feat(ui): add symbolic math support to JS sandbox via nerdamer (#25948)

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

Preload nerdamer (with decimal.js) in the sandboxed worker,
exposing the `nerdamer` global for symbolic computation:
simplify, expand, factor, diff, integrate, solve, laplace,
ilt, limit, partfrac, gcd/lcm, roots, coefficients, and more.

Mirrors the math.js integration pattern from the
feature/sandbox-symbolic-math branch, but uses nerdamer
for a lighter, more focused symbolic math engine.

* Update sandbox-harness.ts

* docs(ui): update sandbox tool description with detailed nerdamer usage guide

* Clarify nerdamer usage in sandbox tool description

Updated the description of the sandbox tool to clarify usage of nerdamer.

* ui: build nerdamer sandbox prelude from vendored source

Replace the vendored all.min.js with the readable nerdamer-prime
source and its two bundled deps (big-integer, decimal.js), licenses
included. A vite plugin bundles and minifies them at build time with
the upstream esbuild flags, exposed as virtual:nerdamer and imported
lazily on first sandbox use. The vendors package.json pins commonjs
so the project level type: module does not break esbuild format
detection. The harness gains a CSP removing network egress from the
worker, and browser tests cover the prelude, exact arithmetic, the
fetch block and the timeout.

Upstream snapshot: together-science/nerdamer-prime@1936145

* feat(ui): make symbolic math (nerdamer) a user-toggleable setting

- Add SYMBOLIC_MATH_ENABLED setting key and registry entry (checkbox, default false)
- Convert SANDBOX_TOOL_DEFINITION to buildSandboxToolDefinition(includeSymbolicMath)
  so the tool description includes/excludes nerdamer API docs dynamically
- Cache sandbox harness per variant ('nerdamer' / 'plain') for instant toggle
- Deprecate SANDBOX_TOOL_DEFINITION constant alias for backward compatibility
- Update tools store to pass symbolic math config into tool definition

* docs(ui): tell LLM to list nerdamer functions first, do not guess

* test(ui): enable symbolic math in sandbox tests via settingsStore config

* style(ui): fix formatting for tools.svelte.ts

---------

Co-authored-by: Pascal <admin@serveurperso.com>

tools/ui/src/lib/services/sandbox.service.ts

@@ -7,9 +7,32 @@ import {
 	SANDBOX_TOOL_NAME,
 	SANDBOX_TRUNCATION_NOTICE
 } from '$lib/constants';
-import { SANDBOX_HARNESS_HTML } from './sandbox-harness';
+import { buildSandboxHarness } from './sandbox-harness';
+import { config } from '$lib/stores/settings.svelte';
 import type { ToolExecutionResult } from '$lib/types';
 
+/** Cached harnesses keyed by whether nerdamer is included. */
+const harnessCache: Record<string, string> = {};
+
+/**
+ * Build the sandbox harness. When symbolic math is enabled, loads the
+ * nerdamer prelude lazily; otherwise builds a plain harness with an empty
+ * prelude. Cached per variant so toggling the setting is instant.
+ */
+async function getHarness(): Promise<string> {
+	const enabled = !!config().symbolicMathEnabled;
+	const key = enabled ? 'nerdamer' : 'plain';
+	if (!harnessCache[key]) {
+		if (enabled) {
+			const { default: nerdamerJs } = await import('virtual:nerdamer');
+			harnessCache[key] = buildSandboxHarness(nerdamerJs);
+		} else {
+			harnessCache[key] = buildSandboxHarness('');
+		}
+	}
+	return harnessCache[key];
+}
+
 interface SandboxReply {
 	logs?: unknown;
 	result?: unknown;
@@ -45,20 +68,22 @@ export class SandboxService {
 	 * timeout or abort. Removing the iframe terminates the worker
 	 * at the browser level, so runaway code cannot outlive it.
 	 */
-	static executeTool(
+	static async executeTool(
 		toolName: string,
 		params: Record<string, unknown>,
 		signal?: AbortSignal
 	): Promise<ToolExecutionResult> {
 		if (toolName !== SANDBOX_TOOL_NAME) {
-			return Promise.resolve({ content: `Unknown frontend tool: ${toolName}`, isError: true });
+			return { content: `Unknown frontend tool: ${toolName}`, isError: true };
 		}
 
 		const code = typeof params.code === 'string' ? params.code : '';
 		if (!code) {
-			return Promise.resolve({ content: 'Missing required parameter: code', isError: true });
+			return { content: 'Missing required parameter: code', isError: true };
 		}
 
+		const harness = await getHarness();
+
 		const requested = Number(params.timeout_ms);
 		const timeoutMs =
 			Number.isFinite(requested) && requested > 0
@@ -69,7 +94,7 @@ export class SandboxService {
 			const iframe = document.createElement('iframe');
 			iframe.setAttribute('sandbox', 'allow-scripts');
 			iframe.style.display = 'none';
-			iframe.srcdoc = SANDBOX_HARNESS_HTML;
+			iframe.srcdoc = harness;
 
 			let settled = false;