Algorithms in Real Algebraic Geometry by Saugata Basu
Book Contents :-
1. Introduction
2. Quantifier elimination and related problems
3. Computing topological invariants of semi-algebraic sets
4. Sums of squares and semi-definite programming
5. Open problems
About this book :-
"Algorithms in Real Algebraic Geometry" by Saugata Basu, Richard Pollack, and Marie-Françoise Roy is a foundational book that explains how to solve mathematical problems involving real polynomial equations using "algorithms", "real algebraic geometry", and "computational methods". The text focuses on turning deep mathematical theory into practical procedures that can be implemented and analyzed.
The book introduces essential concepts such as "semi-algebraic sets", decision problems, and complexity bounds. It explains how algorithms can determine properties like connectivity, feasibility, and topology of solution sets defined by polynomial inequalities. Topics such as quantifier elimination, cylindrical algebraic decomposition, and roadmap algorithms are presented with clarity and logical structure, making advanced ideas more accessible.
Designed mainly for graduate students and researchers, the book balances rigor with usability. It is widely used in "computer science", "mathematics", and "computational geometry", especially for those working on symbolic computation or algorithm design. With clear proofs, structured algorithms, and strong theoretical foundations, the book remains a key reference for understanding how "algorithms", "polynomials", "topology", "complexity", and "real geometry" interact in modern mathematical research.
Book Detail :-
Title:
Algorithms in Real Algebraic Geometry by Saugata Basu
Publisher:
Springer
Year:
2016
Pages:
706
Type:
PDF
Language:
English
ISBN-10 #:
3540330984
ISBN-13 #:
978-3540330981
License:
External Educational Resource
Amazon:
Amazon
About Author :-
The author
Saugata Basu
are internationally respected scholars in "real algebraic geometry", "algorithm design", and "computational mathematics". Their research focuses on developing efficient methods to solve problems involving real polynomial equations and geometric structures. Together, they combine deep expertise in "algorithms", "semi-algebraic geometry", "computational complexity", "symbolic computation", and "topology". Their collaborative work has strongly influenced both mathematical theory and computer science, making them leading authorities in algorithmic real algebraic geometry.
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