certifyRealSolution -- determine whether a given point is an real approximate solution to the system

Synopsis

Usage:

certifyRealSolution(PS, P)
Inputs:
- PS, a polynomial system,
- P, a point,

Description

When the system is real (or rational) polynomial system, this function executes the gamma test based on the value computed by computeConstants, and determine whether a given point is a real approximate solution or not.

i1 : R = RR[x1,x2,y1,y2];

i2 : f = polySystem {3*y1 + 2*y2 -1, 3*x1 + 2*x2 -3.5,x1^2 + y1^2 -1, x2^2 + y2^2 - 1};

i3 : p = point{{.954379,.318431,-.298633,.947949}};

i4 : certifyRealSolution(f,p)

o4 = true

However, an input point is poorly approximated, it gives false even if the point is real. In this case, user should apply newton to the point to get more precise approximation.

i5 : p = point{{.65,.77,.75,-.64}};  -- poorly approximated solution

i6 : certifyRealSolution(f,p)

o6 = false

Ways to use certifyRealSolution :

certifyRealSolution(PolySystem,AbstractPoint)
certifyRealSolution(PolySystem,Matrix)

For the programmer

The object certifyRealSolution is a method function.