Polynomial Complexity Recognizing a Tropical Linear Variety
نویسنده
چکیده
A polynomial complexity algorithm is designed which tests whether a point belongs to a given tropical linear variety.
منابع مشابه
Complexity of tropical Schur polynomials
We study the complexity of computation of a tropical Schur polynomial Tsλ where λ is a partition, and of a tropical polynomial Tmλ obtained by the tropicalization of the monomial symmetric function mλ. Then Tsλ and Tmλ coincide as tropical functions (so, as convex piece-wise linear functions), while differ as tropical polynomials. We prove the following bounds on the complexity of computing ove...
متن کاملTropical differential equations
Tropical differential equations are introduced and an algorithm is designed which tests solvability of a system of tropical linear differential equations within the complexity polynomial in the size of the system and in its coefficients. Moreover, we show that there exists a minimal solution, and the algorithm constructs it (in case of solvability). This extends a similar complexity bound estab...
متن کاملThe tropical Grassmannian
In tropical algebraic geometry, the solution sets of polynomial equations are piecewise-linear. We introduce the tropical variety of a polynomial ideal, and we identify it with a polyhedral subcomplex of the Gröbner fan. The tropical Grassmannian arises in this manner from the ideal of quadratic Plücker relations. It is shown to parametrize all tropical linear spaces. Lines in tropical projecti...
متن کاملTropical Varieties for Exponential Sums and Their Distance to Amoebae
Abstract. Given any n-variate exponential sum, g, the real part of the complex zero set of g forms a sub-analytic variety R(Z(g)) generalizing the amoeba of a complex polynomial. We extend the notion of Archimedean tropical hypersurface to derive a piecewise linear approximation, Trop(g), of R(Z(g)), with explicit bounds — solely as a function of n, the number of terms, and the minimal distance...
متن کاملIdempotent and tropical mathematics. Complexity of algorithms and interval analysis
A very brief introduction to tropical and idempotent mathematics is presented. Tropical mathematics can be treated as a result of a dequantization of the traditional mathematics as the Planck constant tends to zero taking imaginary values. In the framework of idempotent mathematics usually constructions and algorithms are more simple with respect to their traditional analogs. We especially exam...
متن کامل