       RE: Canceling square roots with Simplify

• To: mathgroup at smc.vnet.net
• Subject: [mg18248] RE: [mg18211] Canceling square roots with Simplify
• From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
• Date: Thu, 24 Jun 1999 14:24:27 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```
-----Original Message-----
From: Ersek, Ted R
To: mathgroup at smc.vnet.net
Subject: [mg18248] RE: [mg18211] Canceling square roots with Simplify

Everett G. Farr  wrote:
-----------------------

Try typing in the following in a new session of Mathematica (I'm currently
running ver 3.0 under WinNT).

Simplify[ Sqrt[b^2]*Sqrt[1/b^2] ]

It seems like the b's should cancel, and I should get 1. Why don't I? Is
there any workaround?

---------------------

Everett,
I think WRI left a needed rule out of the Simplify routine.  Anyway I think
you can say in general that:

((zb^(-z1))^z2
and
(zb^z1)^(-z2)
are equal for any (zb,z1,z2).

If I am right the two rules below are worth keeping. They will simplify your
example and *lots* of others.

----------------
In:=
MyRules= {
((zb_^(-1*z1_))^(z2_)):>((zb^z1)^(-z2)),
((zb_^p_?Negative)^z2_):>(zb^(-p))^(-z2)  };

In:=
example=(((z1^(-z2))^z2)^(-z3))^(-z4)
Out=
(((z1^(-z2))^z2)^(-z3))^(-z4)

In:=
example//.MyRules
Out=
(((z1^z2)^z2)^z3)^(-z4)

---------------------

If you have Version 4.0 you can use the following to make Simplify and
FullSimplify use MyRules automatically.

In:=
SetOptions[Simplify,
TransformationFunctions->{Automatic,(#//.MyRules)&}];
SetOptions[FullSimplify,
TransformationFunctions->{Automatic,(#//.MyRules)&}];

----------------
Regards,
Ted Ersek

```

• Prev by Date: RE: Canceling square roots with Simplify
• Next by Date: Re: Canceling square roots with Simplify
• Previous by thread: RE: Canceling square roots with Simplify
• Next by thread: Re: Canceling square roots with Simplify