# certifySolution -- certify whether a given point is an approximate solution to the system

## Synopsis

• Usage:
(points, constants) = certifySolution(PS, P)
• Inputs:
• Outputs:
• points, a list, a list of certified solutions
• constants, a list, a list of constants for each certified solution

## Description

This function executes the alpha test based on the value computed by computeConstants.

 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};

Input should be a list of Point type objects.

 i3 : p = point{{.95,.32,-.30,.95}}; i4 : certifySolution(f,{p}) o4 = ({p}, {(.0505356, .00526407, 9.60011)}) o4 : Sequence

## Ways to use certifySolution :

• "certifySolution(PolySystem,List)"

## For the programmer

The object certifySolution is .