Reducible cubic CNS polynomials View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2007-11

AUTHORS

Shigeki Akiyama, Horst Brunotte, Attila Pethő

ABSTRACT

The concept of a canonical number system can be regarded as a natural generalization of decimal representations of rational integers to elements of residue class rings of polynomial rings. Generators of canonical number systems are CNS polynomials which are known in the linear and quadratic cases, but whose complete description is still open. In the present note reducible CNS polynomials are treated, and the main result is the characterization of reducible cubic CNS polynomials. More... »

PAGES

177-183

References to SciGraph publications

  • 2006. Notes on CNS Polynomials and Integral Interpolation in MORE SETS, GRAPHS AND NUMBERS
  • 2005-08. Generalized radix representations and dynamical systems. I in ACTA MATHEMATICA HUNGARICA
  • 1981-12. Canonical number systems in algebraic number fields in ACTA MATHEMATICA HUNGARICA
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10998-007-4177-y

    DOI

    http://dx.doi.org/10.1007/s10998-007-4177-y

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1027920730


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Department of Mathematics, Faculty of Science, Niigata University, Ikarashi 2-8050, 950-2181, Niigata, Japan", 
              "id": "http://www.grid.ac/institutes/grid.260975.f", 
              "name": [
                "Department of Mathematics, Faculty of Science, Niigata University, Ikarashi 2-8050, 950-2181, Niigata, Japan"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Akiyama", 
            "givenName": "Shigeki", 
            "id": "sg:person.011153327405.03", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011153327405.03"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Haus-Endt-Strasse 88, D-40593, D\u00fcsseldorf, Germany", 
              "id": "http://www.grid.ac/institutes/None", 
              "name": [
                "Haus-Endt-Strasse 88, D-40593, D\u00fcsseldorf, Germany"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Brunotte", 
            "givenName": "Horst", 
            "id": "sg:person.012747025157.36", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012747025157.36"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Computer Science, University of Debrecen, P.O. Box 12, H-4010, Debrecen, Hungary", 
              "id": "http://www.grid.ac/institutes/grid.7122.6", 
              "name": [
                "Department of Computer Science, University of Debrecen, P.O. Box 12, H-4010, Debrecen, Hungary"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Peth\u0151", 
            "givenName": "Attila", 
            "id": "sg:person.013334020373.46", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013334020373.46"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/bf01895142", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050389700", 
              "https://doi.org/10.1007/bf01895142"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-540-32439-3_13", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049444289", 
              "https://doi.org/10.1007/978-3-540-32439-3_13"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10474-005-0221-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047907570", 
              "https://doi.org/10.1007/s10474-005-0221-z"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2007-11", 
        "datePublishedReg": "2007-11-01", 
        "description": "The concept of a canonical number system can be regarded as a natural generalization of decimal representations of rational integers to elements of residue class rings of polynomial rings. Generators of canonical number systems are CNS polynomials which are known in the linear and quadratic cases, but whose complete description is still open. In the present note reducible CNS polynomials are treated, and the main result is the characterization of reducible cubic CNS polynomials.", 
        "genre": "article", 
        "id": "sg:pub.10.1007/s10998-007-4177-y", 
        "inLanguage": "en", 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1136293", 
            "issn": [
              "0031-5303", 
              "1588-2829"
            ], 
            "name": "Periodica Mathematica Hungarica", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "55"
          }
        ], 
        "keywords": [
          "number system", 
          "generator", 
          "system", 
          "characterization", 
          "elements", 
          "polynomials", 
          "complete description", 
          "results", 
          "concept", 
          "ring", 
          "description", 
          "decimal representation", 
          "quadratic case", 
          "main results", 
          "representation", 
          "cases", 
          "generalization", 
          "canonical number systems", 
          "integers", 
          "residue class ring", 
          "natural generalization", 
          "rational integers", 
          "polynomial ring"
        ], 
        "name": "Reducible cubic CNS polynomials", 
        "pagination": "177-183", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1027920730"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s10998-007-4177-y"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s10998-007-4177-y", 
          "https://app.dimensions.ai/details/publication/pub.1027920730"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-05-10T09:58", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220509/entities/gbq_results/article/article_441.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/s10998-007-4177-y"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10998-007-4177-y'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10998-007-4177-y'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10998-007-4177-y'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10998-007-4177-y'


     

    This table displays all metadata directly associated to this object as RDF triples.

