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

## Synopsis

• Usage:
certifyDistinctSoln(PS, P)
• Inputs:
• PS, ,
• P, ,

## 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 = QQ[x1,x2,y1,y2]; i2 : f = polySystem {3*y1 + 2*y2 -1, 3*x1 + 2*x2 -7/2,x1^2 + y1^2 -1, x2^2 + y2^2 - 1}; i3 : p = point{{.954379,.318431,-.298633,.947949}}; i4 : certifyRealSoln(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 newtonOper to the point to get more precise approximation.

 i5 : p = point{{.65,.77,.75,-.64}}; -- poorly approximated solution i6 : certifyRealSoln(f,p) o6 = false

## Ways to use certifyRealSoln :

• "certifyRealSoln(PolySystem,Point)"

## For the programmer

The object certifyRealSoln is .