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

• To: mathgroup at smc.vnet.net
• Subject: [mg46096] Re: how to test if 2 expressions are the same? Mathematica 5.0
• From: bobhanlon at aol.com (Bob Hanlon)
• Date: Fri, 6 Feb 2004 04:15:19 -0500 (EST)
• References: <bvt135\$oj5\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Use Equal (==); however, you will also frequently have to use Simplify or
FullSimplify.

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

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

%//Simplify

True

You may also have to state Assumptions that would make the equality True

a*Log[x] == Log[x^a] // Simplify

a*Log[x] == Log[x^a]

Simplify[%, {Element[{a,x}, Reals], x>0}]

True

Sometimes there are shortcuts using PowerExpand; however, you need to be sure
that the implied assumptions hold.

a*Log[x] == Log[x^a] // PowerExpand

True

Bob Hanlon

In article <bvt135\$oj5\$1 at smc.vnet.net>, nma124 at hotmail.com (steve_H) wrote:

<< 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.

```

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