1.1. TROPICAL HYPERSURFACES 5 x1 1 (1, 1) x2 Figure 2. 1 ⊕ (0 x1) ⊕ (0 x2) 5 + 2x2 (−1, −1) 5 + 2x1 (−5, −1) x1 (0, 0) 0 x2 (−1, −5) 1 + x1 + x2 Figure 3. 0 ⊕ (0 x1) ⊕ (0 x2) ⊕ (1 x1 x2) ⊕ (5 x1 x1) ⊕ (5 x2 x2) 9 + 2x1 3 + x1 + x2 (−9, −3) (−5, −3) x1 (0, 0) 0 x2 1 + 2x2 (−1, −1) Figure 4. 0 ⊕ (0 x1) ⊕ (0 x2) ⊕ (3 x1 x2) ⊕ (9 x1 x1) ⊕ (1 x2 x2) we consider the Newton polytope of S, ΔS := Conv(S) ⊆ NR,

Purchased from American Mathematical Society for the exclusive use of nofirst nolast (email unknown) Copyright 2011 American Mathematical Society. Duplication prohibited. Please report unauthorized use to cust-serv@ams.org. Thank You! Your purchase supports the AMS' mission, programs, and services for the mathematical community.