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Re: get a, b from numbers in the form a+b Pi

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On May 22, 6:58 am, "1.156" <r...@piovere.com> wrote:
> I have lists  of numbers (Mathematica output) all numerically in the
> form a + b*Pi and I'm trying to extract the values of a and b for
> further work.
>
> Here's an example of the best I've been able to do so far:
>
> nums={1/2 (-2+\[Pi]),-2+(3 \[Pi])/4,-(11/3)+(5 \[Pi])/4,5/48 (-64+21
> \[Pi]),-(61/5)+(63 \[Pi])/16,-(338/15)+(231 \[Pi])/32};
> {FullForm[#][[1,1]],FullForm[#][[1,2]]/\[Pi]}&/@nums
>
> When I run this line of code 4 of the six input numbers give me the
> {a,b} I'm looking for but the first and fourth entries fail because the
> form isn't right. Possibly I could patch this scheme to look for a small
> finite set of possibilities of input number form but I suspect I may a
> long way from attacking this problem correctly.
>
> Can someone offer some other ideas on how to pull this off? Many thanks
> for looking at this. Rob
> --
> Sent from my plain desktop PC.

Interesting task you're describing, but I think I found what's
throwing you off.
Your code relies on each expression being of the form a+b Pi, so that
you can FullForm to get it in the form Plus[a,b Pi] and then you pick
off a and b. The cases where it doesnt work for you is when FullForm
has head Times
FullForm[1/2 (-2 + \[Pi])] = Times[Rational[1,2],Plus[-2,Pi]]
The solution: hit it with Expand[] first, so that it does any
multiplication/division and gets it into the form you want.
FullForm[Expand[1/2 (-2 + \[Pi])]] = Plus[-1,Times[Rational[1,2],Pi]]

so the final code is below,
nums = {1/2 (-2 + \[Pi]), -2 + (3 \[Pi])/4, -(11/3) + (5 \[Pi])/4,
   5/48 (-64 + 21 \[Pi]), -(61/5) + (63 \[Pi])/
     16, -(338/15) + (231 \[Pi])/32};
{FullForm[Expand@#][[1, 1]],
   FullForm[Expand@#][[1, 2]]/\[Pi]} & /@ nums

hope that helps!
-Stefan S

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get a, b from numbers in the form a+b Pi "1.156" <rob@piovere.com> - 2011-05-22 10:58 +0000
  Re: get a, b from numbers in the form a+b Pi "Nasser M. Abbasi" <nma@12000.org> - 2011-05-23 10:26 +0000
  Re: get a, b from numbers in the form a+b Pi Albert Retey <awnl@gmx-topmail.de> - 2011-05-23 10:28 +0000
  Re: get a, b from numbers in the form a+b Pi Wolfgang Windsteiger <Wolfgang.Windsteiger@risc.jku.at> - 2011-05-23 10:28 +0000
  Re: get a, b from numbers in the form a+b Pi Peter Breitfeld <phbrf@t-online.de> - 2011-05-23 10:28 +0000
  Re: get a, b from numbers in the form a+b Pi Peter Pein <petsie@dordos.net> - 2011-05-23 10:29 +0000
  Re: get a, b from numbers in the form a+b Pi Roland Franzius <roland.franzius@uos.de> - 2011-05-23 10:22 +0000
  Re: get a, b from numbers in the form a+b Pi Armand Tamzarian <mike.honeychurch@gmail.com> - 2011-05-23 10:26 +0000
  Re: get a, b from numbers in the form a+b Pi Stefan Salanski <wutchamacallit27@gmail.com> - 2011-05-23 10:23 +0000
  Re: get a, b from numbers in the form a+b Pi Ray Koopman <koopman@sfu.ca> - 2011-05-23 10:23 +0000

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