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    <p>There are a few natural ways to do it.</p> <p>You could form the list of arguments to your "percentage decrease" function using <a href="http://reference.wolfram.com/mathematica/ref/Partition.html" rel="nofollow noreferrer">Partition</a>:</p> <pre><code>In[3]:= list = {a, b, c, d, e}; In[4]:= Partition[list, 2, 1] Out[4]= {{a, b}, {b, c}, {c, d}, {d, e}} </code></pre> <p>Then you can <a href="http://reference.wolfram.com/mathematica/ref/Apply.html" rel="nofollow noreferrer">Apply</a> a function to these:</p> <pre><code>In[6]:= f @@@ Partition[list, 2, 1] Out[6]= {f[a, b], f[b, c], f[c, d], f[d, e]} </code></pre> <p>Using your percent decrease function:</p> <pre><code>In[7]:= PercentDecrease[a_, b_] := (b - a)/a In[8]:= PercentDecrease @@@ Partition[list, 2, 1] Out[8]= {(-a + b)/a, (-b + c)/b, (-c + d)/c, (-d + e)/d} </code></pre> <p>(Read about @@@ by looking at the "More Information" notes at <a href="http://reference.wolfram.com/mathematica/ref/Apply.html" rel="nofollow noreferrer">Apply</a>.)</p> <p>Instead of Partition you can use <a href="http://reference.wolfram.com/mathematica/ref/Most.html" rel="nofollow noreferrer">Most</a> and <a href="http://reference.wolfram.com/mathematica/ref/Rest.html" rel="nofollow noreferrer">Rest</a> to form lists of the first and second arguments and then combine them using <a href="http://reference.wolfram.com/mathematica/ref/MapThread.html" rel="nofollow noreferrer">MapThread</a>:</p> <pre><code>In[14]:= MapThread[PercentDecrease, {Most[list], Rest[list]}] Out[14]= {(-a + b)/a, (-b + c)/b, (-c + d)/c, (-d + e)/d} </code></pre> <p>A different way is to form your operation (a subtraction and a division) in two steps like this:</p> <pre><code>In[10]:= Differences[list] / Most[list] Out[10]= {(-a + b)/a, (-b + c)/b, (-c + d)/c, (-d + e)/d} </code></pre> <p>The divide operation (/) <a href="http://reference.wolfram.com/mathematica/ref/Listable.html" rel="nofollow noreferrer">threads</a> over the two lists <code>Differences[list]</code> and <code>Most[list</code>].</p>
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    1. POCalculating percent difference between elements in a list with functional programming in Mathematica?
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    1. USAndrew Moylan
    1. USAndrew Moylan
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    1. COGreat answer! By the way, I like this explanation of @@@ better: http://stackoverflow.com/questions/1141166/in-mathematica-what-does-mean/1141701#1141701
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    2. CO+1, great answer. I personally, like the last one the best. Although, I'd probably write it `Differences[#]/Most[#]& @ list`, but that's just me.
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