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The Product Types Ontology: Class Definition for "Irreducible fraction"

This page is part of http://www.productontology.org/, a huge, precise dictionary of product types and brand names for marking up Web sites with schema.org or the GoodRelations e-commerce standard.

Breaking news: schema.org has just implemented our proposal to define an additionalType property with the use of this service in mind!

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http://www.productontology.org/

On this page: Usage(schema.org/Microdata, RDFa, Facebook) Contact Information Caching Policy License Acknowledgments References

pto:Irreducible_fraction (rdf:type owl:Class)

URI http://www.productontology.org/id/Irreducible_fraction
rdfs:subClassOf gr:ProductOrService, http://schema.org/Product
rdfs:label Irreducible fraction (as a class or brand name of products of services)
Translation(s):  كسر غير قابل للاختزال@ar;  Fracció irreductible@ca;  Gekürzter Bruch@de;  Ανάγωγο κλάσμα@el;  Nereduktebla frakcio@eo;  Fracción irreducible@es;  Murru taandamine@et;  Zatiki laburtezin@eu;  کسر تحویل‌ناپذیر@fa;  Fraction irréductible@fr; 

rdfs:comment

An irreducible fraction (or fraction in lowest terms, simplest form or reduced fraction) is a fraction in which the numerator and denominator are integers that have no other common divisors than 1 (and −1, when negative numbers are considered). In other words, a fraction is irreducible if and only if a and b are coprime, that is, if a and b have a greatest common divisor of 1. In higher mathematics, "irreducible fraction" may also refer to rational fractions such that the numerator and the denominator are coprime polynomials. Every positive rational number can be represented as an irreducible fraction in exactly one way. An equivalent definition is sometimes useful: if a and b are integers, then the fraction is irreducible if and only if there is no other equal fraction such that or where means the absolute value of a.(Two fractions and are equal or equivalent if and only if ad = bc.) For example, and are all irreducible fractions. On the other hand, is reducible since it is equal in value to and the numerator of is less than the numerator of . A fraction that is reducible can be reduced by dividing both the numerator and denominator by a common factor. It can be fully reduced to lowest terms if both are divided by their greatest common divisor. In order to find the greatest common divisor, the Euclidean algorithm or prime factorization can be used. The Euclidean algorithm is commonly preferred because it allows one to reduce fractions with numerators and denominators too large to be easily factored. (Source: Wikipedia, the free encyclopedia, see http://en.wikipedia.org/wiki/Irreducible_fraction)

Note: The extraction of the abstract from the Wikipedia page may sometimes yield imperfect results. We are improving the algorithm regularly.

is rdfs:domain of gr:category gr:color gr:condition gr:depth gr:hasEAN_UCC-13 gr:hasGTIN-14 gr:hasMPN gr:hasManufacturer gr:hasStockKeepingUnit gr:height gr:isAccessoryOrSparePartFor gr:isConsumableFor gr:isSimilarTo gr:weight gr:width
is rdfs:range of gr:includes gr:isAccessoryOrSparePartFor gr:isConsumableFor gr:isSimilarTo

Note: This is a generic list. Some of the properties may not be applicable to this particular type of object.

Trademark Disclaimer:  Since this service returns class descriptions for potentiall any series of characters, it cannot indicate automatically whether a name is a registered trademark or otherwise protected. We assume no liability for the absence of trademark rights and other damages. See the section "License" below for details.

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Usage

The following shows how to model that you offer to sell [a/an/some] Irreducible fraction for $ 19.99.

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Microdata / Use with http://schema.org/Product

One of the most powerful usages of the class definitions from this site is to describe the type of your page and product for the schema.org product markup in Microdata syntax much more precisely.

Simply add the full URI of a class from this site, e.g. http://www.productontology.org/id/Irreducible_fraction as an additional type as follows:

<div itemscope itemtype="http://schema.org/Product">
    <link itemprop="additionalType" href="http://www.productontology.org/id/Irreducible_fraction" />
    <!-- other schema.org properties go in here -->
</div>		

Note: In HTML5, it is valid to use the <link> element in the body of a HTML document.

