feature: add formula rander in the markdown (#611)

* feature: add formula rander in the markdown

* fixed the lint errors

web/tests/markdown-katex.test.ts

@@ -0,0 +1,39 @@
+import { describe, it } from "node:test";
+import assert from "node:assert/strict";
+
+import katex from "katex";
+
+import { katexOptions } from "../src/core/markdown/katex";
+
+function render(expression: string) {
+  return katex.renderToString(expression, {
+    ...katexOptions,
+    displayMode: true,
+  });
+}
+
+describe("markdown physics katex support", () => {
+  it("renders vector calculus operators", () => {
+    assert.doesNotThrow(() => {
+      render("\\curl{\\vect{B}} = \\mu_0 \\vect{J} + \\mu_0 \\varepsilon_0 \\pdv{\\vect{E}}{t}");
+    });
+  });
+
+  it("renders quantum mechanics bra-ket notation", () => {
+    const html = render("\\braket{\\psi}{\\phi}");
+    assert.ok(html.includes("⟨") && html.includes("⟩"));
+  });
+
+  it("renders vector magnitude formula with subscripts and square root", () => {
+  const html = render("(F_1) (F_2), (F=\\sqrt{F_1^2+F_2^2})");
+  assert.ok(html.includes("F"));
+  assert.ok(html.includes("₁") || html.includes("sub")); // subscript check
+  assert.ok(html.includes("√") || html.includes("sqrt")); // square root check
+  });
+
+  it("renders chemical equations via mhchem", () => {
+    assert.doesNotThrow(() => {
+      render("\\ce{H2O ->[\\Delta] H+ + OH-}");
+    });
+  });
+});