       Re: Problem with FullSimplify in Version 5: Rationals are converted to Reals

• To: mathgroup at smc.vnet.net
• Subject: [mg45504] Re: Problem with FullSimplify in Version 5: Rationals are converted to Reals
• From: bobhanlon at aol.com (Bob Hanlon)
• Date: Sat, 10 Jan 2004 16:43:25 -0500 (EST)
• References: <bto17c\$2gp\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```\$Version

5.0 for Mac OS X (November 19, 2003)

expr = Erf[(-(Log/Log) -
Log[10^(-12 + (20 + deltaL)/10)]/Log)/
(Sqrt*Sqrt[0.25302502757884177 +
(0.6089140226261116 - 0.005294904544574884*(20 + deltaL))2])];

Use can use Simplify and a replacement rule rather than FullSimplify

Simplify[expr]/. (a_.*Log[x_] + b_.*Log[y_]) :> Log[x^a*y^b]

Erf[Log[10^(-deltaL/10)]/
(Sqrt[2.518113782096139 - 0.021179618178299536*deltaL]*
Log)]

However, this can be simplified further if deltaL is real

Simplify[%, Element[deltaL, Reals]]

-1.*Erf[(0.1*deltaL)/Sqrt[2.518113782096139 -
0.021179618178299536*deltaL]]

But in that case you don't need anything other than Simplify

Simplify[expr, Element[deltaL, Reals]]

-1.*Erf[(0.1*deltaL)/Sqrt[2.518113782096139 -
0.021179618178299536*deltaL]]

You can use Rationalize to clean this up

Rationalize[%]

-Erf[deltaL/(10*Sqrt[2.518113782096139 -
0.021179618178299536*deltaL])]

Bob Hanlon

In article <bto17c\$2gp\$1 at smc.vnet.net>, oberfeld <oberfeld at uni-mainz.de> wrote:

<< while trying to solve an equation that could be solved without problems
in MA 4.2, Solve[] does not find a solution in Ma 5.0.0.0.

I found that the problem is due to FullSimplify[] in Version 5.

In Version 4.2,
Full Simplify[
Erf    [
(
-(Log/Log) -
Log[10^(-12 + (20 +deltaL)/10)]/Log
)/
(Sqrt*Sqrt[0.25302502757884177 +
(0.6089140226261116 - 0.005294904544574884*
(20 + deltaL))2])
]
]

yields

Out:=-Erf[Log[10^(deltaL/10)]/
(Sqrt[1.012100110315367 + (-0.010653685371740707 +
0.00005607202827231952*deltaL)*deltaL]*Log)]

In Version 5, I get

Out:=0.5 - 0.25*Erf[(0. -
0.30709257318568767*Log[E^(0.2302585092994046*deltaL)])/
Sqrt[0.5060500551576835 + (-0.005326842685870354 +
0.00002803601413615976*deltaL)*
deltaL]] +
0.25*Erf[(0. + 0.30709257318568767*Log[E^(0.2302585092994046*deltaL)])/
Sqrt[0.5060500551576835 + (-0.005326842685870354 +
0.00002803601413615976*deltaL)*
deltaL]]

So, FullSimplify[] in Version 5 has obviously converted *all numbers* to
Reals, while in Version 4.2, Rationals are used where available!!

As a consequence, Solve[] Version 5 can not find a solution to an
equation in which the above term appears.

QUESTION: do you know of a fix available for FullSimplify[] in Version 5
that corrects for this behaviour?
Or are there any Options which can be used to 'reset' FullSimplify[] in
Version 5 to the behavior of Version 4.2??

```

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