Here is a complete example:

<!DOCTYPE html>
<html>
<head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/>
    <title>An offer to sell a / some Irreducible_fraction</title>
</head>
<body>
<div itemscope itemtype="http://schema.org/Product" itemid="#product">
    <link itemprop="additionalType" href="http://www.productontology.org/id/Irreducible_fraction" />
    <span itemprop="name">.. a short name for the object ...</span>
    Product description: 
    <span itemprop="description">... a longer description ...</span>
    <div itemprop="offers" itemscope itemtype="http://schema.org/Offer" itemid="#offer">
        <span itemprop="price">$19.99</span> 
        <link itemprop="availability" href="http://schema.org/InStock" />In stock
    </div>
</div>
</body>
</html>

Turtle Syntax

@prefix foaf: <http://xmlns.com/foaf/0.1/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .
@prefix pto: <http://www.productontology.org/id/> .
@prefix gr: <http://purl.org/goodrelations/v1#> .
@prefix foo: <http://example.com/> .

# The object
foo:myObject a <http://www.productontology.org/id/Irreducible_fraction> ;
	a gr:SomeItems ;
	gr:name "... a short name for the object ..."@en ;
	gr:description "... a longer description ..."@en .

# The agent (person or company) who is offering it
foo:ACMECorp a gr:BusinessEntity ;
	gr:legalName "ACME Corp" ;
	gr:offers foo:Offer .
		
# The offer to sell it
foo:Offer a gr:Offering ;
	gr:includes foo:myObject;
	foaf:page <http://URI_of_the_page_containing_the_offer.com>;
	gr:hasBusinessFunction gr:Sell ;
	gr:validFrom "2011-01-24T00:00:00+01:00"^^xsd:dateTime ;
	gr:validThrough "2011-12-24T00:00:00+01:00"^^xsd:dateTime ;
	gr:hasPriceSpecification
         [ a gr:UnitPriceSpecification ;
           gr:hasCurrency "USD"^^xsd:string ;
           gr:hasCurrencyValue "19.99"^^xsd:float ;
           gr:validThrough "2011-12-24T00:00:00+01:00"^^xsd:dateTime ] .

Note: Replace gr:SomeItems (http://purl.org/goodrelations/v1#SomeItems) by gr:Individual if you are describing a unique object of that kind (e.g. antique furniture).

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RDFa

<!DOCTYPE html>
<html version="HTML+RDFa 1.1" xmlns="http://www.w3.org/1999/xhtml">
<head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/>
    <title>An offer to sell a / some Irreducible_fraction</title>
</head>
<body>
<div xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
     xmlns:rdfs="http://www.w3.org/2000/01/rdf-schema#"
     xmlns:foaf="http://xmlns.com/foaf/0.1/"
     xmlns:gr="http://purl.org/goodrelations/v1#"
     xmlns:pto="http://www.productontology.org/id/"
     xmlns:foo="http://example.com/"
     xmlns:xsd="http://www.w3.org/2001/XMLSchema#">

<!-- The agent (person or company) who is offering it -->
   <div about="#ACMECorp" typeof="gr:BusinessEntity">
      <div property="gr:legalName">ACME Corp</div>
      <div rel="gr:offers">
<!-- The offer to sell it -->	
         <div about="#offer" typeof="gr:Offering">
            <div rel="gr:hasBusinessFunction" resource="http://purl.org/goodrelations/v1#Sell"></div>
            <div rel="gr:includes">
<!-- The object -->	
               <div about="#myObject" typeof="http://www.productontology.org/id/Irreducible_fraction">
                  <div rel="rdf:type" resource="http://purl.org/goodrelations/v1#SomeItems"></div>
                  <div property="gr:description" xml:lang="en">... a longer description ...</div>
                  <div property="gr:name" xml:lang="en">.. a short name for the object ...</div>
               </div>
            </div>
            <div rel="foaf:page" resource="http://URI_of_the_page_containing_the_offer"></div>
            <div rel="gr:hasPriceSpecification">
               <div typeof="gr:UnitPriceSpecification">
                  <div property="gr:hasCurrency" content="USD" datatype="xsd:string">$ </div>
                  <div property="gr:hasCurrencyValue" datatype="xsd:float">19.99</div>
                  <div property="gr:validThrough" content="2011-12-24T00:00:00+01:00" 
					   datatype="xsd:dateTime"></div>
               </div>
            </div>
            <div property="gr:validFrom" content="2011-01-24T00:00:00+01:00"
                 datatype="xsd:dateTime"></div>
            <div property="gr:validThrough" content="2011-12-24T00:00:00+01:00"
                 datatype="xsd:dateTime"></div>
         </div>
      </div>
   </div>
</div>
</body>
</html>

