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<head><title>merge(HashTable,HashTable,Function) -- merge hash tables</title>
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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="_hash_sptables.html" title="">hash tables</a> > <a href="_merge_lp__Hash__Table_cm__Hash__Table_cm__Function_rp.html" title="merge hash tables">merge(HashTable,HashTable,Function)</a></div>
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<div><h1>merge(HashTable,HashTable,Function) -- merge hash tables</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>z = merge(x,y,g)</tt></div>
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<li><span>Function: <a href="_merge_lp__Hash__Table_cm__Hash__Table_cm__Function_rp.html" title="merge hash tables">merge</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>x</tt>, <span>a <a href="___Hash__Table.html">hash table</a></span></span></li>
<li><span><tt>y</tt>, <span>a <a href="___Hash__Table.html">hash table</a></span></span></li>
<li><span><tt>g</tt>, <span>a <a href="___Function.html">function</a></span>, a function of two variables to be used to combine a value of <tt>x</tt> with a value of <tt>y</tt> when the corresponding keys coincide.</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>z</tt>, <span>a <a href="___Hash__Table.html">hash table</a></span>, a new hash table whose keys are the keys occurring in <tt>x</tt> or in <tt>y</tt>; the same values are used, except that if if a key <tt>k</tt> occurs in both arguments, then <tt>g(x#k,y#k)</tt> is used instead, unless <tt>g</tt> evaluated <a href="_continue.html" title="continue with the next iteration of a loop">continue</a>, in which case the key <tt>k</tt> does not appear in the result.</span></li>
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<div class="single"><h2>Description</h2>
<div>If <tt>x</tt> and <tt>y</tt> have the same class and have the same parent, then so will <tt>z</tt>.<p>This function is useful for multiplying monomials or adding polynomials. We illustrate that with a simple-minded implmentation of the free abelian group on the set of strings, representing an element as a type of hash table that associates coefficients to strings.</p>
<table class="examples"><tr><td><pre>i1 : Free = new Type of HashTable
o1 = Free
o1 : Type</pre>
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<tr><td><pre>i2 : p = new Free from { "x" => 2, "y" => 3, "cat" => 5 }
o2 = Free{cat => 5}
x => 2
y => 3
o2 : Free</pre>
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<tr><td><pre>i3 : q = new Free from { "x" => 100, "y" => 200, "dog" => 7 }
o3 = Free{dog => 7}
x => 100
y => 200
o3 : Free</pre>
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<tr><td><pre>i4 : Free + Free := (p,q) -> merge(p,q,plus);</pre>
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<tr><td><pre>i5 : p+q
o5 = Free{cat => 5}
dog => 7
x => 102
y => 203
o5 : Free</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_combine.html" title="combine hash tables">combine</a> -- combine hash tables</span></li>
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