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Re: Assisting FullSimplify

• To: mathgroup at smc.vnet.net
• Subject: [mg56164] Re: [mg56143] Assisting FullSimplify
• From: Chris Chiasson <chris.chiasson at gmail.com>
• Date: Sun, 17 Apr 2005 03:07:13 -0400 (EDT)
• References: <200504160753.DAA24721@smc.vnet.net>
• Reply-to: Chris Chiasson <chris.chiasson at gmail.com>
• Sender: owner-wri-mathgroup at wolfram.com

Hugh,
If you could show what you did manually to go from the original
expression to the final expression, there might be a way to use the
transformation functions option to make simplify do that
automatically.

I was just wondering, what are you doing with all of these
trig/complex expressions?

f = -((2*I)/(4 - 100*((9.42477796076938 + 0.01*I) -
2*k)*(0.047123889803846894*I - k + k1)));

ee = (-1 + Cos[a*k] + I*Sin[a*k])*(6 - 3*Sr + 3*(2 + Sr)*Cos[(-2 +
a)*k] - (2 + Sr)*Cos[2*(-1 + a)*k] -
   2*Cos[a*k] + Sr*Cos[a*k] - 6*I*Sin[(-2 + a)*k] - 3*I*Sr*Sin[(-2 +
a)*k] + 2*I*Sin[2*(-1 + a)*k] +
   I*Sr*Sin[2*(-1 + a)*k] - 2*I*Sin[a*k] + I*Sr*Sin[a*k]);

e1 = (2 c q r w (-1 + Cos[k L2]))/(c S r w (4 Cos[k L1] - Cos[k (L1 -
L2)] - 3 Cos[k (L1 + L2)]) + 2 M (w - w0) (w + w0) Sin[k (L1 + L2)]);

Of course, you don't have to tell if you don't want to.

Regards,

On 4/16/05, Hugh Goyder <h.g.d.goyder at cranfield.ac.uk> wrote:
> I started with the expression e1 below. FullSimplify does not make any
> progress in making it simpler. By a mixture of working on parts of the
> expression, luck and physical reasoning I worked out that the expression is
> the same as that given in e2. (For example I knew the expression should be
> real). Is there anyway that I could have directed FullSimplify to get from
> e1 to e2, by for example setting options?
> 
> (Cutting and pasting the code below into a notebook will make it readable.
> It may then be evaluated.)
> 
> Thanks
> 
> Hugh Goyder
> 
> e1 = (4*I*
> E^(I*(a + b)*k)*(-E^(2*I*a*k) +
> E^(2*I*(1 + ar)*k)))/(E^(2*I*(1 + a + ar)*k)*(-2 + Sr) +
> E^(2*I*(a + b)*k)*(-2 + Sr) - E^(4*I*a*k)*Sr + E^(2*I*(1 + ar)*k)*Sr +
> E^(2*I*(2*a + b)*k)*Sr - E^(2*I*(1 + ar + b)*k)*Sr -
> E^(2*I*a*k)*(2 + Sr) - E^(2*I*(1 + a + ar + b)*k)*(2 + Sr))
> 
> e2 = -(Sin[(1 - a + ar)*k]/((-Cos[(1 + ar)*k])*Cos[b*k] +
> Sr*Cos[a*k]*Sin[(1 - a + ar)*k]*Sin[b*k]))
> 
> FullSimplify[e1]
> 
> FullSimplify[e1 == e2]
> 
> LeafCount[e1]
> 
> LeafCount[e2]
> 
> 


-- 
Chris Chiasson
Kettering University
Mechanical Engineering
Graduate Student
1 810 265 3161

• References:
  • Assisting FullSimplify
    • From: "Hugh Goyder" <h.g.d.goyder@cranfield.ac.uk>