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<head><title>combine -- combine 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="_combine.html" title="combine hash tables">combine</a></div>
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<div><h1>combine -- combine 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 = combine(x,y,f,g,h)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>x</tt>, a hash table</span></li>
<li><span><tt>y</tt>, a hash table of the same class as <tt>x</tt></span></li>
<li><span><tt>f</tt>, a function of two variables to be used for combining a key of <tt>x</tt> with a key of <tt>y</tt> to make a new key for <tt>z</tt>.</span></li>
<li><span><tt>g</tt>, a function of two variables to be used for combining a value of <tt>x</tt> with a value of <tt>y</tt> to make a new value for <tt>z</tt>.</span></li>
<li><span><tt>h</tt>, a function of two variables to be used for combining two values returned by <tt>g</tt> when the corresponding keys returned by <tt>f</tt> turn out to be equal. Its first argument will be the value accumulated so far, and its second argument will be a value just provided by <tt>g</tt>.</span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>z</tt>, a new hash table, of the same class as <tt>x</tt> and <tt>y</tt>, containing the pair <tt>f(p,q) => g(b,c)</tt> whenever <tt>x</tt> contains the pair <tt>p => b</tt> and <tt>y</tt> contains the pair <tt>q => c</tt>, except that <tt>h</tt> is used to combine values when two keys coincide. If <tt>f</tt> or <tt>g</tt> evaluates <a href="_continue.html" title="continue with the next iteration of a loop">continue</a>, then nothing is contributed to the resulting hash table. If <tt>h</tt> evaluates <a href="_continue.html" title="continue with the next iteration of a loop">continue</a>, then, at that point, the entry stored under the key <tt>f(p,q)</tt> in the hash table under construction is removed.</span></li>
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<div class="single"><h2>Description</h2>
<div>The function <tt>f</tt> is applied to every pair <tt>(p,q)</tt> where <tt>p</tt> is a key of <tt>x</tt> and <tt>q</tt> is a key of <tt>y</tt>. The number of times <tt>f</tt> is evaluated is thus the product of the number of keys in <tt>x</tt> and the number of keys in <tt>y</tt>.<p/>
The function <tt>h</tt> should be an associative function, for otherwise the result may depend on internal details about the implementation of hash tables that affect the order in which entries are encountered. If <tt>f</tt>, <tt>g</tt>, and <tt>h</tt> are commutative functions as well, then the result <tt>z</tt> is a commutative function of <tt>x</tt> and <tt>y</tt>.<p/>
The result is mutable if and only if <tt>x</tt> or <tt>y</tt> is.<p/>
This function can be used for multiplying polynomials, where it can be used in code something like this:<pre> combine(x, y, monomialTimes, coeffTimes, coeffPlus)</pre>
We illustrate that with a simple-minded implmentation of the free ring on the English alphabet, representing words as string and polynomials as hash tables that associate coefficients to words.<table class="examples"><tr><td><pre>i1 : Poly = new Type of HashTable
o1 = Poly
o1 : Type</pre>
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<tr><td><pre>i2 : p = new Poly from { "" => 1, "x" => 2, "y" => 3, "cat" => 5 }
o2 = Poly{ => 1 }
cat => 5
x => 2
y => 3
o2 : Poly</pre>
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<tr><td><pre>i3 : Poly * Poly := (p,q) -> combine(p,q,concatenate,times,plus);</pre>
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<tr><td><pre>i4 : p*p
o4 = Poly{ => 1 }
cat => 10
catcat => 25
catx => 10
caty => 15
x => 4
xcat => 10
xx => 4
xy => 6
y => 6
ycat => 15
yx => 6
yy => 9
o4 : Poly</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_merge_lp__Hash__Table_cm__Hash__Table_cm__Function_rp.html" title="merge hash tables">merge</a> -- merge hash tables</span></li>
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