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MathGroup Archive 2004

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Re: solve and simplify. force left hand side to be 0==

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51171] Re: solve and simplify. force left hand side to be 0==
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Thu, 7 Oct 2004 05:25:51 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <ck0bv6$nuk$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

In article <ck0bv6$nuk$1 at smc.vnet.net>,
 sean kim <sean_incali at yahoo.com> wrote:

> consider a system such as, 
> 
> sde = {
> 0==v1-d1 e[0]+k2 es[0]-k1 e[0] s[0],
> 0==-k2 es[0]-k3 es[0]+k1 e[0] s[0],
> 0==k3 es[0]-d3 p[0],
> 0==v2+k2 es[0]-d2 s[0]-k1 e[0] s[0]};
> 
> sv = {e[0],es[0],p[0],s[0]};
> 
> Solve[sde[[1]], e[0]]
> 
> sde1= sde/.%
> 
> %//Simplify
> 
> shows once I simplify the solution, the structure of
> 0== stuff... is lost.
> 
> is there anyway to force Simplify to keep the
> structure so that left hand side is always 0== stuff?

For this particular problem, one way is to apply Simplify (or 
FullSimplify) at the appropriate level. Instead of 

   sde1 // Simplify

try

  Map[FullSimplify, sde1, {3}]

Level {3} is required because sde1 is a list of lists (2 levels), each 
element of the list is an equation, and you want to apply simplification 
to each part of the equation.

If you want to always get an expression of the form 0 == expression, 
then the following will work:

  Map[0 == FullSimplify[Subtract @@ ##] &, sde1, {2}]

The idea is to turn each equation into something that must be 
identically zero, simplify, and re-construct an equation.

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 6488 2734
School of Physics, M013                         Fax: +61 8 6488 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au 
AUSTRALIA                            http://physics.uwa.edu.au/~paul


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