When the system is real (or rational) polynomial system, this function executes the gamma test based on the value computed by computeConstants, and determine whether a given point is a real approximate solution or not.
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 : p = point{{.954379,.318431,-.298633,.947949}}; |
i4 : certifyRealSoln(f,p) o4 = true |
However, an input point is poorly approximated, it gives false even if the point is real. In this case, user should apply newtonOper to the point to get more precise approximation.
i5 : p = point{{.65,.77,.75,-.64}}; -- poorly approximated solution |
i6 : certifyRealSoln(f,p) o6 = false |
The object certifyRealSoln is a method function.