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

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)

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 p comes with cached diagnostics. For example, p.cache.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{cache => CacheTable{...3...}              }
           Coordinates => {.543689, .295598, .160713}

Ways to use solveRationalSystem :

solveRationalSystem(List)

For the programmer

The object solveRationalSystem is a method function with options.

solveRationalSystem -- approximates solutions to a rational system of equations

Synopsis

Description

See also

Ways to use solveRationalSystem :

For the programmer