What good libraries are there for solving a system of non-linear equations in C++?

Question

In a C++ application I\'m coding, I need to solve a system of non-linear equations (N equations, N unknowns).

The systems I\'m solving will be rather sm

Answer 1

Microsoft Z3 https://github.com/Z3Prover/z3/blob/master/examples/c%2B%2B/example.cpp

also consider omnn::math: https://github.com/ohhmm/openmind/blob/master/omnn/math/test/08_System.cpp

Lets say system of equations is like this:

(x-a1)^2 + (y-b1)^2 = c1
(x-a2)^2 + (y-b2)^2 = c2

Then you have couple options:

Valuable a1, a2, b1, b2; // init with values

System sys;
Variable x,y;
sys << (x-a1)^2 + (y-b1)^2 - c1; // addin an equation as an equality to 0
sys << (x-a2)^2 + (y-b2)^2 - c2;

for(auto& solution : sys.Solve(x))
        std::cout << solution;

alternative way is to make single equation (see why):

((x-a1)^2 + (y-b1)^2 - c1)^2 + ((x-a2)^2 + (y-b2)^2 - c2)^2 = 0

Variable x,y;
Valuable a1, a2, b1, b2; // init with values
auto eq = ((x-a1)^2 + (y-b1)^2 - c1)^2 + ((x-a2)^2 + (y-b2)^2 - c2)^2;
eq.SetView(Valuable::View::Equation);  // optional: equation optimizations
// get y function:
auto fn = eq(y);

// show
std::cout << fn << std::endl;

// evaluate
auto evaluate = fn;
evaluate.eval(x, 10);
evaluate.optimize(); // calculate
// show calculated value at x=10:
std::cout << evaluate << std::endl;