Polyhedral Homotopy Continuation Method for solving sparse polynomial system, optimized by only tracing real zeros
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#pragma once
#include <complex>
#include <random>
using dbl = std::complex<double>;
using dbl_complex = std::complex<double>;
inline std::complex<double> operator*(unsigned i, std::complex<double> z)
{
z *= i;
return z;
}
inline bool isnan(std::complex<double> const& z)
{
using std::isnan;
return isnan(z.real()) || isnan(z.imag());
}
inline double rand_real()
{
static std::default_random_engine generator;
static std::uniform_real_distribution<double> distribution(-1.0, 1.0);
return distribution(generator);
}
inline dbl pow(const dbl& z, int power)
{
if (power < 0) {
return pow(1. / z, -power);
} else if (power == 0)
return dbl(1, 0);
else if (power == 1)
return z;
else if (power == 2)
return z * z;
else if (power == 3)
return z * z * z;
else {
unsigned int p(power);
dbl result(1, 0), z_to_the_current_power_of_two = z;
// fast powering algorithm
do {
if ((p & 1) == 1) result *= z_to_the_current_power_of_two;
z_to_the_current_power_of_two *= z_to_the_current_power_of_two;
} while (p >>= 1);
return result;
}
}