@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

psr:-GR8X1BV4-T
  skos:prefLabel "golden ratio"@en, "nombre d'or"@fr ;
  a skos:Concept ;
  skos:broader psr:-V3F2M3LL-D .

psr:-V3F2M3LL-D
  skos:narrower psr:-B2H0L954-0, psr:-GR8X1BV4-T ;
  skos:prefLabel "algebraic number"@en, "nombre algébrique"@fr ;
  skos:definition """An <b>algebraic number</b> is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients.  For example, the golden ratio, <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 (1+{\\\\sqrt {5}})/2}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mo stretchy="false">(</mo>
<br/>        <mn>1</mn>
<br/>        <mo>+</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <msqrt>
<br/>            <mn>5</mn>
<br/>          </msqrt>
<br/>        </mrow>
<br/>        <mo stretchy="false">)</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mo>/</mo>
<br/>        </mrow>
<br/>        <mn>2</mn>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle (1+{\\\\sqrt {5}})/2}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8834bbd69c7f1eddf70573ed4296941c18c25ee5" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:11.235ex; height:3.009ex;" alt="(1+{\\\\sqrt  {5}})/2"></span>, is an algebraic number, because it is a root of the polynomial <span class="texhtml"><i>x</i><sup>2</sup> − <i>x</i> − 1</span>. That is, it is a value for x for which the polynomial evaluates to zero.  As another example, the complex number <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 1+i}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mn>1</mn>
<br/>        <mo>+</mo>
<br/>        <mi>i</mi>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle 1+i}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a65e41a5c0369e908cf26a2452046f19bab946d" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.505ex; width:4.805ex; height:2.343ex;" alt="{\\\\displaystyle 1+i}"></span> is algebraic because it is a root of <span class="texhtml"><i>x</i><sup>4</sup> + 4</span>.
<br/>All integers and rational numbers are algebraic, as are all roots of integers. Real and complex numbers that are not algebraic, such as <span class="texhtml mvar" style="font-style:italic;">π</span> and <span class="texhtml mvar" style="font-style:italic;">e</span>, are called transcendental numbers.
<br/>The set  of algebraic numbers is countably infinite and has measure zero in the Lebesgue measure as a subset of the uncountable complex numbers. In that sense, almost all complex numbers are transcendental. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Algebraic_number">https://en.wikipedia.org/wiki/Algebraic_number</a>)"""@en, """Un nombre algébrique, en mathématiques, est un nombre complexe solution d'une équation polynomiale à coefficients dans le corps <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 \\\\mathbb {Q} }">
         <semantics>
         <mrow class="MJX-TeXAtom-ORD">
         <mstyle displaystyle="true" scriptlevel="0">
         <mrow class="MJX-TeXAtom-ORD">
         <mi mathvariant="double-struck">Q</mi>
         </mrow>
         </mstyle>
         </mrow>
         <annotation encoding="application/x-tex">{\\\\displaystyle \\\\mathbb {Q} }</annotation>
         </semantics>
         </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5909f0b54e4718fa24d5fd34d54189d24a66e9a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.808ex; height:2.509ex;" alt="\\\\mathbb{Q} "></span> des rationnels (autrement dit racine d'un polynôme non nul à coefficients rationnels). Les nombres entiers et rationnels sont algébriques, ainsi que toutes les racines de ces nombres. Les nombres complexes qui ne sont pas algébriques, comme π et e (théorème de Lindemann-Weierstrass), sont dits transcendants. L'étude de ces nombres, de leurs polynômes minimaux et des corps qui les contiennent fait partie de la théorie de Galois. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Nombre_alg%C3%A9brique">https://fr.wikipedia.org/wiki/Nombre_alg%C3%A9brique</a>)"""@fr ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Nombre_alg%C3%A9brique>, <https://en.wikipedia.org/wiki/Algebraic_number> ;
  skos:broader psr:-Z5NBGSJC-F ;
  a skos:Concept ;
  skos:inScheme psr: .

psr:-B2H0L954-0
  skos:prefLabel "constructible number"@en, "nombre constructible"@fr ;
  a skos:Concept ;
  skos:broader psr:-V3F2M3LL-D .

psr: a skos:ConceptScheme .
psr:-Z5NBGSJC-F
  skos:prefLabel "nombre"@fr, "number"@en ;
  a skos:Concept ;
  skos:narrower psr:-V3F2M3LL-D .