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 December 22nd, 2011, 03:39 AM #1 Newbie   Joined: Dec 2011 Posts: 12 Thanks: 0 Mathematica - symbolic representation Hey 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 $..(-2 + n)(-1 + n)*A + (-2 + n)(-1 + n)(-3 + n)*B..$ I would like to get $.. 3!A\binom{n}{3}/n + 4!B\binom{n}{4}/n...$ How can I do that? I appreciate your help! Cheers, maxiim
 December 22nd, 2011, 06:36 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 932 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Mathematica - symbolic representation Generally Mathematica is pretty stupid. You should be able to do it with something like Code: 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. Code: 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.
December 22nd, 2011, 09:16 AM   #3
Newbie

Joined: Dec 2011

Posts: 12
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Re: Mathematica - symbolic representation

Hi CRGreathouse

Quote:
 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

$..(-2 + n)(-1 + n)*A + (-2 + n)(-1 + n)(-3 + n)*B..$

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?

cheers,
maxiim

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