منابع مشابه
Beyond Polyhedral Homotopies
We present a new algorithmic framework which utilizes tropical geometry and homotopy continuation for solving systems of polynomial equations where some of the polynomials are generic elements in linear subspaces of the polynomial ring. This approach generalizes the polyhedral homotopies by Huber and Sturmfels.
متن کاملConstructing Polyhedral Homotopies on Grid-of-Clusters
Polyhedral homotopy continuation is a promising approach to solving large-scale polynomial systems. However, the method faces a computational bottleneck in constructing the homotopy functions because we need to find all mixed cells for polynomial systems. The search for mixed cells can be formulated as a vertex enumeration problem for polyhedra. Among the search methods for solving the problem ...
متن کاملFinding All Mixed Cells for Polyhedral Homotopies
Acknowledgment I would like to express my sincerely gratitude to my adviser Prof. Masakazu Kojima. He introduced me to homotopy methods for solving a polynomial system and in addition, provided a great research environment. A lot of his advice encouraged me to continue to study. I am very thankful for his warm encouragement. I am largely indebted to Dr. Akiko Takeda for valuable suggestions and...
متن کاملAlgebraic Properties of Homotopies
The scheme ExFunc3CondD deals with a non empty set A, three unary functors F , G, and H yielding sets, and three unary predicates P, Q, R, and states that: There exists a function f such that dom f = A and for every element c of A holds if P[c], then f(c) = F(c) and if Q[c], then f(c) = G(c) and if R[c], then f(c) = H(c) provided the parameters meet the following conditions: • For every element...
متن کاملSimulations as Homotopies
We exhibit a model structure on 2-Cat, obtained by transfer from sSet across the adjunction C2 ◦ Sd a Ex ◦ N2. A certain class of homotopies in this model structure turns out to be in 1-to-1 correspondence with strong simulations among labeled transitions systems, formalising the geometric intuition of simulations as deformations. The correspondence still holds in the cubical setting, character...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 2019
ISSN: 0747-7171
DOI: 10.1016/j.jsc.2018.06.019