MCP Calc Tools

Instructions

Implementation Reference

• index.js:422-438 (handler)

  Core handler function implementing the Z-transform calculation using numerical summation of f[n] * z^{-n} from n=0 to limit.

  const zTransform = (expr, n, z, limit = 100) => {
    try {
      const node = math.parse(expr);
      let result = math.complex(0, 0);
      
      for (let k = 0; k <= limit; k++) {
        const scope = { [n]: k };
        const fn = math.evaluate(node, scope);
        const zTerm = math.pow(z, -k);
        result = math.add(result, math.multiply(fn, zTerm));
      }
      
      return result.toString();
    } catch (e) {
      return `Error: ${e.message}`;
    }
  };

• index.js:473-488 (registration)

  Registers the z_transform tool with Genkit AI, specifying name, description, input/output schemas, and handler.

  ai.defineTool(
    {
      name: 'z_transform',
      description: 'Calculate the Z-transform of a function',
      inputSchema: z.object({
        expression: z.string().describe('Function of discrete time'),
        timeVar: z.string().describe('Discrete time variable'),
        zVar: z.string().describe('Z-transform variable'),
        limit: z.number().optional().describe('Upper limit for summation (default: 100)')
      }),
      outputSchema: z.string(),
    },
    async ({ expression, timeVar, zVar, limit = 100 }) => {
      return zTransform(expression, timeVar, zVar, limit);
    }
  );

• index.js:477-483 (schema)

  Defines the input schema (expression, timeVar, zVar, optional limit) and output schema (string) for the z_transform tool.

  inputSchema: z.object({
    expression: z.string().describe('Function of discrete time'),
    timeVar: z.string().describe('Discrete time variable'),
    zVar: z.string().describe('Z-transform variable'),
    limit: z.number().optional().describe('Upper limit for summation (default: 100)')
  }),
  outputSchema: z.string(),