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[1]:= MyRules= { ((zb_^(-1*z1_))^(z2_)):>((zb^z1)^(-z2)), ((zb_^p_?Negative)^z2_):>(zb^(-p))^(-z2) }; In[2]:= example=(((z1^(-z2))^z2)^(-z3))^(-z4) Out[2]= (((z1^(-z2))^z2)^(-z3))^(-z4) In[3]:= example//.MyRules Out[3]= (((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[4]:= SetOptions[Simplify, TransformationFunctions->{Automatic,(#//.MyRules)&}]; SetOptions[FullSimplify, TransformationFunctions->{Automatic,(#//.MyRules)&}]; ---------------- Regards, Ted Ersek