@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:-DW8DQDJ2-X
  skos:definition """Les <b>équations de Cauchy-Riemann</b> en analyse complexe, ainsi nommées en l'honneur d'Augustin Cauchy et Bernhard Riemann, sont les deux équations aux dérivées partielles<center><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 {\\rac {\\\\partial P}{\\\\partial x}}={\\rac {\\\\partial Q}{\\\\partial y}}\\\\quad {\\	ext{et}}\\\\quad {\\rac {\\\\partial P}{\\\\partial y}}=-{\\rac {\\\\partial Q}{\\\\partial x}}}">
<br/>  <semantics>
<br/>    <mrow class="MJX-TeXAtom-ORD">
<br/>      <mstyle displaystyle="true" scriptlevel="0">
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <mi mathvariant="normal">∂<!-- ∂ --></mi>
<br/>              <mi>P</mi>
<br/>            </mrow>
<br/>            <mrow>
<br/>              <mi mathvariant="normal">∂<!-- ∂ --></mi>
<br/>              <mi>x</mi>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>=</mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <mi mathvariant="normal">∂<!-- ∂ --></mi>
<br/>              <mi>Q</mi>
<br/>            </mrow>
<br/>            <mrow>
<br/>              <mi mathvariant="normal">∂<!-- ∂ --></mi>
<br/>              <mi>y</mi>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mspace width="1em"></mspace>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mtext>et</mtext>
<br/>        </mrow>
<br/>        <mspace width="1em"></mspace>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <mi mathvariant="normal">∂<!-- ∂ --></mi>
<br/>              <mi>P</mi>
<br/>            </mrow>
<br/>            <mrow>
<br/>              <mi mathvariant="normal">∂<!-- ∂ --></mi>
<br/>              <mi>y</mi>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>        <mo>=</mo>
<br/>        <mo>−<!-- − --></mo>
<br/>        <mrow class="MJX-TeXAtom-ORD">
<br/>          <mfrac>
<br/>            <mrow>
<br/>              <mi mathvariant="normal">∂<!-- ∂ --></mi>
<br/>              <mi>Q</mi>
<br/>            </mrow>
<br/>            <mrow>
<br/>              <mi mathvariant="normal">∂<!-- ∂ --></mi>
<br/>              <mi>x</mi>
<br/>            </mrow>
<br/>          </mfrac>
<br/>        </mrow>
<br/>      </mstyle>
<br/>    </mrow>
<br/>    <annotation encoding="application/x-tex">{\\\\displaystyle {\\rac {\\\\partial P}{\\\\partial x}}={\\rac {\\\\partial Q}{\\\\partial y}}\\\\quad {\\	ext{et}}\\\\quad {\\rac {\\\\partial P}{\\\\partial y}}=-{\\rac {\\\\partial Q}{\\\\partial x}}}</annotation>
<br/>  </semantics>
<br/></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/625d4df95c51927adc1d618bcaa13803d4356fa8" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:30.372ex; height:6.009ex;" alt="{\\\\displaystyle {\\rac {\\\\partial P}{\\\\partial x}}={\\rac {\\\\partial Q}{\\\\partial y}}\\\\quad {\\	ext{et}}\\\\quad {\\rac {\\\\partial P}{\\\\partial y}}=-{\\rac {\\\\partial Q}{\\\\partial x}}}"></span></center>exprimant une condition nécessaire et suffisante pour qu'une fonction <span class="texhtml"><i>f</i> = <i>P</i> + i <i>Q</i></span> (d'une variable complexe, à valeurs complexes) différentiable au sens réel en un point soit différentiable au sens complexe en ce point.
<br/>En d'autres termes, ce sont les conditions à ajouter à la différentiabilité au sens réel pour obtenir la différentiabilité au sens complexe. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/%C3%89quations_de_Cauchy-Riemann">https://fr.wikipedia.org/wiki/%C3%89quations_de_Cauchy-Riemann</a>)"""@fr, """In the field of complex analysis in mathematics, the <b>Cauchy–Riemann equations</b>, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which form a necessary and sufficient condition for a complex function of a complex variable to be complex differentiable. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Cauchy%E2%80%93Riemann_equations">https://en.wikipedia.org/wiki/Cauchy%E2%80%93Riemann_equations</a>)"""@en ;
  skos:inScheme psr: ;
  skos:prefLabel "Cauchy-Riemann equations"@en, "équations de Cauchy-Riemann"@fr ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Cauchy%E2%80%93Riemann_equations>, <https://fr.wikipedia.org/wiki/%C3%89quations_de_Cauchy-Riemann> ;
  dc:modified "2023-08-23"^^xsd:date ;
  skos:related psr:-ST0RJ5D8-4 ;
  a skos:Concept ;
  skos:broader psr:-RN57KZJ9-9 .

psr:-ST0RJ5D8-4
  skos:prefLabel "fonction holomorphe"@fr, "holomorphic function"@en ;
  a skos:Concept ;
  skos:related psr:-DW8DQDJ2-X .

psr:-RN57KZJ9-9
  skos:prefLabel "analyse complexe"@fr, "complex analysis"@en ;
  a skos:Concept ;
  skos:narrower psr:-DW8DQDJ2-X .