Abstract
This thesis presents several contributions designed to improve the practical application of cylindrical algebraic decomposition (CAD) by broadening its range of uses and improving accessibility. CAD is an important algorithm in symbolic computation with a variety of implementations and applications, yet its high computational complexity can be intimidating and means it should be used with care. However, this also means that seemingly small improvements and specialised methods can lead to significant performance improvements.We present various approaches which help push CAD further in terms of reach, understanding, and application, starting with a detailed yet approachable overview. This is followed by demonstrating how a variety of novel tools and methods can be used to reduce the complexity of a problem, and showing how deeper consideration of problem features can make a significant difference. Additionally, we present the first implementation of CAD in Macaulay2, incorporating recent research and presenting CAD to a wider audience in a practical context. Further, we benchmark two contrasting CAD implementations in Maple, identifying scenarios in which one may be favourable. Finally, we introduce a graphing tool for CAD visualisation, with applications in both communication and research.
These contributions offer new ways to improve CAD and its accessibility, making it more approachable, transparent, and comparable for prospective users and researchers alike.
| Date of Award | 2026 |
|---|---|
| Original language | English |
| Awarding Institution |
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| Supervisor | Gregory Sankaran (Supervisor) & James Davenport (Supervisor) |
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