Real and Imaginary part of a function

[Lorenzo Monacelli]

Dear all,

I have a complex expression and I want to separate imaginary and real part, however I noticed that when I have derivatives on a function, the real and imaginary part separation does not work properly:

t = sy.Symbol("t", real = True)

f = sy.Function("f", real = True)(t)

 Then if I ask sympy the imaginary part of f, it correctly returns 0, however if I ask the immaginary part of the derivative of f, it is not able to see that it is zero:

sy.im(f) # this is zero (ok!)

sy.im(sy.diff(f, t))  # does not simplify to zero

How can I force sympy to set automatically the derivative of f to real numbers?

Thanks in advance for the help,

Bests, 

Lorenzo

[Aaron Meurer]

There is an open issue about this https://github.com/sympy/sympy/issues/11868.

Aaron Meurer

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[Lorenzo Monacelli]

I have found a simple workaround for this problem. I implemented a function that performs a hardcore substitution of the expression:

def parse_imaginary_real(expression):

    """

    It takes an expression and parse correctly the imaginary and real part of first derivatives of a 

    real or imaginary function.

    

    This function works only for first derivatives. 

    It could be extended easily to work with second or higher order derivatives as well.

    

    """

    all_variables = globals()

    

    # Get the variables that are functions

    all_functions = [x for x in all_variables.values() if isinstance(x, sy.Function)]

    

    new_exp = expression

    for f in all_functions:

        if f.is_real:

            new_exp = expression.subs(sy.im(sy.diff(f)), 0).subs(sy.re(sy.diff(f)), sy.diff(f))

        elif f.is_imaginary:

            new_exp = expression.subs(sy.im(sy.diff(f)), sy.diff(f)).subs(sy.re(sy.diff(f)), 0)

    

    return new_exp

This function can be used as simplify to an expression. Indeed, it has still some issues: it does not check the type of the argument, and it simplifies only first derivatives (and I think it could be very slow if many variables have been defined, I do not know very well how the globals() can work if the function is used on a library).

However, for my simple case, it does the job and allows me to go over, simplifying the imaginary and real parts of first derivatives that are zero by definition. I hope it can be useful for other users.

Bests,

Lorenzo

Il giorno venerdì 28 febbraio 2020 20:02:51 UTC+1, Aaron Meurer ha scritto:

There is an open issue about this https://github.com/sympy/sympy/issues/11868.

Aaron Meurer

On Fri, Feb 28, 2020 at 12:00 PM Lorenzo Monacelli
<lorenzo92...@gmail.com> wrote:
>
> Dear all,
> I have a complex expression and I want to separate imaginary and real part, however I noticed that when I have derivatives on a function, the real and imaginary part separation does not work properly:
>
> t = sy.Symbol("t", real = True)
> f = sy.Function("f", real = True)(t)
>
>  Then if I ask sympy the imaginary part of f, it correctly returns 0, however if I ask the immaginary part of the derivative of f, it is not able to see that it is zero:
>
> sy.im(f) # this is zero (ok!)
> sy.im(sy.diff(f, t))  # does not simplify to zero
>
> How can I force sympy to set automatically the derivative of f to real numbers?
> Thanks in advance for the help,
> Bests,
> Lorenzo
>
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> You received this message because you are subscribed to the Google Groups "sympy" group.

> To unsubscribe from this group and stop receiving emails from it, send an email to sy...@googlegroups.com.

[Lorenzo Monacelli]

The code needs a small edit to work properly with many functions (it requires sympy imported as sy):

def parse_imaginary_real(expression):

    """

    It takes an expression and parse correctly the imaginary and real part of first derivatives of a 

    real or imaginary function.

    

    This function works only for first derivatives. 

    It could be extended easily to work with second or higher order derivatives as well.

    

    """

    all_variables = globals()

    

    # Get the variables that are functions

    all_functions = [x for x in all_variables.values() if isinstance(x, sy.Function)]

    

    new_exp = expression

    for f in all_functions:

        if f.is_real:

            new_exp = new_exp.subs(sy.im(sy.diff(f)), 0).subs(sy.re(sy.diff(f)), sy.diff(f))

        elif f.is_imaginary:

            new_exp = new_exp.subs(sy.im(sy.diff(f)), sy.diff(f)).subs(sy.re(sy.diff(f)), 0)

    

    return new_exp