A2
A
2
This Demonstration shows the real part of the Vieta mapping, which is important in singularity theory. The domain is the plane containing the green hexagon; it has been rotated around the origin to make it horizontal for the purpose of the Demonstration. A point in the plane determines a polynomial +px+q with roots , , . The image of (the tip of the arrow from ) has coordinates . When the "show orbit" checkbox is checked, the orbit of the point under the action of the Coxeter group generated by reflections in the red lines (or symmetries of the blue equilateral triangle) is shown together with the image of all the points in the orbit (the set of all the distinct images of the point under transformations by elements of the group ).
x+y+z=0
P=(α,β,γ)
3
x
α
β
γ
Q
P
P
(p,q)
P
A
2
A
2