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

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All the solutions below work provided each number in nums includes both 
a nonzero a and a nonzero b. But all fails otherwise!

On 5/23/2011 6:22 AM, Bob Hanlon wrote:
> 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};
>
> nums /. {Plus ->  List, Pi ->  1}

Fails if List nums includes 2 or Pi or 3Pi, for example.
>
>
> (List @@@ Expand[nums]) /. Pi ->  1

Fails if List nums includes 2, for example, or Pi.
>
>
> {#[[1]], #[[2]]/Pi}&  /@ Expand[nums]

Error if List nums includes, say, 2.
>
>
> #/{1, Pi}&  /@ (List @@@ Expand[nums])
>

Fails if List nums includes 2, for example, or Pi.

>
> ---- "1.156"<rob@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

-- 
Murray Eisenberg                     murray@math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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Re: get a, b from numbers in the form a+b Pi Murray Eisenberg <murray@math.umass.edu> - 2011-05-24 10:00 +0000

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