11. Each node of this diagram represents a simple root . 12. Thus ? 1 is the unique noncompact simple root and the other simple roots are compact. 13. Thus ? 1 is the unique noncompact simple root and the other simple roots are compact. 14. Given a root system, select a set ? of simple roots as in the preceding section. 15. Let moreover be a choice of simple roots . 16. You wouldn't know it from the elaborate meat-and-shellfish dish in Spanish restaurants, but paella has simple roots . 17. This method provides quadratic convergence for simple roots at the cost of two polynomial evaluations per step. 18. A line joining two simple roots indicates that they are at an angle of 120?to each other. 19. The simple roots are used, as all the other roots can be obtained as linear combinations of these. 20. Consequently, the Dynkin diagram is independent of the choice of simple roots ; it is determined by the root system itself.
