We might be able to help if you could share your original expression.
But I don't really understand your question. You say that radcan puts your
expression in the form you want. So use radcan! -- Why would you expect
ratsimp or trigsimp or default simplification to do the same thing as
radcan?
As for representing exponentials as hyperbolic functions, here's an
approach that will often work:
(%i1) ex: %e^(a*x) + %e^(x-b)$
(%i3) subst(%e^(qq*%i*x),%e,ex);
(%o3) %e^(%i*a*qq*x^2)+%e^(%i*qq*x*(x-b))
(%i4) rectform(%);
(%o4) %i*(sin(a*qq*x^2)+sin(qq*x*(x-b)))+cos(a*qq*x^2)+cos(qq*x*(x-b))
(%i5) subst(-%i,qq,%);
(%o5) %i*(-%i*sinh(a*x^2)-%i*sinh(x*(x-b)))+cosh(a*x^2)+cosh(x*(x-b))
(%i6) ratsimp(%);
(%o6) sinh(x^2-b*x)+cosh(x^2-b*x)+sinh(a*x^2)+cosh(a*x^2)
or...:
(%i8) demoivre(%o3);
(%o8) %i*sin(a*qq*x^2)+cos(a*qq*x^2)+%i*sin(qq*x*(x-b))+cos(qq*x*(x-b))
(%i9) subst(-%i,qq,%);
(%o9) sinh(a*x^2)+cosh(a*x^2)+sinh(x*(x-b))+cosh(x*(x-b))
Does this help in your case?
-s
-----------------------------------
On Fri, Apr 27, 2012 at 15:32, David Ronis <David.Ronis at mcgill.ca> wrote:
> I have an expression that ultimately becomes:
>
> f:(exp(x)+exp(x/2))/(exp(x/2)+1);
>
> I've tried various simplification routines:
>
>
> ratsimp(f);
> trigsimp(f);
> radcan(f);
>
>
> The only one that works is radcan(). Is there a flag that
> would make the other ones work? Alternately, is there a function that
> forces the exponentials to be represented as sums of hyperbolic
> functions?
>
>
>
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