sympy: order of result from solving a quadratic equation

Question

I solved a quadratic equation using sympy:

import sympy as sp
q,qm,k,c0,c,vt,vm = sp.symbols('q qm k c0 c vt vm')
c = ( c0 * vt - q * vm) / vt
eq1 = sp.Eq(qm * k * c / (1 + k * c) ,q)
q_solve = sp.solve(eq1,q)

Based on some testing I figured out that only q_solve[0] makes physical sense. Will sympy always put (b - sqrt(b**2 - 4*a*c))/2a in the first place ? I guess, it might change with an upgrade ?

Answer 1

A simple test to answer your question is to symbolically solve the quadratic equation using sympy per below:

import sympy as sp
a, b, c, x = sp.symbols('a b c x')
solve( a*x**2 + b*x + c, x)

this gives you the result:

[(-b + sqrt(-4*a*c + b**2))/(2*a), -(b + sqrt(-4*a*c + b**2))/(2*a)]

which leads me to believe that in general the order is first the + sqrt() solution and then the - sqrt() solution.

For your program q_solve[0] gives you:

(c0*k*vt + k*qm*vm + vt - sqrt(c0**2*k**2*vt**2 - 2*c0*k**2*qm*vm*vt + 2*c0*k*vt**2 + k**2*qm**2*vm**2 + 2*k*qm*vm*vt + vt**2))/(2*k*vm)

this is still the x= (-b + sqrt(b**2-4*a*c))/(2*a) answer, the negative sign from the b term goes away as a result of the distribution of the signs of the variables within the solution