This function applies Newton's method on a given point and given polynomial system.
It converges to an exact solution if a given point is an approximate solution.
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{{.95,.32,-.30,.95}};
|
i4 : newtonOper(f,p)
o4 = {.954379, .318431, -.298633, .947949}
o4 : Point
|
However, if the Jacobian of the system is singular at the point, it just returns the input.
i5 : p = point{{0,.32,0,.95}};
|
i6 : newtonOper(f,p) o6 = p o6 : Point |
The object newtonOper is a method function.