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


I'd think all these would work; some do and some don't:

expr = 1 - Sin[x]^2 == Cos[x]^2; 
simplifiers = {Simplify, FullSimplify, TrigExpand, TrigReduce,
TrigToExp};
Through[Compose[simplifiers, expr]]

{True, True, 1 - Sin[x]^2 == Cos[x]^2,
  1 - Sin[x]^2 == Cos[x]^2, True}

The results for Log, on the other hand, don't surprise me. Simplify
and FullSimplify (correctly) do not assume that x is a positive real,
et cetera. PowerExpand does make that kind of assumption.

expr = a*Log[x] == Log[x^a];
simplifiers = {Simplify, FullSimplify, PowerExpand}; 
Through[Compose[simplifiers, expr]]

{a*Log[x] == Log[x^a], a*Log[x] == Log[x^a], True}

Sometimes subtracting may work when Equal doesn't (but not this time):

expr = a*Log[x] - Log[x^a]; 
simplifiers = {Simplify, FullSimplify, PowerExpand}; 
Through[Compose[simplifiers, expr]]

{a*Log[x] - Log[x^a], a*Log[x] - Log[x^a], 0}

Bobby

nma124 at hotmail.com (steve_H) wrote in message news:<bvt135$oj5$1 at smc.vnet.net>...
> 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


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