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Formalization of a Newton series representation of polynomials

Authors:

Cyril Cohen,

Boris DjalalAuthors Info & Claims

CPP 2016: Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs

Pages 100 - 109

https://doi.org/10.1145/2854065.2854075

Published: 18 January 2016 Publication History

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Abstract

We formalize an algorithm to change the representation of a poly- nomial to a Newton power series. This provides a way to compute efficiently polynomials whose roots are the sums or products of roots of other polynomials, and hence provides a base component of efficient computation for algebraic numbers. In order to achieve this, we formalize a notion of truncated power series and develop an abstract theory of poles of fractions.

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Cited By

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Shishin DHidayat TSultana UShevchenko MJak E(2020) Experimental measurement and thermodynamic model predictions of the distributions of Cu, As, Sb and Sn between liquid lead and PbO–FeO–Fe 2 O 3 –SiO 2 slag International Journal of Materials Research10.3139/146.111942Online publication date: 13-Aug-2020
https://doi.org/10.3139/146.111942
Joosten SThiemann RYamada A(2018)A Verified Implementation of Algebraic Numbers in Isabelle/HOLJournal of Automated Reasoning10.1007/s10817-018-09504-wOnline publication date: 9-Dec-2018
https://doi.org/10.1007/s10817-018-09504-w
Thiemann RYamada A(2016)Algebraic Numbers in Isabelle/HOLInteractive Theorem Proving10.1007/978-3-319-43144-4_24(391-408)Online publication date: 7-Aug-2016
https://doi.org/10.1007/978-3-319-43144-4_24

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Published In

CPP 2016: Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs

January 2016

196 pages

ISBN:9781450341271

DOI:10.1145/2854065

Program Chairs:
Jeremy Avigad
Carnegie Mellon University, USA
,
Adam Chlipala
MIT, USA

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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SIGLOG: ACM Special Interest Group on Logic and Computation

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Association for Computing Machinery

New York, NY, United States

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Published: 18 January 2016

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CPP 2016: Certified Proofs and Programs

January 18 - 19, 2016

FL, St. Petersburg, USA

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Overall Acceptance Rate 18 of 26 submissions, 69%

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Shishin DHidayat TSultana UShevchenko MJak E(2020) Experimental measurement and thermodynamic model predictions of the distributions of Cu, As, Sb and Sn between liquid lead and PbO–FeO–Fe 2 O 3 –SiO 2 slag International Journal of Materials Research10.3139/146.111942Online publication date: 13-Aug-2020
https://doi.org/10.3139/146.111942
Joosten SThiemann RYamada A(2018)A Verified Implementation of Algebraic Numbers in Isabelle/HOLJournal of Automated Reasoning10.1007/s10817-018-09504-wOnline publication date: 9-Dec-2018
https://doi.org/10.1007/s10817-018-09504-w
Thiemann RYamada A(2016)Algebraic Numbers in Isabelle/HOLInteractive Theorem Proving10.1007/978-3-319-43144-4_24(391-408)Online publication date: 7-Aug-2016
https://doi.org/10.1007/978-3-319-43144-4_24

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Recommendations

Finding small degree factors of multivariate supersparse (lacunary) polynomials over algebraic number fields

Interlacing and spacing properties of zeros of polynomials, in particular of orthogonal and Lq-minimal polynomials, q∈[1,∞]

Hahn, Jacobi, and Krawtchouk polynomials of several variables