Do these functions have actual applications? Or are we just playing?
Mathcad is saying that your equation has a root (E(x) =0) at the number given (-221.____)
As demonstrated in the other thread (https://community.ptc.com/t5/PTC-Mathcad/solve-x-fully/td-p/578709) the two first terms ( e^x and -(1/e^(i*x))^i ) cancel out. You're left with (e^pi)*cot(x).
That should give repeated roots at pi/2 +n*pi.
> the two first terms ( e^x and -(1/e^(i*x))^i ) cancel out.
No! Not if we see it as a complex calculation which we have to do as the imaginary unit "i" is involved.
I see. Thanks for reminding me that (a^b)^c=a^(b*c) only when b and c are real numbers. When either one is complex, things become more complex.
This would only be true for one of the infinite number of curves of the family described above, namely the one with k=0:
For all the others muPad is not able to find exact solutions and so will only present one numeric value - and sometimes even a wrong one (or at least we reach the end of the numeric precision of the symbolics here):
To be fair it must be said that we get a better result when we add "float,250" to the last eval, too (we get -2.3*10^-105 which is close enough to zero).
And while muPad is not respecting an assume statement the way we want in that case, its interesting that it still reacts (in a weird way) to assume statements:
BTW, uncle Wolfram also has his troubles with expressions like these. Or does anybody think that Wolfram is correct with this:
x=1.1 IS a correct solution but I would have expected Wolfram telling me that any number is solution like here:
It's about time that you finally realize that Mathcad / muPad is simply not capable of delivering ALL solutions to more complicated equations that are not analytically solvable!
If you insist in getting all solution you will probably have to resort to a different, more capable program with better symbolics.
I guess I just wish learning :
The solution are given, I guess that only are solution of ;
I guess discussing is discussing about difference.
Oh, no ! Now I realize I was wrong with the below. My guessing is not correct ! :
So far, to solve it, I have to solve it "by hand" with root function and guess value. And I still have a query : "Is there a anyway else ? ( as writting a program function to get output at least two solutions at once )
Keep in mind that with E(x) you are not just defining one single curve but rather a family E(x,k) of an infinite number of curves. One of them (k=36) has one root at the given -224,79..
For more details see here: https://community.ptc.com/t5/PTC-Mathcad/solve-x-fully/m-p/578762/highlight/true#M183096
Whenever the symbolics switches to float mode its not capable to give you all roots any more. Similar to numerical solve methods but with the difference that the numerics will respect any guess values or ranges ("root" function) while the symbolics usually will ignore any assume statement in this case.
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