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

psr:-V91WMW66-Q
  dc:modified "2024-10-18"^^xsd:date ;
  a skos:Concept ;
  skos:broader psr:-LCX4HPGN-Z, psr:-SNTKWPJM-D ;
  skos:narrower psr:-J9TLDK49-R, psr:-RZHMZQ9H-2, psr:-PJSZQ3B9-1, psr:-LPBF743P-0, psr:-LK8XNN3X-R, psr:-M8SH22G9-Z ;
  skos:inScheme psr: ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/%C3%89quation_polynomiale>, <https://en.wikipedia.org/wiki/Algebraic_equation> ;
  skos:definition """En mathématiques, une <b>équation polynomiale</b>, ou <b>équation algébrique</b></span>, est une équation de la forme :  <dl><dd><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 P=0}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>P</mi>         <mo>=</mo>         <mn>0</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle P=0}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6f743f37b37ce0c2ddc1db0fdca0e577c19f51d" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.006ex; height:2.176ex;" alt="{\\\\displaystyle P=0}"></span></dd></dl> où <span class="texhtml mvar" style="font-style:italic;">P</span> est un polynôme. Voici un exemple d'équation simple avec une seule inconnue :  <dl><dd><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 7x^{42}-x^{7}+3=0}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mn>7</mn>         <msup>           <mi>x</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>42</mn>           </mrow>         </msup>         <mo>−<!-- − --></mo>         <msup>           <mi>x</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>7</mn>           </mrow>         </msup>         <mo>+</mo>         <mn>3</mn>         <mo>=</mo>         <mn>0</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle 7x^{42}-x^{7}+3=0}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/12747750d8f6f744d047185d302d34a6cdbda813" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:17.856ex; height:2.843ex;" alt="{\\\\displaystyle 7x^{42}-x^{7}+3=0}"></span></dd></dl> Usuellement, le terme <i>équation polynomiale</i> désigne une équation avec une seule inconnue (notée ici <span class="texhtml mvar" style="font-style:italic;">x</span>) :  <dl><dd><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 a_{n}x^{n}+a_{n-1}x^{n-1}+\\\\dots +a_{1}x+a_{0}=0}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>n</mi>           </mrow>         </msub>         <msup>           <mi>x</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>n</mi>           </mrow>         </msup>         <mo>+</mo>         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>n</mi>             <mo>−<!-- − --></mo>             <mn>1</mn>           </mrow>         </msub>         <msup>           <mi>x</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>n</mi>             <mo>−<!-- − --></mo>             <mn>1</mn>           </mrow>         </msup>         <mo>+</mo>         <mo>⋯<!-- ⋯ --></mo>         <mo>+</mo>         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>1</mn>           </mrow>         </msub>         <mi>x</mi>         <mo>+</mo>         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>0</mn>           </mrow>         </msub>         <mo>=</mo>         <mn>0</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\\\\dots +a_{1}x+a_{0}=0}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4453a001b0b668b3043d8bae71ade1c046343070" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:38.437ex; height:3.009ex;" alt="{\\\\displaystyle a_{n}x^{n}+a_{n-1}x^{n-1}+\\\\dots +a_{1}x+a_{0}=0}"></span>,</dd></dl> où l'entier naturel <span class="texhtml mvar" style="font-style:italic;">n</span> et les <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 a_{i}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msub>           <mi>a</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>i</mi>           </mrow>         </msub>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle a_{i}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bc77764b2e74e64a63341054fa90f3e07db275f" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.029ex; height:2.009ex;" alt="{\\\\displaystyle a_{i}}"></span>, appelés <i>coefficients</i> de l’équation, sont connus. Les coefficients sont le plus souvent des nombres réels ou complexes, mais ils peuvent prendre leurs valeurs dans n’importe quel anneau. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/%C3%89quation_polynomiale">https://fr.wikipedia.org/wiki/%C3%89quation_polynomiale</a>)"""@fr, """In mathematics, an <b>algebraic equation</b> or <b>polynomial equation</b> is an equation of the form <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 P=0}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>P</mi>         <mo>=</mo>         <mn>0</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle P=0}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6f743f37b37ce0c2ddc1db0fdca0e577c19f51d" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.006ex; height:2.176ex;" alt="{\\\\displaystyle P=0}"></span>, where <i>P</i> is a polynomial with coefficients in some field, often the field of the rational numbers.  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}-3x+1=0}">   <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>3</mn>         <mi>x</mi>         <mo>+</mo>         <mn>1</mn>         <mo>=</mo>         <mn>0</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle x^{5}-3x+1=0}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/698e1afb9a1d47e492390b6a5a4612ea0dfff0cc" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:15.98ex; height:2.843ex;" alt="{\\\\displaystyle x^{5}-3x+1=0}"></span> is an algebraic equation with integer coefficients and  <dl><dd><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 y^{4}+{\\rac {xy}{2}}-{\\rac {x^{3}}{3}}+xy^{2}+y^{2}+{\\rac {1}{7}}=0}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mi>y</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>4</mn>           </mrow>         </msup>         <mo>+</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mrow>               <mi>x</mi>               <mi>y</mi>             </mrow>             <mn>2</mn>           </mfrac>         </mrow>         <mo>−<!-- − --></mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <msup>               <mi>x</mi>               <mrow class="MJX-TeXAtom-ORD">                 <mn>3</mn>               </mrow>             </msup>             <mn>3</mn>           </mfrac>         </mrow>         <mo>+</mo>         <mi>x</mi>         <msup>           <mi>y</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>+</mo>         <msup>           <mi>y</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>2</mn>           </mrow>         </msup>         <mo>+</mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>1</mn>             <mn>7</mn>           </mfrac>         </mrow>         <mo>=</mo>         <mn>0</mn>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle y^{4}+{\\rac {xy}{2}}-{\\rac {x^{3}}{3}}+xy^{2}+y^{2}+{\\rac {1}{7}}=0}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cebca40bd954fec7e7a5e4bf25de98273e8451bf" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:34.977ex; height:5.843ex;" alt="{\\\\displaystyle y^{4}+{\\rac {xy}{2}}-{\\rac {x^{3}}{3}}+xy^{2}+y^{2}+{\\rac {1}{7}}=0}"></span></dd></dl> is a multivariate polynomial equation over the rationals. For many authors, the term <i>algebraic equation</i> refers only to the univariate case, that is polynomial equations that involve only one variable. On the other hand, a polynomial equation may involve several variables (the <i>multivariate</i> case), in which case the term <i>polynomial equation</i> is usually preferred.  
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Algebraic_equation">https://en.wikipedia.org/wiki/Algebraic_equation</a>)"""@en ;
  skos:prefLabel "équation polynomiale"@fr, "polynomial equation"@en ;
  skos:altLabel "équation algébrique"@fr, "algebraic equation"@en ;
  dc:created "2023-07-13"^^xsd:date .

