@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr: a skos:ConceptScheme .
psr:-SNTKWPJM-D
  skos:prefLabel "polynôme"@fr, "polynomial"@en ;
  a skos:Concept ;
  skos:narrower psr:-P16SBGTJ-4 .

psr:-VF1N8B88-T
  skos:prefLabel "Schinzel's hypothesis H"@en, "hypothèse H de Schinzel"@fr ;
  a skos:Concept ;
  skos:related psr:-P16SBGTJ-4 .

psr:-P16SBGTJ-4
  dc:created "2023-08-17"^^xsd:date ;
  skos:prefLabel "irreducible polynomial"@en, "polynôme irréductible"@fr ;
  a skos:Concept ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Polyn%C3%B4me_irr%C3%A9ductible>, <https://en.wikipedia.org/wiki/Irreducible_polynomial> ;
  skos:inScheme psr: ;
  skos:related psr:-VF1N8B88-T ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:definition """In mathematics, an <b>irreducible polynomial</b> is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials. The property of irreducibility depends on the nature of the coefficients that are accepted for the possible factors, that is, the field to which the coefficients of the polynomial and its possible factors are supposed to belong. For example, the polynomial <span class="texhtml"><i>x</i><sup>2</sup> − 2</span> is a polynomial with integer coefficients, but, as every integer is also a real number, it is also a polynomial with real coefficients. It is irreducible if it is considered as a polynomial with integer coefficients, but it factors as <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\\\\displaystyle \\\\left(x-{\\\\sqrt {2}}\\
ight)\\\\left(x+{\\\\sqrt {2}}\\
ight)}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow>           <mo>(</mo>           <mrow>             <mi>x</mi>             <mo>−<!-- − --></mo>             <mrow class="MJX-TeXAtom-ORD">               <msqrt>                 <mn>2</mn>               </msqrt>             </mrow>           </mrow>           <mo>)</mo>         </mrow>         <mrow>           <mo>(</mo>           <mrow>             <mi>x</mi>             <mo>+</mo>             <mrow class="MJX-TeXAtom-ORD">               <msqrt>                 <mn>2</mn>               </msqrt>             </mrow>           </mrow>           <mo>)</mo>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle \\\\left(x-{\\\\sqrt {2}}\\
ight)\\\\left(x+{\\\\sqrt {2}}\\
ight)}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42c42e511306bea30774a7b19219afbdab45d228" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:19.184ex; height:3.343ex;" alt="{\\\\displaystyle \\\\left(x-{\\\\sqrt {2}}\\
ight)\\\\left(x+{\\\\sqrt {2}}\\
ight)}"></span> if it is considered as a polynomial with real coefficients. One says that the polynomial <span class="texhtml"><i>x</i><sup>2</sup> − 2</span> is irreducible over the integers but not over the reals.  
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Irreducible_polynomial">https://en.wikipedia.org/wiki/Irreducible_polynomial</a>)"""@en, """En algèbre, un polynôme irréductible à coefficients dans un anneau intègre est un polynôme qui n’est ni inversible, ni produit de deux polynômes non inversibles. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Polyn%C3%B4me_irr%C3%A9ductible">https://fr.wikipedia.org/wiki/Polyn%C3%B4me_irr%C3%A9ductible</a>)"""@fr ;
  skos:broader psr:-SNTKWPJM-D .