# certifyCount -- executes alpha-certification on a given system and list of points

## Synopsis

• Usage:
(D, R, CS, C) = certifyCount(PS, P)
• Inputs:
• PS, ,
• P, ,
• Outputs:
• D, a list, a list of certified distinct solutions
• R, a list, a list of certified real solutions
• CS, a list, a list of certified solutions
• C, a list, a list of constants for certified solutions

## Description

When the system solved by solver has lots of points, this function does all procedures of certifySolution, certifyDistinctSoln and certifyRealSoln at once.

 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 : p1 = point{{.954379,.318431,-.298633,.947949}}; p2 = point{{.95, .32, -.30, .95}}; p3 = point{{.652567, .77115, .757776, -.636663}}; p4 = point{{.65, .77, .76, -.64}}; i7 : p5 = point{{.31, .30, .72, -.60}}; -- poorly approximated solution i8 : P = {p1, p2, p3, p4, p5} o8 = {p1, p2, p3, p4, p5} o8 : List i9 : certifyCount(f,P) o9 = HashTable{certifiedDistinct => {p1, p3} } certifiedReal => {p1, p3} certifiedSolutions => {p1, p2, p3, p4} constants => {(.000187221, .0000195696, 9.56696), (.0505356, .00526407, 9.60011), (.000475856, .0000611448, 7.78244), (.0382327, .00492679, 7.76016)} o9 : HashTable

## Ways to use certifyCount :

• "certifyCount(PolySystem,List)"

## For the programmer

The object certifyCount is .