Note: Replace gr:SomeItems (http://purl.org/goodrelations/v1#SomeItems) by gr:Individual if you are describing a unique object of that kind (e.g. antique furniture).

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RDF/XML

<?xml version="1.0" encoding="UTF-8" ?>
<rdf:RDF xmlns:gr="http://purl.org/goodrelations/v1#" 
  xmlns:pto="http://www.productontology.org/id/" 
  xmlns:xsd="http://www.w3.org/2001/XMLSchema#" 
  xmlns:foaf="http://xmlns.com/foaf/0.1/" 
  xmlns:foo="http://example.com/" 
  xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<!-- The object -->
  <rdf:Description rdf:about="http://example.com/myObject">
    <rdf:type rdf:resource="http://www.productontology.org/id/Irreducible_fraction"/>    
    <rdf:type rdf:resource="http://purl.org/goodrelations/v1#SomeItems"/>
    <gr:name xml:lang="en">... a short name for the object ...</gr:name>
    <gr:description xml:lang="en">... a longer description ...</gr:description>
  </rdf:Description>
<!-- The agent (person or company) who is offering it -->
  <gr:BusinessEntity rdf:about="http://example.com/ACMECorp">
    <gr:legalName>ACME Corp</gr:legalName>
    <gr:offers rdf:resource="http://example.com/Offer" />
  </gr:BusinessEntity>
<!-- The offer to sell it -->   
  <gr:Offering rdf:about="http://example.com/Offer">
    <gr:includes rdf:resource="http://example.com/myObject" />
    <foaf:page rdf:resource="http://URI_of_the_page_containing_the_offer"/>
    <gr:hasBusinessFunction rdf:resource="http://purl.org/goodrelations/v1#Sell"/>
    <gr:validFrom rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">
      2011-01-24T00:00:00+01:00</gr:validFrom>
    <gr:validThrough rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">
      2011-12-24T00:00:00+01:00</gr:validThrough>
    <gr:hasPriceSpecification>
      <gr:UnitPriceSpecification>
        <gr:hasCurrency rdf:datatype="http://www.w3.org/2001/XMLSchema#string">USD</gr:hasCurrency>
        <gr:hasCurrencyValue rdf:datatype="http://www.w3.org/2001/XMLSchema#float">19.99</gr:hasCurrencyValue>
        <gr:validThrough rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">
          2011-12-24T00:00:00+01:00</gr:validThrough>
      </gr:UnitPriceSpecification>
    </gr:hasPriceSpecification>
  </gr:Offering>

</rdf:RDF>

Note: Replace gr:SomeItems (http://purl.org/goodrelations/v1#SomeItems) by gr:Individual if you are describing a unique object of that kind (e.g. antique furniture).

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SPARQL Query

prefix foaf: <http://xmlns.com/foaf/0.1/> 
prefix xsd: <http://www.w3.org/2001/XMLSchema#> 
prefix pto: <http://www.productontology.org/id/> 
prefix gr: <http://purl.org/goodrelations/v1#> 
prefix foo: <http://example.com/> 

# Find the cheapest offer for a Irreducible_fraction

SELECT * WHERE{
?company gr:offers ?offer .
?offer a gr:Offering .
?offer gr:hasBusinessFunction gr:Sell .
OPTIONAL {?offer rdfs:label ?label } .
OPTIONAL {?offer gr:name ?label } .
OPTIONAL {?offer rdfs:comment ?label } .
OPTIONAL {?offer gr:description ?label } .
?offer gr:hasPriceSpecification ?p .
?p a gr:UnitPriceSpecification .
?p gr:hasCurrency ?currency .
?p gr:hasCurrencyValue ?price .
?offer gr:includes ?product .
?product a <http://www.productontology.org/id/Irreducible_fraction> .
}
ORDER BY (?price)
LIMIT 10

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Facebook Open Graph Protocol

You can also use the class definitions from this site for better describing the type of your page or product for the Facebook Open Graph Protocol.

