Re: `Collect' with complex numbers??
- To: mathgroup@smc.vnet.net
- Subject: [mg12369] Re: [mg12320] `Collect' with complex numbers??
- From: Daniel Lichtblau <danl@wolfram.com>
- Date: Sun, 10 May 1998 02:04:52 -0400
- References: <199805072252.SAA01018@smc.vnet.net.>
Craig P Earls wrote:
>
> I couldn't figure out how to do an annoyingly straightforward
> transformation with crtesian complex numbers:
>
> Collect[(a+b)c +b d,b]
>
> yields
>
> a c + b(c+d)
>
> Which is good, but
>
> Collect[(a+i)b + c I , I]
>
> yields
>
> (a+I)b +c I
>
> How can I do complex algebra when I can't get this transformation? Using
> ComplexExpand and Re is less than satisfying.
>
> --
> ----------------------------------------------------------------------
> Craig P Earls, LT U.S. Navy cearls@ix.netcom.com
> MIT Naval Construction and Engineering cpearls@mit.edu
> ----------------------------------------------------------------------
The entity I is a number (it is a symbolic convenience for Complex[0,1])
and Collect cannot use a number for its variable. Roughly, this is
because Complex[a,b] is an atomic entity (for integer/rational/real
a,b), hence will not be split for purposes of collection.
You can work around this with simple replacement rules. I do it inside a
module in order to localize the
complexCollect[expr_, var_] := Module[
{myI,e2,v2},
{e2,v2} = {expr,var} /. Complex[a_,b_]->a+myI*b;
Collect[e2,v2] /. myI->I
]
In[18]:= complexCollect[(a+I)b + c I , I] Out[18]= a b + I (b + c)
Daniel Lichtblau
Wolfram Research
- References:
- `Collect' with complex numbers??
- From: Craig P Earls <cearls@ix.netcom.com>
- `Collect' with complex numbers??