Sharif Digital Repository

Tropical algebraic geometry is a fairly new branch in geometry which is called so in honor of Brazilian mathematician Imre Simon who was pioneer of this field.The set equipped with the addition and multiplication is a semifield.Algebraic geometry objects like algebraic varieties can be defined over.Polynomials and rational functions are defined over.The functions that they define are piecewise linear and concave functions and the set of points where they are nonlinear is a tropical variety which is a concave polyhedral. Thus, tropical algebraic geometry is a piecewise linear version of algebraic geometry.Another approach to tropical algebraic geometry comes back to the works of Russian...