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[rushfan]

(10-24-2018 02:18 AM)Anders Wrote:  1. normalized laplace expressions
partfrac() is a great way to normalize the output from Laplace for many (but not all) conversions. Maybe we should add parameter to laplace() to tell laplace() that we want the result in the normalized form..., i.e. laplace(expression of parameter 1, [param 1 (i.e. t)], [param 2 (i.e. s)], [normalized flag]) where the normalized flag is either 1 or 0 for yes and no, with default = 1 for yes.

In the normalized form we want a sum of terms, where each term is a function of s that corresponds 1:1 to each term in the original expression (where each term was a function of t)

Example of common terms (of t and the corresponding terms of s):
unit step : 1 <-> 1/s
ramp: t <-> 1/s^2
sine: sin(a*t) <-> a/(s^2 +a^2)

see more attached

2. Found some issues with laplace and ilaplace/invlaplace

I played around with laplace() and ilaplace() and noticed that they no longer behave like the used to

ilaplace((1/(x^2+1)^2)) (or invlaplace() which is and works the same ilapalce())

results in:

1/4*(-x*e^(i*x)-x*e^(−i*x)−i*e^(i*x)+i*e^(−i*x))

which is correct (if you apply Euler) but it is no longer presented in the usual recognizable formal (like it used to do and indeed the help menu shows it should/did):

1/2*sin(x)-1/2*x*cos(x)

I realize that I had "i" checked in CAS settings and if I uncheck that I get the expected result: 1/2*sin(x)-1/2*x*cos(x).

Is this the way this should work - the transformation being dependent of "i" being checked or not?

I was using a "physical " prime
version is 2.0.0.13865 from 2018 07 06
Hardware version C

Also, the virtual Prime does not behave the same way as the "physical" Prime.

The virtual Prime does not like when you use the familiar parameters s and t but prefers x.

laplace(2*t*e^(-3*t)+5,t,s)
results in
"laplace(2*t*e^(-3*t)+5,t,s) Error: Bad Argument Value"

but:

laplace(2*x*e^(-3*x)+5,x,s)
works fine
(5*s^2+32*s+45)/(s^3+6*s^2+9*s)

The Virtual Prime have the same version and date (version is 2.0.0.13865 from 2018 07 06) as the "real" Prime.

Running simplify( exp2trig( ilaplace(1/(x^2+1)^2))) works for me.

You can create a program to run simplify( exp2trig( ilaplace( ))).