How to get around Meijerg???

[Javier Pérez]

Hello all,

I am trying to move several sympy equations from the Laplace domain to the Time domain but the output of some of the equations are contains calls to the Meijerg method.

How can I get around that issue, please???

Thank you in advance for your help...

[Aaron Meurer]

The hyperexpand() function will try to convert meijerg functions into
simpler functions. However, if this is the result of an integral, it
generally calls hyperexpand() automatically, so likely the issue is
that hyperexpand() does not presently know how to convert it. Or it is
possible that the function in question does not have a closed form
simpler than a Meijerg G-function. If you post the expression you are
getting, we might be able to give more advice for it.

Aaron Meurer

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[Javier Pérez]

Hello Aaron,

First of all, thanks for your answer. As you suggested, here I bring a piece of code with one of the problematic equations (see Section PIECE OF CODE). As a result of certain computation, I get "equ_laplace" in the Laplace domain, then, when I try to move it to the Time domain the output is not a conventional equation (see Section OUTPUT). I have try either force " sym.inverse_laplace_transform()" not to use Meijerg to compute the solution or, reshape the Meijerg output to a conventional equation but with not success yet, unfortunately.

##### PIECE OF CODE ############

import sympy as sym

s = sym.Symbol('s')
t = sym.Symbol('t', positive=True)

# Equation in the Laplace domain
equ_laplace = 470.0*s**2/(1.0*s**4 + 18.7*s**3 + 17.9*s**2 + 4.68*s + 0.131)

# Moving to the Time domain
equ_time = sym.inverse_laplace_transform(equ_laplace, s, t)

print("equ_time =", equ_time)

##############################

#### OUTPUT #################

equ_time = 470.0*meijerg(((-16.7038273656911, 0, 0, 0.968289766789687, 0.517768799450727 - 0.0283089619304889*I, 0.517768799450727 + 0.0283089619304889*I), ()), ((), (-17.7038273656911, -0.031710233210313, 1, 1, -0.482231200549273 - 0.0283089619304889*I, -0.482231200549273 + 0.0283089619304889*I)), exp(t))

##############################

Thank you for your time,

Javier

[David Bailey]

On 14/07/2020 11:49, Javier Perez Rodriguez wrote:

Hello Aaron,

First of all, thanks for your answer. As you suggested, here I bring a piece of code with one of the problematic equations (see Section PIECE OF CODE). As a result of certain computation, I get "equ_laplace" in the Laplace domain, then, when I try to move it to the Time domain the output is not a conventional equation (see Section OUTPUT). I have try either force " sym.inverse_laplace_transform()" not to use Meijerg to compute the solution or, reshape the Meijerg output to a conventional equation but with not success yet, unfortunately.

Javier,

meijerg is a special function - like sin or cos or besselj! So it is a conventional equation, it is just that meijerg isn't that well known:

https://en.wikipedia.org/wiki/Meijer_G-function

You can evaluate it for specific numerical arguments, or manipulate expressions using it just as you can manipulate expressions using sin or cos, or whatever.

David

[Aaron Meurer]

Laplace transforms are something that SymPy doesn't do as well with as
it should. I tried to get a closed form version with exponentials by
using apart(full=True) and finding the transform of the individual
terms, but I ran into a bug
https://github.com/sympy/sympy/issues/19773.

I was able to workaround the bugs to get an answer with

>>> Add(*[inverse_laplace_transform(nsimplify(i), s, t) for i in Add.make_args(apart((equ_laplace), s, full=True).doit())])
(1398726960911182419102898085651241253403000977950623455914670 -
24878179654951949422367214210629217423593456535413826921554823*I)*exp(-482231200549273*t/1000000000000000
- 283089619304889*I*t/10000000000000000)/100000000000000000000000000000000000000000000000000000000000
+ (1398726960911182419102898085651241253403000977950623455914670 +
24878179654951949422367214210629217423593456535413826921554823*I)*exp(-482231200549273*t/1000000000000000
+ 283089619304889*I*t/10000000000000000)/100000000000000000000000000000000000000000000000000000000000
- 281057785843441*exp(-177038273656911*t/10000000000000)/10000000000000
+ 65620080368859*exp(-317102332103131*t/10000000000000000)/500000000000000

Aaron Meurer

On Tue, Jul 14, 2020 at 5:37 AM Javier Perez Rodriguez
<jprgu...@gmail.com> wrote:
>
> Hello Aaron,
>
> First of all, thanks for your answer. As you suggested, here I bring a piece of code with one of the problematic equations (see Section PIECE OF CODE). As a result of certain computation, I get "equ_laplace" in the Laplace domain, then, when I try to move it to the Time domain the output is not a conventional equation (see Section OUTPUT). I have try either force " sym.inverse_laplace_transform()" not to use Meijerg to compute the solution or, reshape the Meijerg output to a conventional equation but with not success yet, unfortunately.
>

> ##### PIECE OF CODE ############
> import sympy as sym
>
> s = sym.Symbol('s')
> t = sym.Symbol('t', positive=True)
>
> # Equation in the Laplace domain
> equ_laplace = 470.0*s**2/(1.0*s**4 + 18.7*s**3 + 17.9*s**2 + 4.68*s + 0.131)
>
> # Moving to the Time domain
> equ_time = sym.inverse_laplace_transform(equ_laplace, s, t)
>
> print("equ_time =", equ_time)
> ##############################
>
> #### OUTPUT #################
> equ_time = 470.0*meijerg(((-16.7038273656911, 0, 0, 0.968289766789687, 0.517768799450727 - 0.0283089619304889*I, 0.517768799450727 + 0.0283089619304889*I), ()), ((), (-17.7038273656911, -0.031710233210313, 1, 1, -0.482231200549273 - 0.0283089619304889*I, -0.482231200549273 + 0.0283089619304889*I)), exp(t))
> ##############################
>
> Thank you for your time,
> Javier
>

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[Javier Pérez]

Hello Aaron,

I posted new comments in the git hub you opened.

https://github.com/sympy/sympy/issues/19773

Thank you in advance,

Javier

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