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Re: how to test if 2 expressions are the same? Mathematica 5.0

• To: mathgroup at smc.vnet.net
• Subject: [mg46095] Re: how to test if 2 expressions are the same? Mathematica 5.0
• From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
• Date: Fri, 6 Feb 2004 04:15:18 -0500 (EST)
• Organization: Universitaet Leipzig
• References: <bvt135$oj5$1@smc.vnet.net>
• Reply-to: kuska at informatik.uni-leipzig.de
• Sender: owner-wri-mathgroup at wolfram.com

Hi,

first of all for complex x  the expressions,
a*Log[x]
and
Log[x^a]

are *not* the same. 

SameQ[] tests to an identity and it does no
simplifications that might be possible.

That's the reason why

1 - Cos[phi]^2 == Sin[phi]^2

is unevaluated while

1 - Cos[phi]^2 == Sin[phi]^2 // FullSimplify

return True.

Regards
  Jens


steve_H wrote:
> 
> hello;
> 
> I am confused.
> 
> many times, I want to find if there is a way to obtain one expression
> from another by tranformation.
> 
> for example, we know that 1-sin^2(x) = cos^2(x), and  a*log(x)=log(x^a),
> etc.., but sometimes this does not seem to work using SameQ:
> 
> SameQ[a Log[x], Log[x^a] ]
> False
> 
> I tried MatchQ and that also gives False.
> 
> what is the right way to do these things in Mathematica? I checked the on-line help,
> and can't seem to see the right command for this.
> 
> many thanks,
> STeve