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Ordered Semiautomatic Rings with Applications to Geometry
The present work looks at semiautomatic rings with automatic addition and comparisons which are dense subrings of the real numbers and asks how these can be used to represent geometric objects such that certain operations and transformations are automatic. The underlying ring has always to be a coun...
Autores principales: | , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7206621/ http://dx.doi.org/10.1007/978-3-030-40608-0_9 |
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author | Gao, Ziyuan Jain, Sanjay Qi, Ji Schlicht, Philipp Stephan, Frank Tarr, Jacob |
author_facet | Gao, Ziyuan Jain, Sanjay Qi, Ji Schlicht, Philipp Stephan, Frank Tarr, Jacob |
author_sort | Gao, Ziyuan |
collection | PubMed |
description | The present work looks at semiautomatic rings with automatic addition and comparisons which are dense subrings of the real numbers and asks how these can be used to represent geometric objects such that certain operations and transformations are automatic. The underlying ring has always to be a countable dense subring of the real numbers and additions and comparisons and multiplications with constants need to be automatic. It is shown that the ring can be selected such that equilateral triangles can be represented and rotations by [Formula: see text] are possible, while the standard representation of the b-adic rationals does not allow this. |
format | Online Article Text |
id | pubmed-7206621 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
record_format | MEDLINE/PubMed |
spelling | pubmed-72066212020-05-08 Ordered Semiautomatic Rings with Applications to Geometry Gao, Ziyuan Jain, Sanjay Qi, Ji Schlicht, Philipp Stephan, Frank Tarr, Jacob Language and Automata Theory and Applications Article The present work looks at semiautomatic rings with automatic addition and comparisons which are dense subrings of the real numbers and asks how these can be used to represent geometric objects such that certain operations and transformations are automatic. The underlying ring has always to be a countable dense subring of the real numbers and additions and comparisons and multiplications with constants need to be automatic. It is shown that the ring can be selected such that equilateral triangles can be represented and rotations by [Formula: see text] are possible, while the standard representation of the b-adic rationals does not allow this. 2020-01-07 /pmc/articles/PMC7206621/ http://dx.doi.org/10.1007/978-3-030-40608-0_9 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
spellingShingle | Article Gao, Ziyuan Jain, Sanjay Qi, Ji Schlicht, Philipp Stephan, Frank Tarr, Jacob Ordered Semiautomatic Rings with Applications to Geometry |
title | Ordered Semiautomatic Rings with Applications to Geometry |
title_full | Ordered Semiautomatic Rings with Applications to Geometry |
title_fullStr | Ordered Semiautomatic Rings with Applications to Geometry |
title_full_unstemmed | Ordered Semiautomatic Rings with Applications to Geometry |
title_short | Ordered Semiautomatic Rings with Applications to Geometry |
title_sort | ordered semiautomatic rings with applications to geometry |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7206621/ http://dx.doi.org/10.1007/978-3-030-40608-0_9 |
work_keys_str_mv | AT gaoziyuan orderedsemiautomaticringswithapplicationstogeometry AT jainsanjay orderedsemiautomaticringswithapplicationstogeometry AT qiji orderedsemiautomaticringswithapplicationstogeometry AT schlichtphilipp orderedsemiautomaticringswithapplicationstogeometry AT stephanfrank orderedsemiautomaticringswithapplicationstogeometry AT tarrjacob orderedsemiautomaticringswithapplicationstogeometry |