Converts the rational system into a Laurent system, invokes the command phc -b and phc -z
Adds slack variables if needed (i.e. if system is overdetermined)
Writes the system to temporary file
Launches the blackbox solver
Stores output of phc in temporary file
Parses and outputs the solutions.
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) The system is not binomial! o3 = {{.543689, .295598, .160713}, {-.771845-1.11514*ii, -.647799+1.72143*ii, ------------------------------------------------------------------------ 2.41964-.606291*ii}, {-.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 => 4.87567 } Coordinates => {.543689, .295598, .160713} LastT => 1 SolutionStatus => Regular |