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December 22nd, 2011, 02:39 AM   #1
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Mathematica - symbolic representation


I have a considerably long formula involving binomial coefficients. I wish to tell Mathematica to give a (symbolic) representation of these binomial coefficients, but I don't know how. For example in

I would like to get

How can I do that?

I appreciate your help!

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December 22nd, 2011, 05:36 AM   #2
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Re: Mathematica - symbolic representation

Generally Mathematica is pretty stupid. You should be able to do it with something like
f[x_] := LeafCount[x] - Count[x, _Binomial, {0, Infinity}] +  15 Count[x, _Plus, {0, Infinity}]
Simplify[(n - 2) (n - 1) A + (n - 3) (n - 2) (n - 1) B, ComplexityFunction -> f]
where the choice of f makes it very expensive to write + or - signs (and free to write binomials) to nudge it in the right direction. But even FullSimplify will just stay at its local minimum; to get the simplified answer you need not only to give it the whole expression, but pass it with Hold.

Simplify[Hold[3! A Binomial[n, 3]/n + 4! B Binomial[n, 4]/n], ComplexityFunction -> f]
You could try some version of /. but that will be fairly inflexible.
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December 22nd, 2011, 08:16 AM   #3
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Re: Mathematica - symbolic representation

Hi CRGreathouse

Thx for your answer.

Generally Mathematica is pretty stupid.
I find Mathematica is some powerful software, however, in some regards (like this one), it can be a bitch!

Back to the problem:
Id like Mathematica to transform the expression I have, that is

to the representation with binomial coefficients without having to type all of them manually.
(I have a large number of terms, so it would be very helpful).

In more general terms, is it possible to transform a given expression in terms of built-in Mathematica functions?

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