Re: Extract Integers

*To*: mathgroup at smc.vnet.net*Subject*: [mg131430] Re: Extract Integers*From*: David Bailey <dave at removedbailey.co.uk>*Date*: Sun, 21 Jul 2013 21:42:37 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <ksg5j9$c1t$1@smc.vnet.net>

On 21/07/2013 09:19, Dana DeLouis wrote: > Hi. I've run out of ideas. Does anyone know the proper way to extract all the integers from the following simplified version of a larger problem I'm working on? > > equ=Series[Exp[x],{x,0,5}] //Normal > > 1+x+x^2/2+x^3/6+x^4/24+x^5/120 > > When trying to extract all the integers, I understand numbers like 120 are part of Rational[1,120] > > equ //FullForm > > << Not shown here >> > > I thought looking at all LevelSpec was the solution, but apparently not. > > Cases[equ, _Integer, Infinity] > {1,2,3,4,5} > > (* Or *) > > Position[equ, _Integer, Infinity] > {{1},{3,2,2},{4,2,2},{5,2,2},{6,2,2}} > > Extract[equ, %] > {1,2,3,4,5} > > Both ways extract from the numerator, but I just can't seem to extract the {2,6,24,120} inside the denominator. > Does anyone know the proper way? > Thanks in advance. :>~ > > Dana > Mac & Math 9 > > This seems a strange sort of thing to wish to do, and I am a bit concerned that it is a class test question. However, you have obviously explored the problem a bit, so (assuming there are no real numbers in your larger problem) here are two suggestions: Flatten[ Cases[equ, _?NumberQ, \[Infinity]] /. x_Rational :> {Numerator[x], Denominator[x]}] {1, 1, 2, 2, 1, 6, 3, 1, 24, 4, 1, 120, 5} This is OK, but it contains some spurious ones because the numerators of 1 are not usually shown within a multiplication. Of course, if you would like those implicit ones, it is ideal. Alternatively, by converting the expression to a string, it is possible to extract all the integers using a string pattern, and then convert them back from strings to integers: Map[ToExpression, StringCases[ToString[eq, InputForm], DigitCharacter ..]] {1, 2, 2, 3, 6, 4, 24, 5, 120} It may be worth discussing your larger problem here, because this seems a rather odd step to need to take! David Bailey http://www.dbaileyconsultancy.co.uk