A Verified Implementation of Algebraic Numbers in Isabelle/HOL
We formalize algebraic numbers in Isabelle/HOL. Our development serves as a verified implementation of algebraic operations on real and complex numbers. We moreover provide algorithms that can identify all the real or complex roots of rational polynomials, and two implementations to display algebrai...
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| Veröffentlicht in: | Journal of automated reasoning 2020-03, Vol.64 (3), p.363-389 |
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| container_end_page | 389 |
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| container_issue | 3 |
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| container_title | Journal of automated reasoning |
| container_volume | 64 |
| creator | Joosten, Sebastiaan J. C. Thiemann, René Yamada, Akihisa |
| description | We formalize algebraic numbers in Isabelle/HOL. Our development serves as a verified implementation of algebraic operations on real and complex numbers. We moreover provide algorithms that can identify all the real or complex roots of rational polynomials, and two implementations to display algebraic numbers, an approximative version and an injective precise one. We obtain verified Haskell code for these operations via Isabelle’s code generator. The development combines various existing formalizations such as matrices, Sturm’s theorem, and polynomial factorization, and it includes new formalizations about bivariate polynomials, unique factorization domains, resultants and subresultants. |
| doi_str_mv | 10.1007/s10817-018-09504-w |
| format | Article |
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| ispartof | Journal of automated reasoning, 2020-03, Vol.64 (3), p.363-389 |
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| language | eng |
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| subjects | Algebra Algorithms Artificial Intelligence Bivariate analysis Complex numbers Computer Science Factorization Mathematical Logic and Formal Languages Mathematical Logic and Foundations Polynomials Resultants Symbolic and Algebraic Manipulation |
| title | A Verified Implementation of Algebraic Numbers in Isabelle/HOL |
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