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<article><h2>Mathematica mode</h2>
<textarea id="mathematicaCode">(* example Mathematica code *)(* Dualisiert wird anhand einer Polarität an einer Quadrik $x^t Q x = 0$ mit regulärer Matrix $Q$ (also mit $det(Q) \neq 0$), z.B. die Identitätsmatrix. $p$ ist eine Liste von Polynomen - ein Ideal. *)dualize::"singular" = "Q must be regular: found Det[Q]==0.";dualize[ Q_, p_ ] := Block[ { m, n, xv, lv, uv, vars, polys, dual }, If[Det[Q] == 0, Message[dualize::"singular"], m = Length[p]; n = Length[Q] - 1; xv = Table[Subscript[x, i], {i, 0, n}]; lv = Table[Subscript[l, i], {i, 1, m}]; uv = Table[Subscript[u, i], {i, 0, n}]; (* Konstruiere Ideal polys. *) If[m == 0, polys = Q.uv, polys = Join[p, Q.uv - Transpose[Outer[D, p, xv]].lv] ]; (* Eliminiere die ersten n + 1 + m Variablen xv und lv aus dem Ideal polys. *) vars = Join[xv, lv]; dual = GroebnerBasis[polys, uv, vars]; (* Ersetze u mit x im Ergebnis. *) ReplaceAll[dual, Rule[u, x]] ] ]</textarea>
<script> var mathematicaEditor = CodeMirror.fromTextArea(document.getElementById('mathematicaCode'), { mode: 'text/x-mathematica', lineNumbers: true, matchBrackets: true });</script>
<p><strong>MIME types defined:</strong> <code>text/x-mathematica</code> (Mathematica).</p></article>
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