feat(app): add initial widgets

src/lib/agents/search/widgets/calculationWidget.ts

@@ -0,0 +1,65 @@
+import z from 'zod';
+import { Widget } from '../types';
+import { evaluate as mathEval } from 'mathjs';
+
+const schema = z.object({
+  type: z.literal('calculation'),
+  expression: z
+    .string()
+    .describe(
+      "A valid mathematical expression to be evaluated (e.g., '2 + 2', '3 * (4 + 5)').",
+    ),
+});
+
+const calculationWidget: Widget<typeof schema> = {
+  name: 'calculation',
+  description: `Performs mathematical calculations and evaluates mathematical expressions. Supports arithmetic operations, algebraic equations, functions, and complex mathematical computations.
+
+**What it provides:**
+- Evaluates mathematical expressions and returns computed results
+- Handles basic arithmetic (+, -, *, /)
+- Supports functions (sqrt, sin, cos, log, etc.)
+- Can process complex expressions with parentheses and order of operations
+
+**When to use:**
+- User asks to calculate, compute, or evaluate a mathematical expression
+- Questions like "what is X", "calculate Y", "how much is Z" where X/Y/Z are math expressions
+- Any request involving numbers and mathematical operations
+
+**Example call:**
+{
+  "type": "calculation",
+  "expression": "25% of 480"
+}
+
+{
+  "type": "calculation", 
+  "expression": "sqrt(144) + 5 * 2"
+}
+
+**Important:** The expression must be valid mathematical syntax that can be evaluated by mathjs. Format percentages as "0.25 * 480" or "25% of 480". Do not include currency symbols, units, or non-mathematical text in the expression.`,
+  schema: schema,
+  execute: async (params, _) => {
+    try {
+      const result = mathEval(params.expression);
+
+      return {
+        type: 'calculation_result',
+        data: {
+          expression: params.expression,
+          result: result,
+        },
+      };
+    } catch (error) {
+      return {
+        type: 'calculation_result',
+        data: {
+          expression: params.expression,
+          result: `Error evaluating expression: ${error}`,
+        },
+      };
+    }
+  },
+};
+
+export default calculationWidget;