This function returns numerical approximations of all complex solutions of a rational system. The function converts the system to a Laurent polynomial system and then calls PHCpack’s blackbox solver.
i1 : R = QQ[x,y,z]; |
i2 : system = {y-x^2, z-x^3, (x+y+z-1)/x}; |
i3 : sols = solveRationalSystem(system) using temporary files /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44753-0/0PHCinput and /var/folders/40/dy88l5qd361391m_3v2m51bm0000gn/T/M2-44753-0/0PHCoutput o3 = {{-.771845+1.11514*ii, -.647799-1.72143*ii, 2.41964+.606291*ii}, ------------------------------------------------------------------------ {.543689, .295598, .160713}, {-.771845-1.11514*ii, -.647799+1.72143*ii, ------------------------------------------------------------------------ 2.41964-.606291*ii}} o3 : List |
The solutions are of type Point. Each Point comes with diagnostics. For example, LastT is the end value of the continuation parameter; if it equals 1, then the solver reached the end of the path properly.
i4 : peek first sols o4 = Point{ConditionNumber => 33.5121 } Coordinates => {-.771845+1.11514*ii, -.647799-1.72143*ii, 2.41964+.606291*ii} LastT => 1 SolutionStatus => Regular |