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Newsgroups: comp.soft-sys.math.maple,sci.math.symbolic
Subject: Re: How to I get Maple to spit out 1?
Date: Thu, 14 Jul 2011 22:30:16 +0200
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Axel Vogt schrieb:
> On 14.07.2011 01:27, Salmon Egg wrote:
> >
> > I already know the answer.
> >
> > If I get to an expression
> >
> >   z := x*exp(-(1/2)*x)/(2*sinh((1/2)*x))*((exp(x)-1)/x)
> >
> > How do I get Maple to spit out 1? simplify does not do it.
> >
> > [...]
> 
> For guessing I often just plot as a first step ...
> 
> Difficult to say, though I would expect that Maple would try
> to convert hyperbolics to exp, as we would do, since other
> exp terms are present.
> 
> [...]

Derive 6.10 handles this automatically. Here is the stepwise
simplification:

x*EXP(-1/2*x)/(2*SINH(1/2*x))*((EXP(x)-1)/x)

" SINH(z) -> #e^z/2-#e^(-z)/2 "

x*#e^(-x/2)*(#e^x-1)/(2*x*(#e^(x/2)/2-#e^(-x/2)/2))

" e^(z)*#e^(w) -> #e^(z+w) "

(x*#e^(x/2)-x*#e^(-x/2))/(2*x*(#e^(x/2)/2-#e^(-x/2)/2))

" one final step "

1

Martin.