TL;DR
This paper proves constructively that every rational semifan in a finite-dimensional real vector space can be extended to a complete rational semifan using polyhedral geometry techniques.
Contribution
It provides a constructive proof that extends rational semifans to complete ones, advancing the understanding of fan completions in polyhedral geometry.
Findings
Every rational semifan can be extended to a complete rational semifan.
The proof uses techniques from polyhedral geometry.
The result applies to finite-dimensional real vector spaces with rational structures.
Abstract
In a finite-dimensional real vector space furnished with a rational structure with respect to a subfield of the field of real numbers, every (simplicial) rational semifan is contained in a complete (simplicial) rational semifan. In this paper this result is proved constructively on use of techniques from polyhedral geometry.
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