       Re: Simplify Binomial

• To: mathgroup at smc.vnet.net
• Subject: [mg127648] Re: Simplify Binomial
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Fri, 10 Aug 2012 02:44:41 -0400 (EDT)
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• References: <20120809013640.A3CF16843@smc.vnet.net>

```You would have to know the internal workings of the FullSimplify
algorithm; however, you can tell FullSimplify that you don't like
Binomial using the ComplexityFunction option.

Binomial[m, n + 1]/Binomial[m, n] // FullSimplify[#] &

Binomial[m, 1 + n]/Binomial[m, n]

f[e_] := 100 Count[e, _Binomial, {0, Infinity}] + LeafCount[e]

Binomial[m, n + 1]/Binomial[m, n] //
FullSimplify[#, ComplexityFunction -> f] &

(m - n)/(1 + n)

Bob Hanlon

On Thu, Aug 9, 2012 at 8:44 AM, Jack L Goldberg 1 <jackgold at umich.edu> wrote:
> Does anyone know why FullSimplify works in the first case and fails in the
> second?  That FunctionExpand works in both is interesting of course, but IMO
> this is only part of the answer.
>
> Jack
>
>
>
> Quoting Bob Hanlon <hanlonr357 at gmail.com>:
>
>> Binomial[m + 1, n + 1]/Binomial[m, n] //
>>  FunctionExpand
>>
>> (1 + m)/(1 + n)
>>
>> Binomial[m, n + 1]/Binomial[m, n] //
>>  FunctionExpand
>>
>> (m - n)/(1 + n)
>>
>>
>> Bob Hanlon
>>
>>
>> On Wed, Aug 8, 2012 at 9:36 PM, Themis Matsoukas <tmatsoukas at me.com>
>> wrote:
>>>
>>> This works:
>>>
>>> FullSimplify[Binomial[m + 1, n + 1]/Binomial[m, n]]
>>>
>>> (1 + m)/(1 + n)
>>>
>>> but this doesn't:
>>>
>>> FullSimplify[Binomial[m, n + 1]/Binomial[m, n]]
>>>
>>> Binomial[m, 1 + n]/Binomial[m, n]
>>>
>>> How do I get Mathematica to simplify the last result to (m-n)/n?
>>>
>>> Thanks
>>>
>>
>>
>>
>>
>
>

```

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