Formalization of Complex Analysis and Matrix Theory
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Beschreibung
This book discusses the formalization of mathematical theories centering on complex analysis and matrix theory, covering topics such as algebraic systems, complex numbers, gauge integration, the Fourier transformation and its discrete counterpart, matrices and their transformation, inner product spaces, and function matrices. The formalization is performed using the interactive theorem prover HOL4, chiefly developed at the University of Cambridge. Many of the developments presented are now integral parts of the library of this prover.
As mathematical developments continue to gain in complexity, sometimes demanding proofs of enormous sizes, formalization has proven to be invaluable in terms of obtaining real confidence in their correctness. This book provides a basis for the computer-aided verification of engineering systems constructed using the principles of complex analysis and matrix theory, as well as building blocks for the formalization of more involved mathematical theories.This book discusses the formalization of mathematical theories centering on complex analysis and matrix theory, covering topics such as algebraic systems, complex numbers, gauge integration, the Fourier transformation and its discrete counterpart, matrices and their transformation, inner product spaces, and function matrices. The formalization is performed using the interactive theorem prover HOL4, chiefly developed at the University of Cambridge. Many of the developments presented are now integral parts of the library of this prover.
As mathematical developments continue to gain in complexity, sometimes demanding proofs of enormous sizes, formalization has proven to be invaluable in terms of obtaining real confidence in their correctness. This book provides a basis for the computer-aided verification of engineering systems constructed using the principles of complex analysis and matrix theory, as well as building blocks for the formalization of more involved mathematicaltheories.
Describes the computer-assisted formalization of complex analysis and matrix theory Includes both the formalization of theoretical results and the verification of algorithms that are practically used Provides detailed information on related developments in the research community and outlines potential future directions, helping put the technical content into perspective
Autor*in
Zhiping Shi
Themen in »Formalization of Complex Analysis and Matrix Theory«
Formalization of Mathematical Theories Mechanization of Mathematical Theories Formal Verification of Computer Algorithms (Formal Verification) Interactive Theorem Proving Interactive Theorem Provers Higher Order Logic Proof Assistants Formalization of Matrix Theory Formalization of Complex Analysis Fourier Analysis Algebraic Systems Gauge Integration Inner-product Spaces Function Matrices