Zero-dimensional tropicalizations in OSCAR
Arman Marti-Shahandeh, Yue Ren, Victoria Schleis
TL;DR
This paper introduces algorithms for computing zero-dimensional tropical varieties within Oscar, addressing practical issues with inexact fields and providing an implementation in Julia.
Contribution
It presents novel algorithms for zero-dimensional tropicalizations and a practical workaround for inexact field computations in existing software.
Findings
Algorithms successfully compute zero-dimensional tropical varieties
Implementation in Julia enhances computational efficiency
Addresses practical issues with inexact polynomial fields
Abstract
We present algorithms for computing zero-dimensional tropical varieties as implemented in OscarZerodimensionalTropicalization.jl. The algorithms include a mathematical workaround for a common practical issue arising when working with polynomials over inexact fields in existing software systems.
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Taxonomy
TopicsPolynomial and algebraic computation · Cryptography and Residue Arithmetic · Numerical Methods and Algorithms