hyp2exp

09012022, 12:18 PM
Post: #1




hyp2exp
Hello, is there the "inverse" function of "hyp2exp"? That is, is there a function that does the reverse process of "hyp2exp"?
Best regards, Roberto. 

09042022, 08:00 PM
Post: #2




RE: hyp2exp
No, but it's fairly easy: subst(expression,exp,cosh+sinh)


09052022, 07:21 AM
Post: #3




RE: hyp2exp  
09052022, 11:50 AM
Post: #4




RE: hyp2exp
(09042022 08:00 PM)parisse Wrote: No, but it's fairly easy: subst(expression,exp,cosh+sinh) Above exp2hyp expression might be "simplified" to sin/cos Just keep in mind, e^(i*x) = cos(x) + i*sin(x) = cosh(i*x) + sinh(i*x) cos(x) = cosh(i*x) i*sin(x) = sinh(i*x) cosh(x) = cos(i*x) i*sinh(x) = sin(i*x) CAS> subst(e^(i*x), exp, x > cosh(x) + sinh(x)) cos(x) + i*sin(x)  Same trick can be used for a "better" exp2trig CAS> f := e^x  e^x // = 2*sinh(x) CAS> exp2trig(f) → e^x  e^x CAS> f(exp = (x > cos(i*x) + sin(i*x)/i)) → 2*i*sin(i*x) Or, in steps, since sinh/cosh tends to "simplify" to sin/cos CAS> f(exp=cosh+sinh)(x=x/i)(x=x*i) → 2*i*sin(i*x) 

09052022, 12:40 PM
Post: #5




RE: hyp2exp
(09052022 07:21 AM)robmio Wrote: Another question: why are inverse hyperbolic functions (ATANH, ACOSH, etc.) automatically represented by the corresponding logarithmic form?For a CAS, it is always simpler to work with a smaller set of functions. cosh and sinh are still used sometimes (in the French curriculum system), they are not replaced, atanh and the like are never used, hence they are replaced (same as for sec/csc etc.) 

09052022, 04:25 PM
Post: #6




RE: hyp2exp
Is this a bug?
acosh(z) should produce nonnegative real part, same as acos(z) CAS> acosh(2.) // ??? −1.31695789692+3.14159265359*i CAS> acosh(2+1e15i) 1.31695789692+3.14159265359*i CAS> acosh(21e15i) 1.316957896923.14159265359*i 

09092022, 11:46 AM
Post: #7




RE: hyp2exp
(09052022 11:50 AM)Albert Chan Wrote:(09042022 08:00 PM)parisse Wrote: No, but it's fairly easy: subst(expression,exp,cosh+sinh) Hello, is there an algorithm that translates the logarithmic formulas of the inverse hyperbolic functions into the inverse hyperbolic functions represented with "acosh", "asinh", "atanh", etc.? For instance: e^x*ln(x+√(x^2+1))ln(ln(√(x+1)*√(x1)+x)) instruction> exp(x)*asinh(x)ln(acosh(x)) Best regards, robmio. 

09132022, 04:00 PM
Post: #8




RE: hyp2exp
(09052022 12:40 PM)parisse Wrote:(09052022 07:21 AM)robmio Wrote: Another question: why are inverse hyperbolic functions (ATANH, ACOSH, etc.) automatically represented by the corresponding logarithmic form?For a CAS, it is always simpler to work with a smaller set of functions. cosh and sinh are still used sometimes (in the French curriculum system), they are not replaced, atanh and the like are never used, hence they are replaced (same as for sec/csc etc.) Dear professor, is there the "inverse" function of "atrig2ln"? That is, is there a function that does the reverse process of "atrig2ln"? Best regards, Roberto. 

09142022, 05:48 PM
Post: #9




RE: hyp2exp
evalc converts complex ln to inverse trig functions. However for Inverse hyperbolic functions, you will have to implement it yourself.


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