@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:-FPPBRRRC-0
  skos:prefLabel "monomial"@en, "monôme"@fr ;
  a skos:Concept ;
  skos:broader psr:-HDLZX4QZ-9 .

psr:-WWGGVH3R-4
  skos:prefLabel "Schur polynomial"@en, "polynôme de Schur"@fr ;
  a skos:Concept ;
  skos:broader psr:-HDLZX4QZ-9 .

psr:-HDLZX4QZ-9
  skos:narrower psr:-CTQ35PSM-B, psr:-FPPBRRRC-0, psr:-H31GC9Q4-H, psr:-WWGGVH3R-4, psr:-TSRP86DW-2 ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Polyn%C3%B4me_homog%C3%A8ne>, <https://en.wikipedia.org/wiki/Homogeneous_polynomial> ;
  skos:definition """En mathématiques, un <b>polynôme homogène</b>, ou <b>forme algébrique</b>, est un polynôme en plusieurs indéterminées dont tous les monômes non nuls sont de même degré total. Par exemple le polynôme <i>x</i><sup>5</sup> + 2<i>x</i><sup>3</sup><i>y</i><sup>2</sup> + 9<i>xy</i><sup>4</sup> est homogène de degré 5 car la somme des exposants est 5 pour chacun des monômes ; les polynômes homogènes de degré 2 sont les formes quadratiques. Les polynômes homogènes sont omniprésents en mathématiques et en physique théorique. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Polyn%C3%B4me_homog%C3%A8ne">https://fr.wikipedia.org/wiki/Polyn%C3%B4me_homog%C3%A8ne</a>)"""@fr, """In mathematics, a <b>homogeneous polynomial</b>, sometimes called quantic in older texts, is a polynomial whose nonzero terms all have the same degree. For example, <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 x^{5}+2x^{3}y^{2}+9xy^{4}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mi>x</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>5</mn>           </mrow>         </msup>         <mo>+</mo>         <mn>2</mn>         <msup>           <mi>x</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>3</mn>           </mrow>         </msup>         <msup>           <mi>y</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>+</mo>         <mn>9</mn>         <mi>x</mi>         <msup>           <mi>y</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>4</mn>           </mrow>         </msup>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle x^{5}+2x^{3}y^{2}+9xy^{4}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/51db9a7b25751430fe980a07982859492343788a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.533ex; height:3.009ex;" alt="{\\\\displaystyle x^{5}+2x^{3}y^{2}+9xy^{4}}"></span> is a homogeneous polynomial of degree 5, in two variables; the sum of the exponents in each term is always 5. The polynomial <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 x^{3}+3x^{2}y+z^{7}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mi>x</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>3</mn>           </mrow>         </msup>         <mo>+</mo>         <mn>3</mn>         <msup>           <mi>x</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mi>y</mi>         <mo>+</mo>         <msup>           <mi>z</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>7</mn>           </mrow>         </msup>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle x^{3}+3x^{2}y+z^{7}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8af258622f68c1c0d67e3e1ca16068c119cb65a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.911ex; height:3.009ex;" alt="{\\\\displaystyle x^{3}+3x^{2}y+z^{7}}"></span> is not homogeneous, because the sum of exponents does not match from term to term. The function defined by a homogeneous polynomial is always a homogeneous function.    
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Homogeneous_polynomial">https://en.wikipedia.org/wiki/Homogeneous_polynomial</a>)"""@en ;
  skos:broader psr:-SNTKWPJM-D ;
  skos:prefLabel "polynôme homogène"@fr, "homogeneous polynomial"@en ;
  dc:modified "2024-10-18"^^xsd:date ;
  a skos:Concept ;
  skos:inScheme psr: ;
  skos:altLabel "forme algébrique"@fr .

psr:-TSRP86DW-2
  skos:prefLabel "polynôme zonal"@fr, "zonal polynomial"@en ;
  a skos:Concept ;
  skos:broader psr:-HDLZX4QZ-9 .

psr:-CTQ35PSM-B
  skos:prefLabel "fonction de Jack"@fr, "Jack function"@en ;
  a skos:Concept ;
  skos:broader psr:-HDLZX4QZ-9 .

psr: a skos:ConceptScheme .
psr:-H31GC9Q4-H
  skos:prefLabel "quadratic form"@en, "forme quadratique"@fr ;
  a skos:Concept ;
  skos:broader psr:-HDLZX4QZ-9 .

psr:-SNTKWPJM-D
  skos:prefLabel "polynôme"@fr, "polynomial"@en ;
  a skos:Concept ;
  skos:narrower psr:-HDLZX4QZ-9 .