Hi,
I think I may have found a bug in Sage's solve() function:
z=var('z'); solve(conjugate(z)==1+i, z)
[z == (I + 1)]
It sems that the conjugate is simply ignored. Obviously this leads to
incorrect result for (almost) all equations involving the conjugate. Yet,
solve()'s docstring simply states: "Algebraically solve an equation or
system of equations (over the complex numbers) for given variables."
There is no warning or error message, solve simply returns an incorrect
result.
I also found this thread:
https://www.ma.utexas.edu/pipermail/maxima/2008/011312.html
---- quote ----
Maxima assumes that variables are real-valued by default (even with
domain:complex), so conjugate(z) will yield z. This can be solved by
declare(z,complex).
But alas, Maxima's solve command knows nothing about "conjugate", so this
doesn't help with the original problem.
The easiest way to solve it is to explicitly solve for the real and
imaginary parts:
z:a+%i*b$
conjugate(z)-3*%i*z-3+6*%i => -3*%i*(%i*b+a)-%i*b+a+6*%i-3
[realpart(%),imagpart(%)] => [3*b+a-3,-b-3*a+6]
solve(%,[a,b]) => [[a = 15/8,b = 3/8]]
subst(%[1],z) => 3*%i/8+15/8
---- quote ----
Another workaround is proposed in a followup message:
https://www.ma.utexas.edu/pipermail/maxima/2008/011313.html
It seems to me that some kind of error checking (or even a workaround) could be
implemented in Sage.
Regards,
Gilles
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