CAS: Hyperbolic Functions, assume (Beta)

11052019, 01:42 PM
(This post was last modified: 11052019 01:45 PM by Eddie W. Shore.)
Post: #1




CAS: Hyperbolic Functions, assume (Beta)
I am testing integrals. I don't notice any simplification when it comes to hyperbolic functions.
Example: (e^x  e^x)/2 doesn't simplify to sinh(x) Just want to confirm whether CAS on the HP Prime hasn't implement algebraic rewriting commands with hyperbolic functions. Why doesn't assume work when we want to use "not equals", example a <> 3 (a is not equals to 3)? Other than this, I have not notice any behavior with Beta software so far. 

11052019, 04:12 PM
Post: #2




RE: CAS: Hyperbolic Functions, assume (Beta)
There is no command to convert to hyperbolic function, because it's not useful in a CAS.
CAS are considering parameters like polynomials, they always assume generic value, that's the reason why assuming something like a!=0 would not do anything. The reason is that otherwise it would lead to combinatorical explosions in complexity. 

11052019, 10:06 PM
Post: #3




RE: CAS: Hyperbolic Functions, assume (Beta)
There are codes especially in electronic and electrical engineering that are needed to expand a trigonometric function in exponential functions and vice versa
At least some functions dedicated to the rewriting of hyperbolic expressions would be very useful for programmers. 

11062019, 08:29 PM
Post: #4




RE: CAS: Hyperbolic Functions, assume (Beta)
You can convert yourself like this:
subst(exp(x)+exp(x),exp,cosh+sinh) 

12092019, 07:38 AM
(This post was last modified: 12092019 07:55 AM by Stevetuc.)
Post: #5




RE: CAS: Hyperbolic Functions, assume (Beta)
(11062019 08:29 PM)parisse Wrote: You can convert yourself like this: It would be useful if the cas handled such cases using simplify eg Code:
Gives result Code:
Rather than the anticipated result sin(th) One would have to create a lot of manual subst to workaround all the trig exp forms And this integral Code:
gives result Code:


12092019, 08:25 AM
(This post was last modified: 12092019 08:45 AM by Stevetuc.)
Post: #6




RE: CAS: Hyperbolic Functions, assume (Beta)
Just found that
Code:
Gives the much nicer result Code:
And Code:
Code:
So it would be handy if the cas had an option to return complex exp results in sincos form, so that simplify could do the above automatically 

12092019, 09:27 AM
Post: #7




RE: CAS: Hyperbolic Functions, assume (Beta)
(12092019 08:25 AM)Stevetuc Wrote: Just found that Assign 'sincos' into a [key] in the User mode 

12092019, 12:02 PM
Post: #8




RE: CAS: Hyperbolic Functions, assume (Beta)
Quote:='CyberAngel' pid='124776' dateline='1575883660' Im using the function on cas command line Code: #cas It use a substitution for real exp and sincos function for complex exp Code: ss((e^xe^(x))/2) Code: ss(1/2*(((i))*e^(i*x)+i*e^(((i))*x))) Still, it would be better built in. 

12092019, 01:12 PM
Post: #9




RE: CAS: Hyperbolic Functions, assume (Beta)
Sometimes you will want exponential form, sometimes trigonometric form. That's the reason why you have commands to rewrite an expression...


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