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Primitive Recursive Ordered Fields and Some Applications. / Selivanov, Victor; Selivanova, Svetlana.

Proceedings of Computer Algebra in Scientific Computing (CASC 2021). . Springer Nature, 2021. p. 353-369 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12865).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Harvard

Selivanov, V & Selivanova, S 2021, Primitive Recursive Ordered Fields and Some Applications. in Proceedings of Computer Algebra in Scientific Computing (CASC 2021). . Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12865, Springer Nature, pp. 353-369, Computer algebra in scientific computing-2021, 13/09/21. https://doi.org/10.1007/978-3-030-85165-1_20

APA

Selivanov, V., & Selivanova, S. (2021). Primitive Recursive Ordered Fields and Some Applications. In Proceedings of Computer Algebra in Scientific Computing (CASC 2021). (pp. 353-369). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12865). Springer Nature. https://doi.org/10.1007/978-3-030-85165-1_20

Vancouver

Selivanov V, Selivanova S. Primitive Recursive Ordered Fields and Some Applications. In Proceedings of Computer Algebra in Scientific Computing (CASC 2021). . Springer Nature. 2021. p. 353-369. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-030-85165-1_20

Author

Selivanov, Victor ; Selivanova, Svetlana. / Primitive Recursive Ordered Fields and Some Applications. Proceedings of Computer Algebra in Scientific Computing (CASC 2021). . Springer Nature, 2021. pp. 353-369 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

BibTeX

@inproceedings{8ca36f05e8184dcf922badd929fce46d,
title = "Primitive Recursive Ordered Fields and Some Applications",
abstract = "We establish primitive recursive versions of some known facts about computable ordered fields of reals and computable reals and apply them to several problems of algebra and analysis. In particular, we find a primitive recursive analogue of Ershov-Madison{\textquoteright}s theorem about the computable real closure, relate primitive recursive fields of reals to the field of primitive recursive reals, give sufficient conditions for primitive recursive root-finding and for computing solution operators of symmetric hyperbolic systems of partial differential equations.",
keywords = "Ordered field, Polynomial, Primitive recursion, Real closure, Root-finding, Solution operators of PDEs, Splitting",
author = "Victor Selivanov and Svetlana Selivanova",
year = "2021",
doi = "10.1007/978-3-030-85165-1_20",
language = "English",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Nature",
pages = "353--369",
booktitle = "Proceedings of Computer Algebra in Scientific Computing (CASC 2021).",
address = "Germany",
note = "Computer algebra in scientific computing-2021 ; Conference date: 13-09-2021",

}

RIS

TY - GEN

T1 - Primitive Recursive Ordered Fields and Some Applications

AU - Selivanov, Victor

AU - Selivanova, Svetlana

PY - 2021

Y1 - 2021

N2 - We establish primitive recursive versions of some known facts about computable ordered fields of reals and computable reals and apply them to several problems of algebra and analysis. In particular, we find a primitive recursive analogue of Ershov-Madison’s theorem about the computable real closure, relate primitive recursive fields of reals to the field of primitive recursive reals, give sufficient conditions for primitive recursive root-finding and for computing solution operators of symmetric hyperbolic systems of partial differential equations.

AB - We establish primitive recursive versions of some known facts about computable ordered fields of reals and computable reals and apply them to several problems of algebra and analysis. In particular, we find a primitive recursive analogue of Ershov-Madison’s theorem about the computable real closure, relate primitive recursive fields of reals to the field of primitive recursive reals, give sufficient conditions for primitive recursive root-finding and for computing solution operators of symmetric hyperbolic systems of partial differential equations.

KW - Ordered field

KW - Polynomial

KW - Primitive recursion

KW - Real closure

KW - Root-finding

KW - Solution operators of PDEs

KW - Splitting

UR - http://www.scopus.com/inward/record.url?scp=85115164426&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-85165-1_20

DO - 10.1007/978-3-030-85165-1_20

M3 - Conference contribution

AN - SCOPUS:85115164426

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 353

EP - 369

BT - Proceedings of Computer Algebra in Scientific Computing (CASC 2021).

PB - Springer Nature

T2 - Computer algebra in scientific computing-2021

Y2 - 13 September 2021

ER -

ID: 126985168