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MathGroup Archive 2006

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Re: List Manipulation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72430] Re: List Manipulation
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Wed, 27 Dec 2006 06:19:21 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <emo866$g29$1@smc.vnet.net>

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.
> 
Among many other possibilities, you could try one of the following:

In[1]:=
list = {a1 + b1*k, a2 + b2*k, a3 + b3*k}

Out[1]=
{a1 + b1*k, a2 + b2*k, a3 + b3*k}

In[2]:=
(Select[#1, FreeQ[#1, k] & ] & ) /@ list

Out[2]=
{a1, a2, a3}

In[3]:=
(Select[#1,  !FreeQ[#1, k] & ] & ) /@ list/k

Out[3]=
{b1, b2, b3}

In[4]:=
list /. (p_) + (q_)*k -> p

Out[4]=
{a1, a2, a3}

In[5]:=
list /. (p_) + (q_)*k -> q

Out[5]=
{b1, b2, b3}

Happy holidays,
Jean-Marc


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