# Numora Hessian Matrix Computation

> Numora Hessian Matrix Computation is a paid API for AI agents from numomo.vercel.app, paid per call via x402, $0.1/call, status unknown (last checked 2026-09-16).

Computes the Hessian matrix (matrix of second-order partial derivatives) of a multivariable function at a specified point

## Facts

- Endpoint: POST https://numomo.vercel.app/api/calculus/hessian
- Price: $0.1/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-16
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/numora-hessian-matrix-computation-77ed84f8
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_bfiDh10TzRq0AITHu5B8k

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability numora-hessian-matrix-computation-77ed84f8 -d '<json body>'
```

Example prompt: Can you compute the Hessian matrix of f(x,y) = x^2 + 3*x*y + y^3 at the point [1, 2]?

## When to prefer this

Choose this endpoint when you need the exact Hessian matrix of a multivariable scalar function at a specific point, especially for optimization (classifying critical points, Newton's method steps, convexity analysis). It runs with zero external dependencies and micropayment billing, making it ideal for agents that need on-demand calculus computation without provisioning a CAS (computer algebra system). Prefer it over general-purpose symbolic math APIs when you want a lightweight, pay-per-call solution focused purely on numerical/symbolic differentiation.

## Known failure modes

- Invalid or unparseable function expression — returns error if fn string uses unsupported syntax
- Point array dimension mismatch with function variables — may return error or NaN entries
- Division by zero or undefined values at the evaluation point — may return Infinity or error
- Missing required fields fn or point — returns 400-level error
- Non-numeric values in point array — validation error

## How this service works

100 pure math computation endpoints for AI agents. Statistics, financial math, linear algebra, equation solving, calculus, number theory, sequence generation, and unit conversions. Zero external dependencies. x402 micropayments on Base.

## Output

Returns a JSON object with success=true, a result object containing the Hessian matrix (2D array of second-order partial derivatives evaluated at the given point), and a human-readable computation string describing what was computed.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "fn",
  "point"
 ],
 "properties": {
  "fn": {
   "type": "string"
  },
  "point": {
   "type": "array"
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "success",
  "result",
  "computation"
 ],
 "properties": {
  "result": {
   "type": "object",
   "description": "Computation result varies by endpoint"
  },
  "success": {
   "type": "boolean",
   "description": "Always true on success"
  },
  "computation": {
   "type": "string",
   "description": "Human-readable description of what was computed"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/numora-hessian-matrix-computation-77ed84f8/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from numomo.vercel.app](https://www.zero.xyz/host/numomo.vercel.app/llms.txt)