Collecting denominators together with Mathematica

[anthony2005]

Hi all,
I have a very simple issue, but can't get round of it.

I have a long sum of rational functions, which is in the form for example

$\frac{n_{1}}{d_{1}}+\frac{n_{2}}{d_{1}}+\frac{n_{3}}{d_{1}}+\frac{n_{4}}{d_{1}}+\frac{n_{5}}{d_{2}}+\frac{n_{6}}{d_{2}}+\frac{n_{7}}{d_{1}\cdot d_{2}}+\frac{n_{8}}{d_{1}\cdot d_{2}}+\frac{n_{9}}{d_{1}\cdot d_{2}}$

and I would like to put it in the form

$\frac{n_{1}+n_{2}+n_{3}+n_{4}}{d_{1}}+\frac{n_{5}+n_{6}}{d_{2}}+\frac{n_{7}+n_{8}+n_{9}}{d_{1}\cdot d_{2}}$

If I use Factor or Simplify it would just put all over one single denominator $d_{1}\cdot d_{2}$, taking also so much time since my expression is huge.

Any help?
Thanks

 

[Bill Simpson]

Figuring out how and why this works will be an educational experience.

In[1]:= f=n1/d1+n2/d1+n3/d1+n4/d1+n5/d2+n6/d2+n7/(d1 d2)+n8/(d1 d2)+n9/(d1 d2);

In[2]:= Plus@@Map[Together[Select[f,Function[x, Denominator[x]==#]]]&,Union[Map[ Denominator,List@@f]]]

Out[2]= (n1 + n2 + n3 + n4)/d1 + (n5 + n6)/d2 + (n7 + n8 + n9)/(d1*d2)

Be careful with that, just in case some oddball input breaks it.

 

[anthony2005]

Wow, it worked. Miracles are hidden in mathematica, but I'll figure out why it worked.
Thanks a lot.

 

[Hepth]

I always find ways to use Collect and get it to look right myself.

Collect[f /. {1/(d1*d2) -> 1/d1d2}, {d1, d2, d1d2}] /. d1d2 -> d1 d2

but the way above with mapping is much better and more robust.

 

[alphy]

Dear fellow scientist,

Thank you for reaching out with your question. It sounds like you are trying to collect the denominators in a long sum of rational functions using Mathematica. This can be a tricky task, especially if your expression is large. Fortunately, there are a few strategies you can use to simplify the process and get the desired result.

One approach is to use the Collect function in Mathematica. This function allows you to collect terms with the same denominator and group them together. You can specify which variables you want to collect, in this case the denominators d_{1} and d_{2}. This will help simplify your expression and put it in the desired form.

Another option is to use the Together function, which will combine terms with common factors in the numerator and denominator. This can help reduce the number of terms in your expression and make it easier to manipulate.

I would also recommend breaking down your expression into smaller chunks and using the aforementioned functions on each chunk individually. This can help prevent Mathematica from taking a long time to process the entire expression at once.

I hope these suggestions help you achieve your desired result. Best of luck with your research!

Sincerely,