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NumericalCertification :: certifyCount

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

Synopsis

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 :

For the programmer

The object certifyCount is a method function.