Sympy nsolve function and multiple solutions
math, python, solver, sympy
Solution
The first call of solve gave me two solutions of the corresponding function. But not the second one. I wonder why?
In general, you cannot solve an equation symbolically and apparently `solve` does exactly that. In other words: Consider yourself lucky if `solve` can solve your equation, the typical technical applications don't have analytic solutions, that is, cannot be solved symbolically.
So the fall-back option is to solve the equation numerically, which starts from an initial point. In the general case, there is no guarantee that `nsolve` will find a solution even if exists one.
Is there a way to get the list all numerical solutions with nsolve or with another function, in just one line?
In general, no. Nevertheless, you can start `nsolve` from a number of initial guesses and keep track of the solutions found. You might want to distribute your initial guesses uniformly in the interval of interest. This is called multi-start method.
Problem
I did this little test program in python to see how `solve` and `nsolve` work. ``` from sympy import * theta = Symbol('theta') phi = Symbol('phi') def F(theta,phi): return sin(theta)*cos(phi)+cos(phi)**2 def G(phi): return ((1 + sqrt(3))*sin(phi) - 4*pi*sin(2*phi)*cos(2*phi)) solution1 = solve(F(pi/2,phi),phi) solution2 = solve(G(phi),phi) solution3 = nsolve(G(phi),0) solution4 = nsolve(G(phi),1) solution5 = nsolve(G(phi),2) solution6 = nsolve(G(phi),3) print solution1, solution2, solution3, solution4, solution5, solution6 ``` And I get this output: ``` [pi/2, pi] [] 0.0 -0.713274788952698 2.27148961717279 3.14159265358979 ``` The first call of solve gave me two solutions of the corresponding function. But not the second one. I wonder why? `nsolve` seems to work with an initial test value, but depending on that value, it gives different numerical solutions. Is there a way to get the list all numerical solutions with `nsolve` or with another function, in just one line?