Computing In Algebraic Geometry: Where Algebra Meets Computation

The intersection of algebra and geometry, known as algebraic geometry, offers a rich and intricate tapestry of mathematical concepts that have captivated scholars for centuries. In recent times, the advent of high-performance computing has revolutionized the way we approach algebraic geometry, opening up new avenues for exploration and discovery.

The book 'Computing In Algebraic Geometry' serves as an indispensable guide to this exciting frontier, providing a comprehensive exploration of the computational techniques and algorithms that have transformed the field. Written by a team of experts in the area, this book is an essential resource for students, researchers, and practitioners seeking to delve into the computational realm of algebraic geometry.

Computing in Algebraic Geometry: A Quick Start using SINGULAR (Algorithms and Computation in Mathematics Book 16)

5 out of 5

Language	:	English
File size	:	3954 KB
Text-to-Speech	:	Enabled
Print length	:	344 pages

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Delving into the Computational Landscape

'Computing In Algebraic Geometry' takes readers on a journey through the intricate landscape of computational algebraic geometry. Beginning with an to the fundamental concepts and algorithms, the book gradually delves deeper into the complexities of the subject.

Key topics covered in the book include:

• Algebraic Varieties: Delving into the representation and manipulation of algebraic varieties, the building blocks of algebraic geometry.
• Algorithms for Computations: Exploring a range of algorithms used for computing intersections, projections, and other geometric operations.
• Computational Complexity: Analyzing the computational complexity of algebraic geometry algorithms, providing insights into their efficiency.
• Geometric Modeling: Harnessing computational techniques to create geometric models, enabling the visualization and analysis of complex shapes.
• Computer Graphics: Utilizing computational algebraic geometry to generate realistic graphics, opening up possibilities in fields such as animation and virtual reality.

Applications in Diverse Fields

Beyond its theoretical underpinnings, 'Computing In Algebraic Geometry' also highlights the practical applications of computational algebraic geometry across a wide range of fields:

• Cryptography: Utilizing algebraic geometry techniques to develop novel cryptographic algorithms for secure communication.
• Robotics: Employing computational algebraic geometry for motion planning and control of robotic systems.
• Medicine: Applying algebraic geometry to model biological processes and advance medical research.
• Finance: Utilizing computational algebraic geometry to analyze financial data and develop risk management strategies.

A Resource for the Computational Age

'Computing In Algebraic Geometry' stands as an invaluable resource for anyone seeking to navigate the computational realm of algebraic geometry. With its clear explanations, detailed examples, and extensive references, the book empowers readers to:

• Understand the fundamental concepts and algorithms of computational algebraic geometry.
• Apply computational techniques to solve complex geometric problems.
• Explore the computational complexity of algebraic geometry algorithms.
• Harness computational algebraic geometry for practical applications in diverse fields.

, 'Computing In Algebraic Geometry' is a tour de force in computational algebraic geometry. Providing a comprehensive guide to the computational techniques and algorithms used in the field, the book unlocks a world of possibilities for students, researchers, and practitioners seeking to explore the intersection of algebra, geometry, and computation. With its clear explanations, in-depth examples, and extensive references, 'Computing In Algebraic Geometry' serves as an indispensable resource for anyone venturing into the computational realm of algebraic geometry.

Computing in Algebraic Geometry: A Quick Start using SINGULAR (Algorithms and Computation in Mathematics Book 16)

5 out of 5

Language	:	English
File size	:	3954 KB
Text-to-Speech	:	Enabled
Print length	:	344 pages

FREE