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Re: efficient term collection algorithm


On Aug 31, 2006, at 4:39 AM, Blake Laing wrote:

> Dear Math Group
>
> I wish to combine terms in a expression which share a denominator,  
> such
> as in the following simple case:
>
> In[1]:=
> a/i+b/j+c/i//.Plus[Times[A_.,Power[denom_,-1]],Times[B_.,Power 
> [denom_,-1]]]:>
>       Factor[Plus[A,B]Power[denom,-1]]//InputForm
> Out[1]//InputForm=
> (a + c)/i + b/j
>
> The actual expression I am working with contains thousands of  
> terms, and
> a pairwise algorithm such as this is wholly inadequate. Will one of  
> you
> please suggest a more efficient way to combine each additive term in a
> large expression with a shared denominator?

As long as the whole expression is a sum, you can transform it to a  
list, sort the terms that have common denominators together, split  
into sublists of a common denominator then combine terms with  
Together.  For example

In[6]:=
Plus @@ Together @ Plus @@@
         Split[Sort[List @@ (a/i + b/j + c/i),
             OrderedQ[{Denominator[#1], Denominator[#2]}] &],
           Denominator[#1] == Denominator[#2] &]
Out[6]=
(a + c)/i + b/j

Regards,

Ssezi


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