feat(ui): add symbolic math support to JS sandbox via nerdamer

tools/ui/src/lib/constants/sandbox.ts

@@ -17,10 +17,12 @@ export const SANDBOX_TOOL_DEFINITION: OpenAIToolDefinition = {
 	type: ToolCallType.FUNCTION,
 	function: {
 		name: SANDBOX_TOOL_NAME,
-		description:
-			'Execute JavaScript in a sandboxed browser worker (no DOM, no page access). ' +
-			'Top level await is supported. Use console.log to print intermediate values; ' +
-			'a top level return statement is captured as the result.',
+		description: `Execute JS in a sandboxed browser worker (no DOM/page access). Top-level await ok; console.log for intermediates; top-level return is captured as result.
+Symbolic/numeric math via \`nerdamer\` (pre-loaded, do not require, use it directly). Object.keys(nerdamer).filter(k=>typeof nerdamer[k]==='function') list functions.
+nerdamer('diff(sin(x)/x,x)') or nerdamer.diff('sin(x)/x','x') → Expression; convert with .toString()/.text()/.toTeX(), or .evaluate() (→ still Expression, then .toString()).
+nerdamer(expr,{x:2}) substitutes only; chain .evaluate() or pass 'numer' for numeric result.
+solve(expr,var)→Symbol[]; solveEquations([eq1,..])→[[var,val],..] pairs.
+Functions: simplify/expand/factor(expr), diff(expr,var[,n]), integrate(expr,var), defint(expr,from,to,var), limit(expr,var,to), laplace(expr,t,s), ilt(expr,s,t), gcd/lcm(a,b), roots/coeffs/partfrac(expr,var), pfactor(n), numer/decimals/erf(expr), product/sum(expr,var,from,to), mean/median/stdev/variance(...vals)`,
 		parameters: {
 			type: JsonSchemaType.OBJECT,
 			properties: {

tools/ui/src/lib/services/sandbox-harness.ts

@@ -1,14 +1,23 @@
+/**
+ * nerdamer-prime.js downloaded from https://raw.githubusercontent.com/together-science/nerdamer-prime/refs/heads/main/all.min.js
+ * Upstream commit for all.min.js: https://github.com/together-science/nerdamer-prime/commit/fffcce3ebd74fefb51fcf90b613f088fcab4fd93
+ */
+import { NEWLINE } from '$lib/constants';
 import WORKER_SHIM from './sandbox-worker.js?raw';
+import NERDAMER_JS from '../vendors/nerdamer-prime.js?raw';
 
 /**
  * Harness loaded as srcdoc into a sandboxed iframe (allow-scripts only).
  * The opaque origin is the security boundary: no access to the app origin,
  * its storage or its API. The harness spawns a worker so model code never
  * runs on a main thread, which makes the parent timeout enforceable by
  * removing the iframe.
+ *
+ * nerdamer is preloaded in the worker, exposing the `nerdamer` global for
+ * symbolic computation (simplify, derivative, integrate, solve, etc.).
  */
 export const SANDBOX_HARNESS_HTML = `<!doctype html><script>
-const SHIM = ${JSON.stringify(WORKER_SHIM)};
+const SHIM = ${JSON.stringify(NERDAMER_JS + NEWLINE + WORKER_SHIM)};
 addEventListener('message', (event) => {
 	const respond = (payload) => parent.postMessage(payload, '*');
 	let worker;

tools/ui/src/lib/services/sandbox-worker.js

@@ -21,7 +21,11 @@ self.onmessage = async (event) => {
 	const reply = { logs, result: null, error: null };
 	try {
 		const AsyncFunction = Object.getPrototypeOf(async function () {}).constructor;
-		const value = await new AsyncFunction(event.data.code)();
+		// Inject `nerdamer` (from preloaded nerdamer-prime.js) into the execution context.
+		// User code can use: nerdamer(expr), nerdamer.solve(), nerdamer.derivative(),
+		// nerdamer.integrate(), nerdamer.expand(), nerdamer.factor(), nerdamer.simplify(),
+		// nerdamer.laplace(), nerdamer.limit(), nerdamer.series(), etc.
+		const value = await new AsyncFunction('nerdamer', event.data.code)(self.nerdamer);
 		if (value !== undefined) reply.result = fmt(value);
 	} catch (err) {
 		reply.error = err instanceof Error ? err.stack || err.message : String(err);