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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*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 >>> >> >> >> >> > >

**References**:**Simplify Binomial***From:*Themis Matsoukas <tmatsoukas@me.com>