psr:-LK8XNN3X-R
  skos:prefLabel "équation du second degré"@fr, "quadratic equation"@en ;
  a skos:Concept ;
  skos:broader psr:-V91WMW66-Q .

psr:-RZHMZQ9H-2
  skos:prefLabel "Bring radical"@en, "radical de Bring"@fr ;
  a skos:Concept ;
  skos:broader psr:-V91WMW66-Q .

psr:-M8SH22G9-Z
  skos:prefLabel "first degree equation"@en, "équation du premier degré"@fr ;
  a skos:Concept ;
  skos:broader psr:-V91WMW66-Q .

psr: a skos:ConceptScheme .
psr:-LCX4HPGN-Z
  skos:prefLabel "équation"@fr, "equation"@en ;
  a skos:Concept ;
  skos:narrower psr:-V91WMW66-Q .

psr:-J9TLDK49-R
  skos:prefLabel "calcul ombral"@fr, "umbral calculus"@en ;
  a skos:Concept ;
  skos:broader psr:-V91WMW66-Q .

psr:-SNTKWPJM-D
  skos:prefLabel "polynôme"@fr, "polynomial"@en ;
  a skos:Concept ;
  skos:narrower psr:-V91WMW66-Q .

psr:-PJSZQ3B9-1
  skos:prefLabel "Diophantine equation"@en, "équation diophantienne"@fr ;
  a skos:Concept ;
  skos:broader psr:-V91WMW66-Q .

psr:-LPBF743P-0
  skos:prefLabel "cubic equation"@en, "équation cubique"@fr ;
  a skos:Concept ;
  skos:broader psr:-V91WMW66-Q .