Re: FullSimplify Question

• To: mathgroup at smc.vnet.net
• Subject: [mg48698] Re: FullSimplify Question
• From: "Dana DeLouis" <delouis at bellsouth.net>
• Date: Thu, 10 Jun 2004 02:44:59 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Thank you Paul.  I've had a total misunderstanding of
"TransformationFunctions."  This cleared that up.
I always thought this was to Simplify the equation into a "final" form that
used the functions supplied by this option.  I never realized that it
actually "changed" the equation.

I now understand why the "Simplified" version below is no way near the
original equation.  Thanks also for the tip on the unique way to add "Print"
to the TransformationFunctions option.  I've not seen that before.  Very
nice. :>)

equ = 4*x^2 + 9*x^3

FullSimplify[equ, TransformationFunctions -> {Sqrt}]

2*x^2 + 3*x^3

Dana

"Paul Abbott" <paul at physics.uwa.edu.au> wrote in message
news:ca1ddp\$fag\$1 at smc.vnet.net...
> In article <c9tmvi\$sek\$1 at smc.vnet.net>,
>  "Dana DeLouis" <delouis at bellsouth.net> wrote:
>
> > Hello.  Hate to ask, but does anyone know what the issue is in the
> > following?
> >
> > This equation basically is 5 when t is less than 0, and 1 when t>=0
> >
> > equ = 5 - 4*UnitStep[t]
> >
> > If I ask to "Simplify" this, by using the Sign function, I get the
> > following, which is not even close
> >
> > FullSimplify[equ, TransformationFunctions -> {Sign}]
> >
> > 1 - UnitStep[t]
>
> From the documentation:
>
>    TransformationFunctions is an option for Simplify and FullSimplify
>    which gives the list of functions to apply to try to t
>
> So Sign is being _applied_ to equ. You can see this more clearly if you
> try
>
>    FullSimplify[equ,
>       TransformationFunctions -> {Sign[Print[{#,Sign[#]}]; #] & }]
>
> printing out the sub-expressions that FullSimplify is attempting to
> simplify by application of Sign.
>
> > The above is 1 when t<0, and 0 when t>=0.
> >
> > I have to use both functions "FourierTransform" and
> > "InverseFourierTransform" to get the correct form.
> >
> > 3 - 2*Sign[t]
>
> The transformation rule, UnitStep[x_] :> (Sign[x] + 1)/2 (valid
> everywhere except at x==0) will do what you want:
>
>    Simplify[equ /. UnitStep[x_] :> (Sign[x] + 1)/2]

> Cheers,
> Paul
>
> --
> Paul Abbott                                   Phone: +61 8 9380 2734
> School of Physics, M013                         Fax: +61 8 9380 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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