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