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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>