abs2(x) == conjugate(x)*x

[benneti]

Hi,
I think the title already describes the problem.
Is this outside the scope of the project?
A simple fix/workaround for own code is:

import Base.abs2
abs2(x::Sym) = x*conjugate(x)

Best,
Benedikt

PS: the same is true when using conj(x)

[jverzani]

Sure, we could add this. Do you want to make a pull request with a simple test?

[benneti]

yeah, no problem

[benneti]

I just checked it in Python and there
simplify(abs(x)**2 - conjugate(x)*x) == 0 is false, too.
Therefore I think this is actually not an issue with the Package and should probably be addressed in the python package.

[jverzani]

No, there is an issue with SymPy. I checked and have abs2 misdefined. I will make it x*conj(x) instead of abs(x)^2. Thanks.

[mzaffalon]

Is there any reason to prefer x*conj(x) to conj(x)*x? Does x commute with its conjugate?

[jverzani]

Well, good question. I was only thinking about something that worked for real and complex numbers here. In base julia, the defn was `real(x)*real(x) + imag(x) * imag(x)` for complex numbers, which is not the same with this definition in SymPy (surprisingly to me). But maybe that one makes more sense.

…

On Mon, Feb 24, 2020 at 2:21 PM Michele Zaffalon ***@***.***> wrote: Is there any reason to prefer x*conj(x) to conj(x)*x? Does x commute with its conjugate? — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#332?email_source=notifications&email_token=AADG6TAIKI2HK2VQIFAH3V3REQM5HA5CNFSM4KYN6AHKYY3PNVWWK3TUL52HS4DFVREXG43VMVBW63LNMVXHJKTDN5WW2ZLOORPWSZGOEMZF7TY#issuecomment-590503887>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AADG6THSJFEXC3ESJUY4YT3REQM5HANCNFSM4KYN6AHA> .

-- John Verzani Department of Mathematics College of Staten Island, CUNY verzani@math.csi.cuny.edu

[benneti]

As far as I understand, sympy simply still has some inconsistencies.
See for example sympy/sympy#10822 , which basically tells you that to get the equality you have to expand with complex=true else it will not realize that stuff like the equality in the title are true.