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};
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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}};
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i7 : p5 = point{{.31, .30, .72, -.60}}; -- poorly approximated solution
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i8 : P = {p1, p2, p3, p4, p5}
o8 = {p1, p2, p3, p4, p5}
o8 : List
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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
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The object certifyCount is a method function.