On Wed, Apr 10, 2019 at 5:28 PM rjf <[email protected]> wrote:
>
>
> I suppose this is a Sage bug; Maxima doesn't have a problem with
> its factor program.
>

Indeed.

sage: ex=exp(2*x)+exp(-2*x); ex
e^(2*x) + e^(-2*x)
sage: maxima(ex).factor().sage()
(e^(4*x) + 1)*e^(-2*x)
sage: bool(maxima(ex).factor().sage()==ex)
True

> 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).
>

Withstanding, I expect

  factor(x) == x

to always be true.

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