitable code for the operation at hand.<p/>
The method installed by the code above is automatically inherited by subclasses of <tt>X</tt> and <tt>Y</tt>. Here is a brief description of the way this works. Suppose <tt>X</tt> is the <a href="_parent.html" title="parent type of an object">parent</a> of <tt>P</tt> and <tt>Y</tt> is the parent of <tt>X</tt>. When a sum <tt>p+q</tt> is evaluated where the class of <tt>p</tt> is <tt>P</tt> and the class of <tt>q</tt> is <tt>Q</tt>, then the binary method for <tt>P+Q</tt> is applied, unless there isn't one, in which case the binary method for <tt>P+Y</tt> is applied, unless there isn't one, in which case the binary method for <tt>X+Q</tt> is applied, unless there isn't one, in which case the binary method for <tt>P+Q</tt> is applied. In general this search for a binary method continues all the way up the chain of parents to the topmost ancestor of everything, which is called <a href="___Thing.html" title="the class of all things">Thing</a>. (See also <a href="_lookup.html" title="look up methods">lookup</a>.)<p/>
As an extreme example of inheritance, the code <pre>Thing + Thing := (x,y) -> ( ... )</pre>
will install a binary method for adding any two things, which will take effect as a last resort whenever more a specifically defined method isn't found.<p/>
The <a href="_new.html" title="new objects and new types">new</a> function also uses a ternary lookup table to find the initialization function for the new thing, and should be thought of as a ternary operator. The initialization function for a new expression created by<pre>new Z of x from y</pre>
is obtained as<pre>lookup(NewMethod,Z,X,Y)</pre>
Here <tt>X</tt> is <tt>class x</tt>, and <tt>Y</tt> is <tt>class y</tt>. The initialization function can be installed with<pre>new Z of X from Y := (z,y) -> ...</pre>
where <tt>z</tt> denotes the new hash table of class <tt>Z</tt> and parent <tt>x</tt> provided to the routine by the system.</div>
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