I suppose this is a Sage bug; Maxima doesn't have a problem with
its factor program.

As you know, polynomial "factoring" is a process that mathematically is 
defined
in a unique factorization domain, which is broken in the example
at least 2 ways, by have a denominator, and by having exponentials.
for example,  e^x-1  factors many ways,  one being (e^(x/2)-1)*(e^(x/2)+1).

RJF


On Wednesday, April 10, 2019 at 12:30:42 PM UTC-7, Bill Page wrote:
>
> sage: sage.version.version 
> '8.6' 
> sage: ex=exp(2*x)+exp(-2*x); ex 
> e^(2*x) + e^(-2*x) 
> sage: factor(ex) 
> 2*e^(2*x) 
> sage: bool(factor(ex)==ex) 
> False 
> sage: bool(factor(e^(2*x)+e^(-2*x))==e^(2*x)+e^(-2*x)) 
> False 
> sage: bool(factor(2^(2*x)+2^(-2*x))==2^(2*x)+2^(-2*x)) 
> True 
>

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