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PHCpack :: solveRationalSystem

solveRationalSystem -- approximates solutions to a rational system of equations

Synopsis

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 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

See also

Ways to use solveRationalSystem :