solveRationalSystem -- approximates solutions to a rational system of equations

Synopsis

• Usage:

  solveRationalSystem (f)

• Inputs:
  • f, a list, a system of rational equations with a finite number of solutions
• Optional inputs:
  • Verbose => ..., default value false, option to specify whether additional output is wanted
• Outputs:
  • a list, containing the solutions of f, each of type Point
• Consequences:

  • converts the rational system into a Laurent system, invokes the commands 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 the output of phc in a temporary file,
  • parses and outputs the solutions.

Description

i1 : R = QQ[x,y,z];

i2 : system = {y-x^2, z-x^3, (x+y+z-1)/x};

i3 : sols = solveRationalSystem(system)

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

i4 : peek first sols

o4 = Point{ConditionNumber => 4.87567                }
           Coordinates => {.543689, .295598, .160713}
           LastT => 1
           SolutionStatus => Regular

See also

• solveSystem -- a numerical blackbox solver
• toLaurentPolynomial -- converts a list of rational polynomials into Laurent polynomials