Hmmm...
sage: assumptions()
[]
sage: (z-4*conjugate(z)).simplify()
-3*z
sage: assume(z,"complex")
sage: (z-4*conjugate(z)).simplify()
z - 4*conjugate(z)
Explicitly telling "var(z,"complex") has the same effect... This seems
directly inherited from Maxima :
(%i29) ratsimp(z-4*conjugate(z));
(%o29) z-4*conjugate(z)
(%i30) ratsimp(x-4*conjugate(x));
(%o30) -3*x
BTW : a two-liner to solve the original problem :
sage: var("a,b", domain="real")
(a, b)
sage: [{z:s.get(a)+I*s.get(b)} for s in solve([E.operator()(*map(foo,
E.operands(
....: ))).subs([real_part(z)==a,imag_part(z)==b]) for foo
in[real_part,imag_part]
....: ],[a,b],solution_dict=True)]
[{z: 3/5*I - 1/3}]
which checks. It works, but it's a bit clumsy.
Maxima is not better :
(%i26) facts();
(%o26) [kind(z,complex)]
(%i27) E:z-4*conjugate(z)=1+3*%i;
(%o27) z-4*conjugate(z) = 3*%i+1
(%i28) solve(E,z);
(%o28) [z = 4*conjugate(z)+3*%i+1]
Nor is SymPy :
>>> z=symbols("z", complex=True)
>>> solve(Eq(z - 4*z.conjugate(),1 + 3*I), z)
[]
Nor is Fricas :
sage: fricas.solve(E,z)
[]
This seems to be an area where we can progress...
--
Emmanuel Charpentier
Le mardi 28 novembre 2017 13:23:41 UTC+1, Eric Gourgoulhon a écrit :
>
> This is probably related to the following:
>
> sage: var('z')
> z
> sage: (z - 4*z.conjugate()).simplify()
> -3*z
>
> which is a bug, given that the documentation of var says:
>
> By default, var returns a complex variable
>
> Eric.
>
>
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