Detecting tropical defects of polynomial equations
نویسندگان
چکیده
منابع مشابه
Tropical Scaling of Polynomial Matrices
The eigenvalues of a matrix polynomial can be determined classically by solving a generalized eigenproblem for a linearized matrix pencil, for instance by writing the matrix polynomial in companion form. We introduce a general scaling technique, based on tropical algebra, which applies in particular to this companion form. This scaling, which is inspired by an earlier work of Akian, Bapat, and ...
متن کاملCoupled systems of equations with entire and polynomial functions
We consider the coupled system$F(x,y)=G(x,y)=0$,where$$F(x, y)=bs 0 {m_1} A_k(y)x^{m_1-k}mbox{ and } G(x, y)=bs 0 {m_2} B_k(y)x^{m_2-k}$$with entire functions $A_k(y), B_k(y)$.We derive a priory estimates for the sums of the rootsof the considered system andfor the counting function of roots.
متن کاملCanonical representation for approximating solution of fuzzy polynomial equations
In this paper, the concept of canonical representation is proposed to find fuzzy roots of fuzzy polynomial equations. We transform fuzzy polynomial equations to system of crisp polynomial equations, this transformation is perform by using canonical representation based on three parameters Value, Ambiguity and Fuzziness.
متن کاملEquations of Tropical Varieties
We introduce a scheme-theoretic enrichment of the principal objects of tropical geometry. Using a category of semiring schemes, we construct tropical hypersurfaces as schemes over idempotent semirings such as T = (R∪{−∞},max,+) by writing them as solution sets to explicit systems of tropical equations that are uniquely determined by tropical linear algebra. We then define a tropicalization func...
متن کاملAn Algorithm for Detecting ” Linear ” Solutions of Nonlinear Polynomial Differential Equations
A symbolic computational algorithm which detects ” linear ”‘ solutions of nonlinear polynomial differential equations of single functions, is developed throughout this paper.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2019
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-019-00916-4