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Re: Assisting FullSimplify
*To*: mathgroup at smc.vnet.net
*Subject*: [mg56163] Re: Assisting FullSimplify
*From*: Peter Pein <petsie at arcor.de>
*Date*: Sun, 17 Apr 2005 03:07:12 -0400 (EDT)
*References*: <d3qht2$oi2$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Hugh Goyder 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]
>
>
In[6]:=
Timing[
e3a = FullSimplify[ComplexExpand[Re[e1],
TargetFunctions -> {Re, Im}]];
e3 = FullSimplify[Numerator[e3a]/
Collect[TrigExpand[ExpandAll[Denominator[e3a]]],
Cos[#1*k]& /@ {a, b}, FullSimplify]]]
Out[6]=
{57.719*Second,
Sin[(1 - a + ar)*k] /
( Cos[(1 + ar)*k]*Cos[b*k] +
Sr*Cos[a*k]*Sin[(-1 + a - ar)*k]*Sin[b*k] ) }
In[7]:=
Simplify[e2 == e3]
LeafCount /@ {e1, e2, e3}
Out[7]=
True
Out[8]=
{148, 45, 43}
--
Peter Pein
Berlin
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