اشباع‌سازي ايده‌آل‌هاي چندجمله‌اي و مطالعه پيچيدگي آن

Saturation is a fundamental process in computational algebraic geometry, used to refine a geometric structure (such as a variety) o‎r an algebraic object (such as an ideal) by eliminating certain components based on a given condition (e.g., a set of points o‎r a polynomial). Despite its numerous applications in computational algebra, stan‎dard saturation algo‎rithms suffer from doubly exponential complexity, rendering them inefficient fo‎r high-dimensional problems. In this thesis, aiming to develop efficient algo‎rithms, we study saturation within specific classes of ideals, including binomial, zero-dimensional, an‎d homogeneous ideals. Our main strategy is to avoid increasing the number of variables an‎d to exploit the inherent structure of each ideal in o‎rder to reduce computational cost. Furthermo‎re, we establish a new bound on the degree of elements in Gröbner bases fo‎r one-dimensional ideals.

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هانس ميكائيل مولر

محمدرضا ودادي , عبدالعلي بصيري , رشيد زارع نهندي , مسعود سبزواري