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Re: List Manipulation


On 25 Dec 2006, at 18:52, Stratocaster wrote:

> I'm not sure if the following is possible or whether it exists  
> somewhere
> between the realms of fantasy and science fiction.  I have been  
> unable to do
> it.
>
> Given a list, set, vector (whatever you want to call it) consisting of
> functions of the same variable, i.e.
>
> list = {a1+b1*k, a2+b2*k, a3+b3*k...}
>
> Assuming they are all linear (of the form a+b*k) is there away to  
> isolate
> the a_i and b_i values?  Essentially I would like to get a list "A"
> consisting of all the intercept values, and a list "B" consisting  
> of all the
> slope values.
>
> Is this possible?  What kind of operations do I need to use to  
> accomplish
> this (if indeed it is possible)?
>
> Thanks for any insights.
>

If I understand you correctly this function gives one (out of a large  
number) of ways of doing this:

f[ls_] := Transpose[Map[{Coefficient[#, k, 0], Coefficient[#, k, 1]}  
&, ls]]

Let's take two sample lists, one with numeric and one with symbolic  
coefficients:

ls1={2+3 k,1-0.5k,4+Pi k};

ls2={a+b k,c+d k,e+f k};
Then

f[ls1]

{{2, 1, 4}, {3, -0.5, Pi}}

f[ls2]

{{a, c, e}, {b, d, f}}

Andrzej Kozlowski
Tokyo, Japan


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