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

- Usage:
    `alpha = certifyRegularSolution(PS, P)`
- Inputs:
  - PS, a polynomial system,
  - P, a point,

## Description

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

    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};

Input can be a AbstractPoint or Matrix representing coordinates or a list of points or matrices.

    i3 : p1 = point{{.95,.32,-.30,.95}};

    i4 : certifyRegularSolution(f,p1)

    o4 = true

## Ways to use certifyRegularSolution:

- `certifyRegularSolution(PolySystem,AbstractPoint)`
- `certifyRegularSolution(PolySystem,Matrix)`

## For the programmer

The object certifyRegularSolution is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NumericalCertification/Documents/DocNumericalCertification.m2:245:0.