Simply define the namespace prefix pto: in the <html> element of your page

<html version="HTML+RDFa 1.1" 
	xmlns="http://www.w3.org/1999/xhtml" 
	xmlns:pto="http://www.productontology.org/id/" 
	>

and use the compact URI (CURIE) pto:Irreducible_fraction in combination with og:type as follows:

	<meta property="og:type" content="pto:Irreducible_fraction"/>

A complete example is here.

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Contact Information

Univ.-Prof. Dr. Martin Hepp

E-Business and Web Science Research Group
Chair of General Management and E-Business
Universität der Bundeswehr München
Werner-Heisenberg-Weg 39
D-85579 Neubiberg, Germany

Phone: +49 89 6004-4217
eMail: mhepp(at)computer.org (preferred mode of communication)
Web: http://www.heppnetz.de/
Web: http://www.unibw.de/ebusiness/

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Caching Policy

In order to minimize the load on the Wikipedia API, all requests are cached internally for 72 hours. This means that changes to the English Wikipedia will be available in this service within 72 hours or less if the same entry has been requested before. Classes not requested within the last six hours are always guaranteed to be in sync with the latest version in Wikipedia.

The RDF/XML dump file is updated every 12 hours only.

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License

The class definition text is taken from Wikipedia, the free encyclopedia under a Creative Commons Attribution-ShareAlike 3.0 Unported (CC BY-SA 3.0) license. Accordingly, the ontology class definitions are available under the very same license.

Trademark Disclaimer:  Since this service returns class descriptions for potentially any series of characters, it cannot indicate automatically whether a name is a registered trademark or otherwise protected. If you want us to block a certain name, please send your request including proof of your rights on the name to our contact address listed below.. Any of the trademarks, service marks, collective marks, design rights or similar rights that are mentioned, used, or cited in this service are the property of their respective owners. Their use here does not imply that you may use them for any purpose other than for the same or a similar informational use as contemplated by the original authors of the underlying Wikipedia articles under the CC-BY-SA and GFDL licensing schemes. Productontology.org is neither endorsed by nor affiliated with any of the holders of any such rights and as such cannot grant any rights to use any otherwise protected materials. Your use of any such or similar incorporeal property is at your own risk.

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Acknowledgements

Thanks to Stefano Bertolo, Julien Chaumond, Bob Ferris, Kingsley Idehen, Axel Polleres, Andreas Radinger, Alex Stolz, and Giovanni Tummarello for very valuable feedback, and to Katharina Siorpaes and Daniel Bachlechner, who contributed to the initial analysis of the stability of Wikipedia URIs back in 2007.

The work on The Product Types Ontology has been supported by the German Federal Ministry of Research (BMBF) by a grant under the KMU Innovativ program as part of the Intelligent Match project (FKZ 01IS10022B).

BMBF logo

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References

Wikipedia: Irreducible fraction, available at http://en.wikipedia.org/wiki/Irreducible_fraction.

Hepp, Martin: GoodRelations: An Ontology for Describing Products and Services Offers on the Web, Proceedings of the 16th International Conference on Knowledge Engineering and Knowledge Management (EKAW2008), Acitrezza, Italy, September 29 - October 3, 2008, Springer LNCS, Vol 5268, pp. 332-347.

Hepp, Martin; Siorpaes, Katharina; Bachlechner, Daniel: Harvesting Wiki Consensus: Using Wikipedia Entries as Vocabulary for Knowledge Management, IEEE Internet Computing, Vol. 11, No. 5, pp. 54-65, Sept-Oct 2007.

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