Forcing Symbolic Variables to Always be Real
I am having a problem, I am trying to do algebra with a function of multiple variables, but Sage is assuming the variables could be complex numbers, which I do not want to do. I have a minimal working example that shows the problem. I am using the method discussed at this Google thread on the issue. I actually want to use the commented out equation, but I can't even get the behaviour right for a purely real (at least conceptually) function.
R, r, L, omega, k, s = var('R r L omega k s') assume(R, 'real') assume(r, 'real') assume(L, 'real') assume(omega, 'real') assume(k, 'real') assume(s, 'real') R.conjugate().simplify() r.conjugate().simplify() L.conjugate().simplify() omega.conjugate().simplify() k.conjugate().simplify() s.conjugate().simplify() #Z(R,r,L,k,omega,s) = R + I * omega * L + ((s * omega**2 * L**2 * k**2) * (r - I * omega * L)) / (r**2 + omega**2 * s **2 * L**2) Z(s,L) = s * L show(Z.diff(s)) Z show(Z) (s, L) |--> L*s (s, L) |--> -(imag_part(L)*D(imag_part)(s) - real_part(L)*D(real_part)(s))/abs(L*s) + (imag_part(L)*imag_part(s) - real_part(L)*real_part(s))*L/(abs(L*s)*conjugate(L)*conjugate(s))
The derivative of the argument of
s*L with respect to
s should be zero by definition, since both
L are purely real variables. Why is Sage assuming the following two things: that real variables all of a sudden become complex, and that
L are related to each other. I want them to be real independent real variables. Always. How do I 'enforce' this?