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Formalization of complex analysis and matrix theory

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 spa...

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Detalles Bibliográficos
Autores principales: Shi, Zhiping, Guan, Yong, Li, Ximeng
Lenguaje:eng
Publicado: Springer 2020
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-981-15-7261-6
http://cds.cern.ch/record/2729462
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author Shi, Zhiping
Guan, Yong
Li, Ximeng
author_facet Shi, Zhiping
Guan, Yong
Li, Ximeng
author_sort Shi, Zhiping
collection CERN
description 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.
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institution Organización Europea para la Investigación Nuclear
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publishDate 2020
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spelling cern-27294622021-04-21T18:05:11Zdoi:10.1007/978-981-15-7261-6http://cds.cern.ch/record/2729462engShi, ZhipingGuan, YongLi, XimengFormalization of complex analysis and matrix theoryMathematical Physics and MathematicsThis 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.Springeroai:cds.cern.ch:27294622020
spellingShingle Mathematical Physics and Mathematics
Shi, Zhiping
Guan, Yong
Li, Ximeng
Formalization of complex analysis and matrix theory
title Formalization of complex analysis and matrix theory
title_full Formalization of complex analysis and matrix theory
title_fullStr Formalization of complex analysis and matrix theory
title_full_unstemmed Formalization of complex analysis and matrix theory
title_short Formalization of complex analysis and matrix theory
title_sort formalization of complex analysis and matrix theory
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-981-15-7261-6
http://cds.cern.ch/record/2729462
work_keys_str_mv AT shizhiping formalizationofcomplexanalysisandmatrixtheory
AT guanyong formalizationofcomplexanalysisandmatrixtheory
AT liximeng formalizationofcomplexanalysisandmatrixtheory