Consider
f := t -> exp(-n*I*t)*(1+exp(exp(I*t)))/cosh(exp(I*t))/(exp(I*t*(1-n)) >*(1+(exp(exp(I*t))-1)/(exp(2*exp(I*t))+1)));
simplify(f(t));
h := t ->(exp(-I*t)*(exp(exp(I*t))+exp(-exp(I*t))-2*cosh(exp(I*t))) >/cosh(exp(I*t)));
simplify(h(t));
g := t -> (1/2)*(exp(exp(I*t))+exp(-exp(I*t)))/cosh(exp(I*t)); >simplify(g(t));
I think every freshman equipped with a formulary can simplify this,
unlike the "world's most powerful math engine".
Or did I miss something?
After simplify(), apply convert(%, exp).
Thanks Rouben!
The situation as I see it is: I want to go from San Francisco
to Los Angles by car and buy a automotive navigation system.
I start, follow the instructions and after a while I find
myself in Las Vegas. So I call the manufacturer and complain.
The manufacturer answers: Hey, there is another button on the
device, the blue one, press it and it will lead you to Los
Angeles. And indeed it does.
So is this OK or absurd? I do know that an algorithmic solution
of simplification problems require some regularizations and
mapping to some standard internal representation before they
can be solved. However it is the promise of a CAS to do this
internally.
In the examples I wanted expressions simplified to 1 or to 0
not to an exponential expression. Other CASs understand this
-- but not Maple.
After simplify(), apply convert(%, exp).
And you example is not a good example, as many examples.
Maple thinks that cosh is more simple than exp, it does not
go that route without being directed.
h := t ->(exp(-I*t)*(exp(exp(I*t))+exp(-exp(I*t))-2*cosh(exp(I*t)))/cosh(exp(I*t)));
simplify(h(t));
Consider
f := t -> exp(-n*I*t)*(1+exp(exp(I*t)))/cosh(exp(I*t))/(exp(I*t*(1-n)) *(1+(exp(exp(I*t))-1)/(exp(2*exp(I*t))+1)));
simplify(f(t));
h := t ->(exp(-I*t)*(exp(exp(I*t))+exp(-exp(I*t))-2*cosh(exp(I*t))) /cosh(exp(I*t)));
simplify(h(t));
g := t -> (1/2)*(exp(exp(I*t))+exp(-exp(I*t)))/cosh(exp(I*t)); simplify(g(t));
I think every freshman equipped with a formulary can simplify this,
unlike the "world's most powerful math engine".
Or did I miss something?
P.S.: If you want to know the solution try Wolfram/Alpha.
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