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mathsymbolic-mathmaxima

How to constrain solutions to be real-valued in Maxima CAS?

I have found myself needing to solve complex-valued equations for two real-valued variables. In Mathematica, this is achievable using the Assuming command as follows:

Mathematica goal

I am interested to see if it is possible to use FOSS tools to achieve the same result. However, in Maxima, I have not found a way to constrain a and b to be purely real. It returns a complex-valued solution with one degree of freedom.

(%i22) solve(%e^(%i*%pi/4) = a*(%i*b+1), [a,b]);
                                  %i + 1
(%o22)             [[a = ------------------------, b = %r4]]
                         sqrt(2) %i %r4 + sqrt(2)

Even using declare(a, real) and declare(b, real) before running solve, it gives the same result. I have also tried to add constraints within the system of equations, but that doesn't work either:

(%i9) solve([x^3=1, imagpart(x)=0], x);
                           sqrt(3) %i - 1          sqrt(3) %i + 1
(%o9)       [[x = 1], [x = --------------], [x = - --------------]]
                                 2                       2

Is solving an equation like this possible in Maxima or any other FOSS CAS?

Solution

  • That's an interesting question. I asked Maxima guys using mailing list (yeah, it's still functioning) and they told me that solve ignores declares and this seems to be the easiest solution:

    %e^(%i*%pi/4) = a*(%i*b+1)$
solve([realpart(%),imagpart(%)],[a,b]);