No Cover Image

Journal article 708 views 92 downloads

The Transrational Numbers as an Abstract Data Type

Jan Aldert Bergstra, John Tucker Orcid Logo

Transmathematica, Volume: 2020, Pages: 1 - 29

Swansea University Author: John Tucker Orcid Logo

  • Bergstra & Tucker-Transrational numbers as an ADT.pdf

    PDF | Version of Record

    Released under the terms of a Creative Commons Attribution Share Alike 4.0 license

    Download (325.35KB)

Check full text

DOI (Published version): 10.36285/tm.47

Abstract

In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element, such as an error element also denoted with a new constant symbol, an unsigned infinity or one or both signed infinities, one positive and one negative. W...

Full description

Published in: Transmathematica
ISSN: 2632-9212
Published: Transmathematica 2020
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa56723
first_indexed 2021-04-22T21:52:11Z
last_indexed 2021-09-17T03:19:27Z
id cronfa56723
recordtype SURis
fullrecord <?xml version="1.0"?><rfc1807><datestamp>2021-09-16T11:20:23.7625530</datestamp><bib-version>v2</bib-version><id>56723</id><entry>2021-04-22</entry><title>The Transrational Numbers as an Abstract Data Type</title><swanseaauthors><author><sid>431b3060563ed44cc68c7056ece2f85e</sid><ORCID>0000-0003-4689-8760</ORCID><firstname>John</firstname><surname>Tucker</surname><name>John Tucker</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2021-04-22</date><deptcode>MACS</deptcode><abstract>In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element, such as an error element also denoted with a new constant symbol, an unsigned infinity or one or both signed infinities, one positive and one negative. We define an enlargement of a field to a transfield, in which division is totalised by setting 1/0 equal to the positive infinite value and -1/0 equal to the negative infinite value , and which also contains an error element to help control their effects. We construct the transrational numbers as a transfield of the field of rational numbers and consider it as an abstract data type. We give it an equational specification under initial algebra semantics.</abstract><type>Journal Article</type><journal>Transmathematica</journal><volume>2020</volume><journalNumber/><paginationStart>1</paginationStart><paginationEnd>29</paginationEnd><publisher>Transmathematica</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint/><issnElectronic>2632-9212</issnElectronic><keywords>Fields, Meadows, Rational numbers, Infinity, Errors</keywords><publishedDay>16</publishedDay><publishedMonth>12</publishedMonth><publishedYear>2020</publishedYear><publishedDate>2020-12-16</publishedDate><doi>10.36285/tm.47</doi><url/><notes/><college>COLLEGE NANME</college><department>Mathematics and Computer Science School</department><CollegeCode>COLLEGE CODE</CollegeCode><DepartmentCode>MACS</DepartmentCode><institution>Swansea University</institution><apcterm/><lastEdited>2021-09-16T11:20:23.7625530</lastEdited><Created>2021-04-22T22:42:06.9929862</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Computer Science</level></path><authors><author><firstname>Jan Aldert</firstname><surname>Bergstra</surname><order>1</order></author><author><firstname>John</firstname><surname>Tucker</surname><orcid>0000-0003-4689-8760</orcid><order>2</order></author></authors><documents><document><filename>56723__19739__aebc3bb3387b488fba0e454a691d6dbb.pdf</filename><originalFilename>Bergstra &amp; Tucker-Transrational numbers as an ADT.pdf</originalFilename><uploaded>2021-04-22T22:51:00.4675550</uploaded><type>Output</type><contentLength>333158</contentLength><contentType>application/pdf</contentType><version>Version of Record</version><cronfaStatus>true</cronfaStatus><documentNotes>Released under the terms of a Creative Commons Attribution Share Alike 4.0 license</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language><licence>http://creativecommons.org/licenses/by-sa/4.0</licence></document></documents><OutputDurs/></rfc1807>
spelling 2021-09-16T11:20:23.7625530 v2 56723 2021-04-22 The Transrational Numbers as an Abstract Data Type 431b3060563ed44cc68c7056ece2f85e 0000-0003-4689-8760 John Tucker John Tucker true false 2021-04-22 MACS In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element, such as an error element also denoted with a new constant symbol, an unsigned infinity or one or both signed infinities, one positive and one negative. We define an enlargement of a field to a transfield, in which division is totalised by setting 1/0 equal to the positive infinite value and -1/0 equal to the negative infinite value , and which also contains an error element to help control their effects. We construct the transrational numbers as a transfield of the field of rational numbers and consider it as an abstract data type. We give it an equational specification under initial algebra semantics. Journal Article Transmathematica 2020 1 29 Transmathematica 2632-9212 Fields, Meadows, Rational numbers, Infinity, Errors 16 12 2020 2020-12-16 10.36285/tm.47 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University 2021-09-16T11:20:23.7625530 2021-04-22T22:42:06.9929862 Faculty of Science and Engineering School of Mathematics and Computer Science - Computer Science Jan Aldert Bergstra 1 John Tucker 0000-0003-4689-8760 2 56723__19739__aebc3bb3387b488fba0e454a691d6dbb.pdf Bergstra & Tucker-Transrational numbers as an ADT.pdf 2021-04-22T22:51:00.4675550 Output 333158 application/pdf Version of Record true Released under the terms of a Creative Commons Attribution Share Alike 4.0 license true eng http://creativecommons.org/licenses/by-sa/4.0
title The Transrational Numbers as an Abstract Data Type
spellingShingle The Transrational Numbers as an Abstract Data Type
John Tucker
title_short The Transrational Numbers as an Abstract Data Type
title_full The Transrational Numbers as an Abstract Data Type
title_fullStr The Transrational Numbers as an Abstract Data Type
title_full_unstemmed The Transrational Numbers as an Abstract Data Type
title_sort The Transrational Numbers as an Abstract Data Type
author_id_str_mv 431b3060563ed44cc68c7056ece2f85e
author_id_fullname_str_mv 431b3060563ed44cc68c7056ece2f85e_***_John Tucker
author John Tucker
author2 Jan Aldert Bergstra
John Tucker
format Journal article
container_title Transmathematica
container_volume 2020
container_start_page 1
publishDate 2020
institution Swansea University
issn 2632-9212
doi_str_mv 10.36285/tm.47
publisher Transmathematica
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Computer Science{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Computer Science
document_store_str 1
active_str 0
description In an arithmetical structure one can make division a total function by defining 1/0 to be an element of the structure, or by adding a new element, such as an error element also denoted with a new constant symbol, an unsigned infinity or one or both signed infinities, one positive and one negative. We define an enlargement of a field to a transfield, in which division is totalised by setting 1/0 equal to the positive infinite value and -1/0 equal to the negative infinite value , and which also contains an error element to help control their effects. We construct the transrational numbers as a transfield of the field of rational numbers and consider it as an abstract data type. We give it an equational specification under initial algebra semantics.
published_date 2020-12-16T20:01:22Z
_version_ 1821346400062930944
score 11.04748

Similar Items