Re: get a, b from numbers in the form a+b Pi
- To: mathgroup at smc.vnet.net
- Subject: [mg119182] Re: get a, b from numbers in the form a+b Pi
- From: Murray Eisenberg <murray at math.umass.edu>
- Date: Tue, 24 May 2011 05:57:33 -0400 (EDT)
Here's a solution that does seem to work also in the case that some of
the entries in the list nums are "degenerate", that is, have zero a or b:
nums = {2, Pi, 3 Pi, 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};
Through[{Re, Im}[#]] & /@ (nums /. Pi :> I)
On 5/23/2011 6:23 AM, Murray Eisenberg wrote:
> Here's another way that also handles the situation where a=0, but not
> the situation where b = 0:
>
> newnums = newnums = Join[{1, 2 Pi}, nums];
> CoefficientList[#, Pi]& /@ Expand[newnums]
>
> The "sneaky" part there is to realize that, since Pi is just a symbol,
> it may be considered the variable in a polynomial!
>
> On 5/22/2011 6:57 AM, 1.156 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 at 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
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