    113 TRIPLES      22 PREDICATES      52 URIs      41 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s10998-007-4177-y schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author Nca73d64333cd453991946866c369c7d3
    4 schema:citation sg:pub.10.1007/978-3-540-32439-3_13
    5 sg:pub.10.1007/bf01895142
    6 sg:pub.10.1007/s10474-005-0221-z
    7 schema:datePublished 2007-11
    8 schema:datePublishedReg 2007-11-01
    9 schema:description The concept of a canonical number system can be regarded as a natural generalization of decimal representations of rational integers to elements of residue class rings of polynomial rings. Generators of canonical number systems are CNS polynomials which are known in the linear and quadratic cases, but whose complete description is still open. In the present note reducible CNS polynomials are treated, and the main result is the characterization of reducible cubic CNS polynomials.
    10 schema:genre article
    11 schema:inLanguage en
    12 schema:isAccessibleForFree true
    13 schema:isPartOf N48768fbf469740a59da0bc2cafb24c29
    14 N726fe041ef2545b0bcfecff901ef27ad
    15 sg:journal.1136293
    16 schema:keywords canonical number systems
    17 cases
    18 characterization
    19 complete description
    20 concept
    21 decimal representation
    22 description
    23 elements
    24 generalization
    25 generator
    26 integers
    27 main results
    28 natural generalization
    29 number system
    30 polynomial ring
    31 polynomials
    32 quadratic case
    33 rational integers
    34 representation
    35 residue class ring
    36 results
    37 ring
    38 system
    39 schema:name Reducible cubic CNS polynomials
    40 schema:pagination 177-183
    41 schema:productId N73728a981bef4577bd3ef0ea5306abf0
    42 Nfb2ef97e016a4bee92132c7b5e3542ef
    43 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027920730
    44 https://doi.org/10.1007/s10998-007-4177-y
    45 schema:sdDatePublished 2022-05-10T09:58
    46 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    47 schema:sdPublisher Nade3577462504894ad52f05f71d7a94e
    48 schema:url https://doi.org/10.1007/s10998-007-4177-y
    49 sgo:license sg:explorer/license/
    50 sgo:sdDataset articles
    51 rdf:type schema:ScholarlyArticle
    52 N1cdc636644454d7eae9b8c282ec3947c rdf:first sg:person.013334020373.46
    53 rdf:rest rdf:nil
    54 N48768fbf469740a59da0bc2cafb24c29 schema:issueNumber 2
    55 rdf:type schema:PublicationIssue
    56 N5f018deea63e4773b50449a04135481b rdf:first sg:person.012747025157.36
    57 rdf:rest N1cdc636644454d7eae9b8c282ec3947c
    58 N726fe041ef2545b0bcfecff901ef27ad schema:volumeNumber 55
    59 rdf:type schema:PublicationVolume
    60 N73728a981bef4577bd3ef0ea5306abf0 schema:name doi
    61 schema:value 10.1007/s10998-007-4177-y
    62 rdf:type schema:PropertyValue
    63 Nade3577462504894ad52f05f71d7a94e schema:name Springer Nature - SN SciGraph project
    64 rdf:type schema:Organization
    65 Nca73d64333cd453991946866c369c7d3 rdf:first sg:person.011153327405.03
    66 rdf:rest N5f018deea63e4773b50449a04135481b
    67 Nfb2ef97e016a4bee92132c7b5e3542ef schema:name dimensions_id
    68 schema:value pub.1027920730
    69 rdf:type schema:PropertyValue
    70 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    71 schema:name Mathematical Sciences
    72 rdf:type schema:DefinedTerm
    73 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    74 schema:name Pure Mathematics
    75 rdf:type schema:DefinedTerm
    76 sg:journal.1136293 schema:issn 0031-5303
    77 1588-2829
    78 schema:name Periodica Mathematica Hungarica
    79 schema:publisher Springer Nature
    80 rdf:type schema:Periodical
    81 sg:person.011153327405.03 schema:affiliation grid-institutes:grid.260975.f
    82 schema:familyName Akiyama
    83 schema:givenName Shigeki
    84 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011153327405.03
    85 rdf:type schema:Person
    86 sg:person.012747025157.36 schema:affiliation grid-institutes:None
    87 schema:familyName Brunotte
    88 schema:givenName Horst
    89 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012747025157.36
    90 rdf:type schema:Person
    91 sg:person.013334020373.46 schema:affiliation grid-institutes:grid.7122.6
    92 schema:familyName Pethő
    93 schema:givenName Attila
    94 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013334020373.46
    95 rdf:type schema:Person
    96 sg:pub.10.1007/978-3-540-32439-3_13 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049444289
    97 https://doi.org/10.1007/978-3-540-32439-3_13
    98 rdf:type schema:CreativeWork
    99 sg:pub.10.1007/bf01895142 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050389700
    100 https://doi.org/10.1007/bf01895142
    101 rdf:type schema:CreativeWork
    102 sg:pub.10.1007/s10474-005-0221-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1047907570
    103 https://doi.org/10.1007/s10474-005-0221-z
    104 rdf:type schema:CreativeWork
    105 grid-institutes:None schema:alternateName Haus-Endt-Strasse 88, D-40593, Düsseldorf, Germany
    106 schema:name Haus-Endt-Strasse 88, D-40593, Düsseldorf, Germany
    107 rdf:type schema:Organization
    108 grid-institutes:grid.260975.f schema:alternateName Department of Mathematics, Faculty of Science, Niigata University, Ikarashi 2-8050, 950-2181, Niigata, Japan
    109 schema:name Department of Mathematics, Faculty of Science, Niigata University, Ikarashi 2-8050, 950-2181, Niigata, Japan
    110 rdf:type schema:Organization
    111 grid-institutes:grid.7122.6 schema:alternateName Department of Computer Science, University of Debrecen, P.O. Box 12, H-4010, Debrecen, Hungary
    112 schema:name Department of Computer Science, University of Debrecen, P.O. Box 12, H-4010, Debrecen, Hungary
    113 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...